LMFDB - Embedded newform 122.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(1,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("122.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.93543 q^{3} +1.00000 q^{4} +3.18953 q^{5} -2.93543 q^{6} +3.42723 q^{7} +1.00000 q^{8} +5.61676 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.93543 q^{3} +1.00000 q^{4} +3.18953 q^{5} -2.93543 q^{6} +3.42723 q^{7} +1.00000 q^{8} +5.61676 q^{9} +3.18953 q^{10} -4.68133 q^{11} -2.93543 q^{12} -2.68133 q^{13} +3.42723 q^{14} -9.36266 q^{15} +1.00000 q^{16} -1.49180 q^{17} +5.61676 q^{18} -1.25410 q^{19} +3.18953 q^{20} -10.0604 q^{21} -4.68133 q^{22} +5.10856 q^{23} -2.93543 q^{24} +5.17313 q^{25} -2.68133 q^{26} -7.68133 q^{27} +3.42723 q^{28} -5.12497 q^{29} -9.36266 q^{30} -8.29809 q^{31} +1.00000 q^{32} +13.7417 q^{33} -1.49180 q^{34} +10.9313 q^{35} +5.61676 q^{36} +5.95184 q^{37} -1.25410 q^{38} +7.87086 q^{39} +3.18953 q^{40} -4.63317 q^{41} -10.0604 q^{42} +5.01641 q^{43} -4.68133 q^{44} +17.9149 q^{45} +5.10856 q^{46} -8.37907 q^{47} -2.93543 q^{48} +4.74590 q^{49} +5.17313 q^{50} +4.37907 q^{51} -2.68133 q^{52} -14.0398 q^{53} -7.68133 q^{54} -14.9313 q^{55} +3.42723 q^{56} +3.68133 q^{57} -5.12497 q^{58} -4.81047 q^{59} -9.36266 q^{60} -1.00000 q^{61} -8.29809 q^{62} +19.2499 q^{63} +1.00000 q^{64} -8.55220 q^{65} +13.7417 q^{66} +13.5358 q^{67} -1.49180 q^{68} -14.9958 q^{69} +10.9313 q^{70} +8.23769 q^{71} +5.61676 q^{72} +10.9518 q^{73} +5.95184 q^{74} -15.1854 q^{75} -1.25410 q^{76} -16.0440 q^{77} +7.87086 q^{78} +9.56860 q^{79} +3.18953 q^{80} +5.69774 q^{81} -4.63317 q^{82} +5.47122 q^{83} -10.0604 q^{84} -4.75814 q^{85} +5.01641 q^{86} +15.0440 q^{87} -4.68133 q^{88} +2.88727 q^{89} +17.9149 q^{90} -9.18953 q^{91} +5.10856 q^{92} +24.3585 q^{93} -8.37907 q^{94} -4.00000 q^{95} -2.93543 q^{96} +0.427229 q^{97} +4.74590 q^{98} -26.2939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} + q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 + q^5 - q^6 + 4 * q^7 + 3 * q^8 + 2 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 2 q^{9} + q^{10} - 7 q^{11} - q^{12} - q^{13} + 4 q^{14} - 14 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} - 3 q^{19} + q^{20} - 6 q^{21} - 7 q^{22} + 2 q^{23} - q^{24} + 10 q^{25} - q^{26} - 16 q^{27} + 4 q^{28} + q^{29} - 14 q^{30} - 3 q^{31} + 3 q^{32} + 10 q^{33} - 6 q^{34} - 7 q^{35} + 2 q^{36} + 7 q^{37} - 3 q^{38} + 8 q^{39} + q^{40} + 4 q^{41} - 6 q^{42} + 12 q^{43} - 7 q^{44} + 17 q^{45} + 2 q^{46} - 8 q^{47} - q^{48} + 15 q^{49} + 10 q^{50} - 4 q^{51} - q^{52} + 11 q^{53} - 16 q^{54} - 5 q^{55} + 4 q^{56} + 4 q^{57} + q^{58} - 23 q^{59} - 14 q^{60} - 3 q^{61} - 3 q^{62} + 25 q^{63} + 3 q^{64} - 3 q^{65} + 10 q^{66} + 21 q^{67} - 6 q^{68} - 13 q^{69} - 7 q^{70} + 27 q^{71} + 2 q^{72} + 22 q^{73} + 7 q^{74} - 5 q^{75} - 3 q^{76} - 27 q^{77} + 8 q^{78} + 3 q^{79} + q^{80} + 7 q^{81} + 4 q^{82} - 11 q^{83} - 6 q^{84} + 20 q^{85} + 12 q^{86} + 24 q^{87} - 7 q^{88} - 10 q^{89} + 17 q^{90} - 19 q^{91} + 2 q^{92} + 27 q^{93} - 8 q^{94} - 12 q^{95} - q^{96} - 5 q^{97} + 15 q^{98} - 25 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + q^5 - q^6 + 4 * q^7 + 3 * q^8 + 2 * q^9 + q^10 - 7 * q^11 - q^12 - q^13 + 4 * q^14 - 14 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 - 3 * q^19 + q^20 - 6 * q^21 - 7 * q^22 + 2 * q^23 - q^24 + 10 * q^25 - q^26 - 16 * q^27 + 4 * q^28 + q^29 - 14 * q^30 - 3 * q^31 + 3 * q^32 + 10 * q^33 - 6 * q^34 - 7 * q^35 + 2 * q^36 + 7 * q^37 - 3 * q^38 + 8 * q^39 + q^40 + 4 * q^41 - 6 * q^42 + 12 * q^43 - 7 * q^44 + 17 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 15 * q^49 + 10 * q^50 - 4 * q^51 - q^52 + 11 * q^53 - 16 * q^54 - 5 * q^55 + 4 * q^56 + 4 * q^57 + q^58 - 23 * q^59 - 14 * q^60 - 3 * q^61 - 3 * q^62 + 25 * q^63 + 3 * q^64 - 3 * q^65 + 10 * q^66 + 21 * q^67 - 6 * q^68 - 13 * q^69 - 7 * q^70 + 27 * q^71 + 2 * q^72 + 22 * q^73 + 7 * q^74 - 5 * q^75 - 3 * q^76 - 27 * q^77 + 8 * q^78 + 3 * q^79 + q^80 + 7 * q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 20 * q^85 + 12 * q^86 + 24 * q^87 - 7 * q^88 - 10 * q^89 + 17 * q^90 - 19 * q^91 + 2 * q^92 + 27 * q^93 - 8 * q^94 - 12 * q^95 - q^96 - 5 * q^97 + 15 * q^98 - 25 * 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
$3$	−2.93543	−1.69477	−0.847386	−	0.530977i	$-0.821825\pi$
$3$	−2.93543	−1.69477	−0.847386	+	0.530977i	$0.821825\pi$
$4$	1.00000	0.500000
$5$	3.18953	1.42640	0.713201	−	0.700959i	$-0.247244\pi$
$5$	3.18953	1.42640	0.713201	+	0.700959i	$0.247244\pi$
$6$	−2.93543	−1.19839
$7$	3.42723	1.29537	0.647685	−	0.761908i	$-0.275737\pi$
$7$	3.42723	1.29537	0.647685	+	0.761908i	$0.275737\pi$
$8$	1.00000	0.353553
$9$	5.61676	1.87225
$10$	3.18953	1.00862
$11$	−4.68133	−1.41147	−0.705737	−	0.708474i	$-0.749384\pi$
$11$	−4.68133	−1.41147	−0.705737	+	0.708474i	$0.749384\pi$
$12$	−2.93543	−0.847386
$13$	−2.68133	−0.743667	−0.371834	−	0.928299i	$-0.621271\pi$
$13$	−2.68133	−0.743667	−0.371834	+	0.928299i	$0.621271\pi$
$14$	3.42723	0.915965
$15$	−9.36266	−2.41743
$16$	1.00000	0.250000
$17$	−1.49180	−0.361814	−0.180907	−	0.983500i	$-0.557903\pi$
$17$	−1.49180	−0.361814	−0.180907	+	0.983500i	$0.557903\pi$
$18$	5.61676	1.32388
$19$	−1.25410	−0.287711	−0.143855	−	0.989599i	$-0.545950\pi$
$19$	−1.25410	−0.287711	−0.143855	+	0.989599i	$0.545950\pi$
$20$	3.18953	0.713201
$21$	−10.0604	−2.19536
$22$	−4.68133	−0.998063
$23$	5.10856	1.06521	0.532604	−	0.846364i	$-0.321213\pi$
$23$	5.10856	1.06521	0.532604	+	0.846364i	$0.321213\pi$
$24$	−2.93543	−0.599193
$25$	5.17313	1.03463
$26$	−2.68133	−0.525852
$27$	−7.68133	−1.47827
$28$	3.42723	0.647685
$29$	−5.12497	−0.951682	−0.475841	−	0.879531i	$-0.657856\pi$
$29$	−5.12497	−0.951682	−0.475841	+	0.879531i	$0.657856\pi$
$30$	−9.36266	−1.70938
$31$	−8.29809	−1.49038	−0.745191	−	0.666851i	$-0.767642\pi$
$31$	−8.29809	−1.49038	−0.745191	+	0.666851i	$0.767642\pi$
$32$	1.00000	0.176777
$33$	13.7417	2.39213
$34$	−1.49180	−0.255841
$35$	10.9313	1.84772
$36$	5.61676	0.936127
$37$	5.95184	0.978476	0.489238	−	0.872150i	$-0.337275\pi$
$37$	5.95184	0.978476	0.489238	+	0.872150i	$0.337275\pi$
$38$	−1.25410	−0.203442
$39$	7.87086	1.26035
$40$	3.18953	0.504310
$41$	−4.63317	−0.723580	−0.361790	−	0.932260i	$-0.617834\pi$
$41$	−4.63317	−0.723580	−0.361790	+	0.932260i	$0.617834\pi$
$42$	−10.0604	−1.55235
$43$	5.01641	0.764995	0.382497	−	0.923957i	$-0.375064\pi$
$43$	5.01641	0.764995	0.382497	+	0.923957i	$0.375064\pi$
$44$	−4.68133	−0.705737
$45$	17.9149	2.67059
$46$	5.10856	0.753216
$47$	−8.37907	−1.22221	−0.611106	−	0.791549i	$-0.709275\pi$
$47$	−8.37907	−1.22221	−0.611106	+	0.791549i	$0.709275\pi$
$48$	−2.93543	−0.423693
$49$	4.74590	0.677985
$50$	5.17313	0.731591
$51$	4.37907	0.613192
$52$	−2.68133	−0.371834
$53$	−14.0398	−1.92852	−0.964259	−	0.264961i	$-0.914641\pi$
$53$	−14.0398	−1.92852	−0.964259	+	0.264961i	$0.914641\pi$
$54$	−7.68133	−1.04530
$55$	−14.9313	−2.01333
$56$	3.42723	0.457983
$57$	3.68133	0.487604
$58$	−5.12497	−0.672941
$59$	−4.81047	−0.626269	−0.313135	−	0.949709i	$-0.601379\pi$
$59$	−4.81047	−0.626269	−0.313135	+	0.949709i	$0.601379\pi$
