LMFDB - Embedded newform 1183.2.a.p.1.5

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			1.5
Root			$-1.10939$ 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)

$f(q)$	$=$	$q+2.10939 q^{2} +2.26165 q^{3} +2.44952 q^{4} +3.60178 q^{5} +4.77070 q^{6} -1.00000 q^{7} +0.948212 q^{8} +2.11505 q^{9} +O(q^{10})$	\(q+2.10939 q^{2} +2.26165 q^{3} +2.44952 q^{4} +3.60178 q^{5} +4.77070 q^{6} -1.00000 q^{7} +0.948212 q^{8} +2.11505 q^{9} +7.59755 q^{10} -0.886384 q^{11} +5.53995 q^{12} -2.10939 q^{14} +8.14596 q^{15} -2.89889 q^{16} -4.96016 q^{17} +4.46147 q^{18} -2.37878 q^{19} +8.82263 q^{20} -2.26165 q^{21} -1.86973 q^{22} -3.85851 q^{23} +2.14452 q^{24} +7.97282 q^{25} -2.00144 q^{27} -2.44952 q^{28} +1.28197 q^{29} +17.1830 q^{30} -8.46921 q^{31} -8.01131 q^{32} -2.00469 q^{33} -10.4629 q^{34} -3.60178 q^{35} +5.18087 q^{36} +9.63812 q^{37} -5.01776 q^{38} +3.41525 q^{40} +12.0841 q^{41} -4.77070 q^{42} -3.64250 q^{43} -2.17122 q^{44} +7.61796 q^{45} -8.13910 q^{46} -2.98229 q^{47} -6.55628 q^{48} +1.00000 q^{49} +16.8178 q^{50} -11.2181 q^{51} +4.92032 q^{53} -4.22181 q^{54} -3.19256 q^{55} -0.948212 q^{56} -5.37995 q^{57} +2.70418 q^{58} +7.32746 q^{59} +19.9537 q^{60} -1.53926 q^{61} -17.8648 q^{62} -2.11505 q^{63} -11.1012 q^{64} -4.22867 q^{66} +8.42649 q^{67} -12.1500 q^{68} -8.72660 q^{69} -7.59755 q^{70} +6.44888 q^{71} +2.00552 q^{72} +7.14859 q^{73} +20.3305 q^{74} +18.0317 q^{75} -5.82686 q^{76} +0.886384 q^{77} +0.757551 q^{79} -10.4412 q^{80} -10.8717 q^{81} +25.4901 q^{82} +4.76766 q^{83} -5.53995 q^{84} -17.8654 q^{85} -7.68344 q^{86} +2.89937 q^{87} -0.840480 q^{88} -3.61884 q^{89} +16.0692 q^{90} -9.45150 q^{92} -19.1544 q^{93} -6.29081 q^{94} -8.56783 q^{95} -18.1188 q^{96} +0.463300 q^{97} +2.10939 q^{98} -1.87475 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.10939	1.49156	0.745781	−	0.666191i	$-0.232076\pi$
$2$	2.10939	1.49156	0.745781	+	0.666191i	$0.232076\pi$
$3$	2.26165	1.30576	0.652882	−	0.757460i	$-0.273560\pi$
$3$	2.26165	1.30576	0.652882	+	0.757460i	$0.273560\pi$
$4$	2.44952	1.22476
$5$	3.60178	1.61076	0.805382	−	0.592756i	$-0.201960\pi$
$5$	3.60178	1.61076	0.805382	+	0.592756i	$0.201960\pi$
$6$	4.77070	1.94763
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.948212	0.335243
$9$	2.11505	0.705018
$10$	7.59755	2.40256
$11$	−0.886384	−0.267255	−0.133627	−	0.991032i	$-0.542663\pi$
$11$	−0.886384	−0.267255	−0.133627	+	0.991032i	$0.542663\pi$
$12$	5.53995	1.59925
$13$	0	0
$13$	0	0
$14$	−2.10939	−0.563758
$15$	8.14596	2.10328
$16$	−2.89889	−0.724723
$17$	−4.96016	−1.20302	−0.601508	−	0.798867i	$-0.705433\pi$
$17$	−4.96016	−1.20302	−0.601508	+	0.798867i	$0.705433\pi$
$18$	4.46147	1.05158
$19$	−2.37878	−0.545729	−0.272864	−	0.962053i	$-0.587971\pi$
$19$	−2.37878	−0.545729	−0.272864	+	0.962053i	$0.587971\pi$
$20$	8.82263	1.97280
$21$	−2.26165	−0.493532
$22$	−1.86973	−0.398628
$23$	−3.85851	−0.804555	−0.402278	−	0.915518i	$-0.631781\pi$
$23$	−3.85851	−0.804555	−0.402278	+	0.915518i	$0.631781\pi$
$24$	2.14452	0.437749
$25$	7.97282	1.59456
$26$	0	0
$27$	−2.00144	−0.385177
$28$	−2.44952	−0.462916
$29$	1.28197	0.238056	0.119028	−	0.992891i	$-0.462022\pi$
$29$	1.28197	0.238056	0.119028	+	0.992891i	$0.462022\pi$
$30$	17.1830	3.13717
$31$	−8.46921	−1.52111	−0.760557	−	0.649271i	$-0.775074\pi$
$31$	−8.46921	−1.52111	−0.760557	+	0.649271i	$0.775074\pi$
$32$	−8.01131	−1.41621
$33$	−2.00469	−0.348972
$34$	−10.4629	−1.79437
$35$	−3.60178	−0.608812
$36$	5.18087	0.863478
$37$	9.63812	1.58450	0.792249	−	0.610198i	$-0.208910\pi$
$37$	9.63812	1.58450	0.792249	+	0.610198i	$0.208910\pi$
$38$	−5.01776	−0.813988
$39$	0	0
$40$	3.41525	0.539998
$41$	12.0841	1.88722	0.943612	−	0.331053i	$-0.107404\pi$
$41$	12.0841	1.88722	0.943612	+	0.331053i	$0.107404\pi$
$42$	−4.77070	−0.736134
$43$	−3.64250	−0.555476	−0.277738	−	0.960657i	$-0.589585\pi$
$43$	−3.64250	−0.555476	−0.277738	+	0.960657i	$0.589585\pi$
$44$	−2.17122	−0.327323
$45$	7.61796	1.13562
$46$	−8.13910	−1.20004
$47$	−2.98229	−0.435012	−0.217506	−	0.976059i	$-0.569792\pi$
$47$	−2.98229	−0.435012	−0.217506	+	0.976059i	$0.569792\pi$
$48$	−6.55628	−0.946317
$49$	1.00000	0.142857
$50$	16.8178	2.37839
$51$	−11.2181	−1.57085
$52$	0	0
$53$	4.92032	0.675858	0.337929	−	0.941172i	$-0.390274\pi$
$53$	4.92032	0.675858	0.337929	+	0.941172i	$0.390274\pi$
$54$	−4.22181	−0.574516
$55$	−3.19256	−0.430485
$56$	−0.948212	−0.126710
$57$	−5.37995	−0.712592
$58$	2.70418	0.355076
$59$	7.32746	0.953954	0.476977	−	0.878916i	$-0.341732\pi$
$59$	7.32746	0.953954	0.476977	+	0.878916i	$0.341732\pi$
$60$	19.9537	2.57601
$61$	−1.53926	−0.197082	−0.0985412	−	0.995133i	$-0.531418\pi$
$61$	−1.53926	−0.197082	−0.0985412	+	0.995133i	$0.531418\pi$
$62$	−17.8648	−2.26884
$63$	−2.11505	−0.266472
$64$	−11.1012	−1.38765
$65$	0	0
$66$	−4.22867	−0.520513
$67$	8.42649	1.02946	0.514730	−	0.857352i	$-0.327892\pi$
$67$	8.42649	1.02946	0.514730	+	0.857352i	$0.327892\pi$
$68$	−12.1500	−1.47341
$69$	−8.72660	−1.05056
$70$	−7.59755	−0.908081
$71$	6.44888	0.765342	0.382671	−	0.923885i	$-0.375004\pi$
$71$	6.44888	0.765342	0.382671	+	0.923885i	$0.375004\pi$
$72$	2.00552	0.236353
$73$	7.14859	0.836679	0.418340	−	0.908291i	$-0.362612\pi$
$73$	7.14859	0.836679	0.418340	+	0.908291i	$0.362612\pi$
$74$	20.3305	2.36338
$75$	18.0317	2.08212
$76$	−5.82686	−0.668386
$77$	0.886384	0.101013
$78$	0	0
$79$	0.757551	0.0852311	0.0426156	−	0.999092i	$-0.486431\pi$
$79$	0.757551	0.0852311	0.0426156	+	0.999092i	$0.486431\pi$
$80$	−10.4412	−1.16736
$81$	−10.8717	−1.20797
