LMFDB - Embedded newform 4830.2.a.bw.1.1

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:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.62721 q^{11} -1.00000 q^{12} +4.20555 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.57834 q^{17} -1.00000 q^{18} -7.83276 q^{19} -1.00000 q^{20} +1.00000 q^{21} +5.62721 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.20555 q^{26} -1.00000 q^{27} -1.00000 q^{28} -7.62721 q^{29} -1.00000 q^{30} +4.57834 q^{31} -1.00000 q^{32} +5.62721 q^{33} +2.57834 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +7.83276 q^{38} -4.20555 q^{39} +1.00000 q^{40} +9.25443 q^{41} -1.00000 q^{42} +1.62721 q^{43} -5.62721 q^{44} -1.00000 q^{45} -1.00000 q^{46} -10.6761 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.57834 q^{51} +4.20555 q^{52} -6.00000 q^{53} +1.00000 q^{54} +5.62721 q^{55} +1.00000 q^{56} +7.83276 q^{57} +7.62721 q^{58} -4.00000 q^{59} +1.00000 q^{60} -9.25443 q^{61} -4.57834 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.20555 q^{65} -5.62721 q^{66} +9.62721 q^{67} -2.57834 q^{68} -1.00000 q^{69} -1.00000 q^{70} +6.78389 q^{71} -1.00000 q^{72} +3.15667 q^{73} +6.00000 q^{74} -1.00000 q^{75} -7.83276 q^{76} +5.62721 q^{77} +4.20555 q^{78} +10.0978 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.25443 q^{82} -11.8328 q^{83} +1.00000 q^{84} +2.57834 q^{85} -1.62721 q^{86} +7.62721 q^{87} +5.62721 q^{88} +3.04888 q^{89} +1.00000 q^{90} -4.20555 q^{91} +1.00000 q^{92} -4.57834 q^{93} +10.6761 q^{94} +7.83276 q^{95} +1.00000 q^{96} -5.36222 q^{97} -1.00000 q^{98} -5.62721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - 3 q^{20} + 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} + 12 q^{31} - 3 q^{32} + 4 q^{33} + 6 q^{34} + 3 q^{35} + 3 q^{36} - 18 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 2 q^{41} - 3 q^{42} - 8 q^{43} - 4 q^{44} - 3 q^{45} - 3 q^{46} - 8 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 6 q^{51} - 2 q^{52} - 18 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} + 10 q^{58} - 12 q^{59} + 3 q^{60} - 2 q^{61} - 12 q^{62} - 3 q^{63} + 3 q^{64} + 2 q^{65} - 4 q^{66} + 16 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} + 4 q^{71} - 3 q^{72} + 6 q^{73} + 18 q^{74} - 3 q^{75} + 4 q^{76} + 4 q^{77} - 2 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} - 8 q^{83} + 3 q^{84} + 6 q^{85} + 8 q^{86} + 10 q^{87} + 4 q^{88} - 2 q^{89} + 3 q^{90} + 2 q^{91} + 3 q^{92} - 12 q^{93} + 8 q^{94} - 4 q^{95} + 3 q^{96} + 2 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 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 - 2 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 6 * 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 + 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 + 12 * q^31 - 3 * q^32 + 4 * q^33 + 6 * q^34 + 3 * q^35 + 3 * q^36 - 18 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 2 * q^41 - 3 * q^42 - 8 * q^43 - 4 * q^44 - 3 * q^45 - 3 * q^46 - 8 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 6 * q^51 - 2 * q^52 - 18 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 + 10 * q^58 - 12 * q^59 + 3 * q^60 - 2 * q^61 - 12 * q^62 - 3 * q^63 + 3 * q^64 + 2 * q^65 - 4 * q^66 + 16 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 + 4 * q^71 - 3 * q^72 + 6 * q^73 + 18 * q^74 - 3 * q^75 + 4 * q^76 + 4 * q^77 - 2 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 - 8 * q^83 + 3 * q^84 + 6 * q^85 + 8 * q^86 + 10 * q^87 + 4 * q^88 - 2 * q^89 + 3 * q^90 + 2 * q^91 + 3 * q^92 - 12 * q^93 + 8 * q^94 - 4 * q^95 + 3 * q^96 + 2 * 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
$11$	−5.62721	−1.69667	−0.848334	−	0.529461i	$-0.822394\pi$
$11$	−5.62721	−1.69667	−0.848334	+	0.529461i	$0.822394\pi$
$12$	−1.00000	−0.288675
$13$	4.20555	1.16641	0.583205	−	0.812325i	$-0.301798\pi$
$13$	4.20555	1.16641	0.583205	+	0.812325i	$0.301798\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.57834	−0.625339	−0.312669	−	0.949862i	$-0.601223\pi$
$17$	−2.57834	−0.625339	−0.312669	+	0.949862i	$0.601223\pi$
$18$	−1.00000	−0.235702
$19$	−7.83276	−1.79696	−0.898480	−	0.439015i	$-0.855327\pi$
$19$	−7.83276	−1.79696	−0.898480	+	0.439015i	$0.855327\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	5.62721	1.19973
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−4.20555	−0.824776
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−7.62721	−1.41634	−0.708169	−	0.706043i	$-0.750479\pi$
$29$	−7.62721	−1.41634	−0.708169	+	0.706043i	$0.750479\pi$
$30$	−1.00000	−0.182574
$31$	4.57834	0.822294	0.411147	−	0.911569i	$-0.365128\pi$
$31$	4.57834	0.822294	0.411147	+	0.911569i	$0.365128\pi$
$32$	−1.00000	−0.176777
$33$	5.62721	0.979572
$34$	2.57834	0.442181
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	7.83276	1.27064
$39$	−4.20555	−0.673427
$40$	1.00000	0.158114
$41$	9.25443	1.44530	0.722649	−	0.691215i	$-0.242924\pi$
$41$	9.25443	1.44530	0.722649	+	0.691215i	$0.242924\pi$
$42$	−1.00000	−0.154303
$43$	1.62721	0.248148	0.124074	−	0.992273i	$-0.460404\pi$
$43$	1.62721	0.248148	0.124074	+	0.992273i	$0.460404\pi$
$44$	−5.62721	−0.848334
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	−10.6761	−1.55727	−0.778634	−	0.627479i	$-0.784087\pi$
$47$	−10.6761	−1.55727	−0.778634	+	0.627479i	$0.784087\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	2.57834	0.361039
$52$	4.20555	0.583205
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	5.62721	0.758773
$56$	1.00000	0.133631
$57$	7.83276	1.03747
$58$	7.62721	1.00150
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.00000	0.129099
$61$	−9.25443	−1.18491	−0.592454	−	0.805604i	$-0.701841\pi$
$61$	−9.25443	−1.18491	−0.592454	+	0.805604i	$0.701841\pi$
$62$	−4.57834	−0.581449
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.20555	−0.521634
