LMFDB - Embedded newform 1106.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1106,2,Mod(1,1106)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1106, 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("1106.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1106 = 2 \cdot 7 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1106.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:	$8.83145446355$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 18x^{7} + 34x^{6} + 105x^{5} - 184x^{4} - 212x^{3} + 342x^{2} + 72x - 108 $ x^9 - 2x^8 - 18x^7 + 34x^6 + 105x^5 - 184x^4 - 212x^3 + 342x^2 + 72x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.87839$ of defining polynomial
Character	$\chi$	$=$	1106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.87839 q^{3} +1.00000 q^{4} +3.85604 q^{5} -1.87839 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.528336 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.87839 q^{3} +1.00000 q^{4} +3.85604 q^{5} -1.87839 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.528336 q^{9} +3.85604 q^{10} -1.86563 q^{11} -1.87839 q^{12} +5.20528 q^{13} +1.00000 q^{14} -7.24313 q^{15} +1.00000 q^{16} +6.37514 q^{17} +0.528336 q^{18} -7.67998 q^{19} +3.85604 q^{20} -1.87839 q^{21} -1.86563 q^{22} +2.91123 q^{23} -1.87839 q^{24} +9.86902 q^{25} +5.20528 q^{26} +4.64274 q^{27} +1.00000 q^{28} -4.62039 q^{29} -7.24313 q^{30} -8.49878 q^{31} +1.00000 q^{32} +3.50438 q^{33} +6.37514 q^{34} +3.85604 q^{35} +0.528336 q^{36} -0.886724 q^{37} -7.67998 q^{38} -9.77753 q^{39} +3.85604 q^{40} -1.01049 q^{41} -1.87839 q^{42} +12.3772 q^{43} -1.86563 q^{44} +2.03728 q^{45} +2.91123 q^{46} -8.86902 q^{47} -1.87839 q^{48} +1.00000 q^{49} +9.86902 q^{50} -11.9750 q^{51} +5.20528 q^{52} +3.13635 q^{53} +4.64274 q^{54} -7.19394 q^{55} +1.00000 q^{56} +14.4260 q^{57} -4.62039 q^{58} +11.0838 q^{59} -7.24313 q^{60} -2.67800 q^{61} -8.49878 q^{62} +0.528336 q^{63} +1.00000 q^{64} +20.0718 q^{65} +3.50438 q^{66} +9.04574 q^{67} +6.37514 q^{68} -5.46842 q^{69} +3.85604 q^{70} +14.5835 q^{71} +0.528336 q^{72} -7.10095 q^{73} -0.886724 q^{74} -18.5378 q^{75} -7.67998 q^{76} -1.86563 q^{77} -9.77753 q^{78} +1.00000 q^{79} +3.85604 q^{80} -10.3059 q^{81} -1.01049 q^{82} +1.00067 q^{83} -1.87839 q^{84} +24.5828 q^{85} +12.3772 q^{86} +8.67888 q^{87} -1.86563 q^{88} +2.73783 q^{89} +2.03728 q^{90} +5.20528 q^{91} +2.91123 q^{92} +15.9640 q^{93} -8.86902 q^{94} -29.6143 q^{95} -1.87839 q^{96} -0.922531 q^{97} +1.00000 q^{98} -0.985680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 2 q^{3} + 9 q^{4} + 4 q^{5} + 2 q^{6} + 9 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 2 * q^3 + 9 * q^4 + 4 * q^5 + 2 * q^6 + 9 * q^7 + 9 * q^8 + 13 * q^9	\( 9 q + 9 q^{2} + 2 q^{3} + 9 q^{4} + 4 q^{5} + 2 q^{6} + 9 q^{7} + 9 q^{8} + 13 q^{9} + 4 q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{13} + 9 q^{14} - 2 q^{15} + 9 q^{16} + 6 q^{17} + 13 q^{18} + 2 q^{19} + 4 q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{24} + 23 q^{25} + 2 q^{26} + 2 q^{27} + 9 q^{28} + 10 q^{29} - 2 q^{30} - 6 q^{31} + 9 q^{32} - 2 q^{33} + 6 q^{34} + 4 q^{35} + 13 q^{36} + 10 q^{37} + 2 q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} + 2 q^{42} + 22 q^{43} + 8 q^{44} - 10 q^{45} - 14 q^{47} + 2 q^{48} + 9 q^{49} + 23 q^{50} + 4 q^{51} + 2 q^{52} + 12 q^{53} + 2 q^{54} - 14 q^{55} + 9 q^{56} + 22 q^{57} + 10 q^{58} - 2 q^{59} - 2 q^{60} + 6 q^{61} - 6 q^{62} + 13 q^{63} + 9 q^{64} - 12 q^{65} - 2 q^{66} + 24 q^{67} + 6 q^{68} - 26 q^{69} + 4 q^{70} + 20 q^{71} + 13 q^{72} - 12 q^{73} + 10 q^{74} + 6 q^{75} + 2 q^{76} + 8 q^{77} - 6 q^{78} + 9 q^{79} + 4 q^{80} - 19 q^{81} + 10 q^{82} - 22 q^{83} + 2 q^{84} + 32 q^{85} + 22 q^{86} - 54 q^{87} + 8 q^{88} + 20 q^{89} - 10 q^{90} + 2 q^{91} - 18 q^{93} - 14 q^{94} - 40 q^{95} + 2 q^{96} - 6 q^{97} + 9 q^{98} + 24 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 2 * q^3 + 9 * q^4 + 4 * q^5 + 2 * q^6 + 9 * q^7 + 9 * q^8 + 13 * q^9 + 4 * q^10 + 8 * q^11 + 2 * q^12 + 2 * q^13 + 9 * q^14 - 2 * q^15 + 9 * q^16 + 6 * q^17 + 13 * q^18 + 2 * q^19 + 4 * q^20 + 2 * q^21 + 8 * q^22 + 2 * q^24 + 23 * q^25 + 2 * q^26 + 2 * q^27 + 9 * q^28 + 10 * q^29 - 2 * q^30 - 6 * q^31 + 9 * q^32 - 2 * q^33 + 6 * q^34 + 4 * q^35 + 13 * q^36 + 10 * q^37 + 2 * q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 + 2 * q^42 + 22 * q^43 + 8 * q^44 - 10 * q^45 - 14 * q^47 + 2 * q^48 + 9 * q^49 + 23 * q^50 + 4 * q^51 + 2 * q^52 + 12 * q^53 + 2 * q^54 - 14 * q^55 + 9 * q^56 + 22 * q^57 + 10 * q^58 - 2 * q^59 - 2 * q^60 + 6 * q^61 - 6 * q^62 + 13 * q^63 + 9 * q^64 - 12 * q^65 - 2 * q^66 + 24 * q^67 + 6 * q^68 - 26 * q^69 + 4 * q^70 + 20 * q^71 + 13 * q^72 - 12 * q^73 + 10 * q^74 + 6 * q^75 + 2 * q^76 + 8 * q^77 - 6 * q^78 + 9 * q^79 + 4 * q^80 - 19 * q^81 + 10 * q^82 - 22 * q^83 + 2 * q^84 + 32 * q^85 + 22 * q^86 - 54 * q^87 + 8 * q^88 + 20 * q^89 - 10 * q^90 + 2 * q^91 - 18 * q^93 - 14 * q^94 - 40 * q^95 + 2 * q^96 - 6 * q^97 + 9 * q^98 + 24 * 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
$3$	−1.87839	−1.08449	−0.542243	−	0.840221i	$-0.682425\pi$
$3$	−1.87839	−1.08449	−0.542243	+	0.840221i	$0.682425\pi$
$4$	1.00000	0.500000
$5$	3.85604	1.72447	0.862236	−	0.506507i	$-0.169063\pi$
$5$	3.85604	1.72447	0.862236	+	0.506507i	$0.169063\pi$
$6$	−1.87839	−0.766848
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0.528336	0.176112
$10$	3.85604	1.21939
$11$	−1.86563	−0.562509	−0.281254	−	0.959633i	$-0.590750\pi$
$11$	−1.86563	−0.562509	−0.281254	+	0.959633i	$0.590750\pi$
$12$	−1.87839	−0.542243
$13$	5.20528	1.44369	0.721843	−	0.692057i	$-0.243295\pi$
$13$	5.20528	1.44369	0.721843	+	0.692057i	$0.243295\pi$
$14$	1.00000	0.267261
$15$	−7.24313	−1.87017
$16$	1.00000	0.250000
$17$	6.37514	1.54620	0.773099	−	0.634285i	$-0.218705\pi$
$17$	6.37514	1.54620	0.773099	+	0.634285i	$0.218705\pi$
$18$	0.528336	0.124530
$19$	−7.67998	−1.76191	−0.880954	−	0.473202i	$-0.843098\pi$
$19$	−7.67998	−1.76191	−0.880954	+	0.473202i	$0.843098\pi$
$20$	3.85604	0.862236
$21$	−1.87839	−0.409898
$22$	−1.86563	−0.397754
$23$	2.91123	0.607034	0.303517	−	0.952826i	$-0.401839\pi$
$23$	2.91123	0.607034	0.303517	+	0.952826i	$0.401839\pi$
$24$	−1.87839	−0.383424
