LMFDB - Embedded newform 4730.2.a.ba.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 21x^{8} + 22x^{7} + 138x^{6} - 154x^{5} - 291x^{4} + 327x^{3} + 97x^{2} - 124x + 16 $ x^10 - x^9 - 21x^8 + 22x^7 + 138x^6 - 154x^5 - 291x^4 + 327x^3 + 97x^2 - 124x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.18792$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.18792 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.18792 q^{6} -0.664484 q^{7} +1.00000 q^{8} +1.78700 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.18792 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.18792 q^{6} -0.664484 q^{7} +1.00000 q^{8} +1.78700 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.18792 q^{12} +6.41837 q^{13} -0.664484 q^{14} +2.18792 q^{15} +1.00000 q^{16} +1.04726 q^{17} +1.78700 q^{18} +2.70107 q^{19} -1.00000 q^{20} +1.45384 q^{21} -1.00000 q^{22} +1.48315 q^{23} -2.18792 q^{24} +1.00000 q^{25} +6.41837 q^{26} +2.65394 q^{27} -0.664484 q^{28} -5.23155 q^{29} +2.18792 q^{30} -9.58464 q^{31} +1.00000 q^{32} +2.18792 q^{33} +1.04726 q^{34} +0.664484 q^{35} +1.78700 q^{36} -8.21694 q^{37} +2.70107 q^{38} -14.0429 q^{39} -1.00000 q^{40} +4.09505 q^{41} +1.45384 q^{42} -1.00000 q^{43} -1.00000 q^{44} -1.78700 q^{45} +1.48315 q^{46} -4.37481 q^{47} -2.18792 q^{48} -6.55846 q^{49} +1.00000 q^{50} -2.29133 q^{51} +6.41837 q^{52} +5.31442 q^{53} +2.65394 q^{54} +1.00000 q^{55} -0.664484 q^{56} -5.90974 q^{57} -5.23155 q^{58} +9.72381 q^{59} +2.18792 q^{60} +10.6419 q^{61} -9.58464 q^{62} -1.18744 q^{63} +1.00000 q^{64} -6.41837 q^{65} +2.18792 q^{66} -0.258038 q^{67} +1.04726 q^{68} -3.24501 q^{69} +0.664484 q^{70} +3.31954 q^{71} +1.78700 q^{72} +2.54730 q^{73} -8.21694 q^{74} -2.18792 q^{75} +2.70107 q^{76} +0.664484 q^{77} -14.0429 q^{78} -2.27557 q^{79} -1.00000 q^{80} -11.1676 q^{81} +4.09505 q^{82} -13.4195 q^{83} +1.45384 q^{84} -1.04726 q^{85} -1.00000 q^{86} +11.4462 q^{87} -1.00000 q^{88} +11.7254 q^{89} -1.78700 q^{90} -4.26490 q^{91} +1.48315 q^{92} +20.9705 q^{93} -4.37481 q^{94} -2.70107 q^{95} -2.18792 q^{96} +4.68733 q^{97} -6.55846 q^{98} -1.78700 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * 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
$3$	−2.18792	−1.26320	−0.631599	−	0.775295i	$-0.717601\pi$
$3$	−2.18792	−1.26320	−0.631599	+	0.775295i	$0.717601\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.18792	−0.893216
$7$	−0.664484	−0.251151	−0.125576	−	0.992084i	$-0.540078\pi$
$7$	−0.664484	−0.251151	−0.125576	+	0.992084i	$0.540078\pi$
$8$	1.00000	0.353553
$9$	1.78700	0.595668
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.18792	−0.631599
$13$	6.41837	1.78013	0.890067	−	0.455829i	$-0.150657\pi$
$13$	6.41837	1.78013	0.890067	+	0.455829i	$0.150657\pi$
$14$	−0.664484	−0.177591
$15$	2.18792	0.564919
$16$	1.00000	0.250000
$17$	1.04726	0.253998	0.126999	−	0.991903i	$-0.459465\pi$
$17$	1.04726	0.253998	0.126999	+	0.991903i	$0.459465\pi$
$18$	1.78700	0.421201
$19$	2.70107	0.619668	0.309834	−	0.950791i	$-0.399726\pi$
$19$	2.70107	0.619668	0.309834	+	0.950791i	$0.399726\pi$
$20$	−1.00000	−0.223607
$21$	1.45384	0.317254
$22$	−1.00000	−0.213201
$23$	1.48315	0.309258	0.154629	−	0.987973i	$-0.450582\pi$
$23$	1.48315	0.309258	0.154629	+	0.987973i	$0.450582\pi$
$24$	−2.18792	−0.446608
$25$	1.00000	0.200000
$26$	6.41837	1.25875
$27$	2.65394	0.510751
$28$	−0.664484	−0.125576
$29$	−5.23155	−0.971475	−0.485737	−	0.874105i	$-0.661449\pi$
$29$	−5.23155	−0.971475	−0.485737	+	0.874105i	$0.661449\pi$
$30$	2.18792	0.399458
$31$	−9.58464	−1.72145	−0.860726	−	0.509068i	$-0.829990\pi$
$31$	−9.58464	−1.72145	−0.860726	+	0.509068i	$0.829990\pi$
$32$	1.00000	0.176777
$33$	2.18792	0.380868
$34$	1.04726	0.179604
$35$	0.664484	0.112318
$36$	1.78700	0.297834
$37$	−8.21694	−1.35086	−0.675429	−	0.737425i	$-0.736041\pi$
$37$	−8.21694	−1.35086	−0.675429	+	0.737425i	$0.736041\pi$
$38$	2.70107	0.438172
$39$	−14.0429	−2.24866
$40$	−1.00000	−0.158114
$41$	4.09505	0.639540	0.319770	−	0.947495i	$-0.396394\pi$
$41$	4.09505	0.639540	0.319770	+	0.947495i	$0.396394\pi$
$42$	1.45384	0.224332
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	−1.78700	−0.266391
$46$	1.48315	0.218678
$47$	−4.37481	−0.638132	−0.319066	−	0.947732i	$-0.603369\pi$
$47$	−4.37481	−0.638132	−0.319066	+	0.947732i	$0.603369\pi$
$48$	−2.18792	−0.315799
$49$	−6.55846	−0.936923
$50$	1.00000	0.141421
$51$	−2.29133	−0.320850
$52$	6.41837	0.890067
$53$	5.31442	0.729992	0.364996	−	0.931009i	$-0.381070\pi$
$53$	5.31442	0.729992	0.364996	+	0.931009i	$0.381070\pi$
$54$	2.65394	0.361155
$55$	1.00000	0.134840
$56$	−0.664484	−0.0887954
$57$	−5.90974	−0.782764
$58$	−5.23155	−0.686936
$59$	9.72381	1.26593	0.632966	−	0.774179i	$-0.281837\pi$
$59$	9.72381	1.26593	0.632966	+	0.774179i	$0.281837\pi$
$60$	2.18792	0.282460
$61$	10.6419	1.36256	0.681281	−	0.732022i	$-0.261423\pi$
$61$	10.6419	1.36256	0.681281	+	0.732022i	$0.261423\pi$
$62$	−9.58464	−1.21725
$63$	−1.18744	−0.149603
$64$	1.00000	0.125000
$65$	−6.41837	−0.796100
$66$	2.18792	0.269315
$67$	−0.258038	−0.0315244	−0.0157622	−	0.999876i	$-0.505017\pi$
$67$	−0.258038	−0.0315244	−0.0157622	+	0.999876i	$0.505017\pi$
$68$	1.04726	0.126999
$69$	−3.24501	−0.390654
$70$	0.664484	0.0794210
$71$	3.31954	0.393957	0.196978	−	0.980408i	$-0.436887\pi$
$71$	3.31954	0.393957	0.196978	+	0.980408i	$0.436887\pi$
$72$	1.78700	0.210601
$73$	2.54730	0.298139	0.149069	−	0.988827i	$-0.452372\pi$
$73$	2.54730	0.298139	0.149069	+	0.988827i	$0.452372\pi$
$74$	−8.21694	−0.955200
$75$	−2.18792	−0.252640
$76$	2.70107	0.309834
$77$	0.664484	0.0757249
$78$	−14.0429	−1.59004
$79$	−2.27557	−0.256021	−0.128011	−	0.991773i	$-0.540859\pi$
$79$	−2.27557	−0.256021	−0.128011	+	0.991773i	$0.540859\pi$
$80$	−1.00000	−0.111803
$81$	−11.1676	−1.24085
$82$	4.09505	0.452223
