LMFDB - Embedded newform 4730.2.a.y.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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - 6x^{5} + 46x^{4} + 26x^{3} - 52x^{2} - 20x + 20 $ x^8 - 13x^6 - 6x^5 + 46x^4 + 26x^3 - 52x^2 - 20x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.939990$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.519165 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.519165 q^{6} +1.27228 q^{7} -1.00000 q^{8} -2.73047 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.519165 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.519165 q^{6} +1.27228 q^{7} -1.00000 q^{8} -2.73047 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.519165 q^{12} -2.54201 q^{13} -1.27228 q^{14} -0.519165 q^{15} +1.00000 q^{16} +3.68579 q^{17} +2.73047 q^{18} -5.88267 q^{19} +1.00000 q^{20} -0.660523 q^{21} +1.00000 q^{22} -5.45078 q^{23} +0.519165 q^{24} +1.00000 q^{25} +2.54201 q^{26} +2.97506 q^{27} +1.27228 q^{28} +5.38271 q^{29} +0.519165 q^{30} +5.02465 q^{31} -1.00000 q^{32} +0.519165 q^{33} -3.68579 q^{34} +1.27228 q^{35} -2.73047 q^{36} -6.04474 q^{37} +5.88267 q^{38} +1.31973 q^{39} -1.00000 q^{40} -3.25054 q^{41} +0.660523 q^{42} -1.00000 q^{43} -1.00000 q^{44} -2.73047 q^{45} +5.45078 q^{46} +1.13076 q^{47} -0.519165 q^{48} -5.38131 q^{49} -1.00000 q^{50} -1.91353 q^{51} -2.54201 q^{52} -7.32857 q^{53} -2.97506 q^{54} -1.00000 q^{55} -1.27228 q^{56} +3.05408 q^{57} -5.38271 q^{58} +7.53550 q^{59} -0.519165 q^{60} +7.49326 q^{61} -5.02465 q^{62} -3.47391 q^{63} +1.00000 q^{64} -2.54201 q^{65} -0.519165 q^{66} +14.1423 q^{67} +3.68579 q^{68} +2.82986 q^{69} -1.27228 q^{70} +11.9818 q^{71} +2.73047 q^{72} +14.3195 q^{73} +6.04474 q^{74} -0.519165 q^{75} -5.88267 q^{76} -1.27228 q^{77} -1.31973 q^{78} -13.2470 q^{79} +1.00000 q^{80} +6.64685 q^{81} +3.25054 q^{82} +10.2077 q^{83} -0.660523 q^{84} +3.68579 q^{85} +1.00000 q^{86} -2.79452 q^{87} +1.00000 q^{88} +5.85808 q^{89} +2.73047 q^{90} -3.23415 q^{91} -5.45078 q^{92} -2.60863 q^{93} -1.13076 q^{94} -5.88267 q^{95} +0.519165 q^{96} +12.6071 q^{97} +5.38131 q^{98} +2.73047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9} - 8 q^{10} - 8 q^{11} + 3 q^{12} + 6 q^{13} - 11 q^{14} + 3 q^{15} + 8 q^{16} + 9 q^{17} - 3 q^{18} + 9 q^{19} + 8 q^{20} + 21 q^{21} + 8 q^{22} - 2 q^{23} - 3 q^{24} + 8 q^{25} - 6 q^{26} + 24 q^{27} + 11 q^{28} - 10 q^{29} - 3 q^{30} + 6 q^{31} - 8 q^{32} - 3 q^{33} - 9 q^{34} + 11 q^{35} + 3 q^{36} + 16 q^{37} - 9 q^{38} + 6 q^{39} - 8 q^{40} - 4 q^{41} - 21 q^{42} - 8 q^{43} - 8 q^{44} + 3 q^{45} + 2 q^{46} - 11 q^{47} + 3 q^{48} + 11 q^{49} - 8 q^{50} + 38 q^{51} + 6 q^{52} - 15 q^{53} - 24 q^{54} - 8 q^{55} - 11 q^{56} - 2 q^{57} + 10 q^{58} - 7 q^{59} + 3 q^{60} + 2 q^{61} - 6 q^{62} + 33 q^{63} + 8 q^{64} + 6 q^{65} + 3 q^{66} + 4 q^{67} + 9 q^{68} - 4 q^{69} - 11 q^{70} - 3 q^{71} - 3 q^{72} + 32 q^{73} - 16 q^{74} + 3 q^{75} + 9 q^{76} - 11 q^{77} - 6 q^{78} + 45 q^{79} + 8 q^{80} + 20 q^{81} + 4 q^{82} + 39 q^{83} + 21 q^{84} + 9 q^{85} + 8 q^{86} + 2 q^{87} + 8 q^{88} - 22 q^{89} - 3 q^{90} + 18 q^{91} - 2 q^{92} + 18 q^{93} + 11 q^{94} + 9 q^{95} - 3 q^{96} + 30 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9 - 8 * q^10 - 8 * q^11 + 3 * q^12 + 6 * q^13 - 11 * q^14 + 3 * q^15 + 8 * q^16 + 9 * q^17 - 3 * q^18 + 9 * q^19 + 8 * q^20 + 21 * q^21 + 8 * q^22 - 2 * q^23 - 3 * q^24 + 8 * q^25 - 6 * q^26 + 24 * q^27 + 11 * q^28 - 10 * q^29 - 3 * q^30 + 6 * q^31 - 8 * q^32 - 3 * q^33 - 9 * q^34 + 11 * q^35 + 3 * q^36 + 16 * q^37 - 9 * q^38 + 6 * q^39 - 8 * q^40 - 4 * q^41 - 21 * q^42 - 8 * q^43 - 8 * q^44 + 3 * q^45 + 2 * q^46 - 11 * q^47 + 3 * q^48 + 11 * q^49 - 8 * q^50 + 38 * q^51 + 6 * q^52 - 15 * q^53 - 24 * q^54 - 8 * q^55 - 11 * q^56 - 2 * q^57 + 10 * q^58 - 7 * q^59 + 3 * q^60 + 2 * q^61 - 6 * q^62 + 33 * q^63 + 8 * q^64 + 6 * q^65 + 3 * q^66 + 4 * q^67 + 9 * q^68 - 4 * q^69 - 11 * q^70 - 3 * q^71 - 3 * q^72 + 32 * q^73 - 16 * q^74 + 3 * q^75 + 9 * q^76 - 11 * q^77 - 6 * q^78 + 45 * q^79 + 8 * q^80 + 20 * q^81 + 4 * q^82 + 39 * q^83 + 21 * q^84 + 9 * q^85 + 8 * q^86 + 2 * q^87 + 8 * q^88 - 22 * q^89 - 3 * q^90 + 18 * q^91 - 2 * q^92 + 18 * q^93 + 11 * q^94 + 9 * q^95 - 3 * q^96 + 30 * q^97 - 11 * q^98 - 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
$3$	−0.519165	−0.299740	−0.149870	−	0.988706i	$-0.547886\pi$
$3$	−0.519165	−0.299740	−0.149870	+	0.988706i	$0.547886\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.519165	0.211948
$7$	1.27228	0.480876	0.240438	−	0.970665i	$-0.422709\pi$
$7$	1.27228	0.480876	0.240438	+	0.970665i	$0.422709\pi$
$8$	−1.00000	−0.353553
$9$	−2.73047	−0.910156
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.519165	−0.149870
$13$	−2.54201	−0.705028	−0.352514	−	0.935807i	$-0.614673\pi$
$13$	−2.54201	−0.705028	−0.352514	+	0.935807i	$0.614673\pi$
$14$	−1.27228	−0.340031
$15$	−0.519165	−0.134048
$16$	1.00000	0.250000
$17$	3.68579	0.893935	0.446968	−	0.894550i	$-0.352504\pi$
$17$	3.68579	0.893935	0.446968	+	0.894550i	$0.352504\pi$
$18$	2.73047	0.643577
$19$	−5.88267	−1.34958	−0.674789	−	0.738011i	$-0.735765\pi$
$19$	−5.88267	−1.34958	−0.674789	+	0.738011i	$0.735765\pi$
$20$	1.00000	0.223607
$21$	−0.660523	−0.144138
$22$	1.00000	0.213201
$23$	−5.45078	−1.13657	−0.568284	−	0.822833i	$-0.692392\pi$
$23$	−5.45078	−1.13657	−0.568284	+	0.822833i	$0.692392\pi$
$24$	0.519165	0.105974
$25$	1.00000	0.200000
$26$	2.54201	0.498530
$27$	2.97506	0.572551
$28$	1.27228	0.240438
$29$	5.38271	0.999544	0.499772	−	0.866157i	$-0.333417\pi$
$29$	5.38271	0.999544	0.499772	+	0.866157i	$0.333417\pi$
$30$	0.519165	0.0947862
$31$	5.02465	0.902454	0.451227	−	0.892409i	$-0.350986\pi$
$31$	5.02465	0.902454	0.451227	+	0.892409i	$0.350986\pi$
$32$	−1.00000	−0.176777
$33$	0.519165	0.0903751
$34$	−3.68579	−0.632108
$35$	1.27228	0.215054
$36$	−2.73047	−0.455078
$37$	−6.04474	−0.993749	−0.496875	−	0.867822i	$-0.665519\pi$
$37$	−6.04474	−0.993749	−0.496875	+	0.867822i	$0.665519\pi$
$38$	5.88267	0.954295
$39$	1.31973	0.211325
$40$	−1.00000	−0.158114
