LMFDB - Embedded newform 6026.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 $ x^20 - 5x^19 - 17x^18 + 115x^17 + 78x^16 - 1083x^15 + 248x^14 + 5359x^13 - 3723x^12 - 14776x^11 + 14837x^10 + 21886x^9 - 28084x^8 - 14682x^7 + 25315x^6 + 2042x^5 - 9137x^4 + 576x^3 + 1159x^2 - 78*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.09509$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.09509 q^{3} +1.00000 q^{4} -0.379683 q^{5} -1.09509 q^{6} -3.84052 q^{7} +1.00000 q^{8} -1.80078 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.09509 q^{3} +1.00000 q^{4} -0.379683 q^{5} -1.09509 q^{6} -3.84052 q^{7} +1.00000 q^{8} -1.80078 q^{9} -0.379683 q^{10} +0.261549 q^{11} -1.09509 q^{12} +2.14179 q^{13} -3.84052 q^{14} +0.415786 q^{15} +1.00000 q^{16} +7.86745 q^{17} -1.80078 q^{18} -1.91617 q^{19} -0.379683 q^{20} +4.20570 q^{21} +0.261549 q^{22} +1.00000 q^{23} -1.09509 q^{24} -4.85584 q^{25} +2.14179 q^{26} +5.25728 q^{27} -3.84052 q^{28} -5.12375 q^{29} +0.415786 q^{30} +8.92123 q^{31} +1.00000 q^{32} -0.286419 q^{33} +7.86745 q^{34} +1.45818 q^{35} -1.80078 q^{36} -2.25819 q^{37} -1.91617 q^{38} -2.34544 q^{39} -0.379683 q^{40} +8.99980 q^{41} +4.20570 q^{42} +0.409214 q^{43} +0.261549 q^{44} +0.683727 q^{45} +1.00000 q^{46} -12.9684 q^{47} -1.09509 q^{48} +7.74957 q^{49} -4.85584 q^{50} -8.61554 q^{51} +2.14179 q^{52} +1.01480 q^{53} +5.25728 q^{54} -0.0993058 q^{55} -3.84052 q^{56} +2.09838 q^{57} -5.12375 q^{58} -14.2800 q^{59} +0.415786 q^{60} -11.2712 q^{61} +8.92123 q^{62} +6.91594 q^{63} +1.00000 q^{64} -0.813200 q^{65} -0.286419 q^{66} +16.2276 q^{67} +7.86745 q^{68} -1.09509 q^{69} +1.45818 q^{70} +7.88829 q^{71} -1.80078 q^{72} -13.1428 q^{73} -2.25819 q^{74} +5.31757 q^{75} -1.91617 q^{76} -1.00448 q^{77} -2.34544 q^{78} +12.1520 q^{79} -0.379683 q^{80} -0.354823 q^{81} +8.99980 q^{82} +4.24057 q^{83} +4.20570 q^{84} -2.98714 q^{85} +0.409214 q^{86} +5.61096 q^{87} +0.261549 q^{88} -17.9751 q^{89} +0.683727 q^{90} -8.22557 q^{91} +1.00000 q^{92} -9.76953 q^{93} -12.9684 q^{94} +0.727538 q^{95} -1.09509 q^{96} -17.6933 q^{97} +7.74957 q^{98} -0.470994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * 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
$3$	−1.09509	−0.632249	−0.316124	−	0.948718i	$-0.602382\pi$
$3$	−1.09509	−0.632249	−0.316124	+	0.948718i	$0.602382\pi$
$4$	1.00000	0.500000
$5$	−0.379683	−0.169799	−0.0848997	−	0.996390i	$-0.527057\pi$
$5$	−0.379683	−0.169799	−0.0848997	+	0.996390i	$0.527057\pi$
$6$	−1.09509	−0.447067
$7$	−3.84052	−1.45158	−0.725789	−	0.687917i	$-0.758525\pi$
$7$	−3.84052	−1.45158	−0.725789	+	0.687917i	$0.758525\pi$
$8$	1.00000	0.353553
$9$	−1.80078	−0.600261
$10$	−0.379683	−0.120066
$11$	0.261549	0.0788600	0.0394300	−	0.999222i	$-0.487446\pi$
$11$	0.261549	0.0788600	0.0394300	+	0.999222i	$0.487446\pi$
$12$	−1.09509	−0.316124
$13$	2.14179	0.594025	0.297012	−	0.954874i	$-0.404010\pi$
$13$	2.14179	0.594025	0.297012	+	0.954874i	$0.404010\pi$
$14$	−3.84052	−1.02642
$15$	0.415786	0.107355
$16$	1.00000	0.250000
$17$	7.86745	1.90814	0.954069	−	0.299588i	$-0.0968494\pi$
$17$	7.86745	1.90814	0.954069	+	0.299588i	$0.0968494\pi$
$18$	−1.80078	−0.424449
$19$	−1.91617	−0.439600	−0.219800	−	0.975545i	$-0.570541\pi$
$19$	−1.91617	−0.439600	−0.219800	+	0.975545i	$0.570541\pi$
$20$	−0.379683	−0.0848997
$21$	4.20570	0.917759
$22$	0.261549	0.0557625
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.09509	−0.223534
$25$	−4.85584	−0.971168
$26$	2.14179	0.420039
$27$	5.25728	1.01176
$28$	−3.84052	−0.725789
$29$	−5.12375	−0.951457	−0.475729	−	0.879592i	$-0.657816\pi$
$29$	−5.12375	−0.951457	−0.475729	+	0.879592i	$0.657816\pi$
$30$	0.415786	0.0759118
$31$	8.92123	1.60230	0.801150	−	0.598463i	$-0.204222\pi$
$31$	8.92123	1.60230	0.801150	+	0.598463i	$0.204222\pi$
$32$	1.00000	0.176777
$33$	−0.286419	−0.0498592
$34$	7.86745	1.34926
$35$	1.45818	0.246477
$36$	−1.80078	−0.300131
$37$	−2.25819	−0.371244	−0.185622	−	0.982621i	$-0.559430\pi$
$37$	−2.25819	−0.371244	−0.185622	+	0.982621i	$0.559430\pi$
$38$	−1.91617	−0.310844
$39$	−2.34544	−0.375571
$40$	−0.379683	−0.0600331
$41$	8.99980	1.40553	0.702766	−	0.711421i	$-0.251948\pi$
$41$	8.99980	1.40553	0.702766	+	0.711421i	$0.251948\pi$
$42$	4.20570	0.648954
$43$	0.409214	0.0624045	0.0312023	−	0.999513i	$-0.490066\pi$
$43$	0.409214	0.0624045	0.0312023	+	0.999513i	$0.490066\pi$
$44$	0.261549	0.0394300
$45$	0.683727	0.101924
$46$	1.00000	0.147442
$47$	−12.9684	−1.89164	−0.945818	−	0.324698i	$-0.894737\pi$
$47$	−12.9684	−1.89164	−0.945818	+	0.324698i	$0.894737\pi$
$48$	−1.09509	−0.158062
$49$	7.74957	1.10708
$50$	−4.85584	−0.686720
$51$	−8.61554	−1.20642
$52$	2.14179	0.297012
$53$	1.01480	0.139394	0.0696969	−	0.997568i	$-0.477797\pi$
$53$	1.01480	0.139394	0.0696969	+	0.997568i	$0.477797\pi$
$54$	5.25728	0.715425
$55$	−0.0993058	−0.0133904
$56$	−3.84052	−0.513211
$57$	2.09838	0.277937
$58$	−5.12375	−0.672782
$59$	−14.2800	−1.85910	−0.929552	−	0.368691i	$-0.879806\pi$
$59$	−14.2800	−1.85910	−0.929552	+	0.368691i	$0.879806\pi$
$60$	0.415786	0.0536777
$61$	−11.2712	−1.44312	−0.721562	−	0.692350i	$-0.756575\pi$
$61$	−11.2712	−1.44312	−0.721562	+	0.692350i	$0.756575\pi$
$62$	8.92123	1.13300
$63$	6.91594	0.871327
$64$	1.00000	0.125000
$65$	−0.813200	−0.100865
$66$	−0.286419	−0.0352558
$67$	16.2276	1.98252	0.991260	−	0.131920i	$-0.0421143\pi$
$67$	16.2276	1.98252	0.991260	+	0.131920i	$0.0421143\pi$
$68$	7.86745	0.954069
$69$	−1.09509	−0.131833
$70$	1.45818	0.174286
$71$	7.88829	0.936168	0.468084	−	0.883684i	$-0.344944\pi$
