LMFDB - Embedded newform 8034.2.a.u.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
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} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.09038$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.28102 q^{5} -1.00000 q^{6} -0.150820 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.28102 q^{5} -1.00000 q^{6} -0.150820 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.28102 q^{10} +2.72872 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.150820 q^{14} +1.28102 q^{15} +1.00000 q^{16} -1.40096 q^{17} +1.00000 q^{18} +2.98505 q^{19} -1.28102 q^{20} +0.150820 q^{21} +2.72872 q^{22} -3.64393 q^{23} -1.00000 q^{24} -3.35899 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.150820 q^{28} -3.13722 q^{29} +1.28102 q^{30} -3.12492 q^{31} +1.00000 q^{32} -2.72872 q^{33} -1.40096 q^{34} +0.193203 q^{35} +1.00000 q^{36} +5.90475 q^{37} +2.98505 q^{38} +1.00000 q^{39} -1.28102 q^{40} -3.58873 q^{41} +0.150820 q^{42} +4.00604 q^{43} +2.72872 q^{44} -1.28102 q^{45} -3.64393 q^{46} -7.94456 q^{47} -1.00000 q^{48} -6.97725 q^{49} -3.35899 q^{50} +1.40096 q^{51} -1.00000 q^{52} +9.76780 q^{53} -1.00000 q^{54} -3.49553 q^{55} -0.150820 q^{56} -2.98505 q^{57} -3.13722 q^{58} +5.94199 q^{59} +1.28102 q^{60} -0.902993 q^{61} -3.12492 q^{62} -0.150820 q^{63} +1.00000 q^{64} +1.28102 q^{65} -2.72872 q^{66} -9.25696 q^{67} -1.40096 q^{68} +3.64393 q^{69} +0.193203 q^{70} -1.84367 q^{71} +1.00000 q^{72} +0.335185 q^{73} +5.90475 q^{74} +3.35899 q^{75} +2.98505 q^{76} -0.411544 q^{77} +1.00000 q^{78} -16.1001 q^{79} -1.28102 q^{80} +1.00000 q^{81} -3.58873 q^{82} +16.7825 q^{83} +0.150820 q^{84} +1.79465 q^{85} +4.00604 q^{86} +3.13722 q^{87} +2.72872 q^{88} -2.76294 q^{89} -1.28102 q^{90} +0.150820 q^{91} -3.64393 q^{92} +3.12492 q^{93} -7.94456 q^{94} -3.82389 q^{95} -1.00000 q^{96} +4.08067 q^{97} -6.97725 q^{98} +2.72872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.28102	−0.572888	−0.286444	−	0.958097i	$-0.592473\pi$
$5$	−1.28102	−0.572888	−0.286444	+	0.958097i	$0.592473\pi$
$6$	−1.00000	−0.408248
$7$	−0.150820	−0.0570045	−0.0285022	−	0.999594i	$-0.509074\pi$
$7$	−0.150820	−0.0570045	−0.0285022	+	0.999594i	$0.509074\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.28102	−0.405093
$11$	2.72872	0.822739	0.411369	−	0.911469i	$-0.365051\pi$
$11$	2.72872	0.822739	0.411369	+	0.911469i	$0.365051\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.150820	−0.0403083
$15$	1.28102	0.330757
$16$	1.00000	0.250000
$17$	−1.40096	−0.339782	−0.169891	−	0.985463i	$-0.554342\pi$
$17$	−1.40096	−0.339782	−0.169891	+	0.985463i	$0.554342\pi$
$18$	1.00000	0.235702
$19$	2.98505	0.684816	0.342408	−	0.939551i	$-0.388757\pi$
$19$	2.98505	0.684816	0.342408	+	0.939551i	$0.388757\pi$
$20$	−1.28102	−0.286444
$21$	0.150820	0.0329116
$22$	2.72872	0.581764
$23$	−3.64393	−0.759812	−0.379906	−	0.925025i	$-0.624044\pi$
$23$	−3.64393	−0.759812	−0.379906	+	0.925025i	$0.624044\pi$
$24$	−1.00000	−0.204124
$25$	−3.35899	−0.671799
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−0.150820	−0.0285022
$29$	−3.13722	−0.582567	−0.291284	−	0.956637i	$-0.594082\pi$
$29$	−3.13722	−0.582567	−0.291284	+	0.956637i	$0.594082\pi$
$30$	1.28102	0.233881
$31$	−3.12492	−0.561252	−0.280626	−	0.959817i	$-0.590542\pi$
$31$	−3.12492	−0.561252	−0.280626	+	0.959817i	$0.590542\pi$
$32$	1.00000	0.176777
$33$	−2.72872	−0.475008
$34$	−1.40096	−0.240262
$35$	0.193203	0.0326572
$36$	1.00000	0.166667
$37$	5.90475	0.970734	0.485367	−	0.874310i	$-0.338686\pi$
$37$	5.90475	0.970734	0.485367	+	0.874310i	$0.338686\pi$
$38$	2.98505	0.484238
$39$	1.00000	0.160128
$40$	−1.28102	−0.202547
$41$	−3.58873	−0.560465	−0.280233	−	0.959932i	$-0.590412\pi$
$41$	−3.58873	−0.560465	−0.280233	+	0.959932i	$0.590412\pi$
$42$	0.150820	0.0232720
$43$	4.00604	0.610915	0.305458	−	0.952206i	$-0.401191\pi$
$43$	4.00604	0.610915	0.305458	+	0.952206i	$0.401191\pi$
$44$	2.72872	0.411369
$45$	−1.28102	−0.190963
$46$	−3.64393	−0.537269
$47$	−7.94456	−1.15883	−0.579416	−	0.815032i	$-0.696719\pi$
$47$	−7.94456	−1.15883	−0.579416	+	0.815032i	$0.696719\pi$
$48$	−1.00000	−0.144338
$49$	−6.97725	−0.996750
$50$	−3.35899	−0.475034
$51$	1.40096	0.196173
$52$	−1.00000	−0.138675
$53$	9.76780	1.34171	0.670855	−	0.741588i	$-0.265927\pi$
$53$	9.76780	1.34171	0.670855	+	0.741588i	$0.265927\pi$
$54$	−1.00000	−0.136083
$55$	−3.49553	−0.471337
$56$	−0.150820	−0.0201541
$57$	−2.98505	−0.395379
$58$	−3.13722	−0.411937
$59$	5.94199	0.773581	0.386791	−	0.922168i	$-0.373584\pi$
$59$	5.94199	0.773581	0.386791	+	0.922168i	$0.373584\pi$
$60$	1.28102	0.165379
$61$	−0.902993	−0.115616	−0.0578082	−	0.998328i	$-0.518411\pi$
$61$	−0.902993	−0.115616	−0.0578082	+	0.998328i	$0.518411\pi$
$62$	−3.12492	−0.396865
$63$	−0.150820	−0.0190015
$64$	1.00000	0.125000
$65$	1.28102	0.158891
$66$	−2.72872	−0.335882
$67$	−9.25696	−1.13092	−0.565459	−	0.824777i	$-0.691301\pi$
$67$	−9.25696	−1.13092	−0.565459	+	0.824777i	$0.691301\pi$
$68$	−1.40096	−0.169891
$69$	3.64393	0.438678
$70$	0.193203	0.0230921
$71$	−1.84367	−0.218804	−0.109402	−	0.993998i	$-0.534894\pi$
$71$	−1.84367	−0.218804	−0.109402	+	0.993998i	$0.534894\pi$
$72$	1.00000	0.117851
$73$	0.335185	0.0392304	0.0196152	−	0.999808i	$-0.493756\pi$
$73$	0.335185	0.0392304	0.0196152	+	0.999808i	$0.493756\pi$
$74$	5.90475	0.686413
$75$	3.35899	0.387863
$76$	2.98505	0.342408
$77$	−0.411544	−0.0468998
$78$	1.00000	0.113228
$79$	−16.1001	−1.81141	−0.905703	−	0.423912i	$-0.860657\pi$
