LMFDB - Embedded newform 1502.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
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} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.88979$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.195838 q^{3} +1.00000 q^{4} -1.22685 q^{5} -0.195838 q^{6} +4.43512 q^{7} -1.00000 q^{8} -2.96165 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.195838 q^{3} +1.00000 q^{4} -1.22685 q^{5} -0.195838 q^{6} +4.43512 q^{7} -1.00000 q^{8} -2.96165 q^{9} +1.22685 q^{10} +2.56757 q^{11} +0.195838 q^{12} -6.10492 q^{13} -4.43512 q^{14} -0.240264 q^{15} +1.00000 q^{16} +2.44520 q^{17} +2.96165 q^{18} -7.58010 q^{19} -1.22685 q^{20} +0.868566 q^{21} -2.56757 q^{22} -5.74567 q^{23} -0.195838 q^{24} -3.49484 q^{25} +6.10492 q^{26} -1.16752 q^{27} +4.43512 q^{28} +8.59131 q^{29} +0.240264 q^{30} -3.25883 q^{31} -1.00000 q^{32} +0.502828 q^{33} -2.44520 q^{34} -5.44123 q^{35} -2.96165 q^{36} -1.07062 q^{37} +7.58010 q^{38} -1.19558 q^{39} +1.22685 q^{40} -6.77075 q^{41} -0.868566 q^{42} +5.01953 q^{43} +2.56757 q^{44} +3.63349 q^{45} +5.74567 q^{46} -7.81131 q^{47} +0.195838 q^{48} +12.6703 q^{49} +3.49484 q^{50} +0.478863 q^{51} -6.10492 q^{52} +8.11472 q^{53} +1.16752 q^{54} -3.15002 q^{55} -4.43512 q^{56} -1.48447 q^{57} -8.59131 q^{58} +2.41074 q^{59} -0.240264 q^{60} -12.4628 q^{61} +3.25883 q^{62} -13.1353 q^{63} +1.00000 q^{64} +7.48981 q^{65} -0.502828 q^{66} +0.828938 q^{67} +2.44520 q^{68} -1.12522 q^{69} +5.44123 q^{70} -5.18583 q^{71} +2.96165 q^{72} +1.45491 q^{73} +1.07062 q^{74} -0.684423 q^{75} -7.58010 q^{76} +11.3875 q^{77} +1.19558 q^{78} +6.32544 q^{79} -1.22685 q^{80} +8.65630 q^{81} +6.77075 q^{82} -13.6114 q^{83} +0.868566 q^{84} -2.99989 q^{85} -5.01953 q^{86} +1.68250 q^{87} -2.56757 q^{88} -8.91664 q^{89} -3.63349 q^{90} -27.0761 q^{91} -5.74567 q^{92} -0.638203 q^{93} +7.81131 q^{94} +9.29964 q^{95} -0.195838 q^{96} -16.0736 q^{97} -12.6703 q^{98} -7.60424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * 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
$3$	0.195838	0.113067	0.0565336	−	0.998401i	$-0.481995\pi$
$3$	0.195838	0.113067	0.0565336	+	0.998401i	$0.481995\pi$
$4$	1.00000	0.500000
$5$	−1.22685	−0.548664	−0.274332	−	0.961635i	$-0.588457\pi$
$5$	−1.22685	−0.548664	−0.274332	+	0.961635i	$0.588457\pi$
$6$	−0.195838	−0.0799506
$7$	4.43512	1.67632	0.838159	−	0.545426i	$-0.183632\pi$
$7$	4.43512	1.67632	0.838159	+	0.545426i	$0.183632\pi$
$8$	−1.00000	−0.353553
$9$	−2.96165	−0.987216
$10$	1.22685	0.387964
$11$	2.56757	0.774152	0.387076	−	0.922048i	$-0.373485\pi$
$11$	2.56757	0.774152	0.387076	+	0.922048i	$0.373485\pi$
$12$	0.195838	0.0565336
$13$	−6.10492	−1.69320	−0.846600	−	0.532230i	$-0.821354\pi$
$13$	−6.10492	−1.69320	−0.846600	+	0.532230i	$0.821354\pi$
$14$	−4.43512	−1.18534
$15$	−0.240264	−0.0620358
$16$	1.00000	0.250000
$17$	2.44520	0.593048	0.296524	−	0.955025i	$-0.404173\pi$
$17$	2.44520	0.593048	0.296524	+	0.955025i	$0.404173\pi$
$18$	2.96165	0.698067
$19$	−7.58010	−1.73899	−0.869497	−	0.493938i	$-0.835557\pi$
$19$	−7.58010	−1.73899	−0.869497	+	0.493938i	$0.835557\pi$
$20$	−1.22685	−0.274332
$21$	0.868566	0.189537
$22$	−2.56757	−0.547408
$23$	−5.74567	−1.19806	−0.599028	−	0.800728i	$-0.704446\pi$
$23$	−5.74567	−1.19806	−0.599028	+	0.800728i	$0.704446\pi$
$24$	−0.195838	−0.0399753
$25$	−3.49484	−0.698968
$26$	6.10492	1.19727
$27$	−1.16752	−0.224689
$28$	4.43512	0.838159
$29$	8.59131	1.59537	0.797683	−	0.603077i	$-0.206059\pi$
$29$	8.59131	1.59537	0.797683	+	0.603077i	$0.206059\pi$
$30$	0.240264	0.0438660
$31$	−3.25883	−0.585303	−0.292652	−	0.956219i	$-0.594538\pi$
$31$	−3.25883	−0.585303	−0.292652	+	0.956219i	$0.594538\pi$
$32$	−1.00000	−0.176777
$33$	0.502828	0.0875312
$34$	−2.44520	−0.419348
$35$	−5.44123	−0.919735
$36$	−2.96165	−0.493608
$37$	−1.07062	−0.176009	−0.0880045	−	0.996120i	$-0.528049\pi$
$37$	−1.07062	−0.176009	−0.0880045	+	0.996120i	$0.528049\pi$
$38$	7.58010	1.22965
$39$	−1.19558	−0.191445
$40$	1.22685	0.193982
$41$	−6.77075	−1.05741	−0.528707	−	0.848804i	$-0.677323\pi$
$41$	−6.77075	−1.05741	−0.528707	+	0.848804i	$0.677323\pi$
$42$	−0.868566	−0.134023
$43$	5.01953	0.765471	0.382736	−	0.923858i	$-0.374982\pi$
$43$	5.01953	0.765471	0.382736	+	0.923858i	$0.374982\pi$
$44$	2.56757	0.387076
$45$	3.63349	0.541649
$46$	5.74567	0.847154
$47$	−7.81131	−1.13940	−0.569698	−	0.821854i	$-0.692940\pi$
$47$	−7.81131	−1.13940	−0.569698	+	0.821854i	$0.692940\pi$
$48$	0.195838	0.0282668
$49$	12.6703	1.81004
$50$	3.49484	0.494245
$51$	0.478863	0.0670543
$52$	−6.10492	−0.846600
$53$	8.11472	1.11464	0.557321	−	0.830297i	$-0.311829\pi$
$53$	8.11472	1.11464	0.557321	+	0.830297i	$0.311829\pi$
$54$	1.16752	0.158879
$55$	−3.15002	−0.424749
$56$	−4.43512	−0.592668
$57$	−1.48447	−0.196623
$58$	−8.59131	−1.12809
$59$	2.41074	0.313852	0.156926	−	0.987610i	$-0.449842\pi$
$59$	2.41074	0.313852	0.156926	+	0.987610i	$0.449842\pi$
$60$	−0.240264	−0.0310179
$61$	−12.4628	−1.59570	−0.797848	−	0.602858i	$-0.794029\pi$
$61$	−12.4628	−1.59570	−0.797848	+	0.602858i	$0.794029\pi$
$62$	3.25883	0.413872
$63$	−13.1353	−1.65489
$64$	1.00000	0.125000
$65$	7.48981	0.928997
$66$	−0.502828	−0.0618939
$67$	0.828938	0.101271	0.0506354	−	0.998717i	$-0.483875\pi$
$67$	0.828938	0.101271	0.0506354	+	0.998717i	$0.483875\pi$
$68$	2.44520	0.296524
$69$	−1.12522	−0.135461
$70$	5.44123	0.650351
$71$	−5.18583	−0.615445	−0.307722	−	0.951476i	$-0.599567\pi$
$71$	−5.18583	−0.615445	−0.307722	+	0.951476i	$0.599567\pi$
$72$	2.96165	0.349033
