LMFDB - Embedded newform 2366.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} +0.801938 q^{5} -0.246980 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.93900 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} +0.801938 q^{5} -0.246980 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.93900 q^{9} -0.801938 q^{10} +3.55496 q^{11} +0.246980 q^{12} +1.00000 q^{14} +0.198062 q^{15} +1.00000 q^{16} -1.22521 q^{17} +2.93900 q^{18} +2.75302 q^{19} +0.801938 q^{20} -0.246980 q^{21} -3.55496 q^{22} +2.29590 q^{23} -0.246980 q^{24} -4.35690 q^{25} -1.46681 q^{27} -1.00000 q^{28} +0.0217703 q^{29} -0.198062 q^{30} +2.58211 q^{31} -1.00000 q^{32} +0.878002 q^{33} +1.22521 q^{34} -0.801938 q^{35} -2.93900 q^{36} +4.40581 q^{37} -2.75302 q^{38} -0.801938 q^{40} +12.6136 q^{41} +0.246980 q^{42} -1.14914 q^{43} +3.55496 q^{44} -2.35690 q^{45} -2.29590 q^{46} -11.0368 q^{47} +0.246980 q^{48} +1.00000 q^{49} +4.35690 q^{50} -0.302602 q^{51} +2.02715 q^{53} +1.46681 q^{54} +2.85086 q^{55} +1.00000 q^{56} +0.679940 q^{57} -0.0217703 q^{58} +5.55496 q^{59} +0.198062 q^{60} -5.43296 q^{61} -2.58211 q^{62} +2.93900 q^{63} +1.00000 q^{64} -0.878002 q^{66} +11.7409 q^{67} -1.22521 q^{68} +0.567040 q^{69} +0.801938 q^{70} +6.75063 q^{71} +2.93900 q^{72} -2.13706 q^{73} -4.40581 q^{74} -1.07606 q^{75} +2.75302 q^{76} -3.55496 q^{77} +11.2349 q^{79} +0.801938 q^{80} +8.45473 q^{81} -12.6136 q^{82} +11.2838 q^{83} -0.246980 q^{84} -0.982542 q^{85} +1.14914 q^{86} +0.00537681 q^{87} -3.55496 q^{88} -11.6136 q^{89} +2.35690 q^{90} +2.29590 q^{92} +0.637727 q^{93} +11.0368 q^{94} +2.20775 q^{95} -0.246980 q^{96} +7.13169 q^{97} -1.00000 q^{98} -10.4480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{5} + 4 q^{6} - 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 2 * q^5 + 4 * q^6 - 3 * q^7 - 3 * q^8 + q^9	$ 3 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{5} + 4 q^{6} - 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + 11 q^{11} - 4 q^{12} + 3 q^{14} + 5 q^{15} + 3 q^{16} - 2 q^{17} - q^{18} + 13 q^{19} - 2 q^{20} + 4 q^{21} - 11 q^{22} - 7 q^{23} + 4 q^{24} - 9 q^{25} - q^{27} - 3 q^{28} - 3 q^{29} - 5 q^{30} + 2 q^{31} - 3 q^{32} - 17 q^{33} + 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} + 7 q^{41} - 4 q^{42} - 17 q^{43} + 11 q^{44} - 3 q^{45} + 7 q^{46} - 5 q^{47} - 4 q^{48} + 3 q^{49} + 9 q^{50} - 9 q^{51} + q^{54} - 5 q^{55} + 3 q^{56} - 22 q^{57} + 3 q^{58} + 17 q^{59} + 5 q^{60} + 3 q^{61} - 2 q^{62} - q^{63} + 3 q^{64} + 17 q^{66} + 21 q^{67} - 2 q^{68} + 21 q^{69} - 2 q^{70} - 16 q^{71} - q^{72} - q^{73} + 12 q^{75} + 13 q^{76} - 11 q^{77} + 10 q^{79} - 2 q^{80} + 3 q^{81} - 7 q^{82} + q^{83} + 4 q^{84} + 13 q^{85} + 17 q^{86} - 3 q^{87} - 11 q^{88} - 4 q^{89} + 3 q^{90} - 7 q^{92} + 9 q^{93} + 5 q^{94} - 11 q^{95} + 4 q^{96} + 19 q^{97} - 3 q^{98} + 13 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 2 * q^5 + 4 * q^6 - 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 + 11 * q^11 - 4 * q^12 + 3 * q^14 + 5 * q^15 + 3 * q^16 - 2 * q^17 - q^18 + 13 * q^19 - 2 * q^20 + 4 * q^21 - 11 * q^22 - 7 * q^23 + 4 * q^24 - 9 * q^25 - q^27 - 3 * q^28 - 3 * q^29 - 5 * q^30 + 2 * q^31 - 3 * q^32 - 17 * q^33 + 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 + 7 * q^41 - 4 * q^42 - 17 * q^43 + 11 * q^44 - 3 * q^45 + 7 * q^46 - 5 * q^47 - 4 * q^48 + 3 * q^49 + 9 * q^50 - 9 * q^51 + q^54 - 5 * q^55 + 3 * q^56 - 22 * q^57 + 3 * q^58 + 17 * q^59 + 5 * q^60 + 3 * q^61 - 2 * q^62 - q^63 + 3 * q^64 + 17 * q^66 + 21 * q^67 - 2 * q^68 + 21 * q^69 - 2 * q^70 - 16 * q^71 - q^72 - q^73 + 12 * q^75 + 13 * q^76 - 11 * q^77 + 10 * q^79 - 2 * q^80 + 3 * q^81 - 7 * q^82 + q^83 + 4 * q^84 + 13 * q^85 + 17 * q^86 - 3 * q^87 - 11 * q^88 - 4 * q^89 + 3 * q^90 - 7 * q^92 + 9 * q^93 + 5 * q^94 - 11 * q^95 + 4 * q^96 + 19 * q^97 - 3 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.246980	0.142594	0.0712969	−	0.997455i	$-0.477286\pi$
$3$	0.246980	0.142594	0.0712969	+	0.997455i	$0.477286\pi$
$4$	1.00000	0.500000
$5$	0.801938	0.358637	0.179319	−	0.983791i	$-0.442611\pi$
$5$	0.801938	0.358637	0.179319	+	0.983791i	$0.442611\pi$
$6$	−0.246980	−0.100829
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.93900	−0.979667
$10$	−0.801938	−0.253595
$11$	3.55496	1.07186	0.535930	−	0.844262i	$-0.319961\pi$
$11$	3.55496	1.07186	0.535930	+	0.844262i	$0.319961\pi$
$12$	0.246980	0.0712969
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	0.198062	0.0511395
$16$	1.00000	0.250000
$17$	−1.22521	−0.297157	−0.148578	−	0.988901i	$-0.547470\pi$
$17$	−1.22521	−0.297157	−0.148578	+	0.988901i	$0.547470\pi$
$18$	2.93900	0.692729
$19$	2.75302	0.631586	0.315793	−	0.948828i	$-0.397729\pi$
$19$	2.75302	0.631586	0.315793	+	0.948828i	$0.397729\pi$
$20$	0.801938	0.179319
$21$	−0.246980	−0.0538954
$22$	−3.55496	−0.757920
$23$	2.29590	0.478728	0.239364	−	0.970930i	$-0.423061\pi$
$23$	2.29590	0.478728	0.239364	+	0.970930i	$0.423061\pi$
$24$	−0.246980	−0.0504145
$25$	−4.35690	−0.871379
$26$	0	0
$27$	−1.46681	−0.282288
$28$	−1.00000	−0.188982
$29$	0.0217703	0.00404264	0.00202132	−	0.999998i	$-0.499357\pi$
$29$	0.0217703	0.00404264	0.00202132	+	0.999998i	$0.499357\pi$
$30$	−0.198062	−0.0361611
$31$	2.58211	0.463760	0.231880	−	0.972744i	$-0.425512\pi$
$31$	2.58211	0.463760	0.231880	+	0.972744i	$0.425512\pi$
$32$	−1.00000	−0.176777
$33$	0.878002	0.152841
$34$	1.22521	0.210122
$35$	−0.801938	−0.135552
$36$	−2.93900	−0.489834
$37$	4.40581	0.724311	0.362156	−	0.932118i	$-0.382041\pi$
$37$	4.40581	0.724311	0.362156	+	0.932118i	$0.382041\pi$
$38$	−2.75302	−0.446599
$39$	0	0
$40$	−0.801938	−0.126797
$41$	12.6136	1.96991	0.984954	−	0.172817i	$-0.0552870\pi$
$41$	12.6136	1.96991	0.984954	+	0.172817i	$0.0552870\pi$
$42$	0.246980	0.0381098
$43$	−1.14914	−0.175243	−0.0876215	−	0.996154i	$-0.527927\pi$
$43$	−1.14914	−0.175243	−0.0876215	+	0.996154i	$0.527927\pi$
$44$	3.55496	0.535930
$45$	−2.35690	−0.351345
