LMFDB - Embedded newform 5610.2.a.cf.1.3

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.10710$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.92682 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.92682 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +6.21419 q^{13} -2.92682 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.09390 q^{19} -1.00000 q^{20} +2.92682 q^{21} +1.00000 q^{22} -3.80653 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.21419 q^{26} +1.00000 q^{27} +2.92682 q^{28} +3.28738 q^{29} +1.00000 q^{30} +7.14101 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -2.92682 q^{35} +1.00000 q^{36} +2.00000 q^{37} +5.09390 q^{38} +6.21419 q^{39} +1.00000 q^{40} +2.87971 q^{41} -2.92682 q^{42} -5.50157 q^{43} -1.00000 q^{44} -1.00000 q^{45} +3.80653 q^{46} +1.00000 q^{48} +1.56626 q^{49} -1.00000 q^{50} -1.00000 q^{51} +6.21419 q^{52} +0.519152 q^{53} -1.00000 q^{54} +1.00000 q^{55} -2.92682 q^{56} -5.09390 q^{57} -3.28738 q^{58} +4.21419 q^{59} -1.00000 q^{60} +10.4284 q^{61} -7.14101 q^{62} +2.92682 q^{63} +1.00000 q^{64} -6.21419 q^{65} +1.00000 q^{66} +11.4545 q^{67} -1.00000 q^{68} -3.80653 q^{69} +2.92682 q^{70} -0.506924 q^{71} -1.00000 q^{72} -4.06783 q^{73} -2.00000 q^{74} +1.00000 q^{75} -5.09390 q^{76} -2.92682 q^{77} -6.21419 q^{78} +14.8533 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.87971 q^{82} +5.75942 q^{83} +2.92682 q^{84} +1.00000 q^{85} +5.50157 q^{86} +3.28738 q^{87} +1.00000 q^{88} +7.85363 q^{89} +1.00000 q^{90} +18.1878 q^{91} -3.80653 q^{92} +7.14101 q^{93} +5.09390 q^{95} -1.00000 q^{96} -6.02072 q^{97} -1.56626 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	2.92682	1.10623	0.553116	−	0.833104i	$-0.313438\pi$
$7$	2.92682	1.10623	0.553116	+	0.833104i	$0.313438\pi$
$8$	−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
$13$	6.21419	1.72351	0.861753	−	0.507327i	$-0.169366\pi$
$13$	6.21419	1.72351	0.861753	+	0.507327i	$0.169366\pi$
$14$	−2.92682	−0.782225
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−5.09390	−1.16862	−0.584311	−	0.811530i	$-0.698635\pi$
$19$	−5.09390	−1.16862	−0.584311	+	0.811530i	$0.698635\pi$
$20$	−1.00000	−0.223607
$21$	2.92682	0.638684
$22$	1.00000	0.213201
$23$	−3.80653	−0.793716	−0.396858	−	0.917880i	$-0.629899\pi$
$23$	−3.80653	−0.793716	−0.396858	+	0.917880i	$0.629899\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−6.21419	−1.21870
$27$	1.00000	0.192450
$28$	2.92682	0.553116
$29$	3.28738	0.610450	0.305225	−	0.952280i	$-0.401268\pi$
$29$	3.28738	0.610450	0.305225	+	0.952280i	$0.401268\pi$
$30$	1.00000	0.182574
$31$	7.14101	1.28256	0.641282	−	0.767306i	$-0.278403\pi$
$31$	7.14101	1.28256	0.641282	+	0.767306i	$0.278403\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−2.92682	−0.494722
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	5.09390	0.826340
$39$	6.21419	0.995067
$40$	1.00000	0.158114
$41$	2.87971	0.449735	0.224868	−	0.974389i	$-0.427805\pi$
$41$	2.87971	0.449735	0.224868	+	0.974389i	$0.427805\pi$
$42$	−2.92682	−0.451618
$43$	−5.50157	−0.838981	−0.419491	−	0.907760i	$-0.637791\pi$
$43$	−5.50157	−0.838981	−0.419491	+	0.907760i	$0.637791\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	3.80653	0.561242
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	1.56626	0.223751
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	6.21419	0.861753
$53$	0.519152	0.0713110	0.0356555	−	0.999364i	$-0.488648\pi$
$53$	0.519152	0.0713110	0.0356555	+	0.999364i	$0.488648\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−2.92682	−0.391112
$57$	−5.09390	−0.674704
$58$	−3.28738	−0.431654
$59$	4.21419	0.548641	0.274321	−	0.961638i	$-0.411547\pi$
$59$	4.21419	0.548641	0.274321	+	0.961638i	$0.411547\pi$
$60$	−1.00000	−0.129099
$61$	10.4284	1.33522	0.667609	−	0.744512i	$-0.267318\pi$
$61$	10.4284	1.33522	0.667609	+	0.744512i	$0.267318\pi$
$62$	−7.14101	−0.906909
$63$	2.92682	0.368744
$64$	1.00000	0.125000
$65$	−6.21419	−0.770776
$66$	1.00000	0.123091
$67$	11.4545	1.39939	0.699693	−	0.714444i	$-0.253320\pi$
$67$	11.4545	1.39939	0.699693	+	0.714444i	$0.253320\pi$
$68$	−1.00000	−0.121268
$69$	−3.80653	−0.458252
$70$	2.92682	0.349822
$71$	−0.506924	−0.0601608	−0.0300804	−	0.999547i	$-0.509576\pi$
$71$	−0.506924	−0.0601608	−0.0300804	+	0.999547i	$0.509576\pi$
$72$	−1.00000	−0.117851
$73$	−4.06783	−0.476103	−0.238052	−	0.971253i	$-0.576509\pi$
$73$	−4.06783	−0.476103	−0.238052	+	0.971253i	$0.576509\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	−5.09390	−0.584311
$77$	−2.92682	−0.333542
$78$	−6.21419	−0.703619
$79$	14.8533	1.67113	0.835565	−	0.549392i	$-0.185141\pi$
$79$	14.8533	1.67113	0.835565	+	0.549392i	$0.185141\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.87971	−0.318011
$83$	5.75942	0.632179	0.316089	−	0.948729i	$-0.397630\pi$
$83$	5.75942	0.632179	0.316089	+	0.948729i	$0.397630\pi$
$84$	2.92682	0.319342
$85$	1.00000	0.108465
$86$	5.50157	0.593249
$87$	3.28738	0.352444
$88$	1.00000	0.106600
$89$	7.85363	0.832484	0.416242	−	0.909254i	$-0.363347\pi$
$89$	7.85363	0.832484	0.416242	+	0.909254i	$0.363347\pi$
$90$	1.00000	0.105409
$91$	18.1878	1.90660
$92$	−3.80653	−0.396858
$93$	7.14101	0.740488
$94$	0	0
$95$	5.09390	0.522623
$96$	−1.00000	−0.102062
$97$	−6.02072	−0.611312	−0.305656	−	0.952142i	$-0.598876\pi$
$97$	−6.02072	−0.611312	−0.305656	+	0.952142i	$0.598876\pi$
$98$	−1.56626	−0.158216
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−15.2139	−1.51384	−0.756919	−	0.653509i	$-0.773296\pi$
$101$	−15.2139	−1.51384	−0.756919	+	0.653509i	$0.773296\pi$
$102$	1.00000	0.0990148