$73$	1.45491	0.170285	0.0851424	−	0.996369i	$-0.472865\pi$
$73$	1.45491	0.170285	0.0851424	+	0.996369i	$0.472865\pi$
$74$	1.07062	0.124457
$75$	−0.684423	−0.0790304
$76$	−7.58010	−0.869497
$77$	11.3875	1.29772
$78$	1.19558	0.135372
$79$	6.32544	0.711667	0.355834	−	0.934549i	$-0.384197\pi$
$79$	6.32544	0.711667	0.355834	+	0.934549i	$0.384197\pi$
$80$	−1.22685	−0.137166
$81$	8.65630	0.961811
$82$	6.77075	0.747705
$83$	−13.6114	−1.49404	−0.747021	−	0.664801i	$-0.768516\pi$
$83$	−13.6114	−1.49404	−0.747021	+	0.664801i	$0.768516\pi$
$84$	0.868566	0.0947683
$85$	−2.99989	−0.325384
$86$	−5.01953	−0.541270
$87$	1.68250	0.180383
$88$	−2.56757	−0.273704
$89$	−8.91664	−0.945162	−0.472581	−	0.881287i	$-0.656678\pi$
$89$	−8.91664	−0.945162	−0.472581	+	0.881287i	$0.656678\pi$
$90$	−3.63349	−0.383004
$91$	−27.0761	−2.83834
$92$	−5.74567	−0.599028
$93$	−0.638203	−0.0661786
$94$	7.81131	0.805675
$95$	9.29964	0.954123
$96$	−0.195838	−0.0199876
$97$	−16.0736	−1.63203	−0.816015	−	0.578031i	$-0.803821\pi$
$97$	−16.0736	−1.63203	−0.816015	+	0.578031i	$0.803821\pi$
$98$	−12.6703	−1.27989
$99$	−7.60424	−0.764255
$100$	−3.49484	−0.349484
$101$	7.98546	0.794583	0.397291	−	0.917693i	$-0.369950\pi$
$101$	7.98546	0.794583	0.397291	+	0.917693i	$0.369950\pi$
$102$	−0.478863	−0.0474145
$103$	−6.46557	−0.637072	−0.318536	−	0.947911i	$-0.603191\pi$
$103$	−6.46557	−0.637072	−0.318536	+	0.947911i	$0.603191\pi$
$104$	6.10492	0.598636
$105$	−1.06560	−0.103992
$106$	−8.11472	−0.788171
$107$	5.44264	0.526160	0.263080	−	0.964774i	$-0.415262\pi$
$107$	5.44264	0.526160	0.263080	+	0.964774i	$0.415262\pi$
$108$	−1.16752	−0.112344
$109$	−17.1945	−1.64693	−0.823466	−	0.567366i	$-0.807963\pi$
$109$	−17.1945	−1.64693	−0.823466	+	0.567366i	$0.807963\pi$
$110$	3.15002	0.300343
$111$	−0.209668	−0.0199008
$112$	4.43512	0.419080
$113$	16.0403	1.50895	0.754474	−	0.656330i	$-0.227892\pi$
$113$	16.0403	1.50895	0.754474	+	0.656330i	$0.227892\pi$
$114$	1.48447	0.139034
$115$	7.04908	0.657330
$116$	8.59131	0.797683
$117$	18.0806	1.67155
$118$	−2.41074	−0.221927
$119$	10.8448	0.994137
$120$	0.240264	0.0219330
$121$	−4.40758	−0.400689
$122$	12.4628	1.12833
$123$	−1.32597	−0.119559
$124$	−3.25883	−0.292652
$125$	10.4219	0.932162
$126$	13.1353	1.17018
$127$	−10.8566	−0.963365	−0.481683	−	0.876346i	$-0.659974\pi$
$127$	−10.8566	−0.963365	−0.481683	+	0.876346i	$0.659974\pi$
$128$	−1.00000	−0.0883883
$129$	0.983015	0.0865497
$130$	−7.48981	−0.656900
$131$	−17.0840	−1.49263	−0.746317	−	0.665591i	$-0.768180\pi$
$131$	−17.0840	−1.49263	−0.746317	+	0.665591i	$0.768180\pi$
$132$	0.502828	0.0437656
$133$	−33.6187	−2.91511
$134$	−0.828938	−0.0716093
$135$	1.43237	0.123279
$136$	−2.44520	−0.209674
$137$	2.08901	0.178476	0.0892380	−	0.996010i	$-0.471557\pi$
$137$	2.08901	0.178476	0.0892380	+	0.996010i	$0.471557\pi$
$138$	1.12522	0.0957852
$139$	3.75645	0.318618	0.159309	−	0.987229i	$-0.449073\pi$
$139$	3.75645	0.318618	0.159309	+	0.987229i	$0.449073\pi$
$140$	−5.44123	−0.459867
$141$	−1.52975	−0.128828
$142$	5.18583	0.435185
$143$	−15.6748	−1.31079
$144$	−2.96165	−0.246804
$145$	−10.5402	−0.875319
$146$	−1.45491	−0.120410
$147$	2.48133	0.204656
$148$	−1.07062	−0.0880045
$149$	18.8194	1.54175	0.770873	−	0.636989i	$-0.219820\pi$
$149$	18.8194	1.54175	0.770873	+	0.636989i	$0.219820\pi$
$150$	0.684423	0.0558829
$151$	−2.86564	−0.233202	−0.116601	−	0.993179i	$-0.537200\pi$
$151$	−2.86564	−0.233202	−0.116601	+	0.993179i	$0.537200\pi$
$152$	7.58010	0.614827
$153$	−7.24182	−0.585466
$154$	−11.3875	−0.917630
$155$	3.99809	0.321135
$156$	−1.19558	−0.0957226
$157$	4.59227	0.366503	0.183251	−	0.983066i	$-0.441338\pi$
$157$	4.59227	0.366503	0.183251	+	0.983066i	$0.441338\pi$
$158$	−6.32544	−0.503225
$159$	1.58917	0.126030
$160$	1.22685	0.0969909
$161$	−25.4828	−2.00832
$162$	−8.65630	−0.680103
$163$	−12.4101	−0.972032	−0.486016	−	0.873950i	$-0.661550\pi$
$163$	−12.4101	−0.972032	−0.486016	+	0.873950i	$0.661550\pi$
$164$	−6.77075	−0.528707
$165$	−0.616894	−0.0480252
$166$	13.6114	1.05645
$167$	4.57005	0.353641	0.176820	−	0.984243i	$-0.443419\pi$
$167$	4.57005	0.353641	0.176820	+	0.984243i	$0.443419\pi$
$168$	−0.868566	−0.0670113
$169$	24.2700	1.86692
$170$	2.99989	0.230081
$171$	22.4496	1.71676
$172$	5.01953	0.382736
$173$	−17.6352	−1.34078	−0.670390	−	0.742009i	$-0.733873\pi$
$173$	−17.6352	−1.34078	−0.670390	+	0.742009i	$0.733873\pi$
$174$	−1.68250	−0.127550
$175$	−15.5000	−1.17169
$176$	2.56757	0.193538
$177$	0.472115	0.0354863
$178$	8.91664	0.668330
$179$	10.2811	0.768444	0.384222	−	0.923241i	$-0.374470\pi$
$179$	10.2811	0.768444	0.384222	+	0.923241i	$0.374470\pi$
$180$	3.63349	0.270825
$181$	−15.8281	−1.17650	−0.588248	−	0.808681i	$-0.700182\pi$
$181$	−15.8281	−1.17650	−0.588248	+	0.808681i	$0.700182\pi$
$182$	27.0761	2.00701
$183$	−2.44069	−0.180421
$184$	5.74567	0.423577
$185$	1.31349	0.0965697
$186$	0.638203	0.0467953
$187$	6.27822	0.459109
$188$	−7.81131	−0.569698
$189$	−5.17808	−0.376650
$190$	−9.29964	−0.674667
$191$	−6.08510	−0.440303	−0.220151	−	0.975466i	$-0.570655\pi$
$191$	−6.08510	−0.440303	−0.220151	+	0.975466i	$0.570655\pi$
$192$	0.195838	0.0141334
$193$	−10.3971	−0.748402	−0.374201	−	0.927348i	$-0.622083\pi$
$193$	−10.3971	−0.748402	−0.374201	+	0.927348i	$0.622083\pi$
$194$	16.0736	1.15402
$195$	1.46679	0.105039
$196$	12.6703	0.905022
$197$	18.9093	1.34723	0.673615	−	0.739082i	$-0.264740\pi$
$197$	18.9093	1.34723	0.673615	+	0.739082i	$0.264740\pi$
$198$	7.60424	0.540410
$199$	−7.20274	−0.510589	−0.255295	−	0.966863i	$-0.582172\pi$
