LMFDB - Embedded newform 4017.2.a.j.1.7

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:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +0.645786 q^{10} -1.77709 q^{11} +0.372378 q^{12} +1.00000 q^{13} +3.89444 q^{14} +0.506188 q^{15} -3.11658 q^{16} -3.59426 q^{17} -1.27578 q^{18} -0.715310 q^{19} +0.188493 q^{20} +3.05259 q^{21} +2.26719 q^{22} -0.238375 q^{23} -3.02664 q^{24} -4.74377 q^{25} -1.27578 q^{26} -1.00000 q^{27} +1.13672 q^{28} +2.95446 q^{29} -0.645786 q^{30} +0.136135 q^{31} -2.07720 q^{32} +1.77709 q^{33} +4.58550 q^{34} +1.54518 q^{35} -0.372378 q^{36} +5.90568 q^{37} +0.912581 q^{38} -1.00000 q^{39} -1.53205 q^{40} -5.81439 q^{41} -3.89444 q^{42} -2.36383 q^{43} +0.661750 q^{44} -0.506188 q^{45} +0.304115 q^{46} -7.27479 q^{47} +3.11658 q^{48} +2.31830 q^{49} +6.05203 q^{50} +3.59426 q^{51} -0.372378 q^{52} -4.12441 q^{53} +1.27578 q^{54} +0.899543 q^{55} -9.23908 q^{56} +0.715310 q^{57} -3.76926 q^{58} -4.06634 q^{59} -0.188493 q^{60} -3.05264 q^{61} -0.173679 q^{62} -3.05259 q^{63} +8.88321 q^{64} -0.506188 q^{65} -2.26719 q^{66} +12.3054 q^{67} +1.33842 q^{68} +0.238375 q^{69} -1.97132 q^{70} +6.06837 q^{71} +3.02664 q^{72} -13.9094 q^{73} -7.53436 q^{74} +4.74377 q^{75} +0.266366 q^{76} +5.42473 q^{77} +1.27578 q^{78} -10.1863 q^{79} +1.57758 q^{80} +1.00000 q^{81} +7.41791 q^{82} +1.65318 q^{83} -1.13672 q^{84} +1.81937 q^{85} +3.01574 q^{86} -2.95446 q^{87} -5.37862 q^{88} -12.4282 q^{89} +0.645786 q^{90} -3.05259 q^{91} +0.0887656 q^{92} -0.136135 q^{93} +9.28105 q^{94} +0.362082 q^{95} +2.07720 q^{96} -15.8471 q^{97} -2.95764 q^{98} -1.77709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.27578	−0.902115	−0.451057	−	0.892495i	$-0.648953\pi$
$2$	−1.27578	−0.902115	−0.451057	+	0.892495i	$0.648953\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.372378	−0.186189
$5$	−0.506188	−0.226374	−0.113187	−	0.993574i	$-0.536106\pi$
$5$	−0.506188	−0.226374	−0.113187	+	0.993574i	$0.536106\pi$
$6$	1.27578	0.520836
$7$	−3.05259	−1.15377	−0.576885	−	0.816825i	$-0.695732\pi$
$7$	−3.05259	−1.15377	−0.576885	+	0.816825i	$0.695732\pi$
$8$	3.02664	1.07008
$9$	1.00000	0.333333
$10$	0.645786	0.204215
$11$	−1.77709	−0.535814	−0.267907	−	0.963445i	$-0.586332\pi$
$11$	−1.77709	−0.535814	−0.267907	+	0.963445i	$0.586332\pi$
$12$	0.372378	0.107496
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.89444	1.04083
$15$	0.506188	0.130697
$16$	−3.11658	−0.779145
$17$	−3.59426	−0.871737	−0.435869	−	0.900010i	$-0.643559\pi$
$17$	−3.59426	−0.871737	−0.435869	+	0.900010i	$0.643559\pi$
$18$	−1.27578	−0.300705
$19$	−0.715310	−0.164103	−0.0820517	−	0.996628i	$-0.526147\pi$
$19$	−0.715310	−0.164103	−0.0820517	+	0.996628i	$0.526147\pi$
$20$	0.188493	0.0421483
$21$	3.05259	0.666129
$22$	2.26719	0.483365
$23$	−0.238375	−0.0497047	−0.0248523	−	0.999691i	$-0.507912\pi$
$23$	−0.238375	−0.0497047	−0.0248523	+	0.999691i	$0.507912\pi$
$24$	−3.02664	−0.617810
$25$	−4.74377	−0.948755
$26$	−1.27578	−0.250202
$27$	−1.00000	−0.192450
$28$	1.13672	0.214819
$29$	2.95446	0.548630	0.274315	−	0.961640i	$-0.411549\pi$
$29$	2.95446	0.548630	0.274315	+	0.961640i	$0.411549\pi$
$30$	−0.645786	−0.117904
$31$	0.136135	0.0244506	0.0122253	−	0.999925i	$-0.496108\pi$
$31$	0.136135	0.0244506	0.0122253	+	0.999925i	$0.496108\pi$
$32$	−2.07720	−0.367200
$33$	1.77709	0.309352
$34$	4.58550	0.786407
$35$	1.54518	0.261184
$36$	−0.372378	−0.0620629
$37$	5.90568	0.970887	0.485444	−	0.874268i	$-0.338658\pi$
$37$	5.90568	0.970887	0.485444	+	0.874268i	$0.338658\pi$
$38$	0.912581	0.148040
$39$	−1.00000	−0.160128
$40$	−1.53205	−0.242238
$41$	−5.81439	−0.908056	−0.454028	−	0.890987i	$-0.650013\pi$
$41$	−5.81439	−0.908056	−0.454028	+	0.890987i	$0.650013\pi$
$42$	−3.89444	−0.600925
$43$	−2.36383	−0.360481	−0.180241	−	0.983623i	$-0.557688\pi$
$43$	−2.36383	−0.360481	−0.180241	+	0.983623i	$0.557688\pi$
$44$	0.661750	0.0997625
$45$	−0.506188	−0.0754580
$46$	0.304115	0.0448393
$47$	−7.27479	−1.06114	−0.530568	−	0.847642i	$-0.678022\pi$
$47$	−7.27479	−1.06114	−0.530568	+	0.847642i	$0.678022\pi$
$48$	3.11658	0.449840
$49$	2.31830	0.331185
$50$	6.05203	0.855886
$51$	3.59426	0.503298
$52$	−0.372378	−0.0516395
$53$	−4.12441	−0.566531	−0.283266	−	0.959041i	$-0.591418\pi$
$53$	−4.12441	−0.566531	−0.283266	+	0.959041i	$0.591418\pi$
$54$	1.27578	0.173612
$55$	0.899543	0.121294
$56$	−9.23908	−1.23462
$57$	0.715310	0.0947452
$58$	−3.76926	−0.494927
$59$	−4.06634	−0.529392	−0.264696	−	0.964332i	$-0.585272\pi$
$59$	−4.06634	−0.529392	−0.264696	+	0.964332i	$0.585272\pi$
$60$	−0.188493	−0.0243343
$61$	−3.05264	−0.390850	−0.195425	−	0.980719i	$-0.562609\pi$
$61$	−3.05264	−0.390850	−0.195425	+	0.980719i	$0.562609\pi$
$62$	−0.173679	−0.0220573
$63$	−3.05259	−0.384590
$64$	8.88321	1.11040
$65$	−0.506188	−0.0627849
$66$	−2.26719	−0.279071
$67$	12.3054	1.50335	0.751673	−	0.659536i	$-0.229247\pi$
$67$	12.3054	1.50335	0.751673	+	0.659536i	$0.229247\pi$
$68$	1.33842	0.162308
$69$	0.238375	0.0286970
$70$	−1.97132	−0.235618
$71$	6.06837	0.720183	0.360091	−	0.932917i	$-0.382746\pi$
$71$	6.06837	0.720183	0.360091	+	0.932917i	$0.382746\pi$
$72$	3.02664	0.356693
$73$	−13.9094	−1.62797	−0.813984	−	0.580888i	$-0.802705\pi$
$73$	−13.9094	−1.62797	−0.813984	+	0.580888i	$0.802705\pi$
$74$	−7.53436	−0.875852
$75$	4.74377	0.547764
$76$	0.266366	0.0305542
$77$	5.42473	0.618206
$78$	1.27578	0.144454
$79$	−10.1863	−1.14605	−0.573027	−	0.819537i	$-0.694231\pi$
$79$	−10.1863	−1.14605	−0.573027	+	0.819537i	$0.694231\pi$