$46$	−2.29590	−0.338512
$47$	−11.0368	−1.60989	−0.804944	−	0.593351i	$-0.797805\pi$
$47$	−11.0368	−1.60989	−0.804944	+	0.593351i	$0.797805\pi$
$48$	0.246980	0.0356484
$49$	1.00000	0.142857
$50$	4.35690	0.616158
$51$	−0.302602	−0.0423727
$52$	0	0
$53$	2.02715	0.278450	0.139225	−	0.990261i	$-0.455539\pi$
$53$	2.02715	0.278450	0.139225	+	0.990261i	$0.455539\pi$
$54$	1.46681	0.199608
$55$	2.85086	0.384409
$56$	1.00000	0.133631
$57$	0.679940	0.0900602
$58$	−0.0217703	−0.00285858
$59$	5.55496	0.723194	0.361597	−	0.932335i	$-0.382232\pi$
$59$	5.55496	0.723194	0.361597	+	0.932335i	$0.382232\pi$
$60$	0.198062	0.0255697
$61$	−5.43296	−0.695619	−0.347810	−	0.937565i	$-0.613074\pi$
$61$	−5.43296	−0.695619	−0.347810	+	0.937565i	$0.613074\pi$
$62$	−2.58211	−0.327928
$63$	2.93900	0.370279
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.878002	−0.108075
$67$	11.7409	1.43438	0.717192	−	0.696876i	$-0.245427\pi$
$67$	11.7409	1.43438	0.717192	+	0.696876i	$0.245427\pi$
$68$	−1.22521	−0.148578
$69$	0.567040	0.0682636
$70$	0.801938	0.0958499
$71$	6.75063	0.801152	0.400576	−	0.916264i	$-0.368810\pi$
$71$	6.75063	0.801152	0.400576	+	0.916264i	$0.368810\pi$
$72$	2.93900	0.346365
$73$	−2.13706	−0.250124	−0.125062	−	0.992149i	$-0.539913\pi$
$73$	−2.13706	−0.250124	−0.125062	+	0.992149i	$0.539913\pi$
$74$	−4.40581	−0.512165
$75$	−1.07606	−0.124253
$76$	2.75302	0.315793
$77$	−3.55496	−0.405125
$78$	0	0
$79$	11.2349	1.26402	0.632012	−	0.774958i	$-0.282229\pi$
$79$	11.2349	1.26402	0.632012	+	0.774958i	$0.282229\pi$
$80$	0.801938	0.0896594
$81$	8.45473	0.939415
$82$	−12.6136	−1.39294
$83$	11.2838	1.23856	0.619280	−	0.785170i	$-0.287425\pi$
$83$	11.2838	1.23856	0.619280	+	0.785170i	$0.287425\pi$
$84$	−0.246980	−0.0269477
$85$	−0.982542	−0.106572
$86$	1.14914	0.123915
$87$	0.00537681	0.000576455 0
$88$	−3.55496	−0.378960
$89$	−11.6136	−1.23104	−0.615518	−	0.788123i	$-0.711053\pi$
$89$	−11.6136	−1.23104	−0.615518	+	0.788123i	$0.711053\pi$
$90$	2.35690	0.248439
$91$	0	0
$92$	2.29590	0.239364
$93$	0.637727	0.0661292
$94$	11.0368	1.13836
$95$	2.20775	0.226510
$96$	−0.246980	−0.0252073
$97$	7.13169	0.724113	0.362057	−	0.932156i	$-0.382075\pi$
$97$	7.13169	0.724113	0.362057	+	0.932156i	$0.382075\pi$
$98$	−1.00000	−0.101015
$99$	−10.4480	−1.05007
$100$	−4.35690	−0.435690
$101$	15.3502	1.52740	0.763701	−	0.645571i	$-0.223380\pi$
$101$	15.3502	1.52740	0.763701	+	0.645571i	$0.223380\pi$
$102$	0.302602	0.0299620
$103$	8.57673	0.845090	0.422545	−	0.906342i	$-0.361137\pi$
$103$	8.57673	0.845090	0.422545	+	0.906342i	$0.361137\pi$
$104$	0	0
$105$	−0.198062	−0.0193289
$106$	−2.02715	−0.196894
$107$	−5.95108	−0.575313	−0.287656	−	0.957734i	$-0.592876\pi$
$107$	−5.95108	−0.575313	−0.287656	+	0.957734i	$0.592876\pi$
$108$	−1.46681	−0.141144
$109$	6.81402	0.652665	0.326332	−	0.945255i	$-0.394187\pi$
$109$	6.81402	0.652665	0.326332	+	0.945255i	$0.394187\pi$
$110$	−2.85086	−0.271818
$111$	1.08815	0.103282
$112$	−1.00000	−0.0944911
$113$	−12.4494	−1.17114	−0.585568	−	0.810623i	$-0.699129\pi$
$113$	−12.4494	−1.17114	−0.585568	+	0.810623i	$0.699129\pi$
$114$	−0.679940	−0.0636822
$115$	1.84117	0.171690
$116$	0.0217703	0.00202132
$117$	0	0
$118$	−5.55496	−0.511375
$119$	1.22521	0.112315
$120$	−0.198062	−0.0180805
$121$	1.63773	0.148884
$122$	5.43296	0.491877
$123$	3.11529	0.280897
$124$	2.58211	0.231880
$125$	−7.50365	−0.671147
$126$	−2.93900	−0.261827
$127$	−12.1371	−1.07699	−0.538495	−	0.842629i	$-0.681007\pi$
$127$	−12.1371	−1.07699	−0.538495	+	0.842629i	$0.681007\pi$
$128$	−1.00000	−0.0883883
$129$	−0.283815	−0.0249885
$130$	0	0
$131$	11.9933	1.04786	0.523930	−	0.851762i	$-0.324466\pi$
$131$	11.9933	1.04786	0.523930	+	0.851762i	$0.324466\pi$
$132$	0.878002	0.0764203
$133$	−2.75302	−0.238717
$134$	−11.7409	−1.01426
$135$	−1.17629	−0.101239
$136$	1.22521	0.105061
$137$	−2.48188	−0.212041	−0.106021	−	0.994364i	$-0.533811\pi$
$137$	−2.48188	−0.212041	−0.106021	+	0.994364i	$0.533811\pi$
$138$	−0.567040	−0.0482696
$139$	−7.20775	−0.611353	−0.305677	−	0.952135i	$-0.598883\pi$
$139$	−7.20775	−0.611353	−0.305677	+	0.952135i	$0.598883\pi$
$140$	−0.801938	−0.0677761
$141$	−2.72587	−0.229560
$142$	−6.75063	−0.566500
$143$	0	0
$144$	−2.93900	−0.244917
$145$	0.0174584	0.00144984
$146$	2.13706	0.176865
$147$	0.246980	0.0203705
$148$	4.40581	0.362156
$149$	−10.3230	−0.845697	−0.422848	−	0.906200i	$-0.638970\pi$
$149$	−10.3230	−0.845697	−0.422848	+	0.906200i	$0.638970\pi$
$150$	1.07606	0.0878603
$151$	−8.62863	−0.702188	−0.351094	−	0.936340i	$-0.614190\pi$
$151$	−8.62863	−0.702188	−0.351094	+	0.936340i	$0.614190\pi$
$152$	−2.75302	−0.223299
$153$	3.60089	0.291115
$154$	3.55496	0.286467
$155$	2.07069	0.166322
$156$	0	0
$157$	18.7114	1.49333	0.746666	−	0.665199i	$-0.231653\pi$
$157$	18.7114	1.49333	0.746666	+	0.665199i	$0.231653\pi$
$158$	−11.2349	−0.893800
$159$	0.500664	0.0397052
$160$	−0.801938	−0.0633987
$161$	−2.29590	−0.180942
$162$	−8.45473	−0.664266
$163$	20.9976	1.64466	0.822330	−	0.569011i	$-0.192674\pi$
$163$	20.9976	1.64466	0.822330	+	0.569011i	$0.192674\pi$
$164$	12.6136	0.984954
$165$	0.704103	0.0548143
$166$	−11.2838	−0.875794
$167$	−9.75063	−0.754526	−0.377263	−	0.926106i	$-0.623135\pi$
$167$	−9.75063	−0.754526	−0.377263	+	0.926106i	$0.623135\pi$
$168$	0.246980	0.0190549
$169$	0	0
$170$	0.982542	0.0753575
$171$	−8.09113	−0.618744
$172$	−1.14914	−0.0876215
$173$	−9.51871	−0.723694	−0.361847	−	0.932237i	$-0.617854\pi$
$173$	−9.51871	−0.723694	−0.361847	+	0.932237i	$0.617854\pi$
$174$	−0.00537681	−0.000407615 0
$175$	4.35690	0.329350
$176$	3.55496	0.267965
$177$	1.37196	0.103123
$178$	11.6136	0.870473
$179$	15.7332	1.17595	0.587976	−	0.808878i	$-0.299925\pi$
$179$	15.7332	1.17595	0.587976	+	0.808878i	$0.299925\pi$
$180$	−2.35690	−0.175673
$181$	10.0543	0.747330	0.373665	−	0.927564i	$-0.378101\pi$
$181$	10.0543	0.747330	0.373665	+	0.927564i	$0.378101\pi$
$182$	0	0
$183$	−1.34183	−0.0991910
$184$	−2.29590	−0.169256
$185$	3.53319	0.259765
