LMFDB - Embedded newform 6034.2.a.n.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.632516 q^{3} +1.00000 q^{4} -0.321740 q^{5} -0.632516 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.59992 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.632516 q^{3} +1.00000 q^{4} -0.321740 q^{5} -0.632516 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.59992 q^{9} +0.321740 q^{10} -6.13579 q^{11} +0.632516 q^{12} -6.17301 q^{13} +1.00000 q^{14} -0.203506 q^{15} +1.00000 q^{16} -4.41675 q^{17} +2.59992 q^{18} -1.95390 q^{19} -0.321740 q^{20} -0.632516 q^{21} +6.13579 q^{22} -1.47676 q^{23} -0.632516 q^{24} -4.89648 q^{25} +6.17301 q^{26} -3.54204 q^{27} -1.00000 q^{28} +7.50658 q^{29} +0.203506 q^{30} +0.883615 q^{31} -1.00000 q^{32} -3.88099 q^{33} +4.41675 q^{34} +0.321740 q^{35} -2.59992 q^{36} -6.01483 q^{37} +1.95390 q^{38} -3.90453 q^{39} +0.321740 q^{40} +5.45149 q^{41} +0.632516 q^{42} -3.62475 q^{43} -6.13579 q^{44} +0.836500 q^{45} +1.47676 q^{46} +3.66636 q^{47} +0.632516 q^{48} +1.00000 q^{49} +4.89648 q^{50} -2.79367 q^{51} -6.17301 q^{52} -11.6099 q^{53} +3.54204 q^{54} +1.97413 q^{55} +1.00000 q^{56} -1.23588 q^{57} -7.50658 q^{58} -10.9745 q^{59} -0.203506 q^{60} +5.31575 q^{61} -0.883615 q^{62} +2.59992 q^{63} +1.00000 q^{64} +1.98611 q^{65} +3.88099 q^{66} +7.75011 q^{67} -4.41675 q^{68} -0.934074 q^{69} -0.321740 q^{70} +3.32133 q^{71} +2.59992 q^{72} -0.297693 q^{73} +6.01483 q^{74} -3.09710 q^{75} -1.95390 q^{76} +6.13579 q^{77} +3.90453 q^{78} +10.3255 q^{79} -0.321740 q^{80} +5.55937 q^{81} -5.45149 q^{82} -10.5391 q^{83} -0.632516 q^{84} +1.42105 q^{85} +3.62475 q^{86} +4.74804 q^{87} +6.13579 q^{88} +14.2235 q^{89} -0.836500 q^{90} +6.17301 q^{91} -1.47676 q^{92} +0.558901 q^{93} -3.66636 q^{94} +0.628649 q^{95} -0.632516 q^{96} -3.57404 q^{97} -1.00000 q^{98} +15.9526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.632516	0.365183	0.182592	−	0.983189i	$-0.441551\pi$
$3$	0.632516	0.365183	0.182592	+	0.983189i	$0.441551\pi$
$4$	1.00000	0.500000
$5$	−0.321740	−0.143887	−0.0719433	−	0.997409i	$-0.522920\pi$
$5$	−0.321740	−0.143887	−0.0719433	+	0.997409i	$0.522920\pi$
$6$	−0.632516	−0.258224
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.59992	−0.866641
$10$	0.321740	0.101743
$11$	−6.13579	−1.85001	−0.925006	−	0.379953i	$-0.875940\pi$
$11$	−6.13579	−1.85001	−0.925006	+	0.379953i	$0.875940\pi$
$12$	0.632516	0.182592
$13$	−6.17301	−1.71209	−0.856043	−	0.516904i	$-0.827084\pi$
$13$	−6.17301	−1.71209	−0.856043	+	0.516904i	$0.827084\pi$
$14$	1.00000	0.267261
$15$	−0.203506	−0.0525450
$16$	1.00000	0.250000
$17$	−4.41675	−1.07122	−0.535610	−	0.844466i	$-0.679918\pi$
$17$	−4.41675	−1.07122	−0.535610	+	0.844466i	$0.679918\pi$
$18$	2.59992	0.612808
$19$	−1.95390	−0.448256	−0.224128	−	0.974560i	$-0.571953\pi$
$19$	−1.95390	−0.448256	−0.224128	+	0.974560i	$0.571953\pi$
$20$	−0.321740	−0.0719433
$21$	−0.632516	−0.138026
$22$	6.13579	1.30816
$23$	−1.47676	−0.307926	−0.153963	−	0.988077i	$-0.549204\pi$
$23$	−1.47676	−0.307926	−0.153963	+	0.988077i	$0.549204\pi$
$24$	−0.632516	−0.129112
$25$	−4.89648	−0.979297
$26$	6.17301	1.21063
$27$	−3.54204	−0.681666
$28$	−1.00000	−0.188982
$29$	7.50658	1.39394	0.696969	−	0.717101i	$-0.254532\pi$
$29$	7.50658	1.39394	0.696969	+	0.717101i	$0.254532\pi$
$30$	0.203506	0.0371549
$31$	0.883615	0.158702	0.0793510	−	0.996847i	$-0.474715\pi$
$31$	0.883615	0.158702	0.0793510	+	0.996847i	$0.474715\pi$
$32$	−1.00000	−0.176777
$33$	−3.88099	−0.675594
$34$	4.41675	0.757466
$35$	0.321740	0.0543840
$36$	−2.59992	−0.433321
$37$	−6.01483	−0.988831	−0.494416	−	0.869226i	$-0.664618\pi$
$37$	−6.01483	−0.988831	−0.494416	+	0.869226i	$0.664618\pi$
$38$	1.95390	0.316965
$39$	−3.90453	−0.625225
$40$	0.321740	0.0508716
$41$	5.45149	0.851380	0.425690	−	0.904869i	$-0.360031\pi$
$41$	5.45149	0.851380	0.425690	+	0.904869i	$0.360031\pi$
$42$	0.632516	0.0975994
$43$	−3.62475	−0.552770	−0.276385	−	0.961047i	$-0.589136\pi$
$43$	−3.62475	−0.552770	−0.276385	+	0.961047i	$0.589136\pi$
$44$	−6.13579	−0.925006
$45$	0.836500	0.124698
$46$	1.47676	0.217736
$47$	3.66636	0.534794	0.267397	−	0.963586i	$-0.413837\pi$
$47$	3.66636	0.534794	0.267397	+	0.963586i	$0.413837\pi$
$48$	0.632516	0.0912958
$49$	1.00000	0.142857
$50$	4.89648	0.692467
$51$	−2.79367	−0.391191
$52$	−6.17301	−0.856043
$53$	−11.6099	−1.59475	−0.797373	−	0.603487i	$-0.793778\pi$
$53$	−11.6099	−1.59475	−0.797373	+	0.603487i	$0.793778\pi$
$54$	3.54204	0.482011
$55$	1.97413	0.266192
$56$	1.00000	0.133631
$57$	−1.23588	−0.163696
$58$	−7.50658	−0.985663
$59$	−10.9745	−1.42876	−0.714378	−	0.699760i	$-0.753290\pi$
$59$	−10.9745	−1.42876	−0.714378	+	0.699760i	$0.753290\pi$
$60$	−0.203506	−0.0262725
$61$	5.31575	0.680611	0.340306	−	0.940315i	$-0.389469\pi$
$61$	5.31575	0.680611	0.340306	+	0.940315i	$0.389469\pi$
$62$	−0.883615	−0.112219
$63$	2.59992	0.327560
$64$	1.00000	0.125000
$65$	1.98611	0.246346
$66$	3.88099	0.477717
$67$	7.75011	0.946827	0.473414	−	0.880840i	$-0.343022\pi$
$67$	7.75011	0.946827	0.473414	+	0.880840i	$0.343022\pi$
$68$	−4.41675	−0.535610
$69$	−0.934074	−0.112449
$70$	−0.321740	−0.0384553
$71$	3.32133	0.394169	0.197085	−	0.980386i	$-0.436853\pi$
$71$	3.32133	0.394169	0.197085	+	0.980386i	$0.436853\pi$
$72$	2.59992	0.306404
$73$	−0.297693	−0.0348423	−0.0174212	−	0.999848i	$-0.505546\pi$
$73$	−0.297693	−0.0348423	−0.0174212	+	0.999848i	$0.505546\pi$
$74$	6.01483	0.699209
$75$	−3.09710	−0.357623
$76$	−1.95390	−0.224128
$77$	6.13579	0.699239
$78$	3.90453	0.442101