$80$	1.57758	0.176378
$81$	1.00000	0.111111
$82$	7.41791	0.819171
$83$	1.65318	0.181460	0.0907298	−	0.995876i	$-0.471080\pi$
$83$	1.65318	0.181460	0.0907298	+	0.995876i	$0.471080\pi$
$84$	−1.13672	−0.124026
$85$	1.81937	0.197339
$86$	3.01574	0.325196
$87$	−2.95446	−0.316752
$88$	−5.37862	−0.573363
$89$	−12.4282	−1.31739	−0.658693	−	0.752412i	$-0.728890\pi$
$89$	−12.4282	−1.31739	−0.658693	+	0.752412i	$0.728890\pi$
$90$	0.645786	0.0680718
$91$	−3.05259	−0.319998
$92$	0.0887656	0.00925445
$93$	−0.136135	−0.0141166
$94$	9.28105	0.957267
$95$	0.362082	0.0371488
$96$	2.07720	0.212003
$97$	−15.8471	−1.60903	−0.804515	−	0.593933i	$-0.797575\pi$
$97$	−15.8471	−1.60903	−0.804515	+	0.593933i	$0.797575\pi$
$98$	−2.95764	−0.298767
$99$	−1.77709	−0.178605
$100$	1.76648	0.176648
$101$	−3.35478	−0.333814	−0.166907	−	0.985973i	$-0.553378\pi$
$101$	−3.35478	−0.333814	−0.166907	+	0.985973i	$0.553378\pi$
$102$	−4.58550	−0.454032
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	3.02664	0.296786
$105$	−1.54518	−0.150794
$106$	5.26185	0.511076
$107$	17.7894	1.71977	0.859883	−	0.510492i	$-0.170537\pi$
$107$	17.7894	1.71977	0.859883	+	0.510492i	$0.170537\pi$
$108$	0.372378	0.0358321
$109$	−16.2712	−1.55849	−0.779247	−	0.626717i	$-0.784398\pi$
$109$	−16.2712	−1.55849	−0.779247	+	0.626717i	$0.784398\pi$
$110$	−1.14762	−0.109421
$111$	−5.90568	−0.560542
$112$	9.51363	0.898954
$113$	−0.902316	−0.0848827	−0.0424414	−	0.999099i	$-0.513514\pi$
$113$	−0.902316	−0.0848827	−0.0424414	+	0.999099i	$0.513514\pi$
$114$	−0.912581	−0.0854710
$115$	0.120663	0.0112519
$116$	−1.10018	−0.102149
$117$	1.00000	0.0924500
$118$	5.18777	0.477573
$119$	10.9718	1.00578
$120$	1.53205	0.139856
$121$	−7.84194	−0.712904
$122$	3.89450	0.352592
$123$	5.81439	0.524266
$124$	−0.0506938	−0.00455243
$125$	4.93218	0.441148
$126$	3.89444	0.346944
$127$	−18.5786	−1.64858	−0.824290	−	0.566168i	$-0.808425\pi$
$127$	−18.5786	−1.64858	−0.824290	+	0.566168i	$0.808425\pi$
$128$	−7.17866	−0.634510
$129$	2.36383	0.208124
$130$	0.645786	0.0566392
$131$	−7.85737	−0.686501	−0.343251	−	0.939244i	$-0.611528\pi$
$131$	−7.85737	−0.686501	−0.343251	+	0.939244i	$0.611528\pi$
$132$	−0.661750	−0.0575979
$133$	2.18355	0.189338
$134$	−15.6990	−1.35619
$135$	0.506188	0.0435657
$136$	−10.8785	−0.932827
$137$	14.1353	1.20766	0.603829	−	0.797114i	$-0.293641\pi$
$137$	14.1353	1.20766	0.603829	+	0.797114i	$0.293641\pi$
$138$	−0.304115	−0.0258880
$139$	16.7119	1.41748	0.708742	−	0.705468i	$-0.249263\pi$
$139$	16.7119	1.41748	0.708742	+	0.705468i	$0.249263\pi$
$140$	−0.575392	−0.0486295
$141$	7.27479	0.612648
$142$	−7.74192	−0.649687
$143$	−1.77709	−0.148608
$144$	−3.11658	−0.259715
$145$	−1.49551	−0.124196
$146$	17.7453	1.46861
$147$	−2.31830	−0.191210
$148$	−2.19914	−0.180768
$149$	1.64008	0.134361	0.0671803	−	0.997741i	$-0.478600\pi$
$149$	1.64008	0.134361	0.0671803	+	0.997741i	$0.478600\pi$
$150$	−6.05203	−0.494146
$151$	−3.05639	−0.248726	−0.124363	−	0.992237i	$-0.539689\pi$
$151$	−3.05639	−0.248726	−0.124363	+	0.992237i	$0.539689\pi$
$152$	−2.16499	−0.175604
$153$	−3.59426	−0.290579
$154$	−6.92078	−0.557693
$155$	−0.0689101	−0.00553499
$156$	0.372378	0.0298141
$157$	8.64949	0.690304	0.345152	−	0.938547i	$-0.387827\pi$
$157$	8.64949	0.690304	0.345152	+	0.938547i	$0.387827\pi$
$158$	12.9956	1.03387
$159$	4.12441	0.327087
$160$	1.05145	0.0831247
$161$	0.727661	0.0573477
$162$	−1.27578	−0.100235
$163$	16.6605	1.30495	0.652474	−	0.757811i	$-0.273731\pi$
$163$	16.6605	1.30495	0.652474	+	0.757811i	$0.273731\pi$
$164$	2.16515	0.169070
$165$	−0.899543	−0.0700293
$166$	−2.10909	−0.163697
$167$	18.1176	1.40198	0.700989	−	0.713172i	$-0.252742\pi$
$167$	18.1176	1.40198	0.700989	+	0.713172i	$0.252742\pi$
$168$	9.23908	0.712811
$169$	1.00000	0.0769231
$170$	−2.32113	−0.178022
$171$	−0.715310	−0.0547012
$172$	0.880239	0.0671176
$173$	−7.61457	−0.578925	−0.289462	−	0.957189i	$-0.593477\pi$
$173$	−7.61457	−0.578925	−0.289462	+	0.957189i	$0.593477\pi$
$174$	3.76926	0.285746
$175$	14.4808	1.09464
$176$	5.53845	0.417477
$177$	4.06634	0.305645
$178$	15.8557	1.18843
$179$	20.9646	1.56696	0.783482	−	0.621414i	$-0.213442\pi$
$179$	20.9646	1.56696	0.783482	+	0.621414i	$0.213442\pi$
$180$	0.188493	0.0140494
$181$	−14.2964	−1.06264	−0.531321	−	0.847171i	$-0.678304\pi$
$181$	−14.2964	−1.06264	−0.531321	+	0.847171i	$0.678304\pi$
$182$	3.89444	0.288675
$183$	3.05264	0.225657
$184$	−0.721476	−0.0531879
$185$	−2.98938	−0.219784
$186$	0.173679	0.0127348
$187$	6.38734	0.467089
$188$	2.70897	0.197572
$189$	3.05259	0.222043
$190$	−0.461937	−0.0335125
$191$	2.42083	0.175165	0.0875824	−	0.996157i	$-0.472086\pi$
$191$	2.42083	0.175165	0.0875824	+	0.996157i	$0.472086\pi$
$192$	−8.88321	−0.641091
$193$	−5.40273	−0.388897	−0.194449	−	0.980913i	$-0.562292\pi$
$193$	−5.40273	−0.388897	−0.194449	+	0.980913i	$0.562292\pi$
$194$	20.2175	1.45153
$195$	0.506188	0.0362489
$196$	−0.863281	−0.0616629
$197$	19.6801	1.40215	0.701073	−	0.713089i	$-0.252705\pi$
$197$	19.6801	1.40215	0.701073	+	0.713089i	$0.252705\pi$
$198$	2.26719	0.161122
$199$	−17.2785	−1.22484	−0.612422	−	0.790531i	$-0.709805\pi$
$199$	−17.2785	−1.22484	−0.612422	+	0.790531i	$0.709805\pi$
$200$	−14.3577	−1.01524
$201$	−12.3054	−0.867957
$202$	4.27998	0.301138
$203$	−9.01876	−0.632993
$204$	−1.33842	−0.0937084
$205$	2.94318	0.205560
$206$	1.27578	0.0888880
$207$	−0.238375	−0.0165682
$208$	−3.11658	−0.216096
$209$	1.27117	0.0879289
$210$	1.97132	0.136034
$211$	15.3626	1.05760	0.528802	−	0.848745i	$-0.322641\pi$