$82$	25.4901	2.81491
$83$	4.76766	0.523319	0.261659	−	0.965160i	$-0.415730\pi$
$83$	4.76766	0.523319	0.261659	+	0.965160i	$0.415730\pi$
$84$	−5.53995	−0.604458
$85$	−17.8654	−1.93778
$86$	−7.68344	−0.828527
$87$	2.89937	0.310845
$88$	−0.840480	−0.0895955
$89$	−3.61884	−0.383596	−0.191798	−	0.981434i	$-0.561432\pi$
$89$	−3.61884	−0.383596	−0.191798	+	0.981434i	$0.561432\pi$
$90$	16.0692	1.69385
$91$	0	0
$92$	−9.45150	−0.985387
$93$	−19.1544	−1.98622
$94$	−6.29081	−0.648848
$95$	−8.56783	−0.879040
$96$	−18.1188	−1.84924
$97$	0.463300	0.0470409	0.0235205	−	0.999723i	$-0.492513\pi$
$97$	0.463300	0.0470409	0.0235205	+	0.999723i	$0.492513\pi$
$98$	2.10939	0.213080
$99$	−1.87475	−0.188419
$100$	19.5296	1.95296
$101$	5.82303	0.579413	0.289707	−	0.957115i	$-0.406442\pi$
$101$	5.82303	0.579413	0.289707	+	0.957115i	$0.406442\pi$
$102$	−23.6634	−2.34303
$103$	8.23888	0.811801	0.405901	−	0.913917i	$-0.366958\pi$
$103$	8.23888	0.811801	0.405901	+	0.913917i	$0.366958\pi$
$104$	0	0
$105$	−8.14596	−0.794964
$106$	10.3789	1.00809
$107$	−3.83260	−0.370511	−0.185256	−	0.982690i	$-0.559311\pi$
$107$	−3.83260	−0.370511	−0.185256	+	0.982690i	$0.559311\pi$
$108$	−4.90256	−0.471749
$109$	10.4180	0.997867	0.498934	−	0.866640i	$-0.333725\pi$
$109$	10.4180	0.997867	0.498934	+	0.866640i	$0.333725\pi$
$110$	−6.73435	−0.642095
$111$	21.7980	2.06898
$112$	2.89889	0.273920
$113$	−4.91011	−0.461904	−0.230952	−	0.972965i	$-0.574184\pi$
$113$	−4.91011	−0.461904	−0.230952	+	0.972965i	$0.574184\pi$
$114$	−11.3484	−1.06288
$115$	−13.8975	−1.29595
$116$	3.14022	0.291562
$117$	0	0
$118$	15.4565	1.42288
$119$	4.96016	0.454697
$120$	7.72409	0.705110
$121$	−10.2143	−0.928575
$122$	−3.24690	−0.293961
$123$	27.3301	2.46427
$124$	−20.7455	−1.86300
$125$	10.7074	0.957702
$126$	−4.46147	−0.397459
$127$	−12.3102	−1.09235	−0.546175	−	0.837671i	$-0.683917\pi$
$127$	−12.3102	−1.09235	−0.546175	+	0.837671i	$0.683917\pi$
$128$	−7.39409	−0.653551
$129$	−8.23805	−0.725320
$130$	0	0
$131$	−8.20265	−0.716669	−0.358335	−	0.933593i	$-0.616655\pi$
$131$	−8.20265	−0.716669	−0.358335	+	0.933593i	$0.616655\pi$
$132$	−4.91053	−0.427406
$133$	2.37878	0.206266
$134$	17.7747	1.53550
$135$	−7.20874	−0.620429
$136$	−4.70328	−0.403303
$137$	7.45555	0.636971	0.318485	−	0.947928i	$-0.396826\pi$
$137$	7.45555	0.636971	0.318485	+	0.947928i	$0.396826\pi$
$138$	−18.4078	−1.56697
$139$	16.6806	1.41483	0.707413	−	0.706800i	$-0.249862\pi$
$139$	16.6806	1.41483	0.707413	+	0.706800i	$0.249862\pi$
$140$	−8.82263	−0.745648
$141$	−6.74490	−0.568023
$142$	13.6032	1.14156
$143$	0	0
$144$	−6.13131	−0.510943
$145$	4.61738	0.383453
$146$	15.0792	1.24796
$147$	2.26165	0.186538
$148$	23.6088	1.94063
$149$	2.52163	0.206580	0.103290	−	0.994651i	$-0.467063\pi$
$149$	2.52163	0.206580	0.103290	+	0.994651i	$0.467063\pi$
$150$	38.0359	3.10562
$151$	15.8972	1.29370	0.646849	−	0.762618i	$-0.276086\pi$
$151$	15.8972	1.29370	0.646849	+	0.762618i	$0.276086\pi$
$152$	−2.25558	−0.182952
$153$	−10.4910	−0.848148
$154$	1.86973	0.150667
$155$	−30.5042	−2.45016
$156$	0	0
$157$	12.9831	1.03616	0.518082	−	0.855331i	$-0.326646\pi$
$157$	12.9831	1.03616	0.518082	+	0.855331i	$0.326646\pi$
$158$	1.59797	0.127128
$159$	11.1280	0.882511
$160$	−28.8550	−2.28119
$161$	3.85851	0.304093
$162$	−22.9327	−1.80176
$163$	−2.31948	−0.181676	−0.0908378	−	0.995866i	$-0.528954\pi$
$163$	−2.31948	−0.181676	−0.0908378	+	0.995866i	$0.528954\pi$
$164$	29.6003	2.31140
$165$	−7.22045	−0.562111
$166$	10.0569	0.780563
$167$	13.7918	1.06724	0.533622	−	0.845723i	$-0.320831\pi$
$167$	13.7918	1.06724	0.533622	+	0.845723i	$0.320831\pi$
$168$	−2.14452	−0.165453
$169$	0	0
$170$	−37.6851	−2.89031
$171$	−5.03124	−0.384748
$172$	−8.92237	−0.680324
$173$	−3.68432	−0.280113	−0.140057	−	0.990143i	$-0.544728\pi$
$173$	−3.68432	−0.280113	−0.140057	+	0.990143i	$0.544728\pi$
$174$	6.11590	0.463645
$175$	−7.97282	−0.602688
$176$	2.56953	0.193686
$177$	16.5721	1.24564
$178$	−7.63353	−0.572157
$179$	−5.89277	−0.440446	−0.220223	−	0.975450i	$-0.570678\pi$
$179$	−5.89277	−0.440446	−0.220223	+	0.975450i	$0.570678\pi$
$180$	18.6603	1.39086
$181$	2.11543	0.157239	0.0786193	−	0.996905i	$-0.474949\pi$
$181$	2.11543	0.157239	0.0786193	+	0.996905i	$0.474949\pi$
$182$	0	0
$183$	−3.48127	−0.257343
$184$	−3.65869	−0.269722
$185$	34.7144	2.55225
$186$	−40.4040	−2.96257
$187$	4.39661	0.321512
$188$	−7.30518	−0.532785
$189$	2.00144	0.145583
$190$	−18.0729	−1.31114
$191$	−11.3667	−0.822462	−0.411231	−	0.911531i	$-0.634901\pi$
$191$	−11.3667	−0.822462	−0.411231	+	0.911531i	$0.634901\pi$
$192$	−25.1070	−1.81194
$193$	−14.0894	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$193$	−14.0894	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$194$	0.977279	0.0701645
$195$	0	0
$196$	2.44952	0.174966
$197$	−22.9571	−1.63563	−0.817814	−	0.575482i	$-0.804814\pi$
$197$	−22.9571	−1.63563	−0.817814	+	0.575482i	$0.804814\pi$
$198$	−3.95458	−0.281040
$199$	−3.14985	−0.223287	−0.111643	−	0.993748i	$-0.535611\pi$
$199$	−3.14985	−0.223287	−0.111643	+	0.993748i	$0.535611\pi$
$200$	7.55992	0.534567
$201$	19.0578	1.34423
$202$	12.2830	0.864231
$203$	−1.28197	−0.0899768
$204$	−27.4791	−1.92392
$205$	43.5244	3.03987
$206$	17.3790	1.21085
$207$	−8.16096	−0.567226
$208$	0	0
$209$	2.10851	0.145849
$210$	−17.1830	−1.18574
$211$	−14.8638	−1.02327	−0.511634	−	0.859203i	$-0.670960\pi$
$211$	−14.8638	−1.02327	−0.511634	+	0.859203i	$0.670960\pi$
$212$	12.0524	0.827764
$213$	14.5851	0.999355
$214$	−8.08444	−0.552641
$215$	−13.1195	−0.894741
$216$	−1.89779	−0.129128
