LMFDB - Embedded newform 4830.2.a.bx.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$38.5677441763$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
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			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.49396 q^{11} -1.00000 q^{12} +1.60388 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.89008 q^{17} -1.00000 q^{18} +0.890084 q^{19} +1.00000 q^{20} +1.00000 q^{21} -4.49396 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.60388 q^{26} -1.00000 q^{27} -1.00000 q^{28} -9.70171 q^{29} +1.00000 q^{30} -5.87800 q^{31} -1.00000 q^{32} -4.49396 q^{33} +2.89008 q^{34} -1.00000 q^{35} +1.00000 q^{36} -7.42758 q^{37} -0.890084 q^{38} -1.60388 q^{39} -1.00000 q^{40} +3.78017 q^{41} -1.00000 q^{42} -4.49396 q^{43} +4.49396 q^{44} +1.00000 q^{45} -1.00000 q^{46} -9.87800 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.89008 q^{51} +1.60388 q^{52} +5.20775 q^{53} +1.00000 q^{54} +4.49396 q^{55} +1.00000 q^{56} -0.890084 q^{57} +9.70171 q^{58} -8.98792 q^{59} -1.00000 q^{60} +3.42758 q^{61} +5.87800 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.60388 q^{65} +4.49396 q^{66} +5.48188 q^{67} -2.89008 q^{68} -1.00000 q^{69} +1.00000 q^{70} +6.27413 q^{71} -1.00000 q^{72} -6.00000 q^{73} +7.42758 q^{74} -1.00000 q^{75} +0.890084 q^{76} -4.49396 q^{77} +1.60388 q^{78} +2.21983 q^{79} +1.00000 q^{80} +1.00000 q^{81} -3.78017 q^{82} +10.3177 q^{83} +1.00000 q^{84} -2.89008 q^{85} +4.49396 q^{86} +9.70171 q^{87} -4.49396 q^{88} +9.79954 q^{89} -1.00000 q^{90} -1.60388 q^{91} +1.00000 q^{92} +5.87800 q^{93} +9.87800 q^{94} +0.890084 q^{95} +1.00000 q^{96} -12.8116 q^{97} -1.00000 q^{98} +4.49396 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 4 q^{26} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 3 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 2 q^{38} + 4 q^{39} - 3 q^{40} + 10 q^{41} - 3 q^{42} - 4 q^{43} + 4 q^{44} + 3 q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} - 2 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 2 q^{57} + 2 q^{58} - 8 q^{59} - 3 q^{60} - 6 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 3 q^{69} + 3 q^{70} + 8 q^{71} - 3 q^{72} - 18 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{76} - 4 q^{77} - 4 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 10 q^{82} + 14 q^{83} + 3 q^{84} - 8 q^{85} + 4 q^{86} + 2 q^{87} - 4 q^{88} - 16 q^{89} - 3 q^{90} + 4 q^{91} + 3 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} + 3 q^{96} - 12 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 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 - 4 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 4 * q^26 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 3 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 + 10 * q^41 - 3 * q^42 - 4 * q^43 + 4 * q^44 + 3 * q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 - 2 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 2 * q^57 + 2 * q^58 - 8 * q^59 - 3 * q^60 - 6 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 3 * q^69 + 3 * q^70 + 8 * q^71 - 3 * q^72 - 18 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^76 - 4 * q^77 - 4 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 10 * q^82 + 14 * q^83 + 3 * q^84 - 8 * q^85 + 4 * q^86 + 2 * q^87 - 4 * q^88 - 16 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 + 3 * q^96 - 12 * 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
$11$	4.49396	1.35498	0.677490	−	0.735532i	$-0.263068\pi$
$11$	4.49396	1.35498	0.677490	+	0.735532i	$0.263068\pi$
$12$	−1.00000	−0.288675
$13$	1.60388	0.444835	0.222418	−	0.974952i	$-0.428605\pi$
$13$	1.60388	0.444835	0.222418	+	0.974952i	$0.428605\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.89008	−0.700948	−0.350474	−	0.936572i	$-0.613980\pi$
$17$	−2.89008	−0.700948	−0.350474	+	0.936572i	$0.613980\pi$
$18$	−1.00000	−0.235702
$19$	0.890084	0.204199	0.102100	−	0.994774i	$-0.467444\pi$
$19$	0.890084	0.204199	0.102100	+	0.994774i	$0.467444\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	−4.49396	−0.958115
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−1.60388	−0.314546
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−9.70171	−1.80156	−0.900781	−	0.434273i	$-0.857005\pi$
$29$	−9.70171	−1.80156	−0.900781	+	0.434273i	$0.857005\pi$
$30$	1.00000	0.182574
$31$	−5.87800	−1.05572	−0.527860	−	0.849331i	$-0.677005\pi$
$31$	−5.87800	−1.05572	−0.527860	+	0.849331i	$0.677005\pi$
$32$	−1.00000	−0.176777
$33$	−4.49396	−0.782298
$34$	2.89008	0.495645
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−7.42758	−1.22109	−0.610544	−	0.791983i	$-0.709049\pi$
$37$	−7.42758	−1.22109	−0.610544	+	0.791983i	$0.709049\pi$
$38$	−0.890084	−0.144391
$39$	−1.60388	−0.256826
$40$	−1.00000	−0.158114
$41$	3.78017	0.590363	0.295181	−	0.955441i	$-0.404620\pi$
$41$	3.78017	0.590363	0.295181	+	0.955441i	$0.404620\pi$
$42$	−1.00000	−0.154303
$43$	−4.49396	−0.685322	−0.342661	−	0.939459i	$-0.611328\pi$
$43$	−4.49396	−0.685322	−0.342661	+	0.939459i	$0.611328\pi$
$44$	4.49396	0.677490
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−9.87800	−1.44085	−0.720427	−	0.693530i	$-0.756054\pi$
$47$	−9.87800	−1.44085	−0.720427	+	0.693530i	$0.756054\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	2.89008	0.404693
$52$	1.60388	0.222418
$53$	5.20775	0.715340	0.357670	−	0.933848i	$-0.383571\pi$
$53$	5.20775	0.715340	0.357670	+	0.933848i	$0.383571\pi$
$54$	1.00000	0.136083
$55$	4.49396	0.605965
$56$	1.00000	0.133631
$57$	−0.890084	−0.117894
$58$	9.70171	1.27390
$59$	−8.98792	−1.17013	−0.585064	−	0.810987i	$-0.698930\pi$
$59$	−8.98792	−1.17013	−0.585064	+	0.810987i	$0.698930\pi$
$60$	−1.00000	−0.129099
$61$	3.42758	0.438857	0.219429	−	0.975629i	$-0.429581\pi$
