LMFDB - Embedded newform 4730.2.a.bb.1.6

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.577714$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.577714 q^{12} +0.00668142 q^{13} +2.69986 q^{14} +0.577714 q^{15} +1.00000 q^{16} -7.50323 q^{17} +2.66625 q^{18} -5.32428 q^{19} -1.00000 q^{20} +1.55974 q^{21} +1.00000 q^{22} -1.99332 q^{23} +0.577714 q^{24} +1.00000 q^{25} -0.00668142 q^{26} +3.27347 q^{27} -2.69986 q^{28} -9.74150 q^{29} -0.577714 q^{30} +1.14932 q^{31} -1.00000 q^{32} +0.577714 q^{33} +7.50323 q^{34} +2.69986 q^{35} -2.66625 q^{36} -9.73188 q^{37} +5.32428 q^{38} -0.00385995 q^{39} +1.00000 q^{40} +9.14180 q^{41} -1.55974 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.66625 q^{45} +1.99332 q^{46} -11.2736 q^{47} -0.577714 q^{48} +0.289218 q^{49} -1.00000 q^{50} +4.33472 q^{51} +0.00668142 q^{52} -2.54838 q^{53} -3.27347 q^{54} +1.00000 q^{55} +2.69986 q^{56} +3.07591 q^{57} +9.74150 q^{58} +6.45474 q^{59} +0.577714 q^{60} +4.27657 q^{61} -1.14932 q^{62} +7.19848 q^{63} +1.00000 q^{64} -0.00668142 q^{65} -0.577714 q^{66} -8.89100 q^{67} -7.50323 q^{68} +1.15157 q^{69} -2.69986 q^{70} -15.7990 q^{71} +2.66625 q^{72} +7.72877 q^{73} +9.73188 q^{74} -0.577714 q^{75} -5.32428 q^{76} +2.69986 q^{77} +0.00385995 q^{78} -4.15910 q^{79} -1.00000 q^{80} +6.10761 q^{81} -9.14180 q^{82} -6.92811 q^{83} +1.55974 q^{84} +7.50323 q^{85} -1.00000 q^{86} +5.62781 q^{87} +1.00000 q^{88} -16.4938 q^{89} -2.66625 q^{90} -0.0180389 q^{91} -1.99332 q^{92} -0.663978 q^{93} +11.2736 q^{94} +5.32428 q^{95} +0.577714 q^{96} +14.4906 q^{97} -0.289218 q^{98} +2.66625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	−0.577714	−0.333544	−0.166772	−	0.985996i	$-0.553334\pi$
$3$	−0.577714	−0.333544	−0.166772	+	0.985996i	$0.553334\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.577714	0.235851
$7$	−2.69986	−1.02045	−0.510225	−	0.860041i	$-0.670438\pi$
$7$	−2.69986	−1.02045	−0.510225	+	0.860041i	$0.670438\pi$
$8$	−1.00000	−0.353553
$9$	−2.66625	−0.888749
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.577714	−0.166772
$13$	0.00668142	0.00185309	0.000926546	−	1.00000i	$-0.499705\pi$
$13$	0.00668142	0.00185309	0.000926546		1.00000i	$0.499705\pi$
$14$	2.69986	0.721567
$15$	0.577714	0.149165
$16$	1.00000	0.250000
$17$	−7.50323	−1.81980	−0.909900	−	0.414828i	$-0.863842\pi$
$17$	−7.50323	−1.81980	−0.909900	+	0.414828i	$0.863842\pi$
$18$	2.66625	0.628440
$19$	−5.32428	−1.22147	−0.610736	−	0.791834i	$-0.709126\pi$
$19$	−5.32428	−1.22147	−0.610736	+	0.791834i	$0.709126\pi$
$20$	−1.00000	−0.223607
$21$	1.55974	0.340364
$22$	1.00000	0.213201
$23$	−1.99332	−0.415636	−0.207818	−	0.978168i	$-0.566636\pi$
$23$	−1.99332	−0.415636	−0.207818	+	0.978168i	$0.566636\pi$
$24$	0.577714	0.117925
$25$	1.00000	0.200000
$26$	−0.00668142	−0.00131033
$27$	3.27347	0.629980
$28$	−2.69986	−0.510225
$29$	−9.74150	−1.80895	−0.904476	−	0.426525i	$-0.859738\pi$
$29$	−9.74150	−1.80895	−0.904476	+	0.426525i	$0.859738\pi$
$30$	−0.577714	−0.105476
$31$	1.14932	0.206424	0.103212	−	0.994659i	$-0.467088\pi$
$31$	1.14932	0.206424	0.103212	+	0.994659i	$0.467088\pi$
$32$	−1.00000	−0.176777
$33$	0.577714	0.100567
$34$	7.50323	1.28679
$35$	2.69986	0.456359
$36$	−2.66625	−0.444374
$37$	−9.73188	−1.59991	−0.799956	−	0.600059i	$-0.795144\pi$
$37$	−9.73188	−1.59991	−0.799956	+	0.600059i	$0.795144\pi$
$38$	5.32428	0.863712
$39$	−0.00385995	−0.000618087 0
$40$	1.00000	0.158114
$41$	9.14180	1.42771	0.713855	−	0.700294i	$-0.246948\pi$
$41$	9.14180	1.42771	0.713855	+	0.700294i	$0.246948\pi$
$42$	−1.55974	−0.240674
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	2.66625	0.397461
$46$	1.99332	0.293899
$47$	−11.2736	−1.64442	−0.822208	−	0.569187i	$-0.807258\pi$
$47$	−11.2736	−1.64442	−0.822208	+	0.569187i	$0.807258\pi$
$48$	−0.577714	−0.0833859
$49$	0.289218	0.0413169
$50$	−1.00000	−0.141421
$51$	4.33472	0.606982
$52$	0.00668142	0.000926546 0
$53$	−2.54838	−0.350047	−0.175023	−	0.984564i	$-0.556000\pi$
$53$	−2.54838	−0.350047	−0.175023	+	0.984564i	$0.556000\pi$
$54$	−3.27347	−0.445463
$55$	1.00000	0.134840
$56$	2.69986	0.360783
$57$	3.07591	0.407414
$58$	9.74150	1.27912
$59$	6.45474	0.840335	0.420168	−	0.907446i	$-0.361971\pi$
$59$	6.45474	0.840335	0.420168	+	0.907446i	$0.361971\pi$
$60$	0.577714	0.0745826
$61$	4.27657	0.547558	0.273779	−	0.961793i	$-0.411726\pi$
$61$	4.27657	0.547558	0.273779	+	0.961793i	$0.411726\pi$
$62$	−1.14932	−0.145964
$63$	7.19848	0.906923
$64$	1.00000	0.125000
$65$	−0.00668142	−0.000828728 0
$66$	−0.577714	−0.0711117
$67$	−8.89100	−1.08621	−0.543104	−	0.839665i	$-0.682751\pi$
$67$	−8.89100	−1.08621	−0.543104	+	0.839665i	$0.682751\pi$
$68$	−7.50323	−0.909900
$69$	1.15157	0.138633
$70$	−2.69986	−0.322694
$71$	−15.7990	−1.87500	−0.937500	−	0.347985i	$-0.886866\pi$
$71$	−15.7990	−1.87500	−0.937500	+	0.347985i	$0.886866\pi$
$72$	2.66625	0.314220
$73$	7.72877	0.904584	0.452292	−	0.891870i	$-0.350606\pi$
$73$	7.72877	0.904584	0.452292	+	0.891870i	$0.350606\pi$
$74$	9.73188	1.13131
$75$	−0.577714	−0.0667087
$76$	−5.32428	−0.610736
$77$	2.69986	0.307677
$78$	0.00385995	0.000437054 0
$79$	−4.15910	−0.467936	−0.233968	−	0.972244i	$-0.575171\pi$
$79$	−4.15910	−0.467936	−0.233968	+	0.972244i	$0.575171\pi$
$80$	−1.00000	−0.111803
$81$	6.10761	0.678623
$82$	−9.14180	−1.00954
$83$	−6.92811	−0.760459	−0.380229	−	0.924892i	$-0.624155\pi$
$83$	−6.92811	−0.760459	−0.380229	+	0.924892i	$0.624155\pi$
$84$	1.55974	0.170182
$85$	7.50323	0.813839
$86$	−1.00000	−0.107833
$87$	5.62781	0.603364