$83$	−13.4195	−1.47298	−0.736492	−	0.676446i	$-0.763519\pi$
$83$	−13.4195	−1.47298	−0.736492	+	0.676446i	$0.763519\pi$
$84$	1.45384	0.158627
$85$	−1.04726	−0.113591
$86$	−1.00000	−0.107833
$87$	11.4462	1.22716
$88$	−1.00000	−0.106600
$89$	11.7254	1.24289	0.621445	−	0.783458i	$-0.286546\pi$
$89$	11.7254	1.24289	0.621445	+	0.783458i	$0.286546\pi$
$90$	−1.78700	−0.188367
$91$	−4.26490	−0.447083
$92$	1.48315	0.154629
$93$	20.9705	2.17453
$94$	−4.37481	−0.451228
$95$	−2.70107	−0.277124
$96$	−2.18792	−0.223304
$97$	4.68733	0.475926	0.237963	−	0.971274i	$-0.423520\pi$
$97$	4.68733	0.475926	0.237963	+	0.971274i	$0.423520\pi$
$98$	−6.55846	−0.662505
$99$	−1.78700	−0.179601
$100$	1.00000	0.100000
$101$	−9.64532	−0.959745	−0.479873	−	0.877338i	$-0.659317\pi$
$101$	−9.64532	−0.959745	−0.479873	+	0.877338i	$0.659317\pi$
$102$	−2.29133	−0.226875
$103$	1.66531	0.164088	0.0820440	−	0.996629i	$-0.473855\pi$
$103$	1.66531	0.164088	0.0820440	+	0.996629i	$0.473855\pi$
$104$	6.41837	0.629373
$105$	−1.45384	−0.141880
$106$	5.31442	0.516182
$107$	10.3940	1.00483	0.502414	−	0.864627i	$-0.332445\pi$
$107$	10.3940	1.00483	0.502414	+	0.864627i	$0.332445\pi$
$108$	2.65394	0.255375
$109$	18.2855	1.75143	0.875715	−	0.482828i	$-0.160390\pi$
$109$	18.2855	1.75143	0.875715	+	0.482828i	$0.160390\pi$
$110$	1.00000	0.0953463
$111$	17.9780	1.70640
$112$	−0.664484	−0.0627878
$113$	11.3554	1.06822	0.534112	−	0.845414i	$-0.320646\pi$
$113$	11.3554	1.06822	0.534112	+	0.845414i	$0.320646\pi$
$114$	−5.90974	−0.553498
$115$	−1.48315	−0.138304
$116$	−5.23155	−0.485737
$117$	11.4697	1.06037
$118$	9.72381	0.895149
$119$	−0.695888	−0.0637920
$120$	2.18792	0.199729
$121$	1.00000	0.0909091
$122$	10.6419	0.963476
$123$	−8.95966	−0.807865
$124$	−9.58464	−0.860726
$125$	−1.00000	−0.0894427
$126$	−1.18744	−0.105785
$127$	9.07108	0.804928	0.402464	−	0.915436i	$-0.368154\pi$
$127$	9.07108	0.804928	0.402464	+	0.915436i	$0.368154\pi$
$128$	1.00000	0.0883883
$129$	2.18792	0.192636
$130$	−6.41837	−0.562928
$131$	14.7644	1.28997	0.644985	−	0.764195i	$-0.276864\pi$
$131$	14.7644	1.28997	0.644985	+	0.764195i	$0.276864\pi$
$132$	2.18792	0.190434
$133$	−1.79482	−0.155630
$134$	−0.258038	−0.0222911
$135$	−2.65394	−0.228415
$136$	1.04726	0.0898019
$137$	14.9880	1.28051	0.640257	−	0.768161i	$-0.278828\pi$
$137$	14.9880	1.28051	0.640257	+	0.768161i	$0.278828\pi$
$138$	−3.24501	−0.276234
$139$	−6.33659	−0.537462	−0.268731	−	0.963215i	$-0.586604\pi$
$139$	−6.33659	−0.537462	−0.268731	+	0.963215i	$0.586604\pi$
$140$	0.664484	0.0561591
$141$	9.57175	0.806087
$142$	3.31954	0.278570
$143$	−6.41837	−0.536731
$144$	1.78700	0.148917
$145$	5.23155	0.434457
$146$	2.54730	0.210816
$147$	14.3494	1.18352
$148$	−8.21694	−0.675429
$149$	23.4720	1.92290	0.961451	−	0.274977i	$-0.0886701\pi$
$149$	23.4720	1.92290	0.961451	+	0.274977i	$0.0886701\pi$
$150$	−2.18792	−0.178643
$151$	20.5670	1.67371	0.836857	−	0.547421i	$-0.184390\pi$
$151$	20.5670	1.67371	0.836857	+	0.547421i	$0.184390\pi$
$152$	2.70107	0.219086
$153$	1.87146	0.151299
$154$	0.664484	0.0535456
$155$	9.58464	0.769857
$156$	−14.0429	−1.12433
$157$	6.80128	0.542801	0.271400	−	0.962467i	$-0.412513\pi$
$157$	6.80128	0.542801	0.271400	+	0.962467i	$0.412513\pi$
$158$	−2.27557	−0.181034
$159$	−11.6275	−0.922124
$160$	−1.00000	−0.0790569
$161$	−0.985528	−0.0776705
$162$	−11.1676	−0.877412
$163$	−6.47629	−0.507262	−0.253631	−	0.967301i	$-0.581625\pi$
$163$	−6.47629	−0.507262	−0.253631	+	0.967301i	$0.581625\pi$
$164$	4.09505	0.319770
$165$	−2.18792	−0.170330
$166$	−13.4195	−1.04156
$167$	−3.67586	−0.284447	−0.142223	−	0.989835i	$-0.545425\pi$
$167$	−3.67586	−0.284447	−0.142223	+	0.989835i	$0.545425\pi$
$168$	1.45384	0.112166
$169$	28.1954	2.16888
$170$	−1.04726	−0.0803213
$171$	4.82683	0.369117
$172$	−1.00000	−0.0762493
$173$	−10.1084	−0.768529	−0.384265	−	0.923223i	$-0.625545\pi$
$173$	−10.1084	−0.768529	−0.384265	+	0.923223i	$0.625545\pi$
$174$	11.4462	0.867736
$175$	−0.664484	−0.0502302
$176$	−1.00000	−0.0753778
$177$	−21.2749	−1.59912
$178$	11.7254	0.878856
$179$	−10.7290	−0.801921	−0.400961	−	0.916095i	$-0.631324\pi$
$179$	−10.7290	−0.801921	−0.400961	+	0.916095i	$0.631324\pi$
$180$	−1.78700	−0.133195
$181$	23.4462	1.74274	0.871372	−	0.490622i	$-0.163231\pi$
$181$	23.4462	1.74274	0.871372	+	0.490622i	$0.163231\pi$
$182$	−4.26490	−0.316135
$183$	−23.2837	−1.72118
$184$	1.48315	0.109339
$185$	8.21694	0.604122
$186$	20.9705	1.53763
$187$	−1.04726	−0.0765833
$188$	−4.37481	−0.319066
$189$	−1.76350	−0.128276
$190$	−2.70107	−0.195956
$191$	−13.2886	−0.961530	−0.480765	−	0.876850i	$-0.659641\pi$
$191$	−13.2886	−0.961530	−0.480765	+	0.876850i	$0.659641\pi$
$192$	−2.18792	−0.157900
$193$	−22.1105	−1.59155	−0.795775	−	0.605592i	$-0.792936\pi$
$193$	−22.1105	−1.59155	−0.795775	+	0.605592i	$0.792936\pi$
$194$	4.68733	0.336531
$195$	14.0429	1.00563
$196$	−6.55846	−0.468462
$197$	−1.03178	−0.0735115	−0.0367558	−	0.999324i	$-0.511702\pi$
$197$	−1.03178	−0.0735115	−0.0367558	+	0.999324i	$0.511702\pi$
$198$	−1.78700	−0.126997
$199$	19.9151	1.41175	0.705873	−	0.708339i	$-0.250555\pi$
$199$	19.9151	1.41175	0.705873	+	0.708339i	$0.250555\pi$
$200$	1.00000	0.0707107
$201$	0.564568	0.0398215
$202$	−9.64532	−0.678642
$203$	3.47628	0.243987
$204$	−2.29133	−0.160425
$205$	−4.09505	−0.286011
$206$	1.66531	0.116028
$207$	2.65039	0.184215
$208$	6.41837	0.445034
$209$	−2.70107	−0.186837
$210$	−1.45384	−0.100324
$211$	11.9331	0.821507	0.410754	−	0.911746i	$-0.365266\pi$
$211$	11.9331	0.821507	0.410754	+	0.911746i	$0.365266\pi$
$212$	5.31442	0.364996
$213$	−7.26290	−0.497646
$214$	10.3940	0.710521
$215$	1.00000	0.0681994
$216$	2.65394	0.180578
$217$	6.36884	0.432345
$218$	18.2855	1.23845
$219$	−5.57329	−0.376608
$220$	1.00000	0.0674200
$221$	6.72171	0.452151
$222$	17.9780	1.20661
