LMFDB - Embedded newform 6014.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.56862 q^{3} +1.00000 q^{4} -3.99872 q^{5} -2.56862 q^{6} +2.48908 q^{7} +1.00000 q^{8} +3.59779 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.56862 q^{3} +1.00000 q^{4} -3.99872 q^{5} -2.56862 q^{6} +2.48908 q^{7} +1.00000 q^{8} +3.59779 q^{9} -3.99872 q^{10} +3.77486 q^{11} -2.56862 q^{12} +5.52625 q^{13} +2.48908 q^{14} +10.2712 q^{15} +1.00000 q^{16} +6.23239 q^{17} +3.59779 q^{18} +4.57858 q^{19} -3.99872 q^{20} -6.39350 q^{21} +3.77486 q^{22} -2.19520 q^{23} -2.56862 q^{24} +10.9897 q^{25} +5.52625 q^{26} -1.53550 q^{27} +2.48908 q^{28} -5.87752 q^{29} +10.2712 q^{30} +1.00000 q^{31} +1.00000 q^{32} -9.69617 q^{33} +6.23239 q^{34} -9.95313 q^{35} +3.59779 q^{36} +10.9406 q^{37} +4.57858 q^{38} -14.1948 q^{39} -3.99872 q^{40} -9.39959 q^{41} -6.39350 q^{42} +7.43538 q^{43} +3.77486 q^{44} -14.3866 q^{45} -2.19520 q^{46} -3.21759 q^{47} -2.56862 q^{48} -0.804476 q^{49} +10.9897 q^{50} -16.0086 q^{51} +5.52625 q^{52} -4.47960 q^{53} -1.53550 q^{54} -15.0946 q^{55} +2.48908 q^{56} -11.7606 q^{57} -5.87752 q^{58} -0.0676113 q^{59} +10.2712 q^{60} +1.67993 q^{61} +1.00000 q^{62} +8.95520 q^{63} +1.00000 q^{64} -22.0979 q^{65} -9.69617 q^{66} -12.0418 q^{67} +6.23239 q^{68} +5.63862 q^{69} -9.95313 q^{70} +4.55968 q^{71} +3.59779 q^{72} +9.15350 q^{73} +10.9406 q^{74} -28.2285 q^{75} +4.57858 q^{76} +9.39594 q^{77} -14.1948 q^{78} -9.61424 q^{79} -3.99872 q^{80} -6.84926 q^{81} -9.39959 q^{82} +13.4605 q^{83} -6.39350 q^{84} -24.9216 q^{85} +7.43538 q^{86} +15.0971 q^{87} +3.77486 q^{88} +17.5257 q^{89} -14.3866 q^{90} +13.7553 q^{91} -2.19520 q^{92} -2.56862 q^{93} -3.21759 q^{94} -18.3084 q^{95} -2.56862 q^{96} +1.00000 q^{97} -0.804476 q^{98} +13.5812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.56862	−1.48299	−0.741496	−	0.670957i	$-0.765883\pi$
$3$	−2.56862	−1.48299	−0.741496	+	0.670957i	$0.765883\pi$
$4$	1.00000	0.500000
$5$	−3.99872	−1.78828	−0.894141	−	0.447786i	$-0.852213\pi$
$5$	−3.99872	−1.78828	−0.894141	+	0.447786i	$0.852213\pi$
$6$	−2.56862	−1.04863
$7$	2.48908	0.940784	0.470392	−	0.882458i	$-0.344112\pi$
$7$	2.48908	0.940784	0.470392	+	0.882458i	$0.344112\pi$
$8$	1.00000	0.353553
$9$	3.59779	1.19926
$10$	−3.99872	−1.26451
$11$	3.77486	1.13816	0.569082	−	0.822281i	$-0.307299\pi$
$11$	3.77486	1.13816	0.569082	+	0.822281i	$0.307299\pi$
$12$	−2.56862	−0.741496
$13$	5.52625	1.53271	0.766353	−	0.642420i	$-0.222070\pi$
$13$	5.52625	1.53271	0.766353	+	0.642420i	$0.222070\pi$
$14$	2.48908	0.665235
$15$	10.2712	2.65201
$16$	1.00000	0.250000
$17$	6.23239	1.51158	0.755789	−	0.654816i	$-0.227254\pi$
$17$	6.23239	1.51158	0.755789	+	0.654816i	$0.227254\pi$
$18$	3.59779	0.848008
$19$	4.57858	1.05040	0.525199	−	0.850979i	$-0.323991\pi$
$19$	4.57858	1.05040	0.525199	+	0.850979i	$0.323991\pi$
$20$	−3.99872	−0.894141
$21$	−6.39350	−1.39518
$22$	3.77486	0.804803
$23$	−2.19520	−0.457730	−0.228865	−	0.973458i	$-0.573501\pi$
$23$	−2.19520	−0.457730	−0.228865	+	0.973458i	$0.573501\pi$
$24$	−2.56862	−0.524317
$25$	10.9897	2.19795
$26$	5.52625	1.08379
$27$	−1.53550	−0.295508
$28$	2.48908	0.470392
$29$	−5.87752	−1.09143	−0.545714	−	0.837971i	$-0.683742\pi$
$29$	−5.87752	−1.09143	−0.545714	+	0.837971i	$0.683742\pi$
$30$	10.2712	1.87525
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−9.69617	−1.68789
$34$	6.23239	1.06885
$35$	−9.95313	−1.68239
$36$	3.59779	0.599632
$37$	10.9406	1.79862	0.899308	−	0.437316i	$-0.144071\pi$
$37$	10.9406	1.79862	0.899308	+	0.437316i	$0.144071\pi$
$38$	4.57858	0.742743
$39$	−14.1948	−2.27299
$40$	−3.99872	−0.632253
$41$	−9.39959	−1.46797	−0.733985	−	0.679166i	$-0.762342\pi$
$41$	−9.39959	−1.46797	−0.733985	+	0.679166i	$0.762342\pi$
$42$	−6.39350	−0.986538
$43$	7.43538	1.13388	0.566942	−	0.823758i	$-0.308126\pi$
$43$	7.43538	1.13388	0.566942	+	0.823758i	$0.308126\pi$
$44$	3.77486	0.569082
$45$	−14.3866	−2.14462
$46$	−2.19520	−0.323664
$47$	−3.21759	−0.469333	−0.234667	−	0.972076i	$-0.575400\pi$
$47$	−3.21759	−0.469333	−0.234667	+	0.972076i	$0.575400\pi$
$48$	−2.56862	−0.370748
$49$	−0.804476	−0.114925
$50$	10.9897	1.55419
$51$	−16.0086	−2.24166
$52$	5.52625	0.766353
$53$	−4.47960	−0.615321	−0.307660	−	0.951496i	$-0.599546\pi$
$53$	−4.47960	−0.615321	−0.307660	+	0.951496i	$0.599546\pi$
$54$	−1.53550	−0.208956
$55$	−15.0946	−2.03536
$56$	2.48908	0.332617
$57$	−11.7606	−1.55773
$58$	−5.87752	−0.771757
$59$	−0.0676113	−0.00880224	−0.00440112	−	0.999990i	$-0.501401\pi$
$59$	−0.0676113	−0.00880224	−0.00440112	+	0.999990i	$0.501401\pi$
$60$	10.2712	1.32600
$61$	1.67993	0.215093	0.107547	−	0.994200i	$-0.465700\pi$
$61$	1.67993	0.215093	0.107547	+	0.994200i	$0.465700\pi$
$62$	1.00000	0.127000
$63$	8.95520	1.12825
$64$	1.00000	0.125000
$65$	−22.0979	−2.74091
$66$	−9.69617	−1.19352
$67$	−12.0418	−1.47114	−0.735569	−	0.677449i	$-0.763085\pi$
$67$	−12.0418	−1.47114	−0.735569	+	0.677449i	$0.763085\pi$
$68$	6.23239	0.755789
$69$	5.63862	0.678810
$70$	−9.95313	−1.18963
$71$	4.55968	0.541134	0.270567	−	0.962701i	$-0.412789\pi$
$71$	4.55968	0.541134	0.270567	+	0.962701i	$0.412789\pi$
$72$	3.59779	0.424004
$73$	9.15350	1.07134	0.535668	−	0.844429i	$-0.320060\pi$
$73$	9.15350	1.07134	0.535668	+	0.844429i	$0.320060\pi$
$74$	10.9406	1.27181
$75$	−28.2285	−3.25954
$76$	4.57858	0.525199
$77$	9.39594	1.07077
$78$	−14.1948	−1.60725
$79$	−9.61424	−1.08169	−0.540843	−	0.841123i	$-0.681895\pi$
