LMFDB - Embedded newform 4830.2.a.by.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, 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("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.41855 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.26180 q^{17} -1.00000 q^{18} -3.41855 q^{19} +1.00000 q^{20} -1.00000 q^{21} -3.41855 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.41855 q^{29} +1.00000 q^{30} -5.26180 q^{31} -1.00000 q^{32} -3.41855 q^{33} +3.26180 q^{34} +1.00000 q^{35} +1.00000 q^{36} +10.6803 q^{37} +3.41855 q^{38} -2.00000 q^{39} -1.00000 q^{40} -6.68035 q^{41} +1.00000 q^{42} +5.26180 q^{43} +3.41855 q^{44} +1.00000 q^{45} -1.00000 q^{46} +3.41855 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +3.26180 q^{51} +2.00000 q^{52} +12.8371 q^{53} +1.00000 q^{54} +3.41855 q^{55} -1.00000 q^{56} +3.41855 q^{57} -5.41855 q^{58} -6.15676 q^{59} -1.00000 q^{60} +6.00000 q^{61} +5.26180 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +3.41855 q^{66} +9.57531 q^{67} -3.26180 q^{68} -1.00000 q^{69} -1.00000 q^{70} -9.57531 q^{71} -1.00000 q^{72} -4.83710 q^{73} -10.6803 q^{74} -1.00000 q^{75} -3.41855 q^{76} +3.41855 q^{77} +2.00000 q^{78} -4.68035 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.68035 q^{82} +3.10504 q^{83} -1.00000 q^{84} -3.26180 q^{85} -5.26180 q^{86} -5.41855 q^{87} -3.41855 q^{88} -0.156755 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} +5.26180 q^{93} -3.41855 q^{94} -3.41855 q^{95} +1.00000 q^{96} +1.31965 q^{97} -1.00000 q^{98} +3.41855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{30} - 8 q^{31} - 3 q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} + 10 q^{37} - 4 q^{38} - 6 q^{39} - 3 q^{40} + 2 q^{41} + 3 q^{42} + 8 q^{43} - 4 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} + 3 q^{54} - 4 q^{55} - 3 q^{56} - 4 q^{57} - 2 q^{58} - 12 q^{59} - 3 q^{60} + 18 q^{61} + 8 q^{62} + 3 q^{63} + 3 q^{64} + 6 q^{65} - 4 q^{66} + 8 q^{67} - 2 q^{68} - 3 q^{69} - 3 q^{70} - 8 q^{71} - 3 q^{72} + 14 q^{73} - 10 q^{74} - 3 q^{75} + 4 q^{76} - 4 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 8 q^{83} - 3 q^{84} - 2 q^{85} - 8 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 3 q^{90} + 6 q^{91} + 3 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{95} + 3 q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 + 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^30 - 8 * q^31 - 3 * q^32 + 4 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 + 10 * q^37 - 4 * q^38 - 6 * q^39 - 3 * q^40 + 2 * q^41 + 3 * q^42 + 8 * q^43 - 4 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 + 3 * q^54 - 4 * q^55 - 3 * q^56 - 4 * q^57 - 2 * q^58 - 12 * q^59 - 3 * q^60 + 18 * q^61 + 8 * q^62 + 3 * q^63 + 3 * q^64 + 6 * q^65 - 4 * q^66 + 8 * q^67 - 2 * q^68 - 3 * q^69 - 3 * q^70 - 8 * q^71 - 3 * q^72 + 14 * q^73 - 10 * q^74 - 3 * q^75 + 4 * q^76 - 4 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 8 * q^83 - 3 * q^84 - 2 * q^85 - 8 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 3 * q^90 + 6 * q^91 + 3 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^95 + 3 * q^96 + 26 * q^97 - 3 * 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
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	3.41855	1.03073	0.515366	−	0.856970i	$-0.327656\pi$
$11$	3.41855	1.03073	0.515366	+	0.856970i	$0.327656\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.26180	−0.791102	−0.395551	−	0.918444i	$-0.629446\pi$
$17$	−3.26180	−0.791102	−0.395551	+	0.918444i	$0.629446\pi$
$18$	−1.00000	−0.235702
$19$	−3.41855	−0.784269	−0.392135	−	0.919908i	$-0.628263\pi$
$19$	−3.41855	−0.784269	−0.392135	+	0.919908i	$0.628263\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−3.41855	−0.728837
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	5.41855	1.00620	0.503100	−	0.864228i	$-0.332193\pi$
$29$	5.41855	1.00620	0.503100	+	0.864228i	$0.332193\pi$
$30$	1.00000	0.182574
$31$	−5.26180	−0.945046	−0.472523	−	0.881318i	$-0.656657\pi$
$31$	−5.26180	−0.945046	−0.472523	+	0.881318i	$0.656657\pi$
$32$	−1.00000	−0.176777
$33$	−3.41855	−0.595093
$34$	3.26180	0.559393
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	10.6803	1.75584	0.877919	−	0.478809i	$-0.158931\pi$
$37$	10.6803	1.75584	0.877919	+	0.478809i	$0.158931\pi$
$38$	3.41855	0.554562
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	−6.68035	−1.04329	−0.521647	−	0.853161i	$-0.674682\pi$
$41$	−6.68035	−1.04329	−0.521647	+	0.853161i	$0.674682\pi$
$42$	1.00000	0.154303
$43$	5.26180	0.802416	0.401208	−	0.915987i	$-0.368590\pi$
$43$	5.26180	0.802416	0.401208	+	0.915987i	$0.368590\pi$
$44$	3.41855	0.515366
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	3.41855	0.498647	0.249323	−	0.968420i	$-0.419792\pi$
$47$	3.41855	0.498647	0.249323	+	0.968420i	$0.419792\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	3.26180	0.456743
$52$	2.00000	0.277350
$53$	12.8371	1.76331	0.881656	−	0.471893i	$-0.156429\pi$
$53$	12.8371	1.76331	0.881656	+	0.471893i	$0.156429\pi$
$54$	1.00000	0.136083
$55$	3.41855	0.460957
$56$	−1.00000	−0.133631
$57$	3.41855	0.452798
$58$	−5.41855	−0.711491
$59$	−6.15676	−0.801541	−0.400771	−	0.916178i	$-0.631258\pi$
$59$	−6.15676	−0.801541	−0.400771	+	0.916178i	$0.631258\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	5.26180	0.668249
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	3.41855	0.420795
$67$	9.57531	1.16981	0.584905	−	0.811102i	$-0.301132\pi$
$67$	9.57531	1.16981	0.584905	+	0.811102i	$0.301132\pi$
$68$	−3.26180	−0.395551
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	−9.57531	−1.13638	−0.568190	−	0.822897i	$-0.692356\pi$
$71$	−9.57531	−1.13638	−0.568190	+	0.822897i	$0.692356\pi$