$61$	3.42758	0.438857	0.219429	+	0.975629i	$0.429581\pi$
$62$	5.87800	0.746507
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	1.60388	0.198936
$66$	4.49396	0.553168
$67$	5.48188	0.669718	0.334859	−	0.942268i	$-0.391311\pi$
$67$	5.48188	0.669718	0.334859	+	0.942268i	$0.391311\pi$
$68$	−2.89008	−0.350474
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	6.27413	0.744602	0.372301	−	0.928112i	$-0.378569\pi$
$71$	6.27413	0.744602	0.372301	+	0.928112i	$0.378569\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	7.42758	0.863439
$75$	−1.00000	−0.115470
$76$	0.890084	0.102100
$77$	−4.49396	−0.512134
$78$	1.60388	0.181603
$79$	2.21983	0.249751	0.124875	−	0.992172i	$-0.460147\pi$
$79$	2.21983	0.249751	0.124875	+	0.992172i	$0.460147\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−3.78017	−0.417450
$83$	10.3177	1.13251	0.566256	−	0.824230i	$-0.308392\pi$
$83$	10.3177	1.13251	0.566256	+	0.824230i	$0.308392\pi$
$84$	1.00000	0.109109
$85$	−2.89008	−0.313474
$86$	4.49396	0.484596
$87$	9.70171	1.04013
$88$	−4.49396	−0.479058
$89$	9.79954	1.03875	0.519375	−	0.854547i	$-0.326165\pi$
$89$	9.79954	1.03875	0.519375	+	0.854547i	$0.326165\pi$
$90$	−1.00000	−0.105409
$91$	−1.60388	−0.168132
$92$	1.00000	0.104257
$93$	5.87800	0.609520
$94$	9.87800	1.01884
$95$	0.890084	0.0913207
$96$	1.00000	0.102062
$97$	−12.8116	−1.30082	−0.650412	−	0.759582i	$-0.725404\pi$
$97$	−12.8116	−1.30082	−0.650412	+	0.759582i	$0.725404\pi$
$98$	−1.00000	−0.101015
$99$	4.49396	0.451660
$100$	1.00000	0.100000
$101$	−3.82371	−0.380473	−0.190237	−	0.981738i	$-0.560926\pi$
$101$	−3.82371	−0.380473	−0.190237	+	0.981738i	$0.560926\pi$
$102$	−2.89008	−0.286161
$103$	−16.6353	−1.63913	−0.819564	−	0.572988i	$-0.805784\pi$
$103$	−16.6353	−1.63913	−0.819564	+	0.572988i	$0.805784\pi$
$104$	−1.60388	−0.157273
$105$	1.00000	0.0975900
$106$	−5.20775	−0.505821
$107$	−17.1836	−1.66120	−0.830600	−	0.556869i	$-0.812002\pi$
$107$	−17.1836	−1.66120	−0.830600	+	0.556869i	$0.812002\pi$
$108$	−1.00000	−0.0962250
$109$	−0.219833	−0.0210561	−0.0105281	−	0.999945i	$-0.503351\pi$
$109$	−0.219833	−0.0210561	−0.0105281	+	0.999945i	$0.503351\pi$
$110$	−4.49396	−0.428482
$111$	7.42758	0.704995
$112$	−1.00000	−0.0944911
$113$	−14.6353	−1.37678	−0.688388	−	0.725342i	$-0.741681\pi$
$113$	−14.6353	−1.37678	−0.688388	+	0.725342i	$0.741681\pi$
$114$	0.890084	0.0833640
$115$	1.00000	0.0932505
$116$	−9.70171	−0.900781
$117$	1.60388	0.148278
$118$	8.98792	0.827405
$119$	2.89008	0.264934
$120$	1.00000	0.0912871
$121$	9.19567	0.835970
$122$	−3.42758	−0.310319
$123$	−3.78017	−0.340846
$124$	−5.87800	−0.527860
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	10.9095	0.968058	0.484029	−	0.875052i	$-0.339173\pi$
$127$	10.9095	0.968058	0.484029	+	0.875052i	$0.339173\pi$
$128$	−1.00000	−0.0883883
$129$	4.49396	0.395671
$130$	−1.60388	−0.140669
$131$	10.4155	0.910007	0.455003	−	0.890490i	$-0.349638\pi$
$131$	10.4155	0.910007	0.455003	+	0.890490i	$0.349638\pi$
$132$	−4.49396	−0.391149
$133$	−0.890084	−0.0771800
$134$	−5.48188	−0.473562
$135$	−1.00000	−0.0860663
$136$	2.89008	0.247823
$137$	2.43967	0.208435	0.104217	−	0.994555i	$-0.466766\pi$
$137$	2.43967	0.208435	0.104217	+	0.994555i	$0.466766\pi$
$138$	1.00000	0.0851257
$139$	5.42758	0.460362	0.230181	−	0.973148i	$-0.426068\pi$
$139$	5.42758	0.460362	0.230181	+	0.973148i	$0.426068\pi$
$140$	−1.00000	−0.0845154
$141$	9.87800	0.831878
$142$	−6.27413	−0.526513
$143$	7.20775	0.602742
$144$	1.00000	0.0833333
$145$	−9.70171	−0.805683
$146$	6.00000	0.496564
$147$	−1.00000	−0.0824786
$148$	−7.42758	−0.610544
$149$	11.4276	0.936184	0.468092	−	0.883680i	$-0.344942\pi$
$149$	11.4276	0.936184	0.468092	+	0.883680i	$0.344942\pi$
$150$	1.00000	0.0816497
$151$	−0.792249	−0.0644723	−0.0322362	−	0.999480i	$-0.510263\pi$
$151$	−0.792249	−0.0644723	−0.0322362	+	0.999480i	$0.510263\pi$
$152$	−0.890084	−0.0721953
$153$	−2.89008	−0.233649
$154$	4.49396	0.362134
$155$	−5.87800	−0.472132
$156$	−1.60388	−0.128413
$157$	−8.21983	−0.656014	−0.328007	−	0.944675i	$-0.606377\pi$
$157$	−8.21983	−0.656014	−0.328007	+	0.944675i	$0.606377\pi$
$158$	−2.21983	−0.176600
$159$	−5.20775	−0.413002
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	−9.18359	−0.719314	−0.359657	−	0.933085i	$-0.617106\pi$
$163$	−9.18359	−0.719314	−0.359657	+	0.933085i	$0.617106\pi$
$164$	3.78017	0.295181
$165$	−4.49396	−0.349854
$166$	−10.3177	−0.800806
$167$	−3.54958	−0.274675	−0.137337	−	0.990524i	$-0.543854\pi$
$167$	−3.54958	−0.274675	−0.137337	+	0.990524i	$0.543854\pi$
$168$	−1.00000	−0.0771517
$169$	−10.4276	−0.802122
$170$	2.89008	0.221659
$171$	0.890084	0.0680664
$172$	−4.49396	−0.342661
$173$	23.2814	1.77005	0.885027	−	0.465540i	$-0.154140\pi$
$173$	23.2814	1.77005	0.885027	+	0.465540i	$0.154140\pi$
$174$	−9.70171	−0.735485
$175$	−1.00000	−0.0755929
$176$	4.49396	0.338745
$177$	8.98792	0.675573
$178$	−9.79954	−0.734507
$179$	−11.4034	−0.852332	−0.426166	−	0.904645i	$-0.640136\pi$
$179$	−11.4034	−0.852332	−0.426166	+	0.904645i	$0.640136\pi$
$180$	1.00000	0.0745356
$181$	−24.5241	−1.82286	−0.911431	−	0.411454i	$-0.865021\pi$
$181$	−24.5241	−1.82286	−0.911431	+	0.411454i	$0.865021\pi$
$182$	1.60388	0.118887
$183$	−3.42758	−0.253374
$184$	−1.00000	−0.0737210
$185$	−7.42758	−0.546087
$186$	−5.87800	−0.430996
$187$	−12.9879	−0.949771
$188$	−9.87800	−0.720427
$189$	1.00000	0.0727393
$190$	−0.890084	−0.0645735
$191$	13.7802	0.997098	0.498549	−	0.866862i	$-0.333866\pi$
$191$	13.7802	0.997098	0.498549	+	0.866862i	$0.333866\pi$
$192$	−1.00000	−0.0721688
$193$	7.18359	0.517086	0.258543	−	0.966000i	$-0.416758\pi$
$193$	7.18359	0.517086	0.258543	+	0.966000i	$0.416758\pi$
$194$	12.8116	0.919821
$195$	−1.60388	−0.114856
$196$	1.00000	0.0714286
$197$	6.63533	0.472748	0.236374	−	0.971662i	$-0.424041\pi$
$197$	6.63533	0.472748	0.236374	+	0.971662i	$0.424041\pi$
