LMFDB - Embedded newform 8021.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66552 q^{2} +1.95620 q^{3} +5.10502 q^{4} -0.546887 q^{5} -5.21429 q^{6} +5.08856 q^{7} -8.27650 q^{8} +0.826707 q^{9} +O(q^{10})$	\(q-2.66552 q^{2} +1.95620 q^{3} +5.10502 q^{4} -0.546887 q^{5} -5.21429 q^{6} +5.08856 q^{7} -8.27650 q^{8} +0.826707 q^{9} +1.45774 q^{10} +4.31177 q^{11} +9.98642 q^{12} +1.00000 q^{13} -13.5637 q^{14} -1.06982 q^{15} +11.8512 q^{16} +3.23041 q^{17} -2.20361 q^{18} +3.31212 q^{19} -2.79187 q^{20} +9.95423 q^{21} -11.4931 q^{22} +3.62437 q^{23} -16.1905 q^{24} -4.70091 q^{25} -2.66552 q^{26} -4.25139 q^{27} +25.9772 q^{28} -9.21801 q^{29} +2.85163 q^{30} -6.46419 q^{31} -15.0366 q^{32} +8.43467 q^{33} -8.61074 q^{34} -2.78287 q^{35} +4.22035 q^{36} -6.44142 q^{37} -8.82854 q^{38} +1.95620 q^{39} +4.52631 q^{40} -8.06232 q^{41} -26.5332 q^{42} +8.75120 q^{43} +22.0117 q^{44} -0.452115 q^{45} -9.66085 q^{46} +9.89622 q^{47} +23.1832 q^{48} +18.8934 q^{49} +12.5304 q^{50} +6.31932 q^{51} +5.10502 q^{52} -8.75086 q^{53} +11.3322 q^{54} -2.35805 q^{55} -42.1155 q^{56} +6.47916 q^{57} +24.5708 q^{58} -13.1454 q^{59} -5.46145 q^{60} +15.3334 q^{61} +17.2305 q^{62} +4.20675 q^{63} +16.3780 q^{64} -0.546887 q^{65} -22.4828 q^{66} +9.61382 q^{67} +16.4913 q^{68} +7.08998 q^{69} +7.41780 q^{70} +2.65086 q^{71} -6.84224 q^{72} +1.64712 q^{73} +17.1698 q^{74} -9.19591 q^{75} +16.9084 q^{76} +21.9407 q^{77} -5.21429 q^{78} +4.98517 q^{79} -6.48125 q^{80} -10.7967 q^{81} +21.4903 q^{82} +6.10657 q^{83} +50.8165 q^{84} -1.76667 q^{85} -23.3265 q^{86} -18.0323 q^{87} -35.6863 q^{88} -4.08703 q^{89} +1.20512 q^{90} +5.08856 q^{91} +18.5025 q^{92} -12.6452 q^{93} -26.3786 q^{94} -1.81136 q^{95} -29.4145 q^{96} +11.8459 q^{97} -50.3609 q^{98} +3.56457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.66552	−1.88481	−0.942405	−	0.334474i	$-0.891441\pi$
$2$	−2.66552	−1.88481	−0.942405	+	0.334474i	$0.891441\pi$
$3$	1.95620	1.12941	0.564705	−	0.825293i	$-0.308990\pi$
$3$	1.95620	1.12941	0.564705	+	0.825293i	$0.308990\pi$
$4$	5.10502	2.55251
$5$	−0.546887	−0.244575	−0.122288	−	0.992495i	$-0.539023\pi$
$5$	−0.546887	−0.244575	−0.122288	+	0.992495i	$0.539023\pi$
$6$	−5.21429	−2.12872
$7$	5.08856	1.92329	0.961647	−	0.274288i	$-0.0884423\pi$
$7$	5.08856	1.92329	0.961647	+	0.274288i	$0.0884423\pi$
$8$	−8.27650	−2.92618
$9$	0.826707	0.275569
$10$	1.45774	0.460978
$11$	4.31177	1.30005	0.650024	−	0.759914i	$-0.274759\pi$
$11$	4.31177	1.30005	0.650024	+	0.759914i	$0.274759\pi$
$12$	9.98642	2.88283
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−13.5637	−3.62505
$15$	−1.06982	−0.276226
$16$	11.8512	2.96279
$17$	3.23041	0.783490	0.391745	−	0.920074i	$-0.371872\pi$
$17$	3.23041	0.783490	0.391745	+	0.920074i	$0.371872\pi$
$18$	−2.20361	−0.519395
$19$	3.31212	0.759853	0.379926	−	0.925017i	$-0.375949\pi$
$19$	3.31212	0.759853	0.379926	+	0.925017i	$0.375949\pi$
$20$	−2.79187	−0.624281
$21$	9.95423	2.17219
$22$	−11.4931	−2.45034
$23$	3.62437	0.755734	0.377867	−	0.925860i	$-0.376658\pi$
$23$	3.62437	0.755734	0.377867	+	0.925860i	$0.376658\pi$
$24$	−16.1905	−3.30486
$25$	−4.70091	−0.940183
$26$	−2.66552	−0.522752
$27$	−4.25139	−0.818180
$28$	25.9772	4.90923
$29$	−9.21801	−1.71174	−0.855871	−	0.517189i	$-0.826978\pi$
$29$	−9.21801	−1.71174	−0.855871	+	0.517189i	$0.826978\pi$
$30$	2.85163	0.520634
$31$	−6.46419	−1.16100	−0.580501	−	0.814259i	$-0.697143\pi$
$31$	−6.46419	−1.16100	−0.580501	+	0.814259i	$0.697143\pi$
$32$	−15.0366	−2.65812
$33$	8.43467	1.46829
$34$	−8.61074	−1.47673
$35$	−2.78287	−0.470391
$36$	4.22035	0.703392
$37$	−6.44142	−1.05896	−0.529481	−	0.848322i	$-0.677613\pi$
$37$	−6.44142	−1.05896	−0.529481	+	0.848322i	$0.677613\pi$
$38$	−8.82854	−1.43218
$39$	1.95620	0.313242
$40$	4.52631	0.715673
$41$	−8.06232	−1.25912	−0.629561	−	0.776951i	$-0.716765\pi$
$41$	−8.06232	−1.25912	−0.629561	+	0.776951i	$0.716765\pi$
$42$	−26.5332	−4.09417
$43$	8.75120	1.33455	0.667273	−	0.744814i	$-0.267462\pi$
$43$	8.75120	1.33455	0.667273	+	0.744814i	$0.267462\pi$
$44$	22.0117	3.31838
$45$	−0.452115	−0.0673974
$46$	−9.66085	−1.42441
$47$	9.89622	1.44351	0.721756	−	0.692147i	$-0.243335\pi$
$47$	9.89622	1.44351	0.721756	+	0.692147i	$0.243335\pi$
$48$	23.1832	3.34621
$49$	18.8934	2.69906
$50$	12.5304	1.77207
$51$	6.31932	0.884882
$52$	5.10502	0.707939
$53$	−8.75086	−1.20202	−0.601011	−	0.799240i	$-0.705235\pi$
$53$	−8.75086	−1.20202	−0.601011	+	0.799240i	$0.705235\pi$
$54$	11.3322	1.54211
$55$	−2.35805	−0.317960
$56$	−42.1155	−5.62791
$57$	6.47916	0.858186
$58$	24.5708	3.22631
$59$	−13.1454	−1.71139	−0.855693	−	0.517483i	$-0.826869\pi$
$59$	−13.1454	−1.71139	−0.855693	+	0.517483i	$0.826869\pi$
$60$	−5.46145	−0.705070
$61$	15.3334	1.96324	0.981622	−	0.190834i	$-0.0611194\pi$
$61$	15.3334	1.96324	0.981622	+	0.190834i	$0.0611194\pi$
$62$	17.2305	2.18827
$63$	4.20675	0.530000
$64$	16.3780	2.04725
$65$	−0.546887	−0.0678330
$66$	−22.4828	−2.76744
$67$	9.61382	1.17452	0.587258	−	0.809400i	$-0.300207\pi$
$67$	9.61382	1.17452	0.587258	+	0.809400i	$0.300207\pi$
$68$	16.4913	1.99987
$69$	7.08998	0.853534
$70$	7.41780	0.886597
$71$	2.65086	0.314599	0.157300	−	0.987551i	$-0.449721\pi$
$71$	2.65086	0.314599	0.157300	+	0.987551i	$0.449721\pi$
$72$	−6.84224	−0.806365
$73$	1.64712	0.192780	0.0963901	−	0.995344i	$-0.469270\pi$
$73$	1.64712	0.192780	0.0963901	+	0.995344i	$0.469270\pi$
$74$	17.1698	1.99594
$75$	−9.19591	−1.06185
