LMFDB - Embedded newform 1339.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} + \cdots - 63 $ x^19 - 9x^18 + 13x^17 + 106x^16 - 351x^15 - 279x^14 + 2337x^13 - 1079x^12 - 6826x^11 + 7199x^10 + 9364x^9 - 14841x^8 - 5183x^7 + 14037x^6 - 108x^5 - 6099x^4 + 855x^3 + 1062x^2 - 135x - 63
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.49720$ of defining polynomial
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49720 q^{2} +1.20166 q^{3} +4.23600 q^{4} +1.95194 q^{5} -3.00079 q^{6} -3.56552 q^{7} -5.58375 q^{8} -1.55601 q^{9} +O(q^{10})$	\(q-2.49720 q^{2} +1.20166 q^{3} +4.23600 q^{4} +1.95194 q^{5} -3.00079 q^{6} -3.56552 q^{7} -5.58375 q^{8} -1.55601 q^{9} -4.87439 q^{10} -3.71318 q^{11} +5.09024 q^{12} +1.00000 q^{13} +8.90381 q^{14} +2.34557 q^{15} +5.47172 q^{16} +4.47263 q^{17} +3.88567 q^{18} +4.17369 q^{19} +8.26844 q^{20} -4.28454 q^{21} +9.27254 q^{22} +2.40008 q^{23} -6.70977 q^{24} -1.18992 q^{25} -2.49720 q^{26} -5.47478 q^{27} -15.1036 q^{28} -2.36737 q^{29} -5.85736 q^{30} +1.26438 q^{31} -2.49648 q^{32} -4.46198 q^{33} -11.1690 q^{34} -6.95969 q^{35} -6.59127 q^{36} -6.06862 q^{37} -10.4225 q^{38} +1.20166 q^{39} -10.8992 q^{40} -5.62509 q^{41} +10.6994 q^{42} +10.2266 q^{43} -15.7290 q^{44} -3.03725 q^{45} -5.99347 q^{46} -12.4452 q^{47} +6.57515 q^{48} +5.71293 q^{49} +2.97146 q^{50} +5.37458 q^{51} +4.23600 q^{52} -8.92080 q^{53} +13.6716 q^{54} -7.24791 q^{55} +19.9090 q^{56} +5.01535 q^{57} +5.91178 q^{58} -4.25547 q^{59} +9.93586 q^{60} -3.39243 q^{61} -3.15742 q^{62} +5.54799 q^{63} -4.70923 q^{64} +1.95194 q^{65} +11.1424 q^{66} +1.10425 q^{67} +18.9461 q^{68} +2.88408 q^{69} +17.3797 q^{70} +0.746206 q^{71} +8.68838 q^{72} -12.8074 q^{73} +15.1546 q^{74} -1.42988 q^{75} +17.6797 q^{76} +13.2394 q^{77} -3.00079 q^{78} +2.59208 q^{79} +10.6805 q^{80} -1.91079 q^{81} +14.0470 q^{82} -13.5324 q^{83} -18.1493 q^{84} +8.73032 q^{85} -25.5379 q^{86} -2.84477 q^{87} +20.7334 q^{88} -10.5047 q^{89} +7.58461 q^{90} -3.56552 q^{91} +10.1667 q^{92} +1.51936 q^{93} +31.0782 q^{94} +8.14680 q^{95} -2.99992 q^{96} -0.496351 q^{97} -14.2663 q^{98} +5.77775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) $ 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * 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 $

$2$	−2.49720	−1.76579	−0.882893	−	0.469574i	$-0.844408\pi$
$2$	−2.49720	−1.76579	−0.882893	+	0.469574i	$0.844408\pi$
$3$	1.20166	0.693779	0.346890	−	0.937906i	$-0.387238\pi$
$3$	1.20166	0.693779	0.346890	+	0.937906i	$0.387238\pi$
$4$	4.23600	2.11800
$5$	1.95194	0.872936	0.436468	−	0.899720i	$-0.356229\pi$
$5$	1.95194	0.872936	0.436468	+	0.899720i	$0.356229\pi$
$6$	−3.00079	−1.22507
$7$	−3.56552	−1.34764	−0.673820	−	0.738896i	$-0.735348\pi$
$7$	−3.56552	−1.34764	−0.673820	+	0.738896i	$0.735348\pi$
$8$	−5.58375	−1.97415
$9$	−1.55601	−0.518671
$10$	−4.87439	−1.54142
$11$	−3.71318	−1.11956	−0.559782	−	0.828640i	$-0.689115\pi$
$11$	−3.71318	−1.11956	−0.559782	+	0.828640i	$0.689115\pi$
$12$	5.09024	1.46943
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	8.90381	2.37964
$15$	2.34557	0.605624
$16$	5.47172	1.36793
$17$	4.47263	1.08477	0.542386	−	0.840130i	$-0.317521\pi$
$17$	4.47263	1.08477	0.542386	+	0.840130i	$0.317521\pi$
$18$	3.88567	0.915862
$19$	4.17369	0.957509	0.478755	−	0.877949i	$-0.341088\pi$
$19$	4.17369	0.957509	0.478755	+	0.877949i	$0.341088\pi$
$20$	8.26844	1.84888
$21$	−4.28454	−0.934964
$22$	9.27254	1.97691
$23$	2.40008	0.500450	0.250225	−	0.968188i	$-0.419495\pi$
$23$	2.40008	0.500450	0.250225	+	0.968188i	$0.419495\pi$
$24$	−6.70977	−1.36963
$25$	−1.18992	−0.237983
$26$	−2.49720	−0.489741
$27$	−5.47478	−1.05362
$28$	−15.1036	−2.85430
$29$	−2.36737	−0.439609	−0.219804	−	0.975544i	$-0.570542\pi$
$29$	−2.36737	−0.439609	−0.219804	+	0.975544i	$0.570542\pi$
$30$	−5.85736	−1.06940
$31$	1.26438	0.227090	0.113545	−	0.993533i	$-0.463779\pi$
$31$	1.26438	0.227090	0.113545	+	0.993533i	$0.463779\pi$
$32$	−2.49648	−0.441320
$33$	−4.46198	−0.776731
$34$	−11.1690	−1.91547
$35$	−6.95969	−1.17640
$36$	−6.59127	−1.09855
$37$	−6.06862	−0.997676	−0.498838	−	0.866695i	$-0.666240\pi$
$37$	−6.06862	−0.997676	−0.498838	+	0.866695i	$0.666240\pi$
$38$	−10.4225	−1.69076
$39$	1.20166	0.192420
$40$	−10.8992	−1.72331
$41$	−5.62509	−0.878491	−0.439246	−	0.898367i	$-0.644754\pi$
$41$	−5.62509	−0.878491	−0.439246	+	0.898367i	$0.644754\pi$
$42$	10.6994	1.65095
$43$	10.2266	1.55954	0.779771	−	0.626065i	$-0.215336\pi$
$43$	10.2266	1.55954	0.779771	+	0.626065i	$0.215336\pi$
$44$	−15.7290	−2.37124
$45$	−3.03725	−0.452766
$46$	−5.99347	−0.883689
$47$	−12.4452	−1.81532	−0.907661	−	0.419704i	$-0.862134\pi$
$47$	−12.4452	−1.81532	−0.907661	+	0.419704i	$0.862134\pi$
$48$	6.57515	0.949041
$49$	5.71293	0.816133
$50$	2.97146	0.420228
$51$	5.37458	0.752592
$52$	4.23600	0.587428
$53$	−8.92080	−1.22537	−0.612683	−	0.790329i	$-0.709910\pi$
$53$	−8.92080	−1.22537	−0.612683	+	0.790329i	$0.709910\pi$
$54$	13.6716	1.86047
$55$	−7.24791	−0.977308
$56$	19.9090	2.66045
$57$	5.01535	0.664300
$58$	5.91178	0.776255
$59$	−4.25547	−0.554016	−0.277008	−	0.960868i	$-0.589343\pi$
$59$	−4.25547	−0.554016	−0.277008	+	0.960868i	$0.589343\pi$
$60$	9.93586	1.28271
$61$	−3.39243	−0.434356	−0.217178	−	0.976132i	$-0.569685\pi$
$61$	−3.39243	−0.434356	−0.217178	+	0.976132i	$0.569685\pi$
$62$	−3.15742	−0.400992
$63$	5.54799	0.698981
$64$	−4.70923	−0.588654
$65$	1.95194	0.242109
$66$	11.1424	1.37154
$67$	1.10425	0.134905	0.0674527	−	0.997722i	$-0.478513\pi$
