LMFDB - Embedded newform 4730.2.a.u.1.4

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.23252.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 2 $ x^4 - x^3 - 6*x^2 + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.95372$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.95372 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.95372 q^{6} -2.77076 q^{7} +1.00000 q^{8} +0.817036 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.95372 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.95372 q^{6} -2.77076 q^{7} +1.00000 q^{8} +0.817036 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.95372 q^{12} -4.27661 q^{13} -2.77076 q^{14} +1.95372 q^{15} +1.00000 q^{16} -5.17126 q^{17} +0.817036 q^{18} -3.13669 q^{19} +1.00000 q^{20} -5.41330 q^{21} -1.00000 q^{22} -6.13669 q^{23} +1.95372 q^{24} +1.00000 q^{25} -4.27661 q^{26} -4.26491 q^{27} -2.77076 q^{28} +1.44787 q^{29} +1.95372 q^{30} +6.54152 q^{31} +1.00000 q^{32} -1.95372 q^{33} -5.17126 q^{34} -2.77076 q^{35} +0.817036 q^{36} -7.30795 q^{37} -3.13669 q^{38} -8.35532 q^{39} +1.00000 q^{40} -2.27661 q^{41} -5.41330 q^{42} -1.00000 q^{43} -1.00000 q^{44} +0.817036 q^{45} -6.13669 q^{46} -2.00000 q^{47} +1.95372 q^{48} +0.677111 q^{49} +1.00000 q^{50} -10.1032 q^{51} -4.27661 q^{52} +4.76752 q^{53} -4.26491 q^{54} -1.00000 q^{55} -2.77076 q^{56} -6.12822 q^{57} +1.44787 q^{58} +6.75906 q^{59} +1.95372 q^{60} +8.55432 q^{61} +6.54152 q^{62} -2.26381 q^{63} +1.00000 q^{64} -4.27661 q^{65} -1.95372 q^{66} -5.80533 q^{67} -5.17126 q^{68} -11.9894 q^{69} -2.77076 q^{70} +2.23357 q^{71} +0.817036 q^{72} -4.50585 q^{73} -7.30795 q^{74} +1.95372 q^{75} -3.13669 q^{76} +2.77076 q^{77} -8.35532 q^{78} +6.89251 q^{79} +1.00000 q^{80} -10.7836 q^{81} -2.27661 q^{82} -14.8772 q^{83} -5.41330 q^{84} -5.17126 q^{85} -1.00000 q^{86} +2.82874 q^{87} -1.00000 q^{88} +14.1032 q^{89} +0.817036 q^{90} +11.8495 q^{91} -6.13669 q^{92} +12.7803 q^{93} -2.00000 q^{94} -3.13669 q^{95} +1.95372 q^{96} -7.01390 q^{97} +0.677111 q^{98} -0.817036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * 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
$3$	1.95372	1.12798	0.563991	−	0.825781i	$-0.309265\pi$
$3$	1.95372	1.12798	0.563991	+	0.825781i	$0.309265\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.95372	0.797604
$7$	−2.77076	−1.04725	−0.523624	−	0.851949i	$-0.675420\pi$
$7$	−2.77076	−1.04725	−0.523624	+	0.851949i	$0.675420\pi$
$8$	1.00000	0.353553
$9$	0.817036	0.272345
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.95372	0.563991
$13$	−4.27661	−1.18612	−0.593059	−	0.805159i	$-0.702080\pi$
$13$	−4.27661	−1.18612	−0.593059	+	0.805159i	$0.702080\pi$
$14$	−2.77076	−0.740517
$15$	1.95372	0.504449
$16$	1.00000	0.250000
$17$	−5.17126	−1.25421	−0.627107	−	0.778933i	$-0.715761\pi$
$17$	−5.17126	−1.25421	−0.627107	+	0.778933i	$0.715761\pi$
$18$	0.817036	0.192577
$19$	−3.13669	−0.719605	−0.359803	−	0.933028i	$-0.617156\pi$
$19$	−3.13669	−0.719605	−0.359803	+	0.933028i	$0.617156\pi$
$20$	1.00000	0.223607
$21$	−5.41330	−1.18128
$22$	−1.00000	−0.213201
$23$	−6.13669	−1.27959	−0.639794	−	0.768547i	$-0.720980\pi$
$23$	−6.13669	−1.27959	−0.639794	+	0.768547i	$0.720980\pi$
$24$	1.95372	0.398802
$25$	1.00000	0.200000
$26$	−4.27661	−0.838713
$27$	−4.26491	−0.820782
$28$	−2.77076	−0.523624
$29$	1.44787	0.268863	0.134431	−	0.990923i	$-0.457079\pi$
$29$	1.44787	0.268863	0.134431	+	0.990923i	$0.457079\pi$
$30$	1.95372	0.356700
$31$	6.54152	1.17489	0.587446	−	0.809263i	$-0.300134\pi$
$31$	6.54152	1.17489	0.587446	+	0.809263i	$0.300134\pi$
$32$	1.00000	0.176777
$33$	−1.95372	−0.340100
$34$	−5.17126	−0.886864
$35$	−2.77076	−0.468344
$36$	0.817036	0.136173
$37$	−7.30795	−1.20142	−0.600710	−	0.799467i	$-0.705115\pi$
$37$	−7.30795	−1.20142	−0.600710	+	0.799467i	$0.705115\pi$
$38$	−3.13669	−0.508838
$39$	−8.35532	−1.33792
$40$	1.00000	0.158114
$41$	−2.27661	−0.355547	−0.177774	−	0.984071i	$-0.556889\pi$
$41$	−2.27661	−0.355547	−0.177774	+	0.984071i	$0.556889\pi$
$42$	−5.41330	−0.835290
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	0.817036	0.121797
$46$	−6.13669	−0.904805
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	1.95372	0.281996
$49$	0.677111	0.0967302
$50$	1.00000	0.141421
$51$	−10.1032	−1.41473
$52$	−4.27661	−0.593059
$53$	4.76752	0.654870	0.327435	−	0.944874i	$-0.393816\pi$
$53$	4.76752	0.654870	0.327435	+	0.944874i	$0.393816\pi$
$54$	−4.26491	−0.580380
$55$	−1.00000	−0.134840
$56$	−2.77076	−0.370258
$57$	−6.12822	−0.811703
$58$	1.44787	0.190115
$59$	6.75906	0.879954	0.439977	−	0.898009i	$-0.354987\pi$
$59$	6.75906	0.879954	0.439977	+	0.898009i	$0.354987\pi$
$60$	1.95372	0.252225
$61$	8.55432	1.09527	0.547634	−	0.836718i	$-0.315529\pi$
$61$	8.55432	1.09527	0.547634	+	0.836718i	$0.315529\pi$
$62$	6.54152	0.830774
$63$	−2.26381	−0.285213
$64$	1.00000	0.125000
$65$	−4.27661	−0.530448
$66$	−1.95372	−0.240487
$67$	−5.80533	−0.709234	−0.354617	−	0.935012i	$-0.615389\pi$
$67$	−5.80533	−0.709234	−0.354617	+	0.935012i	$0.615389\pi$
$68$	−5.17126	−0.627107
$69$	−11.9894	−1.44335
$70$	−2.77076	−0.331169
$71$	2.23357	0.265076	0.132538	−	0.991178i	$-0.457687\pi$
$71$	2.23357	0.265076	0.132538	+	0.991178i	$0.457687\pi$
$72$	0.817036	0.0962887
$73$	−4.50585	−0.527370	−0.263685	−	0.964609i	$-0.584938\pi$
$73$	−4.50585	−0.527370	−0.263685	+	0.964609i	$0.584938\pi$
$74$	−7.30795	−0.849532
$75$	1.95372	0.225597
$76$	−3.13669	−0.359803
$77$	2.77076	0.315757
$78$	−8.35532	−0.946054
$79$	6.89251	0.775467	0.387734	−	0.921771i	$-0.373258\pi$