$76$	16.9084	1.93953
$77$	21.9407	2.50037
$78$	−5.21429	−0.590402
$79$	4.98517	0.560876	0.280438	−	0.959872i	$-0.409520\pi$
$79$	4.98517	0.560876	0.280438	+	0.959872i	$0.409520\pi$
$80$	−6.48125	−0.724626
$81$	−10.7967	−1.19963
$82$	21.4903	2.37321
$83$	6.10657	0.670283	0.335142	−	0.942168i	$-0.391216\pi$
$83$	6.10657	0.670283	0.335142	+	0.942168i	$0.391216\pi$
$84$	50.8165	5.54453
$85$	−1.76667	−0.191622
$86$	−23.3265	−2.51536
$87$	−18.0323	−1.93326
$88$	−35.6863	−3.80418
$89$	−4.08703	−0.433224	−0.216612	−	0.976258i	$-0.569501\pi$
$89$	−4.08703	−0.433224	−0.216612	+	0.976258i	$0.569501\pi$
$90$	1.20512	0.127031
$91$	5.08856	0.533426
$92$	18.5025	1.92902
$93$	−12.6452	−1.31125
$94$	−26.3786	−2.72075
$95$	−1.81136	−0.185841
$96$	−29.4145	−3.00211
$97$	11.8459	1.20277	0.601385	−	0.798959i	$-0.294616\pi$
$97$	11.8459	1.20277	0.601385	+	0.798959i	$0.294616\pi$
$98$	−50.3609	−5.08722
$99$	3.56457	0.358253
$100$	−23.9982	−2.39982
$101$	4.69062	0.466735	0.233367	−	0.972389i	$-0.425026\pi$
$101$	4.69062	0.466735	0.233367	+	0.972389i	$0.425026\pi$
$102$	−16.8443	−1.66783
$103$	9.47457	0.933557	0.466779	−	0.884374i	$-0.345415\pi$
$103$	9.47457	0.933557	0.466779	+	0.884374i	$0.345415\pi$
$104$	−8.27650	−0.811577
$105$	−5.44384	−0.531264
$106$	23.3256	2.26558
$107$	16.1172	1.55811	0.779053	−	0.626958i	$-0.215700\pi$
$107$	16.1172	1.55811	0.779053	+	0.626958i	$0.215700\pi$
$108$	−21.7034	−2.08841
$109$	7.11765	0.681747	0.340873	−	0.940109i	$-0.389277\pi$
$109$	7.11765	0.681747	0.340873	+	0.940109i	$0.389277\pi$
$110$	6.28544	0.599294
$111$	−12.6007	−1.19600
$112$	60.3054	5.69832
$113$	5.11722	0.481388	0.240694	−	0.970601i	$-0.422625\pi$
$113$	5.11722	0.481388	0.240694	+	0.970601i	$0.422625\pi$
$114$	−17.2704	−1.61752
$115$	−1.98212	−0.184834
$116$	−47.0581	−4.36924
$117$	0.826707	0.0764291
$118$	35.0394	3.22564
$119$	16.4381	1.50688
$120$	8.85436	0.808289
$121$	7.59135	0.690123
$122$	−40.8716	−3.70034
$123$	−15.7715	−1.42207
$124$	−32.9998	−2.96347
$125$	5.30531	0.474521
$126$	−11.2132	−0.998950
$127$	−7.42422	−0.658793	−0.329396	−	0.944192i	$-0.606845\pi$
$127$	−7.42422	−0.658793	−0.329396	+	0.944192i	$0.606845\pi$
$128$	−13.5828	−1.20056
$129$	17.1191	1.50725
$130$	1.45774	0.127852
$131$	20.9473	1.83018	0.915089	−	0.403251i	$-0.132120\pi$
$131$	20.9473	1.83018	0.915089	+	0.403251i	$0.132120\pi$
$132$	43.0591	3.74782
$133$	16.8539	1.46142
$134$	−25.6259	−2.21374
$135$	2.32503	0.200107
$136$	−26.7365	−2.29264
$137$	−17.8492	−1.52496	−0.762478	−	0.647014i	$-0.776018\pi$
$137$	−17.8492	−1.52496	−0.762478	+	0.647014i	$0.776018\pi$
$138$	−18.8985	−1.60875
$139$	−7.94108	−0.673553	−0.336777	−	0.941585i	$-0.609337\pi$
$139$	−7.94108	−0.673553	−0.336777	+	0.941585i	$0.609337\pi$
$140$	−14.2066	−1.20068
$141$	19.3590	1.63032
$142$	−7.06593	−0.592960
$143$	4.31177	0.360568
$144$	9.79744	0.816453
$145$	5.04122	0.418650
$146$	−4.39043	−0.363354
$147$	36.9593	3.04835
$148$	−32.8836	−2.70301
$149$	−15.3727	−1.25938	−0.629689	−	0.776847i	$-0.716818\pi$
$149$	−15.3727	−1.25938	−0.629689	+	0.776847i	$0.716818\pi$
$150$	24.5119	2.00139
$151$	14.1205	1.14911	0.574553	−	0.818467i	$-0.305176\pi$
$151$	14.1205	1.14911	0.574553	+	0.818467i	$0.305176\pi$
$152$	−27.4128	−2.22347
$153$	2.67060	0.215905
$154$	−58.4834	−4.71273
$155$	3.53518	0.283953
$156$	9.98642	0.799553
$157$	0.134069	0.0106998	0.00534992	−	0.999986i	$-0.498297\pi$
$157$	0.134069	0.0106998	0.00534992	+	0.999986i	$0.498297\pi$
$158$	−13.2881	−1.05714
$159$	−17.1184	−1.35758
$160$	8.22331	0.650110
$161$	18.4428	1.45350
$162$	28.7788	2.26108
$163$	−2.95807	−0.231694	−0.115847	−	0.993267i	$-0.536958\pi$
$163$	−2.95807	−0.231694	−0.115847	+	0.993267i	$0.536958\pi$
$164$	−41.1583	−3.21392
$165$	−4.61281	−0.359107
$166$	−16.2772	−1.26336
$167$	18.4290	1.42608	0.713040	−	0.701124i	$-0.247318\pi$
$167$	18.4290	1.42608	0.713040	+	0.701124i	$0.247318\pi$
$168$	−82.3861	−6.35623
$169$	1.00000	0.0769231
$170$	4.70911	0.361172
$171$	2.73815	0.209392
$172$	44.6750	3.40644
$173$	−6.28863	−0.478116	−0.239058	−	0.971005i	$-0.576839\pi$
$173$	−6.28863	−0.478116	−0.239058	+	0.971005i	$0.576839\pi$
$174$	48.0654	3.64383
$175$	−23.9209	−1.80825
$176$	51.0995	3.85177
$177$	−25.7150	−1.93286
$178$	10.8941	0.816545
$179$	15.0511	1.12497	0.562485	−	0.826808i	$-0.309845\pi$
$179$	15.0511	1.12497	0.562485	+	0.826808i	$0.309845\pi$
$180$	−2.30806	−0.172032
$181$	−13.4425	−0.999172	−0.499586	−	0.866264i	$-0.666514\pi$
$181$	−13.4425	−0.999172	−0.499586	+	0.866264i	$0.666514\pi$
$182$	−13.5637	−1.00541
$183$	29.9952	2.21731
$184$	−29.9971	−2.21142
$185$	3.52273	0.258996
$186$	33.7062	2.47146
$187$	13.9288	1.01857
$188$	50.5204	3.68458
$189$	−21.6335	−1.57360
$190$	4.82822	0.350276
$191$	5.81668	0.420880	0.210440	−	0.977607i	$-0.432510\pi$
$191$	5.81668	0.420880	0.210440	+	0.977607i	$0.432510\pi$
$192$	32.0386	2.31219
$193$	5.85741	0.421625	0.210813	−	0.977526i	$-0.432389\pi$
$193$	5.85741	0.421625	0.210813	+	0.977526i	$0.432389\pi$
$194$	−31.5756	−2.26699
$195$	−1.06982	−0.0766114
$196$	96.4514	6.88938
$197$	20.1878	1.43832	0.719161	−	0.694844i	$-0.244526\pi$
$197$	20.1878	1.43832	0.719161	+	0.694844i	$0.244526\pi$
$198$	−9.50144	−0.675238
$199$	1.02384	0.0725782	0.0362891	−	0.999341i	$-0.488446\pi$
$199$	1.02384	0.0725782	0.0362891	+	0.999341i	$0.488446\pi$
$200$	38.9071	2.75115
$201$	18.8065	1.32651
$202$	−12.5030	−0.879706
$203$	−46.9064	−3.29218
$204$	32.2603	2.25867
$205$	4.40918	0.307950