$211$	15.3626	1.05760	0.528802	+	0.848745i	$0.322641\pi$
$212$	1.53584	0.105482
$213$	−6.06837	−0.415798
$214$	−22.6954	−1.55143
$215$	1.19654	0.0816037
$216$	−3.02664	−0.205937
$217$	−0.415565	−0.0282104
$218$	20.7585	1.40594
$219$	13.9094	0.939907
$220$	−0.334970	−0.0225837
$221$	−3.59426	−0.241776
$222$	7.53436	0.505673
$223$	17.5213	1.17332	0.586658	−	0.809835i	$-0.300443\pi$
$223$	17.5213	1.17332	0.586658	+	0.809835i	$0.300443\pi$
$224$	6.34083	0.423665
$225$	−4.74377	−0.316252
$226$	1.15116	0.0765740
$227$	−24.0192	−1.59421	−0.797104	−	0.603842i	$-0.793636\pi$
$227$	−24.0192	−1.59421	−0.797104	+	0.603842i	$0.793636\pi$
$228$	−0.266366	−0.0176405
$229$	−2.09099	−0.138177	−0.0690884	−	0.997611i	$-0.522009\pi$
$229$	−2.09099	−0.138177	−0.0690884	+	0.997611i	$0.522009\pi$
$230$	−0.153939	−0.0101505
$231$	−5.42473	−0.356921
$232$	8.94210	0.587077
$233$	−9.15311	−0.599640	−0.299820	−	0.953996i	$-0.596927\pi$
$233$	−9.15311	−0.599640	−0.299820	+	0.953996i	$0.596927\pi$
$234$	−1.27578	−0.0834005
$235$	3.68241	0.240214
$236$	1.51421	0.0985669
$237$	10.1863	0.661674
$238$	−13.9976	−0.907333
$239$	6.93850	0.448814	0.224407	−	0.974495i	$-0.427955\pi$
$239$	6.93850	0.448814	0.224407	+	0.974495i	$0.427955\pi$
$240$	−1.57758	−0.101832
$241$	26.6620	1.71745	0.858724	−	0.512438i	$-0.171258\pi$
$241$	26.6620	1.71745	0.858724	+	0.512438i	$0.171258\pi$
$242$	10.0046	0.643121
$243$	−1.00000	−0.0641500
$244$	1.13673	0.0727719
$245$	−1.17349	−0.0749717
$246$	−7.41791	−0.472948
$247$	−0.715310	−0.0455141
$248$	0.412033	0.0261641
$249$	−1.65318	−0.104766
$250$	−6.29239	−0.397966
$251$	13.4503	0.848978	0.424489	−	0.905433i	$-0.360454\pi$
$251$	13.4503	0.848978	0.424489	+	0.905433i	$0.360454\pi$
$252$	1.13672	0.0716063
$253$	0.423615	0.0266324
$254$	23.7022	1.48721
$255$	−1.81937	−0.113934
$256$	−8.60802	−0.538001
$257$	26.9808	1.68302	0.841509	−	0.540243i	$-0.181668\pi$
$257$	26.9808	1.68302	0.841509	+	0.540243i	$0.181668\pi$
$258$	−3.01574	−0.187752
$259$	−18.0276	−1.12018
$260$	0.188493	0.0116898
$261$	2.95446	0.182877
$262$	10.0243	0.619303
$263$	−5.11106	−0.315161	−0.157581	−	0.987506i	$-0.550369\pi$
$263$	−5.11106	−0.315161	−0.157581	+	0.987506i	$0.550369\pi$
$264$	5.37862	0.331031
$265$	2.08773	0.128248
$266$	−2.78573	−0.170804
$267$	12.4282	0.760593
$268$	−4.58226	−0.279906
$269$	−5.04937	−0.307865	−0.153933	−	0.988081i	$-0.549194\pi$
$269$	−5.04937	−0.307865	−0.153933	+	0.988081i	$0.549194\pi$
$270$	−0.645786	−0.0393013
$271$	−10.8978	−0.661996	−0.330998	−	0.943632i	$-0.607385\pi$
$271$	−10.8978	−0.661996	−0.330998	+	0.943632i	$0.607385\pi$
$272$	11.2018	0.679209
$273$	3.05259	0.184751
$274$	−18.0335	−1.08945
$275$	8.43013	0.508356
$276$	−0.0887656	−0.00534306
$277$	−3.91725	−0.235365	−0.117682	−	0.993051i	$-0.537546\pi$
$277$	−3.91725	−0.235365	−0.117682	+	0.993051i	$0.537546\pi$
$278$	−21.3207	−1.27873
$279$	0.136135	0.00815021
$280$	4.67671	0.279487
$281$	6.75296	0.402848	0.201424	−	0.979504i	$-0.435443\pi$
$281$	6.75296	0.402848	0.201424	+	0.979504i	$0.435443\pi$
$282$	−9.28105	−0.552679
$283$	−6.30052	−0.374527	−0.187263	−	0.982310i	$-0.559962\pi$
$283$	−6.30052	−0.374527	−0.187263	+	0.982310i	$0.559962\pi$
$284$	−2.25972	−0.134090
$285$	−0.362082	−0.0214479
$286$	2.26719	0.134061
$287$	17.7490	1.04769
$288$	−2.07720	−0.122400
$289$	−4.08127	−0.240075
$290$	1.90795	0.112039
$291$	15.8471	0.928974
$292$	5.17953	0.303109
$293$	−14.8568	−0.867943	−0.433971	−	0.900927i	$-0.642888\pi$
$293$	−14.8568	−0.867943	−0.433971	+	0.900927i	$0.642888\pi$
$294$	2.95764	0.172493
$295$	2.05833	0.119841
$296$	17.8744	1.03893
$297$	1.77709	0.103117
$298$	−2.09239	−0.121209
$299$	−0.238375	−0.0137856
$300$	−1.76648	−0.101987
$301$	7.21581	0.415913
$302$	3.89929	0.224379
$303$	3.35478	0.192727
$304$	2.22932	0.127860
$305$	1.54521	0.0884784
$306$	4.58550	0.262136
$307$	2.47596	0.141310	0.0706552	−	0.997501i	$-0.477491\pi$
$307$	2.47596	0.141310	0.0706552	+	0.997501i	$0.477491\pi$
$308$	−2.02005	−0.115103
$309$	1.00000	0.0568880
$310$	0.0879143	0.00499320
$311$	4.91918	0.278941	0.139471	−	0.990226i	$-0.455460\pi$
$311$	4.91918	0.278941	0.139471	+	0.990226i	$0.455460\pi$
$312$	−3.02664	−0.171350
$313$	−22.5452	−1.27433	−0.637166	−	0.770727i	$-0.719893\pi$
$313$	−22.5452	−1.27433	−0.637166	+	0.770727i	$0.719893\pi$
$314$	−11.0349	−0.622734
$315$	1.54518	0.0870612
$316$	3.79317	0.213382
$317$	26.6686	1.49786	0.748930	−	0.662649i	$-0.230568\pi$
$317$	26.6686	1.49786	0.748930	+	0.662649i	$0.230568\pi$
$318$	−5.26185	−0.295070
$319$	−5.25036	−0.293964
$320$	−4.49658	−0.251366
$321$	−17.7894	−0.992907
$322$	−0.928338	−0.0517343
$323$	2.57101	0.143055
$324$	−0.372378	−0.0206876
$325$	−4.74377	−0.263137
$326$	−21.2551	−1.17721
$327$	16.2712	0.899797
$328$	−17.5981	−0.971691
$329$	22.2069	1.22431
$330$	1.14762	0.0631745
$331$	27.3313	1.50226	0.751131	−	0.660153i	$-0.229509\pi$
$331$	27.3313	1.50226	0.751131	+	0.660153i	$0.229509\pi$
$332$	−0.615606	−0.0337858
$333$	5.90568	0.323629
$334$	−23.1141	−1.26475
$335$	−6.22885	−0.340319
$336$	−9.51363	−0.519011
$337$	30.3518	1.65337	0.826683	−	0.562668i	$-0.190225\pi$
$337$	30.3518	1.65337	0.826683	+	0.562668i	$0.190225\pi$
$338$	−1.27578	−0.0693934
$339$	0.902316	0.0490071
$340$	−0.677494	−0.0367423
$341$	−0.241925	−0.0131010
$342$	0.912581	0.0493467
$343$	14.2913	0.771659
$344$	−7.15448	−0.385743
$345$	−0.120663	−0.00649626
$346$	9.71454	0.522257
$347$	25.3945	1.36325	0.681625	−	0.731702i	$-0.261274\pi$
$347$	25.3945	1.36325	0.681625	+	0.731702i	$0.261274\pi$
