LMFDB - Embedded newform 5077.2.a.c.1.20

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:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +O(q^{10})$	\(q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +9.47483 q^{10} +1.22619 q^{11} -6.48530 q^{12} +5.68229 q^{13} +10.6770 q^{14} +6.94611 q^{15} +2.31159 q^{16} +0.875977 q^{17} -0.156736 q^{18} +0.266691 q^{19} -14.6944 q^{20} +7.82741 q^{21} -2.92850 q^{22} +4.72547 q^{23} +7.12553 q^{24} +10.7385 q^{25} -13.5710 q^{26} +5.13777 q^{27} -16.5588 q^{28} +3.52186 q^{29} -16.5894 q^{30} -5.19719 q^{31} +2.61854 q^{32} -2.14692 q^{33} -2.09210 q^{34} +17.7354 q^{35} +0.243080 q^{36} +0.569856 q^{37} -0.636938 q^{38} -9.94909 q^{39} +16.1451 q^{40} +7.28931 q^{41} -18.6942 q^{42} -1.60856 q^{43} +4.54179 q^{44} -0.260352 q^{45} -11.2858 q^{46} +6.34320 q^{47} -4.04734 q^{48} +12.9856 q^{49} -25.6468 q^{50} -1.53374 q^{51} +21.0472 q^{52} -6.00921 q^{53} -12.2706 q^{54} -4.86450 q^{55} +18.1935 q^{56} -0.466947 q^{57} -8.41127 q^{58} +10.6432 q^{59} +25.7283 q^{60} -14.5845 q^{61} +12.4125 q^{62} -0.293384 q^{63} -10.8770 q^{64} -22.5427 q^{65} +5.12750 q^{66} +1.39232 q^{67} +3.24462 q^{68} -8.27378 q^{69} -42.3574 q^{70} +2.69836 q^{71} -0.267077 q^{72} +5.82397 q^{73} -1.36099 q^{74} -18.8020 q^{75} +0.987820 q^{76} -5.48169 q^{77} +23.7614 q^{78} -14.5393 q^{79} -9.17048 q^{80} -9.19257 q^{81} -17.4091 q^{82} +4.36231 q^{83} +28.9927 q^{84} -3.47516 q^{85} +3.84173 q^{86} -6.16640 q^{87} -4.99015 q^{88} -3.79378 q^{89} +0.621799 q^{90} -25.4028 q^{91} +17.5031 q^{92} +9.09973 q^{93} -15.1495 q^{94} -1.05801 q^{95} -4.58479 q^{96} -2.58581 q^{97} -31.0135 q^{98} +0.0804702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.38830	−1.68879	−0.844393	−	0.535724i	$-0.820039\pi$
$2$	−2.38830	−1.68879	−0.844393	+	0.535724i	$0.820039\pi$
$3$	−1.75089	−1.01088	−0.505439	−	0.862862i	$-0.668670\pi$
$3$	−1.75089	−1.01088	−0.505439	+	0.862862i	$0.668670\pi$
$4$	3.70399	1.85200
$5$	−3.96718	−1.77418	−0.887088	−	0.461600i	$-0.847276\pi$
$5$	−3.96718	−1.77418	−0.887088	+	0.461600i	$0.847276\pi$
$6$	4.18166	1.70716
$7$	−4.47052	−1.68970	−0.844849	−	0.535004i	$-0.820310\pi$
$7$	−4.47052	−1.68970	−0.844849	+	0.535004i	$0.820310\pi$
$8$	−4.06966	−1.43884
$9$	0.0656264	0.0218755
$10$	9.47483	2.99620
$11$	1.22619	0.369709	0.184854	−	0.982766i	$-0.440819\pi$
$11$	1.22619	0.369709	0.184854	+	0.982766i	$0.440819\pi$
$12$	−6.48530	−1.87214
$13$	5.68229	1.57598	0.787992	−	0.615685i	$-0.211121\pi$
$13$	5.68229	1.57598	0.787992	+	0.615685i	$0.211121\pi$
$14$	10.6770	2.85354
$15$	6.94611	1.79348
$16$	2.31159	0.577896
$17$	0.875977	0.212456	0.106228	−	0.994342i	$-0.466123\pi$
$17$	0.875977	0.212456	0.106228	+	0.994342i	$0.466123\pi$
$18$	−0.156736	−0.0369430
$19$	0.266691	0.0611830	0.0305915	−	0.999532i	$-0.490261\pi$
$19$	0.266691	0.0611830	0.0305915	+	0.999532i	$0.490261\pi$
$20$	−14.6944	−3.28577
$21$	7.82741	1.70808
$22$	−2.92850	−0.624359
$23$	4.72547	0.985328	0.492664	−	0.870220i	$-0.336023\pi$
$23$	4.72547	0.985328	0.492664	+	0.870220i	$0.336023\pi$
$24$	7.12553	1.45449
$25$	10.7385	2.14770
$26$	−13.5710	−2.66150
$27$	5.13777	0.988765
$28$	−16.5588	−3.12932
$29$	3.52186	0.653993	0.326996	−	0.945026i	$-0.393963\pi$
$29$	3.52186	0.653993	0.326996	+	0.945026i	$0.393963\pi$
$30$	−16.5894	−3.02880
$31$	−5.19719	−0.933443	−0.466722	−	0.884404i	$-0.654565\pi$
$31$	−5.19719	−0.933443	−0.466722	+	0.884404i	$0.654565\pi$
$32$	2.61854	0.462897
$33$	−2.14692	−0.373731
$34$	−2.09210	−0.358792
$35$	17.7354	2.99782
$36$	0.243080	0.0405133
$37$	0.569856	0.0936837	0.0468418	−	0.998902i	$-0.485084\pi$
$37$	0.569856	0.0936837	0.0468418	+	0.998902i	$0.485084\pi$
$38$	−0.636938	−0.103325
$39$	−9.94909	−1.59313
$40$	16.1451	2.55276
$41$	7.28931	1.13840	0.569200	−	0.822199i	$-0.307253\pi$
$41$	7.28931	1.13840	0.569200	+	0.822199i	$0.307253\pi$
$42$	−18.6942	−2.88458
$43$	−1.60856	−0.245303	−0.122651	−	0.992450i	$-0.539140\pi$
$43$	−1.60856	−0.245303	−0.122651	+	0.992450i	$0.539140\pi$
$44$	4.54179	0.684700
$45$	−0.260352	−0.0388110
$46$	−11.2858	−1.66401
$47$	6.34320	0.925251	0.462626	−	0.886554i	$-0.346907\pi$
$47$	6.34320	0.925251	0.462626	+	0.886554i	$0.346907\pi$
$48$	−4.04734	−0.584183
$49$	12.9856	1.85508
$50$	−25.6468	−3.62701
$51$	−1.53374	−0.214767
$52$	21.0472	2.91872
$53$	−6.00921	−0.825429	−0.412714	−	0.910861i	$-0.635419\pi$
$53$	−6.00921	−0.825429	−0.412714	+	0.910861i	$0.635419\pi$
$54$	−12.2706	−1.66981
$55$	−4.86450	−0.655929
$56$	18.1935	2.43121
$57$	−0.466947	−0.0618486
$58$	−8.41127	−1.10445
$59$	10.6432	1.38562	0.692812	−	0.721118i	$-0.256371\pi$
$59$	10.6432	1.38562	0.692812	+	0.721118i	$0.256371\pi$
$60$	25.7283	3.32152
$61$	−14.5845	−1.86736	−0.933678	−	0.358115i	$-0.883420\pi$
$61$	−14.5845	−1.86736	−0.933678	+	0.358115i	$0.883420\pi$
$62$	12.4125	1.57639
$63$	−0.293384	−0.0369630
$64$	−10.8770	−1.35963
$65$	−22.5427	−2.79608
$66$	5.12750	0.631151
$67$	1.39232	0.170099	0.0850495	−	0.996377i	$-0.472895\pi$
$67$	1.39232	0.170099	0.0850495	+	0.996377i	$0.472895\pi$
$68$	3.24462	0.393467
$69$	−8.27378	−0.996047
$70$	−42.3574	−5.06268
$71$	2.69836	0.320236	0.160118	−	0.987098i	$-0.448813\pi$
$71$	2.69836	0.320236	0.160118	+	0.987098i	$0.448813\pi$
$72$	−0.267077	−0.0314753
$73$	5.82397	0.681644	0.340822	−	0.940128i	$-0.389295\pi$
$73$	5.82397	0.681644	0.340822	+	0.940128i	$0.389295\pi$
$74$	−1.36099	−0.158212
$75$	−18.8020	−2.17107
$76$	0.987820	0.113311
$77$	−5.48169	−0.624697