$198$	−4.49396	−0.319372
$199$	18.9638	1.34430	0.672152	−	0.740413i	$-0.265370\pi$
$199$	18.9638	1.34430	0.672152	+	0.740413i	$0.265370\pi$
$200$	−1.00000	−0.0707107
$201$	−5.48188	−0.386662
$202$	3.82371	0.269035
$203$	9.70171	0.680927
$204$	2.89008	0.202346
$205$	3.78017	0.264018
$206$	16.6353	1.15904
$207$	1.00000	0.0695048
$208$	1.60388	0.111209
$209$	4.00000	0.276686
$210$	−1.00000	−0.0690066
$211$	−5.34050	−0.367655	−0.183828	−	0.982958i	$-0.558849\pi$
$211$	−5.34050	−0.367655	−0.183828	+	0.982958i	$0.558849\pi$
$212$	5.20775	0.357670
$213$	−6.27413	−0.429896
$214$	17.1836	1.17465
$215$	−4.49396	−0.306485
$216$	1.00000	0.0680414
$217$	5.87800	0.399025
$218$	0.219833	0.0148889
$219$	6.00000	0.405442
$220$	4.49396	0.302983
$221$	−4.63533	−0.311806
$222$	−7.42758	−0.498507
$223$	4.15213	0.278047	0.139024	−	0.990289i	$-0.455604\pi$
$223$	4.15213	0.278047	0.139024	+	0.990289i	$0.455604\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	14.6353	0.973528
$227$	−14.8659	−0.986686	−0.493343	−	0.869835i	$-0.664225\pi$
$227$	−14.8659	−0.986686	−0.493343	+	0.869835i	$0.664225\pi$
$228$	−0.890084	−0.0589472
$229$	−12.7681	−0.843739	−0.421869	−	0.906657i	$-0.638626\pi$
$229$	−12.7681	−0.843739	−0.421869	+	0.906657i	$0.638626\pi$
$230$	−1.00000	−0.0659380
$231$	4.49396	0.295681
$232$	9.70171	0.636948
$233$	8.21983	0.538499	0.269250	−	0.963070i	$-0.413224\pi$
$233$	8.21983	0.538499	0.269250	+	0.963070i	$0.413224\pi$
$234$	−1.60388	−0.104849
$235$	−9.87800	−0.644370
$236$	−8.98792	−0.585064
$237$	−2.21983	−0.144194
$238$	−2.89008	−0.187336
$239$	2.71379	0.175541	0.0877703	−	0.996141i	$-0.472026\pi$
$239$	2.71379	0.175541	0.0877703	+	0.996141i	$0.472026\pi$
$240$	−1.00000	−0.0645497
$241$	−21.7453	−1.40073	−0.700367	−	0.713783i	$-0.746980\pi$
$241$	−21.7453	−1.40073	−0.700367	+	0.713783i	$0.746980\pi$
$242$	−9.19567	−0.591120
$243$	−1.00000	−0.0641500
$244$	3.42758	0.219429
$245$	1.00000	0.0638877
$246$	3.78017	0.241015
$247$	1.42758	0.0908350
$248$	5.87800	0.373254
$249$	−10.3177	−0.653856
$250$	−1.00000	−0.0632456
$251$	−19.3599	−1.22198	−0.610992	−	0.791636i	$-0.709229\pi$
$251$	−19.3599	−1.22198	−0.610992	+	0.791636i	$0.709229\pi$
$252$	−1.00000	−0.0629941
$253$	4.49396	0.282533
$254$	−10.9095	−0.684520
$255$	2.89008	0.180984
$256$	1.00000	0.0625000
$257$	−24.0629	−1.50100	−0.750502	−	0.660868i	$-0.770188\pi$
$257$	−24.0629	−1.50100	−0.750502	+	0.660868i	$0.770188\pi$
$258$	−4.49396	−0.279782
$259$	7.42758	0.461528
$260$	1.60388	0.0994681
$261$	−9.70171	−0.600521
$262$	−10.4155	−0.643472
$263$	6.76809	0.417338	0.208669	−	0.977986i	$-0.433087\pi$
$263$	6.76809	0.417338	0.208669	+	0.977986i	$0.433087\pi$
$264$	4.49396	0.276584
$265$	5.20775	0.319910
$266$	0.890084	0.0545745
$267$	−9.79954	−0.599722
$268$	5.48188	0.334859
$269$	11.5797	0.706028	0.353014	−	0.935618i	$-0.385157\pi$
$269$	11.5797	0.706028	0.353014	+	0.935618i	$0.385157\pi$
$270$	1.00000	0.0608581
$271$	17.6340	1.07119	0.535595	−	0.844475i	$-0.320087\pi$
$271$	17.6340	1.07119	0.535595	+	0.844475i	$0.320087\pi$
$272$	−2.89008	−0.175237
$273$	1.60388	0.0970710
$274$	−2.43967	−0.147386
$275$	4.49396	0.270996
$276$	−1.00000	−0.0601929
$277$	−13.5060	−0.811499	−0.405750	−	0.913984i	$-0.632990\pi$
$277$	−13.5060	−0.811499	−0.405750	+	0.913984i	$0.632990\pi$
$278$	−5.42758	−0.325525
$279$	−5.87800	−0.351907
$280$	1.00000	0.0597614
$281$	8.90946	0.531494	0.265747	−	0.964043i	$-0.414381\pi$
$281$	8.90946	0.531494	0.265747	+	0.964043i	$0.414381\pi$
$282$	−9.87800	−0.588226
$283$	−15.1642	−0.901419	−0.450709	−	0.892671i	$-0.648829\pi$
$283$	−15.1642	−0.901419	−0.450709	+	0.892671i	$0.648829\pi$
$284$	6.27413	0.372301
$285$	−0.890084	−0.0527240
$286$	−7.20775	−0.426203
$287$	−3.78017	−0.223136
$288$	−1.00000	−0.0589256
$289$	−8.64742	−0.508672
$290$	9.70171	0.569704
$291$	12.8116	0.751031
$292$	−6.00000	−0.351123
$293$	−21.0508	−1.22980	−0.614901	−	0.788604i	$-0.710804\pi$
$293$	−21.0508	−1.22980	−0.614901	+	0.788604i	$0.710804\pi$
$294$	1.00000	0.0583212
$295$	−8.98792	−0.523297
$296$	7.42758	0.431720
$297$	−4.49396	−0.260766
$298$	−11.4276	−0.661982
$299$	1.60388	0.0927545
$300$	−1.00000	−0.0577350
$301$	4.49396	0.259028
$302$	0.792249	0.0455888
$303$	3.82371	0.219666
$304$	0.890084	0.0510498
$305$	3.42758	0.196263
$306$	2.89008	0.165215
$307$	0.195669	0.0111674	0.00558372	−	0.999984i	$-0.498223\pi$
$307$	0.195669	0.0111674	0.00558372	+	0.999984i	$0.498223\pi$
$308$	−4.49396	−0.256067
$309$	16.6353	0.946351
$310$	5.87800	0.333848
$311$	−4.50471	−0.255439	−0.127719	−	0.991810i	$-0.540766\pi$
$311$	−4.50471	−0.255439	−0.127719	+	0.991810i	$0.540766\pi$
$312$	1.60388	0.0908016
$313$	−19.1400	−1.08186	−0.540930	−	0.841068i	$-0.681928\pi$
$313$	−19.1400	−1.08186	−0.540930	+	0.841068i	$0.681928\pi$
$314$	8.21983	0.463872
$315$	−1.00000	−0.0563436
$316$	2.21983	0.124875
$317$	26.3043	1.47739	0.738697	−	0.674037i	$-0.235441\pi$
$317$	26.3043	1.47739	0.738697	+	0.674037i	$0.235441\pi$
$318$	5.20775	0.292036
$319$	−43.5991	−2.44108
$320$	1.00000	0.0559017
$321$	17.1836	0.959094
$322$	1.00000	0.0557278
$323$	−2.57242	−0.143133
$324$	1.00000	0.0555556
$325$	1.60388	0.0889670
$326$	9.18359	0.508632
$327$	0.219833	0.0121568
$328$	−3.78017	−0.208725
$329$	9.87800	0.544592
$330$	4.49396	0.247384
$331$	4.35258	0.239240	0.119620	−	0.992820i	$-0.461832\pi$
$331$	4.35258	0.239240	0.119620	+	0.992820i	$0.461832\pi$
$332$	10.3177	0.566256
$333$	−7.42758	−0.407029
$334$	3.54958	0.194224
$335$	5.48188	0.299507
$336$	1.00000	0.0545545
$337$	−35.4819	−1.93282	−0.966411	−	0.257003i	$-0.917265\pi$
$337$	−35.4819	−1.93282	−0.966411	+	0.257003i	$0.917265\pi$
$338$	10.4276	0.567186
$339$	14.6353	0.794882
$340$	−2.89008	−0.156737
$341$	−26.4155	−1.43048
$342$	−0.890084	−0.0481302
$343$	−1.00000	−0.0539949
$344$	4.49396	0.242298
