LMFDB - Embedded newform 1502.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 20x^{9} - 7x^{8} + 134x^{7} + 70x^{6} - 354x^{5} - 193x^{4} + 341x^{3} + 163x^{2} - 72x - 16 $ x^11 - 20x^9 - 7x^8 + 134x^7 + 70x^6 - 354x^5 - 193x^4 + 341x^3 + 163x^2 - 72*x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37027$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.37027 q^{3} +1.00000 q^{4} -4.42460 q^{5} -3.37027 q^{6} +1.01197 q^{7} +1.00000 q^{8} +8.35874 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.37027 q^{3} +1.00000 q^{4} -4.42460 q^{5} -3.37027 q^{6} +1.01197 q^{7} +1.00000 q^{8} +8.35874 q^{9} -4.42460 q^{10} +3.10827 q^{11} -3.37027 q^{12} -4.40497 q^{13} +1.01197 q^{14} +14.9121 q^{15} +1.00000 q^{16} +0.837325 q^{17} +8.35874 q^{18} +6.78693 q^{19} -4.42460 q^{20} -3.41062 q^{21} +3.10827 q^{22} +2.91493 q^{23} -3.37027 q^{24} +14.5771 q^{25} -4.40497 q^{26} -18.0604 q^{27} +1.01197 q^{28} -6.10598 q^{29} +14.9121 q^{30} -6.14393 q^{31} +1.00000 q^{32} -10.4757 q^{33} +0.837325 q^{34} -4.47757 q^{35} +8.35874 q^{36} -11.5328 q^{37} +6.78693 q^{38} +14.8459 q^{39} -4.42460 q^{40} +6.65699 q^{41} -3.41062 q^{42} -7.74329 q^{43} +3.10827 q^{44} -36.9841 q^{45} +2.91493 q^{46} -3.07265 q^{47} -3.37027 q^{48} -5.97591 q^{49} +14.5771 q^{50} -2.82201 q^{51} -4.40497 q^{52} +11.4980 q^{53} -18.0604 q^{54} -13.7529 q^{55} +1.01197 q^{56} -22.8738 q^{57} -6.10598 q^{58} +0.695479 q^{59} +14.9121 q^{60} +4.68732 q^{61} -6.14393 q^{62} +8.45880 q^{63} +1.00000 q^{64} +19.4902 q^{65} -10.4757 q^{66} -4.54022 q^{67} +0.837325 q^{68} -9.82412 q^{69} -4.47757 q^{70} -7.73693 q^{71} +8.35874 q^{72} -1.55058 q^{73} -11.5328 q^{74} -49.1287 q^{75} +6.78693 q^{76} +3.14548 q^{77} +14.8459 q^{78} -2.20310 q^{79} -4.42460 q^{80} +35.7923 q^{81} +6.65699 q^{82} +6.21840 q^{83} -3.41062 q^{84} -3.70483 q^{85} -7.74329 q^{86} +20.5788 q^{87} +3.10827 q^{88} -0.410844 q^{89} -36.9841 q^{90} -4.45770 q^{91} +2.91493 q^{92} +20.7067 q^{93} -3.07265 q^{94} -30.0295 q^{95} -3.37027 q^{96} -0.409765 q^{97} -5.97591 q^{98} +25.9813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.37027	−1.94583	−0.972914	−	0.231168i	$-0.925745\pi$
$3$	−3.37027	−1.94583	−0.972914	+	0.231168i	$0.925745\pi$
$4$	1.00000	0.500000
$5$	−4.42460	−1.97874	−0.989371	−	0.145416i	$-0.953548\pi$
$5$	−4.42460	−1.97874	−0.989371	+	0.145416i	$0.953548\pi$
$6$	−3.37027	−1.37591
$7$	1.01197	0.382489	0.191245	−	0.981542i	$-0.438748\pi$
$7$	1.01197	0.382489	0.191245	+	0.981542i	$0.438748\pi$
$8$	1.00000	0.353553
$9$	8.35874	2.78625
$10$	−4.42460	−1.39918
$11$	3.10827	0.937180	0.468590	−	0.883416i	$-0.344762\pi$
$11$	3.10827	0.937180	0.468590	+	0.883416i	$0.344762\pi$
$12$	−3.37027	−0.972914
$13$	−4.40497	−1.22172	−0.610859	−	0.791739i	$-0.709176\pi$
$13$	−4.40497	−1.22172	−0.610859	+	0.791739i	$0.709176\pi$
$14$	1.01197	0.270461
$15$	14.9121	3.85029
$16$	1.00000	0.250000
$17$	0.837325	0.203081	0.101541	−	0.994831i	$-0.467623\pi$
$17$	0.837325	0.203081	0.101541	+	0.994831i	$0.467623\pi$
$18$	8.35874	1.97017
$19$	6.78693	1.55703	0.778514	−	0.627627i	$-0.215974\pi$
$19$	6.78693	1.55703	0.778514	+	0.627627i	$0.215974\pi$
$20$	−4.42460	−0.989371
$21$	−3.41062	−0.744258
$22$	3.10827	0.662686
$23$	2.91493	0.607806	0.303903	−	0.952703i	$-0.401710\pi$
$23$	2.91493	0.607806	0.303903	+	0.952703i	$0.401710\pi$
$24$	−3.37027	−0.687954
$25$	14.5771	2.91542
$26$	−4.40497	−0.863885
$27$	−18.0604	−3.47573
$28$	1.01197	0.191245
$29$	−6.10598	−1.13385	−0.566926	−	0.823769i	$-0.691868\pi$
$29$	−6.10598	−1.13385	−0.566926	+	0.823769i	$0.691868\pi$
$30$	14.9121	2.72257
$31$	−6.14393	−1.10348	−0.551741	−	0.834016i	$-0.686036\pi$
$31$	−6.14393	−1.10348	−0.551741	+	0.834016i	$0.686036\pi$
$32$	1.00000	0.176777
$33$	−10.4757	−1.82359
$34$	0.837325	0.143600
$35$	−4.47757	−0.756847
$36$	8.35874	1.39312
$37$	−11.5328	−1.89598	−0.947989	−	0.318303i	$-0.896887\pi$
$37$	−11.5328	−1.89598	−0.947989	+	0.318303i	$0.896887\pi$
$38$	6.78693	1.10099
$39$	14.8459	2.37725
$40$	−4.42460	−0.699591
$41$	6.65699	1.03965	0.519824	−	0.854273i	$-0.325998\pi$
$41$	6.65699	1.03965	0.519824	+	0.854273i	$0.325998\pi$
$42$	−3.41062	−0.526270
$43$	−7.74329	−1.18084	−0.590421	−	0.807096i	$-0.701038\pi$
$43$	−7.74329	−1.18084	−0.590421	+	0.807096i	$0.701038\pi$
$44$	3.10827	0.468590
$45$	−36.9841	−5.51326
$46$	2.91493	0.429784
$47$	−3.07265	−0.448192	−0.224096	−	0.974567i	$-0.571943\pi$
$47$	−3.07265	−0.448192	−0.224096	+	0.974567i	$0.571943\pi$
$48$	−3.37027	−0.486457
$49$	−5.97591	−0.853702
$50$	14.5771	2.06151
$51$	−2.82201	−0.395161
$52$	−4.40497	−0.610859
$53$	11.4980	1.57937	0.789683	−	0.613516i	$-0.210245\pi$
$53$	11.4980	1.57937	0.789683	+	0.613516i	$0.210245\pi$
$54$	−18.0604	−2.45771
$55$	−13.7529	−1.85444
$56$	1.01197	0.135230
$57$	−22.8738	−3.02971
$58$	−6.10598	−0.801755
$59$	0.695479	0.0905436	0.0452718	−	0.998975i	$-0.485585\pi$
$59$	0.695479	0.0905436	0.0452718	+	0.998975i	$0.485585\pi$
$60$	14.9121	1.92514
$61$	4.68732	0.600150	0.300075	−	0.953916i	$-0.402988\pi$
$61$	4.68732	0.600150	0.300075	+	0.953916i	$0.402988\pi$
$62$	−6.14393	−0.780279
$63$	8.45880	1.06571
$64$	1.00000	0.125000
$65$	19.4902	2.41746
$66$	−10.4757	−1.28947
$67$	−4.54022	−0.554676	−0.277338	−	0.960772i	$-0.589452\pi$
$67$	−4.54022	−0.554676	−0.277338	+	0.960772i	$0.589452\pi$
$68$	0.837325	0.101541
$69$	−9.82412	−1.18269
$70$	−4.47757	−0.535172
$71$	−7.73693	−0.918204	−0.459102	−	0.888384i	$-0.651829\pi$
$71$	−7.73693	−0.918204	−0.459102	+	0.888384i	$0.651829\pi$
$72$	8.35874	0.985087
$73$	−1.55058	−0.181482	−0.0907408	−	0.995875i	$-0.528923\pi$
$73$	−1.55058	−0.181482	−0.0907408	+	0.995875i	$0.528923\pi$
$74$	−11.5328	−1.34066
$75$	−49.1287	−5.67290
$76$	6.78693	0.778514
$77$	3.14548	0.358461
$78$	14.8459	1.68097
