LMFDB - Embedded newform 6023.2.a.d.1.117

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.117
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09809 q^{2} -2.95727 q^{3} +2.40199 q^{4} +2.07639 q^{5} -6.20463 q^{6} -4.57253 q^{7} +0.843406 q^{8} +5.74546 q^{9} +O(q^{10})$	\(q+2.09809 q^{2} -2.95727 q^{3} +2.40199 q^{4} +2.07639 q^{5} -6.20463 q^{6} -4.57253 q^{7} +0.843406 q^{8} +5.74546 q^{9} +4.35645 q^{10} -3.38662 q^{11} -7.10333 q^{12} +5.90519 q^{13} -9.59359 q^{14} -6.14045 q^{15} -3.03443 q^{16} -0.0690138 q^{17} +12.0545 q^{18} -1.00000 q^{19} +4.98746 q^{20} +13.5222 q^{21} -7.10543 q^{22} -5.51076 q^{23} -2.49418 q^{24} -0.688608 q^{25} +12.3896 q^{26} -8.11908 q^{27} -10.9832 q^{28} -4.92468 q^{29} -12.8832 q^{30} +8.74743 q^{31} -8.05333 q^{32} +10.0151 q^{33} -0.144797 q^{34} -9.49436 q^{35} +13.8005 q^{36} +3.85663 q^{37} -2.09809 q^{38} -17.4633 q^{39} +1.75124 q^{40} +5.50102 q^{41} +28.3709 q^{42} -3.35099 q^{43} -8.13461 q^{44} +11.9298 q^{45} -11.5621 q^{46} +8.58721 q^{47} +8.97364 q^{48} +13.9081 q^{49} -1.44476 q^{50} +0.204093 q^{51} +14.1842 q^{52} -8.61712 q^{53} -17.0346 q^{54} -7.03193 q^{55} -3.85650 q^{56} +2.95727 q^{57} -10.3324 q^{58} -8.82941 q^{59} -14.7493 q^{60} +7.51328 q^{61} +18.3529 q^{62} -26.2713 q^{63} -10.8278 q^{64} +12.2615 q^{65} +21.0127 q^{66} -7.81128 q^{67} -0.165770 q^{68} +16.2968 q^{69} -19.9200 q^{70} +10.3499 q^{71} +4.84576 q^{72} +13.8978 q^{73} +8.09157 q^{74} +2.03640 q^{75} -2.40199 q^{76} +15.4854 q^{77} -36.6395 q^{78} -6.83957 q^{79} -6.30066 q^{80} +6.77396 q^{81} +11.5416 q^{82} -2.21272 q^{83} +32.4802 q^{84} -0.143300 q^{85} -7.03068 q^{86} +14.5636 q^{87} -2.85629 q^{88} -2.64224 q^{89} +25.0298 q^{90} -27.0017 q^{91} -13.2368 q^{92} -25.8685 q^{93} +18.0167 q^{94} -2.07639 q^{95} +23.8159 q^{96} +6.83868 q^{97} +29.1804 q^{98} -19.4577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	2.09809	1.48357	0.741787	−	0.670635i	$-0.233978\pi$
$2$	2.09809	1.48357	0.741787	+	0.670635i	$0.233978\pi$
$3$	−2.95727	−1.70738	−0.853691	−	0.520780i	$-0.825641\pi$
$3$	−2.95727	−1.70738	−0.853691	+	0.520780i	$0.825641\pi$
$4$	2.40199	1.20099
$5$	2.07639	0.928589	0.464295	−	0.885681i	$-0.346308\pi$
$5$	2.07639	0.928589	0.464295	+	0.885681i	$0.346308\pi$
$6$	−6.20463	−2.53303
$7$	−4.57253	−1.72826	−0.864128	−	0.503272i	$-0.832129\pi$
$7$	−4.57253	−1.72826	−0.864128	+	0.503272i	$0.832129\pi$
$8$	0.843406	0.298189
$9$	5.74546	1.91515
$10$	4.35645	1.37763
$11$	−3.38662	−1.02110	−0.510551	−	0.859847i	$-0.670559\pi$
$11$	−3.38662	−1.02110	−0.510551	+	0.859847i	$0.670559\pi$
$12$	−7.10333	−2.05056
$13$	5.90519	1.63780	0.818902	−	0.573933i	$-0.194583\pi$
$13$	5.90519	1.63780	0.818902	+	0.573933i	$0.194583\pi$
$14$	−9.59359	−2.56400
$15$	−6.14045	−1.58546
$16$	−3.03443	−0.758608
$17$	−0.0690138	−0.0167383	−0.00836916	−	0.999965i	$-0.502664\pi$
$17$	−0.0690138	−0.0167383	−0.00836916	+	0.999965i	$0.502664\pi$
$18$	12.0545	2.84127
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.98746	1.11523
$21$	13.5222	2.95079
$22$	−7.10543	−1.51488
$23$	−5.51076	−1.14907	−0.574537	−	0.818479i	$-0.694818\pi$
$23$	−5.51076	−1.14907	−0.574537	+	0.818479i	$0.694818\pi$
$24$	−2.49418	−0.509122
$25$	−0.688608	−0.137722
$26$	12.3896	2.42980
$27$	−8.11908	−1.56252
$28$	−10.9832	−2.07562
$29$	−4.92468	−0.914489	−0.457245	−	0.889341i	$-0.651164\pi$
$29$	−4.92468	−0.914489	−0.457245	+	0.889341i	$0.651164\pi$
$30$	−12.8832	−2.35214
$31$	8.74743	1.57109	0.785543	−	0.618808i	$-0.212384\pi$
$31$	8.74743	1.57109	0.785543	+	0.618808i	$0.212384\pi$
$32$	−8.05333	−1.42364
$33$	10.0151	1.74341
$34$	−0.144797	−0.0248325
$35$	−9.49436	−1.60484
$36$	13.8005	2.30009
$37$	3.85663	0.634027	0.317013	−	0.948421i	$-0.397320\pi$
$37$	3.85663	0.634027	0.317013	+	0.948421i	$0.397320\pi$
$38$	−2.09809	−0.340355
$39$	−17.4633	−2.79636
$40$	1.75124	0.276895
$41$	5.50102	0.859115	0.429557	−	0.903040i	$-0.358670\pi$
$41$	5.50102	0.859115	0.429557	+	0.903040i	$0.358670\pi$
$42$	28.3709	4.37772
$43$	−3.35099	−0.511021	−0.255510	−	0.966806i	$-0.582243\pi$
$43$	−3.35099	−0.511021	−0.255510	+	0.966806i	$0.582243\pi$
$44$	−8.13461	−1.22634
$45$	11.9298	1.77839
$46$	−11.5621	−1.70474
$47$	8.58721	1.25257	0.626287	−	0.779593i	$-0.284574\pi$
$47$	8.58721	1.25257	0.626287	+	0.779593i	$0.284574\pi$
$48$	8.97364	1.29523
$49$	13.9081	1.98687
$50$	−1.44476	−0.204320
$51$	0.204093	0.0285787
$52$	14.1842	1.96699
$53$	−8.61712	−1.18365	−0.591826	−	0.806066i	$-0.701593\pi$
$53$	−8.61712	−1.18365	−0.591826	+	0.806066i	$0.701593\pi$
$54$	−17.0346	−2.31811
$55$	−7.03193	−0.948185
$56$	−3.85650	−0.515347
$57$	2.95727	0.391700
$58$	−10.3324	−1.35671
$59$	−8.82941	−1.14949	−0.574745	−	0.818332i	$-0.694899\pi$
$59$	−8.82941	−1.14949	−0.574745	+	0.818332i	$0.694899\pi$
$60$	−14.7493	−1.90412
$61$	7.51328	0.961977	0.480989	−	0.876727i	$-0.340278\pi$
$61$	7.51328	0.961977	0.480989	+	0.876727i	$0.340278\pi$
$62$	18.3529	2.33082
$63$	−26.2713	−3.30988
$64$	−10.8278	−1.35347
$65$	12.2615	1.52085
$66$	21.0127	2.58648
$67$	−7.81128	−0.954300	−0.477150	−	0.878822i	$-0.658330\pi$
$67$	−7.81128	−0.954300	−0.477150	+	0.878822i	$0.658330\pi$
$68$	−0.165770	−0.0201026
$69$	16.2968	1.96191
$70$	−19.9200	−2.38090
$71$	10.3499	1.22830	0.614151	−	0.789188i	$-0.289498\pi$
$71$	10.3499	1.22830	0.614151	+	0.789188i	$0.289498\pi$
$72$	4.84576	0.571078
$73$	13.8978	1.62662	0.813308	−	0.581833i	$-0.197664\pi$
$73$	13.8978	1.62662	0.813308	+	0.581833i	$0.197664\pi$