$67$	1.10425	0.134905	0.0674527	+	0.997722i	$0.478513\pi$
$68$	18.9461	2.29755
$69$	2.88408	0.347202
$70$	17.3797	2.07728
$71$	0.746206	0.0885584	0.0442792	−	0.999019i	$-0.485901\pi$
$71$	0.746206	0.0885584	0.0442792	+	0.999019i	$0.485901\pi$
$72$	8.68838	1.02394
$73$	−12.8074	−1.49899	−0.749497	−	0.662008i	$-0.769705\pi$
$73$	−12.8074	−1.49899	−0.749497	+	0.662008i	$0.769705\pi$
$74$	15.1546	1.76168
$75$	−1.42988	−0.165108
$76$	17.6797	2.02801
$77$	13.2394	1.50877
$78$	−3.00079	−0.339772
$79$	2.59208	0.291632	0.145816	−	0.989312i	$-0.453419\pi$
$79$	2.59208	0.291632	0.145816	+	0.989312i	$0.453419\pi$
$80$	10.6805	1.19411
$81$	−1.91079	−0.212310
$82$	14.0470	1.55123
$83$	−13.5324	−1.48537	−0.742687	−	0.669639i	$-0.766449\pi$
$83$	−13.5324	−1.48537	−0.742687	+	0.669639i	$0.766449\pi$
$84$	−18.1493	−1.98026
$85$	8.73032	0.946936
$86$	−25.5379	−2.75382
$87$	−2.84477	−0.304991
$88$	20.7334	2.21019
$89$	−10.5047	−1.11349	−0.556746	−	0.830683i	$-0.687950\pi$
$89$	−10.5047	−1.11349	−0.556746	+	0.830683i	$0.687950\pi$
$90$	7.58461	0.799488
$91$	−3.56552	−0.373768
$92$	10.1667	1.05996
$93$	1.51936	0.157550
$94$	31.0782	3.20547
$95$	8.14680	0.835844
$96$	−2.99992	−0.306178
$97$	−0.496351	−0.0503968	−0.0251984	−	0.999682i	$-0.508022\pi$
$97$	−0.496351	−0.0503968	−0.0251984	+	0.999682i	$0.508022\pi$
$98$	−14.2663	−1.44112
$99$	5.77775	0.580685
$100$	−5.04049	−0.504049
$101$	−16.9889	−1.69046	−0.845232	−	0.534400i	$-0.820538\pi$
$101$	−16.9889	−1.69046	−0.845232	+	0.534400i	$0.820538\pi$
$102$	−13.4214	−1.32892
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−5.58375	−0.547531
$105$	−8.36319	−0.816164
$106$	22.2770	2.16374
$107$	16.9881	1.64230	0.821151	−	0.570710i	$-0.193332\pi$
$107$	16.9881	1.64230	0.821151	+	0.570710i	$0.193332\pi$
$108$	−23.1912	−2.23157
$109$	−8.87158	−0.849743	−0.424872	−	0.905254i	$-0.639681\pi$
$109$	−8.87158	−0.849743	−0.424872	+	0.905254i	$0.639681\pi$
$110$	18.0995	1.72572
$111$	−7.29243	−0.692167
$112$	−19.5095	−1.84348
$113$	−12.4746	−1.17351	−0.586757	−	0.809763i	$-0.699596\pi$
$113$	−12.4746	−1.17351	−0.586757	+	0.809763i	$0.699596\pi$
$114$	−12.5243	−1.17301
$115$	4.68481	0.436861
$116$	−10.0282	−0.931092
$117$	−1.55601	−0.143853
$118$	10.6268	0.978273
$119$	−15.9472	−1.46188
$120$	−13.0971	−1.19560
$121$	2.78768	0.253425
$122$	8.47157	0.766980
$123$	−6.75945	−0.609479
$124$	5.35593	0.480977
$125$	−12.0824	−1.08068
$126$	−13.8544	−1.23425
$127$	13.3772	1.18704	0.593519	−	0.804820i	$-0.297738\pi$
$127$	13.3772	1.18704	0.593519	+	0.804820i	$0.297738\pi$
$128$	16.7528	1.48076
$129$	12.2889	1.08198
$130$	−4.87439	−0.427512
$131$	1.60062	0.139847	0.0699235	−	0.997552i	$-0.477724\pi$
$131$	1.60062	0.139847	0.0699235	+	0.997552i	$0.477724\pi$
$132$	−18.9010	−1.64512
$133$	−14.8814	−1.29038
$134$	−2.75753	−0.238214
$135$	−10.6865	−0.919744
$136$	−24.9740	−2.14150
$137$	12.3908	1.05862	0.529311	−	0.848428i	$-0.322451\pi$
$137$	12.3908	1.05862	0.529311	+	0.848428i	$0.322451\pi$
$138$	−7.20211	−0.613085
$139$	−5.24479	−0.444858	−0.222429	−	0.974949i	$-0.571398\pi$
$139$	−5.24479	−0.444858	−0.222429	+	0.974949i	$0.571398\pi$
$140$	−29.4813	−2.49162
$141$	−14.9549	−1.25943
$142$	−1.86343	−0.156375
$143$	−3.71318	−0.310511
$144$	−8.51406	−0.709505
$145$	−4.62096	−0.383750
$146$	31.9827	2.64690
$147$	6.86500	0.566216
$148$	−25.7067	−2.11308
$149$	−6.64894	−0.544703	−0.272351	−	0.962198i	$-0.587801\pi$
$149$	−6.64894	−0.544703	−0.272351	+	0.962198i	$0.587801\pi$
$150$	3.57068	0.291545
$151$	16.2091	1.31908	0.659539	−	0.751671i	$-0.270752\pi$
$151$	16.2091	1.31908	0.659539	+	0.751671i	$0.270752\pi$
$152$	−23.3048	−1.89027
$153$	−6.95946	−0.562639
$154$	−33.0614	−2.66417
$155$	2.46800	0.198235
$156$	5.09024	0.407545
$157$	18.9845	1.51513	0.757566	−	0.652759i	$-0.226388\pi$
$157$	18.9845	1.51513	0.757566	+	0.652759i	$0.226388\pi$
$158$	−6.47295	−0.514960
$159$	−10.7198	−0.850133
$160$	−4.87299	−0.385244
$161$	−8.55752	−0.674427
$162$	4.77163	0.374894
$163$	16.7107	1.30888	0.654442	−	0.756112i	$-0.272904\pi$
$163$	16.7107	1.30888	0.654442	+	0.756112i	$0.272904\pi$
$164$	−23.8279	−1.86065
$165$	−8.70953	−0.678036
$166$	33.7931	2.62285
$167$	5.92411	0.458422	0.229211	−	0.973377i	$-0.426385\pi$
$167$	5.92411	0.458422	0.229211	+	0.973377i	$0.426385\pi$
$168$	23.9238	1.84576
$169$	1.00000	0.0769231
$170$	−21.8013	−1.67209
$171$	−6.49430	−0.496632
$172$	43.3199	3.30311
$173$	−23.7570	−1.80621	−0.903105	−	0.429421i	$-0.858718\pi$
$173$	−23.7570	−1.80621	−0.903105	+	0.429421i	$0.858718\pi$
$174$	7.10396	0.538549
$175$	4.24267	0.320716
$176$	−20.3175	−1.53149
$177$	−5.11364	−0.384364
$178$	26.2322	1.96619
$179$	−20.5884	−1.53885	−0.769425	−	0.638737i	$-0.779457\pi$
$179$	−20.5884	−1.53885	−0.769425	+	0.638737i	$0.779457\pi$
$180$	−12.8658	−0.958960
$181$	−25.7313	−1.91259	−0.956296	−	0.292401i	$-0.905546\pi$
$181$	−25.7313	−1.91259	−0.956296	+	0.292401i	$0.905546\pi$
$182$	8.90381	0.659994
$183$	−4.07655	−0.301347
$184$	−13.4014	−0.987966
$185$	−11.8456	−0.870907
$186$	−3.79414	−0.278200
$187$	−16.6077	−1.21447
$188$	−52.7180	−3.84486
$189$	19.5204	1.41990
$190$	−20.3442	−1.47592
$191$	−10.4183	−0.753840	−0.376920	−	0.926246i	$-0.623017\pi$
$191$	−10.4183	−0.753840	−0.376920	+	0.926246i	$0.623017\pi$
$192$	−5.65889	−0.408395
$193$	−4.97865	−0.358371	−0.179185	−	0.983815i	$-0.557346\pi$
$193$	−4.97865	−0.358371	−0.179185	+	0.983815i	$0.557346\pi$
$194$	1.23949	0.0889900
$195$	2.34557	0.167970
$196$	24.2000	1.72857
$197$	8.57548	0.610978	0.305489	−	0.952196i	$-0.401180\pi$
