LMFDB - Embedded newform 5610.2.a.cg.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:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
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			$-0.339102$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.88501 q^{13} +1.84556 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.21973 q^{19} -1.00000 q^{20} -1.84556 q^{21} +1.00000 q^{22} -5.95030 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.88501 q^{26} -1.00000 q^{27} +1.84556 q^{28} +6.42170 q^{29} +1.00000 q^{30} -1.84556 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.84556 q^{35} +1.00000 q^{36} +8.57614 q^{37} +5.21973 q^{38} +4.88501 q^{39} -1.00000 q^{40} -10.1047 q^{41} -1.84556 q^{42} +1.03945 q^{43} +1.00000 q^{44} -1.00000 q^{45} -5.95030 q^{46} +10.4395 q^{47} -1.00000 q^{48} -3.59390 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.88501 q^{52} +10.1047 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.84556 q^{56} -5.21973 q^{57} +6.42170 q^{58} +10.1306 q^{59} +1.00000 q^{60} -12.5761 q^{61} -1.84556 q^{62} +1.84556 q^{63} +1.00000 q^{64} +4.88501 q^{65} -1.00000 q^{66} -5.21973 q^{67} +1.00000 q^{68} +5.95030 q^{69} -1.84556 q^{70} +7.69113 q^{71} +1.00000 q^{72} +7.77002 q^{73} +8.57614 q^{74} -1.00000 q^{75} +5.21973 q^{76} +1.84556 q^{77} +4.88501 q^{78} -3.79587 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.1047 q^{82} +3.19388 q^{83} -1.84556 q^{84} -1.00000 q^{85} +1.03945 q^{86} -6.42170 q^{87} +1.00000 q^{88} -7.46115 q^{89} -1.00000 q^{90} -9.01560 q^{91} -5.95030 q^{92} +1.84556 q^{93} +10.4395 q^{94} -5.21973 q^{95} -1.00000 q^{96} +8.25918 q^{97} -3.59390 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 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 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	1.84556	0.697557	0.348779	−	0.937205i	$-0.386596\pi$
$7$	1.84556	0.697557	0.348779	+	0.937205i	$0.386596\pi$
$8$	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
$13$	−4.88501	−1.35486	−0.677429	−	0.735588i	$-0.736906\pi$
$13$	−4.88501	−1.35486	−0.677429	+	0.735588i	$0.736906\pi$
$14$	1.84556	0.493248
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	5.21973	1.19749	0.598744	−	0.800940i	$-0.295667\pi$
$19$	5.21973	1.19749	0.598744	+	0.800940i	$0.295667\pi$
$20$	−1.00000	−0.223607
$21$	−1.84556	−0.402735
$22$	1.00000	0.213201
$23$	−5.95030	−1.24072	−0.620362	−	0.784316i	$-0.713014\pi$
$23$	−5.95030	−1.24072	−0.620362	+	0.784316i	$0.713014\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.88501	−0.958029
$27$	−1.00000	−0.192450
$28$	1.84556	0.348779
$29$	6.42170	1.19248	0.596240	−	0.802806i	$-0.296661\pi$
$29$	6.42170	1.19248	0.596240	+	0.802806i	$0.296661\pi$
$30$	1.00000	0.182574
$31$	−1.84556	−0.331473	−0.165736	−	0.986170i	$-0.553000\pi$
$31$	−1.84556	−0.331473	−0.165736	+	0.986170i	$0.553000\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−1.84556	−0.311957
$36$	1.00000	0.166667
$37$	8.57614	1.40991	0.704954	−	0.709253i	$-0.250968\pi$
$37$	8.57614	1.40991	0.704954	+	0.709253i	$0.250968\pi$
$38$	5.21973	0.846752
$39$	4.88501	0.782228
$40$	−1.00000	−0.158114
$41$	−10.1047	−1.57810	−0.789048	−	0.614332i	$-0.789426\pi$
$41$	−10.1047	−1.57810	−0.789048	+	0.614332i	$0.789426\pi$
$42$	−1.84556	−0.284777
$43$	1.03945	0.158514	0.0792571	−	0.996854i	$-0.474745\pi$
$43$	1.03945	0.158514	0.0792571	+	0.996854i	$0.474745\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−5.95030	−0.877324
$47$	10.4395	1.52275	0.761376	−	0.648311i	$-0.224524\pi$
$47$	10.4395	1.52275	0.761376	+	0.648311i	$0.224524\pi$
$48$	−1.00000	−0.144338
$49$	−3.59390	−0.513414
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	−4.88501	−0.677429
$53$	10.1047	1.38799	0.693996	−	0.719979i	$-0.255848\pi$
$53$	10.1047	1.38799	0.693996	+	0.719979i	$0.255848\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	1.84556	0.246624
$57$	−5.21973	−0.691370
$58$	6.42170	0.843211
$59$	10.1306	1.31889	0.659445	−	0.751753i	$-0.270791\pi$
$59$	10.1306	1.31889	0.659445	+	0.751753i	$0.270791\pi$
$60$	1.00000	0.129099
$61$	−12.5761	−1.61021	−0.805105	−	0.593133i	$-0.797891\pi$
$61$	−12.5761	−1.61021	−0.805105	+	0.593133i	$0.797891\pi$
$62$	−1.84556	−0.234387
$63$	1.84556	0.232519
$64$	1.00000	0.125000
$65$	4.88501	0.605911
$66$	−1.00000	−0.123091
$67$	−5.21973	−0.637691	−0.318846	−	0.947807i	$-0.603295\pi$
$67$	−5.21973	−0.637691	−0.318846	+	0.947807i	$0.603295\pi$
$68$	1.00000	0.121268
$69$	5.95030	0.716332
$70$	−1.84556	−0.220587
$71$	7.69113	0.912769	0.456384	−	0.889783i	$-0.349144\pi$
$71$	7.69113	0.912769	0.456384	+	0.889783i	$0.349144\pi$
$72$	1.00000	0.117851
$73$	7.77002	0.909412	0.454706	−	0.890642i	$-0.349744\pi$
$73$	7.77002	0.909412	0.454706	+	0.890642i	$0.349744\pi$
$74$	8.57614	0.996956
$75$	−1.00000	−0.115470
$76$	5.21973	0.598744
$77$	1.84556	0.210321
$78$	4.88501	0.553118
$79$	−3.79587	−0.427068	−0.213534	−	0.976936i	$-0.568497\pi$
$79$	−3.79587	−0.427068	−0.213534	+	0.976936i	$0.568497\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−10.1047	−1.11588
$83$	3.19388	0.350574	0.175287	−	0.984517i	$-0.443915\pi$
$83$	3.19388	0.350574	0.175287	+	0.984517i	$0.443915\pi$
$84$	−1.84556	−0.201367
$85$	−1.00000	−0.108465
$86$	1.03945	0.112086
$87$	−6.42170	−0.688479
$88$	1.00000	0.106600
$89$	−7.46115	−0.790880	−0.395440	−	0.918492i	$-0.629408\pi$
