LMFDB - Embedded newform 4017.2.a.i.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:	$1$
Dimension:	$25$
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)

$f(q)$	$=$	$q-1.46195 q^{2} -1.00000 q^{3} +0.137285 q^{4} -2.88545 q^{5} +1.46195 q^{6} +1.16184 q^{7} +2.72319 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46195 q^{2} -1.00000 q^{3} +0.137285 q^{4} -2.88545 q^{5} +1.46195 q^{6} +1.16184 q^{7} +2.72319 q^{8} +1.00000 q^{9} +4.21838 q^{10} -4.61255 q^{11} -0.137285 q^{12} -1.00000 q^{13} -1.69855 q^{14} +2.88545 q^{15} -4.25572 q^{16} +4.00427 q^{17} -1.46195 q^{18} +3.52485 q^{19} -0.396131 q^{20} -1.16184 q^{21} +6.74329 q^{22} -0.748303 q^{23} -2.72319 q^{24} +3.32585 q^{25} +1.46195 q^{26} -1.00000 q^{27} +0.159504 q^{28} -9.69267 q^{29} -4.21838 q^{30} -6.27160 q^{31} +0.775262 q^{32} +4.61255 q^{33} -5.85402 q^{34} -3.35244 q^{35} +0.137285 q^{36} +6.26432 q^{37} -5.15314 q^{38} +1.00000 q^{39} -7.85763 q^{40} -4.52300 q^{41} +1.69855 q^{42} +8.06672 q^{43} -0.633236 q^{44} -2.88545 q^{45} +1.09398 q^{46} +6.63141 q^{47} +4.25572 q^{48} -5.65013 q^{49} -4.86221 q^{50} -4.00427 q^{51} -0.137285 q^{52} +5.13914 q^{53} +1.46195 q^{54} +13.3093 q^{55} +3.16391 q^{56} -3.52485 q^{57} +14.1702 q^{58} +9.67410 q^{59} +0.396131 q^{60} +11.7495 q^{61} +9.16873 q^{62} +1.16184 q^{63} +7.37806 q^{64} +2.88545 q^{65} -6.74329 q^{66} +10.8303 q^{67} +0.549728 q^{68} +0.748303 q^{69} +4.90109 q^{70} -2.91859 q^{71} +2.72319 q^{72} -0.273822 q^{73} -9.15809 q^{74} -3.32585 q^{75} +0.483911 q^{76} -5.35905 q^{77} -1.46195 q^{78} -10.5485 q^{79} +12.2797 q^{80} +1.00000 q^{81} +6.61237 q^{82} +3.13724 q^{83} -0.159504 q^{84} -11.5541 q^{85} -11.7931 q^{86} +9.69267 q^{87} -12.5608 q^{88} -14.7275 q^{89} +4.21838 q^{90} -1.16184 q^{91} -0.102731 q^{92} +6.27160 q^{93} -9.69476 q^{94} -10.1708 q^{95} -0.775262 q^{96} +7.12268 q^{97} +8.26018 q^{98} -4.61255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−1.46195	−1.03375	−0.516876	−	0.856060i	$-0.672905\pi$
$2$	−1.46195	−1.03375	−0.516876	+	0.856060i	$0.672905\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.137285	0.0686427
$5$	−2.88545	−1.29041	−0.645207	−	0.764008i	$-0.723229\pi$
$5$	−2.88545	−1.29041	−0.645207	+	0.764008i	$0.723229\pi$
$6$	1.46195	0.596837
$7$	1.16184	0.439135	0.219567	−	0.975597i	$-0.429535\pi$
$7$	1.16184	0.439135	0.219567	+	0.975597i	$0.429535\pi$
$8$	2.72319	0.962792
$9$	1.00000	0.333333
$10$	4.21838	1.33397
$11$	−4.61255	−1.39074	−0.695368	−	0.718654i	$-0.744758\pi$
$11$	−4.61255	−1.39074	−0.695368	+	0.718654i	$0.744758\pi$
$12$	−0.137285	−0.0396309
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.69855	−0.453956
$15$	2.88545	0.745021
$16$	−4.25572	−1.06393
$17$	4.00427	0.971177	0.485589	−	0.874187i	$-0.338605\pi$
$17$	4.00427	0.971177	0.485589	+	0.874187i	$0.338605\pi$
$18$	−1.46195	−0.344584
$19$	3.52485	0.808656	0.404328	−	0.914614i	$-0.367505\pi$
$19$	3.52485	0.808656	0.404328	+	0.914614i	$0.367505\pi$
$20$	−0.396131	−0.0885776
$21$	−1.16184	−0.253535
$22$	6.74329	1.43768
$23$	−0.748303	−0.156032	−0.0780160	−	0.996952i	$-0.524859\pi$
$23$	−0.748303	−0.156032	−0.0780160	+	0.996952i	$0.524859\pi$
$24$	−2.72319	−0.555868
$25$	3.32585	0.665170
$26$	1.46195	0.286711
$27$	−1.00000	−0.192450
$28$	0.159504	0.0301434
$29$	−9.69267	−1.79988	−0.899942	−	0.436010i	$-0.856391\pi$
$29$	−9.69267	−1.79988	−0.899942	+	0.436010i	$0.856391\pi$
$30$	−4.21838	−0.770167
$31$	−6.27160	−1.12641	−0.563206	−	0.826317i	$-0.690432\pi$
$31$	−6.27160	−1.12641	−0.563206	+	0.826317i	$0.690432\pi$
$32$	0.775262	0.137048
$33$	4.61255	0.802941
$34$	−5.85402	−1.00396
$35$	−3.35244	−0.566666
$36$	0.137285	0.0228809
$37$	6.26432	1.02985	0.514924	−	0.857236i	$-0.327820\pi$
$37$	6.26432	1.02985	0.514924	+	0.857236i	$0.327820\pi$
$38$	−5.15314	−0.835950
$39$	1.00000	0.160128
$40$	−7.85763	−1.24240
$41$	−4.52300	−0.706373	−0.353187	−	0.935553i	$-0.614902\pi$
$41$	−4.52300	−0.706373	−0.353187	+	0.935553i	$0.614902\pi$
$42$	1.69855	0.262092
$43$	8.06672	1.23016	0.615082	−	0.788464i	$-0.289123\pi$
$43$	8.06672	1.23016	0.615082	+	0.788464i	$0.289123\pi$
$44$	−0.633236	−0.0954639
$45$	−2.88545	−0.430138
$46$	1.09398	0.161298
$47$	6.63141	0.967291	0.483645	−	0.875264i	$-0.339312\pi$
$47$	6.63141	0.967291	0.483645	+	0.875264i	$0.339312\pi$
$48$	4.25572	0.614261
$49$	−5.65013	−0.807161
$50$	−4.86221	−0.687620
$51$	−4.00427	−0.560710
$52$	−0.137285	−0.0190381
$53$	5.13914	0.705915	0.352958	−	0.935639i	$-0.385176\pi$
$53$	5.13914	0.705915	0.352958	+	0.935639i	$0.385176\pi$
$54$	1.46195	0.198946
$55$	13.3093	1.79462
$56$	3.16391	0.422795
$57$	−3.52485	−0.466878
$58$	14.1702	1.86063
$59$	9.67410	1.25946	0.629731	−	0.776814i	$-0.283165\pi$
$59$	9.67410	1.25946	0.629731	+	0.776814i	$0.283165\pi$
$60$	0.396131	0.0511403
$61$	11.7495	1.50437	0.752185	−	0.658952i	$-0.229000\pi$
$61$	11.7495	1.50437	0.752185	+	0.658952i	$0.229000\pi$
$62$	9.16873	1.16443
$63$	1.16184	0.146378
$64$	7.37806	0.922257
$65$	2.88545	0.357897
$66$	−6.74329	−0.830042
$67$	10.8303	1.32314	0.661568	−	0.749885i	$-0.269891\pi$
$67$	10.8303	1.32314	0.661568	+	0.749885i	$0.269891\pi$
$68$	0.549728	0.0666643
$69$	0.748303	0.0900851
$70$	4.90109	0.585792
$71$	−2.91859	−0.346373	−0.173187	−	0.984889i	$-0.555406\pi$
$71$	−2.91859	−0.346373	−0.173187	+	0.984889i	$0.555406\pi$
$72$	2.72319	0.320931
$73$	−0.273822	−0.0320485	−0.0160242	−	0.999872i	$-0.505101\pi$
$73$	−0.273822	−0.0320485	−0.0160242	+	0.999872i	$0.505101\pi$
$74$	−9.15809	−1.06461
