LMFDB - Embedded newform 8041.2.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02657 q^{2} +2.55915 q^{3} +2.10699 q^{4} -3.25953 q^{5} -5.18630 q^{6} +3.04044 q^{7} -0.216828 q^{8} +3.54925 q^{9} +O(q^{10})$	\(q-2.02657 q^{2} +2.55915 q^{3} +2.10699 q^{4} -3.25953 q^{5} -5.18630 q^{6} +3.04044 q^{7} -0.216828 q^{8} +3.54925 q^{9} +6.60567 q^{10} -1.00000 q^{11} +5.39211 q^{12} +2.88993 q^{13} -6.16167 q^{14} -8.34163 q^{15} -3.77457 q^{16} -1.00000 q^{17} -7.19282 q^{18} +8.33818 q^{19} -6.86781 q^{20} +7.78094 q^{21} +2.02657 q^{22} -8.73652 q^{23} -0.554897 q^{24} +5.62454 q^{25} -5.85664 q^{26} +1.40562 q^{27} +6.40618 q^{28} -3.91827 q^{29} +16.9049 q^{30} +3.01615 q^{31} +8.08309 q^{32} -2.55915 q^{33} +2.02657 q^{34} -9.91041 q^{35} +7.47825 q^{36} -6.85881 q^{37} -16.8979 q^{38} +7.39576 q^{39} +0.706759 q^{40} -0.0237582 q^{41} -15.7686 q^{42} -1.00000 q^{43} -2.10699 q^{44} -11.5689 q^{45} +17.7052 q^{46} -9.03774 q^{47} -9.65969 q^{48} +2.24427 q^{49} -11.3985 q^{50} -2.55915 q^{51} +6.08905 q^{52} -8.62071 q^{53} -2.84860 q^{54} +3.25953 q^{55} -0.659254 q^{56} +21.3387 q^{57} +7.94065 q^{58} -0.122360 q^{59} -17.5758 q^{60} -10.5942 q^{61} -6.11244 q^{62} +10.7913 q^{63} -8.83182 q^{64} -9.41980 q^{65} +5.18630 q^{66} +7.28490 q^{67} -2.10699 q^{68} -22.3581 q^{69} +20.0841 q^{70} -12.8719 q^{71} -0.769579 q^{72} +7.70920 q^{73} +13.8999 q^{74} +14.3941 q^{75} +17.5685 q^{76} -3.04044 q^{77} -14.9880 q^{78} +4.18057 q^{79} +12.3033 q^{80} -7.05056 q^{81} +0.0481476 q^{82} +16.9950 q^{83} +16.3944 q^{84} +3.25953 q^{85} +2.02657 q^{86} -10.0274 q^{87} +0.216828 q^{88} -5.32663 q^{89} +23.4452 q^{90} +8.78665 q^{91} -18.4078 q^{92} +7.71878 q^{93} +18.3156 q^{94} -27.1786 q^{95} +20.6858 q^{96} -11.9933 q^{97} -4.54818 q^{98} -3.54925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−2.02657	−1.43300	−0.716501	−	0.697586i	$-0.754258\pi$
$2$	−2.02657	−1.43300	−0.716501	+	0.697586i	$0.754258\pi$
$3$	2.55915	1.47753	0.738763	−	0.673965i	$-0.235410\pi$
$3$	2.55915	1.47753	0.738763	+	0.673965i	$0.235410\pi$
$4$	2.10699	1.05350
$5$	−3.25953	−1.45771	−0.728853	−	0.684670i	$-0.759946\pi$
$5$	−3.25953	−1.45771	−0.728853	+	0.684670i	$0.759946\pi$
$6$	−5.18630	−2.11730
$7$	3.04044	1.14918	0.574589	−	0.818442i	$-0.305162\pi$
$7$	3.04044	1.14918	0.574589	+	0.818442i	$0.305162\pi$
$8$	−0.216828	−0.0766604
$9$	3.54925	1.18308
$10$	6.60567	2.08890
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.39211	1.55657
$13$	2.88993	0.801521	0.400761	−	0.916183i	$-0.368746\pi$
$13$	2.88993	0.801521	0.400761	+	0.916183i	$0.368746\pi$
$14$	−6.16167	−1.64678
$15$	−8.34163	−2.15380
$16$	−3.77457	−0.943642
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.19282	−1.69536
$19$	8.33818	1.91291	0.956455	−	0.291879i	$-0.0942804\pi$
$19$	8.33818	1.91291	0.956455	+	0.291879i	$0.0942804\pi$
$20$	−6.86781	−1.53569
$21$	7.78094	1.69794
$22$	2.02657	0.432067
$23$	−8.73652	−1.82169	−0.910846	−	0.412747i	$-0.864569\pi$
$23$	−8.73652	−1.82169	−0.910846	+	0.412747i	$0.864569\pi$
$24$	−0.554897	−0.113268
$25$	5.62454	1.12491
$26$	−5.85664	−1.14858
$27$	1.40562	0.270512
$28$	6.40618	1.21065
$29$	−3.91827	−0.727604	−0.363802	−	0.931476i	$-0.618522\pi$
$29$	−3.91827	−0.727604	−0.363802	+	0.931476i	$0.618522\pi$
$30$	16.9049	3.08640
$31$	3.01615	0.541716	0.270858	−	0.962619i	$-0.412693\pi$
$31$	3.01615	0.541716	0.270858	+	0.962619i	$0.412693\pi$
$32$	8.08309	1.42890
$33$	−2.55915	−0.445491
$34$	2.02657	0.347554
$35$	−9.91041	−1.67516
$36$	7.47825	1.24638
$37$	−6.85881	−1.12758	−0.563791	−	0.825917i	$-0.690658\pi$
$37$	−6.85881	−1.12758	−0.563791	+	0.825917i	$0.690658\pi$
$38$	−16.8979	−2.74121
$39$	7.39576	1.18427
$40$	0.706759	0.111748
$41$	−0.0237582	−0.00371040	−0.00185520	−	0.999998i	$-0.500591\pi$
$41$	−0.0237582	−0.00371040	−0.00185520	+	0.999998i	$0.500591\pi$
$42$	−15.7686	−2.43315
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.10699	−0.317641
$45$	−11.5689	−1.72459
$46$	17.7052	2.61049
$47$	−9.03774	−1.31829	−0.659145	−	0.752016i	$-0.729082\pi$
$47$	−9.03774	−1.31829	−0.659145	+	0.752016i	$0.729082\pi$
$48$	−9.65969	−1.39426
$49$	2.24427	0.320610
$50$	−11.3985	−1.61200
$51$	−2.55915	−0.358353
$52$	6.08905	0.844400
$53$	−8.62071	−1.18415	−0.592073	−	0.805885i	$-0.701690\pi$
$53$	−8.62071	−1.18415	−0.592073	+	0.805885i	$0.701690\pi$
$54$	−2.84860	−0.387645
$55$	3.25953	0.439515
$56$	−0.659254	−0.0880965
$57$	21.3387	2.82638
$58$	7.94065	1.04266
$59$	−0.122360	−0.0159300	−0.00796499	−	0.999968i	$-0.502535\pi$
$59$	−0.122360	−0.0159300	−0.00796499	+	0.999968i	$0.502535\pi$
$60$	−17.5758	−2.26902
$61$	−10.5942	−1.35644	−0.678222	−	0.734857i	$-0.737249\pi$
$61$	−10.5942	−1.35644	−0.678222	+	0.734857i	$0.737249\pi$
$62$	−6.11244	−0.776281
$63$	10.7913	1.35957
$64$	−8.83182	−1.10398
$65$	−9.41980	−1.16838
$66$	5.18630	0.638390
$67$	7.28490	0.889992	0.444996	−	0.895532i	$-0.353205\pi$
$67$	7.28490	0.889992	0.444996	+	0.895532i	$0.353205\pi$
$68$	−2.10699	−0.255510
$69$	−22.3581	−2.69160
$70$	20.0841	2.40051
$71$	−12.8719	−1.52761	−0.763807	−	0.645444i	$-0.776672\pi$
$71$	−12.8719	−1.52761	−0.763807	+	0.645444i	$0.776672\pi$
$72$	−0.769579	−0.0906958
$73$	7.70920	0.902293	0.451147	−	0.892450i	$-0.351015\pi$
$73$	7.70920	0.902293	0.451147	+	0.892450i	$0.351015\pi$
$74$	13.8999	1.61583
$75$	14.3941	1.66208
$76$	17.5685	2.01524
$77$	−3.04044	−0.346490
$78$	−14.9880	−1.69706
$79$	4.18057	0.470351	0.235175	−	0.971953i	$-0.424434\pi$
