LMFDB - Embedded newform 4830.2.a.by.1.2

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			1.2
Root			$-1.48119$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.61213 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +6.31265 q^{17} -1.00000 q^{18} +1.61213 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.61213 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.387873 q^{29} +1.00000 q^{30} +4.31265 q^{31} -1.00000 q^{32} +1.61213 q^{33} -6.31265 q^{34} +1.00000 q^{35} +1.00000 q^{36} -3.92478 q^{37} -1.61213 q^{38} -2.00000 q^{39} -1.00000 q^{40} +7.92478 q^{41} +1.00000 q^{42} -4.31265 q^{43} -1.61213 q^{44} +1.00000 q^{45} -1.00000 q^{46} -1.61213 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -6.31265 q^{51} +2.00000 q^{52} +2.77575 q^{53} +1.00000 q^{54} -1.61213 q^{55} -1.00000 q^{56} -1.61213 q^{57} -0.387873 q^{58} -10.7005 q^{59} -1.00000 q^{60} +6.00000 q^{61} -4.31265 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.61213 q^{66} +9.08840 q^{67} +6.31265 q^{68} -1.00000 q^{69} -1.00000 q^{70} -9.08840 q^{71} -1.00000 q^{72} +5.22425 q^{73} +3.92478 q^{74} -1.00000 q^{75} +1.61213 q^{76} -1.61213 q^{77} +2.00000 q^{78} +9.92478 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.92478 q^{82} -11.0132 q^{83} -1.00000 q^{84} +6.31265 q^{85} +4.31265 q^{86} -0.387873 q^{87} +1.61213 q^{88} -4.70052 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} -4.31265 q^{93} +1.61213 q^{94} +1.61213 q^{95} +1.00000 q^{96} +15.9248 q^{97} -1.00000 q^{98} -1.61213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−1.61213	−0.486075	−0.243037	−	0.970017i	$-0.578144\pi$
$11$	−1.61213	−0.486075	−0.243037	+	0.970017i	$0.578144\pi$
$12$	−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
$17$	6.31265	1.53104	0.765521	−	0.643411i	$-0.222481\pi$
$17$	6.31265	1.53104	0.765521	+	0.643411i	$0.222481\pi$
$18$	−1.00000	−0.235702
$19$	1.61213	0.369847	0.184924	−	0.982753i	$-0.440796\pi$
$19$	1.61213	0.369847	0.184924	+	0.982753i	$0.440796\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	1.61213	0.343707
$23$	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
$29$	0.387873	0.0720262	0.0360131	−	0.999351i	$-0.488534\pi$
$29$	0.387873	0.0720262	0.0360131	+	0.999351i	$0.488534\pi$
$30$	1.00000	0.182574
$31$	4.31265	0.774575	0.387287	−	0.921959i	$-0.373412\pi$
$31$	4.31265	0.774575	0.387287	+	0.921959i	$0.373412\pi$
$32$	−1.00000	−0.176777
$33$	1.61213	0.280635
$34$	−6.31265	−1.08261
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−3.92478	−0.645229	−0.322615	−	0.946530i	$-0.604562\pi$
$37$	−3.92478	−0.645229	−0.322615	+	0.946530i	$0.604562\pi$
$38$	−1.61213	−0.261522
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	7.92478	1.23764	0.618821	−	0.785532i	$-0.287611\pi$
$41$	7.92478	1.23764	0.618821	+	0.785532i	$0.287611\pi$
$42$	1.00000	0.154303
$43$	−4.31265	−0.657673	−0.328837	−	0.944387i	$-0.606657\pi$
$43$	−4.31265	−0.657673	−0.328837	+	0.944387i	$0.606657\pi$
$44$	−1.61213	−0.243037
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−1.61213	−0.235153	−0.117576	−	0.993064i	$-0.537513\pi$
$47$	−1.61213	−0.235153	−0.117576	+	0.993064i	$0.537513\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−6.31265	−0.883948
$52$	2.00000	0.277350
$53$	2.77575	0.381278	0.190639	−	0.981660i	$-0.438944\pi$
$53$	2.77575	0.381278	0.190639	+	0.981660i	$0.438944\pi$
$54$	1.00000	0.136083
$55$	−1.61213	−0.217379
$56$	−1.00000	−0.133631
$57$	−1.61213	−0.213531
$58$	−0.387873	−0.0509302
$59$	−10.7005	−1.39309	−0.696545	−	0.717513i	$-0.745280\pi$
$59$	−10.7005	−1.39309	−0.696545	+	0.717513i	$0.745280\pi$
$60$	−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	$0.374508\pi$
$62$	−4.31265	−0.547707
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−1.61213	−0.198439
$67$	9.08840	1.11032	0.555162	−	0.831742i	$-0.312656\pi$
$67$	9.08840	1.11032	0.555162	+	0.831742i	$0.312656\pi$
$68$	6.31265	0.765521
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	−9.08840	−1.07859	−0.539297	−	0.842116i	$-0.681310\pi$
$71$	−9.08840	−1.07859	−0.539297	+	0.842116i	$0.681310\pi$
$72$	−1.00000	−0.117851
$73$	5.22425	0.611453	0.305726	−	0.952119i	$-0.401101\pi$
$73$	5.22425	0.611453	0.305726	+	0.952119i	$0.401101\pi$
$74$	3.92478	0.456246
$75$	−1.00000	−0.115470
$76$	1.61213	0.184924
$77$	−1.61213	−0.183719
$78$	2.00000	0.226455
$79$	9.92478	1.11662	0.558312	−	0.829631i	$-0.311449\pi$
$79$	9.92478	1.11662	0.558312	+	0.829631i	$0.311449\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−7.92478	−0.875145
$83$	−11.0132	−1.20885	−0.604426	−	0.796661i	$-0.706598\pi$
$83$	−11.0132	−1.20885	−0.604426	+	0.796661i	$0.706598\pi$
$84$	−1.00000	−0.109109
$85$	6.31265	0.684703
$86$	4.31265	0.465045
$87$	−0.387873	−0.0415844
$88$	1.61213	0.171853
$89$	−4.70052	−0.498254	−0.249127	−	0.968471i	$-0.580144\pi$
$89$	−4.70052	−0.498254	−0.249127	+	0.968471i	$0.580144\pi$
$90$	−1.00000	−0.105409
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	−4.31265	−0.447201
$94$	1.61213	0.166278
$95$	1.61213	0.165401
$96$	1.00000	0.102062
$97$	15.9248	1.61692	0.808458	−	0.588554i	$-0.200302\pi$
$97$	15.9248	1.61692	0.808458	+	0.588554i	$0.200302\pi$
$98$	−1.00000	−0.101015
$99$	−1.61213	−0.162025
$100$	1.00000	0.100000
$101$	−3.29948	−0.328310	−0.164155	−	0.986435i	$-0.552490\pi$
