LMFDB - Embedded newform 8027.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59099 q^{2} -0.493919 q^{3} +4.71322 q^{4} +1.04082 q^{5} +1.27974 q^{6} -3.08433 q^{7} -7.02991 q^{8} -2.75604 q^{9} +O(q^{10})$	\(q-2.59099 q^{2} -0.493919 q^{3} +4.71322 q^{4} +1.04082 q^{5} +1.27974 q^{6} -3.08433 q^{7} -7.02991 q^{8} -2.75604 q^{9} -2.69675 q^{10} +1.54003 q^{11} -2.32795 q^{12} -4.07681 q^{13} +7.99146 q^{14} -0.514081 q^{15} +8.78797 q^{16} -1.10560 q^{17} +7.14088 q^{18} +4.99259 q^{19} +4.90561 q^{20} +1.52341 q^{21} -3.99020 q^{22} -1.00000 q^{23} +3.47220 q^{24} -3.91669 q^{25} +10.5630 q^{26} +2.84302 q^{27} -14.5371 q^{28} -0.889051 q^{29} +1.33198 q^{30} +5.93778 q^{31} -8.70970 q^{32} -0.760650 q^{33} +2.86459 q^{34} -3.21023 q^{35} -12.9898 q^{36} +8.07764 q^{37} -12.9357 q^{38} +2.01361 q^{39} -7.31687 q^{40} -0.673601 q^{41} -3.94713 q^{42} -5.94857 q^{43} +7.25850 q^{44} -2.86855 q^{45} +2.59099 q^{46} -6.86946 q^{47} -4.34054 q^{48} +2.51309 q^{49} +10.1481 q^{50} +0.546076 q^{51} -19.2149 q^{52} -0.962065 q^{53} -7.36622 q^{54} +1.60290 q^{55} +21.6825 q^{56} -2.46593 q^{57} +2.30352 q^{58} +6.53170 q^{59} -2.42297 q^{60} +10.7169 q^{61} -15.3847 q^{62} +8.50055 q^{63} +4.99079 q^{64} -4.24322 q^{65} +1.97084 q^{66} -15.5793 q^{67} -5.21093 q^{68} +0.493919 q^{69} +8.31767 q^{70} +0.545950 q^{71} +19.3747 q^{72} +7.54944 q^{73} -20.9291 q^{74} +1.93453 q^{75} +23.5312 q^{76} -4.74996 q^{77} -5.21724 q^{78} +2.15473 q^{79} +9.14670 q^{80} +6.86391 q^{81} +1.74529 q^{82} +16.6568 q^{83} +7.18015 q^{84} -1.15073 q^{85} +15.4127 q^{86} +0.439119 q^{87} -10.8263 q^{88} +3.46364 q^{89} +7.43237 q^{90} +12.5742 q^{91} -4.71322 q^{92} -2.93278 q^{93} +17.7987 q^{94} +5.19639 q^{95} +4.30189 q^{96} -1.32557 q^{97} -6.51137 q^{98} -4.24439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.59099	−1.83210	−0.916052	−	0.401059i	$-0.868642\pi$
$2$	−2.59099	−1.83210	−0.916052	+	0.401059i	$0.868642\pi$
$3$	−0.493919	−0.285164	−0.142582	−	0.989783i	$-0.545540\pi$
$3$	−0.493919	−0.285164	−0.142582	+	0.989783i	$0.545540\pi$
$4$	4.71322	2.35661
$5$	1.04082	0.465469	0.232734	−	0.972540i	$-0.425233\pi$
$5$	1.04082	0.465469	0.232734	+	0.972540i	$0.425233\pi$
$6$	1.27974	0.522451
$7$	−3.08433	−1.16577	−0.582883	−	0.812556i	$-0.698076\pi$
$7$	−3.08433	−1.16577	−0.582883	+	0.812556i	$0.698076\pi$
$8$	−7.02991	−2.48545
$9$	−2.75604	−0.918681
$10$	−2.69675	−0.852788
$11$	1.54003	0.464337	0.232168	−	0.972676i	$-0.425418\pi$
$11$	1.54003	0.464337	0.232168	+	0.972676i	$0.425418\pi$
$12$	−2.32795	−0.672020
$13$	−4.07681	−1.13070	−0.565351	−	0.824850i	$-0.691259\pi$
$13$	−4.07681	−1.13070	−0.565351	+	0.824850i	$0.691259\pi$
$14$	7.99146	2.13581
$15$	−0.514081	−0.132735
$16$	8.78797	2.19699
$17$	−1.10560	−0.268147	−0.134074	−	0.990971i	$-0.542806\pi$
$17$	−1.10560	−0.268147	−0.134074	+	0.990971i	$0.542806\pi$
$18$	7.14088	1.68312
$19$	4.99259	1.14538	0.572690	−	0.819772i	$-0.305900\pi$
$19$	4.99259	1.14538	0.572690	+	0.819772i	$0.305900\pi$
$20$	4.90561	1.09693
$21$	1.52341	0.332435
$22$	−3.99020	−0.850714
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.47220	0.708761
$25$	−3.91669	−0.783339
$26$	10.5630	2.07157
$27$	2.84302	0.547139
$28$	−14.5371	−2.74726
$29$	−0.889051	−0.165093	−0.0825463	−	0.996587i	$-0.526305\pi$
$29$	−0.889051	−0.165093	−0.0825463	+	0.996587i	$0.526305\pi$
$30$	1.33198	0.243185
$31$	5.93778	1.06646	0.533228	−	0.845972i	$-0.320979\pi$
$31$	5.93778	1.06646	0.533228	+	0.845972i	$0.320979\pi$
$32$	−8.70970	−1.53967
$33$	−0.760650	−0.132412
$34$	2.86459	0.491274
$35$	−3.21023	−0.542628
$36$	−12.9898	−2.16497
$37$	8.07764	1.32796	0.663978	−	0.747752i	$-0.268867\pi$
$37$	8.07764	1.32796	0.663978	+	0.747752i	$0.268867\pi$
$38$	−12.9357	−2.09845
$39$	2.01361	0.322436
$40$	−7.31687	−1.15690
$41$	−0.673601	−0.105199	−0.0525994	−	0.998616i	$-0.516751\pi$
$41$	−0.673601	−0.105199	−0.0525994	+	0.998616i	$0.516751\pi$
$42$	−3.94713	−0.609056
$43$	−5.94857	−0.907148	−0.453574	−	0.891219i	$-0.649851\pi$
$43$	−5.94857	−0.907148	−0.453574	+	0.891219i	$0.649851\pi$
$44$	7.25850	1.09426
$45$	−2.86855	−0.427618
$46$	2.59099	0.382020
$47$	−6.86946	−1.00201	−0.501007	−	0.865443i	$-0.667037\pi$
$47$	−6.86946	−1.00201	−0.501007	+	0.865443i	$0.667037\pi$
$48$	−4.34054	−0.626503
$49$	2.51309	0.359012
$50$	10.1481	1.43516
$51$	0.546076	0.0764659
$52$	−19.2149	−2.66462
$53$	−0.962065	−0.132150	−0.0660749	−	0.997815i	$-0.521048\pi$
$53$	−0.962065	−0.132150	−0.0660749	+	0.997815i	$0.521048\pi$
$54$	−7.36622	−1.00242
$55$	1.60290	0.216134
$56$	21.6825	2.89745
$57$	−2.46593	−0.326621
$58$	2.30352	0.302467
$59$	6.53170	0.850355	0.425178	−	0.905110i	$-0.360212\pi$
$59$	6.53170	0.850355	0.425178	+	0.905110i	$0.360212\pi$
$60$	−2.42297	−0.312804
$61$	10.7169	1.37216	0.686078	−	0.727528i	$-0.259331\pi$
$61$	10.7169	1.37216	0.686078	+	0.727528i	$0.259331\pi$
$62$	−15.3847	−1.95386
$63$	8.50055	1.07097
$64$	4.99079	0.623849
$65$	−4.24322	−0.526307
$66$	1.97084	0.242593
$67$	−15.5793	−1.90331	−0.951656	−	0.307167i	$-0.900619\pi$
$67$	−15.5793	−1.90331	−0.951656	+	0.307167i	$0.900619\pi$
$68$	−5.21093	−0.631918
$69$	0.493919	0.0594608
$70$	8.31767	0.994152
$71$	0.545950	0.0647923	0.0323962	−	0.999475i	$-0.489686\pi$
$71$	0.545950	0.0647923	0.0323962	+	0.999475i	$0.489686\pi$
$72$	19.3747	2.28333
$73$	7.54944	0.883595	0.441797	−	0.897115i	$-0.354341\pi$
$73$	7.54944	0.883595	0.441797	+	0.897115i	$0.354341\pi$
$74$	−20.9291	−2.43296
$75$	1.93453	0.223380
$76$	23.5312	2.69921