$66$	−5.62721	−0.692662
$67$	9.62721	1.17615	0.588076	−	0.808806i	$-0.299886\pi$
$67$	9.62721	1.17615	0.588076	+	0.808806i	$0.299886\pi$
$68$	−2.57834	−0.312669
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	6.78389	0.805099	0.402550	−	0.915398i	$-0.368124\pi$
$71$	6.78389	0.805099	0.402550	+	0.915398i	$0.368124\pi$
$72$	−1.00000	−0.117851
$73$	3.15667	0.369461	0.184730	−	0.982789i	$-0.440859\pi$
$73$	3.15667	0.369461	0.184730	+	0.982789i	$0.440859\pi$
$74$	6.00000	0.697486
$75$	−1.00000	−0.115470
$76$	−7.83276	−0.898480
$77$	5.62721	0.641280
$78$	4.20555	0.476185
$79$	10.0978	1.13609	0.568043	−	0.822999i	$-0.307701\pi$
$79$	10.0978	1.13609	0.568043	+	0.822999i	$0.307701\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−9.25443	−1.02198
$83$	−11.8328	−1.29881	−0.649407	−	0.760441i	$-0.724983\pi$
$83$	−11.8328	−1.29881	−0.649407	+	0.760441i	$0.724983\pi$
$84$	1.00000	0.109109
$85$	2.57834	0.279660
$86$	−1.62721	−0.175467
$87$	7.62721	0.817723
$88$	5.62721	0.599863
$89$	3.04888	0.323180	0.161590	−	0.986858i	$-0.448338\pi$
$89$	3.04888	0.323180	0.161590	+	0.986858i	$0.448338\pi$
$90$	1.00000	0.105409
$91$	−4.20555	−0.440861
$92$	1.00000	0.104257
$93$	−4.57834	−0.474751
$94$	10.6761	1.10115
$95$	7.83276	0.803625
$96$	1.00000	0.102062
$97$	−5.36222	−0.544451	−0.272226	−	0.962233i	$-0.587760\pi$
$97$	−5.36222	−0.544451	−0.272226	+	0.962233i	$0.587760\pi$
$98$	−1.00000	−0.101015
$99$	−5.62721	−0.565556
$100$	1.00000	0.100000
$101$	8.20555	0.816483	0.408241	−	0.912874i	$-0.366142\pi$
$101$	8.20555	0.816483	0.408241	+	0.912874i	$0.366142\pi$
$102$	−2.57834	−0.255293
$103$	−12.4111	−1.22290	−0.611451	−	0.791282i	$-0.709414\pi$
$103$	−12.4111	−1.22290	−0.611451	+	0.791282i	$0.709414\pi$
$104$	−4.20555	−0.412388
$105$	−1.00000	−0.0975900
$106$	6.00000	0.582772
$107$	−15.2544	−1.47470	−0.737351	−	0.675510i	$-0.763923\pi$
$107$	−15.2544	−1.47470	−0.737351	+	0.675510i	$0.763923\pi$
$108$	−1.00000	−0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−5.62721	−0.536534
$111$	6.00000	0.569495
$112$	−1.00000	−0.0944911
$113$	7.15667	0.673243	0.336622	−	0.941640i	$-0.390716\pi$
$113$	7.15667	0.673243	0.336622	+	0.941640i	$0.390716\pi$
$114$	−7.83276	−0.733605
$115$	−1.00000	−0.0932505
$116$	−7.62721	−0.708169
$117$	4.20555	0.388803
$118$	4.00000	0.368230
$119$	2.57834	0.236356
$120$	−1.00000	−0.0912871
$121$	20.6655	1.87868
$122$	9.25443	0.837856
$123$	−9.25443	−0.834443
$124$	4.57834	0.411147
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	−12.8816	−1.14306	−0.571530	−	0.820581i	$-0.693650\pi$
$127$	−12.8816	−1.14306	−0.571530	+	0.820581i	$0.693650\pi$
$128$	−1.00000	−0.0883883
$129$	−1.62721	−0.143268
$130$	4.20555	0.368851
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	5.62721	0.489786
$133$	7.83276	0.679187
$134$	−9.62721	−0.831665
$135$	1.00000	0.0860663
$136$	2.57834	0.221091
$137$	−4.31335	−0.368514	−0.184257	−	0.982878i	$-0.558988\pi$
$137$	−4.31335	−0.368514	−0.184257	+	0.982878i	$0.558988\pi$
$138$	1.00000	0.0851257
$139$	−14.5089	−1.23062	−0.615312	−	0.788283i	$-0.710970\pi$
$139$	−14.5089	−1.23062	−0.615312	+	0.788283i	$0.710970\pi$
$140$	1.00000	0.0845154
$141$	10.6761	0.899089
$142$	−6.78389	−0.569291
$143$	−23.6655	−1.97901
$144$	1.00000	0.0833333
$145$	7.62721	0.633406
$146$	−3.15667	−0.261248
$147$	−1.00000	−0.0824786
$148$	−6.00000	−0.493197
$149$	16.5089	1.35246	0.676229	−	0.736692i	$-0.263613\pi$
$149$	16.5089	1.35246	0.676229	+	0.736692i	$0.263613\pi$
$150$	1.00000	0.0816497
$151$	10.0978	0.821743	0.410872	−	0.911693i	$-0.365224\pi$
$151$	10.0978	0.821743	0.410872	+	0.911693i	$0.365224\pi$
$152$	7.83276	0.635321
$153$	−2.57834	−0.208446
$154$	−5.62721	−0.453454
$155$	−4.57834	−0.367741
$156$	−4.20555	−0.336713
$157$	18.4111	1.46937	0.734683	−	0.678411i	$-0.237331\pi$
$157$	18.4111	1.46937	0.734683	+	0.678411i	$0.237331\pi$
$158$	−10.0978	−0.803334
$159$	6.00000	0.475831
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	9.25443	0.722649
$165$	−5.62721	−0.438078
$166$	11.8328	0.918401
$167$	24.2439	1.87605	0.938023	−	0.346572i	$-0.112654\pi$
$167$	24.2439	1.87605	0.938023	+	0.346572i	$0.112654\pi$
$168$	−1.00000	−0.0771517
$169$	4.68665	0.360512
$170$	−2.57834	−0.197749
$171$	−7.83276	−0.598986
$172$	1.62721	0.124074
$173$	−17.0872	−1.29911	−0.649557	−	0.760313i	$-0.725046\pi$
$173$	−17.0872	−1.29911	−0.649557	+	0.760313i	$0.725046\pi$
$174$	−7.62721	−0.578218
$175$	−1.00000	−0.0755929
$176$	−5.62721	−0.424167
$177$	4.00000	0.300658
$178$	−3.04888	−0.228523
$179$	−2.84333	−0.212520	−0.106260	−	0.994338i	$-0.533888\pi$
$179$	−2.84333	−0.212520	−0.106260	+	0.994338i	$0.533888\pi$
$180$	−1.00000	−0.0745356
$181$	23.5678	1.75178	0.875889	−	0.482512i	$-0.160275\pi$
$181$	23.5678	1.75178	0.875889	+	0.482512i	$0.160275\pi$
$182$	4.20555	0.311736
$183$	9.25443	0.684107
$184$	−1.00000	−0.0737210
$185$	6.00000	0.441129
$186$	4.57834	0.335700
$187$	14.5089	1.06099
$188$	−10.6761	−0.778634
$189$	1.00000	0.0727393
$190$	−7.83276	−0.568248
$191$	−5.15667	−0.373124	−0.186562	−	0.982443i	$-0.559734\pi$
$191$	−5.15667	−0.373124	−0.186562	+	0.982443i	$0.559734\pi$
$192$	−1.00000	−0.0721688
$193$	−0.0977518	−0.00703633	−0.00351817	−	0.999994i	$-0.501120\pi$
$193$	−0.0977518	−0.00703633	−0.00351817	+	0.999994i	$0.501120\pi$
$194$	5.36222	0.384985
$195$	4.20555	0.301166
$196$	1.00000	0.0714286
$197$	3.15667	0.224904	0.112452	−	0.993657i	$-0.464130\pi$
$197$	3.15667	0.224904	0.112452	+	0.993657i	$0.464130\pi$
$198$	5.62721	0.399909
$199$	−10.0978	−0.715811	−0.357905	−	0.933758i	$-0.616509\pi$
$199$	−10.0978	−0.715811	−0.357905	+	0.933758i	$0.616509\pi$
$200$	−1.00000	−0.0707107
$201$	−9.62721	−0.679051
$202$	−8.20555	−0.577340
$203$	7.62721	0.535325
$204$	2.57834	0.180520