$223$	12.1000	0.810279	0.405139	−	0.914255i	$-0.367223\pi$
$223$	12.1000	0.810279	0.405139	+	0.914255i	$0.367223\pi$
$224$	−0.664484	−0.0443977
$225$	1.78700	0.119134
$226$	11.3554	0.755349
$227$	−28.2560	−1.87542	−0.937710	−	0.347420i	$-0.887058\pi$
$227$	−28.2560	−1.87542	−0.937710	+	0.347420i	$0.887058\pi$
$228$	−5.90974	−0.391382
$229$	9.65951	0.638318	0.319159	−	0.947701i	$-0.396600\pi$
$229$	9.65951	0.638318	0.319159	+	0.947701i	$0.396600\pi$
$230$	−1.48315	−0.0977959
$231$	−1.45384	−0.0956556
$232$	−5.23155	−0.343468
$233$	10.6087	0.694999	0.347499	−	0.937680i	$-0.387031\pi$
$233$	10.6087	0.694999	0.347499	+	0.937680i	$0.387031\pi$
$234$	11.4697	0.749795
$235$	4.37481	0.285381
$236$	9.72381	0.632966
$237$	4.97876	0.323405
$238$	−0.695888	−0.0451077
$239$	−11.9578	−0.773486	−0.386743	−	0.922188i	$-0.626400\pi$
$239$	−11.9578	−0.773486	−0.386743	+	0.922188i	$0.626400\pi$
$240$	2.18792	0.141230
$241$	−20.0705	−1.29285	−0.646427	−	0.762976i	$-0.723737\pi$
$241$	−20.0705	−1.29285	−0.646427	+	0.762976i	$0.723737\pi$
$242$	1.00000	0.0642824
$243$	16.4721	1.05668
$244$	10.6419	0.681281
$245$	6.55846	0.419005
$246$	−8.95966	−0.571247
$247$	17.3365	1.10309
$248$	−9.58464	−0.608625
$249$	29.3609	1.86067
$250$	−1.00000	−0.0632456
$251$	−24.5409	−1.54901	−0.774504	−	0.632569i	$-0.782000\pi$
$251$	−24.5409	−1.54901	−0.774504	+	0.632569i	$0.782000\pi$
$252$	−1.18744	−0.0748014
$253$	−1.48315	−0.0932448
$254$	9.07108	0.569170
$255$	2.29133	0.143488
$256$	1.00000	0.0625000
$257$	2.75951	0.172133	0.0860667	−	0.996289i	$-0.472570\pi$
$257$	2.75951	0.172133	0.0860667	+	0.996289i	$0.472570\pi$
$258$	2.18792	0.136214
$259$	5.46002	0.339269
$260$	−6.41837	−0.398050
$261$	−9.34881	−0.578677
$262$	14.7644	0.912146
$263$	−15.7409	−0.970626	−0.485313	−	0.874340i	$-0.661294\pi$
$263$	−15.7409	−0.970626	−0.485313	+	0.874340i	$0.661294\pi$
$264$	2.18792	0.134657
$265$	−5.31442	−0.326462
$266$	−1.79482	−0.110047
$267$	−25.6543	−1.57002
$268$	−0.258038	−0.0157622
$269$	5.15540	0.314330	0.157165	−	0.987572i	$-0.449765\pi$
$269$	5.15540	0.314330	0.157165	+	0.987572i	$0.449765\pi$
$270$	−2.65394	−0.161514
$271$	23.8725	1.45015	0.725075	−	0.688670i	$-0.241805\pi$
$271$	23.8725	1.45015	0.725075	+	0.688670i	$0.241805\pi$
$272$	1.04726	0.0634995
$273$	9.33127	0.564754
$274$	14.9880	0.905460
$275$	−1.00000	−0.0603023
$276$	−3.24501	−0.195327
$277$	4.42723	0.266006	0.133003	−	0.991116i	$-0.457538\pi$
$277$	4.42723	0.266006	0.133003	+	0.991116i	$0.457538\pi$
$278$	−6.33659	−0.380043
$279$	−17.1278	−1.02541
$280$	0.664484	0.0397105
$281$	−8.24133	−0.491636	−0.245818	−	0.969316i	$-0.579057\pi$
$281$	−8.24133	−0.491636	−0.245818	+	0.969316i	$0.579057\pi$
$282$	9.57175	0.569990
$283$	−20.8967	−1.24218	−0.621091	−	0.783738i	$-0.713310\pi$
$283$	−20.8967	−1.24218	−0.621091	+	0.783738i	$0.713310\pi$
$284$	3.31954	0.196978
$285$	5.90974	0.350063
$286$	−6.41837	−0.379526
$287$	−2.72109	−0.160621
$288$	1.78700	0.105300
$289$	−15.9032	−0.935485
$290$	5.23155	0.307207
$291$	−10.2555	−0.601189
$292$	2.54730	0.149069
$293$	−17.7196	−1.03519	−0.517594	−	0.855626i	$-0.673172\pi$
$293$	−17.7196	−1.03519	−0.517594	+	0.855626i	$0.673172\pi$
$294$	14.3494	0.836874
$295$	−9.72381	−0.566142
$296$	−8.21694	−0.477600
$297$	−2.65394	−0.153997
$298$	23.4720	1.35970
$299$	9.51939	0.550521
$300$	−2.18792	−0.126320
$301$	0.664484	0.0383002
$302$	20.5670	1.18350
$303$	21.1032	1.21235
$304$	2.70107	0.154917
$305$	−10.6419	−0.609356
$306$	1.87146	0.106984
$307$	27.4396	1.56606	0.783031	−	0.621983i	$-0.213673\pi$
$307$	27.4396	1.56606	0.783031	+	0.621983i	$0.213673\pi$
$308$	0.664484	0.0378625
$309$	−3.64357	−0.207276
$310$	9.58464	0.544371
$311$	−2.06599	−0.117152	−0.0585759	−	0.998283i	$-0.518656\pi$
$311$	−2.06599	−0.117152	−0.0585759	+	0.998283i	$0.518656\pi$
$312$	−14.0429	−0.795022
$313$	7.26416	0.410595	0.205297	−	0.978700i	$-0.434184\pi$
$313$	7.26416	0.410595	0.205297	+	0.978700i	$0.434184\pi$
$314$	6.80128	0.383818
$315$	1.18744	0.0669044
$316$	−2.27557	−0.128011
$317$	−2.04050	−0.114606	−0.0573028	−	0.998357i	$-0.518250\pi$
$317$	−2.04050	−0.114606	−0.0573028	+	0.998357i	$0.518250\pi$
$318$	−11.6275	−0.652040
$319$	5.23155	0.292911
$320$	−1.00000	−0.0559017
$321$	−22.7413	−1.26930
$322$	−0.985528	−0.0549213
$323$	2.82873	0.157395
$324$	−11.1676	−0.620424
$325$	6.41837	0.356027
$326$	−6.47629	−0.358688
$327$	−40.0072	−2.21240
$328$	4.09505	0.226111
$329$	2.90699	0.160268
$330$	−2.18792	−0.120441
$331$	14.0407	0.771747	0.385874	−	0.922552i	$-0.373900\pi$
$331$	14.0407	0.771747	0.385874	+	0.922552i	$0.373900\pi$
$332$	−13.4195	−0.736492
$333$	−14.6837	−0.804663
$334$	−3.67586	−0.201134
$335$	0.258038	0.0140981
$336$	1.45384	0.0793134
$337$	25.9514	1.41366	0.706832	−	0.707382i	$-0.250124\pi$
$337$	25.9514	1.41366	0.706832	+	0.707382i	$0.250124\pi$
$338$	28.1954	1.53363
$339$	−24.8447	−1.34938
$340$	−1.04726	−0.0567957
$341$	9.58464	0.519037
$342$	4.82683	0.261005
$343$	9.00938	0.486461
$344$	−1.00000	−0.0539164
$345$	3.24501	0.174706
$346$	−10.1084	−0.543432
$347$	−22.1995	−1.19173	−0.595865	−	0.803085i	$-0.703191\pi$
$347$	−22.1995	−1.19173	−0.595865	+	0.803085i	$0.703191\pi$
$348$	11.4462	0.613582
$349$	17.3796	0.930307	0.465153	−	0.885230i	$-0.345999\pi$
$349$	17.3796	0.930307	0.465153	+	0.885230i	$0.345999\pi$
$350$	−0.664484	−0.0355181
$351$	17.0340	0.909205
$352$	−1.00000	−0.0533002
$353$	10.4940	0.558539	0.279270	−	0.960213i	$-0.409908\pi$
$353$	10.4940	0.558539	0.279270	+	0.960213i	$0.409908\pi$
$354$	−21.2749	−1.13075
$355$	−3.31954	−0.176183
$356$	11.7254	0.621445
$357$	1.52255	0.0805818
$358$	−10.7290	−0.567044
$359$	24.7556	1.30655	0.653274	−	0.757121i	$-0.273395\pi$
$359$	24.7556	1.30655	0.653274	+	0.757121i	$0.273395\pi$
$360$	−1.78700	−0.0941834
$361$	−11.7042	−0.616011
$362$	23.4462	1.23231
