LMFDB - Embedded newform 301.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [301,2,Mod(1,301)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(301, 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("301.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 301 = 7 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	301.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:	$2.40349710084$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.370865$ of defining polynomial
Character	$\chi$	$=$	301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.15948 q^{2} -2.96035 q^{3} +2.66333 q^{4} -3.06159 q^{5} -6.39280 q^{6} -1.00000 q^{7} +1.43245 q^{8} +5.76366 q^{9} +O(q^{10})$	\(q+2.15948 q^{2} -2.96035 q^{3} +2.66333 q^{4} -3.06159 q^{5} -6.39280 q^{6} -1.00000 q^{7} +1.43245 q^{8} +5.76366 q^{9} -6.61142 q^{10} -5.60419 q^{11} -7.88439 q^{12} -2.28475 q^{13} -2.15948 q^{14} +9.06336 q^{15} -2.23332 q^{16} +4.43968 q^{17} +12.4465 q^{18} +4.31440 q^{19} -8.15402 q^{20} +2.96035 q^{21} -12.1021 q^{22} -2.19458 q^{23} -4.24055 q^{24} +4.37331 q^{25} -4.93387 q^{26} -8.18141 q^{27} -2.66333 q^{28} -0.786168 q^{29} +19.5721 q^{30} -6.29928 q^{31} -7.68771 q^{32} +16.5904 q^{33} +9.58738 q^{34} +3.06159 q^{35} +15.3506 q^{36} +7.79584 q^{37} +9.31684 q^{38} +6.76366 q^{39} -4.38557 q^{40} -8.60006 q^{41} +6.39280 q^{42} -1.00000 q^{43} -14.9258 q^{44} -17.6460 q^{45} -4.73914 q^{46} +10.1079 q^{47} +6.61142 q^{48} +1.00000 q^{49} +9.44405 q^{50} -13.1430 q^{51} -6.08506 q^{52} -4.68771 q^{53} -17.6676 q^{54} +17.1577 q^{55} -1.43245 q^{56} -12.7721 q^{57} -1.69771 q^{58} -12.9231 q^{59} +24.1387 q^{60} +4.03664 q^{61} -13.6031 q^{62} -5.76366 q^{63} -12.1348 q^{64} +6.99497 q^{65} +35.8265 q^{66} -5.65058 q^{67} +11.8243 q^{68} +6.49672 q^{69} +6.61142 q^{70} -2.91682 q^{71} +8.25616 q^{72} +12.3600 q^{73} +16.8349 q^{74} -12.9465 q^{75} +11.4907 q^{76} +5.60419 q^{77} +14.6060 q^{78} -5.08698 q^{79} +6.83751 q^{80} +6.92883 q^{81} -18.5716 q^{82} -13.2997 q^{83} +7.88439 q^{84} -13.5925 q^{85} -2.15948 q^{86} +2.32733 q^{87} -8.02772 q^{88} -12.1067 q^{89} -38.1060 q^{90} +2.28475 q^{91} -5.84489 q^{92} +18.6481 q^{93} +21.8278 q^{94} -13.2089 q^{95} +22.7583 q^{96} -13.7366 q^{97} +2.15948 q^{98} -32.3007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9} - q^{10} - 16 q^{11} - 8 q^{12} - 2 q^{13} - 8 q^{15} - 8 q^{17} + 17 q^{18} - 10 q^{19} - 6 q^{20} + 3 q^{21} - 5 q^{22} - 2 q^{23} + 10 q^{24} + 11 q^{25} - 24 q^{26} - 9 q^{27} - 2 q^{28} - 4 q^{29} + 24 q^{30} - 6 q^{31} + 4 q^{32} + 14 q^{33} + 17 q^{34} + 6 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + 11 q^{39} - 20 q^{40} - 16 q^{41} + 10 q^{42} - 5 q^{43} - 11 q^{44} - 14 q^{45} + 17 q^{46} - 11 q^{47} + q^{48} + 5 q^{49} + 12 q^{50} - 6 q^{51} + 24 q^{52} + 19 q^{53} - 23 q^{54} + 25 q^{55} + 3 q^{56} - 5 q^{57} - 31 q^{59} + 43 q^{60} - 2 q^{61} + 7 q^{62} - 6 q^{63} - 17 q^{64} + 6 q^{65} + 59 q^{66} + 11 q^{67} + 13 q^{68} - 17 q^{69} + q^{70} - 15 q^{71} + 23 q^{72} + 13 q^{73} + 22 q^{74} + 4 q^{75} + 34 q^{76} + 16 q^{77} + 17 q^{78} + 24 q^{79} + 11 q^{80} + 5 q^{81} - 36 q^{83} + 8 q^{84} - 19 q^{85} + 23 q^{87} - 13 q^{88} - 15 q^{89} - 17 q^{90} + 2 q^{91} - 35 q^{92} + 39 q^{93} + 32 q^{94} - 14 q^{95} - 2 q^{96} - 13 q^{97} - 63 q^{99}+O(q^{100}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9 - q^10 - 16 * q^11 - 8 * q^12 - 2 * q^13 - 8 * q^15 - 8 * q^17 + 17 * q^18 - 10 * q^19 - 6 * q^20 + 3 * q^21 - 5 * q^22 - 2 * q^23 + 10 * q^24 + 11 * q^25 - 24 * q^26 - 9 * q^27 - 2 * q^28 - 4 * q^29 + 24 * q^30 - 6 * q^31 + 4 * q^32 + 14 * q^33 + 17 * q^34 + 6 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + 11 * q^39 - 20 * q^40 - 16 * q^41 + 10 * q^42 - 5 * q^43 - 11 * q^44 - 14 * q^45 + 17 * q^46 - 11 * q^47 + q^48 + 5 * q^49 + 12 * q^50 - 6 * q^51 + 24 * q^52 + 19 * q^53 - 23 * q^54 + 25 * q^55 + 3 * q^56 - 5 * q^57 - 31 * q^59 + 43 * q^60 - 2 * q^61 + 7 * q^62 - 6 * q^63 - 17 * q^64 + 6 * q^65 + 59 * q^66 + 11 * q^67 + 13 * q^68 - 17 * q^69 + q^70 - 15 * q^71 + 23 * q^72 + 13 * q^73 + 22 * q^74 + 4 * q^75 + 34 * q^76 + 16 * q^77 + 17 * q^78 + 24 * q^79 + 11 * q^80 + 5 * q^81 - 36 * q^83 + 8 * q^84 - 19 * q^85 + 23 * q^87 - 13 * q^88 - 15 * q^89 - 17 * q^90 + 2 * q^91 - 35 * q^92 + 39 * q^93 + 32 * q^94 - 14 * q^95 - 2 * q^96 - 13 * q^97 - 63 * 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 $

$2$	2.15948	1.52698	0.763490	−	0.645820i	$-0.223484\pi$
$2$	2.15948	1.52698	0.763490	+	0.645820i	$0.223484\pi$
$3$	−2.96035	−1.70916	−0.854579	−	0.519321i	$-0.826185\pi$
$3$	−2.96035	−1.70916	−0.854579	+	0.519321i	$0.826185\pi$
$4$	2.66333	1.33167
$5$	−3.06159	−1.36918	−0.684591	−	0.728927i	$-0.740019\pi$
$5$	−3.06159	−1.36918	−0.684591	+	0.728927i	$0.740019\pi$
$6$	−6.39280	−2.60985
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.43245	0.506448
$9$	5.76366	1.92122
$10$	−6.61142	−2.09071
$11$	−5.60419	−1.68973	−0.844863	−	0.534982i	$-0.820318\pi$
$11$	−5.60419	−1.68973	−0.844863	+	0.534982i	$0.820318\pi$
$12$	−7.88439	−2.27603
$13$	−2.28475	−0.633676	−0.316838	−	0.948480i	$-0.602621\pi$
$13$	−2.28475	−0.633676	−0.316838	+	0.948480i	$0.602621\pi$
$14$	−2.15948	−0.577144
$15$	9.06336	2.34015
$16$	−2.23332	−0.558331
$17$	4.43968	1.07678	0.538390	−	0.842696i	$-0.319033\pi$
$17$	4.43968	1.07678	0.538390	+	0.842696i	$0.319033\pi$
$18$	12.4465	2.93367
$19$	4.31440	0.989792	0.494896	−	0.868952i	$-0.335206\pi$
$19$	4.31440	0.989792	0.494896	+	0.868952i	$0.335206\pi$
$20$	−8.15402	−1.82329
$21$	2.96035	0.646001
$22$	−12.1021	−2.58018
$23$	−2.19458	−0.457601	−0.228801	−	0.973473i	$-0.573480\pi$
$23$	−2.19458	−0.457601	−0.228801	+	0.973473i	$0.573480\pi$
$24$	−4.24055	−0.865599
$25$	4.37331	0.874661
$26$	−4.93387	−0.967611
$27$	−8.18141	−1.57451
$28$	−2.66333	−0.503323
$29$	−0.786168	−0.145988	−0.0729939	−	0.997332i	$-0.523255\pi$
$29$	−0.786168	−0.145988	−0.0729939	+	0.997332i	$0.523255\pi$
$30$	19.5721	3.57336
$31$	−6.29928	−1.13138	−0.565692	−	0.824617i	$-0.691391\pi$
$31$	−6.29928	−1.13138	−0.565692	+	0.824617i	$0.691391\pi$
