LMFDB - Embedded newform 5610.2.a.cc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -0.890084 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -0.890084 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.10992 q^{13} -0.890084 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +6.09783 q^{19} +1.00000 q^{20} +0.890084 q^{21} -1.00000 q^{22} -8.31767 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.10992 q^{26} -1.00000 q^{27} -0.890084 q^{28} -6.00000 q^{29} -1.00000 q^{30} -3.20775 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -0.890084 q^{35} +1.00000 q^{36} -3.78017 q^{37} +6.09783 q^{38} +1.10992 q^{39} +1.00000 q^{40} -8.00000 q^{41} +0.890084 q^{42} -4.09783 q^{43} -1.00000 q^{44} +1.00000 q^{45} -8.31767 q^{46} +6.76809 q^{47} -1.00000 q^{48} -6.20775 q^{49} +1.00000 q^{50} +1.00000 q^{51} -1.10992 q^{52} +13.0858 q^{53} -1.00000 q^{54} -1.00000 q^{55} -0.890084 q^{56} -6.09783 q^{57} -6.00000 q^{58} -4.89008 q^{59} -1.00000 q^{60} -0.219833 q^{61} -3.20775 q^{62} -0.890084 q^{63} +1.00000 q^{64} -1.10992 q^{65} +1.00000 q^{66} +11.9758 q^{67} -1.00000 q^{68} +8.31767 q^{69} -0.890084 q^{70} -12.0978 q^{71} +1.00000 q^{72} -2.45042 q^{73} -3.78017 q^{74} -1.00000 q^{75} +6.09783 q^{76} +0.890084 q^{77} +1.10992 q^{78} +14.2935 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} -9.97584 q^{83} +0.890084 q^{84} -1.00000 q^{85} -4.09783 q^{86} +6.00000 q^{87} -1.00000 q^{88} -11.9758 q^{89} +1.00000 q^{90} +0.987918 q^{91} -8.31767 q^{92} +3.20775 q^{93} +6.76809 q^{94} +6.09783 q^{95} -1.00000 q^{96} +0.987918 q^{97} -6.20775 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 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 - 2 * 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} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{20} + 2 q^{21} - 3 q^{22} - 8 q^{23} - 3 q^{24} + 3 q^{25} - 4 q^{26} - 3 q^{27} - 2 q^{28} - 18 q^{29} - 3 q^{30} + 8 q^{31} + 3 q^{32} + 3 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - 10 q^{37} + 4 q^{39} + 3 q^{40} - 24 q^{41} + 2 q^{42} + 6 q^{43} - 3 q^{44} + 3 q^{45} - 8 q^{46} - 3 q^{48} - q^{49} + 3 q^{50} + 3 q^{51} - 4 q^{52} + 2 q^{53} - 3 q^{54} - 3 q^{55} - 2 q^{56} - 18 q^{58} - 14 q^{59} - 3 q^{60} - 2 q^{61} + 8 q^{62} - 2 q^{63} + 3 q^{64} - 4 q^{65} + 3 q^{66} - 2 q^{67} - 3 q^{68} + 8 q^{69} - 2 q^{70} - 18 q^{71} + 3 q^{72} - 4 q^{73} - 10 q^{74} - 3 q^{75} + 2 q^{77} + 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 24 q^{82} + 8 q^{83} + 2 q^{84} - 3 q^{85} + 6 q^{86} + 18 q^{87} - 3 q^{88} + 2 q^{89} + 3 q^{90} - 16 q^{91} - 8 q^{92} - 8 q^{93} - 3 q^{96} - 16 q^{97} - q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 3 * q^12 - 4 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^20 + 2 * q^21 - 3 * q^22 - 8 * q^23 - 3 * q^24 + 3 * q^25 - 4 * q^26 - 3 * q^27 - 2 * q^28 - 18 * q^29 - 3 * q^30 + 8 * q^31 + 3 * q^32 + 3 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - 10 * q^37 + 4 * q^39 + 3 * q^40 - 24 * q^41 + 2 * q^42 + 6 * q^43 - 3 * q^44 + 3 * q^45 - 8 * q^46 - 3 * q^48 - q^49 + 3 * q^50 + 3 * q^51 - 4 * q^52 + 2 * q^53 - 3 * q^54 - 3 * q^55 - 2 * q^56 - 18 * q^58 - 14 * q^59 - 3 * q^60 - 2 * q^61 + 8 * q^62 - 2 * q^63 + 3 * q^64 - 4 * q^65 + 3 * q^66 - 2 * q^67 - 3 * q^68 + 8 * q^69 - 2 * q^70 - 18 * q^71 + 3 * q^72 - 4 * q^73 - 10 * q^74 - 3 * q^75 + 2 * q^77 + 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 24 * q^82 + 8 * q^83 + 2 * q^84 - 3 * q^85 + 6 * q^86 + 18 * q^87 - 3 * q^88 + 2 * q^89 + 3 * q^90 - 16 * q^91 - 8 * q^92 - 8 * q^93 - 3 * q^96 - 16 * q^97 - q^98 - 3 * 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
$7$	−0.890084	−0.336420	−0.168210	−	0.985751i	$-0.553799\pi$
$7$	−0.890084	−0.336420	−0.168210	+	0.985751i	$0.553799\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−1.10992	−0.307835	−0.153918	−	0.988084i	$-0.549189\pi$
$13$	−1.10992	−0.307835	−0.153918	+	0.988084i	$0.549189\pi$
$14$	−0.890084	−0.237885
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	6.09783	1.39894	0.699470	−	0.714662i	$-0.253420\pi$
$19$	6.09783	1.39894	0.699470	+	0.714662i	$0.253420\pi$
$20$	1.00000	0.223607
$21$	0.890084	0.194232
$22$	−1.00000	−0.213201
$23$	−8.31767	−1.73435	−0.867177	−	0.498000i	$-0.834068\pi$
$23$	−8.31767	−1.73435	−0.867177	+	0.498000i	$0.834068\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.10992	−0.217672
$27$	−1.00000	−0.192450
$28$	−0.890084	−0.168210
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	−3.20775	−0.576129	−0.288065	−	0.957611i	$-0.593012\pi$
$31$	−3.20775	−0.576129	−0.288065	+	0.957611i	$0.593012\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	−0.890084	−0.150452
$36$	1.00000	0.166667
$37$	−3.78017	−0.621456	−0.310728	−	0.950499i	$-0.600573\pi$
$37$	−3.78017	−0.621456	−0.310728	+	0.950499i	$0.600573\pi$
$38$	6.09783	0.989199
$39$	1.10992	0.177729
$40$	1.00000	0.158114
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	0.890084	0.137343
$43$	−4.09783	−0.624914	−0.312457	−	0.949932i	$-0.601152\pi$
$43$	−4.09783	−0.624914	−0.312457	+	0.949932i	$0.601152\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−8.31767	−1.22637
$47$	6.76809	0.987227	0.493613	−	0.869681i	$-0.335676\pi$
$47$	6.76809	0.987227	0.493613	+	0.869681i	$0.335676\pi$
$48$	−1.00000	−0.144338
$49$	−6.20775	−0.886822
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−1.10992	−0.153918
$53$	13.0858	1.79747	0.898733	−	0.438496i	$-0.144489\pi$
$53$	13.0858	1.79747	0.898733	+	0.438496i	$0.144489\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−0.890084	−0.118942
$57$	−6.09783	−0.807678
$58$	−6.00000	−0.787839
$59$	−4.89008	−0.636635	−0.318317	−	0.947984i	$-0.603118\pi$
$59$	−4.89008	−0.636635	−0.318317	+	0.947984i	$0.603118\pi$
$60$	−1.00000	−0.129099
$61$	−0.219833	−0.0281467	−0.0140733	−	0.999901i	$-0.504480\pi$