$88$	1.00000	0.106600
$89$	−16.4938	−1.74834	−0.874168	−	0.485624i	$-0.838593\pi$
$89$	−16.4938	−1.74834	−0.874168	+	0.485624i	$0.838593\pi$
$90$	−2.66625	−0.281047
$91$	−0.0180389	−0.00189099
$92$	−1.99332	−0.207818
$93$	−0.663978	−0.0688513
$94$	11.2736	1.16278
$95$	5.32428	0.546259
$96$	0.577714	0.0589627
$97$	14.4906	1.47130	0.735649	−	0.677363i	$-0.236877\pi$
$97$	14.4906	1.47130	0.735649	+	0.677363i	$0.236877\pi$
$98$	−0.289218	−0.0292154
$99$	2.66625	0.267968
$100$	1.00000	0.100000
$101$	14.6386	1.45659	0.728297	−	0.685261i	$-0.240312\pi$
$101$	14.6386	1.45659	0.728297	+	0.685261i	$0.240312\pi$
$102$	−4.33472	−0.429201
$103$	−6.34952	−0.625636	−0.312818	−	0.949813i	$-0.601273\pi$
$103$	−6.34952	−0.625636	−0.312818	+	0.949813i	$0.601273\pi$
$104$	−0.00668142	−0.000655167 0
$105$	−1.55974	−0.152216
$106$	2.54838	0.247520
$107$	11.1643	1.07929	0.539646	−	0.841892i	$-0.318558\pi$
$107$	11.1643	1.07929	0.539646	+	0.841892i	$0.318558\pi$
$108$	3.27347	0.314990
$109$	−7.19300	−0.688964	−0.344482	−	0.938793i	$-0.611945\pi$
$109$	−7.19300	−0.688964	−0.344482	+	0.938793i	$0.611945\pi$
$110$	−1.00000	−0.0953463
$111$	5.62225	0.533640
$112$	−2.69986	−0.255112
$113$	−13.8698	−1.30476	−0.652379	−	0.757893i	$-0.726229\pi$
$113$	−13.8698	−1.30476	−0.652379	+	0.757893i	$0.726229\pi$
$114$	−3.07591	−0.288085
$115$	1.99332	0.185878
$116$	−9.74150	−0.904476
$117$	−0.0178143	−0.00164693
$118$	−6.45474	−0.594207
$119$	20.2576	1.85701
$120$	−0.577714	−0.0527379
$121$	1.00000	0.0909091
$122$	−4.27657	−0.387182
$123$	−5.28135	−0.476203
$124$	1.14932	0.103212
$125$	−1.00000	−0.0894427
$126$	−7.19848	−0.641291
$127$	−12.7904	−1.13497	−0.567484	−	0.823384i	$-0.692083\pi$
$127$	−12.7904	−1.13497	−0.567484	+	0.823384i	$0.692083\pi$
$128$	−1.00000	−0.0883883
$129$	−0.577714	−0.0508649
$130$	0.00668142	0.000585999 0
$131$	−7.85038	−0.685891	−0.342945	−	0.939355i	$-0.611425\pi$
$131$	−7.85038	−0.685891	−0.342945	+	0.939355i	$0.611425\pi$
$132$	0.577714	0.0502836
$133$	14.3748	1.24645
$134$	8.89100	0.768065
$135$	−3.27347	−0.281736
$136$	7.50323	0.643396
$137$	8.10979	0.692866	0.346433	−	0.938075i	$-0.387393\pi$
$137$	8.10979	0.692866	0.346433	+	0.938075i	$0.387393\pi$
$138$	−1.15157	−0.0980280
$139$	9.85552	0.835934	0.417967	−	0.908462i	$-0.362743\pi$
$139$	9.85552	0.835934	0.417967	+	0.908462i	$0.362743\pi$
$140$	2.69986	0.228179
$141$	6.51289	0.548484
$142$	15.7990	1.32583
$143$	−0.00668142	−0.000558728 0
$144$	−2.66625	−0.222187
$145$	9.74150	0.808988
$146$	−7.72877	−0.639637
$147$	−0.167085	−0.0137810
$148$	−9.73188	−0.799956
$149$	12.5027	1.02426	0.512129	−	0.858908i	$-0.328857\pi$
$149$	12.5027	1.02426	0.512129	+	0.858908i	$0.328857\pi$
$150$	0.577714	0.0471702
$151$	11.5357	0.938766	0.469383	−	0.882995i	$-0.344476\pi$
$151$	11.5357	0.938766	0.469383	+	0.882995i	$0.344476\pi$
$152$	5.32428	0.431856
$153$	20.0054	1.61734
$154$	−2.69986	−0.217561
$155$	−1.14932	−0.0923155
$156$	−0.00385995	−0.000309044 0
$157$	−15.0341	−1.19985	−0.599924	−	0.800057i	$-0.704802\pi$
$157$	−15.0341	−1.19985	−0.599924	+	0.800057i	$0.704802\pi$
$158$	4.15910	0.330881
$159$	1.47224	0.116756
$160$	1.00000	0.0790569
$161$	5.38167	0.424135
$162$	−6.10761	−0.479859
$163$	−11.8173	−0.925602	−0.462801	−	0.886462i	$-0.653156\pi$
$163$	−11.8173	−0.925602	−0.462801	+	0.886462i	$0.653156\pi$
$164$	9.14180	0.713855
$165$	−0.577714	−0.0449750
$166$	6.92811	0.537726
$167$	8.98218	0.695062	0.347531	−	0.937669i	$-0.387020\pi$
$167$	8.98218	0.695062	0.347531	+	0.937669i	$0.387020\pi$
$168$	−1.55974	−0.120337
$169$	−13.0000	−0.999997
$170$	−7.50323	−0.575471
$171$	14.1958	1.08558
$172$	1.00000	0.0762493
$173$	0.691126	0.0525453	0.0262727	−	0.999655i	$-0.491636\pi$
$173$	0.691126	0.0525453	0.0262727	+	0.999655i	$0.491636\pi$
$174$	−5.62781	−0.426643
$175$	−2.69986	−0.204090
$176$	−1.00000	−0.0753778
$177$	−3.72899	−0.280288
$178$	16.4938	1.23626
$179$	−11.7502	−0.878249	−0.439125	−	0.898426i	$-0.644711\pi$
$179$	−11.7502	−0.878249	−0.439125	+	0.898426i	$0.644711\pi$
$180$	2.66625	0.198730
$181$	−7.73730	−0.575109	−0.287555	−	0.957764i	$-0.592842\pi$
$181$	−7.73730	−0.575109	−0.287555	+	0.957764i	$0.592842\pi$
$182$	0.0180389	0.00133713
$183$	−2.47063	−0.182635
$184$	1.99332	0.146949
$185$	9.73188	0.715502
$186$	0.663978	0.0486852
$187$	7.50323	0.548690
$188$	−11.2736	−0.822208
$189$	−8.83790	−0.642863
$190$	−5.32428	−0.386264
$191$	0.577591	0.0417930	0.0208965	−	0.999782i	$-0.493348\pi$
$191$	0.577591	0.0417930	0.0208965	+	0.999782i	$0.493348\pi$
$192$	−0.577714	−0.0416929
$193$	−5.27610	−0.379782	−0.189891	−	0.981805i	$-0.560813\pi$
$193$	−5.27610	−0.379782	−0.189891	+	0.981805i	$0.560813\pi$
$194$	−14.4906	−1.04036
$195$	0.00385995	0.000276417 0
$196$	0.289218	0.0206584
$197$	−21.4244	−1.52642	−0.763212	−	0.646148i	$-0.776379\pi$
$197$	−21.4244	−1.52642	−0.763212	+	0.646148i	$0.776379\pi$
$198$	−2.66625	−0.189482
$199$	12.3560	0.875895	0.437948	−	0.899001i	$-0.355706\pi$
$199$	12.3560	0.875895	0.437948	+	0.899001i	$0.355706\pi$
$200$	−1.00000	−0.0707107
$201$	5.13646	0.362298
$202$	−14.6386	−1.02997
$203$	26.3006	1.84594
$204$	4.33472	0.303491
$205$	−9.14180	−0.638491
$206$	6.34952	0.442392
$207$	5.31468	0.369396
$208$	0.00668142	0.000463273 0
$209$	5.32428	0.368288
$210$	1.55974	0.107633
$211$	22.9313	1.57866	0.789329	−	0.613970i	$-0.210428\pi$
$211$	22.9313	1.57866	0.789329	+	0.613970i	$0.210428\pi$
$212$	−2.54838	−0.175023
$213$	9.12733	0.625394
$214$	−11.1643	−0.763175
$215$	−1.00000	−0.0681994