$32$	−7.68771	−1.35901
$33$	16.5904	2.88801
$34$	9.58738	1.64422
$35$	3.06159	0.517502
$36$	15.3506	2.55843
$37$	7.79584	1.28163	0.640814	−	0.767696i	$-0.278597\pi$
$37$	7.79584	1.28163	0.640814	+	0.767696i	$0.278597\pi$
$38$	9.31684	1.51139
$39$	6.76366	1.08305
$40$	−4.38557	−0.693420
$41$	−8.60006	−1.34310	−0.671552	−	0.740958i	$-0.734372\pi$
$41$	−8.60006	−1.34310	−0.671552	+	0.740958i	$0.734372\pi$
$42$	6.39280	0.986430
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−14.9258	−2.25015
$45$	−17.6460	−2.63050
$46$	−4.73914	−0.698748
$47$	10.1079	1.47439	0.737194	−	0.675681i	$-0.236150\pi$
$47$	10.1079	1.47439	0.737194	+	0.675681i	$0.236150\pi$
$48$	6.61142	0.954276
$49$	1.00000	0.142857
$50$	9.44405	1.33559
$51$	−13.1430	−1.84039
$52$	−6.08506	−0.843845
$53$	−4.68771	−0.643906	−0.321953	−	0.946756i	$-0.604339\pi$
$53$	−4.68771	−0.643906	−0.321953	+	0.946756i	$0.604339\pi$
$54$	−17.6676	−2.40425
$55$	17.1577	2.31354
$56$	−1.43245	−0.191419
$57$	−12.7721	−1.69171
$58$	−1.69771	−0.222920
$59$	−12.9231	−1.68245	−0.841225	−	0.540686i	$-0.818165\pi$
$59$	−12.9231	−1.68245	−0.841225	+	0.540686i	$0.818165\pi$
$60$	24.1387	3.11630
$61$	4.03664	0.516839	0.258419	−	0.966033i	$-0.416798\pi$
$61$	4.03664	0.516839	0.258419	+	0.966033i	$0.416798\pi$
$62$	−13.6031	−1.72760
$63$	−5.76366	−0.726153
$64$	−12.1348	−1.51685
$65$	6.99497	0.867619
$66$	35.8265	4.40993
$67$	−5.65058	−0.690329	−0.345164	−	0.938542i	$-0.612177\pi$
$67$	−5.65058	−0.690329	−0.345164	+	0.938542i	$0.612177\pi$
$68$	11.8243	1.43391
$69$	6.49672	0.782113
$70$	6.61142	0.790216
$71$	−2.91682	−0.346162	−0.173081	−	0.984908i	$-0.555372\pi$
$71$	−2.91682	−0.346162	−0.173081	+	0.984908i	$0.555372\pi$
$72$	8.25616	0.972998
$73$	12.3600	1.44662	0.723312	−	0.690522i	$-0.242619\pi$
$73$	12.3600	1.44662	0.723312	+	0.690522i	$0.242619\pi$
$74$	16.8349	1.95702
$75$	−12.9465	−1.49493
$76$	11.4907	1.31807
$77$	5.60419	0.638657
$78$	14.6060	1.65380
$79$	−5.08698	−0.572330	−0.286165	−	0.958180i	$-0.592381\pi$
$79$	−5.08698	−0.572330	−0.286165	+	0.958180i	$0.592381\pi$
$80$	6.83751	0.764457
$81$	6.92883	0.769870
$82$	−18.5716	−2.05089
$83$	−13.2997	−1.45983	−0.729916	−	0.683537i	$-0.760441\pi$
$83$	−13.2997	−1.45983	−0.729916	+	0.683537i	$0.760441\pi$
$84$	7.88439	0.860258
$85$	−13.5925	−1.47431
$86$	−2.15948	−0.232862
$87$	2.32733	0.249516
$88$	−8.02772	−0.855758
$89$	−12.1067	−1.28330	−0.641651	−	0.766996i	$-0.721750\pi$
$89$	−12.1067	−1.28330	−0.641651	+	0.766996i	$0.721750\pi$
$90$	−38.1060	−4.01672
$91$	2.28475	0.239507
$92$	−5.84489	−0.609372
$93$	18.6481	1.93371
$94$	21.8278	2.25136
$95$	−13.2089	−1.35521
$96$	22.7583	2.32276
$97$	−13.7366	−1.39474	−0.697371	−	0.716711i	$-0.745647\pi$
$97$	−13.7366	−1.39474	−0.697371	+	0.716711i	$0.745647\pi$
$98$	2.15948	0.218140
$99$	−32.3007	−3.24634
$100$	11.6476	1.16476
$101$	5.91859	0.588922	0.294461	−	0.955664i	$-0.404860\pi$
$101$	5.91859	0.588922	0.294461	+	0.955664i	$0.404860\pi$
$102$	−28.3820	−2.81023
$103$	−4.77879	−0.470868	−0.235434	−	0.971890i	$-0.575651\pi$
$103$	−4.77879	−0.470868	−0.235434	+	0.971890i	$0.575651\pi$
$104$	−3.27280	−0.320924
$105$	−9.06336	−0.884493
$106$	−10.1230	−0.983232
$107$	3.38490	0.327231	0.163615	−	0.986524i	$-0.447684\pi$
$107$	3.38490	0.327231	0.163615	+	0.986524i	$0.447684\pi$
$108$	−21.7898	−2.09673
$109$	−10.3878	−0.994974	−0.497487	−	0.867471i	$-0.665744\pi$
$109$	−10.3878	−0.994974	−0.497487	+	0.867471i	$0.665744\pi$
$110$	37.0516	3.53273
$111$	−23.0784	−2.19050
$112$	2.23332	0.211029
$113$	12.5575	1.18131	0.590657	−	0.806922i	$-0.298868\pi$
$113$	12.5575	1.18131	0.590657	+	0.806922i	$0.298868\pi$
$114$	−27.5811	−2.58321
$115$	6.71889	0.626540
$116$	−2.09383	−0.194407
$117$	−13.1685	−1.21743
$118$	−27.9072	−2.56907
$119$	−4.43968	−0.406985
$120$	12.9828	1.18516
$121$	20.4069	1.85518
$122$	8.71702	0.789202
$123$	25.4592	2.29558
$124$	−16.7771	−1.50663
$125$	1.91867	0.171611
$126$	−12.4465	−1.10882
$127$	14.8780	1.32021	0.660106	−	0.751172i	$-0.270511\pi$
$127$	14.8780	1.32021	0.660106	+	0.751172i	$0.270511\pi$
$128$	−10.8293	−0.957185
$129$	2.96035	0.260644
$130$	15.1055	1.32484
$131$	−12.6806	−1.10791	−0.553953	−	0.832548i	$-0.686881\pi$
$131$	−12.6806	−1.10791	−0.553953	+	0.832548i	$0.686881\pi$
$132$	44.1856	3.84587
$133$	−4.31440	−0.374106
$134$	−12.2023	−1.05412
$135$	25.0481	2.15580
$136$	6.35962	0.545333
$137$	−1.90599	−0.162840	−0.0814199	−	0.996680i	$-0.525945\pi$
$137$	−1.90599	−0.162840	−0.0814199	+	0.996680i	$0.525945\pi$
$138$	14.0295	1.19427
$139$	13.6140	1.15472	0.577361	−	0.816489i	$-0.304082\pi$
$139$	13.6140	1.15472	0.577361	+	0.816489i	$0.304082\pi$
$140$	8.15402	0.689141
$141$	−29.9229	−2.51996
$142$	−6.29879	−0.528583
$143$	12.8042	1.07074
$144$	−12.8721	−1.07268
$145$	2.40692	0.199884
$146$	26.6910	2.20896
$147$	−2.96035	−0.244165
$148$	20.7629	1.70670
$149$	9.97277	0.817001	0.408500	−	0.912758i	$-0.366052\pi$
$149$	9.97277	0.817001	0.408500	+	0.912758i	$0.366052\pi$
$150$	−27.9577	−2.28273
$151$	−1.38750	−0.112913	−0.0564564	−	0.998405i	$-0.517980\pi$
$151$	−1.38750	−0.112913	−0.0564564	+	0.998405i	$0.517980\pi$
$152$	6.18017	0.501278
$153$	25.5888	2.06873
$154$	12.1021	0.975216
$155$	19.2858	1.54907
$156$	18.0139	1.44227
$157$	2.62142	0.209212	0.104606	−	0.994514i	$-0.466642\pi$
$157$	2.62142	0.209212	0.104606	+	0.994514i	$0.466642\pi$
$158$	−10.9852	−0.873936
$159$	13.8773	1.10054
$160$	23.5366	1.86073
$161$	2.19458	0.172957
$162$	14.9626	1.17558
$163$	−21.7677	−1.70498	−0.852489	−	0.522745i	$-0.824908\pi$
$163$	−21.7677	−1.70498	−0.852489	+	0.522745i	$0.824908\pi$
$164$	−22.9048	−1.78857
$165$	−50.7928	−3.95421
$166$	−28.7204	−2.22913
$167$	11.9396	0.923916	0.461958	−	0.886902i	$-0.347147\pi$
$167$	11.9396	0.923916	0.461958	+	0.886902i	$0.347147\pi$
$168$	4.24055	0.327166
$169$	−7.77991	−0.598454
$170$	−29.3526	−2.25124
$171$	24.8668	1.90161
$172$	−2.66333	−0.203077
$173$	−12.6992	−0.965506	−0.482753	−	0.875757i	$-0.660363\pi$
$173$	−12.6992	−0.965506	−0.482753	+	0.875757i	$0.660363\pi$
$174$	5.02582	0.381006
$175$	−4.37331	−0.330591
$176$	12.5160	0.943427