$79$	4.18057	0.470351	0.235175	+	0.971953i	$0.424434\pi$
$80$	12.3033	1.37555
$81$	−7.05056	−0.783395
$82$	0.0481476	0.00531702
$83$	16.9950	1.86544	0.932722	−	0.360597i	$-0.117427\pi$
$83$	16.9950	1.86544	0.932722	+	0.360597i	$0.117427\pi$
$84$	16.3944	1.78877
$85$	3.25953	0.353546
$86$	2.02657	0.218531
$87$	−10.0274	−1.07505
$88$	0.216828	0.0231140
$89$	−5.32663	−0.564622	−0.282311	−	0.959323i	$-0.591101\pi$
$89$	−5.32663	−0.564622	−0.282311	+	0.959323i	$0.591101\pi$
$90$	23.4452	2.47134
$91$	8.78665	0.921091
$92$	−18.4078	−1.91914
$93$	7.71878	0.800400
$94$	18.3156	1.88911
$95$	−27.1786	−2.78846
$96$	20.6858	2.11124
$97$	−11.9933	−1.21773	−0.608866	−	0.793273i	$-0.708375\pi$
$97$	−11.9933	−1.21773	−0.608866	+	0.793273i	$0.708375\pi$
$98$	−4.54818	−0.459435
$99$	−3.54925	−0.356713
$100$	11.8509	1.18509
$101$	−5.03944	−0.501443	−0.250722	−	0.968059i	$-0.580668\pi$
$101$	−5.03944	−0.501443	−0.250722	+	0.968059i	$0.580668\pi$
$102$	5.18630	0.513521
$103$	−4.65680	−0.458848	−0.229424	−	0.973327i	$-0.573684\pi$
$103$	−4.65680	−0.458848	−0.229424	+	0.973327i	$0.573684\pi$
$104$	−0.626618	−0.0614450
$105$	−25.3622	−2.47510
$106$	17.4705	1.69688
$107$	−1.54468	−0.149330	−0.0746650	−	0.997209i	$-0.523789\pi$
$107$	−1.54468	−0.149330	−0.0746650	+	0.997209i	$0.523789\pi$
$108$	2.96164	0.284984
$109$	−10.0344	−0.961122	−0.480561	−	0.876961i	$-0.659567\pi$
$109$	−10.0344	−0.961122	−0.480561	+	0.876961i	$0.659567\pi$
$110$	−6.60567	−0.629826
$111$	−17.5527	−1.66603
$112$	−11.4763	−1.08441
$113$	−5.65748	−0.532211	−0.266106	−	0.963944i	$-0.585737\pi$
$113$	−5.65748	−0.532211	−0.266106	+	0.963944i	$0.585737\pi$
$114$	−43.2444	−4.05020
$115$	28.4770	2.65549
$116$	−8.25577	−0.766529
$117$	10.2571	0.948268
$118$	0.247972	0.0228277
$119$	−3.04044	−0.278717
$120$	1.80870	0.165111
$121$	1.00000	0.0909091
$122$	21.4698	1.94379
$123$	−0.0608008	−0.00548222
$124$	6.35500	0.570696
$125$	−2.03572	−0.182080
$126$	−21.8693	−1.94827
$127$	−15.5405	−1.37900	−0.689498	−	0.724288i	$-0.742169\pi$
$127$	−15.5405	−1.37900	−0.689498	+	0.724288i	$0.742169\pi$
$128$	1.73215	0.153101
$129$	−2.55915	−0.225321
$130$	19.0899	1.67430
$131$	19.7013	1.72131	0.860656	−	0.509187i	$-0.170054\pi$
$131$	19.7013	1.72131	0.860656	+	0.509187i	$0.170054\pi$
$132$	−5.39211	−0.469323
$133$	25.3517	2.19827
$134$	−14.7634	−1.27536
$135$	−4.58167	−0.394328
$136$	0.216828	0.0185929
$137$	19.4702	1.66345	0.831726	−	0.555187i	$-0.187353\pi$
$137$	19.4702	1.66345	0.831726	+	0.555187i	$0.187353\pi$
$138$	45.3103	3.85707
$139$	−20.2447	−1.71714	−0.858568	−	0.512700i	$-0.828645\pi$
$139$	−20.2447	−1.71714	−0.858568	+	0.512700i	$0.828645\pi$
$140$	−20.8812	−1.76478
$141$	−23.1289	−1.94781
$142$	26.0859	2.18908
$143$	−2.88993	−0.241668
$144$	−13.3969	−1.11641
$145$	12.7717	1.06063
$146$	−15.6232	−1.29299
$147$	5.74343	0.473710
$148$	−14.4515	−1.18790
$149$	−10.4035	−0.852289	−0.426144	−	0.904655i	$-0.640128\pi$
$149$	−10.4035	−0.852289	−0.426144	+	0.904655i	$0.640128\pi$
$150$	−29.1706	−2.38177
$151$	−5.40587	−0.439923	−0.219962	−	0.975509i	$-0.570593\pi$
$151$	−5.40587	−0.439923	−0.219962	+	0.975509i	$0.570593\pi$
$152$	−1.80796	−0.146645
$153$	−3.54925	−0.286940
$154$	6.16167	0.496521
$155$	−9.83123	−0.789664
$156$	15.5828	1.24762
$157$	−8.06075	−0.643318	−0.321659	−	0.946856i	$-0.604240\pi$
$157$	−8.06075	−0.643318	−0.321659	+	0.946856i	$0.604240\pi$
$158$	−8.47222	−0.674014
$159$	−22.0617	−1.74961
$160$	−26.3471	−2.08292
$161$	−26.5629	−2.09345
$162$	14.2885	1.12261
$163$	−0.640726	−0.0501855	−0.0250927	−	0.999685i	$-0.507988\pi$
$163$	−0.640726	−0.0501855	−0.0250927	+	0.999685i	$0.507988\pi$
$164$	−0.0500583	−0.00390890
$165$	8.34163	0.649395
$166$	−34.4416	−2.67319
$167$	12.5146	0.968407	0.484203	−	0.874955i	$-0.339109\pi$
$167$	12.5146	0.968407	0.484203	+	0.874955i	$0.339109\pi$
$168$	−1.68713	−0.130165
$169$	−4.64833	−0.357564
$170$	−6.60567	−0.506632
$171$	29.5943	2.26314
$172$	−2.10699	−0.160657
$173$	7.81461	0.594134	0.297067	−	0.954857i	$-0.403992\pi$
$173$	7.81461	0.594134	0.297067	+	0.954857i	$0.403992\pi$
$174$	20.3213	1.54056
$175$	17.1011	1.29272
$176$	3.77457	0.284519
$177$	−0.313139	−0.0235370
$178$	10.7948	0.809104
$179$	9.75957	0.729465	0.364732	−	0.931112i	$-0.381160\pi$
$179$	9.75957	0.729465	0.364732	+	0.931112i	$0.381160\pi$
$180$	−24.3756	−1.81685
$181$	15.9816	1.18790	0.593950	−	0.804502i	$-0.297568\pi$
$181$	15.9816	1.18790	0.593950	+	0.804502i	$0.297568\pi$
$182$	−17.8068	−1.31993
$183$	−27.1121	−2.00418
$184$	1.89433	0.139652
$185$	22.3565	1.64368
$186$	−15.6427	−1.14698
$187$	1.00000	0.0731272
$188$	−19.0425	−1.38881
$189$	4.27371	0.310867
$190$	55.0793	3.99587
$191$	9.77118	0.707018	0.353509	−	0.935431i	$-0.384988\pi$
$191$	9.77118	0.707018	0.353509	+	0.935431i	$0.384988\pi$
$192$	−22.6020	−1.63116
$193$	−10.5506	−0.759450	−0.379725	−	0.925099i	$-0.623981\pi$
$193$	−10.5506	−0.759450	−0.379725	+	0.925099i	$0.623981\pi$
$194$	24.3052	1.74501
$195$	−24.1067	−1.72632
$196$	4.72866	0.337762
$197$	−7.72618	−0.550467	−0.275234	−	0.961377i	$-0.588755\pi$
$197$	−7.72618	−0.550467	−0.275234	+	0.961377i	$0.588755\pi$
$198$	7.19282	0.511171
$199$	−9.46948	−0.671273	−0.335637	−	0.941992i	$-0.608951\pi$
$199$	−9.46948	−0.671273	−0.335637	+	0.941992i	$0.608951\pi$
$200$	−1.21956	−0.0862360
$201$	18.6432	1.31499
$202$	10.2128	0.718570
$203$	−11.9133	−0.836147
$204$	−5.39211	−0.377523
$205$	0.0774405	0.00540868
$206$	9.43734	0.657531
$207$	−31.0081	−2.15521