$217$	8.46921	0.574927
$218$	21.9757	1.48838
$219$	16.1676	1.09251
$220$	−7.82024	−0.527241
$221$	0	0
$222$	45.9805	3.08601
$223$	4.38089	0.293366	0.146683	−	0.989184i	$-0.453140\pi$
$223$	4.38089	0.293366	0.146683	+	0.989184i	$0.453140\pi$
$224$	8.01131	0.535278
$225$	16.8629	1.12420
$226$	−10.3573	−0.688959
$227$	−13.5663	−0.900428	−0.450214	−	0.892921i	$-0.648652\pi$
$227$	−13.5663	−0.900428	−0.450214	+	0.892921i	$0.648652\pi$
$228$	−13.1783	−0.872754
$229$	−16.5180	−1.09154	−0.545770	−	0.837935i	$-0.683763\pi$
$229$	−16.5180	−1.09154	−0.545770	+	0.837935i	$0.683763\pi$
$230$	−29.3152	−1.93299
$231$	2.00469	0.131899
$232$	1.21558	0.0798068
$233$	−16.5026	−1.08112	−0.540561	−	0.841305i	$-0.681788\pi$
$233$	−16.5026	−1.08112	−0.540561	+	0.841305i	$0.681788\pi$
$234$	0	0
$235$	−10.7416	−0.700702
$236$	17.9488	1.16836
$237$	1.71331	0.111292
$238$	10.4629	0.678210
$239$	−30.4210	−1.96777	−0.983886	−	0.178796i	$-0.942780\pi$
$239$	−30.4210	−1.96777	−0.983886	+	0.178796i	$0.942780\pi$
$240$	−23.6143	−1.52429
$241$	−29.5143	−1.90119	−0.950593	−	0.310440i	$-0.899524\pi$
$241$	−29.5143	−1.90119	−0.950593	+	0.310440i	$0.899524\pi$
$242$	−21.5460	−1.38503
$243$	−18.5837	−1.19214
$244$	−3.77046	−0.241379
$245$	3.60178	0.230109
$246$	57.6497	3.67561
$247$	0	0
$248$	−8.03060	−0.509944
$249$	10.7828	0.683331
$250$	22.5861	1.42847
$251$	−12.9827	−0.819459	−0.409730	−	0.912207i	$-0.634377\pi$
$251$	−12.9827	−0.819459	−0.409730	+	0.912207i	$0.634377\pi$
$252$	−5.18087	−0.326364
$253$	3.42012	0.215021
$254$	−25.9669	−1.62931
$255$	−40.4053	−2.53028
$256$	6.60537	0.412836
$257$	−4.58521	−0.286018	−0.143009	−	0.989721i	$-0.545678\pi$
$257$	−4.58521	−0.286018	−0.143009	+	0.989721i	$0.545678\pi$
$258$	−17.3772	−1.08186
$259$	−9.63812	−0.598884
$260$	0	0
$261$	2.71144	0.167834
$262$	−17.3026	−1.06896
$263$	−2.66499	−0.164330	−0.0821652	−	0.996619i	$-0.526184\pi$
$263$	−2.66499	−0.164330	−0.0821652	+	0.996619i	$0.526184\pi$
$264$	−1.90087	−0.116990
$265$	17.7219	1.08865
$266$	5.01776	0.307659
$267$	−8.18453	−0.500885
$268$	20.6409	1.26084
$269$	11.9256	0.727119	0.363559	−	0.931571i	$-0.381561\pi$
$269$	11.9256	0.727119	0.363559	+	0.931571i	$0.381561\pi$
$270$	−15.2060	−0.925409
$271$	13.0283	0.791414	0.395707	−	0.918377i	$-0.370500\pi$
$271$	13.0283	0.791414	0.395707	+	0.918377i	$0.370500\pi$
$272$	14.3790	0.871853
$273$	0	0
$274$	15.7267	0.950082
$275$	−7.06698	−0.426155
$276$	−21.3760	−1.28668
$277$	21.3649	1.28369	0.641846	−	0.766833i	$-0.278169\pi$
$277$	21.3649	1.28369	0.641846	+	0.766833i	$0.278169\pi$
$278$	35.1858	2.11030
$279$	−17.9128	−1.07241
$280$	−3.41525	−0.204100
$281$	−17.2678	−1.03011	−0.515054	−	0.857158i	$-0.672228\pi$
$281$	−17.2678	−1.03011	−0.515054	+	0.857158i	$0.672228\pi$
$282$	−14.2276	−0.847242
$283$	−21.2402	−1.26260	−0.631299	−	0.775539i	$-0.717478\pi$
$283$	−21.2402	−1.26260	−0.631299	+	0.775539i	$0.717478\pi$
$284$	15.7967	0.937360
$285$	−19.3774	−1.14782
$286$	0	0
$287$	−12.0841	−0.713304
$288$	−16.9444	−0.998456
$289$	7.60320	0.447247
$290$	9.73985	0.571944
$291$	1.04782	0.0614243
$292$	17.5106	1.02473
$293$	−0.420060	−0.0245402	−0.0122701	−	0.999925i	$-0.503906\pi$
$293$	−0.420060	−0.0245402	−0.0122701	+	0.999925i	$0.503906\pi$
$294$	4.77070	0.278233
$295$	26.3919	1.53660
$296$	9.13898	0.531192
$297$	1.77404	0.102940
$298$	5.31910	0.308127
$299$	0	0
$300$	44.1690	2.55010
$301$	3.64250	0.209950
$302$	33.5335	1.92963
$303$	13.1696	0.756577
$304$	6.89581	0.395502
$305$	−5.54409	−0.317453
$306$	−22.1296	−1.26507
$307$	14.0807	0.803628	0.401814	−	0.915721i	$-0.368380\pi$
$307$	14.0807	0.803628	0.401814	+	0.915721i	$0.368380\pi$
$308$	2.17122	0.123717
$309$	18.6335	1.06002
$310$	−64.3453	−3.65456
$311$	10.3848	0.588867	0.294434	−	0.955672i	$-0.404869\pi$
$311$	10.3848	0.588867	0.294434	+	0.955672i	$0.404869\pi$
$312$	0	0
$313$	6.84759	0.387048	0.193524	−	0.981096i	$-0.438008\pi$
$313$	6.84759	0.387048	0.193524	+	0.981096i	$0.438008\pi$
$314$	27.3864	1.54550
$315$	−7.61796	−0.429223
$316$	1.85564	0.104388
$317$	0.701249	0.0393861	0.0196930	−	0.999806i	$-0.493731\pi$
$317$	0.701249	0.0393861	0.0196930	+	0.999806i	$0.493731\pi$
$318$	23.4734	1.31632
$319$	−1.13632	−0.0636217
$320$	−39.9840	−2.23518
$321$	−8.66799	−0.483800
$322$	8.13910	0.453574
$323$	11.7991	0.656520
$324$	−26.6305	−1.47947
$325$	0	0
$326$	−4.89268	−0.270980
$327$	23.5619	1.30298
$328$	11.4583	0.632680
$329$	2.98229	0.164419
$330$	−15.2307	−0.838424
$331$	−4.19865	−0.230778	−0.115389	−	0.993320i	$-0.536812\pi$
$331$	−4.19865	−0.230778	−0.115389	+	0.993320i	$0.536812\pi$
$332$	11.6785	0.640940
$333$	20.3851	1.11710
$334$	29.0923	1.59186
$335$	30.3504	1.65822
$336$	6.55628	0.357674
$337$	20.4278	1.11278	0.556388	−	0.830923i	$-0.312187\pi$
$337$	20.4278	1.11278	0.556388	+	0.830923i	$0.312187\pi$
$338$	0	0
$339$	−11.1049	−0.603138
$340$	−43.7617	−2.37331
$341$	7.50697	0.406525
$342$	−10.6128	−0.573876
$343$	−1.00000	−0.0539949
$344$	−3.45386	−0.186220
$345$	−31.4313	−1.69220
$346$	−7.77165	−0.417807
$347$	7.97000	0.427852	0.213926	−	0.976850i	$-0.431375\pi$
$347$	7.97000	0.427852	0.213926	+	0.976850i	$0.431375\pi$
$348$	7.10207	0.380711
$349$	−21.5972	−1.15607	−0.578037	−	0.816011i	$-0.696181\pi$
$349$	−21.5972	−1.15607	−0.578037	+	0.816011i	$0.696181\pi$
$350$	−16.8178	−0.898947
$351$	0	0
$352$	7.10110	0.378490
$353$	21.6176	1.15059	0.575295	−	0.817946i	$-0.304887\pi$
$353$	21.6176	1.15059	0.575295	+	0.817946i	$0.304887\pi$
$354$	34.9571	1.85795
$355$	23.2275	1.23279
$356$	−8.86441	−0.469813