$74$	8.09157	0.940626
$75$	2.03640	0.235144
$76$	−2.40199	−0.275527
$77$	15.4854	1.76473
$78$	−36.6395	−4.14861
$79$	−6.83957	−0.769512	−0.384756	−	0.923018i	$-0.625714\pi$
$79$	−6.83957	−0.769512	−0.384756	+	0.923018i	$0.625714\pi$
$80$	−6.30066	−0.704435
$81$	6.77396	0.752662
$82$	11.5416	1.27456
$83$	−2.21272	−0.242878	−0.121439	−	0.992599i	$-0.538751\pi$
$83$	−2.21272	−0.242878	−0.121439	+	0.992599i	$0.538751\pi$
$84$	32.4802	3.54388
$85$	−0.143300	−0.0155430
$86$	−7.03068	−0.758137
$87$	14.5636	1.56138
$88$	−2.85629	−0.304482
$89$	−2.64224	−0.280077	−0.140039	−	0.990146i	$-0.544723\pi$
$89$	−2.64224	−0.280077	−0.140039	+	0.990146i	$0.544723\pi$
$90$	25.0298	2.63838
$91$	−27.0017	−2.83054
$92$	−13.2368	−1.38003
$93$	−25.8685	−2.68244
$94$	18.0167	1.85829
$95$	−2.07639	−0.213033
$96$	23.8159	2.43070
$97$	6.83868	0.694363	0.347182	−	0.937798i	$-0.387139\pi$
$97$	6.83868	0.694363	0.347182	+	0.937798i	$0.387139\pi$
$98$	29.1804	2.94767
$99$	−19.4577	−1.95557
$100$	−1.65403	−0.165403
$101$	−3.81718	−0.379824	−0.189912	−	0.981801i	$-0.560820\pi$
$101$	−3.81718	−0.379824	−0.189912	+	0.981801i	$0.560820\pi$
$102$	0.428205	0.0423986
$103$	15.3975	1.51716	0.758580	−	0.651580i	$-0.225894\pi$
$103$	15.3975	1.51716	0.758580	+	0.651580i	$0.225894\pi$
$104$	4.98047	0.488375
$105$	28.0774	2.74008
$106$	−18.0795	−1.75604
$107$	19.9401	1.92769	0.963843	−	0.266470i	$-0.0858572\pi$
$107$	19.9401	1.92769	0.963843	+	0.266470i	$0.0858572\pi$
$108$	−19.5019	−1.87657
$109$	−7.33340	−0.702413	−0.351206	−	0.936298i	$-0.614228\pi$
$109$	−7.33340	−0.702413	−0.351206	+	0.936298i	$0.614228\pi$
$110$	−14.7536	−1.40670
$111$	−11.4051	−1.08253
$112$	13.8750	1.31107
$113$	19.8435	1.86672	0.933358	−	0.358946i	$-0.116864\pi$
$113$	19.8435	1.86672	0.933358	+	0.358946i	$0.116864\pi$
$114$	6.20463	0.581117
$115$	−11.4425	−1.06702
$116$	−11.8290	−1.09830
$117$	33.9280	3.13665
$118$	−18.5249	−1.70536
$119$	0.315568	0.0289281
$120$	−5.17889	−0.472766
$121$	0.469163	0.0426512
$122$	15.7636	1.42716
$123$	−16.2680	−1.46684
$124$	21.0112	1.88686
$125$	−11.8118	−1.05648
$126$	−55.1196	−4.91045
$127$	22.2188	1.97160	0.985798	−	0.167934i	$-0.0537096\pi$
$127$	22.2188	1.97160	0.985798	+	0.167934i	$0.0537096\pi$
$128$	−6.61096	−0.584331
$129$	9.90978	0.872508
$130$	25.7257	2.25629
$131$	1.94268	0.169732	0.0848662	−	0.996392i	$-0.472954\pi$
$131$	1.94268	0.169732	0.0848662	+	0.996392i	$0.472954\pi$
$132$	24.0563	2.09383
$133$	4.57253	0.396489
$134$	−16.3888	−1.41577
$135$	−16.8584	−1.45094
$136$	−0.0582067	−0.00499118
$137$	−22.6864	−1.93823	−0.969114	−	0.246611i	$-0.920683\pi$
$137$	−22.6864	−1.93823	−0.969114	+	0.246611i	$0.920683\pi$
$138$	34.1922	2.91064
$139$	2.32631	0.197315	0.0986577	−	0.995121i	$-0.468545\pi$
$139$	2.32631	0.197315	0.0986577	+	0.995121i	$0.468545\pi$
$140$	−22.8053	−1.92740
$141$	−25.3947	−2.13862
$142$	21.7150	1.82228
$143$	−19.9986	−1.67237
$144$	−17.4342	−1.45285
$145$	−10.2255	−0.849185
$146$	29.1589	2.41321
$147$	−41.1300	−3.39234
$148$	9.26358	0.761462
$149$	−14.5235	−1.18981	−0.594904	−	0.803797i	$-0.702810\pi$
$149$	−14.5235	−1.18981	−0.594904	+	0.803797i	$0.702810\pi$
$150$	4.27256	0.348853
$151$	21.5678	1.75516	0.877580	−	0.479430i	$-0.159157\pi$
$151$	21.5678	1.75516	0.877580	+	0.479430i	$0.159157\pi$
$152$	−0.843406	−0.0684092
$153$	−0.396517	−0.0320565
$154$	32.4898	2.61810
$155$	18.1631	1.45889
$156$	−41.9465	−3.35841
$157$	11.3926	0.909225	0.454612	−	0.890689i	$-0.349778\pi$
$157$	11.3926	0.909225	0.454612	+	0.890689i	$0.349778\pi$
$158$	−14.3500	−1.14163
$159$	25.4832	2.02095
$160$	−16.7218	−1.32198
$161$	25.1981	1.98589
$162$	14.2124	1.11663
$163$	2.60493	0.204034	0.102017	−	0.994783i	$-0.467470\pi$
$163$	2.60493	0.204034	0.102017	+	0.994783i	$0.467470\pi$
$164$	13.2134	1.03179
$165$	20.7953	1.61892
$166$	−4.64250	−0.360328
$167$	−11.0712	−0.856717	−0.428358	−	0.903609i	$-0.640908\pi$
$167$	−11.0712	−0.856717	−0.428358	+	0.903609i	$0.640908\pi$
$168$	11.4047	0.879894
$169$	21.8712	1.68240
$170$	−0.300656	−0.0230592
$171$	−5.74546	−0.439367
$172$	−8.04903	−0.613733
$173$	−10.8150	−0.822247	−0.411123	−	0.911580i	$-0.634863\pi$
$173$	−10.8150	−0.822247	−0.411123	+	0.911580i	$0.634863\pi$
$174$	30.5558	2.31643
$175$	3.14868	0.238018
$176$	10.2765	0.774617
$177$	26.1110	1.96262
$178$	−5.54367	−0.415515
$179$	13.7373	1.02677	0.513387	−	0.858157i	$-0.328391\pi$
$179$	13.7373	1.02677	0.513387	+	0.858157i	$0.328391\pi$
$180$	28.6553	2.13584
$181$	25.8190	1.91911	0.959556	−	0.281518i	$-0.0908380\pi$
$181$	25.8190	1.91911	0.959556	+	0.281518i	$0.0908380\pi$
$182$	−56.6520	−4.19932
$183$	−22.2188	−1.64246
$184$	−4.64781	−0.342641
$185$	8.00787	0.588750
$186$	−54.2746	−3.97960
$187$	0.233723	0.0170915
$188$	20.6264	1.50433
$189$	37.1248	2.70043
$190$	−4.35645	−0.316050
$191$	−20.4813	−1.48197	−0.740986	−	0.671521i	$-0.765641\pi$
$191$	−20.4813	−1.48197	−0.740986	+	0.671521i	$0.765641\pi$
$192$	32.0206	2.31089
$193$	20.5655	1.48034	0.740168	−	0.672422i	$-0.234746\pi$
$193$	20.5655	1.48034	0.740168	+	0.672422i	$0.234746\pi$
$194$	14.3482	1.03014
$195$	−36.2605	−2.59667
$196$	33.4070	2.38621
$197$	13.6758	0.974363	0.487182	−	0.873301i	$-0.338025\pi$
$197$	13.6758	0.974363	0.487182	+	0.873301i	$0.338025\pi$
$198$	−40.8240	−2.90123
$199$	27.2960	1.93496	0.967479	−	0.252950i	$-0.0814009\pi$
$199$	27.2960	1.93496	0.967479	+	0.252950i	$0.0814009\pi$
$200$	−0.580776	−0.0410671
$201$	23.1001	1.62935
$202$	−8.00880	−0.563497
