LMFDB - Embedded newform 5077.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46210 q^{2} -1.32036 q^{3} +4.06192 q^{4} +0.169195 q^{5} +3.25085 q^{6} -3.54943 q^{7} -5.07665 q^{8} -1.25666 q^{9} +O(q^{10})$	\(q-2.46210 q^{2} -1.32036 q^{3} +4.06192 q^{4} +0.169195 q^{5} +3.25085 q^{6} -3.54943 q^{7} -5.07665 q^{8} -1.25666 q^{9} -0.416575 q^{10} +3.99749 q^{11} -5.36319 q^{12} +2.86027 q^{13} +8.73903 q^{14} -0.223398 q^{15} +4.37536 q^{16} -5.33330 q^{17} +3.09401 q^{18} +5.51512 q^{19} +0.687257 q^{20} +4.68651 q^{21} -9.84221 q^{22} +3.23033 q^{23} +6.70300 q^{24} -4.97137 q^{25} -7.04227 q^{26} +5.62031 q^{27} -14.4175 q^{28} -8.35675 q^{29} +0.550028 q^{30} +3.74464 q^{31} -0.619269 q^{32} -5.27812 q^{33} +13.1311 q^{34} -0.600546 q^{35} -5.10444 q^{36} -9.58996 q^{37} -13.5788 q^{38} -3.77658 q^{39} -0.858945 q^{40} +6.73355 q^{41} -11.5387 q^{42} -4.71474 q^{43} +16.2375 q^{44} -0.212620 q^{45} -7.95338 q^{46} -3.91637 q^{47} -5.77705 q^{48} +5.59843 q^{49} +12.2400 q^{50} +7.04187 q^{51} +11.6182 q^{52} +0.0537101 q^{53} -13.8377 q^{54} +0.676356 q^{55} +18.0192 q^{56} -7.28193 q^{57} +20.5751 q^{58} -5.29464 q^{59} -0.907425 q^{60} +13.7639 q^{61} -9.21967 q^{62} +4.46041 q^{63} -7.22603 q^{64} +0.483944 q^{65} +12.9952 q^{66} +8.41718 q^{67} -21.6635 q^{68} -4.26519 q^{69} +1.47860 q^{70} +0.221500 q^{71} +6.37960 q^{72} -2.54322 q^{73} +23.6114 q^{74} +6.56399 q^{75} +22.4020 q^{76} -14.1888 q^{77} +9.29832 q^{78} +1.50274 q^{79} +0.740290 q^{80} -3.65085 q^{81} -16.5787 q^{82} +9.34520 q^{83} +19.0363 q^{84} -0.902369 q^{85} +11.6082 q^{86} +11.0339 q^{87} -20.2939 q^{88} +14.0122 q^{89} +0.523491 q^{90} -10.1523 q^{91} +13.1213 q^{92} -4.94426 q^{93} +9.64247 q^{94} +0.933131 q^{95} +0.817657 q^{96} +6.08190 q^{97} -13.7839 q^{98} -5.02347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.46210	−1.74097	−0.870483	−	0.492199i	$-0.836193\pi$
$2$	−2.46210	−1.74097	−0.870483	+	0.492199i	$0.836193\pi$
$3$	−1.32036	−0.762309	−0.381154	−	0.924511i	$-0.624473\pi$
$3$	−1.32036	−0.762309	−0.381154	+	0.924511i	$0.624473\pi$
$4$	4.06192	2.03096
$5$	0.169195	0.0756664	0.0378332	−	0.999284i	$-0.487954\pi$
$5$	0.169195	0.0756664	0.0378332	+	0.999284i	$0.487954\pi$
$6$	3.25085	1.32715
$7$	−3.54943	−1.34156	−0.670779	−	0.741658i	$-0.734040\pi$
$7$	−3.54943	−1.34156	−0.670779	+	0.741658i	$0.734040\pi$
$8$	−5.07665	−1.79487
$9$	−1.25666	−0.418885
$10$	−0.416575	−0.131733
$11$	3.99749	1.20529	0.602644	−	0.798010i	$-0.294114\pi$
$11$	3.99749	1.20529	0.602644	+	0.798010i	$0.294114\pi$
$12$	−5.36319	−1.54822
$13$	2.86027	0.793297	0.396649	−	0.917971i	$-0.370173\pi$
$13$	2.86027	0.793297	0.396649	+	0.917971i	$0.370173\pi$
$14$	8.73903	2.33561
$15$	−0.223398	−0.0576811
$16$	4.37536	1.09384
$17$	−5.33330	−1.29352	−0.646758	−	0.762695i	$-0.723876\pi$
$17$	−5.33330	−1.29352	−0.646758	+	0.762695i	$0.723876\pi$
$18$	3.09401	0.729265
$19$	5.51512	1.26525	0.632627	−	0.774456i	$-0.281976\pi$
$19$	5.51512	1.26525	0.632627	+	0.774456i	$0.281976\pi$
$20$	0.687257	0.153675
$21$	4.68651	1.02268
$22$	−9.84221	−2.09837
$23$	3.23033	0.673570	0.336785	−	0.941582i	$-0.390660\pi$
$23$	3.23033	0.673570	0.336785	+	0.941582i	$0.390660\pi$
$24$	6.70300	1.36824
$25$	−4.97137	−0.994275
$26$	−7.04227	−1.38110
$27$	5.62031	1.08163
$28$	−14.4175	−2.72465
$29$	−8.35675	−1.55181	−0.775904	−	0.630851i	$-0.782706\pi$
$29$	−8.35675	−1.55181	−0.775904	+	0.630851i	$0.782706\pi$
$30$	0.550028	0.100421
$31$	3.74464	0.672557	0.336279	−	0.941763i	$-0.390832\pi$
$31$	3.74464	0.672557	0.336279	+	0.941763i	$0.390832\pi$
$32$	−0.619269	−0.109472
$33$	−5.27812	−0.918802
$34$	13.1311	2.25197
$35$	−0.600546	−0.101511
$36$	−5.10444	−0.850740
$37$	−9.58996	−1.57658	−0.788290	−	0.615304i	$-0.789033\pi$
$37$	−9.58996	−1.57658	−0.788290	+	0.615304i	$0.789033\pi$
$38$	−13.5788	−2.20276
$39$	−3.77658	−0.604738
$40$	−0.858945	−0.135811
$41$	6.73355	1.05160	0.525802	−	0.850607i	$-0.323765\pi$
$41$	6.73355	1.05160	0.525802	+	0.850607i	$0.323765\pi$
$42$	−11.5387	−1.78045
$43$	−4.71474	−0.718991	−0.359496	−	0.933147i	$-0.617051\pi$
$43$	−4.71474	−0.718991	−0.359496	+	0.933147i	$0.617051\pi$
$44$	16.2375	2.44789
$45$	−0.212620	−0.0316955
$46$	−7.95338	−1.17266
$47$	−3.91637	−0.571261	−0.285630	−	0.958340i	$-0.592203\pi$
$47$	−3.91637	−0.571261	−0.285630	+	0.958340i	$0.592203\pi$
$48$	−5.77705	−0.833845
$49$	5.59843	0.799776
$50$	12.2400	1.73100
$51$	7.04187	0.986058
$52$	11.6182	1.61116
$53$	0.0537101	0.00737764	0.00368882	−	0.999993i	$-0.498826\pi$
$53$	0.0537101	0.00737764	0.00368882	+	0.999993i	$0.498826\pi$
$54$	−13.8377	−1.88308
$55$	0.676356	0.0911998
$56$	18.0192	2.40792
$57$	−7.28193	−0.964515
$58$	20.5751	2.70165
$59$	−5.29464	−0.689303	−0.344651	−	0.938731i	$-0.612003\pi$
$59$	−5.29464	−0.689303	−0.344651	+	0.938731i	$0.612003\pi$
$60$	−0.907425	−0.117148
$61$	13.7639	1.76229	0.881146	−	0.472845i	$-0.156773\pi$
$61$	13.7639	1.76229	0.881146	+	0.472845i	$0.156773\pi$
$62$	−9.21967	−1.17090
$63$	4.46041	0.561959
$64$	−7.22603	−0.903254
$65$	0.483944	0.0600259
$66$	12.9952	1.59960
$67$	8.41718	1.02832	0.514161	−	0.857694i	$-0.328103\pi$
$67$	8.41718	1.02832	0.514161	+	0.857694i	$0.328103\pi$
$68$	−21.6635	−2.62708
$69$	−4.26519	−0.513468
$70$	1.47860	0.176727
$71$	0.221500	0.0262872	0.0131436	−	0.999914i	$-0.495816\pi$
$71$	0.221500	0.0262872	0.0131436	+	0.999914i	$0.495816\pi$
$72$	6.37960	0.751843
$73$	−2.54322	−0.297661	−0.148831	−	0.988863i	$-0.547551\pi$
$73$	−2.54322	−0.297661	−0.148831	+	0.988863i	$0.547551\pi$
