LMFDB - Embedded newform 6422.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6422,2,Mod(1,6422)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6422, 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("6422.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6422 = 2 \cdot 13^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6422.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:	$51.2799281781$
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:	no (minimal twist has level 494)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	6422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.04892 q^{3} +1.00000 q^{4} -0.198062 q^{5} -2.04892 q^{6} +0.890084 q^{7} -1.00000 q^{8} +1.19806 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.04892 q^{3} +1.00000 q^{4} -0.198062 q^{5} -2.04892 q^{6} +0.890084 q^{7} -1.00000 q^{8} +1.19806 q^{9} +0.198062 q^{10} +4.13706 q^{11} +2.04892 q^{12} -0.890084 q^{14} -0.405813 q^{15} +1.00000 q^{16} -2.66487 q^{17} -1.19806 q^{18} +1.00000 q^{19} -0.198062 q^{20} +1.82371 q^{21} -4.13706 q^{22} -8.45473 q^{23} -2.04892 q^{24} -4.96077 q^{25} -3.69202 q^{27} +0.890084 q^{28} -4.13706 q^{29} +0.405813 q^{30} -1.08815 q^{31} -1.00000 q^{32} +8.47650 q^{33} +2.66487 q^{34} -0.176292 q^{35} +1.19806 q^{36} -10.7681 q^{37} -1.00000 q^{38} +0.198062 q^{40} +6.66487 q^{41} -1.82371 q^{42} +6.19567 q^{43} +4.13706 q^{44} -0.237291 q^{45} +8.45473 q^{46} -7.38404 q^{47} +2.04892 q^{48} -6.20775 q^{49} +4.96077 q^{50} -5.46011 q^{51} -3.40581 q^{53} +3.69202 q^{54} -0.819396 q^{55} -0.890084 q^{56} +2.04892 q^{57} +4.13706 q^{58} -7.20775 q^{59} -0.405813 q^{60} -11.9215 q^{61} +1.08815 q^{62} +1.06638 q^{63} +1.00000 q^{64} -8.47650 q^{66} -3.87800 q^{67} -2.66487 q^{68} -17.3230 q^{69} +0.176292 q^{70} -6.07606 q^{71} -1.19806 q^{72} +5.16421 q^{73} +10.7681 q^{74} -10.1642 q^{75} +1.00000 q^{76} +3.68233 q^{77} -15.6582 q^{79} -0.198062 q^{80} -11.1588 q^{81} -6.66487 q^{82} +13.1588 q^{83} +1.82371 q^{84} +0.527811 q^{85} -6.19567 q^{86} -8.47650 q^{87} -4.13706 q^{88} +4.53319 q^{89} +0.237291 q^{90} -8.45473 q^{92} -2.22952 q^{93} +7.38404 q^{94} -0.198062 q^{95} -2.04892 q^{96} -8.18060 q^{97} +6.20775 q^{98} +4.95646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9} + 5 q^{10} + 7 q^{11} - 3 q^{12} - 2 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} - 8 q^{18} + 3 q^{19} - 5 q^{20} - 2 q^{21} - 7 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 6 q^{27} + 2 q^{28} - 7 q^{29} - 12 q^{30} - 7 q^{31} - 3 q^{32} + 9 q^{34} - 8 q^{35} + 8 q^{36} - 12 q^{37} - 3 q^{38} + 5 q^{40} + 21 q^{41} + 2 q^{42} - 18 q^{43} + 7 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{47} - 3 q^{48} - q^{49} + 2 q^{50} + 9 q^{51} + 3 q^{53} + 6 q^{54} - 14 q^{55} - 2 q^{56} - 3 q^{57} + 7 q^{58} - 4 q^{59} + 12 q^{60} - 10 q^{61} + 7 q^{62} + 10 q^{63} + 3 q^{64} + 8 q^{67} - 9 q^{68} - 32 q^{69} + 8 q^{70} - 3 q^{71} - 8 q^{72} + 4 q^{73} + 12 q^{74} - 19 q^{75} + 3 q^{76} + 28 q^{77} - 26 q^{79} - 5 q^{80} - 25 q^{81} - 21 q^{82} + 31 q^{83} - 2 q^{84} + 8 q^{85} + 18 q^{86} - 7 q^{88} + 17 q^{89} + 18 q^{90} - 3 q^{92} + 14 q^{93} + 12 q^{94} - 5 q^{95} + 3 q^{96} - 13 q^{97} + q^{98} + 21 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9 + 5 * q^10 + 7 * q^11 - 3 * q^12 - 2 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 - 8 * q^18 + 3 * q^19 - 5 * q^20 - 2 * q^21 - 7 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 6 * q^27 + 2 * q^28 - 7 * q^29 - 12 * q^30 - 7 * q^31 - 3 * q^32 + 9 * q^34 - 8 * q^35 + 8 * q^36 - 12 * q^37 - 3 * q^38 + 5 * q^40 + 21 * q^41 + 2 * q^42 - 18 * q^43 + 7 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^47 - 3 * q^48 - q^49 + 2 * q^50 + 9 * q^51 + 3 * q^53 + 6 * q^54 - 14 * q^55 - 2 * q^56 - 3 * q^57 + 7 * q^58 - 4 * q^59 + 12 * q^60 - 10 * q^61 + 7 * q^62 + 10 * q^63 + 3 * q^64 + 8 * q^67 - 9 * q^68 - 32 * q^69 + 8 * q^70 - 3 * q^71 - 8 * q^72 + 4 * q^73 + 12 * q^74 - 19 * q^75 + 3 * q^76 + 28 * q^77 - 26 * q^79 - 5 * q^80 - 25 * q^81 - 21 * q^82 + 31 * q^83 - 2 * q^84 + 8 * q^85 + 18 * q^86 - 7 * q^88 + 17 * q^89 + 18 * q^90 - 3 * q^92 + 14 * q^93 + 12 * q^94 - 5 * q^95 + 3 * q^96 - 13 * q^97 + q^98 + 21 * 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
$3$	2.04892	1.18294	0.591471	−	0.806326i	$-0.298547\pi$
$3$	2.04892	1.18294	0.591471	+	0.806326i	$0.298547\pi$
$4$	1.00000	0.500000
$5$	−0.198062	−0.0885761	−0.0442881	−	0.999019i	$-0.514102\pi$
$5$	−0.198062	−0.0885761	−0.0442881	+	0.999019i	$0.514102\pi$
$6$	−2.04892	−0.836467
$7$	0.890084	0.336420	0.168210	−	0.985751i	$-0.446201\pi$
$7$	0.890084	0.336420	0.168210	+	0.985751i	$0.446201\pi$
$8$	−1.00000	−0.353553
$9$	1.19806	0.399354
$10$	0.198062	0.0626328
$11$	4.13706	1.24737	0.623686	−	0.781675i	$-0.285634\pi$
$11$	4.13706	1.24737	0.623686	+	0.781675i	$0.285634\pi$
$12$	2.04892	0.591471
$13$	0	0
$13$	0	0
$14$	−0.890084	−0.237885
$15$	−0.405813	−0.104781
$16$	1.00000	0.250000
$17$	−2.66487	−0.646327	−0.323163	−	0.946343i	$-0.604746\pi$
$17$	−2.66487	−0.646327	−0.323163	+	0.946343i	$0.604746\pi$
$18$	−1.19806	−0.282386
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.198062	−0.0442881
$21$	1.82371	0.397966
$22$	−4.13706	−0.882025
$23$	−8.45473	−1.76293	−0.881467	−	0.472246i	$-0.843443\pi$
$23$	−8.45473	−1.76293	−0.881467	+	0.472246i	$0.843443\pi$
$24$	−2.04892	−0.418234
$25$	−4.96077	−0.992154
$26$	0	0
$27$	−3.69202	−0.710530
$28$	0.890084	0.168210
$29$	−4.13706	−0.768233	−0.384117	−	0.923285i	$-0.625494\pi$
$29$	−4.13706	−0.768233	−0.384117	+	0.923285i	$0.625494\pi$
$30$	0.405813	0.0740910
$31$	−1.08815	−0.195437	−0.0977184	−	0.995214i	$-0.531154\pi$
$31$	−1.08815	−0.195437	−0.0977184	+	0.995214i	$0.531154\pi$
$32$	−1.00000	−0.176777
$33$	8.47650	1.47557
$34$	2.66487	0.457022
$35$	−0.176292	−0.0297988
$36$	1.19806	0.199677
$37$	−10.7681	−1.77026	−0.885131	−	0.465342i	$-0.845932\pi$