$203$	22.5183	1.58047
$204$	0.490228	0.0343228
$205$	11.4223	0.797765
$206$	32.3053	2.25082
$207$	−31.6619	−2.20065
$208$	−17.9189	−1.24245
$209$	3.38662	0.234257
$210$	58.9090	4.06511
$211$	22.2830	1.53403	0.767014	−	0.641631i	$-0.221742\pi$
$211$	22.2830	1.53403	0.767014	+	0.641631i	$0.221742\pi$
$212$	−20.6982	−1.42156
$213$	−30.6074	−2.09718
$214$	41.8362	2.85987
$215$	−6.95795	−0.474528
$216$	−6.84768	−0.465926
$217$	−39.9979	−2.71524
$218$	−15.3861	−1.04208
$219$	−41.0996	−2.77726
$220$	−16.8906	−1.13876
$221$	−0.407540	−0.0274141
$222$	−23.9290	−1.60601
$223$	27.0644	1.81237	0.906184	−	0.422884i	$-0.138982\pi$
$223$	27.0644	1.81237	0.906184	+	0.422884i	$0.138982\pi$
$224$	36.8241	2.46041
$225$	−3.95637	−0.263758
$226$	41.6334	2.76941
$227$	−12.1678	−0.807607	−0.403803	−	0.914846i	$-0.632312\pi$
$227$	−12.1678	−0.807607	−0.403803	+	0.914846i	$0.632312\pi$
$228$	7.10333	0.470430
$229$	−3.47262	−0.229477	−0.114739	−	0.993396i	$-0.536603\pi$
$229$	−3.47262	−0.229477	−0.114739	+	0.993396i	$0.536603\pi$
$230$	−24.0074	−1.58300
$231$	−45.7946	−3.01306
$232$	−4.15350	−0.272691
$233$	−9.11051	−0.596849	−0.298425	−	0.954433i	$-0.596461\pi$
$233$	−9.11051	−0.596849	−0.298425	+	0.954433i	$0.596461\pi$
$234$	71.1841	4.65345
$235$	17.8304	1.16313
$236$	−21.2081	−1.38053
$237$	20.2265	1.31385
$238$	0.662091	0.0429170
$239$	4.04094	0.261387	0.130693	−	0.991423i	$-0.458280\pi$
$239$	4.04094	0.261387	0.130693	+	0.991423i	$0.458280\pi$
$240$	18.6328	1.20274
$241$	−14.3931	−0.927143	−0.463572	−	0.886059i	$-0.653432\pi$
$241$	−14.3931	−0.927143	−0.463572	+	0.886059i	$0.653432\pi$
$242$	0.984347	0.0632762
$243$	4.32481	0.277437
$244$	18.0468	1.15533
$245$	28.8786	1.84498
$246$	−34.1318	−2.17616
$247$	−5.90519	−0.375738
$248$	7.37763	0.468480
$249$	6.54363	0.414686
$250$	−24.7822	−1.56736
$251$	14.6803	0.926611	0.463306	−	0.886199i	$-0.346663\pi$
$251$	14.6803	0.926611	0.463306	+	0.886199i	$0.346663\pi$
$252$	−63.1034	−3.97514
$253$	18.6628	1.17332
$254$	46.6170	2.92501
$255$	0.423776	0.0265379
$256$	7.78511	0.486570
$257$	20.2347	1.26221	0.631103	−	0.775699i	$-0.282602\pi$
$257$	20.2347	1.26221	0.631103	+	0.775699i	$0.282602\pi$
$258$	20.7916	1.29443
$259$	−17.6346	−1.09576
$260$	29.4519	1.82653
$261$	−28.2945	−1.75139
$262$	4.07591	0.251811
$263$	−16.6408	−1.02612	−0.513059	−	0.858354i	$-0.671488\pi$
$263$	−16.6408	−1.02612	−0.513059	+	0.858354i	$0.671488\pi$
$264$	8.44683	0.519866
$265$	−17.8925	−1.09913
$266$	9.59359	0.588221
$267$	7.81383	0.478199
$268$	−18.7626	−1.14611
$269$	6.40281	0.390387	0.195193	−	0.980765i	$-0.437467\pi$
$269$	6.40281	0.390387	0.195193	+	0.980765i	$0.437467\pi$
$270$	−35.3704	−2.15257
$271$	−21.0054	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$271$	−21.0054	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$272$	0.209418	0.0126978
$273$	79.8513	4.83282
$274$	−47.5981	−2.87551
$275$	2.33205	0.140628
$276$	39.1448	2.35624
$277$	−0.305842	−0.0183762	−0.00918812	−	0.999958i	$-0.502925\pi$
$277$	−0.305842	−0.0183762	−0.00918812	+	0.999958i	$0.502925\pi$
$278$	4.88082	0.292732
$279$	50.2580	3.00887
$280$	−8.00760	−0.478545
$281$	−23.7951	−1.41950	−0.709748	−	0.704456i	$-0.751191\pi$
$281$	−23.7951	−1.41950	−0.709748	+	0.704456i	$0.751191\pi$
$282$	−53.2804	−3.17280
$283$	3.19305	0.189807	0.0949036	−	0.995486i	$-0.469746\pi$
$283$	3.19305	0.189807	0.0949036	+	0.995486i	$0.469746\pi$
$284$	24.8602	1.47518
$285$	6.14045	0.363729
$286$	−41.9589	−2.48108
$287$	−25.1536	−1.48477
$288$	−46.2701	−2.72649
$289$	−16.9952	−0.999720
$290$	−21.4541	−1.25983
$291$	−20.2239	−1.18554
$292$	33.3824	1.95356
$293$	−14.6209	−0.854159	−0.427080	−	0.904214i	$-0.640458\pi$
$293$	−14.6209	−0.854159	−0.427080	+	0.904214i	$0.640458\pi$
$294$	−86.2944	−5.03279
$295$	−18.3333	−1.06740
$296$	3.25271	0.189060
$297$	27.4962	1.59549
$298$	−30.4716	−1.76517
$299$	−32.5421	−1.88196
$300$	4.89141	0.282406
$301$	15.3225	0.883174
$302$	45.2511	2.60391
$303$	11.2885	0.648505
$304$	3.03443	0.174037
$305$	15.6005	0.893282
$306$	−0.831928	−0.0475581
$307$	−16.3863	−0.935216	−0.467608	−	0.883936i	$-0.654884\pi$
$307$	−16.3863	−0.935216	−0.467608	+	0.883936i	$0.654884\pi$
$308$	37.1958	2.11943
$309$	−45.5346	−2.59037
$310$	38.1078	2.16438
$311$	0.231206	0.0131105	0.00655524	−	0.999979i	$-0.497913\pi$
$311$	0.231206	0.0131105	0.00655524	+	0.999979i	$0.497913\pi$
$312$	−14.7286	−0.833843
$313$	3.96891	0.224336	0.112168	−	0.993689i	$-0.464221\pi$
$313$	3.96891	0.224336	0.112168	+	0.993689i	$0.464221\pi$
$314$	23.9026	1.34890
$315$	−54.5495	−3.07352
$316$	−16.4286	−0.924178
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	53.4660	2.99823
$319$	16.6780	0.933788
$320$	−22.4826	−1.25682
$321$	−58.9685	−3.29130
$322$	52.8680	2.94622
$323$	0.0690138	0.00384003
$324$	16.2710	0.903942
$325$	−4.06636	−0.225561
$326$	5.46538	0.302699
$327$	21.6869	1.19929
$328$	4.63959	0.256179
$329$	−39.2653	−2.16477
$330$	43.6305	2.40178
$331$	−3.70645	−0.203725	−0.101862	−	0.994798i	$-0.532480\pi$
$331$	−3.70645	−0.203725	−0.101862	+	0.994798i	$0.532480\pi$
$332$	−5.31493	−0.291695
$333$	22.1581	1.21426
$334$	−23.2284	−1.27100
$335$	−16.2193	−0.886152
$336$	−41.0323	−2.23850
$337$	−7.15172	−0.389579	−0.194790	−	0.980845i	$-0.562402\pi$
$337$	−7.15172	−0.389579	−0.194790	+	0.980845i	$0.562402\pi$
$338$	45.8879	2.49597
$339$	−58.6826	−3.18720
$340$	−0.344204	−0.0186671
$341$	−29.6242	−1.60424
$342$	−12.0545	−0.651833
$343$	−31.5874	−1.70556
