LMFDB - Embedded newform 8018.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.32663 q^{3} +1.00000 q^{4} -0.835058 q^{5} +1.32663 q^{6} -1.21991 q^{7} -1.00000 q^{8} -1.24006 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.32663 q^{3} +1.00000 q^{4} -0.835058 q^{5} +1.32663 q^{6} -1.21991 q^{7} -1.00000 q^{8} -1.24006 q^{9} +0.835058 q^{10} -6.01829 q^{11} -1.32663 q^{12} +2.14259 q^{13} +1.21991 q^{14} +1.10781 q^{15} +1.00000 q^{16} +2.45244 q^{17} +1.24006 q^{18} +1.00000 q^{19} -0.835058 q^{20} +1.61836 q^{21} +6.01829 q^{22} +3.47719 q^{23} +1.32663 q^{24} -4.30268 q^{25} -2.14259 q^{26} +5.62498 q^{27} -1.21991 q^{28} -6.70321 q^{29} -1.10781 q^{30} +1.33297 q^{31} -1.00000 q^{32} +7.98402 q^{33} -2.45244 q^{34} +1.01869 q^{35} -1.24006 q^{36} -0.648788 q^{37} -1.00000 q^{38} -2.84242 q^{39} +0.835058 q^{40} +1.73540 q^{41} -1.61836 q^{42} +0.150751 q^{43} -6.01829 q^{44} +1.03553 q^{45} -3.47719 q^{46} +5.81406 q^{47} -1.32663 q^{48} -5.51183 q^{49} +4.30268 q^{50} -3.25347 q^{51} +2.14259 q^{52} +8.36481 q^{53} -5.62498 q^{54} +5.02562 q^{55} +1.21991 q^{56} -1.32663 q^{57} +6.70321 q^{58} -1.82208 q^{59} +1.10781 q^{60} +14.1715 q^{61} -1.33297 q^{62} +1.51276 q^{63} +1.00000 q^{64} -1.78919 q^{65} -7.98402 q^{66} -10.6683 q^{67} +2.45244 q^{68} -4.61294 q^{69} -1.01869 q^{70} +12.2953 q^{71} +1.24006 q^{72} -4.76716 q^{73} +0.648788 q^{74} +5.70804 q^{75} +1.00000 q^{76} +7.34174 q^{77} +2.84242 q^{78} -3.67241 q^{79} -0.835058 q^{80} -3.74205 q^{81} -1.73540 q^{82} +16.9835 q^{83} +1.61836 q^{84} -2.04793 q^{85} -0.150751 q^{86} +8.89265 q^{87} +6.01829 q^{88} -4.74130 q^{89} -1.03553 q^{90} -2.61376 q^{91} +3.47719 q^{92} -1.76836 q^{93} -5.81406 q^{94} -0.835058 q^{95} +1.32663 q^{96} +0.349355 q^{97} +5.51183 q^{98} +7.46306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * 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
$3$	−1.32663	−0.765928	−0.382964	−	0.923763i	$-0.625097\pi$
$3$	−1.32663	−0.765928	−0.382964	+	0.923763i	$0.625097\pi$
$4$	1.00000	0.500000
$5$	−0.835058	−0.373449	−0.186725	−	0.982412i	$-0.559787\pi$
$5$	−0.835058	−0.373449	−0.186725	+	0.982412i	$0.559787\pi$
$6$	1.32663	0.541593
$7$	−1.21991	−0.461081	−0.230541	−	0.973063i	$-0.574049\pi$
$7$	−1.21991	−0.461081	−0.230541	+	0.973063i	$0.574049\pi$
$8$	−1.00000	−0.353553
$9$	−1.24006	−0.413355
$10$	0.835058	0.264069
$11$	−6.01829	−1.81458	−0.907291	−	0.420503i	$-0.861854\pi$
$11$	−6.01829	−1.81458	−0.907291	+	0.420503i	$0.861854\pi$
$12$	−1.32663	−0.382964
$13$	2.14259	0.594248	0.297124	−	0.954839i	$-0.403972\pi$
$13$	2.14259	0.594248	0.297124	+	0.954839i	$0.403972\pi$
$14$	1.21991	0.326034
$15$	1.10781	0.286035
$16$	1.00000	0.250000
$17$	2.45244	0.594804	0.297402	−	0.954752i	$-0.403880\pi$
$17$	2.45244	0.594804	0.297402	+	0.954752i	$0.403880\pi$
$18$	1.24006	0.292286
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.835058	−0.186725
$21$	1.61836	0.353155
$22$	6.01829	1.28310
$23$	3.47719	0.725045	0.362523	−	0.931975i	$-0.381916\pi$
$23$	3.47719	0.725045	0.362523	+	0.931975i	$0.381916\pi$
$24$	1.32663	0.270796
$25$	−4.30268	−0.860536
$26$	−2.14259	−0.420197
$27$	5.62498	1.08253
$28$	−1.21991	−0.230541
$29$	−6.70321	−1.24475	−0.622377	−	0.782718i	$-0.713833\pi$
$29$	−6.70321	−1.24475	−0.622377	+	0.782718i	$0.713833\pi$
$30$	−1.10781	−0.202257
$31$	1.33297	0.239409	0.119705	−	0.992810i	$-0.461805\pi$
$31$	1.33297	0.239409	0.119705	+	0.992810i	$0.461805\pi$
$32$	−1.00000	−0.176777
$33$	7.98402	1.38984
$34$	−2.45244	−0.420590
$35$	1.01869	0.172190
$36$	−1.24006	−0.206677
$37$	−0.648788	−0.106660	−0.0533301	−	0.998577i	$-0.516984\pi$
$37$	−0.648788	−0.106660	−0.0533301	+	0.998577i	$0.516984\pi$
$38$	−1.00000	−0.162221
$39$	−2.84242	−0.455151
$40$	0.835058	0.132034
$41$	1.73540	0.271024	0.135512	−	0.990776i	$-0.456732\pi$
$41$	1.73540	0.271024	0.135512	+	0.990776i	$0.456732\pi$
$42$	−1.61836	−0.249718
$43$	0.150751	0.0229893	0.0114946	−	0.999934i	$-0.496341\pi$
$43$	0.150751	0.0229893	0.0114946	+	0.999934i	$0.496341\pi$
$44$	−6.01829	−0.907291
$45$	1.03553	0.154367
$46$	−3.47719	−0.512684
$47$	5.81406	0.848067	0.424034	−	0.905646i	$-0.360614\pi$
$47$	5.81406	0.848067	0.424034	+	0.905646i	$0.360614\pi$
$48$	−1.32663	−0.191482
$49$	−5.51183	−0.787404
$50$	4.30268	0.608491
$51$	−3.25347	−0.455577
$52$	2.14259	0.297124
$53$	8.36481	1.14899	0.574497	−	0.818506i	$-0.305198\pi$
$53$	8.36481	1.14899	0.574497	+	0.818506i	$0.305198\pi$
$54$	−5.62498	−0.765463
$55$	5.02562	0.677655
$56$	1.21991	0.163017
$57$	−1.32663	−0.175716
$58$	6.70321	0.880174
$59$	−1.82208	−0.237215	−0.118607	−	0.992941i	$-0.537843\pi$
$59$	−1.82208	−0.237215	−0.118607	+	0.992941i	$0.537843\pi$
$60$	1.10781	0.143018
$61$	14.1715	1.81448	0.907238	−	0.420618i	$-0.138187\pi$
$61$	14.1715	1.81448	0.907238	+	0.420618i	$0.138187\pi$
$62$	−1.33297	−0.169288
$63$	1.51276	0.190590
$64$	1.00000	0.125000
$65$	−1.78919	−0.221922
$66$	−7.98402	−0.982765
$67$	−10.6683	−1.30334	−0.651671	−	0.758502i	$-0.725932\pi$
$67$	−10.6683	−1.30334	−0.651671	+	0.758502i	$0.725932\pi$
$68$	2.45244	0.297402
$69$	−4.61294	−0.555332
$70$	−1.01869	−0.121757
$71$	12.2953	1.45919	0.729594	−	0.683880i	$-0.239709\pi$
$71$	12.2953	1.45919	0.729594	+	0.683880i	$0.239709\pi$
$72$	1.24006	0.146143
$73$	−4.76716	−0.557953	−0.278977	−	0.960298i	$-0.589995\pi$
$73$	−4.76716	−0.557953	−0.278977	+	0.960298i	$0.589995\pi$
$74$	0.648788	0.0754201
$75$	5.70804	0.659108
$76$	1.00000	0.114708
$77$	7.34174	0.836669
$78$	2.84242	0.321841
