LMFDB - Embedded newform 1122.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(1,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1122.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.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:	$8.95921510679$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{7}]$
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	$\chi$	$=$	1122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.35026 q^{5} -1.00000 q^{6} -2.96239 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.35026 q^{5} -1.00000 q^{6} -2.96239 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.35026 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -2.96239 q^{14} +3.35026 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +8.31265 q^{19} -3.35026 q^{20} +2.96239 q^{21} -1.00000 q^{22} +2.96239 q^{23} -1.00000 q^{24} +6.22425 q^{25} +4.00000 q^{26} -1.00000 q^{27} -2.96239 q^{28} -2.96239 q^{29} +3.35026 q^{30} +1.73813 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +9.92478 q^{35} +1.00000 q^{36} +7.73813 q^{37} +8.31265 q^{38} -4.00000 q^{39} -3.35026 q^{40} +11.9248 q^{41} +2.96239 q^{42} -7.53690 q^{43} -1.00000 q^{44} -3.35026 q^{45} +2.96239 q^{46} +4.38787 q^{47} -1.00000 q^{48} +1.77575 q^{49} +6.22425 q^{50} +1.00000 q^{51} +4.00000 q^{52} +2.70052 q^{53} -1.00000 q^{54} +3.35026 q^{55} -2.96239 q^{56} -8.31265 q^{57} -2.96239 q^{58} -10.2374 q^{59} +3.35026 q^{60} +0.649738 q^{61} +1.73813 q^{62} -2.96239 q^{63} +1.00000 q^{64} -13.4010 q^{65} +1.00000 q^{66} +9.14903 q^{67} -1.00000 q^{68} -2.96239 q^{69} +9.92478 q^{70} -3.73813 q^{71} +1.00000 q^{72} +5.53690 q^{73} +7.73813 q^{74} -6.22425 q^{75} +8.31265 q^{76} +2.96239 q^{77} -4.00000 q^{78} -13.6629 q^{79} -3.35026 q^{80} +1.00000 q^{81} +11.9248 q^{82} +9.14903 q^{83} +2.96239 q^{84} +3.35026 q^{85} -7.53690 q^{86} +2.96239 q^{87} -1.00000 q^{88} -7.92478 q^{89} -3.35026 q^{90} -11.8496 q^{91} +2.96239 q^{92} -1.73813 q^{93} +4.38787 q^{94} -27.8496 q^{95} -1.00000 q^{96} +14.6253 q^{97} +1.77575 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{11} - 3 q^{12} + 12 q^{13} + 2 q^{14} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 4 q^{19} - 2 q^{21} - 3 q^{22} - 2 q^{23} - 3 q^{24} + 17 q^{25} + 12 q^{26} - 3 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{31} + 3 q^{32} + 3 q^{33} - 3 q^{34} + 8 q^{35} + 3 q^{36} + 14 q^{37} + 4 q^{38} - 12 q^{39} + 14 q^{41} - 2 q^{42} - 3 q^{44} - 2 q^{46} + 14 q^{47} - 3 q^{48} + 7 q^{49} + 17 q^{50} + 3 q^{51} + 12 q^{52} - 12 q^{53} - 3 q^{54} + 2 q^{56} - 4 q^{57} + 2 q^{58} + 12 q^{59} + 12 q^{61} - 4 q^{62} + 2 q^{63} + 3 q^{64} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 2 q^{69} + 8 q^{70} - 2 q^{71} + 3 q^{72} - 6 q^{73} + 14 q^{74} - 17 q^{75} + 4 q^{76} - 2 q^{77} - 12 q^{78} - 10 q^{79} + 3 q^{81} + 14 q^{82} + 4 q^{83} - 2 q^{84} - 2 q^{87} - 3 q^{88} - 2 q^{89} + 8 q^{91} - 2 q^{92} + 4 q^{93} + 14 q^{94} - 40 q^{95} - 3 q^{96} + 2 q^{97} + 7 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^11 - 3 * q^12 + 12 * q^13 + 2 * q^14 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 4 * q^19 - 2 * q^21 - 3 * q^22 - 2 * q^23 - 3 * q^24 + 17 * q^25 + 12 * q^26 - 3 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^31 + 3 * q^32 + 3 * q^33 - 3 * q^34 + 8 * q^35 + 3 * q^36 + 14 * q^37 + 4 * q^38 - 12 * q^39 + 14 * q^41 - 2 * q^42 - 3 * q^44 - 2 * q^46 + 14 * q^47 - 3 * q^48 + 7 * q^49 + 17 * q^50 + 3 * q^51 + 12 * q^52 - 12 * q^53 - 3 * q^54 + 2 * q^56 - 4 * q^57 + 2 * q^58 + 12 * q^59 + 12 * q^61 - 4 * q^62 + 2 * q^63 + 3 * q^64 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 2 * q^69 + 8 * q^70 - 2 * q^71 + 3 * q^72 - 6 * q^73 + 14 * q^74 - 17 * q^75 + 4 * q^76 - 2 * q^77 - 12 * q^78 - 10 * q^79 + 3 * q^81 + 14 * q^82 + 4 * q^83 - 2 * q^84 - 2 * q^87 - 3 * q^88 - 2 * q^89 + 8 * q^91 - 2 * q^92 + 4 * q^93 + 14 * q^94 - 40 * q^95 - 3 * q^96 + 2 * q^97 + 7 * 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
$5$	−3.35026	−1.49828	−0.749141	−	0.662410i	$-0.769534\pi$
$5$	−3.35026	−1.49828	−0.749141	+	0.662410i	$0.769534\pi$
$6$	−1.00000	−0.408248
$7$	−2.96239	−1.11968	−0.559839	−	0.828602i	$-0.689137\pi$
$7$	−2.96239	−1.11968	−0.559839	+	0.828602i	$0.689137\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.35026	−1.05945
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.96239	−0.791732
$15$	3.35026	0.865034
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	8.31265	1.90705	0.953526	−	0.301310i	$-0.0974237\pi$
$19$	8.31265	1.90705	0.953526	+	0.301310i	$0.0974237\pi$
$20$	−3.35026	−0.749141
$21$	2.96239	0.646446
$22$	−1.00000	−0.213201
$23$	2.96239	0.617701	0.308850	−	0.951111i	$-0.400056\pi$
$23$	2.96239	0.617701	0.308850	+	0.951111i	$0.400056\pi$
$24$	−1.00000	−0.204124
$25$	6.22425	1.24485
$26$	4.00000	0.784465
$27$	−1.00000	−0.192450
$28$	−2.96239	−0.559839
$29$	−2.96239	−0.550102	−0.275051	−	0.961430i	$-0.588695\pi$
$29$	−2.96239	−0.550102	−0.275051	+	0.961430i	$0.588695\pi$
$30$	3.35026	0.611671
$31$	1.73813	0.312178	0.156089	−	0.987743i	$-0.450111\pi$
$31$	1.73813	0.312178	0.156089	+	0.987743i	$0.450111\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−1.00000	−0.171499
$35$	9.92478	1.67759
$36$	1.00000	0.166667
$37$	7.73813	1.27214	0.636071	−	0.771631i	$-0.280559\pi$
$37$	7.73813	1.27214	0.636071	+	0.771631i	$0.280559\pi$
$38$	8.31265	1.34849
$39$	−4.00000	−0.640513
$40$	−3.35026	−0.529723
$41$	11.9248	1.86234	0.931169	−	0.364589i	$-0.118790\pi$
$41$	11.9248	1.86234	0.931169	+	0.364589i	$0.118790\pi$
$42$	2.96239	0.457106
$43$	−7.53690	−1.14937	−0.574684	−	0.818376i	$-0.694875\pi$
$43$	−7.53690	−1.14937	−0.574684	+	0.818376i	$0.694875\pi$
$44$	−1.00000	−0.150756
$45$	−3.35026	−0.499428
$46$	2.96239	0.436780
$47$	4.38787	0.640037	0.320019	−	0.947411i	$-0.396311\pi$
$47$	4.38787	0.640037	0.320019	+	0.947411i	$0.396311\pi$
$48$	−1.00000	−0.144338
