LMFDB - Embedded newform 4830.2.a.ca.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:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.470683$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +5.55691 q^{11} -1.00000 q^{12} -6.49828 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.05863 q^{17} +1.00000 q^{18} -1.05863 q^{19} +1.00000 q^{20} +1.00000 q^{21} +5.55691 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.49828 q^{26} -1.00000 q^{27} -1.00000 q^{28} -9.43965 q^{29} -1.00000 q^{30} -5.05863 q^{31} +1.00000 q^{32} -5.55691 q^{33} -3.05863 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -1.05863 q^{38} +6.49828 q^{39} +1.00000 q^{40} -9.11383 q^{41} +1.00000 q^{42} +5.55691 q^{43} +5.55691 q^{44} +1.00000 q^{45} -1.00000 q^{46} -5.05863 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.05863 q^{51} -6.49828 q^{52} -2.00000 q^{53} -1.00000 q^{54} +5.55691 q^{55} -1.00000 q^{56} +1.05863 q^{57} -9.43965 q^{58} +12.9966 q^{59} -1.00000 q^{60} -7.88273 q^{61} -5.05863 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.49828 q^{65} -5.55691 q^{66} -2.44309 q^{67} -3.05863 q^{68} +1.00000 q^{69} -1.00000 q^{70} -3.67418 q^{71} +1.00000 q^{72} +13.1138 q^{73} -2.00000 q^{74} -1.00000 q^{75} -1.05863 q^{76} -5.55691 q^{77} +6.49828 q^{78} +13.2311 q^{79} +1.00000 q^{80} +1.00000 q^{81} -9.11383 q^{82} -15.9379 q^{83} +1.00000 q^{84} -3.05863 q^{85} +5.55691 q^{86} +9.43965 q^{87} +5.55691 q^{88} +0.615547 q^{89} +1.00000 q^{90} +6.49828 q^{91} -1.00000 q^{92} +5.05863 q^{93} -5.05863 q^{94} -1.05863 q^{95} -1.00000 q^{96} -4.61555 q^{97} +1.00000 q^{98} +5.55691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 3 q^{12} - 2 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - 4 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} - 16 q^{31} + 3 q^{32} - 10 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} + 3 q^{42} + 3 q^{45} - 3 q^{46} - 16 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 10 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{54} - 3 q^{56} + 4 q^{57} - 10 q^{58} + 4 q^{59} - 3 q^{60} - 22 q^{61} - 16 q^{62} - 3 q^{63} + 3 q^{64} - 2 q^{65} - 24 q^{67} - 10 q^{68} + 3 q^{69} - 3 q^{70} + 4 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} - 3 q^{75} - 4 q^{76} + 2 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} + 6 q^{82} - 12 q^{83} + 3 q^{84} - 10 q^{85} + 10 q^{87} - 14 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} - 3 q^{96} + 2 q^{97} + 3 q^{98}+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 - 3 * q^12 - 2 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - 4 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 - 16 * q^31 + 3 * q^32 - 10 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 + 3 * q^42 + 3 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 10 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^54 - 3 * q^56 + 4 * q^57 - 10 * q^58 + 4 * q^59 - 3 * q^60 - 22 * q^61 - 16 * q^62 - 3 * q^63 + 3 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 3 * q^69 - 3 * q^70 + 4 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 - 3 * q^75 - 4 * q^76 + 2 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 + 6 * q^82 - 12 * q^83 + 3 * q^84 - 10 * q^85 + 10 * q^87 - 14 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 - 3 * q^96 + 2 * q^97 + 3 * q^98

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
$11$	5.55691	1.67547	0.837736	−	0.546075i	$-0.183879\pi$
$11$	5.55691	1.67547	0.837736	+	0.546075i	$0.183879\pi$
$12$	−1.00000	−0.288675
$13$	−6.49828	−1.80230	−0.901149	−	0.433509i	$-0.857275\pi$
$13$	−6.49828	−1.80230	−0.901149	+	0.433509i	$0.857275\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.05863	−0.741828	−0.370914	−	0.928667i	$-0.620955\pi$
$17$	−3.05863	−0.741828	−0.370914	+	0.928667i	$0.620955\pi$
$18$	1.00000	0.235702
$19$	−1.05863	−0.242867	−0.121434	−	0.992600i	$-0.538749\pi$
$19$	−1.05863	−0.242867	−0.121434	+	0.992600i	$0.538749\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	5.55691	1.18474
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−6.49828	−1.27442
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−9.43965	−1.75290	−0.876449	−	0.481494i	$-0.840094\pi$
$29$	−9.43965	−1.75290	−0.876449	+	0.481494i	$0.840094\pi$
$30$	−1.00000	−0.182574
$31$	−5.05863	−0.908557	−0.454279	−	0.890860i	$-0.650103\pi$
$31$	−5.05863	−0.908557	−0.454279	+	0.890860i	$0.650103\pi$
$32$	1.00000	0.176777
$33$	−5.55691	−0.967335
$34$	−3.05863	−0.524551
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−1.05863	−0.171733
$39$	6.49828	1.04056
$40$	1.00000	0.158114
$41$	−9.11383	−1.42334	−0.711670	−	0.702513i	$-0.752061\pi$
$41$	−9.11383	−1.42334	−0.711670	+	0.702513i	$0.752061\pi$
$42$	1.00000	0.154303
$43$	5.55691	0.847421	0.423711	−	0.905798i	$-0.360727\pi$
$43$	5.55691	0.847421	0.423711	+	0.905798i	$0.360727\pi$
$44$	5.55691	0.837736
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−5.05863	−0.737877	−0.368939	−	0.929454i	$-0.620279\pi$
$47$	−5.05863	−0.737877	−0.368939	+	0.929454i	$0.620279\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	3.05863	0.428294
$52$	−6.49828	−0.901149
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.00000	−0.136083
$55$	5.55691	0.749294
$56$	−1.00000	−0.133631
$57$	1.05863	0.140219
$58$	−9.43965	−1.23949
$59$	12.9966	1.69201	0.846004	−	0.533176i	$-0.179002\pi$
$59$	12.9966	1.69201	0.846004	+	0.533176i	$0.179002\pi$
$60$	−1.00000	−0.129099
$61$	−7.88273	−1.00928	−0.504640	−	0.863330i	$-0.668375\pi$
$61$	−7.88273	−1.00928	−0.504640	+	0.863330i	$0.668375\pi$
$62$	−5.05863	−0.642447
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−6.49828	−0.806013
$66$	−5.55691	−0.684009
