LMFDB - Embedded newform 5610.2.a.cg.1.4

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			1.4
Root			$-2.67673$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.16490 q^{13} +5.13277 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.60629 q^{19} -1.00000 q^{20} -5.13277 q^{21} +1.00000 q^{22} +7.63841 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.16490 q^{26} -1.00000 q^{27} +5.13277 q^{28} +9.23342 q^{29} +1.00000 q^{30} -5.13277 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -5.13277 q^{35} +1.00000 q^{36} +8.10064 q^{37} -4.60629 q^{38} -2.16490 q^{39} -1.00000 q^{40} +6.77118 q^{41} -5.13277 q^{42} -9.29767 q^{43} +1.00000 q^{44} -1.00000 q^{45} +7.63841 q^{46} -9.21257 q^{47} -1.00000 q^{48} +19.3453 q^{49} +1.00000 q^{50} -1.00000 q^{51} +2.16490 q^{52} -6.77118 q^{53} -1.00000 q^{54} -1.00000 q^{55} +5.13277 q^{56} +4.60629 q^{57} +9.23342 q^{58} -2.94703 q^{59} +1.00000 q^{60} -12.1006 q^{61} -5.13277 q^{62} +5.13277 q^{63} +1.00000 q^{64} -2.16490 q^{65} -1.00000 q^{66} +4.60629 q^{67} +1.00000 q^{68} -7.63841 q^{69} -5.13277 q^{70} +14.2655 q^{71} +1.00000 q^{72} -6.32980 q^{73} +8.10064 q^{74} -1.00000 q^{75} -4.60629 q^{76} +5.13277 q^{77} -2.16490 q^{78} +6.50564 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.77118 q^{82} -10.4304 q^{83} -5.13277 q^{84} -1.00000 q^{85} -9.29767 q^{86} -9.23342 q^{87} +1.00000 q^{88} +0.0642530 q^{89} -1.00000 q^{90} +11.1119 q^{91} +7.63841 q^{92} +5.13277 q^{93} -9.21257 q^{94} +4.60629 q^{95} -1.00000 q^{96} -11.9040 q^{97} +19.3453 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	5.13277	1.94001	0.970003	−	0.243094i	$-0.0781625\pi$
$7$	5.13277	1.94001	0.970003	+	0.243094i	$0.0781625\pi$
$8$	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
$13$	2.16490	0.600435	0.300217	−	0.953871i	$-0.402941\pi$
$13$	2.16490	0.600435	0.300217	+	0.953871i	$0.402941\pi$
$14$	5.13277	1.37179
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−4.60629	−1.05675	−0.528377	−	0.849010i	$-0.677199\pi$
$19$	−4.60629	−1.05675	−0.528377	+	0.849010i	$0.677199\pi$
$20$	−1.00000	−0.223607
$21$	−5.13277	−1.12006
$22$	1.00000	0.213201
$23$	7.63841	1.59272	0.796360	−	0.604824i	$-0.206756\pi$
$23$	7.63841	1.59272	0.796360	+	0.604824i	$0.206756\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.16490	0.424571
$27$	−1.00000	−0.192450
$28$	5.13277	0.970003
$29$	9.23342	1.71460	0.857301	−	0.514815i	$-0.172139\pi$
$29$	9.23342	1.71460	0.857301	+	0.514815i	$0.172139\pi$
$30$	1.00000	0.182574
$31$	−5.13277	−0.921873	−0.460936	−	0.887433i	$-0.652486\pi$
$31$	−5.13277	−0.921873	−0.460936	+	0.887433i	$0.652486\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−5.13277	−0.867597
$36$	1.00000	0.166667
$37$	8.10064	1.33174	0.665869	−	0.746069i	$-0.268061\pi$
$37$	8.10064	1.33174	0.665869	+	0.746069i	$0.268061\pi$
$38$	−4.60629	−0.747238
$39$	−2.16490	−0.346661
$40$	−1.00000	−0.158114
$41$	6.77118	1.05748	0.528741	−	0.848783i	$-0.322664\pi$
$41$	6.77118	1.05748	0.528741	+	0.848783i	$0.322664\pi$
$42$	−5.13277	−0.792004
$43$	−9.29767	−1.41788	−0.708941	−	0.705268i	$-0.750827\pi$
$43$	−9.29767	−1.41788	−0.708941	+	0.705268i	$0.750827\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	7.63841	1.12622
$47$	−9.21257	−1.34379	−0.671896	−	0.740646i	$-0.734520\pi$
$47$	−9.21257	−1.34379	−0.671896	+	0.740646i	$0.734520\pi$
$48$	−1.00000	−0.144338
$49$	19.3453	2.76362
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	2.16490	0.300217
$53$	−6.77118	−0.930094	−0.465047	−	0.885286i	$-0.653963\pi$
$53$	−6.77118	−0.930094	−0.465047	+	0.885286i	$0.653963\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	5.13277	0.685895
$57$	4.60629	0.610117
$58$	9.23342	1.21241
$59$	−2.94703	−0.383670	−0.191835	−	0.981427i	$-0.561444\pi$
$59$	−2.94703	−0.383670	−0.191835	+	0.981427i	$0.561444\pi$
$60$	1.00000	0.129099
$61$	−12.1006	−1.54933	−0.774664	−	0.632373i	$-0.782081\pi$
$61$	−12.1006	−1.54933	−0.774664	+	0.632373i	$0.782081\pi$
$62$	−5.13277	−0.651863
$63$	5.13277	0.646668
$64$	1.00000	0.125000
$65$	−2.16490	−0.268523
$66$	−1.00000	−0.123091
$67$	4.60629	0.562747	0.281374	−	0.959598i	$-0.409210\pi$
$67$	4.60629	0.562747	0.281374	+	0.959598i	$0.409210\pi$
$68$	1.00000	0.121268
$69$	−7.63841	−0.919557
$70$	−5.13277	−0.613484
$71$	14.2655	1.69301	0.846504	−	0.532382i	$-0.178703\pi$
$71$	14.2655	1.69301	0.846504	+	0.532382i	$0.178703\pi$
$72$	1.00000	0.117851
$73$	−6.32980	−0.740847	−0.370423	−	0.928863i	$-0.620787\pi$
$73$	−6.32980	−0.740847	−0.370423	+	0.928863i	$0.620787\pi$
$74$	8.10064	0.941681
$75$	−1.00000	−0.115470
$76$	−4.60629	−0.528377
$77$	5.13277	0.584934
$78$	−2.16490	−0.245126
$79$	6.50564	0.731942	0.365971	−	0.930626i	$-0.380737\pi$
$79$	6.50564	0.731942	0.365971	+	0.930626i	$0.380737\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	6.77118	0.747752
$83$	−10.4304	−1.14489	−0.572445	−	0.819943i	$-0.694005\pi$
$83$	−10.4304	−1.14489	−0.572445	+	0.819943i	$0.694005\pi$
$84$	−5.13277	−0.560031
$85$	−1.00000	−0.108465
$86$	−9.29767	−1.00259
$87$	−9.23342	−0.989926
$88$	1.00000	0.106600
$89$	0.0642530	0.00681080	0.00340540	−	0.999994i	$-0.498916\pi$
$89$	0.0642530	0.00681080	0.00340540	+	0.999994i	$0.498916\pi$
$90$	−1.00000	−0.105409
$91$	11.1119	1.16485
$92$	7.63841	0.796360
$93$	5.13277	0.532244
$94$	−9.21257	−0.950204
$95$	4.60629	0.472595
$96$	−1.00000	−0.102062
