LMFDB - Embedded newform 6034.2.a.r.1.9

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:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.69299 q^{3} +1.00000 q^{4} -2.70073 q^{5} -1.69299 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.133772 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.69299 q^{3} +1.00000 q^{4} -2.70073 q^{5} -1.69299 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.133772 q^{9} -2.70073 q^{10} +6.10855 q^{11} -1.69299 q^{12} +6.88905 q^{13} -1.00000 q^{14} +4.57232 q^{15} +1.00000 q^{16} -2.56728 q^{17} -0.133772 q^{18} +4.90740 q^{19} -2.70073 q^{20} +1.69299 q^{21} +6.10855 q^{22} -0.388901 q^{23} -1.69299 q^{24} +2.29395 q^{25} +6.88905 q^{26} +5.30546 q^{27} -1.00000 q^{28} -8.35475 q^{29} +4.57232 q^{30} +2.14742 q^{31} +1.00000 q^{32} -10.3417 q^{33} -2.56728 q^{34} +2.70073 q^{35} -0.133772 q^{36} -11.2451 q^{37} +4.90740 q^{38} -11.6631 q^{39} -2.70073 q^{40} -7.33637 q^{41} +1.69299 q^{42} +3.75094 q^{43} +6.10855 q^{44} +0.361282 q^{45} -0.388901 q^{46} +12.3511 q^{47} -1.69299 q^{48} +1.00000 q^{49} +2.29395 q^{50} +4.34640 q^{51} +6.88905 q^{52} -9.34793 q^{53} +5.30546 q^{54} -16.4976 q^{55} -1.00000 q^{56} -8.30819 q^{57} -8.35475 q^{58} -0.566844 q^{59} +4.57232 q^{60} +4.12954 q^{61} +2.14742 q^{62} +0.133772 q^{63} +1.00000 q^{64} -18.6055 q^{65} -10.3417 q^{66} -8.51140 q^{67} -2.56728 q^{68} +0.658407 q^{69} +2.70073 q^{70} +13.0918 q^{71} -0.133772 q^{72} -8.29642 q^{73} -11.2451 q^{74} -3.88365 q^{75} +4.90740 q^{76} -6.10855 q^{77} -11.6631 q^{78} -0.750981 q^{79} -2.70073 q^{80} -8.58079 q^{81} -7.33637 q^{82} +15.8860 q^{83} +1.69299 q^{84} +6.93355 q^{85} +3.75094 q^{86} +14.1445 q^{87} +6.10855 q^{88} +16.8750 q^{89} +0.361282 q^{90} -6.88905 q^{91} -0.388901 q^{92} -3.63557 q^{93} +12.3511 q^{94} -13.2536 q^{95} -1.69299 q^{96} +10.0875 q^{97} +1.00000 q^{98} -0.817153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.69299	−0.977450	−0.488725	−	0.872438i	$-0.662538\pi$
$3$	−1.69299	−0.977450	−0.488725	+	0.872438i	$0.662538\pi$
$4$	1.00000	0.500000
$5$	−2.70073	−1.20780	−0.603902	−	0.797059i	$-0.706388\pi$
$5$	−2.70073	−1.20780	−0.603902	+	0.797059i	$0.706388\pi$
$6$	−1.69299	−0.691162
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−0.133772	−0.0445907
$10$	−2.70073	−0.854047
$11$	6.10855	1.84180	0.920898	−	0.389803i	$-0.127457\pi$
$11$	6.10855	1.84180	0.920898	+	0.389803i	$0.127457\pi$
$12$	−1.69299	−0.488725
$13$	6.88905	1.91068	0.955339	−	0.295512i	$-0.0954902\pi$
$13$	6.88905	1.91068	0.955339	+	0.295512i	$0.0954902\pi$
$14$	−1.00000	−0.267261
$15$	4.57232	1.18057
$16$	1.00000	0.250000
$17$	−2.56728	−0.622658	−0.311329	−	0.950302i	$-0.600774\pi$
$17$	−2.56728	−0.622658	−0.311329	+	0.950302i	$0.600774\pi$
$18$	−0.133772	−0.0315304
$19$	4.90740	1.12583	0.562917	−	0.826513i	$-0.309679\pi$
$19$	4.90740	1.12583	0.562917	+	0.826513i	$0.309679\pi$
$20$	−2.70073	−0.603902
$21$	1.69299	0.369442
$22$	6.10855	1.30235
$23$	−0.388901	−0.0810914	−0.0405457	−	0.999178i	$-0.512910\pi$
$23$	−0.388901	−0.0810914	−0.0405457	+	0.999178i	$0.512910\pi$
$24$	−1.69299	−0.345581
$25$	2.29395	0.458791
$26$	6.88905	1.35105
$27$	5.30546	1.02104
$28$	−1.00000	−0.188982
$29$	−8.35475	−1.55144	−0.775719	−	0.631079i	$-0.782613\pi$
$29$	−8.35475	−1.55144	−0.775719	+	0.631079i	$0.782613\pi$
$30$	4.57232	0.834788
$31$	2.14742	0.385689	0.192844	−	0.981229i	$-0.438229\pi$
$31$	2.14742	0.385689	0.192844	+	0.981229i	$0.438229\pi$
$32$	1.00000	0.176777
$33$	−10.3417	−1.80026
$34$	−2.56728	−0.440286
$35$	2.70073	0.456507
$36$	−0.133772	−0.0222953
$37$	−11.2451	−1.84869	−0.924343	−	0.381562i	$-0.875386\pi$
$37$	−11.2451	−1.84869	−0.924343	+	0.381562i	$0.875386\pi$
$38$	4.90740	0.796085
$39$	−11.6631	−1.86759
$40$	−2.70073	−0.427023
$41$	−7.33637	−1.14575	−0.572874	−	0.819644i	$-0.694172\pi$
$41$	−7.33637	−1.14575	−0.572874	+	0.819644i	$0.694172\pi$
$42$	1.69299	0.261235
$43$	3.75094	0.572012	0.286006	−	0.958228i	$-0.407672\pi$
$43$	3.75094	0.572012	0.286006	+	0.958228i	$0.407672\pi$
$44$	6.10855	0.920898
$45$	0.361282	0.0538568
$46$	−0.388901	−0.0573403
$47$	12.3511	1.80160	0.900799	−	0.434237i	$-0.142982\pi$
$47$	12.3511	1.80160	0.900799	+	0.434237i	$0.142982\pi$
$48$	−1.69299	−0.244363
$49$	1.00000	0.142857
$50$	2.29395	0.324414
$51$	4.34640	0.608617
$52$	6.88905	0.955339
$53$	−9.34793	−1.28404	−0.642019	−	0.766689i	$-0.721903\pi$
$53$	−9.34793	−1.28404	−0.642019	+	0.766689i	$0.721903\pi$
$54$	5.30546	0.721981
$55$	−16.4976	−2.22453
$56$	−1.00000	−0.133631
$57$	−8.30819	−1.10045
$58$	−8.35475	−1.09703
$59$	−0.566844	−0.0737968	−0.0368984	−	0.999319i	$-0.511748\pi$
$59$	−0.566844	−0.0737968	−0.0368984	+	0.999319i	$0.511748\pi$
$60$	4.57232	0.590284
$61$	4.12954	0.528733	0.264366	−	0.964422i	$-0.414837\pi$
$61$	4.12954	0.528733	0.264366	+	0.964422i	$0.414837\pi$
$62$	2.14742	0.272723
$63$	0.133772	0.0168537
$64$	1.00000	0.125000
$65$	−18.6055	−2.30772
$66$	−10.3417	−1.27298
$67$	−8.51140	−1.03983	−0.519917	−	0.854217i	$-0.674037\pi$
$67$	−8.51140	−1.03983	−0.519917	+	0.854217i	$0.674037\pi$
$68$	−2.56728	−0.311329
$69$	0.658407	0.0792628
$70$	2.70073	0.322799
$71$	13.0918	1.55372	0.776858	−	0.629675i	$-0.216812\pi$
$71$	13.0918	1.55372	0.776858	+	0.629675i	$0.216812\pi$
$72$	−0.133772	−0.0157652
$73$	−8.29642	−0.971022	−0.485511	−	0.874230i	$-0.661366\pi$
$73$	−8.29642	−0.971022	−0.485511	+	0.874230i	$0.661366\pi$
$74$	−11.2451	−1.30722
$75$	−3.88365	−0.448445
$76$	4.90740	0.562917