$77$	−4.74996	−0.541309
$78$	−5.21724	−0.590736
$79$	2.15473	0.242426	0.121213	−	0.992627i	$-0.461322\pi$
$79$	2.15473	0.242426	0.121213	+	0.992627i	$0.461322\pi$
$80$	9.14670	1.02263
$81$	6.86391	0.762657
$82$	1.74529	0.192735
$83$	16.6568	1.82832	0.914159	−	0.405356i	$-0.132852\pi$
$83$	16.6568	1.82832	0.914159	+	0.405356i	$0.132852\pi$
$84$	7.18015	0.783419
$85$	−1.15073	−0.124814
$86$	15.4127	1.66199
$87$	0.439119	0.0470785
$88$	−10.8263	−1.15408
$89$	3.46364	0.367145	0.183572	−	0.983006i	$-0.441234\pi$
$89$	3.46364	0.367145	0.183572	+	0.983006i	$0.441234\pi$
$90$	7.43237	0.783440
$91$	12.5742	1.31814
$92$	−4.71322	−0.491387
$93$	−2.93278	−0.304115
$94$	17.7987	1.83579
$95$	5.19639	0.533138
$96$	4.30189	0.439059
$97$	−1.32557	−0.134591	−0.0672955	−	0.997733i	$-0.521437\pi$
$97$	−1.32557	−0.134591	−0.0672955	+	0.997733i	$0.521437\pi$
$98$	−6.51137	−0.657748
$99$	−4.24439	−0.426578
$100$	−18.4602	−1.84602
$101$	14.1202	1.40501	0.702507	−	0.711677i	$-0.252064\pi$
$101$	14.1202	1.40501	0.702507	+	0.711677i	$0.252064\pi$
$102$	−1.41488	−0.140094
$103$	3.73359	0.367882	0.183941	−	0.982937i	$-0.441114\pi$
$103$	3.73359	0.367882	0.183941	+	0.982937i	$0.441114\pi$
$104$	28.6596	2.81030
$105$	1.58559	0.154738
$106$	2.49270	0.242112
$107$	−16.4910	−1.59424	−0.797122	−	0.603818i	$-0.793645\pi$
$107$	−16.4910	−1.59424	−0.797122	+	0.603818i	$0.793645\pi$
$108$	13.3998	1.28939
$109$	13.5986	1.30251	0.651253	−	0.758860i	$-0.274244\pi$
$109$	13.5986	1.30251	0.651253	+	0.758860i	$0.274244\pi$
$110$	−4.15308	−0.395981
$111$	−3.98970	−0.378686
$112$	−27.1050	−2.56118
$113$	3.79437	0.356944	0.178472	−	0.983945i	$-0.442885\pi$
$113$	3.79437	0.356944	0.178472	+	0.983945i	$0.442885\pi$
$114$	6.38921	0.598404
$115$	−1.04082	−0.0970570
$116$	−4.19029	−0.389059
$117$	11.2359	1.03876
$118$	−16.9236	−1.55794
$119$	3.41003	0.312597
$120$	3.61394	0.329906
$121$	−8.62830	−0.784391
$122$	−27.7673	−2.51393
$123$	0.332704	0.0299989
$124$	27.9860	2.51322
$125$	−9.28068	−0.830089
$126$	−22.0248	−1.96213
$127$	13.6069	1.20742	0.603708	−	0.797205i	$-0.293689\pi$
$127$	13.6069	1.20742	0.603708	+	0.797205i	$0.293689\pi$
$128$	4.48832	0.396715
$129$	2.93811	0.258686
$130$	10.9941	0.964249
$131$	−15.9338	−1.39214	−0.696069	−	0.717975i	$-0.745069\pi$
$131$	−15.9338	−1.39214	−0.696069	+	0.717975i	$0.745069\pi$
$132$	−3.58511	−0.312044
$133$	−15.3988	−1.33524
$134$	40.3657	3.48707
$135$	2.95907	0.254676
$136$	7.77226	0.666466
$137$	16.9321	1.44661	0.723306	−	0.690528i	$-0.242622\pi$
$137$	16.9321	1.44661	0.723306	+	0.690528i	$0.242622\pi$
$138$	−1.27974	−0.108938
$139$	−14.0910	−1.19518	−0.597591	−	0.801801i	$-0.703876\pi$
$139$	−14.0910	−1.19518	−0.597591	+	0.801801i	$0.703876\pi$
$140$	−15.1305	−1.27876
$141$	3.39295	0.285738
$142$	−1.41455	−0.118706
$143$	−6.27841	−0.525027
$144$	−24.2200	−2.01834
$145$	−0.925343	−0.0768455
$146$	−19.5605	−1.61884
$147$	−1.24126	−0.102377
$148$	38.0717	3.12947
$149$	−3.70760	−0.303738	−0.151869	−	0.988401i	$-0.548529\pi$
$149$	−3.70760	−0.303738	−0.151869	+	0.988401i	$0.548529\pi$
$150$	−5.01234	−0.409256
$151$	7.61611	0.619790	0.309895	−	0.950771i	$-0.399706\pi$
$151$	7.61611	0.619790	0.309895	+	0.950771i	$0.399706\pi$
$152$	−35.0975	−2.84678
$153$	3.04708	0.246342
$154$	12.3071	0.991734
$155$	6.18016	0.496402
$156$	9.49058	0.759855
$157$	−7.75834	−0.619183	−0.309592	−	0.950870i	$-0.600192\pi$
$157$	−7.75834	−0.619183	−0.309592	+	0.950870i	$0.600192\pi$
$158$	−5.58288	−0.444150
$159$	0.475182	0.0376844
$160$	−9.06524	−0.716670
$161$	3.08433	0.243079
$162$	−17.7843	−1.39727
$163$	−1.62573	−0.127337	−0.0636686	−	0.997971i	$-0.520280\pi$
$163$	−1.62573	−0.127337	−0.0636686	+	0.997971i	$0.520280\pi$
$164$	−3.17483	−0.247912
$165$	−0.791700	−0.0616338
$166$	−43.1575	−3.34967
$167$	3.02536	0.234109	0.117055	−	0.993125i	$-0.462655\pi$
$167$	3.02536	0.234109	0.117055	+	0.993125i	$0.462655\pi$
$168$	−10.7094	−0.826249
$169$	3.62034	0.278488
$170$	2.98153	0.228673
$171$	−13.7598	−1.05224
$172$	−28.0369	−2.13779
$173$	7.11242	0.540747	0.270374	−	0.962755i	$-0.412853\pi$
$173$	7.11242	0.540747	0.270374	+	0.962755i	$0.412853\pi$
$174$	−1.13775	−0.0862528
$175$	12.0804	0.913190
$176$	13.5337	1.02014
$177$	−3.22613	−0.242491
$178$	−8.97424	−0.672647
$179$	17.6622	1.32013	0.660067	−	0.751206i	$-0.270528\pi$
$179$	17.6622	1.32013	0.660067	+	0.751206i	$0.270528\pi$
$180$	−13.5201	−1.00773
$181$	−1.84621	−0.137228	−0.0686139	−	0.997643i	$-0.521858\pi$
$181$	−1.84621	−0.137228	−0.0686139	+	0.997643i	$0.521858\pi$
$182$	−32.5796	−2.41496
$183$	−5.29327	−0.391290
$184$	7.02991	0.518252
$185$	8.40738	0.618123
$186$	7.59879	0.557171
$187$	−1.70266	−0.124511
$188$	−32.3772	−2.36135
$189$	−8.76880	−0.637837
$190$	−13.4638	−0.976765
$191$	−25.5299	−1.84728	−0.923640	−	0.383261i	$-0.874801\pi$
$191$	−25.5299	−1.84728	−0.923640	+	0.383261i	$0.874801\pi$
$192$	−2.46505	−0.177899
$193$	−5.88066	−0.423299	−0.211650	−	0.977346i	$-0.567884\pi$
$193$	−5.88066	−0.423299	−0.211650	+	0.977346i	$0.567884\pi$
$194$	3.43453	0.246585
$195$	2.09581	0.150084
$196$	11.8447	0.846051
$197$	−2.00289	−0.142700	−0.0713498	−	0.997451i	$-0.522731\pi$
$197$	−2.00289	−0.142700	−0.0713498	+	0.997451i	$0.522731\pi$
$198$	10.9972	0.781535
$199$	8.84619	0.627090	0.313545	−	0.949573i	$-0.398483\pi$
$199$	8.84619	0.627090	0.313545	+	0.949573i	$0.398483\pi$
$200$	27.5340	1.94695
$201$	7.69490	0.542756
$202$	−36.5853	−2.57413
$203$	2.74213	0.192460
$204$	2.57377	0.180200
$205$	−0.701098	−0.0489668