$79$	6.89251	0.775467	0.387734	+	0.921771i	$0.373258\pi$
$80$	1.00000	0.111803
$81$	−10.7836	−1.19817
$82$	−2.27661	−0.251410
$83$	−14.8772	−1.63299	−0.816493	−	0.577355i	$-0.804085\pi$
$83$	−14.8772	−1.63299	−0.816493	+	0.577355i	$0.804085\pi$
$84$	−5.41330	−0.590639
$85$	−5.17126	−0.560902
$86$	−1.00000	−0.107833
$87$	2.82874	0.303273
$88$	−1.00000	−0.106600
$89$	14.1032	1.49494	0.747469	−	0.664297i	$-0.231269\pi$
$89$	14.1032	1.49494	0.747469	+	0.664297i	$0.231269\pi$
$90$	0.817036	0.0861232
$91$	11.8495	1.24216
$92$	−6.13669	−0.639794
$93$	12.7803	1.32526
$94$	−2.00000	−0.206284
$95$	−3.13669	−0.321817
$96$	1.95372	0.199401
$97$	−7.01390	−0.712153	−0.356077	−	0.934457i	$-0.615886\pi$
$97$	−7.01390	−0.712153	−0.356077	+	0.934457i	$0.615886\pi$
$98$	0.677111	0.0683986
$99$	−0.817036	−0.0821152
$100$	1.00000	0.100000
$101$	9.23034	0.918453	0.459226	−	0.888319i	$-0.348127\pi$
$101$	9.23034	0.918453	0.459226	+	0.888319i	$0.348127\pi$
$102$	−10.1032	−1.00037
$103$	11.8840	1.17097	0.585485	−	0.810684i	$-0.300904\pi$
$103$	11.8840	1.17097	0.585485	+	0.810684i	$0.300904\pi$
$104$	−4.27661	−0.419356
$105$	−5.41330	−0.528284
$106$	4.76752	0.463063
$107$	6.78570	0.655999	0.327999	−	0.944678i	$-0.393626\pi$
$107$	6.78570	0.655999	0.327999	+	0.944678i	$0.393626\pi$
$108$	−4.26491	−0.410391
$109$	−8.77186	−0.840191	−0.420096	−	0.907480i	$-0.638004\pi$
$109$	−8.77186	−0.840191	−0.420096	+	0.907480i	$0.638004\pi$
$110$	−1.00000	−0.0953463
$111$	−14.2777	−1.35518
$112$	−2.77076	−0.261812
$113$	−6.94312	−0.653153	−0.326577	−	0.945171i	$-0.605895\pi$
$113$	−6.94312	−0.653153	−0.326577	+	0.945171i	$0.605895\pi$
$114$	−6.12822	−0.573960
$115$	−6.13669	−0.572249
$116$	1.44787	0.134431
$117$	−3.49415	−0.323034
$118$	6.75906	0.622222
$119$	14.3283	1.31347
$120$	1.95372	0.178350
$121$	1.00000	0.0909091
$122$	8.55432	0.774472
$123$	−4.44787	−0.401051
$124$	6.54152	0.587446
$125$	1.00000	0.0894427
$126$	−2.26381	−0.201676
$127$	−8.24204	−0.731363	−0.365681	−	0.930740i	$-0.619164\pi$
$127$	−8.24204	−0.731363	−0.365681	+	0.930740i	$0.619164\pi$
$128$	1.00000	0.0883883
$129$	−1.95372	−0.172016
$130$	−4.27661	−0.375084
$131$	−2.94202	−0.257045	−0.128523	−	0.991707i	$-0.541024\pi$
$131$	−2.94202	−0.257045	−0.128523	+	0.991707i	$0.541024\pi$
$132$	−1.95372	−0.170050
$133$	8.69101	0.753606
$134$	−5.80533	−0.501504
$135$	−4.26491	−0.367065
$136$	−5.17126	−0.443432
$137$	1.10894	0.0947435	0.0473718	−	0.998877i	$-0.484915\pi$
$137$	1.10894	0.0947435	0.0473718	+	0.998877i	$0.484915\pi$
$138$	−11.9894	−1.02060
$139$	−13.3017	−1.12823	−0.564117	−	0.825695i	$-0.690783\pi$
$139$	−13.3017	−1.12823	−0.564117	+	0.825695i	$0.690783\pi$
$140$	−2.77076	−0.234172
$141$	−3.90745	−0.329066
$142$	2.23357	0.187437
$143$	4.27661	0.357628
$144$	0.817036	0.0680864
$145$	1.44787	0.120239
$146$	−4.50585	−0.372907
$147$	1.32289	0.109110
$148$	−7.30795	−0.600710
$149$	11.1133	0.910435	0.455218	−	0.890380i	$-0.349561\pi$
$149$	11.1133	0.910435	0.455218	+	0.890380i	$0.349561\pi$
$150$	1.95372	0.159521
$151$	15.8277	1.28804	0.644020	−	0.765009i	$-0.277265\pi$
$151$	15.8277	1.28804	0.644020	+	0.765009i	$0.277265\pi$
$152$	−3.13669	−0.254419
$153$	−4.22511	−0.341580
$154$	2.77076	0.223274
$155$	6.54152	0.525428
$156$	−8.35532	−0.668961
$157$	10.0719	0.803823	0.401912	−	0.915678i	$-0.368346\pi$
$157$	10.0719	0.803823	0.401912	+	0.915678i	$0.368346\pi$
$158$	6.89251	0.548338
$159$	9.31442	0.738682
$160$	1.00000	0.0790569
$161$	17.0033	1.34005
$162$	−10.7836	−0.847237
$163$	17.1863	1.34613	0.673066	−	0.739583i	$-0.264977\pi$
$163$	17.1863	1.34613	0.673066	+	0.739583i	$0.264977\pi$
$164$	−2.27661	−0.177774
$165$	−1.95372	−0.152097
$166$	−14.8772	−1.15470
$167$	−19.1108	−1.47884	−0.739418	−	0.673246i	$-0.764899\pi$
$167$	−19.1108	−1.47884	−0.739418	+	0.673246i	$0.764899\pi$
$168$	−5.41330	−0.417645
$169$	5.28941	0.406878
$170$	−5.17126	−0.396617
$171$	−2.56279	−0.195981
$172$	−1.00000	−0.0762493
$173$	−13.0591	−0.992863	−0.496432	−	0.868076i	$-0.665357\pi$
$173$	−13.0591	−0.992863	−0.496432	+	0.868076i	$0.665357\pi$
$174$	2.82874	0.214446
$175$	−2.77076	−0.209450
$176$	−1.00000	−0.0753778
$177$	13.2053	0.992573
$178$	14.1032	1.05708
$179$	9.12175	0.681791	0.340896	−	0.940101i	$-0.389270\pi$
$179$	9.12175	0.681791	0.340896	+	0.940101i	$0.389270\pi$
$180$	0.817036	0.0608983
$181$	−0.643585	−0.0478373	−0.0239186	−	0.999714i	$-0.507614\pi$
$181$	−0.643585	−0.0478373	−0.0239186	+	0.999714i	$0.507614\pi$
$182$	11.8495	0.878341
$183$	16.7128	1.23544
$184$	−6.13669	−0.452403
$185$	−7.30795	−0.537291
$186$	12.7803	0.937099
$187$	5.17126	0.378160
$188$	−2.00000	−0.145865
$189$	11.8170	0.859563
$190$	−3.13669	−0.227559
$191$	1.34630	0.0974147	0.0487073	−	0.998813i	$-0.484490\pi$
$191$	1.34630	0.0974147	0.0487073	+	0.998813i	$0.484490\pi$
$192$	1.95372	0.140998
$193$	16.4038	1.18077	0.590385	−	0.807122i	$-0.298976\pi$
$193$	16.4038	1.18077	0.590385	+	0.807122i	$0.298976\pi$
$194$	−7.01390	−0.503568
$195$	−8.35532	−0.598337
$196$	0.677111	0.0483651
$197$	−10.9730	−0.781794	−0.390897	−	0.920434i	$-0.627835\pi$
$197$	−10.9730	−0.781794	−0.390897	+	0.920434i	$0.627835\pi$
$198$	−0.817036	−0.0580642
$199$	−7.55646	−0.535663	−0.267832	−	0.963466i	$-0.586307\pi$
$199$	−7.55646	−0.535663	−0.267832	+	0.963466i	$0.586307\pi$
$200$	1.00000	0.0707107
$201$	−11.3420	−0.800004
$202$	9.23034	0.649444
$203$	−4.01170	−0.281566
$204$	−10.1032	−0.707366
$205$	−2.27661	−0.159006
$206$	11.8840	0.828000
$207$	−5.01390	−0.348490
$208$	−4.27661	−0.296530