$25$	9.86902	1.97380
$26$	5.20528	1.02084
$27$	4.64274	0.893496
$28$	1.00000	0.188982
$29$	−4.62039	−0.857985	−0.428992	−	0.903308i	$-0.641131\pi$
$29$	−4.62039	−0.857985	−0.428992	+	0.903308i	$0.641131\pi$
$30$	−7.24313	−1.32241
$31$	−8.49878	−1.52643	−0.763213	−	0.646147i	$-0.776379\pi$
$31$	−8.49878	−1.52643	−0.763213	+	0.646147i	$0.776379\pi$
$32$	1.00000	0.176777
$33$	3.50438	0.610033
$34$	6.37514	1.09333
$35$	3.85604	0.651789
$36$	0.528336	0.0880560
$37$	−0.886724	−0.145777	−0.0728883	−	0.997340i	$-0.523222\pi$
$37$	−0.886724	−0.145777	−0.0728883	+	0.997340i	$0.523222\pi$
$38$	−7.67998	−1.24586
$39$	−9.77753	−1.56566
$40$	3.85604	0.609693
$41$	−1.01049	−0.157813	−0.0789063	−	0.996882i	$-0.525143\pi$
$41$	−1.01049	−0.157813	−0.0789063	+	0.996882i	$0.525143\pi$
$42$	−1.87839	−0.289841
$43$	12.3772	1.88750	0.943750	−	0.330660i	$-0.107271\pi$
$43$	12.3772	1.88750	0.943750	+	0.330660i	$0.107271\pi$
$44$	−1.86563	−0.281254
$45$	2.03728	0.303700
$46$	2.91123	0.429238
$47$	−8.86902	−1.29368	−0.646840	−	0.762626i	$-0.723910\pi$
$47$	−8.86902	−1.29368	−0.646840	+	0.762626i	$0.723910\pi$
$48$	−1.87839	−0.271122
$49$	1.00000	0.142857
$50$	9.86902	1.39569
$51$	−11.9750	−1.67683
$52$	5.20528	0.721843
$53$	3.13635	0.430810	0.215405	−	0.976525i	$-0.430893\pi$
$53$	3.13635	0.430810	0.215405	+	0.976525i	$0.430893\pi$
$54$	4.64274	0.631797
$55$	−7.19394	−0.970031
$56$	1.00000	0.133631
$57$	14.4260	1.91077
$58$	−4.62039	−0.606687
$59$	11.0838	1.44299	0.721493	−	0.692422i	$-0.243456\pi$
$59$	11.0838	1.44299	0.721493	+	0.692422i	$0.243456\pi$
$60$	−7.24313	−0.935084
$61$	−2.67800	−0.342883	−0.171441	−	0.985194i	$-0.554842\pi$
$61$	−2.67800	−0.342883	−0.171441	+	0.985194i	$0.554842\pi$
$62$	−8.49878	−1.07935
$63$	0.528336	0.0665641
$64$	1.00000	0.125000
$65$	20.0718	2.48960
$66$	3.50438	0.431359
$67$	9.04574	1.10511	0.552557	−	0.833475i	$-0.313652\pi$
$67$	9.04574	1.10511	0.552557	+	0.833475i	$0.313652\pi$
$68$	6.37514	0.773099
$69$	−5.46842	−0.658320
$70$	3.85604	0.460885
$71$	14.5835	1.73074	0.865372	−	0.501131i	$-0.167082\pi$
$71$	14.5835	1.73074	0.865372	+	0.501131i	$0.167082\pi$
$72$	0.528336	0.0622650
$73$	−7.10095	−0.831103	−0.415551	−	0.909570i	$-0.636411\pi$
$73$	−7.10095	−0.831103	−0.415551	+	0.909570i	$0.636411\pi$
$74$	−0.886724	−0.103080
$75$	−18.5378	−2.14056
$76$	−7.67998	−0.880954
$77$	−1.86563	−0.212608
$78$	−9.77753	−1.10709
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	3.85604	0.431118
$81$	−10.3059	−1.14510
$82$	−1.01049	−0.111590
$83$	1.00067	0.109838	0.0549190	−	0.998491i	$-0.482510\pi$
$83$	1.00067	0.109838	0.0549190	+	0.998491i	$0.482510\pi$
$84$	−1.87839	−0.204949
$85$	24.5828	2.66638
$86$	12.3772	1.33466
$87$	8.67888	0.930474
$88$	−1.86563	−0.198877
$89$	2.73783	0.290209	0.145105	−	0.989416i	$-0.453648\pi$
$89$	2.73783	0.290209	0.145105	+	0.989416i	$0.453648\pi$
$90$	2.03728	0.214749
$91$	5.20528	0.545662
$92$	2.91123	0.303517
$93$	15.9640	1.65539
$94$	−8.86902	−0.914770
$95$	−29.6143	−3.03836
$96$	−1.87839	−0.191712
$97$	−0.922531	−0.0936689	−0.0468344	−	0.998903i	$-0.514913\pi$
$97$	−0.922531	−0.0936689	−0.0468344	+	0.998903i	$0.514913\pi$
$98$	1.00000	0.101015
$99$	−0.985680	−0.0990646
$100$	9.86902	0.986902
$101$	−13.5024	−1.34354	−0.671769	−	0.740760i	$-0.734465\pi$
$101$	−13.5024	−1.34354	−0.671769	+	0.740760i	$0.734465\pi$
$102$	−11.9750	−1.18570
$103$	1.35979	0.133984	0.0669919	−	0.997754i	$-0.478660\pi$
$103$	1.35979	0.133984	0.0669919	+	0.997754i	$0.478660\pi$
$104$	5.20528	0.510420
$105$	−7.24313	−0.706857
$106$	3.13635	0.304629
$107$	−7.15720	−0.691913	−0.345956	−	0.938251i	$-0.612445\pi$
$107$	−7.15720	−0.691913	−0.345956	+	0.938251i	$0.612445\pi$
$108$	4.64274	0.446748
$109$	−15.0562	−1.44213	−0.721063	−	0.692869i	$-0.756346\pi$
$109$	−15.0562	−1.44213	−0.721063	+	0.692869i	$0.756346\pi$
$110$	−7.19394	−0.685915
$111$	1.66561	0.158093
$112$	1.00000	0.0944911
$113$	−1.09126	−0.102657	−0.0513285	−	0.998682i	$-0.516346\pi$
$113$	−1.09126	−0.102657	−0.0513285	+	0.998682i	$0.516346\pi$
$114$	14.4260	1.35112
$115$	11.2258	1.04681
$116$	−4.62039	−0.428992
$117$	2.75014	0.254250
$118$	11.0838	1.02034
$119$	6.37514	0.584408
$120$	−7.24313	−0.661204
$121$	−7.51942	−0.683584
$122$	−2.67800	−0.242455
$123$	1.89810	0.171146
$124$	−8.49878	−0.763213
$125$	18.7751	1.67930
$126$	0.528336	0.0470679
$127$	18.5199	1.64337	0.821686	−	0.569941i	$-0.193034\pi$
$127$	18.5199	1.64337	0.821686	+	0.569941i	$0.193034\pi$
$128$	1.00000	0.0883883
$129$	−23.2491	−2.04697
$130$	20.0718	1.76041
$131$	−9.71996	−0.849237	−0.424618	−	0.905372i	$-0.639592\pi$
$131$	−9.71996	−0.849237	−0.424618	+	0.905372i	$0.639592\pi$
$132$	3.50438	0.305017
$133$	−7.67998	−0.665938
$134$	9.04574	0.781433
$135$	17.9026	1.54081
$136$	6.37514	0.546664
$137$	−10.7950	−0.922277	−0.461139	−	0.887328i	$-0.652559\pi$
$137$	−10.7950	−0.922277	−0.461139	+	0.887328i	$0.652559\pi$
$138$	−5.46842	−0.465503
$139$	−8.32130	−0.705803	−0.352902	−	0.935660i	$-0.614805\pi$
$139$	−8.32130	−0.705803	−0.352902	+	0.935660i	$0.614805\pi$
$140$	3.85604	0.325895
$141$	16.6594	1.40298
$142$	14.5835	1.22382
$143$	−9.71113	−0.812086
$144$	0.528336	0.0440280
$145$	−17.8164	−1.47957
$146$	−7.10095	−0.587679
$147$	−1.87839	−0.154927
$148$	−0.886724	−0.0728883
$149$	14.0760	1.15315	0.576574	−	0.817045i	$-0.304389\pi$
$149$	14.0760	1.15315	0.576574	+	0.817045i	$0.304389\pi$
$150$	−18.5378	−1.51361
$151$	−8.68091	−0.706443	−0.353221	−	0.935540i	$-0.614914\pi$
$151$	−8.68091	−0.706443	−0.353221	+	0.935540i	$0.614914\pi$
$152$	−7.67998	−0.622928
$153$	3.36822	0.272304
$154$	−1.86563	−0.150337
$155$	−32.7716	−2.63228
$156$	−9.77753	−0.782829
$157$	−1.40610	−0.112219	−0.0561095	−	0.998425i	$-0.517870\pi$
$157$	−1.40610	−0.112219	−0.0561095	+	0.998425i	$0.517870\pi$
$158$	1.00000	0.0795557
$159$	−5.89127	−0.467208
$160$	3.85604	0.304846
$161$	2.91123	0.229437
$162$	−10.3059	−0.809706
$163$	−13.2078	−1.03452	−0.517258	−	0.855830i	$-0.673047\pi$
$163$	−13.2078	−1.03452	−0.517258	+	0.855830i	$0.673047\pi$
$164$	−1.01049	−0.0789063
$165$	13.5130	1.05199
$166$	1.00067	0.0776672
$167$	−0.149609	−0.0115771	−0.00578853	−	0.999983i	$-0.501843\pi$
$167$	−0.149609	−0.0115771	−0.00578853	+	0.999983i	$0.501843\pi$