$75$	−3.32585	−0.384036
$76$	0.483911	0.0555084
$77$	−5.35905	−0.610720
$78$	−1.46195	−0.165533
$79$	−10.5485	−1.18680	−0.593401	−	0.804907i	$-0.702215\pi$
$79$	−10.5485	−1.18680	−0.593401	+	0.804907i	$0.702215\pi$
$80$	12.2797	1.37291
$81$	1.00000	0.111111
$82$	6.61237	0.730215
$83$	3.13724	0.344357	0.172179	−	0.985066i	$-0.444919\pi$
$83$	3.13724	0.344357	0.172179	+	0.985066i	$0.444919\pi$
$84$	−0.159504	−0.0174033
$85$	−11.5541	−1.25322
$86$	−11.7931	−1.27168
$87$	9.69267	1.03916
$88$	−12.5608	−1.33899
$89$	−14.7275	−1.56111	−0.780556	−	0.625085i	$-0.785064\pi$
$89$	−14.7275	−1.56111	−0.780556	+	0.625085i	$0.785064\pi$
$90$	4.21838	0.444656
$91$	−1.16184	−0.121794
$92$	−0.102731	−0.0107105
$93$	6.27160	0.650334
$94$	−9.69476	−0.999939
$95$	−10.1708	−1.04350
$96$	−0.775262	−0.0791248
$97$	7.12268	0.723199	0.361599	−	0.932334i	$-0.382231\pi$
$97$	7.12268	0.723199	0.361599	+	0.932334i	$0.382231\pi$
$98$	8.26018	0.834404
$99$	−4.61255	−0.463578
$100$	0.456591	0.0456591
$101$	7.73919	0.770078	0.385039	−	0.922900i	$-0.374188\pi$
$101$	7.73919	0.770078	0.385039	+	0.922900i	$0.374188\pi$
$102$	5.85402	0.579634
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.72319	−0.267031
$105$	3.35244	0.327165
$106$	−7.51314	−0.729741
$107$	1.84542	0.178403	0.0892017	−	0.996014i	$-0.471568\pi$
$107$	1.84542	0.178403	0.0892017	+	0.996014i	$0.471568\pi$
$108$	−0.137285	−0.0132103
$109$	11.1916	1.07196	0.535981	−	0.844230i	$-0.319942\pi$
$109$	11.1916	1.07196	0.535981	+	0.844230i	$0.319942\pi$
$110$	−19.4575	−1.85520
$111$	−6.26432	−0.594583
$112$	−4.94448	−0.467209
$113$	−4.47391	−0.420870	−0.210435	−	0.977608i	$-0.567488\pi$
$113$	−4.47391	−0.420870	−0.210435	+	0.977608i	$0.567488\pi$
$114$	5.15314	0.482636
$115$	2.15920	0.201346
$116$	−1.33066	−0.123549
$117$	−1.00000	−0.0924500
$118$	−14.1430	−1.30197
$119$	4.65232	0.426478
$120$	7.85763	0.717301
$121$	10.2756	0.934144
$122$	−17.1771	−1.55514
$123$	4.52300	0.407825
$124$	−0.860999	−0.0773200
$125$	4.83069	0.432070
$126$	−1.69855	−0.151319
$127$	5.77845	0.512754	0.256377	−	0.966577i	$-0.417471\pi$
$127$	5.77845	0.512754	0.256377	+	0.966577i	$0.417471\pi$
$128$	−12.3368	−1.09043
$129$	−8.06672	−0.710235
$130$	−4.21838	−0.369976
$131$	−19.5862	−1.71125	−0.855626	−	0.517594i	$-0.826828\pi$
$131$	−19.5862	−1.71125	−0.855626	+	0.517594i	$0.826828\pi$
$132$	0.633236	0.0551161
$133$	4.09532	0.355109
$134$	−15.8334	−1.36779
$135$	2.88545	0.248340
$136$	10.9044	0.935042
$137$	14.8897	1.27211	0.636057	−	0.771642i	$-0.280564\pi$
$137$	14.8897	1.27211	0.636057	+	0.771642i	$0.280564\pi$
$138$	−1.09398	−0.0931257
$139$	10.1125	0.857729	0.428864	−	0.903369i	$-0.358914\pi$
$139$	10.1125	0.857729	0.428864	+	0.903369i	$0.358914\pi$
$140$	−0.460241	−0.0388975
$141$	−6.63141	−0.558466
$142$	4.26683	0.358064
$143$	4.61255	0.385721
$144$	−4.25572	−0.354644
$145$	27.9678	2.32260
$146$	0.400313	0.0331302
$147$	5.65013	0.466014
$148$	0.860000	0.0706916
$149$	−6.33666	−0.519119	−0.259560	−	0.965727i	$-0.583577\pi$
$149$	−6.33666	−0.519119	−0.259560	+	0.965727i	$0.583577\pi$
$150$	4.86221	0.396998
$151$	15.4668	1.25867	0.629334	−	0.777135i	$-0.283328\pi$
$151$	15.4668	1.25867	0.629334	+	0.777135i	$0.283328\pi$
$152$	9.59883	0.778568
$153$	4.00427	0.323726
$154$	7.83464	0.631333
$155$	18.0964	1.45354
$156$	0.137285	0.0109916
$157$	−7.22099	−0.576298	−0.288149	−	0.957586i	$-0.593040\pi$
$157$	−7.22099	−0.576298	−0.288149	+	0.957586i	$0.593040\pi$
$158$	15.4214	1.22686
$159$	−5.13914	−0.407560
$160$	−2.23698	−0.176849
$161$	−0.869410	−0.0685191
$162$	−1.46195	−0.114861
$163$	−7.87926	−0.617151	−0.308576	−	0.951200i	$-0.599852\pi$
$163$	−7.87926	−0.617151	−0.308576	+	0.951200i	$0.599852\pi$
$164$	−0.620942	−0.0484874
$165$	−13.3093	−1.03613
$166$	−4.58648	−0.355980
$167$	−14.7424	−1.14080	−0.570402	−	0.821365i	$-0.693213\pi$
$167$	−14.7424	−1.14080	−0.570402	+	0.821365i	$0.693213\pi$
$168$	−3.16391	−0.244101
$169$	1.00000	0.0769231
$170$	16.8915	1.29552
$171$	3.52485	0.269552
$172$	1.10744	0.0844418
$173$	9.31628	0.708303	0.354152	−	0.935188i	$-0.384770\pi$
$173$	9.31628	0.708303	0.354152	+	0.935188i	$0.384770\pi$
$174$	−14.1702	−1.07424
$175$	3.86411	0.292099
$176$	19.6297	1.47965
$177$	−9.67410	−0.727150
$178$	21.5308	1.61380
$179$	−6.49926	−0.485778	−0.242889	−	0.970054i	$-0.578095\pi$
$179$	−6.49926	−0.485778	−0.242889	+	0.970054i	$0.578095\pi$
$180$	−0.396131	−0.0295259
$181$	−16.2300	−1.20637	−0.603184	−	0.797602i	$-0.706102\pi$
$181$	−16.2300	−1.20637	−0.603184	+	0.797602i	$0.706102\pi$
$182$	1.69855	0.125905
$183$	−11.7495	−0.868548
$184$	−2.03777	−0.150226
$185$	−18.0754	−1.32893
$186$	−9.16873	−0.672284
$187$	−18.4699	−1.35065
$188$	0.910396	0.0663975
$189$	−1.16184	−0.0845115
$190$	14.8691	1.07872
$191$	−13.2275	−0.957107	−0.478554	−	0.878058i	$-0.658839\pi$
$191$	−13.2275	−0.957107	−0.478554	+	0.878058i	$0.658839\pi$
$192$	−7.37806	−0.532465
$193$	−14.1009	−1.01500	−0.507502	−	0.861651i	$-0.669431\pi$
$193$	−14.1009	−1.01500	−0.507502	+	0.861651i	$0.669431\pi$
$194$	−10.4130	−0.747608
$195$	−2.88545	−0.206632
$196$	−0.775680	−0.0554057
$197$	3.21575	0.229113	0.114556	−	0.993417i	$-0.463455\pi$
$197$	3.21575	0.229113	0.114556	+	0.993417i	$0.463455\pi$
$198$	6.74329	0.479225
$199$	−8.58403	−0.608506	−0.304253	−	0.952591i	$-0.598407\pi$
$199$	−8.58403	−0.608506	−0.304253	+	0.952591i	$0.598407\pi$
$200$	9.05691	0.640420
$201$	−10.8303	−0.763913
$202$	−11.3143	−0.796069
$203$	−11.2613	−0.790391
$204$	−0.549728	−0.0384886
$205$	13.0509	0.911514