$197$	8.57548	0.610978	0.305489	+	0.952196i	$0.401180\pi$
$198$	−14.4282	−1.02537
$199$	24.6372	1.74649	0.873244	−	0.487283i	$-0.162012\pi$
$199$	24.6372	1.74649	0.873244	+	0.487283i	$0.162012\pi$
$200$	6.64419	0.469815
$201$	1.32693	0.0935945
$202$	42.4248	2.98500
$203$	8.44089	0.592434
$204$	22.7667	1.59399
$205$	−10.9799	−0.766867
$206$	−2.49720	−0.173988
$207$	−3.73455	−0.259569
$208$	5.47172	0.379396
$209$	−15.4976	−1.07199
$210$	20.8845	1.44117
$211$	4.54905	0.313169	0.156585	−	0.987665i	$-0.449952\pi$
$211$	4.54905	0.313169	0.156585	+	0.987665i	$0.449952\pi$
$212$	−37.7886	−2.59533
$213$	0.896687	0.0614400
$214$	−42.4227	−2.89996
$215$	19.9617	1.36138
$216$	30.5698	2.08001
$217$	−4.50818	−0.306035
$218$	22.1541	1.50047
$219$	−15.3902	−1.03997
$220$	−30.7022	−2.06994
$221$	4.47263	0.300861
$222$	18.2106	1.22222
$223$	−4.36832	−0.292524	−0.146262	−	0.989246i	$-0.546724\pi$
$223$	−4.36832	−0.292524	−0.146262	+	0.989246i	$0.546724\pi$
$224$	8.90125	0.594740
$225$	1.85152	0.123435
$226$	31.1516	2.07218
$227$	19.9253	1.32249	0.661244	−	0.750171i	$-0.270029\pi$
$227$	19.9253	1.32249	0.661244	+	0.750171i	$0.270029\pi$
$228$	21.2451	1.40699
$229$	8.83708	0.583971	0.291985	−	0.956423i	$-0.405684\pi$
$229$	8.83708	0.583971	0.291985	+	0.956423i	$0.405684\pi$
$230$	−11.6989	−0.771403
$231$	15.9093	1.04675
$232$	13.2188	0.867855
$233$	24.9188	1.63249	0.816243	−	0.577708i	$-0.196053\pi$
$233$	24.9188	1.63249	0.816243	+	0.577708i	$0.196053\pi$
$234$	3.88567	0.254014
$235$	−24.2924	−1.58466
$236$	−18.0262	−1.17341
$237$	3.11480	0.202328
$238$	39.8234	2.58137
$239$	−5.03570	−0.325732	−0.162866	−	0.986648i	$-0.552074\pi$
$239$	−5.03570	−0.325732	−0.162866	+	0.986648i	$0.552074\pi$
$240$	12.8343	0.828452
$241$	−9.27870	−0.597694	−0.298847	−	0.954301i	$-0.596602\pi$
$241$	−9.27870	−0.597694	−0.298847	+	0.954301i	$0.596602\pi$
$242$	−6.96139	−0.447495
$243$	14.1282	0.906326
$244$	−14.3703	−0.919966
$245$	11.1513	0.712431
$246$	16.8797	1.07621
$247$	4.17369	0.265565
$248$	−7.05999	−0.448310
$249$	−16.2614	−1.03052
$250$	30.1721	1.90825
$251$	−25.0029	−1.57817	−0.789085	−	0.614284i	$-0.789445\pi$
$251$	−25.0029	−1.57817	−0.789085	+	0.614284i	$0.789445\pi$
$252$	23.5013	1.48044
$253$	−8.91191	−0.560287
$254$	−33.4056	−2.09606
$255$	10.4909	0.656964
$256$	−32.4167	−2.02605
$257$	5.48158	0.341932	0.170966	−	0.985277i	$-0.445311\pi$
$257$	5.48158	0.341932	0.170966	+	0.985277i	$0.445311\pi$
$258$	−30.6878	−1.91054
$259$	21.6378	1.34451
$260$	8.26844	0.512787
$261$	3.68365	0.228012
$262$	−3.99707	−0.246940
$263$	4.14519	0.255603	0.127802	−	0.991800i	$-0.459208\pi$
$263$	4.14519	0.255603	0.127802	+	0.991800i	$0.459208\pi$
$264$	24.9146	1.53338
$265$	−17.4129	−1.06967
$266$	37.1617	2.27853
$267$	−12.6230	−0.772517
$268$	4.67760	0.285730
$269$	16.1883	0.987016	0.493508	−	0.869741i	$-0.335714\pi$
$269$	16.1883	0.987016	0.493508	+	0.869741i	$0.335714\pi$
$270$	26.6862	1.62407
$271$	−12.0999	−0.735019	−0.367509	−	0.930020i	$-0.619789\pi$
$271$	−12.0999	−0.735019	−0.367509	+	0.930020i	$0.619789\pi$
$272$	24.4730	1.48389
$273$	−4.28454	−0.259312
$274$	−30.9424	−1.86930
$275$	4.41837	0.266438
$276$	12.2170	0.735375
$277$	13.0687	0.785222	0.392611	−	0.919705i	$-0.371572\pi$
$277$	13.0687	0.785222	0.392611	+	0.919705i	$0.371572\pi$
$278$	13.0973	0.785523
$279$	−1.96739	−0.117785
$280$	38.8612	2.32240
$281$	16.4633	0.982119	0.491059	−	0.871126i	$-0.336610\pi$
$281$	16.4633	0.982119	0.491059	+	0.871126i	$0.336610\pi$
$282$	37.3454	2.22389
$283$	2.02675	0.120478	0.0602389	−	0.998184i	$-0.480814\pi$
$283$	2.02675	0.120478	0.0602389	+	0.998184i	$0.480814\pi$
$284$	3.16093	0.187567
$285$	9.78969	0.579891
$286$	9.27254	0.548297
$287$	20.0564	1.18389
$288$	3.88456	0.228900
$289$	3.00440	0.176729
$290$	11.5395	0.677621
$291$	−0.596445	−0.0349642
$292$	−54.2523	−3.17487
$293$	3.47548	0.203040	0.101520	−	0.994834i	$-0.467629\pi$
$293$	3.47548	0.203040	0.101520	+	0.994834i	$0.467629\pi$
$294$	−17.1433	−0.999816
$295$	−8.30644	−0.483620
$296$	33.8857	1.96956
$297$	20.3288	1.17960
$298$	16.6037	0.961829
$299$	2.40008	0.138800
$300$	−6.05696	−0.349699
$301$	−36.4631	−2.10170
$302$	−40.4773	−2.32921
$303$	−20.4149	−1.17281
$304$	22.8372	1.30981
$305$	−6.62183	−0.379165
$306$	17.3792	0.993501
$307$	−4.85491	−0.277084	−0.138542	−	0.990357i	$-0.544242\pi$
$307$	−4.85491	−0.277084	−0.138542	+	0.990357i	$0.544242\pi$
$308$	56.0822	3.19558
$309$	1.20166	0.0683601
$310$	−6.16310	−0.350040
$311$	−18.6369	−1.05680	−0.528402	−	0.848994i	$-0.677209\pi$
$311$	−18.6369	−1.05680	−0.528402	+	0.848994i	$0.677209\pi$
$312$	−6.70977	−0.379866
$313$	9.09422	0.514036	0.257018	−	0.966407i	$-0.417260\pi$
$313$	9.09422	0.514036	0.257018	+	0.966407i	$0.417260\pi$
$314$	−47.4082	−2.67540
$315$	10.8294	0.610166
$316$	10.9801	0.617677
$317$	1.96169	0.110180	0.0550899	−	0.998481i	$-0.482455\pi$
$317$	1.96169	0.110180	0.0550899	+	0.998481i	$0.482455\pi$
$318$	26.7694	1.50115
$319$	8.79044	0.492170
$320$	−9.19215	−0.513857
$321$	20.4139	1.13940
$322$	21.3698	1.19089
$323$	18.6673	1.03868
$324$	−8.09412	−0.449673
$325$	−1.18992	−0.0660047
$326$	−41.7300	−2.31121
$327$	−10.6606	−0.589534
$328$	31.4091	1.73428
$329$	44.3737	2.44640
$330$	21.7494	1.19727
$331$	17.2188	0.946432	0.473216	−	0.880946i	$-0.343093\pi$
$331$	17.2188	0.946432	0.473216	+	0.880946i	$0.343093\pi$
$332$	−57.3233	−3.14603
$333$	9.44285	0.517465
$334$	−14.7937	−0.809475
$335$	2.15543	0.117764
$336$	−23.4438	−1.27897
$337$	−9.09271	−0.495311	−0.247656	−	0.968848i	$-0.579660\pi$