$344$	−2.82624	−0.152381
$345$	33.8385	1.82181
$346$	−22.6908	−1.21986
$347$	21.7437	1.16726	0.583632	−	0.812018i	$-0.301631\pi$
$347$	21.7437	1.16726	0.583632	+	0.812018i	$0.301631\pi$
$348$	34.9816	1.87521
$349$	−22.4980	−1.20429	−0.602146	−	0.798386i	$-0.705687\pi$
$349$	−22.4980	−1.20429	−0.602146	+	0.798386i	$0.705687\pi$
$350$	6.60623	0.353118
$351$	−47.9447	−2.55910
$352$	27.2735	1.45368
$353$	−8.70740	−0.463448	−0.231724	−	0.972782i	$-0.574437\pi$
$353$	−8.70740	−0.463448	−0.231724	+	0.972782i	$0.574437\pi$
$354$	54.7832	2.91169
$355$	21.4903	1.14059
$356$	−6.34663	−0.336371
$357$	−0.933221	−0.0493913
$358$	28.8221	1.52330
$359$	22.4868	1.18681	0.593405	−	0.804904i	$-0.297783\pi$
$359$	22.4868	1.18681	0.593405	+	0.804904i	$0.297783\pi$
$360$	10.0617	0.530297
$361$	1.00000	0.0526316
$362$	54.1706	2.84715
$363$	−1.38744	−0.0728219
$364$	−64.8577	−3.39947
$365$	28.8573	1.51046
$366$	−46.6171	−2.43672
$367$	−2.42714	−0.126696	−0.0633478	−	0.997992i	$-0.520178\pi$
$367$	−2.42714	−0.126696	−0.0633478	+	0.997992i	$0.520178\pi$
$368$	16.7220	0.871696
$369$	31.6059	1.64534
$370$	16.8012	0.873455
$371$	39.4021	2.04565
$372$	−62.1359	−3.22160
$373$	16.1988	0.838742	0.419371	−	0.907815i	$-0.362251\pi$
$373$	16.1988	0.838742	0.419371	+	0.907815i	$0.362251\pi$
$374$	0.490373	0.0253566
$375$	34.9306	1.80381
$376$	7.24250	0.373503
$377$	−29.0811	−1.49775
$378$	77.8912	4.00629
$379$	9.27348	0.476347	0.238173	−	0.971223i	$-0.423451\pi$
$379$	9.27348	0.476347	0.238173	+	0.971223i	$0.423451\pi$
$380$	−4.98746	−0.255851
$381$	−65.7069	−3.36627
$382$	−42.9715	−2.19862
$383$	22.2160	1.13519	0.567593	−	0.823310i	$-0.307875\pi$
$383$	22.2160	1.13519	0.567593	+	0.823310i	$0.307875\pi$
$384$	19.5504	0.997677
$385$	32.1537	1.63871
$386$	43.1483	2.19619
$387$	−19.2530	−0.978684
$388$	16.4264	0.833926
$389$	−5.61632	−0.284759	−0.142379	−	0.989812i	$-0.545475\pi$
$389$	−5.61632	−0.284759	−0.142379	+	0.989812i	$0.545475\pi$
$390$	−76.0778	−3.85235
$391$	0.380319	0.0192335
$392$	11.7301	0.592462
$393$	−5.74503	−0.289798
$394$	28.6932	1.44554
$395$	−14.2016	−0.714560
$396$	−46.7371	−2.34863
$397$	−6.96252	−0.349439	−0.174719	−	0.984618i	$-0.555902\pi$
$397$	−6.96252	−0.349439	−0.174719	+	0.984618i	$0.555902\pi$
$398$	57.2694	2.87066
$399$	−13.5222	−0.676958
$400$	2.08953	0.104477
$401$	−16.0678	−0.802386	−0.401193	−	0.915994i	$-0.631404\pi$
$401$	−16.0678	−0.802386	−0.401193	+	0.915994i	$0.631404\pi$
$402$	48.4661	2.41727
$403$	51.6552	2.57313
$404$	−9.16883	−0.456166
$405$	14.0654	0.698914
$406$	47.2453	2.34475
$407$	−13.0609	−0.647406
$408$	0.172133	0.00852185
$409$	15.4613	0.764512	0.382256	−	0.924056i	$-0.375147\pi$
$409$	15.4613	0.764512	0.382256	+	0.924056i	$0.375147\pi$
$410$	23.9649	1.18354
$411$	67.0898	3.30930
$412$	36.9846	1.82210
$413$	40.3728	1.98661
$414$	−66.4295	−3.26483
$415$	−4.59447	−0.225534
$416$	−47.5564	−2.33164
$417$	−6.87954	−0.336893
$418$	7.10543	0.347538
$419$	−8.20509	−0.400845	−0.200422	−	0.979710i	$-0.564231\pi$
$419$	−8.20509	−0.400845	−0.200422	+	0.979710i	$0.564231\pi$
$420$	67.4416	3.29081
$421$	26.1482	1.27439	0.637193	−	0.770704i	$-0.280095\pi$
$421$	26.1482	1.27439	0.637193	+	0.770704i	$0.280095\pi$
$422$	46.7518	2.27584
$423$	49.3375	2.39887
$424$	−7.26773	−0.352952
$425$	0.0475235	0.00230523
$426$	−64.2170	−3.11133
$427$	−34.3547	−1.66254
$428$	47.8960	2.31514
$429$	59.1413	2.85537
$430$	−14.5984	−0.703998
$431$	−19.6059	−0.944385	−0.472192	−	0.881496i	$-0.656537\pi$
$431$	−19.6059	−0.944385	−0.472192	+	0.881496i	$0.656537\pi$
$432$	24.6368	1.18534
$433$	15.7712	0.757914	0.378957	−	0.925414i	$-0.376283\pi$
$433$	15.7712	0.757914	0.378957	+	0.925414i	$0.376283\pi$
$434$	−83.9193	−4.02826
$435$	30.2397	1.44988
$436$	−17.6147	−0.843593
$437$	5.51076	0.263615
$438$	−86.2308	−4.12027
$439$	18.4488	0.880511	0.440256	−	0.897872i	$-0.354888\pi$
$439$	18.4488	0.880511	0.440256	+	0.897872i	$0.354888\pi$
$440$	−5.93077	−0.282738
$441$	79.9083	3.80516
$442$	−0.855055	−0.0406708
$443$	33.7547	1.60374	0.801868	−	0.597501i	$-0.203840\pi$
$443$	33.7547	1.60374	0.801868	+	0.597501i	$0.203840\pi$
$444$	−27.3949	−1.30011
$445$	−5.48632	−0.260077
$446$	56.7836	2.68878
$447$	42.9498	2.03146
$448$	49.5103	2.33914
$449$	−8.90922	−0.420452	−0.210226	−	0.977653i	$-0.567420\pi$
$449$	−8.90922	−0.420452	−0.210226	+	0.977653i	$0.567420\pi$
$450$	−8.30083	−0.391305
$451$	−18.6298	−0.877245
$452$	47.6638	2.24191
$453$	−63.7818	−2.99673
$454$	−25.5292	−1.19814
$455$	−56.0660	−2.62841
$456$	2.49418	0.116801
$457$	−36.5768	−1.71099	−0.855495	−	0.517811i	$-0.826747\pi$
$457$	−36.5768	−1.71099	−0.855495	+	0.517811i	$0.826747\pi$
$458$	−7.28588	−0.340447
$459$	0.560329	0.0261539
$460$	−27.4847	−1.28148
$461$	−28.9759	−1.34954	−0.674771	−	0.738028i	$-0.735757\pi$
$461$	−28.9759	−1.34954	−0.674771	+	0.738028i	$0.735757\pi$
$462$	−96.0812	−4.47010
$463$	36.7299	1.70698	0.853492	−	0.521107i	$-0.174481\pi$
$463$	36.7299	1.70698	0.853492	+	0.521107i	$0.174481\pi$
$464$	14.9436	0.693739
$465$	−53.7132	−2.49089
$466$	−19.1147	−0.885470
$467$	19.2474	0.890662	0.445331	−	0.895366i	$-0.353086\pi$
$467$	19.2474	0.890662	0.445331	+	0.895366i	$0.353086\pi$
$468$	81.4947	3.76709
$469$	35.7173	1.64927
$470$	37.4098	1.72558
$471$	−33.6909	−1.55239
$472$	−7.44677	−0.342765
$473$	11.3485	0.521805
$474$	42.4370	1.94919
$475$	0.688608	0.0315955
$476$	0.757991	0.0347424
$477$	−49.5093	−2.26688
$478$	8.47827	0.387787
$479$	−8.37131	−0.382495	−0.191248	−	0.981542i	$-0.561253\pi$