$348$	1.10018	0.0589756
$349$	13.8170	0.739607	0.369804	−	0.929110i	$-0.379425\pi$
$349$	13.8170	0.739607	0.369804	+	0.929110i	$0.379425\pi$
$350$	−18.4743	−0.987495
$351$	−1.00000	−0.0533761
$352$	3.69138	0.196751
$353$	10.9712	0.583941	0.291970	−	0.956427i	$-0.405689\pi$
$353$	10.9712	0.583941	0.291970	+	0.956427i	$0.405689\pi$
$354$	−5.18777	−0.275727
$355$	−3.07173	−0.163031
$356$	4.62798	0.245282
$357$	−10.9718	−0.580690
$358$	−26.7462	−1.41358
$359$	22.8471	1.20583	0.602913	−	0.797807i	$-0.294007\pi$
$359$	22.8471	1.20583	0.602913	+	0.797807i	$0.294007\pi$
$360$	−1.53205	−0.0807460
$361$	−18.4883	−0.973070
$362$	18.2391	0.958625
$363$	7.84194	0.411595
$364$	1.13672	0.0595801
$365$	7.04075	0.368530
$366$	−3.89450	−0.203569
$367$	−11.2060	−0.584947	−0.292474	−	0.956274i	$-0.594478\pi$
$367$	−11.2060	−0.584947	−0.292474	+	0.956274i	$0.594478\pi$
$368$	0.742915	0.0387271
$369$	−5.81439	−0.302685
$370$	3.81380	0.198270
$371$	12.5901	0.653647
$372$	0.0506938	0.00262835
$373$	−6.17534	−0.319747	−0.159874	−	0.987138i	$-0.551109\pi$
$373$	−6.17534	−0.319747	−0.159874	+	0.987138i	$0.551109\pi$
$374$	−8.14886	−0.421368
$375$	−4.93218	−0.254697
$376$	−22.0182	−1.13550
$377$	2.95446	0.152163
$378$	−3.89444	−0.200308
$379$	17.3821	0.892857	0.446428	−	0.894819i	$-0.352696\pi$
$379$	17.3821	0.892857	0.446428	+	0.894819i	$0.352696\pi$
$380$	−0.134831	−0.00691669
$381$	18.5786	0.951808
$382$	−3.08845	−0.158019
$383$	9.86224	0.503937	0.251969	−	0.967735i	$-0.418922\pi$
$383$	9.86224	0.503937	0.251969	+	0.967735i	$0.418922\pi$
$384$	7.17866	0.366334
$385$	−2.74593	−0.139946
$386$	6.89271	0.350830
$387$	−2.36383	−0.120160
$388$	5.90111	0.299583
$389$	14.5318	0.736791	0.368396	−	0.929669i	$-0.379907\pi$
$389$	14.5318	0.736791	0.368396	+	0.929669i	$0.379907\pi$
$390$	−0.645786	−0.0327006
$391$	0.856783	0.0433294
$392$	7.01664	0.354394
$393$	7.85737	0.396352
$394$	−25.1075	−1.26490
$395$	5.15621	0.259437
$396$	0.661750	0.0332542
$397$	−21.6455	−1.08635	−0.543177	−	0.839618i	$-0.682779\pi$
$397$	−21.6455	−1.08635	−0.543177	+	0.839618i	$0.682779\pi$
$398$	22.0437	1.10495
$399$	−2.18355	−0.109314
$400$	14.7843	0.739217
$401$	8.98126	0.448503	0.224251	−	0.974531i	$-0.428006\pi$
$401$	8.98126	0.448503	0.224251	+	0.974531i	$0.428006\pi$
$402$	15.6990	0.782997
$403$	0.136135	0.00678139
$404$	1.24925	0.0621523
$405$	−0.506188	−0.0251527
$406$	11.5060	0.571032
$407$	−10.4949	−0.520215
$408$	10.8785	0.538568
$409$	−30.4957	−1.50791	−0.753957	−	0.656923i	$-0.771857\pi$
$409$	−30.4957	−1.50791	−0.753957	+	0.656923i	$0.771857\pi$
$410$	−3.75485	−0.185439
$411$	−14.1353	−0.697242
$412$	0.372378	0.0183457
$413$	12.4129	0.610797
$414$	0.304115	0.0149464
$415$	−0.836818	−0.0410778
$416$	−2.07720	−0.101843
$417$	−16.7119	−0.818385
$418$	−1.62174	−0.0793220
$419$	−4.37964	−0.213959	−0.106980	−	0.994261i	$-0.534118\pi$
$419$	−4.37964	−0.213959	−0.106980	+	0.994261i	$0.534118\pi$
$420$	0.575392	0.0280762
$421$	5.87184	0.286176	0.143088	−	0.989710i	$-0.454297\pi$
$421$	5.87184	0.286176	0.143088	+	0.989710i	$0.454297\pi$
$422$	−19.5993	−0.954080
$423$	−7.27479	−0.353712
$424$	−12.4831	−0.606233
$425$	17.0504	0.827065
$426$	7.74192	0.375097
$427$	9.31845	0.450951
$428$	−6.62437	−0.320201
$429$	1.77709	0.0857989
$430$	−1.52653	−0.0736159
$431$	−18.9790	−0.914187	−0.457094	−	0.889419i	$-0.651110\pi$
$431$	−18.9790	−0.914187	−0.457094	+	0.889419i	$0.651110\pi$
$432$	3.11658	0.149947
$433$	31.1549	1.49721	0.748604	−	0.663017i	$-0.230724\pi$
$433$	31.1549	1.49721	0.748604	+	0.663017i	$0.230724\pi$
$434$	0.530171	0.0254490
$435$	1.49551	0.0717044
$436$	6.05901	0.290174
$437$	0.170512	0.00815671
$438$	−17.7453	−0.847904
$439$	−16.0983	−0.768332	−0.384166	−	0.923264i	$-0.625511\pi$
$439$	−16.0983	−0.768332	−0.384166	+	0.923264i	$0.625511\pi$
$440$	2.72259	0.129794
$441$	2.31830	0.110395
$442$	4.58550	0.218110
$443$	−21.9726	−1.04395	−0.521975	−	0.852961i	$-0.674805\pi$
$443$	−21.9726	−1.04395	−0.521975	+	0.852961i	$0.674805\pi$
$444$	2.19914	0.104367
$445$	6.29100	0.298222
$446$	−22.3534	−1.05847
$447$	−1.64008	−0.0775732
$448$	−27.1168	−1.28115
$449$	20.9980	0.990956	0.495478	−	0.868621i	$-0.334993\pi$
$449$	20.9980	0.990956	0.495478	+	0.868621i	$0.334993\pi$
$450$	6.05203	0.285295
$451$	10.3327	0.486549
$452$	0.336002	0.0158042
$453$	3.05639	0.143602
$454$	30.6432	1.43816
$455$	1.54518	0.0724393
$456$	2.16499	0.101385
$457$	−7.24415	−0.338867	−0.169433	−	0.985542i	$-0.554194\pi$
$457$	−7.24415	−0.338867	−0.169433	+	0.985542i	$0.554194\pi$
$458$	2.66765	0.124651
$459$	3.59426	0.167766
$460$	−0.0449321	−0.00209497
$461$	10.9642	0.510652	0.255326	−	0.966855i	$-0.417817\pi$
$461$	10.9642	0.510652	0.255326	+	0.966855i	$0.417817\pi$
$462$	6.92078	0.321984
$463$	−29.2865	−1.36106	−0.680529	−	0.732721i	$-0.738250\pi$
$463$	−29.2865	−1.36106	−0.680529	+	0.732721i	$0.738250\pi$
$464$	−9.20782	−0.427462
$465$	0.0689101	0.00319563
$466$	11.6774	0.540944
$467$	41.8942	1.93863	0.969317	−	0.245813i	$-0.0790548\pi$
$467$	41.8942	1.93863	0.969317	+	0.245813i	$0.0790548\pi$
$468$	−0.372378	−0.0172132
$469$	−37.5634	−1.73452
$470$	−4.69796	−0.216701
$471$	−8.64949	−0.398547
$472$	−12.3073	−0.566491
$473$	4.20075	0.193151
$474$	−12.9956	−0.596906
$475$	3.39327	0.155694
$476$	−4.08566	−0.187266
$477$	−4.12441	−0.188844
$478$	−8.85202	−0.404882
$479$	1.31516	0.0600912	0.0300456	−	0.999549i	$-0.490435\pi$
$479$	1.31516	0.0600912	0.0300456	+	0.999549i	$0.490435\pi$
$480$	−1.05145	−0.0479920