$206$	1.46195	0.101859
$207$	−0.748303	−0.0520107
$208$	4.25572	0.295081
$209$	−16.2585	−1.12463
$210$	−4.90109	−0.338207
$211$	13.1715	0.906766	0.453383	−	0.891316i	$-0.350217\pi$
$211$	13.1715	0.906766	0.453383	+	0.891316i	$0.350217\pi$
$212$	0.705529	0.0484559
$213$	2.91859	0.199979
$214$	−2.69790	−0.184425
$215$	−23.2762	−1.58742
$216$	−2.72319	−0.185289
$217$	−7.28660	−0.494647
$218$	−16.3615	−1.10814
$219$	0.273822	0.0185032
$220$	1.82717	0.123188
$221$	−4.00427	−0.269356
$222$	9.15809	0.614651
$223$	−6.78808	−0.454563	−0.227282	−	0.973829i	$-0.572984\pi$
$223$	−6.78808	−0.454563	−0.227282	+	0.973829i	$0.572984\pi$
$224$	0.900731	0.0601826
$225$	3.32585	0.221723
$226$	6.54062	0.435075
$227$	13.7629	0.913479	0.456739	−	0.889601i	$-0.349017\pi$
$227$	13.7629	0.913479	0.456739	+	0.889601i	$0.349017\pi$
$228$	−0.483911	−0.0320478
$229$	8.74149	0.577654	0.288827	−	0.957381i	$-0.406735\pi$
$229$	8.74149	0.577654	0.288827	+	0.957381i	$0.406735\pi$
$230$	−3.15663	−0.208142
$231$	5.35905	0.352599
$232$	−26.3950	−1.73291
$233$	17.3561	1.13704	0.568518	−	0.822671i	$-0.307517\pi$
$233$	17.3561	1.13704	0.568518	+	0.822671i	$0.307517\pi$
$234$	1.46195	0.0955704
$235$	−19.1346	−1.24821
$236$	1.32811	0.0864529
$237$	10.5485	0.685200
$238$	−6.80144	−0.440872
$239$	13.8470	0.895690	0.447845	−	0.894111i	$-0.352192\pi$
$239$	13.8470	0.895690	0.447845	+	0.894111i	$0.352192\pi$
$240$	−12.2797	−0.792651
$241$	13.9819	0.900655	0.450327	−	0.892864i	$-0.351307\pi$
$241$	13.9819	0.900655	0.450327	+	0.892864i	$0.351307\pi$
$242$	−15.0224	−0.965674
$243$	−1.00000	−0.0641500
$244$	1.61304	0.103264
$245$	16.3032	1.04157
$246$	−6.61237	−0.421590
$247$	−3.52485	−0.224281
$248$	−17.0787	−1.08450
$249$	−3.13724	−0.198815
$250$	−7.06221	−0.446653
$251$	−12.7819	−0.806786	−0.403393	−	0.915027i	$-0.632169\pi$
$251$	−12.7819	−0.806786	−0.403393	+	0.915027i	$0.632169\pi$
$252$	0.159504	0.0100478
$253$	3.45158	0.216999
$254$	−8.44777	−0.530060
$255$	11.5541	0.723548
$256$	3.27968	0.204980
$257$	−12.0040	−0.748787	−0.374393	−	0.927270i	$-0.622149\pi$
$257$	−12.0040	−0.748787	−0.374393	+	0.927270i	$0.622149\pi$
$258$	11.7931	0.734207
$259$	7.27814	0.452242
$260$	0.396131	0.0245670
$261$	−9.69267	−0.599961
$262$	28.6339	1.76901
$263$	−19.0708	−1.17596	−0.587979	−	0.808876i	$-0.700076\pi$
$263$	−19.0708	−1.17596	−0.587979	+	0.808876i	$0.700076\pi$
$264$	12.5608	0.773066
$265$	−14.8288	−0.910923
$266$	−5.98713	−0.367094
$267$	14.7275	0.901309
$268$	1.48685	0.0908237
$269$	−28.7599	−1.75352	−0.876762	−	0.480925i	$-0.840301\pi$
$269$	−28.7599	−1.75352	−0.876762	+	0.480925i	$0.840301\pi$
$270$	−4.21838	−0.256722
$271$	−31.6479	−1.92247	−0.961235	−	0.275729i	$-0.911081\pi$
$271$	−31.6479	−1.92247	−0.961235	+	0.275729i	$0.911081\pi$
$272$	−17.0411	−1.03327
$273$	1.16184	0.0703178
$274$	−21.7679	−1.31505
$275$	−15.3406	−0.925075
$276$	0.102731	0.00618369
$277$	17.0601	1.02504	0.512522	−	0.858674i	$-0.328711\pi$
$277$	17.0601	1.02504	0.512522	+	0.858674i	$0.328711\pi$
$278$	−14.7839	−0.886679
$279$	−6.27160	−0.375471
$280$	−9.12932	−0.545581
$281$	16.8740	1.00662	0.503308	−	0.864107i	$-0.332116\pi$
$281$	16.8740	1.00662	0.503308	+	0.864107i	$0.332116\pi$
$282$	9.69476	0.577315
$283$	13.9561	0.829605	0.414803	−	0.909911i	$-0.363851\pi$
$283$	13.9561	0.829605	0.414803	+	0.909911i	$0.363851\pi$
$284$	−0.400681	−0.0237760
$285$	10.1708	0.602466
$286$	−6.74329	−0.398739
$287$	−5.25500	−0.310193
$288$	0.775262	0.0456827
$289$	−0.965847	−0.0568145
$290$	−40.8874	−2.40099
$291$	−7.12268	−0.417539
$292$	−0.0375918	−0.00219989
$293$	−31.7431	−1.85445	−0.927225	−	0.374504i	$-0.877813\pi$
$293$	−31.7431	−1.85445	−0.927225	+	0.374504i	$0.877813\pi$
$294$	−8.26018	−0.481743
$295$	−27.9142	−1.62523
$296$	17.0589	0.991529
$297$	4.61255	0.267647
$298$	9.26385	0.536641
$299$	0.748303	0.0432755
$300$	−0.456591	−0.0263613
$301$	9.37225	0.540207
$302$	−22.6116	−1.30115
$303$	−7.73919	−0.444605
$304$	−15.0008	−0.860354
$305$	−33.9027	−1.94126
$306$	−5.85402	−0.334652
$307$	10.7602	0.614117	0.307058	−	0.951691i	$-0.400655\pi$
$307$	10.7602	0.614117	0.307058	+	0.951691i	$0.400655\pi$
$308$	−0.735719	−0.0419215
$309$	1.00000	0.0568880
$310$	−26.4560	−1.50260
$311$	−5.68671	−0.322464	−0.161232	−	0.986917i	$-0.551547\pi$
$311$	−5.68671	−0.322464	−0.161232	+	0.986917i	$0.551547\pi$
$312$	2.72319	0.154170
$313$	4.01308	0.226833	0.113416	−	0.993548i	$-0.463821\pi$
$313$	4.01308	0.226833	0.113416	+	0.993548i	$0.463821\pi$
$314$	10.5567	0.595749
$315$	−3.35244	−0.188889
$316$	−1.44816	−0.0814653
$317$	8.40287	0.471952	0.235976	−	0.971759i	$-0.424171\pi$
$317$	8.40287	0.471952	0.235976	+	0.971759i	$0.424171\pi$
$318$	7.51314	0.421316
$319$	44.7079	2.50316
$320$	−21.2890	−1.19009
$321$	−1.84542	−0.103001
$322$	1.27103	0.0708317
$323$	14.1144	0.785348
$324$	0.137285	0.00762697
$325$	−3.32585	−0.184485
$326$	11.5191	0.637981
$327$	−11.1916	−0.618897
$328$	−12.3170	−0.680091
$329$	7.70465	0.424771
$330$	19.4575	1.07110
$331$	−30.1798	−1.65883	−0.829416	−	0.558631i	$-0.811327\pi$
$331$	−30.1798	−1.65883	−0.829416	+	0.558631i	$0.811327\pi$
$332$	0.430698	0.0236376
$333$	6.26432	0.343283
$334$	21.5527	1.17931
$335$	−31.2505	−1.70739
$336$	4.94448	0.269743
$337$	−33.6112	−1.83092	−0.915460	−	0.402410i	$-0.868173\pi$
$337$	−33.6112	−1.83092	−0.915460	+	0.402410i	$0.868173\pi$
$338$	−1.46195	−0.0795194
$339$	4.47391	0.242990
$340$	−1.58621	−0.0860245
$341$	28.9280	1.56654
$342$	−5.15314	−0.278650
$343$	−14.6974	−0.793587