$206$	−25.2547	−1.75958
$207$	2.99629	0.208257
$208$	11.8512	0.821731
$209$	14.2811	0.987844
$210$	14.5107	1.00133
$211$	25.1691	1.73271	0.866355	−	0.499429i	$-0.166457\pi$
$211$	25.1691	1.73271	0.866355	+	0.499429i	$0.166457\pi$
$212$	−44.6733	−3.06817
$213$	5.18561	0.355312
$214$	−42.9607	−2.93673
$215$	−4.78592	−0.326397
$216$	35.1866	2.39415
$217$	−32.8934	−2.23295
$218$	−18.9723	−1.28496
$219$	3.22208	0.217728
$220$	−12.0379	−0.811595
$221$	3.23041	0.217301
$222$	33.5874	2.25424
$223$	−12.3351	−0.826019	−0.413009	−	0.910727i	$-0.635522\pi$
$223$	−12.3351	−0.826019	−0.413009	+	0.910727i	$0.635522\pi$
$224$	−76.5145	−5.11234
$225$	−3.88628	−0.259085
$226$	−13.6401	−0.907324
$227$	−2.75656	−0.182959	−0.0914796	−	0.995807i	$-0.529160\pi$
$227$	−2.75656	−0.182959	−0.0914796	+	0.995807i	$0.529160\pi$
$228$	33.0762	2.19053
$229$	−15.9414	−1.05344	−0.526720	−	0.850039i	$-0.676578\pi$
$229$	−15.9414	−1.05344	−0.526720	+	0.850039i	$0.676578\pi$
$230$	5.28340	0.348377
$231$	42.9203	2.82395
$232$	76.2929	5.00887
$233$	5.05176	0.330952	0.165476	−	0.986214i	$-0.447084\pi$
$233$	5.05176	0.330952	0.165476	+	0.986214i	$0.447084\pi$
$234$	−2.20361	−0.144054
$235$	−5.41212	−0.353048
$236$	−67.1076	−4.36833
$237$	9.75198	0.633459
$238$	−43.8163	−2.84019
$239$	−21.9768	−1.42156	−0.710781	−	0.703414i	$-0.751658\pi$
$239$	−21.9768	−1.42156	−0.710781	+	0.703414i	$0.751658\pi$
$240$	−12.6786	−0.818401
$241$	−4.87609	−0.314096	−0.157048	−	0.987591i	$-0.550198\pi$
$241$	−4.87609	−0.314096	−0.157048	+	0.987591i	$0.550198\pi$
$242$	−20.2349	−1.30075
$243$	−8.36626	−0.536696
$244$	78.2774	5.01120
$245$	−10.3326	−0.660125
$246$	42.0393	2.68032
$247$	3.31212	0.210745
$248$	53.5009	3.39731
$249$	11.9457	0.757025
$250$	−14.1414	−0.894382
$251$	−15.2350	−0.961626	−0.480813	−	0.876823i	$-0.659658\pi$
$251$	−15.2350	−0.961626	−0.480813	+	0.876823i	$0.659658\pi$
$252$	21.4755	1.35283
$253$	15.6274	0.982489
$254$	19.7894	1.24170
$255$	−3.45596	−0.216420
$256$	3.44935	0.215584
$257$	25.4546	1.58781	0.793907	−	0.608040i	$-0.208044\pi$
$257$	25.4546	1.58781	0.793907	+	0.608040i	$0.208044\pi$
$258$	−45.6313	−2.84088
$259$	−32.7775	−2.03670
$260$	−2.79187	−0.173144
$261$	−7.62059	−0.471703
$262$	−55.8357	−3.44954
$263$	−2.31874	−0.142980	−0.0714898	−	0.997441i	$-0.522775\pi$
$263$	−2.31874	−0.142980	−0.0714898	+	0.997441i	$0.522775\pi$
$264$	−69.8095	−4.29648
$265$	4.78573	0.293985
$266$	−44.9245	−2.75450
$267$	−7.99503	−0.489288
$268$	49.0787	2.99796
$269$	16.2204	0.988976	0.494488	−	0.869185i	$-0.335356\pi$
$269$	16.2204	0.988976	0.494488	+	0.869185i	$0.335356\pi$
$270$	−6.19743	−0.377163
$271$	1.72110	0.104549	0.0522746	−	0.998633i	$-0.483353\pi$
$271$	1.72110	0.104549	0.0522746	+	0.998633i	$0.483353\pi$
$272$	38.2842	2.32132
$273$	9.95423	0.602457
$274$	47.5774	2.87425
$275$	−20.2693	−1.22228
$276$	36.1945	2.17865
$277$	5.49352	0.330074	0.165037	−	0.986287i	$-0.447226\pi$
$277$	5.49352	0.330074	0.165037	+	0.986287i	$0.447226\pi$
$278$	21.1671	1.26952
$279$	−5.34399	−0.319936
$280$	23.0324	1.37645
$281$	−18.5818	−1.10850	−0.554249	−	0.832351i	$-0.686995\pi$
$281$	−18.5818	−1.10850	−0.554249	+	0.832351i	$0.686995\pi$
$282$	−51.6018	−3.07284
$283$	10.1617	0.604050	0.302025	−	0.953300i	$-0.402337\pi$
$283$	10.1617	0.604050	0.302025	+	0.953300i	$0.402337\pi$
$284$	13.5327	0.803017
$285$	−3.54337	−0.209891
$286$	−11.4931	−0.679603
$287$	−41.0256	−2.42166
$288$	−12.4308	−0.732494
$289$	−6.56444	−0.386143
$290$	−13.4375	−0.789076
$291$	23.1729	1.35842
$292$	8.40855	0.492073
$293$	6.73369	0.393387	0.196693	−	0.980465i	$-0.436980\pi$
$293$	6.73369	0.393387	0.196693	+	0.980465i	$0.436980\pi$
$294$	−98.5159	−5.74556
$295$	7.18906	0.418563
$296$	53.3124	3.09872
$297$	−18.3310	−1.06367
$298$	40.9762	2.37369
$299$	3.62437	0.209603
$300$	−46.9453	−2.71039
$301$	44.5310	2.56672
$302$	−37.6384	−2.16585
$303$	9.17578	0.527135
$304$	39.2525	2.25129
$305$	−8.38566	−0.480161
$306$	−7.11856	−0.406941
$307$	−3.27719	−0.187039	−0.0935194	−	0.995617i	$-0.529812\pi$
$307$	−3.27719	−0.187039	−0.0935194	+	0.995617i	$0.529812\pi$
$308$	112.008	6.38223
$309$	18.5341	1.05437
$310$	−9.42312	−0.535197
$311$	30.7262	1.74232	0.871162	−	0.490995i	$-0.163367\pi$
$311$	30.7262	1.74232	0.871162	+	0.490995i	$0.163367\pi$
$312$	−16.1905	−0.916604
$313$	16.4176	0.927979	0.463989	−	0.885841i	$-0.346418\pi$
$313$	16.4176	0.927979	0.463989	+	0.885841i	$0.346418\pi$
$314$	−0.357363	−0.0201672
$315$	−2.30062	−0.129625
$316$	25.4494	1.43164
$317$	−27.2002	−1.52772	−0.763859	−	0.645384i	$-0.776698\pi$
$317$	−27.2002	−1.52772	−0.763859	+	0.645384i	$0.776698\pi$
$318$	45.6295	2.55878
$319$	−39.7459	−2.22535
$320$	−8.95693	−0.500708
$321$	31.5284	1.75974
$322$	−49.1598	−2.73957
$323$	10.6995	0.595337
$324$	−55.1172	−3.06207
$325$	−4.70091	−0.260760
$326$	7.88480	0.436699
$327$	13.9235	0.769972
$328$	66.7277	3.68442
$329$	50.3575	2.77630
$330$	12.2956	0.676849
$331$	25.8426	1.42044	0.710219	−	0.703980i	$-0.248596\pi$
$331$	25.8426	1.42044	0.710219	+	0.703980i	$0.248596\pi$
$332$	31.1742	1.71090
$333$	−5.32516	−0.291817
$334$	−49.1230	−2.68789
$335$	−5.25768	−0.287258
$336$	117.969	6.43575
$337$	12.9232	0.703974	0.351987	−	0.936005i	$-0.385506\pi$
$337$	12.9232	0.703974	0.351987	+	0.936005i	$0.385506\pi$
$338$	−2.66552	−0.144985
$339$	10.0103	0.543684
$340$	−9.01889	−0.489118
$341$	−27.8721	−1.50936
$342$	−7.29861	−0.394664
$343$	60.5205	3.26780
$344$	−72.4293	−3.90512