$79$	−16.1001	−1.81141	−0.905703	+	0.423912i	$0.860657\pi$
$80$	−1.28102	−0.143222
$81$	1.00000	0.111111
$82$	−3.58873	−0.396309
$83$	16.7825	1.84212	0.921058	−	0.389425i	$-0.127326\pi$
$83$	16.7825	1.84212	0.921058	+	0.389425i	$0.127326\pi$
$84$	0.150820	0.0164558
$85$	1.79465	0.194657
$86$	4.00604	0.431982
$87$	3.13722	0.336345
$88$	2.72872	0.290882
$89$	−2.76294	−0.292871	−0.146435	−	0.989220i	$-0.546780\pi$
$89$	−2.76294	−0.292871	−0.146435	+	0.989220i	$0.546780\pi$
$90$	−1.28102	−0.135031
$91$	0.150820	0.0158102
$92$	−3.64393	−0.379906
$93$	3.12492	0.324039
$94$	−7.94456	−0.819418
$95$	−3.82389	−0.392323
$96$	−1.00000	−0.102062
$97$	4.08067	0.414329	0.207165	−	0.978306i	$-0.433576\pi$
$97$	4.08067	0.414329	0.207165	+	0.978306i	$0.433576\pi$
$98$	−6.97725	−0.704809
$99$	2.72872	0.274246
$100$	−3.35899	−0.335899
$101$	7.14976	0.711427	0.355714	−	0.934595i	$-0.384238\pi$
$101$	7.14976	0.711427	0.355714	+	0.934595i	$0.384238\pi$
$102$	1.40096	0.138715
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.193203	−0.0188547
$106$	9.76780	0.948733
$107$	−15.2584	−1.47508	−0.737541	−	0.675302i	$-0.764013\pi$
$107$	−15.2584	−1.47508	−0.737541	+	0.675302i	$0.764013\pi$
$108$	−1.00000	−0.0962250
$109$	−5.77092	−0.552754	−0.276377	−	0.961049i	$-0.589134\pi$
$109$	−5.77092	−0.552754	−0.276377	+	0.961049i	$0.589134\pi$
$110$	−3.49553	−0.333286
$111$	−5.90475	−0.560454
$112$	−0.150820	−0.0142511
$113$	5.63454	0.530053	0.265026	−	0.964241i	$-0.414619\pi$
$113$	5.63454	0.530053	0.265026	+	0.964241i	$0.414619\pi$
$114$	−2.98505	−0.279575
$115$	4.66794	0.435288
$116$	−3.13722	−0.291284
$117$	−1.00000	−0.0924500
$118$	5.94199	0.547005
$119$	0.211292	0.0193691
$120$	1.28102	0.116940
$121$	−3.55411	−0.323101
$122$	−0.902993	−0.0817532
$123$	3.58873	0.323585
$124$	−3.12492	−0.280626
$125$	10.7080	0.957754
$126$	−0.150820	−0.0134361
$127$	−4.97386	−0.441359	−0.220679	−	0.975346i	$-0.570827\pi$
$127$	−4.97386	−0.441359	−0.220679	+	0.975346i	$0.570827\pi$
$128$	1.00000	0.0883883
$129$	−4.00604	−0.352712
$130$	1.28102	0.112353
$131$	5.00665	0.437433	0.218716	−	0.975788i	$-0.429813\pi$
$131$	5.00665	0.437433	0.218716	+	0.975788i	$0.429813\pi$
$132$	−2.72872	−0.237504
$133$	−0.450204	−0.0390376
$134$	−9.25696	−0.799680
$135$	1.28102	0.110252
$136$	−1.40096	−0.120131
$137$	−11.7194	−1.00125	−0.500626	−	0.865663i	$-0.666897\pi$
$137$	−11.7194	−1.00125	−0.500626	+	0.865663i	$0.666897\pi$
$138$	3.64393	0.310192
$139$	−4.04784	−0.343333	−0.171667	−	0.985155i	$-0.554915\pi$
$139$	−4.04784	−0.343333	−0.171667	+	0.985155i	$0.554915\pi$
$140$	0.193203	0.0163286
$141$	7.94456	0.669052
$142$	−1.84367	−0.154718
$143$	−2.72872	−0.228187
$144$	1.00000	0.0833333
$145$	4.01884	0.333746
$146$	0.335185	0.0277401
$147$	6.97725	0.575474
$148$	5.90475	0.485367
$149$	1.10782	0.0907563	0.0453782	−	0.998970i	$-0.485551\pi$
$149$	1.10782	0.0907563	0.0453782	+	0.998970i	$0.485551\pi$
$150$	3.35899	0.274261
$151$	−6.47223	−0.526702	−0.263351	−	0.964700i	$-0.584828\pi$
$151$	−6.47223	−0.526702	−0.263351	+	0.964700i	$0.584828\pi$
$152$	2.98505	0.242119
$153$	−1.40096	−0.113261
$154$	−0.411544	−0.0331632
$155$	4.00308	0.321535
$156$	1.00000	0.0800641
$157$	7.37548	0.588627	0.294314	−	0.955709i	$-0.404909\pi$
$157$	7.37548	0.588627	0.294314	+	0.955709i	$0.404909\pi$
$158$	−16.1001	−1.28086
$159$	−9.76780	−0.774637
$160$	−1.28102	−0.101273
$161$	0.549577	0.0433127
$162$	1.00000	0.0785674
$163$	−3.64977	−0.285872	−0.142936	−	0.989732i	$-0.545654\pi$
$163$	−3.64977	−0.285872	−0.142936	+	0.989732i	$0.545654\pi$
$164$	−3.58873	−0.280233
$165$	3.49553	0.272127
$166$	16.7825	1.30257
$167$	−19.7775	−1.53043	−0.765213	−	0.643777i	$-0.777367\pi$
$167$	−19.7775	−1.53043	−0.765213	+	0.643777i	$0.777367\pi$
$168$	0.150820	0.0116360
$169$	1.00000	0.0769231
$170$	1.79465	0.137643
$171$	2.98505	0.228272
$172$	4.00604	0.305458
$173$	−11.5387	−0.877275	−0.438637	−	0.898664i	$-0.644539\pi$
$173$	−11.5387	−0.877275	−0.438637	+	0.898664i	$0.644539\pi$
$174$	3.13722	0.237832
$175$	0.506603	0.0382956
$176$	2.72872	0.205685
$177$	−5.94199	−0.446627
$178$	−2.76294	−0.207091
$179$	−12.9507	−0.967981	−0.483990	−	0.875073i	$-0.660813\pi$
$179$	−12.9507	−0.967981	−0.483990	+	0.875073i	$0.660813\pi$
$180$	−1.28102	−0.0954814
$181$	−7.09745	−0.527549	−0.263775	−	0.964584i	$-0.584968\pi$
$181$	−7.09745	−0.527549	−0.263775	+	0.964584i	$0.584968\pi$
$182$	0.150820	0.0111795
$183$	0.902993	0.0667512
$184$	−3.64393	−0.268634
$185$	−7.56408	−0.556122
$186$	3.12492	0.229130
$187$	−3.82281	−0.279552
$188$	−7.94456	−0.579416
$189$	0.150820	0.0109705
$190$	−3.82389	−0.277414
$191$	−0.843938	−0.0610652	−0.0305326	−	0.999534i	$-0.509720\pi$
$191$	−0.843938	−0.0610652	−0.0305326	+	0.999534i	$0.509720\pi$
$192$	−1.00000	−0.0721688
$193$	−20.0782	−1.44526	−0.722632	−	0.691233i	$-0.757068\pi$
$193$	−20.0782	−1.44526	−0.722632	+	0.691233i	$0.757068\pi$
$194$	4.08067	0.292975
$195$	−1.28102	−0.0917356
$196$	−6.97725	−0.498375
$197$	20.5882	1.46685	0.733423	−	0.679773i	$-0.237922\pi$
$197$	20.5882	1.46685	0.733423	+	0.679773i	$0.237922\pi$
$198$	2.72872	0.193921
$199$	22.5837	1.60091	0.800456	−	0.599391i	$-0.204591\pi$
$199$	22.5837	1.60091	0.800456	+	0.599391i	$0.204591\pi$
$200$	−3.35899	−0.237517
$201$	9.25696	0.652936
$202$	7.14976	0.503055
$203$	0.473155	0.0332090
$204$	1.40096	0.0980866
$205$	4.59722	0.321084
$206$	1.00000	0.0696733
$207$	−3.64393	−0.253271
$208$	−1.00000	−0.0693375
$209$	8.14534	0.563425
$210$	−0.193203	−0.0133323