$168$	−1.87839	−0.144921
$169$	14.0950	1.08423
$170$	24.5828	1.88541
$171$	−4.05761	−0.310293
$172$	12.3772	0.943750
$173$	−17.3176	−1.31663	−0.658316	−	0.752742i	$-0.728731\pi$
$173$	−17.3176	−1.31663	−0.658316	+	0.752742i	$0.728731\pi$
$174$	8.67888	0.657944
$175$	9.86902	0.746028
$176$	−1.86563	−0.140627
$177$	−20.8196	−1.56490
$178$	2.73783	0.205209
$179$	−2.69095	−0.201131	−0.100566	−	0.994930i	$-0.532065\pi$
$179$	−2.69095	−0.201131	−0.100566	+	0.994930i	$0.532065\pi$
$180$	2.03728	0.151850
$181$	−17.7071	−1.31616	−0.658079	−	0.752949i	$-0.728631\pi$
$181$	−17.7071	−1.31616	−0.658079	+	0.752949i	$0.728631\pi$
$182$	5.20528	0.385841
$183$	5.03032	0.371852
$184$	2.91123	0.214619
$185$	−3.41924	−0.251388
$186$	15.9640	1.17054
$187$	−11.8937	−0.869750
$188$	−8.86902	−0.646840
$189$	4.64274	0.337710
$190$	−29.6143	−2.14845
$191$	−9.83269	−0.711469	−0.355734	−	0.934587i	$-0.615769\pi$
$191$	−9.83269	−0.711469	−0.355734	+	0.934587i	$0.615769\pi$
$192$	−1.87839	−0.135561
$193$	−12.7852	−0.920301	−0.460151	−	0.887841i	$-0.652205\pi$
$193$	−12.7852	−0.920301	−0.460151	+	0.887841i	$0.652205\pi$
$194$	−0.922531	−0.0662339
$195$	−37.7025	−2.69993
$196$	1.00000	0.0714286
$197$	11.8827	0.846610	0.423305	−	0.905987i	$-0.360870\pi$
$197$	11.8827	0.846610	0.423305	+	0.905987i	$0.360870\pi$
$198$	−0.985680	−0.0700492
$199$	2.63169	0.186555	0.0932777	−	0.995640i	$-0.470266\pi$
$199$	2.63169	0.186555	0.0932777	+	0.995640i	$0.470266\pi$
$200$	9.86902	0.697845
$201$	−16.9914	−1.19848
$202$	−13.5024	−0.950025
$203$	−4.62039	−0.324288
$204$	−11.9750	−0.838416
$205$	−3.89650	−0.272144
$206$	1.35979	0.0947409
$207$	1.53811	0.106906
$208$	5.20528	0.360921
$209$	14.3280	0.991088
$210$	−7.24313	−0.499823
$211$	7.59486	0.522852	0.261426	−	0.965224i	$-0.415807\pi$
$211$	7.59486	0.522852	0.261426	+	0.965224i	$0.415807\pi$
$212$	3.13635	0.215405
$213$	−27.3935	−1.87697
$214$	−7.15720	−0.489256
$215$	47.7268	3.25494
$216$	4.64274	0.315898
$217$	−8.49878	−0.576935
$218$	−15.0562	−1.01974
$219$	13.3383	0.901320
$220$	−7.19394	−0.485015
$221$	33.1844	2.23222
$222$	1.66561	0.111789
$223$	−16.0101	−1.07211	−0.536057	−	0.844182i	$-0.680087\pi$
$223$	−16.0101	−1.07211	−0.536057	+	0.844182i	$0.680087\pi$
$224$	1.00000	0.0668153
$225$	5.21416	0.347611
$226$	−1.09126	−0.0725895
$227$	20.0079	1.32797	0.663986	−	0.747745i	$-0.268864\pi$
$227$	20.0079	1.32797	0.663986	+	0.747745i	$0.268864\pi$
$228$	14.4260	0.955383
$229$	3.54676	0.234377	0.117188	−	0.993110i	$-0.462612\pi$
$229$	3.54676	0.234377	0.117188	+	0.993110i	$0.462612\pi$
$230$	11.2258	0.740208
$231$	3.50438	0.230571
$232$	−4.62039	−0.303344
$233$	−19.8857	−1.30276	−0.651379	−	0.758753i	$-0.725809\pi$
$233$	−19.8857	−1.30276	−0.651379	+	0.758753i	$0.725809\pi$
$234$	2.75014	0.179782
$235$	−34.1993	−2.23091
$236$	11.0838	0.721493
$237$	−1.87839	−0.122014
$238$	6.37514	0.413239
$239$	−16.3759	−1.05927	−0.529633	−	0.848227i	$-0.677671\pi$
$239$	−16.3759	−1.05927	−0.529633	+	0.848227i	$0.677671\pi$
$240$	−7.24313	−0.467542
$241$	2.83443	0.182582	0.0912910	−	0.995824i	$-0.470901\pi$
$241$	2.83443	0.182582	0.0912910	+	0.995824i	$0.470901\pi$
$242$	−7.51942	−0.483367
$243$	5.43019	0.348347
$244$	−2.67800	−0.171441
$245$	3.85604	0.246353
$246$	1.89810	0.121018
$247$	−39.9764	−2.54364
$248$	−8.49878	−0.539673
$249$	−1.87965	−0.119118
$250$	18.7751	1.18744
$251$	−24.7377	−1.56143	−0.780714	−	0.624889i	$-0.785144\pi$
$251$	−24.7377	−1.56143	−0.780714	+	0.624889i	$0.785144\pi$
$252$	0.528336	0.0332820
$253$	−5.43128	−0.341462
$254$	18.5199	1.16204
$255$	−46.1760	−2.89165
$256$	1.00000	0.0625000
$257$	24.1854	1.50864	0.754321	−	0.656505i	$-0.227966\pi$
$257$	24.1854	1.50864	0.754321	+	0.656505i	$0.227966\pi$
$258$	−23.2491	−1.44743
$259$	−0.886724	−0.0550984
$260$	20.0718	1.24480
$261$	−2.44112	−0.151101
$262$	−9.71996	−0.600501
$263$	−25.1459	−1.55056	−0.775282	−	0.631616i	$-0.782392\pi$
$263$	−25.1459	−1.55056	−0.775282	+	0.631616i	$0.782392\pi$
$264$	3.50438	0.215679
$265$	12.0939	0.742920
$266$	−7.67998	−0.470890
$267$	−5.14270	−0.314728
$268$	9.04574	0.552557
$269$	−12.8703	−0.784719	−0.392359	−	0.919812i	$-0.628341\pi$
$269$	−12.8703	−0.784719	−0.392359	+	0.919812i	$0.628341\pi$
$270$	17.9026	1.08952
$271$	−31.2087	−1.89579	−0.947897	−	0.318576i	$-0.896795\pi$
$271$	−31.2087	−1.89579	−0.947897	+	0.318576i	$0.896795\pi$
$272$	6.37514	0.386550
$273$	−9.77753	−0.591763
$274$	−10.7950	−0.652149
$275$	−18.4119	−1.11028
$276$	−5.46842	−0.329160
$277$	24.8998	1.49609	0.748043	−	0.663650i	$-0.230994\pi$
$277$	24.8998	1.49609	0.748043	+	0.663650i	$0.230994\pi$
$278$	−8.32130	−0.499078
$279$	−4.49021	−0.268822
$280$	3.85604	0.230442
$281$	−13.5400	−0.807731	−0.403865	−	0.914818i	$-0.632334\pi$
$281$	−13.5400	−0.807731	−0.403865	+	0.914818i	$0.632334\pi$
$282$	16.6594	0.992056
$283$	−11.4031	−0.677843	−0.338921	−	0.940815i	$-0.610062\pi$
$283$	−11.4031	−0.677843	−0.338921	+	0.940815i	$0.610062\pi$
$284$	14.5835	0.865372
$285$	55.6271	3.29506
$286$	−9.71113	−0.574231
$287$	−1.01049	−0.0596476
$288$	0.528336	0.0311325
$289$	23.6424	1.39073
$290$	−17.8164	−1.04621
$291$	1.73287	0.101583
$292$	−7.10095	−0.415551
$293$	−8.50456	−0.496841	−0.248421	−	0.968652i	$-0.579912\pi$
$293$	−8.50456	−0.496841	−0.248421	+	0.968652i	$0.579912\pi$
$294$	−1.87839	−0.109550
$295$	42.7395	2.48839
$296$	−0.886724	−0.0515398
$297$	−8.66164	−0.502599
$298$	14.0760	0.815398
$299$	15.1538	0.876366
$300$	−18.5378	−1.07028
$301$	12.3772	0.713408
$302$	−8.68091	−0.499530
$303$	25.3627	1.45705
$304$	−7.67998	−0.440477
$305$	−10.3265	−0.591292
$306$	3.36822	0.192548
$307$	12.6508	0.722022	0.361011	−	0.932562i	$-0.382432\pi$
$307$	12.6508	0.722022	0.361011	+	0.932562i	$0.382432\pi$
$308$	−1.86563	−0.106304
$309$	−2.55421	−0.145304
$310$	−32.7716	−1.86130
$311$	18.5162	1.04996	0.524980	−	0.851115i	$-0.324073\pi$
$311$	18.5162	1.04996	0.524980	+	0.851115i	$0.324073\pi$
$312$	−9.77753	−0.553544
$313$	−3.62713	−0.205018	−0.102509	−	0.994732i	$-0.532687\pi$
$313$	−3.62713	−0.205018	−0.102509	+	0.994732i	$0.532687\pi$
$314$	−1.40610	−0.0793508
$315$	2.03728	0.114788
$316$	1.00000	0.0562544
$317$	24.2598	1.36257	0.681283	−	0.732020i	$-0.261422\pi$
$317$	24.2598	1.36257	0.681283	+	0.732020i	$0.261422\pi$
