LMFDB - Embedded newform 667.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.43510$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.43510 q^{2} +1.52354 q^{3} +3.92972 q^{4} +3.49556 q^{5} +3.70997 q^{6} -4.87125 q^{7} +4.69905 q^{8} -0.678832 q^{9} +O(q^{10})$	\(q+2.43510 q^{2} +1.52354 q^{3} +3.92972 q^{4} +3.49556 q^{5} +3.70997 q^{6} -4.87125 q^{7} +4.69905 q^{8} -0.678832 q^{9} +8.51205 q^{10} -1.63115 q^{11} +5.98707 q^{12} -5.07695 q^{13} -11.8620 q^{14} +5.32562 q^{15} +3.58324 q^{16} +7.41068 q^{17} -1.65302 q^{18} +0.289958 q^{19} +13.7366 q^{20} -7.42154 q^{21} -3.97201 q^{22} -1.00000 q^{23} +7.15919 q^{24} +7.21896 q^{25} -12.3629 q^{26} -5.60484 q^{27} -19.1426 q^{28} +1.00000 q^{29} +12.9684 q^{30} -1.20829 q^{31} -0.672566 q^{32} -2.48512 q^{33} +18.0458 q^{34} -17.0278 q^{35} -2.66762 q^{36} +2.03076 q^{37} +0.706078 q^{38} -7.73492 q^{39} +16.4258 q^{40} -10.9339 q^{41} -18.0722 q^{42} +5.66129 q^{43} -6.40996 q^{44} -2.37290 q^{45} -2.43510 q^{46} +5.12682 q^{47} +5.45920 q^{48} +16.7291 q^{49} +17.5789 q^{50} +11.2905 q^{51} -19.9510 q^{52} +7.16900 q^{53} -13.6484 q^{54} -5.70179 q^{55} -22.8903 q^{56} +0.441763 q^{57} +2.43510 q^{58} -0.758039 q^{59} +20.9282 q^{60} +11.5695 q^{61} -2.94232 q^{62} +3.30676 q^{63} -8.80424 q^{64} -17.7468 q^{65} -6.05152 q^{66} +3.60778 q^{67} +29.1219 q^{68} -1.52354 q^{69} -41.4644 q^{70} +8.89620 q^{71} -3.18987 q^{72} -2.62827 q^{73} +4.94510 q^{74} +10.9984 q^{75} +1.13945 q^{76} +7.94575 q^{77} -18.8353 q^{78} -3.77211 q^{79} +12.5254 q^{80} -6.50269 q^{81} -26.6251 q^{82} -10.7050 q^{83} -29.1646 q^{84} +25.9045 q^{85} +13.7858 q^{86} +1.52354 q^{87} -7.66486 q^{88} -4.54315 q^{89} -5.77825 q^{90} +24.7311 q^{91} -3.92972 q^{92} -1.84088 q^{93} +12.4843 q^{94} +1.01357 q^{95} -1.02468 q^{96} -2.62406 q^{97} +40.7371 q^{98} +1.10728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	2.43510	1.72188	0.860938	−	0.508710i	$-0.169877\pi$
$2$	2.43510	1.72188	0.860938	+	0.508710i	$0.169877\pi$
$3$	1.52354	0.879615	0.439808	−	0.898092i	$-0.355047\pi$
$3$	1.52354	0.879615	0.439808	+	0.898092i	$0.355047\pi$
$4$	3.92972	1.96486
$5$	3.49556	1.56326	0.781632	−	0.623740i	$-0.214388\pi$
$5$	3.49556	1.56326	0.781632	+	0.623740i	$0.214388\pi$
$6$	3.70997	1.51459
$7$	−4.87125	−1.84116	−0.920581	−	0.390553i	$-0.872284\pi$
$7$	−4.87125	−1.84116	−0.920581	+	0.390553i	$0.872284\pi$
$8$	4.69905	1.66137
$9$	−0.678832	−0.226277
$10$	8.51205	2.69175
$11$	−1.63115	−0.491810	−0.245905	−	0.969294i	$-0.579085\pi$
$11$	−1.63115	−0.491810	−0.245905	+	0.969294i	$0.579085\pi$
$12$	5.98707	1.72832
$13$	−5.07695	−1.40809	−0.704046	−	0.710155i	$-0.748625\pi$
$13$	−5.07695	−1.40809	−0.704046	+	0.710155i	$0.748625\pi$
$14$	−11.8620	−3.17025
$15$	5.32562	1.37507
$16$	3.58324	0.895809
$17$	7.41068	1.79735	0.898677	−	0.438611i	$-0.144529\pi$
$17$	7.41068	1.79735	0.898677	+	0.438611i	$0.144529\pi$
$18$	−1.65302	−0.389621
$19$	0.289958	0.0665210	0.0332605	−	0.999447i	$-0.489411\pi$
$19$	0.289958	0.0665210	0.0332605	+	0.999447i	$0.489411\pi$
$20$	13.7366	3.07159
$21$	−7.42154	−1.61951
$22$	−3.97201	−0.846836
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	7.15919	1.46136
$25$	7.21896	1.44379
$26$	−12.3629	−2.42456
$27$	−5.60484	−1.07865
$28$	−19.1426	−3.61762
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	12.9684	2.36770
$31$	−1.20829	−0.217016	−0.108508	−	0.994096i	$-0.534607\pi$
$31$	−1.20829	−0.217016	−0.108508	+	0.994096i	$0.534607\pi$
$32$	−0.672566	−0.118894
$33$	−2.48512	−0.432604
$34$	18.0458	3.09482
$35$	−17.0278	−2.87822
$36$	−2.66762	−0.444603
$37$	2.03076	0.333855	0.166927	−	0.985969i	$-0.446615\pi$
$37$	2.03076	0.333855	0.166927	+	0.985969i	$0.446615\pi$
$38$	0.706078	0.114541
$39$	−7.73492	−1.23858
$40$	16.4258	2.59715
$41$	−10.9339	−1.70758	−0.853792	−	0.520615i	$-0.825703\pi$
$41$	−10.9339	−1.70758	−0.853792	+	0.520615i	$0.825703\pi$
$42$	−18.0722	−2.78860
$43$	5.66129	0.863339	0.431670	−	0.902032i	$-0.357925\pi$
$43$	5.66129	0.863339	0.431670	+	0.902032i	$0.357925\pi$
$44$	−6.40996	−0.966337
$45$	−2.37290	−0.353731
$46$	−2.43510	−0.359036
$47$	5.12682	0.747823	0.373912	−	0.927464i	$-0.378016\pi$
$47$	5.12682	0.747823	0.373912	+	0.927464i	$0.378016\pi$
$48$	5.45920	0.787967
$49$	16.7291	2.38987
$50$	17.5789	2.48603
$51$	11.2905	1.58098
$52$	−19.9510	−2.76670
$53$	7.16900	0.984737	0.492369	−	0.870387i	$-0.336131\pi$
$53$	7.16900	0.984737	0.492369	+	0.870387i	$0.336131\pi$
$54$	−13.6484	−1.85731
$55$	−5.70179	−0.768829
$56$	−22.8903	−3.05884
$57$	0.441763	0.0585129
$58$	2.43510	0.319744
$59$	−0.758039	−0.0986883	−0.0493441	−	0.998782i	$-0.515713\pi$
$59$	−0.758039	−0.0986883	−0.0493441	+	0.998782i	$0.515713\pi$
$60$	20.9282	2.70182
$61$	11.5695	1.48133	0.740663	−	0.671876i	$-0.234511\pi$
$61$	11.5695	1.48133	0.740663	+	0.671876i	$0.234511\pi$
$62$	−2.94232	−0.373675
$63$	3.30676	0.416613
$64$	−8.80424	−1.10053
$65$	−17.7468	−2.20122
$66$	−6.05152	−0.744890
$67$	3.60778	0.440761	0.220380	−	0.975414i	$-0.429270\pi$
$67$	3.60778	0.440761	0.220380	+	0.975414i	$0.429270\pi$
$68$	29.1219	3.53155
$69$	−1.52354	−0.183412
$70$	−41.4644	−4.95594
$71$	8.89620	1.05579	0.527893	−	0.849311i	$-0.322982\pi$
$71$	8.89620	1.05579	0.527893	+	0.849311i	$0.322982\pi$
$72$	−3.18987	−0.375929
$73$	−2.62827	−0.307616	−0.153808	−	0.988101i	$-0.549154\pi$
$73$	−2.62827	−0.307616	−0.153808	+	0.988101i	$0.549154\pi$
$74$	4.94510	0.574857
$75$	10.9984	1.26998
$76$	1.13945	0.130704
$77$	7.94575	0.905502