$344$	21.9672	1.18439
$345$	−2.15920	−0.116247
$346$	−13.6199	−0.732210
$347$	−15.2588	−0.819134	−0.409567	−	0.912280i	$-0.634320\pi$
$347$	−15.2588	−0.819134	−0.409567	+	0.912280i	$0.634320\pi$
$348$	1.33066	0.0713310
$349$	−11.6548	−0.623867	−0.311933	−	0.950104i	$-0.600977\pi$
$349$	−11.6548	−0.623867	−0.311933	+	0.950104i	$0.600977\pi$
$350$	−5.64912	−0.301958
$351$	1.00000	0.0533761
$352$	−3.57593	−0.190598
$353$	−9.76772	−0.519883	−0.259942	−	0.965624i	$-0.583703\pi$
$353$	−9.76772	−0.519883	−0.259942	+	0.965624i	$0.583703\pi$
$354$	14.1430	0.751693
$355$	8.42147	0.446965
$356$	−2.02187	−0.107159
$357$	−4.65232	−0.246227
$358$	9.50157	0.502174
$359$	−8.36245	−0.441353	−0.220677	−	0.975347i	$-0.570827\pi$
$359$	−8.36245	−0.441353	−0.220677	+	0.975347i	$0.570827\pi$
$360$	−7.85763	−0.414134
$361$	−6.57543	−0.346076
$362$	23.7274	1.24709
$363$	−10.2756	−0.539329
$364$	−0.159504	−0.00836028
$365$	0.790101	0.0413558
$366$	17.1771	0.897863
$367$	−10.9021	−0.569084	−0.284542	−	0.958664i	$-0.591842\pi$
$367$	−10.9021	−0.569084	−0.284542	+	0.958664i	$0.591842\pi$
$368$	3.18457	0.166007
$369$	−4.52300	−0.235458
$370$	26.4253	1.37378
$371$	5.97086	0.309992
$372$	0.860999	0.0446407
$373$	−20.6441	−1.06891	−0.534455	−	0.845197i	$-0.679483\pi$
$373$	−20.6441	−1.06891	−0.534455	+	0.845197i	$0.679483\pi$
$374$	27.0019	1.39624
$375$	−4.83069	−0.249456
$376$	18.0586	0.931300
$377$	9.69267	0.499198
$378$	1.69855	0.0873639
$379$	−36.7183	−1.88609	−0.943047	−	0.332661i	$-0.892054\pi$
$379$	−36.7183	−1.88609	−0.943047	+	0.332661i	$0.892054\pi$
$380$	−1.39630	−0.0716288
$381$	−5.77845	−0.296039
$382$	19.3379	0.989411
$383$	28.4626	1.45437	0.727185	−	0.686442i	$-0.240828\pi$
$383$	28.4626	1.45437	0.727185	+	0.686442i	$0.240828\pi$
$384$	12.3368	0.629562
$385$	15.4633	0.788082
$386$	20.6147	1.04926
$387$	8.06672	0.410054
$388$	0.977841	0.0496423
$389$	−15.9403	−0.808207	−0.404104	−	0.914713i	$-0.632416\pi$
$389$	−15.9403	−0.808207	−0.404104	+	0.914713i	$0.632416\pi$
$390$	4.21838	0.213606
$391$	−2.99641	−0.151535
$392$	−15.3864	−0.777128
$393$	19.5862	0.987992
$394$	−4.70125	−0.236846
$395$	30.4373	1.53147
$396$	−0.633236	−0.0318213
$397$	1.32041	0.0662693	0.0331346	−	0.999451i	$-0.489451\pi$
$397$	1.32041	0.0662693	0.0331346	+	0.999451i	$0.489451\pi$
$398$	12.5494	0.629044
$399$	−4.09532	−0.205022
$400$	−14.1539	−0.707695
$401$	−3.11442	−0.155527	−0.0777634	−	0.996972i	$-0.524778\pi$
$401$	−3.11442	−0.155527	−0.0777634	+	0.996972i	$0.524778\pi$
$402$	15.8334	0.789697
$403$	6.27160	0.312410
$404$	1.06248	0.0528602
$405$	−2.88545	−0.143379
$406$	16.4635	0.817069
$407$	−28.8945	−1.43225
$408$	−10.9044	−0.539847
$409$	−18.0756	−0.893783	−0.446891	−	0.894588i	$-0.647469\pi$
$409$	−18.0756	−0.893783	−0.446891	+	0.894588i	$0.647469\pi$
$410$	−19.0797	−0.942280
$411$	−14.8897	−0.734455
$412$	−0.137285	−0.00676357
$413$	11.2398	0.553073
$414$	1.09398	0.0537661
$415$	−9.05238	−0.444364
$416$	−0.775262	−0.0380103
$417$	−10.1125	−0.495210
$418$	23.7691	1.16258
$419$	0.902861	0.0441076	0.0220538	−	0.999757i	$-0.492979\pi$
$419$	0.902861	0.0441076	0.0220538	+	0.999757i	$0.492979\pi$
$420$	0.460241	0.0224575
$421$	30.0237	1.46327	0.731634	−	0.681698i	$-0.238758\pi$
$421$	30.0237	1.46327	0.731634	+	0.681698i	$0.238758\pi$
$422$	−19.2561	−0.937371
$423$	6.63141	0.322430
$424$	13.9948	0.679650
$425$	13.3176	0.645998
$426$	−4.26683	−0.206728
$427$	13.6511	0.660621
$428$	0.253349	0.0122461
$429$	−4.61255	−0.222696
$430$	34.0285	1.64100
$431$	36.8559	1.77529	0.887644	−	0.460531i	$-0.152341\pi$
$431$	36.8559	1.77529	0.887644	+	0.460531i	$0.152341\pi$
$432$	4.25572	0.204754
$433$	8.03411	0.386095	0.193047	−	0.981189i	$-0.438163\pi$
$433$	8.03411	0.386095	0.193047	+	0.981189i	$0.438163\pi$
$434$	10.6526	0.511342
$435$	−27.9678	−1.34095
$436$	1.53644	0.0735823
$437$	−2.63766	−0.126176
$438$	−0.400313	−0.0191277
$439$	12.1834	0.581481	0.290740	−	0.956802i	$-0.406098\pi$
$439$	12.1834	0.581481	0.290740	+	0.956802i	$0.406098\pi$
$440$	36.2437	1.72785
$441$	−5.65013	−0.269054
$442$	5.85402	0.278447
$443$	−17.3296	−0.823356	−0.411678	−	0.911329i	$-0.635057\pi$
$443$	−17.3296	−0.823356	−0.411678	+	0.911329i	$0.635057\pi$
$444$	−0.860000	−0.0408138
$445$	42.4956	2.01448
$446$	9.92380	0.469906
$447$	6.33666	0.299714
$448$	8.57213	0.404995
$449$	23.6914	1.11807	0.559034	−	0.829145i	$-0.311172\pi$
$449$	23.6914	1.11807	0.559034	+	0.829145i	$0.311172\pi$
$450$	−4.86221	−0.229207
$451$	20.8625	0.982378
$452$	−0.614203	−0.0288897
$453$	−15.4668	−0.726693
$454$	−20.1207	−0.944310
$455$	3.35244	0.157165
$456$	−9.59883	−0.449506
$457$	−10.0290	−0.469135	−0.234567	−	0.972100i	$-0.575367\pi$
$457$	−10.0290	−0.469135	−0.234567	+	0.972100i	$0.575367\pi$
$458$	−12.7796	−0.597151
$459$	−4.00427	−0.186903
$460$	0.296426	0.0138209
$461$	−26.0357	−1.21260	−0.606302	−	0.795235i	$-0.707348\pi$
$461$	−26.0357	−1.21260	−0.606302	+	0.795235i	$0.707348\pi$
$462$	−7.83464	−0.364500
$463$	−1.95681	−0.0909405	−0.0454703	−	0.998966i	$-0.514479\pi$
$463$	−1.95681	−0.0909405	−0.0454703	+	0.998966i	$0.514479\pi$
$464$	41.2493	1.91495
$465$	−18.0964	−0.839201
$466$	−25.3737	−1.17541
$467$	−8.00967	−0.370643	−0.185322	−	0.982678i	$-0.559333\pi$
$467$	−8.00967	−0.370643	−0.185322	+	0.982678i	$0.559333\pi$
$468$	−0.137285	−0.00634602
$469$	12.5831	0.581035
$470$	27.9738	1.29034
$471$	7.22099	0.332726
$472$	26.3444	1.21260
$473$	−37.2081	−1.71083
$474$	−15.4214	−0.708327
$475$	11.7231	0.537893
$476$	0.638696	0.0292746
$477$	5.13914	0.235305