$60$	−9.36266	−1.20871
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−8.29809	−1.05386
$63$	19.2499	2.42526
$64$	1.00000	0.125000
$65$	−8.55220	−1.06077
$66$	13.7417	1.69149
$67$	13.5358	1.65366	0.826830	−	0.562452i	$-0.190142\pi$
$67$	13.5358	1.65366	0.826830	+	0.562452i	$0.190142\pi$
$68$	−1.49180	−0.180907
$69$	−14.9958	−1.80529
$70$	10.9313	1.30654
$71$	8.23769	0.977635	0.488817	−	0.872386i	$-0.337428\pi$
$71$	8.23769	0.977635	0.488817	+	0.872386i	$0.337428\pi$
$72$	5.61676	0.661942
$73$	10.9518	1.28182	0.640908	−	0.767618i	$-0.278558\pi$
$73$	10.9518	1.28182	0.640908	+	0.767618i	$0.278558\pi$
$74$	5.95184	0.691887
$75$	−15.1854	−1.75345
$76$	−1.25410	−0.143855
$77$	−16.0440	−1.82838
$78$	7.87086	0.891200
$79$	9.56860	1.07655	0.538276	−	0.842769i	$-0.319076\pi$
$79$	9.56860	1.07655	0.538276	+	0.842769i	$0.319076\pi$
$80$	3.18953	0.356601
$81$	5.69774	0.633082
$82$	−4.63317	−0.511648
$83$	5.47122	0.600545	0.300272	−	0.953854i	$-0.402922\pi$
$83$	5.47122	0.600545	0.300272	+	0.953854i	$0.402922\pi$
$84$	−10.0604	−1.09768
$85$	−4.75814	−0.516092
$86$	5.01641	0.540933
$87$	15.0440	1.61289
$88$	−4.68133	−0.499032
$89$	2.88727	0.306050	0.153025	−	0.988222i	$-0.451098\pi$
$89$	2.88727	0.306050	0.153025	+	0.988222i	$0.451098\pi$
$90$	17.9149	1.88839
$91$	−9.18953	−0.963325
$92$	5.10856	0.532604
$93$	24.3585	2.52586
$94$	−8.37907	−0.864235
$95$	−4.00000	−0.410391
$96$	−2.93543	−0.299596
$97$	0.427229	0.0433785	0.0216893	−	0.999765i	$-0.493096\pi$
$97$	0.427229	0.0433785	0.0216893	+	0.999765i	$0.493096\pi$
$98$	4.74590	0.479408
$99$	−26.2939	−2.64264
$100$	5.17313	0.517313
$101$	12.6772	1.26142	0.630712	−	0.776017i	$-0.282763\pi$
$101$	12.6772	1.26142	0.630712	+	0.776017i	$0.282763\pi$
$102$	4.37907	0.433592
$103$	−5.23353	−0.515675	−0.257837	−	0.966188i	$-0.583010\pi$
$103$	−5.23353	−0.515675	−0.257837	+	0.966188i	$0.583010\pi$
$104$	−2.68133	−0.262926
$105$	−32.0880	−3.13147
$106$	−14.0398	−1.36367
$107$	−0.366830	−0.0354628	−0.0177314	−	0.999843i	$-0.505644\pi$
$107$	−0.366830	−0.0354628	−0.0177314	+	0.999843i	$0.505644\pi$
$108$	−7.68133	−0.739136
$109$	2.68133	0.256825	0.128412	−	0.991721i	$-0.459012\pi$
$109$	2.68133	0.256825	0.128412	+	0.991721i	$0.459012\pi$
$110$	−14.9313	−1.42364
$111$	−17.4712	−1.65829
$112$	3.42723	0.323843
$113$	4.91903	0.462743	0.231372	−	0.972865i	$-0.425679\pi$
$113$	4.91903	0.462743	0.231372	+	0.972865i	$0.425679\pi$
$114$	3.68133	0.344788
$115$	16.2939	1.51942
$116$	−5.12497	−0.475841
$117$	−15.0604	−1.39233
$118$	−4.81047	−0.442839
$119$	−5.11273	−0.468683
$120$	−9.36266	−0.854690
$121$	10.9149	0.992260
$122$	−1.00000	−0.0905357
$123$	13.6004	1.22630
$124$	−8.29809	−0.745191
$125$	0.552195	0.0493898
$126$	19.2499	1.71492
$127$	12.2499	1.08701	0.543503	−	0.839407i	$-0.317098\pi$
$127$	12.2499	1.08701	0.543503	+	0.839407i	$0.317098\pi$
$128$	1.00000	0.0883883
$129$	−14.7253	−1.29649
$130$	−8.55220	−0.750077
$131$	−19.7417	−1.72484	−0.862421	−	0.506191i	$-0.831053\pi$
$131$	−19.7417	−1.72484	−0.862421	+	0.506191i	$0.831053\pi$
$132$	13.7417	1.19606
$133$	−4.29809	−0.372692
$134$	13.5358	1.16931
$135$	−24.4999	−2.10861
$136$	−1.49180	−0.127921
$137$	−4.89144	−0.417904	−0.208952	−	0.977926i	$-0.567005\pi$
$137$	−4.89144	−0.417904	−0.208952	+	0.977926i	$0.567005\pi$
$138$	−14.9958	−1.27653
$139$	4.04399	0.343007	0.171503	−	0.985184i	$-0.445138\pi$
$139$	4.04399	0.343007	0.171503	+	0.985184i	$0.445138\pi$
$140$	10.9313	0.923860
$141$	24.5962	2.07137
$142$	8.23769	0.691292
$143$	12.5522	1.04967
$144$	5.61676	0.468064
