LMFDB - Embedded newform 2366.2.a.s.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			$1.73205$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.00000 q^{10} -0.732051 q^{11} +0.732051 q^{12} -1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} -5.73205 q^{17} -2.46410 q^{18} +1.46410 q^{19} -1.00000 q^{20} -0.732051 q^{21} -0.732051 q^{22} +1.26795 q^{23} +0.732051 q^{24} -4.00000 q^{25} -4.00000 q^{27} -1.00000 q^{28} -3.00000 q^{29} -0.732051 q^{30} +5.26795 q^{31} +1.00000 q^{32} -0.535898 q^{33} -5.73205 q^{34} +1.00000 q^{35} -2.46410 q^{36} -5.19615 q^{37} +1.46410 q^{38} -1.00000 q^{40} -2.46410 q^{41} -0.732051 q^{42} -12.1962 q^{43} -0.732051 q^{44} +2.46410 q^{45} +1.26795 q^{46} +2.92820 q^{47} +0.732051 q^{48} +1.00000 q^{49} -4.00000 q^{50} -4.19615 q^{51} +1.53590 q^{53} -4.00000 q^{54} +0.732051 q^{55} -1.00000 q^{56} +1.07180 q^{57} -3.00000 q^{58} -10.7321 q^{59} -0.732051 q^{60} -11.7321 q^{61} +5.26795 q^{62} +2.46410 q^{63} +1.00000 q^{64} -0.535898 q^{66} +11.6603 q^{67} -5.73205 q^{68} +0.928203 q^{69} +1.00000 q^{70} +13.8564 q^{71} -2.46410 q^{72} -11.3923 q^{73} -5.19615 q^{74} -2.92820 q^{75} +1.46410 q^{76} +0.732051 q^{77} -3.80385 q^{79} -1.00000 q^{80} +4.46410 q^{81} -2.46410 q^{82} -3.80385 q^{83} -0.732051 q^{84} +5.73205 q^{85} -12.1962 q^{86} -2.19615 q^{87} -0.732051 q^{88} -2.53590 q^{89} +2.46410 q^{90} +1.26795 q^{92} +3.85641 q^{93} +2.92820 q^{94} -1.46410 q^{95} +0.732051 q^{96} +5.46410 q^{97} +1.00000 q^{98} +1.80385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 6 q^{23} - 2 q^{24} - 8 q^{25} - 8 q^{27} - 2 q^{28} - 6 q^{29} + 2 q^{30} + 14 q^{31} + 2 q^{32} - 8 q^{33} - 8 q^{34} + 2 q^{35} + 2 q^{36} - 4 q^{38} - 2 q^{40} + 2 q^{41} + 2 q^{42} - 14 q^{43} + 2 q^{44} - 2 q^{45} + 6 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{49} - 8 q^{50} + 2 q^{51} + 10 q^{53} - 8 q^{54} - 2 q^{55} - 2 q^{56} + 16 q^{57} - 6 q^{58} - 18 q^{59} + 2 q^{60} - 20 q^{61} + 14 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 6 q^{67} - 8 q^{68} - 12 q^{69} + 2 q^{70} + 2 q^{72} - 2 q^{73} + 8 q^{75} - 4 q^{76} - 2 q^{77} - 18 q^{79} - 2 q^{80} + 2 q^{81} + 2 q^{82} - 18 q^{83} + 2 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} + 2 q^{88} - 12 q^{89} - 2 q^{90} + 6 q^{92} - 20 q^{93} - 8 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{97} + 2 q^{98} + 14 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 6 * q^23 - 2 * q^24 - 8 * q^25 - 8 * q^27 - 2 * q^28 - 6 * q^29 + 2 * q^30 + 14 * q^31 + 2 * q^32 - 8 * q^33 - 8 * q^34 + 2 * q^35 + 2 * q^36 - 4 * q^38 - 2 * q^40 + 2 * q^41 + 2 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^45 + 6 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^49 - 8 * q^50 + 2 * q^51 + 10 * q^53 - 8 * q^54 - 2 * q^55 - 2 * q^56 + 16 * q^57 - 6 * q^58 - 18 * q^59 + 2 * q^60 - 20 * q^61 + 14 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 6 * q^67 - 8 * q^68 - 12 * q^69 + 2 * q^70 + 2 * q^72 - 2 * q^73 + 8 * q^75 - 4 * q^76 - 2 * q^77 - 18 * q^79 - 2 * q^80 + 2 * q^81 + 2 * q^82 - 18 * q^83 + 2 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 + 2 * q^88 - 12 * q^89 - 2 * q^90 + 6 * q^92 - 20 * q^93 - 8 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^97 + 2 * q^98 + 14 * 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
$3$	0.732051	0.422650	0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051	0.422650	0.211325	+	0.977416i	$0.432222\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0.732051	0.298858
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.46410	−0.821367
$10$	−1.00000	−0.316228
$11$	−0.732051	−0.220722	−0.110361	−	0.993892i	$-0.535201\pi$
$11$	−0.732051	−0.220722	−0.110361	+	0.993892i	$0.535201\pi$
$12$	0.732051	0.211325
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.732051	−0.189015
$16$	1.00000	0.250000
$17$	−5.73205	−1.39023	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−5.73205	−1.39023	−0.695113	+	0.718900i	$0.744646\pi$
$18$	−2.46410	−0.580794
$19$	1.46410	0.335888	0.167944	−	0.985797i	$-0.446287\pi$
$19$	1.46410	0.335888	0.167944	+	0.985797i	$0.446287\pi$
$20$	−1.00000	−0.223607
$21$	−0.732051	−0.159747
$22$	−0.732051	−0.156074
$23$	1.26795	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$23$	1.26795	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$24$	0.732051	0.149429
$25$	−4.00000	−0.800000
$26$	0	0
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−0.732051	−0.133654
$31$	5.26795	0.946152	0.473076	−	0.881022i	$-0.343144\pi$
$31$	5.26795	0.946152	0.473076	+	0.881022i	$0.343144\pi$
$32$	1.00000	0.176777
$33$	−0.535898	−0.0932879
$34$	−5.73205	−0.983039
$35$	1.00000	0.169031
$36$	−2.46410	−0.410684
$37$	−5.19615	−0.854242	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	−5.19615	−0.854242	−0.427121	+	0.904194i	$0.640472\pi$
$38$	1.46410	0.237509
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−2.46410	−0.384828	−0.192414	−	0.981314i	$-0.561632\pi$
$41$	−2.46410	−0.384828	−0.192414	+	0.981314i	$0.561632\pi$
$42$	−0.732051	−0.112958
$43$	−12.1962	−1.85990	−0.929948	−	0.367691i	$-0.880148\pi$
$43$	−12.1962	−1.85990	−0.929948	+	0.367691i	$0.880148\pi$
$44$	−0.732051	−0.110361
$45$	2.46410	0.367327
$46$	1.26795	0.186949
$47$	2.92820	0.427122	0.213561	−	0.976930i	$-0.431494\pi$
$47$	2.92820	0.427122	0.213561	+	0.976930i	$0.431494\pi$
$48$	0.732051	0.105662
$49$	1.00000	0.142857
$50$	−4.00000	−0.565685
$51$	−4.19615	−0.587579
$52$	0	0
$53$	1.53590	0.210972	0.105486	−	0.994421i	$-0.466360\pi$
$53$	1.53590	0.210972	0.105486	+	0.994421i	$0.466360\pi$
$54$	−4.00000	−0.544331
$55$	0.732051	0.0987097
$56$	−1.00000	−0.133631
$57$	1.07180	0.141963
$58$	−3.00000	−0.393919
$59$	−10.7321	−1.39719	−0.698597	−	0.715515i	$-0.746192\pi$
$59$	−10.7321	−1.39719	−0.698597	+	0.715515i	$0.746192\pi$
$60$	−0.732051	−0.0945074
