LMFDB - Embedded newform 4017.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.607674 q^{2} -1.00000 q^{3} -1.63073 q^{4} -3.70104 q^{5} +0.607674 q^{6} +0.175250 q^{7} +2.20630 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.607674 q^{2} -1.00000 q^{3} -1.63073 q^{4} -3.70104 q^{5} +0.607674 q^{6} +0.175250 q^{7} +2.20630 q^{8} +1.00000 q^{9} +2.24902 q^{10} -2.41053 q^{11} +1.63073 q^{12} -1.00000 q^{13} -0.106495 q^{14} +3.70104 q^{15} +1.92075 q^{16} +1.06768 q^{17} -0.607674 q^{18} -7.45695 q^{19} +6.03540 q^{20} -0.175250 q^{21} +1.46482 q^{22} -1.86155 q^{23} -2.20630 q^{24} +8.69767 q^{25} +0.607674 q^{26} -1.00000 q^{27} -0.285786 q^{28} +4.19094 q^{29} -2.24902 q^{30} -9.41459 q^{31} -5.57980 q^{32} +2.41053 q^{33} -0.648804 q^{34} -0.648606 q^{35} -1.63073 q^{36} -1.36475 q^{37} +4.53140 q^{38} +1.00000 q^{39} -8.16561 q^{40} -11.3794 q^{41} +0.106495 q^{42} -3.16987 q^{43} +3.93093 q^{44} -3.70104 q^{45} +1.13122 q^{46} -0.0643099 q^{47} -1.92075 q^{48} -6.96929 q^{49} -5.28535 q^{50} -1.06768 q^{51} +1.63073 q^{52} -9.84391 q^{53} +0.607674 q^{54} +8.92145 q^{55} +0.386654 q^{56} +7.45695 q^{57} -2.54673 q^{58} +0.754889 q^{59} -6.03540 q^{60} -8.76819 q^{61} +5.72100 q^{62} +0.175250 q^{63} -0.450805 q^{64} +3.70104 q^{65} -1.46482 q^{66} -6.87468 q^{67} -1.74111 q^{68} +1.86155 q^{69} +0.394141 q^{70} +1.97036 q^{71} +2.20630 q^{72} -15.3900 q^{73} +0.829320 q^{74} -8.69767 q^{75} +12.1603 q^{76} -0.422445 q^{77} -0.607674 q^{78} +13.8936 q^{79} -7.10877 q^{80} +1.00000 q^{81} +6.91498 q^{82} -4.54820 q^{83} +0.285786 q^{84} -3.95154 q^{85} +1.92625 q^{86} -4.19094 q^{87} -5.31835 q^{88} +8.54553 q^{89} +2.24902 q^{90} -0.175250 q^{91} +3.03569 q^{92} +9.41459 q^{93} +0.0390794 q^{94} +27.5985 q^{95} +5.57980 q^{96} -12.8195 q^{97} +4.23506 q^{98} -2.41053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	−0.607674	−0.429691	−0.214845	−	0.976648i	$-0.568925\pi$
$2$	−0.607674	−0.429691	−0.214845	+	0.976648i	$0.568925\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.63073	−0.815366
$5$	−3.70104	−1.65515	−0.827577	−	0.561352i	$-0.810281\pi$
$5$	−3.70104	−1.65515	−0.827577	+	0.561352i	$0.810281\pi$
$6$	0.607674	0.248082
$7$	0.175250	0.0662382	0.0331191	−	0.999451i	$-0.489456\pi$
$7$	0.175250	0.0662382	0.0331191	+	0.999451i	$0.489456\pi$
$8$	2.20630	0.780046
$9$	1.00000	0.333333
$10$	2.24902	0.711204
$11$	−2.41053	−0.726802	−0.363401	−	0.931633i	$-0.618384\pi$
$11$	−2.41053	−0.726802	−0.363401	+	0.931633i	$0.618384\pi$
$12$	1.63073	0.470752
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.106495	−0.0284619
$15$	3.70104	0.955604
$16$	1.92075	0.480188
$17$	1.06768	0.258951	0.129476	−	0.991583i	$-0.458671\pi$
$17$	1.06768	0.258951	0.129476	+	0.991583i	$0.458671\pi$
$18$	−0.607674	−0.143230
$19$	−7.45695	−1.71074	−0.855371	−	0.518015i	$-0.826671\pi$
$19$	−7.45695	−1.71074	−0.855371	+	0.518015i	$0.826671\pi$
$20$	6.03540	1.34956
$21$	−0.175250	−0.0382427
$22$	1.46482	0.312300
$23$	−1.86155	−0.388160	−0.194080	−	0.980986i	$-0.562172\pi$
$23$	−1.86155	−0.388160	−0.194080	+	0.980986i	$0.562172\pi$
$24$	−2.20630	−0.450360
$25$	8.69767	1.73953
$26$	0.607674	0.119175
$27$	−1.00000	−0.192450
$28$	−0.285786	−0.0540084
$29$	4.19094	0.778238	0.389119	−	0.921187i	$-0.372779\pi$
$29$	4.19094	0.778238	0.389119	+	0.921187i	$0.372779\pi$
$30$	−2.24902	−0.410614
$31$	−9.41459	−1.69091	−0.845455	−	0.534046i	$-0.820671\pi$
$31$	−9.41459	−1.69091	−0.845455	+	0.534046i	$0.820671\pi$
$32$	−5.57980	−0.986378
$33$	2.41053	0.419619
$34$	−0.648804	−0.111269
$35$	−0.648606	−0.109634
$36$	−1.63073	−0.271789
$37$	−1.36475	−0.224363	−0.112181	−	0.993688i	$-0.535784\pi$
$37$	−1.36475	−0.224363	−0.112181	+	0.993688i	$0.535784\pi$
$38$	4.53140	0.735090
$39$	1.00000	0.160128
$40$	−8.16561	−1.29110
$41$	−11.3794	−1.77717	−0.888583	−	0.458715i	$-0.848310\pi$
$41$	−11.3794	−1.77717	−0.888583	+	0.458715i	$0.848310\pi$
$42$	0.106495	0.0164325
$43$	−3.16987	−0.483401	−0.241700	−	0.970351i	$-0.577705\pi$
$43$	−3.16987	−0.483401	−0.241700	+	0.970351i	$0.577705\pi$
$44$	3.93093	0.592609
$45$	−3.70104	−0.551718
$46$	1.13122	0.166789
$47$	−0.0643099	−0.00938056	−0.00469028	−	0.999989i	$-0.501493\pi$
$47$	−0.0643099	−0.00938056	−0.00469028	+	0.999989i	$0.501493\pi$
$48$	−1.92075	−0.277237
$49$	−6.96929	−0.995612
$50$	−5.28535	−0.747461
$51$	−1.06768	−0.149506
$52$	1.63073	0.226142
$53$	−9.84391	−1.35217	−0.676083	−	0.736826i	$-0.736324\pi$
$53$	−9.84391	−1.35217	−0.676083	+	0.736826i	$0.736324\pi$
$54$	0.607674	0.0826940
$55$	8.92145	1.20297
$56$	0.386654	0.0516689
$57$	7.45695	0.987698
$58$	−2.54673	−0.334402
$59$	0.754889	0.0982781	0.0491391	−	0.998792i	$-0.484352\pi$
$59$	0.754889	0.0982781	0.0491391	+	0.998792i	$0.484352\pi$
$60$	−6.03540	−0.779167
$61$	−8.76819	−1.12265	−0.561326	−	0.827595i	$-0.689709\pi$
$61$	−8.76819	−1.12265	−0.561326	+	0.827595i	$0.689709\pi$
$62$	5.72100	0.726568
$63$	0.175250	0.0220794
$64$	−0.450805	−0.0563506
$65$	3.70104	0.459057
$66$	−1.46482	−0.180306
$67$	−6.87468	−0.839876	−0.419938	−	0.907553i	$-0.637948\pi$
$67$	−6.87468	−0.839876	−0.419938	+	0.907553i	$0.637948\pi$
$68$	−1.74111	−0.211140
$69$	1.86155	0.224104
$70$	0.394141	0.0471089
$71$	1.97036	0.233839	0.116919	−	0.993141i	$-0.462698\pi$
$71$	1.97036	0.233839	0.116919	+	0.993141i	$0.462698\pi$
$72$	2.20630	0.260015
$73$	−15.3900	−1.80126	−0.900630	−	0.434586i	$-0.856895\pi$
$73$	−15.3900	−1.80126	−0.900630	+	0.434586i	$0.856895\pi$
$74$	0.829320	0.0964065
$75$	−8.69767	−1.00432
$76$	12.1603	1.39488