$89$	−7.46115	−0.790880	−0.395440	+	0.918492i	$0.629408\pi$
$90$	−1.00000	−0.105409
$91$	−9.01560	−0.945091
$92$	−5.95030	−0.620362
$93$	1.84556	0.191376
$94$	10.4395	1.07675
$95$	−5.21973	−0.535533
$96$	−1.00000	−0.102062
$97$	8.25918	0.838592	0.419296	−	0.907850i	$-0.362277\pi$
$97$	8.25918	0.838592	0.419296	+	0.907850i	$0.362277\pi$
$98$	−3.59390	−0.363038
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	0.643593	0.0640399	0.0320199	−	0.999487i	$-0.489806\pi$
$101$	0.643593	0.0640399	0.0320199	+	0.999487i	$0.489806\pi$
$102$	−1.00000	−0.0990148
$103$	9.17612	0.904150	0.452075	−	0.891980i	$-0.350684\pi$
$103$	9.17612	0.904150	0.452075	+	0.891980i	$0.350684\pi$
$104$	−4.88501	−0.479015
$105$	1.84556	0.180109
$106$	10.1047	0.981459
$107$	4.73057	0.457322	0.228661	−	0.973506i	$-0.426565\pi$
$107$	4.73057	0.457322	0.228661	+	0.973506i	$0.426565\pi$
$108$	−1.00000	−0.0962250
$109$	−5.55445	−0.532020	−0.266010	−	0.963970i	$-0.585705\pi$
$109$	−5.55445	−0.532020	−0.266010	+	0.963970i	$0.585705\pi$
$110$	−1.00000	−0.0953463
$111$	−8.57614	−0.814011
$112$	1.84556	0.174389
$113$	4.64359	0.436832	0.218416	−	0.975856i	$-0.429911\pi$
$113$	4.64359	0.436832	0.218416	+	0.975856i	$0.429911\pi$
$114$	−5.21973	−0.488872
$115$	5.95030	0.554869
$116$	6.42170	0.596240
$117$	−4.88501	−0.451619
$118$	10.1306	0.932596
$119$	1.84556	0.169183
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−12.5761	−1.13859
$123$	10.1047	0.911114
$124$	−1.84556	−0.165736
$125$	−1.00000	−0.0894427
$126$	1.84556	0.164416
$127$	6.74833	0.598818	0.299409	−	0.954125i	$-0.403211\pi$
$127$	6.74833	0.598818	0.299409	+	0.954125i	$0.403211\pi$
$128$	1.00000	0.0883883
$129$	−1.03945	−0.0915182
$130$	4.88501	0.428444
$131$	−3.19388	−0.279051	−0.139525	−	0.990218i	$-0.544558\pi$
$131$	−3.19388	−0.279051	−0.139525	+	0.990218i	$0.544558\pi$
$132$	−1.00000	−0.0870388
$133$	9.63334	0.835317
$134$	−5.21973	−0.450916
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	15.8456	1.35378	0.676889	−	0.736085i	$-0.263328\pi$
$137$	15.8456	1.35378	0.676889	+	0.736085i	$0.263328\pi$
$138$	5.95030	0.506523
$139$	18.8612	1.59978	0.799891	−	0.600145i	$-0.204890\pi$
$139$	18.8612	1.59978	0.799891	+	0.600145i	$0.204890\pi$
$140$	−1.84556	−0.155979
$141$	−10.4395	−0.879161
$142$	7.69113	0.645425
$143$	−4.88501	−0.408505
$144$	1.00000	0.0833333
$145$	−6.42170	−0.533293
$146$	7.77002	0.643051
$147$	3.59390	0.296420
$148$	8.57614	0.704954
$149$	−15.1203	−1.23871	−0.619353	−	0.785113i	$-0.712605\pi$
$149$	−15.1203	−1.23871	−0.619353	+	0.785113i	$0.712605\pi$
$150$	−1.00000	−0.0816497
$151$	−6.57614	−0.535158	−0.267579	−	0.963536i	$-0.586224\pi$
$151$	−6.57614	−0.535158	−0.267579	+	0.963536i	$0.586224\pi$
$152$	5.21973	0.423376
$153$	1.00000	0.0808452
$154$	1.84556	0.148720
$155$	1.84556	0.148239
$156$	4.88501	0.391114
$157$	−1.79587	−0.143326	−0.0716629	−	0.997429i	$-0.522831\pi$
$157$	−1.79587	−0.143326	−0.0716629	+	0.997429i	$0.522831\pi$
$158$	−3.79587	−0.301983
$159$	−10.1047	−0.801358
$160$	−1.00000	−0.0790569
$161$	−10.9817	−0.865476
$162$	1.00000	0.0785674
$163$	−18.5006	−1.44908	−0.724539	−	0.689234i	$-0.757947\pi$
$163$	−18.5006	−1.44908	−0.724539	+	0.689234i	$0.757947\pi$
$164$	−10.1047	−0.789048
$165$	1.00000	0.0778499
$166$	3.19388	0.247893
$167$	6.07889	0.470399	0.235199	−	0.971947i	$-0.424426\pi$
$167$	6.07889	0.470399	0.235199	+	0.971947i	$0.424426\pi$
$168$	−1.84556	−0.142388
$169$	10.8633	0.835640
$170$	−1.00000	−0.0766965
$171$	5.21973	0.399163
$172$	1.03945	0.0792571
$173$	5.86332	0.445780	0.222890	−	0.974844i	$-0.428451\pi$
$173$	5.86332	0.445780	0.222890	+	0.974844i	$0.428451\pi$
$174$	−6.42170	−0.486828
$175$	1.84556	0.139511
$176$	1.00000	0.0753778
$177$	−10.1306	−0.761461
$178$	−7.46115	−0.559237
$179$	−6.88501	−0.514610	−0.257305	−	0.966330i	$-0.582834\pi$
$179$	−6.88501	−0.514610	−0.257305	+	0.966330i	$0.582834\pi$
$180$	−1.00000	−0.0745356
$181$	9.47891	0.704561	0.352281	−	0.935894i	$-0.385406\pi$
$181$	9.47891	0.704561	0.352281	+	0.935894i	$0.385406\pi$
$182$	−9.01560	−0.668280
$183$	12.5761	0.929655
$184$	−5.95030	−0.438662
$185$	−8.57614	−0.630530
$186$	1.84556	0.135323
$187$	1.00000	0.0731272
$188$	10.4395	0.761376
$189$	−1.84556	−0.134245
$190$	−5.21973	−0.378679
$191$	8.37001	0.605632	0.302816	−	0.953049i	$-0.402073\pi$
$191$	8.37001	0.605632	0.302816	+	0.953049i	$0.402073\pi$
$192$	−1.00000	−0.0721688
$193$	−3.77002	−0.271372	−0.135686	−	0.990752i	$-0.543324\pi$
$193$	−3.77002	−0.271372	−0.135686	+	0.990752i	$0.543324\pi$
$194$	8.25918	0.592974
$195$	−4.88501	−0.349823
$196$	−3.59390	−0.256707
$197$	23.3245	1.66180	0.830900	−	0.556422i	$-0.187826\pi$
$197$	23.3245	1.66180	0.830900	+	0.556422i	$0.187826\pi$
$198$	1.00000	0.0710669
$199$	2.57614	0.182617	0.0913087	−	0.995823i	$-0.470895\pi$
$199$	2.57614	0.182617	0.0913087	+	0.995823i	$0.470895\pi$
$200$	1.00000	0.0707107
$201$	5.21973	0.368171
$202$	0.643593	0.0452830
$203$	11.8517	0.831823
$204$	−1.00000	−0.0700140
$205$	10.1047	0.705746
$206$	9.17612	0.639331
$207$	−5.95030	−0.413575
$208$	−4.88501	−0.338714
$209$	5.21973	0.361056
$210$	1.84556	0.127356
$211$	17.6095	1.21229	0.606144	−	0.795355i	$-0.292716\pi$
$211$	17.6095	1.21229	0.606144	+	0.795355i	$0.292716\pi$
$212$	10.1047	0.693996
$213$	−7.69113	−0.526987
$214$	4.73057	0.323375
$215$	−1.03945	−0.0708897
$216$	−1.00000	−0.0680414
$217$	−3.40610	−0.231221
$218$	−5.55445	−0.376195