$186$	−0.637727	−0.0467604
$187$	−4.35557	−0.318511
$188$	−11.0368	−0.804944
$189$	1.46681	0.106695
$190$	−2.20775	−0.160167
$191$	12.1631	0.880094	0.440047	−	0.897975i	$-0.354962\pi$
$191$	12.1631	0.880094	0.440047	+	0.897975i	$0.354962\pi$
$192$	0.246980	0.0178242
$193$	20.7192	1.49140	0.745699	−	0.666283i	$-0.232116\pi$
$193$	20.7192	1.49140	0.745699	+	0.666283i	$0.232116\pi$
$194$	−7.13169	−0.512025
$195$	0	0
$196$	1.00000	0.0714286
$197$	21.9801	1.56602	0.783010	−	0.622009i	$-0.213683\pi$
$197$	21.9801	1.56602	0.783010	+	0.622009i	$0.213683\pi$
$198$	10.4480	0.742509
$199$	−16.8974	−1.19782	−0.598912	−	0.800815i	$-0.704400\pi$
$199$	−16.8974	−1.19782	−0.598912	+	0.800815i	$0.704400\pi$
$200$	4.35690	0.308079
$201$	2.89977	0.204534
$202$	−15.3502	−1.08004
$203$	−0.0217703	−0.00152797
$204$	−0.302602	−0.0211864
$205$	10.1153	0.706483
$206$	−8.57673	−0.597569
$207$	−6.74764	−0.468994
$208$	0	0
$209$	9.78687	0.676972
$210$	0.198062	0.0136676
$211$	−0.104539	−0.00719679	−0.00359840	−	0.999994i	$-0.501145\pi$
$211$	−0.104539	−0.00719679	−0.00359840	+	0.999994i	$0.501145\pi$
$212$	2.02715	0.139225
$213$	1.66727	0.114239
$214$	5.95108	0.406808
$215$	−0.921543	−0.0628487
$216$	1.46681	0.0998039
$217$	−2.58211	−0.175285
$218$	−6.81402	−0.461504
$219$	−0.527811	−0.0356662
$220$	2.85086	0.192205
$221$	0	0
$222$	−1.08815	−0.0730316
$223$	7.11290	0.476315	0.238158	−	0.971227i	$-0.423457\pi$
$223$	7.11290	0.476315	0.238158	+	0.971227i	$0.423457\pi$
$224$	1.00000	0.0668153
$225$	12.8049	0.853661
$226$	12.4494	0.828119
$227$	−7.72348	−0.512625	−0.256313	−	0.966594i	$-0.582508\pi$
$227$	−7.72348	−0.512625	−0.256313	+	0.966594i	$0.582508\pi$
$228$	0.679940	0.0450301
$229$	22.6939	1.49966	0.749829	−	0.661632i	$-0.230136\pi$
$229$	22.6939	1.49966	0.749829	+	0.661632i	$0.230136\pi$
$230$	−1.84117	−0.121403
$231$	−0.878002	−0.0577683
$232$	−0.0217703	−0.00142929
$233$	−11.2325	−0.735866	−0.367933	−	0.929852i	$-0.619934\pi$
$233$	−11.2325	−0.735866	−0.367933	+	0.929852i	$0.619934\pi$
$234$	0	0
$235$	−8.85086	−0.577366
$236$	5.55496	0.361597
$237$	2.77479	0.180242
$238$	−1.22521	−0.0794185
$239$	−14.2241	−0.920083	−0.460042	−	0.887897i	$-0.652166\pi$
$239$	−14.2241	−0.920083	−0.460042	+	0.887897i	$0.652166\pi$
$240$	0.198062	0.0127849
$241$	16.6431	1.07208	0.536038	−	0.844194i	$-0.319920\pi$
$241$	16.6431	1.07208	0.536038	+	0.844194i	$0.319920\pi$
$242$	−1.63773	−0.105277
$243$	6.48858	0.416243
$244$	−5.43296	−0.347810
$245$	0.801938	0.0512339
$246$	−3.11529	−0.198624
$247$	0	0
$248$	−2.58211	−0.163964
$249$	2.78687	0.176611
$250$	7.50365	0.474572
$251$	−8.47219	−0.534760	−0.267380	−	0.963591i	$-0.586158\pi$
$251$	−8.47219	−0.534760	−0.267380	+	0.963591i	$0.586158\pi$
$252$	2.93900	0.185140
$253$	8.16182	0.513129
$254$	12.1371	0.761547
$255$	−0.242668	−0.0151964
$256$	1.00000	0.0625000
$257$	7.91185	0.493528	0.246764	−	0.969076i	$-0.420633\pi$
$257$	7.91185	0.493528	0.246764	+	0.969076i	$0.420633\pi$
$258$	0.283815	0.0176696
$259$	−4.40581	−0.273764
$260$	0	0
$261$	−0.0639828	−0.00396044
$262$	−11.9933	−0.740948
$263$	−9.71140	−0.598831	−0.299415	−	0.954123i	$-0.596792\pi$
$263$	−9.71140	−0.598831	−0.299415	+	0.954123i	$0.596792\pi$
$264$	−0.878002	−0.0540373
$265$	1.62565	0.0998626
$266$	2.75302	0.168799
$267$	−2.86831	−0.175538
$268$	11.7409	0.717192
$269$	29.6340	1.80682	0.903409	−	0.428781i	$-0.141057\pi$
$269$	29.6340	1.80682	0.903409	+	0.428781i	$0.141057\pi$
$270$	1.17629	0.0715869
$271$	−24.0441	−1.46058	−0.730288	−	0.683139i	$-0.760614\pi$
$271$	−24.0441	−1.46058	−0.730288	+	0.683139i	$0.760614\pi$
$272$	−1.22521	−0.0742892
$273$	0	0
$274$	2.48188	0.149936
$275$	−15.4886	−0.933997
$276$	0.567040	0.0341318
$277$	13.7385	0.825469	0.412735	−	0.910851i	$-0.364574\pi$
$277$	13.7385	0.825469	0.412735	+	0.910851i	$0.364574\pi$
$278$	7.20775	0.432292
$279$	−7.58881	−0.454330
$280$	0.801938	0.0479249
$281$	8.93900	0.533256	0.266628	−	0.963800i	$-0.414090\pi$
$281$	8.93900	0.533256	0.266628	+	0.963800i	$0.414090\pi$
$282$	2.72587	0.162323
$283$	25.2446	1.50063	0.750317	−	0.661078i	$-0.229901\pi$
$283$	25.2446	1.50063	0.750317	+	0.661078i	$0.229901\pi$
$284$	6.75063	0.400576
$285$	0.545269	0.0322990
$286$	0	0
$287$	−12.6136	−0.744555
$288$	2.93900	0.173182
$289$	−15.4989	−0.911698
$290$	−0.0174584	−0.00102519
$291$	1.76138	0.103254
$292$	−2.13706	−0.125062
$293$	−6.96316	−0.406792	−0.203396	−	0.979097i	$-0.565198\pi$
$293$	−6.96316	−0.406792	−0.203396	+	0.979097i	$0.565198\pi$
$294$	−0.246980	−0.0144041
$295$	4.45473	0.259364
$296$	−4.40581	−0.256083
$297$	−5.21446	−0.302573
$298$	10.3230	0.597998
$299$	0	0
$300$	−1.07606	−0.0621266
$301$	1.14914	0.0662356
$302$	8.62863	0.496522
$303$	3.79118	0.217798
$304$	2.75302	0.157897
$305$	−4.35690	−0.249475
$306$	−3.60089	−0.205849
$307$	−17.8823	−1.02060	−0.510299	−	0.859997i	$-0.670465\pi$
$307$	−17.8823	−1.02060	−0.510299	+	0.859997i	$0.670465\pi$
$308$	−3.55496	−0.202563
$309$	2.11828	0.120505
$310$	−2.07069	−0.117607
$311$	16.5254	0.937070	0.468535	−	0.883445i	$-0.344782\pi$
$311$	16.5254	0.937070	0.468535	+	0.883445i	$0.344782\pi$
$312$	0	0
$313$	24.3763	1.37783	0.688914	−	0.724843i	$-0.258088\pi$
$313$	24.3763	1.37783	0.688914	+	0.724843i	$0.258088\pi$
$314$	−18.7114	−1.05595
$315$	2.35690	0.132796
$316$	11.2349	0.632012
$317$	−0.0381637	−0.00214349	−0.00107174	−	0.999999i	$-0.500341\pi$
$317$	−0.0381637	−0.00214349	−0.00107174	+	0.999999i	$0.500341\pi$
$318$	−0.500664	−0.0280758
$319$	0.0773924	0.00433314
$320$	0.801938	0.0448297
$321$	−1.46980	−0.0820360
$322$	2.29590	0.127945
$323$	−3.37303	−0.187680
$324$	8.45473	0.469707
$325$	0	0
$326$	−20.9976	−1.16295
$327$	1.68292	0.0930659
$328$	−12.6136	−0.696468
$329$	11.0368	0.608480
$330$	−0.704103	−0.0387596
$331$	29.4547	1.61898	0.809489	−	0.587135i	$-0.199744\pi$
$331$	29.4547	1.61898	0.809489	+	0.587135i	$0.199744\pi$
$332$	11.2838	0.619280
$333$	−12.9487	−0.709584
$334$	9.75063	0.533531
$335$	9.41550	0.514424