$72$	−1.00000	−0.117851
$73$	−4.83710	−0.566140	−0.283070	−	0.959099i	$-0.591353\pi$
$73$	−4.83710	−0.566140	−0.283070	+	0.959099i	$0.591353\pi$
$74$	−10.6803	−1.24156
$75$	−1.00000	−0.115470
$76$	−3.41855	−0.392135
$77$	3.41855	0.389580
$78$	2.00000	0.226455
$79$	−4.68035	−0.526580	−0.263290	−	0.964717i	$-0.584808\pi$
$79$	−4.68035	−0.526580	−0.263290	+	0.964717i	$0.584808\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	6.68035	0.737721
$83$	3.10504	0.340822	0.170411	−	0.985373i	$-0.445490\pi$
$83$	3.10504	0.340822	0.170411	+	0.985373i	$0.445490\pi$
$84$	−1.00000	−0.109109
$85$	−3.26180	−0.353791
$86$	−5.26180	−0.567394
$87$	−5.41855	−0.580930
$88$	−3.41855	−0.364419
$89$	−0.156755	−0.0166160	−0.00830802	−	0.999965i	$-0.502645\pi$
$89$	−0.156755	−0.0166160	−0.00830802	+	0.999965i	$0.502645\pi$
$90$	−1.00000	−0.105409
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	5.26180	0.545623
$94$	−3.41855	−0.352597
$95$	−3.41855	−0.350736
$96$	1.00000	0.102062
$97$	1.31965	0.133991	0.0669953	−	0.997753i	$-0.478659\pi$
$97$	1.31965	0.133991	0.0669953	+	0.997753i	$0.478659\pi$
$98$	−1.00000	−0.101015
$99$	3.41855	0.343577
$100$	1.00000	0.100000
$101$	−7.84324	−0.780432	−0.390216	−	0.920723i	$-0.627600\pi$
$101$	−7.84324	−0.780432	−0.390216	+	0.920723i	$0.627600\pi$
$102$	−3.26180	−0.322966
$103$	−2.52359	−0.248657	−0.124328	−	0.992241i	$-0.539678\pi$
$103$	−2.52359	−0.248657	−0.124328	+	0.992241i	$0.539678\pi$
$104$	−2.00000	−0.196116
$105$	−1.00000	−0.0975900
$106$	−12.8371	−1.24685
$107$	15.2039	1.46982	0.734910	−	0.678165i	$-0.237224\pi$
$107$	15.2039	1.46982	0.734910	+	0.678165i	$0.237224\pi$
$108$	−1.00000	−0.0962250
$109$	13.5174	1.29474	0.647368	−	0.762177i	$-0.275870\pi$
$109$	13.5174	1.29474	0.647368	+	0.762177i	$0.275870\pi$
$110$	−3.41855	−0.325946
$111$	−10.6803	−1.01373
$112$	1.00000	0.0944911
$113$	−13.5174	−1.27161	−0.635807	−	0.771848i	$-0.719333\pi$
$113$	−13.5174	−1.27161	−0.635807	+	0.771848i	$0.719333\pi$
$114$	−3.41855	−0.320177
$115$	1.00000	0.0932505
$116$	5.41855	0.503100
$117$	2.00000	0.184900
$118$	6.15676	0.566775
$119$	−3.26180	−0.299008
$120$	1.00000	0.0912871
$121$	0.686489	0.0624081
$122$	−6.00000	−0.543214
$123$	6.68035	0.602347
$124$	−5.26180	−0.472523
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	5.57531	0.494728	0.247364	−	0.968923i	$-0.420436\pi$
$127$	5.57531	0.494728	0.247364	+	0.968923i	$0.420436\pi$
$128$	−1.00000	−0.0883883
$129$	−5.26180	−0.463275
$130$	−2.00000	−0.175412
$131$	−4.36683	−0.381532	−0.190766	−	0.981636i	$-0.561097\pi$
$131$	−4.36683	−0.381532	−0.190766	+	0.981636i	$0.561097\pi$
$132$	−3.41855	−0.297547
$133$	−3.41855	−0.296426
$134$	−9.57531	−0.827180
$135$	−1.00000	−0.0860663
$136$	3.26180	0.279697
$137$	−10.9939	−0.939269	−0.469634	−	0.882861i	$-0.655614\pi$
$137$	−10.9939	−0.939269	−0.469634	+	0.882861i	$0.655614\pi$
$138$	1.00000	0.0851257
$139$	−2.15676	−0.182934	−0.0914668	−	0.995808i	$-0.529156\pi$
$139$	−2.15676	−0.182934	−0.0914668	+	0.995808i	$0.529156\pi$
$140$	1.00000	0.0845154
$141$	−3.41855	−0.287894
$142$	9.57531	0.803542
$143$	6.83710	0.571747
$144$	1.00000	0.0833333
$145$	5.41855	0.449986
$146$	4.83710	0.400321
$147$	−1.00000	−0.0824786
$148$	10.6803	0.877919
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	1.00000	0.0816497
$151$	9.36069	0.761762	0.380881	−	0.924624i	$-0.375621\pi$
$151$	9.36069	0.761762	0.380881	+	0.924624i	$0.375621\pi$
$152$	3.41855	0.277281
$153$	−3.26180	−0.263701
$154$	−3.41855	−0.275475
$155$	−5.26180	−0.422638
$156$	−2.00000	−0.160128
$157$	12.5236	0.999491	0.499746	−	0.866172i	$-0.333427\pi$
$157$	12.5236	0.999491	0.499746	+	0.866172i	$0.333427\pi$
$158$	4.68035	0.372348
$159$	−12.8371	−1.01805
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	−0.366835	−0.0287327	−0.0143664	−	0.999897i	$-0.504573\pi$
$163$	−0.366835	−0.0287327	−0.0143664	+	0.999897i	$0.504573\pi$
$164$	−6.68035	−0.521647
$165$	−3.41855	−0.266134
$166$	−3.10504	−0.240998
$167$	11.4186	0.883594	0.441797	−	0.897115i	$-0.354341\pi$
$167$	11.4186	0.883594	0.441797	+	0.897115i	$0.354341\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	3.26180	0.250168
$171$	−3.41855	−0.261423
$172$	5.26180	0.401208
$173$	−22.4124	−1.70398	−0.851992	−	0.523555i	$-0.824605\pi$
$173$	−22.4124	−1.70398	−0.851992	+	0.523555i	$0.824605\pi$
$174$	5.41855	0.410779
$175$	1.00000	0.0755929
$176$	3.41855	0.257683
$177$	6.15676	0.462770
$178$	0.156755	0.0117493
$179$	−23.5174	−1.75778	−0.878888	−	0.477028i	$-0.841714\pi$
$179$	−23.5174	−1.75778	−0.878888	+	0.477028i	$0.841714\pi$
$180$	1.00000	0.0745356
$181$	23.3607	1.73639	0.868193	−	0.496226i	$-0.165281\pi$
$181$	23.3607	1.73639	0.868193	+	0.496226i	$0.165281\pi$
$182$	−2.00000	−0.148250
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	10.6803	0.785235
$186$	−5.26180	−0.385814
$187$	−11.1506	−0.815414
$188$	3.41855	0.249323
$189$	−1.00000	−0.0727393
$190$	3.41855	0.248008
$191$	6.15676	0.445487	0.222744	−	0.974877i	$-0.428499\pi$
$191$	6.15676	0.445487	0.222744	+	0.974877i	$0.428499\pi$
$192$	−1.00000	−0.0721688
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−1.31965	−0.0947456
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	−0.523590	−0.0373043	−0.0186521	−	0.999826i	$-0.505938\pi$
$197$	−0.523590	−0.0373043	−0.0186521	+	0.999826i	$0.505938\pi$
$198$	−3.41855	−0.242946
$199$	8.99386	0.637558	0.318779	−	0.947829i	$-0.396727\pi$
$199$	8.99386	0.637558	0.318779	+	0.947829i	$0.396727\pi$
$200$	−1.00000	−0.0707107
$201$	−9.57531	−0.675390
$202$	7.84324	0.551849
$203$	5.41855	0.380308
$204$	3.26180	0.228371
$205$	−6.68035	−0.466576
$206$	2.52359	0.175827
$207$	1.00000	0.0695048
$208$	2.00000	0.138675
