LMFDB - Embedded newform 8015.2.a.l.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20228 q^{2} -3.01220 q^{3} +2.85005 q^{4} -1.00000 q^{5} +6.63371 q^{6} -1.00000 q^{7} -1.87206 q^{8} +6.07333 q^{9} +O(q^{10})$	\(q-2.20228 q^{2} -3.01220 q^{3} +2.85005 q^{4} -1.00000 q^{5} +6.63371 q^{6} -1.00000 q^{7} -1.87206 q^{8} +6.07333 q^{9} +2.20228 q^{10} -3.78158 q^{11} -8.58492 q^{12} +4.33541 q^{13} +2.20228 q^{14} +3.01220 q^{15} -1.57731 q^{16} +1.42225 q^{17} -13.3752 q^{18} -3.78650 q^{19} -2.85005 q^{20} +3.01220 q^{21} +8.32810 q^{22} -8.43662 q^{23} +5.63900 q^{24} +1.00000 q^{25} -9.54781 q^{26} -9.25749 q^{27} -2.85005 q^{28} -7.89528 q^{29} -6.63371 q^{30} -4.98465 q^{31} +7.21779 q^{32} +11.3909 q^{33} -3.13220 q^{34} +1.00000 q^{35} +17.3093 q^{36} -2.71137 q^{37} +8.33895 q^{38} -13.0591 q^{39} +1.87206 q^{40} -1.56428 q^{41} -6.63371 q^{42} +5.07248 q^{43} -10.7777 q^{44} -6.07333 q^{45} +18.5798 q^{46} -3.10936 q^{47} +4.75116 q^{48} +1.00000 q^{49} -2.20228 q^{50} -4.28410 q^{51} +12.3562 q^{52} +1.42151 q^{53} +20.3876 q^{54} +3.78158 q^{55} +1.87206 q^{56} +11.4057 q^{57} +17.3876 q^{58} -9.60495 q^{59} +8.58492 q^{60} -10.5797 q^{61} +10.9776 q^{62} -6.07333 q^{63} -12.7410 q^{64} -4.33541 q^{65} -25.0859 q^{66} -0.748661 q^{67} +4.05349 q^{68} +25.4128 q^{69} -2.20228 q^{70} +1.44871 q^{71} -11.3696 q^{72} +5.14212 q^{73} +5.97121 q^{74} -3.01220 q^{75} -10.7917 q^{76} +3.78158 q^{77} +28.7599 q^{78} +9.81951 q^{79} +1.57731 q^{80} +9.66538 q^{81} +3.44499 q^{82} +0.0758723 q^{83} +8.58492 q^{84} -1.42225 q^{85} -11.1710 q^{86} +23.7821 q^{87} +7.07932 q^{88} -14.5072 q^{89} +13.3752 q^{90} -4.33541 q^{91} -24.0448 q^{92} +15.0148 q^{93} +6.84769 q^{94} +3.78650 q^{95} -21.7414 q^{96} +8.60767 q^{97} -2.20228 q^{98} -22.9668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−2.20228	−1.55725	−0.778625	−	0.627490i	$-0.784082\pi$
$2$	−2.20228	−1.55725	−0.778625	+	0.627490i	$0.784082\pi$
$3$	−3.01220	−1.73909	−0.869547	−	0.493851i	$-0.835589\pi$
$3$	−3.01220	−1.73909	−0.869547	+	0.493851i	$0.835589\pi$
$4$	2.85005	1.42503
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.63371	2.70820
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.87206	−0.661872
$9$	6.07333	2.02444
$10$	2.20228	0.696423
$11$	−3.78158	−1.14019	−0.570094	−	0.821580i	$-0.693093\pi$
$11$	−3.78158	−1.14019	−0.570094	+	0.821580i	$0.693093\pi$
$12$	−8.58492	−2.47825
$13$	4.33541	1.20243	0.601214	−	0.799088i	$-0.294684\pi$
$13$	4.33541	1.20243	0.601214	+	0.799088i	$0.294684\pi$
$14$	2.20228	0.588585
$15$	3.01220	0.777746
$16$	−1.57731	−0.394327
$17$	1.42225	0.344947	0.172473	−	0.985014i	$-0.444824\pi$
$17$	1.42225	0.344947	0.172473	+	0.985014i	$0.444824\pi$
$18$	−13.3752	−3.15257
$19$	−3.78650	−0.868683	−0.434341	−	0.900748i	$-0.643019\pi$
$19$	−3.78650	−0.868683	−0.434341	+	0.900748i	$0.643019\pi$
$20$	−2.85005	−0.637291
$21$	3.01220	0.657315
$22$	8.32810	1.77556
$23$	−8.43662	−1.75916	−0.879578	−	0.475754i	$-0.842175\pi$
$23$	−8.43662	−1.75916	−0.879578	+	0.475754i	$0.842175\pi$
$24$	5.63900	1.15106
$25$	1.00000	0.200000
$26$	−9.54781	−1.87248
$27$	−9.25749	−1.78160
$28$	−2.85005	−0.538609
$29$	−7.89528	−1.46612	−0.733058	−	0.680166i	$-0.761908\pi$
$29$	−7.89528	−1.46612	−0.733058	+	0.680166i	$0.761908\pi$
$30$	−6.63371	−1.21114
$31$	−4.98465	−0.895270	−0.447635	−	0.894216i	$-0.647734\pi$
$31$	−4.98465	−0.895270	−0.447635	+	0.894216i	$0.647734\pi$
$32$	7.21779	1.27594
$33$	11.3909	1.98289
$34$	−3.13220	−0.537168
$35$	1.00000	0.169031
$36$	17.3093	2.88489
$37$	−2.71137	−0.445747	−0.222873	−	0.974847i	$-0.571544\pi$
$37$	−2.71137	−0.445747	−0.222873	+	0.974847i	$0.571544\pi$
$38$	8.33895	1.35276
$39$	−13.0591	−2.09113
$40$	1.87206	0.295998
$41$	−1.56428	−0.244299	−0.122150	−	0.992512i	$-0.538979\pi$
$41$	−1.56428	−0.244299	−0.122150	+	0.992512i	$0.538979\pi$
$42$	−6.63371	−1.02360
$43$	5.07248	0.773545	0.386773	−	0.922175i	$-0.373590\pi$
$43$	5.07248	0.773545	0.386773	+	0.922175i	$0.373590\pi$
$44$	−10.7777	−1.62480
$45$	−6.07333	−0.905359
$46$	18.5798	2.73945
$47$	−3.10936	−0.453547	−0.226773	−	0.973948i	$-0.572818\pi$
$47$	−3.10936	−0.453547	−0.226773	+	0.973948i	$0.572818\pi$
$48$	4.75116	0.685771
$49$	1.00000	0.142857
$50$	−2.20228	−0.311450
$51$	−4.28410	−0.599894
$52$	12.3562	1.71349
$53$	1.42151	0.195259	0.0976295	−	0.995223i	$-0.468874\pi$
$53$	1.42151	0.195259	0.0976295	+	0.995223i	$0.468874\pi$
$54$	20.3876	2.77440
$55$	3.78158	0.509908
$56$	1.87206	0.250164
$57$	11.4057	1.51072
$58$	17.3876	2.28311
$59$	−9.60495	−1.25046	−0.625229	−	0.780441i	$-0.714994\pi$
$59$	−9.60495	−1.25046	−0.625229	+	0.780441i	$0.714994\pi$
$60$	8.58492	1.10831
$61$	−10.5797	−1.35460	−0.677299	−	0.735708i	$-0.736850\pi$
$61$	−10.5797	−1.35460	−0.677299	+	0.735708i	$0.736850\pi$
$62$	10.9776	1.39416
$63$	−6.07333	−0.765168
$64$	−12.7410	−1.59263
$65$	−4.33541	−0.537742
$66$	−25.0859	−3.08786
$67$	−0.748661	−0.0914636	−0.0457318	−	0.998954i	$-0.514562\pi$
$67$	−0.748661	−0.0914636	−0.0457318	+	0.998954i	$0.514562\pi$
$68$	4.05349	0.491558
$69$	25.4128	3.05934
$70$	−2.20228	−0.263223
$71$	1.44871	0.171930	0.0859650	−	0.996298i	$-0.472603\pi$
$71$	1.44871	0.171930	0.0859650	+	0.996298i	$0.472603\pi$
$72$	−11.3696	−1.33992
$73$	5.14212	0.601840	0.300920	−	0.953649i	$-0.402706\pi$
$73$	5.14212	0.601840	0.300920	+	0.953649i	$0.402706\pi$
$74$	5.97121	0.694139
$75$	−3.01220	−0.347819
$76$	−10.7917	−1.23790
$77$	3.78158	0.430950