$41$	−3.25054	−0.507649	−0.253825	−	0.967250i	$-0.581689\pi$
$41$	−3.25054	−0.507649	−0.253825	+	0.967250i	$0.581689\pi$
$42$	0.660523	0.101921
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	−2.73047	−0.407034
$46$	5.45078	0.803674
$47$	1.13076	0.164938	0.0824688	−	0.996594i	$-0.473720\pi$
$47$	1.13076	0.164938	0.0824688	+	0.996594i	$0.473720\pi$
$48$	−0.519165	−0.0749351
$49$	−5.38131	−0.768758
$50$	−1.00000	−0.141421
$51$	−1.91353	−0.267948
$52$	−2.54201	−0.352514
$53$	−7.32857	−1.00666	−0.503329	−	0.864095i	$-0.667891\pi$
$53$	−7.32857	−1.00666	−0.503329	+	0.864095i	$0.667891\pi$
$54$	−2.97506	−0.404854
$55$	−1.00000	−0.134840
$56$	−1.27228	−0.170015
$57$	3.05408	0.404523
$58$	−5.38271	−0.706784
$59$	7.53550	0.981039	0.490520	−	0.871430i	$-0.336807\pi$
$59$	7.53550	0.981039	0.490520	+	0.871430i	$0.336807\pi$
$60$	−0.519165	−0.0670240
$61$	7.49326	0.959413	0.479707	−	0.877429i	$-0.340743\pi$
$61$	7.49326	0.959413	0.479707	+	0.877429i	$0.340743\pi$
$62$	−5.02465	−0.638131
$63$	−3.47391	−0.437672
$64$	1.00000	0.125000
$65$	−2.54201	−0.315298
$66$	−0.519165	−0.0639049
$67$	14.1423	1.72775	0.863876	−	0.503705i	$-0.168030\pi$
$67$	14.1423	1.72775	0.863876	+	0.503705i	$0.168030\pi$
$68$	3.68579	0.446968
$69$	2.82986	0.340675
$70$	−1.27228	−0.152066
$71$	11.9818	1.42198	0.710989	−	0.703203i	$-0.248248\pi$
$71$	11.9818	1.42198	0.710989	+	0.703203i	$0.248248\pi$
$72$	2.73047	0.321789
$73$	14.3195	1.67597	0.837986	−	0.545692i	$-0.183733\pi$
$73$	14.3195	1.67597	0.837986	+	0.545692i	$0.183733\pi$
$74$	6.04474	0.702687
$75$	−0.519165	−0.0599481
$76$	−5.88267	−0.674789
$77$	−1.27228	−0.144990
$78$	−1.31973	−0.149430
$79$	−13.2470	−1.49040	−0.745201	−	0.666839i	$-0.767647\pi$
$79$	−13.2470	−1.49040	−0.745201	+	0.666839i	$0.767647\pi$
$80$	1.00000	0.111803
$81$	6.64685	0.738539
$82$	3.25054	0.358962
$83$	10.2077	1.12045	0.560223	−	0.828342i	$-0.310716\pi$
$83$	10.2077	1.12045	0.560223	+	0.828342i	$0.310716\pi$
$84$	−0.660523	−0.0720690
$85$	3.68579	0.399780
$86$	1.00000	0.107833
$87$	−2.79452	−0.299604
$88$	1.00000	0.106600
$89$	5.85808	0.620955	0.310478	−	0.950581i	$-0.399511\pi$
$89$	5.85808	0.620955	0.310478	+	0.950581i	$0.399511\pi$
$90$	2.73047	0.287817
$91$	−3.23415	−0.339031
$92$	−5.45078	−0.568284
$93$	−2.60863	−0.270502
$94$	−1.13076	−0.116629
$95$	−5.88267	−0.603549
$96$	0.519165	0.0529871
$97$	12.6071	1.28005	0.640027	−	0.768353i	$-0.278923\pi$
$97$	12.6071	1.28005	0.640027	+	0.768353i	$0.278923\pi$
$98$	5.38131	0.543594
$99$	2.73047	0.274422
$100$	1.00000	0.100000
$101$	6.42507	0.639319	0.319659	−	0.947533i	$-0.396432\pi$
$101$	6.42507	0.639319	0.319659	+	0.947533i	$0.396432\pi$
$102$	1.91353	0.189468
$103$	12.9540	1.27639	0.638197	−	0.769873i	$-0.279681\pi$
$103$	12.9540	1.27639	0.638197	+	0.769873i	$0.279681\pi$
$104$	2.54201	0.249265
$105$	−0.660523	−0.0644604
$106$	7.32857	0.711814
$107$	0.750809	0.0725834	0.0362917	−	0.999341i	$-0.488445\pi$
$107$	0.750809	0.0725834	0.0362917	+	0.999341i	$0.488445\pi$
$108$	2.97506	0.286275
$109$	−11.8619	−1.13616	−0.568080	−	0.822973i	$-0.692314\pi$
$109$	−11.8619	−1.13616	−0.568080	+	0.822973i	$0.692314\pi$
$110$	1.00000	0.0953463
$111$	3.13822	0.297867
$112$	1.27228	0.120219
$113$	−16.9651	−1.59594	−0.797970	−	0.602698i	$-0.794092\pi$
$113$	−16.9651	−1.59594	−0.797970	+	0.602698i	$0.794092\pi$
$114$	−3.05408	−0.286041
$115$	−5.45078	−0.508288
$116$	5.38271	0.499772
$117$	6.94088	0.641685
$118$	−7.53550	−0.693699
$119$	4.68935	0.429872
$120$	0.519165	0.0473931
$121$	1.00000	0.0909091
$122$	−7.49326	−0.678408
$123$	1.68757	0.152163
$124$	5.02465	0.451227
$125$	1.00000	0.0894427
$126$	3.47391	0.309481
$127$	5.47672	0.485980	0.242990	−	0.970029i	$-0.421872\pi$
$127$	5.47672	0.485980	0.242990	+	0.970029i	$0.421872\pi$
$128$	−1.00000	−0.0883883
$129$	0.519165	0.0457100
$130$	2.54201	0.222949
$131$	3.12528	0.273057	0.136528	−	0.990636i	$-0.456405\pi$
$131$	3.12528	0.273057	0.136528	+	0.990636i	$0.456405\pi$
$132$	0.519165	0.0451876
$133$	−7.48440	−0.648979
$134$	−14.1423	−1.22170
$135$	2.97506	0.256052
$136$	−3.68579	−0.316054
$137$	−8.02094	−0.685275	−0.342638	−	0.939468i	$-0.611320\pi$
$137$	−8.02094	−0.685275	−0.342638	+	0.939468i	$0.611320\pi$
$138$	−2.82986	−0.240894
$139$	8.73933	0.741261	0.370630	−	0.928780i	$-0.379142\pi$
$139$	8.73933	0.741261	0.370630	+	0.928780i	$0.379142\pi$
$140$	1.27228	0.107527
$141$	−0.587049	−0.0494385
$142$	−11.9818	−1.00549
$143$	2.54201	0.212574
$144$	−2.73047	−0.227539
$145$	5.38271	0.447010
$146$	−14.3195	−1.18509
$147$	2.79379	0.230428
$148$	−6.04474	−0.496875
$149$	−14.9653	−1.22600	−0.613002	−	0.790082i	$-0.710038\pi$
$149$	−14.9653	−1.22600	−0.613002	+	0.790082i	$0.710038\pi$
$150$	0.519165	0.0423897
$151$	−10.0983	−0.821788	−0.410894	−	0.911683i	$-0.634783\pi$
$151$	−10.0983	−0.821788	−0.410894	+	0.911683i	$0.634783\pi$
$152$	5.88267	0.477148
$153$	−10.0639	−0.813620
$154$	1.27228	0.102523
$155$	5.02465	0.403590
$156$	1.31973	0.105663
$157$	23.5298	1.87788	0.938940	−	0.344080i	$-0.111809\pi$
$157$	23.5298	1.87788	0.938940	+	0.344080i	$0.111809\pi$
$158$	13.2470	1.05387
$159$	3.80474	0.301736
$160$	−1.00000	−0.0790569
$161$	−6.93491	−0.546548
$162$	−6.64685	−0.522226
$163$	−25.2789	−1.98000	−0.990000	−	0.141069i	$-0.954946\pi$
$163$	−25.2789	−1.98000	−0.990000	+	0.141069i	$0.954946\pi$
$164$	−3.25054	−0.253825
$165$	0.519165	0.0404170
$166$	−10.2077	−0.792275
$167$	−6.76796	−0.523721	−0.261860	−	0.965106i	$-0.584336\pi$
$167$	−6.76796	−0.523721	−0.261860	+	0.965106i	$0.584336\pi$
$168$	0.660523	0.0509604
$169$	−6.53817	−0.502936
$170$	−3.68579	−0.282687
$171$	16.0624	1.22833
$172$	−1.00000	−0.0762493
$173$	15.1753	1.15375	0.576877	−	0.816831i	$-0.304271\pi$
$173$	15.1753	1.15375	0.576877	+	0.816831i	$0.304271\pi$
$174$	2.79452	0.211852
$175$	1.27228	0.0961752
$176$	−1.00000	−0.0753778
$177$	−3.91217	−0.294057
$178$	−5.85808	−0.439082
$179$	12.2783	0.917722	0.458861	−	0.888508i	$-0.348258\pi$
$179$	12.2783	0.917722	0.458861	+	0.888508i	$0.348258\pi$
$180$	−2.73047	−0.203517
$181$	−1.18644	−0.0881875	−0.0440937	−	0.999027i	$-0.514040\pi$