$337$	−9.09271	−0.495311	−0.247656	+	0.968848i	$0.579660\pi$
$338$	−2.49720	−0.135830
$339$	−14.9903	−0.814160
$340$	36.9817	2.00561
$341$	−4.69488	−0.254242
$342$	16.2176	0.876946
$343$	4.58908	0.247787
$344$	−57.1027	−3.07877
$345$	5.62956	0.303085
$346$	59.3259	3.18938
$347$	15.1916	0.815526	0.407763	−	0.913088i	$-0.366309\pi$
$347$	15.1916	0.815526	0.407763	+	0.913088i	$0.366309\pi$
$348$	−12.0505	−0.645972
$349$	−1.52981	−0.0818887	−0.0409443	−	0.999161i	$-0.513037\pi$
$349$	−1.52981	−0.0818887	−0.0409443	+	0.999161i	$0.513037\pi$
$350$	−10.5948	−0.566315
$351$	−5.47478	−0.292222
$352$	9.26988	0.494086
$353$	−1.27903	−0.0680757	−0.0340379	−	0.999421i	$-0.510837\pi$
$353$	−1.27903	−0.0680757	−0.0340379	+	0.999421i	$0.510837\pi$
$354$	12.7698	0.678705
$355$	1.45655	0.0773058
$356$	−44.4978	−2.35838
$357$	−19.1632	−1.01422
$358$	51.4134	2.71728
$359$	−18.9826	−1.00187	−0.500933	−	0.865486i	$-0.667010\pi$
$359$	−18.9826	−1.00187	−0.500933	+	0.865486i	$0.667010\pi$
$360$	16.9592	0.893829
$361$	−1.58035	−0.0831762
$362$	64.2562	3.37723
$363$	3.34984	0.175821
$364$	−15.1036	−0.791641
$365$	−24.9993	−1.30853
$366$	10.1799	0.532114
$367$	6.89319	0.359821	0.179911	−	0.983683i	$-0.442419\pi$
$367$	6.89319	0.359821	0.179911	+	0.983683i	$0.442419\pi$
$368$	13.1325	0.684581
$369$	8.75271	0.455648
$370$	29.5809	1.53784
$371$	31.8073	1.65135
$372$	6.43601	0.333692
$373$	−2.30178	−0.119182	−0.0595908	−	0.998223i	$-0.518980\pi$
$373$	−2.30178	−0.119182	−0.0595908	+	0.998223i	$0.518980\pi$
$374$	41.4726	2.14450
$375$	−14.5189	−0.749753
$376$	69.4910	3.58372
$377$	−2.36737	−0.121926
$378$	−48.7464	−2.50724
$379$	−10.8676	−0.558230	−0.279115	−	0.960258i	$-0.590041\pi$
$379$	−10.8676	−0.558230	−0.279115	+	0.960258i	$0.590041\pi$
$380$	34.5099	1.77032
$381$	16.0749	0.823542
$382$	26.0165	1.33112
$383$	21.9407	1.12112	0.560558	−	0.828115i	$-0.310587\pi$
$383$	21.9407	1.12112	0.560558	+	0.828115i	$0.310587\pi$
$384$	20.1312	1.02732
$385$	25.8426	1.31706
$386$	12.4327	0.632807
$387$	−15.9127	−0.808888
$388$	−2.10254	−0.106741
$389$	−12.6449	−0.641120	−0.320560	−	0.947228i	$-0.603871\pi$
$389$	−12.6449	−0.641120	−0.320560	+	0.947228i	$0.603871\pi$
$390$	−5.85736	−0.296599
$391$	10.7346	0.542874
$392$	−31.8995	−1.61117
$393$	1.92341	0.0970230
$394$	−21.4147	−1.07886
$395$	5.05960	0.254576
$396$	24.4746	1.22989
$397$	31.2072	1.56624	0.783121	−	0.621869i	$-0.213626\pi$
$397$	31.2072	1.56624	0.783121	+	0.621869i	$0.213626\pi$
$398$	−61.5241	−3.08393
$399$	−17.8823	−0.895237
$400$	−6.51089	−0.325544
$401$	−21.9450	−1.09588	−0.547941	−	0.836517i	$-0.684588\pi$
$401$	−21.9450	−1.09588	−0.547941	+	0.836517i	$0.684588\pi$
$402$	−3.31361	−0.165268
$403$	1.26438	0.0629834
$404$	−71.9652	−3.58040
$405$	−3.72976	−0.185333
$406$	−21.0786	−1.04611
$407$	22.5339	1.11696
$408$	−30.0103	−1.48573
$409$	26.0105	1.28614	0.643069	−	0.765808i	$-0.277661\pi$
$409$	26.0105	1.28614	0.643069	+	0.765808i	$0.277661\pi$
$410$	27.4189	1.35412
$411$	14.8896	0.734450
$412$	4.23600	0.208693
$413$	15.1730	0.746613
$414$	9.32591	0.458343
$415$	−26.4145	−1.29664
$416$	−2.49648	−0.122400
$417$	−6.30246	−0.308633
$418$	38.7007	1.89291
$419$	−22.4363	−1.09608	−0.548042	−	0.836451i	$-0.684627\pi$
$419$	−22.4363	−1.09608	−0.548042	+	0.836451i	$0.684627\pi$
$420$	−35.4265	−1.72864
$421$	−24.0474	−1.17200	−0.586000	−	0.810311i	$-0.699298\pi$
$421$	−24.0474	−1.17200	−0.586000	+	0.810311i	$0.699298\pi$
$422$	−11.3599	−0.552990
$423$	19.3649	0.941554
$424$	49.8115	2.41906
$425$	−5.32205	−0.258157
$426$	−2.23921	−0.108490
$427$	12.0958	0.585355
$428$	71.9617	3.47840
$429$	−4.46198	−0.215426
$430$	−49.8484	−2.40391
$431$	−0.732398	−0.0352784	−0.0176392	−	0.999844i	$-0.505615\pi$
$431$	−0.732398	−0.0352784	−0.0176392	+	0.999844i	$0.505615\pi$
$432$	−29.9565	−1.44128
$433$	−14.4158	−0.692779	−0.346389	−	0.938091i	$-0.612592\pi$
$433$	−14.4158	−0.692779	−0.346389	+	0.938091i	$0.612592\pi$
$434$	11.2578	0.540393
$435$	−5.55283	−0.266238
$436$	−37.5800	−1.79976
$437$	10.0172	0.479186
$438$	38.4323	1.83637
$439$	7.02425	0.335249	0.167625	−	0.985851i	$-0.446390\pi$
$439$	7.02425	0.335249	0.167625	+	0.985851i	$0.446390\pi$
$440$	40.4705	1.92936
$441$	−8.88938	−0.423304
$442$	−11.1690	−0.531257
$443$	−6.39694	−0.303928	−0.151964	−	0.988386i	$-0.548560\pi$
$443$	−6.39694	−0.303928	−0.151964	+	0.988386i	$0.548560\pi$
$444$	−30.8907	−1.46601
$445$	−20.5045	−0.972007
$446$	10.9086	0.516535
$447$	−7.98977	−0.377903
$448$	16.7908	0.793293
$449$	−16.2459	−0.766691	−0.383346	−	0.923605i	$-0.625228\pi$
$449$	−16.2459	−0.766691	−0.383346	+	0.923605i	$0.625228\pi$
$450$	−4.62362	−0.217960
$451$	20.8870	0.983528
$452$	−52.8426	−2.48551
$453$	19.4778	0.915148
$454$	−49.7574	−2.33523
$455$	−6.95969	−0.326275
$456$	−28.0045	−1.31143
$457$	−24.0157	−1.12341	−0.561703	−	0.827339i	$-0.689853\pi$
$457$	−24.0157	−1.12341	−0.561703	+	0.827339i	$0.689853\pi$
$458$	−22.0679	−1.03117
$459$	−24.4867	−1.14294
$460$	19.8449	0.925273
$461$	25.7481	1.19921	0.599605	−	0.800296i	$-0.295324\pi$
$461$	25.7481	1.19921	0.599605	+	0.800296i	$0.295324\pi$
$462$	−39.7286	−1.84834
$463$	−11.5353	−0.536091	−0.268046	−	0.963406i	$-0.586378\pi$
$463$	−11.5353	−0.536091	−0.268046	+	0.963406i	$0.586378\pi$
$464$	−12.9536	−0.601354
$465$	2.96570	0.137531
$466$	−62.2273	−2.88262
$467$	9.60635	0.444529	0.222264	−	0.974986i	$-0.428655\pi$
$467$	9.60635	0.444529	0.222264	+	0.974986i	$0.428655\pi$
$468$	−6.59127	−0.304682
$469$	−3.93722	−0.181804
$470$	60.6629	2.79817
$471$	22.8130	1.05117