$103$	12.9004	1.27112	0.635559	−	0.772053i	$-0.280770\pi$
$103$	12.9004	1.27112	0.635559	+	0.772053i	$0.280770\pi$
$104$	−6.21419	−0.609352
$105$	−2.92682	−0.285628
$106$	−0.519152	−0.0504245
$107$	4.56626	0.441437	0.220718	−	0.975338i	$-0.429160\pi$
$107$	4.56626	0.441437	0.220718	+	0.975338i	$0.429160\pi$
$108$	1.00000	0.0962250
$109$	−14.0414	−1.34493	−0.672463	−	0.740131i	$-0.734764\pi$
$109$	−14.0414	−1.34493	−0.672463	+	0.740131i	$0.734764\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	2.92682	0.276558
$113$	−12.8533	−1.20914	−0.604569	−	0.796552i	$-0.706655\pi$
$113$	−12.8533	−1.20914	−0.604569	+	0.796552i	$0.706655\pi$
$114$	5.09390	0.477088
$115$	3.80653	0.354961
$116$	3.28738	0.305225
$117$	6.21419	0.574502
$118$	−4.21419	−0.387948
$119$	−2.92682	−0.268301
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−10.4284	−0.944142
$123$	2.87971	0.259655
$124$	7.14101	0.641282
$125$	−1.00000	−0.0894427
$126$	−2.92682	−0.260742
$127$	−15.3203	−1.35946	−0.679729	−	0.733463i	$-0.737903\pi$
$127$	−15.3203	−1.35946	−0.679729	+	0.733463i	$0.737903\pi$
$128$	−1.00000	−0.0883883
$129$	−5.50157	−0.484386
$130$	6.21419	0.545021
$131$	5.75942	0.503203	0.251601	−	0.967831i	$-0.419043\pi$
$131$	5.75942	0.503203	0.251601	+	0.967831i	$0.419043\pi$
$132$	−1.00000	−0.0870388
$133$	−14.9089	−1.29277
$134$	−11.4545	−0.989515
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−14.6077	−1.24802	−0.624010	−	0.781416i	$-0.714498\pi$
$137$	−14.6077	−1.24802	−0.624010	+	0.781416i	$0.714498\pi$
$138$	3.80653	0.324033
$139$	−10.7541	−0.912148	−0.456074	−	0.889942i	$-0.650745\pi$
$139$	−10.7541	−0.912148	−0.456074	+	0.889942i	$0.650745\pi$
$140$	−2.92682	−0.247361
$141$	0	0
$142$	0.506924	0.0425401
$143$	−6.21419	−0.519657
$144$	1.00000	0.0833333
$145$	−3.28738	−0.273002
$146$	4.06783	0.336656
$147$	1.56626	0.129183
$148$	2.00000	0.164399
$149$	5.54868	0.454565	0.227283	−	0.973829i	$-0.427016\pi$
$149$	5.54868	0.454565	0.227283	+	0.973829i	$0.427016\pi$
$150$	−1.00000	−0.0816497
$151$	10.6690	0.868228	0.434114	−	0.900858i	$-0.357061\pi$
$151$	10.6690	0.868228	0.434114	+	0.900858i	$0.357061\pi$
$152$	5.09390	0.413170
$153$	−1.00000	−0.0808452
$154$	2.92682	0.235850
$155$	−7.14101	−0.573580
$156$	6.21419	0.497534
$157$	18.4928	1.47588	0.737942	−	0.674865i	$-0.235798\pi$
$157$	18.4928	1.47588	0.737942	+	0.674865i	$0.235798\pi$
$158$	−14.8533	−1.18167
$159$	0.519152	0.0411714
$160$	1.00000	0.0790569
$161$	−11.1410	−0.878035
$162$	−1.00000	−0.0785674
$163$	−12.8062	−1.00306	−0.501530	−	0.865140i	$-0.667229\pi$
$163$	−12.8062	−1.00306	−0.501530	+	0.865140i	$0.667229\pi$
$164$	2.87971	0.224868
$165$	1.00000	0.0778499
$166$	−5.75942	−0.447018
$167$	18.0936	1.40012	0.700062	−	0.714082i	$-0.253156\pi$
$167$	18.0936	1.40012	0.700062	+	0.714082i	$0.253156\pi$
$168$	−2.92682	−0.225809
$169$	25.6162	1.97048
$170$	−1.00000	−0.0766965
$171$	−5.09390	−0.389541
$172$	−5.50157	−0.419491
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	−3.28738	−0.249215
$175$	2.92682	0.221247
$176$	−1.00000	−0.0753778
$177$	4.21419	0.316758
$178$	−7.85363	−0.588655
$179$	−4.21419	−0.314984	−0.157492	−	0.987520i	$-0.550341\pi$
$179$	−4.21419	−0.314984	−0.157492	+	0.987520i	$0.550341\pi$
$180$	−1.00000	−0.0745356
$181$	2.37783	0.176743	0.0883714	−	0.996088i	$-0.471834\pi$
$181$	2.37783	0.176743	0.0883714	+	0.996088i	$0.471834\pi$
$182$	−18.1878	−1.34817
$183$	10.4284	0.770888
$184$	3.80653	0.280621
$185$	−2.00000	−0.147043
$186$	−7.14101	−0.523604
$187$	1.00000	0.0731272
$188$	0	0
$189$	2.92682	0.212895
$190$	−5.09390	−0.369551
$191$	15.8621	1.14774	0.573872	−	0.818945i	$-0.305441\pi$
$191$	15.8621	1.14774	0.573872	+	0.818945i	$0.305441\pi$
$192$	1.00000	0.0721688
$193$	−12.4962	−0.899497	−0.449749	−	0.893155i	$-0.648486\pi$
$193$	−12.4962	−0.899497	−0.449749	+	0.893155i	$0.648486\pi$
$194$	6.02072	0.432263
$195$	−6.21419	−0.445008
$196$	1.56626	0.111876
$197$	18.3342	1.30626	0.653128	−	0.757248i	$-0.273456\pi$
$197$	18.3342	1.30626	0.653128	+	0.757248i	$0.273456\pi$
$198$	1.00000	0.0710669
$199$	2.24058	0.158830	0.0794152	−	0.996842i	$-0.474695\pi$
$199$	2.24058	0.158830	0.0794152	+	0.996842i	$0.474695\pi$
$200$	−1.00000	−0.0707107
$201$	11.4545	0.807935
$202$	15.2139	1.07045
$203$	9.62155	0.675300
$204$	−1.00000	−0.0700140
$205$	−2.87971	−0.201128
$206$	−12.9004	−0.898816
$207$	−3.80653	−0.264572
$208$	6.21419	0.430877
$209$	5.09390	0.352353
$210$	2.92682	0.201970
$211$	5.28738	0.363998	0.181999	−	0.983299i	$-0.441743\pi$
$211$	5.28738	0.363998	0.181999	+	0.983299i	$0.441743\pi$
$212$	0.519152	0.0356555
$213$	−0.506924	−0.0347339
$214$	−4.56626	−0.312143
$215$	5.50157	0.375204
$216$	−1.00000	−0.0680414
$217$	20.9004	1.41881
$218$	14.0414	0.951006
$219$	−4.06783	−0.274878
$220$	1.00000	0.0674200
$221$	−6.21419	−0.418012
$222$	−2.00000	−0.134231
$223$	6.10271	0.408667	0.204334	−	0.978901i	$-0.434497\pi$
$223$	6.10271	0.408667	0.204334	+	0.978901i	$0.434497\pi$
$224$	−2.92682	−0.195556
$225$	1.00000	0.0666667
$226$	12.8533	0.854990
$227$	−19.0882	−1.26693	−0.633465	−	0.773771i	$-0.718368\pi$
$227$	−19.0882	−1.26693	−0.633465	+	0.773771i	$0.718368\pi$
$228$	−5.09390	−0.337352
$229$	−6.09421	−0.402717	−0.201358	−	0.979518i	$-0.564536\pi$
$229$	−6.09421	−0.402717	−0.201358	+	0.979518i	$0.564536\pi$
$230$	−3.80653	−0.250995
$231$	−2.92682	−0.192570
$232$	−3.28738	−0.215827
$233$	14.8062	0.969988	0.484994	−	0.874518i	$-0.338822\pi$
$233$	14.8062	0.969988	0.484994	+	0.874518i	$0.338822\pi$
$234$	−6.21419	−0.406234
$235$	0	0
$236$	4.21419	0.274321
$237$	14.8533	0.964827
$238$	2.92682	0.189717