$61$	−0.219833	−0.0281467	−0.0140733	+	0.999901i	$0.504480\pi$
$62$	−3.20775	−0.407385
$63$	−0.890084	−0.112140
$64$	1.00000	0.125000
$65$	−1.10992	−0.137668
$66$	1.00000	0.123091
$67$	11.9758	1.46308	0.731541	−	0.681798i	$-0.238802\pi$
$67$	11.9758	1.46308	0.731541	+	0.681798i	$0.238802\pi$
$68$	−1.00000	−0.121268
$69$	8.31767	1.00133
$70$	−0.890084	−0.106385
$71$	−12.0978	−1.43575	−0.717874	−	0.696173i	$-0.754885\pi$
$71$	−12.0978	−1.43575	−0.717874	+	0.696173i	$0.754885\pi$
$72$	1.00000	0.117851
$73$	−2.45042	−0.286800	−0.143400	−	0.989665i	$-0.545804\pi$
$73$	−2.45042	−0.286800	−0.143400	+	0.989665i	$0.545804\pi$
$74$	−3.78017	−0.439436
$75$	−1.00000	−0.115470
$76$	6.09783	0.699470
$77$	0.890084	0.101434
$78$	1.10992	0.125673
$79$	14.2935	1.60814	0.804072	−	0.594531i	$-0.202662\pi$
$79$	14.2935	1.60814	0.804072	+	0.594531i	$0.202662\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−8.00000	−0.883452
$83$	−9.97584	−1.09499	−0.547495	−	0.836809i	$-0.684419\pi$
$83$	−9.97584	−1.09499	−0.547495	+	0.836809i	$0.684419\pi$
$84$	0.890084	0.0971161
$85$	−1.00000	−0.108465
$86$	−4.09783	−0.441881
$87$	6.00000	0.643268
$88$	−1.00000	−0.106600
$89$	−11.9758	−1.26944	−0.634718	−	0.772744i	$-0.718884\pi$
$89$	−11.9758	−1.26944	−0.634718	+	0.772744i	$0.718884\pi$
$90$	1.00000	0.105409
$91$	0.987918	0.103562
$92$	−8.31767	−0.867177
$93$	3.20775	0.332628
$94$	6.76809	0.698075
$95$	6.09783	0.625625
$96$	−1.00000	−0.102062
$97$	0.987918	0.100308	0.0501540	−	0.998741i	$-0.484029\pi$
$97$	0.987918	0.100308	0.0501540	+	0.998741i	$0.484029\pi$
$98$	−6.20775	−0.627078
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−9.42758	−0.938080	−0.469040	−	0.883177i	$-0.655400\pi$
$101$	−9.42758	−0.938080	−0.469040	+	0.883177i	$0.655400\pi$
$102$	1.00000	0.0990148
$103$	10.4155	1.02627	0.513135	−	0.858308i	$-0.328484\pi$
$103$	10.4155	1.02627	0.513135	+	0.858308i	$0.328484\pi$
$104$	−1.10992	−0.108836
$105$	0.890084	0.0868633
$106$	13.0858	1.27100
$107$	−8.19567	−0.792305	−0.396153	−	0.918185i	$-0.629655\pi$
$107$	−8.19567	−0.792305	−0.396153	+	0.918185i	$0.629655\pi$
$108$	−1.00000	−0.0962250
$109$	−17.7560	−1.70072	−0.850358	−	0.526204i	$-0.823615\pi$
$109$	−17.7560	−1.70072	−0.850358	+	0.526204i	$0.823615\pi$
$110$	−1.00000	−0.0953463
$111$	3.78017	0.358798
$112$	−0.890084	−0.0841050
$113$	8.09783	0.761780	0.380890	−	0.924620i	$-0.375618\pi$
$113$	8.09783	0.761780	0.380890	+	0.924620i	$0.375618\pi$
$114$	−6.09783	−0.571115
$115$	−8.31767	−0.775626
$116$	−6.00000	−0.557086
$117$	−1.10992	−0.102612
$118$	−4.89008	−0.450169
$119$	0.890084	0.0815938
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−0.219833	−0.0199027
$123$	8.00000	0.721336
$124$	−3.20775	−0.288065
$125$	1.00000	0.0894427
$126$	−0.890084	−0.0792950
$127$	9.97584	0.885212	0.442606	−	0.896716i	$-0.354054\pi$
$127$	9.97584	0.885212	0.442606	+	0.896716i	$0.354054\pi$
$128$	1.00000	0.0883883
$129$	4.09783	0.360794
$130$	−1.10992	−0.0973461
$131$	−3.56033	−0.311068	−0.155534	−	0.987831i	$-0.549710\pi$
$131$	−3.56033	−0.311068	−0.155534	+	0.987831i	$0.549710\pi$
$132$	1.00000	0.0870388
$133$	−5.42758	−0.470631
$134$	11.9758	1.03455
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	0.659498	0.0563447	0.0281723	−	0.999603i	$-0.491031\pi$
$137$	0.659498	0.0563447	0.0281723	+	0.999603i	$0.491031\pi$
$138$	8.31767	0.708047
$139$	−15.7560	−1.33641	−0.668203	−	0.743979i	$-0.732936\pi$
$139$	−15.7560	−1.33641	−0.668203	+	0.743979i	$0.732936\pi$
$140$	−0.890084	−0.0752258
$141$	−6.76809	−0.569976
$142$	−12.0978	−1.01523
$143$	1.10992	0.0928159
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−2.45042	−0.202798
$147$	6.20775	0.512007
$148$	−3.78017	−0.310728
$149$	−10.7681	−0.882156	−0.441078	−	0.897469i	$-0.645404\pi$
$149$	−10.7681	−0.882156	−0.441078	+	0.897469i	$0.645404\pi$
$150$	−1.00000	−0.0816497
$151$	−12.9879	−1.05694	−0.528471	−	0.848951i	$-0.677234\pi$
$151$	−12.9879	−1.05694	−0.528471	+	0.848951i	$0.677234\pi$
$152$	6.09783	0.494600
$153$	−1.00000	−0.0808452
$154$	0.890084	0.0717250
$155$	−3.20775	−0.257653
$156$	1.10992	0.0888644
$157$	−7.75600	−0.618997	−0.309498	−	0.950900i	$-0.600161\pi$
$157$	−7.75600	−0.618997	−0.309498	+	0.950900i	$0.600161\pi$
$158$	14.2935	1.13713
$159$	−13.0858	−1.03777
$160$	1.00000	0.0790569
$161$	7.40342	0.583471
$162$	1.00000	0.0785674
$163$	−13.1836	−1.03262	−0.516309	−	0.856402i	$-0.672694\pi$
$163$	−13.1836	−1.03262	−0.516309	+	0.856402i	$0.672694\pi$
$164$	−8.00000	−0.624695
$165$	1.00000	0.0778499
$166$	−9.97584	−0.774275
$167$	21.1836	1.63924	0.819618	−	0.572911i	$-0.194186\pi$
$167$	21.1836	1.63924	0.819618	+	0.572911i	$0.194186\pi$
$168$	0.890084	0.0686715
$169$	−11.7681	−0.905237
$170$	−1.00000	−0.0766965
$171$	6.09783	0.466313
$172$	−4.09783	−0.312457
$173$	10.1957	0.775162	0.387581	−	0.921836i	$-0.373311\pi$
$173$	10.1957	0.775162	0.387581	+	0.921836i	$0.373311\pi$
$174$	6.00000	0.454859
$175$	−0.890084	−0.0672840
$176$	−1.00000	−0.0753778
$177$	4.89008	0.367561
$178$	−11.9758	−0.897627
$179$	19.3056	1.44297	0.721484	−	0.692432i	$-0.243461\pi$
$179$	19.3056	1.44297	0.721484	+	0.692432i	$0.243461\pi$
$180$	1.00000	0.0745356
$181$	−18.6353	−1.38515	−0.692577	−	0.721344i	$-0.743525\pi$
$181$	−18.6353	−1.38515	−0.692577	+	0.721344i	$0.743525\pi$
$182$	0.987918	0.0732294
$183$	0.219833	0.0162505
$184$	−8.31767	−0.613187
$185$	−3.78017	−0.277923
$186$	3.20775	0.235204
$187$	1.00000	0.0731272
$188$	6.76809	0.493613
$189$	0.890084	0.0647441
$190$	6.09783	0.442383
$191$	−23.8431	−1.72523	−0.862613	−	0.505865i	$-0.831173\pi$
$191$	−23.8431	−1.72523	−0.862613	+	0.505865i	$0.831173\pi$
$192$	−1.00000	−0.0721688
$193$	4.86592	0.350257	0.175128	−	0.984546i	$-0.443966\pi$
$193$	4.86592	0.350257	0.175128	+	0.984546i	$0.443966\pi$
$194$	0.987918	0.0709284
$195$	1.10992	0.0794828
$196$	−6.20775	−0.443411