$478$	−20.2436	−0.925921
$479$	−41.4577	−1.89425	−0.947125	−	0.320864i	$-0.896027\pi$
$479$	−41.4577	−1.89425	−0.947125	+	0.320864i	$0.896027\pi$
$480$	2.23698	0.102104
$481$	−6.26432	−0.285628
$482$	−20.4408	−0.931053
$483$	0.869410	0.0395595
$484$	1.41069	0.0641222
$485$	−20.5522	−0.933226
$486$	1.46195	0.0663152
$487$	20.4905	0.928515	0.464257	−	0.885700i	$-0.346321\pi$
$487$	20.4905	0.928515	0.464257	+	0.885700i	$0.346321\pi$
$488$	31.9961	1.44840
$489$	7.87926	0.356312
$490$	−23.8344	−1.07673
$491$	6.65040	0.300128	0.150064	−	0.988676i	$-0.452052\pi$
$491$	6.65040	0.300128	0.150064	+	0.988676i	$0.452052\pi$
$492$	0.620942	0.0279942
$493$	−38.8120	−1.74801
$494$	5.15314	0.231851
$495$	13.3093	0.598208
$496$	26.6902	1.19842
$497$	−3.39094	−0.152105
$498$	4.58648	0.205525
$499$	−3.98813	−0.178533	−0.0892665	−	0.996008i	$-0.528452\pi$
$499$	−3.98813	−0.178533	−0.0892665	+	0.996008i	$0.528452\pi$
$500$	0.663183	0.0296585
$501$	14.7424	0.658644
$502$	18.6864	0.834016
$503$	−18.0600	−0.805257	−0.402628	−	0.915363i	$-0.631903\pi$
$503$	−18.0600	−0.805257	−0.402628	+	0.915363i	$0.631903\pi$
$504$	3.16391	0.140932
$505$	−22.3311	−0.993720
$506$	−5.04603	−0.224323
$507$	−1.00000	−0.0444116
$508$	0.793297	0.0351968
$509$	−18.3353	−0.812697	−0.406349	−	0.913718i	$-0.633198\pi$
$509$	−18.3353	−0.812697	−0.406349	+	0.913718i	$0.633198\pi$
$510$	−16.8915	−0.747969
$511$	−0.318138	−0.0140736
$512$	19.8790	0.878535
$513$	−3.52485	−0.155626
$514$	17.5491	0.774059
$515$	2.88545	0.127148
$516$	−1.10744	−0.0487525
$517$	−30.5877	−1.34525
$518$	−10.6403	−0.467506
$519$	−9.31628	−0.408939
$520$	7.85763	0.344580
$521$	21.8576	0.957600	0.478800	−	0.877924i	$-0.341072\pi$
$521$	21.8576	0.957600	0.478800	+	0.877924i	$0.341072\pi$
$522$	14.1702	0.620211
$523$	−1.92595	−0.0842159	−0.0421080	−	0.999113i	$-0.513407\pi$
$523$	−1.92595	−0.0842159	−0.0421080	+	0.999113i	$0.513407\pi$
$524$	−2.68890	−0.117465
$525$	−3.86411	−0.168643
$526$	27.8805	1.21565
$527$	−25.1131	−1.09395
$528$	−19.6297	−0.854274
$529$	−22.4400	−0.975654
$530$	21.6788	0.941669
$531$	9.67410	0.419820
$532$	0.562227	0.0243756
$533$	4.52300	0.195913
$534$	−21.5308	−0.931730
$535$	−5.32487	−0.230214
$536$	29.4930	1.27391
$537$	6.49926	0.280464
$538$	42.0455	1.81271
$539$	26.0615	1.12255
$540$	0.396131	0.0170468
$541$	−32.0842	−1.37941	−0.689704	−	0.724091i	$-0.742259\pi$
$541$	−32.0842	−1.37941	−0.689704	+	0.724091i	$0.742259\pi$
$542$	46.2675	1.98736
$543$	16.2300	0.696497
$544$	3.10436	0.133098
$545$	−32.2929	−1.38327
$546$	−1.69855	−0.0726912
$547$	−7.59182	−0.324603	−0.162301	−	0.986741i	$-0.551892\pi$
$547$	−7.59182	−0.324603	−0.162301	+	0.986741i	$0.551892\pi$
$548$	2.04414	0.0873213
$549$	11.7495	0.501457
$550$	22.4272	0.956298
$551$	−34.1652	−1.45549
$552$	2.03777	0.0867333
$553$	−12.2557	−0.521166
$554$	−24.9410	−1.05964
$555$	18.0754	0.767258
$556$	1.38830	0.0588768
$557$	−22.3955	−0.948928	−0.474464	−	0.880275i	$-0.657358\pi$
$557$	−22.3955	−0.948928	−0.474464	+	0.880275i	$0.657358\pi$
$558$	9.16873	0.388143
$559$	−8.06672	−0.341186
$560$	14.2671	0.602893
$561$	18.4699	0.779798
$562$	−24.6688	−1.04059
$563$	−22.3615	−0.942424	−0.471212	−	0.882020i	$-0.656183\pi$
$563$	−22.3615	−0.942424	−0.471212	+	0.882020i	$0.656183\pi$
$564$	−0.910396	−0.0383346
$565$	12.9093	0.543097
$566$	−20.4031	−0.857606
$567$	1.16184	0.0487927
$568$	−7.94788	−0.333486
$569$	−8.81708	−0.369631	−0.184816	−	0.982773i	$-0.559169\pi$
$569$	−8.81708	−0.369631	−0.184816	+	0.982773i	$0.559169\pi$
$570$	−14.8691	−0.622800
$571$	−7.80626	−0.326682	−0.163341	−	0.986570i	$-0.552227\pi$
$571$	−7.80626	−0.326682	−0.163341	+	0.986570i	$0.552227\pi$
$572$	0.633236	0.0264769
$573$	13.2275	0.552586
$574$	7.68253	0.320663
$575$	−2.48874	−0.103788
$576$	7.37806	0.307419
$577$	42.3421	1.76272	0.881362	−	0.472442i	$-0.156627\pi$
$577$	42.3421	1.76272	0.881362	+	0.472442i	$0.156627\pi$
$578$	1.41202	0.0587321
$579$	14.1009	0.586013
$580$	3.83957	0.159429
$581$	3.64498	0.151219
$582$	10.4130	0.431632
$583$	−23.7045	−0.981741
$584$	−0.745669	−0.0308560
$585$	2.88545	0.119299
$586$	46.4067	1.91704
$587$	7.98179	0.329444	0.164722	−	0.986340i	$-0.447327\pi$
$587$	7.98179	0.329444	0.164722	+	0.986340i	$0.447327\pi$
$588$	0.775680	0.0319885
$589$	−22.1064	−0.910880
$590$	40.8090	1.68008
$591$	−3.21575	−0.132278
$592$	−26.6592	−1.09569
$593$	8.58838	0.352682	0.176341	−	0.984329i	$-0.443574\pi$
$593$	8.58838	0.352682	0.176341	+	0.984329i	$0.443574\pi$
$594$	−6.74329	−0.276681
$595$	−13.4241	−0.550333
$596$	−0.869931	−0.0356338
$597$	8.58403	0.351321
$598$	−1.09398	−0.0447361
$599$	29.5954	1.20923	0.604617	−	0.796516i	$-0.293326\pi$
$599$	29.5954	1.20923	0.604617	+	0.796516i	$0.293326\pi$
$600$	−9.05691	−0.369747
$601$	30.2501	1.23393	0.616964	−	0.786992i	$-0.288363\pi$
$601$	30.2501	1.23393	0.616964	+	0.786992i	$0.288363\pi$
$602$	−13.7017	−0.558440
$603$	10.8303	0.441046
$604$	2.12336	0.0863985
$605$	−29.6497	−1.20543
$606$	11.3143	0.459611
$607$	28.8635	1.17154	0.585768	−	0.810479i	$-0.300793\pi$
$607$	28.8635	1.17154	0.585768	+	0.810479i	$0.300793\pi$
$608$	2.73268	0.110825
$609$	11.2613	0.456333
$610$	49.5638	2.00678
$611$	−6.63141	−0.268278
$612$	0.549728	0.0222214
$613$	−10.2374	−0.413484	−0.206742	−	0.978395i	$-0.566286\pi$
$613$	−10.2374	−0.413484	−0.206742	+	0.978395i	$0.566286\pi$
$614$	−15.7308	−0.634844
$615$	−13.0509	−0.526263
$616$	−14.5937	−0.587997
$617$	−4.39445	−0.176914	−0.0884570	−	0.996080i	$-0.528194\pi$