$479$	−8.37131	−0.382495	−0.191248	+	0.981542i	$0.561253\pi$
$480$	49.4510	2.25712
$481$	22.7741	1.03841
$482$	−30.1981	−1.37549
$483$	−74.5178	−3.39068
$484$	1.12692	0.0512238
$485$	14.1998	0.644778
$486$	9.07385	0.411598
$487$	11.7203	0.531096	0.265548	−	0.964098i	$-0.414447\pi$
$487$	11.7203	0.531096	0.265548	+	0.964098i	$0.414447\pi$
$488$	6.33674	0.286851
$489$	−7.70349	−0.348364
$490$	60.5899	2.73717
$491$	33.2829	1.50204	0.751019	−	0.660281i	$-0.229563\pi$
$491$	33.2829	1.50204	0.751019	+	0.660281i	$0.229563\pi$
$492$	−39.0756	−1.76166
$493$	0.339871	0.0153070
$494$	−12.3896	−0.557435
$495$	−40.4017	−1.81592
$496$	−26.5435	−1.19184
$497$	−47.3251	−2.12282
$498$	13.7291	0.615217
$499$	−13.4713	−0.603060	−0.301530	−	0.953457i	$-0.597497\pi$
$499$	−13.4713	−0.603060	−0.301530	+	0.953457i	$0.597497\pi$
$500$	−28.3717	−1.26882
$501$	32.7406	1.46274
$502$	30.8006	1.37470
$503$	19.8675	0.885846	0.442923	−	0.896560i	$-0.353941\pi$
$503$	19.8675	0.885846	0.442923	+	0.896560i	$0.353941\pi$
$504$	−22.1574	−0.986968
$505$	−7.92596	−0.352701
$506$	39.1563	1.74071
$507$	−64.6792	−2.87251
$508$	53.3692	2.36787
$509$	−1.92411	−0.0852845	−0.0426422	−	0.999090i	$-0.513578\pi$
$509$	−1.92411	−0.0852845	−0.0426422	+	0.999090i	$0.513578\pi$
$510$	0.889121	0.0393709
$511$	−63.5483	−2.81121
$512$	29.5558	1.30619
$513$	8.11908	0.358466
$514$	42.4543	1.87258
$515$	31.9712	1.40882
$516$	23.8032	1.04788
$517$	−29.0816	−1.27901
$518$	−36.9990	−1.62564
$519$	31.9828	1.40389
$520$	10.3414	0.453500
$521$	−24.0459	−1.05347	−0.526736	−	0.850029i	$-0.676584\pi$
$521$	−24.0459	−1.05347	−0.526736	+	0.850029i	$0.676584\pi$
$522$	−59.3645	−2.59832
$523$	−20.9112	−0.914384	−0.457192	−	0.889368i	$-0.651145\pi$
$523$	−20.9112	−0.914384	−0.457192	+	0.889368i	$0.651145\pi$
$524$	4.66629	0.203848
$525$	−9.31152	−0.406388
$526$	−34.9140	−1.52232
$527$	−0.603694	−0.0262973
$528$	−30.3903	−1.32257
$529$	7.36849	0.320369
$530$	−37.5401	−1.63064
$531$	−50.7290	−2.20145
$532$	10.9832	0.476181
$533$	32.4846	1.40706
$534$	16.3941	0.709443
$535$	41.4035	1.79003
$536$	−6.58808	−0.284562
$537$	−40.6249	−1.75310
$538$	13.4337	0.579167
$539$	−47.1013	−2.02880
$540$	−40.4936	−1.74257
$541$	10.6486	0.457819	0.228910	−	0.973448i	$-0.426484\pi$
$541$	10.6486	0.457819	0.228910	+	0.973448i	$0.426484\pi$
$542$	−44.0712	−1.89302
$543$	−76.3539	−3.27666
$544$	0.555791	0.0238293
$545$	−15.2270	−0.652253
$546$	167.535	7.16985
$547$	−26.0177	−1.11244	−0.556219	−	0.831036i	$-0.687748\pi$
$547$	−26.0177	−1.11244	−0.556219	+	0.831036i	$0.687748\pi$
$548$	−54.4924	−2.32780
$549$	43.1673	1.84233
$550$	4.89286	0.208632
$551$	4.92468	0.209798
$552$	13.7448	0.585019
$553$	31.2742	1.32991
$554$	−0.641683	−0.0272625
$555$	−23.6815	−1.00522
$556$	5.58777	0.236974
$557$	−3.01370	−0.127695	−0.0638474	−	0.997960i	$-0.520337\pi$
$557$	−3.01370	−0.127695	−0.0638474	+	0.997960i	$0.520337\pi$
$558$	105.446	4.46388
$559$	−19.7882	−0.836952
$560$	28.8100	1.21744
$561$	−0.691184	−0.0291818
$562$	−49.9243	−2.10593
$563$	−21.5528	−0.908342	−0.454171	−	0.890914i	$-0.650065\pi$
$563$	−21.5528	−0.908342	−0.454171	+	0.890914i	$0.650065\pi$
$564$	−60.9978	−2.56847
$565$	41.2028	1.73341
$566$	6.69931	0.281593
$567$	−30.9742	−1.30079
$568$	8.72913	0.366266
$569$	10.3044	0.431983	0.215991	−	0.976395i	$-0.430702\pi$
$569$	10.3044	0.431983	0.215991	+	0.976395i	$0.430702\pi$
$570$	12.8832	0.539619
$571$	−28.2748	−1.18326	−0.591631	−	0.806209i	$-0.701516\pi$
$571$	−28.2748	−1.18326	−0.591631	+	0.806209i	$0.701516\pi$
$572$	−48.0364	−2.00850
$573$	60.5687	2.53029
$574$	−52.7746	−2.20277
$575$	3.79476	0.158252
$576$	−62.2104	−2.59210
$577$	5.75714	0.239673	0.119836	−	0.992794i	$-0.461763\pi$
$577$	5.75714	0.239673	0.119836	+	0.992794i	$0.461763\pi$
$578$	−35.6576	−1.48316
$579$	−60.8177	−2.52750
$580$	−24.5616	−1.01987
$581$	10.1178	0.419755
$582$	−42.4315	−1.75884
$583$	29.1829	1.20863
$584$	11.7215	0.485039
$585$	70.4478	2.91266
$586$	−30.6759	−1.26721
$587$	6.36394	0.262668	0.131334	−	0.991338i	$-0.458074\pi$
$587$	6.36394	0.262668	0.131334	+	0.991338i	$0.458074\pi$
$588$	−98.7936	−4.07418
$589$	−8.74743	−0.360432
$590$	−38.4649	−1.58357
$591$	−40.4432	−1.66361
$592$	−11.7027	−0.480978
$593$	23.3411	0.958503	0.479251	−	0.877678i	$-0.340908\pi$
$593$	23.3411	0.958503	0.479251	+	0.877678i	$0.340908\pi$
$594$	57.6896	2.36703
$595$	0.655242	0.0268623
$596$	−34.8852	−1.42895
$597$	−80.7216	−3.30371
$598$	−68.2762	−2.79202
$599$	−29.5526	−1.20749	−0.603744	−	0.797178i	$-0.706325\pi$
$599$	−29.5526	−1.20749	−0.603744	+	0.797178i	$0.706325\pi$
$600$	1.71751	0.0701172
$601$	7.40295	0.301973	0.150986	−	0.988536i	$-0.451755\pi$
$601$	7.40295	0.301973	0.150986	+	0.988536i	$0.451755\pi$
$602$	32.1480	1.31026
$603$	−44.8794	−1.82763
$604$	51.8055	2.10794
$605$	0.974165	0.0396055
$606$	23.6842	0.962105
$607$	3.32063	0.134780	0.0673900	−	0.997727i	$-0.478533\pi$
$607$	3.32063	0.134780	0.0673900	+	0.997727i	$0.478533\pi$
$608$	8.05333	0.326606
$609$	−66.5926	−2.69847
$610$	32.7313	1.32525
$611$	50.7091	2.05147
$612$	−0.952428	−0.0384996
$613$	−26.1994	−1.05818	−0.529091	−	0.848565i	$-0.677467\pi$
$613$	−26.1994	−1.05818	−0.529091	+	0.848565i	$0.677467\pi$
$614$	−34.3800	−1.38746
$615$	−33.7787	−1.36209
$616$	13.0605	0.526222
$617$	5.78350	0.232835	0.116417	−	0.993200i	$-0.462859\pi$
$617$	5.78350	0.232835	0.116417	+	0.993200i	$0.462859\pi$
$618$	−95.5357	−3.84301
$619$	15.2634	0.613489	0.306745	−	0.951792i	$-0.400760\pi$
