LMFDB - Embedded newform 5610.2.a.bz.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
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			1.1
Root			$-1.48119$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.96239 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.96239 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.96239 q^{13} +4.96239 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.35026 q^{19} +1.00000 q^{20} -4.96239 q^{21} +1.00000 q^{22} +3.35026 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.96239 q^{26} +1.00000 q^{27} -4.96239 q^{28} +1.22425 q^{29} -1.00000 q^{30} -10.7005 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -4.96239 q^{35} +1.00000 q^{36} +3.92478 q^{37} -3.35026 q^{38} +2.96239 q^{39} -1.00000 q^{40} -7.61213 q^{41} +4.96239 q^{42} -5.73813 q^{43} -1.00000 q^{44} +1.00000 q^{45} -3.35026 q^{46} +4.00000 q^{47} +1.00000 q^{48} +17.6253 q^{49} -1.00000 q^{50} -1.00000 q^{51} +2.96239 q^{52} -1.35026 q^{53} -1.00000 q^{54} -1.00000 q^{55} +4.96239 q^{56} +3.35026 q^{57} -1.22425 q^{58} -14.8872 q^{59} +1.00000 q^{60} -10.0000 q^{61} +10.7005 q^{62} -4.96239 q^{63} +1.00000 q^{64} +2.96239 q^{65} +1.00000 q^{66} -5.08840 q^{67} -1.00000 q^{68} +3.35026 q^{69} +4.96239 q^{70} +5.73813 q^{71} -1.00000 q^{72} +7.73813 q^{73} -3.92478 q^{74} +1.00000 q^{75} +3.35026 q^{76} +4.96239 q^{77} -2.96239 q^{78} +6.05079 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.61213 q^{82} -12.6253 q^{83} -4.96239 q^{84} -1.00000 q^{85} +5.73813 q^{86} +1.22425 q^{87} +1.00000 q^{88} +3.92478 q^{89} -1.00000 q^{90} -14.7005 q^{91} +3.35026 q^{92} -10.7005 q^{93} -4.00000 q^{94} +3.35026 q^{95} -1.00000 q^{96} +16.2374 q^{97} -17.6253 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{20} - 4 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} - 4 q^{28} + 2 q^{29} - 3 q^{30} - 12 q^{31} - 3 q^{32} - 3 q^{33} + 3 q^{34} - 4 q^{35} + 3 q^{36} - 10 q^{37} - 2 q^{39} - 3 q^{40} - 22 q^{41} + 4 q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 12 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} + 4 q^{56} - 2 q^{58} - 12 q^{59} + 3 q^{60} - 30 q^{61} + 12 q^{62} - 4 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 4 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} + 4 q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 22 q^{82} + 4 q^{83} - 4 q^{84} - 3 q^{85} + 8 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} - 24 q^{91} - 12 q^{93} - 12 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^20 - 4 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 - 4 * q^28 + 2 * q^29 - 3 * q^30 - 12 * q^31 - 3 * q^32 - 3 * q^33 + 3 * q^34 - 4 * q^35 + 3 * q^36 - 10 * q^37 - 2 * q^39 - 3 * q^40 - 22 * q^41 + 4 * q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 + 4 * q^56 - 2 * q^58 - 12 * q^59 + 3 * q^60 - 30 * q^61 + 12 * q^62 - 4 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 4 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 + 4 * q^77 + 2 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 22 * q^82 + 4 * q^83 - 4 * q^84 - 3 * q^85 + 8 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 - 24 * q^91 - 12 * q^93 - 12 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−4.96239	−1.87561	−0.937803	−	0.347167i	$-0.887144\pi$
$7$	−4.96239	−1.87561	−0.937803	+	0.347167i	$0.887144\pi$
$8$	−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
$13$	2.96239	0.821619	0.410809	−	0.911721i	$-0.365246\pi$
$13$	2.96239	0.821619	0.410809	+	0.911721i	$0.365246\pi$
$14$	4.96239	1.32625
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.35026	0.768603	0.384301	−	0.923208i	$-0.374442\pi$
$19$	3.35026	0.768603	0.384301	+	0.923208i	$0.374442\pi$
$20$	1.00000	0.223607
$21$	−4.96239	−1.08288
$22$	1.00000	0.213201
$23$	3.35026	0.698578	0.349289	−	0.937015i	$-0.386423\pi$
$23$	3.35026	0.698578	0.349289	+	0.937015i	$0.386423\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−2.96239	−0.580972
$27$	1.00000	0.192450
$28$	−4.96239	−0.937803
$29$	1.22425	0.227338	0.113669	−	0.993519i	$-0.463740\pi$
$29$	1.22425	0.227338	0.113669	+	0.993519i	$0.463740\pi$
$30$	−1.00000	−0.182574
$31$	−10.7005	−1.92187	−0.960935	−	0.276773i	$-0.910735\pi$
$31$	−10.7005	−1.92187	−0.960935	+	0.276773i	$0.910735\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−4.96239	−0.838797
$36$	1.00000	0.166667
$37$	3.92478	0.645229	0.322615	−	0.946530i	$-0.395438\pi$
$37$	3.92478	0.645229	0.322615	+	0.946530i	$0.395438\pi$
$38$	−3.35026	−0.543484
$39$	2.96239	0.474362
$40$	−1.00000	−0.158114
$41$	−7.61213	−1.18881	−0.594407	−	0.804164i	$-0.702613\pi$
$41$	−7.61213	−1.18881	−0.594407	+	0.804164i	$0.702613\pi$
$42$	4.96239	0.765713
$43$	−5.73813	−0.875057	−0.437529	−	0.899204i	$-0.644146\pi$
$43$	−5.73813	−0.875057	−0.437529	+	0.899204i	$0.644146\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−3.35026	−0.493969
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	1.00000	0.144338
$49$	17.6253	2.51790
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	2.96239	0.410809
$53$	−1.35026	−0.185473	−0.0927364	−	0.995691i	$-0.529561\pi$
$53$	−1.35026	−0.185473	−0.0927364	+	0.995691i	$0.529561\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	4.96239	0.663127
$57$	3.35026	0.443753
$58$	−1.22425	−0.160752
$59$	−14.8872	−1.93814	−0.969072	−	0.246778i	$-0.920628\pi$
$59$	−14.8872	−1.93814	−0.969072	+	0.246778i	$0.920628\pi$
$60$	1.00000	0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	10.7005	1.35897
$63$	−4.96239	−0.625202
$64$	1.00000	0.125000
$65$	2.96239	0.367439
$66$	1.00000	0.123091
$67$	−5.08840	−0.621647	−0.310823	−	0.950468i	$-0.600605\pi$
$67$	−5.08840	−0.621647	−0.310823	+	0.950468i	$0.600605\pi$
$68$	−1.00000	−0.121268
$69$	3.35026	0.403324
