LMFDB - Embedded newform 6014.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.60322 q^{3} +1.00000 q^{4} +0.943880 q^{5} +2.60322 q^{6} +3.39783 q^{7} -1.00000 q^{8} +3.77677 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.60322 q^{3} +1.00000 q^{4} +0.943880 q^{5} +2.60322 q^{6} +3.39783 q^{7} -1.00000 q^{8} +3.77677 q^{9} -0.943880 q^{10} -4.92552 q^{11} -2.60322 q^{12} +5.95886 q^{13} -3.39783 q^{14} -2.45713 q^{15} +1.00000 q^{16} +3.05240 q^{17} -3.77677 q^{18} +1.84307 q^{19} +0.943880 q^{20} -8.84531 q^{21} +4.92552 q^{22} -9.14532 q^{23} +2.60322 q^{24} -4.10909 q^{25} -5.95886 q^{26} -2.02211 q^{27} +3.39783 q^{28} +7.00382 q^{29} +2.45713 q^{30} -1.00000 q^{31} -1.00000 q^{32} +12.8222 q^{33} -3.05240 q^{34} +3.20714 q^{35} +3.77677 q^{36} +10.5442 q^{37} -1.84307 q^{38} -15.5123 q^{39} -0.943880 q^{40} -0.125857 q^{41} +8.84531 q^{42} -4.92207 q^{43} -4.92552 q^{44} +3.56482 q^{45} +9.14532 q^{46} -0.237304 q^{47} -2.60322 q^{48} +4.54524 q^{49} +4.10909 q^{50} -7.94607 q^{51} +5.95886 q^{52} +11.0149 q^{53} +2.02211 q^{54} -4.64910 q^{55} -3.39783 q^{56} -4.79792 q^{57} -7.00382 q^{58} -0.664926 q^{59} -2.45713 q^{60} -11.0509 q^{61} +1.00000 q^{62} +12.8328 q^{63} +1.00000 q^{64} +5.62445 q^{65} -12.8222 q^{66} +3.66981 q^{67} +3.05240 q^{68} +23.8073 q^{69} -3.20714 q^{70} +6.13047 q^{71} -3.77677 q^{72} +12.2192 q^{73} -10.5442 q^{74} +10.6969 q^{75} +1.84307 q^{76} -16.7361 q^{77} +15.5123 q^{78} +5.12720 q^{79} +0.943880 q^{80} -6.06631 q^{81} +0.125857 q^{82} +5.62773 q^{83} -8.84531 q^{84} +2.88110 q^{85} +4.92207 q^{86} -18.2325 q^{87} +4.92552 q^{88} +1.41949 q^{89} -3.56482 q^{90} +20.2472 q^{91} -9.14532 q^{92} +2.60322 q^{93} +0.237304 q^{94} +1.73964 q^{95} +2.60322 q^{96} +1.00000 q^{97} -4.54524 q^{98} -18.6026 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.60322	−1.50297	−0.751486	−	0.659749i	$-0.770663\pi$
$3$	−2.60322	−1.50297	−0.751486	+	0.659749i	$0.770663\pi$
$4$	1.00000	0.500000
$5$	0.943880	0.422116	0.211058	−	0.977474i	$-0.432309\pi$
$5$	0.943880	0.422116	0.211058	+	0.977474i	$0.432309\pi$
$6$	2.60322	1.06276
$7$	3.39783	1.28426	0.642129	−	0.766596i	$-0.278051\pi$
$7$	3.39783	1.28426	0.642129	+	0.766596i	$0.278051\pi$
$8$	−1.00000	−0.353553
$9$	3.77677	1.25892
$10$	−0.943880	−0.298481
$11$	−4.92552	−1.48510	−0.742550	−	0.669791i	$-0.766384\pi$
$11$	−4.92552	−1.48510	−0.742550	+	0.669791i	$0.766384\pi$
$12$	−2.60322	−0.751486
$13$	5.95886	1.65269	0.826346	−	0.563163i	$-0.190416\pi$
$13$	5.95886	1.65269	0.826346	+	0.563163i	$0.190416\pi$
$14$	−3.39783	−0.908108
$15$	−2.45713	−0.634428
$16$	1.00000	0.250000
$17$	3.05240	0.740315	0.370157	−	0.928969i	$-0.379304\pi$
$17$	3.05240	0.740315	0.370157	+	0.928969i	$0.379304\pi$
$18$	−3.77677	−0.890194
$19$	1.84307	0.422829	0.211415	−	0.977396i	$-0.432193\pi$
$19$	1.84307	0.422829	0.211415	+	0.977396i	$0.432193\pi$
$20$	0.943880	0.211058
$21$	−8.84531	−1.93020
$22$	4.92552	1.05012
$23$	−9.14532	−1.90693	−0.953465	−	0.301503i	$-0.902512\pi$
$23$	−9.14532	−1.90693	−0.953465	+	0.301503i	$0.902512\pi$
$24$	2.60322	0.531381
$25$	−4.10909	−0.821818
$26$	−5.95886	−1.16863
$27$	−2.02211	−0.389156
$28$	3.39783	0.642129
$29$	7.00382	1.30058	0.650288	−	0.759688i	$-0.274648\pi$
$29$	7.00382	1.30058	0.650288	+	0.759688i	$0.274648\pi$
$30$	2.45713	0.448609
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	12.8222	2.23206
$34$	−3.05240	−0.523482
$35$	3.20714	0.542106
$36$	3.77677	0.629462
$37$	10.5442	1.73345	0.866727	−	0.498782i	$-0.166219\pi$
$37$	10.5442	1.73345	0.866727	+	0.498782i	$0.166219\pi$
$38$	−1.84307	−0.298985
$39$	−15.5123	−2.48395
$40$	−0.943880	−0.149241
$41$	−0.125857	−0.0196556	−0.00982778	−	0.999952i	$-0.503128\pi$
$41$	−0.125857	−0.0196556	−0.00982778	+	0.999952i	$0.503128\pi$
$42$	8.84531	1.36486
$43$	−4.92207	−0.750608	−0.375304	−	0.926902i	$-0.622462\pi$
$43$	−4.92207	−0.750608	−0.375304	+	0.926902i	$0.622462\pi$
$44$	−4.92552	−0.742550
$45$	3.56482	0.531412
$46$	9.14532	1.34840
$47$	−0.237304	−0.0346143	−0.0173072	−	0.999850i	$-0.505509\pi$
$47$	−0.237304	−0.0346143	−0.0173072	+	0.999850i	$0.505509\pi$
$48$	−2.60322	−0.375743
$49$	4.54524	0.649320
$50$	4.10909	0.581113
$51$	−7.94607	−1.11267
$52$	5.95886	0.826346
$53$	11.0149	1.51302	0.756509	−	0.653983i	$-0.226903\pi$
$53$	11.0149	1.51302	0.756509	+	0.653983i	$0.226903\pi$
$54$	2.02211	0.275175
$55$	−4.64910	−0.626884
$56$	−3.39783	−0.454054
$57$	−4.79792	−0.635500
$58$	−7.00382	−0.919647
$59$	−0.664926	−0.0865660	−0.0432830	−	0.999063i	$-0.513782\pi$
$59$	−0.664926	−0.0865660	−0.0432830	+	0.999063i	$0.513782\pi$
$60$	−2.45713	−0.317214
$61$	−11.0509	−1.41492	−0.707460	−	0.706753i	$-0.750159\pi$
$61$	−11.0509	−1.41492	−0.707460	+	0.706753i	$0.750159\pi$
$62$	1.00000	0.127000
$63$	12.8328	1.61678
$64$	1.00000	0.125000
$65$	5.62445	0.697627
$66$	−12.8222	−1.57831
$67$	3.66981	0.448339	0.224170	−	0.974550i	$-0.428033\pi$
$67$	3.66981	0.448339	0.224170	+	0.974550i	$0.428033\pi$
$68$	3.05240	0.370157
$69$	23.8073	2.86606
$70$	−3.20714	−0.383327
$71$	6.13047	0.727553	0.363776	−	0.931486i	$-0.381487\pi$
$71$	6.13047	0.727553	0.363776	+	0.931486i	$0.381487\pi$
$72$	−3.77677	−0.445097
$73$	12.2192	1.43015	0.715073	−	0.699050i	$-0.246393\pi$
$73$	12.2192	1.43015	0.715073	+	0.699050i	$0.246393\pi$
$74$	−10.5442	−1.22574
$75$	10.6969	1.23517
$76$	1.84307	0.211415
$77$	−16.7361	−1.90725
$78$	15.5123	1.75642
$79$	5.12720	0.576855	0.288428	−	0.957502i	$-0.406868\pi$