$239$	10.1464	0.656314	0.328157	−	0.944623i	$-0.393573\pi$
$239$	10.1464	0.656314	0.328157	+	0.944623i	$0.393573\pi$
$240$	−1.00000	−0.0645497
$241$	−25.2380	−1.62573	−0.812863	−	0.582455i	$-0.802092\pi$
$241$	−25.2380	−1.62573	−0.812863	+	0.582455i	$0.802092\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	10.4284	0.667609
$245$	−1.56626	−0.100065
$246$	−2.87971	−0.183604
$247$	−31.6545	−2.01413
$248$	−7.14101	−0.453455
$249$	5.75942	0.364988
$250$	1.00000	0.0632456
$251$	−16.5484	−1.04452	−0.522262	−	0.852785i	$-0.674912\pi$
$251$	−16.5484	−1.04452	−0.522262	+	0.852785i	$0.674912\pi$
$252$	2.92682	0.184372
$253$	3.80653	0.239314
$254$	15.3203	0.961283
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	28.2384	1.76146	0.880730	−	0.473618i	$-0.157052\pi$
$257$	28.2384	1.76146	0.880730	+	0.473618i	$0.157052\pi$
$258$	5.50157	0.342513
$259$	5.85363	0.363727
$260$	−6.21419	−0.385388
$261$	3.28738	0.203483
$262$	−5.75942	−0.355818
$263$	−1.89729	−0.116992	−0.0584961	−	0.998288i	$-0.518631\pi$
$263$	−1.89729	−0.116992	−0.0584961	+	0.998288i	$0.518631\pi$
$264$	1.00000	0.0615457
$265$	−0.519152	−0.0318912
$266$	14.9089	0.914125
$267$	7.85363	0.480635
$268$	11.4545	0.699693
$269$	−17.5188	−1.06814	−0.534071	−	0.845439i	$-0.679339\pi$
$269$	−17.5188	−1.06814	−0.534071	+	0.845439i	$0.679339\pi$
$270$	1.00000	0.0608581
$271$	2.61841	0.159057	0.0795286	−	0.996833i	$-0.474659\pi$
$271$	2.61841	0.159057	0.0795286	+	0.996833i	$0.474659\pi$
$272$	−1.00000	−0.0606339
$273$	18.1878	1.10078
$274$	14.6077	0.882483
$275$	−1.00000	−0.0603023
$276$	−3.80653	−0.229126
$277$	20.3762	1.22429	0.612145	−	0.790746i	$-0.290307\pi$
$277$	20.3762	1.22429	0.612145	+	0.790746i	$0.290307\pi$
$278$	10.7541	0.644986
$279$	7.14101	0.427521
$280$	2.92682	0.174911
$281$	−12.7541	−0.760844	−0.380422	−	0.924813i	$-0.624221\pi$
$281$	−12.7541	−0.760844	−0.380422	+	0.924813i	$0.624221\pi$
$282$	0	0
$283$	20.3342	1.20874	0.604371	−	0.796703i	$-0.293425\pi$
$283$	20.3342	1.20874	0.604371	+	0.796703i	$0.293425\pi$
$284$	−0.506924	−0.0300804
$285$	5.09390	0.301737
$286$	6.21419	0.367453
$287$	8.42839	0.497512
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	3.28738	0.193041
$291$	−6.02072	−0.352941
$292$	−4.06783	−0.238052
$293$	28.2384	1.64970	0.824851	−	0.565350i	$-0.191259\pi$
$293$	28.2384	1.64970	0.824851	+	0.565350i	$0.191259\pi$
$294$	−1.56626	−0.0913461
$295$	−4.21419	−0.245360
$296$	−2.00000	−0.116248
$297$	−1.00000	−0.0580259
$298$	−5.54868	−0.321426
$299$	−23.6545	−1.36797
$300$	1.00000	0.0577350
$301$	−16.1021	−0.928109
$302$	−10.6690	−0.613930
$303$	−15.2139	−0.874015
$304$	−5.09390	−0.292155
$305$	−10.4284	−0.597128
$306$	1.00000	0.0571662
$307$	25.5867	1.46031	0.730154	−	0.683282i	$-0.239448\pi$
$307$	25.5867	1.46031	0.730154	+	0.683282i	$0.239448\pi$
$308$	−2.92682	−0.166771
$309$	12.9004	0.733880
$310$	7.14101	0.405582
$311$	15.5345	0.880882	0.440441	−	0.897782i	$-0.354822\pi$
$311$	15.5345	0.880882	0.440441	+	0.897782i	$0.354822\pi$
$312$	−6.21419	−0.351809
$313$	−15.1532	−0.856512	−0.428256	−	0.903658i	$-0.640872\pi$
$313$	−15.1532	−0.856512	−0.428256	+	0.903658i	$0.640872\pi$
$314$	−18.4928	−1.04361
$315$	−2.92682	−0.164907
$316$	14.8533	0.835565
$317$	17.3640	0.975258	0.487629	−	0.873051i	$-0.337862\pi$
$317$	17.3640	0.975258	0.487629	+	0.873051i	$0.337862\pi$
$318$	−0.519152	−0.0291126
$319$	−3.28738	−0.184058
$320$	−1.00000	−0.0559017
$321$	4.56626	0.254864
$322$	11.1410	0.620864
$323$	5.09390	0.283432
$324$	1.00000	0.0555556
$325$	6.21419	0.344701
$326$	12.8062	0.709271
$327$	−14.0414	−0.776493
$328$	−2.87971	−0.159005
$329$	0	0
$330$	−1.00000	−0.0550482
$331$	−7.32944	−0.402862	−0.201431	−	0.979503i	$-0.564559\pi$
$331$	−7.32944	−0.402862	−0.201431	+	0.979503i	$0.564559\pi$
$332$	5.75942	0.316089
$333$	2.00000	0.109599
$334$	−18.0936	−0.990037
$335$	−11.4545	−0.625824
$336$	2.92682	0.159671
$337$	−0.360558	−0.0196409	−0.00982043	−	0.999952i	$-0.503126\pi$
$337$	−0.360558	−0.0196409	−0.00982043	+	0.999952i	$0.503126\pi$
$338$	−25.6162	−1.39334
$339$	−12.8533	−0.698097
$340$	1.00000	0.0542326
$341$	−7.14101	−0.386707
$342$	5.09390	0.275447
$343$	−15.9036	−0.858712
$344$	5.50157	0.296625
$345$	3.80653	0.204937
$346$	−6.00000	−0.322562
$347$	4.74557	0.254756	0.127378	−	0.991854i	$-0.459344\pi$
$347$	4.74557	0.254756	0.127378	+	0.991854i	$0.459344\pi$
$348$	3.28738	0.176222
$349$	36.6962	1.96431	0.982153	−	0.188086i	$-0.0602284\pi$
$349$	36.6962	1.96431	0.982153	+	0.188086i	$0.0602284\pi$
$350$	−2.92682	−0.156445
$351$	6.21419	0.331689
$352$	1.00000	0.0533002
$353$	−12.5311	−0.666963	−0.333481	−	0.942757i	$-0.608223\pi$
$353$	−12.5311	−0.666963	−0.333481	+	0.942757i	$0.608223\pi$
$354$	−4.21419	−0.223982
$355$	0.506924	0.0269047
$356$	7.85363	0.416242
$357$	−2.92682	−0.154904
$358$	4.21419	0.222727
$359$	−9.24372	−0.487865	−0.243932	−	0.969792i	$-0.578437\pi$
$359$	−9.24372	−0.487865	−0.243932	+	0.969792i	$0.578437\pi$
$360$	1.00000	0.0527046
$361$	6.94785	0.365676
$362$	−2.37783	−0.124976
$363$	1.00000	0.0524864
$364$	18.1878	0.953300
$365$	4.06783	0.212920
$366$	−10.4284	−0.545100
$367$	20.0814	1.04824	0.524119	−	0.851645i	$-0.324395\pi$
$367$	20.0814	1.04824	0.524119	+	0.851645i	$0.324395\pi$
$368$	−3.80653	−0.198429
$369$	2.87971	0.149912
$370$	2.00000	0.103975
$371$	1.51946	0.0788866
$372$	7.14101	0.370244
$373$	−17.6388	−0.913303	−0.456652	−	0.889646i	$-0.650951\pi$
$373$	−17.6388	−0.913303	−0.456652	+	0.889646i	$0.650951\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	20.4284	1.05212
$378$	−2.92682	−0.150539