$79$	−2.20310	−0.247868	−0.123934	−	0.992290i	$-0.539551\pi$
$79$	−2.20310	−0.247868	−0.123934	+	0.992290i	$0.539551\pi$
$80$	−4.42460	−0.494685
$81$	35.7923	3.97692
$82$	6.65699	0.735142
$83$	6.21840	0.682558	0.341279	−	0.939962i	$-0.389140\pi$
$83$	6.21840	0.682558	0.341279	+	0.939962i	$0.389140\pi$
$84$	−3.41062	−0.372129
$85$	−3.70483	−0.401845
$86$	−7.74329	−0.834981
$87$	20.5788	2.20628
$88$	3.10827	0.331343
$89$	−0.410844	−0.0435494	−0.0217747	−	0.999763i	$-0.506932\pi$
$89$	−0.410844	−0.0435494	−0.0217747	+	0.999763i	$0.506932\pi$
$90$	−36.9841	−3.89846
$91$	−4.45770	−0.467294
$92$	2.91493	0.303903
$93$	20.7067	2.14719
$94$	−3.07265	−0.316920
$95$	−30.0295	−3.08096
$96$	−3.37027	−0.343977
$97$	−0.409765	−0.0416054	−0.0208027	−	0.999784i	$-0.506622\pi$
$97$	−0.409765	−0.0416054	−0.0208027	+	0.999784i	$0.506622\pi$
$98$	−5.97591	−0.603658
$99$	25.9813	2.61121
$100$	14.5771	1.45771
$101$	11.3453	1.12890	0.564450	−	0.825467i	$-0.309088\pi$
$101$	11.3453	1.12890	0.564450	+	0.825467i	$0.309088\pi$
$102$	−2.82201	−0.279421
$103$	−18.7018	−1.84274	−0.921372	−	0.388683i	$-0.872930\pi$
$103$	−18.7018	−1.84274	−0.921372	+	0.388683i	$0.872930\pi$
$104$	−4.40497	−0.431943
$105$	15.0906	1.47269
$106$	11.4980	1.11678
$107$	−1.36417	−0.131879	−0.0659397	−	0.997824i	$-0.521005\pi$
$107$	−1.36417	−0.131879	−0.0659397	+	0.997824i	$0.521005\pi$
$108$	−18.0604	−1.73786
$109$	−13.8022	−1.32201	−0.661007	−	0.750380i	$-0.729871\pi$
$109$	−13.8022	−1.32201	−0.661007	+	0.750380i	$0.729871\pi$
$110$	−13.7529	−1.31128
$111$	38.8686	3.68925
$112$	1.01197	0.0956223
$113$	−7.10376	−0.668265	−0.334133	−	0.942526i	$-0.608443\pi$
$113$	−7.10376	−0.668265	−0.334133	+	0.942526i	$0.608443\pi$
$114$	−22.8738	−2.14233
$115$	−12.8974	−1.20269
$116$	−6.10598	−0.566926
$117$	−36.8200	−3.40401
$118$	0.695479	0.0640240
$119$	0.847349	0.0776763
$120$	14.9121	1.36128
$121$	−1.33863	−0.121693
$122$	4.68732	0.424370
$123$	−22.4359	−2.02298
$124$	−6.14393	−0.551741
$125$	−42.3748	−3.79011
$126$	8.45880	0.753570
$127$	−10.0828	−0.894703	−0.447351	−	0.894358i	$-0.647633\pi$
$127$	−10.0828	−0.894703	−0.447351	+	0.894358i	$0.647633\pi$
$128$	1.00000	0.0883883
$129$	26.0970	2.29771
$130$	19.4902	1.70941
$131$	−14.5675	−1.27277	−0.636385	−	0.771372i	$-0.719571\pi$
$131$	−14.5675	−1.27277	−0.636385	+	0.771372i	$0.719571\pi$
$132$	−10.4757	−0.911796
$133$	6.86818	0.595547
$134$	−4.54022	−0.392215
$135$	79.9101	6.87756
$136$	0.837325	0.0718000
$137$	−5.33104	−0.455461	−0.227731	−	0.973724i	$-0.573131\pi$
$137$	−5.33104	−0.455461	−0.227731	+	0.973724i	$0.573131\pi$
$138$	−9.82412	−0.836285
$139$	8.16063	0.692176	0.346088	−	0.938202i	$-0.387510\pi$
$139$	8.16063	0.692176	0.346088	+	0.938202i	$0.387510\pi$
$140$	−4.47757	−0.378424
$141$	10.3557	0.872105
$142$	−7.73693	−0.649268
$143$	−13.6919	−1.14497
$144$	8.35874	0.696561
$145$	27.0165	2.24360
$146$	−1.55058	−0.128327
$147$	20.1405	1.66116
$148$	−11.5328	−0.947989
$149$	7.71440	0.631988	0.315994	−	0.948761i	$-0.397662\pi$
$149$	7.71440	0.631988	0.315994	+	0.948761i	$0.397662\pi$
$150$	−49.1287	−4.01135
$151$	−3.42389	−0.278632	−0.139316	−	0.990248i	$-0.544490\pi$
$151$	−3.42389	−0.278632	−0.139316	+	0.990248i	$0.544490\pi$
$152$	6.78693	0.550493
$153$	6.99898	0.565834
$154$	3.14548	0.253470
$155$	27.1844	2.18350
$156$	14.8459	1.18863
$157$	−11.4200	−0.911414	−0.455707	−	0.890130i	$-0.650614\pi$
$157$	−11.4200	−0.911414	−0.455707	+	0.890130i	$0.650614\pi$
$158$	−2.20310	−0.175269
$159$	−38.7512	−3.07317
$160$	−4.42460	−0.349795
$161$	2.94983	0.232479
$162$	35.7923	2.81211
$163$	3.53561	0.276930	0.138465	−	0.990367i	$-0.455783\pi$
$163$	3.53561	0.276930	0.138465	+	0.990367i	$0.455783\pi$
$164$	6.65699	0.519824
$165$	46.3509	3.60841
$166$	6.21840	0.482641
$167$	2.17734	0.168487	0.0842437	−	0.996445i	$-0.473153\pi$
$167$	2.17734	0.168487	0.0842437	+	0.996445i	$0.473153\pi$
$168$	−3.41062	−0.263135
$169$	6.40374	0.492596
$170$	−3.70483	−0.284147
$171$	56.7302	4.33827
$172$	−7.74329	−0.590421
$173$	−3.23026	−0.245592	−0.122796	−	0.992432i	$-0.539186\pi$
$173$	−3.23026	−0.245592	−0.122796	+	0.992432i	$0.539186\pi$
$174$	20.5788	1.56008
$175$	14.7516	1.11512
$176$	3.10827	0.234295
$177$	−2.34395	−0.176182
$178$	−0.410844	−0.0307941
$179$	−17.6494	−1.31918	−0.659588	−	0.751628i	$-0.729269\pi$
$179$	−17.6494	−1.31918	−0.659588	+	0.751628i	$0.729269\pi$
$180$	−36.9841	−2.75663
$181$	16.6018	1.23400	0.617000	−	0.786963i	$-0.288348\pi$
$181$	16.6018	1.23400	0.617000	+	0.786963i	$0.288348\pi$
$182$	−4.45770	−0.330427
$183$	−15.7976	−1.16779
$184$	2.91493	0.214892
$185$	51.0280	3.75165
$186$	20.7067	1.51829
$187$	2.60264	0.190324
$188$	−3.07265	−0.224096
$189$	−18.2766	−1.32943
$190$	−30.0295	−2.17857
$191$	−2.20202	−0.159332	−0.0796661	−	0.996822i	$-0.525385\pi$
$191$	−2.20202	−0.159332	−0.0796661	+	0.996822i	$0.525385\pi$
$192$	−3.37027	−0.243228
$193$	10.7663	0.774974	0.387487	−	0.921875i	$-0.373343\pi$
$193$	10.7663	0.774974	0.387487	+	0.921875i	$0.373343\pi$
$194$	−0.409765	−0.0294194
$195$	−65.6874	−4.70397
$196$	−5.97591	−0.426851
$197$	18.3371	1.30646	0.653231	−	0.757158i	$-0.273413\pi$
$197$	18.3371	1.30646	0.653231	+	0.757158i	$0.273413\pi$
$198$	25.9813	1.84641
$199$	−7.10967	−0.503991	−0.251995	−	0.967728i	$-0.581087\pi$
$199$	−7.10967	−0.503991	−0.251995	+	0.967728i	$0.581087\pi$
$200$	14.5771	1.03076
$201$	15.3018	1.07930
$202$	11.3453	0.798252
$203$	−6.17908	−0.433686
$204$	−2.82201	−0.197580
$205$	−29.4545	−2.05719
$206$	−18.7018	−1.30302
$207$	24.3652	1.69350
$208$	−4.40497	−0.305430
$209$	21.0956	1.45922
$210$	15.0906	1.04135
$211$	−19.0060	−1.30843	−0.654214	−	0.756310i	$-0.727000\pi$
$211$	−19.0060	−1.30843	−0.654214	+	0.756310i	$0.727000\pi$
$212$	11.4980	0.789683
$213$	26.0755	1.78667
$214$	−1.36417	−0.0932529