$79$	5.12720	0.576855	0.288428	+	0.957502i	$0.406868\pi$
$80$	0.943880	0.105529
$81$	−6.06631	−0.674034
$82$	0.125857	0.0138986
$83$	5.62773	0.617723	0.308862	−	0.951107i	$-0.400052\pi$
$83$	5.62773	0.617723	0.308862	+	0.951107i	$0.400052\pi$
$84$	−8.84531	−0.965102
$85$	2.88110	0.312499
$86$	4.92207	0.530760
$87$	−18.2325	−1.95473
$88$	4.92552	0.525062
$89$	1.41949	0.150465	0.0752326	−	0.997166i	$-0.476030\pi$
$89$	1.41949	0.150465	0.0752326	+	0.997166i	$0.476030\pi$
$90$	−3.56482	−0.375765
$91$	20.2472	2.12248
$92$	−9.14532	−0.953465
$93$	2.60322	0.269942
$94$	0.237304	0.0244760
$95$	1.73964	0.178483
$96$	2.60322	0.265690
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−4.54524	−0.459138
$99$	−18.6026	−1.86963
$100$	−4.10909	−0.410909
$101$	7.63374	0.759586	0.379793	−	0.925072i	$-0.375995\pi$
$101$	7.63374	0.759586	0.379793	+	0.925072i	$0.375995\pi$
$102$	7.94607	0.786778
$103$	8.58181	0.845591	0.422796	−	0.906225i	$-0.361049\pi$
$103$	8.58181	0.845591	0.422796	+	0.906225i	$0.361049\pi$
$104$	−5.95886	−0.584315
$105$	−8.34891	−0.814770
$106$	−11.0149	−1.06987
$107$	−9.73498	−0.941116	−0.470558	−	0.882369i	$-0.655947\pi$
$107$	−9.73498	−0.941116	−0.470558	+	0.882369i	$0.655947\pi$
$108$	−2.02211	−0.194578
$109$	−5.37709	−0.515032	−0.257516	−	0.966274i	$-0.582904\pi$
$109$	−5.37709	−0.515032	−0.257516	+	0.966274i	$0.582904\pi$
$110$	4.64910	0.443274
$111$	−27.4489	−2.60533
$112$	3.39783	0.321065
$113$	−0.703704	−0.0661989	−0.0330995	−	0.999452i	$-0.510538\pi$
$113$	−0.703704	−0.0661989	−0.0330995	+	0.999452i	$0.510538\pi$
$114$	4.79792	0.449366
$115$	−8.63208	−0.804946
$116$	7.00382	0.650288
$117$	22.5053	2.08061
$118$	0.664926	0.0612114
$119$	10.3715	0.950756
$120$	2.45713	0.224304
$121$	13.2607	1.20552
$122$	11.0509	1.00050
$123$	0.327634	0.0295417
$124$	−1.00000	−0.0898027
$125$	−8.59789	−0.769018
$126$	−12.8328	−1.14324
$127$	6.29020	0.558165	0.279083	−	0.960267i	$-0.409970\pi$
$127$	6.29020	0.558165	0.279083	+	0.960267i	$0.409970\pi$
$128$	−1.00000	−0.0883883
$129$	12.8132	1.12814
$130$	−5.62445	−0.493297
$131$	−2.94083	−0.256942	−0.128471	−	0.991713i	$-0.541007\pi$
$131$	−2.94083	−0.256942	−0.128471	+	0.991713i	$0.541007\pi$
$132$	12.8222	1.11603
$133$	6.26243	0.543022
$134$	−3.66981	−0.317024
$135$	−1.90863	−0.164269
$136$	−3.05240	−0.261741
$137$	1.91034	0.163211	0.0816057	−	0.996665i	$-0.473995\pi$
$137$	1.91034	0.163211	0.0816057	+	0.996665i	$0.473995\pi$
$138$	−23.8073	−2.02661
$139$	−6.93880	−0.588541	−0.294271	−	0.955722i	$-0.595077\pi$
$139$	−6.93880	−0.588541	−0.294271	+	0.955722i	$0.595077\pi$
$140$	3.20714	0.271053
$141$	0.617755	0.0520244
$142$	−6.13047	−0.514457
$143$	−29.3505	−2.45441
$144$	3.77677	0.314731
$145$	6.61076	0.548994
$146$	−12.2192	−1.01127
$147$	−11.8323	−0.975909
$148$	10.5442	0.866727
$149$	−18.1575	−1.48752	−0.743760	−	0.668447i	$-0.766959\pi$
$149$	−18.1575	−1.48752	−0.743760	+	0.668447i	$0.766959\pi$
$150$	−10.6969	−0.873397
$151$	15.4787	1.25964	0.629820	−	0.776741i	$-0.283129\pi$
$151$	15.4787	1.25964	0.629820	+	0.776741i	$0.283129\pi$
$152$	−1.84307	−0.149493
$153$	11.5282	0.932000
$154$	16.7361	1.34863
$155$	−0.943880	−0.0758143
$156$	−15.5123	−1.24197
$157$	3.79066	0.302528	0.151264	−	0.988493i	$-0.451666\pi$
$157$	3.79066	0.302528	0.151264	+	0.988493i	$0.451666\pi$
$158$	−5.12720	−0.407898
$159$	−28.6744	−2.27402
$160$	−0.943880	−0.0746203
$161$	−31.0742	−2.44899
$162$	6.06631	0.476614
$163$	−7.08195	−0.554701	−0.277350	−	0.960769i	$-0.589456\pi$
$163$	−7.08195	−0.554701	−0.277350	+	0.960769i	$0.589456\pi$
$164$	−0.125857	−0.00982778
$165$	12.1026	0.942189
$166$	−5.62773	−0.436796
$167$	−10.4345	−0.807446	−0.403723	−	0.914881i	$-0.632284\pi$
$167$	−10.4345	−0.807446	−0.403723	+	0.914881i	$0.632284\pi$
$168$	8.84531	0.682430
$169$	22.5080	1.73139
$170$	−2.88110	−0.220970
$171$	6.96085	0.532310
$172$	−4.92207	−0.375304
$173$	−14.4730	−1.10036	−0.550182	−	0.835045i	$-0.685441\pi$
$173$	−14.4730	−1.10036	−0.550182	+	0.835045i	$0.685441\pi$
$174$	18.2325	1.38220
$175$	−13.9620	−1.05543
$176$	−4.92552	−0.371275
$177$	1.73095	0.130106
$178$	−1.41949	−0.106395
$179$	−8.20683	−0.613407	−0.306704	−	0.951805i	$-0.599226\pi$
$179$	−8.20683	−0.613407	−0.306704	+	0.951805i	$0.599226\pi$
$180$	3.56482	0.265706
$181$	−1.95334	−0.145191	−0.0725953	−	0.997361i	$-0.523128\pi$
$181$	−1.95334	−0.145191	−0.0725953	+	0.997361i	$0.523128\pi$
$182$	−20.2472	−1.50082
$183$	28.7679	2.12658
$184$	9.14532	0.674202
$185$	9.95245	0.731719
$186$	−2.60322	−0.190878
$187$	−15.0346	−1.09944
$188$	−0.237304	−0.0173072
$189$	−6.87079	−0.499776
$190$	−1.73964	−0.126206
$191$	−21.4621	−1.55295	−0.776473	−	0.630151i	$-0.782993\pi$
$191$	−21.4621	−1.55295	−0.776473	+	0.630151i	$0.782993\pi$
$192$	−2.60322	−0.187871
$193$	−6.25506	−0.450249	−0.225125	−	0.974330i	$-0.572279\pi$
$193$	−6.25506	−0.450249	−0.225125	+	0.974330i	$0.572279\pi$
$194$	−1.00000	−0.0717958
$195$	−14.6417	−1.04851
$196$	4.54524	0.324660
$197$	−15.3984	−1.09709	−0.548545	−	0.836121i	$-0.684818\pi$
$197$	−15.3984	−1.09709	−0.548545	+	0.836121i	$0.684818\pi$
$198$	18.6026	1.32203
$199$	−9.26333	−0.656660	−0.328330	−	0.944563i	$-0.606486\pi$
$199$	−9.26333	−0.656660	−0.328330	+	0.944563i	$0.606486\pi$
$200$	4.10909	0.290557
$201$	−9.55334	−0.673841
$202$	−7.63374	−0.537108
$203$	23.7978	1.67028
$204$	−7.94607	−0.556336
$205$	−0.118794	−0.00829692
$206$	−8.58181	−0.597923
$207$	−34.5398	−2.40068
$208$	5.95886	0.413173
$209$	−9.07807	−0.627943