$379$	−10.2406	−0.526023	−0.263012	−	0.964793i	$-0.584716\pi$
$379$	−10.2406	−0.526023	−0.263012	+	0.964793i	$0.584716\pi$
$380$	5.09390	0.261312
$381$	−15.3203	−0.784884
$382$	−15.8621	−0.811577
$383$	12.1357	0.620103	0.310051	−	0.950720i	$-0.399654\pi$
$383$	12.1357	0.620103	0.310051	+	0.950720i	$0.399654\pi$
$384$	−1.00000	−0.0510310
$385$	2.92682	0.149164
$386$	12.4962	0.636040
$387$	−5.50157	−0.279660
$388$	−6.02072	−0.305656
$389$	−11.0295	−0.559219	−0.279610	−	0.960114i	$-0.590205\pi$
$389$	−11.0295	−0.559219	−0.279610	+	0.960114i	$0.590205\pi$
$390$	6.21419	0.314668
$391$	3.80653	0.192504
$392$	−1.56626	−0.0791080
$393$	5.75942	0.290524
$394$	−18.3342	−0.923662
$395$	−14.8533	−0.747352
$396$	−1.00000	−0.0502519
$397$	−12.3235	−0.618497	−0.309248	−	0.950981i	$-0.600077\pi$
$397$	−12.3235	−0.618497	−0.309248	+	0.950981i	$0.600077\pi$
$398$	−2.24058	−0.112310
$399$	−14.9089	−0.746380
$400$	1.00000	0.0500000
$401$	−27.9300	−1.39476	−0.697378	−	0.716704i	$-0.745650\pi$
$401$	−27.9300	−1.39476	−0.697378	+	0.716704i	$0.745650\pi$
$402$	−11.4545	−0.571297
$403$	44.3756	2.21051
$404$	−15.2139	−0.756919
$405$	−1.00000	−0.0496904
$406$	−9.62155	−0.477509
$407$	−2.00000	−0.0991363
$408$	1.00000	0.0495074
$409$	−5.61305	−0.277548	−0.138774	−	0.990324i	$-0.544316\pi$
$409$	−5.61305	−0.277548	−0.138774	+	0.990324i	$0.544316\pi$
$410$	2.87971	0.142219
$411$	−14.6077	−0.720545
$412$	12.9004	0.635559
$413$	12.3342	0.606925
$414$	3.80653	0.187081
$415$	−5.75942	−0.282719
$416$	−6.21419	−0.304676
$417$	−10.7541	−0.526629
$418$	−5.09390	−0.249151
$419$	−10.6599	−0.520768	−0.260384	−	0.965505i	$-0.583849\pi$
$419$	−10.6599	−0.520768	−0.260384	+	0.965505i	$0.583849\pi$
$420$	−2.92682	−0.142814
$421$	8.57475	0.417908	0.208954	−	0.977925i	$-0.432994\pi$
$421$	8.57475	0.417908	0.208954	+	0.977925i	$0.432994\pi$
$422$	−5.28738	−0.257385
$423$	0	0
$424$	−0.519152	−0.0252122
$425$	−1.00000	−0.0485071
$426$	0.506924	0.0245606
$427$	30.5220	1.47706
$428$	4.56626	0.220718
$429$	−6.21419	−0.300024
$430$	−5.50157	−0.265309
$431$	−3.07663	−0.148196	−0.0740980	−	0.997251i	$-0.523608\pi$
$431$	−3.07663	−0.148196	−0.0740980	+	0.997251i	$0.523608\pi$
$432$	1.00000	0.0481125
$433$	−12.8675	−0.618372	−0.309186	−	0.951002i	$-0.600057\pi$
$433$	−12.8675	−0.618372	−0.309186	+	0.951002i	$0.600057\pi$
$434$	−20.9004	−1.00325
$435$	−3.28738	−0.157618
$436$	−14.0414	−0.672463
$437$	19.3901	0.927553
$438$	4.06783	0.194368
$439$	5.72081	0.273039	0.136520	−	0.990637i	$-0.456408\pi$
$439$	5.72081	0.273039	0.136520	+	0.990637i	$0.456408\pi$
$440$	−1.00000	−0.0476731
$441$	1.56626	0.0745838
$442$	6.21419	0.295579
$443$	−8.32913	−0.395729	−0.197864	−	0.980229i	$-0.563401\pi$
$443$	−8.32913	−0.395729	−0.197864	+	0.980229i	$0.563401\pi$
$444$	2.00000	0.0949158
$445$	−7.85363	−0.372298
$446$	−6.10271	−0.288972
$447$	5.54868	0.262443
$448$	2.92682	0.138279
$449$	−3.46013	−0.163294	−0.0816468	−	0.996661i	$-0.526018\pi$
$449$	−3.46013	−0.163294	−0.0816468	+	0.996661i	$0.526018\pi$
$450$	−1.00000	−0.0471405
$451$	−2.87971	−0.135600
$452$	−12.8533	−0.604569
$453$	10.6690	0.501272
$454$	19.0882	0.895855
$455$	−18.1878	−0.852658
$456$	5.09390	0.238544
$457$	−14.8568	−0.694970	−0.347485	−	0.937685i	$-0.612964\pi$
$457$	−14.8568	−0.694970	−0.347485	+	0.937685i	$0.612964\pi$
$458$	6.09421	0.284764
$459$	−1.00000	−0.0466760
$460$	3.80653	0.177480
$461$	31.0323	1.44532	0.722660	−	0.691203i	$-0.242919\pi$
$461$	31.0323	1.44532	0.722660	+	0.691203i	$0.242919\pi$
$462$	2.92682	0.136168
$463$	14.7977	0.687709	0.343854	−	0.939023i	$-0.388267\pi$
$463$	14.7977	0.687709	0.343854	+	0.939023i	$0.388267\pi$
$464$	3.28738	0.152613
$465$	−7.14101	−0.331156
$466$	−14.8062	−0.685885
$467$	17.9507	0.830658	0.415329	−	0.909671i	$-0.363666\pi$
$467$	17.9507	0.830658	0.415329	+	0.909671i	$0.363666\pi$
$468$	6.21419	0.287251
$469$	33.5251	1.54805
$470$	0	0
$471$	18.4928	0.852102
$472$	−4.21419	−0.193974
$473$	5.50157	0.252962
$474$	−14.8533	−0.682236
$475$	−5.09390	−0.233724
$476$	−2.92682	−0.134150
$477$	0.519152	0.0237703
$478$	−10.1464	−0.464084
$479$	16.7833	0.766848	0.383424	−	0.923573i	$-0.374745\pi$
$479$	16.7833	0.766848	0.383424	+	0.923573i	$0.374745\pi$
$480$	1.00000	0.0456435
$481$	12.4284	0.566686
$482$	25.2380	1.14956
$483$	−11.1410	−0.506934
$484$	1.00000	0.0454545
$485$	6.02072	0.273387
$486$	−1.00000	−0.0453609
$487$	1.65360	0.0749318	0.0374659	−	0.999298i	$-0.488071\pi$
$487$	1.65360	0.0749318	0.0374659	+	0.999298i	$0.488071\pi$
$488$	−10.4284	−0.472071
$489$	−12.8062	−0.579117
$490$	1.56626	0.0707564
$491$	−11.7716	−0.531247	−0.265624	−	0.964077i	$-0.585578\pi$
$491$	−11.7716	−0.531247	−0.265624	+	0.964077i	$0.585578\pi$
$492$	2.87971	0.129827
$493$	−3.28738	−0.148056
$494$	31.6545	1.42420
$495$	1.00000	0.0449467
$496$	7.14101	0.320641
$497$	−1.48367	−0.0665519
$498$	−5.75942	−0.258086
$499$	8.13565	0.364202	0.182101	−	0.983280i	$-0.441710\pi$
$499$	8.13565	0.364202	0.182101	+	0.983280i	$0.441710\pi$
$500$	−1.00000	−0.0447214
$501$	18.0936	0.808362
$502$	16.5484	0.738590
$503$	27.8429	1.24145	0.620727	−	0.784027i	$-0.286837\pi$
$503$	27.8429	1.24145	0.620727	+	0.784027i	$0.286837\pi$
$504$	−2.92682	−0.130371
$505$	15.2139	0.677009
$506$	−3.80653	−0.169221
$507$	25.6162	1.13766
$508$	−15.3203	−0.679729
$509$	−11.0295	−0.488875	−0.244438	−	0.969665i	$-0.578603\pi$
$509$	−11.0295	−0.488875	−0.244438	+	0.969665i	$0.578603\pi$
$510$	−1.00000	−0.0442807
$511$	−11.9058	−0.526681
$512$	−1.00000	−0.0441942
$513$	−5.09390	−0.224901
$514$	−28.2384	−1.24554
$515$	−12.9004	−0.568461
$516$	−5.50157	−0.242193