$67$	−2.44309	−0.298470	−0.149235	−	0.988802i	$-0.547681\pi$
$67$	−2.44309	−0.298470	−0.149235	+	0.988802i	$0.547681\pi$
$68$	−3.05863	−0.370914
$69$	1.00000	0.120386
$70$	−1.00000	−0.119523
$71$	−3.67418	−0.436045	−0.218023	−	0.975944i	$-0.569961\pi$
$71$	−3.67418	−0.436045	−0.218023	+	0.975944i	$0.569961\pi$
$72$	1.00000	0.117851
$73$	13.1138	1.53486	0.767429	−	0.641134i	$-0.221536\pi$
$73$	13.1138	1.53486	0.767429	+	0.641134i	$0.221536\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−1.05863	−0.121434
$77$	−5.55691	−0.633269
$78$	6.49828	0.735785
$79$	13.2311	1.48861	0.744307	−	0.667837i	$-0.232780\pi$
$79$	13.2311	1.48861	0.744307	+	0.667837i	$0.232780\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−9.11383	−1.00645
$83$	−15.9379	−1.74941	−0.874707	−	0.484651i	$-0.838947\pi$
$83$	−15.9379	−1.74941	−0.874707	+	0.484651i	$0.838947\pi$
$84$	1.00000	0.109109
$85$	−3.05863	−0.331755
$86$	5.55691	0.599217
$87$	9.43965	1.01204
$88$	5.55691	0.592369
$89$	0.615547	0.0652479	0.0326239	−	0.999468i	$-0.489614\pi$
$89$	0.615547	0.0652479	0.0326239	+	0.999468i	$0.489614\pi$
$90$	1.00000	0.105409
$91$	6.49828	0.681205
$92$	−1.00000	−0.104257
$93$	5.05863	0.524556
$94$	−5.05863	−0.521758
$95$	−1.05863	−0.108613
$96$	−1.00000	−0.102062
$97$	−4.61555	−0.468638	−0.234319	−	0.972160i	$-0.575286\pi$
$97$	−4.61555	−0.468638	−0.234319	+	0.972160i	$0.575286\pi$
$98$	1.00000	0.101015
$99$	5.55691	0.558491
$100$	1.00000	0.100000
$101$	−10.2637	−1.02128	−0.510641	−	0.859794i	$-0.670592\pi$
$101$	−10.2637	−1.02128	−0.510641	+	0.859794i	$0.670592\pi$
$102$	3.05863	0.302850
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−6.49828	−0.637209
$105$	1.00000	0.0975900
$106$	−2.00000	−0.194257
$107$	−1.88273	−0.182011	−0.0910054	−	0.995850i	$-0.529008\pi$
$107$	−1.88273	−0.182011	−0.0910054	+	0.995850i	$0.529008\pi$
$108$	−1.00000	−0.0962250
$109$	1.76547	0.169101	0.0845506	−	0.996419i	$-0.473055\pi$
$109$	1.76547	0.169101	0.0845506	+	0.996419i	$0.473055\pi$
$110$	5.55691	0.529831
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	7.88273	0.741545	0.370773	−	0.928724i	$-0.379093\pi$
$113$	7.88273	0.741545	0.370773	+	0.928724i	$0.379093\pi$
$114$	1.05863	0.0991501
$115$	−1.00000	−0.0932505
$116$	−9.43965	−0.876449
$117$	−6.49828	−0.600766
$118$	12.9966	1.19643
$119$	3.05863	0.280384
$120$	−1.00000	−0.0912871
$121$	19.8793	1.80721
$122$	−7.88273	−0.713669
$123$	9.11383	0.821766
$124$	−5.05863	−0.454279
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−20.6707	−1.83423	−0.917116	−	0.398621i	$-0.869489\pi$
$127$	−20.6707	−1.83423	−0.917116	+	0.398621i	$0.869489\pi$
$128$	1.00000	0.0883883
$129$	−5.55691	−0.489259
$130$	−6.49828	−0.569937
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	−5.55691	−0.483667
$133$	1.05863	0.0917951
$134$	−2.44309	−0.211050
$135$	−1.00000	−0.0860663
$136$	−3.05863	−0.262276
$137$	5.76547	0.492577	0.246289	−	0.969197i	$-0.420789\pi$
$137$	5.76547	0.492577	0.246289	+	0.969197i	$0.420789\pi$
$138$	1.00000	0.0851257
$139$	12.9966	1.10235	0.551177	−	0.834388i	$-0.314179\pi$
$139$	12.9966	1.10235	0.551177	+	0.834388i	$0.314179\pi$
$140$	−1.00000	−0.0845154
$141$	5.05863	0.426014
$142$	−3.67418	−0.308330
$143$	−36.1104	−3.01970
$144$	1.00000	0.0833333
$145$	−9.43965	−0.783920
$146$	13.1138	1.08531
$147$	−1.00000	−0.0824786
$148$	−2.00000	−0.164399
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−1.00000	−0.0816497
$151$	−16.9966	−1.38316	−0.691580	−	0.722300i	$-0.743085\pi$
$151$	−16.9966	−1.38316	−0.691580	+	0.722300i	$0.743085\pi$
$152$	−1.05863	−0.0858665
$153$	−3.05863	−0.247276
$154$	−5.55691	−0.447789
$155$	−5.05863	−0.406319
$156$	6.49828	0.520279
$157$	20.2277	1.61434	0.807171	−	0.590317i	$-0.200997\pi$
$157$	20.2277	1.61434	0.807171	+	0.590317i	$0.200997\pi$
$158$	13.2311	1.05261
$159$	2.00000	0.158610
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−20.9966	−1.64458	−0.822289	−	0.569070i	$-0.807303\pi$
$163$	−20.9966	−1.64458	−0.822289	+	0.569070i	$0.807303\pi$
$164$	−9.11383	−0.711670
$165$	−5.55691	−0.432605
$166$	−15.9379	−1.23702
$167$	−17.8207	−1.37900	−0.689502	−	0.724284i	$-0.742171\pi$
$167$	−17.8207	−1.37900	−0.689502	+	0.724284i	$0.742171\pi$
$168$	1.00000	0.0771517
$169$	29.2277	2.24828
$170$	−3.05863	−0.234586
$171$	−1.05863	−0.0809557
$172$	5.55691	0.423711
$173$	−15.0586	−1.14489	−0.572443	−	0.819944i	$-0.694004\pi$
$173$	−15.0586	−1.14489	−0.572443	+	0.819944i	$0.694004\pi$
$174$	9.43965	0.715618
$175$	−1.00000	−0.0755929
$176$	5.55691	0.418868
$177$	−12.9966	−0.976881
$178$	0.615547	0.0461372
$179$	−10.8793	−0.813157	−0.406578	−	0.913616i	$-0.633278\pi$
$179$	−10.8793	−0.813157	−0.406578	+	0.913616i	$0.633278\pi$
$180$	1.00000	0.0745356
$181$	0.117266	0.00871634	0.00435817	−	0.999991i	$-0.498613\pi$
$181$	0.117266	0.00871634	0.00435817	+	0.999991i	$0.498613\pi$
$182$	6.49828	0.481685
$183$	7.88273	0.582708
$184$	−1.00000	−0.0737210
$185$	−2.00000	−0.147043
$186$	5.05863	0.370917
$187$	−16.9966	−1.24291
$188$	−5.05863	−0.368939
$189$	1.00000	0.0727393
$190$	−1.05863	−0.0768013
$191$	12.1104	0.876277	0.438139	−	0.898907i	$-0.355638\pi$
$191$	12.1104	0.876277	0.438139	+	0.898907i	$0.355638\pi$
$192$	−1.00000	−0.0721688
$193$	−22.9966	−1.65533	−0.827664	−	0.561223i	$-0.810331\pi$
$193$	−22.9966	−1.65533	−0.827664	+	0.561223i	$0.810331\pi$
$194$	−4.61555	−0.331377
$195$	6.49828	0.465352
$196$	1.00000	0.0714286
$197$	11.8827	0.846610	0.423305	−	0.905987i	$-0.360870\pi$
$197$	11.8827	0.846610	0.423305	+	0.905987i	$0.360870\pi$
$198$	5.55691	0.394913
$199$	25.9931	1.84260	0.921302	−	0.388848i	$-0.127127\pi$
$199$	25.9931	1.84260	0.921302	+	0.388848i	$0.127127\pi$
$200$	1.00000	0.0707107
$201$	2.44309	0.172322
$202$	−10.2637	−0.722155
