LMFDB - Embedded newform 2366.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 10x + 14 $ x^3 - x^2 - 10*x + 14
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.52023$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.52023 q^{3} +1.00000 q^{4} +4.16867 q^{5} +1.52023 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.688899 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.52023 q^{3} +1.00000 q^{4} +4.16867 q^{5} +1.52023 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.688899 q^{9} +4.16867 q^{10} +4.64844 q^{11} +1.52023 q^{12} +1.00000 q^{14} +6.33734 q^{15} +1.00000 q^{16} -6.33734 q^{17} -0.688899 q^{18} -2.16867 q^{19} +4.16867 q^{20} +1.52023 q^{21} +4.64844 q^{22} -3.68890 q^{23} +1.52023 q^{24} +12.3778 q^{25} -5.60798 q^{27} +1.00000 q^{28} +5.04046 q^{29} +6.33734 q^{30} -4.64844 q^{31} +1.00000 q^{32} +7.06670 q^{33} -6.33734 q^{34} +4.16867 q^{35} -0.688899 q^{36} -1.68890 q^{37} -2.16867 q^{38} +4.16867 q^{40} -9.68890 q^{41} +1.52023 q^{42} +4.33734 q^{43} +4.64844 q^{44} -2.87179 q^{45} -3.68890 q^{46} +3.35156 q^{47} +1.52023 q^{48} +1.00000 q^{49} +12.3778 q^{50} -9.63421 q^{51} -6.00000 q^{53} -5.60798 q^{54} +19.3778 q^{55} +1.00000 q^{56} -3.29688 q^{57} +5.04046 q^{58} -9.54647 q^{59} +6.33734 q^{60} +0.479769 q^{61} -4.64844 q^{62} -0.688899 q^{63} +1.00000 q^{64} +7.06670 q^{66} +0.311101 q^{67} -6.33734 q^{68} -5.60798 q^{69} +4.16867 q^{70} -6.08092 q^{71} -0.688899 q^{72} -1.35156 q^{73} -1.68890 q^{74} +18.8171 q^{75} -2.16867 q^{76} +4.64844 q^{77} -14.0262 q^{79} +4.16867 q^{80} -6.45872 q^{81} -9.68890 q^{82} +11.4655 q^{83} +1.52023 q^{84} -26.4183 q^{85} +4.33734 q^{86} +7.66266 q^{87} +4.64844 q^{88} -1.66266 q^{89} -2.87179 q^{90} -3.68890 q^{92} -7.06670 q^{93} +3.35156 q^{94} -9.04046 q^{95} +1.52023 q^{96} -2.31110 q^{97} +1.00000 q^{98} -3.20231 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 12 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 12 * q^9	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 12 q^{9} + 2 q^{10} + 7 q^{11} + q^{12} + 3 q^{14} - 2 q^{15} + 3 q^{16} + 2 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{20} + q^{21} + 7 q^{22} + 3 q^{23} + q^{24} + 9 q^{25} - 17 q^{27} + 3 q^{28} + 8 q^{29} - 2 q^{30} - 7 q^{31} + 3 q^{32} - 21 q^{33} + 2 q^{34} + 2 q^{35} + 12 q^{36} + 9 q^{37} + 4 q^{38} + 2 q^{40} - 15 q^{41} + q^{42} - 8 q^{43} + 7 q^{44} - 12 q^{45} + 3 q^{46} + 17 q^{47} + q^{48} + 3 q^{49} + 9 q^{50} + 6 q^{51} - 18 q^{53} - 17 q^{54} + 30 q^{55} + 3 q^{56} + 4 q^{57} + 8 q^{58} + 10 q^{59} - 2 q^{60} + 5 q^{61} - 7 q^{62} + 12 q^{63} + 3 q^{64} - 21 q^{66} + 15 q^{67} + 2 q^{68} - 17 q^{69} + 2 q^{70} - 4 q^{71} + 12 q^{72} - 11 q^{73} + 9 q^{74} + 39 q^{75} + 4 q^{76} + 7 q^{77} - 7 q^{79} + 2 q^{80} + 23 q^{81} - 15 q^{82} + 10 q^{83} + q^{84} - 44 q^{85} - 8 q^{86} + 44 q^{87} + 7 q^{88} - 26 q^{89} - 12 q^{90} + 3 q^{92} + 21 q^{93} + 17 q^{94} - 20 q^{95} + q^{96} - 21 q^{97} + 3 q^{98} + 26 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 12 * q^9 + 2 * q^10 + 7 * q^11 + q^12 + 3 * q^14 - 2 * q^15 + 3 * q^16 + 2 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^20 + q^21 + 7 * q^22 + 3 * q^23 + q^24 + 9 * q^25 - 17 * q^27 + 3 * q^28 + 8 * q^29 - 2 * q^30 - 7 * q^31 + 3 * q^32 - 21 * q^33 + 2 * q^34 + 2 * q^35 + 12 * q^36 + 9 * q^37 + 4 * q^38 + 2 * q^40 - 15 * q^41 + q^42 - 8 * q^43 + 7 * q^44 - 12 * q^45 + 3 * q^46 + 17 * q^47 + q^48 + 3 * q^49 + 9 * q^50 + 6 * q^51 - 18 * q^53 - 17 * q^54 + 30 * q^55 + 3 * q^56 + 4 * q^57 + 8 * q^58 + 10 * q^59 - 2 * q^60 + 5 * q^61 - 7 * q^62 + 12 * q^63 + 3 * q^64 - 21 * q^66 + 15 * q^67 + 2 * q^68 - 17 * q^69 + 2 * q^70 - 4 * q^71 + 12 * q^72 - 11 * q^73 + 9 * q^74 + 39 * q^75 + 4 * q^76 + 7 * q^77 - 7 * q^79 + 2 * q^80 + 23 * q^81 - 15 * q^82 + 10 * q^83 + q^84 - 44 * q^85 - 8 * q^86 + 44 * q^87 + 7 * q^88 - 26 * q^89 - 12 * q^90 + 3 * q^92 + 21 * q^93 + 17 * q^94 - 20 * q^95 + q^96 - 21 * q^97 + 3 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.52023	0.877705	0.438853	−	0.898559i	$-0.355385\pi$
$3$	1.52023	0.877705	0.438853	+	0.898559i	$0.355385\pi$
$4$	1.00000	0.500000
$5$	4.16867	1.86429	0.932143	−	0.362091i	$-0.117937\pi$
$5$	4.16867	1.86429	0.932143	+	0.362091i	$0.117937\pi$
$6$	1.52023	0.620632
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−0.688899	−0.229633
$10$	4.16867	1.31825
$11$	4.64844	1.40156	0.700778	−	0.713379i	$-0.252836\pi$
$11$	4.64844	1.40156	0.700778	+	0.713379i	$0.252836\pi$
$12$	1.52023	0.438853
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	6.33734	1.63629
$16$	1.00000	0.250000
$17$	−6.33734	−1.53703	−0.768515	−	0.639832i	$-0.779004\pi$
$17$	−6.33734	−1.53703	−0.768515	+	0.639832i	$0.779004\pi$
$18$	−0.688899	−0.162375
$19$	−2.16867	−0.497527	−0.248763	−	0.968564i	$-0.580024\pi$
$19$	−2.16867	−0.497527	−0.248763	+	0.968564i	$0.580024\pi$
$20$	4.16867	0.932143
$21$	1.52023	0.331741
$22$	4.64844	0.991050
$23$	−3.68890	−0.769189	−0.384594	−	0.923086i	$-0.625659\pi$
$23$	−3.68890	−0.769189	−0.384594	+	0.923086i	$0.625659\pi$
$24$	1.52023	0.310316
$25$	12.3778	2.47556
$26$	0	0
$27$	−5.60798	−1.07926
$28$	1.00000	0.188982
$29$	5.04046	0.935990	0.467995	−	0.883731i	$-0.344977\pi$
$29$	5.04046	0.935990	0.467995	+	0.883731i	$0.344977\pi$
$30$	6.33734	1.15703
$31$	−4.64844	−0.834884	−0.417442	−	0.908704i	$-0.637073\pi$
$31$	−4.64844	−0.834884	−0.417442	+	0.908704i	$0.637073\pi$
$32$	1.00000	0.176777
$33$	7.06670	1.23015
$34$	−6.33734	−1.08684
$35$	4.16867	0.704634
$36$	−0.688899	−0.114817
$37$	−1.68890	−0.277653	−0.138827	−	0.990317i	$-0.544333\pi$
$37$	−1.68890	−0.277653	−0.138827	+	0.990317i	$0.544333\pi$
$38$	−2.16867	−0.351805
$39$	0	0
$40$	4.16867	0.659124
$41$	−9.68890	−1.51315	−0.756576	−	0.653906i	$-0.773129\pi$
$41$	−9.68890	−1.51315	−0.756576	+	0.653906i	$0.773129\pi$
$42$	1.52023	0.234577
$43$	4.33734	0.661438	0.330719	−	0.943729i	$-0.392709\pi$
$43$	4.33734	0.661438	0.330719	+	0.943729i	$0.392709\pi$
$44$	4.64844	0.700778