$177$	38.2570	2.87557
$178$	−26.1440	−1.95958
$179$	−3.35423	−0.250707	−0.125354	−	0.992112i	$-0.540007\pi$
$179$	−3.35423	−0.250707	−0.125354	+	0.992112i	$0.540007\pi$
$180$	−46.9970	−3.50295
$181$	7.31919	0.544031	0.272016	−	0.962293i	$-0.412310\pi$
$181$	7.31919	0.544031	0.272016	+	0.962293i	$0.412310\pi$
$182$	4.93387	0.365723
$183$	−11.9499	−0.883359
$184$	−3.14363	−0.231751
$185$	−23.8676	−1.75478
$186$	40.2700	2.95274
$187$	−24.8808	−1.81946
$188$	26.9207	1.96339
$189$	8.18141	0.595110
$190$	−28.5243	−2.06937
$191$	17.8052	1.28834	0.644168	−	0.764884i	$-0.277204\pi$
$191$	17.8052	1.28834	0.644168	+	0.764884i	$0.277204\pi$
$192$	35.9231	2.59253
$193$	16.1958	1.16580	0.582899	−	0.812545i	$-0.301918\pi$
$193$	16.1958	1.16580	0.582899	+	0.812545i	$0.301918\pi$
$194$	−29.6639	−2.12974
$195$	−20.7075	−1.48290
$196$	2.66333	0.190238
$197$	26.0132	1.85336	0.926681	−	0.375849i	$-0.122649\pi$
$197$	26.0132	1.85336	0.926681	+	0.375849i	$0.122649\pi$
$198$	−69.7525	−4.95709
$199$	6.08108	0.431076	0.215538	−	0.976495i	$-0.430849\pi$
$199$	6.08108	0.431076	0.215538	+	0.976495i	$0.430849\pi$
$200$	6.26455	0.442970
$201$	16.7277	1.17988
$202$	12.7811	0.899272
$203$	0.786168	0.0551782
$204$	−35.0042	−2.45078
$205$	26.3298	1.83895
$206$	−10.3197	−0.719006
$207$	−12.6488	−0.879153
$208$	5.10259	0.353801
$209$	−24.1787	−1.67248
$210$	−19.5721	−1.35060
$211$	−0.784548	−0.0540105	−0.0270053	−	0.999635i	$-0.508597\pi$
$211$	−0.784548	−0.0540105	−0.0270053	+	0.999635i	$0.508597\pi$
$212$	−12.4849	−0.857468
$213$	8.63479	0.591646
$214$	7.30962	0.499675
$215$	3.06159	0.208798
$216$	−11.7195	−0.797409
$217$	6.29928	0.427623
$218$	−22.4323	−1.51930
$219$	−36.5898	−2.47251
$220$	45.6967	3.08087
$221$	−10.1436	−0.682330
$222$	−49.8372	−3.34486
$223$	8.84124	0.592054	0.296027	−	0.955180i	$-0.404338\pi$
$223$	8.84124	0.592054	0.296027	+	0.955180i	$0.404338\pi$
$224$	7.68771	0.513657
$225$	25.2063	1.68042
$226$	27.1177	1.80384
$227$	−18.2674	−1.21245	−0.606226	−	0.795292i	$-0.707317\pi$
$227$	−18.2674	−1.21245	−0.606226	+	0.795292i	$0.707317\pi$
$228$	−34.0164	−2.25279
$229$	6.14176	0.405859	0.202929	−	0.979193i	$-0.434954\pi$
$229$	6.14176	0.405859	0.202929	+	0.979193i	$0.434954\pi$
$230$	14.5093	0.956713
$231$	−16.5904	−1.09157
$232$	−1.12615	−0.0739352
$233$	−2.07569	−0.135983	−0.0679915	−	0.997686i	$-0.521659\pi$
$233$	−2.07569	−0.135983	−0.0679915	+	0.997686i	$0.521659\pi$
$234$	−28.4371	−1.85899
$235$	−30.9462	−2.01871
$236$	−34.4186	−2.24046
$237$	15.0592	0.978203
$238$	−9.58738	−0.621457
$239$	−20.5572	−1.32973	−0.664866	−	0.746963i	$-0.731511\pi$
$239$	−20.5572	−1.32973	−0.664866	+	0.746963i	$0.731511\pi$
$240$	−20.2414	−1.30658
$241$	−7.99527	−0.515021	−0.257510	−	0.966276i	$-0.582902\pi$
$241$	−7.99527	−0.515021	−0.257510	+	0.966276i	$0.582902\pi$
$242$	44.0683	2.83282
$243$	4.03247	0.258683
$244$	10.7509	0.688257
$245$	−3.06159	−0.195598
$246$	54.9785	3.50530
$247$	−9.85734	−0.627208
$248$	−9.02340	−0.572987
$249$	39.3717	2.49508
$250$	4.14333	0.262047
$251$	3.00554	0.189708	0.0948541	−	0.995491i	$-0.469762\pi$
$251$	3.00554	0.189708	0.0948541	+	0.995491i	$0.469762\pi$
$252$	−15.3506	−0.966994
$253$	12.2988	0.773221
$254$	32.1287	2.01594
$255$	40.2384	2.51983
$256$	0.883907	0.0552442
$257$	−13.3462	−0.832512	−0.416256	−	0.909247i	$-0.636658\pi$
$257$	−13.3462	−0.832512	−0.416256	+	0.909247i	$0.636658\pi$
$258$	6.39280	0.397998
$259$	−7.79584	−0.484410
$260$	18.6299	1.15538
$261$	−4.53121	−0.280475
$262$	−27.3834	−1.69175
$263$	−17.8843	−1.10279	−0.551397	−	0.834243i	$-0.685905\pi$
$263$	−17.8843	−1.10279	−0.551397	+	0.834243i	$0.685905\pi$
$264$	23.7649	1.46263
$265$	14.3518	0.881625
$266$	−9.31684	−0.571252
$267$	35.8399	2.19337
$268$	−15.0494	−0.919287
$269$	−16.2216	−0.989048	−0.494524	−	0.869164i	$-0.664658\pi$
$269$	−16.2216	−0.989048	−0.494524	+	0.869164i	$0.664658\pi$
$270$	54.0907	3.29186
$271$	1.25565	0.0762752	0.0381376	−	0.999272i	$-0.487857\pi$
$271$	1.25565	0.0762752	0.0381376	+	0.999272i	$0.487857\pi$
$272$	−9.91524	−0.601200
$273$	−6.76366	−0.409356
$274$	−4.11594	−0.248653
$275$	−24.5088	−1.47794
$276$	17.3029	1.04151
$277$	9.16483	0.550661	0.275331	−	0.961350i	$-0.411213\pi$
$277$	9.16483	0.550661	0.275331	+	0.961350i	$0.411213\pi$
$278$	29.3990	1.76324
$279$	−36.3069	−2.17364
$280$	4.38557	0.262088
$281$	−10.7641	−0.642133	−0.321067	−	0.947057i	$-0.604041\pi$
$281$	−10.7641	−0.642133	−0.321067	+	0.947057i	$0.604041\pi$
$282$	−64.6178	−3.84793
$283$	28.1255	1.67189	0.835944	−	0.548815i	$-0.184921\pi$
$283$	28.1255	1.67189	0.835944	+	0.548815i	$0.184921\pi$
$284$	−7.76845	−0.460973
$285$	39.1030	2.31626
$286$	27.6503	1.63500
$287$	8.60006	0.507646
$288$	−44.3094	−2.61095
$289$	2.71076	0.159456
$290$	5.19769	0.305219
$291$	40.6652	2.38383
$292$	32.9187	1.92642
$293$	−3.54899	−0.207334	−0.103667	−	0.994612i	$-0.533058\pi$
$293$	−3.54899	−0.207334	−0.103667	+	0.994612i	$0.533058\pi$
$294$	−6.39280	−0.372836
$295$	39.5653	2.30358
$296$	11.1672	0.649078
$297$	45.8502	2.66050
$298$	21.5359	1.24754
$299$	5.01407	0.289971
$300$	−34.4809	−1.99075
$301$	1.00000	0.0576390
$302$	−2.99626	−0.172416
$303$	−17.5211	−1.00656
$304$	−9.63546	−0.552631
$305$	−12.3585	−0.707647
$306$	55.2584	3.15891
$307$	3.16436	0.180600	0.0902998	−	0.995915i	$-0.471217\pi$
$307$	3.16436	0.180600	0.0902998	+	0.995915i	$0.471217\pi$
$308$	14.9258	0.850478
$309$	14.1469	0.804788
$310$	41.6472	2.36540
$311$	−29.6719	−1.68254	−0.841270	−	0.540615i	$-0.818192\pi$
$311$	−29.6719	−1.68254	−0.841270	+	0.540615i	$0.818192\pi$
$312$	9.68861	0.548510
$313$	−14.3347	−0.810244	−0.405122	−	0.914263i	$-0.632771\pi$
$313$	−14.3347	−0.810244	−0.405122	+	0.914263i	$0.632771\pi$
$314$	5.66089	0.319463
$315$	17.6460	0.994237
$316$	−13.5483	−0.762153
$317$	19.9503	1.12052	0.560260	−	0.828317i	$-0.310701\pi$
$317$	19.9503	1.12052	0.560260	+	0.828317i	$0.310701\pi$
$318$	29.9676	1.68050
$319$	4.40584	0.246679
$320$	37.1516	2.07684
$321$	−10.0205	−0.559289
$322$	4.73914	0.264102
$323$	19.1546	1.06579
$324$	18.4538	1.02521
$325$	−9.99192	−0.554252
$326$	−47.0068	−2.60347