$70$	4.96239	0.593119
$71$	5.73813	0.680991	0.340496	−	0.940246i	$-0.389405\pi$
$71$	5.73813	0.680991	0.340496	+	0.940246i	$0.389405\pi$
$72$	−1.00000	−0.117851
$73$	7.73813	0.905680	0.452840	−	0.891592i	$-0.350411\pi$
$73$	7.73813	0.905680	0.452840	+	0.891592i	$0.350411\pi$
$74$	−3.92478	−0.456246
$75$	1.00000	0.115470
$76$	3.35026	0.384301
$77$	4.96239	0.565517
$78$	−2.96239	−0.335424
$79$	6.05079	0.680767	0.340383	−	0.940287i	$-0.389443\pi$
$79$	6.05079	0.680767	0.340383	+	0.940287i	$0.389443\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	7.61213	0.840619
$83$	−12.6253	−1.38581	−0.692903	−	0.721030i	$-0.743669\pi$
$83$	−12.6253	−1.38581	−0.692903	+	0.721030i	$0.743669\pi$
$84$	−4.96239	−0.541441
$85$	−1.00000	−0.108465
$86$	5.73813	0.618759
$87$	1.22425	0.131254
$88$	1.00000	0.106600
$89$	3.92478	0.416026	0.208013	−	0.978126i	$-0.433300\pi$
$89$	3.92478	0.416026	0.208013	+	0.978126i	$0.433300\pi$
$90$	−1.00000	−0.105409
$91$	−14.7005	−1.54103
$92$	3.35026	0.349289
$93$	−10.7005	−1.10959
$94$	−4.00000	−0.412568
$95$	3.35026	0.343730
$96$	−1.00000	−0.102062
$97$	16.2374	1.64866	0.824330	−	0.566109i	$-0.191552\pi$
$97$	16.2374	1.64866	0.824330	+	0.566109i	$0.191552\pi$
$98$	−17.6253	−1.78042
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	6.31265	0.628132	0.314066	−	0.949401i	$-0.398309\pi$
$101$	6.31265	0.628132	0.314066	+	0.949401i	$0.398309\pi$
$102$	1.00000	0.0990148
$103$	13.4010	1.32044	0.660222	−	0.751070i	$-0.270462\pi$
$103$	13.4010	1.32044	0.660222	+	0.751070i	$0.270462\pi$
$104$	−2.96239	−0.290486
$105$	−4.96239	−0.484280
$106$	1.35026	0.131149
$107$	14.5501	1.40661	0.703305	−	0.710889i	$-0.251707\pi$
$107$	14.5501	1.40661	0.703305	+	0.710889i	$0.251707\pi$
$108$	1.00000	0.0962250
$109$	−16.7005	−1.59962	−0.799810	−	0.600253i	$-0.795066\pi$
$109$	−16.7005	−1.59962	−0.799810	+	0.600253i	$0.795066\pi$
$110$	1.00000	0.0953463
$111$	3.92478	0.372523
$112$	−4.96239	−0.468902
$113$	7.27504	0.684378	0.342189	−	0.939631i	$-0.388832\pi$
$113$	7.27504	0.684378	0.342189	+	0.939631i	$0.388832\pi$
$114$	−3.35026	−0.313781
$115$	3.35026	0.312414
$116$	1.22425	0.113669
$117$	2.96239	0.273873
$118$	14.8872	1.37047
$119$	4.96239	0.454901
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	10.0000	0.905357
$123$	−7.61213	−0.686362
$124$	−10.7005	−0.960935
$125$	1.00000	0.0894427
$126$	4.96239	0.442085
$127$	−1.29948	−0.115310	−0.0576549	−	0.998337i	$-0.518362\pi$
$127$	−1.29948	−0.115310	−0.0576549	+	0.998337i	$0.518362\pi$
$128$	−1.00000	−0.0883883
$129$	−5.73813	−0.505215
$130$	−2.96239	−0.259819
$131$	−7.22425	−0.631186	−0.315593	−	0.948895i	$-0.602203\pi$
$131$	−7.22425	−0.631186	−0.315593	+	0.948895i	$0.602203\pi$
$132$	−1.00000	−0.0870388
$133$	−16.6253	−1.44160
$134$	5.08840	0.439571
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	−21.3258	−1.82199	−0.910994	−	0.412419i	$-0.864684\pi$
$137$	−21.3258	−1.82199	−0.910994	+	0.412419i	$0.864684\pi$
$138$	−3.35026	−0.285193
$139$	−21.4010	−1.81521	−0.907607	−	0.419822i	$-0.862093\pi$
$139$	−21.4010	−1.81521	−0.907607	+	0.419822i	$0.862093\pi$
$140$	−4.96239	−0.419398
$141$	4.00000	0.336861
$142$	−5.73813	−0.481534
$143$	−2.96239	−0.247727
$144$	1.00000	0.0833333
$145$	1.22425	0.101669
$146$	−7.73813	−0.640413
$147$	17.6253	1.45371
$148$	3.92478	0.322615
$149$	−12.2374	−1.00253	−0.501265	−	0.865294i	$-0.667132\pi$
$149$	−12.2374	−1.00253	−0.501265	+	0.865294i	$0.667132\pi$
$150$	−1.00000	−0.0816497
$151$	−16.6253	−1.35295	−0.676474	−	0.736467i	$-0.736493\pi$
$151$	−16.6253	−1.35295	−0.676474	+	0.736467i	$0.736493\pi$
$152$	−3.35026	−0.271742
$153$	−1.00000	−0.0808452
$154$	−4.96239	−0.399881
$155$	−10.7005	−0.859487
$156$	2.96239	0.237181
$157$	−8.23743	−0.657418	−0.328709	−	0.944431i	$-0.606614\pi$
$157$	−8.23743	−0.657418	−0.328709	+	0.944431i	$0.606614\pi$
$158$	−6.05079	−0.481375
$159$	−1.35026	−0.107083
$160$	−1.00000	−0.0790569
$161$	−16.6253	−1.31026
$162$	−1.00000	−0.0785674
$163$	−9.14903	−0.716607	−0.358304	−	0.933605i	$-0.616645\pi$
$163$	−9.14903	−0.716607	−0.358304	+	0.933605i	$0.616645\pi$
$164$	−7.61213	−0.594407
$165$	−1.00000	−0.0778499
$166$	12.6253	0.979913
$167$	7.47627	0.578531	0.289266	−	0.957249i	$-0.406589\pi$
$167$	7.47627	0.578531	0.289266	+	0.957249i	$0.406589\pi$
$168$	4.96239	0.382857
$169$	−4.22425	−0.324943
$170$	1.00000	0.0766965
$171$	3.35026	0.256201
$172$	−5.73813	−0.437529
$173$	4.44851	0.338214	0.169107	−	0.985598i	$-0.445912\pi$
$173$	4.44851	0.338214	0.169107	+	0.985598i	$0.445912\pi$
$174$	−1.22425	−0.0928104
$175$	−4.96239	−0.375121
$176$	−1.00000	−0.0753778
$177$	−14.8872	−1.11899
$178$	−3.92478	−0.294174
$179$	14.8872	1.11272	0.556360	−	0.830942i	$-0.312198\pi$
$179$	14.8872	1.11272	0.556360	+	0.830942i	$0.312198\pi$
$180$	1.00000	0.0745356
$181$	−9.22425	−0.685633	−0.342817	−	0.939402i	$-0.611381\pi$
$181$	−9.22425	−0.685633	−0.342817	+	0.939402i	$0.611381\pi$
$182$	14.7005	1.08968
$183$	−10.0000	−0.739221
$184$	−3.35026	−0.246985
$185$	3.92478	0.288555
$186$	10.7005	0.784600
$187$	1.00000	0.0731272
$188$	4.00000	0.291730
$189$	−4.96239	−0.360961
$190$	−3.35026	−0.243054
$191$	8.77575	0.634991	0.317495	−	0.948260i	$-0.397158\pi$
$191$	8.77575	0.634991	0.317495	+	0.948260i	$0.397158\pi$
$192$	1.00000	0.0721688
$193$	−10.1866	−0.733251	−0.366625	−	0.930369i	$-0.619487\pi$
$193$	−10.1866	−0.733251	−0.366625	+	0.930369i	$0.619487\pi$
$194$	−16.2374	−1.16578
$195$	2.96239	0.212141
$196$	17.6253	1.25895
$197$	−17.0738	−1.21646	−0.608229	−	0.793761i	$-0.708120\pi$
$197$	−17.0738	−1.21646	−0.608229	+	0.793761i	$0.708120\pi$
$198$	1.00000	0.0710669
$199$	−25.1490	−1.78277	−0.891384	−	0.453249i	$-0.850265\pi$
$199$	−25.1490	−1.78277	−0.891384	+	0.453249i	$0.850265\pi$
$200$	−1.00000	−0.0707107