$209$	−11.6865	−0.808371
$210$	1.00000	0.0690066
$211$	13.3607	0.919788	0.459894	−	0.887974i	$-0.347887\pi$
$211$	13.3607	0.919788	0.459894	+	0.887974i	$0.347887\pi$
$212$	12.8371	0.881656
$213$	9.57531	0.656089
$214$	−15.2039	−1.03932
$215$	5.26180	0.358851
$216$	1.00000	0.0680414
$217$	−5.26180	−0.357194
$218$	−13.5174	−0.915517
$219$	4.83710	0.326861
$220$	3.41855	0.230479
$221$	−6.52359	−0.438824
$222$	10.6803	0.716818
$223$	−9.67420	−0.647833	−0.323916	−	0.946086i	$-0.605000\pi$
$223$	−9.67420	−0.647833	−0.323916	+	0.946086i	$0.605000\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	13.5174	0.899167
$227$	15.4186	1.02337	0.511683	−	0.859175i	$-0.329022\pi$
$227$	15.4186	1.02337	0.511683	+	0.859175i	$0.329022\pi$
$228$	3.41855	0.226399
$229$	15.3607	1.01506	0.507532	−	0.861633i	$-0.330558\pi$
$229$	15.3607	1.01506	0.507532	+	0.861633i	$0.330558\pi$
$230$	−1.00000	−0.0659380
$231$	−3.41855	−0.224924
$232$	−5.41855	−0.355745
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−2.00000	−0.130744
$235$	3.41855	0.223002
$236$	−6.15676	−0.400771
$237$	4.68035	0.304021
$238$	3.26180	0.211431
$239$	−3.90110	−0.252341	−0.126171	−	0.992009i	$-0.540269\pi$
$239$	−3.90110	−0.252341	−0.126171	+	0.992009i	$0.540269\pi$
$240$	−1.00000	−0.0645497
$241$	9.05172	0.583072	0.291536	−	0.956560i	$-0.405834\pi$
$241$	9.05172	0.583072	0.291536	+	0.956560i	$0.405834\pi$
$242$	−0.686489	−0.0441292
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	1.00000	0.0638877
$246$	−6.68035	−0.425923
$247$	−6.83710	−0.435034
$248$	5.26180	0.334124
$249$	−3.10504	−0.196774
$250$	−1.00000	−0.0632456
$251$	3.20394	0.202231	0.101115	−	0.994875i	$-0.467759\pi$
$251$	3.20394	0.202231	0.101115	+	0.994875i	$0.467759\pi$
$252$	1.00000	0.0629941
$253$	3.41855	0.214922
$254$	−5.57531	−0.349826
$255$	3.26180	0.204262
$256$	1.00000	0.0625000
$257$	7.84324	0.489248	0.244624	−	0.969618i	$-0.421335\pi$
$257$	7.84324	0.489248	0.244624	+	0.969618i	$0.421335\pi$
$258$	5.26180	0.327585
$259$	10.6803	0.663644
$260$	2.00000	0.124035
$261$	5.41855	0.335400
$262$	4.36683	0.269784
$263$	2.52359	0.155611	0.0778056	−	0.996969i	$-0.475209\pi$
$263$	2.52359	0.155611	0.0778056	+	0.996969i	$0.475209\pi$
$264$	3.41855	0.210397
$265$	12.8371	0.788577
$266$	3.41855	0.209605
$267$	0.156755	0.00959328
$268$	9.57531	0.584905
$269$	6.36683	0.388193	0.194096	−	0.980982i	$-0.437823\pi$
$269$	6.36683	0.388193	0.194096	+	0.980982i	$0.437823\pi$
$270$	1.00000	0.0608581
$271$	16.4124	0.996983	0.498491	−	0.866895i	$-0.333888\pi$
$271$	16.4124	0.996983	0.498491	+	0.866895i	$0.333888\pi$
$272$	−3.26180	−0.197775
$273$	−2.00000	−0.121046
$274$	10.9939	0.664163
$275$	3.41855	0.206146
$276$	−1.00000	−0.0601929
$277$	−2.77924	−0.166989	−0.0834943	−	0.996508i	$-0.526608\pi$
$277$	−2.77924	−0.166989	−0.0834943	+	0.996508i	$0.526608\pi$
$278$	2.15676	0.129354
$279$	−5.26180	−0.315015
$280$	−1.00000	−0.0597614
$281$	−10.4124	−0.621152	−0.310576	−	0.950549i	$-0.600522\pi$
$281$	−10.4124	−0.621152	−0.310576	+	0.950549i	$0.600522\pi$
$282$	3.41855	0.203572
$283$	−4.99386	−0.296854	−0.148427	−	0.988923i	$-0.547421\pi$
$283$	−4.99386	−0.296854	−0.148427	+	0.988923i	$0.547421\pi$
$284$	−9.57531	−0.568190
$285$	3.41855	0.202497
$286$	−6.83710	−0.404286
$287$	−6.68035	−0.394328
$288$	−1.00000	−0.0589256
$289$	−6.36069	−0.374158
$290$	−5.41855	−0.318188
$291$	−1.31965	−0.0773595
$292$	−4.83710	−0.283070
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	1.00000	0.0583212
$295$	−6.15676	−0.358460
$296$	−10.6803	−0.620782
$297$	−3.41855	−0.198364
$298$	−6.00000	−0.347571
$299$	2.00000	0.115663
$300$	−1.00000	−0.0577350
$301$	5.26180	0.303285
$302$	−9.36069	−0.538647
$303$	7.84324	0.450583
$304$	−3.41855	−0.196067
$305$	6.00000	0.343559
$306$	3.26180	0.186464
$307$	−15.8843	−0.906564	−0.453282	−	0.891367i	$-0.649747\pi$
$307$	−15.8843	−0.906564	−0.453282	+	0.891367i	$0.649747\pi$
$308$	3.41855	0.194790
$309$	2.52359	0.143562
$310$	5.26180	0.298850
$311$	−4.99386	−0.283176	−0.141588	−	0.989926i	$-0.545221\pi$
$311$	−4.99386	−0.283176	−0.141588	+	0.989926i	$0.545221\pi$
$312$	2.00000	0.113228
$313$	24.3545	1.37660	0.688300	−	0.725426i	$-0.258357\pi$
$313$	24.3545	1.37660	0.688300	+	0.725426i	$0.258357\pi$
$314$	−12.5236	−0.706747
$315$	1.00000	0.0563436
$316$	−4.68035	−0.263290
$317$	27.9877	1.57195	0.785973	−	0.618260i	$-0.212162\pi$
$317$	27.9877	1.57195	0.785973	+	0.618260i	$0.212162\pi$
$318$	12.8371	0.719869
$319$	18.5236	1.03712
$320$	1.00000	0.0559017
$321$	−15.2039	−0.848601
$322$	−1.00000	−0.0557278
$323$	11.1506	0.620437
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	0.366835	0.0203171
$327$	−13.5174	−0.747517
$328$	6.68035	0.368860
$329$	3.41855	0.188471
$330$	3.41855	0.188185
$331$	−2.83710	−0.155941	−0.0779706	−	0.996956i	$-0.524844\pi$
$331$	−2.83710	−0.155941	−0.0779706	+	0.996956i	$0.524844\pi$
$332$	3.10504	0.170411
$333$	10.6803	0.585279
$334$	−11.4186	−0.624795
$335$	9.57531	0.523155
$336$	−1.00000	−0.0545545
$337$	14.5814	0.794302	0.397151	−	0.917753i	$-0.369999\pi$
$337$	14.5814	0.794302	0.397151	+	0.917753i	$0.369999\pi$
$338$	9.00000	0.489535
$339$	13.5174	0.734167
$340$	−3.26180	−0.176896
$341$	−17.9877	−0.974089
$342$	3.41855	0.184854
$343$	1.00000	0.0539949
$344$	−5.26180	−0.283697
$345$	−1.00000	−0.0538382
$346$	22.4124	1.20490
$347$	−32.5113	−1.74530	−0.872649	−	0.488348i	$-0.837600\pi$
$347$	−32.5113	−1.74530	−0.872649	+	0.488348i	$0.837600\pi$
$348$	−5.41855	−0.290465
$349$	2.58145	0.138182	0.0690909	−	0.997610i	$-0.477990\pi$
$349$	2.58145	0.138182	0.0690909	+	0.997610i	$0.477990\pi$
$350$	−1.00000	−0.0534522
$351$	−2.00000	−0.106752
$352$	−3.41855	−0.182209