$97$	−11.9040	−1.20866	−0.604332	−	0.796733i	$-0.706560\pi$
$97$	−11.9040	−1.20866	−0.604332	+	0.796733i	$0.706560\pi$
$98$	19.3453	1.95417
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−8.70693	−0.866372	−0.433186	−	0.901305i	$-0.642611\pi$
$101$	−8.70693	−0.866372	−0.433186	+	0.901305i	$0.642611\pi$
$102$	−1.00000	−0.0990148
$103$	18.0155	1.77512	0.887562	−	0.460688i	$-0.152397\pi$
$103$	18.0155	1.77512	0.887562	+	0.460688i	$0.152397\pi$
$104$	2.16490	0.212286
$105$	5.13277	0.500907
$106$	−6.77118	−0.657676
$107$	0.967873	0.0935679	0.0467839	−	0.998905i	$-0.485103\pi$
$107$	0.967873	0.0935679	0.0467839	+	0.998905i	$0.485103\pi$
$108$	−1.00000	−0.0962250
$109$	7.04767	0.675045	0.337522	−	0.941318i	$-0.390411\pi$
$109$	7.04767	0.675045	0.337522	+	0.941318i	$0.390411\pi$
$110$	−1.00000	−0.0953463
$111$	−8.10064	−0.768879
$112$	5.13277	0.485001
$113$	−4.70693	−0.442791	−0.221395	−	0.975184i	$-0.571061\pi$
$113$	−4.70693	−0.442791	−0.221395	+	0.975184i	$0.571061\pi$
$114$	4.60629	0.431418
$115$	−7.63841	−0.712286
$116$	9.23342	0.857301
$117$	2.16490	0.200145
$118$	−2.94703	−0.271296
$119$	5.13277	0.470520
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−12.1006	−1.09554
$123$	−6.77118	−0.610537
$124$	−5.13277	−0.460936
$125$	−1.00000	−0.0894427
$126$	5.13277	0.457264
$127$	−19.4781	−1.72840	−0.864202	−	0.503146i	$-0.832176\pi$
$127$	−19.4781	−1.72840	−0.864202	+	0.503146i	$0.832176\pi$
$128$	1.00000	0.0883883
$129$	9.29767	0.818614
$130$	−2.16490	−0.189874
$131$	10.4304	0.911312	0.455656	−	0.890156i	$-0.349405\pi$
$131$	10.4304	0.911312	0.455656	+	0.890156i	$0.349405\pi$
$132$	−1.00000	−0.0870388
$133$	−23.6430	−2.05011
$134$	4.60629	0.397922
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	19.1328	1.63462	0.817311	−	0.576196i	$-0.195464\pi$
$137$	19.1328	1.63462	0.817311	+	0.576196i	$0.195464\pi$
$138$	−7.63841	−0.650225
$139$	2.02084	0.171406	0.0857029	−	0.996321i	$-0.472686\pi$
$139$	2.02084	0.171406	0.0857029	+	0.996321i	$0.472686\pi$
$140$	−5.13277	−0.433798
$141$	9.21257	0.775838
$142$	14.2655	1.19714
$143$	2.16490	0.181038
$144$	1.00000	0.0833333
$145$	−9.23342	−0.766794
$146$	−6.32980	−0.523858
$147$	−19.3453	−1.59558
$148$	8.10064	0.665869
$149$	21.8831	1.79273	0.896367	−	0.443312i	$-0.146197\pi$
$149$	21.8831	1.79273	0.896367	+	0.443312i	$0.146197\pi$
$150$	−1.00000	−0.0816497
$151$	−6.10064	−0.496463	−0.248232	−	0.968701i	$-0.579849\pi$
$151$	−6.10064	−0.496463	−0.248232	+	0.968701i	$0.579849\pi$
$152$	−4.60629	−0.373619
$153$	1.00000	0.0808452
$154$	5.13277	0.413611
$155$	5.13277	0.412274
$156$	−2.16490	−0.173331
$157$	8.50564	0.678824	0.339412	−	0.940638i	$-0.389772\pi$
$157$	8.50564	0.678824	0.339412	+	0.940638i	$0.389772\pi$
$158$	6.50564	0.517561
$159$	6.77118	0.536990
$160$	−1.00000	−0.0790569
$161$	39.2062	3.08988
$162$	1.00000	0.0785674
$163$	−0.638078	−0.0499781	−0.0249890	−	0.999688i	$-0.507955\pi$
$163$	−0.638078	−0.0499781	−0.0249890	+	0.999688i	$0.507955\pi$
$164$	6.77118	0.528741
$165$	1.00000	0.0778499
$166$	−10.4304	−0.809559
$167$	−14.5953	−1.12942	−0.564711	−	0.825289i	$-0.691012\pi$
$167$	−14.5953	−1.12942	−0.564711	+	0.825289i	$0.691012\pi$
$168$	−5.13277	−0.396002
$169$	−8.31322	−0.639478
$170$	−1.00000	−0.0766965
$171$	−4.60629	−0.352251
$172$	−9.29767	−0.708941
$173$	−13.3132	−1.01219	−0.506093	−	0.862479i	$-0.668911\pi$
$173$	−13.3132	−1.01219	−0.506093	+	0.862479i	$0.668911\pi$
$174$	−9.23342	−0.699983
$175$	5.13277	0.388001
$176$	1.00000	0.0753778
$177$	2.94703	0.221512
$178$	0.0642530	0.00481597
$179$	0.164898	0.0123251	0.00616253	−	0.999981i	$-0.498038\pi$
$179$	0.164898	0.0123251	0.00616253	+	0.999981i	$0.498038\pi$
$180$	−1.00000	−0.0745356
$181$	−20.5102	−1.52451	−0.762257	−	0.647274i	$-0.775909\pi$
$181$	−20.5102	−1.52451	−0.762257	+	0.647274i	$0.775909\pi$
$182$	11.1119	0.823671
$183$	12.1006	0.894505
$184$	7.63841	0.563111
$185$	−8.10064	−0.595571
$186$	5.13277	0.376353
$187$	1.00000	0.0731272
$188$	−9.21257	−0.671896
$189$	−5.13277	−0.373354
$190$	4.60629	0.334175
$191$	3.58511	0.259409	0.129705	−	0.991553i	$-0.458597\pi$
$191$	3.58511	0.259409	0.129705	+	0.991553i	$0.458597\pi$
$192$	−1.00000	−0.0721688
$193$	10.3298	0.743555	0.371777	−	0.928322i	$-0.378748\pi$
$193$	10.3298	0.743555	0.371777	+	0.928322i	$0.378748\pi$
$194$	−11.9040	−0.854654
$195$	2.16490	0.155032
$196$	19.3453	1.38181
$197$	−3.37747	−0.240635	−0.120317	−	0.992735i	$-0.538391\pi$
$197$	−3.37747	−0.240635	−0.120317	+	0.992735i	$0.538391\pi$
$198$	1.00000	0.0710669
$199$	2.10064	0.148911	0.0744554	−	0.997224i	$-0.476278\pi$
$199$	2.10064	0.148911	0.0744554	+	0.997224i	$0.476278\pi$
$200$	1.00000	0.0707107
$201$	−4.60629	−0.324902
$202$	−8.70693	−0.612618
$203$	47.3930	3.32634
$204$	−1.00000	−0.0700140
$205$	−6.77118	−0.472920
$206$	18.0155	1.25520
$207$	7.63841	0.530906
$208$	2.16490	0.150109
$209$	−4.60629	−0.318623
$210$	5.13277	0.354195
$211$	−25.4573	−1.75255	−0.876275	−	0.481811i	$-0.839979\pi$
$211$	−25.4573	−1.75255	−0.876275	+	0.481811i	$0.839979\pi$
$212$	−6.77118	−0.465047
$213$	−14.2655	−0.977459
$214$	0.967873	0.0661625
$215$	9.29767	0.634096
$216$	−1.00000	−0.0680414
$217$	−26.3453	−1.78844
$218$	7.04767	0.477329
$219$	6.32980	0.427728
$220$	−1.00000	−0.0674200
$221$	2.16490	0.145627
$222$	−8.10064	−0.543680
$223$	8.80298	0.589491	0.294745	−	0.955576i	$-0.404765\pi$
