LMFDB - Embedded newform 5610.2.a.ce.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.679643$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.94272 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.94272 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +1.77585 q^{13} +2.94272 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.94272 q^{19} +1.00000 q^{20} +2.94272 q^{21} +1.00000 q^{22} +4.10959 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.77585 q^{26} -1.00000 q^{27} -2.94272 q^{28} +1.43377 q^{29} +1.00000 q^{30} -8.09337 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -2.94272 q^{35} +1.00000 q^{36} +11.7119 q^{37} +4.94272 q^{38} -1.77585 q^{39} -1.00000 q^{40} +5.88544 q^{41} -2.94272 q^{42} -1.00169 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.10959 q^{46} -9.31921 q^{47} -1.00000 q^{48} +1.65960 q^{49} -1.00000 q^{50} -1.00000 q^{51} +1.77585 q^{52} +1.44998 q^{53} +1.00000 q^{54} -1.00000 q^{55} +2.94272 q^{56} +4.94272 q^{57} -1.43377 q^{58} +2.76919 q^{59} -1.00000 q^{60} +2.65960 q^{61} +8.09337 q^{62} -2.94272 q^{63} +1.00000 q^{64} +1.77585 q^{65} -1.00000 q^{66} +12.5450 q^{67} +1.00000 q^{68} -4.10959 q^{69} +2.94272 q^{70} -8.88375 q^{71} -1.00000 q^{72} -10.6546 q^{73} -11.7119 q^{74} -1.00000 q^{75} -4.94272 q^{76} +2.94272 q^{77} +1.77585 q^{78} -0.998311 q^{79} +1.00000 q^{80} +1.00000 q^{81} -5.88544 q^{82} -3.60729 q^{83} +2.94272 q^{84} +1.00000 q^{85} +1.00169 q^{86} -1.43377 q^{87} +1.00000 q^{88} -8.33374 q^{89} -1.00000 q^{90} -5.22584 q^{91} +4.10959 q^{92} +8.09337 q^{93} +9.31921 q^{94} -4.94272 q^{95} +1.00000 q^{96} +11.1113 q^{97} -1.65960 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 9 q^{19} + 4 q^{20} + q^{21} + 4 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} - 4 q^{27} - q^{28} - 8 q^{29} + 4 q^{30} - q^{31} - 4 q^{32} + 4 q^{33} - 4 q^{34} - q^{35} + 4 q^{36} + q^{37} + 9 q^{38} - 3 q^{39} - 4 q^{40} + 2 q^{41} - q^{42} + 4 q^{43} - 4 q^{44} + 4 q^{45} + q^{46} - 2 q^{47} - 4 q^{48} - 11 q^{49} - 4 q^{50} - 4 q^{51} + 3 q^{52} + 6 q^{53} + 4 q^{54} - 4 q^{55} + q^{56} + 9 q^{57} + 8 q^{58} - 24 q^{59} - 4 q^{60} - 7 q^{61} + q^{62} - q^{63} + 4 q^{64} + 3 q^{65} - 4 q^{66} + 11 q^{67} + 4 q^{68} + q^{69} + q^{70} - 22 q^{71} - 4 q^{72} + 14 q^{73} - q^{74} - 4 q^{75} - 9 q^{76} + q^{77} + 3 q^{78} - 12 q^{79} + 4 q^{80} + 4 q^{81} - 2 q^{82} - 25 q^{83} + q^{84} + 4 q^{85} - 4 q^{86} + 8 q^{87} + 4 q^{88} - 20 q^{89} - 4 q^{90} - 17 q^{91} - q^{92} + q^{93} + 2 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 9 * q^19 + 4 * q^20 + q^21 + 4 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 - 4 * q^27 - q^28 - 8 * q^29 + 4 * q^30 - q^31 - 4 * q^32 + 4 * q^33 - 4 * q^34 - q^35 + 4 * q^36 + q^37 + 9 * q^38 - 3 * q^39 - 4 * q^40 + 2 * q^41 - q^42 + 4 * q^43 - 4 * q^44 + 4 * q^45 + q^46 - 2 * q^47 - 4 * q^48 - 11 * q^49 - 4 * q^50 - 4 * q^51 + 3 * q^52 + 6 * q^53 + 4 * q^54 - 4 * q^55 + q^56 + 9 * q^57 + 8 * q^58 - 24 * q^59 - 4 * q^60 - 7 * q^61 + q^62 - q^63 + 4 * q^64 + 3 * q^65 - 4 * q^66 + 11 * q^67 + 4 * q^68 + q^69 + q^70 - 22 * q^71 - 4 * q^72 + 14 * q^73 - q^74 - 4 * q^75 - 9 * q^76 + q^77 + 3 * q^78 - 12 * q^79 + 4 * q^80 + 4 * q^81 - 2 * q^82 - 25 * q^83 + q^84 + 4 * q^85 - 4 * q^86 + 8 * q^87 + 4 * q^88 - 20 * q^89 - 4 * q^90 - 17 * q^91 - q^92 + q^93 + 2 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 11 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−2.94272	−1.11224	−0.556122	−	0.831101i	$-0.687711\pi$
$7$	−2.94272	−1.11224	−0.556122	+	0.831101i	$0.687711\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	1.77585	0.492533	0.246266	−	0.969202i	$-0.420796\pi$
$13$	1.77585	0.492533	0.246266	+	0.969202i	$0.420796\pi$
$14$	2.94272	0.786475
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−4.94272	−1.13394	−0.566969	−	0.823739i	$-0.691884\pi$
$19$	−4.94272	−1.13394	−0.566969	+	0.823739i	$0.691884\pi$
$20$	1.00000	0.223607
$21$	2.94272	0.642154
$22$	1.00000	0.213201
$23$	4.10959	0.856909	0.428454	−	0.903563i	$-0.359058\pi$
$23$	4.10959	0.856909	0.428454	+	0.903563i	$0.359058\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−1.77585	−0.348273
$27$	−1.00000	−0.192450
$28$	−2.94272	−0.556122
$29$	1.43377	0.266244	0.133122	−	0.991100i	$-0.457500\pi$
$29$	1.43377	0.266244	0.133122	+	0.991100i	$0.457500\pi$
$30$	1.00000	0.182574
$31$	−8.09337	−1.45361	−0.726806	−	0.686842i	$-0.758996\pi$
$31$	−8.09337	−1.45361	−0.726806	+	0.686842i	$0.758996\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	−2.94272	−0.497411
$36$	1.00000	0.166667
$37$	11.7119	1.92543	0.962713	−	0.270523i	$-0.0871967\pi$
$37$	11.7119	1.92543	0.962713	+	0.270523i	$0.0871967\pi$
$38$	4.94272	0.801815
$39$	−1.77585	−0.284364
$40$	−1.00000	−0.158114
$41$	5.88544	0.919151	0.459576	−	0.888139i	$-0.348001\pi$
$41$	5.88544	0.919151	0.459576	+	0.888139i	$0.348001\pi$
$42$	−2.94272	−0.454072
$43$	−1.00169	−0.152756	−0.0763781	−	0.997079i	$-0.524336\pi$
$43$	−1.00169	−0.152756	−0.0763781	+	0.997079i	$0.524336\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−4.10959	−0.605926
$47$	−9.31921	−1.35935	−0.679673	−	0.733515i	$-0.737878\pi$
$47$	−9.31921	−1.35935	−0.679673	+	0.733515i	$0.737878\pi$
$48$	−1.00000	−0.144338
$49$	1.65960	0.237086
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	1.77585	0.246266
$53$	1.44998	0.199171	0.0995853	−	0.995029i	$-0.468248\pi$
$53$	1.44998	0.199171	0.0995853	+	0.995029i	$0.468248\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	2.94272	0.393238
$57$	4.94272	0.654679
$58$	−1.43377	−0.188263
$59$	2.76919	0.360518	0.180259	−	0.983619i	$-0.442306\pi$
$59$	2.76919	0.360518	0.180259	+	0.983619i	$0.442306\pi$
$60$	−1.00000	−0.129099
$61$	2.65960	0.340527	0.170264	−	0.985399i	$-0.445538\pi$
$61$	2.65960	0.340527	0.170264	+	0.985399i	$0.445538\pi$
$62$	8.09337	1.02786