$345$	−3.87742	−0.208753
$346$	16.7625	0.901157
$347$	−20.9250	−1.12331	−0.561656	−	0.827371i	$-0.689835\pi$
$347$	−20.9250	−1.12331	−0.561656	+	0.827371i	$0.689835\pi$
$348$	−92.0550	−4.93466
$349$	11.1487	0.596776	0.298388	−	0.954445i	$-0.403551\pi$
$349$	11.1487	0.596776	0.298388	+	0.954445i	$0.403551\pi$
$350$	63.7617	3.40821
$351$	−4.25139	−0.226922
$352$	−64.8342	−3.45568
$353$	−11.9257	−0.634740	−0.317370	−	0.948302i	$-0.602800\pi$
$353$	−11.9257	−0.634740	−0.317370	+	0.948302i	$0.602800\pi$
$354$	68.5440	3.64307
$355$	−1.44972	−0.0769433
$356$	−20.8644	−1.10581
$357$	32.1563	1.70189
$358$	−40.1190	−2.12035
$359$	−32.9504	−1.73905	−0.869527	−	0.493886i	$-0.835576\pi$
$359$	−32.9504	−1.73905	−0.869527	+	0.493886i	$0.835576\pi$
$360$	3.74193	0.197217
$361$	−8.02986	−0.422624
$362$	35.8313	1.88325
$363$	14.8502	0.779432
$364$	25.9772	1.36157
$365$	−0.900787	−0.0471493
$366$	−79.9529	−4.17921
$367$	13.1036	0.684002	0.342001	−	0.939700i	$-0.388895\pi$
$367$	13.1036	0.684002	0.342001	+	0.939700i	$0.388895\pi$
$368$	42.9530	2.23908
$369$	−6.66517	−0.346975
$370$	−9.38992	−0.488159
$371$	−44.5293	−2.31184
$372$	−64.5541	−3.34698
$373$	−15.5963	−0.807544	−0.403772	−	0.914860i	$-0.632301\pi$
$373$	−15.5963	−0.807544	−0.403772	+	0.914860i	$0.632301\pi$
$374$	−37.1275	−1.91982
$375$	10.3782	0.535929
$376$	−81.9061	−4.22398
$377$	−9.21801	−0.474752
$378$	57.6645	2.96594
$379$	−10.5450	−0.541662	−0.270831	−	0.962627i	$-0.587298\pi$
$379$	−10.5450	−0.541662	−0.270831	+	0.962627i	$0.587298\pi$
$380$	−9.24701	−0.474362
$381$	−14.5232	−0.744048
$382$	−15.5045	−0.793279
$383$	−12.1129	−0.618939	−0.309469	−	0.950909i	$-0.600151\pi$
$383$	−12.1129	−0.618939	−0.309469	+	0.950909i	$0.600151\pi$
$384$	−26.5707	−1.35593
$385$	−11.9991	−0.611530
$386$	−15.6131	−0.794684
$387$	7.23467	0.367759
$388$	60.4736	3.07008
$389$	35.2205	1.78575	0.892875	−	0.450304i	$-0.148684\pi$
$389$	35.2205	1.78575	0.892875	+	0.450304i	$0.148684\pi$
$390$	2.85163	0.144398
$391$	11.7082	0.592110
$392$	−156.372	−7.89796
$393$	40.9771	2.06702
$394$	−53.8111	−2.71096
$395$	−2.72633	−0.137176
$396$	18.1972	0.914443
$397$	7.37343	0.370062	0.185031	−	0.982733i	$-0.440761\pi$
$397$	7.37343	0.370062	0.185031	+	0.982733i	$0.440761\pi$
$398$	−2.72907	−0.136796
$399$	32.9696	1.65054
$400$	−55.7113	−2.78557
$401$	34.0558	1.70066	0.850332	−	0.526246i	$-0.176401\pi$
$401$	34.0558	1.70066	0.850332	+	0.526246i	$0.176401\pi$
$402$	−50.1293	−2.50022
$403$	−6.46419	−0.322004
$404$	23.9457	1.19134
$405$	5.90457	0.293400
$406$	125.030	6.20514
$407$	−27.7739	−1.37670
$408$	−52.3019	−2.58933
$409$	0.204404	0.0101071	0.00505356	−	0.999987i	$-0.498391\pi$
$409$	0.204404	0.0101071	0.00505356	+	0.999987i	$0.498391\pi$
$410$	−11.7528	−0.580428
$411$	−34.9165	−1.72230
$412$	48.3678	2.38291
$413$	−66.8912	−3.29150
$414$	−7.98669	−0.392524
$415$	−3.33961	−0.163935
$416$	−15.0366	−0.737229
$417$	−15.5343	−0.760719
$418$	−38.0666	−1.86190
$419$	−14.4826	−0.707522	−0.353761	−	0.935336i	$-0.615097\pi$
$419$	−14.4826	−0.707522	−0.353761	+	0.935336i	$0.615097\pi$
$420$	−27.7909	−1.35606
$421$	−22.3520	−1.08937	−0.544684	−	0.838641i	$-0.683351\pi$
$421$	−22.3520	−1.08937	−0.544684	+	0.838641i	$0.683351\pi$
$422$	−67.0887	−3.26583
$423$	8.18127	0.397787
$424$	72.4265	3.51734
$425$	−15.1859	−0.736624
$426$	−13.8224	−0.669695
$427$	78.0251	3.77590
$428$	82.2785	3.97708
$429$	8.43467	0.407230
$430$	12.7570	0.615196
$431$	−23.8134	−1.14705	−0.573525	−	0.819188i	$-0.694425\pi$
$431$	−23.8134	−1.14705	−0.573525	+	0.819188i	$0.694425\pi$
$432$	−50.3839	−2.42410
$433$	−2.34725	−0.112802	−0.0564009	−	0.998408i	$-0.517963\pi$
$433$	−2.34725	−0.112802	−0.0564009	+	0.998408i	$0.517963\pi$
$434$	87.6782	4.20869
$435$	9.86161	0.472828
$436$	36.3357	1.74016
$437$	12.0044	0.574246
$438$	−8.58854	−0.410376
$439$	39.1738	1.86966	0.934831	−	0.355092i	$-0.115551\pi$
$439$	39.1738	1.86966	0.934831	+	0.355092i	$0.115551\pi$
$440$	19.5164	0.930408
$441$	15.6193	0.743778
$442$	−8.61074	−0.409571
$443$	−7.33294	−0.348398	−0.174199	−	0.984710i	$-0.555734\pi$
$443$	−7.33294	−0.348398	−0.174199	+	0.984710i	$0.555734\pi$
$444$	−64.3267	−3.05281
$445$	2.23514	0.105956
$446$	32.8795	1.55689
$447$	−30.0720	−1.42236
$448$	83.3405	3.93747
$449$	−2.98362	−0.140806	−0.0704030	−	0.997519i	$-0.522429\pi$
$449$	−2.98362	−0.140806	−0.0704030	+	0.997519i	$0.522429\pi$
$450$	10.3590	0.488326
$451$	−34.7628	−1.63692
$452$	26.1235	1.22875
$453$	27.6224	1.29781
$454$	7.34767	0.344843
$455$	−2.78287	−0.130463
$456$	−53.6248	−2.51121
$457$	15.1433	0.708374	0.354187	−	0.935175i	$-0.384758\pi$
$457$	15.1433	0.708374	0.354187	+	0.935175i	$0.384758\pi$
$458$	42.4923	1.98553
$459$	−13.7337	−0.641036
$460$	−10.1188	−0.471790
$461$	−30.2219	−1.40757	−0.703787	−	0.710411i	$-0.748509\pi$
$461$	−30.2219	−1.40757	−0.703787	+	0.710411i	$0.748509\pi$
$462$	−114.405	−5.32261
$463$	−25.0104	−1.16233	−0.581167	−	0.813784i	$-0.697404\pi$
$463$	−25.0104	−1.16233	−0.581167	+	0.813784i	$0.697404\pi$
$464$	−109.244	−5.07154
$465$	6.91552	0.320699
$466$	−13.4656	−0.623782
$467$	−34.5044	−1.59667	−0.798336	−	0.602213i	$-0.794286\pi$
$467$	−34.5044	−1.59667	−0.798336	+	0.602213i	$0.794286\pi$
$468$	4.22035	0.195086
$469$	48.9205	2.25894
$470$	14.4261	0.665428
$471$	0.262265	0.0120845
$472$	108.798	5.00783
$473$	37.7331	1.73497
$474$	−25.9941	−1.19395
$475$	−15.5700	−0.714400
$476$	83.9170	3.84633
$477$	−7.23439	−0.331240
$478$	58.5797	2.67937