$79$	−3.67241	−0.413178	−0.206589	−	0.978428i	$-0.566236\pi$
$79$	−3.67241	−0.413178	−0.206589	+	0.978428i	$0.566236\pi$
$80$	−0.835058	−0.0933623
$81$	−3.74205	−0.415783
$82$	−1.73540	−0.191643
$83$	16.9835	1.86418	0.932090	−	0.362228i	$-0.117984\pi$
$83$	16.9835	1.86418	0.932090	+	0.362228i	$0.117984\pi$
$84$	1.61836	0.176577
$85$	−2.04793	−0.222129
$86$	−0.150751	−0.0162559
$87$	8.89265	0.953392
$88$	6.01829	0.641552
$89$	−4.74130	−0.502577	−0.251289	−	0.967912i	$-0.580854\pi$
$89$	−4.74130	−0.502577	−0.251289	+	0.967912i	$0.580854\pi$
$90$	−1.03553	−0.109154
$91$	−2.61376	−0.273997
$92$	3.47719	0.362523
$93$	−1.76836	−0.183370
$94$	−5.81406	−0.599674
$95$	−0.835058	−0.0856752
$96$	1.32663	0.135398
$97$	0.349355	0.0354717	0.0177358	−	0.999843i	$-0.494354\pi$
$97$	0.349355	0.0354717	0.0177358	+	0.999843i	$0.494354\pi$
$98$	5.51183	0.556779
$99$	7.46306	0.750066
$100$	−4.30268	−0.430268
$101$	2.29319	0.228181	0.114090	−	0.993470i	$-0.463605\pi$
$101$	2.29319	0.228181	0.114090	+	0.993470i	$0.463605\pi$
$102$	3.25347	0.322142
$103$	0.0518453	0.00510847	0.00255424	−	0.999997i	$-0.499187\pi$
$103$	0.0518453	0.00510847	0.00255424	+	0.999997i	$0.499187\pi$
$104$	−2.14259	−0.210099
$105$	−1.35142	−0.131885
$106$	−8.36481	−0.812462
$107$	11.7707	1.13791	0.568956	−	0.822368i	$-0.307347\pi$
$107$	11.7707	1.13791	0.568956	+	0.822368i	$0.307347\pi$
$108$	5.62498	0.541264
$109$	−10.9711	−1.05084	−0.525419	−	0.850844i	$-0.676091\pi$
$109$	−10.9711	−1.05084	−0.525419	+	0.850844i	$0.676091\pi$
$110$	−5.02562	−0.479174
$111$	0.860699	0.0816940
$112$	−1.21991	−0.115270
$113$	−2.45077	−0.230549	−0.115274	−	0.993334i	$-0.536775\pi$
$113$	−2.45077	−0.230549	−0.115274	+	0.993334i	$0.536775\pi$
$114$	1.32663	0.124250
$115$	−2.90366	−0.270768
$116$	−6.70321	−0.622377
$117$	−2.65695	−0.245635
$118$	1.82208	0.167736
$119$	−2.99175	−0.274253
$120$	−1.10781	−0.101129
$121$	25.2198	2.29271
$122$	−14.1715	−1.28303
$123$	−2.30223	−0.207585
$124$	1.33297	0.119705
$125$	7.76828	0.694816
$126$	−1.51276	−0.134767
$127$	13.5623	1.20346	0.601730	−	0.798699i	$-0.294478\pi$
$127$	13.5623	1.20346	0.601730	+	0.798699i	$0.294478\pi$
$128$	−1.00000	−0.0883883
$129$	−0.199990	−0.0176081
$130$	1.78919	0.156922
$131$	−8.62428	−0.753507	−0.376753	−	0.926314i	$-0.622960\pi$
$131$	−8.62428	−0.753507	−0.376753	+	0.926314i	$0.622960\pi$
$132$	7.98402	0.694919
$133$	−1.21991	−0.105779
$134$	10.6683	0.921602
$135$	−4.69718	−0.404269
$136$	−2.45244	−0.210295
$137$	21.4983	1.83672	0.918362	−	0.395741i	$-0.129512\pi$
$137$	21.4983	1.83672	0.918362	+	0.395741i	$0.129512\pi$
$138$	4.61294	0.392679
$139$	−19.7033	−1.67122	−0.835608	−	0.549326i	$-0.814884\pi$
$139$	−19.7033	−1.67122	−0.835608	+	0.549326i	$0.814884\pi$
$140$	1.01869	0.0860952
$141$	−7.71308	−0.649558
$142$	−12.2953	−1.03180
$143$	−12.8947	−1.07831
$144$	−1.24006	−0.103339
$145$	5.59757	0.464853
$146$	4.76716	0.394533
$147$	7.31214	0.603095
$148$	−0.648788	−0.0533301
$149$	10.2434	0.839176	0.419588	−	0.907715i	$-0.362175\pi$
$149$	10.2434	0.839176	0.419588	+	0.907715i	$0.362175\pi$
$150$	−5.70804	−0.466060
$151$	−0.778611	−0.0633625	−0.0316812	−	0.999498i	$-0.510086\pi$
$151$	−0.778611	−0.0633625	−0.0316812	+	0.999498i	$0.510086\pi$
$152$	−1.00000	−0.0811107
$153$	−3.04118	−0.245865
$154$	−7.34174	−0.591615
$155$	−1.11311	−0.0894072
$156$	−2.84242	−0.227576
$157$	−2.99259	−0.238834	−0.119417	−	0.992844i	$-0.538103\pi$
$157$	−2.99259	−0.238834	−0.119417	+	0.992844i	$0.538103\pi$
$158$	3.67241	0.292161
$159$	−11.0970	−0.880047
$160$	0.835058	0.0660171
$161$	−4.24185	−0.334305
$162$	3.74205	0.294003
$163$	1.89343	0.148305	0.0741525	−	0.997247i	$-0.476375\pi$
$163$	1.89343	0.148305	0.0741525	+	0.997247i	$0.476375\pi$
$164$	1.73540	0.135512
$165$	−6.66712	−0.519034
$166$	−16.9835	−1.31817
$167$	−14.6456	−1.13331	−0.566655	−	0.823955i	$-0.691763\pi$
$167$	−14.6456	−1.13331	−0.566655	+	0.823955i	$0.691763\pi$
$168$	−1.61836	−0.124859
$169$	−8.40930	−0.646869
$170$	2.04793	0.157069
$171$	−1.24006	−0.0948301
$172$	0.150751	0.0114946
$173$	17.2307	1.31003	0.655013	−	0.755618i	$-0.272663\pi$
$173$	17.2307	1.31003	0.655013	+	0.755618i	$0.272663\pi$
$174$	−8.89265	−0.674150
$175$	5.24886	0.396777
$176$	−6.01829	−0.453646
$177$	2.41722	0.181689
$178$	4.74130	0.355376
$179$	−6.82272	−0.509954	−0.254977	−	0.966947i	$-0.582068\pi$
$179$	−6.82272	−0.509954	−0.254977	+	0.966947i	$0.582068\pi$
$180$	1.03553	0.0771835
$181$	1.07770	0.0801045	0.0400523	−	0.999198i	$-0.487248\pi$
$181$	1.07770	0.0801045	0.0400523	+	0.999198i	$0.487248\pi$
$182$	2.61376	0.193745
$183$	−18.8003	−1.38976
$184$	−3.47719	−0.256342
$185$	0.541776	0.0398322
$186$	1.76836	0.129662
$187$	−14.7595	−1.07932
$188$	5.81406	0.424034
$189$	−6.86194	−0.499133
$190$	0.835058	0.0605815
$191$	−7.52129	−0.544221	−0.272111	−	0.962266i	$-0.587722\pi$
$191$	−7.52129	−0.544221	−0.272111	+	0.962266i	$0.587722\pi$
$192$	−1.32663	−0.0957410
$193$	−8.64919	−0.622582	−0.311291	−	0.950315i	$-0.600761\pi$
$193$	−8.64919	−0.622582	−0.311291	+	0.950315i	$0.600761\pi$
$194$	−0.349355	−0.0250822
$195$	2.37359	0.169976
$196$	−5.51183	−0.393702
$197$	12.3933	0.882986	0.441493	−	0.897265i	$-0.354449\pi$
$197$	12.3933	0.882986	0.441493	+	0.897265i	$0.354449\pi$
$198$	−7.46306	−0.530377
$199$	−17.3704	−1.23135	−0.615676	−	0.787999i	$-0.711117\pi$
$199$	−17.3704	−1.23135	−0.615676	+	0.787999i	$0.711117\pi$
$200$	4.30268	0.304245
$201$	14.1529	0.998266
$202$	−2.29319	−0.161348
$203$	8.17728	0.573932
$204$	−3.25347	−0.227789
$205$	−1.44916	−0.101214