$353$	−2.68035	−0.142660	−0.0713302	−	0.997453i	$-0.522724\pi$
$353$	−2.68035	−0.142660	−0.0713302	+	0.997453i	$0.522724\pi$
$354$	−6.15676	−0.327228
$355$	−9.57531	−0.508204
$356$	−0.156755	−0.00830802
$357$	3.26180	0.172633
$358$	23.5174	1.24294
$359$	6.15676	0.324941	0.162471	−	0.986713i	$-0.448054\pi$
$359$	6.15676	0.324941	0.162471	+	0.986713i	$0.448054\pi$
$360$	−1.00000	−0.0527046
$361$	−7.31351	−0.384922
$362$	−23.3607	−1.22781
$363$	−0.686489	−0.0360313
$364$	2.00000	0.104828
$365$	−4.83710	−0.253185
$366$	6.00000	0.313625
$367$	−8.19779	−0.427921	−0.213961	−	0.976842i	$-0.568636\pi$
$367$	−8.19779	−0.427921	−0.213961	+	0.976842i	$0.568636\pi$
$368$	1.00000	0.0521286
$369$	−6.68035	−0.347765
$370$	−10.6803	−0.555245
$371$	12.8371	0.666469
$372$	5.26180	0.272811
$373$	17.3197	0.896778	0.448389	−	0.893839i	$-0.351998\pi$
$373$	17.3197	0.896778	0.448389	+	0.893839i	$0.351998\pi$
$374$	11.1506	0.576584
$375$	−1.00000	−0.0516398
$376$	−3.41855	−0.176298
$377$	10.8371	0.558139
$378$	1.00000	0.0514344
$379$	−24.1978	−1.24296	−0.621479	−	0.783431i	$-0.713468\pi$
$379$	−24.1978	−1.24296	−0.621479	+	0.783431i	$0.713468\pi$
$380$	−3.41855	−0.175368
$381$	−5.57531	−0.285632
$382$	−6.15676	−0.315007
$383$	0.680346	0.0347641	0.0173820	−	0.999849i	$-0.494467\pi$
$383$	0.680346	0.0347641	0.0173820	+	0.999849i	$0.494467\pi$
$384$	1.00000	0.0510310
$385$	3.41855	0.174225
$386$	6.00000	0.305392
$387$	5.26180	0.267472
$388$	1.31965	0.0669953
$389$	12.2101	0.619076	0.309538	−	0.950887i	$-0.399826\pi$
$389$	12.2101	0.619076	0.309538	+	0.950887i	$0.399826\pi$
$390$	2.00000	0.101274
$391$	−3.26180	−0.164956
$392$	−1.00000	−0.0505076
$393$	4.36683	0.220278
$394$	0.523590	0.0263781
$395$	−4.68035	−0.235494
$396$	3.41855	0.171789
$397$	8.63931	0.433594	0.216797	−	0.976217i	$-0.430439\pi$
$397$	8.63931	0.433594	0.216797	+	0.976217i	$0.430439\pi$
$398$	−8.99386	−0.450821
$399$	3.41855	0.171142
$400$	1.00000	0.0500000
$401$	−22.2967	−1.11344	−0.556722	−	0.830699i	$-0.687941\pi$
$401$	−22.2967	−1.11344	−0.556722	+	0.830699i	$0.687941\pi$
$402$	9.57531	0.477573
$403$	−10.5236	−0.524217
$404$	−7.84324	−0.390216
$405$	1.00000	0.0496904
$406$	−5.41855	−0.268918
$407$	36.5113	1.80980
$408$	−3.26180	−0.161483
$409$	39.6742	1.96176	0.980882	−	0.194606i	$-0.0623428\pi$
$409$	39.6742	1.96176	0.980882	+	0.194606i	$0.0623428\pi$
$410$	6.68035	0.329919
$411$	10.9939	0.542287
$412$	−2.52359	−0.124328
$413$	−6.15676	−0.302954
$414$	−1.00000	−0.0491473
$415$	3.10504	0.152420
$416$	−2.00000	−0.0980581
$417$	2.15676	0.105617
$418$	11.6865	0.571605
$419$	−3.63317	−0.177492	−0.0887459	−	0.996054i	$-0.528286\pi$
$419$	−3.63317	−0.177492	−0.0887459	+	0.996054i	$0.528286\pi$
$420$	−1.00000	−0.0487950
$421$	20.1568	0.982380	0.491190	−	0.871052i	$-0.336562\pi$
$421$	20.1568	0.982380	0.491190	+	0.871052i	$0.336562\pi$
$422$	−13.3607	−0.650388
$423$	3.41855	0.166216
$424$	−12.8371	−0.623425
$425$	−3.26180	−0.158220
$426$	−9.57531	−0.463925
$427$	6.00000	0.290360
$428$	15.2039	0.734910
$429$	−6.83710	−0.330098
$430$	−5.26180	−0.253746
$431$	14.3545	0.691434	0.345717	−	0.938339i	$-0.387636\pi$
$431$	14.3545	0.691434	0.345717	+	0.938339i	$0.387636\pi$
$432$	−1.00000	−0.0481125
$433$	14.9939	0.720559	0.360279	−	0.932844i	$-0.382681\pi$
$433$	14.9939	0.720559	0.360279	+	0.932844i	$0.382681\pi$
$434$	5.26180	0.252574
$435$	−5.41855	−0.259800
$436$	13.5174	0.647368
$437$	−3.41855	−0.163531
$438$	−4.83710	−0.231126
$439$	7.78539	0.371576	0.185788	−	0.982590i	$-0.440516\pi$
$439$	7.78539	0.371576	0.185788	+	0.982590i	$0.440516\pi$
$440$	−3.41855	−0.162973
$441$	1.00000	0.0476190
$442$	6.52359	0.310296
$443$	17.4764	0.830329	0.415165	−	0.909746i	$-0.363724\pi$
$443$	17.4764	0.830329	0.415165	+	0.909746i	$0.363724\pi$
$444$	−10.6803	−0.506867
$445$	−0.156755	−0.00743092
$446$	9.67420	0.458087
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	−12.8371	−0.605820	−0.302910	−	0.953019i	$-0.597958\pi$
$449$	−12.8371	−0.605820	−0.302910	+	0.953019i	$0.597958\pi$
$450$	−1.00000	−0.0471405
$451$	−22.8371	−1.07536
$452$	−13.5174	−0.635807
$453$	−9.36069	−0.439804
$454$	−15.4186	−0.723628
$455$	2.00000	0.0937614
$456$	−3.41855	−0.160088
$457$	14.5814	0.682091	0.341046	−	0.940047i	$-0.389219\pi$
$457$	14.5814	0.682091	0.341046	+	0.940047i	$0.389219\pi$
$458$	−15.3607	−0.717758
$459$	3.26180	0.152248
$460$	1.00000	0.0466252
$461$	3.84324	0.178998	0.0894989	−	0.995987i	$-0.471473\pi$
$461$	3.84324	0.178998	0.0894989	+	0.995987i	$0.471473\pi$
$462$	3.41855	0.159045
$463$	26.6225	1.23725	0.618626	−	0.785686i	$-0.287690\pi$
$463$	26.6225	1.23725	0.618626	+	0.785686i	$0.287690\pi$
$464$	5.41855	0.251550
$465$	5.26180	0.244010
$466$	−14.0000	−0.648537
$467$	10.5692	0.489083	0.244541	−	0.969639i	$-0.421363\pi$
$467$	10.5692	0.489083	0.244541	+	0.969639i	$0.421363\pi$
$468$	2.00000	0.0924500
$469$	9.57531	0.442147
$470$	−3.41855	−0.157686
$471$	−12.5236	−0.577057
$472$	6.15676	0.283388
$473$	17.9877	0.827076
$474$	−4.68035	−0.214975
$475$	−3.41855	−0.156854
$476$	−3.26180	−0.149504
$477$	12.8371	0.587770
$478$	3.90110	0.178432
$479$	1.78992	0.0817836	0.0408918	−	0.999164i	$-0.486980\pi$
$479$	1.78992	0.0817836	0.0408918	+	0.999164i	$0.486980\pi$
$480$	1.00000	0.0456435
$481$	21.3607	0.973964
$482$	−9.05172	−0.412294
$483$	−1.00000	−0.0455016
$484$	0.686489	0.0312040
$485$	1.31965	0.0599224
$486$	1.00000	0.0453609
$487$	30.9360	1.40184	0.700922	−	0.713238i	$-0.252772\pi$
$487$	30.9360	1.40184	0.700922	+	0.713238i	$0.252772\pi$
$488$	−6.00000	−0.271607
$489$	0.366835	0.0165889
$490$	−1.00000	−0.0451754
$491$	19.8310	0.894959	0.447479	−	0.894294i	$-0.352322\pi$
$491$	19.8310	0.894959	0.447479	+	0.894294i	$0.352322\pi$
$492$	6.68035	0.301173