$357$	11.2181	0.593727
$358$	−12.4301	−0.656953
$359$	−13.6834	−0.722180	−0.361090	−	0.932531i	$-0.617595\pi$
$359$	−13.6834	−0.722180	−0.361090	+	0.932531i	$0.617595\pi$
$360$	7.22344	0.380708
$361$	−13.3414	−0.702180
$362$	4.46226	0.234531
$363$	−23.1012	−1.21250
$364$	0	0
$365$	25.7477	1.34769
$366$	−7.34335	−0.383843
$367$	−11.4128	−0.595741	−0.297871	−	0.954606i	$-0.596276\pi$
$367$	−11.4128	−0.595741	−0.297871	+	0.954606i	$0.596276\pi$
$368$	11.1854	0.583080
$369$	25.5586	1.33053
$370$	73.2261	3.80685
$371$	−4.92032	−0.255450
$372$	−46.9190	−2.43264
$373$	−31.2808	−1.61966	−0.809830	−	0.586664i	$-0.800441\pi$
$373$	−31.2808	−1.61966	−0.809830	+	0.586664i	$0.800441\pi$
$374$	9.27416	0.479555
$375$	24.2164	1.25053
$376$	−2.82784	−0.145835
$377$	0	0
$378$	4.22181	0.217146
$379$	27.4151	1.40822	0.704108	−	0.710093i	$-0.251347\pi$
$379$	27.4151	1.40822	0.704108	+	0.710093i	$0.251347\pi$
$380$	−20.9871	−1.07661
$381$	−27.8412	−1.42635
$382$	−23.9767	−1.22675
$383$	−16.1006	−0.822705	−0.411352	−	0.911476i	$-0.634943\pi$
$383$	−16.1006	−0.822705	−0.411352	+	0.911476i	$0.634943\pi$
$384$	−16.7228	−0.853383
$385$	3.19256	0.162708
$386$	−29.7199	−1.51271
$387$	−7.70408	−0.391620
$388$	1.13486	0.0576139
$389$	21.1380	1.07174	0.535870	−	0.844301i	$-0.319984\pi$
$389$	21.1380	1.07174	0.535870	+	0.844301i	$0.319984\pi$
$390$	0	0
$391$	19.1388	0.967893
$392$	0.948212	0.0478919
$393$	−18.5515	−0.935800
$394$	−48.4255	−2.43964
$395$	2.72853	0.137287
$396$	−4.59224	−0.230769
$397$	13.0984	0.657390	0.328695	−	0.944436i	$-0.393391\pi$
$397$	13.0984	0.657390	0.328695	+	0.944436i	$0.393391\pi$
$398$	−6.64426	−0.333046
$399$	5.37995	0.269335
$400$	−23.1123	−1.15562
$401$	−19.4447	−0.971022	−0.485511	−	0.874230i	$-0.661367\pi$
$401$	−19.4447	−0.971022	−0.485511	+	0.874230i	$0.661367\pi$
$402$	40.2002	2.00501
$403$	0	0
$404$	14.2636	0.709642
$405$	−39.1575	−1.94575
$406$	−2.70418	−0.134206
$407$	−8.54308	−0.423465
$408$	−10.6372	−0.526618
$409$	−24.0559	−1.18949	−0.594743	−	0.803916i	$-0.702746\pi$
$409$	−24.0559	−1.18949	−0.594743	+	0.803916i	$0.702746\pi$
$410$	91.8098	4.53416
$411$	16.8618	0.831733
$412$	20.1813	0.994261
$413$	−7.32746	−0.360561
$414$	−17.2146	−0.846053
$415$	17.1721	0.842944
$416$	0	0
$417$	37.7256	1.84743
$418$	4.44767	0.217542
$419$	39.0238	1.90644	0.953218	−	0.302283i	$-0.0977487\pi$
$419$	39.0238	1.90644	0.953218	+	0.302283i	$0.0977487\pi$
$420$	−19.9537	−0.973640
$421$	−22.0284	−1.07360	−0.536799	−	0.843710i	$-0.680367\pi$
$421$	−22.0284	−1.07360	−0.536799	+	0.843710i	$0.680367\pi$
$422$	−31.3536	−1.52627
$423$	−6.30771	−0.306691
$424$	4.66551	0.226577
$425$	−39.5465	−1.91828
$426$	30.7657	1.49060
$427$	1.53926	0.0744902
$428$	−9.38803	−0.453787
$429$	0	0
$430$	−27.6741	−1.33456
$431$	−35.8797	−1.72826	−0.864131	−	0.503267i	$-0.832131\pi$
$431$	−35.8797	−1.72826	−0.864131	+	0.503267i	$0.832131\pi$
$432$	5.80195	0.279147
$433$	12.2136	0.586946	0.293473	−	0.955967i	$-0.405189\pi$
$433$	12.2136	0.586946	0.293473	+	0.955967i	$0.405189\pi$
$434$	17.8648	0.857540
$435$	10.4429	0.500699
$436$	25.5192	1.22215
$437$	9.17853	0.439069
$438$	34.1037	1.62954
$439$	−15.7553	−0.751960	−0.375980	−	0.926628i	$-0.622694\pi$
$439$	−15.7553	−0.751960	−0.375980	+	0.926628i	$0.622694\pi$
$440$	−3.02722	−0.144317
$441$	2.11505	0.100717
$442$	0	0
$443$	−15.0706	−0.716028	−0.358014	−	0.933716i	$-0.616546\pi$
$443$	−15.0706	−0.716028	−0.358014	+	0.933716i	$0.616546\pi$
$444$	53.3947	2.53400
$445$	−13.0342	−0.617883
$446$	9.24099	0.437574
$447$	5.70305	0.269745
$448$	11.1012	0.524482
$449$	30.7826	1.45272	0.726360	−	0.687315i	$-0.241211\pi$
$449$	30.7826	1.45272	0.726360	+	0.687315i	$0.241211\pi$
$450$	35.5705	1.67681
$451$	−10.7112	−0.504370
$452$	−12.0274	−0.565722
$453$	35.9540	1.68926
$454$	−28.6166	−1.34304
$455$	0	0
$456$	−5.10133	−0.238892
$457$	−7.75597	−0.362809	−0.181405	−	0.983409i	$-0.558064\pi$
$457$	−7.75597	−0.362809	−0.181405	+	0.983409i	$0.558064\pi$
$458$	−34.8429	−1.62810
$459$	9.92745	0.463374
$460$	−34.0422	−1.58723
$461$	−1.47222	−0.0685681	−0.0342840	−	0.999412i	$-0.510915\pi$
$461$	−1.47222	−0.0685681	−0.0342840	+	0.999412i	$0.510915\pi$
$462$	4.22867	0.196735
$463$	14.0366	0.652335	0.326168	−	0.945312i	$-0.394243\pi$
$463$	14.0366	0.652335	0.326168	+	0.945312i	$0.394243\pi$
$464$	−3.71630	−0.172525
$465$	−68.9898	−3.19933
$466$	−34.8104	−1.61256
$467$	31.3806	1.45212	0.726060	−	0.687631i	$-0.241349\pi$
$467$	31.3806	1.45212	0.726060	+	0.687631i	$0.241349\pi$
$468$	0	0
$469$	−8.42649	−0.389099
$470$	−22.6581	−1.04514
$471$	29.3632	1.35298
$472$	6.94798	0.319807
$473$	3.22865	0.148454
$474$	3.61404	0.165999
$475$	−18.9655	−0.870199
$476$	12.1500	0.556895
$477$	10.4067	0.476492
$478$	−64.1698	−2.93506
$479$	−41.1951	−1.88225	−0.941125	−	0.338059i	$-0.890230\pi$
$479$	−41.1951	−1.88225	−0.941125	+	0.338059i	$0.890230\pi$
$480$	−65.2598	−2.97869
$481$	0	0
$482$	−62.2572	−2.83574
$483$	8.72660	0.397074
$484$	−25.0202	−1.13728
$485$	1.66870	0.0757719
$486$	−39.2002	−1.77816
$487$	−28.3265	−1.28360	−0.641798	−	0.766874i	$-0.721811\pi$
$487$	−28.3265	−1.28360	−0.641798	+	0.766874i	$0.721811\pi$
$488$	−1.45955	−0.0660706
$489$	−5.24584	−0.237225
$490$	7.59755	0.343222
$491$	34.7863	1.56988	0.784941	−	0.619571i	$-0.212693\pi$
$491$	34.7863	1.56988	0.784941	+	0.619571i	$0.212693\pi$
$492$	66.9455	3.01814
$493$	−6.35879	−0.286386
$494$	0	0
$495$	−6.75244	−0.303499
$496$	24.5513	1.10239
$497$	−6.44888	−0.289272
$498$	22.7451	1.01923