$74$	23.6114	2.74477
$75$	6.56399	0.757944
$76$	22.4020	2.56968
$77$	−14.1888	−1.61696
$78$	9.29832	1.05283
$79$	1.50274	0.169071	0.0845356	−	0.996420i	$-0.473059\pi$
$79$	1.50274	0.169071	0.0845356	+	0.996420i	$0.473059\pi$
$80$	0.740290	0.0827670
$81$	−3.65085	−0.405650
$82$	−16.5787	−1.83081
$83$	9.34520	1.02577	0.512885	−	0.858457i	$-0.328577\pi$
$83$	9.34520	1.02577	0.512885	+	0.858457i	$0.328577\pi$
$84$	19.0363	2.07703
$85$	−0.902369	−0.0978756
$86$	11.6082	1.25174
$87$	11.0339	1.18296
$88$	−20.2939	−2.16333
$89$	14.0122	1.48529	0.742643	−	0.669687i	$-0.233572\pi$
$89$	14.0122	1.48529	0.742643	+	0.669687i	$0.233572\pi$
$90$	0.523491	0.0551808
$91$	−10.1523	−1.06425
$92$	13.1213	1.36799
$93$	−4.94426	−0.512696
$94$	9.64247	0.994545
$95$	0.933131	0.0957372
$96$	0.817657	0.0834517
$97$	6.08190	0.617523	0.308762	−	0.951139i	$-0.400085\pi$
$97$	6.08190	0.617523	0.308762	+	0.951139i	$0.400085\pi$
$98$	−13.7839	−1.39238
$99$	−5.02347	−0.504878
$100$	−20.1933	−2.01933
$101$	0.787385	0.0783477	0.0391739	−	0.999232i	$-0.487527\pi$
$101$	0.787385	0.0783477	0.0391739	+	0.999232i	$0.487527\pi$
$102$	−17.3378	−1.71669
$103$	−4.66160	−0.459321	−0.229661	−	0.973271i	$-0.573762\pi$
$103$	−4.66160	−0.459321	−0.229661	+	0.973271i	$0.573762\pi$
$104$	−14.5206	−1.42386
$105$	0.792935	0.0773825
$106$	−0.132239	−0.0128442
$107$	−10.1427	−0.980533	−0.490266	−	0.871573i	$-0.663101\pi$
$107$	−10.1427	−0.980533	−0.490266	+	0.871573i	$0.663101\pi$
$108$	22.8293	2.19675
$109$	−7.02743	−0.673106	−0.336553	−	0.941665i	$-0.609261\pi$
$109$	−7.02743	−0.673106	−0.336553	+	0.941665i	$0.609261\pi$
$110$	−1.66525	−0.158776
$111$	12.6622	1.20184
$112$	−15.5300	−1.46745
$113$	−20.5027	−1.92874	−0.964368	−	0.264565i	$-0.914772\pi$
$113$	−20.5027	−1.92874	−0.964368	+	0.264565i	$0.914772\pi$
$114$	17.9288	1.67919
$115$	0.546556	0.0509666
$116$	−33.9444	−3.15166
$117$	−3.59438	−0.332301
$118$	13.0359	1.20005
$119$	18.9302	1.73533
$120$	1.13411	0.103530
$121$	4.97992	0.452720
$122$	−33.8882	−3.06809
$123$	−8.89070	−0.801647
$124$	15.2104	1.36594
$125$	−1.68711	−0.150899
$126$	−10.9820	−0.978351
$127$	12.8075	1.13649	0.568243	−	0.822861i	$-0.307623\pi$
$127$	12.8075	1.13649	0.568243	+	0.822861i	$0.307623\pi$
$128$	19.0297	1.68201
$129$	6.22515	0.548094
$130$	−1.19152	−0.104503
$131$	−6.74939	−0.589697	−0.294848	−	0.955544i	$-0.595269\pi$
$131$	−6.74939	−0.589697	−0.294848	+	0.955544i	$0.595269\pi$
$132$	−21.4393	−1.86605
$133$	−19.5755	−1.69741
$134$	−20.7239	−1.79027
$135$	0.950929	0.0818429
$136$	27.0753	2.32169
$137$	14.2952	1.22132	0.610659	−	0.791894i	$-0.290905\pi$
$137$	14.2952	1.22132	0.610659	+	0.791894i	$0.290905\pi$
$138$	10.5013	0.893931
$139$	−12.3420	−1.04684	−0.523419	−	0.852075i	$-0.675344\pi$
$139$	−12.3420	−1.04684	−0.523419	+	0.852075i	$0.675344\pi$
$140$	−2.43937	−0.206164
$141$	5.17100	0.435477
$142$	−0.545354	−0.0457651
$143$	11.4339	0.956152
$144$	−5.49833	−0.458194
$145$	−1.41392	−0.117420
$146$	6.26165	0.518218
$147$	−7.39194	−0.609677
$148$	−38.9537	−3.20197
$149$	8.59287	0.703955	0.351977	−	0.936008i	$-0.385509\pi$
$149$	8.59287	0.703955	0.351977	+	0.936008i	$0.385509\pi$
$150$	−16.1612	−1.31955
$151$	7.02814	0.571942	0.285971	−	0.958238i	$-0.407684\pi$
$151$	7.02814	0.571942	0.285971	+	0.958238i	$0.407684\pi$
$152$	−27.9983	−2.27096
$153$	6.70212	0.541835
$154$	34.9342	2.81508
$155$	0.633575	0.0508899
$156$	−15.3402	−1.22820
$157$	11.2757	0.899896	0.449948	−	0.893055i	$-0.351443\pi$
$157$	11.2757	0.899896	0.449948	+	0.893055i	$0.351443\pi$
$158$	−3.69989	−0.294347
$159$	−0.0709165	−0.00562404
$160$	−0.104777	−0.00828337
$161$	−11.4658	−0.903633
$162$	8.98874	0.706222
$163$	20.2313	1.58464	0.792320	−	0.610105i	$-0.208873\pi$
$163$	20.2313	1.58464	0.792320	+	0.610105i	$0.208873\pi$
$164$	27.3512	2.13577
$165$	−0.893031	−0.0695224
$166$	−23.0088	−1.78583
$167$	−18.1560	−1.40495	−0.702476	−	0.711708i	$-0.747922\pi$
$167$	−18.1560	−1.40495	−0.702476	+	0.711708i	$0.747922\pi$
$168$	−23.7918	−1.83558
$169$	−4.81883	−0.370679
$170$	2.22172	0.170398
$171$	−6.93060	−0.529997
$172$	−19.1509	−1.46024
$173$	7.71189	0.586324	0.293162	−	0.956063i	$-0.405293\pi$
$173$	7.71189	0.586324	0.293162	+	0.956063i	$0.405293\pi$
$174$	−27.1665	−2.05949
$175$	17.6455	1.33388
$176$	17.4905	1.31839
$177$	6.99081	0.525462
$178$	−34.4993	−2.58583
$179$	9.76806	0.730099	0.365050	−	0.930988i	$-0.381052\pi$
$179$	9.76806	0.730099	0.365050	+	0.930988i	$0.381052\pi$
$180$	−0.863646	−0.0643724
$181$	21.7268	1.61494	0.807470	−	0.589909i	$-0.200836\pi$
$181$	21.7268	1.61494	0.807470	+	0.589909i	$0.200836\pi$
$182$	24.9960	1.85283
$183$	−18.1733	−1.34341
$184$	−16.3993	−1.20897
$185$	−1.62257	−0.119294
$186$	12.1733	0.892586
$187$	−21.3198	−1.55906
$188$	−15.9080	−1.16021
$189$	−19.9489	−1.45107
$190$	−2.29746	−0.166675
$191$	−17.4175	−1.26029	−0.630145	−	0.776478i	$-0.717004\pi$
$191$	−17.4175	−1.26029	−0.630145	+	0.776478i	$0.717004\pi$
$192$	9.54094	0.688558
$193$	−1.30477	−0.0939196	−0.0469598	−	0.998897i	$-0.514953\pi$
$193$	−1.30477	−0.0939196	−0.0469598	+	0.998897i	$0.514953\pi$
$194$	−14.9742	−1.07509
$195$	−0.638980	−0.0457583
$196$	22.7404	1.62431
$197$	−10.7056	−0.762746	−0.381373	−	0.924421i	$-0.624549\pi$
$197$	−10.7056	−0.762746	−0.381373	+	0.924421i	$0.624549\pi$
$198$	12.3683	0.878974
$199$	−18.3799	−1.30292	−0.651459	−	0.758684i	$-0.725843\pi$
$199$	−18.3799	−1.30292	−0.651459	+	0.758684i	$0.725843\pi$
$200$	25.2379	1.78459
$201$	−11.1137	−0.783899
$202$	−1.93862	−0.136401