$219$	−7.77002	−0.525049
$220$	−1.00000	−0.0674200
$221$	−4.88501	−0.328601
$222$	−8.57614	−0.575593
$223$	19.6156	1.31356	0.656778	−	0.754084i	$-0.271919\pi$
$223$	19.6156	1.31356	0.656778	+	0.754084i	$0.271919\pi$
$224$	1.84556	0.123312
$225$	1.00000	0.0666667
$226$	4.64359	0.308887
$227$	20.3223	1.34884	0.674419	−	0.738348i	$-0.264394\pi$
$227$	20.3223	1.34884	0.674419	+	0.738348i	$0.264394\pi$
$228$	−5.21973	−0.345685
$229$	7.27278	0.480599	0.240299	−	0.970699i	$-0.422754\pi$
$229$	7.27278	0.480599	0.240299	+	0.970699i	$0.422754\pi$
$230$	5.95030	0.392351
$231$	−1.84556	−0.121429
$232$	6.42170	0.421605
$233$	29.1700	1.91099	0.955496	−	0.295003i	$-0.0953208\pi$
$233$	29.1700	1.91099	0.955496	+	0.295003i	$0.0953208\pi$
$234$	−4.88501	−0.319343
$235$	−10.4395	−0.680995
$236$	10.1306	0.659445
$237$	3.79587	0.246568
$238$	1.84556	0.119630
$239$	7.02169	0.454195	0.227098	−	0.973872i	$-0.427076\pi$
$239$	7.02169	0.454195	0.227098	+	0.973872i	$0.427076\pi$
$240$	1.00000	0.0645497
$241$	−16.5680	−1.06724	−0.533621	−	0.845724i	$-0.679169\pi$
$241$	−16.5680	−1.06724	−0.533621	+	0.845724i	$0.679169\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−12.5761	−0.805105
$245$	3.59390	0.229606
$246$	10.1047	0.644255
$247$	−25.4984	−1.62243
$248$	−1.84556	−0.117193
$249$	−3.19388	−0.202404
$250$	−1.00000	−0.0632456
$251$	−21.6333	−1.36548	−0.682742	−	0.730659i	$-0.739213\pi$
$251$	−21.6333	−1.36548	−0.682742	+	0.730659i	$0.739213\pi$
$252$	1.84556	0.116260
$253$	−5.95030	−0.374092
$254$	6.74833	0.423428
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	8.29111	0.517186	0.258593	−	0.965986i	$-0.416741\pi$
$257$	8.29111	0.517186	0.258593	+	0.965986i	$0.416741\pi$
$258$	−1.03945	−0.0647131
$259$	15.8278	0.983492
$260$	4.88501	0.302955
$261$	6.42170	0.397493
$262$	−3.19388	−0.197319
$263$	18.9978	1.17146	0.585728	−	0.810507i	$-0.300809\pi$
$263$	18.9978	1.17146	0.585728	+	0.810507i	$0.300809\pi$
$264$	−1.00000	−0.0615457
$265$	−10.1047	−0.620729
$266$	9.63334	0.590658
$267$	7.46115	0.456615
$268$	−5.21973	−0.318846
$269$	−15.0156	−0.915517	−0.457759	−	0.889077i	$-0.651348\pi$
$269$	−15.0156	−0.915517	−0.457759	+	0.889077i	$0.651348\pi$
$270$	1.00000	0.0608581
$271$	−13.0394	−0.792090	−0.396045	−	0.918231i	$-0.629618\pi$
$271$	−13.0394	−0.792090	−0.396045	+	0.918231i	$0.629618\pi$
$272$	1.00000	0.0606339
$273$	9.01560	0.545649
$274$	15.8456	0.957265
$275$	1.00000	0.0603023
$276$	5.95030	0.358166
$277$	23.3618	1.40367	0.701836	−	0.712339i	$-0.252364\pi$
$277$	23.3618	1.40367	0.701836	+	0.712339i	$0.252364\pi$
$278$	18.8612	1.13122
$279$	−1.84556	−0.110491
$280$	−1.84556	−0.110294
$281$	24.5006	1.46158	0.730791	−	0.682601i	$-0.239151\pi$
$281$	24.5006	1.46158	0.730791	+	0.682601i	$0.239151\pi$
$282$	−10.4395	−0.621661
$283$	−22.2884	−1.32491	−0.662453	−	0.749103i	$-0.730485\pi$
$283$	−22.2884	−1.32491	−0.662453	+	0.749103i	$0.730485\pi$
$284$	7.69113	0.456384
$285$	5.21973	0.309190
$286$	−4.88501	−0.288857
$287$	−18.6489	−1.10081
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−6.42170	−0.377095
$291$	−8.25918	−0.484161
$292$	7.77002	0.454706
$293$	−26.5318	−1.55000	−0.775002	−	0.631959i	$-0.782251\pi$
$293$	−26.5318	−1.55000	−0.775002	+	0.631959i	$0.782251\pi$
$294$	3.59390	0.209600
$295$	−10.1306	−0.589826
$296$	8.57614	0.498478
$297$	−1.00000	−0.0580259
$298$	−15.1203	−0.875898
$299$	29.0673	1.68100
$300$	−1.00000	−0.0577350
$301$	1.91836	0.110573
$302$	−6.57614	−0.378414
$303$	−0.643593	−0.0369734
$304$	5.21973	0.299372
$305$	12.5761	0.720108
$306$	1.00000	0.0571662
$307$	−19.5917	−1.11816	−0.559080	−	0.829114i	$-0.688845\pi$
$307$	−19.5917	−1.11816	−0.559080	+	0.829114i	$0.688845\pi$
$308$	1.84556	0.105161
$309$	−9.17612	−0.522011
$310$	1.84556	0.104821
$311$	6.43946	0.365148	0.182574	−	0.983192i	$-0.441557\pi$
$311$	6.43946	0.365148	0.182574	+	0.983192i	$0.441557\pi$
$312$	4.88501	0.276559
$313$	7.07138	0.399698	0.199849	−	0.979827i	$-0.435955\pi$
$313$	7.07138	0.399698	0.199849	+	0.979827i	$0.435955\pi$
$314$	−1.79587	−0.101347
$315$	−1.84556	−0.103986
$316$	−3.79587	−0.213534
$317$	−24.5523	−1.37899	−0.689497	−	0.724289i	$-0.742168\pi$
$317$	−24.5523	−1.37899	−0.689497	+	0.724289i	$0.742168\pi$
$318$	−10.1047	−0.566646
$319$	6.42170	0.359546
$320$	−1.00000	−0.0559017
$321$	−4.73057	−0.264035
$322$	−10.9817	−0.611984
$323$	5.21973	0.290434
$324$	1.00000	0.0555556
$325$	−4.88501	−0.270972
$326$	−18.5006	−1.02465
$327$	5.55445	0.307162
$328$	−10.1047	−0.557941
$329$	19.2667	1.06221
$330$	1.00000	0.0550482
$331$	24.6312	1.35385	0.676926	−	0.736051i	$-0.263312\pi$
$331$	24.6312	1.35385	0.676926	+	0.736051i	$0.263312\pi$
$332$	3.19388	0.175287
$333$	8.57614	0.469969
$334$	6.07889	0.332622
$335$	5.21973	0.285184
$336$	−1.84556	−0.100684
$337$	−35.1523	−1.91487	−0.957433	−	0.288655i	$-0.906792\pi$
$337$	−35.1523	−1.91487	−0.957433	+	0.288655i	$0.906792\pi$
$338$	10.8633	0.590887
$339$	−4.64359	−0.252205
$340$	−1.00000	−0.0542326
$341$	−1.84556	−0.0999429
$342$	5.21973	0.282251
$343$	−19.5517	−1.05569
$344$	1.03945	0.0560432
$345$	−5.95030	−0.320354
$346$	5.86332	0.315214
$347$	1.56054	0.0837742	0.0418871	−	0.999122i	$-0.486663\pi$
$347$	1.56054	0.0837742	0.0418871	+	0.999122i	$0.486663\pi$
$348$	−6.42170	−0.344239
$349$	2.73866	0.146597	0.0732986	−	0.997310i	$-0.476647\pi$
$349$	2.73866	0.146597	0.0732986	+	0.997310i	$0.476647\pi$
$350$	1.84556	0.0986495