$336$	−0.246980	−0.0134738
$337$	−2.45580	−0.133776	−0.0668879	−	0.997760i	$-0.521307\pi$
$337$	−2.45580	−0.133776	−0.0668879	+	0.997760i	$0.521307\pi$
$338$	0	0
$339$	−3.07474	−0.166997
$340$	−0.982542	−0.0532858
$341$	9.17928	0.497086
$342$	8.09113	0.437518
$343$	−1.00000	−0.0539949
$344$	1.14914	0.0619577
$345$	0.454731	0.0244819
$346$	9.51871	0.511729
$347$	−20.0804	−1.07797	−0.538986	−	0.842315i	$-0.681192\pi$
$347$	−20.0804	−1.07797	−0.538986	+	0.842315i	$0.681192\pi$
$348$	0.00537681	0.000288227 0
$349$	32.9071	1.76147	0.880737	−	0.473605i	$-0.157047\pi$
$349$	32.9071	1.76147	0.880737	+	0.473605i	$0.157047\pi$
$350$	−4.35690	−0.232886
$351$	0	0
$352$	−3.55496	−0.189480
$353$	−35.9788	−1.91496	−0.957480	−	0.288501i	$-0.906843\pi$
$353$	−35.9788	−1.91496	−0.957480	+	0.288501i	$0.906843\pi$
$354$	−1.37196	−0.0729189
$355$	5.41358	0.287323
$356$	−11.6136	−0.615518
$357$	0.302602	0.0160154
$358$	−15.7332	−0.831524
$359$	16.3032	0.860450	0.430225	−	0.902722i	$-0.358434\pi$
$359$	16.3032	0.860450	0.430225	+	0.902722i	$0.358434\pi$
$360$	2.35690	0.124219
$361$	−11.4209	−0.601099
$362$	−10.0543	−0.528442
$363$	0.404485	0.0212300
$364$	0	0
$365$	−1.71379	−0.0897040
$366$	1.34183	0.0701386
$367$	−18.2000	−0.950031	−0.475016	−	0.879977i	$-0.657558\pi$
$367$	−18.2000	−0.950031	−0.475016	+	0.879977i	$0.657558\pi$
$368$	2.29590	0.119682
$369$	−37.0713	−1.92985
$370$	−3.53319	−0.183682
$371$	−2.02715	−0.105244
$372$	0.637727	0.0330646
$373$	31.6407	1.63829	0.819147	−	0.573584i	$-0.194447\pi$
$373$	31.6407	1.63829	0.819147	+	0.573584i	$0.194447\pi$
$374$	4.35557	0.225221
$375$	−1.85325	−0.0957013
$376$	11.0368	0.569181
$377$	0	0
$378$	−1.46681	−0.0754447
$379$	1.51142	0.0776363	0.0388182	−	0.999246i	$-0.487641\pi$
$379$	1.51142	0.0776363	0.0388182	+	0.999246i	$0.487641\pi$
$380$	2.20775	0.113255
$381$	−2.99761	−0.153572
$382$	−12.1631	−0.622321
$383$	−15.0881	−0.770968	−0.385484	−	0.922714i	$-0.625966\pi$
$383$	−15.0881	−0.770968	−0.385484	+	0.922714i	$0.625966\pi$
$384$	−0.246980	−0.0126036
$385$	−2.85086	−0.145293
$386$	−20.7192	−1.05458
$387$	3.37734	0.171680
$388$	7.13169	0.362057
$389$	−9.03252	−0.457967	−0.228984	−	0.973430i	$-0.573540\pi$
$389$	−9.03252	−0.457967	−0.228984	+	0.973430i	$0.573540\pi$
$390$	0	0
$391$	−2.81295	−0.142257
$392$	−1.00000	−0.0505076
$393$	2.96210	0.149418
$394$	−21.9801	−1.10734
$395$	9.00969	0.453327
$396$	−10.4480	−0.525033
$397$	−32.4849	−1.63037	−0.815184	−	0.579202i	$-0.803364\pi$
$397$	−32.4849	−1.63037	−0.815184	+	0.579202i	$0.803364\pi$
$398$	16.8974	0.846989
$399$	−0.679940	−0.0340396
$400$	−4.35690	−0.217845
$401$	−16.0694	−0.802466	−0.401233	−	0.915976i	$-0.631418\pi$
$401$	−16.0694	−0.802466	−0.401233	+	0.915976i	$0.631418\pi$
$402$	−2.89977	−0.144628
$403$	0	0
$404$	15.3502	0.763701
$405$	6.78017	0.336909
$406$	0.0217703	0.00108044
$407$	15.6625	0.776360
$408$	0.302602	0.0149810
$409$	16.5676	0.819217	0.409608	−	0.912261i	$-0.365665\pi$
$409$	16.5676	0.819217	0.409608	+	0.912261i	$0.365665\pi$
$410$	−10.1153	−0.499559
$411$	−0.612973	−0.0302357
$412$	8.57673	0.422545
$413$	−5.55496	−0.273342
$414$	6.74764	0.331629
$415$	9.04892	0.444194
$416$	0	0
$417$	−1.78017	−0.0871752
$418$	−9.78687	−0.478692
$419$	−22.4045	−1.09453	−0.547265	−	0.836959i	$-0.684331\pi$
$419$	−22.4045	−1.09453	−0.547265	+	0.836959i	$0.684331\pi$
$420$	−0.198062	−0.00966445
$421$	−27.8998	−1.35975	−0.679876	−	0.733327i	$-0.737966\pi$
$421$	−27.8998	−1.35975	−0.679876	+	0.733327i	$0.737966\pi$
$422$	0.104539	0.00508890
$423$	32.4373	1.57715
$424$	−2.02715	−0.0984470
$425$	5.33811	0.258936
$426$	−1.66727	−0.0807794
$427$	5.43296	0.262919
$428$	−5.95108	−0.287656
$429$	0	0
$430$	0.921543	0.0444407
$431$	−2.51812	−0.121294	−0.0606468	−	0.998159i	$-0.519316\pi$
$431$	−2.51812	−0.121294	−0.0606468	+	0.998159i	$0.519316\pi$
$432$	−1.46681	−0.0705720
$433$	10.2155	0.490927	0.245463	−	0.969406i	$-0.421060\pi$
$433$	10.2155	0.490927	0.245463	+	0.969406i	$0.421060\pi$
$434$	2.58211	0.123945
$435$	0.00431187	0.000206738 0
$436$	6.81402	0.326332
$437$	6.32065	0.302358
$438$	0.527811	0.0252198
$439$	−22.5985	−1.07857	−0.539284	−	0.842124i	$-0.681305\pi$
$439$	−22.5985	−1.07857	−0.539284	+	0.842124i	$0.681305\pi$
$440$	−2.85086	−0.135909
$441$	−2.93900	−0.139952
$442$	0	0
$443$	−38.4946	−1.82893	−0.914466	−	0.404664i	$-0.867389\pi$
$443$	−38.4946	−1.82893	−0.914466	+	0.404664i	$0.867389\pi$
$444$	1.08815	0.0516411
$445$	−9.31336	−0.441495
$446$	−7.11290	−0.336806
$447$	−2.54958	−0.120591
$448$	−1.00000	−0.0472456
$449$	−30.2150	−1.42594	−0.712968	−	0.701196i	$-0.752650\pi$
$449$	−30.2150	−1.42594	−0.712968	+	0.701196i	$0.752650\pi$
$450$	−12.8049	−0.603630
$451$	44.8407	2.11147
$452$	−12.4494	−0.585568
$453$	−2.13110	−0.100128
$454$	7.72348	0.362481
$455$	0	0
$456$	−0.679940	−0.0318411
$457$	−19.5555	−0.914770	−0.457385	−	0.889269i	$-0.651214\pi$
$457$	−19.5555	−0.914770	−0.457385	+	0.889269i	$0.651214\pi$
$458$	−22.6939	−1.06042
$459$	1.79715	0.0838839
$460$	1.84117	0.0858448
$461$	−16.2935	−0.758864	−0.379432	−	0.925220i	$-0.623881\pi$
$461$	−16.2935	−0.758864	−0.379432	+	0.925220i	$0.623881\pi$
$462$	0.878002	0.0408484
$463$	−12.9554	−0.602088	−0.301044	−	0.953610i	$-0.597335\pi$
$463$	−12.9554	−0.602088	−0.301044	+	0.953610i	$0.597335\pi$
$464$	0.0217703	0.00101066
$465$	0.511418	0.0237164
$466$	11.2325	0.520336
$467$	0.134670	0.00623180	0.00311590	−	0.999995i	$-0.499008\pi$
$467$	0.134670	0.00623180	0.00311590	+	0.999995i	$0.499008\pi$
$468$	0	0
$469$	−11.7409	−0.542146
$470$	8.85086	0.408260
$471$	4.62133	0.212940
$472$	−5.55496	−0.255688
$473$	−4.08516	−0.187836
$474$	−2.77479	−0.127450
$475$	−11.9946	−0.550351
$476$	1.22521	0.0561574
$477$	−5.95779	−0.272788
$478$	14.2241	0.650597
$479$	−40.5013	−1.85055	−0.925275	−	0.379297i	$-0.876166\pi$
$479$	−40.5013	−1.85055	−0.925275	+	0.379297i	$0.876166\pi$
$480$	−0.198062	−0.00904026
$481$	0	0
$482$	−16.6431	−0.758073
$483$	−0.567040	−0.0258012