$77$	−0.422445	−0.0481421
$78$	−0.607674	−0.0688056
$79$	13.8936	1.56315	0.781574	−	0.623812i	$-0.214417\pi$
$79$	13.8936	1.56315	0.781574	+	0.623812i	$0.214417\pi$
$80$	−7.10877	−0.794785
$81$	1.00000	0.111111
$82$	6.91498	0.763632
$83$	−4.54820	−0.499229	−0.249615	−	0.968345i	$-0.580304\pi$
$83$	−4.54820	−0.499229	−0.249615	+	0.968345i	$0.580304\pi$
$84$	0.285786	0.0311818
$85$	−3.95154	−0.428604
$86$	1.92625	0.207713
$87$	−4.19094	−0.449316
$88$	−5.31835	−0.566938
$89$	8.54553	0.905824	0.452912	−	0.891555i	$-0.350385\pi$
$89$	8.54553	0.905824	0.452912	+	0.891555i	$0.350385\pi$
$90$	2.24902	0.237068
$91$	−0.175250	−0.0183712
$92$	3.03569	0.316493
$93$	9.41459	0.976248
$94$	0.0390794	0.00403074
$95$	27.5985	2.83154
$96$	5.57980	0.569485
$97$	−12.8195	−1.30162	−0.650812	−	0.759239i	$-0.725571\pi$
$97$	−12.8195	−1.30162	−0.650812	+	0.759239i	$0.725571\pi$
$98$	4.23506	0.427805
$99$	−2.41053	−0.242267
$100$	−14.1836	−1.41836
$101$	1.10680	0.110131	0.0550654	−	0.998483i	$-0.482463\pi$
$101$	1.10680	0.110131	0.0550654	+	0.998483i	$0.482463\pi$
$102$	0.648804	0.0642412
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.20630	−0.216346
$105$	0.648606	0.0632975
$106$	5.98189	0.581013
$107$	−12.4494	−1.20353	−0.601764	−	0.798674i	$-0.705535\pi$
$107$	−12.4494	−1.20353	−0.601764	+	0.798674i	$0.705535\pi$
$108$	1.63073	0.156917
$109$	−15.8223	−1.51550	−0.757752	−	0.652543i	$-0.773702\pi$
$109$	−15.8223	−1.51550	−0.757752	+	0.652543i	$0.773702\pi$
$110$	−5.42134	−0.516904
$111$	1.36475	0.129536
$112$	0.336611	0.0318068
$113$	20.7135	1.94857	0.974283	−	0.225328i	$-0.0723454\pi$
$113$	20.7135	1.94857	0.974283	+	0.225328i	$0.0723454\pi$
$114$	−4.53140	−0.424404
$115$	6.88967	0.642465
$116$	−6.83430	−0.634549
$117$	−1.00000	−0.0924500
$118$	−0.458726	−0.0422292
$119$	0.187112	0.0171525
$120$	8.16561	0.745414
$121$	−5.18935	−0.471759
$122$	5.32820	0.482393
$123$	11.3794	1.02605
$124$	15.3527	1.37871
$125$	−13.6852	−1.22404
$126$	−0.106495	−0.00948732
$127$	−4.58233	−0.406616	−0.203308	−	0.979115i	$-0.565169\pi$
$127$	−4.58233	−0.406616	−0.203308	+	0.979115i	$0.565169\pi$
$128$	11.4335	1.01059
$129$	3.16987	0.279091
$130$	−2.24902	−0.197252
$131$	11.4292	0.998572	0.499286	−	0.866437i	$-0.333596\pi$
$131$	11.4292	0.998572	0.499286	+	0.866437i	$0.333596\pi$
$132$	−3.93093	−0.342143
$133$	−1.30683	−0.113317
$134$	4.17756	0.360887
$135$	3.70104	0.318535
$136$	2.35563	0.201994
$137$	−7.34776	−0.627762	−0.313881	−	0.949462i	$-0.601629\pi$
$137$	−7.34776	−0.627762	−0.313881	+	0.949462i	$0.601629\pi$
$138$	−1.13122	−0.0962956
$139$	1.57689	0.133750	0.0668749	−	0.997761i	$-0.478697\pi$
$139$	1.57689	0.133750	0.0668749	+	0.997761i	$0.478697\pi$
$140$	1.05770	0.0893922
$141$	0.0643099	0.00541587
$142$	−1.19734	−0.100478
$143$	2.41053	0.201578
$144$	1.92075	0.160063
$145$	−15.5108	−1.28810
$146$	9.35209	0.773985
$147$	6.96929	0.574817
$148$	2.22553	0.182938
$149$	−2.38613	−0.195479	−0.0977395	−	0.995212i	$-0.531161\pi$
$149$	−2.38613	−0.195479	−0.0977395	+	0.995212i	$0.531161\pi$
$150$	5.28535	0.431547
$151$	−8.41294	−0.684635	−0.342318	−	0.939584i	$-0.611212\pi$
$151$	−8.41294	−0.684635	−0.342318	+	0.939584i	$0.611212\pi$
$152$	−16.4523	−1.33446
$153$	1.06768	0.0863171
$154$	0.256709	0.0206862
$155$	34.8438	2.79872
$156$	−1.63073	−0.130563
$157$	−11.5234	−0.919669	−0.459835	−	0.888005i	$-0.652091\pi$
$157$	−11.5234	−0.919669	−0.459835	+	0.888005i	$0.652091\pi$
$158$	−8.44276	−0.671670
$159$	9.84391	0.780673
$160$	20.6510	1.63261
$161$	−0.326237	−0.0257111
$162$	−0.607674	−0.0477434
$163$	15.4712	1.21180	0.605900	−	0.795541i	$-0.292813\pi$
$163$	15.4712	1.21180	0.605900	+	0.795541i	$0.292813\pi$
$164$	18.5568	1.44904
$165$	−8.92145	−0.694534
$166$	2.76382	0.214514
$167$	−12.7459	−0.986307	−0.493154	−	0.869942i	$-0.664156\pi$
$167$	−12.7459	−0.986307	−0.493154	+	0.869942i	$0.664156\pi$
$168$	−0.386654	−0.0298310
$169$	1.00000	0.0769231
$170$	2.40125	0.184167
$171$	−7.45695	−0.570248
$172$	5.16921	0.394148
$173$	−9.01434	−0.685347	−0.342674	−	0.939455i	$-0.611333\pi$
$173$	−9.01434	−0.685347	−0.342674	+	0.939455i	$0.611333\pi$
$174$	2.54673	0.193067
$175$	1.52427	0.115224
$176$	−4.63002	−0.349001
$177$	−0.754889	−0.0567409
$178$	−5.19290	−0.389224
$179$	−13.9344	−1.04151	−0.520754	−	0.853707i	$-0.674349\pi$
$179$	−13.9344	−1.04151	−0.520754	+	0.853707i	$0.674349\pi$
$180$	6.03540	0.449852
$181$	14.1228	1.04974	0.524870	−	0.851183i	$-0.324114\pi$
$181$	14.1228	1.04974	0.524870	+	0.851183i	$0.324114\pi$
$182$	0.106495	0.00789392
$183$	8.76819	0.648163
$184$	−4.10715	−0.302783
$185$	5.05097	0.371355
$186$	−5.72100	−0.419484
$187$	−2.57368	−0.188206
$188$	0.104872	0.00764859
$189$	−0.175250	−0.0127476
$190$	−16.7709	−1.21669
$191$	13.3613	0.966791	0.483396	−	0.875402i	$-0.339403\pi$
$191$	13.3613	0.966791	0.483396	+	0.875402i	$0.339403\pi$
$192$	0.450805	0.0325340
$193$	10.8042	0.777704	0.388852	−	0.921300i	$-0.372872\pi$
$193$	10.8042	0.777704	0.388852	+	0.921300i	$0.372872\pi$
$194$	7.79008	0.559295
$195$	−3.70104	−0.265037
$196$	11.3650	0.811789
$197$	−10.7159	−0.763477	−0.381738	−	0.924270i	$-0.624674\pi$
$197$	−10.7159	−0.763477	−0.381738	+	0.924270i	$0.624674\pi$
$198$	1.46482	0.104100
$199$	−1.40496	−0.0995948	−0.0497974	−	0.998759i	$-0.515858\pi$
$199$	−1.40496	−0.0995948	−0.0497974	+	0.998759i	$0.515858\pi$
$200$	19.1897	1.35692
$201$	6.87468	0.484902
$202$	−0.672574	−0.0473222
$203$	0.734462	0.0515491
$204$	1.74111	0.121902
$205$	42.1156	2.94148
$206$	−0.607674	−0.0423387
$207$	−1.86155	−0.129387
$208$	−1.92075	−0.133180