$197$	−1.01208	−0.0721078	−0.0360539	−	0.999350i	$-0.511479\pi$
$197$	−1.01208	−0.0721078	−0.0360539	+	0.999350i	$0.511479\pi$
$198$	−1.00000	−0.0710669
$199$	15.6474	1.10922	0.554608	−	0.832112i	$-0.312868\pi$
$199$	15.6474	1.10922	0.554608	+	0.832112i	$0.312868\pi$
$200$	1.00000	0.0707107
$201$	−11.9758	−0.844710
$202$	−9.42758	−0.663322
$203$	5.34050	0.374830
$204$	1.00000	0.0700140
$205$	−8.00000	−0.558744
$206$	10.4155	0.725682
$207$	−8.31767	−0.578118
$208$	−1.10992	−0.0769588
$209$	−6.09783	−0.421796
$210$	0.890084	0.0614216
$211$	−4.43967	−0.305639	−0.152820	−	0.988254i	$-0.548835\pi$
$211$	−4.43967	−0.305639	−0.152820	+	0.988254i	$0.548835\pi$
$212$	13.0858	0.898733
$213$	12.0978	0.828930
$214$	−8.19567	−0.560244
$215$	−4.09783	−0.279470
$216$	−1.00000	−0.0680414
$217$	2.85517	0.193821
$218$	−17.7560	−1.20259
$219$	2.45042	0.165584
$220$	−1.00000	−0.0674200
$221$	1.10992	0.0746610
$222$	3.78017	0.253708
$223$	−13.6233	−0.912280	−0.456140	−	0.889908i	$-0.650768\pi$
$223$	−13.6233	−0.912280	−0.456140	+	0.889908i	$0.650768\pi$
$224$	−0.890084	−0.0594712
$225$	1.00000	0.0666667
$226$	8.09783	0.538660
$227$	−20.7439	−1.37682	−0.688411	−	0.725321i	$-0.741692\pi$
$227$	−20.7439	−1.37682	−0.688411	+	0.725321i	$0.741692\pi$
$228$	−6.09783	−0.403839
$229$	−7.78017	−0.514128	−0.257064	−	0.966394i	$-0.582755\pi$
$229$	−7.78017	−0.514128	−0.257064	+	0.966394i	$0.582755\pi$
$230$	−8.31767	−0.548451
$231$	−0.890084	−0.0585632
$232$	−6.00000	−0.393919
$233$	−9.75600	−0.639137	−0.319569	−	0.947563i	$-0.603538\pi$
$233$	−9.75600	−0.639137	−0.319569	+	0.947563i	$0.603538\pi$
$234$	−1.10992	−0.0725575
$235$	6.76809	0.441501
$236$	−4.89008	−0.318317
$237$	−14.2935	−0.928463
$238$	0.890084	0.0576956
$239$	16.7439	1.08307	0.541537	−	0.840677i	$-0.317843\pi$
$239$	16.7439	1.08307	0.541537	+	0.840677i	$0.317843\pi$
$240$	−1.00000	−0.0645497
$241$	6.07367	0.391240	0.195620	−	0.980680i	$-0.437328\pi$
$241$	6.07367	0.391240	0.195620	+	0.980680i	$0.437328\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−0.219833	−0.0140733
$245$	−6.20775	−0.396599
$246$	8.00000	0.510061
$247$	−6.76809	−0.430643
$248$	−3.20775	−0.203692
$249$	9.97584	0.632193
$250$	1.00000	0.0632456
$251$	2.86592	0.180895	0.0904477	−	0.995901i	$-0.471170\pi$
$251$	2.86592	0.180895	0.0904477	+	0.995901i	$0.471170\pi$
$252$	−0.890084	−0.0560700
$253$	8.31767	0.522927
$254$	9.97584	0.625940
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−16.4155	−1.02397	−0.511985	−	0.858994i	$-0.671090\pi$
$257$	−16.4155	−1.02397	−0.511985	+	0.858994i	$0.671090\pi$
$258$	4.09783	0.255120
$259$	3.36467	0.209070
$260$	−1.10992	−0.0688341
$261$	−6.00000	−0.371391
$262$	−3.56033	−0.219958
$263$	12.5483	0.773758	0.386879	−	0.922130i	$-0.373553\pi$
$263$	12.5483	0.773758	0.386879	+	0.922130i	$0.373553\pi$
$264$	1.00000	0.0615457
$265$	13.0858	0.803851
$266$	−5.42758	−0.332786
$267$	11.9758	0.732909
$268$	11.9758	0.731541
$269$	13.7560	0.838718	0.419359	−	0.907820i	$-0.362255\pi$
$269$	13.7560	0.838718	0.419359	+	0.907820i	$0.362255\pi$
$270$	−1.00000	−0.0608581
$271$	18.0629	1.09724	0.548622	−	0.836070i	$-0.315153\pi$
$271$	18.0629	1.09724	0.548622	+	0.836070i	$0.315153\pi$
$272$	−1.00000	−0.0606339
$273$	−0.987918	−0.0597915
$274$	0.659498	0.0398417
$275$	−1.00000	−0.0603023
$276$	8.31767	0.500665
$277$	8.32842	0.500406	0.250203	−	0.968193i	$-0.419503\pi$
$277$	8.32842	0.500406	0.250203	+	0.968193i	$0.419503\pi$
$278$	−15.7560	−0.944982
$279$	−3.20775	−0.192043
$280$	−0.890084	−0.0531927
$281$	1.75600	0.104754	0.0523772	−	0.998627i	$-0.483320\pi$
$281$	1.75600	0.104754	0.0523772	+	0.998627i	$0.483320\pi$
$282$	−6.76809	−0.403034
$283$	−7.40342	−0.440088	−0.220044	−	0.975490i	$-0.570620\pi$
$283$	−7.40342	−0.440088	−0.220044	+	0.975490i	$0.570620\pi$
$284$	−12.0978	−0.717874
$285$	−6.09783	−0.361205
$286$	1.10992	0.0656307
$287$	7.12067	0.420320
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	−0.987918	−0.0579128
$292$	−2.45042	−0.143400
$293$	4.41550	0.257956	0.128978	−	0.991647i	$-0.458830\pi$
$293$	4.41550	0.257956	0.128978	+	0.991647i	$0.458830\pi$
$294$	6.20775	0.362043
$295$	−4.89008	−0.284712
$296$	−3.78017	−0.219718
$297$	1.00000	0.0580259
$298$	−10.7681	−0.623778
$299$	9.23191	0.533895
$300$	−1.00000	−0.0577350
$301$	3.64742	0.210234
$302$	−12.9879	−0.747371
$303$	9.42758	0.541601
$304$	6.09783	0.349735
$305$	−0.219833	−0.0125876
$306$	−1.00000	−0.0571662
$307$	−1.87800	−0.107183	−0.0535916	−	0.998563i	$-0.517067\pi$
$307$	−1.87800	−0.107183	−0.0535916	+	0.998563i	$0.517067\pi$
$308$	0.890084	0.0507172
$309$	−10.4155	−0.592517
$310$	−3.20775	−0.182188
$311$	6.31767	0.358242	0.179121	−	0.983827i	$-0.442675\pi$
$311$	6.31767	0.358242	0.179121	+	0.983827i	$0.442675\pi$
$312$	1.10992	0.0628366
$313$	5.42758	0.306785	0.153393	−	0.988165i	$-0.450980\pi$
$313$	5.42758	0.306785	0.153393	+	0.988165i	$0.450980\pi$
$314$	−7.75600	−0.437697
$315$	−0.890084	−0.0501505
$316$	14.2935	0.804072
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	−13.0858	−0.733813
$319$	6.00000	0.335936
$320$	1.00000	0.0559017
$321$	8.19567	0.457438
$322$	7.40342	0.412576
$323$	−6.09783	−0.339293
$324$	1.00000	0.0555556
$325$	−1.10992	−0.0615671
$326$	−13.1836	−0.730171
$327$	17.7560	0.981909
$328$	−8.00000	−0.441726
$329$	−6.02416	−0.332123
$330$	1.00000	0.0550482
$331$	12.4397	0.683746	0.341873	−	0.939746i	$-0.388939\pi$
$331$	12.4397	0.683746	0.341873	+	0.939746i	$0.388939\pi$
$332$	−9.97584	−0.547495
$333$	−3.78017	−0.207152
$334$	21.1836	1.15911
$335$	11.9758	0.654310
$336$	0.890084	0.0485580
$337$	0.230586	0.0125608	0.00628041	−	0.999980i	$-0.498001\pi$
$337$	0.230586	0.0125608	0.00628041	+	0.999980i	$0.498001\pi$
$338$	−11.7681	−0.640099
$339$	−8.09783	−0.439814
$340$	−1.00000	−0.0542326
$341$	3.20775	0.173709
$342$	6.09783	0.329733
$343$	11.7560	0.634765
$344$	−4.09783	−0.220940
