LMFDB - Embedded newform 4830.2.a.by.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:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.311108$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.80642 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -5.05086 q^{17} -1.00000 q^{18} +5.80642 q^{19} +1.00000 q^{20} -1.00000 q^{21} +5.80642 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -3.80642 q^{29} +1.00000 q^{30} -7.05086 q^{31} -1.00000 q^{32} +5.80642 q^{33} +5.05086 q^{34} +1.00000 q^{35} +1.00000 q^{36} +3.24443 q^{37} -5.80642 q^{38} -2.00000 q^{39} -1.00000 q^{40} +0.755569 q^{41} +1.00000 q^{42} +7.05086 q^{43} -5.80642 q^{44} +1.00000 q^{45} -1.00000 q^{46} -5.80642 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +5.05086 q^{51} +2.00000 q^{52} -5.61285 q^{53} +1.00000 q^{54} -5.80642 q^{55} -1.00000 q^{56} -5.80642 q^{57} +3.80642 q^{58} +4.85728 q^{59} -1.00000 q^{60} +6.00000 q^{61} +7.05086 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -5.80642 q^{66} -10.6637 q^{67} -5.05086 q^{68} -1.00000 q^{69} -1.00000 q^{70} +10.6637 q^{71} -1.00000 q^{72} +13.6128 q^{73} -3.24443 q^{74} -1.00000 q^{75} +5.80642 q^{76} -5.80642 q^{77} +2.00000 q^{78} +2.75557 q^{79} +1.00000 q^{80} +1.00000 q^{81} -0.755569 q^{82} +15.9081 q^{83} -1.00000 q^{84} -5.05086 q^{85} -7.05086 q^{86} +3.80642 q^{87} +5.80642 q^{88} +10.8573 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} +7.05086 q^{93} +5.80642 q^{94} +5.80642 q^{95} +1.00000 q^{96} +8.75557 q^{97} -1.00000 q^{98} -5.80642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{30} - 8 q^{31} - 3 q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} + 10 q^{37} - 4 q^{38} - 6 q^{39} - 3 q^{40} + 2 q^{41} + 3 q^{42} + 8 q^{43} - 4 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} + 3 q^{54} - 4 q^{55} - 3 q^{56} - 4 q^{57} - 2 q^{58} - 12 q^{59} - 3 q^{60} + 18 q^{61} + 8 q^{62} + 3 q^{63} + 3 q^{64} + 6 q^{65} - 4 q^{66} + 8 q^{67} - 2 q^{68} - 3 q^{69} - 3 q^{70} - 8 q^{71} - 3 q^{72} + 14 q^{73} - 10 q^{74} - 3 q^{75} + 4 q^{76} - 4 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 8 q^{83} - 3 q^{84} - 2 q^{85} - 8 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 3 q^{90} + 6 q^{91} + 3 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{95} + 3 q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 + 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^30 - 8 * q^31 - 3 * q^32 + 4 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 + 10 * q^37 - 4 * q^38 - 6 * q^39 - 3 * q^40 + 2 * q^41 + 3 * q^42 + 8 * q^43 - 4 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 + 3 * q^54 - 4 * q^55 - 3 * q^56 - 4 * q^57 - 2 * q^58 - 12 * q^59 - 3 * q^60 + 18 * q^61 + 8 * q^62 + 3 * q^63 + 3 * q^64 + 6 * q^65 - 4 * q^66 + 8 * q^67 - 2 * q^68 - 3 * q^69 - 3 * q^70 - 8 * q^71 - 3 * q^72 + 14 * q^73 - 10 * q^74 - 3 * q^75 + 4 * q^76 - 4 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 8 * q^83 - 3 * q^84 - 2 * q^85 - 8 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 3 * q^90 + 6 * q^91 + 3 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^95 + 3 * q^96 + 26 * q^97 - 3 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−5.80642	−1.75070	−0.875351	−	0.483487i	$-0.839370\pi$
$11$	−5.80642	−1.75070	−0.875351	+	0.483487i	$0.839370\pi$
$12$	−1.00000	−0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−5.05086	−1.22501	−0.612506	−	0.790466i	$-0.709839\pi$
$17$	−5.05086	−1.22501	−0.612506	+	0.790466i	$0.709839\pi$
$18$	−1.00000	−0.235702
$19$	5.80642	1.33208	0.666042	−	0.745914i	$-0.267987\pi$
$19$	5.80642	1.33208	0.666042	+	0.745914i	$0.267987\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	5.80642	1.23793
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−3.80642	−0.706835	−0.353418	−	0.935466i	$-0.614981\pi$
$29$	−3.80642	−0.706835	−0.353418	+	0.935466i	$0.614981\pi$
$30$	1.00000	0.182574
$31$	−7.05086	−1.26637	−0.633185	−	0.774000i	$-0.718253\pi$
$31$	−7.05086	−1.26637	−0.633185	+	0.774000i	$0.718253\pi$
$32$	−1.00000	−0.176777
$33$	5.80642	1.01077
$34$	5.05086	0.866215
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	3.24443	0.533381	0.266691	−	0.963782i	$-0.414070\pi$
$37$	3.24443	0.533381	0.266691	+	0.963782i	$0.414070\pi$
$38$	−5.80642	−0.941926
$39$	−2.00000	−0.320256
$40$	−1.00000	−0.158114
$41$	0.755569	0.118000	0.0590000	−	0.998258i	$-0.481209\pi$
$41$	0.755569	0.118000	0.0590000	+	0.998258i	$0.481209\pi$
$42$	1.00000	0.154303
$43$	7.05086	1.07525	0.537623	−	0.843186i	$-0.319323\pi$
$43$	7.05086	1.07525	0.537623	+	0.843186i	$0.319323\pi$
$44$	−5.80642	−0.875351
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−5.80642	−0.846954	−0.423477	−	0.905907i	$-0.639191\pi$
$47$	−5.80642	−0.846954	−0.423477	+	0.905907i	$0.639191\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	5.05086	0.707261
$52$	2.00000	0.277350
$53$	−5.61285	−0.770984	−0.385492	−	0.922711i	$-0.625968\pi$
$53$	−5.61285	−0.770984	−0.385492	+	0.922711i	$0.625968\pi$
$54$	1.00000	0.136083
$55$	−5.80642	−0.782938
$56$	−1.00000	−0.133631
$57$	−5.80642	−0.769080
$58$	3.80642	0.499808
$59$	4.85728	0.632364	0.316182	−	0.948699i	$-0.397599\pi$
$59$	4.85728	0.632364	0.316182	+	0.948699i	$0.397599\pi$
$60$	−1.00000	−0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	7.05086	0.895459
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	−5.80642	−0.714721
$67$	−10.6637	−1.30278	−0.651389	−	0.758744i	$-0.725814\pi$
$67$	−10.6637	−1.30278	−0.651389	+	0.758744i	$0.725814\pi$
$68$	−5.05086	−0.612506
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	10.6637	1.26555	0.632774	−	0.774336i	$-0.281916\pi$
$71$	10.6637	1.26555	0.632774	+	0.774336i	$0.281916\pi$
$72$	−1.00000	−0.117851