$481$	5.90568	0.269276
$482$	−34.0149	−1.54934
$483$	−0.727661	−0.0331097
$484$	2.92016	0.132735
$485$	8.02161	0.364243
$486$	1.27578	0.0578707
$487$	29.8662	1.35337	0.676683	−	0.736274i	$-0.263417\pi$
$487$	29.8662	1.35337	0.676683	+	0.736274i	$0.263417\pi$
$488$	−9.23923	−0.418240
$489$	−16.6605	−0.753412
$490$	1.49712	0.0676331
$491$	−8.17232	−0.368811	−0.184406	−	0.982850i	$-0.559036\pi$
$491$	−8.17232	−0.368811	−0.184406	+	0.982850i	$0.559036\pi$
$492$	−2.16515	−0.0976125
$493$	−10.6191	−0.478261
$494$	0.912581	0.0410590
$495$	0.899543	0.0404315
$496$	−0.424277	−0.0190506
$497$	−18.5242	−0.830925
$498$	2.10909	0.0945108
$499$	5.99482	0.268365	0.134183	−	0.990957i	$-0.457159\pi$
$499$	5.99482	0.268365	0.134183	+	0.990957i	$0.457159\pi$
$500$	−1.83663	−0.0821368
$501$	−18.1176	−0.809433
$502$	−17.1597	−0.765876
$503$	36.3423	1.62042	0.810212	−	0.586137i	$-0.199352\pi$
$503$	36.3423	1.62042	0.810212	+	0.586137i	$0.199352\pi$
$504$	−9.23908	−0.411541
$505$	1.69815	0.0755667
$506$	−0.540441	−0.0240255
$507$	−1.00000	−0.0444116
$508$	6.91824	0.306947
$509$	13.6721	0.606007	0.303003	−	0.952989i	$-0.402011\pi$
$509$	13.6721	0.606007	0.303003	+	0.952989i	$0.402011\pi$
$510$	2.32113	0.102781
$511$	42.4595	1.87830
$512$	25.3393	1.11985
$513$	0.715310	0.0315817
$514$	−34.4217	−1.51828
$515$	0.506188	0.0223053
$516$	−0.880239	−0.0387504
$517$	12.9280	0.568572
$518$	22.9993	1.01053
$519$	7.61457	0.334242
$520$	−1.53205	−0.0671848
$521$	−5.96539	−0.261348	−0.130674	−	0.991425i	$-0.541714\pi$
$521$	−5.96539	−0.261348	−0.130674	+	0.991425i	$0.541714\pi$
$522$	−3.76926	−0.164976
$523$	18.0919	0.791106	0.395553	−	0.918443i	$-0.370553\pi$
$523$	18.0919	0.791106	0.395553	+	0.918443i	$0.370553\pi$
$524$	2.92591	0.127819
$525$	−14.4808	−0.631993
$526$	6.52060	0.284312
$527$	−0.489307	−0.0213145
$528$	−5.53845	−0.241030
$529$	−22.9432	−0.997529
$530$	−2.66349	−0.115694
$531$	−4.06634	−0.176464
$532$	−0.813104	−0.0352525
$533$	−5.81439	−0.251849
$534$	−15.8557	−0.686142
$535$	−9.00478	−0.389310
$536$	37.2441	1.60870
$537$	−20.9646	−0.904687
$538$	6.44190	0.277730
$539$	−4.11983	−0.177453
$540$	−0.188493	−0.00811145
$541$	−10.5646	−0.454208	−0.227104	−	0.973871i	$-0.572926\pi$
$541$	−10.5646	−0.454208	−0.227104	+	0.973871i	$0.572926\pi$
$542$	13.9033	0.597196
$543$	14.2964	0.613517
$544$	7.46600	0.320102
$545$	8.23626	0.352803
$546$	−3.89444	−0.166667
$547$	−23.2951	−0.996027	−0.498013	−	0.867169i	$-0.665937\pi$
$547$	−23.2951	−0.996027	−0.498013	+	0.867169i	$0.665937\pi$
$548$	−5.26366	−0.224852
$549$	−3.05264	−0.130283
$550$	−10.7550	−0.458595
$551$	−2.11336	−0.0900321
$552$	0.721476	0.0307080
$553$	31.0947	1.32228
$554$	4.99757	0.212326
$555$	2.98938	0.126892
$556$	−6.22313	−0.263920
$557$	−4.54236	−0.192466	−0.0962331	−	0.995359i	$-0.530679\pi$
$557$	−4.54236	−0.192466	−0.0962331	+	0.995359i	$0.530679\pi$
$558$	−0.173679	−0.00735243
$559$	−2.36383	−0.0999796
$560$	−4.81569	−0.203500
$561$	−6.38734	−0.269674
$562$	−8.61531	−0.363415
$563$	−11.5640	−0.487364	−0.243682	−	0.969855i	$-0.578355\pi$
$563$	−11.5640	−0.487364	−0.243682	+	0.969855i	$0.578355\pi$
$564$	−2.70897	−0.114068
$565$	0.456741	0.0192153
$566$	8.03809	0.337866
$567$	−3.05259	−0.128197
$568$	18.3668	0.770652
$569$	25.6662	1.07598	0.537991	−	0.842950i	$-0.319183\pi$
$569$	25.6662	1.07598	0.537991	+	0.842950i	$0.319183\pi$
$570$	0.461937	0.0193484
$571$	−31.6651	−1.32514	−0.662572	−	0.748998i	$-0.730535\pi$
$571$	−31.6651	−1.32514	−0.662572	+	0.748998i	$0.730535\pi$
$572$	0.661750	0.0276691
$573$	−2.42083	−0.101131
$574$	−22.6438	−0.945134
$575$	1.13080	0.0471575
$576$	8.88321	0.370134
$577$	3.75953	0.156511	0.0782556	−	0.996933i	$-0.475065\pi$
$577$	3.75953	0.156511	0.0782556	+	0.996933i	$0.475065\pi$
$578$	5.20681	0.216575
$579$	5.40273	0.224530
$580$	0.556896	0.0231238
$581$	−5.04647	−0.209363
$582$	−20.2175	−0.838041
$583$	7.32946	0.303555
$584$	−42.0986	−1.74205
$585$	−0.506188	−0.0209283
$586$	18.9540	0.782984
$587$	−9.25750	−0.382098	−0.191049	−	0.981580i	$-0.561189\pi$
$587$	−9.25750	−0.382098	−0.191049	+	0.981580i	$0.561189\pi$
$588$	0.863281	0.0356011
$589$	−0.0973791	−0.00401243
$590$	−2.62599	−0.108110
$591$	−19.6801	−0.809530
$592$	−18.4055	−0.756462
$593$	23.2842	0.956168	0.478084	−	0.878314i	$-0.341331\pi$
$593$	23.2842	0.956168	0.478084	+	0.878314i	$0.341331\pi$
$594$	−2.26719	−0.0930237
$595$	−5.55380	−0.227683
$596$	−0.610729	−0.0250165
$597$	17.2785	0.707164
$598$	0.304115	0.0124362
$599$	31.4527	1.28512	0.642561	−	0.766235i	$-0.277872\pi$
$599$	31.4527	1.28512	0.642561	+	0.766235i	$0.277872\pi$
$600$	14.3577	0.586150
$601$	40.8070	1.66455	0.832275	−	0.554362i	$-0.187038\pi$
$601$	40.8070	1.66455	0.832275	+	0.554362i	$0.187038\pi$
$602$	−9.20581	−0.375201
$603$	12.3054	0.501115
$604$	1.13813	0.0463099
$605$	3.96950	0.161383
$606$	−4.27998	−0.173862
$607$	35.9070	1.45742	0.728709	−	0.684823i	$-0.240121\pi$
$607$	35.9070	1.45742	0.728709	+	0.684823i	$0.240121\pi$
$608$	1.48584	0.0602588
$609$	9.01876	0.365459
$610$	−1.97135	−0.0798177
$611$	−7.27479	−0.294306
$612$	1.33842	0.0541026
$613$	6.01339	0.242879	0.121439	−	0.992599i	$-0.461249\pi$
$613$	6.01339	0.242879	0.121439	+	0.992599i	$0.461249\pi$
$614$	−3.15879	−0.127478
$615$	−2.94318	−0.118680
$616$	16.4187	0.661529
$617$	42.9411	1.72874	0.864372	−	0.502852i	$-0.167716\pi$
$617$	42.9411	1.72874	0.864372	+	0.502852i	$0.167716\pi$
$618$	−1.27578	−0.0513195
$619$	5.03275	0.202283	0.101142	−	0.994872i	$-0.467750\pi$