$145$	−16.3463	−1.35748
$146$	10.9518	0.906381
$147$	−13.9313	−1.14903
$148$	5.95184	0.489238
$149$	−3.35148	−0.274564	−0.137282	−	0.990532i	$-0.543837\pi$
$149$	−3.35148	−0.274564	−0.137282	+	0.990532i	$0.543837\pi$
$150$	−15.1854	−1.23988
$151$	−14.2130	−1.15663	−0.578317	−	0.815812i	$-0.696290\pi$
$151$	−14.2130	−1.15663	−0.578317	+	0.815812i	$0.696290\pi$
$152$	−1.25410	−0.101721
$153$	−8.37907	−0.677408
$154$	−16.0440	−1.29286
$155$	−26.4671	−2.12588
$156$	7.87086	0.630174
$157$	−6.74590	−0.538381	−0.269191	−	0.963087i	$-0.586756\pi$
$157$	−6.74590	−0.538381	−0.269191	+	0.963087i	$0.586756\pi$
$158$	9.56860	0.761237
$159$	41.2130	3.26840
$160$	3.18953	0.252155
$161$	17.5082	1.37984
$162$	5.69774	0.447657
$163$	7.95184	0.622836	0.311418	−	0.950273i	$-0.399196\pi$
$163$	7.95184	0.622836	0.311418	+	0.950273i	$0.399196\pi$
$164$	−4.63317	−0.361790
$165$	43.8297	3.41214
$166$	5.47122	0.424649
$167$	8.54102	0.660924	0.330462	−	0.943819i	$-0.392795\pi$
$167$	8.54102	0.660924	0.330462	+	0.943819i	$0.392795\pi$
$168$	−10.0604	−0.776177
$169$	−5.81047	−0.446959
$170$	−4.75814	−0.364932
$171$	−7.04399	−0.538668
$172$	5.01641	0.382497
$173$	3.63317	0.276225	0.138112	−	0.990417i	$-0.455896\pi$
$173$	3.63317	0.276225	0.138112	+	0.990417i	$0.455896\pi$
$174$	15.0440	1.14048
$175$	17.7295	1.34022
$176$	−4.68133	−0.352869
$177$	14.1208	1.06138
$178$	2.88727	0.216410
$179$	−17.6608	−1.32003	−0.660013	−	0.751254i	$-0.729449\pi$
$179$	−17.6608	−1.32003	−0.660013	+	0.751254i	$0.729449\pi$
$180$	17.9149	1.33529
$181$	−1.03698	−0.0770783	−0.0385392	−	0.999257i	$-0.512270\pi$
$181$	−1.03698	−0.0770783	−0.0385392	+	0.999257i	$0.512270\pi$
$182$	−9.18953	−0.681174
$183$	2.93543	0.216993
$184$	5.10856	0.376608
$185$	18.9836	1.39570
$186$	24.3585	1.78605
$187$	6.98359	0.510691
$188$	−8.37907	−0.611106
$189$	−26.3257	−1.91491
$190$	−4.00000	−0.290191
$191$	−3.74590	−0.271044	−0.135522	−	0.990774i	$-0.543271\pi$
$191$	−3.74590	−0.271044	−0.135522	+	0.990774i	$0.543271\pi$
$192$	−2.93543	−0.211847
$193$	−4.97526	−0.358127	−0.179063	−	0.983838i	$-0.557307\pi$
$193$	−4.97526	−0.358127	−0.179063	+	0.983838i	$0.557307\pi$
$194$	0.427229	0.0306733
$195$	25.1044	1.79776
$196$	4.74590	0.338993
$197$	4.46421	0.318062	0.159031	−	0.987274i	$-0.449163\pi$
$197$	4.46421	0.318062	0.159031	+	0.987274i	$0.449163\pi$
$198$	−26.2939	−1.86863
$199$	9.57978	0.679093	0.339546	−	0.940589i	$-0.389726\pi$
$199$	9.57978	0.679093	0.339546	+	0.940589i	$0.389726\pi$
$200$	5.17313	0.365795
$201$	−39.7334	−2.80258
$202$	12.6772	0.891962
$203$	−17.5644	−1.23278
$204$	4.37907	0.306596
$205$	−14.7777	−1.03212
$206$	−5.23353	−0.364637
$207$	28.6936	1.99434
$208$	−2.68133	−0.185917
$209$	5.87086	0.406096
$210$	−32.0880	−2.21428
$211$	6.50820	0.448043	0.224022	−	0.974584i	$-0.428081\pi$
$211$	6.50820	0.448043	0.224022	+	0.974584i	$0.428081\pi$
$212$	−14.0398	−0.964259
$213$	−24.1812	−1.65687
$214$	−0.366830	−0.0250760
$215$	16.0000	1.09119
$216$	−7.68133	−0.522648
$217$	−28.4395	−1.93060
$218$	2.68133	0.181603
$219$	−32.1484	−2.17239
$220$	−14.9313	−1.00667
$221$	4.00000	0.269069
$222$	−17.4712	−1.17259
$223$	−5.22235	−0.349714	−0.174857	−	0.984594i	$-0.555946\pi$
$223$	−5.22235	−0.349714	−0.174857	+	0.984594i	$0.555946\pi$
$224$	3.42723	0.228991
$225$	29.0562	1.93708
$226$	4.91903	0.327209
$227$	7.02759	0.466437	0.233219	−	0.972424i	$-0.425074\pi$
$227$	7.02759	0.466437	0.233219	+	0.972424i	$0.425074\pi$
$228$	3.68133	0.243802
$229$	20.8021	1.37464	0.687322	−	0.726353i	$-0.258786\pi$
$229$	20.8021	1.37464	0.687322	+	0.726353i	$0.258786\pi$