$215$	34.2610	2.33658
$216$	−18.0604	−1.22886
$217$	−6.21748	−0.422070
$218$	−13.8022	−0.934805
$219$	5.22588	0.353132
$220$	−13.7529	−0.927218
$221$	−3.68839	−0.248108
$222$	38.8686	2.60869
$223$	8.99318	0.602228	0.301114	−	0.953588i	$-0.402642\pi$
$223$	8.99318	0.602228	0.301114	+	0.953588i	$0.402642\pi$
$224$	1.01197	0.0676152
$225$	121.846	8.12307
$226$	−7.10376	−0.472535
$227$	−11.8015	−0.783295	−0.391648	−	0.920115i	$-0.628095\pi$
$227$	−11.8015	−0.783295	−0.391648	+	0.920115i	$0.628095\pi$
$228$	−22.8738	−1.51485
$229$	9.27514	0.612919	0.306459	−	0.951884i	$-0.400856\pi$
$229$	9.27514	0.612919	0.306459	+	0.951884i	$0.400856\pi$
$230$	−12.8974	−0.850430
$231$	−10.6011	−0.697504
$232$	−6.10598	−0.400877
$233$	4.52444	0.296406	0.148203	−	0.988957i	$-0.452651\pi$
$233$	4.52444	0.296406	0.148203	+	0.988957i	$0.452651\pi$
$234$	−36.8200	−2.40700
$235$	13.5953	0.886857
$236$	0.695479	0.0452718
$237$	7.42505	0.482309
$238$	0.847349	0.0549255
$239$	−25.5565	−1.65311	−0.826556	−	0.562854i	$-0.809703\pi$
$239$	−25.5565	−1.65311	−0.826556	+	0.562854i	$0.809703\pi$
$240$	14.9121	0.962572
$241$	−5.63701	−0.363111	−0.181556	−	0.983381i	$-0.558113\pi$
$241$	−5.63701	−0.363111	−0.181556	+	0.983381i	$0.558113\pi$
$242$	−1.33863	−0.0860503
$243$	−66.4485	−4.26268
$244$	4.68732	0.300075
$245$	26.4410	1.68926
$246$	−22.4359	−1.43046
$247$	−29.8962	−1.90225
$248$	−6.14393	−0.390140
$249$	−20.9577	−1.32814
$250$	−42.3748	−2.68002
$251$	16.7887	1.05970	0.529848	−	0.848093i	$-0.322249\pi$
$251$	16.7887	1.05970	0.529848	+	0.848093i	$0.322249\pi$
$252$	8.45880	0.532854
$253$	9.06042	0.569623
$254$	−10.0828	−0.632650
$255$	12.4863	0.781921
$256$	1.00000	0.0625000
$257$	4.04789	0.252501	0.126250	−	0.991998i	$-0.459706\pi$
$257$	4.04789	0.252501	0.126250	+	0.991998i	$0.459706\pi$
$258$	26.0970	1.62473
$259$	−11.6708	−0.725191
$260$	19.4902	1.20873
$261$	−51.0383	−3.15919
$262$	−14.5675	−0.899984
$263$	3.16744	0.195313	0.0976564	−	0.995220i	$-0.468865\pi$
$263$	3.16744	0.195313	0.0976564	+	0.995220i	$0.468865\pi$
$264$	−10.4757	−0.644737
$265$	−50.8738	−3.12516
$266$	6.86818	0.421115
$267$	1.38466	0.0847396
$268$	−4.54022	−0.277338
$269$	−20.7995	−1.26817	−0.634085	−	0.773263i	$-0.718623\pi$
$269$	−20.7995	−1.26817	−0.634085	+	0.773263i	$0.718623\pi$
$270$	79.9101	4.86317
$271$	−11.0735	−0.672665	−0.336333	−	0.941743i	$-0.609187\pi$
$271$	−11.0735	−0.672665	−0.336333	+	0.941743i	$0.609187\pi$
$272$	0.837325	0.0507703
$273$	15.0237	0.909274
$274$	−5.33104	−0.322060
$275$	45.3096	2.73227
$276$	−9.82412	−0.591343
$277$	−26.7092	−1.60480	−0.802401	−	0.596785i	$-0.796444\pi$
$277$	−26.7092	−1.60480	−0.802401	+	0.596785i	$0.796444\pi$
$278$	8.16063	0.489442
$279$	−51.3555	−3.07457
$280$	−4.47757	−0.267586
$281$	11.3730	0.678456	0.339228	−	0.940704i	$-0.389834\pi$
$281$	11.3730	0.678456	0.339228	+	0.940704i	$0.389834\pi$
$282$	10.3557	0.616672
$283$	−7.87815	−0.468308	−0.234154	−	0.972200i	$-0.575232\pi$
$283$	−7.87815	−0.468308	−0.234154	+	0.972200i	$0.575232\pi$
$284$	−7.73693	−0.459102
$285$	101.207	5.99501
$286$	−13.6919	−0.809616
$287$	6.73669	0.397654
$288$	8.35874	0.492543
$289$	−16.2989	−0.958758
$290$	27.0165	1.58647
$291$	1.38102	0.0809569
$292$	−1.55058	−0.0907408
$293$	0.338308	0.0197642	0.00988209	−	0.999951i	$-0.496854\pi$
$293$	0.338308	0.0197642	0.00988209	+	0.999951i	$0.496854\pi$
$294$	20.1405	1.17462
$295$	−3.07721	−0.179162
$296$	−11.5328	−0.670329
$297$	−56.1367	−3.25738
$298$	7.71440	0.446883
$299$	−12.8402	−0.742567
$300$	−49.1287	−2.83645
$301$	−7.83599	−0.451659
$302$	−3.42389	−0.197023
$303$	−38.2368	−2.19664
$304$	6.78693	0.389257
$305$	−20.7395	−1.18754
$306$	6.99898	0.400105
$307$	−10.9539	−0.625174	−0.312587	−	0.949889i	$-0.601196\pi$
$307$	−10.9539	−0.625174	−0.312587	+	0.949889i	$0.601196\pi$
$308$	3.14548	0.179231
$309$	63.0302	3.58566
$310$	27.1844	1.54397
$311$	7.44483	0.422158	0.211079	−	0.977469i	$-0.432302\pi$
$311$	7.44483	0.422158	0.211079	+	0.977469i	$0.432302\pi$
$312$	14.8459	0.840486
$313$	−14.2771	−0.806989	−0.403494	−	0.914982i	$-0.632205\pi$
$313$	−14.2771	−0.806989	−0.403494	+	0.914982i	$0.632205\pi$
$314$	−11.4200	−0.644467
$315$	−37.4268	−2.10876
$316$	−2.20310	−0.123934
$317$	13.3667	0.750751	0.375376	−	0.926873i	$-0.377514\pi$
$317$	13.3667	0.750751	0.375376	+	0.926873i	$0.377514\pi$
$318$	−38.7512	−2.17306
$319$	−18.9791	−1.06262
$320$	−4.42460	−0.247343
$321$	4.59763	0.256615
$322$	2.94983	0.164388
$323$	5.68287	0.316203
$324$	35.7923	1.98846
$325$	−64.2116	−3.56182
$326$	3.53561	0.195819
$327$	46.5173	2.57241
$328$	6.65699	0.367571
$329$	−3.10944	−0.171429
$330$	46.3509	2.55153
$331$	23.2440	1.27761	0.638804	−	0.769370i	$-0.279430\pi$
$331$	23.2440	1.27761	0.638804	+	0.769370i	$0.279430\pi$
$332$	6.21840	0.341279
$333$	−96.3995	−5.28266
$334$	2.17734	0.119139
$335$	20.0887	1.09756
$336$	−3.41062	−0.186065
$337$	−6.49715	−0.353922	−0.176961	−	0.984218i	$-0.556627\pi$
$337$	−6.49715	−0.353922	−0.176961	+	0.984218i	$0.556627\pi$
$338$	6.40374	0.348318
$339$	23.9416	1.30033
$340$	−3.70483	−0.200922
$341$	−19.0970	−1.03416
$342$	56.7302	3.06762
$343$	−13.1313	−0.709021
$344$	−7.74329	−0.417490
$345$	43.4678	2.34023
$346$	−3.23026	−0.173660
$347$	−3.41799	−0.183487	−0.0917436	−	0.995783i	$-0.529244\pi$
$347$	−3.41799	−0.183487	−0.0917436	+	0.995783i	$0.529244\pi$
$348$	20.5788	1.10314
$349$	22.7101	1.21564	0.607822	−	0.794073i	$-0.292043\pi$
$349$	22.7101	1.21564	0.607822	+	0.794073i	$0.292043\pi$
$350$	14.7516	0.788506
$351$	79.5555	4.24636
$352$	3.10827	0.165672
$353$	−5.41987	−0.288470	−0.144235	−	0.989543i	$-0.546072\pi$
$353$	−5.41987	−0.288470	−0.144235	+	0.989543i	$0.546072\pi$
$354$	−2.34395	−0.124580
$355$	34.2328	1.81689
$356$	−0.410844	−0.0217747
$357$	−2.85580	−0.151145