$209$	3.13669	0.216969
$210$	−5.41330	−0.373553
$211$	−3.27661	−0.225571	−0.112786	−	0.993619i	$-0.535977\pi$
$211$	−3.27661	−0.225571	−0.112786	+	0.993619i	$0.535977\pi$
$212$	4.76752	0.327435
$213$	4.36379	0.299002
$214$	6.78570	0.463861
$215$	−1.00000	−0.0681994
$216$	−4.26491	−0.290190
$217$	−18.1250	−1.23040
$218$	−8.77186	−0.594105
$219$	−8.80319	−0.594864
$220$	−1.00000	−0.0674200
$221$	22.1155	1.48765
$222$	−14.2777	−0.958257
$223$	−12.2372	−0.819461	−0.409731	−	0.912207i	$-0.634377\pi$
$223$	−12.2372	−0.819461	−0.409731	+	0.912207i	$0.634377\pi$
$224$	−2.77076	−0.185129
$225$	0.817036	0.0544691
$226$	−6.94312	−0.461849
$227$	3.26815	0.216914	0.108457	−	0.994101i	$-0.465409\pi$
$227$	3.26815	0.216914	0.108457	+	0.994101i	$0.465409\pi$
$228$	−6.12822	−0.405851
$229$	−22.5467	−1.48993	−0.744966	−	0.667103i	$-0.767534\pi$
$229$	−22.5467	−1.48993	−0.744966	+	0.667103i	$0.767534\pi$
$230$	−6.13669	−0.404641
$231$	5.41330	0.356169
$232$	1.44787	0.0950574
$233$	6.47706	0.424327	0.212163	−	0.977234i	$-0.431949\pi$
$233$	6.47706	0.424327	0.212163	+	0.977234i	$0.431949\pi$
$234$	−3.49415	−0.228420
$235$	−2.00000	−0.130466
$236$	6.75906	0.439977
$237$	13.4661	0.874714
$238$	14.3283	0.928767
$239$	−22.7558	−1.47195	−0.735976	−	0.677008i	$-0.763276\pi$
$239$	−22.7558	−1.47195	−0.735976	+	0.677008i	$0.763276\pi$
$240$	1.95372	0.126112
$241$	1.57773	0.101631	0.0508153	−	0.998708i	$-0.483818\pi$
$241$	1.57773	0.101631	0.0508153	+	0.998708i	$0.483818\pi$
$242$	1.00000	0.0642824
$243$	−8.27337	−0.530737
$244$	8.55432	0.547634
$245$	0.677111	0.0432591
$246$	−4.44787	−0.283586
$247$	13.4144	0.853538
$248$	6.54152	0.415387
$249$	−29.0660	−1.84198
$250$	1.00000	0.0632456
$251$	5.42824	0.342628	0.171314	−	0.985217i	$-0.445199\pi$
$251$	5.42824	0.342628	0.171314	+	0.985217i	$0.445199\pi$
$252$	−2.26381	−0.142607
$253$	6.13669	0.385810
$254$	−8.24204	−0.517152
$255$	−10.1032	−0.632688
$256$	1.00000	0.0625000
$257$	−11.5197	−0.718582	−0.359291	−	0.933226i	$-0.616981\pi$
$257$	−11.5197	−0.718582	−0.359291	+	0.933226i	$0.616981\pi$
$258$	−1.95372	−0.121634
$259$	20.2486	1.25818
$260$	−4.27661	−0.265224
$261$	1.18296	0.0732236
$262$	−2.94202	−0.181759
$263$	−24.5857	−1.51602	−0.758008	−	0.652245i	$-0.773827\pi$
$263$	−24.5857	−1.51602	−0.758008	+	0.652245i	$0.773827\pi$
$264$	−1.95372	−0.120243
$265$	4.76752	0.292867
$266$	8.69101	0.532880
$267$	27.5538	1.68626
$268$	−5.80533	−0.354617
$269$	−9.52299	−0.580627	−0.290313	−	0.956932i	$-0.593760\pi$
$269$	−9.52299	−0.580627	−0.290313	+	0.956932i	$0.593760\pi$
$270$	−4.26491	−0.259554
$271$	−23.2606	−1.41298	−0.706491	−	0.707722i	$-0.749723\pi$
$271$	−23.2606	−1.41298	−0.706491	+	0.707722i	$0.749723\pi$
$272$	−5.17126	−0.313554
$273$	23.1506	1.40114
$274$	1.10894	0.0669938
$275$	−1.00000	−0.0603023
$276$	−11.9894	−0.721677
$277$	−31.6404	−1.90109	−0.950544	−	0.310591i	$-0.899473\pi$
$277$	−31.6404	−1.90109	−0.950544	+	0.310591i	$0.899473\pi$
$278$	−13.3017	−0.797781
$279$	5.34466	0.319976
$280$	−2.77076	−0.165585
$281$	8.66814	0.517098	0.258549	−	0.965998i	$-0.416756\pi$
$281$	8.66814	0.517098	0.258549	+	0.965998i	$0.416756\pi$
$282$	−3.90745	−0.232685
$283$	23.0613	1.37085	0.685425	−	0.728143i	$-0.259616\pi$
$283$	23.0613	1.37085	0.685425	+	0.728143i	$0.259616\pi$
$284$	2.23357	0.132538
$285$	−6.12822	−0.363004
$286$	4.27661	0.252881
$287$	6.30795	0.372346
$288$	0.817036	0.0481443
$289$	9.74192	0.573054
$290$	1.44787	0.0850219
$291$	−13.7032	−0.803297
$292$	−4.50585	−0.263685
$293$	1.85684	0.108478	0.0542388	−	0.998528i	$-0.482727\pi$
$293$	1.85684	0.108478	0.0542388	+	0.998528i	$0.482727\pi$
$294$	1.32289	0.0771524
$295$	6.75906	0.393527
$296$	−7.30795	−0.424766
$297$	4.26491	0.247475
$298$	11.1133	0.643775
$299$	26.2442	1.51774
$300$	1.95372	0.112798
$301$	2.77076	0.159704
$302$	15.8277	0.910782
$303$	18.0335	1.03600
$304$	−3.13669	−0.179901
$305$	8.55432	0.489819
$306$	−4.22511	−0.241533
$307$	10.9899	0.627229	0.313614	−	0.949550i	$-0.398460\pi$
$307$	10.9899	0.627229	0.313614	+	0.949550i	$0.398460\pi$
$308$	2.77076	0.157879
$309$	23.2181	1.32083
$310$	6.54152	0.371533
$311$	17.9293	1.01668	0.508338	−	0.861158i	$-0.330260\pi$
$311$	17.9293	1.01668	0.508338	+	0.861158i	$0.330260\pi$
$312$	−8.35532	−0.473027
$313$	19.8840	1.12391	0.561956	−	0.827167i	$-0.310049\pi$
$313$	19.8840	1.12391	0.561956	+	0.827167i	$0.310049\pi$
$314$	10.0719	0.568389
$315$	−2.26381	−0.127551
$316$	6.89251	0.387734
$317$	−21.1340	−1.18700	−0.593502	−	0.804833i	$-0.702255\pi$
$317$	−21.1340	−1.18700	−0.593502	+	0.804833i	$0.702255\pi$
$318$	9.31442	0.522327
$319$	−1.44787	−0.0810652
$320$	1.00000	0.0559017
$321$	13.2574	0.739955
$322$	17.0033	0.947556
$323$	16.2206	0.902540
$324$	−10.7836	−0.599087
$325$	−4.27661	−0.237224
$326$	17.1863	0.951858
$327$	−17.1378	−0.947722
$328$	−2.27661	−0.125705
$329$	5.54152	0.305514
$330$	−1.95372	−0.107549
$331$	18.8522	1.03621	0.518105	−	0.855317i	$-0.326638\pi$
$331$	18.8522	1.03621	0.518105	+	0.855317i	$0.326638\pi$
$332$	−14.8772	−0.816493
$333$	−5.97086	−0.327201
$334$	−19.1108	−1.04570
$335$	−5.80533	−0.317179
$336$	−5.41330	−0.295320
$337$	7.11004	0.387309	0.193654	−	0.981070i	$-0.437966\pi$
$337$	7.11004	0.387309	0.193654	+	0.981070i	$0.437966\pi$
$338$	5.28941	0.287706
$339$	−13.5649	−0.736746
$340$	−5.17126	−0.280451
$341$	−6.54152	−0.354243
$342$	−2.56279	−0.138580
$343$	17.5192	0.945948
$344$	−1.00000	−0.0539164
$345$	−11.9894	−0.645487
$346$	−13.0591	−0.702060
$347$	−29.3352	−1.57480	−0.787398	−	0.616445i	$-0.788572\pi$