$181$	−1.18644	−0.0881875	−0.0440937	+	0.999027i	$0.514040\pi$
$182$	3.23415	0.239731
$183$	−3.89024	−0.287575
$184$	5.45078	0.401837
$185$	−6.04474	−0.444418
$186$	2.60863	0.191274
$187$	−3.68579	−0.269532
$188$	1.13076	0.0824688
$189$	3.78510	0.275326
$190$	5.88267	0.426774
$191$	−12.1017	−0.875650	−0.437825	−	0.899060i	$-0.644251\pi$
$191$	−12.1017	−0.875650	−0.437825	+	0.899060i	$0.644251\pi$
$192$	−0.519165	−0.0374675
$193$	24.1625	1.73925	0.869627	−	0.493709i	$-0.164359\pi$
$193$	24.1625	1.73925	0.869627	+	0.493709i	$0.164359\pi$
$194$	−12.6071	−0.905134
$195$	1.31973	0.0945075
$196$	−5.38131	−0.384379
$197$	3.41989	0.243657	0.121828	−	0.992551i	$-0.461124\pi$
$197$	3.41989	0.243657	0.121828	+	0.992551i	$0.461124\pi$
$198$	−2.73047	−0.194046
$199$	5.10184	0.361660	0.180830	−	0.983514i	$-0.442122\pi$
$199$	5.10184	0.361660	0.180830	+	0.983514i	$0.442122\pi$
$200$	−1.00000	−0.0707107
$201$	−7.34217	−0.517877
$202$	−6.42507	−0.452067
$203$	6.84830	0.480657
$204$	−1.91353	−0.133974
$205$	−3.25054	−0.227028
$206$	−12.9540	−0.902547
$207$	14.8832	1.03445
$208$	−2.54201	−0.176257
$209$	5.88267	0.406913
$210$	0.660523	0.0455804
$211$	26.6533	1.83489	0.917445	−	0.397863i	$-0.130248\pi$
$211$	26.6533	1.83489	0.917445	+	0.397863i	$0.130248\pi$
$212$	−7.32857	−0.503329
$213$	−6.22054	−0.426224
$214$	−0.750809	−0.0513242
$215$	−1.00000	−0.0681994
$216$	−2.97506	−0.202427
$217$	6.39276	0.433969
$218$	11.8619	0.803386
$219$	−7.43419	−0.502356
$220$	−1.00000	−0.0674200
$221$	−9.36933	−0.630249
$222$	−3.13822	−0.210624
$223$	24.2533	1.62412	0.812061	−	0.583572i	$-0.198346\pi$
$223$	24.2533	1.62412	0.812061	+	0.583572i	$0.198346\pi$
$224$	−1.27228	−0.0850077
$225$	−2.73047	−0.182031
$226$	16.9651	1.12850
$227$	8.16289	0.541790	0.270895	−	0.962609i	$-0.412680\pi$
$227$	8.16289	0.541790	0.270895	+	0.962609i	$0.412680\pi$
$228$	3.05408	0.202261
$229$	−13.1244	−0.867287	−0.433643	−	0.901085i	$-0.642772\pi$
$229$	−13.1244	−0.867287	−0.433643	+	0.901085i	$0.642772\pi$
$230$	5.45078	0.359414
$231$	0.660523	0.0434592
$232$	−5.38271	−0.353392
$233$	15.4645	1.01311	0.506555	−	0.862207i	$-0.330919\pi$
$233$	15.4645	1.01311	0.506555	+	0.862207i	$0.330919\pi$
$234$	−6.94088	−0.453740
$235$	1.13076	0.0737624
$236$	7.53550	0.490520
$237$	6.87738	0.446734
$238$	−4.68935	−0.303965
$239$	−4.55396	−0.294571	−0.147286	−	0.989094i	$-0.547054\pi$
$239$	−4.55396	−0.294571	−0.147286	+	0.989094i	$0.547054\pi$
$240$	−0.519165	−0.0335120
$241$	−14.7575	−0.950612	−0.475306	−	0.879821i	$-0.657663\pi$
$241$	−14.7575	−0.950612	−0.475306	+	0.879821i	$0.657663\pi$
$242$	−1.00000	−0.0642824
$243$	−12.3760	−0.793921
$244$	7.49326	0.479707
$245$	−5.38131	−0.343799
$246$	−1.68757	−0.107595
$247$	14.9538	0.951490
$248$	−5.02465	−0.319066
$249$	−5.29951	−0.335843
$250$	−1.00000	−0.0632456
$251$	−2.70680	−0.170851	−0.0854257	−	0.996345i	$-0.527225\pi$
$251$	−2.70680	−0.170851	−0.0854257	+	0.996345i	$0.527225\pi$
$252$	−3.47391	−0.218836
$253$	5.45078	0.342688
$254$	−5.47672	−0.343640
$255$	−1.91353	−0.119830
$256$	1.00000	0.0625000
$257$	−10.1501	−0.633146	−0.316573	−	0.948568i	$-0.602532\pi$
$257$	−10.1501	−0.633146	−0.316573	+	0.948568i	$0.602532\pi$
$258$	−0.519165	−0.0323218
$259$	−7.69059	−0.477870
$260$	−2.54201	−0.157649
$261$	−14.6973	−0.909741
$262$	−3.12528	−0.193080
$263$	−18.6359	−1.14914	−0.574570	−	0.818455i	$-0.694831\pi$
$263$	−18.6359	−1.14914	−0.574570	+	0.818455i	$0.694831\pi$
$264$	−0.519165	−0.0319524
$265$	−7.32857	−0.450191
$266$	7.48440	0.458898
$267$	−3.04131	−0.186125
$268$	14.1423	0.863876
$269$	11.5687	0.705354	0.352677	−	0.935745i	$-0.385272\pi$
$269$	11.5687	0.705354	0.352677	+	0.935745i	$0.385272\pi$
$270$	−2.97506	−0.181056
$271$	−9.13856	−0.555128	−0.277564	−	0.960707i	$-0.589527\pi$
$271$	−9.13856	−0.555128	−0.277564	+	0.960707i	$0.589527\pi$
$272$	3.68579	0.223484
$273$	1.67906	0.101621
$274$	8.02094	0.484563
$275$	−1.00000	−0.0603023
$276$	2.82986	0.170337
$277$	22.6874	1.36316	0.681578	−	0.731745i	$-0.261294\pi$
$277$	22.6874	1.36316	0.681578	+	0.731745i	$0.261294\pi$
$278$	−8.73933	−0.524150
$279$	−13.7196	−0.821374
$280$	−1.27228	−0.0760332
$281$	−25.7793	−1.53786	−0.768931	−	0.639331i	$-0.779211\pi$
$281$	−25.7793	−1.53786	−0.768931	+	0.639331i	$0.779211\pi$
$282$	0.587049	0.0349583
$283$	8.81066	0.523740	0.261870	−	0.965103i	$-0.415661\pi$
$283$	8.81066	0.523740	0.261870	+	0.965103i	$0.415661\pi$
$284$	11.9818	0.710989
$285$	3.05408	0.180908
$286$	−2.54201	−0.150312
$287$	−4.13559	−0.244116
$288$	2.73047	0.160894
$289$	−3.41495	−0.200880
$290$	−5.38271	−0.316084
$291$	−6.54515	−0.383684
$292$	14.3195	0.837986
$293$	17.8462	1.04259	0.521293	−	0.853378i	$-0.325450\pi$
$293$	17.8462	1.04259	0.521293	+	0.853378i	$0.325450\pi$
$294$	−2.79379	−0.162937
$295$	7.53550	0.438734
$296$	6.04474	0.351343
$297$	−2.97506	−0.172631
$298$	14.9653	0.866915
$299$	13.8560	0.801311
$300$	−0.519165	−0.0299740
$301$	−1.27228	−0.0733329
$302$	10.0983	0.581092
$303$	−3.33568	−0.191630
$304$	−5.88267	−0.337394
$305$	7.49326	0.429063
$306$	10.0639	0.575316
$307$	30.3155	1.73020	0.865099	−	0.501601i	$-0.167256\pi$
$307$	30.3155	1.73020	0.865099	+	0.501601i	$0.167256\pi$
$308$	−1.27228	−0.0724948
$309$	−6.72526	−0.382587
$310$	−5.02465	−0.285381
$311$	−8.80179	−0.499104	−0.249552	−	0.968361i	$-0.580283\pi$
$311$	−8.80179	−0.499104	−0.249552	+	0.968361i	$0.580283\pi$
$312$	−1.31973	−0.0747148
$313$	−1.97550	−0.111662	−0.0558308	−	0.998440i	$-0.517781\pi$
$313$	−1.97550	−0.111662	−0.0558308	+	0.998440i	$0.517781\pi$
$314$	−23.5298	−1.32786
$315$	−3.47391	−0.195733
$316$	−13.2470	−0.745201
$317$	−21.6943	−1.21847	−0.609236	−	0.792989i	$-0.708524\pi$
$317$	−21.6943	−1.21847	−0.609236	+	0.792989i	$0.708524\pi$
$318$	−3.80474	−0.213359
$319$	−5.38271	−0.301374
$320$	1.00000	0.0559017
$321$	−0.389794	−0.0217562
$322$	6.93491	0.386468
$323$	−21.6823	−1.20644
$324$	6.64685	0.369270
$325$	−2.54201	−0.141006
$326$	25.2789	1.40007
$327$	6.15827	0.340553
$328$	3.25054	0.179481
$329$	1.43864	0.0793145
$330$	−0.519165	−0.0285791
$331$	−23.6074	−1.29758	−0.648790	−	0.760968i	$-0.724725\pi$