$78$	23.7614	2.69045
$79$	−14.5393	−1.63580	−0.817899	−	0.575361i	$-0.804861\pi$
$79$	−14.5393	−1.63580	−0.817899	+	0.575361i	$0.804861\pi$
$80$	−9.17048	−1.02529
$81$	−9.19257	−1.02140
$82$	−17.4091	−1.92251
$83$	4.36231	0.478826	0.239413	−	0.970918i	$-0.423045\pi$
$83$	4.36231	0.478826	0.239413	+	0.970918i	$0.423045\pi$
$84$	28.9927	3.16336
$85$	−3.47516	−0.376934
$86$	3.84173	0.414264
$87$	−6.16640	−0.661107
$88$	−4.99015	−0.531952
$89$	−3.79378	−0.402140	−0.201070	−	0.979577i	$-0.564442\pi$
$89$	−3.79378	−0.402140	−0.201070	+	0.979577i	$0.564442\pi$
$90$	0.621799	0.0655434
$91$	−25.4028	−2.66294
$92$	17.5031	1.82482
$93$	9.09973	0.943598
$94$	−15.1495	−1.56255
$95$	−1.05801	−0.108549
$96$	−4.58479	−0.467933
$97$	−2.58581	−0.262549	−0.131275	−	0.991346i	$-0.541907\pi$
$97$	−2.58581	−0.262549	−0.131275	+	0.991346i	$0.541907\pi$
$98$	−31.0135	−3.13283
$99$	0.0804702	0.00808756
$100$	39.7754	3.97754
$101$	−14.0545	−1.39848	−0.699238	−	0.714889i	$-0.746477\pi$
$101$	−14.0545	−1.39848	−0.699238	+	0.714889i	$0.746477\pi$
$102$	3.66304	0.362695
$103$	2.25317	0.222011	0.111006	−	0.993820i	$-0.464593\pi$
$103$	2.25317	0.222011	0.111006	+	0.993820i	$0.464593\pi$
$104$	−23.1250	−2.26759
$105$	−31.0527	−3.03044
$106$	14.3518	1.39397
$107$	14.0059	1.35400	0.677002	−	0.735981i	$-0.263279\pi$
$107$	14.0059	1.35400	0.677002	+	0.735981i	$0.263279\pi$
$108$	19.0303	1.83119
$109$	4.80541	0.460275	0.230138	−	0.973158i	$-0.426082\pi$
$109$	4.80541	0.460275	0.230138	+	0.973158i	$0.426082\pi$
$110$	11.6179	1.10772
$111$	−0.997756	−0.0947028
$112$	−10.3340	−0.976471
$113$	18.0303	1.69614	0.848072	−	0.529881i	$-0.177764\pi$
$113$	18.0303	1.69614	0.848072	+	0.529881i	$0.177764\pi$
$114$	1.11521	0.104449
$115$	−18.7468	−1.74815
$116$	13.0449	1.21119
$117$	0.372909	0.0344754
$118$	−25.4192	−2.34002
$119$	−3.91608	−0.358986
$120$	−28.2683	−2.58053
$121$	−9.49647	−0.863315
$122$	34.8322	3.15356
$123$	−12.7628	−1.15078
$124$	−19.2504	−1.72873
$125$	−22.7657	−2.03623
$126$	0.700691	0.0624225
$127$	−9.09032	−0.806635	−0.403318	−	0.915060i	$-0.632143\pi$
$127$	−9.09032	−0.806635	−0.403318	+	0.915060i	$0.632143\pi$
$128$	20.7406	1.83323
$129$	2.81641	0.247971
$130$	53.8388	4.72197
$131$	8.77954	0.767072	0.383536	−	0.923526i	$-0.374706\pi$
$131$	8.77954	0.767072	0.383536	+	0.923526i	$0.374706\pi$
$132$	−7.95218	−0.692148
$133$	−1.19225	−0.103381
$134$	−3.32528	−0.287261
$135$	−20.3825	−1.75424
$136$	−3.56493	−0.305690
$137$	−2.42199	−0.206924	−0.103462	−	0.994633i	$-0.532992\pi$
$137$	−2.42199	−0.206924	−0.103462	+	0.994633i	$0.532992\pi$
$138$	19.7603	1.68211
$139$	10.1719	0.862768	0.431384	−	0.902168i	$-0.358025\pi$
$139$	10.1719	0.862768	0.431384	+	0.902168i	$0.358025\pi$
$140$	65.6917	5.55196
$141$	−11.1063	−0.935317
$142$	−6.44449	−0.540810
$143$	6.96755	0.582656
$144$	0.151701	0.0126418
$145$	−13.9719	−1.16030
$146$	−13.9094	−1.15115
$147$	−22.7363	−1.87526
$148$	2.11074	0.173502
$149$	−9.77994	−0.801204	−0.400602	−	0.916252i	$-0.631199\pi$
$149$	−9.77994	−0.801204	−0.400602	+	0.916252i	$0.631199\pi$
$150$	44.9049	3.66647
$151$	14.6506	1.19225	0.596124	−	0.802892i	$-0.296707\pi$
$151$	14.6506	1.19225	0.596124	+	0.802892i	$0.296707\pi$
$152$	−1.08534	−0.0880326
$153$	0.0574873	0.00464757
$154$	13.0919	1.05498
$155$	20.6182	1.65609
$156$	−36.8514	−2.95047
$157$	−2.17862	−0.173873	−0.0869365	−	0.996214i	$-0.527708\pi$
$157$	−2.17862	−0.173873	−0.0869365	+	0.996214i	$0.527708\pi$
$158$	34.7243	2.76251
$159$	10.5215	0.834408
$160$	−10.3882	−0.821262
$161$	−21.1253	−1.66491
$162$	21.9547	1.72492
$163$	22.7026	1.77821	0.889103	−	0.457708i	$-0.151329\pi$
$163$	22.7026	1.77821	0.889103	+	0.457708i	$0.151329\pi$
$164$	26.9996	2.10831
$165$	8.51722	0.663065
$166$	−10.4185	−0.808634
$167$	10.6426	0.823546	0.411773	−	0.911286i	$-0.364910\pi$
$167$	10.6426	0.823546	0.411773	+	0.911286i	$0.364910\pi$
$168$	−31.8549	−2.45766
$169$	19.2885	1.48373
$170$	8.29974	0.636561
$171$	0.0175019	0.00133841
$172$	−5.95809	−0.454300
$173$	3.89438	0.296085	0.148042	−	0.988981i	$-0.452703\pi$
$173$	3.89438	0.296085	0.148042	+	0.988981i	$0.452703\pi$
$174$	14.7272	1.11647
$175$	−48.0068	−3.62897
$176$	2.83443	0.213653
$177$	−18.6351	−1.40070
$178$	9.06071	0.679129
$179$	−13.2651	−0.991481	−0.495741	−	0.868471i	$-0.665103\pi$
$179$	−13.2651	−0.991481	−0.495741	+	0.868471i	$0.665103\pi$
$180$	−0.964342	−0.0718778
$181$	−0.584514	−0.0434466	−0.0217233	−	0.999764i	$-0.506915\pi$
$181$	−0.584514	−0.0434466	−0.0217233	+	0.999764i	$0.506915\pi$
$182$	60.6696	4.49713
$183$	25.5359	1.88767
$184$	−19.2310	−1.41773
$185$	−2.26072	−0.166211
$186$	−21.7329	−1.59353
$187$	1.07411	0.0785468
$188$	23.4952	1.71356
$189$	−22.9685	−1.67072
$190$	2.52685	0.183317
$191$	−24.1022	−1.74397	−0.871986	−	0.489531i	$-0.837168\pi$
$191$	−24.1022	−1.74397	−0.871986	+	0.489531i	$0.837168\pi$
$192$	19.0445	1.37442
$193$	4.48141	0.322579	0.161290	−	0.986907i	$-0.448435\pi$
$193$	4.48141	0.322579	0.161290	+	0.986907i	$0.448435\pi$
$194$	6.17570	0.443389
$195$	39.4698	2.82649
$196$	48.0985	3.43561
$197$	9.85850	0.702389	0.351195	−	0.936302i	$-0.385776\pi$
$197$	9.85850	0.702389	0.351195	+	0.936302i	$0.385776\pi$
$198$	−0.192187	−0.0136582
$199$	−9.18896	−0.651388	−0.325694	−	0.945475i	$-0.605598\pi$
$199$	−9.18896	−0.651388	−0.325694	+	0.945475i	$0.605598\pi$
$200$	−43.7021	−3.09020
$201$	−2.43780	−0.171949
$202$	33.5665	2.36173
$203$	−15.7446	−1.10505
$204$	−5.68097	−0.397748
$205$	−28.9180	−2.01972