$78$	−18.8353	−2.13268
$79$	−3.77211	−0.424395	−0.212198	−	0.977227i	$-0.568062\pi$
$79$	−3.77211	−0.424395	−0.212198	+	0.977227i	$0.568062\pi$
$80$	12.5254	1.40039
$81$	−6.50269	−0.722521
$82$	−26.6251	−2.94025
$83$	−10.7050	−1.17502	−0.587510	−	0.809217i	$-0.699892\pi$
$83$	−10.7050	−1.17502	−0.587510	+	0.809217i	$0.699892\pi$
$84$	−29.1646	−3.18211
$85$	25.9045	2.80974
$86$	13.7858	1.48656
$87$	1.52354	0.163340
$88$	−7.66486	−0.817077
$89$	−4.54315	−0.481573	−0.240786	−	0.970578i	$-0.577405\pi$
$89$	−4.54315	−0.481573	−0.240786	+	0.970578i	$0.577405\pi$
$90$	−5.77825	−0.609081
$91$	24.7311	2.59252
$92$	−3.92972	−0.409701
$93$	−1.84088	−0.190890
$94$	12.4843	1.28766
$95$	1.01357	0.103990
$96$	−1.02468	−0.104581
$97$	−2.62406	−0.266433	−0.133217	−	0.991087i	$-0.542531\pi$
$97$	−2.62406	−0.266433	−0.133217	+	0.991087i	$0.542531\pi$
$98$	40.7371	4.11507
$99$	1.10728	0.111285
$100$	28.3685	2.83685
$101$	18.5441	1.84521	0.922604	−	0.385748i	$-0.126057\pi$
$101$	18.5441	1.84521	0.922604	+	0.385748i	$0.126057\pi$
$102$	27.4934	2.72225
$103$	6.66490	0.656712	0.328356	−	0.944554i	$-0.393505\pi$
$103$	6.66490	0.656712	0.328356	+	0.944554i	$0.393505\pi$
$104$	−23.8568	−2.33936
$105$	−25.9425	−2.53173
$106$	17.4572	1.69560
$107$	−13.0781	−1.26431	−0.632156	−	0.774841i	$-0.717830\pi$
$107$	−13.0781	−1.26431	−0.632156	+	0.774841i	$0.717830\pi$
$108$	−22.0254	−2.11940
$109$	13.3526	1.27895	0.639476	−	0.768811i	$-0.279152\pi$
$109$	13.3526	1.27895	0.639476	+	0.768811i	$0.279152\pi$
$110$	−13.8844	−1.32383
$111$	3.09394	0.293664
$112$	−17.4549	−1.64933
$113$	4.16536	0.391844	0.195922	−	0.980619i	$-0.437230\pi$
$113$	4.16536	0.391844	0.195922	+	0.980619i	$0.437230\pi$
$114$	1.07574	0.100752
$115$	−3.49556	−0.325963
$116$	3.92972	0.364865
$117$	3.44639	0.318619
$118$	−1.84590	−0.169929
$119$	−36.0993	−3.30922
$120$	25.0254	2.28449
$121$	−8.33935	−0.758123
$122$	28.1730	2.55066
$123$	−16.6582	−1.50202
$124$	−4.74825	−0.426405
$125$	7.75651	0.693763
$126$	8.05230	0.717356
$127$	−10.0964	−0.895909	−0.447954	−	0.894056i	$-0.647847\pi$
$127$	−10.0964	−0.895909	−0.447954	+	0.894056i	$0.647847\pi$
$128$	−20.0941	−1.77608
$129$	8.62520	0.759406
$130$	−43.2152	−3.79023
$131$	−20.4223	−1.78430	−0.892151	−	0.451736i	$-0.850805\pi$
$131$	−20.4223	−1.78430	−0.892151	+	0.451736i	$0.850805\pi$
$132$	−9.76581	−0.850005
$133$	−1.41246	−0.122476
$134$	8.78531	0.758935
$135$	−19.5921	−1.68622
$136$	34.8232	2.98606
$137$	−10.9157	−0.932591	−0.466296	−	0.884629i	$-0.654412\pi$
$137$	−10.9157	−0.932591	−0.466296	+	0.884629i	$0.654412\pi$
$138$	−3.70997	−0.315814
$139$	−9.60677	−0.814836	−0.407418	−	0.913242i	$-0.633571\pi$
$139$	−9.60677	−0.814836	−0.407418	+	0.913242i	$0.633571\pi$
$140$	−66.9143	−5.65529
$141$	7.81090	0.657797
$142$	21.6632	1.81793
$143$	8.28126	0.692514
$144$	−2.43241	−0.202701
$145$	3.49556	0.290291
$146$	−6.40011	−0.529677
$147$	25.4875	2.10217
$148$	7.98031	0.655977
$149$	−3.92991	−0.321950	−0.160975	−	0.986958i	$-0.551464\pi$
$149$	−3.92991	−0.321950	−0.160975	+	0.986958i	$0.551464\pi$
$150$	26.7821	2.18675
$151$	9.79351	0.796985	0.398492	−	0.917172i	$-0.369534\pi$
$151$	9.79351	0.796985	0.398492	+	0.917172i	$0.369534\pi$
$152$	1.36253	0.110516
$153$	−5.03060	−0.406700
$154$	19.3487	1.55916
$155$	−4.22367	−0.339253
$156$	−30.3960	−2.43363
$157$	−1.60539	−0.128124	−0.0640621	−	0.997946i	$-0.520406\pi$
$157$	−1.60539	−0.128124	−0.0640621	+	0.997946i	$0.520406\pi$
$158$	−9.18546	−0.730756
$159$	10.9222	0.866190
$160$	−2.35100	−0.185863
$161$	4.87125	0.383909
$162$	−15.8347	−1.24409
$163$	−15.5495	−1.21793	−0.608964	−	0.793198i	$-0.708414\pi$
$163$	−15.5495	−1.21793	−0.608964	+	0.793198i	$0.708414\pi$
$164$	−42.9670	−3.35516
$165$	−8.68689	−0.676274
$166$	−26.0676	−2.02324
$167$	0.764987	0.0591965	0.0295982	−	0.999562i	$-0.490577\pi$
$167$	0.764987	0.0591965	0.0295982	+	0.999562i	$0.490577\pi$
$168$	−34.8742	−2.69060
$169$	12.7754	0.982722
$170$	63.0801	4.83802
$171$	−0.196833	−0.0150522
$172$	22.2473	1.69634
$173$	2.00062	0.152104	0.0760521	−	0.997104i	$-0.475768\pi$
$173$	2.00062	0.152104	0.0760521	+	0.997104i	$0.475768\pi$
$174$	3.70997	0.281252
$175$	−35.1654	−2.65825
$176$	−5.84480	−0.440568
$177$	−1.15490	−0.0868077
$178$	−11.0630	−0.829209
$179$	20.3309	1.51961	0.759803	−	0.650154i	$-0.225296\pi$
$179$	20.3309	1.51961	0.759803	+	0.650154i	$0.225296\pi$
$180$	−9.32482	−0.695031
$181$	5.46867	0.406483	0.203242	−	0.979129i	$-0.434852\pi$
$181$	5.46867	0.406483	0.203242	+	0.979129i	$0.434852\pi$
$182$	60.2227	4.46401
$183$	17.6266	1.30300
$184$	−4.69905	−0.346419
$185$	7.09865	0.521903
$186$	−4.48273	−0.328690
$187$	−12.0879	−0.883957
$188$	20.1469	1.46937
$189$	27.3026	1.98597
$190$	2.46814	0.179058
$191$	6.82852	0.494095	0.247047	−	0.969003i	$-0.420540\pi$
$191$	6.82852	0.494095	0.247047	+	0.969003i	$0.420540\pi$
$192$	−13.4136	−0.968043
$193$	19.2138	1.38304	0.691518	−	0.722359i	$-0.256942\pi$
$193$	19.2138	1.38304	0.691518	+	0.722359i	$0.256942\pi$
$194$	−6.38986	−0.458765
$195$	−27.0379	−1.93622
$196$	65.7407	4.69576
$197$	−10.5750	−0.753440	−0.376720	−	0.926327i	$-0.622948\pi$
$197$	−10.5750	−0.753440	−0.376720	+	0.926327i	$0.622948\pi$
$198$	2.69633	0.191620
$199$	−0.0141811	−0.00100527	−0.000502634	−	1.00000i	$-0.500160\pi$
$199$	−0.0141811	−0.00100527	−0.000502634		1.00000i	$0.500160\pi$
$200$	33.9223	2.39867
$201$	5.49659	0.387700
$202$	45.1568	3.17722
$203$	−4.87125	−0.341895
$204$	44.3683	3.10640
$205$	−38.2200	−2.66940
$206$	16.2297	1.13078