$63$	−2.94272	−0.370748
$64$	1.00000	0.125000
$65$	1.77585	0.220267
$66$	−1.00000	−0.123091
$67$	12.5450	1.53262	0.766311	−	0.642470i	$-0.222090\pi$
$67$	12.5450	1.53262	0.766311	+	0.642470i	$0.222090\pi$
$68$	1.00000	0.121268
$69$	−4.10959	−0.494736
$70$	2.94272	0.351722
$71$	−8.88375	−1.05431	−0.527154	−	0.849770i	$-0.676741\pi$
$71$	−8.88375	−1.05431	−0.527154	+	0.849770i	$0.676741\pi$
$72$	−1.00000	−0.117851
$73$	−10.6546	−1.24703	−0.623515	−	0.781811i	$-0.714296\pi$
$73$	−10.6546	−1.24703	−0.623515	+	0.781811i	$0.714296\pi$
$74$	−11.7119	−1.36148
$75$	−1.00000	−0.115470
$76$	−4.94272	−0.566969
$77$	2.94272	0.335354
$78$	1.77585	0.201076
$79$	−0.998311	−0.112319	−0.0561594	−	0.998422i	$-0.517885\pi$
$79$	−0.998311	−0.112319	−0.0561594	+	0.998422i	$0.517885\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−5.88544	−0.649938
$83$	−3.60729	−0.395952	−0.197976	−	0.980207i	$-0.563437\pi$
$83$	−3.60729	−0.395952	−0.197976	+	0.980207i	$0.563437\pi$
$84$	2.94272	0.321077
$85$	1.00000	0.108465
$86$	1.00169	0.108015
$87$	−1.43377	−0.153716
$88$	1.00000	0.106600
$89$	−8.33374	−0.883374	−0.441687	−	0.897169i	$-0.645620\pi$
$89$	−8.33374	−0.883374	−0.441687	+	0.897169i	$0.645620\pi$
$90$	−1.00000	−0.105409
$91$	−5.22584	−0.547817
$92$	4.10959	0.428454
$93$	8.09337	0.839244
$94$	9.31921	0.961203
$95$	−4.94272	−0.507112
$96$	1.00000	0.102062
$97$	11.1113	1.12818	0.564090	−	0.825714i	$-0.309227\pi$
$97$	11.1113	1.12818	0.564090	+	0.825714i	$0.309227\pi$
$98$	−1.65960	−0.167645
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	19.4238	1.93274	0.966372	−	0.257150i	$-0.0827834\pi$
$101$	19.4238	1.93274	0.966372	+	0.257150i	$0.0827834\pi$
$102$	1.00000	0.0990148
$103$	5.94103	0.585387	0.292694	−	0.956206i	$-0.405448\pi$
$103$	5.94103	0.585387	0.292694	+	0.956206i	$0.405448\pi$
$104$	−1.77585	−0.174137
$105$	2.94272	0.287180
$106$	−1.44998	−0.140835
$107$	12.0378	1.16374	0.581868	−	0.813283i	$-0.302322\pi$
$107$	12.0378	1.16374	0.581868	+	0.813283i	$0.302322\pi$
$108$	−1.00000	−0.0962250
$109$	−14.4305	−1.38219	−0.691095	−	0.722764i	$-0.742871\pi$
$109$	−14.4305	−1.38219	−0.691095	+	0.722764i	$0.742871\pi$
$110$	1.00000	0.0953463
$111$	−11.7119	−1.11165
$112$	−2.94272	−0.278061
$113$	−7.60233	−0.715167	−0.357583	−	0.933881i	$-0.616399\pi$
$113$	−7.60233	−0.715167	−0.357583	+	0.933881i	$0.616399\pi$
$114$	−4.94272	−0.462928
$115$	4.10959	0.383221
$116$	1.43377	0.133122
$117$	1.77585	0.164178
$118$	−2.76919	−0.254925
$119$	−2.94272	−0.269759
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−2.65960	−0.240789
$123$	−5.88544	−0.530672
$124$	−8.09337	−0.726806
$125$	1.00000	0.0894427
$126$	2.94272	0.262158
$127$	−13.0523	−1.15821	−0.579103	−	0.815255i	$-0.696597\pi$
$127$	−13.0523	−1.15821	−0.579103	+	0.815255i	$0.696597\pi$
$128$	−1.00000	−0.0883883
$129$	1.00169	0.0881938
$130$	−1.77585	−0.155753
$131$	−16.1636	−1.41222	−0.706110	−	0.708103i	$-0.749551\pi$
$131$	−16.1636	−1.41222	−0.706110	+	0.708103i	$0.749551\pi$
$132$	1.00000	0.0870388
$133$	14.5450	1.26122
$134$	−12.5450	−1.08373
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−4.20793	−0.359508	−0.179754	−	0.983712i	$-0.557530\pi$
$137$	−4.20793	−0.359508	−0.179754	+	0.983712i	$0.557530\pi$
$138$	4.10959	0.349831
$139$	16.7053	1.41692	0.708461	−	0.705750i	$-0.249390\pi$
$139$	16.7053	1.41692	0.708461	+	0.705750i	$0.249390\pi$
$140$	−2.94272	−0.248705
$141$	9.31921	0.784819
$142$	8.88375	0.745508
$143$	−1.77585	−0.148504
$144$	1.00000	0.0833333
$145$	1.43377	0.119068
$146$	10.6546	0.881784
$147$	−1.65960	−0.136882
$148$	11.7119	0.962713
$149$	−15.7085	−1.28689	−0.643447	−	0.765491i	$-0.722496\pi$
$149$	−15.7085	−1.28689	−0.643447	+	0.765491i	$0.722496\pi$
$150$	1.00000	0.0816497
$151$	−14.9933	−1.22014	−0.610070	−	0.792347i	$-0.708859\pi$
$151$	−14.9933	−1.22014	−0.610070	+	0.792347i	$0.708859\pi$
$152$	4.94272	0.400908
$153$	1.00000	0.0808452
$154$	−2.94272	−0.237131
$155$	−8.09337	−0.650075
$156$	−1.77585	−0.142182
$157$	13.5861	1.08429	0.542145	−	0.840285i	$-0.317612\pi$
$157$	13.5861	1.08429	0.542145	+	0.840285i	$0.317612\pi$
$158$	0.998311	0.0794214
$159$	−1.44998	−0.114991
$160$	−1.00000	−0.0790569
$161$	−12.0934	−0.953091
$162$	−1.00000	−0.0785674
$163$	2.71857	0.212935	0.106468	−	0.994316i	$-0.466046\pi$
$163$	2.71857	0.212935	0.106468	+	0.994316i	$0.466046\pi$
$164$	5.88544	0.459576
$165$	1.00000	0.0778499
$166$	3.60729	0.279980
$167$	−18.8198	−1.45632	−0.728160	−	0.685407i	$-0.759624\pi$
$167$	−18.8198	−1.45632	−0.728160	+	0.685407i	$0.759624\pi$
$168$	−2.94272	−0.227036
$169$	−9.84635	−0.757411
$170$	−1.00000	−0.0766965
$171$	−4.94272	−0.377979
$172$	−1.00169	−0.0763781
$173$	−5.67751	−0.431653	−0.215827	−	0.976432i	$-0.569245\pi$
$173$	−5.67751	−0.431653	−0.215827	+	0.976432i	$0.569245\pi$
$174$	1.43377	0.108694
$175$	−2.94272	−0.222449
$176$	−1.00000	−0.0753778
$177$	−2.76919	−0.208145
$178$	8.33374	0.624640
$179$	−22.2653	−1.66419	−0.832094	−	0.554635i	$-0.812858\pi$
$179$	−22.2653	−1.66419	−0.832094	+	0.554635i	$0.812858\pi$
$180$	1.00000	0.0745356
$181$	−8.27028	−0.614725	−0.307362	−	0.951593i	$-0.599446\pi$
$181$	−8.27028	−0.614725	−0.307362	+	0.951593i	$0.599446\pi$
$182$	5.22584	0.387365
$183$	−2.65960	−0.196604
$184$	−4.10959	−0.302963
$185$	11.7119	0.861077
$186$	−8.09337	−0.593435
$187$	−1.00000	−0.0731272
$188$	−9.31921	−0.679673
$189$	2.94272	0.214051
$190$	4.94272	0.358583
$191$	4.14896	0.300208	0.150104	−	0.988670i	$-0.452039\pi$
$191$	4.14896	0.300208	0.150104	+	0.988670i	$0.452039\pi$
$192$	−1.00000	−0.0721688
$193$	−8.88713	−0.639710	−0.319855	−	0.947467i	$-0.603634\pi$
$193$	−8.88713	−0.639710	−0.319855	+	0.947467i	$0.603634\pi$
$194$	−11.1113	−0.797743
$195$	−1.77585	−0.127171
$196$	1.65960	0.118543
$197$	16.8119	1.19780	0.598901	−	0.800823i	$-0.295604\pi$
$197$	16.8119	1.19780	0.598901	+	0.800823i	$0.295604\pi$