$210$	8.34891	0.576129
$211$	21.5632	1.48447	0.742236	−	0.670139i	$-0.233765\pi$
$211$	21.5632	1.48447	0.742236	+	0.670139i	$0.233765\pi$
$212$	11.0149	0.756509
$213$	−15.9590	−1.09349
$214$	9.73498	0.665469
$215$	−4.64584	−0.316844
$216$	2.02211	0.137587
$217$	−3.39783	−0.230660
$218$	5.37709	0.364183
$219$	−31.8092	−2.14947
$220$	−4.64910	−0.313442
$221$	18.1888	1.22351
$222$	27.4489	1.84225
$223$	16.1706	1.08286	0.541432	−	0.840745i	$-0.317882\pi$
$223$	16.1706	1.08286	0.541432	+	0.840745i	$0.317882\pi$
$224$	−3.39783	−0.227027
$225$	−15.5191	−1.03461
$226$	0.703704	0.0468097
$227$	−1.40540	−0.0932794	−0.0466397	−	0.998912i	$-0.514851\pi$
$227$	−1.40540	−0.0932794	−0.0466397	+	0.998912i	$0.514851\pi$
$228$	−4.79792	−0.317750
$229$	13.9036	0.918775	0.459388	−	0.888236i	$-0.348069\pi$
$229$	13.9036	0.918775	0.459388	+	0.888236i	$0.348069\pi$
$230$	8.63208	0.569182
$231$	43.5677	2.86654
$232$	−7.00382	−0.459823
$233$	29.1204	1.90774	0.953870	−	0.300220i	$-0.0970602\pi$
$233$	29.1204	1.90774	0.953870	+	0.300220i	$0.0970602\pi$
$234$	−22.5053	−1.47122
$235$	−0.223986	−0.0146113
$236$	−0.664926	−0.0432830
$237$	−13.3473	−0.866997
$238$	−10.3715	−0.672286
$239$	23.4522	1.51700	0.758500	−	0.651674i	$-0.225933\pi$
$239$	23.4522	1.51700	0.758500	+	0.651674i	$0.225933\pi$
$240$	−2.45713	−0.158607
$241$	10.3686	0.667902	0.333951	−	0.942590i	$-0.391618\pi$
$241$	10.3686	0.667902	0.333951	+	0.942590i	$0.391618\pi$
$242$	−13.2607	−0.852431
$243$	21.8583	1.40221
$244$	−11.0509	−0.707460
$245$	4.29016	0.274088
$246$	−0.327634	−0.0208892
$247$	10.9826	0.698806
$248$	1.00000	0.0635001
$249$	−14.6502	−0.928421
$250$	8.59789	0.543778
$251$	−14.7944	−0.933816	−0.466908	−	0.884306i	$-0.654632\pi$
$251$	−14.7944	−0.933816	−0.466908	+	0.884306i	$0.654632\pi$
$252$	12.8328	0.808392
$253$	45.0454	2.83198
$254$	−6.29020	−0.394683
$255$	−7.50014	−0.469677
$256$	1.00000	0.0625000
$257$	4.48870	0.279998	0.139999	−	0.990152i	$-0.455290\pi$
$257$	4.48870	0.279998	0.139999	+	0.990152i	$0.455290\pi$
$258$	−12.8132	−0.797718
$259$	35.8274	2.22620
$260$	5.62445	0.348814
$261$	26.4518	1.63733
$262$	2.94083	0.181685
$263$	7.44196	0.458891	0.229445	−	0.973322i	$-0.426309\pi$
$263$	7.44196	0.458891	0.229445	+	0.973322i	$0.426309\pi$
$264$	−12.8222	−0.789153
$265$	10.3968	0.638669
$266$	−6.26243	−0.383974
$267$	−3.69524	−0.226145
$268$	3.66981	0.224170
$269$	−13.1012	−0.798796	−0.399398	−	0.916778i	$-0.630781\pi$
$269$	−13.1012	−0.798796	−0.399398	+	0.916778i	$0.630781\pi$
$270$	1.90863	0.116156
$271$	−1.50469	−0.0914031	−0.0457016	−	0.998955i	$-0.514552\pi$
$271$	−1.50469	−0.0914031	−0.0457016	+	0.998955i	$0.514552\pi$
$272$	3.05240	0.185079
$273$	−52.7080	−3.19003
$274$	−1.91034	−0.115408
$275$	20.2394	1.22048
$276$	23.8073	1.43303
$277$	−9.58471	−0.575890	−0.287945	−	0.957647i	$-0.592972\pi$
$277$	−9.58471	−0.575890	−0.287945	+	0.957647i	$0.592972\pi$
$278$	6.93880	0.416162
$279$	−3.77677	−0.226109
$280$	−3.20714	−0.191663
$281$	2.98829	0.178266	0.0891331	−	0.996020i	$-0.471590\pi$
$281$	2.98829	0.178266	0.0891331	+	0.996020i	$0.471590\pi$
$282$	−0.617755	−0.0367868
$283$	−24.3512	−1.44753	−0.723765	−	0.690046i	$-0.757590\pi$
$283$	−24.3512	−1.44753	−0.723765	+	0.690046i	$0.757590\pi$
$284$	6.13047	0.363776
$285$	−4.52866	−0.268255
$286$	29.3505	1.73553
$287$	−0.427640	−0.0252428
$288$	−3.77677	−0.222548
$289$	−7.68287	−0.451934
$290$	−6.61076	−0.388197
$291$	−2.60322	−0.152604
$292$	12.2192	0.715073
$293$	14.6246	0.854377	0.427188	−	0.904163i	$-0.359504\pi$
$293$	14.6246	0.854377	0.427188	+	0.904163i	$0.359504\pi$
$294$	11.8323	0.690072
$295$	−0.627610	−0.0365409
$296$	−10.5442	−0.612869
$297$	9.95995	0.577935
$298$	18.1575	1.05184
$299$	−54.4957	−3.15157
$300$	10.6969	0.617585
$301$	−16.7243	−0.963975
$302$	−15.4787	−0.890700
$303$	−19.8723	−1.14164
$304$	1.84307	0.105707
$305$	−10.4307	−0.597260
$306$	−11.5282	−0.659024
$307$	5.42257	0.309482	0.154741	−	0.987955i	$-0.450546\pi$
$307$	5.42257	0.309482	0.154741	+	0.987955i	$0.450546\pi$
$308$	−16.7361	−0.953626
$309$	−22.3404	−1.27090
$310$	0.943880	0.0536088
$311$	27.8837	1.58114	0.790570	−	0.612372i	$-0.209784\pi$
$311$	27.8837	1.58114	0.790570	+	0.612372i	$0.209784\pi$
$312$	15.5123	0.878208
$313$	−33.5668	−1.89731	−0.948655	−	0.316313i	$-0.897555\pi$
$313$	−33.5668	−1.89731	−0.948655	+	0.316313i	$0.897555\pi$
$314$	−3.79066	−0.213919
$315$	12.1126	0.682470
$316$	5.12720	0.288428
$317$	−23.5046	−1.32015	−0.660074	−	0.751200i	$-0.729475\pi$
$317$	−23.5046	−1.32015	−0.660074	+	0.751200i	$0.729475\pi$
$318$	28.6744	1.60798
$319$	−34.4974	−1.93149
$320$	0.943880	0.0527645
$321$	25.3423	1.41447
$322$	31.0742	1.73170
$323$	5.62578	0.313027
$324$	−6.06631	−0.337017
$325$	−24.4855	−1.35821
$326$	7.08195	0.392233
$327$	13.9978	0.774079
$328$	0.125857	0.00694929
$329$	−0.806318	−0.0444537
$330$	−12.1026	−0.666228
$331$	34.1598	1.87759	0.938796	−	0.344473i	$-0.111942\pi$
$331$	34.1598	1.87759	0.938796	+	0.344473i	$0.111942\pi$
$332$	5.62773	0.308862
$333$	39.8230	2.18229
$334$	10.4345	0.570950
$335$	3.46386	0.189251
$336$	−8.84531	−0.482551
$337$	10.5476	0.574562	0.287281	−	0.957846i	$-0.407249\pi$
$337$	10.5476	0.574562	0.287281	+	0.957846i	$0.407249\pi$
$338$	−22.5080	−1.22428
$339$	1.83190	0.0994951
$340$	2.88110	0.156249
$341$	4.92552	0.266732
$342$	−6.96085	−0.376400
$343$	−8.34086	−0.450364
$344$	4.92207	0.265380
$345$	22.4712	1.20981
$346$	14.4730	0.778074