$207$	0.678832	0.0471821
$208$	−18.1919	−1.26138
$209$	−0.472966	−0.0327157
$210$	−63.1725	−4.35932
$211$	−8.93797	−0.615316	−0.307658	−	0.951497i	$-0.599545\pi$
$211$	−8.93797	−0.615316	−0.307658	+	0.951497i	$0.599545\pi$
$212$	28.1721	1.93487
$213$	13.5537	0.928685
$214$	−31.8466	−2.17699
$215$	19.7894	1.34963
$216$	−26.3374	−1.79204
$217$	5.88591	0.399561
$218$	32.5150	2.20220
$219$	−4.00427	−0.270584
$220$	−22.4064	−1.51064
$221$	−37.6236	−2.53084
$222$	7.53405	0.505653
$223$	22.4912	1.50612	0.753062	−	0.657950i	$-0.228576\pi$
$223$	22.4912	1.50612	0.753062	+	0.657950i	$0.228576\pi$
$224$	3.27624	0.218903
$225$	−4.90046	−0.326697
$226$	10.1431	0.674707
$227$	12.6937	0.842510	0.421255	−	0.906942i	$-0.361590\pi$
$227$	12.6937	0.842510	0.421255	+	0.906942i	$0.361590\pi$
$228$	1.73600	0.114970
$229$	−19.9279	−1.31687	−0.658437	−	0.752636i	$-0.728782\pi$
$229$	−19.9279	−1.31687	−0.658437	+	0.752636i	$0.728782\pi$
$230$	−8.51205	−0.561268
$231$	12.1056	0.796493
$232$	4.69905	0.308508
$233$	15.8089	1.03568	0.517838	−	0.855479i	$-0.326737\pi$
$233$	15.8089	1.03568	0.517838	+	0.855479i	$0.326737\pi$
$234$	8.39231	0.548623
$235$	17.9211	1.16904
$236$	−2.97888	−0.193908
$237$	−5.74695	−0.373304
$238$	−87.9055	−5.69807
$239$	−28.5189	−1.84474	−0.922368	−	0.386313i	$-0.873748\pi$
$239$	−28.5189	−1.84474	−0.922368	+	0.386313i	$0.873748\pi$
$240$	19.0830	1.23180
$241$	−10.4957	−0.676087	−0.338044	−	0.941130i	$-0.609765\pi$
$241$	−10.4957	−0.676087	−0.338044	+	0.941130i	$0.609765\pi$
$242$	−20.3072	−1.30539
$243$	6.90742	0.443111
$244$	45.4650	2.91060
$245$	58.4777	3.73600
$246$	−40.5643	−2.58629
$247$	−1.47210	−0.0936677
$248$	−5.67783	−0.360543
$249$	−16.3094	−1.03357
$250$	18.8879	1.19457
$251$	0.515831	0.0325589	0.0162795	−	0.999867i	$-0.494818\pi$
$251$	0.515831	0.0325589	0.0162795	+	0.999867i	$0.494818\pi$
$252$	12.9946	0.818585
$253$	1.63115	0.102550
$254$	−24.5857	−1.54264
$255$	39.4665	2.47149
$256$	−31.3226	−1.95766
$257$	11.5127	0.718142	0.359071	−	0.933310i	$-0.383094\pi$
$257$	11.5127	0.718142	0.359071	+	0.933310i	$0.383094\pi$
$258$	21.0032	1.30760
$259$	−9.89234	−0.614680
$260$	−69.7398	−4.32508
$261$	−0.678832	−0.0420186
$262$	−49.7303	−3.07235
$263$	−3.77657	−0.232873	−0.116437	−	0.993198i	$-0.537147\pi$
$263$	−3.77657	−0.232873	−0.116437	+	0.993198i	$0.537147\pi$
$264$	−11.6777	−0.718713
$265$	25.0597	1.53940
$266$	−3.43949	−0.210888
$267$	−6.92166	−0.423599
$268$	14.1776	0.866032
$269$	−13.0119	−0.793348	−0.396674	−	0.917960i	$-0.629836\pi$
$269$	−13.0119	−0.793348	−0.396674	+	0.917960i	$0.629836\pi$
$270$	−47.7087	−2.90346
$271$	−23.5566	−1.43096	−0.715480	−	0.698633i	$-0.753792\pi$
$271$	−23.5566	−1.43096	−0.715480	+	0.698633i	$0.753792\pi$
$272$	26.5542	1.61009
$273$	37.6788	2.28042
$274$	−26.5808	−1.60581
$275$	−11.7752	−0.710072
$276$	−5.98707	−0.360379
$277$	8.30189	0.498812	0.249406	−	0.968399i	$-0.419765\pi$
$277$	8.30189	0.498812	0.249406	+	0.968399i	$0.419765\pi$
$278$	−23.3935	−1.40305
$279$	0.820228	0.0491058
$280$	−80.0144	−4.78178
$281$	−24.5091	−1.46209	−0.731046	−	0.682328i	$-0.760968\pi$
$281$	−24.5091	−1.46209	−0.731046	+	0.682328i	$0.760968\pi$
$282$	19.0203	1.13264
$283$	16.8683	1.00271	0.501357	−	0.865240i	$-0.332834\pi$
$283$	16.8683	1.00271	0.501357	+	0.865240i	$0.332834\pi$
$284$	34.9596	2.07447
$285$	1.54421	0.0914711
$286$	20.1657	1.19242
$287$	53.2617	3.14394
$288$	0.456559	0.0269030
$289$	37.9182	2.23048
$290$	8.51205	0.499845
$291$	−3.99786	−0.234359
$292$	−10.3284	−0.604422
$293$	9.99230	0.583756	0.291878	−	0.956456i	$-0.405720\pi$
$293$	9.99230	0.583756	0.291878	+	0.956456i	$0.405720\pi$
$294$	62.0645	3.61968
$295$	−2.64977	−0.154276
$296$	9.54264	0.554655
$297$	9.14234	0.530492
$298$	−9.56972	−0.554359
$299$	5.07695	0.293607
$300$	43.2204	2.49533
$301$	−27.5776	−1.58955
$302$	23.8482	1.37231
$303$	28.2527	1.62307
$304$	1.03899	0.0595901
$305$	40.4420	2.31570
$306$	−12.2500	−0.700288
$307$	−10.3287	−0.589488	−0.294744	−	0.955576i	$-0.595234\pi$
$307$	−10.3287	−0.589488	−0.294744	+	0.955576i	$0.595234\pi$
$308$	31.2245	1.77918
$309$	10.1542	0.577654
$310$	−10.2851	−0.584152
$311$	21.5343	1.22110	0.610550	−	0.791978i	$-0.290949\pi$
$311$	21.5343	1.22110	0.610550	+	0.791978i	$0.290949\pi$
$312$	−36.3468	−2.05773
$313$	−1.23924	−0.0700459	−0.0350229	−	0.999387i	$-0.511150\pi$
$313$	−1.23924	−0.0700459	−0.0350229	+	0.999387i	$0.511150\pi$
$314$	−3.90929	−0.220614
$315$	11.5590	0.651275
$316$	−14.8233	−0.833876
$317$	−24.4749	−1.37465	−0.687325	−	0.726350i	$-0.741215\pi$
$317$	−24.4749	−1.37465	−0.687325	+	0.726350i	$0.741215\pi$
$318$	26.5968	1.49147
$319$	−1.63115	−0.0913269
$320$	−30.7758	−1.72042
$321$	−19.9250	−1.11211
$322$	11.8620	0.661043
$323$	2.14879	0.119562
$324$	−25.5537	−1.41965
$325$	−36.6503	−2.03299
$326$	−37.8645	−2.09712
$327$	20.3433	1.12498
$328$	−51.3788	−2.83692
$329$	−24.9740	−1.37686
$330$	−21.1535	−1.16446
$331$	5.08020	0.279233	0.139616	−	0.990206i	$-0.455413\pi$
$331$	5.08020	0.279233	0.139616	+	0.990206i	$0.455413\pi$
$332$	−42.0674	−2.30875
$333$	−1.37854	−0.0755437
$334$	1.86282	0.101929
$335$	12.6112	0.689025
$336$	−26.5931	−1.45077
$337$	−30.1891	−1.64450	−0.822252	−	0.569124i	$-0.807282\pi$
$337$	−30.1891	−1.64450	−0.822252	+	0.569124i	$0.807282\pi$
$338$	31.1094	1.69213
$339$	6.34608	0.344672
$340$	101.797	5.52074
$341$	1.97091	0.106731
$342$	−0.479308	−0.0259180
$343$	−47.3930	−2.55898
$344$	26.6027	1.43432
$345$	−5.32562	−0.286722
$346$	4.87171	0.261905
