LMFDB - Embedded newform 2366.2.a.z.1.2

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:	$1$
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			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.55496 q^{3} +1.00000 q^{4} -2.49396 q^{5} -1.55496 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.582105 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.55496 q^{3} +1.00000 q^{4} -2.49396 q^{5} -1.55496 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.582105 q^{9} -2.49396 q^{10} +5.74094 q^{11} -1.55496 q^{12} -1.00000 q^{14} +3.87800 q^{15} +1.00000 q^{16} -0.753020 q^{17} -0.582105 q^{18} +3.89977 q^{19} -2.49396 q^{20} +1.55496 q^{21} +5.74094 q^{22} -4.89008 q^{23} -1.55496 q^{24} +1.21983 q^{25} +5.57002 q^{27} -1.00000 q^{28} +0.890084 q^{29} +3.87800 q^{30} -7.60388 q^{31} +1.00000 q^{32} -8.92692 q^{33} -0.753020 q^{34} +2.49396 q^{35} -0.582105 q^{36} -2.89008 q^{37} +3.89977 q^{38} -2.49396 q^{40} -10.1196 q^{41} +1.55496 q^{42} +11.1860 q^{43} +5.74094 q^{44} +1.45175 q^{45} -4.89008 q^{46} +4.21983 q^{47} -1.55496 q^{48} +1.00000 q^{49} +1.21983 q^{50} +1.17092 q^{51} -1.50604 q^{53} +5.57002 q^{54} -14.3177 q^{55} -1.00000 q^{56} -6.06398 q^{57} +0.890084 q^{58} -10.1032 q^{59} +3.87800 q^{60} -3.82371 q^{61} -7.60388 q^{62} +0.582105 q^{63} +1.00000 q^{64} -8.92692 q^{66} -8.14675 q^{67} -0.753020 q^{68} +7.60388 q^{69} +2.49396 q^{70} +6.59179 q^{71} -0.582105 q^{72} -13.2567 q^{73} -2.89008 q^{74} -1.89679 q^{75} +3.89977 q^{76} -5.74094 q^{77} -17.3056 q^{79} -2.49396 q^{80} -6.91484 q^{81} -10.1196 q^{82} -1.92394 q^{83} +1.55496 q^{84} +1.87800 q^{85} +11.1860 q^{86} -1.38404 q^{87} +5.74094 q^{88} -11.8291 q^{89} +1.45175 q^{90} -4.89008 q^{92} +11.8237 q^{93} +4.21983 q^{94} -9.72587 q^{95} -1.55496 q^{96} -8.75302 q^{97} +1.00000 q^{98} -3.34183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 4 * q^9	\( 3 q + 3 q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 4 q^{9} + 2 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{14} - 8 q^{15} + 3 q^{16} - 7 q^{17} + 4 q^{18} - 11 q^{19} + 2 q^{20} + 5 q^{21} + 3 q^{22} - 14 q^{23} - 5 q^{24} + 5 q^{25} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 14 q^{31} + 3 q^{32} + 2 q^{33} - 7 q^{34} - 2 q^{35} + 4 q^{36} - 8 q^{37} - 11 q^{38} + 2 q^{40} - 9 q^{41} + 5 q^{42} + 19 q^{43} + 3 q^{44} + 26 q^{45} - 14 q^{46} + 14 q^{47} - 5 q^{48} + 3 q^{49} + 5 q^{50} + 14 q^{51} - 14 q^{53} - 8 q^{54} - 26 q^{55} - 3 q^{56} + 16 q^{57} + 2 q^{58} - 9 q^{59} - 8 q^{60} - 4 q^{61} - 14 q^{62} - 4 q^{63} + 3 q^{64} + 2 q^{66} + 3 q^{67} - 7 q^{68} + 14 q^{69} - 2 q^{70} - 8 q^{71} + 4 q^{72} - 13 q^{73} - 8 q^{74} - 27 q^{75} - 11 q^{76} - 3 q^{77} - 16 q^{79} + 2 q^{80} + 27 q^{81} - 9 q^{82} - 21 q^{83} + 5 q^{84} - 14 q^{85} + 19 q^{86} + 6 q^{87} + 3 q^{88} - 25 q^{89} + 26 q^{90} - 14 q^{92} + 28 q^{93} + 14 q^{94} - 40 q^{95} - 5 q^{96} - 31 q^{97} + 3 q^{98} - 31 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 4 * q^9 + 2 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^14 - 8 * q^15 + 3 * q^16 - 7 * q^17 + 4 * q^18 - 11 * q^19 + 2 * q^20 + 5 * q^21 + 3 * q^22 - 14 * q^23 - 5 * q^24 + 5 * q^25 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 14 * q^31 + 3 * q^32 + 2 * q^33 - 7 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 11 * q^38 + 2 * q^40 - 9 * q^41 + 5 * q^42 + 19 * q^43 + 3 * q^44 + 26 * q^45 - 14 * q^46 + 14 * q^47 - 5 * q^48 + 3 * q^49 + 5 * q^50 + 14 * q^51 - 14 * q^53 - 8 * q^54 - 26 * q^55 - 3 * q^56 + 16 * q^57 + 2 * q^58 - 9 * q^59 - 8 * q^60 - 4 * q^61 - 14 * q^62 - 4 * q^63 + 3 * q^64 + 2 * q^66 + 3 * q^67 - 7 * q^68 + 14 * q^69 - 2 * q^70 - 8 * q^71 + 4 * q^72 - 13 * q^73 - 8 * q^74 - 27 * q^75 - 11 * q^76 - 3 * q^77 - 16 * q^79 + 2 * q^80 + 27 * q^81 - 9 * q^82 - 21 * q^83 + 5 * q^84 - 14 * q^85 + 19 * q^86 + 6 * q^87 + 3 * q^88 - 25 * q^89 + 26 * q^90 - 14 * q^92 + 28 * q^93 + 14 * q^94 - 40 * q^95 - 5 * q^96 - 31 * q^97 + 3 * q^98 - 31 * 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
$3$	−1.55496	−0.897755	−0.448878	−	0.893593i	$-0.648176\pi$
$3$	−1.55496	−0.897755	−0.448878	+	0.893593i	$0.648176\pi$
$4$	1.00000	0.500000
$5$	−2.49396	−1.11533	−0.557666	−	0.830065i	$-0.688303\pi$
$5$	−2.49396	−1.11533	−0.557666	+	0.830065i	$0.688303\pi$
$6$	−1.55496	−0.634809
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−0.582105	−0.194035
$10$	−2.49396	−0.788659
$11$	5.74094	1.73096	0.865479	−	0.500945i	$-0.167014\pi$
$11$	5.74094	1.73096	0.865479	+	0.500945i	$0.167014\pi$
$12$	−1.55496	−0.448878
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	3.87800	1.00130
$16$	1.00000	0.250000
$17$	−0.753020	−0.182634	−0.0913171	−	0.995822i	$-0.529108\pi$
$17$	−0.753020	−0.182634	−0.0913171	+	0.995822i	$0.529108\pi$
$18$	−0.582105	−0.137204
$19$	3.89977	0.894669	0.447335	−	0.894367i	$-0.352373\pi$
$19$	3.89977	0.894669	0.447335	+	0.894367i	$0.352373\pi$
$20$	−2.49396	−0.557666
$21$	1.55496	0.339320
$22$	5.74094	1.22397
$23$	−4.89008	−1.01965	−0.509826	−	0.860277i	$-0.670290\pi$
$23$	−4.89008	−1.01965	−0.509826	+	0.860277i	$0.670290\pi$
$24$	−1.55496	−0.317404
$25$	1.21983	0.243967
$26$	0	0
$27$	5.57002	1.07195
$28$	−1.00000	−0.188982
$29$	0.890084	0.165284	0.0826422	−	0.996579i	$-0.473664\pi$
$29$	0.890084	0.165284	0.0826422	+	0.996579i	$0.473664\pi$
$30$	3.87800	0.708023
$31$	−7.60388	−1.36570	−0.682848	−	0.730560i	$-0.739259\pi$
$31$	−7.60388	−1.36570	−0.682848	+	0.730560i	$0.739259\pi$
$32$	1.00000	0.176777
$33$	−8.92692	−1.55398
$34$	−0.753020	−0.129142
$35$	2.49396	0.421556
$36$	−0.582105	−0.0970175
$37$	−2.89008	−0.475127	−0.237563	−	0.971372i	$-0.576349\pi$
$37$	−2.89008	−0.475127	−0.237563	+	0.971372i	$0.576349\pi$
$38$	3.89977	0.632627
$39$	0	0
$40$	−2.49396	−0.394330
$41$	−10.1196	−1.58042	−0.790208	−	0.612838i	$-0.790028\pi$
$41$	−10.1196	−1.58042	−0.790208	+	0.612838i	$0.790028\pi$
$42$	1.55496	0.239935