$363$	−2.18792	−0.114836
$364$	−4.26490	−0.223541
$365$	−2.54730	−0.133332
$366$	−23.2837	−1.21706
$367$	5.50542	0.287380	0.143690	−	0.989623i	$-0.454103\pi$
$367$	5.50542	0.287380	0.143690	+	0.989623i	$0.454103\pi$
$368$	1.48315	0.0773145
$369$	7.31788	0.380953
$370$	8.21694	0.427179
$371$	−3.53134	−0.183338
$372$	20.9705	1.08727
$373$	22.7091	1.17583	0.587916	−	0.808922i	$-0.299948\pi$
$373$	22.7091	1.17583	0.587916	+	0.808922i	$0.299948\pi$
$374$	−1.04726	−0.0541526
$375$	2.18792	0.112984
$376$	−4.37481	−0.225614
$377$	−33.5780	−1.72936
$378$	−1.76350	−0.0907046
$379$	8.45509	0.434309	0.217155	−	0.976137i	$-0.430322\pi$
$379$	8.45509	0.434309	0.217155	+	0.976137i	$0.430322\pi$
$380$	−2.70107	−0.138562
$381$	−19.8468	−1.01678
$382$	−13.2886	−0.679904
$383$	−22.9749	−1.17396	−0.586980	−	0.809601i	$-0.699683\pi$
$383$	−22.9749	−1.17396	−0.586980	+	0.809601i	$0.699683\pi$
$384$	−2.18792	−0.111652
$385$	−0.664484	−0.0338652
$386$	−22.1105	−1.12540
$387$	−1.78700	−0.0908386
$388$	4.68733	0.237963
$389$	28.1152	1.42550	0.712749	−	0.701419i	$-0.247450\pi$
$389$	28.1152	1.42550	0.712749	+	0.701419i	$0.247450\pi$
$390$	14.0429	0.711089
$391$	1.55324	0.0785510
$392$	−6.55846	−0.331252
$393$	−32.3033	−1.62949
$394$	−1.03178	−0.0519805
$395$	2.27557	0.114496
$396$	−1.78700	−0.0898004
$397$	9.55314	0.479458	0.239729	−	0.970840i	$-0.422941\pi$
$397$	9.55314	0.479458	0.239729	+	0.970840i	$0.422941\pi$
$398$	19.9151	0.998255
$399$	3.92692	0.196592
$400$	1.00000	0.0500000
$401$	2.68948	0.134306	0.0671531	−	0.997743i	$-0.478608\pi$
$401$	2.68948	0.134306	0.0671531	+	0.997743i	$0.478608\pi$
$402$	0.564568	0.0281581
$403$	−61.5177	−3.06442
$404$	−9.64532	−0.479873
$405$	11.1676	0.554924
$406$	3.47628	0.172525
$407$	8.21694	0.407299
$408$	−2.29133	−0.113438
$409$	30.3241	1.49943	0.749716	−	0.661760i	$-0.230190\pi$
$409$	30.3241	1.49943	0.749716	+	0.661760i	$0.230190\pi$
$410$	−4.09505	−0.202240
$411$	−32.7926	−1.61754
$412$	1.66531	0.0820440
$413$	−6.46131	−0.317940
$414$	2.65039	0.130260
$415$	13.4195	0.658739
$416$	6.41837	0.314686
$417$	13.8640	0.678921
$418$	−2.70107	−0.132114
$419$	17.4127	0.850667	0.425333	−	0.905037i	$-0.360157\pi$
$419$	17.4127	0.850667	0.425333	+	0.905037i	$0.360157\pi$
$420$	−1.45384	−0.0709401
$421$	21.4546	1.04563	0.522817	−	0.852445i	$-0.324881\pi$
$421$	21.4546	1.04563	0.522817	+	0.852445i	$0.324881\pi$
$422$	11.9331	0.580893
$423$	−7.81781	−0.380115
$424$	5.31442	0.258091
$425$	1.04726	0.0507996
$426$	−7.26290	−0.351889
$427$	−7.07140	−0.342209
$428$	10.3940	0.502414
$429$	14.0429	0.677997
$430$	1.00000	0.0482243
$431$	1.61138	0.0776174	0.0388087	−	0.999247i	$-0.487644\pi$
$431$	1.61138	0.0776174	0.0388087	+	0.999247i	$0.487644\pi$
$432$	2.65394	0.127688
$433$	−21.0490	−1.01155	−0.505776	−	0.862665i	$-0.668794\pi$
$433$	−21.0490	−1.01155	−0.505776	+	0.862665i	$0.668794\pi$
$434$	6.36884	0.305714
$435$	−11.4462	−0.548805
$436$	18.2855	0.875715
$437$	4.00609	0.191637
$438$	−5.57329	−0.266302
$439$	8.05448	0.384419	0.192210	−	0.981354i	$-0.438435\pi$
$439$	8.05448	0.384419	0.192210	+	0.981354i	$0.438435\pi$
$440$	1.00000	0.0476731
$441$	−11.7200	−0.558095
$442$	6.72171	0.319719
$443$	5.83464	0.277212	0.138606	−	0.990348i	$-0.455738\pi$
$443$	5.83464	0.277212	0.138606	+	0.990348i	$0.455738\pi$
$444$	17.9780	0.853200
$445$	−11.7254	−0.555837
$446$	12.1000	0.572954
$447$	−51.3549	−2.42900
$448$	−0.664484	−0.0313939
$449$	40.6353	1.91770	0.958850	−	0.283914i	$-0.0916331\pi$
$449$	40.6353	1.91770	0.958850	+	0.283914i	$0.0916331\pi$
$450$	1.78700	0.0842402
$451$	−4.09505	−0.192828
$452$	11.3554	0.534112
$453$	−44.9989	−2.11423
$454$	−28.2560	−1.32612
$455$	4.26490	0.199942
$456$	−5.90974	−0.276749
$457$	7.35584	0.344092	0.172046	−	0.985089i	$-0.444962\pi$
$457$	7.35584	0.344092	0.172046	+	0.985089i	$0.444962\pi$
$458$	9.65951	0.451359
$459$	2.77937	0.129730
$460$	−1.48315	−0.0691522
$461$	−24.0023	−1.11790	−0.558949	−	0.829202i	$-0.688795\pi$
$461$	−24.0023	−1.11790	−0.558949	+	0.829202i	$0.688795\pi$
$462$	−1.45384	−0.0676387
$463$	18.0702	0.839796	0.419898	−	0.907571i	$-0.362066\pi$
$463$	18.0702	0.839796	0.419898	+	0.907571i	$0.362066\pi$
$464$	−5.23155	−0.242869
$465$	−20.9705	−0.972481
$466$	10.6087	0.491438
$467$	34.7368	1.60743	0.803715	−	0.595015i	$-0.202854\pi$
$467$	34.7368	1.60743	0.803715	+	0.595015i	$0.202854\pi$
$468$	11.4697	0.530185
$469$	0.171462	0.00791739
$470$	4.37481	0.201795
$471$	−14.8807	−0.685665
$472$	9.72381	0.447575
$473$	1.00000	0.0459800
$474$	4.97876	0.228682
$475$	2.70107	0.123934
$476$	−0.695888	−0.0318960
$477$	9.49689	0.434833
$478$	−11.9578	−0.546937
$479$	−12.4270	−0.567806	−0.283903	−	0.958853i	$-0.591629\pi$
$479$	−12.4270	−0.567806	−0.283903	+	0.958853i	$0.591629\pi$
$480$	2.18792	0.0998645
$481$	−52.7394	−2.40471
$482$	−20.0705	−0.914186
$483$	2.15626	0.0981132
$484$	1.00000	0.0454545
$485$	−4.68733	−0.212841
$486$	16.4721	0.747189
$487$	6.31726	0.286262	0.143131	−	0.989704i	$-0.454283\pi$
$487$	6.31726	0.286262	0.143131	+	0.989704i	$0.454283\pi$
$488$	10.6419	0.481738
$489$	14.1696	0.640772
$490$	6.55846	0.296281
$491$	−30.4495	−1.37417	−0.687083	−	0.726579i	$-0.741109\pi$
$491$	−30.4495	−1.37417	−0.687083	+	0.726579i	$0.741109\pi$
$492$	−8.95966	−0.403932
$493$	−5.47880	−0.246753
$494$	17.3365	0.780005
$495$	1.78700	0.0803199
$496$	−9.58464	−0.430363
$497$	−2.20578	−0.0989428
$498$	29.3609	1.31569
$499$	−1.74018	−0.0779014	−0.0389507	−	0.999241i	$-0.512402\pi$
$499$	−1.74018	−0.0779014	−0.0389507	+	0.999241i	$0.512402\pi$
$500$	−1.00000	−0.0447214
$501$	8.04251	0.359313
$502$	−24.5409	−1.09531
$503$	−27.1202	−1.20923	−0.604616	−	0.796517i	$-0.706673\pi$
$503$	−27.1202	−1.20923	−0.604616	+	0.796517i	$0.706673\pi$
$504$	−1.18744	−0.0528926
$505$	9.64532	0.429211
$506$	−1.48315	−0.0659340