$619$	15.2634	0.613489	0.306745	+	0.951792i	$0.400760\pi$
$620$	43.6275	1.75212
$621$	44.7423	1.79545
$622$	0.485091	0.0194504
$623$	12.0817	0.484045
$624$	52.9911	2.12134
$625$	−21.0828	−0.843311
$626$	8.32714	0.332819
$627$	−10.0151	−0.399966
$628$	27.3648	1.09197
$629$	−0.266161	−0.0106125
$630$	−114.450	−4.55979
$631$	−4.28373	−0.170533	−0.0852664	−	0.996358i	$-0.527174\pi$
$631$	−4.28373	−0.170533	−0.0852664	+	0.996358i	$0.527174\pi$
$632$	−5.76853	−0.229460
$633$	−65.8970	−2.61917
$634$	2.09809	0.0833259
$635$	46.1348	1.83080
$636$	61.2103	2.42714
$637$	82.1298	3.25410
$638$	34.9919	1.38534
$639$	59.4647	2.35239
$640$	−13.7269	−0.542604
$641$	34.8438	1.37625	0.688123	−	0.725594i	$-0.258435\pi$
$641$	34.8438	1.37625	0.688123	+	0.725594i	$0.258435\pi$
$642$	−123.721	−4.88289
$643$	19.3609	0.763519	0.381760	−	0.924262i	$-0.375318\pi$
$643$	19.3609	0.763519	0.381760	+	0.924262i	$0.375318\pi$
$644$	60.5256	2.38504
$645$	20.5766	0.810201
$646$	0.144797	0.00569698
$647$	9.76593	0.383938	0.191969	−	0.981401i	$-0.438513\pi$
$647$	9.76593	0.383938	0.191969	+	0.981401i	$0.438513\pi$
$648$	5.71319	0.224435
$649$	29.9018	1.17375
$650$	−8.53160	−0.334637
$651$	118.285	4.63595
$652$	6.25701	0.245043
$653$	−23.6628	−0.925997	−0.462998	−	0.886359i	$-0.653226\pi$
$653$	−23.6628	−0.925997	−0.462998	+	0.886359i	$0.653226\pi$
$654$	45.5010	1.77923
$655$	4.03375	0.157612
$656$	−16.6925	−0.651732
$657$	79.8494	3.11522
$658$	−82.3822	−3.21159
$659$	−27.5402	−1.07281	−0.536407	−	0.843960i	$-0.680219\pi$
$659$	−27.5402	−1.07281	−0.536407	+	0.843960i	$0.680219\pi$
$660$	49.9501	1.94431
$661$	−10.6294	−0.413434	−0.206717	−	0.978401i	$-0.566278\pi$
$661$	−10.6294	−0.413434	−0.206717	+	0.978401i	$0.566278\pi$
$662$	−7.77647	−0.302241
$663$	1.20521	0.0468063
$664$	−1.86622	−0.0724235
$665$	9.49436	0.368176
$666$	46.4898	1.80144
$667$	27.1387	1.05082
$668$	−26.5929	−1.02891
$669$	−80.0369	−3.09440
$670$	−34.0295	−1.31467
$671$	−25.4446	−0.982278
$672$	−108.899	−4.20087
$673$	18.4194	0.710015	0.355008	−	0.934863i	$-0.384478\pi$
$673$	18.4194	0.710015	0.355008	+	0.934863i	$0.384478\pi$
$674$	−15.0050	−0.577970
$675$	5.59087	0.215193
$676$	52.5344	2.02056
$677$	−5.39939	−0.207516	−0.103758	−	0.994603i	$-0.533087\pi$
$677$	−5.39939	−0.207516	−0.103758	+	0.994603i	$0.533087\pi$
$678$	−123.121	−4.72845
$679$	−31.2701	−1.20004
$680$	−0.120860	−0.00463476
$681$	35.9836	1.37889
$682$	−62.1543	−2.38001
$683$	−11.1446	−0.426434	−0.213217	−	0.977005i	$-0.568394\pi$
$683$	−11.1446	−0.426434	−0.213217	+	0.977005i	$0.568394\pi$
$684$	−13.8005	−0.527676
$685$	−47.1058	−1.79982
$686$	−66.2732	−2.53032
$687$	10.2695	0.391806
$688$	10.1683	0.387664
$689$	−50.8857	−1.93859
$690$	70.9964	2.70279
$691$	−15.6042	−0.593613	−0.296807	−	0.954938i	$-0.595922\pi$
$691$	−15.6042	−0.593613	−0.296807	+	0.954938i	$0.595922\pi$
$692$	−25.9774	−0.987513
$693$	88.9709	3.37972
$694$	45.6203	1.73172
$695$	4.83033	0.183225
$696$	12.2830	0.465587
$697$	−0.379647	−0.0143801
$698$	−47.2029	−1.78666
$699$	26.9423	1.01905
$700$	7.56310	0.285858
$701$	21.5755	0.814896	0.407448	−	0.913228i	$-0.366419\pi$
$701$	21.5755	0.814896	0.407448	+	0.913228i	$0.366419\pi$
$702$	−100.592	−3.79661
$703$	−3.85663	−0.145456
$704$	36.6694	1.38203
$705$	−52.7293	−1.98590
$706$	−18.2689	−0.687560
$707$	17.4542	0.656433
$708$	62.7182	2.35709
$709$	−42.0222	−1.57818	−0.789089	−	0.614279i	$-0.789447\pi$
$709$	−42.0222	−1.57818	−0.789089	+	0.614279i	$0.789447\pi$
$710$	45.0887	1.69215
$711$	−39.2965	−1.47373
$712$	−2.22848	−0.0835159
$713$	−48.2050	−1.80529
$714$	−1.95798	−0.0732757
$715$	−41.5249	−1.55294
$716$	32.9968	1.23315
$717$	−11.9502	−0.446287
$718$	47.1795	1.76072
$719$	−5.95280	−0.222002	−0.111001	−	0.993820i	$-0.535406\pi$
$719$	−5.95280	−0.222002	−0.111001	+	0.993820i	$0.535406\pi$
$720$	−36.2002	−1.34910
$721$	−70.4055	−2.62204
$722$	2.09809	0.0780829
$723$	42.5644	1.58299
$724$	62.0169	2.30484
$725$	3.39117	0.125945
$726$	−2.91098	−0.108037
$727$	19.2031	0.712205	0.356103	−	0.934447i	$-0.384105\pi$
$727$	19.2031	0.712205	0.356103	+	0.934447i	$0.384105\pi$
$728$	−22.7734	−0.844037
$729$	−33.1115	−1.22635
$730$	60.5452	2.24088
$731$	0.231264	0.00855363
$732$	−53.3693	−1.97259
$733$	−32.4097	−1.19708	−0.598539	−	0.801093i	$-0.704252\pi$
$733$	−32.4097	−1.19708	−0.598539	+	0.801093i	$0.704252\pi$
$734$	−5.09236	−0.187963
$735$	−85.4018	−3.15009
$736$	44.3800	1.63587
$737$	26.4538	0.974438
$738$	66.3121	2.44098
$739$	−47.4766	−1.74645	−0.873227	−	0.487314i	$-0.837977\pi$
$739$	−47.4766	−1.74645	−0.873227	+	0.487314i	$0.837977\pi$
$740$	19.2348	0.707085
$741$	17.4633	0.641529
$742$	82.6692	3.03488
$743$	−19.6937	−0.722491	−0.361246	−	0.932471i	$-0.617648\pi$
$743$	−19.6937	−0.722491	−0.361246	+	0.932471i	$0.617648\pi$
$744$	−21.8177	−0.799875
$745$	−30.1564	−1.10484
$746$	33.9866	1.24434
$747$	−12.7131	−0.465149
$748$	0.561400	0.0205268
$749$	−91.1770	−3.33154
$750$	73.2876	2.67609
$751$	−35.3237	−1.28898	−0.644490	−	0.764612i	$-0.722930\pi$
$751$	−35.3237	−1.28898	−0.644490	+	0.764612i	$0.722930\pi$
$752$	−26.0573	−0.950212
$753$	−43.4136	−1.58208
$754$	−61.0149	−2.22203
$755$	44.7831	1.62982
$756$	89.1733	3.24320
$757$	27.3711	0.994820	0.497410	−	0.867516i	$-0.334284\pi$
$757$	27.3711	0.994820	0.497410	+	0.867516i	$0.334284\pi$
$758$	19.4566	0.706696
$759$	−55.1911	−2.00331
$760$	−1.75124	−0.0635241
$761$	18.9061	0.685347	0.342673	−	0.939455i	$-0.388668\pi$