$216$	−3.27347	−0.222732
$217$	−3.10299	−0.210645
$218$	7.19300	0.487171
$219$	−4.46502	−0.301718
$220$	1.00000	0.0674200
$221$	−0.0501322	−0.00337226
$222$	−5.62225	−0.377341
$223$	12.5840	0.842688	0.421344	−	0.906901i	$-0.361559\pi$
$223$	12.5840	0.842688	0.421344	+	0.906901i	$0.361559\pi$
$224$	2.69986	0.180392
$225$	−2.66625	−0.177750
$226$	13.8698	0.922603
$227$	13.4424	0.892205	0.446103	−	0.894982i	$-0.352812\pi$
$227$	13.4424	0.892205	0.446103	+	0.894982i	$0.352812\pi$
$228$	3.07591	0.203707
$229$	14.6520	0.968228	0.484114	−	0.875005i	$-0.339142\pi$
$229$	14.6520	0.968228	0.484114	+	0.875005i	$0.339142\pi$
$230$	−1.99332	−0.131436
$231$	−1.55974	−0.102624
$232$	9.74150	0.639561
$233$	−17.1222	−1.12172	−0.560858	−	0.827912i	$-0.689528\pi$
$233$	−17.1222	−1.12172	−0.560858	+	0.827912i	$0.689528\pi$
$234$	0.0178143	0.00116456
$235$	11.2736	0.735405
$236$	6.45474	0.420168
$237$	2.40277	0.156077
$238$	−20.2576	−1.31311
$239$	−4.63878	−0.300058	−0.150029	−	0.988682i	$-0.547937\pi$
$239$	−4.63878	−0.300058	−0.150029	+	0.988682i	$0.547937\pi$
$240$	0.577714	0.0372913
$241$	15.2434	0.981913	0.490956	−	0.871184i	$-0.336647\pi$
$241$	15.2434	0.981913	0.490956	+	0.871184i	$0.336647\pi$
$242$	−1.00000	−0.0642824
$243$	−13.3489	−0.856330
$244$	4.27657	0.273779
$245$	−0.289218	−0.0184775
$246$	5.28135	0.336727
$247$	−0.0355737	−0.00226350
$248$	−1.14932	−0.0729818
$249$	4.00247	0.253646
$250$	1.00000	0.0632456
$251$	5.90920	0.372985	0.186493	−	0.982456i	$-0.440288\pi$
$251$	5.90920	0.372985	0.186493	+	0.982456i	$0.440288\pi$
$252$	7.19848	0.453462
$253$	1.99332	0.125319
$254$	12.7904	0.802544
$255$	−4.33472	−0.271451
$256$	1.00000	0.0625000
$257$	−22.8381	−1.42460	−0.712302	−	0.701873i	$-0.752347\pi$
$257$	−22.8381	−1.42460	−0.712302	+	0.701873i	$0.752347\pi$
$258$	0.577714	0.0359669
$259$	26.2747	1.63263
$260$	−0.00668142	−0.000414364 0
$261$	25.9732	1.60770
$262$	7.85038	0.484998
$263$	2.36294	0.145705	0.0728526	−	0.997343i	$-0.476790\pi$
$263$	2.36294	0.145705	0.0728526	+	0.997343i	$0.476790\pi$
$264$	−0.577714	−0.0355559
$265$	2.54838	0.156546
$266$	−14.3748	−0.881374
$267$	9.52869	0.583146
$268$	−8.89100	−0.543104
$269$	−16.1901	−0.987128	−0.493564	−	0.869709i	$-0.664306\pi$
$269$	−16.1901	−0.987128	−0.493564	+	0.869709i	$0.664306\pi$
$270$	3.27347	0.199217
$271$	−4.34264	−0.263797	−0.131898	−	0.991263i	$-0.542107\pi$
$271$	−4.34264	−0.263797	−0.131898	+	0.991263i	$0.542107\pi$
$272$	−7.50323	−0.454950
$273$	0.0104213	0.000630727 0
$274$	−8.10979	−0.489931
$275$	−1.00000	−0.0603023
$276$	1.15157	0.0693163
$277$	−3.77746	−0.226966	−0.113483	−	0.993540i	$-0.536201\pi$
$277$	−3.77746	−0.226966	−0.113483	+	0.993540i	$0.536201\pi$
$278$	−9.85552	−0.591095
$279$	−3.06437	−0.183459
$280$	−2.69986	−0.161347
$281$	1.26839	0.0756657	0.0378329	−	0.999284i	$-0.487955\pi$
$281$	1.26839	0.0756657	0.0378329	+	0.999284i	$0.487955\pi$
$282$	−6.51289	−0.387837
$283$	−10.1674	−0.604390	−0.302195	−	0.953246i	$-0.597719\pi$
$283$	−10.1674	−0.604390	−0.302195	+	0.953246i	$0.597719\pi$
$284$	−15.7990	−0.937500
$285$	−3.07591	−0.182201
$286$	0.00668142	0.000395081 0
$287$	−24.6815	−1.45691
$288$	2.66625	0.157110
$289$	39.2984	2.31167
$290$	−9.74150	−0.572041
$291$	−8.37143	−0.490742
$292$	7.72877	0.452292
$293$	−18.4822	−1.07974	−0.539872	−	0.841747i	$-0.681527\pi$
$293$	−18.4822	−1.07974	−0.539872	+	0.841747i	$0.681527\pi$
$294$	0.167085	0.00974462
$295$	−6.45474	−0.375809
$296$	9.73188	0.565654
$297$	−3.27347	−0.189946
$298$	−12.5027	−0.724260
$299$	−0.0133182	−0.000770211 0
$300$	−0.577714	−0.0333544
$301$	−2.69986	−0.155617
$302$	−11.5357	−0.663808
$303$	−8.45693	−0.485838
$304$	−5.32428	−0.305368
$305$	−4.27657	−0.244876
$306$	−20.0054	−1.14364
$307$	−8.27918	−0.472517	−0.236259	−	0.971690i	$-0.575921\pi$
$307$	−8.27918	−0.472517	−0.236259	+	0.971690i	$0.575921\pi$
$308$	2.69986	0.153839
$309$	3.66821	0.208677
$310$	1.14932	0.0652769
$311$	14.4629	0.820116	0.410058	−	0.912059i	$-0.365508\pi$
$311$	14.4629	0.820116	0.410058	+	0.912059i	$0.365508\pi$
$312$	0.00385995	0.000218527 0
$313$	−1.07351	−0.0606784	−0.0303392	−	0.999540i	$-0.509659\pi$
$313$	−1.07351	−0.0606784	−0.0303392	+	0.999540i	$0.509659\pi$
$314$	15.0341	0.848421
$315$	−7.19848	−0.405588
$316$	−4.15910	−0.233968
$317$	−18.3258	−1.02928	−0.514638	−	0.857407i	$-0.672074\pi$
$317$	−18.3258	−1.02928	−0.514638	+	0.857407i	$0.672074\pi$
$318$	−1.47224	−0.0825588
$319$	9.74150	0.545420
$320$	−1.00000	−0.0559017
$321$	−6.44977	−0.359991
$322$	−5.38167	−0.299909
$323$	39.9492	2.22284
$324$	6.10761	0.339312
$325$	0.00668142	0.000370619 0
$326$	11.8173	0.654500
$327$	4.15550	0.229800
$328$	−9.14180	−0.504772
$329$	30.4370	1.67804
$330$	0.577714	0.0318021
$331$	−20.6284	−1.13384	−0.566919	−	0.823774i	$-0.691865\pi$
$331$	−20.6284	−1.13384	−0.566919	+	0.823774i	$0.691865\pi$
$332$	−6.92811	−0.380229
$333$	25.9476	1.42192
$334$	−8.98218	−0.491483
$335$	8.89100	0.485767
$336$	1.55974	0.0850911
$337$	4.19893	0.228730	0.114365	−	0.993439i	$-0.463517\pi$
$337$	4.19893	0.228730	0.114365	+	0.993439i	$0.463517\pi$
$338$	13.0000	0.707104
$339$	8.01276	0.435194
$340$	7.50323	0.406920
$341$	−1.14932	−0.0622391
$342$	−14.1958	−0.767623
$343$	18.1181	0.978288
$344$	−1.00000	−0.0539164
$345$	−1.15157	−0.0619984
$346$	−0.691126	−0.0371552
$347$	11.3065	0.606964	0.303482	−	0.952837i	$-0.401851\pi$
$347$	11.3065	0.606964	0.303482	+	0.952837i	$0.401851\pi$
$348$	5.62781	0.301682
$349$	−27.8234	−1.48935	−0.744675	−	0.667427i	$-0.767396\pi$