$71$	7.88829	0.936168	0.468084	+	0.883684i	$0.344944\pi$
$72$	−1.80078	−0.212224
$73$	−13.1428	−1.53824	−0.769122	−	0.639102i	$-0.779306\pi$
$73$	−13.1428	−1.53824	−0.769122	+	0.639102i	$0.779306\pi$
$74$	−2.25819	−0.262509
$75$	5.31757	0.614020
$76$	−1.91617	−0.219800
$77$	−1.00448	−0.114472
$78$	−2.34544	−0.265569
$79$	12.1520	1.36720	0.683601	−	0.729856i	$-0.260413\pi$
$79$	12.1520	1.36720	0.683601	+	0.729856i	$0.260413\pi$
$80$	−0.379683	−0.0424498
$81$	−0.354823	−0.0394247
$82$	8.99980	0.993861
$83$	4.24057	0.465463	0.232732	−	0.972541i	$-0.425234\pi$
$83$	4.24057	0.465463	0.232732	+	0.972541i	$0.425234\pi$
$84$	4.20570	0.458880
$85$	−2.98714	−0.324001
$86$	0.409214	0.0441267
$87$	5.61096	0.601558
$88$	0.261549	0.0278812
$89$	−17.9751	−1.90535	−0.952677	−	0.303984i	$-0.901683\pi$
$89$	−17.9751	−1.90535	−0.952677	+	0.303984i	$0.901683\pi$
$90$	0.683727	0.0720712
$91$	−8.22557	−0.862274
$92$	1.00000	0.104257
$93$	−9.76953	−1.01305
$94$	−12.9684	−1.33759
$95$	0.727538	0.0746438
$96$	−1.09509	−0.111767
$97$	−17.6933	−1.79649	−0.898243	−	0.439500i	$-0.855156\pi$
$97$	−17.6933	−1.79649	−0.898243	+	0.439500i	$0.855156\pi$
$98$	7.74957	0.782825
$99$	−0.470994	−0.0473366
$100$	−4.85584	−0.485584
$101$	18.0472	1.79577	0.897884	−	0.440232i	$-0.145104\pi$
$101$	18.0472	1.79577	0.897884	+	0.440232i	$0.145104\pi$
$102$	−8.61554	−0.853066
$103$	−1.04986	−0.103446	−0.0517229	−	0.998661i	$-0.516471\pi$
$103$	−1.04986	−0.103446	−0.0517229	+	0.998661i	$0.516471\pi$
$104$	2.14179	0.210019
$105$	−1.59683	−0.155835
$106$	1.01480	0.0985662
$107$	8.69987	0.841048	0.420524	−	0.907281i	$-0.361846\pi$
$107$	8.69987	0.841048	0.420524	+	0.907281i	$0.361846\pi$
$108$	5.25728	0.505882
$109$	−12.4180	−1.18943	−0.594713	−	0.803938i	$-0.702734\pi$
$109$	−12.4180	−1.18943	−0.594713	+	0.803938i	$0.702734\pi$
$110$	−0.0993058	−0.00946843
$111$	2.47291	0.234719
$112$	−3.84052	−0.362895
$113$	−18.4230	−1.73309	−0.866546	−	0.499098i	$-0.833665\pi$
$113$	−18.4230	−1.73309	−0.866546	+	0.499098i	$0.833665\pi$
$114$	2.09838	0.196531
$115$	−0.379683	−0.0354056
$116$	−5.12375	−0.475729
$117$	−3.85690	−0.356570
$118$	−14.2800	−1.31458
$119$	−30.2151	−2.76981
$120$	0.415786	0.0379559
$121$	−10.9316	−0.993781
$122$	−11.2712	−1.02044
$123$	−9.85556	−0.888646
$124$	8.92123	0.801150
$125$	3.74209	0.334703
$126$	6.91594	0.616121
$127$	1.46855	0.130313	0.0651564	−	0.997875i	$-0.479245\pi$
$127$	1.46855	0.130313	0.0651564	+	0.997875i	$0.479245\pi$
$128$	1.00000	0.0883883
$129$	−0.448125	−0.0394552
$130$	−0.813200	−0.0713223
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.286419	−0.0249296
$133$	7.35909	0.638114
$134$	16.2276	1.40185
$135$	−1.99610	−0.171797
$136$	7.86745	0.674628
$137$	−11.2182	−0.958432	−0.479216	−	0.877697i	$-0.659079\pi$
$137$	−11.2182	−0.958432	−0.479216	+	0.877697i	$0.659079\pi$
$138$	−1.09509	−0.0932200
$139$	−10.1698	−0.862589	−0.431295	−	0.902211i	$-0.641943\pi$
$139$	−10.1698	−0.862589	−0.431295	+	0.902211i	$0.641943\pi$
$140$	1.45818	0.123239
$141$	14.2015	1.19598
$142$	7.88829	0.661971
$143$	0.560182	0.0468448
$144$	−1.80078	−0.150065
$145$	1.94540	0.161557
$146$	−13.1428	−1.08770
$147$	−8.48645	−0.699951
$148$	−2.25819	−0.185622
$149$	−9.46032	−0.775020	−0.387510	−	0.921866i	$-0.626665\pi$
$149$	−9.46032	−0.775020	−0.387510	+	0.921866i	$0.626665\pi$
$150$	5.31757	0.434178
$151$	9.98401	0.812487	0.406244	−	0.913765i	$-0.366838\pi$
$151$	9.98401	0.812487	0.406244	+	0.913765i	$0.366838\pi$
$152$	−1.91617	−0.155422
$153$	−14.1676	−1.14538
$154$	−1.00448	−0.0809436
$155$	−3.38724	−0.272070
$156$	−2.34544	−0.187786
$157$	−9.47140	−0.755900	−0.377950	−	0.925826i	$-0.623371\pi$
$157$	−9.47140	−0.755900	−0.377950	+	0.925826i	$0.623371\pi$
$158$	12.1520	0.966758
$159$	−1.11130	−0.0881315
$160$	−0.379683	−0.0300166
$161$	−3.84052	−0.302675
$162$	−0.354823	−0.0278775
$163$	−13.5905	−1.06449	−0.532246	−	0.846590i	$-0.678652\pi$
$163$	−13.5905	−1.06449	−0.532246	+	0.846590i	$0.678652\pi$
$164$	8.99980	0.702766
$165$	0.108748	0.00846606
$166$	4.24057	0.329132
$167$	−23.6335	−1.82882	−0.914408	−	0.404795i	$-0.867343\pi$
$167$	−23.6335	−1.82882	−0.914408	+	0.404795i	$0.867343\pi$
$168$	4.20570	0.324477
$169$	−8.41275	−0.647135
$170$	−2.98714	−0.229103
$171$	3.45061	0.263875
$172$	0.409214	0.0312023
$173$	−6.91608	−0.525820	−0.262910	−	0.964820i	$-0.584682\pi$
$173$	−6.91608	−0.525820	−0.262910	+	0.964820i	$0.584682\pi$
$174$	5.61096	0.425366
$175$	18.6489	1.40973
$176$	0.261549	0.0197150
$177$	15.6379	1.17542
$178$	−17.9751	−1.34729
$179$	17.6654	1.32037	0.660187	−	0.751101i	$-0.270477\pi$
$179$	17.6654	1.32037	0.660187	+	0.751101i	$0.270477\pi$
$180$	0.683727	0.0509620
$181$	13.1081	0.974320	0.487160	−	0.873313i	$-0.338033\pi$
$181$	13.1081	0.974320	0.487160	+	0.873313i	$0.338033\pi$
$182$	−8.22557	−0.609720
$183$	12.3429	0.912413
$184$	1.00000	0.0737210
$185$	0.857396	0.0630370
$186$	−9.76953	−0.716336
$187$	2.05773	0.150476
$188$	−12.9684	−0.945818
$189$	−20.1907	−1.46865
$190$	0.727538	0.0527812
$191$	15.2263	1.10174	0.550870	−	0.834591i	$-0.314296\pi$
$191$	15.2263	1.10174	0.550870	+	0.834591i	$0.314296\pi$
$192$	−1.09509	−0.0790311
$193$	20.9529	1.50822	0.754110	−	0.656748i	$-0.228069\pi$
$193$	20.9529	1.50822	0.754110	+	0.656748i	$0.228069\pi$
$194$	−17.6933	−1.27031
$195$	0.890525	0.0637718
$196$	7.74957	0.553541
$197$	−16.2950	−1.16097	−0.580486	−	0.814270i	$-0.697137\pi$
$197$	−16.2950	−1.16097	−0.580486	+	0.814270i	$0.697137\pi$
$198$	−0.470994	−0.0334721
$199$	−16.7787	−1.18941	−0.594704	−	0.803945i	$-0.702731\pi$