$73$	13.6128	1.59326	0.796632	−	0.604465i	$-0.206613\pi$
$73$	13.6128	1.59326	0.796632	+	0.604465i	$0.206613\pi$
$74$	−3.24443	−0.377157
$75$	−1.00000	−0.115470
$76$	5.80642	0.666042
$77$	−5.80642	−0.661703
$78$	2.00000	0.226455
$79$	2.75557	0.310026	0.155013	−	0.987912i	$-0.450458\pi$
$79$	2.75557	0.310026	0.155013	+	0.987912i	$0.450458\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−0.755569	−0.0834386
$83$	15.9081	1.74614	0.873072	−	0.487591i	$-0.162124\pi$
$83$	15.9081	1.74614	0.873072	+	0.487591i	$0.162124\pi$
$84$	−1.00000	−0.109109
$85$	−5.05086	−0.547842
$86$	−7.05086	−0.760313
$87$	3.80642	0.408091
$88$	5.80642	0.618967
$89$	10.8573	1.15087	0.575435	−	0.817848i	$-0.304833\pi$
$89$	10.8573	1.15087	0.575435	+	0.817848i	$0.304833\pi$
$90$	−1.00000	−0.105409
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	7.05086	0.731140
$94$	5.80642	0.598887
$95$	5.80642	0.595727
$96$	1.00000	0.102062
$97$	8.75557	0.888993	0.444497	−	0.895781i	$-0.353383\pi$
$97$	8.75557	0.888993	0.444497	+	0.895781i	$0.353383\pi$
$98$	−1.00000	−0.101015
$99$	−5.80642	−0.583568
$100$	1.00000	0.100000
$101$	−18.8573	−1.87637	−0.938185	−	0.346135i	$-0.887494\pi$
$101$	−18.8573	−1.87637	−0.938185	+	0.346135i	$0.887494\pi$
$102$	−5.05086	−0.500109
$103$	−6.10171	−0.601219	−0.300610	−	0.953747i	$-0.597190\pi$
$103$	−6.10171	−0.601219	−0.300610	+	0.953747i	$0.597190\pi$
$104$	−2.00000	−0.196116
$105$	−1.00000	−0.0975900
$106$	5.61285	0.545168
$107$	11.3461	1.09687	0.548436	−	0.836192i	$-0.315223\pi$
$107$	11.3461	1.09687	0.548436	+	0.836192i	$0.315223\pi$
$108$	−1.00000	−0.0962250
$109$	−12.3684	−1.18468	−0.592340	−	0.805688i	$-0.701796\pi$
$109$	−12.3684	−1.18468	−0.592340	+	0.805688i	$0.701796\pi$
$110$	5.80642	0.553621
$111$	−3.24443	−0.307948
$112$	1.00000	0.0944911
$113$	12.3684	1.16352	0.581761	−	0.813360i	$-0.302364\pi$
$113$	12.3684	1.16352	0.581761	+	0.813360i	$0.302364\pi$
$114$	5.80642	0.543821
$115$	1.00000	0.0932505
$116$	−3.80642	−0.353418
$117$	2.00000	0.184900
$118$	−4.85728	−0.447149
$119$	−5.05086	−0.463011
$120$	1.00000	0.0912871
$121$	22.7146	2.06496
$122$	−6.00000	−0.543214
$123$	−0.755569	−0.0681273
$124$	−7.05086	−0.633185
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−14.6637	−1.30119	−0.650597	−	0.759424i	$-0.725481\pi$
$127$	−14.6637	−1.30119	−0.650597	+	0.759424i	$0.725481\pi$
$128$	−1.00000	−0.0883883
$129$	−7.05086	−0.620793
$130$	−2.00000	−0.175412
$131$	−18.9590	−1.65645	−0.828227	−	0.560392i	$-0.810650\pi$
$131$	−18.9590	−1.65645	−0.828227	+	0.560392i	$0.810650\pi$
$132$	5.80642	0.505384
$133$	5.80642	0.503481
$134$	10.6637	0.921204
$135$	−1.00000	−0.0860663
$136$	5.05086	0.433107
$137$	18.4701	1.57801	0.789005	−	0.614387i	$-0.210597\pi$
$137$	18.4701	1.57801	0.789005	+	0.614387i	$0.210597\pi$
$138$	1.00000	0.0851257
$139$	8.85728	0.751265	0.375632	−	0.926769i	$-0.377426\pi$
$139$	8.85728	0.751265	0.375632	+	0.926769i	$0.377426\pi$
$140$	1.00000	0.0845154
$141$	5.80642	0.488989
$142$	−10.6637	−0.894878
$143$	−11.6128	−0.971115
$144$	1.00000	0.0833333
$145$	−3.80642	−0.316106
$146$	−13.6128	−1.12661
$147$	−1.00000	−0.0824786
$148$	3.24443	0.266691
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	1.00000	0.0816497
$151$	−5.51114	−0.448490	−0.224245	−	0.974533i	$-0.571992\pi$
$151$	−5.51114	−0.448490	−0.224245	+	0.974533i	$0.571992\pi$
$152$	−5.80642	−0.470963
$153$	−5.05086	−0.408337
$154$	5.80642	0.467895
$155$	−7.05086	−0.566338
$156$	−2.00000	−0.160128
$157$	16.1017	1.28506	0.642528	−	0.766262i	$-0.277886\pi$
$157$	16.1017	1.28506	0.642528	+	0.766262i	$0.277886\pi$
$158$	−2.75557	−0.219221
$159$	5.61285	0.445128
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	−14.9590	−1.17168	−0.585839	−	0.810427i	$-0.699235\pi$
$163$	−14.9590	−1.17168	−0.585839	+	0.810427i	$0.699235\pi$
$164$	0.755569	0.0590000
$165$	5.80642	0.452029
$166$	−15.9081	−1.23471
$167$	2.19358	0.169744	0.0848720	−	0.996392i	$-0.472952\pi$
$167$	2.19358	0.169744	0.0848720	+	0.996392i	$0.472952\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	5.05086	0.387383
$171$	5.80642	0.444028
$172$	7.05086	0.537623
$173$	16.2766	1.23748	0.618742	−	0.785595i	$-0.287643\pi$
$173$	16.2766	1.23748	0.618742	+	0.785595i	$0.287643\pi$
$174$	−3.80642	−0.288564
$175$	1.00000	0.0755929
$176$	−5.80642	−0.437676
$177$	−4.85728	−0.365095
$178$	−10.8573	−0.813787
$179$	2.36842	0.177024	0.0885119	−	0.996075i	$-0.471789\pi$
$179$	2.36842	0.177024	0.0885119	+	0.996075i	$0.471789\pi$
$180$	1.00000	0.0745356
$181$	8.48886	0.630972	0.315486	−	0.948930i	$-0.397832\pi$
$181$	8.48886	0.630972	0.315486	+	0.948930i	$0.397832\pi$
$182$	−2.00000	−0.148250
$183$	−6.00000	−0.443533
$184$	−1.00000	−0.0737210
$185$	3.24443	0.238535
$186$	−7.05086	−0.516994
$187$	29.3274	2.14463
$188$	−5.80642	−0.423477
$189$	−1.00000	−0.0727393
$190$	−5.80642	−0.421242
$191$	−4.85728	−0.351460	−0.175730	−	0.984438i	$-0.556229\pi$
$191$	−4.85728	−0.351460	−0.175730	+	0.984438i	$0.556229\pi$
$192$	−1.00000	−0.0721688
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−8.75557	−0.628613
$195$	−2.00000	−0.143223
$196$	1.00000	0.0714286
$197$	−4.10171	−0.292235	−0.146117	−	0.989267i	$-0.546678\pi$
$197$	−4.10171	−0.292235	−0.146117	+	0.989267i	$0.546678\pi$
$198$	5.80642	0.412645
$199$	−20.4701	−1.45109	−0.725544	−	0.688175i	$-0.758412\pi$
$199$	−20.4701	−1.45109	−0.725544	+	0.688175i	$0.758412\pi$
$200$	−1.00000	−0.0707107
$201$	10.6637	0.752160
$202$	18.8573	1.32679
$203$	−3.80642	−0.267159
$204$	5.05086	0.353631
$205$	0.755569	0.0527712
$206$	6.10171	0.425126
$207$	1.00000	0.0695048
$208$	2.00000	0.138675
$209$	−33.7146	−2.33208
$210$	1.00000	0.0690066
$211$	−1.51114	−0.104031	−0.0520155	−	0.998646i	$-0.516565\pi$