$517$	0	0
$518$	−5.85363	−0.257194
$519$	6.00000	0.263371
$520$	6.21419	0.272510
$521$	−14.2556	−0.624551	−0.312275	−	0.949992i	$-0.601091\pi$
$521$	−14.2556	−0.624551	−0.312275	+	0.949992i	$0.601091\pi$
$522$	−3.28738	−0.143885
$523$	−21.7415	−0.950691	−0.475345	−	0.879799i	$-0.657677\pi$
$523$	−21.7415	−0.950691	−0.475345	+	0.879799i	$0.657677\pi$
$524$	5.75942	0.251601
$525$	2.92682	0.127737
$526$	1.89729	0.0827259
$527$	−7.14101	−0.311067
$528$	−1.00000	−0.0435194
$529$	−8.51035	−0.370015
$530$	0.519152	0.0225505
$531$	4.21419	0.182880
$532$	−14.9089	−0.646384
$533$	17.8951	0.775122
$534$	−7.85363	−0.339860
$535$	−4.56626	−0.197417
$536$	−11.4545	−0.494757
$537$	−4.21419	−0.181856
$538$	17.5188	0.755291
$539$	−1.56626	−0.0674635
$540$	−1.00000	−0.0430331
$541$	4.33479	0.186367	0.0931837	−	0.995649i	$-0.470296\pi$
$541$	4.33479	0.186367	0.0931837	+	0.995649i	$0.470296\pi$
$542$	−2.61841	−0.112470
$543$	2.37783	0.102043
$544$	1.00000	0.0428746
$545$	14.0414	0.601469
$546$	−18.1878	−0.778366
$547$	21.8536	0.934394	0.467197	−	0.884153i	$-0.345264\pi$
$547$	21.8536	0.934394	0.467197	+	0.884153i	$0.345264\pi$
$548$	−14.6077	−0.624010
$549$	10.4284	0.445073
$550$	1.00000	0.0426401
$551$	−16.7456	−0.713385
$552$	3.80653	0.162017
$553$	43.4730	1.84866
$554$	−20.3762	−0.865703
$555$	−2.00000	−0.0848953
$556$	−10.7541	−0.456074
$557$	25.7924	1.09286	0.546429	−	0.837506i	$-0.315987\pi$
$557$	25.7924	1.09286	0.546429	+	0.837506i	$0.315987\pi$
$558$	−7.14101	−0.302303
$559$	−34.1878	−1.44599
$560$	−2.92682	−0.123681
$561$	1.00000	0.0422200
$562$	12.7541	0.537998
$563$	−15.2017	−0.640673	−0.320337	−	0.947304i	$-0.603796\pi$
$563$	−15.2017	−0.640673	−0.320337	+	0.947304i	$0.603796\pi$
$564$	0	0
$565$	12.8533	0.540743
$566$	−20.3342	−0.854709
$567$	2.92682	0.122915
$568$	0.506924	0.0212701
$569$	−1.76004	−0.0737848	−0.0368924	−	0.999319i	$-0.511746\pi$
$569$	−1.76004	−0.0737848	−0.0368924	+	0.999319i	$0.511746\pi$
$570$	−5.09390	−0.213360
$571$	6.98615	0.292361	0.146181	−	0.989258i	$-0.453302\pi$
$571$	6.98615	0.292361	0.146181	+	0.989258i	$0.453302\pi$
$572$	−6.21419	−0.259828
$573$	15.8621	0.662650
$574$	−8.42839	−0.351794
$575$	−3.80653	−0.158743
$576$	1.00000	0.0416667
$577$	−30.0829	−1.25237	−0.626183	−	0.779676i	$-0.715384\pi$
$577$	−30.0829	−1.25237	−0.626183	+	0.779676i	$0.715384\pi$
$578$	−1.00000	−0.0415945
$579$	−12.4962	−0.519325
$580$	−3.28738	−0.136501
$581$	16.8568	0.699337
$582$	6.02072	0.249567
$583$	−0.519152	−0.0215011
$584$	4.06783	0.168328
$585$	−6.21419	−0.256925
$586$	−28.2384	−1.16652
$587$	−23.1966	−0.957427	−0.478713	−	0.877971i	$-0.658897\pi$
$587$	−23.1966	−0.957427	−0.478713	+	0.877971i	$0.658897\pi$
$588$	1.56626	0.0645914
$589$	−36.3756	−1.49883
$590$	4.21419	0.173496
$591$	18.3342	0.754167
$592$	2.00000	0.0821995
$593$	5.09735	0.209323	0.104662	−	0.994508i	$-0.466624\pi$
$593$	5.09735	0.209323	0.104662	+	0.994508i	$0.466624\pi$
$594$	1.00000	0.0410305
$595$	2.92682	0.119988
$596$	5.54868	0.227283
$597$	2.24058	0.0917008
$598$	23.6545	0.967304
$599$	21.9557	0.897086	0.448543	−	0.893761i	$-0.351943\pi$
$599$	21.9557	0.897086	0.448543	+	0.893761i	$0.351943\pi$
$600$	−1.00000	−0.0408248
$601$	−4.85332	−0.197971	−0.0989856	−	0.995089i	$-0.531560\pi$
$601$	−4.85332	−0.197971	−0.0989856	+	0.995089i	$0.531560\pi$
$602$	16.1021	0.656272
$603$	11.4545	0.466462
$604$	10.6690	0.434114
$605$	−1.00000	−0.0406558
$606$	15.2139	0.618022
$607$	3.45164	0.140098	0.0700488	−	0.997544i	$-0.477685\pi$
$607$	3.45164	0.140098	0.0700488	+	0.997544i	$0.477685\pi$
$608$	5.09390	0.206585
$609$	9.62155	0.389885
$610$	10.4284	0.422233
$611$	0	0
$612$	−1.00000	−0.0404226
$613$	−13.5345	−0.546654	−0.273327	−	0.961921i	$-0.588124\pi$
$613$	−13.5345	−0.546654	−0.273327	+	0.961921i	$0.588124\pi$
$614$	−25.5867	−1.03259
$615$	−2.87971	−0.116121
$616$	2.92682	0.117925
$617$	38.5084	1.55029	0.775146	−	0.631782i	$-0.217676\pi$
$617$	38.5084	1.55029	0.775146	+	0.631782i	$0.217676\pi$
$618$	−12.9004	−0.518931
$619$	−25.2682	−1.01561	−0.507807	−	0.861471i	$-0.669544\pi$
$619$	−25.2682	−1.01561	−0.507807	+	0.861471i	$0.669544\pi$
$620$	−7.14101	−0.286790
$621$	−3.80653	−0.152751
$622$	−15.5345	−0.622877
$623$	22.9862	0.920921
$624$	6.21419	0.248767
$625$	1.00000	0.0400000
$626$	15.1532	0.605645
$627$	5.09390	0.203431
$628$	18.4928	0.737942
$629$	−2.00000	−0.0797452
$630$	2.92682	0.116607
$631$	20.2230	0.805064	0.402532	−	0.915406i	$-0.368130\pi$
$631$	20.2230	0.805064	0.402532	+	0.915406i	$0.368130\pi$
$632$	−14.8533	−0.590833
$633$	5.28738	0.210154
$634$	−17.3640	−0.689612
$635$	15.3203	0.607968
$636$	0.519152	0.0205857
$637$	9.73303	0.385637
$638$	3.28738	0.130148
$639$	−0.506924	−0.0200536
$640$	1.00000	0.0395285
$641$	−9.35520	−0.369508	−0.184754	−	0.982785i	$-0.559149\pi$
$641$	−9.35520	−0.369508	−0.184754	+	0.982785i	$0.559149\pi$
$642$	−4.56626	−0.180216
$643$	9.52733	0.375721	0.187861	−	0.982196i	$-0.439845\pi$
$643$	9.52733	0.375721	0.187861	+	0.982196i	$0.439845\pi$
$644$	−11.1410	−0.439017
$645$	5.50157	0.216624
$646$	−5.09390	−0.200417
$647$	13.9648	0.549014	0.274507	−	0.961585i	$-0.411485\pi$
$647$	13.9648	0.549014	0.274507	+	0.961585i	$0.411485\pi$
$648$	−1.00000	−0.0392837
$649$	−4.21419	−0.165422
$650$	−6.21419	−0.243741
$651$	20.9004	0.819152
$652$	−12.8062	−0.501530
$653$	−30.7961	−1.20515	−0.602573	−	0.798064i	$-0.705858\pi$
$653$	−30.7961	−1.20515	−0.602573	+	0.798064i	$0.705858\pi$
$654$	14.0414	0.549064
$655$	−5.75942	−0.225039
$656$	2.87971	0.112434
$657$	−4.06783	−0.158701
$658$	0	0
$659$	−29.0659	−1.13225	−0.566124	−	0.824320i	$-0.691558\pi$