$203$	29.6617	2.08184
$204$	28.6035	2.00265
$205$	1.13928	0.0795711
$206$	11.4773	0.799662
$207$	−4.05941	−0.282149
$208$	12.5147	0.867741
$209$	22.0466	1.52500
$210$	−1.95228	−0.134720
$211$	6.17090	0.424822	0.212411	−	0.977180i	$-0.431868\pi$
$211$	6.17090	0.424822	0.212411	+	0.977180i	$0.431868\pi$
$212$	0.218166	0.0149837
$213$	−0.292459	−0.0200389
$214$	24.9723	1.70707
$215$	−0.797711	−0.0544035
$216$	−28.5323	−1.94138
$217$	−13.2913	−0.902274
$218$	17.3022	1.17185
$219$	3.35796	0.226910
$220$	2.74730	0.185223
$221$	−15.2547	−1.02614
$222$	−31.1755	−2.09236
$223$	19.2012	1.28581	0.642904	−	0.765947i	$-0.277730\pi$
$223$	19.2012	1.28581	0.642904	+	0.765947i	$0.277730\pi$
$224$	2.19805	0.146863
$225$	6.24730	0.416487
$226$	50.4797	3.35786
$227$	15.4961	1.02851	0.514257	−	0.857636i	$-0.328068\pi$
$227$	15.4961	1.02851	0.514257	+	0.857636i	$0.328068\pi$
$228$	−29.5786	−1.95889
$229$	19.3748	1.28032	0.640160	−	0.768242i	$-0.278868\pi$
$229$	19.3748	1.28032	0.640160	+	0.768242i	$0.278868\pi$
$230$	−1.34567	−0.0887311
$231$	18.7343	1.23263
$232$	42.4243	2.78529
$233$	−14.8287	−0.971462	−0.485731	−	0.874108i	$-0.661447\pi$
$233$	−14.8287	−0.971462	−0.485731	+	0.874108i	$0.661447\pi$
$234$	8.84971	0.578524
$235$	−0.662630	−0.0432252
$236$	−21.5064	−1.39995
$237$	−1.98415	−0.128884
$238$	−46.6079	−3.02114
$239$	−10.9194	−0.706316	−0.353158	−	0.935564i	$-0.614892\pi$
$239$	−10.9194	−0.706316	−0.353158	+	0.935564i	$0.614892\pi$
$240$	−0.977448	−0.0630940
$241$	14.4695	0.932060	0.466030	−	0.884769i	$-0.345684\pi$
$241$	14.4695	0.932060	0.466030	+	0.884769i	$0.345684\pi$
$242$	−12.2611	−0.788171
$243$	−12.0405	−0.772398
$244$	55.9080	3.57915
$245$	0.947228	0.0605162
$246$	21.8898	1.39564
$247$	15.7747	1.00372
$248$	−19.0102	−1.20715
$249$	−12.3390	−0.781953
$250$	4.15382	0.262711
$251$	14.6765	0.926374	0.463187	−	0.886261i	$-0.346706\pi$
$251$	14.6765	0.926374	0.463187	+	0.886261i	$0.346706\pi$
$252$	18.1178	1.14132
$253$	12.9132	0.811846
$254$	−31.5334	−1.97858
$255$	1.19145	0.0746114
$256$	−32.4010	−2.02506
$257$	−31.1891	−1.94553	−0.972763	−	0.231803i	$-0.925538\pi$
$257$	−31.1891	−1.94553	−0.972763	+	0.231803i	$0.925538\pi$
$258$	−15.3269	−0.954212
$259$	34.0389	2.11507
$260$	1.96574	0.121910
$261$	10.5016	0.650030
$262$	16.6176	1.02664
$263$	0.185728	0.0114525	0.00572625	−	0.999984i	$-0.498177\pi$
$263$	0.185728	0.0114525	0.00572625	+	0.999984i	$0.498177\pi$
$264$	26.7952	1.64913
$265$	0.00908748	0.000558239 0
$266$	48.1968	2.95514
$267$	−18.5011	−1.13225
$268$	34.1899	2.08848
$269$	4.93670	0.300996	0.150498	−	0.988610i	$-0.451912\pi$
$269$	4.93670	0.300996	0.150498	+	0.988610i	$0.451912\pi$
$270$	−2.34128	−0.142486
$271$	14.9955	0.910911	0.455455	−	0.890259i	$-0.349476\pi$
$271$	14.9955	0.910911	0.455455	+	0.890259i	$0.349476\pi$
$272$	−23.3351	−1.41490
$273$	13.4047	0.811290
$274$	−35.1961	−2.12627
$275$	−19.8730	−1.19839
$276$	−17.3249	−1.04283
$277$	−21.8451	−1.31255	−0.656273	−	0.754523i	$-0.727868\pi$
$277$	−21.8451	−1.31255	−0.656273	+	0.754523i	$0.727868\pi$
$278$	30.3873	1.82251
$279$	−4.70572	−0.281724
$280$	3.04876	0.182198
$281$	12.5710	0.749925	0.374962	−	0.927040i	$-0.377656\pi$
$281$	12.5710	0.749925	0.374962	+	0.927040i	$0.377656\pi$
$282$	−12.7315	−0.758151
$283$	−20.6383	−1.22682	−0.613409	−	0.789765i	$-0.710202\pi$
$283$	−20.6383	−1.22682	−0.613409	+	0.789765i	$0.710202\pi$
$284$	0.899714	0.0533882
$285$	−1.23207	−0.0729813
$286$	−28.1514	−1.66463
$287$	−23.9003	−1.41079
$288$	0.778208	0.0458563
$289$	11.4441	0.673183
$290$	3.48121	0.204424
$291$	−8.03028	−0.470744
$292$	−10.3304	−0.604539
$293$	26.1911	1.53010	0.765050	−	0.643971i	$-0.222714\pi$
$293$	26.1911	1.53010	0.765050	+	0.643971i	$0.222714\pi$
$294$	18.1997	1.06143
$295$	−0.895826	−0.0521570
$296$	48.6849	2.82975
$297$	22.4671	1.30367
$298$	−21.1565	−1.22556
$299$	9.23963	0.534341
$300$	26.6624	1.53936
$301$	16.7346	0.964568
$302$	−17.3040	−0.995731
$303$	−1.03963	−0.0597252
$304$	24.1306	1.38399
$305$	2.32879	0.133346
$306$	−16.5013	−0.943315
$307$	10.9430	0.624548	0.312274	−	0.949992i	$-0.398909\pi$
$307$	10.9430	0.624548	0.312274	+	0.949992i	$0.398909\pi$
$308$	−57.6338	−3.28399
$309$	6.15498	0.350145
$310$	−1.55992	−0.0885976
$311$	−10.8061	−0.612759	−0.306380	−	0.951909i	$-0.599118\pi$
$311$	−10.8061	−0.612759	−0.306380	+	0.951909i	$0.599118\pi$
$312$	19.1724	1.08542
$313$	−2.94210	−0.166297	−0.0831486	−	0.996537i	$-0.526498\pi$
$313$	−2.94210	−0.166297	−0.0831486	+	0.996537i	$0.526498\pi$
$314$	−27.7618	−1.56669
$315$	0.754679	0.0425214
$316$	6.10400	0.343377
$317$	−21.5738	−1.21171	−0.605854	−	0.795576i	$-0.707168\pi$
$317$	−21.5738	−1.21171	−0.605854	+	0.795576i	$0.707168\pi$
$318$	0.174603	0.00979127
$319$	−33.4060	−1.87038
$320$	−1.22261	−0.0683459
$321$	13.3920	0.747469
$322$	28.2300	1.57319
$323$	−29.4138	−1.63663
$324$	−14.8295	−0.823859
$325$	−14.2195	−0.788755
$326$	−49.8115	−2.75880
$327$	9.27872	0.513115
$328$	−34.1839	−1.88749
$329$	13.9009	0.766379
$330$	2.19873	0.121036
$331$	34.7767	1.91150	0.955749	−	0.294183i	$-0.0950474\pi$
$331$	34.7767	1.91150	0.955749	+	0.294183i	$0.0950474\pi$
$332$	37.9595	2.08330
$333$	12.0513	0.660406
$334$	44.7018	2.44597
$335$	1.42415	0.0778094
$336$	20.5052	1.11865
$337$	−27.6453	−1.50593	−0.752967	−	0.658058i	$-0.771378\pi$
$337$	−27.6453	−1.50593	−0.752967	+	0.658058i	$0.771378\pi$
$338$	11.8644	0.645340
$339$	27.0709	1.47029
$340$	−3.66535	−0.198782
$341$	14.9692	0.810625
$342$	17.0638	0.922706
$343$	4.97476	0.268612