$230$	16.2939	1.07439
$231$	47.0961	3.09869
$232$	−5.12497	−0.336471
$233$	6.69251	0.438441	0.219220	−	0.975675i	$-0.429649\pi$
$233$	6.69251	0.438441	0.219220	+	0.975675i	$0.429649\pi$
$234$	−15.0604	−0.984529
$235$	−26.7253	−1.74337
$236$	−4.81047	−0.313135
$237$	−28.0880	−1.82451
$238$	−5.11273	−0.331409
$239$	27.9917	1.81063	0.905315	−	0.424741i	$-0.139635\pi$
$239$	27.9917	1.81063	0.905315	+	0.424741i	$0.139635\pi$
$240$	−9.36266	−0.604357
$241$	21.8943	1.41033	0.705167	−	0.709041i	$-0.250872\pi$
$241$	21.8943	1.41033	0.705167	+	0.709041i	$0.250872\pi$
$242$	10.9149	0.701634
$243$	6.31867	0.405343
$244$	−1.00000	−0.0640184
$245$	15.1372	0.967080
$246$	13.6004	0.867127
$247$	3.36266	0.213961
$248$	−8.29809	−0.526929
$249$	−16.0604	−1.01779
$250$	0.552195	0.0349239
$251$	27.3215	1.72452	0.862259	−	0.506467i	$-0.169049\pi$
$251$	27.3215	1.72452	0.862259	+	0.506467i	$0.169049\pi$
$252$	19.2499	1.21263
$253$	−23.9149	−1.50351
$254$	12.2499	0.768629
$255$	13.9672	0.874659
$256$	1.00000	0.0625000
$257$	−0.907847	−0.0566299	−0.0283150	−	0.999599i	$-0.509014\pi$
$257$	−0.907847	−0.0566299	−0.0283150	+	0.999599i	$0.509014\pi$
$258$	−14.7253	−0.916759
$259$	20.3983	1.26749
$260$	−8.55220	−0.530385
$261$	−28.7857	−1.78179
$262$	−19.7417	−1.21965
$263$	−4.69251	−0.289353	−0.144676	−	0.989479i	$-0.546214\pi$
$263$	−4.69251	−0.289353	−0.144676	+	0.989479i	$0.546214\pi$
$264$	13.7417	0.845745
$265$	−44.7805	−2.75084
$266$	−4.29809	−0.263533
$267$	−8.47539	−0.518685
$268$	13.5358	0.826830
$269$	11.6537	0.710541	0.355271	−	0.934763i	$-0.384389\pi$
$269$	11.6537	0.710541	0.355271	+	0.934763i	$0.384389\pi$
$270$	−24.4999	−1.49101
$271$	−19.7089	−1.19723	−0.598616	−	0.801036i	$-0.704282\pi$
$271$	−19.7089	−1.19723	−0.598616	+	0.801036i	$0.704282\pi$
$272$	−1.49180	−0.0904535
$273$	26.9753	1.63262
$274$	−4.89144	−0.295503
$275$	−24.2171	−1.46035
$276$	−14.9958	−0.902643
$277$	−5.12497	−0.307929	−0.153965	−	0.988076i	$-0.549204\pi$
$277$	−5.12497	−0.307929	−0.153965	+	0.988076i	$0.549204\pi$
$278$	4.04399	0.242543
$279$	−46.6084	−2.79037
$280$	10.9313	0.653268
$281$	10.9836	0.655226	0.327613	−	0.944812i	$-0.393756\pi$
$281$	10.9836	0.655226	0.327613	+	0.944812i	$0.393756\pi$
$282$	24.5962	1.46468
$283$	1.32284	0.0786346	0.0393173	−	0.999227i	$-0.487482\pi$
$283$	1.32284	0.0786346	0.0393173	+	0.999227i	$0.487482\pi$
$284$	8.23769	0.488817
$285$	11.7417	0.695520
$286$	12.5522	0.742227
$287$	−15.8789	−0.937304
$288$	5.61676	0.330971
$289$	−14.7745	−0.869091
$290$	−16.3463	−0.959885
$291$	−1.25410	−0.0735167
$292$	10.9518	0.640908
$293$	7.01641	0.409903	0.204951	−	0.978772i	$-0.434296\pi$
$293$	7.01641	0.409903	0.204951	+	0.978772i	$0.434296\pi$
$294$	−13.9313	−0.812488
$295$	−15.3431	−0.893312
$296$	5.95184	0.345944
$297$	35.9588	2.08654
$298$	−3.35148	−0.194146
$299$	−13.6977	−0.792161
$300$	−15.1854	−0.876727
$301$	17.1924	0.990952
$302$	−14.2130	−0.817863
$303$	−37.2130	−2.13783
$304$	−1.25410	−0.0719277
$305$	−3.18953	−0.182632
$306$	−8.37907	−0.478999
$307$	−3.91486	−0.223433	−0.111716	−	0.993740i	$-0.535635\pi$
$307$	−3.91486	−0.223433	−0.111716	+	0.993740i	$0.535635\pi$
$308$	−16.0440	−0.914191
$309$	15.3627	0.873951
$310$	−26.4671	−1.50323
$311$	−3.77348	−0.213975	−0.106987	−	0.994260i	$-0.534120\pi$
$311$	−3.77348	−0.213975	−0.106987	+	0.994260i	$0.534120\pi$
$312$	7.87086	0.445600
$313$	8.72532	0.493184	0.246592	−	0.969119i	$-0.420689\pi$
$313$	8.72532	0.493184	0.246592	+	0.969119i	$0.420689\pi$
$314$	−6.74590	−0.380693
$315$	61.3983	3.45940