$205$	−9.25443	−0.646357
$206$	12.4111	0.864722
$207$	1.00000	0.0695048
$208$	4.20555	0.291602
$209$	44.0766	3.04884
$210$	1.00000	0.0690066
$211$	−0.411100	−0.0283013	−0.0141507	−	0.999900i	$-0.504504\pi$
$211$	−0.411100	−0.0283013	−0.0141507	+	0.999900i	$0.504504\pi$
$212$	−6.00000	−0.412082
$213$	−6.78389	−0.464824
$214$	15.2544	1.04277
$215$	−1.62721	−0.110975
$216$	1.00000	0.0680414
$217$	−4.57834	−0.310798
$218$	−6.00000	−0.406371
$219$	−3.15667	−0.213308
$220$	5.62721	0.379387
$221$	−10.8433	−0.729401
$222$	−6.00000	−0.402694
$223$	−1.45998	−0.0977672	−0.0488836	−	0.998804i	$-0.515566\pi$
$223$	−1.45998	−0.0977672	−0.0488836	+	0.998804i	$0.515566\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−7.15667	−0.476055
$227$	8.57834	0.569364	0.284682	−	0.958622i	$-0.408112\pi$
$227$	8.57834	0.569364	0.284682	+	0.958622i	$0.408112\pi$
$228$	7.83276	0.518737
$229$	−5.66553	−0.374389	−0.187194	−	0.982323i	$-0.559939\pi$
$229$	−5.66553	−0.374389	−0.187194	+	0.982323i	$0.559939\pi$
$230$	1.00000	0.0659380
$231$	−5.62721	−0.370243
$232$	7.62721	0.500751
$233$	7.15667	0.468849	0.234425	−	0.972134i	$-0.424679\pi$
$233$	7.15667	0.468849	0.234425	+	0.972134i	$0.424679\pi$
$234$	−4.20555	−0.274925
$235$	10.6761	0.696431
$236$	−4.00000	−0.260378
$237$	−10.0978	−0.655919
$238$	−2.57834	−0.167129
$239$	6.78389	0.438813	0.219407	−	0.975634i	$-0.429588\pi$
$239$	6.78389	0.438813	0.219407	+	0.975634i	$0.429588\pi$
$240$	1.00000	0.0645497
$241$	24.6761	1.58953	0.794763	−	0.606920i	$-0.207595\pi$
$241$	24.6761	1.58953	0.794763	+	0.606920i	$0.207595\pi$
$242$	−20.6655	−1.32843
$243$	−1.00000	−0.0641500
$244$	−9.25443	−0.592454
$245$	−1.00000	−0.0638877
$246$	9.25443	0.590041
$247$	−32.9411	−2.09599
$248$	−4.57834	−0.290725
$249$	11.8328	0.749871
$250$	1.00000	0.0632456
$251$	7.89220	0.498151	0.249076	−	0.968484i	$-0.419873\pi$
$251$	7.89220	0.498151	0.249076	+	0.968484i	$0.419873\pi$
$252$	−1.00000	−0.0629941
$253$	−5.62721	−0.353780
$254$	12.8816	0.808266
$255$	−2.57834	−0.161462
$256$	1.00000	0.0625000
$257$	22.4111	1.39797	0.698983	−	0.715138i	$-0.253636\pi$
$257$	22.4111	1.39797	0.698983	+	0.715138i	$0.253636\pi$
$258$	1.62721	0.101306
$259$	6.00000	0.372822
$260$	−4.20555	−0.260817
$261$	−7.62721	−0.472113
$262$	4.00000	0.247121
$263$	−5.90225	−0.363948	−0.181974	−	0.983303i	$-0.558249\pi$
$263$	−5.90225	−0.363948	−0.181974	+	0.983303i	$0.558249\pi$
$264$	−5.62721	−0.346331
$265$	6.00000	0.368577
$266$	−7.83276	−0.480258
$267$	−3.04888	−0.186588
$268$	9.62721	0.588076
$269$	−5.36222	−0.326941	−0.163470	−	0.986548i	$-0.552269\pi$
$269$	−5.36222	−0.326941	−0.163470	+	0.986548i	$0.552269\pi$
$270$	−1.00000	−0.0608581
$271$	27.0872	1.64543	0.822715	−	0.568454i	$-0.192458\pi$
$271$	27.0872	1.64543	0.822715	+	0.568454i	$0.192458\pi$
$272$	−2.57834	−0.156335
$273$	4.20555	0.254531
$274$	4.31335	0.260579
$275$	−5.62721	−0.339334
$276$	−1.00000	−0.0601929
$277$	−23.2927	−1.39953	−0.699763	−	0.714376i	$-0.746711\pi$
$277$	−23.2927	−1.39953	−0.699763	+	0.714376i	$0.746711\pi$
$278$	14.5089	0.870183
$279$	4.57834	0.274098
$280$	−1.00000	−0.0597614
$281$	−25.3905	−1.51467	−0.757335	−	0.653027i	$-0.773499\pi$
$281$	−25.3905	−1.51467	−0.757335	+	0.653027i	$0.773499\pi$
$282$	−10.6761	−0.635752
$283$	20.3033	1.20691	0.603453	−	0.797399i	$-0.293791\pi$
$283$	20.3033	1.20691	0.603453	+	0.797399i	$0.293791\pi$
$284$	6.78389	0.402550
$285$	−7.83276	−0.463973
$286$	23.6655	1.39937
$287$	−9.25443	−0.546271
$288$	−1.00000	−0.0589256
$289$	−10.3522	−0.608952
$290$	−7.62721	−0.447885
$291$	5.36222	0.314339
$292$	3.15667	0.184730
$293$	12.0978	0.706758	0.353379	−	0.935480i	$-0.385033\pi$
$293$	12.0978	0.706758	0.353379	+	0.935480i	$0.385033\pi$
$294$	1.00000	0.0583212
$295$	4.00000	0.232889
$296$	6.00000	0.348743
$297$	5.62721	0.326524
$298$	−16.5089	−0.956332
$299$	4.20555	0.243213
$300$	−1.00000	−0.0577350
$301$	−1.62721	−0.0937910
$302$	−10.0978	−0.581060
$303$	−8.20555	−0.471397
$304$	−7.83276	−0.449240
$305$	9.25443	0.529907
$306$	2.57834	0.147394
$307$	−30.9200	−1.76469	−0.882347	−	0.470599i	$-0.844038\pi$
$307$	−30.9200	−1.76469	−0.882347	+	0.470599i	$0.844038\pi$
$308$	5.62721	0.320640
$309$	12.4111	0.706043
$310$	4.57834	0.260032
$311$	24.3033	1.37811	0.689057	−	0.724707i	$-0.258025\pi$
$311$	24.3033	1.37811	0.689057	+	0.724707i	$0.258025\pi$
$312$	4.20555	0.238092
$313$	8.54002	0.482711	0.241355	−	0.970437i	$-0.422408\pi$
$313$	8.54002	0.482711	0.241355	+	0.970437i	$0.422408\pi$
$314$	−18.4111	−1.03900
$315$	1.00000	0.0563436
$316$	10.0978	0.568043
$317$	−26.4111	−1.48340	−0.741698	−	0.670734i	$-0.765979\pi$
$317$	−26.4111	−1.48340	−0.741698	+	0.670734i	$0.765979\pi$
$318$	−6.00000	−0.336463
$319$	42.9200	2.40306
$320$	−1.00000	−0.0559017
$321$	15.2544	0.851419
$322$	1.00000	0.0557278
$323$	20.1955	1.12371
$324$	1.00000	0.0555556
$325$	4.20555	0.233282
$326$	8.00000	0.443079
$327$	−6.00000	−0.331801
$328$	−9.25443	−0.510990
$329$	10.6761	0.588592
$330$	5.62721	0.309768
$331$	−8.41110	−0.462316	−0.231158	−	0.972916i	$-0.574251\pi$
$331$	−8.41110	−0.462316	−0.231158	+	0.972916i	$0.574251\pi$
$332$	−11.8328	−0.649407
$333$	−6.00000	−0.328798
$334$	−24.2439	−1.32657
$335$	−9.62721	−0.525991
$336$	1.00000	0.0545545
$337$	−13.1950	−0.718777	−0.359388	−	0.933188i	$-0.617015\pi$
$337$	−13.1950	−0.718777	−0.359388	+	0.933188i	$0.617015\pi$
$338$	−4.68665	−0.254920
$339$	−7.15667	−0.388697
$340$	2.57834	0.139830
$341$	−25.7633	−1.39516
$342$	7.83276	0.423547
$343$	−1.00000	−0.0539949
$344$	−1.62721	−0.0877334
$345$	1.00000	0.0538382
$346$	17.0872	0.918613
$347$	10.5089	0.564145	0.282072	−	0.959393i	$-0.408978\pi$
$347$	10.5089	0.564145	0.282072	+	0.959393i	$0.408978\pi$
$348$	7.62721	0.408862
$349$	10.1672	0.544240	0.272120	−	0.962263i	$-0.412275\pi$