$211$	−9.96548	−0.686052	−0.343026	−	0.939326i	$-0.611452\pi$
$211$	−9.96548	−0.686052	−0.343026	+	0.939326i	$0.611452\pi$
$212$	9.76780	0.670855
$213$	1.84367	0.126326
$214$	−15.2584	−1.04304
$215$	−5.13181	−0.349986
$216$	−1.00000	−0.0680414
$217$	0.471300	0.0319939
$218$	−5.77092	−0.390856
$219$	−0.335185	−0.0226497
$220$	−3.49553	−0.235669
$221$	1.40096	0.0942386
$222$	−5.90475	−0.396301
$223$	20.8470	1.39602	0.698008	−	0.716090i	$-0.254070\pi$
$223$	20.8470	1.39602	0.698008	+	0.716090i	$0.254070\pi$
$224$	−0.150820	−0.0100771
$225$	−3.35899	−0.223933
$226$	5.63454	0.374804
$227$	−24.5998	−1.63275	−0.816373	−	0.577524i	$-0.804019\pi$
$227$	−24.5998	−1.63275	−0.816373	+	0.577524i	$0.804019\pi$
$228$	−2.98505	−0.197689
$229$	9.47451	0.626093	0.313047	−	0.949738i	$-0.398650\pi$
$229$	9.47451	0.626093	0.313047	+	0.949738i	$0.398650\pi$
$230$	4.66794	0.307795
$231$	0.411544	0.0270776
$232$	−3.13722	−0.205969
$233$	−14.9556	−0.979772	−0.489886	−	0.871786i	$-0.662962\pi$
$233$	−14.9556	−0.979772	−0.489886	+	0.871786i	$0.662962\pi$
$234$	−1.00000	−0.0653720
$235$	10.1771	0.663882
$236$	5.94199	0.386791
$237$	16.1001	1.04582
$238$	0.211292	0.0136960
$239$	7.36802	0.476597	0.238299	−	0.971192i	$-0.423410\pi$
$239$	7.36802	0.476597	0.238299	+	0.971192i	$0.423410\pi$
$240$	1.28102	0.0826893
$241$	−17.2309	−1.10994	−0.554970	−	0.831870i	$-0.687270\pi$
$241$	−17.2309	−1.10994	−0.554970	+	0.831870i	$0.687270\pi$
$242$	−3.55411	−0.228467
$243$	−1.00000	−0.0641500
$244$	−0.902993	−0.0578082
$245$	8.93798	0.571027
$246$	3.58873	0.228809
$247$	−2.98505	−0.189934
$248$	−3.12492	−0.198433
$249$	−16.7825	−1.06355
$250$	10.7080	0.677234
$251$	−0.541779	−0.0341968	−0.0170984	−	0.999854i	$-0.505443\pi$
$251$	−0.541779	−0.0341968	−0.0170984	+	0.999854i	$0.505443\pi$
$252$	−0.150820	−0.00950075
$253$	−9.94326	−0.625127
$254$	−4.97386	−0.312088
$255$	−1.79465	−0.112385
$256$	1.00000	0.0625000
$257$	−22.0984	−1.37846	−0.689231	−	0.724541i	$-0.742052\pi$
$257$	−22.0984	−1.37846	−0.689231	+	0.724541i	$0.742052\pi$
$258$	−4.00604	−0.249405
$259$	−0.890552	−0.0553362
$260$	1.28102	0.0794453
$261$	−3.13722	−0.194189
$262$	5.00665	0.309312
$263$	0.240830	0.0148502	0.00742509	−	0.999972i	$-0.497636\pi$
$263$	0.240830	0.0148502	0.00742509	+	0.999972i	$0.497636\pi$
$264$	−2.72872	−0.167941
$265$	−12.5127	−0.768650
$266$	−0.450204	−0.0276038
$267$	2.76294	0.169089
$268$	−9.25696	−0.565459
$269$	4.72949	0.288362	0.144181	−	0.989551i	$-0.453945\pi$
$269$	4.72949	0.288362	0.144181	+	0.989551i	$0.453945\pi$
$270$	1.28102	0.0779602
$271$	−15.0761	−0.915810	−0.457905	−	0.889001i	$-0.651400\pi$
$271$	−15.0761	−0.915810	−0.457905	+	0.889001i	$0.651400\pi$
$272$	−1.40096	−0.0849455
$273$	−0.150820	−0.00912803
$274$	−11.7194	−0.707993
$275$	−9.16574	−0.552715
$276$	3.64393	0.219339
$277$	−8.53217	−0.512649	−0.256324	−	0.966591i	$-0.582512\pi$
$277$	−8.53217	−0.512649	−0.256324	+	0.966591i	$0.582512\pi$
$278$	−4.04784	−0.242773
$279$	−3.12492	−0.187084
$280$	0.193203	0.0115461
$281$	−2.27292	−0.135591	−0.0677956	−	0.997699i	$-0.521597\pi$
$281$	−2.27292	−0.135591	−0.0677956	+	0.997699i	$0.521597\pi$
$282$	7.94456	0.473091
$283$	−28.5472	−1.69696	−0.848479	−	0.529230i	$-0.822481\pi$
$283$	−28.5472	−1.69696	−0.848479	+	0.529230i	$0.822481\pi$
$284$	−1.84367	−0.109402
$285$	3.82389	0.226508
$286$	−2.72872	−0.161352
$287$	0.541251	0.0319490
$288$	1.00000	0.0589256
$289$	−15.0373	−0.884548
$290$	4.01884	0.235994
$291$	−4.08067	−0.239213
$292$	0.335185	0.0196152
$293$	−27.4011	−1.60079	−0.800395	−	0.599472i	$-0.795377\pi$
$293$	−27.4011	−1.60079	−0.800395	+	0.599472i	$0.795377\pi$
$294$	6.97725	0.406922
$295$	−7.61179	−0.443176
$296$	5.90475	0.343206
$297$	−2.72872	−0.158336
$298$	1.10782	0.0641744
$299$	3.64393	0.210734
$300$	3.35899	0.193932
$301$	−0.604190	−0.0348249
$302$	−6.47223	−0.372435
$303$	−7.14976	−0.410743
$304$	2.98505	0.171204
$305$	1.15675	0.0662353
$306$	−1.40096	−0.0800874
$307$	8.19739	0.467850	0.233925	−	0.972255i	$-0.424843\pi$
$307$	8.19739	0.467850	0.233925	+	0.972255i	$0.424843\pi$
$308$	−0.411544	−0.0234499
$309$	−1.00000	−0.0568880
$310$	4.00308	0.227359
$311$	−10.8072	−0.612822	−0.306411	−	0.951899i	$-0.599128\pi$
$311$	−10.8072	−0.612822	−0.306411	+	0.951899i	$0.599128\pi$
$312$	1.00000	0.0566139
$313$	11.6277	0.657237	0.328618	−	0.944463i	$-0.393417\pi$
$313$	11.6277	0.657237	0.328618	+	0.944463i	$0.393417\pi$
$314$	7.37548	0.416222
$315$	0.193203	0.0108857
$316$	−16.1001	−0.905703
$317$	2.17428	0.122120	0.0610599	−	0.998134i	$-0.480552\pi$
$317$	2.17428	0.122120	0.0610599	+	0.998134i	$0.480552\pi$
$318$	−9.76780	−0.547751
$319$	−8.56059	−0.479301
$320$	−1.28102	−0.0716110
$321$	15.2584	0.851639
$322$	0.549577	0.0306267
$323$	−4.18192	−0.232688
$324$	1.00000	0.0555556
$325$	3.35899	0.186324
$326$	−3.64977	−0.202142
$327$	5.77092	0.319133
$328$	−3.58873	−0.198154
$329$	1.19820	0.0660587
$330$	3.49553	0.192423
$331$	−6.00037	−0.329810	−0.164905	−	0.986309i	$-0.552732\pi$
$331$	−6.00037	−0.329810	−0.164905	+	0.986309i	$0.552732\pi$
$332$	16.7825	0.921058
$333$	5.90475	0.323578
$334$	−19.7775	−1.08218
$335$	11.8583	0.647890
$336$	0.150820	0.00822789
$337$	−29.5946	−1.61212	−0.806060	−	0.591834i	$-0.798404\pi$
$337$	−29.5946	−1.61212	−0.806060	+	0.591834i	$0.798404\pi$
$338$	1.00000	0.0543928
$339$	−5.63454	−0.306026
$340$	1.79465	0.0973286
$341$	−8.52702	−0.461764
$342$	2.98505	0.161413
$343$	2.10805	0.113824
$344$	4.00604	0.215991
$345$	−4.66794	−0.251313
$346$	−11.5387	−0.620327
$347$	−6.78091	−0.364019	−0.182009	−	0.983297i	$-0.558260\pi$