$79$	−9.61424	−1.08169	−0.540843	+	0.841123i	$0.681895\pi$
$80$	−3.99872	−0.447070
$81$	−6.84926	−0.761029
$82$	−9.39959	−1.03801
$83$	13.4605	1.47748	0.738742	−	0.673988i	$-0.235420\pi$
$83$	13.4605	1.47748	0.738742	+	0.673988i	$0.235420\pi$
$84$	−6.39350	−0.697588
$85$	−24.9216	−2.70313
$86$	7.43538	0.801777
$87$	15.0971	1.61858
$88$	3.77486	0.402402
$89$	17.5257	1.85772	0.928862	−	0.370427i	$-0.120789\pi$
$89$	17.5257	1.85772	0.928862	+	0.370427i	$0.120789\pi$
$90$	−14.3866	−1.51648
$91$	13.7553	1.44194
$92$	−2.19520	−0.228865
$93$	−2.56862	−0.266353
$94$	−3.21759	−0.331869
$95$	−18.3084	−1.87841
$96$	−2.56862	−0.262158
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−0.804476	−0.0812643
$99$	13.5812	1.36496
$100$	10.9897	1.09897
$101$	−2.36974	−0.235798	−0.117899	−	0.993026i	$-0.537616\pi$
$101$	−2.36974	−0.235798	−0.117899	+	0.993026i	$0.537616\pi$
$102$	−16.0086	−1.58509
$103$	18.6293	1.83559	0.917797	−	0.397049i	$-0.129966\pi$
$103$	18.6293	1.83559	0.917797	+	0.397049i	$0.129966\pi$
$104$	5.52625	0.541893
$105$	25.5658	2.49497
$106$	−4.47960	−0.435098
$107$	−15.4044	−1.48920	−0.744602	−	0.667509i	$-0.767361\pi$
$107$	−15.4044	−1.48920	−0.744602	+	0.667509i	$0.767361\pi$
$108$	−1.53550	−0.147754
$109$	14.2413	1.36407	0.682033	−	0.731321i	$-0.261096\pi$
$109$	14.2413	1.36407	0.682033	+	0.731321i	$0.261096\pi$
$110$	−15.0946	−1.43921
$111$	−28.1021	−2.66733
$112$	2.48908	0.235196
$113$	−17.6541	−1.66076	−0.830378	−	0.557200i	$-0.811876\pi$
$113$	−17.6541	−1.66076	−0.830378	+	0.557200i	$0.811876\pi$
$114$	−11.7606	−1.10148
$115$	8.77797	0.818550
$116$	−5.87752	−0.545714
$117$	19.8823	1.83812
$118$	−0.0676113	−0.00622412
$119$	15.5129	1.42207
$120$	10.2712	0.937626
$121$	3.24958	0.295416
$122$	1.67993	0.152094
$123$	24.1440	2.17699
$124$	1.00000	0.0898027
$125$	−23.9513	−2.14227
$126$	8.95520	0.797793
$127$	16.8274	1.49319	0.746597	−	0.665276i	$-0.231686\pi$
$127$	16.8274	1.49319	0.746597	+	0.665276i	$0.231686\pi$
$128$	1.00000	0.0883883
$129$	−19.0986	−1.68154
$130$	−22.0979	−1.93811
$131$	13.3297	1.16462	0.582310	−	0.812967i	$-0.302149\pi$
$131$	13.3297	1.16462	0.582310	+	0.812967i	$0.302149\pi$
$132$	−9.69617	−0.843944
$133$	11.3965	0.988198
$134$	−12.0418	−1.04025
$135$	6.14005	0.528451
$136$	6.23239	0.534423
$137$	−7.17933	−0.613371	−0.306686	−	0.951811i	$-0.599220\pi$
$137$	−7.17933	−0.613371	−0.306686	+	0.951811i	$0.599220\pi$
$138$	5.63862	0.479991
$139$	−1.59476	−0.135265	−0.0676327	−	0.997710i	$-0.521545\pi$
$139$	−1.59476	−0.135265	−0.0676327	+	0.997710i	$0.521545\pi$
$140$	−9.95313	−0.841193
$141$	8.26475	0.696017
$142$	4.55968	0.382640
$143$	20.8608	1.74447
$144$	3.59779	0.299816
$145$	23.5026	1.95178
$146$	9.15350	0.757549
$147$	2.06639	0.170433
$148$	10.9406	0.899308
$149$	10.0637	0.824454	0.412227	−	0.911081i	$-0.364751\pi$
$149$	10.0637	0.824454	0.412227	+	0.911081i	$0.364751\pi$
$150$	−28.2285	−2.30484
$151$	−21.0358	−1.71187	−0.855936	−	0.517082i	$-0.827018\pi$
$151$	−21.0358	−1.71187	−0.855936	+	0.517082i	$0.827018\pi$
$152$	4.57858	0.371372
$153$	22.4229	1.81278
$154$	9.39594	0.757146
$155$	−3.99872	−0.321185
$156$	−14.1948	−1.13649
$157$	−0.656314	−0.0523796	−0.0261898	−	0.999657i	$-0.508337\pi$
$157$	−0.656314	−0.0523796	−0.0261898	+	0.999657i	$0.508337\pi$
$158$	−9.61424	−0.764868
$159$	11.5064	0.912516
$160$	−3.99872	−0.316126
$161$	−5.46402	−0.430625
$162$	−6.84926	−0.538129
$163$	−9.74000	−0.762896	−0.381448	−	0.924390i	$-0.624574\pi$
$163$	−9.74000	−0.762896	−0.381448	+	0.924390i	$0.624574\pi$
$164$	−9.39959	−0.733985
$165$	38.7723	3.01842
$166$	13.4605	1.04474
$167$	−15.2409	−1.17938	−0.589688	−	0.807631i	$-0.700749\pi$
$167$	−15.2409	−1.17938	−0.589688	+	0.807631i	$0.700749\pi$
$168$	−6.39350	−0.493269
$169$	17.5394	1.34919
$170$	−24.9216	−1.91140
$171$	16.4728	1.25971
$172$	7.43538	0.566942
$173$	11.8548	0.901302	0.450651	−	0.892700i	$-0.351192\pi$
$173$	11.8548	0.901302	0.450651	+	0.892700i	$0.351192\pi$
$174$	15.0971	1.14451
$175$	27.3544	2.06780
$176$	3.77486	0.284541
$177$	0.173667	0.0130536
$178$	17.5257	1.31361
$179$	−15.1515	−1.13248	−0.566239	−	0.824241i	$-0.691602\pi$
$179$	−15.1515	−1.13248	−0.566239	+	0.824241i	$0.691602\pi$
$180$	−14.3866	−1.07231
$181$	−16.7089	−1.24196	−0.620981	−	0.783826i	$-0.713265\pi$
$181$	−16.7089	−1.24196	−0.620981	+	0.783826i	$0.713265\pi$
$182$	13.7553	1.01961
$183$	−4.31511	−0.318982
$184$	−2.19520	−0.161832
$185$	−43.7482	−3.21643
$186$	−2.56862	−0.188340
$187$	23.5264	1.72042
$188$	−3.21759	−0.234667
$189$	−3.82199	−0.278009
$190$	−18.3084	−1.32823
$191$	−17.8187	−1.28932	−0.644659	−	0.764470i	$-0.723001\pi$
$191$	−17.8187	−1.28932	−0.644659	+	0.764470i	$0.723001\pi$
$192$	−2.56862	−0.185374
$193$	2.99486	0.215575	0.107787	−	0.994174i	$-0.465623\pi$
$193$	2.99486	0.215575	0.107787	+	0.994174i	$0.465623\pi$
$194$	1.00000	0.0717958
$195$	56.7611	4.06474
$196$	−0.804476	−0.0574626
$197$	22.8941	1.63114	0.815568	−	0.578661i	$-0.196425\pi$
$197$	22.8941	1.63114	0.815568	+	0.578661i	$0.196425\pi$
$198$	13.5812	0.965172
$199$	−6.85540	−0.485966	−0.242983	−	0.970030i	$-0.578126\pi$
$199$	−6.85540	−0.485966	−0.242983	+	0.970030i	$0.578126\pi$
$200$	10.9897	0.777093
$201$	30.9307	2.18169
$202$	−2.36974	−0.166735
$203$	−14.6296	−1.02680
$204$	−16.0086	−1.12083
$205$	37.5863	2.62514
$206$	18.6293	1.29796
$207$	−7.89787	−0.548940
$208$	5.52625	0.383176
$209$	17.2835	1.19552
$210$	25.5658	1.76421