$203$	9.43965	0.662533
$204$	3.05863	0.214147
$205$	−9.11383	−0.636537
$206$	−8.00000	−0.557386
$207$	−1.00000	−0.0695048
$208$	−6.49828	−0.450575
$209$	−5.88273	−0.406917
$210$	1.00000	0.0690066
$211$	−4.99656	−0.343978	−0.171989	−	0.985099i	$-0.555019\pi$
$211$	−4.99656	−0.343978	−0.171989	+	0.985099i	$0.555019\pi$
$212$	−2.00000	−0.137361
$213$	3.67418	0.251751
$214$	−1.88273	−0.128701
$215$	5.55691	0.378978
$216$	−1.00000	−0.0680414
$217$	5.05863	0.343402
$218$	1.76547	0.119573
$219$	−13.1138	−0.886150
$220$	5.55691	0.374647
$221$	19.8759	1.33699
$222$	2.00000	0.134231
$223$	−18.3810	−1.23088	−0.615442	−	0.788182i	$-0.711022\pi$
$223$	−18.3810	−1.23088	−0.615442	+	0.788182i	$0.711022\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	7.88273	0.524352
$227$	27.0518	1.79549	0.897744	−	0.440517i	$-0.145205\pi$
$227$	27.0518	1.79549	0.897744	+	0.440517i	$0.145205\pi$
$228$	1.05863	0.0701097
$229$	2.88617	0.190724	0.0953618	−	0.995443i	$-0.469599\pi$
$229$	2.88617	0.190724	0.0953618	+	0.995443i	$0.469599\pi$
$230$	−1.00000	−0.0659380
$231$	5.55691	0.365618
$232$	−9.43965	−0.619743
$233$	−13.3484	−0.874480	−0.437240	−	0.899345i	$-0.644044\pi$
$233$	−13.3484	−0.874480	−0.437240	+	0.899345i	$0.644044\pi$
$234$	−6.49828	−0.424806
$235$	−5.05863	−0.329989
$236$	12.9966	0.846004
$237$	−13.2311	−0.859452
$238$	3.05863	0.198262
$239$	4.32582	0.279814	0.139907	−	0.990165i	$-0.455320\pi$
$239$	4.32582	0.279814	0.139907	+	0.990165i	$0.455320\pi$
$240$	−1.00000	−0.0645497
$241$	8.70683	0.560856	0.280428	−	0.959875i	$-0.409524\pi$
$241$	8.70683	0.560856	0.280428	+	0.959875i	$0.409524\pi$
$242$	19.8793	1.27789
$243$	−1.00000	−0.0641500
$244$	−7.88273	−0.504640
$245$	1.00000	0.0638877
$246$	9.11383	0.581076
$247$	6.87930	0.437719
$248$	−5.05863	−0.321224
$249$	15.9379	1.01003
$250$	1.00000	0.0632456
$251$	21.7294	1.37155	0.685773	−	0.727815i	$-0.259464\pi$
$251$	21.7294	1.37155	0.685773	+	0.727815i	$0.259464\pi$
$252$	−1.00000	−0.0629941
$253$	−5.55691	−0.349360
$254$	−20.6707	−1.29700
$255$	3.05863	0.191539
$256$	1.00000	0.0625000
$257$	19.9931	1.24714	0.623568	−	0.781769i	$-0.285682\pi$
$257$	19.9931	1.24714	0.623568	+	0.781769i	$0.285682\pi$
$258$	−5.55691	−0.345958
$259$	2.00000	0.124274
$260$	−6.49828	−0.403006
$261$	−9.43965	−0.584300
$262$	−4.00000	−0.247121
$263$	−3.76547	−0.232189	−0.116094	−	0.993238i	$-0.537037\pi$
$263$	−3.76547	−0.232189	−0.116094	+	0.993238i	$0.537037\pi$
$264$	−5.55691	−0.342004
$265$	−2.00000	−0.122859
$266$	1.05863	0.0649090
$267$	−0.615547	−0.0376709
$268$	−2.44309	−0.149235
$269$	12.6155	0.769184	0.384592	−	0.923087i	$-0.374342\pi$
$269$	12.6155	0.769184	0.384592	+	0.923087i	$0.374342\pi$
$270$	−1.00000	−0.0608581
$271$	−27.2863	−1.65752	−0.828762	−	0.559601i	$-0.810954\pi$
$271$	−27.2863	−1.65752	−0.828762	+	0.559601i	$0.810954\pi$
$272$	−3.05863	−0.185457
$273$	−6.49828	−0.393294
$274$	5.76547	0.348305
$275$	5.55691	0.335095
$276$	1.00000	0.0601929
$277$	−26.4362	−1.58840	−0.794199	−	0.607658i	$-0.792109\pi$
$277$	−26.4362	−1.58840	−0.794199	+	0.607658i	$0.792109\pi$
$278$	12.9966	0.779482
$279$	−5.05863	−0.302852
$280$	−1.00000	−0.0597614
$281$	−11.7914	−0.703419	−0.351709	−	0.936109i	$-0.614399\pi$
$281$	−11.7914	−0.703419	−0.351709	+	0.936109i	$0.614399\pi$
$282$	5.05863	0.301237
$283$	−29.7294	−1.76723	−0.883614	−	0.468216i	$-0.844897\pi$
$283$	−29.7294	−1.76723	−0.883614	+	0.468216i	$0.844897\pi$
$284$	−3.67418	−0.218023
$285$	1.05863	0.0627080
$286$	−36.1104	−2.13525
$287$	9.11383	0.537972
$288$	1.00000	0.0589256
$289$	−7.64476	−0.449692
$290$	−9.43965	−0.554315
$291$	4.61555	0.270568
$292$	13.1138	0.767429
$293$	−1.00344	−0.0586215	−0.0293107	−	0.999570i	$-0.509331\pi$
$293$	−1.00344	−0.0586215	−0.0293107	+	0.999570i	$0.509331\pi$
$294$	−1.00000	−0.0583212
$295$	12.9966	0.756689
$296$	−2.00000	−0.116248
$297$	−5.55691	−0.322445
$298$	−2.00000	−0.115857
$299$	6.49828	0.375805
$300$	−1.00000	−0.0577350
$301$	−5.55691	−0.320295
$302$	−16.9966	−0.978042
$303$	10.2637	0.589637
$304$	−1.05863	−0.0607168
$305$	−7.88273	−0.451364
$306$	−3.05863	−0.174850
$307$	−30.4622	−1.73857	−0.869284	−	0.494312i	$-0.835420\pi$
$307$	−30.4622	−1.73857	−0.869284	+	0.494312i	$0.835420\pi$
$308$	−5.55691	−0.316635
$309$	8.00000	0.455104
$310$	−5.05863	−0.287311
$311$	−11.5017	−0.652203	−0.326101	−	0.945335i	$-0.605735\pi$
$311$	−11.5017	−0.652203	−0.326101	+	0.945335i	$0.605735\pi$
$312$	6.49828	0.367893
$313$	30.3741	1.71685	0.858424	−	0.512941i	$-0.171444\pi$
$313$	30.3741	1.71685	0.858424	+	0.512941i	$0.171444\pi$
$314$	20.2277	1.14151
$315$	−1.00000	−0.0563436
$316$	13.2311	0.744307
$317$	−10.9966	−0.617628	−0.308814	−	0.951122i	$-0.599932\pi$
$317$	−10.9966	−0.617628	−0.308814	+	0.951122i	$0.599932\pi$
$318$	2.00000	0.112154
$319$	−52.4553	−2.93693
$320$	1.00000	0.0559017
$321$	1.88273	0.105084
$322$	1.00000	0.0557278
$323$	3.23797	0.180165
$324$	1.00000	0.0555556
$325$	−6.49828	−0.360460
$326$	−20.9966	−1.16289
$327$	−1.76547	−0.0976306
$328$	−9.11383	−0.503227
$329$	5.05863	0.278891
$330$	−5.55691	−0.305898
$331$	13.9931	0.769132	0.384566	−	0.923098i	$-0.374351\pi$
$331$	13.9931	0.769132	0.384566	+	0.923098i	$0.374351\pi$
$332$	−15.9379	−0.874707
$333$	−2.00000	−0.109599
$334$	−17.8207	−0.975103
$335$	−2.44309	−0.133480
$336$	1.00000	0.0545545
$337$	−8.20855	−0.447148	−0.223574	−	0.974687i	$-0.571772\pi$
$337$	−8.20855	−0.447148	−0.223574	+	0.974687i	$0.571772\pi$
$338$	29.2277	1.58977
$339$	−7.88273	−0.428131
$340$	−3.05863	−0.165878
$341$	−28.1104	−1.52226
$342$	−1.05863	−0.0572443
$343$	−1.00000	−0.0539949
$344$	5.55691	0.299609
$345$	1.00000	0.0538382
$346$	−15.0586	−0.809557
$347$	3.00344	0.161233	0.0806165	−	0.996745i	$-0.474311\pi$