$484$	1.63773	0.0744422
$485$	5.71917	0.259694
$486$	−6.48858	−0.294328
$487$	13.6789	0.619849	0.309924	−	0.950761i	$-0.399696\pi$
$487$	13.6789	0.619849	0.309924	+	0.950761i	$0.399696\pi$
$488$	5.43296	0.245939
$489$	5.18598	0.234518
$490$	−0.801938	−0.0362279
$491$	−18.5483	−0.837071	−0.418535	−	0.908200i	$-0.637456\pi$
$491$	−18.5483	−0.837071	−0.418535	+	0.908200i	$0.637456\pi$
$492$	3.11529	0.140448
$493$	−0.0266731	−0.00120130
$494$	0	0
$495$	−8.37867	−0.376593
$496$	2.58211	0.115940
$497$	−6.75063	−0.302807
$498$	−2.78687	−0.124883
$499$	−10.4349	−0.467129	−0.233565	−	0.972341i	$-0.575039\pi$
$499$	−10.4349	−0.467129	−0.233565	+	0.972341i	$0.575039\pi$
$500$	−7.50365	−0.335573
$501$	−2.40821	−0.107591
$502$	8.47219	0.378132
$503$	−42.2030	−1.88174	−0.940869	−	0.338772i	$-0.889989\pi$
$503$	−42.2030	−1.88174	−0.940869	+	0.338772i	$0.889989\pi$
$504$	−2.93900	−0.130914
$505$	12.3099	0.547783
$506$	−8.16182	−0.362837
$507$	0	0
$508$	−12.1371	−0.538495
$509$	17.4252	0.772358	0.386179	−	0.922424i	$-0.373795\pi$
$509$	17.4252	0.772358	0.386179	+	0.922424i	$0.373795\pi$
$510$	0.242668	0.0107455
$511$	2.13706	0.0945381
$512$	−1.00000	−0.0441942
$513$	−4.03816	−0.178289
$514$	−7.91185	−0.348977
$515$	6.87800	0.303081
$516$	−0.283815	−0.0124943
$517$	−39.2355	−1.72557
$518$	4.40581	0.193580
$519$	−2.35093	−0.103194
$520$	0	0
$521$	11.9041	0.521527	0.260764	−	0.965403i	$-0.416026\pi$
$521$	11.9041	0.521527	0.260764	+	0.965403i	$0.416026\pi$
$522$	0.0639828	0.00280045
$523$	−16.4470	−0.719175	−0.359588	−	0.933111i	$-0.617083\pi$
$523$	−16.4470	−0.719175	−0.359588	+	0.933111i	$0.617083\pi$
$524$	11.9933	0.523930
$525$	1.07606	0.0469633
$526$	9.71140	0.423437
$527$	−3.16362	−0.137809
$528$	0.878002	0.0382101
$529$	−17.7289	−0.770820
$530$	−1.62565	−0.0706135
$531$	−16.3260	−0.708489
$532$	−2.75302	−0.119359
$533$	0	0
$534$	2.86831	0.124124
$535$	−4.77240	−0.206329
$536$	−11.7409	−0.507131
$537$	3.88577	0.167683
$538$	−29.6340	−1.27761
$539$	3.55496	0.153123
$540$	−1.17629	−0.0506195
$541$	21.2717	0.914543	0.457272	−	0.889327i	$-0.348827\pi$
$541$	21.2717	0.914543	0.457272	+	0.889327i	$0.348827\pi$
$542$	24.0441	1.03278
$543$	2.48321	0.106565
$544$	1.22521	0.0525304
$545$	5.46442	0.234070
$546$	0	0
$547$	−28.8388	−1.23306	−0.616528	−	0.787333i	$-0.711461\pi$
$547$	−28.8388	−1.23306	−0.616528	+	0.787333i	$0.711461\pi$
$548$	−2.48188	−0.106021
$549$	15.9675	0.681475
$550$	15.4886	0.660435
$551$	0.0599340	0.00255327
$552$	−0.567040	−0.0241348
$553$	−11.2349	−0.477756
$554$	−13.7385	−0.583695
$555$	0.872625	0.0370409
$556$	−7.20775	−0.305677
$557$	14.9801	0.634729	0.317365	−	0.948304i	$-0.397202\pi$
$557$	14.9801	0.634729	0.317365	+	0.948304i	$0.397202\pi$
$558$	7.58881	0.321260
$559$	0	0
$560$	−0.801938	−0.0338881
$561$	−1.07574	−0.0454176
$562$	−8.93900	−0.377069
$563$	0.606859	0.0255761	0.0127880	−	0.999918i	$-0.495929\pi$
$563$	0.606859	0.0255761	0.0127880	+	0.999918i	$0.495929\pi$
$564$	−2.72587	−0.114780
$565$	−9.98361	−0.420013
$566$	−25.2446	−1.06111
$567$	−8.45473	−0.355065
$568$	−6.75063	−0.283250
$569$	26.5295	1.11217	0.556087	−	0.831124i	$-0.312302\pi$
$569$	26.5295	1.11217	0.556087	+	0.831124i	$0.312302\pi$
$570$	−0.545269	−0.0228388
$571$	4.38298	0.183422	0.0917110	−	0.995786i	$-0.470766\pi$
$571$	4.38298	0.183422	0.0917110	+	0.995786i	$0.470766\pi$
$572$	0	0
$573$	3.00405	0.125496
$574$	12.6136	0.526480
$575$	−10.0030	−0.417153
$576$	−2.93900	−0.122458
$577$	2.07739	0.0864830	0.0432415	−	0.999065i	$-0.486232\pi$
$577$	2.07739	0.0864830	0.0432415	+	0.999065i	$0.486232\pi$
$578$	15.4989	0.644668
$579$	5.11721	0.212664
$580$	0.0174584	0.000724920 0
$581$	−11.2838	−0.468132
$582$	−1.76138	−0.0730116
$583$	7.20642	0.298460
$584$	2.13706	0.0884323
$585$	0	0
$586$	6.96316	0.287646
$587$	17.9095	0.739203	0.369601	−	0.929190i	$-0.379494\pi$
$587$	17.9095	0.739203	0.369601	+	0.929190i	$0.379494\pi$
$588$	0.246980	0.0101853
$589$	7.10859	0.292904
$590$	−4.45473	−0.183398
$591$	5.42865	0.223305
$592$	4.40581	0.181078
$593$	22.5254	0.925008	0.462504	−	0.886617i	$-0.346951\pi$
$593$	22.5254	0.925008	0.462504	+	0.886617i	$0.346951\pi$
$594$	5.21446	0.213952
$595$	0.982542	0.0402803
$596$	−10.3230	−0.422848
$597$	−4.17331	−0.170802
$598$	0	0
$599$	−45.4596	−1.85743	−0.928715	−	0.370794i	$-0.879086\pi$
$599$	−45.4596	−1.85743	−0.928715	+	0.370794i	$0.879086\pi$
$600$	1.07606	0.0439301
$601$	39.6752	1.61838	0.809192	−	0.587545i	$-0.199905\pi$
$601$	39.6752	1.61838	0.809192	+	0.587545i	$0.199905\pi$
$602$	−1.14914	−0.0468357
$603$	−34.5066	−1.40522
$604$	−8.62863	−0.351094
$605$	1.31336	0.0533955
$606$	−3.79118	−0.154006
$607$	39.1444	1.58882	0.794410	−	0.607382i	$-0.207780\pi$
$607$	39.1444	1.58882	0.794410	+	0.607382i	$0.207780\pi$
$608$	−2.75302	−0.111650
$609$	−0.00537681	−0.000217879 0
$610$	4.35690	0.176406
$611$	0	0
$612$	3.60089	0.145557
$613$	13.8224	0.558281	0.279140	−	0.960250i	$-0.409951\pi$
$613$	13.8224	0.558281	0.279140	+	0.960250i	$0.409951\pi$
$614$	17.8823	0.721671
$615$	2.49827	0.100740
$616$	3.55496	0.143233
$617$	−29.3817	−1.18286	−0.591430	−	0.806356i	$-0.701437\pi$
$617$	−29.3817	−1.18286	−0.591430	+	0.806356i	$0.701437\pi$
$618$	−2.11828	−0.0852096
$619$	45.8920	1.84456	0.922278	−	0.386528i	$-0.126326\pi$
$619$	45.8920	1.84456	0.922278	+	0.386528i	$0.126326\pi$
$620$	2.07069	0.0831608
$621$	−3.36765	−0.135139
$622$	−16.5254	−0.662609
$623$	11.6136	0.465288
$624$	0	0
$625$	15.7670	0.630681
$626$	−24.3763	−0.974272
$627$	2.41716	0.0965320
$628$	18.7114	0.746666
$629$	−5.39804	−0.215234
$630$	−2.35690	−0.0939010
$631$	−45.9014	−1.82731	−0.913654	−	0.406494i	$-0.866751\pi$
$631$	−45.9014	−1.82731	−0.913654	+	0.406494i	$0.866751\pi$
$632$	−11.2349	−0.446900
$633$	−0.0258191	−0.00102622
$634$	0.0381637	0.00151567
$635$	−9.73317	−0.386249
$636$	0.500664	0.0198526
$637$	0	0
$638$	−0.0773924	−0.00306399
$639$	−19.8401	−0.784862
$640$	−0.801938	−0.0316994