$61$	−11.7321	−1.50214	−0.751068	−	0.660225i	$-0.770461\pi$
$61$	−11.7321	−1.50214	−0.751068	+	0.660225i	$0.770461\pi$
$62$	5.26795	0.669030
$63$	2.46410	0.310448
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.535898	−0.0659645
$67$	11.6603	1.42453	0.712263	−	0.701912i	$-0.247670\pi$
$67$	11.6603	1.42453	0.712263	+	0.701912i	$0.247670\pi$
$68$	−5.73205	−0.695113
$69$	0.928203	0.111743
$70$	1.00000	0.119523
$71$	13.8564	1.64445	0.822226	−	0.569160i	$-0.192732\pi$
$71$	13.8564	1.64445	0.822226	+	0.569160i	$0.192732\pi$
$72$	−2.46410	−0.290397
$73$	−11.3923	−1.33337	−0.666684	−	0.745340i	$-0.732287\pi$
$73$	−11.3923	−1.33337	−0.666684	+	0.745340i	$0.732287\pi$
$74$	−5.19615	−0.604040
$75$	−2.92820	−0.338120
$76$	1.46410	0.167944
$77$	0.732051	0.0834249
$78$	0	0
$79$	−3.80385	−0.427966	−0.213983	−	0.976837i	$-0.568644\pi$
$79$	−3.80385	−0.427966	−0.213983	+	0.976837i	$0.568644\pi$
$80$	−1.00000	−0.111803
$81$	4.46410	0.496011
$82$	−2.46410	−0.272115
$83$	−3.80385	−0.417527	−0.208763	−	0.977966i	$-0.566944\pi$
$83$	−3.80385	−0.417527	−0.208763	+	0.977966i	$0.566944\pi$
$84$	−0.732051	−0.0798733
$85$	5.73205	0.621728
$86$	−12.1962	−1.31514
$87$	−2.19615	−0.235452
$88$	−0.732051	−0.0780369
$89$	−2.53590	−0.268805	−0.134402	−	0.990927i	$-0.542911\pi$
$89$	−2.53590	−0.268805	−0.134402	+	0.990927i	$0.542911\pi$
$90$	2.46410	0.259739
$91$	0	0
$92$	1.26795	0.132193
$93$	3.85641	0.399891
$94$	2.92820	0.302021
$95$	−1.46410	−0.150214
$96$	0.732051	0.0747146
$97$	5.46410	0.554795	0.277398	−	0.960755i	$-0.410528\pi$
$97$	5.46410	0.554795	0.277398	+	0.960755i	$0.410528\pi$
$98$	1.00000	0.101015
$99$	1.80385	0.181294
$100$	−4.00000	−0.400000
$101$	1.19615	0.119022	0.0595108	−	0.998228i	$-0.481046\pi$
$101$	1.19615	0.119022	0.0595108	+	0.998228i	$0.481046\pi$
$102$	−4.19615	−0.415481
$103$	−8.39230	−0.826918	−0.413459	−	0.910523i	$-0.635680\pi$
$103$	−8.39230	−0.826918	−0.413459	+	0.910523i	$0.635680\pi$
$104$	0	0
$105$	0.732051	0.0714408
$106$	1.53590	0.149180
$107$	10.9282	1.05647	0.528235	−	0.849098i	$-0.322854\pi$
$107$	10.9282	1.05647	0.528235	+	0.849098i	$0.322854\pi$
$108$	−4.00000	−0.384900
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0.732051	0.0697983
$111$	−3.80385	−0.361045
$112$	−1.00000	−0.0944911
$113$	11.3923	1.07170	0.535849	−	0.844314i	$-0.319992\pi$
$113$	11.3923	1.07170	0.535849	+	0.844314i	$0.319992\pi$
$114$	1.07180	0.100383
$115$	−1.26795	−0.118237
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−10.7321	−0.987965
$119$	5.73205	0.525456
$120$	−0.732051	−0.0668268
$121$	−10.4641	−0.951282
$122$	−11.7321	−1.06217
$123$	−1.80385	−0.162647
$124$	5.26795	0.473076
$125$	9.00000	0.804984
$126$	2.46410	0.219520
$127$	9.85641	0.874615	0.437307	−	0.899312i	$-0.355932\pi$
$127$	9.85641	0.874615	0.437307	+	0.899312i	$0.355932\pi$
$128$	1.00000	0.0883883
$129$	−8.92820	−0.786084
$130$	0	0
$131$	−5.07180	−0.443125	−0.221562	−	0.975146i	$-0.571116\pi$
$131$	−5.07180	−0.443125	−0.221562	+	0.975146i	$0.571116\pi$
$132$	−0.535898	−0.0466440
$133$	−1.46410	−0.126954
$134$	11.6603	1.00729
$135$	4.00000	0.344265
$136$	−5.73205	−0.491519
$137$	−6.12436	−0.523239	−0.261620	−	0.965171i	$-0.584257\pi$
$137$	−6.12436	−0.523239	−0.261620	+	0.965171i	$0.584257\pi$
$138$	0.928203	0.0790139
$139$	−0.339746	−0.0288169	−0.0144084	−	0.999896i	$-0.504587\pi$
$139$	−0.339746	−0.0288169	−0.0144084	+	0.999896i	$0.504587\pi$
$140$	1.00000	0.0845154
$141$	2.14359	0.180523
$142$	13.8564	1.16280
$143$	0	0
$144$	−2.46410	−0.205342
$145$	3.00000	0.249136
$146$	−11.3923	−0.942834
$147$	0.732051	0.0603785
$148$	−5.19615	−0.427121
$149$	17.1962	1.40876	0.704382	−	0.709821i	$-0.251224\pi$
$149$	17.1962	1.40876	0.704382	+	0.709821i	$0.251224\pi$
$150$	−2.92820	−0.239087
$151$	−12.3923	−1.00847	−0.504236	−	0.863566i	$-0.668226\pi$
$151$	−12.3923	−1.00847	−0.504236	+	0.863566i	$0.668226\pi$
$152$	1.46410	0.118754
$153$	14.1244	1.14189
$154$	0.732051	0.0589903
$155$	−5.26795	−0.423132
$156$	0	0
$157$	13.7321	1.09594	0.547968	−	0.836499i	$-0.315401\pi$
$157$	13.7321	1.09594	0.547968	+	0.836499i	$0.315401\pi$
$158$	−3.80385	−0.302618
$159$	1.12436	0.0891672
$160$	−1.00000	−0.0790569
$161$	−1.26795	−0.0999284
$162$	4.46410	0.350733
$163$	−0.732051	−0.0573386	−0.0286693	−	0.999589i	$-0.509127\pi$
$163$	−0.732051	−0.0573386	−0.0286693	+	0.999589i	$0.509127\pi$
$164$	−2.46410	−0.192414
$165$	0.535898	0.0417196
$166$	−3.80385	−0.295236
$167$	5.26795	0.407646	0.203823	−	0.979008i	$-0.434663\pi$
$167$	5.26795	0.407646	0.203823	+	0.979008i	$0.434663\pi$
$168$	−0.732051	−0.0564789
$169$	0	0
$170$	5.73205	0.439628
$171$	−3.60770	−0.275887
$172$	−12.1962	−0.929948
$173$	−20.9282	−1.59114	−0.795571	−	0.605860i	$-0.792829\pi$
$173$	−20.9282	−1.59114	−0.795571	+	0.605860i	$0.792829\pi$
$174$	−2.19615	−0.166490
$175$	4.00000	0.302372
$176$	−0.732051	−0.0551804
$177$	−7.85641	−0.590524
$178$	−2.53590	−0.190074
$179$	16.3923	1.22522	0.612609	−	0.790386i	$-0.290120\pi$
$179$	16.3923	1.22522	0.612609	+	0.790386i	$0.290120\pi$
$180$	2.46410	0.183663
$181$	−3.19615	−0.237568	−0.118784	−	0.992920i	$-0.537900\pi$
$181$	−3.19615	−0.237568	−0.118784	+	0.992920i	$0.537900\pi$
$182$	0	0
$183$	−8.58846	−0.634877
$184$	1.26795	0.0934745
$185$	5.19615	0.382029
$186$	3.85641	0.282765
$187$	4.19615	0.306853
$188$	2.92820	0.213561
$189$	4.00000	0.290957
$190$	−1.46410	−0.106217
$191$	7.12436	0.515500	0.257750	−	0.966212i	$-0.417019\pi$
$191$	7.12436	0.515500	0.257750	+	0.966212i	$0.417019\pi$
$192$	0.732051	0.0528312
$193$	23.1962	1.66970	0.834848	−	0.550481i	$-0.185556\pi$
$193$	23.1962	1.66970	0.834848	+	0.550481i	$0.185556\pi$
$194$	5.46410	0.392300
$195$	0	0
$196$	1.00000	0.0714286
$197$	7.07180	0.503845	0.251922	−	0.967747i	$-0.418937\pi$
$197$	7.07180	0.503845	0.251922	+	0.967747i	$0.418937\pi$
$198$	1.80385	0.128194
$199$	−5.46410	−0.387340	−0.193670	−	0.981067i	$-0.562039\pi$
