LMFDB - Embedded newform 6034.2.a.n.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} -3.76480 q^{10} +5.13106 q^{11} -1.69422 q^{12} +2.53139 q^{13} +1.00000 q^{14} -6.37839 q^{15} +1.00000 q^{16} +1.63388 q^{17} +0.129635 q^{18} +2.24224 q^{19} +3.76480 q^{20} +1.69422 q^{21} -5.13106 q^{22} +4.75107 q^{23} +1.69422 q^{24} +9.17374 q^{25} -2.53139 q^{26} +5.30227 q^{27} -1.00000 q^{28} +3.82147 q^{29} +6.37839 q^{30} +7.14240 q^{31} -1.00000 q^{32} -8.69311 q^{33} -1.63388 q^{34} -3.76480 q^{35} -0.129635 q^{36} +2.28449 q^{37} -2.24224 q^{38} -4.28873 q^{39} -3.76480 q^{40} -6.10878 q^{41} -1.69422 q^{42} -7.09119 q^{43} +5.13106 q^{44} -0.488049 q^{45} -4.75107 q^{46} +1.29990 q^{47} -1.69422 q^{48} +1.00000 q^{49} -9.17374 q^{50} -2.76814 q^{51} +2.53139 q^{52} +1.88649 q^{53} -5.30227 q^{54} +19.3174 q^{55} +1.00000 q^{56} -3.79883 q^{57} -3.82147 q^{58} +7.44350 q^{59} -6.37839 q^{60} -0.00800210 q^{61} -7.14240 q^{62} +0.129635 q^{63} +1.00000 q^{64} +9.53020 q^{65} +8.69311 q^{66} +0.701020 q^{67} +1.63388 q^{68} -8.04934 q^{69} +3.76480 q^{70} -3.28126 q^{71} +0.129635 q^{72} -2.75032 q^{73} -2.28449 q^{74} -15.5423 q^{75} +2.24224 q^{76} -5.13106 q^{77} +4.28873 q^{78} +3.70673 q^{79} +3.76480 q^{80} -8.59429 q^{81} +6.10878 q^{82} +7.74981 q^{83} +1.69422 q^{84} +6.15123 q^{85} +7.09119 q^{86} -6.47438 q^{87} -5.13106 q^{88} -8.90310 q^{89} +0.488049 q^{90} -2.53139 q^{91} +4.75107 q^{92} -12.1008 q^{93} -1.29990 q^{94} +8.44158 q^{95} +1.69422 q^{96} -8.92397 q^{97} -1.00000 q^{98} -0.665163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.69422	−0.978156	−0.489078	−	0.872240i	$-0.662667\pi$
$3$	−1.69422	−0.978156	−0.489078	+	0.872240i	$0.662667\pi$
$4$	1.00000	0.500000
$5$	3.76480	1.68367	0.841836	−	0.539734i	$-0.181475\pi$
$5$	3.76480	1.68367	0.841836	+	0.539734i	$0.181475\pi$
$6$	1.69422	0.691660
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.129635	−0.0432115
$10$	−3.76480	−1.19054
$11$	5.13106	1.54707	0.773536	−	0.633753i	$-0.218486\pi$
$11$	5.13106	1.54707	0.773536	+	0.633753i	$0.218486\pi$
$12$	−1.69422	−0.489078
$13$	2.53139	0.702082	0.351041	−	0.936360i	$-0.385828\pi$
$13$	2.53139	0.702082	0.351041	+	0.936360i	$0.385828\pi$
$14$	1.00000	0.267261
$15$	−6.37839	−1.64689
$16$	1.00000	0.250000
$17$	1.63388	0.396273	0.198137	−	0.980174i	$-0.436511\pi$
$17$	1.63388	0.396273	0.198137	+	0.980174i	$0.436511\pi$
$18$	0.129635	0.0305552
$19$	2.24224	0.514404	0.257202	−	0.966358i	$-0.417199\pi$
$19$	2.24224	0.514404	0.257202	+	0.966358i	$0.417199\pi$
$20$	3.76480	0.841836
$21$	1.69422	0.369708
$22$	−5.13106	−1.09394
$23$	4.75107	0.990668	0.495334	−	0.868703i	$-0.335046\pi$
$23$	4.75107	0.990668	0.495334	+	0.868703i	$0.335046\pi$
$24$	1.69422	0.345830
$25$	9.17374	1.83475
$26$	−2.53139	−0.496447
$27$	5.30227	1.02042
$28$	−1.00000	−0.188982
$29$	3.82147	0.709628	0.354814	−	0.934937i	$-0.384544\pi$
$29$	3.82147	0.709628	0.354814	+	0.934937i	$0.384544\pi$
$30$	6.37839	1.16453
$31$	7.14240	1.28281	0.641406	−	0.767202i	$-0.278351\pi$
$31$	7.14240	1.28281	0.641406	+	0.767202i	$0.278351\pi$
$32$	−1.00000	−0.176777
$33$	−8.69311	−1.51328
$34$	−1.63388	−0.280208
$35$	−3.76480	−0.636368
$36$	−0.129635	−0.0216058
$37$	2.28449	0.375568	0.187784	−	0.982210i	$-0.439870\pi$
$37$	2.28449	0.375568	0.187784	+	0.982210i	$0.439870\pi$
$38$	−2.24224	−0.363739
$39$	−4.28873	−0.686746
$40$	−3.76480	−0.595268
$41$	−6.10878	−0.954031	−0.477015	−	0.878895i	$-0.658281\pi$
$41$	−6.10878	−0.954031	−0.477015	+	0.878895i	$0.658281\pi$
$42$	−1.69422	−0.261423
$43$	−7.09119	−1.08140	−0.540698	−	0.841217i	$-0.681840\pi$
$43$	−7.09119	−1.08140	−0.540698	+	0.841217i	$0.681840\pi$
$44$	5.13106	0.773536
$45$	−0.488049	−0.0727540
$46$	−4.75107	−0.700508
$47$	1.29990	0.189610	0.0948048	−	0.995496i	$-0.469777\pi$
$47$	1.29990	0.189610	0.0948048	+	0.995496i	$0.469777\pi$
$48$	−1.69422	−0.244539
$49$	1.00000	0.142857
$50$	−9.17374	−1.29736
$51$	−2.76814	−0.387617
$52$	2.53139	0.351041
$53$	1.88649	0.259129	0.129564	−	0.991571i	$-0.458642\pi$
$53$	1.88649	0.259129	0.129564	+	0.991571i	$0.458642\pi$
$54$	−5.30227	−0.721548
$55$	19.3174	2.60476
$56$	1.00000	0.133631
$57$	−3.79883	−0.503167
$58$	−3.82147	−0.501783
$59$	7.44350	0.969061	0.484530	−	0.874774i	$-0.338991\pi$
$59$	7.44350	0.969061	0.484530	+	0.874774i	$0.338991\pi$
$60$	−6.37839	−0.823446
$61$	−0.00800210	−0.00102456	−0.000512282	−	1.00000i	$-0.500163\pi$
$61$	−0.00800210	−0.00102456	−0.000512282		1.00000i	$0.500163\pi$
$62$	−7.14240	−0.907085
$63$	0.129635	0.0163324
$64$	1.00000	0.125000
$65$	9.53020	1.18208
$66$	8.69311	1.07005
$67$	0.701020	0.0856432	0.0428216	−	0.999083i	$-0.486365\pi$
$67$	0.701020	0.0856432	0.0428216	+	0.999083i	$0.486365\pi$
$68$	1.63388	0.198137
$69$	−8.04934	−0.969027
$70$	3.76480	0.449980
$71$	−3.28126	−0.389414	−0.194707	−	0.980861i	$-0.562376\pi$
$71$	−3.28126	−0.389414	−0.194707	+	0.980861i	$0.562376\pi$
$72$	0.129635	0.0152776
$73$	−2.75032	−0.321900	−0.160950	−	0.986963i	$-0.551456\pi$
$73$	−2.75032	−0.321900	−0.160950	+	0.986963i	$0.551456\pi$
$74$	−2.28449	−0.265567
$75$	−15.5423	−1.79467
$76$	2.24224	0.257202
$77$	−5.13106	−0.584738
$78$	4.28873	0.485603
$79$	3.70673	0.417040	0.208520	−	0.978018i	$-0.433135\pi$
$79$	3.70673	0.417040	0.208520	+	0.978018i	$0.433135\pi$
$80$	3.76480	0.420918
$81$	−8.59429	−0.954921
$82$	6.10878	0.674601
$83$	7.74981	0.850653	0.425326	−	0.905040i	$-0.360159\pi$
$83$	7.74981	0.850653	0.425326	+	0.905040i	$0.360159\pi$