$209$	17.9752	1.24337
$210$	−0.394141	−0.0271983
$211$	12.1934	0.839428	0.419714	−	0.907656i	$-0.362130\pi$
$211$	12.1934	0.839428	0.419714	+	0.907656i	$0.362130\pi$
$212$	16.0528	1.10251
$213$	−1.97036	−0.135007
$214$	7.56518	0.517145
$215$	11.7318	0.800102
$216$	−2.20630	−0.150120
$217$	−1.64991	−0.112003
$218$	9.61482	0.651198
$219$	15.3900	1.03996
$220$	−14.5485	−0.980860
$221$	−1.06768	−0.0718202
$222$	−0.829320	−0.0556603
$223$	−17.3568	−1.16230	−0.581149	−	0.813797i	$-0.697397\pi$
$223$	−17.3568	−1.16230	−0.581149	+	0.813797i	$0.697397\pi$
$224$	−0.977859	−0.0653359
$225$	8.69767	0.579845
$226$	−12.5871	−0.837280
$227$	18.7074	1.24166	0.620828	−	0.783947i	$-0.286796\pi$
$227$	18.7074	1.24166	0.620828	+	0.783947i	$0.286796\pi$
$228$	−12.1603	−0.805335
$229$	−7.20572	−0.476167	−0.238084	−	0.971245i	$-0.576519\pi$
$229$	−7.20572	−0.476167	−0.238084	+	0.971245i	$0.576519\pi$
$230$	−4.18667	−0.276061
$231$	0.422445	0.0277948
$232$	9.24648	0.607061
$233$	13.7689	0.902033	0.451017	−	0.892516i	$-0.351062\pi$
$233$	13.7689	0.902033	0.451017	+	0.892516i	$0.351062\pi$
$234$	0.607674	0.0397249
$235$	0.238013	0.0155263
$236$	−1.23102	−0.0801326
$237$	−13.8936	−0.902484
$238$	−0.113703	−0.00737026
$239$	14.3537	0.928461	0.464231	−	0.885714i	$-0.346331\pi$
$239$	14.3537	0.928461	0.464231	+	0.885714i	$0.346331\pi$
$240$	7.10877	0.458869
$241$	5.89301	0.379602	0.189801	−	0.981823i	$-0.439216\pi$
$241$	5.89301	0.379602	0.189801	+	0.981823i	$0.439216\pi$
$242$	3.15344	0.202711
$243$	−1.00000	−0.0641500
$244$	14.2986	0.915372
$245$	25.7936	1.64789
$246$	−6.91498	−0.440883
$247$	7.45695	0.474475
$248$	−20.7714	−1.31899
$249$	4.54820	0.288230
$250$	8.31615	0.525960
$251$	−19.6320	−1.23916	−0.619580	−	0.784933i	$-0.712697\pi$
$251$	−19.6320	−1.23916	−0.619580	+	0.784933i	$0.712697\pi$
$252$	−0.285786	−0.0180028
$253$	4.48732	0.282116
$254$	2.78457	0.174719
$255$	3.95154	0.247455
$256$	−6.04625	−0.377891
$257$	15.0363	0.937941	0.468970	−	0.883214i	$-0.344625\pi$
$257$	15.0363	0.937941	0.468970	+	0.883214i	$0.344625\pi$
$258$	−1.92625	−0.119923
$259$	−0.239171	−0.0148614
$260$	−6.03540	−0.374300
$261$	4.19094	0.259413
$262$	−6.94522	−0.429077
$263$	13.1642	0.811737	0.405868	−	0.913932i	$-0.366969\pi$
$263$	13.1642	0.811737	0.405868	+	0.913932i	$0.366969\pi$
$264$	5.31835	0.327322
$265$	36.4327	2.23804
$266$	0.794127	0.0486911
$267$	−8.54553	−0.522978
$268$	11.2108	0.684806
$269$	−6.16484	−0.375877	−0.187938	−	0.982181i	$-0.560181\pi$
$269$	−6.16484	−0.375877	−0.187938	+	0.982181i	$0.560181\pi$
$270$	−2.24902	−0.136871
$271$	18.2669	1.10964	0.554819	−	0.831971i	$-0.312788\pi$
$271$	18.2669	1.10964	0.554819	+	0.831971i	$0.312788\pi$
$272$	2.05076	0.124345
$273$	0.175250	0.0106066
$274$	4.46504	0.269743
$275$	−20.9660	−1.26430
$276$	−3.03569	−0.182727
$277$	−16.7393	−1.00577	−0.502884	−	0.864354i	$-0.667728\pi$
$277$	−16.7393	−1.00577	−0.502884	+	0.864354i	$0.667728\pi$
$278$	−0.958233	−0.0574710
$279$	−9.41459	−0.563637
$280$	−1.43102	−0.0855199
$281$	10.7868	0.643488	0.321744	−	0.946827i	$-0.395731\pi$
$281$	10.7868	0.643488	0.321744	+	0.946827i	$0.395731\pi$
$282$	−0.0390794	−0.00232715
$283$	−1.56963	−0.0933049	−0.0466524	−	0.998911i	$-0.514855\pi$
$283$	−1.56963	−0.0933049	−0.0466524	+	0.998911i	$0.514855\pi$
$284$	−3.21313	−0.190664
$285$	−27.5985	−1.63479
$286$	−1.46482	−0.0866164
$287$	−1.99424	−0.117716
$288$	−5.57980	−0.328793
$289$	−15.8601	−0.932944
$290$	9.42553	0.553486
$291$	12.8195	0.751493
$292$	25.0969	1.46869
$293$	−20.4401	−1.19412	−0.597062	−	0.802195i	$-0.703665\pi$
$293$	−20.4401	−1.19412	−0.597062	+	0.802195i	$0.703665\pi$
$294$	−4.23506	−0.246993
$295$	−2.79387	−0.162665
$296$	−3.01104	−0.175013
$297$	2.41053	0.139873
$298$	1.44999	0.0839955
$299$	1.86155	0.107656
$300$	14.1836	0.818889
$301$	−0.555519	−0.0320196
$302$	5.11233	0.294181
$303$	−1.10680	−0.0635840
$304$	−14.3230	−0.821478
$305$	32.4514	1.85816
$306$	−0.648804	−0.0370897
$307$	22.9313	1.30876	0.654380	−	0.756166i	$-0.272930\pi$
$307$	22.9313	1.30876	0.654380	+	0.756166i	$0.272930\pi$
$308$	0.688894	0.0392534
$309$	−1.00000	−0.0568880
$310$	−21.1736	−1.20258
$311$	1.25238	0.0710158	0.0355079	−	0.999369i	$-0.488695\pi$
$311$	1.25238	0.0710158	0.0355079	+	0.999369i	$0.488695\pi$
$312$	2.20630	0.124907
$313$	−7.06452	−0.399311	−0.199655	−	0.979866i	$-0.563982\pi$
$313$	−7.06452	−0.399311	−0.199655	+	0.979866i	$0.563982\pi$
$314$	7.00249	0.395173
$315$	−0.648606	−0.0365448
$316$	−22.6567	−1.27454
$317$	−0.886239	−0.0497762	−0.0248881	−	0.999690i	$-0.507923\pi$
$317$	−0.886239	−0.0497762	−0.0248881	+	0.999690i	$0.507923\pi$
$318$	−5.98189	−0.335448
$319$	−10.1024	−0.565625
$320$	1.66844	0.0932689
$321$	12.4494	0.694857
$322$	0.198246	0.0110478
$323$	−7.96167	−0.442999
$324$	−1.63073	−0.0905962
$325$	−8.69767	−0.482460
$326$	−9.40146	−0.520699
$327$	15.8223	0.874976
$328$	−25.1064	−1.38627
$329$	−0.0112703	−0.000621352 0
$330$	5.42134	0.298435
$331$	31.0829	1.70847	0.854235	−	0.519887i	$-0.174026\pi$
$331$	31.0829	1.70847	0.854235	+	0.519887i	$0.174026\pi$
$332$	7.41689	0.407055
$333$	−1.36475	−0.0747876
$334$	7.74535	0.423807
$335$	25.4434	1.39012
$336$	−0.336611	−0.0183637
$337$	−8.97644	−0.488978	−0.244489	−	0.969652i	$-0.578620\pi$
$337$	−8.97644	−0.488978	−0.244489	+	0.969652i	$0.578620\pi$
$338$	−0.607674	−0.0330531
$339$	−20.7135	−1.12501
$340$	6.44390	0.349470
$341$	22.6941	1.22896
$342$	4.53140	0.245030
$343$	−2.44812	−0.132186
$344$	−6.99369	−0.377075
$345$	−6.88967	−0.370927
$346$	5.47778	0.294487