$493$	−17.6742	−0.796006
$494$	6.83710	0.307616
$495$	3.41855	0.153652
$496$	−5.26180	−0.236262
$497$	−9.57531	−0.429511
$498$	3.10504	0.139140
$499$	−27.0349	−1.21025	−0.605124	−	0.796131i	$-0.706876\pi$
$499$	−27.0349	−1.21025	−0.605124	+	0.796131i	$0.706876\pi$
$500$	1.00000	0.0447214
$501$	−11.4186	−0.510143
$502$	−3.20394	−0.142999
$503$	−25.8432	−1.15229	−0.576147	−	0.817346i	$-0.695444\pi$
$503$	−25.8432	−1.15229	−0.576147	+	0.817346i	$0.695444\pi$
$504$	−1.00000	−0.0445435
$505$	−7.84324	−0.349020
$506$	−3.41855	−0.151973
$507$	9.00000	0.399704
$508$	5.57531	0.247364
$509$	16.7838	0.743928	0.371964	−	0.928247i	$-0.378685\pi$
$509$	16.7838	0.743928	0.371964	+	0.928247i	$0.378685\pi$
$510$	−3.26180	−0.144435
$511$	−4.83710	−0.213981
$512$	−1.00000	−0.0441942
$513$	3.41855	0.150933
$514$	−7.84324	−0.345951
$515$	−2.52359	−0.111203
$516$	−5.26180	−0.231638
$517$	11.6865	0.513971
$518$	−10.6803	−0.469267
$519$	22.4124	0.983796
$520$	−2.00000	−0.0877058
$521$	−3.84324	−0.168376	−0.0841878	−	0.996450i	$-0.526830\pi$
$521$	−3.84324	−0.168376	−0.0841878	+	0.996450i	$0.526830\pi$
$522$	−5.41855	−0.237164
$523$	22.3545	0.977496	0.488748	−	0.872425i	$-0.337454\pi$
$523$	22.3545	0.977496	0.488748	+	0.872425i	$0.337454\pi$
$524$	−4.36683	−0.190766
$525$	−1.00000	−0.0436436
$526$	−2.52359	−0.110034
$527$	17.1629	0.747628
$528$	−3.41855	−0.148773
$529$	1.00000	0.0434783
$530$	−12.8371	−0.557608
$531$	−6.15676	−0.267180
$532$	−3.41855	−0.148213
$533$	−13.3607	−0.578716
$534$	−0.156755	−0.00678347
$535$	15.2039	0.657323
$536$	−9.57531	−0.413590
$537$	23.5174	1.01485
$538$	−6.36683	−0.274494
$539$	3.41855	0.147247
$540$	−1.00000	−0.0430331
$541$	35.2450	1.51530	0.757650	−	0.652661i	$-0.226347\pi$
$541$	35.2450	1.51530	0.757650	+	0.652661i	$0.226347\pi$
$542$	−16.4124	−0.704973
$543$	−23.3607	−1.00250
$544$	3.26180	0.139848
$545$	13.5174	0.579024
$546$	2.00000	0.0855921
$547$	16.3668	0.699795	0.349898	−	0.936788i	$-0.386216\pi$
$547$	16.3668	0.699795	0.349898	+	0.936788i	$0.386216\pi$
$548$	−10.9939	−0.469634
$549$	6.00000	0.256074
$550$	−3.41855	−0.145767
$551$	−18.5236	−0.789131
$552$	1.00000	0.0425628
$553$	−4.68035	−0.199029
$554$	2.77924	0.118079
$555$	−10.6803	−0.453355
$556$	−2.15676	−0.0914668
$557$	17.1506	0.726695	0.363347	−	0.931654i	$-0.381634\pi$
$557$	17.1506	0.726695	0.363347	+	0.931654i	$0.381634\pi$
$558$	5.26180	0.222750
$559$	10.5236	0.445100
$560$	1.00000	0.0422577
$561$	11.1506	0.470779
$562$	10.4124	0.439221
$563$	−10.5692	−0.445437	−0.222719	−	0.974883i	$-0.571493\pi$
$563$	−10.5692	−0.445437	−0.222719	+	0.974883i	$0.571493\pi$
$564$	−3.41855	−0.143947
$565$	−13.5174	−0.568683
$566$	4.99386	0.209907
$567$	1.00000	0.0419961
$568$	9.57531	0.401771
$569$	13.0517	0.547156	0.273578	−	0.961850i	$-0.411793\pi$
$569$	13.0517	0.547156	0.273578	+	0.961850i	$0.411793\pi$
$570$	−3.41855	−0.143187
$571$	−22.4079	−0.937740	−0.468870	−	0.883267i	$-0.655339\pi$
$571$	−22.4079	−0.937740	−0.468870	+	0.883267i	$0.655339\pi$
$572$	6.83710	0.285874
$573$	−6.15676	−0.257202
$574$	6.68035	0.278832
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	42.9315	1.78726	0.893630	−	0.448804i	$-0.148150\pi$
$577$	42.9315	1.78726	0.893630	+	0.448804i	$0.148150\pi$
$578$	6.36069	0.264570
$579$	6.00000	0.249351
$580$	5.41855	0.224993
$581$	3.10504	0.128819
$582$	1.31965	0.0547014
$583$	43.8843	1.81750
$584$	4.83710	0.200161
$585$	2.00000	0.0826898
$586$	2.00000	0.0826192
$587$	−28.6270	−1.18156	−0.590782	−	0.806831i	$-0.701181\pi$
$587$	−28.6270	−1.18156	−0.590782	+	0.806831i	$0.701181\pi$
$588$	−1.00000	−0.0412393
$589$	17.9877	0.741171
$590$	6.15676	0.253470
$591$	0.523590	0.0215376
$592$	10.6803	0.438960
$593$	22.8781	0.939493	0.469746	−	0.882801i	$-0.344345\pi$
$593$	22.8781	0.939493	0.469746	+	0.882801i	$0.344345\pi$
$594$	3.41855	0.140265
$595$	−3.26180	−0.133721
$596$	6.00000	0.245770
$597$	−8.99386	−0.368094
$598$	−2.00000	−0.0817861
$599$	−32.6102	−1.33242	−0.666208	−	0.745766i	$-0.732084\pi$
$599$	−32.6102	−1.33242	−0.666208	+	0.745766i	$0.732084\pi$
$600$	1.00000	0.0408248
$601$	34.1978	1.39496	0.697479	−	0.716606i	$-0.254305\pi$
$601$	34.1978	1.39496	0.697479	+	0.716606i	$0.254305\pi$
$602$	−5.26180	−0.214455
$603$	9.57531	0.389937
$604$	9.36069	0.380881
$605$	0.686489	0.0279097
$606$	−7.84324	−0.318610
$607$	39.8843	1.61885	0.809427	−	0.587221i	$-0.199778\pi$
$607$	39.8843	1.61885	0.809427	+	0.587221i	$0.199778\pi$
$608$	3.41855	0.138641
$609$	−5.41855	−0.219571
$610$	−6.00000	−0.242933
$611$	6.83710	0.276600
$612$	−3.26180	−0.131850
$613$	−10.7961	−0.436049	−0.218024	−	0.975943i	$-0.569961\pi$
$613$	−10.7961	−0.436049	−0.218024	+	0.975943i	$0.569961\pi$
$614$	15.8843	0.641037
$615$	6.68035	0.269378
$616$	−3.41855	−0.137737
$617$	7.52973	0.303136	0.151568	−	0.988447i	$-0.451568\pi$
$617$	7.52973	0.303136	0.151568	+	0.988447i	$0.451568\pi$
$618$	−2.52359	−0.101514
$619$	−9.62863	−0.387007	−0.193504	−	0.981100i	$-0.561985\pi$
$619$	−9.62863	−0.387007	−0.193504	+	0.981100i	$0.561985\pi$
$620$	−5.26180	−0.211319
$621$	−1.00000	−0.0401286
$622$	4.99386	0.200235
$623$	−0.156755	−0.00628028
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	−24.3545	−0.973404
$627$	11.6865	0.466713
$628$	12.5236	0.499746
$629$	−34.8371	−1.38905
$630$	−1.00000	−0.0398410
$631$	−17.7275	−0.705722	−0.352861	−	0.935676i	$-0.614791\pi$
$631$	−17.7275	−0.705722	−0.352861	+	0.935676i	$0.614791\pi$
$632$	4.68035	0.186174
$633$	−13.3607	−0.531040
$634$	−27.9877	−1.11153
$635$	5.57531	0.221249
$636$	−12.8371	−0.509024
$637$	2.00000	0.0792429
$638$	−18.5236	−0.733356
$639$	−9.57531	−0.378793
$640$	−1.00000	−0.0395285
$641$	−18.4124	−0.727246	−0.363623	−	0.931546i	$-0.618460\pi$