$617$	−4.39445	−0.176914	−0.0884570	+	0.996080i	$0.528194\pi$
$618$	−1.46195	−0.0588081
$619$	20.6519	0.830069	0.415034	−	0.909806i	$-0.363770\pi$
$619$	20.6519	0.830069	0.415034	+	0.909806i	$0.363770\pi$
$620$	2.48437	0.0997749
$621$	0.748303	0.0300284
$622$	8.31366	0.333348
$623$	−17.1110	−0.685539
$624$	−4.25572	−0.170365
$625$	−30.5680	−1.22272
$626$	−5.86691	−0.234489
$627$	16.2585	0.649303
$628$	−0.991337	−0.0395587
$629$	25.0840	1.00016
$630$	4.90109	0.195264
$631$	−23.6714	−0.942343	−0.471171	−	0.882042i	$-0.656169\pi$
$631$	−23.6714	−0.942343	−0.471171	+	0.882042i	$0.656169\pi$
$632$	−28.7256	−1.14264
$633$	−13.1715	−0.523522
$634$	−12.2845	−0.487882
$635$	−16.6734	−0.661665
$636$	−0.705529	−0.0279761
$637$	5.65013	0.223866
$638$	−65.3605	−2.58765
$639$	−2.91859	−0.115458
$640$	35.5974	1.40711
$641$	−47.4694	−1.87493	−0.937464	−	0.348083i	$-0.886833\pi$
$641$	−47.4694	−1.87493	−0.937464	+	0.348083i	$0.886833\pi$
$642$	2.69790	0.106478
$643$	11.3353	0.447022	0.223511	−	0.974701i	$-0.428248\pi$
$643$	11.3353	0.447022	0.223511	+	0.974701i	$0.428248\pi$
$644$	−0.119357	−0.00470334
$645$	23.2762	0.916498
$646$	−20.6345	−0.811855
$647$	−8.77144	−0.344841	−0.172420	−	0.985023i	$-0.555159\pi$
$647$	−8.77144	−0.344841	−0.172420	+	0.985023i	$0.555159\pi$
$648$	2.72319	0.106977
$649$	−44.6223	−1.75158
$650$	4.86221	0.190712
$651$	7.28660	0.285584
$652$	−1.08171	−0.0423629
$653$	26.0859	1.02082	0.510411	−	0.859931i	$-0.329493\pi$
$653$	26.0859	1.02082	0.510411	+	0.859931i	$0.329493\pi$
$654$	16.3615	0.639786
$655$	56.5150	2.20823
$656$	19.2486	0.751532
$657$	−0.273822	−0.0106828
$658$	−11.2638	−0.439108
$659$	34.8112	1.35605	0.678027	−	0.735037i	$-0.262835\pi$
$659$	34.8112	1.35605	0.678027	+	0.735037i	$0.262835\pi$
$660$	−1.82717	−0.0711226
$661$	31.6324	1.23036	0.615178	−	0.788388i	$-0.289084\pi$
$661$	31.6324	1.23036	0.615178	+	0.788388i	$0.289084\pi$
$662$	44.1212	1.71482
$663$	4.00427	0.155513
$664$	8.54331	0.331545
$665$	−11.8168	−0.458238
$666$	−9.15809	−0.354869
$667$	7.25306	0.280840
$668$	−2.02392	−0.0783080
$669$	6.78808	0.262442
$670$	45.6865	1.76502
$671$	−54.1951	−2.09218
$672$	−0.900731	−0.0347465
$673$	8.84056	0.340779	0.170389	−	0.985377i	$-0.445497\pi$
$673$	8.84056	0.340779	0.170389	+	0.985377i	$0.445497\pi$
$674$	49.1378	1.89272
$675$	−3.32585	−0.128012
$676$	0.137285	0.00528021
$677$	−33.3382	−1.28129	−0.640645	−	0.767837i	$-0.721333\pi$
$677$	−33.3382	−1.28129	−0.640645	+	0.767837i	$0.721333\pi$
$678$	−6.54062	−0.251191
$679$	8.27542	0.317582
$680$	−31.4641	−1.20659
$681$	−13.7629	−0.527397
$682$	−42.2912	−1.61941
$683$	44.2161	1.69188	0.845940	−	0.533278i	$-0.179040\pi$
$683$	44.2161	1.69188	0.845940	+	0.533278i	$0.179040\pi$
$684$	0.483911	0.0185028
$685$	−42.9636	−1.64155
$686$	21.4869	0.820372
$687$	−8.74149	−0.333509
$688$	−34.3297	−1.30881
$689$	−5.13914	−0.195786
$690$	3.15663	0.120171
$691$	5.44807	0.207254	0.103627	−	0.994616i	$-0.466955\pi$
$691$	5.44807	0.207254	0.103627	+	0.994616i	$0.466955\pi$
$692$	1.27899	0.0486199
$693$	−5.35905	−0.203573
$694$	22.3075	0.846781
$695$	−29.1791	−1.10683
$696$	26.3950	1.00050
$697$	−18.1113	−0.686014
$698$	17.0387	0.644923
$699$	−17.3561	−0.656469
$700$	0.530486	0.0200505
$701$	18.8679	0.712632	0.356316	−	0.934365i	$-0.384033\pi$
$701$	18.8679	0.712632	0.356316	+	0.934365i	$0.384033\pi$
$702$	−1.46195	−0.0551776
$703$	22.0808	0.832792
$704$	−34.0316	−1.28262
$705$	19.1346	0.720652
$706$	14.2799	0.537430
$707$	8.99171	0.338168
$708$	−1.32811	−0.0499136
$709$	−25.4451	−0.955609	−0.477805	−	0.878466i	$-0.658567\pi$
$709$	−25.4451	−0.955609	−0.477805	+	0.878466i	$0.658567\pi$
$710$	−12.3117	−0.462051
$711$	−10.5485	−0.395601
$712$	−40.1058	−1.50303
$713$	4.69306	0.175756
$714$	6.80144	0.254538
$715$	−13.3093	−0.497739
$716$	−0.892254	−0.0333451
$717$	−13.8470	−0.517127
$718$	12.2254	0.456250
$719$	6.48595	0.241885	0.120943	−	0.992660i	$-0.461408\pi$
$719$	6.48595	0.241885	0.120943	+	0.992660i	$0.461408\pi$
$720$	12.2797	0.457637
$721$	−1.16184	−0.0432692
$722$	9.61293	0.357756
$723$	−13.9819	−0.519993
$724$	−2.22815	−0.0828084
$725$	−32.2364	−1.19723
$726$	15.0224	0.557532
$727$	−38.3435	−1.42208	−0.711041	−	0.703150i	$-0.751776\pi$
$727$	−38.3435	−1.42208	−0.711041	+	0.703150i	$0.751776\pi$
$728$	−3.16391	−0.117262
$729$	1.00000	0.0370370
$730$	−1.15509	−0.0427516
$731$	32.3013	1.19471
$732$	−1.61304	−0.0596195
$733$	1.45473	0.0537317	0.0268659	−	0.999639i	$-0.491447\pi$
$733$	1.45473	0.0537317	0.0268659	+	0.999639i	$0.491447\pi$
$734$	15.9383	0.588292
$735$	−16.3032	−0.601352
$736$	−0.580131	−0.0213839
$737$	−49.9554	−1.84013
$738$	6.61237	0.243405
$739$	36.9272	1.35839	0.679195	−	0.733958i	$-0.262329\pi$
$739$	36.9272	1.35839	0.679195	+	0.733958i	$0.262329\pi$
$740$	−2.48149	−0.0912214
$741$	3.52485	0.129489
$742$	−8.72908	−0.320455
$743$	−13.1779	−0.483449	−0.241724	−	0.970345i	$-0.577713\pi$
$743$	−13.1779	−0.483449	−0.241724	+	0.970345i	$0.577713\pi$
$744$	17.0787	0.626137
$745$	18.2841	0.669879
$746$	30.1805	1.10499
$747$	3.13724	0.114786
$748$	−2.53564	−0.0927123
$749$	2.14408	0.0783431
$750$	7.06221	0.257875
$751$	−30.6927	−1.11999	−0.559996	−	0.828495i	$-0.689197\pi$
$751$	−30.6927	−1.11999	−0.559996	+	0.828495i	$0.689197\pi$
$752$	−28.2215	−1.02913
$753$	12.7819	0.465798
$754$	−14.1702	−0.516047
$755$	−44.6287	−1.62420
$756$	−0.159504	−0.00580110
$757$	40.2796	1.46399	0.731993	−	0.681312i	$-0.238590\pi$
$757$	40.2796	1.46399	0.731993	+	0.681312i	$0.238590\pi$
$758$	53.6802	1.94975
$759$	−3.45158	−0.125285