$84$	1.69422	0.184854
$85$	6.15123	0.667194
$86$	7.09119	0.764663
$87$	−6.47438	−0.694127
$88$	−5.13106	−0.546972
$89$	−8.90310	−0.943727	−0.471864	−	0.881672i	$-0.656419\pi$
$89$	−8.90310	−0.943727	−0.471864	+	0.881672i	$0.656419\pi$
$90$	0.488049	0.0514449
$91$	−2.53139	−0.265362
$92$	4.75107	0.495334
$93$	−12.1008	−1.25479
$94$	−1.29990	−0.134074
$95$	8.44158	0.866088
$96$	1.69422	0.172915
$97$	−8.92397	−0.906092	−0.453046	−	0.891487i	$-0.649663\pi$
$97$	−8.92397	−0.906092	−0.453046	+	0.891487i	$0.649663\pi$
$98$	−1.00000	−0.101015
$99$	−0.665163	−0.0668514
$100$	9.17374	0.917374
$101$	−10.5709	−1.05185	−0.525924	−	0.850532i	$-0.676280\pi$
$101$	−10.5709	−1.05185	−0.525924	+	0.850532i	$0.676280\pi$
$102$	2.76814	0.274087
$103$	0.247124	0.0243498	0.0121749	−	0.999926i	$-0.496125\pi$
$103$	0.247124	0.0243498	0.0121749	+	0.999926i	$0.496125\pi$
$104$	−2.53139	−0.248224
$105$	6.37839	0.622467
$106$	−1.88649	−0.183232
$107$	4.44791	0.429996	0.214998	−	0.976614i	$-0.431026\pi$
$107$	4.44791	0.429996	0.214998	+	0.976614i	$0.431026\pi$
$108$	5.30227	0.510212
$109$	4.93957	0.473125	0.236563	−	0.971616i	$-0.423979\pi$
$109$	4.93957	0.473125	0.236563	+	0.971616i	$0.423979\pi$
$110$	−19.3174	−1.84184
$111$	−3.87042	−0.367364
$112$	−1.00000	−0.0944911
$113$	3.76323	0.354015	0.177008	−	0.984209i	$-0.443358\pi$
$113$	3.76323	0.354015	0.177008	+	0.984209i	$0.443358\pi$
$114$	3.79883	0.355793
$115$	17.8869	1.66796
$116$	3.82147	0.354814
$117$	−0.328156	−0.0303381
$118$	−7.44350	−0.685229
$119$	−1.63388	−0.149777
$120$	6.37839	0.582264
$121$	15.3277	1.39343
$122$	0.00800210	0.000724476 0
$123$	10.3496	0.933190
$124$	7.14240	0.641406
$125$	15.7133	1.40544
$126$	−0.129635	−0.0115488
$127$	−2.90453	−0.257735	−0.128868	−	0.991662i	$-0.541134\pi$
$127$	−2.90453	−0.257735	−0.128868	+	0.991662i	$0.541134\pi$
$128$	−1.00000	−0.0883883
$129$	12.0140	1.05777
$130$	−9.53020	−0.835854
$131$	−7.95468	−0.695003	−0.347502	−	0.937679i	$-0.612970\pi$
$131$	−7.95468	−0.695003	−0.347502	+	0.937679i	$0.612970\pi$
$132$	−8.69311	−0.756638
$133$	−2.24224	−0.194427
$134$	−0.701020	−0.0605589
$135$	19.9620	1.71806
$136$	−1.63388	−0.140104
$137$	−0.336958	−0.0287883	−0.0143941	−	0.999896i	$-0.504582\pi$
$137$	−0.336958	−0.0287883	−0.0143941	+	0.999896i	$0.504582\pi$
$138$	8.04934	0.685206
$139$	13.2883	1.12709	0.563547	−	0.826084i	$-0.309436\pi$
$139$	13.2883	1.12709	0.563547	+	0.826084i	$0.309436\pi$
$140$	−3.76480	−0.318184
$141$	−2.20231	−0.185468
$142$	3.28126	0.275358
$143$	12.9887	1.08617
$144$	−0.129635	−0.0108029
$145$	14.3871	1.19478
$146$	2.75032	0.227618
$147$	−1.69422	−0.139737
$148$	2.28449	0.187784
$149$	−2.03542	−0.166748	−0.0833742	−	0.996518i	$-0.526570\pi$
$149$	−2.03542	−0.166748	−0.0833742	+	0.996518i	$0.526570\pi$
$150$	15.5423	1.26902
$151$	1.78140	0.144968	0.0724842	−	0.997370i	$-0.476907\pi$
$151$	1.78140	0.144968	0.0724842	+	0.997370i	$0.476907\pi$
$152$	−2.24224	−0.181869
$153$	−0.211807	−0.0171236
$154$	5.13106	0.413472
$155$	26.8897	2.15983
$156$	−4.28873	−0.343373
$157$	4.79958	0.383049	0.191524	−	0.981488i	$-0.438657\pi$
$157$	4.79958	0.383049	0.191524	+	0.981488i	$0.438657\pi$
$158$	−3.70673	−0.294892
$159$	−3.19612	−0.253468
$160$	−3.76480	−0.297634
$161$	−4.75107	−0.374437
$162$	8.59429	0.675231
$163$	2.74208	0.214776	0.107388	−	0.994217i	$-0.465751\pi$
$163$	2.74208	0.214776	0.107388	+	0.994217i	$0.465751\pi$
$164$	−6.10878	−0.477015
$165$	−32.7279	−2.54786
$166$	−7.74981	−0.601502
$167$	−17.5930	−1.36139	−0.680693	−	0.732569i	$-0.738321\pi$
$167$	−17.5930	−1.36139	−0.680693	+	0.732569i	$0.738321\pi$
$168$	−1.69422	−0.130712
$169$	−6.59204	−0.507080
$170$	−6.15123	−0.471778
$171$	−0.290672	−0.0222282
$172$	−7.09119	−0.540698
$173$	−14.4727	−1.10034	−0.550168	−	0.835054i	$-0.685436\pi$
$173$	−14.4727	−1.10034	−0.550168	+	0.835054i	$0.685436\pi$
$174$	6.47438	0.490822
$175$	−9.17374	−0.693470
$176$	5.13106	0.386768
$177$	−12.6109	−0.947892
$178$	8.90310	0.667316
$179$	−16.2018	−1.21098	−0.605491	−	0.795852i	$-0.707023\pi$
$179$	−16.2018	−1.21098	−0.605491	+	0.795852i	$0.707023\pi$
$180$	−0.488049	−0.0363770
$181$	3.75290	0.278951	0.139475	−	0.990226i	$-0.455458\pi$
$181$	3.75290	0.278951	0.139475	+	0.990226i	$0.455458\pi$
$182$	2.53139	0.187639
$183$	0.0135573	0.00100218
$184$	−4.75107	−0.350254
$185$	8.60066	0.632333
$186$	12.1008	0.887270
$187$	8.38352	0.613063
$188$	1.29990	0.0948048
$189$	−5.30227	−0.385684
$190$	−8.44158	−0.612416
$191$	15.4237	1.11602	0.558010	−	0.829834i	$-0.311565\pi$
$191$	15.4237	1.11602	0.558010	+	0.829834i	$0.311565\pi$
$192$	−1.69422	−0.122269
$193$	−24.4004	−1.75638	−0.878191	−	0.478310i	$-0.841250\pi$
$193$	−24.4004	−1.75638	−0.878191	+	0.478310i	$0.841250\pi$
$194$	8.92397	0.640704
$195$	−16.1462	−1.15625
$196$	1.00000	0.0714286
$197$	−14.1409	−1.00750	−0.503750	−	0.863849i	$-0.668047\pi$
$197$	−14.1409	−1.00750	−0.503750	+	0.863849i	$0.668047\pi$
$198$	0.665163	0.0472710
$199$	5.58283	0.395756	0.197878	−	0.980227i	$-0.436595\pi$
$199$	5.58283	0.395756	0.197878	+	0.980227i	$0.436595\pi$
$200$	−9.17374	−0.648682
$201$	−1.18768	−0.0837724
$202$	10.5709	0.743768
$203$	−3.82147	−0.268214
$204$	−2.76814	−0.193809
$205$	−22.9983	−1.60627
$206$	−0.247124	−0.0172179
$207$	−0.615904	−0.0428083
$208$	2.53139	0.175521
$209$	11.5050	0.795820
$210$	−6.37839	−0.440151
$211$	19.1382	1.31753	0.658765	−	0.752349i	$-0.271079\pi$
$211$	19.1382	1.31753	0.658765	+	0.752349i	$0.271079\pi$
