LMFDB - Embedded newform 2366.2.a.bh.1.4

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:	$6$
Coefficient field:	6.6.285686784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10x^{4} + 12x^{3} + 21x^{2} + 2x - 2 $ x^6 - 2x^5 - 10x^4 + 12x^3 + 21x^2 + 2*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			1.4
Root			$0.252878$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.252878 q^{3} +1.00000 q^{4} +1.14776 q^{5} +0.252878 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.93605 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.252878 q^{3} +1.00000 q^{4} +1.14776 q^{5} +0.252878 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.93605 q^{9} +1.14776 q^{10} +4.44485 q^{11} +0.252878 q^{12} +1.00000 q^{14} +0.290242 q^{15} +1.00000 q^{16} +2.70976 q^{17} -2.93605 q^{18} +6.56298 q^{19} +1.14776 q^{20} +0.252878 q^{21} +4.44485 q^{22} -2.08000 q^{23} +0.252878 q^{24} -3.68266 q^{25} -1.50110 q^{27} +1.00000 q^{28} +7.19919 q^{29} +0.290242 q^{30} -7.90895 q^{31} +1.00000 q^{32} +1.12400 q^{33} +2.70976 q^{34} +1.14776 q^{35} -2.93605 q^{36} -9.64405 q^{37} +6.56298 q^{38} +1.14776 q^{40} +9.49471 q^{41} +0.252878 q^{42} -3.40320 q^{43} +4.44485 q^{44} -3.36987 q^{45} -2.08000 q^{46} -1.67435 q^{47} +0.252878 q^{48} +1.00000 q^{49} -3.68266 q^{50} +0.685238 q^{51} +13.2815 q^{53} -1.50110 q^{54} +5.10160 q^{55} +1.00000 q^{56} +1.65963 q^{57} +7.19919 q^{58} -0.0677585 q^{59} +0.290242 q^{60} +8.10046 q^{61} -7.90895 q^{62} -2.93605 q^{63} +1.00000 q^{64} +1.12400 q^{66} +0.513495 q^{67} +2.70976 q^{68} -0.525985 q^{69} +1.14776 q^{70} +10.7873 q^{71} -2.93605 q^{72} -8.02452 q^{73} -9.64405 q^{74} -0.931263 q^{75} +6.56298 q^{76} +4.44485 q^{77} +10.7404 q^{79} +1.14776 q^{80} +8.42856 q^{81} +9.49471 q^{82} -15.3479 q^{83} +0.252878 q^{84} +3.11014 q^{85} -3.40320 q^{86} +1.82052 q^{87} +4.44485 q^{88} +10.8596 q^{89} -3.36987 q^{90} -2.08000 q^{92} -2.00000 q^{93} -1.67435 q^{94} +7.53270 q^{95} +0.252878 q^{96} +2.12694 q^{97} +1.00000 q^{98} -13.0503 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * q^98 - 2 * 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
$3$	0.252878	0.145999	0.0729996	−	0.997332i	$-0.476743\pi$
$3$	0.252878	0.145999	0.0729996	+	0.997332i	$0.476743\pi$
$4$	1.00000	0.500000
$5$	1.14776	0.513292	0.256646	−	0.966505i	$-0.417383\pi$
$5$	1.14776	0.513292	0.256646	+	0.966505i	$0.417383\pi$
$6$	0.252878	0.103237
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.93605	−0.978684
$10$	1.14776	0.362952
$11$	4.44485	1.34017	0.670086	−	0.742283i	$-0.266257\pi$
$11$	4.44485	1.34017	0.670086	+	0.742283i	$0.266257\pi$
$12$	0.252878	0.0729996
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	0.290242	0.0749402
$16$	1.00000	0.250000
$17$	2.70976	0.657213	0.328606	−	0.944467i	$-0.393421\pi$
$17$	2.70976	0.657213	0.328606	+	0.944467i	$0.393421\pi$
$18$	−2.93605	−0.692034
$19$	6.56298	1.50565	0.752826	−	0.658220i	$-0.228690\pi$
$19$	6.56298	1.50565	0.752826	+	0.658220i	$0.228690\pi$
$20$	1.14776	0.256646
$21$	0.252878	0.0551825
$22$	4.44485	0.947645
$23$	−2.08000	−0.433709	−0.216855	−	0.976204i	$-0.569580\pi$
$23$	−2.08000	−0.433709	−0.216855	+	0.976204i	$0.569580\pi$
$24$	0.252878	0.0516185
$25$	−3.68266	−0.736531
$26$	0	0
$27$	−1.50110	−0.288886
$28$	1.00000	0.188982
$29$	7.19919	1.33686	0.668428	−	0.743776i	$-0.266967\pi$
$29$	7.19919	1.33686	0.668428	+	0.743776i	$0.266967\pi$
$30$	0.290242	0.0529907
$31$	−7.90895	−1.42049	−0.710245	−	0.703955i	$-0.751416\pi$
$31$	−7.90895	−1.42049	−0.710245	+	0.703955i	$0.751416\pi$
$32$	1.00000	0.176777
$33$	1.12400	0.195664
$34$	2.70976	0.464720
$35$	1.14776	0.194006
$36$	−2.93605	−0.489342
$37$	−9.64405	−1.58547	−0.792736	−	0.609566i	$-0.791344\pi$
$37$	−9.64405	−1.58547	−0.792736	+	0.609566i	$0.791344\pi$
$38$	6.56298	1.06466
$39$	0	0
$40$	1.14776	0.181476
$41$	9.49471	1.48282	0.741412	−	0.671050i	$-0.234157\pi$
$41$	9.49471	1.48282	0.741412	+	0.671050i	$0.234157\pi$
$42$	0.252878	0.0390199
$43$	−3.40320	−0.518983	−0.259491	−	0.965745i	$-0.583555\pi$
$43$	−3.40320	−0.518983	−0.259491	+	0.965745i	$0.583555\pi$
$44$	4.44485	0.670086
$45$	−3.36987	−0.502351
$46$	−2.08000	−0.306679
$47$	−1.67435	−0.244229	−0.122114	−	0.992516i	$-0.538967\pi$
$47$	−1.67435	−0.244229	−0.122114	+	0.992516i	$0.538967\pi$
$48$	0.252878	0.0364998
$49$	1.00000	0.142857
$50$	−3.68266	−0.520806
$51$	0.685238	0.0959525
$52$	0	0
$53$	13.2815	1.82436	0.912180	−	0.409789i	$-0.134398\pi$
$53$	13.2815	1.82436	0.912180	+	0.409789i	$0.134398\pi$
$54$	−1.50110	−0.204273
$55$	5.10160	0.687900
$56$	1.00000	0.133631
$57$	1.65963	0.219824
$58$	7.19919	0.945301
$59$	−0.0677585	−0.00882140	−0.00441070	−	0.999990i	$-0.501404\pi$
$59$	−0.0677585	−0.00882140	−0.00441070	+	0.999990i	$0.501404\pi$
$60$	0.290242	0.0374701
$61$	8.10046	1.03716	0.518579	−	0.855030i	$-0.326461\pi$
$61$	8.10046	1.03716	0.518579	+	0.855030i	$0.326461\pi$
$62$	−7.90895	−1.00444
$63$	−2.93605	−0.369908
$64$	1.00000	0.125000
$65$	0	0
$66$	1.12400	0.138355
$67$	0.513495	0.0627334	0.0313667	−	0.999508i	$-0.490014\pi$
$67$	0.513495	0.0627334	0.0313667	+	0.999508i	$0.490014\pi$
$68$	2.70976	0.328606
$69$	−0.525985	−0.0633212
$70$	1.14776	0.137183
$71$	10.7873	1.28022	0.640109	−	0.768284i	$-0.278889\pi$
$71$	10.7873	1.28022	0.640109	+	0.768284i	$0.278889\pi$
$72$	−2.93605	−0.346017
$73$	−8.02452	−0.939199	−0.469599	−	0.882880i	$-0.655602\pi$
$73$	−8.02452	−0.939199	−0.469599	+	0.882880i	$0.655602\pi$
$74$	−9.64405	−1.12110
$75$	−0.931263	−0.107533
$76$	6.56298	0.752826
$77$	4.44485	0.506538
$78$	0	0
$79$	10.7404	1.20839	0.604193	−	0.796838i	$-0.293496\pi$
$79$	10.7404	1.20839	0.604193	+	0.796838i	$0.293496\pi$
$80$	1.14776	0.128323
$81$	8.42856	0.936507
$82$	9.49471	1.04851
$83$	−15.3479	−1.68465	−0.842327	−	0.538967i	$-0.818815\pi$