$344$	23.9351	1.29049
$345$	−0.721649	−0.0388523
$346$	−18.9874	−1.02077
$347$	−19.4721	−1.04532	−0.522658	−	0.852542i	$-0.675060\pi$
$347$	−19.4721	−1.04532	−0.522658	+	0.852542i	$0.675060\pi$
$348$	44.8188	2.40254
$349$	−20.4946	−1.09705	−0.548526	−	0.836133i	$-0.684811\pi$
$349$	−20.4946	−1.09705	−0.548526	+	0.836133i	$0.684811\pi$
$350$	−43.4450	−2.32223
$351$	16.0756	0.858053
$352$	−2.47552	−0.131946
$353$	−1.27099	−0.0676482	−0.0338241	−	0.999428i	$-0.510769\pi$
$353$	−1.27099	−0.0676482	−0.0338241	+	0.999428i	$0.510769\pi$
$354$	−17.2121	−0.914811
$355$	0.0374767	0.00198905
$356$	56.9163	3.01656
$357$	−24.9946	−1.32285
$358$	−24.0499	−1.27108
$359$	−23.7855	−1.25535	−0.627676	−	0.778474i	$-0.715994\pi$
$359$	−23.7855	−1.25535	−0.627676	+	0.778474i	$0.715994\pi$
$360$	1.07940	0.0568893
$361$	11.4165	0.600870
$362$	−53.4935	−2.81155
$363$	−6.57528	−0.345113
$364$	−41.2380	−2.16146
$365$	−0.430300	−0.0225230
$366$	44.7445	2.33883
$367$	−4.50120	−0.234961	−0.117480	−	0.993075i	$-0.537482\pi$
$367$	−4.50120	−0.234961	−0.117480	+	0.993075i	$0.537482\pi$
$368$	14.1339	0.736779
$369$	−8.46176	−0.440502
$370$	3.99493	0.207687
$371$	−0.190640	−0.00989753
$372$	−20.0832	−1.04127
$373$	33.3294	1.72573	0.862865	−	0.505435i	$-0.168668\pi$
$373$	33.3294	1.72573	0.862865	+	0.505435i	$0.168668\pi$
$374$	52.4915	2.71427
$375$	2.22759	0.115032
$376$	19.8820	1.02534
$377$	−23.9026	−1.23105
$378$	49.1161	2.52626
$379$	3.33806	0.171464	0.0857322	−	0.996318i	$-0.472677\pi$
$379$	3.33806	0.171464	0.0857322	+	0.996318i	$0.472677\pi$
$380$	3.79030	0.194439
$381$	−16.9105	−0.866353
$382$	42.8837	2.19412
$383$	15.4585	0.789893	0.394947	−	0.918704i	$-0.370763\pi$
$383$	15.4585	0.789893	0.394947	+	0.918704i	$0.370763\pi$
$384$	−25.1260	−1.28221
$385$	−2.40068	−0.122350
$386$	3.21248	0.163511
$387$	5.92481	0.301175
$388$	24.7042	1.25417
$389$	5.41256	0.274427	0.137214	−	0.990541i	$-0.456185\pi$
$389$	5.41256	0.274427	0.137214	+	0.990541i	$0.456185\pi$
$390$	1.57323	0.0796636
$391$	−17.2283	−0.871273
$392$	−28.4213	−1.43549
$393$	8.91160	0.449531
$394$	26.3583	1.32791
$395$	0.254256	0.0127930
$396$	−20.4049	−1.02539
$397$	18.5264	0.929815	0.464908	−	0.885359i	$-0.346088\pi$
$397$	18.5264	0.929815	0.464908	+	0.885359i	$0.346088\pi$
$398$	45.2532	2.26834
$399$	25.8467	1.29395
$400$	−21.7516	−1.08758
$401$	−31.5587	−1.57597	−0.787984	−	0.615695i	$-0.788875\pi$
$401$	−31.5587	−1.57597	−0.787984	+	0.615695i	$0.788875\pi$
$402$	27.3630	1.36474
$403$	10.7107	0.533538
$404$	3.19830	0.159121
$405$	−0.617706	−0.0306940
$406$	−73.0299	−3.62441
$407$	−38.3358	−1.90023
$408$	−35.7491	−1.76984
$409$	−31.4062	−1.55294	−0.776469	−	0.630155i	$-0.782991\pi$
$409$	−31.4062	−1.55294	−0.776469	+	0.630155i	$0.782991\pi$
$410$	−2.80503	−0.138531
$411$	−18.8747	−0.931021
$412$	−18.9351	−0.932863
$413$	18.7929	0.924739
$414$	9.99466	0.491211
$415$	1.58116	0.0776162
$416$	−1.77128	−0.0868441
$417$	16.2959	0.798014
$418$	−54.2809	−2.65497
$419$	−24.0384	−1.17435	−0.587177	−	0.809458i	$-0.699761\pi$
$419$	−24.0384	−1.17435	−0.587177	+	0.809458i	$0.699761\pi$
$420$	3.22084	0.157161
$421$	11.7460	0.572463	0.286232	−	0.958160i	$-0.407597\pi$
$421$	11.7460	0.572463	0.286232	+	0.958160i	$0.407597\pi$
$422$	−15.1934	−0.739601
$423$	4.92152	0.239293
$424$	−0.272667	−0.0132419
$425$	26.5138	1.28611
$426$	0.720062	0.0348871
$427$	−48.8541	−2.36422
$428$	−41.1989	−1.99142
$429$	−15.0969	−0.728883
$430$	1.96404	0.0947146
$431$	−24.9992	−1.20417	−0.602085	−	0.798432i	$-0.705663\pi$
$431$	−24.9992	−1.20417	−0.602085	+	0.798432i	$0.705663\pi$
$432$	24.5909	1.18313
$433$	−23.4353	−1.12623	−0.563114	−	0.826379i	$-0.690397\pi$
$433$	−23.4353	−1.12623	−0.563114	+	0.826379i	$0.690397\pi$
$434$	32.7245	1.57083
$435$	1.86688	0.0895101
$436$	−28.5449	−1.36705
$437$	17.8156	0.852238
$438$	−8.26762	−0.395042
$439$	3.56819	0.170300	0.0851502	−	0.996368i	$-0.472863\pi$
$439$	3.56819	0.170300	0.0851502	+	0.996368i	$0.472863\pi$
$440$	−3.43362	−0.163692
$441$	−7.03530	−0.335014
$442$	37.5586	1.78648
$443$	−10.3473	−0.491617	−0.245808	−	0.969318i	$-0.579053\pi$
$443$	−10.3473	−0.491617	−0.245808	+	0.969318i	$0.579053\pi$
$444$	51.4327	2.44089
$445$	2.37079	0.112386
$446$	−47.2752	−2.23855
$447$	−11.3457	−0.536631
$448$	25.6483	1.21177
$449$	−22.8726	−1.07943	−0.539713	−	0.841849i	$-0.681467\pi$
$449$	−22.8726	−1.07943	−0.539713	+	0.841849i	$0.681467\pi$
$450$	−15.3815	−0.725089
$451$	26.9173	1.26749
$452$	−83.2805	−3.91719
$453$	−9.27966	−0.435996
$454$	−38.1529	−1.79061
$455$	−1.71773	−0.0805282
$456$	36.9678	1.73118
$457$	−16.6800	−0.780256	−0.390128	−	0.920761i	$-0.627569\pi$
$457$	−16.6800	−0.780256	−0.390128	+	0.920761i	$0.627569\pi$
$458$	−47.7025	−2.22899
$459$	−29.9748	−1.39910
$460$	2.22007	0.103511
$461$	23.8354	1.11012	0.555062	−	0.831809i	$-0.312695\pi$
$461$	23.8354	1.11012	0.555062	+	0.831809i	$0.312695\pi$
$462$	−46.1256	−2.14596
$463$	−10.7883	−0.501376	−0.250688	−	0.968068i	$-0.580657\pi$
$463$	−10.7883	−0.501376	−0.250688	+	0.968068i	$0.580657\pi$
$464$	−36.5638	−1.69743
$465$	−0.836545	−0.0387939
$466$	36.5098	1.69128
$467$	−5.21607	−0.241371	−0.120686	−	0.992691i	$-0.538509\pi$
$467$	−5.21607	−0.241371	−0.120686	+	0.992691i	$0.538509\pi$
$468$	−14.6001	−0.674889
$469$	−29.8762	−1.37955
$470$	1.63146	0.0752536
$471$	−14.8879	−0.685999
$472$	26.8790	1.23721
$473$	−18.8471	−0.866592
$474$	4.88517	0.224383
$475$	−27.4177	−1.25801
$476$	76.8928	3.52438
$477$	−0.0674951	−0.00309039
$478$	26.8846	1.22967