$347$	−6.78091	−0.364019	−0.182009	+	0.983297i	$0.558260\pi$
$348$	3.13722	0.168173
$349$	26.4372	1.41515	0.707575	−	0.706639i	$-0.249789\pi$
$349$	26.4372	1.41515	0.707575	+	0.706639i	$0.249789\pi$
$350$	0.506603	0.0270791
$351$	1.00000	0.0533761
$352$	2.72872	0.145441
$353$	4.03589	0.214809	0.107404	−	0.994215i	$-0.465746\pi$
$353$	4.03589	0.214809	0.107404	+	0.994215i	$0.465746\pi$
$354$	−5.94199	−0.315813
$355$	2.36178	0.125350
$356$	−2.76294	−0.146435
$357$	−0.211292	−0.0111828
$358$	−12.9507	−0.684466
$359$	−18.6816	−0.985979	−0.492989	−	0.870035i	$-0.664096\pi$
$359$	−18.6816	−0.985979	−0.492989	+	0.870035i	$0.664096\pi$
$360$	−1.28102	−0.0675155
$361$	−10.0895	−0.531027
$362$	−7.09745	−0.373034
$363$	3.55411	0.186542
$364$	0.150820	0.00790510
$365$	−0.429378	−0.0224747
$366$	0.902993	0.0472002
$367$	23.2865	1.21555	0.607773	−	0.794111i	$-0.292063\pi$
$367$	23.2865	1.21555	0.607773	+	0.794111i	$0.292063\pi$
$368$	−3.64393	−0.189953
$369$	−3.58873	−0.186822
$370$	−7.56408	−0.393238
$371$	−1.47318	−0.0764835
$372$	3.12492	0.162020
$373$	−37.0894	−1.92042	−0.960208	−	0.279287i	$-0.909902\pi$
$373$	−37.0894	−1.92042	−0.960208	+	0.279287i	$0.909902\pi$
$374$	−3.82281	−0.197673
$375$	−10.7080	−0.552960
$376$	−7.94456	−0.409709
$377$	3.13722	0.161575
$378$	0.150820	0.00775733
$379$	−29.1903	−1.49941	−0.749703	−	0.661775i	$-0.769804\pi$
$379$	−29.1903	−1.49941	−0.749703	+	0.661775i	$0.769804\pi$
$380$	−3.82389	−0.196162
$381$	4.97386	0.254819
$382$	−0.843938	−0.0431796
$383$	30.5102	1.55900	0.779500	−	0.626402i	$-0.215473\pi$
$383$	30.5102	1.55900	0.779500	+	0.626402i	$0.215473\pi$
$384$	−1.00000	−0.0510310
$385$	0.527195	0.0268684
$386$	−20.0782	−1.02196
$387$	4.00604	0.203638
$388$	4.08067	0.207165
$389$	−17.0921	−0.866606	−0.433303	−	0.901248i	$-0.642652\pi$
$389$	−17.0921	−0.866606	−0.433303	+	0.901248i	$0.642652\pi$
$390$	−1.28102	−0.0648668
$391$	5.10499	0.258171
$392$	−6.97725	−0.352405
$393$	−5.00665	−0.252552
$394$	20.5882	1.03722
$395$	20.6246	1.03773
$396$	2.72872	0.137123
$397$	8.60237	0.431741	0.215870	−	0.976422i	$-0.430741\pi$
$397$	8.60237	0.431741	0.215870	+	0.976422i	$0.430741\pi$
$398$	22.5837	1.13202
$399$	0.450204	0.0225384
$400$	−3.35899	−0.167950
$401$	21.5282	1.07507	0.537534	−	0.843242i	$-0.319356\pi$
$401$	21.5282	1.07507	0.537534	+	0.843242i	$0.319356\pi$
$402$	9.25696	0.461695
$403$	3.12492	0.155663
$404$	7.14976	0.355714
$405$	−1.28102	−0.0636543
$406$	0.473155	0.0234823
$407$	16.1124	0.798661
$408$	1.40096	0.0693577
$409$	25.9873	1.28499	0.642495	−	0.766290i	$-0.277899\pi$
$409$	25.9873	1.28499	0.642495	+	0.766290i	$0.277899\pi$
$410$	4.59722	0.227041
$411$	11.7194	0.578074
$412$	1.00000	0.0492665
$413$	−0.896169	−0.0440976
$414$	−3.64393	−0.179090
$415$	−21.4986	−1.05533
$416$	−1.00000	−0.0490290
$417$	4.04784	0.198223
$418$	8.14534	0.398402
$419$	−12.4578	−0.608602	−0.304301	−	0.952576i	$-0.598423\pi$
$419$	−12.4578	−0.608602	−0.304301	+	0.952576i	$0.598423\pi$
$420$	−0.193203	−0.00942733
$421$	−23.3438	−1.13771	−0.568855	−	0.822438i	$-0.692613\pi$
$421$	−23.3438	−1.13771	−0.568855	+	0.822438i	$0.692613\pi$
$422$	−9.96548	−0.485112
$423$	−7.94456	−0.386278
$424$	9.76780	0.474366
$425$	4.70581	0.228265
$426$	1.84367	0.0893263
$427$	0.136189	0.00659066
$428$	−15.2584	−0.737541
$429$	2.72872	0.131744
$430$	−5.13181	−0.247478
$431$	−31.3495	−1.51005	−0.755025	−	0.655696i	$-0.772375\pi$
$431$	−31.3495	−1.51005	−0.755025	+	0.655696i	$0.772375\pi$
$432$	−1.00000	−0.0481125
$433$	−9.19544	−0.441905	−0.220952	−	0.975285i	$-0.570917\pi$
$433$	−9.19544	−0.441905	−0.220952	+	0.975285i	$0.570917\pi$
$434$	0.471300	0.0226231
$435$	−4.01884	−0.192688
$436$	−5.77092	−0.276377
$437$	−10.8773	−0.520332
$438$	−0.335185	−0.0160158
$439$	−2.52539	−0.120530	−0.0602652	−	0.998182i	$-0.519195\pi$
$439$	−2.52539	−0.120530	−0.0602652	+	0.998182i	$0.519195\pi$
$440$	−3.49553	−0.166643
$441$	−6.97725	−0.332250
$442$	1.40096	0.0666367
$443$	31.9317	1.51712	0.758561	−	0.651602i	$-0.225903\pi$
$443$	31.9317	1.51712	0.758561	+	0.651602i	$0.225903\pi$
$444$	−5.90475	−0.280227
$445$	3.53937	0.167782
$446$	20.8470	0.987133
$447$	−1.10782	−0.0523982
$448$	−0.150820	−0.00712556
$449$	−0.800397	−0.0377730	−0.0188865	−	0.999822i	$-0.506012\pi$
$449$	−0.800397	−0.0377730	−0.0188865	+	0.999822i	$0.506012\pi$
$450$	−3.35899	−0.158345
$451$	−9.79262	−0.461116
$452$	5.63454	0.265026
$453$	6.47223	0.304092
$454$	−24.5998	−1.15453
$455$	−0.193203	−0.00905748
$456$	−2.98505	−0.139788
$457$	33.6699	1.57501	0.787506	−	0.616306i	$-0.211372\pi$
$457$	33.6699	1.57501	0.787506	+	0.616306i	$0.211372\pi$
$458$	9.47451	0.442715
$459$	1.40096	0.0653911
$460$	4.66794	0.217644
$461$	−30.8838	−1.43840	−0.719201	−	0.694802i	$-0.755492\pi$
$461$	−30.8838	−1.43840	−0.719201	+	0.694802i	$0.755492\pi$
$462$	0.411544	0.0191468
$463$	−37.6764	−1.75097	−0.875485	−	0.483245i	$-0.839458\pi$
$463$	−37.6764	−1.75097	−0.875485	+	0.483245i	$0.839458\pi$
$464$	−3.13722	−0.145642
$465$	−4.00308	−0.185638
$466$	−14.9556	−0.692804
$467$	16.0139	0.741033	0.370517	−	0.928826i	$-0.379181\pi$
$467$	16.0139	0.741033	0.370517	+	0.928826i	$0.379181\pi$
$468$	−1.00000	−0.0462250
$469$	1.39613	0.0644674
$470$	10.1771	0.469435
$471$	−7.37548	−0.339844
$472$	5.94199	0.273502
$473$	10.9313	0.502624
$474$	16.1001	0.739504
$475$	−10.0268	−0.460059
$476$	0.211292	0.00968455
$477$	9.76780	0.447237
$478$	7.36802	0.337005
$479$	42.3149	1.93342	0.966708	−	0.255883i	$-0.0823663\pi$