$499$	−0.0694885	−0.00311073	−0.00155537	−	0.999999i	$-0.500495\pi$
$499$	−0.0694885	−0.00311073	−0.00155537	+	0.999999i	$0.500495\pi$
$500$	26.2281	1.17295
$501$	31.1923	1.39357
$502$	−27.3855	−1.22228
$503$	25.7372	1.14756	0.573782	−	0.819008i	$-0.305476\pi$
$503$	25.7372	1.14756	0.573782	+	0.819008i	$0.305476\pi$
$504$	−2.00552	−0.0893329
$505$	20.9733	0.933299
$506$	7.21437	0.320718
$507$	0	0
$508$	−30.1540	−1.33787
$509$	−7.04000	−0.312042	−0.156021	−	0.987754i	$-0.549867\pi$
$509$	−7.04000	−0.312042	−0.156021	+	0.987754i	$0.549867\pi$
$510$	−85.2304	−3.77407
$511$	−7.14859	−0.316235
$512$	28.7215	1.26932
$513$	4.76097	0.210202
$514$	−9.67199	−0.426613
$515$	29.6746	1.30762
$516$	−20.1793	−0.888342
$517$	2.64346	0.116259
$518$	−20.3305	−0.893273
$519$	−8.33263	−0.365762
$520$	0	0
$521$	16.3253	0.715225	0.357613	−	0.933870i	$-0.383591\pi$
$521$	16.3253	0.715225	0.357613	+	0.933870i	$0.383591\pi$
$522$	5.71948	0.250335
$523$	−7.08946	−0.310000	−0.155000	−	0.987914i	$-0.549538\pi$
$523$	−7.08946	−0.310000	−0.155000	+	0.987914i	$0.549538\pi$
$524$	−20.0926	−0.877748
$525$	−18.0317	−0.786968
$526$	−5.62150	−0.245109
$527$	42.0086	1.82993
$528$	5.81138	0.252908
$529$	−8.11189	−0.352691
$530$	37.3824	1.62379
$531$	15.4980	0.672555
$532$	5.82686	0.252626
$533$	0	0
$534$	−17.2644	−0.747102
$535$	−13.8042	−0.596807
$536$	7.99010	0.345120
$537$	−13.3274	−0.575118
$538$	25.1558	1.08454
$539$	−0.886384	−0.0381793
$540$	−17.6579	−0.759877
$541$	25.5162	1.09703	0.548515	−	0.836141i	$-0.315194\pi$
$541$	25.5162	1.09703	0.548515	+	0.836141i	$0.315194\pi$
$542$	27.4818	1.18044
$543$	4.78436	0.205316
$544$	39.7374	1.70373
$545$	37.5235	1.60733
$546$	0	0
$547$	−13.3073	−0.568978	−0.284489	−	0.958679i	$-0.591824\pi$
$547$	−13.3073	−0.568978	−0.284489	+	0.958679i	$0.591824\pi$
$548$	18.2625	0.780136
$549$	−3.25562	−0.138947
$550$	−14.9070	−0.635637
$551$	−3.04952	−0.129914
$552$	−8.27466	−0.352193
$553$	−0.757551	−0.0322143
$554$	45.0669	1.91471
$555$	78.5118	3.33264
$556$	40.8594	1.73282
$557$	17.0071	0.720612	0.360306	−	0.932834i	$-0.382672\pi$
$557$	17.0071	0.720612	0.360306	+	0.932834i	$0.382672\pi$
$558$	−37.7851	−1.59957
$559$	0	0
$560$	10.4412	0.441220
$561$	9.94358	0.419818
$562$	−36.4244	−1.53647
$563$	−24.9193	−1.05022	−0.525111	−	0.851034i	$-0.675976\pi$
$563$	−24.9193	−1.05022	−0.525111	+	0.851034i	$0.675976\pi$
$564$	−16.5218	−0.695691
$565$	−17.6851	−0.744019
$566$	−44.8038	−1.88325
$567$	10.8717	0.456569
$568$	6.11491	0.256576
$569$	5.88129	0.246557	0.123278	−	0.992372i	$-0.460659\pi$
$569$	5.88129	0.246557	0.123278	+	0.992372i	$0.460659\pi$
$570$	−40.8745	−1.71204
$571$	8.92622	0.373551	0.186775	−	0.982403i	$-0.440196\pi$
$571$	8.92622	0.373551	0.186775	+	0.982403i	$0.440196\pi$
$572$	0	0
$573$	−25.7074	−1.07394
$574$	−25.4901	−1.06394
$575$	−30.7632	−1.28291
$576$	−23.4796	−0.978317
$577$	36.1933	1.50675	0.753374	−	0.657592i	$-0.228425\pi$
$577$	36.1933	1.50675	0.753374	+	0.657592i	$0.228425\pi$
$578$	16.0381	0.667097
$579$	−31.8652	−1.32427
$580$	11.3104	0.469638
$581$	−4.76766	−0.197796
$582$	2.21026	0.0916183
$583$	−4.36130	−0.180626
$584$	6.77838	0.280491
$585$	0	0
$586$	−0.886069	−0.0366032
$587$	36.4895	1.50608	0.753041	−	0.657974i	$-0.228586\pi$
$587$	36.4895	1.50608	0.753041	+	0.657974i	$0.228586\pi$
$588$	5.53995	0.228464
$589$	20.1463	0.830116
$590$	55.6708	2.29193
$591$	−51.9210	−2.13574
$592$	−27.9399	−1.14832
$593$	34.9930	1.43699	0.718495	−	0.695533i	$-0.244832\pi$
$593$	34.9930	1.43699	0.718495	+	0.695533i	$0.244832\pi$
$594$	3.74215	0.153542
$595$	17.8654	0.732410
$596$	6.17679	0.253011
$597$	−7.12385	−0.291560
$598$	0	0
$599$	−32.5052	−1.32812	−0.664062	−	0.747677i	$-0.731169\pi$
$599$	−32.5052	−1.32812	−0.664062	+	0.747677i	$0.731169\pi$
$600$	17.0979	0.698018
$601$	20.0780	0.819000	0.409500	−	0.912310i	$-0.365703\pi$
$601$	20.0780	0.819000	0.409500	+	0.912310i	$0.365703\pi$
$602$	7.68344	0.313154
$603$	17.8225	0.725788
$604$	38.9406	1.58447
$605$	−36.7897	−1.49572
$606$	27.7799	1.12848
$607$	9.71601	0.394361	0.197180	−	0.980367i	$-0.436822\pi$
$607$	9.71601	0.394361	0.197180	+	0.980367i	$0.436822\pi$
$608$	19.0571	0.772868
$609$	−2.89937	−0.117488
$610$	−11.6946	−0.473502
$611$	0	0
$612$	−25.6979	−1.03878
$613$	−11.8816	−0.479893	−0.239947	−	0.970786i	$-0.577130\pi$
$613$	−11.8816	−0.479893	−0.239947	+	0.970786i	$0.577130\pi$
$614$	29.7017	1.19866
$615$	98.4368	3.96936
$616$	0.840480	0.0338639
$617$	19.9884	0.804705	0.402352	−	0.915485i	$-0.368193\pi$
$617$	19.9884	0.804705	0.402352	+	0.915485i	$0.368193\pi$
$618$	39.3052	1.58109
$619$	41.7176	1.67677	0.838386	−	0.545078i	$-0.183500\pi$
$619$	41.7176	1.67677	0.838386	+	0.545078i	$0.183500\pi$
$620$	−74.7207	−3.00086
$621$	7.72257	0.309896
$622$	21.9056	0.878333
$623$	3.61884	0.144986
$624$	0	0
$625$	−1.29828	−0.0519312
$626$	14.4442	0.577307
$627$	4.76871	0.190444
$628$	31.8023	1.26905
$629$	−47.8066	−1.90618
$630$	−16.0692	−0.640213
$631$	17.6415	0.702296	0.351148	−	0.936320i	$-0.385791\pi$
$631$	17.6415	0.702296	0.351148	+	0.936320i	$0.385791\pi$
$632$	0.718319	0.0285732
$633$	−33.6168	−1.33615
$634$	1.47921	0.0587468
$635$	−44.3385	−1.75952
$636$	27.2584	1.08086
$637$	0	0
$638$	−2.39694	−0.0948958
$639$	13.6397	0.539580
$640$	−26.6319	−1.05272
$641$	−10.9202	−0.431324	−0.215662	−	0.976468i	$-0.569191\pi$
$641$	−10.9202	−0.431324	−0.215662	+	0.976468i	$0.569191\pi$
$642$	−18.2842	−0.721618
$643$	−17.6351	−0.695462	−0.347731	−	0.937594i	$-0.613048\pi$
$643$	−17.6351	−0.695462	−0.347731	+	0.937594i	$0.613048\pi$