$358$	−17.6494	−0.932798
$359$	−13.7338	−0.724845	−0.362422	−	0.932014i	$-0.618050\pi$
$359$	−13.7338	−0.724845	−0.362422	+	0.932014i	$0.618050\pi$
$360$	−36.9841	−1.94923
$361$	27.0624	1.42434
$362$	16.6018	0.872570
$363$	4.51154	0.236795
$364$	−4.45770	−0.233647
$365$	6.86069	0.359105
$366$	−15.7976	−0.825752
$367$	1.06506	0.0555955	0.0277978	−	0.999614i	$-0.491151\pi$
$367$	1.06506	0.0555955	0.0277978	+	0.999614i	$0.491151\pi$
$368$	2.91493	0.151951
$369$	55.6441	2.89671
$370$	51.0280	2.65282
$371$	11.6356	0.604090
$372$	20.7067	1.07359
$373$	13.1630	0.681554	0.340777	−	0.940144i	$-0.389310\pi$
$373$	13.1630	0.681554	0.340777	+	0.940144i	$0.389310\pi$
$374$	2.60264	0.134579
$375$	142.815	7.37491
$376$	−3.07265	−0.158460
$377$	26.8967	1.38525
$378$	−18.2766	−0.940048
$379$	13.7070	0.704081	0.352040	−	0.935985i	$-0.385488\pi$
$379$	13.7070	0.704081	0.352040	+	0.935985i	$0.385488\pi$
$380$	−30.0295	−1.54048
$381$	33.9817	1.74094
$382$	−2.20202	−0.112665
$383$	−20.8819	−1.06701	−0.533507	−	0.845795i	$-0.679126\pi$
$383$	−20.8819	−1.06701	−0.533507	+	0.845795i	$0.679126\pi$
$384$	−3.37027	−0.171989
$385$	−13.9175	−0.709302
$386$	10.7663	0.547990
$387$	−64.7242	−3.29011
$388$	−0.409765	−0.0208027
$389$	−21.5115	−1.09068	−0.545339	−	0.838215i	$-0.683599\pi$
$389$	−21.5115	−1.09068	−0.545339	+	0.838215i	$0.683599\pi$
$390$	−65.6874	−3.32621
$391$	2.44075	0.123434
$392$	−5.97591	−0.301829
$393$	49.0965	2.47659
$394$	18.3371	0.923809
$395$	9.74784	0.490467
$396$	25.9813	1.30561
$397$	7.62724	0.382800	0.191400	−	0.981512i	$-0.438697\pi$
$397$	7.62724	0.382800	0.191400	+	0.981512i	$0.438697\pi$
$398$	−7.10967	−0.356375
$399$	−23.1476	−1.15883
$400$	14.5771	0.728854
$401$	12.4252	0.620484	0.310242	−	0.950658i	$-0.399590\pi$
$401$	12.4252	0.620484	0.310242	+	0.950658i	$0.399590\pi$
$402$	15.3018	0.763183
$403$	27.0638	1.34814
$404$	11.3453	0.564450
$405$	−158.367	−7.86930
$406$	−6.17908	−0.306663
$407$	−35.8471	−1.77687
$408$	−2.82201	−0.139710
$409$	−23.1972	−1.14703	−0.573513	−	0.819196i	$-0.694420\pi$
$409$	−23.1972	−1.14703	−0.573513	+	0.819196i	$0.694420\pi$
$410$	−29.4545	−1.45466
$411$	17.9671	0.886249
$412$	−18.7018	−0.921372
$413$	0.703804	0.0346320
$414$	24.3652	1.19748
$415$	−27.5139	−1.35061
$416$	−4.40497	−0.215971
$417$	−27.5036	−1.34685
$418$	21.0956	1.03182
$419$	−1.29903	−0.0634616	−0.0317308	−	0.999496i	$-0.510102\pi$
$419$	−1.29903	−0.0634616	−0.0317308	+	0.999496i	$0.510102\pi$
$420$	15.0906	0.736347
$421$	−24.6422	−1.20099	−0.600494	−	0.799629i	$-0.705030\pi$
$421$	−24.6422	−1.20099	−0.600494	+	0.799629i	$0.705030\pi$
$422$	−19.0060	−0.925198
$423$	−25.6835	−1.24877
$424$	11.4980	0.558390
$425$	12.2058	0.592066
$426$	26.0755	1.26336
$427$	4.74344	0.229551
$428$	−1.36417	−0.0659397
$429$	46.1453	2.22791
$430$	34.2610	1.65221
$431$	−9.02540	−0.434738	−0.217369	−	0.976089i	$-0.569748\pi$
$431$	−9.02540	−0.434738	−0.217369	+	0.976089i	$0.569748\pi$
$432$	−18.0604	−0.868932
$433$	−5.76709	−0.277149	−0.138574	−	0.990352i	$-0.544252\pi$
$433$	−5.76709	−0.277149	−0.138574	+	0.990352i	$0.544252\pi$
$434$	−6.21748	−0.298448
$435$	−91.0531	−4.36566
$436$	−13.8022	−0.661007
$437$	19.7835	0.946371
$438$	5.22588	0.249702
$439$	27.2183	1.29906	0.649530	−	0.760336i	$-0.274966\pi$
$439$	27.2183	1.29906	0.649530	+	0.760336i	$0.274966\pi$
$440$	−13.7529	−0.655642
$441$	−49.9511	−2.37862
$442$	−3.68839	−0.175439
$443$	28.9478	1.37535	0.687677	−	0.726017i	$-0.258631\pi$
$443$	28.9478	1.37535	0.687677	+	0.726017i	$0.258631\pi$
$444$	38.8686	1.84462
$445$	1.81782	0.0861730
$446$	8.99318	0.425840
$447$	−25.9996	−1.22974
$448$	1.01197	0.0478111
$449$	−21.4388	−1.01176	−0.505879	−	0.862604i	$-0.668832\pi$
$449$	−21.4388	−1.01176	−0.505879	+	0.862604i	$0.668832\pi$
$450$	121.846	5.74388
$451$	20.6918	0.974337
$452$	−7.10376	−0.334133
$453$	11.5394	0.542171
$454$	−11.8015	−0.553873
$455$	19.7235	0.924654
$456$	−22.8738	−1.07116
$457$	−18.8327	−0.880957	−0.440479	−	0.897763i	$-0.645191\pi$
$457$	−18.8327	−0.880957	−0.440479	+	0.897763i	$0.645191\pi$
$458$	9.27514	0.433399
$459$	−15.1224	−0.705854
$460$	−12.8974	−0.601345
$461$	0.575061	0.0267833	0.0133916	−	0.999910i	$-0.495737\pi$
$461$	0.575061	0.0267833	0.0133916	+	0.999910i	$0.495737\pi$
$462$	−10.6011	−0.493210
$463$	26.2417	1.21955	0.609777	−	0.792573i	$-0.291259\pi$
$463$	26.2417	1.21955	0.609777	+	0.792573i	$0.291259\pi$
$464$	−6.10598	−0.283463
$465$	−91.6189	−4.24872
$466$	4.52444	0.209591
$467$	6.53685	0.302489	0.151245	−	0.988496i	$-0.451672\pi$
$467$	6.53685	0.302489	0.151245	+	0.988496i	$0.451672\pi$
$468$	−36.8200	−1.70200
$469$	−4.59457	−0.212158
$470$	13.5953	0.627102
$471$	38.4885	1.77346
$472$	0.695479	0.0320120
$473$	−24.0683	−1.10666
$474$	7.42505	0.341044
$475$	98.9337	4.53939
$476$	0.847349	0.0388382
$477$	96.1084	4.40050
$478$	−25.5565	−1.16893
$479$	−40.0588	−1.83033	−0.915167	−	0.403074i	$-0.867942\pi$
$479$	−40.0588	−1.83033	−0.915167	+	0.403074i	$0.867942\pi$
$480$	14.9121	0.680641
$481$	50.8015	2.31635
$482$	−5.63701	−0.256759
$483$	−9.94173	−0.452364
$484$	−1.33863	−0.0608467
$485$	1.81305	0.0823262
$486$	−66.4485	−3.01417
$487$	−23.2651	−1.05424	−0.527121	−	0.849790i	$-0.676729\pi$
$487$	−23.2651	−1.05424	−0.527121	+	0.849790i	$0.676729\pi$
$488$	4.68732	0.212185
$489$	−11.9160	−0.538858
$490$	26.4410	1.19448
$491$	−10.0267	−0.452497	−0.226249	−	0.974070i	$-0.572646\pi$
$491$	−10.0267	−0.452497	−0.226249	+	0.974070i	$0.572646\pi$
$492$	−22.4359	−1.01149
$493$	−5.11269	−0.230264
$494$	−29.8962	−1.34509
$495$	−114.957	−5.16692
$496$	−6.14393	−0.275870
$497$	−7.82955	−0.351203
$498$	−20.9577	−0.939137
$499$	−9.65673	−0.432294	−0.216147	−	0.976361i	$-0.569349\pi$
$499$	−9.65673	−0.432294	−0.216147	+	0.976361i	$0.569349\pi$
$500$	−42.3748	−1.89506