$206$	−5.38125	−0.374929
$207$	0.310115	0.0215545
$208$	13.1351	0.910756
$209$	0.327012	0.0226199
$210$	74.1633	5.11776
$211$	2.89258	0.199134	0.0995669	−	0.995031i	$-0.468254\pi$
$211$	2.89258	0.199134	0.0995669	+	0.995031i	$0.468254\pi$
$212$	−22.2581	−1.52869
$213$	−4.72453	−0.323720
$214$	−33.4504	−2.28662
$215$	6.38144	0.435211
$216$	−20.9090	−1.42268
$217$	23.2342	1.57724
$218$	−11.4768	−0.777306
$219$	−10.1971	−0.689059
$220$	−18.0181	−1.21478
$221$	4.97756	0.334827
$222$	2.38294	0.159933
$223$	13.1510	0.880658	0.440329	−	0.897837i	$-0.354862\pi$
$223$	13.1510	0.880658	0.440329	+	0.897837i	$0.354862\pi$
$224$	−11.7063	−0.782157
$225$	0.704731	0.0469820
$226$	−43.0617	−2.86442
$227$	−18.9061	−1.25484	−0.627419	−	0.778682i	$-0.715889\pi$
$227$	−18.9061	−1.25484	−0.627419	+	0.778682i	$0.715889\pi$
$228$	−1.72957	−0.114543
$229$	−4.98989	−0.329741	−0.164871	−	0.986315i	$-0.552721\pi$
$229$	−4.98989	−0.329741	−0.164871	+	0.986315i	$0.552721\pi$
$230$	44.7730	2.95224
$231$	9.59785	0.631492
$232$	−14.3328	−0.940992
$233$	−8.85678	−0.580227	−0.290113	−	0.956992i	$-0.593693\pi$
$233$	−8.85678	−0.580227	−0.290113	+	0.956992i	$0.593693\pi$
$234$	−0.890619	−0.0582216
$235$	−25.1646	−1.64156
$236$	39.4223	2.56617
$237$	25.4568	1.65359
$238$	9.35278	0.606251
$239$	21.5968	1.39698	0.698489	−	0.715620i	$-0.253856\pi$
$239$	21.5968	1.39698	0.698489	+	0.715620i	$0.253856\pi$
$240$	16.0565	1.03644
$241$	−2.44494	−0.157492	−0.0787462	−	0.996895i	$-0.525092\pi$
$241$	−2.44494	−0.157492	−0.0787462	+	0.996895i	$0.525092\pi$
$242$	22.6805	1.45795
$243$	0.681888	0.0437432
$244$	−54.0209	−3.45834
$245$	−51.5161	−3.29124
$246$	30.4815	1.94343
$247$	1.51541	0.0964235
$248$	21.1508	1.34308
$249$	−7.63793	−0.484034
$250$	54.3715	3.43875
$251$	9.13636	0.576682	0.288341	−	0.957528i	$-0.406896\pi$
$251$	9.13636	0.576682	0.288341	+	0.957528i	$0.406896\pi$
$252$	−1.08669	−0.0684553
$253$	5.79430	0.364284
$254$	21.7104	1.36223
$255$	6.08463	0.381035
$256$	−27.7808	−1.73630
$257$	9.89140	0.617009	0.308504	−	0.951223i	$-0.400172\pi$
$257$	9.89140	0.617009	0.308504	+	0.951223i	$0.400172\pi$
$258$	−6.72645	−0.418771
$259$	−2.54755	−0.158297
$260$	−83.4980	−5.17832
$261$	0.231127	0.0143064
$262$	−20.9682	−1.29542
$263$	10.6650	0.657634	0.328817	−	0.944394i	$-0.393350\pi$
$263$	10.6650	0.657634	0.328817	+	0.944394i	$0.393350\pi$
$264$	8.73723	0.537739
$265$	23.8396	1.46446
$266$	2.84745	0.174588
$267$	6.64251	0.406515
$268$	5.15715	0.315023
$269$	19.9580	1.21686	0.608431	−	0.793607i	$-0.291799\pi$
$269$	19.9580	1.21686	0.608431	+	0.793607i	$0.291799\pi$
$270$	48.6795	2.96254
$271$	−0.516063	−0.0313486	−0.0156743	−	0.999877i	$-0.504989\pi$
$271$	−0.516063	−0.0313486	−0.0156743	+	0.999877i	$0.504989\pi$
$272$	2.02490	0.122777
$273$	44.4776	2.69191
$274$	5.78444	0.349451
$275$	13.1674	0.794025
$276$	−30.6461	−1.84468
$277$	−6.75597	−0.405927	−0.202963	−	0.979186i	$-0.565057\pi$
$277$	−6.75597	−0.405927	−0.202963	+	0.979186i	$0.565057\pi$
$278$	−24.2935	−1.45703
$279$	−0.341073	−0.0204195
$280$	−72.1768	−4.31339
$281$	−22.8601	−1.36372	−0.681859	−	0.731484i	$-0.738828\pi$
$281$	−22.8601	−1.36372	−0.681859	+	0.731484i	$0.738828\pi$
$282$	26.5252	1.57955
$283$	−9.64501	−0.573337	−0.286668	−	0.958030i	$-0.592548\pi$
$283$	−9.64501	−0.573337	−0.286668	+	0.958030i	$0.592548\pi$
$284$	9.99469	0.593076
$285$	1.85246	0.109730
$286$	−16.6406	−0.983980
$287$	−32.5870	−1.92355
$288$	0.171846	0.0101261
$289$	−16.2327	−0.954863
$290$	33.3690	1.95950
$291$	4.52748	0.265405
$292$	21.5719	1.26240
$293$	−19.0200	−1.11116	−0.555579	−	0.831464i	$-0.687503\pi$
$293$	−19.0200	−1.11116	−0.555579	+	0.831464i	$0.687503\pi$
$294$	54.3013	3.16692
$295$	−42.2234	−2.45834
$296$	−2.31912	−0.134796
$297$	6.29987	0.365555
$298$	23.3575	1.35306
$299$	26.8515	1.55286
$300$	−69.6425	−4.02081
$301$	7.19110	0.414488
$302$	−34.9901	−2.01345
$303$	24.6080	1.41369
$304$	0.616478	0.0353574
$305$	57.8594	3.31302
$306$	−0.137297	−0.00784875
$307$	−13.8217	−0.788847	−0.394424	−	0.918929i	$-0.629056\pi$
$307$	−13.8217	−0.788847	−0.394424	+	0.918929i	$0.629056\pi$
$308$	−20.3042	−1.15694
$309$	−3.94505	−0.224426
$310$	−49.2425	−2.79679
$311$	25.7073	1.45773	0.728865	−	0.684658i	$-0.240048\pi$
$311$	25.7073	1.45773	0.728865	+	0.684658i	$0.240048\pi$
$312$	40.4894	2.29226
$313$	−10.0156	−0.566116	−0.283058	−	0.959103i	$-0.591349\pi$
$313$	−10.0156	−0.566116	−0.283058	+	0.959103i	$0.591349\pi$
$314$	5.20321	0.293634
$315$	1.16391	0.0655788
$316$	−53.8535	−3.02949
$317$	−24.6014	−1.38175	−0.690876	−	0.722973i	$-0.742775\pi$
$317$	−24.6014	−1.38175	−0.690876	+	0.722973i	$0.742775\pi$
$318$	−25.1285	−1.40914
$319$	4.31845	0.241787
$320$	43.1512	2.41223
$321$	−24.5229	−1.36873
$322$	50.4536	2.81167
$323$	0.233615	0.0129987
$324$	−34.0492	−1.89162
$325$	61.0194	3.38475
$326$	−54.2207	−3.00301
$327$	−8.41377	−0.465282
$328$	−29.6650	−1.63798
$329$	−28.3574	−1.56340
$330$	−20.3417	−1.11977
$331$	2.06549	0.113530	0.0567649	−	0.998388i	$-0.481921\pi$
$331$	2.06549	0.113530	0.0567649	+	0.998388i	$0.481921\pi$
$332$	16.1580	0.886784
$333$	0.0373976	0.00204938
$334$	−25.4177	−1.39079
$335$	−5.52359	−0.301786
$336$	18.0937	0.987093
$337$	22.3314	1.21647	0.608235	−	0.793757i	$-0.291878\pi$
$337$	22.3314	1.21647	0.608235	+	0.793757i	$0.291878\pi$
$338$	−46.0667	−2.50570
$339$	−31.5690	−1.71460
$340$	−12.8720	−0.698081
$341$	−6.37272	−0.345102
$342$	−0.0418000	−0.00226028
$343$	−26.7586	−1.44483
$344$	6.54628	0.352952