$345$	−1.00000	−0.0538382
$346$	−23.2814	−1.25162
$347$	22.9638	1.23276	0.616379	−	0.787449i	$-0.288599\pi$
$347$	22.9638	1.23276	0.616379	+	0.787449i	$0.288599\pi$
$348$	9.70171	0.520066
$349$	−27.0858	−1.44987	−0.724934	−	0.688819i	$-0.758130\pi$
$349$	−27.0858	−1.44987	−0.724934	+	0.688819i	$0.758130\pi$
$350$	1.00000	0.0534522
$351$	−1.60388	−0.0856085
$352$	−4.49396	−0.239529
$353$	−23.1836	−1.23394	−0.616969	−	0.786988i	$-0.711640\pi$
$353$	−23.1836	−1.23394	−0.616969	+	0.786988i	$0.711640\pi$
$354$	−8.98792	−0.477702
$355$	6.27413	0.332996
$356$	9.79954	0.519375
$357$	−2.89008	−0.152959
$358$	11.4034	0.602689
$359$	14.6595	0.773699	0.386849	−	0.922143i	$-0.373563\pi$
$359$	14.6595	0.773699	0.386849	+	0.922143i	$0.373563\pi$
$360$	−1.00000	−0.0527046
$361$	−18.2078	−0.958303
$362$	24.5241	1.28896
$363$	−9.19567	−0.482647
$364$	−1.60388	−0.0840659
$365$	−6.00000	−0.314054
$366$	3.42758	0.179163
$367$	30.1715	1.57494	0.787470	−	0.616353i	$-0.211391\pi$
$367$	30.1715	1.57494	0.787470	+	0.616353i	$0.211391\pi$
$368$	1.00000	0.0521286
$369$	3.78017	0.196788
$370$	7.42758	0.386142
$371$	−5.20775	−0.270373
$372$	5.87800	0.304760
$373$	−24.5241	−1.26981	−0.634905	−	0.772591i	$-0.718961\pi$
$373$	−24.5241	−1.26981	−0.634905	+	0.772591i	$0.718961\pi$
$374$	12.9879	0.671589
$375$	−1.00000	−0.0516398
$376$	9.87800	0.509419
$377$	−15.5603	−0.801398
$378$	−1.00000	−0.0514344
$379$	−0.792249	−0.0406951	−0.0203476	−	0.999793i	$-0.506477\pi$
$379$	−0.792249	−0.0406951	−0.0203476	+	0.999793i	$0.506477\pi$
$380$	0.890084	0.0456603
$381$	−10.9095	−0.558909
$382$	−13.7802	−0.705055
$383$	19.2078	0.981470	0.490735	−	0.871309i	$-0.336728\pi$
$383$	19.2078	0.981470	0.490735	+	0.871309i	$0.336728\pi$
$384$	1.00000	0.0510310
$385$	−4.49396	−0.229033
$386$	−7.18359	−0.365635
$387$	−4.49396	−0.228441
$388$	−12.8116	−0.650412
$389$	12.0629	0.611614	0.305807	−	0.952093i	$-0.401074\pi$
$389$	12.0629	0.611614	0.305807	+	0.952093i	$0.401074\pi$
$390$	1.60388	0.0812154
$391$	−2.89008	−0.146158
$392$	−1.00000	−0.0505076
$393$	−10.4155	−0.525393
$394$	−6.63533	−0.334283
$395$	2.21983	0.111692
$396$	4.49396	0.225830
$397$	−14.3961	−0.722521	−0.361260	−	0.932465i	$-0.617653\pi$
$397$	−14.3961	−0.722521	−0.361260	+	0.932465i	$0.617653\pi$
$398$	−18.9638	−0.950567
$399$	0.890084	0.0445599
$400$	1.00000	0.0500000
$401$	30.3370	1.51496	0.757480	−	0.652859i	$-0.226430\pi$
$401$	30.3370	1.51496	0.757480	+	0.652859i	$0.226430\pi$
$402$	5.48188	0.273411
$403$	−9.42758	−0.469621
$404$	−3.82371	−0.190237
$405$	1.00000	0.0496904
$406$	−9.70171	−0.481488
$407$	−33.3793	−1.65455
$408$	−2.89008	−0.143080
$409$	−35.7318	−1.76683	−0.883413	−	0.468595i	$-0.844760\pi$
$409$	−35.7318	−1.76683	−0.883413	+	0.468595i	$0.844760\pi$
$410$	−3.78017	−0.186689
$411$	−2.43967	−0.120340
$412$	−16.6353	−0.819564
$413$	8.98792	0.442267
$414$	−1.00000	−0.0491473
$415$	10.3177	0.506474
$416$	−1.60388	−0.0786365
$417$	−5.42758	−0.265790
$418$	−4.00000	−0.195646
$419$	−1.27545	−0.0623100	−0.0311550	−	0.999515i	$-0.509919\pi$
$419$	−1.27545	−0.0623100	−0.0311550	+	0.999515i	$0.509919\pi$
$420$	1.00000	0.0487950
$421$	−7.58450	−0.369646	−0.184823	−	0.982772i	$-0.559171\pi$
$421$	−7.58450	−0.369646	−0.184823	+	0.982772i	$0.559171\pi$
$422$	5.34050	0.259972
$423$	−9.87800	−0.480285
$424$	−5.20775	−0.252911
$425$	−2.89008	−0.140190
$426$	6.27413	0.303982
$427$	−3.42758	−0.165872
$428$	−17.1836	−0.830600
$429$	−7.20775	−0.347993
$430$	4.49396	0.216718
$431$	10.7681	0.518680	0.259340	−	0.965786i	$-0.416495\pi$
$431$	10.7681	0.518680	0.259340	+	0.965786i	$0.416495\pi$
$432$	−1.00000	−0.0481125
$433$	−4.42029	−0.212425	−0.106213	−	0.994343i	$-0.533872\pi$
$433$	−4.42029	−0.212425	−0.106213	+	0.994343i	$0.533872\pi$
$434$	−5.87800	−0.282153
$435$	9.70171	0.465161
$436$	−0.219833	−0.0105281
$437$	0.890084	0.0425785
$438$	−6.00000	−0.286691
$439$	22.8659	1.09133	0.545665	−	0.838003i	$-0.316277\pi$
$439$	22.8659	1.09133	0.545665	+	0.838003i	$0.316277\pi$
$440$	−4.49396	−0.214241
$441$	1.00000	0.0476190
$442$	4.63533	0.220480
$443$	34.5241	1.64029	0.820145	−	0.572156i	$-0.193893\pi$
$443$	34.5241	1.64029	0.820145	+	0.572156i	$0.193893\pi$
$444$	7.42758	0.352498
$445$	9.79954	0.464543
$446$	−4.15213	−0.196609
$447$	−11.4276	−0.540506
$448$	−1.00000	−0.0472456
$449$	8.17151	0.385637	0.192819	−	0.981234i	$-0.438237\pi$
$449$	8.17151	0.385637	0.192819	+	0.981234i	$0.438237\pi$
$450$	−1.00000	−0.0471405
$451$	16.9879	0.799930
$452$	−14.6353	−0.688388
$453$	0.792249	0.0372231
$454$	14.8659	0.697692
$455$	−1.60388	−0.0751908
$456$	0.890084	0.0416820
$457$	−2.29829	−0.107509	−0.0537547	−	0.998554i	$-0.517119\pi$
$457$	−2.29829	−0.107509	−0.0537547	+	0.998554i	$0.517119\pi$
$458$	12.7681	0.596613
$459$	2.89008	0.134898
$460$	1.00000	0.0466252
$461$	2.59179	0.120712	0.0603559	−	0.998177i	$-0.480776\pi$
$461$	2.59179	0.120712	0.0603559	+	0.998177i	$0.480776\pi$
$462$	−4.49396	−0.209078
$463$	25.2379	1.17290	0.586452	−	0.809984i	$-0.300524\pi$
$463$	25.2379	1.17290	0.586452	+	0.809984i	$0.300524\pi$
$464$	−9.70171	−0.450391
$465$	5.87800	0.272586
$466$	−8.21983	−0.380776
$467$	24.9288	1.15357	0.576785	−	0.816896i	$-0.304307\pi$
$467$	24.9288	1.15357	0.576785	+	0.816896i	$0.304307\pi$
$468$	1.60388	0.0741392
$469$	−5.48188	−0.253130
$470$	9.87800	0.455638
$471$	8.21983	0.378750
$472$	8.98792	0.413702
$473$	−20.1957	−0.928598
$474$	2.21983	0.101960
$475$	0.890084	0.0408398
$476$	2.89008	0.132467
$477$	5.20775	0.238447
$478$	−2.71379	−0.124126
$479$	−27.4905	−1.25607	−0.628037	−	0.778184i	$-0.716141\pi$
$479$	−27.4905	−1.25607	−0.628037	+	0.778184i	$0.716141\pi$
$480$	1.00000	0.0456435
$481$	−11.9129	−0.543182
$482$	21.7453	0.990469
$483$	1.00000	0.0455016
$484$	9.19567	0.417985
$485$	−12.8116	−0.581746
$486$	1.00000	0.0453609