$83$	−15.3479	−1.68465	−0.842327	+	0.538967i	$0.818815\pi$
$84$	0.252878	0.0275913
$85$	3.11014	0.337342
$86$	−3.40320	−0.366976
$87$	1.82052	0.195180
$88$	4.44485	0.473823
$89$	10.8596	1.15111	0.575555	−	0.817763i	$-0.304786\pi$
$89$	10.8596	1.15111	0.575555	+	0.817763i	$0.304786\pi$
$90$	−3.36987	−0.355216
$91$	0	0
$92$	−2.08000	−0.216855
$93$	−2.00000	−0.207390
$94$	−1.67435	−0.172696
$95$	7.53270	0.772838
$96$	0.252878	0.0258093
$97$	2.12694	0.215958	0.107979	−	0.994153i	$-0.465562\pi$
$97$	2.12694	0.215958	0.107979	+	0.994153i	$0.465562\pi$
$98$	1.00000	0.101015
$99$	−13.0503	−1.31161
$100$	−3.68266	−0.368266
$101$	−6.01888	−0.598901	−0.299451	−	0.954112i	$-0.596803\pi$
$101$	−6.01888	−0.598901	−0.299451	+	0.954112i	$0.596803\pi$
$102$	0.685238	0.0678487
$103$	−5.75670	−0.567224	−0.283612	−	0.958939i	$-0.591533\pi$
$103$	−5.75670	−0.567224	−0.283612	+	0.958939i	$0.591533\pi$
$104$	0	0
$105$	0.290242	0.0283247
$106$	13.2815	1.29002
$107$	−5.54937	−0.536478	−0.268239	−	0.963352i	$-0.586442\pi$
$107$	−5.54937	−0.536478	−0.268239	+	0.963352i	$0.586442\pi$
$108$	−1.50110	−0.144443
$109$	−7.96986	−0.763374	−0.381687	−	0.924292i	$-0.624657\pi$
$109$	−7.96986	−0.763374	−0.381687	+	0.924292i	$0.624657\pi$
$110$	5.10160	0.486419
$111$	−2.43877	−0.231477
$112$	1.00000	0.0944911
$113$	−4.37070	−0.411161	−0.205580	−	0.978640i	$-0.565908\pi$
$113$	−4.37070	−0.411161	−0.205580	+	0.978640i	$0.565908\pi$
$114$	1.65963	0.155439
$115$	−2.38733	−0.222619
$116$	7.19919	0.668428
$117$	0	0
$118$	−0.0677585	−0.00623767
$119$	2.70976	0.248403
$120$	0.290242	0.0264954
$121$	8.75670	0.796063
$122$	8.10046	0.733382
$123$	2.40100	0.216491
$124$	−7.90895	−0.710245
$125$	−9.96557	−0.891347
$126$	−2.93605	−0.261564
$127$	6.86494	0.609165	0.304583	−	0.952486i	$-0.401483\pi$
$127$	6.86494	0.609165	0.304583	+	0.952486i	$0.401483\pi$
$128$	1.00000	0.0883883
$129$	−0.860593	−0.0757710
$130$	0	0
$131$	−16.1996	−1.41537	−0.707683	−	0.706530i	$-0.750259\pi$
$131$	−16.1996	−1.41537	−0.707683	+	0.706530i	$0.750259\pi$
$132$	1.12400	0.0978321
$133$	6.56298	0.569083
$134$	0.513495	0.0443592
$135$	−1.72289	−0.148283
$136$	2.70976	0.232360
$137$	−5.20224	−0.444457	−0.222229	−	0.974995i	$-0.571333\pi$
$137$	−5.20224	−0.444457	−0.222229	+	0.974995i	$0.571333\pi$
$138$	−0.525985	−0.0447749
$139$	5.74027	0.486883	0.243442	−	0.969916i	$-0.421724\pi$
$139$	5.74027	0.486883	0.243442	+	0.969916i	$0.421724\pi$
$140$	1.14776	0.0970030
$141$	−0.423405	−0.0356572
$142$	10.7873	0.905250
$143$	0	0
$144$	−2.93605	−0.244671
$145$	8.26291	0.686198
$146$	−8.02452	−0.664114
$147$	0.252878	0.0208570
$148$	−9.64405	−0.792736
$149$	3.02580	0.247883	0.123941	−	0.992290i	$-0.460447\pi$
$149$	3.02580	0.247883	0.123941	+	0.992290i	$0.460447\pi$
$150$	−0.931263	−0.0760373
$151$	−1.27030	−0.103376	−0.0516879	−	0.998663i	$-0.516460\pi$
$151$	−1.27030	−0.103376	−0.0516879	+	0.998663i	$0.516460\pi$
$152$	6.56298	0.532328
$153$	−7.95599	−0.643204
$154$	4.44485	0.358176
$155$	−9.07754	−0.729126
$156$	0	0
$157$	−4.11859	−0.328699	−0.164350	−	0.986402i	$-0.552553\pi$
$157$	−4.11859	−0.328699	−0.164350	+	0.986402i	$0.552553\pi$
$158$	10.7404	0.854457
$159$	3.35861	0.266355
$160$	1.14776	0.0907380
$161$	−2.08000	−0.163927
$162$	8.42856	0.662211
$163$	11.2191	0.878751	0.439376	−	0.898303i	$-0.355200\pi$
$163$	11.2191	0.878751	0.439376	+	0.898303i	$0.355200\pi$
$164$	9.49471	0.741412
$165$	1.29008	0.100433
$166$	−15.3479	−1.19123
$167$	−3.99739	−0.309327	−0.154664	−	0.987967i	$-0.549429\pi$
$167$	−3.99739	−0.309327	−0.154664	+	0.987967i	$0.549429\pi$
$168$	0.252878	0.0195100
$169$	0	0
$170$	3.11014	0.238537
$171$	−19.2693	−1.47356
$172$	−3.40320	−0.259491
$173$	−12.1679	−0.925109	−0.462555	−	0.886591i	$-0.653067\pi$
$173$	−12.1679	−0.925109	−0.462555	+	0.886591i	$0.653067\pi$
$174$	1.82052	0.138013
$175$	−3.68266	−0.278383
$176$	4.44485	0.335043
$177$	−0.0171346	−0.00128792
$178$	10.8596	0.813958
$179$	−11.8711	−0.887285	−0.443643	−	0.896204i	$-0.646314\pi$
$179$	−11.8711	−0.887285	−0.443643	+	0.896204i	$0.646314\pi$
$180$	−3.36987	−0.251175
$181$	4.79134	0.356137	0.178069	−	0.984018i	$-0.443015\pi$
$181$	4.79134	0.356137	0.178069	+	0.984018i	$0.443015\pi$
$182$	0	0
$183$	2.04843	0.151424
$184$	−2.08000	−0.153339
$185$	−11.0690	−0.813809
$186$	−2.00000	−0.146647
$187$	12.0445	0.880779
$188$	−1.67435	−0.122114
$189$	−1.50110	−0.109189
$190$	7.53270	0.546479
$191$	15.5853	1.12771	0.563855	−	0.825874i	$-0.309318\pi$
$191$	15.5853	1.12771	0.563855	+	0.825874i	$0.309318\pi$
$192$	0.252878	0.0182499
$193$	−17.5855	−1.26583	−0.632916	−	0.774221i	$-0.718142\pi$
$193$	−17.5855	−1.26583	−0.632916	+	0.774221i	$0.718142\pi$
$194$	2.12694	0.152705
$195$	0	0
$196$	1.00000	0.0714286
$197$	0.529815	0.0377477	0.0188739	−	0.999822i	$-0.493992\pi$
$197$	0.529815	0.0377477	0.0188739	+	0.999822i	$0.493992\pi$
$198$	−13.0503	−0.927446
$199$	25.1465	1.78259	0.891294	−	0.453426i	$-0.149799\pi$
$199$	25.1465	1.78259	0.891294	+	0.453426i	$0.149799\pi$
$200$	−3.68266	−0.260403
$201$	0.129852	0.00915902
$202$	−6.01888	−0.423487
$203$	7.19919	0.505284
$204$	0.685238	0.0479763
$205$	10.8976	0.761121
$206$	−5.75670	−0.401088
$207$	6.10698	0.424465
$208$	0	0
$209$	29.1715	2.01783
$210$	0.290242	0.0200286
$211$	5.44170	0.374622	0.187311	−	0.982301i	$-0.440023\pi$
$211$	5.44170	0.374622	0.187311	+	0.982301i	$0.440023\pi$
$212$	13.2815	0.912180
$213$	2.72787	0.186911
$214$	−5.54937	−0.379347
$215$	−3.90604	−0.266390
$216$	−1.50110	−0.102137
$217$	−7.90895	−0.536895
$218$	−7.96986	−0.539787
$219$	−2.02922	−0.137122
$220$	5.10160	0.343950
$221$	0	0
$222$	−2.43877	−0.163679
$223$	−9.24550	−0.619124	−0.309562	−	0.950879i	$-0.600182\pi$
$223$	−9.24550	−0.619124	−0.309562	+	0.950879i	$0.600182\pi$
$224$	1.00000	0.0668153
$225$	10.8125	0.720832