$198$	1.00000	0.0710669
$199$	23.7463	1.68333	0.841666	−	0.539999i	$-0.181575\pi$
$199$	23.7463	1.68333	0.841666	+	0.539999i	$0.181575\pi$
$200$	−1.00000	−0.0707107
$201$	−12.5450	−0.884859
$202$	−19.4238	−1.36666
$203$	−4.21918	−0.296128
$204$	−1.00000	−0.0700140
$205$	5.88544	0.411057
$206$	−5.94103	−0.413931
$207$	4.10959	0.285636
$208$	1.77585	0.123133
$209$	4.94272	0.341895
$210$	−2.94272	−0.203067
$211$	4.60401	0.316953	0.158477	−	0.987363i	$-0.449342\pi$
$211$	4.60401	0.316953	0.158477	+	0.987363i	$0.449342\pi$
$212$	1.44998	0.0995853
$213$	8.88375	0.608705
$214$	−12.0378	−0.822886
$215$	−1.00169	−0.0683146
$216$	1.00000	0.0680414
$217$	23.8165	1.61677
$218$	14.4305	0.977356
$219$	10.6546	0.719973
$220$	−1.00000	−0.0674200
$221$	1.77585	0.119457
$222$	11.7119	0.786052
$223$	29.7497	1.99219	0.996093	−	0.0883049i	$-0.0281450\pi$
$223$	29.7497	1.99219	0.996093	+	0.0883049i	$0.0281450\pi$
$224$	2.94272	0.196619
$225$	1.00000	0.0666667
$226$	7.60233	0.505699
$227$	−4.98209	−0.330673	−0.165337	−	0.986237i	$-0.552871\pi$
$227$	−4.98209	−0.330673	−0.165337	+	0.986237i	$0.552871\pi$
$228$	4.94272	0.327340
$229$	−11.2636	−0.744321	−0.372160	−	0.928168i	$-0.621383\pi$
$229$	−11.2636	−0.744321	−0.372160	+	0.928168i	$0.621383\pi$
$230$	−4.10959	−0.270978
$231$	−2.94272	−0.193617
$232$	−1.43377	−0.0941315
$233$	−10.8709	−0.712177	−0.356089	−	0.934452i	$-0.615890\pi$
$233$	−10.8709	−0.712177	−0.356089	+	0.934452i	$0.615890\pi$
$234$	−1.77585	−0.116091
$235$	−9.31921	−0.607918
$236$	2.76919	0.180259
$237$	0.998311	0.0648473
$238$	2.94272	0.190748
$239$	2.37152	0.153401	0.0767004	−	0.997054i	$-0.475562\pi$
$239$	2.37152	0.153401	0.0767004	+	0.997054i	$0.475562\pi$
$240$	−1.00000	−0.0645497
$241$	−29.2341	−1.88313	−0.941566	−	0.336827i	$-0.890646\pi$
$241$	−29.2341	−1.88313	−0.941566	+	0.336827i	$0.890646\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	2.65960	0.170264
$245$	1.65960	0.106028
$246$	5.88544	0.375242
$247$	−8.77754	−0.558502
$248$	8.09337	0.513930
$249$	3.60729	0.228603
$250$	−1.00000	−0.0632456
$251$	−5.96063	−0.376231	−0.188116	−	0.982147i	$-0.560238\pi$
$251$	−5.96063	−0.376231	−0.188116	+	0.982147i	$0.560238\pi$
$252$	−2.94272	−0.185374
$253$	−4.10959	−0.258368
$254$	13.0523	0.818975
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	12.1523	0.758042	0.379021	−	0.925388i	$-0.376261\pi$
$257$	12.1523	0.758042	0.379021	+	0.925388i	$0.376261\pi$
$258$	−1.00169	−0.0623624
$259$	−34.4649	−2.14154
$260$	1.77585	0.110134
$261$	1.43377	0.0887480
$262$	16.1636	0.998590
$263$	6.54505	0.403585	0.201792	−	0.979428i	$-0.435323\pi$
$263$	6.54505	0.403585	0.201792	+	0.979428i	$0.435323\pi$
$264$	−1.00000	−0.0615457
$265$	1.44998	0.0890718
$266$	−14.5450	−0.891814
$267$	8.33374	0.510016
$268$	12.5450	0.766311
$269$	−29.4794	−1.79739	−0.898696	−	0.438572i	$-0.855484\pi$
$269$	−29.4794	−1.79739	−0.898696	+	0.438572i	$0.855484\pi$
$270$	1.00000	0.0608581
$271$	25.1536	1.52797	0.763985	−	0.645234i	$-0.223240\pi$
$271$	25.1536	1.52797	0.763985	+	0.645234i	$0.223240\pi$
$272$	1.00000	0.0606339
$273$	5.22584	0.316282
$274$	4.20793	0.254210
$275$	−1.00000	−0.0603023
$276$	−4.10959	−0.247368
$277$	−16.8576	−1.01287	−0.506437	−	0.862277i	$-0.669038\pi$
$277$	−16.8576	−1.01287	−0.506437	+	0.862277i	$0.669038\pi$
$278$	−16.7053	−1.00191
$279$	−8.09337	−0.484538
$280$	2.94272	0.175861
$281$	−14.8709	−0.887124	−0.443562	−	0.896244i	$-0.646285\pi$
$281$	−14.8709	−0.887124	−0.443562	+	0.896244i	$0.646285\pi$
$282$	−9.31921	−0.554951
$283$	−23.3059	−1.38539	−0.692696	−	0.721230i	$-0.743577\pi$
$283$	−23.3059	−1.38539	−0.692696	+	0.721230i	$0.743577\pi$
$284$	−8.88375	−0.527154
$285$	4.94272	0.292781
$286$	1.77585	0.105008
$287$	−17.3192	−1.02232
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−1.43377	−0.0841937
$291$	−11.1113	−0.651355
$292$	−10.6546	−0.623515
$293$	−15.3192	−0.894958	−0.447479	−	0.894295i	$-0.647678\pi$
$293$	−15.3192	−0.894958	−0.447479	+	0.894295i	$0.647678\pi$
$294$	1.65960	0.0967901
$295$	2.76919	0.161229
$296$	−11.7119	−0.680741
$297$	1.00000	0.0580259
$298$	15.7085	0.909971
$299$	7.29802	0.422056
$300$	−1.00000	−0.0577350
$301$	2.94769	0.169902
$302$	14.9933	0.862770
$303$	−19.4238	−1.11587
$304$	−4.94272	−0.283484
$305$	2.65960	0.152289
$306$	−1.00000	−0.0571662
$307$	21.9738	1.25411	0.627057	−	0.778974i	$-0.284259\pi$
$307$	21.9738	1.25411	0.627057	+	0.778974i	$0.284259\pi$
$308$	2.94272	0.167677
$309$	−5.94103	−0.337973
$310$	8.09337	0.459673
$311$	−4.34995	−0.246663	−0.123332	−	0.992366i	$-0.539358\pi$
$311$	−4.34995	−0.246663	−0.123332	+	0.992366i	$0.539358\pi$
$312$	1.77585	0.100538
$313$	15.7630	0.890978	0.445489	−	0.895287i	$-0.353030\pi$
$313$	15.7630	0.890978	0.445489	+	0.895287i	$0.353030\pi$
$314$	−13.5861	−0.766708
$315$	−2.94272	−0.165804
$316$	−0.998311	−0.0561594
$317$	9.10341	0.511298	0.255649	−	0.966770i	$-0.417711\pi$
$317$	9.10341	0.511298	0.255649	+	0.966770i	$0.417711\pi$
$318$	1.44998	0.0813111
$319$	−1.43377	−0.0802756
$320$	1.00000	0.0559017
$321$	−12.0378	−0.671883
$322$	12.0934	0.673937
$323$	−4.94272	−0.275020
$324$	1.00000	0.0555556
$325$	1.77585	0.0985066
$326$	−2.71857	−0.150568
$327$	14.4305	0.798008
$328$	−5.88544	−0.324969
$329$	27.4238	1.51192
$330$	−1.00000	−0.0550482
$331$	28.9789	1.59282	0.796412	−	0.604754i	$-0.206728\pi$
$331$	28.9789	1.59282	0.796412	+	0.604754i	$0.206728\pi$
$332$	−3.60729	−0.197976
$333$	11.7119	0.641809
$334$	18.8198	1.02977
$335$	12.5450	0.685409
$336$	2.94272	0.160539
$337$	−17.7580	−0.967342	−0.483671	−	0.875250i	$-0.660697\pi$
$337$	−17.7580	−0.967342	−0.483671	+	0.875250i	$0.660697\pi$
$338$	9.84635	0.535571
$339$	7.60233	0.412902
$340$	1.00000	0.0542326
$341$	8.09337	0.438281
$342$	4.94272	0.267272
$343$	15.7153	0.848546
$344$	1.00169	0.0540074
$345$	−4.10959	−0.221253
$346$	5.67751	0.305225