$331$	−23.6074	−1.29758	−0.648790	+	0.760968i	$0.724725\pi$
$332$	10.2077	0.560223
$333$	16.5050	0.904467
$334$	6.76796	0.370326
$335$	14.1423	0.772674
$336$	−0.660523	−0.0360345
$337$	23.6028	1.28573	0.642863	−	0.765981i	$-0.277746\pi$
$337$	23.6028	1.28573	0.642863	+	0.765981i	$0.277746\pi$
$338$	6.53817	0.355629
$339$	8.80768	0.478367
$340$	3.68579	0.199890
$341$	−5.02465	−0.272100
$342$	−16.0624	−0.868558
$343$	−15.7525	−0.850553
$344$	1.00000	0.0539164
$345$	2.82986	0.152354
$346$	−15.1753	−0.815827
$347$	9.96068	0.534717	0.267359	−	0.963597i	$-0.413849\pi$
$347$	9.96068	0.534717	0.267359	+	0.963597i	$0.413849\pi$
$348$	−2.79452	−0.149802
$349$	10.3103	0.551896	0.275948	−	0.961173i	$-0.411008\pi$
$349$	10.3103	0.551896	0.275948	+	0.961173i	$0.411008\pi$
$350$	−1.27228	−0.0680061
$351$	−7.56264	−0.403664
$352$	1.00000	0.0533002
$353$	14.7849	0.786919	0.393459	−	0.919342i	$-0.371278\pi$
$353$	14.7849	0.786919	0.393459	+	0.919342i	$0.371278\pi$
$354$	3.91217	0.207930
$355$	11.9818	0.635928
$356$	5.85808	0.310478
$357$	−2.43455	−0.128850
$358$	−12.2783	−0.648927
$359$	20.4609	1.07988	0.539942	−	0.841703i	$-0.318446\pi$
$359$	20.4609	1.07988	0.539942	+	0.841703i	$0.318446\pi$
$360$	2.73047	0.143908
$361$	15.6058	0.821360
$362$	1.18644	0.0623579
$363$	−0.519165	−0.0272491
$364$	−3.23415	−0.169515
$365$	14.3195	0.749517
$366$	3.89024	0.203346
$367$	37.4464	1.95469	0.977343	−	0.211664i	$-0.0678882\pi$
$367$	37.4464	1.95469	0.977343	+	0.211664i	$0.0678882\pi$
$368$	−5.45078	−0.284142
$369$	8.87550	0.462040
$370$	6.04474	0.314251
$371$	−9.32399	−0.484077
$372$	−2.60863	−0.135251
$373$	11.9952	0.621087	0.310543	−	0.950559i	$-0.399489\pi$
$373$	11.9952	0.621087	0.310543	+	0.950559i	$0.399489\pi$
$374$	3.68579	0.190588
$375$	−0.519165	−0.0268096
$376$	−1.13076	−0.0583143
$377$	−13.6829	−0.704706
$378$	−3.78510	−0.194685
$379$	9.81487	0.504156	0.252078	−	0.967707i	$-0.418886\pi$
$379$	9.81487	0.504156	0.252078	+	0.967707i	$0.418886\pi$
$380$	−5.88267	−0.301775
$381$	−2.84332	−0.145668
$382$	12.1017	0.619178
$383$	21.3956	1.09327	0.546633	−	0.837372i	$-0.315909\pi$
$383$	21.3956	1.09327	0.546633	+	0.837372i	$0.315909\pi$
$384$	0.519165	0.0264936
$385$	−1.27228	−0.0648413
$386$	−24.1625	−1.22984
$387$	2.73047	0.138797
$388$	12.6071	0.640027
$389$	11.5879	0.587531	0.293765	−	0.955878i	$-0.405092\pi$
$389$	11.5879	0.587531	0.293765	+	0.955878i	$0.405092\pi$
$390$	−1.31973	−0.0668269
$391$	−20.0904	−1.01602
$392$	5.38131	0.271797
$393$	−1.62254	−0.0818462
$394$	−3.41989	−0.172291
$395$	−13.2470	−0.666528
$396$	2.73047	0.137211
$397$	−30.4935	−1.53042	−0.765211	−	0.643779i	$-0.777365\pi$
$397$	−30.4935	−1.53042	−0.765211	+	0.643779i	$0.777365\pi$
$398$	−5.10184	−0.255732
$399$	3.88564	0.194525
$400$	1.00000	0.0500000
$401$	−2.61860	−0.130767	−0.0653833	−	0.997860i	$-0.520827\pi$
$401$	−2.61860	−0.130767	−0.0653833	+	0.997860i	$0.520827\pi$
$402$	7.34217	0.366194
$403$	−12.7727	−0.636255
$404$	6.42507	0.319659
$405$	6.64685	0.330285
$406$	−6.84830	−0.339876
$407$	6.04474	0.299627
$408$	1.91353	0.0947341
$409$	15.7034	0.776485	0.388242	−	0.921557i	$-0.373082\pi$
$409$	15.7034	0.776485	0.388242	+	0.921557i	$0.373082\pi$
$410$	3.25054	0.160533
$411$	4.16420	0.205405
$412$	12.9540	0.638197
$413$	9.58726	0.471758
$414$	−14.8832	−0.731469
$415$	10.2077	0.501078
$416$	2.54201	0.124632
$417$	−4.53716	−0.222186
$418$	−5.88267	−0.287731
$419$	−40.1703	−1.96245	−0.981223	−	0.192876i	$-0.938219\pi$
$419$	−40.1703	−1.96245	−0.981223	+	0.192876i	$0.938219\pi$
$420$	−0.660523	−0.0322302
$421$	31.2999	1.52547	0.762733	−	0.646713i	$-0.223857\pi$
$421$	31.2999	1.52547	0.762733	+	0.646713i	$0.223857\pi$
$422$	−26.6533	−1.29746
$423$	−3.08749	−0.150119
$424$	7.32857	0.355907
$425$	3.68579	0.178787
$426$	6.22054	0.301386
$427$	9.53351	0.461359
$428$	0.750809	0.0362917
$429$	−1.31973	−0.0637170
$430$	1.00000	0.0482243
$431$	−13.0533	−0.628754	−0.314377	−	0.949298i	$-0.601796\pi$
$431$	−13.0533	−0.628754	−0.314377	+	0.949298i	$0.601796\pi$
$432$	2.97506	0.143138
$433$	−23.0956	−1.10991	−0.554953	−	0.831882i	$-0.687264\pi$
$433$	−23.0956	−1.10991	−0.554953	+	0.831882i	$0.687264\pi$
$434$	−6.39276	−0.306862
$435$	−2.79452	−0.133987
$436$	−11.8619	−0.568080
$437$	32.0652	1.53389
$438$	7.43419	0.355220
$439$	27.9394	1.33347	0.666736	−	0.745294i	$-0.267691\pi$
$439$	27.9394	1.33347	0.666736	+	0.745294i	$0.267691\pi$
$440$	1.00000	0.0476731
$441$	14.6935	0.699690
$442$	9.36933	0.445653
$443$	17.1014	0.812511	0.406256	−	0.913759i	$-0.366834\pi$
$443$	17.1014	0.812511	0.406256	+	0.913759i	$0.366834\pi$
$444$	3.13822	0.148933
$445$	5.85808	0.277700
$446$	−24.2533	−1.14843
$447$	7.76945	0.367483
$448$	1.27228	0.0601095
$449$	22.0228	1.03932	0.519659	−	0.854374i	$-0.326059\pi$
$449$	22.0228	1.03932	0.519659	+	0.854374i	$0.326059\pi$
$450$	2.73047	0.128715
$451$	3.25054	0.153062
$452$	−16.9651	−0.797970
$453$	5.24269	0.246323
$454$	−8.16289	−0.383103
$455$	−3.23415	−0.151619
$456$	−3.05408	−0.143020
$457$	19.6651	0.919896	0.459948	−	0.887946i	$-0.347868\pi$
$457$	19.6651	0.919896	0.459948	+	0.887946i	$0.347868\pi$
$458$	13.1244	0.613264
$459$	10.9654	0.511823
$460$	−5.45078	−0.254144
$461$	16.5641	0.771466	0.385733	−	0.922610i	$-0.373949\pi$
$461$	16.5641	0.771466	0.385733	+	0.922610i	$0.373949\pi$
$462$	−0.660523	−0.0307303
$463$	22.6899	1.05449	0.527246	−	0.849713i	$-0.323225\pi$
$463$	22.6899	1.05449	0.527246	+	0.849713i	$0.323225\pi$
$464$	5.38271	0.249886
$465$	−2.60863	−0.120972
$466$	−15.4645	−0.716377
$467$	−14.6484	−0.677847	−0.338924	−	0.940814i	$-0.610063\pi$
$467$	−14.6484	−0.677847	−0.338924	+	0.940814i	$0.610063\pi$
$468$	6.94088	0.320843
$469$	17.9929	0.830834
$470$	−1.13076	−0.0521579
$471$	−12.2158	−0.562877
$472$	−7.53550	−0.346850
$473$	1.00000	0.0459800
$474$	−6.87738	−0.315889
$475$	−5.88267	−0.269916
$476$	4.68935	0.214936
$477$	20.0104	0.916215
$478$	4.55396	0.208293
$479$	−35.0561	−1.60175	−0.800877	−	0.598829i	$-0.795633\pi$
$479$	−35.0561	−1.60175	−0.800877	+	0.598829i	$0.795633\pi$
$480$	0.519165	0.0236966