$327$	30.7516	1.70057
$328$	−12.3192	−0.680212
$329$	−10.1079	−0.557266
$330$	−109.686	−6.03800
$331$	15.4377	0.848532	0.424266	−	0.905538i	$-0.360532\pi$
$331$	15.4377	0.848532	0.424266	+	0.905538i	$0.360532\pi$
$332$	−35.4215	−1.94401
$333$	44.9326	2.46229
$334$	25.7833	1.41080
$335$	17.2997	0.945186
$336$	−6.61142	−0.360682
$337$	−2.66638	−0.145247	−0.0726234	−	0.997359i	$-0.523137\pi$
$337$	−2.66638	−0.145247	−0.0726234	+	0.997359i	$0.523137\pi$
$338$	−16.8005	−0.913827
$339$	−37.1747	−2.01905
$340$	−36.2012	−1.96329
$341$	35.3023	1.91173
$342$	53.6992	2.90372
$343$	−1.00000	−0.0539949
$344$	−1.43245	−0.0772326
$345$	−19.8903	−1.07086
$346$	−27.4237	−1.47431
$347$	−31.6536	−1.69926	−0.849628	−	0.527382i	$-0.823174\pi$
$347$	−31.6536	−1.69926	−0.849628	+	0.527382i	$0.823174\pi$
$348$	6.19846	0.332272
$349$	−0.490839	−0.0262740	−0.0131370	−	0.999914i	$-0.504182\pi$
$349$	−0.490839	−0.0262740	−0.0131370	+	0.999914i	$0.504182\pi$
$350$	−9.44405	−0.504806
$351$	18.6925	0.997732
$352$	43.0834	2.29635
$353$	0.848146	0.0451422	0.0225711	−	0.999745i	$-0.492815\pi$
$353$	0.848146	0.0451422	0.0225711	+	0.999745i	$0.492815\pi$
$354$	82.6150	4.39094
$355$	8.93008	0.473960
$356$	−32.2441	−1.70893
$357$	13.1430	0.695601
$358$	−7.24338	−0.382825
$359$	−7.18360	−0.379136	−0.189568	−	0.981868i	$-0.560709\pi$
$359$	−7.18360	−0.379136	−0.189568	+	0.981868i	$0.560709\pi$
$360$	−25.2770	−1.33221
$361$	−0.385934	−0.0203123
$362$	15.8056	0.830724
$363$	−60.4116	−3.17079
$364$	6.08506	0.318944
$365$	−37.8411	−1.98069
$366$	−25.8054	−1.34887
$367$	25.6500	1.33892	0.669459	−	0.742849i	$-0.266526\pi$
$367$	25.6500	1.33892	0.669459	+	0.742849i	$0.266526\pi$
$368$	4.90120	0.255493
$369$	−49.5679	−2.58040
$370$	−51.5416	−2.67952
$371$	4.68771	0.243374
$372$	49.6660	2.57506
$373$	−27.2258	−1.40970	−0.704850	−	0.709356i	$-0.748986\pi$
$373$	−27.2258	−1.40970	−0.704850	+	0.709356i	$0.748986\pi$
$374$	−53.7295	−2.77829
$375$	−5.67995	−0.293311
$376$	14.4791	0.746701
$377$	1.79620	0.0925090
$378$	17.6676	0.908721
$379$	−1.56025	−0.0801448	−0.0400724	−	0.999197i	$-0.512759\pi$
$379$	−1.56025	−0.0801448	−0.0400724	+	0.999197i	$0.512759\pi$
$380$	−35.1797	−1.80468
$381$	−44.0442	−2.25645
$382$	38.4498	1.96726
$383$	−1.28803	−0.0658155	−0.0329077	−	0.999458i	$-0.510477\pi$
$383$	−1.28803	−0.0658155	−0.0329077	+	0.999458i	$0.510477\pi$
$384$	32.0585	1.63598
$385$	−17.1577	−0.874438
$386$	34.9744	1.78015
$387$	−5.76366	−0.292984
$388$	−36.5852	−1.85733
$389$	−5.25263	−0.266319	−0.133159	−	0.991095i	$-0.542512\pi$
$389$	−5.25263	−0.266319	−0.133159	+	0.991095i	$0.542512\pi$
$390$	−44.7174	−2.26435
$391$	−9.74323	−0.492736
$392$	1.43245	0.0723497
$393$	37.5389	1.89359
$394$	56.1748	2.83005
$395$	15.5742	0.783625
$396$	−86.0274	−4.32304
$397$	−29.9762	−1.50446	−0.752230	−	0.658900i	$-0.771022\pi$
$397$	−29.9762	−1.50446	−0.752230	+	0.658900i	$0.771022\pi$
$398$	13.1319	0.658245
$399$	12.7721	0.639406
$400$	−9.76701	−0.488351
$401$	−19.1682	−0.957215	−0.478608	−	0.878029i	$-0.658858\pi$
$401$	−19.1682	−0.957215	−0.478608	+	0.878029i	$0.658858\pi$
$402$	36.1230	1.80165
$403$	14.3923	0.716931
$404$	15.7632	0.784247
$405$	−21.2132	−1.05409
$406$	1.69771	0.0842560
$407$	−43.6894	−2.16560
$408$	−18.8267	−0.932060
$409$	16.1885	0.800468	0.400234	−	0.916413i	$-0.368929\pi$
$409$	16.1885	0.800468	0.400234	+	0.916413i	$0.368929\pi$
$410$	56.8586	2.80805
$411$	5.64240	0.278319
$412$	−12.7275	−0.627039
$413$	12.9231	0.635906
$414$	−27.3148	−1.34245
$415$	40.7182	1.99878
$416$	17.5645	0.861171
$417$	−40.3021	−1.97360
$418$	−52.2134	−2.55384
$419$	24.1354	1.17909	0.589547	−	0.807734i	$-0.299306\pi$
$419$	24.1354	1.17909	0.589547	+	0.807734i	$0.299306\pi$
$420$	−24.1387	−1.17785
$421$	−12.2771	−0.598351	−0.299175	−	0.954198i	$-0.596712\pi$
$421$	−12.2771	−0.598351	−0.299175	+	0.954198i	$0.596712\pi$
$422$	−1.69421	−0.0824730
$423$	58.2585	2.83263
$424$	−6.71491	−0.326105
$425$	19.4161	0.941818
$426$	18.6466	0.903432
$427$	−4.03664	−0.195347
$428$	9.01512	0.435762
$429$	−37.9049	−1.83006
$430$	6.61142	0.318831
$431$	−23.1061	−1.11298	−0.556492	−	0.830853i	$-0.687853\pi$
$431$	−23.1061	−1.11298	−0.556492	+	0.830853i	$0.687853\pi$
$432$	18.2717	0.879099
$433$	1.04427	0.0501842	0.0250921	−	0.999685i	$-0.492012\pi$
$433$	1.04427	0.0501842	0.0250921	+	0.999685i	$0.492012\pi$
$434$	13.6031	0.652971
$435$	−7.12533	−0.341633
$436$	−27.6663	−1.32497
$437$	−9.46829	−0.452930
$438$	−79.0147	−3.77547
$439$	−20.1886	−0.963551	−0.481776	−	0.876295i	$-0.660008\pi$
$439$	−20.1886	−0.963551	−0.481776	+	0.876295i	$0.660008\pi$
$440$	24.5776	1.17169
$441$	5.76366	0.274460
$442$	−21.9048	−1.04190
$443$	22.5847	1.07303	0.536516	−	0.843890i	$-0.319740\pi$
$443$	22.5847	1.07303	0.536516	+	0.843890i	$0.319740\pi$
$444$	−61.4655	−2.91702
$445$	37.0656	1.75708
$446$	19.0924	0.904054
$447$	−29.5229	−1.39638
$448$	12.1348	0.573314
$449$	11.9241	0.562732	0.281366	−	0.959601i	$-0.409213\pi$
$449$	11.9241	0.562732	0.281366	+	0.959601i	$0.409213\pi$
$450$	54.4323	2.56596
$451$	48.1964	2.26948
$452$	33.4449	1.57312
$453$	4.10747	0.192986
$454$	−39.4481	−1.85139
$455$	−6.99497	−0.327929
$456$	−18.2955	−0.856763
$457$	−18.6028	−0.870204	−0.435102	−	0.900381i	$-0.643288\pi$
$457$	−18.6028	−0.870204	−0.435102	+	0.900381i	$0.643288\pi$
$458$	13.2630	0.619738
$459$	−36.3228	−1.69540
$460$	17.8946	0.834342
$461$	7.64055	0.355856	0.177928	−	0.984044i	$-0.443061\pi$
$461$	7.64055	0.355856	0.177928	+	0.984044i	$0.443061\pi$
$462$	−35.8265	−1.66680
$463$	−24.8632	−1.15549	−0.577744	−	0.816218i	$-0.696067\pi$
$463$	−24.8632	−1.15549	−0.577744	+	0.816218i	$0.696067\pi$
$464$	1.75577	0.0815095
$465$	−57.0926	−2.64761
$466$	−4.48240	−0.207643
$467$	−12.4969	−0.578289	−0.289145	−	0.957285i	$-0.593371\pi$
$467$	−12.4969	−0.578289	−0.289145	+	0.957285i	$0.593371\pi$
$468$	−35.0722	−1.62121
$469$	5.65058	0.260920
$470$	−66.8275	−3.08252
$471$	−7.76032	−0.357577
$472$	−18.5118	−0.852073
$473$	5.60419	0.257681
$474$	32.5201	1.49370
$475$	18.8682	0.865733
$476$	−11.8243	−0.541968
$477$	−27.0184	−1.23709
$478$	−44.3927	−2.03047