$206$	−0.0518453	−0.00361224
$207$	−4.31194	−0.299701
$208$	2.14259	0.148562
$209$	−6.01829	−0.416294
$210$	1.35142	0.0932571
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	8.36481	0.574497
$213$	−16.3113	−1.11763
$214$	−11.7707	−0.804626
$215$	−0.125886	−0.00858534
$216$	−5.62498	−0.382731
$217$	−1.62610	−0.110387
$218$	10.9711	0.743054
$219$	6.32423	0.427352
$220$	5.02562	0.338827
$221$	5.25458	0.353461
$222$	−0.860699	−0.0577663
$223$	−19.6288	−1.31444	−0.657221	−	0.753698i	$-0.728268\pi$
$223$	−19.6288	−1.31444	−0.657221	+	0.753698i	$0.728268\pi$
$224$	1.21991	0.0815084
$225$	5.33560	0.355706
$226$	2.45077	0.163023
$227$	−27.4777	−1.82376	−0.911879	−	0.410460i	$-0.865368\pi$
$227$	−27.4777	−1.82376	−0.911879	+	0.410460i	$0.865368\pi$
$228$	−1.32663	−0.0878579
$229$	15.4613	1.02171	0.510856	−	0.859666i	$-0.329329\pi$
$229$	15.4613	1.02171	0.510856	+	0.859666i	$0.329329\pi$
$230$	2.90366	0.191462
$231$	−9.73975	−0.640828
$232$	6.70321	0.440087
$233$	6.12529	0.401281	0.200641	−	0.979665i	$-0.435698\pi$
$233$	6.12529	0.401281	0.200641	+	0.979665i	$0.435698\pi$
$234$	2.65695	0.173690
$235$	−4.85507	−0.316710
$236$	−1.82208	−0.118607
$237$	4.87191	0.316464
$238$	2.99175	0.193926
$239$	−8.33373	−0.539064	−0.269532	−	0.962991i	$-0.586869\pi$
$239$	−8.33373	−0.539064	−0.269532	+	0.962991i	$0.586869\pi$
$240$	1.10781	0.0715088
$241$	9.56124	0.615894	0.307947	−	0.951404i	$-0.400358\pi$
$241$	9.56124	0.615894	0.307947	+	0.951404i	$0.400358\pi$
$242$	−25.2198	−1.62119
$243$	−11.9106	−0.764068
$244$	14.1715	0.907238
$245$	4.60270	0.294056
$246$	2.30223	0.146785
$247$	2.14259	0.136330
$248$	−1.33297	−0.0846439
$249$	−22.5307	−1.42783
$250$	−7.76828	−0.491309
$251$	18.3551	1.15857	0.579283	−	0.815126i	$-0.303333\pi$
$251$	18.3551	1.15857	0.579283	+	0.815126i	$0.303333\pi$
$252$	1.51276	0.0952950
$253$	−20.9268	−1.31565
$254$	−13.5623	−0.850975
$255$	2.71684	0.170135
$256$	1.00000	0.0625000
$257$	9.19251	0.573413	0.286707	−	0.958018i	$-0.407440\pi$
$257$	9.19251	0.573413	0.286707	+	0.958018i	$0.407440\pi$
$258$	0.199990	0.0124508
$259$	0.791460	0.0491790
$260$	−1.78919	−0.110961
$261$	8.31240	0.514525
$262$	8.62428	0.532810
$263$	7.22747	0.445665	0.222832	−	0.974857i	$-0.428470\pi$
$263$	7.22747	0.445665	0.222832	+	0.974857i	$0.428470\pi$
$264$	−7.98402	−0.491382
$265$	−6.98510	−0.429091
$266$	1.21991	0.0747972
$267$	6.28994	0.384938
$268$	−10.6683	−0.651671
$269$	12.1972	0.743679	0.371840	−	0.928297i	$-0.378727\pi$
$269$	12.1972	0.743679	0.371840	+	0.928297i	$0.378727\pi$
$270$	4.69718	0.285862
$271$	−21.2713	−1.29214	−0.646069	−	0.763279i	$-0.723588\pi$
$271$	−21.2713	−1.29214	−0.646069	+	0.763279i	$0.723588\pi$
$272$	2.45244	0.148701
$273$	3.46748	0.209862
$274$	−21.4983	−1.29876
$275$	25.8948	1.56151
$276$	−4.61294	−0.277666
$277$	20.7960	1.24951	0.624756	−	0.780820i	$-0.285199\pi$
$277$	20.7960	1.24951	0.624756	+	0.780820i	$0.285199\pi$
$278$	19.7033	1.18173
$279$	−1.65297	−0.0989609
$280$	−1.01869	−0.0608785
$281$	−18.7932	−1.12111	−0.560555	−	0.828117i	$-0.689412\pi$
$281$	−18.7932	−1.12111	−0.560555	+	0.828117i	$0.689412\pi$
$282$	7.71308	0.459307
$283$	−24.0594	−1.43019	−0.715093	−	0.699029i	$-0.753616\pi$
$283$	−24.0594	−1.43019	−0.715093	+	0.699029i	$0.753616\pi$
$284$	12.2953	0.729594
$285$	1.10781	0.0656210
$286$	12.8947	0.762482
$287$	−2.11702	−0.124964
$288$	1.24006	0.0730715
$289$	−10.9855	−0.646208
$290$	−5.59757	−0.328700
$291$	−0.463464	−0.0271687
$292$	−4.76716	−0.278977
$293$	4.77232	0.278802	0.139401	−	0.990236i	$-0.455482\pi$
$293$	4.77232	0.278802	0.139401	+	0.990236i	$0.455482\pi$
$294$	−7.31214	−0.426452
$295$	1.52154	0.0885877
$296$	0.648788	0.0377100
$297$	−33.8527	−1.96434
$298$	−10.2434	−0.593387
$299$	7.45021	0.430857
$300$	5.70804	0.329554
$301$	−0.183902	−0.0105999
$302$	0.778611	0.0448040
$303$	−3.04221	−0.174770
$304$	1.00000	0.0573539
$305$	−11.8340	−0.677615
$306$	3.04118	0.173853
$307$	−10.2308	−0.583904	−0.291952	−	0.956433i	$-0.594305\pi$
$307$	−10.2308	−0.583904	−0.291952	+	0.956433i	$0.594305\pi$
$308$	7.34174	0.418335
$309$	−0.0687794	−0.00391272
$310$	1.11311	0.0632204
$311$	−2.94437	−0.166960	−0.0834798	−	0.996509i	$-0.526603\pi$
$311$	−2.94437	−0.166960	−0.0834798	+	0.996509i	$0.526603\pi$
$312$	2.84242	0.160920
$313$	−21.2706	−1.20229	−0.601143	−	0.799142i	$-0.705288\pi$
$313$	−21.2706	−1.20229	−0.601143	+	0.799142i	$0.705288\pi$
$314$	2.99259	0.168881
$315$	−1.26324	−0.0711757
$316$	−3.67241	−0.206589
$317$	19.7225	1.10773	0.553864	−	0.832607i	$-0.313153\pi$
$317$	19.7225	1.10773	0.553864	+	0.832607i	$0.313153\pi$
$318$	11.0970	0.622287
$319$	40.3418	2.25871
$320$	−0.835058	−0.0466812
$321$	−15.6153	−0.871559
$322$	4.24185	0.236389
$323$	2.45244	0.136457
$324$	−3.74205	−0.207892
$325$	−9.21889	−0.511372
$326$	−1.89343	−0.104867
$327$	14.5545	0.804866
$328$	−1.73540	−0.0958214
$329$	−7.09260	−0.391028
$330$	6.66712	0.367013
$331$	6.91530	0.380099	0.190050	−	0.981774i	$-0.439135\pi$
$331$	6.91530	0.380099	0.190050	+	0.981774i	$0.439135\pi$
$332$	16.9835	0.932090
$333$	0.804539	0.0440885
$334$	14.6456	0.801372
$335$	8.90866	0.486732
$336$	1.61836	0.0882887
$337$	−10.6359	−0.579375	−0.289688	−	0.957121i	$-0.593551\pi$
$337$	−10.6359	−0.579375	−0.289688	+	0.957121i	$0.593551\pi$
$338$	8.40930	0.457405
$339$	3.25125	0.176584
$340$	−2.04793	−0.111065
$341$	−8.02222	−0.434428
$342$	1.24006	0.0670550
$343$	15.2633	0.824138
$344$	−0.150751	−0.00812794
$345$	3.85207	0.207388
$346$	−17.2307	−0.926328
$347$	−18.9302	−1.01623	−0.508114	−	0.861290i	$-0.669657\pi$