$351$	4.88501	0.260743
$352$	1.00000	0.0533002
$353$	−5.30671	−0.282448	−0.141224	−	0.989978i	$-0.545104\pi$
$353$	−5.30671	−0.282448	−0.141224	+	0.989978i	$0.545104\pi$
$354$	−10.1306	−0.538435
$355$	−7.69113	−0.408203
$356$	−7.46115	−0.395440
$357$	−1.84556	−0.0976776
$358$	−6.88501	−0.363884
$359$	36.1101	1.90582	0.952909	−	0.303257i	$-0.0980742\pi$
$359$	36.1101	1.90582	0.952909	+	0.303257i	$0.0980742\pi$
$360$	−1.00000	−0.0527046
$361$	8.24558	0.433978
$362$	9.47891	0.498200
$363$	−1.00000	−0.0524864
$364$	−9.01560	−0.472546
$365$	−7.77002	−0.406701
$366$	12.5761	0.657365
$367$	−5.39192	−0.281456	−0.140728	−	0.990048i	$-0.544944\pi$
$367$	−5.39192	−0.281456	−0.140728	+	0.990048i	$0.544944\pi$
$368$	−5.95030	−0.310181
$369$	−10.1047	−0.526032
$370$	−8.57614	−0.445852
$371$	18.6489	0.968205
$372$	1.84556	0.0956880
$373$	26.8789	1.39174	0.695869	−	0.718169i	$-0.255019\pi$
$373$	26.8789	1.39174	0.695869	+	0.718169i	$0.255019\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	10.4395	0.538374
$377$	−31.3701	−1.61564
$378$	−1.84556	−0.0949255
$379$	5.90670	0.303407	0.151703	−	0.988426i	$-0.451524\pi$
$379$	5.90670	0.303407	0.151703	+	0.988426i	$0.451524\pi$
$380$	−5.21973	−0.267766
$381$	−6.74833	−0.345728
$382$	8.37001	0.428247
$383$	1.82171	0.0930852	0.0465426	−	0.998916i	$-0.485180\pi$
$383$	1.82171	0.0930852	0.0465426	+	0.998916i	$0.485180\pi$
$384$	−1.00000	−0.0510310
$385$	−1.84556	−0.0940586
$386$	−3.77002	−0.191889
$387$	1.03945	0.0528380
$388$	8.25918	0.419296
$389$	−1.10890	−0.0562234	−0.0281117	−	0.999605i	$-0.508949\pi$
$389$	−1.10890	−0.0562234	−0.0281117	+	0.999605i	$0.508949\pi$
$390$	−4.88501	−0.247362
$391$	−5.95030	−0.300920
$392$	−3.59390	−0.181519
$393$	3.19388	0.161110
$394$	23.3245	1.17507
$395$	3.79587	0.190991
$396$	1.00000	0.0502519
$397$	33.5917	1.68592	0.842960	−	0.537976i	$-0.180811\pi$
$397$	33.5917	1.68592	0.842960	+	0.537976i	$0.180811\pi$
$398$	2.57614	0.129130
$399$	−9.63334	−0.482270
$400$	1.00000	0.0500000
$401$	38.1856	1.90690	0.953450	−	0.301552i	$-0.0975048\pi$
$401$	38.1856	1.90690	0.953450	+	0.301552i	$0.0975048\pi$
$402$	5.21973	0.260336
$403$	9.01560	0.449099
$404$	0.643593	0.0320199
$405$	−1.00000	−0.0496904
$406$	11.8517	0.588188
$407$	8.57614	0.425103
$408$	−1.00000	−0.0495074
$409$	8.13059	0.402032	0.201016	−	0.979588i	$-0.435576\pi$
$409$	8.13059	0.402032	0.201016	+	0.979588i	$0.435576\pi$
$410$	10.1047	0.499038
$411$	−15.8456	−0.781604
$412$	9.17612	0.452075
$413$	18.6966	0.920001
$414$	−5.95030	−0.292441
$415$	−3.19388	−0.156782
$416$	−4.88501	−0.239507
$417$	−18.8612	−0.923635
$418$	5.21973	0.255305
$419$	−32.6312	−1.59414	−0.797069	−	0.603889i	$-0.793617\pi$
$419$	−32.6312	−1.59414	−0.797069	+	0.603889i	$0.793617\pi$
$420$	1.84556	0.0900543
$421$	−8.93670	−0.435548	−0.217774	−	0.975999i	$-0.569880\pi$
$421$	−8.93670	−0.435548	−0.217774	+	0.975999i	$0.569880\pi$
$422$	17.6095	0.857217
$423$	10.4395	0.507584
$424$	10.1047	0.490730
$425$	1.00000	0.0485071
$426$	−7.69113	−0.372636
$427$	−23.2101	−1.12321
$428$	4.73057	0.228661
$429$	4.88501	0.235851
$430$	−1.03945	−0.0501266
$431$	7.01360	0.337833	0.168917	−	0.985630i	$-0.445973\pi$
$431$	7.01360	0.337833	0.168917	+	0.985630i	$0.445973\pi$
$432$	−1.00000	−0.0481125
$433$	−23.6706	−1.13754	−0.568769	−	0.822497i	$-0.692580\pi$
$433$	−23.6706	−1.13754	−0.568769	+	0.822497i	$0.692580\pi$
$434$	−3.40610	−0.163498
$435$	6.42170	0.307897
$436$	−5.55445	−0.266010
$437$	−31.0590	−1.48575
$438$	−7.77002	−0.371266
$439$	−16.3781	−0.781684	−0.390842	−	0.920458i	$-0.627816\pi$
$439$	−16.3781	−0.781684	−0.390842	+	0.920458i	$0.627816\pi$
$440$	−1.00000	−0.0476731
$441$	−3.59390	−0.171138
$442$	−4.88501	−0.232356
$443$	30.9659	1.47123	0.735617	−	0.677398i	$-0.236892\pi$
$443$	30.9659	1.47123	0.735617	+	0.677398i	$0.236892\pi$
$444$	−8.57614	−0.407005
$445$	7.46115	0.353692
$446$	19.6156	0.928825
$447$	15.1203	0.715167
$448$	1.84556	0.0871947
$449$	8.94614	0.422195	0.211097	−	0.977465i	$-0.432296\pi$
$449$	8.94614	0.422195	0.211097	+	0.977465i	$0.432296\pi$
$450$	1.00000	0.0471405
$451$	−10.1047	−0.475814
$452$	4.64359	0.218416
$453$	6.57614	0.308974
$454$	20.3223	0.953773
$455$	9.01560	0.422658
$456$	−5.21973	−0.244436
$457$	3.63334	0.169961	0.0849803	−	0.996383i	$-0.472917\pi$
$457$	3.63334	0.169961	0.0849803	+	0.996383i	$0.472917\pi$
$458$	7.27278	0.339835
$459$	−1.00000	−0.0466760
$460$	5.95030	0.277434
$461$	−23.7754	−1.10733	−0.553665	−	0.832740i	$-0.686771\pi$
$461$	−23.7754	−1.10733	−0.553665	+	0.832740i	$0.686771\pi$
$462$	−1.84556	−0.0858634
$463$	36.0728	1.67645	0.838223	−	0.545328i	$-0.183595\pi$
$463$	36.0728	1.67645	0.838223	+	0.545328i	$0.183595\pi$
$464$	6.42170	0.298120
$465$	−1.84556	−0.0855860
$466$	29.1700	1.35128
$467$	13.4081	0.620453	0.310226	−	0.950663i	$-0.399595\pi$
$467$	13.4081	0.620453	0.310226	+	0.950663i	$0.399595\pi$
$468$	−4.88501	−0.225810
$469$	−9.63334	−0.444826
$470$	−10.4395	−0.481536
$471$	1.79587	0.0827492
$472$	10.1306	0.466298
$473$	1.03945	0.0477938
$474$	3.79587	0.174350
$475$	5.21973	0.239498
$476$	1.84556	0.0845913
$477$	10.1047	0.462664
$478$	7.02169	0.321165
$479$	21.0592	0.962219	0.481110	−	0.876660i	$-0.340234\pi$
$479$	21.0592	0.962219	0.481110	+	0.876660i	$0.340234\pi$
$480$	1.00000	0.0456435
$481$	−41.8945	−1.91023
$482$	−16.5680	−0.754654
$483$	10.9817	0.499683
$484$	1.00000	0.0454545