$212$	1.88649	0.129564
$213$	5.55917	0.380908
$214$	−4.44791	−0.304053
$215$	−26.6969	−1.82072
$216$	−5.30227	−0.360774
$217$	−7.14240	−0.484857
$218$	−4.93957	−0.334550
$219$	4.65963	0.314868
$220$	19.3174	1.30238
$221$	4.13599	0.278217
$222$	3.87042	0.259766
$223$	−8.10489	−0.542744	−0.271372	−	0.962475i	$-0.587477\pi$
$223$	−8.10489	−0.542744	−0.271372	+	0.962475i	$0.587477\pi$
$224$	1.00000	0.0668153
$225$	−1.18923	−0.0792823
$226$	−3.76323	−0.250327
$227$	−11.5098	−0.763934	−0.381967	−	0.924176i	$-0.624753\pi$
$227$	−11.5098	−0.763934	−0.381967	+	0.924176i	$0.624753\pi$
$228$	−3.79883	−0.251584
$229$	−7.41334	−0.489887	−0.244944	−	0.969537i	$-0.578769\pi$
$229$	−7.41334	−0.489887	−0.244944	+	0.969537i	$0.578769\pi$
$230$	−17.8869	−1.17942
$231$	8.69311	0.571965
$232$	−3.82147	−0.250891
$233$	−26.0542	−1.70687	−0.853433	−	0.521202i	$-0.825484\pi$
$233$	−26.0542	−1.70687	−0.853433	+	0.521202i	$0.825484\pi$
$234$	0.328156	0.0214523
$235$	4.89386	0.319240
$236$	7.44350	0.484530
$237$	−6.28000	−0.407930
$238$	1.63388	0.105909
$239$	−4.13675	−0.267584	−0.133792	−	0.991009i	$-0.542715\pi$
$239$	−4.13675	−0.267584	−0.133792	+	0.991009i	$0.542715\pi$
$240$	−6.37839	−0.411723
$241$	14.4204	0.928897	0.464448	−	0.885600i	$-0.346253\pi$
$241$	14.4204	0.928897	0.464448	+	0.885600i	$0.346253\pi$
$242$	−15.3277	−0.985304
$243$	−1.34625	−0.0863617
$244$	−0.00800210	−0.000512282 0
$245$	3.76480	0.240524
$246$	−10.3496	−0.659865
$247$	5.67598	0.361154
$248$	−7.14240	−0.453543
$249$	−13.1299	−0.832071
$250$	−15.7133	−0.993798
$251$	13.2145	0.834091	0.417046	−	0.908886i	$-0.363066\pi$
$251$	13.2145	0.834091	0.417046	+	0.908886i	$0.363066\pi$
$252$	0.129635	0.00816622
$253$	24.3780	1.53263
$254$	2.90453	0.182246
$255$	−10.4215	−0.652620
$256$	1.00000	0.0625000
$257$	3.32744	0.207560	0.103780	−	0.994600i	$-0.466906\pi$
$257$	3.32744	0.207560	0.103780	+	0.994600i	$0.466906\pi$
$258$	−12.0140	−0.747959
$259$	−2.28449	−0.141951
$260$	9.53020	0.591038
$261$	−0.495394	−0.0306641
$262$	7.95468	0.491442
$263$	−22.8100	−1.40653	−0.703264	−	0.710929i	$-0.748275\pi$
$263$	−22.8100	−1.40653	−0.703264	+	0.710929i	$0.748275\pi$
$264$	8.69311	0.535024
$265$	7.10225	0.436288
$266$	2.24224	0.137480
$267$	15.0838	0.923112
$268$	0.701020	0.0428216
$269$	−2.36176	−0.143999	−0.0719995	−	0.997405i	$-0.522938\pi$
$269$	−2.36176	−0.143999	−0.0719995	+	0.997405i	$0.522938\pi$
$270$	−19.9620	−1.21485
$271$	−6.66509	−0.404875	−0.202438	−	0.979295i	$-0.564886\pi$
$271$	−6.66509	−0.404875	−0.202438	+	0.979295i	$0.564886\pi$
$272$	1.63388	0.0990684
$273$	4.28873	0.259566
$274$	0.336958	0.0203564
$275$	47.0710	2.83849
$276$	−8.04934	−0.484514
$277$	−25.7492	−1.54712	−0.773560	−	0.633723i	$-0.781526\pi$
$277$	−25.7492	−1.54712	−0.773560	+	0.633723i	$0.781526\pi$
$278$	−13.2883	−0.796976
$279$	−0.925902	−0.0554323
$280$	3.76480	0.224990
$281$	7.24230	0.432040	0.216020	−	0.976389i	$-0.430692\pi$
$281$	7.24230	0.432040	0.216020	+	0.976389i	$0.430692\pi$
$282$	2.20231	0.131146
$283$	−5.52079	−0.328177	−0.164089	−	0.986446i	$-0.552468\pi$
$283$	−5.52079	−0.328177	−0.164089	+	0.986446i	$0.552468\pi$
$284$	−3.28126	−0.194707
$285$	−14.3019	−0.847169
$286$	−12.9887	−0.768039
$287$	6.10878	0.360590
$288$	0.129635	0.00763879
$289$	−14.3304	−0.842967
$290$	−14.3871	−0.844838
$291$	15.1191	0.886299
$292$	−2.75032	−0.160950
$293$	4.12082	0.240741	0.120370	−	0.992729i	$-0.461592\pi$
$293$	4.12082	0.240741	0.120370	+	0.992729i	$0.461592\pi$
$294$	1.69422	0.0988086
$295$	28.0233	1.63158
$296$	−2.28449	−0.132783
$297$	27.2063	1.57867
$298$	2.03542	0.117909
$299$	12.0268	0.695530
$300$	−15.5423	−0.897335
$301$	7.09119	0.408729
$302$	−1.78140	−0.102508
$303$	17.9094	1.02887
$304$	2.24224	0.128601
$305$	−0.0301263	−0.00172503
$306$	0.211807	0.0121082
$307$	15.1726	0.865944	0.432972	−	0.901407i	$-0.357465\pi$
$307$	15.1726	0.865944	0.432972	+	0.901407i	$0.357465\pi$
$308$	−5.13106	−0.292369
$309$	−0.418681	−0.0238179
$310$	−26.8897	−1.52723
$311$	−4.58694	−0.260101	−0.130051	−	0.991507i	$-0.541514\pi$
$311$	−4.58694	−0.260101	−0.130051	+	0.991507i	$0.541514\pi$
$312$	4.28873	0.242801
$313$	−0.591030	−0.0334070	−0.0167035	−	0.999860i	$-0.505317\pi$
$313$	−0.591030	−0.0334070	−0.0167035	+	0.999860i	$0.505317\pi$
$314$	−4.79958	−0.270856
$315$	0.488049	0.0274984
$316$	3.70673	0.208520
$317$	18.1207	1.01776	0.508881	−	0.860837i	$-0.330059\pi$
$317$	18.1207	1.01776	0.508881	+	0.860837i	$0.330059\pi$
$318$	3.19612	0.179229
$319$	19.6082	1.09785
$320$	3.76480	0.210459
$321$	−7.53572	−0.420603
$322$	4.75107	0.264767
$323$	3.66354	0.203845
$324$	−8.59429	−0.477461
$325$	23.2224	1.28814
$326$	−2.74208	−0.151870
$327$	−8.36870	−0.462790
$328$	6.10878	0.337301
$329$	−1.29990	−0.0716657
$330$	32.7279	1.80161
$331$	24.2633	1.33363	0.666816	−	0.745223i	$-0.267657\pi$
$331$	24.2633	1.33363	0.666816	+	0.745223i	$0.267657\pi$
$332$	7.74981	0.425326
$333$	−0.296149	−0.0162289
$334$	17.5930	0.962645
$335$	2.63920	0.144195
$336$	1.69422	0.0924270
$337$	20.5308	1.11839	0.559193	−	0.829038i	$-0.311111\pi$
$337$	20.5308	1.11839	0.559193	+	0.829038i	$0.311111\pi$
$338$	6.59204	0.358560
$339$	−6.37573	−0.346282
$340$	6.15123	0.333597
$341$	36.6480	1.98460
$342$	0.290672	0.0157177
$343$	−1.00000	−0.0539949
$344$	7.09119	0.382331
$345$	−30.3042	−1.63152
$346$	14.4727	0.778055
$347$	0.619877	0.0332767	0.0166384	−	0.999862i	$-0.494704\pi$
$347$	0.619877	0.0332767	0.0166384	+	0.999862i	$0.494704\pi$