$43$	11.1860	1.70585	0.852923	−	0.522037i	$-0.174828\pi$
$43$	11.1860	1.70585	0.852923	+	0.522037i	$0.174828\pi$
$44$	5.74094	0.865479
$45$	1.45175	0.216414
$46$	−4.89008	−0.721004
$47$	4.21983	0.615526	0.307763	−	0.951463i	$-0.400420\pi$
$47$	4.21983	0.615526	0.307763	+	0.951463i	$0.400420\pi$
$48$	−1.55496	−0.224439
$49$	1.00000	0.142857
$50$	1.21983	0.172510
$51$	1.17092	0.163961
$52$	0	0
$53$	−1.50604	−0.206871	−0.103435	−	0.994636i	$-0.532983\pi$
$53$	−1.50604	−0.206871	−0.103435	+	0.994636i	$0.532983\pi$
$54$	5.57002	0.757984
$55$	−14.3177	−1.93059
$56$	−1.00000	−0.133631
$57$	−6.06398	−0.803194
$58$	0.890084	0.116874
$59$	−10.1032	−1.31533	−0.657663	−	0.753312i	$-0.728455\pi$
$59$	−10.1032	−1.31533	−0.657663	+	0.753312i	$0.728455\pi$
$60$	3.87800	0.500648
$61$	−3.82371	−0.489576	−0.244788	−	0.969577i	$-0.578718\pi$
$61$	−3.82371	−0.489576	−0.244788	+	0.969577i	$0.578718\pi$
$62$	−7.60388	−0.965693
$63$	0.582105	0.0733384
$64$	1.00000	0.125000
$65$	0	0
$66$	−8.92692	−1.09883
$67$	−8.14675	−0.995284	−0.497642	−	0.867382i	$-0.665801\pi$
$67$	−8.14675	−0.995284	−0.497642	+	0.867382i	$0.665801\pi$
$68$	−0.753020	−0.0913171
$69$	7.60388	0.915399
$70$	2.49396	0.298085
$71$	6.59179	0.782302	0.391151	−	0.920327i	$-0.372077\pi$
$71$	6.59179	0.782302	0.391151	+	0.920327i	$0.372077\pi$
$72$	−0.582105	−0.0686018
$73$	−13.2567	−1.55158	−0.775788	−	0.630994i	$-0.782647\pi$
$73$	−13.2567	−1.55158	−0.775788	+	0.630994i	$0.782647\pi$
$74$	−2.89008	−0.335965
$75$	−1.89679	−0.219022
$76$	3.89977	0.447335
$77$	−5.74094	−0.654241
$78$	0	0
$79$	−17.3056	−1.94703	−0.973515	−	0.228622i	$-0.926578\pi$
$79$	−17.3056	−1.94703	−0.973515	+	0.228622i	$0.926578\pi$
$80$	−2.49396	−0.278833
$81$	−6.91484	−0.768315
$82$	−10.1196	−1.11752
$83$	−1.92394	−0.211179	−0.105590	−	0.994410i	$-0.533673\pi$
$83$	−1.92394	−0.211179	−0.105590	+	0.994410i	$0.533673\pi$
$84$	1.55496	0.169660
$85$	1.87800	0.203698
$86$	11.1860	1.20622
$87$	−1.38404	−0.148385
$88$	5.74094	0.611986
$89$	−11.8291	−1.25388	−0.626940	−	0.779067i	$-0.715693\pi$
$89$	−11.8291	−1.25388	−0.626940	+	0.779067i	$0.715693\pi$
$90$	1.45175	0.153028
$91$	0	0
$92$	−4.89008	−0.509826
$93$	11.8237	1.22606
$94$	4.21983	0.435242
$95$	−9.72587	−0.997854
$96$	−1.55496	−0.158702
$97$	−8.75302	−0.888735	−0.444367	−	0.895845i	$-0.646571\pi$
$97$	−8.75302	−0.888735	−0.444367	+	0.895845i	$0.646571\pi$
$98$	1.00000	0.101015
$99$	−3.34183	−0.335867
$100$	1.21983	0.121983
$101$	3.20775	0.319183	0.159592	−	0.987183i	$-0.448982\pi$
$101$	3.20775	0.319183	0.159592	+	0.987183i	$0.448982\pi$
$102$	1.17092	0.115938
$103$	4.59179	0.452443	0.226221	−	0.974076i	$-0.427363\pi$
$103$	4.59179	0.452443	0.226221	+	0.974076i	$0.427363\pi$
$104$	0	0
$105$	−3.87800	−0.378454
$106$	−1.50604	−0.146280
$107$	−13.6015	−1.31490	−0.657452	−	0.753496i	$-0.728366\pi$
$107$	−13.6015	−1.31490	−0.657452	+	0.753496i	$0.728366\pi$
$108$	5.57002	0.535976
$109$	−14.9095	−1.42807	−0.714034	−	0.700111i	$-0.753134\pi$
$109$	−14.9095	−1.42807	−0.714034	+	0.700111i	$0.753134\pi$
$110$	−14.3177	−1.36514
$111$	4.49396	0.426548
$112$	−1.00000	−0.0944911
$113$	16.9825	1.59758	0.798792	−	0.601608i	$-0.205473\pi$
$113$	16.9825	1.59758	0.798792	+	0.601608i	$0.205473\pi$
$114$	−6.06398	−0.567944
$115$	12.1957	1.13725
$116$	0.890084	0.0826422
$117$	0	0
$118$	−10.1032	−0.930076
$119$	0.753020	0.0690293
$120$	3.87800	0.354012
$121$	21.9584	1.99622
$122$	−3.82371	−0.346182
$123$	15.7356	1.41883
$124$	−7.60388	−0.682848
$125$	9.42758	0.843229
$126$	0.582105	0.0518581
$127$	−0.987918	−0.0876636	−0.0438318	−	0.999039i	$-0.513957\pi$
$127$	−0.987918	−0.0876636	−0.0438318	+	0.999039i	$0.513957\pi$
$128$	1.00000	0.0883883
$129$	−17.3937	−1.53143
$130$	0	0
$131$	−9.13169	−0.797839	−0.398920	−	0.916986i	$-0.630615\pi$
$131$	−9.13169	−0.797839	−0.398920	+	0.916986i	$0.630615\pi$
$132$	−8.92692	−0.776989
$133$	−3.89977	−0.338153
$134$	−8.14675	−0.703772
$135$	−13.8914	−1.19558
$136$	−0.753020	−0.0645710
$137$	18.4209	1.57380	0.786901	−	0.617079i	$-0.211684\pi$
$137$	18.4209	1.57380	0.786901	+	0.617079i	$0.211684\pi$
$138$	7.60388	0.647285
$139$	−9.24698	−0.784319	−0.392159	−	0.919897i	$-0.628272\pi$
$139$	−9.24698	−0.784319	−0.392159	+	0.919897i	$0.628272\pi$
$140$	2.49396	0.210778
$141$	−6.56166	−0.552592
$142$	6.59179	0.553171
$143$	0	0
$144$	−0.582105	−0.0485088
$145$	−2.21983	−0.184347
$146$	−13.2567	−1.09713
$147$	−1.55496	−0.128251
$148$	−2.89008	−0.237563
$149$	−13.5060	−1.10646	−0.553229	−	0.833029i	$-0.686605\pi$
$149$	−13.5060	−1.10646	−0.553229	+	0.833029i	$0.686605\pi$
$150$	−1.89679	−0.154872
$151$	−4.05429	−0.329934	−0.164967	−	0.986299i	$-0.552752\pi$
$151$	−4.05429	−0.329934	−0.164967	+	0.986299i	$0.552752\pi$
$152$	3.89977	0.316313
$153$	0.438337	0.0354375
$154$	−5.74094	−0.462618
$155$	18.9638	1.52321
$156$	0	0
$157$	0.176292	0.0140696	0.00703482	−	0.999975i	$-0.497761\pi$
$157$	0.176292	0.0140696	0.00703482	+	0.999975i	$0.497761\pi$
$158$	−17.3056	−1.37676
$159$	2.34183	0.185719
$160$	−2.49396	−0.197165
$161$	4.89008	0.385393
$162$	−6.91484	−0.543281
$163$	14.3763	1.12604	0.563018	−	0.826444i	$-0.309640\pi$
$163$	14.3763	1.12604	0.563018	+	0.826444i	$0.309640\pi$
$164$	−10.1196	−0.790208
$165$	22.2634	1.73320
$166$	−1.92394	−0.149326
$167$	−24.0194	−1.85868	−0.929338	−	0.369231i	$-0.879621\pi$
$167$	−24.0194	−1.85868	−0.929338	+	0.369231i	$0.879621\pi$
$168$	1.55496	0.119968
$169$	0	0
$170$	1.87800	0.144036
$171$	−2.27008	−0.173597
$172$	11.1860	0.852923
$173$	4.84654	0.368476	0.184238	−	0.982882i	$-0.441018\pi$
$173$	4.84654	0.368476	0.184238	+	0.982882i	$0.441018\pi$
$174$	−1.38404	−0.104924
$175$	−1.21983	−0.0922107
$176$	5.74094	0.432740
$177$	15.7101	1.18084
$178$	−11.8291	−0.886627
$179$	20.9487	1.56578	0.782889	−	0.622161i	$-0.213745\pi$
$179$	20.9487	1.56578	0.782889	+	0.622161i	$0.213745\pi$
$180$	1.45175	0.108207
$181$	−6.53750	−0.485929	−0.242964	−	0.970035i	$-0.578120\pi$