$481$	15.3658	0.700621
$482$	14.7575	0.672184
$483$	3.60037	0.163822
$484$	1.00000	0.0454545
$485$	12.6071	0.572457
$486$	12.3760	0.561387
$487$	11.4679	0.519661	0.259831	−	0.965654i	$-0.416333\pi$
$487$	11.4679	0.519661	0.259831	+	0.965654i	$0.416333\pi$
$488$	−7.49326	−0.339204
$489$	13.1240	0.593486
$490$	5.38131	0.243103
$491$	17.9831	0.811565	0.405782	−	0.913970i	$-0.366999\pi$
$491$	17.9831	0.811565	0.405782	+	0.913970i	$0.366999\pi$
$492$	1.68757	0.0760815
$493$	19.8395	0.893528
$494$	−14.9538	−0.672805
$495$	2.73047	0.122725
$496$	5.02465	0.225614
$497$	15.2442	0.683795
$498$	5.29951	0.237477
$499$	9.46436	0.423683	0.211841	−	0.977304i	$-0.432054\pi$
$499$	9.46436	0.423683	0.211841	+	0.977304i	$0.432054\pi$
$500$	1.00000	0.0447214
$501$	3.51369	0.156980
$502$	2.70680	0.120810
$503$	14.6605	0.653682	0.326841	−	0.945079i	$-0.394016\pi$
$503$	14.6605	0.653682	0.326841	+	0.945079i	$0.394016\pi$
$504$	3.47391	0.154740
$505$	6.42507	0.285912
$506$	−5.45078	−0.242317
$507$	3.39439	0.150750
$508$	5.47672	0.242990
$509$	−11.9624	−0.530226	−0.265113	−	0.964217i	$-0.585409\pi$
$509$	−11.9624	−0.530226	−0.265113	+	0.964217i	$0.585409\pi$
$510$	1.91353	0.0847327
$511$	18.2184	0.805935
$512$	−1.00000	−0.0441942
$513$	−17.5013	−0.772702
$514$	10.1501	0.447702
$515$	12.9540	0.570821
$516$	0.519165	0.0228550
$517$	−1.13076	−0.0497306
$518$	7.69059	0.337905
$519$	−7.87847	−0.345826
$520$	2.54201	0.111475
$521$	−7.87015	−0.344798	−0.172399	−	0.985027i	$-0.555152\pi$
$521$	−7.87015	−0.344798	−0.172399	+	0.985027i	$0.555152\pi$
$522$	14.6973	0.643284
$523$	−11.4230	−0.499494	−0.249747	−	0.968311i	$-0.580347\pi$
$523$	−11.4230	−0.499494	−0.249747	+	0.968311i	$0.580347\pi$
$524$	3.12528	0.136528
$525$	−0.660523	−0.0288276
$526$	18.6359	0.812565
$527$	18.5198	0.806736
$528$	0.519165	0.0225938
$529$	6.71105	0.291785
$530$	7.32857	0.318333
$531$	−20.5754	−0.892898
$532$	−7.48440	−0.324490
$533$	8.26292	0.357907
$534$	3.04131	0.131610
$535$	0.750809	0.0324603
$536$	−14.1423	−0.610852
$537$	−6.37446	−0.275078
$538$	−11.5687	−0.498760
$539$	5.38131	0.231789
$540$	2.97506	0.128026
$541$	26.7384	1.14957	0.574786	−	0.818303i	$-0.305085\pi$
$541$	26.7384	1.14957	0.574786	+	0.818303i	$0.305085\pi$
$542$	9.13856	0.392535
$543$	0.615959	0.0264333
$544$	−3.68579	−0.158027
$545$	−11.8619	−0.508106
$546$	−1.67906	−0.0718571
$547$	6.91090	0.295489	0.147744	−	0.989026i	$-0.452799\pi$
$547$	6.91090	0.295489	0.147744	+	0.989026i	$0.452799\pi$
$548$	−8.02094	−0.342638
$549$	−20.4601	−0.873216
$550$	1.00000	0.0426401
$551$	−31.6647	−1.34896
$552$	−2.82986	−0.120447
$553$	−16.8539	−0.716699
$554$	−22.6874	−0.963897
$555$	3.13822	0.133210
$556$	8.73933	0.370630
$557$	7.43897	0.315199	0.157600	−	0.987503i	$-0.449624\pi$
$557$	7.43897	0.315199	0.157600	+	0.987503i	$0.449624\pi$
$558$	13.7196	0.580799
$559$	2.54201	0.107516
$560$	1.27228	0.0537636
$561$	1.91353	0.0807895
$562$	25.7793	1.08743
$563$	15.2581	0.643053	0.321527	−	0.946901i	$-0.395804\pi$
$563$	15.2581	0.643053	0.321527	+	0.946901i	$0.395804\pi$
$564$	−0.587049	−0.0247192
$565$	−16.9651	−0.713726
$566$	−8.81066	−0.370340
$567$	8.45665	0.355146
$568$	−11.9818	−0.502745
$569$	−19.5439	−0.819321	−0.409661	−	0.912238i	$-0.634353\pi$
$569$	−19.5439	−0.819321	−0.409661	+	0.912238i	$0.634353\pi$
$570$	−3.05408	−0.127921
$571$	39.9943	1.67371	0.836854	−	0.547426i	$-0.184392\pi$
$571$	39.9943	1.67371	0.836854	+	0.547426i	$0.184392\pi$
$572$	2.54201	0.106287
$573$	6.28280	0.262468
$574$	4.13559	0.172616
$575$	−5.45078	−0.227313
$576$	−2.73047	−0.113769
$577$	−6.99263	−0.291107	−0.145553	−	0.989350i	$-0.546496\pi$
$577$	−6.99263	−0.291107	−0.145553	+	0.989350i	$0.546496\pi$
$578$	3.41495	0.142043
$579$	−12.5443	−0.521325
$580$	5.38271	0.223505
$581$	12.9871	0.538795
$582$	6.54515	0.271305
$583$	7.32857	0.303519
$584$	−14.3195	−0.592546
$585$	6.94088	0.286970
$586$	−17.8462	−0.737220
$587$	−3.51905	−0.145247	−0.0726235	−	0.997359i	$-0.523137\pi$
$587$	−3.51905	−0.145247	−0.0726235	+	0.997359i	$0.523137\pi$
$588$	2.79379	0.115214
$589$	−29.5584	−1.21793
$590$	−7.53550	−0.310232
$591$	−1.77549	−0.0730338
$592$	−6.04474	−0.248437
$593$	−11.9878	−0.492280	−0.246140	−	0.969234i	$-0.579162\pi$
$593$	−11.9878	−0.492280	−0.246140	+	0.969234i	$0.579162\pi$
$594$	2.97506	0.122068
$595$	4.68935	0.192245
$596$	−14.9653	−0.613002
$597$	−2.64870	−0.108404
$598$	−13.8560	−0.566613
$599$	−14.6696	−0.599385	−0.299693	−	0.954036i	$-0.596884\pi$
$599$	−14.6696	−0.599385	−0.299693	+	0.954036i	$0.596884\pi$
$600$	0.519165	0.0211948
$601$	−41.0051	−1.67263	−0.836317	−	0.548246i	$-0.815296\pi$
$601$	−41.0051	−1.67263	−0.836317	+	0.548246i	$0.815296\pi$
$602$	1.27228	0.0518542
$603$	−38.6150	−1.57252
$604$	−10.0983	−0.410894
$605$	1.00000	0.0406558
$606$	3.33568	0.135503
$607$	−35.3832	−1.43616	−0.718080	−	0.695960i	$-0.754979\pi$
$607$	−35.3832	−1.43616	−0.718080	+	0.695960i	$0.754979\pi$
$608$	5.88267	0.238574
$609$	−3.55540	−0.144072
$610$	−7.49326	−0.303393
$611$	−2.87440	−0.116286
$612$	−10.0639	−0.406810
$613$	−18.6160	−0.751893	−0.375947	−	0.926641i	$-0.622682\pi$
$613$	−18.6160	−0.751893	−0.375947	+	0.926641i	$0.622682\pi$
$614$	−30.3155	−1.22343
$615$	1.68757	0.0680493
$616$	1.27228	0.0512615
$617$	−4.49290	−0.180877	−0.0904386	−	0.995902i	$-0.528827\pi$
$617$	−4.49290	−0.180877	−0.0904386	+	0.995902i	$0.528827\pi$
$618$	6.72526	0.270530
$619$	23.1031	0.928592	0.464296	−	0.885680i	$-0.346307\pi$
$619$	23.1031	0.928592	0.464296	+	0.885680i	$0.346307\pi$
$620$	5.02465	0.201795
$621$	−16.2164	−0.650742
$622$	8.80179	0.352920
$623$	7.45311	0.298602
$624$	1.31973	0.0528313
$625$	1.00000	0.0400000
$626$	1.97550	0.0789567
$627$	−3.05408	−0.121968
$628$	23.5298	0.938940
$629$	−22.2796	−0.888348
$630$	3.47391	0.138404
$631$	43.3876	1.72723	0.863617	−	0.504149i	$-0.168194\pi$
$631$	43.3876	1.72723	0.863617	+	0.504149i	$0.168194\pi$
$632$	13.2470	0.526937
$633$	−13.8375	−0.549991
$634$	21.6943	0.861590
$635$	5.47672	0.217337
$636$	3.80474	0.150868
$637$	13.6794	0.541996
$638$	5.38271	0.213103
$639$	−32.7159	−1.29422