$223$	8.80298	0.589491	0.294745	+	0.955576i	$0.404765\pi$
$224$	5.13277	0.342948
$225$	1.00000	0.0666667
$226$	−4.70693	−0.313100
$227$	−4.04341	−0.268370	−0.134185	−	0.990956i	$-0.542842\pi$
$227$	−4.04341	−0.268370	−0.134185	+	0.990956i	$0.542842\pi$
$228$	4.60629	0.305059
$229$	−27.0258	−1.78591	−0.892957	−	0.450142i	$-0.851373\pi$
$229$	−27.0258	−1.78591	−0.892957	+	0.450142i	$0.851373\pi$
$230$	−7.63841	−0.503662
$231$	−5.13277	−0.337712
$232$	9.23342	0.606203
$233$	5.75530	0.377042	0.188521	−	0.982069i	$-0.439631\pi$
$233$	5.75530	0.377042	0.188521	+	0.982069i	$0.439631\pi$
$234$	2.16490	0.141524
$235$	9.21257	0.600962
$236$	−2.94703	−0.191835
$237$	−6.50564	−0.422587
$238$	5.13277	0.332708
$239$	19.1483	1.23860	0.619301	−	0.785154i	$-0.287416\pi$
$239$	19.1483	1.23860	0.619301	+	0.785154i	$0.287416\pi$
$240$	1.00000	0.0645497
$241$	10.1695	0.655075	0.327537	−	0.944838i	$-0.393781\pi$
$241$	10.1695	0.655075	0.327537	+	0.944838i	$0.393781\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−12.1006	−0.774664
$245$	−19.3453	−1.23593
$246$	−6.77118	−0.431715
$247$	−9.97214	−0.634512
$248$	−5.13277	−0.325931
$249$	10.4304	0.661002
$250$	−1.00000	−0.0632456
$251$	11.6430	0.734900	0.367450	−	0.930043i	$-0.380231\pi$
$251$	11.6430	0.734900	0.367450	+	0.930043i	$0.380231\pi$
$252$	5.13277	0.323334
$253$	7.63841	0.480223
$254$	−19.4781	−1.22217
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	24.1804	1.50833	0.754167	−	0.656682i	$-0.228041\pi$
$257$	24.1804	1.50833	0.754167	+	0.656682i	$0.228041\pi$
$258$	9.29767	0.578848
$259$	41.5788	2.58358
$260$	−2.16490	−0.134261
$261$	9.23342	0.571534
$262$	10.4304	0.644395
$263$	21.3341	1.31551	0.657757	−	0.753230i	$-0.271505\pi$
$263$	21.3341	1.31551	0.657757	+	0.753230i	$0.271505\pi$
$264$	−1.00000	−0.0615457
$265$	6.77118	0.415951
$266$	−23.6430	−1.44965
$267$	−0.0642530	−0.00393222
$268$	4.60629	0.281374
$269$	5.11193	0.311680	0.155840	−	0.987782i	$-0.450192\pi$
$269$	5.11193	0.311680	0.155840	+	0.987782i	$0.450192\pi$
$270$	1.00000	0.0608581
$271$	−2.70233	−0.164155	−0.0820774	−	0.996626i	$-0.526155\pi$
$271$	−2.70233	−0.164155	−0.0820774	+	0.996626i	$0.526155\pi$
$272$	1.00000	0.0606339
$273$	−11.1119	−0.672524
$274$	19.1328	1.15585
$275$	1.00000	0.0603023
$276$	−7.63841	−0.459778
$277$	−11.3411	−0.681419	−0.340710	−	0.940169i	$-0.610667\pi$
$277$	−11.3411	−0.681419	−0.340710	+	0.940169i	$0.610667\pi$
$278$	2.02084	0.121202
$279$	−5.13277	−0.307291
$280$	−5.13277	−0.306742
$281$	6.63808	0.395995	0.197997	−	0.980203i	$-0.436556\pi$
$281$	6.63808	0.395995	0.197997	+	0.980203i	$0.436556\pi$
$282$	9.21257	0.548601
$283$	32.1377	1.91039	0.955194	−	0.295980i	$-0.0956461\pi$
$283$	32.1377	1.91039	0.955194	+	0.295980i	$0.0956461\pi$
$284$	14.2655	0.846504
$285$	−4.60629	−0.272853
$286$	2.16490	0.128013
$287$	34.7549	2.05152
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−9.23342	−0.542205
$291$	11.9040	0.697822
$292$	−6.32980	−0.370423
$293$	31.5858	1.84526	0.922630	−	0.385685i	$-0.126035\pi$
$293$	31.5858	1.84526	0.922630	+	0.385685i	$0.126035\pi$
$294$	−19.3453	−1.12824
$295$	2.94703	0.171583
$296$	8.10064	0.470840
$297$	−1.00000	−0.0580259
$298$	21.8831	1.26765
$299$	16.5364	0.956324
$300$	−1.00000	−0.0577350
$301$	−47.7228	−2.75070
$302$	−6.10064	−0.351053
$303$	8.70693	0.500200
$304$	−4.60629	−0.264189
$305$	12.1006	0.692881
$306$	1.00000	0.0571662
$307$	1.01128	0.0577169	0.0288584	−	0.999584i	$-0.490813\pi$
$307$	1.01128	0.0577169	0.0288584	+	0.999584i	$0.490813\pi$
$308$	5.13277	0.292467
$309$	−18.0155	−1.02487
$310$	5.13277	0.291522
$311$	−13.2126	−0.749216	−0.374608	−	0.927183i	$-0.622223\pi$
$311$	−13.2126	−0.749216	−0.374608	+	0.927183i	$0.622223\pi$
$312$	−2.16490	−0.122563
$313$	32.7867	1.85322	0.926608	−	0.376029i	$-0.122711\pi$
$313$	32.7867	1.85322	0.926608	+	0.376029i	$0.122711\pi$
$314$	8.50564	0.480001
$315$	−5.13277	−0.289199
$316$	6.50564	0.365971
$317$	−14.2864	−0.802403	−0.401202	−	0.915990i	$-0.631407\pi$
$317$	−14.2864	−0.802403	−0.401202	+	0.915990i	$0.631407\pi$
$318$	6.77118	0.379709
$319$	9.23342	0.516972
$320$	−1.00000	−0.0559017
$321$	−0.967873	−0.0540214
$322$	39.2062	2.18488
$323$	−4.60629	−0.256301
$324$	1.00000	0.0555556
$325$	2.16490	0.120087
$326$	−0.638078	−0.0353398
$327$	−7.04767	−0.389737
$328$	6.77118	0.373876
$329$	−47.2860	−2.60696
$330$	1.00000	0.0550482
$331$	−6.30895	−0.346771	−0.173386	−	0.984854i	$-0.555471\pi$
$331$	−6.30895	−0.346771	−0.173386	+	0.984854i	$0.555471\pi$
$332$	−10.4304	−0.572445
$333$	8.10064	0.443913
$334$	−14.5953	−0.798621
$335$	−4.60629	−0.251668
$336$	−5.13277	−0.280016
$337$	−34.2013	−1.86306	−0.931531	−	0.363661i	$-0.881527\pi$
$337$	−34.2013	−1.86306	−0.931531	+	0.363661i	$0.881527\pi$
$338$	−8.31322	−0.452179
$339$	4.70693	0.255645
$340$	−1.00000	−0.0542326
$341$	−5.13277	−0.277955
$342$	−4.60629	−0.249079
$343$	63.3658	3.42143
$344$	−9.29767	−0.501297
$345$	7.63841	0.411238
$346$	−13.3132	−0.715723
$347$	21.2126	1.13875	0.569375	−	0.822078i	$-0.307185\pi$
$347$	21.2126	1.13875	0.569375	+	0.822078i	$0.307185\pi$
$348$	−9.23342	−0.494963
$349$	25.2380	1.35096	0.675480	−	0.737378i	$-0.263936\pi$
$349$	25.2380	1.35096	0.675480	+	0.737378i	$0.263936\pi$
$350$	5.13277	0.274358
$351$	−2.16490	−0.115554
$352$	1.00000	0.0533002
$353$	−1.06852	−0.0568715	−0.0284358	−	0.999596i	$-0.509053\pi$
$353$	−1.06852	−0.0568715	−0.0284358	+	0.999596i	$0.509053\pi$