$345$	32.8236	1.76716
$346$	−9.30097	−0.500023
$347$	−31.8775	−1.71128	−0.855638	−	0.517575i	$-0.826835\pi$
$347$	−31.8775	−1.71128	−0.855638	+	0.517575i	$0.826835\pi$
$348$	−22.8403	−1.22437
$349$	−33.5954	−1.79832	−0.899160	−	0.437620i	$-0.855822\pi$
$349$	−33.5954	−1.79832	−0.899160	+	0.437620i	$0.855822\pi$
$350$	114.655	6.12856
$351$	29.1943	1.55828
$352$	3.21082	0.171137
$353$	18.5922	0.989562	0.494781	−	0.869018i	$-0.335248\pi$
$353$	18.5922	0.989562	0.494781	+	0.869018i	$0.335248\pi$
$354$	44.5062	2.36548
$355$	−10.7049	−0.568155
$356$	−14.0522	−0.744763
$357$	6.85663	0.362891
$358$	31.6811	1.67440
$359$	28.5402	1.50629	0.753146	−	0.657853i	$-0.228535\pi$
$359$	28.5402	1.50629	0.753146	+	0.657853i	$0.228535\pi$
$360$	1.05954	0.0558428
$361$	−18.9289	−0.996257
$362$	1.39600	0.0733720
$363$	16.6273	0.872707
$364$	−94.0919	−4.93176
$365$	−23.1047	−1.20936
$366$	−60.9875	−3.18787
$367$	20.0744	1.04787	0.523936	−	0.851757i	$-0.324463\pi$
$367$	20.0744	1.04787	0.523936	+	0.851757i	$0.324463\pi$
$368$	10.9233	0.569417
$369$	0.478372	0.0249030
$370$	5.39929	0.280695
$371$	26.8643	1.39473
$372$	33.7053	1.74754
$373$	−9.14764	−0.473647	−0.236823	−	0.971553i	$-0.576106\pi$
$373$	−9.14764	−0.473647	−0.236823	+	0.971553i	$0.576106\pi$
$374$	−2.56530	−0.132649
$375$	39.8604	2.05838
$376$	−25.8147	−1.33129
$377$	20.0122	1.03068
$378$	54.8558	2.82148
$379$	33.3064	1.71083	0.855416	−	0.517941i	$-0.173301\pi$
$379$	33.3064	1.71083	0.855416	+	0.517941i	$0.173301\pi$
$380$	−3.91886	−0.201033
$381$	15.9162	0.815411
$382$	57.5633	2.94520
$383$	−21.7060	−1.10912	−0.554561	−	0.832143i	$-0.687114\pi$
$383$	−21.7060	−1.10912	−0.554561	+	0.832143i	$0.687114\pi$
$384$	−36.3146	−1.85317
$385$	21.7469	1.10832
$386$	−10.7030	−0.544767
$387$	−0.105564	−0.00536612
$388$	−9.57783	−0.486240
$389$	17.8533	0.905198	0.452599	−	0.891714i	$-0.350497\pi$
$389$	17.8533	0.905198	0.452599	+	0.891714i	$0.350497\pi$
$390$	−94.2659	−4.77334
$391$	4.13940	0.209339
$392$	−52.8468	−2.66917
$393$	−15.3720	−0.775417
$394$	−23.5451	−1.18619
$395$	57.6800	2.90220
$396$	0.298061	0.0149781
$397$	9.44450	0.474006	0.237003	−	0.971509i	$-0.423835\pi$
$397$	9.44450	0.474006	0.237003	+	0.971509i	$0.423835\pi$
$398$	21.9460	1.10005
$399$	2.08750	0.104505
$400$	24.8230	1.24115
$401$	−8.13671	−0.406328	−0.203164	−	0.979145i	$-0.565122\pi$
$401$	−8.13671	−0.406328	−0.203164	+	0.979145i	$0.565122\pi$
$402$	5.82222	0.290386
$403$	−29.5320	−1.47109
$404$	−52.0579	−2.58998
$405$	36.4686	1.81214
$406$	37.6028	1.86619
$407$	0.698749	0.0346357
$408$	6.24181	0.309015
$409$	−13.0276	−0.644173	−0.322087	−	0.946710i	$-0.604384\pi$
$409$	−13.0276	−0.644173	−0.322087	+	0.946710i	$0.604384\pi$
$410$	69.0650	3.41088
$411$	4.24064	0.209175
$412$	8.34572	0.411164
$413$	−47.5806	−2.34129
$414$	−0.740650	−0.0364010
$415$	−17.3061	−0.849521
$416$	14.8793	0.729519
$417$	−17.8099	−0.872154
$418$	−0.781004	−0.0382002
$419$	6.07588	0.296826	0.148413	−	0.988925i	$-0.452583\pi$
$419$	6.07588	0.296826	0.148413	+	0.988925i	$0.452583\pi$
$420$	−115.019	−5.61236
$421$	7.86083	0.383113	0.191557	−	0.981482i	$-0.438646\pi$
$421$	7.86083	0.383113	0.191557	+	0.981482i	$0.438646\pi$
$422$	−6.90837	−0.336294
$423$	0.416282	0.0202403
$424$	24.4554	1.18766
$425$	9.40670	0.456292
$426$	11.2836	0.546693
$427$	65.2004	3.15527
$428$	51.8779	2.50761
$429$	−12.1994	−0.588994
$430$	−15.2408	−0.734978
$431$	−29.5516	−1.42345	−0.711726	−	0.702458i	$-0.752086\pi$
$431$	−29.5516	−1.42345	−0.711726	+	0.702458i	$0.752086\pi$
$432$	11.8764	0.571404
$433$	−26.2418	−1.26110	−0.630550	−	0.776149i	$-0.717171\pi$
$433$	−26.2418	−1.26110	−0.630550	+	0.776149i	$0.717171\pi$
$434$	−55.4902	−2.66362
$435$	24.4632	1.17292
$436$	17.7992	0.852428
$437$	1.26024	0.0602853
$438$	24.3539	1.16367
$439$	18.7901	0.896803	0.448401	−	0.893832i	$-0.351994\pi$
$439$	18.7901	0.896803	0.448401	+	0.893832i	$0.351994\pi$
$440$	19.7968	0.943777
$441$	0.852197	0.0405808
$442$	−11.8879	−0.565451
$443$	−25.0243	−1.18894	−0.594471	−	0.804117i	$-0.702638\pi$
$443$	−25.0243	−1.18894	−0.594471	+	0.804117i	$0.702638\pi$
$444$	−3.69568	−0.175389
$445$	15.0506	0.713468
$446$	−31.4086	−1.48724
$447$	17.1236	0.809920
$448$	48.6261	2.29737
$449$	26.6325	1.25686	0.628432	−	0.777864i	$-0.283697\pi$
$449$	26.6325	1.25686	0.628432	+	0.777864i	$0.283697\pi$
$450$	−1.68311	−0.0793426
$451$	8.93805	0.420876
$452$	66.7840	3.14125
$453$	−25.6516	−1.20522
$454$	45.1534	2.11915
$455$	100.778	4.72452
$456$	1.90031	0.0889903
$457$	38.9616	1.82255	0.911273	−	0.411802i	$-0.135101\pi$
$457$	38.9616	1.82255	0.911273	+	0.411802i	$0.135101\pi$
$458$	11.9174	0.556862
$459$	4.50057	0.210069
$460$	−69.4379	−3.23756
$461$	−2.03724	−0.0948837	−0.0474419	−	0.998874i	$-0.515107\pi$
$461$	−2.03724	−0.0948837	−0.0474419	+	0.998874i	$0.515107\pi$
$462$	−22.9226	−1.06646
$463$	−31.5991	−1.46854	−0.734268	−	0.678860i	$-0.762474\pi$
$463$	−31.5991	−1.46854	−0.734268	+	0.678860i	$0.762474\pi$
$464$	8.14108	0.377940
$465$	−36.1003	−1.67411
$466$	21.1527	0.979879
$467$	13.8274	0.639855	0.319927	−	0.947442i	$-0.396342\pi$
$467$	13.8274	0.639855	0.319927	+	0.947442i	$0.396342\pi$
$468$	1.38125	0.0638484
$469$	−6.22440	−0.287416
$470$	60.1008	2.77224
$471$	3.81453	0.175764
$472$	−43.3141	−1.99369
$473$	−1.97239	−0.0906907
$474$	−60.7985	−2.79257
$475$	2.86386	0.131403
$476$	−14.5051	−0.664841
$477$	−0.394363	−0.0180566
$478$	−51.5796	−2.35920
$479$	27.6181	1.26190	0.630951	−	0.775822i	$-0.282665\pi$