$479$	−27.8546	−1.27271	−0.636354	−	0.771397i	$-0.719558\pi$
$479$	−27.8546	−1.27271	−0.636354	+	0.771397i	$0.719558\pi$
$480$	0.138343	0.00631449
$481$	−27.4299	−1.25070
$482$	−35.6252	−1.62268
$483$	15.1390	0.688847
$484$	20.2281	0.919457
$485$	1.02903	0.0467257
$486$	29.6449	1.34472
$487$	−17.9913	−0.815262	−0.407631	−	0.913147i	$-0.633645\pi$
$487$	−17.9913	−0.815262	−0.407631	+	0.913147i	$0.633645\pi$
$488$	−69.8747	−3.16308
$489$	−26.7126	−1.20799
$490$	−2.33217	−0.105357
$491$	−24.8795	−1.12280	−0.561398	−	0.827546i	$-0.689736\pi$
$491$	−24.8795	−1.12280	−0.561398	+	0.827546i	$0.689736\pi$
$492$	−36.1133	−1.62811
$493$	44.5690	2.00729
$494$	−38.8390	−1.74745
$495$	−0.849946	−0.0382022
$496$	16.3842	0.735671
$497$	−0.786197	−0.0352658
$498$	30.3798	1.36135
$499$	42.6055	1.90728	0.953642	−	0.300944i	$-0.0973016\pi$
$499$	42.6055	1.90728	0.953642	+	0.300944i	$0.0973016\pi$
$500$	−6.85290	−0.306471
$501$	23.9724	1.07101
$502$	−36.1350	−1.61279
$503$	21.1065	0.941094	0.470547	−	0.882375i	$-0.344057\pi$
$503$	21.1065	0.941094	0.470547	+	0.882375i	$0.344057\pi$
$504$	−22.6439	−1.00864
$505$	0.133222	0.00592829
$506$	−31.7936	−1.41340
$507$	6.36258	0.282572
$508$	52.0232	2.30816
$509$	−31.8864	−1.41334	−0.706670	−	0.707543i	$-0.749804\pi$
$509$	−31.8864	−1.41334	−0.706670	+	0.707543i	$0.749804\pi$
$510$	−2.93346	−0.129896
$511$	9.02697	0.399330
$512$	41.7149	1.84355
$513$	30.9967	1.36854
$514$	76.7907	3.38709
$515$	−0.788720	−0.0347552
$516$	25.2861	1.11316
$517$	−15.6556	−0.688534
$518$	−83.8070	−3.68227
$519$	−10.1824	−0.446960
$520$	−2.45682	−0.107739
$521$	−37.3289	−1.63541	−0.817705	−	0.575638i	$-0.804754\pi$
$521$	−37.3289	−1.63541	−0.817705	+	0.575638i	$0.804754\pi$
$522$	−25.8558	−1.13168
$523$	7.07527	0.309380	0.154690	−	0.987963i	$-0.450562\pi$
$523$	7.07527	0.309380	0.154690	+	0.987963i	$0.450562\pi$
$524$	−27.4155	−1.19765
$525$	−23.2984	−1.01683
$526$	−0.457281	−0.0199384
$527$	−19.9713	−0.869963
$528$	−23.0937	−1.00502
$529$	−12.5650	−0.546303
$530$	−0.0223743	−0.000971876 0
$531$	6.65353	0.288739
$532$	−79.5142	−3.44738
$533$	19.2598	0.834235
$534$	45.5514	1.97120
$535$	−1.71610	−0.0741933
$536$	−42.7311	−1.84570
$537$	−12.8973	−0.556561
$538$	−12.1546	−0.524023
$539$	22.3797	0.963961
$540$	3.86260	0.166220
$541$	−19.9424	−0.857392	−0.428696	−	0.903449i	$-0.641027\pi$
$541$	−19.9424	−0.857392	−0.428696	+	0.903449i	$0.641027\pi$
$542$	−36.9203	−1.58586
$543$	−28.6871	−1.23108
$544$	3.30275	0.141604
$545$	−1.18901	−0.0509315
$546$	−33.0037	−1.41243
$547$	−0.598732	−0.0255999	−0.0128000	−	0.999918i	$-0.504074\pi$
$547$	−0.598732	−0.0255999	−0.0128000	+	0.999918i	$0.504074\pi$
$548$	58.0658	2.48045
$549$	−17.2965	−0.738198
$550$	48.9293	2.08635
$551$	−46.0884	−1.96343
$552$	21.6529	0.921608
$553$	−5.33386	−0.226819
$554$	53.7848	2.28510
$555$	2.14238	0.0909389
$556$	−50.1324	−2.12609
$557$	6.27659	0.265948	0.132974	−	0.991120i	$-0.457547\pi$
$557$	6.27659	0.265948	0.132974	+	0.991120i	$0.457547\pi$
$558$	11.5859	0.490472
$559$	−13.4855	−0.570374
$560$	−2.62761	−0.111037
$561$	28.1498	1.18848
$562$	−30.9511	−1.30559
$563$	−4.37917	−0.184560	−0.0922801	−	0.995733i	$-0.529416\pi$
$563$	−4.37917	−0.184560	−0.0922801	+	0.995733i	$0.529416\pi$
$564$	21.0042	0.884437
$565$	−3.46896	−0.145940
$566$	50.8134	2.13585
$567$	12.9584	0.544203
$568$	−1.12448	−0.0471820
$569$	−32.1937	−1.34963	−0.674815	−	0.737987i	$-0.735776\pi$
$569$	−32.1937	−1.34963	−0.674815	+	0.737987i	$0.735776\pi$
$570$	3.03347	0.127058
$571$	0.413146	0.0172896	0.00864482	−	0.999963i	$-0.497248\pi$
$571$	0.413146	0.0172896	0.00864482	+	0.999963i	$0.497248\pi$
$572$	46.4437	1.94191
$573$	22.9974	0.960730
$574$	58.8448	2.45613
$575$	−16.0592	−0.669714
$576$	9.08063	0.378360
$577$	28.8719	1.20195	0.600976	−	0.799267i	$-0.294779\pi$
$577$	28.8719	1.20195	0.600976	+	0.799267i	$0.294779\pi$
$578$	−28.1765	−1.17199
$579$	1.72277	0.0715957
$580$	−5.74323	−0.238475
$581$	−33.1701	−1.37613
$582$	19.7713	0.819548
$583$	0.214705	0.00889219
$584$	12.9110	0.534263
$585$	−0.608152	−0.0251440
$586$	−64.4850	−2.66385
$587$	−27.0193	−1.11521	−0.557603	−	0.830108i	$-0.688279\pi$
$587$	−27.0193	−1.11521	−0.557603	+	0.830108i	$0.688279\pi$
$588$	−30.0255	−1.23823
$589$	20.6521	0.850956
$590$	2.20561	0.0908036
$591$	14.1353	0.581448
$592$	−41.9596	−1.72453
$593$	−20.7413	−0.851745	−0.425872	−	0.904783i	$-0.640033\pi$
$593$	−20.7413	−0.851745	−0.425872	+	0.904783i	$0.640033\pi$
$594$	−55.3162	−2.26965
$595$	3.20289	0.131306
$596$	34.9035	1.42970
$597$	24.2681	0.993226
$598$	−22.7489	−0.930270
$599$	−10.7410	−0.438866	−0.219433	−	0.975628i	$-0.570421\pi$
$599$	−10.7410	−0.438866	−0.219433	+	0.975628i	$0.570421\pi$
$600$	−33.3231	−1.36041
$601$	−11.9985	−0.489430	−0.244715	−	0.969595i	$-0.578694\pi$
$601$	−11.9985	−0.489430	−0.244715	+	0.969595i	$0.578694\pi$
$602$	−41.2023	−1.67928
$603$	−10.5775	−0.430749
$604$	28.5478	1.16159
$605$	0.842579	0.0342557
$606$	2.55967	0.103979
$607$	−20.4382	−0.829562	−0.414781	−	0.909921i	$-0.636142\pi$
$607$	−20.4382	−0.829562	−0.414781	+	0.909921i	$0.636142\pi$
$608$	−3.41534	−0.138510
$609$	−39.1640	−1.58701
$610$	−5.73371	−0.232151
$611$	−11.2019	−0.453180
$612$	27.2235	1.10044
$613$	9.89741	0.399753	0.199876	−	0.979821i	$-0.435946\pi$
$613$	9.89741	0.399753	0.199876	+	0.979821i	$0.435946\pi$
$614$	−26.9426	−1.08732
$615$	−1.50426	−0.0606577
$616$	72.0316	2.90224
$617$	−13.9072	−0.559884	−0.279942	−	0.960017i	$-0.590315\pi$
$617$	−13.9072	−0.559884	−0.279942	+	0.960017i	$0.590315\pi$