$641$	49.2476	1.94516	0.972581	−	0.232564i	$-0.0747116\pi$
$641$	49.2476	1.94516	0.972581	+	0.232564i	$0.0747116\pi$
$642$	1.46980	0.0580082
$643$	44.3860	1.75041	0.875206	−	0.483751i	$-0.160726\pi$
$643$	44.3860	1.75041	0.875206	+	0.483751i	$0.160726\pi$
$644$	−2.29590	−0.0904710
$645$	−0.227602	−0.00896183
$646$	3.37303	0.132710
$647$	−0.260980	−0.0102602	−0.00513009	−	0.999987i	$-0.501633\pi$
$647$	−0.260980	−0.0102602	−0.00513009	+	0.999987i	$0.501633\pi$
$648$	−8.45473	−0.332133
$649$	19.7476	0.775163
$650$	0	0
$651$	−0.637727	−0.0249945
$652$	20.9976	0.822330
$653$	−1.24459	−0.0487044	−0.0243522	−	0.999703i	$-0.507752\pi$
$653$	−1.24459	−0.0487044	−0.0243522	+	0.999703i	$0.507752\pi$
$654$	−1.68292	−0.0658075
$655$	9.61788	0.375802
$656$	12.6136	0.492477
$657$	6.28083	0.245039
$658$	−11.0368	−0.430261
$659$	−22.0941	−0.860664	−0.430332	−	0.902671i	$-0.641604\pi$
$659$	−22.0941	−0.860664	−0.430332	+	0.902671i	$0.641604\pi$
$660$	0.704103	0.0274072
$661$	−0.329749	−0.0128257	−0.00641287	−	0.999979i	$-0.502041\pi$
$661$	−0.329749	−0.0128257	−0.00641287	+	0.999979i	$0.502041\pi$
$662$	−29.4547	−1.14479
$663$	0	0
$664$	−11.2838	−0.437897
$665$	−2.20775	−0.0856129
$666$	12.9487	0.501752
$667$	0.0499823	0.00193532
$668$	−9.75063	−0.377263
$669$	1.75674	0.0679195
$670$	−9.41550	−0.363753
$671$	−19.3139	−0.745607
$672$	0.246980	0.00952745
$673$	−31.8495	−1.22771	−0.613855	−	0.789419i	$-0.710382\pi$
$673$	−31.8495	−1.22771	−0.613855	+	0.789419i	$0.710382\pi$
$674$	2.45580	0.0945937
$675$	6.39075	0.245980
$676$	0	0
$677$	−7.04461	−0.270746	−0.135373	−	0.990795i	$-0.543223\pi$
$677$	−7.04461	−0.270746	−0.135373	+	0.990795i	$0.543223\pi$
$678$	3.07474	0.118085
$679$	−7.13169	−0.273689
$680$	0.982542	0.0376788
$681$	−1.90754	−0.0730972
$682$	−9.17928	−0.351493
$683$	−19.2814	−0.737783	−0.368892	−	0.929472i	$-0.620263\pi$
$683$	−19.2814	−0.737783	−0.368892	+	0.929472i	$0.620263\pi$
$684$	−8.09113	−0.309372
$685$	−1.99031	−0.0760459
$686$	1.00000	0.0381802
$687$	5.60494	0.213842
$688$	−1.14914	−0.0438107
$689$	0	0
$690$	−0.454731	−0.0173113
$691$	−17.1903	−0.653950	−0.326975	−	0.945033i	$-0.606029\pi$
$691$	−17.1903	−0.653950	−0.326975	+	0.945033i	$0.606029\pi$
$692$	−9.51871	−0.361847
$693$	10.4480	0.396888
$694$	20.0804	0.762241
$695$	−5.78017	−0.219254
$696$	−0.00537681	−0.000203808 0
$697$	−15.4543	−0.585372
$698$	−32.9071	−1.24555
$699$	−2.77420	−0.104930
$700$	4.35690	0.164675
$701$	2.94571	0.111258	0.0556289	−	0.998452i	$-0.482284\pi$
$701$	2.94571	0.111258	0.0556289	+	0.998452i	$0.482284\pi$
$702$	0	0
$703$	12.1293	0.457465
$704$	3.55496	0.133983
$705$	−2.18598	−0.0823288
$706$	35.9788	1.35408
$707$	−15.3502	−0.577303
$708$	1.37196	0.0515615
$709$	−34.5163	−1.29629	−0.648144	−	0.761518i	$-0.724454\pi$
$709$	−34.5163	−1.29629	−0.648144	+	0.761518i	$0.724454\pi$
$710$	−5.41358	−0.203168
$711$	−33.0194	−1.23832
$712$	11.6136	0.435237
$713$	5.92825	0.222015
$714$	−0.302602	−0.0113246
$715$	0	0
$716$	15.7332	0.587976
$717$	−3.51307	−0.131198
$718$	−16.3032	−0.608430
$719$	−30.4306	−1.13487	−0.567434	−	0.823419i	$-0.692064\pi$
$719$	−30.4306	−1.13487	−0.567434	+	0.823419i	$0.692064\pi$
$720$	−2.35690	−0.0878363
$721$	−8.57673	−0.319414
$722$	11.4209	0.425041
$723$	4.11051	0.152871
$724$	10.0543	0.373665
$725$	−0.0948508	−0.00352267
$726$	−0.404485	−0.0150119
$727$	−45.1973	−1.67628	−0.838138	−	0.545458i	$-0.816356\pi$
$727$	−45.1973	−1.67628	−0.838138	+	0.545458i	$0.816356\pi$
$728$	0	0
$729$	−23.7616	−0.880061
$730$	1.71379	0.0634303
$731$	1.40794	0.0520747
$732$	−1.34183	−0.0495955
$733$	−11.4125	−0.421531	−0.210765	−	0.977537i	$-0.567596\pi$
$733$	−11.4125	−0.421531	−0.210765	+	0.977537i	$0.567596\pi$
$734$	18.2000	0.671774
$735$	0.198062	0.00730564
$736$	−2.29590	−0.0846279
$737$	41.7385	1.53746
$738$	37.0713	1.36461
$739$	32.3744	1.19091	0.595455	−	0.803389i	$-0.296972\pi$
$739$	32.3744	1.19091	0.595455	+	0.803389i	$0.296972\pi$
$740$	3.53319	0.129883
$741$	0	0
$742$	2.02715	0.0744189
$743$	6.13408	0.225038	0.112519	−	0.993650i	$-0.464108\pi$
$743$	6.13408	0.225038	0.112519	+	0.993650i	$0.464108\pi$
$744$	−0.637727	−0.0233802
$745$	−8.27844	−0.303299
$746$	−31.6407	−1.15845
$747$	−33.1631	−1.21338
$748$	−4.35557	−0.159255
$749$	5.95108	0.217448
$750$	1.85325	0.0676710
$751$	−9.17390	−0.334760	−0.167380	−	0.985892i	$-0.553531\pi$
$751$	−9.17390	−0.334760	−0.167380	+	0.985892i	$0.553531\pi$
$752$	−11.0368	−0.402472
$753$	−2.09246	−0.0762534
$754$	0	0
$755$	−6.91962	−0.251831
$756$	1.46681	0.0533474
$757$	−42.0465	−1.52821	−0.764103	−	0.645094i	$-0.776818\pi$
$757$	−42.0465	−1.52821	−0.764103	+	0.645094i	$0.776818\pi$
$758$	−1.51142	−0.0548972
$759$	2.01580	0.0731690
$760$	−2.20775	−0.0800835
$761$	10.6606	0.386445	0.193223	−	0.981155i	$-0.438106\pi$
$761$	10.6606	0.386445	0.193223	+	0.981155i	$0.438106\pi$
$762$	2.99761	0.108592
$763$	−6.81402	−0.246684
$764$	12.1631	0.440047
$765$	2.88769	0.104405
$766$	15.0881	0.545157
$767$	0	0
$768$	0.246980	0.00891211
$769$	4.84894	0.174857	0.0874286	−	0.996171i	$-0.472135\pi$
$769$	4.84894	0.174857	0.0874286	+	0.996171i	$0.472135\pi$
$770$	2.85086	0.102738
$771$	1.95407	0.0703740
$772$	20.7192	0.745699
$773$	−40.8649	−1.46981	−0.734903	−	0.678172i	$-0.762772\pi$
$773$	−40.8649	−1.46981	−0.734903	+	0.678172i	$0.762772\pi$
$774$	−3.37734	−0.121396
$775$	−11.2500	−0.404111
$776$	−7.13169	−0.256013
$777$	−1.08815	−0.0390370
$778$	9.03252	0.323832
$779$	34.7254	1.24417
$780$	0	0
$781$	23.9982	0.858723
$782$	2.81295	0.100591
$783$	−0.0319329	−0.00114119
$784$	1.00000	0.0357143
$785$	15.0054	0.535565
$786$	−2.96210	−0.105655
$787$	54.9788	1.95978	0.979892	−	0.199530i	$-0.0639416\pi$
$787$	54.9788	1.95978	0.979892	+	0.199530i	$0.0639416\pi$
$788$	21.9801	0.783010
$789$	−2.39852	−0.0853895
$790$	−9.00969	−0.320550
$791$	12.4494	0.442648
$792$	10.4480	0.371254
$793$	0	0
$794$	32.4849	1.15284
$795$	0.401501	0.0142398
$796$	−16.8974	−0.598912