$347$	13.7724	0.739339	0.369669	−	0.929163i	$-0.379471\pi$
$347$	13.7724	0.739339	0.369669	+	0.929163i	$0.379471\pi$
$348$	6.83430	0.366357
$349$	−1.25265	−0.0670530	−0.0335265	−	0.999438i	$-0.510674\pi$
$349$	−1.25265	−0.0670530	−0.0335265	+	0.999438i	$0.510674\pi$
$350$	−0.926257	−0.0495105
$351$	1.00000	0.0533761
$352$	13.4503	0.716901
$353$	13.4855	0.717760	0.358880	−	0.933384i	$-0.383159\pi$
$353$	13.4855	0.717760	0.358880	+	0.933384i	$0.383159\pi$
$354$	0.458726	0.0243810
$355$	−7.29237	−0.387039
$356$	−13.9355	−0.738578
$357$	−0.187112	−0.00990299
$358$	8.46759	0.447526
$359$	−22.1188	−1.16738	−0.583692	−	0.811975i	$-0.698392\pi$
$359$	−22.1188	−1.16738	−0.583692	+	0.811975i	$0.698392\pi$
$360$	−8.16561	−0.430365
$361$	36.6062	1.92664
$362$	−8.58206	−0.451063
$363$	5.18935	0.272370
$364$	0.285786	0.0149792
$365$	56.9589	2.98136
$366$	−5.32820	−0.278510
$367$	−3.30929	−0.172744	−0.0863719	−	0.996263i	$-0.527527\pi$
$367$	−3.30929	−0.172744	−0.0863719	+	0.996263i	$0.527527\pi$
$368$	−3.57558	−0.186390
$369$	−11.3794	−0.592389
$370$	−3.06935	−0.159568
$371$	−1.72514	−0.0895650
$372$	−15.3527	−0.795999
$373$	−27.2401	−1.41044	−0.705220	−	0.708988i	$-0.749152\pi$
$373$	−27.2401	−1.41044	−0.705220	+	0.708988i	$0.749152\pi$
$374$	1.56396	0.0808705
$375$	13.6852	0.706702
$376$	−0.141887	−0.00731726
$377$	−4.19094	−0.215844
$378$	0.106495	0.00547750
$379$	−30.5198	−1.56770	−0.783848	−	0.620953i	$-0.786746\pi$
$379$	−30.5198	−1.56770	−0.783848	+	0.620953i	$0.786746\pi$
$380$	−45.0057	−2.30874
$381$	4.58233	0.234760
$382$	−8.11933	−0.415421
$383$	−2.33925	−0.119530	−0.0597650	−	0.998212i	$-0.519035\pi$
$383$	−2.33925	−0.119530	−0.0597650	+	0.998212i	$0.519035\pi$
$384$	−11.4335	−0.583465
$385$	1.56348	0.0796825
$386$	−6.56544	−0.334172
$387$	−3.16987	−0.161134
$388$	20.9052	1.06130
$389$	−26.7857	−1.35809	−0.679045	−	0.734097i	$-0.737606\pi$
$389$	−26.7857	−1.35809	−0.679045	+	0.734097i	$0.737606\pi$
$390$	2.24902	0.113884
$391$	−1.98755	−0.100515
$392$	−15.3764	−0.776623
$393$	−11.4292	−0.576526
$394$	6.51178	0.328059
$395$	−51.4206	−2.58725
$396$	3.93093	0.197536
$397$	−9.38343	−0.470941	−0.235470	−	0.971882i	$-0.575663\pi$
$397$	−9.38343	−0.470941	−0.235470	+	0.971882i	$0.575663\pi$
$398$	0.853756	0.0427949
$399$	1.30683	0.0654234
$400$	16.7061	0.835303
$401$	−0.871614	−0.0435263	−0.0217632	−	0.999763i	$-0.506928\pi$
$401$	−0.871614	−0.0435263	−0.0217632	+	0.999763i	$0.506928\pi$
$402$	−4.17756	−0.208358
$403$	9.41459	0.468974
$404$	−1.80490	−0.0897969
$405$	−3.70104	−0.183906
$406$	−0.446314	−0.0221502
$407$	3.28976	0.163067
$408$	−2.35563	−0.116621
$409$	−21.4479	−1.06053	−0.530264	−	0.847832i	$-0.677907\pi$
$409$	−21.4479	−1.06053	−0.530264	+	0.847832i	$0.677907\pi$
$410$	−25.5926	−1.26393
$411$	7.34776	0.362438
$412$	−1.63073	−0.0803404
$413$	0.132294	0.00650977
$414$	1.13122	0.0555963
$415$	16.8330	0.826302
$416$	5.57980	0.273572
$417$	−1.57689	−0.0772204
$418$	−10.9231	−0.534265
$419$	1.70480	0.0832849	0.0416424	−	0.999133i	$-0.486741\pi$
$419$	1.70480	0.0832849	0.0416424	+	0.999133i	$0.486741\pi$
$420$	−1.05770	−0.0516106
$421$	16.4798	0.803175	0.401587	−	0.915821i	$-0.368459\pi$
$421$	16.4798	0.803175	0.401587	+	0.915821i	$0.368459\pi$
$422$	−7.40961	−0.360694
$423$	−0.0643099	−0.00312685
$424$	−21.7186	−1.05475
$425$	9.28637	0.450455
$426$	1.19734	0.0580111
$427$	−1.53662	−0.0743625
$428$	20.3016	0.981316
$429$	−2.41053	−0.116381
$430$	−7.12911	−0.343796
$431$	15.9800	0.769728	0.384864	−	0.922973i	$-0.374248\pi$
$431$	15.9800	0.769728	0.384864	+	0.922973i	$0.374248\pi$
$432$	−1.92075	−0.0924122
$433$	−38.5326	−1.85176	−0.925879	−	0.377821i	$-0.876673\pi$
$433$	−38.5326	−1.85176	−0.925879	+	0.377821i	$0.876673\pi$
$434$	1.00261	0.0481266
$435$	15.5108	0.743687
$436$	25.8020	1.23569
$437$	13.8815	0.664042
$438$	−9.35209	−0.446860
$439$	−2.16863	−0.103503	−0.0517514	−	0.998660i	$-0.516480\pi$
$439$	−2.16863	−0.103503	−0.0517514	+	0.998660i	$0.516480\pi$
$440$	19.6834	0.938370
$441$	−6.96929	−0.331871
$442$	0.648804	0.0308605
$443$	20.7163	0.984263	0.492132	−	0.870521i	$-0.336218\pi$
$443$	20.7163	0.984263	0.492132	+	0.870521i	$0.336218\pi$
$444$	−2.22553	−0.105619
$445$	−31.6273	−1.49928
$446$	10.5473	0.499429
$447$	2.38613	0.112860
$448$	−0.0790035	−0.00373256
$449$	39.3477	1.85693	0.928467	−	0.371415i	$-0.121127\pi$
$449$	39.3477	1.85693	0.928467	+	0.371415i	$0.121127\pi$
$450$	−5.28535	−0.249154
$451$	27.4304	1.29165
$452$	−33.7782	−1.58879
$453$	8.41294	0.395274
$454$	−11.3680	−0.533528
$455$	0.648606	0.0304071
$456$	16.4523	0.770449
$457$	24.1039	1.12753	0.563767	−	0.825934i	$-0.309352\pi$
$457$	24.1039	1.12753	0.563767	+	0.825934i	$0.309352\pi$
$458$	4.37873	0.204604
$459$	−1.06768	−0.0498352
$460$	−11.2352	−0.523844
$461$	0.355552	0.0165597	0.00827986	−	0.999966i	$-0.497364\pi$
$461$	0.355552	0.0165597	0.00827986	+	0.999966i	$0.497364\pi$
$462$	−0.256709	−0.0119432
$463$	−1.58006	−0.0734318	−0.0367159	−	0.999326i	$-0.511690\pi$
$463$	−1.58006	−0.0734318	−0.0367159	+	0.999326i	$0.511690\pi$
$464$	8.04975	0.373700
$465$	−34.8438	−1.61584
$466$	−8.36703	−0.387595
$467$	−3.46107	−0.160159	−0.0800796	−	0.996788i	$-0.525517\pi$
$467$	−3.46107	−0.160159	−0.0800796	+	0.996788i	$0.525517\pi$
$468$	1.63073	0.0753806
$469$	−1.20479	−0.0556319
$470$	−0.144634	−0.00667149
$471$	11.5234	0.530971
$472$	1.66551	0.0766614
$473$	7.64106	0.351336
$474$	8.44276	0.387789
$475$	−64.8581	−2.97590
$476$	−0.305129	−0.0139856
$477$	−9.84391	−0.450722
$478$	−8.72235	−0.398951
$479$	−31.2672	−1.42863	−0.714317	−	0.699822i	$-0.753263\pi$