$479$	23.3352	1.06621	0.533107	−	0.846048i	$-0.321024\pi$
$479$	23.3352	1.06621	0.533107	+	0.846048i	$0.321024\pi$
$480$	−69.6765	−3.18028
$481$	−17.8116	−0.812137
$482$	−17.2656	−0.786426
$483$	−6.49672	−0.295611
$484$	54.3505	2.47048
$485$	42.0558	1.90966
$486$	8.70802	0.395004
$487$	1.06565	0.0482891	0.0241446	−	0.999708i	$-0.492314\pi$
$487$	1.06565	0.0482891	0.0241446	+	0.999708i	$0.492314\pi$
$488$	5.78229	0.261752
$489$	64.4400	2.91408
$490$	−6.61142	−0.298673
$491$	20.7386	0.935920	0.467960	−	0.883750i	$-0.344989\pi$
$491$	20.7386	0.935920	0.467960	+	0.883750i	$0.344989\pi$
$492$	67.8063	3.05694
$493$	−3.49034	−0.157197
$494$	−21.2867	−0.957733
$495$	98.8912	4.44483
$496$	14.0683	0.631687
$497$	2.91682	0.130837
$498$	85.0223	3.80994
$499$	28.4275	1.27259	0.636296	−	0.771445i	$-0.280466\pi$
$499$	28.4275	1.27259	0.636296	+	0.771445i	$0.280466\pi$
$500$	5.11007	0.228529
$501$	−35.3454	−1.57912
$502$	6.49039	0.289680
$503$	−0.0580937	−0.00259027	−0.00129513	−	0.999999i	$-0.500412\pi$
$503$	−0.0580937	−0.00259027	−0.00129513	+	0.999999i	$0.500412\pi$
$504$	−8.25616	−0.367759
$505$	−18.1203	−0.806342
$506$	26.5590	1.18069
$507$	23.0312	1.02285
$508$	39.6252	1.75808
$509$	4.23923	0.187900	0.0939502	−	0.995577i	$-0.470051\pi$
$509$	4.23923	0.187900	0.0939502	+	0.995577i	$0.470051\pi$
$510$	86.8939	3.84773
$511$	−12.3600	−0.546772
$512$	23.5674	1.04154
$513$	−35.2979	−1.55844
$514$	−28.8208	−1.27123
$515$	14.6307	0.644704
$516$	7.88439	0.347091
$517$	−56.6466	−2.49131
$518$	−16.8349	−0.739684
$519$	37.5942	1.65020
$520$	10.0199	0.439404
$521$	−13.4733	−0.590277	−0.295139	−	0.955454i	$-0.595366\pi$
$521$	−13.4733	−0.590277	−0.295139	+	0.955454i	$0.595366\pi$
$522$	−9.78503	−0.428279
$523$	−8.72990	−0.381732	−0.190866	−	0.981616i	$-0.561130\pi$
$523$	−8.72990	−0.381732	−0.190866	+	0.981616i	$0.561130\pi$
$524$	−33.7726	−1.47536
$525$	12.9465	0.565032
$526$	−38.6207	−1.68394
$527$	−27.9668	−1.21825
$528$	−37.0516	−1.61247
$529$	−18.1838	−0.790601
$530$	30.9924	1.34622
$531$	−74.4846	−3.23236
$532$	−11.4907	−0.498185
$533$	19.6490	0.851093
$534$	77.3954	3.34923
$535$	−10.3632	−0.448039
$536$	−8.09418	−0.349615
$537$	9.92970	0.428498
$538$	−35.0301	−1.51026
$539$	−5.60419	−0.241390
$540$	66.7114	2.87080
$541$	−26.1555	−1.12451	−0.562256	−	0.826963i	$-0.690067\pi$
$541$	−26.1555	−1.12451	−0.562256	+	0.826963i	$0.690067\pi$
$542$	2.71154	0.116471
$543$	−21.6674	−0.929835
$544$	−34.1310	−1.46335
$545$	31.8032	1.36230
$546$	−14.6060	−0.625078
$547$	21.2563	0.908855	0.454427	−	0.890784i	$-0.349844\pi$
$547$	21.2563	0.908855	0.454427	+	0.890784i	$0.349844\pi$
$548$	−5.07629	−0.216848
$549$	23.2658	0.992962
$550$	−52.9262	−2.25678
$551$	−3.39185	−0.144497
$552$	9.30623	0.396099
$553$	5.08698	0.216320
$554$	19.7912	0.840849
$555$	70.6565	2.99920
$556$	36.2585	1.53770
$557$	−19.9294	−0.844436	−0.422218	−	0.906494i	$-0.638748\pi$
$557$	−19.9294	−0.844436	−0.422218	+	0.906494i	$0.638748\pi$
$558$	−78.4039	−3.31910
$559$	2.28475	0.0966347
$560$	−6.83751	−0.288938
$561$	73.6559	3.10975
$562$	−23.2448	−0.980524
$563$	19.6576	0.828469	0.414235	−	0.910170i	$-0.364049\pi$
$563$	19.6576	0.828469	0.414235	+	0.910170i	$0.364049\pi$
$564$	−79.6946	−3.35575
$565$	−38.4460	−1.61744
$566$	60.7363	2.55294
$567$	−6.92883	−0.290984
$568$	−4.17819	−0.175313
$569$	−31.6522	−1.32693	−0.663464	−	0.748208i	$-0.730915\pi$
$569$	−31.6522	−1.32693	−0.663464	+	0.748208i	$0.730915\pi$
$570$	84.4419	3.53688
$571$	−8.84571	−0.370182	−0.185091	−	0.982721i	$-0.559258\pi$
$571$	−8.84571	−0.370182	−0.185091	+	0.982721i	$0.559258\pi$
$572$	34.1018	1.42587
$573$	−52.7095	−2.20197
$574$	18.5716	0.775164
$575$	−9.59756	−0.400246
$576$	−69.9407	−2.91420
$577$	−41.7012	−1.73604	−0.868021	−	0.496527i	$-0.834608\pi$
$577$	−41.7012	−1.73604	−0.868021	+	0.496527i	$0.834608\pi$
$578$	5.85381	0.243486
$579$	−47.9452	−1.99253
$580$	6.41043	0.266179
$581$	13.2997	0.551764
$582$	87.8154	3.64007
$583$	26.2708	1.08803
$584$	17.7050	0.732639
$585$	40.3166	1.66689
$586$	−7.66396	−0.316595
$587$	16.4131	0.677439	0.338720	−	0.940887i	$-0.390006\pi$
$587$	16.4131	0.677439	0.338720	+	0.940887i	$0.390006\pi$
$588$	−7.88439	−0.325147
$589$	−27.1776	−1.11983
$590$	85.4403	3.51752
$591$	−77.0081	−3.16769
$592$	−17.4106	−0.715573
$593$	−9.98650	−0.410096	−0.205048	−	0.978752i	$-0.565735\pi$
$593$	−9.98650	−0.410096	−0.205048	+	0.978752i	$0.565735\pi$
$594$	99.0123	4.06252
$595$	13.5925	0.557237
$596$	26.5608	1.08797
$597$	−18.0021	−0.736777
$598$	10.8278	0.442780
$599$	24.0664	0.983327	0.491663	−	0.870785i	$-0.336389\pi$
$599$	24.0664	0.983327	0.491663	+	0.870785i	$0.336389\pi$
$600$	−18.5452	−0.757106
$601$	−16.7024	−0.681303	−0.340652	−	0.940190i	$-0.610648\pi$
$601$	−16.7024	−0.681303	−0.340652	+	0.940190i	$0.610648\pi$
$602$	2.15948	0.0880136
$603$	−32.5681	−1.32627
$604$	−3.69536	−0.150362
$605$	−62.4776	−2.54007
$606$	−37.8364	−1.53700
$607$	34.4595	1.39867	0.699335	−	0.714794i	$-0.253480\pi$
$607$	34.4595	1.39867	0.699335	+	0.714794i	$0.253480\pi$
$608$	−33.1679	−1.34513
$609$	−2.32733	−0.0943083
$610$	−26.6879	−1.08056
$611$	−23.0940	−0.934285
$612$	68.1515	2.75486
$613$	−12.9422	−0.522731	−0.261366	−	0.965240i	$-0.584173\pi$
$613$	−12.9422	−0.522731	−0.261366	+	0.965240i	$0.584173\pi$
$614$	6.83335	0.275772
$615$	−77.9455	−3.14306
$616$	8.02772	0.323446
$617$	−48.5569	−1.95483	−0.977415	−	0.211331i	$-0.932220\pi$
$617$	−48.5569	−1.95483	−0.977415	+	0.211331i	$0.932220\pi$
$618$	30.5498	1.22889
$619$	−14.7697	−0.593646	−0.296823	−	0.954933i	$-0.595927\pi$
$619$	−14.7697	−0.593646	−0.296823	+	0.954933i	$0.595927\pi$
$620$	51.3644	2.06285
$621$	17.9547	0.720499
$622$	−64.0758	−2.56920
$623$	12.1067	0.485043
$624$	−15.1055	−0.604702
$625$	−27.7407	−1.10963
$626$	−30.9554	−1.23723
$627$	71.5775	2.85853
$628$	6.98171	0.278601
$629$	34.6110	1.38003
$630$	38.1060	1.51818
$631$	4.88412	0.194434	0.0972168	−	0.995263i	$-0.469006\pi$
$631$	4.88412	0.194434	0.0972168	+	0.995263i	$0.469006\pi$
$632$	−7.28685	−0.289855
$633$	2.32254	0.0923126
$634$	43.0822	1.71101
$635$	−45.5504	−1.80761
$636$	36.9597	1.46555