$349$	−27.8234	−1.48935	−0.744675	+	0.667427i	$0.767396\pi$
$350$	2.69986	0.144313
$351$	0.0218714	0.00116741
$352$	1.00000	0.0533002
$353$	−30.2682	−1.61101	−0.805506	−	0.592587i	$-0.798106\pi$
$353$	−30.2682	−1.61101	−0.805506	+	0.592587i	$0.798106\pi$
$354$	3.72899	0.198194
$355$	15.7990	0.838526
$356$	−16.4938	−0.874168
$357$	−11.7031	−0.619395
$358$	11.7502	0.621016
$359$	−0.0533741	−0.00281698	−0.00140849	−	0.999999i	$-0.500448\pi$
$359$	−0.0533741	−0.00281698	−0.00140849	+	0.999999i	$0.500448\pi$
$360$	−2.66625	−0.140524
$361$	9.34792	0.491996
$362$	7.73730	0.406664
$363$	−0.577714	−0.0303221
$364$	−0.0180389	−0.000945494 0
$365$	−7.72877	−0.404542
$366$	2.47063	0.129142
$367$	10.8408	0.565883	0.282942	−	0.959137i	$-0.408690\pi$
$367$	10.8408	0.565883	0.282942	+	0.959137i	$0.408690\pi$
$368$	−1.99332	−0.103909
$369$	−24.3743	−1.26888
$370$	−9.73188	−0.505936
$371$	6.88025	0.357205
$372$	−0.663978	−0.0344257
$373$	−28.6721	−1.48458	−0.742292	−	0.670076i	$-0.766261\pi$
$373$	−28.6721	−1.48458	−0.742292	+	0.670076i	$0.766261\pi$
$374$	−7.50323	−0.387983
$375$	0.577714	0.0298330
$376$	11.2736	0.581389
$377$	−0.0650871	−0.00335216
$378$	8.83790	0.454572
$379$	24.2561	1.24595	0.622977	−	0.782240i	$-0.285923\pi$
$379$	24.2561	1.24595	0.622977	+	0.782240i	$0.285923\pi$
$380$	5.32428	0.273130
$381$	7.38922	0.378561
$382$	−0.577591	−0.0295521
$383$	14.7829	0.755369	0.377684	−	0.925934i	$-0.376720\pi$
$383$	14.7829	0.755369	0.377684	+	0.925934i	$0.376720\pi$
$384$	0.577714	0.0294814
$385$	−2.69986	−0.137597
$386$	5.27610	0.268547
$387$	−2.66625	−0.135533
$388$	14.4906	0.735649
$389$	25.4940	1.29260	0.646298	−	0.763085i	$-0.276316\pi$
$389$	25.4940	1.29260	0.646298	+	0.763085i	$0.276316\pi$
$390$	−0.00385995	−0.000195456 0
$391$	14.9563	0.756374
$392$	−0.289218	−0.0146077
$393$	4.53528	0.228774
$394$	21.4244	1.07934
$395$	4.15910	0.209267
$396$	2.66625	0.133984
$397$	17.7664	0.891669	0.445835	−	0.895115i	$-0.352907\pi$
$397$	17.7664	0.891669	0.445835	+	0.895115i	$0.352907\pi$
$398$	−12.3560	−0.619351
$399$	−8.30451	−0.415746
$400$	1.00000	0.0500000
$401$	−0.144875	−0.00723470	−0.00361735	−	0.999993i	$-0.501151\pi$
$401$	−0.144875	−0.00723470	−0.00361735	+	0.999993i	$0.501151\pi$
$402$	−5.13646	−0.256183
$403$	0.00767908	0.000382522 0
$404$	14.6386	0.728297
$405$	−6.10761	−0.303489
$406$	−26.3006	−1.30528
$407$	9.73188	0.482391
$408$	−4.33472	−0.214601
$409$	−0.871128	−0.0430745	−0.0215373	−	0.999768i	$-0.506856\pi$
$409$	−0.871128	−0.0430745	−0.0215373	+	0.999768i	$0.506856\pi$
$410$	9.14180	0.451481
$411$	−4.68514	−0.231101
$412$	−6.34952	−0.312818
$413$	−17.4269	−0.857520
$414$	−5.31468	−0.261202
$415$	6.92811	0.340088
$416$	−0.00668142	−0.000327584 0
$417$	−5.69367	−0.278820
$418$	−5.32428	−0.260419
$419$	−19.3475	−0.945185	−0.472593	−	0.881281i	$-0.656682\pi$
$419$	−19.3475	−0.945185	−0.472593	+	0.881281i	$0.656682\pi$
$420$	−1.55974	−0.0761078
$421$	−13.3644	−0.651339	−0.325670	−	0.945484i	$-0.605590\pi$
$421$	−13.3644	−0.651339	−0.325670	+	0.945484i	$0.605590\pi$
$422$	−22.9313	−1.11628
$423$	30.0581	1.46147
$424$	2.54838	0.123760
$425$	−7.50323	−0.363960
$426$	−9.12733	−0.442220
$427$	−11.5461	−0.558756
$428$	11.1643	0.539646
$429$	0.00385995	0.000186360 0
$430$	1.00000	0.0482243
$431$	−18.9085	−0.910790	−0.455395	−	0.890290i	$-0.650502\pi$
$431$	−18.9085	−0.910790	−0.455395	+	0.890290i	$0.650502\pi$
$432$	3.27347	0.157495
$433$	−28.0836	−1.34961	−0.674806	−	0.737996i	$-0.735773\pi$
$433$	−28.0836	−1.34961	−0.674806	+	0.737996i	$0.735773\pi$
$434$	3.10299	0.148948
$435$	−5.62781	−0.269833
$436$	−7.19300	−0.344482
$437$	10.6130	0.507688
$438$	4.46502	0.213347
$439$	40.8954	1.95183	0.975916	−	0.218149i	$-0.0700018\pi$
$439$	40.8954	1.95183	0.975916	+	0.218149i	$0.0700018\pi$
$440$	−1.00000	−0.0476731
$441$	−0.771127	−0.0367203
$442$	0.0501322	0.00238455
$443$	40.6426	1.93099	0.965494	−	0.260426i	$-0.0838629\pi$
$443$	40.6426	1.93099	0.965494	+	0.260426i	$0.0838629\pi$
$444$	5.62225	0.266820
$445$	16.4938	0.781880
$446$	−12.5840	−0.595870
$447$	−7.22297	−0.341635
$448$	−2.69986	−0.127556
$449$	20.4364	0.964455	0.482228	−	0.876046i	$-0.339828\pi$
$449$	20.4364	0.964455	0.482228	+	0.876046i	$0.339828\pi$
$450$	2.66625	0.125688
$451$	−9.14180	−0.430471
$452$	−13.8698	−0.652379
$453$	−6.66437	−0.313119
$454$	−13.4424	−0.630884
$455$	0.0180389	0.000845675 0
$456$	−3.07591	−0.144043
$457$	28.6296	1.33923	0.669617	−	0.742706i	$-0.266458\pi$
$457$	28.6296	1.33923	0.669617	+	0.742706i	$0.266458\pi$
$458$	−14.6520	−0.684641
$459$	−24.5616	−1.14644
$460$	1.99332	0.0929390
$461$	7.14878	0.332952	0.166476	−	0.986046i	$-0.446761\pi$
$461$	7.14878	0.332952	0.166476	+	0.986046i	$0.446761\pi$
$462$	1.55974	0.0725659
$463$	−30.9169	−1.43683	−0.718416	−	0.695614i	$-0.755132\pi$
$463$	−30.9169	−1.43683	−0.718416	+	0.695614i	$0.755132\pi$
$464$	−9.74150	−0.452238
$465$	0.663978	0.0307912
$466$	17.1222	0.793172
$467$	19.7877	0.915666	0.457833	−	0.889038i	$-0.348626\pi$
$467$	19.7877	0.915666	0.457833	+	0.889038i	$0.348626\pi$
$468$	−0.0178143	−0.000823467 0
$469$	24.0044	1.10842
$470$	−11.2736	−0.520010
$471$	8.68539	0.400201
$472$	−6.45474	−0.297103
$473$	−1.00000	−0.0459800
$474$	−2.40277	−0.110363
$475$	−5.32428	−0.244295
$476$	20.2576	0.928507
$477$	6.79461	0.311104
$478$	4.63878	0.212173
$479$	−17.7962	−0.813130	−0.406565	−	0.913622i	$-0.633274\pi$
$479$	−17.7962	−0.813130	−0.406565	+	0.913622i	$0.633274\pi$
$480$	−0.577714	−0.0263689
$481$	−0.0650228	−0.00296478
$482$	−15.2434	−0.694317