$211$	8.98960	0.618870	0.309435	−	0.950921i	$-0.399860\pi$
$211$	8.98960	0.618870	0.309435	+	0.950921i	$0.399860\pi$
$212$	−4.47960	−0.307660
$213$	−11.7121	−0.802497
$214$	−15.4044	−1.05303
$215$	−29.7320	−2.02770
$216$	−1.53550	−0.104478
$217$	2.48908	0.168970
$218$	14.2413	0.964540
$219$	−23.5118	−1.58878
$220$	−15.0946	−1.01768
$221$	34.4417	2.31680
$222$	−28.1021	−1.88609
$223$	1.42440	0.0953851	0.0476925	−	0.998862i	$-0.484813\pi$
$223$	1.42440	0.0953851	0.0476925	+	0.998862i	$0.484813\pi$
$224$	2.48908	0.166309
$225$	39.5389	2.63592
$226$	−17.6541	−1.17433
$227$	12.0187	0.797709	0.398855	−	0.917014i	$-0.369408\pi$
$227$	12.0187	0.797709	0.398855	+	0.917014i	$0.369408\pi$
$228$	−11.7606	−0.778866
$229$	−1.75668	−0.116085	−0.0580425	−	0.998314i	$-0.518486\pi$
$229$	−1.75668	−0.116085	−0.0580425	+	0.998314i	$0.518486\pi$
$230$	8.77797	0.578802
$231$	−24.1346	−1.58794
$232$	−5.87752	−0.385878
$233$	−29.2143	−1.91389	−0.956947	−	0.290263i	$-0.906257\pi$
$233$	−29.2143	−1.91389	−0.956947	+	0.290263i	$0.906257\pi$
$234$	19.8823	1.29975
$235$	12.8662	0.839300
$236$	−0.0676113	−0.00440112
$237$	24.6953	1.60413
$238$	15.5129	1.00555
$239$	2.29718	0.148592	0.0742961	−	0.997236i	$-0.476329\pi$
$239$	2.29718	0.148592	0.0742961	+	0.997236i	$0.476329\pi$
$240$	10.2712	0.663002
$241$	−14.6789	−0.945549	−0.472775	−	0.881183i	$-0.656748\pi$
$241$	−14.6789	−0.945549	−0.472775	+	0.881183i	$0.656748\pi$
$242$	3.24958	0.208891
$243$	22.1996	1.42411
$244$	1.67993	0.107547
$245$	3.21687	0.205518
$246$	24.1440	1.53936
$247$	25.3024	1.60995
$248$	1.00000	0.0635001
$249$	−34.5749	−2.19110
$250$	−23.9513	−1.51481
$251$	14.8640	0.938207	0.469104	−	0.883143i	$-0.344577\pi$
$251$	14.8640	0.938207	0.469104	+	0.883143i	$0.344577\pi$
$252$	8.95520	0.564125
$253$	−8.28656	−0.520972
$254$	16.8274	1.05585
$255$	64.0140	4.00871
$256$	1.00000	0.0625000
$257$	−0.261431	−0.0163076	−0.00815382	−	0.999967i	$-0.502595\pi$
$257$	−0.261431	−0.0163076	−0.00815382	+	0.999967i	$0.502595\pi$
$258$	−19.0986	−1.18903
$259$	27.2319	1.69211
$260$	−22.0979	−1.37045
$261$	−21.1461	−1.30891
$262$	13.3297	0.823511
$263$	0.582502	0.0359186	0.0179593	−	0.999839i	$-0.494283\pi$
$263$	0.582502	0.0359186	0.0179593	+	0.999839i	$0.494283\pi$
$264$	−9.69617	−0.596758
$265$	17.9127	1.10037
$266$	11.3965	0.698761
$267$	−45.0169	−2.75499
$268$	−12.0418	−0.735569
$269$	9.99751	0.609559	0.304779	−	0.952423i	$-0.401417\pi$
$269$	9.99751	0.609559	0.304779	+	0.952423i	$0.401417\pi$
$270$	6.14005	0.373671
$271$	−3.96960	−0.241136	−0.120568	−	0.992705i	$-0.538472\pi$
$271$	−3.96960	−0.241136	−0.120568	+	0.992705i	$0.538472\pi$
$272$	6.23239	0.377894
$273$	−35.3320	−2.13839
$274$	−7.17933	−0.433719
$275$	41.4848	2.50163
$276$	5.63862	0.339405
$277$	−4.11837	−0.247449	−0.123724	−	0.992317i	$-0.539484\pi$
$277$	−4.11837	−0.247449	−0.123724	+	0.992317i	$0.539484\pi$
$278$	−1.59476	−0.0956471
$279$	3.59779	0.215394
$280$	−9.95313	−0.594814
$281$	23.7610	1.41746	0.708732	−	0.705478i	$-0.249268\pi$
$281$	23.7610	1.41746	0.708732	+	0.705478i	$0.249268\pi$
$282$	8.26475	0.492159
$283$	−9.59523	−0.570377	−0.285188	−	0.958471i	$-0.592056\pi$
$283$	−9.59523	−0.570377	−0.285188	+	0.958471i	$0.592056\pi$
$284$	4.55968	0.270567
$285$	47.0274	2.78566
$286$	20.8608	1.23353
$287$	−23.3964	−1.38104
$288$	3.59779	0.212002
$289$	21.8427	1.28487
$290$	23.5026	1.38012
$291$	−2.56862	−0.150575
$292$	9.15350	0.535668
$293$	−6.47244	−0.378124	−0.189062	−	0.981965i	$-0.560545\pi$
$293$	−6.47244	−0.378124	−0.189062	+	0.981965i	$0.560545\pi$
$294$	2.06639	0.120514
$295$	0.270358	0.0157409
$296$	10.9406	0.635907
$297$	−5.79632	−0.336336
$298$	10.0637	0.582977
$299$	−12.1312	−0.701565
$300$	−28.2285	−1.62977
$301$	18.5073	1.06674
$302$	−21.0358	−1.21048
$303$	6.08696	0.349687
$304$	4.57858	0.262599
$305$	−6.71758	−0.384648
$306$	22.4229	1.28183
$307$	10.0678	0.574597	0.287299	−	0.957841i	$-0.407243\pi$
$307$	10.0678	0.574597	0.287299	+	0.957841i	$0.407243\pi$
$308$	9.39594	0.535383
$309$	−47.8514	−2.72217
$310$	−3.99872	−0.227112
$311$	3.88436	0.220262	0.110131	−	0.993917i	$-0.464873\pi$
$311$	3.88436	0.220262	0.110131	+	0.993917i	$0.464873\pi$
$312$	−14.1948	−0.803623
$313$	5.46605	0.308959	0.154480	−	0.987996i	$-0.450630\pi$
$313$	5.46605	0.308959	0.154480	+	0.987996i	$0.450630\pi$
$314$	−0.656314	−0.0370379
$315$	−35.8093	−2.01763
$316$	−9.61424	−0.540843
$317$	29.6927	1.66771	0.833854	−	0.551986i	$-0.186130\pi$
$317$	29.6927	1.66771	0.833854	+	0.551986i	$0.186130\pi$
$318$	11.5064	0.645246
$319$	−22.1868	−1.24222
$320$	−3.99872	−0.223535
$321$	39.5681	2.20848
$322$	−5.46402	−0.304498
$323$	28.5355	1.58776
$324$	−6.84926	−0.380514
$325$	60.7321	3.36881
$326$	−9.74000	−0.539449
$327$	−36.5804	−2.02290
$328$	−9.39959	−0.519006
$329$	−8.00883	−0.441541
$330$	38.7723	2.13434
$331$	−22.0643	−1.21277	−0.606383	−	0.795173i	$-0.707380\pi$
$331$	−22.0643	−1.21277	−0.606383	+	0.795173i	$0.707380\pi$
$332$	13.4605	0.738742
$333$	39.3619	2.15702
$334$	−15.2409	−0.833945
$335$	48.1517	2.63081
$336$	−6.39350	−0.348794
$337$	19.4871	1.06153	0.530764	−	0.847520i	$-0.321905\pi$
$337$	19.4871	1.06153	0.530764	+	0.847520i	$0.321905\pi$
$338$	17.5394	0.954018
$339$	45.3466	2.46289
$340$	−24.9216	−1.35156
$341$	3.77486	0.204420
$342$	16.4728	0.890746
$343$	−19.4260	−1.04890
$344$	7.43538	0.400889
$345$	−22.5473	−1.21390
$346$	11.8548	0.637317
$347$	−12.1835	−0.654047	−0.327024	−	0.945016i	$-0.606046\pi$