$347$	24.0211	1.28952	0.644759	−	0.764386i	$-0.276958\pi$
$347$	24.0211	1.28952	0.644759	+	0.764386i	$0.276958\pi$
$348$	−18.2325	−0.977365
$349$	7.34685	0.393268	0.196634	−	0.980477i	$-0.436999\pi$
$349$	7.34685	0.393268	0.196634	+	0.980477i	$0.436999\pi$
$350$	13.9620	0.746300
$351$	−12.0495	−0.643154
$352$	4.92552	0.262531
$353$	−36.9331	−1.96575	−0.982875	−	0.184274i	$-0.941007\pi$
$353$	−36.9331	−1.96575	−0.982875	+	0.184274i	$0.941007\pi$
$354$	−1.73095	−0.0919990
$355$	5.78643	0.307112
$356$	1.41949	0.0752326
$357$	−26.9994	−1.42896
$358$	8.20683	0.433744
$359$	19.2572	1.01635	0.508177	−	0.861253i	$-0.330319\pi$
$359$	19.2572	1.01635	0.508177	+	0.861253i	$0.330319\pi$
$360$	−3.56482	−0.187882
$361$	−15.6031	−0.821216
$362$	1.95334	0.102665
$363$	−34.5206	−1.81186
$364$	20.2472	1.06124
$365$	11.5334	0.603687
$366$	−28.7679	−1.50372
$367$	33.2392	1.73507	0.867537	−	0.497373i	$-0.165702\pi$
$367$	33.2392	1.73507	0.867537	+	0.497373i	$0.165702\pi$
$368$	−9.14532	−0.476733
$369$	−0.475333	−0.0247449
$370$	−9.95245	−0.517403
$371$	37.4269	1.94311
$372$	2.60322	0.134971
$373$	10.1948	0.527865	0.263932	−	0.964541i	$-0.414980\pi$
$373$	10.1948	0.527865	0.263932	+	0.964541i	$0.414980\pi$
$374$	15.0346	0.777422
$375$	22.3822	1.15581
$376$	0.237304	0.0122380
$377$	41.7348	2.14945
$378$	6.87079	0.353395
$379$	13.4101	0.688829	0.344414	−	0.938818i	$-0.388077\pi$
$379$	13.4101	0.688829	0.344414	+	0.938818i	$0.388077\pi$
$380$	1.73964	0.0892414
$381$	−16.3748	−0.838907
$382$	21.4621	1.09810
$383$	27.8266	1.42187	0.710937	−	0.703256i	$-0.248271\pi$
$383$	27.8266	1.42187	0.710937	+	0.703256i	$0.248271\pi$
$384$	2.60322	0.132845
$385$	−15.7968	−0.805081
$386$	6.25506	0.318374
$387$	−18.5895	−0.944959
$388$	1.00000	0.0507673
$389$	28.3819	1.43902	0.719509	−	0.694483i	$-0.244367\pi$
$389$	28.3819	1.43902	0.719509	+	0.694483i	$0.244367\pi$
$390$	14.6417	0.741411
$391$	−27.9151	−1.41173
$392$	−4.54524	−0.229569
$393$	7.65564	0.386176
$394$	15.3984	0.775759
$395$	4.83946	0.243500
$396$	−18.6026	−0.934814
$397$	−28.4753	−1.42913	−0.714567	−	0.699567i	$-0.753376\pi$
$397$	−28.4753	−1.42913	−0.714567	+	0.699567i	$0.753376\pi$
$398$	9.26333	0.464329
$399$	−16.3025	−0.816146
$400$	−4.10909	−0.205455
$401$	21.5792	1.07762	0.538808	−	0.842429i	$-0.318875\pi$
$401$	21.5792	1.07762	0.538808	+	0.842429i	$0.318875\pi$
$402$	9.55334	0.476477
$403$	−5.95886	−0.296832
$404$	7.63374	0.379793
$405$	−5.72587	−0.284521
$406$	−23.7978	−1.18106
$407$	−51.9356	−2.57435
$408$	7.94607	0.393389
$409$	−8.84642	−0.437427	−0.218714	−	0.975789i	$-0.570186\pi$
$409$	−8.84642	−0.437427	−0.218714	+	0.975789i	$0.570186\pi$
$410$	0.118794	0.00586681
$411$	−4.97304	−0.245302
$412$	8.58181	0.422796
$413$	−2.25930	−0.111173
$414$	34.5398	1.69754
$415$	5.31190	0.260751
$416$	−5.95886	−0.292157
$417$	18.0633	0.884561
$418$	9.07807	0.444023
$419$	−16.8814	−0.824710	−0.412355	−	0.911023i	$-0.635294\pi$
$419$	−16.8814	−0.824710	−0.412355	+	0.911023i	$0.635294\pi$
$420$	−8.34891	−0.407385
$421$	3.80313	0.185353	0.0926766	−	0.995696i	$-0.470458\pi$
$421$	3.80313	0.185353	0.0926766	+	0.995696i	$0.470458\pi$
$422$	−21.5632	−1.04968
$423$	−0.896243	−0.0435768
$424$	−11.0149	−0.534933
$425$	−12.5426	−0.608404
$426$	15.9590	0.773215
$427$	−37.5490	−1.81712
$428$	−9.73498	−0.470558
$429$	76.4058	3.68891
$430$	4.64584	0.224042
$431$	−4.69663	−0.226229	−0.113114	−	0.993582i	$-0.536083\pi$
$431$	−4.69663	−0.226229	−0.113114	+	0.993582i	$0.536083\pi$
$432$	−2.02211	−0.0972889
$433$	31.2137	1.50003	0.750017	−	0.661418i	$-0.230045\pi$
$433$	31.2137	1.50003	0.750017	+	0.661418i	$0.230045\pi$
$434$	3.39783	0.163101
$435$	−17.2093	−0.825123
$436$	−5.37709	−0.257516
$437$	−16.8554	−0.806305
$438$	31.8092	1.51990
$439$	20.2783	0.967829	0.483915	−	0.875115i	$-0.339215\pi$
$439$	20.2783	0.967829	0.483915	+	0.875115i	$0.339215\pi$
$440$	4.64910	0.221637
$441$	17.1663	0.817444
$442$	−18.1888	−0.865154
$443$	32.0949	1.52487	0.762437	−	0.647062i	$-0.224003\pi$
$443$	32.0949	1.52487	0.762437	+	0.647062i	$0.224003\pi$
$444$	−27.4489	−1.30267
$445$	1.33982	0.0635137
$446$	−16.1706	−0.765700
$447$	47.2680	2.23570
$448$	3.39783	0.160532
$449$	−21.5708	−1.01799	−0.508995	−	0.860769i	$-0.669983\pi$
$449$	−21.5708	−1.01799	−0.508995	+	0.860769i	$0.669983\pi$
$450$	15.5191	0.731577
$451$	0.619910	0.0291904
$452$	−0.703704	−0.0330995
$453$	−40.2946	−1.89320
$454$	1.40540	0.0659585
$455$	19.1109	0.895934
$456$	4.79792	0.224683
$457$	−10.4505	−0.488852	−0.244426	−	0.969668i	$-0.578599\pi$
$457$	−10.4505	−0.488852	−0.244426	+	0.969668i	$0.578599\pi$
$458$	−13.9036	−0.649672
$459$	−6.17229	−0.288098
$460$	−8.63208	−0.402473
$461$	6.65772	0.310081	0.155040	−	0.987908i	$-0.450449\pi$
$461$	6.65772	0.310081	0.155040	+	0.987908i	$0.450449\pi$
$462$	−43.5677	−2.02695
$463$	40.7385	1.89328	0.946639	−	0.322296i	$-0.104455\pi$
$463$	40.7385	1.89328	0.946639	+	0.322296i	$0.104455\pi$
$464$	7.00382	0.325144
$465$	2.45713	0.113947
$466$	−29.1204	−1.34898
$467$	−5.95721	−0.275667	−0.137833	−	0.990455i	$-0.544014\pi$
$467$	−5.95721	−0.275667	−0.137833	+	0.990455i	$0.544014\pi$
$468$	22.5053	1.04031
$469$	12.4694	0.575783
$470$	0.223986	0.0103317
$471$	−9.86793	−0.454690
$472$	0.664926	0.0306057
$473$	24.2437	1.11473
$474$	13.3473	0.613060
$475$	−7.57334	−0.347489
$476$	10.3715	0.475378
$477$	41.6009	1.90478
$478$	−23.4522	−1.07268
$479$	−36.1575	−1.65208	−0.826040	−	0.563612i	$-0.809411\pi$
$479$	−36.1575	−1.65208	−0.826040	+	0.563612i	$0.809411\pi$