$78$	28.7599	3.25642
$79$	9.81951	1.10478	0.552391	−	0.833585i	$-0.313716\pi$
$79$	9.81951	1.10478	0.552391	+	0.833585i	$0.313716\pi$
$80$	1.57731	0.176348
$81$	9.66538	1.07393
$82$	3.44499	0.380435
$83$	0.0758723	0.00832807	0.00416403	−	0.999991i	$-0.498675\pi$
$83$	0.0758723	0.00832807	0.00416403	+	0.999991i	$0.498675\pi$
$84$	8.58492	0.936692
$85$	−1.42225	−0.154265
$86$	−11.1710	−1.20460
$87$	23.7821	2.54971
$88$	7.07932	0.754658
$89$	−14.5072	−1.53776	−0.768879	−	0.639395i	$-0.779185\pi$
$89$	−14.5072	−1.53776	−0.768879	+	0.639395i	$0.779185\pi$
$90$	13.3752	1.40987
$91$	−4.33541	−0.454475
$92$	−24.0448	−2.50684
$93$	15.0148	1.55696
$94$	6.84769	0.706285
$95$	3.78650	0.388487
$96$	−21.7414	−2.21897
$97$	8.60767	0.873976	0.436988	−	0.899467i	$-0.356045\pi$
$97$	8.60767	0.873976	0.436988	+	0.899467i	$0.356045\pi$
$98$	−2.20228	−0.222464
$99$	−22.9668	−2.30825
$100$	2.85005	0.285005
$101$	−1.83398	−0.182488	−0.0912442	−	0.995829i	$-0.529084\pi$
$101$	−1.83398	−0.182488	−0.0912442	+	0.995829i	$0.529084\pi$
$102$	9.43481	0.934185
$103$	−9.46639	−0.932751	−0.466375	−	0.884587i	$-0.654440\pi$
$103$	−9.46639	−0.932751	−0.466375	+	0.884587i	$0.654440\pi$
$104$	−8.11614	−0.795853
$105$	−3.01220	−0.293960
$106$	−3.13056	−0.304067
$107$	0.955305	0.0923528	0.0461764	−	0.998933i	$-0.485296\pi$
$107$	0.955305	0.0923528	0.0461764	+	0.998933i	$0.485296\pi$
$108$	−26.3843	−2.53883
$109$	3.03723	0.290913	0.145457	−	0.989365i	$-0.453535\pi$
$109$	3.03723	0.290913	0.145457	+	0.989365i	$0.453535\pi$
$110$	−8.32810	−0.794053
$111$	8.16719	0.775195
$112$	1.57731	0.149041
$113$	9.05115	0.851461	0.425730	−	0.904850i	$-0.360017\pi$
$113$	9.05115	0.851461	0.425730	+	0.904850i	$0.360017\pi$
$114$	−25.1186	−2.35257
$115$	8.43662	0.786719
$116$	−22.5020	−2.08925
$117$	26.3304	2.43425
$118$	21.1528	1.94728
$119$	−1.42225	−0.130378
$120$	−5.63900	−0.514768
$121$	3.30031	0.300028
$122$	23.2996	2.10945
$123$	4.71192	0.424859
$124$	−14.2065	−1.27578
$125$	−1.00000	−0.0894427
$126$	13.3752	1.19156
$127$	−15.2615	−1.35424	−0.677122	−	0.735871i	$-0.736773\pi$
$127$	−15.2615	−1.35424	−0.677122	+	0.735871i	$0.736773\pi$
$128$	13.6237	1.20418
$129$	−15.2793	−1.34527
$130$	9.54781	0.837398
$131$	3.03144	0.264858	0.132429	−	0.991192i	$-0.457722\pi$
$131$	3.03144	0.264858	0.132429	+	0.991192i	$0.457722\pi$
$132$	32.4645	2.82567
$133$	3.78650	0.328331
$134$	1.64876	0.142432
$135$	9.25749	0.796758
$136$	−2.66254	−0.228311
$137$	3.14462	0.268663	0.134332	−	0.990936i	$-0.457111\pi$
$137$	3.14462	0.268663	0.134332	+	0.990936i	$0.457111\pi$
$138$	−55.9661	−4.76415
$139$	−11.8717	−1.00695	−0.503473	−	0.864011i	$-0.667945\pi$
$139$	−11.8717	−1.00695	−0.503473	+	0.864011i	$0.667945\pi$
$140$	2.85005	0.240873
$141$	9.36600	0.788760
$142$	−3.19046	−0.267738
$143$	−16.3947	−1.37099
$144$	−9.57951	−0.798292
$145$	7.89528	0.655667
$146$	−11.3244	−0.937215
$147$	−3.01220	−0.248442
$148$	−7.72755	−0.635201
$149$	−18.1012	−1.48291	−0.741454	−	0.671004i	$-0.765863\pi$
$149$	−18.1012	−1.48291	−0.741454	+	0.671004i	$0.765863\pi$
$150$	6.63371	0.541640
$151$	−6.14969	−0.500455	−0.250227	−	0.968187i	$-0.580505\pi$
$151$	−6.14969	−0.500455	−0.250227	+	0.968187i	$0.580505\pi$
$152$	7.08854	0.574957
$153$	8.63781	0.698326
$154$	−8.32810	−0.671097
$155$	4.98465	0.400377
$156$	−37.2192	−2.97992
$157$	17.3907	1.38793	0.693964	−	0.720009i	$-0.255863\pi$
$157$	17.3907	1.38793	0.693964	+	0.720009i	$0.255863\pi$
$158$	−21.6253	−1.72042
$159$	−4.28186	−0.339573
$160$	−7.21779	−0.570616
$161$	8.43662	0.664899
$162$	−21.2859	−1.67238
$163$	−6.62045	−0.518554	−0.259277	−	0.965803i	$-0.583484\pi$
$163$	−6.62045	−0.518554	−0.259277	+	0.965803i	$0.583484\pi$
$164$	−4.45828	−0.348133
$165$	−11.3909	−0.886777
$166$	−0.167092	−0.0129689
$167$	−20.9967	−1.62478	−0.812388	−	0.583118i	$-0.801833\pi$
$167$	−20.9967	−1.62478	−0.812388	+	0.583118i	$0.801833\pi$
$168$	−5.63900	−0.435058
$169$	5.79580	0.445831
$170$	3.13220	0.240229
$171$	−22.9967	−1.75860
$172$	14.4568	1.10232
$173$	−15.8812	−1.20742	−0.603712	−	0.797202i	$-0.706312\pi$
$173$	−15.8812	−1.20742	−0.603712	+	0.797202i	$0.706312\pi$
$174$	−52.3750	−3.97054
$175$	−1.00000	−0.0755929
$176$	5.96470	0.449606
$177$	28.9320	2.17466
$178$	31.9489	2.39467
$179$	8.25045	0.616668	0.308334	−	0.951278i	$-0.400229\pi$
$179$	8.25045	0.616668	0.308334	+	0.951278i	$0.400229\pi$
$180$	−17.3093	−1.29016
$181$	13.4586	1.00037	0.500184	−	0.865919i	$-0.333266\pi$
$181$	13.4586	1.00037	0.500184	+	0.865919i	$0.333266\pi$
$182$	9.54781	0.707731
$183$	31.8683	2.35577
$184$	15.7938	1.16434
$185$	2.71137	0.199344
$186$	−33.0667	−2.42457
$187$	−5.37835	−0.393304
$188$	−8.86184	−0.646316
$189$	9.25749	0.673383
$190$	−8.33895	−0.604971
$191$	9.46567	0.684912	0.342456	−	0.939534i	$-0.388741\pi$
$191$	9.46567	0.684912	0.342456	+	0.939534i	$0.388741\pi$
$192$	38.3784	2.76972
$193$	−16.0525	−1.15549	−0.577743	−	0.816219i	$-0.696066\pi$
$193$	−16.0525	−1.15549	−0.577743	+	0.816219i	$0.696066\pi$
$194$	−18.9565	−1.36100
$195$	13.0591	0.935183
$196$	2.85005	0.203575
$197$	−22.5002	−1.60307	−0.801535	−	0.597948i	$-0.795983\pi$
$197$	−22.5002	−1.60307	−0.801535	+	0.597948i	$0.795983\pi$
$198$	50.5793	3.59452
$199$	−9.28637	−0.658293	−0.329147	−	0.944279i	$-0.606761\pi$
$199$	−9.28637	−0.658293	−0.329147	+	0.944279i	$0.606761\pi$
$200$	−1.87206	−0.132374
$201$	2.25512	0.159064
$202$	4.03895	0.284180
$203$	7.89528	0.554140
$204$	−12.2099	−0.854865
$205$	1.56428	0.109254