$347$	−12.1835	−0.654047	−0.327024	+	0.945016i	$0.606046\pi$
$348$	15.0971	0.809290
$349$	−20.9998	−1.12409	−0.562046	−	0.827106i	$-0.689986\pi$
$349$	−20.9998	−1.12409	−0.562046	+	0.827106i	$0.689986\pi$
$350$	27.3544	1.46215
$351$	−8.48558	−0.452927
$352$	3.77486	0.201201
$353$	−27.0945	−1.44209	−0.721047	−	0.692886i	$-0.756339\pi$
$353$	−27.0945	−1.44209	−0.721047	+	0.692886i	$0.756339\pi$
$354$	0.173667	0.00923032
$355$	−18.2329	−0.967700
$356$	17.5257	0.928862
$357$	−39.8468	−2.10892
$358$	−15.1515	−0.800783
$359$	−5.66785	−0.299138	−0.149569	−	0.988751i	$-0.547789\pi$
$359$	−5.66785	−0.299138	−0.149569	+	0.988751i	$0.547789\pi$
$360$	−14.3866	−0.758239
$361$	1.96338	0.103336
$362$	−16.7089	−0.878199
$363$	−8.34692	−0.438100
$364$	13.7553	0.720972
$365$	−36.6023	−1.91585
$366$	−4.31511	−0.225554
$367$	−16.9432	−0.884430	−0.442215	−	0.896909i	$-0.645807\pi$
$367$	−16.9432	−0.884430	−0.442215	+	0.896909i	$0.645807\pi$
$368$	−2.19520	−0.114433
$369$	−33.8178	−1.76048
$370$	−43.7482	−2.27436
$371$	−11.1501	−0.578884
$372$	−2.56862	−0.133177
$373$	15.5397	0.804614	0.402307	−	0.915505i	$-0.368208\pi$
$373$	15.5397	0.804614	0.402307	+	0.915505i	$0.368208\pi$
$374$	23.5264	1.21652
$375$	61.5218	3.17697
$376$	−3.21759	−0.165934
$377$	−32.4807	−1.67284
$378$	−3.82199	−0.196582
$379$	−34.7018	−1.78251	−0.891255	−	0.453503i	$-0.850174\pi$
$379$	−34.7018	−1.78251	−0.891255	+	0.453503i	$0.850174\pi$
$380$	−18.3084	−0.939203
$381$	−43.2233	−2.21440
$382$	−17.8187	−0.911686
$383$	32.3372	1.65236	0.826178	−	0.563409i	$-0.190511\pi$
$383$	32.3372	1.65236	0.826178	+	0.563409i	$0.190511\pi$
$384$	−2.56862	−0.131079
$385$	−37.5717	−1.91483
$386$	2.99486	0.152435
$387$	26.7510	1.35983
$388$	1.00000	0.0507673
$389$	16.6798	0.845698	0.422849	−	0.906200i	$-0.361030\pi$
$389$	16.6798	0.845698	0.422849	+	0.906200i	$0.361030\pi$
$390$	56.7611	2.87421
$391$	−13.6813	−0.691895
$392$	−0.804476	−0.0406322
$393$	−34.2389	−1.72712
$394$	22.8941	1.15339
$395$	38.4446	1.93436
$396$	13.5812	0.682480
$397$	−17.2010	−0.863296	−0.431648	−	0.902042i	$-0.642068\pi$
$397$	−17.2010	−0.863296	−0.431648	+	0.902042i	$0.642068\pi$
$398$	−6.85540	−0.343630
$399$	−29.2731	−1.46549
$400$	10.9897	0.549487
$401$	−19.1460	−0.956105	−0.478052	−	0.878331i	$-0.658657\pi$
$401$	−19.1460	−0.956105	−0.478052	+	0.878331i	$0.658657\pi$
$402$	30.9307	1.54269
$403$	5.52625	0.275282
$404$	−2.36974	−0.117899
$405$	27.3883	1.36093
$406$	−14.6296	−0.726056
$407$	41.2991	2.04712
$408$	−16.0086	−0.792545
$409$	−8.19984	−0.405456	−0.202728	−	0.979235i	$-0.564981\pi$
$409$	−8.19984	−0.405456	−0.202728	+	0.979235i	$0.564981\pi$
$410$	37.5863	1.85626
$411$	18.4409	0.909624
$412$	18.6293	0.917797
$413$	−0.168290	−0.00828100
$414$	−7.89787	−0.388159
$415$	−53.8248	−2.64216
$416$	5.52625	0.270947
$417$	4.09632	0.200598
$418$	17.2835	0.845364
$419$	6.20134	0.302955	0.151478	−	0.988461i	$-0.451597\pi$
$419$	6.20134	0.302955	0.151478	+	0.988461i	$0.451597\pi$
$420$	25.5658	1.24748
$421$	17.8184	0.868418	0.434209	−	0.900812i	$-0.357028\pi$
$421$	17.8184	0.868418	0.434209	+	0.900812i	$0.357028\pi$
$422$	8.98960	0.437607
$423$	−11.5762	−0.562855
$424$	−4.47960	−0.217549
$425$	68.4924	3.32237
$426$	−11.7121	−0.567451
$427$	4.18149	0.202356
$428$	−15.4044	−0.744602
$429$	−53.5835	−2.58703
$430$	−29.7320	−1.43380
$431$	1.74095	0.0838587	0.0419293	−	0.999121i	$-0.486650\pi$
$431$	1.74095	0.0838587	0.0419293	+	0.999121i	$0.486650\pi$
$432$	−1.53550	−0.0738770
$433$	7.26284	0.349030	0.174515	−	0.984655i	$-0.444164\pi$
$433$	7.26284	0.349030	0.174515	+	0.984655i	$0.444164\pi$
$434$	2.48908	0.119480
$435$	−60.3691	−2.89448
$436$	14.2413	0.682033
$437$	−10.0509	−0.480799
$438$	−23.5118	−1.12344
$439$	27.4372	1.30951	0.654754	−	0.755842i	$-0.272772\pi$
$439$	27.4372	1.30951	0.654754	+	0.755842i	$0.272772\pi$
$440$	−15.0946	−0.719607
$441$	−2.89434	−0.137826
$442$	34.4417	1.63823
$443$	4.19189	0.199163	0.0995814	−	0.995029i	$-0.468250\pi$
$443$	4.19189	0.199163	0.0995814	+	0.995029i	$0.468250\pi$
$444$	−28.1021	−1.33367
$445$	−70.0804	−3.32213
$446$	1.42440	0.0674474
$447$	−25.8499	−1.22266
$448$	2.48908	0.117598
$449$	−26.4848	−1.24989	−0.624947	−	0.780667i	$-0.714879\pi$
$449$	−26.4848	−1.24989	−0.624947	+	0.780667i	$0.714879\pi$
$450$	39.5389	1.86388
$451$	−35.4822	−1.67079
$452$	−17.6541	−0.830378
$453$	54.0330	2.53869
$454$	12.0187	0.564066
$455$	−55.0035	−2.57860
$456$	−11.7606	−0.550741
$457$	−5.23954	−0.245095	−0.122548	−	0.992463i	$-0.539106\pi$
$457$	−5.23954	−0.245095	−0.122548	+	0.992463i	$0.539106\pi$
$458$	−1.75668	−0.0820844
$459$	−9.56987	−0.446683
$460$	8.77797	0.409275
$461$	−10.6726	−0.497072	−0.248536	−	0.968623i	$-0.579950\pi$
$461$	−10.6726	−0.497072	−0.248536	+	0.968623i	$0.579950\pi$
$462$	−24.1346	−1.12284
$463$	24.1562	1.12264	0.561318	−	0.827600i	$-0.310294\pi$
$463$	24.1562	1.12264	0.561318	+	0.827600i	$0.310294\pi$
$464$	−5.87752	−0.272857
$465$	10.2712	0.476314
$466$	−29.2143	−1.35333
$467$	2.16555	0.100210	0.0501048	−	0.998744i	$-0.484044\pi$
$467$	2.16555	0.100210	0.0501048	+	0.998744i	$0.484044\pi$
$468$	19.8823	0.919060
$469$	−29.9730	−1.38402
$470$	12.8662	0.593475
$471$	1.68582	0.0776785
$472$	−0.0676113	−0.00311206
$473$	28.0675	1.29055
$474$	24.6953	1.13429
$475$	50.3174	2.30872
$476$	15.5129	0.711034
$477$	−16.1167	−0.737933
$478$	2.29718	0.105071
$479$	30.8126	1.40786	0.703931	−	0.710269i	$-0.251427\pi$
$479$	30.8126	1.40786	0.703931	+	0.710269i	$0.251427\pi$