$101$	−3.29948	−0.328310	−0.164155	+	0.986435i	$0.552490\pi$
$102$	6.31265	0.625046
$103$	16.6253	1.63814	0.819070	−	0.573694i	$-0.194490\pi$
$103$	16.6253	1.63814	0.819070	+	0.573694i	$0.194490\pi$
$104$	−2.00000	−0.196116
$105$	−1.00000	−0.0975900
$106$	−2.77575	−0.269604
$107$	−18.5501	−1.79330	−0.896652	−	0.442736i	$-0.854008\pi$
$107$	−18.5501	−1.79330	−0.896652	+	0.442736i	$0.854008\pi$
$108$	−1.00000	−0.0962250
$109$	−11.1490	−1.06788	−0.533942	−	0.845521i	$-0.679290\pi$
$109$	−11.1490	−1.06788	−0.533942	+	0.845521i	$0.679290\pi$
$110$	1.61213	0.153710
$111$	3.92478	0.372523
$112$	1.00000	0.0944911
$113$	11.1490	1.04881	0.524406	−	0.851468i	$-0.324287\pi$
$113$	11.1490	1.04881	0.524406	+	0.851468i	$0.324287\pi$
$114$	1.61213	0.150990
$115$	1.00000	0.0932505
$116$	0.387873	0.0360131
$117$	2.00000	0.184900
$118$	10.7005	0.985063
$119$	6.31265	0.578680
$120$	1.00000	0.0912871
$121$	−8.40105	−0.763732
$122$	−6.00000	−0.543214
$123$	−7.92478	−0.714553
$124$	4.31265	0.387287
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	5.08840	0.451522	0.225761	−	0.974183i	$-0.427513\pi$
$127$	5.08840	0.451522	0.225761	+	0.974183i	$0.427513\pi$
$128$	−1.00000	−0.0883883
$129$	4.31265	0.379708
$130$	−2.00000	−0.175412
$131$	19.3258	1.68851	0.844253	−	0.535946i	$-0.180045\pi$
$131$	19.3258	1.68851	0.844253	+	0.535946i	$0.180045\pi$
$132$	1.61213	0.140318
$133$	1.61213	0.139789
$134$	−9.08840	−0.785118
$135$	−1.00000	−0.0860663
$136$	−6.31265	−0.541305
$137$	−5.47627	−0.467869	−0.233935	−	0.972252i	$-0.575160\pi$
$137$	−5.47627	−0.467869	−0.233935	+	0.972252i	$0.575160\pi$
$138$	1.00000	0.0851257
$139$	−6.70052	−0.568331	−0.284165	−	0.958775i	$-0.591717\pi$
$139$	−6.70052	−0.568331	−0.284165	+	0.958775i	$0.591717\pi$
$140$	1.00000	0.0845154
$141$	1.61213	0.135766
$142$	9.08840	0.762681
$143$	−3.22425	−0.269626
$144$	1.00000	0.0833333
$145$	0.387873	0.0322111
$146$	−5.22425	−0.432362
$147$	−1.00000	−0.0824786
$148$	−3.92478	−0.322615
$149$	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
$151$	−19.8496	−1.61533	−0.807667	−	0.589639i	$-0.799270\pi$
$151$	−19.8496	−1.61533	−0.807667	+	0.589639i	$0.799270\pi$
$152$	−1.61213	−0.130761
$153$	6.31265	0.510348
$154$	1.61213	0.129909
$155$	4.31265	0.346400
$156$	−2.00000	−0.160128
$157$	−6.62530	−0.528757	−0.264378	−	0.964419i	$-0.585167\pi$
$157$	−6.62530	−0.528757	−0.264378	+	0.964419i	$0.585167\pi$
$158$	−9.92478	−0.789573
$159$	−2.77575	−0.220131
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	23.3258	1.82702	0.913510	−	0.406817i	$-0.133361\pi$
$163$	23.3258	1.82702	0.913510	+	0.406817i	$0.133361\pi$
$164$	7.92478	0.618821
$165$	1.61213	0.125504
$166$	11.0132	0.854788
$167$	6.38787	0.494308	0.247154	−	0.968976i	$-0.420505\pi$
$167$	6.38787	0.494308	0.247154	+	0.968976i	$0.420505\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	−6.31265	−0.484158
$171$	1.61213	0.123282
$172$	−4.31265	−0.328837
$173$	−11.8641	−0.902014	−0.451007	−	0.892520i	$-0.648935\pi$
$173$	−11.8641	−0.902014	−0.451007	+	0.892520i	$0.648935\pi$
$174$	0.387873	0.0294046
$175$	1.00000	0.0755929
$176$	−1.61213	−0.121519
$177$	10.7005	0.804301
$178$	4.70052	0.352319
$179$	1.14903	0.0858826	0.0429413	−	0.999078i	$-0.486327\pi$
$179$	1.14903	0.0858826	0.0429413	+	0.999078i	$0.486327\pi$
$180$	1.00000	0.0745356
$181$	−5.84955	−0.434794	−0.217397	−	0.976083i	$-0.569757\pi$
$181$	−5.84955	−0.434794	−0.217397	+	0.976083i	$0.569757\pi$
$182$	−2.00000	−0.148250
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	−3.92478	−0.288555
$186$	4.31265	0.316219
$187$	−10.1768	−0.744201
$188$	−1.61213	−0.117576
$189$	−1.00000	−0.0727393
$190$	−1.61213	−0.116956
$191$	10.7005	0.774263	0.387131	−	0.922025i	$-0.373466\pi$
$191$	10.7005	0.774263	0.387131	+	0.922025i	$0.373466\pi$
$192$	−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	$0.569283\pi$
$194$	−15.9248	−1.14333
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	18.6253	1.32700	0.663499	−	0.748177i	$-0.269071\pi$
$197$	18.6253	1.32700	0.663499	+	0.748177i	$0.269071\pi$
$198$	1.61213	0.114569
$199$	3.47627	0.246426	0.123213	−	0.992380i	$-0.460680\pi$
$199$	3.47627	0.246426	0.123213	+	0.992380i	$0.460680\pi$
$200$	−1.00000	−0.0707107
$201$	−9.08840	−0.641046
$202$	3.29948	0.232150
$203$	0.387873	0.0272234
$204$	−6.31265	−0.441974
$205$	7.92478	0.553490
$206$	−16.6253	−1.15834
$207$	1.00000	0.0695048
$208$	2.00000	0.138675
$209$	−2.59895	−0.179773
$210$	1.00000	0.0690066
$211$	−15.8496	−1.09113	−0.545564	−	0.838069i	$-0.683685\pi$
$211$	−15.8496	−1.09113	−0.545564	+	0.838069i	$0.683685\pi$
$212$	2.77575	0.190639
$213$	9.08840	0.622727
$214$	18.5501	1.26806
$215$	−4.31265	−0.294120
$216$	1.00000	0.0680414
$217$	4.31265	0.292762
$218$	11.1490	0.755108
$219$	−5.22425	−0.353022
$220$	−1.61213	−0.108690
$221$	12.6253	0.849270
$222$	−3.92478	−0.263414
$223$	10.4485	0.699684	0.349842	−	0.936809i	$-0.386235\pi$
$223$	10.4485	0.699684	0.349842	+	0.936809i	$0.386235\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−11.1490	−0.741623
$227$	10.3879	0.689467	0.344734	−	0.938701i	$-0.387969\pi$
$227$	10.3879	0.689467	0.344734	+	0.938701i	$0.387969\pi$
$228$	−1.61213	−0.106766
$229$	−13.8496	−0.915204	−0.457602	−	0.889157i	$-0.651292\pi$
$229$	−13.8496	−0.915204	−0.457602	+	0.889157i	$0.651292\pi$