$206$	−9.67369	−0.673998
$207$	2.75604	0.191558
$208$	−35.8268	−2.48414
$209$	7.68875	0.531842
$210$	−4.10825	−0.283496
$211$	−1.46987	−0.101190	−0.0505950	−	0.998719i	$-0.516112\pi$
$211$	−1.46987	−0.101190	−0.0505950	+	0.998719i	$0.516112\pi$
$212$	−4.53442	−0.311425
$213$	−0.269655	−0.0184764
$214$	42.7279	2.92082
$215$	−6.19139	−0.422249
$216$	−19.9862	−1.35989
$217$	−18.3141	−1.24324
$218$	−35.2337	−2.38633
$219$	−3.72881	−0.251970
$220$	7.55479	0.509344
$221$	4.50731	0.303195
$222$	10.3373	0.693792
$223$	−13.4402	−0.900022	−0.450011	−	0.893023i	$-0.648580\pi$
$223$	−13.4402	−0.900022	−0.450011	+	0.893023i	$0.648580\pi$
$224$	26.8636	1.79490
$225$	10.7946	0.719639
$226$	−9.83116	−0.653959
$227$	19.6760	1.30594	0.652970	−	0.757383i	$-0.273523\pi$
$227$	19.6760	1.30594	0.652970	+	0.757383i	$0.273523\pi$
$228$	−11.6225	−0.769718
$229$	−4.21050	−0.278238	−0.139119	−	0.990276i	$-0.544427\pi$
$229$	−4.21050	−0.278238	−0.139119	+	0.990276i	$0.544427\pi$
$230$	2.69675	0.177819
$231$	2.34610	0.154362
$232$	6.24995	0.410329
$233$	−20.2263	−1.32507	−0.662535	−	0.749031i	$-0.730519\pi$
$233$	−20.2263	−1.32507	−0.662535	+	0.749031i	$0.730519\pi$
$234$	−29.1120	−1.90311
$235$	−7.14987	−0.466406
$236$	30.7853	2.00395
$237$	−1.06426	−0.0691312
$238$	−8.83535	−0.572710
$239$	−2.25180	−0.145657	−0.0728285	−	0.997344i	$-0.523203\pi$
$239$	−2.25180	−0.145657	−0.0728285	+	0.997344i	$0.523203\pi$
$240$	−4.51773	−0.291618
$241$	−15.0126	−0.967044	−0.483522	−	0.875332i	$-0.660643\pi$
$241$	−15.0126	−0.967044	−0.483522	+	0.875332i	$0.660643\pi$
$242$	22.3558	1.43709
$243$	−11.9193	−0.764622
$244$	50.5110	3.23363
$245$	2.61567	0.167109
$246$	−0.862033	−0.0549612
$247$	−20.3538	−1.29508
$248$	−41.7420	−2.65062
$249$	−8.22709	−0.521371
$250$	24.0461	1.52081
$251$	−0.810455	−0.0511555	−0.0255777	−	0.999673i	$-0.508143\pi$
$251$	−0.810455	−0.0511555	−0.0255777	+	0.999673i	$0.508143\pi$
$252$	40.0649	2.52385
$253$	−1.54003	−0.0968209
$254$	−35.2553	−2.21211
$255$	0.568367	0.0355925
$256$	−21.6108	−1.35067
$257$	−19.3248	−1.20545	−0.602724	−	0.797950i	$-0.705918\pi$
$257$	−19.3248	−1.20545	−0.602724	+	0.797950i	$0.705918\pi$
$258$	−7.61261	−0.473940
$259$	−24.9141	−1.54809
$260$	−19.9992	−1.24030
$261$	2.45026	0.151668
$262$	41.2842	2.55054
$263$	7.60644	0.469033	0.234517	−	0.972112i	$-0.424649\pi$
$263$	7.60644	0.469033	0.234517	+	0.972112i	$0.424649\pi$
$264$	5.34730	0.329104
$265$	−1.00134	−0.0615116
$266$	39.8981	2.44631
$267$	−1.71075	−0.104696
$268$	−73.4285	−4.48536
$269$	−16.7229	−1.01961	−0.509806	−	0.860290i	$-0.670283\pi$
$269$	−16.7229	−1.01961	−0.509806	+	0.860290i	$0.670283\pi$
$270$	−7.66692	−0.466594
$271$	−1.58955	−0.0965583	−0.0482792	−	0.998834i	$-0.515374\pi$
$271$	−1.58955	−0.0965583	−0.0482792	+	0.998834i	$0.515374\pi$
$272$	−9.71597	−0.589117
$273$	−6.21064	−0.375885
$274$	−43.8710	−2.65034
$275$	−6.03183	−0.363733
$276$	2.32795	0.140126
$277$	3.58668	0.215503	0.107751	−	0.994178i	$-0.465635\pi$
$277$	3.58668	0.215503	0.107751	+	0.994178i	$0.465635\pi$
$278$	36.5096	2.18970
$279$	−16.3648	−0.979734
$280$	22.5676	1.34867
$281$	11.8779	0.708575	0.354287	−	0.935137i	$-0.384723\pi$
$281$	11.8779	0.708575	0.354287	+	0.935137i	$0.384723\pi$
$282$	−8.79110	−0.523502
$283$	−7.69573	−0.457463	−0.228732	−	0.973490i	$-0.573458\pi$
$283$	−7.69573	−0.457463	−0.228732	+	0.973490i	$0.573458\pi$
$284$	2.57318	0.152690
$285$	−2.56659	−0.152032
$286$	16.2673	0.961904
$287$	2.07761	0.122637
$288$	24.0043	1.41447
$289$	−15.7777	−0.928097
$290$	2.39755	0.140789
$291$	0.654723	0.0383805
$292$	35.5821	2.08229
$293$	24.8998	1.45466	0.727330	−	0.686288i	$-0.240761\pi$
$293$	24.8998	1.45466	0.727330	+	0.686288i	$0.240761\pi$
$294$	3.21609	0.187566
$295$	6.79833	0.395814
$296$	−56.7851	−3.30057
$297$	4.37834	0.254057
$298$	9.60634	0.556480
$299$	4.07681	0.235768
$300$	9.11785	0.526419
$301$	18.3473	1.05752
$302$	−19.7333	−1.13552
$303$	−6.97424	−0.400659
$304$	43.8747	2.51639
$305$	11.1543	0.638696
$306$	−7.89494	−0.451324
$307$	−25.8085	−1.47297	−0.736484	−	0.676455i	$-0.763516\pi$
$307$	−25.8085	−1.47297	−0.736484	+	0.676455i	$0.763516\pi$
$308$	−22.3876	−1.27565
$309$	−1.84409	−0.104907
$310$	−16.0127	−0.909461
$311$	11.9418	0.677159	0.338579	−	0.940938i	$-0.390054\pi$
$311$	11.9418	0.677159	0.338579	+	0.940938i	$0.390054\pi$
$312$	−14.1555	−0.801397
$313$	−3.65870	−0.206802	−0.103401	−	0.994640i	$-0.532972\pi$
$313$	−3.65870	−0.206802	−0.103401	+	0.994640i	$0.532972\pi$
$314$	20.1018	1.13441
$315$	8.84754	0.498503
$316$	10.1557	0.571303
$317$	−9.24740	−0.519386	−0.259693	−	0.965691i	$-0.583621\pi$
$317$	−9.24740	−0.519386	−0.259693	+	0.965691i	$0.583621\pi$
$318$	−1.23119	−0.0690417
$319$	−1.36917	−0.0766586
$320$	5.19452	0.290383
$321$	8.14521	0.454621
$322$	−7.99146	−0.445347
$323$	−5.51980	−0.307130
$324$	32.3511	1.79728
$325$	15.9676	0.885723
$326$	4.21226	0.233295
$327$	−6.71659	−0.371428
$328$	4.73536	0.261466
$329$	21.1877	1.16811
$330$	2.05129	0.112920
$331$	11.6597	0.640873	0.320436	−	0.947270i	$-0.396170\pi$
$331$	11.6597	0.640873	0.320436	+	0.947270i	$0.396170\pi$
$332$	78.5070	4.30863
$333$	−22.2623	−1.21997
$334$	−7.83867	−0.428913
$335$	−16.2152	−0.885932
$336$	13.3877	0.730357
$337$	8.96326	0.488260	0.244130	−	0.969743i	$-0.421498\pi$
$337$	8.96326	0.488260	0.244130	+	0.969743i	$0.421498\pi$
$338$	−9.38027	−0.510219
$339$	−1.87411	−0.101788
$340$	−5.42364	−0.294138
$341$	9.14436	0.495195
$342$	35.6515	1.92781
$343$	13.8391	0.747242
$344$	41.8179	2.25467