$206$	20.8477	1.45253
$207$	−51.2384	−3.56132
$208$	−6.83827	−0.474149
$209$	14.3189	0.990462
$210$	6.63371	0.457770
$211$	−15.1645	−1.04397	−0.521985	−	0.852955i	$-0.674808\pi$
$211$	−15.1645	−1.04397	−0.521985	+	0.852955i	$0.674808\pi$
$212$	4.05137	0.278249
$213$	−4.36379	−0.299002
$214$	−2.10385	−0.143816
$215$	−5.07248	−0.345940
$216$	17.3305	1.17919
$217$	4.98465	0.338380
$218$	−6.68883	−0.453025
$219$	−15.4891	−1.04666
$220$	10.7777	0.726632
$221$	6.16605	0.414773
$222$	−17.9865	−1.20717
$223$	−4.53894	−0.303950	−0.151975	−	0.988384i	$-0.548563\pi$
$223$	−4.53894	−0.303950	−0.151975	+	0.988384i	$0.548563\pi$
$224$	−7.21779	−0.482259
$225$	6.07333	0.404889
$226$	−19.9332	−1.32594
$227$	3.67431	0.243873	0.121936	−	0.992538i	$-0.461090\pi$
$227$	3.67431	0.243873	0.121936	+	0.992538i	$0.461090\pi$
$228$	32.5068	2.15282
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−18.5798	−1.22512
$231$	−11.3909	−0.749463
$232$	14.7804	0.970381
$233$	−16.8132	−1.10147	−0.550734	−	0.834681i	$-0.685652\pi$
$233$	−16.8132	−1.10147	−0.550734	+	0.834681i	$0.685652\pi$
$234$	−57.9870	−3.79073
$235$	3.10936	0.202832
$236$	−27.3746	−1.78194
$237$	−29.5783	−1.92132
$238$	3.13220	0.203030
$239$	17.7248	1.14652	0.573262	−	0.819372i	$-0.305678\pi$
$239$	17.7248	1.14652	0.573262	+	0.819372i	$0.305678\pi$
$240$	−4.75116	−0.306686
$241$	18.8485	1.21414	0.607070	−	0.794649i	$-0.292345\pi$
$241$	18.8485	1.21414	0.607070	+	0.794649i	$0.292345\pi$
$242$	−7.26822	−0.467219
$243$	−1.34157	−0.0860617
$244$	−30.1528	−1.93034
$245$	−1.00000	−0.0638877
$246$	−10.3770	−0.661612
$247$	−16.4160	−1.04453
$248$	9.33155	0.592554
$249$	−0.228542	−0.0144833
$250$	2.20228	0.139285
$251$	−4.97088	−0.313759	−0.156880	−	0.987618i	$-0.550143\pi$
$251$	−4.97088	−0.313759	−0.156880	+	0.987618i	$0.550143\pi$
$252$	−17.3093	−1.09038
$253$	31.9037	2.00577
$254$	33.6103	2.10889
$255$	4.28410	0.268281
$256$	−4.52129	−0.282581
$257$	2.41699	0.150768	0.0753840	−	0.997155i	$-0.475982\pi$
$257$	2.41699	0.150768	0.0753840	+	0.997155i	$0.475982\pi$
$258$	33.6493	2.09492
$259$	2.71137	0.168476
$260$	−12.3562	−0.766296
$261$	−47.9507	−2.96807
$262$	−6.67608	−0.412450
$263$	−7.57986	−0.467394	−0.233697	−	0.972309i	$-0.575082\pi$
$263$	−7.57986	−0.467394	−0.233697	+	0.972309i	$0.575082\pi$
$264$	−21.3243	−1.31242
$265$	−1.42151	−0.0873224
$266$	−8.33895	−0.511294
$267$	43.6985	2.67430
$268$	−2.13372	−0.130338
$269$	−15.2830	−0.931820	−0.465910	−	0.884832i	$-0.654273\pi$
$269$	−15.2830	−0.931820	−0.465910	+	0.884832i	$0.654273\pi$
$270$	−20.3876	−1.24075
$271$	1.98963	0.120861	0.0604307	−	0.998172i	$-0.480753\pi$
$271$	1.98963	0.120861	0.0604307	+	0.998172i	$0.480753\pi$
$272$	−2.24333	−0.136022
$273$	13.0591	0.790374
$274$	−6.92535	−0.418376
$275$	−3.78158	−0.228038
$276$	72.4277	4.35964
$277$	−25.7457	−1.54691	−0.773455	−	0.633852i	$-0.781473\pi$
$277$	−25.7457	−1.54691	−0.773455	+	0.633852i	$0.781473\pi$
$278$	26.1449	1.56807
$279$	−30.2734	−1.81242
$280$	−1.87206	−0.111877
$281$	22.8797	1.36489	0.682445	−	0.730937i	$-0.260917\pi$
$281$	22.8797	1.36489	0.682445	+	0.730937i	$0.260917\pi$
$282$	−20.6266	−1.22830
$283$	−6.63277	−0.394277	−0.197139	−	0.980376i	$-0.563165\pi$
$283$	−6.63277	−0.394277	−0.197139	+	0.980376i	$0.563165\pi$
$284$	4.12889	0.245005
$285$	−11.4057	−0.675615
$286$	36.1057	2.13498
$287$	1.56428	0.0923365
$288$	43.8360	2.58306
$289$	−14.9772	−0.881012
$290$	−17.3876	−1.02104
$291$	−25.9280	−1.51993
$292$	14.6553	0.857638
$293$	−6.88190	−0.402045	−0.201023	−	0.979587i	$-0.564426\pi$
$293$	−6.88190	−0.402045	−0.201023	+	0.979587i	$0.564426\pi$
$294$	6.63371	0.386886
$295$	9.60495	0.559222
$296$	5.07584	0.295027
$297$	35.0079	2.03136
$298$	39.8640	2.30926
$299$	−36.5762	−2.11526
$300$	−8.58492	−0.495651
$301$	−5.07248	−0.292373
$302$	13.5434	0.779333
$303$	5.52432	0.317364
$304$	5.97247	0.342545
$305$	10.5797	0.605795
$306$	−19.0229	−1.08747
$307$	9.02278	0.514957	0.257479	−	0.966284i	$-0.417108\pi$
$307$	9.02278	0.514957	0.257479	+	0.966284i	$0.417108\pi$
$308$	10.7777	0.614116
$309$	28.5146	1.62214
$310$	−10.9776	−0.623487
$311$	−24.3545	−1.38102	−0.690510	−	0.723323i	$-0.742614\pi$
$311$	−24.3545	−1.38102	−0.690510	+	0.723323i	$0.742614\pi$
$312$	24.4474	1.38406
$313$	2.98681	0.168824	0.0844122	−	0.996431i	$-0.473099\pi$
$313$	2.98681	0.168824	0.0844122	+	0.996431i	$0.473099\pi$
$314$	−38.2992	−2.16135
$315$	6.07333	0.342194
$316$	27.9861	1.57434
$317$	−20.6349	−1.15897	−0.579487	−	0.814982i	$-0.696747\pi$
$317$	−20.6349	−1.15897	−0.579487	+	0.814982i	$0.696747\pi$
$318$	9.42986	0.528801
$319$	29.8566	1.67165
$320$	12.7410	0.712244
$321$	−2.87757	−0.160610
$322$	−18.5798	−1.03541
$323$	−5.38536	−0.299649
$324$	27.5468	1.53038
$325$	4.33541	0.240485
$326$	14.5801	0.807517
$327$	−9.14872	−0.505926
$328$	2.92842	0.161695
$329$	3.10936	0.171425
$330$	25.0859	1.38093
$331$	−33.8801	−1.86222	−0.931110	−	0.364739i	$-0.881158\pi$
$331$	−33.8801	−1.86222	−0.931110	+	0.364739i	$0.881158\pi$
$332$	0.216240	0.0118677
$333$	−16.4671	−0.902389
$334$	46.2407	2.53018
$335$	0.748661	0.0409037
$336$	−4.75116	−0.259197
$337$	−20.9479	−1.14110	−0.570552	−	0.821261i	$-0.693271\pi$
$337$	−20.9479	−1.14110	−0.570552	+	0.821261i	$0.693271\pi$
$338$	−12.7640	−0.694270
$339$	−27.2639	−1.48077
$340$	−4.05349	−0.219831
$341$	18.8498	1.02078
$342$	50.6452	2.73858
$343$	−1.00000	−0.0539949
$344$	−9.49596	−0.511988
$345$	−25.4128	−1.36818
$346$	34.9749	1.88026