$483$	−3.10907	−0.141468
$484$	1.00000	0.0454545
$485$	−14.4906	−0.657984
$486$	13.3489	0.605517
$487$	22.9534	1.04012	0.520058	−	0.854131i	$-0.325910\pi$
$487$	22.9534	1.04012	0.520058	+	0.854131i	$0.325910\pi$
$488$	−4.27657	−0.193591
$489$	6.82702	0.308729
$490$	0.289218	0.0130655
$491$	3.36504	0.151862	0.0759310	−	0.997113i	$-0.475807\pi$
$491$	3.36504	0.151862	0.0759310	+	0.997113i	$0.475807\pi$
$492$	−5.28135	−0.238102
$493$	73.0927	3.29193
$494$	0.0355737	0.00160054
$495$	−2.66625	−0.119839
$496$	1.14932	0.0516059
$497$	42.6551	1.91334
$498$	−4.00247	−0.179355
$499$	18.9121	0.846624	0.423312	−	0.905984i	$-0.360867\pi$
$499$	18.9121	0.846624	0.423312	+	0.905984i	$0.360867\pi$
$500$	−1.00000	−0.0447214
$501$	−5.18913	−0.231833
$502$	−5.90920	−0.263741
$503$	3.42471	0.152700	0.0763501	−	0.997081i	$-0.475673\pi$
$503$	3.42471	0.152700	0.0763501	+	0.997081i	$0.475673\pi$
$504$	−7.19848	−0.320646
$505$	−14.6386	−0.651409
$506$	−1.99332	−0.0886138
$507$	7.51026	0.333542
$508$	−12.7904	−0.567484
$509$	1.36409	0.0604624	0.0302312	−	0.999543i	$-0.490376\pi$
$509$	1.36409	0.0604624	0.0302312	+	0.999543i	$0.490376\pi$
$510$	4.33472	0.191945
$511$	−20.8666	−0.923082
$512$	−1.00000	−0.0441942
$513$	−17.4289	−0.769503
$514$	22.8381	1.00735
$515$	6.34952	0.279793
$516$	−0.577714	−0.0254325
$517$	11.2736	0.495810
$518$	−26.2747	−1.15444
$519$	−0.399273	−0.0175262
$520$	0.00668142	0.000293000 0
$521$	−8.88322	−0.389181	−0.194590	−	0.980885i	$-0.562338\pi$
$521$	−8.88322	−0.389181	−0.194590	+	0.980885i	$0.562338\pi$
$522$	−25.9732	−1.13682
$523$	−19.2649	−0.842394	−0.421197	−	0.906969i	$-0.638390\pi$
$523$	−19.2649	−0.842394	−0.421197	+	0.906969i	$0.638390\pi$
$524$	−7.85038	−0.342945
$525$	1.55974	0.0680729
$526$	−2.36294	−0.103029
$527$	−8.62360	−0.375650
$528$	0.577714	0.0251418
$529$	−19.0267	−0.827247
$530$	−2.54838	−0.110695
$531$	−17.2099	−0.746847
$532$	14.3748	0.623226
$533$	0.0610802	0.00264568
$534$	−9.52869	−0.412347
$535$	−11.1643	−0.482674
$536$	8.89100	0.384033
$537$	6.78824	0.292934
$538$	16.1901	0.698005
$539$	−0.289218	−0.0124575
$540$	−3.27347	−0.140868
$541$	18.3686	0.789727	0.394864	−	0.918740i	$-0.370792\pi$
$541$	18.3686	0.789727	0.394864	+	0.918740i	$0.370792\pi$
$542$	4.34264	0.186532
$543$	4.46995	0.191824
$544$	7.50323	0.321698
$545$	7.19300	0.308114
$546$	−0.0104213	−0.000445991 0
$547$	−31.0349	−1.32696	−0.663479	−	0.748195i	$-0.730921\pi$
$547$	−31.0349	−1.32696	−0.663479	+	0.748195i	$0.730921\pi$
$548$	8.10979	0.346433
$549$	−11.4024	−0.486642
$550$	1.00000	0.0426401
$551$	51.8665	2.20959
$552$	−1.15157	−0.0490140
$553$	11.2290	0.477505
$554$	3.77746	0.160489
$555$	−5.62225	−0.238651
$556$	9.85552	0.417967
$557$	31.1414	1.31950	0.659751	−	0.751484i	$-0.270662\pi$
$557$	31.1414	1.31950	0.659751	+	0.751484i	$0.270662\pi$
$558$	3.06437	0.129725
$559$	0.00668142	0.000282594 0
$560$	2.69986	0.114090
$561$	−4.33472	−0.183012
$562$	−1.26839	−0.0535038
$563$	14.6683	0.618197	0.309098	−	0.951030i	$-0.399973\pi$
$563$	14.6683	0.618197	0.309098	+	0.951030i	$0.399973\pi$
$564$	6.51289	0.274242
$565$	13.8698	0.583506
$566$	10.1674	0.427368
$567$	−16.4897	−0.692500
$568$	15.7990	0.662913
$569$	−21.0302	−0.881634	−0.440817	−	0.897597i	$-0.645311\pi$
$569$	−21.0302	−0.881634	−0.440817	+	0.897597i	$0.645311\pi$
$570$	3.07591	0.128836
$571$	3.56595	0.149230	0.0746151	−	0.997212i	$-0.476227\pi$
$571$	3.56595	0.149230	0.0746151	+	0.997212i	$0.476227\pi$
$572$	−0.00668142	−0.000279364 0
$573$	−0.333682	−0.0139398
$574$	24.6815	1.03019
$575$	−1.99332	−0.0831271
$576$	−2.66625	−0.111094
$577$	44.3300	1.84548	0.922742	−	0.385419i	$-0.125943\pi$
$577$	44.3300	1.84548	0.922742	+	0.385419i	$0.125943\pi$
$578$	−39.2984	−1.63460
$579$	3.04808	0.126674
$580$	9.74150	0.404494
$581$	18.7049	0.776010
$582$	8.37143	0.347007
$583$	2.54838	0.105543
$584$	−7.72877	−0.319819
$585$	0.0178143	0.000736531 0
$586$	18.4822	0.763495
$587$	−19.6007	−0.809009	−0.404504	−	0.914536i	$-0.632556\pi$
$587$	−19.6007	−0.809009	−0.404504	+	0.914536i	$0.632556\pi$
$588$	−0.167085	−0.00689049
$589$	−6.11929	−0.252141
$590$	6.45474	0.265737
$591$	12.3772	0.509129
$592$	−9.73188	−0.399978
$593$	26.4786	1.08735	0.543674	−	0.839297i	$-0.317033\pi$
$593$	26.4786	1.08735	0.543674	+	0.839297i	$0.317033\pi$
$594$	3.27347	0.134312
$595$	−20.2576	−0.830482
$596$	12.5027	0.512129
$597$	−7.13825	−0.292149
$598$	0.0133182	0.000544622 0
$599$	−15.5145	−0.633906	−0.316953	−	0.948441i	$-0.602660\pi$
$599$	−15.5145	−0.633906	−0.316953	+	0.948441i	$0.602660\pi$
$600$	0.577714	0.0235851
$601$	−13.7412	−0.560515	−0.280257	−	0.959925i	$-0.590420\pi$
$601$	−13.7412	−0.560515	−0.280257	+	0.959925i	$0.590420\pi$
$602$	2.69986	0.110038
$603$	23.7056	0.965366
$604$	11.5357	0.469383
$605$	−1.00000	−0.0406558
$606$	8.45693	0.343539
$607$	11.5673	0.469503	0.234752	−	0.972055i	$-0.424572\pi$
$607$	11.5673	0.469503	0.234752	+	0.972055i	$0.424572\pi$
$608$	5.32428	0.215928
$609$	−15.1943	−0.615703
$610$	4.27657	0.173153
$611$	−0.0753233	−0.00304726
$612$	20.0054	0.808672
$613$	5.55030	0.224174	0.112087	−	0.993698i	$-0.464246\pi$
$613$	5.55030	0.224174	0.112087	+	0.993698i	$0.464246\pi$
$614$	8.27918	0.334120
$615$	5.28135	0.212965
$616$	−2.69986	−0.108780
$617$	−20.1201	−0.810006	−0.405003	−	0.914315i	$-0.632730\pi$
$617$	−20.1201	−0.810006	−0.405003	+	0.914315i	$0.632730\pi$
$618$	−3.66821	−0.147557
$619$	−1.34982	−0.0542538	−0.0271269	−	0.999632i	$-0.508636\pi$
$619$	−1.34982	−0.0542538	−0.0271269	+	0.999632i	$0.508636\pi$