$619$	5.03275	0.202283	0.101142	+	0.994872i	$0.467750\pi$
$620$	0.0256606	0.00103055
$621$	0.238375	0.00956567
$622$	−6.27581	−0.251637
$623$	37.9382	1.51996
$624$	3.11658	0.124763
$625$	21.2223	0.848890
$626$	28.7628	1.14959
$627$	−1.27117	−0.0507658
$628$	−3.22088	−0.128527
$629$	−21.2266	−0.846358
$630$	−1.97132	−0.0785392
$631$	−29.7510	−1.18437	−0.592185	−	0.805802i	$-0.701734\pi$
$631$	−29.7510	−1.18437	−0.592185	+	0.805802i	$0.701734\pi$
$632$	−30.8304	−1.22637
$633$	−15.3626	−0.610608
$634$	−34.0234	−1.35124
$635$	9.40424	0.373196
$636$	−1.53584	−0.0608999
$637$	2.31830	0.0918542
$638$	6.69832	0.265189
$639$	6.06837	0.240061
$640$	3.63375	0.143637
$641$	−38.8127	−1.53301	−0.766505	−	0.642238i	$-0.778006\pi$
$641$	−38.8127	−1.53301	−0.766505	+	0.642238i	$0.778006\pi$
$642$	22.6954	0.895716
$643$	−34.5045	−1.36073	−0.680363	−	0.732875i	$-0.738178\pi$
$643$	−34.5045	−1.36073	−0.680363	+	0.732875i	$0.738178\pi$
$644$	−0.270965	−0.0106775
$645$	−1.19654	−0.0471139
$646$	−3.28006	−0.129052
$647$	−21.0735	−0.828483	−0.414241	−	0.910167i	$-0.635953\pi$
$647$	−21.0735	−0.828483	−0.414241	+	0.910167i	$0.635953\pi$
$648$	3.02664	0.118898
$649$	7.22626	0.283656
$650$	6.05203	0.237380
$651$	0.415565	0.0162873
$652$	−6.20398	−0.242967
$653$	8.74814	0.342341	0.171171	−	0.985241i	$-0.445245\pi$
$653$	8.74814	0.342341	0.171171	+	0.985241i	$0.445245\pi$
$654$	−20.7585	−0.811720
$655$	3.97730	0.155406
$656$	18.1210	0.707507
$657$	−13.9094	−0.542656
$658$	−28.3312	−1.10447
$659$	−4.59733	−0.179087	−0.0895433	−	0.995983i	$-0.528541\pi$
$659$	−4.59733	−0.179087	−0.0895433	+	0.995983i	$0.528541\pi$
$660$	0.334970	0.0130387
$661$	−7.30213	−0.284020	−0.142010	−	0.989865i	$-0.545357\pi$
$661$	−7.30213	−0.284020	−0.142010	+	0.989865i	$0.545357\pi$
$662$	−34.8688	−1.35521
$663$	3.59426	0.139590
$664$	5.00357	0.194176
$665$	−1.10529	−0.0428611
$666$	−7.53436	−0.291951
$667$	−0.704271	−0.0272695
$668$	−6.74657	−0.261033
$669$	−17.5213	−0.677414
$670$	7.94667	0.307006
$671$	5.42482	0.209423
$672$	−6.34083	−0.244603
$673$	−51.1172	−1.97042	−0.985211	−	0.171344i	$-0.945189\pi$
$673$	−51.1172	−1.97042	−0.985211	+	0.171344i	$0.945189\pi$
$674$	−38.7223	−1.49153
$675$	4.74377	0.182588
$676$	−0.372378	−0.0143222
$677$	−12.0934	−0.464788	−0.232394	−	0.972622i	$-0.574656\pi$
$677$	−12.0934	−0.464788	−0.232394	+	0.972622i	$0.574656\pi$
$678$	−1.15116	−0.0442100
$679$	48.3747	1.85645
$680$	5.50659	0.211168
$681$	24.0192	0.920417
$682$	0.308644	0.0118186
$683$	25.9836	0.994234	0.497117	−	0.867684i	$-0.334392\pi$
$683$	25.9836	0.994234	0.497117	+	0.867684i	$0.334392\pi$
$684$	0.266366	0.0101847
$685$	−7.15510	−0.273382
$686$	−18.2326	−0.696125
$687$	2.09099	0.0797764
$688$	7.36708	0.280867
$689$	−4.12441	−0.157127
$690$	0.153939	0.00586037
$691$	30.7103	1.16828	0.584138	−	0.811654i	$-0.301433\pi$
$691$	30.7103	1.16828	0.584138	+	0.811654i	$0.301433\pi$
$692$	2.83549	0.107789
$693$	5.42473	0.206069
$694$	−32.3979	−1.22981
$695$	−8.45936	−0.320882
$696$	−8.94210	−0.338949
$697$	20.8985	0.791586
$698$	−17.6275	−0.667211
$699$	9.15311	0.346202
$700$	−5.39232	−0.203811
$701$	−51.8192	−1.95719	−0.978593	−	0.205806i	$-0.934018\pi$
$701$	−51.8192	−1.95719	−0.978593	+	0.205806i	$0.934018\pi$
$702$	1.27578	0.0481513
$703$	−4.22439	−0.159326
$704$	−15.7863	−0.594968
$705$	−3.68241	−0.138688
$706$	−13.9969	−0.526782
$707$	10.2408	0.385144
$708$	−1.51421	−0.0569076
$709$	−31.7882	−1.19383	−0.596915	−	0.802305i	$-0.703607\pi$
$709$	−31.7882	−1.19383	−0.596915	+	0.802305i	$0.703607\pi$
$710$	3.91887	0.147072
$711$	−10.1863	−0.382018
$712$	−37.6157	−1.40971
$713$	−0.0324513	−0.00121531
$714$	13.9976	0.523849
$715$	0.899543	0.0336410
$716$	−7.80673	−0.291751
$717$	−6.93850	−0.259123
$718$	−29.1480	−1.08779
$719$	−33.9686	−1.26681	−0.633407	−	0.773819i	$-0.718344\pi$
$719$	−33.9686	−1.26681	−0.633407	+	0.773819i	$0.718344\pi$
$720$	1.57758	0.0587928
$721$	3.05259	0.113684
$722$	23.5871	0.877821
$723$	−26.6620	−0.991569
$724$	5.32365	0.197852
$725$	−14.0153	−0.520515
$726$	−10.0046	−0.371306
$727$	−16.9776	−0.629663	−0.314832	−	0.949148i	$-0.601948\pi$
$727$	−16.9776	−0.629663	−0.314832	+	0.949148i	$0.601948\pi$
$728$	−9.23908	−0.342423
$729$	1.00000	0.0370370
$730$	−8.98247	−0.332456
$731$	8.49625	0.314245
$732$	−1.13673	−0.0420149
$733$	−20.9167	−0.772576	−0.386288	−	0.922378i	$-0.626243\pi$
$733$	−20.9167	−0.772576	−0.386288	+	0.922378i	$0.626243\pi$
$734$	14.2964	0.527690
$735$	1.17349	0.0432849
$736$	0.495153	0.0182516
$737$	−21.8679	−0.805513
$738$	7.41791	0.273057
$739$	12.0997	0.445095	0.222548	−	0.974922i	$-0.428563\pi$
$739$	12.0997	0.445095	0.222548	+	0.974922i	$0.428563\pi$
$740$	1.11318	0.0409213
$741$	0.715310	0.0262776
$742$	−16.0623	−0.589664
$743$	15.0790	0.553194	0.276597	−	0.960986i	$-0.410793\pi$
$743$	15.0790	0.553194	0.276597	+	0.960986i	$0.410793\pi$
$744$	−0.412033	−0.0151059
$745$	−0.830189	−0.0304158
$746$	7.87840	0.288449
$747$	1.65318	0.0604866
$748$	−2.37850	−0.0869667
$749$	−54.3037	−1.98421
$750$	6.29239	0.229766
$751$	21.9237	0.800009	0.400004	−	0.916513i	$-0.369009\pi$
$751$	21.9237	0.800009	0.400004	+	0.916513i	$0.369009\pi$
$752$	22.6725	0.826779
$753$	−13.4503	−0.490158
$754$	−3.76926	−0.137268
$755$	1.54711	0.0563050
$756$	−1.13672	−0.0413419
$757$	−2.99591	−0.108888	−0.0544440	−	0.998517i	$-0.517339\pi$
$757$	−2.99591	−0.108888	−0.0544440	+	0.998517i	$0.517339\pi$
$758$	−22.1757	−0.805459
$759$	−0.423615	−0.0153762
$760$	1.09589	0.0397521
$761$	4.79728	0.173901	0.0869506	−	0.996213i	$-0.472288\pi$