$479$	−31.2672	−1.42863	−0.714317	+	0.699822i	$0.753263\pi$
$480$	−20.6510	−0.942586
$481$	1.36475	0.0622270
$482$	−3.58103	−0.163111
$483$	0.326237	0.0148443
$484$	8.46245	0.384657
$485$	47.4455	2.15439
$486$	0.607674	0.0275647
$487$	21.5604	0.976997	0.488498	−	0.872565i	$-0.337545\pi$
$487$	21.5604	0.976997	0.488498	+	0.872565i	$0.337545\pi$
$488$	−19.3453	−0.875720
$489$	−15.4712	−0.699633
$490$	−15.6741	−0.708084
$491$	−27.6411	−1.24743	−0.623713	−	0.781654i	$-0.714376\pi$
$491$	−27.6411	−1.24743	−0.623713	+	0.781654i	$0.714376\pi$
$492$	−18.5568	−0.836604
$493$	4.47460	0.201526
$494$	−4.53140	−0.203877
$495$	8.92145	0.400990
$496$	−18.0831	−0.811955
$497$	0.345305	0.0154891
$498$	−2.76382	−0.123850
$499$	5.06624	0.226796	0.113398	−	0.993550i	$-0.463826\pi$
$499$	5.06624	0.226796	0.113398	+	0.993550i	$0.463826\pi$
$500$	22.3169	0.998043
$501$	12.7459	0.569445
$502$	11.9299	0.532455
$503$	−12.4681	−0.555926	−0.277963	−	0.960592i	$-0.589659\pi$
$503$	−12.4681	−0.555926	−0.277963	+	0.960592i	$0.589659\pi$
$504$	0.386654	0.0172230
$505$	−4.09631	−0.182283
$506$	−2.72683	−0.121222
$507$	−1.00000	−0.0444116
$508$	7.47256	0.331541
$509$	9.98530	0.442591	0.221295	−	0.975207i	$-0.428972\pi$
$509$	9.98530	0.442591	0.221295	+	0.975207i	$0.428972\pi$
$510$	−2.40125	−0.106329
$511$	−2.69709	−0.119312
$512$	−19.1929	−0.848215
$513$	7.45695	0.329233
$514$	−9.13719	−0.403024
$515$	−3.70104	−0.163087
$516$	−5.16921	−0.227562
$517$	0.155021	0.00681780
$518$	0.145338	0.00638580
$519$	9.01434	0.395685
$520$	8.16561	0.358085
$521$	27.7640	1.21636	0.608180	−	0.793799i	$-0.291900\pi$
$521$	27.7640	1.21636	0.608180	+	0.793799i	$0.291900\pi$
$522$	−2.54673	−0.111467
$523$	−29.4356	−1.28713	−0.643565	−	0.765392i	$-0.722545\pi$
$523$	−29.4356	−1.28713	−0.643565	+	0.765392i	$0.722545\pi$
$524$	−18.6379	−0.814202
$525$	−1.52427	−0.0665244
$526$	−7.99952	−0.348796
$527$	−10.0518	−0.437864
$528$	4.63002	0.201496
$529$	−19.5346	−0.849332
$530$	−22.1392	−0.961665
$531$	0.754889	0.0327594
$532$	2.13109	0.0923945
$533$	11.3794	0.492897
$534$	5.19290	0.224719
$535$	46.0757	1.99202
$536$	−15.1676	−0.655141
$537$	13.9344	0.601315
$538$	3.74621	0.161511
$539$	16.7997	0.723613
$540$	−6.03540	−0.259722
$541$	−21.3146	−0.916388	−0.458194	−	0.888852i	$-0.651504\pi$
$541$	−21.3146	−0.916388	−0.458194	+	0.888852i	$0.651504\pi$
$542$	−11.1004	−0.476801
$543$	−14.1228	−0.606067
$544$	−5.95746	−0.255424
$545$	58.5590	2.50839
$546$	−0.106495	−0.00455756
$547$	−15.1916	−0.649544	−0.324772	−	0.945792i	$-0.605288\pi$
$547$	−15.1916	−0.649544	−0.324772	+	0.945792i	$0.605288\pi$
$548$	11.9822	0.511855
$549$	−8.76819	−0.374217
$550$	12.7405	0.543256
$551$	−31.2516	−1.33136
$552$	4.10715	0.174812
$553$	2.43485	0.103540
$554$	10.1721	0.432169
$555$	−5.05097	−0.214402
$556$	−2.57148	−0.109055
$557$	−21.3760	−0.905732	−0.452866	−	0.891579i	$-0.649598\pi$
$557$	−21.3760	−0.905732	−0.452866	+	0.891579i	$0.649598\pi$
$558$	5.72100	0.242189
$559$	3.16987	0.134071
$560$	−1.24581	−0.0526451
$561$	2.57368	0.108661
$562$	−6.55488	−0.276501
$563$	4.86168	0.204895	0.102448	−	0.994738i	$-0.467333\pi$
$563$	4.86168	0.204895	0.102448	+	0.994738i	$0.467333\pi$
$564$	−0.104872	−0.00441591
$565$	−76.6616	−3.22518
$566$	0.953824	0.0400922
$567$	0.175250	0.00735980
$568$	4.34721	0.182405
$569$	−15.0851	−0.632398	−0.316199	−	0.948693i	$-0.602407\pi$
$569$	−15.0851	−0.632398	−0.316199	+	0.948693i	$0.602407\pi$
$570$	16.7709	0.702455
$571$	−26.0913	−1.09189	−0.545944	−	0.837822i	$-0.683829\pi$
$571$	−26.0913	−1.09189	−0.545944	+	0.837822i	$0.683829\pi$
$572$	−3.93093	−0.164360
$573$	−13.3613	−0.558177
$574$	1.21185	0.0505816
$575$	−16.1912	−0.675218
$576$	−0.450805	−0.0187835
$577$	31.9302	1.32927	0.664637	−	0.747167i	$-0.268586\pi$
$577$	31.9302	1.32927	0.664637	+	0.747167i	$0.268586\pi$
$578$	9.63774	0.400877
$579$	−10.8042	−0.449008
$580$	25.2940	1.05028
$581$	−0.797071	−0.0330681
$582$	−7.79008	−0.322909
$583$	23.7290	0.982756
$584$	−33.9549	−1.40507
$585$	3.70104	0.153019
$586$	12.4209	0.513104
$587$	−18.6395	−0.769334	−0.384667	−	0.923055i	$-0.625684\pi$
$587$	−18.6395	−0.769334	−0.384667	+	0.923055i	$0.625684\pi$
$588$	−11.3650	−0.468686
$589$	70.2042	2.89271
$590$	1.69776	0.0698958
$591$	10.7159	0.440793
$592$	−2.62134	−0.107736
$593$	8.54173	0.350767	0.175383	−	0.984500i	$-0.443884\pi$
$593$	8.54173	0.350767	0.175383	+	0.984500i	$0.443884\pi$
$594$	−1.46482	−0.0601021
$595$	−0.692507	−0.0283900
$596$	3.89113	0.159387
$597$	1.40496	0.0575011
$598$	−1.13122	−0.0462589
$599$	−30.6954	−1.25418	−0.627090	−	0.778947i	$-0.715754\pi$
$599$	−30.6954	−1.25418	−0.627090	+	0.778947i	$0.715754\pi$
$600$	−19.1897	−0.783416
$601$	−21.0363	−0.858088	−0.429044	−	0.903284i	$-0.641149\pi$
$601$	−21.0363	−0.858088	−0.429044	+	0.903284i	$0.641149\pi$
$602$	0.337575	0.0137585
$603$	−6.87468	−0.279959
$604$	13.7193	0.558228
$605$	19.2060	0.780834
$606$	0.672574	0.0273215
$607$	−21.9905	−0.892568	−0.446284	−	0.894891i	$-0.647253\pi$
$607$	−21.9905	−0.892568	−0.446284	+	0.894891i	$0.647253\pi$
$608$	41.6083	1.68744
$609$	−0.734462	−0.0297619
$610$	−19.7199	−0.798435
$611$	0.0643099	0.00260170
$612$	−1.74111	−0.0703801
$613$	10.3908	0.419682	0.209841	−	0.977736i	$-0.432705\pi$
$613$	10.3908	0.419682	0.209841	+	0.977736i	$0.432705\pi$
$614$	−13.9348	−0.562362
$615$	−42.1156	−1.69827
$616$	−0.932041	−0.0375530
$617$	6.69071	0.269358	0.134679	−	0.990889i	$-0.457000\pi$
$617$	6.69071	0.269358	0.134679	+	0.990889i	$0.457000\pi$
$618$	0.607674	0.0244442