$620$	−1.14932	−0.0461578
$621$	−6.52507	−0.261842
$622$	−14.4629	−0.579910
$623$	44.5308	1.78409
$624$	−0.00385995	−0.000154522 0
$625$	1.00000	0.0400000
$626$	1.07351	0.0429061
$627$	−3.07591	−0.122840
$628$	−15.0341	−0.599924
$629$	73.0205	2.91152
$630$	7.19848	0.286794
$631$	34.8854	1.38877	0.694384	−	0.719605i	$-0.255677\pi$
$631$	34.8854	1.38877	0.694384	+	0.719605i	$0.255677\pi$
$632$	4.15910	0.165440
$633$	−13.2478	−0.526551
$634$	18.3258	0.727809
$635$	12.7904	0.507573
$636$	1.47224	0.0583779
$637$	0.00193239	7.65640e−5 0
$638$	−9.74150	−0.385670
$639$	42.1241	1.66640
$640$	1.00000	0.0395285
$641$	−8.36971	−0.330584	−0.165292	−	0.986245i	$-0.552857\pi$
$641$	−8.36971	−0.330584	−0.165292	+	0.986245i	$0.552857\pi$
$642$	6.44977	0.254552
$643$	28.7586	1.13413	0.567065	−	0.823673i	$-0.308079\pi$
$643$	28.7586	1.13413	0.567065	+	0.823673i	$0.308079\pi$
$644$	5.38167	0.212068
$645$	0.577714	0.0227475
$646$	−39.9492	−1.57178
$647$	−46.0375	−1.80992	−0.904960	−	0.425497i	$-0.860099\pi$
$647$	−46.0375	−1.80992	−0.904960	+	0.425497i	$0.860099\pi$
$648$	−6.10761	−0.239929
$649$	−6.45474	−0.253371
$650$	−0.00668142	−0.000262067 0
$651$	1.79264	0.0702593
$652$	−11.8173	−0.462801
$653$	−12.6529	−0.495148	−0.247574	−	0.968869i	$-0.579633\pi$
$653$	−12.6529	−0.495148	−0.247574	+	0.968869i	$0.579633\pi$
$654$	−4.15550	−0.162493
$655$	7.85038	0.306740
$656$	9.14180	0.356927
$657$	−20.6068	−0.803948
$658$	−30.4370	−1.18656
$659$	33.1773	1.29240	0.646202	−	0.763166i	$-0.276356\pi$
$659$	33.1773	1.29240	0.646202	+	0.763166i	$0.276356\pi$
$660$	−0.577714	−0.0224875
$661$	15.1291	0.588455	0.294227	−	0.955735i	$-0.404938\pi$
$661$	15.1291	0.588455	0.294227	+	0.955735i	$0.404938\pi$
$662$	20.6284	0.801744
$663$	0.0289621	0.00112479
$664$	6.92811	0.268863
$665$	−14.3748	−0.557430
$666$	−25.9476	−1.00545
$667$	19.4179	0.751865
$668$	8.98218	0.347531
$669$	−7.26996	−0.281073
$670$	−8.89100	−0.343489
$671$	−4.27657	−0.165095
$672$	−1.55974	−0.0601685
$673$	33.3925	1.28719	0.643594	−	0.765367i	$-0.277443\pi$
$673$	33.3925	1.28719	0.643594	+	0.765367i	$0.277443\pi$
$674$	−4.19893	−0.161737
$675$	3.27347	0.125996
$676$	−13.0000	−0.499998
$677$	−50.5639	−1.94333	−0.971664	−	0.236365i	$-0.924044\pi$
$677$	−50.5639	−1.94333	−0.971664	+	0.236365i	$0.924044\pi$
$678$	−8.01276	−0.307728
$679$	−39.1225	−1.50138
$680$	−7.50323	−0.287736
$681$	−7.76588	−0.297589
$682$	1.14932	0.0440097
$683$	−39.3871	−1.50710	−0.753552	−	0.657388i	$-0.771661\pi$
$683$	−39.3871	−1.50710	−0.753552	+	0.657388i	$0.771661\pi$
$684$	14.1958	0.542791
$685$	−8.10979	−0.309859
$686$	−18.1181	−0.691754
$687$	−8.46464	−0.322946
$688$	1.00000	0.0381246
$689$	−0.0170268	−0.000648669 0
$690$	1.15157	0.0438395
$691$	−43.6230	−1.65950	−0.829748	−	0.558139i	$-0.811516\pi$
$691$	−43.6230	−1.65950	−0.829748	+	0.558139i	$0.811516\pi$
$692$	0.691126	0.0262727
$693$	−7.19848	−0.273448
$694$	−11.3065	−0.429188
$695$	−9.85552	−0.373841
$696$	−5.62781	−0.213321
$697$	−68.5930	−2.59815
$698$	27.8234	1.05313
$699$	9.89176	0.374141
$700$	−2.69986	−0.102045
$701$	−3.67861	−0.138939	−0.0694695	−	0.997584i	$-0.522131\pi$
$701$	−3.67861	−0.138939	−0.0694695	+	0.997584i	$0.522131\pi$
$702$	−0.0218714	−0.000825484 0
$703$	51.8152	1.95425
$704$	−1.00000	−0.0376889
$705$	−6.51289	−0.245290
$706$	30.2682	1.13916
$707$	−39.5221	−1.48638
$708$	−3.72899	−0.140144
$709$	−1.47094	−0.0552423	−0.0276212	−	0.999618i	$-0.508793\pi$
$709$	−1.47094	−0.0552423	−0.0276212	+	0.999618i	$0.508793\pi$
$710$	−15.7990	−0.592927
$711$	11.0892	0.415877
$712$	16.4938	0.618130
$713$	−2.29096	−0.0857971
$714$	11.7031	0.437978
$715$	0.00668142	0.000249871 0
$716$	−11.7502	−0.439125
$717$	2.67989	0.100082
$718$	0.0533741	0.00199190
$719$	22.4756	0.838200	0.419100	−	0.907940i	$-0.362346\pi$
$719$	22.4756	0.838200	0.419100	+	0.907940i	$0.362346\pi$
$720$	2.66625	0.0993651
$721$	17.1428	0.638430
$722$	−9.34792	−0.347893
$723$	−8.80632	−0.327511
$724$	−7.73730	−0.287555
$725$	−9.74150	−0.361790
$726$	0.577714	0.0214410
$727$	−30.1579	−1.11850	−0.559248	−	0.829001i	$-0.688910\pi$
$727$	−30.1579	−1.11850	−0.559248	+	0.829001i	$0.688910\pi$
$728$	0.0180389	0.000668565 0
$729$	−10.6110	−0.393000
$730$	7.72877	0.286055
$731$	−7.50323	−0.277517
$732$	−2.47063	−0.0913173
$733$	6.75176	0.249382	0.124691	−	0.992196i	$-0.460206\pi$
$733$	6.75176	0.249382	0.124691	+	0.992196i	$0.460206\pi$
$734$	−10.8408	−0.400140
$735$	0.167085	0.00616304
$736$	1.99332	0.0734747
$737$	8.89100	0.327504
$738$	24.3743	0.897230
$739$	4.36909	0.160719	0.0803597	−	0.996766i	$-0.474393\pi$
$739$	4.36909	0.160719	0.0803597	+	0.996766i	$0.474393\pi$
$740$	9.73188	0.357751
$741$	0.0205515	0.000754976 0
$742$	−6.88025	−0.252582
$743$	−8.81851	−0.323520	−0.161760	−	0.986830i	$-0.551717\pi$
$743$	−8.81851	−0.323520	−0.161760	+	0.986830i	$0.551717\pi$
$744$	0.663978	0.0243426
$745$	−12.5027	−0.458062
$746$	28.6721	1.04976
$747$	18.4720	0.675857
$748$	7.50323	0.274345
$749$	−30.1420	−1.10136
$750$	−0.577714	−0.0210951
$751$	−16.8820	−0.616031	−0.308016	−	0.951381i	$-0.599665\pi$
$751$	−16.8820	−0.616031	−0.308016	+	0.951381i	$0.599665\pi$
$752$	−11.2736	−0.411104
$753$	−3.41383	−0.124407
$754$	0.0650871	0.00237033
$755$	−11.5357	−0.419829
$756$	−8.83790	−0.321431
$757$	−45.6446	−1.65898	−0.829490	−	0.558521i	$-0.811369\pi$
$757$	−45.6446	−1.65898	−0.829490	+	0.558521i	$0.811369\pi$
$758$	−24.2561	−0.881023
$759$	−1.15157	−0.0417993
$760$	−5.32428	−0.193132
$761$	−39.5567	−1.43393	−0.716964	−	0.697110i	$-0.754469\pi$