$479$	42.3149	1.93342	0.966708	+	0.255883i	$0.0823663\pi$
$480$	1.28102	0.0584702
$481$	−5.90475	−0.269233
$482$	−17.2309	−0.784846
$483$	−0.549577	−0.0250066
$484$	−3.55411	−0.161550
$485$	−5.22741	−0.237364
$486$	−1.00000	−0.0453609
$487$	19.0950	0.865277	0.432638	−	0.901568i	$-0.357583\pi$
$487$	19.0950	0.865277	0.432638	+	0.901568i	$0.357583\pi$
$488$	−0.902993	−0.0408766
$489$	3.64977	0.165048
$490$	8.93798	0.403777
$491$	15.1094	0.681879	0.340939	−	0.940085i	$-0.389255\pi$
$491$	15.1094	0.681879	0.340939	+	0.940085i	$0.389255\pi$
$492$	3.58873	0.161792
$493$	4.39511	0.197946
$494$	−2.98505	−0.134304
$495$	−3.49553	−0.157112
$496$	−3.12492	−0.140313
$497$	0.278062	0.0124728
$498$	−16.7825	−0.752041
$499$	40.9281	1.83219	0.916096	−	0.400958i	$-0.131323\pi$
$499$	40.9281	1.83219	0.916096	+	0.400958i	$0.131323\pi$
$500$	10.7080	0.478877
$501$	19.7775	0.883592
$502$	−0.541779	−0.0241808
$503$	0.585088	0.0260878	0.0130439	−	0.999915i	$-0.495848\pi$
$503$	0.585088	0.0260878	0.0130439	+	0.999915i	$0.495848\pi$
$504$	−0.150820	−0.00671804
$505$	−9.15896	−0.407568
$506$	−9.94326	−0.442032
$507$	−1.00000	−0.0444116
$508$	−4.97386	−0.220679
$509$	25.0019	1.10819	0.554095	−	0.832453i	$-0.313064\pi$
$509$	25.0019	1.10819	0.554095	+	0.832453i	$0.313064\pi$
$510$	−1.79465	−0.0794685
$511$	−0.0505525	−0.00223631
$512$	1.00000	0.0441942
$513$	−2.98505	−0.131793
$514$	−22.0984	−0.974720
$515$	−1.28102	−0.0564484
$516$	−4.00604	−0.176356
$517$	−21.6784	−0.953416
$518$	−0.890552	−0.0391286
$519$	11.5387	0.506495
$520$	1.28102	0.0561763
$521$	−35.7955	−1.56823	−0.784114	−	0.620617i	$-0.786882\pi$
$521$	−35.7955	−1.56823	−0.784114	+	0.620617i	$0.786882\pi$
$522$	−3.13722	−0.137312
$523$	−0.377713	−0.0165163	−0.00825813	−	0.999966i	$-0.502629\pi$
$523$	−0.377713	−0.0165163	−0.00825813	+	0.999966i	$0.502629\pi$
$524$	5.00665	0.218716
$525$	−0.506603	−0.0221100
$526$	0.240830	0.0105007
$527$	4.37788	0.190703
$528$	−2.72872	−0.118752
$529$	−9.72176	−0.422685
$530$	−12.5127	−0.543518
$531$	5.94199	0.257860
$532$	−0.450204	−0.0195188
$533$	3.58873	0.155445
$534$	2.76294	0.119564
$535$	19.5462	0.845058
$536$	−9.25696	−0.399840
$537$	12.9507	0.558864
$538$	4.72949	0.203903
$539$	−19.0389	−0.820065
$540$	1.28102	0.0551262
$541$	−29.5904	−1.27219	−0.636094	−	0.771611i	$-0.719451\pi$
$541$	−29.5904	−1.27219	−0.636094	+	0.771611i	$0.719451\pi$
$542$	−15.0761	−0.647575
$543$	7.09745	0.304581
$544$	−1.40096	−0.0600655
$545$	7.39265	0.316666
$546$	−0.150820	−0.00645449
$547$	−14.1742	−0.606043	−0.303021	−	0.952984i	$-0.597995\pi$
$547$	−14.1742	−0.606043	−0.303021	+	0.952984i	$0.597995\pi$
$548$	−11.7194	−0.500626
$549$	−0.902993	−0.0385388
$550$	−9.16574	−0.390829
$551$	−9.36475	−0.398952
$552$	3.64393	0.155096
$553$	2.42822	0.103258
$554$	−8.53217	−0.362497
$555$	7.56408	0.321077
$556$	−4.04784	−0.171667
$557$	39.8874	1.69008	0.845042	−	0.534699i	$-0.179575\pi$
$557$	39.8874	1.69008	0.845042	+	0.534699i	$0.179575\pi$
$558$	−3.12492	−0.132288
$559$	−4.00604	−0.169437
$560$	0.193203	0.00816430
$561$	3.82281	0.161399
$562$	−2.27292	−0.0958775
$563$	−11.0471	−0.465581	−0.232791	−	0.972527i	$-0.574786\pi$
$563$	−11.0471	−0.465581	−0.232791	+	0.972527i	$0.574786\pi$
$564$	7.94456	0.334526
$565$	−7.21794	−0.303661
$566$	−28.5472	−1.19993
$567$	−0.150820	−0.00633383
$568$	−1.84367	−0.0773588
$569$	−45.8253	−1.92110	−0.960549	−	0.278110i	$-0.910292\pi$
$569$	−45.8253	−1.92110	−0.960549	+	0.278110i	$0.910292\pi$
$570$	3.82389	0.160165
$571$	22.5709	0.944561	0.472281	−	0.881448i	$-0.343431\pi$
$571$	22.5709	0.944561	0.472281	+	0.881448i	$0.343431\pi$
$572$	−2.72872	−0.114093
$573$	0.843938	0.0352560
$574$	0.541251	0.0225914
$575$	12.2400	0.510441
$576$	1.00000	0.0416667
$577$	9.86893	0.410849	0.205425	−	0.978673i	$-0.434142\pi$
$577$	9.86893	0.410849	0.205425	+	0.978673i	$0.434142\pi$
$578$	−15.0373	−0.625470
$579$	20.0782	0.834423
$580$	4.01884	0.166873
$581$	−2.53113	−0.105009
$582$	−4.08067	−0.169149
$583$	26.6536	1.10388
$584$	0.335185	0.0138701
$585$	1.28102	0.0529635
$586$	−27.4011	−1.13193
$587$	44.6576	1.84322	0.921608	−	0.388123i	$-0.126876\pi$
$587$	44.6576	1.84322	0.921608	+	0.388123i	$0.126876\pi$
$588$	6.97725	0.287737
$589$	−9.32803	−0.384355
$590$	−7.61179	−0.313373
$591$	−20.5882	−0.846884
$592$	5.90475	0.242684
$593$	13.0883	0.537474	0.268737	−	0.963214i	$-0.413394\pi$
$593$	13.0883	0.537474	0.268737	+	0.963214i	$0.413394\pi$
$594$	−2.72872	−0.111961
$595$	−0.270669	−0.0110963
$596$	1.10782	0.0453782
$597$	−22.5837	−0.924287
$598$	3.64393	0.149011
$599$	19.9139	0.813660	0.406830	−	0.913504i	$-0.366634\pi$
$599$	19.9139	0.813660	0.406830	+	0.913504i	$0.366634\pi$
$600$	3.35899	0.137130
$601$	13.3652	0.545177	0.272589	−	0.962131i	$-0.412120\pi$
$601$	13.3652	0.545177	0.272589	+	0.962131i	$0.412120\pi$
$602$	−0.604190	−0.0246249
$603$	−9.25696	−0.376973
$604$	−6.47223	−0.263351
$605$	4.55288	0.185101
$606$	−7.14976	−0.290439
$607$	−28.3327	−1.14999	−0.574995	−	0.818157i	$-0.694996\pi$
$607$	−28.3327	−1.14999	−0.574995	+	0.818157i	$0.694996\pi$
$608$	2.98505	0.121060
$609$	−0.473155	−0.0191732
$610$	1.15675	0.0468354
$611$	7.94456	0.321402
$612$	−1.40096	−0.0566303
$613$	−14.6877	−0.593230	−0.296615	−	0.954997i	$-0.595858\pi$
$613$	−14.6877	−0.593230	−0.296615	+	0.954997i	$0.595858\pi$
$614$	8.19739	0.330820
$615$	−4.59722	−0.185378
$616$	−0.411544	−0.0165816
$617$	39.2554	1.58036	0.790182	−	0.612873i	$-0.209986\pi$
$617$	39.2554	1.58036	0.790182	+	0.612873i	$0.209986\pi$
$618$	−1.00000	−0.0402259
