LMFDB - Embedded newform 1183.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.879640$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} +O(q^{10})$	\(q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} -0.203187 q^{10} -0.364618 q^{11} +1.15615 q^{12} -0.120360 q^{14} +0.983005 q^{15} +3.91329 q^{16} -3.18555 q^{17} -0.320270 q^{18} +1.44391 q^{19} +3.35188 q^{20} +0.582292 q^{21} -0.0438854 q^{22} -5.08321 q^{23} +0.279323 q^{24} -2.15010 q^{25} +3.29632 q^{27} +1.98551 q^{28} +8.19662 q^{29} +0.118314 q^{30} -4.69775 q^{31} +1.43040 q^{32} +0.212314 q^{33} -0.383412 q^{34} +1.68817 q^{35} +5.28332 q^{36} +6.31584 q^{37} +0.173789 q^{38} +0.809806 q^{40} +5.82732 q^{41} +0.0700846 q^{42} -0.773122 q^{43} +0.723954 q^{44} +4.49210 q^{45} -0.611815 q^{46} +12.7905 q^{47} -2.27868 q^{48} +1.00000 q^{49} -0.258786 q^{50} +1.85492 q^{51} +1.37110 q^{53} +0.396744 q^{54} +0.615536 q^{55} +0.479696 q^{56} -0.840776 q^{57} +0.986544 q^{58} +9.36197 q^{59} -1.95177 q^{60} -9.02484 q^{61} -0.565421 q^{62} +2.66094 q^{63} -7.65442 q^{64} +0.0255541 q^{66} +13.4759 q^{67} +6.32495 q^{68} +2.95991 q^{69} +0.203187 q^{70} -7.08115 q^{71} +1.27644 q^{72} -2.16083 q^{73} +0.760173 q^{74} +1.25198 q^{75} -2.86690 q^{76} +0.364618 q^{77} -6.88781 q^{79} -6.60628 q^{80} +6.06339 q^{81} +0.701376 q^{82} +0.567380 q^{83} -1.15615 q^{84} +5.37773 q^{85} -0.0930528 q^{86} -4.77282 q^{87} +0.174906 q^{88} -1.13893 q^{89} +0.540669 q^{90} +10.0928 q^{92} +2.73547 q^{93} +1.53947 q^{94} -2.43755 q^{95} -0.832908 q^{96} +7.92785 q^{97} +0.120360 q^{98} +0.970225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	$ 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) $ 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 4 * q^11 + 2 * q^12 - 4 * q^14 + 20 * q^15 + 8 * q^16 - 4 * q^17 - 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 + 6 * q^27 - 4 * q^28 - 8 * q^29 + 8 * q^30 - 14 * q^31 + 8 * q^32 + 16 * q^33 - 2 * q^34 - 6 * q^35 - 10 * q^36 + 12 * q^37 - 2 * q^38 + 46 * q^40 + 28 * q^41 - 4 * q^42 + 2 * q^43 - 20 * q^44 + 16 * q^45 + 20 * q^46 + 14 * q^47 + 2 * q^48 + 6 * q^49 + 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 + 6 * q^55 - 12 * q^56 + 4 * q^58 - 2 * q^59 - 14 * q^61 - 4 * q^62 - 4 * q^63 + 26 * q^64 - 26 * q^66 + 24 * q^67 + 8 * q^68 + 4 * q^69 - 12 * q^70 + 4 * q^71 + 8 * q^72 + 36 * q^73 - 6 * q^74 + 46 * q^75 - 26 * q^76 - 4 * q^77 - 28 * q^79 + 36 * q^80 - 2 * q^81 + 14 * q^82 + 26 * q^83 - 2 * q^84 - 20 * q^85 - 24 * q^86 + 2 * q^87 - 14 * q^88 + 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 + 4 * q^98 + 16 * 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 $

$2$	0.120360	0.0851073	0.0425536	−	0.999094i	$-0.486451\pi$
$2$	0.120360	0.0851073	0.0425536	+	0.999094i	$0.486451\pi$
$3$	−0.582292	−0.336186	−0.168093	−	0.985771i	$-0.553761\pi$
$3$	−0.582292	−0.336186	−0.168093	+	0.985771i	$0.553761\pi$
$4$	−1.98551	−0.992757
$5$	−1.68817	−0.754971	−0.377485	−	0.926016i	$-0.623211\pi$
$5$	−1.68817	−0.754971	−0.377485	+	0.926016i	$0.623211\pi$
$6$	−0.0700846	−0.0286119
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.479696	−0.169598
$9$	−2.66094	−0.886979
$10$	−0.203187	−0.0642535
$11$	−0.364618	−0.109936	−0.0549682	−	0.998488i	$-0.517506\pi$
$11$	−0.364618	−0.109936	−0.0549682	+	0.998488i	$0.517506\pi$
$12$	1.15615	0.333751
$13$	0	0
$13$	0	0
$14$	−0.120360	−0.0321675
$15$	0.983005	0.253811
$16$	3.91329	0.978323
$17$	−3.18555	−0.772609	−0.386304	−	0.922371i	$-0.626249\pi$
$17$	−3.18555	−0.772609	−0.386304	+	0.922371i	$0.626249\pi$
$18$	−0.320270	−0.0754884
$19$	1.44391	0.331255	0.165628	−	0.986188i	$-0.447035\pi$
$19$	1.44391	0.331255	0.165628	+	0.986188i	$0.447035\pi$
$20$	3.35188	0.749502
$21$	0.582292	0.127067
$22$	−0.0438854	−0.00935640
$23$	−5.08321	−1.05992	−0.529962	−	0.848022i	$-0.677794\pi$
$23$	−5.08321	−1.05992	−0.529962	+	0.848022i	$0.677794\pi$
$24$	0.279323	0.0570166
$25$	−2.15010	−0.430020
$26$	0	0
$27$	3.29632	0.634377
$28$	1.98551	0.375227
$29$	8.19662	1.52207	0.761037	−	0.648709i	$-0.224691\pi$
$29$	8.19662	1.52207	0.761037	+	0.648709i	$0.224691\pi$
$30$	0.118314	0.0216012
$31$	−4.69775	−0.843742	−0.421871	−	0.906656i	$-0.638626\pi$
$31$	−4.69775	−0.843742	−0.421871	+	0.906656i	$0.638626\pi$
$32$	1.43040	0.252861
$33$	0.212314	0.0369592
$34$	−0.383412	−0.0657546
$35$	1.68817	0.285352
$36$	5.28332	0.880554
$37$	6.31584	1.03832	0.519159	−	0.854678i	$-0.326245\pi$
$37$	6.31584	1.03832	0.519159	+	0.854678i	$0.326245\pi$
$38$	0.173789	0.0281922
$39$	0	0
$40$	0.809806	0.128042
$41$	5.82732	0.910074	0.455037	−	0.890472i	$-0.349626\pi$
$41$	5.82732	0.910074	0.455037	+	0.890472i	$0.349626\pi$
$42$	0.0700846	0.0108143
$43$	−0.773122	−0.117900	−0.0589500	−	0.998261i	$-0.518775\pi$
$43$	−0.773122	−0.117900	−0.0589500	+	0.998261i	$0.518775\pi$
$44$	0.723954	0.109140
$45$	4.49210	0.669643
$46$	−0.611815	−0.0902072
$47$	12.7905	1.86569	0.932846	−	0.360275i	$-0.117317\pi$
$47$	12.7905	1.86569	0.932846	+	0.360275i	$0.117317\pi$
$48$	−2.27868	−0.328899
$49$	1.00000	0.142857
$50$	−0.258786	−0.0365978
$51$	1.85492	0.259741
$52$	0	0
$53$	1.37110	0.188334	0.0941672	−	0.995556i	$-0.469981\pi$
$53$	1.37110	0.188334	0.0941672	+	0.995556i	$0.469981\pi$
$54$	0.396744	0.0539901
$55$	0.615536	0.0829988
$56$	0.479696	0.0641021
$57$	−0.840776	−0.111363
$58$	0.986544	0.129540
$59$	9.36197	1.21882	0.609412	−	0.792854i	$-0.291405\pi$
$59$	9.36197	1.21882	0.609412	+	0.792854i	$0.291405\pi$
$60$	−1.95177	−0.251972
$61$	−9.02484	−1.15551	−0.577756	−	0.816209i	$-0.696072\pi$
$61$	−9.02484	−1.15551	−0.577756	+	0.816209i	$0.696072\pi$
$62$	−0.565421	−0.0718086
$63$	2.66094	0.335246
$64$	−7.65442	−0.956802
$65$	0	0
$66$	0.0255541	0.00314549
$67$	13.4759	1.64635	0.823174	−	0.567789i	$-0.192201\pi$
$67$	13.4759	1.64635	0.823174	+	0.567789i	$0.192201\pi$
$68$	6.32495	0.767013
$69$	2.95991	0.356332
$70$	0.203187	0.0242855
$71$	−7.08115	−0.840378	−0.420189	−	0.907437i	$-0.638036\pi$