$230$	−1.00000	−0.0659380
$231$	1.61213	0.106070
$232$	−0.387873	−0.0254651
$233$	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
$235$	−1.61213	−0.105164
$236$	−10.7005	−0.696545
$237$	−9.92478	−0.644684
$238$	−6.31265	−0.409188
$239$	−23.5369	−1.52248	−0.761238	−	0.648473i	$-0.775408\pi$
$239$	−23.5369	−1.52248	−0.761238	+	0.648473i	$0.775408\pi$
$240$	−1.00000	−0.0645497
$241$	27.7137	1.78520	0.892598	−	0.450853i	$-0.148880\pi$
$241$	27.7137	1.78520	0.892598	+	0.450853i	$0.148880\pi$
$242$	8.40105	0.540040
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	1.00000	0.0638877
$246$	7.92478	0.505265
$247$	3.22425	0.205154
$248$	−4.31265	−0.273854
$249$	11.0132	0.697932
$250$	−1.00000	−0.0632456
$251$	−30.5501	−1.92830	−0.964152	−	0.265351i	$-0.914512\pi$
$251$	−30.5501	−1.92830	−0.964152	+	0.265351i	$0.914512\pi$
$252$	1.00000	0.0629941
$253$	−1.61213	−0.101354
$254$	−5.08840	−0.319274
$255$	−6.31265	−0.395313
$256$	1.00000	0.0625000
$257$	3.29948	0.205816	0.102908	−	0.994691i	$-0.467185\pi$
$257$	3.29948	0.205816	0.102908	+	0.994691i	$0.467185\pi$
$258$	−4.31265	−0.268494
$259$	−3.92478	−0.243874
$260$	2.00000	0.124035
$261$	0.387873	0.0240087
$262$	−19.3258	−1.19395
$263$	−16.6253	−1.02516	−0.512580	−	0.858639i	$-0.671310\pi$
$263$	−16.6253	−1.02516	−0.512580	+	0.858639i	$0.671310\pi$
$264$	−1.61213	−0.0992195
$265$	2.77575	0.170513
$266$	−1.61213	−0.0988458
$267$	4.70052	0.287667
$268$	9.08840	0.555162
$269$	−17.3258	−1.05637	−0.528187	−	0.849128i	$-0.677128\pi$
$269$	−17.3258	−1.05637	−0.528187	+	0.849128i	$0.677128\pi$
$270$	1.00000	0.0608581
$271$	5.86414	0.356221	0.178111	−	0.984010i	$-0.443001\pi$
$271$	5.86414	0.356221	0.178111	+	0.984010i	$0.443001\pi$
$272$	6.31265	0.382761
$273$	−2.00000	−0.121046
$274$	5.47627	0.330834
$275$	−1.61213	−0.0972149
$276$	−1.00000	−0.0601929
$277$	31.4617	1.89035	0.945175	−	0.326565i	$-0.105891\pi$
$277$	31.4617	1.89035	0.945175	+	0.326565i	$0.105891\pi$
$278$	6.70052	0.401871
$279$	4.31265	0.258192
$280$	−1.00000	−0.0597614
$281$	0.135857	0.00810456	0.00405228	−	0.999992i	$-0.498710\pi$
$281$	0.135857	0.00810456	0.00405228	+	0.999992i	$0.498710\pi$
$282$	−1.61213	−0.0960008
$283$	0.523730	0.0311325	0.0155663	−	0.999879i	$-0.495045\pi$
$283$	0.523730	0.0311325	0.0155663	+	0.999879i	$0.495045\pi$
$284$	−9.08840	−0.539297
$285$	−1.61213	−0.0954942
$286$	3.22425	0.190654
$287$	7.92478	0.467785
$288$	−1.00000	−0.0589256
$289$	22.8496	1.34409
$290$	−0.387873	−0.0227767
$291$	−15.9248	−0.933527
$292$	5.22425	0.305726
$293$	−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
$295$	−10.7005	−0.623009
$296$	3.92478	0.228123
$297$	1.61213	0.0935451
$298$	−6.00000	−0.347571
$299$	2.00000	0.115663
$300$	−1.00000	−0.0577350
$301$	−4.31265	−0.248577
$302$	19.8496	1.14221
$303$	3.29948	0.189550
$304$	1.61213	0.0924618
$305$	6.00000	0.343559
$306$	−6.31265	−0.360870
$307$	32.4749	1.85344	0.926719	−	0.375755i	$-0.122617\pi$
$307$	32.4749	1.85344	0.926719	+	0.375755i	$0.122617\pi$
$308$	−1.61213	−0.0918595
$309$	−16.6253	−0.945780
$310$	−4.31265	−0.244942
$311$	0.523730	0.0296980	0.0148490	−	0.999890i	$-0.495273\pi$
$311$	0.523730	0.0296980	0.0148490	+	0.999890i	$0.495273\pi$
$312$	2.00000	0.113228
$313$	−10.3733	−0.586333	−0.293166	−	0.956061i	$-0.594709\pi$
$313$	−10.3733	−0.586333	−0.293166	+	0.956061i	$0.594709\pi$
$314$	6.62530	0.373887
$315$	1.00000	0.0563436
$316$	9.92478	0.558312
$317$	16.9525	0.952149	0.476075	−	0.879405i	$-0.342059\pi$
$317$	16.9525	0.952149	0.476075	+	0.879405i	$0.342059\pi$
$318$	2.77575	0.155656
$319$	−0.625301	−0.0350101
$320$	1.00000	0.0559017
$321$	18.5501	1.03536
$322$	−1.00000	−0.0557278
$323$	10.1768	0.566252
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	−23.3258	−1.29190
$327$	11.1490	0.616543
$328$	−7.92478	−0.437573
$329$	−1.61213	−0.0888794
$330$	−1.61213	−0.0887447
$331$	7.22425	0.397081	0.198540	−	0.980093i	$-0.436380\pi$
$331$	7.22425	0.397081	0.198540	+	0.980093i	$0.436380\pi$
$332$	−11.0132	−0.604426
$333$	−3.92478	−0.215076
$334$	−6.38787	−0.349529
$335$	9.08840	0.496552
$336$	−1.00000	−0.0545545
$337$	19.6121	1.06834	0.534170	−	0.845377i	$-0.320624\pi$
$337$	19.6121	1.06834	0.534170	+	0.845377i	$0.320624\pi$
$338$	9.00000	0.489535
$339$	−11.1490	−0.605532
$340$	6.31265	0.342352
$341$	−6.95254	−0.376501
$342$	−1.61213	−0.0871738
$343$	1.00000	0.0539949
$344$	4.31265	0.232523
$345$	−1.00000	−0.0538382
$346$	11.8641	0.637820
$347$	−2.32724	−0.124933	−0.0624664	−	0.998047i	$-0.519897\pi$
$347$	−2.32724	−0.124933	−0.0624664	+	0.998047i	$0.519897\pi$
$348$	−0.387873	−0.0207922
$349$	7.61213	0.407468	0.203734	−	0.979026i	$-0.434692\pi$
$349$	7.61213	0.407468	0.203734	+	0.979026i	$0.434692\pi$
$350$	−1.00000	−0.0534522
$351$	−2.00000	−0.106752
$352$	1.61213	0.0859267
$353$	11.9248	0.634692	0.317346	−	0.948310i	$-0.397208\pi$
$353$	11.9248	0.634692	0.317346	+	0.948310i	$0.397208\pi$
$354$	−10.7005	−0.568726
$355$	−9.08840	−0.482362
$356$	−4.70052	−0.249127
$357$	−6.31265	−0.334101
$358$	−1.14903	−0.0607282
$359$	10.7005	0.564752	0.282376	−	0.959304i	$-0.408877\pi$
$359$	10.7005	0.564752	0.282376	+	0.959304i	$0.408877\pi$
$360$	−1.00000	−0.0527046
$361$	−16.4010	−0.863213
$362$	5.84955	0.307446
$363$	8.40105	0.440941
$364$	2.00000	0.104828
$365$	5.22425	0.273450