$487$	2.11721	0.0959400	0.0479700	−	0.998849i	$-0.484725\pi$
$487$	2.11721	0.0959400	0.0479700	+	0.998849i	$0.484725\pi$
$488$	−3.42758	−0.155159
$489$	9.18359	0.415296
$490$	−1.00000	−0.0451754
$491$	−34.2586	−1.54607	−0.773034	−	0.634364i	$-0.781262\pi$
$491$	−34.2586	−1.54607	−0.773034	+	0.634364i	$0.781262\pi$
$492$	−3.78017	−0.170423
$493$	28.0388	1.26280
$494$	−1.42758	−0.0642300
$495$	4.49396	0.201988
$496$	−5.87800	−0.263930
$497$	−6.27413	−0.281433
$498$	10.3177	0.462346
$499$	−34.1715	−1.52973	−0.764863	−	0.644193i	$-0.777194\pi$
$499$	−34.1715	−1.52973	−0.764863	+	0.644193i	$0.777194\pi$
$500$	1.00000	0.0447214
$501$	3.54958	0.158584
$502$	19.3599	0.864074
$503$	−11.2948	−0.503612	−0.251806	−	0.967778i	$-0.581024\pi$
$503$	−11.2948	−0.503612	−0.251806	+	0.967778i	$0.581024\pi$
$504$	1.00000	0.0445435
$505$	−3.82371	−0.170153
$506$	−4.49396	−0.199781
$507$	10.4276	0.463105
$508$	10.9095	0.484029
$509$	−15.3840	−0.681886	−0.340943	−	0.940084i	$-0.610746\pi$
$509$	−15.3840	−0.681886	−0.340943	+	0.940084i	$0.610746\pi$
$510$	−2.89008	−0.127975
$511$	6.00000	0.265424
$512$	−1.00000	−0.0441942
$513$	−0.890084	−0.0392982
$514$	24.0629	1.06137
$515$	−16.6353	−0.733040
$516$	4.49396	0.197836
$517$	−44.3913	−1.95233
$518$	−7.42758	−0.326349
$519$	−23.2814	−1.02194
$520$	−1.60388	−0.0703346
$521$	−3.73663	−0.163705	−0.0818523	−	0.996644i	$-0.526084\pi$
$521$	−3.73663	−0.163705	−0.0818523	+	0.996644i	$0.526084\pi$
$522$	9.70171	0.424632
$523$	10.4203	0.455647	0.227824	−	0.973702i	$-0.426839\pi$
$523$	10.4203	0.455647	0.227824	+	0.973702i	$0.426839\pi$
$524$	10.4155	0.455003
$525$	1.00000	0.0436436
$526$	−6.76809	−0.295103
$527$	16.9879	0.740005
$528$	−4.49396	−0.195574
$529$	1.00000	0.0434783
$530$	−5.20775	−0.226210
$531$	−8.98792	−0.390042
$532$	−0.890084	−0.0385900
$533$	6.06292	0.262614
$534$	9.79954	0.424068
$535$	−17.1836	−0.742911
$536$	−5.48188	−0.236781
$537$	11.4034	0.492094
$538$	−11.5797	−0.499237
$539$	4.49396	0.193569
$540$	−1.00000	−0.0430331
$541$	−31.8189	−1.36800	−0.684001	−	0.729481i	$-0.739762\pi$
$541$	−31.8189	−1.36800	−0.684001	+	0.729481i	$0.739762\pi$
$542$	−17.6340	−0.757445
$543$	24.5241	1.05243
$544$	2.89008	0.123911
$545$	−0.219833	−0.00941659
$546$	−1.60388	−0.0686395
$547$	−5.67158	−0.242499	−0.121250	−	0.992622i	$-0.538690\pi$
$547$	−5.67158	−0.242499	−0.121250	+	0.992622i	$0.538690\pi$
$548$	2.43967	0.104217
$549$	3.42758	0.146286
$550$	−4.49396	−0.191623
$551$	−8.63533	−0.367878
$552$	1.00000	0.0425628
$553$	−2.21983	−0.0943969
$554$	13.5060	0.573817
$555$	7.42758	0.315283
$556$	5.42758	0.230181
$557$	−43.0267	−1.82310	−0.911549	−	0.411191i	$-0.865113\pi$
$557$	−43.0267	−1.82310	−0.911549	+	0.411191i	$0.865113\pi$
$558$	5.87800	0.248836
$559$	−7.20775	−0.304855
$560$	−1.00000	−0.0422577
$561$	12.9879	0.548350
$562$	−8.90946	−0.375823
$563$	−3.70650	−0.156210	−0.0781051	−	0.996945i	$-0.524887\pi$
$563$	−3.70650	−0.156210	−0.0781051	+	0.996945i	$0.524887\pi$
$564$	9.87800	0.415939
$565$	−14.6353	−0.615713
$566$	15.1642	0.637399
$567$	−1.00000	−0.0419961
$568$	−6.27413	−0.263257
$569$	−4.03013	−0.168952	−0.0844759	−	0.996426i	$-0.526922\pi$
$569$	−4.03013	−0.168952	−0.0844759	+	0.996426i	$0.526922\pi$
$570$	0.890084	0.0372815
$571$	−47.4034	−1.98377	−0.991886	−	0.127133i	$-0.959423\pi$
$571$	−47.4034	−1.98377	−0.991886	+	0.127133i	$0.959423\pi$
$572$	7.20775	0.301371
$573$	−13.7802	−0.575675
$574$	3.78017	0.157781
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−3.97584	−0.165516	−0.0827581	−	0.996570i	$-0.526373\pi$
$577$	−3.97584	−0.165516	−0.0827581	+	0.996570i	$0.526373\pi$
$578$	8.64742	0.359685
$579$	−7.18359	−0.298540
$580$	−9.70171	−0.402842
$581$	−10.3177	−0.428049
$582$	−12.8116	−0.531059
$583$	23.4034	0.969271
$584$	6.00000	0.248282
$585$	1.60388	0.0663121
$586$	21.0508	0.869602
$587$	−36.9879	−1.52665	−0.763327	−	0.646012i	$-0.776436\pi$
$587$	−36.9879	−1.52665	−0.763327	+	0.646012i	$0.776436\pi$
$588$	−1.00000	−0.0412393
$589$	−5.23191	−0.215577
$590$	8.98792	0.370027
$591$	−6.63533	−0.272941
$592$	−7.42758	−0.305272
$593$	−39.5749	−1.62515	−0.812574	−	0.582858i	$-0.801934\pi$
$593$	−39.5749	−1.62515	−0.812574	+	0.582858i	$0.801934\pi$
$594$	4.49396	0.184389
$595$	2.89008	0.118482
$596$	11.4276	0.468092
$597$	−18.9638	−0.776135
$598$	−1.60388	−0.0655873
$599$	−7.17496	−0.293161	−0.146581	−	0.989199i	$-0.546827\pi$
$599$	−7.17496	−0.293161	−0.146581	+	0.989199i	$0.546827\pi$
$600$	1.00000	0.0408248
$601$	−4.02416	−0.164149	−0.0820745	−	0.996626i	$-0.526155\pi$
$601$	−4.02416	−0.164149	−0.0820745	+	0.996626i	$0.526155\pi$
$602$	−4.49396	−0.183160
$603$	5.48188	0.223239
$604$	−0.792249	−0.0322362
$605$	9.19567	0.373857
$606$	−3.82371	−0.155328
$607$	0.787463	0.0319621	0.0159811	−	0.999872i	$-0.494913\pi$
$607$	0.787463	0.0319621	0.0159811	+	0.999872i	$0.494913\pi$
$608$	−0.890084	−0.0360977
$609$	−9.70171	−0.393133
$610$	−3.42758	−0.138779
$611$	−15.8431	−0.640943
$612$	−2.89008	−0.116825
$613$	−2.35258	−0.0950200	−0.0475100	−	0.998871i	$-0.515129\pi$
$613$	−2.35258	−0.0950200	−0.0475100	+	0.998871i	$0.515129\pi$
$614$	−0.195669	−0.00789657
$615$	−3.78017	−0.152431
$616$	4.49396	0.181067
$617$	19.8189	0.797880	0.398940	−	0.916977i	$-0.369378\pi$
$617$	19.8189	0.797880	0.398940	+	0.916977i	$0.369378\pi$
$618$	−16.6353	−0.669171
$619$	41.4771	1.66711	0.833553	−	0.552440i	$-0.186303\pi$
$619$	41.4771	1.66711	0.833553	+	0.552440i	$0.186303\pi$
$620$	−5.87800	−0.236066
$621$	−1.00000	−0.0401286
$622$	4.50471	0.180623
$623$	−9.79954	−0.392610
$624$	−1.60388	−0.0642064
$625$	1.00000	0.0400000
$626$	19.1400	0.764990
$627$	−4.00000	−0.159745
$628$	−8.21983	−0.328007
$629$	21.4663	0.855919
$630$	1.00000	0.0398410
$631$	12.9008	0.513574	0.256787	−	0.966468i	$-0.417336\pi$
$631$	12.9008	0.513574	0.256787	+	0.966468i	$0.417336\pi$