$345$	0.514081	0.0276772
$346$	−18.4282	−0.990706
$347$	28.2080	1.51429	0.757143	−	0.653249i	$-0.226594\pi$
$347$	28.2080	1.51429	0.757143	+	0.653249i	$0.226594\pi$
$348$	2.06966	0.110946
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−31.3001	−1.67306
$351$	−11.5904	−0.618652
$352$	−13.4132	−0.714927
$353$	17.0910	0.909661	0.454831	−	0.890578i	$-0.349700\pi$
$353$	17.0910	0.909661	0.454831	+	0.890578i	$0.349700\pi$
$354$	8.35886	0.444269
$355$	0.568236	0.0301588
$356$	16.3249	0.865216
$357$	−1.68428	−0.0891415
$358$	−45.7625	−2.41862
$359$	−4.40870	−0.232682	−0.116341	−	0.993209i	$-0.537117\pi$
$359$	−4.40870	−0.232682	−0.116341	+	0.993209i	$0.537117\pi$
$360$	20.1656	1.06282
$361$	5.92597	0.311893
$362$	4.78351	0.251416
$363$	4.26168	0.223680
$364$	59.2650	3.10633
$365$	7.85761	0.411286
$366$	13.7148	0.716884
$367$	−28.1054	−1.46709	−0.733545	−	0.679641i	$-0.762136\pi$
$367$	−28.1054	−1.46709	−0.733545	+	0.679641i	$0.762136\pi$
$368$	−8.78797	−0.458105
$369$	1.85648	0.0966443
$370$	−21.7834	−1.13247
$371$	2.96733	0.154056
$372$	−13.8228	−0.716680
$373$	−14.3417	−0.742588	−0.371294	−	0.928515i	$-0.621086\pi$
$373$	−14.3417	−0.742588	−0.371294	+	0.928515i	$0.621086\pi$
$374$	4.41156	0.228116
$375$	4.58390	0.236712
$376$	48.2916	2.49045
$377$	3.62449	0.186671
$378$	22.7199	1.16858
$379$	0.457949	0.0235233	0.0117616	−	0.999931i	$-0.496256\pi$
$379$	0.457949	0.0235233	0.0117616	+	0.999931i	$0.496256\pi$
$380$	24.4917	1.25640
$381$	−6.72070	−0.344312
$382$	66.1477	3.38441
$383$	7.02370	0.358895	0.179447	−	0.983768i	$-0.442569\pi$
$383$	7.02370	0.358895	0.179447	+	0.983768i	$0.442569\pi$
$384$	−2.21687	−0.113129
$385$	−4.94386	−0.251962
$386$	15.2367	0.775529
$387$	16.3945	0.833380
$388$	−6.24769	−0.317178
$389$	−1.22277	−0.0619968	−0.0309984	−	0.999519i	$-0.509869\pi$
$389$	−1.22277	−0.0619968	−0.0309984	+	0.999519i	$0.509869\pi$
$390$	−5.43021	−0.274969
$391$	1.10560	0.0559125
$392$	−17.6668	−0.892306
$393$	7.86998	0.396988
$394$	5.18945	0.261441
$395$	2.24269	0.112842
$396$	−20.0047	−1.00528
$397$	7.55745	0.379298	0.189649	−	0.981852i	$-0.439265\pi$
$397$	7.55745	0.379298	0.189649	+	0.981852i	$0.439265\pi$
$398$	−22.9204	−1.14889
$399$	7.60575	0.380764
$400$	−34.4198	−1.72099
$401$	19.4304	0.970308	0.485154	−	0.874429i	$-0.338764\pi$
$401$	19.4304	0.970308	0.485154	+	0.874429i	$0.338764\pi$
$402$	−19.9374	−0.994386
$403$	−24.2072	−1.20584
$404$	66.5516	3.31107
$405$	7.14410	0.354993
$406$	−7.10482	−0.352606
$407$	12.4398	0.616619
$408$	−3.83886	−0.190052
$409$	−8.27788	−0.409315	−0.204657	−	0.978834i	$-0.565608\pi$
$409$	−8.27788	−0.409315	−0.204657	+	0.978834i	$0.565608\pi$
$410$	1.81654	0.0897123
$411$	−8.36311	−0.412522
$412$	17.5972	0.866953
$413$	−20.1459	−0.991316
$414$	−7.14088	−0.350955
$415$	17.3367	0.851025
$416$	35.5078	1.74091
$417$	6.95981	0.340823
$418$	−19.9214	−0.974390
$419$	−10.2028	−0.498438	−0.249219	−	0.968447i	$-0.580174\pi$
$419$	−10.2028	−0.498438	−0.249219	+	0.968447i	$0.580174\pi$
$420$	7.47325	0.364657
$421$	30.8417	1.50313	0.751567	−	0.659657i	$-0.229298\pi$
$421$	30.8417	1.50313	0.751567	+	0.659657i	$0.229298\pi$
$422$	3.80841	0.185391
$423$	18.9325	0.920531
$424$	6.76323	0.328451
$425$	4.33029	0.210050
$426$	0.698672	0.0338508
$427$	−33.0544	−1.59961
$428$	−77.7256	−3.75701
$429$	3.10102	0.149719
$430$	16.0418	0.773605
$431$	22.2983	1.07407	0.537035	−	0.843560i	$-0.319544\pi$
$431$	22.2983	1.07407	0.537035	+	0.843560i	$0.319544\pi$
$432$	24.9844	1.20206
$433$	−35.6803	−1.71468	−0.857342	−	0.514747i	$-0.827886\pi$
$433$	−35.6803	−1.71468	−0.857342	+	0.514747i	$0.827886\pi$
$434$	47.4515	2.27774
$435$	0.457044	0.0219136
$436$	64.0930	3.06950
$437$	−4.99259	−0.238828
$438$	9.66130	0.461635
$439$	−5.25922	−0.251009	−0.125504	−	0.992093i	$-0.540055\pi$
$439$	−5.25922	−0.251009	−0.125504	+	0.992093i	$0.540055\pi$
$440$	−11.2682	−0.537191
$441$	−6.92618	−0.329818
$442$	−11.6784	−0.555484
$443$	24.5849	1.16806	0.584032	−	0.811731i	$-0.301474\pi$
$443$	24.5849	1.16806	0.584032	+	0.811731i	$0.301474\pi$
$444$	−18.8043	−0.892413
$445$	3.60502	0.170894
$446$	34.8234	1.64893
$447$	1.83125	0.0866153
$448$	−15.3933	−0.727263
$449$	−35.4231	−1.67172	−0.835859	−	0.548945i	$-0.815030\pi$
$449$	−35.4231	−1.67172	−0.835859	+	0.548945i	$0.815030\pi$
$450$	−27.9686	−1.31845
$451$	−1.03737	−0.0488477
$452$	17.8837	0.841178
$453$	−3.76174	−0.176742
$454$	−50.9802	−2.39262
$455$	13.0875	0.613551
$456$	17.3353	0.811799
$457$	−7.14372	−0.334169	−0.167084	−	0.985943i	$-0.553435\pi$
$457$	−7.14372	−0.334169	−0.167084	+	0.985943i	$0.553435\pi$
$458$	10.9093	0.509760
$459$	−3.14324	−0.146714
$460$	−4.90561	−0.228725
$461$	2.78997	0.129942	0.0649709	−	0.997887i	$-0.479305\pi$
$461$	2.78997	0.129942	0.0649709	+	0.997887i	$0.479305\pi$
$462$	−6.07870	−0.282807
$463$	12.7671	0.593338	0.296669	−	0.954980i	$-0.404124\pi$
$463$	12.7671	0.593338	0.296669	+	0.954980i	$0.404124\pi$
$464$	−7.81296	−0.362707
$465$	−3.05250	−0.141556
$466$	52.4061	2.42767
$467$	17.5190	0.810685	0.405342	−	0.914165i	$-0.367152\pi$
$467$	17.5190	0.810685	0.405342	+	0.914165i	$0.367152\pi$
$468$	52.9570	2.44794
$469$	48.0516	2.21882
$470$	18.5252	0.854505
$471$	3.83199	0.176569
$472$	−45.9173	−2.11351
$473$	−9.16098	−0.421222
$474$	2.75749	0.126656
$475$	−19.5544	−0.897220
$476$	16.0722	0.736669
$477$	2.65149	0.121404
$478$	5.83439	0.266859
$479$	−25.9050	−1.18363	−0.591815	−	0.806074i	$-0.701588\pi$
$479$	−25.9050	−1.18363	−0.591815	+	0.806074i	$0.701588\pi$