$45$	−2.87179	−0.428102
$46$	−3.68890	−0.543899
$47$	3.35156	0.488876	0.244438	−	0.969665i	$-0.421397\pi$
$47$	3.35156	0.488876	0.244438	+	0.969665i	$0.421397\pi$
$48$	1.52023	0.219426
$49$	1.00000	0.142857
$50$	12.3778	1.75049
$51$	−9.63421	−1.34906
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−5.60798	−0.763149
$55$	19.3778	2.61290
$56$	1.00000	0.133631
$57$	−3.29688	−0.436682
$58$	5.04046	0.661845
$59$	−9.54647	−1.24284	−0.621422	−	0.783476i	$-0.713445\pi$
$59$	−9.54647	−1.24284	−0.621422	+	0.783476i	$0.713445\pi$
$60$	6.33734	0.818147
$61$	0.479769	0.0614282	0.0307141	−	0.999528i	$-0.490222\pi$
$61$	0.479769	0.0614282	0.0307141	+	0.999528i	$0.490222\pi$
$62$	−4.64844	−0.590352
$63$	−0.688899	−0.0867931
$64$	1.00000	0.125000
$65$	0	0
$66$	7.06670	0.869850
$67$	0.311101	0.0380070	0.0190035	−	0.999819i	$-0.493951\pi$
$67$	0.311101	0.0380070	0.0190035	+	0.999819i	$0.493951\pi$
$68$	−6.33734	−0.768515
$69$	−5.60798	−0.675121
$70$	4.16867	0.498251
$71$	−6.08092	−0.721673	−0.360836	−	0.932629i	$-0.617509\pi$
$71$	−6.08092	−0.721673	−0.360836	+	0.932629i	$0.617509\pi$
$72$	−0.688899	−0.0811875
$73$	−1.35156	−0.158188	−0.0790942	−	0.996867i	$-0.525203\pi$
$73$	−1.35156	−0.158188	−0.0790942	+	0.996867i	$0.525203\pi$
$74$	−1.68890	−0.196331
$75$	18.8171	2.17281
$76$	−2.16867	−0.248763
$77$	4.64844	0.529739
$78$	0	0
$79$	−14.0262	−1.57807	−0.789037	−	0.614345i	$-0.789420\pi$
$79$	−14.0262	−1.57807	−0.789037	+	0.614345i	$0.789420\pi$
$80$	4.16867	0.466071
$81$	−6.45872	−0.717636
$82$	−9.68890	−1.06996
$83$	11.4655	1.25851	0.629254	−	0.777200i	$-0.283361\pi$
$83$	11.4655	1.25851	0.629254	+	0.777200i	$0.283361\pi$
$84$	1.52023	0.165871
$85$	−26.4183	−2.86546
$86$	4.33734	0.467707
$87$	7.66266	0.821524
$88$	4.64844	0.495525
$89$	−1.66266	−0.176242	−0.0881209	−	0.996110i	$-0.528086\pi$
$89$	−1.66266	−0.176242	−0.0881209	+	0.996110i	$0.528086\pi$
$90$	−2.87179	−0.302713
$91$	0	0
$92$	−3.68890	−0.384594
$93$	−7.06670	−0.732782
$94$	3.35156	0.345687
$95$	−9.04046	−0.927532
$96$	1.52023	0.155158
$97$	−2.31110	−0.234657	−0.117328	−	0.993093i	$-0.537433\pi$
$97$	−2.31110	−0.234657	−0.117328	+	0.993093i	$0.537433\pi$
$98$	1.00000	0.101015
$99$	−3.20231	−0.321844
$100$	12.3778	1.23778
$101$	15.8576	1.57789	0.788943	−	0.614466i	$-0.210628\pi$
$101$	15.8576	1.57789	0.788943	+	0.614466i	$0.210628\pi$
$102$	−9.63421	−0.953929
$103$	0.337337	0.0332388	0.0166194	−	0.999862i	$-0.494710\pi$
$103$	0.337337	0.0332388	0.0166194	+	0.999862i	$0.494710\pi$
$104$	0	0
$105$	6.33734	0.618461
$106$	−6.00000	−0.582772
$107$	7.37780	0.713239	0.356619	−	0.934250i	$-0.383929\pi$
$107$	7.37780	0.713239	0.356619	+	0.934250i	$0.383929\pi$
$108$	−5.60798	−0.539628
$109$	8.08092	0.774012	0.387006	−	0.922077i	$-0.373509\pi$
$109$	8.08092	0.774012	0.387006	+	0.922077i	$0.373509\pi$
$110$	19.3778	1.84760
$111$	−2.56752	−0.243698
$112$	1.00000	0.0944911
$113$	3.68890	0.347022	0.173511	−	0.984832i	$-0.444489\pi$
$113$	3.68890	0.347022	0.173511	+	0.984832i	$0.444489\pi$
$114$	−3.29688	−0.308781
$115$	−15.3778	−1.43399
$116$	5.04046	0.467995
$117$	0	0
$118$	−9.54647	−0.878824
$119$	−6.33734	−0.580943
$120$	6.33734	0.578517
$121$	10.6080	0.964362
$122$	0.479769	0.0434363
$123$	−14.7294	−1.32810
$124$	−4.64844	−0.417442
$125$	30.7556	2.75086
$126$	−0.688899	−0.0613720
$127$	2.39202	0.212258	0.106129	−	0.994352i	$-0.466154\pi$
$127$	2.39202	0.212258	0.106129	+	0.994352i	$0.466154\pi$
$128$	1.00000	0.0883883
$129$	6.59375	0.580548
$130$	0	0
$131$	8.42508	0.736103	0.368051	−	0.929805i	$-0.380025\pi$
$131$	8.42508	0.736103	0.368051	+	0.929805i	$0.380025\pi$
$132$	7.06670	0.615077
$133$	−2.16867	−0.188047
$134$	0.311101	0.0268750
$135$	−23.3778	−2.01204
$136$	−6.33734	−0.543422
$137$	−6.08092	−0.519528	−0.259764	−	0.965672i	$-0.583645\pi$
$137$	−6.08092	−0.519528	−0.259764	+	0.965672i	$0.583645\pi$
$138$	−5.60798	−0.477383
$139$	−2.16867	−0.183944	−0.0919720	−	0.995762i	$-0.529317\pi$
$139$	−2.16867	−0.183944	−0.0919720	+	0.995762i	$0.529317\pi$
$140$	4.16867	0.352317
$141$	5.09515	0.429089
$142$	−6.08092	−0.510300
$143$	0	0
$144$	−0.688899	−0.0574083
$145$	21.0120	1.74495
$146$	−1.35156	−0.111856
$147$	1.52023	0.125386
$148$	−1.68890	−0.138827
$149$	8.72936	0.715137	0.357569	−	0.933887i	$-0.383606\pi$
$149$	8.72936	0.715137	0.357569	+	0.933887i	$0.383606\pi$
$150$	18.8171	1.53641
$151$	−10.3373	−0.841241	−0.420620	−	0.907237i	$-0.638188\pi$
$151$	−10.3373	−0.841241	−0.420620	+	0.907237i	$0.638188\pi$
$152$	−2.16867	−0.175902
$153$	4.36579	0.352953
$154$	4.64844	0.374582
$155$	−19.3778	−1.55646
$156$	0	0
$157$	−1.60115	−0.127786	−0.0638929	−	0.997957i	$-0.520352\pi$
$157$	−1.60115	−0.127786	−0.0638929	+	0.997957i	$0.520352\pi$
$158$	−14.0262	−1.11587
$159$	−9.12138	−0.723373
$160$	4.16867	0.329562
$161$	−3.68890	−0.290726
$162$	−6.45872	−0.507445
$163$	18.4183	1.44263	0.721315	−	0.692607i	$-0.243538\pi$
$163$	18.4183	1.44263	0.721315	+	0.692607i	$0.243538\pi$
$164$	−9.68890	−0.756576
$165$	29.4587	2.29336
$166$	11.4655	0.889899
$167$	−5.74358	−0.444452	−0.222226	−	0.974995i	$-0.571332\pi$
$167$	−5.74358	−0.444452	−0.222226	+	0.974995i	$0.571332\pi$
$168$	1.52023	0.117288
$169$	0	0
$170$	−26.4183	−2.02619
$171$	1.49399	0.114249
$172$	4.33734	0.330719
$173$	−22.2496	−1.69161	−0.845803	−	0.533496i	$-0.820878\pi$
$173$	−22.2496	−1.69161	−0.845803	+	0.533496i	$0.820878\pi$
$174$	7.66266	0.580905
$175$	12.3778	0.935674
$176$	4.64844	0.350389
$177$	−14.5128	−1.09085
$178$	−1.66266	−0.124622
$179$	14.5938	1.09079	0.545394	−	0.838180i	$-0.316380\pi$
$179$	14.5938	1.09079	0.545394	+	0.838180i	$0.316380\pi$
$180$	−2.87179	−0.214051
$181$	−19.5727	−1.45483	−0.727414	−	0.686199i	$-0.759278\pi$
$181$	−19.5727	−1.45483	−0.727414	+	0.686199i	$0.759278\pi$
$182$	0	0
$183$	0.729360	0.0539159
$184$	−3.68890	−0.271949
$185$	−7.04046	−0.517625
$186$	−7.06670	−0.518155
$187$	−29.4587	−2.15423
$188$	3.35156	0.244438
$189$	−5.60798	−0.407920
$190$	−9.04046	−0.655864
$191$	6.95954	0.503575	0.251787	−	0.967783i	$-0.418982\pi$