$181$	−6.53750	−0.485929	−0.242964	+	0.970035i	$0.578120\pi$
$182$	0	0
$183$	5.94571	0.439519
$184$	−4.89008	−0.360502
$185$	7.20775	0.529924
$186$	11.8237	0.866956
$187$	−4.32304	−0.316132
$188$	4.21983	0.307763
$189$	−5.57002	−0.405160
$190$	−9.72587	−0.705589
$191$	−13.1293	−0.950002	−0.475001	−	0.879985i	$-0.657552\pi$
$191$	−13.1293	−0.950002	−0.475001	+	0.879985i	$0.657552\pi$
$192$	−1.55496	−0.112219
$193$	−5.40581	−0.389119	−0.194559	−	0.980891i	$-0.562328\pi$
$193$	−5.40581	−0.389119	−0.194559	+	0.980891i	$0.562328\pi$
$194$	−8.75302	−0.628430
$195$	0	0
$196$	1.00000	0.0714286
$197$	−8.71379	−0.620832	−0.310416	−	0.950601i	$-0.600468\pi$
$197$	−8.71379	−0.620832	−0.310416	+	0.950601i	$0.600468\pi$
$198$	−3.34183	−0.237494
$199$	23.5690	1.67076	0.835380	−	0.549673i	$-0.185248\pi$
$199$	23.5690	1.67076	0.835380	+	0.549673i	$0.185248\pi$
$200$	1.21983	0.0862552
$201$	12.6679	0.893522
$202$	3.20775	0.225697
$203$	−0.890084	−0.0624716
$204$	1.17092	0.0819805
$205$	25.2379	1.76269
$206$	4.59179	0.319925
$207$	2.84654	0.197848
$208$	0	0
$209$	22.3884	1.54863
$210$	−3.87800	−0.267608
$211$	19.7952	1.36276	0.681380	−	0.731930i	$-0.261380\pi$
$211$	19.7952	1.36276	0.681380	+	0.731930i	$0.261380\pi$
$212$	−1.50604	−0.103435
$213$	−10.2500	−0.702316
$214$	−13.6015	−0.929778
$215$	−27.8974	−1.90259
$216$	5.57002	0.378992
$217$	7.60388	0.516185
$218$	−14.9095	−1.00980
$219$	20.6136	1.39294
$220$	−14.3177	−0.965297
$221$	0	0
$222$	4.49396	0.301615
$223$	23.7211	1.58848	0.794241	−	0.607603i	$-0.207869\pi$
$223$	23.7211	1.58848	0.794241	+	0.607603i	$0.207869\pi$
$224$	−1.00000	−0.0668153
$225$	−0.710071	−0.0473381
$226$	16.9825	1.12966
$227$	6.88471	0.456954	0.228477	−	0.973549i	$-0.426625\pi$
$227$	6.88471	0.456954	0.228477	+	0.973549i	$0.426625\pi$
$228$	−6.06398	−0.401597
$229$	−7.28621	−0.481486	−0.240743	−	0.970589i	$-0.577391\pi$
$229$	−7.28621	−0.481486	−0.240743	+	0.970589i	$0.577391\pi$
$230$	12.1957	0.804159
$231$	8.92692	0.587348
$232$	0.890084	0.0584369
$233$	−0.445042	−0.0291557	−0.0145778	−	0.999894i	$-0.504640\pi$
$233$	−0.445042	−0.0291557	−0.0145778	+	0.999894i	$0.504640\pi$
$234$	0	0
$235$	−10.5241	−0.686516
$236$	−10.1032	−0.657663
$237$	26.9095	1.74796
$238$	0.753020	0.0488111
$239$	−23.5797	−1.52524	−0.762622	−	0.646844i	$-0.776089\pi$
$239$	−23.5797	−1.52524	−0.762622	+	0.646844i	$0.776089\pi$
$240$	3.87800	0.250324
$241$	−8.21983	−0.529486	−0.264743	−	0.964319i	$-0.585287\pi$
$241$	−8.21983	−0.529486	−0.264743	+	0.964319i	$0.585287\pi$
$242$	21.9584	1.41154
$243$	−5.95779	−0.382192
$244$	−3.82371	−0.244788
$245$	−2.49396	−0.159333
$246$	15.7356	1.00326
$247$	0	0
$248$	−7.60388	−0.482847
$249$	2.99164	0.189587
$250$	9.42758	0.596253
$251$	−15.7409	−0.993559	−0.496780	−	0.867877i	$-0.665484\pi$
$251$	−15.7409	−0.993559	−0.496780	+	0.867877i	$0.665484\pi$
$252$	0.582105	0.0366692
$253$	−28.0737	−1.76498
$254$	−0.987918	−0.0619875
$255$	−2.92021	−0.182871
$256$	1.00000	0.0625000
$257$	8.77910	0.547625	0.273813	−	0.961783i	$-0.411715\pi$
$257$	8.77910	0.547625	0.273813	+	0.961783i	$0.411715\pi$
$258$	−17.3937	−1.08289
$259$	2.89008	0.179581
$260$	0	0
$261$	−0.518122	−0.0320710
$262$	−9.13169	−0.564157
$263$	−3.32975	−0.205321	−0.102661	−	0.994716i	$-0.532736\pi$
$263$	−3.32975	−0.205321	−0.102661	+	0.994716i	$0.532736\pi$
$264$	−8.92692	−0.549414
$265$	3.75600	0.230730
$266$	−3.89977	−0.239110
$267$	18.3937	1.12568
$268$	−8.14675	−0.497642
$269$	4.84654	0.295499	0.147749	−	0.989025i	$-0.452797\pi$
$269$	4.84654	0.295499	0.147749	+	0.989025i	$0.452797\pi$
$270$	−13.8914	−0.845404
$271$	−27.5991	−1.67653	−0.838263	−	0.545267i	$-0.816428\pi$
$271$	−27.5991	−1.67653	−0.838263	+	0.545267i	$0.816428\pi$
$272$	−0.753020	−0.0456586
$273$	0	0
$274$	18.4209	1.11285
$275$	7.00298	0.422296
$276$	7.60388	0.457700
$277$	−10.4698	−0.629069	−0.314535	−	0.949246i	$-0.601848\pi$
$277$	−10.4698	−0.629069	−0.314535	+	0.949246i	$0.601848\pi$
$278$	−9.24698	−0.554597
$279$	4.42626	0.264993
$280$	2.49396	0.149043
$281$	13.0901	0.780888	0.390444	−	0.920627i	$-0.372322\pi$
$281$	13.0901	0.780888	0.390444	+	0.920627i	$0.372322\pi$
$282$	−6.56166	−0.390741
$283$	−13.2403	−0.787053	−0.393526	−	0.919313i	$-0.628745\pi$
$283$	−13.2403	−0.787053	−0.393526	+	0.919313i	$0.628745\pi$
$284$	6.59179	0.391151
$285$	15.1233	0.895829
$286$	0	0
$287$	10.1196	0.597341
$288$	−0.582105	−0.0343009
$289$	−16.4330	−0.966645
$290$	−2.21983	−0.130353
$291$	13.6106	0.797866
$292$	−13.2567	−0.775788
$293$	16.6703	0.973886	0.486943	−	0.873434i	$-0.338112\pi$
$293$	16.6703	0.973886	0.486943	+	0.873434i	$0.338112\pi$
$294$	−1.55496	−0.0906870
$295$	25.1970	1.46703
$296$	−2.89008	−0.167983
$297$	31.9772	1.85550
$298$	−13.5060	−0.782384
$299$	0	0
$300$	−1.89679	−0.109511
$301$	−11.1860	−0.644749
$302$	−4.05429	−0.233298
$303$	−4.98792	−0.286548
$304$	3.89977	0.223667
$305$	9.53617	0.546040
$306$	0.438337	0.0250581
$307$	11.6625	0.665613	0.332806	−	0.942995i	$-0.392004\pi$
$307$	11.6625	0.665613	0.332806	+	0.942995i	$0.392004\pi$
$308$	−5.74094	−0.327120
$309$	−7.14005	−0.406183
$310$	18.9638	1.07707
$311$	6.29350	0.356872	0.178436	−	0.983952i	$-0.442896\pi$
$311$	6.29350	0.356872	0.178436	+	0.983952i	$0.442896\pi$
$312$	0	0
$313$	27.2470	1.54009	0.770045	−	0.637989i	$-0.220234\pi$
$313$	27.2470	1.54009	0.770045	+	0.637989i	$0.220234\pi$
$314$	0.176292	0.00994873
$315$	−1.45175	−0.0817967
$316$	−17.3056	−0.973515
$317$	23.4819	1.31887	0.659437	−	0.751760i	$-0.270795\pi$
$317$	23.4819	1.31887	0.659437	+	0.751760i	$0.270795\pi$
$318$	2.34183	0.131323
$319$	5.10992	0.286100
$320$	−2.49396	−0.139417
$321$	21.1497	1.18046
$322$	4.89008	0.272514
$323$	−2.93661	−0.163397
$324$	−6.91484	−0.384158
$325$	0	0
$326$	14.3763	0.796228
$327$	23.1836	1.28206
$328$	−10.1196	−0.558762
$329$	−4.21983	−0.232647
$330$	22.2634	1.22556
$331$	−17.6233	−0.968662	−0.484331	−	0.874885i	$-0.660937\pi$