$619$	−3.30713	−0.132925	−0.0664625	−	0.997789i	$-0.521171\pi$
$619$	−3.30713	−0.132925	−0.0664625	+	0.997789i	$0.521171\pi$
$620$	4.00308	0.160767
$621$	3.64393	0.146226
$622$	−10.8072	−0.433331
$623$	0.416706	0.0166950
$624$	1.00000	0.0400320
$625$	3.07782	0.123113
$626$	11.6277	0.464736
$627$	−8.14534	−0.325294
$628$	7.37548	0.294314
$629$	−8.27229	−0.329838
$630$	0.193203	0.00769738
$631$	5.25893	0.209355	0.104677	−	0.994506i	$-0.466619\pi$
$631$	5.25893	0.209355	0.104677	+	0.994506i	$0.466619\pi$
$632$	−16.1001	−0.640429
$633$	9.96548	0.396092
$634$	2.17428	0.0863518
$635$	6.37160	0.252849
$636$	−9.76780	−0.387318
$637$	6.97725	0.276449
$638$	−8.56059	−0.338917
$639$	−1.84367	−0.0729346
$640$	−1.28102	−0.0506367
$641$	10.3035	0.406963	0.203481	−	0.979079i	$-0.434774\pi$
$641$	10.3035	0.406963	0.203481	+	0.979079i	$0.434774\pi$
$642$	15.2584	0.602200
$643$	−43.6334	−1.72073	−0.860367	−	0.509675i	$-0.829766\pi$
$643$	−43.6334	−1.72073	−0.860367	+	0.509675i	$0.829766\pi$
$644$	0.549577	0.0216564
$645$	5.13181	0.202065
$646$	−4.18192	−0.164535
$647$	−20.2545	−0.796285	−0.398143	−	0.917323i	$-0.630345\pi$
$647$	−20.2545	−0.796285	−0.398143	+	0.917323i	$0.630345\pi$
$648$	1.00000	0.0392837
$649$	16.2140	0.636455
$650$	3.35899	0.131751
$651$	−0.471300	−0.0184717
$652$	−3.64977	−0.142936
$653$	−8.08179	−0.316265	−0.158132	−	0.987418i	$-0.550547\pi$
$653$	−8.08179	−0.316265	−0.158132	+	0.987418i	$0.550547\pi$
$654$	5.77092	0.225661
$655$	−6.41360	−0.250600
$656$	−3.58873	−0.140116
$657$	0.335185	0.0130768
$658$	1.19820	0.0467105
$659$	−7.51841	−0.292876	−0.146438	−	0.989220i	$-0.546781\pi$
$659$	−7.51841	−0.292876	−0.146438	+	0.989220i	$0.546781\pi$
$660$	3.49553	0.136063
$661$	−30.0203	−1.16765	−0.583826	−	0.811879i	$-0.698445\pi$
$661$	−30.0203	−1.16765	−0.583826	+	0.811879i	$0.698445\pi$
$662$	−6.00037	−0.233211
$663$	−1.40096	−0.0544087
$664$	16.7825	0.651286
$665$	0.576719	0.0223642
$666$	5.90475	0.228804
$667$	11.4318	0.442642
$668$	−19.7775	−0.765213
$669$	−20.8470	−0.805990
$670$	11.8583	0.458127
$671$	−2.46401	−0.0951221
$672$	0.150820	0.00581800
$673$	−42.8641	−1.65229	−0.826145	−	0.563457i	$-0.809471\pi$
$673$	−42.8641	−1.65229	−0.826145	+	0.563457i	$0.809471\pi$
$674$	−29.5946	−1.13994
$675$	3.35899	0.129288
$676$	1.00000	0.0384615
$677$	0.963303	0.0370227	0.0185114	−	0.999829i	$-0.494107\pi$
$677$	0.963303	0.0370227	0.0185114	+	0.999829i	$0.494107\pi$
$678$	−5.63454	−0.216393
$679$	−0.615445	−0.0236186
$680$	1.79465	0.0688217
$681$	24.5998	0.942667
$682$	−8.52702	−0.326516
$683$	15.6086	0.597247	0.298624	−	0.954371i	$-0.403472\pi$
$683$	15.6086	0.597247	0.298624	+	0.954371i	$0.403472\pi$
$684$	2.98505	0.114136
$685$	15.0127	0.573606
$686$	2.10805	0.0804856
$687$	−9.47451	−0.361475
$688$	4.00604	0.152729
$689$	−9.76780	−0.372124
$690$	−4.66794	−0.177705
$691$	−22.4466	−0.853911	−0.426955	−	0.904273i	$-0.640414\pi$
$691$	−22.4466	−0.853911	−0.426955	+	0.904273i	$0.640414\pi$
$692$	−11.5387	−0.438637
$693$	−0.411544	−0.0156333
$694$	−6.78091	−0.257400
$695$	5.18535	0.196692
$696$	3.13722	0.118916
$697$	5.02765	0.190436
$698$	26.4372	1.00066
$699$	14.9556	0.565672
$700$	0.506603	0.0191478
$701$	25.8603	0.976729	0.488365	−	0.872640i	$-0.337594\pi$
$701$	25.8603	0.976729	0.488365	+	0.872640i	$0.337594\pi$
$702$	1.00000	0.0377426
$703$	17.6259	0.664775
$704$	2.72872	0.102842
$705$	−10.1771	−0.383292
$706$	4.03589	0.151893
$707$	−1.07832	−0.0405546
$708$	−5.94199	−0.223314
$709$	−45.2787	−1.70048	−0.850238	−	0.526398i	$-0.823542\pi$
$709$	−45.2787	−1.70048	−0.850238	+	0.526398i	$0.823542\pi$
$710$	2.36178	0.0886359
$711$	−16.1001	−0.603802
$712$	−2.76294	−0.103545
$713$	11.3870	0.426446
$714$	−0.211292	−0.00790740
$715$	3.49553	0.130725
$716$	−12.9507	−0.483990
$717$	−7.36802	−0.275164
$718$	−18.6816	−0.697192
$719$	40.0792	1.49470	0.747351	−	0.664430i	$-0.231325\pi$
$719$	40.0792	1.49470	0.747351	+	0.664430i	$0.231325\pi$
$720$	−1.28102	−0.0477407
$721$	−0.150820	−0.00561682
$722$	−10.0895	−0.375492
$723$	17.2309	0.640824
$724$	−7.09745	−0.263775
$725$	10.5379	0.391368
$726$	3.55411	0.131905
$727$	15.8930	0.589439	0.294719	−	0.955584i	$-0.404774\pi$
$727$	15.8930	0.589439	0.294719	+	0.955584i	$0.404774\pi$
$728$	0.150820	0.00558975
$729$	1.00000	0.0370370
$730$	−0.429378	−0.0158920
$731$	−5.61229	−0.207578
$732$	0.902993	0.0333756
$733$	−27.2646	−1.00704	−0.503520	−	0.863983i	$-0.667962\pi$
$733$	−27.2646	−1.00704	−0.503520	+	0.863983i	$0.667962\pi$
$734$	23.2865	0.859521
$735$	−8.93798	−0.329682
$736$	−3.64393	−0.134317
$737$	−25.2596	−0.930450
$738$	−3.58873	−0.132103
$739$	−1.30291	−0.0479282	−0.0239641	−	0.999713i	$-0.507629\pi$
$739$	−1.30291	−0.0479282	−0.0239641	+	0.999713i	$0.507629\pi$
$740$	−7.56408	−0.278061
$741$	2.98505	0.109658
$742$	−1.47318	−0.0540820
$743$	50.0208	1.83508	0.917542	−	0.397638i	$-0.130170\pi$
$743$	50.0208	1.83508	0.917542	+	0.397638i	$0.130170\pi$
$744$	3.12492	0.114565
$745$	−1.41914	−0.0519932
$746$	−37.0894	−1.35794
$747$	16.7825	0.614039
$748$	−3.82281	−0.139776
$749$	2.30126	0.0840863
$750$	−10.7080	−0.391001
$751$	8.50695	0.310423	0.155212	−	0.987881i	$-0.450394\pi$
$751$	8.50695	0.310423	0.155212	+	0.987881i	$0.450394\pi$
$752$	−7.94456	−0.289708
$753$	0.541779	0.0197435
$754$	3.13722	0.114251
$755$	8.29104	0.301742
$756$	0.150820	0.00548526
$757$	2.59046	0.0941520	0.0470760	−	0.998891i	$-0.485010\pi$
$757$	2.59046	0.0941520	0.0470760	+	0.998891i	$0.485010\pi$
$758$	−29.1903	−1.06024
$759$	9.94326	0.360917
$760$	−3.82389	−0.138707