$637$	−2.28475	−0.0905252
$638$	9.51429	0.376674
$639$	−16.8115	−0.665055
$640$	33.1549	1.31056
$641$	−5.77830	−0.228229	−0.114115	−	0.993468i	$-0.536403\pi$
$641$	−5.77830	−0.228229	−0.114115	+	0.993468i	$0.536403\pi$
$642$	−21.6390	−0.854024
$643$	15.4517	0.609354	0.304677	−	0.952456i	$-0.401451\pi$
$643$	15.4517	0.609354	0.304677	+	0.952456i	$0.401451\pi$
$644$	5.84489	0.230321
$645$	−9.06336	−0.356869
$646$	41.3638	1.62744
$647$	−33.8319	−1.33007	−0.665035	−	0.746812i	$-0.731584\pi$
$647$	−33.8319	−1.33007	−0.665035	+	0.746812i	$0.731584\pi$
$648$	9.92521	0.389899
$649$	72.4237	2.84288
$650$	−21.5773	−0.846332
$651$	−18.6481	−0.730875
$652$	−57.9746	−2.27046
$653$	5.61833	0.219862	0.109931	−	0.993939i	$-0.464937\pi$
$653$	5.61833	0.219862	0.109931	+	0.993939i	$0.464937\pi$
$654$	66.4073	2.59673
$655$	38.8226	1.51693
$656$	19.2067	0.749897
$657$	71.2386	2.77928
$658$	−21.8278	−0.850934
$659$	−1.50406	−0.0585900	−0.0292950	−	0.999571i	$-0.509326\pi$
$659$	−1.50406	−0.0585900	−0.0292950	+	0.999571i	$0.509326\pi$
$660$	−135.278	−5.26569
$661$	−27.9240	−1.08612	−0.543060	−	0.839694i	$-0.682734\pi$
$661$	−27.9240	−1.08612	−0.543060	+	0.839694i	$0.682734\pi$
$662$	33.3373	1.29569
$663$	30.0285	1.16621
$664$	−19.0512	−0.739328
$665$	13.2089	0.512220
$666$	97.0308	3.75987
$667$	1.72531	0.0668042
$668$	31.7992	1.23035
$669$	−26.1732	−1.01191
$670$	37.3584	1.44328
$671$	−22.6221	−0.873316
$672$	−22.7583	−0.877920
$673$	13.3571	0.514879	0.257439	−	0.966294i	$-0.417121\pi$
$673$	13.3571	0.514879	0.257439	+	0.966294i	$0.417121\pi$
$674$	−5.75797	−0.221789
$675$	−35.7798	−1.37717
$676$	−20.7205	−0.796941
$677$	21.4623	0.824863	0.412431	−	0.910989i	$-0.364680\pi$
$677$	21.4623	0.824863	0.412431	+	0.910989i	$0.364680\pi$
$678$	−80.2779	−3.08305
$679$	13.7366	0.527163
$680$	−19.4705	−0.746661
$681$	54.0780	2.07227
$682$	76.2345	2.91917
$683$	−23.1335	−0.885178	−0.442589	−	0.896725i	$-0.645940\pi$
$683$	−23.1335	−0.885178	−0.442589	+	0.896725i	$0.645940\pi$
$684$	66.2285	2.53231
$685$	5.83536	0.222958
$686$	−2.15948	−0.0824491
$687$	−18.1817	−0.693677
$688$	2.23332	0.0851447
$689$	10.7103	0.408028
$690$	−42.9525	−1.63517
$691$	6.16979	0.234710	0.117355	−	0.993090i	$-0.462558\pi$
$691$	6.16979	0.234710	0.117355	+	0.993090i	$0.462558\pi$
$692$	−33.8223	−1.28573
$693$	32.3007	1.22700
$694$	−68.3553	−2.59473
$695$	−41.6803	−1.58103
$696$	3.33379	0.126367
$697$	−38.1815	−1.44623
$698$	−1.05995	−0.0401199
$699$	6.14477	0.232417
$700$	−11.6476	−0.440237
$701$	50.1789	1.89523	0.947616	−	0.319412i	$-0.103485\pi$
$701$	50.1789	1.89523	0.947616	+	0.319412i	$0.103485\pi$
$702$	40.3660	1.52352
$703$	33.6344	1.26854
$704$	68.0055	2.56306
$705$	91.6115	3.45029
$706$	1.83155	0.0689313
$707$	−5.91859	−0.222592
$708$	101.891	3.82930
$709$	31.0345	1.16553	0.582763	−	0.812642i	$-0.301972\pi$
$709$	31.0345	1.16553	0.582763	+	0.812642i	$0.301972\pi$
$710$	19.2843	0.723726
$711$	−29.3197	−1.09957
$712$	−17.3422	−0.649926
$713$	13.8243	0.517723
$714$	28.3820	1.06217
$715$	−39.2011	−1.46604
$716$	−8.93344	−0.333858
$717$	60.8564	2.27272
$718$	−15.5128	−0.578933
$719$	12.4752	0.465247	0.232623	−	0.972567i	$-0.425269\pi$
$719$	12.4752	0.465247	0.232623	+	0.972567i	$0.425269\pi$
$720$	39.4091	1.46869
$721$	4.77879	0.177971
$722$	−0.833414	−0.0310165
$723$	23.6688	0.880252
$724$	19.4934	0.724468
$725$	−3.43815	−0.127690
$726$	−130.457	−4.84173
$727$	−12.4191	−0.460599	−0.230300	−	0.973120i	$-0.573971\pi$
$727$	−12.4191	−0.460599	−0.230300	+	0.973120i	$0.573971\pi$
$728$	3.27280	0.121298
$729$	−32.7240	−1.21200
$730$	−81.7168	−3.02448
$731$	−4.43968	−0.164207
$732$	−31.8265	−1.17634
$733$	−8.85155	−0.326939	−0.163470	−	0.986548i	$-0.552269\pi$
$733$	−8.85155	−0.326939	−0.163470	+	0.986548i	$0.552269\pi$
$734$	55.3905	2.04450
$735$	9.06336	0.334307
$736$	16.8713	0.621884
$737$	31.6669	1.16647
$738$	−107.041	−3.94022
$739$	19.6485	0.722781	0.361390	−	0.932415i	$-0.382302\pi$
$739$	19.6485	0.722781	0.361390	+	0.932415i	$0.382302\pi$
$740$	−63.5674	−2.33679
$741$	29.1812	1.07200
$742$	10.1230	0.371627
$743$	31.4306	1.15308	0.576539	−	0.817070i	$-0.304403\pi$
$743$	31.4306	1.15308	0.576539	+	0.817070i	$0.304403\pi$
$744$	26.7124	0.979325
$745$	−30.5325	−1.11862
$746$	−58.7935	−2.15258
$747$	−76.6550	−2.80466
$748$	−66.2659	−2.42292
$749$	−3.38490	−0.123682
$750$	−12.2657	−0.447880
$751$	−18.7919	−0.685725	−0.342862	−	0.939386i	$-0.611396\pi$
$751$	−18.7919	−0.685725	−0.342862	+	0.939386i	$0.611396\pi$
$752$	−22.5742	−0.823197
$753$	−8.89745	−0.324241
$754$	3.87885	0.141259
$755$	4.24794	0.154598
$756$	21.7898	0.792488
$757$	−48.4191	−1.75982	−0.879911	−	0.475139i	$-0.842398\pi$
$757$	−48.4191	−1.75982	−0.879911	+	0.475139i	$0.842398\pi$
$758$	−3.36933	−0.122380
$759$	−36.4088	−1.32156
$760$	−18.9211	−0.686341
$761$	11.9107	0.431764	0.215882	−	0.976419i	$-0.430737\pi$
$761$	11.9107	0.431764	0.215882	+	0.976419i	$0.430737\pi$
$762$	−95.1123	−3.44555
$763$	10.3878	0.376065
$764$	47.4211	1.71563
$765$	−78.3424	−2.83247
$766$	−2.78148	−0.100499
$767$	29.5262	1.06613
$768$	−2.61667	−0.0944211
$769$	0.900391	0.0324689	0.0162345	−	0.999868i	$-0.494832\pi$
$769$	0.900391	0.0324689	0.0162345	+	0.999868i	$0.494832\pi$
$770$	−37.0516	−1.33525
$771$	39.5094	1.42290
$772$	43.1348	1.55245
$773$	16.5477	0.595179	0.297590	−	0.954694i	$-0.403817\pi$
$773$	16.5477	0.595179	0.297590	+	0.954694i	$0.403817\pi$
$774$	−12.4465	−0.447380
$775$	−27.5487	−0.989578
$776$	−19.6770	−0.706364
$777$	23.0784	0.827933
$778$	−11.3429	−0.406663
$779$	−37.1041	−1.32939
$780$	−55.1511	−1.97472
$781$	16.3464	0.584920
$782$	−21.0403	−0.752398
$783$	6.43196	0.229860
$784$	−2.23332	−0.0797616
$785$	−8.02570	−0.286450
$786$	81.0643	2.89147
$787$	44.4006	1.58271	0.791355	−	0.611356i	$-0.209376\pi$
$787$	44.4006	1.58271	0.791355	+	0.611356i	$0.209376\pi$
$788$	69.2817	2.46806
$789$	52.9438	1.88485
$790$	33.6322	1.19658
$791$	−12.5575	−0.446495
$792$	−46.2691	−1.64410
$793$	−9.22272	−0.327508
$794$	−64.7328	−2.29728
$795$	−42.4864	−1.50684
$796$	16.1959	0.574050
$797$	−15.1025	−0.534959	−0.267479	−	0.963564i	$-0.586191\pi$