$480$	4.47749	0.204369
$481$	−32.9310	−1.50152
$482$	38.8974	1.77173
$483$	−1.52341	−0.0693175
$484$	−40.6671	−1.84850
$485$	−1.37968	−0.0626479
$486$	30.8827	1.40087
$487$	16.2044	0.734293	0.367146	−	0.930163i	$-0.380335\pi$
$487$	16.2044	0.734293	0.367146	+	0.930163i	$0.380335\pi$
$488$	−75.3387	−3.41042
$489$	0.802980	0.0363120
$490$	−6.77717	−0.306161
$491$	−19.6575	−0.887129	−0.443565	−	0.896242i	$-0.646286\pi$
$491$	−19.6575	−0.887129	−0.443565	+	0.896242i	$0.646286\pi$
$492$	1.56811	0.0706958
$493$	0.982934	0.0442691
$494$	52.7365	2.37273
$495$	−4.41765	−0.198559
$496$	52.1810	2.34300
$497$	−1.68389	−0.0755328
$498$	21.3163	0.955206
$499$	−23.2278	−1.03982	−0.519910	−	0.854221i	$-0.674034\pi$
$499$	−23.2278	−1.03982	−0.519910	+	0.854221i	$0.674034\pi$
$500$	−43.7418	−1.95619
$501$	−1.49428	−0.0667596
$502$	2.09988	0.0937222
$503$	−39.6320	−1.76710	−0.883552	−	0.468334i	$-0.844855\pi$
$503$	−39.6320	−1.76710	−0.883552	+	0.468334i	$0.844855\pi$
$504$	−59.7581	−2.66184
$505$	14.6966	0.653990
$506$	3.99020	0.177386
$507$	−1.78816	−0.0794148
$508$	64.1322	2.84541
$509$	13.6249	0.603914	0.301957	−	0.953322i	$-0.402360\pi$
$509$	13.6249	0.603914	0.301957	+	0.953322i	$0.402360\pi$
$510$	−1.47263	−0.0652092
$511$	−23.2849	−1.03007
$512$	47.0166	2.07786
$513$	14.1940	0.626682
$514$	50.0703	2.20851
$515$	3.88600	0.171238
$516$	13.8479	0.609622
$517$	−10.5792	−0.465272
$518$	64.5522	2.83626
$519$	−3.51296	−0.154202
$520$	29.8295	1.30811
$521$	−19.9162	−0.872543	−0.436272	−	0.899815i	$-0.643701\pi$
$521$	−19.9162	−0.872543	−0.436272	+	0.899815i	$0.643701\pi$
$522$	−6.34861	−0.277871
$523$	20.7161	0.905850	0.452925	−	0.891549i	$-0.350381\pi$
$523$	20.7161	0.905850	0.452925	+	0.891549i	$0.350381\pi$
$524$	−75.0992	−3.28073
$525$	−5.96672	−0.260409
$526$	−19.7082	−0.859318
$527$	−6.56480	−0.285967
$528$	−6.68457	−0.290909
$529$	1.00000	0.0434783
$530$	2.59445	0.112696
$531$	−18.0017	−0.781205
$532$	−72.5778	−3.14665
$533$	2.74614	0.118949
$534$	4.43254	0.191815
$535$	−17.1642	−0.742071
$536$	109.521	4.73058
$537$	−8.72369	−0.376455
$538$	43.3288	1.86804
$539$	3.87023	0.166703
$540$	13.9467	0.600172
$541$	−7.07231	−0.304063	−0.152031	−	0.988376i	$-0.548581\pi$
$541$	−7.07231	−0.304063	−0.152031	+	0.988376i	$0.548581\pi$
$542$	4.11851	0.176905
$543$	0.911879	0.0391325
$544$	9.62944	0.412859
$545$	14.1537	0.606276
$546$	16.0917	0.688661
$547$	−21.4137	−0.915585	−0.457792	−	0.889059i	$-0.651360\pi$
$547$	−21.4137	−0.915585	−0.457792	+	0.889059i	$0.651360\pi$
$548$	79.8049	3.40910
$549$	−29.5362	−1.26057
$550$	15.6284	0.666397
$551$	−4.43867	−0.189094
$552$	−3.47220	−0.147787
$553$	−6.64590	−0.282612
$554$	−9.29304	−0.394824
$555$	−4.15256	−0.176266
$556$	−66.4139	−2.81658
$557$	22.6576	0.960034	0.480017	−	0.877259i	$-0.340630\pi$
$557$	22.6576	0.960034	0.480017	+	0.877259i	$0.340630\pi$
$558$	42.4009	1.79497
$559$	24.2512	1.02571
$560$	−28.2114	−1.19215
$561$	0.840974	0.0355060
$562$	−30.7754	−1.29818
$563$	17.3308	0.730406	0.365203	−	0.930928i	$-0.381000\pi$
$563$	17.3308	0.730406	0.365203	+	0.930928i	$0.381000\pi$
$564$	15.9917	0.673373
$565$	3.94926	0.166146
$566$	19.9395	0.838121
$567$	−21.1706	−0.889080
$568$	−3.83798	−0.161038
$569$	−5.81475	−0.243767	−0.121883	−	0.992544i	$-0.538893\pi$
$569$	−5.81475	−0.243767	−0.121883	+	0.992544i	$0.538893\pi$
$570$	6.65001	0.278538
$571$	34.8800	1.45968	0.729841	−	0.683616i	$-0.239594\pi$
$571$	34.8800	1.45968	0.729841	+	0.683616i	$0.239594\pi$
$572$	−29.5915	−1.23728
$573$	12.6097	0.526778
$574$	−5.38306	−0.224684
$575$	3.91669	0.163337
$576$	−13.7549	−0.573119
$577$	−36.3441	−1.51303	−0.756513	−	0.653979i	$-0.773099\pi$
$577$	−36.3441	−1.51303	−0.756513	+	0.653979i	$0.773099\pi$
$578$	40.8797	1.70037
$579$	2.90457	0.120710
$580$	−4.36134	−0.181095
$581$	−51.3750	−2.13139
$582$	−1.69638	−0.0703171
$583$	−1.48161	−0.0613620
$584$	−53.0718	−2.19613
$585$	11.6945	0.483508
$586$	−64.5150	−2.66509
$587$	−18.0171	−0.743646	−0.371823	−	0.928304i	$-0.621267\pi$
$587$	−18.0171	−0.743646	−0.371823	+	0.928304i	$0.621267\pi$
$588$	−5.85033	−0.241263
$589$	29.6449	1.22150
$590$	−17.6144	−0.725173
$591$	0.989263	0.0406928
$592$	70.9861	2.91751
$593$	9.37467	0.384971	0.192486	−	0.981300i	$-0.438345\pi$
$593$	9.37467	0.384971	0.192486	+	0.981300i	$0.438345\pi$
$594$	−11.3442	−0.465459
$595$	3.54923	0.145504
$596$	−17.4747	−0.715792
$597$	−4.36930	−0.178823
$598$	−10.5630	−0.431951
$599$	−14.0152	−0.572644	−0.286322	−	0.958133i	$-0.592433\pi$
$599$	−14.0152	−0.572644	−0.286322	+	0.958133i	$0.592433\pi$
$600$	−13.5996	−0.555199
$601$	−36.6407	−1.49461	−0.747303	−	0.664483i	$-0.768652\pi$
$601$	−36.6407	−1.49461	−0.747303	+	0.664483i	$0.768652\pi$
$602$	−47.5377	−1.93749
$603$	42.9372	1.74854
$604$	35.8964	1.46060
$605$	−8.98051	−0.365110
$606$	18.0702	0.734050
$607$	−33.0031	−1.33956	−0.669778	−	0.742561i	$-0.733611\pi$
$607$	−33.0031	−1.33956	−0.669778	+	0.742561i	$0.733611\pi$
$608$	−43.4840	−1.76351
$609$	−1.35439	−0.0548826
$610$	−28.9008	−1.17016
$611$	28.0054	1.13298
$612$	14.3615	0.580531
$613$	−39.0190	−1.57596	−0.787981	−	0.615699i	$-0.788874\pi$
$613$	−39.0190	−1.57596	−0.787981	+	0.615699i	$0.788874\pi$
$614$	66.8695	2.69863
$615$	0.346286	0.0139636
$616$	33.3918	1.34539
$617$	−0.577879	−0.0232645	−0.0116323	−	0.999932i	$-0.503703\pi$
$617$	−0.577879	−0.0232645	−0.0116323	+	0.999932i	$0.503703\pi$
$618$	4.77802	0.192200
$619$	25.8612	1.03945	0.519724	−	0.854334i	$-0.326035\pi$
$619$	25.8612	1.03945	0.519724	+	0.854334i	$0.326035\pi$