$79$	10.3255	1.16170	0.580852	−	0.814009i	$-0.302719\pi$
$79$	10.3255	1.16170	0.580852	+	0.814009i	$0.302719\pi$
$80$	−0.321740	−0.0359716
$81$	5.55937	0.617708
$82$	−5.45149	−0.602017
$83$	−10.5391	−1.15682	−0.578411	−	0.815746i	$-0.696327\pi$
$83$	−10.5391	−1.15682	−0.578411	+	0.815746i	$0.696327\pi$
$84$	−0.632516	−0.0690132
$85$	1.42105	0.154134
$86$	3.62475	0.390867
$87$	4.74804	0.509043
$88$	6.13579	0.654078
$89$	14.2235	1.50769	0.753846	−	0.657051i	$-0.228196\pi$
$89$	14.2235	1.50769	0.753846	+	0.657051i	$0.228196\pi$
$90$	−0.836500	−0.0881748
$91$	6.17301	0.647108
$92$	−1.47676	−0.153963
$93$	0.558901	0.0579553
$94$	−3.66636	−0.378156
$95$	0.628649	0.0644981
$96$	−0.632516	−0.0645559
$97$	−3.57404	−0.362889	−0.181444	−	0.983401i	$-0.558077\pi$
$97$	−3.57404	−0.362889	−0.181444	+	0.983401i	$0.558077\pi$
$98$	−1.00000	−0.101015
$99$	15.9526	1.60330
$100$	−4.89648	−0.489648
$101$	−6.37269	−0.634106	−0.317053	−	0.948408i	$-0.602693\pi$
$101$	−6.37269	−0.634106	−0.317053	+	0.948408i	$0.602693\pi$
$102$	2.79367	0.276614
$103$	3.02702	0.298261	0.149131	−	0.988818i	$-0.452353\pi$
$103$	3.02702	0.298261	0.149131	+	0.988818i	$0.452353\pi$
$104$	6.17301	0.605314
$105$	0.203506	0.0198601
$106$	11.6099	1.12766
$107$	−1.85798	−0.179618	−0.0898090	−	0.995959i	$-0.528626\pi$
$107$	−1.85798	−0.179618	−0.0898090	+	0.995959i	$0.528626\pi$
$108$	−3.54204	−0.340833
$109$	−9.44677	−0.904837	−0.452418	−	0.891806i	$-0.649439\pi$
$109$	−9.44677	−0.904837	−0.452418	+	0.891806i	$0.649439\pi$
$110$	−1.97413	−0.188226
$111$	−3.80447	−0.361105
$112$	−1.00000	−0.0944911
$113$	12.4241	1.16876	0.584380	−	0.811480i	$-0.301338\pi$
$113$	12.4241	1.16876	0.584380	+	0.811480i	$0.301338\pi$
$114$	1.23588	0.115750
$115$	0.475133	0.0443064
$116$	7.50658	0.696969
$117$	16.0494	1.48376
$118$	10.9745	1.01028
$119$	4.41675	0.404883
$120$	0.203506	0.0185775
$121$	26.6480	2.42254
$122$	−5.31575	−0.481265
$123$	3.44816	0.310910
$124$	0.883615	0.0793510
$125$	3.18410	0.284794
$126$	−2.59992	−0.231620
$127$	−9.62882	−0.854419	−0.427210	−	0.904153i	$-0.640503\pi$
$127$	−9.62882	−0.854419	−0.427210	+	0.904153i	$0.640503\pi$
$128$	−1.00000	−0.0883883
$129$	−2.29272	−0.201862
$130$	−1.98611	−0.174193
$131$	14.6100	1.27648	0.638242	−	0.769836i	$-0.279662\pi$
$131$	14.6100	1.27648	0.638242	+	0.769836i	$0.279662\pi$
$132$	−3.88099	−0.337797
$133$	1.95390	0.169425
$134$	−7.75011	−0.669508
$135$	1.13962	0.0980826
$136$	4.41675	0.378733
$137$	4.48617	0.383280	0.191640	−	0.981465i	$-0.438619\pi$
$137$	4.48617	0.383280	0.191640	+	0.981465i	$0.438619\pi$
$138$	0.934074	0.0795137
$139$	−13.0596	−1.10770	−0.553852	−	0.832615i	$-0.686842\pi$
$139$	−13.0596	−1.10770	−0.553852	+	0.832615i	$0.686842\pi$
$140$	0.321740	0.0271920
$141$	2.31903	0.195298
$142$	−3.32133	−0.278720
$143$	37.8763	3.16738
$144$	−2.59992	−0.216660
$145$	−2.41517	−0.200569
$146$	0.297693	0.0246372
$147$	0.632516	0.0521691
$148$	−6.01483	−0.494416
$149$	−5.14666	−0.421631	−0.210815	−	0.977526i	$-0.567612\pi$
$149$	−5.14666	−0.421631	−0.210815	+	0.977526i	$0.567612\pi$
$150$	3.09710	0.252878
$151$	13.4881	1.09764	0.548822	−	0.835939i	$-0.315076\pi$
$151$	13.4881	1.09764	0.548822	+	0.835939i	$0.315076\pi$
$152$	1.95390	0.158483
$153$	11.4832	0.928363
$154$	−6.13579	−0.494436
$155$	−0.284294	−0.0228351
$156$	−3.90453	−0.312613
$157$	−5.47952	−0.437313	−0.218657	−	0.975802i	$-0.570167\pi$
$157$	−5.47952	−0.437313	−0.218657	+	0.975802i	$0.570167\pi$
$158$	−10.3255	−0.821449
$159$	−7.34347	−0.582375
$160$	0.321740	0.0254358
$161$	1.47676	0.116385
$162$	−5.55937	−0.436785
$163$	−11.4391	−0.895983	−0.447991	−	0.894038i	$-0.647860\pi$
$163$	−11.4391	−0.895983	−0.447991	+	0.894038i	$0.647860\pi$
$164$	5.45149	0.425690
$165$	1.24867	0.0972088
$166$	10.5391	0.817996
$167$	−8.45450	−0.654228	−0.327114	−	0.944985i	$-0.606076\pi$
$167$	−8.45450	−0.654228	−0.327114	+	0.944985i	$0.606076\pi$
$168$	0.632516	0.0487997
$169$	25.1061	1.93124
$170$	−1.42105	−0.108989
$171$	5.08000	0.388477
$172$	−3.62475	−0.276385
$173$	−12.9740	−0.986398	−0.493199	−	0.869916i	$-0.664173\pi$
$173$	−12.9740	−0.986398	−0.493199	+	0.869916i	$0.664173\pi$
$174$	−4.74804	−0.359948
$175$	4.89648	0.370139
$176$	−6.13579	−0.462503
$177$	−6.94154	−0.521758
$178$	−14.2235	−1.06610
$179$	18.4980	1.38260	0.691301	−	0.722567i	$-0.257038\pi$
$179$	18.4980	1.38260	0.691301	+	0.722567i	$0.257038\pi$
$180$	0.836500	0.0623490
$181$	−7.81010	−0.580520	−0.290260	−	0.956948i	$-0.593742\pi$
$181$	−7.81010	−0.580520	−0.290260	+	0.956948i	$0.593742\pi$
$182$	−6.17301	−0.457574
$183$	3.36230	0.248548
$184$	1.47676	0.108868
$185$	1.93521	0.142280
$186$	−0.558901	−0.0409806
$187$	27.1003	1.98177
$188$	3.66636	0.267397
$189$	3.54204	0.257646
$190$	−0.628649	−0.0456070
$191$	−13.4955	−0.976503	−0.488252	−	0.872703i	$-0.662365\pi$
$191$	−13.4955	−0.976503	−0.488252	+	0.872703i	$0.662365\pi$
$192$	0.632516	0.0456479
$193$	−0.696223	−0.0501152	−0.0250576	−	0.999686i	$-0.507977\pi$
$193$	−0.696223	−0.0501152	−0.0250576	+	0.999686i	$0.507977\pi$
$194$	3.57404	0.256601
$195$	1.25624	0.0899615
$196$	1.00000	0.0714286
$197$	−8.60111	−0.612804	−0.306402	−	0.951902i	$-0.599125\pi$
$197$	−8.60111	−0.612804	−0.306402	+	0.951902i	$0.599125\pi$
$198$	−15.9526	−1.13370
$199$	−11.1122	−0.787724	−0.393862	−	0.919170i	$-0.628861\pi$
$199$	−11.1122	−0.787724	−0.393862	+	0.919170i	$0.628861\pi$
$200$	4.89648	0.346234
$201$	4.90207	0.345766
$202$	6.37269	0.448381
$203$	−7.50658	−0.526859
$204$	−2.79367	−0.195596
$205$	−1.75396	−0.122502
$206$	−3.02702	−0.210902