$366$	6.00000	0.313625
$367$	31.0738	1.62204	0.811020	−	0.585019i	$-0.198913\pi$
$367$	31.0738	1.62204	0.811020	+	0.585019i	$0.198913\pi$
$368$	1.00000	0.0521286
$369$	7.92478	0.412547
$370$	3.92478	0.204039
$371$	2.77575	0.144110
$372$	−4.31265	−0.223601
$373$	31.9248	1.65300	0.826501	−	0.562935i	$-0.190328\pi$
$373$	31.9248	1.65300	0.826501	+	0.562935i	$0.190328\pi$
$374$	10.1768	0.526229
$375$	−1.00000	−0.0516398
$376$	1.61213	0.0831391
$377$	0.775746	0.0399530
$378$	1.00000	0.0514344
$379$	15.0738	0.774290	0.387145	−	0.922019i	$-0.373461\pi$
$379$	15.0738	0.774290	0.387145	+	0.922019i	$0.373461\pi$
$380$	1.61213	0.0827004
$381$	−5.08840	−0.260686
$382$	−10.7005	−0.547486
$383$	−13.9248	−0.711523	−0.355761	−	0.934577i	$-0.615778\pi$
$383$	−13.9248	−0.711523	−0.355761	+	0.934577i	$0.615778\pi$
$384$	1.00000	0.0510310
$385$	−1.61213	−0.0821616
$386$	6.00000	0.305392
$387$	−4.31265	−0.219224
$388$	15.9248	0.808458
$389$	−16.0263	−0.812568	−0.406284	−	0.913747i	$-0.633176\pi$
$389$	−16.0263	−0.812568	−0.406284	+	0.913747i	$0.633176\pi$
$390$	2.00000	0.101274
$391$	6.31265	0.319244
$392$	−1.00000	−0.0505076
$393$	−19.3258	−0.974859
$394$	−18.6253	−0.938329
$395$	9.92478	0.499370
$396$	−1.61213	−0.0810124
$397$	37.8496	1.89961	0.949807	−	0.312835i	$-0.101279\pi$
$397$	37.8496	1.89961	0.949807	+	0.312835i	$0.101279\pi$
$398$	−3.47627	−0.174250
$399$	−1.61213	−0.0807073
$400$	1.00000	0.0500000
$401$	36.6107	1.82825	0.914126	−	0.405431i	$-0.132878\pi$
$401$	36.6107	1.82825	0.914126	+	0.405431i	$0.132878\pi$
$402$	9.08840	0.453288
$403$	8.62530	0.429657
$404$	−3.29948	−0.164155
$405$	1.00000	0.0496904
$406$	−0.387873	−0.0192498
$407$	6.32724	0.313630
$408$	6.31265	0.312523
$409$	19.5515	0.966759	0.483380	−	0.875411i	$-0.339409\pi$
$409$	19.5515	0.966759	0.483380	+	0.875411i	$0.339409\pi$
$410$	−7.92478	−0.391377
$411$	5.47627	0.270124
$412$	16.6253	0.819070
$413$	−10.7005	−0.526538
$414$	−1.00000	−0.0491473
$415$	−11.0132	−0.540615
$416$	−2.00000	−0.0980581
$417$	6.70052	0.328126
$418$	2.59895	0.127119
$419$	−27.3258	−1.33495	−0.667477	−	0.744630i	$-0.732626\pi$
$419$	−27.3258	−1.33495	−0.667477	+	0.744630i	$0.732626\pi$
$420$	−1.00000	−0.0487950
$421$	24.7005	1.20383	0.601915	−	0.798560i	$-0.294405\pi$
$421$	24.7005	1.20383	0.601915	+	0.798560i	$0.294405\pi$
$422$	15.8496	0.771544
$423$	−1.61213	−0.0783843
$424$	−2.77575	−0.134802
$425$	6.31265	0.306209
$426$	−9.08840	−0.440334
$427$	6.00000	0.290360
$428$	−18.5501	−0.896652
$429$	3.22425	0.155668
$430$	4.31265	0.207974
$431$	−20.3733	−0.981347	−0.490673	−	0.871344i	$-0.663249\pi$
$431$	−20.3733	−0.981347	−0.490673	+	0.871344i	$0.663249\pi$
$432$	−1.00000	−0.0481125
$433$	9.47627	0.455400	0.227700	−	0.973731i	$-0.426879\pi$
$433$	9.47627	0.455400	0.227700	+	0.973731i	$0.426879\pi$
$434$	−4.31265	−0.207014
$435$	−0.387873	−0.0185971
$436$	−11.1490	−0.533942
$437$	1.61213	0.0771185
$438$	5.22425	0.249624
$439$	−20.9380	−0.999314	−0.499657	−	0.866223i	$-0.666541\pi$
$439$	−20.9380	−0.999314	−0.499657	+	0.866223i	$0.666541\pi$
$440$	1.61213	0.0768551
$441$	1.00000	0.0476190
$442$	−12.6253	−0.600524
$443$	36.6253	1.74012	0.870060	−	0.492945i	$-0.164080\pi$
$443$	36.6253	1.74012	0.870060	+	0.492945i	$0.164080\pi$
$444$	3.92478	0.186262
$445$	−4.70052	−0.222826
$446$	−10.4485	−0.494751
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	−2.77575	−0.130996	−0.0654978	−	0.997853i	$-0.520864\pi$
$449$	−2.77575	−0.130996	−0.0654978	+	0.997853i	$0.520864\pi$
$450$	−1.00000	−0.0471405
$451$	−12.7757	−0.601586
$452$	11.1490	0.524406
$453$	19.8496	0.932613
$454$	−10.3879	−0.487527
$455$	2.00000	0.0937614
$456$	1.61213	0.0754948
$457$	19.6121	0.917417	0.458708	−	0.888587i	$-0.348312\pi$
$457$	19.6121	0.917417	0.458708	+	0.888587i	$0.348312\pi$
$458$	13.8496	0.647147
$459$	−6.31265	−0.294649
$460$	1.00000	0.0466252
$461$	−0.700523	−0.0326266	−0.0163133	−	0.999867i	$-0.505193\pi$
$461$	−0.700523	−0.0326266	−0.0163133	+	0.999867i	$0.505193\pi$
$462$	−1.61213	−0.0750029
$463$	−12.1622	−0.565226	−0.282613	−	0.959234i	$-0.591201\pi$
$463$	−12.1622	−0.565226	−0.282613	+	0.959234i	$0.591201\pi$
$464$	0.387873	0.0180066
$465$	−4.31265	−0.199994
$466$	−14.0000	−0.648537
$467$	4.56467	0.211228	0.105614	−	0.994407i	$-0.466319\pi$
$467$	4.56467	0.211228	0.105614	+	0.994407i	$0.466319\pi$
$468$	2.00000	0.0924500
$469$	9.08840	0.419663
$470$	1.61213	0.0743619
$471$	6.62530	0.305278
$472$	10.7005	0.492532
$473$	6.95254	0.319678
$474$	9.92478	0.455860
$475$	1.61213	0.0739695
$476$	6.31265	0.289340
$477$	2.77575	0.127093
$478$	23.5369	1.07655
$479$	30.0263	1.37194	0.685969	−	0.727630i	$-0.259378\pi$
$479$	30.0263	1.37194	0.685969	+	0.727630i	$0.259378\pi$
$480$	1.00000	0.0456435
$481$	−7.84955	−0.357909
$482$	−27.7137	−1.26232
$483$	−1.00000	−0.0455016
$484$	−8.40105	−0.381866
$485$	15.9248	0.723107
$486$	1.00000	0.0453609
$487$	1.23884	0.0561373	0.0280686	−	0.999606i	$-0.491064\pi$
$487$	1.23884	0.0561373	0.0280686	+	0.999606i	$0.491064\pi$
$488$	−6.00000	−0.271607
$489$	−23.3258	−1.05483
$490$	−1.00000	−0.0451754
$491$	4.25202	0.191891	0.0959454	−	0.995387i	$-0.469413\pi$
$491$	4.25202	0.191891	0.0959454	+	0.995387i	$0.469413\pi$
$492$	−7.92478	−0.357277
$493$	2.44851	0.110275
$494$	−3.22425	−0.145066
$495$	−1.61213	−0.0724597