$641$	−18.4124	−0.727246	−0.363623	+	0.931546i	$0.618460\pi$
$642$	15.2039	0.600052
$643$	−17.8432	−0.703669	−0.351834	−	0.936062i	$-0.614442\pi$
$643$	−17.8432	−0.703669	−0.351834	+	0.936062i	$0.614442\pi$
$644$	1.00000	0.0394055
$645$	−5.26180	−0.207183
$646$	−11.1506	−0.438715
$647$	−9.09275	−0.357473	−0.178737	−	0.983897i	$-0.557201\pi$
$647$	−9.09275	−0.357473	−0.178737	+	0.983897i	$0.557201\pi$
$648$	−1.00000	−0.0392837
$649$	−21.0472	−0.826174
$650$	−2.00000	−0.0784465
$651$	5.26180	0.206226
$652$	−0.366835	−0.0143664
$653$	16.8371	0.658887	0.329443	−	0.944175i	$-0.393139\pi$
$653$	16.8371	0.658887	0.329443	+	0.944175i	$0.393139\pi$
$654$	13.5174	0.528574
$655$	−4.36683	−0.170626
$656$	−6.68035	−0.260824
$657$	−4.83710	−0.188713
$658$	−3.41855	−0.133269
$659$	−27.4186	−1.06808	−0.534038	−	0.845461i	$-0.679326\pi$
$659$	−27.4186	−1.06808	−0.534038	+	0.845461i	$0.679326\pi$
$660$	−3.41855	−0.133067
$661$	19.0472	0.740849	0.370425	−	0.928862i	$-0.379212\pi$
$661$	19.0472	0.740849	0.370425	+	0.928862i	$0.379212\pi$
$662$	2.83710	0.110267
$663$	6.52359	0.253355
$664$	−3.10504	−0.120499
$665$	−3.41855	−0.132566
$666$	−10.6803	−0.413855
$667$	5.41855	0.209807
$668$	11.4186	0.441797
$669$	9.67420	0.374026
$670$	−9.57531	−0.369926
$671$	20.5113	0.791830
$672$	1.00000	0.0385758
$673$	−26.5113	−1.02194	−0.510968	−	0.859600i	$-0.670713\pi$
$673$	−26.5113	−1.02194	−0.510968	+	0.859600i	$0.670713\pi$
$674$	−14.5814	−0.561656
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	38.3956	1.47566	0.737831	−	0.674985i	$-0.235850\pi$
$677$	38.3956	1.47566	0.737831	+	0.674985i	$0.235850\pi$
$678$	−13.5174	−0.519134
$679$	1.31965	0.0506437
$680$	3.26180	0.125084
$681$	−15.4186	−0.590840
$682$	17.9877	0.688785
$683$	10.8371	0.414670	0.207335	−	0.978270i	$-0.433521\pi$
$683$	10.8371	0.414670	0.207335	+	0.978270i	$0.433521\pi$
$684$	−3.41855	−0.130712
$685$	−10.9939	−0.420054
$686$	−1.00000	−0.0381802
$687$	−15.3607	−0.586047
$688$	5.26180	0.200604
$689$	25.6742	0.978109
$690$	1.00000	0.0380693
$691$	8.99386	0.342142	0.171071	−	0.985259i	$-0.445277\pi$
$691$	8.99386	0.342142	0.171071	+	0.985259i	$0.445277\pi$
$692$	−22.4124	−0.851992
$693$	3.41855	0.129860
$694$	32.5113	1.23411
$695$	−2.15676	−0.0818104
$696$	5.41855	0.205390
$697$	21.7899	0.825352
$698$	−2.58145	−0.0977093
$699$	−14.0000	−0.529529
$700$	1.00000	0.0377964
$701$	16.5236	0.624087	0.312044	−	0.950068i	$-0.398986\pi$
$701$	16.5236	0.624087	0.312044	+	0.950068i	$0.398986\pi$
$702$	2.00000	0.0754851
$703$	−36.5113	−1.37705
$704$	3.41855	0.128841
$705$	−3.41855	−0.128750
$706$	2.68035	0.100876
$707$	−7.84324	−0.294976
$708$	6.15676	0.231385
$709$	37.5174	1.40900	0.704499	−	0.709705i	$-0.251172\pi$
$709$	37.5174	1.40900	0.704499	+	0.709705i	$0.251172\pi$
$710$	9.57531	0.359355
$711$	−4.68035	−0.175527
$712$	0.156755	0.00587466
$713$	−5.26180	−0.197056
$714$	−3.26180	−0.122070
$715$	6.83710	0.255693
$716$	−23.5174	−0.878888
$717$	3.90110	0.145689
$718$	−6.15676	−0.229768
$719$	−23.7152	−0.884429	−0.442215	−	0.896909i	$-0.645807\pi$
$719$	−23.7152	−0.884429	−0.442215	+	0.896909i	$0.645807\pi$
$720$	1.00000	0.0372678
$721$	−2.52359	−0.0939834
$722$	7.31351	0.272181
$723$	−9.05172	−0.336637
$724$	23.3607	0.868193
$725$	5.41855	0.201240
$726$	0.686489	0.0254780
$727$	−19.6865	−0.730131	−0.365066	−	0.930982i	$-0.618953\pi$
$727$	−19.6865	−0.730131	−0.365066	+	0.930982i	$0.618953\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	4.83710	0.179029
$731$	−17.1629	−0.634793
$732$	−6.00000	−0.221766
$733$	−32.5236	−1.20129	−0.600643	−	0.799517i	$-0.705089\pi$
$733$	−32.5236	−1.20129	−0.600643	+	0.799517i	$0.705089\pi$
$734$	8.19779	0.302586
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	32.7337	1.20576
$738$	6.68035	0.245907
$739$	−44.8248	−1.64891	−0.824454	−	0.565929i	$-0.808517\pi$
$739$	−44.8248	−1.64891	−0.824454	+	0.565929i	$0.808517\pi$
$740$	10.6803	0.392617
$741$	6.83710	0.251167
$742$	−12.8371	−0.471265
$743$	−47.6619	−1.74855	−0.874273	−	0.485434i	$-0.838661\pi$
$743$	−47.6619	−1.74855	−0.874273	+	0.485434i	$0.838661\pi$
$744$	−5.26180	−0.192907
$745$	6.00000	0.219823
$746$	−17.3197	−0.634118
$747$	3.10504	0.113607
$748$	−11.1506	−0.407707
$749$	15.2039	0.555540
$750$	1.00000	0.0365148
$751$	−31.4017	−1.14587	−0.572933	−	0.819602i	$-0.694194\pi$
$751$	−31.4017	−1.14587	−0.572933	+	0.819602i	$0.694194\pi$
$752$	3.41855	0.124662
$753$	−3.20394	−0.116758
$754$	−10.8371	−0.394664
$755$	9.36069	0.340670
$756$	−1.00000	−0.0363696
$757$	11.8432	0.430450	0.215225	−	0.976564i	$-0.430952\pi$
$757$	11.8432	0.430450	0.215225	+	0.976564i	$0.430952\pi$
$758$	24.1978	0.878903
$759$	−3.41855	−0.124086
$760$	3.41855	0.124004
$761$	−10.9939	−0.398527	−0.199264	−	0.979946i	$-0.563855\pi$
$761$	−10.9939	−0.398527	−0.199264	+	0.979946i	$0.563855\pi$
$762$	5.57531	0.201972
$763$	13.5174	0.489364
$764$	6.15676	0.222744
$765$	−3.26180	−0.117930
$766$	−0.680346	−0.0245819
$767$	−12.3135	−0.444615
$768$	−1.00000	−0.0360844
$769$	−0.738205	−0.0266203	−0.0133102	−	0.999911i	$-0.504237\pi$
$769$	−0.738205	−0.0266203	−0.0133102	+	0.999911i	$0.504237\pi$
$770$	−3.41855	−0.123196
$771$	−7.84324	−0.282468
$772$	−6.00000	−0.215945
$773$	−20.5236	−0.738182	−0.369091	−	0.929393i	$-0.620331\pi$
$773$	−20.5236	−0.738182	−0.369091	+	0.929393i	$0.620331\pi$
$774$	−5.26180	−0.189131
$775$	−5.26180	−0.189009
$776$	−1.31965	−0.0473728
$777$	−10.6803	−0.383155
$778$	−12.2101	−0.437753
$779$	22.8371	0.818224
$780$	−2.00000	−0.0716115
$781$	−32.7337	−1.17130
$782$	3.26180	0.116642
$783$	−5.41855	−0.193643
$784$	1.00000	0.0357143
$785$	12.5236	0.446986
$786$	−4.36683	−0.155760
$787$	26.4703	0.943563	0.471782	−	0.881715i	$-0.343611\pi$