$37$	−10.7681	−1.77026	−0.885131	+	0.465342i	$0.845932\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	0.198062	0.0313164
$41$	6.66487	1.04088	0.520439	−	0.853899i	$-0.325768\pi$
$41$	6.66487	1.04088	0.520439	+	0.853899i	$0.325768\pi$
$42$	−1.82371	−0.281404
$43$	6.19567	0.944831	0.472415	−	0.881376i	$-0.343382\pi$
$43$	6.19567	0.944831	0.472415	+	0.881376i	$0.343382\pi$
$44$	4.13706	0.623686
$45$	−0.237291	−0.0353732
$46$	8.45473	1.24658
$47$	−7.38404	−1.07707	−0.538537	−	0.842602i	$-0.681023\pi$
$47$	−7.38404	−1.07707	−0.538537	+	0.842602i	$0.681023\pi$
$48$	2.04892	0.295736
$49$	−6.20775	−0.886822
$50$	4.96077	0.701559
$51$	−5.46011	−0.764568
$52$	0	0
$53$	−3.40581	−0.467824	−0.233912	−	0.972258i	$-0.575153\pi$
$53$	−3.40581	−0.467824	−0.233912	+	0.972258i	$0.575153\pi$
$54$	3.69202	0.502420
$55$	−0.819396	−0.110487
$56$	−0.890084	−0.118942
$57$	2.04892	0.271386
$58$	4.13706	0.543223
$59$	−7.20775	−0.938369	−0.469185	−	0.883100i	$-0.655452\pi$
$59$	−7.20775	−0.938369	−0.469185	+	0.883100i	$0.655452\pi$
$60$	−0.405813	−0.0523903
$61$	−11.9215	−1.52640	−0.763199	−	0.646164i	$-0.776372\pi$
$61$	−11.9215	−1.52640	−0.763199	+	0.646164i	$0.776372\pi$
$62$	1.08815	0.138195
$63$	1.06638	0.134351
$64$	1.00000	0.125000
$65$	0	0
$66$	−8.47650	−1.04339
$67$	−3.87800	−0.473773	−0.236887	−	0.971537i	$-0.576127\pi$
$67$	−3.87800	−0.473773	−0.236887	+	0.971537i	$0.576127\pi$
$68$	−2.66487	−0.323163
$69$	−17.3230	−2.08545
$70$	0.176292	0.0210709
$71$	−6.07606	−0.721096	−0.360548	−	0.932741i	$-0.617410\pi$
$71$	−6.07606	−0.721096	−0.360548	+	0.932741i	$0.617410\pi$
$72$	−1.19806	−0.141193
$73$	5.16421	0.604425	0.302213	−	0.953241i	$-0.402275\pi$
$73$	5.16421	0.604425	0.302213	+	0.953241i	$0.402275\pi$
$74$	10.7681	1.25176
$75$	−10.1642	−1.17366
$76$	1.00000	0.114708
$77$	3.68233	0.419641
$78$	0	0
$79$	−15.6582	−1.76168	−0.880841	−	0.473412i	$-0.843022\pi$
$79$	−15.6582	−1.76168	−0.880841	+	0.473412i	$0.843022\pi$
$80$	−0.198062	−0.0221440
$81$	−11.1588	−1.23987
$82$	−6.66487	−0.736012
$83$	13.1588	1.44437	0.722185	−	0.691700i	$-0.243138\pi$
$83$	13.1588	1.44437	0.722185	+	0.691700i	$0.243138\pi$
$84$	1.82371	0.198983
$85$	0.527811	0.0572491
$86$	−6.19567	−0.668096
$87$	−8.47650	−0.908776
$88$	−4.13706	−0.441012
$89$	4.53319	0.480517	0.240258	−	0.970709i	$-0.422768\pi$
$89$	4.53319	0.480517	0.240258	+	0.970709i	$0.422768\pi$
$90$	0.237291	0.0250127
$91$	0	0
$92$	−8.45473	−0.881467
$93$	−2.22952	−0.231191
$94$	7.38404	0.761606
$95$	−0.198062	−0.0203208
$96$	−2.04892	−0.209117
$97$	−8.18060	−0.830614	−0.415307	−	0.909681i	$-0.636326\pi$
$97$	−8.18060	−0.830614	−0.415307	+	0.909681i	$0.636326\pi$
$98$	6.20775	0.627078
$99$	4.95646	0.498143
$100$	−4.96077	−0.496077
$101$	1.32975	0.132315	0.0661575	−	0.997809i	$-0.478926\pi$
$101$	1.32975	0.132315	0.0661575	+	0.997809i	$0.478926\pi$
$102$	5.46011	0.540631
$103$	−0.670251	−0.0660418	−0.0330209	−	0.999455i	$-0.510513\pi$
$103$	−0.670251	−0.0660418	−0.0330209	+	0.999455i	$0.510513\pi$
$104$	0	0
$105$	−0.361208	−0.0352503
$106$	3.40581	0.330802
$107$	13.1075	1.26715	0.633576	−	0.773680i	$-0.281586\pi$
$107$	13.1075	1.26715	0.633576	+	0.773680i	$0.281586\pi$
$108$	−3.69202	−0.355265
$109$	15.0858	1.44495	0.722477	−	0.691395i	$-0.243004\pi$
$109$	15.0858	1.44495	0.722477	+	0.691395i	$0.243004\pi$
$110$	0.819396	0.0781264
$111$	−22.0629	−2.09412
$112$	0.890084	0.0841050
$113$	19.5254	1.83680	0.918398	−	0.395657i	$-0.129483\pi$
$113$	19.5254	1.83680	0.918398	+	0.395657i	$0.129483\pi$
$114$	−2.04892	−0.191899
$115$	1.67456	0.156154
$116$	−4.13706	−0.384117
$117$	0	0
$118$	7.20775	0.663527
$119$	−2.37196	−0.217437
$120$	0.405813	0.0370455
$121$	6.11529	0.555936
$122$	11.9215	1.07933
$123$	13.6558	1.23130
$124$	−1.08815	−0.0977184
$125$	1.97285	0.176457
$126$	−1.06638	−0.0950003
$127$	−13.2078	−1.17200	−0.585999	−	0.810312i	$-0.699298\pi$
$127$	−13.2078	−1.17200	−0.585999	+	0.810312i	$0.699298\pi$
$128$	−1.00000	−0.0883883
$129$	12.6944	1.11768
$130$	0	0
$131$	14.9879	1.30950	0.654750	−	0.755845i	$-0.272774\pi$
$131$	14.9879	1.30950	0.654750	+	0.755845i	$0.272774\pi$
$132$	8.47650	0.737785
$133$	0.890084	0.0771800
$134$	3.87800	0.335008
$135$	0.731250	0.0629360
$136$	2.66487	0.228511
$137$	−17.3056	−1.47852	−0.739258	−	0.673422i	$-0.764824\pi$
$137$	−17.3056	−1.47852	−0.739258	+	0.673422i	$0.764824\pi$
$138$	17.3230	1.47464
$139$	14.4155	1.22271	0.611353	−	0.791358i	$-0.290625\pi$
$139$	14.4155	1.22271	0.611353	+	0.791358i	$0.290625\pi$
$140$	−0.176292	−0.0148994
$141$	−15.1293	−1.27412
$142$	6.07606	0.509892
$143$	0	0
$144$	1.19806	0.0998385
$145$	0.819396	0.0680471
$146$	−5.16421	−0.427393
$147$	−12.7192	−1.04906
$148$	−10.7681	−0.885131
$149$	−5.38942	−0.441518	−0.220759	−	0.975328i	$-0.570854\pi$
$149$	−5.38942	−0.441518	−0.220759	+	0.975328i	$0.570854\pi$
$150$	10.1642	0.829904
$151$	15.9366	1.29690	0.648451	−	0.761256i	$-0.275417\pi$
$151$	15.9366	1.29690	0.648451	+	0.761256i	$0.275417\pi$
$152$	−1.00000	−0.0811107
$153$	−3.19269	−0.258113
$154$	−3.68233	−0.296731
$155$	0.215521	0.0173110
$156$	0	0
$157$	−10.5483	−0.841842	−0.420921	−	0.907097i	$-0.638293\pi$
$157$	−10.5483	−0.841842	−0.420921	+	0.907097i	$0.638293\pi$
$158$	15.6582	1.24570
$159$	−6.97823	−0.553410
$160$	0.198062	0.0156582
$161$	−7.52542	−0.593086
$162$	11.1588	0.876721
$163$	5.59850	0.438508	0.219254	−	0.975668i	$-0.429638\pi$
$163$	5.59850	0.438508	0.219254	+	0.975668i	$0.429638\pi$
$164$	6.66487	0.520439
$165$	−1.67887	−0.130700
$166$	−13.1588	−1.02132
$167$	−13.8485	−1.07163	−0.535813	−	0.844337i	$-0.679995\pi$
$167$	−13.8485	−1.07163	−0.535813	+	0.844337i	$0.679995\pi$
$168$	−1.82371	−0.140702
$169$	0	0
$170$	−0.527811	−0.0404813
$171$	1.19806	0.0916181
$172$	6.19567	0.472415
$173$	15.4523	1.17482	0.587410	−	0.809290i	$-0.300148\pi$
$173$	15.4523	1.17482	0.587410	+	0.809290i	$0.300148\pi$
$174$	8.47650	0.642602
$175$	−4.41550	−0.333781
$176$	4.13706	0.311843
$177$	−14.7681	−1.11004
$178$	−4.53319	−0.339777