$318$	−5.89127	−0.330366
$319$	8.61994	0.482624
$320$	3.85604	0.215559
$321$	13.4440	0.750370
$322$	2.91123	0.162237
$323$	−48.9609	−2.72426
$324$	−10.3059	−0.572548
$325$	51.3710	2.84955
$326$	−13.2078	−0.731513
$327$	28.2814	1.56397
$328$	−1.01049	−0.0557952
$329$	−8.86902	−0.488965
$330$	13.5130	0.743866
$331$	5.21689	0.286746	0.143373	−	0.989669i	$-0.454205\pi$
$331$	5.21689	0.286746	0.143373	+	0.989669i	$0.454205\pi$
$332$	1.00067	0.0549190
$333$	−0.468489	−0.0256730
$334$	−0.149609	−0.00818622
$335$	34.8807	1.90574
$336$	−1.87839	−0.102474
$337$	−0.803326	−0.0437600	−0.0218800	−	0.999761i	$-0.506965\pi$
$337$	−0.803326	−0.0437600	−0.0218800	+	0.999761i	$0.506965\pi$
$338$	14.0950	0.766665
$339$	2.04981	0.111330
$340$	24.5828	1.33319
$341$	15.8556	0.858628
$342$	−4.05761	−0.219410
$343$	1.00000	0.0539949
$344$	12.3772	0.667332
$345$	−21.0864	−1.13525
$346$	−17.3176	−0.930999
$347$	−0.411194	−0.0220740	−0.0110370	−	0.999939i	$-0.503513\pi$
$347$	−0.411194	−0.0220740	−0.0110370	+	0.999939i	$0.503513\pi$
$348$	8.67888	0.465237
$349$	27.7621	1.48607	0.743035	−	0.669253i	$-0.233386\pi$
$349$	27.7621	1.48607	0.743035	+	0.669253i	$0.233386\pi$
$350$	9.86902	0.527521
$351$	24.1668	1.28993
$352$	−1.86563	−0.0994384
$353$	26.9944	1.43677	0.718384	−	0.695647i	$-0.244882\pi$
$353$	26.9944	1.43677	0.718384	+	0.695647i	$0.244882\pi$
$354$	−20.8196	−1.10655
$355$	56.2345	2.98462
$356$	2.73783	0.145105
$357$	−11.9750	−0.633783
$358$	−2.69095	−0.142221
$359$	6.30961	0.333009	0.166504	−	0.986041i	$-0.446752\pi$
$359$	6.30961	0.333009	0.166504	+	0.986041i	$0.446752\pi$
$360$	2.03728	0.107374
$361$	39.9820	2.10432
$362$	−17.7071	−0.930664
$363$	14.1244	0.741338
$364$	5.20528	0.272831
$365$	−27.3815	−1.43321
$366$	5.03032	0.262939
$367$	−1.93352	−0.100929	−0.0504645	−	0.998726i	$-0.516070\pi$
$367$	−1.93352	−0.100929	−0.0504645	+	0.998726i	$0.516070\pi$
$368$	2.91123	0.151758
$369$	−0.533881	−0.0277927
$370$	−3.41924	−0.177758
$371$	3.13635	0.162831
$372$	15.9640	0.827694
$373$	10.3719	0.537035	0.268517	−	0.963275i	$-0.413466\pi$
$373$	10.3719	0.537035	0.268517	+	0.963275i	$0.413466\pi$
$374$	−11.8937	−0.615006
$375$	−35.2669	−1.82118
$376$	−8.86902	−0.457385
$377$	−24.0504	−1.23866
$378$	4.64274	0.238797
$379$	13.5247	0.694715	0.347358	−	0.937733i	$-0.387079\pi$
$379$	13.5247	0.694715	0.347358	+	0.937733i	$0.387079\pi$
$380$	−29.6143	−1.51918
$381$	−34.7874	−1.78221
$382$	−9.83269	−0.503084
$383$	0.718186	0.0366976	0.0183488	−	0.999832i	$-0.494159\pi$
$383$	0.718186	0.0366976	0.0183488	+	0.999832i	$0.494159\pi$
$384$	−1.87839	−0.0958560
$385$	−7.19394	−0.366637
$386$	−12.7852	−0.650751
$387$	6.53930	0.332411
$388$	−0.922531	−0.0468344
$389$	−6.15026	−0.311830	−0.155915	−	0.987770i	$-0.549833\pi$
$389$	−6.15026	−0.311830	−0.155915	+	0.987770i	$0.549833\pi$
$390$	−37.7025	−1.90914
$391$	18.5595	0.938594
$392$	1.00000	0.0505076
$393$	18.2578	0.920986
$394$	11.8827	0.598644
$395$	3.85604	0.194018
$396$	−0.985680	−0.0495323
$397$	−28.0784	−1.40922	−0.704608	−	0.709597i	$-0.748877\pi$
$397$	−28.0784	−1.40922	−0.704608	+	0.709597i	$0.748877\pi$
$398$	2.63169	0.131915
$399$	14.4260	0.722202
$400$	9.86902	0.493451
$401$	−15.5964	−0.778846	−0.389423	−	0.921059i	$-0.627326\pi$
$401$	−15.5964	−0.778846	−0.389423	+	0.921059i	$0.627326\pi$
$402$	−16.9914	−0.847454
$403$	−44.2385	−2.20368
$404$	−13.5024	−0.671769
$405$	−39.7398	−1.97469
$406$	−4.62039	−0.229306
$407$	1.65430	0.0820006
$408$	−11.9750	−0.592850
$409$	34.3848	1.70022	0.850109	−	0.526607i	$-0.176536\pi$
$409$	34.3848	1.70022	0.850109	+	0.526607i	$0.176536\pi$
$410$	−3.89650	−0.192435
$411$	20.2771	1.00020
$412$	1.35979	0.0669919
$413$	11.0838	0.545397
$414$	1.53811	0.0755939
$415$	3.85863	0.189413
$416$	5.20528	0.255210
$417$	15.6306	0.765434
$418$	14.3280	0.700805
$419$	−17.0949	−0.835139	−0.417569	−	0.908645i	$-0.637118\pi$
$419$	−17.0949	−0.835139	−0.417569	+	0.908645i	$0.637118\pi$
$420$	−7.24313	−0.353428
$421$	6.56918	0.320162	0.160081	−	0.987104i	$-0.448824\pi$
$421$	6.56918	0.320162	0.160081	+	0.987104i	$0.448824\pi$
$422$	7.59486	0.369712
$423$	−4.68582	−0.227833
$424$	3.13635	0.152314
$425$	62.9164	3.05189
$426$	−27.3935	−1.32722
$427$	−2.67800	−0.129597
$428$	−7.15720	−0.345956
$429$	18.2413	0.880697
$430$	47.7268	2.30159
$431$	16.0542	0.773305	0.386653	−	0.922225i	$-0.373631\pi$
$431$	16.0542	0.773305	0.386653	+	0.922225i	$0.373631\pi$
$432$	4.64274	0.223374
$433$	−20.1815	−0.969861	−0.484930	−	0.874553i	$-0.661155\pi$
$433$	−20.1815	−0.969861	−0.484930	+	0.874553i	$0.661155\pi$
$434$	−8.49878	−0.407954
$435$	33.4661	1.60458
$436$	−15.0562	−0.721063
$437$	−22.3582	−1.06954
$438$	13.3383	0.637330
$439$	26.6643	1.27262	0.636309	−	0.771434i	$-0.280460\pi$
$439$	26.6643	1.27262	0.636309	+	0.771434i	$0.280460\pi$
$440$	−7.19394	−0.342958
$441$	0.528336	0.0251589
$442$	33.1844	1.57842
$443$	40.0990	1.90516	0.952581	−	0.304285i	$-0.0984174\pi$
$443$	40.0990	1.90516	0.952581	+	0.304285i	$0.0984174\pi$
$444$	1.66561	0.0790464
$445$	10.5572	0.500458
$446$	−16.0101	−0.758099
$447$	−26.4401	−1.25057
$448$	1.00000	0.0472456
$449$	−25.5669	−1.20658	−0.603288	−	0.797524i	$-0.706143\pi$
$449$	−25.5669	−1.20658	−0.603288	+	0.797524i	$0.706143\pi$
$450$	5.21416	0.245798
$451$	1.88521	0.0887710
$452$	−1.09126	−0.0513285
$453$	16.3061	0.766128
$454$	20.0079	0.939017
$455$	20.0718	0.940979
$456$	14.4260	0.675558
$457$	21.5768	1.00932	0.504660	−	0.863318i	$-0.331618\pi$
$457$	21.5768	1.00932	0.504660	+	0.863318i	$0.331618\pi$
$458$	3.54676	0.165729
$459$	29.5981	1.38152
$460$	11.2258	0.523406
$461$	−17.3805	−0.809492	−0.404746	−	0.914429i	$-0.632640\pi$
$461$	−17.3805	−0.809492	−0.404746	+	0.914429i	$0.632640\pi$
$462$	3.50438	0.163038
$463$	−29.4456	−1.36845	−0.684227	−	0.729269i	$-0.739860\pi$
$463$	−29.4456	−1.36845	−0.684227	+	0.729269i	$0.739860\pi$
$464$	−4.62039	−0.214496
$465$	61.5577	2.85467
$466$	−19.8857	−0.921189
$467$	−37.9100	−1.75427	−0.877133	−	0.480247i	$-0.840547\pi$
$467$	−37.9100	−1.75427	−0.877133	+	0.480247i	$0.840547\pi$
$468$	2.75014	0.127125
$469$	9.04574	0.417694
$470$	−34.1993	−1.57749
$471$	2.64120	0.121700
$472$	11.0838	0.510172
$473$	−23.0912	−1.06174
$474$	−1.87839	−0.0862772