$347$	−29.3352	−1.57480	−0.787398	+	0.616445i	$0.788572\pi$
$348$	2.82874	0.151636
$349$	−10.2363	−0.547937	−0.273968	−	0.961739i	$-0.588336\pi$
$349$	−10.2363	−0.547937	−0.273968	+	0.961739i	$0.588336\pi$
$350$	−2.77076	−0.148103
$351$	18.2394	0.973545
$352$	−1.00000	−0.0533002
$353$	12.3632	0.658029	0.329015	−	0.944325i	$-0.393283\pi$
$353$	12.3632	0.658029	0.329015	+	0.944325i	$0.393283\pi$
$354$	13.2053	0.701855
$355$	2.23357	0.118546
$356$	14.1032	0.747469
$357$	27.9936	1.48158
$358$	9.12175	0.482099
$359$	−8.81130	−0.465043	−0.232521	−	0.972591i	$-0.574698\pi$
$359$	−8.81130	−0.465043	−0.232521	+	0.972591i	$0.574698\pi$
$360$	0.817036	0.0430616
$361$	−9.16119	−0.482168
$362$	−0.643585	−0.0338261
$363$	1.95372	0.102544
$364$	11.8495	0.621081
$365$	−4.50585	−0.235847
$366$	16.7128	0.873591
$367$	−13.3379	−0.696232	−0.348116	−	0.937452i	$-0.613178\pi$
$367$	−13.3379	−0.696232	−0.348116	+	0.937452i	$0.613178\pi$
$368$	−6.13669	−0.319897
$369$	−1.86008	−0.0968316
$370$	−7.30795	−0.379922
$371$	−13.2097	−0.685811
$372$	12.7803	0.662629
$373$	−10.6978	−0.553913	−0.276957	−	0.960882i	$-0.589326\pi$
$373$	−10.6978	−0.553913	−0.276957	+	0.960882i	$0.589326\pi$
$374$	5.17126	0.267399
$375$	1.95372	0.100890
$376$	−2.00000	−0.103142
$377$	−6.19198	−0.318903
$378$	11.8170	0.607803
$379$	24.5996	1.26359	0.631797	−	0.775134i	$-0.282318\pi$
$379$	24.5996	1.26359	0.631797	+	0.775134i	$0.282318\pi$
$380$	−3.13669	−0.160909
$381$	−16.1027	−0.824965
$382$	1.34630	0.0688826
$383$	−5.22491	−0.266980	−0.133490	−	0.991050i	$-0.542618\pi$
$383$	−5.22491	−0.266980	−0.133490	+	0.991050i	$0.542618\pi$
$384$	1.95372	0.0997005
$385$	2.77076	0.141211
$386$	16.4038	0.834931
$387$	−0.817036	−0.0415323
$388$	−7.01390	−0.356077
$389$	−19.4319	−0.985236	−0.492618	−	0.870246i	$-0.663960\pi$
$389$	−19.4319	−0.985236	−0.492618	+	0.870246i	$0.663960\pi$
$390$	−8.35532	−0.423088
$391$	31.7344	1.60488
$392$	0.677111	0.0341993
$393$	−5.74789	−0.289943
$394$	−10.9730	−0.552812
$395$	6.89251	0.346800
$396$	−0.817036	−0.0410576
$397$	21.3251	1.07028	0.535138	−	0.844765i	$-0.320260\pi$
$397$	21.3251	1.07028	0.535138	+	0.844765i	$0.320260\pi$
$398$	−7.55646	−0.378771
$399$	16.9798	0.850055
$400$	1.00000	0.0500000
$401$	5.62456	0.280877	0.140439	−	0.990089i	$-0.455149\pi$
$401$	5.62456	0.280877	0.140439	+	0.990089i	$0.455149\pi$
$402$	−11.3420	−0.565688
$403$	−27.9755	−1.39356
$404$	9.23034	0.459226
$405$	−10.7836	−0.535839
$406$	−4.01170	−0.199098
$407$	7.30795	0.362241
$408$	−10.1032	−0.500184
$409$	−5.76588	−0.285105	−0.142552	−	0.989787i	$-0.545531\pi$
$409$	−5.76588	−0.285105	−0.142552	+	0.989787i	$0.545531\pi$
$410$	−2.27661	−0.112434
$411$	2.16657	0.106869
$412$	11.8840	0.585485
$413$	−18.7277	−0.921531
$414$	−5.01390	−0.246420
$415$	−14.8772	−0.730293
$416$	−4.27661	−0.209678
$417$	−25.9878	−1.27263
$418$	3.13669	0.153420
$419$	34.6825	1.69435	0.847177	−	0.531312i	$-0.178301\pi$
$419$	34.6825	1.69435	0.847177	+	0.531312i	$0.178301\pi$
$420$	−5.41330	−0.264142
$421$	−0.480251	−0.0234060	−0.0117030	−	0.999932i	$-0.503725\pi$
$421$	−0.480251	−0.0234060	−0.0117030	+	0.999932i	$0.503725\pi$
$422$	−3.27661	−0.159503
$423$	−1.63407	−0.0794513
$424$	4.76752	0.231531
$425$	−5.17126	−0.250843
$426$	4.36379	0.211426
$427$	−23.7020	−1.14702
$428$	6.78570	0.327999
$429$	8.35532	0.403399
$430$	−1.00000	−0.0482243
$431$	−30.6921	−1.47839	−0.739193	−	0.673493i	$-0.764793\pi$
$431$	−30.6921	−1.47839	−0.739193	+	0.673493i	$0.764793\pi$
$432$	−4.26491	−0.205195
$433$	13.0591	0.627579	0.313790	−	0.949493i	$-0.398401\pi$
$433$	13.0591	0.627579	0.313790	+	0.949493i	$0.398401\pi$
$434$	−18.1250	−0.870027
$435$	2.82874	0.135628
$436$	−8.77186	−0.420096
$437$	19.2489	0.920798
$438$	−8.80319	−0.420633
$439$	3.21754	0.153565	0.0767823	−	0.997048i	$-0.475535\pi$
$439$	3.21754	0.153565	0.0767823	+	0.997048i	$0.475535\pi$
$440$	−1.00000	−0.0476731
$441$	0.553225	0.0263440
$442$	22.1155	1.05193
$443$	25.7683	1.22429	0.612144	−	0.790747i	$-0.290307\pi$
$443$	25.7683	1.22429	0.612144	+	0.790747i	$0.290307\pi$
$444$	−14.2777	−0.677590
$445$	14.1032	0.668556
$446$	−12.2372	−0.579447
$447$	21.7123	1.02696
$448$	−2.77076	−0.130906
$449$	−11.9074	−0.561947	−0.280974	−	0.959715i	$-0.590657\pi$
$449$	−11.9074	−0.561947	−0.280974	+	0.959715i	$0.590657\pi$
$450$	0.817036	0.0385155
$451$	2.27661	0.107201
$452$	−6.94312	−0.326577
$453$	30.9229	1.45289
$454$	3.26815	0.153382
$455$	11.8495	0.555512
$456$	−6.12822	−0.286980
$457$	−25.4574	−1.19085	−0.595424	−	0.803411i	$-0.703016\pi$
$457$	−25.4574	−1.19085	−0.595424	+	0.803411i	$0.703016\pi$
$458$	−22.5467	−1.05354
$459$	22.0549	1.02944
$460$	−6.13669	−0.286125
$461$	−32.3026	−1.50448	−0.752240	−	0.658889i	$-0.771027\pi$
$461$	−32.3026	−1.50448	−0.752240	+	0.658889i	$0.771027\pi$
$462$	5.41330	0.251849
$463$	−14.7814	−0.686951	−0.343475	−	0.939162i	$-0.611604\pi$
$463$	−14.7814	−0.686951	−0.343475	+	0.939162i	$0.611604\pi$
$464$	1.44787	0.0672157
$465$	12.7803	0.592673
$466$	6.47706	0.300044
$467$	5.70740	0.264107	0.132053	−	0.991243i	$-0.457843\pi$
$467$	5.70740	0.264107	0.132053	+	0.991243i	$0.457843\pi$
$468$	−3.49415	−0.161517
$469$	16.0852	0.742745
$470$	−2.00000	−0.0922531
$471$	19.6777	0.906699
$472$	6.75906	0.311111
$473$	1.00000	0.0459800
$474$	13.4661	0.618516
$475$	−3.13669	−0.143921
$476$	14.3283	0.656737
$477$	3.89524	0.178351
$478$	−22.7558	−1.04083
$479$	32.9883	1.50727	0.753637	−	0.657291i	$-0.228298\pi$
$479$	32.9883	1.50727	0.753637	+	0.657291i	$0.228298\pi$