$479$	−38.8642	−1.77575	−0.887875	−	0.460085i	$-0.847819\pi$
$479$	−38.8642	−1.77575	−0.887875	+	0.460085i	$0.847819\pi$
$480$	16.0864	0.734241
$481$	−6.44142	−0.293703
$482$	12.9973	0.592012
$483$	36.0778	1.64160
$484$	38.7540	1.76154
$485$	−6.47838	−0.294168
$486$	22.3005	1.01157
$487$	8.76289	0.397084	0.198542	−	0.980092i	$-0.436379\pi$
$487$	8.76289	0.397084	0.198542	+	0.980092i	$0.436379\pi$
$488$	−126.907	−5.74481
$489$	−5.78656	−0.261677
$490$	27.5418	1.24421
$491$	7.11925	0.321287	0.160644	−	0.987012i	$-0.448643\pi$
$491$	7.11925	0.321287	0.160644	+	0.987012i	$0.448643\pi$
$492$	−80.5137	−3.62984
$493$	−29.7780	−1.34113
$494$	−8.82854	−0.397215
$495$	−1.94942	−0.0876198
$496$	−76.6082	−3.43981
$497$	13.4891	0.605067
$498$	−31.8414	−1.42685
$499$	25.6400	1.14780	0.573901	−	0.818925i	$-0.305429\pi$
$499$	25.6400	1.14780	0.573901	+	0.818925i	$0.305429\pi$
$500$	27.0837	1.21122
$501$	36.0508	1.61063
$502$	40.6093	1.81248
$503$	−22.2128	−0.990419	−0.495209	−	0.868774i	$-0.664909\pi$
$503$	−22.2128	−0.990419	−0.495209	+	0.868774i	$0.664909\pi$
$504$	−34.8171	−1.55088
$505$	−2.56524	−0.114152
$506$	−41.6553	−1.85181
$507$	1.95620	0.0868778
$508$	−37.9008	−1.68157
$509$	5.80802	0.257436	0.128718	−	0.991681i	$-0.458914\pi$
$509$	5.80802	0.257436	0.128718	+	0.991681i	$0.458914\pi$
$510$	9.21194	0.407911
$511$	8.38145	0.370773
$512$	17.9714	0.794229
$513$	−14.0811	−0.621696
$514$	−67.8498	−2.99273
$515$	−5.18152	−0.228325
$516$	87.3931	3.84727
$517$	42.6702	1.87663
$518$	87.3693	3.83879
$519$	−12.3018	−0.539989
$520$	4.52631	0.198492
$521$	5.01502	0.219712	0.109856	−	0.993948i	$-0.464961\pi$
$521$	5.01502	0.219712	0.109856	+	0.993948i	$0.464961\pi$
$522$	20.3129	0.889070
$523$	−25.0774	−1.09656	−0.548280	−	0.836295i	$-0.684717\pi$
$523$	−25.0774	−1.09656	−0.548280	+	0.836295i	$0.684717\pi$
$524$	106.937	4.67155
$525$	−46.7940	−2.04226
$526$	6.18065	0.269489
$527$	−20.8820	−0.909634
$528$	99.9607	4.35023
$529$	−9.86394	−0.428867
$530$	−12.7565	−0.554106
$531$	−10.8674	−0.471605
$532$	86.0396	3.73029
$533$	−8.06232	−0.349218
$534$	21.3110	0.922215
$535$	−8.81428	−0.381075
$536$	−79.5688	−3.43685
$537$	29.4429	1.27055
$538$	−43.2359	−1.86403
$539$	81.4642	3.50891
$540$	11.8693	0.510774
$541$	−42.1749	−1.81324	−0.906619	−	0.421950i	$-0.861346\pi$
$541$	−42.1749	−1.81324	−0.906619	+	0.421950i	$0.861346\pi$
$542$	−4.58762	−0.197055
$543$	−26.2961	−1.12848
$544$	−48.5743	−2.08261
$545$	−3.89255	−0.166739
$546$	−26.5332	−1.13552
$547$	−28.5566	−1.22099	−0.610495	−	0.792020i	$-0.709030\pi$
$547$	−28.5566	−1.22099	−0.610495	+	0.792020i	$0.709030\pi$
$548$	−91.1203	−3.89246
$549$	12.6762	0.541009
$550$	54.0282	2.30377
$551$	−30.5312	−1.30067
$552$	−58.6802	−2.49760
$553$	25.3673	1.07873
$554$	−14.6431	−0.622126
$555$	6.89115	0.292513
$556$	−40.5393	−1.71925
$557$	8.59940	0.364368	0.182184	−	0.983264i	$-0.441683\pi$
$557$	8.59940	0.364368	0.182184	+	0.983264i	$0.441683\pi$
$558$	14.2445	0.603019
$559$	8.75120	0.370136
$560$	−32.9803	−1.39367
$561$	27.2475	1.15039
$562$	49.5303	2.08931
$563$	14.3389	0.604312	0.302156	−	0.953258i	$-0.402294\pi$
$563$	14.3389	0.604312	0.302156	+	0.953258i	$0.402294\pi$
$564$	98.8278	4.16140
$565$	−2.79854	−0.117736
$566$	−27.0863	−1.13852
$567$	−54.9395	−2.30724
$568$	−21.9398	−0.920575
$569$	9.95587	0.417372	0.208686	−	0.977983i	$-0.433081\pi$
$569$	9.95587	0.417372	0.208686	+	0.977983i	$0.433081\pi$
$570$	9.44494	0.395605
$571$	−16.3302	−0.683396	−0.341698	−	0.939810i	$-0.611002\pi$
$571$	−16.3302	−0.683396	−0.341698	+	0.939810i	$0.611002\pi$
$572$	22.0117	0.920354
$573$	11.3786	0.475347
$574$	109.355	4.56438
$575$	−17.0379	−0.710528
$576$	13.5398	0.564159
$577$	−35.1636	−1.46388	−0.731939	−	0.681370i	$-0.761384\pi$
$577$	−35.1636	−1.46388	−0.731939	+	0.681370i	$0.761384\pi$
$578$	17.4977	0.727807
$579$	11.4582	0.476188
$580$	25.7355	1.06861
$581$	31.0737	1.28915
$582$	−61.7680	−2.56037
$583$	−37.7317	−1.56269
$584$	−13.6323	−0.564111
$585$	−0.452115	−0.0186927
$586$	−17.9488	−0.741459
$587$	−15.9690	−0.659112	−0.329556	−	0.944136i	$-0.606899\pi$
$587$	−15.9690	−0.659112	−0.329556	+	0.944136i	$0.606899\pi$
$588$	188.678	7.78094
$589$	−21.4102	−0.882191
$590$	−19.1626	−0.788912
$591$	39.4913	1.62446
$592$	−76.3383	−3.13749
$593$	27.8958	1.14554	0.572771	−	0.819715i	$-0.305868\pi$
$593$	27.8958	1.14554	0.572771	+	0.819715i	$0.305868\pi$
$594$	48.8617	2.00482
$595$	−8.98982	−0.368546
$596$	−78.4777	−3.21457
$597$	2.00284	0.0819706
$598$	−9.66085	−0.395061
$599$	22.8399	0.933212	0.466606	−	0.884465i	$-0.345477\pi$
$599$	22.8399	0.933212	0.466606	+	0.884465i	$0.345477\pi$
$600$	76.1100	3.10718
$601$	−38.0646	−1.55269	−0.776344	−	0.630309i	$-0.782928\pi$
$601$	−38.0646	−1.55269	−0.776344	+	0.630309i	$0.782928\pi$
$602$	−118.698	−4.83779
$603$	7.94781	0.323660
$604$	72.0851	2.93310
$605$	−4.15161	−0.168787
$606$	−24.4583	−0.993549
$607$	−3.06235	−0.124297	−0.0621484	−	0.998067i	$-0.519795\pi$
$607$	−3.06235	−0.124297	−0.0621484	+	0.998067i	$0.519795\pi$
$608$	−49.8029	−2.01978
$609$	−91.7582	−3.71823
$610$	22.3522	0.905013
$611$	9.89622	0.400358
$612$	13.6335	0.551101
$613$	−29.3799	−1.18664	−0.593322	−	0.804966i	$-0.702184\pi$
$613$	−29.3799	−1.18664	−0.593322	+	0.804966i	$0.702184\pi$
$614$	8.73542	0.352533
$615$	8.62522	0.347803
$616$	−181.592	−7.31656
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−49.4031	−1.98729
$619$	21.6630	0.870709	0.435355	−	0.900259i	$-0.356623\pi$