$347$	24.2947	1.30421	0.652105	−	0.758129i	$-0.273886\pi$
$347$	24.2947	1.30421	0.652105	+	0.758129i	$0.273886\pi$
$348$	−1.43377	−0.0768580
$349$	−18.9349	−1.01356	−0.506780	−	0.862076i	$-0.669164\pi$
$349$	−18.9349	−1.01356	−0.506780	+	0.862076i	$0.669164\pi$
$350$	2.94272	0.157295
$351$	−1.77585	−0.0947880
$352$	1.00000	0.0533002
$353$	9.97544	0.530939	0.265469	−	0.964119i	$-0.414473\pi$
$353$	9.97544	0.530939	0.265469	+	0.964119i	$0.414473\pi$
$354$	2.76919	0.147181
$355$	−8.88375	−0.471501
$356$	−8.33374	−0.441687
$357$	2.94272	0.155745
$358$	22.2653	1.17676
$359$	−35.2749	−1.86174	−0.930868	−	0.365355i	$-0.880947\pi$
$359$	−35.2749	−1.86174	−0.930868	+	0.365355i	$0.880947\pi$
$360$	−1.00000	−0.0527046
$361$	5.43049	0.285815
$362$	8.27028	0.434676
$363$	−1.00000	−0.0524864
$364$	−5.22584	−0.273908
$365$	−10.6546	−0.557689
$366$	2.65960	0.139020
$367$	14.9821	0.782059	0.391029	−	0.920378i	$-0.372119\pi$
$367$	14.9821	0.782059	0.391029	+	0.920378i	$0.372119\pi$
$368$	4.10959	0.214227
$369$	5.88544	0.306384
$370$	−11.7119	−0.608873
$371$	−4.26690	−0.221526
$372$	8.09337	0.419622
$373$	−4.58780	−0.237547	−0.118774	−	0.992921i	$-0.537896\pi$
$373$	−4.58780	−0.237547	−0.118774	+	0.992921i	$0.537896\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	9.31921	0.480602
$377$	2.54616	0.131134
$378$	−2.94272	−0.151357
$379$	−30.7642	−1.58025	−0.790126	−	0.612944i	$-0.789985\pi$
$379$	−30.7642	−1.58025	−0.790126	+	0.612944i	$0.789985\pi$
$380$	−4.94272	−0.253556
$381$	13.0523	0.668690
$382$	−4.14896	−0.212279
$383$	−25.3192	−1.29375	−0.646876	−	0.762596i	$-0.723925\pi$
$383$	−25.3192	−1.29375	−0.646876	+	0.762596i	$0.723925\pi$
$384$	1.00000	0.0510310
$385$	2.94272	0.149975
$386$	8.88713	0.452343
$387$	−1.00169	−0.0509187
$388$	11.1113	0.564090
$389$	−17.2652	−0.875381	−0.437690	−	0.899126i	$-0.644203\pi$
$389$	−17.2652	−0.875381	−0.437690	+	0.899126i	$0.644203\pi$
$390$	1.77585	0.0899238
$391$	4.10959	0.207831
$392$	−1.65960	−0.0838227
$393$	16.1636	0.815345
$394$	−16.8119	−0.846974
$395$	−0.998311	−0.0502305
$396$	−1.00000	−0.0502519
$397$	−36.5907	−1.83643	−0.918217	−	0.396077i	$-0.870371\pi$
$397$	−36.5907	−1.83643	−0.918217	+	0.396077i	$0.870371\pi$
$398$	−23.7463	−1.19030
$399$	−14.5450	−0.728163
$400$	1.00000	0.0500000
$401$	−12.2586	−0.612163	−0.306081	−	0.952005i	$-0.599018\pi$
$401$	−12.2586	−0.612163	−0.306081	+	0.952005i	$0.599018\pi$
$402$	12.5450	0.625690
$403$	−14.3726	−0.715952
$404$	19.4238	0.966372
$405$	1.00000	0.0496904
$406$	4.21918	0.209394
$407$	−11.7119	−0.580538
$408$	1.00000	0.0495074
$409$	21.5418	1.06517	0.532586	−	0.846376i	$-0.321220\pi$
$409$	21.5418	1.06517	0.532586	+	0.846376i	$0.321220\pi$
$410$	−5.88544	−0.290661
$411$	4.20793	0.207562
$412$	5.94103	0.292694
$413$	−8.14896	−0.400984
$414$	−4.10959	−0.201975
$415$	−3.60729	−0.177075
$416$	−1.77585	−0.0870683
$417$	−16.7053	−0.818060
$418$	−4.94272	−0.241756
$419$	−3.12909	−0.152866	−0.0764329	−	0.997075i	$-0.524353\pi$
$419$	−3.12909	−0.152866	−0.0764329	+	0.997075i	$0.524353\pi$
$420$	2.94272	0.143590
$421$	−11.5940	−0.565056	−0.282528	−	0.959259i	$-0.591173\pi$
$421$	−11.5940	−0.565056	−0.282528	+	0.959259i	$0.591173\pi$
$422$	−4.60401	−0.224120
$423$	−9.31921	−0.453115
$424$	−1.44998	−0.0704175
$425$	1.00000	0.0485071
$426$	−8.88375	−0.430419
$427$	−7.82647	−0.378750
$428$	12.0378	0.581868
$429$	1.77585	0.0857389
$430$	1.00169	0.0483057
$431$	−20.6006	−0.992298	−0.496149	−	0.868237i	$-0.665253\pi$
$431$	−20.6006	−0.992298	−0.496149	+	0.868237i	$0.665253\pi$
$432$	−1.00000	−0.0481125
$433$	26.2570	1.26183	0.630914	−	0.775852i	$-0.282680\pi$
$433$	26.2570	1.26183	0.630914	+	0.775852i	$0.282680\pi$
$434$	−23.8165	−1.14323
$435$	−1.43377	−0.0687439
$436$	−14.4305	−0.691095
$437$	−20.3126	−0.971681
$438$	−10.6546	−0.509098
$439$	22.8414	1.09016	0.545080	−	0.838384i	$-0.316499\pi$
$439$	22.8414	1.09016	0.545080	+	0.838384i	$0.316499\pi$
$440$	1.00000	0.0476731
$441$	1.65960	0.0790288
$442$	−1.77585	−0.0844687
$443$	−7.38652	−0.350944	−0.175472	−	0.984484i	$-0.556145\pi$
$443$	−7.38652	−0.350944	−0.175472	+	0.984484i	$0.556145\pi$
$444$	−11.7119	−0.555823
$445$	−8.33374	−0.395057
$446$	−29.7497	−1.40869
$447$	15.7085	0.742988
$448$	−2.94272	−0.139030
$449$	13.4666	0.635527	0.317764	−	0.948170i	$-0.397068\pi$
$449$	13.4666	0.635527	0.317764	+	0.948170i	$0.397068\pi$
$450$	−1.00000	−0.0471405
$451$	−5.88544	−0.277135
$452$	−7.60233	−0.357583
$453$	14.9933	0.704449
$454$	4.98209	0.233821
$455$	−5.22584	−0.244991
$456$	−4.94272	−0.231464
$457$	−34.2648	−1.60284	−0.801421	−	0.598101i	$-0.795922\pi$
$457$	−34.2648	−1.60284	−0.801421	+	0.598101i	$0.795922\pi$
$458$	11.2636	0.526314
$459$	−1.00000	−0.0466760
$460$	4.10959	0.191611
$461$	−7.55170	−0.351718	−0.175859	−	0.984415i	$-0.556270\pi$
$461$	−7.55170	−0.351718	−0.175859	+	0.984415i	$0.556270\pi$
$462$	2.94272	0.136908
$463$	−32.7352	−1.52133	−0.760666	−	0.649143i	$-0.775128\pi$
$463$	−32.7352	−1.52133	−0.760666	+	0.649143i	$0.775128\pi$
$464$	1.43377	0.0665610
$465$	8.09337	0.375321
$466$	10.8709	0.503585
$467$	3.90363	0.180638	0.0903192	−	0.995913i	$-0.471211\pi$
$467$	3.90363	0.180638	0.0903192	+	0.995913i	$0.471211\pi$
$468$	1.77585	0.0820888
$469$	−36.9166	−1.70465
$470$	9.31921	0.429863
$471$	−13.5861	−0.626015
$472$	−2.76919	−0.127462
$473$	1.00169	0.0460577
$474$	−0.998311	−0.0458540
$475$	−4.94272	−0.226788
$476$	−2.94272	−0.134879
$477$	1.44998	0.0663902
$478$	−2.37152	−0.108471
$479$	−8.10669	−0.370404	−0.185202	−	0.982700i	$-0.559294\pi$
$479$	−8.10669	−0.370404	−0.185202	+	0.982700i	$0.559294\pi$
$480$	1.00000	0.0456435
$481$	20.7986	0.948336
$482$	29.2341	1.33158
$483$	12.0934	0.550267
$484$	1.00000	0.0454545
$485$	11.1113	0.504537
$486$	1.00000	0.0453609
$487$	−30.5239	−1.38317	−0.691584	−	0.722296i	$-0.743087\pi$
$487$	−30.5239	−1.38317	−0.691584	+	0.722296i	$0.743087\pi$