$345$	8.31767	0.447808
$346$	10.1957	0.548123
$347$	29.6233	1.59026	0.795130	−	0.606439i	$-0.207403\pi$
$347$	29.6233	1.59026	0.795130	+	0.606439i	$0.207403\pi$
$348$	6.00000	0.321634
$349$	−23.3056	−1.24752	−0.623760	−	0.781616i	$-0.714396\pi$
$349$	−23.3056	−1.24752	−0.623760	+	0.781616i	$0.714396\pi$
$350$	−0.890084	−0.0475770
$351$	1.10992	0.0592429
$352$	−1.00000	−0.0533002
$353$	−10.0000	−0.532246	−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000	−0.532246	−0.266123	+	0.963939i	$0.585743\pi$
$354$	4.89008	0.259905
$355$	−12.0978	−0.642086
$356$	−11.9758	−0.634718
$357$	−0.890084	−0.0471082
$358$	19.3056	1.02033
$359$	−18.7681	−0.990542	−0.495271	−	0.868739i	$-0.664931\pi$
$359$	−18.7681	−0.990542	−0.495271	+	0.868739i	$0.664931\pi$
$360$	1.00000	0.0527046
$361$	18.1836	0.957031
$362$	−18.6353	−0.979451
$363$	−1.00000	−0.0524864
$364$	0.987918	0.0517810
$365$	−2.45042	−0.128261
$366$	0.219833	0.0114908
$367$	−29.0508	−1.51644	−0.758221	−	0.651998i	$-0.773931\pi$
$367$	−29.0508	−1.51644	−0.758221	+	0.651998i	$0.773931\pi$
$368$	−8.31767	−0.433588
$369$	−8.00000	−0.416463
$370$	−3.78017	−0.196522
$371$	−11.6474	−0.604704
$372$	3.20775	0.166314
$373$	−0.670251	−0.0347043	−0.0173521	−	0.999849i	$-0.505524\pi$
$373$	−0.670251	−0.0347043	−0.0173521	+	0.999849i	$0.505524\pi$
$374$	1.00000	0.0517088
$375$	−1.00000	−0.0516398
$376$	6.76809	0.349037
$377$	6.65950	0.342982
$378$	0.890084	0.0457810
$379$	25.0750	1.28802	0.644008	−	0.765019i	$-0.277270\pi$
$379$	25.0750	1.28802	0.644008	+	0.765019i	$0.277270\pi$
$380$	6.09783	0.312812
$381$	−9.97584	−0.511078
$382$	−23.8431	−1.21992
$383$	−24.0388	−1.22832	−0.614161	−	0.789180i	$-0.710506\pi$
$383$	−24.0388	−1.22832	−0.614161	+	0.789180i	$0.710506\pi$
$384$	−1.00000	−0.0510310
$385$	0.890084	0.0453629
$386$	4.86592	0.247669
$387$	−4.09783	−0.208305
$388$	0.987918	0.0501540
$389$	−26.4892	−1.34305	−0.671527	−	0.740980i	$-0.734361\pi$
$389$	−26.4892	−1.34305	−0.671527	+	0.740980i	$0.734361\pi$
$390$	1.10992	0.0562028
$391$	8.31767	0.420643
$392$	−6.20775	−0.313539
$393$	3.56033	0.179595
$394$	−1.01208	−0.0509879
$395$	14.2935	0.719184
$396$	−1.00000	−0.0502519
$397$	8.76809	0.440058	0.220029	−	0.975493i	$-0.429385\pi$
$397$	8.76809	0.440058	0.220029	+	0.975493i	$0.429385\pi$
$398$	15.6474	0.784334
$399$	5.42758	0.271719
$400$	1.00000	0.0500000
$401$	3.41683	0.170628	0.0853142	−	0.996354i	$-0.472811\pi$
$401$	3.41683	0.170628	0.0853142	+	0.996354i	$0.472811\pi$
$402$	−11.9758	−0.597300
$403$	3.56033	0.177353
$404$	−9.42758	−0.469040
$405$	1.00000	0.0496904
$406$	5.34050	0.265045
$407$	3.78017	0.187376
$408$	1.00000	0.0495074
$409$	−7.53617	−0.372640	−0.186320	−	0.982489i	$-0.559656\pi$
$409$	−7.53617	−0.372640	−0.186320	+	0.982489i	$0.559656\pi$
$410$	−8.00000	−0.395092
$411$	−0.659498	−0.0325306
$412$	10.4155	0.513135
$413$	4.35258	0.214177
$414$	−8.31767	−0.408791
$415$	−9.97584	−0.489695
$416$	−1.10992	−0.0544181
$417$	15.7560	0.771575
$418$	−6.09783	−0.298255
$419$	−13.0750	−0.638756	−0.319378	−	0.947627i	$-0.603474\pi$
$419$	−13.0750	−0.638756	−0.319378	+	0.947627i	$0.603474\pi$
$420$	0.890084	0.0434316
$421$	−28.8552	−1.40631	−0.703157	−	0.711034i	$-0.748227\pi$
$421$	−28.8552	−1.40631	−0.703157	+	0.711034i	$0.748227\pi$
$422$	−4.43967	−0.216120
$423$	6.76809	0.329076
$424$	13.0858	0.635500
$425$	−1.00000	−0.0485071
$426$	12.0978	0.586142
$427$	0.195669	0.00946910
$428$	−8.19567	−0.396153
$429$	−1.10992	−0.0535873
$430$	−4.09783	−0.197615
$431$	7.62325	0.367199	0.183600	−	0.983001i	$-0.441225\pi$
$431$	7.62325	0.367199	0.183600	+	0.983001i	$0.441225\pi$
$432$	−1.00000	−0.0481125
$433$	16.5724	0.796420	0.398210	−	0.917294i	$-0.369632\pi$
$433$	16.5724	0.796420	0.398210	+	0.917294i	$0.369632\pi$
$434$	2.85517	0.137052
$435$	6.00000	0.287678
$436$	−17.7560	−0.850358
$437$	−50.7198	−2.42626
$438$	2.45042	0.117086
$439$	18.7332	0.894085	0.447043	−	0.894513i	$-0.352477\pi$
$439$	18.7332	0.894085	0.447043	+	0.894513i	$0.352477\pi$
$440$	−1.00000	−0.0476731
$441$	−6.20775	−0.295607
$442$	1.10992	0.0527933
$443$	−12.7573	−0.606119	−0.303060	−	0.952972i	$-0.598008\pi$
$443$	−12.7573	−0.606119	−0.303060	+	0.952972i	$0.598008\pi$
$444$	3.78017	0.179399
$445$	−11.9758	−0.567709
$446$	−13.6233	−0.645080
$447$	10.7681	0.509313
$448$	−0.890084	−0.0420525
$449$	26.6848	1.25934	0.629668	−	0.776865i	$-0.283191\pi$
$449$	26.6848	1.25934	0.629668	+	0.776865i	$0.283191\pi$
$450$	1.00000	0.0471405
$451$	8.00000	0.376705
$452$	8.09783	0.380890
$453$	12.9879	0.610226
$454$	−20.7439	−0.973561
$455$	0.987918	0.0463143
$456$	−6.09783	−0.285557
$457$	−31.1836	−1.45871	−0.729353	−	0.684137i	$-0.760179\pi$
$457$	−31.1836	−1.45871	−0.729353	+	0.684137i	$0.760179\pi$
$458$	−7.78017	−0.363543
$459$	1.00000	0.0466760
$460$	−8.31767	−0.387813
$461$	−8.74392	−0.407245	−0.203623	−	0.979049i	$-0.565272\pi$
$461$	−8.74392	−0.407245	−0.203623	+	0.979049i	$0.565272\pi$
$462$	−0.890084	−0.0414104
$463$	−6.32842	−0.294107	−0.147053	−	0.989129i	$-0.546979\pi$
$463$	−6.32842	−0.294107	−0.147053	+	0.989129i	$0.546979\pi$
$464$	−6.00000	−0.278543
$465$	3.20775	0.148756
$466$	−9.75600	−0.451938
$467$	−17.8538	−0.826177	−0.413089	−	0.910691i	$-0.635550\pi$
$467$	−17.8538	−0.826177	−0.413089	+	0.910691i	$0.635550\pi$
$468$	−1.10992	−0.0513059
$469$	−10.6595	−0.492210
$470$	6.76809	0.312189
$471$	7.75600	0.357378
$472$	−4.89008	−0.225084
$473$	4.09783	0.188419
$474$	−14.2935	−0.656522
$475$	6.09783	0.279788
$476$	0.890084	0.0407969
$477$	13.0858	0.599155
$478$	16.7439	0.765849
$479$	2.10859	0.0963439	0.0481719	−	0.998839i	$-0.484660\pi$
$479$	2.10859	0.0963439	0.0481719	+	0.998839i	$0.484660\pi$
$480$	−1.00000	−0.0456435
$481$	4.19567	0.191306
$482$	6.07367	0.276648
$483$	−7.40342	−0.336867
$484$	1.00000	0.0454545
$485$	0.987918	0.0448591
$486$	−1.00000	−0.0453609