$179$	−12.7114	−0.950095	−0.475047	−	0.879960i	$-0.657569\pi$
$179$	−12.7114	−0.950095	−0.475047	+	0.879960i	$0.657569\pi$
$180$	−0.237291	−0.0176866
$181$	13.4765	1.00170	0.500850	−	0.865534i	$-0.333021\pi$
$181$	13.4765	1.00170	0.500850	+	0.865534i	$0.333021\pi$
$182$	0	0
$183$	−24.4263	−1.80564
$184$	8.45473	0.623291
$185$	2.13275	0.156803
$186$	2.22952	0.163476
$187$	−11.0248	−0.806210
$188$	−7.38404	−0.538537
$189$	−3.28621	−0.239036
$190$	0.198062	0.0143689
$191$	18.5157	1.33975	0.669876	−	0.742473i	$-0.266347\pi$
$191$	18.5157	1.33975	0.669876	+	0.742473i	$0.266347\pi$
$192$	2.04892	0.147868
$193$	3.55496	0.255891	0.127946	−	0.991781i	$-0.459162\pi$
$193$	3.55496	0.255891	0.127946	+	0.991781i	$0.459162\pi$
$194$	8.18060	0.587333
$195$	0	0
$196$	−6.20775	−0.443411
$197$	2.19567	0.156435	0.0782175	−	0.996936i	$-0.475077\pi$
$197$	2.19567	0.156435	0.0782175	+	0.996936i	$0.475077\pi$
$198$	−4.95646	−0.352240
$199$	−15.2228	−1.07912	−0.539558	−	0.841948i	$-0.681409\pi$
$199$	−15.2228	−1.07912	−0.539558	+	0.841948i	$0.681409\pi$
$200$	4.96077	0.350780
$201$	−7.94571	−0.560447
$202$	−1.32975	−0.0935608
$203$	−3.68233	−0.258449
$204$	−5.46011	−0.382284
$205$	−1.32006	−0.0921970
$206$	0.670251	0.0466986
$207$	−10.1293	−0.704035
$208$	0	0
$209$	4.13706	0.286167
$210$	0.361208	0.0249257
$211$	−17.2905	−1.19033	−0.595164	−	0.803604i	$-0.702913\pi$
$211$	−17.2905	−1.19033	−0.595164	+	0.803604i	$0.702913\pi$
$212$	−3.40581	−0.233912
$213$	−12.4494	−0.853016
$214$	−13.1075	−0.896012
$215$	−1.22713	−0.0836895
$216$	3.69202	0.251210
$217$	−0.968541	−0.0657489
$218$	−15.0858	−1.02174
$219$	10.5810	0.715000
$220$	−0.819396	−0.0552437
$221$	0	0
$222$	22.0629	1.48077
$223$	−19.8726	−1.33077	−0.665385	−	0.746501i	$-0.731732\pi$
$223$	−19.8726	−1.33077	−0.665385	+	0.746501i	$0.731732\pi$
$224$	−0.890084	−0.0594712
$225$	−5.94331	−0.396221
$226$	−19.5254	−1.29881
$227$	4.76809	0.316469	0.158234	−	0.987402i	$-0.449420\pi$
$227$	4.76809	0.316469	0.158234	+	0.987402i	$0.449420\pi$
$228$	2.04892	0.135693
$229$	23.8931	1.57890	0.789449	−	0.613816i	$-0.210366\pi$
$229$	23.8931	1.57890	0.789449	+	0.613816i	$0.210366\pi$
$230$	−1.67456	−0.110417
$231$	7.54480	0.496411
$232$	4.13706	0.271612
$233$	11.7778	0.771588	0.385794	−	0.922585i	$-0.373928\pi$
$233$	11.7778	0.771588	0.385794	+	0.922585i	$0.373928\pi$
$234$	0	0
$235$	1.46250	0.0954030
$236$	−7.20775	−0.469185
$237$	−32.0823	−2.08397
$238$	2.37196	0.153751
$239$	12.2983	0.795510	0.397755	−	0.917492i	$-0.369789\pi$
$239$	12.2983	0.795510	0.397755	+	0.917492i	$0.369789\pi$
$240$	−0.405813	−0.0261951
$241$	−0.613564	−0.0395231	−0.0197616	−	0.999805i	$-0.506291\pi$
$241$	−0.613564	−0.0395231	−0.0197616	+	0.999805i	$0.506291\pi$
$242$	−6.11529	−0.393106
$243$	−11.7875	−0.756166
$244$	−11.9215	−0.763199
$245$	1.22952	0.0785512
$246$	−13.6558	−0.870661
$247$	0	0
$248$	1.08815	0.0690973
$249$	26.9614	1.70861
$250$	−1.97285	−0.124774
$251$	−21.1836	−1.33710	−0.668548	−	0.743669i	$-0.733084\pi$
$251$	−21.1836	−1.33710	−0.668548	+	0.743669i	$0.733084\pi$
$252$	1.06638	0.0671754
$253$	−34.9778	−2.19903
$254$	13.2078	0.828728
$255$	1.08144	0.0677225
$256$	1.00000	0.0625000
$257$	15.1535	0.945247	0.472623	−	0.881265i	$-0.343307\pi$
$257$	15.1535	0.945247	0.472623	+	0.881265i	$0.343307\pi$
$258$	−12.6944	−0.790320
$259$	−9.58450	−0.595552
$260$	0	0
$261$	−4.95646	−0.306797
$262$	−14.9879	−0.925957
$263$	−9.45712	−0.583151	−0.291576	−	0.956548i	$-0.594179\pi$
$263$	−9.45712	−0.583151	−0.291576	+	0.956548i	$0.594179\pi$
$264$	−8.47650	−0.521693
$265$	0.674563	0.0414381
$266$	−0.890084	−0.0545745
$267$	9.28813	0.568424
$268$	−3.87800	−0.236887
$269$	−13.4034	−0.817221	−0.408610	−	0.912709i	$-0.633987\pi$
$269$	−13.4034	−0.817221	−0.408610	+	0.912709i	$0.633987\pi$
$270$	−0.731250	−0.0445025
$271$	24.7138	1.50126	0.750628	−	0.660725i	$-0.229751\pi$
$271$	24.7138	1.50126	0.750628	+	0.660725i	$0.229751\pi$
$272$	−2.66487	−0.161582
$273$	0	0
$274$	17.3056	1.04547
$275$	−20.5230	−1.23758
$276$	−17.3230	−1.04272
$277$	8.78746	0.527987	0.263994	−	0.964524i	$-0.414960\pi$
$277$	8.78746	0.527987	0.263994	+	0.964524i	$0.414960\pi$
$278$	−14.4155	−0.864584
$279$	−1.30367	−0.0780485
$280$	0.176292	0.0105355
$281$	17.7168	1.05689	0.528447	−	0.848966i	$-0.322774\pi$
$281$	17.7168	1.05689	0.528447	+	0.848966i	$0.322774\pi$
$282$	15.1293	0.900936
$283$	−9.96508	−0.592363	−0.296181	−	0.955132i	$-0.595713\pi$
$283$	−9.96508	−0.592363	−0.296181	+	0.955132i	$0.595713\pi$
$284$	−6.07606	−0.360548
$285$	−0.405813	−0.0240383
$286$	0	0
$287$	5.93230	0.350172
$288$	−1.19806	−0.0705965
$289$	−9.89844	−0.582261
$290$	−0.819396	−0.0481166
$291$	−16.7614	−0.982570
$292$	5.16421	0.302213
$293$	−11.1099	−0.649048	−0.324524	−	0.945877i	$-0.605204\pi$
$293$	−11.1099	−0.649048	−0.324524	+	0.945877i	$0.605204\pi$
$294$	12.7192	0.741797
$295$	1.42758	0.0831171
$296$	10.7681	0.625882
$297$	−15.2741	−0.886295
$298$	5.38942	0.312201
$299$	0	0
$300$	−10.1642	−0.586831
$301$	5.51466	0.317860
$302$	−15.9366	−0.917049
$303$	2.72455	0.156521
$304$	1.00000	0.0573539
$305$	2.36121	0.135202
$306$	3.19269	0.182514
$307$	−9.83446	−0.561282	−0.280641	−	0.959813i	$-0.590547\pi$
$307$	−9.83446	−0.561282	−0.280641	+	0.959813i	$0.590547\pi$
$308$	3.68233	0.209820
$309$	−1.37329	−0.0781237
$310$	−0.215521	−0.0122408
$311$	11.8726	0.673235	0.336617	−	0.941642i	$-0.390717\pi$
$311$	11.8726	0.673235	0.336617	+	0.941642i	$0.390717\pi$
$312$	0	0
$313$	−8.81402	−0.498198	−0.249099	−	0.968478i	$-0.580134\pi$
$313$	−8.81402	−0.498198	−0.249099	+	0.968478i	$0.580134\pi$
$314$	10.5483	0.595272
$315$	−0.211209	−0.0119003
$316$	−15.6582	−0.880841
$317$	12.7138	0.714078	0.357039	−	0.934090i	$-0.383786\pi$
$317$	12.7138	0.714078	0.357039	+	0.934090i	$0.383786\pi$
$318$	6.97823	0.391320
$319$	−17.1153	−0.958272
$320$	−0.198062	−0.0110720
$321$	26.8562	1.49897
$322$	7.52542	0.419375
$323$	−2.66487	−0.148278
$324$	−11.1588	−0.619935