$761$	18.9061	0.685347	0.342673	+	0.939455i	$0.388668\pi$
$762$	−137.859	−4.99411
$763$	33.5322	1.21395
$764$	−49.1957	−1.77984
$765$	−0.823323	−0.0297673
$766$	46.6112	1.68413
$767$	−52.1393	−1.88264
$768$	−23.0227	−0.830760
$769$	36.1212	1.30256	0.651282	−	0.758836i	$-0.274232\pi$
$769$	36.1212	1.30256	0.651282	+	0.758836i	$0.274232\pi$
$770$	67.4615	2.43114
$771$	−59.8396	−2.15507
$772$	49.3980	1.77787
$773$	−2.00907	−0.0722613	−0.0361307	−	0.999347i	$-0.511503\pi$
$773$	−2.00907	−0.0722613	−0.0361307	+	0.999347i	$0.511503\pi$
$774$	−40.3945	−1.45195
$775$	−6.02355	−0.216372
$776$	5.76778	0.207051
$777$	52.1503	1.87088
$778$	−11.7835	−0.422461
$779$	−5.50102	−0.197094
$780$	−87.0973	−3.11858
$781$	−35.0510	−1.25422
$782$	0.797944	0.0285344
$783$	39.9839	1.42891
$784$	−42.2031	−1.50725
$785$	23.6554	0.844296
$786$	−12.0536	−0.429937
$787$	−17.0263	−0.606922	−0.303461	−	0.952844i	$-0.598142\pi$
$787$	−17.0263	−0.606922	−0.303461	+	0.952844i	$0.598142\pi$
$788$	32.8492	1.17020
$789$	49.2115	1.75197
$790$	−29.7963	−1.06010
$791$	−90.7350	−3.22616
$792$	−16.4107	−0.583129
$793$	44.3673	1.57553
$794$	−14.6080	−0.518419
$795$	52.9130	1.87663
$796$	65.5645	2.32387
$797$	22.8986	0.811111	0.405556	−	0.914070i	$-0.367078\pi$
$797$	22.8986	0.811111	0.405556	+	0.914070i	$0.367078\pi$
$798$	−28.3709	−1.00432
$799$	−0.592636	−0.0209660
$800$	5.54559	0.196066
$801$	−15.1809	−0.536391
$802$	−33.7116	−1.19040
$803$	−47.0666	−1.66094
$804$	55.4861	1.95684
$805$	52.3212	1.84408
$806$	108.377	3.81743
$807$	−18.9349	−0.666539
$808$	−3.21943	−0.113259
$809$	−27.2878	−0.959390	−0.479695	−	0.877435i	$-0.659253\pi$
$809$	−27.2878	−0.959390	−0.479695	+	0.877435i	$0.659253\pi$
$810$	29.5104	1.03689
$811$	−2.55656	−0.0897729	−0.0448865	−	0.998992i	$-0.514293\pi$
$811$	−2.55656	−0.0897729	−0.0448865	+	0.998992i	$0.514293\pi$
$812$	54.0886	1.89814
$813$	62.1186	2.17860
$814$	−27.4030	−0.960476
$815$	5.40885	0.189464
$816$	−0.619306	−0.0216800
$817$	3.35099	0.117236
$818$	32.4392	1.13421
$819$	−155.137	−5.42093
$820$	27.4361	0.958111
$821$	43.8221	1.52940	0.764702	−	0.644384i	$-0.222886\pi$
$821$	43.8221	1.52940	0.764702	+	0.644384i	$0.222886\pi$
$822$	140.761	4.90959
$823$	−40.9220	−1.42645	−0.713226	−	0.700934i	$-0.752767\pi$
$823$	−40.9220	−1.42645	−0.713226	+	0.700934i	$0.752767\pi$
$824$	12.9863	0.452400
$825$	−6.89651	−0.240106
$826$	84.7057	2.94729
$827$	−32.7137	−1.13757	−0.568783	−	0.822488i	$-0.692586\pi$
$827$	−32.7137	−1.13757	−0.568783	+	0.822488i	$0.692586\pi$
$828$	−76.0514	−2.64297
$829$	27.1440	0.942752	0.471376	−	0.881932i	$-0.343758\pi$
$829$	27.1440	0.942752	0.471376	+	0.881932i	$0.343758\pi$
$830$	−9.63963	−0.334596
$831$	0.904457	0.0313753
$832$	−63.9399	−2.21672
$833$	−0.959849	−0.0332568
$834$	−14.4339	−0.499805
$835$	−22.9882	−0.795538
$836$	8.13461	0.281341
$837$	−71.0211	−2.45485
$838$	−17.2150	−0.594683
$839$	39.1610	1.35199	0.675994	−	0.736907i	$-0.263715\pi$
$839$	39.1610	1.35199	0.675994	+	0.736907i	$0.263715\pi$
$840$	23.6806	0.817060
$841$	−4.74756	−0.163709
$842$	54.8614	1.89065
$843$	70.3686	2.42362
$844$	53.5236	1.84236
$845$	45.4132	1.56226
$846$	103.515	3.55890
$847$	−2.14527	−0.0737122
$848$	26.1481	0.897928
$849$	−9.44272	−0.324073
$850$	0.0997086	0.00341998
$851$	−21.2530	−0.728543
$852$	−73.5185	−2.51870
$853$	50.0059	1.71217	0.856085	−	0.516834i	$-0.172890\pi$
$853$	50.0059	1.71217	0.856085	+	0.516834i	$0.172890\pi$
$854$	−72.0794	−2.46651
$855$	−11.9298	−0.407991
$856$	16.8176	0.574815
$857$	−43.1532	−1.47408	−0.737042	−	0.675847i	$-0.763778\pi$
$857$	−43.1532	−1.47408	−0.737042	+	0.675847i	$0.763778\pi$
$858$	124.084	4.23615
$859$	18.5447	0.632738	0.316369	−	0.948636i	$-0.397536\pi$
$859$	18.5447	0.632738	0.316369	+	0.948636i	$0.397536\pi$
$860$	−16.7129	−0.569906
$861$	74.3861	2.53507
$862$	−41.1350	−1.40106
$863$	5.98428	0.203707	0.101854	−	0.994799i	$-0.467523\pi$
$863$	5.98428	0.203707	0.101854	+	0.994799i	$0.467523\pi$
$864$	65.3856	2.22446
$865$	−22.4561	−0.763529
$866$	33.0893	1.12442
$867$	50.2596	1.70690
$868$	−96.0745	−3.26098
$869$	23.1630	0.785750
$870$	63.4457	2.15101
$871$	−46.1271	−1.56296
$872$	−6.18503	−0.209452
$873$	39.2914	1.32981
$874$	11.5621	0.391093
$875$	54.0097	1.82586
$876$	−98.7208	−3.33547
$877$	−19.0770	−0.644185	−0.322092	−	0.946708i	$-0.604386\pi$
$877$	−19.0770	−0.644185	−0.322092	+	0.946708i	$0.604386\pi$
$878$	38.7072	1.30630
$879$	43.2378	1.45838
$880$	21.3379	0.719301
$881$	−13.7296	−0.462563	−0.231282	−	0.972887i	$-0.574292\pi$
$881$	−13.7296	−0.462563	−0.231282	+	0.972887i	$0.574292\pi$
$882$	167.655	5.64524
$883$	−17.3643	−0.584355	−0.292177	−	0.956364i	$-0.594380\pi$
$883$	−17.3643	−0.584355	−0.292177	+	0.956364i	$0.594380\pi$
$884$	−0.978905	−0.0329241
$885$	54.2165	1.82247
$886$	70.8205	2.37926
$887$	7.15659	0.240295	0.120147	−	0.992756i	$-0.461663\pi$
$887$	7.15659	0.240295	0.120147	+	0.992756i	$0.461663\pi$
$888$	−9.61914	−0.322797
$889$	−101.596	−3.40742
$890$	−11.5108	−0.385843
$891$	−22.9408	−0.768545
$892$	65.0084	2.17664
$893$	−8.58721	−0.287360
$894$	90.1127	3.01382
$895$	28.5240	0.953451
$896$	30.2288	1.00987
$897$	96.2358	3.21322
$898$	−18.6924	−0.623772
$899$	−43.0783	−1.43674
$900$	−9.50316	−0.316772
$901$	0.594701	0.0198123
$902$	−39.0871	−1.30146
$903$	−45.3128	−1.50792
$904$	16.7361	0.556634
$905$	53.6103	1.78207
$906$	−133.820	−4.44587
$907$	−2.55564	−0.0848588	−0.0424294	−	0.999099i	$-0.513510\pi$
$907$	−2.55564	−0.0848588	−0.0424294	+	0.999099i	$0.513510\pi$