$191$	6.95954	0.503575	0.251787	+	0.967783i	$0.418982\pi$
$192$	1.52023	0.109713
$193$	13.3778	0.962955	0.481477	−	0.876458i	$-0.340100\pi$
$193$	13.3778	0.962955	0.481477	+	0.876458i	$0.340100\pi$
$194$	−2.31110	−0.165927
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0262	−0.714340	−0.357170	−	0.934039i	$-0.616258\pi$
$197$	−10.0262	−0.714340	−0.357170	+	0.934039i	$0.616258\pi$
$198$	−3.20231	−0.227578
$199$	12.3373	0.874571	0.437285	−	0.899323i	$-0.355940\pi$
$199$	12.3373	0.874571	0.437285	+	0.899323i	$0.355940\pi$
$200$	12.3778	0.875243
$201$	0.472945	0.0333590
$202$	15.8576	1.11573
$203$	5.04046	0.353771
$204$	−9.63421	−0.674530
$205$	−40.3898	−2.82095
$206$	0.337337	0.0235034
$207$	2.54128	0.176631
$208$	0	0
$209$	−10.0809	−0.697312
$210$	6.33734	0.437318
$211$	−6.75560	−0.465074	−0.232537	−	0.972587i	$-0.574703\pi$
$211$	−6.75560	−0.465074	−0.232537	+	0.972587i	$0.574703\pi$
$212$	−6.00000	−0.412082
$213$	−9.24440	−0.633416
$214$	7.37780	0.504336
$215$	18.0809	1.23311
$216$	−5.60798	−0.381575
$217$	−4.64844	−0.315557
$218$	8.08092	0.547309
$219$	−2.05469	−0.138843
$220$	19.3778	1.30645
$221$	0	0
$222$	−2.56752	−0.172320
$223$	2.39202	0.160182	0.0800909	−	0.996788i	$-0.474479\pi$
$223$	2.39202	0.160182	0.0800909	+	0.996788i	$0.474479\pi$
$224$	1.00000	0.0668153
$225$	−8.52706	−0.568470
$226$	3.68890	0.245382
$227$	−13.2091	−0.876721	−0.438360	−	0.898799i	$-0.644441\pi$
$227$	−13.2091	−0.876721	−0.438360	+	0.898799i	$0.644441\pi$
$228$	−3.29688	−0.218341
$229$	13.2901	0.878231	0.439116	−	0.898431i	$-0.355292\pi$
$229$	13.2901	0.878231	0.439116	+	0.898431i	$0.355292\pi$
$230$	−15.3778	−1.01398
$231$	7.06670	0.464955
$232$	5.04046	0.330922
$233$	7.76982	0.509018	0.254509	−	0.967070i	$-0.418086\pi$
$233$	7.76982	0.509018	0.254509	+	0.967070i	$0.418086\pi$
$234$	0	0
$235$	13.9716	0.911403
$236$	−9.54647	−0.621422
$237$	−21.3231	−1.38509
$238$	−6.33734	−0.410789
$239$	29.0929	1.88187	0.940933	−	0.338594i	$-0.109951\pi$
$239$	29.0929	1.88187	0.940933	+	0.338594i	$0.109951\pi$
$240$	6.33734	0.409073
$241$	4.59375	0.295910	0.147955	−	0.988994i	$-0.452731\pi$
$241$	4.59375	0.295910	0.147955	+	0.988994i	$0.452731\pi$
$242$	10.6080	0.681907
$243$	7.00519	0.449383
$244$	0.479769	0.0307141
$245$	4.16867	0.266326
$246$	−14.7294	−0.939110
$247$	0	0
$248$	−4.64844	−0.295176
$249$	17.4303	1.10460
$250$	30.7556	1.94515
$251$	22.5322	1.42222	0.711111	−	0.703079i	$-0.248192\pi$
$251$	22.5322	1.42222	0.711111	+	0.703079i	$0.248192\pi$
$252$	−0.688899	−0.0433966
$253$	−17.1476	−1.07806
$254$	2.39202	0.150089
$255$	−40.1618	−2.51503
$256$	1.00000	0.0625000
$257$	−3.91908	−0.244465	−0.122233	−	0.992501i	$-0.539005\pi$
$257$	−3.91908	−0.244465	−0.122233	+	0.992501i	$0.539005\pi$
$258$	6.59375	0.410509
$259$	−1.68890	−0.104943
$260$	0	0
$261$	−3.47237	−0.214934
$262$	8.42508	0.520503
$263$	13.7151	0.845711	0.422856	−	0.906197i	$-0.361028\pi$
$263$	13.7151	0.845711	0.422856	+	0.906197i	$0.361028\pi$
$264$	7.06670	0.434925
$265$	−25.0120	−1.53648
$266$	−2.16867	−0.132970
$267$	−2.52763	−0.154688
$268$	0.311101	0.0190035
$269$	29.4918	1.79815	0.899073	−	0.437799i	$-0.144242\pi$
$269$	29.4918	1.79815	0.899073	+	0.437799i	$0.144242\pi$
$270$	−23.3778	−1.42273
$271$	−1.76982	−0.107509	−0.0537545	−	0.998554i	$-0.517119\pi$
$271$	−1.76982	−0.107509	−0.0537545	+	0.998554i	$0.517119\pi$
$272$	−6.33734	−0.384258
$273$	0	0
$274$	−6.08092	−0.367362
$275$	57.5374	3.46964
$276$	−5.60798	−0.337561
$277$	3.91908	0.235475	0.117737	−	0.993045i	$-0.462436\pi$
$277$	3.91908	0.235475	0.117737	+	0.993045i	$0.462436\pi$
$278$	−2.16867	−0.130068
$279$	3.20231	0.191717
$280$	4.16867	0.249126
$281$	−2.08092	−0.124137	−0.0620687	−	0.998072i	$-0.519770\pi$
$281$	−2.08092	−0.124137	−0.0620687	+	0.998072i	$0.519770\pi$
$282$	5.09515	0.303412
$283$	11.9385	0.709670	0.354835	−	0.934929i	$-0.384537\pi$
$283$	11.9385	0.709670	0.354835	+	0.934929i	$0.384537\pi$
$284$	−6.08092	−0.360836
$285$	−13.7436	−0.814100
$286$	0	0
$287$	−9.68890	−0.571918
$288$	−0.688899	−0.0405938
$289$	23.1618	1.36246
$290$	21.0120	1.23387
$291$	−3.51341	−0.205960
$292$	−1.35156	−0.0790942
$293$	−12.5060	−0.730609	−0.365304	−	0.930888i	$-0.619035\pi$
$293$	−12.5060	−0.730609	−0.365304	+	0.930888i	$0.619035\pi$
$294$	1.52023	0.0886616
$295$	−39.7961	−2.31702
$296$	−1.68890	−0.0981653
$297$	−26.0683	−1.51264
$298$	8.72936	0.505678
$299$	0	0
$300$	18.8171	1.08641
$301$	4.33734	0.250000
$302$	−10.3373	−0.594847
$303$	24.1072	1.38492
$304$	−2.16867	−0.124382
$305$	2.00000	0.114520
$306$	4.36579	0.249575
$307$	−13.3846	−0.763901	−0.381950	−	0.924183i	$-0.624747\pi$
$307$	−13.3846	−0.763901	−0.381950	+	0.924183i	$0.624747\pi$
$308$	4.64844	0.264869
$309$	0.512830	0.0291739
$310$	−19.3778	−1.10058
$311$	24.6747	1.39917	0.699586	−	0.714548i	$-0.253368\pi$
$311$	24.6747	1.39917	0.699586	+	0.714548i	$0.253368\pi$
$312$	0	0
$313$	13.0405	0.737090	0.368545	−	0.929610i	$-0.379856\pi$
$313$	13.0405	0.737090	0.368545	+	0.929610i	$0.379856\pi$
$314$	−1.60115	−0.0903583
$315$	−2.87179	−0.161807
$316$	−14.0262	−0.789037
$317$	−11.2706	−0.633022	−0.316511	−	0.948589i	$-0.602511\pi$
$317$	−11.2706	−0.633022	−0.316511	+	0.948589i	$0.602511\pi$
$318$	−9.12138	−0.511502
$319$	23.4303	1.31184
$320$	4.16867	0.233036
$321$	11.2160	0.626014
$322$	−3.68890	−0.205574
$323$	13.7436	0.764714
$324$	−6.45872	−0.358818
$325$	0	0
$326$	18.4183	1.02009
$327$	12.2849	0.679355
$328$	−9.68890	−0.534980
$329$	3.35156	0.184778
$330$	29.4587	1.62165
$331$	−16.0262	−0.880882	−0.440441	−	0.897782i	$-0.645178\pi$
$331$	−16.0262	−0.880882	−0.440441	+	0.897782i	$0.645178\pi$
$332$	11.4655	0.629254
$333$	1.16348	0.0637584
$334$	−5.74358	−0.314275
$335$	1.29688	0.0708559
$336$	1.52023	0.0829354
$337$	27.8507	1.51713	0.758563	−	0.651599i	$-0.225902\pi$
$337$	27.8507	1.51713	0.758563	+	0.651599i	$0.225902\pi$
$338$	0	0
$339$	5.60798	0.304584
$340$	−26.4183	−1.43273
$341$	−21.6080	−1.17014
$342$	1.49399	0.0807859
$343$	1.00000	0.0539949
$344$	4.33734	0.233854
$345$	−23.3778	−1.25862