$71$	−7.08115	−0.840378	−0.420189	+	0.907437i	$0.638036\pi$
$72$	1.27644	0.150430
$73$	−2.16083	−0.252906	−0.126453	−	0.991973i	$-0.540359\pi$
$73$	−2.16083	−0.252906	−0.126453	+	0.991973i	$0.540359\pi$
$74$	0.760173	0.0883684
$75$	1.25198	0.144567
$76$	−2.86690	−0.328856
$77$	0.364618	0.0415521
$78$	0	0
$79$	−6.88781	−0.774940	−0.387470	−	0.921882i	$-0.626651\pi$
$79$	−6.88781	−0.774940	−0.387470	+	0.921882i	$0.626651\pi$
$80$	−6.60628	−0.738605
$81$	6.06339	0.673710
$82$	0.701376	0.0774540
$83$	0.567380	0.0622780	0.0311390	−	0.999515i	$-0.490087\pi$
$83$	0.567380	0.0622780	0.0311390	+	0.999515i	$0.490087\pi$
$84$	−1.15615	−0.126146
$85$	5.37773	0.583297
$86$	−0.0930528	−0.0100341
$87$	−4.77282	−0.511700
$88$	0.174906	0.0186450
$89$	−1.13893	−0.120727	−0.0603634	−	0.998176i	$-0.519226\pi$
$89$	−1.13893	−0.120727	−0.0603634	+	0.998176i	$0.519226\pi$
$90$	0.540669	0.0569915
$91$	0	0
$92$	10.0928	1.05225
$93$	2.73547	0.283655
$94$	1.53947	0.158784
$95$	−2.43755	−0.250088
$96$	−0.832908	−0.0850083
$97$	7.92785	0.804952	0.402476	−	0.915431i	$-0.368150\pi$
$97$	7.92785	0.804952	0.402476	+	0.915431i	$0.368150\pi$
$98$	0.120360	0.0121582
$99$	0.970225	0.0975113
$100$	4.26905	0.426905
$101$	−15.5464	−1.54693	−0.773465	−	0.633839i	$-0.781478\pi$
$101$	−15.5464	−1.54693	−0.773465	+	0.633839i	$0.781478\pi$
$102$	0.223258	0.0221058
$103$	10.2982	1.01471	0.507354	−	0.861738i	$-0.330624\pi$
$103$	10.2982	1.01471	0.507354	+	0.861738i	$0.330624\pi$
$104$	0	0
$105$	−0.983005	−0.0959315
$106$	0.165025	0.0160286
$107$	−13.1244	−1.26878	−0.634391	−	0.773012i	$-0.718749\pi$
$107$	−13.1244	−1.26878	−0.634391	+	0.773012i	$0.718749\pi$
$108$	−6.54488	−0.629782
$109$	10.4459	1.00054	0.500268	−	0.865871i	$-0.333235\pi$
$109$	10.4459	1.00054	0.500268	+	0.865871i	$0.333235\pi$
$110$	0.0740858	0.00706380
$111$	−3.67766	−0.349068
$112$	−3.91329	−0.369771
$113$	4.95262	0.465903	0.232952	−	0.972488i	$-0.425162\pi$
$113$	4.95262	0.465903	0.232952	+	0.972488i	$0.425162\pi$
$114$	−0.101196	−0.00947784
$115$	8.58130	0.800211
$116$	−16.2745	−1.51105
$117$	0	0
$118$	1.12681	0.103731
$119$	3.18555	0.292019
$120$	−0.471544	−0.0430458
$121$	−10.8671	−0.987914
$122$	−1.08623	−0.0983425
$123$	−3.39320	−0.305955
$124$	9.32746	0.837630
$125$	12.0705	1.07962
$126$	0.320270	0.0285319
$127$	8.06731	0.715858	0.357929	−	0.933749i	$-0.383483\pi$
$127$	8.06731	0.715858	0.357929	+	0.933749i	$0.383483\pi$
$128$	−3.78208	−0.334291
$129$	0.450183	0.0396364
$130$	0	0
$131$	18.9039	1.65164	0.825820	−	0.563934i	$-0.190713\pi$
$131$	18.9039	1.65164	0.825820	+	0.563934i	$0.190713\pi$
$132$	−0.421553	−0.0366915
$133$	−1.44391	−0.125203
$134$	1.62196	0.140116
$135$	−5.56473	−0.478936
$136$	1.52809	0.131033
$137$	−18.2255	−1.55711	−0.778554	−	0.627577i	$-0.784047\pi$
$137$	−18.2255	−1.55711	−0.778554	+	0.627577i	$0.784047\pi$
$138$	0.356255	0.0303264
$139$	5.25085	0.445371	0.222686	−	0.974890i	$-0.428518\pi$
$139$	5.25085	0.445371	0.222686	+	0.974890i	$0.428518\pi$
$140$	−3.35188	−0.283285
$141$	−7.44783	−0.627220
$142$	−0.852287	−0.0715223
$143$	0	0
$144$	−10.4130	−0.867751
$145$	−13.8372	−1.14912
$146$	−0.260077	−0.0215241
$147$	−0.582292	−0.0480266
$148$	−12.5402	−1.03080
$149$	9.27309	0.759681	0.379841	−	0.925052i	$-0.375979\pi$
$149$	9.27309	0.759681	0.379841	+	0.925052i	$0.375979\pi$
$150$	0.150689	0.0123037
$151$	−14.0132	−1.14038	−0.570189	−	0.821513i	$-0.693130\pi$
$151$	−14.0132	−1.14038	−0.570189	+	0.821513i	$0.693130\pi$
$152$	−0.692636	−0.0561802
$153$	8.47654	0.685287
$154$	0.0438854	0.00353639
$155$	7.93059	0.637000
$156$	0	0
$157$	−17.1825	−1.37131	−0.685656	−	0.727925i	$-0.740485\pi$
$157$	−17.1825	−1.37131	−0.685656	+	0.727925i	$0.740485\pi$
$158$	−0.829017	−0.0659530
$159$	−0.798378	−0.0633155
$160$	−2.41474	−0.190902
$161$	5.08321	0.400613
$162$	0.729789	0.0573376
$163$	−11.7927	−0.923679	−0.461840	−	0.886963i	$-0.652810\pi$
$163$	−11.7927	−0.923679	−0.461840	+	0.886963i	$0.652810\pi$
$164$	−11.5702	−0.903482
$165$	−0.358422	−0.0279031
$166$	0.0682898	0.00530031
$167$	4.31687	0.334049	0.167025	−	0.985953i	$-0.446584\pi$
$167$	4.31687	0.334049	0.167025	+	0.985953i	$0.446584\pi$
$168$	−0.279323	−0.0215502
$169$	0	0
$170$	0.647263	0.0496428
$171$	−3.84214	−0.293816
$172$	1.53504	0.117046
$173$	12.5197	0.951855	0.475928	−	0.879484i	$-0.342112\pi$
$173$	12.5197	0.951855	0.475928	+	0.879484i	$0.342112\pi$
$174$	−0.574457	−0.0435494
$175$	2.15010	0.162532
$176$	−1.42686	−0.107553
$177$	−5.45140	−0.409752
$178$	−0.137082	−0.0102747
$179$	−6.59534	−0.492959	−0.246479	−	0.969148i	$-0.579274\pi$
$179$	−6.59534	−0.492959	−0.246479	+	0.969148i	$0.579274\pi$
$180$	−8.91913	−0.664792
$181$	11.0157	0.818791	0.409395	−	0.912357i	$-0.365740\pi$
$181$	11.0157	0.818791	0.409395	+	0.912357i	$0.365740\pi$
$182$	0	0
$183$	5.25509	0.388468
$184$	2.43840	0.179761
$185$	−10.6622	−0.783899
$186$	0.329240	0.0241411
$187$	1.16151	0.0849379
$188$	−25.3958	−1.85218
$189$	−3.29632	−0.239772
$190$	−0.293384	−0.0212843
$191$	5.93213	0.429234	0.214617	−	0.976698i	$-0.431150\pi$
$191$	5.93213	0.429234	0.214617	+	0.976698i	$0.431150\pi$
$192$	4.45711	0.321664
$193$	4.19595	0.302031	0.151016	−	0.988531i	$-0.451746\pi$
$193$	4.19595	0.302031	0.151016	+	0.988531i	$0.451746\pi$
$194$	0.954196	0.0685073
$195$	0	0
$196$	−1.98551	−0.141822
$197$	−5.78494	−0.412160	−0.206080	−	0.978535i	$-0.566071\pi$
$197$	−5.78494	−0.412160	−0.206080	+	0.978535i	$0.566071\pi$
$198$	0.116776	0.00829893
$199$	11.9598	0.847805	0.423903	−	0.905708i	$-0.360660\pi$
$199$	11.9598	0.847805	0.423903	+	0.905708i	$0.360660\pi$
$200$	1.03139	0.0729305
$201$	−7.84693	−0.553480
$202$	−1.87117	−0.131655
$203$	−8.19662	−0.575290
$204$	−3.68297	−0.257859
$205$	−9.83748	−0.687079
$206$	1.23949	0.0863590
$207$	13.5261	0.940129
$208$	0	0
$209$	−0.526475	−0.0364170
$210$	−0.118314	−0.00816447
$211$	−8.23591	−0.566983	−0.283492	−	0.958975i	$-0.591493\pi$