$632$	−2.21983	−0.0883002
$633$	5.34050	0.212266
$634$	−26.3043	−1.04468
$635$	10.9095	0.432929
$636$	−5.20775	−0.206501
$637$	1.60388	0.0635479
$638$	43.5991	1.72610
$639$	6.27413	0.248201
$640$	−1.00000	−0.0395285
$641$	5.34913	0.211278	0.105639	−	0.994405i	$-0.466311\pi$
$641$	5.34913	0.211278	0.105639	+	0.994405i	$0.466311\pi$
$642$	−17.1836	−0.678182
$643$	3.49529	0.137841	0.0689203	−	0.997622i	$-0.478045\pi$
$643$	3.49529	0.137841	0.0689203	+	0.997622i	$0.478045\pi$
$644$	−1.00000	−0.0394055
$645$	4.49396	0.176949
$646$	2.57242	0.101210
$647$	−2.56166	−0.100709	−0.0503547	−	0.998731i	$-0.516035\pi$
$647$	−2.56166	−0.100709	−0.0503547	+	0.998731i	$0.516035\pi$
$648$	−1.00000	−0.0392837
$649$	−40.3913	−1.58550
$650$	−1.60388	−0.0629092
$651$	−5.87800	−0.230377
$652$	−9.18359	−0.359657
$653$	35.8672	1.40359	0.701797	−	0.712377i	$-0.252381\pi$
$653$	35.8672	1.40359	0.701797	+	0.712377i	$0.252381\pi$
$654$	−0.219833	−0.00859613
$655$	10.4155	0.406967
$656$	3.78017	0.147591
$657$	−6.00000	−0.234082
$658$	−9.87800	−0.385085
$659$	−39.6534	−1.54468	−0.772338	−	0.635211i	$-0.780913\pi$
$659$	−39.6534	−1.54468	−0.772338	+	0.635211i	$0.780913\pi$
$660$	−4.49396	−0.174927
$661$	−15.6233	−0.607674	−0.303837	−	0.952724i	$-0.598268\pi$
$661$	−15.6233	−0.607674	−0.303837	+	0.952724i	$0.598268\pi$
$662$	−4.35258	−0.169168
$663$	4.63533	0.180021
$664$	−10.3177	−0.400403
$665$	−0.890084	−0.0345160
$666$	7.42758	0.287813
$667$	−9.70171	−0.375652
$668$	−3.54958	−0.137337
$669$	−4.15213	−0.160531
$670$	−5.48188	−0.211783
$671$	15.4034	0.594642
$672$	−1.00000	−0.0385758
$673$	−13.7560	−0.530255	−0.265127	−	0.964213i	$-0.585414\pi$
$673$	−13.7560	−0.530255	−0.265127	+	0.964213i	$0.585414\pi$
$674$	35.4819	1.36671
$675$	−1.00000	−0.0384900
$676$	−10.4276	−0.401061
$677$	−26.3913	−1.01430	−0.507151	−	0.861857i	$-0.669301\pi$
$677$	−26.3913	−1.01430	−0.507151	+	0.861857i	$0.669301\pi$
$678$	−14.6353	−0.562067
$679$	12.8116	0.491665
$680$	2.89008	0.110830
$681$	14.8659	0.569663
$682$	26.4155	1.01150
$683$	−8.54825	−0.327090	−0.163545	−	0.986536i	$-0.552293\pi$
$683$	−8.54825	−0.327090	−0.163545	+	0.986536i	$0.552293\pi$
$684$	0.890084	0.0340332
$685$	2.43967	0.0932148
$686$	1.00000	0.0381802
$687$	12.7681	0.487133
$688$	−4.49396	−0.171331
$689$	8.35258	0.318208
$690$	1.00000	0.0380693
$691$	25.7802	0.980724	0.490362	−	0.871519i	$-0.336865\pi$
$691$	25.7802	0.980724	0.490362	+	0.871519i	$0.336865\pi$
$692$	23.2814	0.885027
$693$	−4.49396	−0.170711
$694$	−22.9638	−0.871692
$695$	5.42758	0.205880
$696$	−9.70171	−0.367742
$697$	−10.9250	−0.413814
$698$	27.0858	1.02521
$699$	−8.21983	−0.310903
$700$	−1.00000	−0.0377964
$701$	−27.9758	−1.05663	−0.528316	−	0.849048i	$-0.677177\pi$
$701$	−27.9758	−1.05663	−0.528316	+	0.849048i	$0.677177\pi$
$702$	1.60388	0.0605344
$703$	−6.61117	−0.249345
$704$	4.49396	0.169372
$705$	9.87800	0.372027
$706$	23.1836	0.872526
$707$	3.82371	0.143805
$708$	8.98792	0.337787
$709$	−2.59658	−0.0975166	−0.0487583	−	0.998811i	$-0.515526\pi$
$709$	−2.59658	−0.0975166	−0.0487583	+	0.998811i	$0.515526\pi$
$710$	−6.27413	−0.235464
$711$	2.21983	0.0832502
$712$	−9.79954	−0.367253
$713$	−5.87800	−0.220133
$714$	2.89008	0.108159
$715$	7.20775	0.269555
$716$	−11.4034	−0.426166
$717$	−2.71379	−0.101348
$718$	−14.6595	−0.547088
$719$	−2.61596	−0.0975587	−0.0487794	−	0.998810i	$-0.515533\pi$
$719$	−2.61596	−0.0975587	−0.0487794	+	0.998810i	$0.515533\pi$
$720$	1.00000	0.0372678
$721$	16.6353	0.619532
$722$	18.2078	0.677622
$723$	21.7453	0.808715
$724$	−24.5241	−0.911431
$725$	−9.70171	−0.360312
$726$	9.19567	0.341283
$727$	−27.8646	−1.03344	−0.516720	−	0.856154i	$-0.672847\pi$
$727$	−27.8646	−1.03344	−0.516720	+	0.856154i	$0.672847\pi$
$728$	1.60388	0.0594436
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	12.9879	0.480376
$732$	−3.42758	−0.126687
$733$	45.2680	1.67201	0.836006	−	0.548720i	$-0.184885\pi$
$733$	45.2680	1.67201	0.836006	+	0.548720i	$0.184885\pi$
$734$	−30.1715	−1.11365
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	24.6353	0.907454
$738$	−3.78017	−0.139150
$739$	−19.4034	−0.713766	−0.356883	−	0.934149i	$-0.616161\pi$
$739$	−19.4034	−0.713766	−0.356883	+	0.934149i	$0.616161\pi$
$740$	−7.42758	−0.273043
$741$	−1.42758	−0.0524436
$742$	5.20775	0.191183
$743$	−28.5870	−1.04876	−0.524378	−	0.851486i	$-0.675702\pi$
$743$	−28.5870	−1.04876	−0.524378	+	0.851486i	$0.675702\pi$
$744$	−5.87800	−0.215498
$745$	11.4276	0.418674
$746$	24.5241	0.897891
$747$	10.3177	0.377504
$748$	−12.9879	−0.474885
$749$	17.1836	0.627875
$750$	1.00000	0.0365148
$751$	10.6810	0.389755	0.194878	−	0.980828i	$-0.437569\pi$
$751$	10.6810	0.389755	0.194878	+	0.980828i	$0.437569\pi$
$752$	−9.87800	−0.360214
$753$	19.3599	0.705513
$754$	15.5603	0.566674
$755$	−0.792249	−0.0288329
$756$	1.00000	0.0363696
$757$	10.0871	0.366621	0.183311	−	0.983055i	$-0.441319\pi$
$757$	10.0871	0.366621	0.183311	+	0.983055i	$0.441319\pi$
$758$	0.792249	0.0287758
$759$	−4.49396	−0.163120
$760$	−0.890084	−0.0322867
$761$	29.4034	1.06587	0.532937	−	0.846155i	$-0.321088\pi$
$761$	29.4034	1.06587	0.532937	+	0.846155i	$0.321088\pi$
$762$	10.9095	0.395208
$763$	0.219833	0.00795847
$764$	13.7802	0.498549
$765$	−2.89008	−0.104491
$766$	−19.2078	−0.694004
$767$	−14.4155	−0.520514
$768$	−1.00000	−0.0360844
$769$	16.7788	0.605060	0.302530	−	0.953140i	$-0.402169\pi$
$769$	16.7788	0.605060	0.302530	+	0.953140i	$0.402169\pi$
$770$	4.49396	0.161951
$771$	24.0629	0.866605
$772$	7.18359	0.258543
$773$	2.04833	0.0736732	0.0368366	−	0.999321i	$-0.488272\pi$
$773$	2.04833	0.0736732	0.0368366	+	0.999321i	$0.488272\pi$
$774$	4.49396	0.161532
$775$	−5.87800	−0.211144
$776$	12.8116	0.459911
$777$	−7.42758	−0.266463
$778$	−12.0629	−0.432477
$779$	3.36467	0.120552
$780$	−1.60388	−0.0574280
$781$	28.1957	1.00892