$496$	4.31265	0.193644
$497$	−9.08840	−0.407670
$498$	−11.0132	−0.493512
$499$	22.2981	0.998198	0.499099	−	0.866545i	$-0.333664\pi$
$499$	22.2981	0.998198	0.499099	+	0.866545i	$0.333664\pi$
$500$	1.00000	0.0447214
$501$	−6.38787	−0.285389
$502$	30.5501	1.36352
$503$	−21.2995	−0.949697	−0.474848	−	0.880068i	$-0.657497\pi$
$503$	−21.2995	−0.949697	−0.474848	+	0.880068i	$0.657497\pi$
$504$	−1.00000	−0.0445435
$505$	−3.29948	−0.146825
$506$	1.61213	0.0716678
$507$	9.00000	0.399704
$508$	5.08840	0.225761
$509$	39.5026	1.75092	0.875461	−	0.483288i	$-0.160558\pi$
$509$	39.5026	1.75092	0.875461	+	0.483288i	$0.160558\pi$
$510$	6.31265	0.279529
$511$	5.22425	0.231107
$512$	−1.00000	−0.0441942
$513$	−1.61213	−0.0711771
$514$	−3.29948	−0.145534
$515$	16.6253	0.732598
$516$	4.31265	0.189854
$517$	2.59895	0.114302
$518$	3.92478	0.172445
$519$	11.8641	0.520778
$520$	−2.00000	−0.0877058
$521$	0.700523	0.0306905	0.0153452	−	0.999882i	$-0.495115\pi$
$521$	0.700523	0.0306905	0.0153452	+	0.999882i	$0.495115\pi$
$522$	−0.387873	−0.0169767
$523$	−12.3733	−0.541046	−0.270523	−	0.962714i	$-0.587197\pi$
$523$	−12.3733	−0.541046	−0.270523	+	0.962714i	$0.587197\pi$
$524$	19.3258	0.844253
$525$	−1.00000	−0.0436436
$526$	16.6253	0.724898
$527$	27.2243	1.18591
$528$	1.61213	0.0701588
$529$	1.00000	0.0434783
$530$	−2.77575	−0.120571
$531$	−10.7005	−0.464363
$532$	1.61213	0.0698946
$533$	15.8496	0.686520
$534$	−4.70052	−0.203412
$535$	−18.5501	−0.801990
$536$	−9.08840	−0.392559
$537$	−1.14903	−0.0495843
$538$	17.3258	0.746969
$539$	−1.61213	−0.0694392
$540$	−1.00000	−0.0430331
$541$	−42.3244	−1.81967	−0.909834	−	0.414972i	$-0.863791\pi$
$541$	−42.3244	−1.81967	−0.909834	+	0.414972i	$0.863791\pi$
$542$	−5.86414	−0.251887
$543$	5.84955	0.251028
$544$	−6.31265	−0.270653
$545$	−11.1490	−0.477572
$546$	2.00000	0.0855921
$547$	−7.32582	−0.313230	−0.156615	−	0.987660i	$-0.550058\pi$
$547$	−7.32582	−0.313230	−0.156615	+	0.987660i	$0.550058\pi$
$548$	−5.47627	−0.233935
$549$	6.00000	0.256074
$550$	1.61213	0.0687413
$551$	0.625301	0.0266387
$552$	1.00000	0.0425628
$553$	9.92478	0.422044
$554$	−31.4617	−1.33668
$555$	3.92478	0.166598
$556$	−6.70052	−0.284165
$557$	16.1768	0.685433	0.342716	−	0.939439i	$-0.388653\pi$
$557$	16.1768	0.685433	0.342716	+	0.939439i	$0.388653\pi$
$558$	−4.31265	−0.182569
$559$	−8.62530	−0.364811
$560$	1.00000	0.0422577
$561$	10.1768	0.429665
$562$	−0.135857	−0.00573079
$563$	−4.56467	−0.192378	−0.0961889	−	0.995363i	$-0.530665\pi$
$563$	−4.56467	−0.192378	−0.0961889	+	0.995363i	$0.530665\pi$
$564$	1.61213	0.0678828
$565$	11.1490	0.469043
$566$	−0.523730	−0.0220140
$567$	1.00000	0.0419961
$568$	9.08840	0.381341
$569$	31.7137	1.32951	0.664754	−	0.747063i	$-0.268536\pi$
$569$	31.7137	1.32951	0.664754	+	0.747063i	$0.268536\pi$
$570$	1.61213	0.0675246
$571$	45.1002	1.88738	0.943691	−	0.330827i	$-0.107328\pi$
$571$	45.1002	1.88738	0.943691	+	0.330827i	$0.107328\pi$
$572$	−3.22425	−0.134813
$573$	−10.7005	−0.447021
$574$	−7.92478	−0.330774
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−43.7255	−1.82031	−0.910157	−	0.414263i	$-0.864039\pi$
$577$	−43.7255	−1.82031	−0.910157	+	0.414263i	$0.864039\pi$
$578$	−22.8496	−0.950416
$579$	6.00000	0.249351
$580$	0.387873	0.0161056
$581$	−11.0132	−0.456903
$582$	15.9248	0.660103
$583$	−4.47486	−0.185330
$584$	−5.22425	−0.216181
$585$	2.00000	0.0826898
$586$	2.00000	0.0826192
$587$	−46.8021	−1.93173	−0.965865	−	0.259048i	$-0.916591\pi$
$587$	−46.8021	−1.93173	−0.965865	+	0.259048i	$0.916591\pi$
$588$	−1.00000	−0.0412393
$589$	6.95254	0.286474
$590$	10.7005	0.440534
$591$	−18.6253	−0.766142
$592$	−3.92478	−0.161307
$593$	−30.9986	−1.27296	−0.636480	−	0.771293i	$-0.719610\pi$
$593$	−30.9986	−1.27296	−0.636480	+	0.771293i	$0.719610\pi$
$594$	−1.61213	−0.0661464
$595$	6.31265	0.258793
$596$	6.00000	0.245770
$597$	−3.47627	−0.142274
$598$	−2.00000	−0.0817861
$599$	17.2097	0.703168	0.351584	−	0.936156i	$-0.385643\pi$
$599$	17.2097	0.703168	0.351584	+	0.936156i	$0.385643\pi$
$600$	1.00000	0.0408248
$601$	−5.07381	−0.206965	−0.103482	−	0.994631i	$-0.532999\pi$
$601$	−5.07381	−0.206965	−0.103482	+	0.994631i	$0.532999\pi$
$602$	4.31265	0.175771
$603$	9.08840	0.370108
$604$	−19.8496	−0.807667
$605$	−8.40105	−0.341551
$606$	−3.29948	−0.134032
$607$	−8.47486	−0.343984	−0.171992	−	0.985098i	$-0.555020\pi$
$607$	−8.47486	−0.343984	−0.171992	+	0.985098i	$0.555020\pi$
$608$	−1.61213	−0.0653804
$609$	−0.387873	−0.0157174
$610$	−6.00000	−0.242933
$611$	−3.22425	−0.130439
$612$	6.31265	0.255174
$613$	−44.5501	−1.79936	−0.899680	−	0.436549i	$-0.856200\pi$
$613$	−44.5501	−1.79936	−0.899680	+	0.436549i	$0.856200\pi$
$614$	−32.4749	−1.31058
$615$	−7.92478	−0.319558
$616$	1.61213	0.0649544
$617$	−6.10157	−0.245640	−0.122820	−	0.992429i	$-0.539194\pi$
$617$	−6.10157	−0.245640	−0.122820	+	0.992429i	$0.539194\pi$
$618$	16.6253	0.668768
$619$	23.6385	0.950111	0.475055	−	0.879956i	$-0.342428\pi$
$619$	23.6385	0.950111	0.475055	+	0.879956i	$0.342428\pi$
$620$	4.31265	0.173200
$621$	−1.00000	−0.0401286
$622$	−0.523730	−0.0209997
$623$	−4.70052	−0.188322
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	10.3733	0.414600
$627$	2.59895	0.103792
$628$	−6.62530	−0.264378
$629$	−24.7757	−0.987874
$630$	−1.00000	−0.0398410
$631$	35.1754	1.40031	0.700155	−	0.713991i	$-0.253114\pi$