$354$	2.94703	0.156633
$355$	−14.2655	−0.757136
$356$	0.0642530	0.00340540
$357$	−5.13277	−0.271655
$358$	0.164898	0.00871513
$359$	−24.8192	−1.30991	−0.654953	−	0.755669i	$-0.727312\pi$
$359$	−24.8192	−1.30991	−0.654953	+	0.755669i	$0.727312\pi$
$360$	−1.00000	−0.0527046
$361$	2.21787	0.116730
$362$	−20.5102	−1.07799
$363$	−1.00000	−0.0524864
$364$	11.1119	0.582423
$365$	6.32980	0.331317
$366$	12.1006	0.632511
$367$	30.1850	1.57565	0.787823	−	0.615901i	$-0.211208\pi$
$367$	30.1850	1.57565	0.787823	+	0.615901i	$0.211208\pi$
$368$	7.63841	0.398180
$369$	6.77118	0.352494
$370$	−8.10064	−0.421132
$371$	−34.7549	−1.80439
$372$	5.13277	0.266122
$373$	−12.4251	−0.643350	−0.321675	−	0.946850i	$-0.604246\pi$
$373$	−12.4251	−0.643350	−0.321675	+	0.946850i	$0.604246\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−9.21257	−0.475102
$377$	19.9894	1.02951
$378$	−5.13277	−0.264001
$379$	10.9834	0.564180	0.282090	−	0.959388i	$-0.408972\pi$
$379$	10.9834	0.564180	0.282090	+	0.959388i	$0.408972\pi$
$380$	4.60629	0.236297
$381$	19.4781	0.997894
$382$	3.58511	0.183430
$383$	−4.68149	−0.239213	−0.119606	−	0.992821i	$-0.538163\pi$
$383$	−4.68149	−0.239213	−0.119606	+	0.992821i	$0.538163\pi$
$384$	−1.00000	−0.0510310
$385$	−5.13277	−0.261590
$386$	10.3298	0.525773
$387$	−9.29767	−0.472627
$388$	−11.9040	−0.604332
$389$	24.0953	1.22168	0.610841	−	0.791753i	$-0.290831\pi$
$389$	24.0953	1.22168	0.610841	+	0.791753i	$0.290831\pi$
$390$	2.16490	0.109624
$391$	7.63841	0.386291
$392$	19.3453	0.977087
$393$	−10.4304	−0.526146
$394$	−3.37747	−0.170154
$395$	−6.50564	−0.327334
$396$	1.00000	0.0502519
$397$	12.9887	0.651885	0.325943	−	0.945390i	$-0.394318\pi$
$397$	12.9887	0.651885	0.325943	+	0.945390i	$0.394318\pi$
$398$	2.10064	0.105296
$399$	23.6430	1.18363
$400$	1.00000	0.0500000
$401$	−5.35662	−0.267497	−0.133749	−	0.991015i	$-0.542701\pi$
$401$	−5.35662	−0.267497	−0.133749	+	0.991015i	$0.542701\pi$
$402$	−4.60629	−0.229741
$403$	−11.1119	−0.553524
$404$	−8.70693	−0.433186
$405$	−1.00000	−0.0496904
$406$	47.3930	2.35208
$407$	8.10064	0.401534
$408$	−1.00000	−0.0495074
$409$	−4.94703	−0.244615	−0.122307	−	0.992492i	$-0.539029\pi$
$409$	−4.94703	−0.244615	−0.122307	+	0.992492i	$0.539029\pi$
$410$	−6.77118	−0.334405
$411$	−19.1328	−0.943750
$412$	18.0155	0.887562
$413$	−15.1264	−0.744323
$414$	7.63841	0.375407
$415$	10.4304	0.512010
$416$	2.16490	0.106143
$417$	−2.02084	−0.0989612
$418$	−4.60629	−0.225301
$419$	−1.69105	−0.0826131	−0.0413066	−	0.999147i	$-0.513152\pi$
$419$	−1.69105	−0.0826131	−0.0413066	+	0.999147i	$0.513152\pi$
$420$	5.13277	0.250454
$421$	−9.48341	−0.462193	−0.231097	−	0.972931i	$-0.574231\pi$
$421$	−9.48341	−0.462193	−0.231097	+	0.972931i	$0.574231\pi$
$422$	−25.4573	−1.23924
$423$	−9.21257	−0.447931
$424$	−6.77118	−0.328838
$425$	1.00000	0.0485071
$426$	−14.2655	−0.691168
$427$	−62.1098	−3.00571
$428$	0.967873	0.0467839
$429$	−2.16490	−0.104522
$430$	9.29767	0.448373
$431$	−7.12182	−0.343046	−0.171523	−	0.985180i	$-0.554869\pi$
$431$	−7.12182	−0.343046	−0.171523	+	0.985180i	$0.554869\pi$
$432$	−1.00000	−0.0481125
$433$	17.6066	0.846120	0.423060	−	0.906102i	$-0.360956\pi$
$433$	17.6066	0.846120	0.423060	+	0.906102i	$0.360956\pi$
$434$	−26.3453	−1.26462
$435$	9.23342	0.442708
$436$	7.04767	0.337522
$437$	−35.1847	−1.68311
$438$	6.32980	0.302449
$439$	−37.8552	−1.80673	−0.903366	−	0.428870i	$-0.858912\pi$
$439$	−37.8552	−1.80673	−0.903366	+	0.428870i	$0.858912\pi$
$440$	−1.00000	−0.0476731
$441$	19.3453	0.921207
$442$	2.16490	0.102974
$443$	−2.75034	−0.130673	−0.0653363	−	0.997863i	$-0.520812\pi$
$443$	−2.75034	−0.130673	−0.0653363	+	0.997863i	$0.520812\pi$
$444$	−8.10064	−0.384440
$445$	−0.0642530	−0.00304588
$446$	8.80298	0.416833
$447$	−21.8831	−1.03504
$448$	5.13277	0.242501
$449$	3.68575	0.173941	0.0869707	−	0.996211i	$-0.472281\pi$
$449$	3.68575	0.173941	0.0869707	+	0.996211i	$0.472281\pi$
$450$	1.00000	0.0471405
$451$	6.77118	0.318843
$452$	−4.70693	−0.221395
$453$	6.10064	0.286633
$454$	−4.04341	−0.189767
$455$	−11.1119	−0.520935
$456$	4.60629	0.215709
$457$	−29.6430	−1.38664	−0.693321	−	0.720629i	$-0.743853\pi$
$457$	−29.6430	−1.38664	−0.693321	+	0.720629i	$0.743853\pi$
$458$	−27.0258	−1.26283
$459$	−1.00000	−0.0466760
$460$	−7.63841	−0.356143
$461$	34.3778	1.60113	0.800567	−	0.599243i	$-0.204532\pi$
$461$	34.3778	1.60113	0.800567	+	0.599243i	$0.204532\pi$
$462$	−5.13277	−0.238798
$463$	−16.8556	−0.783345	−0.391673	−	0.920105i	$-0.628103\pi$
$463$	−16.8556	−0.783345	−0.391673	+	0.920105i	$0.628103\pi$
$464$	9.23342	0.428651
$465$	−5.13277	−0.238027
$466$	5.75530	0.266609
$467$	30.3552	1.40467	0.702337	−	0.711845i	$-0.252140\pi$
$467$	30.3552	1.40467	0.702337	+	0.711845i	$0.252140\pi$
$468$	2.16490	0.100072
$469$	23.6430	1.09173
$470$	9.21257	0.424944
$471$	−8.50564	−0.391919
$472$	−2.94703	−0.135648
$473$	−9.29767	−0.427507
$474$	−6.50564	−0.298814
$475$	−4.60629	−0.211351
$476$	5.13277	0.235260
$477$	−6.77118	−0.310031
$478$	19.1483	0.875824
$479$	−17.7338	−0.810276	−0.405138	−	0.914256i	$-0.632777\pi$
$479$	−17.7338	−0.810276	−0.405138	+	0.914256i	$0.632777\pi$
$480$	1.00000	0.0456435
$481$	17.5371	0.799622
$482$	10.1695	0.463208
$483$	−39.2062	−1.78395
$484$	1.00000	0.0454545
$485$	11.9040	0.540531
$486$	−1.00000	−0.0453609
$487$	−29.5255	−1.33793	−0.668963	−	0.743296i	$-0.733262\pi$