$77$	−6.10855	−0.696134
$78$	−11.6631	−1.32059
$79$	−0.750981	−0.0844920	−0.0422460	−	0.999107i	$-0.513451\pi$
$79$	−0.750981	−0.0844920	−0.0422460	+	0.999107i	$0.513451\pi$
$80$	−2.70073	−0.301951
$81$	−8.58079	−0.953421
$82$	−7.33637	−0.810166
$83$	15.8860	1.74371	0.871857	−	0.489761i	$-0.162916\pi$
$83$	15.8860	1.74371	0.871857	+	0.489761i	$0.162916\pi$
$84$	1.69299	0.184721
$85$	6.93355	0.752049
$86$	3.75094	0.404474
$87$	14.1445	1.51645
$88$	6.10855	0.651173
$89$	16.8750	1.78875	0.894373	−	0.447321i	$-0.147622\pi$
$89$	16.8750	1.78875	0.894373	+	0.447321i	$0.147622\pi$
$90$	0.361282	0.0380825
$91$	−6.88905	−0.722168
$92$	−0.388901	−0.0405457
$93$	−3.63557	−0.376992
$94$	12.3511	1.27392
$95$	−13.2536	−1.35979
$96$	−1.69299	−0.172790
$97$	10.0875	1.02423	0.512116	−	0.858916i	$-0.328862\pi$
$97$	10.0875	1.02423	0.512116	+	0.858916i	$0.328862\pi$
$98$	1.00000	0.101015
$99$	−0.817153	−0.0821269
$100$	2.29395	0.229395
$101$	10.2272	1.01764	0.508822	−	0.860872i	$-0.330081\pi$
$101$	10.2272	1.01764	0.508822	+	0.860872i	$0.330081\pi$
$102$	4.34640	0.430357
$103$	−7.20624	−0.710052	−0.355026	−	0.934856i	$-0.615528\pi$
$103$	−7.20624	−0.710052	−0.355026	+	0.934856i	$0.615528\pi$
$104$	6.88905	0.675527
$105$	−4.57232	−0.446213
$106$	−9.34793	−0.907951
$107$	3.17309	0.306754	0.153377	−	0.988168i	$-0.450985\pi$
$107$	3.17309	0.306754	0.153377	+	0.988168i	$0.450985\pi$
$108$	5.30546	0.510518
$109$	−18.9314	−1.81330	−0.906650	−	0.421884i	$-0.861369\pi$
$109$	−18.9314	−1.81330	−0.906650	+	0.421884i	$0.861369\pi$
$110$	−16.4976	−1.57298
$111$	19.0379	1.80700
$112$	−1.00000	−0.0944911
$113$	2.42294	0.227931	0.113965	−	0.993485i	$-0.463645\pi$
$113$	2.42294	0.227931	0.113965	+	0.993485i	$0.463645\pi$
$114$	−8.30819	−0.778133
$115$	1.05032	0.0979426
$116$	−8.35475	−0.775719
$117$	−0.921562	−0.0851984
$118$	−0.566844	−0.0521822
$119$	2.56728	0.235343
$120$	4.57232	0.417394
$121$	26.3144	2.39222
$122$	4.12954	0.373871
$123$	12.4204	1.11991
$124$	2.14742	0.192844
$125$	7.30830	0.653675
$126$	0.133772	0.0119174
$127$	−1.69509	−0.150415	−0.0752075	−	0.997168i	$-0.523962\pi$
$127$	−1.69509	−0.150415	−0.0752075	+	0.997168i	$0.523962\pi$
$128$	1.00000	0.0883883
$129$	−6.35031	−0.559114
$130$	−18.6055	−1.63181
$131$	−3.84249	−0.335720	−0.167860	−	0.985811i	$-0.553686\pi$
$131$	−3.84249	−0.335720	−0.167860	+	0.985811i	$0.553686\pi$
$132$	−10.3417	−0.900132
$133$	−4.90740	−0.425525
$134$	−8.51140	−0.735273
$135$	−14.3286	−1.23321
$136$	−2.56728	−0.220143
$137$	−8.23371	−0.703453	−0.351727	−	0.936103i	$-0.614405\pi$
$137$	−8.23371	−0.703453	−0.351727	+	0.936103i	$0.614405\pi$
$138$	0.658407	0.0560473
$139$	−15.1215	−1.28259	−0.641295	−	0.767295i	$-0.721602\pi$
$139$	−15.1215	−1.28259	−0.641295	+	0.767295i	$0.721602\pi$
$140$	2.70073	0.228254
$141$	−20.9104	−1.76097
$142$	13.0918	1.09864
$143$	42.0821	3.51908
$144$	−0.133772	−0.0111477
$145$	22.5639	1.87383
$146$	−8.29642	−0.686616
$147$	−1.69299	−0.139636
$148$	−11.2451	−0.924343
$149$	14.6652	1.20142	0.600710	−	0.799467i	$-0.294885\pi$
$149$	14.6652	1.20142	0.600710	+	0.799467i	$0.294885\pi$
$150$	−3.88365	−0.317099
$151$	15.8911	1.29320	0.646602	−	0.762828i	$-0.276190\pi$
$151$	15.8911	1.29320	0.646602	+	0.762828i	$0.276190\pi$
$152$	4.90740	0.398042
$153$	0.343431	0.0277647
$154$	−6.10855	−0.492241
$155$	−5.79962	−0.465836
$156$	−11.6631	−0.933797
$157$	16.3131	1.30192	0.650962	−	0.759111i	$-0.274366\pi$
$157$	16.3131	1.30192	0.650962	+	0.759111i	$0.274366\pi$
$158$	−0.750981	−0.0597449
$159$	15.8260	1.25508
$160$	−2.70073	−0.213512
$161$	0.388901	0.0306497
$162$	−8.58079	−0.674170
$163$	−2.75178	−0.215536	−0.107768	−	0.994176i	$-0.534370\pi$
$163$	−2.75178	−0.215536	−0.107768	+	0.994176i	$0.534370\pi$
$164$	−7.33637	−0.572874
$165$	27.9303	2.17437
$166$	15.8860	1.23299
$167$	13.8896	1.07481	0.537405	−	0.843324i	$-0.319404\pi$
$167$	13.8896	1.07481	0.537405	+	0.843324i	$0.319404\pi$
$168$	1.69299	0.130617
$169$	34.4590	2.65069
$170$	6.93355	0.531779
$171$	−0.656472	−0.0502017
$172$	3.75094	0.286006
$173$	6.68855	0.508521	0.254261	−	0.967136i	$-0.418168\pi$
$173$	6.68855	0.508521	0.254261	+	0.967136i	$0.418168\pi$
$174$	14.1445	1.07229
$175$	−2.29395	−0.173407
$176$	6.10855	0.460449
$177$	0.959663	0.0721327
$178$	16.8750	1.26483
$179$	−11.3523	−0.848512	−0.424256	−	0.905542i	$-0.639464\pi$
$179$	−11.3523	−0.848512	−0.424256	+	0.905542i	$0.639464\pi$
$180$	0.361282	0.0269284
$181$	−5.35454	−0.398000	−0.199000	−	0.979999i	$-0.563769\pi$
$181$	−5.35454	−0.398000	−0.199000	+	0.979999i	$0.563769\pi$
$182$	−6.88905	−0.510650
$183$	−6.99128	−0.516810
$184$	−0.388901	−0.0286701
$185$	30.3701	2.23285
$186$	−3.63557	−0.266573
$187$	−15.6824	−1.14681
$188$	12.3511	0.900799
$189$	−5.30546	−0.385915
$190$	−13.2536	−0.961515
$191$	21.9405	1.58756	0.793778	−	0.608207i	$-0.208111\pi$
$191$	21.9405	1.58756	0.793778	+	0.608207i	$0.208111\pi$
$192$	−1.69299	−0.122181
$193$	−4.03662	−0.290562	−0.145281	−	0.989390i	$-0.546409\pi$
$193$	−4.03662	−0.290562	−0.145281	+	0.989390i	$0.546409\pi$
$194$	10.0875	0.724241
$195$	31.4990	2.25569
$196$	1.00000	0.0714286
$197$	18.0779	1.28800	0.644000	−	0.765025i	$-0.277274\pi$
$197$	18.0779	1.28800	0.644000	+	0.765025i	$0.277274\pi$
$198$	−0.817153	−0.0580725
$199$	−19.6165	−1.39058	−0.695288	−	0.718731i	$-0.744723\pi$
$199$	−19.6165	−1.39058	−0.695288	+	0.718731i	$0.744723\pi$
$200$	2.29395	0.162207
$201$	14.4098	1.01639
$202$	10.2272	0.719582
$203$	8.35475	0.586388
$204$	4.34640	0.304309