$485$	−8.25918	−0.375030
$486$	−1.00000	−0.0453609
$487$	−22.1481	−1.00363	−0.501813	−	0.864976i	$-0.667334\pi$
$487$	−22.1481	−1.00363	−0.501813	+	0.864976i	$0.667334\pi$
$488$	−12.5761	−0.569295
$489$	18.5006	0.836626
$490$	3.59390	0.162356
$491$	−11.5864	−0.522886	−0.261443	−	0.965219i	$-0.584198\pi$
$491$	−11.5864	−0.522886	−0.261443	+	0.965219i	$0.584198\pi$
$492$	10.1047	0.455557
$493$	6.42170	0.289219
$494$	−25.4984	−1.14723
$495$	−1.00000	−0.0449467
$496$	−1.84556	−0.0828682
$497$	14.1945	0.636709
$498$	−3.19388	−0.143121
$499$	−30.9223	−1.38427	−0.692136	−	0.721767i	$-0.743330\pi$
$499$	−30.9223	−1.38427	−0.692136	+	0.721767i	$0.743330\pi$
$500$	−1.00000	−0.0447214
$501$	−6.07889	−0.271585
$502$	−21.6333	−0.965543
$503$	−36.4190	−1.62384	−0.811921	−	0.583768i	$-0.801578\pi$
$503$	−36.4190	−1.62384	−0.811921	+	0.583768i	$0.801578\pi$
$504$	1.84556	0.0822079
$505$	−0.643593	−0.0286395
$506$	−5.95030	−0.264523
$507$	−10.8633	−0.482457
$508$	6.74833	0.299409
$509$	−6.26117	−0.277522	−0.138761	−	0.990326i	$-0.544312\pi$
$509$	−6.26117	−0.277522	−0.138761	+	0.990326i	$0.544312\pi$
$510$	1.00000	0.0442807
$511$	14.3401	0.634367
$512$	1.00000	0.0441942
$513$	−5.21973	−0.230457
$514$	8.29111	0.365705
$515$	−9.17612	−0.404348
$516$	−1.03945	−0.0457591
$517$	10.4395	0.459127
$518$	15.8278	0.695434
$519$	−5.86332	−0.257371
$520$	4.88501	0.214222
$521$	6.34616	0.278030	0.139015	−	0.990290i	$-0.455606\pi$
$521$	6.34616	0.278030	0.139015	+	0.990290i	$0.455606\pi$
$522$	6.42170	0.281070
$523$	13.9184	0.608608	0.304304	−	0.952575i	$-0.401576\pi$
$523$	13.9184	0.608608	0.304304	+	0.952575i	$0.401576\pi$
$524$	−3.19388	−0.139525
$525$	−1.84556	−0.0805470
$526$	18.9978	0.828345
$527$	−1.84556	−0.0803940
$528$	−1.00000	−0.0435194
$529$	12.4061	0.539396
$530$	−10.1047	−0.438922
$531$	10.1306	0.439630
$532$	9.63334	0.417658
$533$	49.3618	2.13809
$534$	7.46115	0.322875
$535$	−4.73057	−0.204521
$536$	−5.21973	−0.225458
$537$	6.88501	0.297110
$538$	−15.0156	−0.647368
$539$	−3.59390	−0.154800
$540$	1.00000	0.0430331
$541$	8.74833	0.376120	0.188060	−	0.982158i	$-0.439780\pi$
$541$	8.74833	0.376120	0.188060	+	0.982158i	$0.439780\pi$
$542$	−13.0394	−0.560092
$543$	−9.47891	−0.406779
$544$	1.00000	0.0428746
$545$	5.55445	0.237926
$546$	9.01560	0.385832
$547$	0.706723	0.0302173	0.0151086	−	0.999886i	$-0.495191\pi$
$547$	0.706723	0.0302173	0.0151086	+	0.999886i	$0.495191\pi$
$548$	15.8456	0.676889
$549$	−12.5761	−0.536736
$550$	1.00000	0.0426401
$551$	33.5195	1.42798
$552$	5.95030	0.253262
$553$	−7.00551	−0.297905
$554$	23.3618	0.992546
$555$	8.57614	0.364037
$556$	18.8612	0.799891
$557$	−23.5223	−0.996671	−0.498336	−	0.866984i	$-0.666055\pi$
$557$	−23.5223	−0.996671	−0.498336	+	0.866984i	$0.666055\pi$
$558$	−1.84556	−0.0781289
$559$	−5.07771	−0.214764
$560$	−1.84556	−0.0779893
$561$	−1.00000	−0.0422200
$562$	24.5006	1.03350
$563$	4.08498	0.172162	0.0860808	−	0.996288i	$-0.472566\pi$
$563$	4.08498	0.172162	0.0860808	+	0.996288i	$0.472566\pi$
$564$	−10.4395	−0.439581
$565$	−4.64359	−0.195357
$566$	−22.2884	−0.936850
$567$	1.84556	0.0775064
$568$	7.69113	0.322713
$569$	11.4239	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$569$	11.4239	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$570$	5.21973	0.218630
$571$	−19.3184	−0.808449	−0.404224	−	0.914660i	$-0.632459\pi$
$571$	−19.3184	−0.808449	−0.404224	+	0.914660i	$0.632459\pi$
$572$	−4.88501	−0.204253
$573$	−8.37001	−0.349662
$574$	−18.6489	−0.778392
$575$	−5.95030	−0.248145
$576$	1.00000	0.0416667
$577$	10.2095	0.425026	0.212513	−	0.977158i	$-0.431835\pi$
$577$	10.2095	0.425026	0.212513	+	0.977158i	$0.431835\pi$
$578$	1.00000	0.0415945
$579$	3.77002	0.156677
$580$	−6.42170	−0.266647
$581$	5.89451	0.244546
$582$	−8.25918	−0.342354
$583$	10.1047	0.418496
$584$	7.77002	0.321526
$585$	4.88501	0.201970
$586$	−26.5318	−1.09602
$587$	4.16587	0.171944	0.0859720	−	0.996298i	$-0.472600\pi$
$587$	4.16587	0.171944	0.0859720	+	0.996298i	$0.472600\pi$
$588$	3.59390	0.148210
$589$	−9.63334	−0.396935
$590$	−10.1306	−0.417070
$591$	−23.3245	−0.959440
$592$	8.57614	0.352477
$593$	14.2612	0.585636	0.292818	−	0.956168i	$-0.405407\pi$
$593$	14.2612	0.585636	0.292818	+	0.956168i	$0.405407\pi$
$594$	−1.00000	−0.0410305
$595$	−1.84556	−0.0756607
$596$	−15.1203	−0.619353
$597$	−2.57614	−0.105434
$598$	29.0673	1.18865
$599$	1.26333	0.0516185	0.0258092	−	0.999667i	$-0.491784\pi$
$599$	1.26333	0.0516185	0.0258092	+	0.999667i	$0.491784\pi$
$600$	−1.00000	−0.0408248
$601$	−4.98975	−0.203536	−0.101768	−	0.994808i	$-0.532450\pi$
$601$	−4.98975	−0.203536	−0.101768	+	0.994808i	$0.532450\pi$
$602$	1.91836	0.0781867
$603$	−5.21973	−0.212564
$604$	−6.57614	−0.267579
$605$	−1.00000	−0.0406558
$606$	−0.643593	−0.0261442
$607$	−44.3340	−1.79946	−0.899730	−	0.436446i	$-0.856237\pi$
$607$	−44.3340	−1.79946	−0.899730	+	0.436446i	$0.856237\pi$
$608$	5.21973	0.211688
$609$	−11.8517	−0.480253
$610$	12.5761	0.509193
$611$	−50.9969	−2.06311
$612$	1.00000	0.0404226
$613$	−34.4190	−1.39017	−0.695084	−	0.718928i	$-0.744633\pi$
$613$	−34.4190	−1.39017	−0.695084	+	0.718928i	$0.744633\pi$
$614$	−19.5917	−0.790658
$615$	−10.1047	−0.407462
$616$	1.84556	0.0743599
$617$	4.02585	0.162074	0.0810372	−	0.996711i	$-0.474177\pi$
$617$	4.02585	0.162074	0.0810372	+	0.996711i	$0.474177\pi$
$618$	−9.17612	−0.369118
$619$	−5.06330	−0.203511	−0.101756	−	0.994809i	$-0.532446\pi$