$331$	−17.6233	−0.968662	−0.484331	+	0.874885i	$0.660937\pi$
$332$	−1.92394	−0.105590
$333$	1.68233	0.0921913
$334$	−24.0194	−1.31428
$335$	20.3177	1.11007
$336$	1.55496	0.0848299
$337$	22.7463	1.23907	0.619535	−	0.784969i	$-0.287321\pi$
$337$	22.7463	1.23907	0.619535	+	0.784969i	$0.287321\pi$
$338$	0	0
$339$	−26.4071	−1.43424
$340$	1.87800	0.101849
$341$	−43.6534	−2.36396
$342$	−2.27008	−0.122752
$343$	−1.00000	−0.0539949
$344$	11.1860	0.603108
$345$	−18.9638	−1.02097
$346$	4.84654	0.260552
$347$	0.987918	0.0530342	0.0265171	−	0.999648i	$-0.491558\pi$
$347$	0.987918	0.0530342	0.0265171	+	0.999648i	$0.491558\pi$
$348$	−1.38404	−0.0741925
$349$	−3.05562	−0.163564	−0.0817819	−	0.996650i	$-0.526061\pi$
$349$	−3.05562	−0.163564	−0.0817819	+	0.996650i	$0.526061\pi$
$350$	−1.21983	−0.0652028
$351$	0	0
$352$	5.74094	0.305993
$353$	29.1444	1.55120	0.775599	−	0.631226i	$-0.217448\pi$
$353$	29.1444	1.55120	0.775599	+	0.631226i	$0.217448\pi$
$354$	15.7101	0.834981
$355$	−16.4397	−0.872527
$356$	−11.8291	−0.626940
$357$	−1.17092	−0.0619714
$358$	20.9487	1.10717
$359$	−33.6969	−1.77846	−0.889228	−	0.457465i	$-0.848758\pi$
$359$	−33.6969	−1.77846	−0.889228	+	0.457465i	$0.848758\pi$
$360$	1.45175	0.0765138
$361$	−3.79178	−0.199567
$362$	−6.53750	−0.343603
$363$	−34.1444	−1.79211
$364$	0	0
$365$	33.0616	1.73052
$366$	5.94571	0.310787
$367$	0.0193774	0.00101149	0.000505745	−	1.00000i	$-0.499839\pi$
$367$	0.0193774	0.00101149	0.000505745		1.00000i	$0.499839\pi$
$368$	−4.89008	−0.254913
$369$	5.89067	0.306656
$370$	7.20775	0.374713
$371$	1.50604	0.0781897
$372$	11.8237	0.613031
$373$	−8.76809	−0.453994	−0.226997	−	0.973895i	$-0.572891\pi$
$373$	−8.76809	−0.453994	−0.226997	+	0.973895i	$0.572891\pi$
$374$	−4.32304	−0.223539
$375$	−14.6595	−0.757013
$376$	4.21983	0.217621
$377$	0	0
$378$	−5.57002	−0.286491
$379$	−25.4873	−1.30919	−0.654596	−	0.755979i	$-0.727161\pi$
$379$	−25.4873	−1.30919	−0.654596	+	0.755979i	$0.727161\pi$
$380$	−9.72587	−0.498927
$381$	1.53617	0.0787005
$382$	−13.1293	−0.671753
$383$	10.4590	0.534432	0.267216	−	0.963637i	$-0.413896\pi$
$383$	10.4590	0.534432	0.267216	+	0.963637i	$0.413896\pi$
$384$	−1.55496	−0.0793511
$385$	14.3177	0.729696
$386$	−5.40581	−0.275149
$387$	−6.51142	−0.330994
$388$	−8.75302	−0.444367
$389$	−11.9952	−0.608182	−0.304091	−	0.952643i	$-0.598353\pi$
$389$	−11.9952	−0.608182	−0.304091	+	0.952643i	$0.598353\pi$
$390$	0	0
$391$	3.68233	0.186224
$392$	1.00000	0.0505076
$393$	14.1994	0.716264
$394$	−8.71379	−0.438994
$395$	43.1594	2.17159
$396$	−3.34183	−0.167933
$397$	0.371961	0.0186682	0.00933410	−	0.999956i	$-0.497029\pi$
$397$	0.371961	0.0186682	0.00933410	+	0.999956i	$0.497029\pi$
$398$	23.5690	1.18141
$399$	6.06398	0.303579
$400$	1.21983	0.0609916
$401$	−9.35557	−0.467195	−0.233597	−	0.972333i	$-0.575050\pi$
$401$	−9.35557	−0.467195	−0.233597	+	0.972333i	$0.575050\pi$
$402$	12.6679	0.631815
$403$	0	0
$404$	3.20775	0.159592
$405$	17.2453	0.856927
$406$	−0.890084	−0.0441741
$407$	−16.5918	−0.822425
$408$	1.17092	0.0579689
$409$	29.2083	1.44426	0.722130	−	0.691758i	$-0.243163\pi$
$409$	29.2083	1.44426	0.722130	+	0.691758i	$0.243163\pi$
$410$	25.2379	1.24641
$411$	−28.6437	−1.41289
$412$	4.59179	0.226221
$413$	10.1032	0.497147
$414$	2.84654	0.139900
$415$	4.79822	0.235535
$416$	0	0
$417$	14.3787	0.704126
$418$	22.3884	1.09505
$419$	−10.2198	−0.499271	−0.249636	−	0.968340i	$-0.580311\pi$
$419$	−10.2198	−0.499271	−0.249636	+	0.968340i	$0.580311\pi$
$420$	−3.87800	−0.189227
$421$	1.01208	0.0493258	0.0246629	−	0.999696i	$-0.492149\pi$
$421$	1.01208	0.0493258	0.0246629	+	0.999696i	$0.492149\pi$
$422$	19.7952	0.963617
$423$	−2.45639	−0.119434
$424$	−1.50604	−0.0731398
$425$	−0.918559	−0.0445566
$426$	−10.2500	−0.496612
$427$	3.82371	0.185042
$428$	−13.6015	−0.657452
$429$	0	0
$430$	−27.8974	−1.34533
$431$	−4.73795	−0.228219	−0.114110	−	0.993468i	$-0.536402\pi$
$431$	−4.73795	−0.228219	−0.114110	+	0.993468i	$0.536402\pi$
$432$	5.57002	0.267988
$433$	3.72050	0.178796	0.0893978	−	0.995996i	$-0.471506\pi$
$433$	3.72050	0.178796	0.0893978	+	0.995996i	$0.471506\pi$
$434$	7.60388	0.364998
$435$	3.45175	0.165499
$436$	−14.9095	−0.714034
$437$	−19.0702	−0.912252
$438$	20.6136	0.984954
$439$	−23.7318	−1.13266	−0.566329	−	0.824179i	$-0.691637\pi$
$439$	−23.7318	−1.13266	−0.566329	+	0.824179i	$0.691637\pi$
$440$	−14.3177	−0.682568
$441$	−0.582105	−0.0277193
$442$	0	0
$443$	−19.9124	−0.946069	−0.473034	−	0.881044i	$-0.656841\pi$
$443$	−19.9124	−0.946069	−0.473034	+	0.881044i	$0.656841\pi$
$444$	4.49396	0.213274
$445$	29.5013	1.39849
$446$	23.7211	1.12323
$447$	21.0013	0.993329
$448$	−1.00000	−0.0472456
$449$	−21.2489	−1.00280	−0.501399	−	0.865216i	$-0.667181\pi$
$449$	−21.2489	−1.00280	−0.501399	+	0.865216i	$0.667181\pi$
$450$	−0.710071	−0.0334731
$451$	−58.0960	−2.73564
$452$	16.9825	0.798792
$453$	6.30426	0.296200
$454$	6.88471	0.323115
$455$	0	0
$456$	−6.06398	−0.283972
$457$	−24.8068	−1.16042	−0.580208	−	0.814469i	$-0.697029\pi$
$457$	−24.8068	−1.16042	−0.580208	+	0.814469i	$0.697029\pi$
$458$	−7.28621	−0.340462
$459$	−4.19434	−0.195775
$460$	12.1957	0.568626
$461$	6.40688	0.298398	0.149199	−	0.988807i	$-0.452330\pi$
$461$	6.40688	0.298398	0.149199	+	0.988807i	$0.452330\pi$
$462$	8.92692	0.415318
$463$	−27.8780	−1.29560	−0.647800	−	0.761810i	$-0.724311\pi$
$463$	−27.8780	−1.29560	−0.647800	+	0.761810i	$0.724311\pi$
$464$	0.890084	0.0413211
$465$	−29.4878	−1.36747
$466$	−0.445042	−0.0206162
$467$	22.6300	1.04719	0.523595	−	0.851967i	$-0.324591\pi$
$467$	22.6300	1.04719	0.523595	+	0.851967i	$0.324591\pi$
$468$	0	0
$469$	8.14675	0.376182
$470$	−10.5241	−0.485440
$471$	−0.274127	−0.0126311
$472$	−10.1032	−0.465038
$473$	64.2180	2.95275
$474$	26.9095	1.23599
$475$	4.75707	0.218269
$476$	0.753020	0.0345146
$477$	0.876674	0.0401402
$478$	−23.5797	−1.07851
$479$	38.2801	1.74906	0.874531	−	0.484969i	$-0.161169\pi$
$479$	38.2801	1.74906	0.874531	+	0.484969i	$0.161169\pi$