$325$	0	0
$326$	−5.59850	−0.310072
$327$	30.9095	1.70930
$328$	−6.66487	−0.368006
$329$	−6.57242	−0.362349
$330$	1.67887	0.0924190
$331$	18.1715	0.998796	0.499398	−	0.866373i	$-0.333554\pi$
$331$	18.1715	0.998796	0.499398	+	0.866373i	$0.333554\pi$
$332$	13.1588	0.722185
$333$	−12.9008	−0.706962
$334$	13.8485	0.757754
$335$	0.768086	0.0419650
$336$	1.82371	0.0994914
$337$	13.9323	0.758941	0.379470	−	0.925204i	$-0.376106\pi$
$337$	13.9323	0.758941	0.379470	+	0.925204i	$0.376106\pi$
$338$	0	0
$339$	40.0060	2.17283
$340$	0.527811	0.0286246
$341$	−4.50173	−0.243782
$342$	−1.19806	−0.0647838
$343$	−11.7560	−0.634765
$344$	−6.19567	−0.334048
$345$	3.43104	0.184721
$346$	−15.4523	−0.830723
$347$	−8.02416	−0.430760	−0.215380	−	0.976530i	$-0.569099\pi$
$347$	−8.02416	−0.430760	−0.215380	+	0.976530i	$0.569099\pi$
$348$	−8.47650	−0.454388
$349$	−10.7192	−0.573784	−0.286892	−	0.957963i	$-0.592622\pi$
$349$	−10.7192	−0.573784	−0.286892	+	0.957963i	$0.592622\pi$
$350$	4.41550	0.236019
$351$	0	0
$352$	−4.13706	−0.220506
$353$	−36.1172	−1.92233	−0.961163	−	0.275983i	$-0.910997\pi$
$353$	−36.1172	−1.92233	−0.961163	+	0.275983i	$0.910997\pi$
$354$	14.7681	0.784915
$355$	1.20344	0.0638719
$356$	4.53319	0.240258
$357$	−4.85995	−0.257216
$358$	12.7114	0.671818
$359$	−32.3129	−1.70541	−0.852704	−	0.522394i	$-0.825039\pi$
$359$	−32.3129	−1.70541	−0.852704	+	0.522394i	$0.825039\pi$
$360$	0.237291	0.0125063
$361$	1.00000	0.0526316
$362$	−13.4765	−0.708309
$363$	12.5297	0.657640
$364$	0	0
$365$	−1.02284	−0.0535376
$366$	24.4263	1.27678
$367$	5.24027	0.273540	0.136770	−	0.990603i	$-0.456328\pi$
$367$	5.24027	0.273540	0.136770	+	0.990603i	$0.456328\pi$
$368$	−8.45473	−0.440733
$369$	7.98493	0.415679
$370$	−2.13275	−0.110876
$371$	−3.03146	−0.157386
$372$	−2.22952	−0.115595
$373$	−14.6213	−0.757064	−0.378532	−	0.925588i	$-0.623571\pi$
$373$	−14.6213	−0.757064	−0.378532	+	0.925588i	$0.623571\pi$
$374$	11.0248	0.570076
$375$	4.04221	0.208739
$376$	7.38404	0.380803
$377$	0	0
$378$	3.28621	0.169024
$379$	14.8116	0.760822	0.380411	−	0.924818i	$-0.375783\pi$
$379$	14.8116	0.760822	0.380411	+	0.924818i	$0.375783\pi$
$380$	−0.198062	−0.0101604
$381$	−27.0616	−1.38641
$382$	−18.5157	−0.947347
$383$	−12.2524	−0.626066	−0.313033	−	0.949742i	$-0.601345\pi$
$383$	−12.2524	−0.626066	−0.313033	+	0.949742i	$0.601345\pi$
$384$	−2.04892	−0.104558
$385$	−0.729331	−0.0371702
$386$	−3.55496	−0.180943
$387$	7.42280	0.377322
$388$	−8.18060	−0.415307
$389$	33.6969	1.70850	0.854251	−	0.519861i	$-0.174016\pi$
$389$	33.6969	1.70850	0.854251	+	0.519861i	$0.174016\pi$
$390$	0	0
$391$	22.5308	1.13943
$392$	6.20775	0.313539
$393$	30.7090	1.54906
$394$	−2.19567	−0.110616
$395$	3.10129	0.156043
$396$	4.95646	0.249071
$397$	0.198062	0.00994046	0.00497023	−	0.999988i	$-0.498418\pi$
$397$	0.198062	0.00994046	0.00497023	+	0.999988i	$0.498418\pi$
$398$	15.2228	0.763051
$399$	1.82371	0.0912996
$400$	−4.96077	−0.248039
$401$	−7.22952	−0.361025	−0.180513	−	0.983573i	$-0.557776\pi$
$401$	−7.22952	−0.361025	−0.180513	+	0.983573i	$0.557776\pi$
$402$	7.94571	0.396296
$403$	0	0
$404$	1.32975	0.0661575
$405$	2.21014	0.109823
$406$	3.68233	0.182751
$407$	−44.5483	−2.20817
$408$	5.46011	0.270316
$409$	−10.5483	−0.521578	−0.260789	−	0.965396i	$-0.583983\pi$
$409$	−10.5483	−0.521578	−0.260789	+	0.965396i	$0.583983\pi$
$410$	1.32006	0.0651931
$411$	−35.4577	−1.74900
$412$	−0.670251	−0.0330209
$413$	−6.41550	−0.315686
$414$	10.1293	0.497828
$415$	−2.60627	−0.127937
$416$	0	0
$417$	29.5362	1.44639
$418$	−4.13706	−0.202350
$419$	−9.92154	−0.484699	−0.242350	−	0.970189i	$-0.577918\pi$
$419$	−9.92154	−0.484699	−0.242350	+	0.970189i	$0.577918\pi$
$420$	−0.361208	−0.0176251
$421$	25.4577	1.24073	0.620367	−	0.784312i	$-0.286984\pi$
$421$	25.4577	1.24073	0.620367	+	0.784312i	$0.286984\pi$
$422$	17.2905	0.841689
$423$	−8.84654	−0.430134
$424$	3.40581	0.165401
$425$	13.2198	0.641256
$426$	12.4494	0.603173
$427$	−10.6112	−0.513511
$428$	13.1075	0.633576
$429$	0	0
$430$	1.22713	0.0591774
$431$	1.26145	0.0607621	0.0303811	−	0.999538i	$-0.490328\pi$
$431$	1.26145	0.0607621	0.0303811	+	0.999538i	$0.490328\pi$
$432$	−3.69202	−0.177632
$433$	−5.78017	−0.277777	−0.138889	−	0.990308i	$-0.544353\pi$
$433$	−5.78017	−0.277777	−0.138889	+	0.990308i	$0.544353\pi$
$434$	0.968541	0.0464915
$435$	1.67887	0.0804959
$436$	15.0858	0.722477
$437$	−8.45473	−0.404445
$438$	−10.5810	−0.505582
$439$	15.6668	0.747735	0.373868	−	0.927482i	$-0.378031\pi$
$439$	15.6668	0.747735	0.373868	+	0.927482i	$0.378031\pi$
$440$	0.819396	0.0390632
$441$	−7.43727	−0.354156
$442$	0	0
$443$	4.89008	0.232335	0.116167	−	0.993230i	$-0.462939\pi$
$443$	4.89008	0.232335	0.116167	+	0.993230i	$0.462939\pi$
$444$	−22.0629	−1.04706
$445$	−0.897853	−0.0425623
$446$	19.8726	0.940996
$447$	−11.0425	−0.522291
$448$	0.890084	0.0420525
$449$	−0.347207	−0.0163857	−0.00819286	−	0.999966i	$-0.502608\pi$
$449$	−0.347207	−0.0163857	−0.00819286	+	0.999966i	$0.502608\pi$
$450$	5.94331	0.280170
$451$	27.5730	1.29836
$452$	19.5254	0.918398
$453$	32.6528	1.53416
$454$	−4.76809	−0.223777
$455$	0	0
$456$	−2.04892	−0.0959493
$457$	−31.7754	−1.48639	−0.743195	−	0.669075i	$-0.766690\pi$
$457$	−31.7754	−1.48639	−0.743195	+	0.669075i	$0.766690\pi$
$458$	−23.8931	−1.11645
$459$	9.83877	0.459235
$460$	1.67456	0.0780769
$461$	28.2543	1.31593	0.657966	−	0.753047i	$-0.271417\pi$
$461$	28.2543	1.31593	0.657966	+	0.753047i	$0.271417\pi$
$462$	−7.54480	−0.351016
$463$	2.42029	0.112480	0.0562402	−	0.998417i	$-0.482089\pi$
$463$	2.42029	0.112480	0.0562402	+	0.998417i	$0.482089\pi$
$464$	−4.13706	−0.192058
$465$	0.441584	0.0204780
$466$	−11.7778	−0.545595
$467$	−10.5724	−0.489233	−0.244617	−	0.969620i	$-0.578662\pi$
$467$	−10.5724	−0.489233	−0.244617	+	0.969620i	$0.578662\pi$
$468$	0	0
$469$	−3.45175	−0.159387
$470$	−1.46250	−0.0674601
$471$	−21.6125	−0.995851
$472$	7.20775	0.331764
$473$	25.6319	1.17855
$474$	32.0823	1.47359
$475$	−4.96077	−0.227616