$619$	−5.06330	−0.203511	−0.101756	+	0.994809i	$0.532446\pi$
$620$	1.84556	0.0741196
$621$	5.95030	0.238777
$622$	6.43946	0.258199
$623$	−13.7700	−0.551684
$624$	4.88501	0.195557
$625$	1.00000	0.0400000
$626$	7.07138	0.282629
$627$	−5.21973	−0.208456
$628$	−1.79587	−0.0716629
$629$	8.57614	0.341953
$630$	−1.84556	−0.0735290
$631$	5.13610	0.204465	0.102232	−	0.994761i	$-0.467401\pi$
$631$	5.13610	0.204465	0.102232	+	0.994761i	$0.467401\pi$
$632$	−3.79587	−0.150991
$633$	−17.6095	−0.699914
$634$	−24.5523	−0.975096
$635$	−6.74833	−0.267799
$636$	−10.1047	−0.400679
$637$	17.5562	0.695603
$638$	6.42170	0.254238
$639$	7.69113	0.304256
$640$	−1.00000	−0.0395285
$641$	−49.5890	−1.95865	−0.979324	−	0.202300i	$-0.935159\pi$
$641$	−49.5890	−1.95865	−0.979324	+	0.202300i	$0.935159\pi$
$642$	−4.73057	−0.186701
$643$	−47.3957	−1.86910	−0.934552	−	0.355827i	$-0.884199\pi$
$643$	−47.3957	−1.86910	−0.934552	+	0.355827i	$0.884199\pi$
$644$	−10.9817	−0.432738
$645$	1.03945	0.0409282
$646$	5.21973	0.205368
$647$	28.1101	1.10512	0.552561	−	0.833473i	$-0.313651\pi$
$647$	28.1101	1.10512	0.552561	+	0.833473i	$0.313651\pi$
$648$	1.00000	0.0392837
$649$	10.1306	0.397660
$650$	−4.88501	−0.191606
$651$	3.40610	0.133496
$652$	−18.5006	−0.724539
$653$	−20.7739	−0.812947	−0.406474	−	0.913662i	$-0.633242\pi$
$653$	−20.7739	−0.812947	−0.406474	+	0.913662i	$0.633242\pi$
$654$	5.55445	0.217196
$655$	3.19388	0.124795
$656$	−10.1047	−0.394524
$657$	7.77002	0.303137
$658$	19.2667	0.751094
$659$	−36.8870	−1.43691	−0.718457	−	0.695572i	$-0.755151\pi$
$659$	−36.8870	−1.43691	−0.718457	+	0.695572i	$0.755151\pi$
$660$	1.00000	0.0389249
$661$	36.6345	1.42492	0.712459	−	0.701714i	$-0.247581\pi$
$661$	36.6345	1.42492	0.712459	+	0.701714i	$0.247581\pi$
$662$	24.6312	0.957318
$663$	4.88501	0.189718
$664$	3.19388	0.123947
$665$	−9.63334	−0.373565
$666$	8.57614	0.332319
$667$	−38.2111	−1.47954
$668$	6.07889	0.235199
$669$	−19.6156	−0.758382
$670$	5.21973	0.201656
$671$	−12.5761	−0.485496
$672$	−1.84556	−0.0711942
$673$	−37.2312	−1.43516	−0.717578	−	0.696478i	$-0.754749\pi$
$673$	−37.2312	−1.43516	−0.717578	+	0.696478i	$0.754749\pi$
$674$	−35.1523	−1.35401
$675$	−1.00000	−0.0384900
$676$	10.8633	0.417820
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	−4.64359	−0.178336
$679$	15.2428	0.584966
$680$	−1.00000	−0.0383482
$681$	−20.3223	−0.778752
$682$	−1.84556	−0.0706703
$683$	−39.3201	−1.50454	−0.752272	−	0.658853i	$-0.771042\pi$
$683$	−39.3201	−1.50454	−0.752272	+	0.658853i	$0.771042\pi$
$684$	5.21973	0.199581
$685$	−15.8456	−0.605428
$686$	−19.5517	−0.746488
$687$	−7.27278	−0.277474
$688$	1.03945	0.0396285
$689$	−49.3618	−1.88053
$690$	−5.95030	−0.226524
$691$	−38.8373	−1.47744	−0.738720	−	0.674012i	$-0.764570\pi$
$691$	−38.8373	−1.47744	−0.738720	+	0.674012i	$0.764570\pi$
$692$	5.86332	0.222890
$693$	1.84556	0.0701072
$694$	1.56054	0.0592373
$695$	−18.8612	−0.715445
$696$	−6.42170	−0.243414
$697$	−10.1047	−0.382744
$698$	2.73866	0.103660
$699$	−29.1700	−1.10331
$700$	1.84556	0.0697557
$701$	43.9848	1.66128	0.830642	−	0.556806i	$-0.187973\pi$
$701$	43.9848	1.66128	0.830642	+	0.556806i	$0.187973\pi$
$702$	4.88501	0.184373
$703$	44.7651	1.68835
$704$	1.00000	0.0376889
$705$	10.4395	0.393173
$706$	−5.30671	−0.199721
$707$	1.18779	0.0446715
$708$	−10.1306	−0.380731
$709$	7.28719	0.273676	0.136838	−	0.990593i	$-0.456306\pi$
$709$	7.28719	0.273676	0.136838	+	0.990593i	$0.456306\pi$
$710$	−7.69113	−0.288643
$711$	−3.79587	−0.142356
$712$	−7.46115	−0.279618
$713$	10.9817	0.411266
$714$	−1.84556	−0.0690685
$715$	4.88501	0.182689
$716$	−6.88501	−0.257305
$717$	−7.02169	−0.262230
$718$	36.1101	1.34762
$719$	−30.6651	−1.14362	−0.571808	−	0.820388i	$-0.693758\pi$
$719$	−30.6651	−1.14362	−0.571808	+	0.820388i	$0.693758\pi$
$720$	−1.00000	−0.0372678
$721$	16.9351	0.630697
$722$	8.24558	0.306869
$723$	16.5680	0.616172
$724$	9.47891	0.352281
$725$	6.42170	0.238496
$726$	−1.00000	−0.0371135
$727$	−3.57830	−0.132712	−0.0663559	−	0.997796i	$-0.521137\pi$
$727$	−3.57830	−0.132712	−0.0663559	+	0.997796i	$0.521137\pi$
$728$	−9.01560	−0.334140
$729$	1.00000	0.0370370
$730$	−7.77002	−0.287581
$731$	1.03945	0.0384453
$732$	12.5761	0.464827
$733$	6.17220	0.227975	0.113988	−	0.993482i	$-0.463638\pi$
$733$	6.17220	0.227975	0.113988	+	0.993482i	$0.463638\pi$
$734$	−5.39192	−0.199020
$735$	−3.59390	−0.132563
$736$	−5.95030	−0.219331
$737$	−5.21973	−0.192271
$738$	−10.1047	−0.371961
$739$	−23.2986	−0.857054	−0.428527	−	0.903529i	$-0.640967\pi$
$739$	−23.2986	−0.857054	−0.428527	+	0.903529i	$0.640967\pi$
$740$	−8.57614	−0.315265
$741$	25.4984	0.936708
$742$	18.6489	0.684624
$743$	6.71281	0.246269	0.123135	−	0.992390i	$-0.460705\pi$
$743$	6.71281	0.246269	0.123135	+	0.992390i	$0.460705\pi$
$744$	1.84556	0.0676616
$745$	15.1203	0.553966
$746$	26.8789	0.984107
$747$	3.19388	0.116858
$748$	1.00000	0.0365636
$749$	8.73057	0.319008
$750$	1.00000	0.0365148
$751$	−48.8568	−1.78281	−0.891406	−	0.453206i	$-0.850280\pi$
$751$	−48.8568	−1.78281	−0.891406	+	0.453206i	$0.850280\pi$
$752$	10.4395	0.380688
$753$	21.6333	0.788363
$754$	−31.3701	−1.14243
$755$	6.57614	0.239330
$756$	−1.84556	−0.0671225
$757$	2.98640	0.108543	0.0542713	−	0.998526i	$-0.482716\pi$
$757$	2.98640	0.108543	0.0542713	+	0.998526i	$0.482716\pi$
$758$	5.90670	0.214541
$759$	5.95030	0.215982
$760$	−5.21973	−0.189339