$316$	9.56860	0.538276
$317$	−14.1208	−0.793103	−0.396551	−	0.918012i	$-0.629793\pi$
$317$	−14.1208	−0.793103	−0.396551	+	0.918012i	$0.629793\pi$
$318$	41.2130	2.31111
$319$	23.9917	1.34328
$320$	3.18953	0.178300
$321$	1.07681	0.0601014
$322$	17.5082	0.975694
$323$	1.87086	0.104098
$324$	5.69774	0.316541
$325$	−13.8709	−0.769417
$326$	7.95184	0.440412
$327$	−7.87086	−0.435260
$328$	−4.63317	−0.255824
$329$	−28.7170	−1.58322
$330$	43.8297	2.41275
$331$	−27.1484	−1.49221	−0.746105	−	0.665828i	$-0.768078\pi$
$331$	−27.1484	−1.49221	−0.746105	+	0.665828i	$0.768078\pi$
$332$	5.47122	0.300272
$333$	33.4301	1.83196
$334$	8.54102	0.467344
$335$	43.1729	2.35879
$336$	−10.0604	−0.548840
$337$	−4.46705	−0.243336	−0.121668	−	0.992571i	$-0.538824\pi$
$337$	−4.46705	−0.243336	−0.121668	+	0.992571i	$0.538824\pi$
$338$	−5.81047	−0.316048
$339$	−14.4395	−0.784244
$340$	−4.75814	−0.258046
$341$	38.8461	2.10364
$342$	−7.04399	−0.380895
$343$	−7.72532	−0.417128
$344$	5.01641	0.270467
$345$	−47.8297	−2.57507
$346$	3.63317	0.195320
$347$	31.4835	1.69012	0.845060	−	0.534671i	$-0.179564\pi$
$347$	31.4835	1.69012	0.845060	+	0.534671i	$0.179564\pi$
$348$	15.0440	0.806443
$349$	−32.8789	−1.75997	−0.879984	−	0.475002i	$-0.842447\pi$
$349$	−32.8789	−1.75997	−0.879984	+	0.475002i	$0.842447\pi$
$350$	17.7295	0.947681
$351$	20.5962	1.09934
$352$	−4.68133	−0.249516
$353$	−31.1278	−1.65677	−0.828383	−	0.560162i	$-0.810739\pi$
$353$	−31.1278	−1.65677	−0.828383	+	0.560162i	$0.810739\pi$
$354$	14.1208	0.750512
$355$	26.2744	1.39450
$356$	2.88727	0.153025
$357$	15.0081	0.794311
$358$	−17.6608	−0.933400
$359$	2.20488	0.116369	0.0581846	−	0.998306i	$-0.481469\pi$
$359$	2.20488	0.116369	0.0581846	+	0.998306i	$0.481469\pi$
$360$	17.9149	0.944196
$361$	−17.4272	−0.917223
$362$	−1.03698	−0.0545026
$363$	−32.0398	−1.68165
$364$	−9.18953	−0.481662
$365$	34.9313	1.82839
$366$	2.93543	0.153438
$367$	−8.72532	−0.455458	−0.227729	−	0.973725i	$-0.573130\pi$
$367$	−8.72532	−0.455458	−0.227729	+	0.973725i	$0.573130\pi$
$368$	5.10856	0.266302
$369$	−26.0234	−1.35472
$370$	18.9836	0.986910
$371$	−48.1177	−2.49815
$372$	24.3585	1.26293
$373$	31.0562	1.60803	0.804015	−	0.594609i	$-0.202693\pi$
$373$	31.0562	1.60803	0.804015	+	0.594609i	$0.202693\pi$
$374$	6.98359	0.361113
$375$	−1.62093	−0.0837046
$376$	−8.37907	−0.432117
$377$	13.7417	0.707735
$378$	−26.3257	−1.35405
$379$	12.3913	0.636499	0.318249	−	0.948007i	$-0.396905\pi$
$379$	12.3913	0.636499	0.318249	+	0.948007i	$0.396905\pi$
$380$	−4.00000	−0.205196
$381$	−35.9588	−1.84223
$382$	−3.74590	−0.191657
$383$	−20.3145	−1.03802	−0.519011	−	0.854767i	$-0.673700\pi$
$383$	−20.3145	−1.03802	−0.519011	+	0.854767i	$0.673700\pi$
$384$	−2.93543	−0.149798
$385$	−51.1729	−2.60801
$386$	−4.97526	−0.253234
$387$	28.1760	1.43226
$388$	0.427229	0.0216893
$389$	7.09215	0.359586	0.179793	−	0.983704i	$-0.442457\pi$
$389$	7.09215	0.359586	0.179793	+	0.983704i	$0.442457\pi$
$390$	25.1044	1.27121
$391$	−7.62093	−0.385407
$392$	4.74590	0.239704
$393$	57.9505	2.92322
$394$	4.46421	0.224904
$395$	30.5194	1.53560
$396$	−26.2939	−1.32132
$397$	30.1637	1.51387	0.756937	−	0.653488i	$-0.226695\pi$
$397$	30.1637	1.51387	0.756937	+	0.653488i	$0.226695\pi$
$398$	9.57978	0.480191
$399$	12.6168	0.631628
$400$	5.17313	0.258656
$401$	−6.88727	−0.343934	−0.171967	−	0.985103i	$-0.555012\pi$
$401$	−6.88727	−0.343934	−0.171967	+	0.985103i	$0.555012\pi$
$402$	−39.7334	−1.98172
$403$	22.2499	1.10835
$404$	12.6772	0.630712
$405$	18.1731	0.903030
$406$	−17.5644	−0.871708
$407$	−27.8625	−1.38109
$408$	4.37907	0.216796