$347$	−18.9302	−1.01623	−0.508114	+	0.861290i	$0.669657\pi$
$348$	8.89265	0.476696
$349$	12.4884	0.668490	0.334245	−	0.942486i	$-0.391519\pi$
$349$	12.4884	0.668490	0.334245	+	0.942486i	$0.391519\pi$
$350$	−5.24886	−0.280563
$351$	12.0520	0.643290
$352$	6.01829	0.320776
$353$	7.91788	0.421426	0.210713	−	0.977548i	$-0.432421\pi$
$353$	7.91788	0.421426	0.210713	+	0.977548i	$0.432421\pi$
$354$	−2.41722	−0.128474
$355$	−10.2673	−0.544933
$356$	−4.74130	−0.251289
$357$	3.96893	0.210058
$358$	6.82272	0.360592
$359$	5.09362	0.268831	0.134415	−	0.990925i	$-0.457084\pi$
$359$	5.09362	0.268831	0.134415	+	0.990925i	$0.457084\pi$
$360$	−1.03553	−0.0545770
$361$	1.00000	0.0526316
$362$	−1.07770	−0.0566425
$363$	−33.4572	−1.75605
$364$	−2.61376	−0.136998
$365$	3.98085	0.208367
$366$	18.8003	0.982707
$367$	15.7754	0.823468	0.411734	−	0.911304i	$-0.364923\pi$
$367$	15.7754	0.823468	0.411734	+	0.911304i	$0.364923\pi$
$368$	3.47719	0.181261
$369$	−2.15201	−0.112029
$370$	−0.541776	−0.0281656
$371$	−10.2043	−0.529780
$372$	−1.76836	−0.0916851
$373$	11.3090	0.585556	0.292778	−	0.956180i	$-0.405420\pi$
$373$	11.3090	0.585556	0.292778	+	0.956180i	$0.405420\pi$
$374$	14.7595	0.763195
$375$	−10.3056	−0.532179
$376$	−5.81406	−0.299837
$377$	−14.3622	−0.739693
$378$	6.86194	0.352940
$379$	9.19113	0.472117	0.236058	−	0.971739i	$-0.424144\pi$
$379$	9.19113	0.472117	0.236058	+	0.971739i	$0.424144\pi$
$380$	−0.835058	−0.0428376
$381$	−17.9921	−0.921764
$382$	7.52129	0.384823
$383$	20.0925	1.02668	0.513340	−	0.858185i	$-0.328408\pi$
$383$	20.0925	1.02668	0.513340	+	0.858185i	$0.328408\pi$
$384$	1.32663	0.0676991
$385$	−6.13078	−0.312454
$386$	8.64919	0.440232
$387$	−0.186941	−0.00950273
$388$	0.349355	0.0177358
$389$	15.5872	0.790301	0.395151	−	0.918616i	$-0.370692\pi$
$389$	15.5872	0.790301	0.395151	+	0.918616i	$0.370692\pi$
$390$	−2.37359	−0.120191
$391$	8.52761	0.431260
$392$	5.51183	0.278389
$393$	11.4412	0.577132
$394$	−12.3933	−0.624365
$395$	3.06667	0.154301
$396$	7.46306	0.375033
$397$	22.5225	1.13037	0.565185	−	0.824964i	$-0.308805\pi$
$397$	22.5225	1.13037	0.565185	+	0.824964i	$0.308805\pi$
$398$	17.3704	0.870698
$399$	1.61836	0.0810193
$400$	−4.30268	−0.215134
$401$	−8.58135	−0.428532	−0.214266	−	0.976775i	$-0.568736\pi$
$401$	−8.58135	−0.428532	−0.214266	+	0.976775i	$0.568736\pi$
$402$	−14.1529	−0.705880
$403$	2.85602	0.142269
$404$	2.29319	0.114090
$405$	3.12483	0.155274
$406$	−8.17728	−0.405832
$407$	3.90459	0.193544
$408$	3.25347	0.161071
$409$	4.02833	0.199188	0.0995940	−	0.995028i	$-0.468246\pi$
$409$	4.02833	0.199188	0.0995940	+	0.995028i	$0.468246\pi$
$410$	1.44916	0.0715689
$411$	−28.5202	−1.40680
$412$	0.0518453	0.00255424
$413$	2.22277	0.109375
$414$	4.31194	0.211920
$415$	−14.1822	−0.696177
$416$	−2.14259	−0.105049
$417$	26.1390	1.28003
$418$	6.01829	0.294364
$419$	−33.3063	−1.62712	−0.813560	−	0.581481i	$-0.802474\pi$
$419$	−33.3063	−1.62712	−0.813560	+	0.581481i	$0.802474\pi$
$420$	−1.35142	−0.0659427
$421$	−29.4299	−1.43433	−0.717163	−	0.696906i	$-0.754559\pi$
$421$	−29.4299	−1.43433	−0.717163	+	0.696906i	$0.754559\pi$
$422$	−1.00000	−0.0486792
$423$	−7.20980	−0.350552
$424$	−8.36481	−0.406231
$425$	−10.5521	−0.511850
$426$	16.3113	0.790286
$427$	−17.2879	−0.836620
$428$	11.7707	0.568956
$429$	17.1065	0.825909
$430$	0.125886	0.00607075
$431$	8.74995	0.421470	0.210735	−	0.977543i	$-0.432414\pi$
$431$	8.74995	0.421470	0.210735	+	0.977543i	$0.432414\pi$
$432$	5.62498	0.270632
$433$	−20.3495	−0.977934	−0.488967	−	0.872302i	$-0.662626\pi$
$433$	−20.3495	−0.977934	−0.488967	+	0.872302i	$0.662626\pi$
$434$	1.62610	0.0780554
$435$	−7.42588	−0.356044
$436$	−10.9711	−0.525419
$437$	3.47719	0.166337
$438$	−6.32423	−0.302183
$439$	−13.8335	−0.660236	−0.330118	−	0.943940i	$-0.607088\pi$
$439$	−13.8335	−0.660236	−0.330118	+	0.943940i	$0.607088\pi$
$440$	−5.02562	−0.239587
$441$	6.83502	0.325477
$442$	−5.25458	−0.249935
$443$	−33.7861	−1.60523	−0.802613	−	0.596500i	$-0.796558\pi$
$443$	−33.7861	−1.60523	−0.802613	+	0.596500i	$0.796558\pi$
$444$	0.860699	0.0408470
$445$	3.95926	0.187687
$446$	19.6288	0.929451
$447$	−13.5892	−0.642748
$448$	−1.21991	−0.0576351
$449$	7.89776	0.372719	0.186359	−	0.982482i	$-0.440331\pi$
$449$	7.89776	0.372719	0.186359	+	0.982482i	$0.440331\pi$
$450$	−5.33560	−0.251522
$451$	−10.4441	−0.491795
$452$	−2.45077	−0.115274
$453$	1.03293	0.0485311
$454$	27.4777	1.28959
$455$	2.18264	0.102324
$456$	1.32663	0.0621249
$457$	16.6019	0.776603	0.388302	−	0.921532i	$-0.373062\pi$
$457$	16.6019	0.776603	0.388302	+	0.921532i	$0.373062\pi$
$458$	−15.4613	−0.722459
$459$	13.7949	0.643892
$460$	−2.90366	−0.135384
$461$	24.4549	1.13898	0.569489	−	0.821999i	$-0.307141\pi$
$461$	24.4549	1.13898	0.569489	+	0.821999i	$0.307141\pi$
$462$	9.73975	0.453134
$463$	8.34239	0.387704	0.193852	−	0.981031i	$-0.437902\pi$
$463$	8.34239	0.387704	0.193852	+	0.981031i	$0.437902\pi$
$464$	−6.70321	−0.311189
$465$	1.47668	0.0684795
$466$	−6.12529	−0.283749
$467$	−35.5595	−1.64550	−0.822750	−	0.568404i	$-0.807561\pi$
$467$	−35.5595	−1.64550	−0.822750	+	0.568404i	$0.807561\pi$
$468$	−2.65695	−0.122818
$469$	13.0143	0.600946
$470$	4.85507	0.223948
$471$	3.97004	0.182930
$472$	1.82208	0.0838681
$473$	−0.907262	−0.0417160
$474$	−4.87191	−0.223774
$475$	−4.30268	−0.197420
$476$	−2.99175	−0.137126
$477$	−10.3729	−0.474942
$478$	8.33373	0.381176
$479$	−20.6884	−0.945278	−0.472639	−	0.881256i	$-0.656699\pi$
$479$	−20.6884	−0.945278	−0.472639	+	0.881256i	$0.656699\pi$
$480$	−1.10781	−0.0505644