$205$	19.8136	1.38384
$206$	−7.20624	−0.502083
$207$	0.0520240	0.00361592
$208$	6.88905	0.477670
$209$	29.9771	2.07356
$210$	−4.57232	−0.315520
$211$	18.7257	1.28913	0.644565	−	0.764550i	$-0.277039\pi$
$211$	18.7257	1.28913	0.644565	+	0.764550i	$0.277039\pi$
$212$	−9.34793	−0.642019
$213$	−22.1644	−1.51868
$214$	3.17309	0.216908
$215$	−10.1303	−0.690879
$216$	5.30546	0.360991
$217$	−2.14742	−0.145777
$218$	−18.9314	−1.28220
$219$	14.0458	0.949126
$220$	−16.4976	−1.11226
$221$	−17.6861	−1.18970
$222$	19.0379	1.27774
$223$	−16.6725	−1.11647	−0.558236	−	0.829682i	$-0.688522\pi$
$223$	−16.6725	−1.11647	−0.558236	+	0.829682i	$0.688522\pi$
$224$	−1.00000	−0.0668153
$225$	−0.306867	−0.0204578
$226$	2.42294	0.161171
$227$	3.64286	0.241785	0.120893	−	0.992666i	$-0.461424\pi$
$227$	3.64286	0.241785	0.120893	+	0.992666i	$0.461424\pi$
$228$	−8.30819	−0.550223
$229$	−17.0672	−1.12784	−0.563918	−	0.825831i	$-0.690706\pi$
$229$	−17.0672	−1.12784	−0.563918	+	0.825831i	$0.690706\pi$
$230$	1.05032	0.0692558
$231$	10.3417	0.680436
$232$	−8.35475	−0.548516
$233$	7.52723	0.493125	0.246563	−	0.969127i	$-0.420699\pi$
$233$	7.52723	0.493125	0.246563	+	0.969127i	$0.420699\pi$
$234$	−0.921562	−0.0602444
$235$	−33.3571	−2.17598
$236$	−0.566844	−0.0368984
$237$	1.27141	0.0825868
$238$	2.56728	0.166412
$239$	9.22233	0.596543	0.298272	−	0.954481i	$-0.403590\pi$
$239$	9.22233	0.596543	0.298272	+	0.954481i	$0.403590\pi$
$240$	4.57232	0.295142
$241$	−1.77519	−0.114350	−0.0571749	−	0.998364i	$-0.518209\pi$
$241$	−1.77519	−0.114350	−0.0571749	+	0.998364i	$0.518209\pi$
$242$	26.3144	1.69155
$243$	−1.38915	−0.0891138
$244$	4.12954	0.264366
$245$	−2.70073	−0.172543
$246$	12.4204	0.791897
$247$	33.8073	2.15111
$248$	2.14742	0.136362
$249$	−26.8949	−1.70439
$250$	7.30830	0.462218
$251$	25.8164	1.62951	0.814757	−	0.579802i	$-0.196870\pi$
$251$	25.8164	1.62951	0.814757	+	0.579802i	$0.196870\pi$
$252$	0.133772	0.00842684
$253$	−2.37562	−0.149354
$254$	−1.69509	−0.106359
$255$	−11.7385	−0.735090
$256$	1.00000	0.0625000
$257$	6.01768	0.375372	0.187686	−	0.982229i	$-0.439901\pi$
$257$	6.01768	0.375372	0.187686	+	0.982229i	$0.439901\pi$
$258$	−6.35031	−0.395353
$259$	11.2451	0.698738
$260$	−18.6055	−1.15386
$261$	1.11763	0.0691797
$262$	−3.84249	−0.237390
$263$	−18.0814	−1.11494	−0.557472	−	0.830195i	$-0.688229\pi$
$263$	−18.0814	−1.11494	−0.557472	+	0.830195i	$0.688229\pi$
$264$	−10.3417	−0.636490
$265$	25.2463	1.55087
$266$	−4.90740	−0.300892
$267$	−28.5693	−1.74841
$268$	−8.51140	−0.519917
$269$	−7.34143	−0.447615	−0.223807	−	0.974633i	$-0.571849\pi$
$269$	−7.34143	−0.447615	−0.223807	+	0.974633i	$0.571849\pi$
$270$	−14.3286	−0.872012
$271$	−3.72160	−0.226071	−0.113036	−	0.993591i	$-0.536057\pi$
$271$	−3.72160	−0.226071	−0.113036	+	0.993591i	$0.536057\pi$
$272$	−2.56728	−0.155664
$273$	11.6631	0.705884
$274$	−8.23371	−0.497417
$275$	14.0127	0.845000
$276$	0.658407	0.0396314
$277$	1.75844	0.105654	0.0528271	−	0.998604i	$-0.483177\pi$
$277$	1.75844	0.105654	0.0528271	+	0.998604i	$0.483177\pi$
$278$	−15.1215	−0.906927
$279$	−0.287265	−0.0171981
$280$	2.70073	0.161400
$281$	18.4479	1.10051	0.550256	−	0.834996i	$-0.314530\pi$
$281$	18.4479	1.10051	0.550256	+	0.834996i	$0.314530\pi$
$282$	−20.9104	−1.24520
$283$	−17.6969	−1.05197	−0.525987	−	0.850493i	$-0.676304\pi$
$283$	−17.6969	−1.05197	−0.525987	+	0.850493i	$0.676304\pi$
$284$	13.0918	0.776858
$285$	22.4382	1.32912
$286$	42.0821	2.48837
$287$	7.33637	0.433052
$288$	−0.133772	−0.00788259
$289$	−10.4091	−0.612297
$290$	22.5639	1.32500
$291$	−17.0781	−1.00114
$292$	−8.29642	−0.485511
$293$	−13.9945	−0.817567	−0.408783	−	0.912631i	$-0.634047\pi$
$293$	−13.9945	−0.817567	−0.408783	+	0.912631i	$0.634047\pi$
$294$	−1.69299	−0.0987374
$295$	1.53089	0.0891320
$296$	−11.2451	−0.653609
$297$	32.4086	1.88054
$298$	14.6652	0.849532
$299$	−2.67916	−0.154940
$300$	−3.88365	−0.224223
$301$	−3.75094	−0.216200
$302$	15.8911	0.914433
$303$	−17.3146	−0.994696
$304$	4.90740	0.281459
$305$	−11.1528	−0.638606
$306$	0.343431	0.0196326
$307$	0.494156	0.0282030	0.0141015	−	0.999901i	$-0.495511\pi$
$307$	0.494156	0.0282030	0.0141015	+	0.999901i	$0.495511\pi$
$308$	−6.10855	−0.348067
$309$	12.2001	0.694041
$310$	−5.79962	−0.329396
$311$	15.6473	0.887277	0.443638	−	0.896206i	$-0.353687\pi$
$311$	15.6473	0.887277	0.443638	+	0.896206i	$0.353687\pi$
$312$	−11.6631	−0.660294
$313$	16.7702	0.947905	0.473953	−	0.880550i	$-0.342827\pi$
$313$	16.7702	0.947905	0.473953	+	0.880550i	$0.342827\pi$
$314$	16.3131	0.920599
$315$	−0.361282	−0.0203560
$316$	−0.750981	−0.0422460
$317$	−18.2061	−1.02256	−0.511279	−	0.859415i	$-0.670828\pi$
$317$	−18.2061	−1.02256	−0.511279	+	0.859415i	$0.670828\pi$
$318$	15.8260	0.887478
$319$	−51.0354	−2.85743
$320$	−2.70073	−0.150976
$321$	−5.37202	−0.299837
$322$	0.388901	0.0216726
$323$	−12.5987	−0.701009
$324$	−8.58079	−0.476711
$325$	15.8032	0.876602
$326$	−2.75178	−0.152407
$327$	32.0507	1.77241
$328$	−7.33637	−0.405083
$329$	−12.3511	−0.680940
$330$	27.9303	1.53751
$331$	26.9765	1.48276	0.741382	−	0.671084i	$-0.234171\pi$
$331$	26.9765	1.48276	0.741382	+	0.671084i	$0.234171\pi$
$332$	15.8860	0.871857
$333$	1.50428	0.0824342
$334$	13.8896	0.760006
$335$	22.9870	1.25591
$336$	1.69299	0.0923604
$337$	8.19239	0.446268	0.223134	−	0.974788i	$-0.428371\pi$
$337$	8.19239	0.446268	0.223134	+	0.974788i	$0.428371\pi$
$338$	34.4590	1.87432
$339$	−4.10202	−0.222791
$340$	6.93355	0.376024
$341$	13.1176	0.710360
$342$	−0.656472	−0.0354980
$343$	−1.00000	−0.0539949