$348$	−6.47438	−0.347063
$349$	0.293252	0.0156974	0.00784871	−	0.999969i	$-0.497502\pi$
$349$	0.293252	0.0156974	0.00784871	+	0.999969i	$0.497502\pi$
$350$	9.17374	0.490357
$351$	13.4221	0.716421
$352$	−5.13106	−0.273486
$353$	−30.7987	−1.63925	−0.819625	−	0.572900i	$-0.805818\pi$
$353$	−30.7987	−1.63925	−0.819625	+	0.572900i	$0.805818\pi$
$354$	12.6109	0.670261
$355$	−12.3533	−0.655646
$356$	−8.90310	−0.471864
$357$	2.76814	0.146505
$358$	16.2018	0.856294
$359$	−13.9496	−0.736231	−0.368116	−	0.929780i	$-0.619997\pi$
$359$	−13.9496	−0.736231	−0.368116	+	0.929780i	$0.619997\pi$
$360$	0.488049	0.0257224
$361$	−13.9724	−0.735388
$362$	−3.75290	−0.197248
$363$	−25.9685	−1.36299
$364$	−2.53139	−0.132681
$365$	−10.3544	−0.541974
$366$	−0.0135573	−0.000708650 0
$367$	−18.7430	−0.978376	−0.489188	−	0.872178i	$-0.662707\pi$
$367$	−18.7430	−0.978376	−0.489188	+	0.872178i	$0.662707\pi$
$368$	4.75107	0.247667
$369$	0.791909	0.0412251
$370$	−8.60066	−0.447127
$371$	−1.88649	−0.0979416
$372$	−12.1008	−0.627395
$373$	0.233693	0.0121002	0.00605009	−	0.999982i	$-0.498074\pi$
$373$	0.233693	0.0121002	0.00605009	+	0.999982i	$0.498074\pi$
$374$	−8.38352	−0.433501
$375$	−26.6217	−1.37474
$376$	−1.29990	−0.0670372
$377$	9.67364	0.498218
$378$	5.30227	0.272720
$379$	22.0112	1.13064	0.565319	−	0.824873i	$-0.308753\pi$
$379$	22.0112	1.13064	0.565319	+	0.824873i	$0.308753\pi$
$380$	8.44158	0.433044
$381$	4.92090	0.252105
$382$	−15.4237	−0.789145
$383$	6.39092	0.326561	0.163280	−	0.986580i	$-0.447792\pi$
$383$	6.39092	0.326561	0.163280	+	0.986580i	$0.447792\pi$
$384$	1.69422	0.0864576
$385$	−19.3174	−0.984507
$386$	24.4004	1.24195
$387$	0.919264	0.0467288
$388$	−8.92397	−0.453046
$389$	26.6128	1.34932	0.674662	−	0.738127i	$-0.264289\pi$
$389$	26.6128	1.34932	0.674662	+	0.738127i	$0.264289\pi$
$390$	16.1462	0.817595
$391$	7.76267	0.392575
$392$	−1.00000	−0.0505076
$393$	13.4769	0.679821
$394$	14.1409	0.712411
$395$	13.9551	0.702158
$396$	−0.665163	−0.0334257
$397$	−6.68899	−0.335711	−0.167856	−	0.985812i	$-0.553684\pi$
$397$	−6.68899	−0.335711	−0.167856	+	0.985812i	$0.553684\pi$
$398$	−5.58283	−0.279842
$399$	3.79883	0.190179
$400$	9.17374	0.458687
$401$	−8.28110	−0.413538	−0.206769	−	0.978390i	$-0.566295\pi$
$401$	−8.28110	−0.413538	−0.206769	+	0.978390i	$0.566295\pi$
$402$	1.18768	0.0592360
$403$	18.0802	0.900640
$404$	−10.5709	−0.525924
$405$	−32.3558	−1.60777
$406$	3.82147	0.189656
$407$	11.7218	0.581031
$408$	2.76814	0.137043
$409$	3.04974	0.150800	0.0753999	−	0.997153i	$-0.475977\pi$
$409$	3.04974	0.150800	0.0753999	+	0.997153i	$0.475977\pi$
$410$	22.9983	1.13581
$411$	0.570880	0.0281594
$412$	0.247124	0.0121749
$413$	−7.44350	−0.366271
$414$	0.615904	0.0302700
$415$	29.1765	1.43222
$416$	−2.53139	−0.124112
$417$	−22.5132	−1.10247
$418$	−11.5050	−0.562730
$419$	33.0604	1.61511	0.807554	−	0.589794i	$-0.200791\pi$
$419$	33.0604	1.61511	0.807554	+	0.589794i	$0.200791\pi$
$420$	6.37839	0.311233
$421$	26.2130	1.27754	0.638771	−	0.769397i	$-0.279443\pi$
$421$	26.2130	1.27754	0.638771	+	0.769397i	$0.279443\pi$
$422$	−19.1382	−0.931635
$423$	−0.168512	−0.00819333
$424$	−1.88649	−0.0916159
$425$	14.9888	0.727062
$426$	−5.55917	−0.269342
$427$	0.00800210	0.000387249 0
$428$	4.44791	0.214998
$429$	−22.0057	−1.06245
$430$	26.6969	1.28744
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.30227	0.255106
$433$	15.9959	0.768713	0.384356	−	0.923185i	$-0.374423\pi$
$433$	15.9959	0.768713	0.384356	+	0.923185i	$0.374423\pi$
$434$	7.14240	0.342846
$435$	−24.3748	−1.16868
$436$	4.93957	0.236563
$437$	10.6530	0.509604
$438$	−4.65963	−0.222646
$439$	−31.2755	−1.49270	−0.746350	−	0.665554i	$-0.768195\pi$
$439$	−31.2755	−1.49270	−0.746350	+	0.665554i	$0.768195\pi$
$440$	−19.3174	−0.920922
$441$	−0.129635	−0.00617308
$442$	−4.13599	−0.196729
$443$	−26.1389	−1.24190	−0.620949	−	0.783851i	$-0.713253\pi$
$443$	−26.1389	−1.24190	−0.620949	+	0.783851i	$0.713253\pi$
$444$	−3.87042	−0.183682
$445$	−33.5184	−1.58893
$446$	8.10489	0.383778
$447$	3.44845	0.163106
$448$	−1.00000	−0.0472456
$449$	14.1690	0.668678	0.334339	−	0.942453i	$-0.391487\pi$
$449$	14.1690	0.668678	0.334339	+	0.942453i	$0.391487\pi$
$450$	1.18923	0.0560611
$451$	−31.3445	−1.47595
$452$	3.76323	0.177008
$453$	−3.01808	−0.141802
$454$	11.5098	0.540183
$455$	−9.53020	−0.446783
$456$	3.79883	0.177897
$457$	14.2280	0.665557	0.332779	−	0.943005i	$-0.392014\pi$
$457$	14.2280	0.665557	0.332779	+	0.943005i	$0.392014\pi$
$458$	7.41334	0.346402
$459$	8.66327	0.404367
$460$	17.8869	0.833979
$461$	19.6352	0.914504	0.457252	−	0.889337i	$-0.348834\pi$
$461$	19.6352	0.914504	0.457252	+	0.889337i	$0.348834\pi$
$462$	−8.69311	−0.404440
$463$	−12.0254	−0.558867	−0.279433	−	0.960165i	$-0.590147\pi$
$463$	−12.0254	−0.558867	−0.279433	+	0.960165i	$0.590147\pi$
$464$	3.82147	0.177407
$465$	−45.5570	−2.11265
$466$	26.0542	1.20694
$467$	−2.49381	−0.115400	−0.0576998	−	0.998334i	$-0.518377\pi$
$467$	−2.49381	−0.115400	−0.0576998	+	0.998334i	$0.518377\pi$
$468$	−0.328156	−0.0151690
$469$	−0.701020	−0.0323701
$470$	−4.89386	−0.225737
$471$	−8.13153	−0.374681
$472$	−7.44350	−0.342615
$473$	−36.3853	−1.67300
$474$	6.28000	0.288450
$475$	20.5697	0.943803
$476$	−1.63388	−0.0748886
$477$	−0.244554	−0.0111974
$478$	4.13675	0.189210
$479$	23.9177	1.09283	0.546415	−	0.837515i	$-0.315992\pi$
$479$	23.9177	1.09283	0.546415	+	0.837515i	$0.315992\pi$
$480$	6.37839	0.291132
$481$	5.78295	0.263680
$482$	−14.4204	−0.656829