$346$	−22.2496	−1.19615
$347$	−2.41826	−0.129819	−0.0649095	−	0.997891i	$-0.520676\pi$
$347$	−2.41826	−0.129819	−0.0649095	+	0.997891i	$0.520676\pi$
$348$	7.66266	0.410762
$349$	−19.0998	−1.02239	−0.511193	−	0.859466i	$-0.670796\pi$
$349$	−19.0998	−1.02239	−0.511193	+	0.859466i	$0.670796\pi$
$350$	12.3778	0.661621
$351$	0	0
$352$	4.64844	0.247763
$353$	−18.0262	−0.959440	−0.479720	−	0.877422i	$-0.659262\pi$
$353$	−18.0262	−0.959440	−0.479720	+	0.877422i	$0.659262\pi$
$354$	−14.5128	−0.771348
$355$	−25.3493	−1.34540
$356$	−1.66266	−0.0881209
$357$	−9.63421	−0.509897
$358$	14.5938	0.771304
$359$	28.3089	1.49409	0.747043	−	0.664776i	$-0.231473\pi$
$359$	28.3089	1.49409	0.747043	+	0.664776i	$0.231473\pi$
$360$	−2.87179	−0.151357
$361$	−14.2969	−0.752467
$362$	−19.5727	−1.02872
$363$	16.1266	0.846425
$364$	0	0
$365$	−5.63421	−0.294908
$366$	0.729360	0.0381243
$367$	−2.08092	−0.108623	−0.0543116	−	0.998524i	$-0.517296\pi$
$367$	−2.08092	−0.108623	−0.0543116	+	0.998524i	$0.517296\pi$
$368$	−3.68890	−0.192297
$369$	6.67467	0.347470
$370$	−7.04046	−0.366016
$371$	−6.00000	−0.311504
$372$	−7.06670	−0.366391
$373$	−28.0809	−1.45398	−0.726988	−	0.686651i	$-0.759080\pi$
$373$	−28.0809	−1.45398	−0.726988	+	0.686651i	$0.759080\pi$
$374$	−29.4587	−1.52327
$375$	46.7556	2.41445
$376$	3.35156	0.172844
$377$	0	0
$378$	−5.60798	−0.288443
$379$	−5.01201	−0.257450	−0.128725	−	0.991680i	$-0.541088\pi$
$379$	−5.01201	−0.257450	−0.128725	+	0.991680i	$0.541088\pi$
$380$	−9.04046	−0.463766
$381$	3.63643	0.186300
$382$	6.95954	0.356081
$383$	4.81028	0.245794	0.122897	−	0.992419i	$-0.460782\pi$
$383$	4.81028	0.245794	0.122897	+	0.992419i	$0.460782\pi$
$384$	1.52023	0.0775789
$385$	19.3778	0.987584
$386$	13.3778	0.680912
$387$	−2.98799	−0.151888
$388$	−2.31110	−0.117328
$389$	−35.0120	−1.77518	−0.887590	−	0.460635i	$-0.847622\pi$
$389$	−35.0120	−1.77518	−0.887590	+	0.460635i	$0.847622\pi$
$390$	0	0
$391$	23.3778	1.18227
$392$	1.00000	0.0505076
$393$	12.8081	0.646082
$394$	−10.0262	−0.505114
$395$	−58.4707	−2.94198
$396$	−3.20231	−0.160922
$397$	−23.2616	−1.16747	−0.583733	−	0.811946i	$-0.698409\pi$
$397$	−23.2616	−1.16747	−0.583733	+	0.811946i	$0.698409\pi$
$398$	12.3373	0.618415
$399$	−3.29688	−0.165050
$400$	12.3778	0.618890
$401$	−10.6222	−0.530447	−0.265224	−	0.964187i	$-0.585446\pi$
$401$	−10.6222	−0.530447	−0.265224	+	0.964187i	$0.585446\pi$
$402$	0.472945	0.0235884
$403$	0	0
$404$	15.8576	0.788943
$405$	−26.9243	−1.33788
$406$	5.04046	0.250154
$407$	−7.85074	−0.389147
$408$	−9.63421	−0.476965
$409$	12.5938	0.622721	0.311360	−	0.950292i	$-0.399215\pi$
$409$	12.5938	0.622721	0.311360	+	0.950292i	$0.399215\pi$
$410$	−40.3898	−1.99471
$411$	−9.24440	−0.455993
$412$	0.337337	0.0166194
$413$	−9.54647	−0.469751
$414$	2.54128	0.124897
$415$	47.7961	2.34622
$416$	0	0
$417$	−3.29688	−0.161449
$418$	−10.0809	−0.493074
$419$	19.9385	0.974059	0.487029	−	0.873386i	$-0.338080\pi$
$419$	19.9385	0.974059	0.487029	+	0.873386i	$0.338080\pi$
$420$	6.33734	0.309230
$421$	13.3516	0.650715	0.325358	−	0.945591i	$-0.394515\pi$
$421$	13.3516	0.650715	0.325358	+	0.945591i	$0.394515\pi$
$422$	−6.75560	−0.328857
$423$	−2.30889	−0.112262
$424$	−6.00000	−0.291386
$425$	−78.4423	−3.80501
$426$	−9.24440	−0.447893
$427$	0.479769	0.0232177
$428$	7.37780	0.356619
$429$	0	0
$430$	18.0809	0.871939
$431$	−9.04046	−0.435464	−0.217732	−	0.976009i	$-0.569866\pi$
$431$	−9.04046	−0.435464	−0.217732	+	0.976009i	$0.569866\pi$
$432$	−5.60798	−0.269814
$433$	−5.82451	−0.279908	−0.139954	−	0.990158i	$-0.544695\pi$
$433$	−5.82451	−0.279908	−0.139954	+	0.990158i	$0.544695\pi$
$434$	−4.64844	−0.223132
$435$	31.9431	1.53155
$436$	8.08092	0.387006
$437$	8.00000	0.382692
$438$	−2.05469	−0.0981767
$439$	−16.8365	−0.803563	−0.401782	−	0.915736i	$-0.631609\pi$
$439$	−16.8365	−0.803563	−0.401782	+	0.915736i	$0.631609\pi$
$440$	19.3778	0.923800
$441$	−0.688899	−0.0328047
$442$	0	0
$443$	22.0809	1.04910	0.524548	−	0.851381i	$-0.324234\pi$
$443$	22.0809	1.04910	0.524548	+	0.851381i	$0.324234\pi$
$444$	−2.56752	−0.121849
$445$	−6.93109	−0.328565
$446$	2.39202	0.113266
$447$	13.2706	0.627680
$448$	1.00000	0.0472456
$449$	−28.0525	−1.32388	−0.661939	−	0.749558i	$-0.730266\pi$
$449$	−28.0525	−1.32388	−0.661939	+	0.749558i	$0.730266\pi$
$450$	−8.52706	−0.401969
$451$	−45.0382	−2.12077
$452$	3.68890	0.173511
$453$	−15.7151	−0.738361
$454$	−13.2091	−0.619935
$455$	0	0
$456$	−3.29688	−0.154390
$457$	−38.5653	−1.80401	−0.902004	−	0.431727i	$-0.857904\pi$
$457$	−38.5653	−1.80401	−0.902004	+	0.431727i	$0.857904\pi$
$458$	13.2901	0.621003
$459$	35.5396	1.65885
$460$	−15.3778	−0.716994
$461$	16.7909	0.782029	0.391014	−	0.920385i	$-0.372124\pi$
$461$	16.7909	0.782029	0.391014	+	0.920385i	$0.372124\pi$
$462$	7.06670	0.328773
$463$	17.9716	0.835209	0.417604	−	0.908629i	$-0.362870\pi$
$463$	17.9716	0.835209	0.417604	+	0.908629i	$0.362870\pi$
$464$	5.04046	0.233998
$465$	−29.4587	−1.36612
$466$	7.76982	0.359930
$467$	−34.8433	−1.61236	−0.806179	−	0.591672i	$-0.798468\pi$
$467$	−34.8433	−1.61236	−0.806179	+	0.591672i	$0.798468\pi$
$468$	0	0
$469$	0.311101	0.0143653
$470$	13.9716	0.644460
$471$	−2.43412	−0.112158
$472$	−9.54647	−0.439412
$473$	20.1618	0.927043
$474$	−21.3231	−0.979403
$475$	−26.8433	−1.23166
$476$	−6.33734	−0.290471
$477$	4.13340	0.189255
$478$	29.0929	1.33068
$479$	−30.4183	−1.38985	−0.694923	−	0.719084i	$-0.744562\pi$
$479$	−30.4183	−1.38985	−0.694923	+	0.719084i	$0.744562\pi$
$480$	6.33734	0.289259
$481$	0	0
$482$	4.59375	0.209240
$483$	−5.60798	−0.255172
$484$	10.6080	0.482181
$485$	−9.63421	−0.437467
$486$	7.00519	0.317762
$487$	−6.95954	−0.315367	−0.157683	−	0.987490i	$-0.550403\pi$
$487$	−6.95954	−0.315367	−0.157683	+	0.987490i	$0.550403\pi$
$488$	0.479769	0.0217181
$489$	28.0000	1.26620
$490$	4.16867	0.188321
$491$	−38.6462	−1.74408	−0.872040	−	0.489435i	$-0.837203\pi$
$491$	−38.6462	−1.74408	−0.872040	+	0.489435i	$0.837203\pi$
$492$	−14.7294	−0.664051
$493$	−31.9431	−1.43864
$494$	0	0
$495$	−13.3493	−0.600009