$476$	−2.37196	−0.108719
$477$	−4.08038	−0.186828
$478$	−12.2983	−0.562511
$479$	29.0616	1.32786	0.663929	−	0.747796i	$-0.268888\pi$
$479$	29.0616	1.32786	0.663929	+	0.747796i	$0.268888\pi$
$480$	0.405813	0.0185228
$481$	0	0
$482$	0.613564	0.0279471
$483$	−15.4190	−0.701587
$484$	6.11529	0.277968
$485$	1.62027	0.0735726
$486$	11.7875	0.534690
$487$	−11.9366	−0.540899	−0.270450	−	0.962734i	$-0.587172\pi$
$487$	−11.9366	−0.540899	−0.270450	+	0.962734i	$0.587172\pi$
$488$	11.9215	0.539663
$489$	11.4709	0.518730
$490$	−1.22952	−0.0555441
$491$	−29.3163	−1.32303	−0.661514	−	0.749933i	$-0.730086\pi$
$491$	−29.3163	−1.32303	−0.661514	+	0.749933i	$0.730086\pi$
$492$	13.6558	0.615650
$493$	11.0248	0.496530
$494$	0	0
$495$	−0.981688	−0.0441236
$496$	−1.08815	−0.0488592
$497$	−5.40821	−0.242591
$498$	−26.9614	−1.20817
$499$	−1.30499	−0.0584196	−0.0292098	−	0.999573i	$-0.509299\pi$
$499$	−1.30499	−0.0584196	−0.0292098	+	0.999573i	$0.509299\pi$
$500$	1.97285	0.0882287
$501$	−28.3744	−1.26767
$502$	21.1836	0.945470
$503$	−6.13275	−0.273446	−0.136723	−	0.990609i	$-0.543657\pi$
$503$	−6.13275	−0.273446	−0.136723	+	0.990609i	$0.543657\pi$
$504$	−1.06638	−0.0475002
$505$	−0.263373	−0.0117199
$506$	34.9778	1.55495
$507$	0	0
$508$	−13.2078	−0.585999
$509$	22.6219	1.00270	0.501350	−	0.865245i	$-0.332837\pi$
$509$	22.6219	1.00270	0.501350	+	0.865245i	$0.332837\pi$
$510$	−1.08144	−0.0478870
$511$	4.59658	0.203341
$512$	−1.00000	−0.0441942
$513$	−3.69202	−0.163007
$514$	−15.1535	−0.668390
$515$	0.132751	0.00584973
$516$	12.6944	0.558840
$517$	−30.5483	−1.34351
$518$	9.58450	0.421119
$519$	31.6606	1.38974
$520$	0	0
$521$	−11.0858	−0.485676	−0.242838	−	0.970067i	$-0.578078\pi$
$521$	−11.0858	−0.485676	−0.242838	+	0.970067i	$0.578078\pi$
$522$	4.95646	0.216938
$523$	−35.0834	−1.53409	−0.767044	−	0.641594i	$-0.778273\pi$
$523$	−35.0834	−1.53409	−0.767044	+	0.641594i	$0.778273\pi$
$524$	14.9879	0.654750
$525$	−9.04700	−0.394843
$526$	9.45712	0.412350
$527$	2.89977	0.126316
$528$	8.47650	0.368892
$529$	48.4825	2.10793
$530$	−0.674563	−0.0293011
$531$	−8.63533	−0.374742
$532$	0.890084	0.0385900
$533$	0	0
$534$	−9.28813	−0.401937
$535$	−2.59611	−0.112239
$536$	3.87800	0.167504
$537$	−26.0446	−1.12391
$538$	13.4034	0.577862
$539$	−25.6819	−1.10620
$540$	0.731250	0.0314680
$541$	−17.8261	−0.766404	−0.383202	−	0.923665i	$-0.625179\pi$
$541$	−17.8261	−0.766404	−0.383202	+	0.923665i	$0.625179\pi$
$542$	−24.7138	−1.06155
$543$	27.6122	1.18495
$544$	2.66487	0.114256
$545$	−2.98792	−0.127988
$546$	0	0
$547$	−13.1075	−0.560437	−0.280219	−	0.959936i	$-0.590407\pi$
$547$	−13.1075	−0.560437	−0.280219	+	0.959936i	$0.590407\pi$
$548$	−17.3056	−0.739258
$549$	−14.2828	−0.609573
$550$	20.5230	0.875105
$551$	−4.13706	−0.176245
$552$	17.3230	0.737318
$553$	−13.9371	−0.592665
$554$	−8.78746	−0.373344
$555$	4.36983	0.185489
$556$	14.4155	0.611353
$557$	35.4534	1.50221	0.751104	−	0.660183i	$-0.229521\pi$
$557$	35.4534	1.50221	0.751104	+	0.660183i	$0.229521\pi$
$558$	1.30367	0.0551886
$559$	0	0
$560$	−0.176292	−0.00744970
$561$	−22.5888	−0.953700
$562$	−17.7168	−0.747337
$563$	3.14914	0.132721	0.0663603	−	0.997796i	$-0.478861\pi$
$563$	3.14914	0.132721	0.0663603	+	0.997796i	$0.478861\pi$
$564$	−15.1293	−0.637058
$565$	−3.86725	−0.162696
$566$	9.96508	0.418864
$567$	−9.93230	−0.417117
$568$	6.07606	0.254946
$569$	20.3827	0.854488	0.427244	−	0.904136i	$-0.359485\pi$
$569$	20.3827	0.854488	0.427244	+	0.904136i	$0.359485\pi$
$570$	0.405813	0.0169976
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	0	0
$573$	37.9372	1.58485
$574$	−5.93230	−0.247609
$575$	41.9420	1.74910
$576$	1.19806	0.0499193
$577$	30.6219	1.27481	0.637404	−	0.770530i	$-0.280008\pi$
$577$	30.6219	1.27481	0.637404	+	0.770530i	$0.280008\pi$
$578$	9.89844	0.411721
$579$	7.28382	0.302705
$580$	0.819396	0.0340236
$581$	11.7125	0.485915
$582$	16.7614	0.694782
$583$	−14.0901	−0.583551
$584$	−5.16421	−0.213697
$585$	0	0
$586$	11.1099	0.458946
$587$	−3.40342	−0.140474	−0.0702371	−	0.997530i	$-0.522376\pi$
$587$	−3.40342	−0.140474	−0.0702371	+	0.997530i	$0.522376\pi$
$588$	−12.7192	−0.524530
$589$	−1.08815	−0.0448363
$590$	−1.42758	−0.0587727
$591$	4.49875	0.185054
$592$	−10.7681	−0.442566
$593$	4.31767	0.177305	0.0886527	−	0.996063i	$-0.471744\pi$
$593$	4.31767	0.177305	0.0886527	+	0.996063i	$0.471744\pi$
$594$	15.2741	0.626705
$595$	0.469796	0.0192598
$596$	−5.38942	−0.220759
$597$	−31.1903	−1.27653
$598$	0	0
$599$	−13.0616	−0.533682	−0.266841	−	0.963741i	$-0.585980\pi$
$599$	−13.0616	−0.533682	−0.266841	+	0.963741i	$0.585980\pi$
$600$	10.1642	0.414952
$601$	−42.7284	−1.74293	−0.871464	−	0.490460i	$-0.836829\pi$
$601$	−42.7284	−1.74293	−0.871464	+	0.490460i	$0.836829\pi$
$602$	−5.51466	−0.224761
$603$	−4.64609	−0.189203
$604$	15.9366	0.648451
$605$	−1.21121	−0.0492426
$606$	−2.72455	−0.110677
$607$	−43.9168	−1.78253	−0.891263	−	0.453487i	$-0.850180\pi$
$607$	−43.9168	−1.78253	−0.891263	+	0.453487i	$0.850180\pi$
$608$	−1.00000	−0.0405554
$609$	−7.54480	−0.305731
$610$	−2.36121	−0.0956025
$611$	0	0
$612$	−3.19269	−0.129057
$613$	1.42519	0.0575629	0.0287815	−	0.999586i	$-0.490837\pi$
$613$	1.42519	0.0575629	0.0287815	+	0.999586i	$0.490837\pi$
$614$	9.83446	0.396887
$615$	−2.70469	−0.109064
$616$	−3.68233	−0.148365
$617$	−12.4832	−0.502555	−0.251277	−	0.967915i	$-0.580851\pi$
$617$	−12.4832	−0.502555	−0.251277	+	0.967915i	$0.580851\pi$
$618$	1.37329	0.0552418
$619$	−36.1148	−1.45158	−0.725789	−	0.687918i	$-0.758525\pi$
$619$	−36.1148	−1.45158	−0.725789	+	0.687918i	$0.758525\pi$
$620$	0.215521	0.00865552
$621$	31.2150	1.25262
$622$	−11.8726	−0.476049
$623$	4.03492	0.161656
$624$	0	0
$625$	24.4131	0.976524
$626$	8.81402	0.352279
$627$	8.47650	0.338519
$628$	−10.5483	−0.420921
$629$	28.6956	1.14417
$630$	0.211209	0.00841476
$631$	2.85517	0.113662	0.0568312	−	0.998384i	$-0.481900\pi$
$631$	2.85517	0.113662	0.0568312	+	0.998384i	$0.481900\pi$
$632$	15.6582	0.622849
$633$	−35.4268	−1.40809