$347$	3.00344	0.161233	0.0806165	+	0.996745i	$0.474311\pi$
$348$	9.43965	0.506018
$349$	27.4036	1.46688	0.733439	−	0.679755i	$-0.237914\pi$
$349$	27.4036	1.46688	0.733439	+	0.679755i	$0.237914\pi$
$350$	−1.00000	−0.0534522
$351$	6.49828	0.346853
$352$	5.55691	0.296185
$353$	−1.11383	−0.0592831	−0.0296416	−	0.999561i	$-0.509437\pi$
$353$	−1.11383	−0.0592831	−0.0296416	+	0.999561i	$0.509437\pi$
$354$	−12.9966	−0.690759
$355$	−3.67418	−0.195005
$356$	0.615547	0.0326239
$357$	−3.05863	−0.161880
$358$	−10.8793	−0.574989
$359$	−20.1104	−1.06139	−0.530693	−	0.847564i	$-0.678068\pi$
$359$	−20.1104	−1.06139	−0.530693	+	0.847564i	$0.678068\pi$
$360$	1.00000	0.0527046
$361$	−17.8793	−0.941016
$362$	0.117266	0.00616338
$363$	−19.8793	−1.04339
$364$	6.49828	0.340602
$365$	13.1138	0.686409
$366$	7.88273	0.412037
$367$	26.4622	1.38132	0.690658	−	0.723182i	$-0.257321\pi$
$367$	26.4622	1.38132	0.690658	+	0.723182i	$0.257321\pi$
$368$	−1.00000	−0.0521286
$369$	−9.11383	−0.474447
$370$	−2.00000	−0.103975
$371$	2.00000	0.103835
$372$	5.05863	0.262278
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	−16.9966	−0.878871
$375$	−1.00000	−0.0516398
$376$	−5.05863	−0.260879
$377$	61.3415	3.15925
$378$	1.00000	0.0514344
$379$	−19.8759	−1.02095	−0.510477	−	0.859891i	$-0.670531\pi$
$379$	−19.8759	−1.02095	−0.510477	+	0.859891i	$0.670531\pi$
$380$	−1.05863	−0.0543067
$381$	20.6707	1.05899
$382$	12.1104	0.619621
$383$	−19.1138	−0.976671	−0.488336	−	0.872656i	$-0.662396\pi$
$383$	−19.1138	−0.976671	−0.488336	+	0.872656i	$0.662396\pi$
$384$	−1.00000	−0.0510310
$385$	−5.55691	−0.283207
$386$	−22.9966	−1.17049
$387$	5.55691	0.282474
$388$	−4.61555	−0.234319
$389$	24.1173	1.22279	0.611397	−	0.791324i	$-0.290608\pi$
$389$	24.1173	1.22279	0.611397	+	0.791324i	$0.290608\pi$
$390$	6.49828	0.329053
$391$	3.05863	0.154682
$392$	1.00000	0.0505076
$393$	4.00000	0.201773
$394$	11.8827	0.598643
$395$	13.2311	0.665729
$396$	5.55691	0.279245
$397$	−6.49828	−0.326139	−0.163070	−	0.986615i	$-0.552140\pi$
$397$	−6.49828	−0.326139	−0.163070	+	0.986615i	$0.552140\pi$
$398$	25.9931	1.30292
$399$	−1.05863	−0.0529979
$400$	1.00000	0.0500000
$401$	−0.677618	−0.0338386	−0.0169193	−	0.999857i	$-0.505386\pi$
$401$	−0.677618	−0.0338386	−0.0169193	+	0.999857i	$0.505386\pi$
$402$	2.44309	0.121850
$403$	32.8724	1.63749
$404$	−10.2637	−0.510641
$405$	1.00000	0.0496904
$406$	9.43965	0.468482
$407$	−11.1138	−0.550892
$408$	3.05863	0.151425
$409$	−14.9966	−0.741532	−0.370766	−	0.928726i	$-0.620905\pi$
$409$	−14.9966	−0.741532	−0.370766	+	0.928726i	$0.620905\pi$
$410$	−9.11383	−0.450100
$411$	−5.76547	−0.284390
$412$	−8.00000	−0.394132
$413$	−12.9966	−0.639519
$414$	−1.00000	−0.0491473
$415$	−15.9379	−0.782362
$416$	−6.49828	−0.318604
$417$	−12.9966	−0.636444
$418$	−5.88273	−0.287734
$419$	−20.0812	−0.981030	−0.490515	−	0.871433i	$-0.663191\pi$
$419$	−20.0812	−0.981030	−0.490515	+	0.871433i	$0.663191\pi$
$420$	1.00000	0.0487950
$421$	10.8862	0.530560	0.265280	−	0.964171i	$-0.414536\pi$
$421$	10.8862	0.530560	0.265280	+	0.964171i	$0.414536\pi$
$422$	−4.99656	−0.243229
$423$	−5.05863	−0.245959
$424$	−2.00000	−0.0971286
$425$	−3.05863	−0.148366
$426$	3.67418	0.178015
$427$	7.88273	0.381472
$428$	−1.88273	−0.0910054
$429$	36.1104	1.74343
$430$	5.55691	0.267978
$431$	−2.76891	−0.133373	−0.0666867	−	0.997774i	$-0.521243\pi$
$431$	−2.76891	−0.133373	−0.0666867	+	0.997774i	$0.521243\pi$
$432$	−1.00000	−0.0481125
$433$	−8.85008	−0.425308	−0.212654	−	0.977128i	$-0.568211\pi$
$433$	−8.85008	−0.425308	−0.212654	+	0.977128i	$0.568211\pi$
$434$	5.05863	0.242822
$435$	9.43965	0.452596
$436$	1.76547	0.0845506
$437$	1.05863	0.0506413
$438$	−13.1138	−0.626603
$439$	20.4070	0.973973	0.486986	−	0.873410i	$-0.338096\pi$
$439$	20.4070	0.973973	0.486986	+	0.873410i	$0.338096\pi$
$440$	5.55691	0.264915
$441$	1.00000	0.0476190
$442$	19.8759	0.945398
$443$	25.2311	1.19877	0.599383	−	0.800463i	$-0.295413\pi$
$443$	25.2311	1.19877	0.599383	+	0.800463i	$0.295413\pi$
$444$	2.00000	0.0949158
$445$	0.615547	0.0291797
$446$	−18.3810	−0.870366
$447$	2.00000	0.0945968
$448$	−1.00000	−0.0472456
$449$	23.8827	1.12710	0.563548	−	0.826083i	$-0.309436\pi$
$449$	23.8827	1.12710	0.563548	+	0.826083i	$0.309436\pi$
$450$	1.00000	0.0471405
$451$	−50.6448	−2.38477
$452$	7.88273	0.370773
$453$	16.9966	0.798568
$454$	27.0518	1.26960
$455$	6.49828	0.304644
$456$	1.05863	0.0495750
$457$	13.0225	0.609169	0.304584	−	0.952485i	$-0.401482\pi$
$457$	13.0225	0.609169	0.304584	+	0.952485i	$0.401482\pi$
$458$	2.88617	0.134862
$459$	3.05863	0.142765
$460$	−1.00000	−0.0466252
$461$	−2.26375	−0.105433	−0.0527166	−	0.998610i	$-0.516788\pi$
$461$	−2.26375	−0.105433	−0.0527166	+	0.998610i	$0.516788\pi$
$462$	5.55691	0.258531
$463$	−19.2051	−0.892537	−0.446269	−	0.894899i	$-0.647247\pi$
$463$	−19.2051	−0.892537	−0.446269	+	0.894899i	$0.647247\pi$
$464$	−9.43965	−0.438225
$465$	5.05863	0.234588
$466$	−13.3484	−0.618351
$467$	30.1656	1.39590	0.697948	−	0.716148i	$-0.254096\pi$
$467$	30.1656	1.39590	0.697948	+	0.716148i	$0.254096\pi$
$468$	−6.49828	−0.300383
$469$	2.44309	0.112811
$470$	−5.05863	−0.233337
$471$	−20.2277	−0.932041
$472$	12.9966	0.598215
$473$	30.8793	1.41983
$474$	−13.2311	−0.607724
$475$	−1.05863	−0.0485734
$476$	3.05863	0.140192
$477$	−2.00000	−0.0915737
$478$	4.32582	0.197858
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	−1.00000	−0.0456435
$481$	12.9966	0.592592
$482$	8.70683	0.396585
$483$	−1.00000	−0.0455016
$484$	19.8793	0.903604
$485$	−4.61555	−0.209581
$486$	−1.00000	−0.0453609
$487$	24.7811	1.12294	0.561470	−	0.827497i	$-0.310236\pi$
$487$	24.7811	1.12294	0.561470	+	0.827497i	$0.310236\pi$
$488$	−7.88273	−0.356835
$489$	20.9966	0.949497
$490$	1.00000	0.0451754