$199$	−5.46410	−0.387340	−0.193670	+	0.981067i	$0.562039\pi$
$200$	−4.00000	−0.282843
$201$	8.53590	0.602076
$202$	1.19615	0.0841610
$203$	3.00000	0.210559
$204$	−4.19615	−0.293789
$205$	2.46410	0.172100
$206$	−8.39230	−0.584720
$207$	−3.12436	−0.217158
$208$	0	0
$209$	−1.07180	−0.0741377
$210$	0.732051	0.0505163
$211$	−21.2679	−1.46415	−0.732073	−	0.681226i	$-0.761447\pi$
$211$	−21.2679	−1.46415	−0.732073	+	0.681226i	$0.761447\pi$
$212$	1.53590	0.105486
$213$	10.1436	0.695028
$214$	10.9282	0.747037
$215$	12.1962	0.831771
$216$	−4.00000	−0.272166
$217$	−5.26795	−0.357612
$218$	−10.0000	−0.677285
$219$	−8.33975	−0.563548
$220$	0.732051	0.0493549
$221$	0	0
$222$	−3.80385	−0.255298
$223$	12.3923	0.829850	0.414925	−	0.909856i	$-0.363808\pi$
$223$	12.3923	0.829850	0.414925	+	0.909856i	$0.363808\pi$
$224$	−1.00000	−0.0668153
$225$	9.85641	0.657094
$226$	11.3923	0.757805
$227$	−1.26795	−0.0841567	−0.0420784	−	0.999114i	$-0.513398\pi$
$227$	−1.26795	−0.0841567	−0.0420784	+	0.999114i	$0.513398\pi$
$228$	1.07180	0.0709815
$229$	24.3923	1.61189	0.805944	−	0.591991i	$-0.201658\pi$
$229$	24.3923	1.61189	0.805944	+	0.591991i	$0.201658\pi$
$230$	−1.26795	−0.0836061
$231$	0.535898	0.0352595
$232$	−3.00000	−0.196960
$233$	−4.39230	−0.287749	−0.143875	−	0.989596i	$-0.545956\pi$
$233$	−4.39230	−0.287749	−0.143875	+	0.989596i	$0.545956\pi$
$234$	0	0
$235$	−2.92820	−0.191015
$236$	−10.7321	−0.698597
$237$	−2.78461	−0.180880
$238$	5.73205	0.371554
$239$	−29.5167	−1.90927	−0.954637	−	0.297772i	$-0.903756\pi$
$239$	−29.5167	−1.90927	−0.954637	+	0.297772i	$0.903756\pi$
$240$	−0.732051	−0.0472537
$241$	−15.3923	−0.991506	−0.495753	−	0.868464i	$-0.665108\pi$
$241$	−15.3923	−0.991506	−0.495753	+	0.868464i	$0.665108\pi$
$242$	−10.4641	−0.672658
$243$	15.2679	0.979439
$244$	−11.7321	−0.751068
$245$	−1.00000	−0.0638877
$246$	−1.80385	−0.115009
$247$	0	0
$248$	5.26795	0.334515
$249$	−2.78461	−0.176467
$250$	9.00000	0.569210
$251$	22.9282	1.44722	0.723608	−	0.690212i	$-0.242483\pi$
$251$	22.9282	1.44722	0.723608	+	0.690212i	$0.242483\pi$
$252$	2.46410	0.155224
$253$	−0.928203	−0.0583556
$254$	9.85641	0.618446
$255$	4.19615	0.262773
$256$	1.00000	0.0625000
$257$	1.33975	0.0835711	0.0417855	−	0.999127i	$-0.486695\pi$
$257$	1.33975	0.0835711	0.0417855	+	0.999127i	$0.486695\pi$
$258$	−8.92820	−0.555846
$259$	5.19615	0.322873
$260$	0	0
$261$	7.39230	0.457572
$262$	−5.07180	−0.313337
$263$	−20.5885	−1.26954	−0.634769	−	0.772702i	$-0.718905\pi$
$263$	−20.5885	−1.26954	−0.634769	+	0.772702i	$0.718905\pi$
$264$	−0.535898	−0.0329823
$265$	−1.53590	−0.0943495
$266$	−1.46410	−0.0897698
$267$	−1.85641	−0.113610
$268$	11.6603	0.712263
$269$	−28.7846	−1.75503	−0.877514	−	0.479550i	$-0.840800\pi$
$269$	−28.7846	−1.75503	−0.877514	+	0.479550i	$0.840800\pi$
$270$	4.00000	0.243432
$271$	−7.12436	−0.432774	−0.216387	−	0.976308i	$-0.569427\pi$
$271$	−7.12436	−0.432774	−0.216387	+	0.976308i	$0.569427\pi$
$272$	−5.73205	−0.347557
$273$	0	0
$274$	−6.12436	−0.369986
$275$	2.92820	0.176577
$276$	0.928203	0.0558713
$277$	9.39230	0.564329	0.282164	−	0.959366i	$-0.408948\pi$
$277$	9.39230	0.564329	0.282164	+	0.959366i	$0.408948\pi$
$278$	−0.339746	−0.0203766
$279$	−12.9808	−0.777138
$280$	1.00000	0.0597614
$281$	16.6603	0.993867	0.496934	−	0.867789i	$-0.334459\pi$
$281$	16.6603	0.993867	0.496934	+	0.867789i	$0.334459\pi$
$282$	2.14359	0.127649
$283$	−10.5885	−0.629418	−0.314709	−	0.949188i	$-0.601907\pi$
$283$	−10.5885	−0.629418	−0.314709	+	0.949188i	$0.601907\pi$
$284$	13.8564	0.822226
$285$	−1.07180	−0.0634878
$286$	0	0
$287$	2.46410	0.145451
$288$	−2.46410	−0.145199
$289$	15.8564	0.932730
$290$	3.00000	0.176166
$291$	4.00000	0.234484
$292$	−11.3923	−0.666684
$293$	17.3923	1.01607	0.508035	−	0.861337i	$-0.330372\pi$
$293$	17.3923	1.01607	0.508035	+	0.861337i	$0.330372\pi$
$294$	0.732051	0.0426941
$295$	10.7321	0.624844
$296$	−5.19615	−0.302020
$297$	2.92820	0.169912
$298$	17.1962	0.996146
$299$	0	0
$300$	−2.92820	−0.169060
$301$	12.1962	0.702975
$302$	−12.3923	−0.713097
$303$	0.875644	0.0503045
$304$	1.46410	0.0839720
$305$	11.7321	0.671775
$306$	14.1244	0.807436
$307$	23.5167	1.34217	0.671083	−	0.741382i	$-0.265829\pi$
$307$	23.5167	1.34217	0.671083	+	0.741382i	$0.265829\pi$
$308$	0.732051	0.0417125
$309$	−6.14359	−0.349497
$310$	−5.26795	−0.299199
$311$	−10.1962	−0.578171	−0.289085	−	0.957303i	$-0.593351\pi$
$311$	−10.1962	−0.578171	−0.289085	+	0.957303i	$0.593351\pi$
$312$	0	0
$313$	−32.0000	−1.80875	−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000	−1.80875	−0.904373	+	0.426742i	$0.859661\pi$
$314$	13.7321	0.774944
$315$	−2.46410	−0.138836
$316$	−3.80385	−0.213983
$317$	7.05256	0.396111	0.198056	−	0.980191i	$-0.436537\pi$
$317$	7.05256	0.396111	0.198056	+	0.980191i	$0.436537\pi$
$318$	1.12436	0.0630507
$319$	2.19615	0.122961
$320$	−1.00000	−0.0559017
$321$	8.00000	0.446516
$322$	−1.26795	−0.0706600
$323$	−8.39230	−0.466960
$324$	4.46410	0.248006
$325$	0	0
$326$	−0.732051	−0.0405445
$327$	−7.32051	−0.404825
$328$	−2.46410	−0.136057
$329$	−2.92820	−0.161437
$330$	0.535898	0.0295002
$331$	−4.33975	−0.238534	−0.119267	−	0.992862i	$-0.538054\pi$
$331$	−4.33975	−0.238534	−0.119267	+	0.992862i	$0.538054\pi$
$332$	−3.80385	−0.208763
$333$	12.8038	0.701647
$334$	5.26795	0.288249
$335$	−11.6603	−0.637068
$336$	−0.732051	−0.0399366
$337$	6.32051	0.344300	0.172150	−	0.985071i	$-0.444929\pi$
$337$	6.32051	0.344300	0.172150	+	0.985071i	$0.444929\pi$
$338$	0	0
$339$	8.33975	0.452953
$340$	5.73205	0.310864
$341$	−3.85641	−0.208836
$342$	−3.60770	−0.195082
$343$	−1.00000	−0.0539949
$344$	−12.1962	−0.657572
$345$	−0.928203	−0.0499728
$346$	−20.9282	−1.12511
$347$	28.9808	1.55577	0.777884	−	0.628407i	$-0.216293\pi$
$347$	28.9808	1.55577	0.777884	+	0.628407i	$0.216293\pi$
$348$	−2.19615	−0.117726
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	−0.732051	−0.0390184