$201$	−5.08840	−0.358908
$202$	−6.31265	−0.444157
$203$	−6.07522	−0.426397
$204$	−1.00000	−0.0700140
$205$	−7.61213	−0.531654
$206$	−13.4010	−0.933695
$207$	3.35026	0.232859
$208$	2.96239	0.205405
$209$	−3.35026	−0.231742
$210$	4.96239	0.342437
$211$	−4.77575	−0.328776	−0.164388	−	0.986396i	$-0.552565\pi$
$211$	−4.77575	−0.328776	−0.164388	+	0.986396i	$0.552565\pi$
$212$	−1.35026	−0.0927364
$213$	5.73813	0.393171
$214$	−14.5501	−0.994623
$215$	−5.73813	−0.391338
$216$	−1.00000	−0.0680414
$217$	53.1002	3.60467
$218$	16.7005	1.13110
$219$	7.73813	0.522895
$220$	−1.00000	−0.0674200
$221$	−2.96239	−0.199272
$222$	−3.92478	−0.263414
$223$	−16.3733	−1.09644	−0.548218	−	0.836335i	$-0.684694\pi$
$223$	−16.3733	−1.09644	−0.548218	+	0.836335i	$0.684694\pi$
$224$	4.96239	0.331564
$225$	1.00000	0.0666667
$226$	−7.27504	−0.483928
$227$	−20.6253	−1.36895	−0.684475	−	0.729037i	$-0.739968\pi$
$227$	−20.6253	−1.36895	−0.684475	+	0.729037i	$0.739968\pi$
$228$	3.35026	0.221877
$229$	−8.70052	−0.574947	−0.287473	−	0.957789i	$-0.592815\pi$
$229$	−8.70052	−0.574947	−0.287473	+	0.957789i	$0.592815\pi$
$230$	−3.35026	−0.220910
$231$	4.96239	0.326501
$232$	−1.22425	−0.0803762
$233$	3.14903	0.206300	0.103150	−	0.994666i	$-0.467108\pi$
$233$	3.14903	0.206300	0.103150	+	0.994666i	$0.467108\pi$
$234$	−2.96239	−0.193657
$235$	4.00000	0.260931
$236$	−14.8872	−0.969072
$237$	6.05079	0.393041
$238$	−4.96239	−0.321664
$239$	−8.37328	−0.541623	−0.270811	−	0.962632i	$-0.587292\pi$
$239$	−8.37328	−0.541623	−0.270811	+	0.962632i	$0.587292\pi$
$240$	1.00000	0.0645497
$241$	−14.1260	−0.909936	−0.454968	−	0.890508i	$-0.650349\pi$
$241$	−14.1260	−0.909936	−0.454968	+	0.890508i	$0.650349\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	17.6253	1.12604
$246$	7.61213	0.485331
$247$	9.92478	0.631498
$248$	10.7005	0.679484
$249$	−12.6253	−0.800096
$250$	−1.00000	−0.0632456
$251$	−1.73813	−0.109710	−0.0548551	−	0.998494i	$-0.517470\pi$
$251$	−1.73813	−0.109710	−0.0548551	+	0.998494i	$0.517470\pi$
$252$	−4.96239	−0.312601
$253$	−3.35026	−0.210629
$254$	1.29948	0.0815364
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	8.07522	0.503719	0.251859	−	0.967764i	$-0.418958\pi$
$257$	8.07522	0.503719	0.251859	+	0.967764i	$0.418958\pi$
$258$	5.73813	0.357241
$259$	−19.4763	−1.21020
$260$	2.96239	0.183720
$261$	1.22425	0.0757794
$262$	7.22425	0.446316
$263$	−8.37328	−0.516319	−0.258159	−	0.966102i	$-0.583116\pi$
$263$	−8.37328	−0.516319	−0.258159	+	0.966102i	$0.583116\pi$
$264$	1.00000	0.0615457
$265$	−1.35026	−0.0829459
$266$	16.6253	1.01936
$267$	3.92478	0.240192
$268$	−5.08840	−0.310823
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−1.00000	−0.0608581
$271$	−21.7743	−1.32270	−0.661348	−	0.750079i	$-0.730015\pi$
$271$	−21.7743	−1.32270	−0.661348	+	0.750079i	$0.730015\pi$
$272$	−1.00000	−0.0606339
$273$	−14.7005	−0.889716
$274$	21.3258	1.28834
$275$	−1.00000	−0.0603023
$276$	3.35026	0.201662
$277$	10.7757	0.647452	0.323726	−	0.946151i	$-0.395064\pi$
$277$	10.7757	0.647452	0.323726	+	0.946151i	$0.395064\pi$
$278$	21.4010	1.28355
$279$	−10.7005	−0.640624
$280$	4.96239	0.296559
$281$	9.47627	0.565307	0.282653	−	0.959222i	$-0.408785\pi$
$281$	9.47627	0.565307	0.282653	+	0.959222i	$0.408785\pi$
$282$	−4.00000	−0.238197
$283$	2.55008	0.151586	0.0757932	−	0.997124i	$-0.475851\pi$
$283$	2.55008	0.151586	0.0757932	+	0.997124i	$0.475851\pi$
$284$	5.73813	0.340496
$285$	3.35026	0.198452
$286$	2.96239	0.175170
$287$	37.7743	2.22975
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−1.22425	−0.0718907
$291$	16.2374	0.951855
$292$	7.73813	0.452840
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	−17.6253	−1.02793
$295$	−14.8872	−0.866764
$296$	−3.92478	−0.228123
$297$	−1.00000	−0.0580259
$298$	12.2374	0.708895
$299$	9.92478	0.573965
$300$	1.00000	0.0577350
$301$	28.4749	1.64126
$302$	16.6253	0.956679
$303$	6.31265	0.362652
$304$	3.35026	0.192151
$305$	−10.0000	−0.572598
$306$	1.00000	0.0571662
$307$	−4.43866	−0.253328	−0.126664	−	0.991946i	$-0.540427\pi$
$307$	−4.43866	−0.253328	−0.126664	+	0.991946i	$0.540427\pi$
$308$	4.96239	0.282758
$309$	13.4010	0.762359
$310$	10.7005	0.607749
$311$	−25.8397	−1.46524	−0.732618	−	0.680640i	$-0.761702\pi$
$311$	−25.8397	−1.46524	−0.732618	+	0.680640i	$0.761702\pi$
$312$	−2.96239	−0.167712
$313$	4.38787	0.248017	0.124009	−	0.992281i	$-0.460425\pi$
$313$	4.38787	0.248017	0.124009	+	0.992281i	$0.460425\pi$
$314$	8.23743	0.464865
$315$	−4.96239	−0.279599
$316$	6.05079	0.340383
$317$	−10.2520	−0.575811	−0.287905	−	0.957659i	$-0.592959\pi$
$317$	−10.2520	−0.575811	−0.287905	+	0.957659i	$0.592959\pi$
$318$	1.35026	0.0757189
$319$	−1.22425	−0.0685450
$320$	1.00000	0.0559017
$321$	14.5501	0.812106
$322$	16.6253	0.926492
$323$	−3.35026	−0.186414
$324$	1.00000	0.0555556
$325$	2.96239	0.164324
$326$	9.14903	0.506718
$327$	−16.7005	−0.923541
$328$	7.61213	0.420309
$329$	−19.8496	−1.09434
$330$	1.00000	0.0550482
$331$	−11.0738	−0.608672	−0.304336	−	0.952565i	$-0.598434\pi$
$331$	−11.0738	−0.608672	−0.304336	+	0.952565i	$0.598434\pi$
$332$	−12.6253	−0.692903
$333$	3.92478	0.215076
$334$	−7.47627	−0.409083
$335$	−5.08840	−0.278009
$336$	−4.96239	−0.270720
$337$	−4.11142	−0.223963	−0.111982	−	0.993710i	$-0.535720\pi$
$337$	−4.11142	−0.223963	−0.111982	+	0.993710i	$0.535720\pi$
$338$	4.22425	0.229769
$339$	7.27504	0.395126
$340$	−1.00000	−0.0542326
$341$	10.7005	0.579466
$342$	−3.35026	−0.181161
$343$	−52.7269	−2.84698
$344$	5.73813	0.309379
$345$	3.35026	0.180372
$346$	−4.44851	−0.239153
$347$	−18.0263	−0.967705	−0.483853	−	0.875150i	$-0.660763\pi$
$347$	−18.0263	−0.967705	−0.483853	+	0.875150i	$0.660763\pi$
$348$	1.22425	0.0656269
$349$	11.1246	0.595486	0.297743	−	0.954646i	$-0.403766\pi$
$349$	11.1246	0.595486	0.297743	+	0.954646i	$0.403766\pi$