$347$	−19.5114	−1.04743	−0.523714	−	0.851894i	$-0.675454\pi$
$347$	−19.5114	−1.04743	−0.523714	+	0.851894i	$0.675454\pi$
$348$	67.7803	3.63341
$349$	7.17450	0.384042	0.192021	−	0.981391i	$-0.438496\pi$
$349$	7.17450	0.384042	0.192021	+	0.981391i	$0.438496\pi$
$350$	2.20228	0.117717
$351$	−40.1350	−2.14225
$352$	−27.2946	−1.45481
$353$	9.41706	0.501219	0.250610	−	0.968088i	$-0.419369\pi$
$353$	9.41706	0.501219	0.250610	+	0.968088i	$0.419369\pi$
$354$	−63.7165	−3.38649
$355$	−1.44871	−0.0768894
$356$	−41.3462	−2.19134
$357$	4.28410	0.226739
$358$	−18.1698	−0.960306
$359$	9.33033	0.492436	0.246218	−	0.969214i	$-0.420812\pi$
$359$	9.33033	0.492436	0.246218	+	0.969214i	$0.420812\pi$
$360$	11.3696	0.599232
$361$	−4.66241	−0.245390
$362$	−29.6396	−1.55782
$363$	−9.94119	−0.521777
$364$	−12.3562	−0.647638
$365$	−5.14212	−0.269151
$366$	−70.1830	−3.66852
$367$	18.0824	0.943895	0.471948	−	0.881627i	$-0.343551\pi$
$367$	18.0824	0.943895	0.471948	+	0.881627i	$0.343551\pi$
$368$	13.3071	0.693682
$369$	−9.50039	−0.494571
$370$	−5.97121	−0.310428
$371$	−1.42151	−0.0738009
$372$	42.7928	2.21871
$373$	5.68094	0.294148	0.147074	−	0.989125i	$-0.453014\pi$
$373$	5.68094	0.294148	0.147074	+	0.989125i	$0.453014\pi$
$374$	11.8447	0.612473
$375$	3.01220	0.155549
$376$	5.82090	0.300190
$377$	−34.2293	−1.76290
$378$	−20.3876	−1.04863
$379$	−18.6051	−0.955681	−0.477841	−	0.878447i	$-0.658580\pi$
$379$	−18.6051	−0.955681	−0.477841	+	0.878447i	$0.658580\pi$
$380$	10.7917	0.553604
$381$	45.9708	2.35516
$382$	−20.8461	−1.06658
$383$	−21.3436	−1.09060	−0.545302	−	0.838239i	$-0.683585\pi$
$383$	−21.3436	−1.09060	−0.545302	+	0.838239i	$0.683585\pi$
$384$	−41.0373	−2.09418
$385$	−3.78158	−0.192727
$386$	35.3522	1.79938
$387$	30.8068	1.56600
$388$	24.5323	1.24544
$389$	−33.8583	−1.71668	−0.858341	−	0.513079i	$-0.828505\pi$
$389$	−33.8583	−1.71668	−0.858341	+	0.513079i	$0.828505\pi$
$390$	−28.7599	−1.45631
$391$	−11.9990	−0.606815
$392$	−1.87206	−0.0945531
$393$	−9.13129	−0.460613
$394$	49.5517	2.49638
$395$	−9.81951	−0.494073
$396$	−65.4565	−3.28931
$397$	17.2818	0.867351	0.433675	−	0.901069i	$-0.357216\pi$
$397$	17.2818	0.867351	0.433675	+	0.901069i	$0.357216\pi$
$398$	20.4512	1.02513
$399$	−11.4057	−0.570999
$400$	−1.57731	−0.0788653
$401$	−34.5449	−1.72509	−0.862545	−	0.505980i	$-0.831131\pi$
$401$	−34.5449	−1.72509	−0.862545	+	0.505980i	$0.831131\pi$
$402$	−4.96641	−0.247702
$403$	−21.6105	−1.07650
$404$	−5.22695	−0.260051
$405$	−9.66538	−0.480277
$406$	−17.3876	−0.862934
$407$	10.2533	0.508235
$408$	8.02008	0.397053
$409$	23.5760	1.16576	0.582879	−	0.812559i	$-0.301926\pi$
$409$	23.5760	1.16576	0.582879	+	0.812559i	$0.301926\pi$
$410$	−3.44499	−0.170136
$411$	−9.47222	−0.467230
$412$	−26.9797	−1.32919
$413$	9.60495	0.472629
$414$	112.841	5.54586
$415$	−0.0758723	−0.00372442
$416$	31.2921	1.53422
$417$	35.7600	1.75117
$418$	−31.5344	−1.54240
$419$	−36.7564	−1.79567	−0.897833	−	0.440336i	$-0.854859\pi$
$419$	−36.7564	−1.79567	−0.897833	+	0.440336i	$0.854859\pi$
$420$	−8.58492	−0.418901
$421$	1.34267	0.0654375	0.0327188	−	0.999465i	$-0.489583\pi$
$421$	1.34267	0.0654375	0.0327188	+	0.999465i	$0.489583\pi$
$422$	33.3966	1.62572
$423$	−18.8842	−0.918180
$424$	−2.66114	−0.129236
$425$	1.42225	0.0689893
$426$	9.61031	0.465621
$427$	10.5797	0.511990
$428$	2.72267	0.131605
$429$	49.3840	2.38428
$430$	11.1710	0.538715
$431$	−7.49466	−0.361005	−0.180503	−	0.983575i	$-0.557772\pi$
$431$	−7.49466	−0.361005	−0.180503	+	0.983575i	$0.557772\pi$
$432$	14.6019	0.702534
$433$	−7.35574	−0.353495	−0.176747	−	0.984256i	$-0.556558\pi$
$433$	−7.35574	−0.353495	−0.176747	+	0.984256i	$0.556558\pi$
$434$	−10.9776	−0.526942
$435$	−23.7821	−1.14027
$436$	8.65625	0.414559
$437$	31.9453	1.52815
$438$	34.1114	1.62990
$439$	−9.15590	−0.436987	−0.218494	−	0.975838i	$-0.570114\pi$
$439$	−9.15590	−0.436987	−0.218494	+	0.975838i	$0.570114\pi$
$440$	−7.07932	−0.337493
$441$	6.07333	0.289206
$442$	−13.5794	−0.645906
$443$	17.1794	0.816216	0.408108	−	0.912934i	$-0.366189\pi$
$443$	17.1794	0.816216	0.408108	+	0.912934i	$0.366189\pi$
$444$	23.2769	1.10467
$445$	14.5072	0.687706
$446$	9.99602	0.473325
$447$	54.5244	2.57892
$448$	12.7410	0.601956
$449$	−4.72940	−0.223194	−0.111597	−	0.993754i	$-0.535597\pi$
$449$	−4.72940	−0.223194	−0.111597	+	0.993754i	$0.535597\pi$
$450$	−13.3752	−0.630513
$451$	5.91544	0.278547
$452$	25.7963	1.21335
$453$	18.5241	0.870337
$454$	−8.09188	−0.379771
$455$	4.33541	0.203247
$456$	−21.3521	−0.999903
$457$	27.6705	1.29437	0.647185	−	0.762333i	$-0.275946\pi$
$457$	27.6705	1.29437	0.647185	+	0.762333i	$0.275946\pi$
$458$	−2.20228	−0.102906
$459$	−13.1665	−0.614559
$460$	24.0448	1.12109
$461$	−29.1383	−1.35711	−0.678553	−	0.734551i	$-0.737393\pi$
$461$	−29.1383	−1.35711	−0.678553	+	0.734551i	$0.737393\pi$
$462$	25.0859	1.16710
$463$	−34.8120	−1.61785	−0.808926	−	0.587910i	$-0.799951\pi$
$463$	−34.8120	−1.61785	−0.808926	+	0.587910i	$0.799951\pi$
$464$	12.4533	0.578129
$465$	−15.0148	−0.696293
$466$	37.0274	1.71526
$467$	−3.58396	−0.165846	−0.0829228	−	0.996556i	$-0.526426\pi$
$467$	−3.58396	−0.165846	−0.0829228	+	0.996556i	$0.526426\pi$
$468$	75.0430	3.46887
$469$	0.748661	0.0345700
$470$	−6.84769	−0.315860
$471$	−52.3842	−2.41374
$472$	17.9810	0.827643
$473$	−19.1819	−0.881987
$474$	65.1398	2.99197
$475$	−3.78650	−0.173737
$476$	−4.05349	−0.185792
$477$	8.63328	0.395291
$478$	−39.0351	−1.78543
$479$	24.9792	1.14133	0.570664	−	0.821184i	$-0.306686\pi$