$211$	−1.51114	−0.104031	−0.0520155	+	0.998646i	$0.516565\pi$
$212$	−5.61285	−0.385492
$213$	−10.6637	−0.730665
$214$	−11.3461	−0.775606
$215$	7.05086	0.480864
$216$	1.00000	0.0680414
$217$	−7.05086	−0.478643
$218$	12.3684	0.837695
$219$	−13.6128	−0.919871
$220$	−5.80642	−0.391469
$221$	−10.1017	−0.679515
$222$	3.24443	0.217752
$223$	27.2257	1.82317	0.911584	−	0.411115i	$-0.134860\pi$
$223$	27.2257	1.82317	0.911584	+	0.411115i	$0.134860\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−12.3684	−0.822735
$227$	6.19358	0.411082	0.205541	−	0.978648i	$-0.434105\pi$
$227$	6.19358	0.411082	0.205541	+	0.978648i	$0.434105\pi$
$228$	−5.80642	−0.384540
$229$	0.488863	0.0323049	0.0161525	−	0.999870i	$-0.494858\pi$
$229$	0.488863	0.0323049	0.0161525	+	0.999870i	$0.494858\pi$
$230$	−1.00000	−0.0659380
$231$	5.80642	0.382035
$232$	3.80642	0.249904
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−2.00000	−0.130744
$235$	−5.80642	−0.378769
$236$	4.85728	0.316182
$237$	−2.75557	−0.178993
$238$	5.05086	0.327398
$239$	−20.5620	−1.33004	−0.665022	−	0.746823i	$-0.731578\pi$
$239$	−20.5620	−1.33004	−0.665022	+	0.746823i	$0.731578\pi$
$240$	−1.00000	−0.0645497
$241$	−14.7654	−0.951124	−0.475562	−	0.879682i	$-0.657755\pi$
$241$	−14.7654	−0.951124	−0.475562	+	0.879682i	$0.657755\pi$
$242$	−22.7146	−1.46015
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	1.00000	0.0638877
$246$	0.755569	0.0481733
$247$	11.6128	0.738908
$248$	7.05086	0.447730
$249$	−15.9081	−1.00814
$250$	−1.00000	−0.0632456
$251$	−0.653858	−0.0412712	−0.0206356	−	0.999787i	$-0.506569\pi$
$251$	−0.653858	−0.0412712	−0.0206356	+	0.999787i	$0.506569\pi$
$252$	1.00000	0.0629941
$253$	−5.80642	−0.365047
$254$	14.6637	0.920083
$255$	5.05086	0.316297
$256$	1.00000	0.0625000
$257$	18.8573	1.17628	0.588142	−	0.808757i	$-0.299859\pi$
$257$	18.8573	1.17628	0.588142	+	0.808757i	$0.299859\pi$
$258$	7.05086	0.438967
$259$	3.24443	0.201599
$260$	2.00000	0.124035
$261$	−3.80642	−0.235612
$262$	18.9590	1.17129
$263$	6.10171	0.376248	0.188124	−	0.982145i	$-0.439759\pi$
$263$	6.10171	0.376248	0.188124	+	0.982145i	$0.439759\pi$
$264$	−5.80642	−0.357361
$265$	−5.61285	−0.344794
$266$	−5.80642	−0.356015
$267$	−10.8573	−0.664455
$268$	−10.6637	−0.651389
$269$	20.9590	1.27789	0.638946	−	0.769252i	$-0.279371\pi$
$269$	20.9590	1.27789	0.638946	+	0.769252i	$0.279371\pi$
$270$	1.00000	0.0608581
$271$	−22.2766	−1.35320	−0.676602	−	0.736349i	$-0.736548\pi$
$271$	−22.2766	−1.35320	−0.676602	+	0.736349i	$0.736548\pi$
$272$	−5.05086	−0.306253
$273$	−2.00000	−0.121046
$274$	−18.4701	−1.11582
$275$	−5.80642	−0.350141
$276$	−1.00000	−0.0601929
$277$	21.3176	1.28085	0.640424	−	0.768021i	$-0.278759\pi$
$277$	21.3176	1.28085	0.640424	+	0.768021i	$0.278759\pi$
$278$	−8.85728	−0.531224
$279$	−7.05086	−0.422124
$280$	−1.00000	−0.0597614
$281$	28.2766	1.68684	0.843419	−	0.537257i	$-0.180539\pi$
$281$	28.2766	1.68684	0.843419	+	0.537257i	$0.180539\pi$
$282$	−5.80642	−0.345768
$283$	24.4701	1.45460	0.727299	−	0.686321i	$-0.240775\pi$
$283$	24.4701	1.45460	0.727299	+	0.686321i	$0.240775\pi$
$284$	10.6637	0.632774
$285$	−5.80642	−0.343943
$286$	11.6128	0.686682
$287$	0.755569	0.0445998
$288$	−1.00000	−0.0589256
$289$	8.51114	0.500655
$290$	3.80642	0.223521
$291$	−8.75557	−0.513261
$292$	13.6128	0.796632
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	1.00000	0.0583212
$295$	4.85728	0.282802
$296$	−3.24443	−0.188579
$297$	5.80642	0.336923
$298$	−6.00000	−0.347571
$299$	2.00000	0.115663
$300$	−1.00000	−0.0577350
$301$	7.05086	0.406405
$302$	5.51114	0.317130
$303$	18.8573	1.08332
$304$	5.80642	0.333021
$305$	6.00000	0.343559
$306$	5.05086	0.288738
$307$	−4.59057	−0.261998	−0.130999	−	0.991383i	$-0.541818\pi$
$307$	−4.59057	−0.261998	−0.130999	+	0.991383i	$0.541818\pi$
$308$	−5.80642	−0.330852
$309$	6.10171	0.347114
$310$	7.05086	0.400462
$311$	24.4701	1.38757	0.693787	−	0.720180i	$-0.255941\pi$
$311$	24.4701	1.38757	0.693787	+	0.720180i	$0.255941\pi$
$312$	2.00000	0.113228
$313$	−19.9813	−1.12941	−0.564704	−	0.825294i	$-0.691010\pi$
$313$	−19.9813	−1.12941	−0.564704	+	0.825294i	$0.691010\pi$
$314$	−16.1017	−0.908672
$315$	1.00000	0.0563436
$316$	2.75557	0.155013
$317$	−30.9403	−1.73778	−0.868889	−	0.495007i	$-0.835165\pi$
$317$	−30.9403	−1.73778	−0.868889	+	0.495007i	$0.835165\pi$
$318$	−5.61285	−0.314753
$319$	22.1017	1.23746
$320$	1.00000	0.0559017
$321$	−11.3461	−0.633280
$322$	−1.00000	−0.0557278
$323$	−29.3274	−1.63182
$324$	1.00000	0.0555556
$325$	2.00000	0.110940
$326$	14.9590	0.828502
$327$	12.3684	0.683975
$328$	−0.755569	−0.0417193
$329$	−5.80642	−0.320119
$330$	−5.80642	−0.319633
$331$	15.6128	0.858160	0.429080	−	0.903267i	$-0.358838\pi$
$331$	15.6128	0.858160	0.429080	+	0.903267i	$0.358838\pi$
$332$	15.9081	0.873072
$333$	3.24443	0.177794
$334$	−2.19358	−0.120027
$335$	−10.6637	−0.582620
$336$	−1.00000	−0.0545545
$337$	23.8064	1.29682	0.648409	−	0.761292i	$-0.275435\pi$
$337$	23.8064	1.29682	0.648409	+	0.761292i	$0.275435\pi$
$338$	9.00000	0.489535
$339$	−12.3684	−0.671760
$340$	−5.05086	−0.273921
$341$	40.9403	2.21704
$342$	−5.80642	−0.313975
$343$	1.00000	0.0539949
$344$	−7.05086	−0.380157
$345$	−1.00000	−0.0538382
$346$	−16.2766	−0.875033
$347$	22.8385	1.22604	0.613019	−	0.790068i	$-0.289955\pi$
$347$	22.8385	1.22604	0.613019	+	0.790068i	$0.289955\pi$
$348$	3.80642	0.204046
$349$	11.8064	0.631983	0.315992	−	0.948762i	$-0.397663\pi$
$349$	11.8064	0.631983	0.315992	+	0.948762i	$0.397663\pi$
$350$	−1.00000	−0.0534522
$351$	−2.00000	−0.106752
$352$	5.80642	0.309483
$353$	4.75557	0.253113	0.126557	−	0.991959i	$-0.459607\pi$
$353$	4.75557	0.253113	0.126557	+	0.991959i	$0.459607\pi$
$354$	4.85728	0.258161
$355$	10.6637	0.565971
$356$	10.8573	0.575435
$357$	5.05086	0.267320