$761$	−39.5567	−1.43393	−0.716964	+	0.697110i	$0.754469\pi$
$762$	−7.38922	−0.267683
$763$	19.4201	0.703053
$764$	0.577591	0.0208965
$765$	−20.0054	−0.723298
$766$	−14.7829	−0.534126
$767$	0.0431268	0.00155722
$768$	−0.577714	−0.0208465
$769$	−17.6786	−0.637507	−0.318753	−	0.947838i	$-0.603264\pi$
$769$	−17.6786	−0.637507	−0.318753	+	0.947838i	$0.603264\pi$
$770$	2.69986	0.0972960
$771$	13.1939	0.475167
$772$	−5.27610	−0.189891
$773$	−24.8237	−0.892848	−0.446424	−	0.894822i	$-0.647303\pi$
$773$	−24.8237	−0.892848	−0.446424	+	0.894822i	$0.647303\pi$
$774$	2.66625	0.0958362
$775$	1.14932	0.0412848
$776$	−14.4906	−0.520182
$777$	−15.1793	−0.544553
$778$	−25.4940	−0.914004
$779$	−48.6735	−1.74391
$780$	0.00385995	0.000138208 0
$781$	15.7990	0.565334
$782$	−14.9563	−0.534837
$783$	−31.8885	−1.13960
$784$	0.289218	0.0103292
$785$	15.0341	0.536588
$786$	−4.53528	−0.161768
$787$	−13.5929	−0.484534	−0.242267	−	0.970210i	$-0.577891\pi$
$787$	−13.5929	−0.484534	−0.242267	+	0.970210i	$0.577891\pi$
$788$	−21.4244	−0.763212
$789$	−1.36511	−0.0485991
$790$	−4.15910	−0.147974
$791$	37.4464	1.33144
$792$	−2.66625	−0.0947409
$793$	0.0285735	0.00101468
$794$	−17.7664	−0.630505
$795$	−1.47224	−0.0522148
$796$	12.3560	0.437948
$797$	−28.6756	−1.01574	−0.507872	−	0.861433i	$-0.669568\pi$
$797$	−28.6756	−1.01574	−0.507872	+	0.861433i	$0.669568\pi$
$798$	8.30451	0.293977
$799$	84.5880	2.99251
$800$	−1.00000	−0.0353553
$801$	43.9764	1.55383
$802$	0.144875	0.00511571
$803$	−7.72877	−0.272742
$804$	5.13646	0.181149
$805$	−5.38167	−0.189679
$806$	−0.00767908	−0.000270484 0
$807$	9.35325	0.329250
$808$	−14.6386	−0.514984
$809$	−53.7637	−1.89023	−0.945116	−	0.326736i	$-0.894051\pi$
$809$	−53.7637	−1.89023	−0.945116	+	0.326736i	$0.894051\pi$
$810$	6.10761	0.214599
$811$	−7.62688	−0.267816	−0.133908	−	0.990994i	$-0.542753\pi$
$811$	−7.62688	−0.267816	−0.133908	+	0.990994i	$0.542753\pi$
$812$	26.3006	0.922972
$813$	2.50880	0.0879876
$814$	−9.73188	−0.341102
$815$	11.8173	0.413942
$816$	4.33472	0.151746
$817$	−5.32428	−0.186273
$818$	0.871128	0.0304583
$819$	0.0480961	0.00168061
$820$	−9.14180	−0.319246
$821$	−18.2915	−0.638376	−0.319188	−	0.947691i	$-0.603410\pi$
$821$	−18.2915	−0.638376	−0.319188	+	0.947691i	$0.603410\pi$
$822$	4.68514	0.163413
$823$	30.4628	1.06187	0.530933	−	0.847414i	$-0.321842\pi$
$823$	30.4628	1.06187	0.530933	+	0.847414i	$0.321842\pi$
$824$	6.34952	0.221196
$825$	0.577714	0.0201134
$826$	17.4269	0.606358
$827$	−27.5902	−0.959406	−0.479703	−	0.877431i	$-0.659256\pi$
$827$	−27.5902	−0.959406	−0.479703	+	0.877431i	$0.659256\pi$
$828$	5.31468	0.184698
$829$	−35.3817	−1.22886	−0.614428	−	0.788973i	$-0.710613\pi$
$829$	−35.3817	−1.22886	−0.614428	+	0.788973i	$0.710613\pi$
$830$	−6.92811	−0.240478
$831$	2.18229	0.0757030
$832$	0.00668142	0.000231637 0
$833$	−2.17007	−0.0751884
$834$	5.69367	0.197156
$835$	−8.98218	−0.310841
$836$	5.32428	0.184144
$837$	3.76226	0.130043
$838$	19.3475	0.668347
$839$	−23.5199	−0.811998	−0.405999	−	0.913873i	$-0.633076\pi$
$839$	−23.5199	−0.811998	−0.405999	+	0.913873i	$0.633076\pi$
$840$	1.55974	0.0538163
$841$	65.8969	2.27231
$842$	13.3644	0.460566
$843$	−0.732767	−0.0252378
$844$	22.9313	0.789329
$845$	13.0000	0.447212
$846$	−30.0581	−1.03342
$847$	−2.69986	−0.0927681
$848$	−2.54838	−0.0875117
$849$	5.87386	0.201590
$850$	7.50323	0.257359
$851$	19.3987	0.664980
$852$	9.12733	0.312697
$853$	18.9000	0.647124	0.323562	−	0.946207i	$-0.395120\pi$
$853$	18.9000	0.647124	0.323562	+	0.946207i	$0.395120\pi$
$854$	11.5461	0.395100
$855$	−14.1958	−0.485487
$856$	−11.1643	−0.381587
$857$	−40.3890	−1.37966	−0.689831	−	0.723971i	$-0.742315\pi$
$857$	−40.3890	−1.37966	−0.689831	+	0.723971i	$0.742315\pi$
$858$	−0.00385995	−0.000131777 0
$859$	−37.2036	−1.26937	−0.634685	−	0.772771i	$-0.718870\pi$
$859$	−37.2036	−1.26937	−0.634685	+	0.772771i	$0.718870\pi$
$860$	−1.00000	−0.0340997
$861$	14.2589	0.485941
$862$	18.9085	0.644025
$863$	−42.9220	−1.46108	−0.730541	−	0.682869i	$-0.760732\pi$
$863$	−42.9220	−1.46108	−0.730541	+	0.682869i	$0.760732\pi$
$864$	−3.27347	−0.111366
$865$	−0.691126	−0.0234990
$866$	28.0836	0.954319
$867$	−22.7032	−0.771043
$868$	−3.10299	−0.105322
$869$	4.15910	0.141088
$870$	5.62781	0.190800
$871$	−0.0594045	−0.00201284
$872$	7.19300	0.243586
$873$	−38.6355	−1.30761
$874$	−10.6130	−0.358989
$875$	2.69986	0.0912718
$876$	−4.46502	−0.150859
$877$	−31.0755	−1.04934	−0.524672	−	0.851304i	$-0.675812\pi$
$877$	−31.0755	−1.04934	−0.524672	+	0.851304i	$0.675812\pi$
$878$	−40.8954	−1.38015
$879$	10.6775	0.360142
$880$	1.00000	0.0337100
$881$	−21.8002	−0.734468	−0.367234	−	0.930129i	$-0.619695\pi$
$881$	−21.8002	−0.734468	−0.367234	+	0.930129i	$0.619695\pi$
$882$	0.771127	0.0259652
$883$	26.3278	0.886002	0.443001	−	0.896521i	$-0.353914\pi$
$883$	26.3278	0.886002	0.443001	+	0.896521i	$0.353914\pi$
$884$	−0.0501322	−0.00168613
$885$	3.72899	0.125349
$886$	−40.6426	−1.36541
$887$	28.0714	0.942546	0.471273	−	0.881987i	$-0.343795\pi$
$887$	28.0714	0.942546	0.471273	+	0.881987i	$0.343795\pi$
$888$	−5.62225	−0.188670
$889$	34.5323	1.15818
$890$	−16.4938	−0.552872
$891$	−6.10761	−0.204613
$892$	12.5840	0.421344
$893$	60.0235	2.00861
$894$	7.22297	0.241572
$895$	11.7502	0.392765
$896$	2.69986	0.0901958
$897$	0.00769411	0.000256899 0
$898$	−20.4364	−0.681973
$899$	−11.1961	−0.373411
$900$	−2.66625	−0.0888749
$901$	19.1211	0.637015
$902$	9.14180	0.304389
$903$	1.55974	0.0519051
$904$	13.8698	0.461302
$905$	7.73730	0.257197