$797$	−15.1025	−0.534959	−0.267479	+	0.963564i	$0.586191\pi$
$798$	27.5811	0.976361
$799$	44.8758	1.58759
$800$	−33.6207	−1.18867
$801$	−69.7787	−2.46551
$802$	−41.3933	−1.46165
$803$	−69.2675	−2.44440
$804$	44.5514	1.57121
$805$	−6.71889	−0.236810
$806$	31.0798	1.09474
$807$	48.0216	1.69044
$808$	8.47809	0.298258
$809$	−14.6960	−0.516682	−0.258341	−	0.966054i	$-0.583176\pi$
$809$	−14.6960	−0.516682	−0.258341	+	0.966054i	$0.583176\pi$
$810$	−45.8094	−1.60958
$811$	−29.5152	−1.03642	−0.518210	−	0.855253i	$-0.673401\pi$
$811$	−29.5152	−1.03642	−0.518210	+	0.855253i	$0.673401\pi$
$812$	2.09383	0.0734789
$813$	−3.71716	−0.130366
$814$	−94.3461	−3.30683
$815$	66.6437	2.33443
$816$	29.3526	1.02755
$817$	−4.31440	−0.150942
$818$	34.9586	1.22230
$819$	13.1685	0.460146
$820$	70.1251	2.44887
$821$	22.4477	0.783429	0.391714	−	0.920087i	$-0.371882\pi$
$821$	22.4477	0.783429	0.391714	+	0.920087i	$0.371882\pi$
$822$	12.1846	0.424988
$823$	42.5781	1.48418	0.742089	−	0.670301i	$-0.233835\pi$
$823$	42.5781	1.48418	0.742089	+	0.670301i	$0.233835\pi$
$824$	−6.84538	−0.238470
$825$	72.5547	2.52603
$826$	27.9072	0.971016
$827$	−14.6348	−0.508901	−0.254450	−	0.967086i	$-0.581895\pi$
$827$	−14.6348	−0.508901	−0.254450	+	0.967086i	$0.581895\pi$
$828$	−33.6880	−1.17074
$829$	32.5807	1.13157	0.565787	−	0.824552i	$-0.308573\pi$
$829$	32.5807	1.13157	0.565787	+	0.824552i	$0.308573\pi$
$830$	87.9299	3.05209
$831$	−27.1311	−0.941167
$832$	27.7249	0.961189
$833$	4.43968	0.153826
$834$	−87.0314	−3.01365
$835$	−36.5542	−1.26501
$836$	−64.3960	−2.22718
$837$	51.5370	1.78138
$838$	52.1199	1.80045
$839$	−32.1116	−1.10862	−0.554308	−	0.832312i	$-0.687017\pi$
$839$	−32.1116	−1.10862	−0.554308	+	0.832312i	$0.687017\pi$
$840$	−12.9828	−0.447950
$841$	−28.3819	−0.978688
$842$	−26.5121	−0.913669
$843$	31.8655	1.09751
$844$	−2.08951	−0.0719240
$845$	23.8188	0.819393
$846$	125.808	4.32536
$847$	−20.4069	−0.701191
$848$	10.4692	0.359513
$849$	−83.2613	−2.85752
$850$	41.9285	1.43814
$851$	−17.1086	−0.586475
$852$	22.9973	0.787875
$853$	0.586270	0.0200735	0.0100367	−	0.999950i	$-0.496805\pi$
$853$	0.586270	0.0200735	0.0100367	+	0.999950i	$0.496805\pi$
$854$	−8.71702	−0.298290
$855$	−76.1317	−2.60365
$856$	4.84871	0.165725
$857$	51.3326	1.75349	0.876744	−	0.480958i	$-0.159711\pi$
$857$	51.3326	1.75349	0.876744	+	0.480958i	$0.159711\pi$
$858$	−81.8546	−2.79447
$859$	3.80324	0.129765	0.0648824	−	0.997893i	$-0.479333\pi$
$859$	3.80324	0.129765	0.0648824	+	0.997893i	$0.479333\pi$
$860$	8.15402	0.278050
$861$	−25.4592	−0.867646
$862$	−49.8971	−1.69950
$863$	29.1919	0.993703	0.496851	−	0.867836i	$-0.334489\pi$
$863$	29.1919	0.993703	0.496851	+	0.867836i	$0.334489\pi$
$864$	62.8963	2.13978
$865$	38.8798	1.32195
$866$	2.25507	0.0766303
$867$	−8.02478	−0.272536
$868$	16.7771	0.569451
$869$	28.5084	0.967082
$870$	−15.3870	−0.521667
$871$	12.9102	0.437445
$872$	−14.8801	−0.503902
$873$	−79.1732	−2.67961
$874$	−20.4465	−0.691615
$875$	−1.91867	−0.0648630
$876$	−97.4508	−3.29256
$877$	22.3726	0.755469	0.377735	−	0.925914i	$-0.376703\pi$
$877$	22.3726	0.755469	0.377735	+	0.925914i	$0.376703\pi$
$878$	−43.5969	−1.47132
$879$	10.5063	0.354367
$880$	−38.3187	−1.29172
$881$	9.10600	0.306789	0.153394	−	0.988165i	$-0.450980\pi$
$881$	9.10600	0.306789	0.153394	+	0.988165i	$0.450980\pi$
$882$	12.4465	0.419095
$883$	4.77425	0.160666	0.0803332	−	0.996768i	$-0.474402\pi$
$883$	4.77425	0.160666	0.0803332	+	0.996768i	$0.474402\pi$
$884$	−27.0157	−0.908636
$885$	−117.127	−3.93718
$886$	48.7711	1.63850
$887$	55.8728	1.87603	0.938013	−	0.346601i	$-0.112664\pi$
$887$	55.8728	1.87603	0.938013	+	0.346601i	$0.112664\pi$
$888$	−33.0587	−1.10938
$889$	−14.8780	−0.498993
$890$	80.0422	2.68302
$891$	−38.8305	−1.30087
$892$	23.5472	0.788418
$893$	43.6095	1.45934
$894$	−63.7539	−2.13225
$895$	10.2693	0.343264
$896$	10.8293	0.361782
$897$	−14.8434	−0.495606
$898$	25.7497	0.859280
$899$	4.95229	0.165168
$900$	67.1327	2.23776
$901$	−20.8119	−0.693346
$902$	104.079	3.46545
$903$	−2.96035	−0.0985142
$904$	17.9881	0.598274
$905$	−22.4083	−0.744878
$906$	8.86998	0.294685
$907$	−35.0756	−1.16467	−0.582333	−	0.812951i	$-0.697860\pi$
$907$	−35.0756	−1.16467	−0.582333	+	0.812951i	$0.697860\pi$
$908$	−48.6523	−1.61458
$909$	34.1128	1.13145
$910$	−15.1055	−0.500741
$911$	2.84582	0.0942863	0.0471432	−	0.998888i	$-0.484988\pi$
$911$	2.84582	0.0942863	0.0471432	+	0.998888i	$0.484988\pi$
$912$	28.5243	0.944535
$913$	74.5340	2.46672
$914$	−40.1724	−1.32878
$915$	36.5855	1.20948
$916$	16.3575	0.540469
$917$	12.6806	0.418749
$918$	−78.4383	−2.58885
$919$	20.4770	0.675472	0.337736	−	0.941241i	$-0.390339\pi$
$919$	20.4770	0.675472	0.337736	+	0.941241i	$0.390339\pi$
$920$	9.62448	0.317310
$921$	−9.36761	−0.308673
$922$	16.4996	0.543385
$923$	6.66420	0.219355
$924$	−44.1856	−1.45360
$925$	34.0936	1.12099
$926$	−53.6914	−1.76441
$927$	−27.5433	−0.904642
$928$	6.04383	0.198399
$929$	5.23252	0.171673	0.0858366	−	0.996309i	$-0.472644\pi$
$929$	5.23252	0.171673	0.0858366	+	0.996309i	$0.472644\pi$
$930$	−123.290	−4.04284
$931$	4.31440	0.141399
$932$	−5.52826	−0.181084
$933$	87.8392	2.87573
$934$	−26.9868	−0.883036
$935$	76.1747	2.49118
$936$	−18.8633	−0.616566
$937$	37.1942	1.21508	0.607540	−	0.794289i	$-0.292156\pi$
$937$	37.1942	1.21508	0.607540	+	0.794289i	$0.292156\pi$
$938$	12.2023	0.398419
$939$	42.4357	1.38484
$940$	−82.4200	−2.68824
$941$	−14.0998	−0.459641	−0.229820	−	0.973233i	$-0.573814\pi$
$941$	−14.0998	−0.459641	−0.229820	+	0.973233i	$0.573814\pi$
$942$	−16.7582	−0.546012
$943$	18.8735	0.614606
$944$	28.8616	0.939364
$945$	−25.0481	−0.814814
$946$	12.1021	0.393473
$947$	56.8196	1.84639	0.923195	−	0.384331i	$-0.125568\pi$
$947$	56.8196	1.84639	0.923195	+	0.384331i	$0.125568\pi$
$948$	40.1078	1.30264
$949$	−28.2394	−0.916691
$950$	40.7454	1.32196
$951$	−59.0598	−1.91515
$952$	−6.35962	−0.206117
$953$	37.8521	1.22615	0.613074	−	0.790025i	$-0.289933\pi$
$953$	37.8521	1.22615	0.613074	+	0.790025i	$0.289933\pi$
$954$	−58.3455	−1.88901
$955$	−54.5120	−1.76397
$956$	−54.7506	−1.77076
$957$	−13.0428	−0.421614