$344$	3.75094	0.202237
$345$	−1.77818	−0.0957340
$346$	6.68855	0.359579
$347$	10.9966	0.590329	0.295165	−	0.955446i	$-0.404625\pi$
$347$	10.9966	0.590329	0.295165	+	0.955446i	$0.404625\pi$
$348$	14.1445	0.758227
$349$	3.35190	0.179423	0.0897116	−	0.995968i	$-0.471405\pi$
$349$	3.35190	0.179423	0.0897116	+	0.995968i	$0.471405\pi$
$350$	−2.29395	−0.122617
$351$	36.5495	1.95087
$352$	6.10855	0.325587
$353$	−3.61552	−0.192434	−0.0962172	−	0.995360i	$-0.530674\pi$
$353$	−3.61552	−0.192434	−0.0962172	+	0.995360i	$0.530674\pi$
$354$	0.959663	0.0510055
$355$	−35.3576	−1.87659
$356$	16.8750	0.894373
$357$	−4.34640	−0.230036
$358$	−11.3523	−0.599988
$359$	22.4872	1.18683	0.593415	−	0.804897i	$-0.297779\pi$
$359$	22.4872	1.18683	0.593415	+	0.804897i	$0.297779\pi$
$360$	0.361282	0.0190413
$361$	5.08254	0.267502
$362$	−5.35454	−0.281429
$363$	−44.5501	−2.33827
$364$	−6.88905	−0.361084
$365$	22.4064	1.17280
$366$	−6.99128	−0.365440
$367$	2.92972	0.152930	0.0764650	−	0.997072i	$-0.475637\pi$
$367$	2.92972	0.152930	0.0764650	+	0.997072i	$0.475637\pi$
$368$	−0.388901	−0.0202729
$369$	0.981400	0.0510897
$370$	30.3701	1.57886
$371$	9.34793	0.485320
$372$	−3.63557	−0.188496
$373$	−29.9912	−1.55289	−0.776443	−	0.630188i	$-0.782978\pi$
$373$	−29.9912	−1.55289	−0.776443	+	0.630188i	$0.782978\pi$
$374$	−15.6824	−0.810916
$375$	−12.3729	−0.638934
$376$	12.3511	0.636961
$377$	−57.5563	−2.96430
$378$	−5.30546	−0.272883
$379$	3.08060	0.158240	0.0791198	−	0.996865i	$-0.474789\pi$
$379$	3.08060	0.158240	0.0791198	+	0.996865i	$0.474789\pi$
$380$	−13.2536	−0.679894
$381$	2.86978	0.147023
$382$	21.9405	1.12257
$383$	8.83854	0.451628	0.225814	−	0.974170i	$-0.427496\pi$
$383$	8.83854	0.451628	0.225814	+	0.974170i	$0.427496\pi$
$384$	−1.69299	−0.0863952
$385$	16.4976	0.840793
$386$	−4.03662	−0.205458
$387$	−0.501770	−0.0255064
$388$	10.0875	0.512116
$389$	23.9546	1.21455	0.607273	−	0.794493i	$-0.292263\pi$
$389$	23.9546	1.21455	0.607273	+	0.794493i	$0.292263\pi$
$390$	31.4990	1.59501
$391$	0.998419	0.0504922
$392$	1.00000	0.0505076
$393$	6.50530	0.328149
$394$	18.0779	0.910754
$395$	2.02820	0.102050
$396$	−0.817153	−0.0410635
$397$	16.1770	0.811901	0.405950	−	0.913895i	$-0.366941\pi$
$397$	16.1770	0.811901	0.405950	+	0.913895i	$0.366941\pi$
$398$	−19.6165	−0.983286
$399$	8.30819	0.415930
$400$	2.29395	0.114698
$401$	−24.7623	−1.23657	−0.618284	−	0.785955i	$-0.712172\pi$
$401$	−24.7623	−1.23657	−0.618284	+	0.785955i	$0.712172\pi$
$402$	14.4098	0.718693
$403$	14.7937	0.736927
$404$	10.2272	0.508822
$405$	23.1744	1.15155
$406$	8.35475	0.414639
$407$	−68.6914	−3.40490
$408$	4.34640	0.215179
$409$	21.3835	1.05735	0.528673	−	0.848826i	$-0.322690\pi$
$409$	21.3835	1.05735	0.528673	+	0.848826i	$0.322690\pi$
$410$	19.8136	0.978522
$411$	13.9396	0.687591
$412$	−7.20624	−0.355026
$413$	0.566844	0.0278926
$414$	0.0520240	0.00255684
$415$	−42.9038	−2.10606
$416$	6.88905	0.337763
$417$	25.6006	1.25367
$418$	29.9771	1.46623
$419$	−18.7177	−0.914417	−0.457209	−	0.889359i	$-0.651151\pi$
$419$	−18.7177	−0.914417	−0.457209	+	0.889359i	$0.651151\pi$
$420$	−4.57232	−0.223107
$421$	−7.66189	−0.373417	−0.186709	−	0.982415i	$-0.559782\pi$
$421$	−7.66189	−0.373417	−0.186709	+	0.982415i	$0.559782\pi$
$422$	18.7257	0.911552
$423$	−1.65224	−0.0803344
$424$	−9.34793	−0.453976
$425$	−5.88923	−0.285670
$426$	−22.1644	−1.07387
$427$	−4.12954	−0.199842
$428$	3.17309	0.153377
$429$	−71.2447	−3.43973
$430$	−10.1303	−0.488525
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.30546	0.255259
$433$	31.8943	1.53274	0.766371	−	0.642399i	$-0.222061\pi$
$433$	31.8943	1.53274	0.766371	+	0.642399i	$0.222061\pi$
$434$	−2.14742	−0.103080
$435$	−38.2006	−1.83158
$436$	−18.9314	−0.906650
$437$	−1.90849	−0.0912955
$438$	14.0458	0.671134
$439$	−25.6138	−1.22248	−0.611240	−	0.791445i	$-0.709329\pi$
$439$	−25.6138	−1.22248	−0.611240	+	0.791445i	$0.709329\pi$
$440$	−16.4976	−0.786490
$441$	−0.133772	−0.00637010
$442$	−17.6861	−0.841244
$443$	26.3425	1.25157	0.625786	−	0.779995i	$-0.284778\pi$
$443$	26.3425	1.25157	0.625786	+	0.779995i	$0.284778\pi$
$444$	19.0379	0.903500
$445$	−45.5749	−2.16046
$446$	−16.6725	−0.789465
$447$	−24.8281	−1.17433
$448$	−1.00000	−0.0472456
$449$	34.4152	1.62415	0.812076	−	0.583551i	$-0.198337\pi$
$449$	34.4152	1.62415	0.812076	+	0.583551i	$0.198337\pi$
$450$	−0.306867	−0.0144658
$451$	−44.8145	−2.11023
$452$	2.42294	0.113965
$453$	−26.9036	−1.26404
$454$	3.64286	0.170968
$455$	18.6055	0.872238
$456$	−8.30819	−0.389067
$457$	−2.73568	−0.127970	−0.0639848	−	0.997951i	$-0.520381\pi$
$457$	−2.73568	−0.127970	−0.0639848	+	0.997951i	$0.520381\pi$
$458$	−17.0672	−0.797500
$459$	−13.6206	−0.635756
$460$	1.05032	0.0489713
$461$	−31.9249	−1.48689	−0.743446	−	0.668796i	$-0.766810\pi$
$461$	−31.9249	−1.48689	−0.743446	+	0.668796i	$0.766810\pi$
$462$	10.3417	0.481141
$463$	20.5332	0.954261	0.477130	−	0.878833i	$-0.341677\pi$
$463$	20.5332	0.954261	0.477130	+	0.878833i	$0.341677\pi$
$464$	−8.35475	−0.387859
$465$	9.81871	0.455332
$466$	7.52723	0.348692
$467$	6.80434	0.314867	0.157434	−	0.987530i	$-0.449678\pi$
$467$	6.80434	0.314867	0.157434	+	0.987530i	$0.449678\pi$
$468$	−0.921562	−0.0425992
$469$	8.51140	0.393020
$470$	−33.3571	−1.53865
$471$	−27.6179	−1.27257
$472$	−0.566844	−0.0260911
$473$	22.9128	1.05353
$474$	1.27141	0.0583977
$475$	11.2573	0.516522
$476$	2.56728	0.117671
$477$	1.25049	0.0572561
$478$	9.22233	0.421820
$479$	28.7253	1.31249	0.656247	−	0.754546i	$-0.272143\pi$