$479$	27.6181	1.26190	0.630951	+	0.775822i	$0.282665\pi$
$480$	18.1887	0.830196
$481$	3.23809	0.147644
$482$	5.83926	0.265971
$483$	36.9881	1.68302
$484$	−35.1749	−1.59886
$485$	10.2584	0.465809
$486$	−1.62856	−0.0738728
$487$	1.88156	0.0852616	0.0426308	−	0.999091i	$-0.486426\pi$
$487$	1.88156	0.0852616	0.0426308	+	0.999091i	$0.486426\pi$
$488$	59.3539	2.68683
$489$	−39.7498	−1.79755
$490$	123.036	5.55820
$491$	14.5676	0.657425	0.328713	−	0.944430i	$-0.393385\pi$
$491$	14.5676	0.657425	0.328713	+	0.944430i	$0.393385\pi$
$492$	−47.2734	−2.13125
$493$	3.08507	0.138945
$494$	−3.61927	−0.162839
$495$	−0.319240	−0.0143488
$496$	−12.0138	−0.539434
$497$	−12.0631	−0.541102
$498$	18.2417	0.817430
$499$	26.0109	1.16441	0.582203	−	0.813044i	$-0.302191\pi$
$499$	26.0109	1.16441	0.582203	+	0.813044i	$0.302191\pi$
$500$	−84.3242	−3.77109
$501$	−18.6340	−0.832505
$502$	−21.8204	−0.973892
$503$	−38.5668	−1.71961	−0.859805	−	0.510623i	$-0.829415\pi$
$503$	−38.5668	−1.71961	−0.859805	+	0.510623i	$0.829415\pi$
$504$	1.19397	0.0531838
$505$	55.7568	2.48115
$506$	−13.8385	−0.615198
$507$	−33.7720	−1.49987
$508$	−33.6705	−1.49389
$509$	−35.8752	−1.59014	−0.795070	−	0.606518i	$-0.792566\pi$
$509$	−35.8752	−1.59014	−0.795070	+	0.606518i	$0.792566\pi$
$510$	−14.5320	−0.643486
$511$	−26.0362	−1.15177
$512$	24.8677	1.09901
$513$	1.37020	0.0604956
$514$	−23.6237	−1.04200
$515$	−8.93872	−0.393887
$516$	10.4320	0.459242
$517$	7.77795	0.342074
$518$	6.08433	0.267330
$519$	−6.81865	−0.299306
$520$	91.7410	4.02311
$521$	33.2903	1.45847	0.729236	−	0.684262i	$-0.239875\pi$
$521$	33.2903	1.45847	0.729236	+	0.684262i	$0.239875\pi$
$522$	−0.552002	−0.0241605
$523$	18.2217	0.796781	0.398390	−	0.917216i	$-0.369569\pi$
$523$	18.2217	0.796781	0.398390	+	0.917216i	$0.369569\pi$
$524$	32.5194	1.42062
$525$	84.0547	3.66845
$526$	−25.4713	−1.11060
$527$	−4.55262	−0.198315
$528$	−4.96279	−0.215978
$529$	−0.669974	−0.0291293
$530$	−56.9363	−2.47315
$531$	0.698474	0.0303112
$532$	−4.41607	−0.191461
$533$	41.4200	1.79410
$534$	−15.8643	−0.686517
$535$	−55.5640	−2.40224
$536$	−5.66627	−0.244745
$537$	23.2258	1.00227
$538$	−47.6658	−2.05502
$539$	15.9227	0.685840
$540$	−75.4966	−3.24886
$541$	44.9009	1.93044	0.965220	−	0.261437i	$-0.0841964\pi$
$541$	44.9009	1.93044	0.965220	+	0.261437i	$0.0841964\pi$
$542$	1.23251	0.0529410
$543$	1.02342	0.0439192
$544$	2.29378	0.0983452
$545$	−19.0639	−0.816610
$546$	−106.226	−4.54606
$547$	0.380055	0.0162500	0.00812499	−	0.999967i	$-0.497414\pi$
$547$	0.380055	0.0162500	0.00812499	+	0.999967i	$0.497414\pi$
$548$	−8.97103	−0.383223
$549$	−0.957129	−0.0408493
$550$	−31.4478	−1.34094
$551$	0.939247	0.0400133
$552$	33.6715	1.43315
$553$	64.9982	2.76401
$554$	16.1353	0.685523
$555$	3.95828	0.168020
$556$	37.6766	1.59784
$557$	39.4224	1.67038	0.835190	−	0.549962i	$-0.185358\pi$
$557$	39.4224	1.67038	0.835190	+	0.549962i	$0.185358\pi$
$558$	0.814586	0.0344842
$559$	−9.14030	−0.386594
$560$	40.9968	1.73243
$561$	−1.88065	−0.0794013
$562$	54.5968	2.30303
$563$	−41.6216	−1.75414	−0.877070	−	0.480362i	$-0.840505\pi$
$563$	−41.6216	−1.75414	−0.877070	+	0.480362i	$0.840505\pi$
$564$	−41.1376	−1.73220
$565$	−71.5293	−3.00926
$566$	23.0352	0.968243
$567$	41.0956	1.72585
$568$	−10.9814	−0.460768
$569$	−16.2989	−0.683285	−0.341643	−	0.939830i	$-0.610983\pi$
$569$	−16.2989	−0.683285	−0.341643	+	0.939830i	$0.610983\pi$
$570$	−4.42424	−0.185311
$571$	−30.4043	−1.27238	−0.636191	−	0.771532i	$-0.719491\pi$
$571$	−30.4043	−1.27238	−0.636191	+	0.771532i	$0.719491\pi$
$572$	25.8078	1.07908
$573$	42.2003	1.76294
$574$	77.8277	3.24847
$575$	50.7445	2.11619
$576$	−0.713822	−0.0297426
$577$	−5.84694	−0.243411	−0.121706	−	0.992566i	$-0.538836\pi$
$577$	−5.84694	−0.243411	−0.121706	+	0.992566i	$0.538836\pi$
$578$	38.7685	1.61256
$579$	−7.84647	−0.326088
$580$	−51.7517	−2.14887
$581$	−19.5018	−0.809071
$582$	−10.8130	−0.448213
$583$	−7.36841	−0.305168
$584$	−23.7015	−0.980777
$585$	−1.47940	−0.0611655
$586$	45.4254	1.87651
$587$	32.2394	1.33066	0.665331	−	0.746549i	$-0.268290\pi$
$587$	32.2394	1.33066	0.665331	+	0.746549i	$0.268290\pi$
$588$	−84.2153	−3.47298
$589$	−1.38604	−0.0571109
$590$	100.842	4.15162
$591$	−17.2612	−0.710030
$592$	1.31727	0.0541395
$593$	17.5483	0.720621	0.360311	−	0.932832i	$-0.382671\pi$
$593$	17.5483	0.720621	0.360311	+	0.932832i	$0.382671\pi$
$594$	−15.0460	−0.617345
$595$	15.5358	0.636905
$596$	−36.2249	−1.48383
$597$	16.0889	0.658474
$598$	−64.1295	−2.62245
$599$	5.08583	0.207801	0.103901	−	0.994588i	$-0.466868\pi$
$599$	5.08583	0.207801	0.103901	+	0.994588i	$0.466868\pi$
$600$	76.5177	3.12382
$601$	27.6760	1.12893	0.564463	−	0.825458i	$-0.309083\pi$
$601$	27.6760	1.12893	0.564463	+	0.825458i	$0.309083\pi$
$602$	−17.1745	−0.699981
$603$	0.0913730	0.00372100
$604$	54.2657	2.20804
$605$	37.6742	1.53167
$606$	−58.7713	−2.38742
$607$	21.5227	0.873580	0.436790	−	0.899564i	$-0.356115\pi$
$607$	21.5227	0.873580	0.436790	+	0.899564i	$0.356115\pi$
$608$	0.698341	0.0283215
$609$	27.5670	1.11707
$610$	−138.186	−5.59498
$611$	36.0439	1.45818
$612$	0.212933	0.00860729
$613$	3.21425	0.129822	0.0649112	−	0.997891i	$-0.479324\pi$
$613$	3.21425	0.129822	0.0649112	+	0.997891i	$0.479324\pi$
$614$	33.0105	1.33219
$615$	50.6324	2.04169
$616$	22.3086	0.898839
$617$	−17.2829	−0.695785	−0.347893	−	0.937534i	$-0.613103\pi$
$617$	−17.2829	−0.695785	−0.347893	+	0.937534i	$0.613103\pi$
$618$	9.42199	0.379008
$619$	−18.1292	−0.728673	−0.364337	−	0.931267i	$-0.618704\pi$