$350$	4.96239	0.265251
$351$	2.96239	0.158121
$352$	1.00000	0.0533002
$353$	−17.4763	−0.930168	−0.465084	−	0.885267i	$-0.653976\pi$
$353$	−17.4763	−0.930168	−0.465084	+	0.885267i	$0.653976\pi$
$354$	14.8872	0.791244
$355$	5.73813	0.304549
$356$	3.92478	0.208013
$357$	4.96239	0.262637
$358$	−14.8872	−0.786811
$359$	12.1016	0.638696	0.319348	−	0.947637i	$-0.396536\pi$
$359$	12.1016	0.638696	0.319348	+	0.947637i	$0.396536\pi$
$360$	−1.00000	−0.0527046
$361$	−7.77575	−0.409250
$362$	9.22425	0.484816
$363$	1.00000	0.0524864
$364$	−14.7005	−0.770517
$365$	7.73813	0.405032
$366$	10.0000	0.522708
$367$	−1.86414	−0.0973075	−0.0486537	−	0.998816i	$-0.515493\pi$
$367$	−1.86414	−0.0973075	−0.0486537	+	0.998816i	$0.515493\pi$
$368$	3.35026	0.174644
$369$	−7.61213	−0.396271
$370$	−3.92478	−0.204039
$371$	6.70052	0.347874
$372$	−10.7005	−0.554796
$373$	−17.8134	−0.922341	−0.461170	−	0.887312i	$-0.652570\pi$
$373$	−17.8134	−0.922341	−0.461170	+	0.887312i	$0.652570\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−4.00000	−0.206284
$377$	3.62672	0.186785
$378$	4.96239	0.255238
$379$	−10.7005	−0.549649	−0.274824	−	0.961494i	$-0.588620\pi$
$379$	−10.7005	−0.549649	−0.274824	+	0.961494i	$0.588620\pi$
$380$	3.35026	0.171865
$381$	−1.29948	−0.0665742
$382$	−8.77575	−0.449006
$383$	27.3258	1.39628	0.698142	−	0.715959i	$-0.254010\pi$
$383$	27.3258	1.39628	0.698142	+	0.715959i	$0.254010\pi$
$384$	−1.00000	−0.0510310
$385$	4.96239	0.252907
$386$	10.1866	0.518486
$387$	−5.73813	−0.291686
$388$	16.2374	0.824330
$389$	−5.66291	−0.287121	−0.143561	−	0.989642i	$-0.545855\pi$
$389$	−5.66291	−0.287121	−0.143561	+	0.989642i	$0.545855\pi$
$390$	−2.96239	−0.150006
$391$	−3.35026	−0.169430
$392$	−17.6253	−0.890212
$393$	−7.22425	−0.364415
$394$	17.0738	0.860166
$395$	6.05079	0.304448
$396$	−1.00000	−0.0502519
$397$	26.9986	1.35502	0.677510	−	0.735513i	$-0.263059\pi$
$397$	26.9986	1.35502	0.677510	+	0.735513i	$0.263059\pi$
$398$	25.1490	1.26061
$399$	−16.6253	−0.832306
$400$	1.00000	0.0500000
$401$	−8.88717	−0.443804	−0.221902	−	0.975069i	$-0.571226\pi$
$401$	−8.88717	−0.443804	−0.221902	+	0.975069i	$0.571226\pi$
$402$	5.08840	0.253786
$403$	−31.6991	−1.57905
$404$	6.31265	0.314066
$405$	1.00000	0.0496904
$406$	6.07522	0.301508
$407$	−3.92478	−0.194544
$408$	1.00000	0.0495074
$409$	18.9986	0.939420	0.469710	−	0.882821i	$-0.344359\pi$
$409$	18.9986	0.939420	0.469710	+	0.882821i	$0.344359\pi$
$410$	7.61213	0.375936
$411$	−21.3258	−1.05193
$412$	13.4010	0.660222
$413$	73.8759	3.63520
$414$	−3.35026	−0.164656
$415$	−12.6253	−0.619752
$416$	−2.96239	−0.145243
$417$	−21.4010	−1.04801
$418$	3.35026	0.163867
$419$	−12.6253	−0.616786	−0.308393	−	0.951259i	$-0.599791\pi$
$419$	−12.6253	−0.616786	−0.308393	+	0.951259i	$0.599791\pi$
$420$	−4.96239	−0.242140
$421$	7.55149	0.368037	0.184019	−	0.982923i	$-0.441089\pi$
$421$	7.55149	0.368037	0.184019	+	0.982923i	$0.441089\pi$
$422$	4.77575	0.232480
$423$	4.00000	0.194487
$424$	1.35026	0.0655745
$425$	−1.00000	−0.0485071
$426$	−5.73813	−0.278014
$427$	49.6239	2.40147
$428$	14.5501	0.703305
$429$	−2.96239	−0.143025
$430$	5.73813	0.276717
$431$	13.2097	0.636287	0.318144	−	0.948043i	$-0.396941\pi$
$431$	13.2097	0.636287	0.318144	+	0.948043i	$0.396941\pi$
$432$	1.00000	0.0481125
$433$	−7.25060	−0.348442	−0.174221	−	0.984707i	$-0.555741\pi$
$433$	−7.25060	−0.348442	−0.174221	+	0.984707i	$0.555741\pi$
$434$	−53.1002	−2.54889
$435$	1.22425	0.0586985
$436$	−16.7005	−0.799810
$437$	11.2243	0.536929
$438$	−7.73813	−0.369742
$439$	17.9003	0.854337	0.427168	−	0.904172i	$-0.359511\pi$
$439$	17.9003	0.854337	0.427168	+	0.904172i	$0.359511\pi$
$440$	1.00000	0.0476731
$441$	17.6253	0.839300
$442$	2.96239	0.140906
$443$	−8.64974	−0.410961	−0.205481	−	0.978661i	$-0.565876\pi$
$443$	−8.64974	−0.410961	−0.205481	+	0.978661i	$0.565876\pi$
$444$	3.92478	0.186262
$445$	3.92478	0.186052
$446$	16.3733	0.775298
$447$	−12.2374	−0.578810
$448$	−4.96239	−0.234451
$449$	9.66291	0.456021	0.228011	−	0.973659i	$-0.426778\pi$
$449$	9.66291	0.456021	0.228011	+	0.973659i	$0.426778\pi$
$450$	−1.00000	−0.0471405
$451$	7.61213	0.358441
$452$	7.27504	0.342189
$453$	−16.6253	−0.781125
$454$	20.6253	0.967993
$455$	−14.7005	−0.689171
$456$	−3.35026	−0.156890
$457$	−33.1754	−1.55188	−0.775939	−	0.630807i	$-0.782724\pi$
$457$	−33.1754	−1.55188	−0.775939	+	0.630807i	$0.782724\pi$
$458$	8.70052	0.406549
$459$	−1.00000	−0.0466760
$460$	3.35026	0.156207
$461$	9.78892	0.455915	0.227958	−	0.973671i	$-0.426795\pi$
$461$	9.78892	0.455915	0.227958	+	0.973671i	$0.426795\pi$
$462$	−4.96239	−0.230871
$463$	19.1754	0.891155	0.445578	−	0.895243i	$-0.352998\pi$
$463$	19.1754	0.891155	0.445578	+	0.895243i	$0.352998\pi$
$464$	1.22425	0.0568346
$465$	−10.7005	−0.496225
$466$	−3.14903	−0.145876
$467$	31.9756	1.47965	0.739826	−	0.672798i	$-0.234908\pi$
$467$	31.9756	1.47965	0.739826	+	0.672798i	$0.234908\pi$
$468$	2.96239	0.136936
$469$	25.2506	1.16596
$470$	−4.00000	−0.184506
$471$	−8.23743	−0.379561
$472$	14.8872	0.685237
$473$	5.73813	0.263840
$474$	−6.05079	−0.277922
$475$	3.35026	0.153721
$476$	4.96239	0.227451
$477$	−1.35026	−0.0618242
$478$	8.37328	0.382985
$479$	10.2374	0.467760	0.233880	−	0.972265i	$-0.424858\pi$
$479$	10.2374	0.467760	0.233880	+	0.972265i	$0.424858\pi$
$480$	−1.00000	−0.0456435
$481$	11.6267	0.530133
$482$	14.1260	0.643422
$483$	−16.6253	−0.756477
$484$	1.00000	0.0454545
$485$	16.2374	0.737304
$486$	−1.00000	−0.0453609
$487$	−31.3865	−1.42226	−0.711128	−	0.703062i	$-0.751815\pi$
$487$	−31.3865	−1.42226	−0.711128	+	0.703062i	$0.751815\pi$
$488$	10.0000	0.452679
$489$	−9.14903	−0.413733
$490$	−17.6253	−0.796230
$491$	9.86414	0.445163	0.222581	−	0.974914i	$-0.428552\pi$
$491$	9.86414	0.445163	0.222581	+	0.974914i	$0.428552\pi$