$620$	29.1284	1.16983
$621$	−2.84302	−0.114086
$622$	−30.9411	−1.24063
$623$	−10.6830	−0.428005
$624$	17.6956	0.708389
$625$	9.92395	0.396958
$626$	9.47964	0.378883
$627$	−3.79762	−0.151662
$628$	−36.5667	−1.45917
$629$	−8.93064	−0.356088
$630$	−22.9239	−0.913309
$631$	−29.4821	−1.17366	−0.586832	−	0.809709i	$-0.699625\pi$
$631$	−29.4821	−1.17366	−0.586832	+	0.809709i	$0.699625\pi$
$632$	−15.1476	−0.602537
$633$	0.725996	0.0288557
$634$	23.9599	0.951569
$635$	14.1623	0.562015
$636$	2.23964	0.0888073
$637$	−10.2454	−0.405936
$638$	3.54749	0.140447
$639$	−1.50466	−0.0595235
$640$	4.67154	0.184659
$641$	21.6399	0.854727	0.427363	−	0.904080i	$-0.359443\pi$
$641$	21.6399	0.854727	0.427363	+	0.904080i	$0.359443\pi$
$642$	−21.1041	−0.832914
$643$	−17.4356	−0.687594	−0.343797	−	0.939044i	$-0.611713\pi$
$643$	−17.4356	−0.687594	−0.343797	+	0.939044i	$0.611713\pi$
$644$	14.5371	0.572842
$645$	3.05804	0.120410
$646$	14.3017	0.562695
$647$	12.3634	0.486054	0.243027	−	0.970020i	$-0.421860\pi$
$647$	12.3634	0.486054	0.243027	+	0.970020i	$0.421860\pi$
$648$	−48.2527	−1.89554
$649$	10.0590	0.394851
$650$	−41.3718	−1.62274
$651$	9.04566	0.354527
$652$	−7.66243	−0.300084
$653$	−1.28030	−0.0501019	−0.0250510	−	0.999686i	$-0.507975\pi$
$653$	−1.28030	−0.0501019	−0.0250510	+	0.999686i	$0.507975\pi$
$654$	17.4026	0.680495
$655$	−16.5842	−0.647997
$656$	−5.91959	−0.231121
$657$	−20.8066	−0.811742
$658$	−54.8970	−2.14011
$659$	35.6733	1.38964	0.694818	−	0.719186i	$-0.255485\pi$
$659$	35.6733	1.38964	0.694818	+	0.719186i	$0.255485\pi$
$660$	−3.73145	−0.145247
$661$	−16.9333	−0.658628	−0.329314	−	0.944220i	$-0.606817\pi$
$661$	−16.9333	−0.658628	−0.329314	+	0.944220i	$0.606817\pi$
$662$	−30.2100	−1.17415
$663$	−2.22625	−0.0864602
$664$	−117.096	−4.54419
$665$	−16.0274	−0.621515
$666$	57.6815	2.23511
$667$	0.889051	0.0344242
$668$	14.2592	0.551704
$669$	6.63836	0.256654
$670$	42.0134	1.62312
$671$	16.5043	0.637143
$672$	−13.2684	−0.511841
$673$	−4.97991	−0.191961	−0.0959806	−	0.995383i	$-0.530599\pi$
$673$	−4.97991	−0.191961	−0.0959806	+	0.995383i	$0.530599\pi$
$674$	−23.2237	−0.894543
$675$	−11.1352	−0.428595
$676$	17.0635	0.656287
$677$	21.8102	0.838235	0.419117	−	0.907932i	$-0.362340\pi$
$677$	21.8102	0.838235	0.419117	+	0.907932i	$0.362340\pi$
$678$	4.85580	0.186486
$679$	4.08849	0.156902
$680$	8.08952	0.310219
$681$	−9.71834	−0.372407
$682$	−23.6929	−0.907249
$683$	27.0346	1.03445	0.517224	−	0.855850i	$-0.326965\pi$
$683$	27.0346	1.03445	0.517224	+	0.855850i	$0.326965\pi$
$684$	−64.8529	−2.47971
$685$	17.6233	0.673353
$686$	−35.8570	−1.36903
$687$	2.07964	0.0793434
$688$	−52.2758	−1.99300
$689$	3.92215	0.149422
$690$	−1.33198	−0.0507075
$691$	−38.9043	−1.47999	−0.739994	−	0.672614i	$-0.765172\pi$
$691$	−38.9043	−1.47999	−0.739994	+	0.672614i	$0.765172\pi$
$692$	33.5224	1.27433
$693$	13.0911	0.497290
$694$	−73.0867	−2.77433
$695$	−14.6662	−0.556321
$696$	−3.08697	−0.117011
$697$	0.744733	0.0282088
$698$	2.59099	0.0980703
$699$	9.99015	0.377862
$700$	56.9374	2.15203
$701$	−11.4857	−0.433809	−0.216905	−	0.976193i	$-0.569596\pi$
$701$	−11.4857	−0.433809	−0.216905	+	0.976193i	$0.569596\pi$
$702$	30.0307	1.13343
$703$	40.3284	1.52101
$704$	7.68598	0.289676
$705$	3.53146	0.133002
$706$	−44.2825	−1.66659
$707$	−43.5514	−1.63792
$708$	−15.2054	−0.571456
$709$	−15.9828	−0.600248	−0.300124	−	0.953900i	$-0.597028\pi$
$709$	−15.9828	−0.600248	−0.300124	+	0.953900i	$0.597028\pi$
$710$	−1.47229	−0.0552541
$711$	−5.93853	−0.222712
$712$	−24.3490	−0.912519
$713$	−5.93778	−0.222371
$714$	4.36394	0.163316
$715$	−6.53469	−0.244384
$716$	83.2457	3.11104
$717$	1.11221	0.0415361
$718$	11.4229	0.426298
$719$	−2.39711	−0.0893971	−0.0446986	−	0.999001i	$-0.514233\pi$
$719$	−2.39711	−0.0893971	−0.0446986	+	0.999001i	$0.514233\pi$
$720$	−25.2087	−0.939473
$721$	−11.5156	−0.428864
$722$	−15.3541	−0.571421
$723$	7.41499	0.275766
$724$	−8.70159	−0.323392
$725$	3.48214	0.129323
$726$	−11.0420	−0.409806
$727$	40.1501	1.48909	0.744543	−	0.667575i	$-0.232668\pi$
$727$	40.1501	1.48909	0.744543	+	0.667575i	$0.232668\pi$
$728$	−88.3955	−3.27616
$729$	−14.7046	−0.544614
$730$	−20.3590	−0.753519
$731$	6.57673	0.243249
$732$	−24.9483	−0.922116
$733$	−46.0439	−1.70067	−0.850335	−	0.526242i	$-0.823601\pi$
$733$	−46.0439	−1.70067	−0.850335	+	0.526242i	$0.823601\pi$
$734$	72.8207	2.68786
$735$	−1.29193	−0.0476535
$736$	8.70970	0.321044
$737$	−23.9926	−0.883778
$738$	−4.81010	−0.177062
$739$	−4.26930	−0.157049	−0.0785244	−	0.996912i	$-0.525021\pi$
$739$	−4.26930	−0.157049	−0.0785244	+	0.996912i	$0.525021\pi$
$740$	39.6258	1.45667
$741$	10.0531	0.369311
$742$	−7.68830	−0.282246
$743$	−8.38114	−0.307474	−0.153737	−	0.988112i	$-0.549131\pi$
$743$	−8.38114	−0.307474	−0.153737	+	0.988112i	$0.549131\pi$
$744$	20.6172	0.755862
$745$	−3.85894	−0.141381
$746$	37.1593	1.36050
$747$	−45.9068	−1.67964
$748$	−8.02499	−0.293423
$749$	50.8636	1.85852
$750$	−11.8768	−0.433680
$751$	−52.9722	−1.93298	−0.966491	−	0.256702i	$-0.917364\pi$
$751$	−52.9722	−1.93298	−0.966491	+	0.256702i	$0.917364\pi$
$752$	−60.3686	−2.20142
$753$	0.400299	0.0145877
$754$	−9.39101	−0.342000
$755$	7.92700	0.288493
$756$	−41.3293	−1.50313
$757$	−4.46244	−0.162190	−0.0810951	−	0.996706i	$-0.525842\pi$
$757$	−4.46244	−0.162190	−0.0810951	+	0.996706i	$0.525842\pi$
$758$	−1.18654	−0.0430971
$759$	0.760650	0.0276099
$760$	−36.5301	−1.32509
$761$	−21.1643	−0.767205	−0.383602	−	0.923498i	$-0.625317\pi$
$761$	−21.1643	−0.767205	−0.383602	+	0.923498i	$0.625317\pi$