$640$	−1.00000	−0.0395285
$641$	−34.7726	−1.37344	−0.686718	−	0.726923i	$-0.740949\pi$
$641$	−34.7726	−1.37344	−0.686718	+	0.726923i	$0.740949\pi$
$642$	0.389794	0.0153839
$643$	29.6904	1.17087	0.585437	−	0.810718i	$-0.300923\pi$
$643$	29.6904	1.17087	0.585437	+	0.810718i	$0.300923\pi$
$644$	−6.93491	−0.273274
$645$	0.519165	0.0204421
$646$	21.6823	0.853078
$647$	7.20887	0.283410	0.141705	−	0.989909i	$-0.454742\pi$
$647$	7.20887	0.283410	0.141705	+	0.989909i	$0.454742\pi$
$648$	−6.64685	−0.261113
$649$	−7.53550	−0.295794
$650$	2.54201	0.0997060
$651$	−3.31890	−0.130078
$652$	−25.2789	−0.990000
$653$	−3.51579	−0.137583	−0.0687917	−	0.997631i	$-0.521914\pi$
$653$	−3.51579	−0.137583	−0.0687917	+	0.997631i	$0.521914\pi$
$654$	−6.15827	−0.240807
$655$	3.12528	0.122115
$656$	−3.25054	−0.126912
$657$	−39.0990	−1.52540
$658$	−1.43864	−0.0560839
$659$	4.42359	0.172319	0.0861593	−	0.996281i	$-0.472541\pi$
$659$	4.42359	0.172319	0.0861593	+	0.996281i	$0.472541\pi$
$660$	0.519165	0.0202085
$661$	−31.1087	−1.20999	−0.604994	−	0.796230i	$-0.706824\pi$
$661$	−31.1087	−1.20999	−0.604994	+	0.796230i	$0.706824\pi$
$662$	23.6074	0.917527
$663$	4.86423	0.188911
$664$	−10.2077	−0.396137
$665$	−7.48440	−0.290232
$666$	−16.5050	−0.639555
$667$	−29.3400	−1.13605
$668$	−6.76796	−0.261860
$669$	−12.5915	−0.486815
$670$	−14.1423	−0.546363
$671$	−7.49326	−0.289274
$672$	0.660523	0.0254802
$673$	−42.0507	−1.62094	−0.810468	−	0.585783i	$-0.800787\pi$
$673$	−42.0507	−1.62094	−0.810468	+	0.585783i	$0.800787\pi$
$674$	−23.6028	−0.909146
$675$	2.97506	0.114510
$676$	−6.53817	−0.251468
$677$	37.2313	1.43092	0.715458	−	0.698656i	$-0.246218\pi$
$677$	37.2313	1.43092	0.715458	+	0.698656i	$0.246218\pi$
$678$	−8.80768	−0.338257
$679$	16.0397	0.615547
$680$	−3.68579	−0.141344
$681$	−4.23789	−0.162396
$682$	5.02465	0.192404
$683$	31.3054	1.19787	0.598935	−	0.800798i	$-0.295591\pi$
$683$	31.3054	1.19787	0.598935	+	0.800798i	$0.295591\pi$
$684$	16.0624	0.614163
$685$	−8.02094	−0.306465
$686$	15.7525	0.601432
$687$	6.81375	0.259961
$688$	−1.00000	−0.0381246
$689$	18.6293	0.709721
$690$	−2.82986	−0.107731
$691$	0.431993	0.0164338	0.00821690	−	0.999966i	$-0.497384\pi$
$691$	0.431993	0.0164338	0.00821690	+	0.999966i	$0.497384\pi$
$692$	15.1753	0.576877
$693$	3.47391	0.131963
$694$	−9.96068	−0.378102
$695$	8.73933	0.331502
$696$	2.79452	0.105926
$697$	−11.9808	−0.453806
$698$	−10.3103	−0.390249
$699$	−8.02862	−0.303670
$700$	1.27228	0.0480876
$701$	−28.5463	−1.07818	−0.539090	−	0.842248i	$-0.681232\pi$
$701$	−28.5463	−1.07818	−0.539090	+	0.842248i	$0.681232\pi$
$702$	7.56264	0.285434
$703$	35.5592	1.34114
$704$	−1.00000	−0.0376889
$705$	−0.587049	−0.0221096
$706$	−14.7849	−0.556436
$707$	8.17448	0.307433
$708$	−3.91217	−0.147028
$709$	−12.7064	−0.477198	−0.238599	−	0.971118i	$-0.576688\pi$
$709$	−12.7064	−0.477198	−0.238599	+	0.971118i	$0.576688\pi$
$710$	−11.9818	−0.449669
$711$	36.1705	1.35650
$712$	−5.85808	−0.219541
$713$	−27.3883	−1.02570
$714$	2.43455	0.0911107
$715$	2.54201	0.0950659
$716$	12.2783	0.458861
$717$	2.36426	0.0882948
$718$	−20.4609	−0.763593
$719$	8.33948	0.311010	0.155505	−	0.987835i	$-0.450300\pi$
$719$	8.33948	0.311010	0.155505	+	0.987835i	$0.450300\pi$
$720$	−2.73047	−0.101759
$721$	16.4811	0.613787
$722$	−15.6058	−0.580789
$723$	7.66156	0.284937
$724$	−1.18644	−0.0440937
$725$	5.38271	0.199909
$726$	0.519165	0.0192680
$727$	36.5320	1.35490	0.677448	−	0.735570i	$-0.263086\pi$
$727$	36.5320	1.35490	0.677448	+	0.735570i	$0.263086\pi$
$728$	3.23415	0.119866
$729$	−13.5154	−0.500569
$730$	−14.3195	−0.529989
$731$	−3.68579	−0.136324
$732$	−3.89024	−0.143787
$733$	1.47574	0.0545078	0.0272539	−	0.999629i	$-0.491324\pi$
$733$	1.47574	0.0545078	0.0272539	+	0.999629i	$0.491324\pi$
$734$	−37.4464	−1.38217
$735$	2.79379	0.103050
$736$	5.45078	0.200919
$737$	−14.1423	−0.520937
$738$	−8.87550	−0.326712
$739$	−2.84455	−0.104638	−0.0523192	−	0.998630i	$-0.516661\pi$
$739$	−2.84455	−0.104638	−0.0523192	+	0.998630i	$0.516661\pi$
$740$	−6.04474	−0.222209
$741$	−7.76351	−0.285200
$742$	9.32399	0.342294
$743$	−46.4676	−1.70473	−0.852365	−	0.522947i	$-0.824833\pi$
$743$	−46.4676	−1.70473	−0.852365	+	0.522947i	$0.824833\pi$
$744$	2.60863	0.0956369
$745$	−14.9653	−0.548285
$746$	−11.9952	−0.439175
$747$	−27.8719	−1.01978
$748$	−3.68579	−0.134766
$749$	0.955237	0.0349036
$750$	0.519165	0.0189572
$751$	33.9883	1.24025	0.620125	−	0.784503i	$-0.287082\pi$
$751$	33.9883	1.24025	0.620125	+	0.784503i	$0.287082\pi$
$752$	1.13076	0.0412344
$753$	1.40528	0.0512111
$754$	13.6829	0.498303
$755$	−10.0983	−0.367515
$756$	3.78510	0.137663
$757$	−6.84798	−0.248894	−0.124447	−	0.992226i	$-0.539716\pi$
$757$	−6.84798	−0.248894	−0.124447	+	0.992226i	$0.539716\pi$
$758$	−9.81487	−0.356492
$759$	−2.82986	−0.102717
$760$	5.88267	0.213387
$761$	37.5136	1.35987	0.679933	−	0.733274i	$-0.262009\pi$
$761$	37.5136	1.35987	0.679933	+	0.733274i	$0.262009\pi$
$762$	2.84332	0.103003
$763$	−15.0916	−0.546352
$764$	−12.1017	−0.437825
$765$	−10.0639	−0.363862
$766$	−21.3956	−0.773056
$767$	−19.1554	−0.691660
$768$	−0.519165	−0.0187338
$769$	9.92139	0.357775	0.178887	−	0.983870i	$-0.442750\pi$
$769$	9.92139	0.357775	0.178887	+	0.983870i	$0.442750\pi$
$770$	1.27228	0.0458497
$771$	5.26958	0.189779
$772$	24.1625	0.869627
$773$	−12.0791	−0.434456	−0.217228	−	0.976121i	$-0.569702\pi$
$773$	−12.0791	−0.434456	−0.217228	+	0.976121i	$0.569702\pi$
$774$	−2.73047	−0.0981446
$775$	5.02465	0.180491
$776$	−12.6071	−0.452567
$777$	3.99269	0.143237
$778$	−11.5879	−0.415447
$779$	19.1219	0.685112
$780$	1.31973	0.0472538
$781$	−11.9818	−0.428742
$782$	20.0904	0.718433
$783$	16.0139	0.572290
$784$	−5.38131	−0.192190
$785$	23.5298	0.839814
$786$	1.62254	0.0578740
$787$	−2.71226	−0.0966815	−0.0483407	−	0.998831i	$-0.515393\pi$
$787$	−2.71226	−0.0966815	−0.0483407	+	0.998831i	$0.515393\pi$
$788$	3.41989	0.121828
$789$	9.67513	0.344444
$790$	13.2470	0.471307
$791$	−21.5843	−0.767449
$792$	−2.73047	−0.0970229
$793$	−19.0480	−0.676413
$794$	30.4935	1.08217
$795$	3.80474	0.134940
$796$	5.10184	0.180830