$619$	−34.4294	−1.38384	−0.691918	−	0.721976i	$-0.743234\pi$
$619$	−34.4294	−1.38384	−0.691918	+	0.721976i	$0.743234\pi$
$620$	−56.8208	−2.28198
$621$	1.86155	0.0747015
$622$	−0.761037	−0.0305148
$623$	1.49760	0.0600002
$624$	1.92075	0.0768916
$625$	7.16114	0.286445
$626$	4.29293	0.171580
$627$	−17.9752	−0.717860
$628$	18.7916	0.749867
$629$	−1.45712	−0.0580990
$630$	0.394141	0.0157030
$631$	38.2230	1.52164	0.760818	−	0.648966i	$-0.224798\pi$
$631$	38.2230	1.52164	0.760818	+	0.648966i	$0.224798\pi$
$632$	30.6534	1.21933
$633$	−12.1934	−0.484644
$634$	0.538545	0.0213883
$635$	16.9594	0.673013
$636$	−16.0528	−0.636534
$637$	6.96929	0.276133
$638$	6.13896	0.243044
$639$	1.97036	0.0779462
$640$	−42.3159	−1.67268
$641$	−34.6774	−1.36967	−0.684837	−	0.728696i	$-0.740127\pi$
$641$	−34.6774	−1.36967	−0.684837	+	0.728696i	$0.740127\pi$
$642$	−7.56518	−0.298574
$643$	−15.4502	−0.609295	−0.304647	−	0.952465i	$-0.598539\pi$
$643$	−15.4502	−0.609295	−0.304647	+	0.952465i	$0.598539\pi$
$644$	0.532005	0.0209639
$645$	−11.7318	−0.461939
$646$	4.83810	0.190353
$647$	22.5870	0.887987	0.443993	−	0.896030i	$-0.353561\pi$
$647$	22.5870	0.887987	0.443993	+	0.896030i	$0.353561\pi$
$648$	2.20630	0.0866717
$649$	−1.81968	−0.0714287
$650$	5.28535	0.207309
$651$	1.64991	0.0646649
$652$	−25.2294	−0.988060
$653$	38.9665	1.52488	0.762438	−	0.647061i	$-0.224002\pi$
$653$	38.9665	1.52488	0.762438	+	0.647061i	$0.224002\pi$
$654$	−9.61482	−0.375969
$655$	−42.2998	−1.65279
$656$	−21.8570	−0.853374
$657$	−15.3900	−0.600420
$658$	0.00684867	0.000266989 0
$659$	−16.4608	−0.641220	−0.320610	−	0.947211i	$-0.603888\pi$
$659$	−16.4608	−0.641220	−0.320610	+	0.947211i	$0.603888\pi$
$660$	14.5485	0.566300
$661$	0.614700	0.0239091	0.0119545	−	0.999929i	$-0.496195\pi$
$661$	0.614700	0.0239091	0.0119545	+	0.999929i	$0.496195\pi$
$662$	−18.8883	−0.734113
$663$	1.06768	0.0414654
$664$	−10.0347	−0.389422
$665$	4.83663	0.187556
$666$	0.829320	0.0321355
$667$	−7.80165	−0.302081
$668$	20.7851	0.804201
$669$	17.3568	0.671054
$670$	−15.4613	−0.597323
$671$	21.1360	0.815945
$672$	0.977859	0.0377217
$673$	5.40825	0.208473	0.104236	−	0.994553i	$-0.466760\pi$
$673$	5.40825	0.208473	0.104236	+	0.994553i	$0.466760\pi$
$674$	5.45475	0.210109
$675$	−8.69767	−0.334774
$676$	−1.63073	−0.0627205
$677$	44.1168	1.69555	0.847774	−	0.530358i	$-0.177942\pi$
$677$	44.1168	1.69555	0.847774	+	0.530358i	$0.177942\pi$
$678$	12.5871	0.483404
$679$	−2.24662	−0.0862173
$680$	−8.71829	−0.334331
$681$	−18.7074	−0.716871
$682$	−13.7906	−0.528071
$683$	11.4548	0.438307	0.219153	−	0.975690i	$-0.429671\pi$
$683$	11.4548	0.438307	0.219153	+	0.975690i	$0.429671\pi$
$684$	12.1603	0.464960
$685$	27.1943	1.03904
$686$	1.48766	0.0567990
$687$	7.20572	0.274915
$688$	−6.08853	−0.232123
$689$	9.84391	0.375023
$690$	4.18667	0.159384
$691$	−30.8570	−1.17385	−0.586927	−	0.809640i	$-0.699663\pi$
$691$	−30.8570	−1.17385	−0.586927	+	0.809640i	$0.699663\pi$
$692$	14.7000	0.558809
$693$	−0.422445	−0.0160474
$694$	−8.36910	−0.317687
$695$	−5.83611	−0.221376
$696$	−9.24648	−0.350487
$697$	−12.1496	−0.460200
$698$	0.761205	0.0288120
$699$	−13.7689	−0.520789
$700$	−2.48567	−0.0939495
$701$	−5.11953	−0.193362	−0.0966809	−	0.995315i	$-0.530823\pi$
$701$	−5.11953	−0.193362	−0.0966809	+	0.995315i	$0.530823\pi$
$702$	−0.607674	−0.0229352
$703$	10.1768	0.383827
$704$	1.08668	0.0409557
$705$	−0.238013	−0.00896409
$706$	−8.19479	−0.308415
$707$	0.193967	0.00729487
$708$	1.23102	0.0462646
$709$	27.2838	1.02466	0.512332	−	0.858787i	$-0.328782\pi$
$709$	27.2838	1.02466	0.512332	+	0.858787i	$0.328782\pi$
$710$	4.43138	0.166307
$711$	13.8936	0.521049
$712$	18.8540	0.706584
$713$	17.5257	0.656344
$714$	0.113703	0.00425522
$715$	−8.92145	−0.333643
$716$	22.7233	0.849210
$717$	−14.3537	−0.536047
$718$	13.4410	0.501614
$719$	36.4810	1.36051	0.680255	−	0.732975i	$-0.261869\pi$
$719$	36.4810	1.36051	0.680255	+	0.732975i	$0.261869\pi$
$720$	−7.10877	−0.264928
$721$	0.175250	0.00652665
$722$	−22.2446	−0.827859
$723$	−5.89301	−0.219163
$724$	−23.0305	−0.855922
$725$	36.4514	1.35377
$726$	−3.15344	−0.117035
$727$	26.0379	0.965691	0.482846	−	0.875705i	$-0.339603\pi$
$727$	26.0379	0.965691	0.482846	+	0.875705i	$0.339603\pi$
$728$	−0.386654	−0.0143304
$729$	1.00000	0.0370370
$730$	−34.6124	−1.28106
$731$	−3.38442	−0.125177
$732$	−14.2986	−0.528490
$733$	−4.08545	−0.150900	−0.0754498	−	0.997150i	$-0.524039\pi$
$733$	−4.08545	−0.150900	−0.0754498	+	0.997150i	$0.524039\pi$
$734$	2.01097	0.0742264
$735$	−25.7936	−0.951411
$736$	10.3871	0.382873
$737$	16.5716	0.610423
$738$	6.91498	0.254544
$739$	−19.5835	−0.720391	−0.360196	−	0.932877i	$-0.617290\pi$
$739$	−19.5835	−0.720391	−0.360196	+	0.932877i	$0.617290\pi$
$740$	−8.23678	−0.302790
$741$	−7.45695	−0.273938
$742$	1.04833	0.0384853
$743$	−7.32203	−0.268619	−0.134310	−	0.990939i	$-0.542882\pi$
$743$	−7.32203	−0.268619	−0.134310	+	0.990939i	$0.542882\pi$
$744$	20.7714	0.761518
$745$	8.83114	0.323548
$746$	16.5531	0.606053
$747$	−4.54820	−0.166410
$748$	4.19699	0.153457
$749$	−2.18176	−0.0797196
$750$	−8.31615	−0.303663
$751$	37.1493	1.35560	0.677799	−	0.735247i	$-0.262934\pi$
$751$	37.1493	1.35560	0.677799	+	0.735247i	$0.262934\pi$
$752$	−0.123523	−0.00450443
$753$	19.6320	0.715429
$754$	2.54673	0.0927463
$755$	31.1366	1.13318
$756$	0.285786	0.0103939
$757$	20.3654	0.740194	0.370097	−	0.928993i	$-0.379325\pi$
$757$	20.3654	0.740194	0.370097	+	0.928993i	$0.379325\pi$
$758$	18.5461	0.673624
$759$	−4.48732	−0.162879
$760$	60.8905	2.20873
$761$	40.4009	1.46453	0.732266	−	0.681019i	$-0.238463\pi$