$207$	3.83946	0.266861
$208$	−6.17301	−0.428022
$209$	11.9888	0.829279
$210$	−0.203506	−0.0140432
$211$	−28.9543	−1.99329	−0.996647	−	0.0818258i	$-0.973925\pi$
$211$	−28.9543	−1.99329	−0.996647	+	0.0818258i	$0.973925\pi$
$212$	−11.6099	−0.797373
$213$	2.10079	0.143944
$214$	1.85798	0.127009
$215$	1.16623	0.0795362
$216$	3.54204	0.241005
$217$	−0.883615	−0.0599837
$218$	9.44677	0.639816
$219$	−0.188296	−0.0127238
$220$	1.97413	0.133096
$221$	27.2647	1.83402
$222$	3.80447	0.255340
$223$	−8.37454	−0.560801	−0.280400	−	0.959883i	$-0.590467\pi$
$223$	−8.37454	−0.560801	−0.280400	+	0.959883i	$0.590467\pi$
$224$	1.00000	0.0668153
$225$	12.7305	0.848699
$226$	−12.4241	−0.826438
$227$	20.3147	1.34833	0.674167	−	0.738579i	$-0.264503\pi$
$227$	20.3147	1.34833	0.674167	+	0.738579i	$0.264503\pi$
$228$	−1.23588	−0.0818479
$229$	−4.69795	−0.310449	−0.155225	−	0.987879i	$-0.549610\pi$
$229$	−4.69795	−0.310449	−0.155225	+	0.987879i	$0.549610\pi$
$230$	−0.475133	−0.0313293
$231$	3.88099	0.255350
$232$	−7.50658	−0.492831
$233$	−8.39479	−0.549961	−0.274980	−	0.961450i	$-0.588671\pi$
$233$	−8.39479	−0.549961	−0.274980	+	0.961450i	$0.588671\pi$
$234$	−16.0494	−1.04918
$235$	−1.17962	−0.0769497
$236$	−10.9745	−0.714378
$237$	6.53102	0.424235
$238$	−4.41675	−0.286295
$239$	−15.1964	−0.982973	−0.491487	−	0.870885i	$-0.663546\pi$
$239$	−15.1964	−0.982973	−0.491487	+	0.870885i	$0.663546\pi$
$240$	−0.203506	−0.0131362
$241$	25.8121	1.66270	0.831352	−	0.555747i	$-0.187567\pi$
$241$	25.8121	1.66270	0.831352	+	0.555747i	$0.187567\pi$
$242$	−26.6480	−1.71300
$243$	14.1425	0.907243
$244$	5.31575	0.340306
$245$	−0.321740	−0.0205552
$246$	−3.44816	−0.219847
$247$	12.0615	0.767453
$248$	−0.883615	−0.0561096
$249$	−6.66618	−0.422452
$250$	−3.18410	−0.201380
$251$	18.5296	1.16958	0.584790	−	0.811185i	$-0.301177\pi$
$251$	18.5296	1.16958	0.584790	+	0.811185i	$0.301177\pi$
$252$	2.59992	0.163780
$253$	9.06109	0.569666
$254$	9.62882	0.604166
$255$	0.898834	0.0562872
$256$	1.00000	0.0625000
$257$	10.9871	0.685359	0.342680	−	0.939452i	$-0.388665\pi$
$257$	10.9871	0.685359	0.342680	+	0.939452i	$0.388665\pi$
$258$	2.29272	0.142738
$259$	6.01483	0.373743
$260$	1.98611	0.123173
$261$	−19.5165	−1.20804
$262$	−14.6100	−0.902610
$263$	−4.06441	−0.250622	−0.125311	−	0.992117i	$-0.539993\pi$
$263$	−4.06441	−0.250622	−0.125311	+	0.992117i	$0.539993\pi$
$264$	3.88099	0.238858
$265$	3.73538	0.229463
$266$	−1.95390	−0.119802
$267$	8.99662	0.550584
$268$	7.75011	0.473414
$269$	−8.60242	−0.524499	−0.262250	−	0.965000i	$-0.584464\pi$
$269$	−8.60242	−0.524499	−0.262250	+	0.965000i	$0.584464\pi$
$270$	−1.13962	−0.0693549
$271$	−19.0069	−1.15459	−0.577294	−	0.816537i	$-0.695891\pi$
$271$	−19.0069	−1.15459	−0.577294	+	0.816537i	$0.695891\pi$
$272$	−4.41675	−0.267805
$273$	3.90453	0.236313
$274$	−4.48617	−0.271020
$275$	30.0438	1.81171
$276$	−0.934074	−0.0562247
$277$	−30.6634	−1.84239	−0.921193	−	0.389105i	$-0.872784\pi$
$277$	−30.6634	−1.84239	−0.921193	+	0.389105i	$0.872784\pi$
$278$	13.0596	0.783264
$279$	−2.29733	−0.137538
$280$	−0.321740	−0.0192277
$281$	−27.5384	−1.64280	−0.821402	−	0.570350i	$-0.806808\pi$
$281$	−27.5384	−1.64280	−0.821402	+	0.570350i	$0.806808\pi$
$282$	−2.31903	−0.138096
$283$	−1.18924	−0.0706932	−0.0353466	−	0.999375i	$-0.511254\pi$
$283$	−1.18924	−0.0706932	−0.0353466	+	0.999375i	$0.511254\pi$
$284$	3.32133	0.197085
$285$	0.397631	0.0235536
$286$	−37.8763	−2.23968
$287$	−5.45149	−0.321792
$288$	2.59992	0.153202
$289$	2.50768	0.147510
$290$	2.41517	0.141824
$291$	−2.26064	−0.132521
$292$	−0.297693	−0.0174212
$293$	−9.16357	−0.535342	−0.267671	−	0.963510i	$-0.586254\pi$
$293$	−9.16357	−0.535342	−0.267671	+	0.963510i	$0.586254\pi$
$294$	−0.632516	−0.0368891
$295$	3.53093	0.205579
$296$	6.01483	0.349605
$297$	21.7332	1.26109
$298$	5.14666	0.298138
$299$	9.11606	0.527195
$300$	−3.09710	−0.178811
$301$	3.62475	0.208927
$302$	−13.4881	−0.776152
$303$	−4.03083	−0.231565
$304$	−1.95390	−0.112064
$305$	−1.71029	−0.0979309
$306$	−11.4832	−0.656451
$307$	−28.0502	−1.60091	−0.800456	−	0.599391i	$-0.795409\pi$
$307$	−28.0502	−1.60091	−0.800456	+	0.599391i	$0.795409\pi$
$308$	6.13579	0.349619
$309$	1.91464	0.108920
$310$	0.284294	0.0161468
$311$	−1.11890	−0.0634471	−0.0317235	−	0.999497i	$-0.510100\pi$
$311$	−1.11890	−0.0634471	−0.0317235	+	0.999497i	$0.510100\pi$
$312$	3.90453	0.221051
$313$	−10.7012	−0.604865	−0.302432	−	0.953171i	$-0.597799\pi$
$313$	−10.7012	−0.604865	−0.302432	+	0.953171i	$0.597799\pi$
$314$	5.47952	0.309227
$315$	−0.836500	−0.0471314
$316$	10.3255	0.580852
$317$	−4.27822	−0.240289	−0.120144	−	0.992756i	$-0.538336\pi$
$317$	−4.27822	−0.240289	−0.120144	+	0.992756i	$0.538336\pi$
$318$	7.34347	0.411801
$319$	−46.0589	−2.57880
$320$	−0.321740	−0.0179858
$321$	−1.17520	−0.0655935
$322$	−1.47676	−0.0822966
$323$	8.62990	0.480181
$324$	5.55937	0.308854
$325$	30.2261	1.67664
$326$	11.4391	0.633555
$327$	−5.97524	−0.330431
$328$	−5.45149	−0.301008
$329$	−3.66636	−0.202133
$330$	−1.24867	−0.0687370
$331$	1.17775	0.0647351	0.0323675	−	0.999476i	$-0.489695\pi$
$331$	1.17775	0.0647351	0.0323675	+	0.999476i	$0.489695\pi$
$332$	−10.5391	−0.578411
$333$	15.6381	0.856962
$334$	8.45450	0.462609
$335$	−2.49352	−0.136236
$336$	−0.632516	−0.0345066
$337$	−7.61369	−0.414744	−0.207372	−	0.978262i	$-0.566491\pi$
$337$	−7.61369	−0.414744	−0.207372	+	0.978262i	$0.566491\pi$
$338$	−25.1061	−1.36559
$339$	7.85844	0.426812
$340$	1.42105	0.0770670
$341$	−5.42168	−0.293600
$342$	−5.08000	−0.274695
$343$	−1.00000	−0.0539949