$631$	35.1754	1.40031	0.700155	+	0.713991i	$0.253114\pi$
$632$	−9.92478	−0.394786
$633$	15.8496	0.629963
$634$	−16.9525	−0.673271
$635$	5.08840	0.201927
$636$	−2.77575	−0.110065
$637$	2.00000	0.0792429
$638$	0.625301	0.0247559
$639$	−9.08840	−0.359531
$640$	−1.00000	−0.0395285
$641$	−7.86414	−0.310615	−0.155307	−	0.987866i	$-0.549637\pi$
$641$	−7.86414	−0.310615	−0.155307	+	0.987866i	$0.549637\pi$
$642$	−18.5501	−0.732113
$643$	−13.2995	−0.524480	−0.262240	−	0.965003i	$-0.584461\pi$
$643$	−13.2995	−0.524480	−0.262240	+	0.965003i	$0.584461\pi$
$644$	1.00000	0.0394055
$645$	4.31265	0.169810
$646$	−10.1768	−0.400401
$647$	16.0606	0.631409	0.315704	−	0.948858i	$-0.397759\pi$
$647$	16.0606	0.631409	0.315704	+	0.948858i	$0.397759\pi$
$648$	−1.00000	−0.0392837
$649$	17.2506	0.677145
$650$	−2.00000	−0.0784465
$651$	−4.31265	−0.169026
$652$	23.3258	0.913510
$653$	6.77575	0.265155	0.132578	−	0.991173i	$-0.457675\pi$
$653$	6.77575	0.265155	0.132578	+	0.991173i	$0.457675\pi$
$654$	−11.1490	−0.435962
$655$	19.3258	0.755122
$656$	7.92478	0.309411
$657$	5.22425	0.203818
$658$	1.61213	0.0628472
$659$	−22.3879	−0.872108	−0.436054	−	0.899921i	$-0.643624\pi$
$659$	−22.3879	−0.872108	−0.436054	+	0.899921i	$0.643624\pi$
$660$	1.61213	0.0627520
$661$	−19.2506	−0.748762	−0.374381	−	0.927275i	$-0.622145\pi$
$661$	−19.2506	−0.748762	−0.374381	+	0.927275i	$0.622145\pi$
$662$	−7.22425	−0.280779
$663$	−12.6253	−0.490326
$664$	11.0132	0.427394
$665$	1.61213	0.0625156
$666$	3.92478	0.152082
$667$	0.387873	0.0150185
$668$	6.38787	0.247154
$669$	−10.4485	−0.403963
$670$	−9.08840	−0.351115
$671$	−9.67276	−0.373413
$672$	1.00000	0.0385758
$673$	3.67276	0.141575	0.0707873	−	0.997491i	$-0.477449\pi$
$673$	3.67276	0.141575	0.0707873	+	0.997491i	$0.477449\pi$
$674$	−19.6121	−0.755431
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−40.1476	−1.54300	−0.771499	−	0.636230i	$-0.780493\pi$
$677$	−40.1476	−1.54300	−0.771499	+	0.636230i	$0.780493\pi$
$678$	11.1490	0.428176
$679$	15.9248	0.611137
$680$	−6.31265	−0.242079
$681$	−10.3879	−0.398064
$682$	6.95254	0.266226
$683$	0.775746	0.0296831	0.0148416	−	0.999890i	$-0.495276\pi$
$683$	0.775746	0.0296831	0.0148416	+	0.999890i	$0.495276\pi$
$684$	1.61213	0.0616412
$685$	−5.47627	−0.209238
$686$	−1.00000	−0.0381802
$687$	13.8496	0.528393
$688$	−4.31265	−0.164418
$689$	5.55149	0.211495
$690$	1.00000	0.0380693
$691$	3.47627	0.132244	0.0661218	−	0.997812i	$-0.478937\pi$
$691$	3.47627	0.132244	0.0661218	+	0.997812i	$0.478937\pi$
$692$	−11.8641	−0.451007
$693$	−1.61213	−0.0612396
$694$	2.32724	0.0883408
$695$	−6.70052	−0.254165
$696$	0.387873	0.0147023
$697$	50.0263	1.89488
$698$	−7.61213	−0.288123
$699$	−14.0000	−0.529529
$700$	1.00000	0.0377964
$701$	−2.62530	−0.0991562	−0.0495781	−	0.998770i	$-0.515788\pi$
$701$	−2.62530	−0.0991562	−0.0495781	+	0.998770i	$0.515788\pi$
$702$	2.00000	0.0754851
$703$	−6.32724	−0.238636
$704$	−1.61213	−0.0607593
$705$	1.61213	0.0607162
$706$	−11.9248	−0.448795
$707$	−3.29948	−0.124090
$708$	10.7005	0.402150
$709$	12.8510	0.482628	0.241314	−	0.970447i	$-0.422422\pi$
$709$	12.8510	0.482628	0.241314	+	0.970447i	$0.422422\pi$
$710$	9.08840	0.341081
$711$	9.92478	0.372208
$712$	4.70052	0.176160
$713$	4.31265	0.161510
$714$	6.31265	0.236245
$715$	−3.22425	−0.120580
$716$	1.14903	0.0429413
$717$	23.5369	0.879002
$718$	−10.7005	−0.399340
$719$	40.2228	1.50006	0.750029	−	0.661405i	$-0.230039\pi$
$719$	40.2228	1.50006	0.750029	+	0.661405i	$0.230039\pi$
$720$	1.00000	0.0372678
$721$	16.6253	0.619159
$722$	16.4010	0.610384
$723$	−27.7137	−1.03068
$724$	−5.84955	−0.217397
$725$	0.387873	0.0144052
$726$	−8.40105	−0.311792
$727$	−10.5990	−0.393093	−0.196547	−	0.980494i	$-0.562973\pi$
$727$	−10.5990	−0.393093	−0.196547	+	0.980494i	$0.562973\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−5.22425	−0.193358
$731$	−27.2243	−1.00693
$732$	−6.00000	−0.221766
$733$	−13.3747	−0.494006	−0.247003	−	0.969015i	$-0.579446\pi$
$733$	−13.3747	−0.494006	−0.247003	+	0.969015i	$0.579446\pi$
$734$	−31.0738	−1.14696
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	−14.6516	−0.539700
$738$	−7.92478	−0.291715
$739$	−23.7283	−0.872859	−0.436430	−	0.899738i	$-0.643757\pi$
$739$	−23.7283	−0.872859	−0.436430	+	0.899738i	$0.643757\pi$
$740$	−3.92478	−0.144278
$741$	−3.22425	−0.118446
$742$	−2.77575	−0.101901
$743$	−16.5040	−0.605474	−0.302737	−	0.953074i	$-0.597900\pi$
$743$	−16.5040	−0.605474	−0.302737	+	0.953074i	$0.597900\pi$
$744$	4.31265	0.158109
$745$	6.00000	0.219823
$746$	−31.9248	−1.16885
$747$	−11.0132	−0.402951
$748$	−10.1768	−0.372100
$749$	−18.5501	−0.677805
$750$	1.00000	0.0365148
$751$	41.6239	1.51888	0.759439	−	0.650579i	$-0.225474\pi$
$751$	41.6239	1.51888	0.759439	+	0.650579i	$0.225474\pi$
$752$	−1.61213	−0.0587882
$753$	30.5501	1.11331
$754$	−0.775746	−0.0282510
$755$	−19.8496	−0.722399
$756$	−1.00000	−0.0363696
$757$	7.29948	0.265304	0.132652	−	0.991163i	$-0.457651\pi$
$757$	7.29948	0.265304	0.132652	+	0.991163i	$0.457651\pi$
$758$	−15.0738	−0.547505
$759$	1.61213	0.0585165
$760$	−1.61213	−0.0584780
$761$	−5.47627	−0.198515	−0.0992573	−	0.995062i	$-0.531647\pi$
$761$	−5.47627	−0.198515	−0.0992573	+	0.995062i	$0.531647\pi$
$762$	5.08840	0.184333
$763$	−11.1490	−0.403622
$764$	10.7005	0.387131
$765$	6.31265	0.228234