$496$	−4.64844	−0.208721
$497$	−6.08092	−0.272767
$498$	17.4303	0.781069
$499$	14.2827	0.639379	0.319690	−	0.947522i	$-0.396421\pi$
$499$	14.2827	0.639379	0.319690	+	0.947522i	$0.396421\pi$
$500$	30.7556	1.37543
$501$	−8.73157	−0.390098
$502$	22.5322	1.00566
$503$	20.0525	0.894096	0.447048	−	0.894510i	$-0.352475\pi$
$503$	20.0525	0.894096	0.447048	+	0.894510i	$0.352475\pi$
$504$	−0.688899	−0.0306860
$505$	66.1049	2.94163
$506$	−17.1476	−0.762305
$507$	0	0
$508$	2.39202	0.106129
$509$	−8.84334	−0.391974	−0.195987	−	0.980606i	$-0.562791\pi$
$509$	−8.84334	−0.391974	−0.195987	+	0.980606i	$0.562791\pi$
$510$	−40.1618	−1.77840
$511$	−1.35156	−0.0597896
$512$	1.00000	0.0441942
$513$	12.1618	0.536959
$514$	−3.91908	−0.172863
$515$	1.40625	0.0619667
$516$	6.59375	0.290274
$517$	15.5795	0.685187
$518$	−1.68890	−0.0742060
$519$	−33.8245	−1.48473
$520$	0	0
$521$	−22.9595	−1.00588	−0.502938	−	0.864323i	$-0.667748\pi$
$521$	−22.9595	−1.00588	−0.502938	+	0.864323i	$0.667748\pi$
$522$	−3.47237	−0.151981
$523$	2.76463	0.120889	0.0604445	−	0.998172i	$-0.480748\pi$
$523$	2.76463	0.120889	0.0604445	+	0.998172i	$0.480748\pi$
$524$	8.42508	0.368051
$525$	18.8171	0.821246
$526$	13.7151	0.598008
$527$	29.4587	1.28324
$528$	7.06670	0.307539
$529$	−9.39202	−0.408349
$530$	−25.0120	−1.08645
$531$	6.57655	0.285398
$532$	−2.16867	−0.0940237
$533$	0	0
$534$	−2.52763	−0.109381
$535$	30.7556	1.32968
$536$	0.311101	0.0134375
$537$	22.1859	0.957391
$538$	29.4918	1.27148
$539$	4.64844	0.200222
$540$	−23.3778	−1.00602
$541$	−33.7676	−1.45178	−0.725891	−	0.687809i	$-0.758573\pi$
$541$	−33.7676	−1.45178	−0.725891	+	0.687809i	$0.758573\pi$
$542$	−1.76982	−0.0760203
$543$	−29.7550	−1.27691
$544$	−6.33734	−0.271711
$545$	33.6867	1.44298
$546$	0	0
$547$	23.0405	0.985139	0.492569	−	0.870273i	$-0.336058\pi$
$547$	23.0405	0.985139	0.492569	+	0.870273i	$0.336058\pi$
$548$	−6.08092	−0.259764
$549$	−0.330513	−0.0141059
$550$	57.5374	2.45340
$551$	−10.9311	−0.465680
$552$	−5.60798	−0.238691
$553$	−14.0262	−0.596456
$554$	3.91908	0.166506
$555$	−10.7031	−0.454322
$556$	−2.16867	−0.0919720
$557$	−19.9453	−0.845110	−0.422555	−	0.906337i	$-0.638867\pi$
$557$	−19.9453	−0.845110	−0.422555	+	0.906337i	$0.638867\pi$
$558$	3.20231	0.135564
$559$	0	0
$560$	4.16867	0.176158
$561$	−44.7840	−1.89078
$562$	−2.08092	−0.0877784
$563$	−34.6416	−1.45997	−0.729985	−	0.683463i	$-0.760473\pi$
$563$	−34.6416	−1.45997	−0.729985	+	0.683463i	$0.760473\pi$
$564$	5.09515	0.214544
$565$	15.3778	0.646949
$566$	11.9385	0.501812
$567$	−6.45872	−0.271241
$568$	−6.08092	−0.255150
$569$	22.9573	0.962421	0.481211	−	0.876605i	$-0.340197\pi$
$569$	22.9573	0.962421	0.481211	+	0.876605i	$0.340197\pi$
$570$	−13.7436	−0.575655
$571$	42.3089	1.77057	0.885286	−	0.465047i	$-0.153963\pi$
$571$	42.3089	1.77057	0.885286	+	0.465047i	$0.153963\pi$
$572$	0	0
$573$	10.5801	0.441990
$574$	−9.68890	−0.404407
$575$	−45.6605	−1.90417
$576$	−0.688899	−0.0287041
$577$	12.9311	0.538328	0.269164	−	0.963094i	$-0.413253\pi$
$577$	12.9311	0.538328	0.269164	+	0.963094i	$0.413253\pi$
$578$	23.1618	0.963406
$579$	20.3373	0.845191
$580$	21.0120	0.872476
$581$	11.4655	0.475671
$582$	−3.51341	−0.145635
$583$	−27.8906	−1.15511
$584$	−1.35156	−0.0559280
$585$	0	0
$586$	−12.5060	−0.516618
$587$	38.3830	1.58424	0.792118	−	0.610368i	$-0.208979\pi$
$587$	38.3830	1.58424	0.792118	+	0.610368i	$0.208979\pi$
$588$	1.52023	0.0626932
$589$	10.0809	0.415377
$590$	−39.7961	−1.63838
$591$	−15.2422	−0.626980
$592$	−1.68890	−0.0694133
$593$	−24.9311	−1.02380	−0.511899	−	0.859046i	$-0.671058\pi$
$593$	−24.9311	−1.02380	−0.511899	+	0.859046i	$0.671058\pi$
$594$	−26.0683	−1.06960
$595$	−26.4183	−1.08304
$596$	8.72936	0.357569
$597$	18.7556	0.767615
$598$	0	0
$599$	−48.7818	−1.99317	−0.996586	−	0.0825632i	$-0.973689\pi$
$599$	−48.7818	−1.99317	−0.996586	+	0.0825632i	$0.973689\pi$
$600$	18.8171	0.768205
$601$	30.0525	1.22587	0.612933	−	0.790135i	$-0.289990\pi$
$601$	30.0525	1.22587	0.612933	+	0.790135i	$0.289990\pi$
$602$	4.33734	0.176777
$603$	−0.214317	−0.00872767
$604$	−10.3373	−0.420620
$605$	44.2211	1.79785
$606$	24.1072	0.979286
$607$	4.05247	0.164485	0.0822424	−	0.996612i	$-0.473792\pi$
$607$	4.05247	0.164485	0.0822424	+	0.996612i	$0.473792\pi$
$608$	−2.16867	−0.0879511
$609$	7.66266	0.310507
$610$	2.00000	0.0809776
$611$	0	0
$612$	4.36579	0.176476
$613$	40.9573	1.65425	0.827125	−	0.562017i	$-0.189975\pi$
$613$	40.9573	1.65425	0.827125	+	0.562017i	$0.189975\pi$
$614$	−13.3846	−0.540159
$615$	−61.4018	−2.47596
$616$	4.64844	0.187291
$617$	−9.37780	−0.377536	−0.188768	−	0.982022i	$-0.560449\pi$
$617$	−9.37780	−0.377536	−0.188768	+	0.982022i	$0.560449\pi$
$618$	0.512830	0.0206291
$619$	−24.4251	−0.981727	−0.490864	−	0.871236i	$-0.663319\pi$
$619$	−24.4251	−0.981727	−0.490864	+	0.871236i	$0.663319\pi$
$620$	−19.3778	−0.778231
$621$	20.6873	0.830151
$622$	24.6747	0.989364
$623$	−1.66266	−0.0666132
$624$	0	0
$625$	66.3209	2.65284
$626$	13.0405	0.521202
$627$	−15.3253	−0.612035
$628$	−1.60115	−0.0638929
$629$	10.7031	0.426761
$630$	−2.87179	−0.114415
$631$	−4.51283	−0.179653	−0.0898265	−	0.995957i	$-0.528631\pi$
$631$	−4.51283	−0.179653	−0.0898265	+	0.995957i	$0.528631\pi$
$632$	−14.0262	−0.557934
$633$	−10.2701	−0.408198
$634$	−11.2706	−0.447614
$635$	9.97155	0.395709
$636$	−9.12138	−0.361686
$637$	0	0
$638$	23.4303	0.927613
$639$	4.18914	0.165720
$640$	4.16867	0.164781
$641$	−0.201730	−0.00796784	−0.00398392	−	0.999992i	$-0.501268\pi$
$641$	−0.201730	−0.00796784	−0.00398392	+	0.999992i	$0.501268\pi$
$642$	11.2160	0.442658
$643$	−37.8838	−1.49399	−0.746996	−	0.664829i	$-0.768504\pi$
$643$	−37.8838	−1.49399	−0.746996	+	0.664829i	$0.768504\pi$
$644$	−3.68890	−0.145363
$645$	27.4872	1.08231
$646$	13.7436	0.540734
$647$	−25.6342	−1.00778	−0.503892	−	0.863766i	$-0.668099\pi$
$647$	−25.6342	−1.00778	−0.503892	+	0.863766i	$0.668099\pi$
$648$	−6.45872	−0.253723
$649$	−44.3762	−1.74192
$650$	0	0
$651$	−7.06670	−0.276966
$652$	18.4183	0.721315
$653$	−49.1454	−1.92321	−0.961604	−	0.274440i	$-0.911507\pi$