$226$	−4.37070	−0.290735
$227$	−1.50478	−0.0998756	−0.0499378	−	0.998752i	$-0.515902\pi$
$227$	−1.50478	−0.0998756	−0.0499378	+	0.998752i	$0.515902\pi$
$228$	1.65963	0.109912
$229$	−25.4380	−1.68099	−0.840496	−	0.541818i	$-0.817736\pi$
$229$	−25.4380	−1.68099	−0.840496	+	0.541818i	$0.817736\pi$
$230$	−2.38733	−0.157416
$231$	1.12400	0.0739541
$232$	7.19919	0.472650
$233$	−12.1004	−0.792724	−0.396362	−	0.918094i	$-0.629727\pi$
$233$	−12.1004	−0.792724	−0.396362	+	0.918094i	$0.629727\pi$
$234$	0	0
$235$	−1.92174	−0.125361
$236$	−0.0677585	−0.00441070
$237$	2.71600	0.176423
$238$	2.70976	0.175648
$239$	5.57964	0.360917	0.180458	−	0.983583i	$-0.442242\pi$
$239$	5.57964	0.360917	0.180458	+	0.983583i	$0.442242\pi$
$240$	0.290242	0.0187350
$241$	−23.2430	−1.49722	−0.748608	−	0.663013i	$-0.769277\pi$
$241$	−23.2430	−1.49722	−0.748608	+	0.663013i	$0.769277\pi$
$242$	8.75670	0.562902
$243$	6.63469	0.425616
$244$	8.10046	0.518579
$245$	1.14776	0.0733274
$246$	2.40100	0.153082
$247$	0	0
$248$	−7.90895	−0.502219
$249$	−3.88115	−0.245958
$250$	−9.96557	−0.630278
$251$	−23.7414	−1.49855	−0.749273	−	0.662261i	$-0.769597\pi$
$251$	−23.7414	−1.49855	−0.749273	+	0.662261i	$0.769597\pi$
$252$	−2.93605	−0.184954
$253$	−9.24528	−0.581246
$254$	6.86494	0.430745
$255$	0.786486	0.0492517
$256$	1.00000	0.0625000
$257$	7.01039	0.437296	0.218648	−	0.975804i	$-0.429835\pi$
$257$	7.01039	0.437296	0.218648	+	0.975804i	$0.429835\pi$
$258$	−0.860593	−0.0535782
$259$	−9.64405	−0.599252
$260$	0	0
$261$	−21.1372	−1.30836
$262$	−16.1996	−1.00081
$263$	30.8452	1.90200	0.950998	−	0.309196i	$-0.100060\pi$
$263$	30.8452	1.90200	0.950998	+	0.309196i	$0.100060\pi$
$264$	1.12400	0.0691777
$265$	15.2440	0.936429
$266$	6.56298	0.402402
$267$	2.74614	0.168061
$268$	0.513495	0.0313667
$269$	−5.63191	−0.343383	−0.171692	−	0.985151i	$-0.554923\pi$
$269$	−5.63191	−0.343383	−0.171692	+	0.985151i	$0.554923\pi$
$270$	−1.72289	−0.104852
$271$	−3.00481	−0.182529	−0.0912645	−	0.995827i	$-0.529091\pi$
$271$	−3.00481	−0.182529	−0.0912645	+	0.995827i	$0.529091\pi$
$272$	2.70976	0.164303
$273$	0	0
$274$	−5.20224	−0.314279
$275$	−16.3689	−0.987080
$276$	−0.525985	−0.0316606
$277$	−24.1732	−1.45243	−0.726214	−	0.687469i	$-0.758722\pi$
$277$	−24.1732	−1.45243	−0.726214	+	0.687469i	$0.758722\pi$
$278$	5.74027	0.344278
$279$	23.2211	1.39021
$280$	1.14776	0.0685915
$281$	1.74575	0.104143	0.0520713	−	0.998643i	$-0.483418\pi$
$281$	1.74575	0.104143	0.0520713	+	0.998643i	$0.483418\pi$
$282$	−0.423405	−0.0252134
$283$	26.1143	1.55233	0.776167	−	0.630527i	$-0.217161\pi$
$283$	26.1143	1.55233	0.776167	+	0.630527i	$0.217161\pi$
$284$	10.7873	0.640109
$285$	1.90485	0.112834
$286$	0	0
$287$	9.49471	0.560455
$288$	−2.93605	−0.173009
$289$	−9.65721	−0.568071
$290$	8.26291	0.485215
$291$	0.537855	0.0315296
$292$	−8.02452	−0.469599
$293$	5.65535	0.330389	0.165194	−	0.986261i	$-0.447175\pi$
$293$	5.65535	0.330389	0.165194	+	0.986261i	$0.447175\pi$
$294$	0.252878	0.0147481
$295$	−0.0777701	−0.00452795
$296$	−9.64405	−0.560549
$297$	−6.67215	−0.387158
$298$	3.02580	0.175280
$299$	0	0
$300$	−0.931263	−0.0537665
$301$	−3.40320	−0.196157
$302$	−1.27030	−0.0730977
$303$	−1.52204	−0.0874391
$304$	6.56298	0.376413
$305$	9.29735	0.532365
$306$	−7.95599	−0.454814
$307$	−20.4767	−1.16867	−0.584333	−	0.811514i	$-0.698644\pi$
$307$	−20.4767	−1.16867	−0.584333	+	0.811514i	$0.698644\pi$
$308$	4.44485	0.253269
$309$	−1.45574	−0.0828143
$310$	−9.07754	−0.515570
$311$	−1.23712	−0.0701506	−0.0350753	−	0.999385i	$-0.511167\pi$
$311$	−1.23712	−0.0701506	−0.0350753	+	0.999385i	$0.511167\pi$
$312$	0	0
$313$	−9.01151	−0.509361	−0.254680	−	0.967025i	$-0.581970\pi$
$313$	−9.01151	−0.509361	−0.254680	+	0.967025i	$0.581970\pi$
$314$	−4.11859	−0.232426
$315$	−3.36987	−0.189871
$316$	10.7404	0.604193
$317$	0.580644	0.0326122	0.0163061	−	0.999867i	$-0.494809\pi$
$317$	0.580644	0.0326122	0.0163061	+	0.999867i	$0.494809\pi$
$318$	3.35861	0.188342
$319$	31.9993	1.79162
$320$	1.14776	0.0641615
$321$	−1.40331	−0.0783253
$322$	−2.08000	−0.115914
$323$	17.7841	0.989533
$324$	8.42856	0.468254
$325$	0	0
$326$	11.2191	0.621371
$327$	−2.01540	−0.111452
$328$	9.49471	0.524257
$329$	−1.67435	−0.0923097
$330$	1.29008	0.0710167
$331$	−31.3654	−1.72400	−0.861999	−	0.506910i	$-0.830788\pi$
$331$	−31.3654	−1.72400	−0.861999	+	0.506910i	$0.830788\pi$
$332$	−15.3479	−0.842327
$333$	28.3154	1.55168
$334$	−3.99739	−0.218727
$335$	0.589367	0.0322005
$336$	0.252878	0.0137956
$337$	−9.43033	−0.513703	−0.256851	−	0.966451i	$-0.582685\pi$
$337$	−9.43033	−0.513703	−0.256851	+	0.966451i	$0.582685\pi$
$338$	0	0
$339$	−1.10525	−0.0600292
$340$	3.11014	0.168671
$341$	−35.1541	−1.90370
$342$	−19.2693	−1.04196
$343$	1.00000	0.0539949
$344$	−3.40320	−0.183488
$345$	−0.603703	−0.0325023
$346$	−12.1679	−0.654151
$347$	6.47300	0.347489	0.173744	−	0.984791i	$-0.444413\pi$
$347$	6.47300	0.347489	0.173744	+	0.984791i	$0.444413\pi$
$348$	1.82052	0.0975900
$349$	9.90515	0.530211	0.265105	−	0.964219i	$-0.414593\pi$
$349$	9.90515	0.530211	0.265105	+	0.964219i	$0.414593\pi$
$350$	−3.68266	−0.196846
$351$	0	0
$352$	4.44485	0.236911
$353$	−28.7758	−1.53158	−0.765790	−	0.643090i	$-0.777652\pi$
$353$	−28.7758	−1.53158	−0.765790	+	0.643090i	$0.777652\pi$
$354$	−0.0171346	−0.000910695 0
$355$	12.3812	0.657125
$356$	10.8596	0.575555
$357$	0.685238	0.0362666
$358$	−11.8711	−0.627406
$359$	12.1382	0.640631	0.320315	−	0.947311i	$-0.396211\pi$
$359$	12.1382	0.640631	0.320315	+	0.947311i	$0.396211\pi$
$360$	−3.36987	−0.177608
$361$	24.0727	1.26699
$362$	4.79134	0.251827
$363$	2.21438	0.116225
$364$	0	0
$365$	−9.21019	−0.482083
$366$	2.04843	0.107073
$367$	−27.0775	−1.41343	−0.706717	−	0.707496i	$-0.749825\pi$
$367$	−27.0775	−1.41343	−0.706717	+	0.707496i	$0.749825\pi$
$368$	−2.08000	−0.108427
$369$	−27.8770	−1.45122