$199$	−16.7787	−1.18941	−0.594704	+	0.803945i	$0.702731\pi$
$200$	−4.85584	−0.343360
$201$	−17.7707	−1.25345
$202$	18.0472	1.26980
$203$	19.6779	1.38112
$204$	−8.61554	−0.603209
$205$	−3.41707	−0.238659
$206$	−1.04986	−0.0731473
$207$	−1.80078	−0.125163
$208$	2.14179	0.148506
$209$	−0.501173	−0.0346669
$210$	−1.59683	−0.110192
$211$	−23.1807	−1.59583	−0.797913	−	0.602773i	$-0.794062\pi$
$211$	−23.1807	−1.59583	−0.797913	+	0.602773i	$0.794062\pi$
$212$	1.01480	0.0696969
$213$	−8.63837	−0.591891
$214$	8.69987	0.594711
$215$	−0.155372	−0.0105963
$216$	5.25728	0.357712
$217$	−34.2621	−2.32587
$218$	−12.4180	−0.841051
$219$	14.3925	0.972553
$220$	−0.0993058	−0.00669519
$221$	16.8504	1.13348
$222$	2.47291	0.165971
$223$	12.7776	0.855652	0.427826	−	0.903861i	$-0.359280\pi$
$223$	12.7776	0.855652	0.427826	+	0.903861i	$0.359280\pi$
$224$	−3.84052	−0.256605
$225$	8.74432	0.582955
$226$	−18.4230	−1.22548
$227$	−7.80777	−0.518220	−0.259110	−	0.965848i	$-0.583429\pi$
$227$	−7.80777	−0.518220	−0.259110	+	0.965848i	$0.583429\pi$
$228$	2.09838	0.138968
$229$	−12.8485	−0.849053	−0.424527	−	0.905415i	$-0.639560\pi$
$229$	−12.8485	−0.849053	−0.424527	+	0.905415i	$0.639560\pi$
$230$	−0.379683	−0.0250356
$231$	1.10000	0.0723745
$232$	−5.12375	−0.336391
$233$	−18.3254	−1.20053	−0.600267	−	0.799800i	$-0.704939\pi$
$233$	−18.3254	−1.20053	−0.600267	+	0.799800i	$0.704939\pi$
$234$	−3.85690	−0.252133
$235$	4.92388	0.321199
$236$	−14.2800	−0.929552
$237$	−13.3075	−0.864412
$238$	−30.2151	−1.95855
$239$	−20.6913	−1.33841	−0.669206	−	0.743077i	$-0.733365\pi$
$239$	−20.6913	−1.33841	−0.669206	+	0.743077i	$0.733365\pi$
$240$	0.415786	0.0268389
$241$	15.5075	0.998923	0.499461	−	0.866336i	$-0.333531\pi$
$241$	15.5075	0.998923	0.499461	+	0.866336i	$0.333531\pi$
$242$	−10.9316	−0.702709
$243$	−15.3833	−0.986837
$244$	−11.2712	−0.721562
$245$	−2.94238	−0.187982
$246$	−9.85556	−0.628368
$247$	−4.10403	−0.261133
$248$	8.92123	0.566499
$249$	−4.64380	−0.294289
$250$	3.74209	0.236671
$251$	−1.96952	−0.124315	−0.0621576	−	0.998066i	$-0.519798\pi$
$251$	−1.96952	−0.124315	−0.0621576	+	0.998066i	$0.519798\pi$
$252$	6.91594	0.435663
$253$	0.261549	0.0164435
$254$	1.46855	0.0921451
$255$	3.27118	0.204849
$256$	1.00000	0.0625000
$257$	6.44580	0.402078	0.201039	−	0.979583i	$-0.435568\pi$
$257$	6.44580	0.402078	0.201039	+	0.979583i	$0.435568\pi$
$258$	−0.448125	−0.0278990
$259$	8.67261	0.538890
$260$	−0.813200	−0.0504325
$261$	9.22678	0.571123
$262$	−1.00000	−0.0617802
$263$	−5.05238	−0.311543	−0.155772	−	0.987793i	$-0.549786\pi$
$263$	−5.05238	−0.311543	−0.155772	+	0.987793i	$0.549786\pi$
$264$	−0.286419	−0.0176279
$265$	−0.385303	−0.0236690
$266$	7.35909	0.451215
$267$	19.6843	1.20466
$268$	16.2276	0.991260
$269$	−4.10023	−0.249995	−0.124998	−	0.992157i	$-0.539892\pi$
$269$	−4.10023	−0.249995	−0.124998	+	0.992157i	$0.539892\pi$
$270$	−1.99610	−0.121479
$271$	−9.83874	−0.597661	−0.298831	−	0.954306i	$-0.596597\pi$
$271$	−9.83874	−0.597661	−0.298831	+	0.954306i	$0.596597\pi$
$272$	7.86745	0.477034
$273$	9.00771	0.545172
$274$	−11.2182	−0.677713
$275$	−1.27004	−0.0765864
$276$	−1.09509	−0.0659165
$277$	19.1602	1.15122	0.575612	−	0.817723i	$-0.304764\pi$
$277$	19.1602	1.15122	0.575612	+	0.817723i	$0.304764\pi$
$278$	−10.1698	−0.609943
$279$	−16.0652	−0.961799
$280$	1.45818	0.0871429
$281$	−10.9363	−0.652403	−0.326202	−	0.945300i	$-0.605769\pi$
$281$	−10.9363	−0.652403	−0.326202	+	0.945300i	$0.605769\pi$
$282$	14.2015	0.845689
$283$	16.9832	1.00954	0.504772	−	0.863252i	$-0.331576\pi$
$283$	16.9832	1.00954	0.504772	+	0.863252i	$0.331576\pi$
$284$	7.88829	0.468084
$285$	−0.796718	−0.0471935
$286$	0.560182	0.0331243
$287$	−34.5639	−2.04024
$288$	−1.80078	−0.106112
$289$	44.8968	2.64099
$290$	1.94540	0.114238
$291$	19.3757	1.13583
$292$	−13.1428	−0.769122
$293$	−7.98815	−0.466673	−0.233336	−	0.972396i	$-0.574964\pi$
$293$	−7.98815	−0.466673	−0.233336	+	0.972396i	$0.574964\pi$
$294$	−8.48645	−0.494940
$295$	5.42189	0.315675
$296$	−2.25819	−0.131255
$297$	1.37504	0.0797877
$298$	−9.46032	−0.548022
$299$	2.14179	0.123863
$300$	5.31757	0.307010
$301$	−1.57159	−0.0905851
$302$	9.98401	0.574515
$303$	−19.7633	−1.13537
$304$	−1.91617	−0.109900
$305$	4.27946	0.245041
$306$	−14.1676	−0.809907
$307$	13.1475	0.750368	0.375184	−	0.926950i	$-0.377580\pi$
$307$	13.1475	0.750368	0.375184	+	0.926950i	$0.377580\pi$
$308$	−1.00448	−0.0572358
$309$	1.14969	0.0654035
$310$	−3.38724	−0.192382
$311$	−12.4572	−0.706384	−0.353192	−	0.935551i	$-0.614904\pi$
$311$	−12.4572	−0.706384	−0.353192	+	0.935551i	$0.614904\pi$
$312$	−2.34544	−0.132785
$313$	14.9622	0.845712	0.422856	−	0.906197i	$-0.361028\pi$
$313$	14.9622	0.845712	0.422856	+	0.906197i	$0.361028\pi$
$314$	−9.47140	−0.534502
$315$	−2.62587	−0.147951
$316$	12.1520	0.683601
$317$	−31.1550	−1.74984	−0.874919	−	0.484269i	$-0.839086\pi$
$317$	−31.1550	−1.74984	−0.874919	+	0.484269i	$0.839086\pi$
$318$	−1.11130	−0.0623184
$319$	−1.34011	−0.0750320
$320$	−0.379683	−0.0212249
$321$	−9.52711	−0.531751
$322$	−3.84052	−0.214024
$323$	−15.0754	−0.838817
$324$	−0.354823	−0.0197124
$325$	−10.4002	−0.576898
$326$	−13.5905	−0.752710
$327$	13.5988	0.752013
$328$	8.99980	0.496931
$329$	49.8054	2.74586
$330$	0.108748	0.00598641
$331$	15.3719	0.844915	0.422457	−	0.906383i	$-0.361168\pi$
$331$	15.3719	0.844915	0.422457	+	0.906383i	$0.361168\pi$
$332$	4.24057	0.232732
$333$	4.06651	0.222844
$334$	−23.6335	−1.29317
$335$	−6.16136	−0.336631
$336$	4.20570	0.229440
$337$	13.1891	0.718454	0.359227	−	0.933250i	$-0.383040\pi$
$337$	13.1891	0.718454	0.359227	+	0.933250i	$0.383040\pi$