$480$	3.87800	0.177006
$481$	0	0
$482$	−8.21983	−0.374403
$483$	−7.60388	−0.345988
$484$	21.9584	0.998108
$485$	21.8297	0.991235
$486$	−5.95779	−0.270251
$487$	7.58450	0.343686	0.171843	−	0.985124i	$-0.445028\pi$
$487$	7.58450	0.343686	0.171843	+	0.985124i	$0.445028\pi$
$488$	−3.82371	−0.173091
$489$	−22.3545	−1.01091
$490$	−2.49396	−0.112666
$491$	21.2325	0.958210	0.479105	−	0.877758i	$-0.340961\pi$
$491$	21.2325	0.958210	0.479105	+	0.877758i	$0.340961\pi$
$492$	15.7356	0.709414
$493$	−0.670251	−0.0301866
$494$	0	0
$495$	8.33439	0.374603
$496$	−7.60388	−0.341424
$497$	−6.59179	−0.295682
$498$	2.99164	0.134059
$499$	−23.6082	−1.05685	−0.528424	−	0.848981i	$-0.677217\pi$
$499$	−23.6082	−1.05685	−0.528424	+	0.848981i	$0.677217\pi$
$500$	9.42758	0.421614
$501$	37.3491	1.66864
$502$	−15.7409	−0.702552
$503$	−28.2150	−1.25805	−0.629023	−	0.777386i	$-0.716545\pi$
$503$	−28.2150	−1.25805	−0.629023	+	0.777386i	$0.716545\pi$
$504$	0.582105	0.0259290
$505$	−8.00000	−0.355995
$506$	−28.0737	−1.24803
$507$	0	0
$508$	−0.987918	−0.0438318
$509$	18.1414	0.804102	0.402051	−	0.915617i	$-0.368297\pi$
$509$	18.1414	0.804102	0.402051	+	0.915617i	$0.368297\pi$
$510$	−2.92021	−0.129309
$511$	13.2567	0.586440
$512$	1.00000	0.0441942
$513$	21.7218	0.959042
$514$	8.77910	0.387230
$515$	−11.4517	−0.504624
$516$	−17.3937	−0.765716
$517$	24.2258	1.06545
$518$	2.89008	0.126983
$519$	−7.53617	−0.330801
$520$	0	0
$521$	36.4644	1.59754	0.798768	−	0.601640i	$-0.205486\pi$
$521$	36.4644	1.59754	0.798768	+	0.601640i	$0.205486\pi$
$522$	−0.518122	−0.0226776
$523$	1.05993	0.0463477	0.0231738	−	0.999731i	$-0.492623\pi$
$523$	1.05993	0.0463477	0.0231738	+	0.999731i	$0.492623\pi$
$524$	−9.13169	−0.398920
$525$	1.89679	0.0827826
$526$	−3.32975	−0.145184
$527$	5.72587	0.249423
$528$	−8.92692	−0.388494
$529$	0.912919	0.0396921
$530$	3.75600	0.163150
$531$	5.88113	0.255219
$532$	−3.89977	−0.169077
$533$	0	0
$534$	18.3937	0.795975
$535$	33.9215	1.46656
$536$	−8.14675	−0.351886
$537$	−32.5743	−1.40569
$538$	4.84654	0.208949
$539$	5.74094	0.247280
$540$	−13.8914	−0.597791
$541$	−22.2693	−0.957434	−0.478717	−	0.877969i	$-0.658898\pi$
$541$	−22.2693	−0.957434	−0.478717	+	0.877969i	$0.658898\pi$
$542$	−27.5991	−1.18548
$543$	10.1655	0.436245
$544$	−0.753020	−0.0322855
$545$	37.1836	1.59277
$546$	0	0
$547$	−26.4644	−1.13154	−0.565768	−	0.824564i	$-0.691420\pi$
$547$	−26.4644	−1.13154	−0.565768	+	0.824564i	$0.691420\pi$
$548$	18.4209	0.786901
$549$	2.22580	0.0949948
$550$	7.00298	0.298608
$551$	3.47112	0.147875
$552$	7.60388	0.323642
$553$	17.3056	0.735908
$554$	−10.4698	−0.444819
$555$	−11.2078	−0.475743
$556$	−9.24698	−0.392159
$557$	42.5676	1.80365	0.901824	−	0.432103i	$-0.142228\pi$
$557$	42.5676	1.80365	0.901824	+	0.432103i	$0.142228\pi$
$558$	4.42626	0.187378
$559$	0	0
$560$	2.49396	0.105389
$561$	6.72215	0.283809
$562$	13.0901	0.552171
$563$	15.5991	0.657423	0.328712	−	0.944430i	$-0.393386\pi$
$563$	15.5991	0.657423	0.328712	+	0.944430i	$0.393386\pi$
$564$	−6.56166	−0.276296
$565$	−42.3538	−1.78184
$566$	−13.2403	−0.556530
$567$	6.91484	0.290396
$568$	6.59179	0.276586
$569$	17.1890	0.720599	0.360299	−	0.932837i	$-0.382675\pi$
$569$	17.1890	0.720599	0.360299	+	0.932837i	$0.382675\pi$
$570$	15.1233	0.633446
$571$	0.841166	0.0352017	0.0176009	−	0.999845i	$-0.494397\pi$
$571$	0.841166	0.0352017	0.0176009	+	0.999845i	$0.494397\pi$
$572$	0	0
$573$	20.4155	0.852870
$574$	10.1196	0.422384
$575$	−5.96508	−0.248761
$576$	−0.582105	−0.0242544
$577$	−40.4916	−1.68569	−0.842843	−	0.538160i	$-0.819120\pi$
$577$	−40.4916	−1.68569	−0.842843	+	0.538160i	$0.819120\pi$
$578$	−16.4330	−0.683521
$579$	8.40581	0.349334
$580$	−2.21983	−0.0921735
$581$	1.92394	0.0798183
$582$	13.6106	0.564177
$583$	−8.64609	−0.358084
$584$	−13.2567	−0.548565
$585$	0	0
$586$	16.6703	0.688642
$587$	4.33944	0.179108	0.0895539	−	0.995982i	$-0.471456\pi$
$587$	4.33944	0.179108	0.0895539	+	0.995982i	$0.471456\pi$
$588$	−1.55496	−0.0641254
$589$	−29.6534	−1.22185
$590$	25.1970	1.03734
$591$	13.5496	0.557355
$592$	−2.89008	−0.118782
$593$	40.9487	1.68156	0.840781	−	0.541376i	$-0.182096\pi$
$593$	40.9487	1.68156	0.840781	+	0.541376i	$0.182096\pi$
$594$	31.9772	1.31204
$595$	−1.87800	−0.0769906
$596$	−13.5060	−0.553229
$597$	−36.6487	−1.49993
$598$	0	0
$599$	10.1280	0.413817	0.206909	−	0.978360i	$-0.433660\pi$
$599$	10.1280	0.413817	0.206909	+	0.978360i	$0.433660\pi$
$600$	−1.89679	−0.0774361
$601$	40.3782	1.64706	0.823530	−	0.567272i	$-0.192001\pi$
$601$	40.3782	1.64706	0.823530	+	0.567272i	$0.192001\pi$
$602$	−11.1860	−0.455907
$603$	4.74227	0.193120
$604$	−4.05429	−0.164967
$605$	−54.7633	−2.22644
$606$	−4.98792	−0.202620
$607$	−5.79092	−0.235046	−0.117523	−	0.993070i	$-0.537495\pi$
$607$	−5.79092	−0.235046	−0.117523	+	0.993070i	$0.537495\pi$
$608$	3.89977	0.158157
$609$	1.38404	0.0560843
$610$	9.53617	0.386108
$611$	0	0
$612$	0.438337	0.0177187
$613$	−30.2500	−1.22178	−0.610892	−	0.791714i	$-0.709189\pi$
$613$	−30.2500	−1.22178	−0.610892	+	0.791714i	$0.709189\pi$
$614$	11.6625	0.470659
$615$	−39.2438	−1.58246
$616$	−5.74094	−0.231309
$617$	−2.75196	−0.110790	−0.0553948	−	0.998465i	$-0.517642\pi$
$617$	−2.75196	−0.110790	−0.0553948	+	0.998465i	$0.517642\pi$
$618$	−7.14005	−0.287215
$619$	−8.28275	−0.332912	−0.166456	−	0.986049i	$-0.553232\pi$
$619$	−8.28275	−0.332912	−0.166456	+	0.986049i	$0.553232\pi$
$620$	18.9638	0.761603
$621$	−27.2379	−1.09302
$622$	6.29350	0.252347
$623$	11.8291	0.473922
$624$	0	0
$625$	−29.6112	−1.18445
$626$	27.2470	1.08901
$627$	−34.8130	−1.39030
$628$	0.176292	0.00703482
$629$	2.17629	0.0867744
$630$	−1.45175	−0.0578390
$631$	44.0689	1.75435	0.877177	−	0.480167i	$-0.159424\pi$
$631$	44.0689	1.75435	0.877177	+	0.480167i	$0.159424\pi$
$632$	−17.3056	−0.688379
$633$	−30.7808	−1.22343
$634$	23.4819	0.932584
$635$	2.46383	0.0977740
$636$	2.34183	0.0928596
$637$	0	0
$638$	5.10992	0.202304
$639$	−3.83712	−0.151794
$640$	−2.49396	−0.0985824