$479$	28.7253	1.31249	0.656247	+	0.754546i	$0.272143\pi$
$480$	4.57232	0.208697
$481$	−77.4682	−3.53224
$482$	−1.77519	−0.0808576
$483$	−0.658407	−0.0299585
$484$	26.3144	1.19611
$485$	−27.2437	−1.23707
$486$	−1.38915	−0.0630130
$487$	−8.93883	−0.405057	−0.202529	−	0.979276i	$-0.564916\pi$
$487$	−8.93883	−0.405057	−0.202529	+	0.979276i	$0.564916\pi$
$488$	4.12954	0.186935
$489$	4.65875	0.210676
$490$	−2.70073	−0.122007
$491$	−36.8490	−1.66297	−0.831486	−	0.555546i	$-0.812509\pi$
$491$	−36.8490	−1.66297	−0.831486	+	0.555546i	$0.812509\pi$
$492$	12.4204	0.559956
$493$	21.4490	0.966015
$494$	33.8073	1.52106
$495$	2.20691	0.0991933
$496$	2.14742	0.0964222
$497$	−13.0918	−0.587250
$498$	−26.8949	−1.20519
$499$	22.8717	1.02388	0.511939	−	0.859022i	$-0.328928\pi$
$499$	22.8717	1.02388	0.511939	+	0.859022i	$0.328928\pi$
$500$	7.30830	0.326837
$501$	−23.5150	−1.05057
$502$	25.8164	1.15224
$503$	−37.9954	−1.69413	−0.847066	−	0.531488i	$-0.821633\pi$
$503$	−37.9954	−1.69413	−0.847066	+	0.531488i	$0.821633\pi$
$504$	0.133772	0.00595868
$505$	−27.6209	−1.22911
$506$	−2.37562	−0.105609
$507$	−58.3388	−2.59092
$508$	−1.69509	−0.0752075
$509$	−12.4768	−0.553026	−0.276513	−	0.961010i	$-0.589179\pi$
$509$	−12.4768	−0.553026	−0.276513	+	0.961010i	$0.589179\pi$
$510$	−11.7385	−0.519787
$511$	8.29642	0.367012
$512$	1.00000	0.0441942
$513$	26.0360	1.14952
$514$	6.01768	0.265428
$515$	19.4621	0.857604
$516$	−6.35031	−0.279557
$517$	75.4475	3.31818
$518$	11.2451	0.494082
$519$	−11.3237	−0.497054
$520$	−18.6055	−0.815904
$521$	16.8621	0.738743	0.369371	−	0.929282i	$-0.379573\pi$
$521$	16.8621	0.738743	0.369371	+	0.929282i	$0.379573\pi$
$522$	1.11763	0.0489174
$523$	23.5222	1.02855	0.514276	−	0.857625i	$-0.328061\pi$
$523$	23.5222	1.02855	0.514276	+	0.857625i	$0.328061\pi$
$524$	−3.84249	−0.167860
$525$	3.88365	0.169496
$526$	−18.0814	−0.788385
$527$	−5.51305	−0.240152
$528$	−10.3417	−0.450066
$529$	−22.8488	−0.993424
$530$	25.2463	1.09663
$531$	0.0758278	0.00329065
$532$	−4.90740	−0.212763
$533$	−50.5406	−2.18916
$534$	−28.5693	−1.23631
$535$	−8.56966	−0.370499
$536$	−8.51140	−0.367637
$537$	19.2194	0.829378
$538$	−7.34143	−0.316511
$539$	6.10855	0.263114
$540$	−14.3286	−0.616606
$541$	−28.5342	−1.22678	−0.613391	−	0.789780i	$-0.710195\pi$
$541$	−28.5342	−1.22678	−0.613391	+	0.789780i	$0.710195\pi$
$542$	−3.72160	−0.159857
$543$	9.06521	0.389025
$544$	−2.56728	−0.110071
$545$	51.1286	2.19011
$546$	11.6631	0.499135
$547$	18.3035	0.782601	0.391301	−	0.920263i	$-0.372025\pi$
$547$	18.3035	0.782601	0.391301	+	0.920263i	$0.372025\pi$
$548$	−8.23371	−0.351727
$549$	−0.552416	−0.0235766
$550$	14.0127	0.597505
$551$	−41.0001	−1.74666
$552$	0.658407	0.0280236
$553$	0.750981	0.0319350
$554$	1.75844	0.0747088
$555$	−51.4163	−2.18250
$556$	−15.1215	−0.641295
$557$	38.6577	1.63798	0.818991	−	0.573807i	$-0.194534\pi$
$557$	38.6577	1.63798	0.818991	+	0.573807i	$0.194534\pi$
$558$	−0.287265	−0.0121609
$559$	25.8404	1.09293
$560$	2.70073	0.114127
$561$	26.5502	1.12095
$562$	18.4479	0.778179
$563$	10.2832	0.433386	0.216693	−	0.976240i	$-0.430473\pi$
$563$	10.2832	0.433386	0.216693	+	0.976240i	$0.430473\pi$
$564$	−20.9104	−0.880486
$565$	−6.54371	−0.275296
$566$	−17.6969	−0.743858
$567$	8.58079	0.360359
$568$	13.0918	0.549322
$569$	−27.6457	−1.15897	−0.579483	−	0.814984i	$-0.696746\pi$
$569$	−27.6457	−1.15897	−0.579483	+	0.814984i	$0.696746\pi$
$570$	22.4382	0.939833
$571$	46.3975	1.94167	0.970837	−	0.239742i	$-0.0770629\pi$
$571$	46.3975	1.94167	0.970837	+	0.239742i	$0.0770629\pi$
$572$	42.0821	1.75954
$573$	−37.1451	−1.55176
$574$	7.33637	0.306214
$575$	−0.892121	−0.0372040
$576$	−0.133772	−0.00557383
$577$	−12.6141	−0.525130	−0.262565	−	0.964914i	$-0.584568\pi$
$577$	−12.6141	−0.525130	−0.262565	+	0.964914i	$0.584568\pi$
$578$	−10.4091	−0.432960
$579$	6.83397	0.284010
$580$	22.5639	0.936917
$581$	−15.8860	−0.659062
$582$	−17.0781	−0.707910
$583$	−57.1023	−2.36494
$584$	−8.29642	−0.343308
$585$	2.48889	0.102903
$586$	−13.9945	−0.578107
$587$	3.32805	0.137363	0.0686816	−	0.997639i	$-0.478121\pi$
$587$	3.32805	0.137363	0.0686816	+	0.997639i	$0.478121\pi$
$588$	−1.69299	−0.0698179
$589$	10.5383	0.434221
$590$	1.53089	0.0630259
$591$	−30.6059	−1.25896
$592$	−11.2451	−0.462172
$593$	−32.3643	−1.32904	−0.664521	−	0.747270i	$-0.731364\pi$
$593$	−32.3643	−1.32904	−0.664521	+	0.747270i	$0.731364\pi$
$594$	32.4086	1.32974
$595$	−6.93355	−0.284248
$596$	14.6652	0.600710
$597$	33.2106	1.35922
$598$	−2.67916	−0.109559
$599$	7.38223	0.301630	0.150815	−	0.988562i	$-0.451810\pi$
$599$	7.38223	0.301630	0.150815	+	0.988562i	$0.451810\pi$
$600$	−3.88365	−0.158549
$601$	1.85351	0.0756061	0.0378031	−	0.999285i	$-0.487964\pi$
$601$	1.85351	0.0756061	0.0378031	+	0.999285i	$0.487964\pi$
$602$	−3.75094	−0.152877
$603$	1.13859	0.0463669
$604$	15.8911	0.646602
$605$	−71.0681	−2.88933
$606$	−17.3146	−0.703356
$607$	1.71021	0.0694154	0.0347077	−	0.999398i	$-0.488950\pi$
$607$	1.71021	0.0694154	0.0347077	+	0.999398i	$0.488950\pi$
$608$	4.90740	0.199021
$609$	−14.1445	−0.573166
$610$	−11.1528	−0.451563
$611$	85.0875	3.44227
$612$	0.343431	0.0138824
$613$	−3.24964	−0.131252	−0.0656259	−	0.997844i	$-0.520904\pi$
$613$	−3.24964	−0.131252	−0.0656259	+	0.997844i	$0.520904\pi$
$614$	0.494156	0.0199425
$615$	−33.5442	−1.35263
$616$	−6.10855	−0.246120
$617$	−35.8273	−1.44235	−0.721177	−	0.692751i	$-0.756398\pi$
$617$	−35.8273	−1.44235	−0.721177	+	0.692751i	$0.756398\pi$
$618$	12.2001	0.490761
$619$	19.5037	0.783919	0.391959	−	0.919983i	$-0.371797\pi$