$338$	−8.41275	−0.457593
$339$	20.1748	1.09574
$340$	−2.98714	−0.162000
$341$	2.33334	0.126357
$342$	3.45061	0.186588
$343$	−2.87874	−0.155437
$344$	0.409214	0.0220633
$345$	0.415786	0.0223852
$346$	−6.91608	−0.371811
$347$	10.9286	0.586675	0.293338	−	0.956009i	$-0.405234\pi$
$347$	10.9286	0.586675	0.293338	+	0.956009i	$0.405234\pi$
$348$	5.61096	0.300779
$349$	17.1764	0.919430	0.459715	−	0.888066i	$-0.347951\pi$
$349$	17.1764	0.919430	0.459715	+	0.888066i	$0.347951\pi$
$350$	18.6489	0.996828
$351$	11.2600	0.601012
$352$	0.261549	0.0139406
$353$	16.4062	0.873212	0.436606	−	0.899653i	$-0.356180\pi$
$353$	16.4062	0.873212	0.436606	+	0.899653i	$0.356180\pi$
$354$	15.6379	0.831145
$355$	−2.99505	−0.158961
$356$	−17.9751	−0.952677
$357$	33.0881	1.75121
$358$	17.6654	0.933645
$359$	−4.91396	−0.259349	−0.129674	−	0.991557i	$-0.541393\pi$
$359$	−4.91396	−0.259349	−0.129674	+	0.991557i	$0.541393\pi$
$360$	0.683727	0.0360356
$361$	−15.3283	−0.806752
$362$	13.1081	0.688949
$363$	11.9710	0.628317
$364$	−8.22557	−0.431137
$365$	4.99008	0.261193
$366$	12.3429	0.645173
$367$	27.5827	1.43981	0.719904	−	0.694074i	$-0.244186\pi$
$367$	27.5827	1.43981	0.719904	+	0.694074i	$0.244186\pi$
$368$	1.00000	0.0521286
$369$	−16.2067	−0.843687
$370$	0.857396	0.0445739
$371$	−3.89736	−0.202341
$372$	−9.76953	−0.506526
$373$	−36.5714	−1.89360	−0.946798	−	0.321829i	$-0.895703\pi$
$373$	−36.5714	−1.89360	−0.946798	+	0.321829i	$0.895703\pi$
$374$	2.05773	0.106402
$375$	−4.09792	−0.211616
$376$	−12.9684	−0.668794
$377$	−10.9740	−0.565189
$378$	−20.1907	−1.03850
$379$	7.75161	0.398174	0.199087	−	0.979982i	$-0.436202\pi$
$379$	7.75161	0.398174	0.199087	+	0.979982i	$0.436202\pi$
$380$	0.727538	0.0373219
$381$	−1.60819	−0.0823901
$382$	15.2263	0.779048
$383$	−8.94818	−0.457231	−0.228615	−	0.973517i	$-0.573420\pi$
$383$	−8.94818	−0.457231	−0.228615	+	0.973517i	$0.573420\pi$
$384$	−1.09509	−0.0558834
$385$	0.381385	0.0194372
$386$	20.9529	1.06647
$387$	−0.736906	−0.0374590
$388$	−17.6933	−0.898243
$389$	−1.85160	−0.0938798	−0.0469399	−	0.998898i	$-0.514947\pi$
$389$	−1.85160	−0.0938798	−0.0469399	+	0.998898i	$0.514947\pi$
$390$	0.890525	0.0450935
$391$	7.86745	0.397874
$392$	7.74957	0.391412
$393$	1.09509	0.0552398
$394$	−16.2950	−0.820931
$395$	−4.61389	−0.232150
$396$	−0.470994	−0.0236683
$397$	−28.7208	−1.44146	−0.720729	−	0.693217i	$-0.756193\pi$
$397$	−28.7208	−1.44146	−0.720729	+	0.693217i	$0.756193\pi$
$398$	−16.7787	−0.841039
$399$	−8.05885	−0.403447
$400$	−4.85584	−0.242792
$401$	22.3340	1.11531	0.557654	−	0.830073i	$-0.311701\pi$
$401$	22.3340	1.11531	0.557654	+	0.830073i	$0.311701\pi$
$402$	−17.7707	−0.886320
$403$	19.1074	0.951806
$404$	18.0472	0.897884
$405$	0.134720	0.00669430
$406$	19.6779	0.976596
$407$	−0.590628	−0.0292763
$408$	−8.61554	−0.426533
$409$	12.0914	0.597881	0.298940	−	0.954272i	$-0.403367\pi$
$409$	12.0914	0.597881	0.298940	+	0.954272i	$0.403367\pi$
$410$	−3.41707	−0.168757
$411$	12.2849	0.605967
$412$	−1.04986	−0.0517229
$413$	54.8428	2.69864
$414$	−1.80078	−0.0885037
$415$	−1.61007	−0.0790354
$416$	2.14179	0.105010
$417$	11.1368	0.545371
$418$	−0.501173	−0.0245132
$419$	−19.4906	−0.952177	−0.476088	−	0.879397i	$-0.657946\pi$
$419$	−19.4906	−0.952177	−0.476088	+	0.879397i	$0.657946\pi$
$420$	−1.59683	−0.0779175
$421$	−17.9165	−0.873196	−0.436598	−	0.899657i	$-0.643817\pi$
$421$	−17.9165	−0.873196	−0.436598	+	0.899657i	$0.643817\pi$
$422$	−23.1807	−1.12842
$423$	23.3533	1.13548
$424$	1.01480	0.0492831
$425$	−38.2031	−1.85312
$426$	−8.63837	−0.418530
$427$	43.2871	2.09481
$428$	8.69987	0.420524
$429$	−0.613449	−0.0296176
$430$	−0.155372	−0.00749268
$431$	−29.2287	−1.40789	−0.703947	−	0.710252i	$-0.748581\pi$
$431$	−29.2287	−1.40789	−0.703947	+	0.710252i	$0.748581\pi$
$432$	5.25728	0.252941
$433$	−9.82049	−0.471943	−0.235971	−	0.971760i	$-0.575827\pi$
$433$	−9.82049	−0.471943	−0.235971	+	0.971760i	$0.575827\pi$
$434$	−34.2621	−1.64464
$435$	−2.13038	−0.102144
$436$	−12.4180	−0.594713
$437$	−1.91617	−0.0916630
$438$	14.3925	0.687699
$439$	−21.5346	−1.02779	−0.513895	−	0.857853i	$-0.671798\pi$
$439$	−21.5346	−1.02779	−0.513895	+	0.857853i	$0.671798\pi$
$440$	−0.0993058	−0.00473422
$441$	−13.9553	−0.664538
$442$	16.8504	0.801492
$443$	3.10840	0.147684	0.0738422	−	0.997270i	$-0.476474\pi$
$443$	3.10840	0.147684	0.0738422	+	0.997270i	$0.476474\pi$
$444$	2.47291	0.117359
$445$	6.82483	0.323528
$446$	12.7776	0.605038
$447$	10.3599	0.490005
$448$	−3.84052	−0.181447
$449$	−20.5764	−0.971062	−0.485531	−	0.874220i	$-0.661374\pi$
$449$	−20.5764	−0.971062	−0.485531	+	0.874220i	$0.661374\pi$
$450$	8.74432	0.412211
$451$	2.35389	0.110840
$452$	−18.4230	−0.866546
$453$	−10.9334	−0.513694
$454$	−7.80777	−0.366437
$455$	3.12311	0.146414
$456$	2.09838	0.0982654
$457$	30.0123	1.40392	0.701958	−	0.712218i	$-0.252309\pi$
$457$	30.0123	1.40392	0.701958	+	0.712218i	$0.252309\pi$
$458$	−12.8485	−0.600371
$459$	41.3614	1.93058
$460$	−0.379683	−0.0177028
$461$	20.4534	0.952611	0.476305	−	0.879280i	$-0.341976\pi$
$461$	20.4534	0.952611	0.476305	+	0.879280i	$0.341976\pi$
$462$	1.10000	0.0511765
$463$	−22.6020	−1.05040	−0.525201	−	0.850978i	$-0.676010\pi$
$463$	−22.6020	−1.05040	−0.525201	+	0.850978i	$0.676010\pi$
$464$	−5.12375	−0.237864
$465$	3.70932	0.172016
$466$	−18.3254	−0.848906
$467$	26.9318	1.24625	0.623127	−	0.782120i	$-0.285862\pi$
$467$	26.9318	1.24625	0.623127	+	0.782120i	$0.285862\pi$
$468$	−3.85690	−0.178285
$469$	−62.3225	−2.87779
$470$	4.92388	0.227122
$471$	10.3720	0.477917
$472$	−14.2800	−0.657292