$353$	−36.1769	−1.92550	−0.962751	−	0.270388i	$-0.912848\pi$
$353$	−36.1769	−1.92550	−0.962751	+	0.270388i	$0.912848\pi$
$354$	−7.85641	−0.417563
$355$	−13.8564	−0.735422
$356$	−2.53590	−0.134402
$357$	4.19615	0.222084
$358$	16.3923	0.866360
$359$	−16.3923	−0.865153	−0.432576	−	0.901597i	$-0.642395\pi$
$359$	−16.3923	−0.865153	−0.432576	+	0.901597i	$0.642395\pi$
$360$	2.46410	0.129870
$361$	−16.8564	−0.887179
$362$	−3.19615	−0.167986
$363$	−7.66025	−0.402059
$364$	0	0
$365$	11.3923	0.596300
$366$	−8.58846	−0.448926
$367$	33.9090	1.77003	0.885017	−	0.465559i	$-0.154147\pi$
$367$	33.9090	1.77003	0.885017	+	0.465559i	$0.154147\pi$
$368$	1.26795	0.0660964
$369$	6.07180	0.316085
$370$	5.19615	0.270135
$371$	−1.53590	−0.0797399
$372$	3.85641	0.199945
$373$	−32.4641	−1.68093	−0.840464	−	0.541868i	$-0.817717\pi$
$373$	−32.4641	−1.68093	−0.840464	+	0.541868i	$0.817717\pi$
$374$	4.19615	0.216978
$375$	6.58846	0.340226
$376$	2.92820	0.151011
$377$	0	0
$378$	4.00000	0.205738
$379$	22.1962	1.14014	0.570070	−	0.821596i	$-0.306916\pi$
$379$	22.1962	1.14014	0.570070	+	0.821596i	$0.306916\pi$
$380$	−1.46410	−0.0751068
$381$	7.21539	0.369656
$382$	7.12436	0.364514
$383$	−32.5885	−1.66519	−0.832596	−	0.553880i	$-0.813146\pi$
$383$	−32.5885	−1.66519	−0.832596	+	0.553880i	$0.813146\pi$
$384$	0.732051	0.0373573
$385$	−0.732051	−0.0373088
$386$	23.1962	1.18065
$387$	30.0526	1.52766
$388$	5.46410	0.277398
$389$	24.3205	1.23310	0.616549	−	0.787316i	$-0.288530\pi$
$389$	24.3205	1.23310	0.616549	+	0.787316i	$0.288530\pi$
$390$	0	0
$391$	−7.26795	−0.367556
$392$	1.00000	0.0505076
$393$	−3.71281	−0.187287
$394$	7.07180	0.356272
$395$	3.80385	0.191392
$396$	1.80385	0.0906468
$397$	−29.4641	−1.47876	−0.739380	−	0.673288i	$-0.764881\pi$
$397$	−29.4641	−1.47876	−0.739380	+	0.673288i	$0.764881\pi$
$398$	−5.46410	−0.273891
$399$	−1.07180	−0.0536570
$400$	−4.00000	−0.200000
$401$	33.0526	1.65057	0.825283	−	0.564719i	$-0.191016\pi$
$401$	33.0526	1.65057	0.825283	+	0.564719i	$0.191016\pi$
$402$	8.53590	0.425732
$403$	0	0
$404$	1.19615	0.0595108
$405$	−4.46410	−0.221823
$406$	3.00000	0.148888
$407$	3.80385	0.188550
$408$	−4.19615	−0.207741
$409$	−26.3205	−1.30147	−0.650733	−	0.759307i	$-0.725538\pi$
$409$	−26.3205	−1.30147	−0.650733	+	0.759307i	$0.725538\pi$
$410$	2.46410	0.121693
$411$	−4.48334	−0.221147
$412$	−8.39230	−0.413459
$413$	10.7321	0.528090
$414$	−3.12436	−0.153554
$415$	3.80385	0.186724
$416$	0	0
$417$	−0.248711	−0.0121794
$418$	−1.07180	−0.0524233
$419$	5.12436	0.250341	0.125171	−	0.992135i	$-0.460052\pi$
$419$	5.12436	0.250341	0.125171	+	0.992135i	$0.460052\pi$
$420$	0.732051	0.0357204
$421$	14.1244	0.688379	0.344189	−	0.938900i	$-0.388154\pi$
$421$	14.1244	0.688379	0.344189	+	0.938900i	$0.388154\pi$
$422$	−21.2679	−1.03531
$423$	−7.21539	−0.350824
$424$	1.53590	0.0745898
$425$	22.9282	1.11218
$426$	10.1436	0.491459
$427$	11.7321	0.567754
$428$	10.9282	0.528235
$429$	0	0
$430$	12.1962	0.588151
$431$	26.5359	1.27819	0.639095	−	0.769128i	$-0.279309\pi$
$431$	26.5359	1.27819	0.639095	+	0.769128i	$0.279309\pi$
$432$	−4.00000	−0.192450
$433$	21.7321	1.04438	0.522188	−	0.852830i	$-0.325116\pi$
$433$	21.7321	1.04438	0.522188	+	0.852830i	$0.325116\pi$
$434$	−5.26795	−0.252870
$435$	2.19615	0.105297
$436$	−10.0000	−0.478913
$437$	1.85641	0.0888040
$438$	−8.33975	−0.398488
$439$	−19.2679	−0.919609	−0.459805	−	0.888020i	$-0.652081\pi$
$439$	−19.2679	−0.919609	−0.459805	+	0.888020i	$0.652081\pi$
$440$	0.732051	0.0348992
$441$	−2.46410	−0.117338
$442$	0	0
$443$	35.3205	1.67813	0.839064	−	0.544033i	$-0.183103\pi$
$443$	35.3205	1.67813	0.839064	+	0.544033i	$0.183103\pi$
$444$	−3.80385	−0.180523
$445$	2.53590	0.120213
$446$	12.3923	0.586793
$447$	12.5885	0.595414
$448$	−1.00000	−0.0472456
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	9.85641	0.464635
$451$	1.80385	0.0849399
$452$	11.3923	0.535849
$453$	−9.07180	−0.426230
$454$	−1.26795	−0.0595078
$455$	0	0
$456$	1.07180	0.0501915
$457$	−14.2679	−0.667427	−0.333713	−	0.942675i	$-0.608302\pi$
$457$	−14.2679	−0.667427	−0.333713	+	0.942675i	$0.608302\pi$
$458$	24.3923	1.13978
$459$	22.9282	1.07020
$460$	−1.26795	−0.0591184
$461$	−8.32051	−0.387525	−0.193762	−	0.981048i	$-0.562069\pi$
$461$	−8.32051	−0.387525	−0.193762	+	0.981048i	$0.562069\pi$
$462$	0.535898	0.0249322
$463$	3.94744	0.183453	0.0917266	−	0.995784i	$-0.470761\pi$
$463$	3.94744	0.183453	0.0917266	+	0.995784i	$0.470761\pi$
$464$	−3.00000	−0.139272
$465$	−3.85641	−0.178837
$466$	−4.39230	−0.203470
$467$	−24.7321	−1.14446	−0.572231	−	0.820092i	$-0.693922\pi$
$467$	−24.7321	−1.14446	−0.572231	+	0.820092i	$0.693922\pi$
$468$	0	0
$469$	−11.6603	−0.538421
$470$	−2.92820	−0.135068
$471$	10.0526	0.463197
$472$	−10.7321	−0.493983
$473$	8.92820	0.410519
$474$	−2.78461	−0.127901
$475$	−5.85641	−0.268710
$476$	5.73205	0.262728
$477$	−3.78461	−0.173285
$478$	−29.5167	−1.35006
$479$	−32.1962	−1.47108	−0.735540	−	0.677481i	$-0.763071\pi$
$479$	−32.1962	−1.47108	−0.735540	+	0.677481i	$0.763071\pi$
$480$	−0.732051	−0.0334134
$481$	0	0
$482$	−15.3923	−0.701100
$483$	−0.928203	−0.0422347
$484$	−10.4641	−0.475641
$485$	−5.46410	−0.248112
$486$	15.2679	0.692568
$487$	−31.3205	−1.41927	−0.709634	−	0.704571i	$-0.751140\pi$
$487$	−31.3205	−1.41927	−0.709634	+	0.704571i	$0.751140\pi$
$488$	−11.7321	−0.531085
$489$	−0.535898	−0.0242342
$490$	−1.00000	−0.0451754
$491$	−27.7128	−1.25066	−0.625331	−	0.780360i	$-0.715036\pi$
$491$	−27.7128	−1.25066	−0.625331	+	0.780360i	$0.715036\pi$
$492$	−1.80385	−0.0813237
$493$	17.1962	0.774476
$494$	0	0
$495$	−1.80385	−0.0810769
$496$	5.26795	0.236538
$497$	−13.8564	−0.621545
$498$	−2.78461	−0.124781
$499$	11.2679	0.504423	0.252211	−	0.967672i	$-0.418842\pi$
$499$	11.2679	0.504423	0.252211	+	0.967672i	$0.418842\pi$
$500$	9.00000	0.402492
$501$	3.85641	0.172292
$502$	22.9282	1.02334
$503$	20.7321	0.924396	0.462198	−	0.886777i	$-0.347061\pi$