$472$	23.7615	1.09371
$473$	−37.9732	−1.74601
$474$	−7.77829	−0.357269
$475$	−4.96634	−0.227871
$476$	−67.5526	−3.09627
$477$	13.8809	0.635562
$478$	12.5751	0.575173
$479$	−25.8231	−1.17989	−0.589943	−	0.807445i	$-0.700850\pi$
$479$	−25.8231	−1.17989	−0.589943	+	0.807445i	$0.700850\pi$
$480$	−5.85568	−0.267274
$481$	−6.06862	−0.276705
$482$	23.1708	1.05540
$483$	−10.2832	−0.467903
$484$	11.8086	0.536756
$485$	−0.968849	−0.0439932
$486$	−35.2810	−1.60038
$487$	−8.51661	−0.385925	−0.192962	−	0.981206i	$-0.561810\pi$
$487$	−8.51661	−0.385925	−0.192962	+	0.981206i	$0.561810\pi$
$488$	18.9425	0.857485
$489$	20.0806	0.908076
$490$	−27.8471	−1.25800
$491$	13.1537	0.593618	0.296809	−	0.954937i	$-0.404078\pi$
$491$	13.1537	0.593618	0.296809	+	0.954937i	$0.404078\pi$
$492$	−28.6331	−1.29088
$493$	−10.5883	−0.476875
$494$	−10.4225	−0.468932
$495$	11.2778	0.506901
$496$	6.91835	0.310643
$497$	−2.66061	−0.119345
$498$	40.6078	1.81968
$499$	23.0973	1.03398	0.516989	−	0.855992i	$-0.327053\pi$
$499$	23.0973	1.03398	0.516989	+	0.855992i	$0.327053\pi$
$500$	−51.1810	−2.28888
$501$	7.11877	0.318043
$502$	62.4373	2.78671
$503$	−34.5435	−1.54022	−0.770109	−	0.637913i	$-0.779798\pi$
$503$	−34.5435	−1.54022	−0.770109	+	0.637913i	$0.779798\pi$
$504$	−30.9786	−1.37990
$505$	−33.1615	−1.47567
$506$	22.2548	0.989347
$507$	1.20166	0.0533676
$508$	56.6660	2.51415
$509$	34.7968	1.54234	0.771170	−	0.636630i	$-0.219672\pi$
$509$	34.7968	1.54234	0.771170	+	0.636630i	$0.219672\pi$
$510$	−26.1978	−1.16006
$511$	45.6651	2.02010
$512$	47.4453	2.09681
$513$	−22.8500	−1.00885
$514$	−13.6886	−0.603778
$515$	1.95194	0.0860129
$516$	52.0558	2.29163
$517$	46.2113	2.03237
$518$	−54.0339	−2.37411
$519$	−28.5478	−1.25311
$520$	−10.8992	−0.477960
$521$	8.77346	0.384372	0.192186	−	0.981359i	$-0.438442\pi$
$521$	8.77346	0.384372	0.192186	+	0.981359i	$0.438442\pi$
$522$	−9.19880	−0.402621
$523$	−0.0881980	−0.00385663	−0.00192831	−	0.999998i	$-0.500614\pi$
$523$	−0.0881980	−0.00385663	−0.00192831	+	0.999998i	$0.500614\pi$
$524$	6.78024	0.296196
$525$	5.09825	0.222506
$526$	−10.3514	−0.451341
$527$	5.65511	0.246341
$528$	−24.4147	−1.06251
$529$	−17.2396	−0.749549
$530$	43.4835	1.88880
$531$	6.62157	0.287352
$532$	−63.0375	−2.73302
$533$	−5.62509	−0.243650
$534$	31.5222	1.36410
$535$	33.1598	1.43362
$536$	−6.16584	−0.266324
$537$	−24.7403	−1.06762
$538$	−40.4253	−1.74286
$539$	−21.2131	−0.913713
$540$	−45.2679	−1.94802
$541$	34.6552	1.48994	0.744972	−	0.667096i	$-0.232463\pi$
$541$	34.6552	1.48994	0.744972	+	0.667096i	$0.232463\pi$
$542$	30.2159	1.29789
$543$	−30.9203	−1.32692
$544$	−11.1658	−0.478731
$545$	−17.3168	−0.741771
$546$	10.6994	0.457890
$547$	1.66015	0.0709829	0.0354914	−	0.999370i	$-0.488700\pi$
$547$	1.66015	0.0709829	0.0354914	+	0.999370i	$0.488700\pi$
$548$	52.4877	2.24216
$549$	5.27866	0.225288
$550$	−11.0335	−0.470472
$551$	−9.88064	−0.420929
$552$	−16.1040	−0.685430
$553$	−9.24212	−0.393015
$554$	−32.6351	−1.38653
$555$	−14.2344	−0.604217
$556$	−22.2170	−0.942209
$557$	7.87838	0.333818	0.166909	−	0.985972i	$-0.446621\pi$
$557$	7.87838	0.333818	0.166909	+	0.985972i	$0.446621\pi$
$558$	4.91298	0.207983
$559$	10.2266	0.432539
$560$	−38.0815	−1.60924
$561$	−19.9568	−0.842575
$562$	−41.1122	−1.73421
$563$	2.69731	0.113678	0.0568391	−	0.998383i	$-0.481898\pi$
$563$	2.69731	0.113678	0.0568391	+	0.998383i	$0.481898\pi$
$564$	−63.3491	−2.66748
$565$	−24.3498	−1.02440
$566$	−5.06120	−0.212738
$567$	6.81296	0.286117
$568$	−4.16663	−0.174828
$569$	27.3651	1.14720	0.573602	−	0.819134i	$-0.305546\pi$
$569$	27.3651	1.14720	0.573602	+	0.819134i	$0.305546\pi$
$570$	−24.4468	−1.02396
$571$	−3.96589	−0.165967	−0.0829837	−	0.996551i	$-0.526445\pi$
$571$	−3.96589	−0.165967	−0.0829837	+	0.996551i	$0.526445\pi$
$572$	−15.7290	−0.657664
$573$	−12.5192	−0.522999
$574$	−50.0847	−2.09050
$575$	−2.85589	−0.119099
$576$	7.32762	0.305317
$577$	10.2712	0.427596	0.213798	−	0.976878i	$-0.431417\pi$
$577$	10.2712	0.427596	0.213798	+	0.976878i	$0.431417\pi$
$578$	−7.50258	−0.312066
$579$	−5.98264	−0.248630
$580$	−19.5744	−0.812783
$581$	48.2500	2.00175
$582$	1.48944	0.0617394
$583$	33.1245	1.37188
$584$	71.5134	2.95924
$585$	−3.03725	−0.125575
$586$	−8.67897	−0.358525
$587$	−13.2140	−0.545402	−0.272701	−	0.962099i	$-0.587917\pi$
$587$	−13.2140	−0.545402	−0.272701	+	0.962099i	$0.587917\pi$
$588$	29.0802	1.19925
$589$	5.27714	0.217441
$590$	20.7428	0.853970
$591$	10.3048	0.423883
$592$	−33.2058	−1.36475
$593$	35.2784	1.44871	0.724356	−	0.689427i	$-0.242137\pi$
$593$	35.2784	1.44871	0.724356	+	0.689427i	$0.242137\pi$
$594$	−50.7651	−2.08292
$595$	−31.1281	−1.27613
$596$	−28.1649	−1.15368
$597$	29.6056	1.21168
$598$	−5.99347	−0.245091
$599$	13.3169	0.544113	0.272057	−	0.962281i	$-0.412296\pi$
$599$	13.3169	0.544113	0.272057	+	0.962281i	$0.412296\pi$
$600$	7.98406	0.325948
$601$	−27.2643	−1.11213	−0.556067	−	0.831137i	$-0.687690\pi$
$601$	−27.2643	−1.11213	−0.556067	+	0.831137i	$0.687690\pi$
$602$	91.0557	3.71115
$603$	−1.71822	−0.0699714
$604$	68.6618	2.79381
$605$	5.44139	0.221224
$606$	50.9802	2.07093
$607$	−37.7518	−1.53230	−0.766149	−	0.642662i	$-0.777830\pi$
$607$	−37.7518	−1.53230	−0.766149	+	0.642662i	$0.777830\pi$
$608$	−10.4195	−0.422568
$609$	10.1431	0.411018
$610$	16.5360	0.669524
$611$	−12.4452	−0.503480
$612$	−29.4803	−1.19167
$613$	−24.6496	−0.995588	−0.497794	−	0.867295i	$-0.665856\pi$
$613$	−24.6496	−0.995588	−0.497794	+	0.867295i	$0.665856\pi$
$614$	12.1237	0.489272
$615$	−13.1941	−0.532036
$616$	−73.9255	−2.97854