$760$	−27.6970	−1.00468
$761$	−45.2010	−1.63853	−0.819267	−	0.573412i	$-0.805619\pi$
$761$	−45.2010	−1.63853	−0.819267	+	0.573412i	$0.805619\pi$
$762$	8.44777	0.306031
$763$	13.0029	0.470735
$764$	−1.81594	−0.0656984
$765$	−11.5541	−0.417740
$766$	−41.6107	−1.50346
$767$	−9.67410	−0.349312
$768$	−3.27968	−0.118345
$769$	51.9622	1.87380	0.936902	−	0.349591i	$-0.113680\pi$
$769$	51.9622	1.87380	0.936902	+	0.349591i	$0.113680\pi$
$770$	−22.6065	−0.814681
$771$	12.0040	0.432312
$772$	−1.93585	−0.0696726
$773$	46.9734	1.68952	0.844759	−	0.535147i	$-0.179744\pi$
$773$	46.9734	1.68952	0.844759	+	0.535147i	$0.179744\pi$
$774$	−11.7931	−0.423894
$775$	−20.8584	−0.749255
$776$	19.3964	0.696290
$777$	−7.27814	−0.261102
$778$	23.3039	0.835486
$779$	−15.9429	−0.571213
$780$	−0.396131	−0.0141838
$781$	13.4622	0.481714
$782$	4.38058	0.156649
$783$	9.69267	0.346388
$784$	24.0454	0.858763
$785$	20.8358	0.743663
$786$	−28.6339	−1.02134
$787$	−18.5071	−0.659707	−0.329853	−	0.944032i	$-0.606999\pi$
$787$	−18.5071	−0.659707	−0.329853	+	0.944032i	$0.606999\pi$
$788$	0.441476	0.0157269
$789$	19.0708	0.678939
$790$	−44.4977	−1.58316
$791$	−5.19798	−0.184819
$792$	−12.5608	−0.446330
$793$	−11.7495	−0.417237
$794$	−1.93036	−0.0685060
$795$	14.8288	0.525922
$796$	−1.17846	−0.0417695
$797$	47.1287	1.66939	0.834693	−	0.550716i	$-0.185645\pi$
$797$	47.1287	1.66939	0.834693	+	0.550716i	$0.185645\pi$
$798$	5.98713	0.211942
$799$	26.5539	0.939411
$800$	2.57840	0.0911603
$801$	−14.7275	−0.520371
$802$	4.55312	0.160776
$803$	1.26302	0.0445709
$804$	−1.48685	−0.0524371
$805$	2.50864	0.0884180
$806$	−9.16873	−0.322955
$807$	28.7599	1.01240
$808$	21.0753	0.741425
$809$	11.5336	0.405499	0.202750	−	0.979231i	$-0.435012\pi$
$809$	11.5336	0.405499	0.202750	+	0.979231i	$0.435012\pi$
$810$	4.21838	0.148219
$811$	21.1641	0.743171	0.371586	−	0.928399i	$-0.378814\pi$
$811$	21.1641	0.743171	0.371586	+	0.928399i	$0.378814\pi$
$812$	−1.54602	−0.0542546
$813$	31.6479	1.10994
$814$	42.2421	1.48059
$815$	22.7352	0.796381
$816$	17.0411	0.596556
$817$	28.4340	0.994779
$818$	26.4256	0.923950
$819$	−1.16184	−0.0405980
$820$	1.79170	0.0625688
$821$	6.31458	0.220381	0.110190	−	0.993911i	$-0.464854\pi$
$821$	6.31458	0.220381	0.110190	+	0.993911i	$0.464854\pi$
$822$	21.7679	0.759244
$823$	−40.5117	−1.41215	−0.706074	−	0.708138i	$-0.749535\pi$
$823$	−40.5117	−1.41215	−0.706074	+	0.708138i	$0.749535\pi$
$824$	−2.72319	−0.0948667
$825$	15.3406	0.534092
$826$	−16.4319	−0.571740
$827$	−21.4248	−0.745014	−0.372507	−	0.928029i	$-0.621502\pi$
$827$	−21.4248	−0.745014	−0.372507	+	0.928029i	$0.621502\pi$
$828$	−0.102731	−0.00357016
$829$	7.88717	0.273933	0.136966	−	0.990576i	$-0.456265\pi$
$829$	7.88717	0.273933	0.136966	+	0.990576i	$0.456265\pi$
$830$	13.2341	0.459362
$831$	−17.0601	−0.591809
$832$	−7.37806	−0.255788
$833$	−22.6246	−0.783896
$834$	14.7839	0.511924
$835$	42.5387	1.47211
$836$	−2.23206	−0.0771974
$837$	6.27160	0.216778
$838$	−1.31993	−0.0455963
$839$	−24.9432	−0.861135	−0.430567	−	0.902558i	$-0.641687\pi$
$839$	−24.9432	−0.861135	−0.430567	+	0.902558i	$0.641687\pi$
$840$	9.12932	0.314992
$841$	64.9479	2.23958
$842$	−43.8931	−1.51266
$843$	−16.8740	−0.581170
$844$	1.80826	0.0622429
$845$	−2.88545	−0.0992627
$846$	−9.69476	−0.333313
$847$	11.9386	0.410215
$848$	−21.8708	−0.751045
$849$	−13.9561	−0.478973
$850$	−19.4696	−0.667801
$851$	−4.68761	−0.160689
$852$	0.400681	0.0137271
$853$	3.49654	0.119719	0.0598597	−	0.998207i	$-0.480935\pi$
$853$	3.49654	0.119719	0.0598597	+	0.998207i	$0.480935\pi$
$854$	−19.9571	−0.682918
$855$	−10.1708	−0.347834
$856$	5.02542	0.171765
$857$	12.6995	0.433805	0.216903	−	0.976193i	$-0.430405\pi$
$857$	12.6995	0.433805	0.216903	+	0.976193i	$0.430405\pi$
$858$	6.74329	0.230212
$859$	34.3103	1.17065	0.585326	−	0.810798i	$-0.300966\pi$
$859$	34.3103	1.17065	0.585326	+	0.810798i	$0.300966\pi$
$860$	−3.19548	−0.108965
$861$	5.25500	0.179090
$862$	−53.8814	−1.83521
$863$	−32.7382	−1.11442	−0.557211	−	0.830371i	$-0.688128\pi$
$863$	−32.7382	−1.11442	−0.557211	+	0.830371i	$0.688128\pi$
$864$	−0.775262	−0.0263749
$865$	−26.8817	−0.914005
$866$	−11.7454	−0.399126
$867$	0.965847	0.0328019
$868$	−1.00034	−0.0339539
$869$	48.6556	1.65053
$870$	40.8874	1.38621
$871$	−10.8303	−0.366972
$872$	30.4768	1.03208
$873$	7.12268	0.241066
$874$	3.85611	0.130435
$875$	5.61249	0.189737
$876$	0.0375918	0.00127011
$877$	−27.2250	−0.919322	−0.459661	−	0.888095i	$-0.652029\pi$
$877$	−27.2250	−0.919322	−0.459661	+	0.888095i	$0.652029\pi$
$878$	−17.8114	−0.601107
$879$	31.7431	1.07067
$880$	−56.6407	−1.90936
$881$	−30.1593	−1.01609	−0.508047	−	0.861329i	$-0.669632\pi$
$881$	−30.1593	−1.01609	−0.508047	+	0.861329i	$0.669632\pi$
$882$	8.26018	0.278135
$883$	−18.4125	−0.619629	−0.309814	−	0.950797i	$-0.600267\pi$
$883$	−18.4125	−0.619629	−0.309814	+	0.950797i	$0.600267\pi$
$884$	−0.549728	−0.0184893
$885$	27.9142	0.938325
$886$	25.3350	0.851146
$887$	−36.8349	−1.23679	−0.618397	−	0.785866i	$-0.712217\pi$
$887$	−36.8349	−1.23679	−0.618397	+	0.785866i	$0.712217\pi$
$888$	−17.0589	−0.572460
$889$	6.71364	0.225168
$890$	−62.1262	−2.08247
$891$	−4.61255	−0.154526
$892$	−0.931904	−0.0312025
$893$	23.3747	0.782206
$894$	−9.26385	−0.309830
$895$	18.7533	0.626855
$896$	−14.3335	−0.478847
$897$	−0.748303	−0.0249851
$898$	−34.6356	−1.15580
$899$	60.7885	2.02741
$900$	0.456591	0.0152197
$901$	20.5785	0.685569
$902$	−30.4999	−1.01554
$903$	−9.37225	−0.311889
$904$	−12.1833	−0.405211
$905$	46.8310	1.55672
$906$	22.6116	0.751220