$761$	18.6275	0.675248	0.337624	−	0.941281i	$-0.390377\pi$
$761$	18.6275	0.675248	0.337624	+	0.941281i	$0.390377\pi$
$762$	4.97386	0.180184
$763$	0.870369	0.0315095
$764$	−0.843938	−0.0305326
$765$	1.79465	0.0648857
$766$	30.5102	1.10238
$767$	−5.94199	−0.214553
$768$	−1.00000	−0.0360844
$769$	−43.8157	−1.58003	−0.790017	−	0.613085i	$-0.789928\pi$
$769$	−43.8157	−1.58003	−0.790017	+	0.613085i	$0.789928\pi$
$770$	0.527195	0.0189988
$771$	22.0984	0.795856
$772$	−20.0782	−0.722632
$773$	37.8594	1.36171	0.680854	−	0.732419i	$-0.261609\pi$
$773$	37.8594	1.36171	0.680854	+	0.732419i	$0.261609\pi$
$774$	4.00604	0.143994
$775$	10.4966	0.377049
$776$	4.08067	0.146487
$777$	0.890552	0.0319484
$778$	−17.0921	−0.612783
$779$	−10.7125	−0.383816
$780$	−1.28102	−0.0458678
$781$	−5.03086	−0.180018
$782$	5.10499	0.182554
$783$	3.13722	0.112115
$784$	−6.97725	−0.249188
$785$	−9.44811	−0.337218
$786$	−5.00665	−0.178581
$787$	−25.1829	−0.897675	−0.448837	−	0.893613i	$-0.648162\pi$
$787$	−25.1829	−0.897675	−0.448837	+	0.893613i	$0.648162\pi$
$788$	20.5882	0.733423
$789$	−0.240830	−0.00857376
$790$	20.6246	0.733789
$791$	−0.849799	−0.0302154
$792$	2.72872	0.0969607
$793$	0.902993	0.0320662
$794$	8.60237	0.305287
$795$	12.5127	0.443780
$796$	22.5837	0.800456
$797$	48.0587	1.70233	0.851164	−	0.524900i	$-0.175897\pi$
$797$	48.0587	1.70233	0.851164	+	0.524900i	$0.175897\pi$
$798$	0.450204	0.0159370
$799$	11.1300	0.393750
$800$	−3.35899	−0.118758
$801$	−2.76294	−0.0976236
$802$	21.5282	0.760187
$803$	0.914624	0.0322764
$804$	9.25696	0.326468
$805$	−0.704018	−0.0248134
$806$	3.12492	0.110071
$807$	−4.72949	−0.166486
$808$	7.14976	0.251528
$809$	8.29979	0.291805	0.145903	−	0.989299i	$-0.453391\pi$
$809$	8.29979	0.291805	0.145903	+	0.989299i	$0.453391\pi$
$810$	−1.28102	−0.0450104
$811$	−2.18178	−0.0766126	−0.0383063	−	0.999266i	$-0.512196\pi$
$811$	−2.18178	−0.0766126	−0.0383063	+	0.999266i	$0.512196\pi$
$812$	0.473155	0.0166045
$813$	15.0761	0.528743
$814$	16.1124	0.564738
$815$	4.67542	0.163773
$816$	1.40096	0.0490433
$817$	11.9582	0.418365
$818$	25.9873	0.908626
$819$	0.150820	0.00527007
$820$	4.59722	0.160542
$821$	12.8939	0.450001	0.225000	−	0.974359i	$-0.427762\pi$
$821$	12.8939	0.450001	0.225000	+	0.974359i	$0.427762\pi$
$822$	11.7194	0.408760
$823$	26.5924	0.926954	0.463477	−	0.886109i	$-0.346602\pi$
$823$	26.5924	0.926954	0.463477	+	0.886109i	$0.346602\pi$
$824$	1.00000	0.0348367
$825$	9.16574	0.319110
$826$	−0.896169	−0.0311817
$827$	1.16399	0.0404760	0.0202380	−	0.999795i	$-0.493558\pi$
$827$	1.16399	0.0404760	0.0202380	+	0.999795i	$0.493558\pi$
$828$	−3.64393	−0.126635
$829$	33.3658	1.15884	0.579421	−	0.815028i	$-0.303279\pi$
$829$	33.3658	1.15884	0.579421	+	0.815028i	$0.303279\pi$
$830$	−21.4986	−0.746229
$831$	8.53217	0.295978
$832$	−1.00000	−0.0346688
$833$	9.77483	0.338678
$834$	4.04784	0.140165
$835$	25.3353	0.876764
$836$	8.14534	0.281712
$837$	3.12492	0.108013
$838$	−12.4578	−0.430347
$839$	23.2408	0.802360	0.401180	−	0.915999i	$-0.368600\pi$
$839$	23.2408	0.802360	0.401180	+	0.915999i	$0.368600\pi$
$840$	−0.193203	−0.00666613
$841$	−19.1578	−0.660615
$842$	−23.3438	−0.804482
$843$	2.27292	0.0782836
$844$	−9.96548	−0.343026
$845$	−1.28102	−0.0440683
$846$	−7.94456	−0.273139
$847$	0.536030	0.0184182
$848$	9.76780	0.335428
$849$	28.5472	0.979739
$850$	4.70581	0.161408
$851$	−21.5165	−0.737576
$852$	1.84367	0.0631632
$853$	45.3688	1.55340	0.776700	−	0.629871i	$-0.216892\pi$
$853$	45.3688	1.55340	0.776700	+	0.629871i	$0.216892\pi$
$854$	0.136189	0.00466030
$855$	−3.82389	−0.130774
$856$	−15.2584	−0.521520
$857$	19.5853	0.669021	0.334510	−	0.942392i	$-0.391429\pi$
$857$	19.5853	0.669021	0.334510	+	0.942392i	$0.391429\pi$
$858$	2.72872	0.0931568
$859$	1.16712	0.0398217	0.0199108	−	0.999802i	$-0.493662\pi$
$859$	1.16712	0.0398217	0.0199108	+	0.999802i	$0.493662\pi$
$860$	−5.13181	−0.174993
$861$	−0.541251	−0.0184458
$862$	−31.3495	−1.06777
$863$	15.1698	0.516384	0.258192	−	0.966094i	$-0.416873\pi$
$863$	15.1698	0.516384	0.258192	+	0.966094i	$0.416873\pi$
$864$	−1.00000	−0.0340207
$865$	14.7813	0.502580
$866$	−9.19544	−0.312474
$867$	15.0373	0.510694
$868$	0.471300	0.0159970
$869$	−43.9327	−1.49031
$870$	−4.01884	−0.136251
$871$	9.25696	0.313660
$872$	−5.77092	−0.195428
$873$	4.08067	0.138110
$874$	−10.8773	−0.367930
$875$	−1.61498	−0.0545963
$876$	−0.335185	−0.0113248
$877$	16.2391	0.548356	0.274178	−	0.961679i	$-0.411594\pi$
$877$	16.2391	0.548356	0.274178	+	0.961679i	$0.411594\pi$
$878$	−2.52539	−0.0852278
$879$	27.4011	0.924217
$880$	−3.49553	−0.117834
$881$	−7.29834	−0.245887	−0.122944	−	0.992414i	$-0.539233\pi$
$881$	−7.29834	−0.245887	−0.122944	+	0.992414i	$0.539233\pi$
$882$	−6.97725	−0.234936
$883$	11.7787	0.396385	0.198192	−	0.980163i	$-0.436493\pi$
$883$	11.7787	0.396385	0.198192	+	0.980163i	$0.436493\pi$
$884$	1.40096	0.0471193
$885$	7.61179	0.255868
$886$	31.9317	1.07277
$887$	−25.8323	−0.867364	−0.433682	−	0.901066i	$-0.642786\pi$
$887$	−25.8323	−0.867364	−0.433682	+	0.901066i	$0.642786\pi$
$888$	−5.90475	−0.198150
$889$	0.750156	0.0251594
$890$	3.53937	0.118640
$891$	2.72872	0.0914154
$892$	20.8470	0.698008
$893$	−23.7149	−0.793588
$894$	−1.10782	−0.0370511
$895$	16.5901	0.554545
$896$	−0.150820	−0.00503853
$897$	−3.64393	−0.121667
$898$	−0.800397	−0.0267096
$899$	9.80357	0.326967
$900$	−3.35899	−0.111966
$901$	−13.6843	−0.455889
$902$	−9.79262	−0.326059
$903$	0.604190	0.0201062
$904$	5.63454	0.187402
$905$	9.09196	0.302227
$906$	6.47223	0.215025