$641$	11.0339	0.435811	0.217905	−	0.975970i	$-0.430078\pi$
$641$	11.0339	0.435811	0.217905	+	0.975970i	$0.430078\pi$
$642$	21.1497	0.834713
$643$	−29.5230	−1.16427	−0.582137	−	0.813091i	$-0.697783\pi$
$643$	−29.5230	−1.16427	−0.582137	+	0.813091i	$0.697783\pi$
$644$	4.89008	0.192696
$645$	43.3793	1.70806
$646$	−2.93661	−0.115539
$647$	−37.7125	−1.48263	−0.741315	−	0.671157i	$-0.765798\pi$
$647$	−37.7125	−1.48263	−0.741315	+	0.671157i	$0.765798\pi$
$648$	−6.91484	−0.271640
$649$	−58.0019	−2.27677
$650$	0	0
$651$	−11.8237	−0.463408
$652$	14.3763	0.563018
$653$	44.9288	1.75820	0.879101	−	0.476636i	$-0.158144\pi$
$653$	44.9288	1.75820	0.879101	+	0.476636i	$0.158144\pi$
$654$	23.1836	0.906550
$655$	22.7741	0.889856
$656$	−10.1196	−0.395104
$657$	7.71678	0.301060
$658$	−4.21983	−0.164506
$659$	26.0140	1.01336	0.506681	−	0.862134i	$-0.330872\pi$
$659$	26.0140	1.01336	0.506681	+	0.862134i	$0.330872\pi$
$660$	22.2634	0.866601
$661$	31.0401	1.20732	0.603660	−	0.797242i	$-0.293709\pi$
$661$	31.0401	1.20732	0.603660	+	0.797242i	$0.293709\pi$
$662$	−17.6233	−0.684947
$663$	0	0
$664$	−1.92394	−0.0746632
$665$	9.72587	0.377153
$666$	1.68233	0.0651891
$667$	−4.35258	−0.168533
$668$	−24.0194	−0.929338
$669$	−36.8853	−1.42607
$670$	20.3177	0.784940
$671$	−21.9517	−0.847435
$672$	1.55496	0.0599838
$673$	16.1140	0.621148	0.310574	−	0.950549i	$-0.399479\pi$
$673$	16.1140	0.621148	0.310574	+	0.950549i	$0.399479\pi$
$674$	22.7463	0.876155
$675$	6.79450	0.261520
$676$	0	0
$677$	−37.2379	−1.43117	−0.715584	−	0.698527i	$-0.753839\pi$
$677$	−37.2379	−1.43117	−0.715584	+	0.698527i	$0.753839\pi$
$678$	−26.4071	−1.01416
$679$	8.75302	0.335910
$680$	1.87800	0.0720181
$681$	−10.7054	−0.410233
$682$	−43.6534	−1.67157
$683$	27.8864	1.06704	0.533521	−	0.845787i	$-0.320869\pi$
$683$	27.8864	1.06704	0.533521	+	0.845787i	$0.320869\pi$
$684$	−2.27008	−0.0867986
$685$	−45.9409	−1.75531
$686$	−1.00000	−0.0381802
$687$	11.3297	0.432257
$688$	11.1860	0.426462
$689$	0	0
$690$	−18.9638	−0.721938
$691$	14.7114	0.559648	0.279824	−	0.960051i	$-0.409724\pi$
$691$	14.7114	0.559648	0.279824	+	0.960051i	$0.409724\pi$
$692$	4.84654	0.184238
$693$	3.34183	0.126946
$694$	0.987918	0.0375009
$695$	23.0616	0.874776
$696$	−1.38404	−0.0524620
$697$	7.62027	0.288638
$698$	−3.05562	−0.115657
$699$	0.692021	0.0261747
$700$	−1.21983	−0.0461053
$701$	−9.61463	−0.363140	−0.181570	−	0.983378i	$-0.558118\pi$
$701$	−9.61463	−0.363140	−0.181570	+	0.983378i	$0.558118\pi$
$702$	0	0
$703$	−11.2707	−0.425081
$704$	5.74094	0.216370
$705$	16.3645	0.616323
$706$	29.1444	1.09686
$707$	−3.20775	−0.120640
$708$	15.7101	0.590421
$709$	−39.7259	−1.49194	−0.745968	−	0.665982i	$-0.768013\pi$
$709$	−39.7259	−1.49194	−0.745968	+	0.665982i	$0.768013\pi$
$710$	−16.4397	−0.616970
$711$	10.0737	0.377792
$712$	−11.8291	−0.443314
$713$	37.1836	1.39254
$714$	−1.17092	−0.0438204
$715$	0	0
$716$	20.9487	0.782889
$717$	36.6655	1.36930
$718$	−33.6969	−1.25756
$719$	40.0194	1.49247	0.746235	−	0.665682i	$-0.231859\pi$
$719$	40.0194	1.49247	0.746235	+	0.665682i	$0.231859\pi$
$720$	1.45175	0.0541034
$721$	−4.59179	−0.171007
$722$	−3.79178	−0.141115
$723$	12.7815	0.475349
$724$	−6.53750	−0.242964
$725$	1.08575	0.0403239
$726$	−34.1444	−1.26722
$727$	11.4819	0.425839	0.212920	−	0.977070i	$-0.431703\pi$
$727$	11.4819	0.425839	0.212920	+	0.977070i	$0.431703\pi$
$728$	0	0
$729$	30.0086	1.11143
$730$	33.0616	1.22366
$731$	−8.42327	−0.311546
$732$	5.94571	0.219760
$733$	−41.5883	−1.53610	−0.768050	−	0.640390i	$-0.778773\pi$
$733$	−41.5883	−1.53610	−0.768050	+	0.640390i	$0.778773\pi$
$734$	0.0193774	0.000715231 0
$735$	3.87800	0.143042
$736$	−4.89008	−0.180251
$737$	−46.7700	−1.72280
$738$	5.89067	0.216839
$739$	−52.9778	−1.94882	−0.974409	−	0.224782i	$-0.927833\pi$
$739$	−52.9778	−1.94882	−0.974409	+	0.224782i	$0.927833\pi$
$740$	7.20775	0.264962
$741$	0	0
$742$	1.50604	0.0552885
$743$	−3.63401	−0.133319	−0.0666594	−	0.997776i	$-0.521234\pi$
$743$	−3.63401	−0.133319	−0.0666594	+	0.997776i	$0.521234\pi$
$744$	11.8237	0.433478
$745$	33.6835	1.23407
$746$	−8.76809	−0.321022
$747$	1.11993	0.0409762
$748$	−4.32304	−0.158066
$749$	13.6015	0.496987
$750$	−14.6595	−0.535289
$751$	−11.8914	−0.433924	−0.216962	−	0.976180i	$-0.569615\pi$
$751$	−11.8914	−0.433924	−0.216962	+	0.976180i	$0.569615\pi$
$752$	4.21983	0.153881
$753$	24.4765	0.891973
$754$	0	0
$755$	10.1112	0.367986
$756$	−5.57002	−0.202580
$757$	−0.0892109	−0.00324243	−0.00162121	−	0.999999i	$-0.500516\pi$
$757$	−0.0892109	−0.00324243	−0.00162121	+	0.999999i	$0.500516\pi$
$758$	−25.4873	−0.925739
$759$	43.6534	1.58452
$760$	−9.72587	−0.352795
$761$	−33.2314	−1.20464	−0.602319	−	0.798255i	$-0.705757\pi$
$761$	−33.2314	−1.20464	−0.602319	+	0.798255i	$0.705757\pi$
$762$	1.53617	0.0556496
$763$	14.9095	0.539759
$764$	−13.1293	−0.475001
$765$	−1.09319	−0.0395245
$766$	10.4590	0.377901
$767$	0	0
$768$	−1.55496	−0.0561097
$769$	−38.5332	−1.38954	−0.694771	−	0.719231i	$-0.744494\pi$
$769$	−38.5332	−1.38954	−0.694771	+	0.719231i	$0.744494\pi$
$770$	14.3177	0.515973
$771$	−13.6511	−0.491634
$772$	−5.40581	−0.194559
$773$	−47.7995	−1.71923	−0.859615	−	0.510942i	$-0.829297\pi$
$773$	−47.7995	−1.71923	−0.859615	+	0.510942i	$0.829297\pi$
$774$	−6.51142	−0.234048
$775$	−9.27545	−0.333184
$776$	−8.75302	−0.314215
$777$	−4.49396	−0.161220
$778$	−11.9952	−0.430049
$779$	−39.4642	−1.41395
$780$	0	0
$781$	37.8431	1.35413
$782$	3.68233	0.131680
$783$	4.95779	0.177177
$784$	1.00000	0.0357143
$785$	−0.439665	−0.0156923
$786$	14.1994	0.506475
$787$	11.0573	0.394149	0.197075	−	0.980388i	$-0.436856\pi$
$787$	11.0573	0.394149	0.197075	+	0.980388i	$0.436856\pi$
$788$	−8.71379	−0.310416
$789$	5.17762	0.184328
$790$	43.1594	1.53554
$791$	−16.9825	−0.603830
$792$	−3.34183	−0.118747
$793$	0	0
$794$	0.371961	0.0132004
$795$	−5.84043	−0.207139
$796$	23.5690	0.835380
$797$	−39.4422	−1.39711	−0.698557	−	0.715555i	$-0.746174\pi$