$199$	−7.20274	−0.510589	−0.255295	+	0.966863i	$0.582172\pi$
$200$	3.49484	0.247123
$201$	0.162338	0.0114504
$202$	−7.98546	−0.561855
$203$	38.1035	2.67434
$204$	0.478863	0.0335271
$205$	8.30669	0.580165
$206$	6.46557	0.450478
$207$	17.0167	1.18274
$208$	−6.10492	−0.423300
$209$	−19.4624	−1.34625
$210$	1.06560	0.0735333
$211$	8.17050	0.562480	0.281240	−	0.959637i	$-0.409254\pi$
$211$	8.17050	0.562480	0.281240	+	0.959637i	$0.409254\pi$
$212$	8.11472	0.557321
$213$	−1.01558	−0.0695866
$214$	−5.44264	−0.372051
$215$	−6.15821	−0.419986
$216$	1.16752	0.0794395
$217$	−14.4533	−0.981155
$218$	17.1945	1.16456
$219$	0.284928	0.0192536
$220$	−3.15002	−0.212374
$221$	−14.9277	−1.00415
$222$	0.209668	0.0140720
$223$	−7.71630	−0.516721	−0.258361	−	0.966049i	$-0.583182\pi$
$223$	−7.71630	−0.516721	−0.258361	+	0.966049i	$0.583182\pi$
$224$	−4.43512	−0.296334
$225$	10.3505	0.690032
$226$	−16.0403	−1.06699
$227$	6.88010	0.456648	0.228324	−	0.973585i	$-0.426675\pi$
$227$	6.88010	0.456648	0.228324	+	0.973585i	$0.426675\pi$
$228$	−1.48447	−0.0983116
$229$	25.3052	1.67222	0.836108	−	0.548565i	$-0.184826\pi$
$229$	25.3052	1.67222	0.836108	+	0.548565i	$0.184826\pi$
$230$	−7.04908	−0.464802
$231$	2.23010	0.146730
$232$	−8.59131	−0.564047
$233$	−16.5849	−1.08651	−0.543255	−	0.839567i	$-0.682809\pi$
$233$	−16.5849	−1.08651	−0.543255	+	0.839567i	$0.682809\pi$
$234$	−18.0806	−1.18197
$235$	9.58330	0.625145
$236$	2.41074	0.156926
$237$	1.23876	0.0804662
$238$	−10.8448	−0.702961
$239$	−16.7337	−1.08242	−0.541208	−	0.840889i	$-0.682033\pi$
$239$	−16.7337	−1.08242	−0.541208	+	0.840889i	$0.682033\pi$
$240$	−0.240264	−0.0155090
$241$	−2.58061	−0.166232	−0.0831159	−	0.996540i	$-0.526487\pi$
$241$	−2.58061	−0.166232	−0.0831159	+	0.996540i	$0.526487\pi$
$242$	4.40758	0.283330
$243$	5.19779	0.333438
$244$	−12.4628	−0.797848
$245$	−15.5445	−0.993105
$246$	1.32597	0.0845408
$247$	46.2759	2.94446
$248$	3.25883	0.206936
$249$	−2.66562	−0.168927
$250$	−10.4219	−0.659138
$251$	22.1392	1.39742	0.698708	−	0.715407i	$-0.253759\pi$
$251$	22.1392	1.39742	0.698708	+	0.715407i	$0.253759\pi$
$252$	−13.1353	−0.827444
$253$	−14.7524	−0.927477
$254$	10.8566	0.681202
$255$	−0.587493	−0.0367902
$256$	1.00000	0.0625000
$257$	−6.96277	−0.434326	−0.217163	−	0.976135i	$-0.569680\pi$
$257$	−6.96277	−0.434326	−0.217163	+	0.976135i	$0.569680\pi$
$258$	−0.983015	−0.0611998
$259$	−4.74833	−0.295047
$260$	7.48981	0.464498
$261$	−25.4444	−1.57497
$262$	17.0840	1.05545
$263$	11.8091	0.728180	0.364090	−	0.931364i	$-0.381380\pi$
$263$	11.8091	0.728180	0.364090	+	0.931364i	$0.381380\pi$
$264$	−0.502828	−0.0309469
$265$	−9.95554	−0.611564
$266$	33.6187	2.06129
$267$	−1.74622	−0.106867
$268$	0.828938	0.0506354
$269$	1.46252	0.0891716	0.0445858	−	0.999006i	$-0.485803\pi$
$269$	1.46252	0.0891716	0.0445858	+	0.999006i	$0.485803\pi$
$270$	−1.43237	−0.0871711
$271$	−27.8539	−1.69200	−0.846002	−	0.533180i	$-0.820997\pi$
$271$	−27.8539	−1.69200	−0.846002	+	0.533180i	$0.820997\pi$
$272$	2.44520	0.148262
$273$	−5.30252	−0.320923
$274$	−2.08901	−0.126202
$275$	−8.97325	−0.541108
$276$	−1.12522	−0.0677304
$277$	−23.5494	−1.41495	−0.707473	−	0.706741i	$-0.750165\pi$
$277$	−23.5494	−1.41495	−0.707473	+	0.706741i	$0.750165\pi$
$278$	−3.75645	−0.225297
$279$	9.65151	0.577821
$280$	5.44123	0.325175
$281$	−26.1214	−1.55827	−0.779137	−	0.626854i	$-0.784342\pi$
$281$	−26.1214	−1.55827	−0.779137	+	0.626854i	$0.784342\pi$
$282$	1.52975	0.0910954
$283$	23.1965	1.37889	0.689444	−	0.724339i	$-0.257855\pi$
$283$	23.1965	1.37889	0.689444	+	0.724339i	$0.257855\pi$
$284$	−5.18583	−0.307722
$285$	1.82122	0.107880
$286$	15.6748	0.926871
$287$	−30.0291	−1.77256
$288$	2.96165	0.174517
$289$	−11.0210	−0.648294
$290$	10.5402	0.618944
$291$	−3.14783	−0.184529
$292$	1.45491	0.0851424
$293$	17.6348	1.03023	0.515117	−	0.857120i	$-0.327749\pi$
$293$	17.6348	1.03023	0.515117	+	0.857120i	$0.327749\pi$
$294$	−2.48133	−0.144714
$295$	−2.95762	−0.172199
$296$	1.07062	0.0622286
$297$	−2.99768	−0.173943
$298$	−18.8194	−1.09018
$299$	35.0769	2.02855
$300$	−0.684423	−0.0395152
$301$	22.2622	1.28317
$302$	2.86564	0.164899
$303$	1.56386	0.0898412
$304$	−7.58010	−0.434749
$305$	15.2900	0.875501
$306$	7.24182	0.413987
$307$	29.8945	1.70617	0.853083	−	0.521775i	$-0.174730\pi$
$307$	29.8945	1.70617	0.853083	+	0.521775i	$0.174730\pi$
$308$	11.3875	0.648862
$309$	−1.26621	−0.0720319
$310$	−3.99809	−0.227076
$311$	22.8223	1.29414	0.647068	−	0.762432i	$-0.275995\pi$
$311$	22.8223	1.29414	0.647068	+	0.762432i	$0.275995\pi$
$312$	1.19558	0.0676861
$313$	−8.49540	−0.480189	−0.240094	−	0.970750i	$-0.577178\pi$
$313$	−8.49540	−0.480189	−0.240094	+	0.970750i	$0.577178\pi$
$314$	−4.59227	−0.259157
$315$	16.1150	0.907977
$316$	6.32544	0.355834
$317$	−7.07015	−0.397099	−0.198550	−	0.980091i	$-0.563623\pi$
$317$	−7.07015	−0.397099	−0.198550	+	0.980091i	$0.563623\pi$
$318$	−1.58917	−0.0891163
$319$	22.0588	1.23505
$320$	−1.22685	−0.0685830
$321$	1.06588	0.0594914
$322$	25.4828	1.42010
$323$	−18.5349	−1.03131
$324$	8.65630	0.480905
$325$	21.3357	1.18349
$326$	12.4101	0.687331
$327$	−3.36733	−0.186214
$328$	6.77075	0.373852
$329$	−34.6441	−1.90999
$330$	0.616894	0.0339589
$331$	21.6983	1.19264	0.596322	−	0.802745i	$-0.296628\pi$
$331$	21.6983	1.19264	0.596322	+	0.802745i	$0.296628\pi$
$332$	−13.6114	−0.747021
$333$	3.17080	0.173759
$334$	−4.57005	−0.250062
$335$	−1.01698	−0.0555637
$336$	0.868566	0.0473841
$337$	15.2293	0.829595	0.414798	−	0.909914i	$-0.363852\pi$
$337$	15.2293	0.829595	0.414798	+	0.909914i	$0.363852\pi$
$338$	−24.2700	−1.32012