$492$	−7.61213	−0.343181
$493$	−1.22425	−0.0551376
$494$	−9.92478	−0.446537
$495$	−1.00000	−0.0449467
$496$	−10.7005	−0.480468
$497$	−28.4749	−1.27727
$498$	12.6253	0.565753
$499$	−8.15045	−0.364864	−0.182432	−	0.983218i	$-0.558397\pi$
$499$	−8.15045	−0.364864	−0.182432	+	0.983218i	$0.558397\pi$
$500$	1.00000	0.0447214
$501$	7.47627	0.334015
$502$	1.73813	0.0775768
$503$	−10.9525	−0.488350	−0.244175	−	0.969731i	$-0.578517\pi$
$503$	−10.9525	−0.488350	−0.244175	+	0.969731i	$0.578517\pi$
$504$	4.96239	0.221042
$505$	6.31265	0.280909
$506$	3.35026	0.148937
$507$	−4.22425	−0.187606
$508$	−1.29948	−0.0576549
$509$	14.1866	0.628812	0.314406	−	0.949289i	$-0.398195\pi$
$509$	14.1866	0.628812	0.314406	+	0.949289i	$0.398195\pi$
$510$	1.00000	0.0442807
$511$	−38.3996	−1.69870
$512$	−1.00000	−0.0441942
$513$	3.35026	0.147918
$514$	−8.07522	−0.356183
$515$	13.4010	0.590521
$516$	−5.73813	−0.252607
$517$	−4.00000	−0.175920
$518$	19.4763	0.855738
$519$	4.44851	0.195268
$520$	−2.96239	−0.129909
$521$	22.8119	0.999409	0.499705	−	0.866196i	$-0.333442\pi$
$521$	22.8119	0.999409	0.499705	+	0.866196i	$0.333442\pi$
$522$	−1.22425	−0.0535841
$523$	−11.8134	−0.516562	−0.258281	−	0.966070i	$-0.583156\pi$
$523$	−11.8134	−0.516562	−0.258281	+	0.966070i	$0.583156\pi$
$524$	−7.22425	−0.315593
$525$	−4.96239	−0.216576
$526$	8.37328	0.365093
$527$	10.7005	0.466122
$528$	−1.00000	−0.0435194
$529$	−11.7757	−0.511989
$530$	1.35026	0.0586516
$531$	−14.8872	−0.646048
$532$	−16.6253	−0.720798
$533$	−22.5501	−0.976752
$534$	−3.92478	−0.169842
$535$	14.5501	0.629055
$536$	5.08840	0.219785
$537$	14.8872	0.642429
$538$	−14.0000	−0.603583
$539$	−17.6253	−0.759175
$540$	1.00000	0.0430331
$541$	−23.4010	−1.00609	−0.503045	−	0.864260i	$-0.667787\pi$
$541$	−23.4010	−1.00609	−0.503045	+	0.864260i	$0.667787\pi$
$542$	21.7743	0.935288
$543$	−9.22425	−0.395851
$544$	1.00000	0.0428746
$545$	−16.7005	−0.715372
$546$	14.7005	0.629124
$547$	−26.2981	−1.12442	−0.562212	−	0.826993i	$-0.690049\pi$
$547$	−26.2981	−1.12442	−0.562212	+	0.826993i	$0.690049\pi$
$548$	−21.3258	−0.910994
$549$	−10.0000	−0.426790
$550$	1.00000	0.0426401
$551$	4.10157	0.174733
$552$	−3.35026	−0.142597
$553$	−30.0263	−1.27685
$554$	−10.7757	−0.457818
$555$	3.92478	0.166598
$556$	−21.4010	−0.907607
$557$	34.6253	1.46712	0.733561	−	0.679624i	$-0.237857\pi$
$557$	34.6253	1.46712	0.733561	+	0.679624i	$0.237857\pi$
$558$	10.7005	0.452989
$559$	−16.9986	−0.718964
$560$	−4.96239	−0.209699
$561$	1.00000	0.0422200
$562$	−9.47627	−0.399732
$563$	0.775746	0.0326938	0.0163469	−	0.999866i	$-0.494796\pi$
$563$	0.775746	0.0326938	0.0163469	+	0.999866i	$0.494796\pi$
$564$	4.00000	0.168430
$565$	7.27504	0.306063
$566$	−2.55008	−0.107188
$567$	−4.96239	−0.208401
$568$	−5.73813	−0.240767
$569$	3.77433	0.158228	0.0791141	−	0.996866i	$-0.474791\pi$
$569$	3.77433	0.158228	0.0791141	+	0.996866i	$0.474791\pi$
$570$	−3.35026	−0.140327
$571$	−38.1476	−1.59643	−0.798214	−	0.602374i	$-0.794222\pi$
$571$	−38.1476	−1.59643	−0.798214	+	0.602374i	$0.794222\pi$
$572$	−2.96239	−0.123864
$573$	8.77575	0.366612
$574$	−37.7743	−1.57667
$575$	3.35026	0.139716
$576$	1.00000	0.0416667
$577$	−32.2981	−1.34459	−0.672293	−	0.740285i	$-0.734690\pi$
$577$	−32.2981	−1.34459	−0.672293	+	0.740285i	$0.734690\pi$
$578$	−1.00000	−0.0415945
$579$	−10.1866	−0.423342
$580$	1.22425	0.0508344
$581$	62.6516	2.59923
$582$	−16.2374	−0.673063
$583$	1.35026	0.0559221
$584$	−7.73813	−0.320206
$585$	2.96239	0.122480
$586$	−10.0000	−0.413096
$587$	37.4979	1.54770	0.773852	−	0.633367i	$-0.218328\pi$
$587$	37.4979	1.54770	0.773852	+	0.633367i	$0.218328\pi$
$588$	17.6253	0.726855
$589$	−35.8496	−1.47716
$590$	14.8872	0.612895
$591$	−17.0738	−0.702323
$592$	3.92478	0.161307
$593$	14.6253	0.600589	0.300295	−	0.953847i	$-0.402915\pi$
$593$	14.6253	0.600589	0.300295	+	0.953847i	$0.402915\pi$
$594$	1.00000	0.0410305
$595$	4.96239	0.203438
$596$	−12.2374	−0.501265
$597$	−25.1490	−1.02928
$598$	−9.92478	−0.405854
$599$	38.9234	1.59037	0.795183	−	0.606370i	$-0.207375\pi$
$599$	38.9234	1.59037	0.795183	+	0.606370i	$0.207375\pi$
$600$	−1.00000	−0.0408248
$601$	3.79877	0.154955	0.0774775	−	0.996994i	$-0.475313\pi$
$601$	3.79877	0.154955	0.0774775	+	0.996994i	$0.475313\pi$
$602$	−28.4749	−1.16055
$603$	−5.08840	−0.207216
$604$	−16.6253	−0.676474
$605$	1.00000	0.0406558
$606$	−6.31265	−0.256434
$607$	−19.4109	−0.787864	−0.393932	−	0.919140i	$-0.628885\pi$
$607$	−19.4109	−0.787864	−0.393932	+	0.919140i	$0.628885\pi$
$608$	−3.35026	−0.135871
$609$	−6.07522	−0.246180
$610$	10.0000	0.404888
$611$	11.8496	0.479382
$612$	−1.00000	−0.0404226
$613$	−8.26187	−0.333694	−0.166847	−	0.985983i	$-0.553359\pi$
$613$	−8.26187	−0.333694	−0.166847	+	0.985983i	$0.553359\pi$
$614$	4.43866	0.179130
$615$	−7.61213	−0.306951
$616$	−4.96239	−0.199940
$617$	20.3028	0.817360	0.408680	−	0.912678i	$-0.365989\pi$
$617$	20.3028	0.817360	0.408680	+	0.912678i	$0.365989\pi$
$618$	−13.4010	−0.539069
$619$	−22.2981	−0.896235	−0.448117	−	0.893975i	$-0.647905\pi$
$619$	−22.2981	−0.896235	−0.448117	+	0.893975i	$0.647905\pi$
$620$	−10.7005	−0.429743
$621$	3.35026	0.134441
$622$	25.8397	1.03608
$623$	−19.4763	−0.780300
$624$	2.96239	0.118590
$625$	1.00000	0.0400000
$626$	−4.38787	−0.175375
$627$	−3.35026	−0.133797
$628$	−8.23743	−0.328709
$629$	−3.92478	−0.156491
$630$	4.96239	0.197706
$631$	19.4763	0.775338	0.387669	−	0.921799i	$-0.373280\pi$
$631$	19.4763	0.775338	0.387669	+	0.921799i	$0.373280\pi$
$632$	−6.05079	−0.240687
$633$	−4.77575	−0.189819
$634$	10.2520	0.407160
$635$	−1.29948	−0.0515682
$636$	−1.35026	−0.0535414
$637$	52.2130	2.06875
$638$	1.22425	0.0484687
$639$	5.73813	0.226997
$640$	−1.00000	−0.0395285
$641$	−50.1378	−1.98032	−0.990161	−	0.139930i	$-0.955312\pi$