$797$	−39.4422	−1.39711	−0.698557	+	0.715555i	$0.746174\pi$
$798$	6.06398	0.214663
$799$	−3.17762	−0.112416
$800$	1.21983	0.0431276
$801$	6.88577	0.243297
$802$	−9.35557	−0.330357
$803$	−76.1057	−2.68571
$804$	12.6679	0.446761
$805$	−12.1957	−0.429841
$806$	0	0
$807$	−7.53617	−0.265286
$808$	3.20775	0.112848
$809$	11.4735	0.403387	0.201694	−	0.979449i	$-0.435355\pi$
$809$	11.4735	0.403387	0.201694	+	0.979449i	$0.435355\pi$
$810$	17.2453	0.605939
$811$	31.7797	1.11594	0.557968	−	0.829862i	$-0.311581\pi$
$811$	31.7797	1.11594	0.557968	+	0.829862i	$0.311581\pi$
$812$	−0.890084	−0.0312358
$813$	42.9154	1.50511
$814$	−16.5918	−0.581542
$815$	−35.8538	−1.25591
$816$	1.17092	0.0409902
$817$	43.6228	1.52617
$818$	29.2083	1.02125
$819$	0	0
$820$	25.2379	0.881345
$821$	−8.35258	−0.291507	−0.145754	−	0.989321i	$-0.546561\pi$
$821$	−8.35258	−0.291507	−0.145754	+	0.989321i	$0.546561\pi$
$822$	−28.6437	−0.999064
$823$	11.8431	0.412824	0.206412	−	0.978465i	$-0.433821\pi$
$823$	11.8431	0.412824	0.206412	+	0.978465i	$0.433821\pi$
$824$	4.59179	0.159963
$825$	−10.8893	−0.379118
$826$	10.1032	0.351536
$827$	38.8558	1.35115	0.675574	−	0.737293i	$-0.263896\pi$
$827$	38.8558	1.35115	0.675574	+	0.737293i	$0.263896\pi$
$828$	2.84654	0.0989242
$829$	40.9724	1.42303	0.711515	−	0.702671i	$-0.248009\pi$
$829$	40.9724	1.42303	0.711515	+	0.702671i	$0.248009\pi$
$830$	4.79822	0.166549
$831$	16.2801	0.564750
$832$	0	0
$833$	−0.753020	−0.0260906
$834$	14.3787	0.497892
$835$	59.9033	2.07304
$836$	22.3884	0.774317
$837$	−42.3538	−1.46396
$838$	−10.2198	−0.353038
$839$	−22.4263	−0.774240	−0.387120	−	0.922029i	$-0.626530\pi$
$839$	−22.4263	−0.774240	−0.387120	+	0.922029i	$0.626530\pi$
$840$	−3.87800	−0.133804
$841$	−28.2078	−0.972681
$842$	1.01208	0.0348786
$843$	−20.3545	−0.701046
$844$	19.7952	0.681380
$845$	0	0
$846$	−2.45639	−0.0844523
$847$	−21.9584	−0.754499
$848$	−1.50604	−0.0517177
$849$	20.5881	0.706581
$850$	−0.918559	−0.0315063
$851$	14.1328	0.484464
$852$	−10.2500	−0.351158
$853$	7.59312	0.259984	0.129992	−	0.991515i	$-0.458505\pi$
$853$	7.59312	0.259984	0.129992	+	0.991515i	$0.458505\pi$
$854$	3.82371	0.130845
$855$	5.66148	0.193619
$856$	−13.6015	−0.464889
$857$	−25.2529	−0.862624	−0.431312	−	0.902203i	$-0.641949\pi$
$857$	−25.2529	−0.862624	−0.431312	+	0.902203i	$0.641949\pi$
$858$	0	0
$859$	−3.77479	−0.128794	−0.0643971	−	0.997924i	$-0.520512\pi$
$859$	−3.77479	−0.128794	−0.0643971	+	0.997924i	$0.520512\pi$
$860$	−27.8974	−0.951293
$861$	−15.7356	−0.536267
$862$	−4.73795	−0.161375
$863$	−11.2862	−0.384187	−0.192093	−	0.981377i	$-0.561528\pi$
$863$	−11.2862	−0.384187	−0.192093	+	0.981377i	$0.561528\pi$
$864$	5.57002	0.189496
$865$	−12.0871	−0.410973
$866$	3.72050	0.126428
$867$	25.5526	0.867811
$868$	7.60388	0.258092
$869$	−99.3503	−3.37023
$870$	3.45175	0.117025
$871$	0	0
$872$	−14.9095	−0.504898
$873$	5.09518	0.172446
$874$	−19.0702	−0.645060
$875$	−9.42758	−0.318710
$876$	20.6136	0.696468
$877$	22.1608	0.748315	0.374158	−	0.927365i	$-0.377932\pi$
$877$	22.1608	0.748315	0.374158	+	0.927365i	$0.377932\pi$
$878$	−23.7318	−0.800911
$879$	−25.9215	−0.874312
$880$	−14.3177	−0.482648
$881$	−13.6142	−0.458673	−0.229336	−	0.973347i	$-0.573656\pi$
$881$	−13.6142	−0.458673	−0.229336	+	0.973347i	$0.573656\pi$
$882$	−0.582105	−0.0196005
$883$	−51.2073	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$883$	−51.2073	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$884$	0	0
$885$	−39.1803	−1.31703
$886$	−19.9124	−0.668972
$887$	−12.7875	−0.429361	−0.214680	−	0.976684i	$-0.568871\pi$
$887$	−12.7875	−0.429361	−0.214680	+	0.976684i	$0.568871\pi$
$888$	4.49396	0.150807
$889$	0.987918	0.0331337
$890$	29.5013	0.988884
$891$	−39.6977	−1.32992
$892$	23.7211	0.794241
$893$	16.4564	0.550692
$894$	21.0013	0.702389
$895$	−52.2452	−1.74636
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−21.2489	−0.709085
$899$	−6.76809	−0.225728
$900$	−0.710071	−0.0236690
$901$	1.13408	0.0377817
$902$	−58.0960	−1.93439
$903$	17.3937	0.578827
$904$	16.9825	0.564831
$905$	16.3043	0.541972
$906$	6.30426	0.209445
$907$	−6.41491	−0.213004	−0.106502	−	0.994313i	$-0.533965\pi$
$907$	−6.41491	−0.213004	−0.106502	+	0.994313i	$0.533965\pi$
$908$	6.88471	0.228477
$909$	−1.86725	−0.0619327
$910$	0	0
$911$	−21.1750	−0.701558	−0.350779	−	0.936458i	$-0.614083\pi$
$911$	−21.1750	−0.701558	−0.350779	+	0.936458i	$0.614083\pi$
$912$	−6.06398	−0.200799
$913$	−11.0452	−0.365543
$914$	−24.8068	−0.820537
$915$	−14.8283	−0.490210
$916$	−7.28621	−0.240743
$917$	9.13169	0.301555
$918$	−4.19434	−0.138434
$919$	24.3263	0.802450	0.401225	−	0.915979i	$-0.368584\pi$
$919$	24.3263	0.802450	0.401225	+	0.915979i	$0.368584\pi$
$920$	12.1957	0.402079
$921$	−18.1347	−0.597558
$922$	6.40688	0.210999
$923$	0	0
$924$	8.92692	0.293674
$925$	−3.52542	−0.115915
$926$	−27.8780	−0.916128
$927$	−2.67291	−0.0877898
$928$	0.890084	0.0292184
$929$	7.69932	0.252606	0.126303	−	0.991992i	$-0.459689\pi$
$929$	7.69932	0.252606	0.126303	+	0.991992i	$0.459689\pi$
$930$	−29.4878	−0.966945
$931$	3.89977	0.127810
$932$	−0.445042	−0.0145778
$933$	−9.78614	−0.320384
$934$	22.6300	0.740475
$935$	10.7815	0.352593
$936$	0	0
$937$	8.80061	0.287503	0.143752	−	0.989614i	$-0.454083\pi$
$937$	8.80061	0.287503	0.143752	+	0.989614i	$0.454083\pi$
$938$	8.14675	0.266001
$939$	−42.3679	−1.38262
$940$	−10.5241	−0.343258
$941$	22.0253	0.718006	0.359003	−	0.933336i	$-0.383117\pi$
$941$	22.0253	0.718006	0.359003	+	0.933336i	$0.383117\pi$
$942$	−0.274127	−0.00893153
$943$	49.4857	1.61148
$944$	−10.1032	−0.328832
$945$	13.8914	0.451888
$946$	64.2180	2.08791
$947$	10.7899	0.350623	0.175312	−	0.984513i	$-0.443907\pi$
$947$	10.7899	0.350623	0.175312	+	0.984513i	$0.443907\pi$
$948$	26.9095	0.873979
$949$	0	0
$950$	4.75707	0.154340
$951$	−36.5133	−1.18403
$952$	0.753020	0.0244055
$953$	21.7149	0.703413	0.351707	−	0.936110i	$-0.385601\pi$
$953$	21.7149	0.703413	0.351707	+	0.936110i	$0.385601\pi$