$49$	1.77575	0.253678
$50$	6.22425	0.880242
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	2.70052	0.370945	0.185473	−	0.982649i	$-0.440618\pi$
$53$	2.70052	0.370945	0.185473	+	0.982649i	$0.440618\pi$
$54$	−1.00000	−0.136083
$55$	3.35026	0.451749
$56$	−2.96239	−0.395866
$57$	−8.31265	−1.10104
$58$	−2.96239	−0.388981
$59$	−10.2374	−1.33280	−0.666400	−	0.745595i	$-0.732166\pi$
$59$	−10.2374	−1.33280	−0.666400	+	0.745595i	$0.732166\pi$
$60$	3.35026	0.432517
$61$	0.649738	0.0831905	0.0415952	−	0.999135i	$-0.486756\pi$
$61$	0.649738	0.0831905	0.0415952	+	0.999135i	$0.486756\pi$
$62$	1.73813	0.220743
$63$	−2.96239	−0.373226
$64$	1.00000	0.125000
$65$	−13.4010	−1.66220
$66$	1.00000	0.123091
$67$	9.14903	1.11773	0.558866	−	0.829258i	$-0.311237\pi$
$67$	9.14903	1.11773	0.558866	+	0.829258i	$0.311237\pi$
$68$	−1.00000	−0.121268
$69$	−2.96239	−0.356630
$70$	9.92478	1.18624
$71$	−3.73813	−0.443635	−0.221817	−	0.975088i	$-0.571199\pi$
$71$	−3.73813	−0.443635	−0.221817	+	0.975088i	$0.571199\pi$
$72$	1.00000	0.117851
$73$	5.53690	0.648046	0.324023	−	0.946049i	$-0.394965\pi$
$73$	5.53690	0.648046	0.324023	+	0.946049i	$0.394965\pi$
$74$	7.73813	0.899540
$75$	−6.22425	−0.718715
$76$	8.31265	0.953526
$77$	2.96239	0.337596
$78$	−4.00000	−0.452911
$79$	−13.6629	−1.53720	−0.768599	−	0.639731i	$-0.779046\pi$
$79$	−13.6629	−1.53720	−0.768599	+	0.639731i	$0.779046\pi$
$80$	−3.35026	−0.374571
$81$	1.00000	0.111111
$82$	11.9248	1.31687
$83$	9.14903	1.00424	0.502118	−	0.864799i	$-0.332554\pi$
$83$	9.14903	1.00424	0.502118	+	0.864799i	$0.332554\pi$
$84$	2.96239	0.323223
$85$	3.35026	0.363387
$86$	−7.53690	−0.812725
$87$	2.96239	0.317601
$88$	−1.00000	−0.106600
$89$	−7.92478	−0.840025	−0.420012	−	0.907518i	$-0.637974\pi$
$89$	−7.92478	−0.840025	−0.420012	+	0.907518i	$0.637974\pi$
$90$	−3.35026	−0.353149
$91$	−11.8496	−1.24217
$92$	2.96239	0.308850
$93$	−1.73813	−0.180236
$94$	4.38787	0.452575
$95$	−27.8496	−2.85730
$96$	−1.00000	−0.102062
$97$	14.6253	1.48497	0.742487	−	0.669860i	$-0.233646\pi$
$97$	14.6253	1.48497	0.742487	+	0.669860i	$0.233646\pi$
$98$	1.77575	0.179377
$99$	−1.00000	−0.100504
$100$	6.22425	0.622425
$101$	−11.1490	−1.10937	−0.554685	−	0.832060i	$-0.687161\pi$
$101$	−11.1490	−1.10937	−0.554685	+	0.832060i	$0.687161\pi$
$102$	1.00000	0.0990148
$103$	10.7005	1.05435	0.527177	−	0.849756i	$-0.323250\pi$
$103$	10.7005	1.05435	0.527177	+	0.849756i	$0.323250\pi$
$104$	4.00000	0.392232
$105$	−9.92478	−0.968559
$106$	2.70052	0.262298
$107$	12.6253	1.22053	0.610267	−	0.792196i	$-0.291062\pi$
$107$	12.6253	1.22053	0.610267	+	0.792196i	$0.291062\pi$
$108$	−1.00000	−0.0962250
$109$	6.57452	0.629724	0.314862	−	0.949137i	$-0.398042\pi$
$109$	6.57452	0.629724	0.314862	+	0.949137i	$0.398042\pi$
$110$	3.35026	0.319435
$111$	−7.73813	−0.734471
$112$	−2.96239	−0.279919
$113$	4.23743	0.398624	0.199312	−	0.979936i	$-0.436129\pi$
$113$	4.23743	0.398624	0.199312	+	0.979936i	$0.436129\pi$
$114$	−8.31265	−0.778551
$115$	−9.92478	−0.925490
$116$	−2.96239	−0.275051
$117$	4.00000	0.369800
$118$	−10.2374	−0.942432
$119$	2.96239	0.271562
$120$	3.35026	0.305836
$121$	1.00000	0.0909091
$122$	0.649738	0.0588245
$123$	−11.9248	−1.07522
$124$	1.73813	0.156089
$125$	−4.10157	−0.366856
$126$	−2.96239	−0.263911
$127$	−13.0132	−1.15473	−0.577366	−	0.816485i	$-0.695919\pi$
$127$	−13.0132	−1.15473	−0.577366	+	0.816485i	$0.695919\pi$
$128$	1.00000	0.0883883
$129$	7.53690	0.663587
$130$	−13.4010	−1.17535
$131$	−5.29948	−0.463017	−0.231509	−	0.972833i	$-0.574366\pi$
$131$	−5.29948	−0.463017	−0.231509	+	0.972833i	$0.574366\pi$
$132$	1.00000	0.0870388
$133$	−24.6253	−2.13528
$134$	9.14903	0.790356
$135$	3.35026	0.288345
$136$	−1.00000	−0.0857493
$137$	−5.22425	−0.446338	−0.223169	−	0.974780i	$-0.571640\pi$
$137$	−5.22425	−0.446338	−0.223169	+	0.974780i	$0.571640\pi$
$138$	−2.96239	−0.252175
$139$	11.8496	1.00507	0.502533	−	0.864558i	$-0.332402\pi$
$139$	11.8496	1.00507	0.502533	+	0.864558i	$0.332402\pi$
$140$	9.92478	0.838797
$141$	−4.38787	−0.369526
$142$	−3.73813	−0.313697
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	9.92478	0.824208
$146$	5.53690	0.458237
$147$	−1.77575	−0.146461
$148$	7.73813	0.636071
$149$	2.77575	0.227398	0.113699	−	0.993515i	$-0.463730\pi$
$149$	2.77575	0.227398	0.113699	+	0.993515i	$0.463730\pi$
$150$	−6.22425	−0.508208
$151$	2.06063	0.167692	0.0838460	−	0.996479i	$-0.473280\pi$
$151$	2.06063	0.167692	0.0838460	+	0.996479i	$0.473280\pi$
$152$	8.31265	0.674245
$153$	−1.00000	−0.0808452
$154$	2.96239	0.238716
$155$	−5.82321	−0.467731
$156$	−4.00000	−0.320256
$157$	18.6253	1.48646	0.743230	−	0.669036i	$-0.233293\pi$
$157$	18.6253	1.48646	0.743230	+	0.669036i	$0.233293\pi$
$158$	−13.6629	−1.08696
$159$	−2.70052	−0.214165
$160$	−3.35026	−0.264861
$161$	−8.77575	−0.691626
$162$	1.00000	0.0785674
$163$	−7.22425	−0.565847	−0.282924	−	0.959142i	$-0.591304\pi$
$163$	−7.22425	−0.565847	−0.282924	+	0.959142i	$0.591304\pi$
$164$	11.9248	0.931169
$165$	−3.35026	−0.260818
$166$	9.14903	0.710103
$167$	−8.96239	−0.693530	−0.346765	−	0.937952i	$-0.612720\pi$
$167$	−8.96239	−0.693530	−0.346765	+	0.937952i	$0.612720\pi$
$168$	2.96239	0.228553
$169$	3.00000	0.230769
$170$	3.35026	0.256953
$171$	8.31265	0.635684
$172$	−7.53690	−0.574684
$173$	15.2144	1.15673	0.578365	−	0.815778i	$-0.303691\pi$
$173$	15.2144	1.15673	0.578365	+	0.815778i	$0.303691\pi$
$174$	2.96239	0.224578
$175$	−18.4387	−1.39383
$176$	−1.00000	−0.0753778
$177$	10.2374	0.769492
$178$	−7.92478	−0.593987
$179$	−6.38787	−0.477452	−0.238726	−	0.971087i	$-0.576730\pi$
$179$	−6.38787	−0.477452	−0.238726	+	0.971087i	$0.576730\pi$
$180$	−3.35026	−0.249714
$181$	6.96239	0.517510	0.258755	−	0.965943i	$-0.416688\pi$
$181$	6.96239	0.517510	0.258755	+	0.965943i	$0.416688\pi$
$182$	−11.8496	−0.878347
$183$	−0.649738	−0.0480300
$184$	2.96239	0.218390
$185$	−25.9248	−1.90603
$186$	−1.73813	−0.127446
$187$	1.00000	0.0731272
$188$	4.38787	0.320019