$475$	−75.7938	−3.47766
$476$	6.37514	0.292204
$477$	1.65705	0.0758709
$478$	−16.3759	−0.749015
$479$	−23.1491	−1.05771	−0.528854	−	0.848713i	$-0.677378\pi$
$479$	−23.1491	−1.05771	−0.528854	+	0.848713i	$0.677378\pi$
$480$	−7.24313	−0.330602
$481$	−4.61565	−0.210456
$482$	2.83443	0.129105
$483$	−5.46842	−0.248822
$484$	−7.51942	−0.341792
$485$	−3.55731	−0.161529
$486$	5.43019	0.246318
$487$	24.6596	1.11744	0.558718	−	0.829358i	$-0.311294\pi$
$487$	24.6596	1.11744	0.558718	+	0.829358i	$0.311294\pi$
$488$	−2.67800	−0.121227
$489$	24.8094	1.12192
$490$	3.85604	0.174198
$491$	4.33822	0.195781	0.0978906	−	0.995197i	$-0.468790\pi$
$491$	4.33822	0.195781	0.0978906	+	0.995197i	$0.468790\pi$
$492$	1.89810	0.0855729
$493$	−29.4556	−1.32662
$494$	−39.9764	−1.79863
$495$	−3.80082	−0.170834
$496$	−8.49878	−0.381606
$497$	14.5835	0.654159
$498$	−1.87965	−0.0842291
$499$	24.9946	1.11891	0.559456	−	0.828860i	$-0.311010\pi$
$499$	24.9946	1.11891	0.559456	+	0.828860i	$0.311010\pi$
$500$	18.7751	0.839649
$501$	0.281023	0.0125552
$502$	−24.7377	−1.10410
$503$	−24.0839	−1.07385	−0.536924	−	0.843630i	$-0.680414\pi$
$503$	−24.0839	−1.07385	−0.536924	+	0.843630i	$0.680414\pi$
$504$	0.528336	0.0235340
$505$	−52.0657	−2.31689
$506$	−5.43128	−0.241450
$507$	−26.4758	−1.17583
$508$	18.5199	0.821686
$509$	−34.5526	−1.53152	−0.765758	−	0.643128i	$-0.777636\pi$
$509$	−34.5526	−1.53152	−0.765758	+	0.643128i	$0.777636\pi$
$510$	−46.1760	−2.04471
$511$	−7.10095	−0.314127
$512$	1.00000	0.0441942
$513$	−35.6561	−1.57426
$514$	24.1854	1.06677
$515$	5.24339	0.231051
$516$	−23.2491	−1.02348
$517$	16.5463	0.727706
$518$	−0.886724	−0.0389604
$519$	32.5291	1.42787
$520$	20.0718	0.880205
$521$	−21.9878	−0.963302	−0.481651	−	0.876363i	$-0.659963\pi$
$521$	−21.9878	−0.963302	−0.481651	+	0.876363i	$0.659963\pi$
$522$	−2.44112	−0.106845
$523$	33.9780	1.48575	0.742877	−	0.669428i	$-0.233461\pi$
$523$	33.9780	1.48575	0.742877	+	0.669428i	$0.233461\pi$
$524$	−9.71996	−0.424618
$525$	−18.5378	−0.809058
$526$	−25.1459	−1.09641
$527$	−54.1809	−2.36016
$528$	3.50438	0.152508
$529$	−14.5247	−0.631510
$530$	12.0939	0.525324
$531$	5.85596	0.254127
$532$	−7.67998	−0.332969
$533$	−5.25991	−0.227832
$534$	−5.14270	−0.222546
$535$	−27.5984	−1.19318
$536$	9.04574	0.390717
$537$	5.05465	0.218124
$538$	−12.8703	−0.554880
$539$	−1.86563	−0.0803584
$540$	17.9026	0.770404
$541$	−21.8636	−0.939989	−0.469995	−	0.882669i	$-0.655744\pi$
$541$	−21.8636	−0.939989	−0.469995	+	0.882669i	$0.655744\pi$
$542$	−31.2087	−1.34053
$543$	33.2608	1.42736
$544$	6.37514	0.273332
$545$	−58.0574	−2.48691
$546$	−9.77753	−0.418440
$547$	38.3837	1.64117	0.820584	−	0.571526i	$-0.193648\pi$
$547$	38.3837	1.64117	0.820584	+	0.571526i	$0.193648\pi$
$548$	−10.7950	−0.461139
$549$	−1.41488	−0.0603858
$550$	−18.4119	−0.785088
$551$	35.4845	1.51169
$552$	−5.46842	−0.232751
$553$	1.00000	0.0425243
$554$	24.8998	1.05789
$555$	6.42266	0.272627
$556$	−8.32130	−0.352902
$557$	−14.1692	−0.600369	−0.300184	−	0.953881i	$-0.597048\pi$
$557$	−14.1692	−0.600369	−0.300184	+	0.953881i	$0.597048\pi$
$558$	−4.49021	−0.190086
$559$	64.4266	2.72496
$560$	3.85604	0.162947
$561$	22.3409	0.943233
$562$	−13.5400	−0.571152
$563$	3.58134	0.150935	0.0754677	−	0.997148i	$-0.475955\pi$
$563$	3.58134	0.150935	0.0754677	+	0.997148i	$0.475955\pi$
$564$	16.6594	0.701489
$565$	−4.20794	−0.177029
$566$	−11.4031	−0.479307
$567$	−10.3059	−0.432806
$568$	14.5835	0.611910
$569$	20.2937	0.850758	0.425379	−	0.905015i	$-0.360141\pi$
$569$	20.2937	0.850758	0.425379	+	0.905015i	$0.360141\pi$
$570$	55.6271	2.32996
$571$	−38.9283	−1.62910	−0.814550	−	0.580093i	$-0.803016\pi$
$571$	−38.9283	−1.62910	−0.814550	+	0.580093i	$0.803016\pi$
$572$	−9.71113	−0.406043
$573$	18.4696	0.771578
$574$	−1.01049	−0.0421772
$575$	28.7310	1.19817
$576$	0.528336	0.0220140
$577$	−1.92754	−0.0802444	−0.0401222	−	0.999195i	$-0.512775\pi$
$577$	−1.92754	−0.0802444	−0.0401222	+	0.999195i	$0.512775\pi$
$578$	23.6424	0.983394
$579$	24.0156	0.998055
$580$	−17.8164	−0.739786
$581$	1.00067	0.0415149
$582$	1.73287	0.0718298
$583$	−5.85126	−0.242335
$584$	−7.10095	−0.293839
$585$	10.6046	0.438448
$586$	−8.50456	−0.351320
$587$	−18.8684	−0.778782	−0.389391	−	0.921072i	$-0.627315\pi$
$587$	−18.8684	−0.778782	−0.389391	+	0.921072i	$0.627315\pi$
$588$	−1.87839	−0.0774634
$589$	65.2704	2.68942
$590$	42.7395	1.75956
$591$	−22.3204	−0.918138
$592$	−0.886724	−0.0364441
$593$	−36.2327	−1.48790	−0.743950	−	0.668235i	$-0.767050\pi$
$593$	−36.2327	−1.48790	−0.743950	+	0.668235i	$0.767050\pi$
$594$	−8.66164	−0.355391
$595$	24.5828	1.00780
$596$	14.0760	0.576574
$597$	−4.94333	−0.202317
$598$	15.1538	0.619684
$599$	−15.4831	−0.632622	−0.316311	−	0.948656i	$-0.602444\pi$
$599$	−15.4831	−0.632622	−0.316311	+	0.948656i	$0.602444\pi$
$600$	−18.5378	−0.756804
$601$	−8.66101	−0.353290	−0.176645	−	0.984275i	$-0.556524\pi$
$601$	−8.66101	−0.353290	−0.176645	+	0.984275i	$0.556524\pi$
$602$	12.3772	0.504456
$603$	4.77919	0.194624
$604$	−8.68091	−0.353221
$605$	−28.9952	−1.17882
$606$	25.3627	1.03029
$607$	12.5387	0.508929	0.254465	−	0.967082i	$-0.418101\pi$
$607$	12.5387	0.508929	0.254465	+	0.967082i	$0.418101\pi$
$608$	−7.67998	−0.311464
$609$	8.67888	0.351686
$610$	−10.3265	−0.418106
$611$	−46.1658	−1.86767
$612$	3.36822	0.136152
$613$	29.2290	1.18055	0.590275	−	0.807203i	$-0.299019\pi$
$613$	29.2290	1.18055	0.590275	+	0.807203i	$0.299019\pi$
$614$	12.6508	0.510546
$615$	7.31914	0.295136
$616$	−1.86563	−0.0751684
$617$	7.72468	0.310984	0.155492	−	0.987837i	$-0.450304\pi$
$617$	7.72468	0.310984	0.155492	+	0.987837i	$0.450304\pi$
$618$	−2.55421	−0.102745
$619$	29.9723	1.20469	0.602345	−	0.798236i	$-0.294233\pi$
$619$	29.9723	1.20469	0.602345	+	0.798236i	$0.294233\pi$
$620$	−32.7716	−1.31614
$621$	13.5161	0.542382
$622$	18.5162	0.742433
$623$	2.73783	0.109689
$624$	−9.77753	−0.391415
$625$	23.0525	0.922099
$626$	−3.62713	−0.144969
$627$	−26.9135	−1.07482
$628$	−1.40610	−0.0561095
$629$	−5.65299	−0.225400
$630$	2.03728	0.0811673
$631$	0.571939	0.0227685	0.0113843	−	0.999935i	$-0.496376\pi$
$631$	0.571939	0.0227685	0.0113843	+	0.999935i	$0.496376\pi$
$632$	1.00000	0.0397779
$633$	−14.2661	−0.567026
$634$	24.2598	0.963480
$635$	71.4132	2.83395
$636$	−5.89127	−0.233604