$339$	3.14131	0.170612
$340$	−2.99989	−0.162692
$341$	−8.36728	−0.453114
$342$	−22.4496	−1.21393
$343$	25.1485	1.35789
$344$	−5.01953	−0.270635
$345$	1.38048	0.0743224
$346$	17.6352	0.948075
$347$	−11.0076	−0.590918	−0.295459	−	0.955355i	$-0.595472\pi$
$347$	−11.0076	−0.590918	−0.295459	+	0.955355i	$0.595472\pi$
$348$	1.68250	0.0901917
$349$	29.4160	1.57460	0.787302	−	0.616567i	$-0.211477\pi$
$349$	29.4160	1.57460	0.787302	+	0.616567i	$0.211477\pi$
$350$	15.5000	0.828512
$351$	7.12760	0.380443
$352$	−2.56757	−0.136852
$353$	2.29414	0.122105	0.0610525	−	0.998135i	$-0.480554\pi$
$353$	2.29414	0.122105	0.0610525	+	0.998135i	$0.480554\pi$
$354$	−0.472115	−0.0250926
$355$	6.36223	0.337672
$356$	−8.91664	−0.472581
$357$	2.12382	0.112404
$358$	−10.2811	−0.543372
$359$	9.43942	0.498194	0.249097	−	0.968479i	$-0.419866\pi$
$359$	9.43942	0.498194	0.249097	+	0.968479i	$0.419866\pi$
$360$	−3.63349	−0.191502
$361$	38.4579	2.02410
$362$	15.8281	0.831908
$363$	−0.863172	−0.0453048
$364$	−27.0761	−1.41917
$365$	−1.78496	−0.0934291
$366$	2.44069	0.127577
$367$	29.6835	1.54946	0.774732	−	0.632289i	$-0.217885\pi$
$367$	29.6835	1.54946	0.774732	+	0.632289i	$0.217885\pi$
$368$	−5.74567	−0.299514
$369$	20.0526	1.04390
$370$	−1.31349	−0.0682851
$371$	35.9898	1.86850
$372$	−0.638203	−0.0330893
$373$	14.1212	0.731167	0.365583	−	0.930779i	$-0.380869\pi$
$373$	14.1212	0.731167	0.365583	+	0.930779i	$0.380869\pi$
$374$	−6.27822	−0.324639
$375$	2.04100	0.105397
$376$	7.81131	0.402838
$377$	−52.4492	−2.70127
$378$	5.17808	0.266332
$379$	0.975424	0.0501042	0.0250521	−	0.999686i	$-0.492025\pi$
$379$	0.975424	0.0501042	0.0250521	+	0.999686i	$0.492025\pi$
$380$	9.29964	0.477061
$381$	−2.12613	−0.108925
$382$	6.08510	0.311341
$383$	−3.96578	−0.202642	−0.101321	−	0.994854i	$-0.532307\pi$
$383$	−3.96578	−0.202642	−0.101321	+	0.994854i	$0.532307\pi$
$384$	−0.195838	−0.00999382
$385$	−13.9707	−0.712014
$386$	10.3971	0.529200
$387$	−14.8661	−0.755685
$388$	−16.0736	−0.816015
$389$	32.4075	1.64313	0.821563	−	0.570118i	$-0.193103\pi$
$389$	32.4075	1.64313	0.821563	+	0.570118i	$0.193103\pi$
$390$	−1.46679	−0.0742738
$391$	−14.0493	−0.710505
$392$	−12.6703	−0.639947
$393$	−3.34569	−0.168768
$394$	−18.9093	−0.952636
$395$	−7.76036	−0.390466
$396$	−7.60424	−0.382127
$397$	−33.0348	−1.65797	−0.828985	−	0.559271i	$-0.811081\pi$
$397$	−33.0348	−1.65797	−0.828985	+	0.559271i	$0.811081\pi$
$398$	7.20274	0.361041
$399$	−6.58381	−0.329603
$400$	−3.49484	−0.174742
$401$	15.3046	0.764275	0.382138	−	0.924105i	$-0.375188\pi$
$401$	15.3046	0.764275	0.382138	+	0.924105i	$0.375188\pi$
$402$	−0.162338	−0.00809666
$403$	19.8949	0.991035
$404$	7.98546	0.397291
$405$	−10.6200	−0.527711
$406$	−38.1035	−1.89104
$407$	−2.74889	−0.136258
$408$	−0.478863	−0.0237073
$409$	−24.1616	−1.19471	−0.597356	−	0.801976i	$-0.703782\pi$
$409$	−24.1616	−1.19471	−0.597356	+	0.801976i	$0.703782\pi$
$410$	−8.30669	−0.410238
$411$	0.409107	0.0201798
$412$	−6.46557	−0.318536
$413$	10.6919	0.526116
$414$	−17.0167	−0.836323
$415$	16.6991	0.819726
$416$	6.10492	0.299318
$417$	0.735656	0.0360252
$418$	19.4624	0.951939
$419$	21.2258	1.03695	0.518474	−	0.855093i	$-0.326500\pi$
$419$	21.2258	1.03695	0.518474	+	0.855093i	$0.326500\pi$
$420$	−1.06560	−0.0519959
$421$	−29.2639	−1.42623	−0.713117	−	0.701045i	$-0.752717\pi$
$421$	−29.2639	−1.42623	−0.713117	+	0.701045i	$0.752717\pi$
$422$	−8.17050	−0.397734
$423$	23.1343	1.12483
$424$	−8.11472	−0.394086
$425$	−8.54559	−0.414522
$426$	1.01558	0.0492052
$427$	−55.2740	−2.67490
$428$	5.44264	0.263080
$429$	−3.06972	−0.148208
$430$	6.15821	0.296975
$431$	20.8670	1.00513	0.502564	−	0.864540i	$-0.332390\pi$
$431$	20.8670	1.00513	0.502564	+	0.864540i	$0.332390\pi$
$432$	−1.16752	−0.0561722
$433$	19.0730	0.916588	0.458294	−	0.888801i	$-0.348461\pi$
$433$	19.0730	0.916588	0.458294	+	0.888801i	$0.348461\pi$
$434$	14.4533	0.693781
$435$	−2.06418	−0.0989698
$436$	−17.1945	−0.823466
$437$	43.5528	2.08341
$438$	−0.284928	−0.0136144
$439$	15.9645	0.761945	0.380973	−	0.924586i	$-0.375589\pi$
$439$	15.9645	0.761945	0.380973	+	0.924586i	$0.375589\pi$
$440$	3.15002	0.150171
$441$	−37.5250	−1.78690
$442$	14.9277	0.710040
$443$	−22.7314	−1.08000	−0.540000	−	0.841665i	$-0.681576\pi$
$443$	−22.7314	−1.08000	−0.540000	+	0.841665i	$0.681576\pi$
$444$	−0.209668	−0.00995042
$445$	10.9394	0.518576
$446$	7.71630	0.365377
$447$	3.68555	0.174321
$448$	4.43512	0.209540
$449$	12.7994	0.604040	0.302020	−	0.953302i	$-0.402339\pi$
$449$	12.7994	0.604040	0.302020	+	0.953302i	$0.402339\pi$
$450$	−10.3505	−0.487927
$451$	−17.3844	−0.818599
$452$	16.0403	0.754474
$453$	−0.561201	−0.0263675
$454$	−6.88010	−0.322899
$455$	33.2182	1.55729
$456$	1.48447	0.0695168
$457$	10.5942	0.495575	0.247787	−	0.968814i	$-0.420297\pi$
$457$	10.5942	0.495575	0.247787	+	0.968814i	$0.420297\pi$
$458$	−25.3052	−1.18244
$459$	−2.85481	−0.133251
$460$	7.04908	0.328665
$461$	36.4791	1.69900	0.849499	−	0.527590i	$-0.176904\pi$
$461$	36.4791	1.69900	0.849499	+	0.527590i	$0.176904\pi$
$462$	−2.23010	−0.103754
$463$	32.9285	1.53032	0.765158	−	0.643842i	$-0.222661\pi$
$463$	32.9285	1.53032	0.765158	+	0.643842i	$0.222661\pi$
$464$	8.59131	0.398841
$465$	0.782979	0.0363098
$466$	16.5849	0.768279
$467$	−32.1211	−1.48639	−0.743193	−	0.669077i	$-0.766690\pi$
$467$	−32.1211	−1.48639	−0.743193	+	0.669077i	$0.766690\pi$
$468$	18.0806	0.835777
$469$	3.67644	0.169762
$470$	−9.58330	−0.442045
$471$	0.899341	0.0414394
$472$	−2.41074	−0.110963
$473$	12.8880	0.592591
$474$	−1.23876	−0.0568982
$475$	26.4912	1.21550