$488$	−2.65960	−0.120395
$489$	−2.71857	−0.122938
$490$	−1.65960	−0.0749733
$491$	−37.4081	−1.68820	−0.844102	−	0.536183i	$-0.819866\pi$
$491$	−37.4081	−1.68820	−0.844102	+	0.536183i	$0.819866\pi$
$492$	−5.88544	−0.265336
$493$	1.43377	0.0645737
$494$	8.77754	0.394920
$495$	−1.00000	−0.0449467
$496$	−8.09337	−0.363403
$497$	26.1424	1.17265
$498$	−3.60729	−0.161647
$499$	2.76629	0.123836	0.0619182	−	0.998081i	$-0.480278\pi$
$499$	2.76629	0.123836	0.0619182	+	0.998081i	$0.480278\pi$
$500$	1.00000	0.0447214
$501$	18.8198	0.840807
$502$	5.96063	0.266036
$503$	−44.2245	−1.97187	−0.985937	−	0.167117i	$-0.946554\pi$
$503$	−44.2245	−1.97187	−0.985937	+	0.167117i	$0.946554\pi$
$504$	2.94272	0.131079
$505$	19.4238	0.864349
$506$	4.10959	0.182694
$507$	9.84635	0.437292
$508$	−13.0523	−0.579103
$509$	−12.8493	−0.569537	−0.284769	−	0.958596i	$-0.591917\pi$
$509$	−12.8493	−0.569537	−0.284769	+	0.958596i	$0.591917\pi$
$510$	1.00000	0.0442807
$511$	31.3536	1.38700
$512$	−1.00000	−0.0441942
$513$	4.94272	0.218226
$514$	−12.1523	−0.536017
$515$	5.94103	0.261793
$516$	1.00169	0.0440969
$517$	9.31921	0.409858
$518$	34.4649	1.51430
$519$	5.67751	0.249215
$520$	−1.77585	−0.0778763
$521$	18.5135	0.811093	0.405546	−	0.914074i	$-0.367081\pi$
$521$	18.5135	0.811093	0.405546	+	0.914074i	$0.367081\pi$
$522$	−1.43377	−0.0627543
$523$	15.6334	0.683599	0.341799	−	0.939773i	$-0.388964\pi$
$523$	15.6334	0.683599	0.341799	+	0.939773i	$0.388964\pi$
$524$	−16.1636	−0.706110
$525$	2.94272	0.128431
$526$	−6.54505	−0.285378
$527$	−8.09337	−0.352553
$528$	1.00000	0.0435194
$529$	−6.11128	−0.265708
$530$	−1.44998	−0.0629833
$531$	2.76919	0.120173
$532$	14.5450	0.630608
$533$	10.4517	0.452712
$534$	−8.33374	−0.360636
$535$	12.0378	0.520439
$536$	−12.5450	−0.541863
$537$	22.2653	0.960819
$538$	29.4794	1.27095
$539$	−1.65960	−0.0714842
$540$	−1.00000	−0.0430331
$541$	20.7874	0.893719	0.446860	−	0.894604i	$-0.352542\pi$
$541$	20.7874	0.893719	0.446860	+	0.894604i	$0.352542\pi$
$542$	−25.1536	−1.08044
$543$	8.27028	0.354912
$544$	−1.00000	−0.0428746
$545$	−14.4305	−0.618134
$546$	−5.22584	−0.223645
$547$	−38.4973	−1.64603	−0.823013	−	0.568022i	$-0.807709\pi$
$547$	−38.4973	−1.64603	−0.823013	+	0.568022i	$0.807709\pi$
$548$	−4.20793	−0.179754
$549$	2.65960	0.113509
$550$	1.00000	0.0426401
$551$	−7.08671	−0.301904
$552$	4.10959	0.174916
$553$	2.93775	0.124926
$554$	16.8576	0.716211
$555$	−11.7119	−0.497143
$556$	16.7053	0.708461
$557$	−30.1935	−1.27934	−0.639670	−	0.768650i	$-0.720929\pi$
$557$	−30.1935	−1.27934	−0.639670	+	0.768650i	$0.720929\pi$
$558$	8.09337	0.342620
$559$	−1.77885	−0.0752374
$560$	−2.94272	−0.124353
$561$	1.00000	0.0422200
$562$	14.8709	0.627292
$563$	−41.1357	−1.73366	−0.866832	−	0.498600i	$-0.833848\pi$
$563$	−41.1357	−1.73366	−0.866832	+	0.498600i	$0.833848\pi$
$564$	9.31921	0.392409
$565$	−7.60233	−0.319832
$566$	23.3059	0.979620
$567$	−2.94272	−0.123583
$568$	8.88375	0.372754
$569$	−38.1946	−1.60120	−0.800601	−	0.599198i	$-0.795486\pi$
$569$	−38.1946	−1.60120	−0.800601	+	0.599198i	$0.795486\pi$
$570$	−4.94272	−0.207028
$571$	−13.1702	−0.551158	−0.275579	−	0.961278i	$-0.588870\pi$
$571$	−13.1702	−0.551158	−0.275579	+	0.961278i	$0.588870\pi$
$572$	−1.77585	−0.0742521
$573$	−4.14896	−0.173325
$574$	17.3192	0.722890
$575$	4.10959	0.171382
$576$	1.00000	0.0416667
$577$	−42.0278	−1.74964	−0.874821	−	0.484446i	$-0.839021\pi$
$577$	−42.0278	−1.74964	−0.874821	+	0.484446i	$0.839021\pi$
$578$	−1.00000	−0.0415945
$579$	8.88713	0.369337
$580$	1.43377	0.0595340
$581$	10.6153	0.440395
$582$	11.1113	0.460577
$583$	−1.44998	−0.0600522
$584$	10.6546	0.440892
$585$	1.77585	0.0734224
$586$	15.3192	0.632831
$587$	1.98181	0.0817982	0.0408991	−	0.999163i	$-0.486978\pi$
$587$	1.98181	0.0817982	0.0408991	+	0.999163i	$0.486978\pi$
$588$	−1.65960	−0.0684409
$589$	40.0033	1.64831
$590$	−2.76919	−0.114006
$591$	−16.8119	−0.691551
$592$	11.7119	0.481357
$593$	−29.9266	−1.22894	−0.614469	−	0.788941i	$-0.710630\pi$
$593$	−29.9266	−1.22894	−0.614469	+	0.788941i	$0.710630\pi$
$594$	−1.00000	−0.0410305
$595$	−2.94272	−0.120640
$596$	−15.7085	−0.643447
$597$	−23.7463	−0.971872
$598$	−7.29802	−0.298438
$599$	−20.2968	−0.829305	−0.414653	−	0.909980i	$-0.636097\pi$
$599$	−20.2968	−0.829305	−0.414653	+	0.909980i	$0.636097\pi$
$600$	1.00000	0.0408248
$601$	36.3532	1.48288	0.741440	−	0.671020i	$-0.234143\pi$
$601$	36.3532	1.48288	0.741440	+	0.671020i	$0.234143\pi$
$602$	−2.94769	−0.120139
$603$	12.5450	0.510874
$604$	−14.9933	−0.610070
$605$	1.00000	0.0406558
$606$	19.4238	0.789039
$607$	14.1897	0.575944	0.287972	−	0.957639i	$-0.407019\pi$
$607$	14.1897	0.575944	0.287972	+	0.957639i	$0.407019\pi$
$608$	4.94272	0.200454
$609$	4.21918	0.170970
$610$	−2.65960	−0.107684
$611$	−16.5495	−0.669523
$612$	1.00000	0.0404226
$613$	−34.9215	−1.41047	−0.705234	−	0.708975i	$-0.749158\pi$
$613$	−34.9215	−1.41047	−0.705234	+	0.708975i	$0.749158\pi$
$614$	−21.9738	−0.886792
$615$	−5.88544	−0.237324
$616$	−2.94272	−0.118566
$617$	0.498917	0.0200856	0.0100428	−	0.999950i	$-0.496803\pi$
$617$	0.498917	0.0200856	0.0100428	+	0.999950i	$0.496803\pi$
$618$	5.94103	0.238983
$619$	49.3549	1.98374	0.991871	−	0.127248i	$-0.0406146\pi$
$619$	49.3549	1.98374	0.991871	+	0.127248i	$0.0406146\pi$
$620$	−8.09337	−0.325038
$621$	−4.10959	−0.164912
$622$	4.34995	0.174417
$623$	24.5239	0.982528
$624$	−1.77585	−0.0710910
$625$	1.00000	0.0400000
$626$	−15.7630	−0.630017
$627$	−4.94272	−0.197393
$628$	13.5861	0.542145
$629$	11.7119	0.466985
$630$	2.94272	0.117241
$631$	−10.7019	−0.426035	−0.213018	−	0.977048i	$-0.568329\pi$
$631$	−10.7019	−0.426035	−0.213018	+	0.977048i	$0.568329\pi$
$632$	0.998311	0.0397107
$633$	−4.60401	−0.182993
$634$	−9.10341	−0.361543
$635$	−13.0523	−0.517965
$636$	−1.44998	−0.0574956
$637$	2.94721	0.116773
$638$	1.43377	0.0567634
$639$	−8.88375	−0.351436