$483$	8.04934	0.366258
$484$	15.3277	0.696715
$485$	−33.5970	−1.52556
$486$	1.34625	0.0610669
$487$	13.4212	0.608171	0.304085	−	0.952645i	$-0.401649\pi$
$487$	13.4212	0.608171	0.304085	+	0.952645i	$0.401649\pi$
$488$	0.00800210	0.000362238 0
$489$	−4.64567	−0.210084
$490$	−3.76480	−0.170076
$491$	−12.6746	−0.571995	−0.285998	−	0.958230i	$-0.592325\pi$
$491$	−12.6746	−0.571995	−0.285998	+	0.958230i	$0.592325\pi$
$492$	10.3496	0.466595
$493$	6.24381	0.281207
$494$	−5.67598	−0.255375
$495$	−2.50421	−0.112556
$496$	7.14240	0.320703
$497$	3.28126	0.147185
$498$	13.1299	0.588363
$499$	30.7009	1.37436	0.687181	−	0.726486i	$-0.258848\pi$
$499$	30.7009	1.37436	0.687181	+	0.726486i	$0.258848\pi$
$500$	15.7133	0.702721
$501$	29.8063	1.33165
$502$	−13.2145	−0.589792
$503$	−5.63591	−0.251293	−0.125646	−	0.992075i	$-0.540100\pi$
$503$	−5.63591	−0.251293	−0.125646	+	0.992075i	$0.540100\pi$
$504$	−0.129635	−0.00577439
$505$	−39.7975	−1.77096
$506$	−24.3780	−1.08374
$507$	11.1683	0.496003
$508$	−2.90453	−0.128868
$509$	40.0652	1.77586	0.887930	−	0.459979i	$-0.152143\pi$
$509$	40.0652	1.77586	0.887930	+	0.459979i	$0.152143\pi$
$510$	10.4215	0.461472
$511$	2.75032	0.121667
$512$	−1.00000	−0.0441942
$513$	11.8890	0.524910
$514$	−3.32744	−0.146767
$515$	0.930373	0.0409971
$516$	12.0140	0.528887
$517$	6.66985	0.293340
$518$	2.28449	0.100375
$519$	24.5198	1.07630
$520$	−9.53020	−0.417927
$521$	−12.7582	−0.558947	−0.279474	−	0.960153i	$-0.590160\pi$
$521$	−12.7582	−0.558947	−0.279474	+	0.960153i	$0.590160\pi$
$522$	0.495394	0.0216828
$523$	−22.1792	−0.969829	−0.484915	−	0.874561i	$-0.661149\pi$
$523$	−22.1792	−0.969829	−0.484915	+	0.874561i	$0.661149\pi$
$524$	−7.95468	−0.347502
$525$	15.5423	0.678321
$526$	22.8100	0.994565
$527$	11.6698	0.508344
$528$	−8.69311	−0.378319
$529$	−0.427289	−0.0185778
$530$	−7.10225	−0.308502
$531$	−0.964935	−0.0418746
$532$	−2.24224	−0.0972133
$533$	−15.4637	−0.669808
$534$	−15.0838	−0.652739
$535$	16.7455	0.723972
$536$	−0.701020	−0.0302794
$537$	27.4494	1.18453
$538$	2.36176	0.101823
$539$	5.13106	0.221010
$540$	19.9620	0.859029
$541$	−6.75570	−0.290450	−0.145225	−	0.989399i	$-0.546391\pi$
$541$	−6.75570	−0.290450	−0.145225	+	0.989399i	$0.546391\pi$
$542$	6.66509	0.286290
$543$	−6.35821	−0.272857
$544$	−1.63388	−0.0700519
$545$	18.5965	0.796587
$546$	−4.28873	−0.183541
$547$	20.5399	0.878221	0.439110	−	0.898433i	$-0.355294\pi$
$547$	20.5399	0.878221	0.439110	+	0.898433i	$0.355294\pi$
$548$	−0.336958	−0.0143941
$549$	0.00103735	4.42730e−5 0
$550$	−47.0710	−2.00711
$551$	8.56863	0.365036
$552$	8.04934	0.342603
$553$	−3.70673	−0.157626
$554$	25.7492	1.09398
$555$	−14.5714	−0.618520
$556$	13.2883	0.563547
$557$	30.3295	1.28510	0.642550	−	0.766244i	$-0.277876\pi$
$557$	30.3295	1.28510	0.642550	+	0.766244i	$0.277876\pi$
$558$	0.925902	0.0391966
$559$	−17.9506	−0.759230
$560$	−3.76480	−0.159092
$561$	−14.2035	−0.599671
$562$	−7.24230	−0.305498
$563$	34.3651	1.44831	0.724157	−	0.689635i	$-0.242229\pi$
$563$	34.3651	1.44831	0.724157	+	0.689635i	$0.242229\pi$
$564$	−2.20231	−0.0927339
$565$	14.1678	0.596045
$566$	5.52079	0.232056
$567$	8.59429	0.360926
$568$	3.28126	0.137679
$569$	37.0801	1.55448	0.777240	−	0.629204i	$-0.216619\pi$
$569$	37.0801	1.55448	0.777240	+	0.629204i	$0.216619\pi$
$570$	14.3019	0.599039
$571$	4.16167	0.174161	0.0870803	−	0.996201i	$-0.472246\pi$
$571$	4.16167	0.174161	0.0870803	+	0.996201i	$0.472246\pi$
$572$	12.9887	0.543086
$573$	−26.1311	−1.09164
$574$	−6.10878	−0.254975
$575$	43.5851	1.81763
$576$	−0.129635	−0.00540144
$577$	2.02887	0.0844628	0.0422314	−	0.999108i	$-0.486553\pi$
$577$	2.02887	0.0844628	0.0422314	+	0.999108i	$0.486553\pi$
$578$	14.3304	0.596068
$579$	41.3396	1.71801
$580$	14.3871	0.597390
$581$	−7.74981	−0.321516
$582$	−15.1191	−0.626708
$583$	9.67967	0.400891
$584$	2.75032	0.113809
$585$	−1.23544	−0.0510793
$586$	−4.12082	−0.170229
$587$	6.09047	0.251380	0.125690	−	0.992070i	$-0.459885\pi$
$587$	6.09047	0.251380	0.125690	+	0.992070i	$0.459885\pi$
$588$	−1.69422	−0.0698683
$589$	16.0149	0.659884
$590$	−28.0233	−1.15370
$591$	23.9578	0.985492
$592$	2.28449	0.0938920
$593$	−6.16953	−0.253352	−0.126676	−	0.991944i	$-0.540431\pi$
$593$	−6.16953	−0.253352	−0.126676	+	0.991944i	$0.540431\pi$
$594$	−27.2063	−1.11629
$595$	−6.15123	−0.252176
$596$	−2.03542	−0.0833742
$597$	−9.45852	−0.387111
$598$	−12.0268	−0.491814
$599$	11.2936	0.461444	0.230722	−	0.973020i	$-0.425891\pi$
$599$	11.2936	0.461444	0.230722	+	0.973020i	$0.425891\pi$
$600$	15.5423	0.634512
$601$	−18.5052	−0.754844	−0.377422	−	0.926041i	$-0.623189\pi$
$601$	−18.5052	−0.754844	−0.377422	+	0.926041i	$0.623189\pi$
$602$	−7.09119	−0.289015
$603$	−0.0908764	−0.00370077
$604$	1.78140	0.0724842
$605$	57.7059	2.34608
$606$	−17.9094	−0.727521
$607$	32.3535	1.31319	0.656593	−	0.754245i	$-0.271997\pi$
$607$	32.3535	1.31319	0.656593	+	0.754245i	$0.271997\pi$
$608$	−2.24224	−0.0909347
$609$	6.47438	0.262355
$610$	0.0301263	0.00121978
$611$	3.29056	0.133122
$612$	−0.211807	−0.00856179
$613$	−33.5095	−1.35344	−0.676718	−	0.736243i	$-0.736598\pi$
$613$	−33.5095	−1.35344	−0.676718	+	0.736243i	$0.736598\pi$
$614$	−15.1726	−0.612315
$615$	38.9641	1.57119
$616$	5.13106	0.206736
$617$	−41.2052	−1.65886	−0.829429	−	0.558612i	$-0.811334\pi$
$617$	−41.2052	−1.65886	−0.829429	+	0.558612i	$0.811334\pi$
$618$	0.418681	0.0168418
$619$	−20.2632	−0.814448	−0.407224	−	0.913328i	$-0.633503\pi$
$619$	−20.2632	−0.814448	−0.407224	+	0.913328i	$0.633503\pi$