$211$	−8.23591	−0.566983	−0.283492	+	0.958975i	$0.591493\pi$
$212$	−2.72233	−0.186970
$213$	4.12330	0.282524
$214$	−1.57965	−0.107983
$215$	1.30516	0.0890110
$216$	−1.58123	−0.107589
$217$	4.69775	0.318904
$218$	1.25727	0.0851528
$219$	1.25823	0.0850234
$220$	−1.22215	−0.0823976
$221$	0	0
$222$	−0.442643	−0.0297082
$223$	−15.3015	−1.02466	−0.512331	−	0.858788i	$-0.671218\pi$
$223$	−15.3015	−1.02466	−0.512331	+	0.858788i	$0.671218\pi$
$224$	−1.43040	−0.0955723
$225$	5.72127	0.381418
$226$	0.596097	0.0396518
$227$	−6.95467	−0.461598	−0.230799	−	0.973002i	$-0.574134\pi$
$227$	−6.95467	−0.461598	−0.230799	+	0.973002i	$0.574134\pi$
$228$	1.66937	0.110557
$229$	27.4219	1.81209	0.906045	−	0.423180i	$-0.139086\pi$
$229$	27.4219	1.81209	0.906045	+	0.423180i	$0.139086\pi$
$230$	1.03284	0.0681038
$231$	−0.212314	−0.0139693
$232$	−3.93188	−0.258141
$233$	−6.85333	−0.448976	−0.224488	−	0.974477i	$-0.572071\pi$
$233$	−6.85333	−0.448976	−0.224488	+	0.974477i	$0.572071\pi$
$234$	0	0
$235$	−21.5926	−1.40854
$236$	−18.5883	−1.21000
$237$	4.01072	0.260524
$238$	0.383412	0.0248529
$239$	22.0754	1.42794	0.713970	−	0.700177i	$-0.246895\pi$
$239$	22.0754	1.42794	0.713970	+	0.700177i	$0.246895\pi$
$240$	3.84679	0.248309
$241$	−15.7971	−1.01758	−0.508790	−	0.860890i	$-0.669907\pi$
$241$	−15.7971	−1.01758	−0.508790	+	0.860890i	$0.669907\pi$
$242$	−1.30796	−0.0840787
$243$	−13.4196	−0.860869
$244$	17.9189	1.14714
$245$	−1.68817	−0.107853
$246$	−0.408405	−0.0260390
$247$	0	0
$248$	2.25349	0.143097
$249$	−0.330381	−0.0209370
$250$	1.45281	0.0918838
$251$	22.5567	1.42376	0.711882	−	0.702299i	$-0.247843\pi$
$251$	22.5567	1.42376	0.711882	+	0.702299i	$0.247843\pi$
$252$	−5.28332	−0.332818
$253$	1.85343	0.116524
$254$	0.970981	0.0609247
$255$	−3.13141	−0.196097
$256$	14.8536	0.928352
$257$	20.4129	1.27332	0.636660	−	0.771145i	$-0.280315\pi$
$257$	20.4129	1.27332	0.636660	+	0.771145i	$0.280315\pi$
$258$	0.0541839	0.00337334
$259$	−6.31584	−0.392447
$260$	0	0
$261$	−21.8107	−1.35005
$262$	2.27527	0.140567
$263$	−29.5402	−1.82153	−0.910764	−	0.412927i	$-0.864506\pi$
$263$	−29.5402	−1.82153	−0.910764	+	0.412927i	$0.864506\pi$
$264$	−0.101846	−0.00626820
$265$	−2.31464	−0.142187
$266$	−0.173789	−0.0106557
$267$	0.663193	0.0405867
$268$	−26.7567	−1.63442
$269$	27.9163	1.70209	0.851043	−	0.525096i	$-0.175971\pi$
$269$	27.9163	1.70209	0.851043	+	0.525096i	$0.175971\pi$
$270$	−0.669770	−0.0407609
$271$	−29.4491	−1.78890	−0.894451	−	0.447165i	$-0.852434\pi$
$271$	−29.4491	−1.78890	−0.894451	+	0.447165i	$0.852434\pi$
$272$	−12.4660	−0.755861
$273$	0	0
$274$	−2.19362	−0.132521
$275$	0.783965	0.0472748
$276$	−5.87695	−0.353751
$277$	6.85854	0.412090	0.206045	−	0.978543i	$-0.433941\pi$
$277$	6.85854	0.412090	0.206045	+	0.978543i	$0.433941\pi$
$278$	0.631992	0.0379043
$279$	12.5004	0.748381
$280$	−0.809806	−0.0483952
$281$	29.0940	1.73561	0.867803	−	0.496909i	$-0.165532\pi$
$281$	29.0940	1.73561	0.867803	+	0.496909i	$0.165532\pi$
$282$	−0.896420	−0.0533810
$283$	11.6102	0.690156	0.345078	−	0.938574i	$-0.387853\pi$
$283$	11.6102	0.690156	0.345078	+	0.938574i	$0.387853\pi$
$284$	14.0597	0.834291
$285$	1.41937	0.0840761
$286$	0	0
$287$	−5.82732	−0.343976
$288$	−3.80619	−0.224282
$289$	−6.85229	−0.403076
$290$	−1.66545	−0.0977985
$291$	−4.61633	−0.270614
$292$	4.29035	0.251074
$293$	17.7886	1.03922	0.519610	−	0.854403i	$-0.326077\pi$
$293$	17.7886	1.03922	0.519610	+	0.854403i	$0.326077\pi$
$294$	−0.0700846	−0.00408742
$295$	−15.8046	−0.920177
$296$	−3.02968	−0.176097
$297$	−1.20190	−0.0697412
$298$	1.11611	0.0646544
$299$	0	0
$300$	−2.48583	−0.143520
$301$	0.773122	0.0445620
$302$	−1.68663	−0.0970546
$303$	9.05257	0.520057
$304$	5.65043	0.324074
$305$	15.2354	0.872378
$306$	1.02024	0.0583230
$307$	−9.07966	−0.518204	−0.259102	−	0.965850i	$-0.583427\pi$
$307$	−9.07966	−0.518204	−0.259102	+	0.965850i	$0.583427\pi$
$308$	−0.723954	−0.0412511
$309$	−5.99654	−0.341131
$310$	0.954525	0.0542134
$311$	1.57073	0.0890677	0.0445338	−	0.999008i	$-0.485820\pi$
$311$	1.57073	0.0890677	0.0445338	+	0.999008i	$0.485820\pi$
$312$	0	0
$313$	20.6232	1.16569	0.582846	−	0.812582i	$-0.301939\pi$
$313$	20.6232	1.16569	0.582846	+	0.812582i	$0.301939\pi$
$314$	−2.06808	−0.116709
$315$	−4.49210	−0.253101
$316$	13.6758	0.769327
$317$	30.5435	1.71549	0.857747	−	0.514072i	$-0.171863\pi$
$317$	30.5435	1.71549	0.857747	+	0.514072i	$0.171863\pi$
$318$	−0.0960927	−0.00538861
$319$	−2.98863	−0.167331
$320$	12.9219	0.722358
$321$	7.64223	0.426548
$322$	0.611815	0.0340951
$323$	−4.59964	−0.255931
$324$	−12.0389	−0.668830
$325$	0	0
$326$	−1.41937	−0.0786118
$327$	−6.08256	−0.336366
$328$	−2.79534	−0.154347
$329$	−12.7905	−0.705165
$330$	−0.0431396	−0.00237476
$331$	−25.8531	−1.42101	−0.710507	−	0.703690i	$-0.751534\pi$
$331$	−25.8531	−1.42101	−0.710507	+	0.703690i	$0.751534\pi$
$332$	−1.12654	−0.0618269
$333$	−16.8060	−0.920965
$334$	0.519578	0.0284300
$335$	−22.7496	−1.24294
$336$	2.27868	0.124312
$337$	21.3954	1.16548	0.582742	−	0.812657i	$-0.301980\pi$
$337$	21.3954	1.16548	0.582742	+	0.812657i	$0.301980\pi$
$338$	0	0
$339$	−2.88387	−0.156630
$340$	−10.6776	−0.579072
$341$	1.71289	0.0927580
$342$	−0.462440	−0.0250059
$343$	−1.00000	−0.0539949
$344$	0.370863	0.0199956
$345$	−4.99682	−0.269020
$346$	1.50687	0.0810098
$347$	2.20883	0.118576	0.0592882	−	0.998241i	$-0.481117\pi$
$347$	2.20883	0.118576	0.0592882	+	0.998241i	$0.481117\pi$
$348$	9.47651	0.507994
$349$	−11.2912	−0.604402	−0.302201	−	0.953244i	$-0.597721\pi$
$349$	−11.2912	−0.604402	−0.302201	+	0.953244i	$0.597721\pi$
$350$	0.258786	0.0138327
$351$	0	0
$352$	−0.521548	−0.0277986
$353$	35.6433	1.89710	0.948552	−	0.316623i	$-0.102549\pi$
$353$	35.6433	1.89710	0.948552	+	0.316623i	$0.102549\pi$
$354$	−0.656130	−0.0348729
$355$	11.9542	0.634461
$356$	2.26137	0.119852
$357$	−1.85492	−0.0981727
$358$	−0.793815	−0.0419544
$359$	−19.3218	−1.01976	−0.509882	−	0.860244i	$-0.670311\pi$
$359$	−19.3218	−1.01976	−0.509882	+	0.860244i	$0.670311\pi$