$370$	−11.0690	−0.575450
$371$	13.2815	0.689543
$372$	−2.00000	−0.103695
$373$	−15.6332	−0.809457	−0.404729	−	0.914437i	$-0.632634\pi$
$373$	−15.6332	−0.809457	−0.404729	+	0.914437i	$0.632634\pi$
$374$	12.0445	0.622805
$375$	−2.52007	−0.130136
$376$	−1.67435	−0.0863478
$377$	0	0
$378$	−1.50110	−0.0772081
$379$	37.3308	1.91756	0.958778	−	0.284155i	$-0.0917131\pi$
$379$	37.3308	1.91756	0.958778	+	0.284155i	$0.0917131\pi$
$380$	7.53270	0.386419
$381$	1.73599	0.0889376
$382$	15.5853	0.797411
$383$	−37.8964	−1.93642	−0.968209	−	0.250144i	$-0.919522\pi$
$383$	−37.8964	−1.93642	−0.968209	+	0.250144i	$0.919522\pi$
$384$	0.252878	0.0129046
$385$	5.10160	0.260002
$386$	−17.5855	−0.895078
$387$	9.99196	0.507920
$388$	2.12694	0.107979
$389$	10.1053	0.512361	0.256180	−	0.966629i	$-0.417536\pi$
$389$	10.1053	0.512361	0.256180	+	0.966629i	$0.417536\pi$
$390$	0	0
$391$	−5.63629	−0.285039
$392$	1.00000	0.0505076
$393$	−4.09652	−0.206642
$394$	0.529815	0.0266917
$395$	12.3273	0.620254
$396$	−13.0503	−0.655803
$397$	−5.50839	−0.276458	−0.138229	−	0.990400i	$-0.544141\pi$
$397$	−5.50839	−0.276458	−0.138229	+	0.990400i	$0.544141\pi$
$398$	25.1465	1.26048
$399$	1.65963	0.0830856
$400$	−3.68266	−0.184133
$401$	−26.7495	−1.33581	−0.667903	−	0.744249i	$-0.732808\pi$
$401$	−26.7495	−1.33581	−0.667903	+	0.744249i	$0.732808\pi$
$402$	0.129852	0.00647641
$403$	0	0
$404$	−6.01888	−0.299451
$405$	9.67393	0.480701
$406$	7.19919	0.357290
$407$	−42.8663	−2.12481
$408$	0.685238	0.0339243
$409$	−31.9995	−1.58227	−0.791137	−	0.611639i	$-0.790510\pi$
$409$	−31.9995	−1.58227	−0.791137	+	0.611639i	$0.790510\pi$
$410$	10.8976	0.538194
$411$	−1.31553	−0.0648904
$412$	−5.75670	−0.283612
$413$	−0.0677585	−0.00333418
$414$	6.10698	0.300142
$415$	−17.6157	−0.864719
$416$	0	0
$417$	1.45159	0.0710846
$418$	29.1715	1.42682
$419$	11.6956	0.571370	0.285685	−	0.958324i	$-0.407779\pi$
$419$	11.6956	0.571370	0.285685	+	0.958324i	$0.407779\pi$
$420$	0.290242	0.0141624
$421$	−25.8565	−1.26017	−0.630084	−	0.776527i	$-0.716979\pi$
$421$	−25.8565	−1.26017	−0.630084	+	0.776527i	$0.716979\pi$
$422$	5.44170	0.264898
$423$	4.91597	0.239023
$424$	13.2815	0.645009
$425$	−9.97911	−0.484058
$426$	2.72787	0.132166
$427$	8.10046	0.392009
$428$	−5.54937	−0.268239
$429$	0	0
$430$	−3.90604	−0.188366
$431$	−10.7062	−0.515700	−0.257850	−	0.966185i	$-0.583014\pi$
$431$	−10.7062	−0.515700	−0.257850	+	0.966185i	$0.583014\pi$
$432$	−1.50110	−0.0722216
$433$	22.4299	1.07791	0.538956	−	0.842334i	$-0.318819\pi$
$433$	22.4299	1.07791	0.538956	+	0.842334i	$0.318819\pi$
$434$	−7.90895	−0.379642
$435$	2.08951	0.100184
$436$	−7.96986	−0.381687
$437$	−13.6510	−0.653015
$438$	−2.02922	−0.0969601
$439$	−12.7183	−0.607009	−0.303505	−	0.952830i	$-0.598157\pi$
$439$	−12.7183	−0.607009	−0.303505	+	0.952830i	$0.598157\pi$
$440$	5.10160	0.243209
$441$	−2.93605	−0.139812
$442$	0	0
$443$	−7.86448	−0.373653	−0.186826	−	0.982393i	$-0.559820\pi$
$443$	−7.86448	−0.373653	−0.186826	+	0.982393i	$0.559820\pi$
$444$	−2.43877	−0.115739
$445$	12.4641	0.590856
$446$	−9.24550	−0.437787
$447$	0.765157	0.0361907
$448$	1.00000	0.0472456
$449$	16.8373	0.794600	0.397300	−	0.917689i	$-0.369947\pi$
$449$	16.8373	0.794600	0.397300	+	0.917689i	$0.369947\pi$
$450$	10.8125	0.509705
$451$	42.2025	1.98724
$452$	−4.37070	−0.205580
$453$	−0.321232	−0.0150928
$454$	−1.50478	−0.0706227
$455$	0	0
$456$	1.65963	0.0777195
$457$	−9.19764	−0.430248	−0.215124	−	0.976587i	$-0.569015\pi$
$457$	−9.19764	−0.430248	−0.215124	+	0.976587i	$0.569015\pi$
$458$	−25.4380	−1.18864
$459$	−4.06761	−0.189860
$460$	−2.38733	−0.111310
$461$	−21.8021	−1.01542	−0.507712	−	0.861527i	$-0.669509\pi$
$461$	−21.8021	−1.01542	−0.507712	+	0.861527i	$0.669509\pi$
$462$	1.12400	0.0522934
$463$	26.0636	1.21128	0.605638	−	0.795740i	$-0.292918\pi$
$463$	26.0636	1.21128	0.605638	+	0.795740i	$0.292918\pi$
$464$	7.19919	0.334214
$465$	−2.29551	−0.106452
$466$	−12.1004	−0.560541
$467$	−28.6668	−1.32654	−0.663271	−	0.748379i	$-0.730832\pi$
$467$	−28.6668	−1.32654	−0.663271	+	0.748379i	$0.730832\pi$
$468$	0	0
$469$	0.513495	0.0237110
$470$	−1.92174	−0.0886433
$471$	−1.04150	−0.0479898
$472$	−0.0677585	−0.00311884
$473$	−15.1267	−0.695526
$474$	2.71600	0.124750
$475$	−24.1692	−1.10896
$476$	2.70976	0.124202
$477$	−38.9953	−1.78547
$478$	5.57964	0.255207
$479$	−17.9762	−0.821356	−0.410678	−	0.911781i	$-0.634708\pi$
$479$	−17.9762	−0.821356	−0.410678	+	0.911781i	$0.634708\pi$
$480$	0.290242	0.0132477
$481$	0	0
$482$	−23.2430	−1.05869
$483$	−0.525985	−0.0239332
$484$	8.75670	0.398032
$485$	2.44120	0.110849
$486$	6.63469	0.300956
$487$	21.9216	0.993363	0.496681	−	0.867933i	$-0.334552\pi$
$487$	21.9216	0.993363	0.496681	+	0.867933i	$0.334552\pi$
$488$	8.10046	0.366691
$489$	2.83707	0.128297
$490$	1.14776	0.0518503
$491$	−21.6006	−0.974822	−0.487411	−	0.873173i	$-0.662059\pi$
$491$	−21.6006	−0.974822	−0.487411	+	0.873173i	$0.662059\pi$
$492$	2.40100	0.108246
$493$	19.5081	0.878599
$494$	0	0
$495$	−14.9786	−0.673237
$496$	−7.90895	−0.355122
$497$	10.7873	0.483877
$498$	−3.88115	−0.173919
$499$	38.6105	1.72844	0.864221	−	0.503112i	$-0.167812\pi$
$499$	38.6105	1.72844	0.864221	+	0.503112i	$0.167812\pi$
$500$	−9.96557	−0.445674
$501$	−1.01085	−0.0451615
$502$	−23.7414	−1.05963
$503$	−9.47007	−0.422249	−0.211125	−	0.977459i	$-0.567713\pi$
$503$	−9.47007	−0.422249	−0.211125	+	0.977459i	$0.567713\pi$
$504$	−2.93605	−0.130782
$505$	−6.90820	−0.307411
$506$	−9.24528	−0.411003
$507$	0	0
$508$	6.86494	0.304583
$509$	−13.0530	−0.578565	−0.289283	−	0.957244i	$-0.593417\pi$
$509$	−13.0530	−0.578565	−0.289283	+	0.957244i	$0.593417\pi$
$510$	0.786486	0.0348262
$511$	−8.02452	−0.354984
$512$	1.00000	0.0441942
$513$	−9.85167	−0.434962
$514$	7.01039	0.309215
$515$	−6.60728	−0.291152
$516$	−0.860593	−0.0378855
$517$	−7.44222	−0.327309