$358$	−2.36842	−0.125175
$359$	−4.85728	−0.256357	−0.128179	−	0.991751i	$-0.540913\pi$
$359$	−4.85728	−0.256357	−0.128179	+	0.991751i	$0.540913\pi$
$360$	−1.00000	−0.0527046
$361$	14.7146	0.774450
$362$	−8.48886	−0.446165
$363$	−22.7146	−1.19221
$364$	2.00000	0.104828
$365$	13.6128	0.712529
$366$	6.00000	0.313625
$367$	25.1240	1.31146	0.655731	−	0.754995i	$-0.272361\pi$
$367$	25.1240	1.31146	0.655731	+	0.754995i	$0.272361\pi$
$368$	1.00000	0.0521286
$369$	0.755569	0.0393333
$370$	−3.24443	−0.168670
$371$	−5.61285	−0.291405
$372$	7.05086	0.365570
$373$	24.7556	1.28179	0.640897	−	0.767627i	$-0.278562\pi$
$373$	24.7556	1.28179	0.640897	+	0.767627i	$0.278562\pi$
$374$	−29.3274	−1.51648
$375$	−1.00000	−0.0516398
$376$	5.80642	0.299443
$377$	−7.61285	−0.392082
$378$	1.00000	0.0514344
$379$	9.12399	0.468668	0.234334	−	0.972156i	$-0.424709\pi$
$379$	9.12399	0.468668	0.234334	+	0.972156i	$0.424709\pi$
$380$	5.80642	0.297863
$381$	14.6637	0.751244
$382$	4.85728	0.248520
$383$	−6.75557	−0.345193	−0.172597	−	0.984993i	$-0.555216\pi$
$383$	−6.75557	−0.345193	−0.172597	+	0.984993i	$0.555216\pi$
$384$	1.00000	0.0510310
$385$	−5.80642	−0.295923
$386$	6.00000	0.305392
$387$	7.05086	0.358415
$388$	8.75557	0.444497
$389$	37.8163	1.91736	0.958680	−	0.284485i	$-0.0918226\pi$
$389$	37.8163	1.91736	0.958680	+	0.284485i	$0.0918226\pi$
$390$	2.00000	0.101274
$391$	−5.05086	−0.255433
$392$	−1.00000	−0.0505076
$393$	18.9590	0.956354
$394$	4.10171	0.206641
$395$	2.75557	0.138648
$396$	−5.80642	−0.291784
$397$	23.5111	1.17999	0.589995	−	0.807407i	$-0.299130\pi$
$397$	23.5111	1.17999	0.589995	+	0.807407i	$0.299130\pi$
$398$	20.4701	1.02607
$399$	−5.80642	−0.290685
$400$	1.00000	0.0500000
$401$	27.6860	1.38257	0.691286	−	0.722581i	$-0.257045\pi$
$401$	27.6860	1.38257	0.691286	+	0.722581i	$0.257045\pi$
$402$	−10.6637	−0.531857
$403$	−14.1017	−0.702456
$404$	−18.8573	−0.938185
$405$	1.00000	0.0496904
$406$	3.80642	0.188910
$407$	−18.8385	−0.933792
$408$	−5.05086	−0.250055
$409$	2.77430	0.137181	0.0685903	−	0.997645i	$-0.478150\pi$
$409$	2.77430	0.137181	0.0685903	+	0.997645i	$0.478150\pi$
$410$	−0.755569	−0.0373149
$411$	−18.4701	−0.911064
$412$	−6.10171	−0.300610
$413$	4.85728	0.239011
$414$	−1.00000	−0.0491473
$415$	15.9081	0.780900
$416$	−2.00000	−0.0980581
$417$	−8.85728	−0.433743
$418$	33.7146	1.64903
$419$	10.9590	0.535382	0.267691	−	0.963505i	$-0.413739\pi$
$419$	10.9590	0.535382	0.267691	+	0.963505i	$0.413739\pi$
$420$	−1.00000	−0.0487950
$421$	9.14272	0.445589	0.222794	−	0.974865i	$-0.428482\pi$
$421$	9.14272	0.445589	0.222794	+	0.974865i	$0.428482\pi$
$422$	1.51114	0.0735610
$423$	−5.80642	−0.282318
$424$	5.61285	0.272584
$425$	−5.05086	−0.245002
$426$	10.6637	0.516658
$427$	6.00000	0.290360
$428$	11.3461	0.548436
$429$	11.6128	0.560674
$430$	−7.05086	−0.340022
$431$	−29.9813	−1.44415	−0.722073	−	0.691817i	$-0.756811\pi$
$431$	−29.9813	−1.44415	−0.722073	+	0.691817i	$0.756811\pi$
$432$	−1.00000	−0.0481125
$433$	−14.4701	−0.695390	−0.347695	−	0.937608i	$-0.613036\pi$
$433$	−14.4701	−0.695390	−0.347695	+	0.937608i	$0.613036\pi$
$434$	7.05086	0.338452
$435$	3.80642	0.182504
$436$	−12.3684	−0.592340
$437$	5.80642	0.277759
$438$	13.6128	0.650447
$439$	13.1526	0.627738	0.313869	−	0.949466i	$-0.398375\pi$
$439$	13.1526	0.627738	0.313869	+	0.949466i	$0.398375\pi$
$440$	5.80642	0.276810
$441$	1.00000	0.0476190
$442$	10.1017	0.480489
$443$	13.8983	0.660328	0.330164	−	0.943924i	$-0.392896\pi$
$443$	13.8983	0.660328	0.330164	+	0.943924i	$0.392896\pi$
$444$	−3.24443	−0.153974
$445$	10.8573	0.514684
$446$	−27.2257	−1.28917
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	5.61285	0.264887	0.132443	−	0.991191i	$-0.457718\pi$
$449$	5.61285	0.264887	0.132443	+	0.991191i	$0.457718\pi$
$450$	−1.00000	−0.0471405
$451$	−4.38715	−0.206583
$452$	12.3684	0.581761
$453$	5.51114	0.258936
$454$	−6.19358	−0.290679
$455$	2.00000	0.0937614
$456$	5.80642	0.271911
$457$	23.8064	1.11362	0.556809	−	0.830641i	$-0.312026\pi$
$457$	23.8064	1.11362	0.556809	+	0.830641i	$0.312026\pi$
$458$	−0.488863	−0.0228430
$459$	5.05086	0.235754
$460$	1.00000	0.0466252
$461$	14.8573	0.691972	0.345986	−	0.938240i	$-0.387544\pi$
$461$	14.8573	0.691972	0.345986	+	0.938240i	$0.387544\pi$
$462$	−5.80642	−0.270139
$463$	13.5397	0.629244	0.314622	−	0.949217i	$-0.398122\pi$
$463$	13.5397	0.629244	0.314622	+	0.949217i	$0.398122\pi$
$464$	−3.80642	−0.176709
$465$	7.05086	0.326976
$466$	−14.0000	−0.648537
$467$	−39.1338	−1.81090	−0.905449	−	0.424455i	$-0.860466\pi$
$467$	−39.1338	−1.81090	−0.905449	+	0.424455i	$0.860466\pi$
$468$	2.00000	0.0924500
$469$	−10.6637	−0.492404
$470$	5.80642	0.267830
$471$	−16.1017	−0.741928
$472$	−4.85728	−0.223574
$473$	−40.9403	−1.88243
$474$	2.75557	0.126567
$475$	5.80642	0.266417
$476$	−5.05086	−0.231506
$477$	−5.61285	−0.256995
$478$	20.5620	0.940484
$479$	−23.8163	−1.08819	−0.544097	−	0.839023i	$-0.683127\pi$
$479$	−23.8163	−1.08819	−0.544097	+	0.839023i	$0.683127\pi$
$480$	1.00000	0.0456435
$481$	6.48886	0.295867
$482$	14.7654	0.672546
$483$	−1.00000	−0.0455016
$484$	22.7146	1.03248
$485$	8.75557	0.397570
$486$	1.00000	0.0453609
$487$	−4.17484	−0.189180	−0.0945900	−	0.995516i	$-0.530154\pi$
$487$	−4.17484	−0.189180	−0.0945900	+	0.995516i	$0.530154\pi$
$488$	−6.00000	−0.271607
$489$	14.9590	0.676469
$490$	−1.00000	−0.0451754
$491$	−28.0830	−1.26737	−0.633683	−	0.773592i	$-0.718458\pi$
$491$	−28.0830	−1.26737	−0.633683	+	0.773592i	$0.718458\pi$
$492$	−0.755569	−0.0340637
$493$	19.2257	0.865882
$494$	−11.6128	−0.522487
$495$	−5.80642	−0.260979
$496$	−7.05086	−0.316593
$497$	10.6637	0.478332
$498$	15.9081	0.712861
$499$	24.7368	1.10737	0.553686	−	0.832725i	$-0.313221\pi$
$499$	24.7368	1.10737	0.553686	+	0.832725i	$0.313221\pi$