$619$	19.5037	0.783919	0.391959	+	0.919983i	$0.371797\pi$
$620$	−5.79962	−0.232918
$621$	−2.06330	−0.0827972
$622$	15.6473	0.627399
$623$	−16.8750	−0.676083
$624$	−11.6631	−0.466898
$625$	−31.2075	−1.24830
$626$	16.7702	0.670270
$627$	−50.7510	−2.02680
$628$	16.3131	0.650962
$629$	28.8694	1.15110
$630$	−0.361282	−0.0143938
$631$	−15.9378	−0.634474	−0.317237	−	0.948346i	$-0.602755\pi$
$631$	−15.9378	−0.634474	−0.317237	+	0.948346i	$0.602755\pi$
$632$	−0.750981	−0.0298724
$633$	−31.7025	−1.26006
$634$	−18.2061	−0.723058
$635$	4.57799	0.181672
$636$	15.8260	0.627541
$637$	6.88905	0.272954
$638$	−51.0354	−2.02051
$639$	−1.75132	−0.0692813
$640$	−2.70073	−0.106756
$641$	28.5966	1.12950	0.564748	−	0.825263i	$-0.308973\pi$
$641$	28.5966	1.12950	0.564748	+	0.825263i	$0.308973\pi$
$642$	−5.37202	−0.212017
$643$	49.5048	1.95228	0.976139	−	0.217145i	$-0.0696744\pi$
$643$	49.5048	1.95228	0.976139	+	0.217145i	$0.0696744\pi$
$644$	0.388901	0.0153248
$645$	17.1505	0.675300
$646$	−12.5987	−0.495688
$647$	−23.6910	−0.931388	−0.465694	−	0.884946i	$-0.654195\pi$
$647$	−23.6910	−0.931388	−0.465694	+	0.884946i	$0.654195\pi$
$648$	−8.58079	−0.337085
$649$	−3.46259	−0.135919
$650$	15.8032	0.619851
$651$	3.63557	0.142489
$652$	−2.75178	−0.107768
$653$	−8.56739	−0.335268	−0.167634	−	0.985849i	$-0.553613\pi$
$653$	−8.56739	−0.335268	−0.167634	+	0.985849i	$0.553613\pi$
$654$	32.0507	1.25328
$655$	10.3775	0.405483
$656$	−7.33637	−0.286437
$657$	1.10983	0.0432985
$658$	−12.3511	−0.481497
$659$	37.2528	1.45116	0.725582	−	0.688135i	$-0.241571\pi$
$659$	37.2528	1.45116	0.725582	+	0.688135i	$0.241571\pi$
$660$	27.9303	1.08718
$661$	16.3747	0.636901	0.318450	−	0.947940i	$-0.396838\pi$
$661$	16.3747	0.636901	0.318450	+	0.947940i	$0.396838\pi$
$662$	26.9765	1.04847
$663$	29.9425	1.16287
$664$	15.8860	0.616496
$665$	13.2536	0.513951
$666$	1.50428	0.0582897
$667$	3.24917	0.125808
$668$	13.8896	0.537405
$669$	28.2264	1.09130
$670$	22.9870	0.888066
$671$	25.2255	0.973819
$672$	1.69299	0.0653087
$673$	46.0240	1.77409	0.887047	−	0.461679i	$-0.152753\pi$
$673$	46.0240	1.77409	0.887047	+	0.461679i	$0.152753\pi$
$674$	8.19239	0.315559
$675$	12.1705	0.468442
$676$	34.4590	1.32535
$677$	18.6668	0.717425	0.358712	−	0.933448i	$-0.383216\pi$
$677$	18.6668	0.717425	0.358712	+	0.933448i	$0.383216\pi$
$678$	−4.10202	−0.157537
$679$	−10.0875	−0.387123
$680$	6.93355	0.265889
$681$	−6.16734	−0.236333
$682$	13.1176	0.502300
$683$	−7.53758	−0.288418	−0.144209	−	0.989547i	$-0.546064\pi$
$683$	−7.53758	−0.288418	−0.144209	+	0.989547i	$0.546064\pi$
$684$	−0.656472	−0.0251008
$685$	22.2370	0.849634
$686$	−1.00000	−0.0381802
$687$	28.8947	1.10240
$688$	3.75094	0.143003
$689$	−64.3984	−2.45338
$690$	−1.77818	−0.0676942
$691$	13.2969	0.505839	0.252920	−	0.967487i	$-0.418609\pi$
$691$	13.2969	0.505839	0.252920	+	0.967487i	$0.418609\pi$
$692$	6.68855	0.254261
$693$	0.817153	0.0310411
$694$	10.9966	0.417426
$695$	40.8391	1.54912
$696$	14.1445	0.536147
$697$	18.8345	0.713409
$698$	3.35190	0.126871
$699$	−12.7435	−0.482005
$700$	−2.29395	−0.0867033
$701$	46.7240	1.76474	0.882371	−	0.470554i	$-0.155946\pi$
$701$	46.7240	1.76474	0.882371	+	0.470554i	$0.155946\pi$
$702$	36.5495	1.37947
$703$	−55.1843	−2.08131
$704$	6.10855	0.230225
$705$	56.4734	2.12691
$706$	−3.61552	−0.136072
$707$	−10.2272	−0.384633
$708$	0.959663	0.0360663
$709$	11.3101	0.424759	0.212380	−	0.977187i	$-0.431879\pi$
$709$	11.3101	0.424759	0.212380	+	0.977187i	$0.431879\pi$
$710$	−35.3576	−1.32695
$711$	0.100460	0.00376756
$712$	16.8750	0.632417
$713$	−0.835135	−0.0312760
$714$	−4.34640	−0.162660
$715$	−113.652	−4.25036
$716$	−11.3523	−0.424256
$717$	−15.6134	−0.583091
$718$	22.4872	0.839216
$719$	−5.06525	−0.188902	−0.0944510	−	0.995530i	$-0.530110\pi$
$719$	−5.06525	−0.188902	−0.0944510	+	0.995530i	$0.530110\pi$
$720$	0.361282	0.0134642
$721$	7.20624	0.268375
$722$	5.08254	0.189153
$723$	3.00538	0.111771
$724$	−5.35454	−0.199000
$725$	−19.1654	−0.711786
$726$	−44.5501	−1.65341
$727$	−27.3412	−1.01403	−0.507015	−	0.861937i	$-0.669251\pi$
$727$	−27.3412	−1.01403	−0.507015	+	0.861937i	$0.669251\pi$
$728$	−6.88905	−0.255325
$729$	28.0942	1.04053
$730$	22.4064	0.829298
$731$	−9.62972	−0.356168
$732$	−6.99128	−0.258405
$733$	3.05494	0.112837	0.0564184	−	0.998407i	$-0.482032\pi$
$733$	3.05494	0.112837	0.0564184	+	0.998407i	$0.482032\pi$
$734$	2.92972	0.108138
$735$	4.57232	0.168653
$736$	−0.388901	−0.0143351
$737$	−51.9923	−1.91516
$738$	0.981400	0.0361258
$739$	23.7044	0.871981	0.435991	−	0.899951i	$-0.356398\pi$
$739$	23.7044	0.871981	0.435991	+	0.899951i	$0.356398\pi$
$740$	30.3701	1.11643
$741$	−57.2355	−2.10260
$742$	9.34793	0.343173
$743$	−11.2893	−0.414163	−0.207082	−	0.978324i	$-0.566397\pi$
$743$	−11.2893	−0.414163	−0.207082	+	0.978324i	$0.566397\pi$
$744$	−3.63557	−0.133287
$745$	−39.6068	−1.45108
$746$	−29.9912	−1.09806
$747$	−2.12510	−0.0777534
$748$	−15.6824	−0.573405
$749$	−3.17309	−0.115942
$750$	−12.3729	−0.451795
$751$	49.2861	1.79848	0.899238	−	0.437460i	$-0.144122\pi$
$751$	49.2861	1.79848	0.899238	+	0.437460i	$0.144122\pi$
$752$	12.3511	0.450399
$753$	−43.7070	−1.59277
$754$	−57.5563	−2.09608
$755$	−42.9177	−1.56194
$756$	−5.30546	−0.192958
$757$	−11.0247	−0.400699	−0.200349	−	0.979725i	$-0.564208\pi$
$757$	−11.0247	−0.400699	−0.200349	+	0.979725i	$0.564208\pi$
$758$	3.08060	0.111892
$759$	4.02191	0.145986
$760$	−13.2536	−0.480757
$761$	−42.1339	−1.52735	−0.763677	−	0.645599i	$-0.776608\pi$