$344$	3.62475	0.195434
$345$	0.300529	0.0161800
$346$	12.9740	0.697489
$347$	6.02573	0.323478	0.161739	−	0.986834i	$-0.448290\pi$
$347$	6.02573	0.323478	0.161739	+	0.986834i	$0.448290\pi$
$348$	4.74804	0.254521
$349$	−6.80816	−0.364433	−0.182216	−	0.983258i	$-0.558327\pi$
$349$	−6.80816	−0.364433	−0.182216	+	0.983258i	$0.558327\pi$
$350$	−4.89648	−0.261728
$351$	21.8651	1.16707
$352$	6.13579	0.327039
$353$	12.2006	0.649372	0.324686	−	0.945822i	$-0.394741\pi$
$353$	12.2006	0.649372	0.324686	+	0.945822i	$0.394741\pi$
$354$	6.94154	0.368939
$355$	−1.06860	−0.0567156
$356$	14.2235	0.753846
$357$	2.79367	0.147856
$358$	−18.4980	−0.977648
$359$	35.8380	1.89146	0.945729	−	0.324957i	$-0.105350\pi$
$359$	35.8380	1.89146	0.945729	+	0.324957i	$0.105350\pi$
$360$	−0.836500	−0.0440874
$361$	−15.1823	−0.799066
$362$	7.81010	0.410490
$363$	16.8553	0.884673
$364$	6.17301	0.323554
$365$	0.0957797	0.00501334
$366$	−3.36230	−0.175750
$367$	−32.0340	−1.67216	−0.836081	−	0.548607i	$-0.815158\pi$
$367$	−32.0340	−1.67216	−0.836081	+	0.548607i	$0.815158\pi$
$368$	−1.47676	−0.0769814
$369$	−14.1735	−0.737841
$370$	−1.93521	−0.100607
$371$	11.6099	0.602757
$372$	0.558901	0.0289777
$373$	25.7329	1.33240	0.666201	−	0.745772i	$-0.267919\pi$
$373$	25.7329	1.33240	0.666201	+	0.745772i	$0.267919\pi$
$374$	−27.1003	−1.40132
$375$	2.01399	0.104002
$376$	−3.66636	−0.189078
$377$	−46.3383	−2.38654
$378$	−3.54204	−0.182183
$379$	−25.3657	−1.30295	−0.651474	−	0.758671i	$-0.725849\pi$
$379$	−25.3657	−1.30295	−0.651474	+	0.758671i	$0.725849\pi$
$380$	0.628649	0.0322490
$381$	−6.09038	−0.312020
$382$	13.4955	0.690492
$383$	21.4946	1.09832	0.549161	−	0.835717i	$-0.314947\pi$
$383$	21.4946	1.09832	0.549161	+	0.835717i	$0.314947\pi$
$384$	−0.632516	−0.0322780
$385$	−1.97413	−0.100611
$386$	0.696223	0.0354368
$387$	9.42408	0.479053
$388$	−3.57404	−0.181444
$389$	3.47999	0.176443	0.0882213	−	0.996101i	$-0.471882\pi$
$389$	3.47999	0.176443	0.0882213	+	0.996101i	$0.471882\pi$
$390$	−1.25624	−0.0636124
$391$	6.52248	0.329856
$392$	−1.00000	−0.0505076
$393$	9.24107	0.466150
$394$	8.60111	0.433318
$395$	−3.32211	−0.167154
$396$	15.9526	0.801648
$397$	33.7381	1.69327	0.846633	−	0.532178i	$-0.178626\pi$
$397$	33.7381	1.69327	0.846633	+	0.532178i	$0.178626\pi$
$398$	11.1122	0.557005
$399$	1.23588	0.0618712
$400$	−4.89648	−0.244824
$401$	−12.1011	−0.604300	−0.302150	−	0.953260i	$-0.597704\pi$
$401$	−12.1011	−0.604300	−0.302150	+	0.953260i	$0.597704\pi$
$402$	−4.90207	−0.244493
$403$	−5.45457	−0.271711
$404$	−6.37269	−0.317053
$405$	−1.78867	−0.0888799
$406$	7.50658	0.372546
$407$	36.9057	1.82935
$408$	2.79367	0.138307
$409$	1.22236	0.0604417	0.0302208	−	0.999543i	$-0.490379\pi$
$409$	1.22236	0.0604417	0.0302208	+	0.999543i	$0.490379\pi$
$410$	1.75396	0.0866221
$411$	2.83758	0.139967
$412$	3.02702	0.149131
$413$	10.9745	0.540019
$414$	−3.83946	−0.188699
$415$	3.39087	0.166451
$416$	6.17301	0.302657
$417$	−8.26042	−0.404515
$418$	−11.9888	−0.586389
$419$	5.23734	0.255861	0.127931	−	0.991783i	$-0.459167\pi$
$419$	5.23734	0.255861	0.127931	+	0.991783i	$0.459167\pi$
$420$	0.203506	0.00993007
$421$	−6.17262	−0.300835	−0.150418	−	0.988623i	$-0.548062\pi$
$421$	−6.17262	−0.300835	−0.150418	+	0.988623i	$0.548062\pi$
$422$	28.9543	1.40947
$423$	−9.53226	−0.463474
$424$	11.6099	0.563828
$425$	21.6265	1.04904
$426$	−2.10079	−0.101784
$427$	−5.31575	−0.257247
$428$	−1.85798	−0.0898090
$429$	23.9574	1.15667
$430$	−1.16623	−0.0562406
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−3.54204	−0.170417
$433$	−27.5362	−1.32330	−0.661652	−	0.749811i	$-0.730144\pi$
$433$	−27.5362	−1.32330	−0.661652	+	0.749811i	$0.730144\pi$
$434$	0.883615	0.0424149
$435$	−1.52763	−0.0732444
$436$	−9.44677	−0.452418
$437$	2.88545	0.138030
$438$	0.188296	0.00899711
$439$	−13.7298	−0.655289	−0.327645	−	0.944801i	$-0.606255\pi$
$439$	−13.7298	−0.655289	−0.327645	+	0.944801i	$0.606255\pi$
$440$	−1.97413	−0.0941130
$441$	−2.59992	−0.123806
$442$	−27.2647	−1.29685
$443$	−3.62468	−0.172214	−0.0861068	−	0.996286i	$-0.527443\pi$
$443$	−3.62468	−0.172214	−0.0861068	+	0.996286i	$0.527443\pi$
$444$	−3.80447	−0.180552
$445$	−4.57628	−0.216937
$446$	8.37454	0.396546
$447$	−3.25535	−0.153973
$448$	−1.00000	−0.0472456
$449$	27.5415	1.29976	0.649882	−	0.760035i	$-0.274818\pi$
$449$	27.5415	1.29976	0.649882	+	0.760035i	$0.274818\pi$
$450$	−12.7305	−0.600121
$451$	−33.4492	−1.57506
$452$	12.4241	0.584380
$453$	8.53143	0.400841
$454$	−20.3147	−0.953416
$455$	−1.98611	−0.0931101
$456$	1.23588	0.0578752
$457$	7.70717	0.360526	0.180263	−	0.983618i	$-0.442305\pi$
$457$	7.70717	0.360526	0.180263	+	0.983618i	$0.442305\pi$
$458$	4.69795	0.219521
$459$	15.6443	0.730214
$460$	0.475133	0.0221532
$461$	−7.23951	−0.337178	−0.168589	−	0.985686i	$-0.553921\pi$
$461$	−7.23951	−0.337178	−0.168589	+	0.985686i	$0.553921\pi$
$462$	−3.88099	−0.180560
$463$	−28.3503	−1.31755	−0.658775	−	0.752340i	$-0.728925\pi$
$463$	−28.3503	−1.31755	−0.658775	+	0.752340i	$0.728925\pi$
$464$	7.50658	0.348484
$465$	−0.179821	−0.00833899
$466$	8.39479	0.388881
$467$	−36.0164	−1.66664	−0.833320	−	0.552791i	$-0.813563\pi$
$467$	−36.0164	−1.66664	−0.833320	+	0.552791i	$0.813563\pi$
$468$	16.0494	0.741882
$469$	−7.75011	−0.357867
$470$	1.17962	0.0544116
$471$	−3.46589	−0.159700
$472$	10.9745	0.505141
$473$	22.2408	1.02263
$474$	−6.53102	−0.299979
$475$	9.56726	0.438976
$476$	4.41675	0.202441
$477$	30.1849	1.38207
$478$	15.1964	0.695067
$479$	22.3916	1.02310	0.511548	−	0.859254i	$-0.329072\pi$