$480$	1.95372	0.0891749
$481$	31.2533	1.42503
$482$	1.57773	0.0718636
$483$	33.2197	1.51155
$484$	1.00000	0.0454545
$485$	−7.01390	−0.318485
$486$	−8.27337	−0.375288
$487$	−18.6230	−0.843887	−0.421943	−	0.906622i	$-0.638652\pi$
$487$	−18.6230	−0.843887	−0.421943	+	0.906622i	$0.638652\pi$
$488$	8.55432	0.387236
$489$	33.5772	1.51841
$490$	0.677111	0.0305888
$491$	−35.1571	−1.58662	−0.793309	−	0.608819i	$-0.791644\pi$
$491$	−35.1571	−1.58662	−0.793309	+	0.608819i	$0.791644\pi$
$492$	−4.44787	−0.200526
$493$	−7.48732	−0.337212
$494$	13.4144	0.603542
$495$	−0.817036	−0.0367231
$496$	6.54152	0.293723
$497$	−6.18870	−0.277601
$498$	−29.0660	−1.30248
$499$	19.7547	0.884343	0.442171	−	0.896931i	$-0.354208\pi$
$499$	19.7547	0.884343	0.442171	+	0.896931i	$0.354208\pi$
$500$	1.00000	0.0447214
$501$	−37.3372	−1.66810
$502$	5.42824	0.242274
$503$	−16.4743	−0.734554	−0.367277	−	0.930112i	$-0.619710\pi$
$503$	−16.4743	−0.734554	−0.367277	+	0.930112i	$0.619710\pi$
$504$	−2.26381	−0.100838
$505$	9.23034	0.410745
$506$	6.13669	0.272809
$507$	10.3341	0.458951
$508$	−8.24204	−0.365681
$509$	−37.2405	−1.65065	−0.825327	−	0.564655i	$-0.809009\pi$
$509$	−37.2405	−1.65065	−0.825327	+	0.564655i	$0.809009\pi$
$510$	−10.1032	−0.447378
$511$	12.4846	0.552288
$512$	1.00000	0.0441942
$513$	13.3777	0.590639
$514$	−11.5197	−0.508114
$515$	11.8840	0.523673
$516$	−1.95372	−0.0860079
$517$	2.00000	0.0879599
$518$	20.2486	0.889671
$519$	−25.5138	−1.11993
$520$	−4.27661	−0.187542
$521$	−44.3426	−1.94269	−0.971343	−	0.237683i	$-0.923612\pi$
$521$	−44.3426	−1.94269	−0.971343	+	0.237683i	$0.923612\pi$
$522$	1.18296	0.0517769
$523$	9.32129	0.407591	0.203796	−	0.979013i	$-0.434672\pi$
$523$	9.32129	0.407591	0.203796	+	0.979013i	$0.434672\pi$
$524$	−2.94202	−0.128523
$525$	−5.41330	−0.236256
$526$	−24.5857	−1.07199
$527$	−33.8279	−1.47357
$528$	−1.95372	−0.0850249
$529$	14.6589	0.637345
$530$	4.76752	0.207088
$531$	5.52239	0.239651
$532$	8.69101	0.376803
$533$	9.73619	0.421721
$534$	27.5538	1.19237
$535$	6.78570	0.293371
$536$	−5.80533	−0.250752
$537$	17.8214	0.769049
$538$	−9.52299	−0.410565
$539$	−0.677111	−0.0291653
$540$	−4.26491	−0.183532
$541$	5.90531	0.253889	0.126944	−	0.991910i	$-0.459483\pi$
$541$	5.90531	0.253889	0.126944	+	0.991910i	$0.459483\pi$
$542$	−23.2606	−0.999129
$543$	−1.25739	−0.0539597
$544$	−5.17126	−0.221716
$545$	−8.77186	−0.375745
$546$	23.1506	0.990754
$547$	20.5298	0.877792	0.438896	−	0.898538i	$-0.355370\pi$
$547$	20.5298	0.877792	0.438896	+	0.898538i	$0.355370\pi$
$548$	1.10894	0.0473718
$549$	6.98919	0.298291
$550$	−1.00000	−0.0426401
$551$	−4.54152	−0.193475
$552$	−11.9894	−0.510302
$553$	−19.0975	−0.812107
$554$	−31.6404	−1.34427
$555$	−14.2777	−0.606055
$556$	−13.3017	−0.564117
$557$	−3.79521	−0.160808	−0.0804042	−	0.996762i	$-0.525621\pi$
$557$	−3.79521	−0.160808	−0.0804042	+	0.996762i	$0.525621\pi$
$558$	5.34466	0.226257
$559$	4.27661	0.180881
$560$	−2.77076	−0.117086
$561$	10.1032	0.426558
$562$	8.66814	0.365643
$563$	26.9959	1.13774	0.568871	−	0.822427i	$-0.307380\pi$
$563$	26.9959	1.13774	0.568871	+	0.822427i	$0.307380\pi$
$564$	−3.90745	−0.164533
$565$	−6.94312	−0.292099
$566$	23.0613	0.969337
$567$	29.8787	1.25479
$568$	2.23357	0.0937187
$569$	−45.9479	−1.92623	−0.963117	−	0.269083i	$-0.913280\pi$
$569$	−45.9479	−1.92623	−0.963117	+	0.269083i	$0.913280\pi$
$570$	−6.12822	−0.256683
$571$	−42.0916	−1.76148	−0.880738	−	0.473603i	$-0.842953\pi$
$571$	−42.0916	−1.76148	−0.880738	+	0.473603i	$0.842953\pi$
$572$	4.27661	0.178814
$573$	2.63029	0.109882
$574$	6.30795	0.263289
$575$	−6.13669	−0.255918
$576$	0.817036	0.0340432
$577$	16.8336	0.700793	0.350397	−	0.936601i	$-0.386047\pi$
$577$	16.8336	0.700793	0.350397	+	0.936601i	$0.386047\pi$
$578$	9.74192	0.405211
$579$	32.0485	1.33189
$580$	1.44787	0.0601196
$581$	41.2212	1.71014
$582$	−13.7032	−0.568017
$583$	−4.76752	−0.197451
$584$	−4.50585	−0.186453
$585$	−3.49415	−0.144465
$586$	1.85684	0.0767052
$587$	−5.64473	−0.232983	−0.116492	−	0.993192i	$-0.537165\pi$
$587$	−5.64473	−0.232983	−0.116492	+	0.993192i	$0.537165\pi$
$588$	1.32289	0.0545550
$589$	−20.5187	−0.845458
$590$	6.75906	0.278266
$591$	−21.4382	−0.881850
$592$	−7.30795	−0.300355
$593$	−15.5568	−0.638842	−0.319421	−	0.947613i	$-0.603488\pi$
$593$	−15.5568	−0.638842	−0.319421	+	0.947613i	$0.603488\pi$
$594$	4.26491	0.174991
$595$	14.3283	0.587404
$596$	11.1133	0.455218
$597$	−14.7632	−0.604219
$598$	26.2442	1.07321
$599$	10.4272	0.426044	0.213022	−	0.977047i	$-0.431669\pi$
$599$	10.4272	0.426044	0.213022	+	0.977047i	$0.431669\pi$
$600$	1.95372	0.0797604
$601$	−22.7991	−0.929993	−0.464996	−	0.885313i	$-0.653944\pi$
$601$	−22.7991	−0.929993	−0.464996	+	0.885313i	$0.653944\pi$
$602$	2.77076	0.112928
$603$	−4.74317	−0.193157
$604$	15.8277	0.644020
$605$	1.00000	0.0406558
$606$	18.0335	0.732562
$607$	23.7081	0.962284	0.481142	−	0.876643i	$-0.340222\pi$
$607$	23.7081	0.962284	0.481142	+	0.876643i	$0.340222\pi$
$608$	−3.13669	−0.127209
$609$	−7.83776	−0.317602
$610$	8.55432	0.346354
$611$	8.55322	0.346026
$612$	−4.22511	−0.170790
$613$	−0.251011	−0.0101382	−0.00506912	−	0.999987i	$-0.501614\pi$
$613$	−0.251011	−0.0101382	−0.00506912	+	0.999987i	$0.501614\pi$
$614$	10.9899	0.443518
$615$	−4.44787	−0.179355
$616$	2.77076	0.111637
$617$	44.7570	1.80185	0.900924	−	0.433977i	$-0.142890\pi$
$617$	44.7570	1.80185	0.900924	+	0.433977i	$0.142890\pi$
$618$	23.2181	0.933970
$619$	−4.26850	−0.171565	−0.0857827	−	0.996314i	$-0.527339\pi$
$619$	−4.26850	−0.171565	−0.0857827	+	0.996314i	$0.527339\pi$