$620$	26.8897	1.07992
$621$	25.1915	1.01090
$622$	4.58694	0.183919
$623$	8.90310	0.356695
$624$	−4.28873	−0.171686
$625$	13.2888	0.531554
$626$	0.591030	0.0236223
$627$	−19.4920	−0.778436
$628$	4.79958	0.191524
$629$	3.73258	0.148828
$630$	−0.488049	−0.0194443
$631$	−22.9496	−0.913610	−0.456805	−	0.889567i	$-0.651006\pi$
$631$	−22.9496	−0.913610	−0.456805	+	0.889567i	$0.651006\pi$
$632$	−3.70673	−0.147446
$633$	−32.4243	−1.28875
$634$	−18.1207	−0.719666
$635$	−10.9350	−0.433941
$636$	−3.19612	−0.126734
$637$	2.53139	0.100297
$638$	−19.6082	−0.776294
$639$	0.425365	0.0168272
$640$	−3.76480	−0.148817
$641$	−24.5916	−0.971310	−0.485655	−	0.874151i	$-0.661419\pi$
$641$	−24.5916	−0.971310	−0.485655	+	0.874151i	$0.661419\pi$
$642$	7.53572	0.297411
$643$	34.8580	1.37467	0.687333	−	0.726342i	$-0.258781\pi$
$643$	34.8580	1.37467	0.687333	+	0.726342i	$0.258781\pi$
$644$	−4.75107	−0.187219
$645$	45.2304	1.78094
$646$	−3.66354	−0.144140
$647$	16.9996	0.668322	0.334161	−	0.942516i	$-0.391547\pi$
$647$	16.9996	0.668322	0.334161	+	0.942516i	$0.391547\pi$
$648$	8.59429	0.337616
$649$	38.1930	1.49921
$650$	−23.2224	−0.910856
$651$	12.1008	0.474266
$652$	2.74208	0.107388
$653$	20.4074	0.798602	0.399301	−	0.916820i	$-0.369253\pi$
$653$	20.4074	0.798602	0.399301	+	0.916820i	$0.369253\pi$
$654$	8.36870	0.327242
$655$	−29.9478	−1.17016
$656$	−6.10878	−0.238508
$657$	0.356536	0.0139098
$658$	1.29990	0.0506753
$659$	32.3364	1.25965	0.629824	−	0.776738i	$-0.283127\pi$
$659$	32.3364	1.25965	0.629824	+	0.776738i	$0.283127\pi$
$660$	−32.7279	−1.27393
$661$	−33.5586	−1.30528	−0.652639	−	0.757669i	$-0.726338\pi$
$661$	−33.5586	−1.30528	−0.652639	+	0.757669i	$0.726338\pi$
$662$	−24.2633	−0.943020
$663$	−7.00725	−0.272139
$664$	−7.74981	−0.300751
$665$	−8.44158	−0.327350
$666$	0.296149	0.0114755
$667$	18.1561	0.703006
$668$	−17.5930	−0.680693
$669$	13.7314	0.530888
$670$	−2.63920	−0.101961
$671$	−0.0410592	−0.00158507
$672$	−1.69422	−0.0653558
$673$	18.8291	0.725810	0.362905	−	0.931826i	$-0.381785\pi$
$673$	18.8291	0.725810	0.362905	+	0.931826i	$0.381785\pi$
$674$	−20.5308	−0.790818
$675$	48.6417	1.87222
$676$	−6.59204	−0.253540
$677$	23.0258	0.884954	0.442477	−	0.896780i	$-0.354100\pi$
$677$	23.0258	0.884954	0.442477	+	0.896780i	$0.354100\pi$
$678$	6.37573	0.244858
$679$	8.92397	0.342471
$680$	−6.15123	−0.235889
$681$	19.5001	0.747247
$682$	−36.6480	−1.40333
$683$	18.5392	0.709381	0.354690	−	0.934984i	$-0.384586\pi$
$683$	18.5392	0.709381	0.354690	+	0.934984i	$0.384586\pi$
$684$	−0.290672	−0.0111141
$685$	−1.26858	−0.0484700
$686$	1.00000	0.0381802
$687$	12.5598	0.479186
$688$	−7.09119	−0.270349
$689$	4.77544	0.181930
$690$	30.3042	1.15366
$691$	1.70733	0.0649497	0.0324749	−	0.999473i	$-0.489661\pi$
$691$	1.70733	0.0649497	0.0324749	+	0.999473i	$0.489661\pi$
$692$	−14.4727	−0.550168
$693$	0.665163	0.0252674
$694$	−0.619877	−0.0235302
$695$	50.0277	1.89766
$696$	6.47438	0.245411
$697$	−9.98099	−0.378057
$698$	−0.293252	−0.0110997
$699$	44.1414	1.66958
$700$	−9.17374	−0.346735
$701$	−8.58039	−0.324077	−0.162039	−	0.986784i	$-0.551807\pi$
$701$	−8.58039	−0.324077	−0.162039	+	0.986784i	$0.551807\pi$
$702$	−13.4221	−0.506586
$703$	5.12237	0.193194
$704$	5.13106	0.193384
$705$	−8.29126	−0.312267
$706$	30.7987	1.15912
$707$	10.5709	0.397561
$708$	−12.6109	−0.473946
$709$	−40.6934	−1.52827	−0.764136	−	0.645055i	$-0.776834\pi$
$709$	−40.6934	−1.52827	−0.764136	+	0.645055i	$0.776834\pi$
$710$	12.3533	0.463611
$711$	−0.480521	−0.0180209
$712$	8.90310	0.333658
$713$	33.9341	1.27084
$714$	−2.76814	−0.103595
$715$	48.9000	1.82876
$716$	−16.2018	−0.605491
$717$	7.00854	0.261739
$718$	13.9496	0.520594
$719$	1.09263	0.0407482	0.0203741	−	0.999792i	$-0.493514\pi$
$719$	1.09263	0.0407482	0.0203741	+	0.999792i	$0.493514\pi$
$720$	−0.488049	−0.0181885
$721$	−0.247124	−0.00920338
$722$	13.9724	0.519998
$723$	−24.4312	−0.908605
$724$	3.75290	0.139475
$725$	35.0571	1.30199
$726$	25.9685	0.963781
$727$	−1.68744	−0.0625837	−0.0312918	−	0.999510i	$-0.509962\pi$
$727$	−1.68744	−0.0625837	−0.0312918	+	0.999510i	$0.509962\pi$
$728$	2.53139	0.0938197
$729$	28.0637	1.03940
$730$	10.3544	0.383234
$731$	−11.5861	−0.428529
$732$	0.0135573	0.000501092 0
$733$	7.42652	0.274305	0.137152	−	0.990550i	$-0.456205\pi$
$733$	7.42652	0.274305	0.137152	+	0.990550i	$0.456205\pi$
$734$	18.7430	0.691817
$735$	−6.37839	−0.235270
$736$	−4.75107	−0.175127
$737$	3.59697	0.132496
$738$	−0.791909	−0.0291506
$739$	−32.7878	−1.20612	−0.603060	−	0.797696i	$-0.706052\pi$
$739$	−32.7878	−1.20612	−0.603060	+	0.797696i	$0.706052\pi$
$740$	8.60066	0.316166
$741$	−9.61634	−0.353265
$742$	1.88649	0.0692551
$743$	−21.9863	−0.806599	−0.403299	−	0.915068i	$-0.632137\pi$
$743$	−21.9863	−0.806599	−0.403299	+	0.915068i	$0.632137\pi$
$744$	12.1008	0.443635
$745$	−7.66297	−0.280750
$746$	−0.233693	−0.00855613
$747$	−1.00464	−0.0367580
$748$	8.38352	0.306532
$749$	−4.44791	−0.162523
$750$	26.6217	0.972089
$751$	−20.6369	−0.753051	−0.376525	−	0.926406i	$-0.622881\pi$
$751$	−20.6369	−0.753051	−0.376525	+	0.926406i	$0.622881\pi$
$752$	1.29990	0.0474024
$753$	−22.3882	−0.815871
$754$	−9.67364	−0.352293
$755$	6.70663	0.244079
$756$	−5.30227	−0.192842
$757$	23.4349	0.851756	0.425878	−	0.904781i	$-0.359965\pi$
$757$	23.4349	0.851756	0.425878	+	0.904781i	$0.359965\pi$
$758$	−22.0112	−0.799481
$759$	−41.3016	−1.49915
$760$	−8.44158	−0.306208
$761$	32.1036	1.16375	0.581876	−	0.813277i	$-0.302319\pi$