$349$	10.1672	0.544240	0.272120	+	0.962263i	$0.412275\pi$
$350$	1.00000	0.0534522
$351$	−4.20555	−0.224476
$352$	5.62721	0.299931
$353$	−5.66553	−0.301546	−0.150773	−	0.988568i	$-0.548176\pi$
$353$	−5.66553	−0.301546	−0.150773	+	0.988568i	$0.548176\pi$
$354$	−4.00000	−0.212598
$355$	−6.78389	−0.360051
$356$	3.04888	0.161590
$357$	−2.57834	−0.136460
$358$	2.84333	0.150274
$359$	26.1744	1.38143	0.690715	−	0.723127i	$-0.257296\pi$
$359$	26.1744	1.38143	0.690715	+	0.723127i	$0.257296\pi$
$360$	1.00000	0.0527046
$361$	42.3522	2.22906
$362$	−23.5678	−1.23869
$363$	−20.6655	−1.08466
$364$	−4.20555	−0.220431
$365$	−3.15667	−0.165228
$366$	−9.25443	−0.483737
$367$	−32.6066	−1.70205	−0.851025	−	0.525124i	$-0.824019\pi$
$367$	−32.6066	−1.70205	−0.851025	+	0.525124i	$0.824019\pi$
$368$	1.00000	0.0521286
$369$	9.25443	0.481766
$370$	−6.00000	−0.311925
$371$	6.00000	0.311504
$372$	−4.57834	−0.237376
$373$	34.8222	1.80303	0.901513	−	0.432753i	$-0.142458\pi$
$373$	34.8222	1.80303	0.901513	+	0.432753i	$0.142458\pi$
$374$	−14.5089	−0.750235
$375$	1.00000	0.0516398
$376$	10.6761	0.550577
$377$	−32.0766	−1.65203
$378$	−1.00000	−0.0514344
$379$	23.2544	1.19450	0.597250	−	0.802055i	$-0.296260\pi$
$379$	23.2544	1.19450	0.597250	+	0.802055i	$0.296260\pi$
$380$	7.83276	0.401812
$381$	12.8816	0.659946
$382$	5.15667	0.263838
$383$	15.2544	0.779465	0.389732	−	0.920928i	$-0.372568\pi$
$383$	15.2544	0.779465	0.389732	+	0.920928i	$0.372568\pi$
$384$	1.00000	0.0510310
$385$	−5.62721	−0.286789
$386$	0.0977518	0.00497544
$387$	1.62721	0.0827159
$388$	−5.36222	−0.272226
$389$	−5.66553	−0.287254	−0.143627	−	0.989632i	$-0.545876\pi$
$389$	−5.66553	−0.287254	−0.143627	+	0.989632i	$0.545876\pi$
$390$	−4.20555	−0.212956
$391$	−2.57834	−0.130392
$392$	−1.00000	−0.0505076
$393$	4.00000	0.201773
$394$	−3.15667	−0.159031
$395$	−10.0978	−0.508073
$396$	−5.62721	−0.282778
$397$	35.5366	1.78353	0.891765	−	0.452498i	$-0.149467\pi$
$397$	35.5366	1.78353	0.891765	+	0.452498i	$0.149467\pi$
$398$	10.0978	0.506155
$399$	−7.83276	−0.392129
$400$	1.00000	0.0500000
$401$	−23.6272	−1.17989	−0.589943	−	0.807445i	$-0.700850\pi$
$401$	−23.6272	−1.17989	−0.589943	+	0.807445i	$0.700850\pi$
$402$	9.62721	0.480162
$403$	19.2544	0.959131
$404$	8.20555	0.408241
$405$	−1.00000	−0.0496904
$406$	−7.62721	−0.378532
$407$	33.7633	1.67358
$408$	−2.57834	−0.127647
$409$	28.9200	1.43000	0.715000	−	0.699125i	$-0.246427\pi$
$409$	28.9200	1.43000	0.715000	+	0.699125i	$0.246427\pi$
$410$	9.25443	0.457044
$411$	4.31335	0.212762
$412$	−12.4111	−0.611451
$413$	4.00000	0.196827
$414$	−1.00000	−0.0491473
$415$	11.8328	0.580847
$416$	−4.20555	−0.206194
$417$	14.5089	0.710502
$418$	−44.0766	−2.15586
$419$	31.7733	1.55223	0.776114	−	0.630592i	$-0.217188\pi$
$419$	31.7733	1.55223	0.776114	+	0.630592i	$0.217188\pi$
$420$	−1.00000	−0.0487950
$421$	20.8433	1.01584	0.507921	−	0.861404i	$-0.330414\pi$
$421$	20.8433	1.01584	0.507921	+	0.861404i	$0.330414\pi$
$422$	0.411100	0.0200120
$423$	−10.6761	−0.519089
$424$	6.00000	0.291386
$425$	−2.57834	−0.125068
$426$	6.78389	0.328680
$427$	9.25443	0.447853
$428$	−15.2544	−0.737351
$429$	23.6655	1.14258
$430$	1.62721	0.0784712
$431$	−6.09775	−0.293718	−0.146859	−	0.989157i	$-0.546916\pi$
$431$	−6.09775	−0.293718	−0.146859	+	0.989157i	$0.546916\pi$
$432$	−1.00000	−0.0481125
$433$	33.1466	1.59293	0.796463	−	0.604688i	$-0.206702\pi$
$433$	33.1466	1.59293	0.796463	+	0.604688i	$0.206702\pi$
$434$	4.57834	0.219767
$435$	−7.62721	−0.365697
$436$	6.00000	0.287348
$437$	−7.83276	−0.374692
$438$	3.15667	0.150832
$439$	24.9894	1.19268	0.596340	−	0.802732i	$-0.296621\pi$
$439$	24.9894	1.19268	0.596340	+	0.802732i	$0.296621\pi$
$440$	−5.62721	−0.268267
$441$	1.00000	0.0476190
$442$	10.8433	0.515764
$443$	−16.1955	−0.769472	−0.384736	−	0.923027i	$-0.625707\pi$
$443$	−16.1955	−0.769472	−0.384736	+	0.923027i	$0.625707\pi$
$444$	6.00000	0.284747
$445$	−3.04888	−0.144531
$446$	1.45998	0.0691319
$447$	−16.5089	−0.780842
$448$	−1.00000	−0.0472456
$449$	−5.66553	−0.267373	−0.133686	−	0.991024i	$-0.542681\pi$
$449$	−5.66553	−0.267373	−0.133686	+	0.991024i	$0.542681\pi$
$450$	−1.00000	−0.0471405
$451$	−52.0766	−2.45219
$452$	7.15667	0.336622
$453$	−10.0978	−0.474434
$454$	−8.57834	−0.402601
$455$	4.20555	0.197159
$456$	−7.83276	−0.366803
$457$	10.3517	0.484230	0.242115	−	0.970248i	$-0.422159\pi$
$457$	10.3517	0.484230	0.242115	+	0.970248i	$0.422159\pi$
$458$	5.66553	0.264733
$459$	2.57834	0.120346
$460$	−1.00000	−0.0466252
$461$	41.0278	1.91085	0.955426	−	0.295229i	$-0.0953961\pi$
$461$	41.0278	1.91085	0.955426	+	0.295229i	$0.0953961\pi$
$462$	5.62721	0.261802
$463$	23.5295	1.09351	0.546753	−	0.837294i	$-0.315864\pi$
$463$	23.5295	1.09351	0.546753	+	0.837294i	$0.315864\pi$
$464$	−7.62721	−0.354084
$465$	4.57834	0.212315
$466$	−7.15667	−0.331527
$467$	1.51941	0.0703101	0.0351551	−	0.999382i	$-0.488807\pi$
$467$	1.51941	0.0703101	0.0351551	+	0.999382i	$0.488807\pi$
$468$	4.20555	0.194402
$469$	−9.62721	−0.444543
$470$	−10.6761	−0.492451
$471$	−18.4111	−0.848339
$472$	4.00000	0.184115
$473$	−9.15667	−0.421024
$474$	10.0978	0.463805
$475$	−7.83276	−0.359392
$476$	2.57834	0.118178
$477$	−6.00000	−0.274721
$478$	−6.78389	−0.310288
$479$	−26.9200	−1.23000	−0.615002	−	0.788526i	$-0.710845\pi$
$479$	−26.9200	−1.23000	−0.615002	+	0.788526i	$0.710845\pi$
$480$	−1.00000	−0.0456435
$481$	−25.2333	−1.15054
$482$	−24.6761	−1.12397
$483$	1.00000	0.0455016
$484$	20.6655	0.939342
$485$	5.36222	0.243486
$486$	1.00000	0.0453609
$487$	−17.2927	−0.783609	−0.391804	−	0.920049i	$-0.628149\pi$
$487$	−17.2927	−0.783609	−0.391804	+	0.920049i	$0.628149\pi$
$488$	9.25443	0.418928
$489$	8.00000	0.361773
$490$	1.00000	0.0451754
$491$	29.9789	1.35293	0.676464	−	0.736476i	$-0.263512\pi$