$620$	6.54152	0.262714
$621$	26.1724	1.05026
$622$	17.9293	0.718898
$623$	−39.0766	−1.56557
$624$	−8.35532	−0.334480
$625$	1.00000	0.0400000
$626$	19.8840	0.794726
$627$	6.12822	0.244738
$628$	10.0719	0.401912
$629$	37.7913	1.50684
$630$	−2.26381	−0.0901924
$631$	2.62291	0.104416	0.0522082	−	0.998636i	$-0.483374\pi$
$631$	2.62291	0.104416	0.0522082	+	0.998636i	$0.483374\pi$
$632$	6.89251	0.274169
$633$	−6.40160	−0.254441
$634$	−21.1340	−0.839339
$635$	−8.24204	−0.327075
$636$	9.31442	0.369341
$637$	−2.89574	−0.114734
$638$	−1.44787	−0.0573218
$639$	1.82491	0.0721924
$640$	1.00000	0.0395285
$641$	15.8554	0.626252	0.313126	−	0.949712i	$-0.398624\pi$
$641$	15.8554	0.626252	0.313126	+	0.949712i	$0.398624\pi$
$642$	13.2574	0.523227
$643$	31.3170	1.23502	0.617511	−	0.786562i	$-0.288141\pi$
$643$	31.3170	1.23502	0.617511	+	0.786562i	$0.288141\pi$
$644$	17.0033	0.670023
$645$	−1.95372	−0.0769278
$646$	16.2206	0.638192
$647$	−10.2453	−0.402783	−0.201392	−	0.979511i	$-0.564546\pi$
$647$	−10.2453	−0.402783	−0.201392	+	0.979511i	$0.564546\pi$
$648$	−10.7836	−0.423618
$649$	−6.75906	−0.265316
$650$	−4.27661	−0.167743
$651$	−35.4112	−1.38787
$652$	17.1863	0.673066
$653$	22.2736	0.871632	0.435816	−	0.900036i	$-0.356460\pi$
$653$	22.2736	0.871632	0.435816	+	0.900036i	$0.356460\pi$
$654$	−17.1378	−0.670140
$655$	−2.94202	−0.114954
$656$	−2.27661	−0.0888868
$657$	−3.68145	−0.143627
$658$	5.54152	0.216031
$659$	−22.2252	−0.865769	−0.432885	−	0.901449i	$-0.642504\pi$
$659$	−22.2252	−0.865769	−0.432885	+	0.901449i	$0.642504\pi$
$660$	−1.95372	−0.0760486
$661$	−42.3034	−1.64541	−0.822705	−	0.568469i	$-0.807536\pi$
$661$	−42.3034	−1.64541	−0.822705	+	0.568469i	$0.807536\pi$
$662$	18.8522	0.732712
$663$	43.2075	1.67804
$664$	−14.8772	−0.577348
$665$	8.69101	0.337023
$666$	−5.97086	−0.231366
$667$	−8.88513	−0.344034
$668$	−19.1108	−0.739418
$669$	−23.9080	−0.924338
$670$	−5.80533	−0.224280
$671$	−8.55432	−0.330236
$672$	−5.41330	−0.208823
$673$	−16.1329	−0.621878	−0.310939	−	0.950430i	$-0.600643\pi$
$673$	−16.1329	−0.621878	−0.310939	+	0.950430i	$0.600643\pi$
$674$	7.11004	0.273869
$675$	−4.26491	−0.164156
$676$	5.28941	0.203439
$677$	42.4692	1.63222	0.816112	−	0.577894i	$-0.196125\pi$
$677$	42.4692	1.63222	0.816112	+	0.577894i	$0.196125\pi$
$678$	−13.5649	−0.520958
$679$	19.4338	0.745802
$680$	−5.17126	−0.198309
$681$	6.38505	0.244676
$682$	−6.54152	−0.250488
$683$	−14.5043	−0.554990	−0.277495	−	0.960727i	$-0.589504\pi$
$683$	−14.5043	−0.554990	−0.277495	+	0.960727i	$0.589504\pi$
$684$	−2.56279	−0.0979906
$685$	1.10894	0.0423706
$686$	17.5192	0.668886
$687$	−44.0501	−1.68062
$688$	−1.00000	−0.0381246
$689$	−20.3888	−0.776753
$690$	−11.9894	−0.456428
$691$	−33.5331	−1.27566	−0.637830	−	0.770177i	$-0.720168\pi$
$691$	−33.5331	−1.27566	−0.637830	+	0.770177i	$0.720168\pi$
$692$	−13.0591	−0.496432
$693$	2.26381	0.0859951
$694$	−29.3352	−1.11355
$695$	−13.3017	−0.504561
$696$	2.82874	0.107223
$697$	11.7730	0.445932
$698$	−10.2363	−0.387450
$699$	12.6544	0.478633
$700$	−2.77076	−0.104725
$701$	3.90531	0.147501	0.0737507	−	0.997277i	$-0.476503\pi$
$701$	3.90531	0.147501	0.0737507	+	0.997277i	$0.476503\pi$
$702$	18.2394	0.688400
$703$	22.9227	0.864548
$704$	−1.00000	−0.0376889
$705$	−3.90745	−0.147163
$706$	12.3632	0.465297
$707$	−25.5750	−0.961849
$708$	13.2053	0.496287
$709$	−24.0399	−0.902836	−0.451418	−	0.892313i	$-0.649082\pi$
$709$	−24.0399	−0.902836	−0.451418	+	0.892313i	$0.649082\pi$
$710$	2.23357	0.0838245
$711$	5.63143	0.211195
$712$	14.1032	0.528540
$713$	−40.1433	−1.50338
$714$	27.9936	1.04763
$715$	4.27661	0.159936
$716$	9.12175	0.340896
$717$	−44.4586	−1.66034
$718$	−8.81130	−0.328835
$719$	−15.6319	−0.582973	−0.291486	−	0.956575i	$-0.594150\pi$
$719$	−15.6319	−0.582973	−0.291486	+	0.956575i	$0.594150\pi$
$720$	0.817036	0.0304491
$721$	−32.9278	−1.22630
$722$	−9.16119	−0.340944
$723$	3.08245	0.114637
$724$	−0.643585	−0.0239186
$725$	1.44787	0.0537726
$726$	1.95372	0.0725095
$727$	−44.0883	−1.63514	−0.817572	−	0.575827i	$-0.804680\pi$
$727$	−44.0883	−1.63514	−0.817572	+	0.575827i	$0.804680\pi$
$728$	11.8495	0.439170
$729$	16.1868	0.599511
$730$	−4.50585	−0.166769
$731$	5.17126	0.191266
$732$	16.7128	0.617722
$733$	38.8095	1.43346	0.716731	−	0.697350i	$-0.245638\pi$
$733$	38.8095	1.43346	0.716731	+	0.697350i	$0.245638\pi$
$734$	−13.3379	−0.492310
$735$	1.32289	0.0487955
$736$	−6.13669	−0.226201
$737$	5.80533	0.213842
$738$	−1.86008	−0.0684703
$739$	0.886180	0.0325987	0.0162993	−	0.999867i	$-0.494812\pi$
$739$	0.886180	0.0325987	0.0162993	+	0.999867i	$0.494812\pi$
$740$	−7.30795	−0.268645
$741$	26.2080	0.962776
$742$	−13.2097	−0.484942
$743$	51.1425	1.87624	0.938119	−	0.346314i	$-0.112567\pi$
$743$	51.1425	1.87624	0.938119	+	0.346314i	$0.112567\pi$
$744$	12.7803	0.468549
$745$	11.1133	0.407159
$746$	−10.6978	−0.391676
$747$	−12.1552	−0.444736
$748$	5.17126	0.189080
$749$	−18.8016	−0.686994
$750$	1.95372	0.0713399
$751$	−22.1076	−0.806718	−0.403359	−	0.915042i	$-0.632157\pi$
$751$	−22.1076	−0.806718	−0.403359	+	0.915042i	$0.632157\pi$
$752$	−2.00000	−0.0729325
$753$	10.6053	0.386478
$754$	−6.19198	−0.225499
$755$	15.8277	0.576029
$756$	11.8170	0.429781
$757$	−23.8383	−0.866418	−0.433209	−	0.901294i	$-0.642619\pi$
$757$	−23.8383	−0.866418	−0.433209	+	0.901294i	$0.642619\pi$
$758$	24.5996	0.893496
$759$	11.9894	0.435187
$760$	−3.13669	−0.113780
$761$	38.2797	1.38764	0.693819	−	0.720149i	$-0.255927\pi$
$761$	38.2797	1.38764	0.693819	+	0.720149i	$0.255927\pi$