$653$	−49.1454	−1.92321	−0.961604	+	0.274440i	$0.911507\pi$
$654$	12.2849	0.480376
$655$	35.1214	1.37231
$656$	−9.68890	−0.378288
$657$	0.931090	0.0363253
$658$	3.35156	0.130657
$659$	−7.66266	−0.298495	−0.149247	−	0.988800i	$-0.547685\pi$
$659$	−7.66266	−0.298495	−0.149247	+	0.988800i	$0.547685\pi$
$660$	29.4587	1.14668
$661$	−15.0336	−0.584741	−0.292370	−	0.956305i	$-0.594444\pi$
$661$	−15.0336	−0.584741	−0.292370	+	0.956305i	$0.594444\pi$
$662$	−16.0262	−0.622877
$663$	0	0
$664$	11.4655	0.444949
$665$	−9.04046	−0.350574
$666$	1.16348	0.0450840
$667$	−18.5938	−0.719953
$668$	−5.74358	−0.222226
$669$	3.63643	0.140592
$670$	1.29688	0.0501027
$671$	2.23018	0.0860951
$672$	1.52023	0.0586442
$673$	16.4445	0.633889	0.316944	−	0.948444i	$-0.397343\pi$
$673$	16.4445	0.633889	0.316944	+	0.948444i	$0.397343\pi$
$674$	27.8507	1.07277
$675$	−69.4144	−2.67176
$676$	0	0
$677$	−6.38520	−0.245403	−0.122702	−	0.992444i	$-0.539156\pi$
$677$	−6.38520	−0.245403	−0.122702	+	0.992444i	$0.539156\pi$
$678$	5.60798	0.215373
$679$	−2.31110	−0.0886919
$680$	−26.4183	−1.01309
$681$	−20.0809	−0.769503
$682$	−21.6080	−0.827412
$683$	33.1476	1.26836	0.634179	−	0.773186i	$-0.281338\pi$
$683$	33.1476	1.26836	0.634179	+	0.773186i	$0.281338\pi$
$684$	1.49399	0.0571243
$685$	−25.3493	−0.968549
$686$	1.00000	0.0381802
$687$	20.2039	0.770828
$688$	4.33734	0.165359
$689$	0	0
$690$	−23.3778	−0.889978
$691$	−25.0473	−0.952844	−0.476422	−	0.879217i	$-0.658066\pi$
$691$	−25.0473	−0.952844	−0.476422	+	0.879217i	$0.658066\pi$
$692$	−22.2496	−0.845803
$693$	−3.20231	−0.121646
$694$	−2.41826	−0.0917959
$695$	−9.04046	−0.342924
$696$	7.66266	0.290452
$697$	61.4018	2.32576
$698$	−19.0998	−0.722937
$699$	11.8119	0.446768
$700$	12.3778	0.467837
$701$	14.4992	0.547627	0.273813	−	0.961783i	$-0.411715\pi$
$701$	14.4992	0.547627	0.273813	+	0.961783i	$0.411715\pi$
$702$	0	0
$703$	3.66266	0.138140
$704$	4.64844	0.175195
$705$	21.2400	0.799944
$706$	−18.0262	−0.678426
$707$	15.8576	0.596385
$708$	−14.5128	−0.545426
$709$	32.4445	1.21848	0.609239	−	0.792986i	$-0.291475\pi$
$709$	32.4445	1.21848	0.609239	+	0.792986i	$0.291475\pi$
$710$	−25.3493	−0.951344
$711$	9.66266	0.362378
$712$	−1.66266	−0.0623109
$713$	17.1476	0.642183
$714$	−9.63421	−0.360551
$715$	0	0
$716$	14.5938	0.545394
$717$	44.2280	1.65172
$718$	28.3089	1.05648
$719$	46.4183	1.73111	0.865554	−	0.500815i	$-0.166966\pi$
$719$	46.4183	1.73111	0.865554	+	0.500815i	$0.166966\pi$
$720$	−2.87179	−0.107025
$721$	0.337337	0.0125631
$722$	−14.2969	−0.532075
$723$	6.98356	0.259721
$724$	−19.5727	−0.727414
$725$	62.3898	2.31710
$726$	16.1266	0.598513
$727$	4.28486	0.158917	0.0794584	−	0.996838i	$-0.474681\pi$
$727$	4.28486	0.158917	0.0794584	+	0.996838i	$0.474681\pi$
$728$	0	0
$729$	30.0257	1.11206
$730$	−5.63421	−0.208532
$731$	−27.4872	−1.01665
$732$	0.729360	0.0269579
$733$	15.7083	0.580200	0.290100	−	0.956996i	$-0.406311\pi$
$733$	15.7083	0.580200	0.290100	+	0.956996i	$0.406311\pi$
$734$	−2.08092	−0.0768082
$735$	6.33734	0.233756
$736$	−3.68890	−0.135975
$737$	1.44613	0.0532690
$738$	6.67467	0.245698
$739$	46.9311	1.72639	0.863194	−	0.504872i	$-0.168460\pi$
$739$	46.9311	1.72639	0.863194	+	0.504872i	$0.168460\pi$
$740$	−7.04046	−0.258812
$741$	0	0
$742$	−6.00000	−0.220267
$743$	−3.58174	−0.131401	−0.0657007	−	0.997839i	$-0.520928\pi$
$743$	−3.58174	−0.131401	−0.0657007	+	0.997839i	$0.520928\pi$
$744$	−7.06670	−0.259078
$745$	36.3898	1.33322
$746$	−28.0809	−1.02812
$747$	−7.89860	−0.288995
$748$	−29.4587	−1.07712
$749$	7.37780	0.269579
$750$	46.7556	1.70727
$751$	−1.09515	−0.0399625	−0.0199812	−	0.999800i	$-0.506361\pi$
$751$	−1.09515	−0.0399625	−0.0199812	+	0.999800i	$0.506361\pi$
$752$	3.35156	0.122219
$753$	34.2542	1.24829
$754$	0	0
$755$	−43.0929	−1.56831
$756$	−5.60798	−0.203960
$757$	−19.7436	−0.717593	−0.358796	−	0.933416i	$-0.616813\pi$
$757$	−19.7436	−0.717593	−0.358796	+	0.933416i	$0.616813\pi$
$758$	−5.01201	−0.182044
$759$	−26.0683	−0.946221
$760$	−9.04046	−0.327932
$761$	1.57953	0.0572578	0.0286289	−	0.999590i	$-0.490886\pi$
$761$	1.57953	0.0572578	0.0286289	+	0.999590i	$0.490886\pi$
$762$	3.63643	0.131734
$763$	8.08092	0.292549
$764$	6.95954	0.251787
$765$	18.1995	0.658005
$766$	4.81028	0.173803
$767$	0	0
$768$	1.52023	0.0548566
$769$	−29.6889	−1.07061	−0.535305	−	0.844659i	$-0.679803\pi$
$769$	−29.6889	−1.07061	−0.535305	+	0.844659i	$0.679803\pi$
$770$	19.3778	0.698327
$771$	−5.95790	−0.214569
$772$	13.3778	0.481477
$773$	−18.2496	−0.656392	−0.328196	−	0.944610i	$-0.606441\pi$
$773$	−18.2496	−0.656392	−0.328196	+	0.944610i	$0.606441\pi$
$774$	−2.98799	−0.107401
$775$	−57.5374	−2.06681
$776$	−2.31110	−0.0829637
$777$	−2.56752	−0.0921091
$778$	−35.0120	−1.25524
$779$	21.0120	0.752833
$780$	0	0
$781$	−28.2668	−1.01147
$782$	23.3778	0.835988
$783$	−28.2668	−1.01017
$784$	1.00000	0.0357143
$785$	−6.67467	−0.238229
$786$	12.8081	0.456849
$787$	20.0877	0.716051	0.358025	−	0.933712i	$-0.383450\pi$
$787$	20.0877	0.716051	0.358025	+	0.933712i	$0.383450\pi$
$788$	−10.0262	−0.357170
$789$	20.8502	0.742286
$790$	−58.4707	−2.08030
$791$	3.68890	0.131162
$792$	−3.20231	−0.113789
$793$	0	0
$794$	−23.2616	−0.825523
$795$	−38.0240	−1.34857
$796$	12.3373	0.437285
$797$	−12.1424	−0.430107	−0.215054	−	0.976602i	$-0.568993\pi$
$797$	−12.1424	−0.430107	−0.215054	+	0.976602i	$0.568993\pi$
$798$	−3.29688	−0.116708
$799$	−21.2400	−0.751416
$800$	12.3778	0.437621
$801$	1.14541	0.0404710
$802$	−10.6222	−0.375083
$803$	−6.28265	−0.221710
$804$	0.472945	0.0166795
$805$	−15.3778	−0.541996
$806$	0	0
$807$	44.8343	1.57824
$808$	15.8576	0.557867
$809$	31.8906	1.12121	0.560607	−	0.828082i	$-0.310568\pi$
$809$	31.8906	1.12121	0.560607	+	0.828082i	$0.310568\pi$
$810$	−26.9243	−0.946022
$811$	44.0172	1.54565	0.772826	−	0.634617i	$-0.218842\pi$
$811$	44.0172	1.54565	0.772826	+	0.634617i	$0.218842\pi$
$812$	5.04046	0.176886
$813$	−2.69054	−0.0943612
$814$	−7.85074	−0.275168
$815$	76.7796	2.68947
$816$	−9.63421	−0.337265
$817$	−9.40625	−0.329083
$818$	12.5938	0.440330