$641$	−50.1378	−1.98032	−0.990161	+	0.139930i	$0.955312\pi$
$642$	−14.5501	−0.574246
$643$	11.3747	0.448574	0.224287	−	0.974523i	$-0.427995\pi$
$643$	11.3747	0.448574	0.224287	+	0.974523i	$0.427995\pi$
$644$	−16.6253	−0.655129
$645$	−5.73813	−0.225939
$646$	3.35026	0.131814
$647$	−18.0263	−0.708689	−0.354344	−	0.935115i	$-0.615296\pi$
$647$	−18.0263	−0.708689	−0.354344	+	0.935115i	$0.615296\pi$
$648$	−1.00000	−0.0392837
$649$	14.8872	0.584372
$650$	−2.96239	−0.116194
$651$	53.1002	2.08116
$652$	−9.14903	−0.358304
$653$	−21.8496	−0.855039	−0.427520	−	0.904006i	$-0.640612\pi$
$653$	−21.8496	−0.855039	−0.427520	+	0.904006i	$0.640612\pi$
$654$	16.7005	0.653042
$655$	−7.22425	−0.282275
$656$	−7.61213	−0.297204
$657$	7.73813	0.301893
$658$	19.8496	0.773816
$659$	−37.0884	−1.44476	−0.722379	−	0.691497i	$-0.756952\pi$
$659$	−37.0884	−1.44476	−0.722379	+	0.691497i	$0.756952\pi$
$660$	−1.00000	−0.0389249
$661$	31.6239	1.23003	0.615013	−	0.788517i	$-0.289151\pi$
$661$	31.6239	1.23003	0.615013	+	0.788517i	$0.289151\pi$
$662$	11.0738	0.430396
$663$	−2.96239	−0.115050
$664$	12.6253	0.489957
$665$	−16.6253	−0.644702
$666$	−3.92478	−0.152082
$667$	4.10157	0.158813
$668$	7.47627	0.289266
$669$	−16.3733	−0.633028
$670$	5.08840	0.196582
$671$	10.0000	0.386046
$672$	4.96239	0.191428
$673$	−3.73813	−0.144095	−0.0720473	−	0.997401i	$-0.522953\pi$
$673$	−3.73813	−0.144095	−0.0720473	+	0.997401i	$0.522953\pi$
$674$	4.11142	0.158366
$675$	1.00000	0.0384900
$676$	−4.22425	−0.162471
$677$	−17.0738	−0.656200	−0.328100	−	0.944643i	$-0.606408\pi$
$677$	−17.0738	−0.656200	−0.328100	+	0.944643i	$0.606408\pi$
$678$	−7.27504	−0.279396
$679$	−80.5764	−3.09224
$680$	1.00000	0.0383482
$681$	−20.6253	−0.790363
$682$	−10.7005	−0.409744
$683$	0.150446	0.00575664	0.00287832	−	0.999996i	$-0.499084\pi$
$683$	0.150446	0.00575664	0.00287832	+	0.999996i	$0.499084\pi$
$684$	3.35026	0.128100
$685$	−21.3258	−0.814818
$686$	52.7269	2.01312
$687$	−8.70052	−0.331946
$688$	−5.73813	−0.218764
$689$	−4.00000	−0.152388
$690$	−3.35026	−0.127542
$691$	9.77433	0.371833	0.185917	−	0.982566i	$-0.440475\pi$
$691$	9.77433	0.371833	0.185917	+	0.982566i	$0.440475\pi$
$692$	4.44851	0.169107
$693$	4.96239	0.188506
$694$	18.0263	0.684271
$695$	−21.4010	−0.811788
$696$	−1.22425	−0.0464052
$697$	7.61213	0.288330
$698$	−11.1246	−0.421072
$699$	3.14903	0.119107
$700$	−4.96239	−0.187561
$701$	45.6385	1.72374	0.861871	−	0.507128i	$-0.169293\pi$
$701$	45.6385	1.72374	0.861871	+	0.507128i	$0.169293\pi$
$702$	−2.96239	−0.111808
$703$	13.1490	0.495925
$704$	−1.00000	−0.0376889
$705$	4.00000	0.150649
$706$	17.4763	0.657728
$707$	−31.3258	−1.17813
$708$	−14.8872	−0.559494
$709$	−45.6991	−1.71627	−0.858133	−	0.513427i	$-0.828376\pi$
$709$	−45.6991	−1.71627	−0.858133	+	0.513427i	$0.828376\pi$
$710$	−5.73813	−0.215348
$711$	6.05079	0.226922
$712$	−3.92478	−0.147087
$713$	−35.8496	−1.34258
$714$	−4.96239	−0.185713
$715$	−2.96239	−0.110787
$716$	14.8872	0.556360
$717$	−8.37328	−0.312706
$718$	−12.1016	−0.451627
$719$	42.8872	1.59942	0.799711	−	0.600386i	$-0.204986\pi$
$719$	42.8872	1.59942	0.799711	+	0.600386i	$0.204986\pi$
$720$	1.00000	0.0372678
$721$	−66.5012	−2.47663
$722$	7.77575	0.289383
$723$	−14.1260	−0.525352
$724$	−9.22425	−0.342817
$725$	1.22425	0.0454676
$726$	−1.00000	−0.0371135
$727$	−36.3536	−1.34828	−0.674140	−	0.738604i	$-0.735486\pi$
$727$	−36.3536	−1.34828	−0.674140	+	0.738604i	$0.735486\pi$
$728$	14.7005	0.544838
$729$	1.00000	0.0370370
$730$	−7.73813	−0.286401
$731$	5.73813	0.212233
$732$	−10.0000	−0.369611
$733$	4.63515	0.171203	0.0856016	−	0.996329i	$-0.472719\pi$
$733$	4.63515	0.171203	0.0856016	+	0.996329i	$0.472719\pi$
$734$	1.86414	0.0688068
$735$	17.6253	0.650119
$736$	−3.35026	−0.123492
$737$	5.08840	0.187433
$738$	7.61213	0.280206
$739$	11.9756	0.440528	0.220264	−	0.975440i	$-0.429308\pi$
$739$	11.9756	0.440528	0.220264	+	0.975440i	$0.429308\pi$
$740$	3.92478	0.144278
$741$	9.92478	0.364596
$742$	−6.70052	−0.245984
$743$	−16.7757	−0.615442	−0.307721	−	0.951477i	$-0.599566\pi$
$743$	−16.7757	−0.615442	−0.307721	+	0.951477i	$0.599566\pi$
$744$	10.7005	0.392300
$745$	−12.2374	−0.448345
$746$	17.8134	0.652193
$747$	−12.6253	−0.461936
$748$	1.00000	0.0365636
$749$	−72.2031	−2.63825
$750$	−1.00000	−0.0365148
$751$	32.4749	1.18502	0.592512	−	0.805562i	$-0.298136\pi$
$751$	32.4749	1.18502	0.592512	+	0.805562i	$0.298136\pi$
$752$	4.00000	0.145865
$753$	−1.73813	−0.0633412
$754$	−3.62672	−0.132077
$755$	−16.6253	−0.605057
$756$	−4.96239	−0.180480
$757$	47.7137	1.73418	0.867092	−	0.498148i	$-0.165986\pi$
$757$	47.7137	1.73418	0.867092	+	0.498148i	$0.165986\pi$
$758$	10.7005	0.388661
$759$	−3.35026	−0.121607
$760$	−3.35026	−0.121527
$761$	25.5975	0.927910	0.463955	−	0.885859i	$-0.346430\pi$
$761$	25.5975	0.927910	0.463955	+	0.885859i	$0.346430\pi$
$762$	1.29948	0.0470751
$763$	82.8745	3.00026
$764$	8.77575	0.317495
$765$	−1.00000	−0.0361551
$766$	−27.3258	−0.987322
$767$	−44.1016	−1.59242
$768$	1.00000	0.0360844
$769$	18.7466	0.676019	0.338009	−	0.941143i	$-0.390246\pi$
$769$	18.7466	0.676019	0.338009	+	0.941143i	$0.390246\pi$
$770$	−4.96239	−0.178832
$771$	8.07522	0.290822
$772$	−10.1866	−0.366625
$773$	30.6009	1.10064	0.550318	−	0.834955i	$-0.314506\pi$
$773$	30.6009	1.10064	0.550318	+	0.834955i	$0.314506\pi$
$774$	5.73813	0.206253
$775$	−10.7005	−0.384374
$776$	−16.2374	−0.582890
$777$	−19.4763	−0.698707
$778$	5.66291	0.203025
$779$	−25.5026	−0.913726
$780$	2.96239	0.106071
$781$	−5.73813	−0.205327
$782$	3.35026	0.119805
$783$	1.22425	0.0437513
$784$	17.6253	0.629475
$785$	−8.23743	−0.294006
$786$	7.22425	0.257681
$787$	54.7729	1.95244	0.976222	−	0.216774i	$-0.0695535\pi$
$787$	54.7729	1.95244	0.976222	+	0.216774i	$0.0695535\pi$
$788$	−17.0738	−0.608229