$487$	−12.6112	−0.571467	−0.285733	−	0.958309i	$-0.592237\pi$
$487$	−12.6112	−0.571467	−0.285733	+	0.958309i	$0.592237\pi$
$488$	−0.219833	−0.00995135
$489$	13.1836	0.596182
$490$	−6.20775	−0.280438
$491$	−2.98792	−0.134843	−0.0674214	−	0.997725i	$-0.521477\pi$
$491$	−2.98792	−0.134843	−0.0674214	+	0.997725i	$0.521477\pi$
$492$	8.00000	0.360668
$493$	6.00000	0.270226
$494$	−6.76809	−0.304511
$495$	−1.00000	−0.0449467
$496$	−3.20775	−0.144032
$497$	10.7681	0.483015
$498$	9.97584	0.447028
$499$	−14.3284	−0.641428	−0.320714	−	0.947176i	$-0.603923\pi$
$499$	−14.3284	−0.641428	−0.320714	+	0.947176i	$0.603923\pi$
$500$	1.00000	0.0447214
$501$	−21.1836	−0.946413
$502$	2.86592	0.127912
$503$	12.9879	0.579103	0.289551	−	0.957162i	$-0.406494\pi$
$503$	12.9879	0.579103	0.289551	+	0.957162i	$0.406494\pi$
$504$	−0.890084	−0.0396475
$505$	−9.42758	−0.419522
$506$	8.31767	0.369765
$507$	11.7681	0.522639
$508$	9.97584	0.442606
$509$	−4.07367	−0.180562	−0.0902812	−	0.995916i	$-0.528777\pi$
$509$	−4.07367	−0.180562	−0.0902812	+	0.995916i	$0.528777\pi$
$510$	1.00000	0.0442807
$511$	2.18108	0.0964852
$512$	1.00000	0.0441942
$513$	−6.09783	−0.269226
$514$	−16.4155	−0.724057
$515$	10.4155	0.458962
$516$	4.09783	0.180397
$517$	−6.76809	−0.297660
$518$	3.36467	0.147835
$519$	−10.1957	−0.447540
$520$	−1.10992	−0.0486730
$521$	−3.48666	−0.152753	−0.0763767	−	0.997079i	$-0.524335\pi$
$521$	−3.48666	−0.152753	−0.0763767	+	0.997079i	$0.524335\pi$
$522$	−6.00000	−0.262613
$523$	38.4650	1.68196	0.840979	−	0.541068i	$-0.181980\pi$
$523$	38.4650	1.68196	0.840979	+	0.541068i	$0.181980\pi$
$524$	−3.56033	−0.155534
$525$	0.890084	0.0388464
$526$	12.5483	0.547130
$527$	3.20775	0.139732
$528$	1.00000	0.0435194
$529$	46.1836	2.00798
$530$	13.0858	0.568409
$531$	−4.89008	−0.212212
$532$	−5.42758	−0.235316
$533$	8.87933	0.384606
$534$	11.9758	0.518245
$535$	−8.19567	−0.354330
$536$	11.9758	0.517277
$537$	−19.3056	−0.833098
$538$	13.7560	0.593063
$539$	6.20775	0.267387
$540$	−1.00000	−0.0430331
$541$	−13.0508	−0.561099	−0.280550	−	0.959840i	$-0.590517\pi$
$541$	−13.0508	−0.561099	−0.280550	+	0.959840i	$0.590517\pi$
$542$	18.0629	0.775869
$543$	18.6353	0.799719
$544$	−1.00000	−0.0428746
$545$	−17.7560	−0.760584
$546$	−0.987918	−0.0422790
$547$	−15.0121	−0.641870	−0.320935	−	0.947101i	$-0.603997\pi$
$547$	−15.0121	−0.641870	−0.320935	+	0.947101i	$0.603997\pi$
$548$	0.659498	0.0281723
$549$	−0.219833	−0.00938222
$550$	−1.00000	−0.0426401
$551$	−36.5870	−1.55866
$552$	8.31767	0.354023
$553$	−12.7224	−0.541012
$554$	8.32842	0.353841
$555$	3.78017	0.160459
$556$	−15.7560	−0.668203
$557$	−21.2948	−0.902291	−0.451145	−	0.892450i	$-0.648984\pi$
$557$	−21.2948	−0.902291	−0.451145	+	0.892450i	$0.648984\pi$
$558$	−3.20775	−0.135795
$559$	4.54825	0.192371
$560$	−0.890084	−0.0376129
$561$	−1.00000	−0.0422200
$562$	1.75600	0.0740726
$563$	27.5603	1.16153	0.580765	−	0.814071i	$-0.302754\pi$
$563$	27.5603	1.16153	0.580765	+	0.814071i	$0.302754\pi$
$564$	−6.76809	−0.284988
$565$	8.09783	0.340678
$566$	−7.40342	−0.311189
$567$	−0.890084	−0.0373800
$568$	−12.0978	−0.507614
$569$	−40.0629	−1.67952	−0.839762	−	0.542954i	$-0.817306\pi$
$569$	−40.0629	−1.67952	−0.839762	+	0.542954i	$0.817306\pi$
$570$	−6.09783	−0.255410
$571$	34.6112	1.44843	0.724216	−	0.689573i	$-0.242202\pi$
$571$	34.6112	1.44843	0.724216	+	0.689573i	$0.242202\pi$
$572$	1.10992	0.0464079
$573$	23.8431	0.996059
$574$	7.12067	0.297211
$575$	−8.31767	−0.346871
$576$	1.00000	0.0416667
$577$	40.9638	1.70534	0.852672	−	0.522447i	$-0.174981\pi$
$577$	40.9638	1.70534	0.852672	+	0.522447i	$0.174981\pi$
$578$	1.00000	0.0415945
$579$	−4.86592	−0.202221
$580$	−6.00000	−0.249136
$581$	8.87933	0.368377
$582$	−0.987918	−0.0409505
$583$	−13.0858	−0.541957
$584$	−2.45042	−0.101399
$585$	−1.10992	−0.0458894
$586$	4.41550	0.182403
$587$	13.3927	0.552775	0.276387	−	0.961046i	$-0.410863\pi$
$587$	13.3927	0.552775	0.276387	+	0.961046i	$0.410863\pi$
$588$	6.20775	0.256003
$589$	−19.5603	−0.805970
$590$	−4.89008	−0.201322
$591$	1.01208	0.0416315
$592$	−3.78017	−0.155364
$593$	31.1836	1.28056	0.640278	−	0.768143i	$-0.278819\pi$
$593$	31.1836	1.28056	0.640278	+	0.768143i	$0.278819\pi$
$594$	1.00000	0.0410305
$595$	0.890084	0.0364899
$596$	−10.7681	−0.441078
$597$	−15.6474	−0.640406
$598$	9.23191	0.377521
$599$	−5.69309	−0.232613	−0.116307	−	0.993213i	$-0.537106\pi$
$599$	−5.69309	−0.232613	−0.116307	+	0.993213i	$0.537106\pi$
$600$	−1.00000	−0.0408248
$601$	−28.4892	−1.16210	−0.581049	−	0.813869i	$-0.697357\pi$
$601$	−28.4892	−1.16210	−0.581049	+	0.813869i	$0.697357\pi$
$602$	3.64742	0.148658
$603$	11.9758	0.487694
$604$	−12.9879	−0.528471
$605$	1.00000	0.0406558
$606$	9.42758	0.382969
$607$	−30.4263	−1.23496	−0.617482	−	0.786585i	$-0.711847\pi$
$607$	−30.4263	−1.23496	−0.617482	+	0.786585i	$0.711847\pi$
$608$	6.09783	0.247300
$609$	−5.34050	−0.216408
$610$	−0.219833	−0.00890076
$611$	−7.51201	−0.303903
$612$	−1.00000	−0.0404226
$613$	31.3297	1.26540	0.632698	−	0.774398i	$-0.281947\pi$
$613$	31.3297	1.26540	0.632698	+	0.774398i	$0.281947\pi$
$614$	−1.87800	−0.0757900
$615$	8.00000	0.322591
$616$	0.890084	0.0358625
$617$	3.46250	0.139395	0.0696975	−	0.997568i	$-0.477797\pi$
$617$	3.46250	0.139395	0.0696975	+	0.997568i	$0.477797\pi$
$618$	−10.4155	−0.418973
$619$	38.7198	1.55628	0.778139	−	0.628092i	$-0.216164\pi$
$619$	38.7198	1.55628	0.778139	+	0.628092i	$0.216164\pi$
$620$	−3.20775	−0.128826
$621$	8.31767	0.333776
$622$	6.31767	0.253315
$623$	10.6595	0.427064
$624$	1.10992	0.0444322
$625$	1.00000	0.0400000
$626$	5.42758	0.216930
$627$	6.09783	0.243524
$628$	−7.75600	−0.309498
$629$	3.78017	0.150725
$630$	−0.890084	−0.0354618
$631$	6.13275	0.244141	0.122070	−	0.992521i	$-0.461047\pi$
$631$	6.13275	0.244141	0.122070	+	0.992521i	$0.461047\pi$
$632$	14.2935	0.568565
$633$	4.43967	0.176461
$634$	−22.0000	−0.873732
$635$	9.97584	0.395879