$473$	0.107030	0.00492123
$474$	−13.3075	−0.611232
$475$	9.30463	0.426926
$476$	−30.2151	−1.38491
$477$	−1.82744	−0.0836727
$478$	−20.6913	−0.946400
$479$	9.79929	0.447741	0.223871	−	0.974619i	$-0.428131\pi$
$479$	9.79929	0.447741	0.223871	+	0.974619i	$0.428131\pi$
$480$	0.415786	0.0189779
$481$	−4.83656	−0.220528
$482$	15.5075	0.706345
$483$	4.20570	0.191366
$484$	−10.9316	−0.496891
$485$	6.71786	0.305042
$486$	−15.3833	−0.697799
$487$	28.8284	1.30634	0.653169	−	0.757212i	$-0.273439\pi$
$487$	28.8284	1.30634	0.653169	+	0.757212i	$0.273439\pi$
$488$	−11.2712	−0.510221
$489$	14.8828	0.673024
$490$	−2.94238	−0.132923
$491$	−13.9082	−0.627669	−0.313835	−	0.949478i	$-0.601614\pi$
$491$	−13.9082	−0.627669	−0.313835	+	0.949478i	$0.601614\pi$
$492$	−9.85556	−0.444323
$493$	−40.3109	−1.81551
$494$	−4.10403	−0.184649
$495$	0.178828	0.00803773
$496$	8.92123	0.400575
$497$	−30.2951	−1.35892
$498$	−4.64380	−0.208094
$499$	12.2317	0.547567	0.273784	−	0.961791i	$-0.411725\pi$
$499$	12.2317	0.547567	0.273784	+	0.961791i	$0.411725\pi$
$500$	3.74209	0.167352
$501$	25.8807	1.15627
$502$	−1.96952	−0.0879041
$503$	16.0728	0.716651	0.358326	−	0.933597i	$-0.383348\pi$
$503$	16.0728	0.716651	0.358326	+	0.933597i	$0.383348\pi$
$504$	6.91594	0.308061
$505$	−6.85223	−0.304920
$506$	0.261549	0.0116273
$507$	9.21269	0.409150
$508$	1.46855	0.0651564
$509$	16.1127	0.714183	0.357092	−	0.934069i	$-0.383768\pi$
$509$	16.1127	0.714183	0.357092	+	0.934069i	$0.383768\pi$
$510$	3.27118	0.144850
$511$	50.4750	2.23288
$512$	1.00000	0.0441942
$513$	−10.0738	−0.444771
$514$	6.44580	0.284312
$515$	0.398614	0.0175650
$516$	−0.448125	−0.0197276
$517$	−3.39187	−0.149174
$518$	8.67261	0.381053
$519$	7.57371	0.332449
$520$	−0.813200	−0.0356612
$521$	−2.63788	−0.115568	−0.0577838	−	0.998329i	$-0.518403\pi$
$521$	−2.63788	−0.115568	−0.0577838	+	0.998329i	$0.518403\pi$
$522$	9.22678	0.403845
$523$	−6.08479	−0.266069	−0.133035	−	0.991111i	$-0.542472\pi$
$523$	−6.08479	−0.266069	−0.133035	+	0.991111i	$0.542472\pi$
$524$	−1.00000	−0.0436852
$525$	−20.4222	−0.891298
$526$	−5.05238	−0.220294
$527$	70.1874	3.05741
$528$	−0.286419	−0.0124648
$529$	1.00000	0.0434783
$530$	−0.385303	−0.0167365
$531$	25.7153	1.11595
$532$	7.35909	0.319057
$533$	19.2756	0.834921
$534$	19.6843	0.851822
$535$	−3.30319	−0.142809
$536$	16.2276	0.700927
$537$	−19.3451	−0.834805
$538$	−4.10023	−0.176773
$539$	2.02689	0.0873045
$540$	−1.99610	−0.0858984
$541$	−31.8727	−1.37031	−0.685156	−	0.728396i	$-0.740266\pi$
$541$	−31.8727	−1.37031	−0.685156	+	0.728396i	$0.740266\pi$
$542$	−9.83874	−0.422610
$543$	−14.3546	−0.616013
$544$	7.86745	0.337314
$545$	4.71489	0.201964
$546$	9.00771	0.385494
$547$	5.33149	0.227958	0.113979	−	0.993483i	$-0.463640\pi$
$547$	5.33149	0.227958	0.113979	+	0.993483i	$0.463640\pi$
$548$	−11.2182	−0.479216
$549$	20.2969	0.866251
$550$	−1.27004	−0.0541547
$551$	9.81800	0.418261
$552$	−1.09509	−0.0466100
$553$	−46.6698	−1.98460
$554$	19.1602	0.814038
$555$	−0.938923	−0.0398551
$556$	−10.1698	−0.431295
$557$	46.7775	1.98203	0.991014	−	0.133761i	$-0.0427056\pi$
$557$	46.7775	1.98203	0.991014	+	0.133761i	$0.0427056\pi$
$558$	−16.0652	−0.680095
$559$	0.876449	0.0370698
$560$	1.45818	0.0616193
$561$	−2.25339	−0.0951381
$562$	−10.9363	−0.461319
$563$	20.0832	0.846405	0.423202	−	0.906035i	$-0.360906\pi$
$563$	20.0832	0.846405	0.423202	+	0.906035i	$0.360906\pi$
$564$	14.2015	0.597992
$565$	6.99490	0.294278
$566$	16.9832	0.713856
$567$	1.36270	0.0572281
$568$	7.88829	0.330985
$569$	−12.4335	−0.521239	−0.260619	−	0.965442i	$-0.583927\pi$
$569$	−12.4335	−0.521239	−0.260619	+	0.965442i	$0.583927\pi$
$570$	−0.796718	−0.0333708
$571$	−12.9858	−0.543438	−0.271719	−	0.962377i	$-0.587592\pi$
$571$	−12.9858	−0.543438	−0.271719	+	0.962377i	$0.587592\pi$
$572$	0.560182	0.0234224
$573$	−16.6742	−0.696574
$574$	−34.5639	−1.44267
$575$	−4.85584	−0.202503
$576$	−1.80078	−0.0750327
$577$	−32.7949	−1.36527	−0.682634	−	0.730761i	$-0.739166\pi$
$577$	−32.7949	−1.36527	−0.682634	+	0.730761i	$0.739166\pi$
$578$	44.8968	1.86746
$579$	−22.9452	−0.953570
$580$	1.94540	0.0807784
$581$	−16.2860	−0.675657
$582$	19.3757	0.803150
$583$	0.265421	0.0109926
$584$	−13.1428	−0.543851
$585$	1.46440	0.0605454
$586$	−7.98815	−0.329987
$587$	−11.1631	−0.460749	−0.230374	−	0.973102i	$-0.573995\pi$
$587$	−11.1631	−0.460749	−0.230374	+	0.973102i	$0.573995\pi$
$588$	−8.48645	−0.349975
$589$	−17.0946	−0.704372
$590$	5.42189	0.223216
$591$	17.8445	0.734023
$592$	−2.25819	−0.0928110
$593$	−24.4498	−1.00403	−0.502016	−	0.864859i	$-0.667408\pi$
$593$	−24.4498	−1.00403	−0.502016	+	0.864859i	$0.667408\pi$
$594$	1.37504	0.0564184
$595$	11.4722	0.470312
$596$	−9.46032	−0.387510
$597$	18.3741	0.752002
$598$	2.14179	0.0875842
$599$	−1.20215	−0.0491187	−0.0245593	−	0.999698i	$-0.507818\pi$
$599$	−1.20215	−0.0491187	−0.0245593	+	0.999698i	$0.507818\pi$
$600$	5.31757	0.217089
$601$	16.7062	0.681461	0.340730	−	0.940161i	$-0.389326\pi$
$601$	16.7062	0.681461	0.340730	+	0.940161i	$0.389326\pi$
$602$	−1.57159	−0.0640534
$603$	−29.2225	−1.19003
$604$	9.98401	0.406244
$605$	4.15054	0.168743
$606$	−19.7633	−0.802829
$607$	−9.10179	−0.369430	−0.184715	−	0.982792i	$-0.559136\pi$
$607$	−9.10179	−0.369430	−0.184715	+	0.982792i	$0.559136\pi$
$608$	−1.91617	−0.0777111
$609$	−21.5490	−0.873209
$610$	4.27946	0.173270
$611$	−27.7755	−1.12368
$612$	−14.1676	−0.572691
$613$	−46.6655	−1.88480	−0.942400	−	0.334488i	$-0.891437\pi$
$613$	−46.6655	−1.88480	−0.942400	+	0.334488i	$0.891437\pi$
$614$	13.1475	0.530590
$615$	3.74199	0.150892
$616$	−1.00448	−0.0404718