$644$	9.45150	0.372441
$645$	−29.6716	−1.16832
$646$	24.8889	0.979241
$647$	16.6726	0.655469	0.327735	−	0.944770i	$-0.393715\pi$
$647$	16.6726	0.655469	0.327735	+	0.944770i	$0.393715\pi$
$648$	−10.3087	−0.404963
$649$	−6.49495	−0.254949
$650$	0	0
$651$	19.1544	0.750719
$652$	−5.68161	−0.222509
$653$	−6.77329	−0.265059	−0.132530	−	0.991179i	$-0.542310\pi$
$653$	−6.77329	−0.265059	−0.132530	+	0.991179i	$0.542310\pi$
$654$	49.7013	1.94347
$655$	−29.5441	−1.15439
$656$	−35.0306	−1.36772
$657$	15.1197	0.589874
$658$	6.29081	0.245241
$659$	33.5361	1.30638	0.653190	−	0.757194i	$-0.273430\pi$
$659$	33.5361	1.30638	0.653190	+	0.757194i	$0.273430\pi$
$660$	−17.6866	−0.688451
$661$	25.1661	0.978848	0.489424	−	0.872046i	$-0.337207\pi$
$661$	25.1661	0.978848	0.489424	+	0.872046i	$0.337207\pi$
$662$	−8.85657	−0.344221
$663$	0	0
$664$	4.52075	0.175439
$665$	8.56783	0.332246
$666$	43.0002	1.66622
$667$	−4.94651	−0.191529
$668$	33.7833	1.30712
$669$	9.90802	0.383066
$670$	64.0207	2.47334
$671$	1.36438	0.0526713
$672$	18.1188	0.698947
$673$	−1.85468	−0.0714927	−0.0357464	−	0.999361i	$-0.511381\pi$
$673$	−1.85468	−0.0714927	−0.0357464	+	0.999361i	$0.511381\pi$
$674$	43.0902	1.65977
$675$	−15.9571	−0.614189
$676$	0	0
$677$	−14.7209	−0.565770	−0.282885	−	0.959154i	$-0.591291\pi$
$677$	−14.7209	−0.565770	−0.282885	+	0.959154i	$0.591291\pi$
$678$	−23.4246	−0.899618
$679$	−0.463300	−0.0177798
$680$	−16.9402	−0.649627
$681$	−30.6822	−1.17575
$682$	15.8351	0.606358
$683$	7.94353	0.303951	0.151975	−	0.988384i	$-0.451437\pi$
$683$	7.94353	0.303951	0.151975	+	0.988384i	$0.451437\pi$
$684$	−12.3241	−0.471224
$685$	26.8533	1.02601
$686$	−2.10939	−0.0805368
$687$	−37.3579	−1.42529
$688$	10.5592	0.402566
$689$	0	0
$690$	−66.3008	−2.52403
$691$	10.2307	0.389193	0.194597	−	0.980883i	$-0.437660\pi$
$691$	10.2307	0.389193	0.194597	+	0.980883i	$0.437660\pi$
$692$	−9.02481	−0.343072
$693$	1.87475	0.0712159
$694$	16.8118	0.638168
$695$	60.0797	2.27895
$696$	2.74922	0.104209
$697$	−59.9392	−2.27036
$698$	−45.5570	−1.72436
$699$	−37.3231	−1.41169
$700$	−19.5296	−0.738148
$701$	16.5978	0.626891	0.313445	−	0.949606i	$-0.398517\pi$
$701$	16.5978	0.626891	0.313445	+	0.949606i	$0.398517\pi$
$702$	0	0
$703$	−22.9269	−0.864706
$704$	9.83992	0.370856
$705$	−24.2936	−0.914951
$706$	45.5999	1.71618
$707$	−5.82303	−0.218998
$708$	40.5938	1.52561
$709$	47.8659	1.79764	0.898820	−	0.438318i	$-0.144426\pi$
$709$	47.8659	1.79764	0.898820	+	0.438318i	$0.144426\pi$
$710$	48.9957	1.83878
$711$	1.60226	0.0600895
$712$	−3.43142	−0.128598
$713$	32.6785	1.22382
$714$	23.6634	0.885581
$715$	0	0
$716$	−14.4344	−0.539441
$717$	−68.8017	−2.56944
$718$	−28.8635	−1.07718
$719$	−38.0922	−1.42060	−0.710300	−	0.703899i	$-0.751441\pi$
$719$	−38.0922	−1.42060	−0.710300	+	0.703899i	$0.751441\pi$
$720$	−22.0836	−0.823009
$721$	−8.23888	−0.306832
$722$	−28.1423	−1.04735
$723$	−66.7511	−2.48250
$724$	5.18179	0.192580
$725$	10.2209	0.379596
$726$	−48.7294	−1.80852
$727$	−15.4059	−0.571374	−0.285687	−	0.958323i	$-0.592222\pi$
$727$	−15.4059	−0.571374	−0.285687	+	0.958323i	$0.592222\pi$
$728$	0	0
$729$	−9.41460	−0.348689
$730$	54.3118	2.01017
$731$	18.0674	0.668246
$732$	−8.52744	−0.315183
$733$	−11.6298	−0.429557	−0.214778	−	0.976663i	$-0.568903\pi$
$733$	−11.6298	−0.429557	−0.214778	+	0.976663i	$0.568903\pi$
$734$	−24.0740	−0.888586
$735$	8.14596	0.300468
$736$	30.9117	1.13942
$737$	−7.46911	−0.275128
$738$	53.9130	1.98456
$739$	−2.68901	−0.0989168	−0.0494584	−	0.998776i	$-0.515750\pi$
$739$	−2.68901	−0.0989168	−0.0494584	+	0.998776i	$0.515750\pi$
$740$	85.0336	3.12590
$741$	0	0
$742$	−10.3789	−0.381020
$743$	−2.46720	−0.0905126	−0.0452563	−	0.998975i	$-0.514410\pi$
$743$	−2.46720	−0.0905126	−0.0452563	+	0.998975i	$0.514410\pi$
$744$	−18.1624	−0.665866
$745$	9.08236	0.332752
$746$	−65.9835	−2.41583
$747$	10.0839	0.368949
$748$	10.7696	0.393775
$749$	3.83260	0.140040
$750$	51.0819	1.86525
$751$	−37.9185	−1.38366	−0.691832	−	0.722058i	$-0.743196\pi$
$751$	−37.9185	−1.38366	−0.691832	+	0.722058i	$0.743196\pi$
$752$	8.64534	0.315263
$753$	−29.3623	−1.07002
$754$	0	0
$755$	57.2583	2.08384
$756$	4.90256	0.178304
$757$	34.6451	1.25920	0.629598	−	0.776921i	$-0.283219\pi$
$757$	34.6451	1.25920	0.629598	+	0.776921i	$0.283219\pi$
$758$	57.8290	2.10044
$759$	7.73512	0.280767
$760$	−8.12411	−0.294692
$761$	22.8595	0.828655	0.414328	−	0.910128i	$-0.364017\pi$
$761$	22.8595	0.828655	0.414328	+	0.910128i	$0.364017\pi$
$762$	−58.7280	−2.12749
$763$	−10.4180	−0.377158
$764$	−27.8428	−1.00732
$765$	−37.7863	−1.36617
$766$	−33.9625	−1.22712
$767$	0	0
$768$	14.9390	0.539065
$769$	−51.8275	−1.86895	−0.934473	−	0.356034i	$-0.884129\pi$
$769$	−51.8275	−1.86895	−0.934473	+	0.356034i	$0.884129\pi$
$770$	6.73435	0.242689
$771$	−10.3701	−0.373471
$772$	−34.5122	−1.24212
$773$	5.69966	0.205003	0.102501	−	0.994733i	$-0.467315\pi$
$773$	5.69966	0.205003	0.102501	+	0.994733i	$0.467315\pi$
$774$	−16.2509	−0.584126
$775$	−67.5234	−2.42551
$776$	0.439306	0.0157702
$777$	−21.7980	−0.782001
$778$	44.5883	1.59857
$779$	−28.7454	−1.02991
$780$	0	0
$781$	−5.71619	−0.204541
$782$	40.3712	1.44367
$783$	−2.56579	−0.0916938
$784$	−2.89889	−0.103532
$785$	46.7622	1.66902
$786$	−39.1324	−1.39580
$787$	−16.8141	−0.599358	−0.299679	−	0.954040i	$-0.596880\pi$
$787$	−16.8141	−0.599358	−0.299679	+	0.954040i	$0.596880\pi$
$788$	−56.2340	−2.00325
$789$	−6.02727	−0.214577
$790$	5.75553	0.204773
$791$	4.91011	0.174583
$792$	−1.77766	−0.0631664
$793$	0	0
$794$	27.6296	0.980539
$795$	40.0807	1.42152