$617$	−41.5805	−1.67397	−0.836984	−	0.547227i	$-0.815684\pi$
$617$	−41.5805	−1.67397	−0.836984	+	0.547227i	$0.815684\pi$
$618$	−3.00079	−0.120709
$619$	−4.08790	−0.164306	−0.0821532	−	0.996620i	$-0.526180\pi$
$619$	−4.08790	−0.164306	−0.0821532	+	0.996620i	$0.526180\pi$
$620$	10.4545	0.419862
$621$	−13.1399	−0.527286
$622$	46.5402	1.86609
$623$	37.4546	1.50059
$624$	6.57515	0.263217
$625$	−17.6345	−0.705381
$626$	−22.7101	−0.907677
$627$	−18.6229	−0.743727
$628$	80.4186	3.20905
$629$	−27.1427	−1.08225
$630$	−27.0431	−1.07742
$631$	−20.7515	−0.826103	−0.413051	−	0.910708i	$-0.635537\pi$
$631$	−20.7515	−0.826103	−0.413051	+	0.910708i	$0.635537\pi$
$632$	−14.4735	−0.575726
$633$	5.46641	0.217270
$634$	−4.89874	−0.194554
$635$	26.1116	1.03621
$636$	−45.4090	−1.80058
$637$	5.71293	0.226354
$638$	−21.9515	−0.869068
$639$	−1.16111	−0.0459327
$640$	32.7006	1.29260
$641$	45.0789	1.78051	0.890255	−	0.455463i	$-0.150526\pi$
$641$	45.0789	1.78051	0.890255	+	0.455463i	$0.150526\pi$
$642$	−50.9777	−2.01193
$643$	−9.46005	−0.373068	−0.186534	−	0.982448i	$-0.559725\pi$
$643$	−9.46005	−0.373068	−0.186534	+	0.982448i	$0.559725\pi$
$644$	−36.2497	−1.42844
$645$	23.9872	0.944497
$646$	−46.6161	−1.83408
$647$	−38.7702	−1.52422	−0.762108	−	0.647450i	$-0.775835\pi$
$647$	−38.7702	−1.52422	−0.762108	+	0.647450i	$0.775835\pi$
$648$	10.6694	0.419133
$649$	15.8013	0.620256
$650$	2.97146	0.116550
$651$	−5.41730	−0.212321
$652$	70.7866	2.77222
$653$	10.9164	0.427194	0.213597	−	0.976922i	$-0.431482\pi$
$653$	10.9164	0.427194	0.213597	+	0.976922i	$0.431482\pi$
$654$	26.6217	1.04099
$655$	3.12433	0.122077
$656$	−30.7789	−1.20171
$657$	19.9285	0.777484
$658$	−110.810	−4.31982
$659$	47.3207	1.84335	0.921676	−	0.387959i	$-0.126820\pi$
$659$	47.3207	1.84335	0.921676	+	0.387959i	$0.126820\pi$
$660$	−36.8936	−1.43608
$661$	25.1177	0.976966	0.488483	−	0.872574i	$-0.337551\pi$
$661$	25.1177	0.976966	0.488483	+	0.872574i	$0.337551\pi$
$662$	−42.9988	−1.67120
$663$	5.37458	0.208731
$664$	75.5615	2.93236
$665$	−29.0476	−1.12642
$666$	−23.5807	−0.913733
$667$	−5.68186	−0.220002
$668$	25.0946	0.970938
$669$	−5.24923	−0.202947
$670$	−5.38254	−0.207946
$671$	12.5967	0.486289
$672$	10.6963	0.412618
$673$	45.1706	1.74120	0.870599	−	0.491992i	$-0.163731\pi$
$673$	45.1706	1.74120	0.870599	+	0.491992i	$0.163731\pi$
$674$	22.7063	0.874614
$675$	6.51453	0.250744
$676$	4.23600	0.162923
$677$	−12.4779	−0.479565	−0.239782	−	0.970827i	$-0.577076\pi$
$677$	−12.4779	−0.479565	−0.239782	+	0.970827i	$0.577076\pi$
$678$	37.4337	1.43763
$679$	1.76975	0.0679167
$680$	−48.7479	−1.86940
$681$	23.9434	0.917514
$682$	11.7240	0.448937
$683$	−3.69855	−0.141521	−0.0707606	−	0.997493i	$-0.522543\pi$
$683$	−3.69855	−0.141521	−0.0707606	+	0.997493i	$0.522543\pi$
$684$	−27.5099	−1.05187
$685$	24.1862	0.924109
$686$	−11.4598	−0.437539
$687$	10.6192	0.405147
$688$	55.9571	2.13334
$689$	−8.92080	−0.339855
$690$	−14.0581	−0.535184
$691$	4.16224	0.158339	0.0791696	−	0.996861i	$-0.474773\pi$
$691$	4.16224	0.158339	0.0791696	+	0.996861i	$0.474773\pi$
$692$	−100.635	−3.82555
$693$	−20.6007	−0.782555
$694$	−37.9364	−1.44005
$695$	−10.2375	−0.388332
$696$	15.8845	0.602099
$697$	−25.1589	−0.952963
$698$	3.82023	0.144598
$699$	29.9440	1.13259
$700$	17.9720	0.679276
$701$	33.3548	1.25979	0.629897	−	0.776679i	$-0.283097\pi$
$701$	33.3548	1.25979	0.629897	+	0.776679i	$0.283097\pi$
$702$	13.6716	0.516002
$703$	−25.3285	−0.955284
$704$	17.4862	0.659036
$705$	−29.1912	−1.09940
$706$	3.19398	0.120207
$707$	60.5744	2.27814
$708$	−21.6614	−0.814084
$709$	−0.499562	−0.0187614	−0.00938072	−	0.999956i	$-0.502986\pi$
$709$	−0.499562	−0.0187614	−0.00938072	+	0.999956i	$0.502986\pi$
$710$	−3.63730	−0.136506
$711$	−4.03331	−0.151261
$712$	58.6554	2.19820
$713$	3.03462	0.113647
$714$	47.8542	1.79090
$715$	−7.24791	−0.271057
$716$	−87.2126	−3.25929
$717$	−6.05120	−0.225986
$718$	47.4034	1.76908
$719$	−46.2363	−1.72432	−0.862161	−	0.506635i	$-0.830889\pi$
$719$	−46.2363	−1.72432	−0.862161	+	0.506635i	$0.830889\pi$
$720$	−16.6190	−0.619352
$721$	−3.56552	−0.132787
$722$	3.94644	0.146871
$723$	−11.1499	−0.414668
$724$	−108.998	−4.05087
$725$	2.81697	0.104619
$726$	−8.36523	−0.310463
$727$	20.6085	0.764325	0.382163	−	0.924095i	$-0.375179\pi$
$727$	20.6085	0.764325	0.382163	+	0.924095i	$0.375179\pi$
$728$	19.9090	0.737875
$729$	22.7097	0.841100
$730$	62.4284	2.31058
$731$	45.7398	1.69175
$732$	−17.2683	−0.638253
$733$	42.3451	1.56405	0.782027	−	0.623245i	$-0.214186\pi$
$733$	42.3451	1.56405	0.782027	+	0.623245i	$0.214186\pi$
$734$	−17.2137	−0.635368
$735$	13.4001	0.494270
$736$	−5.99175	−0.220859
$737$	−4.10027	−0.151035
$738$	−21.8573	−0.804577
$739$	−33.5858	−1.23547	−0.617737	−	0.786385i	$-0.711950\pi$
$739$	−33.5858	−1.23547	−0.617737	+	0.786385i	$0.711950\pi$
$740$	−50.1781	−1.84458
$741$	5.01535	0.184244
$742$	−79.4291	−2.91594
$743$	34.4001	1.26202	0.631008	−	0.775776i	$-0.282641\pi$
$743$	34.4001	1.26202	0.631008	+	0.775776i	$0.282641\pi$
$744$	−8.48372	−0.311028
$745$	−12.9784	−0.475490
$746$	5.74800	0.210449
$747$	21.0566	0.770420
$748$	−70.3501	−2.57225
$749$	−60.5714	−2.21323
$750$	36.2566	1.32390
$751$	−25.1142	−0.916430	−0.458215	−	0.888841i	$-0.651511\pi$
$751$	−25.1142	−0.916430	−0.458215	+	0.888841i	$0.651511\pi$
$752$	−68.0968	−2.48323
$753$	−30.0450	−1.09490
$754$	5.91178	0.215294
$755$	31.6392	1.15147
$756$	82.6886	3.00736
$757$	−42.7689	−1.55446	−0.777232	−	0.629214i	$-0.783377\pi$
$757$	−42.7689	−1.55446	−0.777232	+	0.629214i	$0.783377\pi$
$758$	27.1385	0.985715