$208$	−10.9082	−0.756349
$209$	−8.33818	−0.576764
$210$	51.3984	3.54682
$211$	12.9206	0.889494	0.444747	−	0.895656i	$-0.353294\pi$
$211$	12.9206	0.889494	0.444747	+	0.895656i	$0.353294\pi$
$212$	−18.1638	−1.24749
$213$	−32.9412	−2.25709
$214$	3.13041	0.213990
$215$	3.25953	0.222298
$216$	−0.304779	−0.0207376
$217$	9.17042	0.622529
$218$	20.3354	1.37729
$219$	19.7290	1.33316
$220$	6.86781	0.463028
$221$	−2.88993	−0.194397
$222$	35.5719	2.38743
$223$	8.74127	0.585359	0.292679	−	0.956211i	$-0.405453\pi$
$223$	8.74127	0.585359	0.292679	+	0.956211i	$0.405453\pi$
$224$	24.5761	1.64206
$225$	19.9629	1.33086
$226$	11.4653	0.762660
$227$	14.6266	0.970799	0.485399	−	0.874293i	$-0.338674\pi$
$227$	14.6266	0.970799	0.485399	+	0.874293i	$0.338674\pi$
$228$	44.9604	2.97758
$229$	−13.0833	−0.864568	−0.432284	−	0.901738i	$-0.642292\pi$
$229$	−13.0833	−0.864568	−0.432284	+	0.901738i	$0.642292\pi$
$230$	−57.7106	−3.80533
$231$	−7.78094	−0.511948
$232$	0.849592	0.0557785
$233$	28.7731	1.88499	0.942494	−	0.334223i	$-0.108474\pi$
$233$	28.7731	1.88499	0.942494	+	0.334223i	$0.108474\pi$
$234$	−20.7867	−1.35887
$235$	29.4588	1.92168
$236$	−0.257813	−0.0167822
$237$	10.6987	0.694956
$238$	6.16167	0.399402
$239$	19.9574	1.29094	0.645470	−	0.763786i	$-0.276662\pi$
$239$	19.9574	1.29094	0.645470	+	0.763786i	$0.276662\pi$
$240$	31.4861	2.03242
$241$	10.9302	0.704075	0.352038	−	0.935986i	$-0.385489\pi$
$241$	10.9302	0.704075	0.352038	+	0.935986i	$0.385489\pi$
$242$	−2.02657	−0.130273
$243$	−22.2603	−1.42800
$244$	−22.3218	−1.42901
$245$	−7.31527	−0.467355
$246$	0.123217	0.00785604
$247$	24.0967	1.53324
$248$	−0.653987	−0.0415282
$249$	43.4928	2.75624
$250$	4.12552	0.260921
$251$	−17.9686	−1.13417	−0.567084	−	0.823660i	$-0.691929\pi$
$251$	−17.9686	−1.13417	−0.567084	+	0.823660i	$0.691929\pi$
$252$	22.7372	1.43231
$253$	8.73652	0.549261
$254$	31.4939	1.97610
$255$	8.34163	0.522373
$256$	14.1533	0.884583
$257$	−24.5411	−1.53083	−0.765416	−	0.643535i	$-0.777467\pi$
$257$	−24.5411	−1.53083	−0.765416	+	0.643535i	$0.777467\pi$
$258$	5.18630	0.322885
$259$	−20.8538	−1.29579
$260$	−19.8475	−1.23089
$261$	−13.9069	−0.860818
$262$	−39.9261	−2.46664
$263$	−13.9072	−0.857554	−0.428777	−	0.903410i	$-0.641055\pi$
$263$	−13.9072	−0.857554	−0.428777	+	0.903410i	$0.641055\pi$
$264$	0.554897	0.0341515
$265$	28.0995	1.72614
$266$	−51.3771	−3.15013
$267$	−13.6317	−0.834243
$268$	15.3492	0.937604
$269$	−14.7066	−0.896674	−0.448337	−	0.893865i	$-0.647984\pi$
$269$	−14.7066	−0.896674	−0.448337	+	0.893865i	$0.647984\pi$
$270$	9.28509	0.565073
$271$	19.4408	1.18095	0.590473	−	0.807058i	$-0.298941\pi$
$271$	19.4408	1.18095	0.590473	+	0.807058i	$0.298941\pi$
$272$	3.77457	0.228867
$273$	22.4864	1.36094
$274$	−39.4578	−2.38373
$275$	−5.62454	−0.339173
$276$	−47.1083	−2.83559
$277$	6.22571	0.374067	0.187033	−	0.982354i	$-0.440113\pi$
$277$	6.22571	0.374067	0.187033	+	0.982354i	$0.440113\pi$
$278$	41.0274	2.46066
$279$	10.7051	0.640896
$280$	2.14886	0.128419
$281$	6.24993	0.372839	0.186420	−	0.982470i	$-0.440312\pi$
$281$	6.24993	0.372839	0.186420	+	0.982470i	$0.440312\pi$
$282$	46.8725	2.79121
$283$	−29.9267	−1.77896	−0.889480	−	0.456974i	$-0.848933\pi$
$283$	−29.9267	−1.77896	−0.889480	+	0.456974i	$0.848933\pi$
$284$	−27.1210	−1.60934
$285$	−69.5541	−4.12003
$286$	5.85664	0.346311
$287$	−0.0722353	−0.00426391
$288$	28.6889	1.69051
$289$	1.00000	0.0588235
$290$	−25.8828	−1.51989
$291$	−30.6926	−1.79923
$292$	16.2432	0.950563
$293$	20.5015	1.19771	0.598856	−	0.800857i	$-0.295622\pi$
$293$	20.5015	1.19771	0.598856	+	0.800857i	$0.295622\pi$
$294$	−11.6395	−0.678828
$295$	0.398838	0.0232212
$296$	1.48719	0.0864409
$297$	−1.40562	−0.0815626
$298$	21.0835	1.22133
$299$	−25.2479	−1.46012
$300$	30.3282	1.75100
$301$	−3.04044	−0.175248
$302$	10.9554	0.630411
$303$	−12.8967	−0.740896
$304$	−31.4730	−1.80510
$305$	34.5320	1.97730
$306$	7.19282	0.411186
$307$	−29.0408	−1.65744	−0.828722	−	0.559660i	$-0.810932\pi$
$307$	−29.0408	−1.65744	−0.828722	+	0.559660i	$0.810932\pi$
$308$	−6.40618	−0.365026
$309$	−11.9175	−0.677960
$310$	19.9237	1.13159
$311$	21.4914	1.21867	0.609334	−	0.792914i	$-0.291437\pi$
$311$	21.4914	1.21867	0.609334	+	0.792914i	$0.291437\pi$
$312$	−1.60361	−0.0907866
$313$	−14.4809	−0.818508	−0.409254	−	0.912420i	$-0.634211\pi$
$313$	−14.4809	−0.818508	−0.409254	+	0.912420i	$0.634211\pi$
$314$	16.3357	0.921876
$315$	−35.1745	−1.98186
$316$	8.80843	0.495513
$317$	6.57217	0.369130	0.184565	−	0.982820i	$-0.440912\pi$
$317$	6.57217	0.369130	0.184565	+	0.982820i	$0.440912\pi$
$318$	44.7096	2.50719
$319$	3.91827	0.219381
$320$	28.7876	1.60928
$321$	−3.95307	−0.220639
$322$	53.8316	2.99992
$323$	−8.33818	−0.463949
$324$	−14.8555	−0.825304
$325$	16.2545	0.901638
$326$	1.29848	0.0719159
$327$	−25.6796	−1.42008
$328$	0.00515145	0.000284441 0
$329$	−27.4787	−1.51495
$330$	−16.9049	−0.930585
$331$	−32.9573	−1.81150	−0.905749	−	0.423815i	$-0.860691\pi$
$331$	−32.9573	−1.81150	−0.905749	+	0.423815i	$0.860691\pi$
$332$	35.8083	1.96524
$333$	−24.3437	−1.33403
$334$	−25.3617	−1.38773
$335$	−23.7454	−1.29735
$336$	−29.3697	−1.60225
$337$	−1.17969	−0.0642617	−0.0321309	−	0.999484i	$-0.510229\pi$
$337$	−1.17969	−0.0642617	−0.0321309	+	0.999484i	$0.510229\pi$
$338$	9.42016	0.512389
$339$	−14.4784	−0.786356
$340$	6.86781	0.372459
$341$	−3.01615	−0.163334
$342$	−59.9750	−3.24308
$343$	−14.4595	−0.780740
$344$	0.216828	0.0116906
$345$	72.8769	3.92356
$346$	−15.8369	−0.851395