$796$	−7.71562	−0.273473
$797$	42.1301	1.49233	0.746163	−	0.665764i	$-0.231894\pi$
$797$	42.1301	1.49233	0.746163	+	0.665764i	$0.231894\pi$
$798$	11.3484	0.401729
$799$	14.7926	0.523326
$800$	−63.8727	−2.25824
$801$	−7.65403	−0.270442
$802$	−41.0164	−1.44834
$803$	−6.33640	−0.223607
$804$	46.6824	1.64636
$805$	13.8975	0.489823
$806$	0	0
$807$	26.9716	0.949445
$808$	5.52147	0.194245
$809$	−30.1686	−1.06067	−0.530336	−	0.847787i	$-0.677934\pi$
$809$	−30.1686	−1.06067	−0.530336	+	0.847787i	$0.677934\pi$
$810$	−82.5984	−2.90221
$811$	23.7929	0.835480	0.417740	−	0.908567i	$-0.362822\pi$
$811$	23.7929	0.835480	0.417740	+	0.908567i	$0.362822\pi$
$812$	−3.14022	−0.110200
$813$	29.4655	1.03340
$814$	−18.0207	−0.631624
$815$	−8.35425	−0.292637
$816$	32.5202	1.13843
$817$	8.66468	0.303139
$818$	−50.7432	−1.77419
$819$	0	0
$820$	106.614	3.72312
$821$	−35.8847	−1.25239	−0.626193	−	0.779668i	$-0.715388\pi$
$821$	−35.8847	−1.25239	−0.626193	+	0.779668i	$0.715388\pi$
$822$	35.5682	1.24058
$823$	−12.2346	−0.426470	−0.213235	−	0.977001i	$-0.568400\pi$
$823$	−12.2346	−0.426470	−0.213235	+	0.977001i	$0.568400\pi$
$824$	7.81220	0.272151
$825$	−15.9830	−0.556457
$826$	−15.4565	−0.537799
$827$	27.3474	0.950962	0.475481	−	0.879726i	$-0.342274\pi$
$827$	27.3474	0.950962	0.475481	+	0.879726i	$0.342274\pi$
$828$	−19.9904	−0.694715
$829$	23.5738	0.818751	0.409376	−	0.912366i	$-0.365747\pi$
$829$	23.5738	0.818751	0.409376	+	0.912366i	$0.365747\pi$
$830$	36.2226	1.25730
$831$	48.3199	1.67620
$832$	0	0
$833$	−4.96016	−0.171859
$834$	79.5779	2.75556
$835$	49.6751	1.71908
$836$	5.16483	0.178630
$837$	16.9506	0.585898
$838$	82.3163	2.84357
$839$	10.5883	0.365549	0.182775	−	0.983155i	$-0.441492\pi$
$839$	10.5883	0.365549	0.182775	+	0.983155i	$0.441492\pi$
$840$	−7.72409	−0.266507
$841$	−27.3565	−0.943329
$842$	−46.4664	−1.60134
$843$	−39.0536	−1.34508
$844$	−36.4092	−1.25326
$845$	0	0
$846$	−13.3054	−0.457449
$847$	10.2143	0.350968
$848$	−14.2635	−0.489810
$849$	−48.0379	−1.64866
$850$	−83.4188	−2.86124
$851$	−37.1888	−1.27482
$852$	35.7265	1.22397
$853$	21.3925	0.732464	0.366232	−	0.930524i	$-0.380648\pi$
$853$	21.3925	0.732464	0.366232	+	0.930524i	$0.380648\pi$
$854$	3.24690	0.111107
$855$	−18.1214	−0.619739
$856$	−3.63412	−0.124212
$857$	7.22129	0.246675	0.123337	−	0.992365i	$-0.460640\pi$
$857$	7.22129	0.246675	0.123337	+	0.992365i	$0.460640\pi$
$858$	0	0
$859$	57.1073	1.94848	0.974238	−	0.225524i	$-0.0724095\pi$
$859$	57.1073	1.94848	0.974238	+	0.225524i	$0.0724095\pi$
$860$	−32.1364	−1.09584
$861$	−27.3301	−0.931406
$862$	−75.6841	−2.57781
$863$	51.3361	1.74750	0.873751	−	0.486374i	$-0.161681\pi$
$863$	51.3361	1.74750	0.873751	+	0.486374i	$0.161681\pi$
$864$	16.0341	0.545493
$865$	−13.2701	−0.451197
$866$	25.7631	0.875467
$867$	17.1958	0.583999
$868$	20.7455	0.704148
$869$	−0.671481	−0.0227784
$870$	22.0281	0.746823
$871$	0	0
$872$	9.87851	0.334528
$873$	0.979903	0.0331647
$874$	19.3611	0.654899
$875$	−10.7074	−0.361977
$876$	39.6029	1.33806
$877$	21.4277	0.723563	0.361781	−	0.932263i	$-0.382169\pi$
$877$	21.4277	0.723563	0.361781	+	0.932263i	$0.382169\pi$
$878$	−33.2341	−1.12160
$879$	−0.950027	−0.0320436
$880$	9.25489	0.311982
$881$	29.0619	0.979120	0.489560	−	0.871970i	$-0.337157\pi$
$881$	29.0619	0.979120	0.489560	+	0.871970i	$0.337157\pi$
$882$	4.46147	0.150225
$883$	−4.83594	−0.162742	−0.0813711	−	0.996684i	$-0.525930\pi$
$883$	−4.83594	−0.162742	−0.0813711	+	0.996684i	$0.525930\pi$
$884$	0	0
$885$	59.6892	2.00643
$886$	−31.7899	−1.06800
$887$	−24.9898	−0.839075	−0.419538	−	0.907738i	$-0.637808\pi$
$887$	−24.9898	−0.839075	−0.419538	+	0.907738i	$0.637808\pi$
$888$	20.6692	0.693612
$889$	12.3102	0.412869
$890$	−27.4943	−0.921611
$891$	9.63651	0.322835
$892$	10.7311	0.359303
$893$	7.09420	0.237398
$894$	12.0299	0.402341
$895$	−21.2244	−0.709455
$896$	7.39409	0.247019
$897$	0	0
$898$	64.9324	2.16682
$899$	−10.8573	−0.362111
$900$	41.3061	1.37687
$901$	−24.4056	−0.813068
$902$	−22.5940	−0.752300
$903$	8.23805	0.274145
$904$	−4.65582	−0.154850
$905$	7.61931	0.253274
$906$	75.8409	2.51964
$907$	15.0412	0.499435	0.249717	−	0.968319i	$-0.419662\pi$
$907$	15.0412	0.499435	0.249717	+	0.968319i	$0.419662\pi$
$908$	−33.2310	−1.10281
$909$	12.3160	0.408497
$910$	0	0
$911$	−9.22150	−0.305522	−0.152761	−	0.988263i	$-0.548816\pi$
$911$	−9.22150	−0.305522	−0.152761	+	0.988263i	$0.548816\pi$
$912$	15.5959	0.516432
$913$	−4.22598	−0.139860
$914$	−16.3604	−0.541153
$915$	−12.5388	−0.414519
$916$	−40.4612	−1.33687
$917$	8.20265	0.270875
$918$	20.9409	0.691151
$919$	−45.0803	−1.48706	−0.743531	−	0.668701i	$-0.766851\pi$
$919$	−45.0803	−1.48706	−0.743531	+	0.668701i	$0.766851\pi$
$920$	−13.1778	−0.434459
$921$	31.8456	1.04935
$922$	−3.10548	−0.102274
$923$	0	0
$924$	4.91053	0.161544
$925$	76.8430	2.52658
$926$	29.6086	0.972999
$927$	17.4257	0.572334
$928$	−10.2703	−0.337139
$929$	46.9169	1.53929	0.769647	−	0.638469i	$-0.220432\pi$
$929$	46.9169	1.53929	0.769647	+	0.638469i	$0.220432\pi$
$930$	−145.526	−4.77200
$931$	−2.37878	−0.0779612
$932$	−40.4235	−1.32412
$933$	23.4867	0.768921
$934$	66.1939	2.16593
$935$	15.8356	0.517880
$936$	0	0
$937$	−28.3912	−0.927501	−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912	−0.927501	−0.463750	+	0.885966i	$0.653497\pi$
$938$	−17.7747	−0.580366
$939$	15.4868	0.505394
$940$	−26.3117	−0.858192
$941$	17.8718	0.582603	0.291302	−	0.956631i	$-0.405912\pi$
$941$	17.8718	0.582603	0.291302	+	0.956631i	$0.405912\pi$
$942$	61.9384	2.01806
$943$	−46.6268	−1.51838
$944$	−21.2415	−0.691353