$491$	19.3484	0.873179	0.436590	−	0.899661i	$-0.356186\pi$
$491$	19.3484	0.873179	0.436590	+	0.899661i	$0.356186\pi$
$492$	9.11383	0.410883
$493$	28.8724	1.30035
$494$	6.87930	0.309514
$495$	5.55691	0.249765
$496$	−5.05863	−0.227139
$497$	3.67418	0.164810
$498$	15.9379	0.714196
$499$	20.5275	0.918937	0.459468	−	0.888194i	$-0.348040\pi$
$499$	20.5275	0.918937	0.459468	+	0.888194i	$0.348040\pi$
$500$	1.00000	0.0447214
$501$	17.8207	0.796168
$502$	21.7294	0.969830
$503$	21.2311	0.946648	0.473324	−	0.880888i	$-0.343054\pi$
$503$	21.2311	0.946648	0.473324	+	0.880888i	$0.343054\pi$
$504$	−1.00000	−0.0445435
$505$	−10.2637	−0.456731
$506$	−5.55691	−0.247035
$507$	−29.2277	−1.29805
$508$	−20.6707	−0.917116
$509$	−12.7259	−0.564067	−0.282034	−	0.959405i	$-0.591009\pi$
$509$	−12.7259	−0.564067	−0.282034	+	0.959405i	$0.591009\pi$
$510$	3.05863	0.135439
$511$	−13.1138	−0.580122
$512$	1.00000	0.0441942
$513$	1.05863	0.0467398
$514$	19.9931	0.881859
$515$	−8.00000	−0.352522
$516$	−5.55691	−0.244630
$517$	−28.1104	−1.23629
$518$	2.00000	0.0878750
$519$	15.0586	0.661001
$520$	−6.49828	−0.284968
$521$	−27.8398	−1.21968	−0.609841	−	0.792524i	$-0.708767\pi$
$521$	−27.8398	−1.21968	−0.609841	+	0.792524i	$0.708767\pi$
$522$	−9.43965	−0.413162
$523$	14.7259	0.643920	0.321960	−	0.946753i	$-0.395658\pi$
$523$	14.7259	0.643920	0.321960	+	0.946753i	$0.395658\pi$
$524$	−4.00000	−0.174741
$525$	1.00000	0.0436436
$526$	−3.76547	−0.164182
$527$	15.4725	0.673993
$528$	−5.55691	−0.241834
$529$	1.00000	0.0434783
$530$	−2.00000	−0.0868744
$531$	12.9966	0.564003
$532$	1.05863	0.0458976
$533$	59.2242	2.56529
$534$	−0.615547	−0.0266373
$535$	−1.88273	−0.0813977
$536$	−2.44309	−0.105525
$537$	10.8793	0.469476
$538$	12.6155	0.543895
$539$	5.55691	0.239353
$540$	−1.00000	−0.0430331
$541$	10.8862	0.468033	0.234017	−	0.972233i	$-0.424813\pi$
$541$	10.8862	0.468033	0.234017	+	0.972233i	$0.424813\pi$
$542$	−27.2863	−1.17205
$543$	−0.117266	−0.00503238
$544$	−3.05863	−0.131138
$545$	1.76547	0.0756243
$546$	−6.49828	−0.278101
$547$	42.7552	1.82808	0.914039	−	0.405626i	$-0.132946\pi$
$547$	42.7552	1.82808	0.914039	+	0.405626i	$0.132946\pi$
$548$	5.76547	0.246289
$549$	−7.88273	−0.336427
$550$	5.55691	0.236948
$551$	9.99312	0.425721
$552$	1.00000	0.0425628
$553$	−13.2311	−0.562643
$554$	−26.4362	−1.12317
$555$	2.00000	0.0848953
$556$	12.9966	0.551177
$557$	−5.76547	−0.244291	−0.122145	−	0.992512i	$-0.538977\pi$
$557$	−5.76547	−0.244291	−0.122145	+	0.992512i	$0.538977\pi$
$558$	−5.05863	−0.214149
$559$	−36.1104	−1.52731
$560$	−1.00000	−0.0422577
$561$	16.9966	0.717595
$562$	−11.7914	−0.497392
$563$	−22.1656	−0.934168	−0.467084	−	0.884213i	$-0.654695\pi$
$563$	−22.1656	−0.934168	−0.467084	+	0.884213i	$0.654695\pi$
$564$	5.05863	0.213007
$565$	7.88273	0.331629
$566$	−29.7294	−1.24962
$567$	−1.00000	−0.0419961
$568$	−3.67418	−0.154165
$569$	7.32238	0.306970	0.153485	−	0.988151i	$-0.450950\pi$
$569$	7.32238	0.306970	0.153485	+	0.988151i	$0.450950\pi$
$570$	1.05863	0.0443413
$571$	8.23453	0.344604	0.172302	−	0.985044i	$-0.444879\pi$
$571$	8.23453	0.344604	0.172302	+	0.985044i	$0.444879\pi$
$572$	−36.1104	−1.50985
$573$	−12.1104	−0.505919
$574$	9.11383	0.380404
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	−11.2311	−0.467557	−0.233778	−	0.972290i	$-0.575109\pi$
$577$	−11.2311	−0.467557	−0.233778	+	0.972290i	$0.575109\pi$
$578$	−7.64476	−0.317980
$579$	22.9966	0.955705
$580$	−9.43965	−0.391960
$581$	15.9379	0.661217
$582$	4.61555	0.191321
$583$	−11.1138	−0.460288
$584$	13.1138	0.542654
$585$	−6.49828	−0.268671
$586$	−1.00344	−0.0414516
$587$	5.99312	0.247363	0.123681	−	0.992322i	$-0.460530\pi$
$587$	5.99312	0.247363	0.123681	+	0.992322i	$0.460530\pi$
$588$	−1.00000	−0.0412393
$589$	5.35524	0.220659
$590$	12.9966	0.535060
$591$	−11.8827	−0.488790
$592$	−2.00000	−0.0821995
$593$	24.2277	0.994911	0.497455	−	0.867490i	$-0.334268\pi$
$593$	24.2277	0.994911	0.497455	+	0.867490i	$0.334268\pi$
$594$	−5.55691	−0.228003
$595$	3.05863	0.125392
$596$	−2.00000	−0.0819232
$597$	−25.9931	−1.06383
$598$	6.49828	0.265734
$599$	3.32926	0.136030	0.0680149	−	0.997684i	$-0.478333\pi$
$599$	3.32926	0.136030	0.0680149	+	0.997684i	$0.478333\pi$
$600$	−1.00000	−0.0408248
$601$	11.1207	0.453623	0.226811	−	0.973939i	$-0.427170\pi$
$601$	11.1207	0.453623	0.226811	+	0.973939i	$0.427170\pi$
$602$	−5.55691	−0.226483
$603$	−2.44309	−0.0994901
$604$	−16.9966	−0.691580
$605$	19.8793	0.808208
$606$	10.2637	0.416936
$607$	−4.96735	−0.201618	−0.100809	−	0.994906i	$-0.532143\pi$
$607$	−4.96735	−0.201618	−0.100809	+	0.994906i	$0.532143\pi$
$608$	−1.05863	−0.0429332
$609$	−9.43965	−0.382514
$610$	−7.88273	−0.319163
$611$	32.8724	1.32988
$612$	−3.05863	−0.123638
$613$	−28.1173	−1.13565	−0.567823	−	0.823151i	$-0.692214\pi$
$613$	−28.1173	−1.13565	−0.567823	+	0.823151i	$0.692214\pi$
$614$	−30.4622	−1.22935
$615$	9.11383	0.367505
$616$	−5.55691	−0.223894
$617$	13.1138	0.527943	0.263971	−	0.964530i	$-0.414968\pi$
$617$	13.1138	0.527943	0.263971	+	0.964530i	$0.414968\pi$
$618$	8.00000	0.321807
$619$	−39.1621	−1.57406	−0.787030	−	0.616915i	$-0.788382\pi$
$619$	−39.1621	−1.57406	−0.787030	+	0.616915i	$0.788382\pi$
$620$	−5.05863	−0.203160
$621$	1.00000	0.0401286
$622$	−11.5017	−0.461177
$623$	−0.615547	−0.0246614
$624$	6.49828	0.260139
$625$	1.00000	0.0400000
$626$	30.3741	1.21399
$627$	5.88273	0.234934
$628$	20.2277	0.807171
$629$	6.11727	0.243911
$630$	−1.00000	−0.0398410
$631$	−47.6933	−1.89864	−0.949320	−	0.314312i	$-0.898226\pi$
$631$	−47.6933	−1.89864	−0.949320	+	0.314312i	$0.898226\pi$
$632$	13.2311	0.526305
$633$	4.99656	0.198596
$634$	−10.9966	−0.436729
$635$	−20.6707	−0.820293
$636$	2.00000	0.0793052
$637$	−6.49828	−0.257471
$638$	−52.4553	−2.07673
$639$	−3.67418	−0.145348