$189$	2.96239	0.215482
$190$	−27.8496	−2.02042
$191$	13.0132	0.941600	0.470800	−	0.882240i	$-0.343965\pi$
$191$	13.0132	0.941600	0.470800	+	0.882240i	$0.343965\pi$
$192$	−1.00000	−0.0721688
$193$	5.68735	0.409384	0.204692	−	0.978826i	$-0.434381\pi$
$193$	5.68735	0.409384	0.204692	+	0.978826i	$0.434381\pi$
$194$	14.6253	1.05004
$195$	13.4010	0.959669
$196$	1.77575	0.126839
$197$	−14.4387	−1.02871	−0.514356	−	0.857577i	$-0.671969\pi$
$197$	−14.4387	−1.02871	−0.514356	+	0.857577i	$0.671969\pi$
$198$	−1.00000	−0.0710669
$199$	−12.1866	−0.863888	−0.431944	−	0.901900i	$-0.642172\pi$
$199$	−12.1866	−0.863888	−0.431944	+	0.901900i	$0.642172\pi$
$200$	6.22425	0.440121
$201$	−9.14903	−0.645323
$202$	−11.1490	−0.784443
$203$	8.77575	0.615937
$204$	1.00000	0.0700140
$205$	−39.9511	−2.79031
$206$	10.7005	0.745541
$207$	2.96239	0.205900
$208$	4.00000	0.277350
$209$	−8.31265	−0.574998
$210$	−9.92478	−0.684875
$211$	22.5501	1.55241	0.776206	−	0.630480i	$-0.217142\pi$
$211$	22.5501	1.55241	0.776206	+	0.630480i	$0.217142\pi$
$212$	2.70052	0.185473
$213$	3.73813	0.256133
$214$	12.6253	0.863048
$215$	25.2506	1.72208
$216$	−1.00000	−0.0680414
$217$	−5.14903	−0.349539
$218$	6.57452	0.445282
$219$	−5.53690	−0.374149
$220$	3.35026	0.225875
$221$	−4.00000	−0.269069
$222$	−7.73813	−0.519350
$223$	−3.47627	−0.232788	−0.116394	−	0.993203i	$-0.537134\pi$
$223$	−3.47627	−0.232788	−0.116394	+	0.993203i	$0.537134\pi$
$224$	−2.96239	−0.197933
$225$	6.22425	0.414950
$226$	4.23743	0.281869
$227$	25.7743	1.71070	0.855351	−	0.518049i	$-0.173341\pi$
$227$	25.7743	1.71070	0.855351	+	0.518049i	$0.173341\pi$
$228$	−8.31265	−0.550519
$229$	6.77575	0.447754	0.223877	−	0.974617i	$-0.428129\pi$
$229$	6.77575	0.447754	0.223877	+	0.974617i	$0.428129\pi$
$230$	−9.92478	−0.654420
$231$	−2.96239	−0.194911
$232$	−2.96239	−0.194490
$233$	20.2981	1.32977	0.664885	−	0.746946i	$-0.268480\pi$
$233$	20.2981	1.32977	0.664885	+	0.746946i	$0.268480\pi$
$234$	4.00000	0.261488
$235$	−14.7005	−0.958956
$236$	−10.2374	−0.666400
$237$	13.6629	0.887502
$238$	2.96239	0.192023
$239$	−17.1490	−1.10928	−0.554639	−	0.832091i	$-0.687144\pi$
$239$	−17.1490	−1.10928	−0.554639	+	0.832091i	$0.687144\pi$
$240$	3.35026	0.216258
$241$	22.9380	1.47756	0.738782	−	0.673945i	$-0.235401\pi$
$241$	22.9380	1.47756	0.738782	+	0.673945i	$0.235401\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	0.649738	0.0415952
$245$	−5.94921	−0.380081
$246$	−11.9248	−0.760296
$247$	33.2506	2.11569
$248$	1.73813	0.110372
$249$	−9.14903	−0.579796
$250$	−4.10157	−0.259406
$251$	−4.83638	−0.305270	−0.152635	−	0.988283i	$-0.548776\pi$
$251$	−4.83638	−0.305270	−0.152635	+	0.988283i	$0.548776\pi$
$252$	−2.96239	−0.186613
$253$	−2.96239	−0.186244
$254$	−13.0132	−0.816519
$255$	−3.35026	−0.209802
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	7.53690	0.469227
$259$	−22.9234	−1.42439
$260$	−13.4010	−0.831098
$261$	−2.96239	−0.183367
$262$	−5.29948	−0.327403
$263$	−23.3258	−1.43833	−0.719166	−	0.694838i	$-0.755476\pi$
$263$	−23.3258	−1.43833	−0.719166	+	0.694838i	$0.755476\pi$
$264$	1.00000	0.0615457
$265$	−9.04746	−0.555781
$266$	−24.6253	−1.50987
$267$	7.92478	0.484988
$268$	9.14903	0.558866
$269$	2.05079	0.125039	0.0625193	−	0.998044i	$-0.480087\pi$
$269$	2.05079	0.125039	0.0625193	+	0.998044i	$0.480087\pi$
$270$	3.35026	0.203890
$271$	−16.3879	−0.995492	−0.497746	−	0.867323i	$-0.665839\pi$
$271$	−16.3879	−0.995492	−0.497746	+	0.867323i	$0.665839\pi$
$272$	−1.00000	−0.0606339
$273$	11.8496	0.717168
$274$	−5.22425	−0.315609
$275$	−6.22425	−0.375337
$276$	−2.96239	−0.178315
$277$	−18.9478	−1.13846	−0.569231	−	0.822177i	$-0.692759\pi$
$277$	−18.9478	−1.13846	−0.569231	+	0.822177i	$0.692759\pi$
$278$	11.8496	0.710689
$279$	1.73813	0.104059
$280$	9.92478	0.593119
$281$	−23.4010	−1.39599	−0.697995	−	0.716103i	$-0.745924\pi$
$281$	−23.4010	−1.39599	−0.697995	+	0.716103i	$0.745924\pi$
$282$	−4.38787	−0.261294
$283$	−22.5501	−1.34046	−0.670231	−	0.742152i	$-0.733805\pi$
$283$	−22.5501	−1.34046	−0.670231	+	0.742152i	$0.733805\pi$
$284$	−3.73813	−0.221817
$285$	27.8496	1.64967
$286$	−4.00000	−0.236525
$287$	−35.3258	−2.08522
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	9.92478	0.582803
$291$	−14.6253	−0.857350
$292$	5.53690	0.324023
$293$	0.598953	0.0349912	0.0174956	−	0.999847i	$-0.494431\pi$
$293$	0.598953	0.0349912	0.0174956	+	0.999847i	$0.494431\pi$
$294$	−1.77575	−0.103564
$295$	34.2981	1.99691
$296$	7.73813	0.449770
$297$	1.00000	0.0580259
$298$	2.77575	0.160795
$299$	11.8496	0.685277
$300$	−6.22425	−0.359357
$301$	22.3272	1.28692
$302$	2.06063	0.118576
$303$	11.1490	0.640495
$304$	8.31265	0.476763
$305$	−2.17679	−0.124643
$306$	−1.00000	−0.0571662
$307$	−13.0884	−0.746994	−0.373497	−	0.927631i	$-0.621841\pi$
$307$	−13.0884	−0.746994	−0.373497	+	0.927631i	$0.621841\pi$
$308$	2.96239	0.168798
$309$	−10.7005	−0.608732
$310$	−5.82321	−0.330736
$311$	−9.81336	−0.556464	−0.278232	−	0.960514i	$-0.589748\pi$
$311$	−9.81336	−0.556464	−0.278232	+	0.960514i	$0.589748\pi$
$312$	−4.00000	−0.226455
$313$	29.4763	1.66610	0.833049	−	0.553200i	$-0.186593\pi$
$313$	29.4763	1.66610	0.833049	+	0.553200i	$0.186593\pi$
$314$	18.6253	1.05109
$315$	9.92478	0.559198
$316$	−13.6629	−0.768599
$317$	−25.2750	−1.41959	−0.709794	−	0.704410i	$-0.751212\pi$
$317$	−25.2750	−1.41959	−0.709794	+	0.704410i	$0.751212\pi$
$318$	−2.70052	−0.151438
$319$	2.96239	0.165862
$320$	−3.35026	−0.187285
$321$	−12.6253	−0.704676
$322$	−8.77575	−0.489053
$323$	−8.31265	−0.462528
$324$	1.00000	0.0555556
$325$	24.8970	1.38104
$326$	−7.22425	−0.400114
$327$	−6.57452	−0.363572
$328$	11.9248	0.658436
$329$	−12.9986	−0.716635
$330$	−3.35026	−0.184426
$331$	−5.55149	−0.305138	−0.152569	−	0.988293i	$-0.548755\pi$
$331$	−5.55149	−0.305138	−0.152569	+	0.988293i	$0.548755\pi$
$332$	9.14903	0.502118
$333$	7.73813	0.424047
$334$	−8.96239	−0.490400
$335$	−30.6516	−1.67468
$336$	2.96239	0.161612