$360$	−2.15484	−0.113570
$361$	−16.9151	−0.890270
$362$	1.32585	0.0696851
$363$	6.32780	0.332123
$364$	0	0
$365$	3.64783	0.190936
$366$	0.632502	0.0330614
$367$	−3.72065	−0.194216	−0.0971082	−	0.995274i	$-0.530959\pi$
$367$	−3.72065	−0.194216	−0.0971082	+	0.995274i	$0.530959\pi$
$368$	−19.8921	−1.03695
$369$	−15.5061	−0.807217
$370$	−1.28330	−0.0667155
$371$	−1.37110	−0.0711837
$372$	−5.43130	−0.281600
$373$	−3.51276	−0.181884	−0.0909420	−	0.995856i	$-0.528988\pi$
$373$	−3.51276	−0.181884	−0.0909420	+	0.995856i	$0.528988\pi$
$374$	0.139799	0.00722884
$375$	−7.02858	−0.362954
$376$	−6.13557	−0.316418
$377$	0	0
$378$	−0.396744	−0.0204063
$379$	−25.0163	−1.28500	−0.642500	−	0.766285i	$-0.722103\pi$
$379$	−25.0163	−1.28500	−0.642500	+	0.766285i	$0.722103\pi$
$380$	4.83980	0.248276
$381$	−4.69753	−0.240662
$382$	0.713990	0.0365309
$383$	−22.4654	−1.14793	−0.573964	−	0.818881i	$-0.694595\pi$
$383$	−22.4654	−1.14793	−0.573964	+	0.818881i	$0.694595\pi$
$384$	2.20227	0.112384
$385$	−0.615536	−0.0313706
$386$	0.505024	0.0257051
$387$	2.05723	0.104575
$388$	−15.7409	−0.799121
$389$	−13.3364	−0.676184	−0.338092	−	0.941113i	$-0.609781\pi$
$389$	−13.3364	−0.676184	−0.338092	+	0.941113i	$0.609781\pi$
$390$	0	0
$391$	16.1928	0.818906
$392$	−0.479696	−0.0242283
$393$	−11.0076	−0.555259
$394$	−0.696274	−0.0350778
$395$	11.6278	0.585057
$396$	−1.92640	−0.0968050
$397$	25.8333	1.29654	0.648268	−	0.761412i	$-0.275494\pi$
$397$	25.8333	1.29654	0.648268	+	0.761412i	$0.275494\pi$
$398$	1.43948	0.0721544
$399$	0.840776	0.0420914
$400$	−8.41396	−0.420698
$401$	17.5605	0.876930	0.438465	−	0.898748i	$-0.355522\pi$
$401$	17.5605	0.876930	0.438465	+	0.898748i	$0.355522\pi$
$402$	−0.944456	−0.0471052
$403$	0	0
$404$	30.8677	1.53572
$405$	−10.2360	−0.508631
$406$	−0.986544	−0.0489613
$407$	−2.30287	−0.114149
$408$	−0.889797	−0.0440515
$409$	14.5282	0.718373	0.359186	−	0.933266i	$-0.383054\pi$
$409$	14.5282	0.718373	0.359186	+	0.933266i	$0.383054\pi$
$410$	−1.18404	−0.0584755
$411$	10.6126	0.523479
$412$	−20.4471	−1.00736
$413$	−9.36197	−0.460672
$414$	1.62800	0.0800119
$415$	−0.957831	−0.0470181
$416$	0	0
$417$	−3.05753	−0.149728
$418$	−0.0633664	−0.00309935
$419$	−4.60192	−0.224819	−0.112409	−	0.993662i	$-0.535857\pi$
$419$	−4.60192	−0.224819	−0.112409	+	0.993662i	$0.535857\pi$
$420$	1.95177	0.0952366
$421$	−19.2645	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$421$	−19.2645	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$422$	−0.991273	−0.0482544
$423$	−34.0348	−1.65483
$424$	−0.657709	−0.0319412
$425$	6.84924	0.332237
$426$	0.496280	0.0240448
$427$	9.02484	0.436743
$428$	26.0587	1.25959
$429$	0	0
$430$	0.157089	0.00757548
$431$	28.3651	1.36630	0.683149	−	0.730279i	$-0.260610\pi$
$431$	28.3651	1.36630	0.683149	+	0.730279i	$0.260610\pi$
$432$	12.8995	0.620625
$433$	−12.5203	−0.601686	−0.300843	−	0.953674i	$-0.597268\pi$
$433$	−12.5203	−0.601686	−0.300843	+	0.953674i	$0.597268\pi$
$434$	0.565421	0.0271411
$435$	8.05732	0.386319
$436$	−20.7405	−0.993288
$437$	−7.33969	−0.351105
$438$	0.151441	0.00723611
$439$	31.7273	1.51426	0.757132	−	0.653262i	$-0.226600\pi$
$439$	31.7273	1.51426	0.757132	+	0.653262i	$0.226600\pi$
$440$	−0.295270	−0.0140764
$441$	−2.66094	−0.126711
$442$	0	0
$443$	1.73048	0.0822177	0.0411088	−	0.999155i	$-0.486911\pi$
$443$	1.73048	0.0822177	0.0411088	+	0.999155i	$0.486911\pi$
$444$	7.30205	0.346540
$445$	1.92271	0.0911452
$446$	−1.84168	−0.0872062
$447$	−5.39965	−0.255394
$448$	7.65442	0.361637
$449$	10.5564	0.498186	0.249093	−	0.968480i	$-0.419868\pi$
$449$	10.5564	0.498186	0.249093	+	0.968480i	$0.419868\pi$
$450$	0.688612	0.0324615
$451$	−2.12475	−0.100050
$452$	−9.83349	−0.462528
$453$	8.15978	0.383380
$454$	−0.837063	−0.0392853
$455$	0	0
$456$	0.403317	0.0188870
$457$	7.94894	0.371836	0.185918	−	0.982565i	$-0.440474\pi$
$457$	7.94894	0.371836	0.185918	+	0.982565i	$0.440474\pi$
$458$	3.30050	0.154222
$459$	−10.5006	−0.490125
$460$	−17.0383	−0.794415
$461$	10.8918	0.507284	0.253642	−	0.967298i	$-0.418371\pi$
$461$	10.8918	0.507284	0.253642	+	0.967298i	$0.418371\pi$
$462$	−0.0255541	−0.00118889
$463$	35.8227	1.66482	0.832411	−	0.554158i	$-0.186960\pi$
$463$	35.8227	1.66482	0.832411	+	0.554158i	$0.186960\pi$
$464$	32.0757	1.48908
$465$	−4.61792	−0.214151
$466$	−0.824866	−0.0382112
$467$	19.8983	0.920785	0.460393	−	0.887715i	$-0.347709\pi$
$467$	19.8983	0.920785	0.460393	+	0.887715i	$0.347709\pi$
$468$	0	0
$469$	−13.4759	−0.622261
$470$	−2.59888	−0.119877
$471$	10.0052	0.461017
$472$	−4.49090	−0.206710
$473$	0.281894	0.0129615
$474$	0.482730	0.0221725
$475$	−3.10454	−0.142446
$476$	−6.32495	−0.289904
$477$	−3.64840	−0.167049
$478$	2.65699	0.121528
$479$	26.2902	1.20123	0.600615	−	0.799538i	$-0.294922\pi$
$479$	26.2902	1.20123	0.600615	+	0.799538i	$0.294922\pi$
$480$	1.40609	0.0641788
$481$	0	0
$482$	−1.90134	−0.0866035
$483$	−2.95991	−0.134681
$484$	21.5767	0.980758
$485$	−13.3835	−0.607715
$486$	−1.61518	−0.0732662
$487$	6.37962	0.289088	0.144544	−	0.989498i	$-0.453828\pi$
$487$	6.37962	0.289088	0.144544	+	0.989498i	$0.453828\pi$
$488$	4.32918	0.195973
$489$	6.86682	0.310528
$490$	−0.203187	−0.00917907
$491$	−2.96768	−0.133929	−0.0669647	−	0.997755i	$-0.521331\pi$
$491$	−2.96768	−0.133929	−0.0669647	+	0.997755i	$0.521331\pi$
$492$	6.73725	0.303739
$493$	−26.1107	−1.17597
$494$	0	0
$495$	−1.63790	−0.0736182
$496$	−18.3837	−0.825452
$497$	7.08115	0.317633
$498$	−0.0397646	−0.00178189
$499$	−28.1331	−1.25941	−0.629704	−	0.776835i	$-0.716824\pi$
$499$	−28.1331	−1.25941	−0.629704	+	0.776835i	$0.716824\pi$
$500$	−23.9662	−1.07180
$501$	−2.51368	−0.112303
$502$	2.71492	0.121173
$503$	−31.5376	−1.40619	−0.703097	−	0.711094i	$-0.748200\pi$
$503$	−31.5376	−1.40619	−0.703097	+	0.711094i	$0.748200\pi$
$504$	−1.27644	−0.0568572
$505$	26.2450	1.16789
$506$	0.223079	0.00991706
$507$	0	0
$508$	−16.0178	−0.710673
$509$	−13.5944	−0.602560	−0.301280	−	0.953536i	$-0.597414\pi$