$761$	40.4009	1.46453	0.732266	+	0.681019i	$0.238463\pi$
$762$	−2.78457	−0.100874
$763$	−2.77286	−0.100384
$764$	−21.7887	−0.788289
$765$	−3.95154	−0.142868
$766$	1.42150	0.0513609
$767$	−0.754889	−0.0272574
$768$	6.04625	0.218175
$769$	−25.1602	−0.907301	−0.453651	−	0.891180i	$-0.649879\pi$
$769$	−25.1602	−0.907301	−0.453651	+	0.891180i	$0.649879\pi$
$770$	−0.950089	−0.0342388
$771$	−15.0363	−0.541520
$772$	−17.6188	−0.634113
$773$	27.7781	0.999110	0.499555	−	0.866282i	$-0.333497\pi$
$773$	27.7781	0.999110	0.499555	+	0.866282i	$0.333497\pi$
$774$	1.92625	0.0692376
$775$	−81.8850	−2.94140
$776$	−28.2837	−1.01533
$777$	0.239171	0.00858023
$778$	16.2770	0.583558
$779$	84.8558	3.04027
$780$	6.03540	0.216102
$781$	−4.74960	−0.169954
$782$	1.20778	0.0431902
$783$	−4.19094	−0.149772
$784$	−13.3863	−0.478081
$785$	42.6486	1.52219
$786$	6.94522	0.247728
$787$	5.85605	0.208745	0.104373	−	0.994538i	$-0.466717\pi$
$787$	5.85605	0.208745	0.104373	+	0.994538i	$0.466717\pi$
$788$	17.4748	0.622513
$789$	−13.1642	−0.468656
$790$	31.2470	1.11172
$791$	3.63005	0.129070
$792$	−5.31835	−0.188979
$793$	8.76819	0.311368
$794$	5.70207	0.202359
$795$	−36.4327	−1.29213
$796$	2.29111	0.0812062
$797$	47.5074	1.68280	0.841400	−	0.540414i	$-0.181732\pi$
$797$	47.5074	1.68280	0.841400	+	0.540414i	$0.181732\pi$
$798$	−0.794127	−0.0281118
$799$	−0.0686626	−0.00242911
$800$	−48.5312	−1.71584
$801$	8.54553	0.301941
$802$	0.529658	0.0187029
$803$	37.0980	1.30916
$804$	−11.2108	−0.395373
$805$	1.20741	0.0425558
$806$	−5.72100	−0.201514
$807$	6.16484	0.217013
$808$	2.44194	0.0859070
$809$	−38.7893	−1.36376	−0.681879	−	0.731465i	$-0.738837\pi$
$809$	−38.7893	−1.36376	−0.681879	+	0.731465i	$0.738837\pi$
$810$	2.24902	0.0790227
$811$	17.6912	0.621223	0.310612	−	0.950537i	$-0.399466\pi$
$811$	17.6912	0.621223	0.310612	+	0.950537i	$0.399466\pi$
$812$	−1.19771	−0.0420314
$813$	−18.2669	−0.640650
$814$	−1.99910	−0.0700684
$815$	−57.2596	−2.00572
$816$	−2.05076	−0.0717908
$817$	23.6376	0.826974
$818$	13.0333	0.455699
$819$	−0.175250	−0.00612373
$820$	−68.6793	−2.39839
$821$	4.22481	0.147447	0.0737235	−	0.997279i	$-0.476512\pi$
$821$	4.22481	0.147447	0.0737235	+	0.997279i	$0.476512\pi$
$822$	−4.46504	−0.155736
$823$	41.0154	1.42971	0.714853	−	0.699275i	$-0.246494\pi$
$823$	41.0154	1.42971	0.714853	+	0.699275i	$0.246494\pi$
$824$	2.20630	0.0768602
$825$	20.9660	0.729942
$826$	−0.0803918	−0.00279719
$827$	22.2323	0.773092	0.386546	−	0.922270i	$-0.373668\pi$
$827$	22.2323	0.773092	0.386546	+	0.922270i	$0.373668\pi$
$828$	3.03569	0.105498
$829$	−40.5849	−1.40957	−0.704786	−	0.709420i	$-0.748957\pi$
$829$	−40.5849	−1.40957	−0.704786	+	0.709420i	$0.748957\pi$
$830$	−10.2290	−0.355054
$831$	16.7393	0.580680
$832$	0.450805	0.0156288
$833$	−7.44100	−0.257815
$834$	0.958233	0.0331809
$835$	47.1730	1.63249
$836$	−29.3127	−1.01380
$837$	9.41459	0.325416
$838$	−1.03596	−0.0357867
$839$	4.42025	0.152604	0.0763020	−	0.997085i	$-0.475689\pi$
$839$	4.42025	0.152604	0.0763020	+	0.997085i	$0.475689\pi$
$840$	1.43102	0.0493749
$841$	−11.4360	−0.394346
$842$	−10.0143	−0.345117
$843$	−10.7868	−0.371518
$844$	−19.8842	−0.684441
$845$	−3.70104	−0.127320
$846$	0.0390794	0.00134358
$847$	−0.909434	−0.0312485
$848$	−18.9077	−0.649293
$849$	1.56963	0.0538696
$850$	−5.64309	−0.193556
$851$	2.54054	0.0870887
$852$	3.21313	0.110080
$853$	5.67326	0.194249	0.0971244	−	0.995272i	$-0.469036\pi$
$853$	5.67326	0.194249	0.0971244	+	0.995272i	$0.469036\pi$
$854$	0.933767	0.0319529
$855$	27.5985	0.943847
$856$	−27.4671	−0.938807
$857$	−20.8763	−0.713122	−0.356561	−	0.934272i	$-0.616051\pi$
$857$	−20.8763	−0.713122	−0.356561	+	0.934272i	$0.616051\pi$
$858$	1.46482	0.0500080
$859$	46.4262	1.58404	0.792021	−	0.610494i	$-0.209029\pi$
$859$	46.4262	1.58404	0.792021	+	0.610494i	$0.209029\pi$
$860$	−19.1314	−0.652376
$861$	1.99424	0.0679636
$862$	−9.71061	−0.330745
$863$	25.9442	0.883150	0.441575	−	0.897224i	$-0.354420\pi$
$863$	25.9442	0.883150	0.441575	+	0.897224i	$0.354420\pi$
$864$	5.57980	0.189828
$865$	33.3624	1.13436
$866$	23.4152	0.795683
$867$	15.8601	0.538636
$868$	2.69056	0.0913234
$869$	−33.4908	−1.13610
$870$	−9.42553	−0.319555
$871$	6.87468	0.232940
$872$	−34.9088	−1.18216
$873$	−12.8195	−0.433875
$874$	−8.43543	−0.285333
$875$	−2.39833	−0.0810785
$876$	−25.0969	−0.847947
$877$	−7.13026	−0.240772	−0.120386	−	0.992727i	$-0.538413\pi$
$877$	−7.13026	−0.240772	−0.120386	+	0.992727i	$0.538413\pi$
$878$	1.31782	0.0444742
$879$	20.4401	0.689428
$880$	17.1359	0.577651
$881$	−45.0251	−1.51694	−0.758468	−	0.651711i	$-0.774052\pi$
$881$	−45.0251	−1.51694	−0.758468	+	0.651711i	$0.774052\pi$
$882$	4.23506	0.142602
$883$	10.3553	0.348485	0.174242	−	0.984703i	$-0.444252\pi$
$883$	10.3553	0.348485	0.174242	+	0.984703i	$0.444252\pi$
$884$	1.74111	0.0585598
$885$	2.79387	0.0939149
$886$	−12.5888	−0.422929
$887$	−32.1826	−1.08059	−0.540293	−	0.841477i	$-0.681687\pi$
$887$	−32.1826	−1.08059	−0.540293	+	0.841477i	$0.681687\pi$
$888$	3.01104	0.101044
$889$	−0.803054	−0.0269336
$890$	19.2191	0.644226
$891$	−2.41053	−0.0807557
$892$	28.3043	0.947699
$893$	0.479556	0.0160477
$894$	−1.44999	−0.0484948
$895$	51.5718	1.72386
$896$	2.00373	0.0669398
$897$	−1.86155	−0.0621554
$898$	−23.9106	−0.797907
$899$	−39.4560	−1.31593
$900$	−14.1836	−0.472786
$901$	−10.5102	−0.350145
$902$	−16.6688	−0.555009
$903$	0.555519	0.0184865
$904$	45.7003	1.51997
$905$	−52.2690	−1.73748
$906$	−5.11233	−0.169846
$907$	−10.3838	−0.344790	−0.172395	−	0.985028i	$-0.555151\pi$