$507$	−61.6894	−2.73972
$508$	9.07108	0.402464
$509$	18.8648	0.836169	0.418085	−	0.908408i	$-0.362702\pi$
$509$	18.8648	0.836169	0.418085	+	0.908408i	$0.362702\pi$
$510$	2.29133	0.101462
$511$	−1.69264	−0.0748779
$512$	1.00000	0.0441942
$513$	7.16848	0.316496
$514$	2.75951	0.121717
$515$	−1.66531	−0.0733824
$516$	2.18792	0.0963179
$517$	4.37481	0.192404
$518$	5.46002	0.239900
$519$	22.1165	0.970805
$520$	−6.41837	−0.281464
$521$	19.4389	0.851635	0.425818	−	0.904809i	$-0.359986\pi$
$521$	19.4389	0.851635	0.425818	+	0.904809i	$0.359986\pi$
$522$	−9.34881	−0.409186
$523$	12.5466	0.548626	0.274313	−	0.961640i	$-0.411550\pi$
$523$	12.5466	0.548626	0.274313	+	0.961640i	$0.411550\pi$
$524$	14.7644	0.644985
$525$	1.45384	0.0634507
$526$	−15.7409	−0.686336
$527$	−10.0376	−0.437246
$528$	2.18792	0.0952171
$529$	−20.8003	−0.904360
$530$	−5.31442	−0.230844
$531$	17.3765	0.754076
$532$	−1.79482	−0.0778152
$533$	26.2835	1.13847
$534$	−25.6543	−1.11017
$535$	−10.3940	−0.449373
$536$	−0.258038	−0.0111456
$537$	23.4742	1.01299
$538$	5.15540	0.222265
$539$	6.55846	0.282493
$540$	−2.65394	−0.114207
$541$	−31.4406	−1.35174	−0.675869	−	0.737022i	$-0.736232\pi$
$541$	−31.4406	−1.35174	−0.675869	+	0.737022i	$0.736232\pi$
$542$	23.8725	1.02541
$543$	−51.2985	−2.20143
$544$	1.04726	0.0449010
$545$	−18.2855	−0.783264
$546$	9.33127	0.399341
$547$	−18.6869	−0.798994	−0.399497	−	0.916735i	$-0.630815\pi$
$547$	−18.6869	−0.798994	−0.399497	+	0.916735i	$0.630815\pi$
$548$	14.9880	0.640257
$549$	19.0172	0.811634
$550$	−1.00000	−0.0426401
$551$	−14.1308	−0.601992
$552$	−3.24501	−0.138117
$553$	1.51208	0.0643000
$554$	4.42723	0.188095
$555$	−17.9780	−0.763125
$556$	−6.33659	−0.268731
$557$	−34.4687	−1.46049	−0.730243	−	0.683187i	$-0.760593\pi$
$557$	−34.4687	−1.46049	−0.730243	+	0.683187i	$0.760593\pi$
$558$	−17.1278	−0.725078
$559$	−6.41837	−0.271468
$560$	0.664484	0.0280796
$561$	2.29133	0.0967399
$562$	−8.24133	−0.347639
$563$	8.34644	0.351760	0.175880	−	0.984412i	$-0.443723\pi$
$563$	8.34644	0.351760	0.175880	+	0.984412i	$0.443723\pi$
$564$	9.57175	0.403044
$565$	−11.3554	−0.477725
$566$	−20.8967	−0.878355
$567$	7.42071	0.311640
$568$	3.31954	0.139285
$569$	45.6393	1.91330	0.956649	−	0.291243i	$-0.0940688\pi$
$569$	45.6393	1.91330	0.956649	+	0.291243i	$0.0940688\pi$
$570$	5.90974	0.247532
$571$	32.8332	1.37403	0.687014	−	0.726644i	$-0.258921\pi$
$571$	32.8332	1.37403	0.687014	+	0.726644i	$0.258921\pi$
$572$	−6.41837	−0.268365
$573$	29.0744	1.21460
$574$	−2.72109	−0.113576
$575$	1.48315	0.0618516
$576$	1.78700	0.0744585
$577$	27.5903	1.14860	0.574300	−	0.818645i	$-0.305274\pi$
$577$	27.5903	1.14860	0.574300	+	0.818645i	$0.305274\pi$
$578$	−15.9032	−0.661488
$579$	48.3761	2.01044
$580$	5.23155	0.217228
$581$	8.91706	0.369942
$582$	−10.2555	−0.425105
$583$	−5.31442	−0.220101
$584$	2.54730	0.105408
$585$	−11.4697	−0.474212
$586$	−17.7196	−0.731989
$587$	−32.7782	−1.35290	−0.676450	−	0.736488i	$-0.736483\pi$
$587$	−32.7782	−1.35290	−0.676450	+	0.736488i	$0.736483\pi$
$588$	14.3494	0.591759
$589$	−25.8888	−1.06673
$590$	−9.72381	−0.400323
$591$	2.25746	0.0928596
$592$	−8.21694	−0.337714
$593$	12.4214	0.510087	0.255044	−	0.966930i	$-0.417910\pi$
$593$	12.4214	0.510087	0.255044	+	0.966930i	$0.417910\pi$
$594$	−2.65394	−0.108892
$595$	0.695888	0.0285286
$596$	23.4720	0.961451
$597$	−43.5727	−1.78331
$598$	9.51939	0.389277
$599$	29.4467	1.20316	0.601580	−	0.798812i	$-0.294538\pi$
$599$	29.4467	1.20316	0.601580	+	0.798812i	$0.294538\pi$
$600$	−2.18792	−0.0893216
$601$	2.97902	0.121517	0.0607584	−	0.998153i	$-0.480648\pi$
$601$	2.97902	0.121517	0.0607584	+	0.998153i	$0.480648\pi$
$602$	0.664484	0.0270823
$603$	−0.461115	−0.0187781
$604$	20.5670	0.836857
$605$	−1.00000	−0.0406558
$606$	21.1032	0.857259
$607$	31.5484	1.28051	0.640255	−	0.768162i	$-0.278829\pi$
$607$	31.5484	1.28051	0.640255	+	0.768162i	$0.278829\pi$
$608$	2.70107	0.109543
$609$	−7.60583	−0.308204
$610$	−10.6419	−0.430880
$611$	−28.0792	−1.13596
$612$	1.87146	0.0756493
$613$	−30.7009	−1.24000	−0.619998	−	0.784603i	$-0.712867\pi$
$613$	−30.7009	−1.24000	−0.619998	+	0.784603i	$0.712867\pi$
$614$	27.4396	1.10737
$615$	8.95966	0.361288
$616$	0.664484	0.0267728
$617$	−13.8559	−0.557817	−0.278908	−	0.960318i	$-0.589973\pi$
$617$	−13.8559	−0.557817	−0.278908	+	0.960318i	$0.589973\pi$
$618$	−3.64357	−0.146566
$619$	15.2936	0.614700	0.307350	−	0.951596i	$-0.400558\pi$
$619$	15.2936	0.614700	0.307350	+	0.951596i	$0.400558\pi$
$620$	9.58464	0.384928
$621$	3.93619	0.157954
$622$	−2.06599	−0.0828388
$623$	−7.79134	−0.312153
$624$	−14.0429	−0.562165
$625$	1.00000	0.0400000
$626$	7.26416	0.290334
$627$	5.90974	0.236012
$628$	6.80128	0.271400
$629$	−8.60529	−0.343115
$630$	1.18744	0.0473086
$631$	−26.7511	−1.06494	−0.532472	−	0.846447i	$-0.678737\pi$
$631$	−26.7511	−1.06494	−0.532472	+	0.846447i	$0.678737\pi$
$632$	−2.27557	−0.0905172
$633$	−26.1087	−1.03773
$634$	−2.04050	−0.0810384
$635$	−9.07108	−0.359975
$636$	−11.6275	−0.461062
$637$	−42.0946	−1.66785
$638$	5.23155	0.207119
$639$	5.93203	0.234668
$640$	−1.00000	−0.0395285
$641$	−19.4343	−0.767610	−0.383805	−	0.923414i	$-0.625387\pi$
$641$	−19.4343	−0.767610	−0.383805	+	0.923414i	$0.625387\pi$
$642$	−22.7413	−0.897529
$643$	−28.2014	−1.11216	−0.556078	−	0.831130i	$-0.687694\pi$
$643$	−28.2014	−1.11216	−0.556078	+	0.831130i	$0.687694\pi$
$644$	−0.985528	−0.0388353
$645$	−2.18792	−0.0861494
$646$	2.82873	0.111295
$647$	−1.65299	−0.0649859	−0.0324929	−	0.999472i	$-0.510345\pi$
$647$	−1.65299	−0.0649859	−0.0324929	+	0.999472i	$0.510345\pi$
$648$	−11.1676	−0.438706
$649$	−9.72381	−0.381693
$650$	6.41837	0.251749
$651$	−13.9345	−0.546137
$652$	−6.47629	−0.253631
$653$	−24.6203	−0.963469	−0.481734	−	0.876317i	$-0.659993\pi$
$653$	−24.6203	−0.963469	−0.481734	+	0.876317i	$0.659993\pi$