$634$	−12.7138	−0.504929
$635$	2.61596	0.103811
$636$	−6.97823	−0.276705
$637$	0	0
$638$	17.1153	0.677601
$639$	−7.27950	−0.287973
$640$	0.198062	0.00782910
$641$	−19.0508	−0.752463	−0.376231	−	0.926526i	$-0.622780\pi$
$641$	−19.0508	−0.752463	−0.376231	+	0.926526i	$0.622780\pi$
$642$	−26.8562	−1.05993
$643$	50.0877	1.97526	0.987632	−	0.156787i	$-0.0501135\pi$
$643$	50.0877	1.97526	0.987632	+	0.156787i	$0.0501135\pi$
$644$	−7.52542	−0.296543
$645$	−2.51428	−0.0989999
$646$	2.66487	0.104848
$647$	4.00836	0.157585	0.0787925	−	0.996891i	$-0.474894\pi$
$647$	4.00836	0.157585	0.0787925	+	0.996891i	$0.474894\pi$
$648$	11.1588	0.438360
$649$	−29.8189	−1.17050
$650$	0	0
$651$	−1.98446	−0.0777771
$652$	5.59850	0.219254
$653$	14.8116	0.579624	0.289812	−	0.957084i	$-0.406407\pi$
$653$	14.8116	0.579624	0.289812	+	0.957084i	$0.406407\pi$
$654$	−30.9095	−1.20866
$655$	−2.96854	−0.115990
$656$	6.66487	0.260220
$657$	6.18705	0.241380
$658$	6.57242	0.256219
$659$	13.0019	0.506483	0.253241	−	0.967403i	$-0.418503\pi$
$659$	13.0019	0.506483	0.253241	+	0.967403i	$0.418503\pi$
$660$	−1.67887	−0.0653501
$661$	−2.18705	−0.0850662	−0.0425331	−	0.999095i	$-0.513543\pi$
$661$	−2.18705	−0.0850662	−0.0425331	+	0.999095i	$0.513543\pi$
$662$	−18.1715	−0.706256
$663$	0	0
$664$	−13.1588	−0.510662
$665$	−0.176292	−0.00683631
$666$	12.9008	0.499897
$667$	34.9778	1.35434
$668$	−13.8485	−0.535813
$669$	−40.7174	−1.57422
$670$	−0.768086	−0.0296737
$671$	−49.3202	−1.90398
$672$	−1.82371	−0.0703511
$673$	−40.6762	−1.56795	−0.783977	−	0.620790i	$-0.786812\pi$
$673$	−40.6762	−1.56795	−0.783977	+	0.620790i	$0.786812\pi$
$674$	−13.9323	−0.536652
$675$	18.3153	0.704955
$676$	0	0
$677$	−1.47757	−0.0567875	−0.0283937	−	0.999597i	$-0.509039\pi$
$677$	−1.47757	−0.0567875	−0.0283937	+	0.999597i	$0.509039\pi$
$678$	−40.0060	−1.53642
$679$	−7.28142	−0.279435
$680$	−0.527811	−0.0202406
$681$	9.76941	0.374365
$682$	4.50173	0.172380
$683$	48.2210	1.84513	0.922563	−	0.385847i	$-0.126091\pi$
$683$	48.2210	1.84513	0.922563	+	0.385847i	$0.126091\pi$
$684$	1.19806	0.0458091
$685$	3.42758	0.130961
$686$	11.7560	0.448846
$687$	48.9549	1.86775
$688$	6.19567	0.236208
$689$	0	0
$690$	−3.43104	−0.130618
$691$	−9.73019	−0.370154	−0.185077	−	0.982724i	$-0.559253\pi$
$691$	−9.73019	−0.370154	−0.185077	+	0.982724i	$0.559253\pi$
$692$	15.4523	0.587410
$693$	4.41166	0.167585
$694$	8.02416	0.304593
$695$	−2.85517	−0.108303
$696$	8.47650	0.321301
$697$	−17.7611	−0.672748
$698$	10.7192	0.405727
$699$	24.1317	0.912744
$700$	−4.41550	−0.166890
$701$	33.2030	1.25406	0.627029	−	0.778996i	$-0.284271\pi$
$701$	33.2030	1.25406	0.627029	+	0.778996i	$0.284271\pi$
$702$	0	0
$703$	−10.7681	−0.406126
$704$	4.13706	0.155921
$705$	2.99654	0.112856
$706$	36.1172	1.35929
$707$	1.18359	0.0445134
$708$	−14.7681	−0.555019
$709$	−12.1715	−0.457111	−0.228555	−	0.973531i	$-0.573400\pi$
$709$	−12.1715	−0.457111	−0.228555	+	0.973531i	$0.573400\pi$
$710$	−1.20344	−0.0451643
$711$	−18.7595	−0.703535
$712$	−4.53319	−0.169888
$713$	9.19998	0.344542
$714$	4.85995	0.181879
$715$	0	0
$716$	−12.7114	−0.475047
$717$	25.1982	0.941043
$718$	32.3129	1.20591
$719$	−8.43967	−0.314746	−0.157373	−	0.987539i	$-0.550303\pi$
$719$	−8.43967	−0.314746	−0.157373	+	0.987539i	$0.550303\pi$
$720$	−0.237291	−0.00884331
$721$	−0.596580	−0.0222178
$722$	−1.00000	−0.0372161
$723$	−1.25714	−0.0467536
$724$	13.4765	0.500850
$725$	20.5230	0.762206
$726$	−12.5297	−0.465022
$727$	16.8498	0.624924	0.312462	−	0.949930i	$-0.398846\pi$
$727$	16.8498	0.624924	0.312462	+	0.949930i	$0.398846\pi$
$728$	0	0
$729$	9.32496	0.345369
$730$	1.02284	0.0378568
$731$	−16.5107	−0.610670
$732$	−24.4263	−0.902820
$733$	−50.3086	−1.85819	−0.929095	−	0.369842i	$-0.879412\pi$
$733$	−50.3086	−1.85819	−0.929095	+	0.369842i	$0.879412\pi$
$734$	−5.24027	−0.193422
$735$	2.51919	0.0929216
$736$	8.45473	0.311646
$737$	−16.0435	−0.590971
$738$	−7.98493	−0.293930
$739$	9.67324	0.355836	0.177918	−	0.984045i	$-0.443064\pi$
$739$	9.67324	0.355836	0.177918	+	0.984045i	$0.443064\pi$
$740$	2.13275	0.0784015
$741$	0	0
$742$	3.03146	0.111288
$743$	−41.6364	−1.52749	−0.763746	−	0.645517i	$-0.776642\pi$
$743$	−41.6364	−1.52749	−0.763746	+	0.645517i	$0.776642\pi$
$744$	2.22952	0.0817382
$745$	1.06744	0.0391080
$746$	14.6213	0.535325
$747$	15.7651	0.576815
$748$	−11.0248	−0.403105
$749$	11.6668	0.426295
$750$	−4.04221	−0.147601
$751$	−43.1680	−1.57522	−0.787612	−	0.616171i	$-0.788683\pi$
$751$	−43.1680	−1.57522	−0.787612	+	0.616171i	$0.788683\pi$
$752$	−7.38404	−0.269268
$753$	−43.4034	−1.58171
$754$	0	0
$755$	−3.15644	−0.114875
$756$	−3.28621	−0.119518
$757$	23.1535	0.841527	0.420763	−	0.907170i	$-0.361762\pi$
$757$	23.1535	0.841527	0.420763	+	0.907170i	$0.361762\pi$
$758$	−14.8116	−0.537982
$759$	−71.6665	−2.60133
$760$	0.198062	0.00718447
$761$	22.2258	0.805685	0.402842	−	0.915269i	$-0.368022\pi$
$761$	22.2258	0.805685	0.402842	+	0.915269i	$0.368022\pi$
$762$	27.0616	0.980338
$763$	13.4276	0.486111
$764$	18.5157	0.669876
$765$	0.632351	0.0228627
$766$	12.2524	0.442696
$767$	0	0
$768$	2.04892	0.0739339
$769$	14.8552	0.535691	0.267846	−	0.963462i	$-0.413688\pi$
$769$	14.8552	0.535691	0.267846	+	0.963462i	$0.413688\pi$
$770$	0.729331	0.0262833
$771$	31.0482	1.11817
$772$	3.55496	0.127946
$773$	−0.537500	−0.0193325	−0.00966626	−	0.999953i	$-0.503077\pi$
$773$	−0.537500	−0.0193325	−0.00966626	+	0.999953i	$0.503077\pi$
$774$	−7.42280	−0.266807
$775$	5.39804	0.193903
$776$	8.18060	0.293667
$777$	−19.6378	−0.704504
$778$	−33.6969	−1.20809
$779$	6.66487	0.238794
$780$	0	0
$781$	−25.1371	−0.899475
$782$	−22.5308	−0.805700
$783$	15.2741	0.545853
$784$	−6.20775	−0.221705
$785$	2.08921	0.0745671
$786$	−30.7090	−1.09535
$787$	36.1124	1.28727	0.643634	−	0.765333i	$-0.277426\pi$
$787$	36.1124	1.28727	0.643634	+	0.765333i	$0.277426\pi$
$788$	2.19567	0.0782175
$789$	−19.3769	−0.689835
$790$	−3.10129	−0.110339
$791$	17.3793	0.617935
$792$	−4.95646	−0.176120
$793$	0	0