$337$	−28.3879	−1.54639	−0.773193	−	0.634171i	$-0.781342\pi$
$337$	−28.3879	−1.54639	−0.773193	+	0.634171i	$0.781342\pi$
$338$	3.00000	0.163178
$339$	−4.23743	−0.230145
$340$	3.35026	0.181693
$341$	−1.73813	−0.0941253
$342$	8.31265	0.449497
$343$	15.4763	0.835640
$344$	−7.53690	−0.406363
$345$	9.92478	0.534332
$346$	15.2144	0.817931
$347$	26.0263	1.39717	0.698584	−	0.715528i	$-0.253814\pi$
$347$	26.0263	1.39717	0.698584	+	0.715528i	$0.253814\pi$
$348$	2.96239	0.158801
$349$	18.4485	0.987526	0.493763	−	0.869597i	$-0.335621\pi$
$349$	18.4485	0.987526	0.493763	+	0.869597i	$0.335621\pi$
$350$	−18.4387	−0.985588
$351$	−4.00000	−0.213504
$352$	−1.00000	−0.0533002
$353$	8.70052	0.463082	0.231541	−	0.972825i	$-0.425623\pi$
$353$	8.70052	0.463082	0.231541	+	0.972825i	$0.425623\pi$
$354$	10.2374	0.544113
$355$	12.5237	0.664691
$356$	−7.92478	−0.420012
$357$	−2.96239	−0.156786
$358$	−6.38787	−0.337610
$359$	−14.1768	−0.748223	−0.374111	−	0.927384i	$-0.622052\pi$
$359$	−14.1768	−0.748223	−0.374111	+	0.927384i	$0.622052\pi$
$360$	−3.35026	−0.176574
$361$	50.1002	2.63685
$362$	6.96239	0.365935
$363$	−1.00000	−0.0524864
$364$	−11.8496	−0.621085
$365$	−18.5501	−0.970955
$366$	−0.649738	−0.0339624
$367$	−21.2144	−1.10738	−0.553691	−	0.832722i	$-0.686781\pi$
$367$	−21.2144	−1.10738	−0.553691	+	0.832722i	$0.686781\pi$
$368$	2.96239	0.154425
$369$	11.9248	0.620779
$370$	−25.9248	−1.34776
$371$	−8.00000	−0.415339
$372$	−1.73813	−0.0901181
$373$	36.0000	1.86401	0.932005	−	0.362446i	$-0.118058\pi$
$373$	36.0000	1.86401	0.932005	+	0.362446i	$0.118058\pi$
$374$	1.00000	0.0517088
$375$	4.10157	0.211804
$376$	4.38787	0.226287
$377$	−11.8496	−0.610283
$378$	2.96239	0.152369
$379$	−9.40105	−0.482899	−0.241450	−	0.970413i	$-0.577623\pi$
$379$	−9.40105	−0.482899	−0.241450	+	0.970413i	$0.577623\pi$
$380$	−27.8496	−1.42865
$381$	13.0132	0.666685
$382$	13.0132	0.665812
$383$	−29.0132	−1.48250	−0.741252	−	0.671227i	$-0.765768\pi$
$383$	−29.0132	−1.48250	−0.741252	+	0.671227i	$0.765768\pi$
$384$	−1.00000	−0.0510310
$385$	−9.92478	−0.505813
$386$	5.68735	0.289478
$387$	−7.53690	−0.383122
$388$	14.6253	0.742487
$389$	33.1002	1.67824	0.839122	−	0.543943i	$-0.183069\pi$
$389$	33.1002	1.67824	0.839122	+	0.543943i	$0.183069\pi$
$390$	13.4010	0.678588
$391$	−2.96239	−0.149814
$392$	1.77575	0.0896887
$393$	5.29948	0.267323
$394$	−14.4387	−0.727409
$395$	45.7743	2.30316
$396$	−1.00000	−0.0502519
$397$	18.1866	0.912761	0.456381	−	0.889785i	$-0.349146\pi$
$397$	18.1866	0.912761	0.456381	+	0.889785i	$0.349146\pi$
$398$	−12.1866	−0.610861
$399$	24.6253	1.23281
$400$	6.22425	0.311213
$401$	1.16362	0.0581084	0.0290542	−	0.999578i	$-0.490750\pi$
$401$	1.16362	0.0581084	0.0290542	+	0.999578i	$0.490750\pi$
$402$	−9.14903	−0.456312
$403$	6.95254	0.346331
$404$	−11.1490	−0.554685
$405$	−3.35026	−0.166476
$406$	8.77575	0.435533
$407$	−7.73813	−0.383565
$408$	1.00000	0.0495074
$409$	0.850969	0.0420777	0.0210389	−	0.999779i	$-0.493303\pi$
$409$	0.850969	0.0420777	0.0210389	+	0.999779i	$0.493303\pi$
$410$	−39.9511	−1.97305
$411$	5.22425	0.257693
$412$	10.7005	0.527177
$413$	30.3272	1.49231
$414$	2.96239	0.145593
$415$	−30.6516	−1.50463
$416$	4.00000	0.196116
$417$	−11.8496	−0.580275
$418$	−8.31265	−0.406585
$419$	30.3996	1.48512	0.742560	−	0.669780i	$-0.233612\pi$
$419$	30.3996	1.48512	0.742560	+	0.669780i	$0.233612\pi$
$420$	−9.92478	−0.484280
$421$	3.44992	0.168139	0.0840695	−	0.996460i	$-0.473208\pi$
$421$	3.44992	0.168139	0.0840695	+	0.996460i	$0.473208\pi$
$422$	22.5501	1.09772
$423$	4.38787	0.213346
$424$	2.70052	0.131149
$425$	−6.22425	−0.301921
$426$	3.73813	0.181113
$427$	−1.92478	−0.0931465
$428$	12.6253	0.610267
$429$	4.00000	0.193122
$430$	25.2506	1.21769
$431$	17.9902	0.866555	0.433278	−	0.901261i	$-0.357357\pi$
$431$	17.9902	0.866555	0.433278	+	0.901261i	$0.357357\pi$
$432$	−1.00000	−0.0481125
$433$	25.0738	1.20497	0.602485	−	0.798130i	$-0.294177\pi$
$433$	25.0738	1.20497	0.602485	+	0.798130i	$0.294177\pi$
$434$	−5.14903	−0.247161
$435$	−9.92478	−0.475857
$436$	6.57452	0.314862
$437$	24.6253	1.17799
$438$	−5.53690	−0.264564
$439$	−23.5877	−1.12578	−0.562889	−	0.826532i	$-0.690310\pi$
$439$	−23.5877	−1.12578	−0.562889	+	0.826532i	$0.690310\pi$
$440$	3.35026	0.159717
$441$	1.77575	0.0845593
$442$	−4.00000	−0.190261
$443$	24.6859	1.17286	0.586432	−	0.809998i	$-0.300532\pi$
$443$	24.6859	1.17286	0.586432	+	0.809998i	$0.300532\pi$
$444$	−7.73813	−0.367236
$445$	26.5501	1.25859
$446$	−3.47627	−0.164606
$447$	−2.77575	−0.131288
$448$	−2.96239	−0.139960
$449$	−38.4142	−1.81288	−0.906440	−	0.422336i	$-0.861210\pi$
$449$	−38.4142	−1.81288	−0.906440	+	0.422336i	$0.861210\pi$
$450$	6.22425	0.293414
$451$	−11.9248	−0.561516
$452$	4.23743	0.199312
$453$	−2.06063	−0.0968170
$454$	25.7743	1.20965
$455$	39.6991	1.86112
$456$	−8.31265	−0.389276
$457$	−16.7005	−0.781218	−0.390609	−	0.920557i	$-0.627735\pi$
$457$	−16.7005	−0.781218	−0.390609	+	0.920557i	$0.627735\pi$
$458$	6.77575	0.316610
$459$	1.00000	0.0466760
$460$	−9.92478	−0.462745
$461$	−18.3733	−0.855729	−0.427865	−	0.903843i	$-0.640734\pi$
$461$	−18.3733	−0.855729	−0.427865	+	0.903843i	$0.640734\pi$
$462$	−2.96239	−0.137823
$463$	−16.1016	−0.748303	−0.374152	−	0.927368i	$-0.622066\pi$
$463$	−16.1016	−0.748303	−0.374152	+	0.927368i	$0.622066\pi$
$464$	−2.96239	−0.137525
$465$	5.82321	0.270045
$466$	20.2981	0.940290
$467$	−11.6385	−0.538564	−0.269282	−	0.963061i	$-0.586786\pi$
$467$	−11.6385	−0.538564	−0.269282	+	0.963061i	$0.586786\pi$
$468$	4.00000	0.184900
$469$	−27.1030	−1.25150
$470$	−14.7005	−0.678085
$471$	−18.6253	−0.858209
$472$	−10.2374	−0.471216
$473$	7.53690	0.346547
$474$	13.6629	0.627558
$475$	51.7400	2.37400
$476$	2.96239	0.135781
$477$	2.70052	0.123648
$478$	−17.1490	−0.784378
$479$	−11.0376	−0.504321	−0.252161	−	0.967685i	$-0.581141\pi$
$479$	−11.0376	−0.504321	−0.252161	+	0.967685i	$0.581141\pi$
$480$	3.35026	0.152918
$481$	30.9525	1.41131
$482$	22.9380	1.04480