$907$	−45.8058	−1.52096	−0.760479	−	0.649363i	$-0.775036\pi$
$907$	−45.8058	−1.52096	−0.760479	+	0.649363i	$0.775036\pi$
$908$	1.88945	0.0627037
$909$	7.73919	0.256693
$910$	−4.90109	−0.162469
$911$	−21.5960	−0.715508	−0.357754	−	0.933816i	$-0.616457\pi$
$911$	−21.5960	−0.715508	−0.357754	+	0.933816i	$0.616457\pi$
$912$	15.0008	0.496726
$913$	−14.4707	−0.478910
$914$	14.6618	0.484969
$915$	33.9027	1.12079
$916$	1.20008	0.0396517
$917$	−22.7560	−0.751470
$918$	5.85402	0.193211
$919$	−58.4858	−1.92927	−0.964635	−	0.263590i	$-0.915093\pi$
$919$	−58.4858	−1.92927	−0.964635	+	0.263590i	$0.915093\pi$
$920$	5.87989	0.193854
$921$	−10.7602	−0.354560
$922$	38.0628	1.25353
$923$	2.91859	0.0960667
$924$	0.735719	0.0242034
$925$	20.8342	0.685023
$926$	2.86075	0.0940099
$927$	−1.00000	−0.0328443
$928$	−7.51436	−0.246671
$929$	−49.2285	−1.61513	−0.807567	−	0.589776i	$-0.799216\pi$
$929$	−49.2285	−1.61513	−0.807567	+	0.589776i	$0.799216\pi$
$930$	26.4560	0.867525
$931$	−19.9158	−0.652715
$932$	2.38274	0.0780493
$933$	5.68671	0.186175
$934$	11.7097	0.383153
$935$	53.2940	1.74290
$936$	−2.72319	−0.0890102
$937$	−15.1554	−0.495105	−0.247553	−	0.968874i	$-0.579626\pi$
$937$	−15.1554	−0.495105	−0.247553	+	0.968874i	$0.579626\pi$
$938$	−18.3959	−0.600646
$939$	−4.01308	−0.130962
$940$	−2.62691	−0.0856803
$941$	−27.7373	−0.904210	−0.452105	−	0.891965i	$-0.649327\pi$
$941$	−27.7373	−0.904210	−0.452105	+	0.891965i	$0.649327\pi$
$942$	−10.5567	−0.343956
$943$	3.38457	0.110217
$944$	−41.1703	−1.33998
$945$	3.35244	0.109055
$946$	54.3963	1.76857
$947$	34.3520	1.11629	0.558145	−	0.829743i	$-0.311513\pi$
$947$	34.3520	1.11629	0.558145	+	0.829743i	$0.311513\pi$
$948$	1.44816	0.0470340
$949$	0.273822	0.00888864
$950$	−17.1386	−0.556048
$951$	−8.40287	−0.272482
$952$	12.6691	0.410609
$953$	51.4051	1.66517	0.832587	−	0.553894i	$-0.186859\pi$
$953$	51.4051	1.66517	0.832587	+	0.553894i	$0.186859\pi$
$954$	−7.51314	−0.243247
$955$	38.1673	1.23506
$956$	1.90100	0.0614826
$957$	−44.7079	−1.44520
$958$	60.6089	1.95818
$959$	17.2995	0.558629
$960$	21.2890	0.687101
$961$	8.33293	0.268804
$962$	9.15809	0.295269
$963$	1.84542	0.0594678
$964$	1.91951	0.0618234
$965$	40.6875	1.30978
$966$	−1.27103	−0.0408947
$967$	−23.0327	−0.740680	−0.370340	−	0.928896i	$-0.620759\pi$
$967$	−23.0327	−0.740680	−0.370340	+	0.928896i	$0.620759\pi$
$968$	27.9824	0.899387
$969$	−14.1144	−0.453421
$970$	30.0462	0.964724
$971$	41.9207	1.34530	0.672649	−	0.739961i	$-0.265156\pi$
$971$	41.9207	1.34530	0.672649	+	0.739961i	$0.265156\pi$
$972$	−0.137285	−0.00440343
$973$	11.7491	0.376658
$974$	−29.9561	−0.959854
$975$	3.32585	0.106512
$976$	−50.0026	−1.60055
$977$	17.0423	0.545231	0.272615	−	0.962123i	$-0.412111\pi$
$977$	17.0423	0.545231	0.272615	+	0.962123i	$0.412111\pi$
$978$	−11.5191	−0.368339
$979$	67.9313	2.17109
$980$	2.23819	0.0714963
$981$	11.1916	0.357320
$982$	−9.72252	−0.310258
$983$	9.37173	0.298912	0.149456	−	0.988768i	$-0.452248\pi$
$983$	9.37173	0.298912	0.149456	+	0.988768i	$0.452248\pi$
$984$	12.3170	0.392651
$985$	−9.27890	−0.295650
$986$	56.7411	1.80700
$987$	−7.70465	−0.245242
$988$	−0.483911	−0.0153952
$989$	−6.03635	−0.191945
$990$	−19.4575	−0.618399
$991$	−5.90294	−0.187513	−0.0937565	−	0.995595i	$-0.529888\pi$
$991$	−5.90294	−0.187513	−0.0937565	+	0.995595i	$0.529888\pi$
$992$	−4.86213	−0.154373
$993$	30.1798	0.957727
$994$	4.95738	0.157238
$995$	24.7688	0.785224
$996$	−0.430698	−0.0136472
$997$	−17.8947	−0.566732	−0.283366	−	0.959012i	$-0.591451\pi$
$997$	−17.8947	−0.566732	−0.283366	+	0.959012i	$0.591451\pi$
$998$	5.83042	0.184559
$999$	−6.26432	−0.198194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.46195 q^{2} -1.00000 q^{3} +0.137285 q^{4} -2.88545 q^{5} +1.46195 q^{6} +1.16184 q^{7} +2.72319 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46195 q^{2} -1.00000 q^{3} +0.137285 q^{4} -2.88545 q^{5} +1.46195 q^{6} +1.16184 q^{7} +2.72319 q^{8} +1.00000 q^{9} +4.21838 q^{10} -4.61255 q^{11} -0.137285 q^{12} -1.00000 q^{13} -1.69855 q^{14} +2.88545 q^{15} -4.25572 q^{16} +4.00427 q^{17} -1.46195 q^{18} +3.52485 q^{19} -0.396131 q^{20} -1.16184 q^{21} +6.74329 q^{22} -0.748303 q^{23} -2.72319 q^{24} +3.32585 q^{25} +1.46195 q^{26} -1.00000 q^{27} +0.159504 q^{28} -9.69267 q^{29} -4.21838 q^{30} -6.27160 q^{31} +0.775262 q^{32} +4.61255 q^{33} -5.85402 q^{34} -3.35244 q^{35} +0.137285 q^{36} +6.26432 q^{37} -5.15314 q^{38} +1.00000 q^{39} -7.85763 q^{40} -4.52300 q^{41} +1.69855 q^{42} +8.06672 q^{43} -0.633236 q^{44} -2.88545 q^{45} +1.09398 q^{46} +6.63141 q^{47} +4.25572 q^{48} -5.65013 q^{49} -4.86221 q^{50} -4.00427 q^{51} -0.137285 q^{52} +5.13914 q^{53} +1.46195 q^{54} +13.3093 q^{55} +3.16391 q^{56} -3.52485 q^{57} +14.1702 q^{58} +9.67410 q^{59} +0.396131 q^{60} +11.7495 q^{61} +9.16873 q^{62} +1.16184 q^{63} +7.37806 q^{64} +2.88545 q^{65} -6.74329 q^{66} +10.8303 q^{67} +0.549728 q^{68} +0.748303 q^{69} +4.90109 q^{70} -2.91859 q^{71} +2.72319 q^{72} -0.273822 q^{73} -9.15809 q^{74} -3.32585 q^{75} +0.483911 q^{76} -5.35905 q^{77} -1.46195 q^{78} -10.5485 q^{79} +12.2797 q^{80} +1.00000 q^{81} +6.61237 q^{82} +3.13724 q^{83} -0.159504 q^{84} -11.5541 q^{85} -11.7931 q^{86} +9.69267 q^{87} -12.5608 q^{88} -14.7275 q^{89} +4.21838 q^{90} -1.16184 q^{91} -0.102731 q^{92} +6.27160 q^{93} -9.69476 q^{94} -10.1708 q^{95} -0.775262 q^{96} +7.12268 q^{97} +8.26018 q^{98} -4.61255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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