$347$	2.02485	0.108700	0.0543498	−	0.998522i	$-0.482691\pi$
$347$	2.02485	0.108700	0.0543498	+	0.998522i	$0.482691\pi$
$348$	−21.1278	−1.13257
$349$	−22.7080	−1.21553	−0.607767	−	0.794116i	$-0.707934\pi$
$349$	−22.7080	−1.21553	−0.607767	+	0.794116i	$0.707934\pi$
$350$	−34.6566	−1.85247
$351$	4.06215	0.216821
$352$	−8.08309	−0.430830
$353$	−4.34326	−0.231168	−0.115584	−	0.993298i	$-0.536874\pi$
$353$	−4.34326	−0.231168	−0.115584	+	0.993298i	$0.536874\pi$
$354$	0.634598	0.0337285
$355$	41.9564	2.22681
$356$	−11.2232	−0.594827
$357$	−7.78094	−0.411811
$358$	−19.7785	−1.04532
$359$	−33.4108	−1.76336	−0.881678	−	0.471851i	$-0.843586\pi$
$359$	−33.4108	−1.76336	−0.881678	+	0.471851i	$0.843586\pi$
$360$	2.50847	0.132208
$361$	50.5253	2.65923
$362$	−32.3878	−1.70226
$363$	2.55915	0.134321
$364$	18.5134	0.970366
$365$	−25.1284	−1.31528
$366$	54.9446	2.87200
$367$	35.4437	1.85014	0.925072	−	0.379792i	$-0.124004\pi$
$367$	35.4437	1.85014	0.925072	+	0.379792i	$0.124004\pi$
$368$	32.9766	1.71902
$369$	−0.0843238	−0.00438972
$370$	−45.3071	−2.35540
$371$	−26.2107	−1.36079
$372$	16.2634	0.843219
$373$	−7.24223	−0.374988	−0.187494	−	0.982266i	$-0.560037\pi$
$373$	−7.24223	−0.374988	−0.187494	+	0.982266i	$0.560037\pi$
$374$	−2.02657	−0.104792
$375$	−5.20970	−0.269028
$376$	1.95964	0.101061
$377$	−11.3235	−0.583190
$378$	−8.66099	−0.445473
$379$	−21.3275	−1.09552	−0.547761	−	0.836635i	$-0.684520\pi$
$379$	−21.3275	−1.09552	−0.547761	+	0.836635i	$0.684520\pi$
$380$	−57.2651	−2.93764
$381$	−39.7704	−2.03750
$382$	−19.8020	−1.01316
$383$	12.6202	0.644860	0.322430	−	0.946593i	$-0.395500\pi$
$383$	12.6202	0.644860	0.322430	+	0.946593i	$0.395500\pi$
$384$	4.43282	0.226211
$385$	9.91041	0.505081
$386$	21.3816	1.08829
$387$	−3.54925	−0.180419
$388$	−25.2697	−1.28288
$389$	−16.2467	−0.823740	−0.411870	−	0.911243i	$-0.635124\pi$
$389$	−16.2467	−0.823740	−0.411870	+	0.911243i	$0.635124\pi$
$390$	48.8540	2.47382
$391$	8.73652	0.441825
$392$	−0.486622	−0.0245781
$393$	50.4186	2.54328
$394$	15.6577	0.788821
$395$	−13.6267	−0.685633
$396$	−7.47825	−0.375796
$397$	−21.3689	−1.07247	−0.536237	−	0.844067i	$-0.680155\pi$
$397$	−21.3689	−1.07247	−0.536237	+	0.844067i	$0.680155\pi$
$398$	19.1906	0.961937
$399$	64.8789	3.24801
$400$	−21.2302	−1.06151
$401$	−12.1090	−0.604696	−0.302348	−	0.953198i	$-0.597770\pi$
$401$	−12.1090	−0.604696	−0.302348	+	0.953198i	$0.597770\pi$
$402$	−37.7817	−1.88438
$403$	8.71645	0.434197
$404$	−10.6181	−0.528269
$405$	22.9815	1.14196
$406$	24.1431	1.19820
$407$	6.85881	0.339979
$408$	0.554897	0.0274715
$409$	−3.75547	−0.185696	−0.0928481	−	0.995680i	$-0.529597\pi$
$409$	−3.75547	−0.185696	−0.0928481	+	0.995680i	$0.529597\pi$
$410$	−0.156939	−0.00775065
$411$	49.8272	2.45779
$412$	−9.81184	−0.483395
$413$	−0.372030	−0.0183064
$414$	62.8402	3.08843
$415$	−55.3957	−2.71927
$416$	23.3595	1.14530
$417$	−51.8093	−2.53711
$418$	16.8979	0.826505
$419$	2.39542	0.117024	0.0585119	−	0.998287i	$-0.481364\pi$
$419$	2.39542	0.117024	0.0585119	+	0.998287i	$0.481364\pi$
$420$	−53.4380	−2.60751
$421$	−6.31668	−0.307856	−0.153928	−	0.988082i	$-0.549192\pi$
$421$	−6.31668	−0.307856	−0.153928	+	0.988082i	$0.549192\pi$
$422$	−26.1846	−1.27465
$423$	−32.0772	−1.55965
$424$	1.86921	0.0907771
$425$	−5.62454	−0.272830
$426$	66.7576	3.23442
$427$	−32.2109	−1.55880
$428$	−3.25463	−0.157319
$429$	−7.39576	−0.357071
$430$	−6.60567	−0.318554
$431$	−12.2055	−0.587919	−0.293959	−	0.955818i	$-0.594973\pi$
$431$	−12.2055	−0.587919	−0.293959	+	0.955818i	$0.594973\pi$
$432$	−5.30562	−0.255267
$433$	−19.3230	−0.928604	−0.464302	−	0.885677i	$-0.653695\pi$
$433$	−19.3230	−0.928604	−0.464302	+	0.885677i	$0.653695\pi$
$434$	−18.5845	−0.892085
$435$	32.6848	1.56711
$436$	−21.1424	−1.01254
$437$	−72.8467	−3.48473
$438$	−39.9822	−1.91043
$439$	−28.4308	−1.35693	−0.678464	−	0.734633i	$-0.737354\pi$
$439$	−28.4308	−1.35693	−0.678464	+	0.734633i	$0.737354\pi$
$440$	−0.706759	−0.0336934
$441$	7.96549	0.379309
$442$	5.85664	0.278572
$443$	−16.3248	−0.775613	−0.387807	−	0.921741i	$-0.626767\pi$
$443$	−16.3248	−0.775613	−0.387807	+	0.921741i	$0.626767\pi$
$444$	−36.9835	−1.75516
$445$	17.3623	0.823053
$446$	−17.7148	−0.838821
$447$	−26.6241	−1.25928
$448$	−26.8526	−1.26867
$449$	−5.19775	−0.245297	−0.122648	−	0.992450i	$-0.539139\pi$
$449$	−5.19775	−0.245297	−0.122648	+	0.992450i	$0.539139\pi$
$450$	−40.4563	−1.90713
$451$	0.0237582	0.00111873
$452$	−11.9203	−0.560683
$453$	−13.8344	−0.649998
$454$	−29.6418	−1.39116
$455$	−28.6403	−1.34268
$456$	−4.62683	−0.216671
$457$	23.7406	1.11054	0.555270	−	0.831670i	$-0.312615\pi$
$457$	23.7406	1.11054	0.555270	+	0.831670i	$0.312615\pi$
$458$	26.5142	1.23893
$459$	−1.40562	−0.0656089
$460$	60.0008	2.79755
$461$	−29.6074	−1.37896	−0.689478	−	0.724307i	$-0.742160\pi$
$461$	−29.6074	−1.37896	−0.689478	+	0.724307i	$0.742160\pi$
$462$	15.7686	0.733623
$463$	33.5579	1.55957	0.779784	−	0.626049i	$-0.215329\pi$
$463$	33.5579	1.55957	0.779784	+	0.626049i	$0.215329\pi$
$464$	14.7898	0.686598
$465$	−25.1596	−1.16675
$466$	−58.3107	−2.70119
$467$	−15.7475	−0.728706	−0.364353	−	0.931261i	$-0.618710\pi$
$467$	−15.7475	−0.728706	−0.364353	+	0.931261i	$0.618710\pi$
$468$	21.6116	0.998996
$469$	22.1493	1.02276
$470$	−59.7004	−2.75377
$471$	−20.6287	−0.950519
$472$	0.0265312	0.00122120
$473$	1.00000	0.0459800
$474$	−21.6817	−0.995873
$475$	46.8985	2.15185
$476$	−6.40618	−0.293627
$477$	−30.5971	−1.40094
$478$	−40.4452	−1.84992
$479$	25.1894	1.15093	0.575467	−	0.817825i	$-0.304820\pi$