$640$	−1.00000	−0.0395285
$641$	−6.87381	−0.271499	−0.135750	−	0.990743i	$-0.543344\pi$
$641$	−6.87381	−0.271499	−0.135750	+	0.990743i	$0.543344\pi$
$642$	12.0378	0.475093
$643$	33.6464	1.32688	0.663442	−	0.748228i	$-0.269095\pi$
$643$	33.6464	1.32688	0.663442	+	0.748228i	$0.269095\pi$
$644$	−12.0934	−0.476546
$645$	1.00169	0.0394415
$646$	4.94272	0.194469
$647$	−14.7888	−0.581407	−0.290704	−	0.956813i	$-0.593889\pi$
$647$	−14.7888	−0.581407	−0.290704	+	0.956813i	$0.593889\pi$
$648$	−1.00000	−0.0392837
$649$	−2.76919	−0.108700
$650$	−1.77585	−0.0696547
$651$	−23.8165	−0.933444
$652$	2.71857	0.106468
$653$	49.7353	1.94629	0.973146	−	0.230190i	$-0.0739348\pi$
$653$	49.7353	1.94629	0.973146	+	0.230190i	$0.0739348\pi$
$654$	−14.4305	−0.564277
$655$	−16.1636	−0.631564
$656$	5.88544	0.229788
$657$	−10.6546	−0.415677
$658$	−27.4238	−1.06909
$659$	−17.3059	−0.674142	−0.337071	−	0.941479i	$-0.609436\pi$
$659$	−17.3059	−0.674142	−0.337071	+	0.941479i	$0.609436\pi$
$660$	1.00000	0.0389249
$661$	26.0357	1.01267	0.506336	−	0.862336i	$-0.331000\pi$
$661$	26.0357	1.01267	0.506336	+	0.862336i	$0.331000\pi$
$662$	−28.9789	−1.12630
$663$	−1.77585	−0.0689684
$664$	3.60729	0.139990
$665$	14.5450	0.564033
$666$	−11.7119	−0.453827
$667$	5.89220	0.228147
$668$	−18.8198	−0.728160
$669$	−29.7497	−1.15019
$670$	−12.5450	−0.484657
$671$	−2.65960	−0.102673
$672$	−2.94272	−0.113518
$673$	9.75129	0.375885	0.187942	−	0.982180i	$-0.439818\pi$
$673$	9.75129	0.375885	0.187942	+	0.982180i	$0.439818\pi$
$674$	17.7580	0.684014
$675$	−1.00000	−0.0384900
$676$	−9.84635	−0.378706
$677$	37.0443	1.42373	0.711865	−	0.702316i	$-0.247851\pi$
$677$	37.0443	1.42373	0.711865	+	0.702316i	$0.247851\pi$
$678$	−7.60233	−0.291966
$679$	−32.6974	−1.25481
$680$	−1.00000	−0.0383482
$681$	4.98209	0.190914
$682$	−8.09337	−0.309911
$683$	−39.4007	−1.50762	−0.753812	−	0.657090i	$-0.771787\pi$
$683$	−39.4007	−1.50762	−0.753812	+	0.657090i	$0.771787\pi$
$684$	−4.94272	−0.188990
$685$	−4.20793	−0.160777
$686$	−15.7153	−0.600013
$687$	11.2636	0.429734
$688$	−1.00169	−0.0381890
$689$	2.57496	0.0980981
$690$	4.10959	0.156449
$691$	−35.2556	−1.34119	−0.670594	−	0.741825i	$-0.733961\pi$
$691$	−35.2556	−1.34119	−0.670594	+	0.741825i	$0.733961\pi$
$692$	−5.67751	−0.215827
$693$	2.94272	0.111785
$694$	−24.2947	−0.922216
$695$	16.7053	0.633666
$696$	1.43377	0.0543468
$697$	5.88544	0.222927
$698$	18.9349	0.716695
$699$	10.8709	0.411176
$700$	−2.94272	−0.111224
$701$	−32.4284	−1.22480	−0.612402	−	0.790546i	$-0.709797\pi$
$701$	−32.4284	−1.22480	−0.612402	+	0.790546i	$0.709797\pi$
$702$	1.77585	0.0670252
$703$	−57.8887	−2.18331
$704$	−1.00000	−0.0376889
$705$	9.31921	0.350982
$706$	−9.97544	−0.375430
$707$	−57.1589	−2.14968
$708$	−2.76919	−0.104073
$709$	13.2047	0.495911	0.247956	−	0.968771i	$-0.420241\pi$
$709$	13.2047	0.495911	0.247956	+	0.968771i	$0.420241\pi$
$710$	8.88375	0.333401
$711$	−0.998311	−0.0374396
$712$	8.33374	0.312320
$713$	−33.2604	−1.24561
$714$	−2.94272	−0.110129
$715$	−1.77585	−0.0664131
$716$	−22.2653	−0.832094
$717$	−2.37152	−0.0885660
$718$	35.2749	1.31645
$719$	−16.3175	−0.608541	−0.304270	−	0.952586i	$-0.598413\pi$
$719$	−16.3175	−0.608541	−0.304270	+	0.952586i	$0.598413\pi$
$720$	1.00000	0.0372678
$721$	−17.4828	−0.651093
$722$	−5.43049	−0.202102
$723$	29.2341	1.08723
$724$	−8.27028	−0.307362
$725$	1.43377	0.0532488
$726$	1.00000	0.0371135
$727$	−23.3126	−0.864618	−0.432309	−	0.901725i	$-0.642301\pi$
$727$	−23.3126	−0.864618	−0.432309	+	0.901725i	$0.642301\pi$
$728$	5.22584	0.193682
$729$	1.00000	0.0370370
$730$	10.6546	0.394346
$731$	−1.00169	−0.0370488
$732$	−2.65960	−0.0983018
$733$	−3.24543	−0.119873	−0.0599364	−	0.998202i	$-0.519090\pi$
$733$	−3.24543	−0.119873	−0.0599364	+	0.998202i	$0.519090\pi$
$734$	−14.9821	−0.552999
$735$	−1.65960	−0.0612154
$736$	−4.10959	−0.151481
$737$	−12.5450	−0.462103
$738$	−5.88544	−0.216646
$739$	−21.2631	−0.782177	−0.391089	−	0.920353i	$-0.627901\pi$
$739$	−21.2631	−0.782177	−0.391089	+	0.920353i	$0.627901\pi$
$740$	11.7119	0.430539
$741$	8.77754	0.322451
$742$	4.26690	0.156643
$743$	33.6549	1.23468	0.617340	−	0.786697i	$-0.288210\pi$
$743$	33.6549	1.23468	0.617340	+	0.786697i	$0.288210\pi$
$744$	−8.09337	−0.296717
$745$	−15.7085	−0.575516
$746$	4.58780	0.167971
$747$	−3.60729	−0.131984
$748$	−1.00000	−0.0365636
$749$	−35.4238	−1.29436
$750$	1.00000	0.0365148
$751$	47.6975	1.74051	0.870253	−	0.492605i	$-0.163955\pi$
$751$	47.6975	1.74051	0.870253	+	0.492605i	$0.163955\pi$
$752$	−9.31921	−0.339837
$753$	5.96063	0.217217
$754$	−2.54616	−0.0927257
$755$	−14.9933	−0.545664
$756$	2.94272	0.107026
$757$	−32.6796	−1.18776	−0.593880	−	0.804554i	$-0.702405\pi$
$757$	−32.6796	−1.18776	−0.593880	+	0.804554i	$0.702405\pi$
$758$	30.7642	1.11741
$759$	4.10959	0.149169
$760$	4.94272	0.179291
$761$	36.2358	1.31355	0.656773	−	0.754088i	$-0.271921\pi$
$761$	36.2358	1.31355	0.656773	+	0.754088i	$0.271921\pi$
$762$	−13.0523	−0.472835
$763$	42.4649	1.53733
$764$	4.14896	0.150104
$765$	1.00000	0.0361551
$766$	25.3192	0.914820
$767$	4.91768	0.177567
$768$	−1.00000	−0.0360844
$769$	−21.4563	−0.773733	−0.386866	−	0.922136i	$-0.626443\pi$
$769$	−21.4563	−0.773733	−0.386866	+	0.922136i	$0.626443\pi$
$770$	−2.94272	−0.106048
$771$	−12.1523	−0.437656
$772$	−8.88713	−0.319855
$773$	14.4845	0.520971	0.260485	−	0.965478i	$-0.416117\pi$
$773$	14.4845	0.520971	0.260485	+	0.965478i	$0.416117\pi$
$774$	1.00169	0.0360050
$775$	−8.09337	−0.290723
$776$	−11.1113	−0.398872
$777$	34.4649	1.23642
$778$	17.2652	0.618988
$779$	−29.0901	−1.04226
$780$	−1.77585	−0.0635857
$781$	8.88375	0.317886
$782$	−4.10959	−0.146959
$783$	−1.43377	−0.0512387
$784$	1.65960	0.0592716
$785$	13.5861	0.484909
$786$	−16.1636	−0.576536
$787$	−9.67948	−0.345036	−0.172518	−	0.985006i	$-0.555190\pi$
$787$	−9.67948	−0.345036	−0.172518	+	0.985006i	$0.555190\pi$
$788$	16.8119	0.598901