$907$	−4.96342	−0.164808	−0.0824039	−	0.996599i	$-0.526260\pi$
$907$	−4.96342	−0.164808	−0.0824039	+	0.996599i	$0.526260\pi$
$908$	−24.5998	−0.816373
$909$	7.14976	0.237142
$910$	−0.193203	−0.00640461
$911$	−35.7281	−1.18372	−0.591862	−	0.806040i	$-0.701607\pi$
$911$	−35.7281	−1.18372	−0.591862	+	0.806040i	$0.701607\pi$
$912$	−2.98505	−0.0988447
$913$	45.7946	1.51558
$914$	33.6699	1.11370
$915$	−1.15675	−0.0382410
$916$	9.47451	0.313047
$917$	−0.755101	−0.0249356
$918$	1.40096	0.0462385
$919$	42.1350	1.38991	0.694953	−	0.719055i	$-0.255425\pi$
$919$	42.1350	1.38991	0.694953	+	0.719055i	$0.255425\pi$
$920$	4.66794	0.153897
$921$	−8.19739	−0.270113
$922$	−30.8838	−1.01710
$923$	1.84367	0.0606853
$924$	0.411544	0.0135388
$925$	−19.8340	−0.652138
$926$	−37.6764	−1.23812
$927$	1.00000	0.0328443
$928$	−3.13722	−0.102984
$929$	16.7166	0.548455	0.274227	−	0.961665i	$-0.411578\pi$
$929$	16.7166	0.548455	0.274227	+	0.961665i	$0.411578\pi$
$930$	−4.00308	−0.131266
$931$	−20.8274	−0.682591
$932$	−14.9556	−0.489886
$933$	10.8072	0.353813
$934$	16.0139	0.523990
$935$	4.89709	0.160152
$936$	−1.00000	−0.0326860
$937$	−9.39603	−0.306955	−0.153477	−	0.988152i	$-0.549047\pi$
$937$	−9.39603	−0.306955	−0.153477	+	0.988152i	$0.549047\pi$
$938$	1.39613	0.0455853
$939$	−11.6277	−0.379456
$940$	10.1771	0.331941
$941$	−25.9136	−0.844760	−0.422380	−	0.906419i	$-0.638805\pi$
$941$	−25.9136	−0.844760	−0.422380	+	0.906419i	$0.638805\pi$
$942$	−7.37548	−0.240306
$943$	13.0771	0.425848
$944$	5.94199	0.193395
$945$	−0.193203	−0.00628488
$946$	10.9313	0.355409
$947$	−18.7307	−0.608665	−0.304333	−	0.952566i	$-0.598433\pi$
$947$	−18.7307	−0.608665	−0.304333	+	0.952566i	$0.598433\pi$
$948$	16.1001	0.522908
$949$	−0.335185	−0.0108806
$950$	−10.0268	−0.325311
$951$	−2.17428	−0.0705059
$952$	0.211292	0.00684801
$953$	13.5448	0.438760	0.219380	−	0.975639i	$-0.429597\pi$
$953$	13.5448	0.438760	0.219380	+	0.975639i	$0.429597\pi$
$954$	9.76780	0.316244
$955$	1.08110	0.0349835
$956$	7.36802	0.238299
$957$	8.56059	0.276724
$958$	42.3149	1.36713
$959$	1.76751	0.0570759
$960$	1.28102	0.0413447
$961$	−21.2349	−0.684996
$962$	−5.90475	−0.190377
$963$	−15.2584	−0.491694
$964$	−17.2309	−0.554970
$965$	25.7206	0.827975
$966$	−0.549577	−0.0176823
$967$	33.9145	1.09062	0.545309	−	0.838235i	$-0.316412\pi$
$967$	33.9145	1.09062	0.545309	+	0.838235i	$0.316412\pi$
$968$	−3.55411	−0.114233
$969$	4.18192	0.134343
$970$	−5.22741	−0.167842
$971$	−4.58464	−0.147128	−0.0735641	−	0.997290i	$-0.523437\pi$
$971$	−4.58464	−0.147128	−0.0735641	+	0.997290i	$0.523437\pi$
$972$	−1.00000	−0.0320750
$973$	0.610494	0.0195715
$974$	19.0950	0.611843
$975$	−3.35899	−0.107574
$976$	−0.902993	−0.0289041
$977$	−17.3668	−0.555613	−0.277807	−	0.960637i	$-0.589607\pi$
$977$	−17.3668	−0.555613	−0.277807	+	0.960637i	$0.589607\pi$
$978$	3.64977	0.116707
$979$	−7.53927	−0.240956
$980$	8.93798	0.285513
$981$	−5.77092	−0.184251
$982$	15.1094	0.482161
$983$	57.3276	1.82847	0.914233	−	0.405190i	$-0.132794\pi$
$983$	57.3276	1.82847	0.914233	+	0.405190i	$0.132794\pi$
$984$	3.58873	0.114404
$985$	−26.3738	−0.840339
$986$	4.39511	0.139969
$987$	−1.19820	−0.0381390
$988$	−2.98505	−0.0949669
$989$	−14.5977	−0.464181
$990$	−3.49553	−0.111095
$991$	44.0372	1.39889	0.699444	−	0.714687i	$-0.253431\pi$
$991$	44.0372	1.39889	0.699444	+	0.714687i	$0.253431\pi$
$992$	−3.12492	−0.0992163
$993$	6.00037	0.190416
$994$	0.278062	0.00881960
$995$	−28.9300	−0.917144
$996$	−16.7825	−0.531773
$997$	36.7645	1.16434	0.582172	−	0.813066i	$-0.302203\pi$
$997$	36.7645	1.16434	0.582172	+	0.813066i	$0.302203\pi$
$998$	40.9281	1.29556
$999$	−5.90475	−0.186818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.4	✓	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.28102 q^{5} -1.00000 q^{6} -0.150820 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.28102 q^{5} -1.00000 q^{6} -0.150820 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.28102 q^{10} +2.72872 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.150820 q^{14} +1.28102 q^{15} +1.00000 q^{16} -1.40096 q^{17} +1.00000 q^{18} +2.98505 q^{19} -1.28102 q^{20} +0.150820 q^{21} +2.72872 q^{22} -3.64393 q^{23} -1.00000 q^{24} -3.35899 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.150820 q^{28} -3.13722 q^{29} +1.28102 q^{30} -3.12492 q^{31} +1.00000 q^{32} -2.72872 q^{33} -1.40096 q^{34} +0.193203 q^{35} +1.00000 q^{36} +5.90475 q^{37} +2.98505 q^{38} +1.00000 q^{39} -1.28102 q^{40} -3.58873 q^{41} +0.150820 q^{42} +4.00604 q^{43} +2.72872 q^{44} -1.28102 q^{45} -3.64393 q^{46} -7.94456 q^{47} -1.00000 q^{48} -6.97725 q^{49} -3.35899 q^{50} +1.40096 q^{51} -1.00000 q^{52} +9.76780 q^{53} -1.00000 q^{54} -3.49553 q^{55} -0.150820 q^{56} -2.98505 q^{57} -3.13722 q^{58} +5.94199 q^{59} +1.28102 q^{60} -0.902993 q^{61} -3.12492 q^{62} -0.150820 q^{63} +1.00000 q^{64} +1.28102 q^{65} -2.72872 q^{66} -9.25696 q^{67} -1.40096 q^{68} +3.64393 q^{69} +0.193203 q^{70} -1.84367 q^{71} +1.00000 q^{72} +0.335185 q^{73} +5.90475 q^{74} +3.35899 q^{75} +2.98505 q^{76} -0.411544 q^{77} +1.00000 q^{78} -16.1001 q^{79} -1.28102 q^{80} +1.00000 q^{81} -3.58873 q^{82} +16.7825 q^{83} +0.150820 q^{84} +1.79465 q^{85} +4.00604 q^{86} +3.13722 q^{87} +2.72872 q^{88} -2.76294 q^{89} -1.28102 q^{90} +0.150820 q^{91} -3.64393 q^{92} +3.12492 q^{93} -7.94456 q^{94} -3.82389 q^{95} -1.00000 q^{96} +4.08067 q^{97} -6.97725 q^{98} +2.72872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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