$500$	1.00000	0.0447214
$501$	−2.19358	−0.0980018
$502$	0.653858	0.0291831
$503$	−36.8573	−1.64338	−0.821692	−	0.569931i	$-0.806970\pi$
$503$	−36.8573	−1.64338	−0.821692	+	0.569931i	$0.806970\pi$
$504$	−1.00000	−0.0445435
$505$	−18.8573	−0.839138
$506$	5.80642	0.258127
$507$	9.00000	0.399704
$508$	−14.6637	−0.650597
$509$	−38.2864	−1.69701	−0.848507	−	0.529184i	$-0.822498\pi$
$509$	−38.2864	−1.69701	−0.848507	+	0.529184i	$0.822498\pi$
$510$	−5.05086	−0.223656
$511$	13.6128	0.602197
$512$	−1.00000	−0.0441942
$513$	−5.80642	−0.256360
$514$	−18.8573	−0.831759
$515$	−6.10171	−0.268873
$516$	−7.05086	−0.310397
$517$	33.7146	1.48276
$518$	−3.24443	−0.142552
$519$	−16.2766	−0.714461
$520$	−2.00000	−0.0877058
$521$	−14.8573	−0.650909	−0.325455	−	0.945558i	$-0.605517\pi$
$521$	−14.8573	−0.650909	−0.325455	+	0.945558i	$0.605517\pi$
$522$	3.80642	0.166603
$523$	−21.9813	−0.961174	−0.480587	−	0.876947i	$-0.659576\pi$
$523$	−21.9813	−0.961174	−0.480587	+	0.876947i	$0.659576\pi$
$524$	−18.9590	−0.828227
$525$	−1.00000	−0.0436436
$526$	−6.10171	−0.266047
$527$	35.6128	1.55132
$528$	5.80642	0.252692
$529$	1.00000	0.0434783
$530$	5.61285	0.243807
$531$	4.85728	0.210788
$532$	5.80642	0.251740
$533$	1.51114	0.0654546
$534$	10.8573	0.469840
$535$	11.3461	0.490536
$536$	10.6637	0.460602
$537$	−2.36842	−0.102205
$538$	−20.9590	−0.903606
$539$	−5.80642	−0.250100
$540$	−1.00000	−0.0430331
$541$	9.07944	0.390355	0.195178	−	0.980768i	$-0.437472\pi$
$541$	9.07944	0.390355	0.195178	+	0.980768i	$0.437472\pi$
$542$	22.2766	0.956860
$543$	−8.48886	−0.364292
$544$	5.05086	0.216554
$545$	−12.3684	−0.529805
$546$	2.00000	0.0855921
$547$	30.9590	1.32371	0.661855	−	0.749632i	$-0.269769\pi$
$547$	30.9590	1.32371	0.661855	+	0.749632i	$0.269769\pi$
$548$	18.4701	0.789005
$549$	6.00000	0.256074
$550$	5.80642	0.247587
$551$	−22.1017	−0.941565
$552$	1.00000	0.0425628
$553$	2.75557	0.117179
$554$	−21.3176	−0.905696
$555$	−3.24443	−0.137718
$556$	8.85728	0.375632
$557$	−23.3274	−0.988414	−0.494207	−	0.869344i	$-0.664541\pi$
$557$	−23.3274	−0.988414	−0.494207	+	0.869344i	$0.664541\pi$
$558$	7.05086	0.298486
$559$	14.1017	0.596439
$560$	1.00000	0.0422577
$561$	−29.3274	−1.23820
$562$	−28.2766	−1.19277
$563$	39.1338	1.64929	0.824647	−	0.565648i	$-0.191374\pi$
$563$	39.1338	1.64929	0.824647	+	0.565648i	$0.191374\pi$
$564$	5.80642	0.244495
$565$	12.3684	0.520343
$566$	−24.4701	−1.02856
$567$	1.00000	0.0419961
$568$	−10.6637	−0.447439
$569$	−10.7654	−0.451310	−0.225655	−	0.974207i	$-0.572452\pi$
$569$	−10.7654	−0.451310	−0.225655	+	0.974207i	$0.572452\pi$
$570$	5.80642	0.243204
$571$	−14.6923	−0.614853	−0.307426	−	0.951572i	$-0.599468\pi$
$571$	−14.6923	−0.614853	−0.307426	+	0.951572i	$0.599468\pi$
$572$	−11.6128	−0.485558
$573$	4.85728	0.202916
$574$	−0.755569	−0.0315368
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	38.7940	1.61502	0.807508	−	0.589857i	$-0.200816\pi$
$577$	38.7940	1.61502	0.807508	+	0.589857i	$0.200816\pi$
$578$	−8.51114	−0.354017
$579$	6.00000	0.249351
$580$	−3.80642	−0.158053
$581$	15.9081	0.659981
$582$	8.75557	0.362930
$583$	32.5906	1.34976
$584$	−13.6128	−0.563304
$585$	2.00000	0.0826898
$586$	2.00000	0.0826192
$587$	15.4291	0.636828	0.318414	−	0.947952i	$-0.396850\pi$
$587$	15.4291	0.636828	0.318414	+	0.947952i	$0.396850\pi$
$588$	−1.00000	−0.0412393
$589$	−40.9403	−1.68691
$590$	−4.85728	−0.199971
$591$	4.10171	0.168722
$592$	3.24443	0.133345
$593$	−17.8796	−0.734225	−0.367113	−	0.930176i	$-0.619654\pi$
$593$	−17.8796	−0.734225	−0.367113	+	0.930176i	$0.619654\pi$
$594$	−5.80642	−0.238240
$595$	−5.05086	−0.207065
$596$	6.00000	0.245770
$597$	20.4701	0.837787
$598$	−2.00000	−0.0817861
$599$	39.4005	1.60986	0.804931	−	0.593368i	$-0.202202\pi$
$599$	39.4005	1.60986	0.804931	+	0.593368i	$0.202202\pi$
$600$	1.00000	0.0408248
$601$	0.876015	0.0357334	0.0178667	−	0.999840i	$-0.494313\pi$
$601$	0.876015	0.0357334	0.0178667	+	0.999840i	$0.494313\pi$
$602$	−7.05086	−0.287371
$603$	−10.6637	−0.434260
$604$	−5.51114	−0.224245
$605$	22.7146	0.923478
$606$	−18.8573	−0.766025
$607$	28.5906	1.16046	0.580228	−	0.814454i	$-0.302964\pi$
$607$	28.5906	1.16046	0.580228	+	0.814454i	$0.302964\pi$
$608$	−5.80642	−0.235482
$609$	3.80642	0.154244
$610$	−6.00000	−0.242933
$611$	−11.6128	−0.469806
$612$	−5.05086	−0.204169
$613$	−14.6539	−0.591864	−0.295932	−	0.955209i	$-0.595630\pi$
$613$	−14.6539	−0.591864	−0.295932	+	0.955209i	$0.595630\pi$
$614$	4.59057	0.185260
$615$	−0.755569	−0.0304675
$616$	5.80642	0.233947
$617$	40.5718	1.63336	0.816680	−	0.577090i	$-0.195812\pi$
$617$	40.5718	1.63336	0.816680	+	0.577090i	$0.195812\pi$
$618$	−6.10171	−0.245447
$619$	−26.0098	−1.04542	−0.522712	−	0.852509i	$-0.675080\pi$
$619$	−26.0098	−1.04542	−0.522712	+	0.852509i	$0.675080\pi$
$620$	−7.05086	−0.283169
$621$	−1.00000	−0.0401286
$622$	−24.4701	−0.981163
$623$	10.8573	0.434988
$624$	−2.00000	−0.0800641
$625$	1.00000	0.0400000
$626$	19.9813	0.798612
$627$	33.7146	1.34643
$628$	16.1017	0.642528
$629$	−16.3872	−0.653399
$630$	−1.00000	−0.0398410
$631$	−17.4479	−0.694588	−0.347294	−	0.937756i	$-0.612899\pi$
$631$	−17.4479	−0.694588	−0.347294	+	0.937756i	$0.612899\pi$
$632$	−2.75557	−0.109611
$633$	1.51114	0.0600623
$634$	30.9403	1.22879
$635$	−14.6637	−0.581911
$636$	5.61285	0.222564
$637$	2.00000	0.0792429
$638$	−22.1017	−0.875015
$639$	10.6637	0.421850
$640$	−1.00000	−0.0395285
$641$	20.2766	0.800876	0.400438	−	0.916324i	$-0.368858\pi$
$641$	20.2766	0.800876	0.400438	+	0.916324i	$0.368858\pi$
$642$	11.3461	0.447796
$643$	−28.8573	−1.13802	−0.569010	−	0.822331i	$-0.692673\pi$
$643$	−28.8573	−1.13802	−0.569010	+	0.822331i	$0.692673\pi$
$644$	1.00000	0.0394055
$645$	−7.05086	−0.277627
$646$	29.3274	1.15387
$647$	37.0321	1.45588	0.727941	−	0.685639i	$-0.240477\pi$