$476$	10.8448	0.497069
$477$	−24.0329	−1.10039
$478$	16.7337	0.765383
$479$	17.6285	0.805468	0.402734	−	0.915317i	$-0.368060\pi$
$479$	17.6285	0.805468	0.402734	+	0.915317i	$0.368060\pi$
$480$	0.240264	0.0109665
$481$	6.53605	0.298018
$482$	2.58061	0.117544
$483$	−4.99050	−0.227075
$484$	−4.40758	−0.200344
$485$	19.7199	0.895435
$486$	−5.19779	−0.235776
$487$	−18.3058	−0.829514	−0.414757	−	0.909932i	$-0.636133\pi$
$487$	−18.3058	−0.829514	−0.414757	+	0.909932i	$0.636133\pi$
$488$	12.4628	0.564164
$489$	−2.43037	−0.109905
$490$	15.5445	0.702231
$491$	4.45179	0.200907	0.100453	−	0.994942i	$-0.467971\pi$
$491$	4.45179	0.200907	0.100453	+	0.994942i	$0.467971\pi$
$492$	−1.32597	−0.0597794
$493$	21.0075	0.946128
$494$	−46.2759	−2.08205
$495$	9.32926	0.419319
$496$	−3.25883	−0.146326
$497$	−22.9998	−1.03168
$498$	2.66562	0.119449
$499$	26.0799	1.16750	0.583748	−	0.811935i	$-0.301586\pi$
$499$	26.0799	1.16750	0.583748	+	0.811935i	$0.301586\pi$
$500$	10.4219	0.466081
$501$	0.894989	0.0399852
$502$	−22.1392	−0.988122
$503$	−21.7516	−0.969857	−0.484928	−	0.874554i	$-0.661154\pi$
$503$	−21.7516	−0.969857	−0.484928	+	0.874554i	$0.661154\pi$
$504$	13.1353	0.585091
$505$	−9.79695	−0.435959
$506$	14.7524	0.655825
$507$	4.75299	0.211088
$508$	−10.8566	−0.481683
$509$	−2.31596	−0.102653	−0.0513266	−	0.998682i	$-0.516345\pi$
$509$	−2.31596	−0.102653	−0.0513266	+	0.998682i	$0.516345\pi$
$510$	0.587493	0.0260146
$511$	6.45272	0.285452
$512$	−1.00000	−0.0441942
$513$	8.84990	0.390733
$514$	6.96277	0.307115
$515$	7.93228	0.349538
$516$	0.983015	0.0432748
$517$	−20.0561	−0.882066
$518$	4.74833	0.208630
$519$	−3.45365	−0.151598
$520$	−7.48981	−0.328450
$521$	13.2000	0.578304	0.289152	−	0.957283i	$-0.406627\pi$
$521$	13.2000	0.578304	0.289152	+	0.957283i	$0.406627\pi$
$522$	25.4444	1.11367
$523$	−10.9206	−0.477526	−0.238763	−	0.971078i	$-0.576742\pi$
$523$	−10.9206	−0.477526	−0.238763	+	0.971078i	$0.576742\pi$
$524$	−17.0840	−0.746317
$525$	−3.03550	−0.132480
$526$	−11.8091	−0.514901
$527$	−7.96849	−0.347113
$528$	0.502828	0.0218828
$529$	10.0128	0.435338
$530$	9.95554	0.432441
$531$	−7.13977	−0.309840
$532$	−33.6187	−1.45755
$533$	41.3349	1.79041
$534$	1.74622	0.0755662
$535$	−6.67730	−0.288685
$536$	−0.828938	−0.0358047
$537$	2.01343	0.0868858
$538$	−1.46252	−0.0630539
$539$	32.5319	1.40125
$540$	1.43237	0.0616393
$541$	−5.57023	−0.239483	−0.119741	−	0.992805i	$-0.538207\pi$
$541$	−5.57023	−0.239483	−0.119741	+	0.992805i	$0.538207\pi$
$542$	27.8539	1.19643
$543$	−3.09975	−0.133023
$544$	−2.44520	−0.104837
$545$	21.0950	0.903612
$546$	5.30252	0.226927
$547$	−19.2153	−0.821585	−0.410792	−	0.911729i	$-0.634748\pi$
$547$	−19.2153	−0.821585	−0.410792	+	0.911729i	$0.634748\pi$
$548$	2.08901	0.0892380
$549$	36.9104	1.57530
$550$	8.97325	0.382621
$551$	−65.1229	−2.77433
$552$	1.12522	0.0478926
$553$	28.0541	1.19298
$554$	23.5494	1.00052
$555$	0.257231	0.0109189
$556$	3.75645	0.159309
$557$	−22.9302	−0.971584	−0.485792	−	0.874074i	$-0.661469\pi$
$557$	−22.9302	−0.971584	−0.485792	+	0.874074i	$0.661469\pi$
$558$	−9.65151	−0.408581
$559$	−30.6438	−1.29610
$560$	−5.44123	−0.229934
$561$	1.22952	0.0519102
$562$	26.1214	1.10187
$563$	−35.5336	−1.49756	−0.748782	−	0.662816i	$-0.769361\pi$
$563$	−35.5336	−1.49756	−0.748782	+	0.662816i	$0.769361\pi$
$564$	−1.52975	−0.0644142
$565$	−19.6791	−0.827905
$566$	−23.1965	−0.975021
$567$	38.3917	1.61230
$568$	5.18583	0.217593
$569$	−18.7536	−0.786191	−0.393096	−	0.919498i	$-0.628596\pi$
$569$	−18.7536	−0.786191	−0.393096	+	0.919498i	$0.628596\pi$
$570$	−1.82122	−0.0762827
$571$	20.4171	0.854430	0.427215	−	0.904150i	$-0.359495\pi$
$571$	20.4171	0.854430	0.427215	+	0.904150i	$0.359495\pi$
$572$	−15.6748	−0.655397
$573$	−1.19169	−0.0497838
$574$	30.0291	1.25339
$575$	20.0802	0.837403
$576$	−2.96165	−0.123402
$577$	1.99303	0.0829710	0.0414855	−	0.999139i	$-0.486791\pi$
$577$	1.99303	0.0829710	0.0414855	+	0.999139i	$0.486791\pi$
$578$	11.0210	0.458413
$579$	−2.03616	−0.0846197
$580$	−10.5402	−0.437659
$581$	−60.3681	−2.50449
$582$	3.14783	0.130482
$583$	20.8351	0.862903
$584$	−1.45491	−0.0602048
$585$	−22.1822	−0.917121
$586$	−17.6348	−0.728485
$587$	−18.2774	−0.754391	−0.377195	−	0.926134i	$-0.623111\pi$
$587$	−18.2774	−0.754391	−0.377195	+	0.926134i	$0.623111\pi$
$588$	2.48133	0.102328
$589$	24.7023	1.01784
$590$	2.95762	0.121763
$591$	3.70316	0.152328
$592$	−1.07062	−0.0440022
$593$	−21.1065	−0.866740	−0.433370	−	0.901216i	$-0.642676\pi$
$593$	−21.1065	−0.866740	−0.433370	+	0.901216i	$0.642676\pi$
$594$	2.99768	0.122996
$595$	−13.3049	−0.545447
$596$	18.8194	0.770873
$597$	−1.41057	−0.0577309
$598$	−35.0769	−1.43440
$599$	−11.5521	−0.472004	−0.236002	−	0.971753i	$-0.575837\pi$
$599$	−11.5521	−0.472004	−0.236002	+	0.971753i	$0.575837\pi$
$600$	0.684423	0.0279415
$601$	−32.7106	−1.33429	−0.667147	−	0.744926i	$-0.732485\pi$
$601$	−32.7106	−1.33429	−0.667147	+	0.744926i	$0.732485\pi$
$602$	−22.2622	−0.907341
$603$	−2.45502	−0.0999762
$604$	−2.86564	−0.116601
$605$	5.40743	0.219843
$606$	−1.56386	−0.0635273
$607$	−9.00627	−0.365553	−0.182777	−	0.983154i	$-0.558509\pi$
$607$	−9.00627	−0.365553	−0.182777	+	0.983154i	$0.558509\pi$
$608$	7.58010	0.307414
$609$	7.46211	0.302380
$610$	−15.2900	−0.619073
$611$	47.6874	1.92923
$612$	−7.24182	−0.292733
$613$	46.6693	1.88496	0.942478	−	0.334268i	$-0.108489\pi$
$613$	46.6693	1.88496	0.942478	+	0.334268i	$0.108489\pi$
$614$	−29.8945	−1.20644
$615$	1.62677	0.0655976
$616$	−11.3875	−0.458815
$617$	−21.3494	−0.859493	−0.429747	−	0.902950i	$-0.641397\pi$