$761$	−42.1339	−1.52735	−0.763677	+	0.645599i	$0.776608\pi$
$762$	2.86978	0.103961
$763$	18.9314	0.685363
$764$	21.9405	0.793778
$765$	−0.927514	−0.0335344
$766$	8.83854	0.319349
$767$	−3.90501	−0.141002
$768$	−1.69299	−0.0610907
$769$	−32.9467	−1.18809	−0.594045	−	0.804432i	$-0.702470\pi$
$769$	−32.9467	−1.18809	−0.594045	+	0.804432i	$0.702470\pi$
$770$	16.4976	0.594531
$771$	−10.1879	−0.366908
$772$	−4.03662	−0.145281
$773$	39.7351	1.42917	0.714586	−	0.699547i	$-0.246615\pi$
$773$	39.7351	1.42917	0.714586	+	0.699547i	$0.246615\pi$
$774$	−0.501770	−0.0180358
$775$	4.92609	0.176950
$776$	10.0875	0.362121
$777$	−19.0379	−0.682981
$778$	23.9546	0.858814
$779$	−36.0025	−1.28992
$780$	31.4990	1.12784
$781$	79.9722	2.86163
$782$	0.998419	0.0357034
$783$	−44.3258	−1.58407
$784$	1.00000	0.0357143
$785$	−44.0572	−1.57247
$786$	6.50530	0.232037
$787$	27.5298	0.981330	0.490665	−	0.871348i	$-0.336754\pi$
$787$	27.5298	0.981330	0.490665	+	0.871348i	$0.336754\pi$
$788$	18.0779	0.644000
$789$	30.6116	1.08980
$790$	2.02820	0.0721601
$791$	−2.42294	−0.0861498
$792$	−0.817153	−0.0290363
$793$	28.4486	1.01024
$794$	16.1770	0.574100
$795$	−42.7418	−1.51589
$796$	−19.6165	−0.695288
$797$	7.98329	0.282783	0.141391	−	0.989954i	$-0.454842\pi$
$797$	7.98329	0.282783	0.141391	+	0.989954i	$0.454842\pi$
$798$	8.30819	0.294107
$799$	−31.7089	−1.12178
$800$	2.29395	0.0811036
$801$	−2.25740	−0.0797614
$802$	−24.7623	−0.874386
$803$	−50.6791	−1.78843
$804$	14.4098	0.508193
$805$	−1.05032	−0.0370188
$806$	14.7937	0.521086
$807$	12.4290	0.437521
$808$	10.2272	0.359791
$809$	−36.2004	−1.27274	−0.636368	−	0.771385i	$-0.719564\pi$
$809$	−36.2004	−1.27274	−0.636368	+	0.771385i	$0.719564\pi$
$810$	23.1744	0.814266
$811$	−16.6216	−0.583664	−0.291832	−	0.956470i	$-0.594265\pi$
$811$	−16.6216	−0.583664	−0.291832	+	0.956470i	$0.594265\pi$
$812$	8.35475	0.293194
$813$	6.30065	0.220974
$814$	−68.6914	−2.40763
$815$	7.43183	0.260326
$816$	4.34640	0.152154
$817$	18.4073	0.643991
$818$	21.3835	0.747656
$819$	0.921562	0.0322020
$820$	19.8136	0.691920
$821$	−0.512079	−0.0178717	−0.00893585	−	0.999960i	$-0.502844\pi$
$821$	−0.512079	−0.0178717	−0.00893585	+	0.999960i	$0.502844\pi$
$822$	13.9396	0.486200
$823$	−34.1172	−1.18925	−0.594625	−	0.804003i	$-0.702699\pi$
$823$	−34.1172	−1.18925	−0.594625	+	0.804003i	$0.702699\pi$
$824$	−7.20624	−0.251041
$825$	−23.7235	−0.825945
$826$	0.566844	0.0197230
$827$	−39.0336	−1.35733	−0.678666	−	0.734447i	$-0.737441\pi$
$827$	−39.0336	−1.35733	−0.678666	+	0.734447i	$0.737441\pi$
$828$	0.0520240	0.00180796
$829$	56.5560	1.96427	0.982136	−	0.188171i	$-0.0602561\pi$
$829$	56.5560	1.96427	0.982136	+	0.188171i	$0.0602561\pi$
$830$	−42.9038	−1.48921
$831$	−2.97702	−0.103272
$832$	6.88905	0.238835
$833$	−2.56728	−0.0889511
$834$	25.6006	0.886477
$835$	−37.5121	−1.29816
$836$	29.9771	1.03678
$837$	11.3931	0.393802
$838$	−18.7177	−0.646591
$839$	43.7536	1.51054	0.755271	−	0.655412i	$-0.227505\pi$
$839$	43.7536	1.51054	0.755271	+	0.655412i	$0.227505\pi$
$840$	−4.57232	−0.157760
$841$	40.8018	1.40696
$842$	−7.66189	−0.264046
$843$	−31.2322	−1.07570
$844$	18.7257	0.644565
$845$	−93.0645	−3.20152
$846$	−1.65224	−0.0568050
$847$	−26.3144	−0.904172
$848$	−9.34793	−0.321009
$849$	29.9608	1.02825
$850$	−5.88923	−0.201999
$851$	4.37324	0.149913
$852$	−22.1644	−0.759341
$853$	−5.41990	−0.185574	−0.0927869	−	0.995686i	$-0.529578\pi$
$853$	−5.41990	−0.185574	−0.0927869	+	0.995686i	$0.529578\pi$
$854$	−4.12954	−0.141310
$855$	1.77296	0.0606338
$856$	3.17309	0.108454
$857$	49.2311	1.68170	0.840851	−	0.541267i	$-0.182055\pi$
$857$	49.2311	1.68170	0.840851	+	0.541267i	$0.182055\pi$
$858$	−71.2447	−2.43225
$859$	3.06077	0.104432	0.0522161	−	0.998636i	$-0.483372\pi$
$859$	3.06077	0.104432	0.0522161	+	0.998636i	$0.483372\pi$
$860$	−10.1303	−0.345440
$861$	−12.4204	−0.423287
$862$	−1.00000	−0.0340601
$863$	−50.8791	−1.73194	−0.865972	−	0.500092i	$-0.833299\pi$
$863$	−50.8791	−1.73194	−0.865972	+	0.500092i	$0.833299\pi$
$864$	5.30546	0.180495
$865$	−18.0640	−0.614194
$866$	31.8943	1.08381
$867$	17.6225	0.598490
$868$	−2.14742	−0.0728883
$869$	−4.58741	−0.155617
$870$	−38.2006	−1.29512
$871$	−58.6355	−1.98679
$872$	−18.9314	−0.641098
$873$	−1.34943	−0.0456712
$874$	−1.90849	−0.0645556
$875$	−7.30830	−0.247066
$876$	14.0458	0.474563
$877$	−32.5670	−1.09971	−0.549854	−	0.835261i	$-0.685317\pi$
$877$	−32.5670	−1.09971	−0.549854	+	0.835261i	$0.685317\pi$
$878$	−25.6138	−0.864424
$879$	23.6926	0.799131
$880$	−16.4976	−0.556132
$881$	−4.88076	−0.164437	−0.0822185	−	0.996614i	$-0.526201\pi$
$881$	−4.88076	−0.164437	−0.0822185	+	0.996614i	$0.526201\pi$
$882$	−0.133772	−0.00450434
$883$	55.2859	1.86052	0.930259	−	0.366903i	$-0.119582\pi$
$883$	55.2859	1.86052	0.930259	+	0.366903i	$0.119582\pi$
$884$	−17.6861	−0.594849
$885$	−2.59179	−0.0871222
$886$	26.3425	0.884995
$887$	30.1603	1.01268	0.506342	−	0.862333i	$-0.330997\pi$
$887$	30.1603	1.01268	0.506342	+	0.862333i	$0.330997\pi$
$888$	19.0379	0.638871
$889$	1.69509	0.0568515
$890$	−45.5749	−1.52767
$891$	−52.4162	−1.75601
$892$	−16.6725	−0.558236
$893$	60.6119	2.02830
$894$	−24.8281	−0.830376
$895$	30.6596	1.02484
$896$	−1.00000	−0.0334077
$897$	4.53579	0.151446
$898$	34.4152	1.14845
$899$	−17.9412	−0.598372
$900$	−0.306867	−0.0102289
$901$	23.9988	0.799516
$902$	−44.8145	−1.49216
$903$	6.35031	0.211325
$904$	2.42294	0.0805857
$905$	14.4612	0.480706
$906$	−26.9036	−0.893813
$907$	30.5142	1.01321	0.506603	−	0.862179i	$-0.330901\pi$