$491$	29.9789	1.35293	0.676464	+	0.736476i	$0.263512\pi$
$492$	−9.25443	−0.417222
$493$	19.6655	0.885691
$494$	32.9411	1.48209
$495$	5.62721	0.252924
$496$	4.57834	0.205573
$497$	−6.78389	−0.304299
$498$	−11.8328	−0.530239
$499$	−32.4111	−1.45092	−0.725460	−	0.688264i	$-0.758373\pi$
$499$	−32.4111	−1.45092	−0.725460	+	0.688264i	$0.758373\pi$
$500$	−1.00000	−0.0447214
$501$	−24.2439	−1.08314
$502$	−7.89220	−0.352246
$503$	15.5889	0.695075	0.347537	−	0.937666i	$-0.387018\pi$
$503$	15.5889	0.695075	0.347537	+	0.937666i	$0.387018\pi$
$504$	1.00000	0.0445435
$505$	−8.20555	−0.365142
$506$	5.62721	0.250160
$507$	−4.68665	−0.208142
$508$	−12.8816	−0.571530
$509$	22.7144	1.00680	0.503399	−	0.864054i	$-0.332083\pi$
$509$	22.7144	1.00680	0.503399	+	0.864054i	$0.332083\pi$
$510$	2.57834	0.114171
$511$	−3.15667	−0.139643
$512$	−1.00000	−0.0441942
$513$	7.83276	0.345825
$514$	−22.4111	−0.988511
$515$	12.4111	0.546898
$516$	−1.62721	−0.0716341
$517$	60.0766	2.64217
$518$	−6.00000	−0.263625
$519$	17.0872	0.750044
$520$	4.20555	0.184426
$521$	−44.2822	−1.94004	−0.970019	−	0.243030i	$-0.921859\pi$
$521$	−44.2822	−1.94004	−0.970019	+	0.243030i	$0.921859\pi$
$522$	7.62721	0.333834
$523$	−30.4011	−1.32935	−0.664673	−	0.747135i	$-0.731429\pi$
$523$	−30.4011	−1.32935	−0.664673	+	0.747135i	$0.731429\pi$
$524$	−4.00000	−0.174741
$525$	1.00000	0.0436436
$526$	5.90225	0.257350
$527$	−11.8045	−0.514212
$528$	5.62721	0.244893
$529$	1.00000	0.0434783
$530$	−6.00000	−0.260623
$531$	−4.00000	−0.173585
$532$	7.83276	0.339593
$533$	38.9200	1.68581
$534$	3.04888	0.131938
$535$	15.2544	0.659506
$536$	−9.62721	−0.415832
$537$	2.84333	0.122699
$538$	5.36222	0.231182
$539$	−5.62721	−0.242381
$540$	1.00000	0.0430331
$541$	13.8811	0.596796	0.298398	−	0.954442i	$-0.403548\pi$
$541$	13.8811	0.596796	0.298398	+	0.954442i	$0.403548\pi$
$542$	−27.0872	−1.16349
$543$	−23.5678	−1.01139
$544$	2.57834	0.110545
$545$	−6.00000	−0.257012
$546$	−4.20555	−0.179981
$547$	0.822200	0.0351548	0.0175774	−	0.999846i	$-0.494405\pi$
$547$	0.822200	0.0351548	0.0175774	+	0.999846i	$0.494405\pi$
$548$	−4.31335	−0.184257
$549$	−9.25443	−0.394969
$550$	5.62721	0.239945
$551$	59.7422	2.54510
$552$	1.00000	0.0425628
$553$	−10.0978	−0.429400
$554$	23.2927	0.989614
$555$	−6.00000	−0.254686
$556$	−14.5089	−0.615312
$557$	11.4911	0.486896	0.243448	−	0.969914i	$-0.421722\pi$
$557$	11.4911	0.486896	0.243448	+	0.969914i	$0.421722\pi$
$558$	−4.57834	−0.193816
$559$	6.84333	0.289442
$560$	1.00000	0.0422577
$561$	−14.5089	−0.612564
$562$	25.3905	1.07103
$563$	−10.3416	−0.435847	−0.217924	−	0.975966i	$-0.569928\pi$
$563$	−10.3416	−0.435847	−0.217924	+	0.975966i	$0.569928\pi$
$564$	10.6761	0.449544
$565$	−7.15667	−0.301084
$566$	−20.3033	−0.853411
$567$	−1.00000	−0.0419961
$568$	−6.78389	−0.284646
$569$	−19.8227	−0.831012	−0.415506	−	0.909591i	$-0.636395\pi$
$569$	−19.8227	−0.831012	−0.415506	+	0.909591i	$0.636395\pi$
$570$	7.83276	0.328078
$571$	26.7244	1.11838	0.559192	−	0.829038i	$-0.311112\pi$
$571$	26.7244	1.11838	0.559192	+	0.829038i	$0.311112\pi$
$572$	−23.6655	−0.989505
$573$	5.15667	0.215423
$574$	9.25443	0.386272
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−26.4111	−1.09951	−0.549754	−	0.835326i	$-0.685279\pi$
$577$	−26.4111	−1.09951	−0.549754	+	0.835326i	$0.685279\pi$
$578$	10.3522	0.430594
$579$	0.0977518	0.00406243
$580$	7.62721	0.316703
$581$	11.8328	0.490906
$582$	−5.36222	−0.222271
$583$	33.7633	1.39833
$584$	−3.15667	−0.130624
$585$	−4.20555	−0.173878
$586$	−12.0978	−0.499754
$587$	9.68665	0.399811	0.199905	−	0.979815i	$-0.435936\pi$
$587$	9.68665	0.399811	0.199905	+	0.979815i	$0.435936\pi$
$588$	−1.00000	−0.0412393
$589$	−35.8610	−1.47763
$590$	−4.00000	−0.164677
$591$	−3.15667	−0.129848
$592$	−6.00000	−0.246598
$593$	28.0978	1.15384	0.576918	−	0.816802i	$-0.304255\pi$
$593$	28.0978	1.15384	0.576918	+	0.816802i	$0.304255\pi$
$594$	−5.62721	−0.230887
$595$	−2.57834	−0.105702
$596$	16.5089	0.676229
$597$	10.0978	0.413273
$598$	−4.20555	−0.171978
$599$	3.19499	0.130544	0.0652718	−	0.997868i	$-0.479209\pi$
$599$	3.19499	0.130544	0.0652718	+	0.997868i	$0.479209\pi$
$600$	1.00000	0.0408248
$601$	6.74557	0.275158	0.137579	−	0.990491i	$-0.456068\pi$
$601$	6.74557	0.275158	0.137579	+	0.990491i	$0.456068\pi$
$602$	1.62721	0.0663203
$603$	9.62721	0.392050
$604$	10.0978	0.410872
$605$	−20.6655	−0.840173
$606$	8.20555	0.333328
$607$	36.7144	1.49019	0.745096	−	0.666957i	$-0.232404\pi$
$607$	36.7144	1.49019	0.745096	+	0.666957i	$0.232404\pi$
$608$	7.83276	0.317660
$609$	−7.62721	−0.309070
$610$	−9.25443	−0.374701
$611$	−44.8988	−1.81641
$612$	−2.57834	−0.104223
$613$	45.8610	1.85231	0.926155	−	0.377144i	$-0.123094\pi$
$613$	45.8610	1.85231	0.926155	+	0.377144i	$0.123094\pi$
$614$	30.9200	1.24783
$615$	9.25443	0.373174
$616$	−5.62721	−0.226727
$617$	6.94108	0.279437	0.139719	−	0.990191i	$-0.455380\pi$
$617$	6.94108	0.279437	0.139719	+	0.990191i	$0.455380\pi$
$618$	−12.4111	−0.499248
$619$	22.3416	0.897985	0.448993	−	0.893535i	$-0.351783\pi$
$619$	22.3416	0.897985	0.448993	+	0.893535i	$0.351783\pi$
$620$	−4.57834	−0.183870
$621$	−1.00000	−0.0401286
$622$	−24.3033	−0.974474
$623$	−3.04888	−0.122151
$624$	−4.20555	−0.168357
$625$	1.00000	0.0400000
$626$	−8.54002	−0.341328
$627$	−44.0766	−1.76025
$628$	18.4111	0.734683
$629$	15.4700	0.616830
$630$	−1.00000	−0.0398410
$631$	−10.0978	−0.401985	−0.200993	−	0.979593i	$-0.564417\pi$
$631$	−10.0978	−0.401985	−0.200993	+	0.979593i	$0.564417\pi$
$632$	−10.0978	−0.401667
$633$	0.411100	0.0163398
$634$	26.4111	1.04892
$635$	12.8816	0.511192
$636$	6.00000	0.237915
$637$	4.20555	0.166630
$638$	−42.9200	−1.69922
$639$	6.78389	0.268366
$640$	1.00000	0.0395285
$641$	−34.2127	−1.35132	−0.675660	−	0.737213i	$-0.736141\pi$