$347$	−15.1414	−0.812831	−0.406416	−	0.913688i	$-0.633221\pi$
$347$	−15.1414	−0.812831	−0.406416	+	0.913688i	$0.633221\pi$
$348$	5.98707	0.320941
$349$	25.2696	1.35265	0.676325	−	0.736603i	$-0.263571\pi$
$349$	25.2696	1.35265	0.676325	+	0.736603i	$0.263571\pi$
$350$	−85.6313	−4.57718
$351$	28.4555	1.51884
$352$	1.09706	0.0584733
$353$	−21.9355	−1.16751	−0.583755	−	0.811930i	$-0.698417\pi$
$353$	−21.9355	−1.16751	−0.583755	+	0.811930i	$0.698417\pi$
$354$	−2.81230	−0.149472
$355$	31.0972	1.65047
$356$	−17.8533	−0.946222
$357$	−54.9987	−2.91084
$358$	49.5079	2.61657
$359$	−11.5228	−0.608148	−0.304074	−	0.952648i	$-0.598347\pi$
$359$	−11.5228	−0.608148	−0.304074	+	0.952648i	$0.598347\pi$
$360$	−11.1504	−0.587676
$361$	−18.9159	−0.995575
$362$	13.3168	0.699914
$363$	−12.7053	−0.666856
$364$	97.1862	5.09394
$365$	−9.18729	−0.480885
$366$	42.9226	2.24360
$367$	30.2955	1.58141	0.790707	−	0.612195i	$-0.209713\pi$
$367$	30.2955	1.58141	0.790707	+	0.612195i	$0.209713\pi$
$368$	−3.58324	−0.186789
$369$	7.42226	0.386387
$370$	17.2859	0.898652
$371$	−34.9220	−1.81306
$372$	−7.23414	−0.375073
$373$	12.2767	0.635664	0.317832	−	0.948147i	$-0.397045\pi$
$373$	12.2767	0.635664	0.317832	+	0.948147i	$0.397045\pi$
$374$	−29.4353	−1.52207
$375$	11.8173	0.610245
$376$	24.0912	1.24241
$377$	−5.07695	−0.261476
$378$	66.4846	3.41960
$379$	−10.3849	−0.533438	−0.266719	−	0.963774i	$-0.585940\pi$
$379$	−10.3849	−0.533438	−0.266719	+	0.963774i	$0.585940\pi$
$380$	3.98303	0.204325
$381$	−15.3822	−0.788055
$382$	16.6281	0.850770
$383$	22.4826	1.14880	0.574402	−	0.818573i	$-0.305234\pi$
$383$	22.4826	1.14880	0.574402	+	0.818573i	$0.305234\pi$
$384$	−30.6141	−1.56227
$385$	27.7749	1.41554
$386$	46.7874	2.38142
$387$	−3.84307	−0.195354
$388$	−10.3118	−0.523504
$389$	−9.81702	−0.497743	−0.248871	−	0.968537i	$-0.580060\pi$
$389$	−9.81702	−0.497743	−0.248871	+	0.968537i	$0.580060\pi$
$390$	−65.8400	−3.33394
$391$	−7.41068	−0.374774
$392$	78.6110	3.97046
$393$	−31.1141	−1.56950
$394$	−25.7513	−1.29733
$395$	−13.1856	−0.663441
$396$	4.35128	0.218660
$397$	1.40591	0.0705608	0.0352804	−	0.999377i	$-0.488768\pi$
$397$	1.40591	0.0705608	0.0352804	+	0.999377i	$0.488768\pi$
$398$	−0.0345323	−0.00173095
$399$	−2.15194	−0.107732
$400$	25.8672	1.29336
$401$	−12.9350	−0.645943	−0.322971	−	0.946409i	$-0.604682\pi$
$401$	−12.9350	−0.645943	−0.322971	+	0.946409i	$0.604682\pi$
$402$	13.3848	0.667571
$403$	6.13444	0.305578
$404$	72.8731	3.62557
$405$	−22.7306	−1.12949
$406$	−11.8620	−0.588701
$407$	−3.31247	−0.164193
$408$	53.0545	2.62659
$409$	25.6740	1.26950	0.634748	−	0.772720i	$-0.281104\pi$
$409$	25.6740	1.26950	0.634748	+	0.772720i	$0.281104\pi$
$410$	−93.0696	−4.59638
$411$	−16.6305	−0.820321
$412$	26.1912	1.29035
$413$	3.69260	0.181701
$414$	1.65302	0.0812417
$415$	−37.4198	−1.83687
$416$	3.41458	0.167414
$417$	−14.6363	−0.716742
$418$	−1.15172	−0.0563324
$419$	2.80144	0.136859	0.0684297	−	0.997656i	$-0.478201\pi$
$419$	2.80144	0.136859	0.0684297	+	0.997656i	$0.478201\pi$
$420$	−101.947	−4.97448
$421$	23.0333	1.12258	0.561288	−	0.827621i	$-0.310306\pi$
$421$	23.0333	1.12258	0.561288	+	0.827621i	$0.310306\pi$
$422$	−21.7649	−1.05950
$423$	−3.48025	−0.169215
$424$	33.6875	1.63601
$425$	53.4974	2.59501
$426$	33.0046	1.59908
$427$	−56.3581	−2.72736
$428$	−51.3934	−2.48419
$429$	12.6168	0.609146
$430$	48.1892	2.32389
$431$	11.6913	0.563150	0.281575	−	0.959539i	$-0.409143\pi$
$431$	11.6913	0.563150	0.281575	+	0.959539i	$0.409143\pi$
$432$	−20.0835	−0.966266
$433$	9.89512	0.475529	0.237765	−	0.971323i	$-0.423585\pi$
$433$	9.89512	0.475529	0.237765	+	0.971323i	$0.423585\pi$
$434$	14.3328	0.687995
$435$	5.32562	0.255344
$436$	52.4721	2.51296
$437$	−0.289958	−0.0138706
$438$	−9.75081	−0.465912
$439$	−25.3217	−1.20854	−0.604269	−	0.796780i	$-0.706535\pi$
$439$	−25.3217	−1.20854	−0.604269	+	0.796780i	$0.706535\pi$
$440$	−26.7930	−1.27731
$441$	−11.3563	−0.540774
$442$	−91.6174	−4.35779
$443$	35.7692	1.69944	0.849722	−	0.527230i	$-0.176769\pi$
$443$	35.7692	1.69944	0.849722	+	0.527230i	$0.176769\pi$
$444$	12.1583	0.577007
$445$	−15.8809	−0.752825
$446$	54.7684	2.59336
$447$	−5.98736	−0.283193
$448$	42.8877	2.02625
$449$	22.9074	1.08106	0.540532	−	0.841323i	$-0.318223\pi$
$449$	22.9074	1.08106	0.540532	+	0.841323i	$0.318223\pi$
$450$	−11.9331	−0.562532
$451$	17.8348	0.839807
$452$	16.3687	0.769918
$453$	14.9208	0.701040
$454$	30.9104	1.45070
$455$	86.4491	4.05280
$456$	2.07587	0.0972113
$457$	16.8884	0.790005	0.395002	−	0.918680i	$-0.370744\pi$
$457$	16.8884	0.790005	0.395002	+	0.918680i	$0.370744\pi$
$458$	−48.5265	−2.26749
$459$	−41.5357	−1.93872
$460$	−13.7366	−0.640471
$461$	28.9020	1.34610	0.673050	−	0.739597i	$-0.264984\pi$
$461$	28.9020	1.34610	0.673050	+	0.739597i	$0.264984\pi$
$462$	29.4785	1.37146
$463$	−12.8535	−0.597351	−0.298675	−	0.954355i	$-0.596545\pi$
$463$	−12.8535	−0.597351	−0.298675	+	0.954355i	$0.596545\pi$
$464$	3.58324	0.166348
$465$	−6.43492	−0.298412
$466$	38.4963	1.78330
$467$	−7.93973	−0.367407	−0.183703	−	0.982982i	$-0.558809\pi$
$467$	−7.93973	−0.367407	−0.183703	+	0.982982i	$0.558809\pi$
$468$	13.5433	0.626041
$469$	−17.5744	−0.811511
$470$	43.6397	2.01295
$471$	−2.44588	−0.112700
$472$	−3.56207	−0.163957
$473$	−9.23442	−0.424599
$474$	−13.9944	−0.642784
$475$	2.09320	0.0960425
$476$	−141.860	−6.50215
$477$	−4.86654	−0.222824
$478$	−69.4464	−3.17641
$479$	32.7143	1.49475	0.747377	−	0.664400i	$-0.231313\pi$
$479$	32.7143	1.49475	0.747377	+	0.664400i	$0.231313\pi$
$480$	−3.58183	−0.163488