$797$	−27.0446	−0.957969	−0.478985	−	0.877823i	$-0.658995\pi$
$797$	−27.0446	−0.957969	−0.478985	+	0.877823i	$0.658995\pi$
$798$	0.679940	0.0240696
$799$	13.5224	0.478389
$800$	4.35690	0.154040
$801$	34.1323	1.20600
$802$	16.0694	0.567429
$803$	−7.59717	−0.268098
$804$	2.89977	0.102267
$805$	−1.84117	−0.0648926
$806$	0	0
$807$	7.31900	0.257641
$808$	−15.3502	−0.540018
$809$	19.7060	0.692827	0.346413	−	0.938082i	$-0.387399\pi$
$809$	19.7060	0.692827	0.346413	+	0.938082i	$0.387399\pi$
$810$	−6.78017	−0.238231
$811$	36.7743	1.29132	0.645660	−	0.763625i	$-0.276582\pi$
$811$	36.7743	1.29132	0.645660	+	0.763625i	$0.276582\pi$
$812$	−0.0217703	−0.000763986 0
$813$	−5.93841	−0.208269
$814$	−15.6625	−0.548970
$815$	16.8388	0.589837
$816$	−0.302602	−0.0105932
$817$	−3.16362	−0.110681
$818$	−16.5676	−0.579274
$819$	0	0
$820$	10.1153	0.353241
$821$	−22.2620	−0.776951	−0.388475	−	0.921459i	$-0.626998\pi$
$821$	−22.2620	−0.776951	−0.388475	+	0.921459i	$0.626998\pi$
$822$	0.612973	0.0213799
$823$	−38.8133	−1.35295	−0.676473	−	0.736467i	$-0.736492\pi$
$823$	−38.8133	−1.35295	−0.676473	+	0.736467i	$0.736492\pi$
$824$	−8.57673	−0.298784
$825$	−3.82536	−0.133182
$826$	5.55496	0.193282
$827$	−41.1094	−1.42952	−0.714758	−	0.699372i	$-0.753463\pi$
$827$	−41.1094	−1.42952	−0.714758	+	0.699372i	$0.753463\pi$
$828$	−6.74764	−0.234497
$829$	28.5418	0.991298	0.495649	−	0.868523i	$-0.334930\pi$
$829$	28.5418	0.991298	0.495649	+	0.868523i	$0.334930\pi$
$830$	−9.04892	−0.314093
$831$	3.39314	0.117707
$832$	0	0
$833$	−1.22521	−0.0424510
$834$	1.78017	0.0616422
$835$	−7.81940	−0.270601
$836$	9.78687	0.338486
$837$	−3.78746	−0.130914
$838$	22.4045	0.773950
$839$	5.15154	0.177851	0.0889254	−	0.996038i	$-0.471657\pi$
$839$	5.15154	0.177851	0.0889254	+	0.996038i	$0.471657\pi$
$840$	0.198062	0.00683380
$841$	−28.9995	−0.999984
$842$	27.8998	0.961490
$843$	2.20775	0.0760390
$844$	−0.104539	−0.00359840
$845$	0	0
$846$	−32.4373	−1.11522
$847$	−1.63773	−0.0562730
$848$	2.02715	0.0696125
$849$	6.23490	0.213981
$850$	−5.33811	−0.183096
$851$	10.1153	0.346748
$852$	1.66727	0.0571196
$853$	−21.0170	−0.719608	−0.359804	−	0.933028i	$-0.617156\pi$
$853$	−21.0170	−0.719608	−0.359804	+	0.933028i	$0.617156\pi$
$854$	−5.43296	−0.185912
$855$	−6.48858	−0.221905
$856$	5.95108	0.203404
$857$	−42.6185	−1.45582	−0.727910	−	0.685673i	$-0.759508\pi$
$857$	−42.6185	−1.45582	−0.727910	+	0.685673i	$0.759508\pi$
$858$	0	0
$859$	−22.3526	−0.762660	−0.381330	−	0.924439i	$-0.624534\pi$
$859$	−22.3526	−0.762660	−0.381330	+	0.924439i	$0.624534\pi$
$860$	−0.921543	−0.0314243
$861$	−3.11529	−0.106169
$862$	2.51812	0.0857676
$863$	−3.09916	−0.105497	−0.0527484	−	0.998608i	$-0.516798\pi$
$863$	−3.09916	−0.105497	−0.0527484	+	0.998608i	$0.516798\pi$
$864$	1.46681	0.0499020
$865$	−7.63342	−0.259544
$866$	−10.2155	−0.347138
$867$	−3.82790	−0.130002
$868$	−2.58211	−0.0876424
$869$	39.9396	1.35486
$870$	−0.00431187	−0.000146186 0
$871$	0	0
$872$	−6.81402	−0.230752
$873$	−20.9600	−0.709390
$874$	−6.32065	−0.213799
$875$	7.50365	0.253670
$876$	−0.527811	−0.0178331
$877$	−25.7627	−0.869945	−0.434972	−	0.900444i	$-0.643242\pi$
$877$	−25.7627	−0.869945	−0.434972	+	0.900444i	$0.643242\pi$
$878$	22.5985	0.762662
$879$	−1.71976	−0.0580060
$880$	2.85086	0.0961023
$881$	11.6418	0.392221	0.196111	−	0.980582i	$-0.437169\pi$
$881$	11.6418	0.392221	0.196111	+	0.980582i	$0.437169\pi$
$882$	2.93900	0.0989613
$883$	22.1564	0.745624	0.372812	−	0.927907i	$-0.378394\pi$
$883$	22.1564	0.745624	0.372812	+	0.927907i	$0.378394\pi$
$884$	0	0
$885$	1.10023	0.0369837
$886$	38.4946	1.29325
$887$	−11.6950	−0.392680	−0.196340	−	0.980536i	$-0.562906\pi$
$887$	−11.6950	−0.392680	−0.196340	+	0.980536i	$0.562906\pi$
$888$	−1.08815	−0.0365158
$889$	12.1371	0.407064
$890$	9.31336	0.312184
$891$	30.0562	1.00692
$892$	7.11290	0.238158
$893$	−30.3846	−1.01678
$894$	2.54958	0.0852708
$895$	12.6170	0.421741
$896$	1.00000	0.0334077
$897$	0	0
$898$	30.2150	1.00829
$899$	0.0562131	0.00187481
$900$	12.8049	0.426831
$901$	−2.48368	−0.0827434
$902$	−44.8407	−1.49303
$903$	0.283815	0.00944478
$904$	12.4494	0.414059
$905$	8.06292	0.268020
$906$	2.13110	0.0708009
$907$	−55.9579	−1.85805	−0.929026	−	0.370015i	$-0.879353\pi$
$907$	−55.9579	−1.85805	−0.929026	+	0.370015i	$0.879353\pi$
$908$	−7.72348	−0.256313
$909$	−45.1142	−1.49634
$910$	0	0
$911$	−32.6426	−1.08150	−0.540749	−	0.841184i	$-0.681859\pi$
$911$	−32.6426	−1.08150	−0.540749	+	0.841184i	$0.681859\pi$
$912$	0.679940	0.0225151
$913$	40.1135	1.32756
$914$	19.5555	0.646840
$915$	−1.07606	−0.0355736
$916$	22.6939	0.749829
$917$	−11.9933	−0.396054
$918$	−1.79715	−0.0593149
$919$	15.9420	0.525878	0.262939	−	0.964813i	$-0.415308\pi$
$919$	15.9420	0.525878	0.262939	+	0.964813i	$0.415308\pi$
$920$	−1.84117	−0.0607015
$921$	−4.41657	−0.145531
$922$	16.2935	0.536598
$923$	0	0
$924$	−0.878002	−0.0288842
$925$	−19.1957	−0.631150
$926$	12.9554	0.425741
$927$	−25.2070	−0.827907
$928$	−0.0217703	−0.000714644 0
$929$	5.73364	0.188115	0.0940574	−	0.995567i	$-0.470016\pi$
$929$	5.73364	0.188115	0.0940574	+	0.995567i	$0.470016\pi$
$930$	−0.511418	−0.0167700
$931$	2.75302	0.0902266
$932$	−11.2325	−0.367933
$933$	4.08144	0.133620
$934$	−0.134670	−0.00440655
$935$	−3.49289	−0.114230
$936$	0	0
$937$	28.0479	0.916283	0.458142	−	0.888879i	$-0.348515\pi$
$937$	28.0479	0.916283	0.458142	+	0.888879i	$0.348515\pi$
$938$	11.7409	0.383355
$939$	6.02044	0.196470
$940$	−8.85086	−0.288683
$941$	37.0344	1.20729	0.603644	−	0.797254i	$-0.293715\pi$
$941$	37.0344	1.20729	0.603644	+	0.797254i	$0.293715\pi$
$942$	−4.62133	−0.150571
$943$	28.9594	0.943049
$944$	5.55496	0.180798
$945$	1.17629	0.0382648
$946$	4.08516	0.132820
$947$	−28.3370	−0.920830	−0.460415	−	0.887704i	$-0.652299\pi$
$947$	−28.3370	−0.920830	−0.460415	+	0.887704i	$0.652299\pi$
$948$	2.77479	0.0901210
$949$	0	0
$950$	11.9946	0.389157
$951$	−0.00942566	−0.000305648 0
$952$	−1.22521	−0.0397093
$953$	10.3918	0.336624	0.168312	−	0.985734i	$-0.446168\pi$