$487$	−29.5255	−1.33793	−0.668963	+	0.743296i	$0.733262\pi$
$488$	−12.1006	−0.547770
$489$	0.638078	0.0288549
$490$	−19.3453	−0.873934
$491$	−35.0367	−1.58119	−0.790593	−	0.612342i	$-0.790227\pi$
$491$	−35.0367	−1.58119	−0.790593	+	0.612342i	$0.790227\pi$
$492$	−6.77118	−0.305269
$493$	9.23342	0.415852
$494$	−9.97214	−0.448668
$495$	−1.00000	−0.0449467
$496$	−5.13277	−0.230468
$497$	73.2218	3.28445
$498$	10.4304	0.467399
$499$	−15.8715	−0.710506	−0.355253	−	0.934770i	$-0.615605\pi$
$499$	−15.8715	−0.710506	−0.355253	+	0.934770i	$0.615605\pi$
$500$	−1.00000	−0.0447214
$501$	14.5953	0.652072
$502$	11.6430	0.519653
$503$	31.0847	1.38600	0.693000	−	0.720938i	$-0.256289\pi$
$503$	31.0847	1.38600	0.693000	+	0.720938i	$0.256289\pi$
$504$	5.13277	0.228632
$505$	8.70693	0.387453
$506$	7.63841	0.339569
$507$	8.31322	0.369203
$508$	−19.4781	−0.864202
$509$	19.8941	0.881789	0.440894	−	0.897559i	$-0.354661\pi$
$509$	19.8941	0.881789	0.440894	+	0.897559i	$0.354661\pi$
$510$	1.00000	0.0442807
$511$	−32.4894	−1.43725
$512$	1.00000	0.0441942
$513$	4.60629	0.203372
$514$	24.1804	1.06655
$515$	−18.0155	−0.793860
$516$	9.29767	0.409307
$517$	−9.21257	−0.405168
$518$	41.5788	1.82687
$519$	13.3132	0.584385
$520$	−2.16490	−0.0949371
$521$	−8.22915	−0.360526	−0.180263	−	0.983618i	$-0.557695\pi$
$521$	−8.22915	−0.360526	−0.180263	+	0.983618i	$0.557695\pi$
$522$	9.23342	0.404136
$523$	−35.7228	−1.56205	−0.781025	−	0.624500i	$-0.785303\pi$
$523$	−35.7228	−1.56205	−0.781025	+	0.624500i	$0.785303\pi$
$524$	10.4304	0.455656
$525$	−5.13277	−0.224013
$526$	21.3341	0.930209
$527$	−5.13277	−0.223587
$528$	−1.00000	−0.0435194
$529$	35.3453	1.53675
$530$	6.77118	0.294121
$531$	−2.94703	−0.127890
$532$	−23.6430	−1.02505
$533$	14.6589	0.634948
$534$	−0.0642530	−0.00278050
$535$	−0.967873	−0.0418448
$536$	4.60629	0.198961
$537$	−0.164898	−0.00711587
$538$	5.11193	0.220391
$539$	19.3453	0.833263
$540$	1.00000	0.0430331
$541$	−17.4781	−0.751443	−0.375721	−	0.926733i	$-0.622605\pi$
$541$	−17.4781	−0.751443	−0.375721	+	0.926733i	$0.622605\pi$
$542$	−2.70233	−0.116075
$543$	20.5102	0.880179
$544$	1.00000	0.0428746
$545$	−7.04767	−0.301889
$546$	−11.1119	−0.475547
$547$	−12.8464	−0.549272	−0.274636	−	0.961548i	$-0.588557\pi$
$547$	−12.8464	−0.549272	−0.274636	+	0.961548i	$0.588557\pi$
$548$	19.1328	0.817311
$549$	−12.1006	−0.516443
$550$	1.00000	0.0426401
$551$	−42.5318	−1.81191
$552$	−7.63841	−0.325112
$553$	33.3920	1.41997
$554$	−11.3411	−0.481836
$555$	8.10064	0.343853
$556$	2.02084	0.0857029
$557$	−17.7864	−0.753634	−0.376817	−	0.926288i	$-0.622981\pi$
$557$	−17.7864	−0.753634	−0.376817	+	0.926288i	$0.622981\pi$
$558$	−5.13277	−0.217288
$559$	−20.1285	−0.851345
$560$	−5.13277	−0.216899
$561$	−1.00000	−0.0422200
$562$	6.63808	0.280010
$563$	15.6649	0.660197	0.330099	−	0.943946i	$-0.392918\pi$
$563$	15.6649	0.660197	0.330099	+	0.943946i	$0.392918\pi$
$564$	9.21257	0.387919
$565$	4.70693	0.198022
$566$	32.1377	1.35085
$567$	5.13277	0.215556
$568$	14.2655	0.598569
$569$	11.8994	0.498847	0.249423	−	0.968395i	$-0.419759\pi$
$569$	11.8994	0.498847	0.249423	+	0.968395i	$0.419759\pi$
$570$	−4.60629	−0.192936
$571$	39.6377	1.65879	0.829393	−	0.558665i	$-0.188686\pi$
$571$	39.6377	1.65879	0.829393	+	0.558665i	$0.188686\pi$
$572$	2.16490	0.0905189
$573$	−3.58511	−0.149770
$574$	34.7549	1.45064
$575$	7.63841	0.318544
$576$	1.00000	0.0416667
$577$	−23.5424	−0.980082	−0.490041	−	0.871700i	$-0.663018\pi$
$577$	−23.5424	−0.980082	−0.490041	+	0.871700i	$0.663018\pi$
$578$	1.00000	0.0415945
$579$	−10.3298	−0.429292
$580$	−9.23342	−0.383397
$581$	−53.5371	−2.22109
$582$	11.9040	0.493435
$583$	−6.77118	−0.280434
$584$	−6.32980	−0.261929
$585$	−2.16490	−0.0895075
$586$	31.5858	1.30480
$587$	−10.9205	−0.450739	−0.225369	−	0.974273i	$-0.572359\pi$
$587$	−10.9205	−0.450739	−0.225369	+	0.974273i	$0.572359\pi$
$588$	−19.3453	−0.797789
$589$	23.6430	0.974193
$590$	2.94703	0.121327
$591$	3.37747	0.138931
$592$	8.10064	0.332934
$593$	−11.8941	−0.488430	−0.244215	−	0.969721i	$-0.578530\pi$
$593$	−11.8941	−0.488430	−0.244215	+	0.969721i	$0.578530\pi$
$594$	−1.00000	−0.0410305
$595$	−5.13277	−0.210423
$596$	21.8831	0.896367
$597$	−2.10064	−0.0859737
$598$	16.5364	0.676223
$599$	−27.2281	−1.11251	−0.556255	−	0.831011i	$-0.687762\pi$
$599$	−27.2281	−1.11251	−0.556255	+	0.831011i	$0.687762\pi$
$600$	−1.00000	−0.0408248
$601$	18.9361	0.772419	0.386209	−	0.922411i	$-0.373784\pi$
$601$	18.9361	0.772419	0.386209	+	0.922411i	$0.373784\pi$
$602$	−47.7228	−1.94504
$603$	4.60629	0.187582
$604$	−6.10064	−0.248232
$605$	−1.00000	−0.0406558
$606$	8.70693	0.353695
$607$	34.7496	1.41044	0.705222	−	0.708986i	$-0.250847\pi$
$607$	34.7496	1.41044	0.705222	+	0.708986i	$0.250847\pi$
$608$	−4.60629	−0.186810
$609$	−47.3930	−1.92046
$610$	12.1006	0.489941
$611$	−19.9443	−0.806859
$612$	1.00000	0.0404226
$613$	33.0847	1.33628	0.668140	−	0.744036i	$-0.267091\pi$
$613$	33.0847	1.33628	0.668140	+	0.744036i	$0.267091\pi$
$614$	1.01128	0.0408120
$615$	6.77118	0.273040
$616$	5.13277	0.206805
$617$	7.82416	0.314989	0.157494	−	0.987520i	$-0.449658\pi$
$617$	7.82416	0.314989	0.157494	+	0.987520i	$0.449658\pi$
$618$	−18.0155	−0.724692
$619$	−4.51659	−0.181537	−0.0907685	−	0.995872i	$-0.528932\pi$
$619$	−4.51659	−0.181537	−0.0907685	+	0.995872i	$0.528932\pi$
$620$	5.13277	0.206137
$621$	−7.63841	−0.306519
$622$	−13.2126	−0.529776