$641$	−34.2127	−1.35132	−0.675660	+	0.737213i	$0.736141\pi$
$642$	−15.2544	−0.602044
$643$	13.4600	0.530810	0.265405	−	0.964137i	$-0.414494\pi$
$643$	13.4600	0.530810	0.265405	+	0.964137i	$0.414494\pi$
$644$	−1.00000	−0.0394055
$645$	1.62721	0.0640714
$646$	−20.1955	−0.794581
$647$	21.8116	0.857504	0.428752	−	0.903422i	$-0.358953\pi$
$647$	21.8116	0.857504	0.428752	+	0.903422i	$0.358953\pi$
$648$	−1.00000	−0.0392837
$649$	22.5089	0.883550
$650$	−4.20555	−0.164955
$651$	4.57834	0.179439
$652$	−8.00000	−0.313304
$653$	7.56777	0.296150	0.148075	−	0.988976i	$-0.452692\pi$
$653$	7.56777	0.296150	0.148075	+	0.988976i	$0.452692\pi$
$654$	6.00000	0.234619
$655$	4.00000	0.156293
$656$	9.25443	0.361325
$657$	3.15667	0.123154
$658$	−10.6761	−0.416197
$659$	−35.8016	−1.39463	−0.697316	−	0.716764i	$-0.745623\pi$
$659$	−35.8016	−1.39463	−0.697316	+	0.716764i	$0.745623\pi$
$660$	−5.62721	−0.219039
$661$	−47.9789	−1.86616	−0.933081	−	0.359666i	$-0.882891\pi$
$661$	−47.9789	−1.86616	−0.933081	+	0.359666i	$0.882891\pi$
$662$	8.41110	0.326907
$663$	10.8433	0.421120
$664$	11.8328	0.459200
$665$	−7.83276	−0.303742
$666$	6.00000	0.232495
$667$	−7.62721	−0.295327
$668$	24.2439	0.938023
$669$	1.45998	0.0564459
$670$	9.62721	0.371932
$671$	52.0766	2.01040
$672$	−1.00000	−0.0385758
$673$	10.3345	0.398365	0.199182	−	0.979962i	$-0.436171\pi$
$673$	10.3345	0.398365	0.199182	+	0.979962i	$0.436171\pi$
$674$	13.1950	0.508252
$675$	−1.00000	−0.0384900
$676$	4.68665	0.180256
$677$	16.5089	0.634487	0.317243	−	0.948344i	$-0.397243\pi$
$677$	16.5089	0.634487	0.317243	+	0.948344i	$0.397243\pi$
$678$	7.15667	0.274850
$679$	5.36222	0.205783
$680$	−2.57834	−0.0988747
$681$	−8.57834	−0.328723
$682$	25.7633	0.986527
$683$	−1.68665	−0.0645379	−0.0322690	−	0.999479i	$-0.510273\pi$
$683$	−1.68665	−0.0645379	−0.0322690	+	0.999479i	$0.510273\pi$
$684$	−7.83276	−0.299493
$685$	4.31335	0.164805
$686$	1.00000	0.0381802
$687$	5.66553	0.216153
$688$	1.62721	0.0620369
$689$	−25.2333	−0.961312
$690$	−1.00000	−0.0380693
$691$	43.8610	1.66855	0.834276	−	0.551347i	$-0.185886\pi$
$691$	43.8610	1.66855	0.834276	+	0.551347i	$0.185886\pi$
$692$	−17.0872	−0.649557
$693$	5.62721	0.213760
$694$	−10.5089	−0.398911
$695$	14.5089	0.550352
$696$	−7.62721	−0.289109
$697$	−23.8610	−0.903801
$698$	−10.1672	−0.384836
$699$	−7.15667	−0.270690
$700$	−1.00000	−0.0377964
$701$	−25.2544	−0.953847	−0.476923	−	0.878945i	$-0.658248\pi$
$701$	−25.2544	−0.953847	−0.476923	+	0.878945i	$0.658248\pi$
$702$	4.20555	0.158728
$703$	46.9966	1.77251
$704$	−5.62721	−0.212084
$705$	−10.6761	−0.402085
$706$	5.66553	0.213225
$707$	−8.20555	−0.308601
$708$	4.00000	0.150329
$709$	−11.9789	−0.449876	−0.224938	−	0.974373i	$-0.572218\pi$
$709$	−11.9789	−0.449876	−0.224938	+	0.974373i	$0.572218\pi$
$710$	6.78389	0.254595
$711$	10.0978	0.378695
$712$	−3.04888	−0.114261
$713$	4.57834	0.171460
$714$	2.57834	0.0964918
$715$	23.6655	0.885040
$716$	−2.84333	−0.106260
$717$	−6.78389	−0.253349
$718$	−26.1744	−0.976819
$719$	1.57885	0.0588813	0.0294406	−	0.999567i	$-0.490627\pi$
$719$	1.57885	0.0588813	0.0294406	+	0.999567i	$0.490627\pi$
$720$	−1.00000	−0.0372678
$721$	12.4111	0.462214
$722$	−42.3522	−1.57618
$723$	−24.6761	−0.917714
$724$	23.5678	0.875889
$725$	−7.62721	−0.283268
$726$	20.6655	0.766970
$727$	−5.90225	−0.218902	−0.109451	−	0.993992i	$-0.534909\pi$
$727$	−5.90225	−0.218902	−0.109451	+	0.993992i	$0.534909\pi$
$728$	4.20555	0.155868
$729$	1.00000	0.0370370
$730$	3.15667	0.116834
$731$	−4.19550	−0.155176
$732$	9.25443	0.342053
$733$	−17.6655	−0.652491	−0.326246	−	0.945285i	$-0.605784\pi$
$733$	−17.6655	−0.652491	−0.326246	+	0.945285i	$0.605784\pi$
$734$	32.6066	1.20353
$735$	1.00000	0.0368856
$736$	−1.00000	−0.0368605
$737$	−54.1744	−1.99554
$738$	−9.25443	−0.340660
$739$	−10.5089	−0.386574	−0.193287	−	0.981142i	$-0.561915\pi$
$739$	−10.5089	−0.386574	−0.193287	+	0.981142i	$0.561915\pi$
$740$	6.00000	0.220564
$741$	32.9411	1.21012
$742$	−6.00000	−0.220267
$743$	−49.4288	−1.81337	−0.906683	−	0.421812i	$-0.861394\pi$
$743$	−49.4288	−1.81337	−0.906683	+	0.421812i	$0.861394\pi$
$744$	4.57834	0.167850
$745$	−16.5089	−0.604838
$746$	−34.8222	−1.27493
$747$	−11.8328	−0.432938
$748$	14.5089	0.530496
$749$	15.2544	0.557385
$750$	−1.00000	−0.0365148
$751$	−35.1355	−1.28211	−0.641057	−	0.767493i	$-0.721504\pi$
$751$	−35.1355	−1.28211	−0.641057	+	0.767493i	$0.721504\pi$
$752$	−10.6761	−0.389317
$753$	−7.89220	−0.287608
$754$	32.0766	1.16816
$755$	−10.0978	−0.367495
$756$	1.00000	0.0363696
$757$	0.843326	0.0306512	0.0153256	−	0.999883i	$-0.495122\pi$
$757$	0.843326	0.0306512	0.0153256	+	0.999883i	$0.495122\pi$
$758$	−23.2544	−0.844639
$759$	5.62721	0.204255
$760$	−7.83276	−0.284124
$761$	−23.2333	−0.842206	−0.421103	−	0.907013i	$-0.638357\pi$
$761$	−23.2333	−0.842206	−0.421103	+	0.907013i	$0.638357\pi$
$762$	−12.8816	−0.466653
$763$	−6.00000	−0.217215
$764$	−5.15667	−0.186562
$765$	2.57834	0.0932200
$766$	−15.2544	−0.551165
$767$	−16.8222	−0.607414
$768$	−1.00000	−0.0360844
$769$	−6.77384	−0.244271	−0.122135	−	0.992513i	$-0.538974\pi$
$769$	−6.77384	−0.244271	−0.122135	+	0.992513i	$0.538974\pi$
$770$	5.62721	0.202791
$771$	−22.4111	−0.807116
$772$	−0.0977518	−0.00351817
$773$	27.7633	0.998576	0.499288	−	0.866436i	$-0.333595\pi$
$773$	27.7633	0.998576	0.499288	+	0.866436i	$0.333595\pi$
$774$	−1.62721	−0.0584890
$775$	4.57834	0.164459
$776$	5.36222	0.192493
$777$	−6.00000	−0.215249
$778$	5.66553	0.203119
$779$	−72.4877	−2.59714
$780$	4.20555	0.150583
$781$	−38.1744	−1.36599
$782$	2.57834	0.0922011
$783$	7.62721	0.272574
$784$	1.00000	0.0357143
$785$	−18.4111	−0.657120
$786$	−4.00000	−0.142675
$787$	−50.6933	−1.80702	−0.903510	−	0.428567i	$-0.859019\pi$
$787$	−50.6933	−1.80702	−0.903510	+	0.428567i	$0.859019\pi$
$788$	3.15667	0.112452