$503$	20.7321	0.924396	0.462198	+	0.886777i	$0.347061\pi$
$504$	2.46410	0.109760
$505$	−1.19615	−0.0532281
$506$	−0.928203	−0.0412637
$507$	0	0
$508$	9.85641	0.437307
$509$	−27.3923	−1.21414	−0.607071	−	0.794647i	$-0.707656\pi$
$509$	−27.3923	−1.21414	−0.607071	+	0.794647i	$0.707656\pi$
$510$	4.19615	0.185809
$511$	11.3923	0.503966
$512$	1.00000	0.0441942
$513$	−5.85641	−0.258567
$514$	1.33975	0.0590937
$515$	8.39230	0.369809
$516$	−8.92820	−0.393042
$517$	−2.14359	−0.0942751
$518$	5.19615	0.228306
$519$	−15.3205	−0.672496
$520$	0	0
$521$	44.3731	1.94402	0.972010	−	0.234941i	$-0.0754896\pi$
$521$	44.3731	1.94402	0.972010	+	0.234941i	$0.0754896\pi$
$522$	7.39230	0.323552
$523$	21.4641	0.938560	0.469280	−	0.883050i	$-0.344514\pi$
$523$	21.4641	0.938560	0.469280	+	0.883050i	$0.344514\pi$
$524$	−5.07180	−0.221562
$525$	2.92820	0.127797
$526$	−20.5885	−0.897699
$527$	−30.1962	−1.31537
$528$	−0.535898	−0.0233220
$529$	−21.3923	−0.930100
$530$	−1.53590	−0.0667152
$531$	26.4449	1.14761
$532$	−1.46410	−0.0634769
$533$	0	0
$534$	−1.85641	−0.0803346
$535$	−10.9282	−0.472467
$536$	11.6603	0.503646
$537$	12.0000	0.517838
$538$	−28.7846	−1.24099
$539$	−0.732051	−0.0315317
$540$	4.00000	0.172133
$541$	−8.26795	−0.355467	−0.177733	−	0.984079i	$-0.556876\pi$
$541$	−8.26795	−0.355467	−0.177733	+	0.984079i	$0.556876\pi$
$542$	−7.12436	−0.306017
$543$	−2.33975	−0.100408
$544$	−5.73205	−0.245760
$545$	10.0000	0.428353
$546$	0	0
$547$	−30.4449	−1.30173	−0.650864	−	0.759194i	$-0.725593\pi$
$547$	−30.4449	−1.30173	−0.650864	+	0.759194i	$0.725593\pi$
$548$	−6.12436	−0.261620
$549$	28.9090	1.23380
$550$	2.92820	0.124859
$551$	−4.39230	−0.187118
$552$	0.928203	0.0395070
$553$	3.80385	0.161756
$554$	9.39230	0.399041
$555$	3.80385	0.161464
$556$	−0.339746	−0.0144084
$557$	−26.1244	−1.10692	−0.553462	−	0.832874i	$-0.686694\pi$
$557$	−26.1244	−1.10692	−0.553462	+	0.832874i	$0.686694\pi$
$558$	−12.9808	−0.549519
$559$	0	0
$560$	1.00000	0.0422577
$561$	3.07180	0.129691
$562$	16.6603	0.702770
$563$	−28.4449	−1.19881	−0.599404	−	0.800447i	$-0.704596\pi$
$563$	−28.4449	−1.19881	−0.599404	+	0.800447i	$0.704596\pi$
$564$	2.14359	0.0902616
$565$	−11.3923	−0.479278
$566$	−10.5885	−0.445066
$567$	−4.46410	−0.187475
$568$	13.8564	0.581402
$569$	−11.3205	−0.474580	−0.237290	−	0.971439i	$-0.576259\pi$
$569$	−11.3205	−0.474580	−0.237290	+	0.971439i	$0.576259\pi$
$570$	−1.07180	−0.0448926
$571$	−5.46410	−0.228666	−0.114333	−	0.993443i	$-0.536473\pi$
$571$	−5.46410	−0.228666	−0.114333	+	0.993443i	$0.536473\pi$
$572$	0	0
$573$	5.21539	0.217876
$574$	2.46410	0.102850
$575$	−5.07180	−0.211509
$576$	−2.46410	−0.102671
$577$	34.1769	1.42280	0.711402	−	0.702786i	$-0.248061\pi$
$577$	34.1769	1.42280	0.711402	+	0.702786i	$0.248061\pi$
$578$	15.8564	0.659540
$579$	16.9808	0.705696
$580$	3.00000	0.124568
$581$	3.80385	0.157810
$582$	4.00000	0.165805
$583$	−1.12436	−0.0465661
$584$	−11.3923	−0.471417
$585$	0	0
$586$	17.3923	0.718469
$587$	−28.7846	−1.18807	−0.594034	−	0.804440i	$-0.702466\pi$
$587$	−28.7846	−1.18807	−0.594034	+	0.804440i	$0.702466\pi$
$588$	0.732051	0.0301893
$589$	7.71281	0.317801
$590$	10.7321	0.441832
$591$	5.17691	0.212950
$592$	−5.19615	−0.213561
$593$	3.14359	0.129092	0.0645460	−	0.997915i	$-0.479440\pi$
$593$	3.14359	0.129092	0.0645460	+	0.997915i	$0.479440\pi$
$594$	2.92820	0.120146
$595$	−5.73205	−0.234991
$596$	17.1962	0.704382
$597$	−4.00000	−0.163709
$598$	0	0
$599$	30.9282	1.26369	0.631846	−	0.775094i	$-0.282297\pi$
$599$	30.9282	1.26369	0.631846	+	0.775094i	$0.282297\pi$
$600$	−2.92820	−0.119543
$601$	−23.0526	−0.940333	−0.470167	−	0.882578i	$-0.655806\pi$
$601$	−23.0526	−0.940333	−0.470167	+	0.882578i	$0.655806\pi$
$602$	12.1962	0.497078
$603$	−28.7321	−1.17006
$604$	−12.3923	−0.504236
$605$	10.4641	0.425426
$606$	0.875644	0.0355706
$607$	−9.85641	−0.400059	−0.200030	−	0.979790i	$-0.564104\pi$
$607$	−9.85641	−0.400059	−0.200030	+	0.979790i	$0.564104\pi$
$608$	1.46410	0.0593772
$609$	2.19615	0.0889926
$610$	11.7321	0.475017
$611$	0	0
$612$	14.1244	0.570943
$613$	15.9808	0.645457	0.322728	−	0.946492i	$-0.395400\pi$
$613$	15.9808	0.645457	0.322728	+	0.946492i	$0.395400\pi$
$614$	23.5167	0.949055
$615$	1.80385	0.0727382
$616$	0.732051	0.0294952
$617$	33.1962	1.33643	0.668213	−	0.743970i	$-0.267059\pi$
$617$	33.1962	1.33643	0.668213	+	0.743970i	$0.267059\pi$
$618$	−6.14359	−0.247132
$619$	−34.0526	−1.36869	−0.684344	−	0.729159i	$-0.739911\pi$
$619$	−34.0526	−1.36869	−0.684344	+	0.729159i	$0.739911\pi$
$620$	−5.26795	−0.211566
$621$	−5.07180	−0.203524
$622$	−10.1962	−0.408828
$623$	2.53590	0.101599
$624$	0	0
$625$	11.0000	0.440000
$626$	−32.0000	−1.27898
$627$	−0.784610	−0.0313343
$628$	13.7321	0.547968
$629$	29.7846	1.18759
$630$	−2.46410	−0.0981722
$631$	10.5359	0.419427	0.209714	−	0.977763i	$-0.432747\pi$
$631$	10.5359	0.419427	0.209714	+	0.977763i	$0.432747\pi$
$632$	−3.80385	−0.151309
$633$	−15.5692	−0.618821
$634$	7.05256	0.280093
$635$	−9.85641	−0.391140
$636$	1.12436	0.0445836
$637$	0	0
$638$	2.19615	0.0869465
$639$	−34.1436	−1.35070
$640$	−1.00000	−0.0395285
$641$	44.4641	1.75623	0.878113	−	0.478453i	$-0.158802\pi$
$641$	44.4641	1.75623	0.878113	+	0.478453i	$0.158802\pi$
$642$	8.00000	0.315735
$643$	−35.7128	−1.40838	−0.704188	−	0.710014i	$-0.748689\pi$
$643$	−35.7128	−1.40838	−0.704188	+	0.710014i	$0.748689\pi$
$644$	−1.26795	−0.0499642
$645$	8.92820	0.351548
$646$	−8.39230	−0.330191
$647$	−13.8564	−0.544752	−0.272376	−	0.962191i	$-0.587809\pi$
$647$	−13.8564	−0.544752	−0.272376	+	0.962191i	$0.587809\pi$
$648$	4.46410	0.175366
$649$	7.85641	0.308391
$650$	0	0
$651$	−3.85641	−0.151144
$652$	−0.732051	−0.0286693
$653$	12.3923	0.484948	0.242474	−	0.970158i	$-0.422041\pi$
$653$	12.3923	0.484948	0.242474	+	0.970158i	$0.422041\pi$
$654$	−7.32051	−0.286255
$655$	5.07180	0.198171
$656$	−2.46410	−0.0962070
$657$	28.0718	1.09519