$619$	−18.1292	−0.728673	−0.364337	+	0.931267i	$0.618704\pi$
$620$	76.3697	3.06708
$621$	24.2784	0.974258
$622$	−61.3969	−2.46179
$623$	16.9602	0.679496
$624$	−22.9982	−0.920664
$625$	36.6232	1.46493
$626$	23.9203	0.956049
$627$	−0.572563	−0.0228660
$628$	−8.06960	−0.322012
$629$	0.499181	0.0199036
$630$	−2.77977	−0.110749
$631$	−16.4951	−0.656660	−0.328330	−	0.944563i	$-0.606486\pi$
$631$	−16.4951	−0.656660	−0.328330	+	0.944563i	$0.606486\pi$
$632$	59.1699	2.35365
$633$	−5.06461	−0.201300
$634$	58.7556	2.33348
$635$	36.0629	1.43111
$636$	38.9715	1.54532
$637$	73.7878	2.92358
$638$	−10.3138	−0.408326
$639$	0.177083	0.00700531
$640$	−82.2817	−3.25247
$641$	−1.00007	−0.0395002	−0.0197501	−	0.999805i	$-0.506287\pi$
$641$	−1.00007	−0.0395002	−0.0197501	+	0.999805i	$0.506287\pi$
$642$	58.5681	2.31150
$643$	26.8659	1.05949	0.529745	−	0.848157i	$-0.322288\pi$
$643$	26.8659	1.05949	0.529745	+	0.848157i	$0.322288\pi$
$644$	−78.2480	−3.08340
$645$	−11.1732	−0.439945
$646$	−0.557943	−0.0219520
$647$	24.1605	0.949846	0.474923	−	0.880027i	$-0.342476\pi$
$647$	24.1605	0.949846	0.474923	+	0.880027i	$0.342476\pi$
$648$	37.4106	1.46963
$649$	13.0505	0.512278
$650$	−145.733	−5.71611
$651$	−40.6805	−1.59440
$652$	84.0903	3.29323
$653$	14.2181	0.556399	0.278200	−	0.960523i	$-0.410262\pi$
$653$	14.2181	0.556399	0.278200	+	0.960523i	$0.410262\pi$
$654$	20.0946	0.785762
$655$	−34.8300	−1.36092
$656$	16.8499	0.657877
$657$	0.382206	0.0149113
$658$	67.7262	2.64024
$659$	47.6450	1.85598	0.927992	−	0.372600i	$-0.121534\pi$
$659$	47.6450	1.85598	0.927992	+	0.372600i	$0.121534\pi$
$660$	31.5477	1.22799
$661$	2.81472	0.109480	0.0547399	−	0.998501i	$-0.482567\pi$
$661$	2.81472	0.109480	0.0547399	+	0.998501i	$0.482567\pi$
$662$	−4.93302	−0.191727
$663$	−8.71518	−0.338469
$664$	−17.7531	−0.688954
$665$	4.72985	0.183416
$666$	−0.0893168	−0.00346096
$667$	16.6424	0.644397
$668$	39.4200	1.52520
$669$	−23.0260	−0.890238
$670$	13.1920	0.509652
$671$	−17.8833	−0.690378
$672$	20.4964	0.790666
$673$	23.2842	0.897541	0.448770	−	0.893647i	$-0.351862\pi$
$673$	23.2842	0.897541	0.448770	+	0.893647i	$0.351862\pi$
$674$	−53.3342	−2.05436
$675$	55.1721	2.12357
$676$	71.4443	2.74786
$677$	−0.235205	−0.00903967	−0.00451983	−	0.999990i	$-0.501439\pi$
$677$	−0.235205	−0.00903967	−0.00451983	+	0.999990i	$0.501439\pi$
$678$	75.3965	2.89558
$679$	11.5599	0.443629
$680$	14.1427	0.542348
$681$	33.1025	1.26849
$682$	15.2200	0.582804
$683$	26.4028	1.01028	0.505138	−	0.863039i	$-0.331442\pi$
$683$	26.4028	1.01028	0.505138	+	0.863039i	$0.331442\pi$
$684$	0.0648271	0.00247873
$685$	9.60846	0.367120
$686$	63.9077	2.44001
$687$	8.73676	0.333328
$688$	−3.71832	−0.141760
$689$	−34.1461	−1.30086
$690$	−78.3927	−2.98436
$691$	−30.7440	−1.16956	−0.584779	−	0.811193i	$-0.698819\pi$
$691$	−30.7440	−1.16956	−0.584779	+	0.811193i	$0.698819\pi$
$692$	14.4248	0.548348
$693$	−0.359744	−0.0136655
$694$	76.1332	2.88998
$695$	−40.3537	−1.53070
$696$	25.0951	0.951228
$697$	6.38527	0.241859
$698$	80.2360	3.03698
$699$	15.5073	0.586539
$700$	−177.817	−6.72085
$701$	−22.4258	−0.847011	−0.423506	−	0.905893i	$-0.639201\pi$
$701$	−22.4258	−0.847011	−0.423506	+	0.905893i	$0.639201\pi$
$702$	−69.7249	−2.63160
$703$	0.151975	0.00573185
$704$	−13.3373	−0.502668
$705$	44.0606	1.65942
$706$	−44.4038	−1.67116
$707$	62.8310	2.36300
$708$	−69.0242	−2.59409
$709$	−30.5979	−1.14913	−0.574565	−	0.818459i	$-0.694829\pi$
$709$	−30.5979	−1.14913	−0.574565	+	0.818459i	$0.694829\pi$
$710$	25.5665	0.959492
$711$	−0.954162	−0.0357839
$712$	15.4394	0.578616
$713$	−24.5592	−0.919747
$714$	−16.3757	−0.612846
$715$	−27.6415	−1.03373
$716$	−49.1339	−1.83622
$717$	−37.8136	−1.41218
$718$	−68.1626	−2.54380
$719$	4.84100	0.180539	0.0902694	−	0.995917i	$-0.471227\pi$
$719$	4.84100	0.180539	0.0902694	+	0.995917i	$0.471227\pi$
$720$	−0.601826	−0.0224287
$721$	−10.0728	−0.375132
$722$	45.2079	1.68246
$723$	4.28083	0.159206
$724$	−2.16504	−0.0804630
$725$	37.8196	1.40458
$726$	−39.7110	−1.47382
$727$	−1.97527	−0.0732586	−0.0366293	−	0.999329i	$-0.511662\pi$
$727$	−1.97527	−0.0732586	−0.0366293	+	0.999329i	$0.511662\pi$
$728$	103.381	3.83154
$729$	26.3838	0.977178
$730$	55.1811	2.04234
$731$	−1.40906	−0.0521160
$732$	94.5849	3.49596
$733$	−21.1541	−0.781343	−0.390672	−	0.920530i	$-0.627757\pi$
$733$	−21.1541	−0.781343	−0.390672	+	0.920530i	$0.627757\pi$
$734$	−47.9437	−1.76963
$735$	90.1992	3.32705
$736$	12.3738	0.456106
$737$	1.70724	0.0628871
$738$	−1.14250	−0.0420559
$739$	−30.0492	−1.10538	−0.552689	−	0.833387i	$-0.686398\pi$
$739$	−30.0492	−1.10538	−0.552689	+	0.833387i	$0.686398\pi$
$740$	−8.37369	−0.307823
$741$	−2.65333	−0.0974724
$742$	−64.1601	−2.35539
$743$	0.927757	0.0340361	0.0170181	−	0.999855i	$-0.494583\pi$
$743$	0.927757	0.0340361	0.0170181	+	0.999855i	$0.494583\pi$
$744$	−37.0328	−1.35769
$745$	38.7988	1.42148
$746$	21.8473	0.799888
$747$	0.286283	0.0104745
$748$	3.97850	0.145468
$749$	−62.6138	−2.28786
$750$	−95.1987	−3.47616
$751$	−1.39640	−0.0509553	−0.0254777	−	0.999675i	$-0.508111\pi$
$751$	−1.39640	−0.0509553	−0.0254777	+	0.999675i	$0.508111\pi$
$752$	14.6629	0.534700
$753$	−15.9968	−0.582955
$754$	−47.7953	−1.74060
$755$	−58.1215	−2.11526
$756$	−85.0753	−3.09416
$757$	−26.1273	−0.949612	−0.474806	−	0.880090i	$-0.657482\pi$
$757$	−26.1273	−0.949612	−0.474806	+	0.880090i	$0.657482\pi$
$758$	−79.5457	−2.88923
$759$	−10.1452	−0.368247
$760$	4.30573	0.156185
$761$	0.995374	0.0360823	0.0180411	−	0.999837i	$-0.494257\pi$