$789$	5.90225	0.210126
$790$	10.0978	0.359262
$791$	−7.15667	−0.254462
$792$	5.62721	0.199954
$793$	−38.9200	−1.38209
$794$	−35.5366	−1.26115
$795$	−6.00000	−0.212798
$796$	−10.0978	−0.357905
$797$	−45.6655	−1.61756	−0.808778	−	0.588114i	$-0.799871\pi$
$797$	−45.6655	−1.61756	−0.808778	+	0.588114i	$0.799871\pi$
$798$	7.83276	0.277277
$799$	27.5266	0.973820
$800$	−1.00000	−0.0353553
$801$	3.04888	0.107727
$802$	23.6272	0.834306
$803$	−17.7633	−0.626852
$804$	−9.62721	−0.339526
$805$	1.00000	0.0352454
$806$	−19.2544	−0.678208
$807$	5.36222	0.188759
$808$	−8.20555	−0.288670
$809$	17.7844	0.625266	0.312633	−	0.949874i	$-0.398789\pi$
$809$	17.7844	0.625266	0.312633	+	0.949874i	$0.398789\pi$
$810$	1.00000	0.0351364
$811$	48.8222	1.71438	0.857190	−	0.515001i	$-0.172208\pi$
$811$	48.8222	1.71438	0.857190	+	0.515001i	$0.172208\pi$
$812$	7.62721	0.267663
$813$	−27.0872	−0.949989
$814$	−33.7633	−1.18340
$815$	8.00000	0.280228
$816$	2.57834	0.0902599
$817$	−12.7456	−0.445911
$818$	−28.9200	−1.01116
$819$	−4.20555	−0.146954
$820$	−9.25443	−0.323179
$821$	−32.6650	−1.14002	−0.570008	−	0.821639i	$-0.693060\pi$
$821$	−32.6650	−1.14002	−0.570008	+	0.821639i	$0.693060\pi$
$822$	−4.31335	−0.150445
$823$	−51.3905	−1.79136	−0.895680	−	0.444699i	$-0.853311\pi$
$823$	−51.3905	−1.79136	−0.895680	+	0.444699i	$0.853311\pi$
$824$	12.4111	0.432361
$825$	5.62721	0.195914
$826$	−4.00000	−0.139178
$827$	−4.94108	−0.171818	−0.0859091	−	0.996303i	$-0.527379\pi$
$827$	−4.94108	−0.171818	−0.0859091	+	0.996303i	$0.527379\pi$
$828$	1.00000	0.0347524
$829$	38.8505	1.34933	0.674666	−	0.738123i	$-0.264288\pi$
$829$	38.8505	1.34933	0.674666	+	0.738123i	$0.264288\pi$
$830$	−11.8328	−0.410721
$831$	23.2927	0.808016
$832$	4.20555	0.145801
$833$	−2.57834	−0.0893341
$834$	−14.5089	−0.502400
$835$	−24.2439	−0.838993
$836$	44.0766	1.52442
$837$	−4.57834	−0.158250
$838$	−31.7733	−1.09759
$839$	−48.1533	−1.66243	−0.831217	−	0.555947i	$-0.812356\pi$
$839$	−48.1533	−1.66243	−0.831217	+	0.555947i	$0.812356\pi$
$840$	1.00000	0.0345033
$841$	29.1744	1.00601
$842$	−20.8433	−0.718308
$843$	25.3905	0.874495
$844$	−0.411100	−0.0141507
$845$	−4.68665	−0.161226
$846$	10.6761	0.367051
$847$	−20.6655	−0.710076
$848$	−6.00000	−0.206041
$849$	−20.3033	−0.696808
$850$	2.57834	0.0884362
$851$	−6.00000	−0.205677
$852$	−6.78389	−0.232412
$853$	18.7144	0.640769	0.320384	−	0.947288i	$-0.396188\pi$
$853$	18.7144	0.640769	0.320384	+	0.947288i	$0.396188\pi$
$854$	−9.25443	−0.316680
$855$	7.83276	0.267875
$856$	15.2544	0.521386
$857$	11.1567	0.381105	0.190552	−	0.981677i	$-0.438972\pi$
$857$	11.1567	0.381105	0.190552	+	0.981677i	$0.438972\pi$
$858$	−23.6655	−0.807928
$859$	−31.6655	−1.08041	−0.540207	−	0.841532i	$-0.681654\pi$
$859$	−31.6655	−1.08041	−0.540207	+	0.841532i	$0.681654\pi$
$860$	−1.62721	−0.0554875
$861$	9.25443	0.315390
$862$	6.09775	0.207690
$863$	47.1155	1.60383	0.801914	−	0.597439i	$-0.203815\pi$
$863$	47.1155	1.60383	0.801914	+	0.597439i	$0.203815\pi$
$864$	1.00000	0.0340207
$865$	17.0872	0.580982
$866$	−33.1466	−1.12637
$867$	10.3522	0.351578
$868$	−4.57834	−0.155399
$869$	−56.8222	−1.92756
$870$	7.62721	0.258587
$871$	40.4877	1.37187
$872$	−6.00000	−0.203186
$873$	−5.36222	−0.181484
$874$	7.83276	0.264947
$875$	1.00000	0.0338062
$876$	−3.15667	−0.106654
$877$	−20.2539	−0.683926	−0.341963	−	0.939713i	$-0.611092\pi$
$877$	−20.2539	−0.683926	−0.341963	+	0.939713i	$0.611092\pi$
$878$	−24.9894	−0.843353
$879$	−12.0978	−0.408047
$880$	5.62721	0.189693
$881$	21.0278	0.708443	0.354221	−	0.935162i	$-0.384746\pi$
$881$	21.0278	0.708443	0.354221	+	0.935162i	$0.384746\pi$
$882$	−1.00000	−0.0336718
$883$	34.7044	1.16789	0.583947	−	0.811792i	$-0.301507\pi$
$883$	34.7044	1.16789	0.583947	+	0.811792i	$0.301507\pi$
$884$	−10.8433	−0.364701
$885$	−4.00000	−0.134459
$886$	16.1955	0.544099
$887$	−40.0283	−1.34402	−0.672009	−	0.740543i	$-0.734568\pi$
$887$	−40.0283	−1.34402	−0.672009	+	0.740543i	$0.734568\pi$
$888$	−6.00000	−0.201347
$889$	12.8816	0.432036
$890$	3.04888	0.102199
$891$	−5.62721	−0.188519
$892$	−1.45998	−0.0488836
$893$	83.6233	2.79835
$894$	16.5089	0.552139
$895$	2.84333	0.0950419
$896$	1.00000	0.0334077
$897$	−4.20555	−0.140419
$898$	5.66553	0.189061
$899$	−34.9200	−1.16465
$900$	1.00000	0.0333333
$901$	15.4700	0.515381
$902$	52.0766	1.73396
$903$	1.62721	0.0541503
$904$	−7.15667	−0.238027
$905$	−23.5678	−0.783419
$906$	10.0978	0.335475
$907$	23.8016	0.790319	0.395159	−	0.918613i	$-0.370689\pi$
$907$	23.8016	0.790319	0.395159	+	0.918613i	$0.370689\pi$
$908$	8.57834	0.284682
$909$	8.20555	0.272161
$910$	−4.20555	−0.139413
$911$	29.4288	0.975020	0.487510	−	0.873117i	$-0.337905\pi$
$911$	29.4288	0.975020	0.487510	+	0.873117i	$0.337905\pi$
$912$	7.83276	0.259369
$913$	66.5855	2.20366
$914$	−10.3517	−0.342403
$915$	−9.25443	−0.305942
$916$	−5.66553	−0.187194
$917$	4.00000	0.132092
$918$	−2.57834	−0.0850978
$919$	4.19550	0.138397	0.0691984	−	0.997603i	$-0.477956\pi$
$919$	4.19550	0.138397	0.0691984	+	0.997603i	$0.477956\pi$
$920$	1.00000	0.0329690
$921$	30.9200	1.01885
$922$	−41.0278	−1.35118
$923$	28.5300	0.939076
$924$	−5.62721	−0.185122
$925$	−6.00000	−0.197279
$926$	−23.5295	−0.773226
$927$	−12.4111	−0.407634
$928$	7.62721	0.250376
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	−4.57834	−0.150130
$931$	−7.83276	−0.256708
$932$	7.15667	0.234425
$933$	−24.3033	−0.795654
$934$	−1.51941	−0.0497168
$935$	−14.5089	−0.474490
$936$	−4.20555	−0.137463
$937$	−61.0278	−1.99369	−0.996845	−	0.0793747i	$-0.974708\pi$
$937$	−61.0278	−1.99369	−0.996845	+	0.0793747i	$0.974708\pi$
$938$	9.62721	0.314340
$939$	−8.54002	−0.278693
$940$	10.6761	0.348216
$941$	10.8222	0.352794	0.176397	−	0.984319i	$-0.443556\pi$
$941$	10.8222	0.352794	0.176397	+	0.984319i	$0.443556\pi$
$942$	18.4111	0.599866