$640$	1.00000	0.0395285
$641$	−19.7914	−0.781715	−0.390858	−	0.920451i	$-0.627822\pi$
$641$	−19.7914	−0.781715	−0.390858	+	0.920451i	$0.627822\pi$
$642$	1.88273	0.0743056
$643$	28.6087	1.12822	0.564108	−	0.825701i	$-0.309220\pi$
$643$	28.6087	1.12822	0.564108	+	0.825701i	$0.309220\pi$
$644$	1.00000	0.0394055
$645$	−5.55691	−0.218803
$646$	3.23797	0.127396
$647$	−25.1690	−0.989496	−0.494748	−	0.869036i	$-0.664740\pi$
$647$	−25.1690	−0.989496	−0.494748	+	0.869036i	$0.664740\pi$
$648$	1.00000	0.0392837
$649$	72.2208	2.83491
$650$	−6.49828	−0.254884
$651$	−5.05863	−0.198263
$652$	−20.9966	−0.822289
$653$	9.58289	0.375008	0.187504	−	0.982264i	$-0.439960\pi$
$653$	9.58289	0.375008	0.187504	+	0.982264i	$0.439960\pi$
$654$	−1.76547	−0.0690352
$655$	−4.00000	−0.156293
$656$	−9.11383	−0.355835
$657$	13.1138	0.511619
$658$	5.05863	0.197206
$659$	1.44652	0.0563486	0.0281743	−	0.999603i	$-0.491031\pi$
$659$	1.44652	0.0563486	0.0281743	+	0.999603i	$0.491031\pi$
$660$	−5.55691	−0.216303
$661$	9.11383	0.354487	0.177243	−	0.984167i	$-0.443282\pi$
$661$	9.11383	0.354487	0.177243	+	0.984167i	$0.443282\pi$
$662$	13.9931	0.543858
$663$	−19.8759	−0.771914
$664$	−15.9379	−0.618512
$665$	1.05863	0.0410520
$666$	−2.00000	−0.0774984
$667$	9.43965	0.365505
$668$	−17.8207	−0.689502
$669$	18.3810	0.710651
$670$	−2.44309	−0.0943846
$671$	−43.8037	−1.69102
$672$	1.00000	0.0385758
$673$	30.1104	1.16067	0.580335	−	0.814378i	$-0.302922\pi$
$673$	30.1104	1.16067	0.580335	+	0.814378i	$0.302922\pi$
$674$	−8.20855	−0.316182
$675$	−1.00000	−0.0384900
$676$	29.2277	1.12414
$677$	−21.7655	−0.836515	−0.418257	−	0.908329i	$-0.637359\pi$
$677$	−21.7655	−0.836515	−0.418257	+	0.908329i	$0.637359\pi$
$678$	−7.88273	−0.302735
$679$	4.61555	0.177128
$680$	−3.05863	−0.117293
$681$	−27.0518	−1.03663
$682$	−28.1104	−1.07640
$683$	−30.9897	−1.18579	−0.592894	−	0.805281i	$-0.702015\pi$
$683$	−30.9897	−1.18579	−0.592894	+	0.805281i	$0.702015\pi$
$684$	−1.05863	−0.0404779
$685$	5.76547	0.220287
$686$	−1.00000	−0.0381802
$687$	−2.88617	−0.110114
$688$	5.55691	0.211855
$689$	12.9966	0.495130
$690$	1.00000	0.0380693
$691$	−16.8862	−0.642380	−0.321190	−	0.947015i	$-0.604083\pi$
$691$	−16.8862	−0.642380	−0.321190	+	0.947015i	$0.604083\pi$
$692$	−15.0586	−0.572443
$693$	−5.55691	−0.211090
$694$	3.00344	0.114009
$695$	12.9966	0.492988
$696$	9.43965	0.357809
$697$	27.8759	1.05587
$698$	27.4036	1.03724
$699$	13.3484	0.504881
$700$	−1.00000	−0.0377964
$701$	−15.1070	−0.570582	−0.285291	−	0.958441i	$-0.592090\pi$
$701$	−15.1070	−0.570582	−0.285291	+	0.958441i	$0.592090\pi$
$702$	6.49828	0.245262
$703$	2.11727	0.0798542
$704$	5.55691	0.209434
$705$	5.05863	0.190519
$706$	−1.11383	−0.0419195
$707$	10.2637	0.386008
$708$	−12.9966	−0.488441
$709$	−5.11383	−0.192054	−0.0960269	−	0.995379i	$-0.530613\pi$
$709$	−5.11383	−0.192054	−0.0960269	+	0.995379i	$0.530613\pi$
$710$	−3.67418	−0.137890
$711$	13.2311	0.496205
$712$	0.615547	0.0230686
$713$	5.05863	0.189447
$714$	−3.05863	−0.114466
$715$	−36.1104	−1.35045
$716$	−10.8793	−0.406578
$717$	−4.32582	−0.161551
$718$	−20.1104	−0.750513
$719$	15.2672	0.569370	0.284685	−	0.958621i	$-0.408111\pi$
$719$	15.2672	0.569370	0.284685	+	0.958621i	$0.408111\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	−17.8793	−0.665398
$723$	−8.70683	−0.323811
$724$	0.117266	0.00435817
$725$	−9.43965	−0.350580
$726$	−19.8793	−0.737790
$727$	28.7620	1.06672	0.533362	−	0.845887i	$-0.320928\pi$
$727$	28.7620	1.06672	0.533362	+	0.845887i	$0.320928\pi$
$728$	6.49828	0.240842
$729$	1.00000	0.0370370
$730$	13.1138	0.485365
$731$	−16.9966	−0.628641
$732$	7.88273	0.291354
$733$	−3.64820	−0.134749	−0.0673747	−	0.997728i	$-0.521462\pi$
$733$	−3.64820	−0.134749	−0.0673747	+	0.997728i	$0.521462\pi$
$734$	26.4622	0.976737
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	−13.5760	−0.500079
$738$	−9.11383	−0.335485
$739$	−9.23109	−0.339571	−0.169786	−	0.985481i	$-0.554308\pi$
$739$	−9.23109	−0.339571	−0.169786	+	0.985481i	$0.554308\pi$
$740$	−2.00000	−0.0735215
$741$	−6.87930	−0.252717
$742$	2.00000	0.0734223
$743$	−27.4588	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$743$	−27.4588	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$744$	5.05863	0.185458
$745$	−2.00000	−0.0732743
$746$	−2.00000	−0.0732252
$747$	−15.9379	−0.583138
$748$	−16.9966	−0.621456
$749$	1.88273	0.0687936
$750$	−1.00000	−0.0365148
$751$	38.2277	1.39495	0.697474	−	0.716611i	$-0.254307\pi$
$751$	38.2277	1.39495	0.697474	+	0.716611i	$0.254307\pi$
$752$	−5.05863	−0.184469
$753$	−21.7294	−0.791862
$754$	61.3415	2.23393
$755$	−16.9966	−0.618568
$756$	1.00000	0.0363696
$757$	1.88961	0.0686790	0.0343395	−	0.999410i	$-0.489067\pi$
$757$	1.88961	0.0686790	0.0343395	+	0.999410i	$0.489067\pi$
$758$	−19.8759	−0.721924
$759$	5.55691	0.201703
$760$	−1.05863	−0.0384007
$761$	24.6967	0.895255	0.447628	−	0.894220i	$-0.352269\pi$
$761$	24.6967	0.895255	0.447628	+	0.894220i	$0.352269\pi$
$762$	20.6707	0.748822
$763$	−1.76547	−0.0639142
$764$	12.1104	0.438139
$765$	−3.05863	−0.110585
$766$	−19.1138	−0.690611
$767$	−84.4553	−3.04950
$768$	−1.00000	−0.0360844
$769$	52.0414	1.87666	0.938331	−	0.345738i	$-0.112371\pi$
$769$	52.0414	1.87666	0.938331	+	0.345738i	$0.112371\pi$
$770$	−5.55691	−0.200257
$771$	−19.9931	−0.720035
$772$	−22.9966	−0.827664
$773$	36.8793	1.32646	0.663228	−	0.748417i	$-0.269186\pi$
$773$	36.8793	1.32646	0.663228	+	0.748417i	$0.269186\pi$
$774$	5.55691	0.199739
$775$	−5.05863	−0.181711
$776$	−4.61555	−0.165688
$777$	−2.00000	−0.0717496
$778$	24.1173	0.864646
$779$	9.64820	0.345683
$780$	6.49828	0.232676
$781$	−20.4171	−0.730582
$782$	3.05863	0.109376
$783$	9.43965	0.337345
$784$	1.00000	0.0357143
$785$	20.2277	0.721956
$786$	4.00000	0.142675