$619$	21.6630	0.870709	0.435355	+	0.900259i	$0.356623\pi$
$620$	18.0472	0.724792
$621$	−15.4086	−0.618326
$622$	−81.9015	−3.28395
$623$	−20.7971	−0.833218
$624$	23.1832	0.928072
$625$	20.6032	0.824127
$626$	−43.7615	−1.74906
$627$	27.9366	1.11568
$628$	0.684422	0.0273114
$629$	−20.8084	−0.829687
$630$	6.13235	0.244319
$631$	5.74721	0.228793	0.114396	−	0.993435i	$-0.463507\pi$
$631$	5.74721	0.228793	0.114396	+	0.993435i	$0.463507\pi$
$632$	−41.2598	−1.64123
$633$	49.2356	1.95694
$634$	72.5029	2.87946
$635$	4.06021	0.161125
$636$	−87.3897	−3.46523
$637$	18.8934	0.748585
$638$	105.944	4.19435
$639$	2.19148	0.0866938
$640$	7.42828	0.293629
$641$	−33.6064	−1.32737	−0.663687	−	0.748010i	$-0.731009\pi$
$641$	−33.6064	−1.32737	−0.663687	+	0.748010i	$0.731009\pi$
$642$	−84.0396	−3.31678
$643$	−33.6896	−1.32859	−0.664295	−	0.747471i	$-0.731268\pi$
$643$	−33.6896	−1.32859	−0.664295	+	0.747471i	$0.731268\pi$
$644$	94.1510	3.71007
$645$	−9.36220	−0.368636
$646$	−28.5198	−1.12210
$647$	−11.2549	−0.442476	−0.221238	−	0.975220i	$-0.571010\pi$
$647$	−11.2549	−0.442476	−0.221238	+	0.975220i	$0.571010\pi$
$648$	89.3587	3.51034
$649$	−56.6800	−2.22488
$650$	12.5304	0.491483
$651$	−64.3460	−2.52192
$652$	−15.1010	−0.591400
$653$	−20.1713	−0.789364	−0.394682	−	0.918818i	$-0.629145\pi$
$653$	−20.1713	−0.789364	−0.394682	+	0.918818i	$0.629145\pi$
$654$	−37.1135	−1.45125
$655$	−11.4558	−0.447617
$656$	−95.5479	−3.73052
$657$	1.36168	0.0531243
$658$	−134.229	−5.23280
$659$	30.6622	1.19443	0.597215	−	0.802081i	$-0.296274\pi$
$659$	30.6622	1.19443	0.597215	+	0.802081i	$0.296274\pi$
$660$	−23.5485	−0.916624
$661$	14.4913	0.563645	0.281823	−	0.959467i	$-0.409061\pi$
$661$	14.4913	0.563645	0.281823	+	0.959467i	$0.409061\pi$
$662$	−68.8841	−2.67726
$663$	6.31932	0.245422
$664$	−50.5410	−1.96137
$665$	−9.21720	−0.357428
$666$	14.1943	0.550020
$667$	−33.4095	−1.29362
$668$	94.0804	3.64008
$669$	−24.1299	−0.932915
$670$	14.0145	0.541426
$671$	66.1142	2.55231
$672$	−149.677	−5.77393
$673$	27.9253	1.07644	0.538221	−	0.842804i	$-0.319097\pi$
$673$	27.9253	1.07644	0.538221	+	0.842804i	$0.319097\pi$
$674$	−34.4472	−1.32686
$675$	19.9854	0.769239
$676$	5.10502	0.196347
$677$	5.79643	0.222775	0.111387	−	0.993777i	$-0.464471\pi$
$677$	5.79643	0.222775	0.111387	+	0.993777i	$0.464471\pi$
$678$	−26.6827	−1.02474
$679$	60.2786	2.31328
$680$	14.6219	0.560723
$681$	−5.39237	−0.206636
$682$	74.2937	2.84485
$683$	−8.31609	−0.318206	−0.159103	−	0.987262i	$-0.550860\pi$
$683$	−8.31609	−0.318206	−0.159103	+	0.987262i	$0.550860\pi$
$684$	13.9783	0.534474
$685$	9.76148	0.372967
$686$	−161.319	−6.15918
$687$	−31.1846	−1.18977
$688$	103.712	3.95398
$689$	−8.75086	−0.333381
$690$	10.3354	0.393461
$691$	37.3351	1.42029	0.710147	−	0.704054i	$-0.248629\pi$
$691$	37.3351	1.42029	0.710147	+	0.704054i	$0.248629\pi$
$692$	−32.1036	−1.22039
$693$	18.1385	0.689025
$694$	55.7760	2.11723
$695$	4.34288	0.164735
$696$	149.244	5.65707
$697$	−26.0446	−0.986510
$698$	−29.7171	−1.12481
$699$	9.88224	0.373781
$700$	−122.117	−4.61557
$701$	1.50508	0.0568460	0.0284230	−	0.999596i	$-0.490951\pi$
$701$	1.50508	0.0568460	0.0284230	+	0.999596i	$0.490951\pi$
$702$	11.3322	0.427706
$703$	−21.3348	−0.804655
$704$	70.6182	2.66152
$705$	−10.5872	−0.398736
$706$	31.7882	1.19637
$707$	23.8685	0.897668
$708$	−131.276	−4.93364
$709$	12.2721	0.460889	0.230445	−	0.973085i	$-0.425982\pi$
$709$	12.2721	0.460889	0.230445	+	0.973085i	$0.425982\pi$
$710$	3.86427	0.145023
$711$	4.12128	0.154560
$712$	33.8263	1.26769
$713$	−23.4286	−0.877409
$714$	−85.7133	−3.20774
$715$	−2.35805	−0.0881861
$716$	76.8360	2.87149
$717$	−42.9910	−1.60553
$718$	87.8300	3.27779
$719$	19.9981	0.745802	0.372901	−	0.927871i	$-0.378363\pi$
$719$	19.9981	0.745802	0.372901	+	0.927871i	$0.378363\pi$
$720$	−5.35810	−0.199684
$721$	48.2119	1.79551
$722$	21.4038	0.796566
$723$	−9.53858	−0.354744
$724$	−68.6241	−2.55039
$725$	43.3331	1.60935
$726$	−39.5835	−1.46908
$727$	21.9043	0.812385	0.406193	−	0.913787i	$-0.366856\pi$
$727$	21.9043	0.812385	0.406193	+	0.913787i	$0.366856\pi$
$728$	−42.1155	−1.56090
$729$	16.0240	0.593481
$730$	2.40107	0.0888675
$731$	28.2700	1.04560
$732$	153.126	5.65970
$733$	24.0500	0.888308	0.444154	−	0.895950i	$-0.353504\pi$
$733$	24.0500	0.888308	0.444154	+	0.895950i	$0.353504\pi$
$734$	−34.9279	−1.28921
$735$	−20.2126	−0.745552
$736$	−54.4981	−2.00883
$737$	41.4526	1.52693
$738$	17.7662	0.653982
$739$	−49.4572	−1.81931	−0.909656	−	0.415362i	$-0.863655\pi$
$739$	−49.4572	−1.81931	−0.909656	+	0.415362i	$0.863655\pi$
$740$	17.9836	0.661090
$741$	6.47916	0.238018
$742$	118.694	4.35739
$743$	−15.8472	−0.581379	−0.290689	−	0.956817i	$-0.593885\pi$
$743$	−15.8472	−0.581379	−0.290689	+	0.956817i	$0.593885\pi$
$744$	104.658	3.83696
$745$	8.40712	0.308013
$746$	41.5722	1.52207
$747$	5.04834	0.184709
$748$	71.1067	2.59992
$749$	82.0132	2.99670
$750$	−27.6634	−1.01012
$751$	−51.7162	−1.88715	−0.943576	−	0.331155i	$-0.892562\pi$
$751$	−51.7162	−1.88715	−0.943576	+	0.331155i	$0.892562\pi$
$752$	117.282	4.27683
$753$	−29.8027	−1.08607
$754$	24.5708	0.894817
$755$	−7.72230	−0.281043
$756$	−110.439	−4.01663
$757$	−18.0122	−0.654663	−0.327332	−	0.944910i	$-0.606149\pi$
$757$	−18.0122	−0.654663	−0.327332	+	0.944910i	$0.606149\pi$
$758$	28.1080	1.02093
$759$	30.5704	1.10963
$760$	14.9917	0.543806
$761$	−12.7880	−0.463564	−0.231782	−	0.972768i	$-0.574456\pi$
$761$	−12.7880	−0.463564	−0.231782	+	0.972768i	$0.574456\pi$