$659$	−29.0659	−1.13225	−0.566124	+	0.824320i	$0.691558\pi$
$660$	1.00000	0.0389249
$661$	26.8913	1.04595	0.522975	−	0.852348i	$-0.324822\pi$
$661$	26.8913	1.04595	0.522975	+	0.852348i	$0.324822\pi$
$662$	7.32944	0.284867
$663$	−6.21419	−0.241339
$664$	−5.75942	−0.223509
$665$	14.9089	0.578143
$666$	−2.00000	−0.0774984
$667$	−12.5135	−0.484524
$668$	18.0936	0.700062
$669$	6.10271	0.235944
$670$	11.4545	0.442524
$671$	−10.4284	−0.402583
$672$	−2.92682	−0.112904
$673$	41.8687	1.61392	0.806960	−	0.590607i	$-0.201111\pi$
$673$	41.8687	1.61392	0.806960	+	0.590607i	$0.201111\pi$
$674$	0.360558	0.0138882
$675$	1.00000	0.0384900
$676$	25.6162	0.985238
$677$	32.8046	1.26078	0.630392	−	0.776277i	$-0.282894\pi$
$677$	32.8046	1.26078	0.630392	+	0.776277i	$0.282894\pi$
$678$	12.8533	0.493629
$679$	−17.6215	−0.676253
$680$	−1.00000	−0.0383482
$681$	−19.0882	−0.731463
$682$	7.14101	0.273443
$683$	38.2990	1.46547	0.732735	−	0.680514i	$-0.238243\pi$
$683$	38.2990	1.46547	0.732735	+	0.680514i	$0.238243\pi$
$684$	−5.09390	−0.194770
$685$	14.6077	0.558131
$686$	15.9036	0.607201
$687$	−6.09421	−0.232509
$688$	−5.50157	−0.209745
$689$	3.22611	0.122905
$690$	−3.80653	−0.144912
$691$	42.1947	1.60516	0.802581	−	0.596543i	$-0.203460\pi$
$691$	42.1947	1.60516	0.802581	+	0.596543i	$0.203460\pi$
$692$	6.00000	0.228086
$693$	−2.92682	−0.111181
$694$	−4.74557	−0.180139
$695$	10.7541	0.407925
$696$	−3.28738	−0.124608
$697$	−2.87971	−0.109077
$698$	−36.6962	−1.38897
$699$	14.8062	0.560023
$700$	2.92682	0.110623
$701$	25.0261	0.945222	0.472611	−	0.881271i	$-0.343312\pi$
$701$	25.0261	0.945222	0.472611	+	0.881271i	$0.343312\pi$
$702$	−6.21419	−0.234540
$703$	−10.1878	−0.384240
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	12.5311	0.471614
$707$	−44.5283	−1.67466
$708$	4.21419	0.158379
$709$	−29.4145	−1.10469	−0.552343	−	0.833617i	$-0.686266\pi$
$709$	−29.4145	−1.10469	−0.552343	+	0.833617i	$0.686266\pi$
$710$	−0.506924	−0.0190245
$711$	14.8533	0.557043
$712$	−7.85363	−0.294327
$713$	−27.1825	−1.01799
$714$	2.92682	0.109533
$715$	6.21419	0.232398
$716$	−4.21419	−0.157492
$717$	10.1464	0.378923
$718$	9.24372	0.344972
$719$	−22.9875	−0.857288	−0.428644	−	0.903474i	$-0.641008\pi$
$719$	−22.9875	−0.857288	−0.428644	+	0.903474i	$0.641008\pi$
$720$	−1.00000	−0.0372678
$721$	37.7572	1.40615
$722$	−6.94785	−0.258572
$723$	−25.2380	−0.938613
$724$	2.37783	0.0883714
$725$	3.28738	0.122090
$726$	−1.00000	−0.0371135
$727$	−34.4086	−1.27614	−0.638071	−	0.769977i	$-0.720268\pi$
$727$	−34.4086	−1.27614	−0.638071	+	0.769977i	$0.720268\pi$
$728$	−18.1878	−0.674085
$729$	1.00000	0.0370370
$730$	−4.06783	−0.150557
$731$	5.50157	0.203483
$732$	10.4284	0.385444
$733$	18.2386	0.673660	0.336830	−	0.941566i	$-0.390645\pi$
$733$	18.2386	0.673660	0.336830	+	0.941566i	$0.390645\pi$
$734$	−20.0814	−0.741217
$735$	−1.56626	−0.0577723
$736$	3.80653	0.140310
$737$	−11.4545	−0.421931
$738$	−2.87971	−0.106004
$739$	−35.6931	−1.31299	−0.656496	−	0.754329i	$-0.727962\pi$
$739$	−35.6931	−1.31299	−0.656496	+	0.754329i	$0.727962\pi$
$740$	−2.00000	−0.0735215
$741$	−31.6545	−1.16286
$742$	−1.51946	−0.0557812
$743$	−46.2707	−1.69751	−0.848753	−	0.528789i	$-0.822646\pi$
$743$	−46.2707	−1.69751	−0.848753	+	0.528789i	$0.822646\pi$
$744$	−7.14101	−0.261802
$745$	−5.54868	−0.203288
$746$	17.6388	0.645803
$747$	5.75942	0.210726
$748$	1.00000	0.0365636
$749$	13.3646	0.488332
$750$	1.00000	0.0365148
$751$	13.5801	0.495545	0.247773	−	0.968818i	$-0.420301\pi$
$751$	13.5801	0.495545	0.247773	+	0.968818i	$0.420301\pi$
$752$	0	0
$753$	−16.5484	−0.603056
$754$	−20.4284	−0.743958
$755$	−10.6690	−0.388283
$756$	2.92682	0.106447
$757$	6.33791	0.230355	0.115178	−	0.993345i	$-0.463256\pi$
$757$	6.33791	0.230355	0.115178	+	0.993345i	$0.463256\pi$
$758$	10.2406	0.371955
$759$	3.80653	0.138168
$760$	−5.09390	−0.184775
$761$	−7.83443	−0.283998	−0.141999	−	0.989867i	$-0.545353\pi$
$761$	−7.83443	−0.283998	−0.141999	+	0.989867i	$0.545353\pi$
$762$	15.3203	0.554997
$763$	−41.0967	−1.48780
$764$	15.8621	0.573872
$765$	1.00000	0.0361551
$766$	−12.1357	−0.438479
$767$	26.1878	0.945587
$768$	1.00000	0.0360844
$769$	22.5640	0.813680	0.406840	−	0.913499i	$-0.366631\pi$
$769$	22.5640	0.813680	0.406840	+	0.913499i	$0.366631\pi$
$770$	−2.92682	−0.105475
$771$	28.2384	1.01698
$772$	−12.4962	−0.449749
$773$	−46.2327	−1.66287	−0.831437	−	0.555619i	$-0.812481\pi$
$773$	−46.2327	−1.66287	−0.831437	+	0.555619i	$0.812481\pi$
$774$	5.50157	0.197750
$775$	7.14101	0.256513
$776$	6.02072	0.216131
$777$	5.85363	0.209998
$778$	11.0295	0.395428
$779$	−14.6690	−0.525570
$780$	−6.21419	−0.222504
$781$	0.506924	0.0181392
$782$	−3.80653	−0.136121
$783$	3.28738	0.117481
$784$	1.56626	0.0559378
$785$	−18.4928	−0.660035
$786$	−5.75942	−0.205432
$787$	6.48054	0.231006	0.115503	−	0.993307i	$-0.463152\pi$
$787$	6.48054	0.231006	0.115503	+	0.993307i	$0.463152\pi$
$788$	18.3342	0.653128
$789$	−1.89729	−0.0675454
$790$	14.8533	0.528458
$791$	−37.6193	−1.33759
$792$	1.00000	0.0355335
$793$	64.8040	2.30126
$794$	12.3235	0.437343
$795$	−0.519152	−0.0184124
$796$	2.24058	0.0794152
$797$	−37.8043	−1.33910	−0.669549	−	0.742768i	$-0.733512\pi$
$797$	−37.8043	−1.33910	−0.669549	+	0.742768i	$0.733512\pi$
$798$	14.9089	0.527770
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	7.85363	0.277495
$802$	27.9300	0.986241
$803$	4.06783	0.143551
$804$	11.4545	0.403968
$805$	11.1410	0.392669
$806$	−44.3756	−1.56306
$807$	−17.5188	−0.616692
$808$	15.2139	0.535223
$809$	2.68119	0.0942657	0.0471329	−	0.998889i	$-0.484992\pi$