$479$	22.3916	1.02310	0.511548	+	0.859254i	$0.329072\pi$
$480$	0.203506	0.00928873
$481$	37.1296	1.69296
$482$	−25.8121	−1.17571
$483$	0.934074	0.0425019
$484$	26.6480	1.21127
$485$	1.14991	0.0522148
$486$	−14.1425	−0.641518
$487$	14.9153	0.675878	0.337939	−	0.941168i	$-0.390270\pi$
$487$	14.9153	0.675878	0.337939	+	0.941168i	$0.390270\pi$
$488$	−5.31575	−0.240632
$489$	−7.23544	−0.327198
$490$	0.321740	0.0145347
$491$	26.1480	1.18004	0.590021	−	0.807388i	$-0.299119\pi$
$491$	26.1480	1.18004	0.590021	+	0.807388i	$0.299119\pi$
$492$	3.44816	0.155455
$493$	−33.1547	−1.49321
$494$	−12.0615	−0.542671
$495$	−5.13259	−0.230693
$496$	0.883615	0.0396755
$497$	−3.32133	−0.148982
$498$	6.66618	0.298719
$499$	7.04939	0.315574	0.157787	−	0.987473i	$-0.449564\pi$
$499$	7.04939	0.315574	0.157787	+	0.987473i	$0.449564\pi$
$500$	3.18410	0.142397
$501$	−5.34761	−0.238913
$502$	−18.5296	−0.827018
$503$	34.3551	1.53182	0.765909	−	0.642948i	$-0.222289\pi$
$503$	34.3551	1.53182	0.765909	+	0.642948i	$0.222289\pi$
$504$	−2.59992	−0.115810
$505$	2.05035	0.0912393
$506$	−9.06109	−0.402815
$507$	15.8800	0.705256
$508$	−9.62882	−0.427210
$509$	−25.2305	−1.11832	−0.559160	−	0.829060i	$-0.688876\pi$
$509$	−25.2305	−1.11832	−0.559160	+	0.829060i	$0.688876\pi$
$510$	−0.898834	−0.0398011
$511$	0.297693	0.0131692
$512$	−1.00000	−0.0441942
$513$	6.92081	0.305561
$514$	−10.9871	−0.484622
$515$	−0.973914	−0.0429158
$516$	−2.29272	−0.100931
$517$	−22.4960	−0.989375
$518$	−6.01483	−0.264276
$519$	−8.20629	−0.360216
$520$	−1.98611	−0.0870965
$521$	−13.1434	−0.575825	−0.287912	−	0.957657i	$-0.592961\pi$
$521$	−13.1434	−0.575825	−0.287912	+	0.957657i	$0.592961\pi$
$522$	19.5165	0.854216
$523$	−9.64825	−0.421889	−0.210944	−	0.977498i	$-0.567654\pi$
$523$	−9.64825	−0.421889	−0.210944	+	0.977498i	$0.567654\pi$
$524$	14.6100	0.638242
$525$	3.09710	0.135169
$526$	4.06441	0.177217
$527$	−3.90271	−0.170005
$528$	−3.88099	−0.168898
$529$	−20.8192	−0.905182
$530$	−3.73538	−0.162255
$531$	28.5328	1.23822
$532$	1.95390	0.0847125
$533$	−33.6522	−1.45764
$534$	−8.99662	−0.389322
$535$	0.597788	0.0258446
$536$	−7.75011	−0.334754
$537$	11.7003	0.504904
$538$	8.60242	0.370877
$539$	−6.13579	−0.264287
$540$	1.13962	0.0490413
$541$	28.9398	1.24422	0.622109	−	0.782930i	$-0.286276\pi$
$541$	28.9398	1.24422	0.622109	+	0.782930i	$0.286276\pi$
$542$	19.0069	0.816417
$543$	−4.94001	−0.211996
$544$	4.41675	0.189367
$545$	3.03941	0.130194
$546$	−3.90453	−0.167099
$547$	29.8837	1.27773	0.638867	−	0.769317i	$-0.279403\pi$
$547$	29.8837	1.27773	0.638867	+	0.769317i	$0.279403\pi$
$548$	4.48617	0.191640
$549$	−13.8205	−0.589846
$550$	−30.0438	−1.28107
$551$	−14.6671	−0.624841
$552$	0.934074	0.0397568
$553$	−10.3255	−0.439083
$554$	30.6634	1.30276
$555$	1.22405	0.0519581
$556$	−13.0596	−0.553852
$557$	17.1092	0.724942	0.362471	−	0.931995i	$-0.381933\pi$
$557$	17.1092	0.724942	0.362471	+	0.931995i	$0.381933\pi$
$558$	2.29733	0.0972538
$559$	22.3757	0.946390
$560$	0.321740	0.0135960
$561$	17.1414	0.723709
$562$	27.5384	1.16164
$563$	4.80060	0.202321	0.101161	−	0.994870i	$-0.467744\pi$
$563$	4.80060	0.202321	0.101161	+	0.994870i	$0.467744\pi$
$564$	2.31903	0.0976489
$565$	−3.99733	−0.168169
$566$	1.18924	0.0499876
$567$	−5.55937	−0.233472
$568$	−3.32133	−0.139360
$569$	26.4806	1.11013	0.555063	−	0.831808i	$-0.312694\pi$
$569$	26.4806	1.11013	0.555063	+	0.831808i	$0.312694\pi$
$570$	−0.397631	−0.0166549
$571$	−30.2918	−1.26767	−0.633837	−	0.773467i	$-0.718521\pi$
$571$	−30.2918	−1.26767	−0.633837	+	0.773467i	$0.718521\pi$
$572$	37.8763	1.58369
$573$	−8.53615	−0.356603
$574$	5.45149	0.227541
$575$	7.23093	0.301551
$576$	−2.59992	−0.108330
$577$	−0.526807	−0.0219313	−0.0109656	−	0.999940i	$-0.503491\pi$
$577$	−0.526807	−0.0219313	−0.0109656	+	0.999940i	$0.503491\pi$
$578$	−2.50768	−0.104306
$579$	−0.440372	−0.0183012
$580$	−2.41517	−0.100284
$581$	10.5391	0.437237
$582$	2.26064	0.0937065
$583$	71.2361	2.95030
$584$	0.297693	0.0123186
$585$	−5.16372	−0.213494
$586$	9.16357	0.378544
$587$	−0.581325	−0.0239938	−0.0119969	−	0.999928i	$-0.503819\pi$
$587$	−0.581325	−0.0239938	−0.0119969	+	0.999928i	$0.503819\pi$
$588$	0.632516	0.0260845
$589$	−1.72650	−0.0711391
$590$	−3.53093	−0.145366
$591$	−5.44034	−0.223786
$592$	−6.01483	−0.247208
$593$	−36.5333	−1.50024	−0.750122	−	0.661300i	$-0.770005\pi$
$593$	−36.5333	−1.50024	−0.750122	+	0.661300i	$0.770005\pi$
$594$	−21.7332	−0.891726
$595$	−1.42105	−0.0582572
$596$	−5.14666	−0.210815
$597$	−7.02865	−0.287664
$598$	−9.11606	−0.372783
$599$	−20.0761	−0.820287	−0.410143	−	0.912021i	$-0.634521\pi$
$599$	−20.0761	−0.820287	−0.410143	+	0.912021i	$0.634521\pi$
$600$	3.09710	0.126439
$601$	−23.5206	−0.959425	−0.479713	−	0.877426i	$-0.659259\pi$
$601$	−23.5206	−0.959425	−0.479713	+	0.877426i	$0.659259\pi$
$602$	−3.62475	−0.147734
$603$	−20.1497	−0.820559
$604$	13.4881	0.548822
$605$	−8.57372	−0.348571
$606$	4.03083	0.163741
$607$	20.3789	0.827156	0.413578	−	0.910469i	$-0.364279\pi$
$607$	20.3789	0.827156	0.413578	+	0.910469i	$0.364279\pi$
$608$	1.95390	0.0792413
$609$	−4.74804	−0.192400
$610$	1.71029	0.0692476
$611$	−22.6325	−0.915613
$612$	11.4832	0.464181
$613$	9.08688	0.367016	0.183508	−	0.983018i	$-0.441255\pi$
$613$	9.08688	0.367016	0.183508	+	0.983018i	$0.441255\pi$
$614$	28.0502	1.13202
$615$	−1.10941	−0.0447358
$616$	−6.13579	−0.247218
$617$	−12.4079	−0.499522	−0.249761	−	0.968308i	$-0.580352\pi$
$617$	−12.4079	−0.499522	−0.249761	+	0.968308i	$0.580352\pi$
$618$	−1.91464	−0.0770181
$619$	−14.9496	−0.600877	−0.300439	−	0.953801i	$-0.597133\pi$