$509$	−13.5944	−0.602560	−0.301280	+	0.953536i	$0.597414\pi$
$510$	−0.376896	−0.0166892
$511$	2.16083	0.0955893
$512$	9.35193	0.413301
$513$	4.75958	0.210140
$514$	2.45689	0.108369
$515$	−17.3850	−0.766074
$516$	−0.893844	−0.0393493
$517$	−4.66366	−0.205108
$518$	−0.760173	−0.0334001
$519$	−7.29012	−0.320001
$520$	0	0
$521$	8.78344	0.384810	0.192405	−	0.981316i	$-0.438371\pi$
$521$	8.78344	0.384810	0.192405	+	0.981316i	$0.438371\pi$
$522$	−2.62513	−0.114899
$523$	32.5698	1.42418	0.712088	−	0.702090i	$-0.247749\pi$
$523$	32.5698	1.42418	0.712088	+	0.702090i	$0.247749\pi$
$524$	−37.5339	−1.63968
$525$	−1.25198	−0.0546411
$526$	−3.55546	−0.155025
$527$	14.9649	0.651882
$528$	0.830847	0.0361580
$529$	2.83905	0.123437
$530$	−0.278589	−0.0121011
$531$	−24.9116	−1.08107
$532$	2.86690	0.124296
$533$	0	0
$534$	0.0798218	0.00345423
$535$	22.1561	0.957894
$536$	−6.46435	−0.279218
$537$	3.84041	0.165726
$538$	3.36000	0.144860
$539$	−0.364618	−0.0157052
$540$	11.0488	0.475467
$541$	6.94870	0.298748	0.149374	−	0.988781i	$-0.452274\pi$
$541$	6.94870	0.298748	0.149374	+	0.988781i	$0.452274\pi$
$542$	−3.54448	−0.152249
$543$	−6.41436	−0.275266
$544$	−4.55659	−0.195362
$545$	−17.6344	−0.755375
$546$	0	0
$547$	10.9095	0.466457	0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095	0.466457	0.233229	+	0.972422i	$0.425071\pi$
$548$	36.1870	1.54583
$549$	24.0145	1.02491
$550$	0.0943579	0.00402343
$551$	11.8352	0.504194
$552$	−1.41986	−0.0604332
$553$	6.88781	0.292900
$554$	0.825493	0.0350718
$555$	6.20850	0.263536
$556$	−10.4256	−0.442145
$557$	34.6295	1.46730	0.733650	−	0.679527i	$-0.237815\pi$
$557$	34.6295	1.46730	0.733650	+	0.679527i	$0.237815\pi$
$558$	1.50455	0.0636927
$559$	0	0
$560$	6.60628	0.279166
$561$	−0.676337	−0.0285550
$562$	3.50176	0.147713
$563$	9.13679	0.385070	0.192535	−	0.981290i	$-0.438329\pi$
$563$	9.13679	0.385070	0.192535	+	0.981290i	$0.438329\pi$
$564$	14.7878	0.622677
$565$	−8.36084	−0.351743
$566$	1.39740	0.0587373
$567$	−6.06339	−0.254638
$568$	3.39680	0.142527
$569$	18.3000	0.767176	0.383588	−	0.923504i	$-0.374688\pi$
$569$	18.3000	0.767176	0.383588	+	0.923504i	$0.374688\pi$
$570$	0.170835	0.00715549
$571$	10.1791	0.425981	0.212990	−	0.977054i	$-0.431680\pi$
$571$	10.1791	0.425981	0.212990	+	0.977054i	$0.431680\pi$
$572$	0	0
$573$	−3.45423	−0.144303
$574$	−0.701376	−0.0292748
$575$	10.9294	0.455788
$576$	20.3679	0.848663
$577$	19.5165	0.812482	0.406241	−	0.913766i	$-0.366839\pi$
$577$	19.5165	0.812482	0.406241	+	0.913766i	$0.366839\pi$
$578$	−0.824740	−0.0343047
$579$	−2.44327	−0.101539
$580$	27.4740	1.14080
$581$	−0.567380	−0.0235389
$582$	−0.555621	−0.0230312
$583$	−0.499926	−0.0207048
$584$	1.03654	0.0428923
$585$	0	0
$586$	2.14103	0.0884453
$587$	35.3900	1.46070	0.730351	−	0.683072i	$-0.239357\pi$
$587$	35.3900	1.46070	0.730351	+	0.683072i	$0.239357\pi$
$588$	1.15615	0.0476788
$589$	−6.78312	−0.279494
$590$	−1.90223	−0.0783137
$591$	3.36852	0.138562
$592$	24.7157	1.01581
$593$	18.0881	0.742790	0.371395	−	0.928475i	$-0.378880\pi$
$593$	18.0881	0.742790	0.371395	+	0.928475i	$0.378880\pi$
$594$	−0.144660	−0.00593548
$595$	−5.37773	−0.220465
$596$	−18.4118	−0.754179
$597$	−6.96407	−0.285021
$598$	0	0
$599$	9.05992	0.370178	0.185089	−	0.982722i	$-0.440743\pi$
$599$	9.05992	0.370178	0.185089	+	0.982722i	$0.440743\pi$
$600$	−0.600572	−0.0245182
$601$	29.2881	1.19469	0.597343	−	0.801986i	$-0.296223\pi$
$601$	29.2881	1.19469	0.597343	+	0.801986i	$0.296223\pi$
$602$	0.0930528	0.00379255
$603$	−35.8586	−1.46028
$604$	27.8234	1.13212
$605$	18.3454	0.745846
$606$	1.08957	0.0442606
$607$	−39.3650	−1.59777	−0.798887	−	0.601481i	$-0.794578\pi$
$607$	−39.3650	−1.59777	−0.798887	+	0.601481i	$0.794578\pi$
$608$	2.06536	0.0837613
$609$	4.77282	0.193405
$610$	1.83373	0.0742457
$611$	0	0
$612$	−16.8303	−0.680324
$613$	−5.53316	−0.223482	−0.111741	−	0.993737i	$-0.535643\pi$
$613$	−5.53316	−0.223482	−0.111741	+	0.993737i	$0.535643\pi$
$614$	−1.09283	−0.0441029
$615$	5.72829	0.230987
$616$	−0.174906	−0.00704716
$617$	12.5815	0.506514	0.253257	−	0.967399i	$-0.418498\pi$
$617$	12.5815	0.506514	0.253257	+	0.967399i	$0.418498\pi$
$618$	−0.721742	−0.0290327
$619$	−22.3955	−0.900149	−0.450075	−	0.892991i	$-0.648603\pi$
$619$	−22.3955	−0.900149	−0.450075	+	0.892991i	$0.648603\pi$
$620$	−15.7463	−0.632386
$621$	−16.7559	−0.672390
$622$	0.189052	0.00758031
$623$	1.13893	0.0456305
$624$	0	0
$625$	−9.62659	−0.385064
$626$	2.48221	0.0992090
$627$	0.306562	0.0122429
$628$	34.1161	1.36138
$629$	−20.1194	−0.802213
$630$	−0.540669	−0.0215408
$631$	−1.94888	−0.0775836	−0.0387918	−	0.999247i	$-0.512351\pi$
$631$	−1.94888	−0.0775836	−0.0387918	+	0.999247i	$0.512351\pi$
$632$	3.30406	0.131428
$633$	4.79570	0.190612
$634$	3.67621	0.146001
$635$	−13.6190	−0.540452
$636$	1.58519	0.0628569
$637$	0	0
$638$	−0.359712	−0.0142411
$639$	18.8425	0.745397
$640$	6.38477	0.252380
$641$	10.4210	0.411605	0.205803	−	0.978594i	$-0.434019\pi$
$641$	10.4210	0.411605	0.205803	+	0.978594i	$0.434019\pi$
$642$	0.919818	0.0363023
$643$	15.2706	0.602214	0.301107	−	0.953590i	$-0.402644\pi$
$643$	15.2706	0.602214	0.301107	+	0.953590i	$0.402644\pi$
$644$	−10.0928	−0.397712
$645$	−0.759983	−0.0299243
$646$	−0.553612	−0.0217816
$647$	17.5066	0.688254	0.344127	−	0.938923i	$-0.388175\pi$
$647$	17.5066	0.688254	0.344127	+	0.938923i	$0.388175\pi$
$648$	−2.90858	−0.114260
$649$	−3.41354	−0.133993
$650$	0	0
$651$	−2.73547	−0.107211
$652$	23.4147	0.916989
$653$	−10.1834	−0.398506	−0.199253	−	0.979948i	$-0.563852\pi$
$653$	−10.1834	−0.398506	−0.199253	+	0.979948i	$0.563852\pi$
$654$	−0.732096	−0.0286272
$655$	−31.9129	−1.24694
$656$	22.8040	0.890346
$657$	5.74982	0.224322
$658$	−1.53947	−0.0600147
$659$	−43.8587	−1.70849	−0.854247	−	0.519867i	$-0.825981\pi$
$659$	−43.8587	−1.70849	−0.854247	+	0.519867i	$0.825981\pi$
$660$	0.711651	0.0277010
$661$	−32.9270	−1.28071	−0.640356	−	0.768078i	$-0.721213\pi$
$661$	−32.9270	−1.28071	−0.640356	+	0.768078i	$0.721213\pi$