$647$	37.0321	1.45588	0.727941	+	0.685639i	$0.240477\pi$
$648$	−1.00000	−0.0392837
$649$	−28.2034	−1.10708
$650$	−2.00000	−0.0784465
$651$	7.05086	0.276345
$652$	−14.9590	−0.585839
$653$	−1.61285	−0.0631156	−0.0315578	−	0.999502i	$-0.510047\pi$
$653$	−1.61285	−0.0631156	−0.0315578	+	0.999502i	$0.510047\pi$
$654$	−12.3684	−0.483643
$655$	−18.9590	−0.740789
$656$	0.755569	0.0295000
$657$	13.6128	0.531088
$658$	5.80642	0.226358
$659$	−18.1936	−0.708721	−0.354361	−	0.935109i	$-0.615301\pi$
$659$	−18.1936	−0.708721	−0.354361	+	0.935109i	$0.615301\pi$
$660$	5.80642	0.226015
$661$	26.2034	1.01919	0.509597	−	0.860413i	$-0.329794\pi$
$661$	26.2034	1.01919	0.509597	+	0.860413i	$0.329794\pi$
$662$	−15.6128	−0.606811
$663$	10.1017	0.392318
$664$	−15.9081	−0.617355
$665$	5.80642	0.225163
$666$	−3.24443	−0.125719
$667$	−3.80642	−0.147385
$668$	2.19358	0.0848720
$669$	−27.2257	−1.05261
$670$	10.6637	0.411975
$671$	−34.8385	−1.34493
$672$	1.00000	0.0385758
$673$	28.8385	1.11164	0.555822	−	0.831301i	$-0.312404\pi$
$673$	28.8385	1.11164	0.555822	+	0.831301i	$0.312404\pi$
$674$	−23.8064	−0.916989
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−28.2480	−1.08566	−0.542829	−	0.839843i	$-0.682647\pi$
$677$	−28.2480	−1.08566	−0.542829	+	0.839843i	$0.682647\pi$
$678$	12.3684	0.475006
$679$	8.75557	0.336008
$680$	5.05086	0.193691
$681$	−6.19358	−0.237338
$682$	−40.9403	−1.56768
$683$	−7.61285	−0.291298	−0.145649	−	0.989336i	$-0.546527\pi$
$683$	−7.61285	−0.291298	−0.145649	+	0.989336i	$0.546527\pi$
$684$	5.80642	0.222014
$685$	18.4701	0.705707
$686$	−1.00000	−0.0381802
$687$	−0.488863	−0.0186513
$688$	7.05086	0.268811
$689$	−11.2257	−0.427665
$690$	1.00000	0.0380693
$691$	−20.4701	−0.778720	−0.389360	−	0.921086i	$-0.627304\pi$
$691$	−20.4701	−0.778720	−0.389360	+	0.921086i	$0.627304\pi$
$692$	16.2766	0.618742
$693$	−5.80642	−0.220568
$694$	−22.8385	−0.866939
$695$	8.85728	0.335976
$696$	−3.80642	−0.144282
$697$	−3.81627	−0.144551
$698$	−11.8064	−0.446880
$699$	−14.0000	−0.529529
$700$	1.00000	0.0377964
$701$	20.1017	0.759231	0.379616	−	0.925144i	$-0.376056\pi$
$701$	20.1017	0.759231	0.379616	+	0.925144i	$0.376056\pi$
$702$	2.00000	0.0754851
$703$	18.8385	0.710509
$704$	−5.80642	−0.218838
$705$	5.80642	0.218683
$706$	−4.75557	−0.178978
$707$	−18.8573	−0.709201
$708$	−4.85728	−0.182548
$709$	11.6316	0.436833	0.218417	−	0.975856i	$-0.429911\pi$
$709$	11.6316	0.436833	0.218417	+	0.975856i	$0.429911\pi$
$710$	−10.6637	−0.400202
$711$	2.75557	0.103342
$712$	−10.8573	−0.406894
$713$	−7.05086	−0.264057
$714$	−5.05086	−0.189024
$715$	−11.6128	−0.434296
$716$	2.36842	0.0885119
$717$	20.5620	0.767902
$718$	4.85728	0.181272
$719$	35.4924	1.32364	0.661822	−	0.749661i	$-0.269784\pi$
$719$	35.4924	1.32364	0.661822	+	0.749661i	$0.269784\pi$
$720$	1.00000	0.0372678
$721$	−6.10171	−0.227240
$722$	−14.7146	−0.547619
$723$	14.7654	0.549132
$724$	8.48886	0.315486
$725$	−3.80642	−0.141367
$726$	22.7146	0.843016
$727$	−41.7146	−1.54711	−0.773554	−	0.633731i	$-0.781523\pi$
$727$	−41.7146	−1.54711	−0.773554	+	0.633731i	$0.781523\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−13.6128	−0.503834
$731$	−35.6128	−1.31719
$732$	−6.00000	−0.221766
$733$	−36.1017	−1.33345	−0.666724	−	0.745305i	$-0.732304\pi$
$733$	−36.1017	−1.33345	−0.666724	+	0.745305i	$0.732304\pi$
$734$	−25.1240	−0.927343
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	61.9180	2.28078
$738$	−0.755569	−0.0278129
$739$	32.5531	1.19749	0.598743	−	0.800942i	$-0.295667\pi$
$739$	32.5531	1.19749	0.598743	+	0.800942i	$0.295667\pi$
$740$	3.24443	0.119268
$741$	−11.6128	−0.426609
$742$	5.61285	0.206054
$743$	48.1659	1.76704	0.883519	−	0.468396i	$-0.155168\pi$
$743$	48.1659	1.76704	0.883519	+	0.468396i	$0.155168\pi$
$744$	−7.05086	−0.258497
$745$	6.00000	0.219823
$746$	−24.7556	−0.906366
$747$	15.9081	0.582048
$748$	29.3274	1.07232
$749$	11.3461	0.414579
$750$	1.00000	0.0365148
$751$	5.77784	0.210837	0.105418	−	0.994428i	$-0.466382\pi$
$751$	5.77784	0.210837	0.105418	+	0.994428i	$0.466382\pi$
$752$	−5.80642	−0.211738
$753$	0.653858	0.0238279
$754$	7.61285	0.277244
$755$	−5.51114	−0.200571
$756$	−1.00000	−0.0363696
$757$	22.8573	0.830762	0.415381	−	0.909648i	$-0.363648\pi$
$757$	22.8573	0.830762	0.415381	+	0.909648i	$0.363648\pi$
$758$	−9.12399	−0.331398
$759$	5.80642	0.210760
$760$	−5.80642	−0.210621
$761$	18.4701	0.669542	0.334771	−	0.942300i	$-0.391341\pi$
$761$	18.4701	0.669542	0.334771	+	0.942300i	$0.391341\pi$
$762$	−14.6637	−0.531210
$763$	−12.3684	−0.447767
$764$	−4.85728	−0.175730
$765$	−5.05086	−0.182614
$766$	6.75557	0.244089
$767$	9.71456	0.350772
$768$	−1.00000	−0.0360844
$769$	1.05086	0.0378948	0.0189474	−	0.999820i	$-0.493968\pi$
$769$	1.05086	0.0378948	0.0189474	+	0.999820i	$0.493968\pi$
$770$	5.80642	0.209249
$771$	−18.8573	−0.679128
$772$	−6.00000	−0.215945
$773$	−24.1017	−0.866878	−0.433439	−	0.901183i	$-0.642700\pi$
$773$	−24.1017	−0.866878	−0.433439	+	0.901183i	$0.642700\pi$
$774$	−7.05086	−0.253438
$775$	−7.05086	−0.253274
$776$	−8.75557	−0.314307
$777$	−3.24443	−0.116393
$778$	−37.8163	−1.35578
$779$	4.38715	0.157186
$780$	−2.00000	−0.0716115
$781$	−61.9180	−2.21560
$782$	5.05086	0.180618
$783$	3.80642	0.136030
$784$	1.00000	0.0357143
$785$	16.1017	0.574695
$786$	−18.9590	−0.676245
$787$	−6.57184	−0.234261	−0.117130	−	0.993117i	$-0.537370\pi$
$787$	−6.57184	−0.234261	−0.117130	+	0.993117i	$0.537370\pi$
$788$	−4.10171	−0.146117
$789$	−6.10171	−0.217227
$790$	−2.75557	−0.0980387
$791$	12.3684	0.439770
$792$	5.80642	0.206322
$793$	12.0000	0.426132
$794$	−23.5111	−0.834379
$795$	5.61285	0.199067
$796$	−20.4701	−0.725544
$797$	−52.3051	−1.85274	−0.926371	−	0.376611i	$-0.877089\pi$
$797$	−52.3051	−1.85274	−0.926371	+	0.376611i	$0.877089\pi$