$618$	−15.1542	−0.609590
$619$	−0.791104	−0.0317972	−0.0158986	−	0.999874i	$-0.505061\pi$
$619$	−0.791104	−0.0317972	−0.0158986	+	0.999874i	$0.505061\pi$
$620$	2.57353	0.103355
$621$	18.1554	0.728553
$622$	26.6057	1.06679
$623$	−49.7352	−1.99260
$624$	−16.5239	−0.661487
$625$	24.5714	0.982857
$626$	7.24373	0.289518
$627$	−29.1094	−1.16252
$628$	45.8009	1.82765
$629$	51.1461	2.03933
$630$	−1.85809	−0.0740282
$631$	−39.5103	−1.57288	−0.786440	−	0.617667i	$-0.788078\pi$
$631$	−39.5103	−1.57288	−0.786440	+	0.617667i	$0.788078\pi$
$632$	−7.62888	−0.303460
$633$	−8.14780	−0.323846
$634$	53.1169	2.10954
$635$	2.16697	0.0859938
$636$	−0.288057	−0.0114222
$637$	16.0131	0.634460
$638$	82.2488	3.25626
$639$	−0.278349	−0.0110113
$640$	3.21974	0.127271
$641$	20.9546	0.827656	0.413828	−	0.910355i	$-0.364191\pi$
$641$	20.9546	0.827656	0.413828	+	0.910355i	$0.364191\pi$
$642$	−32.9724	−1.30132
$643$	−35.9454	−1.41755	−0.708774	−	0.705436i	$-0.750751\pi$
$643$	−35.9454	−1.41755	−0.708774	+	0.705436i	$0.750751\pi$
$644$	−46.5732	−1.83524
$645$	1.05326	0.0414722
$646$	72.4196	2.84931
$647$	−15.5668	−0.611995	−0.305998	−	0.952032i	$-0.598990\pi$
$647$	−15.5668	−0.611995	−0.305998	+	0.952032i	$0.598990\pi$
$648$	18.5341	0.728088
$649$	−21.1653	−0.830809
$650$	35.0098	1.37320
$651$	17.5493	0.687811
$652$	82.1781	3.21834
$653$	−35.9850	−1.40820	−0.704101	−	0.710100i	$-0.748650\pi$
$653$	−35.9850	−1.40820	−0.704101	+	0.710100i	$0.748650\pi$
$654$	−22.8451	−0.893315
$655$	−1.14196	−0.0446202
$656$	29.4618	1.15029
$657$	3.19595	0.124686
$658$	−34.2253	−1.33424
$659$	−22.6152	−0.880962	−0.440481	−	0.897762i	$-0.645192\pi$
$659$	−22.6152	−0.880962	−0.440481	+	0.897762i	$0.645192\pi$
$660$	−3.62742	−0.141197
$661$	4.77585	0.185759	0.0928796	−	0.995677i	$-0.470393\pi$
$661$	4.77585	0.185759	0.0928796	+	0.995677i	$0.470393\pi$
$662$	−85.6235	−3.32785
$663$	20.1417	0.782237
$664$	−47.4423	−1.84112
$665$	−3.31208	−0.128437
$666$	−29.6714	−1.14974
$667$	−26.9950	−1.04525
$668$	−73.7482	−2.85340
$669$	−25.3524	−0.980182
$670$	−3.50638	−0.135463
$671$	55.0212	2.12407
$672$	−2.90221	−0.111955
$673$	8.78595	0.338673	0.169337	−	0.985558i	$-0.445837\pi$
$673$	8.78595	0.338673	0.169337	+	0.985558i	$0.445837\pi$
$674$	68.0654	2.62178
$675$	−27.9406	−1.07544
$676$	−19.5737	−0.752835
$677$	21.4585	0.824716	0.412358	−	0.911022i	$-0.364705\pi$
$677$	21.4585	0.824716	0.412358	+	0.911022i	$0.364705\pi$
$678$	−66.6513	−2.55973
$679$	−21.5873	−0.828443
$680$	4.58101	0.175674
$681$	−20.4604	−0.784045
$682$	−36.8555	−1.41127
$683$	−44.2816	−1.69439	−0.847194	−	0.531283i	$-0.821710\pi$
$683$	−44.2816	−1.69439	−0.847194	+	0.531283i	$0.821710\pi$
$684$	−28.1516	−1.07640
$685$	2.41867	0.0924126
$686$	−12.2483	−0.467644
$687$	−25.5816	−0.975999
$688$	−20.6287	−0.786462
$689$	0.153626	0.00585267
$690$	1.77677	0.0676405
$691$	−3.64309	−0.138590	−0.0692948	−	0.997596i	$-0.522075\pi$
$691$	−3.64309	−0.138590	−0.0692948	+	0.997596i	$0.522075\pi$
$692$	31.3251	1.19080
$693$	17.8304	0.677322
$694$	47.9422	1.81986
$695$	−2.08821	−0.0792104
$696$	−56.0152	−2.12325
$697$	−35.9121	−1.36027
$698$	50.4598	1.90993
$699$	19.5792	0.740554
$700$	71.6747	2.70905
$701$	0.704344	0.0266027	0.0133014	−	0.999912i	$-0.495766\pi$
$701$	0.704344	0.0266027	0.0133014	+	0.999912i	$0.495766\pi$
$702$	−39.5797	−1.49384
$703$	−52.8897	−1.99477
$704$	−28.8860	−1.08868
$705$	0.874909	0.0329510
$706$	3.12931	0.117773
$707$	−2.79477	−0.105108
$708$	28.3961	1.06719
$709$	−21.8987	−0.822423	−0.411212	−	0.911540i	$-0.634894\pi$
$709$	−21.8987	−0.822423	−0.411212	+	0.911540i	$0.634894\pi$
$710$	−0.0922712	−0.00346288
$711$	−1.88842	−0.0708214
$712$	−71.1349	−2.66589
$713$	12.0964	0.453014
$714$	61.5391	2.30304
$715$	1.93456	0.0723485
$716$	39.6771	1.48280
$717$	14.4175	0.538431
$718$	58.5623	2.18553
$719$	36.2276	1.35106	0.675530	−	0.737333i	$-0.263915\pi$
$719$	36.2276	1.35106	0.675530	+	0.737333i	$0.263915\pi$
$720$	−0.930290	−0.0346699
$721$	16.5460	0.616206
$722$	−28.1086	−1.04609
$723$	−19.1049	−0.710518
$724$	88.2525	3.27988
$725$	41.5445	1.54292
$726$	16.1890	0.600829
$727$	−28.1123	−1.04263	−0.521313	−	0.853366i	$-0.674558\pi$
$727$	−28.1123	−1.04263	−0.521313	+	0.853366i	$0.674558\pi$
$728$	51.5399	1.91019
$729$	26.8503	0.994456
$730$	1.05944	0.0392117
$731$	25.1451	0.930027
$732$	−73.8186	−2.72841
$733$	30.9352	1.14262	0.571308	−	0.820736i	$-0.306436\pi$
$733$	30.9352	1.14262	0.571308	+	0.820736i	$0.306436\pi$
$734$	11.0824	0.409059
$735$	−1.25068	−0.0461320
$736$	−2.00044	−0.0737373
$737$	33.6476	1.23942
$738$	20.8337	0.766898
$739$	−24.0088	−0.883180	−0.441590	−	0.897217i	$-0.645585\pi$
$739$	−24.0088	−0.883180	−0.441590	+	0.897217i	$0.645585\pi$
$740$	−6.59077	−0.242281
$741$	−20.8283	−0.765147
$742$	0.469374	0.0172313
$743$	−13.2743	−0.486988	−0.243494	−	0.969902i	$-0.578294\pi$
$743$	−13.2743	−0.486988	−0.243494	+	0.969902i	$0.578294\pi$
$744$	25.1003	0.920222
$745$	1.45387	0.0532657
$746$	−82.0601	−3.00444
$747$	−11.7437	−0.429680
$748$	−86.5994	−3.16639
$749$	36.0008	1.31544
$750$	−5.48453	−0.200267
$751$	11.5469	0.421351	0.210676	−	0.977556i	$-0.432434\pi$
$751$	11.5469	0.421351	0.210676	+	0.977556i	$0.432434\pi$
$752$	−17.1355	−0.624868
$753$	−19.3783	−0.706183
$754$	58.8505	2.14321
$755$	1.18913	0.0432768
$756$	−81.0308	−2.94706
$757$	−0.0376926	−0.00136996	−0.000684980	−	1.00000i	$-0.500218\pi$
$757$	−0.0376926	−0.00136996	−0.000684980		1.00000i	$0.500218\pi$
$758$	−8.21862	−0.298514
$759$	−17.0500	−0.618878
$760$	−4.73718	−0.171836