$479$	24.9792	1.14133	0.570664	+	0.821184i	$0.306686\pi$
$480$	21.7414	0.992355
$481$	−11.7549	−0.535978
$482$	−41.5098	−1.89072
$483$	−25.4128	−1.15632
$484$	9.40606	0.427548
$485$	−8.60767	−0.390854
$486$	2.95451	0.134020
$487$	4.02620	0.182445	0.0912223	−	0.995831i	$-0.470923\pi$
$487$	4.02620	0.182445	0.0912223	+	0.995831i	$0.470923\pi$
$488$	19.8059	0.896570
$489$	19.9421	0.901813
$490$	2.20228	0.0994890
$491$	−18.3784	−0.829407	−0.414703	−	0.909957i	$-0.636115\pi$
$491$	−18.3784	−0.829407	−0.414703	+	0.909957i	$0.636115\pi$
$492$	13.4292	0.605436
$493$	−11.2291	−0.505732
$494$	36.1528	1.62659
$495$	22.9668	1.03228
$496$	7.86232	0.353029
$497$	−1.44871	−0.0649834
$498$	0.503315	0.0225541
$499$	−3.51102	−0.157175	−0.0785874	−	0.996907i	$-0.525041\pi$
$499$	−3.51102	−0.157175	−0.0785874	+	0.996907i	$0.525041\pi$
$500$	−2.85005	−0.127458
$501$	63.2463	2.82564
$502$	10.9473	0.488601
$503$	19.7903	0.882405	0.441202	−	0.897408i	$-0.354552\pi$
$503$	19.7903	0.882405	0.441202	+	0.897408i	$0.354552\pi$
$504$	11.3696	0.506443
$505$	1.83398	0.0816113
$506$	−70.2610	−3.12348
$507$	−17.4581	−0.775341
$508$	−43.4962	−1.92983
$509$	38.5748	1.70980	0.854899	−	0.518795i	$-0.173619\pi$
$509$	38.5748	1.70980	0.854899	+	0.518795i	$0.173619\pi$
$510$	−9.43481	−0.417780
$511$	−5.14212	−0.227474
$512$	−17.2903	−0.764129
$513$	35.0535	1.54765
$514$	−5.32291	−0.234783
$515$	9.46639	0.417139
$516$	−43.5468	−1.91704
$517$	11.7583	0.517128
$518$	−5.97121	−0.262360
$519$	47.8373	2.09982
$520$	8.11614	0.355916
$521$	−27.2196	−1.19251	−0.596256	−	0.802794i	$-0.703346\pi$
$521$	−27.2196	−1.19251	−0.596256	+	0.802794i	$0.703346\pi$
$522$	105.601	4.62203
$523$	6.38232	0.279079	0.139540	−	0.990216i	$-0.455438\pi$
$523$	6.38232	0.279079	0.139540	+	0.990216i	$0.455438\pi$
$524$	8.63976	0.377429
$525$	3.01220	0.131463
$526$	16.6930	0.727849
$527$	−7.08943	−0.308820
$528$	−17.9669	−0.781907
$529$	48.1765	2.09463
$530$	3.13056	0.135983
$531$	−58.3341	−2.53148
$532$	10.7917	0.467881
$533$	−6.78180	−0.293752
$534$	−96.2364	−4.16456
$535$	−0.955305	−0.0413014
$536$	1.40154	0.0605371
$537$	−24.8520	−1.07244
$538$	33.6575	1.45108
$539$	−3.78158	−0.162884
$540$	26.3843	1.13540
$541$	−26.9115	−1.15702	−0.578508	−	0.815677i	$-0.696365\pi$
$541$	−26.9115	−1.15702	−0.578508	+	0.815677i	$0.696365\pi$
$542$	−4.38173	−0.188211
$543$	−40.5399	−1.73973
$544$	10.2655	0.440130
$545$	−3.03723	−0.130100
$546$	−28.7599	−1.23081
$547$	28.9162	1.23637	0.618183	−	0.786034i	$-0.287869\pi$
$547$	28.9162	1.23637	0.618183	+	0.786034i	$0.287869\pi$
$548$	8.96234	0.382852
$549$	−64.2543	−2.74231
$550$	8.32810	0.355111
$551$	29.8955	1.27359
$552$	−47.5741	−2.02489
$553$	−9.81951	−0.417568
$554$	56.6993	2.40892
$555$	−8.16719	−0.346678
$556$	−33.8350	−1.43493
$557$	−14.7611	−0.625449	−0.312725	−	0.949844i	$-0.601242\pi$
$557$	−14.7611	−0.625449	−0.312725	+	0.949844i	$0.601242\pi$
$558$	66.6707	2.82240
$559$	21.9913	0.930132
$560$	−1.57731	−0.0666534
$561$	16.2007	0.683992
$562$	−50.3877	−2.12548
$563$	−10.9805	−0.462774	−0.231387	−	0.972862i	$-0.574326\pi$
$563$	−10.9805	−0.462774	−0.231387	+	0.972862i	$0.574326\pi$
$564$	26.6936	1.12400
$565$	−9.05115	−0.380785
$566$	14.6072	0.613988
$567$	−9.66538	−0.405908
$568$	−2.71206	−0.113796
$569$	33.1740	1.39073	0.695363	−	0.718659i	$-0.255244\pi$
$569$	33.1740	1.39073	0.695363	+	0.718659i	$0.255244\pi$
$570$	25.1186	1.05210
$571$	−14.6394	−0.612640	−0.306320	−	0.951929i	$-0.599098\pi$
$571$	−14.6394	−0.612640	−0.306320	+	0.951929i	$0.599098\pi$
$572$	−46.7257	−1.95370
$573$	−28.5125	−1.19113
$574$	−3.44499	−0.143791
$575$	−8.43662	−0.351831
$576$	−77.3804	−3.22418
$577$	−36.5018	−1.51959	−0.759794	−	0.650164i	$-0.774700\pi$
$577$	−36.5018	−1.51959	−0.759794	+	0.650164i	$0.774700\pi$
$578$	32.9840	1.37196
$579$	48.3534	2.00950
$580$	22.5020	0.934343
$581$	−0.0758723	−0.00314771
$582$	57.1008	2.36690
$583$	−5.37553	−0.222632
$584$	−9.62635	−0.398341
$585$	−26.3304	−1.08863
$586$	15.1559	0.626085
$587$	10.5598	0.435848	0.217924	−	0.975966i	$-0.430071\pi$
$587$	10.5598	0.435848	0.217924	+	0.975966i	$0.430071\pi$
$588$	−8.58492	−0.354036
$589$	18.8744	0.777705
$590$	−21.1528	−0.870848
$591$	67.7749	2.78789
$592$	4.27666	0.175770
$593$	36.9143	1.51589	0.757945	−	0.652318i	$-0.226203\pi$
$593$	36.9143	1.51589	0.757945	+	0.652318i	$0.226203\pi$
$594$	−77.0973	−3.16334
$595$	1.42225	0.0583066
$596$	−51.5894	−2.11318
$597$	27.9724	1.14483
$598$	80.5512	3.29398
$599$	−32.5743	−1.33095	−0.665475	−	0.746420i	$-0.731771\pi$
$599$	−32.5743	−1.33095	−0.665475	+	0.746420i	$0.731771\pi$
$600$	5.63900	0.230211
$601$	18.4055	0.750776	0.375388	−	0.926868i	$-0.377509\pi$
$601$	18.4055	0.750776	0.375388	+	0.926868i	$0.377509\pi$
$602$	11.1710	0.455297
$603$	−4.54687	−0.185163
$604$	−17.5269	−0.713161
$605$	−3.30031	−0.134177
$606$	−12.1661	−0.494215
$607$	−18.7941	−0.762830	−0.381415	−	0.924404i	$-0.624563\pi$
$607$	−18.7941	−0.762830	−0.381415	+	0.924404i	$0.624563\pi$
$608$	−27.3302	−1.10838
$609$	−23.7821	−0.963701
$610$	−23.2996	−0.943373
$611$	−13.4804	−0.545357
$612$	24.6182	0.995132
$613$	16.8509	0.680601	0.340300	−	0.940317i	$-0.389471\pi$
$613$	16.8509	0.680601	0.340300	+	0.940317i	$0.389471\pi$
$614$	−19.8707	−0.801917
$615$	−4.71192	−0.190003
$616$	−7.07932	−0.285234
$617$	19.4653	0.783645	0.391822	−	0.920041i	$-0.371845\pi$
$617$	19.4653	0.783645	0.391822	+	0.920041i	$0.371845\pi$
$618$	−62.7973	−2.52608
$619$	21.4252	0.861152	0.430576	−	0.902554i	$-0.358310\pi$