$481$	−1.39009	−0.0633826
$482$	−9.56124	−0.435503
$483$	5.62735	0.256053
$484$	25.2198	1.14635
$485$	−0.291732	−0.0132469
$486$	11.9106	0.540277
$487$	−16.7711	−0.759973	−0.379987	−	0.924992i	$-0.624071\pi$
$487$	−16.7711	−0.759973	−0.379987	+	0.924992i	$0.624071\pi$
$488$	−14.1715	−0.641514
$489$	−2.51187	−0.113591
$490$	−4.60270	−0.207929
$491$	−9.19757	−0.415081	−0.207540	−	0.978226i	$-0.566546\pi$
$491$	−9.19757	−0.415081	−0.207540	+	0.978226i	$0.566546\pi$
$492$	−2.30223	−0.103792
$493$	−16.4392	−0.740385
$494$	−2.14259	−0.0963998
$495$	−6.23209	−0.280112
$496$	1.33297	0.0598523
$497$	−14.9992	−0.672804
$498$	22.5307	1.00963
$499$	13.0176	0.582748	0.291374	−	0.956609i	$-0.405888\pi$
$499$	13.0176	0.582748	0.291374	+	0.956609i	$0.405888\pi$
$500$	7.76828	0.347408
$501$	19.4292	0.868034
$502$	−18.3551	−0.819230
$503$	−14.1036	−0.628849	−0.314425	−	0.949282i	$-0.601812\pi$
$503$	−14.1036	−0.628849	−0.314425	+	0.949282i	$0.601812\pi$
$504$	−1.51276	−0.0673837
$505$	−1.91495	−0.0852140
$506$	20.9268	0.930308
$507$	11.1560	0.495455
$508$	13.5623	0.601730
$509$	10.5420	0.467264	0.233632	−	0.972325i	$-0.424939\pi$
$509$	10.5420	0.467264	0.233632	+	0.972325i	$0.424939\pi$
$510$	−2.71684	−0.120304
$511$	5.81548	0.257262
$512$	−1.00000	−0.0441942
$513$	5.62498	0.248349
$514$	−9.19251	−0.405464
$515$	−0.0432939	−0.00190776
$516$	−0.199990	−0.00880407
$517$	−34.9907	−1.53889
$518$	−0.791460	−0.0347748
$519$	−22.8587	−1.00339
$520$	1.78919	0.0784612
$521$	8.89666	0.389770	0.194885	−	0.980826i	$-0.437567\pi$
$521$	8.89666	0.389770	0.194885	+	0.980826i	$0.437567\pi$
$522$	−8.31240	−0.363824
$523$	31.6302	1.38309	0.691546	−	0.722333i	$-0.256930\pi$
$523$	31.6302	1.38309	0.691546	+	0.722333i	$0.256930\pi$
$524$	−8.62428	−0.376753
$525$	−6.96328	−0.303902
$526$	−7.22747	−0.315133
$527$	3.26904	0.142402
$528$	7.98402	0.347460
$529$	−10.9091	−0.474309
$530$	6.98510	0.303413
$531$	2.25950	0.0980538
$532$	−1.21991	−0.0528896
$533$	3.71825	0.161055
$534$	−6.28994	−0.272192
$535$	−9.82919	−0.424953
$536$	10.6683	0.460801
$537$	9.05120	0.390588
$538$	−12.1972	−0.525861
$539$	33.1718	1.42881
$540$	−4.69718	−0.202135
$541$	1.42836	0.0614102	0.0307051	−	0.999528i	$-0.490225\pi$
$541$	1.42836	0.0614102	0.0307051	+	0.999528i	$0.490225\pi$
$542$	21.2713	0.913680
$543$	−1.42970	−0.0613543
$544$	−2.45244	−0.105148
$545$	9.16148	0.392435
$546$	−3.46748	−0.148395
$547$	−11.3165	−0.483857	−0.241928	−	0.970294i	$-0.577780\pi$
$547$	−11.3165	−0.483857	−0.241928	+	0.970294i	$0.577780\pi$
$548$	21.4983	0.918362
$549$	−17.5736	−0.750022
$550$	−25.8948	−1.10416
$551$	−6.70321	−0.285566
$552$	4.61294	0.196340
$553$	4.47999	0.190508
$554$	−20.7960	−0.883538
$555$	−0.718734	−0.0305086
$556$	−19.7033	−0.835608
$557$	−12.4616	−0.528015	−0.264007	−	0.964521i	$-0.585044\pi$
$557$	−12.4616	−0.528015	−0.264007	+	0.964521i	$0.585044\pi$
$558$	1.65297	0.0699759
$559$	0.322998	0.0136613
$560$	1.01869	0.0430476
$561$	19.5803	0.826682
$562$	18.7932	0.792745
$563$	−12.7234	−0.536226	−0.268113	−	0.963387i	$-0.586400\pi$
$563$	−12.7234	−0.536226	−0.268113	+	0.963387i	$0.586400\pi$
$564$	−7.71308	−0.324779
$565$	2.04653	0.0860983
$566$	24.0594	1.01129
$567$	4.56495	0.191710
$568$	−12.2953	−0.515901
$569$	−14.6752	−0.615218	−0.307609	−	0.951513i	$-0.599529\pi$
$569$	−14.6752	−0.615218	−0.307609	+	0.951513i	$0.599529\pi$
$570$	−1.10781	−0.0464010
$571$	1.95223	0.0816984	0.0408492	−	0.999165i	$-0.486994\pi$
$571$	1.95223	0.0816984	0.0408492	+	0.999165i	$0.486994\pi$
$572$	−12.8947	−0.539156
$573$	9.97794	0.416834
$574$	2.11702	0.0883628
$575$	−14.9612	−0.623927
$576$	−1.24006	−0.0516693
$577$	7.13543	0.297052	0.148526	−	0.988909i	$-0.452547\pi$
$577$	7.13543	0.297052	0.148526	+	0.988909i	$0.452547\pi$
$578$	10.9855	0.456938
$579$	11.4742	0.476853
$580$	5.59757	0.232426
$581$	−20.7182	−0.859538
$582$	0.463464	0.0192112
$583$	−50.3418	−2.08495
$584$	4.76716	0.197266
$585$	2.21871	0.0917323
$586$	−4.77232	−0.197143
$587$	−12.4144	−0.512397	−0.256199	−	0.966624i	$-0.582470\pi$
$587$	−12.4144	−0.512397	−0.256199	+	0.966624i	$0.582470\pi$
$588$	7.31214	0.301547
$589$	1.33297	0.0549242
$590$	−1.52154	−0.0626410
$591$	−16.4413	−0.676303
$592$	−0.648788	−0.0266650
$593$	−4.83160	−0.198410	−0.0992051	−	0.995067i	$-0.531630\pi$
$593$	−4.83160	−0.198410	−0.0992051	+	0.995067i	$0.531630\pi$
$594$	33.8527	1.38899
$595$	2.49828	0.102420
$596$	10.2434	0.419588
$597$	23.0440	0.943127
$598$	−7.45021	−0.304662
$599$	−10.3610	−0.423339	−0.211670	−	0.977341i	$-0.567890\pi$
$599$	−10.3610	−0.423339	−0.211670	+	0.977341i	$0.567890\pi$
$600$	−5.70804	−0.233030
$601$	10.5292	0.429495	0.214748	−	0.976670i	$-0.431107\pi$
$601$	10.5292	0.429495	0.214748	+	0.976670i	$0.431107\pi$
$602$	0.183902	0.00749528
$603$	13.2294	0.538742
$604$	−0.778611	−0.0316812
$605$	−21.0600	−0.856211
$606$	3.04221	0.123581
$607$	−28.1769	−1.14366	−0.571832	−	0.820371i	$-0.693767\pi$
$607$	−28.1769	−1.14366	−0.571832	+	0.820371i	$0.693767\pi$
$608$	−1.00000	−0.0405554
$609$	−10.8482	−0.439591
$610$	11.8340	0.479146
$611$	12.4572	0.503962
$612$	−3.04118	−0.122933
$613$	−4.71109	−0.190279	−0.0951395	−	0.995464i	$-0.530330\pi$
$613$	−4.71109	−0.190279	−0.0951395	+	0.995464i	$0.530330\pi$
$614$	10.2308	0.412882
$615$	1.92249	0.0775224
$616$	−7.34174	−0.295807
$617$	−15.6295	−0.629218	−0.314609	−	0.949221i	$-0.601873\pi$
$617$	−15.6295	−0.629218	−0.314609	+	0.949221i	$0.601873\pi$
$618$	0.0687794	0.00276671
$619$	−25.4192	−1.02168	−0.510842	−	0.859675i	$-0.670666\pi$