$761$	33.1191	1.20057	0.600284	−	0.799787i	$-0.295054\pi$
$761$	33.1191	1.20057	0.600284	+	0.799787i	$0.295054\pi$
$762$	41.6354	1.50829
$763$	24.9434	0.903010
$764$	−70.7487	−2.55960
$765$	1.13397	0.0409986
$766$	−38.0604	−1.37518
$767$	−15.1441	−0.546822
$768$	42.7809	1.54372
$769$	−34.3121	−1.23733	−0.618663	−	0.785657i	$-0.712325\pi$
$769$	−34.3121	−1.23733	−0.618663	+	0.785657i	$0.712325\pi$
$770$	5.91070	0.213007
$771$	41.1808	1.48309
$772$	−5.29989	−0.190747
$773$	32.3342	1.16298	0.581490	−	0.813553i	$-0.302470\pi$
$773$	32.3342	1.16298	0.581490	+	0.813553i	$0.302470\pi$
$774$	−14.5875	−0.524335
$775$	−18.6160	−0.668706
$776$	−30.8757	−1.10837
$777$	−44.9435	−1.61234
$778$	−13.3262	−0.477769
$779$	37.1363	1.33055
$780$	−2.59549	−0.0929333
$781$	0.885443	0.0316836
$782$	42.4178	1.51686
$783$	−46.9675	−1.67848
$784$	24.4952	0.874828
$785$	1.90779	0.0680918
$786$	−21.9412	−0.782618
$787$	−8.26138	−0.294486	−0.147243	−	0.989100i	$-0.547040\pi$
$787$	−8.26138	−0.294486	−0.147243	+	0.989100i	$0.547040\pi$
$788$	−43.4855	−1.54911
$789$	−0.245228	−0.00873034
$790$	−0.626003	−0.0222722
$791$	72.7730	2.58751
$792$	25.5024	0.906188
$793$	39.3686	1.39802
$794$	−45.6139	−1.61878
$795$	−0.0119987	−0.000425551 0
$796$	−74.6578	−2.64618
$797$	15.1899	0.538055	0.269028	−	0.963132i	$-0.413298\pi$
$797$	15.1899	0.538055	0.269028	+	0.963132i	$0.413298\pi$
$798$	−63.6370	−2.25273
$799$	20.8872	0.738935
$800$	3.07862	0.108846
$801$	−17.6085	−0.622165
$802$	77.7007	2.74371
$803$	−10.1665	−0.358768
$804$	−45.1429	−1.59207
$805$	−1.93996	−0.0683746
$806$	−26.3708	−0.928871
$807$	−6.51820	−0.229452
$808$	−3.99728	−0.140624
$809$	47.6124	1.67396	0.836981	−	0.547232i	$-0.184319\pi$
$809$	47.6124	1.67396	0.836981	+	0.547232i	$0.184319\pi$
$810$	1.52085	0.0534373
$811$	3.59576	0.126264	0.0631321	−	0.998005i	$-0.479891\pi$
$811$	3.59576	0.126264	0.0631321	+	0.998005i	$0.479891\pi$
$812$	120.483	4.22814
$813$	−19.7994	−0.694395
$814$	94.3863	3.30824
$815$	3.42304	0.119904
$816$	30.8107	1.07859
$817$	−26.0024	−0.909707
$818$	77.3252	2.70361
$819$	12.7580	0.445800
$820$	4.62768	0.161606
$821$	−0.785262	−0.0274058	−0.0137029	−	0.999906i	$-0.504362\pi$
$821$	−0.785262	−0.0274058	−0.0137029	+	0.999906i	$0.504362\pi$
$822$	46.4714	1.62088
$823$	−30.7316	−1.07124	−0.535618	−	0.844460i	$-0.679921\pi$
$823$	−30.7316	−1.07124	−0.535618	+	0.844460i	$0.679921\pi$
$824$	23.6653	0.824421
$825$	26.2395	0.913542
$826$	−46.2700	−1.60994
$827$	−15.3308	−0.533104	−0.266552	−	0.963821i	$-0.585884\pi$
$827$	−15.3308	−0.533104	−0.266552	+	0.963821i	$0.585884\pi$
$828$	−16.4890	−0.573033
$829$	−8.18978	−0.284443	−0.142221	−	0.989835i	$-0.545425\pi$
$829$	−8.18978	−0.284443	−0.142221	+	0.989835i	$0.545425\pi$
$830$	−3.89298	−0.135127
$831$	28.8434	1.00057
$832$	−20.6684	−0.716549
$833$	−29.8581	−1.03452
$834$	−40.1221	−1.38931
$835$	−3.07190	−0.106308
$836$	89.5517	3.09721
$837$	21.0460	0.727457
$838$	59.1850	2.04451
$839$	−37.6531	−1.29993	−0.649965	−	0.759964i	$-0.725217\pi$
$839$	−37.6531	−1.29993	−0.649965	+	0.759964i	$0.725217\pi$
$840$	−4.02546	−0.138891
$841$	40.8352	1.40811
$842$	−28.9197	−0.996639
$843$	−16.5983	−0.571674
$844$	25.0657	0.862798
$845$	−0.815323	−0.0280480
$846$	−12.1173	−0.416600
$847$	−17.6759	−0.607350
$848$	0.235001	0.00806997
$849$	27.2499	0.935214
$850$	−65.2796	−2.23907
$851$	−30.9787	−1.06194
$852$	−1.18794	−0.0406983
$853$	42.8397	1.46680	0.733401	−	0.679796i	$-0.237932\pi$
$853$	42.8397	1.46680	0.733401	+	0.679796i	$0.237932\pi$
$854$	120.284	4.11602
$855$	−1.17262	−0.0401029
$856$	51.4910	1.75993
$857$	3.01476	0.102982	0.0514910	−	0.998673i	$-0.483603\pi$
$857$	3.01476	0.102982	0.0514910	+	0.998673i	$0.483603\pi$
$858$	37.1699	1.26896
$859$	30.0584	1.02558	0.512790	−	0.858514i	$-0.328612\pi$
$859$	30.0584	1.02558	0.512790	+	0.858514i	$0.328612\pi$
$860$	−3.24024	−0.110491
$861$	31.5569	1.07546
$862$	61.5505	2.09642
$863$	−42.5846	−1.44960	−0.724798	−	0.688961i	$-0.758067\pi$
$863$	−42.5846	−1.44960	−0.724798	+	0.688961i	$0.758067\pi$
$864$	−3.48048	−0.118408
$865$	1.30481	0.0443650
$866$	57.7000	1.96073
$867$	−15.1103	−0.513173
$868$	−53.9883	−1.83248
$869$	6.00718	0.203780
$870$	−4.59644	−0.155834
$871$	24.0754	0.815765
$872$	35.6758	1.20814
$873$	−7.64286	−0.258671
$874$	−43.8638	−1.48372
$875$	5.98827	0.202440
$876$	13.6398	0.460845
$877$	50.4619	1.70398	0.851988	−	0.523561i	$-0.175397\pi$
$877$	50.4619	1.70398	0.851988	+	0.523561i	$0.175397\pi$
$878$	−8.78523	−0.296487
$879$	−34.5816	−1.16641
$880$	2.95930	0.0997581
$881$	29.0089	0.977335	0.488668	−	0.872470i	$-0.337483\pi$
$881$	29.0089	0.977335	0.488668	+	0.872470i	$0.337483\pi$
$882$	17.3216	0.583249
$883$	−44.4641	−1.49633	−0.748167	−	0.663510i	$-0.769066\pi$
$883$	−44.4641	−1.49633	−0.748167	+	0.663510i	$0.769066\pi$
$884$	−61.9634	−2.08406
$885$	1.18281	0.0397598
$886$	25.4761	0.855888
$887$	22.9297	0.769905	0.384952	−	0.922936i	$-0.374218\pi$
$887$	22.9297	0.769905	0.384952	+	0.922936i	$0.374218\pi$
$888$	−64.2814	−2.15714
$889$	−45.4595	−1.52466
$890$	−5.83711	−0.195661
$891$	−14.5942	−0.488925
$892$	77.9938	2.61142
$893$	−21.5992	−0.722790
$894$	27.9341	0.934256
$895$	1.65271	0.0552439
$896$	−67.5446	−2.25651
$897$	−12.1996	−0.407333
$898$	56.3146	1.87924
$899$	−31.2930	−1.04368
$900$	25.3761	0.845869
$901$	−0.286452	−0.00954310
$902$	−66.2730	−2.20665
$903$	−22.0957	−0.735299
$904$	104.085	3.46182
$905$	3.67607	0.122197
$906$	22.8474	0.759055
$907$	−23.0339	−0.764827	−0.382414	−	0.923991i	$-0.624907\pi$