$789$	−8.37328	−0.298097
$790$	−6.05079	−0.215277
$791$	−36.1016	−1.28362
$792$	1.00000	0.0355335
$793$	−29.6239	−1.05198
$794$	−26.9986	−0.958144
$795$	−1.35026	−0.0478888
$796$	−25.1490	−0.891384
$797$	29.7235	1.05286	0.526431	−	0.850218i	$-0.323530\pi$
$797$	29.7235	1.05286	0.526431	+	0.850218i	$0.323530\pi$
$798$	16.6253	0.588529
$799$	−4.00000	−0.141510
$800$	−1.00000	−0.0353553
$801$	3.92478	0.138675
$802$	8.88717	0.313817
$803$	−7.73813	−0.273073
$804$	−5.08840	−0.179454
$805$	−16.6253	−0.585965
$806$	31.6991	1.11655
$807$	14.0000	0.492823
$808$	−6.31265	−0.222078
$809$	44.1886	1.55359	0.776793	−	0.629756i	$-0.216845\pi$
$809$	44.1886	1.55359	0.776793	+	0.629756i	$0.216845\pi$
$810$	−1.00000	−0.0351364
$811$	−17.2995	−0.607467	−0.303733	−	0.952757i	$-0.598233\pi$
$811$	−17.2995	−0.607467	−0.303733	+	0.952757i	$0.598233\pi$
$812$	−6.07522	−0.213199
$813$	−21.7743	−0.763659
$814$	3.92478	0.137563
$815$	−9.14903	−0.320477
$816$	−1.00000	−0.0350070
$817$	−19.2243	−0.672572
$818$	−18.9986	−0.664270
$819$	−14.7005	−0.513678
$820$	−7.61213	−0.265827
$821$	−4.17679	−0.145771	−0.0728855	−	0.997340i	$-0.523221\pi$
$821$	−4.17679	−0.145771	−0.0728855	+	0.997340i	$0.523221\pi$
$822$	21.3258	0.743824
$823$	−17.3112	−0.603432	−0.301716	−	0.953398i	$-0.597559\pi$
$823$	−17.3112	−0.603432	−0.301716	+	0.953398i	$0.597559\pi$
$824$	−13.4010	−0.466848
$825$	−1.00000	−0.0348155
$826$	−73.8759	−2.57047
$827$	−41.7743	−1.45264	−0.726318	−	0.687359i	$-0.758770\pi$
$827$	−41.7743	−1.45264	−0.726318	+	0.687359i	$0.758770\pi$
$828$	3.35026	0.116430
$829$	10.4749	0.363807	0.181903	−	0.983316i	$-0.441774\pi$
$829$	10.4749	0.363807	0.181903	+	0.983316i	$0.441774\pi$
$830$	12.6253	0.438231
$831$	10.7757	0.373806
$832$	2.96239	0.102702
$833$	−17.6253	−0.610680
$834$	21.4010	0.741058
$835$	7.47627	0.258727
$836$	−3.35026	−0.115871
$837$	−10.7005	−0.369864
$838$	12.6253	0.436134
$839$	41.1655	1.42119	0.710596	−	0.703600i	$-0.248425\pi$
$839$	41.1655	1.42119	0.710596	+	0.703600i	$0.248425\pi$
$840$	4.96239	0.171219
$841$	−27.5012	−0.948317
$842$	−7.55149	−0.260242
$843$	9.47627	0.326380
$844$	−4.77575	−0.164388
$845$	−4.22425	−0.145319
$846$	−4.00000	−0.137523
$847$	−4.96239	−0.170510
$848$	−1.35026	−0.0463682
$849$	2.55008	0.0875184
$850$	1.00000	0.0342997
$851$	13.1490	0.450743
$852$	5.73813	0.196585
$853$	17.7283	0.607005	0.303502	−	0.952831i	$-0.401844\pi$
$853$	17.7283	0.607005	0.303502	+	0.952831i	$0.401844\pi$
$854$	−49.6239	−1.69809
$855$	3.35026	0.114577
$856$	−14.5501	−0.497311
$857$	−26.7466	−0.913645	−0.456823	−	0.889558i	$-0.651013\pi$
$857$	−26.7466	−0.913645	−0.456823	+	0.889558i	$0.651013\pi$
$858$	2.96239	0.101134
$859$	−13.6728	−0.466509	−0.233254	−	0.972416i	$-0.574937\pi$
$859$	−13.6728	−0.466509	−0.233254	+	0.972416i	$0.574937\pi$
$860$	−5.73813	−0.195669
$861$	37.7743	1.28735
$862$	−13.2097	−0.449923
$863$	50.9037	1.73278	0.866390	−	0.499367i	$-0.166434\pi$
$863$	50.9037	1.73278	0.866390	+	0.499367i	$0.166434\pi$
$864$	−1.00000	−0.0340207
$865$	4.44851	0.151254
$866$	7.25060	0.246385
$867$	1.00000	0.0339618
$868$	53.1002	1.80234
$869$	−6.05079	−0.205259
$870$	−1.22425	−0.0415061
$871$	−15.0738	−0.510757
$872$	16.7005	0.565551
$873$	16.2374	0.549554
$874$	−11.2243	−0.379666
$875$	−4.96239	−0.167759
$876$	7.73813	0.261447
$877$	−0.0263477	−0.000889697 0	−0.000444849	−	1.00000i	$-0.500142\pi$
$877$	−0.0263477	−0.000889697 0	−0.000444849		1.00000i	$0.500142\pi$
$878$	−17.9003	−0.604107
$879$	10.0000	0.337292
$880$	−1.00000	−0.0337100
$881$	20.2619	0.682640	0.341320	−	0.939947i	$-0.389126\pi$
$881$	20.2619	0.682640	0.341320	+	0.939947i	$0.389126\pi$
$882$	−17.6253	−0.593475
$883$	14.0870	0.474065	0.237032	−	0.971502i	$-0.423825\pi$
$883$	14.0870	0.474065	0.237032	+	0.971502i	$0.423825\pi$
$884$	−2.96239	−0.0996359
$885$	−14.8872	−0.500427
$886$	8.64974	0.290594
$887$	5.29948	0.177939	0.0889695	−	0.996034i	$-0.471643\pi$
$887$	5.29948	0.177939	0.0889695	+	0.996034i	$0.471643\pi$
$888$	−3.92478	−0.131707
$889$	6.44851	0.216276
$890$	−3.92478	−0.131559
$891$	−1.00000	−0.0335013
$892$	−16.3733	−0.548218
$893$	13.4010	0.448449
$894$	12.2374	0.409281
$895$	14.8872	0.497623
$896$	4.96239	0.165782
$897$	9.92478	0.331379
$898$	−9.66291	−0.322456
$899$	−13.1002	−0.436915
$900$	1.00000	0.0333333
$901$	1.35026	0.0449837
$902$	−7.61213	−0.253456
$903$	28.4749	0.947584
$904$	−7.27504	−0.241964
$905$	−9.22425	−0.306625
$906$	16.6253	0.552339
$907$	48.9789	1.62632	0.813159	−	0.582042i	$-0.197746\pi$
$907$	48.9789	1.62632	0.813159	+	0.582042i	$0.197746\pi$
$908$	−20.6253	−0.684475
$909$	6.31265	0.209377
$910$	14.7005	0.487318
$911$	−29.0640	−0.962932	−0.481466	−	0.876465i	$-0.659896\pi$
$911$	−29.0640	−0.962932	−0.481466	+	0.876465i	$0.659896\pi$
$912$	3.35026	0.110938
$913$	12.6253	0.417836
$914$	33.1754	1.09734
$915$	−10.0000	−0.330590
$916$	−8.70052	−0.287473
$917$	35.8496	1.18386
$918$	1.00000	0.0330049
$919$	56.3244	1.85797	0.928985	−	0.370116i	$-0.120682\pi$
$919$	56.3244	1.85797	0.928985	+	0.370116i	$0.120682\pi$
$920$	−3.35026	−0.110455
$921$	−4.43866	−0.146259
$922$	−9.78892	−0.322381
$923$	16.9986	0.559515
$924$	4.96239	0.163251
$925$	3.92478	0.129046
$926$	−19.1754	−0.630142
$927$	13.4010	0.440148
$928$	−1.22425	−0.0401881
$929$	30.1378	0.988788	0.494394	−	0.869238i	$-0.335390\pi$
$929$	30.1378	0.988788	0.494394	+	0.869238i	$0.335390\pi$
$930$	10.7005	0.350884
$931$	59.0494	1.93526
$932$	3.14903	0.103150
$933$	−25.8397	−0.845954
$934$	−31.9756	−1.04627
$935$	1.00000	0.0327035
$936$	−2.96239	−0.0968287
$937$	40.0752	1.30920	0.654600	−	0.755975i	$-0.272837\pi$
$937$	40.0752	1.30920	0.654600	+	0.755975i	$0.272837\pi$
$938$	−25.2506	−0.824461
$939$	4.38787	0.143193
$940$	4.00000	0.130466
$941$	23.6728	0.771710	0.385855	−	0.922559i	$-0.373907\pi$