$619$	−14.9496	−0.600877	−0.300439	+	0.953801i	$0.597133\pi$
$620$	−0.284294	−0.0114175
$621$	5.23074	0.209903
$622$	1.11890	0.0448638
$623$	−14.2235	−0.569854
$624$	−3.90453	−0.156306
$625$	23.4580	0.938319
$626$	10.7012	0.427704
$627$	7.58308	0.302839
$628$	−5.47952	−0.218657
$629$	26.5660	1.05925
$630$	0.836500	0.0333269
$631$	42.0127	1.67250	0.836251	−	0.548348i	$-0.184743\pi$
$631$	42.0127	1.67250	0.836251	+	0.548348i	$0.184743\pi$
$632$	−10.3255	−0.410724
$633$	−18.3140	−0.727918
$634$	4.27822	0.169910
$635$	3.09798	0.122939
$636$	−7.34347	−0.291187
$637$	−6.17301	−0.244584
$638$	46.0589	1.82349
$639$	−8.63520	−0.341603
$640$	0.321740	0.0127179
$641$	−13.3344	−0.526676	−0.263338	−	0.964704i	$-0.584823\pi$
$641$	−13.3344	−0.526676	−0.263338	+	0.964704i	$0.584823\pi$
$642$	1.17520	0.0463816
$643$	4.62498	0.182392	0.0911958	−	0.995833i	$-0.470931\pi$
$643$	4.62498	0.182392	0.0911958	+	0.995833i	$0.470931\pi$
$644$	1.47676	0.0581925
$645$	0.737659	0.0290453
$646$	−8.62990	−0.339539
$647$	11.8158	0.464528	0.232264	−	0.972653i	$-0.425387\pi$
$647$	11.8158	0.464528	0.232264	+	0.972653i	$0.425387\pi$
$648$	−5.55937	−0.218393
$649$	67.3372	2.64321
$650$	−30.2261	−1.18556
$651$	−0.558901	−0.0219050
$652$	−11.4391	−0.447991
$653$	−6.96223	−0.272453	−0.136227	−	0.990678i	$-0.543498\pi$
$653$	−6.96223	−0.272453	−0.136227	+	0.990678i	$0.543498\pi$
$654$	5.97524	0.233650
$655$	−4.70063	−0.183669
$656$	5.45149	0.212845
$657$	0.773979	0.0301958
$658$	3.66636	0.142930
$659$	17.9936	0.700933	0.350466	−	0.936575i	$-0.386023\pi$
$659$	17.9936	0.700933	0.350466	+	0.936575i	$0.386023\pi$
$660$	1.24867	0.0486044
$661$	−37.6774	−1.46548	−0.732741	−	0.680508i	$-0.761759\pi$
$661$	−37.6774	−1.46548	−0.732741	+	0.680508i	$0.761759\pi$
$662$	−1.17775	−0.0457746
$663$	17.2453	0.669753
$664$	10.5391	0.408998
$665$	−0.628649	−0.0243780
$666$	−15.6381	−0.605963
$667$	−11.0854	−0.429229
$668$	−8.45450	−0.327114
$669$	−5.29703	−0.204795
$670$	2.49352	0.0963332
$671$	−32.6163	−1.25914
$672$	0.632516	0.0243998
$673$	−11.4214	−0.440262	−0.220131	−	0.975470i	$-0.570648\pi$
$673$	−11.4214	−0.440262	−0.220131	+	0.975470i	$0.570648\pi$
$674$	7.61369	0.293268
$675$	17.3436	0.667554
$676$	25.1061	0.965620
$677$	46.1621	1.77415	0.887077	−	0.461622i	$-0.152732\pi$
$677$	46.1621	1.77415	0.887077	+	0.461622i	$0.152732\pi$
$678$	−7.85844	−0.301801
$679$	3.57404	0.137159
$680$	−1.42105	−0.0544946
$681$	12.8494	0.492389
$682$	5.42168	0.207607
$683$	16.0903	0.615680	0.307840	−	0.951438i	$-0.400394\pi$
$683$	16.0903	0.615680	0.307840	+	0.951438i	$0.400394\pi$
$684$	5.08000	0.194239
$685$	−1.44338	−0.0551488
$686$	1.00000	0.0381802
$687$	−2.97153	−0.113371
$688$	−3.62475	−0.138192
$689$	71.6682	2.73034
$690$	−0.300529	−0.0114410
$691$	31.2068	1.18716	0.593581	−	0.804774i	$-0.297714\pi$
$691$	31.2068	1.18716	0.593581	+	0.804774i	$0.297714\pi$
$692$	−12.9740	−0.493199
$693$	−15.9526	−0.605989
$694$	−6.02573	−0.228734
$695$	4.20181	0.159384
$696$	−4.74804	−0.179974
$697$	−24.0779	−0.912015
$698$	6.80816	0.257693
$699$	−5.30984	−0.200837
$700$	4.89648	0.185070
$701$	−20.4699	−0.773136	−0.386568	−	0.922261i	$-0.626340\pi$
$701$	−20.4699	−0.773136	−0.386568	+	0.922261i	$0.626340\pi$
$702$	−21.8651	−0.825244
$703$	11.7524	0.443250
$704$	−6.13579	−0.231251
$705$	−0.746126	−0.0281007
$706$	−12.2006	−0.459176
$707$	6.37269	0.239670
$708$	−6.94154	−0.260879
$709$	13.6881	0.514068	0.257034	−	0.966402i	$-0.417255\pi$
$709$	13.6881	0.514068	0.257034	+	0.966402i	$0.417255\pi$
$710$	1.06860	0.0401040
$711$	−26.8454	−1.00678
$712$	−14.2235	−0.533050
$713$	−1.30489	−0.0488684
$714$	−2.79367	−0.104550
$715$	−12.1863	−0.455743
$716$	18.4980	0.691301
$717$	−9.61197	−0.358965
$718$	−35.8380	−1.33746
$719$	−28.8229	−1.07491	−0.537457	−	0.843291i	$-0.680615\pi$
$719$	−28.8229	−1.07491	−0.537457	+	0.843291i	$0.680615\pi$
$720$	0.836500	0.0311745
$721$	−3.02702	−0.112732
$722$	15.1823	0.565025
$723$	16.3266	0.607192
$724$	−7.81010	−0.290260
$725$	−36.7559	−1.36508
$726$	−16.8553	−0.625558
$727$	33.8736	1.25630	0.628152	−	0.778091i	$-0.283812\pi$
$727$	33.8736	1.25630	0.628152	+	0.778091i	$0.283812\pi$
$728$	−6.17301	−0.228787
$729$	−7.73274	−0.286398
$730$	−0.0957797	−0.00354497
$731$	16.0096	0.592138
$732$	3.36230	0.124274
$733$	20.6247	0.761791	0.380896	−	0.924618i	$-0.375616\pi$
$733$	20.6247	0.761791	0.380896	+	0.924618i	$0.375616\pi$
$734$	32.0340	1.18240
$735$	−0.203506	−0.00750643
$736$	1.47676	0.0544341
$737$	−47.5531	−1.75164
$738$	14.1735	0.521733
$739$	38.7895	1.42690	0.713448	−	0.700708i	$-0.247132\pi$
$739$	38.7895	1.42690	0.713448	+	0.700708i	$0.247132\pi$
$740$	1.93521	0.0711398
$741$	7.62908	0.280261
$742$	−11.6099	−0.426214
$743$	16.3465	0.599697	0.299848	−	0.953987i	$-0.403064\pi$
$743$	16.3465	0.599697	0.299848	+	0.953987i	$0.403064\pi$
$744$	−0.558901	−0.0204903
$745$	1.65589	0.0606670
$746$	−25.7329	−0.942150
$747$	27.4010	1.00255
$748$	27.1003	0.990884
$749$	1.85798	0.0678892
$750$	−2.01399	−0.0735406
$751$	−48.9778	−1.78723	−0.893613	−	0.448838i	$-0.851838\pi$
$751$	−48.9778	−1.78723	−0.893613	+	0.448838i	$0.851838\pi$
$752$	3.66636	0.133698
$753$	11.7203	0.427111
$754$	46.3383	1.68754
$755$	−4.33966	−0.157936
$756$	3.54204	0.128823
$757$	−6.59531	−0.239711	−0.119855	−	0.992791i	$-0.538243\pi$
$757$	−6.59531	−0.239711	−0.119855	+	0.992791i	$0.538243\pi$
$758$	25.3657	0.921323
$759$	5.73129	0.208033
$760$	−0.628649	−0.0228035
$761$	17.9108	0.649265	0.324632	−	0.945840i	$-0.394759\pi$