$907$	30.5142	1.01321	0.506603	+	0.862179i	$0.330901\pi$
$908$	3.64286	0.120893
$909$	−1.36811	−0.0453774
$910$	18.6055	0.616765
$911$	53.8735	1.78491	0.892454	−	0.451138i	$-0.148982\pi$
$911$	53.8735	1.78491	0.892454	+	0.451138i	$0.148982\pi$
$912$	−8.30819	−0.275112
$913$	97.0403	3.21157
$914$	−2.73568	−0.0904881
$915$	18.8816	0.624206
$916$	−17.0672	−0.563918
$917$	3.84249	0.126890
$918$	−13.6206	−0.449547
$919$	−12.2878	−0.405336	−0.202668	−	0.979248i	$-0.564961\pi$
$919$	−12.2878	−0.405336	−0.202668	+	0.979248i	$0.564961\pi$
$920$	1.05032	0.0346279
$921$	−0.836603	−0.0275670
$922$	−31.9249	−1.05139
$923$	90.1904	2.96865
$924$	10.3417	0.340218
$925$	−25.7958	−0.848160
$926$	20.5332	0.674764
$927$	0.963994	0.0316617
$928$	−8.35475	−0.274258
$929$	18.1019	0.593904	0.296952	−	0.954892i	$-0.404030\pi$
$929$	18.1019	0.593904	0.296952	+	0.954892i	$0.404030\pi$
$930$	9.81871	0.321968
$931$	4.90740	0.160833
$932$	7.52723	0.246563
$933$	−26.4908	−0.867269
$934$	6.80434	0.222645
$935$	42.3539	1.38512
$936$	−0.921562	−0.0301222
$937$	−7.59014	−0.247959	−0.123979	−	0.992285i	$-0.539566\pi$
$937$	−7.59014	−0.247959	−0.123979	+	0.992285i	$0.539566\pi$
$938$	8.51140	0.277907
$939$	−28.3918	−0.926530
$940$	−33.3571	−1.08799
$941$	48.4948	1.58089	0.790443	−	0.612535i	$-0.209850\pi$
$941$	48.4948	1.58089	0.790443	+	0.612535i	$0.209850\pi$
$942$	−27.6179	−0.899840
$943$	2.85312	0.0929103
$944$	−0.566844	−0.0184492
$945$	14.3286	0.466110
$946$	22.9128	0.744959
$947$	45.6212	1.48249	0.741245	−	0.671235i	$-0.234236\pi$
$947$	45.6212	1.48249	0.741245	+	0.671235i	$0.234236\pi$
$948$	1.27141	0.0412934
$949$	−57.1544	−1.85531
$950$	11.2573	0.365237
$951$	30.8229	0.999500
$952$	2.56728	0.0832061
$953$	15.9812	0.517683	0.258842	−	0.965920i	$-0.416659\pi$
$953$	15.9812	0.517683	0.258842	+	0.965920i	$0.416659\pi$
$954$	1.25049	0.0404862
$955$	−59.2553	−1.91746
$956$	9.22233	0.298272
$957$	86.4026	2.79300
$958$	28.7253	0.928074
$959$	8.23371	0.265880
$960$	4.57232	0.147571
$961$	−26.3886	−0.851244
$962$	−77.4682	−2.49767
$963$	−0.424470	−0.0136784
$964$	−1.77519	−0.0571749
$965$	10.9018	0.350942
$966$	−0.658407	−0.0211839
$967$	−9.21313	−0.296274	−0.148137	−	0.988967i	$-0.547328\pi$
$967$	−9.21313	−0.296274	−0.148137	+	0.988967i	$0.547328\pi$
$968$	26.3144	0.845776
$969$	21.3295	0.685202
$970$	−27.2437	−0.874742
$971$	−20.8659	−0.669617	−0.334809	−	0.942286i	$-0.608672\pi$
$971$	−20.8659	−0.669617	−0.334809	+	0.942286i	$0.608672\pi$
$972$	−1.38915	−0.0445569
$973$	15.1215	0.484773
$974$	−8.93883	−0.286419
$975$	−26.7547	−0.856835
$976$	4.12954	0.132183
$977$	−3.02710	−0.0968456	−0.0484228	−	0.998827i	$-0.515419\pi$
$977$	−3.02710	−0.0968456	−0.0484228	+	0.998827i	$0.515419\pi$
$978$	4.65875	0.148970
$979$	103.082	3.29451
$980$	−2.70073	−0.0862717
$981$	2.53249	0.0808562
$982$	−36.8490	−1.17590
$983$	18.9198	0.603449	0.301724	−	0.953395i	$-0.402438\pi$
$983$	18.9198	0.603449	0.301724	+	0.953395i	$0.402438\pi$
$984$	12.4204	0.395949
$985$	−48.8237	−1.55565
$986$	21.4490	0.683076
$987$	20.9104	0.665585
$988$	33.8073	1.07555
$989$	−1.45874	−0.0463853
$990$	2.20691	0.0701402
$991$	−9.96983	−0.316702	−0.158351	−	0.987383i	$-0.550618\pi$
$991$	−9.96983	−0.316702	−0.158351	+	0.987383i	$0.550618\pi$
$992$	2.14742	0.0681808
$993$	−45.6711	−1.44933
$994$	−13.0918	−0.415248
$995$	52.9789	1.67954
$996$	−26.8949	−0.852197
$997$	−26.5311	−0.840249	−0.420124	−	0.907466i	$-0.638014\pi$
$997$	−26.5311	−0.840249	−0.420124	+	0.907466i	$0.638014\pi$
$998$	22.8717	0.723991
$999$	−59.6605	−1.88757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.9	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.69299 q^{3} +1.00000 q^{4} -2.70073 q^{5} -1.69299 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.133772 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.69299 q^{3} +1.00000 q^{4} -2.70073 q^{5} -1.69299 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.133772 q^{9} -2.70073 q^{10} +6.10855 q^{11} -1.69299 q^{12} +6.88905 q^{13} -1.00000 q^{14} +4.57232 q^{15} +1.00000 q^{16} -2.56728 q^{17} -0.133772 q^{18} +4.90740 q^{19} -2.70073 q^{20} +1.69299 q^{21} +6.10855 q^{22} -0.388901 q^{23} -1.69299 q^{24} +2.29395 q^{25} +6.88905 q^{26} +5.30546 q^{27} -1.00000 q^{28} -8.35475 q^{29} +4.57232 q^{30} +2.14742 q^{31} +1.00000 q^{32} -10.3417 q^{33} -2.56728 q^{34} +2.70073 q^{35} -0.133772 q^{36} -11.2451 q^{37} +4.90740 q^{38} -11.6631 q^{39} -2.70073 q^{40} -7.33637 q^{41} +1.69299 q^{42} +3.75094 q^{43} +6.10855 q^{44} +0.361282 q^{45} -0.388901 q^{46} +12.3511 q^{47} -1.69299 q^{48} +1.00000 q^{49} +2.29395 q^{50} +4.34640 q^{51} +6.88905 q^{52} -9.34793 q^{53} +5.30546 q^{54} -16.4976 q^{55} -1.00000 q^{56} -8.30819 q^{57} -8.35475 q^{58} -0.566844 q^{59} +4.57232 q^{60} +4.12954 q^{61} +2.14742 q^{62} +0.133772 q^{63} +1.00000 q^{64} -18.6055 q^{65} -10.3417 q^{66} -8.51140 q^{67} -2.56728 q^{68} +0.658407 q^{69} +2.70073 q^{70} +13.0918 q^{71} -0.133772 q^{72} -8.29642 q^{73} -11.2451 q^{74} -3.88365 q^{75} +4.90740 q^{76} -6.10855 q^{77} -11.6631 q^{78} -0.750981 q^{79} -2.70073 q^{80} -8.58079 q^{81} -7.33637 q^{82} +15.8860 q^{83} +1.69299 q^{84} +6.93355 q^{85} +3.75094 q^{86} +14.1445 q^{87} +6.10855 q^{88} +16.8750 q^{89} +0.361282 q^{90} -6.88905 q^{91} -0.388901 q^{92} -3.63557 q^{93} +12.3511 q^{94} -13.2536 q^{95} -1.69299 q^{96} +10.0875 q^{97} +1.00000 q^{98} -0.817153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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