$662$	−3.11167	−0.120939
$663$	0	0
$664$	−0.272170	−0.0105622
$665$	2.43755	0.0945243
$666$	−2.02277	−0.0783808
$667$	−41.6651	−1.61328
$668$	−8.57120	−0.331630
$669$	8.90992	0.344478
$670$	−2.73814	−0.105784
$671$	3.29062	0.127033
$672$	0.832908	0.0321301
$673$	26.6845	1.02861	0.514307	−	0.857606i	$-0.328049\pi$
$673$	26.6845	1.02861	0.514307	+	0.857606i	$0.328049\pi$
$674$	2.57515	0.0991912
$675$	−7.08740	−0.272794
$676$	0	0
$677$	29.5328	1.13504	0.567519	−	0.823361i	$-0.307904\pi$
$677$	29.5328	1.13504	0.567519	+	0.823361i	$0.307904\pi$
$678$	−0.347102	−0.0133304
$679$	−7.92785	−0.304243
$680$	−2.57968	−0.0989261
$681$	4.04965	0.155183
$682$	0.206163	0.00789438
$683$	18.2880	0.699771	0.349885	−	0.936793i	$-0.386221\pi$
$683$	18.2880	0.699771	0.349885	+	0.936793i	$0.386221\pi$
$684$	7.62863	0.291688
$685$	30.7676	1.17557
$686$	−0.120360	−0.00459536
$687$	−15.9676	−0.609200
$688$	−3.02545	−0.115344
$689$	0	0
$690$	−0.601417	−0.0228956
$691$	10.3406	0.393376	0.196688	−	0.980466i	$-0.436981\pi$
$691$	10.3406	0.393376	0.196688	+	0.980466i	$0.436981\pi$
$692$	−24.8580	−0.944961
$693$	−0.970225	−0.0368558
$694$	0.265855	0.0100917
$695$	−8.86430	−0.336242
$696$	2.28950	0.0867834
$697$	−18.5632	−0.703131
$698$	−1.35900	−0.0514390
$699$	3.99064	0.150940
$700$	−4.26905	−0.161355
$701$	−41.6959	−1.57483	−0.787415	−	0.616423i	$-0.788581\pi$
$701$	−41.6959	−1.57483	−0.787415	+	0.616423i	$0.788581\pi$
$702$	0	0
$703$	9.11948	0.343948
$704$	2.79094	0.105188
$705$	12.5732	0.473533
$706$	4.29003	0.161457
$707$	15.5464	0.584684
$708$	10.8238	0.406784
$709$	−0.0109463	−0.000411095 0	−0.000205548	−	1.00000i	$-0.500065\pi$
$709$	−0.0109463	−0.000411095 0	−0.000205548		1.00000i	$0.500065\pi$
$710$	1.43880	0.0539972
$711$	18.3280	0.687355
$712$	0.546342	0.0204750
$713$	23.8797	0.894301
$714$	−0.223258	−0.00835521
$715$	0	0
$716$	13.0951	0.489388
$717$	−12.8543	−0.480054
$718$	−2.32557	−0.0867894
$719$	−25.4660	−0.949722	−0.474861	−	0.880061i	$-0.657502\pi$
$719$	−25.4660	−0.949722	−0.474861	+	0.880061i	$0.657502\pi$
$720$	17.5789	0.655127
$721$	−10.2982	−0.383523
$722$	−2.03590	−0.0757685
$723$	9.19853	0.342097
$724$	−21.8718	−0.812860
$725$	−17.6235	−0.654521
$726$	0.761613	0.0282661
$727$	23.5565	0.873663	0.436831	−	0.899543i	$-0.356101\pi$
$727$	23.5565	0.873663	0.436831	+	0.899543i	$0.356101\pi$
$728$	0	0
$729$	−10.3760	−0.384297
$730$	0.439053	0.0162501
$731$	2.46282	0.0910905
$732$	−10.4341	−0.385654
$733$	6.23249	0.230202	0.115101	−	0.993354i	$-0.463281\pi$
$733$	6.23249	0.230202	0.115101	+	0.993354i	$0.463281\pi$
$734$	−0.447817	−0.0165292
$735$	0.983005	0.0362587
$736$	−7.27100	−0.268013
$737$	−4.91357	−0.180994
$738$	−1.86632	−0.0687000
$739$	1.29718	0.0477174	0.0238587	−	0.999715i	$-0.492405\pi$
$739$	1.29718	0.0477174	0.0238587	+	0.999715i	$0.492405\pi$
$740$	21.1699	0.778221
$741$	0	0
$742$	−0.165025	−0.00605825
$743$	−6.06942	−0.222665	−0.111333	−	0.993783i	$-0.535512\pi$
$743$	−6.06942	−0.222665	−0.111333	+	0.993783i	$0.535512\pi$
$744$	−1.31219	−0.0481073
$745$	−15.6545	−0.573537
$746$	−0.422796	−0.0154797
$747$	−1.50976	−0.0552393
$748$	−2.30619	−0.0843227
$749$	13.1244	0.479555
$750$	−0.845960	−0.0308901
$751$	−36.6046	−1.33572	−0.667860	−	0.744287i	$-0.732790\pi$
$751$	−36.6046	−1.33572	−0.667860	+	0.744287i	$0.732790\pi$
$752$	50.0531	1.82525
$753$	−13.1346	−0.478650
$754$	0	0
$755$	23.6566	0.860952
$756$	6.54488	0.238035
$757$	11.6798	0.424510	0.212255	−	0.977214i	$-0.431919\pi$
$757$	11.6798	0.424510	0.212255	+	0.977214i	$0.431919\pi$
$758$	−3.01096	−0.109363
$759$	−1.07924	−0.0391739
$760$	1.16928	0.0424144
$761$	39.7688	1.44162	0.720810	−	0.693133i	$-0.243770\pi$
$761$	39.7688	1.44162	0.720810	+	0.693133i	$0.243770\pi$
$762$	−0.565394	−0.0204821
$763$	−10.4459	−0.378167
$764$	−11.7783	−0.426125
$765$	−14.3098	−0.517372
$766$	−2.70393	−0.0976970
$767$	0	0
$768$	−8.64915	−0.312099
$769$	9.95937	0.359144	0.179572	−	0.983745i	$-0.442529\pi$
$769$	9.95937	0.359144	0.179572	+	0.983745i	$0.442529\pi$
$770$	−0.0740858	−0.00266987
$771$	−11.8863	−0.428073
$772$	−8.33112	−0.299843
$773$	12.7518	0.458649	0.229324	−	0.973350i	$-0.426348\pi$
$773$	12.7518	0.458649	0.229324	+	0.973350i	$0.426348\pi$
$774$	0.247608	0.00890007
$775$	10.1006	0.362825
$776$	−3.80296	−0.136518
$777$	3.67766	0.131935
$778$	−1.60517	−0.0575482
$779$	8.41411	0.301467
$780$	0	0
$781$	2.58192	0.0923882
$782$	1.94897	0.0696949
$783$	27.0186	0.965568
$784$	3.91329	0.139760
$785$	29.0069	1.03530
$786$	−1.32487	−0.0472566
$787$	−8.68773	−0.309684	−0.154842	−	0.987939i	$-0.549487\pi$
$787$	−8.68773	−0.309684	−0.154842	+	0.987939i	$0.549487\pi$
$788$	11.4861	0.409174
$789$	17.2010	0.612373
$790$	1.39952	0.0497926
$791$	−4.95262	−0.176095
$792$	−0.465413	−0.0165377
$793$	0	0
$794$	3.10929	0.110345
$795$	1.34779	0.0478013
$796$	−23.7463	−0.841664
$797$	38.7438	1.37237	0.686187	−	0.727425i	$-0.259283\pi$
$797$	38.7438	1.37237	0.686187	+	0.727425i	$0.259283\pi$
$798$	0.101196	0.00358229
$799$	−40.7449	−1.44145
$800$	−3.07549	−0.108735
$801$	3.03063	0.107082
$802$	2.11358	0.0746331
$803$	0.787876	0.0278036
$804$	15.5802	0.549471
$805$	−8.58130	−0.302451
$806$	0	0
$807$	−16.2554	−0.572218
$808$	7.45757	0.262356
$809$	28.8550	1.01449	0.507244	−	0.861802i	$-0.330664\pi$
$809$	28.8550	1.01449	0.507244	+	0.861802i	$0.330664\pi$
$810$	−1.23200	−0.0432882
$811$	−12.3917	−0.435131	−0.217566	−	0.976046i	$-0.569812\pi$
$811$	−12.3917	−0.435131	−0.217566	+	0.976046i	$0.569812\pi$
$812$	16.2745	0.571123
$813$	17.1479	0.601405
$814$	−0.277173	−0.00971491
$815$	19.9081	0.697351
$816$	7.25884	0.254110
$817$	−1.11632	−0.0390549
$818$	1.74861	0.0611388
$819$	0	0
$820$	19.5324	0.682103
$821$	−41.0238	−1.43174	−0.715870	−	0.698233i	$-0.753970\pi$
$821$	−41.0238	−1.43174	−0.715870	+	0.698233i	$0.753970\pi$
$822$	1.27733	0.0445519
$823$	−2.13613	−0.0744608	−0.0372304	−	0.999307i	$-0.511854\pi$
$823$	−2.13613	−0.0744608	−0.0372304	+	0.999307i	$0.511854\pi$