$654$	−40.0072	−1.56441
$655$	−14.7644	−0.576892
$656$	4.09505	0.159885
$657$	4.55203	0.177592
$658$	2.90699	0.113326
$659$	−27.3629	−1.06591	−0.532953	−	0.846145i	$-0.678918\pi$
$659$	−27.3629	−1.06591	−0.532953	+	0.846145i	$0.678918\pi$
$660$	−2.18792	−0.0851648
$661$	31.2085	1.21387	0.606934	−	0.794752i	$-0.292399\pi$
$661$	31.2085	1.21387	0.606934	+	0.794752i	$0.292399\pi$
$662$	14.0407	0.545708
$663$	−14.7066	−0.571156
$664$	−13.4195	−0.520779
$665$	1.79482	0.0696001
$666$	−14.6837	−0.568982
$667$	−7.75917	−0.300436
$668$	−3.67586	−0.142223
$669$	−26.4740	−1.02354
$670$	0.258038	0.00996889
$671$	−10.6419	−0.410828
$672$	1.45384	0.0560830
$673$	46.3135	1.78525	0.892627	−	0.450797i	$-0.148860\pi$
$673$	46.3135	1.78525	0.892627	+	0.450797i	$0.148860\pi$
$674$	25.9514	0.999611
$675$	2.65394	0.102150
$676$	28.1954	1.08444
$677$	−23.6496	−0.908928	−0.454464	−	0.890765i	$-0.650169\pi$
$677$	−23.6496	−0.908928	−0.454464	+	0.890765i	$0.650169\pi$
$678$	−24.8447	−0.954155
$679$	−3.11466	−0.119529
$680$	−1.04726	−0.0401606
$681$	61.8220	2.36903
$682$	9.58464	0.367015
$683$	0.800311	0.0306230	0.0153115	−	0.999883i	$-0.495126\pi$
$683$	0.800311	0.0306230	0.0153115	+	0.999883i	$0.495126\pi$
$684$	4.82683	0.184558
$685$	−14.9880	−0.572663
$686$	9.00938	0.343980
$687$	−21.1343	−0.806322
$688$	−1.00000	−0.0381246
$689$	34.1099	1.29948
$690$	3.24501	0.123536
$691$	−47.9012	−1.82225	−0.911123	−	0.412135i	$-0.864783\pi$
$691$	−47.9012	−1.82225	−0.911123	+	0.412135i	$0.864783\pi$
$692$	−10.1084	−0.384265
$693$	1.18744	0.0451069
$694$	−22.1995	−0.842680
$695$	6.33659	0.240360
$696$	11.4462	0.433868
$697$	4.28859	0.162442
$698$	17.3796	0.657826
$699$	−23.2110	−0.877921
$700$	−0.664484	−0.0251151
$701$	37.6804	1.42317	0.711584	−	0.702601i	$-0.247978\pi$
$701$	37.6804	1.42317	0.711584	+	0.702601i	$0.247978\pi$
$702$	17.0340	0.642905
$703$	−22.1946	−0.837084
$704$	−1.00000	−0.0376889
$705$	−9.57175	−0.360493
$706$	10.4940	0.394947
$707$	6.40916	0.241041
$708$	−21.2749	−0.799561
$709$	−6.17728	−0.231993	−0.115996	−	0.993250i	$-0.537006\pi$
$709$	−6.17728	−0.231993	−0.115996	+	0.993250i	$0.537006\pi$
$710$	−3.31954	−0.124580
$711$	−4.06645	−0.152504
$712$	11.7254	0.439428
$713$	−14.2155	−0.532373
$714$	1.52255	0.0569800
$715$	6.41837	0.240033
$716$	−10.7290	−0.400961
$717$	26.1627	0.977066
$718$	24.7556	0.923869
$719$	−20.6106	−0.768644	−0.384322	−	0.923199i	$-0.625565\pi$
$719$	−20.6106	−0.768644	−0.384322	+	0.923199i	$0.625565\pi$
$720$	−1.78700	−0.0665977
$721$	−1.10657	−0.0412109
$722$	−11.7042	−0.435586
$723$	43.9127	1.63313
$724$	23.4462	0.871372
$725$	−5.23155	−0.194295
$726$	−2.18792	−0.0812014
$727$	28.6070	1.06098	0.530488	−	0.847692i	$-0.322009\pi$
$727$	28.6070	1.06098	0.530488	+	0.847692i	$0.322009\pi$
$728$	−4.26490	−0.158068
$729$	−2.53676	−0.0939541
$730$	−2.54730	−0.0942798
$731$	−1.04726	−0.0387344
$732$	−23.2837	−0.860592
$733$	15.1868	0.560938	0.280469	−	0.959863i	$-0.409510\pi$
$733$	15.1868	0.560938	0.280469	+	0.959863i	$0.409510\pi$
$734$	5.50542	0.203209
$735$	−14.3494	−0.529286
$736$	1.48315	0.0546696
$737$	0.258038	0.00950496
$738$	7.31788	0.269375
$739$	27.1512	0.998771	0.499386	−	0.866380i	$-0.333559\pi$
$739$	27.1512	0.998771	0.499386	+	0.866380i	$0.333559\pi$
$740$	8.21694	0.302061
$741$	−37.9309	−1.39342
$742$	−3.53134	−0.129640
$743$	−22.7436	−0.834383	−0.417192	−	0.908818i	$-0.636986\pi$
$743$	−22.7436	−0.834383	−0.417192	+	0.908818i	$0.636986\pi$
$744$	20.9705	0.768814
$745$	−23.4720	−0.859948
$746$	22.7091	0.831439
$747$	−23.9808	−0.877410
$748$	−1.04726	−0.0382917
$749$	−6.90666	−0.252364
$750$	2.18792	0.0798916
$751$	32.8509	1.19874	0.599372	−	0.800470i	$-0.295417\pi$
$751$	32.8509	1.19874	0.599372	+	0.800470i	$0.295417\pi$
$752$	−4.37481	−0.159533
$753$	53.6936	1.95670
$754$	−33.5780	−1.22284
$755$	−20.5670	−0.748508
$756$	−1.76350	−0.0641379
$757$	17.5560	0.638084	0.319042	−	0.947741i	$-0.396639\pi$
$757$	17.5560	0.638084	0.319042	+	0.947741i	$0.396639\pi$
$758$	8.45509	0.307103
$759$	3.24501	0.117787
$760$	−2.70107	−0.0979782
$761$	−11.4347	−0.414506	−0.207253	−	0.978287i	$-0.566452\pi$
$761$	−11.4347	−0.414506	−0.207253	+	0.978287i	$0.566452\pi$
$762$	−19.8468	−0.718974
$763$	−12.1504	−0.439874
$764$	−13.2886	−0.480765
$765$	−1.87146	−0.0676628
$766$	−22.9749	−0.830116
$767$	62.4110	2.25353
$768$	−2.18792	−0.0789499
$769$	−31.2432	−1.12666	−0.563330	−	0.826232i	$-0.690480\pi$
$769$	−31.2432	−1.12666	−0.563330	+	0.826232i	$0.690480\pi$
$770$	−0.664484	−0.0239463
$771$	−6.03759	−0.217439
$772$	−22.1105	−0.795775
$773$	−44.3955	−1.59679	−0.798397	−	0.602131i	$-0.794319\pi$
$773$	−44.3955	−1.59679	−0.798397	+	0.602131i	$0.794319\pi$
$774$	−1.78700	−0.0642326
$775$	−9.58464	−0.344290
$776$	4.68733	0.168265
$777$	−11.9461	−0.428564
$778$	28.1152	1.00798
$779$	11.0610	0.396303
$780$	14.0429	0.502816
$781$	−3.31954	−0.118783
$782$	1.55324	0.0555439
$783$	−13.8842	−0.496182
$784$	−6.55846	−0.234231
$785$	−6.80128	−0.242748
$786$	−32.3033	−1.15222
$787$	−30.1340	−1.07416	−0.537080	−	0.843531i	$-0.680473\pi$
$787$	−30.1340	−1.07416	−0.537080	+	0.843531i	$0.680473\pi$
$788$	−1.03178	−0.0367558
$789$	34.4399	1.22609
$790$	2.27557	0.0809610
$791$	−7.54547	−0.268286
$792$	−1.78700	−0.0634984
$793$	68.3039	2.42554
$794$	9.55314	0.339028
$795$	11.6275	0.412386
$796$	19.9151	0.705873
$797$	−44.4182	−1.57337	−0.786687	−	0.617352i	$-0.788206\pi$
$797$	−44.4182	−1.57337	−0.786687	+	0.617352i	$0.788206\pi$
$798$	3.92692	0.139012
$799$	−4.58157	−0.162084
$800$	1.00000	0.0353553
$801$	20.9533	0.740350
$802$	2.68948	0.0949688
$803$	−2.54730	−0.0898922
$804$	0.564568	0.0199108
$805$	0.985528	0.0347353
$806$	−61.5177	−2.16687
$807$	−11.2796	−0.397061
$808$	−9.64532	−0.339321
$809$	23.8771	0.839476	0.419738	−	0.907645i	$-0.362122\pi$