$797$	15.2469	0.540075	0.270037	−	0.962850i	$-0.412964\pi$
$797$	15.2469	0.540075	0.270037	+	0.962850i	$0.412964\pi$
$798$	−3.88564	−0.137550
$799$	4.16773	0.147444
$800$	−1.00000	−0.0353553
$801$	−15.9953	−0.565166
$802$	2.61860	0.0924659
$803$	−14.3195	−0.505325
$804$	−7.34217	−0.258938
$805$	−6.93491	−0.244424
$806$	12.7727	0.449900
$807$	−6.00605	−0.211423
$808$	−6.42507	−0.226033
$809$	46.9209	1.64965	0.824825	−	0.565388i	$-0.191274\pi$
$809$	46.9209	1.64965	0.824825	+	0.565388i	$0.191274\pi$
$810$	−6.64685	−0.233547
$811$	45.5650	1.60000	0.800002	−	0.599998i	$-0.204832\pi$
$811$	45.5650	1.60000	0.800002	+	0.599998i	$0.204832\pi$
$812$	6.84830	0.240328
$813$	4.74443	0.166394
$814$	−6.04474	−0.211868
$815$	−25.2789	−0.885483
$816$	−1.91353	−0.0669871
$817$	5.88267	0.205809
$818$	−15.7034	−0.549057
$819$	8.83074	0.308571
$820$	−3.25054	−0.113514
$821$	−29.5995	−1.03303	−0.516516	−	0.856278i	$-0.672771\pi$
$821$	−29.5995	−1.03303	−0.516516	+	0.856278i	$0.672771\pi$
$822$	−4.16420	−0.145243
$823$	−27.4184	−0.955744	−0.477872	−	0.878430i	$-0.658592\pi$
$823$	−27.4184	−0.955744	−0.477872	+	0.878430i	$0.658592\pi$
$824$	−12.9540	−0.451273
$825$	0.519165	0.0180750
$826$	−9.58726	−0.333583
$827$	32.4460	1.12826	0.564128	−	0.825687i	$-0.309212\pi$
$827$	32.4460	1.12826	0.564128	+	0.825687i	$0.309212\pi$
$828$	14.8832	0.517227
$829$	5.48029	0.190338	0.0951692	−	0.995461i	$-0.469661\pi$
$829$	5.48029	0.190338	0.0951692	+	0.995461i	$0.469661\pi$
$830$	−10.2077	−0.354316
$831$	−11.7785	−0.408593
$832$	−2.54201	−0.0881285
$833$	−19.8344	−0.687220
$834$	4.53716	0.157109
$835$	−6.76796	−0.234215
$836$	5.88267	0.203456
$837$	14.9486	0.516701
$838$	40.1703	1.38766
$839$	44.7395	1.54458	0.772289	−	0.635272i	$-0.219112\pi$
$839$	44.7395	1.54458	0.772289	+	0.635272i	$0.219112\pi$
$840$	0.660523	0.0227902
$841$	−0.0264446	−0.000911883 0
$842$	−31.2999	−1.07867
$843$	13.3837	0.460960
$844$	26.6533	0.917445
$845$	−6.53817	−0.224920
$846$	3.08749	0.106150
$847$	1.27228	0.0437160
$848$	−7.32857	−0.251664
$849$	−4.57419	−0.156986
$850$	−3.68579	−0.126422
$851$	32.9486	1.12946
$852$	−6.22054	−0.213112
$853$	−9.82773	−0.336495	−0.168247	−	0.985745i	$-0.553811\pi$
$853$	−9.82773	−0.336495	−0.168247	+	0.985745i	$0.553811\pi$
$854$	−9.53351	−0.326230
$855$	16.0624	0.549324
$856$	−0.750809	−0.0256621
$857$	34.8660	1.19100	0.595501	−	0.803355i	$-0.296954\pi$
$857$	34.8660	1.19100	0.595501	+	0.803355i	$0.296954\pi$
$858$	1.31973	0.0450547
$859$	38.7955	1.32369	0.661843	−	0.749642i	$-0.269775\pi$
$859$	38.7955	1.32369	0.661843	+	0.749642i	$0.269775\pi$
$860$	−1.00000	−0.0340997
$861$	2.14706	0.0731715
$862$	13.0533	0.444596
$863$	−21.8871	−0.745046	−0.372523	−	0.928023i	$-0.621507\pi$
$863$	−21.8871	−0.745046	−0.372523	+	0.928023i	$0.621507\pi$
$864$	−2.97506	−0.101214
$865$	15.1753	0.515974
$866$	23.0956	0.784822
$867$	1.77293	0.0602117
$868$	6.39276	0.216984
$869$	13.2470	0.449373
$870$	2.79452	0.0947430
$871$	−35.9498	−1.21811
$872$	11.8619	0.401693
$873$	−34.4232	−1.16505
$874$	−32.0652	−1.08462
$875$	1.27228	0.0430109
$876$	−7.43419	−0.251178
$877$	−51.5007	−1.73906	−0.869528	−	0.493884i	$-0.835577\pi$
$877$	−51.5007	−1.73906	−0.869528	+	0.493884i	$0.835577\pi$
$878$	−27.9394	−0.942908
$879$	−9.26513	−0.312505
$880$	−1.00000	−0.0337100
$881$	−42.8349	−1.44315	−0.721573	−	0.692338i	$-0.756581\pi$
$881$	−42.8349	−1.44315	−0.721573	+	0.692338i	$0.756581\pi$
$882$	−14.6935	−0.494755
$883$	36.5283	1.22928	0.614638	−	0.788810i	$-0.289302\pi$
$883$	36.5283	1.22928	0.614638	+	0.788810i	$0.289302\pi$
$884$	−9.36933	−0.315125
$885$	−3.91217	−0.131506
$886$	−17.1014	−0.574532
$887$	47.7178	1.60221	0.801103	−	0.598526i	$-0.204247\pi$
$887$	47.7178	1.60221	0.801103	+	0.598526i	$0.204247\pi$
$888$	−3.13822	−0.105312
$889$	6.96791	0.233696
$890$	−5.85808	−0.196363
$891$	−6.64685	−0.222678
$892$	24.2533	0.812061
$893$	−6.65186	−0.222596
$894$	−7.76945	−0.259849
$895$	12.2783	0.410418
$896$	−1.27228	−0.0425038
$897$	−7.19354	−0.240185
$898$	−22.0228	−0.734909
$899$	27.0462	0.902043
$900$	−2.73047	−0.0910156
$901$	−27.0116	−0.899886
$902$	−3.25054	−0.108231
$903$	0.660523	0.0219808
$904$	16.9651	0.564250
$905$	−1.18644	−0.0394386
$906$	−5.24269	−0.174177
$907$	−49.3201	−1.63765	−0.818823	−	0.574046i	$-0.805373\pi$
$907$	−49.3201	−1.63765	−0.818823	+	0.574046i	$0.805373\pi$
$908$	8.16289	0.270895
$909$	−17.5435	−0.581880
$910$	3.23415	0.107211
$911$	−29.0555	−0.962653	−0.481327	−	0.876541i	$-0.659845\pi$
$911$	−29.0555	−0.962653	−0.481327	+	0.876541i	$0.659845\pi$
$912$	3.05408	0.101131
$913$	−10.2077	−0.337827
$914$	−19.6651	−0.650465
$915$	−3.89024	−0.128607
$916$	−13.1244	−0.433643
$917$	3.97622	0.131307
$918$	−10.9654	−0.361914
$919$	−13.2874	−0.438311	−0.219156	−	0.975690i	$-0.570330\pi$
$919$	−13.2874	−0.438311	−0.219156	+	0.975690i	$0.570330\pi$
$920$	5.45078	0.179707
$921$	−15.7388	−0.518610
$922$	−16.5641	−0.545509
$923$	−30.4579	−1.00253
$924$	0.660523	0.0217296
$925$	−6.04474	−0.198750
$926$	−22.6899	−0.745638
$927$	−35.3704	−1.16172
$928$	−5.38271	−0.176696
$929$	16.0197	0.525588	0.262794	−	0.964852i	$-0.415356\pi$
$929$	16.0197	0.525588	0.262794	+	0.964852i	$0.415356\pi$
$930$	2.60863	0.0855402
$931$	31.6565	1.03750
$932$	15.4645	0.506555
$933$	4.56959	0.149602
$934$	14.6484	0.479310
$935$	−3.68579	−0.120538
$936$	−6.94088	−0.226870
$937$	42.4087	1.38543	0.692716	−	0.721210i	$-0.256414\pi$
$937$	42.4087	1.38543	0.692716	+	0.721210i	$0.256414\pi$
$938$	−17.9929	−0.587488
$939$	1.02561	0.0334695
$940$	1.13076	0.0368812
$941$	−11.8225	−0.385403	−0.192702	−	0.981257i	$-0.561725\pi$
$941$	−11.8225	−0.385403	−0.192702	+	0.981257i	$0.561725\pi$
$942$	12.2158	0.398014
$943$	17.7180	0.576977
$944$	7.53550	0.245260
$945$	3.78510	0.123129
$946$	−1.00000	−0.0325128
$947$	−50.7642	−1.64962	−0.824808	−	0.565413i	$-0.808717\pi$
$947$	−50.7642	−1.64962	−0.824808	+	0.565413i	$0.808717\pi$
$948$	6.87738	0.223367
$949$	−36.4004	−1.18161
$950$	5.88267	0.190859
$951$	11.2629	0.365225
$952$	−4.68935	−0.151983
$953$	−18.0745	−0.585490	−0.292745	−	0.956191i	$-0.594569\pi$