$761$	0.995374	0.0360823	0.0180411	+	0.999837i	$0.494257\pi$
$762$	−38.0127	−1.37705
$763$	−21.4827	−0.777726
$764$	−89.2743	−3.22983
$765$	−0.228062	−0.00824561
$766$	51.8404	1.87307
$767$	60.4777	2.18372
$768$	48.6412	1.75519
$769$	−36.2952	−1.30884	−0.654419	−	0.756132i	$-0.727087\pi$
$769$	−36.2952	−1.30884	−0.654419	+	0.756132i	$0.727087\pi$
$770$	−51.9381	−1.87172
$771$	−17.3188	−0.623721
$772$	16.5991	0.597416
$773$	−38.5863	−1.38785	−0.693926	−	0.720046i	$-0.744121\pi$
$773$	−38.5863	−1.38785	−0.693926	+	0.720046i	$0.744121\pi$
$774$	0.252119	0.00906222
$775$	−55.8101	−2.00476
$776$	10.5234	0.377767
$777$	4.46049	0.160019
$778$	−42.6391	−1.52868
$779$	1.94399	0.0696507
$780$	146.196	5.23466
$781$	3.30869	0.118394
$782$	−9.88615	−0.353528
$783$	18.0945	0.646645
$784$	30.0173	1.07204
$785$	8.64299	0.308481
$786$	36.7131	1.30951
$787$	−16.3109	−0.581421	−0.290710	−	0.956811i	$-0.593892\pi$
$787$	−16.3109	−0.581421	−0.290710	+	0.956811i	$0.593892\pi$
$788$	36.5158	1.30082
$789$	−18.6733	−0.664788
$790$	−137.757	−4.90119
$791$	−80.6047	−2.86597
$792$	−0.327486	−0.0116367
$793$	−82.8735	−2.94292
$794$	−22.5563	−0.800494
$795$	−41.7406	−1.48039
$796$	−34.0359	−1.20637
$797$	−5.43112	−0.192380	−0.0961900	−	0.995363i	$-0.530666\pi$
$797$	−5.43112	−0.192380	−0.0961900	+	0.995363i	$0.530666\pi$
$798$	−4.98557	−0.176487
$799$	5.55650	0.196575
$800$	28.1193	0.994166
$801$	−0.248972	−0.00879701
$802$	19.4329	0.686201
$803$	7.14127	0.252010
$804$	−9.02961	−0.318450
$805$	83.8079	2.95384
$806$	70.5313	2.48436
$807$	−34.9443	−1.23010
$808$	57.1971	2.01219
$809$	−12.5539	−0.441372	−0.220686	−	0.975345i	$-0.570830\pi$
$809$	−12.5539	−0.441372	−0.220686	+	0.975345i	$0.570830\pi$
$810$	−87.0981	−3.06031
$811$	27.3730	0.961194	0.480597	−	0.876941i	$-0.340420\pi$
$811$	27.3730	0.961194	0.480597	+	0.876941i	$0.340420\pi$
$812$	−58.3177	−2.04655
$813$	0.903571	0.0316896
$814$	−1.66882	−0.0584923
$815$	−90.0653	−3.15485
$816$	−3.54538	−0.124113
$817$	−0.428987	−0.0150084
$818$	31.1139	1.08787
$819$	−1.66710	−0.0582531
$820$	−107.112	−3.74052
$821$	11.5797	0.404134	0.202067	−	0.979372i	$-0.435234\pi$
$821$	11.5797	0.404134	0.202067	+	0.979372i	$0.435234\pi$
$822$	−10.1279	−0.353252
$823$	−5.47179	−0.190734	−0.0953672	−	0.995442i	$-0.530403\pi$
$823$	−5.47179	−0.190734	−0.0953672	+	0.995442i	$0.530403\pi$
$824$	−9.16961	−0.319439
$825$	−23.0547	−0.802663
$826$	113.637	3.95393
$827$	11.2074	0.389719	0.194860	−	0.980831i	$-0.437575\pi$
$827$	11.2074	0.389719	0.194860	+	0.980831i	$0.437575\pi$
$828$	1.14867	0.0399189
$829$	31.7906	1.10413	0.552067	−	0.833800i	$-0.313839\pi$
$829$	31.7906	1.10413	0.552067	+	0.833800i	$0.313839\pi$
$830$	41.3321	1.43466
$831$	11.8290	0.410343
$832$	−61.8066	−2.14276
$833$	11.3751	0.394123
$834$	42.5354	1.47288
$835$	−42.2210	−1.46112
$836$	1.21125	0.0418920
$837$	−26.7020	−0.922956
$838$	−14.5111	−0.501276
$839$	−21.3064	−0.735580	−0.367790	−	0.929909i	$-0.619885\pi$
$839$	−21.3064	−0.735580	−0.367790	+	0.929909i	$0.619885\pi$
$840$	126.374	4.36032
$841$	−16.5965	−0.572293
$842$	−18.7740	−0.646996
$843$	40.0256	1.37855
$844$	10.7141	0.368795
$845$	−76.5208	−2.63239
$846$	−0.994208	−0.0341816
$847$	42.4542	1.45874
$848$	−13.8908	−0.477012
$849$	16.8874	0.579574
$850$	−22.4661	−0.770579
$851$	2.69283	0.0923091
$852$	−17.4996	−0.599528
$853$	33.3108	1.14054	0.570270	−	0.821458i	$-0.306839\pi$
$853$	33.3108	1.14054	0.570270	+	0.821458i	$0.306839\pi$
$854$	−155.718	−5.32857
$855$	−0.0694334	−0.00237457
$856$	−56.9993	−1.94820
$857$	12.2290	0.417734	0.208867	−	0.977944i	$-0.433022\pi$
$857$	12.2290	0.417734	0.208867	+	0.977944i	$0.433022\pi$
$858$	29.1359	0.994685
$859$	8.43378	0.287757	0.143878	−	0.989595i	$-0.454043\pi$
$859$	8.43378	0.287757	0.143878	+	0.989595i	$0.454043\pi$
$860$	23.6368	0.806009
$861$	57.0564	1.94448
$862$	70.5782	2.40390
$863$	−42.4917	−1.44643	−0.723217	−	0.690621i	$-0.757337\pi$
$863$	−42.4917	−1.44643	−0.723217	+	0.690621i	$0.757337\pi$
$864$	13.4535	0.457697
$865$	−15.4497	−0.525306
$866$	62.6734	2.12973
$867$	28.4217	0.965250
$868$	86.0592	2.92104
$869$	−17.8279	−0.604769
$870$	−58.4256	−1.98081
$871$	7.91157	0.268073
$872$	−19.5564	−0.662263
$873$	−0.169697	−0.00574339
$874$	−3.00983	−0.101809
$875$	101.775	3.44061
$876$	−37.7702	−1.27614
$877$	35.9175	1.21285	0.606424	−	0.795142i	$-0.292603\pi$
$877$	35.9175	1.21285	0.606424	+	0.795142i	$0.292603\pi$
$878$	−44.8765	−1.51451
$879$	33.3019	1.12325
$880$	−11.2447	−0.379059
$881$	−25.4978	−0.859044	−0.429522	−	0.903056i	$-0.641318\pi$
$881$	−25.4978	−0.859044	−0.429522	+	0.903056i	$0.641318\pi$
$882$	−2.03530	−0.0685323
$883$	−49.7463	−1.67410	−0.837048	−	0.547130i	$-0.815720\pi$
$883$	−49.7463	−1.67410	−0.837048	+	0.547130i	$0.815720\pi$
$884$	18.4369	0.620099
$885$	73.9287	2.48509
$886$	59.7657	2.00787
$887$	28.0467	0.941716	0.470858	−	0.882209i	$-0.343944\pi$
$887$	28.0467	0.941716	0.470858	+	0.882209i	$0.343944\pi$
$888$	4.06052	0.136262
$889$	40.6385	1.36297
$890$	−35.9455	−1.20489
$891$	−11.2718	−0.377620
$892$	48.7113	1.63098
$893$	1.69167	0.0566097
$894$	−40.8964	−1.36778
$895$	52.6251	1.75906
$896$	−92.7213	−3.09760
$897$	−47.0141	−1.56975
$898$	−63.6064	−2.12257
$899$	−18.3038	−0.610465
$900$	2.61032	0.0870106
$901$	−5.26393	−0.175367
$902$	−21.3468	−0.710770
$903$	−12.5908	−0.418997
$904$	−73.3769	−2.44048
$905$	2.31887	0.0770819
$906$	61.2639	2.03536
$907$	−49.1046	−1.63049	−0.815246	−	0.579114i	$-0.803398\pi$