$658$	−2.92820	−0.114153
$659$	8.78461	0.342200	0.171100	−	0.985254i	$-0.445268\pi$
$659$	8.78461	0.342200	0.171100	+	0.985254i	$0.445268\pi$
$660$	0.535898	0.0208598
$661$	−1.92820	−0.0749984	−0.0374992	−	0.999297i	$-0.511939\pi$
$661$	−1.92820	−0.0749984	−0.0374992	+	0.999297i	$0.511939\pi$
$662$	−4.33975	−0.168669
$663$	0	0
$664$	−3.80385	−0.147618
$665$	1.46410	0.0567754
$666$	12.8038	0.496139
$667$	−3.80385	−0.147286
$668$	5.26795	0.203823
$669$	9.07180	0.350736
$670$	−11.6603	−0.450475
$671$	8.58846	0.331554
$672$	−0.732051	−0.0282395
$673$	21.7846	0.839735	0.419867	−	0.907585i	$-0.362077\pi$
$673$	21.7846	0.839735	0.419867	+	0.907585i	$0.362077\pi$
$674$	6.32051	0.243457
$675$	16.0000	0.615840
$676$	0	0
$677$	27.8564	1.07061	0.535304	−	0.844659i	$-0.320197\pi$
$677$	27.8564	1.07061	0.535304	+	0.844659i	$0.320197\pi$
$678$	8.33975	0.320286
$679$	−5.46410	−0.209693
$680$	5.73205	0.219814
$681$	−0.928203	−0.0355688
$682$	−3.85641	−0.147669
$683$	6.53590	0.250089	0.125045	−	0.992151i	$-0.460093\pi$
$683$	6.53590	0.250089	0.125045	+	0.992151i	$0.460093\pi$
$684$	−3.60770	−0.137944
$685$	6.12436	0.234000
$686$	−1.00000	−0.0381802
$687$	17.8564	0.681264
$688$	−12.1962	−0.464974
$689$	0	0
$690$	−0.928203	−0.0353361
$691$	5.85641	0.222788	0.111394	−	0.993776i	$-0.464468\pi$
$691$	5.85641	0.222788	0.111394	+	0.993776i	$0.464468\pi$
$692$	−20.9282	−0.795571
$693$	−1.80385	−0.0685225
$694$	28.9808	1.10009
$695$	0.339746	0.0128873
$696$	−2.19615	−0.0832449
$697$	14.1244	0.534998
$698$	2.00000	0.0757011
$699$	−3.21539	−0.121617
$700$	4.00000	0.151186
$701$	14.5359	0.549013	0.274507	−	0.961585i	$-0.411485\pi$
$701$	14.5359	0.549013	0.274507	+	0.961585i	$0.411485\pi$
$702$	0	0
$703$	−7.60770	−0.286930
$704$	−0.732051	−0.0275902
$705$	−2.14359	−0.0807324
$706$	−36.1769	−1.36154
$707$	−1.19615	−0.0449859
$708$	−7.85641	−0.295262
$709$	−6.51666	−0.244738	−0.122369	−	0.992485i	$-0.539049\pi$
$709$	−6.51666	−0.244738	−0.122369	+	0.992485i	$0.539049\pi$
$710$	−13.8564	−0.520022
$711$	9.37307	0.351517
$712$	−2.53590	−0.0950368
$713$	6.67949	0.250149
$714$	4.19615	0.157037
$715$	0	0
$716$	16.3923	0.612609
$717$	−21.6077	−0.806954
$718$	−16.3923	−0.611755
$719$	−6.19615	−0.231077	−0.115539	−	0.993303i	$-0.536859\pi$
$719$	−6.19615	−0.231077	−0.115539	+	0.993303i	$0.536859\pi$
$720$	2.46410	0.0918316
$721$	8.39230	0.312546
$722$	−16.8564	−0.627330
$723$	−11.2679	−0.419060
$724$	−3.19615	−0.118784
$725$	12.0000	0.445669
$726$	−7.66025	−0.284299
$727$	53.8564	1.99742	0.998712	−	0.0507424i	$-0.0161587\pi$
$727$	53.8564	1.99742	0.998712	+	0.0507424i	$0.0161587\pi$
$728$	0	0
$729$	−2.21539	−0.0820515
$730$	11.3923	0.421648
$731$	69.9090	2.58568
$732$	−8.58846	−0.317439
$733$	−2.46410	−0.0910137	−0.0455068	−	0.998964i	$-0.514490\pi$
$733$	−2.46410	−0.0910137	−0.0455068	+	0.998964i	$0.514490\pi$
$734$	33.9090	1.25160
$735$	−0.732051	−0.0270021
$736$	1.26795	0.0467372
$737$	−8.53590	−0.314424
$738$	6.07180	0.223506
$739$	−6.53590	−0.240427	−0.120213	−	0.992748i	$-0.538358\pi$
$739$	−6.53590	−0.240427	−0.120213	+	0.992748i	$0.538358\pi$
$740$	5.19615	0.191014
$741$	0	0
$742$	−1.53590	−0.0563846
$743$	−5.07180	−0.186066	−0.0930331	−	0.995663i	$-0.529656\pi$
$743$	−5.07180	−0.186066	−0.0930331	+	0.995663i	$0.529656\pi$
$744$	3.85641	0.141383
$745$	−17.1962	−0.630018
$746$	−32.4641	−1.18860
$747$	9.37307	0.342943
$748$	4.19615	0.153427
$749$	−10.9282	−0.399308
$750$	6.58846	0.240576
$751$	6.44486	0.235176	0.117588	−	0.993062i	$-0.462484\pi$
$751$	6.44486	0.235176	0.117588	+	0.993062i	$0.462484\pi$
$752$	2.92820	0.106781
$753$	16.7846	0.611665
$754$	0	0
$755$	12.3923	0.451002
$756$	4.00000	0.145479
$757$	−44.3923	−1.61347	−0.806733	−	0.590916i	$-0.798766\pi$
$757$	−44.3923	−1.61347	−0.806733	+	0.590916i	$0.798766\pi$
$758$	22.1962	0.806201
$759$	−0.679492	−0.0246640
$760$	−1.46410	−0.0531085
$761$	18.2487	0.661515	0.330758	−	0.943716i	$-0.392696\pi$
$761$	18.2487	0.661515	0.330758	+	0.943716i	$0.392696\pi$
$762$	7.21539	0.261386
$763$	10.0000	0.362024
$764$	7.12436	0.257750
$765$	−14.1244	−0.510667
$766$	−32.5885	−1.17747
$767$	0	0
$768$	0.732051	0.0264156
$769$	0.392305	0.0141469	0.00707344	−	0.999975i	$-0.497748\pi$
$769$	0.392305	0.0141469	0.00707344	+	0.999975i	$0.497748\pi$
$770$	−0.732051	−0.0263813
$771$	0.980762	0.0353213
$772$	23.1962	0.834848
$773$	−46.2487	−1.66345	−0.831725	−	0.555187i	$-0.812647\pi$
$773$	−46.2487	−1.66345	−0.831725	+	0.555187i	$0.812647\pi$
$774$	30.0526	1.08022
$775$	−21.0718	−0.756921
$776$	5.46410	0.196150
$777$	3.80385	0.136462
$778$	24.3205	0.871932
$779$	−3.60770	−0.129259
$780$	0	0
$781$	−10.1436	−0.362966
$782$	−7.26795	−0.259901
$783$	12.0000	0.428845
$784$	1.00000	0.0357143
$785$	−13.7321	−0.490118
$786$	−3.71281	−0.132432
$787$	−44.9808	−1.60339	−0.801696	−	0.597733i	$-0.796068\pi$
$787$	−44.9808	−1.60339	−0.801696	+	0.597733i	$0.796068\pi$
$788$	7.07180	0.251922
$789$	−15.0718	−0.536570
$790$	3.80385	0.135335
$791$	−11.3923	−0.405064
$792$	1.80385	0.0640969
$793$	0	0
$794$	−29.4641	−1.04564
$795$	−1.12436	−0.0398768
$796$	−5.46410	−0.193670
$797$	−8.92820	−0.316253	−0.158127	−	0.987419i	$-0.550545\pi$
$797$	−8.92820	−0.316253	−0.158127	+	0.987419i	$0.550545\pi$
$798$	−1.07180	−0.0379412
$799$	−16.7846	−0.593797
$800$	−4.00000	−0.141421
$801$	6.24871	0.220787
$802$	33.0526	1.16713
$803$	8.33975	0.294303
$804$	8.53590	0.301038
$805$	1.26795	0.0446893
$806$	0	0
$807$	−21.0718	−0.741762
$808$	1.19615	0.0420805
$809$	−7.24871	−0.254851	−0.127426	−	0.991848i	$-0.540671\pi$
$809$	−7.24871	−0.254851	−0.127426	+	0.991848i	$0.540671\pi$
$810$	−4.46410	−0.156853
$811$	−20.8756	−0.733043	−0.366522	−	0.930410i	$-0.619451\pi$
$811$	−20.8756	−0.733043	−0.366522	+	0.930410i	$0.619451\pi$
$812$	3.00000	0.105279
$813$	−5.21539	−0.182912
$814$	3.80385	0.133325
$815$	0.732051	0.0256426
$816$	−4.19615	−0.146895