$798$	5.80642	0.205545
$799$	29.3274	1.03753
$800$	−1.00000	−0.0353553
$801$	10.8573	0.383623
$802$	−27.6860	−0.977626
$803$	−79.0420	−2.78933
$804$	10.6637	0.376080
$805$	1.00000	0.0352454
$806$	14.1017	0.496712
$807$	−20.9590	−0.737791
$808$	18.8573	0.663397
$809$	−18.7368	−0.658752	−0.329376	−	0.944199i	$-0.606838\pi$
$809$	−18.7368	−0.658752	−0.329376	+	0.944199i	$0.606838\pi$
$810$	−1.00000	−0.0351364
$811$	−46.7753	−1.64250	−0.821251	−	0.570567i	$-0.806723\pi$
$811$	−46.7753	−1.64250	−0.821251	+	0.570567i	$0.806723\pi$
$812$	−3.80642	−0.133579
$813$	22.2766	0.781273
$814$	18.8385	0.660291
$815$	−14.9590	−0.523991
$816$	5.05086	0.176815
$817$	40.9403	1.43232
$818$	−2.77430	−0.0970013
$819$	2.00000	0.0698857
$820$	0.755569	0.0263856
$821$	21.9081	0.764599	0.382300	−	0.924038i	$-0.375132\pi$
$821$	21.9081	0.764599	0.382300	+	0.924038i	$0.375132\pi$
$822$	18.4701	0.644220
$823$	−13.7234	−0.478369	−0.239185	−	0.970974i	$-0.576880\pi$
$823$	−13.7234	−0.478369	−0.239185	+	0.970974i	$0.576880\pi$
$824$	6.10171	0.212563
$825$	5.80642	0.202154
$826$	−4.85728	−0.169006
$827$	8.85728	0.307998	0.153999	−	0.988071i	$-0.450785\pi$
$827$	8.85728	0.307998	0.153999	+	0.988071i	$0.450785\pi$
$828$	1.00000	0.0347524
$829$	−11.0696	−0.384463	−0.192231	−	0.981350i	$-0.561572\pi$
$829$	−11.0696	−0.384463	−0.192231	+	0.981350i	$0.561572\pi$
$830$	−15.9081	−0.552179
$831$	−21.3176	−0.739498
$832$	2.00000	0.0693375
$833$	−5.05086	−0.175002
$834$	8.85728	0.306702
$835$	2.19358	0.0759118
$836$	−33.7146	−1.16604
$837$	7.05086	0.243713
$838$	−10.9590	−0.378572
$839$	−26.8385	−0.926569	−0.463285	−	0.886210i	$-0.653329\pi$
$839$	−26.8385	−0.926569	−0.463285	+	0.886210i	$0.653329\pi$
$840$	1.00000	0.0345033
$841$	−14.5111	−0.500384
$842$	−9.14272	−0.315079
$843$	−28.2766	−0.973896
$844$	−1.51114	−0.0520155
$845$	−9.00000	−0.309609
$846$	5.80642	0.199629
$847$	22.7146	0.780481
$848$	−5.61285	−0.192746
$849$	−24.4701	−0.839813
$850$	5.05086	0.173243
$851$	3.24443	0.111218
$852$	−10.6637	−0.365332
$853$	2.94025	0.100672	0.0503362	−	0.998732i	$-0.483971\pi$
$853$	2.94025	0.100672	0.0503362	+	0.998732i	$0.483971\pi$
$854$	−6.00000	−0.205316
$855$	5.80642	0.198576
$856$	−11.3461	−0.387803
$857$	35.4479	1.21088	0.605438	−	0.795893i	$-0.292998\pi$
$857$	35.4479	1.21088	0.605438	+	0.795893i	$0.292998\pi$
$858$	−11.6128	−0.396456
$859$	−18.7556	−0.639932	−0.319966	−	0.947429i	$-0.603671\pi$
$859$	−18.7556	−0.639932	−0.319966	+	0.947429i	$0.603671\pi$
$860$	7.05086	0.240432
$861$	−0.755569	−0.0257497
$862$	29.9813	1.02117
$863$	21.5111	0.732248	0.366124	−	0.930566i	$-0.380685\pi$
$863$	21.5111	0.732248	0.366124	+	0.930566i	$0.380685\pi$
$864$	1.00000	0.0340207
$865$	16.2766	0.553419
$866$	14.4701	0.491715
$867$	−8.51114	−0.289053
$868$	−7.05086	−0.239322
$869$	−16.0000	−0.542763
$870$	−3.80642	−0.129050
$871$	−21.3274	−0.722652
$872$	12.3684	0.418847
$873$	8.75557	0.296331
$874$	−5.80642	−0.196405
$875$	1.00000	0.0338062
$876$	−13.6128	−0.459936
$877$	−48.9501	−1.65293	−0.826464	−	0.562990i	$-0.809651\pi$
$877$	−48.9501	−1.65293	−0.826464	+	0.562990i	$0.809651\pi$
$878$	−13.1526	−0.443878
$879$	2.00000	0.0674583
$880$	−5.80642	−0.195735
$881$	−49.1624	−1.65632	−0.828162	−	0.560489i	$-0.810613\pi$
$881$	−49.1624	−1.65632	−0.828162	+	0.560489i	$0.810613\pi$
$882$	−1.00000	−0.0336718
$883$	−14.0187	−0.471768	−0.235884	−	0.971781i	$-0.575799\pi$
$883$	−14.0187	−0.471768	−0.235884	+	0.971781i	$0.575799\pi$
$884$	−10.1017	−0.339757
$885$	−4.85728	−0.163276
$886$	−13.8983	−0.466922
$887$	−19.9081	−0.668450	−0.334225	−	0.942493i	$-0.608474\pi$
$887$	−19.9081	−0.668450	−0.334225	+	0.942493i	$0.608474\pi$
$888$	3.24443	0.108876
$889$	−14.6637	−0.491805
$890$	−10.8573	−0.363937
$891$	−5.80642	−0.194523
$892$	27.2257	0.911584
$893$	−33.7146	−1.12821
$894$	6.00000	0.200670
$895$	2.36842	0.0791674
$896$	−1.00000	−0.0334077
$897$	−2.00000	−0.0667781
$898$	−5.61285	−0.187303
$899$	26.8385	0.895116
$900$	1.00000	0.0333333
$901$	28.3497	0.944465
$902$	4.38715	0.146076
$903$	−7.05086	−0.234638
$904$	−12.3684	−0.411367
$905$	8.48886	0.282179
$906$	−5.51114	−0.183095
$907$	10.6637	0.354082	0.177041	−	0.984203i	$-0.443347\pi$
$907$	10.6637	0.354082	0.177041	+	0.984203i	$0.443347\pi$
$908$	6.19358	0.205541
$909$	−18.8573	−0.625456
$910$	−2.00000	−0.0662994
$911$	26.1847	0.867537	0.433769	−	0.901024i	$-0.357184\pi$
$911$	26.1847	0.867537	0.433769	+	0.901024i	$0.357184\pi$
$912$	−5.80642	−0.192270
$913$	−92.3694	−3.05698
$914$	−23.8064	−0.787447
$915$	−6.00000	−0.198354
$916$	0.488863	0.0161525
$917$	−18.9590	−0.626081
$918$	−5.05086	−0.166703
$919$	8.32387	0.274579	0.137290	−	0.990531i	$-0.456161\pi$
$919$	8.32387	0.274579	0.137290	+	0.990531i	$0.456161\pi$
$920$	−1.00000	−0.0329690
$921$	4.59057	0.151265
$922$	−14.8573	−0.489298
$923$	21.3274	0.702000
$924$	5.80642	0.191017
$925$	3.24443	0.106676
$926$	−13.5397	−0.444943
$927$	−6.10171	−0.200406
$928$	3.80642	0.124952
$929$	34.4701	1.13093	0.565464	−	0.824773i	$-0.308697\pi$
$929$	34.4701	1.13093	0.565464	+	0.824773i	$0.308697\pi$
$930$	−7.05086	−0.231207
$931$	5.80642	0.190298
$932$	14.0000	0.458585
$933$	−24.4701	−0.801116
$934$	39.1338	1.28050
$935$	29.3274	0.959109
$936$	−2.00000	−0.0653720
$937$	−23.5941	−0.770786	−0.385393	−	0.922753i	$-0.625934\pi$
$937$	−23.5941	−0.770786	−0.385393	+	0.922753i	$0.625934\pi$
$938$	10.6637	0.348182
$939$	19.9813	0.652064
$940$	−5.80642	−0.189385
$941$	−32.4514	−1.05789	−0.528943	−	0.848658i	$-0.677411\pi$
$941$	−32.4514	−1.05789	−0.528943	+	0.848658i	$0.677411\pi$
$942$	16.1017	0.524622
$943$	0.755569	0.0246047
$944$	4.85728	0.158091
$945$	−1.00000	−0.0325300
$946$	40.9403	1.33108
$947$	32.2034	1.04647	0.523235	−	0.852188i	$-0.324725\pi$