$945$	7.20874	0.234500
$946$	6.81048	0.221428
$947$	−9.52234	−0.309435	−0.154717	−	0.987959i	$-0.549447\pi$
$947$	−9.52234	−0.309435	−0.154717	+	0.987959i	$0.549447\pi$
$948$	4.19680	0.136306
$949$	0	0
$950$	−40.0057	−1.29796
$951$	1.58598	0.0514289
$952$	4.70328	0.152434
$953$	−13.4180	−0.434652	−0.217326	−	0.976099i	$-0.569733\pi$
$953$	−13.4180	−0.434652	−0.217326	+	0.976099i	$0.569733\pi$
$954$	21.9519	0.710718
$955$	−40.9402	−1.32479
$956$	−74.5169	−2.41005
$957$	−2.56996	−0.0830749
$958$	−86.8964	−2.80749
$959$	−7.45555	−0.240752
$960$	−90.4298	−2.91861
$961$	40.7275	1.31379
$962$	0	0
$963$	−8.10615	−0.261217
$964$	−72.2960	−2.32850
$965$	−50.7468	−1.63360
$966$	18.4078	0.592261
$967$	−12.9316	−0.415851	−0.207926	−	0.978145i	$-0.566671\pi$
$967$	−12.9316	−0.415851	−0.207926	+	0.978145i	$0.566671\pi$
$968$	−9.68534	−0.311299
$969$	26.6854	0.857260
$970$	3.51994	0.113019
$971$	47.5213	1.52503	0.762516	−	0.646969i	$-0.223964\pi$
$971$	47.5213	1.52503	0.762516	+	0.646969i	$0.223964\pi$
$972$	−45.5211	−1.46009
$973$	−16.6806	−0.534754
$974$	−59.7515	−1.91456
$975$	0	0
$976$	4.46216	0.142830
$977$	36.4942	1.16755	0.583776	−	0.811915i	$-0.301575\pi$
$977$	36.4942	1.16755	0.583776	+	0.811915i	$0.301575\pi$
$978$	−11.0655	−0.353836
$979$	3.20768	0.102518
$980$	8.82263	0.281829
$981$	22.0347	0.703514
$982$	73.3777	2.34158
$983$	−44.1843	−1.40926	−0.704629	−	0.709576i	$-0.748887\pi$
$983$	−44.1843	−1.40926	−0.704629	+	0.709576i	$0.748887\pi$
$984$	25.9147	0.826130
$985$	−82.6865	−2.63461
$986$	−13.4132	−0.427162
$987$	6.74490	0.214692
$988$	0	0
$989$	14.0546	0.446911
$990$	−14.2435	−0.452689
$991$	−50.7097	−1.61085	−0.805424	−	0.592699i	$-0.798062\pi$
$991$	−50.7097	−1.61085	−0.805424	+	0.592699i	$0.798062\pi$
$992$	67.8495	2.15422
$993$	−9.49586	−0.301342
$994$	−13.6032	−0.431467
$995$	−11.3451	−0.359663
$996$	26.4126	0.836916
$997$	−50.2768	−1.59228	−0.796141	−	0.605111i	$-0.793129\pi$
$997$	−50.2768	−1.59228	−0.796141	+	0.605111i	$0.793129\pi$
$998$	−0.146578	−0.00463985
$999$	−19.2901	−0.610312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.p.1.5		6
7.6	odd	2		8281.2.a.ch.1.5		6
13.2	odd	12		91.2.q.a.43.6	yes	12
13.5	odd	4		1183.2.c.i.337.2		12
13.7	odd	12		91.2.q.a.36.6	✓	12
13.8	odd	4		1183.2.c.i.337.11		12
13.12	even	2		1183.2.a.m.1.2		6
39.2	even	12		819.2.ct.a.316.1		12
39.20	even	12		819.2.ct.a.127.1		12
52.7	even	12		1456.2.cc.c.673.5		12
52.15	even	12		1456.2.cc.c.225.5		12
91.2	odd	12		637.2.k.h.459.1		12
91.20	even	12		637.2.q.h.491.6		12
91.33	even	12		637.2.u.i.361.1		12
91.41	even	12		637.2.q.h.589.6		12
91.46	odd	12		637.2.k.h.569.6		12
91.54	even	12		637.2.k.g.459.1		12
91.59	even	12		637.2.k.g.569.6		12
91.67	odd	12		637.2.u.h.30.1		12
91.72	odd	12		637.2.u.h.361.1		12
91.80	even	12		637.2.u.i.30.1		12
91.90	odd	2		8281.2.a.by.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	13.7	odd	12
91.2.q.a.43.6	yes	12	13.2	odd	12
637.2.k.g.459.1		12	91.54	even	12
637.2.k.g.569.6		12	91.59	even	12
637.2.k.h.459.1		12	91.2	odd	12
637.2.k.h.569.6		12	91.46	odd	12
637.2.q.h.491.6		12	91.20	even	12
637.2.q.h.589.6		12	91.41	even	12
637.2.u.h.30.1		12	91.67	odd	12
637.2.u.h.361.1		12	91.72	odd	12
637.2.u.i.30.1		12	91.80	even	12
637.2.u.i.361.1		12	91.33	even	12
819.2.ct.a.127.1		12	39.20	even	12
819.2.ct.a.316.1		12	39.2	even	12
1183.2.a.m.1.2		6	13.12	even	2
1183.2.a.p.1.5		6	1.1	even	1	trivial
1183.2.c.i.337.2		12	13.5	odd	4
1183.2.c.i.337.11		12	13.8	odd	4
1456.2.cc.c.225.5		12	52.15	even	12
1456.2.cc.c.673.5		12	52.7	even	12
8281.2.a.by.1.2		6	91.90	odd	2
8281.2.a.ch.1.5		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)

\(f(q)\)	\(=\)	\(q+2.10939 q^{2} +2.26165 q^{3} +2.44952 q^{4} +3.60178 q^{5} +4.77070 q^{6} -1.00000 q^{7} +0.948212 q^{8} +2.11505 q^{9} +O(q^{10})\)	\(q+2.10939 q^{2} +2.26165 q^{3} +2.44952 q^{4} +3.60178 q^{5} +4.77070 q^{6} -1.00000 q^{7} +0.948212 q^{8} +2.11505 q^{9} +7.59755 q^{10} -0.886384 q^{11} +5.53995 q^{12} -2.10939 q^{14} +8.14596 q^{15} -2.89889 q^{16} -4.96016 q^{17} +4.46147 q^{18} -2.37878 q^{19} +8.82263 q^{20} -2.26165 q^{21} -1.86973 q^{22} -3.85851 q^{23} +2.14452 q^{24} +7.97282 q^{25} -2.00144 q^{27} -2.44952 q^{28} +1.28197 q^{29} +17.1830 q^{30} -8.46921 q^{31} -8.01131 q^{32} -2.00469 q^{33} -10.4629 q^{34} -3.60178 q^{35} +5.18087 q^{36} +9.63812 q^{37} -5.01776 q^{38} +3.41525 q^{40} +12.0841 q^{41} -4.77070 q^{42} -3.64250 q^{43} -2.17122 q^{44} +7.61796 q^{45} -8.13910 q^{46} -2.98229 q^{47} -6.55628 q^{48} +1.00000 q^{49} +16.8178 q^{50} -11.2181 q^{51} +4.92032 q^{53} -4.22181 q^{54} -3.19256 q^{55} -0.948212 q^{56} -5.37995 q^{57} +2.70418 q^{58} +7.32746 q^{59} +19.9537 q^{60} -1.53926 q^{61} -17.8648 q^{62} -2.11505 q^{63} -11.1012 q^{64} -4.22867 q^{66} +8.42649 q^{67} -12.1500 q^{68} -8.72660 q^{69} -7.59755 q^{70} +6.44888 q^{71} +2.00552 q^{72} +7.14859 q^{73} +20.3305 q^{74} +18.0317 q^{75} -5.82686 q^{76} +0.886384 q^{77} +0.757551 q^{79} -10.4412 q^{80} -10.8717 q^{81} +25.4901 q^{82} +4.76766 q^{83} -5.53995 q^{84} -17.8654 q^{85} -7.68344 q^{86} +2.89937 q^{87} -0.840480 q^{88} -3.61884 q^{89} +16.0692 q^{90} -9.45150 q^{92} -19.1544 q^{93} -6.29081 q^{94} -8.56783 q^{95} -18.1188 q^{96} +0.463300 q^{97} +2.10939 q^{98} -1.87475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 4 q^{4} + 6 q^{5} + 4 q^{6} - 6 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 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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