$409$	−10.4342	−0.515940	−0.257970	−	0.966153i	$-0.583054\pi$
$409$	−10.4342	−0.515940	−0.257970	+	0.966153i	$0.583054\pi$
$410$	−14.7777	−0.729816
$411$	14.3585	0.708252
$412$	−5.23353	−0.257837
$413$	−16.4866	−0.811251
$414$	28.6936	1.41021
$415$	17.4506	0.856618
$416$	−2.68133	−0.131463
$417$	−11.8709	−0.581319
$418$	5.87086	0.287153
$419$	29.0409	1.41874	0.709370	−	0.704836i	$-0.248980\pi$
$419$	29.0409	1.41874	0.709370	+	0.704836i	$0.248980\pi$
$420$	−32.0880	−1.56573
$421$	−14.9630	−0.729253	−0.364626	−	0.931154i	$-0.618803\pi$
$421$	−14.9630	−0.729253	−0.364626	+	0.931154i	$0.618803\pi$
$422$	6.50820	0.316814
$423$	−47.0632	−2.28829
$424$	−14.0398	−0.681834
$425$	−7.71725	−0.374342
$426$	−24.1812	−1.17158
$427$	−3.42723	−0.165855
$428$	−0.366830	−0.0177314
$429$	−36.8461	−1.77895
$430$	16.0000	0.771589
$431$	−14.9753	−0.721333	−0.360666	−	0.932695i	$-0.617451\pi$
$431$	−14.9753	−0.721333	−0.360666	+	0.932695i	$0.617451\pi$
$432$	−7.68133	−0.369568
$433$	23.3215	1.12076	0.560380	−	0.828236i	$-0.310655\pi$
$433$	23.3215	1.12076	0.560380	+	0.828236i	$0.310655\pi$
$434$	−28.4395	−1.36514
$435$	47.9833	2.30062
$436$	2.68133	0.128412
$437$	−6.40665	−0.306472
$438$	−32.1484	−1.53611
$439$	−16.1208	−0.769404	−0.384702	−	0.923041i	$-0.625696\pi$
$439$	−16.1208	−0.769404	−0.384702	+	0.923041i	$0.625696\pi$
$440$	−14.9313	−0.711820
$441$	26.6566	1.26936
$442$	4.00000	0.190261
$443$	−39.4436	−1.87402	−0.937012	−	0.349298i	$-0.886420\pi$
$443$	−39.4436	−1.87402	−0.937012	+	0.349298i	$0.886420\pi$
$444$	−17.4712	−0.829147
$445$	9.20905	0.436551
$446$	−5.22235	−0.247285
$447$	9.83805	0.465324
$448$	3.42723	0.161921
$449$	20.1250	0.949756	0.474878	−	0.880052i	$-0.342492\pi$
$449$	20.1250	0.949756	0.474878	+	0.880052i	$0.342492\pi$
$450$	29.0562	1.36972
$451$	21.6894	1.02131
$452$	4.91903	0.231372
$453$	41.7212	1.96023
$454$	7.02759	0.329821
$455$	−29.3103	−1.37409
$456$	3.68133	0.172394
$457$	−14.9836	−0.700903	−0.350451	−	0.936581i	$-0.613972\pi$
$457$	−14.9836	−0.700903	−0.350451	+	0.936581i	$0.613972\pi$
$458$	20.8021	0.972020
$459$	11.4590	0.534860
$460$	16.2939	0.759708
$461$	−29.5798	−1.37767	−0.688834	−	0.724919i	$-0.741877\pi$
$461$	−29.5798	−1.37767	−0.688834	+	0.724919i	$0.741877\pi$
$462$	47.0961	2.19111
$463$	−10.4119	−0.483881	−0.241941	−	0.970291i	$-0.577784\pi$
$463$	−10.4119	−0.483881	−0.241941	+	0.970291i	$0.577784\pi$
$464$	−5.12497	−0.237921
$465$	77.6922	3.60289
$466$	6.69251	0.310024
$467$	−22.8656	−1.05810	−0.529048	−	0.848592i	$-0.677451\pi$
$467$	−22.8656	−1.05810	−0.529048	+	0.848592i	$0.677451\pi$
$468$	−15.0604	−0.696167
$469$	46.3902	2.14210
$470$	−26.7253	−1.23275
$471$	19.8021	0.912434
$472$	−4.81047	−0.221420
$473$	−23.4835	−1.07977
$474$	−28.0880	−1.29012
$475$	−6.48763	−0.297673
$476$	−5.11273	−0.234342
$477$	−78.8584	−3.61068
$478$	27.9917	1.28031
$479$	−11.2747	−0.515153	−0.257577	−	0.966258i	$-0.582924\pi$
$479$	−11.2747	−0.515153	−0.257577	+	0.966258i	$0.582924\pi$
$480$	−9.36266	−0.427345
$481$	−15.9588	−0.727661
$482$	21.8943	0.997257
$483$	−51.3941	−2.33851
$484$	10.9149	0.496130
$485$	1.36266	0.0618753
$486$	6.31867	0.286621
$487$	−27.7969	−1.25960	−0.629799	−	0.776758i	$-0.716863\pi$
$487$	−27.7969	−1.25960	−0.629799	+	0.776758i	$0.716863\pi$
$488$	−1.00000	−0.0452679
$489$	−23.3421	−1.05557
$490$	15.1372	0.683829
$491$	−38.2294	−1.72527	−0.862633	−	0.505830i	$-0.831186\pi$
$491$	−38.2294	−1.72527	−0.862633	+	0.505830i	$0.831186\pi$
$492$	13.6004	0.613151
$493$	7.64541	0.344332
$494$	3.36266	0.151293
$495$	−83.8654	−3.76947