$761$	17.9108	0.649265	0.324632	+	0.945840i	$0.394759\pi$
$762$	6.09038	0.220631
$763$	9.44677	0.341996
$764$	−13.4955	−0.488252
$765$	−3.69461	−0.133579
$766$	−21.4946	−0.776631
$767$	67.7456	2.44615
$768$	0.632516	0.0228240
$769$	−37.5827	−1.35527	−0.677634	−	0.735400i	$-0.736994\pi$
$769$	−37.5827	−1.35527	−0.677634	+	0.735400i	$0.736994\pi$
$770$	1.97413	0.0711428
$771$	6.94955	0.250282
$772$	−0.696223	−0.0250576
$773$	−5.64442	−0.203016	−0.101508	−	0.994835i	$-0.532367\pi$
$773$	−5.64442	−0.203016	−0.101508	+	0.994835i	$0.532367\pi$
$774$	−9.42408	−0.338742
$775$	−4.32661	−0.155416
$776$	3.57404	0.128301
$777$	3.80447	0.136485
$778$	−3.47999	−0.124764
$779$	−10.6517	−0.381637
$780$	1.25624	0.0449808
$781$	−20.3790	−0.729217
$782$	−6.52248	−0.233243
$783$	−26.5886	−0.950200
$784$	1.00000	0.0357143
$785$	1.76298	0.0629235
$786$	−9.24107	−0.329618
$787$	−19.8074	−0.706058	−0.353029	−	0.935612i	$-0.614848\pi$
$787$	−19.8074	−0.706058	−0.353029	+	0.935612i	$0.614848\pi$
$788$	−8.60111	−0.306402
$789$	−2.57081	−0.0915231
$790$	3.32211	0.118195
$791$	−12.4241	−0.441750
$792$	−15.9526	−0.566851
$793$	−32.8142	−1.16527
$794$	−33.7381	−1.19732
$795$	2.36269	0.0837959
$796$	−11.1122	−0.393862
$797$	−10.1365	−0.359053	−0.179527	−	0.983753i	$-0.557457\pi$
$797$	−10.1365	−0.359053	−0.179527	+	0.983753i	$0.557457\pi$
$798$	−1.23588	−0.0437495
$799$	−16.1934	−0.572881
$800$	4.89648	0.173117
$801$	−36.9801	−1.30663
$802$	12.1011	0.427305
$803$	1.82658	0.0644587
$804$	4.90207	0.172883
$805$	−0.475133	−0.0167462
$806$	5.45457	0.192129
$807$	−5.44117	−0.191538
$808$	6.37269	0.224190
$809$	−45.3280	−1.59365	−0.796824	−	0.604211i	$-0.793488\pi$
$809$	−45.3280	−1.59365	−0.796824	+	0.604211i	$0.793488\pi$
$810$	1.78867	0.0628476
$811$	37.0438	1.30078	0.650392	−	0.759598i	$-0.274604\pi$
$811$	37.0438	1.30078	0.650392	+	0.759598i	$0.274604\pi$
$812$	−7.50658	−0.263429
$813$	−12.0222	−0.421636
$814$	−36.9057	−1.29355
$815$	3.68043	0.128920
$816$	−2.79367	−0.0977979
$817$	7.08242	0.247783
$818$	−1.22236	−0.0427387
$819$	−16.0494	−0.560810
$820$	−1.75396	−0.0612511
$821$	13.6798	0.477430	0.238715	−	0.971090i	$-0.423274\pi$
$821$	13.6798	0.477430	0.238715	+	0.971090i	$0.423274\pi$
$822$	−2.83758	−0.0989719
$823$	42.9795	1.49817	0.749086	−	0.662473i	$-0.230493\pi$
$823$	42.9795	1.49817	0.749086	+	0.662473i	$0.230493\pi$
$824$	−3.02702	−0.105451
$825$	19.0032	0.661606
$826$	−10.9745	−0.381851
$827$	−52.7622	−1.83472	−0.917360	−	0.398059i	$-0.869684\pi$
$827$	−52.7622	−1.83472	−0.917360	+	0.398059i	$0.869684\pi$
$828$	3.83946	0.133431
$829$	33.3332	1.15771	0.578854	−	0.815431i	$-0.303500\pi$
$829$	33.3332	1.15771	0.578854	+	0.815431i	$0.303500\pi$
$830$	−3.39087	−0.117699
$831$	−19.3951	−0.672809
$832$	−6.17301	−0.214011
$833$	−4.41675	−0.153031
$834$	8.26042	0.286035
$835$	2.72015	0.0941347
$836$	11.9888	0.414640
$837$	−3.12980	−0.108182
$838$	−5.23734	−0.180921
$839$	−39.5637	−1.36589	−0.682945	−	0.730469i	$-0.739301\pi$
$839$	−39.5637	−1.36589	−0.682945	+	0.730469i	$0.739301\pi$
$840$	−0.203506	−0.00702162
$841$	27.3488	0.943063
$842$	6.17262	0.212723
$843$	−17.4185	−0.599925
$844$	−28.9543	−0.996647
$845$	−8.07764	−0.277879
$846$	9.53226	0.327726
$847$	−26.6480	−0.915635
$848$	−11.6099	−0.398686
$849$	−0.752216	−0.0258160
$850$	−21.6265	−0.741784
$851$	8.88245	0.304486
$852$	2.10079	0.0719720
$853$	−15.1560	−0.518930	−0.259465	−	0.965752i	$-0.583546\pi$
$853$	−15.1560	−0.518930	−0.259465	+	0.965752i	$0.583546\pi$
$854$	5.31575	0.181901
$855$	−1.63444	−0.0558967
$856$	1.85798	0.0635046
$857$	20.7256	0.707973	0.353987	−	0.935251i	$-0.384826\pi$
$857$	20.7256	0.707973	0.353987	+	0.935251i	$0.384826\pi$
$858$	−23.9574	−0.817892
$859$	4.74521	0.161904	0.0809522	−	0.996718i	$-0.474204\pi$
$859$	4.74521	0.161904	0.0809522	+	0.996718i	$0.474204\pi$
$860$	1.16623	0.0397681
$861$	−3.44816	−0.117513
$862$	−1.00000	−0.0340601
$863$	44.3775	1.51063	0.755315	−	0.655362i	$-0.227484\pi$
$863$	44.3775	1.51063	0.755315	+	0.655362i	$0.227484\pi$
$864$	3.54204	0.120503
$865$	4.17427	0.141929
$866$	27.5362	0.935717
$867$	1.58615	0.0538684
$868$	−0.883615	−0.0299918
$869$	−63.3549	−2.14917
$870$	1.52763	0.0517916
$871$	−47.8416	−1.62105
$872$	9.44677	0.319908
$873$	9.29223	0.314494
$874$	−2.88545	−0.0976017
$875$	−3.18410	−0.107642
$876$	−0.188296	−0.00636192
$877$	34.5448	1.16649	0.583247	−	0.812295i	$-0.301782\pi$
$877$	34.5448	1.16649	0.583247	+	0.812295i	$0.301782\pi$
$878$	13.7298	0.463360
$879$	−5.79611	−0.195498
$880$	1.97413	0.0665480
$881$	39.6145	1.33465	0.667323	−	0.744768i	$-0.267440\pi$
$881$	39.6145	1.33465	0.667323	+	0.744768i	$0.267440\pi$
$882$	2.59992	0.0875440
$883$	16.6696	0.560976	0.280488	−	0.959857i	$-0.409504\pi$
$883$	16.6696	0.560976	0.280488	+	0.959857i	$0.409504\pi$
$884$	27.2647	0.917010
$885$	2.23337	0.0750740
$886$	3.62468	0.121773
$887$	9.13035	0.306567	0.153284	−	0.988182i	$-0.451015\pi$
$887$	9.13035	0.306567	0.153284	+	0.988182i	$0.451015\pi$
$888$	3.80447	0.127670
$889$	9.62882	0.322940
$890$	4.57628	0.153397
$891$	−34.1112	−1.14277
$892$	−8.37454	−0.280400
$893$	−7.16372	−0.239725
$894$	3.25535	0.108875
$895$	−5.95154	−0.198938
$896$	1.00000	0.0334077
$897$	5.76605	0.192523
$898$	−27.5415	−0.919072
$899$	6.63293	0.221221
$900$	12.7305	0.424349
$901$	51.2781	1.70832
$902$	33.4492	1.11374
$903$	2.29272	0.0762968
$904$	−12.4241	−0.413219
$905$	2.51282	0.0835291
$906$	−8.53143	−0.283438
$907$	32.8657	1.09129	0.545644	−	0.838017i	$-0.316285\pi$
$907$	32.8657	1.09129	0.545644	+	0.838017i	$0.316285\pi$