$819$	0	0
$820$	−40.3898	−1.41047
$821$	−7.58174	−0.264605	−0.132302	−	0.991209i	$-0.542237\pi$
$821$	−7.58174	−0.264605	−0.132302	+	0.991209i	$0.542237\pi$
$822$	−9.24440	−0.322436
$823$	−0.0546856	−0.00190622	−0.000953110	−	1.00000i	$-0.500303\pi$
$823$	−0.0546856	−0.00190622	−0.000953110		1.00000i	$0.500303\pi$
$824$	0.337337	0.0117517
$825$	87.4702	3.04532
$826$	−9.54647	−0.332164
$827$	34.2428	1.19074	0.595369	−	0.803453i	$-0.297006\pi$
$827$	34.2428	1.19074	0.595369	+	0.803453i	$0.297006\pi$
$828$	2.54128	0.0883156
$829$	−43.5989	−1.51425	−0.757127	−	0.653268i	$-0.773398\pi$
$829$	−43.5989	−1.51425	−0.757127	+	0.653268i	$0.773398\pi$
$830$	47.7961	1.65903
$831$	5.95790	0.206677
$832$	0	0
$833$	−6.33734	−0.219576
$834$	−3.29688	−0.114161
$835$	−23.9431	−0.828585
$836$	−10.0809	−0.348656
$837$	26.0683	0.901053
$838$	19.9385	0.688764
$839$	24.6484	0.850959	0.425479	−	0.904968i	$-0.360106\pi$
$839$	24.6484	0.850959	0.425479	+	0.904968i	$0.360106\pi$
$840$	6.33734	0.218659
$841$	−3.59375	−0.123923
$842$	13.3516	0.460125
$843$	−3.16348	−0.108956
$844$	−6.75560	−0.232537
$845$	0	0
$846$	−2.30889	−0.0793812
$847$	10.6080	0.364494
$848$	−6.00000	−0.206041
$849$	18.1493	0.622881
$850$	−78.4423	−2.69055
$851$	6.23018	0.213568
$852$	−9.24440	−0.316708
$853$	−44.0456	−1.50809	−0.754047	−	0.656820i	$-0.771901\pi$
$853$	−44.0456	−1.50809	−0.754047	+	0.656820i	$0.771901\pi$
$854$	0.479769	0.0164174
$855$	6.22797	0.212992
$856$	7.37780	0.252168
$857$	32.4707	1.10918	0.554590	−	0.832124i	$-0.312875\pi$
$857$	32.4707	1.10918	0.554590	+	0.832124i	$0.312875\pi$
$858$	0	0
$859$	−19.9385	−0.680292	−0.340146	−	0.940373i	$-0.610477\pi$
$859$	−19.9385	−0.680292	−0.340146	+	0.940373i	$0.610477\pi$
$860$	18.0809	0.616554
$861$	−14.7294	−0.501975
$862$	−9.04046	−0.307919
$863$	45.4587	1.54743	0.773716	−	0.633532i	$-0.218396\pi$
$863$	45.4587	1.54743	0.773716	+	0.633532i	$0.218396\pi$
$864$	−5.60798	−0.190787
$865$	−92.7512	−3.15363
$866$	−5.82451	−0.197925
$867$	35.2113	1.19584
$868$	−4.64844	−0.157778
$869$	−65.2001	−2.21176
$870$	31.9431	1.08297
$871$	0	0
$872$	8.08092	0.273655
$873$	1.59212	0.0538849
$874$	8.00000	0.270604
$875$	30.7556	1.03973
$876$	−2.05469	−0.0694214
$877$	0.120808	0.00407938	0.00203969	−	0.999998i	$-0.499351\pi$
$877$	0.120808	0.00407938	0.00203969	+	0.999998i	$0.499351\pi$
$878$	−16.8365	−0.568205
$879$	−19.0120	−0.641259
$880$	19.3778	0.653225
$881$	22.7840	0.767614	0.383807	−	0.923413i	$-0.374613\pi$
$881$	22.7840	0.767614	0.383807	+	0.923413i	$0.374613\pi$
$882$	−0.688899	−0.0231964
$883$	28.6747	0.964980	0.482490	−	0.875902i	$-0.339733\pi$
$883$	28.6747	0.964980	0.482490	+	0.875902i	$0.339733\pi$
$884$	0	0
$885$	−60.4992	−2.03366
$886$	22.0809	0.741823
$887$	−33.0120	−1.10843	−0.554217	−	0.832372i	$-0.686982\pi$
$887$	−33.0120	−1.10843	−0.554217	+	0.832372i	$0.686982\pi$
$888$	−2.56752	−0.0861602
$889$	2.39202	0.0802259
$890$	−6.93109	−0.232331
$891$	−30.0230	−1.00581
$892$	2.39202	0.0800909
$893$	−7.26843	−0.243229
$894$	13.2706	0.443837
$895$	60.8365	2.03354
$896$	1.00000	0.0334077
$897$	0	0
$898$	−28.0525	−0.936123
$899$	−23.4303	−0.781443
$900$	−8.52706	−0.284235
$901$	38.0240	1.26676
$902$	−45.0382	−1.49961
$903$	6.59375	0.219426
$904$	3.68890	0.122691
$905$	−81.5921	−2.71221
$906$	−15.7151	−0.522100
$907$	−24.5128	−0.813935	−0.406968	−	0.913443i	$-0.633414\pi$
$907$	−24.5128	−0.813935	−0.406968	+	0.913443i	$0.633414\pi$
$908$	−13.2091	−0.438360
$909$	−10.9243	−0.362335
$910$	0	0
$911$	45.5112	1.50785	0.753927	−	0.656959i	$-0.228157\pi$
$911$	45.5112	1.50785	0.753927	+	0.656959i	$0.228157\pi$
$912$	−3.29688	−0.109170
$913$	53.2969	1.76387
$914$	−38.5653	−1.27563
$915$	3.04046	0.100515
$916$	13.2901	0.439116
$917$	8.42508	0.278221
$918$	35.5396	1.17298
$919$	11.4850	0.378854	0.189427	−	0.981895i	$-0.439337\pi$
$919$	11.4850	0.378854	0.189427	+	0.981895i	$0.439337\pi$
$920$	−15.3778	−0.506991
$921$	−20.3477	−0.670480
$922$	16.7909	0.552978
$923$	0	0
$924$	7.06670	0.232477
$925$	−20.9049	−0.687347
$926$	17.9716	0.590582
$927$	−0.232391	−0.00763273
$928$	5.04046	0.165461
$929$	−45.2810	−1.48562	−0.742811	−	0.669501i	$-0.766508\pi$
$929$	−45.2810	−1.48562	−0.742811	+	0.669501i	$0.766508\pi$
$930$	−29.4587	−0.965989
$931$	−2.16867	−0.0710752
$932$	7.76982	0.254509
$933$	37.5112	1.22806
$934$	−34.8433	−1.14011
$935$	−122.804	−4.01611
$936$	0	0
$937$	36.7556	1.20075	0.600377	−	0.799717i	$-0.295017\pi$
$937$	36.7556	1.20075	0.600377	+	0.799717i	$0.295017\pi$
$938$	0.311101	0.0101578
$939$	19.8245	0.646948
$940$	13.9716	0.455702
$941$	−27.5465	−0.897989	−0.448995	−	0.893534i	$-0.648218\pi$
$941$	−27.5465	−0.897989	−0.448995	+	0.893534i	$0.648218\pi$
$942$	−2.43412	−0.0793079
$943$	35.7414	1.16390
$944$	−9.54647	−0.310711
$945$	−23.3778	−0.760480
$946$	20.1618	0.655518
$947$	−48.4423	−1.57416	−0.787081	−	0.616849i	$-0.788409\pi$
$947$	−48.4423	−1.57416	−0.787081	+	0.616849i	$0.788409\pi$
$948$	−21.3231	−0.692543
$949$	0	0
$950$	−26.8433	−0.870913
$951$	−17.1340	−0.555607
$952$	−6.33734	−0.205394
$953$	40.7556	1.32020	0.660102	−	0.751176i	$-0.270513\pi$
$953$	40.7556	1.32020	0.660102	+	0.751176i	$0.270513\pi$
$954$	4.13340	0.133824
$955$	29.0120	0.938807
$956$	29.0929	0.940933
$957$	35.6194	1.15141
$958$	−30.4183	−0.982769
$959$	−6.08092	−0.196363
$960$	6.33734	0.204537
$961$	−9.39202	−0.302968
$962$	0	0
$963$	−5.08256	−0.163783
$964$	4.59375	0.147955
$965$	55.7676	1.79522
$966$	−5.60798	−0.180434
$967$	40.6326	1.30666	0.653328	−	0.757075i	$-0.273372\pi$
$967$	40.6326	1.30666	0.653328	+	0.757075i	$0.273372\pi$
$968$	10.6080	0.340953
$969$	20.8934	0.671193
$970$	−9.63421	−0.309336
$971$	−3.61480	−0.116005	−0.0580023	−	0.998316i	$-0.518473\pi$
$971$	−3.61480	−0.116005	−0.0580023	+	0.998316i	$0.518473\pi$
$972$	7.00519	0.224691
$973$	−2.16867	−0.0695243
$974$	−6.95954	−0.222998
$975$	0	0
$976$	0.479769	0.0153570
$977$	−54.8081	−1.75347	−0.876733	−	0.480978i	$-0.840282\pi$
$977$	−54.8081	−1.75347	−0.876733	+	0.480978i	$0.840282\pi$
$978$	28.0000	0.895341