$637$	5.20528	0.206241
$638$	8.61994	0.341267
$639$	7.70499	0.304805
$640$	3.85604	0.152423
$641$	−31.7563	−1.25430	−0.627149	−	0.778900i	$-0.715778\pi$
$641$	−31.7563	−1.25430	−0.627149	+	0.778900i	$0.715778\pi$
$642$	13.4440	0.530592
$643$	30.3943	1.19863	0.599317	−	0.800512i	$-0.295439\pi$
$643$	30.3943	1.19863	0.599317	+	0.800512i	$0.295439\pi$
$644$	2.91123	0.114719
$645$	−89.6494	−3.52994
$646$	−48.9609	−1.92634
$647$	3.99972	0.157245	0.0786226	−	0.996904i	$-0.474948\pi$
$647$	3.99972	0.157245	0.0786226	+	0.996904i	$0.474948\pi$
$648$	−10.3059	−0.404853
$649$	−20.6782	−0.811692
$650$	51.3710	2.01494
$651$	15.9640	0.625678
$652$	−13.2078	−0.517258
$653$	50.2763	1.96746	0.983731	−	0.179646i	$-0.0574954\pi$
$653$	50.2763	1.96746	0.983731	+	0.179646i	$0.0574954\pi$
$654$	28.2814	1.10589
$655$	−37.4805	−1.46449
$656$	−1.01049	−0.0394532
$657$	−3.75169	−0.146367
$658$	−8.86902	−0.345750
$659$	27.7055	1.07925	0.539627	−	0.841904i	$-0.318565\pi$
$659$	27.7055	1.07925	0.539627	+	0.841904i	$0.318565\pi$
$660$	13.5130	0.525993
$661$	8.61648	0.335142	0.167571	−	0.985860i	$-0.446408\pi$
$661$	8.61648	0.335142	0.167571	+	0.985860i	$0.446408\pi$
$662$	5.21689	0.202760
$663$	−62.3331	−2.42082
$664$	1.00067	0.0388336
$665$	−29.6143	−1.14839
$666$	−0.468489	−0.0181536
$667$	−13.4510	−0.520826
$668$	−0.149609	−0.00578853
$669$	30.0731	1.16269
$670$	34.8807	1.34756
$671$	4.99616	0.192875
$672$	−1.87839	−0.0724603
$673$	27.0928	1.04435	0.522176	−	0.852838i	$-0.325120\pi$
$673$	27.0928	1.04435	0.522176	+	0.852838i	$0.325120\pi$
$674$	−0.803326	−0.0309430
$675$	45.8193	1.76359
$676$	14.0950	0.542114
$677$	−5.85457	−0.225009	−0.112505	−	0.993651i	$-0.535887\pi$
$677$	−5.85457	−0.225009	−0.112505	+	0.993651i	$0.535887\pi$
$678$	2.04981	0.0787223
$679$	−0.922531	−0.0354035
$680$	24.5828	0.942706
$681$	−37.5826	−1.44017
$682$	15.8556	0.607141
$683$	15.7397	0.602261	0.301131	−	0.953583i	$-0.402636\pi$
$683$	15.7397	0.602261	0.301131	+	0.953583i	$0.402636\pi$
$684$	−4.05761	−0.155147
$685$	−41.6258	−1.59044
$686$	1.00000	0.0381802
$687$	−6.66219	−0.254178
$688$	12.3772	0.471875
$689$	16.3256	0.621955
$690$	−21.0864	−0.802746
$691$	−17.2600	−0.656602	−0.328301	−	0.944573i	$-0.606476\pi$
$691$	−17.2600	−0.656602	−0.328301	+	0.944573i	$0.606476\pi$
$692$	−17.3176	−0.658316
$693$	−0.985680	−0.0374429
$694$	−0.411194	−0.0156087
$695$	−32.0872	−1.21714
$696$	8.67888	0.328972
$697$	−6.44204	−0.244010
$698$	27.7621	1.05081
$699$	37.3531	1.41282
$700$	9.86902	0.373014
$701$	−18.4974	−0.698637	−0.349318	−	0.937004i	$-0.613587\pi$
$701$	−18.4974	−0.698637	−0.349318	+	0.937004i	$0.613587\pi$
$702$	24.1668	0.912116
$703$	6.81002	0.256845
$704$	−1.86563	−0.0703136
$705$	64.2395	2.41940
$706$	26.9944	1.01595
$707$	−13.5024	−0.507810
$708$	−20.8196	−0.782450
$709$	12.0588	0.452879	0.226440	−	0.974025i	$-0.427291\pi$
$709$	12.0588	0.452879	0.226440	+	0.974025i	$0.427291\pi$
$710$	56.2345	2.11044
$711$	0.528336	0.0198142
$712$	2.73783	0.102604
$713$	−24.7419	−0.926591
$714$	−11.9750	−0.448152
$715$	−37.4465	−1.40042
$716$	−2.69095	−0.100566
$717$	30.7602	1.14876
$718$	6.30961	0.235473
$719$	−37.2308	−1.38848	−0.694238	−	0.719745i	$-0.744259\pi$
$719$	−37.2308	−1.38848	−0.694238	+	0.719745i	$0.744259\pi$
$720$	2.03728	0.0759251
$721$	1.35979	0.0506411
$722$	39.9820	1.48798
$723$	−5.32416	−0.198008
$724$	−17.7071	−0.658079
$725$	−45.5987	−1.69349
$726$	14.1244	0.524205
$727$	40.5928	1.50551	0.752753	−	0.658303i	$-0.228726\pi$
$727$	40.5928	1.50551	0.752753	+	0.658303i	$0.228726\pi$
$728$	5.20528	0.192921
$729$	20.7176	0.767319
$730$	−27.3815	−1.01344
$731$	78.9061	2.91845
$732$	5.03032	0.185926
$733$	36.9757	1.36573	0.682865	−	0.730545i	$-0.260734\pi$
$733$	36.9757	1.36573	0.682865	+	0.730545i	$0.260734\pi$
$734$	−1.93352	−0.0713676
$735$	−7.24313	−0.267167
$736$	2.91123	0.107309
$737$	−16.8760	−0.621636
$738$	−0.533881	−0.0196524
$739$	−8.31934	−0.306032	−0.153016	−	0.988224i	$-0.548899\pi$
$739$	−8.31934	−0.306032	−0.153016	+	0.988224i	$0.548899\pi$
$740$	−3.41924	−0.125694
$741$	75.0912	2.75855
$742$	3.13635	0.115139
$743$	−10.9011	−0.399924	−0.199962	−	0.979804i	$-0.564082\pi$
$743$	−10.9011	−0.399924	−0.199962	+	0.979804i	$0.564082\pi$
$744$	15.9640	0.585268
$745$	54.2774	1.98857
$746$	10.3719	0.379741
$747$	0.528691	0.0193438
$748$	−11.8937	−0.434875
$749$	−7.15720	−0.261518
$750$	−35.2669	−1.28777
$751$	37.2585	1.35958	0.679791	−	0.733406i	$-0.262070\pi$
$751$	37.2585	1.35958	0.679791	+	0.733406i	$0.262070\pi$
$752$	−8.86902	−0.323420
$753$	46.4669	1.69335
$754$	−24.0504	−0.875865
$755$	−33.4739	−1.21824
$756$	4.64274	0.168855
$757$	28.6413	1.04099	0.520493	−	0.853866i	$-0.325748\pi$
$757$	28.6413	1.04099	0.520493	+	0.853866i	$0.325748\pi$
$758$	13.5247	0.491238
$759$	10.2020	0.370311
$760$	−29.6143	−1.07422
$761$	−37.3313	−1.35326	−0.676629	−	0.736324i	$-0.736560\pi$
$761$	−37.3313	−1.35326	−0.676629	+	0.736324i	$0.736560\pi$
$762$	−34.7874	−1.26022
$763$	−15.0562	−0.545072
$764$	−9.83269	−0.355734
$765$	12.9880	0.469581
$766$	0.718186	0.0259491
$767$	57.6942	2.08322
$768$	−1.87839	−0.0677804
$769$	−3.51120	−0.126617	−0.0633086	−	0.997994i	$-0.520165\pi$
$769$	−3.51120	−0.126617	−0.0633086	+	0.997994i	$0.520165\pi$
$770$	−7.19394	−0.259252
$771$	−45.4295	−1.63610
$772$	−12.7852	−0.460151
$773$	16.5248	0.594354	0.297177	−	0.954822i	$-0.403955\pi$
$773$	16.5248	0.594354	0.297177	+	0.954822i	$0.403955\pi$
$774$	6.53930	0.235050
$775$	−83.8746	−3.01286
$776$	−0.922531	−0.0331169
$777$	1.66561	0.0597535
$778$	−6.15026	−0.220497
$779$	7.76057	0.278051
$780$	−37.7025	−1.34997
$781$	−27.2074	−0.973558
$782$	18.5595	0.663686
$783$	−21.4513	−0.766606
$784$	1.00000	0.0357143
$785$	−5.42197	−0.193518
$786$	18.2578	0.651236
$787$	−17.4656	−0.622580	−0.311290	−	0.950315i	$-0.600761\pi$
$787$	−17.4656	−0.622580	−0.311290	+	0.950315i	$0.600761\pi$
$788$	11.8827	0.423305
$789$	47.2337	1.68157
$790$	3.85604	0.137192
$791$	−1.09126	−0.0388007
$792$	−0.985680	−0.0350246
$793$	−13.9397	−0.495015
$794$	−28.0784	−0.996466
$795$	−22.7170	−0.805687
$796$	2.63169	0.0932777
$797$	21.6403	0.766538	0.383269	−	0.923637i	$-0.374798\pi$
$797$	21.6403	0.766538	0.383269	+	0.923637i	$0.374798\pi$
$798$	14.4260	0.510674