$824$	−4.93999	−0.172093
$825$	−0.456496	−0.0158932
$826$	−1.12681	−0.0392066
$827$	−8.54938	−0.297291	−0.148645	−	0.988891i	$-0.547491\pi$
$827$	−8.54938	−0.297291	−0.148645	+	0.988891i	$0.547491\pi$
$828$	−26.8563	−0.933320
$829$	−14.7569	−0.512528	−0.256264	−	0.966607i	$-0.582492\pi$
$829$	−14.7569	−0.512528	−0.256264	+	0.966607i	$0.582492\pi$
$830$	−0.115284	−0.00400158
$831$	−3.99367	−0.138539
$832$	0	0
$833$	−3.18555	−0.110373
$834$	−0.368004	−0.0127429
$835$	−7.28758	−0.252197
$836$	1.04532	0.0361532
$837$	−15.4853	−0.535250
$838$	−0.553887	−0.0191337
$839$	−26.9716	−0.931164	−0.465582	−	0.885005i	$-0.654155\pi$
$839$	−26.9716	−0.931164	−0.465582	+	0.885005i	$0.654155\pi$
$840$	0.471544	0.0162698
$841$	38.1845	1.31671
$842$	−2.31867	−0.0799068
$843$	−16.9412	−0.583487
$844$	16.3525	0.562877
$845$	0	0
$846$	−4.09643	−0.140838
$847$	10.8671	0.373396
$848$	5.36549	0.184252
$849$	−6.76053	−0.232021
$850$	0.824374	0.0282758
$851$	−32.1047	−1.10054
$852$	−8.18686	−0.280477
$853$	−25.6332	−0.877665	−0.438832	−	0.898569i	$-0.644608\pi$
$853$	−25.6332	−0.877665	−0.438832	+	0.898569i	$0.644608\pi$
$854$	1.08623	0.0371700
$855$	6.48618	0.221823
$856$	6.29572	0.215183
$857$	11.7653	0.401894	0.200947	−	0.979602i	$-0.435598\pi$
$857$	11.7653	0.401894	0.200947	+	0.979602i	$0.435598\pi$
$858$	0	0
$859$	−21.7761	−0.742992	−0.371496	−	0.928435i	$-0.621155\pi$
$859$	−21.7761	−0.742992	−0.371496	+	0.928435i	$0.621155\pi$
$860$	−2.59141	−0.0883663
$861$	3.39320	0.115640
$862$	3.41402	0.116282
$863$	41.0575	1.39761	0.698807	−	0.715310i	$-0.253715\pi$
$863$	41.0575	1.39761	0.698807	+	0.715310i	$0.253715\pi$
$864$	4.71504	0.160409
$865$	−21.1353	−0.718623
$866$	−1.50694	−0.0512079
$867$	3.99003	0.135509
$868$	−9.32746	−0.316594
$869$	2.51142	0.0851942
$870$	0.969778	0.0328785
$871$	0	0
$872$	−5.01085	−0.169689
$873$	−21.0955	−0.713975
$874$	−0.883404	−0.0298816
$875$	−12.0705	−0.408059
$876$	−2.49824	−0.0844076
$877$	6.89112	0.232696	0.116348	−	0.993208i	$-0.462881\pi$
$877$	6.89112	0.232696	0.116348	+	0.993208i	$0.462881\pi$
$878$	3.81870	0.128875
$879$	−10.3582	−0.349372
$880$	2.40877	0.0811996
$881$	−10.6458	−0.358665	−0.179332	−	0.983789i	$-0.557394\pi$
$881$	−10.6458	−0.358665	−0.179332	+	0.983789i	$0.557394\pi$
$882$	−0.320270	−0.0107841
$883$	−21.3844	−0.719641	−0.359821	−	0.933022i	$-0.617162\pi$
$883$	−21.3844	−0.719641	−0.359821	+	0.933022i	$0.617162\pi$
$884$	0	0
$885$	9.20286	0.309351
$886$	0.208281	0.00699732
$887$	−34.1150	−1.14547	−0.572735	−	0.819740i	$-0.694118\pi$
$887$	−34.1150	−1.14547	−0.572735	+	0.819740i	$0.694118\pi$
$888$	1.76416	0.0592013
$889$	−8.06731	−0.270569
$890$	0.231417	0.00775712
$891$	−2.21082	−0.0740653
$892$	30.3813	1.01724
$893$	18.4684	0.618020
$894$	−0.649901	−0.0217359
$895$	11.1340	0.372169
$896$	3.78208	0.126350
$897$	0	0
$898$	1.27056	0.0423992
$899$	−38.5057	−1.28424
$900$	−11.3597	−0.378655
$901$	−4.36769	−0.145509
$902$	−0.255734	−0.00851502
$903$	−0.450183	−0.0149811
$904$	−2.37575	−0.0790163
$905$	−18.5963	−0.618163
$906$	0.982110	0.0326284
$907$	42.1515	1.39962	0.699810	−	0.714329i	$-0.253268\pi$
$907$	42.1515	1.39962	0.699810	+	0.714329i	$0.253268\pi$
$908$	13.8086	0.458254
$909$	41.3681	1.37209
$910$	0	0
$911$	20.9947	0.695584	0.347792	−	0.937572i	$-0.386932\pi$
$911$	20.9947	0.695584	0.347792	+	0.937572i	$0.386932\pi$
$912$	−3.29020	−0.108949
$913$	−0.206877	−0.00684663
$914$	0.956734	0.0316459
$915$	−8.87147	−0.293282
$916$	−54.4466	−1.79897
$917$	−18.9039	−0.624261
$918$	−1.26385	−0.0417132
$919$	−14.2940	−0.471515	−0.235757	−	0.971812i	$-0.575757\pi$
$919$	−14.2940	−0.471515	−0.235757	+	0.971812i	$0.575757\pi$
$920$	−4.11642	−0.135714
$921$	5.28701	0.174213
$922$	1.31094	0.0431736
$923$	0	0
$924$	0.421553	0.0138681
$925$	−13.5797	−0.446497
$926$	4.31162	0.141689
$927$	−27.4027	−0.900024
$928$	11.7244	0.384872
$929$	6.80723	0.223338	0.111669	−	0.993745i	$-0.464380\pi$
$929$	6.80723	0.223338	0.111669	+	0.993745i	$0.464380\pi$
$930$	−0.555812	−0.0182258
$931$	1.44391	0.0473221
$932$	13.6074	0.445724
$933$	−0.914621	−0.0299433
$934$	2.39496	0.0783655
$935$	−1.96082	−0.0641256
$936$	0	0
$937$	−5.22890	−0.170821	−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890	−0.170821	−0.0854104	+	0.996346i	$0.527220\pi$
$938$	−1.62196	−0.0529590
$939$	−12.0087	−0.391890
$940$	42.8723	1.39834
$941$	−56.4403	−1.83990	−0.919951	−	0.392033i	$-0.871772\pi$
$941$	−56.4403	−1.83990	−0.919951	+	0.392033i	$0.871772\pi$
$942$	1.20423	0.0392359
$943$	−29.6215	−0.964609
$944$	36.6361	1.19240
$945$	5.56473	0.181021
$946$	0.0339287	0.00110312
$947$	−5.85027	−0.190108	−0.0950541	−	0.995472i	$-0.530302\pi$
$947$	−5.85027	−0.190108	−0.0950541	+	0.995472i	$0.530302\pi$
$948$	−7.96334	−0.258637
$949$	0	0
$950$	−0.373662	−0.0121232
$951$	−17.7852	−0.576726
$952$	−1.52809	−0.0495258
$953$	−21.7484	−0.704499	−0.352249	−	0.935906i	$-0.614583\pi$
$953$	−21.7484	−0.704499	−0.352249	+	0.935906i	$0.614583\pi$
$954$	−0.439121	−0.0142171
$955$	−10.0144	−0.324059
$956$	−43.8310	−1.41760
$957$	1.74026	0.0562546
$958$	3.16429	0.102233
$959$	18.2255	0.588532
$960$	−7.52433	−0.242847
$961$	−8.93110	−0.288100
$962$	0	0
$963$	34.9232	1.12538
$964$	31.3654	1.01021
$965$	−7.08346	−0.228025
$966$	−0.356255	−0.0114623
$967$	13.3251	0.428507	0.214253	−	0.976778i	$-0.431268\pi$
$967$	13.3251	0.428507	0.214253	+	0.976778i	$0.431268\pi$
$968$	5.21288	0.167548
$969$	2.67833	0.0860404
$970$	−1.61084	−0.0517210
$971$	7.46185	0.239462	0.119731	−	0.992806i	$-0.461797\pi$
$971$	7.46185	0.239462	0.119731	+	0.992806i	$0.461797\pi$
$972$	26.6448	0.854633
$973$	−5.25085	−0.168335
$974$	0.767850	0.0246035
$975$	0	0
$976$	−35.3168	−1.13046
$977$	10.9605	0.350656	0.175328	−	0.984510i	$-0.443901\pi$
$977$	10.9605	0.350656	0.175328	+	0.984510i	$0.443901\pi$
$978$	0.826490	0.0264282
$979$	0.415276	0.0132723
$980$	3.35188	0.107072
$981$	−27.7959	−0.887453
$982$	−0.357189	−0.0113984