$907$	−49.1046	−1.63049	−0.815246	+	0.579114i	$0.803398\pi$
$908$	−70.0279	−2.32396
$909$	−0.922348	−0.0305923
$910$	−240.687	−7.97871
$911$	−33.6278	−1.11414	−0.557069	−	0.830466i	$-0.688074\pi$
$911$	−33.6278	−1.11414	−0.557069	+	0.830466i	$0.688074\pi$
$912$	−1.07939	−0.0357421
$913$	5.34900	0.177026
$914$	−93.0521	−3.07789
$915$	−101.306	−3.34906
$916$	−18.4825	−0.610680
$917$	−39.2491	−1.29612
$918$	−10.7487	−0.354761
$919$	−38.9312	−1.28422	−0.642112	−	0.766611i	$-0.721941\pi$
$919$	−38.9312	−1.28422	−0.642112	+	0.766611i	$0.721941\pi$
$920$	76.2929	2.51530
$921$	24.2004	0.797429
$922$	4.86555	0.160238
$923$	15.3328	0.504687
$924$	35.5504	1.16952
$925$	6.11940	0.201205
$926$	75.4683	2.48004
$927$	0.147867	0.00485660
$928$	9.22214	0.302732
$929$	17.3666	0.569780	0.284890	−	0.958560i	$-0.408043\pi$
$929$	17.3666	0.569780	0.284890	+	0.958560i	$0.408043\pi$
$930$	86.2184	2.82721
$931$	3.46313	0.113499
$932$	−32.8055	−1.07458
$933$	−45.0108	−1.47359
$934$	−33.0240	−1.08058
$935$	−4.26119	−0.139356
$936$	−1.51761	−0.0496046
$937$	−10.8030	−0.352920	−0.176460	−	0.984308i	$-0.556465\pi$
$937$	−10.8030	−0.352920	−0.176460	+	0.984308i	$0.556465\pi$
$938$	14.8658	0.485384
$939$	17.5363	0.572275
$940$	−93.2097	−3.04016
$941$	25.7914	0.840774	0.420387	−	0.907345i	$-0.361894\pi$
$941$	25.7914	0.840774	0.420387	+	0.907345i	$0.361894\pi$
$942$	−9.11027	−0.296829
$943$	34.4454	1.12170
$944$	24.6026	0.800748
$945$	91.1203	2.96414
$946$	4.71067	0.153157
$947$	−21.5238	−0.699430	−0.349715	−	0.936856i	$-0.613722\pi$
$947$	−21.5238	−0.699430	−0.349715	+	0.936856i	$0.613722\pi$
$948$	94.2917	3.06245
$949$	33.0935	1.07426
$950$	−6.83977	−0.221911
$951$	43.0744	1.39678
$952$	15.9371	0.516524
$953$	−35.6681	−1.15540	−0.577702	−	0.816248i	$-0.696050\pi$
$953$	−35.6681	−1.15540	−0.577702	+	0.816248i	$0.696050\pi$
$954$	0.941859	0.0304938
$955$	95.6177	3.09412
$956$	79.9943	2.58720
$957$	−7.56115	−0.244417
$958$	−65.9604	−2.13108
$959$	10.8275	0.349640
$960$	−75.5532	−2.43847
$961$	−3.98920	−0.128684
$962$	−7.73353	−0.249339
$963$	0.919159	0.0296195
$964$	−9.05604	−0.291675
$965$	−17.7786	−0.572312
$966$	−88.3389	−2.84226
$967$	9.01500	0.289903	0.144951	−	0.989439i	$-0.453697\pi$
$967$	9.01500	0.289903	0.144951	+	0.989439i	$0.453697\pi$
$968$	38.6474	1.24217
$969$	−0.409035	−0.0131401
$970$	−24.5001	−0.786651
$971$	38.0223	1.22019	0.610096	−	0.792327i	$-0.291131\pi$
$971$	38.0223	1.22019	0.610096	+	0.792327i	$0.291131\pi$
$972$	2.52571	0.0810122
$973$	−45.4736	−1.45782
$974$	−4.49373	−0.143989
$975$	−106.838	−3.42157
$976$	−33.7133	−1.07914
$977$	−2.12682	−0.0680429	−0.0340214	−	0.999421i	$-0.510831\pi$
$977$	−2.12682	−0.0680429	−0.0340214	+	0.999421i	$0.510831\pi$
$978$	94.9347	3.03568
$979$	−4.65188	−0.148675
$980$	−190.815	−6.09537
$981$	0.315362	0.0100687
$982$	−34.7918	−1.11025
$983$	6.58974	0.210180	0.105090	−	0.994463i	$-0.466487\pi$
$983$	6.58974	0.210180	0.105090	+	0.994463i	$0.466487\pi$
$984$	51.9402	1.65579
$985$	−39.1105	−1.24616
$986$	−7.36808	−0.234648
$987$	49.6508	1.58040
$988$	5.61308	0.178576
$989$	−7.60119	−0.241704
$990$	0.762442	0.0242320
$991$	−20.7147	−0.658025	−0.329012	−	0.944326i	$-0.606716\pi$
$991$	−20.7147	−0.658025	−0.329012	+	0.944326i	$0.606716\pi$
$992$	−13.6091	−0.432088
$993$	−3.61646	−0.114765
$994$	28.8102	0.913805
$995$	36.4543	1.15568
$996$	−28.2909	−0.896430
$997$	47.8293	1.51477	0.757384	−	0.652969i	$-0.226477\pi$
$997$	47.8293	1.51477	0.757384	+	0.652969i	$0.226477\pi$
$998$	−62.1218	−1.96643
$999$	2.92779	0.0926312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.20	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.20	✓	216	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)

\(f(q)\)	\(=\)	\(q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +O(q^{10})\)	\(q-2.38830 q^{2} -1.75089 q^{3} +3.70399 q^{4} -3.96718 q^{5} +4.18166 q^{6} -4.47052 q^{7} -4.06966 q^{8} +0.0656264 q^{9} +9.47483 q^{10} +1.22619 q^{11} -6.48530 q^{12} +5.68229 q^{13} +10.6770 q^{14} +6.94611 q^{15} +2.31159 q^{16} +0.875977 q^{17} -0.156736 q^{18} +0.266691 q^{19} -14.6944 q^{20} +7.82741 q^{21} -2.92850 q^{22} +4.72547 q^{23} +7.12553 q^{24} +10.7385 q^{25} -13.5710 q^{26} +5.13777 q^{27} -16.5588 q^{28} +3.52186 q^{29} -16.5894 q^{30} -5.19719 q^{31} +2.61854 q^{32} -2.14692 q^{33} -2.09210 q^{34} +17.7354 q^{35} +0.243080 q^{36} +0.569856 q^{37} -0.636938 q^{38} -9.94909 q^{39} +16.1451 q^{40} +7.28931 q^{41} -18.6942 q^{42} -1.60856 q^{43} +4.54179 q^{44} -0.260352 q^{45} -11.2858 q^{46} +6.34320 q^{47} -4.04734 q^{48} +12.9856 q^{49} -25.6468 q^{50} -1.53374 q^{51} +21.0472 q^{52} -6.00921 q^{53} -12.2706 q^{54} -4.86450 q^{55} +18.1935 q^{56} -0.466947 q^{57} -8.41127 q^{58} +10.6432 q^{59} +25.7283 q^{60} -14.5845 q^{61} +12.4125 q^{62} -0.293384 q^{63} -10.8770 q^{64} -22.5427 q^{65} +5.12750 q^{66} +1.39232 q^{67} +3.24462 q^{68} -8.27378 q^{69} -42.3574 q^{70} +2.69836 q^{71} -0.267077 q^{72} +5.82397 q^{73} -1.36099 q^{74} -18.8020 q^{75} +0.987820 q^{76} -5.48169 q^{77} +23.7614 q^{78} -14.5393 q^{79} -9.17048 q^{80} -9.19257 q^{81} -17.4091 q^{82} +4.36231 q^{83} +28.9927 q^{84} -3.47516 q^{85} +3.84173 q^{86} -6.16640 q^{87} -4.99015 q^{88} -3.79378 q^{89} +0.621799 q^{90} -25.4028 q^{91} +17.5031 q^{92} +9.09973 q^{93} -15.1495 q^{94} -1.05801 q^{95} -4.58479 q^{96} -2.58581 q^{97} -31.0135 q^{98} +0.0804702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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