$636$	−13.0858	−0.518884
$637$	6.89008	0.272995
$638$	6.00000	0.237542
$639$	−12.0978	−0.478583
$640$	1.00000	0.0395285
$641$	12.5133	0.494247	0.247124	−	0.968984i	$-0.420515\pi$
$641$	12.5133	0.494247	0.247124	+	0.968984i	$0.420515\pi$
$642$	8.19567	0.323457
$643$	44.8310	1.76796	0.883981	−	0.467523i	$-0.154853\pi$
$643$	44.8310	1.76796	0.883981	+	0.467523i	$0.154853\pi$
$644$	7.40342	0.291736
$645$	4.09783	0.161352
$646$	−6.09783	−0.239916
$647$	−37.8189	−1.48682	−0.743408	−	0.668839i	$-0.766792\pi$
$647$	−37.8189	−1.48682	−0.743408	+	0.668839i	$0.766792\pi$
$648$	1.00000	0.0392837
$649$	4.89008	0.191953
$650$	−1.10992	−0.0435345
$651$	−2.85517	−0.111903
$652$	−13.1836	−0.516309
$653$	26.8310	1.04998	0.524989	−	0.851109i	$-0.324069\pi$
$653$	26.8310	1.04998	0.524989	+	0.851109i	$0.324069\pi$
$654$	17.7560	0.694315
$655$	−3.56033	−0.139114
$656$	−8.00000	−0.312348
$657$	−2.45042	−0.0955999
$658$	−6.02416	−0.234846
$659$	−0.132751	−0.00517126	−0.00258563	−	0.999997i	$-0.500823\pi$
$659$	−0.132751	−0.00517126	−0.00258563	+	0.999997i	$0.500823\pi$
$660$	1.00000	0.0389249
$661$	46.1957	1.79680	0.898402	−	0.439175i	$-0.144729\pi$
$661$	46.1957	1.79680	0.898402	+	0.439175i	$0.144729\pi$
$662$	12.4397	0.483481
$663$	−1.10992	−0.0431056
$664$	−9.97584	−0.387138
$665$	−5.42758	−0.210473
$666$	−3.78017	−0.146479
$667$	49.9060	1.93237
$668$	21.1836	0.819618
$669$	13.6233	0.526705
$670$	11.9758	0.462667
$671$	0.219833	0.00848654
$672$	0.890084	0.0343357
$673$	39.3297	1.51605	0.758025	−	0.652225i	$-0.226164\pi$
$673$	39.3297	1.51605	0.758025	+	0.652225i	$0.226164\pi$
$674$	0.230586	0.00888185
$675$	−1.00000	−0.0384900
$676$	−11.7681	−0.452619
$677$	−2.98792	−0.114835	−0.0574175	−	0.998350i	$-0.518287\pi$
$677$	−2.98792	−0.114835	−0.0574175	+	0.998350i	$0.518287\pi$
$678$	−8.09783	−0.310995
$679$	−0.879330	−0.0337456
$680$	−1.00000	−0.0383482
$681$	20.7439	0.794909
$682$	3.20775	0.122831
$683$	37.2707	1.42612	0.713061	−	0.701102i	$-0.247308\pi$
$683$	37.2707	1.42612	0.713061	+	0.701102i	$0.247308\pi$
$684$	6.09783	0.233157
$685$	0.659498	0.0251981
$686$	11.7560	0.448846
$687$	7.78017	0.296832
$688$	−4.09783	−0.156228
$689$	−14.5241	−0.553324
$690$	8.31767	0.316648
$691$	21.7318	0.826718	0.413359	−	0.910568i	$-0.364355\pi$
$691$	21.7318	0.826718	0.413359	+	0.910568i	$0.364355\pi$
$692$	10.1957	0.387581
$693$	0.890084	0.0338115
$694$	29.6233	1.12448
$695$	−15.7560	−0.597659
$696$	6.00000	0.227429
$697$	8.00000	0.303022
$698$	−23.3056	−0.882129
$699$	9.75600	0.369006
$700$	−0.890084	−0.0336420
$701$	−44.4784	−1.67993	−0.839963	−	0.542643i	$-0.817424\pi$
$701$	−44.4784	−1.67993	−0.839963	+	0.542643i	$0.817424\pi$
$702$	1.10992	0.0418911
$703$	−23.0508	−0.869379
$704$	−1.00000	−0.0376889
$705$	−6.76809	−0.254901
$706$	−10.0000	−0.376355
$707$	8.39134	0.315589
$708$	4.89008	0.183781
$709$	36.0844	1.35518	0.677590	−	0.735440i	$-0.263025\pi$
$709$	36.0844	1.35518	0.677590	+	0.735440i	$0.263025\pi$
$710$	−12.0978	−0.454024
$711$	14.2935	0.536048
$712$	−11.9758	−0.448813
$713$	26.6810	0.999211
$714$	−0.890084	−0.0333105
$715$	1.10992	0.0415085
$716$	19.3056	0.721484
$717$	−16.7439	−0.625313
$718$	−18.7681	−0.700419
$719$	5.63401	0.210113	0.105056	−	0.994466i	$-0.466498\pi$
$719$	5.63401	0.210113	0.105056	+	0.994466i	$0.466498\pi$
$720$	1.00000	0.0372678
$721$	−9.27067	−0.345258
$722$	18.1836	0.676723
$723$	−6.07367	−0.225882
$724$	−18.6353	−0.692577
$725$	−6.00000	−0.222834
$726$	−1.00000	−0.0371135
$727$	−4.39134	−0.162866	−0.0814329	−	0.996679i	$-0.525950\pi$
$727$	−4.39134	−0.162866	−0.0814329	+	0.996679i	$0.525950\pi$
$728$	0.987918	0.0366147
$729$	1.00000	0.0370370
$730$	−2.45042	−0.0906941
$731$	4.09783	0.151564
$732$	0.219833	0.00812524
$733$	0.0349168	0.00128968	0.000644841	−	1.00000i	$-0.499795\pi$
$733$	0.0349168	0.00128968	0.000644841		1.00000i	$0.499795\pi$
$734$	−29.0508	−1.07229
$735$	6.20775	0.228976
$736$	−8.31767	−0.306593
$737$	−11.9758	−0.441136
$738$	−8.00000	−0.294484
$739$	−9.85384	−0.362479	−0.181240	−	0.983439i	$-0.558011\pi$
$739$	−9.85384	−0.362479	−0.181240	+	0.983439i	$0.558011\pi$
$740$	−3.78017	−0.138962
$741$	6.76809	0.248632
$742$	−11.6474	−0.427590
$743$	8.98792	0.329735	0.164867	−	0.986316i	$-0.447280\pi$
$743$	8.98792	0.329735	0.164867	+	0.986316i	$0.447280\pi$
$744$	3.20775	0.117602
$745$	−10.7681	−0.394512
$746$	−0.670251	−0.0245396
$747$	−9.97584	−0.364997
$748$	1.00000	0.0365636
$749$	7.29483	0.266547
$750$	−1.00000	−0.0365148
$751$	31.3551	1.14416	0.572082	−	0.820197i	$-0.306136\pi$
$751$	31.3551	1.14416	0.572082	+	0.820197i	$0.306136\pi$
$752$	6.76809	0.246807
$753$	−2.86592	−0.104440
$754$	6.65950	0.242525
$755$	−12.9879	−0.472679
$756$	0.890084	0.0323720
$757$	−14.0242	−0.509717	−0.254858	−	0.966978i	$-0.582029\pi$
$757$	−14.0242	−0.509717	−0.254858	+	0.966978i	$0.582029\pi$
$758$	25.0750	0.910765
$759$	−8.31767	−0.301912
$760$	6.09783	0.221192
$761$	−15.7802	−0.572031	−0.286015	−	0.958225i	$-0.592331\pi$
$761$	−15.7802	−0.572031	−0.286015	+	0.958225i	$0.592331\pi$
$762$	−9.97584	−0.361386
$763$	15.8043	0.572155
$764$	−23.8431	−0.862613
$765$	−1.00000	−0.0361551
$766$	−24.0388	−0.868556
$767$	5.42758	0.195979
$768$	−1.00000	−0.0360844
$769$	2.68366	0.0967753	0.0483876	−	0.998829i	$-0.484592\pi$
$769$	2.68366	0.0967753	0.0483876	+	0.998829i	$0.484592\pi$
$770$	0.890084	0.0320764
$771$	16.4155	0.591190
$772$	4.86592	0.175128
$773$	−1.96508	−0.0706791	−0.0353396	−	0.999375i	$-0.511251\pi$
$773$	−1.96508	−0.0706791	−0.0353396	+	0.999375i	$0.511251\pi$
$774$	−4.09783	−0.147294
$775$	−3.20775	−0.115226
$776$	0.987918	0.0354642
$777$	−3.36467	−0.120707
$778$	−26.4892	−0.949683
$779$	−48.7827	−1.74782
$780$	1.10992	0.0397414
$781$	12.0978	0.432895
$782$	8.31767	0.297439
$783$	6.00000	0.214423
$784$	−6.20775	−0.221705
$785$	−7.75600	−0.276824
$786$	3.56033	0.126993