$480$	2.45713	0.112152
$481$	62.8314	2.86487
$482$	−10.3686	−0.472278
$483$	80.8931	3.68076
$484$	13.2607	0.602760
$485$	0.943880	0.0428594
$486$	−21.8583	−0.991512
$487$	−24.7559	−1.12180	−0.560898	−	0.827885i	$-0.689544\pi$
$487$	−24.7559	−1.12180	−0.560898	+	0.827885i	$0.689544\pi$
$488$	11.0509	0.500250
$489$	18.4359	0.833700
$490$	−4.29016	−0.193810
$491$	31.8772	1.43860	0.719298	−	0.694702i	$-0.244464\pi$
$491$	31.8772	1.43860	0.719298	+	0.694702i	$0.244464\pi$
$492$	0.327634	0.0147709
$493$	21.3784	0.962836
$494$	−10.9826	−0.494130
$495$	−17.5586	−0.789199
$496$	−1.00000	−0.0449013
$497$	20.8303	0.934366
$498$	14.6502	0.656493
$499$	23.9291	1.07121	0.535607	−	0.844467i	$-0.320083\pi$
$499$	23.9291	1.07121	0.535607	+	0.844467i	$0.320083\pi$
$500$	−8.59789	−0.384509
$501$	27.1633	1.21357
$502$	14.7944	0.660307
$503$	38.5431	1.71855	0.859275	−	0.511514i	$-0.170915\pi$
$503$	38.5431	1.71855	0.859275	+	0.511514i	$0.170915\pi$
$504$	−12.8328	−0.571619
$505$	7.20534	0.320633
$506$	−45.0454	−2.00251
$507$	−58.5935	−2.60223
$508$	6.29020	0.279083
$509$	29.6895	1.31596	0.657982	−	0.753033i	$-0.271410\pi$
$509$	29.6895	1.31596	0.657982	+	0.753033i	$0.271410\pi$
$510$	7.50014	0.332112
$511$	41.5186	1.83668
$512$	−1.00000	−0.0441942
$513$	−3.72689	−0.164546
$514$	−4.48870	−0.197988
$515$	8.10020	0.356937
$516$	12.8132	0.564072
$517$	1.16884	0.0514057
$518$	−35.8274	−1.57416
$519$	37.6765	1.65381
$520$	−5.62445	−0.246648
$521$	−7.73803	−0.339009	−0.169505	−	0.985529i	$-0.554217\pi$
$521$	−7.73803	−0.339009	−0.169505	+	0.985529i	$0.554217\pi$
$522$	−26.4518	−1.15777
$523$	18.4790	0.808029	0.404014	−	0.914753i	$-0.367615\pi$
$523$	18.4790	0.808029	0.404014	+	0.914753i	$0.367615\pi$
$524$	−2.94083	−0.128471
$525$	36.3462	1.58628
$526$	−7.44196	−0.324485
$527$	−3.05240	−0.132964
$528$	12.8222	0.558016
$529$	60.6368	2.63638
$530$	−10.3968	−0.451607
$531$	−2.51127	−0.108980
$532$	6.26243	0.271511
$533$	−0.749964	−0.0324846
$534$	3.69524	0.159909
$535$	−9.18865	−0.397260
$536$	−3.66981	−0.158512
$537$	21.3642	0.921934
$538$	13.1012	0.564834
$539$	−22.3876	−0.964304
$540$	−1.90863	−0.0821344
$541$	16.9124	0.727121	0.363560	−	0.931571i	$-0.381561\pi$
$541$	16.9124	0.727121	0.363560	+	0.931571i	$0.381561\pi$
$542$	1.50469	0.0646318
$543$	5.08498	0.218217
$544$	−3.05240	−0.130870
$545$	−5.07533	−0.217403
$546$	52.7080	2.25569
$547$	2.70305	0.115574	0.0577871	−	0.998329i	$-0.481596\pi$
$547$	2.70305	0.115574	0.0577871	+	0.998329i	$0.481596\pi$
$548$	1.91034	0.0816057
$549$	−41.7366	−1.78128
$550$	−20.2394	−0.863011
$551$	12.9085	0.549922
$552$	−23.8073	−1.01331
$553$	17.4214	0.740831
$554$	9.58471	0.407215
$555$	−25.9085	−1.09975
$556$	−6.93880	−0.294271
$557$	−11.9261	−0.505323	−0.252661	−	0.967555i	$-0.581306\pi$
$557$	−11.9261	−0.505323	−0.252661	+	0.967555i	$0.581306\pi$
$558$	3.77677	0.159884
$559$	−29.3299	−1.24052
$560$	3.20714	0.135526
$561$	39.1385	1.65243
$562$	−2.98829	−0.126053
$563$	−10.7211	−0.451840	−0.225920	−	0.974146i	$-0.572539\pi$
$563$	−10.7211	−0.451840	−0.225920	+	0.974146i	$0.572539\pi$
$564$	0.617755	0.0260122
$565$	−0.664212	−0.0279436
$566$	24.3512	1.02356
$567$	−20.6123	−0.865634
$568$	−6.13047	−0.257229
$569$	38.8924	1.63046	0.815228	−	0.579140i	$-0.196612\pi$
$569$	38.8924	1.63046	0.815228	+	0.579140i	$0.196612\pi$
$570$	4.52866	0.189685
$571$	−42.2831	−1.76949	−0.884745	−	0.466075i	$-0.845668\pi$
$571$	−42.2831	−1.76949	−0.884745	+	0.466075i	$0.845668\pi$
$572$	−29.3505	−1.22721
$573$	55.8707	2.33403
$574$	0.427640	0.0178494
$575$	37.5789	1.56715
$576$	3.77677	0.157366
$577$	22.3446	0.930220	0.465110	−	0.885253i	$-0.346015\pi$
$577$	22.3446	0.930220	0.465110	+	0.885253i	$0.346015\pi$
$578$	7.68287	0.319565
$579$	16.2833	0.676712
$580$	6.61076	0.274497
$581$	19.1221	0.793316
$582$	2.60322	0.107907
$583$	−54.2543	−2.24698
$584$	−12.2192	−0.505633
$585$	21.2423	0.878260
$586$	−14.6246	−0.604136
$587$	−20.1445	−0.831453	−0.415727	−	0.909490i	$-0.636473\pi$
$587$	−20.1445	−0.831453	−0.415727	+	0.909490i	$0.636473\pi$
$588$	−11.8323	−0.487955
$589$	−1.84307	−0.0759423
$590$	0.627610	0.0258383
$591$	40.0854	1.64889
$592$	10.5442	0.433364
$593$	−43.4503	−1.78429	−0.892145	−	0.451749i	$-0.850800\pi$
$593$	−43.4503	−1.78429	−0.892145	+	0.451749i	$0.850800\pi$
$594$	−9.95995	−0.408662
$595$	9.78947	0.401329
$596$	−18.1575	−0.743760
$597$	24.1145	0.986942
$598$	54.4957	2.22849
$599$	26.0697	1.06518	0.532590	−	0.846374i	$-0.321219\pi$
$599$	26.0697	1.06518	0.532590	+	0.846374i	$0.321219\pi$
$600$	−10.6969	−0.436698
$601$	8.59095	0.350432	0.175216	−	0.984530i	$-0.443938\pi$
$601$	8.59095	0.350432	0.175216	+	0.984530i	$0.443938\pi$
$602$	16.7243	0.681633
$603$	13.8600	0.564425
$604$	15.4787	0.629820
$605$	12.5165	0.508869
$606$	19.8723	0.807259
$607$	−1.32215	−0.0536642	−0.0268321	−	0.999640i	$-0.508542\pi$
$607$	−1.32215	−0.0536642	−0.0268321	+	0.999640i	$0.508542\pi$
$608$	−1.84307	−0.0747463
$609$	−61.9509	−2.51038
$610$	10.4307	0.422327
$611$	−1.41406	−0.0572068
$612$	11.5282	0.466000
$613$	7.71102	0.311445	0.155723	−	0.987801i	$-0.450229\pi$
$613$	7.71102	0.311445	0.155723	+	0.987801i	$0.450229\pi$
$614$	−5.42257	−0.218837
$615$	0.309247	0.0124700
$616$	16.7361	0.674315
$617$	8.84793	0.356204	0.178102	−	0.984012i	$-0.443004\pi$
$617$	8.84793	0.356204	0.178102	+	0.984012i	$0.443004\pi$
$618$	22.3404	0.898662
$619$	0.758445	0.0304845	0.0152422	−	0.999884i	$-0.495148\pi$
$619$	0.758445	0.0304845	0.0152422	+	0.999884i	$0.495148\pi$