$762$	17.4133	0.630816
$763$	−41.9425	−1.51842
$764$	−120.328	−4.35331
$765$	3.17146	0.114664
$766$	−18.1983	−0.657532
$767$	−26.6285	−0.961499
$768$	10.6740	0.385164
$769$	39.2220	1.41438	0.707191	−	0.707022i	$-0.249962\pi$
$769$	39.2220	1.41438	0.707191	+	0.707022i	$0.249962\pi$
$770$	12.8095	0.461621
$771$	9.54488	0.343750
$772$	−27.7168	−0.997551
$773$	−54.3795	−1.95589	−0.977947	−	0.208854i	$-0.933027\pi$
$773$	−54.3795	−1.95589	−0.977947	+	0.208854i	$0.933027\pi$
$774$	−42.4780	−1.52684
$775$	−23.2564	−0.835396
$776$	9.31862	0.334519
$777$	12.3055	0.441459
$778$	3.16818	0.113585
$779$	−3.36302	−0.120493
$780$	9.87799	0.353689
$781$	0.840780	0.0300855
$782$	−2.86459	−0.102438
$783$	−2.52759	−0.0903287
$784$	22.0849	0.788747
$785$	−8.07504	−0.288211
$786$	−20.3910	−0.727324
$787$	−44.0280	−1.56943	−0.784714	−	0.619857i	$-0.787190\pi$
$787$	−44.0280	−1.56943	−0.784714	+	0.619857i	$0.787190\pi$
$788$	−9.44003	−0.336287
$789$	−3.75696	−0.133751
$790$	−5.81077	−0.206738
$791$	−11.7031	−0.416114
$792$	29.8377	1.06024
$793$	−43.6906	−1.55150
$794$	−19.5813	−0.694913
$795$	0.494579	0.0175409
$796$	41.6940	1.47780
$797$	10.5976	0.375388	0.187694	−	0.982228i	$-0.439899\pi$
$797$	10.5976	0.375388	0.187694	+	0.982228i	$0.439899\pi$
$798$	−19.7064	−0.697599
$799$	7.59486	0.268687
$800$	34.1132	1.20609
$801$	−9.54593	−0.337289
$802$	−50.3439	−1.77771
$803$	11.6264	0.410286
$804$	36.2677	1.27906
$805$	3.21023	0.113146
$806$	62.7205	2.20923
$807$	8.25974	0.290757
$808$	−99.2638	−3.49209
$809$	11.9519	0.420208	0.210104	−	0.977679i	$-0.432620\pi$
$809$	11.9519	0.420208	0.210104	+	0.977679i	$0.432620\pi$
$810$	−18.5103	−0.650385
$811$	35.9658	1.26293	0.631466	−	0.775404i	$-0.282454\pi$
$811$	35.9658	1.26293	0.631466	+	0.775404i	$0.282454\pi$
$812$	12.9242	0.453552
$813$	0.785109	0.0275350
$814$	−32.2314	−1.12971
$815$	−1.69210	−0.0592716
$816$	4.79890	0.167995
$817$	−29.6988	−1.03903
$818$	21.4479	0.749908
$819$	−34.6551	−1.21095
$820$	−3.30443	−0.115396
$821$	39.5656	1.38085	0.690424	−	0.723405i	$-0.257424\pi$
$821$	39.5656	1.38085	0.690424	+	0.723405i	$0.257424\pi$
$822$	21.6687	0.755783
$823$	−11.3838	−0.396815	−0.198408	−	0.980120i	$-0.563577\pi$
$823$	−11.3838	−0.396815	−0.198408	+	0.980120i	$0.563577\pi$
$824$	−26.2468	−0.914351
$825$	2.97923	0.103724
$826$	52.1978	1.81619
$827$	29.4020	1.02241	0.511204	−	0.859460i	$-0.329200\pi$
$827$	29.4020	1.02241	0.511204	+	0.859460i	$0.329200\pi$
$828$	12.9898	0.451428
$829$	−5.78035	−0.200760	−0.100380	−	0.994949i	$-0.532006\pi$
$829$	−5.78035	−0.200760	−0.100380	+	0.994949i	$0.532006\pi$
$830$	−44.9192	−1.55917
$831$	−1.77153	−0.0614537
$832$	−20.3465	−0.705388
$833$	−2.77846	−0.0962681
$834$	−18.0328	−0.624424
$835$	3.14886	0.108971
$836$	36.2387	1.25334
$837$	16.8812	0.583500
$838$	26.4353	0.913191
$839$	−27.6049	−0.953027	−0.476513	−	0.879167i	$-0.658100\pi$
$839$	−27.6049	−0.953027	−0.476513	+	0.879167i	$0.658100\pi$
$840$	−11.1466	−0.384594
$841$	−28.2096	−0.972744
$842$	−79.9105	−2.75390
$843$	−5.86671	−0.202060
$844$	−6.92781	−0.238465
$845$	3.76813	0.129628
$846$	−49.0539	−1.68651
$847$	26.6125	0.914417
$848$	−8.45460	−0.290332
$849$	3.80106	0.130452
$850$	−11.2197	−0.384834
$851$	−8.07764	−0.276898
$852$	−1.27094	−0.0435417
$853$	−50.8252	−1.74022	−0.870111	−	0.492856i	$-0.835953\pi$
$853$	−50.8252	−1.74022	−0.870111	+	0.492856i	$0.835953\pi$
$854$	85.6435	2.93066
$855$	−14.3215	−0.489784
$856$	115.930	3.96241
$857$	−56.0261	−1.91382	−0.956908	−	0.290392i	$-0.906214\pi$
$857$	−56.0261	−1.91382	−0.956908	+	0.290392i	$0.906214\pi$
$858$	−8.03471	−0.274301
$859$	−42.6447	−1.45502	−0.727509	−	0.686098i	$-0.759322\pi$
$859$	−42.6447	−1.45502	−0.727509	+	0.686098i	$0.759322\pi$
$860$	−29.1814	−0.995076
$861$	−1.02617	−0.0349718
$862$	−57.7745	−1.96781
$863$	0.0241911	0.000823476 0	0.000411738	−	1.00000i	$-0.499869\pi$
$863$	0.0241911	0.000823476 0	0.000411738		1.00000i	$0.499869\pi$
$864$	−24.7619	−0.842415
$865$	7.40275	0.251701
$866$	92.4471	3.14148
$867$	7.79288	0.264660
$868$	−86.3181	−2.92983
$869$	3.31835	0.112567
$870$	−1.18420	−0.0401480
$871$	63.5137	2.15208
$872$	−95.5967	−3.23731
$873$	3.65332	0.123646
$874$	12.9357	0.437558
$875$	28.6247	0.967690
$876$	−17.5747	−0.593793
$877$	36.6305	1.23692	0.618461	−	0.785815i	$-0.287756\pi$
$877$	36.6305	1.23692	0.618461	+	0.785815i	$0.287756\pi$
$878$	13.6266	0.459874
$879$	−12.2985	−0.414817
$880$	14.0862	0.474846
$881$	−13.7493	−0.463227	−0.231613	−	0.972808i	$-0.574400\pi$
$881$	−13.7493	−0.463227	−0.231613	+	0.972808i	$0.574400\pi$
$882$	17.9456	0.604261
$883$	−9.78357	−0.329243	−0.164622	−	0.986357i	$-0.552640\pi$
$883$	−9.78357	−0.329243	−0.164622	+	0.986357i	$0.552640\pi$
$884$	21.2439	0.714511
$885$	−3.35782	−0.112872
$886$	−63.6992	−2.14002
$887$	−0.0934998	−0.00313942	−0.00156971	−	0.999999i	$-0.500500\pi$
$887$	−0.0934998	−0.00313942	−0.00156971	+	0.999999i	$0.500500\pi$
$888$	28.0472	0.941203
$889$	−41.9681	−1.40757
$890$	−9.34057	−0.313097
$891$	10.5706	0.354130
$892$	−63.3465	−2.12100
$893$	−34.2964	−1.14768
$894$	−4.74475	−0.158688
$895$	18.3832	0.614482
$896$	−13.8435	−0.462478
$897$	−2.01361	−0.0672325
$898$	91.7807	3.06276
$899$	−5.27899	−0.176064
$900$	50.8772	1.69591
$901$	1.06366	0.0354356
$902$	2.68781	0.0894941
$903$	−9.06210	−0.301568
$904$	−26.6741	−0.887166
$905$	−1.92157	−0.0638753
$906$	9.74662	0.323810
$907$	−15.0213	−0.498775	−0.249387	−	0.968404i	$-0.580229\pi$
$907$	−15.0213	−0.498775	−0.249387	+	0.968404i	$0.580229\pi$