$480$	10.2712	0.468813
$481$	60.4602	2.75675
$482$	−14.6789	−0.668604
$483$	14.0350	0.638614
$484$	3.24958	0.147708
$485$	−3.99872	−0.181572
$486$	22.1996	1.00700
$487$	−5.22519	−0.236776	−0.118388	−	0.992967i	$-0.537773\pi$
$487$	−5.22519	−0.236776	−0.118388	+	0.992967i	$0.537773\pi$
$488$	1.67993	0.0760470
$489$	25.0183	1.13137
$490$	3.21687	0.145323
$491$	24.4311	1.10256	0.551280	−	0.834321i	$-0.314140\pi$
$491$	24.4311	1.10256	0.551280	+	0.834321i	$0.314140\pi$
$492$	24.1440	1.08849
$493$	−36.6310	−1.64978
$494$	25.3024	1.13841
$495$	−54.3073	−2.44093
$496$	1.00000	0.0449013
$497$	11.3494	0.509090
$498$	−34.5749	−1.54934
$499$	−18.2592	−0.817395	−0.408697	−	0.912670i	$-0.634017\pi$
$499$	−18.2592	−0.817395	−0.408697	+	0.912670i	$0.634017\pi$
$500$	−23.9513	−1.07114
$501$	39.1481	1.74901
$502$	14.8640	0.663413
$503$	14.4991	0.646481	0.323241	−	0.946317i	$-0.395228\pi$
$503$	14.4991	0.646481	0.323241	+	0.946317i	$0.395228\pi$
$504$	8.95520	0.398896
$505$	9.47594	0.421674
$506$	−8.28656	−0.368383
$507$	−45.0520	−2.00083
$508$	16.8274	0.746597
$509$	19.9684	0.885083	0.442542	−	0.896748i	$-0.354077\pi$
$509$	19.9684	0.885083	0.442542	+	0.896748i	$0.354077\pi$
$510$	64.0140	2.83459
$511$	22.7838	1.00790
$512$	1.00000	0.0441942
$513$	−7.03043	−0.310401
$514$	−0.261431	−0.0115312
$515$	−74.4931	−3.28256
$516$	−19.0986	−0.840771
$517$	−12.1459	−0.534178
$518$	27.2319	1.19650
$519$	−30.4504	−1.33662
$520$	−22.0979	−0.969057
$521$	−27.9548	−1.22472	−0.612361	−	0.790578i	$-0.709780\pi$
$521$	−27.9548	−1.22472	−0.612361	+	0.790578i	$0.709780\pi$
$522$	−21.1461	−0.925541
$523$	−18.1581	−0.793996	−0.396998	−	0.917819i	$-0.629948\pi$
$523$	−18.1581	−0.793996	−0.396998	+	0.917819i	$0.629948\pi$
$524$	13.3297	0.582310
$525$	−70.2629	−3.06653
$526$	0.582502	0.0253983
$527$	6.23239	0.271487
$528$	−9.69617	−0.421972
$529$	−18.1811	−0.790483
$530$	17.9127	0.778077
$531$	−0.243251	−0.0105562
$532$	11.3965	0.494099
$533$	−51.9445	−2.24997
$534$	−45.0169	−1.94807
$535$	61.5981	2.66312
$536$	−12.0418	−0.520126
$537$	38.9185	1.67946
$538$	9.99751	0.431023
$539$	−3.03679	−0.130804
$540$	6.14005	0.264226
$541$	−7.00816	−0.301304	−0.150652	−	0.988587i	$-0.548137\pi$
$541$	−7.00816	−0.301304	−0.150652	+	0.988587i	$0.548137\pi$
$542$	−3.96960	−0.170509
$543$	42.9187	1.84182
$544$	6.23239	0.267212
$545$	−56.9468	−2.43933
$546$	−35.3320	−1.51207
$547$	11.5252	0.492784	0.246392	−	0.969170i	$-0.420755\pi$
$547$	11.5252	0.492784	0.246392	+	0.969170i	$0.420755\pi$
$548$	−7.17933	−0.306686
$549$	6.04405	0.257954
$550$	41.4848	1.76892
$551$	−26.9107	−1.14643
$552$	5.63862	0.239996
$553$	−23.9306	−1.01763
$554$	−4.11837	−0.174973
$555$	112.372	4.76994
$556$	−1.59476	−0.0676327
$557$	35.8588	1.51939	0.759693	−	0.650282i	$-0.225349\pi$
$557$	35.8588	1.51939	0.759693	+	0.650282i	$0.225349\pi$
$558$	3.59779	0.152307
$559$	41.0897	1.73791
$560$	−9.95313	−0.420597
$561$	−60.4304	−2.55137
$562$	23.7610	1.00230
$563$	25.4679	1.07334	0.536671	−	0.843791i	$-0.319681\pi$
$563$	25.4679	1.07334	0.536671	+	0.843791i	$0.319681\pi$
$564$	8.26475	0.348009
$565$	70.5937	2.96990
$566$	−9.59523	−0.403317
$567$	−17.0484	−0.715964
$568$	4.55968	0.191320
$569$	−6.09259	−0.255415	−0.127707	−	0.991812i	$-0.540762\pi$
$569$	−6.09259	−0.255415	−0.127707	+	0.991812i	$0.540762\pi$
$570$	47.0274	1.96976
$571$	27.0734	1.13299	0.566494	−	0.824066i	$-0.308300\pi$
$571$	27.0734	1.13299	0.566494	+	0.824066i	$0.308300\pi$
$572$	20.8608	0.872235
$573$	45.7695	1.91205
$574$	−23.3964	−0.976545
$575$	−24.1247	−1.00607
$576$	3.59779	0.149908
$577$	−35.1607	−1.46376	−0.731880	−	0.681434i	$-0.761357\pi$
$577$	−35.1607	−1.46376	−0.731880	+	0.681434i	$0.761357\pi$
$578$	21.8427	0.908537
$579$	−7.69266	−0.319696
$580$	23.5026	0.975891
$581$	33.5043	1.38999
$582$	−2.56862	−0.106473
$583$	−16.9099	−0.700336
$584$	9.15350	0.378775
$585$	−79.5037	−3.28707
$586$	−6.47244	−0.267374
$587$	−0.926276	−0.0382315	−0.0191158	−	0.999817i	$-0.506085\pi$
$587$	−0.926276	−0.0382315	−0.0191158	+	0.999817i	$0.506085\pi$
$588$	2.06639	0.0852165
$589$	4.57858	0.188657
$590$	0.270358	0.0111305
$591$	−58.8061	−2.41896
$592$	10.9406	0.449654
$593$	1.24907	0.0512932	0.0256466	−	0.999671i	$-0.491836\pi$
$593$	1.24907	0.0512932	0.0256466	+	0.999671i	$0.491836\pi$
$594$	−5.79632	−0.237826
$595$	−62.0318	−2.54306
$596$	10.0637	0.412227
$597$	17.6089	0.720684
$598$	−12.1312	−0.496082
$599$	27.1535	1.10946	0.554731	−	0.832030i	$-0.312821\pi$
$599$	27.1535	1.10946	0.554731	+	0.832030i	$0.312821\pi$
$600$	−28.2285	−1.15242
$601$	2.74790	0.112089	0.0560446	−	0.998428i	$-0.482151\pi$
$601$	2.74790	0.112089	0.0560446	+	0.998428i	$0.482151\pi$
$602$	18.5073	0.754300
$603$	−43.3239	−1.76428
$604$	−21.0358	−0.855936
$605$	−12.9941	−0.528287
$606$	6.08696	0.247266
$607$	−4.14219	−0.168126	−0.0840631	−	0.996460i	$-0.526790\pi$
$607$	−4.14219	−0.168126	−0.0840631	+	0.996460i	$0.526790\pi$
$608$	4.57858	0.185686
$609$	37.5779	1.52273
$610$	−6.71758	−0.271987
$611$	−17.7812	−0.719350
$612$	22.4229	0.906391
$613$	38.0165	1.53547	0.767736	−	0.640767i	$-0.221383\pi$
$613$	38.0165	1.53547	0.767736	+	0.640767i	$0.221383\pi$
$614$	10.0678	0.406302
$615$	−96.5449	−3.89307
$616$	9.39594	0.378573
$617$	−45.6904	−1.83942	−0.919712	−	0.392593i	$-0.871578\pi$
$617$	−45.6904	−1.83942	−0.919712	+	0.392593i	$0.871578\pi$
$618$	−47.8514	−1.92487
$619$	10.7710	0.432924	0.216462	−	0.976291i	$-0.430548\pi$