$794$	−0.198062	−0.00702897
$795$	1.38212	0.0490189
$796$	−15.2228	−0.539558
$797$	20.4413	0.724069	0.362034	−	0.932165i	$-0.382082\pi$
$797$	20.4413	0.724069	0.362034	+	0.932165i	$0.382082\pi$
$798$	−1.82371	−0.0645586
$799$	19.6775	0.696142
$800$	4.96077	0.175390
$801$	5.43104	0.191896
$802$	7.22952	0.255283
$803$	21.3647	0.753943
$804$	−7.94571	−0.280223
$805$	1.49050	0.0525333
$806$	0	0
$807$	−27.4625	−0.966726
$808$	−1.32975	−0.0467804
$809$	35.5271	1.24907	0.624533	−	0.780999i	$-0.285289\pi$
$809$	35.5271	1.24907	0.624533	+	0.780999i	$0.285289\pi$
$810$	−2.21014	−0.0776565
$811$	−12.9250	−0.453858	−0.226929	−	0.973911i	$-0.572869\pi$
$811$	−12.9250	−0.453858	−0.226929	+	0.973911i	$0.572869\pi$
$812$	−3.68233	−0.129225
$813$	50.6365	1.77590
$814$	44.5483	1.56142
$815$	−1.10885	−0.0388414
$816$	−5.46011	−0.191142
$817$	6.19567	0.216759
$818$	10.5483	0.368811
$819$	0	0
$820$	−1.32006	−0.0460985
$821$	−41.4905	−1.44803	−0.724014	−	0.689785i	$-0.757705\pi$
$821$	−41.4905	−1.44803	−0.724014	+	0.689785i	$0.757705\pi$
$822$	35.4577	1.23673
$823$	2.29185	0.0798888	0.0399444	−	0.999202i	$-0.487282\pi$
$823$	2.29185	0.0798888	0.0399444	+	0.999202i	$0.487282\pi$
$824$	0.670251	0.0233493
$825$	−42.0500	−1.46399
$826$	6.41550	0.223224
$827$	28.0194	0.974329	0.487165	−	0.873310i	$-0.338031\pi$
$827$	28.0194	0.974329	0.487165	+	0.873310i	$0.338031\pi$
$828$	−10.1293	−0.352017
$829$	−20.1497	−0.699829	−0.349915	−	0.936782i	$-0.613789\pi$
$829$	−20.1497	−0.699829	−0.349915	+	0.936782i	$0.613789\pi$
$830$	2.60627	0.0904649
$831$	18.0048	0.624579
$832$	0	0
$833$	16.5429	0.573177
$834$	−29.5362	−1.02275
$835$	2.74286	0.0949205
$836$	4.13706	0.143083
$837$	4.01746	0.138864
$838$	9.92154	0.342734
$839$	−46.7348	−1.61347	−0.806733	−	0.590917i	$-0.798766\pi$
$839$	−46.7348	−1.61347	−0.806733	+	0.590917i	$0.798766\pi$
$840$	0.361208	0.0124629
$841$	−11.8847	−0.409817
$842$	−25.4577	−0.877331
$843$	36.3002	1.25025
$844$	−17.2905	−0.595164
$845$	0	0
$846$	8.84654	0.304150
$847$	5.44312	0.187028
$848$	−3.40581	−0.116956
$849$	−20.4176	−0.700731
$850$	−13.2198	−0.453437
$851$	91.0413	3.12085
$852$	−12.4494	−0.426508
$853$	−9.02608	−0.309047	−0.154524	−	0.987989i	$-0.549384\pi$
$853$	−9.02608	−0.309047	−0.154524	+	0.987989i	$0.549384\pi$
$854$	10.6112	0.363107
$855$	−0.237291	−0.00811518
$856$	−13.1075	−0.448006
$857$	−14.0194	−0.478893	−0.239446	−	0.970910i	$-0.576966\pi$
$857$	−14.0194	−0.478893	−0.239446	+	0.970910i	$0.576966\pi$
$858$	0	0
$859$	−32.1500	−1.09694	−0.548472	−	0.836169i	$-0.684790\pi$
$859$	−32.1500	−1.09694	−0.548472	+	0.836169i	$0.684790\pi$
$860$	−1.22713	−0.0418447
$861$	12.1548	0.414234
$862$	−1.26145	−0.0429653
$863$	−31.5357	−1.07349	−0.536744	−	0.843745i	$-0.680346\pi$
$863$	−31.5357	−1.07349	−0.536744	+	0.843745i	$0.680346\pi$
$864$	3.69202	0.125605
$865$	−3.06052	−0.104061
$866$	5.78017	0.196418
$867$	−20.2811	−0.688782
$868$	−0.968541	−0.0328744
$869$	−64.7788	−2.19747
$870$	−1.67887	−0.0569192
$871$	0	0
$872$	−15.0858	−0.510868
$873$	−9.80087	−0.331709
$874$	8.45473	0.285986
$875$	1.75600	0.0593638
$876$	10.5810	0.357500
$877$	−39.3551	−1.32893	−0.664464	−	0.747321i	$-0.731340\pi$
$877$	−39.3551	−1.32893	−0.664464	+	0.747321i	$0.731340\pi$
$878$	−15.6668	−0.528729
$879$	−22.7633	−0.767787
$880$	−0.819396	−0.0276218
$881$	−39.9734	−1.34674	−0.673370	−	0.739306i	$-0.735154\pi$
$881$	−39.9734	−1.34674	−0.673370	+	0.739306i	$0.735154\pi$
$882$	7.43727	0.250426
$883$	30.1366	1.01418	0.507088	−	0.861894i	$-0.330722\pi$
$883$	30.1366	1.01418	0.507088	+	0.861894i	$0.330722\pi$
$884$	0	0
$885$	2.92500	0.0983228
$886$	−4.89008	−0.164286
$887$	−34.0823	−1.14437	−0.572186	−	0.820124i	$-0.693904\pi$
$887$	−34.0823	−1.14437	−0.572186	+	0.820124i	$0.693904\pi$
$888$	22.0629	0.740383
$889$	−11.7560	−0.394284
$890$	0.897853	0.0300961
$891$	−46.1648	−1.54658
$892$	−19.8726	−0.665385
$893$	−7.38404	−0.247098
$894$	11.0425	0.369316
$895$	2.51765	0.0841557
$896$	−0.890084	−0.0297356
$897$	0	0
$898$	0.347207	0.0115865
$899$	4.50173	0.150141
$900$	−5.94331	−0.198110
$901$	9.07606	0.302368
$902$	−27.5730	−0.918081
$903$	11.2991	0.376010
$904$	−19.5254	−0.649406
$905$	−2.66919	−0.0887268
$906$	−32.6528	−1.08482
$907$	35.2403	1.17013	0.585067	−	0.810985i	$-0.301068\pi$
$907$	35.2403	1.17013	0.585067	+	0.810985i	$0.301068\pi$
$908$	4.76809	0.158234
$909$	1.59312	0.0528405
$910$	0	0
$911$	23.8237	0.789315	0.394657	−	0.918828i	$-0.370863\pi$
$911$	23.8237	0.789315	0.394657	+	0.918828i	$0.370863\pi$
$912$	2.04892	0.0678464
$913$	54.4389	1.80167
$914$	31.7754	1.05104
$915$	4.83792	0.159937
$916$	23.8931	0.789449
$917$	13.3405	0.440542
$918$	−9.83877	−0.324728
$919$	−19.1675	−0.632276	−0.316138	−	0.948713i	$-0.602386\pi$
$919$	−19.1675	−0.632276	−0.316138	+	0.948713i	$0.602386\pi$
$920$	−1.67456	−0.0552087
$921$	−20.1500	−0.663965
$922$	−28.2543	−0.930505
$923$	0	0
$924$	7.54480	0.248206
$925$	53.4180	1.75637
$926$	−2.42029	−0.0795356
$927$	−0.803003	−0.0263741
$928$	4.13706	0.135806
$929$	−59.9120	−1.96565	−0.982824	−	0.184545i	$-0.940919\pi$
$929$	−59.9120	−1.96565	−0.982824	+	0.184545i	$0.940919\pi$
$930$	−0.441584	−0.0144801
$931$	−6.20775	−0.203451
$932$	11.7778	0.385794
$933$	24.3260	0.796398
$934$	10.5724	0.345940
$935$	2.18359	0.0714110
$936$	0	0
$937$	−45.9057	−1.49968	−0.749838	−	0.661622i	$-0.769868\pi$
$937$	−45.9057	−1.49968	−0.749838	+	0.661622i	$0.769868\pi$
$938$	3.45175	0.112704
$939$	−18.0592	−0.589340
$940$	1.46250	0.0477015
$941$	16.8009	0.547693	0.273846	−	0.961773i	$-0.411704\pi$
$941$	16.8009	0.547693	0.273846	+	0.961773i	$0.411704\pi$
$942$	21.6125	0.704173
$943$	−56.3497	−1.83500
$944$	−7.20775	−0.234592
$945$	0.650874	0.0211729
$946$	−25.6319	−0.833364
$947$	−8.02774	−0.260866	−0.130433	−	0.991457i	$-0.541637\pi$
$947$	−8.02774	−0.260866	−0.130433	+	0.991457i	$0.541637\pi$
$948$	−32.0823	−1.04198
$949$	0	0
$950$	4.96077	0.160949
$951$	26.0495	0.844713
$952$	2.37196	0.0768757