$766$	13.9248	0.503123
$767$	−21.4010	−0.772747
$768$	−1.00000	−0.0360844
$769$	−10.3127	−0.371884	−0.185942	−	0.982561i	$-0.559534\pi$
$769$	−10.3127	−0.371884	−0.185942	+	0.982561i	$0.559534\pi$
$770$	1.61213	0.0580970
$771$	−3.29948	−0.118828
$772$	−6.00000	−0.215945
$773$	−1.37470	−0.0494445	−0.0247222	−	0.999694i	$-0.507870\pi$
$773$	−1.37470	−0.0494445	−0.0247222	+	0.999694i	$0.507870\pi$
$774$	4.31265	0.155015
$775$	4.31265	0.154915
$776$	−15.9248	−0.571666
$777$	3.92478	0.140801
$778$	16.0263	0.574572
$779$	12.7757	0.457739
$780$	−2.00000	−0.0716115
$781$	14.6516	0.524277
$782$	−6.31265	−0.225740
$783$	−0.387873	−0.0138615
$784$	1.00000	0.0357143
$785$	−6.62530	−0.236467
$786$	19.3258	0.689329
$787$	40.1016	1.42947	0.714733	−	0.699397i	$-0.246548\pi$
$787$	40.1016	1.42947	0.714733	+	0.699397i	$0.246548\pi$
$788$	18.6253	0.663499
$789$	16.6253	0.591876
$790$	−9.92478	−0.353108
$791$	11.1490	0.396414
$792$	1.61213	0.0572844
$793$	12.0000	0.426132
$794$	−37.8496	−1.34323
$795$	−2.77575	−0.0984456
$796$	3.47627	0.123213
$797$	15.8759	0.562353	0.281177	−	0.959656i	$-0.409275\pi$
$797$	15.8759	0.562353	0.281177	+	0.959656i	$0.409275\pi$
$798$	1.61213	0.0570687
$799$	−10.1768	−0.360029
$800$	−1.00000	−0.0353553
$801$	−4.70052	−0.166085
$802$	−36.6107	−1.29277
$803$	−8.42216	−0.297212
$804$	−9.08840	−0.320523
$805$	1.00000	0.0352454
$806$	−8.62530	−0.303813
$807$	17.3258	0.609898
$808$	3.29948	0.116075
$809$	−16.2981	−0.573009	−0.286505	−	0.958079i	$-0.592493\pi$
$809$	−16.2981	−0.573009	−0.286505	+	0.958079i	$0.592493\pi$
$810$	−1.00000	−0.0351364
$811$	45.3522	1.59253	0.796265	−	0.604948i	$-0.206806\pi$
$811$	45.3522	1.59253	0.796265	+	0.604948i	$0.206806\pi$
$812$	0.387873	0.0136117
$813$	−5.86414	−0.205664
$814$	−6.32724	−0.221770
$815$	23.3258	0.817068
$816$	−6.31265	−0.220987
$817$	−6.95254	−0.243239
$818$	−19.5515	−0.683602
$819$	2.00000	0.0698857
$820$	7.92478	0.276745
$821$	−5.01317	−0.174961	−0.0874805	−	0.996166i	$-0.527882\pi$
$821$	−5.01317	−0.174961	−0.0874805	+	0.996166i	$0.527882\pi$
$822$	−5.47627	−0.191007
$823$	−41.8641	−1.45929	−0.729646	−	0.683825i	$-0.760315\pi$
$823$	−41.8641	−1.45929	−0.729646	+	0.683825i	$0.760315\pi$
$824$	−16.6253	−0.579170
$825$	1.61213	0.0561271
$826$	10.7005	0.372319
$827$	−6.70052	−0.233000	−0.116500	−	0.993191i	$-0.537168\pi$
$827$	−6.70052	−0.233000	−0.116500	+	0.993191i	$0.537168\pi$
$828$	1.00000	0.0347524
$829$	−9.31406	−0.323491	−0.161745	−	0.986833i	$-0.551712\pi$
$829$	−9.31406	−0.323491	−0.161745	+	0.986833i	$0.551712\pi$
$830$	11.0132	0.382273
$831$	−31.4617	−1.09139
$832$	2.00000	0.0693375
$833$	6.31265	0.218720
$834$	−6.70052	−0.232020
$835$	6.38787	0.221061
$836$	−2.59895	−0.0898867
$837$	−4.31265	−0.149067
$838$	27.3258	0.943955
$839$	−1.67276	−0.0577501	−0.0288751	−	0.999583i	$-0.509192\pi$
$839$	−1.67276	−0.0577501	−0.0288751	+	0.999583i	$0.509192\pi$
$840$	1.00000	0.0345033
$841$	−28.8496	−0.994812
$842$	−24.7005	−0.851236
$843$	−0.135857	−0.00467917
$844$	−15.8496	−0.545564
$845$	−9.00000	−0.309609
$846$	1.61213	0.0554261
$847$	−8.40105	−0.288663
$848$	2.77575	0.0953195
$849$	−0.523730	−0.0179744
$850$	−6.31265	−0.216522
$851$	−3.92478	−0.134540
$852$	9.08840	0.311363
$853$	−44.9525	−1.53915	−0.769573	−	0.638559i	$-0.779531\pi$
$853$	−44.9525	−1.53915	−0.769573	+	0.638559i	$0.779531\pi$
$854$	−6.00000	−0.205316
$855$	1.61213	0.0551336
$856$	18.5501	0.634029
$857$	−17.1754	−0.586700	−0.293350	−	0.956005i	$-0.594770\pi$
$857$	−17.1754	−0.586700	−0.293350	+	0.956005i	$0.594770\pi$
$858$	−3.22425	−0.110074
$859$	−25.9248	−0.884542	−0.442271	−	0.896881i	$-0.645827\pi$
$859$	−25.9248	−0.884542	−0.442271	+	0.896881i	$0.645827\pi$
$860$	−4.31265	−0.147060
$861$	−7.92478	−0.270076
$862$	20.3733	0.693917
$863$	35.8496	1.22033	0.610167	−	0.792273i	$-0.291103\pi$
$863$	35.8496	1.22033	0.610167	+	0.792273i	$0.291103\pi$
$864$	1.00000	0.0340207
$865$	−11.8641	−0.403393
$866$	−9.47627	−0.322017
$867$	−22.8496	−0.776012
$868$	4.31265	0.146381
$869$	−16.0000	−0.542763
$870$	0.387873	0.0131501
$871$	18.1768	0.615897
$872$	11.1490	0.377554
$873$	15.9248	0.538972
$874$	−1.61213	−0.0545310
$875$	1.00000	0.0338062
$876$	−5.22425	−0.176511
$877$	48.5910	1.64080	0.820401	−	0.571789i	$-0.193750\pi$
$877$	48.5910	1.64080	0.820401	+	0.571789i	$0.193750\pi$
$878$	20.9380	0.706622
$879$	2.00000	0.0674583
$880$	−1.61213	−0.0543448
$881$	34.5764	1.16491	0.582455	−	0.812863i	$-0.302092\pi$
$881$	34.5764	1.16491	0.582455	+	0.812863i	$0.302092\pi$
$882$	−1.00000	−0.0336718
$883$	−23.6267	−0.795102	−0.397551	−	0.917580i	$-0.630140\pi$
$883$	−23.6267	−0.795102	−0.397551	+	0.917580i	$0.630140\pi$
$884$	12.6253	0.424635
$885$	10.7005	0.359694
$886$	−36.6253	−1.23045
$887$	7.01317	0.235479	0.117740	−	0.993044i	$-0.462435\pi$
$887$	7.01317	0.235479	0.117740	+	0.993044i	$0.462435\pi$
$888$	−3.92478	−0.131707
$889$	5.08840	0.170659
$890$	4.70052	0.157562
$891$	−1.61213	−0.0540083
$892$	10.4485	0.349842
$893$	−2.59895	−0.0869706
$894$	6.00000	0.200670
$895$	1.14903	0.0384079
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	2.77575	0.0926279
$899$	1.67276	0.0557897
$900$	1.00000	0.0333333
$901$	17.5223	0.583753
$902$	12.7757	0.425386
$903$	4.31265	0.143516
$904$	−11.1490	−0.370811
$905$	−5.84955	−0.194446
$906$	−19.8496	−0.659457