$623$	0.329796	0.0132130
$624$	−2.16490	−0.0866653
$625$	1.00000	0.0400000
$626$	32.7867	1.31042
$627$	4.60629	0.183957
$628$	8.50564	0.339412
$629$	8.10064	0.322994
$630$	−5.13277	−0.204495
$631$	−48.3390	−1.92435	−0.962173	−	0.272441i	$-0.912169\pi$
$631$	−48.3390	−1.92435	−0.962173	+	0.272441i	$0.912169\pi$
$632$	6.50564	0.258780
$633$	25.4573	1.01184
$634$	−14.2864	−0.567385
$635$	19.4781	0.772965
$636$	6.77118	0.268495
$637$	41.8807	1.65937
$638$	9.23342	0.365554
$639$	14.2655	0.564336
$640$	−1.00000	−0.0395285
$641$	41.3294	1.63241	0.816207	−	0.577759i	$-0.196073\pi$
$641$	41.3294	1.63241	0.816207	+	0.577759i	$0.196073\pi$
$642$	−0.967873	−0.0381989
$643$	−42.7532	−1.68602	−0.843011	−	0.537896i	$-0.819219\pi$
$643$	−42.7532	−1.68602	−0.843011	+	0.537896i	$0.819219\pi$
$644$	39.2062	1.54494
$645$	−9.29767	−0.366095
$646$	−4.60629	−0.181232
$647$	−32.8192	−1.29026	−0.645128	−	0.764075i	$-0.723196\pi$
$647$	−32.8192	−1.29026	−0.645128	+	0.764075i	$0.723196\pi$
$648$	1.00000	0.0392837
$649$	−2.94703	−0.115681
$650$	2.16490	0.0849143
$651$	26.3453	1.03256
$652$	−0.638078	−0.0249890
$653$	−41.2645	−1.61481	−0.807403	−	0.590001i	$-0.799127\pi$
$653$	−41.2645	−1.61481	−0.807403	+	0.590001i	$0.799127\pi$
$654$	−7.04767	−0.275586
$655$	−10.4304	−0.407551
$656$	6.77118	0.264370
$657$	−6.32980	−0.246949
$658$	−47.2860	−1.84340
$659$	−23.8450	−0.928869	−0.464435	−	0.885607i	$-0.653742\pi$
$659$	−23.8450	−0.928869	−0.464435	+	0.885607i	$0.653742\pi$
$660$	1.00000	0.0389249
$661$	−32.3669	−1.25892	−0.629462	−	0.777031i	$-0.716725\pi$
$661$	−32.3669	−1.25892	−0.629462	+	0.777031i	$0.716725\pi$
$662$	−6.30895	−0.245204
$663$	−2.16490	−0.0840777
$664$	−10.4304	−0.404780
$665$	23.6430	0.916837
$666$	8.10064	0.313894
$667$	70.5286	2.73088
$668$	−14.5953	−0.564711
$669$	−8.80298	−0.340343
$670$	−4.60629	−0.177956
$671$	−12.1006	−0.467140
$672$	−5.13277	−0.198001
$673$	−15.6060	−0.601565	−0.300783	−	0.953693i	$-0.597248\pi$
$673$	−15.6060	−0.601565	−0.300783	+	0.953693i	$0.597248\pi$
$674$	−34.2013	−1.31738
$675$	−1.00000	−0.0384900
$676$	−8.31322	−0.319739
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	4.70693	0.180769
$679$	−61.1003	−2.34481
$680$	−1.00000	−0.0383482
$681$	4.04341	0.154944
$682$	−5.13277	−0.196544
$683$	−17.2907	−0.661608	−0.330804	−	0.943699i	$-0.607320\pi$
$683$	−17.2907	−0.661608	−0.330804	+	0.943699i	$0.607320\pi$
$684$	−4.60629	−0.176126
$685$	−19.1328	−0.731026
$686$	63.3658	2.41932
$687$	27.0258	1.03110
$688$	−9.29767	−0.354470
$689$	−14.6589	−0.558460
$690$	7.63841	0.290789
$691$	−12.2066	−0.464360	−0.232180	−	0.972673i	$-0.574586\pi$
$691$	−12.2066	−0.464360	−0.232180	+	0.972673i	$0.574586\pi$
$692$	−13.3132	−0.506093
$693$	5.13277	0.194978
$694$	21.2126	0.805218
$695$	−2.02084	−0.0766550
$696$	−9.23342	−0.349992
$697$	6.77118	0.256477
$698$	25.2380	0.955273
$699$	−5.75530	−0.217686
$700$	5.13277	0.194001
$701$	−47.9202	−1.80992	−0.904960	−	0.425497i	$-0.860099\pi$
$701$	−47.9202	−1.80992	−0.904960	+	0.425497i	$0.860099\pi$
$702$	−2.16490	−0.0817088
$703$	−37.3139	−1.40732
$704$	1.00000	0.0376889
$705$	−9.21257	−0.346966
$706$	−1.06852	−0.0402142
$707$	−44.6907	−1.68077
$708$	2.94703	0.110756
$709$	−11.4139	−0.428657	−0.214328	−	0.976762i	$-0.568756\pi$
$709$	−11.4139	−0.428657	−0.214328	+	0.976762i	$0.568756\pi$
$710$	−14.2655	−0.535376
$711$	6.50564	0.243981
$712$	0.0642530	0.00240798
$713$	−39.2062	−1.46828
$714$	−5.13277	−0.192089
$715$	−2.16490	−0.0809626
$716$	0.164898	0.00616253
$717$	−19.1483	−0.715107
$718$	−24.8192	−0.926244
$719$	−29.7853	−1.11081	−0.555403	−	0.831581i	$-0.687436\pi$
$719$	−29.7853	−1.11081	−0.555403	+	0.831581i	$0.687436\pi$
$720$	−1.00000	−0.0372678
$721$	92.4697	3.44375
$722$	2.21787	0.0825405
$723$	−10.1695	−0.378208
$724$	−20.5102	−0.762257
$725$	9.23342	0.342920
$726$	−1.00000	−0.0371135
$727$	−0.766584	−0.0284310	−0.0142155	−	0.999899i	$-0.504525\pi$
$727$	−0.766584	−0.0284310	−0.0142155	+	0.999899i	$0.504525\pi$
$728$	11.1119	0.411835
$729$	1.00000	0.0370370
$730$	6.32980	0.234276
$731$	−9.29767	−0.343887
$732$	12.1006	0.447253
$733$	−19.5788	−0.723158	−0.361579	−	0.932341i	$-0.617762\pi$
$733$	−19.5788	−0.723158	−0.361579	+	0.932341i	$0.617762\pi$
$734$	30.1850	1.11415
$735$	19.3453	0.713564
$736$	7.63841	0.281556
$737$	4.60629	0.169675
$738$	6.77118	0.249251
$739$	7.20162	0.264916	0.132458	−	0.991189i	$-0.457713\pi$
$739$	7.20162	0.264916	0.132458	+	0.991189i	$0.457713\pi$
$740$	−8.10064	−0.297786
$741$	9.97214	0.366336
$742$	−34.7549	−1.27589
$743$	25.4139	0.932344	0.466172	−	0.884694i	$-0.345633\pi$
$743$	25.4139	0.932344	0.466172	+	0.884694i	$0.345633\pi$
$744$	5.13277	0.188177
$745$	−21.8831	−0.801735
$746$	−12.4251	−0.454917
$747$	−10.4304	−0.381630
$748$	1.00000	0.0365636
$749$	4.96787	0.181522
$750$	1.00000	0.0365148
$751$	−36.6890	−1.33880	−0.669400	−	0.742902i	$-0.733449\pi$
$751$	−36.6890	−1.33880	−0.669400	+	0.742902i	$0.733449\pi$
$752$	−9.21257	−0.335948
$753$	−11.6430	−0.424295
$754$	19.9894	0.727971
$755$	6.10064	0.222025
$756$	−5.13277	−0.186677
$757$	17.1218	0.622303	0.311152	−	0.950360i	$-0.399285\pi$
$757$	17.1218	0.622303	0.311152	+	0.950360i	$0.399285\pi$
$758$	10.9834	0.398936
$759$	−7.63841	−0.277257
$760$	4.60629	0.167088
$761$	−34.0579	−1.23460	−0.617299	−	0.786729i	$-0.711773\pi$
$761$	−34.0579	−1.23460	−0.617299	+	0.786729i	$0.711773\pi$