$481$	−10.3101	−0.470098
$482$	−25.5581	−1.16414
$483$	7.42154	0.337692
$484$	−32.7713	−1.48960
$485$	−9.17258	−0.416505
$486$	16.8203	0.762983
$487$	6.76700	0.306642	0.153321	−	0.988176i	$-0.451003\pi$
$487$	6.76700	0.306642	0.153321	+	0.988176i	$0.451003\pi$
$488$	54.3658	2.46103
$489$	−23.6902	−1.07131
$490$	142.399	6.43294
$491$	−14.2398	−0.642634	−0.321317	−	0.946972i	$-0.604126\pi$
$491$	−14.2398	−0.642634	−0.321317	+	0.946972i	$0.604126\pi$
$492$	−65.4619	−2.95125
$493$	7.41068	0.333760
$494$	−3.58472	−0.161284
$495$	3.87055	0.173968
$496$	−4.32960	−0.194405
$497$	−43.3357	−1.94387
$498$	−39.7150	−1.77967
$499$	−5.53838	−0.247932	−0.123966	−	0.992286i	$-0.539561\pi$
$499$	−5.53838	−0.247932	−0.123966	+	0.992286i	$0.539561\pi$
$500$	30.4809	1.36315
$501$	1.16549	0.0520701
$502$	1.25610	0.0560625
$503$	35.3182	1.57476	0.787381	−	0.616466i	$-0.211436\pi$
$503$	35.3182	1.57476	0.787381	+	0.616466i	$0.211436\pi$
$504$	15.5386	0.692146
$505$	64.8221	2.88455
$506$	3.97201	0.176578
$507$	19.4638	0.864417
$508$	−39.6759	−1.76033
$509$	−24.8206	−1.10015	−0.550076	−	0.835114i	$-0.685401\pi$
$509$	−24.8206	−1.10015	−0.550076	+	0.835114i	$0.685401\pi$
$510$	96.1049	4.25560
$511$	12.8030	0.566371
$512$	−36.0856	−1.59477
$513$	−1.62517	−0.0717530
$514$	28.0346	1.23655
$515$	23.2976	1.02661
$516$	33.8946	1.49213
$517$	−8.36261	−0.367787
$518$	−24.0889	−1.05840
$519$	3.04802	0.133793
$520$	−83.3931	−3.65703
$521$	25.3463	1.11044	0.555221	−	0.831703i	$-0.312634\pi$
$521$	25.3463	1.11044	0.555221	+	0.831703i	$0.312634\pi$
$522$	−1.65302	−0.0723509
$523$	−1.12658	−0.0492617	−0.0246309	−	0.999697i	$-0.507841\pi$
$523$	−1.12658	−0.0492617	−0.0246309	+	0.999697i	$0.507841\pi$
$524$	−80.2538	−3.50590
$525$	−53.5758	−2.33824
$526$	−9.19633	−0.400979
$527$	−8.95428	−0.390054
$528$	−8.90477	−0.387530
$529$	1.00000	0.0434783
$530$	61.0228	2.65066
$531$	0.514581	0.0223309
$532$	−5.55057	−0.240648
$533$	55.5107	2.40443
$534$	−16.8549	−0.729385
$535$	−45.7154	−1.97645
$536$	16.9532	0.732265
$537$	30.9750	1.33667
$538$	−31.6852	−1.36605
$539$	−27.2877	−1.17536
$540$	−76.9913	−3.31318
$541$	−37.1099	−1.59548	−0.797740	−	0.603001i	$-0.793972\pi$
$541$	−37.1099	−1.59548	−0.797740	+	0.603001i	$0.793972\pi$
$542$	−57.3626	−2.46394
$543$	8.33173	0.357549
$544$	−4.98417	−0.213695
$545$	46.6750	1.99934
$546$	91.7516	3.92661
$547$	4.86456	0.207993	0.103997	−	0.994578i	$-0.466837\pi$
$547$	4.86456	0.207993	0.103997	+	0.994578i	$0.466837\pi$
$548$	−42.8956	−1.83241
$549$	−7.85376	−0.335190
$550$	−28.6738	−1.22266
$551$	0.289958	0.0123526
$552$	−7.15919	−0.304715
$553$	18.3749	0.781380
$554$	20.2159	0.858893
$555$	10.8151	0.459074
$556$	−37.7519	−1.60104
$557$	−23.4839	−0.995043	−0.497521	−	0.867452i	$-0.665756\pi$
$557$	−23.4839	−0.995043	−0.497521	+	0.867452i	$0.665756\pi$
$558$	1.99734	0.0845540
$559$	−28.7421	−1.21566
$560$	−61.0145	−2.57833
$561$	−18.4164	−0.777542
$562$	−59.6822	−2.51754
$563$	−42.1697	−1.77724	−0.888620	−	0.458645i	$-0.848335\pi$
$563$	−42.1697	−1.77724	−0.888620	+	0.458645i	$0.848335\pi$
$564$	30.6946	1.29248
$565$	14.5603	0.612555
$566$	41.0759	1.72655
$567$	31.6763	1.33028
$568$	41.8037	1.75405
$569$	−2.21802	−0.0929842	−0.0464921	−	0.998919i	$-0.514804\pi$
$569$	−2.21802	−0.0929842	−0.0464921	+	0.998919i	$0.514804\pi$
$570$	3.76031	0.157502
$571$	19.4117	0.812353	0.406177	−	0.913795i	$-0.366862\pi$
$571$	19.4117	0.812353	0.406177	+	0.913795i	$0.366862\pi$
$572$	32.5430	1.36069
$573$	10.4035	0.434613
$574$	129.698	5.41347
$575$	−7.21896	−0.301051
$576$	5.97659	0.249025
$577$	−1.65159	−0.0687565	−0.0343782	−	0.999409i	$-0.510945\pi$
$577$	−1.65159	−0.0687565	−0.0343782	+	0.999409i	$0.510945\pi$
$578$	92.3346	3.84061
$579$	29.2729	1.21654
$580$	13.7366	0.570380
$581$	52.1465	2.16340
$582$	−9.73520	−0.403537
$583$	−11.6937	−0.484304
$584$	−12.3504	−0.511063
$585$	12.0471	0.498085
$586$	24.3322	1.00516
$587$	−17.7277	−0.731698	−0.365849	−	0.930674i	$-0.619221\pi$
$587$	−17.7277	−0.731698	−0.365849	+	0.930674i	$0.619221\pi$
$588$	100.158	4.13047
$589$	−0.350355	−0.0144361
$590$	−6.45246	−0.265644
$591$	−16.1115	−0.662737
$592$	7.27669	0.299070
$593$	−1.20316	−0.0494078	−0.0247039	−	0.999695i	$-0.507864\pi$
$593$	−1.20316	−0.0494078	−0.0247039	+	0.999695i	$0.507864\pi$
$594$	22.2625	0.913442
$595$	−126.187	−5.17318
$596$	−15.4434	−0.632587
$597$	−0.0216054	−0.000884249 0
$598$	12.3629	0.505556
$599$	−36.3309	−1.48444	−0.742221	−	0.670155i	$-0.766227\pi$
$599$	−36.3309	−1.48444	−0.742221	+	0.670155i	$0.766227\pi$
$600$	51.6819	2.10990
$601$	−2.62167	−0.106940	−0.0534701	−	0.998569i	$-0.517028\pi$
$601$	−2.62167	−0.106940	−0.0534701	+	0.998569i	$0.517028\pi$
$602$	−67.1543	−2.73700
$603$	−2.44908	−0.0997341
$604$	38.4857	1.56596
$605$	−29.1507	−1.18515
$606$	68.7981	2.79473
$607$	−6.15983	−0.250020	−0.125010	−	0.992155i	$-0.539896\pi$
$607$	−6.15983	−0.250020	−0.125010	+	0.992155i	$0.539896\pi$
$608$	−0.195016	−0.00790895
$609$	−7.42154	−0.300736
$610$	98.4804	3.98735
$611$	−26.0286	−1.05300
$612$	−19.7688	−0.799108
$613$	18.2042	0.735259	0.367630	−	0.929972i	$-0.380169\pi$
$613$	18.2042	0.735259	0.367630	+	0.929972i	$0.380169\pi$
$614$	−25.1513	−1.01502
$615$	−58.2297	−2.34805
$616$	37.3375	1.50437
$617$	7.55796	0.304272	0.152136	−	0.988360i	$-0.451385\pi$
$617$	7.55796	0.304272	0.152136	+	0.988360i	$0.451385\pi$
$618$	24.7266	0.994649
$619$	−3.36490	−0.135247	−0.0676233	−	0.997711i	$-0.521542\pi$
$619$	−3.36490	−0.135247	−0.0676233	+	0.997711i	$0.521542\pi$