$759$	−10.7091	−0.388715
$760$	−45.4897	−1.65008
$761$	17.4860	0.633867	0.316933	−	0.948448i	$-0.397347\pi$
$761$	17.4860	0.633867	0.316933	+	0.948448i	$0.397347\pi$
$762$	−40.1422	−1.45420
$763$	31.6318	1.14515
$764$	−44.1319	−1.59664
$765$	−13.5845	−0.491148
$766$	−54.7902	−1.97965
$767$	−4.25547	−0.153656
$768$	−38.9539	−1.40563
$769$	41.1380	1.48347	0.741737	−	0.670691i	$-0.234003\pi$
$769$	41.1380	1.48347	0.741737	+	0.670691i	$0.234003\pi$
$770$	−64.5340	−2.32565
$771$	6.58700	0.237225
$772$	−21.0896	−0.759030
$773$	−23.3825	−0.841009	−0.420505	−	0.907290i	$-0.638147\pi$
$773$	−23.3825	−0.841009	−0.420505	+	0.907290i	$0.638147\pi$
$774$	39.7372	1.42832
$775$	−1.50451	−0.0540436
$776$	2.77150	0.0994910
$777$	26.0013	0.932791
$778$	31.5768	1.13208
$779$	−23.4774	−0.841164
$780$	9.93586	0.355761
$781$	−2.77080	−0.0991469
$782$	−26.8066	−0.958600
$783$	12.9608	0.463181
$784$	31.2595	1.11641
$785$	37.0568	1.32261
$786$	−4.80313	−0.171322
$787$	−54.3993	−1.93912	−0.969562	−	0.244846i	$-0.921263\pi$
$787$	−54.3993	−1.93912	−0.969562	+	0.244846i	$0.921263\pi$
$788$	36.3258	1.29405
$789$	4.98111	0.177332
$790$	−12.6348	−0.449527
$791$	44.4786	1.58148
$792$	−32.2615	−1.14636
$793$	−3.39243	−0.120469
$794$	−77.9305	−2.76565
$795$	−20.9244	−0.742112
$796$	104.363	3.69907
$797$	6.51372	0.230728	0.115364	−	0.993323i	$-0.463197\pi$
$797$	6.51372	0.230728	0.115364	+	0.993323i	$0.463197\pi$
$798$	44.6558	1.58080
$799$	−55.6628	−1.96921
$800$	2.97060	0.105027
$801$	16.3454	0.577535
$802$	54.8011	1.93509
$803$	47.5562	1.67822
$804$	5.62089	0.198233
$805$	−16.7038	−0.588731
$806$	−3.15742	−0.111215
$807$	19.4528	0.684771
$808$	94.8620	3.33723
$809$	−46.8039	−1.64554	−0.822768	−	0.568377i	$-0.807571\pi$
$809$	−46.8039	−1.64554	−0.822768	+	0.568377i	$0.807571\pi$
$810$	9.31394	0.327259
$811$	35.2587	1.23810	0.619051	−	0.785351i	$-0.287518\pi$
$811$	35.2587	1.23810	0.619051	+	0.785351i	$0.287518\pi$
$812$	35.7556	1.25478
$813$	−14.5400	−0.509941
$814$	−56.2716	−1.97232
$815$	32.6184	1.14257
$816$	29.4082	1.02949
$817$	42.6826	1.49328
$818$	−64.9535	−2.27105
$819$	5.54799	0.193862
$820$	−46.5107	−1.62422
$821$	19.6320	0.685162	0.342581	−	0.939488i	$-0.388699\pi$
$821$	19.6320	0.685162	0.342581	+	0.939488i	$0.388699\pi$
$822$	−37.1823	−1.29688
$823$	16.0107	0.558098	0.279049	−	0.960277i	$-0.409981\pi$
$823$	16.0107	0.558098	0.279049	+	0.960277i	$0.409981\pi$
$824$	−5.58375	−0.194519
$825$	5.30938	0.184849
$826$	−37.8899	−1.31836
$827$	27.9513	0.971962	0.485981	−	0.873969i	$-0.338462\pi$
$827$	27.9513	0.971962	0.485981	+	0.873969i	$0.338462\pi$
$828$	−15.8196	−0.549768
$829$	0.256685	0.00891504	0.00445752	−	0.999990i	$-0.498581\pi$
$829$	0.256685	0.00891504	0.00445752	+	0.999990i	$0.498581\pi$
$830$	65.9622	2.28958
$831$	15.7041	0.544770
$832$	−4.70923	−0.163263
$833$	25.5518	0.885317
$834$	15.7385	0.544980
$835$	11.5635	0.400173
$836$	−65.6480	−2.27048
$837$	−6.92222	−0.239267
$838$	56.0279	1.93545
$839$	−10.1746	−0.351267	−0.175634	−	0.984456i	$-0.556197\pi$
$839$	−10.1746	−0.351267	−0.175634	+	0.984456i	$0.556197\pi$
$840$	46.6979	1.61123
$841$	−23.3956	−0.806744
$842$	60.0512	2.06950
$843$	19.7833	0.681373
$844$	19.2698	0.663293
$845$	1.95194	0.0671489
$846$	−48.3580	−1.66258
$847$	−9.93953	−0.341526
$848$	−48.8121	−1.67622
$849$	2.43547	0.0835850
$850$	13.2902	0.455851
$851$	−14.5652	−0.499287
$852$	3.79837	0.130130
$853$	−31.0893	−1.06448	−0.532238	−	0.846595i	$-0.678649\pi$
$853$	−31.0893	−1.06448	−0.532238	+	0.846595i	$0.678649\pi$
$854$	−30.2055	−1.03361
$855$	−12.6765	−0.433528
$856$	−94.8573	−3.24216
$857$	8.87382	0.303124	0.151562	−	0.988448i	$-0.451570\pi$
$857$	8.87382	0.303124	0.151562	+	0.988448i	$0.451570\pi$
$858$	11.1424	0.380397
$859$	−23.7687	−0.810978	−0.405489	−	0.914100i	$-0.632899\pi$
$859$	−23.7687	−0.810978	−0.405489	+	0.914100i	$0.632899\pi$
$860$	84.5580	2.88340
$861$	24.1009	0.821358
$862$	1.82894	0.0622941
$863$	−49.0900	−1.67104	−0.835521	−	0.549459i	$-0.814834\pi$
$863$	−49.0900	−1.67104	−0.835521	+	0.549459i	$0.814834\pi$
$864$	13.6677	0.464984
$865$	−46.3723	−1.57670
$866$	35.9991	1.22330
$867$	3.61027	0.122611
$868$	−19.0967	−0.648183
$869$	−9.62486	−0.326501
$870$	13.8665	0.470119
$871$	1.10425	0.0374160
$872$	49.5367	1.67752
$873$	0.772328	0.0261393
$874$	−25.0149	−0.846140
$875$	43.0799	1.45637
$876$	−65.1928	−2.20266
$877$	26.1436	0.882808	0.441404	−	0.897308i	$-0.354481\pi$
$877$	26.1436	0.882808	0.441404	+	0.897308i	$0.354481\pi$
$878$	−17.5410	−0.591979
$879$	4.17635	0.140865
$880$	−39.6585	−1.33689
$881$	12.0657	0.406503	0.203251	−	0.979127i	$-0.434849\pi$
$881$	12.0657	0.406503	0.203251	+	0.979127i	$0.434849\pi$
$882$	22.1986	0.747465
$883$	18.7406	0.630670	0.315335	−	0.948980i	$-0.397883\pi$
$883$	18.7406	0.630670	0.315335	+	0.948980i	$0.397883\pi$
$884$	18.9461	0.637225
$885$	−9.98153	−0.335525
$886$	15.9744	0.536672
$887$	−45.5093	−1.52805	−0.764026	−	0.645185i	$-0.776780\pi$
$887$	−45.5093	−1.52805	−0.764026	+	0.645185i	$0.776780\pi$
$888$	40.7191	1.36644
$889$	−47.6968	−1.59970
$890$	51.2038	1.71636
$891$	7.09510	0.237695
$892$	−18.5042	−0.619566
$893$	−51.9424	−1.73819
$894$	19.9521	0.667296
$895$	−40.1874	−1.34332
$896$	−59.7326	−1.99553
$897$	2.88408	0.0962965
$898$	40.5692	1.35381
$899$	−2.99326	−0.0998307
$900$	7.84306	0.261435
$901$	−39.8994	−1.32924
$902$	−52.1589	−1.73670
$903$	−43.8163	−1.45812
$904$	69.6552	2.31670
$905$	−50.2260	−1.66957
$906$	−48.6400	−1.61596
$907$	10.0551	0.333873	0.166937	−	0.985968i	$-0.446612\pi$