$809$	23.8771	0.839476	0.419738	+	0.907645i	$0.362122\pi$
$810$	11.1676	0.392390
$811$	−26.2100	−0.920356	−0.460178	−	0.887827i	$-0.652214\pi$
$811$	−26.2100	−0.920356	−0.460178	+	0.887827i	$0.652214\pi$
$812$	3.47628	0.121994
$813$	−52.2311	−1.83183
$814$	8.21694	0.288004
$815$	6.47629	0.226855
$816$	−2.29133	−0.0802125
$817$	−2.70107	−0.0944985
$818$	30.3241	1.06026
$819$	−7.62140	−0.266313
$820$	−4.09505	−0.143005
$821$	−16.4160	−0.572924	−0.286462	−	0.958092i	$-0.592479\pi$
$821$	−16.4160	−0.572924	−0.286462	+	0.958092i	$0.592479\pi$
$822$	−32.7926	−1.14377
$823$	−36.4431	−1.27033	−0.635164	−	0.772377i	$-0.719068\pi$
$823$	−36.4431	−1.27033	−0.635164	+	0.772377i	$0.719068\pi$
$824$	1.66531	0.0580139
$825$	2.18792	0.0761737
$826$	−6.46131	−0.224818
$827$	48.5975	1.68990	0.844950	−	0.534845i	$-0.179630\pi$
$827$	48.5975	1.68990	0.844950	+	0.534845i	$0.179630\pi$
$828$	2.65039	0.0921076
$829$	−39.1316	−1.35910	−0.679548	−	0.733631i	$-0.737824\pi$
$829$	−39.1316	−1.35910	−0.679548	+	0.733631i	$0.737824\pi$
$830$	13.4195	0.465799
$831$	−9.68643	−0.336018
$832$	6.41837	0.222517
$833$	−6.86842	−0.237977
$834$	13.8640	0.480070
$835$	3.67586	0.127209
$836$	−2.70107	−0.0934185
$837$	−25.4371	−0.879233
$838$	17.4127	0.601512
$839$	−37.4621	−1.29334	−0.646668	−	0.762771i	$-0.723838\pi$
$839$	−37.4621	−1.29334	−0.646668	+	0.762771i	$0.723838\pi$
$840$	−1.45384	−0.0501622
$841$	−1.63087	−0.0562371
$842$	21.4546	0.739374
$843$	18.0314	0.621034
$844$	11.9331	0.410754
$845$	−28.1954	−0.969952
$846$	−7.81781	−0.268782
$847$	−0.664484	−0.0228319
$848$	5.31442	0.182498
$849$	45.7204	1.56912
$850$	1.04726	0.0359208
$851$	−12.1870	−0.417763
$852$	−7.26290	−0.248823
$853$	−17.1654	−0.587733	−0.293866	−	0.955846i	$-0.594942\pi$
$853$	−17.1654	−0.587733	−0.293866	+	0.955846i	$0.594942\pi$
$854$	−7.07140	−0.241978
$855$	−4.82683	−0.165074
$856$	10.3940	0.355261
$857$	−30.2044	−1.03176	−0.515882	−	0.856660i	$-0.672536\pi$
$857$	−30.2044	−1.03176	−0.515882	+	0.856660i	$0.672536\pi$
$858$	14.0429	0.479416
$859$	−47.0823	−1.60643	−0.803213	−	0.595692i	$-0.796878\pi$
$859$	−47.0823	−1.60643	−0.803213	+	0.595692i	$0.796878\pi$
$860$	1.00000	0.0340997
$861$	5.95354	0.202896
$862$	1.61138	0.0548838
$863$	23.8280	0.811116	0.405558	−	0.914069i	$-0.367077\pi$
$863$	23.8280	0.811116	0.405558	+	0.914069i	$0.367077\pi$
$864$	2.65394	0.0902889
$865$	10.1084	0.343697
$866$	−21.0490	−0.715275
$867$	34.7951	1.18170
$868$	6.36884	0.216172
$869$	2.27557	0.0771933
$870$	−11.4462	−0.388063
$871$	−1.65618	−0.0561176
$872$	18.2855	0.619224
$873$	8.37628	0.283494
$874$	4.00609	0.135508
$875$	0.664484	0.0224636
$876$	−5.57329	−0.188304
$877$	−28.2915	−0.955335	−0.477667	−	0.878541i	$-0.658518\pi$
$877$	−28.2915	−0.955335	−0.477667	+	0.878541i	$0.658518\pi$
$878$	8.05448	0.271825
$879$	38.7691	1.30765
$880$	1.00000	0.0337100
$881$	−35.4660	−1.19488	−0.597440	−	0.801914i	$-0.703815\pi$
$881$	−35.4660	−1.19488	−0.597440	+	0.801914i	$0.703815\pi$
$882$	−11.7200	−0.394633
$883$	25.3583	0.853375	0.426687	−	0.904399i	$-0.359680\pi$
$883$	25.3583	0.853375	0.426687	+	0.904399i	$0.359680\pi$
$884$	6.72171	0.226075
$885$	21.2749	0.715149
$886$	5.83464	0.196019
$887$	9.51569	0.319506	0.159753	−	0.987157i	$-0.448930\pi$
$887$	9.51569	0.319506	0.159753	+	0.987157i	$0.448930\pi$
$888$	17.9780	0.603303
$889$	−6.02758	−0.202159
$890$	−11.7254	−0.393036
$891$	11.1676	0.374130
$892$	12.1000	0.405139
$893$	−11.8167	−0.395430
$894$	−51.3549	−1.71757
$895$	10.7290	0.358630
$896$	−0.664484	−0.0221988
$897$	−20.8277	−0.695417
$898$	40.6353	1.35602
$899$	50.1425	1.67235
$900$	1.78700	0.0595668
$901$	5.56559	0.185417
$902$	−4.09505	−0.136350
$903$	−1.45384	−0.0483807
$904$	11.3554	0.377674
$905$	−23.4462	−0.779379
$906$	−44.9989	−1.49499
$907$	13.3134	0.442065	0.221033	−	0.975266i	$-0.429057\pi$
$907$	13.3134	0.442065	0.221033	+	0.975266i	$0.429057\pi$
$908$	−28.2560	−0.937710
$909$	−17.2362	−0.571690
$910$	4.26490	0.141380
$911$	55.4930	1.83857	0.919283	−	0.393598i	$-0.128770\pi$
$911$	55.4930	1.83857	0.919283	+	0.393598i	$0.128770\pi$
$912$	−5.90974	−0.195691
$913$	13.4195	0.444122
$914$	7.35584	0.243310
$915$	23.2837	0.769737
$916$	9.65951	0.319159
$917$	−9.81069	−0.323977
$918$	2.77937	0.0917328
$919$	15.6044	0.514743	0.257372	−	0.966312i	$-0.417144\pi$
$919$	15.6044	0.514743	0.257372	+	0.966312i	$0.417144\pi$
$920$	−1.48315	−0.0488980
$921$	−60.0358	−1.97825
$922$	−24.0023	−0.790474
$923$	21.3060	0.701297
$924$	−1.45384	−0.0478278
$925$	−8.21694	−0.270171
$926$	18.0702	0.593825
$927$	2.97592	0.0977420
$928$	−5.23155	−0.171734
$929$	28.9557	0.950006	0.475003	−	0.879984i	$-0.342447\pi$
$929$	28.9557	0.950006	0.475003	+	0.879984i	$0.342447\pi$
$930$	−20.9705	−0.687648
$931$	−17.7149	−0.580582
$932$	10.6087	0.347499
$933$	4.52023	0.147986
$934$	34.7368	1.13662
$935$	1.04726	0.0342491
$936$	11.4697	0.374897
$937$	0.216760	0.00708125	0.00354063	−	0.999994i	$-0.498873\pi$
$937$	0.216760	0.00708125	0.00354063	+	0.999994i	$0.498873\pi$
$938$	0.171462	0.00559844
$939$	−15.8934	−0.518662
$940$	4.37481	0.142691
$941$	5.71974	0.186458	0.0932291	−	0.995645i	$-0.470281\pi$
$941$	5.71974	0.186458	0.0932291	+	0.995645i	$0.470281\pi$
$942$	−14.8807	−0.484838
$943$	6.07357	0.197783
$944$	9.72381	0.316483
$945$	1.76350	0.0573666
$946$	1.00000	0.0325128
$947$	20.9761	0.681631	0.340815	−	0.940130i	$-0.389297\pi$
$947$	20.9761	0.681631	0.340815	+	0.940130i	$0.389297\pi$
$948$	4.97876	0.161703
$949$	16.3495	0.530727
$950$	2.70107	0.0876343
$951$	4.46445	0.144770
$952$	−0.695888	−0.0225539
$953$	51.4263	1.66586	0.832931	−	0.553377i	$-0.186661\pi$
$953$	51.4263	1.66586	0.832931	+	0.553377i	$0.186661\pi$
$954$	9.49689	0.307473
$955$	13.2886	0.430009
$956$	−11.9578	−0.386743
$957$	−11.4462	−0.370004
$958$	−12.4270	−0.401499
$959$	−9.95930	−0.321602