$787$	26.4703	0.943563	0.471782	+	0.881715i	$0.343611\pi$
$788$	−0.523590	−0.0186521
$789$	−2.52359	−0.0898422
$790$	4.68035	0.166519
$791$	−13.5174	−0.480625
$792$	−3.41855	−0.121473
$793$	12.0000	0.426132
$794$	−8.63931	−0.306598
$795$	−12.8371	−0.455285
$796$	8.99386	0.318779
$797$	−41.5708	−1.47251	−0.736256	−	0.676703i	$-0.763408\pi$
$797$	−41.5708	−1.47251	−0.736256	+	0.676703i	$0.763408\pi$
$798$	−3.41855	−0.121015
$799$	−11.1506	−0.394480
$800$	−1.00000	−0.0353553
$801$	−0.156755	−0.00553868
$802$	22.2967	0.787323
$803$	−16.5359	−0.583538
$804$	−9.57531	−0.337695
$805$	1.00000	0.0352454
$806$	10.5236	0.370678
$807$	−6.36683	−0.224123
$808$	7.84324	0.275924
$809$	33.0349	1.16145	0.580723	−	0.814102i	$-0.302770\pi$
$809$	33.0349	1.16145	0.580723	+	0.814102i	$0.302770\pi$
$810$	−1.00000	−0.0351364
$811$	−6.57691	−0.230947	−0.115473	−	0.993311i	$-0.536838\pi$
$811$	−6.57691	−0.230947	−0.115473	+	0.993311i	$0.536838\pi$
$812$	5.41855	0.190154
$813$	−16.4124	−0.575608
$814$	−36.5113	−1.27972
$815$	−0.366835	−0.0128497
$816$	3.26180	0.114186
$817$	−17.9877	−0.629310
$818$	−39.6742	−1.38718
$819$	2.00000	0.0698857
$820$	−6.68035	−0.233288
$821$	9.10504	0.317768	0.158884	−	0.987297i	$-0.449210\pi$
$821$	9.10504	0.317768	0.158884	+	0.987297i	$0.449210\pi$
$822$	−10.9939	−0.383455
$823$	−52.4124	−1.82698	−0.913491	−	0.406859i	$-0.866624\pi$
$823$	−52.4124	−1.82698	−0.913491	+	0.406859i	$0.866624\pi$
$824$	2.52359	0.0879134
$825$	−3.41855	−0.119019
$826$	6.15676	0.214221
$827$	−2.15676	−0.0749977	−0.0374989	−	0.999297i	$-0.511939\pi$
$827$	−2.15676	−0.0749977	−0.0374989	+	0.999297i	$0.511939\pi$
$828$	1.00000	0.0347524
$829$	−53.6163	−1.86217	−0.931086	−	0.364799i	$-0.881138\pi$
$829$	−53.6163	−1.86217	−0.931086	+	0.364799i	$0.881138\pi$
$830$	−3.10504	−0.107778
$831$	2.77924	0.0964109
$832$	2.00000	0.0693375
$833$	−3.26180	−0.113015
$834$	−2.15676	−0.0746823
$835$	11.4186	0.395155
$836$	−11.6865	−0.404186
$837$	5.26180	0.181874
$838$	3.63317	0.125506
$839$	28.5113	0.984320	0.492160	−	0.870505i	$-0.336208\pi$
$839$	28.5113	0.984320	0.492160	+	0.870505i	$0.336208\pi$
$840$	1.00000	0.0345033
$841$	0.360692	0.0124377
$842$	−20.1568	−0.694648
$843$	10.4124	0.358622
$844$	13.3607	0.459894
$845$	−9.00000	−0.309609
$846$	−3.41855	−0.117532
$847$	0.686489	0.0235880
$848$	12.8371	0.440828
$849$	4.99386	0.171389
$850$	3.26180	0.111879
$851$	10.6803	0.366118
$852$	9.57531	0.328045
$853$	−55.9877	−1.91698	−0.958491	−	0.285121i	$-0.907966\pi$
$853$	−55.9877	−1.91698	−0.958491	+	0.285121i	$0.907966\pi$
$854$	−6.00000	−0.205316
$855$	−3.41855	−0.116912
$856$	−15.2039	−0.519660
$857$	35.7275	1.22043	0.610215	−	0.792236i	$-0.291083\pi$
$857$	35.7275	1.22043	0.610215	+	0.792236i	$0.291083\pi$
$858$	6.83710	0.233415
$859$	−11.3197	−0.386222	−0.193111	−	0.981177i	$-0.561858\pi$
$859$	−11.3197	−0.386222	−0.193111	+	0.981177i	$0.561858\pi$
$860$	5.26180	0.179426
$861$	6.68035	0.227666
$862$	−14.3545	−0.488918
$863$	6.63931	0.226005	0.113002	−	0.993595i	$-0.463953\pi$
$863$	6.63931	0.226005	0.113002	+	0.993595i	$0.463953\pi$
$864$	1.00000	0.0340207
$865$	−22.4124	−0.762045
$866$	−14.9939	−0.509512
$867$	6.36069	0.216020
$868$	−5.26180	−0.178597
$869$	−16.0000	−0.542763
$870$	5.41855	0.183706
$871$	19.1506	0.648894
$872$	−13.5174	−0.457759
$873$	1.31965	0.0446635
$874$	3.41855	0.115634
$875$	1.00000	0.0338062
$876$	4.83710	0.163431
$877$	26.3591	0.890083	0.445042	−	0.895510i	$-0.353189\pi$
$877$	26.3591	0.890083	0.445042	+	0.895510i	$0.353189\pi$
$878$	−7.78539	−0.262744
$879$	2.00000	0.0674583
$880$	3.41855	0.115239
$881$	−27.4140	−0.923602	−0.461801	−	0.886984i	$-0.652797\pi$
$881$	−27.4140	−0.923602	−0.461801	+	0.886984i	$0.652797\pi$
$882$	−1.00000	−0.0336718
$883$	−58.3545	−1.96379	−0.981893	−	0.189434i	$-0.939335\pi$
$883$	−58.3545	−1.96379	−0.981893	+	0.189434i	$0.939335\pi$
$884$	−6.52359	−0.219412
$885$	6.15676	0.206957
$886$	−17.4764	−0.587131
$887$	−7.10504	−0.238564	−0.119282	−	0.992860i	$-0.538059\pi$
$887$	−7.10504	−0.238564	−0.119282	+	0.992860i	$0.538059\pi$
$888$	10.6803	0.358409
$889$	5.57531	0.186990
$890$	0.156755	0.00525446
$891$	3.41855	0.114526
$892$	−9.67420	−0.323916
$893$	−11.6865	−0.391073
$894$	6.00000	0.200670
$895$	−23.5174	−0.786102
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	12.8371	0.428380
$899$	−28.5113	−0.950905
$900$	1.00000	0.0333333
$901$	−41.8720	−1.39496
$902$	22.8371	0.760392
$903$	−5.26180	−0.175102
$904$	13.5174	0.449584
$905$	23.3607	0.776536
$906$	9.36069	0.310988
$907$	−9.57531	−0.317943	−0.158971	−	0.987283i	$-0.550818\pi$
$907$	−9.57531	−0.317943	−0.158971	+	0.987283i	$0.550818\pi$
$908$	15.4186	0.511683
$909$	−7.84324	−0.260144
$910$	−2.00000	−0.0662994
$911$	−25.3074	−0.838471	−0.419235	−	0.907878i	$-0.637702\pi$
$911$	−25.3074	−0.838471	−0.419235	+	0.907878i	$0.637702\pi$
$912$	3.41855	0.113200
$913$	10.6147	0.351296
$914$	−14.5814	−0.482311
$915$	−6.00000	−0.198354
$916$	15.3607	0.507532
$917$	−4.36683	−0.144206
$918$	−3.26180	−0.107655
$919$	41.9253	1.38299	0.691494	−	0.722382i	$-0.256953\pi$
$919$	41.9253	1.38299	0.691494	+	0.722382i	$0.256953\pi$
$920$	−1.00000	−0.0329690
$921$	15.8843	0.523405
$922$	−3.84324	−0.126571
$923$	−19.1506	−0.630350
$924$	−3.41855	−0.112462
$925$	10.6803	0.351168
$926$	−26.6225	−0.874869
$927$	−2.52359	−0.0828856
$928$	−5.41855	−0.177873
$929$	5.00614	0.164246	0.0821231	−	0.996622i	$-0.473830\pi$
$929$	5.00614	0.164246	0.0821231	+	0.996622i	$0.473830\pi$
$930$	−5.26180	−0.172541
$931$	−3.41855	−0.112038
$932$	14.0000	0.458585
$933$	4.99386	0.163492
$934$	−10.5692	−0.345834
$935$	−11.1506	−0.364664
$936$	−2.00000	−0.0653720