$479$	25.1894	1.15093	0.575467	+	0.817825i	$0.304820\pi$
$480$	−67.4261	−3.07757
$481$	−19.8215	−0.903781
$482$	−22.1508	−1.00894
$483$	−67.9784	−3.09312
$484$	2.10699	0.0957724
$485$	39.0924	1.77510
$486$	45.1121	2.04633
$487$	−38.0696	−1.72510	−0.862548	−	0.505974i	$-0.831133\pi$
$487$	−38.0696	−1.72510	−0.862548	+	0.505974i	$0.831133\pi$
$488$	2.29712	0.103986
$489$	−1.63971	−0.0741504
$490$	14.8249	0.669722
$491$	37.2898	1.68286	0.841432	−	0.540363i	$-0.181713\pi$
$491$	37.2898	1.68286	0.841432	+	0.540363i	$0.181713\pi$
$492$	−0.128107	−0.00577550
$493$	3.91827	0.176470
$494$	−48.8338	−2.19714
$495$	11.5689	0.519984
$496$	−11.3847	−0.511186
$497$	−39.1363	−1.75550
$498$	−88.1412	−3.94970
$499$	30.5469	1.36747	0.683734	−	0.729731i	$-0.260355\pi$
$499$	30.5469	1.36747	0.683734	+	0.729731i	$0.260355\pi$
$500$	−4.28924	−0.191821
$501$	32.0267	1.43085
$502$	36.4147	1.62527
$503$	36.7018	1.63645	0.818226	−	0.574896i	$-0.194958\pi$
$503$	36.7018	1.63645	0.818226	+	0.574896i	$0.194958\pi$
$504$	−2.33986	−0.104226
$505$	16.4262	0.730957
$506$	−17.7052	−0.787092
$507$	−11.8958	−0.528310
$508$	−32.7437	−1.45277
$509$	20.8694	0.925019	0.462510	−	0.886614i	$-0.346949\pi$
$509$	20.8694	0.925019	0.462510	+	0.886614i	$0.346949\pi$
$510$	−16.9049	−0.748562
$511$	23.4393	1.03690
$512$	−32.1470	−1.42071
$513$	11.7203	0.517466
$514$	49.7343	2.19369
$515$	15.1790	0.668866
$516$	−5.39211	−0.237375
$517$	9.03774	0.397479
$518$	42.2617	1.85687
$519$	19.9988	0.877849
$520$	2.04248	0.0895687
$521$	11.1934	0.490393	0.245196	−	0.969473i	$-0.421148\pi$
$521$	11.1934	0.490393	0.245196	+	0.969473i	$0.421148\pi$
$522$	28.1834	1.23355
$523$	−4.44012	−0.194153	−0.0970764	−	0.995277i	$-0.530949\pi$
$523$	−4.44012	−0.194153	−0.0970764	+	0.995277i	$0.530949\pi$
$524$	41.5105	1.81340
$525$	43.7642	1.91003
$526$	28.1839	1.22888
$527$	−3.01615	−0.131386
$528$	9.65969	0.420384
$529$	53.3268	2.31856
$530$	−56.9456	−2.47356
$531$	−0.434288	−0.0188465
$532$	53.4159	2.31587
$533$	−0.0686594	−0.00297397
$534$	27.6255	1.19547
$535$	5.03493	0.217679
$536$	−1.57957	−0.0682272
$537$	24.9762	1.07780
$538$	29.8039	1.28494
$539$	−2.24427	−0.0966676
$540$	−9.65355	−0.415423
$541$	−1.88172	−0.0809016	−0.0404508	−	0.999182i	$-0.512879\pi$
$541$	−1.88172	−0.0809016	−0.0404508	+	0.999182i	$0.512879\pi$
$542$	−39.3982	−1.69230
$543$	40.8992	1.75515
$544$	−8.08309	−0.346560
$545$	32.7075	1.40103
$546$	−45.5702	−1.95022
$547$	−12.5095	−0.534867	−0.267433	−	0.963576i	$-0.586176\pi$
$547$	−12.5095	−0.534867	−0.267433	+	0.963576i	$0.586176\pi$
$548$	41.0236	1.75244
$549$	−37.6014	−1.60479
$550$	11.3985	0.486035
$551$	−32.6713	−1.39184
$552$	4.84787	0.206339
$553$	12.7108	0.540517
$554$	−12.6169	−0.536039
$555$	57.2137	2.42859
$556$	−42.6555	−1.80900
$557$	38.7431	1.64160	0.820798	−	0.571219i	$-0.193529\pi$
$557$	38.7431	1.64160	0.820798	+	0.571219i	$0.193529\pi$
$558$	−21.6946	−0.918406
$559$	−2.88993	−0.122231
$560$	37.4075	1.58076
$561$	2.55915	0.108047
$562$	−12.6659	−0.534280
$563$	32.2774	1.36033	0.680166	−	0.733058i	$-0.261908\pi$
$563$	32.2774	1.36033	0.680166	+	0.733058i	$0.261908\pi$
$564$	−48.7325	−2.05201
$565$	18.4407	0.775808
$566$	60.6487	2.54925
$567$	−21.4368	−0.900261
$568$	2.79100	0.117108
$569$	−42.4634	−1.78016	−0.890080	−	0.455804i	$-0.849352\pi$
$569$	−42.4634	−1.78016	−0.890080	+	0.455804i	$0.849352\pi$
$570$	140.956	5.90401
$571$	−8.99550	−0.376450	−0.188225	−	0.982126i	$-0.560273\pi$
$571$	−8.99550	−0.376450	−0.188225	+	0.982126i	$0.560273\pi$
$572$	−6.08905	−0.254596
$573$	25.0059	1.04464
$574$	0.146390	0.00611020
$575$	−49.1390	−2.04924
$576$	−31.3464	−1.30610
$577$	−9.92261	−0.413084	−0.206542	−	0.978438i	$-0.566221\pi$
$577$	−9.92261	−0.413084	−0.206542	+	0.978438i	$0.566221\pi$
$578$	−2.02657	−0.0842943
$579$	−27.0006	−1.12211
$580$	26.9099	1.11737
$581$	51.6723	2.14373
$582$	62.2007	2.57830
$583$	8.62071	0.357033
$584$	−1.67157	−0.0691702
$585$	−33.4333	−1.38230
$586$	−41.5478	−1.71632
$587$	13.0553	0.538848	0.269424	−	0.963022i	$-0.413167\pi$
$587$	13.0553	0.538848	0.269424	+	0.963022i	$0.413167\pi$
$588$	12.1014	0.499052
$589$	25.1492	1.03626
$590$	−0.808273	−0.0332761
$591$	−19.7725	−0.813330
$592$	25.8891	1.06403
$593$	26.0149	1.06830	0.534152	−	0.845388i	$-0.320631\pi$
$593$	26.0149	1.06830	0.534152	+	0.845388i	$0.320631\pi$
$594$	2.84860	0.116879
$595$	9.91041	0.406287
$596$	−21.9201	−0.897883
$597$	−24.2338	−0.991824
$598$	51.1667	2.09236
$599$	11.8208	0.482983	0.241491	−	0.970403i	$-0.422363\pi$
$599$	11.8208	0.482983	0.241491	+	0.970403i	$0.422363\pi$
$600$	−3.12104	−0.127416
$601$	−11.5228	−0.470025	−0.235013	−	0.971992i	$-0.575513\pi$
$601$	−11.5228	−0.470025	−0.235013	+	0.971992i	$0.575513\pi$
$602$	6.16167	0.251131
$603$	25.8560	1.05294
$604$	−11.3901	−0.463458
$605$	−3.25953	−0.132519
$606$	26.1361	1.06171
$607$	−14.9968	−0.608702	−0.304351	−	0.952560i	$-0.598440\pi$
$607$	−14.9968	−0.608702	−0.304351	+	0.952560i	$0.598440\pi$
$608$	67.3983	2.73336
$609$	−30.4878	−1.23543
$610$	−69.9816	−2.83347
$611$	−26.1184	−1.05664
$612$	−7.47825	−0.302290
$613$	4.65850	0.188155	0.0940774	−	0.995565i	$-0.470010\pi$
$613$	4.65850	0.188155	0.0940774	+	0.995565i	$0.470010\pi$
$614$	58.8532	2.37512
$615$	0.198182	0.00799147
$616$	0.659254	0.0265621
$617$	−1.47789	−0.0594977	−0.0297488	−	0.999557i	$-0.509471\pi$
$617$	−1.47789	−0.0594977	−0.0297488	+	0.999557i	$0.509471\pi$
$618$	24.1516	0.971519
$619$	4.34496	0.174639	0.0873194	−	0.996180i	$-0.472170\pi$