$761$	32.1036	1.16375	0.581876	+	0.813277i	$0.302319\pi$
$762$	−4.92090	−0.178265
$763$	−4.93957	−0.178824
$764$	15.4237	0.558010
$765$	−0.797412	−0.0288305
$766$	−6.39092	−0.230913
$767$	18.8424	0.680361
$768$	−1.69422	−0.0611347
$769$	−28.6301	−1.03243	−0.516214	−	0.856459i	$-0.672659\pi$
$769$	−28.6301	−1.03243	−0.516214	+	0.856459i	$0.672659\pi$
$770$	19.3174	0.696151
$771$	−5.63740	−0.203026
$772$	−24.4004	−0.878191
$773$	−12.4854	−0.449070	−0.224535	−	0.974466i	$-0.572086\pi$
$773$	−12.4854	−0.449070	−0.224535	+	0.974466i	$0.572086\pi$
$774$	−0.919264	−0.0330423
$775$	65.5225	2.35364
$776$	8.92397	0.320352
$777$	3.87042	0.138851
$778$	−26.6128	−0.954116
$779$	−13.6973	−0.490757
$780$	−16.1462	−0.578127
$781$	−16.8363	−0.602452
$782$	−7.76267	−0.277593
$783$	20.2625	0.724121
$784$	1.00000	0.0357143
$785$	18.0695	0.644928
$786$	−13.4769	−0.480706
$787$	−34.2854	−1.22214	−0.611071	−	0.791576i	$-0.709261\pi$
$787$	−34.2854	−1.22214	−0.611071	+	0.791576i	$0.709261\pi$
$788$	−14.1409	−0.503750
$789$	38.6451	1.37580
$790$	−13.9551	−0.496501
$791$	−3.76323	−0.133805
$792$	0.665163	0.0236355
$793$	−0.0202565	−0.000719328 0
$794$	6.68899	0.237384
$795$	−12.0327	−0.426758
$796$	5.58283	0.197878
$797$	24.7988	0.878419	0.439209	−	0.898385i	$-0.355259\pi$
$797$	24.7988	0.878419	0.439209	+	0.898385i	$0.355259\pi$
$798$	−3.79883	−0.134477
$799$	2.12387	0.0751373
$800$	−9.17374	−0.324341
$801$	1.15415	0.0407799
$802$	8.28110	0.292416
$803$	−14.1120	−0.498003
$804$	−1.18768	−0.0418862
$805$	−17.8869	−0.630429
$806$	−18.0802	−0.636849
$807$	4.00133	0.140853
$808$	10.5709	0.371884
$809$	−29.1838	−1.02605	−0.513024	−	0.858374i	$-0.671475\pi$
$809$	−29.1838	−1.02605	−0.513024	+	0.858374i	$0.671475\pi$
$810$	32.3558	1.13687
$811$	36.1041	1.26778	0.633892	−	0.773421i	$-0.281456\pi$
$811$	36.1041	1.26778	0.633892	+	0.773421i	$0.281456\pi$
$812$	−3.82147	−0.134107
$813$	11.2921	0.396031
$814$	−11.7218	−0.410851
$815$	10.3234	0.361612
$816$	−2.76814	−0.0969043
$817$	−15.9001	−0.556275
$818$	−3.04974	−0.106632
$819$	0.328156	0.0114667
$820$	−22.9983	−0.803137
$821$	39.8232	1.38984	0.694920	−	0.719087i	$-0.255440\pi$
$821$	39.8232	1.38984	0.694920	+	0.719087i	$0.255440\pi$
$822$	−0.570880	−0.0199117
$823$	−17.9944	−0.627244	−0.313622	−	0.949548i	$-0.601542\pi$
$823$	−17.9944	−0.627244	−0.313622	+	0.949548i	$0.601542\pi$
$824$	−0.247124	−0.00860897
$825$	−79.7484	−2.77648
$826$	7.44350	0.258992
$827$	−12.4662	−0.433493	−0.216747	−	0.976228i	$-0.569545\pi$
$827$	−12.4662	−0.433493	−0.216747	+	0.976228i	$0.569545\pi$
$828$	−0.615904	−0.0214041
$829$	−48.1453	−1.67215	−0.836077	−	0.548612i	$-0.815157\pi$
$829$	−48.1453	−1.67215	−0.836077	+	0.548612i	$0.815157\pi$
$830$	−29.1765	−1.01273
$831$	43.6247	1.51332
$832$	2.53139	0.0877603
$833$	1.63388	0.0566105
$834$	22.5132	0.779567
$835$	−66.2341	−2.29213
$836$	11.5050	0.397910
$837$	37.8709	1.30901
$838$	−33.0604	−1.14205
$839$	−18.6641	−0.644358	−0.322179	−	0.946679i	$-0.604415\pi$
$839$	−18.6641	−0.644358	−0.322179	+	0.946679i	$0.604415\pi$
$840$	−6.37839	−0.220075
$841$	−14.3964	−0.496428
$842$	−26.2130	−0.903358
$843$	−12.2700	−0.422602
$844$	19.1382	0.658765
$845$	−24.8177	−0.853756
$846$	0.168512	0.00579356
$847$	−15.3277	−0.526667
$848$	1.88649	0.0647822
$849$	9.35341	0.321008
$850$	−14.9888	−0.514111
$851$	10.8538	0.372063
$852$	5.55917	0.190454
$853$	34.9018	1.19502	0.597508	−	0.801863i	$-0.296158\pi$
$853$	34.9018	1.19502	0.597508	+	0.801863i	$0.296158\pi$
$854$	−0.00800210	−0.000273826 0
$855$	−1.09432	−0.0374250
$856$	−4.44791	−0.152027
$857$	−35.3858	−1.20876	−0.604378	−	0.796697i	$-0.706578\pi$
$857$	−35.3858	−1.20876	−0.604378	+	0.796697i	$0.706578\pi$
$858$	22.0057	0.751262
$859$	−16.8970	−0.576518	−0.288259	−	0.957552i	$-0.593076\pi$
$859$	−16.8970	−0.576518	−0.288259	+	0.957552i	$0.593076\pi$
$860$	−26.6969	−0.910358
$861$	−10.3496	−0.352713
$862$	−1.00000	−0.0340601
$863$	−13.6174	−0.463543	−0.231772	−	0.972770i	$-0.574452\pi$
$863$	−13.6174	−0.463543	−0.231772	+	0.972770i	$0.574452\pi$
$864$	−5.30227	−0.180387
$865$	−54.4867	−1.85260
$866$	−15.9959	−0.543562
$867$	24.2789	0.824553
$868$	−7.14240	−0.242429
$869$	19.0194	0.645190
$870$	24.3748	0.826383
$871$	1.77456	0.0601286
$872$	−4.93957	−0.167275
$873$	1.15686	0.0391536
$874$	−10.6530	−0.360344
$875$	−15.7133	−0.531207
$876$	4.65963	0.157434
$877$	55.3170	1.86792	0.933961	−	0.357376i	$-0.116328\pi$
$877$	55.3170	1.86792	0.933961	+	0.357376i	$0.116328\pi$
$878$	31.2755	1.05550
$879$	−6.98156	−0.235482
$880$	19.3174	0.651190
$881$	37.1653	1.25213	0.626066	−	0.779770i	$-0.284664\pi$
$881$	37.1653	1.25213	0.626066	+	0.779770i	$0.284664\pi$
$882$	0.129635	0.00436503
$883$	20.0043	0.673199	0.336599	−	0.941648i	$-0.390723\pi$
$883$	20.0043	0.673199	0.336599	+	0.941648i	$0.390723\pi$
$884$	4.13599	0.139108
$885$	−47.4775	−1.59594
$886$	26.1389	0.878155
$887$	35.2378	1.18317	0.591585	−	0.806242i	$-0.298502\pi$
$887$	35.2378	1.18317	0.591585	+	0.806242i	$0.298502\pi$
$888$	3.87042	0.129883
$889$	2.90453	0.0974148
$890$	33.5184	1.12354
$891$	−44.0978	−1.47733
$892$	−8.10489	−0.271372
$893$	2.91468	0.0975360
$894$	−3.44845	−0.115333
$895$	−60.9967	−2.03890
$896$	1.00000	0.0334077
$897$	−20.3761	−0.680337
$898$	−14.1690	−0.472827
$899$	27.2944	0.910320
$900$	−1.18923	−0.0396412
$901$	3.08229	0.102686
$902$	31.3445	1.04366
$903$	−12.0140	−0.399801
$904$	−3.76323	−0.125163
$905$	14.1289	0.469661
$906$	3.01808	0.100269