$617$	−21.3494	−0.859493	−0.429747	+	0.902950i	$0.641397\pi$
$618$	1.26621	0.0509342
$619$	−32.5035	−1.30643	−0.653214	−	0.757174i	$-0.726580\pi$
$619$	−32.5035	−1.30643	−0.653214	+	0.757174i	$0.726580\pi$
$620$	3.99809	0.160567
$621$	6.70818	0.269190
$622$	−22.8223	−0.915092
$623$	−39.5464	−1.58439
$624$	−1.19558	−0.0478613
$625$	4.68812	0.187525
$626$	8.49540	0.339545
$627$	−3.81149	−0.152216
$628$	4.59227	0.183251
$629$	−2.61788	−0.104382
$630$	−16.1150	−0.642037
$631$	7.22769	0.287730	0.143865	−	0.989597i	$-0.454047\pi$
$631$	7.22769	0.287730	0.143865	+	0.989597i	$0.454047\pi$
$632$	−6.32544	−0.251612
$633$	1.60009	0.0635980
$634$	7.07015	0.280791
$635$	13.3194	0.528563
$636$	1.58917	0.0630148
$637$	−77.3511	−3.06476
$638$	−22.0588	−0.873316
$639$	15.3586	0.607577
$640$	1.22685	0.0484955
$641$	19.5701	0.772973	0.386486	−	0.922295i	$-0.373689\pi$
$641$	19.5701	0.772973	0.386486	+	0.922295i	$0.373689\pi$
$642$	−1.06588	−0.0420668
$643$	−21.7473	−0.857629	−0.428814	−	0.903393i	$-0.641069\pi$
$643$	−21.7473	−0.857629	−0.428814	+	0.903393i	$0.641069\pi$
$644$	−25.4828	−1.00416
$645$	−1.20601	−0.0474866
$646$	18.5349	0.729244
$647$	−21.9316	−0.862219	−0.431110	−	0.902300i	$-0.641878\pi$
$647$	−21.9316	−0.862219	−0.431110	+	0.902300i	$0.641878\pi$
$648$	−8.65630	−0.340051
$649$	6.18975	0.242969
$650$	−21.3357	−0.836856
$651$	−2.83051	−0.110936
$652$	−12.4101	−0.486016
$653$	−10.4369	−0.408429	−0.204215	−	0.978926i	$-0.565464\pi$
$653$	−10.4369	−0.408429	−0.204215	+	0.978926i	$0.565464\pi$
$654$	3.36733	0.131673
$655$	20.9595	0.818954
$656$	−6.77075	−0.264353
$657$	−4.30894	−0.168108
$658$	34.6441	1.35057
$659$	−38.8293	−1.51258	−0.756288	−	0.654239i	$-0.772989\pi$
$659$	−38.8293	−1.51258	−0.756288	+	0.654239i	$0.772989\pi$
$660$	−0.616894	−0.0240126
$661$	−8.09749	−0.314956	−0.157478	−	0.987522i	$-0.550336\pi$
$661$	−8.09749	−0.314956	−0.157478	+	0.987522i	$0.550336\pi$
$662$	−21.6983	−0.843326
$663$	−2.92342	−0.113536
$664$	13.6114	0.528223
$665$	41.2450	1.59941
$666$	−3.17080	−0.122866
$667$	−49.3628	−1.91134
$668$	4.57005	0.176820
$669$	−1.51114	−0.0584242
$670$	1.01698	0.0392894
$671$	−31.9991	−1.23531
$672$	−0.868566	−0.0335056
$673$	3.56906	0.137577	0.0687886	−	0.997631i	$-0.478087\pi$
$673$	3.56906	0.137577	0.0687886	+	0.997631i	$0.478087\pi$
$674$	−15.2293	−0.586612
$675$	4.08029	0.157050
$676$	24.2700	0.933462
$677$	8.05068	0.309413	0.154706	−	0.987960i	$-0.450557\pi$
$677$	8.05068	0.309413	0.154706	+	0.987960i	$0.450557\pi$
$678$	−3.14131	−0.120641
$679$	−71.2885	−2.73580
$680$	2.99989	0.115041
$681$	1.34739	0.0516319
$682$	8.36728	0.320400
$683$	−26.3364	−1.00773	−0.503867	−	0.863781i	$-0.668090\pi$
$683$	−26.3364	−1.00773	−0.503867	+	0.863781i	$0.668090\pi$
$684$	22.4496	0.858381
$685$	−2.56290	−0.0979233
$686$	−25.1485	−0.960173
$687$	4.95573	0.189073
$688$	5.01953	0.191368
$689$	−49.5397	−1.88731
$690$	−1.38048	−0.0525539
$691$	34.5388	1.31392	0.656959	−	0.753927i	$-0.271843\pi$
$691$	34.5388	1.31392	0.656959	+	0.753927i	$0.271843\pi$
$692$	−17.6352	−0.670390
$693$	−33.7257	−1.28113
$694$	11.0076	0.417842
$695$	−4.60860	−0.174814
$696$	−1.68250	−0.0637752
$697$	−16.5558	−0.627097
$698$	−29.4160	−1.11341
$699$	−3.24795	−0.122849
$700$	−15.5000	−0.585847
$701$	−51.7485	−1.95451	−0.977256	−	0.212062i	$-0.931982\pi$
$701$	−51.7485	−1.95451	−0.977256	+	0.212062i	$0.931982\pi$
$702$	−7.12760	−0.269014
$703$	8.11541	0.306078
$704$	2.56757	0.0967690
$705$	1.87677	0.0706834
$706$	−2.29414	−0.0863412
$707$	35.4165	1.33197
$708$	0.472115	0.0177432
$709$	−45.9466	−1.72556	−0.862780	−	0.505580i	$-0.831279\pi$
$709$	−45.9466	−1.72556	−0.862780	+	0.505580i	$0.831279\pi$
$710$	−6.36223	−0.238770
$711$	−18.7337	−0.702569
$712$	8.91664	0.334165
$713$	18.7242	0.701226
$714$	−2.12382	−0.0794818
$715$	19.2306	0.719185
$716$	10.2811	0.384222
$717$	−3.27710	−0.122386
$718$	−9.43942	−0.352276
$719$	23.6955	0.883694	0.441847	−	0.897091i	$-0.354323\pi$
$719$	23.6955	0.883694	0.441847	+	0.897091i	$0.354323\pi$
$720$	3.63349	0.135412
$721$	−28.6756	−1.06793
$722$	−38.4579	−1.43125
$723$	−0.505382	−0.0187953
$724$	−15.8281	−0.588248
$725$	−30.0252	−1.11511
$726$	0.863172	0.0320353
$727$	38.9693	1.44529	0.722646	−	0.691218i	$-0.242926\pi$
$727$	38.9693	1.44529	0.722646	+	0.691218i	$0.242926\pi$
$728$	27.0761	1.00351
$729$	−24.9510	−0.924110
$730$	1.78496	0.0660644
$731$	12.2738	0.453961
$732$	−2.44069	−0.0902105
$733$	−9.84533	−0.363645	−0.181823	−	0.983331i	$-0.558200\pi$
$733$	−9.84533	−0.363645	−0.181823	+	0.983331i	$0.558200\pi$
$734$	−29.6835	−1.09564
$735$	−3.04421	−0.112288
$736$	5.74567	0.211788
$737$	2.12836	0.0783990
$738$	−20.0526	−0.738146
$739$	7.68370	0.282650	0.141325	−	0.989963i	$-0.454864\pi$
$739$	7.68370	0.282650	0.141325	+	0.989963i	$0.454864\pi$
$740$	1.31349	0.0482848
$741$	9.06258	0.332922
$742$	−35.9898	−1.32123
$743$	−30.8070	−1.13020	−0.565099	−	0.825023i	$-0.691162\pi$
$743$	−30.8070	−1.13020	−0.565099	+	0.825023i	$0.691162\pi$
$744$	0.638203	0.0233977
$745$	−23.0886	−0.845900
$746$	−14.1212	−0.517013
$747$	40.3121	1.47494
$748$	6.27822	0.229555
$749$	24.1388	0.882012
$750$	−2.04100	−0.0745269
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−7.81131	−0.284849
$753$	4.33570	0.158002
$754$	52.4492	1.91009
$755$	3.51571	0.127950
$756$	−5.17808	−0.188325
$757$	8.43607	0.306614	0.153307	−	0.988179i	$-0.451008\pi$
$757$	8.43607	0.306614	0.153307	+	0.988179i	$0.451008\pi$
$758$	−0.975424	−0.0354290
$759$	−2.88909	−0.104867
$760$	−9.29964	−0.337333