$782$	2.89008	0.103349
$783$	9.70171	0.346711
$784$	1.00000	0.0357143
$785$	−8.21983	−0.293378
$786$	10.4155	0.371509
$787$	−22.6547	−0.807553	−0.403777	−	0.914858i	$-0.632303\pi$
$787$	−22.6547	−0.807553	−0.403777	+	0.914858i	$0.632303\pi$
$788$	6.63533	0.236374
$789$	−6.76809	−0.240950
$790$	−2.21983	−0.0789781
$791$	14.6353	0.520373
$792$	−4.49396	−0.159686
$793$	5.49742	0.195219
$794$	14.3961	0.510899
$795$	−5.20775	−0.184700
$796$	18.9638	0.672152
$797$	−21.7560	−0.770637	−0.385319	−	0.922784i	$-0.625908\pi$
$797$	−21.7560	−0.770637	−0.385319	+	0.922784i	$0.625908\pi$
$798$	−0.890084	−0.0315086
$799$	28.5483	1.00996
$800$	−1.00000	−0.0353553
$801$	9.79954	0.346250
$802$	−30.3370	−1.07124
$803$	−26.9638	−0.951530
$804$	−5.48188	−0.193331
$805$	−1.00000	−0.0352454
$806$	9.42758	0.332072
$807$	−11.5797	−0.407625
$808$	3.82371	0.134518
$809$	17.8646	0.628086	0.314043	−	0.949409i	$-0.398316\pi$
$809$	17.8646	0.628086	0.314043	+	0.949409i	$0.398316\pi$
$810$	−1.00000	−0.0351364
$811$	−2.85517	−0.100258	−0.0501292	−	0.998743i	$-0.515963\pi$
$811$	−2.85517	−0.100258	−0.0501292	+	0.998743i	$0.515963\pi$
$812$	9.70171	0.340463
$813$	−17.6340	−0.618452
$814$	33.3793	1.16994
$815$	−9.18359	−0.321687
$816$	2.89008	0.101173
$817$	−4.00000	−0.139942
$818$	35.7318	1.24933
$819$	−1.60388	−0.0560439
$820$	3.78017	0.132009
$821$	8.36121	0.291808	0.145904	−	0.989299i	$-0.453391\pi$
$821$	8.36121	0.291808	0.145904	+	0.989299i	$0.453391\pi$
$822$	2.43967	0.0850931
$823$	31.7405	1.10640	0.553202	−	0.833047i	$-0.313406\pi$
$823$	31.7405	1.10640	0.553202	+	0.833047i	$0.313406\pi$
$824$	16.6353	0.579519
$825$	−4.49396	−0.156460
$826$	−8.98792	−0.312730
$827$	43.1594	1.50080	0.750400	−	0.660984i	$-0.229861\pi$
$827$	43.1594	1.50080	0.750400	+	0.660984i	$0.229861\pi$
$828$	1.00000	0.0347524
$829$	42.6461	1.48116	0.740580	−	0.671968i	$-0.234551\pi$
$829$	42.6461	1.48116	0.740580	+	0.671968i	$0.234551\pi$
$830$	−10.3177	−0.358131
$831$	13.5060	0.468519
$832$	1.60388	0.0556044
$833$	−2.89008	−0.100135
$834$	5.42758	0.187942
$835$	−3.54958	−0.122838
$836$	4.00000	0.138343
$837$	5.87800	0.203173
$838$	1.27545	0.0440598
$839$	24.9396	0.861010	0.430505	−	0.902588i	$-0.358335\pi$
$839$	24.9396	0.861010	0.430505	+	0.902588i	$0.358335\pi$
$840$	−1.00000	−0.0345033
$841$	65.1232	2.24563
$842$	7.58450	0.261379
$843$	−8.90946	−0.306858
$844$	−5.34050	−0.183828
$845$	−10.4276	−0.358720
$846$	9.87800	0.339613
$847$	−9.19567	−0.315967
$848$	5.20775	0.178835
$849$	15.1642	0.520434
$850$	2.89008	0.0991291
$851$	−7.42758	−0.254614
$852$	−6.27413	−0.214948
$853$	26.7004	0.914204	0.457102	−	0.889414i	$-0.348887\pi$
$853$	26.7004	0.914204	0.457102	+	0.889414i	$0.348887\pi$
$854$	3.42758	0.117289
$855$	0.890084	0.0304402
$856$	17.1836	0.587323
$857$	−16.3767	−0.559419	−0.279710	−	0.960085i	$-0.590238\pi$
$857$	−16.3767	−0.559419	−0.279710	+	0.960085i	$0.590238\pi$
$858$	7.20775	0.246069
$859$	21.3405	0.728129	0.364064	−	0.931374i	$-0.381389\pi$
$859$	21.3405	0.728129	0.364064	+	0.931374i	$0.381389\pi$
$860$	−4.49396	−0.153243
$861$	3.78017	0.128828
$862$	−10.7681	−0.366762
$863$	22.8164	0.776680	0.388340	−	0.921516i	$-0.373049\pi$
$863$	22.8164	0.776680	0.388340	+	0.921516i	$0.373049\pi$
$864$	1.00000	0.0340207
$865$	23.2814	0.791592
$866$	4.42029	0.150207
$867$	8.64742	0.293682
$868$	5.87800	0.199512
$869$	9.97584	0.338407
$870$	−9.70171	−0.328919
$871$	8.79225	0.297914
$872$	0.219833	0.00744447
$873$	−12.8116	−0.433608
$874$	−0.890084	−0.0301075
$875$	−1.00000	−0.0338062
$876$	6.00000	0.202721
$877$	5.54480	0.187234	0.0936172	−	0.995608i	$-0.470157\pi$
$877$	5.54480	0.187234	0.0936172	+	0.995608i	$0.470157\pi$
$878$	−22.8659	−0.771687
$879$	21.0508	0.710027
$880$	4.49396	0.151491
$881$	27.5797	0.929184	0.464592	−	0.885525i	$-0.346201\pi$
$881$	27.5797	0.929184	0.464592	+	0.885525i	$0.346201\pi$
$882$	−1.00000	−0.0336718
$883$	−15.5991	−0.524951	−0.262476	−	0.964939i	$-0.584539\pi$
$883$	−15.5991	−0.524951	−0.262476	+	0.964939i	$0.584539\pi$
$884$	−4.63533	−0.155903
$885$	8.98792	0.302126
$886$	−34.5241	−1.15986
$887$	13.6125	0.457063	0.228531	−	0.973537i	$-0.426608\pi$
$887$	13.6125	0.457063	0.228531	+	0.973537i	$0.426608\pi$
$888$	−7.42758	−0.249253
$889$	−10.9095	−0.365892
$890$	−9.79954	−0.328481
$891$	4.49396	0.150553
$892$	4.15213	0.139024
$893$	−8.79225	−0.294221
$894$	11.4276	0.382196
$895$	−11.4034	−0.381174
$896$	1.00000	0.0334077
$897$	−1.60388	−0.0535518
$898$	−8.17151	−0.272687
$899$	57.0267	1.90195
$900$	1.00000	0.0333333
$901$	−15.0508	−0.501416
$902$	−16.9879	−0.565636
$903$	−4.49396	−0.149550
$904$	14.6353	0.486764
$905$	−24.5241	−0.815208
$906$	−0.792249	−0.0263207
$907$	−0.249964	−0.00829990	−0.00414995	−	0.999991i	$-0.501321\pi$
$907$	−0.249964	−0.00829990	−0.00414995	+	0.999991i	$0.501321\pi$
$908$	−14.8659	−0.493343
$909$	−3.82371	−0.126824
$910$	1.60388	0.0531680
$911$	34.3284	1.13735	0.568676	−	0.822562i	$-0.307456\pi$
$911$	34.3284	1.13735	0.568676	+	0.822562i	$0.307456\pi$
$912$	−0.890084	−0.0294736
$913$	46.3672	1.53453
$914$	2.29829	0.0760207
$915$	−3.42758	−0.113312
$916$	−12.7681	−0.421869
$917$	−10.4155	−0.343950
$918$	−2.89008	−0.0953870
$919$	22.3069	0.735837	0.367919	−	0.929858i	$-0.380071\pi$
$919$	22.3069	0.735837	0.367919	+	0.929858i	$0.380071\pi$
$920$	−1.00000	−0.0329690
$921$	−0.195669	−0.00644752
$922$	−2.59179	−0.0853562
$923$	10.0629	0.331225
$924$	4.49396	0.147840
$925$	−7.42758	−0.244217
$926$	−25.2379	−0.829368
$927$	−16.6353	−0.546376
$928$	9.70171	0.318474
$929$	−23.0267	−0.755481	−0.377740	−	0.925912i	$-0.623299\pi$
$929$	−23.0267	−0.755481	−0.377740	+	0.925912i	$0.623299\pi$
$930$	−5.87800	−0.192747
$931$	0.890084	0.0291713
$932$	8.21983	0.269250
$933$	4.50471	0.147478
$934$	−24.9288	−0.815697
$935$	−12.9879	−0.424750