$761$	4.00335	0.145121	0.0725607	−	0.997364i	$-0.476883\pi$
$761$	4.00335	0.145121	0.0725607	+	0.997364i	$0.476883\pi$
$762$	−6.74833	−0.244466
$763$	−10.2511	−0.371114
$764$	8.37001	0.302816
$765$	−1.00000	−0.0361551
$766$	1.82171	0.0658212
$767$	−49.4880	−1.78691
$768$	−1.00000	−0.0360844
$769$	8.49115	0.306199	0.153099	−	0.988211i	$-0.451075\pi$
$769$	8.49115	0.306199	0.153099	+	0.988211i	$0.451075\pi$
$770$	−1.84556	−0.0665095
$771$	−8.29111	−0.298597
$772$	−3.77002	−0.135686
$773$	−11.5803	−0.416514	−0.208257	−	0.978074i	$-0.566779\pi$
$773$	−11.5803	−0.416514	−0.208257	+	0.978074i	$0.566779\pi$
$774$	1.03945	0.0373621
$775$	−1.84556	−0.0662946
$776$	8.25918	0.296487
$777$	−15.8278	−0.567819
$778$	−1.10890	−0.0397559
$779$	−52.7440	−1.88975
$780$	−4.88501	−0.174911
$781$	7.69113	0.275210
$782$	−5.95030	−0.212782
$783$	−6.42170	−0.229493
$784$	−3.59390	−0.128353
$785$	1.79587	0.0640972
$786$	3.19388	0.113922
$787$	−32.6905	−1.16529	−0.582646	−	0.812726i	$-0.697983\pi$
$787$	−32.6905	−1.16529	−0.582646	+	0.812726i	$0.697983\pi$
$788$	23.3245	0.830900
$789$	−18.9978	−0.676341
$790$	3.79587	0.135051
$791$	8.57004	0.304716
$792$	1.00000	0.0355335
$793$	61.4346	2.18160
$794$	33.5917	1.19213
$795$	10.1047	0.358378
$796$	2.57614	0.0913087
$797$	15.7898	0.559303	0.279651	−	0.960102i	$-0.409781\pi$
$797$	15.7898	0.559303	0.279651	+	0.960102i	$0.409781\pi$
$798$	−9.63334	−0.341017
$799$	10.4395	0.369322
$800$	1.00000	0.0353553
$801$	−7.46115	−0.263627
$802$	38.1856	1.34838
$803$	7.77002	0.274198
$804$	5.21973	0.184086
$805$	10.9817	0.387053
$806$	9.01560	0.317561
$807$	15.0156	0.528574
$808$	0.643593	0.0226415
$809$	41.8704	1.47209	0.736043	−	0.676935i	$-0.236692\pi$
$809$	41.8704	1.47209	0.736043	+	0.676935i	$0.236692\pi$
$810$	−1.00000	−0.0351364
$811$	−11.1089	−0.390086	−0.195043	−	0.980795i	$-0.562485\pi$
$811$	−11.1089	−0.390086	−0.195043	+	0.980795i	$0.562485\pi$
$812$	11.8517	0.415912
$813$	13.0394	0.457313
$814$	8.57614	0.300593
$815$	18.5006	0.648048
$816$	−1.00000	−0.0350070
$817$	5.42563	0.189819
$818$	8.13059	0.284279
$819$	−9.01560	−0.315030
$820$	10.1047	0.352873
$821$	18.0490	0.629913	0.314956	−	0.949106i	$-0.398010\pi$
$821$	18.0490	0.629913	0.314956	+	0.949106i	$0.398010\pi$
$822$	−15.8456	−0.552677
$823$	−20.0215	−0.697906	−0.348953	−	0.937140i	$-0.613463\pi$
$823$	−20.0215	−0.697906	−0.348953	+	0.937140i	$0.613463\pi$
$824$	9.17612	0.319665
$825$	−1.00000	−0.0348155
$826$	18.6966	0.650539
$827$	−23.4434	−0.815206	−0.407603	−	0.913159i	$-0.633635\pi$
$827$	−23.4434	−0.815206	−0.407603	+	0.913159i	$0.633635\pi$
$828$	−5.95030	−0.206787
$829$	19.9584	0.693184	0.346592	−	0.938016i	$-0.387339\pi$
$829$	19.9584	0.693184	0.346592	+	0.938016i	$0.387339\pi$
$830$	−3.19388	−0.110861
$831$	−23.3618	−0.810410
$832$	−4.88501	−0.169357
$833$	−3.59390	−0.124521
$834$	−18.8612	−0.653109
$835$	−6.07889	−0.210369
$836$	5.21973	0.180528
$837$	1.84556	0.0637920
$838$	−32.6312	−1.12723
$839$	−32.1740	−1.11077	−0.555384	−	0.831594i	$-0.687429\pi$
$839$	−32.1740	−1.11077	−0.555384	+	0.831594i	$0.687429\pi$
$840$	1.84556	0.0636780
$841$	12.2382	0.422008
$842$	−8.93670	−0.307979
$843$	−24.5006	−0.843845
$844$	17.6095	0.606144
$845$	−10.8633	−0.373710
$846$	10.4395	0.358916
$847$	1.84556	0.0634143
$848$	10.1047	0.346998
$849$	22.2884	0.764935
$850$	1.00000	0.0342997
$851$	−51.0306	−1.74931
$852$	−7.69113	−0.263494
$853$	−19.6257	−0.671970	−0.335985	−	0.941867i	$-0.609069\pi$
$853$	−19.6257	−0.671970	−0.335985	+	0.941867i	$0.609069\pi$
$854$	−23.2101	−0.794232
$855$	−5.21973	−0.178511
$856$	4.73057	0.161688
$857$	−9.25502	−0.316145	−0.158073	−	0.987427i	$-0.550528\pi$
$857$	−9.25502	−0.316145	−0.158073	+	0.987427i	$0.550528\pi$
$858$	4.88501	0.166771
$859$	−47.3957	−1.61712	−0.808560	−	0.588414i	$-0.799753\pi$
$859$	−47.3957	−1.61712	−0.808560	+	0.588414i	$0.799753\pi$
$860$	−1.03945	−0.0354448
$861$	18.6489	0.635554
$862$	7.01360	0.238884
$863$	20.8789	0.710727	0.355363	−	0.934728i	$-0.384357\pi$
$863$	20.8789	0.710727	0.355363	+	0.934728i	$0.384357\pi$
$864$	−1.00000	−0.0340207
$865$	−5.86332	−0.199359
$866$	−23.6706	−0.804361
$867$	−1.00000	−0.0339618
$868$	−3.40610	−0.115611
$869$	−3.79587	−0.128766
$870$	6.42170	0.217716
$871$	25.4984	0.863981
$872$	−5.55445	−0.188097
$873$	8.25918	0.279531
$874$	−31.0590	−1.05059
$875$	−1.84556	−0.0623914
$876$	−7.77002	−0.262525
$877$	−12.8612	−0.434290	−0.217145	−	0.976139i	$-0.569675\pi$
$877$	−12.8612	−0.434290	−0.217145	+	0.976139i	$0.569675\pi$
$878$	−16.3781	−0.552734
$879$	26.5318	0.894895
$880$	−1.00000	−0.0337100
$881$	−31.9184	−1.07536	−0.537679	−	0.843150i	$-0.680699\pi$
$881$	−31.9184	−1.07536	−0.537679	+	0.843150i	$0.680699\pi$
$882$	−3.59390	−0.121013
$883$	−8.73866	−0.294079	−0.147040	−	0.989131i	$-0.546975\pi$
$883$	−8.73866	−0.294079	−0.147040	+	0.989131i	$0.546975\pi$
$884$	−4.88501	−0.164301
$885$	10.1306	0.340536
$886$	30.9659	1.04032
$887$	3.59173	0.120599	0.0602993	−	0.998180i	$-0.480794\pi$
$887$	3.59173	0.120599	0.0602993	+	0.998180i	$0.480794\pi$
$888$	−8.57614	−0.287796
$889$	12.4545	0.417710
$890$	7.46115	0.250098
$891$	1.00000	0.0335013
$892$	19.6156	0.656778
$893$	54.4912	1.82348
$894$	15.1203	0.505700
$895$	6.88501	0.230141
$896$	1.84556	0.0616559
$897$	−29.0673	−0.970529
$898$	8.94614	0.298537
$899$	−11.8517	−0.395275
$900$	1.00000	0.0333333
$901$	10.1047	0.336638
$902$	−10.1047	−0.336451
$903$	−1.91836	−0.0638392