$789$	−6.54505	−0.233010
$790$	0.998311	0.0355183
$791$	22.3715	0.795440
$792$	1.00000	0.0355335
$793$	4.72306	0.167721
$794$	36.5907	1.29856
$795$	−1.44998	−0.0514257
$796$	23.7463	0.841666
$797$	−19.1718	−0.679101	−0.339551	−	0.940588i	$-0.610275\pi$
$797$	−19.1718	−0.679101	−0.339551	+	0.940588i	$0.610275\pi$
$798$	14.5450	0.514889
$799$	−9.31921	−0.329690
$800$	−1.00000	−0.0353553
$801$	−8.33374	−0.294458
$802$	12.2586	0.432865
$803$	10.6546	0.375994
$804$	−12.5450	−0.442430
$805$	−12.0934	−0.426235
$806$	14.3726	0.506254
$807$	29.4794	1.03772
$808$	−19.4238	−0.683328
$809$	−50.2981	−1.76839	−0.884194	−	0.467120i	$-0.845292\pi$
$809$	−50.2981	−1.76839	−0.884194	+	0.467120i	$0.845292\pi$
$810$	−1.00000	−0.0351364
$811$	38.0145	1.33487	0.667435	−	0.744668i	$-0.267392\pi$
$811$	38.0145	1.33487	0.667435	+	0.744668i	$0.267392\pi$
$812$	−4.21918	−0.148064
$813$	−25.1536	−0.882174
$814$	11.7119	0.410502
$815$	2.71857	0.0952274
$816$	−1.00000	−0.0350070
$817$	4.95107	0.173216
$818$	−21.5418	−0.753190
$819$	−5.22584	−0.182606
$820$	5.88544	0.205529
$821$	−13.6907	−0.477810	−0.238905	−	0.971043i	$-0.576788\pi$
$821$	−13.6907	−0.477810	−0.238905	+	0.971043i	$0.576788\pi$
$822$	−4.20793	−0.146768
$823$	−27.2013	−0.948177	−0.474088	−	0.880477i	$-0.657222\pi$
$823$	−27.2013	−0.948177	−0.474088	+	0.880477i	$0.657222\pi$
$824$	−5.94103	−0.206966
$825$	1.00000	0.0348155
$826$	8.14896	0.283539
$827$	12.2737	0.426797	0.213398	−	0.976965i	$-0.431547\pi$
$827$	12.2737	0.426797	0.213398	+	0.976965i	$0.431547\pi$
$828$	4.10959	0.142818
$829$	54.5794	1.89562	0.947811	−	0.318832i	$-0.103290\pi$
$829$	54.5794	1.89562	0.947811	+	0.318832i	$0.103290\pi$
$830$	3.60729	0.125211
$831$	16.8576	0.584784
$832$	1.77585	0.0615666
$833$	1.65960	0.0575019
$834$	16.7053	0.578456
$835$	−18.8198	−0.651287
$836$	4.94272	0.170948
$837$	8.09337	0.279748
$838$	3.12909	0.108093
$839$	−35.0414	−1.20976	−0.604882	−	0.796315i	$-0.706780\pi$
$839$	−35.0414	−1.20976	−0.604882	+	0.796315i	$0.706780\pi$
$840$	−2.94272	−0.101534
$841$	−26.9443	−0.929114
$842$	11.5940	0.399555
$843$	14.8709	0.512181
$844$	4.60401	0.158477
$845$	−9.84635	−0.338725
$846$	9.31921	0.320401
$847$	−2.94272	−0.101113
$848$	1.44998	0.0497927
$849$	23.3059	0.799856
$850$	−1.00000	−0.0342997
$851$	48.1312	1.64991
$852$	8.88375	0.304352
$853$	25.8888	0.886416	0.443208	−	0.896419i	$-0.353840\pi$
$853$	25.8888	0.886416	0.443208	+	0.896419i	$0.353840\pi$
$854$	7.82647	0.267816
$855$	−4.94272	−0.169037
$856$	−12.0378	−0.411443
$857$	8.70395	0.297321	0.148661	−	0.988888i	$-0.452504\pi$
$857$	8.70395	0.297321	0.148661	+	0.988888i	$0.452504\pi$
$858$	−1.77585	−0.0606266
$859$	−24.3735	−0.831613	−0.415806	−	0.909453i	$-0.636501\pi$
$859$	−24.3735	−0.831613	−0.415806	+	0.909453i	$0.636501\pi$
$860$	−1.00169	−0.0341573
$861$	17.3192	0.590237
$862$	20.6006	0.701660
$863$	−24.3105	−0.827538	−0.413769	−	0.910382i	$-0.635788\pi$
$863$	−24.3105	−0.827538	−0.413769	+	0.910382i	$0.635788\pi$
$864$	1.00000	0.0340207
$865$	−5.67751	−0.193041
$866$	−26.2570	−0.892248
$867$	−1.00000	−0.0339618
$868$	23.8165	0.808386
$869$	0.998311	0.0338654
$870$	1.43377	0.0486093
$871$	22.2781	0.754866
$872$	14.4305	0.488678
$873$	11.1113	0.376060
$874$	20.3126	0.687082
$875$	−2.94272	−0.0994821
$876$	10.6546	0.359987
$877$	26.6251	0.899066	0.449533	−	0.893264i	$-0.351590\pi$
$877$	26.6251	0.899066	0.449533	+	0.893264i	$0.351590\pi$
$878$	−22.8414	−0.770859
$879$	15.3192	0.516704
$880$	−1.00000	−0.0337100
$881$	26.2063	0.882914	0.441457	−	0.897282i	$-0.354462\pi$
$881$	26.2063	0.882914	0.441457	+	0.897282i	$0.354462\pi$
$882$	−1.65960	−0.0558818
$883$	26.0445	0.876468	0.438234	−	0.898861i	$-0.355604\pi$
$883$	26.0445	0.876468	0.438234	+	0.898861i	$0.355604\pi$
$884$	1.77585	0.0597284
$885$	−2.76919	−0.0930854
$886$	7.38652	0.248155
$887$	5.38942	0.180959	0.0904796	−	0.995898i	$-0.471160\pi$
$887$	5.38942	0.180959	0.0904796	+	0.995898i	$0.471160\pi$
$888$	11.7119	0.393026
$889$	38.4093	1.28821
$890$	8.33374	0.279347
$891$	−1.00000	−0.0335013
$892$	29.7497	0.996093
$893$	46.0622	1.54141
$894$	−15.7085	−0.525372
$895$	−22.2653	−0.744247
$896$	2.94272	0.0983094
$897$	−7.29802	−0.243674
$898$	−13.4666	−0.449386
$899$	−11.6040	−0.387016
$900$	1.00000	0.0333333
$901$	1.44998	0.0483060
$902$	5.88544	0.195964
$903$	−2.94769	−0.0980930
$904$	7.60233	0.252850
$905$	−8.27028	−0.274913
$906$	−14.9933	−0.498120
$907$	27.1523	0.901579	0.450789	−	0.892630i	$-0.351143\pi$
$907$	27.1523	0.901579	0.450789	+	0.892630i	$0.351143\pi$
$908$	−4.98209	−0.165337
$909$	19.4238	0.644248
$910$	5.22584	0.173235
$911$	50.1773	1.66245	0.831224	−	0.555938i	$-0.187641\pi$
$911$	50.1773	1.66245	0.831224	+	0.555938i	$0.187641\pi$
$912$	4.94272	0.163670
$913$	3.60729	0.119384
$914$	34.2648	1.13338
$915$	−2.65960	−0.0879238
$916$	−11.2636	−0.372160
$917$	47.5649	1.57073
$918$	1.00000	0.0330049
$919$	17.1471	0.565630	0.282815	−	0.959174i	$-0.408732\pi$
$919$	17.1471	0.565630	0.282815	+	0.959174i	$0.408732\pi$
$920$	−4.10959	−0.135489
$921$	−21.9738	−0.724063
$922$	7.55170	0.248702
$923$	−15.7762	−0.519281
$924$	−2.94272	−0.0968084
$925$	11.7119	0.385085
$926$	32.7352	1.07574
$927$	5.94103	0.195129
$928$	−1.43377	−0.0470657
$929$	−38.5891	−1.26607	−0.633034	−	0.774124i	$-0.718191\pi$
$929$	−38.5891	−1.26607	−0.633034	+	0.774124i	$0.718191\pi$
$930$	−8.09337	−0.265392
$931$	−8.20296	−0.268841
$932$	−10.8709	−0.356089
$933$	4.34995	0.142411
$934$	−3.90363	−0.127731
$935$	−1.00000	−0.0327035
$936$	−1.77585	−0.0580455
$937$	47.7119	1.55868	0.779340	−	0.626601i	$-0.215554\pi$
$937$	47.7119	1.55868	0.779340	+	0.626601i	$0.215554\pi$
$938$	36.9166	1.20537
$939$	−15.7630	−0.514406
$940$	−9.31921	−0.303959
$941$	7.60185	0.247813	0.123907	−	0.992294i	$-0.460458\pi$
$941$	7.60185	0.247813	0.123907	+	0.992294i	$0.460458\pi$
$942$	13.5861	0.442659