$907$	10.0551	0.333873	0.166937	+	0.985968i	$0.446612\pi$
$908$	84.4036	2.80103
$909$	26.4350	0.876794
$910$	17.3797	0.576133
$911$	23.7526	0.786958	0.393479	−	0.919334i	$-0.371271\pi$
$911$	23.7526	0.786958	0.393479	+	0.919334i	$0.371271\pi$
$912$	27.4426	0.908716
$913$	50.2482	1.66297
$914$	59.9719	1.98369
$915$	−7.95719	−0.263056
$916$	37.4339	1.23685
$917$	−5.70705	−0.188463
$918$	61.1480	2.01819
$919$	−8.84979	−0.291928	−0.145964	−	0.989290i	$-0.546628\pi$
$919$	−8.84979	−0.291928	−0.145964	+	0.989290i	$0.546628\pi$
$920$	−26.1588	−0.862430
$921$	−5.83395	−0.192235
$922$	−64.2982	−2.11755
$923$	0.746206	0.0245617
$924$	67.3917	2.21702
$925$	7.22116	0.237430
$926$	28.8060	0.946623
$927$	−1.55601	−0.0511061
$928$	5.91008	0.194008
$929$	52.0290	1.70702	0.853509	−	0.521078i	$-0.174470\pi$
$929$	52.0290	1.70702	0.853509	+	0.521078i	$0.174470\pi$
$930$	−7.40595	−0.242851
$931$	23.8440	0.781454
$932$	105.556	3.45761
$933$	−22.3953	−0.733188
$934$	−23.9890	−0.784943
$935$	−32.4172	−1.06016
$936$	8.68838	0.283988
$937$	−16.1818	−0.528637	−0.264319	−	0.964435i	$-0.585147\pi$
$937$	−16.1818	−0.528637	−0.264319	+	0.964435i	$0.585147\pi$
$938$	9.83202	0.321027
$939$	10.9282	0.356627
$940$	−102.903	−3.35631
$941$	−29.5618	−0.963686	−0.481843	−	0.876258i	$-0.660032\pi$
$941$	−29.5618	−0.963686	−0.481843	+	0.876258i	$0.660032\pi$
$942$	−56.9686	−1.85614
$943$	−13.5006	−0.439641
$944$	−23.2848	−0.757854
$945$	38.1028	1.23948
$946$	94.8266	3.08308
$947$	52.0868	1.69260	0.846298	−	0.532711i	$-0.178827\pi$
$947$	52.0868	1.69260	0.846298	+	0.532711i	$0.178827\pi$
$948$	13.1943	0.428532
$949$	−12.8074	−0.415746
$950$	12.4019	0.402372
$951$	2.35729	0.0764404
$952$	89.0453	2.88598
$953$	−46.3857	−1.50258	−0.751289	−	0.659973i	$-0.770568\pi$
$953$	−46.3857	−1.50258	−0.751289	+	0.659973i	$0.770568\pi$
$954$	−34.6633	−1.12227
$955$	−20.3359	−0.658054
$956$	−21.3312	−0.689901
$957$	10.5631	0.341458
$958$	64.4854	2.08343
$959$	−44.1798	−1.42664
$960$	−11.0458	−0.356503
$961$	−29.4013	−0.948430
$962$	15.1546	0.488603
$963$	−26.4337	−0.851814
$964$	−39.3046	−1.26592
$965$	−9.71804	−0.312835
$966$	25.6793	0.826217
$967$	−15.9337	−0.512392	−0.256196	−	0.966625i	$-0.582469\pi$
$967$	−15.9337	−0.512392	−0.256196	+	0.966625i	$0.582469\pi$
$968$	−15.5657	−0.500300
$969$	22.4318	0.720613
$970$	2.41941	0.0776825
$971$	32.5168	1.04351	0.521757	−	0.853094i	$-0.325277\pi$
$971$	32.5168	1.04351	0.521757	+	0.853094i	$0.325277\pi$
$972$	59.8472	1.91960
$973$	18.7004	0.599508
$974$	21.2677	0.681460
$975$	−1.42988	−0.0457927
$976$	−18.5624	−0.594168
$977$	−24.3793	−0.779964	−0.389982	−	0.920822i	$-0.627519\pi$
$977$	−24.3793	−0.779964	−0.389982	+	0.920822i	$0.627519\pi$
$978$	−50.1453	−1.60347
$979$	39.0057	1.24663
$980$	47.2370	1.50893
$981$	13.8043	0.440737
$982$	−32.8474	−1.04820
$983$	−28.1671	−0.898391	−0.449195	−	0.893434i	$-0.648289\pi$
$983$	−28.1671	−0.898391	−0.449195	+	0.893434i	$0.648289\pi$
$984$	37.7430	1.20320
$985$	16.7389	0.533344
$986$	26.4412	0.842059
$987$	53.3221	1.69726
$988$	17.6797	0.562468
$989$	24.5446	0.780473
$990$	−28.1630	−0.895079
$991$	16.0984	0.511383	0.255692	−	0.966758i	$-0.417697\pi$
$991$	16.0984	0.511383	0.255692	+	0.966758i	$0.417697\pi$
$992$	−3.15651	−0.100219
$993$	20.6912	0.656615
$994$	6.64408	0.210737
$995$	48.0905	1.52457
$996$	−68.8832	−2.18265
$997$	−28.4832	−0.902072	−0.451036	−	0.892506i	$-0.648945\pi$
$997$	−28.4832	−0.902072	−0.451036	+	0.892506i	$0.648945\pi$
$998$	−57.6786	−1.82578
$999$	33.2244	1.05117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.d.1.3	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.d.1.3	✓	19	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49720 q^{2} +1.20166 q^{3} +4.23600 q^{4} +1.95194 q^{5} -3.00079 q^{6} -3.56552 q^{7} -5.58375 q^{8} -1.55601 q^{9} +O(q^{10})\)	\(q-2.49720 q^{2} +1.20166 q^{3} +4.23600 q^{4} +1.95194 q^{5} -3.00079 q^{6} -3.56552 q^{7} -5.58375 q^{8} -1.55601 q^{9} -4.87439 q^{10} -3.71318 q^{11} +5.09024 q^{12} +1.00000 q^{13} +8.90381 q^{14} +2.34557 q^{15} +5.47172 q^{16} +4.47263 q^{17} +3.88567 q^{18} +4.17369 q^{19} +8.26844 q^{20} -4.28454 q^{21} +9.27254 q^{22} +2.40008 q^{23} -6.70977 q^{24} -1.18992 q^{25} -2.49720 q^{26} -5.47478 q^{27} -15.1036 q^{28} -2.36737 q^{29} -5.85736 q^{30} +1.26438 q^{31} -2.49648 q^{32} -4.46198 q^{33} -11.1690 q^{34} -6.95969 q^{35} -6.59127 q^{36} -6.06862 q^{37} -10.4225 q^{38} +1.20166 q^{39} -10.8992 q^{40} -5.62509 q^{41} +10.6994 q^{42} +10.2266 q^{43} -15.7290 q^{44} -3.03725 q^{45} -5.99347 q^{46} -12.4452 q^{47} +6.57515 q^{48} +5.71293 q^{49} +2.97146 q^{50} +5.37458 q^{51} +4.23600 q^{52} -8.92080 q^{53} +13.6716 q^{54} -7.24791 q^{55} +19.9090 q^{56} +5.01535 q^{57} +5.91178 q^{58} -4.25547 q^{59} +9.93586 q^{60} -3.39243 q^{61} -3.15742 q^{62} +5.54799 q^{63} -4.70923 q^{64} +1.95194 q^{65} +11.1424 q^{66} +1.10425 q^{67} +18.9461 q^{68} +2.88408 q^{69} +17.3797 q^{70} +0.746206 q^{71} +8.68838 q^{72} -12.8074 q^{73} +15.1546 q^{74} -1.42988 q^{75} +17.6797 q^{76} +13.2394 q^{77} -3.00079 q^{78} +2.59208 q^{79} +10.6805 q^{80} -1.91079 q^{81} +14.0470 q^{82} -13.5324 q^{83} -18.1493 q^{84} +8.73032 q^{85} -25.5379 q^{86} -2.84477 q^{87} +20.7334 q^{88} -10.5047 q^{89} +7.58461 q^{90} -3.56552 q^{91} +10.1667 q^{92} +1.51936 q^{93} +31.0782 q^{94} +8.14680 q^{95} -2.99992 q^{96} -0.496351 q^{97} -14.2663 q^{98} +5.77775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

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