$762$	−16.1027	−0.583338
$763$	24.3047	0.879890
$764$	1.34630	0.0487073
$765$	−4.22511	−0.152759
$766$	−5.22491	−0.188784
$767$	−28.9059	−1.04373
$768$	1.95372	0.0704989
$769$	−4.98774	−0.179863	−0.0899313	−	0.995948i	$-0.528665\pi$
$769$	−4.98774	−0.179863	−0.0899313	+	0.995948i	$0.528665\pi$
$770$	2.77076	0.0998513
$771$	−22.5064	−0.810548
$772$	16.4038	0.590385
$773$	−7.43328	−0.267357	−0.133678	−	0.991025i	$-0.542679\pi$
$773$	−7.43328	−0.267357	−0.133678	+	0.991025i	$0.542679\pi$
$774$	−0.817036	−0.0293678
$775$	6.54152	0.234978
$776$	−7.01390	−0.251784
$777$	39.5601	1.41921
$778$	−19.4319	−0.696667
$779$	7.14102	0.255854
$780$	−8.35532	−0.299168
$781$	−2.23357	−0.0799235
$782$	31.7344	1.13482
$783$	−6.17504	−0.220678
$784$	0.677111	0.0241825
$785$	10.0719	0.359481
$786$	−5.74789	−0.205021
$787$	−15.5525	−0.554388	−0.277194	−	0.960814i	$-0.589404\pi$
$787$	−15.5525	−0.554388	−0.277194	+	0.960814i	$0.589404\pi$
$788$	−10.9730	−0.390897
$789$	−48.0336	−1.71004
$790$	6.89251	0.245224
$791$	19.2377	0.684014
$792$	−0.817036	−0.0290321
$793$	−36.5835	−1.29912
$794$	21.3251	0.756799
$795$	9.31442	0.330348
$796$	−7.55646	−0.267832
$797$	22.8257	0.808528	0.404264	−	0.914642i	$-0.367528\pi$
$797$	22.8257	0.808528	0.404264	+	0.914642i	$0.367528\pi$
$798$	16.9798	0.601079
$799$	10.3425	0.365892
$800$	1.00000	0.0353553
$801$	11.5228	0.407139
$802$	5.62456	0.198610
$803$	4.50585	0.159008
$804$	−11.3420	−0.400002
$805$	17.0033	0.599287
$806$	−27.9755	−0.985397
$807$	−18.6053	−0.654937
$808$	9.23034	0.324722
$809$	23.5660	0.828536	0.414268	−	0.910155i	$-0.364038\pi$
$809$	23.5660	0.828536	0.414268	+	0.910155i	$0.364038\pi$
$810$	−10.7836	−0.378896
$811$	−11.3640	−0.399044	−0.199522	−	0.979893i	$-0.563939\pi$
$811$	−11.3640	−0.399044	−0.199522	+	0.979893i	$0.563939\pi$
$812$	−4.01170	−0.140783
$813$	−45.4448	−1.59382
$814$	7.30795	0.256143
$815$	17.1863	0.602008
$816$	−10.1032	−0.353683
$817$	3.13669	0.109739
$818$	−5.76588	−0.201599
$819$	9.68145	0.338297
$820$	−2.27661	−0.0795028
$821$	−39.4526	−1.37691	−0.688453	−	0.725281i	$-0.741710\pi$
$821$	−39.4526	−1.37691	−0.688453	+	0.725281i	$0.741710\pi$
$822$	2.16657	0.0755679
$823$	−47.1272	−1.64275	−0.821375	−	0.570389i	$-0.806793\pi$
$823$	−47.1272	−1.64275	−0.821375	+	0.570389i	$0.806793\pi$
$824$	11.8840	0.414000
$825$	−1.95372	−0.0680199
$826$	−18.7277	−0.651621
$827$	23.3804	0.813015	0.406508	−	0.913647i	$-0.366746\pi$
$827$	23.3804	0.813015	0.406508	+	0.913647i	$0.366746\pi$
$828$	−5.01390	−0.174245
$829$	14.4304	0.501188	0.250594	−	0.968092i	$-0.419374\pi$
$829$	14.4304	0.501188	0.250594	+	0.968092i	$0.419374\pi$
$830$	−14.8772	−0.516395
$831$	−61.8166	−2.14439
$832$	−4.27661	−0.148265
$833$	−3.50152	−0.121320
$834$	−25.9878	−0.899884
$835$	−19.1108	−0.661356
$836$	3.13669	0.108485
$837$	−27.8990	−0.964330
$838$	34.6825	1.19809
$839$	41.8318	1.44420	0.722098	−	0.691791i	$-0.243178\pi$
$839$	41.8318	1.44420	0.722098	+	0.691791i	$0.243178\pi$
$840$	−5.41330	−0.186777
$841$	−26.9037	−0.927713
$842$	−0.480251	−0.0165505
$843$	16.9352	0.583278
$844$	−3.27661	−0.112786
$845$	5.28941	0.181961
$846$	−1.63407	−0.0561806
$847$	−2.77076	−0.0952044
$848$	4.76752	0.163717
$849$	45.0553	1.54630
$850$	−5.17126	−0.177373
$851$	44.8466	1.53732
$852$	4.36379	0.149501
$853$	−15.6570	−0.536085	−0.268043	−	0.963407i	$-0.586377\pi$
$853$	−15.6570	−0.536085	−0.268043	+	0.963407i	$0.586377\pi$
$854$	−23.7020	−0.811065
$855$	−2.56279	−0.0876455
$856$	6.78570	0.231931
$857$	−0.733996	−0.0250728	−0.0125364	−	0.999921i	$-0.503991\pi$
$857$	−0.733996	−0.0250728	−0.0125364	+	0.999921i	$0.503991\pi$
$858$	8.35532	0.285246
$859$	−38.2560	−1.30528	−0.652639	−	0.757669i	$-0.726338\pi$
$859$	−38.2560	−1.30528	−0.652639	+	0.757669i	$0.726338\pi$
$860$	−1.00000	−0.0340997
$861$	12.3240	0.420000
$862$	−30.6921	−1.04538
$863$	−4.25644	−0.144891	−0.0724455	−	0.997372i	$-0.523080\pi$
$863$	−4.25644	−0.144891	−0.0724455	+	0.997372i	$0.523080\pi$
$864$	−4.26491	−0.145095
$865$	−13.0591	−0.444022
$866$	13.0591	0.443765
$867$	19.0330	0.646395
$868$	−18.1250	−0.615202
$869$	−6.89251	−0.233812
$870$	2.82874	0.0959033
$871$	24.8272	0.841236
$872$	−8.77186	−0.297053
$873$	−5.73061	−0.193952
$874$	19.2489	0.651103
$875$	−2.77076	−0.0936688
$876$	−8.80319	−0.297432
$877$	−25.2311	−0.851993	−0.425996	−	0.904725i	$-0.640076\pi$
$877$	−25.2311	−0.851993	−0.425996	+	0.904725i	$0.640076\pi$
$878$	3.21754	0.108587
$879$	3.62775	0.122361
$880$	−1.00000	−0.0337100
$881$	−47.8076	−1.61068	−0.805340	−	0.592813i	$-0.798017\pi$
$881$	−47.8076	−1.61068	−0.805340	+	0.592813i	$0.798017\pi$
$882$	0.553225	0.0186280
$883$	−0.129858	−0.00437008	−0.00218504	−	0.999998i	$-0.500696\pi$
$883$	−0.129858	−0.00437008	−0.00218504	+	0.999998i	$0.500696\pi$
$884$	22.1155	0.743824
$885$	13.2053	0.443892
$886$	25.7683	0.865702
$887$	−6.59412	−0.221409	−0.110704	−	0.993853i	$-0.535311\pi$
$887$	−6.59412	−0.221409	−0.110704	+	0.993853i	$0.535311\pi$
$888$	−14.2777	−0.479129
$889$	22.8367	0.765919
$890$	14.1032	0.472741
$891$	10.7836	0.361263
$892$	−12.2372	−0.409731
$893$	6.27337	0.209930
$894$	21.7123	0.726167
$895$	9.12175	0.304906
$896$	−2.77076	−0.0925646
$897$	51.2740	1.71199
$898$	−11.9074	−0.397357
$899$	9.47128	0.315885
$900$	0.817036	0.0272345
$901$	−24.6541	−0.821347
$902$	2.27661	0.0758029
$903$	5.41330	0.180143
$904$	−6.94312	−0.230925
$905$	−0.643585	−0.0213935
$906$	30.9229	1.02735
$907$	15.9094	0.528263	0.264131	−	0.964487i	$-0.414915\pi$
$907$	15.9094	0.528263	0.264131	+	0.964487i	$0.414915\pi$