$761$	29.2118	1.05893	0.529464	−	0.848332i	$-0.322393\pi$
$761$	29.2118	1.05893	0.529464	+	0.848332i	$0.322393\pi$
$762$	2.12613	0.0770216
$763$	−76.2596	−2.76078
$764$	−6.08510	−0.220151
$765$	8.88462	0.321224
$766$	3.96578	0.143289
$767$	−14.7174	−0.531414
$768$	0.195838	0.00706670
$769$	7.26914	0.262132	0.131066	−	0.991374i	$-0.458160\pi$
$769$	7.26914	0.262132	0.131066	+	0.991374i	$0.458160\pi$
$770$	13.9707	0.503470
$771$	−1.36358	−0.0491080
$772$	−10.3971	−0.374201
$773$	−19.0566	−0.685417	−0.342709	−	0.939442i	$-0.611344\pi$
$773$	−19.0566	−0.685417	−0.342709	+	0.939442i	$0.611344\pi$
$774$	14.8661	0.534350
$775$	11.3891	0.409108
$776$	16.0736	0.577010
$777$	−0.929904	−0.0333601
$778$	−32.4075	−1.16187
$779$	51.3230	1.83884
$780$	1.46679	0.0525195
$781$	−13.3150	−0.476448
$782$	14.0493	0.502403
$783$	−10.0305	−0.358461
$784$	12.6703	0.452511
$785$	−5.63402	−0.201087
$786$	3.34569	0.119337
$787$	−26.9585	−0.960965	−0.480483	−	0.877004i	$-0.659539\pi$
$787$	−26.9585	−0.960965	−0.480483	+	0.877004i	$0.659539\pi$
$788$	18.9093	0.673615
$789$	2.31267	0.0823332
$790$	7.76036	0.276101
$791$	71.1408	2.52948
$792$	7.60424	0.270205
$793$	76.0843	2.70183
$794$	33.0348	1.17236
$795$	−1.94967	−0.0691478
$796$	−7.20274	−0.255295
$797$	43.5374	1.54217	0.771087	−	0.636730i	$-0.219713\pi$
$797$	43.5374	1.54217	0.771087	+	0.636730i	$0.219713\pi$
$798$	6.58381	0.233064
$799$	−19.1002	−0.675717
$800$	3.49484	0.123561
$801$	26.4079	0.933079
$802$	−15.3046	−0.540424
$803$	3.73560	0.131826
$804$	0.162338	0.00572521
$805$	31.2635	1.10189
$806$	−19.8949	−0.700768
$807$	0.286418	0.0100824
$808$	−7.98546	−0.280927
$809$	−38.0278	−1.33699	−0.668494	−	0.743718i	$-0.733061\pi$
$809$	−38.0278	−1.33699	−0.668494	+	0.743718i	$0.733061\pi$
$810$	10.6200	0.373148
$811$	21.5368	0.756261	0.378130	−	0.925752i	$-0.376567\pi$
$811$	21.5368	0.756261	0.378130	+	0.925752i	$0.376567\pi$
$812$	38.1035	1.33717
$813$	−5.45485	−0.191310
$814$	2.74889	0.0963487
$815$	15.2253	0.533319
$816$	0.478863	0.0167636
$817$	−38.0485	−1.33115
$818$	24.1616	0.844789
$819$	80.1897	2.80206
$820$	8.30669	0.290082
$821$	−24.1514	−0.842890	−0.421445	−	0.906854i	$-0.638477\pi$
$821$	−24.1514	−0.842890	−0.421445	+	0.906854i	$0.638477\pi$
$822$	−0.409107	−0.0142693
$823$	−37.4131	−1.30414	−0.652070	−	0.758159i	$-0.726099\pi$
$823$	−37.4131	−1.30414	−0.652070	+	0.758159i	$0.726099\pi$
$824$	6.46557	0.225239
$825$	−1.75730	−0.0611815
$826$	−10.6919	−0.372020
$827$	3.57493	0.124313	0.0621563	−	0.998066i	$-0.480202\pi$
$827$	3.57493	0.124313	0.0621563	+	0.998066i	$0.480202\pi$
$828$	17.0167	0.591370
$829$	40.2822	1.39906	0.699529	−	0.714604i	$-0.253393\pi$
$829$	40.2822	1.39906	0.699529	+	0.714604i	$0.253393\pi$
$830$	−16.6991	−0.579634
$831$	−4.61187	−0.159984
$832$	−6.10492	−0.211650
$833$	30.9814	1.07344
$834$	−0.735656	−0.0254737
$835$	−5.60676	−0.194030
$836$	−19.4624	−0.673123
$837$	3.80474	0.131511
$838$	−21.2258	−0.733234
$839$	31.4171	1.08464	0.542319	−	0.840173i	$-0.317546\pi$
$839$	31.4171	1.08464	0.542319	+	0.840173i	$0.317546\pi$
$840$	1.06560	0.0367667
$841$	44.8105	1.54519
$842$	29.2639	1.00850
$843$	−5.11557	−0.176190
$844$	8.17050	0.281240
$845$	−29.7757	−1.02431
$846$	−23.1343	−0.795375
$847$	−19.5481	−0.671682
$848$	8.11472	0.278661
$849$	4.54276	0.155907
$850$	8.54559	0.293111
$851$	6.15144	0.210869
$852$	−1.01558	−0.0347933
$853$	−41.0197	−1.40449	−0.702244	−	0.711937i	$-0.747818\pi$
$853$	−41.0197	−1.40449	−0.702244	+	0.711937i	$0.747818\pi$
$854$	55.2740	1.89144
$855$	−27.5423	−0.941925
$856$	−5.44264	−0.186026
$857$	13.5703	0.463554	0.231777	−	0.972769i	$-0.425546\pi$
$857$	13.5703	0.463554	0.231777	+	0.972769i	$0.425546\pi$
$858$	3.06972	0.104799
$859$	24.0842	0.821741	0.410870	−	0.911694i	$-0.365225\pi$
$859$	24.0842	0.821741	0.410870	+	0.911694i	$0.365225\pi$
$860$	−6.15821	−0.209993
$861$	−5.88084	−0.200419
$862$	−20.8670	−0.710732
$863$	−30.7413	−1.04644	−0.523222	−	0.852196i	$-0.675270\pi$
$863$	−30.7413	−1.04644	−0.523222	+	0.852196i	$0.675270\pi$
$864$	1.16752	0.0397198
$865$	21.6358	0.735638
$866$	−19.0730	−0.648126
$867$	−2.15833	−0.0733008
$868$	−14.4533	−0.490577
$869$	16.2410	0.550938
$870$	2.06418	0.0699822
$871$	−5.06060	−0.171472
$872$	17.1945	0.582278
$873$	47.6044	1.61117
$874$	−43.5528	−1.47319
$875$	46.2223	1.56260
$876$	0.284928	0.00962681
$877$	54.0347	1.82462	0.912311	−	0.409498i	$-0.134296\pi$
$877$	54.0347	1.82462	0.912311	+	0.409498i	$0.134296\pi$
$878$	−15.9645	−0.538777
$879$	3.45356	0.116486
$880$	−3.15002	−0.106187
$881$	7.84866	0.264428	0.132214	−	0.991221i	$-0.457791\pi$
$881$	7.84866	0.264428	0.132214	+	0.991221i	$0.457791\pi$
$882$	37.5250	1.26353
$883$	−1.38590	−0.0466392	−0.0233196	−	0.999728i	$-0.507424\pi$
$883$	−1.38590	−0.0466392	−0.0233196	+	0.999728i	$0.507424\pi$
$884$	−14.9277	−0.502074
$885$	−0.579214	−0.0194701
$886$	22.7314	0.763675
$887$	13.8533	0.465147	0.232573	−	0.972579i	$-0.425285\pi$
$887$	13.8533	0.465147	0.232573	+	0.972579i	$0.425285\pi$
$888$	0.209668	0.00703601
$889$	−48.1502	−1.61491
$890$	−10.9394	−0.366688
$891$	22.2257	0.744588
$892$	−7.71630	−0.258361
$893$	59.2105	1.98140
$894$	−3.68555	−0.123263
$895$	−12.6133	−0.421618
$896$	−4.43512	−0.148167
$897$	6.86939	0.229362
$898$	−12.7994	−0.427121
$899$	−27.9976	−0.933773
$900$	10.3505	0.345016
$901$	19.8421	0.661037
$902$	17.3844	0.578837
$903$	4.35979	0.145085
$904$	−16.0403	−0.533494
$905$	19.4187	0.645501
$906$	0.561201	0.0186447
$907$	3.66099	0.121561	0.0607806	−	0.998151i	$-0.480641\pi$
$907$	3.66099	0.121561	0.0607806	+	0.998151i	$0.480641\pi$