$483$	8.77575	0.399310
$484$	1.00000	0.0454545
$485$	−48.9986	−2.22491
$486$	−1.00000	−0.0453609
$487$	−30.1114	−1.36448	−0.682239	−	0.731129i	$-0.738994\pi$
$487$	−30.1114	−1.36448	−0.682239	+	0.731129i	$0.738994\pi$
$488$	0.649738	0.0294123
$489$	7.22425	0.326692
$490$	−5.94921	−0.268758
$491$	6.17679	0.278755	0.139377	−	0.990239i	$-0.455490\pi$
$491$	6.17679	0.278755	0.139377	+	0.990239i	$0.455490\pi$
$492$	−11.9248	−0.537610
$493$	2.96239	0.133419
$494$	33.2506	1.49602
$495$	3.35026	0.150583
$496$	1.73813	0.0780446
$497$	11.0738	0.496728
$498$	−9.14903	−0.409978
$499$	33.6531	1.50652	0.753259	−	0.657724i	$-0.228481\pi$
$499$	33.6531	1.50652	0.753259	+	0.657724i	$0.228481\pi$
$500$	−4.10157	−0.183428
$501$	8.96239	0.400410
$502$	−4.83638	−0.215858
$503$	−34.2130	−1.52548	−0.762741	−	0.646704i	$-0.776147\pi$
$503$	−34.2130	−1.52548	−0.762741	+	0.646704i	$0.776147\pi$
$504$	−2.96239	−0.131955
$505$	37.3522	1.66215
$506$	−2.96239	−0.131694
$507$	−3.00000	−0.133235
$508$	−13.0132	−0.577366
$509$	9.40105	0.416694	0.208347	−	0.978055i	$-0.433192\pi$
$509$	9.40105	0.416694	0.208347	+	0.978055i	$0.433192\pi$
$510$	−3.35026	−0.148352
$511$	−16.4025	−0.725602
$512$	1.00000	0.0441942
$513$	−8.31265	−0.367012
$514$	2.00000	0.0882162
$515$	−35.8496	−1.57972
$516$	7.53690	0.331794
$517$	−4.38787	−0.192978
$518$	−22.9234	−1.00719
$519$	−15.2144	−0.667838
$520$	−13.4010	−0.587675
$521$	27.4617	1.20312	0.601559	−	0.798828i	$-0.294546\pi$
$521$	27.4617	1.20312	0.601559	+	0.798828i	$0.294546\pi$
$522$	−2.96239	−0.129660
$523$	40.1622	1.75617	0.878085	−	0.478504i	$-0.158821\pi$
$523$	40.1622	1.75617	0.878085	+	0.478504i	$0.158821\pi$
$524$	−5.29948	−0.231509
$525$	18.4387	0.804729
$526$	−23.3258	−1.01705
$527$	−1.73813	−0.0757143
$528$	1.00000	0.0435194
$529$	−14.2243	−0.618446
$530$	−9.04746	−0.392997
$531$	−10.2374	−0.444267
$532$	−24.6253	−1.06764
$533$	47.6991	2.06608
$534$	7.92478	0.342939
$535$	−42.2981	−1.82870
$536$	9.14903	0.395178
$537$	6.38787	0.275657
$538$	2.05079	0.0884156
$539$	−1.77575	−0.0764868
$540$	3.35026	0.144172
$541$	−37.5271	−1.61341	−0.806707	−	0.590952i	$-0.798752\pi$
$541$	−37.5271	−1.61341	−0.806707	+	0.590952i	$0.798752\pi$
$542$	−16.3879	−0.703919
$543$	−6.96239	−0.298785
$544$	−1.00000	−0.0428746
$545$	−22.0263	−0.943505
$546$	11.8496	0.507114
$547$	−38.0263	−1.62589	−0.812945	−	0.582341i	$-0.802137\pi$
$547$	−38.0263	−1.62589	−0.812945	+	0.582341i	$0.802137\pi$
$548$	−5.22425	−0.223169
$549$	0.649738	0.0277302
$550$	−6.22425	−0.265403
$551$	−24.6253	−1.04907
$552$	−2.96239	−0.126088
$553$	40.4749	1.72117
$554$	−18.9478	−0.805015
$555$	25.9248	1.10045
$556$	11.8496	0.502533
$557$	42.1016	1.78390	0.891950	−	0.452133i	$-0.149337\pi$
$557$	42.1016	1.78390	0.891950	+	0.452133i	$0.149337\pi$
$558$	1.73813	0.0735811
$559$	−30.1476	−1.27511
$560$	9.92478	0.419398
$561$	−1.00000	−0.0422200
$562$	−23.4010	−0.987114
$563$	29.2995	1.23483	0.617413	−	0.786639i	$-0.288181\pi$
$563$	29.2995	1.23483	0.617413	+	0.786639i	$0.288181\pi$
$564$	−4.38787	−0.184763
$565$	−14.1965	−0.597251
$566$	−22.5501	−0.947850
$567$	−2.96239	−0.124409
$568$	−3.73813	−0.156849
$569$	34.4749	1.44526	0.722631	−	0.691234i	$-0.242933\pi$
$569$	34.4749	1.44526	0.722631	+	0.691234i	$0.242933\pi$
$570$	27.8496	1.16649
$571$	−4.15045	−0.173691	−0.0868454	−	0.996222i	$-0.527679\pi$
$571$	−4.15045	−0.173691	−0.0868454	+	0.996222i	$0.527679\pi$
$572$	−4.00000	−0.167248
$573$	−13.0132	−0.543633
$574$	−35.3258	−1.47447
$575$	18.4387	0.768945
$576$	1.00000	0.0416667
$577$	−21.8496	−0.909609	−0.454804	−	0.890591i	$-0.650291\pi$
$577$	−21.8496	−0.909609	−0.454804	+	0.890591i	$0.650291\pi$
$578$	1.00000	0.0415945
$579$	−5.68735	−0.236358
$580$	9.92478	0.412104
$581$	−27.1030	−1.12442
$582$	−14.6253	−0.606238
$583$	−2.70052	−0.111844
$584$	5.53690	0.229119
$585$	−13.4010	−0.554065
$586$	0.598953	0.0247425
$587$	−48.2638	−1.99206	−0.996030	−	0.0890227i	$-0.971626\pi$
$587$	−48.2638	−1.99206	−0.996030	+	0.0890227i	$0.971626\pi$
$588$	−1.77575	−0.0732305
$589$	14.4485	0.595340
$590$	34.2981	1.41203
$591$	14.4387	0.593927
$592$	7.73813	0.318035
$593$	45.5778	1.87166	0.935829	−	0.352455i	$-0.114653\pi$
$593$	45.5778	1.87166	0.935829	+	0.352455i	$0.114653\pi$
$594$	1.00000	0.0410305
$595$	−9.92478	−0.406876
$596$	2.77575	0.113699
$597$	12.1866	0.498766
$598$	11.8496	0.484564
$599$	−6.93795	−0.283477	−0.141738	−	0.989904i	$-0.545269\pi$
$599$	−6.93795	−0.283477	−0.141738	+	0.989904i	$0.545269\pi$
$600$	−6.22425	−0.254104
$601$	−14.3127	−0.583825	−0.291913	−	0.956445i	$-0.594292\pi$
$601$	−14.3127	−0.583825	−0.291913	+	0.956445i	$0.594292\pi$
$602$	22.3272	0.909990
$603$	9.14903	0.372577
$604$	2.06063	0.0838460
$605$	−3.35026	−0.136208
$606$	11.1490	0.452898
$607$	45.8858	1.86245	0.931223	−	0.364451i	$-0.118743\pi$
$607$	45.8858	1.86245	0.931223	+	0.364451i	$0.118743\pi$
$608$	8.31265	0.337122
$609$	−8.77575	−0.355611
$610$	−2.17679	−0.0881358
$611$	17.5515	0.710057
$612$	−1.00000	−0.0404226
$613$	24.9986	1.00968	0.504842	−	0.863212i	$-0.331551\pi$
$613$	24.9986	1.00968	0.504842	+	0.863212i	$0.331551\pi$
$614$	−13.0884	−0.528205
$615$	39.9511	1.61098
$616$	2.96239	0.119358
$617$	32.3390	1.30192	0.650960	−	0.759112i	$-0.274367\pi$
$617$	32.3390	1.30192	0.650960	+	0.759112i	$0.274367\pi$
$618$	−10.7005	−0.430438
$619$	−3.32582	−0.133676	−0.0668381	−	0.997764i	$-0.521291\pi$
$619$	−3.32582	−0.133676	−0.0668381	+	0.997764i	$0.521291\pi$
$620$	−5.82321	−0.233866
$621$	−2.96239	−0.118877
$622$	−9.81336	−0.393480
$623$	23.4763	0.940557
$624$	−4.00000	−0.160128
$625$	−17.3799	−0.695197
$626$	29.4763	1.17811
$627$	8.31265	0.331975
$628$	18.6253	0.743230
$629$	−7.73813	−0.308540
$630$	9.92478	0.395413
$631$	−25.9248	−1.03205	−0.516025	−	0.856574i	$-0.672589\pi$
$631$	−25.9248	−1.03205	−0.516025	+	0.856574i	$0.672589\pi$
$632$	−13.6629	−0.543481
$633$	−22.5501	−0.896285
$634$	−25.2750	−1.00380
$635$	43.5975	1.73012