$619$	10.7710	0.432924	0.216462	+	0.976291i	$0.430548\pi$
$620$	−3.99872	−0.160592
$621$	3.37073	0.135263
$622$	3.88436	0.155749
$623$	43.6230	1.74772
$624$	−14.1948	−0.568247
$625$	40.8258	1.63303
$626$	5.46605	0.218467
$627$	−44.3947	−1.77295
$628$	−0.656314	−0.0261898
$629$	68.1858	2.71875
$630$	−35.8093	−1.42668
$631$	29.4168	1.17106	0.585532	−	0.810649i	$-0.300886\pi$
$631$	29.4168	1.17106	0.585532	+	0.810649i	$0.300886\pi$
$632$	−9.61424	−0.382434
$633$	−23.0908	−0.917779
$634$	29.6927	1.17925
$635$	−67.2882	−2.67025
$636$	11.5064	0.456258
$637$	−4.44573	−0.176146
$638$	−22.1868	−0.878385
$639$	16.4048	0.648963
$640$	−3.99872	−0.158063
$641$	−26.1421	−1.03255	−0.516276	−	0.856422i	$-0.672682\pi$
$641$	−26.1421	−1.03255	−0.516276	+	0.856422i	$0.672682\pi$
$642$	39.5681	1.56163
$643$	42.2819	1.66743	0.833717	−	0.552192i	$-0.186208\pi$
$643$	42.2819	1.66743	0.833717	+	0.552192i	$0.186208\pi$
$644$	−5.46402	−0.215313
$645$	76.3701	3.00707
$646$	28.5355	1.12271
$647$	34.5989	1.36022	0.680112	−	0.733108i	$-0.261931\pi$
$647$	34.5989	1.36022	0.680112	+	0.733108i	$0.261931\pi$
$648$	−6.84926	−0.269064
$649$	−0.255223	−0.0100184
$650$	60.7321	2.38211
$651$	−6.39350	−0.250581
$652$	−9.74000	−0.381448
$653$	34.9185	1.36647	0.683234	−	0.730199i	$-0.260573\pi$
$653$	34.9185	1.36647	0.683234	+	0.730199i	$0.260573\pi$
$654$	−36.5804	−1.43041
$655$	−53.3016	−2.08267
$656$	−9.39959	−0.366992
$657$	32.9324	1.28482
$658$	−8.00883	−0.312217
$659$	38.7767	1.51053	0.755263	−	0.655422i	$-0.227509\pi$
$659$	38.7767	1.51053	0.755263	+	0.655422i	$0.227509\pi$
$660$	38.7723	1.50921
$661$	7.20755	0.280341	0.140171	−	0.990127i	$-0.455235\pi$
$661$	7.20755	0.280341	0.140171	+	0.990127i	$0.455235\pi$
$662$	−22.0643	−0.857555
$663$	−88.4677	−3.43580
$664$	13.4605	0.522370
$665$	−45.5712	−1.76718
$666$	39.3619	1.52524
$667$	12.9023	0.499580
$668$	−15.2409	−0.589688
$669$	−3.65875	−0.141455
$670$	48.1517	1.86026
$671$	6.34152	0.244811
$672$	−6.39350	−0.246634
$673$	−22.9400	−0.884273	−0.442136	−	0.896948i	$-0.645779\pi$
$673$	−22.9400	−0.884273	−0.442136	+	0.896948i	$0.645779\pi$
$674$	19.4871	0.750614
$675$	−16.8748	−0.649512
$676$	17.5394	0.674593
$677$	−33.9685	−1.30552	−0.652758	−	0.757567i	$-0.726388\pi$
$677$	−33.9685	−1.30552	−0.652758	+	0.757567i	$0.726388\pi$
$678$	45.3466	1.74152
$679$	2.48908	0.0955222
$680$	−24.9216	−0.955699
$681$	−30.8714	−1.18300
$682$	3.77486	0.144547
$683$	−13.5034	−0.516692	−0.258346	−	0.966052i	$-0.583177\pi$
$683$	−13.5034	−0.516692	−0.258346	+	0.966052i	$0.583177\pi$
$684$	16.4728	0.629853
$685$	28.7081	1.09688
$686$	−19.4260	−0.741687
$687$	4.51225	0.172153
$688$	7.43538	0.283471
$689$	−24.7554	−0.943106
$690$	−22.5473	−0.858359
$691$	25.2902	0.962084	0.481042	−	0.876698i	$-0.340258\pi$
$691$	25.2902	0.962084	0.481042	+	0.876698i	$0.340258\pi$
$692$	11.8548	0.450651
$693$	33.8046	1.28413
$694$	−12.1835	−0.462481
$695$	6.37698	0.241893
$696$	15.0971	0.572254
$697$	−58.5820	−2.21895
$698$	−20.9998	−0.794853
$699$	75.0404	2.83829
$700$	27.3544	1.03390
$701$	11.5972	0.438021	0.219010	−	0.975723i	$-0.429717\pi$
$701$	11.5972	0.438021	0.219010	+	0.975723i	$0.429717\pi$
$702$	−8.48558	−0.320267
$703$	50.0922	1.88926
$704$	3.77486	0.142270
$705$	−33.0484	−1.24467
$706$	−27.0945	−1.01971
$707$	−5.89848	−0.221835
$708$	0.173667	0.00652682
$709$	−3.70897	−0.139293	−0.0696466	−	0.997572i	$-0.522187\pi$
$709$	−3.70897	−0.139293	−0.0696466	+	0.997572i	$0.522187\pi$
$710$	−18.2329	−0.684267
$711$	−34.5901	−1.29723
$712$	17.5257	0.656804
$713$	−2.19520	−0.0822108
$714$	−39.8468	−1.49123
$715$	−83.4165	−3.11960
$716$	−15.1515	−0.566239
$717$	−5.90058	−0.220361
$718$	−5.66785	−0.211522
$719$	39.5026	1.47320	0.736599	−	0.676330i	$-0.236431\pi$
$719$	39.5026	1.47320	0.736599	+	0.676330i	$0.236431\pi$
$720$	−14.3866	−0.536156
$721$	46.3697	1.72690
$722$	1.96338	0.0730694
$723$	37.7044	1.40224
$724$	−16.7089	−0.620981
$725$	−64.5925	−2.39891
$726$	−8.34692	−0.309783
$727$	−12.6490	−0.469125	−0.234562	−	0.972101i	$-0.575366\pi$
$727$	−12.6490	−0.469125	−0.234562	+	0.972101i	$0.575366\pi$
$728$	13.7553	0.509805
$729$	−36.4746	−1.35091
$730$	−36.6023	−1.35471
$731$	46.3402	1.71395
$732$	−4.31511	−0.159491
$733$	5.04112	0.186198	0.0930990	−	0.995657i	$-0.470323\pi$
$733$	5.04112	0.186198	0.0930990	+	0.995657i	$0.470323\pi$
$734$	−16.9432	−0.625386
$735$	−8.26291	−0.304782
$736$	−2.19520	−0.0809160
$737$	−45.4561	−1.67440
$738$	−33.8178	−1.24485
$739$	−37.7326	−1.38802	−0.694009	−	0.719967i	$-0.744157\pi$
$739$	−37.7326	−1.38802	−0.694009	+	0.719967i	$0.744157\pi$
$740$	−43.7482	−1.60822
$741$	−64.9921	−2.38754
$742$	−11.1501	−0.409333
$743$	−7.47998	−0.274414	−0.137207	−	0.990542i	$-0.543813\pi$
$743$	−7.47998	−0.274414	−0.137207	+	0.990542i	$0.543813\pi$
$744$	−2.56862	−0.0941701
$745$	−40.2421	−1.47436
$746$	15.5397	0.568948
$747$	48.4282	1.77189
$748$	23.5264	0.860211
$749$	−38.3429	−1.40102
$750$	61.5218	2.24646
$751$	28.8935	1.05434	0.527169	−	0.849760i	$-0.323253\pi$
$751$	28.8935	1.05434	0.527169	+	0.849760i	$0.323253\pi$
$752$	−3.21759	−0.117333
$753$	−38.1799	−1.39135
$754$	−32.4807	−1.18288
$755$	84.1164	3.06131
$756$	−3.82199	−0.139005
$757$	15.0969	0.548707	0.274353	−	0.961629i	$-0.411536\pi$
$757$	15.0969	0.548707	0.274353	+	0.961629i	$0.411536\pi$
$758$	−34.7018	−1.26042
$759$	21.2850	0.772597
$760$	−18.3084	−0.664117
$761$	−49.6562	−1.80003	−0.900017	−	0.435854i	$-0.856446\pi$