$904$	4.64359	0.154444
$905$	−9.47891	−0.315089
$906$	6.57614	0.218478
$907$	−21.0911	−0.700320	−0.350160	−	0.936690i	$-0.613873\pi$
$907$	−21.0911	−0.700320	−0.350160	+	0.936690i	$0.613873\pi$
$908$	20.3223	0.674419
$909$	0.643593	0.0213466
$910$	9.01560	0.298864
$911$	−31.6434	−1.04839	−0.524197	−	0.851597i	$-0.675634\pi$
$911$	−31.6434	−1.04839	−0.524197	+	0.851597i	$0.675634\pi$
$912$	−5.21973	−0.172843
$913$	3.19388	0.105702
$914$	3.63334	0.120180
$915$	−12.5761	−0.415754
$916$	7.27278	0.240299
$917$	−5.89451	−0.194654
$918$	−1.00000	−0.0330049
$919$	−12.4590	−0.410984	−0.205492	−	0.978659i	$-0.565879\pi$
$919$	−12.4590	−0.410984	−0.205492	+	0.978659i	$0.565879\pi$
$920$	5.95030	0.196176
$921$	19.5917	0.645570
$922$	−23.7754	−0.783000
$923$	−37.5712	−1.23667
$924$	−1.84556	−0.0607146
$925$	8.57614	0.281982
$926$	36.0728	1.18543
$927$	9.17612	0.301383
$928$	6.42170	0.210803
$929$	8.11892	0.266373	0.133187	−	0.991091i	$-0.457479\pi$
$929$	8.11892	0.266373	0.133187	+	0.991091i	$0.457479\pi$
$930$	−1.84556	−0.0605184
$931$	−18.7592	−0.614807
$932$	29.1700	0.955496
$933$	−6.43946	−0.210818
$934$	13.4081	0.438726
$935$	−1.00000	−0.0327035
$936$	−4.88501	−0.159672
$937$	3.63334	0.118696	0.0593481	−	0.998237i	$-0.481098\pi$
$937$	3.63334	0.118696	0.0593481	+	0.998237i	$0.481098\pi$
$938$	−9.63334	−0.314540
$939$	−7.07138	−0.230766
$940$	−10.4395	−0.340498
$941$	−1.77834	−0.0579721	−0.0289861	−	0.999580i	$-0.509228\pi$
$941$	−1.77834	−0.0579721	−0.0289861	+	0.999580i	$0.509228\pi$
$942$	1.79587	0.0585125
$943$	60.1263	1.95798
$944$	10.1306	0.329722
$945$	1.84556	0.0600362
$946$	1.03945	0.0337953
$947$	12.8434	0.417354	0.208677	−	0.977985i	$-0.433084\pi$
$947$	12.8434	0.417354	0.208677	+	0.977985i	$0.433084\pi$
$948$	3.79587	0.123284
$949$	−37.9566	−1.23212
$950$	5.21973	0.169350
$951$	24.5523	0.796162
$952$	1.84556	0.0598151
$953$	49.4568	1.60206	0.801032	−	0.598622i	$-0.204285\pi$
$953$	49.4568	1.60206	0.801032	+	0.598622i	$0.204285\pi$
$954$	10.1047	0.327153
$955$	−8.37001	−0.270847
$956$	7.02169	0.227098
$957$	−6.42170	−0.207584
$958$	21.0592	0.680392
$959$	29.2440	0.944338
$960$	1.00000	0.0322749
$961$	−27.5939	−0.890126
$962$	−41.8945	−1.35073
$963$	4.73057	0.152441
$964$	−16.5680	−0.533621
$965$	3.77002	0.121361
$966$	10.9817	0.353329
$967$	28.1101	0.903959	0.451980	−	0.892028i	$-0.350718\pi$
$967$	28.1101	0.903959	0.451980	+	0.892028i	$0.350718\pi$
$968$	1.00000	0.0321412
$969$	−5.21973	−0.167682
$970$	−8.25918	−0.265186
$971$	−30.5244	−0.979576	−0.489788	−	0.871842i	$-0.662926\pi$
$971$	−30.5244	−0.979576	−0.489788	+	0.871842i	$0.662926\pi$
$972$	−1.00000	−0.0320750
$973$	34.8095	1.11594
$974$	−22.1481	−0.709671
$975$	4.88501	0.156446
$976$	−12.5761	−0.402552
$977$	−4.84949	−0.155149	−0.0775745	−	0.996987i	$-0.524718\pi$
$977$	−4.84949	−0.155149	−0.0775745	+	0.996987i	$0.524718\pi$
$978$	18.5006	0.591584
$979$	−7.46115	−0.238459
$980$	3.59390	0.114803
$981$	−5.55445	−0.177340
$982$	−11.5864	−0.369736
$983$	16.9702	0.541266	0.270633	−	0.962683i	$-0.412767\pi$
$983$	16.9702	0.541266	0.270633	+	0.962683i	$0.412767\pi$
$984$	10.1047	0.322127
$985$	−23.3245	−0.743179
$986$	6.42170	0.204509
$987$	−19.2667	−0.613265
$988$	−25.4984	−0.811213
$989$	−6.18502	−0.196672
$990$	−1.00000	−0.0317821
$991$	−0.249505	−0.00792579	−0.00396290	−	0.999992i	$-0.501261\pi$
$991$	−0.249505	−0.00792579	−0.00396290	+	0.999992i	$0.501261\pi$
$992$	−1.84556	−0.0585967
$993$	−24.6312	−0.781647
$994$	14.1945	0.450221
$995$	−2.57614	−0.0816690
$996$	−3.19388	−0.101202
$997$	−34.4055	−1.08963	−0.544817	−	0.838555i	$-0.683401\pi$
$997$	−34.4055	−1.08963	−0.544817	+	0.838555i	$0.683401\pi$
$998$	−30.9223	−0.978828
$999$	−8.57614	−0.271337

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cg.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.84556 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.88501 q^{13} +1.84556 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.21973 q^{19} -1.00000 q^{20} -1.84556 q^{21} +1.00000 q^{22} -5.95030 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.88501 q^{26} -1.00000 q^{27} +1.84556 q^{28} +6.42170 q^{29} +1.00000 q^{30} -1.84556 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.84556 q^{35} +1.00000 q^{36} +8.57614 q^{37} +5.21973 q^{38} +4.88501 q^{39} -1.00000 q^{40} -10.1047 q^{41} -1.84556 q^{42} +1.03945 q^{43} +1.00000 q^{44} -1.00000 q^{45} -5.95030 q^{46} +10.4395 q^{47} -1.00000 q^{48} -3.59390 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.88501 q^{52} +10.1047 q^{53} -1.00000 q^{54} -1.00000 q^{55} +1.84556 q^{56} -5.21973 q^{57} +6.42170 q^{58} +10.1306 q^{59} +1.00000 q^{60} -12.5761 q^{61} -1.84556 q^{62} +1.84556 q^{63} +1.00000 q^{64} +4.88501 q^{65} -1.00000 q^{66} -5.21973 q^{67} +1.00000 q^{68} +5.95030 q^{69} -1.84556 q^{70} +7.69113 q^{71} +1.00000 q^{72} +7.77002 q^{73} +8.57614 q^{74} -1.00000 q^{75} +5.21973 q^{76} +1.84556 q^{77} +4.88501 q^{78} -3.79587 q^{79} -1.00000 q^{80} +1.00000 q^{81} -10.1047 q^{82} +3.19388 q^{83} -1.84556 q^{84} -1.00000 q^{85} +1.03945 q^{86} -6.42170 q^{87} +1.00000 q^{88} -7.46115 q^{89} -1.00000 q^{90} -9.01560 q^{91} -5.95030 q^{92} +1.84556 q^{93} +10.4395 q^{94} -5.21973 q^{95} -1.00000 q^{96} +8.25918 q^{97} -3.59390 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

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