$501$	−7.33822	−0.327847
$502$	16.7887	0.749318
$503$	−22.8731	−1.01986	−0.509930	−	0.860216i	$-0.670329\pi$
$503$	−22.8731	−1.01986	−0.509930	+	0.860216i	$0.670329\pi$
$504$	8.45880	0.376785
$505$	−50.1984	−2.23380
$506$	9.06042	0.402785
$507$	−21.5824	−0.958506
$508$	−10.0828	−0.447351
$509$	−19.7297	−0.874506	−0.437253	−	0.899339i	$-0.644048\pi$
$509$	−19.7297	−0.874506	−0.437253	+	0.899339i	$0.644048\pi$
$510$	12.4863	0.552902
$511$	−1.56914	−0.0694147
$512$	1.00000	0.0441942
$513$	−122.575	−5.41181
$514$	4.04789	0.178545
$515$	82.7480	3.64631
$516$	26.0970	1.14886
$517$	−9.55065	−0.420037
$518$	−11.6708	−0.512788
$519$	10.8869	0.477880
$520$	19.4902	0.854703
$521$	36.4751	1.59800	0.799001	−	0.601330i	$-0.205362\pi$
$521$	36.4751	1.59800	0.799001	+	0.601330i	$0.205362\pi$
$522$	−51.0383	−2.23389
$523$	−29.3323	−1.28261	−0.641305	−	0.767286i	$-0.721607\pi$
$523$	−29.3323	−1.28261	−0.641305	+	0.767286i	$0.721607\pi$
$524$	−14.5675	−0.636385
$525$	−49.7169	−2.16982
$526$	3.16744	0.138107
$527$	−5.14446	−0.224096
$528$	−10.4757	−0.455898
$529$	−14.5032	−0.630572
$530$	−50.8738	−2.20982
$531$	5.81332	0.252277
$532$	6.86818	0.297773
$533$	−29.3238	−1.27016
$534$	1.38466	0.0599200
$535$	6.03592	0.260955
$536$	−4.54022	−0.196108
$537$	59.4832	2.56689
$538$	−20.7995	−0.896732
$539$	−18.5748	−0.800073
$540$	79.9101	3.43878
$541$	25.3512	1.08993	0.544967	−	0.838457i	$-0.316542\pi$
$541$	25.3512	1.08993	0.544967	+	0.838457i	$0.316542\pi$
$542$	−11.0735	−0.475646
$543$	−55.9525	−2.40115
$544$	0.837325	0.0359000
$545$	61.0693	2.61592
$546$	15.0237	0.642954
$547$	2.31623	0.0990349	0.0495174	−	0.998773i	$-0.484232\pi$
$547$	2.31623	0.0990349	0.0495174	+	0.998773i	$0.484232\pi$
$548$	−5.33104	−0.227731
$549$	39.1801	1.67217
$550$	45.3096	1.93201
$551$	−41.4409	−1.76544
$552$	−9.82412	−0.418142
$553$	−2.22948	−0.0948069
$554$	−26.7092	−1.13477
$555$	−171.978	−7.30006
$556$	8.16063	0.346088
$557$	0.647764	0.0274466	0.0137233	−	0.999906i	$-0.495632\pi$
$557$	0.647764	0.0274466	0.0137233	+	0.999906i	$0.495632\pi$
$558$	−51.3555	−2.17405
$559$	34.1090	1.44266
$560$	−4.47757	−0.189212
$561$	−8.77159	−0.370337
$562$	11.3730	0.479741
$563$	−4.47832	−0.188739	−0.0943693	−	0.995537i	$-0.530083\pi$
$563$	−4.47832	−0.188739	−0.0943693	+	0.995537i	$0.530083\pi$
$564$	10.3557	0.436053
$565$	31.4313	1.32232
$566$	−7.87815	−0.331143
$567$	36.2208	1.52113
$568$	−7.73693	−0.324634
$569$	10.2606	0.430148	0.215074	−	0.976598i	$-0.431001\pi$
$569$	10.2606	0.430148	0.215074	+	0.976598i	$0.431001\pi$
$570$	101.207	4.23911
$571$	25.8134	1.08026	0.540128	−	0.841583i	$-0.318376\pi$
$571$	25.8134	1.08026	0.540128	+	0.841583i	$0.318376\pi$
$572$	−13.6919	−0.572485
$573$	7.42139	0.310033
$574$	6.73669	0.281184
$575$	42.4912	1.77201
$576$	8.35874	0.348281
$577$	3.22878	0.134416	0.0672078	−	0.997739i	$-0.478591\pi$
$577$	3.22878	0.134416	0.0672078	+	0.997739i	$0.478591\pi$
$578$	−16.2989	−0.677944
$579$	−36.2853	−1.50797
$580$	27.0165	1.12180
$581$	6.29284	0.261071
$582$	1.38102	0.0572451
$583$	35.7388	1.48015
$584$	−1.55058	−0.0641634
$585$	162.914	6.73565
$586$	0.338308	0.0139754
$587$	5.12940	0.211713	0.105857	−	0.994381i	$-0.466242\pi$
$587$	5.12940	0.211713	0.105857	+	0.994381i	$0.466242\pi$
$588$	20.1405	0.830579
$589$	−41.6984	−1.71815
$590$	−3.07721	−0.126687
$591$	−61.8010	−2.54215
$592$	−11.5328	−0.473995
$593$	8.21495	0.337348	0.168674	−	0.985672i	$-0.446052\pi$
$593$	8.21495	0.337348	0.168674	+	0.985672i	$0.446052\pi$
$594$	−56.1367	−2.30332
$595$	−3.74918	−0.153701
$596$	7.71440	0.315994
$597$	23.9615	0.980679
$598$	−12.8402	−0.525074
$599$	32.6790	1.33523	0.667614	−	0.744507i	$-0.267316\pi$
$599$	32.6790	1.33523	0.667614	+	0.744507i	$0.267316\pi$
$600$	−49.1287	−2.00567
$601$	3.90564	0.159314	0.0796572	−	0.996822i	$-0.474617\pi$
$601$	3.90564	0.159314	0.0796572	+	0.996822i	$0.474617\pi$
$602$	−7.83599	−0.319371
$603$	−37.9505	−1.54546
$604$	−3.42389	−0.139316
$605$	5.92289	0.240800
$606$	−38.2368	−1.55326
$607$	40.6566	1.65020	0.825099	−	0.564988i	$-0.191119\pi$
$607$	40.6566	1.65020	0.825099	+	0.564988i	$0.191119\pi$
$608$	6.78693	0.275246
$609$	20.8252	0.843879
$610$	−20.7395	−0.839719
$611$	13.5349	0.547565
$612$	6.99898	0.282917
$613$	−44.7149	−1.80602	−0.903009	−	0.429621i	$-0.858647\pi$
$613$	−44.7149	−1.80602	−0.903009	+	0.429621i	$0.858647\pi$
$614$	−10.9539	−0.442065
$615$	99.2698	4.00294
$616$	3.14548	0.126735
$617$	5.17087	0.208172	0.104086	−	0.994568i	$-0.466808\pi$
$617$	5.17087	0.208172	0.104086	+	0.994568i	$0.466808\pi$
$618$	63.0302	2.53545
$619$	18.6735	0.750550	0.375275	−	0.926913i	$-0.377548\pi$
$619$	18.6735	0.750550	0.375275	+	0.926913i	$0.377548\pi$
$620$	27.1844	1.09175
$621$	−52.6449	−2.11257
$622$	7.44483	0.298510
$623$	−0.415763	−0.0166572
$624$	14.8459	0.594313
$625$	114.606	4.58424
$626$	−14.2771	−0.570627
$627$	−71.0981	−2.83938
$628$	−11.4200	−0.455707
$629$	−9.65669	−0.385037
$630$	−37.4268	−1.49112
$631$	−41.8213	−1.66488	−0.832440	−	0.554115i	$-0.813057\pi$
$631$	−41.8213	−1.66488	−0.832440	+	0.554115i	$0.813057\pi$
$632$	−2.20310	−0.0876347
$633$	64.0554	2.54597
$634$	13.3667	0.530861
$635$	44.6123	1.77039
$636$	−38.7512	−1.53659
$637$	26.3237	1.04298
$638$	−18.9791	−0.751389
$639$	−64.6709	−2.55834
$640$	−4.42460	−0.174898
$641$	19.2467	0.760199	0.380100	−	0.924946i	$-0.375890\pi$
$641$	19.2467	0.760199	0.380100	+	0.924946i	$0.375890\pi$
$642$	4.59763	0.181454
$643$	−6.29861	−0.248393	−0.124196	−	0.992258i	$-0.539635\pi$
$643$	−6.29861	−0.248393	−0.124196	+	0.992258i	$0.539635\pi$
$644$	2.94983	0.116240
$645$	−115.469	−4.54658
$646$	5.68287	0.223589
$647$	−21.3429	−0.839076	−0.419538	−	0.907738i	$-0.637808\pi$
$647$	−21.3429	−0.839076	−0.419538	+	0.907738i	$0.637808\pi$
$648$	35.7923	1.40605
$649$	2.16174	0.0848557