$620$	−0.943880	−0.0379071
$621$	18.4929	0.742093
$622$	−27.8837	−1.11803
$623$	4.82317	0.193236
$624$	−15.5123	−0.620987
$625$	12.4301	0.497203
$626$	33.5668	1.34160
$627$	23.6322	0.943781
$628$	3.79066	0.151264
$629$	32.1851	1.28330
$630$	−12.1126	−0.482579
$631$	−32.4563	−1.29206	−0.646032	−	0.763310i	$-0.723573\pi$
$631$	−32.4563	−1.29206	−0.646032	+	0.763310i	$0.723573\pi$
$632$	−5.12720	−0.203949
$633$	−56.1338	−2.23112
$634$	23.5046	0.933486
$635$	5.93720	0.235610
$636$	−28.6744	−1.13701
$637$	27.0844	1.07312
$638$	34.4974	1.36577
$639$	23.1534	0.915934
$640$	−0.943880	−0.0373101
$641$	36.8852	1.45688	0.728440	−	0.685110i	$-0.240246\pi$
$641$	36.8852	1.45688	0.728440	+	0.685110i	$0.240246\pi$
$642$	−25.3423	−1.00018
$643$	7.32347	0.288810	0.144405	−	0.989519i	$-0.453873\pi$
$643$	7.32347	0.288810	0.144405	+	0.989519i	$0.453873\pi$
$644$	−31.0742	−1.22450
$645$	12.0942	0.476207
$646$	−5.62578	−0.221343
$647$	15.2996	0.601489	0.300745	−	0.953705i	$-0.402765\pi$
$647$	15.2996	0.601489	0.300745	+	0.953705i	$0.402765\pi$
$648$	6.06631	0.238307
$649$	3.27510	0.128559
$650$	24.4855	0.960401
$651$	8.84531	0.346675
$652$	−7.08195	−0.277350
$653$	−3.77084	−0.147564	−0.0737821	−	0.997274i	$-0.523507\pi$
$653$	−3.77084	−0.147564	−0.0737821	+	0.997274i	$0.523507\pi$
$654$	−13.9978	−0.547356
$655$	−2.77579	−0.108459
$656$	−0.125857	−0.00491389
$657$	46.1490	1.80045
$658$	0.806318	0.0314335
$659$	−11.8184	−0.460380	−0.230190	−	0.973146i	$-0.573935\pi$
$659$	−11.8184	−0.460380	−0.230190	+	0.973146i	$0.573935\pi$
$660$	12.1026	0.471094
$661$	−40.0352	−1.55719	−0.778594	−	0.627529i	$-0.784067\pi$
$661$	−40.0352	−1.55719	−0.778594	+	0.627529i	$0.784067\pi$
$662$	−34.1598	−1.32766
$663$	−47.3495	−1.83890
$664$	−5.62773	−0.218398
$665$	5.91098	0.229218
$666$	−39.8230	−1.54311
$667$	−64.0521	−2.48011
$668$	−10.4345	−0.403723
$669$	−42.0957	−1.62751
$670$	−3.46386	−0.133821
$671$	54.4313	2.10130
$672$	8.84531	0.341215
$673$	19.5891	0.755103	0.377552	−	0.925989i	$-0.376766\pi$
$673$	19.5891	0.755103	0.377552	+	0.925989i	$0.376766\pi$
$674$	−10.5476	−0.406277
$675$	8.30904	0.319815
$676$	22.5080	0.865694
$677$	5.86578	0.225440	0.112720	−	0.993627i	$-0.464044\pi$
$677$	5.86578	0.225440	0.112720	+	0.993627i	$0.464044\pi$
$678$	−1.83190	−0.0703537
$679$	3.39783	0.130397
$680$	−2.88110	−0.110485
$681$	3.65856	0.140196
$682$	−4.92552	−0.188608
$683$	23.4115	0.895817	0.447908	−	0.894079i	$-0.352169\pi$
$683$	23.4115	0.895817	0.447908	+	0.894079i	$0.352169\pi$
$684$	6.96085	0.266155
$685$	1.80313	0.0688941
$686$	8.34086	0.318456
$687$	−36.1942	−1.38089
$688$	−4.92207	−0.187652
$689$	65.6365	2.50055
$690$	−22.4712	−0.855465
$691$	40.1663	1.52800	0.763998	−	0.645218i	$-0.223234\pi$
$691$	40.1663	1.52800	0.763998	+	0.645218i	$0.223234\pi$
$692$	−14.4730	−0.550182
$693$	−63.2083	−2.40108
$694$	−24.0211	−0.911827
$695$	−6.54939	−0.248433
$696$	18.2325	0.691101
$697$	−0.384165	−0.0145513
$698$	−7.34685	−0.278083
$699$	−75.8069	−2.86728
$700$	−13.9620	−0.527713
$701$	8.23963	0.311207	0.155603	−	0.987820i	$-0.450268\pi$
$701$	8.23963	0.311207	0.155603	+	0.987820i	$0.450268\pi$
$702$	12.0495	0.454779
$703$	19.4337	0.732955
$704$	−4.92552	−0.185637
$705$	0.583086	0.0219603
$706$	36.9331	1.38999
$707$	25.9381	0.975505
$708$	1.73095	0.0650531
$709$	−0.720184	−0.0270471	−0.0135235	−	0.999909i	$-0.504305\pi$
$709$	−0.720184	−0.0270471	−0.0135235	+	0.999909i	$0.504305\pi$
$710$	−5.78643	−0.217161
$711$	19.3643	0.726217
$712$	−1.41949	−0.0531975
$713$	9.14532	0.342495
$714$	26.9994	1.01043
$715$	−27.7033	−1.03605
$716$	−8.20683	−0.306704
$717$	−61.0514	−2.28001
$718$	−19.2572	−0.718671
$719$	12.9755	0.483906	0.241953	−	0.970288i	$-0.422212\pi$
$719$	12.9755	0.483906	0.241953	+	0.970288i	$0.422212\pi$
$720$	3.56482	0.132853
$721$	29.1595	1.08596
$722$	15.6031	0.580687
$723$	−26.9919	−1.00384
$724$	−1.95334	−0.0725953
$725$	−28.7793	−1.06884
$726$	34.5206	1.28118
$727$	−44.7453	−1.65951	−0.829756	−	0.558126i	$-0.811521\pi$
$727$	−44.7453	−1.65951	−0.829756	+	0.558126i	$0.811521\pi$
$728$	−20.2472	−0.750411
$729$	−38.7031	−1.43345
$730$	−11.5334	−0.426871
$731$	−15.0241	−0.555687
$732$	28.7679	1.06329
$733$	38.4453	1.42001	0.710005	−	0.704197i	$-0.248693\pi$
$733$	38.4453	1.42001	0.710005	+	0.704197i	$0.248693\pi$
$734$	−33.2392	−1.22688
$735$	−11.1682	−0.411947
$736$	9.14532	0.337101
$737$	−18.0757	−0.665828
$738$	0.475333	0.0174973
$739$	−39.1013	−1.43837	−0.719183	−	0.694821i	$-0.755484\pi$
$739$	−39.1013	−1.43837	−0.719183	+	0.694821i	$0.755484\pi$
$740$	9.95245	0.365859
$741$	−28.5901	−1.05029
$742$	−37.4269	−1.37398
$743$	19.4499	0.713549	0.356775	−	0.934191i	$-0.383876\pi$
$743$	19.4499	0.713549	0.356775	+	0.934191i	$0.383876\pi$
$744$	−2.60322	−0.0954388
$745$	−17.1385	−0.627906
$746$	−10.1948	−0.373257
$747$	21.2546	0.777667
$748$	−15.0346	−0.549721
$749$	−33.0778	−1.20864
$750$	−22.3822	−0.817283
$751$	5.36717	0.195851	0.0979254	−	0.995194i	$-0.468779\pi$
$751$	5.36717	0.195851	0.0979254	+	0.995194i	$0.468779\pi$
$752$	−0.237304	−0.00865358
$753$	38.5132	1.40350
$754$	−41.7348	−1.51989
$755$	14.6101	0.531714
$756$	−6.87079	−0.249888
$757$	10.5094	0.381971	0.190985	−	0.981593i	$-0.438832\pi$
$757$	10.5094	0.381971	0.190985	+	0.981593i	$0.438832\pi$
$758$	−13.4101	−0.487076
$759$	−117.263	−4.25639
$760$	−1.73964	−0.0631032
$761$	35.2595	1.27816	0.639078	−	0.769142i	$-0.279316\pi$
$761$	35.2595	1.27816	0.639078	+	0.769142i	$0.279316\pi$