$518$	−9.64405	−0.423735
$519$	−3.07700	−0.135065
$520$	0	0
$521$	10.3444	0.453196	0.226598	−	0.973988i	$-0.427240\pi$
$521$	10.3444	0.453196	0.226598	+	0.973988i	$0.427240\pi$
$522$	−21.1372	−0.925151
$523$	−2.13368	−0.0932993	−0.0466497	−	0.998911i	$-0.514854\pi$
$523$	−2.13368	−0.0932993	−0.0466497	+	0.998911i	$0.514854\pi$
$524$	−16.1996	−0.707683
$525$	−0.931263	−0.0406437
$526$	30.8452	1.34491
$527$	−21.4313	−0.933564
$528$	1.12400	0.0489160
$529$	−18.6736	−0.811896
$530$	15.2440	0.662156
$531$	0.198942	0.00863336
$532$	6.56298	0.284541
$533$	0	0
$534$	2.74614	0.118837
$535$	−6.36932	−0.275370
$536$	0.513495	0.0221796
$537$	−3.00193	−0.129543
$538$	−5.63191	−0.242809
$539$	4.44485	0.191453
$540$	−1.72289	−0.0741415
$541$	8.41225	0.361671	0.180836	−	0.983513i	$-0.442120\pi$
$541$	8.41225	0.361671	0.180836	+	0.983513i	$0.442120\pi$
$542$	−3.00481	−0.129068
$543$	1.21162	0.0519958
$544$	2.70976	0.116180
$545$	−9.14745	−0.391834
$546$	0	0
$547$	−1.00730	−0.0430692	−0.0215346	−	0.999768i	$-0.506855\pi$
$547$	−1.00730	−0.0430692	−0.0215346	+	0.999768i	$0.506855\pi$
$548$	−5.20224	−0.222229
$549$	−23.7834	−1.01505
$550$	−16.3689	−0.697971
$551$	47.2482	2.01284
$552$	−0.525985	−0.0223874
$553$	10.7404	0.456727
$554$	−24.1732	−1.02702
$555$	−2.79911	−0.118816
$556$	5.74027	0.243442
$557$	43.7905	1.85546	0.927732	−	0.373247i	$-0.121756\pi$
$557$	43.7905	1.85546	0.927732	+	0.373247i	$0.121756\pi$
$558$	23.2211	0.983028
$559$	0	0
$560$	1.14776	0.0485015
$561$	3.04578	0.128593
$562$	1.74575	0.0736399
$563$	4.22667	0.178133	0.0890665	−	0.996026i	$-0.471612\pi$
$563$	4.22667	0.178133	0.0890665	+	0.996026i	$0.471612\pi$
$564$	−0.423405	−0.0178286
$565$	−5.01650	−0.211046
$566$	26.1143	1.09767
$567$	8.42856	0.353966
$568$	10.7873	0.452625
$569$	9.42639	0.395175	0.197587	−	0.980285i	$-0.436689\pi$
$569$	9.42639	0.395175	0.197587	+	0.980285i	$0.436689\pi$
$570$	1.90485	0.0797855
$571$	−25.5304	−1.06842	−0.534208	−	0.845353i	$-0.679390\pi$
$571$	−25.5304	−1.06842	−0.534208	+	0.845353i	$0.679390\pi$
$572$	0	0
$573$	3.94117	0.164645
$574$	9.49471	0.396301
$575$	7.65992	0.319441
$576$	−2.93605	−0.122336
$577$	31.7623	1.32228	0.661141	−	0.750262i	$-0.270073\pi$
$577$	31.7623	1.32228	0.661141	+	0.750262i	$0.270073\pi$
$578$	−9.65721	−0.401687
$579$	−4.44698	−0.184810
$580$	8.26291	0.343099
$581$	−15.3479	−0.636739
$582$	0.537855	0.0222948
$583$	59.0345	2.44496
$584$	−8.02452	−0.332057
$585$	0	0
$586$	5.65535	0.233620
$587$	34.3442	1.41754	0.708768	−	0.705441i	$-0.249251\pi$
$587$	34.3442	1.41754	0.708768	+	0.705441i	$0.249251\pi$
$588$	0.252878	0.0104285
$589$	−51.9063	−2.13876
$590$	−0.0777701	−0.00320175
$591$	0.133978	0.00551114
$592$	−9.64405	−0.396368
$593$	−15.1751	−0.623168	−0.311584	−	0.950219i	$-0.600860\pi$
$593$	−15.1751	−0.623168	−0.311584	+	0.950219i	$0.600860\pi$
$594$	−6.67215	−0.273762
$595$	3.11014	0.127503
$596$	3.02580	0.123941
$597$	6.35899	0.260256
$598$	0	0
$599$	7.48641	0.305886	0.152943	−	0.988235i	$-0.451125\pi$
$599$	7.48641	0.305886	0.152943	+	0.988235i	$0.451125\pi$
$600$	−0.931263	−0.0380187
$601$	36.4142	1.48537	0.742683	−	0.669643i	$-0.233553\pi$
$601$	36.4142	1.48537	0.742683	+	0.669643i	$0.233553\pi$
$602$	−3.40320	−0.138704
$603$	−1.50765	−0.0613962
$604$	−1.27030	−0.0516879
$605$	10.0505	0.408613
$606$	−1.52204	−0.0618288
$607$	4.52337	0.183598	0.0917989	−	0.995778i	$-0.470738\pi$
$607$	4.52337	0.183598	0.0917989	+	0.995778i	$0.470738\pi$
$608$	6.56298	0.266164
$609$	1.82052	0.0737711
$610$	9.29735	0.376439
$611$	0	0
$612$	−7.95599	−0.321602
$613$	40.2337	1.62502	0.812512	−	0.582945i	$-0.198100\pi$
$613$	40.2337	1.62502	0.812512	+	0.582945i	$0.198100\pi$
$614$	−20.4767	−0.826372
$615$	2.75576	0.111123
$616$	4.44485	0.179088
$617$	−39.5031	−1.59034	−0.795168	−	0.606390i	$-0.792617\pi$
$617$	−39.5031	−1.59034	−0.795168	+	0.606390i	$0.792617\pi$
$618$	−1.45574	−0.0585585
$619$	22.9229	0.921348	0.460674	−	0.887569i	$-0.347608\pi$
$619$	22.9229	0.921348	0.460674	+	0.887569i	$0.347608\pi$
$620$	−9.07754	−0.364563
$621$	3.12228	0.125293
$622$	−1.23712	−0.0496039
$623$	10.8596	0.435079
$624$	0	0
$625$	6.97525	0.279010
$626$	−9.01151	−0.360172
$627$	7.37682	0.294602
$628$	−4.11859	−0.164350
$629$	−26.1330	−1.04199
$630$	−3.36987	−0.134259
$631$	−3.60147	−0.143372	−0.0716862	−	0.997427i	$-0.522838\pi$
$631$	−3.60147	−0.143372	−0.0716862	+	0.997427i	$0.522838\pi$
$632$	10.7404	0.427229
$633$	1.37609	0.0546945
$634$	0.580644	0.0230603
$635$	7.87928	0.312680
$636$	3.35861	0.133178
$637$	0	0
$638$	31.9993	1.26687
$639$	−31.6721	−1.25293
$640$	1.14776	0.0453690
$641$	5.21856	0.206121	0.103060	−	0.994675i	$-0.467137\pi$
$641$	5.21856	0.206121	0.103060	+	0.994675i	$0.467137\pi$
$642$	−1.40331	−0.0553843
$643$	20.9008	0.824248	0.412124	−	0.911128i	$-0.364787\pi$
$643$	20.9008	0.824248	0.412124	+	0.911128i	$0.364787\pi$
$644$	−2.08000	−0.0819634
$645$	−0.987751	−0.0388927
$646$	17.7841	0.699706
$647$	−7.62110	−0.299617	−0.149808	−	0.988715i	$-0.547866\pi$
$647$	−7.62110	−0.299617	−0.149808	+	0.988715i	$0.547866\pi$
$648$	8.42856	0.331105
$649$	−0.301176	−0.0118222
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	11.2191	0.439376
$653$	−25.7819	−1.00892	−0.504462	−	0.863434i	$-0.668309\pi$
$653$	−25.7819	−1.00892	−0.504462	+	0.863434i	$0.668309\pi$
$654$	−2.01540	−0.0788084
$655$	−18.5932	−0.726495
$656$	9.49471	0.370706
$657$	23.5604	0.919179
$658$	−1.67435	−0.0652728
$659$	15.6593	0.609999	0.305000	−	0.952352i	$-0.401344\pi$
$659$	15.6593	0.609999	0.305000	+	0.952352i	$0.401344\pi$
$660$	1.29008	0.0502164
$661$	−31.6889	−1.23255	−0.616277	−	0.787529i	$-0.711360\pi$
$661$	−31.6889	−1.23255	−0.616277	+	0.787529i	$0.711360\pi$
$662$	−31.3654	−1.21905
$663$	0	0
$664$	−15.3479	−0.595615
$665$	7.53270	0.292105
$666$	28.3154	1.09720