$787$	−21.3845	−0.762273	−0.381137	−	0.924519i	$-0.624467\pi$
$787$	−21.3845	−0.762273	−0.381137	+	0.924519i	$0.624467\pi$
$788$	11.8827	0.423305
$789$	3.76547	0.134054
$790$	13.2311	0.470741
$791$	−7.88273	−0.280278
$792$	5.55691	0.197456
$793$	51.2242	1.81903
$794$	−6.49828	−0.230615
$795$	2.00000	0.0709327
$796$	25.9931	0.921302
$797$	26.1104	0.924877	0.462439	−	0.886651i	$-0.346975\pi$
$797$	26.1104	0.924877	0.462439	+	0.886651i	$0.346975\pi$
$798$	−1.05863	−0.0374752
$799$	15.4725	0.547378
$800$	1.00000	0.0353553
$801$	0.615547	0.0217493
$802$	−0.677618	−0.0239275
$803$	72.8724	2.57161
$804$	2.44309	0.0861610
$805$	1.00000	0.0352454
$806$	32.8724	1.15788
$807$	−12.6155	−0.444088
$808$	−10.2637	−0.361077
$809$	46.7620	1.64407	0.822033	−	0.569440i	$-0.192840\pi$
$809$	46.7620	1.64407	0.822033	+	0.569440i	$0.192840\pi$
$810$	1.00000	0.0351364
$811$	23.4588	0.823748	0.411874	−	0.911241i	$-0.364874\pi$
$811$	23.4588	0.823748	0.411874	+	0.911241i	$0.364874\pi$
$812$	9.43965	0.331267
$813$	27.2863	0.956972
$814$	−11.1138	−0.389539
$815$	−20.9966	−0.735477
$816$	3.05863	0.107074
$817$	−5.88273	−0.205811
$818$	−14.9966	−0.524342
$819$	6.49828	0.227068
$820$	−9.11383	−0.318269
$821$	−10.4362	−0.364226	−0.182113	−	0.983278i	$-0.558294\pi$
$821$	−10.4362	−0.364226	−0.182113	+	0.983278i	$0.558294\pi$
$822$	−5.76547	−0.201094
$823$	−26.4293	−0.921269	−0.460634	−	0.887590i	$-0.652378\pi$
$823$	−26.4293	−0.921269	−0.460634	+	0.887590i	$0.652378\pi$
$824$	−8.00000	−0.278693
$825$	−5.55691	−0.193467
$826$	−12.9966	−0.452208
$827$	−30.3380	−1.05496	−0.527479	−	0.849568i	$-0.676863\pi$
$827$	−30.3380	−1.05496	−0.527479	+	0.849568i	$0.676863\pi$
$828$	−1.00000	−0.0347524
$829$	−31.4036	−1.09069	−0.545345	−	0.838211i	$-0.683601\pi$
$829$	−31.4036	−1.09069	−0.545345	+	0.838211i	$0.683601\pi$
$830$	−15.9379	−0.553214
$831$	26.4362	0.917062
$832$	−6.49828	−0.225287
$833$	−3.05863	−0.105975
$834$	−12.9966	−0.450034
$835$	−17.8207	−0.616709
$836$	−5.88273	−0.203459
$837$	5.05863	0.174852
$838$	−20.0812	−0.693693
$839$	−0.996562	−0.0344051	−0.0172026	−	0.999852i	$-0.505476\pi$
$839$	−0.996562	−0.0344051	−0.0172026	+	0.999852i	$0.505476\pi$
$840$	1.00000	0.0345033
$841$	60.1070	2.07265
$842$	10.8862	0.375162
$843$	11.7914	0.406119
$844$	−4.99656	−0.171989
$845$	29.2277	1.00546
$846$	−5.05863	−0.173919
$847$	−19.8793	−0.683061
$848$	−2.00000	−0.0686803
$849$	29.7294	1.02031
$850$	−3.05863	−0.104910
$851$	2.00000	0.0685591
$852$	3.67418	0.125875
$853$	−45.1950	−1.54745	−0.773724	−	0.633523i	$-0.781608\pi$
$853$	−45.1950	−1.54745	−0.773724	+	0.633523i	$0.781608\pi$
$854$	7.88273	0.269742
$855$	−1.05863	−0.0362045
$856$	−1.88273	−0.0643505
$857$	−7.12070	−0.243239	−0.121619	−	0.992577i	$-0.538809\pi$
$857$	−7.12070	−0.243239	−0.121619	+	0.992577i	$0.538809\pi$
$858$	36.1104	1.23279
$859$	−41.5760	−1.41856	−0.709278	−	0.704929i	$-0.750979\pi$
$859$	−41.5760	−1.41856	−0.709278	+	0.704929i	$0.750979\pi$
$860$	5.55691	0.189489
$861$	−9.11383	−0.310598
$862$	−2.76891	−0.0943093
$863$	−1.46563	−0.0498905	−0.0249453	−	0.999689i	$-0.507941\pi$
$863$	−1.46563	−0.0498905	−0.0249453	+	0.999689i	$0.507941\pi$
$864$	−1.00000	−0.0340207
$865$	−15.0586	−0.512009
$866$	−8.85008	−0.300738
$867$	7.64476	0.259630
$868$	5.05863	0.171701
$869$	73.5241	2.49413
$870$	9.43965	0.320034
$871$	15.8759	0.537933
$872$	1.76547	0.0597863
$873$	−4.61555	−0.156213
$874$	1.05863	0.0358088
$875$	−1.00000	−0.0338062
$876$	−13.1138	−0.443075
$877$	51.1982	1.72884	0.864421	−	0.502769i	$-0.167685\pi$
$877$	51.1982	1.72884	0.864421	+	0.502769i	$0.167685\pi$
$878$	20.4070	0.688703
$879$	1.00344	0.0338451
$880$	5.55691	0.187324
$881$	8.96047	0.301886	0.150943	−	0.988542i	$-0.451769\pi$
$881$	8.96047	0.301886	0.150943	+	0.988542i	$0.451769\pi$
$882$	1.00000	0.0336718
$883$	−7.23797	−0.243577	−0.121789	−	0.992556i	$-0.538863\pi$
$883$	−7.23797	−0.243577	−0.121789	+	0.992556i	$0.538863\pi$
$884$	19.8759	0.668497
$885$	−12.9966	−0.436875
$886$	25.2311	0.847655
$887$	33.2932	1.11788	0.558938	−	0.829210i	$-0.311209\pi$
$887$	33.2932	1.11788	0.558938	+	0.829210i	$0.311209\pi$
$888$	2.00000	0.0671156
$889$	20.6707	0.693274
$890$	0.615547	0.0206332
$891$	5.55691	0.186164
$892$	−18.3810	−0.615442
$893$	5.35524	0.179206
$894$	2.00000	0.0668900
$895$	−10.8793	−0.363655
$896$	−1.00000	−0.0334077
$897$	−6.49828	−0.216971
$898$	23.8827	0.796977
$899$	47.7517	1.59261
$900$	1.00000	0.0333333
$901$	6.11727	0.203796
$902$	−50.6448	−1.68629
$903$	5.55691	0.184923
$904$	7.88273	0.262176
$905$	0.117266	0.00389806
$906$	16.9966	0.564673
$907$	−38.5535	−1.28015	−0.640074	−	0.768314i	$-0.721096\pi$
$907$	−38.5535	−1.28015	−0.640074	+	0.768314i	$0.721096\pi$
$908$	27.0518	0.897744
$909$	−10.2637	−0.340427
$910$	6.49828	0.215416
$911$	−52.7620	−1.74808	−0.874042	−	0.485850i	$-0.838510\pi$
$911$	−52.7620	−1.74808	−0.874042	+	0.485850i	$0.838510\pi$
$912$	1.05863	0.0350548
$913$	−88.5657	−2.93110
$914$	13.0225	0.430747
$915$	7.88273	0.260595
$916$	2.88617	0.0953618
$917$	4.00000	0.132092
$918$	3.05863	0.100950
$919$	12.7620	0.420981	0.210490	−	0.977596i	$-0.432494\pi$
$919$	12.7620	0.420981	0.210490	+	0.977596i	$0.432494\pi$
$920$	−1.00000	−0.0329690
$921$	30.4622	1.00376
$922$	−2.26375	−0.0745526
$923$	23.8759	0.785883
$924$	5.55691	0.182809
$925$	−2.00000	−0.0657596
$926$	−19.2051	−0.631119
$927$	−8.00000	−0.262754
$928$	−9.43965	−0.309872
$929$	13.2380	0.434324	0.217162	−	0.976136i	$-0.430320\pi$
$929$	13.2380	0.434324	0.217162	+	0.976136i	$0.430320\pi$
$930$	5.05863	0.165879
$931$	−1.05863	−0.0346953
$932$	−13.3484	−0.437240
$933$	11.5017	0.376549
$934$	30.1656	0.987048
$935$	−16.9966	−0.555847
$936$	−6.49828	−0.212403
$937$	−48.2569	−1.57648	−0.788242	−	0.615366i	$-0.789008\pi$