$799$	−56.5412	−2.00029
$800$	9.86902	0.348923
$801$	1.44649	0.0511093
$802$	−15.5964	−0.550727
$803$	13.2477	0.467503
$804$	−16.9914	−0.599241
$805$	11.2258	0.395658
$806$	−44.2385	−1.55824
$807$	24.1755	0.851017
$808$	−13.5024	−0.475013
$809$	−16.0385	−0.563883	−0.281941	−	0.959432i	$-0.590978\pi$
$809$	−16.0385	−0.563883	−0.281941	+	0.959432i	$0.590978\pi$
$810$	−39.7398	−1.39631
$811$	30.4116	1.06790	0.533949	−	0.845517i	$-0.320708\pi$
$811$	30.4116	1.06790	0.533949	+	0.845517i	$0.320708\pi$
$812$	−4.62039	−0.162144
$813$	58.6220	2.05596
$814$	1.65430	0.0579832
$815$	−50.9298	−1.78399
$816$	−11.9750	−0.419208
$817$	−95.0563	−3.32560
$818$	34.3848	1.20224
$819$	2.75014	0.0960976
$820$	−3.89650	−0.136072
$821$	35.2421	1.22996	0.614979	−	0.788543i	$-0.289164\pi$
$821$	35.2421	1.22996	0.614979	+	0.788543i	$0.289164\pi$
$822$	20.2771	0.707247
$823$	−28.4851	−0.992930	−0.496465	−	0.868057i	$-0.665369\pi$
$823$	−28.4851	−0.992930	−0.496465	+	0.868057i	$0.665369\pi$
$824$	1.35979	0.0473704
$825$	34.5848	1.20409
$826$	11.0838	0.385654
$827$	43.0780	1.49797	0.748984	−	0.662588i	$-0.230542\pi$
$827$	43.0780	1.49797	0.748984	+	0.662588i	$0.230542\pi$
$828$	1.53811	0.0534530
$829$	36.7251	1.27552	0.637758	−	0.770237i	$-0.279862\pi$
$829$	36.7251	1.27552	0.637758	+	0.770237i	$0.279862\pi$
$830$	3.85863	0.133935
$831$	−46.7715	−1.62249
$832$	5.20528	0.180461
$833$	6.37514	0.220885
$834$	15.6306	0.541244
$835$	−0.576896	−0.0199643
$836$	14.3280	0.495544
$837$	−39.4576	−1.36385
$838$	−17.0949	−0.590532
$839$	8.03469	0.277388	0.138694	−	0.990335i	$-0.455710\pi$
$839$	8.03469	0.277388	0.138694	+	0.990335i	$0.455710\pi$
$840$	−7.24313	−0.249912
$841$	−7.65199	−0.263862
$842$	6.56918	0.226389
$843$	25.4334	0.875974
$844$	7.59486	0.261426
$845$	54.3507	1.86972
$846$	−4.68582	−0.161102
$847$	−7.51942	−0.258370
$848$	3.13635	0.107703
$849$	21.4194	0.735111
$850$	62.9164	2.15801
$851$	−2.58146	−0.0884913
$852$	−27.3935	−0.938484
$853$	32.2647	1.10472	0.552361	−	0.833605i	$-0.313727\pi$
$853$	32.2647	1.10472	0.552361	+	0.833605i	$0.313727\pi$
$854$	−2.67800	−0.0916393
$855$	−15.6463	−0.535092
$856$	−7.15720	−0.244628
$857$	−52.0405	−1.77767	−0.888834	−	0.458229i	$-0.848484\pi$
$857$	−52.0405	−1.77767	−0.888834	+	0.458229i	$0.848484\pi$
$858$	18.2413	0.622746
$859$	11.7565	0.401126	0.200563	−	0.979681i	$-0.435723\pi$
$859$	11.7565	0.401126	0.200563	+	0.979681i	$0.435723\pi$
$860$	47.7268	1.62747
$861$	1.89810	0.0646870
$862$	16.0542	0.546809
$863$	−52.5235	−1.78792	−0.893960	−	0.448146i	$-0.852085\pi$
$863$	−52.5235	−1.78792	−0.893960	+	0.448146i	$0.852085\pi$
$864$	4.64274	0.157949
$865$	−66.7772	−2.27049
$866$	−20.1815	−0.685795
$867$	−44.4096	−1.50823
$868$	−8.49878	−0.288467
$869$	−1.86563	−0.0632872
$870$	33.4661	1.13461
$871$	47.0856	1.59544
$872$	−15.0562	−0.509869
$873$	−0.487407	−0.0164962
$874$	−22.3582	−0.756277
$875$	18.7751	0.634715
$876$	13.3383	0.450660
$877$	29.7252	1.00375	0.501874	−	0.864941i	$-0.332644\pi$
$877$	29.7252	1.00375	0.501874	+	0.864941i	$0.332644\pi$
$878$	26.6643	0.899877
$879$	15.9748	0.538818
$880$	−7.19394	−0.242508
$881$	57.5296	1.93822	0.969110	−	0.246628i	$-0.0793226\pi$
$881$	57.5296	1.93822	0.969110	+	0.246628i	$0.0793226\pi$
$882$	0.528336	0.0177900
$883$	−36.3790	−1.22425	−0.612125	−	0.790761i	$-0.709685\pi$
$883$	−36.3790	−1.22425	−0.612125	+	0.790761i	$0.709685\pi$
$884$	33.1844	1.11611
$885$	−80.2813	−2.69863
$886$	40.0990	1.34715
$887$	29.0270	0.974630	0.487315	−	0.873226i	$-0.337976\pi$
$887$	29.0270	0.974630	0.487315	+	0.873226i	$0.337976\pi$
$888$	1.66561	0.0558943
$889$	18.5199	0.621136
$890$	10.5572	0.353877
$891$	19.2269	0.644127
$892$	−16.0101	−0.536057
$893$	68.1139	2.27934
$894$	−26.4401	−0.884289
$895$	−10.3764	−0.346845
$896$	1.00000	0.0334077
$897$	−28.4647	−0.950407
$898$	−25.5669	−0.853178
$899$	39.2677	1.30965
$900$	5.21416	0.173805
$901$	19.9946	0.666118
$902$	1.88521	0.0627706
$903$	−23.2491	−0.773682
$904$	−1.09126	−0.0362947
$905$	−68.2792	−2.26968
$906$	16.3061	0.541734
$907$	−5.85817	−0.194517	−0.0972587	−	0.995259i	$-0.531007\pi$
$907$	−5.85817	−0.194517	−0.0972587	+	0.995259i	$0.531007\pi$
$908$	20.0079	0.663986
$909$	−7.13380	−0.236613
$910$	20.0718	0.665372
$911$	−8.57108	−0.283972	−0.141986	−	0.989869i	$-0.545349\pi$
$911$	−8.57108	−0.283972	−0.141986	+	0.989869i	$0.545349\pi$
$912$	14.4260	0.477691
$913$	−1.86688	−0.0617849
$914$	21.5768	0.713697
$915$	19.3971	0.641248
$916$	3.54676	0.117188
$917$	−9.71996	−0.320981
$918$	29.5981	0.976883
$919$	−42.0669	−1.38766	−0.693829	−	0.720140i	$-0.744078\pi$
$919$	−42.0669	−1.38766	−0.693829	+	0.720140i	$0.744078\pi$
$920$	11.2258	0.370104
$921$	−23.7632	−0.783023
$922$	−17.3805	−0.572398
$923$	75.9112	2.49865
$924$	3.50438	0.115285
$925$	−8.75110	−0.287734
$926$	−29.4456	−0.967643
$927$	0.718425	0.0235962
$928$	−4.62039	−0.151672
$929$	−7.63156	−0.250383	−0.125192	−	0.992133i	$-0.539955\pi$
$929$	−7.63156	−0.250383	−0.125192	+	0.992133i	$0.539955\pi$
$930$	61.5577	2.01856
$931$	−7.67998	−0.251701
$932$	−19.8857	−0.651379
$933$	−34.7806	−1.13867
$934$	−37.9100	−1.24045
$935$	−45.8624	−1.49986
$936$	2.75014	0.0898911
$937$	−21.4895	−0.702032	−0.351016	−	0.936369i	$-0.614164\pi$
$937$	−21.4895	−0.702032	−0.351016	+	0.936369i	$0.614164\pi$
$938$	9.04574	0.295354
$939$	6.81316	0.222339
$940$	−34.1993	−1.11546
$941$	−25.6947	−0.837623	−0.418811	−	0.908073i	$-0.637553\pi$
$941$	−25.6947	−0.837623	−0.418811	+	0.908073i	$0.637553\pi$
$942$	2.64120	0.0860549
$943$	−2.94178	−0.0957976
$944$	11.0838	0.360746
$945$	17.9026	0.582371
$946$	−23.0912	−0.750760
$947$	24.7311	0.803654	0.401827	−	0.915716i	$-0.368375\pi$
$947$	24.7311	0.803654	0.401827	+	0.915716i	$0.368375\pi$
$948$	−1.87839	−0.0610072
$949$	−36.9624	−1.19985
$950$	−75.7938	−2.45908
$951$	−45.5693	−1.47769
$952$	6.37514	0.206619
$953$	23.3326	0.755817	0.377908	−	0.925843i	$-0.376643\pi$
$953$	23.3326	0.755817	0.377908	+	0.925843i	$0.376643\pi$
$954$	1.65705	0.0536488
$955$	−37.9152	−1.22691
$956$	−16.3759	−0.529633
$957$	−16.1916	−0.523400
$958$	−23.1491	−0.747913
$959$	−10.7950	−0.348588
$960$	−7.24313	−0.233771
$961$	41.2292	1.32997
$962$	−4.61565	−0.148815
$963$	−3.78141	−0.121854
$964$	2.83443	0.0912910