$907$	−9.08840	−0.301775	−0.150888	−	0.988551i	$-0.548213\pi$
$907$	−9.08840	−0.301775	−0.150888	+	0.988551i	$0.548213\pi$
$908$	10.3879	0.344734
$909$	−3.29948	−0.109437
$910$	−2.00000	−0.0662994
$911$	−28.8773	−0.956748	−0.478374	−	0.878156i	$-0.658774\pi$
$911$	−28.8773	−0.956748	−0.478374	+	0.878156i	$0.658774\pi$
$912$	−1.61213	−0.0533829
$913$	17.7546	0.587593
$914$	−19.6121	−0.648711
$915$	−6.00000	−0.198354
$916$	−13.8496	−0.457602
$917$	19.3258	0.638195
$918$	6.31265	0.208349
$919$	−50.2492	−1.65757	−0.828784	−	0.559569i	$-0.810967\pi$
$919$	−50.2492	−1.65757	−0.828784	+	0.559569i	$0.810967\pi$
$920$	−1.00000	−0.0329690
$921$	−32.4749	−1.07008
$922$	0.700523	0.0230705
$923$	−18.1768	−0.598296
$924$	1.61213	0.0530351
$925$	−3.92478	−0.129046
$926$	12.1622	0.399675
$927$	16.6253	0.546047
$928$	−0.387873	−0.0127326
$929$	10.5237	0.345272	0.172636	−	0.984986i	$-0.444772\pi$
$929$	10.5237	0.345272	0.172636	+	0.984986i	$0.444772\pi$
$930$	4.31265	0.141417
$931$	1.61213	0.0528353
$932$	14.0000	0.458585
$933$	−0.523730	−0.0171462
$934$	−4.56467	−0.149360
$935$	−10.1768	−0.332817
$936$	−2.00000	−0.0653720
$937$	−5.59754	−0.182864	−0.0914318	−	0.995811i	$-0.529144\pi$
$937$	−5.59754	−0.182864	−0.0914318	+	0.995811i	$0.529144\pi$
$938$	−9.08840	−0.296747
$939$	10.3733	0.338519
$940$	−1.61213	−0.0525818
$941$	1.10299	0.0359563	0.0179781	−	0.999838i	$-0.494277\pi$
$941$	1.10299	0.0359563	0.0179781	+	0.999838i	$0.494277\pi$
$942$	−6.62530	−0.215864
$943$	7.92478	0.258066
$944$	−10.7005	−0.348272
$945$	−1.00000	−0.0325300
$946$	−6.95254	−0.226047
$947$	−13.2506	−0.430587	−0.215293	−	0.976549i	$-0.569071\pi$
$947$	−13.2506	−0.430587	−0.215293	+	0.976549i	$0.569071\pi$
$948$	−9.92478	−0.322342
$949$	10.4485	0.339173
$950$	−1.61213	−0.0523043
$951$	−16.9525	−0.549724
$952$	−6.31265	−0.204594
$953$	−4.85097	−0.157138	−0.0785692	−	0.996909i	$-0.525035\pi$
$953$	−4.85097	−0.157138	−0.0785692	+	0.996909i	$0.525035\pi$
$954$	−2.77575	−0.0898681
$955$	10.7005	0.346261
$956$	−23.5369	−0.761238
$957$	0.625301	0.0202131
$958$	−30.0263	−0.970107
$959$	−5.47627	−0.176838
$960$	−1.00000	−0.0322749
$961$	−12.4010	−0.400034
$962$	7.84955	0.253080
$963$	−18.5501	−0.597768
$964$	27.7137	0.892598
$965$	−6.00000	−0.193147
$966$	1.00000	0.0321745
$967$	2.28630	0.0735225	0.0367613	−	0.999324i	$-0.488296\pi$
$967$	2.28630	0.0735225	0.0367613	+	0.999324i	$0.488296\pi$
$968$	8.40105	0.270020
$969$	−10.1768	−0.326926
$970$	−15.9248	−0.511314
$971$	−42.3996	−1.36067	−0.680334	−	0.732902i	$-0.738165\pi$
$971$	−42.3996	−1.36067	−0.680334	+	0.732902i	$0.738165\pi$
$972$	−1.00000	−0.0320750
$973$	−6.70052	−0.214809
$974$	−1.23884	−0.0396951
$975$	−2.00000	−0.0640513
$976$	6.00000	0.192055
$977$	16.8510	0.539110	0.269555	−	0.962985i	$-0.413123\pi$
$977$	16.8510	0.539110	0.269555	+	0.962985i	$0.413123\pi$
$978$	23.3258	0.745878
$979$	7.57784	0.242189
$980$	1.00000	0.0319438
$981$	−11.1490	−0.355961
$982$	−4.25202	−0.135687
$983$	−33.0278	−1.05342	−0.526711	−	0.850044i	$-0.676575\pi$
$983$	−33.0278	−1.05342	−0.526711	+	0.850044i	$0.676575\pi$
$984$	7.92478	0.252633
$985$	18.6253	0.593451
$986$	−2.44851	−0.0779764
$987$	1.61213	0.0513146
$988$	3.22425	0.102577
$989$	−4.31265	−0.137134
$990$	1.61213	0.0512368
$991$	14.6516	0.465425	0.232712	−	0.972546i	$-0.425240\pi$
$991$	14.6516	0.465425	0.232712	+	0.972546i	$0.425240\pi$
$992$	−4.31265	−0.136927
$993$	−7.22425	−0.229255
$994$	9.08840	0.288266
$995$	3.47627	0.110205
$996$	11.0132	0.348966
$997$	28.2981	0.896209	0.448104	−	0.893981i	$-0.352099\pi$
$997$	28.2981	0.896209	0.448104	+	0.893981i	$0.352099\pi$
$998$	−22.2981	−0.705833
$999$	3.92478	0.124174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.by.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.by.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.61213 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +6.31265 q^{17} -1.00000 q^{18} +1.61213 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.61213 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.387873 q^{29} +1.00000 q^{30} +4.31265 q^{31} -1.00000 q^{32} +1.61213 q^{33} -6.31265 q^{34} +1.00000 q^{35} +1.00000 q^{36} -3.92478 q^{37} -1.61213 q^{38} -2.00000 q^{39} -1.00000 q^{40} +7.92478 q^{41} +1.00000 q^{42} -4.31265 q^{43} -1.61213 q^{44} +1.00000 q^{45} -1.00000 q^{46} -1.61213 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -6.31265 q^{51} +2.00000 q^{52} +2.77575 q^{53} +1.00000 q^{54} -1.61213 q^{55} -1.00000 q^{56} -1.61213 q^{57} -0.387873 q^{58} -10.7005 q^{59} -1.00000 q^{60} +6.00000 q^{61} -4.31265 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.61213 q^{66} +9.08840 q^{67} +6.31265 q^{68} -1.00000 q^{69} -1.00000 q^{70} -9.08840 q^{71} -1.00000 q^{72} +5.22425 q^{73} +3.92478 q^{74} -1.00000 q^{75} +1.61213 q^{76} -1.61213 q^{77} +2.00000 q^{78} +9.92478 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.92478 q^{82} -11.0132 q^{83} -1.00000 q^{84} +6.31265 q^{85} +4.31265 q^{86} -0.387873 q^{87} +1.61213 q^{88} -4.70052 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} -4.31265 q^{93} +1.61213 q^{94} +1.61213 q^{95} +1.00000 q^{96} +15.9248 q^{97} -1.00000 q^{98} -1.61213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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