$762$	16.3748	0.593197
$763$	−18.2704	−0.661434
$764$	−21.4621	−0.776473
$765$	10.8812	0.393412
$766$	−27.8266	−1.00542
$767$	−3.96220	−0.143067
$768$	−2.60322	−0.0939357
$769$	33.8759	1.22160	0.610799	−	0.791786i	$-0.290849\pi$
$769$	33.8759	1.22160	0.610799	+	0.791786i	$0.290849\pi$
$770$	15.7968	0.569278
$771$	−11.6851	−0.420829
$772$	−6.25506	−0.225125
$773$	−46.8080	−1.68357	−0.841784	−	0.539814i	$-0.818494\pi$
$773$	−46.8080	−1.68357	−0.841784	+	0.539814i	$0.818494\pi$
$774$	18.5895	0.668187
$775$	4.10909	0.147603
$776$	−1.00000	−0.0358979
$777$	−93.2666	−3.34592
$778$	−28.3819	−1.01754
$779$	−0.231963	−0.00831094
$780$	−14.6417	−0.524257
$781$	−30.1957	−1.08049
$782$	27.9151	0.998243
$783$	−14.1625	−0.506127
$784$	4.54524	0.162330
$785$	3.57793	0.127702
$786$	−7.65564	−0.273068
$787$	−51.7963	−1.84634	−0.923169	−	0.384395i	$-0.874410\pi$
$787$	−51.7963	−1.84634	−0.923169	+	0.384395i	$0.874410\pi$
$788$	−15.3984	−0.548545
$789$	−19.3731	−0.689700
$790$	−4.83946	−0.172180
$791$	−2.39107	−0.0850165
$792$	18.6026	0.661013
$793$	−65.8507	−2.33843
$794$	28.4753	1.01055
$795$	−27.0651	−0.959902
$796$	−9.26333	−0.328330
$797$	−31.0792	−1.10088	−0.550440	−	0.834875i	$-0.685540\pi$
$797$	−31.0792	−1.10088	−0.550440	+	0.834875i	$0.685540\pi$
$798$	16.3025	0.577103
$799$	−0.724346	−0.0256255
$800$	4.10909	0.145278
$801$	5.36107	0.189424
$802$	−21.5792	−0.761990
$803$	−60.1857	−2.12391
$804$	−9.55334	−0.336920
$805$	−29.3303	−1.03376
$806$	5.95886	0.209892
$807$	34.1054	1.20057
$808$	−7.63374	−0.268554
$809$	−20.9892	−0.737941	−0.368970	−	0.929441i	$-0.620290\pi$
$809$	−20.9892	−0.737941	−0.368970	+	0.929441i	$0.620290\pi$
$810$	5.72587	0.201186
$811$	32.0763	1.12635	0.563176	−	0.826337i	$-0.309579\pi$
$811$	32.0763	1.12635	0.563176	+	0.826337i	$0.309579\pi$
$812$	23.7978	0.835138
$813$	3.91703	0.137376
$814$	51.9356	1.82034
$815$	−6.68451	−0.234148
$816$	−7.94607	−0.278168
$817$	−9.07171	−0.317379
$818$	8.84642	0.309308
$819$	76.4690	2.67204
$820$	−0.118794	−0.00414846
$821$	−20.9590	−0.731475	−0.365738	−	0.930718i	$-0.619183\pi$
$821$	−20.9590	−0.731475	−0.365738	+	0.930718i	$0.619183\pi$
$822$	4.97304	0.173455
$823$	7.07555	0.246638	0.123319	−	0.992367i	$-0.460646\pi$
$823$	7.07555	0.246638	0.123319	+	0.992367i	$0.460646\pi$
$824$	−8.58181	−0.298962
$825$	−52.6877	−1.83435
$826$	2.25930	0.0786112
$827$	31.2046	1.08509	0.542546	−	0.840026i	$-0.317461\pi$
$827$	31.2046	1.08509	0.542546	+	0.840026i	$0.317461\pi$
$828$	−34.5398	−1.20034
$829$	45.4524	1.57863	0.789313	−	0.613990i	$-0.210437\pi$
$829$	45.4524	1.57863	0.789313	+	0.613990i	$0.210437\pi$
$830$	−5.31190	−0.184379
$831$	24.9512	0.865546
$832$	5.95886	0.206586
$833$	13.8739	0.480701
$834$	−18.0633	−0.625479
$835$	−9.84892	−0.340836
$836$	−9.07807	−0.313972
$837$	2.02211	0.0698944
$838$	16.8814	0.583158
$839$	23.5673	0.813635	0.406817	−	0.913510i	$-0.366639\pi$
$839$	23.5673	0.813635	0.406817	+	0.913510i	$0.366639\pi$
$840$	8.34891	0.288065
$841$	20.0535	0.691499
$842$	−3.80313	−0.131065
$843$	−7.77918	−0.267929
$844$	21.5632	0.742236
$845$	21.2449	0.730846
$846$	0.896243	0.0308135
$847$	45.0576	1.54820
$848$	11.0149	0.378255
$849$	63.3917	2.17560
$850$	12.5426	0.430207
$851$	−96.4300	−3.30558
$852$	−15.9590	−0.546746
$853$	−6.72373	−0.230216	−0.115108	−	0.993353i	$-0.536721\pi$
$853$	−6.72373	−0.230216	−0.115108	+	0.993353i	$0.536721\pi$
$854$	37.5490	1.28490
$855$	6.57021	0.224696
$856$	9.73498	0.332735
$857$	−8.75050	−0.298911	−0.149456	−	0.988768i	$-0.547752\pi$
$857$	−8.75050	−0.298911	−0.149456	+	0.988768i	$0.547752\pi$
$858$	−76.4058	−2.60845
$859$	18.0800	0.616880	0.308440	−	0.951244i	$-0.400193\pi$
$859$	18.0800	0.616880	0.308440	+	0.951244i	$0.400193\pi$
$860$	−4.64584	−0.158422
$861$	1.11324	0.0379392
$862$	4.69663	0.159968
$863$	−42.6432	−1.45159	−0.725795	−	0.687911i	$-0.758528\pi$
$863$	−42.6432	−1.45159	−0.725795	+	0.687911i	$0.758528\pi$
$864$	2.02211	0.0687936
$865$	−13.6608	−0.464481
$866$	−31.2137	−1.06068
$867$	20.0002	0.679244
$868$	−3.39783	−0.115330
$869$	−25.2541	−0.856688
$870$	17.2093	0.583450
$871$	21.8679	0.740966
$872$	5.37709	0.182091
$873$	3.77677	0.127824
$874$	16.8554	0.570144
$875$	−29.2141	−0.987618
$876$	−31.8092	−1.07473
$877$	26.6281	0.899167	0.449584	−	0.893238i	$-0.351572\pi$
$877$	26.6281	0.899167	0.449584	+	0.893238i	$0.351572\pi$
$878$	−20.2783	−0.684359
$879$	−38.0710	−1.28410
$880$	−4.64910	−0.156721
$881$	−16.1605	−0.544461	−0.272230	−	0.962232i	$-0.587761\pi$
$881$	−16.1605	−0.544461	−0.272230	+	0.962232i	$0.587761\pi$
$882$	−17.1663	−0.578020
$883$	−1.14040	−0.0383775	−0.0191887	−	0.999816i	$-0.506108\pi$
$883$	−1.14040	−0.0383775	−0.0191887	+	0.999816i	$0.506108\pi$
$884$	18.1888	0.611756
$885$	1.63381	0.0549199
$886$	−32.0949	−1.07825
$887$	−17.3995	−0.584217	−0.292108	−	0.956385i	$-0.594357\pi$
$887$	−17.3995	−0.584217	−0.292108	+	0.956385i	$0.594357\pi$
$888$	27.4489	0.921125
$889$	21.3730	0.716829
$890$	−1.33982	−0.0449110
$891$	29.8797	1.00101
$892$	16.1706	0.541432
$893$	−0.437367	−0.0146359
$894$	−47.2680	−1.58088
$895$	−7.74626	−0.258929
$896$	−3.39783	−0.113513
$897$	141.864	4.73672
$898$	21.5708	0.719828
$899$	−7.00382	−0.233590
$900$	−15.5191	−0.517303
$901$	33.6220	1.12011
$902$	−0.619910	−0.0206408
$903$	43.5372	1.44883
$904$	0.703704	0.0234049
$905$	−1.84372	−0.0612872
$906$	40.2946	1.33870
$907$	−17.8505	−0.592715	−0.296357	−	0.955077i	$-0.595772\pi$