$908$	20.3147	0.674167
$909$	16.5685	0.549542
$910$	1.98611	0.0658388
$911$	24.8503	0.823326	0.411663	−	0.911336i	$-0.364948\pi$
$911$	24.8503	0.823326	0.411663	+	0.911336i	$0.364948\pi$
$912$	−1.23588	−0.0409239
$913$	64.6660	2.14013
$914$	−7.70717	−0.254930
$915$	−1.08179	−0.0357627
$916$	−4.69795	−0.155225
$917$	−14.6100	−0.482465
$918$	−15.6443	−0.516339
$919$	50.4332	1.66364	0.831819	−	0.555047i	$-0.187300\pi$
$919$	50.4332	1.66364	0.831819	+	0.555047i	$0.187300\pi$
$920$	−0.475133	−0.0156647
$921$	−17.7422	−0.584627
$922$	7.23951	0.238421
$923$	−20.5026	−0.674851
$924$	3.88099	0.127675
$925$	29.4515	0.968359
$926$	28.3503	0.931649
$927$	−7.87002	−0.258485
$928$	−7.50658	−0.246416
$929$	40.6057	1.33223	0.666115	−	0.745849i	$-0.267956\pi$
$929$	40.6057	1.33223	0.666115	+	0.745849i	$0.267956\pi$
$930$	0.179821	0.00589656
$931$	−1.95390	−0.0640366
$932$	−8.39479	−0.274980
$933$	−0.707723	−0.0231698
$934$	36.0164	1.17849
$935$	−8.71924	−0.285150
$936$	−16.0494	−0.524590
$937$	−6.83152	−0.223176	−0.111588	−	0.993755i	$-0.535594\pi$
$937$	−6.83152	−0.223176	−0.111588	+	0.993755i	$0.535594\pi$
$938$	7.75011	0.253050
$939$	−6.76865	−0.220887
$940$	−1.17962	−0.0384748
$941$	51.2219	1.66978	0.834892	−	0.550413i	$-0.185530\pi$
$941$	51.2219	1.66978	0.834892	+	0.550413i	$0.185530\pi$
$942$	3.46589	0.112925
$943$	−8.05055	−0.262162
$944$	−10.9745	−0.357189
$945$	−1.13962	−0.0370718
$946$	−22.2408	−0.723109
$947$	1.34548	0.0437223	0.0218612	−	0.999761i	$-0.493041\pi$
$947$	1.34548	0.0437223	0.0218612	+	0.999761i	$0.493041\pi$
$948$	6.53102	0.212118
$949$	1.83766	0.0596530
$950$	−9.56726	−0.310403
$951$	−2.70604	−0.0877495
$952$	−4.41675	−0.143148
$953$	−0.269103	−0.00871709	−0.00435854	−	0.999991i	$-0.501387\pi$
$953$	−0.269103	−0.00871709	−0.00435854	+	0.999991i	$0.501387\pi$
$954$	−30.1849	−0.977273
$955$	4.34206	0.140506
$956$	−15.1964	−0.491487
$957$	−29.1330	−0.941735
$958$	−22.3916	−0.723439
$959$	−4.48617	−0.144866
$960$	−0.203506	−0.00656812
$961$	−30.2192	−0.974814
$962$	−37.1296	−1.19711
$963$	4.83061	0.155664
$964$	25.8121	0.831352
$965$	0.224003	0.00721091
$966$	−0.934074	−0.0300533
$967$	10.4188	0.335046	0.167523	−	0.985868i	$-0.446423\pi$
$967$	10.4188	0.335046	0.167523	+	0.985868i	$0.446423\pi$
$968$	−26.6480	−0.856498
$969$	5.45855	0.175354
$970$	−1.14991	−0.0369215
$971$	33.6892	1.08114	0.540568	−	0.841300i	$-0.318209\pi$
$971$	33.6892	1.08114	0.540568	+	0.841300i	$0.318209\pi$
$972$	14.1425	0.453621
$973$	13.0596	0.418672
$974$	−14.9153	−0.477918
$975$	19.1185	0.612281
$976$	5.31575	0.170153
$977$	−40.8827	−1.30795	−0.653976	−	0.756515i	$-0.726900\pi$
$977$	−40.8827	−1.30795	−0.653976	+	0.756515i	$0.726900\pi$
$978$	7.23544	0.231364
$979$	−87.2727	−2.78925
$980$	−0.321740	−0.0102776
$981$	24.5609	0.784169
$982$	−26.1480	−0.834416
$983$	−7.36339	−0.234856	−0.117428	−	0.993081i	$-0.537465\pi$
$983$	−7.36339	−0.234856	−0.117428	+	0.993081i	$0.537465\pi$
$984$	−3.44816	−0.109923
$985$	2.76732	0.0881742
$986$	33.1547	1.05586
$987$	−2.31903	−0.0738157
$988$	12.0615	0.383727
$989$	5.35289	0.170212
$990$	5.13259	0.163124
$991$	1.35098	0.0429152	0.0214576	−	0.999770i	$-0.493169\pi$
$991$	1.35098	0.0429152	0.0214576	+	0.999770i	$0.493169\pi$
$992$	−0.883615	−0.0280548
$993$	0.744947	0.0236402
$994$	3.32133	0.105346
$995$	3.57524	0.113343
$996$	−6.66618	−0.211226
$997$	−15.7053	−0.497393	−0.248697	−	0.968581i	$-0.580002\pi$
$997$	−15.7053	−0.497393	−0.248697	+	0.968581i	$0.580002\pi$
$998$	−7.04939	−0.223144
$999$	21.3048	0.674053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.13	✓	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.632516 q^{3} +1.00000 q^{4} -0.321740 q^{5} -0.632516 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.59992 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.632516 q^{3} +1.00000 q^{4} -0.321740 q^{5} -0.632516 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.59992 q^{9} +0.321740 q^{10} -6.13579 q^{11} +0.632516 q^{12} -6.17301 q^{13} +1.00000 q^{14} -0.203506 q^{15} +1.00000 q^{16} -4.41675 q^{17} +2.59992 q^{18} -1.95390 q^{19} -0.321740 q^{20} -0.632516 q^{21} +6.13579 q^{22} -1.47676 q^{23} -0.632516 q^{24} -4.89648 q^{25} +6.17301 q^{26} -3.54204 q^{27} -1.00000 q^{28} +7.50658 q^{29} +0.203506 q^{30} +0.883615 q^{31} -1.00000 q^{32} -3.88099 q^{33} +4.41675 q^{34} +0.321740 q^{35} -2.59992 q^{36} -6.01483 q^{37} +1.95390 q^{38} -3.90453 q^{39} +0.321740 q^{40} +5.45149 q^{41} +0.632516 q^{42} -3.62475 q^{43} -6.13579 q^{44} +0.836500 q^{45} +1.47676 q^{46} +3.66636 q^{47} +0.632516 q^{48} +1.00000 q^{49} +4.89648 q^{50} -2.79367 q^{51} -6.17301 q^{52} -11.6099 q^{53} +3.54204 q^{54} +1.97413 q^{55} +1.00000 q^{56} -1.23588 q^{57} -7.50658 q^{58} -10.9745 q^{59} -0.203506 q^{60} +5.31575 q^{61} -0.883615 q^{62} +2.59992 q^{63} +1.00000 q^{64} +1.98611 q^{65} +3.88099 q^{66} +7.75011 q^{67} -4.41675 q^{68} -0.934074 q^{69} -0.321740 q^{70} +3.32133 q^{71} +2.59992 q^{72} -0.297693 q^{73} +6.01483 q^{74} -3.09710 q^{75} -1.95390 q^{76} +6.13579 q^{77} +3.90453 q^{78} +10.3255 q^{79} -0.321740 q^{80} +5.55937 q^{81} -5.45149 q^{82} -10.5391 q^{83} -0.632516 q^{84} +1.42105 q^{85} +3.62475 q^{86} +4.74804 q^{87} +6.13579 q^{88} +14.2235 q^{89} -0.836500 q^{90} +6.17301 q^{91} -1.47676 q^{92} +0.558901 q^{93} -3.66636 q^{94} +0.628649 q^{95} -0.632516 q^{96} -3.57404 q^{97} -1.00000 q^{98} +15.9526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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