$636$	−2.70052	−0.107083
$637$	7.10299	0.281431
$638$	2.96239	0.117282
$639$	−3.73813	−0.147878
$640$	−3.35026	−0.132431
$641$	−42.3127	−1.67125	−0.835625	−	0.549301i	$-0.814894\pi$
$641$	−42.3127	−1.67125	−0.835625	+	0.549301i	$0.814894\pi$
$642$	−12.6253	−0.498281
$643$	−35.9511	−1.41777	−0.708887	−	0.705322i	$-0.750802\pi$
$643$	−35.9511	−1.41777	−0.708887	+	0.705322i	$0.750802\pi$
$644$	−8.77575	−0.345813
$645$	−25.2506	−0.994241
$646$	−8.31265	−0.327057
$647$	6.71511	0.263998	0.131999	−	0.991250i	$-0.457860\pi$
$647$	6.71511	0.263998	0.131999	+	0.991250i	$0.457860\pi$
$648$	1.00000	0.0392837
$649$	10.2374	0.401854
$650$	24.8970	0.976541
$651$	5.14903	0.201806
$652$	−7.22425	−0.282924
$653$	5.42548	0.212316	0.106158	−	0.994349i	$-0.466145\pi$
$653$	5.42548	0.212316	0.106158	+	0.994349i	$0.466145\pi$
$654$	−6.57452	−0.257084
$655$	17.7546	0.693731
$656$	11.9248	0.465584
$657$	5.53690	0.216015
$658$	−12.9986	−0.506738
$659$	43.3258	1.68773	0.843867	−	0.536552i	$-0.180273\pi$
$659$	43.3258	1.68773	0.843867	+	0.536552i	$0.180273\pi$
$660$	−3.35026	−0.130409
$661$	−33.1754	−1.29037	−0.645186	−	0.764025i	$-0.723220\pi$
$661$	−33.1754	−1.29037	−0.645186	+	0.764025i	$0.723220\pi$
$662$	−5.55149	−0.215765
$663$	4.00000	0.155347
$664$	9.14903	0.355051
$665$	82.5012	3.19926
$666$	7.73813	0.299847
$667$	−8.77575	−0.339798
$668$	−8.96239	−0.346765
$669$	3.47627	0.134400
$670$	−30.6516	−1.18418
$671$	−0.649738	−0.0250829
$672$	2.96239	0.114277
$673$	3.08840	0.119049	0.0595245	−	0.998227i	$-0.481042\pi$
$673$	3.08840	0.119049	0.0595245	+	0.998227i	$0.481042\pi$
$674$	−28.3879	−1.09346
$675$	−6.22425	−0.239572
$676$	3.00000	0.115385
$677$	46.6615	1.79335	0.896674	−	0.442692i	$-0.145977\pi$
$677$	46.6615	1.79335	0.896674	+	0.442692i	$0.145977\pi$
$678$	−4.23743	−0.162737
$679$	−43.3258	−1.66269
$680$	3.35026	0.128477
$681$	−25.7743	−0.987675
$682$	−1.73813	−0.0665566
$683$	−38.7005	−1.48083	−0.740417	−	0.672148i	$-0.765372\pi$
$683$	−38.7005	−1.48083	−0.740417	+	0.672148i	$0.765372\pi$
$684$	8.31265	0.317842
$685$	17.5026	0.668741
$686$	15.4763	0.590887
$687$	−6.77575	−0.258511
$688$	−7.53690	−0.287342
$689$	10.8021	0.411527
$690$	9.92478	0.377830
$691$	51.0738	1.94294	0.971470	−	0.237164i	$-0.0762179\pi$
$691$	51.0738	1.94294	0.971470	+	0.237164i	$0.0762179\pi$
$692$	15.2144	0.578365
$693$	2.96239	0.112532
$694$	26.0263	0.987947
$695$	−39.6991	−1.50587
$696$	2.96239	0.112289
$697$	−11.9248	−0.451683
$698$	18.4485	0.698286
$699$	−20.2981	−0.767743
$700$	−18.4387	−0.696916
$701$	−9.32582	−0.352232	−0.176116	−	0.984369i	$-0.556353\pi$
$701$	−9.32582	−0.352232	−0.176116	+	0.984369i	$0.556353\pi$
$702$	−4.00000	−0.150970
$703$	64.3244	2.42604
$704$	−1.00000	−0.0376889
$705$	14.7005	0.553654
$706$	8.70052	0.327449
$707$	33.0278	1.24214
$708$	10.2374	0.384746
$709$	−42.5402	−1.59763	−0.798816	−	0.601576i	$-0.794540\pi$
$709$	−42.5402	−1.59763	−0.798816	+	0.601576i	$0.794540\pi$
$710$	12.5237	0.470007
$711$	−13.6629	−0.512399
$712$	−7.92478	−0.296994
$713$	5.14903	0.192833
$714$	−2.96239	−0.110865
$715$	13.4010	0.501171
$716$	−6.38787	−0.238726
$717$	17.1490	0.640442
$718$	−14.1768	−0.529073
$719$	−24.2130	−0.902992	−0.451496	−	0.892273i	$-0.649110\pi$
$719$	−24.2130	−0.902992	−0.451496	+	0.892273i	$0.649110\pi$
$720$	−3.35026	−0.124857
$721$	−31.6991	−1.18054
$722$	50.1002	1.86453
$723$	−22.9380	−0.853072
$724$	6.96239	0.258755
$725$	−18.4387	−0.684795
$726$	−1.00000	−0.0371135
$727$	10.0263	0.371857	0.185928	−	0.982563i	$-0.440471\pi$
$727$	10.0263	0.371857	0.185928	+	0.982563i	$0.440471\pi$
$728$	−11.8496	−0.439174
$729$	1.00000	0.0370370
$730$	−18.5501	−0.686569
$731$	7.53690	0.278762
$732$	−0.649738	−0.0240150
$733$	6.59895	0.243738	0.121869	−	0.992546i	$-0.461111\pi$
$733$	6.59895	0.243738	0.121869	+	0.992546i	$0.461111\pi$
$734$	−21.2144	−0.783038
$735$	5.94921	0.219440
$736$	2.96239	0.109195
$737$	−9.14903	−0.337009
$738$	11.9248	0.438957
$739$	15.5369	0.571534	0.285767	−	0.958299i	$-0.407752\pi$
$739$	15.5369	0.571534	0.285767	+	0.958299i	$0.407752\pi$
$740$	−25.9248	−0.953014
$741$	−33.2506	−1.22149
$742$	−8.00000	−0.293689
$743$	39.0376	1.43215	0.716076	−	0.698023i	$-0.245937\pi$
$743$	39.0376	1.43215	0.716076	+	0.698023i	$0.245937\pi$
$744$	−1.73813	−0.0637231
$745$	−9.29948	−0.340706
$746$	36.0000	1.31805
$747$	9.14903	0.334746
$748$	1.00000	0.0365636
$749$	−37.4010	−1.36660
$750$	4.10157	0.149768
$751$	−20.0362	−0.731131	−0.365566	−	0.930786i	$-0.619124\pi$
$751$	−20.0362	−0.731131	−0.365566	+	0.930786i	$0.619124\pi$
$752$	4.38787	0.160009
$753$	4.83638	0.176248
$754$	−11.8496	−0.431535
$755$	−6.90366	−0.251250
$756$	2.96239	0.107741
$757$	−23.4010	−0.850526	−0.425263	−	0.905070i	$-0.639818\pi$
$757$	−23.4010	−0.850526	−0.425263	+	0.905070i	$0.639818\pi$
$758$	−9.40105	−0.341461
$759$	2.96239	0.107528
$760$	−27.8496	−1.01021
$761$	13.3747	0.484832	0.242416	−	0.970172i	$-0.422060\pi$
$761$	13.3747	0.484832	0.242416	+	0.970172i	$0.422060\pi$
$762$	13.0132	0.471418
$763$	−19.4763	−0.705088
$764$	13.0132	0.470800
$765$	3.35026	0.121129
$766$	−29.0132	−1.04829
$767$	−40.9497	−1.47861
$768$	−1.00000	−0.0360844
$769$	6.92619	0.249765	0.124882	−	0.992172i	$-0.460145\pi$
$769$	6.92619	0.249765	0.124882	+	0.992172i	$0.460145\pi$
$770$	−9.92478	−0.357664
$771$	−2.00000	−0.0720282
$772$	5.68735	0.204692
$773$	13.5515	0.487413	0.243707	−	0.969849i	$-0.421637\pi$
$773$	13.5515	0.487413	0.243707	+	0.969849i	$0.421637\pi$
$774$	−7.53690	−0.270908
$775$	10.8186	0.388615
$776$	14.6253	0.525018
$777$	22.9234	0.822371
$778$	33.1002	1.18670
$779$	99.1265	3.55158
$780$	13.4010	0.479834
$781$	3.73813	0.133761
$782$	−2.96239	−0.105935
$783$	2.96239	0.105867
$784$	1.77575	0.0634195
$785$	−62.3996	−2.22714
$786$	5.29948	0.189026
$787$	2.07522	0.0739737	0.0369869	−	0.999316i	$-0.488224\pi$
$787$	2.07522	0.0739737	0.0369869	+	0.999316i	$0.488224\pi$
$788$	−14.4387	−0.514356
$789$	23.3258	0.830421