$650$	−64.2116	−2.51859
$651$	20.9546	0.821275
$652$	3.53561	0.138465
$653$	−0.527195	−0.0206308	−0.0103154	−	0.999947i	$-0.503284\pi$
$653$	−0.527195	−0.0206308	−0.0103154	+	0.999947i	$0.503284\pi$
$654$	46.5173	1.81897
$655$	64.4554	2.51848
$656$	6.65699	0.259912
$657$	−12.9609	−0.505652
$658$	−3.10944	−0.121218
$659$	−23.7627	−0.925664	−0.462832	−	0.886446i	$-0.653167\pi$
$659$	−23.7627	−0.925664	−0.462832	+	0.886446i	$0.653167\pi$
$660$	46.3509	1.80421
$661$	−21.4149	−0.832944	−0.416472	−	0.909149i	$-0.636734\pi$
$661$	−21.4149	−0.832944	−0.416472	+	0.909149i	$0.636734\pi$
$662$	23.2440	0.903405
$663$	12.4309	0.482775
$664$	6.21840	0.241321
$665$	−30.3889	−1.17843
$666$	−96.3995	−3.73541
$667$	−17.7985	−0.689162
$668$	2.17734	0.0842437
$669$	−30.3095	−1.17183
$670$	20.0887	0.776092
$671$	14.5695	0.562449
$672$	−3.41062	−0.131567
$673$	37.0634	1.42869	0.714344	−	0.699795i	$-0.246725\pi$
$673$	37.0634	1.42869	0.714344	+	0.699795i	$0.246725\pi$
$674$	−6.49715	−0.250261
$675$	−263.268	−10.1332
$676$	6.40374	0.246298
$677$	11.4825	0.441309	0.220654	−	0.975352i	$-0.429181\pi$
$677$	11.4825	0.441309	0.220654	+	0.975352i	$0.429181\pi$
$678$	23.9416	0.919471
$679$	−0.414671	−0.0159136
$680$	−3.70483	−0.142074
$681$	39.7744	1.52416
$682$	−19.0970	−0.731262
$683$	−22.2499	−0.851370	−0.425685	−	0.904871i	$-0.639967\pi$
$683$	−22.2499	−0.851370	−0.425685	+	0.904871i	$0.639967\pi$
$684$	56.7302	2.16913
$685$	23.5877	0.901240
$686$	−13.1313	−0.501354
$687$	−31.2598	−1.19263
$688$	−7.74329	−0.295210
$689$	−50.6481	−1.92954
$690$	43.4678	1.65479
$691$	−49.5690	−1.88569	−0.942847	−	0.333227i	$-0.891862\pi$
$691$	−49.5690	−1.88569	−0.942847	+	0.333227i	$0.891862\pi$
$692$	−3.23026	−0.122796
$693$	26.2923	0.998761
$694$	−3.41799	−0.129745
$695$	−36.1075	−1.36964
$696$	20.5788	0.780038
$697$	5.57407	0.211133
$698$	22.7101	0.859590
$699$	−15.2486	−0.576755
$700$	14.7516	0.557558
$701$	40.6492	1.53530	0.767650	−	0.640870i	$-0.221426\pi$
$701$	40.6492	1.53530	0.767650	+	0.640870i	$0.221426\pi$
$702$	79.5555	3.00263
$703$	−78.2722	−2.95209
$704$	3.10827	0.117148
$705$	−45.8197	−1.72567
$706$	−5.41987	−0.203979
$707$	11.4811	0.431792
$708$	−2.34395	−0.0880911
$709$	33.6256	1.26284	0.631419	−	0.775442i	$-0.282473\pi$
$709$	33.6256	1.26284	0.631419	+	0.775442i	$0.282473\pi$
$710$	34.2328	1.28473
$711$	−18.4152	−0.690622
$712$	−0.410844	−0.0153970
$713$	−17.9091	−0.670702
$714$	−2.85580	−0.106875
$715$	60.5810	2.26560
$716$	−17.6494	−0.659588
$717$	86.1323	3.21667
$718$	−13.7338	−0.512543
$719$	−4.91154	−0.183170	−0.0915848	−	0.995797i	$-0.529193\pi$
$719$	−4.91154	−0.183170	−0.0915848	+	0.995797i	$0.529193\pi$
$720$	−36.9841	−1.37831
$721$	−18.9257	−0.704829
$722$	27.0624	1.00716
$723$	18.9982	0.706552
$724$	16.6018	0.617000
$725$	−89.0074	−3.30565
$726$	4.51154	0.167439
$727$	53.1905	1.97273	0.986364	−	0.164581i	$-0.0526271\pi$
$727$	53.1905	1.97273	0.986364	+	0.164581i	$0.0526271\pi$
$728$	−4.45770	−0.165213
$729$	116.573	4.31751
$730$	6.86069	0.253926
$731$	−6.48365	−0.239807
$732$	−15.7976	−0.583895
$733$	35.1039	1.29659	0.648296	−	0.761388i	$-0.275482\pi$
$733$	35.1039	1.29659	0.648296	+	0.761388i	$0.275482\pi$
$734$	1.06506	0.0393120
$735$	−89.1135	−3.28700
$736$	2.91493	0.107446
$737$	−14.1122	−0.519831
$738$	55.6441	2.04829
$739$	−3.23147	−0.118872	−0.0594358	−	0.998232i	$-0.518930\pi$
$739$	−3.23147	−0.118872	−0.0594358	+	0.998232i	$0.518930\pi$
$740$	51.0280	1.87582
$741$	100.758	3.70145
$742$	11.6356	0.427156
$743$	34.2500	1.25651	0.628256	−	0.778007i	$-0.283769\pi$
$743$	34.2500	1.25651	0.628256	+	0.778007i	$0.283769\pi$
$744$	20.7067	0.759145
$745$	−34.1331	−1.25054
$746$	13.1630	0.481931
$747$	51.9780	1.90177
$748$	2.60264	0.0951618
$749$	−1.38050	−0.0504425
$750$	142.815	5.21485
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	−3.07265	−0.112048
$753$	−56.5826	−2.06198
$754$	26.8967	0.979519
$755$	15.1494	0.551341
$756$	−18.2766	−0.664714
$757$	−24.8512	−0.903231	−0.451616	−	0.892213i	$-0.649152\pi$
$757$	−24.8512	−0.903231	−0.451616	+	0.892213i	$0.649152\pi$
$758$	13.7070	0.497860
$759$	−30.5361	−1.10839
$760$	−30.0295	−1.08928
$761$	18.1567	0.658179	0.329090	−	0.944299i	$-0.393258\pi$
$761$	18.1567	0.658179	0.329090	+	0.944299i	$0.393258\pi$
$762$	33.9817	1.23103
$763$	−13.9675	−0.505656
$764$	−2.20202	−0.0796661
$765$	−30.9677	−1.11964
$766$	−20.8819	−0.754493
$767$	−3.06356	−0.110619
$768$	−3.37027	−0.121614
$769$	21.8013	0.786175	0.393088	−	0.919501i	$-0.371407\pi$
$769$	21.8013	0.786175	0.393088	+	0.919501i	$0.371407\pi$
$770$	−13.9175	−0.501552
$771$	−13.6425	−0.491323
$772$	10.7663	0.387487
$773$	14.6863	0.528228	0.264114	−	0.964491i	$-0.414920\pi$
$773$	14.6863	0.528228	0.264114	+	0.964491i	$0.414920\pi$
$774$	−64.7242	−2.32646
$775$	−89.5605	−3.21711
$776$	−0.409765	−0.0147097
$777$	39.3339	1.41110
$778$	−21.5115	−0.771226
$779$	45.1806	1.61876
$780$	−65.6874	−2.35198
$781$	−24.0485	−0.860523
$782$	2.44075	0.0872809
$783$	110.277	3.94096
$784$	−5.97591	−0.213426
$785$	50.5289	1.80345
$786$	49.0965	1.75121
$787$	−24.0035	−0.855632	−0.427816	−	0.903866i	$-0.640717\pi$
$787$	−24.0035	−0.855632	−0.427816	+	0.903866i	$0.640717\pi$
$788$	18.3371	0.653231
$789$	−10.6751	−0.380045
$790$	9.74784	0.346813
$791$	−7.18880	−0.255604
$792$	25.9813	0.923204
$793$	−20.6475	−0.733215
$794$	7.62724	0.270681
$795$	171.459	6.08101
$796$	−7.10967	−0.251995
$797$	30.3664	1.07563	0.537816	−	0.843062i	$-0.319250\pi$
$797$	30.3664	1.07563	0.537816	+	0.843062i	$0.319250\pi$
$798$	−23.1476	−0.819417
$799$	−2.57281	−0.0910194
$800$	14.5771	0.515378
$801$	−3.43414	−0.121339
$802$	12.4252	0.438749
$803$	−4.81963	−0.170081
$804$	15.3018	0.539652
$805$	−13.0518	−0.460016
$806$	27.0638	0.953282
$807$	70.1001	2.46764