$908$	6.88010	0.228324
$909$	−23.6501	−0.784425
$910$	−33.2182	−1.10117
$911$	18.0843	0.599159	0.299580	−	0.954071i	$-0.403154\pi$
$911$	18.0843	0.599159	0.299580	+	0.954071i	$0.403154\pi$
$912$	−1.48447	−0.0491558
$913$	−34.9481	−1.15661
$914$	−10.5942	−0.350424
$915$	2.99436	0.0989904
$916$	25.3052	0.836108
$917$	−75.7695	−2.50213
$918$	2.85481	0.0942229
$919$	0.467794	0.0154311	0.00771555	−	0.999970i	$-0.497544\pi$
$919$	0.467794	0.0154311	0.00771555	+	0.999970i	$0.497544\pi$
$920$	−7.04908	−0.232401
$921$	5.85447	0.192911
$922$	−36.4791	−1.20137
$923$	31.6591	1.04207
$924$	2.23010	0.0733650
$925$	3.74165	0.123025
$926$	−32.9285	−1.08210
$927$	19.1487	0.628927
$928$	−8.59131	−0.282023
$929$	22.4674	0.737131	0.368565	−	0.929602i	$-0.379849\pi$
$929$	22.4674	0.737131	0.368565	+	0.929602i	$0.379849\pi$
$930$	−0.782979	−0.0256749
$931$	−96.0421	−3.14765
$932$	−16.5849	−0.543255
$933$	4.46948	0.146324
$934$	32.1211	1.05103
$935$	−7.70243	−0.251897
$936$	−18.0806	−0.590983
$937$	−40.5856	−1.32587	−0.662937	−	0.748676i	$-0.730690\pi$
$937$	−40.5856	−1.32587	−0.662937	+	0.748676i	$0.730690\pi$
$938$	−3.67644	−0.120040
$939$	−1.66372	−0.0542936
$940$	9.58330	0.312573
$941$	18.2094	0.593610	0.296805	−	0.954938i	$-0.404079\pi$
$941$	18.2094	0.593610	0.296805	+	0.954938i	$0.404079\pi$
$942$	−0.899341	−0.0293021
$943$	38.9025	1.26684
$944$	2.41074	0.0784630
$945$	6.35273	0.206654
$946$	−12.8880	−0.419025
$947$	2.02565	0.0658249	0.0329125	−	0.999458i	$-0.489522\pi$
$947$	2.02565	0.0658249	0.0329125	+	0.999458i	$0.489522\pi$
$948$	1.23876	0.0402331
$949$	−8.88213	−0.288326
$950$	−26.4912	−0.859489
$951$	−1.38460	−0.0448989
$952$	−10.8448	−0.351481
$953$	−25.4702	−0.825061	−0.412530	−	0.910944i	$-0.635355\pi$
$953$	−25.4702	−0.825061	−0.412530	+	0.910944i	$0.635355\pi$
$954$	24.0329	0.778095
$955$	7.46550	0.241578
$956$	−16.7337	−0.541208
$957$	4.31995	0.139644
$958$	−17.6285	−0.569552
$959$	9.26501	0.299183
$960$	−0.240264	−0.00775448
$961$	−20.3800	−0.657420
$962$	−6.53605	−0.210731
$963$	−16.1192	−0.519433
$964$	−2.58061	−0.0831159
$965$	12.7557	0.410621
$966$	4.99050	0.160567
$967$	44.9853	1.44663	0.723315	−	0.690518i	$-0.242617\pi$
$967$	44.9853	1.44663	0.723315	+	0.690518i	$0.242617\pi$
$968$	4.40758	0.141665
$969$	−3.62983	−0.116607
$970$	−19.7199	−0.633168
$971$	−0.331546	−0.0106398	−0.00531991	−	0.999986i	$-0.501693\pi$
$971$	−0.331546	−0.0106398	−0.00531991	+	0.999986i	$0.501693\pi$
$972$	5.19779	0.166719
$973$	16.6603	0.534105
$974$	18.3058	0.586555
$975$	4.17835	0.133814
$976$	−12.4628	−0.398924
$977$	−29.2620	−0.936174	−0.468087	−	0.883682i	$-0.655057\pi$
$977$	−29.2620	−0.936174	−0.468087	+	0.883682i	$0.655057\pi$
$978$	2.43037	0.0777145
$979$	−22.8941	−0.731699
$980$	−15.5445	−0.496552
$981$	50.9240	1.62588
$982$	−4.45179	−0.142062
$983$	−42.8250	−1.36590	−0.682952	−	0.730463i	$-0.739304\pi$
$983$	−42.8250	−1.36590	−0.682952	+	0.730463i	$0.739304\pi$
$984$	1.32597	0.0422704
$985$	−23.1988	−0.739177
$986$	−21.0075	−0.669014
$987$	−6.78463	−0.215957
$988$	46.2759	1.47223
$989$	−28.8406	−0.917077
$990$	−9.32926	−0.296503
$991$	−18.5464	−0.589144	−0.294572	−	0.955629i	$-0.595177\pi$
$991$	−18.5464	−0.589144	−0.294572	+	0.955629i	$0.595177\pi$
$992$	3.25883	0.103468
$993$	4.24934	0.134849
$994$	22.9998	0.729509
$995$	8.83668	0.280142
$996$	−2.66562	−0.0844635
$997$	9.57802	0.303339	0.151669	−	0.988431i	$-0.451535\pi$
$997$	9.57802	0.303339	0.151669	+	0.988431i	$0.451535\pi$
$998$	−26.0799	−0.825544
$999$	1.24997	0.0395472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.7	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.7	✓	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.195838 q^{3} +1.00000 q^{4} -1.22685 q^{5} -0.195838 q^{6} +4.43512 q^{7} -1.00000 q^{8} -2.96165 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.195838 q^{3} +1.00000 q^{4} -1.22685 q^{5} -0.195838 q^{6} +4.43512 q^{7} -1.00000 q^{8} -2.96165 q^{9} +1.22685 q^{10} +2.56757 q^{11} +0.195838 q^{12} -6.10492 q^{13} -4.43512 q^{14} -0.240264 q^{15} +1.00000 q^{16} +2.44520 q^{17} +2.96165 q^{18} -7.58010 q^{19} -1.22685 q^{20} +0.868566 q^{21} -2.56757 q^{22} -5.74567 q^{23} -0.195838 q^{24} -3.49484 q^{25} +6.10492 q^{26} -1.16752 q^{27} +4.43512 q^{28} +8.59131 q^{29} +0.240264 q^{30} -3.25883 q^{31} -1.00000 q^{32} +0.502828 q^{33} -2.44520 q^{34} -5.44123 q^{35} -2.96165 q^{36} -1.07062 q^{37} +7.58010 q^{38} -1.19558 q^{39} +1.22685 q^{40} -6.77075 q^{41} -0.868566 q^{42} +5.01953 q^{43} +2.56757 q^{44} +3.63349 q^{45} +5.74567 q^{46} -7.81131 q^{47} +0.195838 q^{48} +12.6703 q^{49} +3.49484 q^{50} +0.478863 q^{51} -6.10492 q^{52} +8.11472 q^{53} +1.16752 q^{54} -3.15002 q^{55} -4.43512 q^{56} -1.48447 q^{57} -8.59131 q^{58} +2.41074 q^{59} -0.240264 q^{60} -12.4628 q^{61} +3.25883 q^{62} -13.1353 q^{63} +1.00000 q^{64} +7.48981 q^{65} -0.502828 q^{66} +0.828938 q^{67} +2.44520 q^{68} -1.12522 q^{69} +5.44123 q^{70} -5.18583 q^{71} +2.96165 q^{72} +1.45491 q^{73} +1.07062 q^{74} -0.684423 q^{75} -7.58010 q^{76} +11.3875 q^{77} +1.19558 q^{78} +6.32544 q^{79} -1.22685 q^{80} +8.65630 q^{81} +6.77075 q^{82} -13.6114 q^{83} +0.868566 q^{84} -2.99989 q^{85} -5.01953 q^{86} +1.68250 q^{87} -2.56757 q^{88} -8.91664 q^{89} -3.63349 q^{90} -27.0761 q^{91} -5.74567 q^{92} -0.638203 q^{93} +7.81131 q^{94} +9.29964 q^{95} -0.195838 q^{96} -16.0736 q^{97} -12.6703 q^{98} -7.60424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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