$620$	−16.5978	−0.666584
$621$	5.60484	0.224914
$622$	52.4382	2.10258
$623$	22.1308	0.886653
$624$	−27.7160	−1.10953
$625$	−8.98142	−0.359257
$626$	−3.01767	−0.120610
$627$	−0.720581	−0.0287772
$628$	−6.30873	−0.251746
$629$	15.0493	0.600055
$630$	28.1473	1.12142
$631$	4.41948	0.175937	0.0879684	−	0.996123i	$-0.471963\pi$
$631$	4.41948	0.175937	0.0879684	+	0.996123i	$0.471963\pi$
$632$	−17.7253	−0.705076
$633$	−13.6173	−0.541241
$634$	−59.5989	−2.36698
$635$	−35.2925	−1.40054
$636$	42.9213	1.70194
$637$	−84.9329	−3.36516
$638$	−3.97201	−0.157254
$639$	−6.03902	−0.238900
$640$	−70.2401	−2.77648
$641$	27.1330	1.07169	0.535845	−	0.844316i	$-0.319993\pi$
$641$	27.1330	1.07169	0.535845	+	0.844316i	$0.319993\pi$
$642$	−48.5195	−1.91491
$643$	18.4069	0.725896	0.362948	−	0.931809i	$-0.381770\pi$
$643$	18.4069	0.725896	0.362948	+	0.931809i	$0.381770\pi$
$644$	19.1426	0.754326
$645$	30.1499	1.18715
$646$	5.23252	0.205871
$647$	31.4390	1.23600	0.617998	−	0.786180i	$-0.287944\pi$
$647$	31.4390	1.23600	0.617998	+	0.786180i	$0.287944\pi$
$648$	−30.5565	−1.20037
$649$	1.23648	0.0485359
$650$	−89.2471	−3.50056
$651$	8.96740	0.351460
$652$	−61.1049	−2.39305
$653$	−3.57315	−0.139828	−0.0699140	−	0.997553i	$-0.522272\pi$
$653$	−3.57315	−0.139828	−0.0699140	+	0.997553i	$0.522272\pi$
$654$	49.5379	1.93708
$655$	−71.3874	−2.78934
$656$	−39.1786	−1.52967
$657$	1.78415	0.0696065
$658$	−60.8143	−2.37079
$659$	4.59543	0.179012	0.0895062	−	0.995986i	$-0.471471\pi$
$659$	4.59543	0.179012	0.0895062	+	0.995986i	$0.471471\pi$
$660$	−34.1370	−1.32878
$661$	−29.4071	−1.14380	−0.571901	−	0.820322i	$-0.693794\pi$
$661$	−29.4071	−1.14380	−0.571901	+	0.820322i	$0.693794\pi$
$662$	12.3708	0.480804
$663$	−57.3210	−2.22616
$664$	−50.3031	−1.95214
$665$	−4.93735	−0.191462
$666$	−3.35689	−0.130077
$667$	−1.00000	−0.0387202
$668$	3.00618	0.116313
$669$	34.2662	1.32481
$670$	30.7096	1.18642
$671$	−18.8716	−0.728532
$672$	4.99148	0.192550
$673$	25.9468	1.00018	0.500088	−	0.865975i	$-0.333301\pi$
$673$	25.9468	1.00018	0.500088	+	0.865975i	$0.333301\pi$
$674$	−73.5134	−2.83163
$675$	−40.4611	−1.55735
$676$	50.2037	1.93091
$677$	12.6758	0.487170	0.243585	−	0.969880i	$-0.421677\pi$
$677$	12.6758	0.487170	0.243585	+	0.969880i	$0.421677\pi$
$678$	15.4534	0.593482
$679$	12.7825	0.490547
$680$	121.727	4.66800
$681$	19.3393	0.741085
$682$	4.79936	0.183777
$683$	41.1437	1.57432	0.787159	−	0.616750i	$-0.211551\pi$
$683$	41.1437	1.57432	0.787159	+	0.616750i	$0.211551\pi$
$684$	−0.773498	−0.0295754
$685$	−38.1565	−1.45789
$686$	−115.407	−4.40625
$687$	−30.3609	−1.15834
$688$	20.2858	0.773387
$689$	−36.3966	−1.38660
$690$	−12.9684	−0.493700
$691$	−44.6369	−1.69807	−0.849035	−	0.528337i	$-0.822816\pi$
$691$	−44.6369	−1.69807	−0.849035	+	0.528337i	$0.822816\pi$
$692$	7.86187	0.298863
$693$	−5.39382	−0.204894
$694$	−36.8708	−1.39959
$695$	−33.5811	−1.27380
$696$	7.15919	0.271368
$697$	−81.0274	−3.06913
$698$	61.5340	2.32910
$699$	24.0855	0.910996
$700$	−138.190	−5.22309
$701$	−18.9701	−0.716489	−0.358244	−	0.933628i	$-0.616625\pi$
$701$	−18.9701	−0.716489	−0.358244	+	0.933628i	$0.616625\pi$
$702$	69.2920	2.61526
$703$	0.588836	0.0222084
$704$	14.3610	0.541252
$705$	27.3035	1.02831
$706$	−53.4152	−2.01031
$707$	−90.3331	−3.39733
$708$	−4.53843	−0.170565
$709$	−12.2432	−0.459802	−0.229901	−	0.973214i	$-0.573840\pi$
$709$	−12.2432	−0.459802	−0.229901	+	0.973214i	$0.573840\pi$
$710$	75.7249	2.84191
$711$	2.56063	0.0960309
$712$	−21.3485	−0.800069
$713$	1.20829	0.0452509
$714$	−133.927	−5.01211
$715$	28.9477	1.08258
$716$	79.8948	2.98581
$717$	−43.4497	−1.62266
$718$	−28.0591	−1.04716
$719$	6.46404	0.241068	0.120534	−	0.992709i	$-0.461539\pi$
$719$	6.46404	0.241068	0.120534	+	0.992709i	$0.461539\pi$
$720$	−8.50265	−0.316875
$721$	−32.4664	−1.20911
$722$	−46.0622	−1.71426
$723$	−15.9906	−0.594696
$724$	21.4903	0.798682
$725$	7.21896	0.268105
$726$	−30.9387	−1.14824
$727$	12.3230	0.457034	0.228517	−	0.973540i	$-0.426612\pi$
$727$	12.3230	0.457034	0.228517	+	0.973540i	$0.426612\pi$
$728$	116.213	4.30713
$729$	30.0318	1.11229
$730$	−22.3720	−0.828024
$731$	41.9541	1.55173
$732$	69.2676	2.56020
$733$	19.1603	0.707702	0.353851	−	0.935302i	$-0.384872\pi$
$733$	19.1603	0.707702	0.353851	+	0.935302i	$0.384872\pi$
$734$	73.7726	2.72300
$735$	89.0930	3.28625
$736$	0.672566	0.0247911
$737$	−5.88483	−0.216771
$738$	18.0739	0.665311
$739$	32.4622	1.19414	0.597071	−	0.802189i	$-0.296331\pi$
$739$	32.4622	1.19414	0.597071	+	0.802189i	$0.296331\pi$
$740$	27.8957	1.02546
$741$	−2.24281	−0.0823915
$742$	−85.0386	−3.12187
$743$	−13.5331	−0.496481	−0.248240	−	0.968698i	$-0.579852\pi$
$743$	−13.5331	−0.496481	−0.248240	+	0.968698i	$0.579852\pi$
$744$	−8.65040	−0.317139
$745$	−13.7372	−0.503293
$746$	29.8950	1.09453
$747$	7.26686	0.265880
$748$	−47.5021	−1.73685
$749$	63.7069	2.32780
$750$	28.7764	1.05077
$751$	−27.8722	−1.01707	−0.508535	−	0.861041i	$-0.669813\pi$
$751$	−27.8722	−1.01707	−0.508535	+	0.861041i	$0.669813\pi$
$752$	18.3706	0.669907
$753$	0.785888	0.0286393
$754$	−12.3629	−0.450229
$755$	34.2338	1.24590
$756$	107.291	3.90215
$757$	−41.0638	−1.49249	−0.746245	−	0.665672i	$-0.768145\pi$
$757$	−41.0638	−1.49249	−0.746245	+	0.665672i	$0.768145\pi$
$758$	−25.2883	−0.918514
$759$	2.48512	0.0902041
$760$	4.76281	0.172765
$761$	38.0521	1.37939	0.689694	−	0.724101i	$-0.257745\pi$
$761$	38.0521	1.37939	0.689694	+	0.724101i	$0.257745\pi$
$762$	−37.4573	−1.35693
$763$	−65.0441	−2.35476
$764$	26.8342	0.970826