$762$	38.7120	1.40239
$763$	36.2186	1.31120
$764$	29.6943	1.07430
$765$	−1.46052	−0.0528052
$766$	32.2872	1.16658
$767$	−13.1454	−0.474653
$768$	6.74761	0.243483
$769$	−9.62972	−0.347257	−0.173628	−	0.984811i	$-0.555549\pi$
$769$	−9.62972	−0.347257	−0.173628	+	0.984811i	$0.555549\pi$
$770$	31.9839	1.15262
$771$	49.7942	1.79329
$772$	29.9022	1.07620
$773$	20.3494	0.731918	0.365959	−	0.930631i	$-0.380741\pi$
$773$	20.3494	0.731918	0.365959	+	0.930631i	$0.380741\pi$
$774$	−19.2842	−0.693156
$775$	30.3876	1.09156
$776$	−98.0427	−3.51953
$777$	−64.1193	−2.30027
$778$	−93.8811	−3.36580
$779$	−26.7034	−0.956747
$780$	−5.46145	−0.195551
$781$	11.4299	0.408994
$782$	−31.2085	−1.11601
$783$	39.1894	1.40051
$784$	223.909	7.99676
$785$	−0.0733204	−0.00261692
$786$	−109.226	−3.89595
$787$	−9.93411	−0.354113	−0.177056	−	0.984201i	$-0.556657\pi$
$787$	−9.93411	−0.354113	−0.177056	+	0.984201i	$0.556657\pi$
$788$	103.059	3.67133
$789$	−4.53591	−0.161483
$790$	7.26709	0.258552
$791$	26.0393	0.925850
$792$	−29.5021	−1.04831
$793$	15.3334	0.544506
$794$	−19.6541	−0.697496
$795$	9.36184	0.332030
$796$	5.22673	0.185256
$797$	−7.28756	−0.258139	−0.129069	−	0.991636i	$-0.541199\pi$
$797$	−7.28756	−0.258139	−0.129069	+	0.991636i	$0.541199\pi$
$798$	−87.8812	−3.11096
$799$	31.9689	1.13098
$800$	70.6857	2.49912
$801$	−3.37877	−0.119383
$802$	−90.7765	−3.20543
$803$	7.10198	0.250623
$804$	96.0077	3.38593
$805$	−10.0862	−0.355490
$806$	17.2305	0.606917
$807$	31.7303	1.11696
$808$	−38.8219	−1.36575
$809$	−7.31487	−0.257177	−0.128588	−	0.991698i	$-0.541045\pi$
$809$	−7.31487	−0.257177	−0.128588	+	0.991698i	$0.541045\pi$
$810$	−15.7388	−0.553004
$811$	29.1668	1.02418	0.512092	−	0.858930i	$-0.328871\pi$
$811$	29.1668	1.02418	0.512092	+	0.858930i	$0.328871\pi$
$812$	−239.458	−8.40333
$813$	3.36680	0.118079
$814$	74.0320	2.59482
$815$	1.61773	0.0566666
$816$	74.8914	2.62172
$817$	28.9850	1.01406
$818$	−0.544843	−0.0190500
$819$	4.20675	0.146996
$820$	22.5089	0.786046
$821$	19.2566	0.672059	0.336029	−	0.941851i	$-0.390916\pi$
$821$	19.2566	0.672059	0.336029	+	0.941851i	$0.390916\pi$
$822$	93.0707	3.24621
$823$	−26.9887	−0.940768	−0.470384	−	0.882462i	$-0.655885\pi$
$823$	−26.9887	−0.940768	−0.470384	+	0.882462i	$0.655885\pi$
$824$	−78.4163	−2.73176
$825$	−39.6507	−1.38046
$826$	178.300	6.20385
$827$	29.4890	1.02543	0.512716	−	0.858558i	$-0.328639\pi$
$827$	29.4890	1.02543	0.512716	+	0.858558i	$0.328639\pi$
$828$	15.2961	0.531577
$829$	−50.3478	−1.74865	−0.874326	−	0.485339i	$-0.838696\pi$
$829$	−50.3478	−1.74865	−0.874326	+	0.485339i	$0.838696\pi$
$830$	8.90180	0.308986
$831$	10.7464	0.372789
$832$	16.3780	0.567806
$833$	61.0336	2.11469
$834$	41.4071	1.43381
$835$	−10.0786	−0.348784
$836$	72.9053	2.52148
$837$	27.4818	0.949910
$838$	38.6038	1.33354
$839$	−35.9444	−1.24094	−0.620469	−	0.784231i	$-0.713058\pi$
$839$	−35.9444	−1.24094	−0.620469	+	0.784231i	$0.713058\pi$
$840$	45.0559	1.55458
$841$	55.9718	1.93006
$842$	59.5797	2.05325
$843$	−36.3497	−1.25195
$844$	128.489	4.42276
$845$	−0.546887	−0.0188135
$846$	−21.8074	−0.749753
$847$	38.6290	1.32731
$848$	−103.708	−3.56134
$849$	19.8783	0.682221
$850$	40.4784	1.38840
$851$	−23.3461	−0.800294
$852$	26.4726	0.906937
$853$	−8.25046	−0.282490	−0.141245	−	0.989975i	$-0.545111\pi$
$853$	−8.25046	−0.282490	−0.141245	+	0.989975i	$0.545111\pi$
$854$	−207.978	−7.11685
$855$	−1.49746	−0.0512121
$856$	−133.394	−4.55931
$857$	−20.1091	−0.686915	−0.343457	−	0.939168i	$-0.611598\pi$
$857$	−20.1091	−0.686915	−0.343457	+	0.939168i	$0.611598\pi$
$858$	−22.4828	−0.767551
$859$	7.75479	0.264590	0.132295	−	0.991210i	$-0.457765\pi$
$859$	7.75479	0.264590	0.132295	+	0.991210i	$0.457765\pi$
$860$	−24.4322	−0.833131
$861$	−80.2541	−2.73505
$862$	63.4751	2.16197
$863$	−45.9226	−1.56322	−0.781612	−	0.623765i	$-0.785602\pi$
$863$	−45.9226	−1.56322	−0.781612	+	0.623765i	$0.785602\pi$
$864$	63.9263	2.17482
$865$	3.43917	0.116935
$866$	6.25666	0.212610
$867$	−12.8413	−0.436114
$868$	−167.921	−5.69963
$869$	21.4949	0.729165
$870$	−26.2864	−0.891191
$871$	9.61382	0.325752
$872$	−58.9092	−1.99492
$873$	9.79310	0.331446
$874$	−31.9979	−1.08234
$875$	26.9964	0.912644
$876$	16.4488	0.555753
$877$	2.46426	0.0832122	0.0416061	−	0.999134i	$-0.486753\pi$
$877$	2.46426	0.0832122	0.0416061	+	0.999134i	$0.486753\pi$
$878$	−104.419	−3.52396
$879$	13.1724	0.444295
$880$	−27.9457	−0.942048
$881$	−34.0110	−1.14586	−0.572931	−	0.819604i	$-0.694194\pi$
$881$	−34.0110	−1.14586	−0.572931	+	0.819604i	$0.694194\pi$
$882$	−41.6337	−1.40188
$883$	10.3285	0.347580	0.173790	−	0.984783i	$-0.444399\pi$
$883$	10.3285	0.347580	0.173790	+	0.984783i	$0.444399\pi$
$884$	16.4913	0.554663
$885$	14.0632	0.472730
$886$	19.5461	0.656665
$887$	−12.9168	−0.433704	−0.216852	−	0.976204i	$-0.569579\pi$
$887$	−12.9168	−0.433704	−0.216852	+	0.976204i	$0.569579\pi$
$888$	104.290	3.49973
$889$	−37.7786	−1.26705
$890$	−5.95783	−0.199707
$891$	−46.5528	−1.55958
$892$	−62.9709	−2.10842
$893$	32.7775	1.09686
$894$	80.1576	2.68087
$895$	−8.23124	−0.275140
$896$	−69.1171	−2.30904
$897$	7.08998	0.236728
$898$	7.95292	0.265392
$899$	59.5870	1.98734
$900$	−19.8395	−0.661317
$901$	−28.2689	−0.941773
$902$	92.6612	3.08528
$903$	87.1114	2.89889
$904$	−42.3527	−1.40863
$905$	7.35152	0.244373
$906$	−73.6281	−2.44613
$907$	38.4015	1.27510	0.637551	−	0.770408i	$-0.279948\pi$
$907$	38.4015	1.27510	0.637551	+	0.770408i	$0.279948\pi$