$907$	−17.8505	−0.592715	−0.296357	+	0.955077i	$0.595772\pi$
$908$	−1.40540	−0.0466397
$909$	28.8309	0.956261
$910$	−19.1109	−0.633521
$911$	41.1644	1.36384	0.681919	−	0.731427i	$-0.261146\pi$
$911$	41.1644	1.36384	0.681919	+	0.731427i	$0.261146\pi$
$912$	−4.79792	−0.158875
$913$	−27.7195	−0.917380
$914$	10.4505	0.345670
$915$	27.1534	0.897665
$916$	13.9036	0.459388
$917$	−9.99244	−0.329979
$918$	6.17229	0.203716
$919$	−41.7214	−1.37626	−0.688132	−	0.725586i	$-0.741569\pi$
$919$	−41.7214	−1.37626	−0.688132	+	0.725586i	$0.741569\pi$
$920$	8.63208	0.284591
$921$	−14.1162	−0.465143
$922$	−6.65772	−0.219260
$923$	36.5306	1.20242
$924$	43.5677	1.43327
$925$	−43.3271	−1.42458
$926$	−40.7385	−1.33875
$927$	32.4116	1.06454
$928$	−7.00382	−0.229912
$929$	−15.3786	−0.504555	−0.252277	−	0.967655i	$-0.581180\pi$
$929$	−15.3786	−0.504555	−0.252277	+	0.967655i	$0.581180\pi$
$930$	−2.45713	−0.0805725
$931$	8.37719	0.274551
$932$	29.1204	0.953870
$933$	−72.5875	−2.37641
$934$	5.95721	0.194926
$935$	−14.1909	−0.464092
$936$	−22.5053	−0.735608
$937$	18.8147	0.614651	0.307325	−	0.951605i	$-0.400566\pi$
$937$	18.8147	0.614651	0.307325	+	0.951605i	$0.400566\pi$
$938$	−12.4694	−0.407140
$939$	87.3820	2.85160
$940$	−0.223986	−0.00730563
$941$	37.4847	1.22197	0.610984	−	0.791643i	$-0.290774\pi$
$941$	37.4847	1.22197	0.610984	+	0.791643i	$0.290774\pi$
$942$	9.86793	0.321515
$943$	1.15100	0.0374818
$944$	−0.664926	−0.0216415
$945$	−6.48520	−0.210964
$946$	−24.2437	−0.788232
$947$	−43.7679	−1.42227	−0.711133	−	0.703058i	$-0.751818\pi$
$947$	−43.7679	−1.42227	−0.711133	+	0.703058i	$0.751818\pi$
$948$	−13.3473	−0.433499
$949$	72.8124	2.36359
$950$	7.57334	0.245712
$951$	61.1877	1.98415
$952$	−10.3715	−0.336143
$953$	8.77123	0.284128	0.142064	−	0.989857i	$-0.454626\pi$
$953$	8.77123	0.284128	0.142064	+	0.989857i	$0.454626\pi$
$954$	−41.6009	−1.34688
$955$	−20.2577	−0.655523
$956$	23.4522	0.758500
$957$	89.8045	2.90297
$958$	36.1575	1.16820
$959$	6.49101	0.209606
$960$	−2.45713	−0.0793035
$961$	1.00000	0.0322581
$962$	−62.8314	−2.02577
$963$	−36.7668	−1.18479
$964$	10.3686	0.333951
$965$	−5.90403	−0.190057
$966$	−80.8931	−2.60269
$967$	10.4397	0.335718	0.167859	−	0.985811i	$-0.446315\pi$
$967$	10.4397	0.335718	0.167859	+	0.985811i	$0.446315\pi$
$968$	−13.2607	−0.426215
$969$	−14.6452	−0.470470
$970$	−0.943880	−0.0303062
$971$	−41.1833	−1.32163	−0.660817	−	0.750547i	$-0.729790\pi$
$971$	−41.1833	−1.32163	−0.660817	+	0.750547i	$0.729790\pi$
$972$	21.8583	0.701105
$973$	−23.5769	−0.755839
$974$	24.7559	0.793230
$975$	63.7412	2.04135
$976$	−11.0509	−0.353730
$977$	−19.6394	−0.628319	−0.314159	−	0.949370i	$-0.601723\pi$
$977$	−19.6394	−0.628319	−0.314159	+	0.949370i	$0.601723\pi$
$978$	−18.4359	−0.589515
$979$	−6.99170	−0.223456
$980$	4.29016	0.137044
$981$	−20.3081	−0.648386
$982$	−31.8772	−1.01724
$983$	−4.82611	−0.153929	−0.0769645	−	0.997034i	$-0.524523\pi$
$983$	−4.82611	−0.153929	−0.0769645	+	0.997034i	$0.524523\pi$
$984$	−0.327634	−0.0104446
$985$	−14.5342	−0.463099
$986$	−21.3784	−0.680828
$987$	2.09903	0.0668127
$988$	10.9826	0.349403
$989$	45.0139	1.43136
$990$	17.5586	0.558048
$991$	24.0654	0.764461	0.382231	−	0.924067i	$-0.375156\pi$
$991$	24.0654	0.764461	0.382231	+	0.924067i	$0.375156\pi$
$992$	1.00000	0.0317500
$993$	−88.9256	−2.82197
$994$	−20.8303	−0.660696
$995$	−8.74347	−0.277187
$996$	−14.6502	−0.464210
$997$	−7.34272	−0.232546	−0.116273	−	0.993217i	$-0.537095\pi$
$997$	−7.34272	−0.232546	−0.116273	+	0.993217i	$0.537095\pi$
$998$	−23.9291	−0.757463
$999$	−21.3215	−0.674584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.5	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.60322 q^{3} +1.00000 q^{4} +0.943880 q^{5} +2.60322 q^{6} +3.39783 q^{7} -1.00000 q^{8} +3.77677 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.60322 q^{3} +1.00000 q^{4} +0.943880 q^{5} +2.60322 q^{6} +3.39783 q^{7} -1.00000 q^{8} +3.77677 q^{9} -0.943880 q^{10} -4.92552 q^{11} -2.60322 q^{12} +5.95886 q^{13} -3.39783 q^{14} -2.45713 q^{15} +1.00000 q^{16} +3.05240 q^{17} -3.77677 q^{18} +1.84307 q^{19} +0.943880 q^{20} -8.84531 q^{21} +4.92552 q^{22} -9.14532 q^{23} +2.60322 q^{24} -4.10909 q^{25} -5.95886 q^{26} -2.02211 q^{27} +3.39783 q^{28} +7.00382 q^{29} +2.45713 q^{30} -1.00000 q^{31} -1.00000 q^{32} +12.8222 q^{33} -3.05240 q^{34} +3.20714 q^{35} +3.77677 q^{36} +10.5442 q^{37} -1.84307 q^{38} -15.5123 q^{39} -0.943880 q^{40} -0.125857 q^{41} +8.84531 q^{42} -4.92207 q^{43} -4.92552 q^{44} +3.56482 q^{45} +9.14532 q^{46} -0.237304 q^{47} -2.60322 q^{48} +4.54524 q^{49} +4.10909 q^{50} -7.94607 q^{51} +5.95886 q^{52} +11.0149 q^{53} +2.02211 q^{54} -4.64910 q^{55} -3.39783 q^{56} -4.79792 q^{57} -7.00382 q^{58} -0.664926 q^{59} -2.45713 q^{60} -11.0509 q^{61} +1.00000 q^{62} +12.8328 q^{63} +1.00000 q^{64} +5.62445 q^{65} -12.8222 q^{66} +3.66981 q^{67} +3.05240 q^{68} +23.8073 q^{69} -3.20714 q^{70} +6.13047 q^{71} -3.77677 q^{72} +12.2192 q^{73} -10.5442 q^{74} +10.6969 q^{75} +1.84307 q^{76} -16.7361 q^{77} +15.5123 q^{78} +5.12720 q^{79} +0.943880 q^{80} -6.06631 q^{81} +0.125857 q^{82} +5.62773 q^{83} -8.84531 q^{84} +2.88110 q^{85} +4.92207 q^{86} -18.2325 q^{87} +4.92552 q^{88} +1.41949 q^{89} -3.56482 q^{90} +20.2472 q^{91} -9.14532 q^{92} +2.60322 q^{93} +0.237304 q^{94} +1.73964 q^{95} +2.60322 q^{96} +1.00000 q^{97} -4.54524 q^{98} -18.6026 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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