$619$	4.34496	0.174639	0.0873194	+	0.996180i	$0.472170\pi$
$620$	−20.7143	−0.831908
$621$	−12.2803	−0.492790
$622$	−43.5540	−1.74635
$623$	−16.1953	−0.648851
$624$	−27.9158	−1.11753
$625$	−21.4872	−0.859489
$626$	29.3466	1.17292
$627$	−21.3387	−0.852185
$628$	−16.9839	−0.677733
$629$	6.85881	0.273479
$630$	71.2837	2.84001
$631$	16.5213	0.657701	0.328851	−	0.944382i	$-0.393339\pi$
$631$	16.5213	0.657701	0.328851	+	0.944382i	$0.393339\pi$
$632$	−0.906466	−0.0360573
$633$	33.0659	1.31425
$634$	−13.3190	−0.528964
$635$	50.6547	2.01017
$636$	−46.4838	−1.84320
$637$	6.48578	0.256976
$638$	−7.94065	−0.314374
$639$	−45.6857	−1.80730
$640$	−5.64598	−0.223177
$641$	18.5618	0.733147	0.366573	−	0.930389i	$-0.380531\pi$
$641$	18.5618	0.733147	0.366573	+	0.930389i	$0.380531\pi$
$642$	8.01118	0.316176
$643$	−48.2244	−1.90179	−0.950893	−	0.309521i	$-0.899831\pi$
$643$	−48.2244	−1.90179	−0.950893	+	0.309521i	$0.899831\pi$
$644$	−55.9678	−2.20544
$645$	8.34163	0.328451
$646$	16.8979	0.664840
$647$	−22.1623	−0.871290	−0.435645	−	0.900119i	$-0.643480\pi$
$647$	−22.1623	−0.871290	−0.435645	+	0.900119i	$0.643480\pi$
$648$	1.52876	0.0600554
$649$	0.122360	0.00480307
$650$	−32.9409	−1.29205
$651$	23.4685	0.919802
$652$	−1.35000	−0.0528702
$653$	−18.3901	−0.719659	−0.359830	−	0.933018i	$-0.617165\pi$
$653$	−18.3901	−0.719659	−0.359830	+	0.933018i	$0.617165\pi$
$654$	52.0415	2.03498
$655$	−64.2171	−2.50917
$656$	0.0896768	0.00350129
$657$	27.3619	1.06749
$658$	55.6876	2.17093
$659$	0.399685	0.0155695	0.00778477	−	0.999970i	$-0.497522\pi$
$659$	0.399685	0.0155695	0.00778477	+	0.999970i	$0.497522\pi$
$660$	17.5758	0.684135
$661$	1.07879	0.0419601	0.0209800	−	0.999780i	$-0.493321\pi$
$661$	1.07879	0.0419601	0.0209800	+	0.999780i	$0.493321\pi$
$662$	66.7903	2.59588
$663$	−7.39576	−0.287227
$664$	−3.68500	−0.143006
$665$	−82.6348	−3.20444
$666$	49.3342	1.91166
$667$	34.2321	1.32547
$668$	26.3681	1.02021
$669$	22.3702	0.864883
$670$	48.1217	1.85910
$671$	10.5942	0.408983
$672$	62.8940	2.42619
$673$	9.36242	0.360895	0.180447	−	0.983585i	$-0.442245\pi$
$673$	9.36242	0.360895	0.180447	+	0.983585i	$0.442245\pi$
$674$	2.39072	0.0920872
$675$	7.90599	0.304302
$676$	−9.79399	−0.376692
$677$	−31.4519	−1.20880	−0.604398	−	0.796683i	$-0.706586\pi$
$677$	−31.4519	−1.20880	−0.604398	+	0.796683i	$0.706586\pi$
$678$	29.3414	1.12685
$679$	−36.4648	−1.39939
$680$	−0.706759	−0.0271030
$681$	37.4316	1.43438
$682$	6.11244	0.234058
$683$	−14.4700	−0.553681	−0.276840	−	0.960916i	$-0.589287\pi$
$683$	−14.4700	−0.553681	−0.276840	+	0.960916i	$0.589287\pi$
$684$	62.3550	2.38420
$685$	−63.4637	−2.42482
$686$	29.3032	1.11880
$687$	−33.4821	−1.27742
$688$	3.77457	0.143904
$689$	−24.9132	−0.949118
$690$	−147.690	−5.62247
$691$	16.6530	0.633509	0.316755	−	0.948508i	$-0.397407\pi$
$691$	16.6530	0.633509	0.316755	+	0.948508i	$0.397407\pi$
$692$	16.4653	0.625918
$693$	−10.7913	−0.409927
$694$	−4.10350	−0.155767
$695$	65.9883	2.50308
$696$	2.17423	0.0824142
$697$	0.0237582	0.000899905 0
$698$	46.0195	1.74186
$699$	73.6347	2.78512
$700$	36.0319	1.36188
$701$	−51.1165	−1.93065	−0.965323	−	0.261060i	$-0.915928\pi$
$701$	−51.1165	−1.93065	−0.965323	+	0.261060i	$0.915928\pi$
$702$	−8.23224	−0.310706
$703$	−57.1901	−2.15696
$704$	8.83182	0.332862
$705$	75.3895	2.83933
$706$	8.80192	0.331265
$707$	−15.3221	−0.576248
$708$	−0.659781	−0.0247961
$709$	−7.14979	−0.268516	−0.134258	−	0.990946i	$-0.542865\pi$
$709$	−7.14979	−0.268516	−0.134258	+	0.990946i	$0.542865\pi$
$710$	−85.0276	−3.19103
$711$	14.8379	0.556465
$712$	1.15496	0.0432841
$713$	−26.3507	−0.986840
$714$	15.7686	0.590126
$715$	9.41980	0.352281
$716$	20.5633	0.768488
$717$	51.0741	1.90740
$718$	67.7094	2.52689
$719$	−18.3003	−0.682486	−0.341243	−	0.939975i	$-0.610848\pi$
$719$	−18.3003	−0.682486	−0.341243	+	0.939975i	$0.610848\pi$
$720$	43.6676	1.62740
$721$	−14.1587	−0.527298
$722$	−102.393	−3.81068
$723$	27.9720	1.04029
$724$	33.6730	1.25145
$725$	−22.0385	−0.818488
$726$	−5.18630	−0.192482
$727$	32.9511	1.22209	0.611045	−	0.791596i	$-0.290749\pi$
$727$	32.9511	1.22209	0.611045	+	0.791596i	$0.290749\pi$
$728$	−1.90519	−0.0706112
$729$	−35.8158	−1.32651
$730$	50.9244	1.88480
$731$	1.00000	0.0369863
$732$	−57.1250	−2.11140
$733$	−21.3433	−0.788331	−0.394166	−	0.919039i	$-0.628966\pi$
$733$	−21.3433	−0.788331	−0.394166	+	0.919039i	$0.628966\pi$
$734$	−71.8291	−2.65126
$735$	−18.7209	−0.690530
$736$	−70.6181	−2.60302
$737$	−7.28490	−0.268343
$738$	0.170888	0.00629048
$739$	38.9036	1.43109	0.715546	−	0.698566i	$-0.246178\pi$
$739$	38.9036	1.43109	0.715546	+	0.698566i	$0.246178\pi$
$740$	47.1050	1.73162
$741$	61.6672	2.26540
$742$	53.1179	1.95002
$743$	−33.5357	−1.23031	−0.615154	−	0.788407i	$-0.710906\pi$
$743$	−33.5357	−1.23031	−0.615154	+	0.788407i	$0.710906\pi$
$744$	−1.67365	−0.0613590
$745$	33.9106	1.24239
$746$	14.6769	0.537359
$747$	60.3196	2.20698
$748$	2.10699	0.0770393
$749$	−4.69651	−0.171607
$750$	10.5578	0.385518
$751$	47.6710	1.73954	0.869770	−	0.493457i	$-0.164267\pi$
$751$	47.6710	1.73954	0.869770	+	0.493457i	$0.164267\pi$
$752$	34.1136	1.24399
$753$	−45.9844	−1.67576
$754$	22.9479	0.835713
$755$	17.6206	0.641279
$756$	9.00468	0.327497
$757$	−14.6980	−0.534208	−0.267104	−	0.963668i	$-0.586067\pi$
$757$	−14.6980	−0.534208	−0.267104	+	0.963668i	$0.586067\pi$
$758$	43.2218	1.56989
$759$	22.3581	0.811547
$760$	5.89309	0.213765
$761$	20.2590	0.734387	0.367194	−	0.930145i	$-0.380319\pi$