$937$	−48.2569	−1.57648	−0.788242	+	0.615366i	$0.789008\pi$
$938$	2.44309	0.0797696
$939$	−30.3741	−0.991223
$940$	−5.05863	−0.164994
$941$	−12.4622	−0.406256	−0.203128	−	0.979152i	$-0.565111\pi$
$941$	−12.4622	−0.406256	−0.203128	+	0.979152i	$0.565111\pi$
$942$	−20.2277	−0.659053
$943$	9.11383	0.296787
$944$	12.9966	0.423002
$945$	1.00000	0.0325300
$946$	30.8793	1.00397
$947$	30.9897	1.00703	0.503515	−	0.863987i	$-0.332040\pi$
$947$	30.9897	1.00703	0.503515	+	0.863987i	$0.332040\pi$
$948$	−13.2311	−0.429726
$949$	−85.2173	−2.76627
$950$	−1.05863	−0.0343466
$951$	10.9966	0.356588
$952$	3.05863	0.0991309
$953$	−3.41367	−0.110580	−0.0552898	−	0.998470i	$-0.517608\pi$
$953$	−3.41367	−0.110580	−0.0552898	+	0.998470i	$0.517608\pi$
$954$	−2.00000	−0.0647524
$955$	12.1104	0.391883
$956$	4.32582	0.139907
$957$	52.4553	1.69564
$958$	16.0000	0.516937
$959$	−5.76547	−0.186177
$960$	−1.00000	−0.0322749
$961$	−5.41023	−0.174524
$962$	12.9966	0.419026
$963$	−1.88273	−0.0606702
$964$	8.70683	0.280428
$965$	−22.9966	−0.740286
$966$	−1.00000	−0.0321745
$967$	−27.2051	−0.874858	−0.437429	−	0.899253i	$-0.644111\pi$
$967$	−27.2051	−0.874858	−0.437429	+	0.899253i	$0.644111\pi$
$968$	19.8793	0.638945
$969$	−3.23797	−0.104019
$970$	−4.61555	−0.148196
$971$	−3.79468	−0.121777	−0.0608886	−	0.998145i	$-0.519393\pi$
$971$	−3.79468	−0.121777	−0.0608886	+	0.998145i	$0.519393\pi$
$972$	−1.00000	−0.0320750
$973$	−12.9966	−0.416651
$974$	24.7811	0.794039
$975$	6.49828	0.208112
$976$	−7.88273	−0.252320
$977$	48.8793	1.56379	0.781894	−	0.623412i	$-0.214254\pi$
$977$	48.8793	1.56379	0.781894	+	0.623412i	$0.214254\pi$
$978$	20.9966	0.671396
$979$	3.42054	0.109321
$980$	1.00000	0.0319438
$981$	1.76547	0.0563670
$982$	19.3484	0.617431
$983$	38.8793	1.24006	0.620028	−	0.784579i	$-0.287121\pi$
$983$	38.8793	1.24006	0.620028	+	0.784579i	$0.287121\pi$
$984$	9.11383	0.290538
$985$	11.8827	0.378615
$986$	28.8724	0.919485
$987$	−5.05863	−0.161018
$988$	6.87930	0.218860
$989$	−5.55691	−0.176700
$990$	5.55691	0.176610
$991$	36.7620	1.16778	0.583892	−	0.811831i	$-0.301529\pi$
$991$	36.7620	1.16778	0.583892	+	0.811831i	$0.301529\pi$
$992$	−5.05863	−0.160612
$993$	−13.9931	−0.444058
$994$	3.67418	0.116538
$995$	25.9931	0.824037
$996$	15.9379	0.505013
$997$	−44.2569	−1.40163	−0.700815	−	0.713343i	$-0.747180\pi$
$997$	−44.2569	−1.40163	−0.700815	+	0.713343i	$0.747180\pi$
$998$	20.5275	0.649787
$999$	2.00000	0.0632772

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +5.55691 q^{11} -1.00000 q^{12} -6.49828 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.05863 q^{17} +1.00000 q^{18} -1.05863 q^{19} +1.00000 q^{20} +1.00000 q^{21} +5.55691 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.49828 q^{26} -1.00000 q^{27} -1.00000 q^{28} -9.43965 q^{29} -1.00000 q^{30} -5.05863 q^{31} +1.00000 q^{32} -5.55691 q^{33} -3.05863 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -1.05863 q^{38} +6.49828 q^{39} +1.00000 q^{40} -9.11383 q^{41} +1.00000 q^{42} +5.55691 q^{43} +5.55691 q^{44} +1.00000 q^{45} -1.00000 q^{46} -5.05863 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.05863 q^{51} -6.49828 q^{52} -2.00000 q^{53} -1.00000 q^{54} +5.55691 q^{55} -1.00000 q^{56} +1.05863 q^{57} -9.43965 q^{58} +12.9966 q^{59} -1.00000 q^{60} -7.88273 q^{61} -5.05863 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.49828 q^{65} -5.55691 q^{66} -2.44309 q^{67} -3.05863 q^{68} +1.00000 q^{69} -1.00000 q^{70} -3.67418 q^{71} +1.00000 q^{72} +13.1138 q^{73} -2.00000 q^{74} -1.00000 q^{75} -1.05863 q^{76} -5.55691 q^{77} +6.49828 q^{78} +13.2311 q^{79} +1.00000 q^{80} +1.00000 q^{81} -9.11383 q^{82} -15.9379 q^{83} +1.00000 q^{84} -3.05863 q^{85} +5.55691 q^{86} +9.43965 q^{87} +5.55691 q^{88} +0.615547 q^{89} +1.00000 q^{90} +6.49828 q^{91} -1.00000 q^{92} +5.05863 q^{93} -5.05863 q^{94} -1.05863 q^{95} -1.00000 q^{96} -4.61555 q^{97} +1.00000 q^{98} +5.55691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{12} - 2 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - 4 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} - 16 q^{31} + 3 q^{32} - 10 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} + 3 q^{42} + 3 q^{45} - 3 q^{46} - 16 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 10 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{54} - 3 q^{56} + 4 q^{57} - 10 q^{58} + 4 q^{59} - 3 q^{60} - 22 q^{61} - 16 q^{62} - 3 q^{63} + 3 q^{64} - 2 q^{65} - 24 q^{67} - 10 q^{68} + 3 q^{69} - 3 q^{70} + 4 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} - 3 q^{75} - 4 q^{76} + 2 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} + 6 q^{82} - 12 q^{83} + 3 q^{84} - 10 q^{85} + 10 q^{87} - 14 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} - 3 q^{96} + 2 q^{97} + 3 q^{98}+O(q^{100}) \) 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 - 3 * q^12 - 2 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - 4 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 - 16 * q^31 + 3 * q^32 - 10 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 + 3 * q^42 + 3 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 10 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^54 - 3 * q^56 + 4 * q^57 - 10 * q^58 + 4 * q^59 - 3 * q^60 - 22 * q^61 - 16 * q^62 - 3 * q^63 + 3 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 3 * q^69 - 3 * q^70 + 4 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 - 3 * q^75 - 4 * q^76 + 2 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 + 6 * q^82 - 12 * q^83 + 3 * q^84 - 10 * q^85 + 10 * q^87 - 14 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 - 3 * q^96 + 2 * q^97 + 3 * q^98

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