$936$	−1.60388	−0.0524243
$937$	−44.1280	−1.44160	−0.720799	−	0.693144i	$-0.756225\pi$
$937$	−44.1280	−1.44160	−0.720799	+	0.693144i	$0.756225\pi$
$938$	5.48188	0.178990
$939$	19.1400	0.624612
$940$	−9.87800	−0.322185
$941$	14.3913	0.469144	0.234572	−	0.972099i	$-0.424631\pi$
$941$	14.3913	0.469144	0.234572	+	0.972099i	$0.424631\pi$
$942$	−8.21983	−0.267817
$943$	3.78017	0.123099
$944$	−8.98792	−0.292532
$945$	1.00000	0.0325300
$946$	20.1957	0.656618
$947$	38.6112	1.25469	0.627347	−	0.778740i	$-0.284141\pi$
$947$	38.6112	1.25469	0.627347	+	0.778740i	$0.284141\pi$
$948$	−2.21983	−0.0720968
$949$	−9.62325	−0.312384
$950$	−0.890084	−0.0288781
$951$	−26.3043	−0.852974
$952$	−2.89008	−0.0936682
$953$	0.659498	0.0213632	0.0106816	−	0.999943i	$-0.496600\pi$
$953$	0.659498	0.0213632	0.0106816	+	0.999943i	$0.496600\pi$
$954$	−5.20775	−0.168607
$955$	13.7802	0.445916
$956$	2.71379	0.0877703
$957$	43.5991	1.40936
$958$	27.4905	0.888178
$959$	−2.43967	−0.0787809
$960$	−1.00000	−0.0322749
$961$	3.55091	0.114545
$962$	11.9129	0.384088
$963$	−17.1836	−0.553733
$964$	−21.7453	−0.700367
$965$	7.18359	0.231248
$966$	−1.00000	−0.0321745
$967$	−11.9845	−0.385394	−0.192697	−	0.981258i	$-0.561723\pi$
$967$	−11.9845	−0.385394	−0.192697	+	0.981258i	$0.561723\pi$
$968$	−9.19567	−0.295560
$969$	2.57242	0.0826379
$970$	12.8116	0.411357
$971$	29.4228	0.944223	0.472111	−	0.881539i	$-0.343492\pi$
$971$	29.4228	0.944223	0.472111	+	0.881539i	$0.343492\pi$
$972$	−1.00000	−0.0320750
$973$	−5.42758	−0.174000
$974$	−2.11721	−0.0678398
$975$	−1.60388	−0.0513651
$976$	3.42758	0.109714
$977$	−32.9154	−1.05306	−0.526529	−	0.850157i	$-0.676507\pi$
$977$	−32.9154	−1.05306	−0.526529	+	0.850157i	$0.676507\pi$
$978$	−9.18359	−0.293659
$979$	44.0388	1.40748
$980$	1.00000	0.0319438
$981$	−0.219833	−0.00701871
$982$	34.2586	1.09324
$983$	17.6233	0.562094	0.281047	−	0.959694i	$-0.409318\pi$
$983$	17.6233	0.562094	0.281047	+	0.959694i	$0.409318\pi$
$984$	3.78017	0.120507
$985$	6.63533	0.211419
$986$	−28.0388	−0.892936
$987$	−9.87800	−0.314420
$988$	1.42758	0.0454175
$989$	−4.49396	−0.142900
$990$	−4.49396	−0.142827
$991$	8.96641	0.284827	0.142414	−	0.989807i	$-0.454514\pi$
$991$	8.96641	0.284827	0.142414	+	0.989807i	$0.454514\pi$
$992$	5.87800	0.186627
$993$	−4.35258	−0.138125
$994$	6.27413	0.199003
$995$	18.9638	0.601191
$996$	−10.3177	−0.326928
$997$	7.84522	0.248460	0.124230	−	0.992253i	$-0.460354\pi$
$997$	7.84522	0.248460	0.124230	+	0.992253i	$0.460354\pi$
$998$	34.1715	1.08168
$999$	7.42758	0.234998

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.49396 q^{11} -1.00000 q^{12} +1.60388 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.89008 q^{17} -1.00000 q^{18} +0.890084 q^{19} +1.00000 q^{20} +1.00000 q^{21} -4.49396 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.60388 q^{26} -1.00000 q^{27} -1.00000 q^{28} -9.70171 q^{29} +1.00000 q^{30} -5.87800 q^{31} -1.00000 q^{32} -4.49396 q^{33} +2.89008 q^{34} -1.00000 q^{35} +1.00000 q^{36} -7.42758 q^{37} -0.890084 q^{38} -1.60388 q^{39} -1.00000 q^{40} +3.78017 q^{41} -1.00000 q^{42} -4.49396 q^{43} +4.49396 q^{44} +1.00000 q^{45} -1.00000 q^{46} -9.87800 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +2.89008 q^{51} +1.60388 q^{52} +5.20775 q^{53} +1.00000 q^{54} +4.49396 q^{55} +1.00000 q^{56} -0.890084 q^{57} +9.70171 q^{58} -8.98792 q^{59} -1.00000 q^{60} +3.42758 q^{61} +5.87800 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.60388 q^{65} +4.49396 q^{66} +5.48188 q^{67} -2.89008 q^{68} -1.00000 q^{69} +1.00000 q^{70} +6.27413 q^{71} -1.00000 q^{72} -6.00000 q^{73} +7.42758 q^{74} -1.00000 q^{75} +0.890084 q^{76} -4.49396 q^{77} +1.60388 q^{78} +2.21983 q^{79} +1.00000 q^{80} +1.00000 q^{81} -3.78017 q^{82} +10.3177 q^{83} +1.00000 q^{84} -2.89008 q^{85} +4.49396 q^{86} +9.70171 q^{87} -4.49396 q^{88} +9.79954 q^{89} -1.00000 q^{90} -1.60388 q^{91} +1.00000 q^{92} +5.87800 q^{93} +9.87800 q^{94} +0.890084 q^{95} +1.00000 q^{96} -12.8116 q^{97} -1.00000 q^{98} +4.49396 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 4 q^{26} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 3 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 2 q^{38} + 4 q^{39} - 3 q^{40} + 10 q^{41} - 3 q^{42} - 4 q^{43} + 4 q^{44} + 3 q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} - 2 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 2 q^{57} + 2 q^{58} - 8 q^{59} - 3 q^{60} - 6 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 3 q^{69} + 3 q^{70} + 8 q^{71} - 3 q^{72} - 18 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{76} - 4 q^{77} - 4 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 10 q^{82} + 14 q^{83} + 3 q^{84} - 8 q^{85} + 4 q^{86} + 2 q^{87} - 4 q^{88} - 16 q^{89} - 3 q^{90} + 4 q^{91} + 3 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} + 3 q^{96} - 12 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 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 - 4 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 4 * q^26 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 3 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 + 10 * q^41 - 3 * q^42 - 4 * q^43 + 4 * q^44 + 3 * q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 - 2 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 2 * q^57 + 2 * q^58 - 8 * q^59 - 3 * q^60 - 6 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 3 * q^69 + 3 * q^70 + 8 * q^71 - 3 * q^72 - 18 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^76 - 4 * q^77 - 4 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 10 * q^82 + 14 * q^83 + 3 * q^84 - 8 * q^85 + 4 * q^86 + 2 * q^87 - 4 * q^88 - 16 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 + 3 * q^96 - 12 * q^97 - 3 * q^98 + 4 * q^99

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