$761$	4.79728	0.173901	0.0869506	+	0.996213i	$0.472288\pi$
$762$	−23.7022	−0.858640
$763$	49.6691	1.79814
$764$	−0.901461	−0.0326137
$765$	1.81937	0.0657796
$766$	−12.5821	−0.454609
$767$	−4.06634	−0.146827
$768$	8.60802	0.310615
$769$	−31.6564	−1.14156	−0.570779	−	0.821103i	$-0.693359\pi$
$769$	−31.6564	−1.14156	−0.570779	+	0.821103i	$0.693359\pi$
$770$	3.50322	0.126247
$771$	−26.9808	−0.971691
$772$	2.01186	0.0724083
$773$	−38.0532	−1.36868	−0.684340	−	0.729163i	$-0.739910\pi$
$773$	−38.0532	−1.36868	−0.684340	+	0.729163i	$0.739910\pi$
$774$	3.01574	0.108399
$775$	−0.645795	−0.0231977
$776$	−47.9635	−1.72179
$777$	18.0276	0.646736
$778$	−18.5394	−0.664671
$779$	4.15910	0.149015
$780$	−0.188493	−0.00674913
$781$	−10.7841	−0.385884
$782$	−1.09307	−0.0390881
$783$	−2.95446	−0.105584
$784$	−7.22515	−0.258041
$785$	−4.37827	−0.156267
$786$	−10.0243	−0.357555
$787$	38.5758	1.37508	0.687539	−	0.726148i	$-0.258691\pi$
$787$	38.5758	1.37508	0.687539	+	0.726148i	$0.258691\pi$
$788$	−7.32842	−0.261064
$789$	5.11106	0.181959
$790$	−6.57820	−0.234042
$791$	2.75440	0.0979351
$792$	−5.37862	−0.191121
$793$	−3.05264	−0.108402
$794$	27.6149	0.980017
$795$	−2.08773	−0.0740440
$796$	6.43414	0.228052
$797$	35.8686	1.27053	0.635266	−	0.772294i	$-0.280891\pi$
$797$	35.8686	1.27053	0.635266	+	0.772294i	$0.280891\pi$
$798$	2.78573	0.0986139
$799$	26.1475	0.925032
$800$	9.85376	0.348383
$801$	−12.4282	−0.439129
$802$	−11.4581	−0.404601
$803$	24.7182	0.872287
$804$	4.58226	0.161604
$805$	−0.368333	−0.0129820
$806$	−0.173679	−0.00611759
$807$	5.04937	0.177746
$808$	−10.1537	−0.357207
$809$	−43.6710	−1.53539	−0.767696	−	0.640814i	$-0.778597\pi$
$809$	−43.6710	−1.53539	−0.767696	+	0.640814i	$0.778597\pi$
$810$	0.645786	0.0226906
$811$	42.7642	1.50166	0.750828	−	0.660498i	$-0.229655\pi$
$811$	42.7642	1.50166	0.750828	+	0.660498i	$0.229655\pi$
$812$	3.35838	0.117856
$813$	10.8978	0.382203
$814$	13.3893	0.469293
$815$	−8.43332	−0.295406
$816$	−11.2018	−0.392142
$817$	1.69088	0.0591563
$818$	38.9059	1.36031
$819$	−3.05259	−0.106666
$820$	−1.09597	−0.0382730
$821$	−2.57276	−0.0897898	−0.0448949	−	0.998992i	$-0.514295\pi$
$821$	−2.57276	−0.0897898	−0.0448949	+	0.998992i	$0.514295\pi$
$822$	18.0335	0.628992
$823$	44.5744	1.55377	0.776883	−	0.629645i	$-0.216800\pi$
$823$	44.5744	1.55377	0.776883	+	0.629645i	$0.216800\pi$
$824$	−3.02664	−0.105438
$825$	−8.43013	−0.293499
$826$	−15.8361	−0.551009
$827$	9.11085	0.316815	0.158408	−	0.987374i	$-0.449364\pi$
$827$	9.11085	0.316815	0.158408	+	0.987374i	$0.449364\pi$
$828$	0.0887656	0.00308482
$829$	12.1320	0.421361	0.210680	−	0.977555i	$-0.432432\pi$
$829$	12.1320	0.421361	0.210680	+	0.977555i	$0.432432\pi$
$830$	1.06760	0.0370569
$831$	3.91725	0.135888
$832$	8.88321	0.307970
$833$	−8.33256	−0.288706
$834$	21.3207	0.738277
$835$	−9.17089	−0.317372
$836$	−0.473356	−0.0163714
$837$	−0.136135	−0.00470553
$838$	5.58747	0.193016
$839$	−53.8711	−1.85984	−0.929918	−	0.367767i	$-0.880122\pi$
$839$	−53.8711	−1.85984	−0.929918	+	0.367767i	$0.880122\pi$
$840$	−4.67671	−0.161362
$841$	−20.2711	−0.699005
$842$	−7.49119	−0.258164
$843$	−6.75296	−0.232584
$844$	−5.72068	−0.196914
$845$	−0.506188	−0.0174134
$846$	9.28105	0.319089
$847$	23.9382	0.822527
$848$	12.8541	0.441410
$849$	6.30052	0.216233
$850$	−21.7526	−0.746107
$851$	−1.40777	−0.0482576
$852$	2.25972	0.0774169
$853$	1.06628	0.0365089	0.0182544	−	0.999833i	$-0.494189\pi$
$853$	1.06628	0.0365089	0.0182544	+	0.999833i	$0.494189\pi$
$854$	−11.8883	−0.406810
$855$	0.362082	0.0123829
$856$	53.8421	1.84028
$857$	−16.6961	−0.570328	−0.285164	−	0.958479i	$-0.592048\pi$
$857$	−16.6961	−0.570328	−0.285164	+	0.958479i	$0.592048\pi$
$858$	−2.26719	−0.0774004
$859$	−1.34068	−0.0457434	−0.0228717	−	0.999738i	$-0.507281\pi$
$859$	−1.34068	−0.0457434	−0.0228717	+	0.999738i	$0.507281\pi$
$860$	−0.445566	−0.0151937
$861$	−17.7490	−0.604883
$862$	24.2131	0.824702
$863$	−7.94115	−0.270320	−0.135160	−	0.990824i	$-0.543155\pi$
$863$	−7.94115	−0.270320	−0.135160	+	0.990824i	$0.543155\pi$
$864$	2.07720	0.0706677
$865$	3.85440	0.131054
$866$	−39.7469	−1.35065
$867$	4.08127	0.138607
$868$	0.154747	0.00525246
$869$	18.1021	0.614071
$870$	−1.90795	−0.0646856
$871$	12.3054	0.416953
$872$	−49.2469	−1.66771
$873$	−15.8471	−0.536343
$874$	−0.217537	−0.00735829
$875$	−15.0559	−0.508983
$876$	−5.17953	−0.175000
$877$	51.0387	1.72346	0.861728	−	0.507370i	$-0.169382\pi$
$877$	51.0387	1.72346	0.861728	+	0.507370i	$0.169382\pi$
$878$	20.5380	0.693124
$879$	14.8568	0.501107
$880$	−2.80350	−0.0945059
$881$	25.6095	0.862805	0.431403	−	0.902160i	$-0.358019\pi$
$881$	25.6095	0.862805	0.431403	+	0.902160i	$0.358019\pi$
$882$	−2.95764	−0.0995890
$883$	−53.5333	−1.80154	−0.900769	−	0.434298i	$-0.856997\pi$
$883$	−53.5333	−1.80154	−0.900769	+	0.434298i	$0.856997\pi$
$884$	1.33842	0.0450160
$885$	−2.05833	−0.0691901
$886$	28.0323	0.941763
$887$	26.0123	0.873409	0.436704	−	0.899605i	$-0.356146\pi$
$887$	26.0123	0.873409	0.436704	+	0.899605i	$0.356146\pi$
$888$	−17.8744	−0.599824
$889$	56.7127	1.90208
$890$	−8.02595	−0.269031
$891$	−1.77709	−0.0595349
$892$	−6.52456	−0.218458
$893$	5.20373	0.174136
$894$	2.09239	0.0699799
$895$	−10.6120	−0.354720
$896$	21.9135	0.732078
$897$	0.238375	0.00795912
$898$	−26.7889	−0.893956
$899$	0.402207	0.0134144
$900$	1.76648	0.0588825
$901$	14.8242	0.493866
$902$	−13.1823	−0.438923
$903$	−7.21581	−0.240127
$904$	−2.73098	−0.0908312
$905$	7.23666	0.240555
$906$	−3.89929	−0.129545