$765$	−17.5848	−0.635780
$766$	54.7473	1.97810
$767$	3.84852	0.138962
$768$	−47.7212	−1.72199
$769$	22.2151	0.801097	0.400549	−	0.916276i	$-0.368820\pi$
$769$	22.2151	0.801097	0.400549	+	0.916276i	$0.368820\pi$
$770$	67.6346	2.43738
$771$	17.5400	0.631689
$772$	75.5046	2.71747
$773$	42.9479	1.54473	0.772365	−	0.635179i	$-0.219074\pi$
$773$	42.9479	1.54473	0.772365	+	0.635179i	$0.219074\pi$
$774$	−9.35825	−0.336375
$775$	−8.72262	−0.313326
$776$	−12.3306	−0.442643
$777$	−15.0714	−0.540682
$778$	−23.9054	−0.857051
$779$	−3.17037	−0.113590
$780$	−106.251	−3.80441
$781$	−14.5110	−0.519246
$782$	−18.0458	−0.645315
$783$	−5.60484	−0.200301
$784$	59.9444	2.14087
$785$	−5.61175	−0.200292
$786$	−75.7660	−2.70248
$787$	31.1228	1.10941	0.554703	−	0.832048i	$-0.312832\pi$
$787$	31.1228	1.10941	0.554703	+	0.832048i	$0.312832\pi$
$788$	−41.5569	−1.48040
$789$	−5.75375	−0.204839
$790$	−32.1084	−1.14236
$791$	−20.2905	−0.721448
$792$	5.20315	0.184886
$793$	−58.7379	−2.08584
$794$	3.42354	0.121497
$795$	38.1794	1.35408
$796$	−0.0557275	−0.00197521
$797$	24.1202	0.854383	0.427191	−	0.904161i	$-0.359503\pi$
$797$	24.1202	0.854383	0.427191	+	0.904161i	$0.359503\pi$
$798$	−5.24019	−0.185501
$799$	37.9932	1.34410
$800$	−4.85523	−0.171658
$801$	3.08403	0.108969
$802$	−31.4980	−1.11223
$803$	4.28711	0.151289
$804$	21.6000	0.761775
$805$	17.0278	0.600150
$806$	14.9380	0.526168
$807$	−19.8241	−0.697841
$808$	87.1398	3.06557
$809$	−22.2731	−0.783081	−0.391541	−	0.920161i	$-0.628058\pi$
$809$	−22.2731	−0.783081	−0.391541	+	0.920161i	$0.628058\pi$
$810$	−55.3512	−1.94484
$811$	−38.2815	−1.34424	−0.672122	−	0.740440i	$-0.734617\pi$
$811$	−38.2815	−1.34424	−0.672122	+	0.740440i	$0.734617\pi$
$812$	−19.1426	−0.671775
$813$	−35.8893	−1.25869
$814$	−8.06621	−0.282720
$815$	−54.3541	−1.90394
$816$	40.4564	1.41626
$817$	1.64154	0.0574302
$818$	62.5187	2.18591
$819$	−16.7883	−0.586629
$820$	−150.194	−5.24500
$821$	17.3465	0.605395	0.302698	−	0.953087i	$-0.402113\pi$
$821$	17.3465	0.605395	0.302698	+	0.953087i	$0.402113\pi$
$822$	−40.4969	−1.41249
$823$	5.80452	0.202333	0.101166	−	0.994870i	$-0.467743\pi$
$823$	5.80452	0.202333	0.101166	+	0.994870i	$0.467743\pi$
$824$	31.3187	1.09104
$825$	−17.9400	−0.624590
$826$	8.99186	0.312867
$827$	−27.5059	−0.956475	−0.478237	−	0.878231i	$-0.658724\pi$
$827$	−27.5059	−0.956475	−0.478237	+	0.878231i	$0.658724\pi$
$828$	2.66762	0.0927060
$829$	18.3056	0.635779	0.317890	−	0.948128i	$-0.397026\pi$
$829$	18.3056	0.635779	0.317890	+	0.948128i	$0.397026\pi$
$830$	−91.1210	−3.16286
$831$	12.6482	0.438763
$832$	44.6986	1.54965
$833$	123.974	4.29545
$834$	−35.6408	−1.23414
$835$	2.67406	0.0925397
$836$	−1.85862	−0.0642817
$837$	6.77229	0.234085
$838$	6.82179	0.235655
$839$	−0.291572	−0.0100662	−0.00503308	−	0.999987i	$-0.501602\pi$
$839$	−0.291572	−0.0100662	−0.00503308	+	0.999987i	$0.501602\pi$
$840$	−121.905	−4.20612
$841$	1.00000	0.0344828
$842$	56.0885	1.93294
$843$	−37.3406	−1.28608
$844$	−35.1237	−1.20901
$845$	44.6572	1.53625
$846$	−8.47475	−0.291368
$847$	40.6231	1.39583
$848$	25.6882	0.882136
$849$	25.6994	0.882003
$850$	130.272	4.46828
$851$	−2.03076	−0.0696135
$852$	53.2622	1.82473
$853$	−25.6773	−0.879175	−0.439587	−	0.898200i	$-0.644875\pi$
$853$	−25.6773	−0.879175	−0.439587	+	0.898200i	$0.644875\pi$
$854$	−137.238	−4.69618
$855$	−0.688042	−0.0235305
$856$	−61.4549	−2.10048
$857$	−40.3915	−1.37975	−0.689874	−	0.723930i	$-0.742334\pi$
$857$	−40.3915	−1.37975	−0.689874	+	0.723930i	$0.742334\pi$
$858$	30.7232	1.04887
$859$	−5.56391	−0.189838	−0.0949191	−	0.995485i	$-0.530259\pi$
$859$	−5.56391	−0.189838	−0.0949191	+	0.995485i	$0.530259\pi$
$860$	77.7668	2.65182
$861$	81.1462	2.76545
$862$	28.4695	0.969674
$863$	42.7773	1.45616	0.728078	−	0.685494i	$-0.240414\pi$
$863$	42.7773	1.45616	0.728078	+	0.685494i	$0.240414\pi$
$864$	3.76962	0.128245
$865$	6.99329	0.237779
$866$	24.0956	0.818802
$867$	57.7698	1.96197
$868$	23.1299	0.785081
$869$	6.15287	0.208722
$870$	12.9684	0.439671
$871$	−18.3165	−0.620631
$872$	62.7448	2.12481
$873$	1.78130	0.0602878
$874$	−0.706078	−0.0238834
$875$	−37.7839	−1.27733
$876$	−15.7357	−0.531658
$877$	−44.3278	−1.49684	−0.748422	−	0.663223i	$-0.769188\pi$
$877$	−44.3278	−1.49684	−0.748422	+	0.663223i	$0.769188\pi$
$878$	−61.6609	−2.08095
$879$	15.2236	0.513481
$880$	−20.4308	−0.688724
$881$	−30.0372	−1.01198	−0.505990	−	0.862539i	$-0.668873\pi$
$881$	−30.0372	−1.01198	−0.505990	+	0.862539i	$0.668873\pi$
$882$	−27.6536	−0.931146
$883$	−29.4304	−0.990411	−0.495205	−	0.868776i	$-0.664907\pi$
$883$	−29.4304	−0.990411	−0.495205	+	0.868776i	$0.664907\pi$
$884$	−147.850	−4.97274
$885$	−4.03703	−0.135703
$886$	87.1016	2.92623
$887$	−57.8556	−1.94260	−0.971301	−	0.237854i	$-0.923556\pi$
$887$	−57.8556	−1.94260	−0.971301	+	0.237854i	$0.923556\pi$
$888$	14.5386	0.487883
$889$	49.1820	1.64951
$890$	−38.6715	−1.29627
$891$	10.6069	0.355343
$892$	88.3841	2.95932
$893$	1.48656	0.0497460
$894$	−14.5798	−0.487622
$895$	71.0681	2.37554
$896$	97.8833	3.27005
$897$	7.73492	0.258262
$898$	55.7817	1.86146
$899$	−1.20829	−0.0402988
$900$	−19.2574	−0.641914
$901$	53.1271	1.76992
$902$	43.4295	1.44604
$903$	−42.0155	−1.39819
$904$	19.5732	0.650996
$905$	19.1161	0.635440
$906$	36.3336	1.20710
$907$	−27.2768	−0.905710	−0.452855	−	0.891584i	$-0.649595\pi$
$907$	−27.2768	−0.905710	−0.452855	+	0.891584i	$0.649595\pi$
$908$	49.8826	1.65541
$909$	−12.5883	−0.417529
$910$	210.512	6.97842
$911$	−24.0599	−0.797139	−0.398569	−	0.917138i	$-0.630493\pi$