$907$	−23.0339	−0.764827	−0.382414	+	0.923991i	$0.624907\pi$
$908$	62.9440	2.08887
$909$	−0.989472	−0.0328187
$910$	4.22921	0.140197
$911$	−41.4837	−1.37441	−0.687207	−	0.726461i	$-0.741164\pi$
$911$	−41.4837	−1.37441	−0.687207	+	0.726461i	$0.741164\pi$
$912$	−31.8611	−1.05503
$913$	37.3574	1.23635
$914$	41.0677	1.35840
$915$	−3.07484	−0.101651
$916$	78.6987	2.60028
$917$	23.9565	0.791112
$918$	73.8009	2.43579
$919$	−37.7969	−1.24681	−0.623403	−	0.781901i	$-0.714250\pi$
$919$	−37.7969	−1.24681	−0.623403	+	0.781901i	$0.714250\pi$
$920$	−2.77467	−0.0914783
$921$	−14.4486	−0.476098
$922$	−58.6850	−1.93269
$923$	0.633550	0.0208535
$924$	76.0972	2.50341
$925$	47.6752	1.56755
$926$	26.5619	0.872879
$927$	5.85803	0.192403
$928$	5.17507	0.169880
$929$	29.9285	0.981923	0.490961	−	0.871181i	$-0.336646\pi$
$929$	29.9285	0.981923	0.490961	+	0.871181i	$0.336646\pi$
$930$	2.05966	0.0675388
$931$	30.8760	1.01192
$932$	−60.2331	−1.97300
$933$	14.2680	0.467112
$934$	12.8425	0.420219
$935$	−3.60721	−0.117968
$936$	18.2474	0.596435
$937$	25.1844	0.822737	0.411369	−	0.911469i	$-0.365051\pi$
$937$	25.1844	0.822737	0.411369	+	0.911469i	$0.365051\pi$
$938$	73.5580	2.40175
$939$	3.88462	0.126770
$940$	−2.69155	−0.0877887
$941$	−21.3905	−0.697310	−0.348655	−	0.937251i	$-0.613362\pi$
$941$	−21.3905	−0.697310	−0.348655	+	0.937251i	$0.613362\pi$
$942$	36.6555	1.19430
$943$	21.7516	0.708329
$944$	−23.1660	−0.753988
$945$	−3.37525	−0.109797
$946$	46.4035	1.50871
$947$	31.8054	1.03354	0.516768	−	0.856125i	$-0.327135\pi$
$947$	31.8054	1.03354	0.516768	+	0.856125i	$0.327135\pi$
$948$	−8.05947	−0.261759
$949$	−7.27431	−0.236134
$950$	67.5051	2.19015
$951$	28.4852	0.923695
$952$	−96.1018	−3.11468
$953$	−49.9949	−1.61949	−0.809746	−	0.586780i	$-0.800395\pi$
$953$	−49.9949	−1.61949	−0.809746	+	0.586780i	$0.800395\pi$
$954$	0.166179	0.00538026
$955$	−2.94696	−0.0953615
$956$	−44.3537	−1.43450
$957$	44.1079	1.42581
$958$	68.5806	2.21574
$959$	−50.7396	−1.63847
$960$	1.61428	0.0521007
$961$	−16.9777	−0.547667
$962$	67.5351	2.17742
$963$	12.7459	0.410731
$964$	58.7738	1.89298
$965$	−0.220761	−0.00710655
$966$	−37.2736	−1.19926
$967$	−37.0330	−1.19090	−0.595450	−	0.803392i	$-0.703026\pi$
$967$	−37.0330	−1.19090	−0.595450	+	0.803392i	$0.703026\pi$
$968$	−25.2813	−0.812573
$969$	38.8367	1.24761
$970$	−2.53357	−0.0813479
$971$	16.6259	0.533550	0.266775	−	0.963759i	$-0.414042\pi$
$971$	16.6259	0.533550	0.266775	+	0.963759i	$0.414042\pi$
$972$	−48.9076	−1.56871
$973$	43.8072	1.40439
$974$	44.2963	1.41934
$975$	18.7748	0.601275
$976$	60.2222	1.92767
$977$	−38.5124	−1.23212	−0.616060	−	0.787699i	$-0.711272\pi$
$977$	−38.5124	−1.23212	−0.616060	+	0.787699i	$0.711272\pi$
$978$	65.7690	2.10306
$979$	56.0135	1.79020
$980$	3.84756	0.122906
$981$	8.83106	0.281954
$982$	61.2557	1.95475
$983$	−25.1978	−0.803686	−0.401843	−	0.915709i	$-0.631630\pi$
$983$	−25.1978	−0.803686	−0.401843	+	0.915709i	$0.631630\pi$
$984$	45.1350	1.43885
$985$	−1.81134	−0.0577142
$986$	−109.733	−3.49462
$987$	−18.3541	−0.584218
$988$	64.0758	2.03852
$989$	−15.2302	−0.484291
$990$	2.09265	0.0665088
$991$	5.76984	0.183285	0.0916424	−	0.995792i	$-0.470788\pi$
$991$	5.76984	0.183285	0.0916424	+	0.995792i	$0.470788\pi$
$992$	−2.31894	−0.0736264
$993$	−45.9176	−1.45715
$994$	1.93569	0.0613965
$995$	−3.10979	−0.0985871
$996$	−50.1201	−1.58812
$997$	43.5079	1.37791	0.688955	−	0.724804i	$-0.258070\pi$
$997$	43.5079	1.37791	0.688955	+	0.724804i	$0.258070\pi$
$998$	−104.899	−3.32052
$999$	−53.8985	−1.70527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.19	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.19	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46210 q^{2} -1.32036 q^{3} +4.06192 q^{4} +0.169195 q^{5} +3.25085 q^{6} -3.54943 q^{7} -5.07665 q^{8} -1.25666 q^{9} +O(q^{10})\)	\(q-2.46210 q^{2} -1.32036 q^{3} +4.06192 q^{4} +0.169195 q^{5} +3.25085 q^{6} -3.54943 q^{7} -5.07665 q^{8} -1.25666 q^{9} -0.416575 q^{10} +3.99749 q^{11} -5.36319 q^{12} +2.86027 q^{13} +8.73903 q^{14} -0.223398 q^{15} +4.37536 q^{16} -5.33330 q^{17} +3.09401 q^{18} +5.51512 q^{19} +0.687257 q^{20} +4.68651 q^{21} -9.84221 q^{22} +3.23033 q^{23} +6.70300 q^{24} -4.97137 q^{25} -7.04227 q^{26} +5.62031 q^{27} -14.4175 q^{28} -8.35675 q^{29} +0.550028 q^{30} +3.74464 q^{31} -0.619269 q^{32} -5.27812 q^{33} +13.1311 q^{34} -0.600546 q^{35} -5.10444 q^{36} -9.58996 q^{37} -13.5788 q^{38} -3.77658 q^{39} -0.858945 q^{40} +6.73355 q^{41} -11.5387 q^{42} -4.71474 q^{43} +16.2375 q^{44} -0.212620 q^{45} -7.95338 q^{46} -3.91637 q^{47} -5.77705 q^{48} +5.59843 q^{49} +12.2400 q^{50} +7.04187 q^{51} +11.6182 q^{52} +0.0537101 q^{53} -13.8377 q^{54} +0.676356 q^{55} +18.0192 q^{56} -7.28193 q^{57} +20.5751 q^{58} -5.29464 q^{59} -0.907425 q^{60} +13.7639 q^{61} -9.21967 q^{62} +4.46041 q^{63} -7.22603 q^{64} +0.483944 q^{65} +12.9952 q^{66} +8.41718 q^{67} -21.6635 q^{68} -4.26519 q^{69} +1.47860 q^{70} +0.221500 q^{71} +6.37960 q^{72} -2.54322 q^{73} +23.6114 q^{74} +6.56399 q^{75} +22.4020 q^{76} -14.1888 q^{77} +9.29832 q^{78} +1.50274 q^{79} +0.740290 q^{80} -3.65085 q^{81} -16.5787 q^{82} +9.34520 q^{83} +19.0363 q^{84} -0.902369 q^{85} +11.6082 q^{86} +11.0339 q^{87} -20.2939 q^{88} +14.0122 q^{89} +0.523491 q^{90} -10.1523 q^{91} +13.1213 q^{92} -4.94426 q^{93} +9.64247 q^{94} +0.933131 q^{95} +0.817657 q^{96} +6.08190 q^{97} -13.7839 q^{98} -5.02347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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