$762$	19.4781	0.705618
$763$	36.1741	1.30959
$764$	3.58511	0.129705
$765$	−1.00000	−0.0361551
$766$	−4.68149	−0.169149
$767$	−6.38002	−0.230369
$768$	−1.00000	−0.0360844
$769$	−3.56426	−0.128531	−0.0642653	−	0.997933i	$-0.520470\pi$
$769$	−3.56426	−0.128531	−0.0642653	+	0.997933i	$0.520470\pi$
$770$	−5.13277	−0.184972
$771$	−24.1804	−0.870837
$772$	10.3298	0.371777
$773$	−2.77648	−0.0998631	−0.0499315	−	0.998753i	$-0.515900\pi$
$773$	−2.77648	−0.0998631	−0.0499315	+	0.998753i	$0.515900\pi$
$774$	−9.29767	−0.334198
$775$	−5.13277	−0.184375
$776$	−11.9040	−0.427327
$777$	−41.5788	−1.49163
$778$	24.0953	0.863860
$779$	−31.1900	−1.11750
$780$	2.16490	0.0775158
$781$	14.2655	0.510461
$782$	7.63841	0.273149
$783$	−9.23342	−0.329975
$784$	19.3453	0.690905
$785$	−8.50564	−0.303579
$786$	−10.4304	−0.372042
$787$	33.3867	1.19011	0.595053	−	0.803686i	$-0.297131\pi$
$787$	33.3867	1.19011	0.595053	+	0.803686i	$0.297131\pi$
$788$	−3.37747	−0.120317
$789$	−21.3341	−0.759513
$790$	−6.50564	−0.231460
$791$	−24.1596	−0.859016
$792$	1.00000	0.0355335
$793$	−26.1967	−0.930271
$794$	12.9887	0.460952
$795$	−6.77118	−0.240149
$796$	2.10064	0.0744554
$797$	−26.7659	−0.948096	−0.474048	−	0.880499i	$-0.657208\pi$
$797$	−26.7659	−0.948096	−0.474048	+	0.880499i	$0.657208\pi$
$798$	23.6430	0.836954
$799$	−9.21257	−0.325917
$800$	1.00000	0.0353553
$801$	0.0642530	0.00227027
$802$	−5.35662	−0.189149
$803$	−6.32980	−0.223374
$804$	−4.60629	−0.162451
$805$	−39.2062	−1.38184
$806$	−11.1119	−0.391401
$807$	−5.11193	−0.179948
$808$	−8.70693	−0.306309
$809$	15.5671	0.547312	0.273656	−	0.961828i	$-0.411767\pi$
$809$	15.5671	0.547312	0.273656	+	0.961828i	$0.411767\pi$
$810$	−1.00000	−0.0351364
$811$	14.0953	0.494955	0.247477	−	0.968894i	$-0.420398\pi$
$811$	14.0953	0.494955	0.247477	+	0.968894i	$0.420398\pi$
$812$	47.3930	1.66317
$813$	2.70233	0.0947749
$814$	8.10064	0.283927
$815$	0.638078	0.0223509
$816$	−1.00000	−0.0350070
$817$	42.8277	1.49835
$818$	−4.94703	−0.172969
$819$	11.1119	0.388282
$820$	−6.77118	−0.236460
$821$	−44.6698	−1.55899	−0.779494	−	0.626410i	$-0.784524\pi$
$821$	−44.6698	−1.55899	−0.779494	+	0.626410i	$0.784524\pi$
$822$	−19.1328	−0.667332
$823$	−28.4923	−0.993178	−0.496589	−	0.867986i	$-0.665414\pi$
$823$	−28.4923	−0.993178	−0.496589	+	0.867986i	$0.665414\pi$
$824$	18.0155	0.627601
$825$	−1.00000	−0.0348155
$826$	−15.1264	−0.526316
$827$	−38.3817	−1.33466	−0.667332	−	0.744760i	$-0.732564\pi$
$827$	−38.3817	−1.33466	−0.667332	+	0.744760i	$0.732564\pi$
$828$	7.63841	0.265453
$829$	32.6317	1.13335	0.566673	−	0.823942i	$-0.308230\pi$
$829$	32.6317	1.13335	0.566673	+	0.823942i	$0.308230\pi$
$830$	10.4304	0.362046
$831$	11.3411	0.393418
$832$	2.16490	0.0750543
$833$	19.3453	0.670276
$834$	−2.02084	−0.0699761
$835$	14.5953	0.505093
$836$	−4.60629	−0.159312
$837$	5.13277	0.177415
$838$	−1.69105	−0.0584163
$839$	−43.3496	−1.49659	−0.748297	−	0.663363i	$-0.769128\pi$
$839$	−43.3496	−1.49659	−0.748297	+	0.663363i	$0.769128\pi$
$840$	5.13277	0.177097
$841$	56.2560	1.93986
$842$	−9.48341	−0.326820
$843$	−6.63808	−0.228628
$844$	−25.4573	−0.876275
$845$	8.31322	0.285983
$846$	−9.21257	−0.316735
$847$	5.13277	0.176364
$848$	−6.77118	−0.232523
$849$	−32.1377	−1.10296
$850$	1.00000	0.0342997
$851$	61.8761	2.12108
$852$	−14.2655	−0.488729
$853$	−29.0830	−0.995784	−0.497892	−	0.867239i	$-0.665892\pi$
$853$	−29.0830	−0.995784	−0.497892	+	0.867239i	$0.665892\pi$
$854$	−62.1098	−2.12536
$855$	4.60629	0.157532
$856$	0.967873	0.0330812
$857$	2.57979	0.0881240	0.0440620	−	0.999029i	$-0.485970\pi$
$857$	2.57979	0.0881240	0.0440620	+	0.999029i	$0.485970\pi$
$858$	−2.16490	−0.0739084
$859$	−42.7532	−1.45872	−0.729361	−	0.684130i	$-0.760182\pi$
$859$	−42.7532	−1.45872	−0.729361	+	0.684130i	$0.760182\pi$
$860$	9.29767	0.317048
$861$	−34.7549	−1.18445
$862$	−7.12182	−0.242570
$863$	−18.4251	−0.627199	−0.313600	−	0.949555i	$-0.601535\pi$
$863$	−18.4251	−0.627199	−0.313600	+	0.949555i	$0.601535\pi$
$864$	−1.00000	−0.0340207
$865$	13.3132	0.452663
$866$	17.6066	0.598297
$867$	−1.00000	−0.0339618
$868$	−26.3453	−0.894219
$869$	6.50564	0.220689
$870$	9.23342	0.313042
$871$	9.97214	0.337893
$872$	7.04767	0.238664
$873$	−11.9040	−0.402888
$874$	−35.1847	−1.19014
$875$	−5.13277	−0.173519
$876$	6.32980	0.213864
$877$	3.97916	0.134367	0.0671833	−	0.997741i	$-0.478599\pi$
$877$	3.97916	0.134367	0.0671833	+	0.997741i	$0.478599\pi$
$878$	−37.8552	−1.27755
$879$	−31.5858	−1.06536
$880$	−1.00000	−0.0337100
$881$	17.7228	0.597097	0.298548	−	0.954395i	$-0.403498\pi$
$881$	17.7228	0.597097	0.298548	+	0.954395i	$0.403498\pi$
$882$	19.3453	0.651392
$883$	−31.2380	−1.05124	−0.525621	−	0.850719i	$-0.676167\pi$
$883$	−31.2380	−1.05124	−0.525621	+	0.850719i	$0.676167\pi$
$884$	2.16490	0.0728134
$885$	−2.94703	−0.0990633
$886$	−2.75034	−0.0923994
$887$	−17.0113	−0.571183	−0.285591	−	0.958351i	$-0.592190\pi$
$887$	−17.0113	−0.571183	−0.285591	+	0.958351i	$0.592190\pi$
$888$	−8.10064	−0.271840
$889$	−99.9767	−3.35311
$890$	−0.0642530	−0.00215377
$891$	1.00000	0.0335013
$892$	8.80298	0.294745
$893$	42.4357	1.42006
$894$	−21.8831	−0.731881
$895$	−0.164898	−0.00551193
$896$	5.13277	0.171474
$897$	−16.5364	−0.552134
$898$	3.68575	0.122995
$899$	−47.3930	−1.58065
$900$	1.00000	0.0333333
$901$	−6.77118	−0.225581
$902$	6.77118	0.225456
$903$	47.7228	1.58812
$904$	−4.70693	−0.156550
$905$	20.5102	0.681783