$979$	−7.72878	−0.247013
$980$	4.16867	0.133163
$981$	−5.56694	−0.177739
$982$	−38.6462	−1.23325
$983$	−53.5248	−1.70718	−0.853589	−	0.520948i	$-0.825579\pi$
$983$	−53.5248	−1.70718	−0.853589	+	0.520948i	$0.825579\pi$
$984$	−14.7294	−0.469555
$985$	−41.7961	−1.33173
$986$	−31.9431	−1.01728
$987$	5.09515	0.162180
$988$	0	0
$989$	−16.0000	−0.508770
$990$	−13.3493	−0.424270
$991$	21.9738	0.698020	0.349010	−	0.937119i	$-0.386518\pi$
$991$	21.9738	0.698020	0.349010	+	0.937119i	$0.386518\pi$
$992$	−4.64844	−0.147588
$993$	−24.3636	−0.773155
$994$	−6.08092	−0.192875
$995$	51.4303	1.63045
$996$	17.4303	0.552299
$997$	8.81711	0.279241	0.139620	−	0.990205i	$-0.455412\pi$
$997$	8.81711	0.279241	0.139620	+	0.990205i	$0.455412\pi$
$998$	14.2827	0.452109
$999$	9.47131	0.299659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bc.1.2		3
13.5	odd	4		182.2.d.b.155.2	✓	6
13.8	odd	4		182.2.d.b.155.5	yes	6
13.12	even	2		2366.2.a.x.1.2		3
39.5	even	4		1638.2.c.i.883.6		6
39.8	even	4		1638.2.c.i.883.1		6
52.31	even	4		1456.2.k.b.337.3		6
52.47	even	4		1456.2.k.b.337.4		6
91.5	even	12		1274.2.n.n.753.2		12
91.18	odd	12		1274.2.n.m.961.5		12
91.31	even	12		1274.2.n.n.961.5		12
91.34	even	4		1274.2.d.l.883.5		6
91.44	odd	12		1274.2.n.m.753.2		12
91.47	even	12		1274.2.n.n.753.5		12
91.60	odd	12		1274.2.n.m.961.2		12
91.73	even	12		1274.2.n.n.961.2		12
91.83	even	4		1274.2.d.l.883.2		6
91.86	odd	12		1274.2.n.m.753.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.d.b.155.2	✓	6	13.5	odd	4
182.2.d.b.155.5	yes	6	13.8	odd	4
1274.2.d.l.883.2		6	91.83	even	4
1274.2.d.l.883.5		6	91.34	even	4
1274.2.n.m.753.2		12	91.44	odd	12
1274.2.n.m.753.5		12	91.86	odd	12
1274.2.n.m.961.2		12	91.60	odd	12
1274.2.n.m.961.5		12	91.18	odd	12
1274.2.n.n.753.2		12	91.5	even	12
1274.2.n.n.753.5		12	91.47	even	12
1274.2.n.n.961.2		12	91.73	even	12
1274.2.n.n.961.5		12	91.31	even	12
1456.2.k.b.337.3		6	52.31	even	4
1456.2.k.b.337.4		6	52.47	even	4
1638.2.c.i.883.1		6	39.8	even	4
1638.2.c.i.883.6		6	39.5	even	4
2366.2.a.x.1.2		3	13.12	even	2
2366.2.a.bc.1.2		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.52023 q^{3} +1.00000 q^{4} +4.16867 q^{5} +1.52023 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.688899 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.52023 q^{3} +1.00000 q^{4} +4.16867 q^{5} +1.52023 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.688899 q^{9} +4.16867 q^{10} +4.64844 q^{11} +1.52023 q^{12} +1.00000 q^{14} +6.33734 q^{15} +1.00000 q^{16} -6.33734 q^{17} -0.688899 q^{18} -2.16867 q^{19} +4.16867 q^{20} +1.52023 q^{21} +4.64844 q^{22} -3.68890 q^{23} +1.52023 q^{24} +12.3778 q^{25} -5.60798 q^{27} +1.00000 q^{28} +5.04046 q^{29} +6.33734 q^{30} -4.64844 q^{31} +1.00000 q^{32} +7.06670 q^{33} -6.33734 q^{34} +4.16867 q^{35} -0.688899 q^{36} -1.68890 q^{37} -2.16867 q^{38} +4.16867 q^{40} -9.68890 q^{41} +1.52023 q^{42} +4.33734 q^{43} +4.64844 q^{44} -2.87179 q^{45} -3.68890 q^{46} +3.35156 q^{47} +1.52023 q^{48} +1.00000 q^{49} +12.3778 q^{50} -9.63421 q^{51} -6.00000 q^{53} -5.60798 q^{54} +19.3778 q^{55} +1.00000 q^{56} -3.29688 q^{57} +5.04046 q^{58} -9.54647 q^{59} +6.33734 q^{60} +0.479769 q^{61} -4.64844 q^{62} -0.688899 q^{63} +1.00000 q^{64} +7.06670 q^{66} +0.311101 q^{67} -6.33734 q^{68} -5.60798 q^{69} +4.16867 q^{70} -6.08092 q^{71} -0.688899 q^{72} -1.35156 q^{73} -1.68890 q^{74} +18.8171 q^{75} -2.16867 q^{76} +4.64844 q^{77} -14.0262 q^{79} +4.16867 q^{80} -6.45872 q^{81} -9.68890 q^{82} +11.4655 q^{83} +1.52023 q^{84} -26.4183 q^{85} +4.33734 q^{86} +7.66266 q^{87} +4.64844 q^{88} -1.66266 q^{89} -2.87179 q^{90} -3.68890 q^{92} -7.06670 q^{93} +3.35156 q^{94} -9.04046 q^{95} +1.52023 q^{96} -2.31110 q^{97} +1.00000 q^{98} -3.20231 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 12 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 12 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 2 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 12 q^{9} + 2 q^{10} + 7 q^{11} + q^{12} + 3 q^{14} - 2 q^{15} + 3 q^{16} + 2 q^{17} + 12 q^{18} + 4 q^{19} + 2 q^{20} + q^{21} + 7 q^{22} + 3 q^{23} + q^{24} + 9 q^{25} - 17 q^{27} + 3 q^{28} + 8 q^{29} - 2 q^{30} - 7 q^{31} + 3 q^{32} - 21 q^{33} + 2 q^{34} + 2 q^{35} + 12 q^{36} + 9 q^{37} + 4 q^{38} + 2 q^{40} - 15 q^{41} + q^{42} - 8 q^{43} + 7 q^{44} - 12 q^{45} + 3 q^{46} + 17 q^{47} + q^{48} + 3 q^{49} + 9 q^{50} + 6 q^{51} - 18 q^{53} - 17 q^{54} + 30 q^{55} + 3 q^{56} + 4 q^{57} + 8 q^{58} + 10 q^{59} - 2 q^{60} + 5 q^{61} - 7 q^{62} + 12 q^{63} + 3 q^{64} - 21 q^{66} + 15 q^{67} + 2 q^{68} - 17 q^{69} + 2 q^{70} - 4 q^{71} + 12 q^{72} - 11 q^{73} + 9 q^{74} + 39 q^{75} + 4 q^{76} + 7 q^{77} - 7 q^{79} + 2 q^{80} + 23 q^{81} - 15 q^{82} + 10 q^{83} + q^{84} - 44 q^{85} - 8 q^{86} + 44 q^{87} + 7 q^{88} - 26 q^{89} - 12 q^{90} + 3 q^{92} + 21 q^{93} + 17 q^{94} - 20 q^{95} + q^{96} - 21 q^{97} + 3 q^{98} + 26 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 2 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 12 * q^9 + 2 * q^10 + 7 * q^11 + q^12 + 3 * q^14 - 2 * q^15 + 3 * q^16 + 2 * q^17 + 12 * q^18 + 4 * q^19 + 2 * q^20 + q^21 + 7 * q^22 + 3 * q^23 + q^24 + 9 * q^25 - 17 * q^27 + 3 * q^28 + 8 * q^29 - 2 * q^30 - 7 * q^31 + 3 * q^32 - 21 * q^33 + 2 * q^34 + 2 * q^35 + 12 * q^36 + 9 * q^37 + 4 * q^38 + 2 * q^40 - 15 * q^41 + q^42 - 8 * q^43 + 7 * q^44 - 12 * q^45 + 3 * q^46 + 17 * q^47 + q^48 + 3 * q^49 + 9 * q^50 + 6 * q^51 - 18 * q^53 - 17 * q^54 + 30 * q^55 + 3 * q^56 + 4 * q^57 + 8 * q^58 + 10 * q^59 - 2 * q^60 + 5 * q^61 - 7 * q^62 + 12 * q^63 + 3 * q^64 - 21 * q^66 + 15 * q^67 + 2 * q^68 - 17 * q^69 + 2 * q^70 - 4 * q^71 + 12 * q^72 - 11 * q^73 + 9 * q^74 + 39 * q^75 + 4 * q^76 + 7 * q^77 - 7 * q^79 + 2 * q^80 + 23 * q^81 - 15 * q^82 + 10 * q^83 + q^84 - 44 * q^85 - 8 * q^86 + 44 * q^87 + 7 * q^88 - 26 * q^89 - 12 * q^90 + 3 * q^92 + 21 * q^93 + 17 * q^94 - 20 * q^95 + q^96 - 21 * q^97 + 3 * q^98 + 26 * q^99

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