$907$	−10.3838	−0.344790	−0.172395	+	0.985028i	$0.555151\pi$
$908$	−30.5068	−1.01240
$909$	1.10680	0.0367103
$910$	−0.394141	−0.0130657
$911$	32.3724	1.07255	0.536273	−	0.844044i	$-0.319832\pi$
$911$	32.3724	1.07255	0.536273	+	0.844044i	$0.319832\pi$
$912$	14.3230	0.474280
$913$	10.9636	0.362841
$914$	−14.6473	−0.484491
$915$	−32.4514	−1.07281
$916$	11.7506	0.388250
$917$	2.00296	0.0661437
$918$	0.648804	0.0214137
$919$	40.1853	1.32559	0.662795	−	0.748801i	$-0.269370\pi$
$919$	40.1853	1.32559	0.662795	+	0.748801i	$0.269370\pi$
$920$	15.2007	0.501152
$921$	−22.9313	−0.755613
$922$	−0.216060	−0.00711555
$923$	−1.97036	−0.0648551
$924$	−0.688894	−0.0226630
$925$	−11.8701	−0.390287
$926$	0.960164	0.0315530
$927$	1.00000	0.0328443
$928$	−23.3846	−0.767637
$929$	−0.0358157	−0.00117507	−0.000587537	−	1.00000i	$-0.500187\pi$
$929$	−0.0358157	−0.00117507	−0.000587537		1.00000i	$0.500187\pi$
$930$	21.1736	0.694311
$931$	51.9697	1.70324
$932$	−22.4535	−0.735487
$933$	−1.25238	−0.0410010
$934$	2.10320	0.0688189
$935$	9.52529	0.311510
$936$	−2.20630	−0.0721152
$937$	−27.9085	−0.911730	−0.455865	−	0.890049i	$-0.650670\pi$
$937$	−27.9085	−0.911730	−0.455865	+	0.890049i	$0.650670\pi$
$938$	0.732118	0.0239045
$939$	7.06452	0.230542
$940$	−0.388136	−0.0126596
$941$	−28.6279	−0.933244	−0.466622	−	0.884457i	$-0.654529\pi$
$941$	−28.6279	−0.933244	−0.466622	+	0.884457i	$0.654529\pi$
$942$	−7.00249	−0.228153
$943$	21.1834	0.689826
$944$	1.44995	0.0471920
$945$	0.648606	0.0210992
$946$	−4.64328	−0.150966
$947$	−45.5261	−1.47940	−0.739700	−	0.672937i	$-0.765033\pi$
$947$	−45.5261	−1.47940	−0.739700	+	0.672937i	$0.765033\pi$
$948$	22.6567	0.735855
$949$	15.3900	0.499580
$950$	39.4126	1.27871
$951$	0.886239	0.0287383
$952$	0.412825	0.0133797
$953$	−4.25942	−0.137976	−0.0689880	−	0.997617i	$-0.521977\pi$
$953$	−4.25942	−0.137976	−0.0689880	+	0.997617i	$0.521977\pi$
$954$	5.98189	0.193671
$955$	−49.4507	−1.60019
$956$	−23.4070	−0.757036
$957$	10.1024	0.326564
$958$	19.0003	0.613871
$959$	−1.28769	−0.0415818
$960$	−1.66844	−0.0538488
$961$	57.6345	1.85918
$962$	−0.829320	−0.0267384
$963$	−12.4494	−0.401176
$964$	−9.60991	−0.309515
$965$	−39.9868	−1.28722
$966$	−0.198246	−0.00637845
$967$	−57.3345	−1.84375	−0.921876	−	0.387485i	$-0.873344\pi$
$967$	−57.3345	−1.84375	−0.921876	+	0.387485i	$0.873344\pi$
$968$	−11.4493	−0.367994
$969$	7.96167	0.255766
$970$	−28.8314	−0.925720
$971$	−46.6378	−1.49668	−0.748339	−	0.663317i	$-0.769148\pi$
$971$	−46.6378	−1.49668	−0.748339	+	0.663317i	$0.769148\pi$
$972$	1.63073	0.0523058
$973$	0.276349	0.00885935
$974$	−13.1017	−0.419806
$975$	8.69767	0.278548
$976$	−16.8415	−0.539084
$977$	−58.8977	−1.88431	−0.942153	−	0.335184i	$-0.891202\pi$
$977$	−58.8977	−1.88431	−0.942153	+	0.335184i	$0.891202\pi$
$978$	9.40146	0.300626
$979$	−20.5992	−0.658354
$980$	−42.0624	−1.34364
$981$	−15.8223	−0.505168
$982$	16.7968	0.536007
$983$	40.6002	1.29495	0.647473	−	0.762089i	$-0.275826\pi$
$983$	40.6002	1.29495	0.647473	+	0.762089i	$0.275826\pi$
$984$	25.1064	0.800364
$985$	39.6600	1.26367
$986$	−2.71910	−0.0865938
$987$	0.0112703	0.000358738 0
$988$	−12.1603	−0.386870
$989$	5.90088	0.187637
$990$	−5.42134	−0.172301
$991$	−21.6351	−0.687263	−0.343632	−	0.939105i	$-0.611657\pi$
$991$	−21.6351	−0.687263	−0.343632	+	0.939105i	$0.611657\pi$
$992$	52.5315	1.66788
$993$	−31.0829	−0.986386
$994$	−0.209833	−0.00665550
$995$	5.19980	0.164845
$996$	−7.41689	−0.235013
$997$	13.7556	0.435643	0.217822	−	0.975989i	$-0.430105\pi$
$997$	13.7556	0.435643	0.217822	+	0.975989i	$0.430105\pi$
$998$	−3.07863	−0.0974522
$999$	1.36475	0.0431786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.9	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.607674 q^{2} -1.00000 q^{3} -1.63073 q^{4} -3.70104 q^{5} +0.607674 q^{6} +0.175250 q^{7} +2.20630 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.607674 q^{2} -1.00000 q^{3} -1.63073 q^{4} -3.70104 q^{5} +0.607674 q^{6} +0.175250 q^{7} +2.20630 q^{8} +1.00000 q^{9} +2.24902 q^{10} -2.41053 q^{11} +1.63073 q^{12} -1.00000 q^{13} -0.106495 q^{14} +3.70104 q^{15} +1.92075 q^{16} +1.06768 q^{17} -0.607674 q^{18} -7.45695 q^{19} +6.03540 q^{20} -0.175250 q^{21} +1.46482 q^{22} -1.86155 q^{23} -2.20630 q^{24} +8.69767 q^{25} +0.607674 q^{26} -1.00000 q^{27} -0.285786 q^{28} +4.19094 q^{29} -2.24902 q^{30} -9.41459 q^{31} -5.57980 q^{32} +2.41053 q^{33} -0.648804 q^{34} -0.648606 q^{35} -1.63073 q^{36} -1.36475 q^{37} +4.53140 q^{38} +1.00000 q^{39} -8.16561 q^{40} -11.3794 q^{41} +0.106495 q^{42} -3.16987 q^{43} +3.93093 q^{44} -3.70104 q^{45} +1.13122 q^{46} -0.0643099 q^{47} -1.92075 q^{48} -6.96929 q^{49} -5.28535 q^{50} -1.06768 q^{51} +1.63073 q^{52} -9.84391 q^{53} +0.607674 q^{54} +8.92145 q^{55} +0.386654 q^{56} +7.45695 q^{57} -2.54673 q^{58} +0.754889 q^{59} -6.03540 q^{60} -8.76819 q^{61} +5.72100 q^{62} +0.175250 q^{63} -0.450805 q^{64} +3.70104 q^{65} -1.46482 q^{66} -6.87468 q^{67} -1.74111 q^{68} +1.86155 q^{69} +0.394141 q^{70} +1.97036 q^{71} +2.20630 q^{72} -15.3900 q^{73} +0.829320 q^{74} -8.69767 q^{75} +12.1603 q^{76} -0.422445 q^{77} -0.607674 q^{78} +13.8936 q^{79} -7.10877 q^{80} +1.00000 q^{81} +6.91498 q^{82} -4.54820 q^{83} +0.285786 q^{84} -3.95154 q^{85} +1.92625 q^{86} -4.19094 q^{87} -5.31835 q^{88} +8.54553 q^{89} +2.24902 q^{90} -0.175250 q^{91} +3.03569 q^{92} +9.41459 q^{93} +0.0390794 q^{94} +27.5985 q^{95} +5.57980 q^{96} -12.8195 q^{97} +4.23506 q^{98} -2.41053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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