$908$	3.26815	0.108457
$909$	7.54152	0.250136
$910$	11.8495	0.392806
$911$	−3.23627	−0.107222	−0.0536112	−	0.998562i	$-0.517073\pi$
$911$	−3.23627	−0.107222	−0.0536112	+	0.998562i	$0.517073\pi$
$912$	−6.12822	−0.202926
$913$	14.8772	0.492364
$914$	−25.4574	−0.842057
$915$	16.7128	0.552507
$916$	−22.5467	−0.744966
$917$	8.15163	0.269191
$918$	22.0549	0.727922
$919$	43.0570	1.42032	0.710159	−	0.704041i	$-0.248623\pi$
$919$	43.0570	1.42032	0.710159	+	0.704041i	$0.248623\pi$
$920$	−6.13669	−0.202321
$921$	21.4713	0.707503
$922$	−32.3026	−1.06383
$923$	−9.55213	−0.314412
$924$	5.41330	0.178084
$925$	−7.30795	−0.240284
$926$	−14.7814	−0.485748
$927$	9.70969	0.318908
$928$	1.44787	0.0475287
$929$	31.3145	1.02740	0.513698	−	0.857971i	$-0.328275\pi$
$929$	31.3145	1.02740	0.513698	+	0.857971i	$0.328275\pi$
$930$	12.7803	0.419083
$931$	−2.12389	−0.0696076
$932$	6.47706	0.212163
$933$	35.0288	1.14679
$934$	5.70740	0.186752
$935$	5.17126	0.169118
$936$	−3.49415	−0.114210
$937$	56.4665	1.84468	0.922340	−	0.386379i	$-0.126274\pi$
$937$	56.4665	1.84468	0.922340	+	0.386379i	$0.126274\pi$
$938$	16.0852	0.525200
$939$	38.8479	1.26775
$940$	−2.00000	−0.0652328
$941$	−35.7523	−1.16549	−0.582745	−	0.812655i	$-0.698022\pi$
$941$	−35.7523	−1.16549	−0.582745	+	0.812655i	$0.698022\pi$
$942$	19.6777	0.641133
$943$	13.9709	0.454954
$944$	6.75906	0.219989
$945$	11.8170	0.384408
$946$	1.00000	0.0325128
$947$	−1.42067	−0.0461656	−0.0230828	−	0.999734i	$-0.507348\pi$
$947$	−1.42067	−0.0461656	−0.0230828	+	0.999734i	$0.507348\pi$
$948$	13.4661	0.437357
$949$	19.2698	0.625524
$950$	−3.13669	−0.101768
$951$	−41.2900	−1.33892
$952$	14.3283	0.464383
$953$	5.29410	0.171493	0.0857464	−	0.996317i	$-0.472673\pi$
$953$	5.29410	0.171493	0.0857464	+	0.996317i	$0.472673\pi$
$954$	3.89524	0.126113
$955$	1.34630	0.0435652
$956$	−22.7558	−0.735976
$957$	−2.82874	−0.0914402
$958$	32.9883	1.06580
$959$	−3.07262	−0.0992201
$960$	1.95372	0.0630562
$961$	11.7915	0.380371
$962$	31.2533	1.00765
$963$	5.54417	0.178658
$964$	1.57773	0.0508153
$965$	16.4038	0.528057
$966$	33.2197	1.06883
$967$	25.7973	0.829584	0.414792	−	0.909916i	$-0.363854\pi$
$967$	25.7973	0.829584	0.414792	+	0.909916i	$0.363854\pi$
$968$	1.00000	0.0321412
$969$	31.6906	1.01805
$970$	−7.01390	−0.225203
$971$	−26.8681	−0.862237	−0.431118	−	0.902295i	$-0.641881\pi$
$971$	−26.8681	−0.862237	−0.431118	+	0.902295i	$0.641881\pi$
$972$	−8.27337	−0.265369
$973$	36.8557	1.18154
$974$	−18.6230	−0.596718
$975$	−8.35532	−0.267584
$976$	8.55432	0.273817
$977$	22.7492	0.727811	0.363906	−	0.931436i	$-0.381443\pi$
$977$	22.7492	0.727811	0.363906	+	0.931436i	$0.381443\pi$
$978$	33.5772	1.07368
$979$	−14.1032	−0.450741
$980$	0.677111	0.0216295
$981$	−7.16693	−0.228822
$982$	−35.1571	−1.12191
$983$	38.2987	1.22154	0.610769	−	0.791809i	$-0.290860\pi$
$983$	38.2987	1.22154	0.610769	+	0.791809i	$0.290860\pi$
$984$	−4.44787	−0.141793
$985$	−10.9730	−0.349629
$986$	−7.48732	−0.238445
$987$	10.8266	0.344614
$988$	13.4144	0.426769
$989$	6.13669	0.195135
$990$	−0.817036	−0.0259671
$991$	−11.1843	−0.355280	−0.177640	−	0.984096i	$-0.556846\pi$
$991$	−11.1843	−0.355280	−0.177640	+	0.984096i	$0.556846\pi$
$992$	6.54152	0.207693
$993$	36.8320	1.16883
$994$	−6.18870	−0.196294
$995$	−7.55646	−0.239556
$996$	−29.0660	−0.920990
$997$	−2.25425	−0.0713928	−0.0356964	−	0.999363i	$-0.511365\pi$
$997$	−2.25425	−0.0713928	−0.0356964	+	0.999363i	$0.511365\pi$
$998$	19.7547	0.625325
$999$	31.1677	0.986103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.u.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.u.1.4	✓	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.95372 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.95372 q^{6} -2.77076 q^{7} +1.00000 q^{8} +0.817036 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.95372 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.95372 q^{6} -2.77076 q^{7} +1.00000 q^{8} +0.817036 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.95372 q^{12} -4.27661 q^{13} -2.77076 q^{14} +1.95372 q^{15} +1.00000 q^{16} -5.17126 q^{17} +0.817036 q^{18} -3.13669 q^{19} +1.00000 q^{20} -5.41330 q^{21} -1.00000 q^{22} -6.13669 q^{23} +1.95372 q^{24} +1.00000 q^{25} -4.27661 q^{26} -4.26491 q^{27} -2.77076 q^{28} +1.44787 q^{29} +1.95372 q^{30} +6.54152 q^{31} +1.00000 q^{32} -1.95372 q^{33} -5.17126 q^{34} -2.77076 q^{35} +0.817036 q^{36} -7.30795 q^{37} -3.13669 q^{38} -8.35532 q^{39} +1.00000 q^{40} -2.27661 q^{41} -5.41330 q^{42} -1.00000 q^{43} -1.00000 q^{44} +0.817036 q^{45} -6.13669 q^{46} -2.00000 q^{47} +1.95372 q^{48} +0.677111 q^{49} +1.00000 q^{50} -10.1032 q^{51} -4.27661 q^{52} +4.76752 q^{53} -4.26491 q^{54} -1.00000 q^{55} -2.77076 q^{56} -6.12822 q^{57} +1.44787 q^{58} +6.75906 q^{59} +1.95372 q^{60} +8.55432 q^{61} +6.54152 q^{62} -2.26381 q^{63} +1.00000 q^{64} -4.27661 q^{65} -1.95372 q^{66} -5.80533 q^{67} -5.17126 q^{68} -11.9894 q^{69} -2.77076 q^{70} +2.23357 q^{71} +0.817036 q^{72} -4.50585 q^{73} -7.30795 q^{74} +1.95372 q^{75} -3.13669 q^{76} +2.77076 q^{77} -8.35532 q^{78} +6.89251 q^{79} +1.00000 q^{80} -10.7836 q^{81} -2.27661 q^{82} -14.8772 q^{83} -5.41330 q^{84} -5.17126 q^{85} -1.00000 q^{86} +2.82874 q^{87} -1.00000 q^{88} +14.1032 q^{89} +0.817036 q^{90} +11.8495 q^{91} -6.13669 q^{92} +12.7803 q^{93} -2.00000 q^{94} -3.13669 q^{95} +1.95372 q^{96} -7.01390 q^{97} +0.677111 q^{98} -0.817036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * q^99

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