$761$	−49.6562	−1.80003	−0.900017	+	0.435854i	$0.856446\pi$
$762$	−43.2233	−1.56581
$763$	35.4477	1.28329
$764$	−17.8187	−0.644659
$765$	−89.6627	−3.24176
$766$	32.3372	1.16839
$767$	−0.373637	−0.0134912
$768$	−2.56862	−0.0926870
$769$	17.3584	0.625961	0.312980	−	0.949760i	$-0.398673\pi$
$769$	17.3584	0.625961	0.312980	+	0.949760i	$0.398673\pi$
$770$	−37.5717	−1.35399
$771$	0.671517	0.0241841
$772$	2.99486	0.107787
$773$	−38.2195	−1.37466	−0.687331	−	0.726345i	$-0.741218\pi$
$773$	−38.2195	−1.37466	−0.687331	+	0.726345i	$0.741218\pi$
$774$	26.7510	0.961543
$775$	10.9897	0.394763
$776$	1.00000	0.0358979
$777$	−69.9484	−2.50938
$778$	16.6798	0.597999
$779$	−43.0368	−1.54195
$780$	56.7611	2.03237
$781$	17.2121	0.615899
$782$	−13.6813	−0.489243
$783$	9.02496	0.322526
$784$	−0.804476	−0.0287313
$785$	2.62442	0.0936694
$786$	−34.2389	−1.22126
$787$	−12.1287	−0.432340	−0.216170	−	0.976356i	$-0.569357\pi$
$787$	−12.1287	−0.432340	−0.216170	+	0.976356i	$0.569357\pi$
$788$	22.8941	0.815568
$789$	−1.49622	−0.0532670
$790$	38.4446	1.36780
$791$	−43.9424	−1.56241
$792$	13.5812	0.482586
$793$	9.28373	0.329675
$794$	−17.2010	−0.610442
$795$	−46.0108	−1.63184
$796$	−6.85540	−0.242983
$797$	−48.6755	−1.72418	−0.862088	−	0.506758i	$-0.830844\pi$
$797$	−48.6755	−1.72418	−0.862088	+	0.506758i	$0.830844\pi$
$798$	−29.2731	−1.03626
$799$	−20.0533	−0.709433
$800$	10.9897	0.388546
$801$	63.0540	2.22790
$802$	−19.1460	−0.676068
$803$	34.5532	1.21936
$804$	30.9307	1.09084
$805$	21.8491	0.770079
$806$	5.52625	0.194654
$807$	−25.6798	−0.903970
$808$	−2.36974	−0.0833673
$809$	−8.85326	−0.311264	−0.155632	−	0.987815i	$-0.549741\pi$
$809$	−8.85326	−0.311264	−0.155632	+	0.987815i	$0.549741\pi$
$810$	27.3883	0.962325
$811$	10.5182	0.369343	0.184672	−	0.982800i	$-0.440878\pi$
$811$	10.5182	0.369343	0.184672	+	0.982800i	$0.440878\pi$
$812$	−14.6296	−0.513399
$813$	10.1964	0.357603
$814$	41.2991	1.44753
$815$	38.9475	1.36427
$816$	−16.0086	−0.560414
$817$	34.0435	1.19103
$818$	−8.19984	−0.286701
$819$	49.4887	1.72927
$820$	37.5863	1.31257
$821$	15.4342	0.538656	0.269328	−	0.963049i	$-0.413198\pi$
$821$	15.4342	0.538656	0.269328	+	0.963049i	$0.413198\pi$
$822$	18.4409	0.643202
$823$	−29.1217	−1.01512	−0.507560	−	0.861617i	$-0.669452\pi$
$823$	−29.1217	−1.01512	−0.507560	+	0.861617i	$0.669452\pi$
$824$	18.6293	0.648981
$825$	−106.559	−3.70989
$826$	−0.168290	−0.00585555
$827$	−22.3665	−0.777761	−0.388880	−	0.921288i	$-0.627138\pi$
$827$	−22.3665	−0.777761	−0.388880	+	0.921288i	$0.627138\pi$
$828$	−7.89787	−0.274470
$829$	−27.9612	−0.971134	−0.485567	−	0.874199i	$-0.661387\pi$
$829$	−27.9612	−0.971134	−0.485567	+	0.874199i	$0.661387\pi$
$830$	−53.8248	−1.86829
$831$	10.5785	0.366965
$832$	5.52625	0.191588
$833$	−5.01381	−0.173718
$834$	4.09632	0.141844
$835$	60.9441	2.10906
$836$	17.2835	0.597762
$837$	−1.53550	−0.0530748
$838$	6.20134	0.214222
$839$	17.1819	0.593185	0.296592	−	0.955004i	$-0.404150\pi$
$839$	17.1819	0.593185	0.296592	+	0.955004i	$0.404150\pi$
$840$	25.5658	0.882104
$841$	5.54528	0.191217
$842$	17.8184	0.614064
$843$	−61.0329	−2.10209
$844$	8.98960	0.309435
$845$	−70.1352	−2.41272
$846$	−11.5762	−0.397998
$847$	8.08846	0.277923
$848$	−4.47960	−0.153830
$849$	24.6465	0.845864
$850$	68.4924	2.34927
$851$	−24.0167	−0.823281
$852$	−11.7121	−0.401249
$853$	−30.3957	−1.04073	−0.520364	−	0.853945i	$-0.674204\pi$
$853$	−30.3957	−1.04073	−0.520364	+	0.853945i	$0.674204\pi$
$854$	4.18149	0.143088
$855$	−65.8700	−2.25271
$856$	−15.4044	−0.526513
$857$	−53.0756	−1.81303	−0.906514	−	0.422175i	$-0.861267\pi$
$857$	−53.0756	−1.81303	−0.906514	+	0.422175i	$0.861267\pi$
$858$	−53.5835	−1.82931
$859$	5.80244	0.197977	0.0989884	−	0.995089i	$-0.468439\pi$
$859$	5.80244	0.197977	0.0989884	+	0.995089i	$0.468439\pi$
$860$	−29.7320	−1.01385
$861$	60.0963	2.04808
$862$	1.74095	0.0592970
$863$	1.11871	0.0380812	0.0190406	−	0.999819i	$-0.493939\pi$
$863$	1.11871	0.0380812	0.0190406	+	0.999819i	$0.493939\pi$
$864$	−1.53550	−0.0522389
$865$	−47.4039	−1.61178
$866$	7.26284	0.246802
$867$	−56.1056	−1.90545
$868$	2.48908	0.0844849
$869$	−36.2924	−1.23114
$870$	−60.3691	−2.04670
$871$	−66.5459	−2.25482
$872$	14.2413	0.482270
$873$	3.59779	0.121767
$874$	−10.0509	−0.339976
$875$	−59.6168	−2.01541
$876$	−23.5118	−0.794391
$877$	−50.8503	−1.71709	−0.858547	−	0.512736i	$-0.828632\pi$
$877$	−50.8503	−1.71709	−0.858547	+	0.512736i	$0.828632\pi$
$878$	27.4372	0.925961
$879$	16.6252	0.560755
$880$	−15.0946	−0.508839
$881$	44.8975	1.51264	0.756318	−	0.654204i	$-0.226996\pi$
$881$	44.8975	1.51264	0.756318	+	0.654204i	$0.226996\pi$
$882$	−2.89434	−0.0974575
$883$	25.9141	0.872079	0.436039	−	0.899928i	$-0.356381\pi$
$883$	25.9141	0.872079	0.436039	+	0.899928i	$0.356381\pi$
$884$	34.4417	1.15840
$885$	−0.694447	−0.0233436
$886$	4.19189	0.140829
$887$	−5.91344	−0.198554	−0.0992770	−	0.995060i	$-0.531653\pi$
$887$	−5.91344	−0.198554	−0.0992770	+	0.995060i	$0.531653\pi$
$888$	−28.1021	−0.943045
$889$	41.8849	1.40477
$890$	−70.0804	−2.34910
$891$	−25.8550	−0.866175
$892$	1.42440	0.0476925
$893$	−14.7320	−0.492987
$894$	−25.8499	−0.864550
$895$	60.5867	2.02519
$896$	2.48908	0.0831544
$897$	31.1604	1.04042
$898$	−26.4848	−0.883808
$899$	−5.87752	−0.196026
$900$	39.5389	1.31796
$901$	−27.9187	−0.930105
$902$	−35.4822	−1.18143
$903$	−47.5381	−1.58197
$904$	−17.6541	−0.587166
$905$	66.8141	2.22098
$906$	54.0330	1.79513
$907$	−16.7549	−0.556336	−0.278168	−	0.960532i	$-0.589727\pi$