$617$	−17.1449	−0.690226	−0.345113	−	0.938561i	$-0.612159\pi$
$617$	−17.1449	−0.690226	−0.345113	+	0.938561i	$0.612159\pi$
$618$	1.14969	0.0462473
$619$	−15.8943	−0.638844	−0.319422	−	0.947613i	$-0.603489\pi$
$619$	−15.8943	−0.638844	−0.319422	+	0.947613i	$0.603489\pi$
$620$	−3.38724	−0.136035
$621$	5.25728	0.210967
$622$	−12.4572	−0.499489
$623$	69.0336	2.76577
$624$	−2.34544	−0.0938928
$625$	22.8584	0.914336
$626$	14.9622	0.598009
$627$	0.548828	0.0219181
$628$	−9.47140	−0.377950
$629$	−17.7662	−0.708385
$630$	−2.62587	−0.104617
$631$	−34.9191	−1.39011	−0.695054	−	0.718958i	$-0.744620\pi$
$631$	−34.9191	−1.39011	−0.695054	+	0.718958i	$0.744620\pi$
$632$	12.1520	0.483379
$633$	25.3849	1.00896
$634$	−31.1550	−1.23732
$635$	−0.557584	−0.0221270
$636$	−1.11130	−0.0440658
$637$	16.5979	0.657634
$638$	−1.34011	−0.0530556
$639$	−14.2051	−0.561946
$640$	−0.379683	−0.0150083
$641$	2.89033	0.114161	0.0570806	−	0.998370i	$-0.481821\pi$
$641$	2.89033	0.114161	0.0570806	+	0.998370i	$0.481821\pi$
$642$	−9.52711	−0.376005
$643$	25.6773	1.01261	0.506307	−	0.862353i	$-0.331010\pi$
$643$	25.6773	1.01261	0.506307	+	0.862353i	$0.331010\pi$
$644$	−3.84052	−0.151338
$645$	0.170145	0.00669947
$646$	−15.0754	−0.593133
$647$	−19.0684	−0.749658	−0.374829	−	0.927094i	$-0.622299\pi$
$647$	−19.0684	−0.749658	−0.374829	+	0.927094i	$0.622299\pi$
$648$	−0.354823	−0.0139388
$649$	−3.73493	−0.146609
$650$	−10.4002	−0.407928
$651$	37.5200	1.47053
$652$	−13.5905	−0.532246
$653$	7.02984	0.275099	0.137549	−	0.990495i	$-0.456077\pi$
$653$	7.02984	0.275099	0.137549	+	0.990495i	$0.456077\pi$
$654$	13.5988	0.531754
$655$	0.379683	0.0148354
$656$	8.99980	0.351383
$657$	23.6673	0.923348
$658$	49.8054	1.94161
$659$	17.6964	0.689352	0.344676	−	0.938722i	$-0.387989\pi$
$659$	17.6964	0.689352	0.344676	+	0.938722i	$0.387989\pi$
$660$	0.108748	0.00423303
$661$	−2.97008	−0.115523	−0.0577614	−	0.998330i	$-0.518396\pi$
$661$	−2.97008	−0.115523	−0.0577614	+	0.998330i	$0.518396\pi$
$662$	15.3719	0.597445
$663$	−18.4527	−0.716642
$664$	4.24057	0.164566
$665$	−2.79412	−0.108351
$666$	4.06651	0.157574
$667$	−5.12375	−0.198393
$668$	−23.6335	−0.914408
$669$	−13.9926	−0.540985
$670$	−6.16136	−0.238034
$671$	−2.94796	−0.113805
$672$	4.20570	0.162238
$673$	11.5169	0.443943	0.221971	−	0.975053i	$-0.428751\pi$
$673$	11.5169	0.443943	0.221971	+	0.975053i	$0.428751\pi$
$674$	13.1891	0.508024
$675$	−25.5285	−0.982592
$676$	−8.41275	−0.323567
$677$	11.6180	0.446515	0.223257	−	0.974760i	$-0.428331\pi$
$677$	11.6180	0.446515	0.223257	+	0.974760i	$0.428331\pi$
$678$	20.1748	0.774809
$679$	67.9515	2.60774
$680$	−2.98714	−0.114551
$681$	8.55019	0.327644
$682$	2.33334	0.0893482
$683$	−38.0195	−1.45478	−0.727388	−	0.686226i	$-0.759266\pi$
$683$	−38.0195	−1.45478	−0.727388	+	0.686226i	$0.759266\pi$
$684$	3.45061	0.131938
$685$	4.25934	0.162741
$686$	−2.87874	−0.109911
$687$	14.0702	0.536813
$688$	0.409214	0.0156011
$689$	2.17349	0.0828033
$690$	0.415786	0.0158287
$691$	−35.1699	−1.33793	−0.668963	−	0.743295i	$-0.733262\pi$
$691$	−35.1699	−1.33793	−0.668963	+	0.743295i	$0.733262\pi$
$692$	−6.91608	−0.262910
$693$	1.80886	0.0687129
$694$	10.9286	0.414842
$695$	3.86129	0.146467
$696$	5.61096	0.212683
$697$	70.8055	2.68195
$698$	17.1764	0.650135
$699$	20.0679	0.759036
$700$	18.6489	0.704864
$701$	14.3599	0.542366	0.271183	−	0.962528i	$-0.412585\pi$
$701$	14.3599	0.542366	0.271183	+	0.962528i	$0.412585\pi$
$702$	11.2600	0.424980
$703$	4.32708	0.163199
$704$	0.261549	0.00985751
$705$	−5.39208	−0.203077
$706$	16.4062	0.617454
$707$	−69.3107	−2.60670
$708$	15.6379	0.587708
$709$	−15.9456	−0.598851	−0.299426	−	0.954120i	$-0.596795\pi$
$709$	−15.9456	−0.598851	−0.299426	+	0.954120i	$0.596795\pi$
$710$	−2.99505	−0.112402
$711$	−21.8831	−0.820679
$712$	−17.9751	−0.673645
$713$	8.92123	0.334103
$714$	33.0881	1.23829
$715$	−0.212692	−0.00795422
$716$	17.6654	0.660187
$717$	22.6588	0.846209
$718$	−4.91396	−0.183387
$719$	10.9815	0.409543	0.204771	−	0.978810i	$-0.434355\pi$
$719$	10.9815	0.409543	0.204771	+	0.978810i	$0.434355\pi$
$720$	0.683727	0.0254810
$721$	4.03201	0.150160
$722$	−15.3283	−0.570460
$723$	−16.9820	−0.631568
$724$	13.1081	0.487160
$725$	24.8801	0.924025
$726$	11.9710	0.444287
$727$	14.0636	0.521590	0.260795	−	0.965394i	$-0.416015\pi$
$727$	14.0636	0.521590	0.260795	+	0.965394i	$0.416015\pi$
$728$	−8.22557	−0.304860
$729$	17.9105	0.663351
$730$	4.99008	0.184691
$731$	3.21947	0.119076
$732$	12.3429	0.456206
$733$	47.7484	1.76363	0.881814	−	0.471597i	$-0.156322\pi$
$733$	47.7484	1.76363	0.881814	+	0.471597i	$0.156322\pi$
$734$	27.5827	1.01810
$735$	3.22216	0.118851
$736$	1.00000	0.0368605
$737$	4.24432	0.156342
$738$	−16.2067	−0.596577
$739$	−15.6823	−0.576884	−0.288442	−	0.957497i	$-0.593137\pi$
$739$	−15.6823	−0.576884	−0.288442	+	0.957497i	$0.593137\pi$
$740$	0.857396	0.0315185
$741$	4.49427	0.165101
$742$	−3.89736	−0.143077
$743$	−6.99514	−0.256627	−0.128313	−	0.991734i	$-0.540956\pi$
$743$	−6.99514	−0.256627	−0.128313	+	0.991734i	$0.540956\pi$
$744$	−9.76953	−0.358168
$745$	3.59192	0.131598
$746$	−36.5714	−1.33897
$747$	−7.63636	−0.279400
$748$	2.05773	0.0752379
$749$	−33.4120	−1.22085
$750$	−4.09792	−0.149635
$751$	9.40697	0.343265	0.171633	−	0.985161i	$-0.445096\pi$
$751$	9.40697	0.343265	0.171633	+	0.985161i	$0.445096\pi$
$752$	−12.9684	−0.472909
$753$	2.15680	0.0785981
$754$	−10.9740	−0.399649
$755$	−3.79076	−0.137960
$756$	−20.1907	−0.734327
$757$	−41.2104	−1.49782	−0.748909	−	0.662673i	$-0.769422\pi$
$757$	−41.2104	−1.49782	−0.748909	+	0.662673i	$0.769422\pi$