$619$	21.4252	0.861152	0.430576	+	0.902554i	$0.358310\pi$
$620$	14.2065	0.570547
$621$	78.1019	3.13412
$622$	53.6356	2.15059
$623$	14.5072	0.581218
$624$	20.5982	0.824589
$625$	1.00000	0.0400000
$626$	−6.57780	−0.262902
$627$	−43.1315	−1.72250
$628$	49.5644	1.97783
$629$	−3.85625	−0.153759
$630$	−13.3752	−0.532881
$631$	6.59963	0.262727	0.131364	−	0.991334i	$-0.458064\pi$
$631$	6.59963	0.262727	0.131364	+	0.991334i	$0.458064\pi$
$632$	−18.3827	−0.731223
$633$	45.6786	1.81556
$634$	45.4440	1.80481
$635$	15.2615	0.605636
$636$	−12.2035	−0.483901
$637$	4.33541	0.171775
$638$	−65.7527	−2.60317
$639$	8.79848	0.348063
$640$	−13.6237	−0.538525
$641$	−1.68300	−0.0664747	−0.0332373	−	0.999447i	$-0.510582\pi$
$641$	−1.68300	−0.0664747	−0.0332373	+	0.999447i	$0.510582\pi$
$642$	6.33722	0.250110
$643$	40.3837	1.59258	0.796289	−	0.604916i	$-0.206793\pi$
$643$	40.3837	1.59258	0.796289	+	0.604916i	$0.206793\pi$
$644$	24.0448	0.947498
$645$	15.2793	0.601622
$646$	11.8601	0.466629
$647$	20.9387	0.823183	0.411592	−	0.911368i	$-0.364973\pi$
$647$	20.9387	0.823183	0.411592	+	0.911368i	$0.364973\pi$
$648$	−18.0941	−0.710805
$649$	36.3219	1.42576
$650$	−9.54781	−0.374496
$651$	−15.0148	−0.588475
$652$	−18.8686	−0.738952
$653$	−29.4081	−1.15083	−0.575414	−	0.817863i	$-0.695159\pi$
$653$	−29.4081	−1.15083	−0.575414	+	0.817863i	$0.695159\pi$
$654$	20.1481	0.787852
$655$	−3.03144	−0.118448
$656$	2.46735	0.0963337
$657$	31.2298	1.21839
$658$	−6.84769	−0.266951
$659$	16.2680	0.633712	0.316856	−	0.948474i	$-0.397373\pi$
$659$	16.2680	0.633712	0.316856	+	0.948474i	$0.397373\pi$
$660$	−32.4645	−1.26368
$661$	−23.2298	−0.903534	−0.451767	−	0.892136i	$-0.649206\pi$
$661$	−23.2298	−0.903534	−0.451767	+	0.892136i	$0.649206\pi$
$662$	74.6136	2.89994
$663$	−18.5734	−0.721329
$664$	−0.142037	−0.00551211
$665$	−3.78650	−0.146834
$666$	36.2651	1.40525
$667$	66.6095	2.57913
$668$	−59.8418	−2.31535
$669$	13.6722	0.528597
$670$	−1.64876	−0.0636973
$671$	40.0081	1.54450
$672$	21.7414	0.838693
$673$	13.4306	0.517712	0.258856	−	0.965916i	$-0.416654\pi$
$673$	13.4306	0.517712	0.258856	+	0.965916i	$0.416654\pi$
$674$	46.1332	1.77698
$675$	−9.25749	−0.356321
$676$	16.5183	0.635321
$677$	31.6062	1.21473	0.607363	−	0.794424i	$-0.292227\pi$
$677$	31.6062	1.21473	0.607363	+	0.794424i	$0.292227\pi$
$678$	60.0427	2.30593
$679$	−8.60767	−0.330332
$680$	2.66254	0.102104
$681$	−11.0678	−0.424118
$682$	−41.5127	−1.58960
$683$	24.8793	0.951981	0.475991	−	0.879450i	$-0.342090\pi$
$683$	24.8793	0.951981	0.475991	+	0.879450i	$0.342090\pi$
$684$	−65.5417	−2.50605
$685$	−3.14462	−0.120150
$686$	2.20228	0.0840836
$687$	−3.01220	−0.114923
$688$	−8.00085	−0.305029
$689$	6.16282	0.234785
$690$	55.9661	2.13059
$691$	0.365424	0.0139014	0.00695069	−	0.999976i	$-0.497788\pi$
$691$	0.365424	0.0139014	0.00695069	+	0.999976i	$0.497788\pi$
$692$	−45.2622	−1.72061
$693$	22.9668	0.872435
$694$	42.9697	1.63111
$695$	11.8717	0.450320
$696$	−44.5215	−1.68758
$697$	−2.22480	−0.0842703
$698$	−15.8003	−0.598050
$699$	50.6446	1.91556
$700$	−2.85005	−0.107722
$701$	23.3790	0.883012	0.441506	−	0.897258i	$-0.354444\pi$
$701$	23.3790	0.883012	0.441506	+	0.897258i	$0.354444\pi$
$702$	88.3887	3.33602
$703$	10.2666	0.387212
$704$	48.1811	1.81589
$705$	−9.36600	−0.352744
$706$	−20.7390	−0.780524
$707$	1.83398	0.0689741
$708$	82.4578	3.09895
$709$	7.45475	0.279969	0.139984	−	0.990154i	$-0.455295\pi$
$709$	7.45475	0.279969	0.139984	+	0.990154i	$0.455295\pi$
$710$	3.19046	0.119736
$711$	59.6371	2.23657
$712$	27.1582	1.01780
$713$	42.0536	1.57492
$714$	−9.43481	−0.353089
$715$	16.3947	0.613127
$716$	23.5142	0.878768
$717$	−53.3907	−1.99391
$718$	−20.5480	−0.766846
$719$	−41.4309	−1.54511	−0.772555	−	0.634947i	$-0.781022\pi$
$719$	−41.4309	−1.54511	−0.772555	+	0.634947i	$0.781022\pi$
$720$	9.57951	0.357007
$721$	9.46639	0.352547
$722$	10.2680	0.382134
$723$	−56.7754	−2.11150
$724$	38.3576	1.42555
$725$	−7.89528	−0.293223
$726$	21.8933	0.812537
$727$	−10.5579	−0.391569	−0.195785	−	0.980647i	$-0.562725\pi$
$727$	−10.5579	−0.391569	−0.195785	+	0.980647i	$0.562725\pi$
$728$	8.11614	0.300804
$729$	−24.9551	−0.924262
$730$	11.3244	0.419135
$731$	7.21434	0.266832
$732$	90.8263	3.35704
$733$	38.9965	1.44037	0.720184	−	0.693783i	$-0.244057\pi$
$733$	38.9965	1.44037	0.720184	+	0.693783i	$0.244057\pi$
$734$	−39.8226	−1.46988
$735$	3.01220	0.111107
$736$	−60.8937	−2.24457
$737$	2.83112	0.104286
$738$	20.9225	0.770170
$739$	6.56544	0.241514	0.120757	−	0.992682i	$-0.461468\pi$
$739$	6.56544	0.241514	0.120757	+	0.992682i	$0.461468\pi$
$740$	7.72755	0.284070
$741$	49.4484	1.81653
$742$	3.13056	0.114926
$743$	11.5345	0.423161	0.211581	−	0.977361i	$-0.432139\pi$
$743$	11.5345	0.423161	0.211581	+	0.977361i	$0.432139\pi$
$744$	−28.1085	−1.03051
$745$	18.1012	0.663177
$746$	−12.5110	−0.458062
$747$	0.460798	0.0168597
$748$	−15.3286	−0.560469
$749$	−0.955305	−0.0349061
$750$	−6.63371	−0.242229
$751$	15.9499	0.582019	0.291010	−	0.956720i	$-0.406009\pi$
$751$	15.9499	0.582019	0.291010	+	0.956720i	$0.406009\pi$
$752$	4.90441	0.178846
$753$	14.9733	0.545657
$754$	75.3826	2.74527
$755$	6.14969	0.223810
$756$	26.3843	0.959589
$757$	−36.4971	−1.32651	−0.663255	−	0.748394i	$-0.730825\pi$
$757$	−36.4971	−1.32651	−0.663255	+	0.748394i	$0.730825\pi$
$758$	40.9738	1.48823
$759$	−96.1003	−3.48822
$760$	−7.08854	−0.257128
$761$	29.2799	1.06140	0.530698	−	0.847561i	$-0.321930\pi$
$761$	29.2799	1.06140	0.530698	+	0.847561i	$0.321930\pi$