$790$	45.7743	1.62858
$791$	−12.5529	−0.446330
$792$	−1.00000	−0.0355335
$793$	2.59895	0.0922915
$794$	18.1866	0.645420
$795$	9.04746	0.320880
$796$	−12.1866	−0.431944
$797$	1.14903	0.0407008	0.0203504	−	0.999793i	$-0.493522\pi$
$797$	1.14903	0.0407008	0.0203504	+	0.999793i	$0.493522\pi$
$798$	24.6253	0.871726
$799$	−4.38787	−0.155232
$800$	6.22425	0.220061
$801$	−7.92478	−0.280008
$802$	1.16362	0.0410888
$803$	−5.53690	−0.195393
$804$	−9.14903	−0.322661
$805$	29.4010	1.03625
$806$	6.95254	0.244893
$807$	−2.05079	−0.0721911
$808$	−11.1490	−0.392222
$809$	17.9511	0.631128	0.315564	−	0.948904i	$-0.397806\pi$
$809$	17.9511	0.631128	0.315564	+	0.948904i	$0.397806\pi$
$810$	−3.35026	−0.117716
$811$	32.7269	1.14920	0.574598	−	0.818436i	$-0.305158\pi$
$811$	32.7269	1.14920	0.574598	+	0.818436i	$0.305158\pi$
$812$	8.77575	0.307968
$813$	16.3879	0.574748
$814$	−7.73813	−0.271221
$815$	24.2031	0.847799
$816$	1.00000	0.0350070
$817$	−62.6516	−2.19190
$818$	0.850969	0.0297534
$819$	−11.8496	−0.414057
$820$	−39.9511	−1.39515
$821$	5.28963	0.184609	0.0923046	−	0.995731i	$-0.470577\pi$
$821$	5.28963	0.184609	0.0923046	+	0.995731i	$0.470577\pi$
$822$	5.22425	0.182217
$823$	16.1866	0.564231	0.282115	−	0.959380i	$-0.408964\pi$
$823$	16.1866	0.564231	0.282115	+	0.959380i	$0.408964\pi$
$824$	10.7005	0.372770
$825$	6.22425	0.216701
$826$	30.3272	1.05522
$827$	−21.6239	−0.751936	−0.375968	−	0.926633i	$-0.622690\pi$
$827$	−21.6239	−0.751936	−0.375968	+	0.926633i	$0.622690\pi$
$828$	2.96239	0.102950
$829$	−21.2243	−0.737149	−0.368574	−	0.929598i	$-0.620154\pi$
$829$	−21.2243	−0.737149	−0.368574	+	0.929598i	$0.620154\pi$
$830$	−30.6516	−1.06393
$831$	18.9478	0.657292
$832$	4.00000	0.138675
$833$	−1.77575	−0.0615260
$834$	−11.8496	−0.410317
$835$	30.0263	1.03910
$836$	−8.31265	−0.287499
$837$	−1.73813	−0.0600787
$838$	30.3996	1.05014
$839$	−8.36344	−0.288738	−0.144369	−	0.989524i	$-0.546115\pi$
$839$	−8.36344	−0.288738	−0.144369	+	0.989524i	$0.546115\pi$
$840$	−9.92478	−0.342437
$841$	−20.2243	−0.697388
$842$	3.44992	0.118892
$843$	23.4010	0.805975
$844$	22.5501	0.776206
$845$	−10.0508	−0.345758
$846$	4.38787	0.150858
$847$	−2.96239	−0.101789
$848$	2.70052	0.0927364
$849$	22.5501	0.773917
$850$	−6.22425	−0.213490
$851$	22.9234	0.785803
$852$	3.73813	0.128066
$853$	−35.1509	−1.20355	−0.601773	−	0.798667i	$-0.705539\pi$
$853$	−35.1509	−1.20355	−0.601773	+	0.798667i	$0.705539\pi$
$854$	−1.92478	−0.0658645
$855$	−27.8496	−0.952435
$856$	12.6253	0.431524
$857$	−43.3522	−1.48088	−0.740441	−	0.672121i	$-0.765383\pi$
$857$	−43.3522	−1.48088	−0.740441	+	0.672121i	$0.765383\pi$
$858$	4.00000	0.136558
$859$	−27.6991	−0.945081	−0.472541	−	0.881309i	$-0.656663\pi$
$859$	−27.6991	−0.945081	−0.472541	+	0.881309i	$0.656663\pi$
$860$	25.2506	0.861038
$861$	35.3258	1.20390
$862$	17.9902	0.612747
$863$	27.0884	0.922100	0.461050	−	0.887374i	$-0.347473\pi$
$863$	27.0884	0.922100	0.461050	+	0.887374i	$0.347473\pi$
$864$	−1.00000	−0.0340207
$865$	−50.9722	−1.73311
$866$	25.0738	0.852043
$867$	−1.00000	−0.0339618
$868$	−5.14903	−0.174769
$869$	13.6629	0.463483
$870$	−9.92478	−0.336481
$871$	36.5961	1.24001
$872$	6.57452	0.222641
$873$	14.6253	0.494991
$874$	24.6253	0.832963
$875$	12.1504	0.410760
$876$	−5.53690	−0.187075
$877$	−25.4255	−0.858558	−0.429279	−	0.903172i	$-0.641232\pi$
$877$	−25.4255	−0.858558	−0.429279	+	0.903172i	$0.641232\pi$
$878$	−23.5877	−0.796046
$879$	−0.598953	−0.0202022
$880$	3.35026	0.112937
$881$	−41.1147	−1.38519	−0.692595	−	0.721326i	$-0.743533\pi$
$881$	−41.1147	−1.38519	−0.692595	+	0.721326i	$0.743533\pi$
$882$	1.77575	0.0597925
$883$	−35.3258	−1.18881	−0.594404	−	0.804166i	$-0.702612\pi$
$883$	−35.3258	−1.18881	−0.594404	+	0.804166i	$0.702612\pi$
$884$	−4.00000	−0.134535
$885$	−34.2981	−1.15292
$886$	24.6859	0.829340
$887$	−22.7367	−0.763424	−0.381712	−	0.924281i	$-0.624665\pi$
$887$	−22.7367	−0.763424	−0.381712	+	0.924281i	$0.624665\pi$
$888$	−7.73813	−0.259675
$889$	38.5501	1.29293
$890$	26.5501	0.889961
$891$	−1.00000	−0.0335013
$892$	−3.47627	−0.116394
$893$	36.4749	1.22058
$894$	−2.77575	−0.0928348
$895$	21.4010	0.715358
$896$	−2.96239	−0.0989665
$897$	−11.8496	−0.395645
$898$	−38.4142	−1.28190
$899$	−5.14903	−0.171730
$900$	6.22425	0.207475
$901$	−2.70052	−0.0899675
$902$	−11.9248	−0.397052
$903$	−22.3272	−0.743004
$904$	4.23743	0.140935
$905$	−23.3258	−0.775377
$906$	−2.06063	−0.0684600
$907$	−13.6728	−0.453997	−0.226998	−	0.973895i	$-0.572891\pi$
$907$	−13.6728	−0.453997	−0.226998	+	0.973895i	$0.572891\pi$
$908$	25.7743	0.855351
$909$	−11.1490	−0.369790
$910$	39.6991	1.31601
$911$	23.0640	0.764143	0.382072	−	0.924133i	$-0.375211\pi$
$911$	23.0640	0.764143	0.382072	+	0.924133i	$0.375211\pi$
$912$	−8.31265	−0.275259
$913$	−9.14903	−0.302789
$914$	−16.7005	−0.552404
$915$	2.17679	0.0719626
$916$	6.77575	0.223877
$917$	15.6991	0.518430
$918$	1.00000	0.0330049
$919$	39.9365	1.31738	0.658692	−	0.752412i	$-0.271110\pi$
$919$	39.9365	1.31738	0.658692	+	0.752412i	$0.271110\pi$
$920$	−9.92478	−0.327210
$921$	13.0884	0.431277
$922$	−18.3733	−0.605092
$923$	−14.9525	−0.492169
$924$	−2.96239	−0.0974554
$925$	48.1641	1.58363
$926$	−16.1016	−0.529130
$927$	10.7005	0.351451
$928$	−2.96239	−0.0972452
$929$	−12.2863	−0.403101	−0.201550	−	0.979478i	$-0.564598\pi$
$929$	−12.2863	−0.403101	−0.201550	+	0.979478i	$0.564598\pi$
$930$	5.82321	0.190950
$931$	14.7612	0.483777
$932$	20.2981	0.664885
$933$	9.81336	0.321275
$934$	−11.6385	−0.380823
$935$	−3.35026	−0.109565
$936$	4.00000	0.130744
$937$	−29.0249	−0.948203	−0.474102	−	0.880470i	$-0.657227\pi$
$937$	−29.0249	−0.948203	−0.474102	+	0.880470i	$0.657227\pi$
$938$	−27.1030	−0.884944
$939$	−29.4763	−0.961922
$940$	−14.7005	−0.479478
$941$	−44.4650	−1.44952	−0.724759	−	0.689003i	$-0.758049\pi$
$941$	−44.4650	−1.44952	−0.724759	+	0.689003i	$0.758049\pi$
$942$	−18.6253	−0.606845
$943$	35.3258	1.15037
$944$	−10.2374	−0.333200