$758$	7.75161	0.281551
$759$	−0.286419	−0.0103964
$760$	0.727538	0.0263906
$761$	−24.7278	−0.896382	−0.448191	−	0.893938i	$-0.647932\pi$
$761$	−24.7278	−0.896382	−0.448191	+	0.893938i	$0.647932\pi$
$762$	−1.60819	−0.0582586
$763$	47.6914	1.72655
$764$	15.2263	0.550870
$765$	5.37919	0.194485
$766$	−8.94818	−0.323311
$767$	−30.5848	−1.10435
$768$	−1.09509	−0.0395156
$769$	21.4644	0.774025	0.387012	−	0.922075i	$-0.373507\pi$
$769$	21.4644	0.774025	0.387012	+	0.922075i	$0.373507\pi$
$770$	0.381385	0.0137442
$771$	−7.05871	−0.254213
$772$	20.9529	0.754110
$773$	−47.4466	−1.70654	−0.853268	−	0.521473i	$-0.825383\pi$
$773$	−47.4466	−1.70654	−0.853268	+	0.521473i	$0.825383\pi$
$774$	−0.736906	−0.0264875
$775$	−43.3201	−1.55610
$776$	−17.6933	−0.635153
$777$	−9.49727	−0.340713
$778$	−1.85160	−0.0663830
$779$	−17.2452	−0.617872
$780$	0.890525	0.0318859
$781$	2.06318	0.0738263
$782$	7.86745	0.281339
$783$	−26.9370	−0.962650
$784$	7.74957	0.276770
$785$	3.59613	0.128351
$786$	1.09509	0.0390605
$787$	22.7349	0.810411	0.405206	−	0.914226i	$-0.367200\pi$
$787$	22.7349	0.810411	0.405206	+	0.914226i	$0.367200\pi$
$788$	−16.2950	−0.580486
$789$	5.53280	0.196973
$790$	−4.61389	−0.164155
$791$	70.7539	2.51572
$792$	−0.470994	−0.0167360
$793$	−24.1404	−0.857251
$794$	−28.7208	−1.01926
$795$	0.421940	0.0149647
$796$	−16.7787	−0.594704
$797$	−49.3831	−1.74924	−0.874619	−	0.484811i	$-0.838888\pi$
$797$	−49.3831	−1.74924	−0.874619	+	0.484811i	$0.838888\pi$
$798$	−8.05885	−0.285280
$799$	−102.028	−3.60950
$800$	−4.85584	−0.171680
$801$	32.3692	1.14371
$802$	22.3340	0.788642
$803$	−3.43748	−0.121306
$804$	−17.7707	−0.626723
$805$	1.45818	0.0513941
$806$	19.1074	0.673029
$807$	4.49011	0.158059
$808$	18.0472	0.634900
$809$	46.8279	1.64638	0.823191	−	0.567765i	$-0.192192\pi$
$809$	46.8279	1.64638	0.823191	+	0.567765i	$0.192192\pi$
$810$	0.134720	0.00473358
$811$	−35.7060	−1.25381	−0.626904	−	0.779097i	$-0.715678\pi$
$811$	−35.7060	−1.25381	−0.626904	+	0.779097i	$0.715678\pi$
$812$	19.6779	0.690558
$813$	10.7743	0.377871
$814$	−0.590628	−0.0207015
$815$	5.16009	0.180750
$816$	−8.61554	−0.301604
$817$	−0.784125	−0.0274330
$818$	12.0914	0.422766
$819$	14.8125	0.517590
$820$	−3.41707	−0.119329
$821$	19.3854	0.676554	0.338277	−	0.941047i	$-0.390156\pi$
$821$	19.3854	0.676554	0.338277	+	0.941047i	$0.390156\pi$
$822$	12.2849	0.428484
$823$	−34.5453	−1.20417	−0.602087	−	0.798431i	$-0.705664\pi$
$823$	−34.5453	−1.20417	−0.602087	+	0.798431i	$0.705664\pi$
$824$	−1.04986	−0.0365736
$825$	1.39081	0.0484216
$826$	54.8428	1.90822
$827$	34.0948	1.18559	0.592796	−	0.805353i	$-0.298024\pi$
$827$	34.0948	1.18559	0.592796	+	0.805353i	$0.298024\pi$
$828$	−1.80078	−0.0625816
$829$	2.66335	0.0925020	0.0462510	−	0.998930i	$-0.485273\pi$
$829$	2.66335	0.0925020	0.0462510	+	0.998930i	$0.485273\pi$
$830$	−1.61007	−0.0558865
$831$	−20.9821	−0.727860
$832$	2.14179	0.0742531
$833$	60.9694	2.11246
$834$	11.1368	0.385636
$835$	8.97324	0.310532
$836$	−0.501173	−0.0173334
$837$	46.9014	1.62115
$838$	−19.4906	−0.673291
$839$	19.3650	0.668553	0.334276	−	0.942475i	$-0.391508\pi$
$839$	19.3650	0.668553	0.334276	+	0.942475i	$0.391508\pi$
$840$	−1.59683	−0.0550960
$841$	−2.74714	−0.0947290
$842$	−17.9165	−0.617443
$843$	11.9762	0.412481
$844$	−23.1807	−0.797913
$845$	3.19418	0.109883
$846$	23.3533	0.802903
$847$	41.9830	1.44255
$848$	1.01480	0.0348484
$849$	−18.5981	−0.638283
$850$	−38.2031	−1.31036
$851$	−2.25819	−0.0774097
$852$	−8.63837	−0.295946
$853$	38.1566	1.30646	0.653229	−	0.757161i	$-0.273414\pi$
$853$	38.1566	1.30646	0.653229	+	0.757161i	$0.273414\pi$
$854$	43.2871	1.48125
$855$	−1.31014	−0.0448058
$856$	8.69987	0.297355
$857$	−43.2704	−1.47809	−0.739045	−	0.673656i	$-0.764723\pi$
$857$	−43.2704	−1.47809	−0.739045	+	0.673656i	$0.764723\pi$
$858$	−0.613449	−0.0209428
$859$	41.4898	1.41561	0.707807	−	0.706405i	$-0.249684\pi$
$859$	41.4898	1.41561	0.707807	+	0.706405i	$0.249684\pi$
$860$	−0.155372	−0.00529813
$861$	37.8505	1.28994
$862$	−29.2287	−0.995532
$863$	−41.4904	−1.41235	−0.706176	−	0.708037i	$-0.749581\pi$
$863$	−41.4904	−1.41235	−0.706176	+	0.708037i	$0.749581\pi$
$864$	5.25728	0.178856
$865$	2.62592	0.0892839
$866$	−9.82049	−0.333714
$867$	−49.1659	−1.66976
$868$	−34.2621	−1.16293
$869$	3.17834	0.107818
$870$	−2.13038	−0.0722268
$871$	34.7561	1.17767
$872$	−12.4180	−0.420526
$873$	31.8619	1.07836
$874$	−1.91617	−0.0648155
$875$	−14.3716	−0.485848
$876$	14.3925	0.486276
$877$	7.13006	0.240765	0.120382	−	0.992728i	$-0.461588\pi$
$877$	7.13006	0.240765	0.120382	+	0.992728i	$0.461588\pi$
$878$	−21.5346	−0.726757
$879$	8.74772	0.295053
$880$	−0.0993058	−0.00334760
$881$	23.4481	0.789987	0.394993	−	0.918684i	$-0.370747\pi$
$881$	23.4481	0.789987	0.394993	+	0.918684i	$0.370747\pi$
$882$	−13.9553	−0.469900
$883$	−49.4679	−1.66473	−0.832364	−	0.554229i	$-0.813013\pi$
$883$	−49.4679	−1.66473	−0.832364	+	0.554229i	$0.813013\pi$
$884$	16.8504	0.566740
$885$	−5.93744	−0.199585
$886$	3.10840	0.104429
$887$	9.61588	0.322870	0.161435	−	0.986883i	$-0.448388\pi$
$887$	9.61588	0.322870	0.161435	+	0.986883i	$0.448388\pi$
$888$	2.47291	0.0829856
$889$	−5.63999	−0.189159
$890$	6.82483	0.228769
$891$	−0.0928036	−0.00310904
$892$	12.7776	0.427826
$893$	24.8497	0.831563
$894$	10.3599	0.346486
$895$	−6.70725	−0.224199
$896$	−3.84052	−0.128303
$897$	−2.34544	−0.0783120
$898$	−20.5764	−0.686644
$899$	−45.7102	−1.52452
$900$	8.74432	0.291477
$901$	7.98390	0.265982
$902$	2.35389	0.0783760
$903$	1.72103	0.0572723
$904$	−18.4230	−0.612740
$905$	−4.97694	−0.165439
$906$	−10.9334	−0.363237