$809$	2.68119	0.0942657	0.0471329	+	0.998889i	$0.484992\pi$
$810$	1.00000	0.0351364
$811$	38.9089	1.36628	0.683139	−	0.730289i	$-0.260615\pi$
$811$	38.9089	1.36628	0.683139	+	0.730289i	$0.260615\pi$
$812$	9.62155	0.337650
$813$	2.61841	0.0918317
$814$	2.00000	0.0701000
$815$	12.8062	0.448582
$816$	−1.00000	−0.0350070
$817$	28.0245	0.980452
$818$	5.61305	0.196256
$819$	18.1878	0.635533
$820$	−2.87971	−0.100564
$821$	−43.6630	−1.52385	−0.761924	−	0.647666i	$-0.775745\pi$
$821$	−43.6630	−1.52385	−0.761924	+	0.647666i	$0.775745\pi$
$822$	14.6077	0.509502
$823$	−11.8414	−0.412765	−0.206383	−	0.978471i	$-0.566169\pi$
$823$	−11.8414	−0.412765	−0.206383	+	0.978471i	$0.566169\pi$
$824$	−12.9004	−0.449408
$825$	−1.00000	−0.0348155
$826$	−12.3342	−0.429161
$827$	1.00598	0.0349813	0.0174906	−	0.999847i	$-0.494432\pi$
$827$	1.00598	0.0349813	0.0174906	+	0.999847i	$0.494432\pi$
$828$	−3.80653	−0.132286
$829$	−54.0584	−1.87753	−0.938763	−	0.344563i	$-0.888027\pi$
$829$	−54.0584	−1.87753	−0.938763	+	0.344563i	$0.888027\pi$
$830$	5.75942	0.199912
$831$	20.3762	0.706844
$832$	6.21419	0.215438
$833$	−1.56626	−0.0542676
$834$	10.7541	0.372383
$835$	−18.0936	−0.626155
$836$	5.09390	0.176176
$837$	7.14101	0.246829
$838$	10.6599	0.368238
$839$	−40.9070	−1.41227	−0.706133	−	0.708079i	$-0.749562\pi$
$839$	−40.9070	−1.41227	−0.706133	+	0.708079i	$0.749562\pi$
$840$	2.92682	0.100985
$841$	−18.1932	−0.627350
$842$	−8.57475	−0.295505
$843$	−12.7541	−0.439273
$844$	5.28738	0.181999
$845$	−25.6162	−0.881224
$846$	0	0
$847$	2.92682	0.100567
$848$	0.519152	0.0178277
$849$	20.3342	0.697867
$850$	1.00000	0.0342997
$851$	−7.61305	−0.260972
$852$	−0.506924	−0.0173669
$853$	49.9450	1.71008	0.855042	−	0.518558i	$-0.173531\pi$
$853$	49.9450	1.71008	0.855042	+	0.518558i	$0.173531\pi$
$854$	−30.5220	−1.04444
$855$	5.09390	0.174208
$856$	−4.56626	−0.156072
$857$	18.7120	0.639190	0.319595	−	0.947554i	$-0.396453\pi$
$857$	18.7120	0.639190	0.319595	+	0.947554i	$0.396453\pi$
$858$	6.21419	0.212149
$859$	12.9249	0.440991	0.220496	−	0.975388i	$-0.429232\pi$
$859$	12.9249	0.440991	0.220496	+	0.975388i	$0.429232\pi$
$860$	5.50157	0.187602
$861$	8.42839	0.287239
$862$	3.07663	0.104790
$863$	−18.7733	−0.639049	−0.319525	−	0.947578i	$-0.603523\pi$
$863$	−18.7733	−0.639049	−0.319525	+	0.947578i	$0.603523\pi$
$864$	−1.00000	−0.0340207
$865$	−6.00000	−0.204006
$866$	12.8675	0.437255
$867$	1.00000	0.0339618
$868$	20.9004	0.709407
$869$	−14.8533	−0.503864
$870$	3.28738	0.111452
$871$	71.1802	2.41185
$872$	14.0414	0.475503
$873$	−6.02072	−0.203771
$874$	−19.3901	−0.655879
$875$	−2.92682	−0.0989445
$876$	−4.06783	−0.137439
$877$	−35.1818	−1.18801	−0.594003	−	0.804463i	$-0.702453\pi$
$877$	−35.1818	−1.18801	−0.594003	+	0.804463i	$0.702453\pi$
$878$	−5.72081	−0.193068
$879$	28.2384	0.952456
$880$	1.00000	0.0337100
$881$	29.6724	0.999688	0.499844	−	0.866115i	$-0.333391\pi$
$881$	29.6724	0.999688	0.499844	+	0.866115i	$0.333391\pi$
$882$	−1.56626	−0.0527387
$883$	8.76104	0.294832	0.147416	−	0.989075i	$-0.452904\pi$
$883$	8.76104	0.294832	0.147416	+	0.989075i	$0.452904\pi$
$884$	−6.21419	−0.209006
$885$	−4.21419	−0.141659
$886$	8.32913	0.279822
$887$	17.2783	0.580147	0.290074	−	0.957004i	$-0.406320\pi$
$887$	17.2783	0.580147	0.290074	+	0.957004i	$0.406320\pi$
$888$	−2.00000	−0.0671156
$889$	−44.8398	−1.50388
$890$	7.85363	0.263254
$891$	−1.00000	−0.0335013
$892$	6.10271	0.204334
$893$	0	0
$894$	−5.54868	−0.185575
$895$	4.21419	0.140865
$896$	−2.92682	−0.0977781
$897$	−23.6545	−0.789801
$898$	3.46013	0.115466
$899$	23.4752	0.782941
$900$	1.00000	0.0333333
$901$	−0.519152	−0.0172955
$902$	2.87971	0.0958839
$903$	−16.1021	−0.535844
$904$	12.8533	0.427495
$905$	−2.37783	−0.0790418
$906$	−10.6690	−0.354453
$907$	9.52733	0.316350	0.158175	−	0.987411i	$-0.449439\pi$
$907$	9.52733	0.316350	0.158175	+	0.987411i	$0.449439\pi$
$908$	−19.0882	−0.633465
$909$	−15.2139	−0.504613
$910$	18.1878	0.602920
$911$	30.2550	1.00239	0.501197	−	0.865333i	$-0.332893\pi$
$911$	30.2550	1.00239	0.501197	+	0.865333i	$0.332893\pi$
$912$	−5.09390	−0.168676
$913$	−5.75942	−0.190609
$914$	14.8568	0.491418
$915$	−10.4284	−0.344752
$916$	−6.09421	−0.201358
$917$	16.8568	0.556660
$918$	1.00000	0.0330049
$919$	−6.62531	−0.218549	−0.109274	−	0.994012i	$-0.534853\pi$
$919$	−6.62531	−0.218549	−0.109274	+	0.994012i	$0.534853\pi$
$920$	−3.80653	−0.125497
$921$	25.5867	0.843109
$922$	−31.0323	−1.02200
$923$	−3.15012	−0.103688
$924$	−2.92682	−0.0962852
$925$	2.00000	0.0657596
$926$	−14.7977	−0.486283
$927$	12.9004	0.423706
$928$	−3.28738	−0.107913
$929$	−25.1981	−0.826724	−0.413362	−	0.910567i	$-0.635646\pi$
$929$	−25.1981	−0.826724	−0.413362	+	0.910567i	$0.635646\pi$
$930$	7.14101	0.234163
$931$	−7.97837	−0.261481
$932$	14.8062	0.484994
$933$	15.5345	0.508577
$934$	−17.9507	−0.587364
$935$	−1.00000	−0.0327035
$936$	−6.21419	−0.203117
$937$	38.7525	1.26599	0.632994	−	0.774157i	$-0.281826\pi$
$937$	38.7525	1.26599	0.632994	+	0.774157i	$0.281826\pi$
$938$	−33.5251	−1.09463
$939$	−15.1532	−0.494507
$940$	0	0
$941$	21.3373	0.695576	0.347788	−	0.937573i	$-0.386933\pi$
$941$	21.3373	0.695576	0.347788	+	0.937573i	$0.386933\pi$
$942$	−18.4928	−0.602527
$943$	−10.9617	−0.356962
$944$	4.21419	0.137160
$945$	−2.92682	−0.0952094
$946$	−5.50157	−0.178871
$947$	18.4391	0.599190	0.299595	−	0.954066i	$-0.403148\pi$
$947$	18.4391	0.599190	0.299595	+	0.954066i	$0.403148\pi$
$948$	14.8533	0.482414
$949$	−25.2783	−0.820567
$950$	5.09390	0.165268
$951$	17.3640	0.563066
$952$	2.92682	0.0948587
$953$	8.53331	0.276421	0.138211	−	0.990403i	$-0.455865\pi$
$953$	8.53331	0.276421	0.138211	+	0.990403i	$0.455865\pi$