$761$	20.2590	0.734387	0.367194	+	0.930145i	$0.380319\pi$
$762$	80.5977	2.91975
$763$	−30.5090	−1.10450
$764$	20.5878	0.744841
$765$	11.5689	0.418275
$766$	−25.5757	−0.924087
$767$	−0.353613	−0.0127682
$768$	36.2205	1.30699
$769$	−12.8221	−0.462377	−0.231189	−	0.972909i	$-0.574261\pi$
$769$	−12.8221	−0.462377	−0.231189	+	0.972909i	$0.574261\pi$
$770$	−20.0841	−0.723782
$771$	−62.8044	−2.26185
$772$	−22.2301	−0.800077
$773$	−9.45325	−0.340010	−0.170005	−	0.985443i	$-0.554378\pi$
$773$	−9.45325	−0.340010	−0.170005	+	0.985443i	$0.554378\pi$
$774$	7.19282	0.258540
$775$	16.9645	0.609381
$776$	2.60048	0.0933518
$777$	−53.3680	−1.91457
$778$	32.9251	1.18042
$779$	−0.198100	−0.00709767
$780$	−50.7926	−1.81867
$781$	12.8719	0.460593
$782$	−17.7052	−0.633136
$783$	−5.50761	−0.196826
$784$	−8.47115	−0.302541
$785$	26.2743	0.937768
$786$	−102.177	−3.64453
$787$	−12.2613	−0.437069	−0.218535	−	0.975829i	$-0.570128\pi$
$787$	−12.2613	−0.437069	−0.218535	+	0.975829i	$0.570128\pi$
$788$	−16.2790	−0.579915
$789$	−35.5906	−1.26706
$790$	27.6155	0.982514
$791$	−17.2012	−0.611605
$792$	0.769579	0.0273458
$793$	−30.6164	−1.08722
$794$	43.3056	1.53686
$795$	71.9108	2.55041
$796$	−19.9521	−0.707184
$797$	−12.4030	−0.439336	−0.219668	−	0.975575i	$-0.570497\pi$
$797$	−12.4030	−0.439336	−0.219668	+	0.975575i	$0.570497\pi$
$798$	−131.482	−4.65441
$799$	9.03774	0.319732
$800$	45.4637	1.60738
$801$	−18.9056	−0.667995
$802$	24.5398	0.866531
$803$	−7.70920	−0.272052
$804$	39.2810	1.38533
$805$	86.5825	3.05163
$806$	−17.6645	−0.622206
$807$	−37.6363	−1.32486
$808$	1.09269	0.0384409
$809$	−24.3665	−0.856682	−0.428341	−	0.903617i	$-0.640902\pi$
$809$	−24.3665	−0.856682	−0.428341	+	0.903617i	$0.640902\pi$
$810$	−46.5737	−1.63643
$811$	−7.92032	−0.278120	−0.139060	−	0.990284i	$-0.544408\pi$
$811$	−7.92032	−0.278120	−0.139060	+	0.990284i	$0.544408\pi$
$812$	−25.1012	−0.880878
$813$	49.7520	1.74488
$814$	−13.8999	−0.487191
$815$	2.08846	0.0731557
$816$	9.65969	0.338157
$817$	−8.33818	−0.291716
$818$	7.61074	0.266103
$819$	31.1860	1.08973
$820$	0.163167	0.00569803
$821$	35.5010	1.23900	0.619498	−	0.784999i	$-0.287336\pi$
$821$	35.5010	1.23900	0.619498	+	0.784999i	$0.287336\pi$
$822$	−100.978	−3.52203
$823$	−27.2380	−0.949456	−0.474728	−	0.880132i	$-0.657454\pi$
$823$	−27.2380	−0.949456	−0.474728	+	0.880132i	$0.657454\pi$
$824$	1.00973	0.0351755
$825$	−14.3941	−0.501137
$826$	0.753944	0.0262331
$827$	−26.3329	−0.915686	−0.457843	−	0.889033i	$-0.651378\pi$
$827$	−26.3329	−0.915686	−0.457843	+	0.889033i	$0.651378\pi$
$828$	−65.3339	−2.27051
$829$	13.4609	0.467517	0.233759	−	0.972295i	$-0.424897\pi$
$829$	13.4609	0.467517	0.233759	+	0.972295i	$0.424897\pi$
$830$	112.263	3.89672
$831$	15.9325	0.552694
$832$	−25.5233	−0.884862
$833$	−2.24427	−0.0777594
$834$	104.995	3.63569
$835$	−40.7916	−1.41165
$836$	−17.5685	−0.607619
$837$	4.23957	0.146541
$838$	−4.85449	−0.167695
$839$	−42.8477	−1.47927	−0.739634	−	0.673010i	$-0.765001\pi$
$839$	−42.8477	−1.47927	−0.739634	+	0.673010i	$0.765001\pi$
$840$	5.49925	0.189742
$841$	−13.6472	−0.470592
$842$	12.8012	0.441159
$843$	15.9945	0.550880
$844$	27.2237	0.937078
$845$	15.1514	0.521223
$846$	65.0068	2.23498
$847$	3.04044	0.104471
$848$	32.5394	1.11741
$849$	−76.5870	−2.62846
$850$	11.3985	0.390967
$851$	59.9222	2.05411
$852$	−69.4068	−2.37784
$853$	−31.6409	−1.08336	−0.541682	−	0.840584i	$-0.682212\pi$
$853$	−31.6409	−1.08336	−0.541682	+	0.840584i	$0.682212\pi$
$854$	65.2778	2.23376
$855$	−96.4636	−3.29899
$856$	0.334931	0.0114477
$857$	30.0257	1.02566	0.512829	−	0.858491i	$-0.328598\pi$
$857$	30.0257	1.02566	0.512829	+	0.858491i	$0.328598\pi$
$858$	14.9880	0.511683
$859$	−3.70446	−0.126395	−0.0631974	−	0.998001i	$-0.520130\pi$
$859$	−3.70446	−0.126395	−0.0631974	+	0.998001i	$0.520130\pi$
$860$	6.86781	0.234190
$861$	−0.184861	−0.00630005
$862$	24.7353	0.842489
$863$	−17.9681	−0.611643	−0.305821	−	0.952089i	$-0.598931\pi$
$863$	−17.9681	−0.611643	−0.305821	+	0.952089i	$0.598931\pi$
$864$	11.3618	0.386536
$865$	−25.4720	−0.866073
$866$	39.1594	1.33069
$867$	2.55915	0.0869133
$868$	19.3220	0.655832
$869$	−4.18057	−0.141816
$870$	−66.2380	−2.24568
$871$	21.0528	0.713348
$872$	2.17574	0.0736800
$873$	−42.5672	−1.44068
$874$	147.629	4.99363
$875$	−6.18947	−0.209242
$876$	41.5689	1.40448
$877$	−32.7033	−1.10431	−0.552157	−	0.833740i	$-0.686195\pi$
$877$	−32.7033	−1.10431	−0.552157	+	0.833740i	$0.686195\pi$
$878$	57.6171	1.94448
$879$	52.4665	1.76965
$880$	−12.3033	−0.414745
$881$	−35.1116	−1.18294	−0.591471	−	0.806327i	$-0.701452\pi$
$881$	−35.1116	−1.18294	−0.591471	+	0.806327i	$0.701452\pi$
$882$	−16.1426	−0.543551
$883$	13.4576	0.452884	0.226442	−	0.974025i	$-0.427291\pi$
$883$	13.4576	0.452884	0.226442	+	0.974025i	$0.427291\pi$
$884$	−6.08905	−0.204797
$885$	1.02069	0.0343100
$886$	33.0833	1.11146
$887$	13.2888	0.446196	0.223098	−	0.974796i	$-0.428383\pi$
$887$	13.2888	0.446196	0.223098	+	0.974796i	$0.428383\pi$
$888$	3.80593	0.127719
$889$	−47.2499	−1.58471
$890$	−35.1860	−1.17944
$891$	7.05056	0.236203
$892$	18.4178	0.616674
$893$	−75.3584	−2.52177
$894$	53.9557	1.80455
$895$	−31.8116	−1.06335
$896$	5.26648	0.175941
$897$	−64.6132	−2.15737
$898$	10.5336	0.351511
$899$	−11.8181	−0.394155
$900$	42.0617	1.40206
$901$	8.62071	0.287197
$902$	−0.0481476	−0.00160314
$903$	−7.78094	−0.258934
$904$	1.22670	0.0407995
$905$	−52.0924	−1.73161
$906$	28.0365	0.931449
$907$	12.4164	0.412278	0.206139	−	0.978523i	$-0.433910\pi$