$958$	50.3918	1.62809
$959$	1.90599	0.0615477
$960$	−109.982	−3.54965
$961$	8.68090	0.280029
$962$	−38.4636	−1.24012
$963$	19.5094	0.628683
$964$	−21.2941	−0.685836
$965$	−49.5848	−1.59619
$966$	−14.0295	−0.451392
$967$	−19.8838	−0.639419	−0.319710	−	0.947516i	$-0.603585\pi$
$967$	−19.8838	−0.639419	−0.319710	+	0.947516i	$0.603585\pi$
$968$	29.2319	0.939550
$969$	−56.7042	−1.82160
$970$	90.8185	2.91601
$971$	21.3968	0.686656	0.343328	−	0.939216i	$-0.388446\pi$
$971$	21.3968	0.686656	0.343328	+	0.939216i	$0.388446\pi$
$972$	10.7398	0.344480
$973$	−13.6140	−0.436444
$974$	2.30124	0.0737365
$975$	29.5796	0.947305
$976$	−9.01512	−0.288567
$977$	21.2517	0.679901	0.339950	−	0.940443i	$-0.389590\pi$
$977$	21.2517	0.679901	0.339950	+	0.940443i	$0.389590\pi$
$978$	139.157	4.44974
$979$	67.8480	2.16843
$980$	−8.15402	−0.260471
$981$	−59.8720	−1.91157
$982$	44.7845	1.42913
$983$	−33.6426	−1.07303	−0.536516	−	0.843890i	$-0.680260\pi$
$983$	−33.6426	−1.07303	−0.536516	+	0.843890i	$0.680260\pi$
$984$	36.4690	1.16259
$985$	−79.6416	−2.53759
$986$	−7.53729	−0.240036
$987$	29.9229	0.952456
$988$	−26.2534	−0.835231
$989$	2.19458	0.0697835
$990$	213.553	6.78717
$991$	8.60201	0.273252	0.136626	−	0.990623i	$-0.456374\pi$
$991$	8.60201	0.273252	0.136626	+	0.990623i	$0.456374\pi$
$992$	48.4270	1.53756
$993$	−45.7009	−1.45028
$994$	6.29879	0.199786
$995$	−18.6177	−0.590222
$996$	104.860	3.32262
$997$	−54.2799	−1.71906	−0.859531	−	0.511083i	$-0.829245\pi$
$997$	−54.2799	−1.71906	−0.859531	+	0.511083i	$0.829245\pi$
$998$	61.3886	1.94322
$999$	−63.7810	−2.01794

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	301.2.a.b.1.5	✓	5
3.2	odd	2		2709.2.a.k.1.1		5
4.3	odd	2		4816.2.a.s.1.5		5
5.4	even	2		7525.2.a.g.1.1		5
7.6	odd	2		2107.2.a.f.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
301.2.a.b.1.5	✓	5	1.1	even	1	trivial
2107.2.a.f.1.5		5	7.6	odd	2
2709.2.a.k.1.1		5	3.2	odd	2
4816.2.a.s.1.5		5	4.3	odd	2
7525.2.a.g.1.1		5	5.4	even	2

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:	\( N \)	\(=\)	\( 301 = 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	301.a (trivial)

\(f(q)\)	\(=\)	\(q+2.15948 q^{2} -2.96035 q^{3} +2.66333 q^{4} -3.06159 q^{5} -6.39280 q^{6} -1.00000 q^{7} +1.43245 q^{8} +5.76366 q^{9} +O(q^{10})\)	\(q+2.15948 q^{2} -2.96035 q^{3} +2.66333 q^{4} -3.06159 q^{5} -6.39280 q^{6} -1.00000 q^{7} +1.43245 q^{8} +5.76366 q^{9} -6.61142 q^{10} -5.60419 q^{11} -7.88439 q^{12} -2.28475 q^{13} -2.15948 q^{14} +9.06336 q^{15} -2.23332 q^{16} +4.43968 q^{17} +12.4465 q^{18} +4.31440 q^{19} -8.15402 q^{20} +2.96035 q^{21} -12.1021 q^{22} -2.19458 q^{23} -4.24055 q^{24} +4.37331 q^{25} -4.93387 q^{26} -8.18141 q^{27} -2.66333 q^{28} -0.786168 q^{29} +19.5721 q^{30} -6.29928 q^{31} -7.68771 q^{32} +16.5904 q^{33} +9.58738 q^{34} +3.06159 q^{35} +15.3506 q^{36} +7.79584 q^{37} +9.31684 q^{38} +6.76366 q^{39} -4.38557 q^{40} -8.60006 q^{41} +6.39280 q^{42} -1.00000 q^{43} -14.9258 q^{44} -17.6460 q^{45} -4.73914 q^{46} +10.1079 q^{47} +6.61142 q^{48} +1.00000 q^{49} +9.44405 q^{50} -13.1430 q^{51} -6.08506 q^{52} -4.68771 q^{53} -17.6676 q^{54} +17.1577 q^{55} -1.43245 q^{56} -12.7721 q^{57} -1.69771 q^{58} -12.9231 q^{59} +24.1387 q^{60} +4.03664 q^{61} -13.6031 q^{62} -5.76366 q^{63} -12.1348 q^{64} +6.99497 q^{65} +35.8265 q^{66} -5.65058 q^{67} +11.8243 q^{68} +6.49672 q^{69} +6.61142 q^{70} -2.91682 q^{71} +8.25616 q^{72} +12.3600 q^{73} +16.8349 q^{74} -12.9465 q^{75} +11.4907 q^{76} +5.60419 q^{77} +14.6060 q^{78} -5.08698 q^{79} +6.83751 q^{80} +6.92883 q^{81} -18.5716 q^{82} -13.2997 q^{83} +7.88439 q^{84} -13.5925 q^{85} -2.15948 q^{86} +2.32733 q^{87} -8.02772 q^{88} -12.1067 q^{89} -38.1060 q^{90} +2.28475 q^{91} -5.84489 q^{92} +18.6481 q^{93} +21.8278 q^{94} -13.2089 q^{95} +22.7583 q^{96} -13.7366 q^{97} +2.15948 q^{98} -32.3007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9	\( 5 q - 3 q^{3} + 2 q^{4} - 6 q^{5} - 10 q^{6} - 5 q^{7} - 3 q^{8} + 6 q^{9} - q^{10} - 16 q^{11} - 8 q^{12} - 2 q^{13} - 8 q^{15} - 8 q^{17} + 17 q^{18} - 10 q^{19} - 6 q^{20} + 3 q^{21} - 5 q^{22} - 2 q^{23} + 10 q^{24} + 11 q^{25} - 24 q^{26} - 9 q^{27} - 2 q^{28} - 4 q^{29} + 24 q^{30} - 6 q^{31} + 4 q^{32} + 14 q^{33} + 17 q^{34} + 6 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + 11 q^{39} - 20 q^{40} - 16 q^{41} + 10 q^{42} - 5 q^{43} - 11 q^{44} - 14 q^{45} + 17 q^{46} - 11 q^{47} + q^{48} + 5 q^{49} + 12 q^{50} - 6 q^{51} + 24 q^{52} + 19 q^{53} - 23 q^{54} + 25 q^{55} + 3 q^{56} - 5 q^{57} - 31 q^{59} + 43 q^{60} - 2 q^{61} + 7 q^{62} - 6 q^{63} - 17 q^{64} + 6 q^{65} + 59 q^{66} + 11 q^{67} + 13 q^{68} - 17 q^{69} + q^{70} - 15 q^{71} + 23 q^{72} + 13 q^{73} + 22 q^{74} + 4 q^{75} + 34 q^{76} + 16 q^{77} + 17 q^{78} + 24 q^{79} + 11 q^{80} + 5 q^{81} - 36 q^{83} + 8 q^{84} - 19 q^{85} + 23 q^{87} - 13 q^{88} - 15 q^{89} - 17 q^{90} + 2 q^{91} - 35 q^{92} + 39 q^{93} + 32 q^{94} - 14 q^{95} - 2 q^{96} - 13 q^{97} - 63 q^{99}+O(q^{100}) \) 5 * q - 3 * q^3 + 2 * q^4 - 6 * q^5 - 10 * q^6 - 5 * q^7 - 3 * q^8 + 6 * q^9 - q^10 - 16 * q^11 - 8 * q^12 - 2 * q^13 - 8 * q^15 - 8 * q^17 + 17 * q^18 - 10 * q^19 - 6 * q^20 + 3 * q^21 - 5 * q^22 - 2 * q^23 + 10 * q^24 + 11 * q^25 - 24 * q^26 - 9 * q^27 - 2 * q^28 - 4 * q^29 + 24 * q^30 - 6 * q^31 + 4 * q^32 + 14 * q^33 + 17 * q^34 + 6 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + 11 * q^39 - 20 * q^40 - 16 * q^41 + 10 * q^42 - 5 * q^43 - 11 * q^44 - 14 * q^45 + 17 * q^46 - 11 * q^47 + q^48 + 5 * q^49 + 12 * q^50 - 6 * q^51 + 24 * q^52 + 19 * q^53 - 23 * q^54 + 25 * q^55 + 3 * q^56 - 5 * q^57 - 31 * q^59 + 43 * q^60 - 2 * q^61 + 7 * q^62 - 6 * q^63 - 17 * q^64 + 6 * q^65 + 59 * q^66 + 11 * q^67 + 13 * q^68 - 17 * q^69 + q^70 - 15 * q^71 + 23 * q^72 + 13 * q^73 + 22 * q^74 + 4 * q^75 + 34 * q^76 + 16 * q^77 + 17 * q^78 + 24 * q^79 + 11 * q^80 + 5 * q^81 - 36 * q^83 + 8 * q^84 - 19 * q^85 + 23 * q^87 - 13 * q^88 - 15 * q^89 - 17 * q^90 + 2 * q^91 - 35 * q^92 + 39 * q^93 + 32 * q^94 - 14 * q^95 - 2 * q^96 - 13 * q^97 - 63 * q^99

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