$762$	−101.241	−3.66756
$763$	−3.03723	−0.109955
$764$	26.9777	0.976017
$765$	−8.63781	−0.312301
$766$	47.0046	1.69834
$767$	−41.6414	−1.50358
$768$	13.6190	0.491434
$769$	31.3181	1.12936	0.564680	−	0.825310i	$-0.309000\pi$
$769$	31.3181	1.12936	0.564680	+	0.825310i	$0.309000\pi$
$770$	8.32810	0.300124
$771$	−7.28046	−0.262199
$772$	−45.7505	−1.64660
$773$	1.29537	0.0465911	0.0232956	−	0.999729i	$-0.492584\pi$
$773$	1.29537	0.0465911	0.0232956	+	0.999729i	$0.492584\pi$
$774$	−67.8454	−2.43865
$775$	−4.98465	−0.179054
$776$	−16.1140	−0.578460
$777$	−8.16719	−0.292996
$778$	74.5655	2.67330
$779$	5.92314	0.212219
$780$	37.2192	1.33266
$781$	−5.47840	−0.196032
$782$	26.4252	0.944963
$783$	73.0904	2.61204
$784$	−1.57731	−0.0563324
$785$	−17.3907	−0.620700
$786$	20.1097	0.717289
$787$	41.5502	1.48111	0.740553	−	0.671998i	$-0.234564\pi$
$787$	41.5502	1.48111	0.740553	+	0.671998i	$0.234564\pi$
$788$	−64.1267	−2.28442
$789$	22.8320	0.812842
$790$	21.6253	0.769395
$791$	−9.05115	−0.321822
$792$	42.9951	1.52776
$793$	−45.8676	−1.62881
$794$	−38.0595	−1.35068
$795$	4.28186	0.151862
$796$	−26.4666	−0.938085
$797$	−21.9005	−0.775756	−0.387878	−	0.921711i	$-0.626792\pi$
$797$	−21.9005	−0.775756	−0.387878	+	0.921711i	$0.626792\pi$
$798$	25.1186	0.889187
$799$	−4.42229	−0.156449
$800$	7.21779	0.255187
$801$	−88.1069	−3.11310
$802$	76.0777	2.68640
$803$	−19.4453	−0.686211
$804$	6.42720	0.226670
$805$	−8.43662	−0.297352
$806$	47.5925	1.67637
$807$	46.0354	1.62052
$808$	3.43332	0.120784
$809$	9.39275	0.330232	0.165116	−	0.986274i	$-0.447200\pi$
$809$	9.39275	0.330232	0.165116	+	0.986274i	$0.447200\pi$
$810$	21.2859	0.747910
$811$	−31.7952	−1.11648	−0.558240	−	0.829680i	$-0.688523\pi$
$811$	−31.7952	−1.11648	−0.558240	+	0.829680i	$0.688523\pi$
$812$	22.5020	0.789664
$813$	−5.99316	−0.210189
$814$	−22.5806	−0.791449
$815$	6.62045	0.231904
$816$	6.75734	0.236554
$817$	−19.2069	−0.671965
$818$	−51.9210	−1.81538
$819$	−26.3304	−0.920059
$820$	4.45828	0.155690
$821$	−28.5619	−0.996818	−0.498409	−	0.866942i	$-0.666082\pi$
$821$	−28.5619	−0.996818	−0.498409	+	0.866942i	$0.666082\pi$
$822$	20.8605	0.727594
$823$	−7.52021	−0.262138	−0.131069	−	0.991373i	$-0.541841\pi$
$823$	−7.52021	−0.262138	−0.131069	+	0.991373i	$0.541841\pi$
$824$	17.7216	0.617361
$825$	11.3909	0.396579
$826$	−21.1528	−0.736001
$827$	−29.9178	−1.04034	−0.520171	−	0.854062i	$-0.674132\pi$
$827$	−29.9178	−1.04034	−0.520171	+	0.854062i	$0.674132\pi$
$828$	−146.032	−5.07497
$829$	−30.9662	−1.07550	−0.537750	−	0.843104i	$-0.680726\pi$
$829$	−30.9662	−1.07550	−0.537750	+	0.843104i	$0.680726\pi$
$830$	0.167092	0.00579986
$831$	77.5511	2.69022
$832$	−55.2375	−1.91502
$833$	1.42225	0.0492781
$834$	−78.7536	−2.72701
$835$	20.9967	0.726622
$836$	40.8097	1.41143
$837$	46.1453	1.59502
$838$	80.9479	2.79630
$839$	29.6014	1.02196	0.510978	−	0.859594i	$-0.329284\pi$
$839$	29.6014	1.02196	0.510978	+	0.859594i	$0.329284\pi$
$840$	5.63900	0.194564
$841$	33.3354	1.14950
$842$	−2.95693	−0.101903
$843$	−68.9183	−2.37367
$844$	−43.2197	−1.48768
$845$	−5.79580	−0.199382
$846$	41.5883	1.42984
$847$	−3.30031	−0.113400
$848$	−2.24215	−0.0769958
$849$	19.9792	0.685685
$850$	−3.13220	−0.107434
$851$	22.8748	0.784138
$852$	−12.4370	−0.426086
$853$	−3.48457	−0.119309	−0.0596547	−	0.998219i	$-0.519000\pi$
$853$	−3.48457	−0.119309	−0.0596547	+	0.998219i	$0.519000\pi$
$854$	−23.2996	−0.797296
$855$	22.9967	0.786470
$856$	−1.78838	−0.0611257
$857$	−5.86120	−0.200215	−0.100107	−	0.994977i	$-0.531919\pi$
$857$	−5.86120	−0.200215	−0.100107	+	0.994977i	$0.531919\pi$
$858$	−108.758	−3.71292
$859$	−13.8263	−0.471746	−0.235873	−	0.971784i	$-0.575795\pi$
$859$	−13.8263	−0.471746	−0.235873	+	0.971784i	$0.575795\pi$
$860$	−14.4568	−0.492973
$861$	−4.71192	−0.160582
$862$	16.5054	0.562175
$863$	−46.9250	−1.59735	−0.798673	−	0.601766i	$-0.794464\pi$
$863$	−46.9250	−1.59735	−0.798673	+	0.601766i	$0.794464\pi$
$864$	−66.8186	−2.27321
$865$	15.8812	0.539977
$866$	16.1994	0.550479
$867$	45.1143	1.53216
$868$	14.2065	0.482201
$869$	−37.1332	−1.25966
$870$	52.3750	1.77568
$871$	−3.24576	−0.109978
$872$	−5.68586	−0.192547
$873$	52.2772	1.76932
$874$	−70.3525	−2.37971
$875$	1.00000	0.0338062
$876$	−44.1447	−1.49151
$877$	−49.1993	−1.66134	−0.830671	−	0.556763i	$-0.812043\pi$
$877$	−49.1993	−1.66134	−0.830671	+	0.556763i	$0.812043\pi$
$878$	20.1639	0.680498
$879$	20.7297	0.699194
$880$	−5.96470	−0.201070
$881$	26.5334	0.893934	0.446967	−	0.894550i	$-0.352504\pi$
$881$	26.5334	0.893934	0.446967	+	0.894550i	$0.352504\pi$
$882$	−13.3752	−0.450366
$883$	26.7806	0.901238	0.450619	−	0.892716i	$-0.351203\pi$
$883$	26.7806	0.901238	0.450619	+	0.892716i	$0.351203\pi$
$884$	17.5736	0.591063
$885$	−28.9320	−0.972539
$886$	−37.8338	−1.27105
$887$	22.7884	0.765158	0.382579	−	0.923923i	$-0.375036\pi$
$887$	22.7884	0.765158	0.382579	+	0.923923i	$0.375036\pi$
$888$	−15.2894	−0.513080
$889$	15.2615	0.511856
$890$	−31.9489	−1.07093
$891$	−36.5504	−1.22448
$892$	−12.9362	−0.433136
$893$	11.7736	0.393988
$894$	−120.078	−4.01601
$895$	−8.25045	−0.275782
$896$	−13.6237	−0.455137
$897$	110.175	3.67863
$898$	10.4155	0.347569
$899$	39.3552	1.31257
$900$	17.3093	0.576977
$901$	2.02174	0.0673539
$902$	−13.0275	−0.433767
$903$	15.2793	0.508463
$904$	−16.9443	−0.563558
$905$	−13.4586	−0.447378
$906$	−40.7953	−1.35533
$907$	−36.1619	−1.20074	−0.600368	−	0.799724i	$-0.704979\pi$
$907$	−36.1619	−1.20074	−0.600368	+	0.799724i	$0.704979\pi$