$619$	−25.4192	−1.02168	−0.510842	+	0.859675i	$0.670666\pi$
$620$	−1.11311	−0.0447036
$621$	19.5591	0.784881
$622$	2.94437	0.118058
$623$	5.78394	0.231729
$624$	−2.84242	−0.113788
$625$	15.0264	0.601057
$626$	21.2706	0.850144
$627$	7.98402	0.318851
$628$	−2.99259	−0.119417
$629$	−1.59111	−0.0634419
$630$	1.26324	0.0503288
$631$	23.1347	0.920977	0.460489	−	0.887666i	$-0.347674\pi$
$631$	23.1347	0.920977	0.460489	+	0.887666i	$0.347674\pi$
$632$	3.67241	0.146080
$633$	−1.32663	−0.0527286
$634$	−19.7225	−0.783282
$635$	−11.3253	−0.449432
$636$	−11.0970	−0.440023
$637$	−11.8096	−0.467914
$638$	−40.3418	−1.59715
$639$	−15.2470	−0.603162
$640$	0.835058	0.0330086
$641$	−23.7970	−0.939925	−0.469962	−	0.882686i	$-0.655733\pi$
$641$	−23.7970	−0.939925	−0.469962	+	0.882686i	$0.655733\pi$
$642$	15.6153	0.616285
$643$	−9.34353	−0.368473	−0.184236	−	0.982882i	$-0.558981\pi$
$643$	−9.34353	−0.368473	−0.184236	+	0.982882i	$0.558981\pi$
$644$	−4.24185	−0.167152
$645$	0.167003	0.00657575
$646$	−2.45244	−0.0964900
$647$	−30.2788	−1.19038	−0.595191	−	0.803584i	$-0.702923\pi$
$647$	−30.2788	−1.19038	−0.595191	+	0.803584i	$0.702923\pi$
$648$	3.74205	0.147002
$649$	10.9658	0.430446
$650$	9.21889	0.361594
$651$	2.15723	0.0845485
$652$	1.89343	0.0741525
$653$	−33.2321	−1.30047	−0.650237	−	0.759731i	$-0.725330\pi$
$653$	−33.2321	−1.30047	−0.650237	+	0.759731i	$0.725330\pi$
$654$	−14.5545	−0.569126
$655$	7.20177	0.281397
$656$	1.73540	0.0677559
$657$	5.91158	0.230633
$658$	7.09260	0.276498
$659$	−10.4936	−0.408772	−0.204386	−	0.978890i	$-0.565520\pi$
$659$	−10.4936	−0.408772	−0.204386	+	0.978890i	$0.565520\pi$
$660$	−6.66712	−0.259517
$661$	−7.91295	−0.307778	−0.153889	−	0.988088i	$-0.549180\pi$
$661$	−7.91295	−0.307778	−0.153889	+	0.988088i	$0.549180\pi$
$662$	−6.91530	−0.268771
$663$	−6.97086	−0.270726
$664$	−16.9835	−0.659087
$665$	1.01869	0.0395032
$666$	−0.804539	−0.0311752
$667$	−23.3084	−0.902503
$668$	−14.6456	−0.566655
$669$	26.0401	1.00677
$670$	−8.90866	−0.344172
$671$	−85.2882	−3.29252
$672$	−1.61836	−0.0624295
$673$	−36.9976	−1.42615	−0.713077	−	0.701086i	$-0.752699\pi$
$673$	−36.9976	−1.42615	−0.713077	+	0.701086i	$0.752699\pi$
$674$	10.6359	0.409680
$675$	−24.2025	−0.931553
$676$	−8.40930	−0.323434
$677$	−34.9850	−1.34458	−0.672291	−	0.740287i	$-0.734690\pi$
$677$	−34.9850	−1.34458	−0.672291	+	0.740287i	$0.734690\pi$
$678$	−3.25125	−0.124863
$679$	−0.426181	−0.0163553
$680$	2.04793	0.0785346
$681$	36.4526	1.39687
$682$	8.02222	0.307187
$683$	27.6506	1.05802	0.529010	−	0.848616i	$-0.322563\pi$
$683$	27.6506	1.05802	0.529010	+	0.848616i	$0.322563\pi$
$684$	−1.24006	−0.0474150
$685$	−17.9523	−0.685924
$686$	−15.2633	−0.582754
$687$	−20.5114	−0.782557
$688$	0.150751	0.00574732
$689$	17.9224	0.682788
$690$	−3.85207	−0.146646
$691$	−49.1666	−1.87039	−0.935193	−	0.354140i	$-0.884774\pi$
$691$	−49.1666	−1.87039	−0.935193	+	0.354140i	$0.884774\pi$
$692$	17.2307	0.655013
$693$	−9.10423	−0.345841
$694$	18.9302	0.718582
$695$	16.4534	0.624114
$696$	−8.89265	−0.337075
$697$	4.25596	0.161206
$698$	−12.4884	−0.472694
$699$	−8.12597	−0.307352
$700$	5.24886	0.198388
$701$	−13.8652	−0.523680	−0.261840	−	0.965111i	$-0.584329\pi$
$701$	−13.8652	−0.523680	−0.261840	+	0.965111i	$0.584329\pi$
$702$	−12.0520	−0.454875
$703$	−0.648788	−0.0244695
$704$	−6.01829	−0.226823
$705$	6.44087	0.242577
$706$	−7.91788	−0.297993
$707$	−2.79748	−0.105210
$708$	2.41722	0.0908447
$709$	17.8574	0.670650	0.335325	−	0.942103i	$-0.391154\pi$
$709$	17.8574	0.670650	0.335325	+	0.942103i	$0.391154\pi$
$710$	10.2673	0.385326
$711$	4.55402	0.170789
$712$	4.74130	0.177688
$713$	4.63501	0.173583
$714$	−3.96893	−0.148533
$715$	10.7679	0.402695
$716$	−6.82272	−0.254977
$717$	11.0557	0.412884
$718$	−5.09362	−0.190092
$719$	−26.5009	−0.988318	−0.494159	−	0.869372i	$-0.664524\pi$
$719$	−26.5009	−0.988318	−0.494159	+	0.869372i	$0.664524\pi$
$720$	1.03553	0.0385918
$721$	−0.0632464	−0.00235542
$722$	−1.00000	−0.0372161
$723$	−12.6842	−0.471730
$724$	1.07770	0.0400523
$725$	28.8417	1.07116
$726$	33.4572	1.24171
$727$	6.42640	0.238342	0.119171	−	0.992874i	$-0.461976\pi$
$727$	6.42640	0.238342	0.119171	+	0.992874i	$0.461976\pi$
$728$	2.61376	0.0968724
$729$	27.0271	1.00100
$730$	−3.98085	−0.147338
$731$	0.369708	0.0136741
$732$	−18.8003	−0.694879
$733$	−44.4394	−1.64141	−0.820703	−	0.571356i	$-0.806418\pi$
$733$	−44.4394	−1.64141	−0.820703	+	0.571356i	$0.806418\pi$
$734$	−15.7754	−0.582280
$735$	−6.10606	−0.225225
$736$	−3.47719	−0.128171
$737$	64.2050	2.36502
$738$	2.15201	0.0792164
$739$	15.8495	0.583035	0.291517	−	0.956566i	$-0.405840\pi$
$739$	15.8495	0.583035	0.291517	+	0.956566i	$0.405840\pi$
$740$	0.541776	0.0199161
$741$	−2.84242	−0.104419
$742$	10.2043	0.374611
$743$	19.1836	0.703779	0.351889	−	0.936042i	$-0.385539\pi$
$743$	19.1836	0.703779	0.351889	+	0.936042i	$0.385539\pi$
$744$	1.76836	0.0648311
$745$	−8.55387	−0.313390
$746$	−11.3090	−0.414050
$747$	−21.0606	−0.770567
$748$	−14.7595	−0.539661
$749$	−14.3591	−0.524670
$750$	10.3056	0.376307
$751$	−38.3526	−1.39951	−0.699753	−	0.714385i	$-0.746707\pi$
$751$	−38.3526	−1.39951	−0.699753	+	0.714385i	$0.746707\pi$
$752$	5.81406	0.212017
$753$	−24.3504	−0.887378
$754$	14.3622	0.523042
$755$	0.650185	0.0236627
$756$	−6.86194	−0.249566
$757$	3.80166	0.138174	0.0690868	−	0.997611i	$-0.477991\pi$
$757$	3.80166	0.138174	0.0690868	+	0.997611i	$0.477991\pi$
$758$	−9.19113	−0.333837
$759$	27.7620	1.00770
$760$	0.835058	0.0302907
$761$	−28.5150	−1.03367	−0.516835	−	0.856085i	$-0.672890\pi$