$907$	−14.1824	−0.470918	−0.235459	−	0.971884i	$-0.575659\pi$
$907$	−14.1824	−0.470918	−0.235459	+	0.971884i	$0.575659\pi$
$908$	8.94420	0.296824
$909$	−3.35478	−0.111271
$910$	−1.97132	−0.0653486
$911$	−14.2700	−0.472786	−0.236393	−	0.971657i	$-0.575965\pi$
$911$	−14.2700	−0.472786	−0.236393	+	0.971657i	$0.575965\pi$
$912$	−2.22932	−0.0738202
$913$	−2.93785	−0.0972286
$914$	9.24196	0.305697
$915$	−1.54521	−0.0510830
$916$	0.778639	0.0257270
$917$	23.9853	0.792065
$918$	−4.58550	−0.151344
$919$	−34.3479	−1.13303	−0.566517	−	0.824050i	$-0.691709\pi$
$919$	−34.3479	−1.13303	−0.566517	+	0.824050i	$0.691709\pi$
$920$	0.365202	0.0120404
$921$	−2.47596	−0.0815856
$922$	−13.9879	−0.460667
$923$	6.06837	0.199743
$924$	2.02005	0.0664547
$925$	−28.0152	−0.921134
$926$	37.3632	1.22783
$927$	−1.00000	−0.0328443
$928$	−6.13701	−0.201457
$929$	16.2958	0.534647	0.267324	−	0.963607i	$-0.413861\pi$
$929$	16.2958	0.534647	0.267324	+	0.963607i	$0.413861\pi$
$930$	−0.0879143	−0.00288282
$931$	−1.65830	−0.0543486
$932$	3.40841	0.111646
$933$	−4.91918	−0.161047
$934$	−53.4480	−1.74887
$935$	−3.23320	−0.105737
$936$	3.02664	0.0989288
$937$	−33.8529	−1.10593	−0.552963	−	0.833206i	$-0.686503\pi$
$937$	−33.8529	−1.10593	−0.552963	+	0.833206i	$0.686503\pi$
$938$	47.9227	1.56473
$939$	22.5452	0.735736
$940$	−1.37125	−0.0447251
$941$	46.8092	1.52594	0.762969	−	0.646435i	$-0.223741\pi$
$941$	46.8092	1.52594	0.762969	+	0.646435i	$0.223741\pi$
$942$	11.0349	0.359536
$943$	1.38601	0.0451346
$944$	12.6731	0.412473
$945$	−1.54518	−0.0502648
$946$	−5.35925	−0.174244
$947$	−52.0261	−1.69062	−0.845311	−	0.534275i	$-0.820585\pi$
$947$	−52.0261	−1.69062	−0.845311	+	0.534275i	$0.820585\pi$
$948$	−3.79317	−0.123196
$949$	−13.9094	−0.451517
$950$	−4.32908	−0.140454
$951$	−26.6686	−0.864790
$952$	33.2077	1.07627
$953$	9.23155	0.299039	0.149520	−	0.988759i	$-0.452227\pi$
$953$	9.23155	0.299039	0.149520	+	0.988759i	$0.452227\pi$
$954$	5.26185	0.170359
$955$	−1.22539	−0.0396528
$956$	−2.58374	−0.0835642
$957$	5.25036	0.169720
$958$	−1.67786	−0.0542092
$959$	−43.1492	−1.39336
$960$	4.49658	0.145126
$961$	−30.9815	−0.999402
$962$	−7.53436	−0.242918
$963$	17.7894	0.573255
$964$	−9.92832	−0.319770
$965$	2.73480	0.0880363
$966$	0.928338	0.0298688
$967$	−36.9716	−1.18893	−0.594463	−	0.804123i	$-0.702635\pi$
$967$	−36.9716	−1.18893	−0.594463	+	0.804123i	$0.702635\pi$
$968$	−23.7347	−0.762863
$969$	−2.57101	−0.0825929
$970$	−10.2338	−0.328589
$971$	−34.7886	−1.11642	−0.558210	−	0.829700i	$-0.688512\pi$
$971$	−34.7886	−1.11642	−0.558210	+	0.829700i	$0.688512\pi$
$972$	0.372378	0.0119440
$973$	−51.0145	−1.63545
$974$	−38.1028	−1.22089
$975$	4.74377	0.151922
$976$	9.51379	0.304529
$977$	−9.71591	−0.310839	−0.155420	−	0.987849i	$-0.549673\pi$
$977$	−9.71591	−0.310839	−0.155420	+	0.987849i	$0.549673\pi$
$978$	21.2551	0.679664
$979$	22.0861	0.705873
$980$	0.436983	0.0139589
$981$	−16.2712	−0.519498
$982$	10.4261	0.332710
$983$	9.45583	0.301594	0.150797	−	0.988565i	$-0.451816\pi$
$983$	9.45583	0.301594	0.150797	+	0.988565i	$0.451816\pi$
$984$	17.5981	0.561006
$985$	−9.96181	−0.317410
$986$	13.5477	0.431447
$987$	−22.2069	−0.706854
$988$	0.266366	0.00847422
$989$	0.563480	0.0179176
$990$	−1.14762	−0.0364738
$991$	−10.9428	−0.347610	−0.173805	−	0.984780i	$-0.555606\pi$
$991$	−10.9428	−0.347610	−0.173805	+	0.984780i	$0.555606\pi$
$992$	−0.282780	−0.00897828
$993$	−27.3313	−0.867332
$994$	23.6329	0.749590
$995$	8.74619	0.277273
$996$	0.615606	0.0195062
$997$	34.6737	1.09813	0.549063	−	0.835781i	$-0.314985\pi$
$997$	34.6737	1.09813	0.549063	+	0.835781i	$0.314985\pi$
$998$	−7.64810	−0.242096
$999$	−5.90568	−0.186847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.7	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.7	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.27578 q^{2} -1.00000 q^{3} -0.372378 q^{4} -0.506188 q^{5} +1.27578 q^{6} -3.05259 q^{7} +3.02664 q^{8} +1.00000 q^{9} +0.645786 q^{10} -1.77709 q^{11} +0.372378 q^{12} +1.00000 q^{13} +3.89444 q^{14} +0.506188 q^{15} -3.11658 q^{16} -3.59426 q^{17} -1.27578 q^{18} -0.715310 q^{19} +0.188493 q^{20} +3.05259 q^{21} +2.26719 q^{22} -0.238375 q^{23} -3.02664 q^{24} -4.74377 q^{25} -1.27578 q^{26} -1.00000 q^{27} +1.13672 q^{28} +2.95446 q^{29} -0.645786 q^{30} +0.136135 q^{31} -2.07720 q^{32} +1.77709 q^{33} +4.58550 q^{34} +1.54518 q^{35} -0.372378 q^{36} +5.90568 q^{37} +0.912581 q^{38} -1.00000 q^{39} -1.53205 q^{40} -5.81439 q^{41} -3.89444 q^{42} -2.36383 q^{43} +0.661750 q^{44} -0.506188 q^{45} +0.304115 q^{46} -7.27479 q^{47} +3.11658 q^{48} +2.31830 q^{49} +6.05203 q^{50} +3.59426 q^{51} -0.372378 q^{52} -4.12441 q^{53} +1.27578 q^{54} +0.899543 q^{55} -9.23908 q^{56} +0.715310 q^{57} -3.76926 q^{58} -4.06634 q^{59} -0.188493 q^{60} -3.05264 q^{61} -0.173679 q^{62} -3.05259 q^{63} +8.88321 q^{64} -0.506188 q^{65} -2.26719 q^{66} +12.3054 q^{67} +1.33842 q^{68} +0.238375 q^{69} -1.97132 q^{70} +6.06837 q^{71} +3.02664 q^{72} -13.9094 q^{73} -7.53436 q^{74} +4.74377 q^{75} +0.266366 q^{76} +5.42473 q^{77} +1.27578 q^{78} -10.1863 q^{79} +1.57758 q^{80} +1.00000 q^{81} +7.41791 q^{82} +1.65318 q^{83} -1.13672 q^{84} +1.81937 q^{85} +3.01574 q^{86} -2.95446 q^{87} -5.37862 q^{88} -12.4282 q^{89} +0.645786 q^{90} -3.05259 q^{91} +0.0887656 q^{92} -0.136135 q^{93} +9.28105 q^{94} +0.362082 q^{95} +2.07720 q^{96} -15.8471 q^{97} -2.95764 q^{98} -1.77709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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