$667$	−14.9743	−0.579807
$668$	−3.99739	−0.154664
$669$	−2.33798	−0.0903916
$670$	0.589367	0.0227692
$671$	36.0054	1.38997
$672$	0.252878	0.00975498
$673$	16.7728	0.646546	0.323273	−	0.946306i	$-0.395217\pi$
$673$	16.7728	0.646546	0.323273	+	0.946306i	$0.395217\pi$
$674$	−9.43033	−0.363243
$675$	5.52803	0.212774
$676$	0	0
$677$	−8.34791	−0.320836	−0.160418	−	0.987049i	$-0.551284\pi$
$677$	−8.34791	−0.320836	−0.160418	+	0.987049i	$0.551284\pi$
$678$	−1.10525	−0.0424470
$679$	2.12694	0.0816243
$680$	3.11014	0.119268
$681$	−0.380525	−0.0145818
$682$	−35.1541	−1.34612
$683$	27.1789	1.03997	0.519986	−	0.854175i	$-0.325937\pi$
$683$	27.1789	1.03997	0.519986	+	0.854175i	$0.325937\pi$
$684$	−19.2693	−0.736778
$685$	−5.97090	−0.228136
$686$	1.00000	0.0381802
$687$	−6.43271	−0.245423
$688$	−3.40320	−0.129746
$689$	0	0
$690$	−0.603703	−0.0229826
$691$	−26.2582	−0.998909	−0.499454	−	0.866340i	$-0.666466\pi$
$691$	−26.2582	−0.998909	−0.499454	+	0.866340i	$0.666466\pi$
$692$	−12.1679	−0.462555
$693$	−13.0503	−0.495741
$694$	6.47300	0.245712
$695$	6.58842	0.249913
$696$	1.82052	0.0690066
$697$	25.7284	0.974531
$698$	9.90515	0.374916
$699$	−3.05993	−0.115737
$700$	−3.68266	−0.139191
$701$	26.4443	0.998786	0.499393	−	0.866376i	$-0.333556\pi$
$701$	26.4443	0.998786	0.499393	+	0.866376i	$0.333556\pi$
$702$	0	0
$703$	−63.2937	−2.38717
$704$	4.44485	0.167522
$705$	−0.485966	−0.0183025
$706$	−28.7758	−1.08299
$707$	−6.01888	−0.226363
$708$	−0.0171346	−0.000643959 0
$709$	−11.6264	−0.436640	−0.218320	−	0.975877i	$-0.570058\pi$
$709$	−11.6264	−0.436640	−0.218320	+	0.975877i	$0.570058\pi$
$710$	12.3812	0.464658
$711$	−31.5343	−1.18263
$712$	10.8596	0.406979
$713$	16.4506	0.616080
$714$	0.685238	0.0256444
$715$	0	0
$716$	−11.8711	−0.443643
$717$	1.41097	0.0526935
$718$	12.1382	0.452994
$719$	−44.8758	−1.67359	−0.836793	−	0.547519i	$-0.815572\pi$
$719$	−44.8758	−1.67359	−0.836793	+	0.547519i	$0.815572\pi$
$720$	−3.36987	−0.125588
$721$	−5.75670	−0.214391
$722$	24.0727	0.895894
$723$	−5.87765	−0.218592
$724$	4.79134	0.178069
$725$	−26.5122	−0.984637
$726$	2.21438	0.0821832
$727$	−19.5156	−0.723793	−0.361896	−	0.932218i	$-0.617871\pi$
$727$	−19.5156	−0.723793	−0.361896	+	0.932218i	$0.617871\pi$
$728$	0	0
$729$	−23.6079	−0.874368
$730$	−9.21019	−0.340884
$731$	−9.22184	−0.341082
$732$	2.04843	0.0757121
$733$	10.7037	0.395349	0.197675	−	0.980268i	$-0.436661\pi$
$733$	10.7037	0.395349	0.197675	+	0.980268i	$0.436661\pi$
$734$	−27.0775	−0.999449
$735$	0.290242	0.0107057
$736$	−2.08000	−0.0766697
$737$	2.28241	0.0840736
$738$	−27.8770	−1.02616
$739$	0.477606	0.0175690	0.00878452	−	0.999961i	$-0.497204\pi$
$739$	0.477606	0.0175690	0.00878452	+	0.999961i	$0.497204\pi$
$740$	−11.0690	−0.406905
$741$	0	0
$742$	13.2815	0.487581
$743$	−9.73434	−0.357118	−0.178559	−	0.983929i	$-0.557144\pi$
$743$	−9.73434	−0.357118	−0.178559	+	0.983929i	$0.557144\pi$
$744$	−2.00000	−0.0733236
$745$	3.47287	0.127236
$746$	−15.6332	−0.572373
$747$	45.0623	1.64874
$748$	12.0445	0.440389
$749$	−5.54937	−0.202769
$750$	−2.52007	−0.0920200
$751$	36.2167	1.32157	0.660784	−	0.750576i	$-0.270224\pi$
$751$	36.2167	1.32157	0.660784	+	0.750576i	$0.270224\pi$
$752$	−1.67435	−0.0610571
$753$	−6.00369	−0.218787
$754$	0	0
$755$	−1.45800	−0.0530619
$756$	−1.50110	−0.0545944
$757$	46.4694	1.68896	0.844479	−	0.535589i	$-0.179910\pi$
$757$	46.4694	1.68896	0.844479	+	0.535589i	$0.179910\pi$
$758$	37.3308	1.35592
$759$	−2.33793	−0.0848614
$760$	7.53270	0.273240
$761$	−21.3663	−0.774527	−0.387263	−	0.921969i	$-0.626580\pi$
$761$	−21.3663	−0.774527	−0.387263	+	0.921969i	$0.626580\pi$
$762$	1.73599	0.0628884
$763$	−7.96986	−0.288528
$764$	15.5853	0.563855
$765$	−9.13153	−0.330151
$766$	−37.8964	−1.36925
$767$	0	0
$768$	0.252878	0.00912495
$769$	45.9914	1.65849	0.829246	−	0.558884i	$-0.188770\pi$
$769$	45.9914	1.65849	0.829246	+	0.558884i	$0.188770\pi$
$770$	5.10160	0.183849
$771$	1.77277	0.0638449
$772$	−17.5855	−0.632916
$773$	19.9479	0.717475	0.358737	−	0.933439i	$-0.383207\pi$
$773$	19.9479	0.717475	0.358737	+	0.933439i	$0.383207\pi$
$774$	9.99196	0.359154
$775$	29.1260	1.04624
$776$	2.12694	0.0763526
$777$	−2.43877	−0.0874903
$778$	10.1053	0.362294
$779$	62.3136	2.23262
$780$	0	0
$781$	47.9479	1.71571
$782$	−5.63629	−0.201553
$783$	−10.8067	−0.386200
$784$	1.00000	0.0357143
$785$	−4.72714	−0.168719
$786$	−4.09652	−0.146118
$787$	−43.9625	−1.56709	−0.783546	−	0.621334i	$-0.786591\pi$
$787$	−43.9625	−1.56709	−0.783546	+	0.621334i	$0.786591\pi$
$788$	0.529815	0.0188739
$789$	7.80007	0.277690
$790$	12.3273	0.438586
$791$	−4.37070	−0.155404
$792$	−13.0503	−0.463723
$793$	0	0
$794$	−5.50839	−0.195485
$795$	3.85486	0.136718
$796$	25.1465	0.891294
$797$	31.9724	1.13252	0.566260	−	0.824226i	$-0.308390\pi$
$797$	31.9724	1.13252	0.566260	+	0.824226i	$0.308390\pi$
$798$	1.65963	0.0587504
$799$	−4.53707	−0.160510
$800$	−3.68266	−0.130202
$801$	−31.8842	−1.12657
$802$	−26.7495	−0.944557
$803$	−35.6678	−1.25869
$804$	0.129852	0.00457951
$805$	−2.38733	−0.0841423
$806$	0	0
$807$	−1.42419	−0.0501337
$808$	−6.01888	−0.211744
$809$	−28.1731	−0.990514	−0.495257	−	0.868746i	$-0.664926\pi$
$809$	−28.1731	−0.990514	−0.495257	+	0.868746i	$0.664926\pi$
$810$	9.67393	0.339907
$811$	−39.0534	−1.37135	−0.685675	−	0.727908i	$-0.740493\pi$
$811$	−39.0534	−1.37135	−0.685675	+	0.727908i	$0.740493\pi$
$812$	7.19919	0.252642
$813$	−0.759850	−0.0266491
$814$	−42.8663	−1.50246
$815$	12.8768	0.451056
$816$	0.685238	0.0239881
$817$	−22.3351	−0.781407
$818$	−31.9995	−1.11884
$819$	0	0
$820$	10.8976	0.380561
$821$	−23.5839	−0.823084	−0.411542	−	0.911391i	$-0.635010\pi$
$821$	−23.5839	−0.823084	−0.411542	+	0.911391i	$0.635010\pi$
$822$	−1.31553	−0.0458844
$823$	24.7133	0.861450	0.430725	−	0.902483i	$-0.358258\pi$
$823$	24.7133	0.861450	0.430725	+	0.902483i	$0.358258\pi$