$965$	−49.3003	−1.58703
$966$	−5.46842	−0.175943
$967$	22.2355	0.715046	0.357523	−	0.933904i	$-0.383621\pi$
$967$	22.2355	0.715046	0.357523	+	0.933904i	$0.383621\pi$
$968$	−7.51942	−0.241683
$969$	91.9675	2.95442
$970$	−3.55731	−0.114218
$971$	−3.40613	−0.109308	−0.0546539	−	0.998505i	$-0.517406\pi$
$971$	−3.40613	−0.109308	−0.0546539	+	0.998505i	$0.517406\pi$
$972$	5.43019	0.174173
$973$	−8.32130	−0.266769
$974$	24.6596	0.790146
$975$	−96.4947	−3.09030
$976$	−2.67800	−0.0857207
$977$	−4.68889	−0.150011	−0.0750055	−	0.997183i	$-0.523897\pi$
$977$	−4.68889	−0.150011	−0.0750055	+	0.997183i	$0.523897\pi$
$978$	24.8094	0.793317
$979$	−5.10777	−0.163245
$980$	3.85604	0.123177
$981$	−7.95476	−0.253976
$982$	4.33822	0.138438
$983$	−37.5712	−1.19833	−0.599167	−	0.800624i	$-0.704502\pi$
$983$	−37.5712	−1.19833	−0.599167	+	0.800624i	$0.704502\pi$
$984$	1.89810	0.0605092
$985$	45.8203	1.45996
$986$	−29.4556	−0.938059
$987$	16.6594	0.530276
$988$	−39.9764	−1.27182
$989$	36.0328	1.14578
$990$	−3.80082	−0.120798
$991$	−32.2415	−1.02419	−0.512093	−	0.858930i	$-0.671130\pi$
$991$	−32.2415	−1.02419	−0.512093	+	0.858930i	$0.671130\pi$
$992$	−8.49878	−0.269836
$993$	−9.79933	−0.310972
$994$	14.5835	0.462561
$995$	10.1479	0.321710
$996$	−1.87965	−0.0595590
$997$	−52.2009	−1.65322	−0.826610	−	0.562775i	$-0.809734\pi$
$997$	−52.2009	−1.65322	−0.826610	+	0.562775i	$0.809734\pi$
$998$	24.9946	0.791190
$999$	−4.11683	−0.130251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1106.2.a.l.1.3	✓	9
3.2	odd	2		9954.2.a.bn.1.1		9
4.3	odd	2		8848.2.a.t.1.7		9
7.6	odd	2		7742.2.a.bj.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1106.2.a.l.1.3	✓	9	1.1	even	1	trivial
7742.2.a.bj.1.7		9	7.6	odd	2
8848.2.a.t.1.7		9	4.3	odd	2
9954.2.a.bn.1.1		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1106 = 2 \cdot 7 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1106.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.87839 q^{3} +1.00000 q^{4} +3.85604 q^{5} -1.87839 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.528336 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.87839 q^{3} +1.00000 q^{4} +3.85604 q^{5} -1.87839 q^{6} +1.00000 q^{7} +1.00000 q^{8} +0.528336 q^{9} +3.85604 q^{10} -1.86563 q^{11} -1.87839 q^{12} +5.20528 q^{13} +1.00000 q^{14} -7.24313 q^{15} +1.00000 q^{16} +6.37514 q^{17} +0.528336 q^{18} -7.67998 q^{19} +3.85604 q^{20} -1.87839 q^{21} -1.86563 q^{22} +2.91123 q^{23} -1.87839 q^{24} +9.86902 q^{25} +5.20528 q^{26} +4.64274 q^{27} +1.00000 q^{28} -4.62039 q^{29} -7.24313 q^{30} -8.49878 q^{31} +1.00000 q^{32} +3.50438 q^{33} +6.37514 q^{34} +3.85604 q^{35} +0.528336 q^{36} -0.886724 q^{37} -7.67998 q^{38} -9.77753 q^{39} +3.85604 q^{40} -1.01049 q^{41} -1.87839 q^{42} +12.3772 q^{43} -1.86563 q^{44} +2.03728 q^{45} +2.91123 q^{46} -8.86902 q^{47} -1.87839 q^{48} +1.00000 q^{49} +9.86902 q^{50} -11.9750 q^{51} +5.20528 q^{52} +3.13635 q^{53} +4.64274 q^{54} -7.19394 q^{55} +1.00000 q^{56} +14.4260 q^{57} -4.62039 q^{58} +11.0838 q^{59} -7.24313 q^{60} -2.67800 q^{61} -8.49878 q^{62} +0.528336 q^{63} +1.00000 q^{64} +20.0718 q^{65} +3.50438 q^{66} +9.04574 q^{67} +6.37514 q^{68} -5.46842 q^{69} +3.85604 q^{70} +14.5835 q^{71} +0.528336 q^{72} -7.10095 q^{73} -0.886724 q^{74} -18.5378 q^{75} -7.67998 q^{76} -1.86563 q^{77} -9.77753 q^{78} +1.00000 q^{79} +3.85604 q^{80} -10.3059 q^{81} -1.01049 q^{82} +1.00067 q^{83} -1.87839 q^{84} +24.5828 q^{85} +12.3772 q^{86} +8.67888 q^{87} -1.86563 q^{88} +2.73783 q^{89} +2.03728 q^{90} +5.20528 q^{91} +2.91123 q^{92} +15.9640 q^{93} -8.86902 q^{94} -29.6143 q^{95} -1.87839 q^{96} -0.922531 q^{97} +1.00000 q^{98} -0.985680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 2 q^{3} + 9 q^{4} + 4 q^{5} + 2 q^{6} + 9 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 2 * q^3 + 9 * q^4 + 4 * q^5 + 2 * q^6 + 9 * q^7 + 9 * q^8 + 13 * q^9	\( 9 q + 9 q^{2} + 2 q^{3} + 9 q^{4} + 4 q^{5} + 2 q^{6} + 9 q^{7} + 9 q^{8} + 13 q^{9} + 4 q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{13} + 9 q^{14} - 2 q^{15} + 9 q^{16} + 6 q^{17} + 13 q^{18} + 2 q^{19} + 4 q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{24} + 23 q^{25} + 2 q^{26} + 2 q^{27} + 9 q^{28} + 10 q^{29} - 2 q^{30} - 6 q^{31} + 9 q^{32} - 2 q^{33} + 6 q^{34} + 4 q^{35} + 13 q^{36} + 10 q^{37} + 2 q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} + 2 q^{42} + 22 q^{43} + 8 q^{44} - 10 q^{45} - 14 q^{47} + 2 q^{48} + 9 q^{49} + 23 q^{50} + 4 q^{51} + 2 q^{52} + 12 q^{53} + 2 q^{54} - 14 q^{55} + 9 q^{56} + 22 q^{57} + 10 q^{58} - 2 q^{59} - 2 q^{60} + 6 q^{61} - 6 q^{62} + 13 q^{63} + 9 q^{64} - 12 q^{65} - 2 q^{66} + 24 q^{67} + 6 q^{68} - 26 q^{69} + 4 q^{70} + 20 q^{71} + 13 q^{72} - 12 q^{73} + 10 q^{74} + 6 q^{75} + 2 q^{76} + 8 q^{77} - 6 q^{78} + 9 q^{79} + 4 q^{80} - 19 q^{81} + 10 q^{82} - 22 q^{83} + 2 q^{84} + 32 q^{85} + 22 q^{86} - 54 q^{87} + 8 q^{88} + 20 q^{89} - 10 q^{90} + 2 q^{91} - 18 q^{93} - 14 q^{94} - 40 q^{95} + 2 q^{96} - 6 q^{97} + 9 q^{98} + 24 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 2 * q^3 + 9 * q^4 + 4 * q^5 + 2 * q^6 + 9 * q^7 + 9 * q^8 + 13 * q^9 + 4 * q^10 + 8 * q^11 + 2 * q^12 + 2 * q^13 + 9 * q^14 - 2 * q^15 + 9 * q^16 + 6 * q^17 + 13 * q^18 + 2 * q^19 + 4 * q^20 + 2 * q^21 + 8 * q^22 + 2 * q^24 + 23 * q^25 + 2 * q^26 + 2 * q^27 + 9 * q^28 + 10 * q^29 - 2 * q^30 - 6 * q^31 + 9 * q^32 - 2 * q^33 + 6 * q^34 + 4 * q^35 + 13 * q^36 + 10 * q^37 + 2 * q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 + 2 * q^42 + 22 * q^43 + 8 * q^44 - 10 * q^45 - 14 * q^47 + 2 * q^48 + 9 * q^49 + 23 * q^50 + 4 * q^51 + 2 * q^52 + 12 * q^53 + 2 * q^54 - 14 * q^55 + 9 * q^56 + 22 * q^57 + 10 * q^58 - 2 * q^59 - 2 * q^60 + 6 * q^61 - 6 * q^62 + 13 * q^63 + 9 * q^64 - 12 * q^65 - 2 * q^66 + 24 * q^67 + 6 * q^68 - 26 * q^69 + 4 * q^70 + 20 * q^71 + 13 * q^72 - 12 * q^73 + 10 * q^74 + 6 * q^75 + 2 * q^76 + 8 * q^77 - 6 * q^78 + 9 * q^79 + 4 * q^80 - 19 * q^81 + 10 * q^82 - 22 * q^83 + 2 * q^84 + 32 * q^85 + 22 * q^86 - 54 * q^87 + 8 * q^88 + 20 * q^89 - 10 * q^90 + 2 * q^91 - 18 * q^93 - 14 * q^94 - 40 * q^95 + 2 * q^96 - 6 * q^97 + 9 * q^98 + 24 * q^99

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