$908$	10.4720	0.347525
$909$	−11.1384	−0.369437
$910$	−9.54781	−0.316507
$911$	−47.5345	−1.57489	−0.787444	−	0.616387i	$-0.788596\pi$
$911$	−47.5345	−1.57489	−0.787444	+	0.616387i	$0.788596\pi$
$912$	−17.9903	−0.595717
$913$	−0.286917	−0.00949556
$914$	−60.9382	−2.01566
$915$	−31.8683	−1.05353
$916$	2.85005	0.0941684
$917$	−3.03144	−0.100107
$918$	28.9963	0.957021
$919$	−7.87020	−0.259614	−0.129807	−	0.991539i	$-0.541436\pi$
$919$	−7.87020	−0.259614	−0.129807	+	0.991539i	$0.541436\pi$
$920$	−15.7938	−0.520707
$921$	−27.1784	−0.895558
$922$	64.1708	2.11335
$923$	6.28074	0.206733
$924$	−32.4645	−1.06800
$925$	−2.71137	−0.0891493
$926$	76.6660	2.51940
$927$	−57.4925	−1.88830
$928$	−56.9864	−1.87067
$929$	56.1990	1.84383	0.921915	−	0.387392i	$-0.126624\pi$
$929$	56.1990	1.84383	0.921915	+	0.387392i	$0.126624\pi$
$930$	33.0667	1.08430
$931$	−3.78650	−0.124098
$932$	−47.9185	−1.56962
$933$	73.3607	2.40172
$934$	7.89289	0.258263
$935$	5.37835	0.175891
$936$	−49.2920	−1.61116
$937$	40.8418	1.33424	0.667122	−	0.744948i	$-0.267526\pi$
$937$	40.8418	1.33424	0.667122	+	0.744948i	$0.267526\pi$
$938$	−1.64876	−0.0538341
$939$	−8.99686	−0.293601
$940$	8.86184	0.289041
$941$	−32.4457	−1.05770	−0.528850	−	0.848715i	$-0.677377\pi$
$941$	−32.4457	−1.05770	−0.528850	+	0.848715i	$0.677377\pi$
$942$	115.365	3.75879
$943$	13.1972	0.429761
$944$	15.1500	0.493089
$945$	−9.25749	−0.301146
$946$	42.2441	1.37347
$947$	17.9499	0.583292	0.291646	−	0.956526i	$-0.405797\pi$
$947$	17.9499	0.583292	0.291646	+	0.956526i	$0.405797\pi$
$948$	−84.2997	−2.73793
$949$	22.2932	0.723669
$950$	8.33895	0.270551
$951$	62.1565	2.01556
$952$	2.66254	0.0862933
$953$	−1.98786	−0.0643929	−0.0321965	−	0.999482i	$-0.510250\pi$
$953$	−1.98786	−0.0643929	−0.0321965	+	0.999482i	$0.510250\pi$
$954$	−19.0129	−0.615566
$955$	−9.46567	−0.306302
$956$	50.5167	1.63383
$957$	−89.9339	−2.90715
$958$	−55.0112	−1.77733
$959$	−3.14462	−0.101545
$960$	−38.3784	−1.23866
$961$	−6.15325	−0.198492
$962$	25.8876	0.834651
$963$	5.80189	0.186963
$964$	53.7192	1.73018
$965$	16.0525	0.516749
$966$	55.9661	1.80068
$967$	47.0012	1.51146	0.755728	−	0.654885i	$-0.227283\pi$
$967$	47.0012	1.51146	0.755728	+	0.654885i	$0.227283\pi$
$968$	−6.17837	−0.198580
$969$	16.2218	0.521118
$970$	18.9565	0.608657
$971$	−53.3009	−1.71051	−0.855254	−	0.518210i	$-0.826599\pi$
$971$	−53.3009	−1.71051	−0.855254	+	0.518210i	$0.826599\pi$
$972$	−3.82354	−0.122640
$973$	11.8717	0.380590
$974$	−8.86684	−0.284112
$975$	−13.0591	−0.418226
$976$	16.6875	0.534154
$977$	−18.5001	−0.591871	−0.295935	−	0.955208i	$-0.595631\pi$
$977$	−18.5001	−0.591871	−0.295935	+	0.955208i	$0.595631\pi$
$978$	−43.9182	−1.40435
$979$	54.8600	1.75333
$980$	−2.85005	−0.0910416
$981$	18.4461	0.588938
$982$	40.4745	1.29159
$983$	−38.3996	−1.22476	−0.612379	−	0.790564i	$-0.709787\pi$
$983$	−38.3996	−1.22476	−0.612379	+	0.790564i	$0.709787\pi$
$984$	−8.82097	−0.281202
$985$	22.5002	0.716915
$986$	24.7296	0.787551
$987$	−9.36600	−0.298123
$988$	−46.7866	−1.48848
$989$	−42.7945	−1.36079
$990$	−50.5793	−1.60752
$991$	−36.0994	−1.14673	−0.573367	−	0.819298i	$-0.694363\pi$
$991$	−36.0994	−1.14673	−0.573367	+	0.819298i	$0.694363\pi$
$992$	−35.9782	−1.14231
$993$	102.054	3.23857
$994$	3.19046	0.101195
$995$	9.28637	0.294398
$996$	−0.651358	−0.0206391
$997$	2.67421	0.0846931	0.0423465	−	0.999103i	$-0.486517\pi$
$997$	2.67421	0.0846931	0.0423465	+	0.999103i	$0.486517\pi$
$998$	7.73226	0.244761
$999$	25.1005	0.794144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.9	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.9	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20228 q^{2} -3.01220 q^{3} +2.85005 q^{4} -1.00000 q^{5} +6.63371 q^{6} -1.00000 q^{7} -1.87206 q^{8} +6.07333 q^{9} +O(q^{10})\)	\(q-2.20228 q^{2} -3.01220 q^{3} +2.85005 q^{4} -1.00000 q^{5} +6.63371 q^{6} -1.00000 q^{7} -1.87206 q^{8} +6.07333 q^{9} +2.20228 q^{10} -3.78158 q^{11} -8.58492 q^{12} +4.33541 q^{13} +2.20228 q^{14} +3.01220 q^{15} -1.57731 q^{16} +1.42225 q^{17} -13.3752 q^{18} -3.78650 q^{19} -2.85005 q^{20} +3.01220 q^{21} +8.32810 q^{22} -8.43662 q^{23} +5.63900 q^{24} +1.00000 q^{25} -9.54781 q^{26} -9.25749 q^{27} -2.85005 q^{28} -7.89528 q^{29} -6.63371 q^{30} -4.98465 q^{31} +7.21779 q^{32} +11.3909 q^{33} -3.13220 q^{34} +1.00000 q^{35} +17.3093 q^{36} -2.71137 q^{37} +8.33895 q^{38} -13.0591 q^{39} +1.87206 q^{40} -1.56428 q^{41} -6.63371 q^{42} +5.07248 q^{43} -10.7777 q^{44} -6.07333 q^{45} +18.5798 q^{46} -3.10936 q^{47} +4.75116 q^{48} +1.00000 q^{49} -2.20228 q^{50} -4.28410 q^{51} +12.3562 q^{52} +1.42151 q^{53} +20.3876 q^{54} +3.78158 q^{55} +1.87206 q^{56} +11.4057 q^{57} +17.3876 q^{58} -9.60495 q^{59} +8.58492 q^{60} -10.5797 q^{61} +10.9776 q^{62} -6.07333 q^{63} -12.7410 q^{64} -4.33541 q^{65} -25.0859 q^{66} -0.748661 q^{67} +4.05349 q^{68} +25.4128 q^{69} -2.20228 q^{70} +1.44871 q^{71} -11.3696 q^{72} +5.14212 q^{73} +5.97121 q^{74} -3.01220 q^{75} -10.7917 q^{76} +3.78158 q^{77} +28.7599 q^{78} +9.81951 q^{79} +1.57731 q^{80} +9.66538 q^{81} +3.44499 q^{82} +0.0758723 q^{83} +8.58492 q^{84} -1.42225 q^{85} -11.1710 q^{86} +23.7821 q^{87} +7.07932 q^{88} -14.5072 q^{89} +13.3752 q^{90} -4.33541 q^{91} -24.0448 q^{92} +15.0148 q^{93} +6.84769 q^{94} +3.78650 q^{95} -21.7414 q^{96} +8.60767 q^{97} -2.20228 q^{98} -22.9668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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