$983$	−16.1441	−0.514918	−0.257459	−	0.966289i	$-0.582885\pi$
$983$	−16.1441	−0.514918	−0.257459	+	0.966289i	$0.582885\pi$
$984$	1.62771	0.0518893
$985$	9.76593	0.311168
$986$	−3.14268	−0.100083
$987$	7.44783	0.237067
$988$	0	0
$989$	3.92994	0.124965
$990$	−0.197138	−0.00626544
$991$	6.71496	0.213308	0.106654	−	0.994296i	$-0.465986\pi$
$991$	6.71496	0.213308	0.106654	+	0.994296i	$0.465986\pi$
$992$	−6.71965	−0.213349
$993$	15.0540	0.477725
$994$	0.852287	0.0270329
$995$	−20.1901	−0.640068
$996$	0.655975	0.0207854
$997$	−18.4411	−0.584037	−0.292018	−	0.956413i	$-0.594327\pi$
$997$	−18.4411	−0.584037	−0.292018	+	0.956413i	$0.594327\pi$
$998$	−3.38609	−0.107185
$999$	20.8190	0.658684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.p.1.3		6
7.6	odd	2		8281.2.a.ch.1.3		6
13.5	odd	4		1183.2.c.i.337.6		12
13.6	odd	12		91.2.q.a.36.3	✓	12
13.8	odd	4		1183.2.c.i.337.7		12
13.11	odd	12		91.2.q.a.43.3	yes	12
13.12	even	2		1183.2.a.m.1.4		6
39.11	even	12		819.2.ct.a.316.4		12
39.32	even	12		819.2.ct.a.127.4		12
52.11	even	12		1456.2.cc.c.225.3		12
52.19	even	12		1456.2.cc.c.673.3		12
91.6	even	12		637.2.q.h.491.3		12
91.11	odd	12		637.2.u.h.30.4		12
91.19	even	12		637.2.u.i.361.4		12
91.24	even	12		637.2.u.i.30.4		12
91.32	odd	12		637.2.k.h.569.3		12
91.37	odd	12		637.2.k.h.459.4		12
91.45	even	12		637.2.k.g.569.3		12
91.58	odd	12		637.2.u.h.361.4		12
91.76	even	12		637.2.q.h.589.3		12
91.89	even	12		637.2.k.g.459.4		12
91.90	odd	2		8281.2.a.by.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	13.6	odd	12
91.2.q.a.43.3	yes	12	13.11	odd	12
637.2.k.g.459.4		12	91.89	even	12
637.2.k.g.569.3		12	91.45	even	12
637.2.k.h.459.4		12	91.37	odd	12
637.2.k.h.569.3		12	91.32	odd	12
637.2.q.h.491.3		12	91.6	even	12
637.2.q.h.589.3		12	91.76	even	12
637.2.u.h.30.4		12	91.11	odd	12
637.2.u.h.361.4		12	91.58	odd	12
637.2.u.i.30.4		12	91.24	even	12
637.2.u.i.361.4		12	91.19	even	12
819.2.ct.a.127.4		12	39.32	even	12
819.2.ct.a.316.4		12	39.11	even	12
1183.2.a.m.1.4		6	13.12	even	2
1183.2.a.p.1.3		6	1.1	even	1	trivial
1183.2.c.i.337.6		12	13.5	odd	4
1183.2.c.i.337.7		12	13.8	odd	4
1456.2.cc.c.225.3		12	52.11	even	12
1456.2.cc.c.673.3		12	52.19	even	12
8281.2.a.by.1.4		6	91.90	odd	2
8281.2.a.ch.1.3		6	7.6	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} +O(q^{10})\)	\(q+0.120360 q^{2} -0.582292 q^{3} -1.98551 q^{4} -1.68817 q^{5} -0.0700846 q^{6} -1.00000 q^{7} -0.479696 q^{8} -2.66094 q^{9} -0.203187 q^{10} -0.364618 q^{11} +1.15615 q^{12} -0.120360 q^{14} +0.983005 q^{15} +3.91329 q^{16} -3.18555 q^{17} -0.320270 q^{18} +1.44391 q^{19} +3.35188 q^{20} +0.582292 q^{21} -0.0438854 q^{22} -5.08321 q^{23} +0.279323 q^{24} -2.15010 q^{25} +3.29632 q^{27} +1.98551 q^{28} +8.19662 q^{29} +0.118314 q^{30} -4.69775 q^{31} +1.43040 q^{32} +0.212314 q^{33} -0.383412 q^{34} +1.68817 q^{35} +5.28332 q^{36} +6.31584 q^{37} +0.173789 q^{38} +0.809806 q^{40} +5.82732 q^{41} +0.0700846 q^{42} -0.773122 q^{43} +0.723954 q^{44} +4.49210 q^{45} -0.611815 q^{46} +12.7905 q^{47} -2.27868 q^{48} +1.00000 q^{49} -0.258786 q^{50} +1.85492 q^{51} +1.37110 q^{53} +0.396744 q^{54} +0.615536 q^{55} +0.479696 q^{56} -0.840776 q^{57} +0.986544 q^{58} +9.36197 q^{59} -1.95177 q^{60} -9.02484 q^{61} -0.565421 q^{62} +2.66094 q^{63} -7.65442 q^{64} +0.0255541 q^{66} +13.4759 q^{67} +6.32495 q^{68} +2.95991 q^{69} +0.203187 q^{70} -7.08115 q^{71} +1.27644 q^{72} -2.16083 q^{73} +0.760173 q^{74} +1.25198 q^{75} -2.86690 q^{76} +0.364618 q^{77} -6.88781 q^{79} -6.60628 q^{80} +6.06339 q^{81} +0.701376 q^{82} +0.567380 q^{83} -1.15615 q^{84} +5.37773 q^{85} -0.0930528 q^{86} -4.77282 q^{87} +0.174906 q^{88} -1.13893 q^{89} +0.540669 q^{90} +10.0928 q^{92} +2.73547 q^{93} +1.53947 q^{94} -2.43755 q^{95} -0.832908 q^{96} +7.92785 q^{97} +0.120360 q^{98} +0.970225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9	\( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9} + 12 q^{10} + 4 q^{11} + 2 q^{12} - 4 q^{14} + 20 q^{15} + 8 q^{16} - 4 q^{17} - 16 q^{18} + 2 q^{19} + 26 q^{20} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 10 q^{25} + 6 q^{27} - 4 q^{28} - 8 q^{29} + 8 q^{30} - 14 q^{31} + 8 q^{32} + 16 q^{33} - 2 q^{34} - 6 q^{35} - 10 q^{36} + 12 q^{37} - 2 q^{38} + 46 q^{40} + 28 q^{41} - 4 q^{42} + 2 q^{43} - 20 q^{44} + 16 q^{45} + 20 q^{46} + 14 q^{47} + 2 q^{48} + 6 q^{49} + 32 q^{50} - 26 q^{51} - 22 q^{53} + 14 q^{54} + 6 q^{55} - 12 q^{56} + 4 q^{58} - 2 q^{59} - 14 q^{61} - 4 q^{62} - 4 q^{63} + 26 q^{64} - 26 q^{66} + 24 q^{67} + 8 q^{68} + 4 q^{69} - 12 q^{70} + 4 q^{71} + 8 q^{72} + 36 q^{73} - 6 q^{74} + 46 q^{75} - 26 q^{76} - 4 q^{77} - 28 q^{79} + 36 q^{80} - 2 q^{81} + 14 q^{82} + 26 q^{83} - 2 q^{84} - 20 q^{85} - 24 q^{86} + 2 q^{87} - 14 q^{88} + 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} - 42 q^{96} + 24 q^{97} + 4 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q + 4 * q^2 + 4 * q^4 + 6 * q^5 + 4 * q^6 - 6 * q^7 + 12 * q^8 + 4 * q^9 + 12 * q^10 + 4 * q^11 + 2 * q^12 - 4 * q^14 + 20 * q^15 + 8 * q^16 - 4 * q^17 - 16 * q^18 + 2 * q^19 + 26 * q^20 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 10 * q^25 + 6 * q^27 - 4 * q^28 - 8 * q^29 + 8 * q^30 - 14 * q^31 + 8 * q^32 + 16 * q^33 - 2 * q^34 - 6 * q^35 - 10 * q^36 + 12 * q^37 - 2 * q^38 + 46 * q^40 + 28 * q^41 - 4 * q^42 + 2 * q^43 - 20 * q^44 + 16 * q^45 + 20 * q^46 + 14 * q^47 + 2 * q^48 + 6 * q^49 + 32 * q^50 - 26 * q^51 - 22 * q^53 + 14 * q^54 + 6 * q^55 - 12 * q^56 + 4 * q^58 - 2 * q^59 - 14 * q^61 - 4 * q^62 - 4 * q^63 + 26 * q^64 - 26 * q^66 + 24 * q^67 + 8 * q^68 + 4 * q^69 - 12 * q^70 + 4 * q^71 + 8 * q^72 + 36 * q^73 - 6 * q^74 + 46 * q^75 - 26 * q^76 - 4 * q^77 - 28 * q^79 + 36 * q^80 - 2 * q^81 + 14 * q^82 + 26 * q^83 - 2 * q^84 - 20 * q^85 - 24 * q^86 + 2 * q^87 - 14 * q^88 + 42 * q^89 - 12 * q^90 + 12 * q^92 - 4 * q^94 - 22 * q^95 - 42 * q^96 + 24 * q^97 + 4 * q^98 + 16 * q^99

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