$954$	−0.519152	−0.0168082
$955$	−15.8621	−0.513286
$956$	10.1464	0.328157
$957$	−3.28738	−0.106266
$958$	−16.7833	−0.542243
$959$	−42.7541	−1.38060
$960$	−1.00000	−0.0322749
$961$	19.9940	0.644968
$962$	−12.4284	−0.400707
$963$	4.56626	0.147146
$964$	−25.2380	−0.812863
$965$	12.4962	0.402267
$966$	11.1410	0.358456
$967$	−17.8536	−0.574134	−0.287067	−	0.957910i	$-0.592680\pi$
$967$	−17.8536	−0.574134	−0.287067	+	0.957910i	$0.592680\pi$
$968$	−1.00000	−0.0321412
$969$	5.09390	0.163640
$970$	−6.02072	−0.193314
$971$	28.0672	0.900719	0.450360	−	0.892847i	$-0.351296\pi$
$971$	28.0672	0.900719	0.450360	+	0.892847i	$0.351296\pi$
$972$	1.00000	0.0320750
$973$	−31.4752	−1.00905
$974$	−1.65360	−0.0529848
$975$	6.21419	0.199013
$976$	10.4284	0.333804
$977$	−42.1872	−1.34969	−0.674844	−	0.737961i	$-0.735789\pi$
$977$	−42.1872	−1.34969	−0.674844	+	0.737961i	$0.735789\pi$
$978$	12.8062	0.409498
$979$	−7.85363	−0.251003
$980$	−1.56626	−0.0500323
$981$	−14.0414	−0.448309
$982$	11.7716	0.375648
$983$	−19.9353	−0.635837	−0.317918	−	0.948118i	$-0.602984\pi$
$983$	−19.9353	−0.635837	−0.317918	+	0.948118i	$0.602984\pi$
$984$	−2.87971	−0.0918018
$985$	−18.3342	−0.584175
$986$	3.28738	0.104691
$987$	0	0
$988$	−31.6545	−1.00706
$989$	20.9419	0.665913
$990$	−1.00000	−0.0317821
$991$	−20.7648	−0.659615	−0.329807	−	0.944048i	$-0.606984\pi$
$991$	−20.7648	−0.659615	−0.329807	+	0.944048i	$0.606984\pi$
$992$	−7.14101	−0.226727
$993$	−7.32944	−0.232593
$994$	1.48367	0.0470593
$995$	−2.24058	−0.0710311
$996$	5.75942	0.182494
$997$	−27.6284	−0.875002	−0.437501	−	0.899218i	$-0.644136\pi$
$997$	−27.6284	−0.875002	−0.437501	+	0.899218i	$0.644136\pi$
$998$	−8.13565	−0.257530
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cf.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cf.1.3	✓	4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.92682 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +2.92682 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +6.21419 q^{13} -2.92682 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -5.09390 q^{19} -1.00000 q^{20} +2.92682 q^{21} +1.00000 q^{22} -3.80653 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.21419 q^{26} +1.00000 q^{27} +2.92682 q^{28} +3.28738 q^{29} +1.00000 q^{30} +7.14101 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -2.92682 q^{35} +1.00000 q^{36} +2.00000 q^{37} +5.09390 q^{38} +6.21419 q^{39} +1.00000 q^{40} +2.87971 q^{41} -2.92682 q^{42} -5.50157 q^{43} -1.00000 q^{44} -1.00000 q^{45} +3.80653 q^{46} +1.00000 q^{48} +1.56626 q^{49} -1.00000 q^{50} -1.00000 q^{51} +6.21419 q^{52} +0.519152 q^{53} -1.00000 q^{54} +1.00000 q^{55} -2.92682 q^{56} -5.09390 q^{57} -3.28738 q^{58} +4.21419 q^{59} -1.00000 q^{60} +10.4284 q^{61} -7.14101 q^{62} +2.92682 q^{63} +1.00000 q^{64} -6.21419 q^{65} +1.00000 q^{66} +11.4545 q^{67} -1.00000 q^{68} -3.80653 q^{69} +2.92682 q^{70} -0.506924 q^{71} -1.00000 q^{72} -4.06783 q^{73} -2.00000 q^{74} +1.00000 q^{75} -5.09390 q^{76} -2.92682 q^{77} -6.21419 q^{78} +14.8533 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.87971 q^{82} +5.75942 q^{83} +2.92682 q^{84} +1.00000 q^{85} +5.50157 q^{86} +3.28738 q^{87} +1.00000 q^{88} +7.85363 q^{89} +1.00000 q^{90} +18.1878 q^{91} -3.80653 q^{92} +7.14101 q^{93} +5.09390 q^{95} -1.00000 q^{96} -6.02072 q^{97} -1.56626 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 5 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 6 q^{13} - 5 q^{14} - 4 q^{15} + 4 q^{16} - 4 q^{17} - 4 q^{18} + 8 q^{19} - 4 q^{20} + 5 q^{21} + 4 q^{22} + q^{23} - 4 q^{24} + 4 q^{25} - 6 q^{26} + 4 q^{27} + 5 q^{28} + q^{29} + 4 q^{30} + 3 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{34} - 5 q^{35} + 4 q^{36} + 8 q^{37} - 8 q^{38} + 6 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} + 9 q^{43} - 4 q^{44} - 4 q^{45} - q^{46} + 4 q^{48} + 5 q^{49} - 4 q^{50} - 4 q^{51} + 6 q^{52} - 2 q^{53} - 4 q^{54} + 4 q^{55} - 5 q^{56} + 8 q^{57} - q^{58} - 2 q^{59} - 4 q^{60} + 4 q^{61} - 3 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 4 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} + 5 q^{70} - 10 q^{71} - 4 q^{72} + 16 q^{73} - 8 q^{74} + 4 q^{75} + 8 q^{76} - 5 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} + 4 q^{81} - 2 q^{82} + 4 q^{83} + 5 q^{84} + 4 q^{85} - 9 q^{86} + q^{87} + 4 q^{88} + 18 q^{89} + 4 q^{90} + 16 q^{91} + q^{92} + 3 q^{93} - 8 q^{95} - 4 q^{96} + 11 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 5 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 6 * q^13 - 5 * q^14 - 4 * q^15 + 4 * q^16 - 4 * q^17 - 4 * q^18 + 8 * q^19 - 4 * q^20 + 5 * q^21 + 4 * q^22 + q^23 - 4 * q^24 + 4 * q^25 - 6 * q^26 + 4 * q^27 + 5 * q^28 + q^29 + 4 * q^30 + 3 * q^31 - 4 * q^32 - 4 * q^33 + 4 * q^34 - 5 * q^35 + 4 * q^36 + 8 * q^37 - 8 * q^38 + 6 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 + 9 * q^43 - 4 * q^44 - 4 * q^45 - q^46 + 4 * q^48 + 5 * q^49 - 4 * q^50 - 4 * q^51 + 6 * q^52 - 2 * q^53 - 4 * q^54 + 4 * q^55 - 5 * q^56 + 8 * q^57 - q^58 - 2 * q^59 - 4 * q^60 + 4 * q^61 - 3 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 4 * q^66 + 12 * q^67 - 4 * q^68 + q^69 + 5 * q^70 - 10 * q^71 - 4 * q^72 + 16 * q^73 - 8 * q^74 + 4 * q^75 + 8 * q^76 - 5 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 + 4 * q^81 - 2 * q^82 + 4 * q^83 + 5 * q^84 + 4 * q^85 - 9 * q^86 + q^87 + 4 * q^88 + 18 * q^89 + 4 * q^90 + 16 * q^91 + q^92 + 3 * q^93 - 8 * q^95 - 4 * q^96 + 11 * q^97 - 5 * q^98 - 4 * q^99

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