$907$	−16.3214	−0.541943	−0.270972	−	0.962587i	$-0.587345\pi$
$907$	−16.3214	−0.541943	−0.270972	+	0.962587i	$0.587345\pi$
$908$	−11.5098	−0.381967
$909$	1.37036	0.0454519
$910$	9.53020	0.315923
$911$	−12.9312	−0.428430	−0.214215	−	0.976787i	$-0.568719\pi$
$911$	−12.9312	−0.428430	−0.214215	+	0.976787i	$0.568719\pi$
$912$	−3.79883	−0.125792
$913$	39.7647	1.31602
$914$	−14.2280	−0.470620
$915$	0.0510405	0.00168735
$916$	−7.41334	−0.244944
$917$	7.95468	0.262687
$918$	−8.66327	−0.285930
$919$	4.11729	0.135817	0.0679085	−	0.997692i	$-0.478367\pi$
$919$	4.11729	0.135817	0.0679085	+	0.997692i	$0.478367\pi$
$920$	−17.8869	−0.589712
$921$	−25.7056	−0.847028
$922$	−19.6352	−0.646652
$923$	−8.30617	−0.273401
$924$	8.69311	0.285982
$925$	20.9573	0.689073
$926$	12.0254	0.395179
$927$	−0.0320358	−0.00105219
$928$	−3.82147	−0.125446
$929$	21.3527	0.700559	0.350280	−	0.936645i	$-0.386087\pi$
$929$	21.3527	0.700559	0.350280	+	0.936645i	$0.386087\pi$
$930$	45.5570	1.49387
$931$	2.24224	0.0734863
$932$	−26.0542	−0.853433
$933$	7.77126	0.254420
$934$	2.49381	0.0815998
$935$	31.5623	1.03220
$936$	0.328156	0.0107261
$937$	−19.5021	−0.637104	−0.318552	−	0.947905i	$-0.603197\pi$
$937$	−19.5021	−0.637104	−0.318552	+	0.947905i	$0.603197\pi$
$938$	0.701020	0.0228891
$939$	1.00133	0.0326772
$940$	4.89386	0.159620
$941$	−5.14134	−0.167603	−0.0838014	−	0.996482i	$-0.526706\pi$
$941$	−5.14134	−0.167603	−0.0838014	+	0.996482i	$0.526706\pi$
$942$	8.13153	0.264940
$943$	−29.0233	−0.945127
$944$	7.44350	0.242265
$945$	−19.9620	−0.649365
$946$	36.3853	1.18299
$947$	57.8513	1.87991	0.939957	−	0.341293i	$-0.110865\pi$
$947$	57.8513	1.87991	0.939957	+	0.341293i	$0.110865\pi$
$948$	−6.28000	−0.203965
$949$	−6.96214	−0.226000
$950$	−20.5697	−0.667369
$951$	−30.7004	−0.995529
$952$	1.63388	0.0529543
$953$	−43.7561	−1.41740	−0.708700	−	0.705510i	$-0.750718\pi$
$953$	−43.7561	−1.41740	−0.708700	+	0.705510i	$0.750718\pi$
$954$	0.244554	0.00791773
$955$	58.0672	1.87901
$956$	−4.13675	−0.133792
$957$	−33.2204	−1.07386
$958$	−23.9177	−0.772747
$959$	0.336958	0.0108809
$960$	−6.37839	−0.205862
$961$	20.0138	0.645607
$962$	−5.78295	−0.186450
$963$	−0.576604	−0.0185808
$964$	14.4204	0.464448
$965$	−91.8628	−2.95717
$966$	−8.04934	−0.258983
$967$	−33.2809	−1.07024	−0.535121	−	0.844775i	$-0.679734\pi$
$967$	−33.2809	−1.07024	−0.535121	+	0.844775i	$0.679734\pi$
$968$	−15.3277	−0.492652
$969$	−6.20682	−0.199392
$970$	33.5970	1.07873
$971$	3.31961	0.106531	0.0532657	−	0.998580i	$-0.483037\pi$
$971$	3.31961	0.106531	0.0532657	+	0.998580i	$0.483037\pi$
$972$	−1.34625	−0.0431808
$973$	−13.2883	−0.426002
$974$	−13.4212	−0.430042
$975$	−39.3437	−1.26001
$976$	−0.00800210	−0.000256141 0
$977$	4.02190	0.128672	0.0643360	−	0.997928i	$-0.479507\pi$
$977$	4.02190	0.128672	0.0643360	+	0.997928i	$0.479507\pi$
$978$	4.64567	0.148552
$979$	−45.6823	−1.46001
$980$	3.76480	0.120262
$981$	−0.640339	−0.0204445
$982$	12.6746	0.404462
$983$	−23.2274	−0.740838	−0.370419	−	0.928865i	$-0.620786\pi$
$983$	−23.2274	−0.740838	−0.370419	+	0.928865i	$0.620786\pi$
$984$	−10.3496	−0.329933
$985$	−53.2379	−1.69630
$986$	−6.24381	−0.198843
$987$	2.20231	0.0701002
$988$	5.67598	0.180577
$989$	−33.6908	−1.07130
$990$	2.50421	0.0795889
$991$	39.7385	1.26234	0.631168	−	0.775646i	$-0.282576\pi$
$991$	39.7385	1.26234	0.631168	+	0.775646i	$0.282576\pi$
$992$	−7.14240	−0.226771
$993$	−41.1072	−1.30450
$994$	−3.28126	−0.104075
$995$	21.0183	0.666324
$996$	−13.1299	−0.416035
$997$	−4.20588	−0.133202	−0.0666009	−	0.997780i	$-0.521215\pi$
$997$	−4.20588	−0.133202	−0.0666009	+	0.997780i	$0.521215\pi$
$998$	−30.7009	−0.971821
$999$	12.1130	0.383238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.69422 q^{3} +1.00000 q^{4} +3.76480 q^{5} +1.69422 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.129635 q^{9} -3.76480 q^{10} +5.13106 q^{11} -1.69422 q^{12} +2.53139 q^{13} +1.00000 q^{14} -6.37839 q^{15} +1.00000 q^{16} +1.63388 q^{17} +0.129635 q^{18} +2.24224 q^{19} +3.76480 q^{20} +1.69422 q^{21} -5.13106 q^{22} +4.75107 q^{23} +1.69422 q^{24} +9.17374 q^{25} -2.53139 q^{26} +5.30227 q^{27} -1.00000 q^{28} +3.82147 q^{29} +6.37839 q^{30} +7.14240 q^{31} -1.00000 q^{32} -8.69311 q^{33} -1.63388 q^{34} -3.76480 q^{35} -0.129635 q^{36} +2.28449 q^{37} -2.24224 q^{38} -4.28873 q^{39} -3.76480 q^{40} -6.10878 q^{41} -1.69422 q^{42} -7.09119 q^{43} +5.13106 q^{44} -0.488049 q^{45} -4.75107 q^{46} +1.29990 q^{47} -1.69422 q^{48} +1.00000 q^{49} -9.17374 q^{50} -2.76814 q^{51} +2.53139 q^{52} +1.88649 q^{53} -5.30227 q^{54} +19.3174 q^{55} +1.00000 q^{56} -3.79883 q^{57} -3.82147 q^{58} +7.44350 q^{59} -6.37839 q^{60} -0.00800210 q^{61} -7.14240 q^{62} +0.129635 q^{63} +1.00000 q^{64} +9.53020 q^{65} +8.69311 q^{66} +0.701020 q^{67} +1.63388 q^{68} -8.04934 q^{69} +3.76480 q^{70} -3.28126 q^{71} +0.129635 q^{72} -2.75032 q^{73} -2.28449 q^{74} -15.5423 q^{75} +2.24224 q^{76} -5.13106 q^{77} +4.28873 q^{78} +3.70673 q^{79} +3.76480 q^{80} -8.59429 q^{81} +6.10878 q^{82} +7.74981 q^{83} +1.69422 q^{84} +6.15123 q^{85} +7.09119 q^{86} -6.47438 q^{87} -5.13106 q^{88} -8.90310 q^{89} +0.488049 q^{90} -2.53139 q^{91} +4.75107 q^{92} -12.1008 q^{93} -1.29990 q^{94} +8.44158 q^{95} +1.69422 q^{96} -8.92397 q^{97} -1.00000 q^{98} -0.665163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 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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