$817$	−17.8564	−0.624717
$818$	−26.3205	−0.920275
$819$	0	0
$820$	2.46410	0.0860502
$821$	−30.9282	−1.07940	−0.539701	−	0.841857i	$-0.681463\pi$
$821$	−30.9282	−1.07940	−0.539701	+	0.841857i	$0.681463\pi$
$822$	−4.48334	−0.156374
$823$	2.24871	0.0783851	0.0391926	−	0.999232i	$-0.487521\pi$
$823$	2.24871	0.0783851	0.0391926	+	0.999232i	$0.487521\pi$
$824$	−8.39230	−0.292360
$825$	2.14359	0.0746303
$826$	10.7321	0.373416
$827$	20.4449	0.710938	0.355469	−	0.934688i	$-0.384321\pi$
$827$	20.4449	0.710938	0.355469	+	0.934688i	$0.384321\pi$
$828$	−3.12436	−0.108579
$829$	−6.41154	−0.222682	−0.111341	−	0.993782i	$-0.535515\pi$
$829$	−6.41154	−0.222682	−0.111341	+	0.993782i	$0.535515\pi$
$830$	3.80385	0.132033
$831$	6.87564	0.238513
$832$	0	0
$833$	−5.73205	−0.198604
$834$	−0.248711	−0.00861217
$835$	−5.26795	−0.182305
$836$	−1.07180	−0.0370689
$837$	−21.0718	−0.728348
$838$	5.12436	0.177018
$839$	31.7128	1.09485	0.547424	−	0.836855i	$-0.315609\pi$
$839$	31.7128	1.09485	0.547424	+	0.836855i	$0.315609\pi$
$840$	0.732051	0.0252582
$841$	−20.0000	−0.689655
$842$	14.1244	0.486757
$843$	12.1962	0.420058
$844$	−21.2679	−0.732073
$845$	0	0
$846$	−7.21539	−0.248070
$847$	10.4641	0.359551
$848$	1.53590	0.0527430
$849$	−7.75129	−0.266024
$850$	22.9282	0.786431
$851$	−6.58846	−0.225849
$852$	10.1436	0.347514
$853$	19.0000	0.650548	0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000	0.650548	0.325274	+	0.945620i	$0.394544\pi$
$854$	11.7321	0.401463
$855$	3.60770	0.123381
$856$	10.9282	0.373518
$857$	−0.947441	−0.0323640	−0.0161820	−	0.999869i	$-0.505151\pi$
$857$	−0.947441	−0.0323640	−0.0161820	+	0.999869i	$0.505151\pi$
$858$	0	0
$859$	−32.8372	−1.12039	−0.560195	−	0.828361i	$-0.689274\pi$
$859$	−32.8372	−1.12039	−0.560195	+	0.828361i	$0.689274\pi$
$860$	12.1962	0.415885
$861$	1.80385	0.0614750
$862$	26.5359	0.903816
$863$	−44.4449	−1.51292	−0.756460	−	0.654040i	$-0.773073\pi$
$863$	−44.4449	−1.51292	−0.756460	+	0.654040i	$0.773073\pi$
$864$	−4.00000	−0.136083
$865$	20.9282	0.711580
$866$	21.7321	0.738485
$867$	11.6077	0.394218
$868$	−5.26795	−0.178806
$869$	2.78461	0.0944614
$870$	2.19615	0.0744565
$871$	0	0
$872$	−10.0000	−0.338643
$873$	−13.4641	−0.455691
$874$	1.85641	0.0627939
$875$	−9.00000	−0.304256
$876$	−8.33975	−0.281774
$877$	−1.87564	−0.0633360	−0.0316680	−	0.999498i	$-0.510082\pi$
$877$	−1.87564	−0.0633360	−0.0316680	+	0.999498i	$0.510082\pi$
$878$	−19.2679	−0.650262
$879$	12.7321	0.429441
$880$	0.732051	0.0246774
$881$	−34.3731	−1.15806	−0.579029	−	0.815307i	$-0.696568\pi$
$881$	−34.3731	−1.15806	−0.579029	+	0.815307i	$0.696568\pi$
$882$	−2.46410	−0.0829706
$883$	−23.5167	−0.791399	−0.395699	−	0.918380i	$-0.629498\pi$
$883$	−23.5167	−0.791399	−0.395699	+	0.918380i	$0.629498\pi$
$884$	0	0
$885$	7.85641	0.264090
$886$	35.3205	1.18662
$887$	2.92820	0.0983194	0.0491597	−	0.998791i	$-0.484346\pi$
$887$	2.92820	0.0983194	0.0491597	+	0.998791i	$0.484346\pi$
$888$	−3.80385	−0.127649
$889$	−9.85641	−0.330573
$890$	2.53590	0.0850035
$891$	−3.26795	−0.109480
$892$	12.3923	0.414925
$893$	4.28719	0.143465
$894$	12.5885	0.421021
$895$	−16.3923	−0.547934
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	−15.8038	−0.527088
$900$	9.85641	0.328547
$901$	−8.80385	−0.293299
$902$	1.80385	0.0600616
$903$	8.92820	0.297112
$904$	11.3923	0.378902
$905$	3.19615	0.106244
$906$	−9.07180	−0.301390
$907$	−22.0526	−0.732243	−0.366122	−	0.930567i	$-0.619315\pi$
$907$	−22.0526	−0.732243	−0.366122	+	0.930567i	$0.619315\pi$
$908$	−1.26795	−0.0420784
$909$	−2.94744	−0.0977605
$910$	0	0
$911$	−40.1051	−1.32874	−0.664371	−	0.747403i	$-0.731300\pi$
$911$	−40.1051	−1.32874	−0.664371	+	0.747403i	$0.731300\pi$
$912$	1.07180	0.0354907
$913$	2.78461	0.0921571
$914$	−14.2679	−0.471942
$915$	8.58846	0.283926
$916$	24.3923	0.805944
$917$	5.07180	0.167485
$918$	22.9282	0.756743
$919$	0.784610	0.0258819	0.0129409	−	0.999916i	$-0.495881\pi$
$919$	0.784610	0.0258819	0.0129409	+	0.999916i	$0.495881\pi$
$920$	−1.26795	−0.0418030
$921$	17.2154	0.567266
$922$	−8.32051	−0.274021
$923$	0	0
$924$	0.535898	0.0176298
$925$	20.7846	0.683394
$926$	3.94744	0.129721
$927$	20.6795	0.679204
$928$	−3.00000	−0.0984798
$929$	55.1051	1.80794	0.903970	−	0.427596i	$-0.140639\pi$
$929$	55.1051	1.80794	0.903970	+	0.427596i	$0.140639\pi$
$930$	−3.85641	−0.126457
$931$	1.46410	0.0479840
$932$	−4.39230	−0.143875
$933$	−7.46410	−0.244364
$934$	−24.7321	−0.809257
$935$	−4.19615	−0.137229
$936$	0	0
$937$	55.5885	1.81600	0.907998	−	0.418975i	$-0.137610\pi$
$937$	55.5885	1.81600	0.907998	+	0.418975i	$0.137610\pi$
$938$	−11.6603	−0.380721
$939$	−23.4256	−0.764466
$940$	−2.92820	−0.0955075
$941$	−11.3205	−0.369038	−0.184519	−	0.982829i	$-0.559073\pi$
$941$	−11.3205	−0.369038	−0.184519	+	0.982829i	$0.559073\pi$
$942$	10.0526	0.327530
$943$	−3.12436	−0.101743
$944$	−10.7321	−0.349299
$945$	−4.00000	−0.130120
$946$	8.92820	0.290281
$947$	−53.1244	−1.72631	−0.863155	−	0.504939i	$-0.831515\pi$
$947$	−53.1244	−1.72631	−0.863155	+	0.504939i	$0.831515\pi$
$948$	−2.78461	−0.0904399
$949$	0	0
$950$	−5.85641	−0.190007
$951$	5.16283	0.167416
$952$	5.73205	0.185777
$953$	37.1769	1.20428	0.602139	−	0.798391i	$-0.294315\pi$
$953$	37.1769	1.20428	0.602139	+	0.798391i	$0.294315\pi$
$954$	−3.78461	−0.122531
$955$	−7.12436	−0.230539
$956$	−29.5167	−0.954637
$957$	1.60770	0.0519694
$958$	−32.1962	−1.04021
$959$	6.12436	0.197766
$960$	−0.732051	−0.0236268
$961$	−3.24871	−0.104797
$962$	0	0
$963$	−26.9282	−0.867749
$964$	−15.3923	−0.495753
$965$	−23.1962	−0.746711
$966$	−0.928203	−0.0298644
$967$	13.5167	0.434666	0.217333	−	0.976097i	$-0.430264\pi$
$967$	13.5167	0.434666	0.217333	+	0.976097i	$0.430264\pi$
$968$	−10.4641	−0.336329
$969$	−6.14359	−0.197361
$970$	−5.46410	−0.175442
$971$	−20.3923	−0.654420	−0.327210	−	0.944952i	$-0.606108\pi$
$971$	−20.3923	−0.654420	−0.327210	+	0.944952i	$0.606108\pi$
$972$	15.2679	0.489720