$953$	−18.0745	−0.585490	−0.292745	+	0.956191i	$0.594569\pi$
$954$	−20.0104	−0.647862
$955$	−12.1017	−0.391603
$956$	−4.55396	−0.147286
$957$	2.79452	0.0903339
$958$	35.0561	1.13261
$959$	−10.2049	−0.329532
$960$	−0.519165	−0.0167560
$961$	−5.75287	−0.185576
$962$	−15.3658	−0.495414
$963$	−2.05006	−0.0660622
$964$	−14.7575	−0.475306
$965$	24.1625	0.777818
$966$	−3.60037	−0.115840
$967$	56.5629	1.81894	0.909471	−	0.415768i	$-0.136487\pi$
$967$	56.5629	1.81894	0.909471	+	0.415768i	$0.136487\pi$
$968$	−1.00000	−0.0321412
$969$	11.2567	0.361617
$970$	−12.6071	−0.404788
$971$	−8.98684	−0.288401	−0.144201	−	0.989548i	$-0.546061\pi$
$971$	−8.98684	−0.288401	−0.144201	+	0.989548i	$0.546061\pi$
$972$	−12.3760	−0.396960
$973$	11.1189	0.356454
$974$	−11.4679	−0.367456
$975$	1.31973	0.0422650
$976$	7.49326	0.239853
$977$	−29.9909	−0.959495	−0.479747	−	0.877407i	$-0.659272\pi$
$977$	−29.9909	−0.959495	−0.479747	+	0.877407i	$0.659272\pi$
$978$	−13.1240	−0.419658
$979$	−5.85808	−0.187225
$980$	−5.38131	−0.171900
$981$	32.3884	1.03408
$982$	−17.9831	−0.573863
$983$	−24.0264	−0.766323	−0.383161	−	0.923681i	$-0.625165\pi$
$983$	−24.0264	−0.766323	−0.383161	+	0.923681i	$0.625165\pi$
$984$	−1.68757	−0.0537977
$985$	3.41989	0.108967
$986$	−19.8395	−0.631819
$987$	−0.746890	−0.0237738
$988$	14.9538	0.475745
$989$	5.45078	0.173325
$990$	−2.73047	−0.0867799
$991$	−52.1958	−1.65805	−0.829027	−	0.559209i	$-0.811105\pi$
$991$	−52.1958	−1.65805	−0.829027	+	0.559209i	$0.811105\pi$
$992$	−5.02465	−0.159533
$993$	12.2561	0.388937
$994$	−15.2442	−0.483516
$995$	5.10184	0.161739
$996$	−5.29951	−0.167921
$997$	31.6163	1.00130	0.500649	−	0.865651i	$-0.333095\pi$
$997$	31.6163	1.00130	0.500649	+	0.865651i	$0.333095\pi$
$998$	−9.46436	−0.299589
$999$	−17.9835	−0.568972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.y.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.y.1.3	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.519165 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.519165 q^{6} +1.27228 q^{7} -1.00000 q^{8} -2.73047 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.519165 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.519165 q^{6} +1.27228 q^{7} -1.00000 q^{8} -2.73047 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.519165 q^{12} -2.54201 q^{13} -1.27228 q^{14} -0.519165 q^{15} +1.00000 q^{16} +3.68579 q^{17} +2.73047 q^{18} -5.88267 q^{19} +1.00000 q^{20} -0.660523 q^{21} +1.00000 q^{22} -5.45078 q^{23} +0.519165 q^{24} +1.00000 q^{25} +2.54201 q^{26} +2.97506 q^{27} +1.27228 q^{28} +5.38271 q^{29} +0.519165 q^{30} +5.02465 q^{31} -1.00000 q^{32} +0.519165 q^{33} -3.68579 q^{34} +1.27228 q^{35} -2.73047 q^{36} -6.04474 q^{37} +5.88267 q^{38} +1.31973 q^{39} -1.00000 q^{40} -3.25054 q^{41} +0.660523 q^{42} -1.00000 q^{43} -1.00000 q^{44} -2.73047 q^{45} +5.45078 q^{46} +1.13076 q^{47} -0.519165 q^{48} -5.38131 q^{49} -1.00000 q^{50} -1.91353 q^{51} -2.54201 q^{52} -7.32857 q^{53} -2.97506 q^{54} -1.00000 q^{55} -1.27228 q^{56} +3.05408 q^{57} -5.38271 q^{58} +7.53550 q^{59} -0.519165 q^{60} +7.49326 q^{61} -5.02465 q^{62} -3.47391 q^{63} +1.00000 q^{64} -2.54201 q^{65} -0.519165 q^{66} +14.1423 q^{67} +3.68579 q^{68} +2.82986 q^{69} -1.27228 q^{70} +11.9818 q^{71} +2.73047 q^{72} +14.3195 q^{73} +6.04474 q^{74} -0.519165 q^{75} -5.88267 q^{76} -1.27228 q^{77} -1.31973 q^{78} -13.2470 q^{79} +1.00000 q^{80} +6.64685 q^{81} +3.25054 q^{82} +10.2077 q^{83} -0.660523 q^{84} +3.68579 q^{85} +1.00000 q^{86} -2.79452 q^{87} +1.00000 q^{88} +5.85808 q^{89} +2.73047 q^{90} -3.23415 q^{91} -5.45078 q^{92} -2.60863 q^{93} -1.13076 q^{94} -5.88267 q^{95} +0.519165 q^{96} +12.6071 q^{97} +5.38131 q^{98} +2.73047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9	\( 8 q - 8 q^{2} + 3 q^{3} + 8 q^{4} + 8 q^{5} - 3 q^{6} + 11 q^{7} - 8 q^{8} + 3 q^{9} - 8 q^{10} - 8 q^{11} + 3 q^{12} + 6 q^{13} - 11 q^{14} + 3 q^{15} + 8 q^{16} + 9 q^{17} - 3 q^{18} + 9 q^{19} + 8 q^{20} + 21 q^{21} + 8 q^{22} - 2 q^{23} - 3 q^{24} + 8 q^{25} - 6 q^{26} + 24 q^{27} + 11 q^{28} - 10 q^{29} - 3 q^{30} + 6 q^{31} - 8 q^{32} - 3 q^{33} - 9 q^{34} + 11 q^{35} + 3 q^{36} + 16 q^{37} - 9 q^{38} + 6 q^{39} - 8 q^{40} - 4 q^{41} - 21 q^{42} - 8 q^{43} - 8 q^{44} + 3 q^{45} + 2 q^{46} - 11 q^{47} + 3 q^{48} + 11 q^{49} - 8 q^{50} + 38 q^{51} + 6 q^{52} - 15 q^{53} - 24 q^{54} - 8 q^{55} - 11 q^{56} - 2 q^{57} + 10 q^{58} - 7 q^{59} + 3 q^{60} + 2 q^{61} - 6 q^{62} + 33 q^{63} + 8 q^{64} + 6 q^{65} + 3 q^{66} + 4 q^{67} + 9 q^{68} - 4 q^{69} - 11 q^{70} - 3 q^{71} - 3 q^{72} + 32 q^{73} - 16 q^{74} + 3 q^{75} + 9 q^{76} - 11 q^{77} - 6 q^{78} + 45 q^{79} + 8 q^{80} + 20 q^{81} + 4 q^{82} + 39 q^{83} + 21 q^{84} + 9 q^{85} + 8 q^{86} + 2 q^{87} + 8 q^{88} - 22 q^{89} - 3 q^{90} + 18 q^{91} - 2 q^{92} + 18 q^{93} + 11 q^{94} + 9 q^{95} - 3 q^{96} + 30 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 3 * q^3 + 8 * q^4 + 8 * q^5 - 3 * q^6 + 11 * q^7 - 8 * q^8 + 3 * q^9 - 8 * q^10 - 8 * q^11 + 3 * q^12 + 6 * q^13 - 11 * q^14 + 3 * q^15 + 8 * q^16 + 9 * q^17 - 3 * q^18 + 9 * q^19 + 8 * q^20 + 21 * q^21 + 8 * q^22 - 2 * q^23 - 3 * q^24 + 8 * q^25 - 6 * q^26 + 24 * q^27 + 11 * q^28 - 10 * q^29 - 3 * q^30 + 6 * q^31 - 8 * q^32 - 3 * q^33 - 9 * q^34 + 11 * q^35 + 3 * q^36 + 16 * q^37 - 9 * q^38 + 6 * q^39 - 8 * q^40 - 4 * q^41 - 21 * q^42 - 8 * q^43 - 8 * q^44 + 3 * q^45 + 2 * q^46 - 11 * q^47 + 3 * q^48 + 11 * q^49 - 8 * q^50 + 38 * q^51 + 6 * q^52 - 15 * q^53 - 24 * q^54 - 8 * q^55 - 11 * q^56 - 2 * q^57 + 10 * q^58 - 7 * q^59 + 3 * q^60 + 2 * q^61 - 6 * q^62 + 33 * q^63 + 8 * q^64 + 6 * q^65 + 3 * q^66 + 4 * q^67 + 9 * q^68 - 4 * q^69 - 11 * q^70 - 3 * q^71 - 3 * q^72 + 32 * q^73 - 16 * q^74 + 3 * q^75 + 9 * q^76 - 11 * q^77 - 6 * q^78 + 45 * q^79 + 8 * q^80 + 20 * q^81 + 4 * q^82 + 39 * q^83 + 21 * q^84 + 9 * q^85 + 8 * q^86 + 2 * q^87 + 8 * q^88 - 22 * q^89 - 3 * q^90 + 18 * q^91 - 2 * q^92 + 18 * q^93 + 11 * q^94 + 9 * q^95 - 3 * q^96 + 30 * q^97 - 11 * q^98 - 3 * q^99

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