$906$	6.10064	0.202680
$907$	−18.3506	−0.609323	−0.304662	−	0.952461i	$-0.598543\pi$
$907$	−18.3506	−0.609323	−0.304662	+	0.952461i	$0.598543\pi$
$908$	−4.04341	−0.134185
$909$	−8.70693	−0.288791
$910$	−11.1119	−0.368357
$911$	−18.6370	−0.617472	−0.308736	−	0.951148i	$-0.599906\pi$
$911$	−18.6370	−0.617472	−0.308736	+	0.951148i	$0.599906\pi$
$912$	4.60629	0.152529
$913$	−10.4304	−0.345197
$914$	−29.6430	−0.980504
$915$	−12.1006	−0.400035
$916$	−27.0258	−0.892957
$917$	53.5371	1.76795
$918$	−1.00000	−0.0330049
$919$	−7.26981	−0.239809	−0.119904	−	0.992785i	$-0.538259\pi$
$919$	−7.26981	−0.239809	−0.119904	+	0.992785i	$0.538259\pi$
$920$	−7.63841	−0.251831
$921$	−1.01128	−0.0333229
$922$	34.3778	1.13217
$923$	30.8834	1.01654
$924$	−5.13277	−0.168856
$925$	8.10064	0.266348
$926$	−16.8556	−0.553909
$927$	18.0155	0.591708
$928$	9.23342	0.303102
$929$	49.7592	1.63255	0.816273	−	0.577666i	$-0.196036\pi$
$929$	49.7592	1.63255	0.816273	+	0.577666i	$0.196036\pi$
$930$	−5.13277	−0.168310
$931$	−89.1102	−2.92047
$932$	5.75530	0.188521
$933$	13.2126	0.432560
$934$	30.3552	0.993254
$935$	−1.00000	−0.0327035
$936$	2.16490	0.0707619
$937$	−29.6430	−0.968395	−0.484198	−	0.874959i	$-0.660888\pi$
$937$	−29.6430	−0.968395	−0.484198	+	0.874959i	$0.660888\pi$
$938$	23.6430	0.771972
$939$	−32.7867	−1.06995
$940$	9.21257	0.300481
$941$	28.9781	0.944660	0.472330	−	0.881422i	$-0.343413\pi$
$941$	28.9781	0.944660	0.472330	+	0.881422i	$0.343413\pi$
$942$	−8.50564	−0.277129
$943$	51.7211	1.68427
$944$	−2.94703	−0.0959176
$945$	5.13277	0.166969
$946$	−9.29767	−0.302293
$947$	18.4668	0.600091	0.300046	−	0.953925i	$-0.402998\pi$
$947$	18.4668	0.600091	0.300046	+	0.953925i	$0.402998\pi$
$948$	−6.50564	−0.211293
$949$	−13.7034	−0.444830
$950$	−4.60629	−0.149448
$951$	14.2864	0.463268
$952$	5.13277	0.166354
$953$	46.6039	1.50965	0.754824	−	0.655928i	$-0.227722\pi$
$953$	46.6039	1.50965	0.754824	+	0.655928i	$0.227722\pi$
$954$	−6.77118	−0.219225
$955$	−3.58511	−0.116011
$956$	19.1483	0.619301
$957$	−9.23342	−0.298474
$958$	−17.7338	−0.572952
$959$	98.2041	3.17118
$960$	1.00000	0.0322749
$961$	−4.65466	−0.150150
$962$	17.5371	0.565418
$963$	0.967873	0.0311893
$964$	10.1695	0.327537
$965$	−10.3298	−0.332528
$966$	−39.2062	−1.26144
$967$	−32.8192	−1.05539	−0.527697	−	0.849433i	$-0.676944\pi$
$967$	−32.8192	−1.05539	−0.527697	+	0.849433i	$0.676944\pi$
$968$	1.00000	0.0321412
$969$	4.60629	0.147975
$970$	11.9040	0.382213
$971$	−22.4523	−0.720530	−0.360265	−	0.932850i	$-0.617314\pi$
$971$	−22.4523	−0.720530	−0.360265	+	0.932850i	$0.617314\pi$
$972$	−1.00000	−0.0320750
$973$	10.3725	0.332528
$974$	−29.5255	−0.946057
$975$	−2.16490	−0.0693322
$976$	−12.1006	−0.387332
$977$	−42.7271	−1.36696	−0.683480	−	0.729969i	$-0.739534\pi$
$977$	−42.7271	−1.36696	−0.683480	+	0.729969i	$0.739534\pi$
$978$	0.638078	0.0204035
$979$	0.0642530	0.00205353
$980$	−19.3453	−0.617964
$981$	7.04767	0.225015
$982$	−35.0367	−1.11807
$983$	−21.4185	−0.683143	−0.341571	−	0.939856i	$-0.610959\pi$
$983$	−21.4185	−0.683143	−0.341571	+	0.939856i	$0.610959\pi$
$984$	−6.77118	−0.215857
$985$	3.37747	0.107615
$986$	9.23342	0.294052
$987$	47.2860	1.50513
$988$	−9.97214	−0.317256
$989$	−71.0194	−2.25829
$990$	−1.00000	−0.0317821
$991$	−28.8122	−0.915249	−0.457624	−	0.889146i	$-0.651300\pi$
$991$	−28.8122	−0.915249	−0.457624	+	0.889146i	$0.651300\pi$
$992$	−5.13277	−0.162966
$993$	6.30895	0.200209
$994$	73.2218	2.32245
$995$	−2.10064	−0.0665949
$996$	10.4304	0.330501
$997$	15.3069	0.484773	0.242387	−	0.970180i	$-0.422070\pi$
$997$	15.3069	0.484773	0.242387	+	0.970180i	$0.422070\pi$
$998$	−15.8715	−0.502403
$999$	−8.10064	−0.256293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cg.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cg.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +5.13277 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.16490 q^{13} +5.13277 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.60629 q^{19} -1.00000 q^{20} -5.13277 q^{21} +1.00000 q^{22} +7.63841 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.16490 q^{26} -1.00000 q^{27} +5.13277 q^{28} +9.23342 q^{29} +1.00000 q^{30} -5.13277 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -5.13277 q^{35} +1.00000 q^{36} +8.10064 q^{37} -4.60629 q^{38} -2.16490 q^{39} -1.00000 q^{40} +6.77118 q^{41} -5.13277 q^{42} -9.29767 q^{43} +1.00000 q^{44} -1.00000 q^{45} +7.63841 q^{46} -9.21257 q^{47} -1.00000 q^{48} +19.3453 q^{49} +1.00000 q^{50} -1.00000 q^{51} +2.16490 q^{52} -6.77118 q^{53} -1.00000 q^{54} -1.00000 q^{55} +5.13277 q^{56} +4.60629 q^{57} +9.23342 q^{58} -2.94703 q^{59} +1.00000 q^{60} -12.1006 q^{61} -5.13277 q^{62} +5.13277 q^{63} +1.00000 q^{64} -2.16490 q^{65} -1.00000 q^{66} +4.60629 q^{67} +1.00000 q^{68} -7.63841 q^{69} -5.13277 q^{70} +14.2655 q^{71} +1.00000 q^{72} -6.32980 q^{73} +8.10064 q^{74} -1.00000 q^{75} -4.60629 q^{76} +5.13277 q^{77} -2.16490 q^{78} +6.50564 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.77118 q^{82} -10.4304 q^{83} -5.13277 q^{84} -1.00000 q^{85} -9.29767 q^{86} -9.23342 q^{87} +1.00000 q^{88} +0.0642530 q^{89} -1.00000 q^{90} +11.1119 q^{91} +7.63841 q^{92} +5.13277 q^{93} -9.21257 q^{94} +4.60629 q^{95} -1.00000 q^{96} -11.9040 q^{97} +19.3453 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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