$907$	12.4164	0.412278	0.206139	+	0.978523i	$0.433910\pi$
$908$	30.8181	1.02273
$909$	−17.8863	−0.593250
$910$	58.0417	1.92406
$911$	26.6922	0.884350	0.442175	−	0.896929i	$-0.354207\pi$
$911$	26.6922	0.884350	0.442175	+	0.896929i	$0.354207\pi$
$912$	−80.5443	−2.66709
$913$	−16.9950	−0.562452
$914$	−48.1121	−1.59141
$915$	88.3727	2.92151
$916$	−27.5664	−0.910819
$917$	59.9007	1.97809
$918$	2.84860	0.0940177
$919$	26.1594	0.862919	0.431460	−	0.902132i	$-0.357999\pi$
$919$	26.1594	0.862919	0.431460	+	0.902132i	$0.357999\pi$
$920$	−6.17462	−0.203571
$921$	−74.3197	−2.44892
$922$	60.0016	1.97605
$923$	−37.1989	−1.22442
$924$	−16.3944	−0.539336
$925$	−38.5777	−1.26843
$926$	−68.0075	−2.23487
$927$	−16.5282	−0.542856
$928$	−31.6717	−1.03968
$929$	−13.1967	−0.432970	−0.216485	−	0.976286i	$-0.569459\pi$
$929$	−13.1967	−0.432970	−0.216485	+	0.976286i	$0.569459\pi$
$930$	50.9877	1.67195
$931$	18.7131	0.613298
$932$	60.6247	1.98583
$933$	54.9999	1.80061
$934$	31.9134	1.04424
$935$	−3.25953	−0.106598
$936$	−2.22403	−0.0726946
$937$	48.6401	1.58900	0.794502	−	0.607262i	$-0.207732\pi$
$937$	48.6401	1.58900	0.794502	+	0.607262i	$0.207732\pi$
$938$	−44.8871	−1.46562
$939$	−37.0588	−1.20937
$940$	62.0695	2.02448
$941$	12.1121	0.394843	0.197421	−	0.980319i	$-0.436743\pi$
$941$	12.1121	0.394843	0.197421	+	0.980319i	$0.436743\pi$
$942$	41.8055	1.36210
$943$	0.207564	0.00675921
$944$	0.461858	0.0150322
$945$	−13.9303	−0.453153
$946$	−2.02657	−0.0658895
$947$	−3.07767	−0.100011	−0.0500054	−	0.998749i	$-0.515924\pi$
$947$	−3.07767	−0.100011	−0.0500054	+	0.998749i	$0.515924\pi$
$948$	22.5421	0.732133
$949$	22.2790	0.723207
$950$	−95.0431	−3.08361
$951$	16.8192	0.545399
$952$	0.659254	0.0213665
$953$	−28.4517	−0.921640	−0.460820	−	0.887494i	$-0.652445\pi$
$953$	−28.4517	−0.921640	−0.460820	+	0.887494i	$0.652445\pi$
$954$	62.0072	2.00756
$955$	−31.8495	−1.03062
$956$	42.0502	1.36000
$957$	10.0274	0.324141
$958$	−51.0482	−1.64929
$959$	59.1980	1.91160
$960$	73.6718	2.37775
$961$	−21.9028	−0.706543
$962$	40.1696	1.29512
$963$	−5.48246	−0.176670
$964$	23.0298	0.741741
$965$	34.3900	1.10705
$966$	137.763	4.43245
$967$	1.29759	0.0417277	0.0208639	−	0.999782i	$-0.493358\pi$
$967$	1.29759	0.0417277	0.0208639	+	0.999782i	$0.493358\pi$
$968$	−0.216828	−0.00696913
$969$	−21.3387	−0.685497
$970$	−79.2236	−2.54372
$971$	47.7571	1.53260	0.766299	−	0.642484i	$-0.222096\pi$
$971$	47.7571	1.53260	0.766299	+	0.642484i	$0.222096\pi$
$972$	−46.9023	−1.50439
$973$	−61.5529	−1.97329
$974$	77.1507	2.47207
$975$	41.5978	1.33219
$976$	39.9884	1.28000
$977$	−56.4776	−1.80688	−0.903440	−	0.428715i	$-0.858967\pi$
$977$	−56.4776	−1.80688	−0.903440	+	0.428715i	$0.858967\pi$
$978$	3.32300	0.106258
$979$	5.32663	0.170240
$980$	−15.4132	−0.492357
$981$	−35.6147	−1.13709
$982$	−75.5704	−2.41155
$983$	30.5986	0.975942	0.487971	−	0.872860i	$-0.337737\pi$
$983$	30.5986	0.975942	0.487971	+	0.872860i	$0.337737\pi$
$984$	0.0131833	0.000420269 0
$985$	25.1837	0.802420
$986$	−7.94065	−0.252882
$987$	−70.3222	−2.23838
$988$	50.7717	1.61526
$989$	8.73652	0.277805
$990$	−23.4452	−0.745138
$991$	−13.2983	−0.422435	−0.211218	−	0.977439i	$-0.567743\pi$
$991$	−13.2983	−0.422435	−0.211218	+	0.977439i	$0.567743\pi$
$992$	24.3798	0.774059
$993$	−84.3427	−2.67654
$994$	79.3124	2.51564
$995$	30.8661	0.978520
$996$	91.6390	2.90369
$997$	40.6832	1.28845	0.644224	−	0.764837i	$-0.277180\pi$
$997$	40.6832	1.28845	0.644224	+	0.764837i	$0.277180\pi$
$998$	−61.9055	−1.95958
$999$	−9.64091	−0.305025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.14	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.14	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02657 q^{2} +2.55915 q^{3} +2.10699 q^{4} -3.25953 q^{5} -5.18630 q^{6} +3.04044 q^{7} -0.216828 q^{8} +3.54925 q^{9} +O(q^{10})\)	\(q-2.02657 q^{2} +2.55915 q^{3} +2.10699 q^{4} -3.25953 q^{5} -5.18630 q^{6} +3.04044 q^{7} -0.216828 q^{8} +3.54925 q^{9} +6.60567 q^{10} -1.00000 q^{11} +5.39211 q^{12} +2.88993 q^{13} -6.16167 q^{14} -8.34163 q^{15} -3.77457 q^{16} -1.00000 q^{17} -7.19282 q^{18} +8.33818 q^{19} -6.86781 q^{20} +7.78094 q^{21} +2.02657 q^{22} -8.73652 q^{23} -0.554897 q^{24} +5.62454 q^{25} -5.85664 q^{26} +1.40562 q^{27} +6.40618 q^{28} -3.91827 q^{29} +16.9049 q^{30} +3.01615 q^{31} +8.08309 q^{32} -2.55915 q^{33} +2.02657 q^{34} -9.91041 q^{35} +7.47825 q^{36} -6.85881 q^{37} -16.8979 q^{38} +7.39576 q^{39} +0.706759 q^{40} -0.0237582 q^{41} -15.7686 q^{42} -1.00000 q^{43} -2.10699 q^{44} -11.5689 q^{45} +17.7052 q^{46} -9.03774 q^{47} -9.65969 q^{48} +2.24427 q^{49} -11.3985 q^{50} -2.55915 q^{51} +6.08905 q^{52} -8.62071 q^{53} -2.84860 q^{54} +3.25953 q^{55} -0.659254 q^{56} +21.3387 q^{57} +7.94065 q^{58} -0.122360 q^{59} -17.5758 q^{60} -10.5942 q^{61} -6.11244 q^{62} +10.7913 q^{63} -8.83182 q^{64} -9.41980 q^{65} +5.18630 q^{66} +7.28490 q^{67} -2.10699 q^{68} -22.3581 q^{69} +20.0841 q^{70} -12.8719 q^{71} -0.769579 q^{72} +7.70920 q^{73} +13.8999 q^{74} +14.3941 q^{75} +17.5685 q^{76} -3.04044 q^{77} -14.9880 q^{78} +4.18057 q^{79} +12.3033 q^{80} -7.05056 q^{81} +0.0481476 q^{82} +16.9950 q^{83} +16.3944 q^{84} +3.25953 q^{85} +2.02657 q^{86} -10.0274 q^{87} +0.216828 q^{88} -5.32663 q^{89} +23.4452 q^{90} +8.78665 q^{91} -18.4078 q^{92} +7.71878 q^{93} +18.3156 q^{94} -27.1786 q^{95} +20.6858 q^{96} -11.9933 q^{97} -4.54818 q^{98} -3.54925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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