$808$	11.3453	0.399126
$809$	6.32739	0.222459	0.111230	−	0.993795i	$-0.464521\pi$
$809$	6.32739	0.222459	0.111230	+	0.993795i	$0.464521\pi$
$810$	−158.367	−5.56443
$811$	−45.4362	−1.59548	−0.797740	−	0.603002i	$-0.793971\pi$
$811$	−45.4362	−1.59548	−0.797740	+	0.603002i	$0.793971\pi$
$812$	−6.17908	−0.216843
$813$	37.3206	1.30889
$814$	−35.8471	−1.25644
$815$	−15.6436	−0.547973
$816$	−2.82201	−0.0987902
$817$	−52.5532	−1.83860
$818$	−23.1972	−0.811070
$819$	−37.2608	−1.30200
$820$	−29.4545	−1.02860
$821$	−10.9946	−0.383715	−0.191858	−	0.981423i	$-0.561451\pi$
$821$	−10.9946	−0.383715	−0.191858	+	0.981423i	$0.561451\pi$
$822$	17.9671	0.626673
$823$	23.1220	0.805981	0.402990	−	0.915204i	$-0.367971\pi$
$823$	23.1220	0.805981	0.402990	+	0.915204i	$0.367971\pi$
$824$	−18.7018	−0.651508
$825$	−152.706	−5.31653
$826$	0.703804	0.0244885
$827$	−10.2721	−0.357196	−0.178598	−	0.983922i	$-0.557156\pi$
$827$	−10.2721	−0.357196	−0.178598	+	0.983922i	$0.557156\pi$
$828$	24.3652	0.846748
$829$	−40.2127	−1.39664	−0.698322	−	0.715783i	$-0.746070\pi$
$829$	−40.2127	−1.39664	−0.698322	+	0.715783i	$0.746070\pi$
$830$	−27.5139	−0.955022
$831$	90.0174	3.12267
$832$	−4.40497	−0.152715
$833$	−5.00378	−0.173371
$834$	−27.5036	−0.952370
$835$	−9.63384	−0.333393
$836$	21.0956	0.729608
$837$	110.962	3.83540
$838$	−1.29903	−0.0448741
$839$	39.4506	1.36199	0.680993	−	0.732290i	$-0.261549\pi$
$839$	39.4506	1.36199	0.680993	+	0.732290i	$0.261549\pi$
$840$	15.0906	0.520676
$841$	8.28303	0.285622
$842$	−24.6422	−0.849227
$843$	−38.3301	−1.32016
$844$	−19.0060	−0.654214
$845$	−28.3340	−0.974719
$846$	−25.6835	−0.883017
$847$	−1.35465	−0.0465464
$848$	11.4980	0.394841
$849$	26.5515	0.911246
$850$	12.2058	0.418654
$851$	−33.6173	−1.15239
$852$	26.0755	0.893334
$853$	44.9960	1.54063	0.770317	−	0.637661i	$-0.220098\pi$
$853$	44.9960	1.54063	0.770317	+	0.637661i	$0.220098\pi$
$854$	4.74344	0.162317
$855$	−251.008	−8.58430
$856$	−1.36417	−0.0466264
$857$	21.9341	0.749253	0.374626	−	0.927176i	$-0.377771\pi$
$857$	21.9341	0.749253	0.374626	+	0.927176i	$0.377771\pi$
$858$	46.1453	1.57537
$859$	−10.3585	−0.353426	−0.176713	−	0.984262i	$-0.556546\pi$
$859$	−10.3585	−0.353426	−0.176713	+	0.984262i	$0.556546\pi$
$860$	34.2610	1.16829
$861$	−22.7045	−0.773766
$862$	−9.02540	−0.307406
$863$	18.8531	0.641766	0.320883	−	0.947119i	$-0.396020\pi$
$863$	18.8531	0.641766	0.320883	+	0.947119i	$0.396020\pi$
$864$	−18.0604	−0.614428
$865$	14.2926	0.485964
$866$	−5.76709	−0.195974
$867$	54.9317	1.86558
$868$	−6.21748	−0.211035
$869$	−6.84785	−0.232297
$870$	−91.0531	−3.08699
$871$	19.9995	0.677658
$872$	−13.8022	−0.467402
$873$	−3.42512	−0.115923
$874$	19.7835	0.669185
$875$	−42.8820	−1.44968
$876$	5.22588	0.176566
$877$	42.6701	1.44087	0.720433	−	0.693525i	$-0.243943\pi$
$877$	42.6701	1.44087	0.720433	+	0.693525i	$0.243943\pi$
$878$	27.2183	0.918573
$879$	−1.14019	−0.0384577
$880$	−13.7529	−0.463609
$881$	−46.2687	−1.55883	−0.779417	−	0.626506i	$-0.784485\pi$
$881$	−46.2687	−1.55883	−0.779417	+	0.626506i	$0.784485\pi$
$882$	−49.9511	−1.68194
$883$	22.8696	0.769622	0.384811	−	0.922995i	$-0.374267\pi$
$883$	22.8696	0.769622	0.384811	+	0.922995i	$0.374267\pi$
$884$	−3.68839	−0.124054
$885$	10.3711	0.348619
$886$	28.9478	0.972522
$887$	−35.0691	−1.17751	−0.588753	−	0.808313i	$-0.700381\pi$
$887$	−35.0691	−1.17751	−0.588753	+	0.808313i	$0.700381\pi$
$888$	38.8686	1.30435
$889$	−10.2035	−0.342214
$890$	1.81782	0.0609335
$891$	111.252	3.72709
$892$	8.99318	0.301114
$893$	−20.8539	−0.697848
$894$	−25.9996	−0.869557
$895$	78.0914	2.61031
$896$	1.01197	0.0338076
$897$	43.2749	1.44491
$898$	−21.4388	−0.715421
$899$	37.5147	1.25119
$900$	121.846	4.06153
$901$	9.62752	0.320739
$902$	20.6918	0.688960
$903$	26.4094	0.878851
$904$	−7.10376	−0.236267
$905$	−73.4562	−2.44177
$906$	11.5394	0.383373
$907$	−46.7248	−1.55147	−0.775736	−	0.631058i	$-0.782621\pi$
$907$	−46.7248	−1.55147	−0.775736	+	0.631058i	$0.782621\pi$
$908$	−11.8015	−0.391648
$909$	94.8324	3.14539
$910$	19.7235	0.653829
$911$	28.6807	0.950233	0.475116	−	0.879923i	$-0.342406\pi$
$911$	28.6807	0.950233	0.475116	+	0.879923i	$0.342406\pi$
$912$	−22.8738	−0.757427
$913$	19.3285	0.639680
$914$	−18.8327	−0.622931
$915$	69.8979	2.31075
$916$	9.27514	0.306459
$917$	−14.7419	−0.486821
$918$	−15.1224	−0.499114
$919$	5.20560	0.171717	0.0858585	−	0.996307i	$-0.472637\pi$
$919$	5.20560	0.171717	0.0858585	+	0.996307i	$0.472637\pi$
$920$	−12.8974	−0.425215
$921$	36.9177	1.21648
$922$	0.575061	0.0189386
$923$	34.0809	1.12179
$924$	−10.6011	−0.348752
$925$	−168.114	−5.52757
$926$	26.2417	0.862355
$927$	−156.323	−5.13434
$928$	−6.10598	−0.200439
$929$	−4.58031	−0.150275	−0.0751376	−	0.997173i	$-0.523940\pi$
$929$	−4.58031	−0.150275	−0.0751376	+	0.997173i	$0.523940\pi$
$930$	−91.6189	−3.00430
$931$	−40.5581	−1.32924
$932$	4.52444	0.148203
$933$	−25.0911	−0.821446
$934$	6.53685	0.213892
$935$	−11.5156	−0.376601
$936$	−36.8200	−1.20350
$937$	−34.4785	−1.12636	−0.563182	−	0.826333i	$-0.690423\pi$
$937$	−34.4785	−1.12636	−0.563182	+	0.826333i	$0.690423\pi$
$938$	−4.59457	−0.150018
$939$	48.1177	1.57026
$940$	13.5953	0.443428
$941$	−46.4194	−1.51323	−0.756615	−	0.653860i	$-0.773148\pi$
$941$	−46.4194	−1.51323	−0.756615	+	0.653860i	$0.773148\pi$
$942$	38.4885	1.25402
$943$	19.4047	0.631904
$944$	0.695479	0.0226359
$945$	80.8667	2.63059
$946$	−24.0683	−0.782527
$947$	−44.9704	−1.46134	−0.730671	−	0.682730i	$-0.760793\pi$
$947$	−44.9704	−1.46134	−0.730671	+	0.682730i	$0.760793\pi$
$948$	7.42505	0.241155
$949$	6.83025	0.221719
$950$	98.9337	3.20983
$951$	−45.0496	−1.46083
$952$	0.847349	0.0274627
$953$	44.6213	1.44543	0.722713	−	0.691148i	$-0.242895\pi$
$953$	44.6213	1.44543	0.722713	+	0.691148i	$0.242895\pi$
$954$	96.1084	3.11162
$955$	9.74304	0.315277