$761$	−28.5150	−1.03367	−0.516835	+	0.856085i	$0.672890\pi$
$762$	17.9921	0.651786
$763$	13.3837	0.484521
$764$	−7.52129	−0.272111
$765$	2.53956	0.0918182
$766$	−20.0925	−0.725973
$767$	−3.90398	−0.140964
$768$	−1.32663	−0.0478705
$769$	41.5686	1.49900	0.749501	−	0.662004i	$-0.230294\pi$
$769$	41.5686	1.49900	0.749501	+	0.662004i	$0.230294\pi$
$770$	6.13078	0.220938
$771$	−12.1950	−0.439193
$772$	−8.64919	−0.311291
$773$	24.5093	0.881539	0.440769	−	0.897620i	$-0.354706\pi$
$773$	24.5093	0.881539	0.440769	+	0.897620i	$0.354706\pi$
$774$	0.186941	0.00671945
$775$	−5.73536	−0.206020
$776$	−0.349355	−0.0125411
$777$	−1.04997	−0.0376675
$778$	−15.5872	−0.558828
$779$	1.73540	0.0621771
$780$	2.37359	0.0849880
$781$	−73.9969	−2.64782
$782$	−8.52761	−0.304947
$783$	−37.7054	−1.34748
$784$	−5.51183	−0.196851
$785$	2.49898	0.0891926
$786$	−11.4412	−0.408094
$787$	−37.5666	−1.33910	−0.669552	−	0.742765i	$-0.733514\pi$
$787$	−37.5666	−1.33910	−0.669552	+	0.742765i	$0.733514\pi$
$788$	12.3933	0.441493
$789$	−9.58815	−0.341347
$790$	−3.06667	−0.109107
$791$	2.98970	0.106302
$792$	−7.46306	−0.265188
$793$	30.3638	1.07825
$794$	−22.5225	−0.799292
$795$	9.26661	0.328653
$796$	−17.3704	−0.615676
$797$	14.5798	0.516444	0.258222	−	0.966086i	$-0.416863\pi$
$797$	14.5798	0.516444	0.258222	+	0.966086i	$0.416863\pi$
$798$	−1.61836	−0.0572893
$799$	14.2586	0.504434
$800$	4.30268	0.152123
$801$	5.87952	0.207743
$802$	8.58135	0.303018
$803$	28.6901	1.01245
$804$	14.1529	0.499133
$805$	3.54219	0.124846
$806$	−2.85602	−0.100599
$807$	−16.1812	−0.569605
$808$	−2.29319	−0.0806742
$809$	21.4149	0.752906	0.376453	−	0.926436i	$-0.377144\pi$
$809$	21.4149	0.752906	0.376453	+	0.926436i	$0.377144\pi$
$810$	−3.12483	−0.109795
$811$	−32.5212	−1.14198	−0.570988	−	0.820959i	$-0.693440\pi$
$811$	−32.5212	−1.14198	−0.570988	+	0.820959i	$0.693440\pi$
$812$	8.17728	0.286966
$813$	28.2190	0.989685
$814$	−3.90459	−0.136856
$815$	−1.58113	−0.0553844
$816$	−3.25347	−0.113894
$817$	0.150751	0.00527411
$818$	−4.02833	−0.140847
$819$	3.24123	0.113258
$820$	−1.44916	−0.0506068
$821$	−28.6808	−1.00097	−0.500484	−	0.865746i	$-0.666844\pi$
$821$	−28.6808	−1.00097	−0.500484	+	0.865746i	$0.666844\pi$
$822$	28.5202	0.994757
$823$	−27.7716	−0.968056	−0.484028	−	0.875052i	$-0.660827\pi$
$823$	−27.7716	−0.968056	−0.484028	+	0.875052i	$0.660827\pi$
$824$	−0.0518453	−0.00180612
$825$	−34.3527	−1.19601
$826$	−2.22277	−0.0773400
$827$	−14.7189	−0.511826	−0.255913	−	0.966700i	$-0.582376\pi$
$827$	−14.7189	−0.511826	−0.255913	+	0.966700i	$0.582376\pi$
$828$	−4.31194	−0.149850
$829$	25.1082	0.872042	0.436021	−	0.899936i	$-0.356387\pi$
$829$	25.1082	0.872042	0.436021	+	0.899936i	$0.356387\pi$
$830$	14.1822	0.492271
$831$	−27.5885	−0.957036
$832$	2.14259	0.0742810
$833$	−13.5174	−0.468351
$834$	−26.1390	−0.905118
$835$	12.2299	0.423234
$836$	−6.01829	−0.208147
$837$	7.49795	0.259167
$838$	33.3063	1.15055
$839$	19.1620	0.661546	0.330773	−	0.943710i	$-0.392691\pi$
$839$	19.1620	0.661546	0.330773	+	0.943710i	$0.392691\pi$
$840$	1.35142	0.0466285
$841$	15.9330	0.549413
$842$	29.4299	1.01422
$843$	24.9316	0.858690
$844$	1.00000	0.0344214
$845$	7.02225	0.241573
$846$	7.20980	0.247878
$847$	−30.7658	−1.05712
$848$	8.36481	0.287249
$849$	31.9179	1.09542
$850$	10.5521	0.361933
$851$	−2.25596	−0.0773334
$852$	−16.3113	−0.558816
$853$	−9.55614	−0.327196	−0.163598	−	0.986527i	$-0.552310\pi$
$853$	−9.55614	−0.327196	−0.163598	+	0.986527i	$0.552310\pi$
$854$	17.2879	0.591580
$855$	1.03553	0.0354142
$856$	−11.7707	−0.402313
$857$	−9.44060	−0.322485	−0.161242	−	0.986915i	$-0.551550\pi$
$857$	−9.44060	−0.322485	−0.161242	+	0.986915i	$0.551550\pi$
$858$	−17.1065	−0.584006
$859$	0.833897	0.0284522	0.0142261	−	0.999899i	$-0.495472\pi$
$859$	0.833897	0.0284522	0.0142261	+	0.999899i	$0.495472\pi$
$860$	−0.125886	−0.00429267
$861$	2.80850	0.0957133
$862$	−8.74995	−0.298024
$863$	11.1246	0.378684	0.189342	−	0.981911i	$-0.439364\pi$
$863$	11.1246	0.378684	0.189342	+	0.981911i	$0.439364\pi$
$864$	−5.62498	−0.191366
$865$	−14.3886	−0.489228
$866$	20.3495	0.691504
$867$	14.5737	0.494949
$868$	−1.62610	−0.0551935
$869$	22.1016	0.749745
$870$	7.42588	0.251761
$871$	−22.8578	−0.774509
$872$	10.9711	0.371527
$873$	−0.433223	−0.0146624
$874$	−3.47719	−0.117618
$875$	−9.47657	−0.320366
$876$	6.32423	0.213676
$877$	15.3338	0.517786	0.258893	−	0.965906i	$-0.416642\pi$
$877$	15.3338	0.517786	0.258893	+	0.965906i	$0.416642\pi$
$878$	13.8335	0.466857
$879$	−6.33109	−0.213542
$880$	5.02562	0.169414
$881$	−18.3873	−0.619483	−0.309742	−	0.950821i	$-0.600243\pi$
$881$	−18.3873	−0.619483	−0.309742	+	0.950821i	$0.600243\pi$
$882$	−6.83502	−0.230147
$883$	49.6687	1.67149	0.835743	−	0.549121i	$-0.185037\pi$
$883$	49.6687	1.67149	0.835743	+	0.549121i	$0.185037\pi$
$884$	5.25458	0.176731
$885$	−2.01852	−0.0678518
$886$	33.7861	1.13507
$887$	29.0750	0.976242	0.488121	−	0.872776i	$-0.337682\pi$
$887$	29.0750	0.976242	0.488121	+	0.872776i	$0.337682\pi$
$888$	−0.860699	−0.0288832
$889$	−16.5447	−0.554893
$890$	−3.95926	−0.132715
$891$	22.5207	0.754473
$892$	−19.6288	−0.657221
$893$	5.81406	0.194560
$894$	13.5892	0.454491
$895$	5.69737	0.190442
$896$	1.21991	0.0407542
$897$	−9.88364	−0.330005
$898$	−7.89776	−0.263552
$899$	−8.93520	−0.298006
$900$	5.33560	0.177853
$901$	20.5142	0.683427
$902$	10.4441	0.347752
$903$	0.243969	0.00811878
$904$	2.45077	0.0815113
$905$	−0.899939	−0.0299150
$906$	−1.03293	−0.0343167
$907$	40.7895	1.35439	0.677196	−	0.735803i	$-0.263195\pi$
$907$	40.7895	1.35439	0.677196	+	0.735803i	$0.263195\pi$