$824$	−5.75670	−0.200544
$825$	−4.13933	−0.144113
$826$	−0.0677585	−0.00235762
$827$	45.2456	1.57334	0.786672	−	0.617371i	$-0.211802\pi$
$827$	45.2456	1.57334	0.786672	+	0.617371i	$0.211802\pi$
$828$	6.10698	0.212232
$829$	44.8129	1.55642	0.778208	−	0.628006i	$-0.216129\pi$
$829$	44.8129	1.55642	0.778208	+	0.628006i	$0.216129\pi$
$830$	−17.6157	−0.611449
$831$	−6.11287	−0.212053
$832$	0	0
$833$	2.70976	0.0938875
$834$	1.45159	0.0502644
$835$	−4.58802	−0.158775
$836$	29.1715	1.00892
$837$	11.8721	0.410360
$838$	11.6956	0.404019
$839$	30.8895	1.06642	0.533212	−	0.845982i	$-0.320985\pi$
$839$	30.8895	1.06642	0.533212	+	0.845982i	$0.320985\pi$
$840$	0.290242	0.0100143
$841$	22.8284	0.787186
$842$	−25.8565	−0.891073
$843$	0.441461	0.0152047
$844$	5.44170	0.187311
$845$	0	0
$846$	4.91597	0.169015
$847$	8.75670	0.300884
$848$	13.2815	0.456090
$849$	6.60373	0.226640
$850$	−9.97911	−0.342281
$851$	20.0596	0.687634
$852$	2.72787	0.0934553
$853$	−27.9201	−0.955965	−0.477982	−	0.878369i	$-0.658632\pi$
$853$	−27.9201	−0.955965	−0.477982	+	0.878369i	$0.658632\pi$
$854$	8.10046	0.277192
$855$	−22.1164	−0.756365
$856$	−5.54937	−0.189673
$857$	17.5921	0.600935	0.300468	−	0.953792i	$-0.402857\pi$
$857$	17.5921	0.600935	0.300468	+	0.953792i	$0.402857\pi$
$858$	0	0
$859$	22.1337	0.755193	0.377596	−	0.925970i	$-0.376751\pi$
$859$	22.1337	0.755193	0.377596	+	0.925970i	$0.376751\pi$
$860$	−3.90604	−0.133195
$861$	2.40100	0.0818259
$862$	−10.7062	−0.364655
$863$	4.58867	0.156200	0.0781000	−	0.996946i	$-0.475115\pi$
$863$	4.58867	0.156200	0.0781000	+	0.996946i	$0.475115\pi$
$864$	−1.50110	−0.0510684
$865$	−13.9658	−0.474851
$866$	22.4299	0.762199
$867$	−2.44210	−0.0829379
$868$	−7.90895	−0.268447
$869$	47.7393	1.61944
$870$	2.08951	0.0708410
$871$	0	0
$872$	−7.96986	−0.269893
$873$	−6.24480	−0.211354
$874$	−13.6510	−0.461751
$875$	−9.96557	−0.336898
$876$	−2.02922	−0.0685611
$877$	−39.9812	−1.35007	−0.675035	−	0.737786i	$-0.735872\pi$
$877$	−39.9812	−1.35007	−0.675035	+	0.737786i	$0.735872\pi$
$878$	−12.7183	−0.429220
$879$	1.43011	0.0482365
$880$	5.10160	0.171975
$881$	−47.9096	−1.61412	−0.807058	−	0.590472i	$-0.798942\pi$
$881$	−47.9096	−1.61412	−0.807058	+	0.590472i	$0.798942\pi$
$882$	−2.93605	−0.0988620
$883$	−34.0091	−1.14450	−0.572248	−	0.820080i	$-0.693929\pi$
$883$	−34.0091	−1.14450	−0.572248	+	0.820080i	$0.693929\pi$
$884$	0	0
$885$	−0.0196664	−0.000661077 0
$886$	−7.86448	−0.264212
$887$	3.77343	0.126699	0.0633497	−	0.997991i	$-0.479822\pi$
$887$	3.77343	0.126699	0.0633497	+	0.997991i	$0.479822\pi$
$888$	−2.43877	−0.0818397
$889$	6.86494	0.230243
$890$	12.4641	0.417798
$891$	37.4637	1.25508
$892$	−9.24550	−0.309562
$893$	−10.9887	−0.367723
$894$	0.765157	0.0255907
$895$	−13.6251	−0.455436
$896$	1.00000	0.0334077
$897$	0	0
$898$	16.8373	0.561867
$899$	−56.9381	−1.89899
$900$	10.8125	0.360416
$901$	35.9898	1.19899
$902$	42.2025	1.40519
$903$	−0.860593	−0.0286388
$904$	−4.37070	−0.145367
$905$	5.49929	0.182802
$906$	−0.321232	−0.0106722
$907$	14.2751	0.473996	0.236998	−	0.971510i	$-0.423837\pi$
$907$	14.2751	0.473996	0.236998	+	0.971510i	$0.423837\pi$
$908$	−1.50478	−0.0499378
$909$	17.6718	0.586135
$910$	0	0
$911$	17.4161	0.577020	0.288510	−	0.957477i	$-0.406840\pi$
$911$	17.4161	0.577020	0.288510	+	0.957477i	$0.406840\pi$
$912$	1.65963	0.0549560
$913$	−68.2192	−2.25773
$914$	−9.19764	−0.304231
$915$	2.35110	0.0777248
$916$	−25.4380	−0.840496
$917$	−16.1996	−0.534958
$918$	−4.06761	−0.134251
$919$	36.2358	1.19531	0.597654	−	0.801754i	$-0.296100\pi$
$919$	36.2358	1.19531	0.597654	+	0.801754i	$0.296100\pi$
$920$	−2.38733	−0.0787079
$921$	−5.17810	−0.170624
$922$	−21.8021	−0.718013
$923$	0	0
$924$	1.12400	0.0369770
$925$	35.5157	1.16775
$926$	26.0636	0.856502
$927$	16.9020	0.555133
$928$	7.19919	0.236325
$929$	−14.3940	−0.472253	−0.236126	−	0.971722i	$-0.575878\pi$
$929$	−14.3940	−0.472253	−0.236126	+	0.971722i	$0.575878\pi$
$930$	−2.29551	−0.0752728
$931$	6.56298	0.215093
$932$	−12.1004	−0.396362
$933$	−0.312840	−0.0102419
$934$	−28.6668	−0.938007
$935$	13.8241	0.452097
$936$	0	0
$937$	−6.25633	−0.204385	−0.102193	−	0.994765i	$-0.532586\pi$
$937$	−6.25633	−0.204385	−0.102193	+	0.994765i	$0.532586\pi$
$938$	0.513495	0.0167662
$939$	−2.27881	−0.0743663
$940$	−1.92174	−0.0626803
$941$	29.1506	0.950284	0.475142	−	0.879909i	$-0.342397\pi$
$941$	29.1506	0.950284	0.475142	+	0.879909i	$0.342397\pi$
$942$	−1.04150	−0.0339339
$943$	−19.7490	−0.643115
$944$	−0.0677585	−0.00220535
$945$	−1.72289	−0.0560457
$946$	−15.1267	−0.491811
$947$	−10.8994	−0.354183	−0.177091	−	0.984194i	$-0.556669\pi$
$947$	−10.8994	−0.354183	−0.177091	+	0.984194i	$0.556669\pi$
$948$	2.71600	0.0882116
$949$	0	0
$950$	−24.1692	−0.784153
$951$	0.146832	0.00476135
$952$	2.70976	0.0878238
$953$	27.5305	0.891799	0.445900	−	0.895083i	$-0.352884\pi$
$953$	27.5305	0.891799	0.445900	+	0.895083i	$0.352884\pi$
$954$	−38.9953	−1.26252
$955$	17.8881	0.578844
$956$	5.57964	0.180458
$957$	8.09193	0.261575
$958$	−17.9762	−0.580786
$959$	−5.20224	−0.167989
$960$	0.290242	0.00936752
$961$	31.5515	1.01779
$962$	0	0
$963$	16.2932	0.525042
$964$	−23.2430	−0.748608
$965$	−20.1838	−0.649741
$966$	−0.525985	−0.0169233
$967$	21.0297	0.676271	0.338135	−	0.941097i	$-0.390204\pi$
$967$	21.0297	0.676271	0.338135	+	0.941097i	$0.390204\pi$
$968$	8.75670	0.281451
$969$	4.49720	0.144471
$970$	2.44120	0.0783823
$971$	4.36820	0.140182	0.0700911	−	0.997541i	$-0.477671\pi$
$971$	4.36820	0.140182	0.0700911	+	0.997541i	$0.477671\pi$
$972$	6.63469	0.212808
$973$	5.74027	0.184025
$974$	21.9216	0.702414
$975$	0	0
$976$	8.10046	0.259290
$977$	54.1358	1.73196	0.865978	−	0.500082i	$-0.166697\pi$
$977$	54.1358	1.73196	0.865978	+	0.500082i	$0.166697\pi$
$978$	2.83707	0.0907196
$979$	48.2691	1.54269
$980$	1.14776	0.0366637
$981$	23.3999	0.747102