$960$	2.18792	0.0706149
$961$	60.8653	1.96340
$962$	−52.7394	−1.70039
$963$	18.5742	0.598545
$964$	−20.0705	−0.646427
$965$	22.1105	0.711763
$966$	2.15626	0.0693765
$967$	−33.1191	−1.06504	−0.532520	−	0.846418i	$-0.678755\pi$
$967$	−33.1191	−1.06504	−0.532520	+	0.846418i	$0.678755\pi$
$968$	1.00000	0.0321412
$969$	−6.18904	−0.198821
$970$	−4.68733	−0.150501
$971$	−7.42504	−0.238281	−0.119140	−	0.992877i	$-0.538014\pi$
$971$	−7.42504	−0.238281	−0.119140	+	0.992877i	$0.538014\pi$
$972$	16.4721	0.528342
$973$	4.21056	0.134984
$974$	6.31726	0.202418
$975$	−14.0429	−0.449732
$976$	10.6419	0.340640
$977$	−18.5449	−0.593304	−0.296652	−	0.954986i	$-0.595870\pi$
$977$	−18.5449	−0.593304	−0.296652	+	0.954986i	$0.595870\pi$
$978$	14.1696	0.453094
$979$	−11.7254	−0.374745
$980$	6.55846	0.209502
$981$	32.6762	1.04327
$982$	−30.4495	−0.971681
$983$	−1.74986	−0.0558119	−0.0279059	−	0.999611i	$-0.508884\pi$
$983$	−1.74986	−0.0558119	−0.0279059	+	0.999611i	$0.508884\pi$
$984$	−8.95966	−0.285623
$985$	1.03178	0.0328754
$986$	−5.47880	−0.174481
$987$	−6.36027	−0.202450
$988$	17.3365	0.551547
$989$	−1.48315	−0.0471614
$990$	1.78700	0.0567947
$991$	−51.5356	−1.63708	−0.818541	−	0.574449i	$-0.805216\pi$
$991$	−51.5356	−1.63708	−0.818541	+	0.574449i	$0.805216\pi$
$992$	−9.58464	−0.304313
$993$	−30.7200	−0.974869
$994$	−2.20578	−0.0699631
$995$	−19.9151	−0.631352
$996$	29.3609	0.930335
$997$	−47.4086	−1.50145	−0.750723	−	0.660617i	$-0.770295\pi$
$997$	−47.4086	−1.50145	−0.750723	+	0.660617i	$0.770295\pi$
$998$	−1.74018	−0.0550846
$999$	−21.8073	−0.689952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.ba.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.ba.1.3	✓	10	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.18792 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.18792 q^{6} -0.664484 q^{7} +1.00000 q^{8} +1.78700 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.18792 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.18792 q^{6} -0.664484 q^{7} +1.00000 q^{8} +1.78700 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.18792 q^{12} +6.41837 q^{13} -0.664484 q^{14} +2.18792 q^{15} +1.00000 q^{16} +1.04726 q^{17} +1.78700 q^{18} +2.70107 q^{19} -1.00000 q^{20} +1.45384 q^{21} -1.00000 q^{22} +1.48315 q^{23} -2.18792 q^{24} +1.00000 q^{25} +6.41837 q^{26} +2.65394 q^{27} -0.664484 q^{28} -5.23155 q^{29} +2.18792 q^{30} -9.58464 q^{31} +1.00000 q^{32} +2.18792 q^{33} +1.04726 q^{34} +0.664484 q^{35} +1.78700 q^{36} -8.21694 q^{37} +2.70107 q^{38} -14.0429 q^{39} -1.00000 q^{40} +4.09505 q^{41} +1.45384 q^{42} -1.00000 q^{43} -1.00000 q^{44} -1.78700 q^{45} +1.48315 q^{46} -4.37481 q^{47} -2.18792 q^{48} -6.55846 q^{49} +1.00000 q^{50} -2.29133 q^{51} +6.41837 q^{52} +5.31442 q^{53} +2.65394 q^{54} +1.00000 q^{55} -0.664484 q^{56} -5.90974 q^{57} -5.23155 q^{58} +9.72381 q^{59} +2.18792 q^{60} +10.6419 q^{61} -9.58464 q^{62} -1.18744 q^{63} +1.00000 q^{64} -6.41837 q^{65} +2.18792 q^{66} -0.258038 q^{67} +1.04726 q^{68} -3.24501 q^{69} +0.664484 q^{70} +3.31954 q^{71} +1.78700 q^{72} +2.54730 q^{73} -8.21694 q^{74} -2.18792 q^{75} +2.70107 q^{76} +0.664484 q^{77} -14.0429 q^{78} -2.27557 q^{79} -1.00000 q^{80} -11.1676 q^{81} +4.09505 q^{82} -13.4195 q^{83} +1.45384 q^{84} -1.04726 q^{85} -1.00000 q^{86} +11.4462 q^{87} -1.00000 q^{88} +11.7254 q^{89} -1.78700 q^{90} -4.26490 q^{91} +1.48315 q^{92} +20.9705 q^{93} -4.37481 q^{94} -2.70107 q^{95} -2.18792 q^{96} +4.68733 q^{97} -6.55846 q^{98} -1.78700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - 10 q^{5} - q^{6} + 3 q^{7} + 10 q^{8} + 13 q^{9} - 10 q^{10} - 10 q^{11} - q^{12} + 6 q^{13} + 3 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} + 13 q^{18} + 3 q^{19} - 10 q^{20} + 11 q^{21} - 10 q^{22} - 6 q^{23} - q^{24} + 10 q^{25} + 6 q^{26} + 8 q^{27} + 3 q^{28} + 14 q^{29} + q^{30} + 6 q^{31} + 10 q^{32} + q^{33} + 3 q^{34} - 3 q^{35} + 13 q^{36} + 10 q^{37} + 3 q^{38} + 24 q^{39} - 10 q^{40} + 26 q^{41} + 11 q^{42} - 10 q^{43} - 10 q^{44} - 13 q^{45} - 6 q^{46} + 3 q^{47} - q^{48} + 33 q^{49} + 10 q^{50} + 18 q^{51} + 6 q^{52} - 9 q^{53} + 8 q^{54} + 10 q^{55} + 3 q^{56} + 18 q^{57} + 14 q^{58} - 9 q^{59} + q^{60} + 22 q^{61} + 6 q^{62} - q^{63} + 10 q^{64} - 6 q^{65} + q^{66} + 18 q^{67} + 3 q^{68} + 6 q^{69} - 3 q^{70} + 27 q^{71} + 13 q^{72} + 28 q^{73} + 10 q^{74} - q^{75} + 3 q^{76} - 3 q^{77} + 24 q^{78} + 3 q^{79} - 10 q^{80} + 30 q^{81} + 26 q^{82} - 11 q^{83} + 11 q^{84} - 3 q^{85} - 10 q^{86} + 30 q^{87} - 10 q^{88} + 16 q^{89} - 13 q^{90} + 32 q^{91} - 6 q^{92} + 52 q^{93} + 3 q^{94} - 3 q^{95} - q^{96} + 22 q^{97} + 33 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - 10 * q^5 - q^6 + 3 * q^7 + 10 * q^8 + 13 * q^9 - 10 * q^10 - 10 * q^11 - q^12 + 6 * q^13 + 3 * q^14 + q^15 + 10 * q^16 + 3 * q^17 + 13 * q^18 + 3 * q^19 - 10 * q^20 + 11 * q^21 - 10 * q^22 - 6 * q^23 - q^24 + 10 * q^25 + 6 * q^26 + 8 * q^27 + 3 * q^28 + 14 * q^29 + q^30 + 6 * q^31 + 10 * q^32 + q^33 + 3 * q^34 - 3 * q^35 + 13 * q^36 + 10 * q^37 + 3 * q^38 + 24 * q^39 - 10 * q^40 + 26 * q^41 + 11 * q^42 - 10 * q^43 - 10 * q^44 - 13 * q^45 - 6 * q^46 + 3 * q^47 - q^48 + 33 * q^49 + 10 * q^50 + 18 * q^51 + 6 * q^52 - 9 * q^53 + 8 * q^54 + 10 * q^55 + 3 * q^56 + 18 * q^57 + 14 * q^58 - 9 * q^59 + q^60 + 22 * q^61 + 6 * q^62 - q^63 + 10 * q^64 - 6 * q^65 + q^66 + 18 * q^67 + 3 * q^68 + 6 * q^69 - 3 * q^70 + 27 * q^71 + 13 * q^72 + 28 * q^73 + 10 * q^74 - q^75 + 3 * q^76 - 3 * q^77 + 24 * q^78 + 3 * q^79 - 10 * q^80 + 30 * q^81 + 26 * q^82 - 11 * q^83 + 11 * q^84 - 3 * q^85 - 10 * q^86 + 30 * q^87 - 10 * q^88 + 16 * q^89 - 13 * q^90 + 32 * q^91 - 6 * q^92 + 52 * q^93 + 3 * q^94 - 3 * q^95 - q^96 + 22 * q^97 + 33 * q^98 - 13 * q^99

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