$945$	−9.92478	−0.322853
$946$	7.53690	0.245046
$947$	2.02635	0.0658475	0.0329237	−	0.999458i	$-0.489518\pi$
$947$	2.02635	0.0658475	0.0329237	+	0.999458i	$0.489518\pi$
$948$	13.6629	0.443751
$949$	22.1476	0.718942
$950$	51.7400	1.67867
$951$	25.2750	0.819599
$952$	2.96239	0.0960116
$953$	19.5515	0.633335	0.316667	−	0.948537i	$-0.397436\pi$
$953$	19.5515	0.633335	0.316667	+	0.948537i	$0.397436\pi$
$954$	2.70052	0.0874327
$955$	−43.5975	−1.41078
$956$	−17.1490	−0.554639
$957$	−2.96239	−0.0957604
$958$	−11.0376	−0.356609
$959$	15.4763	0.499755
$960$	3.35026	0.108129
$961$	−27.9789	−0.902545
$962$	30.9525	0.997950
$963$	12.6253	0.406845
$964$	22.9380	0.738782
$965$	−19.0541	−0.613374
$966$	8.77575	0.282355
$967$	23.4128	0.752905	0.376453	−	0.926436i	$-0.377144\pi$
$967$	23.4128	0.752905	0.376453	+	0.926436i	$0.377144\pi$
$968$	1.00000	0.0321412
$969$	8.31265	0.267041
$970$	−48.9986	−1.57325
$971$	−10.2374	−0.328535	−0.164267	−	0.986416i	$-0.552526\pi$
$971$	−10.2374	−0.328535	−0.164267	+	0.986416i	$0.552526\pi$
$972$	−1.00000	−0.0320750
$973$	−35.1030	−1.12535
$974$	−30.1114	−0.964832
$975$	−24.8970	−0.797343
$976$	0.649738	0.0207976
$977$	−6.77575	−0.216775	−0.108388	−	0.994109i	$-0.534569\pi$
$977$	−6.77575	−0.216775	−0.108388	+	0.994109i	$0.534569\pi$
$978$	7.22425	0.231006
$979$	7.92478	0.253277
$980$	−5.94921	−0.190041
$981$	6.57452	0.209908
$982$	6.17679	0.197109
$983$	−11.8594	−0.378256	−0.189128	−	0.981952i	$-0.560566\pi$
$983$	−11.8594	−0.378256	−0.189128	+	0.981952i	$0.560566\pi$
$984$	−11.9248	−0.380148
$985$	48.3733	1.54130
$986$	2.96239	0.0943417
$987$	12.9986	0.413750
$988$	33.2506	1.05784
$989$	−22.3272	−0.709965
$990$	3.35026	0.106478
$991$	−45.5877	−1.44814	−0.724070	−	0.689726i	$-0.757731\pi$
$991$	−45.5877	−1.44814	−0.724070	+	0.689726i	$0.757731\pi$
$992$	1.73813	0.0551858
$993$	5.55149	0.176171
$994$	11.0738	0.351240
$995$	40.8284	1.29435
$996$	−9.14903	−0.289898
$997$	7.87399	0.249372	0.124686	−	0.992196i	$-0.460208\pi$
$997$	7.87399	0.249372	0.124686	+	0.992196i	$0.460208\pi$
$998$	33.6531	1.06527
$999$	−7.73813	−0.244824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.a.s.1.1	✓	3
3.2	odd	2		3366.2.a.z.1.3		3
4.3	odd	2		8976.2.a.bx.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.a.s.1.1	✓	3	1.1	even	1	trivial
3366.2.a.z.1.3		3	3.2	odd	2
8976.2.a.bx.1.1		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.35026 q^{5} -1.00000 q^{6} -2.96239 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.35026 q^{5} -1.00000 q^{6} -2.96239 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.35026 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.00000 q^{13} -2.96239 q^{14} +3.35026 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +8.31265 q^{19} -3.35026 q^{20} +2.96239 q^{21} -1.00000 q^{22} +2.96239 q^{23} -1.00000 q^{24} +6.22425 q^{25} +4.00000 q^{26} -1.00000 q^{27} -2.96239 q^{28} -2.96239 q^{29} +3.35026 q^{30} +1.73813 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} +9.92478 q^{35} +1.00000 q^{36} +7.73813 q^{37} +8.31265 q^{38} -4.00000 q^{39} -3.35026 q^{40} +11.9248 q^{41} +2.96239 q^{42} -7.53690 q^{43} -1.00000 q^{44} -3.35026 q^{45} +2.96239 q^{46} +4.38787 q^{47} -1.00000 q^{48} +1.77575 q^{49} +6.22425 q^{50} +1.00000 q^{51} +4.00000 q^{52} +2.70052 q^{53} -1.00000 q^{54} +3.35026 q^{55} -2.96239 q^{56} -8.31265 q^{57} -2.96239 q^{58} -10.2374 q^{59} +3.35026 q^{60} +0.649738 q^{61} +1.73813 q^{62} -2.96239 q^{63} +1.00000 q^{64} -13.4010 q^{65} +1.00000 q^{66} +9.14903 q^{67} -1.00000 q^{68} -2.96239 q^{69} +9.92478 q^{70} -3.73813 q^{71} +1.00000 q^{72} +5.53690 q^{73} +7.73813 q^{74} -6.22425 q^{75} +8.31265 q^{76} +2.96239 q^{77} -4.00000 q^{78} -13.6629 q^{79} -3.35026 q^{80} +1.00000 q^{81} +11.9248 q^{82} +9.14903 q^{83} +2.96239 q^{84} +3.35026 q^{85} -7.53690 q^{86} +2.96239 q^{87} -1.00000 q^{88} -7.92478 q^{89} -3.35026 q^{90} -11.8496 q^{91} +2.96239 q^{92} -1.73813 q^{93} +4.38787 q^{94} -27.8496 q^{95} -1.00000 q^{96} +14.6253 q^{97} +1.77575 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{11} - 3 q^{12} + 12 q^{13} + 2 q^{14} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 4 q^{19} - 2 q^{21} - 3 q^{22} - 2 q^{23} - 3 q^{24} + 17 q^{25} + 12 q^{26} - 3 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{31} + 3 q^{32} + 3 q^{33} - 3 q^{34} + 8 q^{35} + 3 q^{36} + 14 q^{37} + 4 q^{38} - 12 q^{39} + 14 q^{41} - 2 q^{42} - 3 q^{44} - 2 q^{46} + 14 q^{47} - 3 q^{48} + 7 q^{49} + 17 q^{50} + 3 q^{51} + 12 q^{52} - 12 q^{53} - 3 q^{54} + 2 q^{56} - 4 q^{57} + 2 q^{58} + 12 q^{59} + 12 q^{61} - 4 q^{62} + 2 q^{63} + 3 q^{64} + 3 q^{66} + 4 q^{67} - 3 q^{68} + 2 q^{69} + 8 q^{70} - 2 q^{71} + 3 q^{72} - 6 q^{73} + 14 q^{74} - 17 q^{75} + 4 q^{76} - 2 q^{77} - 12 q^{78} - 10 q^{79} + 3 q^{81} + 14 q^{82} + 4 q^{83} - 2 q^{84} - 2 q^{87} - 3 q^{88} - 2 q^{89} + 8 q^{91} - 2 q^{92} + 4 q^{93} + 14 q^{94} - 40 q^{95} - 3 q^{96} + 2 q^{97} + 7 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^11 - 3 * q^12 + 12 * q^13 + 2 * q^14 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 4 * q^19 - 2 * q^21 - 3 * q^22 - 2 * q^23 - 3 * q^24 + 17 * q^25 + 12 * q^26 - 3 * q^27 + 2 * q^28 + 2 * q^29 - 4 * q^31 + 3 * q^32 + 3 * q^33 - 3 * q^34 + 8 * q^35 + 3 * q^36 + 14 * q^37 + 4 * q^38 - 12 * q^39 + 14 * q^41 - 2 * q^42 - 3 * q^44 - 2 * q^46 + 14 * q^47 - 3 * q^48 + 7 * q^49 + 17 * q^50 + 3 * q^51 + 12 * q^52 - 12 * q^53 - 3 * q^54 + 2 * q^56 - 4 * q^57 + 2 * q^58 + 12 * q^59 + 12 * q^61 - 4 * q^62 + 2 * q^63 + 3 * q^64 + 3 * q^66 + 4 * q^67 - 3 * q^68 + 2 * q^69 + 8 * q^70 - 2 * q^71 + 3 * q^72 - 6 * q^73 + 14 * q^74 - 17 * q^75 + 4 * q^76 - 2 * q^77 - 12 * q^78 - 10 * q^79 + 3 * q^81 + 14 * q^82 + 4 * q^83 - 2 * q^84 - 2 * q^87 - 3 * q^88 - 2 * q^89 + 8 * q^91 - 2 * q^92 + 4 * q^93 + 14 * q^94 - 40 * q^95 - 3 * q^96 + 2 * q^97 + 7 * q^98 - 3 * q^99

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