$943$	9.25443	0.301366
$944$	−4.00000	−0.130189
$945$	−1.00000	−0.0325300
$946$	9.15667	0.297709
$947$	25.2333	0.819972	0.409986	−	0.912092i	$-0.365534\pi$
$947$	25.2333	0.819972	0.409986	+	0.912092i	$0.365534\pi$
$948$	−10.0978	−0.327960
$949$	13.2756	0.430943
$950$	7.83276	0.254128
$951$	26.4111	0.856439
$952$	−2.57834	−0.0835644
$953$	7.97887	0.258461	0.129231	−	0.991615i	$-0.458749\pi$
$953$	7.97887	0.258461	0.129231	+	0.991615i	$0.458749\pi$
$954$	6.00000	0.194257
$955$	5.15667	0.166866
$956$	6.78389	0.219407
$957$	−42.9200	−1.38741
$958$	26.9200	0.869744
$959$	4.31335	0.139285
$960$	1.00000	0.0322749
$961$	−10.0388	−0.323833
$962$	25.2333	0.813554
$963$	−15.2544	−0.491567
$964$	24.6761	0.794763
$965$	0.0977518	0.00314674
$966$	−1.00000	−0.0321745
$967$	−53.9194	−1.73393	−0.866966	−	0.498367i	$-0.833933\pi$
$967$	−53.9194	−1.73393	−0.866966	+	0.498367i	$0.833933\pi$
$968$	−20.6655	−0.664215
$969$	−20.1955	−0.648773
$970$	−5.36222	−0.172171
$971$	12.5189	0.401751	0.200875	−	0.979617i	$-0.435621\pi$
$971$	12.5189	0.401751	0.200875	+	0.979617i	$0.435621\pi$
$972$	−1.00000	−0.0320750
$973$	14.5089	0.465132
$974$	17.2927	0.554095
$975$	−4.20555	−0.134685
$976$	−9.25443	−0.296227
$977$	24.4322	0.781656	0.390828	−	0.920464i	$-0.372189\pi$
$977$	24.4322	0.781656	0.390828	+	0.920464i	$0.372189\pi$
$978$	−8.00000	−0.255812
$979$	−17.1567	−0.548330
$980$	−1.00000	−0.0319438
$981$	6.00000	0.191565
$982$	−29.9789	−0.956664
$983$	32.0766	1.02309	0.511543	−	0.859258i	$-0.329074\pi$
$983$	32.0766	1.02309	0.511543	+	0.859258i	$0.329074\pi$
$984$	9.25443	0.295020
$985$	−3.15667	−0.100580
$986$	−19.6655	−0.626278
$987$	−10.6761	−0.339824
$988$	−32.9411	−1.04800
$989$	1.62721	0.0517424
$990$	−5.62721	−0.178845
$991$	−50.9200	−1.61753	−0.808763	−	0.588135i	$-0.799862\pi$
$991$	−50.9200	−1.61753	−0.808763	+	0.588135i	$0.799862\pi$
$992$	−4.57834	−0.145362
$993$	8.41110	0.266918
$994$	6.78389	0.215172
$995$	10.0978	0.320120
$996$	11.8328	0.374935
$997$	−19.7944	−0.626897	−0.313448	−	0.949605i	$-0.601484\pi$
$997$	−19.7944	−0.626897	−0.313448	+	0.949605i	$0.601484\pi$
$998$	32.4111	1.02596
$999$	6.00000	0.189832

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bw.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.62721 q^{11} -1.00000 q^{12} +4.20555 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.57834 q^{17} -1.00000 q^{18} -7.83276 q^{19} -1.00000 q^{20} +1.00000 q^{21} +5.62721 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.20555 q^{26} -1.00000 q^{27} -1.00000 q^{28} -7.62721 q^{29} -1.00000 q^{30} +4.57834 q^{31} -1.00000 q^{32} +5.62721 q^{33} +2.57834 q^{34} +1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +7.83276 q^{38} -4.20555 q^{39} +1.00000 q^{40} +9.25443 q^{41} -1.00000 q^{42} +1.62721 q^{43} -5.62721 q^{44} -1.00000 q^{45} -1.00000 q^{46} -10.6761 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.57834 q^{51} +4.20555 q^{52} -6.00000 q^{53} +1.00000 q^{54} +5.62721 q^{55} +1.00000 q^{56} +7.83276 q^{57} +7.62721 q^{58} -4.00000 q^{59} +1.00000 q^{60} -9.25443 q^{61} -4.57834 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.20555 q^{65} -5.62721 q^{66} +9.62721 q^{67} -2.57834 q^{68} -1.00000 q^{69} -1.00000 q^{70} +6.78389 q^{71} -1.00000 q^{72} +3.15667 q^{73} +6.00000 q^{74} -1.00000 q^{75} -7.83276 q^{76} +5.62721 q^{77} +4.20555 q^{78} +10.0978 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.25443 q^{82} -11.8328 q^{83} +1.00000 q^{84} +2.57834 q^{85} -1.62721 q^{86} +7.62721 q^{87} +5.62721 q^{88} +3.04888 q^{89} +1.00000 q^{90} -4.20555 q^{91} +1.00000 q^{92} -4.57834 q^{93} +10.6761 q^{94} +7.83276 q^{95} +1.00000 q^{96} -5.36222 q^{97} -1.00000 q^{98} -5.62721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - 3 q^{20} + 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} + 12 q^{31} - 3 q^{32} + 4 q^{33} + 6 q^{34} + 3 q^{35} + 3 q^{36} - 18 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 2 q^{41} - 3 q^{42} - 8 q^{43} - 4 q^{44} - 3 q^{45} - 3 q^{46} - 8 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 6 q^{51} - 2 q^{52} - 18 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} + 10 q^{58} - 12 q^{59} + 3 q^{60} - 2 q^{61} - 12 q^{62} - 3 q^{63} + 3 q^{64} + 2 q^{65} - 4 q^{66} + 16 q^{67} - 6 q^{68} - 3 q^{69} - 3 q^{70} + 4 q^{71} - 3 q^{72} + 6 q^{73} + 18 q^{74} - 3 q^{75} + 4 q^{76} + 4 q^{77} - 2 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} - 8 q^{83} + 3 q^{84} + 6 q^{85} + 8 q^{86} + 10 q^{87} + 4 q^{88} - 2 q^{89} + 3 q^{90} + 2 q^{91} + 3 q^{92} - 12 q^{93} + 8 q^{94} - 4 q^{95} + 3 q^{96} + 2 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 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 - 2 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 6 * 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 + 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 + 12 * q^31 - 3 * q^32 + 4 * q^33 + 6 * q^34 + 3 * q^35 + 3 * q^36 - 18 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 2 * q^41 - 3 * q^42 - 8 * q^43 - 4 * q^44 - 3 * q^45 - 3 * q^46 - 8 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 6 * q^51 - 2 * q^52 - 18 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 + 10 * q^58 - 12 * q^59 + 3 * q^60 - 2 * q^61 - 12 * q^62 - 3 * q^63 + 3 * q^64 + 2 * q^65 - 4 * q^66 + 16 * q^67 - 6 * q^68 - 3 * q^69 - 3 * q^70 + 4 * q^71 - 3 * q^72 + 6 * q^73 + 18 * q^74 - 3 * q^75 + 4 * q^76 + 4 * q^77 - 2 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 - 8 * q^83 + 3 * q^84 + 6 * q^85 + 8 * q^86 + 10 * q^87 + 4 * q^88 - 2 * q^89 + 3 * q^90 + 2 * q^91 + 3 * q^92 - 12 * q^93 + 8 * q^94 - 4 * q^95 + 3 * q^96 + 2 * q^97 - 3 * q^98 - 4 * q^99

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