$956$	−25.5565	−0.826556
$957$	63.9647	2.06768
$958$	−40.0588	−1.29424
$959$	−5.39486	−0.174209
$960$	14.9121	0.481286
$961$	6.74782	0.217672
$962$	50.8015	1.63791
$963$	−11.4028	−0.367449
$964$	−5.63701	−0.181556
$965$	−47.6365	−1.53347
$966$	−9.94173	−0.319870
$967$	−13.8239	−0.444546	−0.222273	−	0.974985i	$-0.571348\pi$
$967$	−13.8239	−0.444546	−0.222273	+	0.974985i	$0.571348\pi$
$968$	−1.33863	−0.0430251
$969$	−19.1528	−0.615277
$970$	1.81305	0.0582134
$971$	22.4420	0.720198	0.360099	−	0.932914i	$-0.382743\pi$
$971$	22.4420	0.720198	0.360099	+	0.932914i	$0.382743\pi$
$972$	−66.4485	−2.13134
$973$	8.25832	0.264750
$974$	−23.2651	−0.745462
$975$	216.411	6.93068
$976$	4.68732	0.150038
$977$	−50.3278	−1.61013	−0.805065	−	0.593187i	$-0.797870\pi$
$977$	−50.3278	−1.61013	−0.805065	+	0.593187i	$0.797870\pi$
$978$	−11.9160	−0.381030
$979$	−1.27702	−0.0408136
$980$	26.4410	0.844628
$981$	−115.369	−3.68346
$982$	−10.0267	−0.319964
$983$	−2.60164	−0.0829796	−0.0414898	−	0.999139i	$-0.513210\pi$
$983$	−2.60164	−0.0829796	−0.0414898	+	0.999139i	$0.513210\pi$
$984$	−22.4359	−0.715230
$985$	−81.1342	−2.58515
$986$	−5.11269	−0.162821
$987$	10.4796	0.333571
$988$	−29.8962	−0.951125
$989$	−22.5712	−0.717722
$990$	−114.957	−3.65356
$991$	−4.59847	−0.146075	−0.0730375	−	0.997329i	$-0.523269\pi$
$991$	−4.59847	−0.146075	−0.0730375	+	0.997329i	$0.523269\pi$
$992$	−6.14393	−0.195070
$993$	−78.3387	−2.48600
$994$	−7.82955	−0.248338
$995$	31.4574	0.997268
$996$	−20.9577	−0.664070
$997$	62.4682	1.97839	0.989194	−	0.146613i	$-0.0468373\pi$
$997$	62.4682	1.97839	0.989194	+	0.146613i	$0.0468373\pi$
$998$	−9.65673	−0.305678
$999$	208.287	6.58990

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.f.1.1	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.37027 q^{3} +1.00000 q^{4} -4.42460 q^{5} -3.37027 q^{6} +1.01197 q^{7} +1.00000 q^{8} +8.35874 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.37027 q^{3} +1.00000 q^{4} -4.42460 q^{5} -3.37027 q^{6} +1.01197 q^{7} +1.00000 q^{8} +8.35874 q^{9} -4.42460 q^{10} +3.10827 q^{11} -3.37027 q^{12} -4.40497 q^{13} +1.01197 q^{14} +14.9121 q^{15} +1.00000 q^{16} +0.837325 q^{17} +8.35874 q^{18} +6.78693 q^{19} -4.42460 q^{20} -3.41062 q^{21} +3.10827 q^{22} +2.91493 q^{23} -3.37027 q^{24} +14.5771 q^{25} -4.40497 q^{26} -18.0604 q^{27} +1.01197 q^{28} -6.10598 q^{29} +14.9121 q^{30} -6.14393 q^{31} +1.00000 q^{32} -10.4757 q^{33} +0.837325 q^{34} -4.47757 q^{35} +8.35874 q^{36} -11.5328 q^{37} +6.78693 q^{38} +14.8459 q^{39} -4.42460 q^{40} +6.65699 q^{41} -3.41062 q^{42} -7.74329 q^{43} +3.10827 q^{44} -36.9841 q^{45} +2.91493 q^{46} -3.07265 q^{47} -3.37027 q^{48} -5.97591 q^{49} +14.5771 q^{50} -2.82201 q^{51} -4.40497 q^{52} +11.4980 q^{53} -18.0604 q^{54} -13.7529 q^{55} +1.01197 q^{56} -22.8738 q^{57} -6.10598 q^{58} +0.695479 q^{59} +14.9121 q^{60} +4.68732 q^{61} -6.14393 q^{62} +8.45880 q^{63} +1.00000 q^{64} +19.4902 q^{65} -10.4757 q^{66} -4.54022 q^{67} +0.837325 q^{68} -9.82412 q^{69} -4.47757 q^{70} -7.73693 q^{71} +8.35874 q^{72} -1.55058 q^{73} -11.5328 q^{74} -49.1287 q^{75} +6.78693 q^{76} +3.14548 q^{77} +14.8459 q^{78} -2.20310 q^{79} -4.42460 q^{80} +35.7923 q^{81} +6.65699 q^{82} +6.21840 q^{83} -3.41062 q^{84} -3.70483 q^{85} -7.74329 q^{86} +20.5788 q^{87} +3.10827 q^{88} -0.410844 q^{89} -36.9841 q^{90} -4.45770 q^{91} +2.91493 q^{92} +20.7067 q^{93} -3.07265 q^{94} -30.0295 q^{95} -3.37027 q^{96} -0.409765 q^{97} -5.97591 q^{98} +25.9813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 12 q^{5} - 11 q^{6} - 9 q^{7} + 11 q^{8} + 18 q^{9} - 12 q^{10} - 7 q^{11} - 11 q^{12} - 21 q^{13} - 9 q^{14} - 3 q^{15} + 11 q^{16} - 16 q^{17} + 18 q^{18} - 22 q^{19} - 12 q^{20} - q^{21} - 7 q^{22} - 2 q^{23} - 11 q^{24} + 19 q^{25} - 21 q^{26} - 44 q^{27} - 9 q^{28} + 4 q^{29} - 3 q^{30} - 28 q^{31} + 11 q^{32} - 13 q^{33} - 16 q^{34} - 11 q^{35} + 18 q^{36} - 22 q^{37} - 22 q^{38} + 9 q^{39} - 12 q^{40} - 5 q^{41} - q^{42} - 7 q^{43} - 7 q^{44} - 23 q^{45} - 2 q^{46} - 31 q^{47} - 11 q^{48} - 2 q^{49} + 19 q^{50} - 6 q^{51} - 21 q^{52} - 17 q^{53} - 44 q^{54} - 18 q^{55} - 9 q^{56} + 7 q^{57} + 4 q^{58} - 18 q^{59} - 3 q^{60} - 18 q^{61} - 28 q^{62} - 27 q^{63} + 11 q^{64} + 22 q^{65} - 13 q^{66} - 11 q^{67} - 16 q^{68} + 9 q^{69} - 11 q^{70} - 16 q^{71} + 18 q^{72} - 33 q^{73} - 22 q^{74} - 21 q^{75} - 22 q^{76} + 9 q^{78} + 9 q^{79} - 12 q^{80} + 71 q^{81} - 5 q^{82} - 18 q^{83} - q^{84} - 8 q^{85} - 7 q^{86} - 17 q^{87} - 7 q^{88} - 23 q^{90} - 22 q^{91} - 2 q^{92} + 8 q^{93} - 31 q^{94} - 23 q^{95} - 11 q^{96} - 66 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 12 * q^5 - 11 * q^6 - 9 * q^7 + 11 * q^8 + 18 * q^9 - 12 * q^10 - 7 * q^11 - 11 * q^12 - 21 * q^13 - 9 * q^14 - 3 * q^15 + 11 * q^16 - 16 * q^17 + 18 * q^18 - 22 * q^19 - 12 * q^20 - q^21 - 7 * q^22 - 2 * q^23 - 11 * q^24 + 19 * q^25 - 21 * q^26 - 44 * q^27 - 9 * q^28 + 4 * q^29 - 3 * q^30 - 28 * q^31 + 11 * q^32 - 13 * q^33 - 16 * q^34 - 11 * q^35 + 18 * q^36 - 22 * q^37 - 22 * q^38 + 9 * q^39 - 12 * q^40 - 5 * q^41 - q^42 - 7 * q^43 - 7 * q^44 - 23 * q^45 - 2 * q^46 - 31 * q^47 - 11 * q^48 - 2 * q^49 + 19 * q^50 - 6 * q^51 - 21 * q^52 - 17 * q^53 - 44 * q^54 - 18 * q^55 - 9 * q^56 + 7 * q^57 + 4 * q^58 - 18 * q^59 - 3 * q^60 - 18 * q^61 - 28 * q^62 - 27 * q^63 + 11 * q^64 + 22 * q^65 - 13 * q^66 - 11 * q^67 - 16 * q^68 + 9 * q^69 - 11 * q^70 - 16 * q^71 + 18 * q^72 - 33 * q^73 - 22 * q^74 - 21 * q^75 - 22 * q^76 + 9 * q^78 + 9 * q^79 - 12 * q^80 + 71 * q^81 - 5 * q^82 - 18 * q^83 - q^84 - 8 * q^85 - 7 * q^86 - 17 * q^87 - 7 * q^88 - 23 * q^90 - 22 * q^91 - 2 * q^92 + 8 * q^93 - 31 * q^94 - 23 * q^95 - 11 * q^96 - 66 * q^97 - 2 * q^98 - 5 * q^99

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