$787$	−35.1594	−1.25330	−0.626649	−	0.779302i	$-0.715574\pi$
$787$	−35.1594	−1.25330	−0.626649	+	0.779302i	$0.715574\pi$
$788$	−1.01208	−0.0360539
$789$	−12.5483	−0.446730
$790$	14.2935	0.508540
$791$	−7.20775	−0.256278
$792$	−1.00000	−0.0355335
$793$	0.243996	0.00866454
$794$	8.76809	0.311168
$795$	−13.0858	−0.464104
$796$	15.6474	0.554608
$797$	45.9168	1.62645	0.813227	−	0.581946i	$-0.197708\pi$
$797$	45.9168	1.62645	0.813227	+	0.581946i	$0.197708\pi$
$798$	5.42758	0.192134
$799$	−6.76809	−0.239438
$800$	1.00000	0.0353553
$801$	−11.9758	−0.423145
$802$	3.41683	0.120652
$803$	2.45042	0.0864734
$804$	−11.9758	−0.422355
$805$	7.40342	0.260936
$806$	3.56033	0.125407
$807$	−13.7560	−0.484234
$808$	−9.42758	−0.331661
$809$	−26.6112	−0.935599	−0.467799	−	0.883835i	$-0.654953\pi$
$809$	−26.6112	−0.935599	−0.467799	+	0.883835i	$0.654953\pi$
$810$	1.00000	0.0351364
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	5.34050	0.187415
$813$	−18.0629	−0.633494
$814$	3.78017	0.132495
$815$	−13.1836	−0.461801
$816$	1.00000	0.0350070
$817$	−24.9879	−0.874217
$818$	−7.53617	−0.263496
$819$	0.987918	0.0345207
$820$	−8.00000	−0.279372
$821$	8.96376	0.312837	0.156419	−	0.987691i	$-0.450005\pi$
$821$	8.96376	0.312837	0.156419	+	0.987691i	$0.450005\pi$
$822$	−0.659498	−0.0230026
$823$	41.6862	1.45309	0.726544	−	0.687120i	$-0.241125\pi$
$823$	41.6862	1.45309	0.726544	+	0.687120i	$0.241125\pi$
$824$	10.4155	0.362841
$825$	1.00000	0.0348155
$826$	4.35258	0.151446
$827$	−17.2922	−0.601308	−0.300654	−	0.953733i	$-0.597205\pi$
$827$	−17.2922	−0.601308	−0.300654	+	0.953733i	$0.597205\pi$
$828$	−8.31767	−0.289059
$829$	3.97584	0.138087	0.0690433	−	0.997614i	$-0.478005\pi$
$829$	3.97584	0.138087	0.0690433	+	0.997614i	$0.478005\pi$
$830$	−9.97584	−0.346266
$831$	−8.32842	−0.288910
$832$	−1.10992	−0.0384794
$833$	6.20775	0.215086
$834$	15.7560	0.545586
$835$	21.1836	0.733088
$836$	−6.09783	−0.210898
$837$	3.20775	0.110876
$838$	−13.0750	−0.451668
$839$	−42.9530	−1.48290	−0.741451	−	0.671007i	$-0.765862\pi$
$839$	−42.9530	−1.48290	−0.741451	+	0.671007i	$0.765862\pi$
$840$	0.890084	0.0307108
$841$	7.00000	0.241379
$842$	−28.8552	−0.994415
$843$	−1.75600	−0.0604800
$844$	−4.43967	−0.152820
$845$	−11.7681	−0.404834
$846$	6.76809	0.232692
$847$	−0.890084	−0.0305836
$848$	13.0858	0.449367
$849$	7.40342	0.254085
$850$	−1.00000	−0.0342997
$851$	31.4422	1.07782
$852$	12.0978	0.414465
$853$	−35.3793	−1.21136	−0.605681	−	0.795707i	$-0.707099\pi$
$853$	−35.3793	−1.21136	−0.605681	+	0.795707i	$0.707099\pi$
$854$	0.195669	0.00669567
$855$	6.09783	0.208542
$856$	−8.19567	−0.280122
$857$	−16.0242	−0.547375	−0.273687	−	0.961819i	$-0.588243\pi$
$857$	−16.0242	−0.547375	−0.273687	+	0.961819i	$0.588243\pi$
$858$	−1.10992	−0.0378919
$859$	49.9758	1.70515	0.852577	−	0.522602i	$-0.175039\pi$
$859$	49.9758	1.70515	0.852577	+	0.522602i	$0.175039\pi$
$860$	−4.09783	−0.139735
$861$	−7.12067	−0.242672
$862$	7.62325	0.259649
$863$	−19.6689	−0.669538	−0.334769	−	0.942300i	$-0.608658\pi$
$863$	−19.6689	−0.669538	−0.334769	+	0.942300i	$0.608658\pi$
$864$	−1.00000	−0.0340207
$865$	10.1957	0.346663
$866$	16.5724	0.563154
$867$	−1.00000	−0.0339618
$868$	2.85517	0.0969107
$869$	−14.2935	−0.484874
$870$	6.00000	0.203419
$871$	−13.2922	−0.450388
$872$	−17.7560	−0.601294
$873$	0.987918	0.0334360
$874$	−50.7198	−1.71562
$875$	−0.890084	−0.0300903
$876$	2.45042	0.0827920
$877$	−18.5966	−0.627962	−0.313981	−	0.949429i	$-0.601663\pi$
$877$	−18.5966	−0.627962	−0.313981	+	0.949429i	$0.601663\pi$
$878$	18.7332	0.632214
$879$	−4.41550	−0.148931
$880$	−1.00000	−0.0337100
$881$	−3.24267	−0.109248	−0.0546241	−	0.998507i	$-0.517396\pi$
$881$	−3.24267	−0.109248	−0.0546241	+	0.998507i	$0.517396\pi$
$882$	−6.20775	−0.209026
$883$	41.3163	1.39041	0.695203	−	0.718814i	$-0.255315\pi$
$883$	41.3163	1.39041	0.695203	+	0.718814i	$0.255315\pi$
$884$	1.10992	0.0373305
$885$	4.89008	0.164378
$886$	−12.7573	−0.428591
$887$	50.2801	1.68824	0.844120	−	0.536154i	$-0.180123\pi$
$887$	50.2801	1.68824	0.844120	+	0.536154i	$0.180123\pi$
$888$	3.78017	0.126854
$889$	−8.87933	−0.297803
$890$	−11.9758	−0.401431
$891$	−1.00000	−0.0335013
$892$	−13.6233	−0.456140
$893$	41.2707	1.38107
$894$	10.7681	0.360139
$895$	19.3056	0.645315
$896$	−0.890084	−0.0297356
$897$	−9.23191	−0.308245
$898$	26.6848	0.890485
$899$	19.2465	0.641907
$900$	1.00000	0.0333333
$901$	−13.0858	−0.435950
$902$	8.00000	0.266371
$903$	−3.64742	−0.121378
$904$	8.09783	0.269330
$905$	−18.6353	−0.619459
$906$	12.9879	0.431495
$907$	45.5362	1.51200	0.756002	−	0.654569i	$-0.227150\pi$
$907$	45.5362	1.51200	0.756002	+	0.654569i	$0.227150\pi$
$908$	−20.7439	−0.688411
$909$	−9.42758	−0.312693
$910$	0.987918	0.0327492
$911$	10.3177	0.341840	0.170920	−	0.985285i	$-0.445326\pi$
$911$	10.3177	0.341840	0.170920	+	0.985285i	$0.445326\pi$
$912$	−6.09783	−0.201919
$913$	9.97584	0.330152
$914$	−31.1836	−1.03146
$915$	0.219833	0.00726744
$916$	−7.78017	−0.257064
$917$	3.16900	0.104649
$918$	1.00000	0.0330049
$919$	−5.69309	−0.187798	−0.0938988	−	0.995582i	$-0.529933\pi$
$919$	−5.69309	−0.187798	−0.0938988	+	0.995582i	$0.529933\pi$
$920$	−8.31767	−0.274225
$921$	1.87800	0.0618823
$922$	−8.74392	−0.287966
$923$	13.4276	0.441974
$924$	−0.890084	−0.0292816
$925$	−3.78017	−0.124291
$926$	−6.32842	−0.207965
$927$	10.4155	0.342090
$928$	−6.00000	−0.196960
$929$	15.8780	0.520940	0.260470	−	0.965482i	$-0.416122\pi$
$929$	15.8780	0.520940	0.260470	+	0.965482i	$0.416122\pi$
$930$	3.20775	0.105186
$931$	−37.8538	−1.24061
$932$	−9.75600	−0.319569
$933$	−6.31767	−0.206831
$934$	−17.8538	−0.584195
$935$	1.00000	0.0327035
$936$	−1.10992	−0.0362787
$937$	41.8431	1.36695	0.683477	−	0.729972i	$-0.260467\pi$
$937$	41.8431	1.36695	0.683477	+	0.729972i	$0.260467\pi$
$938$	−10.6595	−0.348045
$939$	−5.42758	−0.177122
$940$	6.76809	0.220751
$941$	24.2586	0.790807	0.395404	−	0.918507i	$-0.370605\pi$