$908$	−29.2270	−0.969931
$909$	−21.9315	−0.727422
$910$	−117.632	−3.89945
$911$	5.90515	0.195646	0.0978231	−	0.995204i	$-0.468812\pi$
$911$	5.90515	0.195646	0.0978231	+	0.995204i	$0.468812\pi$
$912$	−8.97364	−0.297147
$913$	7.49364	0.248003
$914$	−76.7414	−2.53838
$915$	−46.1349	−1.52517
$916$	−8.34119	−0.275601
$917$	−8.88296	−0.293341
$918$	1.17562	0.0388013
$919$	10.2472	0.338024	0.169012	−	0.985614i	$-0.445942\pi$
$919$	10.2472	0.338024	0.169012	+	0.985614i	$0.445942\pi$
$920$	−9.65065	−0.318173
$921$	48.4588	1.59677
$922$	−60.7940	−2.00214
$923$	61.1179	2.01172
$924$	−109.998	−3.61867
$925$	−2.65571	−0.0873192
$926$	77.0627	2.53244
$927$	88.4657	2.90559
$928$	39.6600	1.30190
$929$	2.31175	0.0758461	0.0379230	−	0.999281i	$-0.487926\pi$
$929$	2.31175	0.0758461	0.0379230	+	0.999281i	$0.487926\pi$
$930$	−112.695	−3.69542
$931$	−13.9081	−0.455819
$932$	−21.8833	−0.716812
$933$	−0.683739	−0.0223846
$934$	40.3827	1.32136
$935$	0.485301	0.0158710
$936$	28.6151	0.935314
$937$	8.74287	0.285617	0.142809	−	0.989750i	$-0.454387\pi$
$937$	8.74287	0.285617	0.142809	+	0.989750i	$0.454387\pi$
$938$	74.9382	2.44682
$939$	−11.7372	−0.383027
$940$	42.8284	1.39691
$941$	41.6964	1.35926	0.679632	−	0.733553i	$-0.262139\pi$
$941$	41.6964	1.35926	0.679632	+	0.733553i	$0.262139\pi$
$942$	−70.6866	−2.30309
$943$	−30.3148	−0.987186
$944$	26.7922	0.872013
$945$	77.0855	2.50759
$946$	23.8102	0.774136
$947$	38.5929	1.25410	0.627050	−	0.778979i	$-0.284262\pi$
$947$	38.5929	1.25410	0.627050	+	0.778979i	$0.284262\pi$
$948$	48.5837	1.57793
$949$	82.0692	2.66408
$950$	1.44476	0.0468743
$951$	−2.95727	−0.0958961
$952$	0.266152	0.00862603
$953$	−35.5709	−1.15225	−0.576127	−	0.817360i	$-0.695437\pi$
$953$	−35.5709	−1.15225	−0.576127	+	0.817360i	$0.695437\pi$
$954$	−103.875	−3.36308
$955$	−42.5271	−1.37614
$956$	9.70629	0.313924
$957$	−49.3214	−1.59433
$958$	−17.5638	−0.567460
$959$	103.734	3.34976
$960$	66.4873	2.14587
$961$	45.5176	1.46831
$962$	47.7822	1.54056
$963$	114.565	3.69182
$964$	−34.5721	−1.11349
$965$	42.7019	1.37462
$966$	−156.345	−5.03032
$967$	−7.11531	−0.228813	−0.114406	−	0.993434i	$-0.536497\pi$
$967$	−7.11531	−0.228813	−0.114406	+	0.993434i	$0.536497\pi$
$968$	0.395695	0.0127181
$969$	−0.204093	−0.00655640
$970$	29.7924	0.956577
$971$	0.544683	0.0174797	0.00873986	−	0.999962i	$-0.497218\pi$
$971$	0.544683	0.0174797	0.00873986	+	0.999962i	$0.497218\pi$
$972$	10.3881	0.333200
$973$	−10.6371	−0.341011
$974$	24.5902	0.787920
$975$	12.0253	0.385119
$976$	−22.7985	−0.729764
$977$	−39.1454	−1.25237	−0.626187	−	0.779673i	$-0.715385\pi$
$977$	−39.1454	−1.25237	−0.626187	+	0.779673i	$0.715385\pi$
$978$	−16.1626	−0.516824
$979$	8.94826	0.285988
$980$	69.3659	2.21581
$981$	−42.1338	−1.34523
$982$	69.8306	2.22839
$983$	−18.3721	−0.585978	−0.292989	−	0.956116i	$-0.594650\pi$
$983$	−18.3721	−0.585978	−0.292989	+	0.956116i	$0.594650\pi$
$984$	−13.7205	−0.437395
$985$	28.3964	0.904784
$986$	0.713080	0.0227091
$987$	116.118	3.69608
$988$	−14.1842	−0.451259
$989$	18.4665	0.587200
$990$	−84.7665	−2.69405
$991$	−22.4670	−0.713688	−0.356844	−	0.934164i	$-0.616147\pi$
$991$	−22.4670	−0.713688	−0.356844	+	0.934164i	$0.616147\pi$
$992$	−70.4459	−2.23666
$993$	10.9610	0.347836
$994$	−99.2924	−3.14936
$995$	56.6770	1.79678
$996$	15.7177	0.498035
$997$	43.6002	1.38083	0.690417	−	0.723412i	$-0.257427\pi$
$997$	43.6002	1.38083	0.690417	+	0.723412i	$0.257427\pi$
$998$	−28.2641	−0.894684
$999$	−31.3123	−0.990678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.117	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.117	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09809 q^{2} -2.95727 q^{3} +2.40199 q^{4} +2.07639 q^{5} -6.20463 q^{6} -4.57253 q^{7} +0.843406 q^{8} +5.74546 q^{9} +O(q^{10})\)	\(q+2.09809 q^{2} -2.95727 q^{3} +2.40199 q^{4} +2.07639 q^{5} -6.20463 q^{6} -4.57253 q^{7} +0.843406 q^{8} +5.74546 q^{9} +4.35645 q^{10} -3.38662 q^{11} -7.10333 q^{12} +5.90519 q^{13} -9.59359 q^{14} -6.14045 q^{15} -3.03443 q^{16} -0.0690138 q^{17} +12.0545 q^{18} -1.00000 q^{19} +4.98746 q^{20} +13.5222 q^{21} -7.10543 q^{22} -5.51076 q^{23} -2.49418 q^{24} -0.688608 q^{25} +12.3896 q^{26} -8.11908 q^{27} -10.9832 q^{28} -4.92468 q^{29} -12.8832 q^{30} +8.74743 q^{31} -8.05333 q^{32} +10.0151 q^{33} -0.144797 q^{34} -9.49436 q^{35} +13.8005 q^{36} +3.85663 q^{37} -2.09809 q^{38} -17.4633 q^{39} +1.75124 q^{40} +5.50102 q^{41} +28.3709 q^{42} -3.35099 q^{43} -8.13461 q^{44} +11.9298 q^{45} -11.5621 q^{46} +8.58721 q^{47} +8.97364 q^{48} +13.9081 q^{49} -1.44476 q^{50} +0.204093 q^{51} +14.1842 q^{52} -8.61712 q^{53} -17.0346 q^{54} -7.03193 q^{55} -3.85650 q^{56} +2.95727 q^{57} -10.3324 q^{58} -8.82941 q^{59} -14.7493 q^{60} +7.51328 q^{61} +18.3529 q^{62} -26.2713 q^{63} -10.8278 q^{64} +12.2615 q^{65} +21.0127 q^{66} -7.81128 q^{67} -0.165770 q^{68} +16.2968 q^{69} -19.9200 q^{70} +10.3499 q^{71} +4.84576 q^{72} +13.8978 q^{73} +8.09157 q^{74} +2.03640 q^{75} -2.40199 q^{76} +15.4854 q^{77} -36.6395 q^{78} -6.83957 q^{79} -6.30066 q^{80} +6.77396 q^{81} +11.5416 q^{82} -2.21272 q^{83} +32.4802 q^{84} -0.143300 q^{85} -7.03068 q^{86} +14.5636 q^{87} -2.85629 q^{88} -2.64224 q^{89} +25.0298 q^{90} -27.0017 q^{91} -13.2368 q^{92} -25.8685 q^{93} +18.0167 q^{94} -2.07639 q^{95} +23.8159 q^{96} +6.83868 q^{97} +29.1804 q^{98} -19.4577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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