$947$	32.2034	1.04647	0.523235	+	0.852188i	$0.324725\pi$
$948$	−2.75557	−0.0894967
$949$	27.2257	0.883783
$950$	−5.80642	−0.188385
$951$	30.9403	1.00331
$952$	5.05086	0.163699
$953$	−3.63158	−0.117639	−0.0588193	−	0.998269i	$-0.518734\pi$
$953$	−3.63158	−0.117639	−0.0588193	+	0.998269i	$0.518734\pi$
$954$	5.61285	0.181723
$955$	−4.85728	−0.157178
$956$	−20.5620	−0.665022
$957$	−22.1017	−0.714447
$958$	23.8163	0.769469
$959$	18.4701	0.596431
$960$	−1.00000	−0.0322749
$961$	18.7146	0.603695
$962$	−6.48886	−0.209209
$963$	11.3461	0.365624
$964$	−14.7654	−0.475562
$965$	−6.00000	−0.193147
$966$	1.00000	0.0321745
$967$	44.7654	1.43956	0.719779	−	0.694203i	$-0.244243\pi$
$967$	44.7654	1.43956	0.719779	+	0.694203i	$0.244243\pi$
$968$	−22.7146	−0.730074
$969$	29.3274	0.942132
$970$	−8.75557	−0.281124
$971$	1.83500	0.0588881	0.0294440	−	0.999566i	$-0.490626\pi$
$971$	1.83500	0.0588881	0.0294440	+	0.999566i	$0.490626\pi$
$972$	−1.00000	−0.0320750
$973$	8.85728	0.283951
$974$	4.17484	0.133771
$975$	−2.00000	−0.0640513
$976$	6.00000	0.192055
$977$	15.6316	0.500099	0.250049	−	0.968233i	$-0.419553\pi$
$977$	15.6316	0.500099	0.250049	+	0.968233i	$0.419553\pi$
$978$	−14.9590	−0.478336
$979$	−63.0420	−2.01483
$980$	1.00000	0.0319438
$981$	−12.3684	−0.394893
$982$	28.0830	0.896164
$983$	7.69582	0.245459	0.122729	−	0.992440i	$-0.460835\pi$
$983$	7.69582	0.245459	0.122729	+	0.992440i	$0.460835\pi$
$984$	0.755569	0.0240867
$985$	−4.10171	−0.130691
$986$	−19.2257	−0.612271
$987$	5.80642	0.184821
$988$	11.6128	0.369454
$989$	7.05086	0.224204
$990$	5.80642	0.184540
$991$	−61.9180	−1.96689	−0.983445	−	0.181208i	$-0.941999\pi$
$991$	−61.9180	−1.96689	−0.983445	+	0.181208i	$0.941999\pi$
$992$	7.05086	0.223865
$993$	−15.6128	−0.495459
$994$	−10.6637	−0.338232
$995$	−20.4701	−0.648947
$996$	−15.9081	−0.504069
$997$	30.7368	0.973445	0.486723	−	0.873557i	$-0.338192\pi$
$997$	30.7368	0.973445	0.486723	+	0.873557i	$0.338192\pi$
$998$	−24.7368	−0.783031
$999$	−3.24443	−0.102649

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.by.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.80642 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -5.05086 q^{17} -1.00000 q^{18} +5.80642 q^{19} +1.00000 q^{20} -1.00000 q^{21} +5.80642 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -3.80642 q^{29} +1.00000 q^{30} -7.05086 q^{31} -1.00000 q^{32} +5.80642 q^{33} +5.05086 q^{34} +1.00000 q^{35} +1.00000 q^{36} +3.24443 q^{37} -5.80642 q^{38} -2.00000 q^{39} -1.00000 q^{40} +0.755569 q^{41} +1.00000 q^{42} +7.05086 q^{43} -5.80642 q^{44} +1.00000 q^{45} -1.00000 q^{46} -5.80642 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +5.05086 q^{51} +2.00000 q^{52} -5.61285 q^{53} +1.00000 q^{54} -5.80642 q^{55} -1.00000 q^{56} -5.80642 q^{57} +3.80642 q^{58} +4.85728 q^{59} -1.00000 q^{60} +6.00000 q^{61} +7.05086 q^{62} +1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -5.80642 q^{66} -10.6637 q^{67} -5.05086 q^{68} -1.00000 q^{69} -1.00000 q^{70} +10.6637 q^{71} -1.00000 q^{72} +13.6128 q^{73} -3.24443 q^{74} -1.00000 q^{75} +5.80642 q^{76} -5.80642 q^{77} +2.00000 q^{78} +2.75557 q^{79} +1.00000 q^{80} +1.00000 q^{81} -0.755569 q^{82} +15.9081 q^{83} -1.00000 q^{84} -5.05086 q^{85} -7.05086 q^{86} +3.80642 q^{87} +5.80642 q^{88} +10.8573 q^{89} -1.00000 q^{90} +2.00000 q^{91} +1.00000 q^{92} +7.05086 q^{93} +5.80642 q^{94} +5.80642 q^{95} +1.00000 q^{96} +8.75557 q^{97} -1.00000 q^{98} -5.80642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 4 q^{11} - 3 q^{12} + 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 2 q^{17} - 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} + 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} - 3 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{30} - 8 q^{31} - 3 q^{32} + 4 q^{33} + 2 q^{34} + 3 q^{35} + 3 q^{36} + 10 q^{37} - 4 q^{38} - 6 q^{39} - 3 q^{40} + 2 q^{41} + 3 q^{42} + 8 q^{43} - 4 q^{44} + 3 q^{45} - 3 q^{46} - 4 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 2 q^{51} + 6 q^{52} + 10 q^{53} + 3 q^{54} - 4 q^{55} - 3 q^{56} - 4 q^{57} - 2 q^{58} - 12 q^{59} - 3 q^{60} + 18 q^{61} + 8 q^{62} + 3 q^{63} + 3 q^{64} + 6 q^{65} - 4 q^{66} + 8 q^{67} - 2 q^{68} - 3 q^{69} - 3 q^{70} - 8 q^{71} - 3 q^{72} + 14 q^{73} - 10 q^{74} - 3 q^{75} + 4 q^{76} - 4 q^{77} + 6 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 2 q^{82} + 8 q^{83} - 3 q^{84} - 2 q^{85} - 8 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 3 q^{90} + 6 q^{91} + 3 q^{92} + 8 q^{93} + 4 q^{94} + 4 q^{95} + 3 q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 4 * q^11 - 3 * q^12 + 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 2 * q^17 - 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 + 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 - 3 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^30 - 8 * q^31 - 3 * q^32 + 4 * q^33 + 2 * q^34 + 3 * q^35 + 3 * q^36 + 10 * q^37 - 4 * q^38 - 6 * q^39 - 3 * q^40 + 2 * q^41 + 3 * q^42 + 8 * q^43 - 4 * q^44 + 3 * q^45 - 3 * q^46 - 4 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 2 * q^51 + 6 * q^52 + 10 * q^53 + 3 * q^54 - 4 * q^55 - 3 * q^56 - 4 * q^57 - 2 * q^58 - 12 * q^59 - 3 * q^60 + 18 * q^61 + 8 * q^62 + 3 * q^63 + 3 * q^64 + 6 * q^65 - 4 * q^66 + 8 * q^67 - 2 * q^68 - 3 * q^69 - 3 * q^70 - 8 * q^71 - 3 * q^72 + 14 * q^73 - 10 * q^74 - 3 * q^75 + 4 * q^76 - 4 * q^77 + 6 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 8 * q^83 - 3 * q^84 - 2 * q^85 - 8 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 3 * q^90 + 6 * q^91 + 3 * q^92 + 8 * q^93 + 4 * q^94 + 4 * q^95 + 3 * q^96 + 26 * q^97 - 3 * q^98 - 4 * q^99

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