$982$	−21.6006	−0.689303
$983$	−44.3574	−1.41478	−0.707391	−	0.706823i	$-0.750128\pi$
$983$	−44.3574	−1.41478	−0.707391	+	0.706823i	$0.750128\pi$
$984$	2.40100	0.0765411
$985$	0.608097	0.0193756
$986$	19.5081	0.621264
$987$	−0.423405	−0.0134771
$988$	0	0
$989$	7.07864	0.225088
$990$	−14.9786	−0.476050
$991$	27.3873	0.869985	0.434992	−	0.900434i	$-0.356751\pi$
$991$	27.3873	0.869985	0.434992	+	0.900434i	$0.356751\pi$
$992$	−7.90895	−0.251109
$993$	−7.93162	−0.251702
$994$	10.7873	0.342152
$995$	28.8620	0.914988
$996$	−3.88115	−0.122979
$997$	−45.8033	−1.45061	−0.725303	−	0.688430i	$-0.758300\pi$
$997$	−45.8033	−1.45061	−0.725303	+	0.688430i	$0.758300\pi$
$998$	38.6105	1.22219
$999$	14.4766	0.458021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bh.1.4		6
13.5	odd	4		2366.2.d.r.337.4		12
13.6	odd	12		182.2.m.b.127.2	yes	12
13.8	odd	4		2366.2.d.r.337.10		12
13.11	odd	12		182.2.m.b.43.2	✓	12
13.12	even	2		2366.2.a.bf.1.4		6
39.11	even	12		1638.2.bj.g.1135.5		12
39.32	even	12		1638.2.bj.g.127.5		12
52.11	even	12		1456.2.cc.d.225.4		12
52.19	even	12		1456.2.cc.d.673.4		12
91.6	even	12		1274.2.m.c.491.2		12
91.11	odd	12		1274.2.v.e.667.5		12
91.19	even	12		1274.2.v.d.361.5		12
91.24	even	12		1274.2.v.d.667.5		12
91.32	odd	12		1274.2.o.d.569.2		12
91.37	odd	12		1274.2.o.d.459.5		12
91.45	even	12		1274.2.o.e.569.2		12
91.58	odd	12		1274.2.v.e.361.5		12
91.76	even	12		1274.2.m.c.589.2		12
91.89	even	12		1274.2.o.e.459.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.2	✓	12	13.11	odd	12
182.2.m.b.127.2	yes	12	13.6	odd	12
1274.2.m.c.491.2		12	91.6	even	12
1274.2.m.c.589.2		12	91.76	even	12
1274.2.o.d.459.5		12	91.37	odd	12
1274.2.o.d.569.2		12	91.32	odd	12
1274.2.o.e.459.5		12	91.89	even	12
1274.2.o.e.569.2		12	91.45	even	12
1274.2.v.d.361.5		12	91.19	even	12
1274.2.v.d.667.5		12	91.24	even	12
1274.2.v.e.361.5		12	91.58	odd	12
1274.2.v.e.667.5		12	91.11	odd	12
1456.2.cc.d.225.4		12	52.11	even	12
1456.2.cc.d.673.4		12	52.19	even	12
1638.2.bj.g.127.5		12	39.32	even	12
1638.2.bj.g.1135.5		12	39.11	even	12
2366.2.a.bf.1.4		6	13.12	even	2
2366.2.a.bh.1.4		6	1.1	even	1	trivial
2366.2.d.r.337.4		12	13.5	odd	4
2366.2.d.r.337.10		12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.252878 q^{3} +1.00000 q^{4} +1.14776 q^{5} +0.252878 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.93605 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.252878 q^{3} +1.00000 q^{4} +1.14776 q^{5} +0.252878 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.93605 q^{9} +1.14776 q^{10} +4.44485 q^{11} +0.252878 q^{12} +1.00000 q^{14} +0.290242 q^{15} +1.00000 q^{16} +2.70976 q^{17} -2.93605 q^{18} +6.56298 q^{19} +1.14776 q^{20} +0.252878 q^{21} +4.44485 q^{22} -2.08000 q^{23} +0.252878 q^{24} -3.68266 q^{25} -1.50110 q^{27} +1.00000 q^{28} +7.19919 q^{29} +0.290242 q^{30} -7.90895 q^{31} +1.00000 q^{32} +1.12400 q^{33} +2.70976 q^{34} +1.14776 q^{35} -2.93605 q^{36} -9.64405 q^{37} +6.56298 q^{38} +1.14776 q^{40} +9.49471 q^{41} +0.252878 q^{42} -3.40320 q^{43} +4.44485 q^{44} -3.36987 q^{45} -2.08000 q^{46} -1.67435 q^{47} +0.252878 q^{48} +1.00000 q^{49} -3.68266 q^{50} +0.685238 q^{51} +13.2815 q^{53} -1.50110 q^{54} +5.10160 q^{55} +1.00000 q^{56} +1.65963 q^{57} +7.19919 q^{58} -0.0677585 q^{59} +0.290242 q^{60} +8.10046 q^{61} -7.90895 q^{62} -2.93605 q^{63} +1.00000 q^{64} +1.12400 q^{66} +0.513495 q^{67} +2.70976 q^{68} -0.525985 q^{69} +1.14776 q^{70} +10.7873 q^{71} -2.93605 q^{72} -8.02452 q^{73} -9.64405 q^{74} -0.931263 q^{75} +6.56298 q^{76} +4.44485 q^{77} +10.7404 q^{79} +1.14776 q^{80} +8.42856 q^{81} +9.49471 q^{82} -15.3479 q^{83} +0.252878 q^{84} +3.11014 q^{85} -3.40320 q^{86} +1.82052 q^{87} +4.44485 q^{88} +10.8596 q^{89} -3.36987 q^{90} -2.08000 q^{92} -2.00000 q^{93} -1.67435 q^{94} +7.53270 q^{95} +0.252878 q^{96} +2.12694 q^{97} +1.00000 q^{98} -13.0503 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 6 q^{14} + 14 q^{15} + 6 q^{16} + 4 q^{17} + 6 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 2 q^{22} - 6 q^{23} + 2 q^{24} + 12 q^{25} + 20 q^{27} + 6 q^{28} + 10 q^{29} + 14 q^{30} - 2 q^{31} + 6 q^{32} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{38} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 26 q^{43} + 2 q^{44} - 6 q^{45} - 6 q^{46} - 8 q^{47} + 2 q^{48} + 6 q^{49} + 12 q^{50} + 18 q^{51} + 18 q^{53} + 20 q^{54} + 6 q^{55} + 6 q^{56} - 28 q^{57} + 10 q^{58} + 2 q^{59} + 14 q^{60} + 28 q^{61} - 2 q^{62} + 6 q^{63} + 6 q^{64} + 6 q^{67} + 4 q^{68} + 32 q^{69} - 2 q^{70} + 4 q^{71} + 6 q^{72} - 22 q^{73} - 48 q^{75} - 4 q^{76} + 2 q^{77} + 22 q^{79} - 2 q^{80} + 34 q^{81} + 6 q^{82} - 10 q^{83} + 2 q^{84} + 32 q^{85} + 26 q^{86} - 2 q^{87} + 2 q^{88} - 4 q^{89} - 6 q^{90} - 6 q^{92} - 12 q^{93} - 8 q^{94} + 32 q^{95} + 2 q^{96} - 12 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 6 * q^14 + 14 * q^15 + 6 * q^16 + 4 * q^17 + 6 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 12 * q^25 + 20 * q^27 + 6 * q^28 + 10 * q^29 + 14 * q^30 - 2 * q^31 + 6 * q^32 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^38 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 26 * q^43 + 2 * q^44 - 6 * q^45 - 6 * q^46 - 8 * q^47 + 2 * q^48 + 6 * q^49 + 12 * q^50 + 18 * q^51 + 18 * q^53 + 20 * q^54 + 6 * q^55 + 6 * q^56 - 28 * q^57 + 10 * q^58 + 2 * q^59 + 14 * q^60 + 28 * q^61 - 2 * q^62 + 6 * q^63 + 6 * q^64 + 6 * q^67 + 4 * q^68 + 32 * q^69 - 2 * q^70 + 4 * q^71 + 6 * q^72 - 22 * q^73 - 48 * q^75 - 4 * q^76 + 2 * q^77 + 22 * q^79 - 2 * q^80 + 34 * q^81 + 6 * q^82 - 10 * q^83 + 2 * q^84 + 32 * q^85 + 26 * q^86 - 2 * q^87 + 2 * q^88 - 4 * q^89 - 6 * q^90 - 6 * q^92 - 12 * q^93 - 8 * q^94 + 32 * q^95 + 2 * q^96 - 12 * q^97 + 6 * q^98 - 2 * q^99

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