$953$	23.1353	0.749425	0.374712	−	0.927141i	$-0.377741\pi$
$953$	23.1353	0.749425	0.374712	+	0.927141i	$0.377741\pi$
$954$	4.08038	0.132107
$955$	−3.66727	−0.118670
$956$	12.2983	0.397755
$957$	−35.0678	−1.13358
$958$	−29.0616	−0.938937
$959$	−15.4034	−0.497402
$960$	−0.405813	−0.0130976
$961$	−29.8159	−0.961804
$962$	0	0
$963$	15.7036	0.506042
$964$	−0.613564	−0.0197616
$965$	−0.704103	−0.0226659
$966$	15.4190	0.496097
$967$	−3.93495	−0.126540	−0.0632698	−	0.997996i	$-0.520153\pi$
$967$	−3.93495	−0.126540	−0.0632698	+	0.997996i	$0.520153\pi$
$968$	−6.11529	−0.196553
$969$	−5.46011	−0.175404
$970$	−1.62027	−0.0520237
$971$	−9.46011	−0.303589	−0.151795	−	0.988412i	$-0.548505\pi$
$971$	−9.46011	−0.303589	−0.151795	+	0.988412i	$0.548505\pi$
$972$	−11.7875	−0.378083
$973$	12.8310	0.411343
$974$	11.9366	0.382474
$975$	0	0
$976$	−11.9215	−0.381599
$977$	33.8340	1.08245	0.541223	−	0.840879i	$-0.317962\pi$
$977$	33.8340	1.08245	0.541223	+	0.840879i	$0.317962\pi$
$978$	−11.4709	−0.366798
$979$	18.7541	0.599383
$980$	1.22952	0.0392756
$981$	18.0737	0.577048
$982$	29.3163	0.935522
$983$	−13.7614	−0.438920	−0.219460	−	0.975622i	$-0.570430\pi$
$983$	−13.7614	−0.438920	−0.219460	+	0.975622i	$0.570430\pi$
$984$	−13.6558	−0.435330
$985$	−0.434879	−0.0138564
$986$	−11.0248	−0.351100
$987$	−13.4663	−0.428638
$988$	0	0
$989$	−52.3827	−1.66567
$990$	0.981688	0.0312001
$991$	24.7525	0.786291	0.393145	−	0.919476i	$-0.371387\pi$
$991$	24.7525	0.786291	0.393145	+	0.919476i	$0.371387\pi$
$992$	1.08815	0.0345487
$993$	37.2319	1.18152
$994$	5.40821	0.171538
$995$	3.01507	0.0955840
$996$	26.9614	0.854303
$997$	58.4951	1.85256	0.926280	−	0.376836i	$-0.122988\pi$
$997$	58.4951	1.85256	0.926280	+	0.376836i	$0.122988\pi$
$998$	1.30499	0.0413089
$999$	39.7560	1.25782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6422.2.a.k.1.3		3
13.5	odd	4		494.2.d.b.77.6	yes	6
13.8	odd	4		494.2.d.b.77.3	✓	6
13.12	even	2		6422.2.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.b.77.3	✓	6	13.8	odd	4
494.2.d.b.77.6	yes	6	13.5	odd	4
6422.2.a.k.1.3		3	1.1	even	1	trivial
6422.2.a.t.1.3		3	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6422 = 2 \cdot 13^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6422.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.04892 q^{3} +1.00000 q^{4} -0.198062 q^{5} -2.04892 q^{6} +0.890084 q^{7} -1.00000 q^{8} +1.19806 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.04892 q^{3} +1.00000 q^{4} -0.198062 q^{5} -2.04892 q^{6} +0.890084 q^{7} -1.00000 q^{8} +1.19806 q^{9} +0.198062 q^{10} +4.13706 q^{11} +2.04892 q^{12} -0.890084 q^{14} -0.405813 q^{15} +1.00000 q^{16} -2.66487 q^{17} -1.19806 q^{18} +1.00000 q^{19} -0.198062 q^{20} +1.82371 q^{21} -4.13706 q^{22} -8.45473 q^{23} -2.04892 q^{24} -4.96077 q^{25} -3.69202 q^{27} +0.890084 q^{28} -4.13706 q^{29} +0.405813 q^{30} -1.08815 q^{31} -1.00000 q^{32} +8.47650 q^{33} +2.66487 q^{34} -0.176292 q^{35} +1.19806 q^{36} -10.7681 q^{37} -1.00000 q^{38} +0.198062 q^{40} +6.66487 q^{41} -1.82371 q^{42} +6.19567 q^{43} +4.13706 q^{44} -0.237291 q^{45} +8.45473 q^{46} -7.38404 q^{47} +2.04892 q^{48} -6.20775 q^{49} +4.96077 q^{50} -5.46011 q^{51} -3.40581 q^{53} +3.69202 q^{54} -0.819396 q^{55} -0.890084 q^{56} +2.04892 q^{57} +4.13706 q^{58} -7.20775 q^{59} -0.405813 q^{60} -11.9215 q^{61} +1.08815 q^{62} +1.06638 q^{63} +1.00000 q^{64} -8.47650 q^{66} -3.87800 q^{67} -2.66487 q^{68} -17.3230 q^{69} +0.176292 q^{70} -6.07606 q^{71} -1.19806 q^{72} +5.16421 q^{73} +10.7681 q^{74} -10.1642 q^{75} +1.00000 q^{76} +3.68233 q^{77} -15.6582 q^{79} -0.198062 q^{80} -11.1588 q^{81} -6.66487 q^{82} +13.1588 q^{83} +1.82371 q^{84} +0.527811 q^{85} -6.19567 q^{86} -8.47650 q^{87} -4.13706 q^{88} +4.53319 q^{89} +0.237291 q^{90} -8.45473 q^{92} -2.22952 q^{93} +7.38404 q^{94} -0.198062 q^{95} -2.04892 q^{96} -8.18060 q^{97} +6.20775 q^{98} +4.95646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9} + 5 q^{10} + 7 q^{11} - 3 q^{12} - 2 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} - 8 q^{18} + 3 q^{19} - 5 q^{20} - 2 q^{21} - 7 q^{22} - 3 q^{23} + 3 q^{24} - 2 q^{25} - 6 q^{27} + 2 q^{28} - 7 q^{29} - 12 q^{30} - 7 q^{31} - 3 q^{32} + 9 q^{34} - 8 q^{35} + 8 q^{36} - 12 q^{37} - 3 q^{38} + 5 q^{40} + 21 q^{41} + 2 q^{42} - 18 q^{43} + 7 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{47} - 3 q^{48} - q^{49} + 2 q^{50} + 9 q^{51} + 3 q^{53} + 6 q^{54} - 14 q^{55} - 2 q^{56} - 3 q^{57} + 7 q^{58} - 4 q^{59} + 12 q^{60} - 10 q^{61} + 7 q^{62} + 10 q^{63} + 3 q^{64} + 8 q^{67} - 9 q^{68} - 32 q^{69} + 8 q^{70} - 3 q^{71} - 8 q^{72} + 4 q^{73} + 12 q^{74} - 19 q^{75} + 3 q^{76} + 28 q^{77} - 26 q^{79} - 5 q^{80} - 25 q^{81} - 21 q^{82} + 31 q^{83} - 2 q^{84} + 8 q^{85} + 18 q^{86} - 7 q^{88} + 17 q^{89} + 18 q^{90} - 3 q^{92} + 14 q^{93} + 12 q^{94} - 5 q^{95} + 3 q^{96} - 13 q^{97} + q^{98} + 21 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 - 3 * q^8 + 8 * q^9 + 5 * q^10 + 7 * q^11 - 3 * q^12 - 2 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 - 8 * q^18 + 3 * q^19 - 5 * q^20 - 2 * q^21 - 7 * q^22 - 3 * q^23 + 3 * q^24 - 2 * q^25 - 6 * q^27 + 2 * q^28 - 7 * q^29 - 12 * q^30 - 7 * q^31 - 3 * q^32 + 9 * q^34 - 8 * q^35 + 8 * q^36 - 12 * q^37 - 3 * q^38 + 5 * q^40 + 21 * q^41 + 2 * q^42 - 18 * q^43 + 7 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^47 - 3 * q^48 - q^49 + 2 * q^50 + 9 * q^51 + 3 * q^53 + 6 * q^54 - 14 * q^55 - 2 * q^56 - 3 * q^57 + 7 * q^58 - 4 * q^59 + 12 * q^60 - 10 * q^61 + 7 * q^62 + 10 * q^63 + 3 * q^64 + 8 * q^67 - 9 * q^68 - 32 * q^69 + 8 * q^70 - 3 * q^71 - 8 * q^72 + 4 * q^73 + 12 * q^74 - 19 * q^75 + 3 * q^76 + 28 * q^77 - 26 * q^79 - 5 * q^80 - 25 * q^81 - 21 * q^82 + 31 * q^83 - 2 * q^84 + 8 * q^85 + 18 * q^86 - 7 * q^88 + 17 * q^89 + 18 * q^90 - 3 * q^92 + 14 * q^93 + 12 * q^94 - 5 * q^95 + 3 * q^96 - 13 * q^97 + q^98 + 21 * q^99

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