$907$	18.1234	0.601776	0.300888	−	0.953659i	$-0.402717\pi$
$907$	18.1234	0.601776	0.300888	+	0.953659i	$0.402717\pi$
$908$	−7.80777	−0.259110
$909$	−32.4992	−1.07793
$910$	3.12311	0.103530
$911$	31.5588	1.04559	0.522794	−	0.852459i	$-0.324890\pi$
$911$	31.5588	1.04559	0.522794	+	0.852459i	$0.324890\pi$
$912$	2.09838	0.0694842
$913$	1.10912	0.0367065
$914$	30.0123	0.992719
$915$	−4.68639	−0.154927
$916$	−12.8485	−0.424527
$917$	3.84052	0.126825
$918$	41.3614	1.36513
$919$	−15.8506	−0.522864	−0.261432	−	0.965222i	$-0.584195\pi$
$919$	−15.8506	−0.522864	−0.261432	+	0.965222i	$0.584195\pi$
$920$	−0.379683	−0.0125178
$921$	−14.3977	−0.474419
$922$	20.4534	0.673598
$923$	16.8950	0.556107
$924$	1.10000	0.0361873
$925$	10.9654	0.360540
$926$	−22.6020	−0.742746
$927$	1.89057	0.0620946
$928$	−5.12375	−0.168195
$929$	−25.7148	−0.843674	−0.421837	−	0.906672i	$-0.638615\pi$
$929$	−25.7148	−0.843674	−0.421837	+	0.906672i	$0.638615\pi$
$930$	3.70932	0.121633
$931$	−14.8495	−0.486673
$932$	−18.3254	−0.600267
$933$	13.6417	0.446611
$934$	26.9318	0.881235
$935$	−0.781283	−0.0255507
$936$	−3.85690	−0.126067
$937$	55.2573	1.80518	0.902588	−	0.430505i	$-0.141664\pi$
$937$	55.2573	1.80518	0.902588	+	0.430505i	$0.141664\pi$
$938$	−62.3225	−2.03490
$939$	−16.3849	−0.534701
$940$	4.92388	0.160599
$941$	12.7048	0.414166	0.207083	−	0.978323i	$-0.433603\pi$
$941$	12.7048	0.414166	0.207083	+	0.978323i	$0.433603\pi$
$942$	10.3720	0.337938
$943$	8.99980	0.293074
$944$	−14.2800	−0.464776
$945$	7.66605	0.249377
$946$	0.107030	0.00347983
$947$	9.15188	0.297396	0.148698	−	0.988883i	$-0.452492\pi$
$947$	9.15188	0.297396	0.148698	+	0.988883i	$0.452492\pi$
$948$	−13.3075	−0.432206
$949$	−28.1490	−0.913755
$950$	9.30463	0.301882
$951$	34.1174	1.10633
$952$	−30.2151	−0.979276
$953$	15.0559	0.487709	0.243855	−	0.969812i	$-0.421588\pi$
$953$	15.0559	0.487709	0.243855	+	0.969812i	$0.421588\pi$
$954$	−1.82744	−0.0591655
$955$	−5.78119	−0.187075
$956$	−20.6913	−0.669206
$957$	1.46754	0.0474389
$958$	9.79929	0.316601
$959$	43.0835	1.39124
$960$	0.415786	0.0134194
$961$	48.5884	1.56737
$962$	−4.83656	−0.155937
$963$	−15.6666	−0.504849
$964$	15.5075	0.499461
$965$	−7.95544	−0.256095
$966$	4.20570	0.135316
$967$	13.8544	0.445529	0.222764	−	0.974872i	$-0.428492\pi$
$967$	13.8544	0.445529	0.222764	+	0.974872i	$0.428492\pi$
$968$	−10.9316	−0.351355
$969$	16.5089	0.530341
$970$	6.71786	0.215697
$971$	13.9417	0.447409	0.223705	−	0.974657i	$-0.428185\pi$
$971$	13.9417	0.447409	0.223705	+	0.974657i	$0.428185\pi$
$972$	−15.3833	−0.493419
$973$	39.0572	1.25212
$974$	28.8284	0.923721
$975$	11.3891	0.364743
$976$	−11.2712	−0.360781
$977$	−41.1704	−1.31716	−0.658579	−	0.752512i	$-0.728842\pi$
$977$	−41.1704	−1.31716	−0.658579	+	0.752512i	$0.728842\pi$
$978$	14.8828	0.475900
$979$	−4.70137	−0.150256
$980$	−2.94238	−0.0939909
$981$	22.3621	0.713966
$982$	−13.9082	−0.443829
$983$	22.2356	0.709207	0.354604	−	0.935017i	$-0.384616\pi$
$983$	22.2356	0.709207	0.354604	+	0.935017i	$0.384616\pi$
$984$	−9.85556	−0.314184
$985$	6.18694	0.197132
$986$	−40.3109	−1.28376
$987$	−54.5412	−1.73607
$988$	−4.10403	−0.130567
$989$	0.409214	0.0130122
$990$	0.178828	0.00568354
$991$	−54.2048	−1.72187	−0.860936	−	0.508713i	$-0.830121\pi$
$991$	−54.2048	−1.72187	−0.860936	+	0.508713i	$0.830121\pi$
$992$	8.92123	0.283249
$993$	−16.8335	−0.534196
$994$	−30.2951	−0.960903
$995$	6.37058	0.201961
$996$	−4.64380	−0.147144
$997$	−41.9581	−1.32883	−0.664413	−	0.747365i	$-0.731318\pi$
$997$	−41.9581	−1.32883	−0.664413	+	0.747365i	$0.731318\pi$
$998$	12.2317	0.387188
$999$	−11.8719	−0.375611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.8	✓	20	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.09509 q^{3} +1.00000 q^{4} -0.379683 q^{5} -1.09509 q^{6} -3.84052 q^{7} +1.00000 q^{8} -1.80078 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.09509 q^{3} +1.00000 q^{4} -0.379683 q^{5} -1.09509 q^{6} -3.84052 q^{7} +1.00000 q^{8} -1.80078 q^{9} -0.379683 q^{10} +0.261549 q^{11} -1.09509 q^{12} +2.14179 q^{13} -3.84052 q^{14} +0.415786 q^{15} +1.00000 q^{16} +7.86745 q^{17} -1.80078 q^{18} -1.91617 q^{19} -0.379683 q^{20} +4.20570 q^{21} +0.261549 q^{22} +1.00000 q^{23} -1.09509 q^{24} -4.85584 q^{25} +2.14179 q^{26} +5.25728 q^{27} -3.84052 q^{28} -5.12375 q^{29} +0.415786 q^{30} +8.92123 q^{31} +1.00000 q^{32} -0.286419 q^{33} +7.86745 q^{34} +1.45818 q^{35} -1.80078 q^{36} -2.25819 q^{37} -1.91617 q^{38} -2.34544 q^{39} -0.379683 q^{40} +8.99980 q^{41} +4.20570 q^{42} +0.409214 q^{43} +0.261549 q^{44} +0.683727 q^{45} +1.00000 q^{46} -12.9684 q^{47} -1.09509 q^{48} +7.74957 q^{49} -4.85584 q^{50} -8.61554 q^{51} +2.14179 q^{52} +1.01480 q^{53} +5.25728 q^{54} -0.0993058 q^{55} -3.84052 q^{56} +2.09838 q^{57} -5.12375 q^{58} -14.2800 q^{59} +0.415786 q^{60} -11.2712 q^{61} +8.92123 q^{62} +6.91594 q^{63} +1.00000 q^{64} -0.813200 q^{65} -0.286419 q^{66} +16.2276 q^{67} +7.86745 q^{68} -1.09509 q^{69} +1.45818 q^{70} +7.88829 q^{71} -1.80078 q^{72} -13.1428 q^{73} -2.25819 q^{74} +5.31757 q^{75} -1.91617 q^{76} -1.00448 q^{77} -2.34544 q^{78} +12.1520 q^{79} -0.379683 q^{80} -0.354823 q^{81} +8.99980 q^{82} +4.24057 q^{83} +4.20570 q^{84} -2.98714 q^{85} +0.409214 q^{86} +5.61096 q^{87} +0.261549 q^{88} -17.9751 q^{89} +0.683727 q^{90} -8.22557 q^{91} +1.00000 q^{92} -9.76953 q^{93} -12.9684 q^{94} +0.727538 q^{95} -1.09509 q^{96} -17.6933 q^{97} +7.74957 q^{98} -0.470994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

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