$907$	−16.7549	−0.556336	−0.278168	+	0.960532i	$0.589727\pi$
$908$	12.0187	0.398855
$909$	−8.52585	−0.282785
$910$	−55.0035	−1.82335
$911$	51.9160	1.72005	0.860027	−	0.510248i	$-0.170446\pi$
$911$	51.9160	1.72005	0.860027	+	0.510248i	$0.170446\pi$
$912$	−11.7606	−0.389433
$913$	50.8116	1.68162
$914$	−5.23954	−0.173308
$915$	17.2549	0.570429
$916$	−1.75668	−0.0580425
$917$	33.1787	1.09566
$918$	−9.56987	−0.315853
$919$	−18.9379	−0.624703	−0.312352	−	0.949967i	$-0.601117\pi$
$919$	−18.9379	−0.624703	−0.312352	+	0.949967i	$0.601117\pi$
$920$	8.77797	0.289401
$921$	−25.8602	−0.852123
$922$	−10.6726	−0.351483
$923$	25.1979	0.829399
$924$	−24.1346	−0.793969
$925$	120.234	3.95327
$926$	24.1562	0.793823
$927$	67.0242	2.20136
$928$	−5.87752	−0.192939
$929$	4.62856	0.151858	0.0759291	−	0.997113i	$-0.475808\pi$
$929$	4.62856	0.151858	0.0759291	+	0.997113i	$0.475808\pi$
$930$	10.2712	0.336805
$931$	−3.68336	−0.120717
$932$	−29.2143	−0.956947
$933$	−9.97744	−0.326647
$934$	2.16555	0.0708589
$935$	−94.0755	−3.07660
$936$	19.8823	0.649873
$937$	−28.6398	−0.935622	−0.467811	−	0.883829i	$-0.654957\pi$
$937$	−28.6398	−0.935622	−0.467811	+	0.883829i	$0.654957\pi$
$938$	−29.9730	−0.978653
$939$	−14.0402	−0.458184
$940$	12.8662	0.419650
$941$	21.1194	0.688472	0.344236	−	0.938883i	$-0.388138\pi$
$941$	21.1194	0.688472	0.344236	+	0.938883i	$0.388138\pi$
$942$	1.68582	0.0549270
$943$	20.6340	0.671934
$944$	−0.0676113	−0.00220056
$945$	15.2831	0.497159
$946$	28.0675	0.912554
$947$	−42.6435	−1.38573	−0.692864	−	0.721068i	$-0.743652\pi$
$947$	−42.6435	−1.38573	−0.692864	+	0.721068i	$0.743652\pi$
$948$	24.6953	0.802066
$949$	50.5845	1.64204
$950$	50.3174	1.63251
$951$	−76.2691	−2.47320
$952$	15.5129	0.502777
$953$	36.6548	1.18737	0.593683	−	0.804699i	$-0.297673\pi$
$953$	36.6548	1.18737	0.593683	+	0.804699i	$0.297673\pi$
$954$	−16.1167	−0.521797
$955$	71.2521	2.30566
$956$	2.29718	0.0742961
$957$	56.9895	1.84221
$958$	30.8126	0.995508
$959$	−17.8699	−0.577050
$960$	10.2712	0.331501
$961$	1.00000	0.0322581
$962$	60.4602	1.94932
$963$	−55.4220	−1.78595
$964$	−14.6789	−0.472775
$965$	−11.9756	−0.385509
$966$	14.0350	0.451568
$967$	−22.8313	−0.734204	−0.367102	−	0.930181i	$-0.619650\pi$
$967$	−22.8313	−0.734204	−0.367102	+	0.930181i	$0.619650\pi$
$968$	3.24958	0.104445
$969$	−73.2968	−2.35463
$970$	−3.99872	−0.128391
$971$	27.0635	0.868510	0.434255	−	0.900790i	$-0.357012\pi$
$971$	27.0635	0.868510	0.434255	+	0.900790i	$0.357012\pi$
$972$	22.1996	0.712054
$973$	−3.96948	−0.127256
$974$	−5.22519	−0.167426
$975$	−155.997	−4.99592
$976$	1.67993	0.0537734
$977$	−29.3611	−0.939346	−0.469673	−	0.882841i	$-0.655628\pi$
$977$	−29.3611	−0.939346	−0.469673	+	0.882841i	$0.655628\pi$
$978$	25.0183	0.799998
$979$	66.1572	2.11439
$980$	3.21687	0.102759
$981$	51.2371	1.63588
$982$	24.4311	0.779627
$983$	54.8497	1.74943	0.874717	−	0.484634i	$-0.161047\pi$
$983$	54.8497	1.74943	0.874717	+	0.484634i	$0.161047\pi$
$984$	24.1440	0.769681
$985$	−91.5470	−2.91693
$986$	−36.6310	−1.16657
$987$	20.5716	0.654802
$988$	25.3024	0.804975
$989$	−16.3221	−0.519013
$990$	−54.3073	−1.72600
$991$	12.9666	0.411897	0.205949	−	0.978563i	$-0.433972\pi$
$991$	12.9666	0.411897	0.205949	+	0.978563i	$0.433972\pi$
$992$	1.00000	0.0317500
$993$	56.6748	1.79852
$994$	11.3494	0.359981
$995$	27.4128	0.869045
$996$	−34.5749	−1.09555
$997$	42.5417	1.34731	0.673655	−	0.739046i	$-0.264724\pi$
$997$	42.5417	1.34731	0.673655	+	0.739046i	$0.264724\pi$
$998$	−18.2592	−0.577985
$999$	−16.7993	−0.531505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.5	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.56862 q^{3} +1.00000 q^{4} -3.99872 q^{5} -2.56862 q^{6} +2.48908 q^{7} +1.00000 q^{8} +3.59779 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.56862 q^{3} +1.00000 q^{4} -3.99872 q^{5} -2.56862 q^{6} +2.48908 q^{7} +1.00000 q^{8} +3.59779 q^{9} -3.99872 q^{10} +3.77486 q^{11} -2.56862 q^{12} +5.52625 q^{13} +2.48908 q^{14} +10.2712 q^{15} +1.00000 q^{16} +6.23239 q^{17} +3.59779 q^{18} +4.57858 q^{19} -3.99872 q^{20} -6.39350 q^{21} +3.77486 q^{22} -2.19520 q^{23} -2.56862 q^{24} +10.9897 q^{25} +5.52625 q^{26} -1.53550 q^{27} +2.48908 q^{28} -5.87752 q^{29} +10.2712 q^{30} +1.00000 q^{31} +1.00000 q^{32} -9.69617 q^{33} +6.23239 q^{34} -9.95313 q^{35} +3.59779 q^{36} +10.9406 q^{37} +4.57858 q^{38} -14.1948 q^{39} -3.99872 q^{40} -9.39959 q^{41} -6.39350 q^{42} +7.43538 q^{43} +3.77486 q^{44} -14.3866 q^{45} -2.19520 q^{46} -3.21759 q^{47} -2.56862 q^{48} -0.804476 q^{49} +10.9897 q^{50} -16.0086 q^{51} +5.52625 q^{52} -4.47960 q^{53} -1.53550 q^{54} -15.0946 q^{55} +2.48908 q^{56} -11.7606 q^{57} -5.87752 q^{58} -0.0676113 q^{59} +10.2712 q^{60} +1.67993 q^{61} +1.00000 q^{62} +8.95520 q^{63} +1.00000 q^{64} -22.0979 q^{65} -9.69617 q^{66} -12.0418 q^{67} +6.23239 q^{68} +5.63862 q^{69} -9.95313 q^{70} +4.55968 q^{71} +3.59779 q^{72} +9.15350 q^{73} +10.9406 q^{74} -28.2285 q^{75} +4.57858 q^{76} +9.39594 q^{77} -14.1948 q^{78} -9.61424 q^{79} -3.99872 q^{80} -6.84926 q^{81} -9.39959 q^{82} +13.4605 q^{83} -6.39350 q^{84} -24.9216 q^{85} +7.43538 q^{86} +15.0971 q^{87} +3.77486 q^{88} +17.5257 q^{89} -14.3866 q^{90} +13.7553 q^{91} -2.19520 q^{92} -2.56862 q^{93} -3.21759 q^{94} -18.3084 q^{95} -2.56862 q^{96} +1.00000 q^{97} -0.804476 q^{98} +13.5812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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