$953$	10.3918	0.336624	0.168312	+	0.985734i	$0.446168\pi$
$954$	5.95779	0.192890
$955$	9.75409	0.315635
$956$	−14.2241	−0.460042
$957$	0.0191143	0.000617879 0
$958$	40.5013	1.30854
$959$	2.48188	0.0801440
$960$	0.198062	0.00639243
$961$	−24.3327	−0.784927
$962$	0	0
$963$	17.4902	0.563615
$964$	16.6431	0.536038
$965$	16.6155	0.534871
$966$	0.567040	0.0182442
$967$	51.7773	1.66505	0.832523	−	0.553991i	$-0.186896\pi$
$967$	51.7773	1.66505	0.832523	+	0.553991i	$0.186896\pi$
$968$	−1.63773	−0.0526385
$969$	−0.833069	−0.0267620
$970$	−5.71917	−0.183631
$971$	4.59478	0.147453	0.0737267	−	0.997278i	$-0.476511\pi$
$971$	4.59478	0.147453	0.0737267	+	0.997278i	$0.476511\pi$
$972$	6.48858	0.208121
$973$	7.20775	0.231070
$974$	−13.6789	−0.438299
$975$	0	0
$976$	−5.43296	−0.173905
$977$	12.4577	0.398558	0.199279	−	0.979943i	$-0.436140\pi$
$977$	12.4577	0.398558	0.199279	+	0.979943i	$0.436140\pi$
$978$	−5.18598	−0.165829
$979$	−41.2857	−1.31950
$980$	0.801938	0.0256170
$981$	−20.0264	−0.639394
$982$	18.5483	0.591899
$983$	14.1226	0.450441	0.225220	−	0.974308i	$-0.427690\pi$
$983$	14.1226	0.450441	0.225220	+	0.974308i	$0.427690\pi$
$984$	−3.11529	−0.0993119
$985$	17.6267	0.561634
$986$	0.0266731	0.000849446 0
$987$	2.72587	0.0867655
$988$	0	0
$989$	−2.63832	−0.0838936
$990$	8.37867	0.266291
$991$	28.2898	0.898655	0.449327	−	0.893367i	$-0.351664\pi$
$991$	28.2898	0.898655	0.449327	+	0.893367i	$0.351664\pi$
$992$	−2.58211	−0.0819819
$993$	7.27472	0.230856
$994$	6.75063	0.214117
$995$	−13.5506	−0.429584
$996$	2.78687	0.0883054
$997$	59.8044	1.89403	0.947013	−	0.321195i	$-0.104085\pi$
$997$	59.8044	1.89403	0.947013	+	0.321195i	$0.104085\pi$
$998$	10.4349	0.330310
$999$	−6.46250	−0.204464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.v.1.3	✓	3
13.5	odd	4		2366.2.d.n.337.6		6
13.8	odd	4		2366.2.d.n.337.3		6
13.12	even	2		2366.2.a.ba.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.v.1.3	✓	3	1.1	even	1	trivial
2366.2.a.ba.1.3	yes	3	13.12	even	2
2366.2.d.n.337.3		6	13.8	odd	4
2366.2.d.n.337.6		6	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} +0.801938 q^{5} -0.246980 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.93900 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.246980 q^{3} +1.00000 q^{4} +0.801938 q^{5} -0.246980 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.93900 q^{9} -0.801938 q^{10} +3.55496 q^{11} +0.246980 q^{12} +1.00000 q^{14} +0.198062 q^{15} +1.00000 q^{16} -1.22521 q^{17} +2.93900 q^{18} +2.75302 q^{19} +0.801938 q^{20} -0.246980 q^{21} -3.55496 q^{22} +2.29590 q^{23} -0.246980 q^{24} -4.35690 q^{25} -1.46681 q^{27} -1.00000 q^{28} +0.0217703 q^{29} -0.198062 q^{30} +2.58211 q^{31} -1.00000 q^{32} +0.878002 q^{33} +1.22521 q^{34} -0.801938 q^{35} -2.93900 q^{36} +4.40581 q^{37} -2.75302 q^{38} -0.801938 q^{40} +12.6136 q^{41} +0.246980 q^{42} -1.14914 q^{43} +3.55496 q^{44} -2.35690 q^{45} -2.29590 q^{46} -11.0368 q^{47} +0.246980 q^{48} +1.00000 q^{49} +4.35690 q^{50} -0.302602 q^{51} +2.02715 q^{53} +1.46681 q^{54} +2.85086 q^{55} +1.00000 q^{56} +0.679940 q^{57} -0.0217703 q^{58} +5.55496 q^{59} +0.198062 q^{60} -5.43296 q^{61} -2.58211 q^{62} +2.93900 q^{63} +1.00000 q^{64} -0.878002 q^{66} +11.7409 q^{67} -1.22521 q^{68} +0.567040 q^{69} +0.801938 q^{70} +6.75063 q^{71} +2.93900 q^{72} -2.13706 q^{73} -4.40581 q^{74} -1.07606 q^{75} +2.75302 q^{76} -3.55496 q^{77} +11.2349 q^{79} +0.801938 q^{80} +8.45473 q^{81} -12.6136 q^{82} +11.2838 q^{83} -0.246980 q^{84} -0.982542 q^{85} +1.14914 q^{86} +0.00537681 q^{87} -3.55496 q^{88} -11.6136 q^{89} +2.35690 q^{90} +2.29590 q^{92} +0.637727 q^{93} +11.0368 q^{94} +2.20775 q^{95} -0.246980 q^{96} +7.13169 q^{97} -1.00000 q^{98} -10.4480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{5} + 4 q^{6} - 3 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 2 * q^5 + 4 * q^6 - 3 * q^7 - 3 * q^8 + q^9	\( 3 q - 3 q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{5} + 4 q^{6} - 3 q^{7} - 3 q^{8} + q^{9} + 2 q^{10} + 11 q^{11} - 4 q^{12} + 3 q^{14} + 5 q^{15} + 3 q^{16} - 2 q^{17} - q^{18} + 13 q^{19} - 2 q^{20} + 4 q^{21} - 11 q^{22} - 7 q^{23} + 4 q^{24} - 9 q^{25} - q^{27} - 3 q^{28} - 3 q^{29} - 5 q^{30} + 2 q^{31} - 3 q^{32} - 17 q^{33} + 2 q^{34} + 2 q^{35} + q^{36} - 13 q^{38} + 2 q^{40} + 7 q^{41} - 4 q^{42} - 17 q^{43} + 11 q^{44} - 3 q^{45} + 7 q^{46} - 5 q^{47} - 4 q^{48} + 3 q^{49} + 9 q^{50} - 9 q^{51} + q^{54} - 5 q^{55} + 3 q^{56} - 22 q^{57} + 3 q^{58} + 17 q^{59} + 5 q^{60} + 3 q^{61} - 2 q^{62} - q^{63} + 3 q^{64} + 17 q^{66} + 21 q^{67} - 2 q^{68} + 21 q^{69} - 2 q^{70} - 16 q^{71} - q^{72} - q^{73} + 12 q^{75} + 13 q^{76} - 11 q^{77} + 10 q^{79} - 2 q^{80} + 3 q^{81} - 7 q^{82} + q^{83} + 4 q^{84} + 13 q^{85} + 17 q^{86} - 3 q^{87} - 11 q^{88} - 4 q^{89} + 3 q^{90} - 7 q^{92} + 9 q^{93} + 5 q^{94} - 11 q^{95} + 4 q^{96} + 19 q^{97} - 3 q^{98} + 13 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 4 * q^3 + 3 * q^4 - 2 * q^5 + 4 * q^6 - 3 * q^7 - 3 * q^8 + q^9 + 2 * q^10 + 11 * q^11 - 4 * q^12 + 3 * q^14 + 5 * q^15 + 3 * q^16 - 2 * q^17 - q^18 + 13 * q^19 - 2 * q^20 + 4 * q^21 - 11 * q^22 - 7 * q^23 + 4 * q^24 - 9 * q^25 - q^27 - 3 * q^28 - 3 * q^29 - 5 * q^30 + 2 * q^31 - 3 * q^32 - 17 * q^33 + 2 * q^34 + 2 * q^35 + q^36 - 13 * q^38 + 2 * q^40 + 7 * q^41 - 4 * q^42 - 17 * q^43 + 11 * q^44 - 3 * q^45 + 7 * q^46 - 5 * q^47 - 4 * q^48 + 3 * q^49 + 9 * q^50 - 9 * q^51 + q^54 - 5 * q^55 + 3 * q^56 - 22 * q^57 + 3 * q^58 + 17 * q^59 + 5 * q^60 + 3 * q^61 - 2 * q^62 - q^63 + 3 * q^64 + 17 * q^66 + 21 * q^67 - 2 * q^68 + 21 * q^69 - 2 * q^70 - 16 * q^71 - q^72 - q^73 + 12 * q^75 + 13 * q^76 - 11 * q^77 + 10 * q^79 - 2 * q^80 + 3 * q^81 - 7 * q^82 + q^83 + 4 * q^84 + 13 * q^85 + 17 * q^86 - 3 * q^87 - 11 * q^88 - 4 * q^89 + 3 * q^90 - 7 * q^92 + 9 * q^93 + 5 * q^94 - 11 * q^95 + 4 * q^96 + 19 * q^97 - 3 * q^98 + 13 * q^99

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