$941$	24.2586	0.790807	0.395404	+	0.918507i	$0.370605\pi$
$942$	7.75600	0.252704
$943$	66.5413	2.16688
$944$	−4.89008	−0.159159
$945$	0.890084	0.0289544
$946$	4.09783	0.133232
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	−14.2935	−0.464231
$949$	2.71976	0.0882871
$950$	6.09783	0.197840
$951$	22.0000	0.713399
$952$	0.890084	0.0288478
$953$	−4.11124	−0.133176	−0.0665881	−	0.997781i	$-0.521211\pi$
$953$	−4.11124	−0.133176	−0.0665881	+	0.997781i	$0.521211\pi$
$954$	13.0858	0.423667
$955$	−23.8431	−0.771544
$956$	16.7439	0.541537
$957$	−6.00000	−0.193952
$958$	2.10859	0.0681254
$959$	−0.587008	−0.0189555
$960$	−1.00000	−0.0322749
$961$	−20.7103	−0.668075
$962$	4.19567	0.135274
$963$	−8.19567	−0.264102
$964$	6.07367	0.195620
$965$	4.86592	0.156640
$966$	−7.40342	−0.238201
$967$	−44.8525	−1.44236	−0.721180	−	0.692748i	$-0.756400\pi$
$967$	−44.8525	−1.44236	−0.721180	+	0.692748i	$0.756400\pi$
$968$	1.00000	0.0321412
$969$	6.09783	0.195891
$970$	0.987918	0.0317201
$971$	22.6219	0.725972	0.362986	−	0.931795i	$-0.381757\pi$
$971$	22.6219	0.725972	0.362986	+	0.931795i	$0.381757\pi$
$972$	−1.00000	−0.0320750
$973$	14.0242	0.449594
$974$	−12.6112	−0.404088
$975$	1.10992	0.0355458
$976$	−0.219833	−0.00703667
$977$	−37.2465	−1.19162	−0.595811	−	0.803125i	$-0.703169\pi$
$977$	−37.2465	−1.19162	−0.595811	+	0.803125i	$0.703169\pi$
$978$	13.1836	0.421565
$979$	11.9758	0.382749
$980$	−6.20775	−0.198299
$981$	−17.7560	−0.566906
$982$	−2.98792	−0.0953483
$983$	−31.3900	−1.00119	−0.500593	−	0.865683i	$-0.666885\pi$
$983$	−31.3900	−1.00119	−0.500593	+	0.865683i	$0.666885\pi$
$984$	8.00000	0.255031
$985$	−1.01208	−0.0322476
$986$	6.00000	0.191079
$987$	6.02416	0.191751
$988$	−6.76809	−0.215321
$989$	34.0844	1.08382
$990$	−1.00000	−0.0317821
$991$	4.15691	0.132049	0.0660244	−	0.997818i	$-0.478968\pi$
$991$	4.15691	0.132049	0.0660244	+	0.997818i	$0.478968\pi$
$992$	−3.20775	−0.101846
$993$	−12.4397	−0.394761
$994$	10.7681	0.341543
$995$	15.6474	0.496056
$996$	9.97584	0.316096
$997$	−12.5241	−0.396642	−0.198321	−	0.980137i	$-0.563549\pi$
$997$	−12.5241	−0.396642	−0.198321	+	0.980137i	$0.563549\pi$
$998$	−14.3284	−0.453558
$999$	3.78017	0.119599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cc.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cc.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -0.890084 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -0.890084 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -1.10992 q^{13} -0.890084 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +6.09783 q^{19} +1.00000 q^{20} +0.890084 q^{21} -1.00000 q^{22} -8.31767 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.10992 q^{26} -1.00000 q^{27} -0.890084 q^{28} -6.00000 q^{29} -1.00000 q^{30} -3.20775 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -0.890084 q^{35} +1.00000 q^{36} -3.78017 q^{37} +6.09783 q^{38} +1.10992 q^{39} +1.00000 q^{40} -8.00000 q^{41} +0.890084 q^{42} -4.09783 q^{43} -1.00000 q^{44} +1.00000 q^{45} -8.31767 q^{46} +6.76809 q^{47} -1.00000 q^{48} -6.20775 q^{49} +1.00000 q^{50} +1.00000 q^{51} -1.10992 q^{52} +13.0858 q^{53} -1.00000 q^{54} -1.00000 q^{55} -0.890084 q^{56} -6.09783 q^{57} -6.00000 q^{58} -4.89008 q^{59} -1.00000 q^{60} -0.219833 q^{61} -3.20775 q^{62} -0.890084 q^{63} +1.00000 q^{64} -1.10992 q^{65} +1.00000 q^{66} +11.9758 q^{67} -1.00000 q^{68} +8.31767 q^{69} -0.890084 q^{70} -12.0978 q^{71} +1.00000 q^{72} -2.45042 q^{73} -3.78017 q^{74} -1.00000 q^{75} +6.09783 q^{76} +0.890084 q^{77} +1.10992 q^{78} +14.2935 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} -9.97584 q^{83} +0.890084 q^{84} -1.00000 q^{85} -4.09783 q^{86} +6.00000 q^{87} -1.00000 q^{88} -11.9758 q^{89} +1.00000 q^{90} +0.987918 q^{91} -8.31767 q^{92} +3.20775 q^{93} +6.76809 q^{94} +6.09783 q^{95} -1.00000 q^{96} +0.987918 q^{97} -6.20775 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{11} - 3 q^{12} - 4 q^{13} - 2 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{20} + 2 q^{21} - 3 q^{22} - 8 q^{23} - 3 q^{24} + 3 q^{25} - 4 q^{26} - 3 q^{27} - 2 q^{28} - 18 q^{29} - 3 q^{30} + 8 q^{31} + 3 q^{32} + 3 q^{33} - 3 q^{34} - 2 q^{35} + 3 q^{36} - 10 q^{37} + 4 q^{39} + 3 q^{40} - 24 q^{41} + 2 q^{42} + 6 q^{43} - 3 q^{44} + 3 q^{45} - 8 q^{46} - 3 q^{48} - q^{49} + 3 q^{50} + 3 q^{51} - 4 q^{52} + 2 q^{53} - 3 q^{54} - 3 q^{55} - 2 q^{56} - 18 q^{58} - 14 q^{59} - 3 q^{60} - 2 q^{61} + 8 q^{62} - 2 q^{63} + 3 q^{64} - 4 q^{65} + 3 q^{66} - 2 q^{67} - 3 q^{68} + 8 q^{69} - 2 q^{70} - 18 q^{71} + 3 q^{72} - 4 q^{73} - 10 q^{74} - 3 q^{75} + 2 q^{77} + 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 24 q^{82} + 8 q^{83} + 2 q^{84} - 3 q^{85} + 6 q^{86} + 18 q^{87} - 3 q^{88} + 2 q^{89} + 3 q^{90} - 16 q^{91} - 8 q^{92} - 8 q^{93} - 3 q^{96} - 16 q^{97} - q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 3 * q^11 - 3 * q^12 - 4 * q^13 - 2 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^20 + 2 * q^21 - 3 * q^22 - 8 * q^23 - 3 * q^24 + 3 * q^25 - 4 * q^26 - 3 * q^27 - 2 * q^28 - 18 * q^29 - 3 * q^30 + 8 * q^31 + 3 * q^32 + 3 * q^33 - 3 * q^34 - 2 * q^35 + 3 * q^36 - 10 * q^37 + 4 * q^39 + 3 * q^40 - 24 * q^41 + 2 * q^42 + 6 * q^43 - 3 * q^44 + 3 * q^45 - 8 * q^46 - 3 * q^48 - q^49 + 3 * q^50 + 3 * q^51 - 4 * q^52 + 2 * q^53 - 3 * q^54 - 3 * q^55 - 2 * q^56 - 18 * q^58 - 14 * q^59 - 3 * q^60 - 2 * q^61 + 8 * q^62 - 2 * q^63 + 3 * q^64 - 4 * q^65 + 3 * q^66 - 2 * q^67 - 3 * q^68 + 8 * q^69 - 2 * q^70 - 18 * q^71 + 3 * q^72 - 4 * q^73 - 10 * q^74 - 3 * q^75 + 2 * q^77 + 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 24 * q^82 + 8 * q^83 + 2 * q^84 - 3 * q^85 + 6 * q^86 + 18 * q^87 - 3 * q^88 + 2 * q^89 + 3 * q^90 - 16 * q^91 - 8 * q^92 - 8 * q^93 - 3 * q^96 - 16 * q^97 - q^98 - 3 * q^99

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