$937$	39.1917	1.28034	0.640168	−	0.768235i	$-0.278865\pi$
$937$	39.1917	1.28034	0.640168	+	0.768235i	$0.278865\pi$
$938$	−9.57531	−0.312645
$939$	−24.3545	−0.794781
$940$	3.41855	0.111501
$941$	41.3484	1.34792	0.673960	−	0.738768i	$-0.264592\pi$
$941$	41.3484	1.34792	0.673960	+	0.738768i	$0.264592\pi$
$942$	12.5236	0.408041
$943$	−6.68035	−0.217542
$944$	−6.15676	−0.200385
$945$	−1.00000	−0.0325300
$946$	−17.9877	−0.584831
$947$	25.0472	0.813924	0.406962	−	0.913445i	$-0.366588\pi$
$947$	25.0472	0.813924	0.406962	+	0.913445i	$0.366588\pi$
$948$	4.68035	0.152011
$949$	−9.67420	−0.314038
$950$	3.41855	0.110912
$951$	−27.9877	−0.907564
$952$	3.26180	0.105715
$953$	−29.5174	−0.956164	−0.478082	−	0.878315i	$-0.658668\pi$
$953$	−29.5174	−0.956164	−0.478082	+	0.878315i	$0.658668\pi$
$954$	−12.8371	−0.415617
$955$	6.15676	0.199228
$956$	−3.90110	−0.126171
$957$	−18.5236	−0.598783
$958$	−1.78992	−0.0578297
$959$	−10.9939	−0.355010
$960$	−1.00000	−0.0322749
$961$	−3.31351	−0.106887
$962$	−21.3607	−0.688696
$963$	15.2039	0.489940
$964$	9.05172	0.291536
$965$	−6.00000	−0.193147
$966$	1.00000	0.0321745
$967$	20.9483	0.673651	0.336826	−	0.941567i	$-0.390647\pi$
$967$	20.9483	0.673651	0.336826	+	0.941567i	$0.390647\pi$
$968$	−0.686489	−0.0220646
$969$	−11.1506	−0.358209
$970$	−1.31965	−0.0423715
$971$	20.5646	0.659950	0.329975	−	0.943990i	$-0.392960\pi$
$971$	20.5646	0.659950	0.329975	+	0.943990i	$0.392960\pi$
$972$	−1.00000	−0.0320750
$973$	−2.15676	−0.0691424
$974$	−30.9360	−0.991253
$975$	−2.00000	−0.0640513
$976$	6.00000	0.192055
$977$	41.5174	1.32826	0.664130	−	0.747617i	$-0.268802\pi$
$977$	41.5174	1.32826	0.664130	+	0.747617i	$0.268802\pi$
$978$	−0.366835	−0.0117301
$979$	−0.535877	−0.0171267
$980$	1.00000	0.0319438
$981$	13.5174	0.431579
$982$	−19.8310	−0.632831
$983$	−58.6681	−1.87122	−0.935610	−	0.353035i	$-0.885150\pi$
$983$	−58.6681	−1.87122	−0.935610	+	0.353035i	$0.885150\pi$
$984$	−6.68035	−0.212962
$985$	−0.523590	−0.0166830
$986$	17.6742	0.562861
$987$	−3.41855	−0.108814
$988$	−6.83710	−0.217517
$989$	5.26180	0.167315
$990$	−3.41855	−0.108649
$991$	−32.7337	−1.03982	−0.519910	−	0.854221i	$-0.674034\pi$
$991$	−32.7337	−1.03982	−0.519910	+	0.854221i	$0.674034\pi$
$992$	5.26180	0.167062
$993$	2.83710	0.0900327
$994$	9.57531	0.303710
$995$	8.99386	0.285124
$996$	−3.10504	−0.0983869
$997$	−21.0349	−0.666182	−0.333091	−	0.942895i	$-0.608092\pi$
$997$	−21.0349	−0.666182	−0.333091	+	0.942895i	$0.608092\pi$
$998$	27.0349	0.855775
$999$	−10.6803	−0.337911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.by.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.by.1.3	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.41855 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.26180 q^{17} -1.00000 q^{18} -3.41855 q^{19} +1.00000 q^{20} -1.00000 q^{21} -3.41855 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.41855 q^{29} +1.00000 q^{30} -5.26180 q^{31} -1.00000 q^{32} -3.41855 q^{33} +3.26180 q^{34} +1.00000 q^{35} +1.00000 q^{36} +10.6803 q^{37} +3.41855 q^{38} -2.00000 q^{39} -1.00000 q^{40} -6.68035 q^{41} +1.00000 q^{42} +5.26180 q^{43} +3.41855 q^{44} +1.00000 q^{45} -1.00000 q^{46} +3.41855 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +3.26180 q^{51} +2.00000 q^{52} +12.8371 q^{53} +1.00000 q^{54} +3.41855 q^{55} -1.00000 q^{56} +3.41855 q^{57} -5.41855 q^{58} -6.15676 q^{59} -1.00000 q^{60} +6.00000 q^{61} +5.26180 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} +3.41855 q^{66} +9.57531 q^{67} -3.26180 q^{68} -1.00000 q^{69} -1.00000 q^{70} -9.57531 q^{71} -1.00000 q^{72} -4.83710 q^{73} -10.6803 q^{74} -1.00000 q^{75} -3.41855 q^{76} +3.41855 q^{77} +2.00000 q^{78} -4.68035 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.68035 q^{82} +3.10504 q^{83} -1.00000 q^{84} -3.26180 q^{85} -5.26180 q^{86} -5.41855 q^{87} -3.41855 q^{88} -0.156755 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} +5.26180 q^{93} -3.41855 q^{94} -3.41855 q^{95} +1.00000 q^{96} +1.31965 q^{97} -1.00000 q^{98} +3.41855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{30} - 8 q^{31} - 3 q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} + 10 q^{37} - 4 q^{38} - 6 q^{39} - 3 q^{40} + 2 q^{41} + 3 q^{42} + 8 q^{43} - 4 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} + 3 q^{54} - 4 q^{55} - 3 q^{56} - 4 q^{57} - 2 q^{58} - 12 q^{59} - 3 q^{60} + 18 q^{61} + 8 q^{62} + 3 q^{63} + 3 q^{64} + 6 q^{65} - 4 q^{66} + 8 q^{67} - 2 q^{68} - 3 q^{69} - 3 q^{70} - 8 q^{71} - 3 q^{72} + 14 q^{73} - 10 q^{74} - 3 q^{75} + 4 q^{76} - 4 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 8 q^{83} - 3 q^{84} - 2 q^{85} - 8 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 3 q^{90} + 6 q^{91} + 3 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{95} + 3 q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 + 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^30 - 8 * q^31 - 3 * q^32 + 4 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 + 10 * q^37 - 4 * q^38 - 6 * q^39 - 3 * q^40 + 2 * q^41 + 3 * q^42 + 8 * q^43 - 4 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 + 3 * q^54 - 4 * q^55 - 3 * q^56 - 4 * q^57 - 2 * q^58 - 12 * q^59 - 3 * q^60 + 18 * q^61 + 8 * q^62 + 3 * q^63 + 3 * q^64 + 6 * q^65 - 4 * q^66 + 8 * q^67 - 2 * q^68 - 3 * q^69 - 3 * q^70 - 8 * q^71 - 3 * q^72 + 14 * q^73 - 10 * q^74 - 3 * q^75 + 4 * q^76 - 4 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 8 * q^83 - 3 * q^84 - 2 * q^85 - 8 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 3 * q^90 + 6 * q^91 + 3 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^95 + 3 * q^96 + 26 * q^97 - 3 * q^98 - 4 * q^99

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