$906$	6.66437	0.221409
$907$	−46.6685	−1.54960	−0.774801	−	0.632206i	$-0.782150\pi$
$907$	−46.6685	−1.54960	−0.774801	+	0.632206i	$0.782150\pi$
$908$	13.4424	0.446103
$909$	−39.0301	−1.29455
$910$	−0.0180389	−0.000597983 0
$911$	−5.96756	−0.197714	−0.0988570	−	0.995102i	$-0.531519\pi$
$911$	−5.96756	−0.197714	−0.0988570	+	0.995102i	$0.531519\pi$
$912$	3.07591	0.101854
$913$	6.92811	0.229287
$914$	−28.6296	−0.946982
$915$	2.47063	0.0816767
$916$	14.6520	0.484114
$917$	21.1949	0.699917
$918$	24.5616	0.810653
$919$	24.0451	0.793175	0.396587	−	0.917997i	$-0.370194\pi$
$919$	24.0451	0.793175	0.396587	+	0.917997i	$0.370194\pi$
$920$	−1.99332	−0.0657178
$921$	4.78300	0.157605
$922$	−7.14878	−0.235433
$923$	−0.105560	−0.00347455
$924$	−1.55974	−0.0513118
$925$	−9.73188	−0.319982
$926$	30.9169	1.01599
$927$	16.9294	0.556034
$928$	9.74150	0.319781
$929$	−58.4345	−1.91717	−0.958587	−	0.284799i	$-0.908073\pi$
$929$	−58.4345	−1.91717	−0.958587	+	0.284799i	$0.908073\pi$
$930$	−0.663978	−0.0217727
$931$	−1.53988	−0.0504674
$932$	−17.1222	−0.560858
$933$	−8.35543	−0.273544
$934$	−19.7877	−0.647474
$935$	−7.50323	−0.245382
$936$	0.0178143	0.000582279 0
$937$	−34.6629	−1.13239	−0.566195	−	0.824272i	$-0.691585\pi$
$937$	−34.6629	−1.13239	−0.566195	+	0.824272i	$0.691585\pi$
$938$	−24.0044	−0.783772
$939$	0.620182	0.0202389
$940$	11.2736	0.367703
$941$	−52.5919	−1.71445	−0.857224	−	0.514944i	$-0.827813\pi$
$941$	−52.5919	−1.71445	−0.857224	+	0.514944i	$0.827813\pi$
$942$	−8.68539	−0.282985
$943$	−18.2225	−0.593407
$944$	6.45474	0.210084
$945$	8.83790	0.287497
$946$	1.00000	0.0325128
$947$	−13.6195	−0.442575	−0.221288	−	0.975209i	$-0.571026\pi$
$947$	−13.6195	−0.442575	−0.221288	+	0.975209i	$0.571026\pi$
$948$	2.40277	0.0780385
$949$	0.0516392	0.00167628
$950$	5.32428	0.172742
$951$	10.5870	0.343309
$952$	−20.2576	−0.656553
$953$	−23.5761	−0.763704	−0.381852	−	0.924223i	$-0.624714\pi$
$953$	−23.5761	−0.763704	−0.381852	+	0.924223i	$0.624714\pi$
$954$	−6.79461	−0.219983
$955$	−0.577591	−0.0186904
$956$	−4.63878	−0.150029
$957$	−5.62781	−0.181921
$958$	17.7962	0.574970
$959$	−21.8953	−0.707035
$960$	0.577714	0.0186456
$961$	−29.6791	−0.957389
$962$	0.0650228	0.00209642
$963$	−29.7667	−0.959220
$964$	15.2434	0.490956
$965$	5.27610	0.169844
$966$	3.10907	0.100033
$967$	9.55469	0.307258	0.153629	−	0.988129i	$-0.450904\pi$
$967$	9.55469	0.307258	0.153629	+	0.988129i	$0.450904\pi$
$968$	−1.00000	−0.0321412
$969$	−23.0793	−0.741412
$970$	14.4906	0.465265
$971$	55.4199	1.77851	0.889255	−	0.457413i	$-0.151224\pi$
$971$	55.4199	1.77851	0.889255	+	0.457413i	$0.151224\pi$
$972$	−13.3489	−0.428165
$973$	−26.6085	−0.853029
$974$	−22.9534	−0.735473
$975$	−0.00385995	−0.000123617 0
$976$	4.27657	0.136890
$977$	36.1687	1.15714	0.578569	−	0.815633i	$-0.303611\pi$
$977$	36.1687	1.15714	0.578569	+	0.815633i	$0.303611\pi$
$978$	−6.82702	−0.218304
$979$	16.4938	0.527143
$980$	−0.289218	−0.00923873
$981$	19.1783	0.612316
$982$	−3.36504	−0.107383
$983$	5.87258	0.187306	0.0936531	−	0.995605i	$-0.470146\pi$
$983$	5.87258	0.187306	0.0936531	+	0.995605i	$0.470146\pi$
$984$	5.28135	0.168363
$985$	21.4244	0.682638
$986$	−73.0927	−2.32775
$987$	−17.5839	−0.559701
$988$	−0.0355737	−0.00113175
$989$	−1.99332	−0.0633838
$990$	2.66625	0.0847389
$991$	7.69550	0.244456	0.122228	−	0.992502i	$-0.460996\pi$
$991$	7.69550	0.244456	0.122228	+	0.992502i	$0.460996\pi$
$992$	−1.14932	−0.0364909
$993$	11.9173	0.378184
$994$	−42.6551	−1.35294
$995$	−12.3560	−0.391712
$996$	4.00247	0.126823
$997$	22.1929	0.702855	0.351427	−	0.936215i	$-0.385696\pi$
$997$	22.1929	0.702855	0.351427	+	0.936215i	$0.385696\pi$
$998$	−18.9121	−0.598653
$999$	−31.8570	−1.00791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.6	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.577714 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.577714 q^{6} -2.69986 q^{7} -1.00000 q^{8} -2.66625 q^{9} +1.00000 q^{10} -1.00000 q^{11} -0.577714 q^{12} +0.00668142 q^{13} +2.69986 q^{14} +0.577714 q^{15} +1.00000 q^{16} -7.50323 q^{17} +2.66625 q^{18} -5.32428 q^{19} -1.00000 q^{20} +1.55974 q^{21} +1.00000 q^{22} -1.99332 q^{23} +0.577714 q^{24} +1.00000 q^{25} -0.00668142 q^{26} +3.27347 q^{27} -2.69986 q^{28} -9.74150 q^{29} -0.577714 q^{30} +1.14932 q^{31} -1.00000 q^{32} +0.577714 q^{33} +7.50323 q^{34} +2.69986 q^{35} -2.66625 q^{36} -9.73188 q^{37} +5.32428 q^{38} -0.00385995 q^{39} +1.00000 q^{40} +9.14180 q^{41} -1.55974 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.66625 q^{45} +1.99332 q^{46} -11.2736 q^{47} -0.577714 q^{48} +0.289218 q^{49} -1.00000 q^{50} +4.33472 q^{51} +0.00668142 q^{52} -2.54838 q^{53} -3.27347 q^{54} +1.00000 q^{55} +2.69986 q^{56} +3.07591 q^{57} +9.74150 q^{58} +6.45474 q^{59} +0.577714 q^{60} +4.27657 q^{61} -1.14932 q^{62} +7.19848 q^{63} +1.00000 q^{64} -0.00668142 q^{65} -0.577714 q^{66} -8.89100 q^{67} -7.50323 q^{68} +1.15157 q^{69} -2.69986 q^{70} -15.7990 q^{71} +2.66625 q^{72} +7.72877 q^{73} +9.73188 q^{74} -0.577714 q^{75} -5.32428 q^{76} +2.69986 q^{77} +0.00385995 q^{78} -4.15910 q^{79} -1.00000 q^{80} +6.10761 q^{81} -9.14180 q^{82} -6.92811 q^{83} +1.55974 q^{84} +7.50323 q^{85} -1.00000 q^{86} +5.62781 q^{87} +1.00000 q^{88} -16.4938 q^{89} -2.66625 q^{90} -0.0180389 q^{91} -1.99332 q^{92} -0.663978 q^{93} +11.2736 q^{94} +5.32428 q^{95} +0.577714 q^{96} +14.4906 q^{97} -0.289218 q^{98} +2.66625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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