$908$	−14.0723	−0.467005
$909$	3.87777	0.128618
$910$	7.41780	0.245898
$911$	16.9957	0.563093	0.281546	−	0.959548i	$-0.409153\pi$
$911$	16.9957	0.563093	0.281546	+	0.959548i	$0.409153\pi$
$912$	76.7856	2.54263
$913$	26.3301	0.871400
$914$	−40.3649	−1.33515
$915$	−16.4040	−0.542300
$916$	−81.3813	−2.68891
$917$	106.592	3.51997
$918$	36.6076	1.20823
$919$	−7.89351	−0.260383	−0.130191	−	0.991489i	$-0.541559\pi$
$919$	−7.89351	−0.260383	−0.130191	+	0.991489i	$0.541559\pi$
$920$	16.4050	0.540858
$921$	−6.41082	−0.211244
$922$	80.5572	2.65301
$923$	2.65086	0.0872541
$924$	219.109	7.20816
$925$	30.2806	0.995618
$926$	66.6659	2.19078
$927$	7.83269	0.257259
$928$	138.607	4.55001
$929$	−47.8581	−1.57017	−0.785087	−	0.619386i	$-0.787382\pi$
$929$	−47.8581	−1.57017	−0.785087	+	0.619386i	$0.787382\pi$
$930$	−18.4335	−0.604457
$931$	62.5774	2.05089
$932$	25.7893	0.844758
$933$	60.1066	1.96780
$934$	91.9722	3.00942
$935$	−7.61748	−0.249118
$936$	−6.84224	−0.223645
$937$	−8.58484	−0.280455	−0.140227	−	0.990119i	$-0.544783\pi$
$937$	−8.58484	−0.280455	−0.140227	+	0.990119i	$0.544783\pi$
$938$	−130.399	−4.25767
$939$	32.1161	1.04807
$940$	−27.6290	−0.901157
$941$	57.8969	1.88738	0.943692	−	0.330825i	$-0.107327\pi$
$941$	57.8969	1.88738	0.943692	+	0.330825i	$0.107327\pi$
$942$	−0.699072	−0.0227770
$943$	−29.2208	−0.951561
$944$	−155.788	−5.07048
$945$	11.8311	0.384864
$946$	−100.579	−3.27009
$947$	−26.0394	−0.846168	−0.423084	−	0.906090i	$-0.639053\pi$
$947$	−26.0394	−0.846168	−0.423084	+	0.906090i	$0.639053\pi$
$948$	49.7840	1.61691
$949$	1.64712	0.0534676
$950$	41.5022	1.34651
$951$	−53.2090	−1.72542
$952$	−136.050	−4.40942
$953$	47.1319	1.52675	0.763376	−	0.645954i	$-0.223540\pi$
$953$	47.1319	1.52675	0.763376	+	0.645954i	$0.223540\pi$
$954$	19.2834	0.624325
$955$	−3.18107	−0.102937
$956$	−112.192	−3.62855
$957$	−77.7509	−2.51333
$958$	103.593	3.34695
$959$	−90.8265	−2.93294
$960$	−17.5215	−0.565505
$961$	10.7858	0.347928
$962$	17.1698	0.553575
$963$	13.3242	0.429366
$964$	−24.8925	−0.801733
$965$	−3.20334	−0.103119
$966$	−96.1663	−3.09410
$967$	−31.1151	−1.00060	−0.500298	−	0.865854i	$-0.666776\pi$
$967$	−31.1151	−1.00060	−0.500298	+	0.865854i	$0.666776\pi$
$968$	−62.8298	−2.01943
$969$	20.9304	0.672380
$970$	17.2683	0.554451
$971$	−21.3787	−0.686075	−0.343037	−	0.939322i	$-0.611456\pi$
$971$	−21.3787	−0.686075	−0.343037	+	0.939322i	$0.611456\pi$
$972$	−42.7099	−1.36992
$973$	−40.4087	−1.29544
$974$	−23.3577	−0.748428
$975$	−9.19591	−0.294505
$976$	181.719	5.81669
$977$	−41.8133	−1.33773	−0.668864	−	0.743385i	$-0.733219\pi$
$977$	−41.8133	−1.33773	−0.668864	+	0.743385i	$0.733219\pi$
$978$	15.4242	0.493212
$979$	−17.6223	−0.563212
$980$	−52.7480	−1.68497
$981$	5.88421	0.187868
$982$	−18.9765	−0.605565
$983$	−1.98304	−0.0632491	−0.0316246	−	0.999500i	$-0.510068\pi$
$983$	−1.98304	−0.0632491	−0.0316246	+	0.999500i	$0.510068\pi$
$984$	130.533	4.16123
$985$	−11.0405	−0.351778
$986$	79.3739	2.52778
$987$	98.5092	3.13558
$988$	16.9084	0.537929
$989$	31.7176	1.00856
$990$	5.19622	0.165147
$991$	35.0228	1.11253	0.556267	−	0.831003i	$-0.312233\pi$
$991$	35.0228	1.11253	0.556267	+	0.831003i	$0.312233\pi$
$992$	97.1993	3.08608
$993$	50.5533	1.60426
$994$	−35.9554	−1.14044
$995$	−0.559926	−0.0177508
$996$	60.9828	1.93231
$997$	−11.1173	−0.352087	−0.176044	−	0.984382i	$-0.556330\pi$
$997$	−11.1173	−0.352087	−0.176044	+	0.984382i	$0.556330\pi$
$998$	−68.3439	−2.16339
$999$	27.3850	0.866422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.7	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.7	✓	174	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66552 q^{2} +1.95620 q^{3} +5.10502 q^{4} -0.546887 q^{5} -5.21429 q^{6} +5.08856 q^{7} -8.27650 q^{8} +0.826707 q^{9} +O(q^{10})\)	\(q-2.66552 q^{2} +1.95620 q^{3} +5.10502 q^{4} -0.546887 q^{5} -5.21429 q^{6} +5.08856 q^{7} -8.27650 q^{8} +0.826707 q^{9} +1.45774 q^{10} +4.31177 q^{11} +9.98642 q^{12} +1.00000 q^{13} -13.5637 q^{14} -1.06982 q^{15} +11.8512 q^{16} +3.23041 q^{17} -2.20361 q^{18} +3.31212 q^{19} -2.79187 q^{20} +9.95423 q^{21} -11.4931 q^{22} +3.62437 q^{23} -16.1905 q^{24} -4.70091 q^{25} -2.66552 q^{26} -4.25139 q^{27} +25.9772 q^{28} -9.21801 q^{29} +2.85163 q^{30} -6.46419 q^{31} -15.0366 q^{32} +8.43467 q^{33} -8.61074 q^{34} -2.78287 q^{35} +4.22035 q^{36} -6.44142 q^{37} -8.82854 q^{38} +1.95620 q^{39} +4.52631 q^{40} -8.06232 q^{41} -26.5332 q^{42} +8.75120 q^{43} +22.0117 q^{44} -0.452115 q^{45} -9.66085 q^{46} +9.89622 q^{47} +23.1832 q^{48} +18.8934 q^{49} +12.5304 q^{50} +6.31932 q^{51} +5.10502 q^{52} -8.75086 q^{53} +11.3322 q^{54} -2.35805 q^{55} -42.1155 q^{56} +6.47916 q^{57} +24.5708 q^{58} -13.1454 q^{59} -5.46145 q^{60} +15.3334 q^{61} +17.2305 q^{62} +4.20675 q^{63} +16.3780 q^{64} -0.546887 q^{65} -22.4828 q^{66} +9.61382 q^{67} +16.4913 q^{68} +7.08998 q^{69} +7.41780 q^{70} +2.65086 q^{71} -6.84224 q^{72} +1.64712 q^{73} +17.1698 q^{74} -9.19591 q^{75} +16.9084 q^{76} +21.9407 q^{77} -5.21429 q^{78} +4.98517 q^{79} -6.48125 q^{80} -10.7967 q^{81} +21.4903 q^{82} +6.10657 q^{83} +50.8165 q^{84} -1.76667 q^{85} -23.3265 q^{86} -18.0323 q^{87} -35.6863 q^{88} -4.08703 q^{89} +1.20512 q^{90} +5.08856 q^{91} +18.5025 q^{92} -12.6452 q^{93} -26.3786 q^{94} -1.81136 q^{95} -29.4145 q^{96} +11.8459 q^{97} -50.3609 q^{98} +3.56457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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