$973$	0.339746	0.0108918
$974$	−31.3205	−1.00357
$975$	0	0
$976$	−11.7321	−0.375534
$977$	24.1244	0.771807	0.385903	−	0.922539i	$-0.373890\pi$
$977$	24.1244	0.771807	0.385903	+	0.922539i	$0.373890\pi$
$978$	−0.535898	−0.0171361
$979$	1.85641	0.0593310
$980$	−1.00000	−0.0319438
$981$	24.6410	0.786727
$982$	−27.7128	−0.884351
$983$	−44.1051	−1.40673	−0.703367	−	0.710826i	$-0.748321\pi$
$983$	−44.1051	−1.40673	−0.703367	+	0.710826i	$0.748321\pi$
$984$	−1.80385	−0.0575046
$985$	−7.07180	−0.225326
$986$	17.1962	0.547637
$987$	−2.14359	−0.0682313
$988$	0	0
$989$	−15.4641	−0.491730
$990$	−1.80385	−0.0573300
$991$	−45.3731	−1.44132	−0.720661	−	0.693287i	$-0.756162\pi$
$991$	−45.3731	−1.44132	−0.720661	+	0.693287i	$0.756162\pi$
$992$	5.26795	0.167258
$993$	−3.17691	−0.100816
$994$	−13.8564	−0.439499
$995$	5.46410	0.173224
$996$	−2.78461	−0.0882337
$997$	−21.9808	−0.696138	−0.348069	−	0.937469i	$-0.613162\pi$
$997$	−21.9808	−0.696138	−0.348069	+	0.937469i	$0.613162\pi$
$998$	11.2679	0.356681
$999$	20.7846	0.657596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.s.1.2		2
13.2	odd	12		182.2.m.a.43.2	✓	4
13.5	odd	4		2366.2.d.k.337.2		4
13.7	odd	12		182.2.m.a.127.2	yes	4
13.8	odd	4		2366.2.d.k.337.4		4
13.12	even	2		2366.2.a.q.1.2		2
39.2	even	12		1638.2.bj.c.1135.1		4
39.20	even	12		1638.2.bj.c.127.1		4
52.7	even	12		1456.2.cc.b.673.2		4
52.15	even	12		1456.2.cc.b.225.2		4
91.2	odd	12		1274.2.o.b.459.1		4
91.20	even	12		1274.2.m.a.491.2		4
91.33	even	12		1274.2.v.b.361.1		4
91.41	even	12		1274.2.m.a.589.2		4
91.46	odd	12		1274.2.o.b.569.2		4
91.54	even	12		1274.2.o.a.459.1		4
91.59	even	12		1274.2.o.a.569.2		4
91.67	odd	12		1274.2.v.a.667.1		4
91.72	odd	12		1274.2.v.a.361.1		4
91.80	even	12		1274.2.v.b.667.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.a.43.2	✓	4	13.2	odd	12
182.2.m.a.127.2	yes	4	13.7	odd	12
1274.2.m.a.491.2		4	91.20	even	12
1274.2.m.a.589.2		4	91.41	even	12
1274.2.o.a.459.1		4	91.54	even	12
1274.2.o.a.569.2		4	91.59	even	12
1274.2.o.b.459.1		4	91.2	odd	12
1274.2.o.b.569.2		4	91.46	odd	12
1274.2.v.a.361.1		4	91.72	odd	12
1274.2.v.a.667.1		4	91.67	odd	12
1274.2.v.b.361.1		4	91.33	even	12
1274.2.v.b.667.1		4	91.80	even	12
1456.2.cc.b.225.2		4	52.15	even	12
1456.2.cc.b.673.2		4	52.7	even	12
1638.2.bj.c.127.1		4	39.20	even	12
1638.2.bj.c.1135.1		4	39.2	even	12
2366.2.a.q.1.2		2	13.12	even	2
2366.2.a.s.1.2		2	1.1	even	1	trivial
2366.2.d.k.337.2		4	13.5	odd	4
2366.2.d.k.337.4		4	13.8	odd	4

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.732051 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.00000 q^{10} -0.732051 q^{11} +0.732051 q^{12} -1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} -5.73205 q^{17} -2.46410 q^{18} +1.46410 q^{19} -1.00000 q^{20} -0.732051 q^{21} -0.732051 q^{22} +1.26795 q^{23} +0.732051 q^{24} -4.00000 q^{25} -4.00000 q^{27} -1.00000 q^{28} -3.00000 q^{29} -0.732051 q^{30} +5.26795 q^{31} +1.00000 q^{32} -0.535898 q^{33} -5.73205 q^{34} +1.00000 q^{35} -2.46410 q^{36} -5.19615 q^{37} +1.46410 q^{38} -1.00000 q^{40} -2.46410 q^{41} -0.732051 q^{42} -12.1962 q^{43} -0.732051 q^{44} +2.46410 q^{45} +1.26795 q^{46} +2.92820 q^{47} +0.732051 q^{48} +1.00000 q^{49} -4.00000 q^{50} -4.19615 q^{51} +1.53590 q^{53} -4.00000 q^{54} +0.732051 q^{55} -1.00000 q^{56} +1.07180 q^{57} -3.00000 q^{58} -10.7321 q^{59} -0.732051 q^{60} -11.7321 q^{61} +5.26795 q^{62} +2.46410 q^{63} +1.00000 q^{64} -0.535898 q^{66} +11.6603 q^{67} -5.73205 q^{68} +0.928203 q^{69} +1.00000 q^{70} +13.8564 q^{71} -2.46410 q^{72} -11.3923 q^{73} -5.19615 q^{74} -2.92820 q^{75} +1.46410 q^{76} +0.732051 q^{77} -3.80385 q^{79} -1.00000 q^{80} +4.46410 q^{81} -2.46410 q^{82} -3.80385 q^{83} -0.732051 q^{84} +5.73205 q^{85} -12.1962 q^{86} -2.19615 q^{87} -0.732051 q^{88} -2.53590 q^{89} +2.46410 q^{90} +1.26795 q^{92} +3.85641 q^{93} +2.92820 q^{94} -1.46410 q^{95} +0.732051 q^{96} +5.46410 q^{97} +1.00000 q^{98} +1.80385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{14} + 2 q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} + 6 q^{23} - 2 q^{24} - 8 q^{25} - 8 q^{27} - 2 q^{28} - 6 q^{29} + 2 q^{30} + 14 q^{31} + 2 q^{32} - 8 q^{33} - 8 q^{34} + 2 q^{35} + 2 q^{36} - 4 q^{38} - 2 q^{40} + 2 q^{41} + 2 q^{42} - 14 q^{43} + 2 q^{44} - 2 q^{45} + 6 q^{46} - 8 q^{47} - 2 q^{48} + 2 q^{49} - 8 q^{50} + 2 q^{51} + 10 q^{53} - 8 q^{54} - 2 q^{55} - 2 q^{56} + 16 q^{57} - 6 q^{58} - 18 q^{59} + 2 q^{60} - 20 q^{61} + 14 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 6 q^{67} - 8 q^{68} - 12 q^{69} + 2 q^{70} + 2 q^{72} - 2 q^{73} + 8 q^{75} - 4 q^{76} - 2 q^{77} - 18 q^{79} - 2 q^{80} + 2 q^{81} + 2 q^{82} - 18 q^{83} + 2 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} + 2 q^{88} - 12 q^{89} - 2 q^{90} + 6 q^{92} - 20 q^{93} - 8 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{97} + 2 q^{98} + 14 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^14 + 2 * q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 + 6 * q^23 - 2 * q^24 - 8 * q^25 - 8 * q^27 - 2 * q^28 - 6 * q^29 + 2 * q^30 + 14 * q^31 + 2 * q^32 - 8 * q^33 - 8 * q^34 + 2 * q^35 + 2 * q^36 - 4 * q^38 - 2 * q^40 + 2 * q^41 + 2 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^45 + 6 * q^46 - 8 * q^47 - 2 * q^48 + 2 * q^49 - 8 * q^50 + 2 * q^51 + 10 * q^53 - 8 * q^54 - 2 * q^55 - 2 * q^56 + 16 * q^57 - 6 * q^58 - 18 * q^59 + 2 * q^60 - 20 * q^61 + 14 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 6 * q^67 - 8 * q^68 - 12 * q^69 + 2 * q^70 + 2 * q^72 - 2 * q^73 + 8 * q^75 - 4 * q^76 - 2 * q^77 - 18 * q^79 - 2 * q^80 + 2 * q^81 + 2 * q^82 - 18 * q^83 + 2 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 + 2 * q^88 - 12 * q^89 - 2 * q^90 + 6 * q^92 - 20 * q^93 - 8 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^97 + 2 * q^98 + 14 * q^99

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