$943$	24.1867	0.787629
$944$	2.76919	0.0901296
$945$	2.94272	0.0957267
$946$	−1.00169	−0.0325677
$947$	59.5418	1.93485	0.967424	−	0.253163i	$-0.0814708\pi$
$947$	59.5418	1.93485	0.967424	+	0.253163i	$0.0814708\pi$
$948$	0.998311	0.0324236
$949$	−18.9211	−0.614203
$950$	4.94272	0.160363
$951$	−9.10341	−0.295198
$952$	2.94272	0.0953741
$953$	−11.6086	−0.376040	−0.188020	−	0.982165i	$-0.560207\pi$
$953$	−11.6086	−0.376040	−0.188020	+	0.982165i	$0.560207\pi$
$954$	−1.44998	−0.0469450
$955$	4.14896	0.134257
$956$	2.37152	0.0767004
$957$	1.43377	0.0463471
$958$	8.10669	0.261915
$959$	12.3828	0.399860
$960$	−1.00000	−0.0322749
$961$	34.5027	1.11299
$962$	−20.7986	−0.670575
$963$	12.0378	0.387912
$964$	−29.2341	−0.941566
$965$	−8.88713	−0.286087
$966$	−12.0934	−0.389098
$967$	−44.1323	−1.41920	−0.709599	−	0.704606i	$-0.751124\pi$
$967$	−44.1323	−1.41920	−0.709599	+	0.704606i	$0.751124\pi$
$968$	−1.00000	−0.0321412
$969$	4.94272	0.158783
$970$	−11.1113	−0.356762
$971$	27.0350	0.867594	0.433797	−	0.901011i	$-0.357174\pi$
$971$	27.0350	0.867594	0.433797	+	0.901011i	$0.357174\pi$
$972$	−1.00000	−0.0320750
$973$	−49.1589	−1.57596
$974$	30.5239	0.978048
$975$	−1.77585	−0.0568728
$976$	2.65960	0.0851319
$977$	−24.1912	−0.773946	−0.386973	−	0.922091i	$-0.626479\pi$
$977$	−24.1912	−0.773946	−0.386973	+	0.922091i	$0.626479\pi$
$978$	2.71857	0.0869304
$979$	8.33374	0.266347
$980$	1.65960	0.0530141
$981$	−14.4305	−0.460730
$982$	37.4081	1.19374
$983$	43.6057	1.39081	0.695403	−	0.718620i	$-0.255226\pi$
$983$	43.6057	1.39081	0.695403	+	0.718620i	$0.255226\pi$
$984$	5.88544	0.187621
$985$	16.8119	0.535673
$986$	−1.43377	−0.0456605
$987$	−27.4238	−0.872910
$988$	−8.77754	−0.279251
$989$	−4.11653	−0.130898
$990$	1.00000	0.0317821
$991$	8.65960	0.275081	0.137541	−	0.990496i	$-0.456080\pi$
$991$	8.65960	0.275081	0.137541	+	0.990496i	$0.456080\pi$
$992$	8.09337	0.256965
$993$	−28.9789	−0.919618
$994$	−26.1424	−0.829187
$995$	23.7463	0.752809
$996$	3.60729	0.114302
$997$	32.0398	1.01471	0.507355	−	0.861737i	$-0.330623\pi$
$997$	32.0398	1.01471	0.507355	+	0.861737i	$0.330623\pi$
$998$	−2.76629	−0.0875655
$999$	−11.7119	−0.370549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ce.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ce.1.1	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.94272 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.94272 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +1.77585 q^{13} +2.94272 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -4.94272 q^{19} +1.00000 q^{20} +2.94272 q^{21} +1.00000 q^{22} +4.10959 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.77585 q^{26} -1.00000 q^{27} -2.94272 q^{28} +1.43377 q^{29} +1.00000 q^{30} -8.09337 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -2.94272 q^{35} +1.00000 q^{36} +11.7119 q^{37} +4.94272 q^{38} -1.77585 q^{39} -1.00000 q^{40} +5.88544 q^{41} -2.94272 q^{42} -1.00169 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.10959 q^{46} -9.31921 q^{47} -1.00000 q^{48} +1.65960 q^{49} -1.00000 q^{50} -1.00000 q^{51} +1.77585 q^{52} +1.44998 q^{53} +1.00000 q^{54} -1.00000 q^{55} +2.94272 q^{56} +4.94272 q^{57} -1.43377 q^{58} +2.76919 q^{59} -1.00000 q^{60} +2.65960 q^{61} +8.09337 q^{62} -2.94272 q^{63} +1.00000 q^{64} +1.77585 q^{65} -1.00000 q^{66} +12.5450 q^{67} +1.00000 q^{68} -4.10959 q^{69} +2.94272 q^{70} -8.88375 q^{71} -1.00000 q^{72} -10.6546 q^{73} -11.7119 q^{74} -1.00000 q^{75} -4.94272 q^{76} +2.94272 q^{77} +1.77585 q^{78} -0.998311 q^{79} +1.00000 q^{80} +1.00000 q^{81} -5.88544 q^{82} -3.60729 q^{83} +2.94272 q^{84} +1.00000 q^{85} +1.00169 q^{86} -1.43377 q^{87} +1.00000 q^{88} -8.33374 q^{89} -1.00000 q^{90} -5.22584 q^{91} +4.10959 q^{92} +8.09337 q^{93} +9.31921 q^{94} -4.94272 q^{95} +1.00000 q^{96} +11.1113 q^{97} -1.65960 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} + 3 q^{13} + q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 9 q^{19} + 4 q^{20} + q^{21} + 4 q^{22} - q^{23} + 4 q^{24} + 4 q^{25} - 3 q^{26} - 4 q^{27} - q^{28} - 8 q^{29} + 4 q^{30} - q^{31} - 4 q^{32} + 4 q^{33} - 4 q^{34} - q^{35} + 4 q^{36} + q^{37} + 9 q^{38} - 3 q^{39} - 4 q^{40} + 2 q^{41} - q^{42} + 4 q^{43} - 4 q^{44} + 4 q^{45} + q^{46} - 2 q^{47} - 4 q^{48} - 11 q^{49} - 4 q^{50} - 4 q^{51} + 3 q^{52} + 6 q^{53} + 4 q^{54} - 4 q^{55} + q^{56} + 9 q^{57} + 8 q^{58} - 24 q^{59} - 4 q^{60} - 7 q^{61} + q^{62} - q^{63} + 4 q^{64} + 3 q^{65} - 4 q^{66} + 11 q^{67} + 4 q^{68} + q^{69} + q^{70} - 22 q^{71} - 4 q^{72} + 14 q^{73} - q^{74} - 4 q^{75} - 9 q^{76} + q^{77} + 3 q^{78} - 12 q^{79} + 4 q^{80} + 4 q^{81} - 2 q^{82} - 25 q^{83} + q^{84} + 4 q^{85} - 4 q^{86} + 8 q^{87} + 4 q^{88} - 20 q^{89} - 4 q^{90} - 17 q^{91} - q^{92} + q^{93} + 2 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - q^7 - 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 + 3 * q^13 + q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 9 * q^19 + 4 * q^20 + q^21 + 4 * q^22 - q^23 + 4 * q^24 + 4 * q^25 - 3 * q^26 - 4 * q^27 - q^28 - 8 * q^29 + 4 * q^30 - q^31 - 4 * q^32 + 4 * q^33 - 4 * q^34 - q^35 + 4 * q^36 + q^37 + 9 * q^38 - 3 * q^39 - 4 * q^40 + 2 * q^41 - q^42 + 4 * q^43 - 4 * q^44 + 4 * q^45 + q^46 - 2 * q^47 - 4 * q^48 - 11 * q^49 - 4 * q^50 - 4 * q^51 + 3 * q^52 + 6 * q^53 + 4 * q^54 - 4 * q^55 + q^56 + 9 * q^57 + 8 * q^58 - 24 * q^59 - 4 * q^60 - 7 * q^61 + q^62 - q^63 + 4 * q^64 + 3 * q^65 - 4 * q^66 + 11 * q^67 + 4 * q^68 + q^69 + q^70 - 22 * q^71 - 4 * q^72 + 14 * q^73 - q^74 - 4 * q^75 - 9 * q^76 + q^77 + 3 * q^78 - 12 * q^79 + 4 * q^80 + 4 * q^81 - 2 * q^82 - 25 * q^83 + q^84 + 4 * q^85 - 4 * q^86 + 8 * q^87 + 4 * q^88 - 20 * q^89 - 4 * q^90 - 17 * q^91 - q^92 + q^93 + 2 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 11 * q^98 - 4 * q^99

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