$908$	−27.4777	−0.911879
$909$	−2.84370	−0.0943197
$910$	−2.18264	−0.0723539
$911$	−1.49946	−0.0496793	−0.0248396	−	0.999691i	$-0.507908\pi$
$911$	−1.49946	−0.0496793	−0.0248396	+	0.999691i	$0.507908\pi$
$912$	−1.32663	−0.0439290
$913$	−102.211	−3.38271
$914$	−16.6019	−0.549141
$915$	15.6993	0.519004
$916$	15.4613	0.510856
$917$	10.5208	0.347428
$918$	−13.7949	−0.455300
$919$	−5.02672	−0.165816	−0.0829081	−	0.996557i	$-0.526421\pi$
$919$	−5.02672	−0.165816	−0.0829081	+	0.996557i	$0.526421\pi$
$920$	2.90366	0.0957308
$921$	13.5725	0.447228
$922$	−24.4549	−0.805380
$923$	26.3439	0.867120
$924$	−9.73975	−0.320414
$925$	2.79153	0.0917848
$926$	−8.34239	−0.274148
$927$	−0.0642915	−0.00211161
$928$	6.70321	0.220044
$929$	−8.49136	−0.278592	−0.139296	−	0.990251i	$-0.544484\pi$
$929$	−8.49136	−0.278592	−0.139296	+	0.990251i	$0.544484\pi$
$930$	−1.47668	−0.0484223
$931$	−5.51183	−0.180643
$932$	6.12529	0.200641
$933$	3.90607	0.127879
$934$	35.5595	1.16354
$935$	12.3250	0.403072
$936$	2.65695	0.0868452
$937$	−32.6723	−1.06736	−0.533679	−	0.845687i	$-0.679191\pi$
$937$	−32.6723	−1.06736	−0.533679	+	0.845687i	$0.679191\pi$
$938$	−13.0143	−0.424933
$939$	28.2181	0.920864
$940$	−4.85507	−0.158355
$941$	43.2567	1.41013	0.705065	−	0.709143i	$-0.250918\pi$
$941$	43.2567	1.41013	0.705065	+	0.709143i	$0.250918\pi$
$942$	−3.97004	−0.129351
$943$	6.03432	0.196505
$944$	−1.82208	−0.0593037
$945$	5.73012	0.186401
$946$	0.907262	0.0294976
$947$	35.1358	1.14176	0.570880	−	0.821034i	$-0.306602\pi$
$947$	35.1358	1.14176	0.570880	+	0.821034i	$0.306602\pi$
$948$	4.87191	0.158232
$949$	−10.2141	−0.331563
$950$	4.30268	0.139597
$951$	−26.1644	−0.848439
$952$	2.99175	0.0969631
$953$	−26.3622	−0.853955	−0.426977	−	0.904262i	$-0.640422\pi$
$953$	−26.3622	−0.853955	−0.426977	+	0.904262i	$0.640422\pi$
$954$	10.3729	0.335835
$955$	6.28071	0.203239
$956$	−8.33373	−0.269532
$957$	−53.5185	−1.73001
$958$	20.6884	0.668413
$959$	−26.2259	−0.846879
$960$	1.10781	0.0357544
$961$	−29.2232	−0.942683
$962$	1.39009	0.0448183
$963$	−14.5964	−0.470362
$964$	9.56124	0.307947
$965$	7.22258	0.232503
$966$	−5.62735	−0.181057
$967$	−34.2020	−1.09986	−0.549930	−	0.835210i	$-0.685346\pi$
$967$	−34.2020	−1.09986	−0.549930	+	0.835210i	$0.685346\pi$
$968$	−25.2198	−0.810595
$969$	−3.25347	−0.104517
$970$	0.291732	0.00936695
$971$	13.3023	0.426890	0.213445	−	0.976955i	$-0.431532\pi$
$971$	13.3023	0.426890	0.213445	+	0.976955i	$0.431532\pi$
$972$	−11.9106	−0.382034
$973$	24.0362	0.770566
$974$	16.7711	0.537382
$975$	12.2300	0.391674
$976$	14.1715	0.453619
$977$	−24.1108	−0.771374	−0.385687	−	0.922630i	$-0.626036\pi$
$977$	−24.1108	−0.771374	−0.385687	+	0.922630i	$0.626036\pi$
$978$	2.51187	0.0803209
$979$	28.5345	0.911968
$980$	4.60270	0.147028
$981$	13.6048	0.434369
$982$	9.19757	0.293506
$983$	15.7753	0.503154	0.251577	−	0.967837i	$-0.419051\pi$
$983$	15.7753	0.503154	0.251577	+	0.967837i	$0.419051\pi$
$984$	2.30223	0.0733923
$985$	−10.3491	−0.329750
$986$	16.4392	0.523531
$987$	9.40923	0.299499
$988$	2.14259	0.0681650
$989$	0.524190	0.0166683
$990$	6.23209	0.198069
$991$	58.0092	1.84272	0.921361	−	0.388709i	$-0.127079\pi$
$991$	58.0092	1.84272	0.921361	+	0.388709i	$0.127079\pi$
$992$	−1.33297	−0.0423220
$993$	−9.17402	−0.291129
$994$	14.9992	0.475744
$995$	14.5053	0.459848
$996$	−22.5307	−0.713913
$997$	−16.9949	−0.538234	−0.269117	−	0.963107i	$-0.586732\pi$
$997$	−16.9949	−0.538234	−0.269117	+	0.963107i	$0.586732\pi$
$998$	−13.0176	−0.412065
$999$	−3.64942	−0.115463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.12	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.12	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.32663 q^{3} +1.00000 q^{4} -0.835058 q^{5} +1.32663 q^{6} -1.21991 q^{7} -1.00000 q^{8} -1.24006 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.32663 q^{3} +1.00000 q^{4} -0.835058 q^{5} +1.32663 q^{6} -1.21991 q^{7} -1.00000 q^{8} -1.24006 q^{9} +0.835058 q^{10} -6.01829 q^{11} -1.32663 q^{12} +2.14259 q^{13} +1.21991 q^{14} +1.10781 q^{15} +1.00000 q^{16} +2.45244 q^{17} +1.24006 q^{18} +1.00000 q^{19} -0.835058 q^{20} +1.61836 q^{21} +6.01829 q^{22} +3.47719 q^{23} +1.32663 q^{24} -4.30268 q^{25} -2.14259 q^{26} +5.62498 q^{27} -1.21991 q^{28} -6.70321 q^{29} -1.10781 q^{30} +1.33297 q^{31} -1.00000 q^{32} +7.98402 q^{33} -2.45244 q^{34} +1.01869 q^{35} -1.24006 q^{36} -0.648788 q^{37} -1.00000 q^{38} -2.84242 q^{39} +0.835058 q^{40} +1.73540 q^{41} -1.61836 q^{42} +0.150751 q^{43} -6.01829 q^{44} +1.03553 q^{45} -3.47719 q^{46} +5.81406 q^{47} -1.32663 q^{48} -5.51183 q^{49} +4.30268 q^{50} -3.25347 q^{51} +2.14259 q^{52} +8.36481 q^{53} -5.62498 q^{54} +5.02562 q^{55} +1.21991 q^{56} -1.32663 q^{57} +6.70321 q^{58} -1.82208 q^{59} +1.10781 q^{60} +14.1715 q^{61} -1.33297 q^{62} +1.51276 q^{63} +1.00000 q^{64} -1.78919 q^{65} -7.98402 q^{66} -10.6683 q^{67} +2.45244 q^{68} -4.61294 q^{69} -1.01869 q^{70} +12.2953 q^{71} +1.24006 q^{72} -4.76716 q^{73} +0.648788 q^{74} +5.70804 q^{75} +1.00000 q^{76} +7.34174 q^{77} +2.84242 q^{78} -3.67241 q^{79} -0.835058 q^{80} -3.74205 q^{81} -1.73540 q^{82} +16.9835 q^{83} +1.61836 q^{84} -2.04793 q^{85} -0.150751 q^{86} +8.89265 q^{87} +6.01829 q^{88} -4.74130 q^{89} -1.03553 q^{90} -2.61376 q^{91} +3.47719 q^{92} -1.76836 q^{93} -5.81406 q^{94} -0.835058 q^{95} +1.32663 q^{96} +0.349355 q^{97} +5.51183 q^{98} +7.46306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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