$954$	0.876674	0.0283834
$955$	32.7439	1.05957
$956$	−23.5797	−0.762622
$957$	−7.94571	−0.256848
$958$	38.2801	1.23677
$959$	−18.4209	−0.594841
$960$	3.87800	0.125162
$961$	26.8189	0.865127
$962$	0	0
$963$	7.91749	0.255138
$964$	−8.21983	−0.264743
$965$	13.4819	0.433997
$966$	−7.60388	−0.244651
$967$	−36.6112	−1.17734	−0.588668	−	0.808375i	$-0.700347\pi$
$967$	−36.6112	−1.17734	−0.588668	+	0.808375i	$0.700347\pi$
$968$	21.9584	0.705769
$969$	4.56630	0.146691
$970$	21.8297	0.700909
$971$	30.8683	0.990611	0.495306	−	0.868719i	$-0.335056\pi$
$971$	30.8683	0.990611	0.495306	+	0.868719i	$0.335056\pi$
$972$	−5.95779	−0.191096
$973$	9.24698	0.296445
$974$	7.58450	0.243023
$975$	0	0
$976$	−3.82371	−0.122394
$977$	18.8769	0.603927	0.301963	−	0.953320i	$-0.402358\pi$
$977$	18.8769	0.603927	0.301963	+	0.953320i	$0.402358\pi$
$978$	−22.3545	−0.714818
$979$	−67.9101	−2.17041
$980$	−2.49396	−0.0796666
$981$	8.67887	0.277095
$982$	21.2325	0.677556
$983$	−26.1473	−0.833971	−0.416985	−	0.908913i	$-0.636913\pi$
$983$	−26.1473	−0.833971	−0.416985	+	0.908913i	$0.636913\pi$
$984$	15.7356	0.501631
$985$	21.7318	0.692434
$986$	−0.670251	−0.0213451
$987$	6.56166	0.208860
$988$	0	0
$989$	−54.7004	−1.73937
$990$	8.33439	0.264884
$991$	7.17496	0.227920	0.113960	−	0.993485i	$-0.463646\pi$
$991$	7.17496	0.227920	0.113960	+	0.993485i	$0.463646\pi$
$992$	−7.60388	−0.241423
$993$	27.4034	0.869621
$994$	−6.59179	−0.209079
$995$	−58.7800	−1.86345
$996$	2.99164	0.0947937
$997$	−30.0000	−0.950110	−0.475055	−	0.879956i	$-0.657572\pi$
$997$	−30.0000	−0.950110	−0.475055	+	0.879956i	$0.657572\pi$
$998$	−23.6082	−0.747304
$999$	−16.0978	−0.509313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.z.1.2	yes	3
13.5	odd	4		2366.2.d.m.337.2		6
13.8	odd	4		2366.2.d.m.337.5		6
13.12	even	2		2366.2.a.u.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.u.1.2	✓	3	13.12	even	2
2366.2.a.z.1.2	yes	3	1.1	even	1	trivial
2366.2.d.m.337.2		6	13.5	odd	4
2366.2.d.m.337.5		6	13.8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.55496 q^{3} +1.00000 q^{4} -2.49396 q^{5} -1.55496 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.582105 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.55496 q^{3} +1.00000 q^{4} -2.49396 q^{5} -1.55496 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.582105 q^{9} -2.49396 q^{10} +5.74094 q^{11} -1.55496 q^{12} -1.00000 q^{14} +3.87800 q^{15} +1.00000 q^{16} -0.753020 q^{17} -0.582105 q^{18} +3.89977 q^{19} -2.49396 q^{20} +1.55496 q^{21} +5.74094 q^{22} -4.89008 q^{23} -1.55496 q^{24} +1.21983 q^{25} +5.57002 q^{27} -1.00000 q^{28} +0.890084 q^{29} +3.87800 q^{30} -7.60388 q^{31} +1.00000 q^{32} -8.92692 q^{33} -0.753020 q^{34} +2.49396 q^{35} -0.582105 q^{36} -2.89008 q^{37} +3.89977 q^{38} -2.49396 q^{40} -10.1196 q^{41} +1.55496 q^{42} +11.1860 q^{43} +5.74094 q^{44} +1.45175 q^{45} -4.89008 q^{46} +4.21983 q^{47} -1.55496 q^{48} +1.00000 q^{49} +1.21983 q^{50} +1.17092 q^{51} -1.50604 q^{53} +5.57002 q^{54} -14.3177 q^{55} -1.00000 q^{56} -6.06398 q^{57} +0.890084 q^{58} -10.1032 q^{59} +3.87800 q^{60} -3.82371 q^{61} -7.60388 q^{62} +0.582105 q^{63} +1.00000 q^{64} -8.92692 q^{66} -8.14675 q^{67} -0.753020 q^{68} +7.60388 q^{69} +2.49396 q^{70} +6.59179 q^{71} -0.582105 q^{72} -13.2567 q^{73} -2.89008 q^{74} -1.89679 q^{75} +3.89977 q^{76} -5.74094 q^{77} -17.3056 q^{79} -2.49396 q^{80} -6.91484 q^{81} -10.1196 q^{82} -1.92394 q^{83} +1.55496 q^{84} +1.87800 q^{85} +11.1860 q^{86} -1.38404 q^{87} +5.74094 q^{88} -11.8291 q^{89} +1.45175 q^{90} -4.89008 q^{92} +11.8237 q^{93} +4.21983 q^{94} -9.72587 q^{95} -1.55496 q^{96} -8.75302 q^{97} +1.00000 q^{98} -3.34183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 4 * q^9	\( 3 q + 3 q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} - 5 q^{6} - 3 q^{7} + 3 q^{8} + 4 q^{9} + 2 q^{10} + 3 q^{11} - 5 q^{12} - 3 q^{14} - 8 q^{15} + 3 q^{16} - 7 q^{17} + 4 q^{18} - 11 q^{19} + 2 q^{20} + 5 q^{21} + 3 q^{22} - 14 q^{23} - 5 q^{24} + 5 q^{25} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 8 q^{30} - 14 q^{31} + 3 q^{32} + 2 q^{33} - 7 q^{34} - 2 q^{35} + 4 q^{36} - 8 q^{37} - 11 q^{38} + 2 q^{40} - 9 q^{41} + 5 q^{42} + 19 q^{43} + 3 q^{44} + 26 q^{45} - 14 q^{46} + 14 q^{47} - 5 q^{48} + 3 q^{49} + 5 q^{50} + 14 q^{51} - 14 q^{53} - 8 q^{54} - 26 q^{55} - 3 q^{56} + 16 q^{57} + 2 q^{58} - 9 q^{59} - 8 q^{60} - 4 q^{61} - 14 q^{62} - 4 q^{63} + 3 q^{64} + 2 q^{66} + 3 q^{67} - 7 q^{68} + 14 q^{69} - 2 q^{70} - 8 q^{71} + 4 q^{72} - 13 q^{73} - 8 q^{74} - 27 q^{75} - 11 q^{76} - 3 q^{77} - 16 q^{79} + 2 q^{80} + 27 q^{81} - 9 q^{82} - 21 q^{83} + 5 q^{84} - 14 q^{85} + 19 q^{86} + 6 q^{87} + 3 q^{88} - 25 q^{89} + 26 q^{90} - 14 q^{92} + 28 q^{93} + 14 q^{94} - 40 q^{95} - 5 q^{96} - 31 q^{97} + 3 q^{98} - 31 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 - 5 * q^6 - 3 * q^7 + 3 * q^8 + 4 * q^9 + 2 * q^10 + 3 * q^11 - 5 * q^12 - 3 * q^14 - 8 * q^15 + 3 * q^16 - 7 * q^17 + 4 * q^18 - 11 * q^19 + 2 * q^20 + 5 * q^21 + 3 * q^22 - 14 * q^23 - 5 * q^24 + 5 * q^25 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 8 * q^30 - 14 * q^31 + 3 * q^32 + 2 * q^33 - 7 * q^34 - 2 * q^35 + 4 * q^36 - 8 * q^37 - 11 * q^38 + 2 * q^40 - 9 * q^41 + 5 * q^42 + 19 * q^43 + 3 * q^44 + 26 * q^45 - 14 * q^46 + 14 * q^47 - 5 * q^48 + 3 * q^49 + 5 * q^50 + 14 * q^51 - 14 * q^53 - 8 * q^54 - 26 * q^55 - 3 * q^56 + 16 * q^57 + 2 * q^58 - 9 * q^59 - 8 * q^60 - 4 * q^61 - 14 * q^62 - 4 * q^63 + 3 * q^64 + 2 * q^66 + 3 * q^67 - 7 * q^68 + 14 * q^69 - 2 * q^70 - 8 * q^71 + 4 * q^72 - 13 * q^73 - 8 * q^74 - 27 * q^75 - 11 * q^76 - 3 * q^77 - 16 * q^79 + 2 * q^80 + 27 * q^81 - 9 * q^82 - 21 * q^83 + 5 * q^84 - 14 * q^85 + 19 * q^86 + 6 * q^87 + 3 * q^88 - 25 * q^89 + 26 * q^90 - 14 * q^92 + 28 * q^93 + 14 * q^94 - 40 * q^95 - 5 * q^96 - 31 * q^97 + 3 * q^98 - 31 * q^99

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