$941$	23.6728	0.771710	0.385855	+	0.922559i	$0.373907\pi$
$942$	8.23743	0.268390
$943$	−25.5026	−0.830479
$944$	−14.8872	−0.484536
$945$	−4.96239	−0.161427
$946$	−5.73813	−0.186563
$947$	−26.8218	−0.871591	−0.435796	−	0.900046i	$-0.643533\pi$
$947$	−26.8218	−0.871591	−0.435796	+	0.900046i	$0.643533\pi$
$948$	6.05079	0.196520
$949$	22.9234	0.744124
$950$	−3.35026	−0.108697
$951$	−10.2520	−0.332444
$952$	−4.96239	−0.160832
$953$	50.4749	1.63504	0.817520	−	0.575900i	$-0.195348\pi$
$953$	50.4749	1.63504	0.817520	+	0.575900i	$0.195348\pi$
$954$	1.35026	0.0437163
$955$	8.77575	0.283976
$956$	−8.37328	−0.270811
$957$	−1.22425	−0.0395745
$958$	−10.2374	−0.330756
$959$	105.827	3.41733
$960$	1.00000	0.0322749
$961$	83.5012	2.69359
$962$	−11.6267	−0.374860
$963$	14.5501	0.468870
$964$	−14.1260	−0.454968
$965$	−10.1866	−0.327920
$966$	16.6253	0.534910
$967$	49.9248	1.60547	0.802736	−	0.596334i	$-0.203377\pi$
$967$	49.9248	1.60547	0.802736	+	0.596334i	$0.203377\pi$
$968$	−1.00000	−0.0321412
$969$	−3.35026	−0.107626
$970$	−16.2374	−0.521352
$971$	−56.0165	−1.79765	−0.898827	−	0.438303i	$-0.855580\pi$
$971$	−56.0165	−1.79765	−0.898827	+	0.438303i	$0.855580\pi$
$972$	1.00000	0.0320750
$973$	106.200	3.40463
$974$	31.3865	1.00569
$975$	2.96239	0.0948724
$976$	−10.0000	−0.320092
$977$	11.9248	0.381507	0.190754	−	0.981638i	$-0.438907\pi$
$977$	11.9248	0.381507	0.190754	+	0.981638i	$0.438907\pi$
$978$	9.14903	0.292554
$979$	−3.92478	−0.125436
$980$	17.6253	0.563020
$981$	−16.7005	−0.533207
$982$	−9.86414	−0.314777
$983$	−3.72355	−0.118763	−0.0593813	−	0.998235i	$-0.518913\pi$
$983$	−3.72355	−0.118763	−0.0593813	+	0.998235i	$0.518913\pi$
$984$	7.61213	0.242666
$985$	−17.0738	−0.544017
$986$	1.22425	0.0389882
$987$	−19.8496	−0.631818
$988$	9.92478	0.315749
$989$	−19.2243	−0.611296
$990$	1.00000	0.0317821
$991$	−28.0000	−0.889449	−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000	−0.889449	−0.444725	+	0.895667i	$0.646698\pi$
$992$	10.7005	0.339742
$993$	−11.0738	−0.351417
$994$	28.4749	0.903168
$995$	−25.1490	−0.797278
$996$	−12.6253	−0.400048
$997$	−48.9037	−1.54879	−0.774397	−	0.632700i	$-0.781947\pi$
$997$	−48.9037	−1.54879	−0.774397	+	0.632700i	$0.781947\pi$
$998$	8.15045	0.257998
$999$	3.92478	0.124174

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.96239 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -4.96239 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.96239 q^{13} +4.96239 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.35026 q^{19} +1.00000 q^{20} -4.96239 q^{21} +1.00000 q^{22} +3.35026 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.96239 q^{26} +1.00000 q^{27} -4.96239 q^{28} +1.22425 q^{29} -1.00000 q^{30} -10.7005 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -4.96239 q^{35} +1.00000 q^{36} +3.92478 q^{37} -3.35026 q^{38} +2.96239 q^{39} -1.00000 q^{40} -7.61213 q^{41} +4.96239 q^{42} -5.73813 q^{43} -1.00000 q^{44} +1.00000 q^{45} -3.35026 q^{46} +4.00000 q^{47} +1.00000 q^{48} +17.6253 q^{49} -1.00000 q^{50} -1.00000 q^{51} +2.96239 q^{52} -1.35026 q^{53} -1.00000 q^{54} -1.00000 q^{55} +4.96239 q^{56} +3.35026 q^{57} -1.22425 q^{58} -14.8872 q^{59} +1.00000 q^{60} -10.0000 q^{61} +10.7005 q^{62} -4.96239 q^{63} +1.00000 q^{64} +2.96239 q^{65} +1.00000 q^{66} -5.08840 q^{67} -1.00000 q^{68} +3.35026 q^{69} +4.96239 q^{70} +5.73813 q^{71} -1.00000 q^{72} +7.73813 q^{73} -3.92478 q^{74} +1.00000 q^{75} +3.35026 q^{76} +4.96239 q^{77} -2.96239 q^{78} +6.05079 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.61213 q^{82} -12.6253 q^{83} -4.96239 q^{84} -1.00000 q^{85} +5.73813 q^{86} +1.22425 q^{87} +1.00000 q^{88} +3.92478 q^{89} -1.00000 q^{90} -14.7005 q^{91} +3.35026 q^{92} -10.7005 q^{93} -4.00000 q^{94} +3.35026 q^{95} -1.00000 q^{96} +16.2374 q^{97} -17.6253 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 3 q^{20} - 4 q^{21} + 3 q^{22} - 3 q^{24} + 3 q^{25} + 2 q^{26} + 3 q^{27} - 4 q^{28} + 2 q^{29} - 3 q^{30} - 12 q^{31} - 3 q^{32} - 3 q^{33} + 3 q^{34} - 4 q^{35} + 3 q^{36} - 10 q^{37} - 2 q^{39} - 3 q^{40} - 22 q^{41} + 4 q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 12 q^{47} + 3 q^{48} + 11 q^{49} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} + 4 q^{56} - 2 q^{58} - 12 q^{59} + 3 q^{60} - 30 q^{61} + 12 q^{62} - 4 q^{63} + 3 q^{64} - 2 q^{65} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 4 q^{70} + 8 q^{71} - 3 q^{72} + 14 q^{73} + 10 q^{74} + 3 q^{75} + 4 q^{77} + 2 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 22 q^{82} + 4 q^{83} - 4 q^{84} - 3 q^{85} + 8 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} - 3 q^{90} - 24 q^{91} - 12 q^{93} - 12 q^{94} - 3 q^{96} + 6 q^{97} - 11 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 - 4 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 3 * q^20 - 4 * q^21 + 3 * q^22 - 3 * q^24 + 3 * q^25 + 2 * q^26 + 3 * q^27 - 4 * q^28 + 2 * q^29 - 3 * q^30 - 12 * q^31 - 3 * q^32 - 3 * q^33 + 3 * q^34 - 4 * q^35 + 3 * q^36 - 10 * q^37 - 2 * q^39 - 3 * q^40 - 22 * q^41 + 4 * q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 12 * q^47 + 3 * q^48 + 11 * q^49 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 + 4 * q^56 - 2 * q^58 - 12 * q^59 + 3 * q^60 - 30 * q^61 + 12 * q^62 - 4 * q^63 + 3 * q^64 - 2 * q^65 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 4 * q^70 + 8 * q^71 - 3 * q^72 + 14 * q^73 + 10 * q^74 + 3 * q^75 + 4 * q^77 + 2 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 22 * q^82 + 4 * q^83 - 4 * q^84 - 3 * q^85 + 8 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 - 3 * q^90 - 24 * q^91 - 12 * q^93 - 12 * q^94 - 3 * q^96 + 6 * q^97 - 11 * q^98 - 3 * q^99

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