$911$	−24.0599	−0.797139	−0.398569	+	0.917138i	$0.630493\pi$
$912$	1.58294	0.0524164
$913$	17.4614	0.577887
$914$	41.1249	1.36029
$915$	61.6150	2.03693
$916$	−78.3110	−2.58747
$917$	99.4821	3.28519
$918$	−101.144	−3.33824
$919$	−38.2959	−1.26326	−0.631632	−	0.775269i	$-0.717615\pi$
$919$	−38.2959	−1.26326	−0.631632	+	0.775269i	$0.717615\pi$
$920$	−16.4258	−0.541544
$921$	−15.7361	−0.518522
$922$	70.3792	2.31782
$923$	−45.1656	−1.48664
$924$	47.5718	1.56500
$925$	14.6600	0.482017
$926$	−31.2995	−1.02856
$927$	−4.52435	−0.148599
$928$	−0.672566	−0.0220781
$929$	16.9016	0.554523	0.277262	−	0.960794i	$-0.410573\pi$
$929$	16.9016	0.554523	0.277262	+	0.960794i	$0.410573\pi$
$930$	−15.6697	−0.513829
$931$	4.85075	0.158977
$932$	62.1245	2.03495
$933$	32.8084	1.07410
$934$	−19.3340	−0.632629
$935$	−42.2541	−1.38186
$936$	16.1948	0.529343
$937$	0.00392697	0.000128289 0	6.41443e−5	−	1.00000i	$-0.499980\pi$
$937$	0.00392697	0.000128289 0	6.41443e−5		1.00000i	$0.499980\pi$
$938$	−42.7955	−1.39732
$939$	−1.88803	−0.0616134
$940$	70.4249	2.29701
$941$	−25.9434	−0.845731	−0.422865	−	0.906193i	$-0.638976\pi$
$941$	−25.9434	−0.845731	−0.422865	+	0.906193i	$0.638976\pi$
$942$	−5.95595	−0.194055
$943$	10.9339	0.356056
$944$	−2.71623	−0.0884058
$945$	95.4380	3.10460
$946$	−22.4867	−0.731107
$947$	17.3620	0.564188	0.282094	−	0.959387i	$-0.408971\pi$
$947$	17.3620	0.564188	0.282094	+	0.959387i	$0.408971\pi$
$948$	−22.5839	−0.733490
$949$	13.3436	0.433151
$950$	5.09715	0.165373
$951$	−37.2885	−1.20916
$952$	−169.633	−5.49782
$953$	28.5774	0.925713	0.462857	−	0.886433i	$-0.346825\pi$
$953$	28.5774	0.925713	0.462857	+	0.886433i	$0.346825\pi$
$954$	−11.8505	−0.383675
$955$	23.8695	0.772400
$956$	−112.071	−3.62464
$957$	−2.48512	−0.0803325
$958$	79.6626	2.57378
$959$	53.1732	1.71705
$960$	−46.8880	−1.51331
$961$	−29.5400	−0.952904
$962$	−25.1060	−0.809451
$963$	8.87785	0.286085
$964$	−41.2451	−1.32842
$965$	67.1629	2.16205
$966$	18.0722	0.581464
$967$	−3.08127	−0.0990869	−0.0495435	−	0.998772i	$-0.515777\pi$
$967$	−3.08127	−0.0990869	−0.0495435	+	0.998772i	$0.515777\pi$
$968$	−39.1870	−1.25952
$969$	3.27376	0.105168
$970$	−22.3362	−0.717171
$971$	−10.1788	−0.326652	−0.163326	−	0.986572i	$-0.552222\pi$
$971$	−10.1788	−0.326652	−0.163326	+	0.986572i	$0.552222\pi$
$972$	27.1442	0.870651
$973$	46.7970	1.50024
$974$	16.4783	0.528000
$975$	−55.8381	−1.78825
$976$	41.4563	1.32699
$977$	−51.5899	−1.65051	−0.825253	−	0.564763i	$-0.808968\pi$
$977$	−51.5899	−1.65051	−0.825253	+	0.564763i	$0.808968\pi$
$978$	−57.6880	−1.84466
$979$	7.41056	0.236843
$980$	229.801	7.34072
$981$	−9.06419	−0.289397
$982$	−34.6754	−1.10654
$983$	−40.0166	−1.27633	−0.638166	−	0.769899i	$-0.720307\pi$
$983$	−40.0166	−1.27633	−0.638166	+	0.769899i	$0.720307\pi$
$984$	−78.2776	−2.49540
$985$	−36.9657	−1.17783
$986$	18.0458	0.574694
$987$	−38.0489	−1.21111
$988$	−5.78495	−0.184044
$989$	−5.66129	−0.180019
$990$	9.42519	0.299552
$991$	−16.9438	−0.538238	−0.269119	−	0.963107i	$-0.586733\pi$
$991$	−16.9438	−0.538238	−0.269119	+	0.963107i	$0.586733\pi$
$992$	0.812657	0.0258019
$993$	7.73987	0.245617
$994$	−105.527	−3.34710
$995$	−0.0495708	−0.00157150
$996$	−64.0913	−2.03081
$997$	15.0505	0.476655	0.238327	−	0.971185i	$-0.423401\pi$
$997$	15.0505	0.476655	0.238327	+	0.971185i	$0.423401\pi$
$998$	−13.4865	−0.426908
$999$	−11.3821	−0.360113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.12	✓	13
3.2	odd	2		6003.2.a.o.1.2		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.12	✓	13	1.1	even	1	trivial
6003.2.a.o.1.2		13	3.2	odd	2

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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.43510 q^{2} +1.52354 q^{3} +3.92972 q^{4} +3.49556 q^{5} +3.70997 q^{6} -4.87125 q^{7} +4.69905 q^{8} -0.678832 q^{9} +O(q^{10})\)	\(q+2.43510 q^{2} +1.52354 q^{3} +3.92972 q^{4} +3.49556 q^{5} +3.70997 q^{6} -4.87125 q^{7} +4.69905 q^{8} -0.678832 q^{9} +8.51205 q^{10} -1.63115 q^{11} +5.98707 q^{12} -5.07695 q^{13} -11.8620 q^{14} +5.32562 q^{15} +3.58324 q^{16} +7.41068 q^{17} -1.65302 q^{18} +0.289958 q^{19} +13.7366 q^{20} -7.42154 q^{21} -3.97201 q^{22} -1.00000 q^{23} +7.15919 q^{24} +7.21896 q^{25} -12.3629 q^{26} -5.60484 q^{27} -19.1426 q^{28} +1.00000 q^{29} +12.9684 q^{30} -1.20829 q^{31} -0.672566 q^{32} -2.48512 q^{33} +18.0458 q^{34} -17.0278 q^{35} -2.66762 q^{36} +2.03076 q^{37} +0.706078 q^{38} -7.73492 q^{39} +16.4258 q^{40} -10.9339 q^{41} -18.0722 q^{42} +5.66129 q^{43} -6.40996 q^{44} -2.37290 q^{45} -2.43510 q^{46} +5.12682 q^{47} +5.45920 q^{48} +16.7291 q^{49} +17.5789 q^{50} +11.2905 q^{51} -19.9510 q^{52} +7.16900 q^{53} -13.6484 q^{54} -5.70179 q^{55} -22.8903 q^{56} +0.441763 q^{57} +2.43510 q^{58} -0.758039 q^{59} +20.9282 q^{60} +11.5695 q^{61} -2.94232 q^{62} +3.30676 q^{63} -8.80424 q^{64} -17.7468 q^{65} -6.05152 q^{66} +3.60778 q^{67} +29.1219 q^{68} -1.52354 q^{69} -41.4644 q^{70} +8.89620 q^{71} -3.18987 q^{72} -2.62827 q^{73} +4.94510 q^{74} +10.9984 q^{75} +1.13945 q^{76} +7.94575 q^{77} -18.8353 q^{78} -3.77211 q^{79} +12.5254 q^{80} -6.50269 q^{81} -26.6251 q^{82} -10.7050 q^{83} -29.1646 q^{84} +25.9045 q^{85} +13.7858 q^{86} +1.52354 q^{87} -7.66486 q^{88} -4.54315 q^{89} -5.77825 q^{90} +24.7311 q^{91} -3.92972 q^{92} -1.84088 q^{93} +12.4843 q^{94} +1.01357 q^{95} -1.02468 q^{96} -2.62406 q^{97} +40.7371 q^{98} +1.10728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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