$908$	92.7371	3.07759
$909$	−38.9159	−1.29076
$910$	−33.9095	−1.12409
$911$	−7.85743	−0.260328	−0.130164	−	0.991492i	$-0.541550\pi$
$911$	−7.85743	−0.260328	−0.130164	+	0.991492i	$0.541550\pi$
$912$	−21.6706	−0.717584
$913$	25.6519	0.848956
$914$	18.5093	0.612232
$915$	−5.50934	−0.182133
$916$	−19.8450	−0.655697
$917$	49.1449	1.62291
$918$	8.14409	0.268795
$919$	22.0703	0.728031	0.364015	−	0.931393i	$-0.381406\pi$
$919$	22.0703	0.728031	0.364015	+	0.931393i	$0.381406\pi$
$920$	7.31687	0.241230
$921$	12.7473	0.420038
$922$	−7.22878	−0.238067
$923$	−2.22573	−0.0732608
$924$	11.0577	0.363770
$925$	−31.6377	−1.04024
$926$	−33.0794	−1.08706
$927$	−10.2899	−0.337966
$928$	7.74337	0.254189
$929$	−10.9985	−0.360848	−0.180424	−	0.983589i	$-0.557747\pi$
$929$	−10.9985	−0.360848	−0.180424	+	0.983589i	$0.557747\pi$
$930$	7.90898	0.259346
$931$	12.5468	0.411205
$932$	−95.3309	−3.12267
$933$	−5.89829	−0.193101
$934$	−45.3916	−1.48526
$935$	−1.77216	−0.0579558
$936$	−78.9870	−2.58177
$937$	0.663284	0.0216686	0.0108343	−	0.999941i	$-0.496551\pi$
$937$	0.663284	0.0216686	0.0108343	+	0.999941i	$0.496551\pi$
$938$	−124.501	−4.06511
$939$	1.80710	0.0589725
$940$	−33.6989	−1.09914
$941$	−33.1570	−1.08089	−0.540444	−	0.841380i	$-0.681744\pi$
$941$	−33.1570	−1.08089	−0.540444	+	0.841380i	$0.681744\pi$
$942$	−9.92864	−0.323493
$943$	0.673601	0.0219355
$944$	57.4004	1.86822
$945$	−9.12675	−0.296893
$946$	23.7360	0.771724
$947$	49.8714	1.62060	0.810302	−	0.586013i	$-0.199303\pi$
$947$	49.8714	1.62060	0.810302	+	0.586013i	$0.199303\pi$
$948$	−5.01609	−0.162915
$949$	−30.7776	−0.999083
$950$	50.6653	1.64380
$951$	4.56746	0.148110
$952$	−23.9722	−0.776944
$953$	35.9790	1.16547	0.582737	−	0.812661i	$-0.301982\pi$
$953$	35.9790	1.16547	0.582737	+	0.812661i	$0.301982\pi$
$954$	−6.86999	−0.222424
$955$	−26.5721	−0.859851
$956$	−10.6132	−0.343256
$957$	0.676257	0.0218603
$958$	67.1195	2.16853
$959$	−52.2243	−1.68641
$960$	−2.56567	−0.0828067
$961$	4.25720	0.137329
$962$	85.3238	2.75095
$963$	45.4499	1.46460
$964$	−70.7575	−2.27894
$965$	−6.12071	−0.197033
$966$	3.94713	0.126997
$967$	−6.85436	−0.220421	−0.110211	−	0.993908i	$-0.535153\pi$
$967$	−6.85436	−0.220421	−0.110211	+	0.993908i	$0.535153\pi$
$968$	60.6562	1.94956
$969$	2.72633	0.0875825
$970$	3.57473	0.114778
$971$	−40.5820	−1.30234	−0.651169	−	0.758933i	$-0.725721\pi$
$971$	−40.5820	−1.30234	−0.651169	+	0.758933i	$0.725721\pi$
$972$	−56.1781	−1.80191
$973$	43.4613	1.39330
$974$	−41.9855	−1.34530
$975$	−7.88670	−0.252576
$976$	94.1796	3.01462
$977$	−2.62549	−0.0839967	−0.0419984	−	0.999118i	$-0.513372\pi$
$977$	−2.62549	−0.0839967	−0.0419984	+	0.999118i	$0.513372\pi$
$978$	−2.08051	−0.0665274
$979$	5.33411	0.170479
$980$	12.3282	0.393811
$981$	−37.4783	−1.19659
$982$	50.9323	1.62531
$983$	−18.9340	−0.603902	−0.301951	−	0.953323i	$-0.597638\pi$
$983$	−18.9340	−0.603902	−0.301951	+	0.953323i	$0.597638\pi$
$984$	−2.33888	−0.0745608
$985$	−2.08464	−0.0664223
$986$	−2.54677	−0.0811057
$987$	−10.4650	−0.333104
$988$	−95.9320	−3.05200
$989$	5.94857	0.189153
$990$	11.4461	0.363780
$991$	−12.0335	−0.382258	−0.191129	−	0.981565i	$-0.561215\pi$
$991$	−12.0335	−0.382258	−0.191129	+	0.981565i	$0.561215\pi$
$992$	−51.7163	−1.64199
$993$	−5.75892	−0.182754
$994$	4.36294	0.138384
$995$	9.20729	0.291891
$996$	−38.7761	−1.22867
$997$	12.0982	0.383153	0.191577	−	0.981478i	$-0.438640\pi$
$997$	12.0982	0.383153	0.191577	+	0.981478i	$0.438640\pi$
$998$	60.1829	1.90506
$999$	22.9649	0.726577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.7	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.7	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59099 q^{2} -0.493919 q^{3} +4.71322 q^{4} +1.04082 q^{5} +1.27974 q^{6} -3.08433 q^{7} -7.02991 q^{8} -2.75604 q^{9} +O(q^{10})\)	\(q-2.59099 q^{2} -0.493919 q^{3} +4.71322 q^{4} +1.04082 q^{5} +1.27974 q^{6} -3.08433 q^{7} -7.02991 q^{8} -2.75604 q^{9} -2.69675 q^{10} +1.54003 q^{11} -2.32795 q^{12} -4.07681 q^{13} +7.99146 q^{14} -0.514081 q^{15} +8.78797 q^{16} -1.10560 q^{17} +7.14088 q^{18} +4.99259 q^{19} +4.90561 q^{20} +1.52341 q^{21} -3.99020 q^{22} -1.00000 q^{23} +3.47220 q^{24} -3.91669 q^{25} +10.5630 q^{26} +2.84302 q^{27} -14.5371 q^{28} -0.889051 q^{29} +1.33198 q^{30} +5.93778 q^{31} -8.70970 q^{32} -0.760650 q^{33} +2.86459 q^{34} -3.21023 q^{35} -12.9898 q^{36} +8.07764 q^{37} -12.9357 q^{38} +2.01361 q^{39} -7.31687 q^{40} -0.673601 q^{41} -3.94713 q^{42} -5.94857 q^{43} +7.25850 q^{44} -2.86855 q^{45} +2.59099 q^{46} -6.86946 q^{47} -4.34054 q^{48} +2.51309 q^{49} +10.1481 q^{50} +0.546076 q^{51} -19.2149 q^{52} -0.962065 q^{53} -7.36622 q^{54} +1.60290 q^{55} +21.6825 q^{56} -2.46593 q^{57} +2.30352 q^{58} +6.53170 q^{59} -2.42297 q^{60} +10.7169 q^{61} -15.3847 q^{62} +8.50055 q^{63} +4.99079 q^{64} -4.24322 q^{65} +1.97084 q^{66} -15.5793 q^{67} -5.21093 q^{68} +0.493919 q^{69} +8.31767 q^{70} +0.545950 q^{71} +19.3747 q^{72} +7.54944 q^{73} -20.9291 q^{74} +1.93453 q^{75} +23.5312 q^{76} -4.74996 q^{77} -5.21724 q^{78} +2.15473 q^{79} +9.14670 q^{80} +6.86391 q^{81} +1.74529 q^{82} +16.6568 q^{83} +7.18015 q^{84} -1.15073 q^{85} +15.4127 q^{86} +0.439119 q^{87} -10.8263 q^{88} +3.46364 q^{89} +7.43237 q^{90} +12.5742 q^{91} -4.71322 q^{92} -2.93278 q^{93} +17.7987 q^{94} +5.19639 q^{95} +4.30189 q^{96} -1.32557 q^{97} -6.51137 q^{98} -4.24439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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