$496$	−8.29809	−0.372595
$497$	28.2325	1.26640
$498$	−16.0604	−0.719684
$499$	38.0768	1.70455	0.852276	−	0.523092i	$-0.175222\pi$
$499$	38.0768	1.70455	0.852276	+	0.523092i	$0.175222\pi$
$500$	0.552195	0.0246949
$501$	−25.0716	−1.12012
$502$	27.3215	1.21942
$503$	−1.14554	−0.0510772	−0.0255386	−	0.999674i	$-0.508130\pi$
$503$	−1.14554	−0.0510772	−0.0255386	+	0.999674i	$0.508130\pi$
$504$	19.2499	0.857460
$505$	40.4342	1.79930
$506$	−23.9149	−1.06315
$507$	17.0562	0.757494
$508$	12.2499	0.543503
$509$	37.2077	1.64920	0.824602	−	0.565714i	$-0.191399\pi$
$509$	37.2077	1.64920	0.824602	+	0.565714i	$0.191399\pi$
$510$	13.9672	0.618477
$511$	37.5345	1.66043
$512$	1.00000	0.0441942
$513$	9.63317	0.425315
$514$	−0.907847	−0.0400434
$515$	−16.6925	−0.735560
$516$	−14.7253	−0.648246
$517$	39.2252	1.72512
$518$	20.3983	0.896251
$519$	−10.6649	−0.468138
$520$	−8.55220	−0.375039
$521$	40.1760	1.76014	0.880071	−	0.474843i	$-0.157495\pi$
$521$	40.1760	1.76014	0.880071	+	0.474843i	$0.157495\pi$
$522$	−28.7857	−1.25992
$523$	0.0768054	0.00335847	0.00167923	−	0.999999i	$-0.499465\pi$
$523$	0.0768054	0.00335847	0.00167923	+	0.999999i	$0.499465\pi$
$524$	−19.7417	−0.862421
$525$	−52.0437	−2.27137
$526$	−4.69251	−0.204603
$527$	12.3791	0.539241
$528$	13.7417	0.598032
$529$	3.09738	0.134669
$530$	−44.7805	−1.94514
$531$	−27.0192	−1.17254
$532$	−4.29809	−0.186346
$533$	12.4231	0.538102
$534$	−8.47539	−0.366766
$535$	−1.17002	−0.0505843
$536$	13.5358	0.584657
$537$	51.8420	2.23715
$538$	11.6537	0.502429
$539$	−22.2171	−0.956959
$540$	−24.4999	−1.05431
$541$	27.8227	1.19619	0.598096	−	0.801425i	$-0.295924\pi$
$541$	27.8227	1.19619	0.598096	+	0.801425i	$0.295924\pi$
$542$	−19.7089	−0.846570
$543$	3.04399	0.130630
$544$	−1.49180	−0.0639603
$545$	8.55220	0.366336
$546$	26.9753	1.15443
$547$	−20.1648	−0.862184	−0.431092	−	0.902308i	$-0.641872\pi$
$547$	−20.1648	−0.862184	−0.431092	+	0.902308i	$0.641872\pi$
$548$	−4.89144	−0.208952
$549$	−5.61676	−0.239718
$550$	−24.2171	−1.03262
$551$	6.42723	0.273809
$552$	−14.9958	−0.638265
$553$	32.7938	1.39453
$554$	−5.12497	−0.217739
$555$	−55.7251	−2.36540
$556$	4.04399	0.171503
$557$	−26.8461	−1.13751	−0.568753	−	0.822508i	$-0.692574\pi$
$557$	−26.8461	−1.13751	−0.568753	+	0.822508i	$0.692574\pi$
$558$	−46.6084	−1.97309
$559$	−13.4506	−0.568902
$560$	10.9313	0.461930
$561$	−20.4999	−0.865505
$562$	10.9836	0.463315
$563$	16.3463	0.688912	0.344456	−	0.938802i	$-0.388063\pi$
$563$	16.3463	0.688912	0.344456	+	0.938802i	$0.388063\pi$
$564$	24.5962	1.03569
$565$	15.6894	0.660058
$566$	1.32284	0.0556030
$567$	19.5275	0.820076
$568$	8.23769	0.345646
$569$	10.6178	0.445122	0.222561	−	0.974919i	$-0.428558\pi$
$569$	10.6178	0.445122	0.222561	+	0.974919i	$0.428558\pi$
$570$	11.7417	0.491807
$571$	−46.3226	−1.93854	−0.969270	−	0.246001i	$-0.920883\pi$
$571$	−46.3226	−1.93854	−0.969270	+	0.246001i	$0.920883\pi$
$572$	12.5522	0.524834
$573$	10.9958	0.459357
$574$	−15.8789	−0.662774
$575$	26.4272	1.10209
$576$	5.61676	0.234032
$577$	−8.94244	−0.372279	−0.186139	−	0.982523i	$-0.559598\pi$
$577$	−8.94244	−0.372279	−0.186139	+	0.982523i	$0.559598\pi$
$578$	−14.7745	−0.614540
$579$	14.6045	0.606943
$580$	−16.3463	−0.678741
$581$	18.7511	0.777928
$582$	−1.25410	−0.0519842
$583$	65.7251	2.72205
$584$	10.9518	0.453190
$585$	−48.0357	−1.98603
$586$	7.01641	0.289845
$587$	−13.9365	−0.575221	−0.287610	−	0.957748i	$-0.592861\pi$
$587$	−13.9365	−0.575221	−0.287610	+	0.957748i	$0.592861\pi$
$588$	−13.9313	−0.574516
$589$	10.4067	0.428799
$590$	−15.3431	−0.631667
$591$	−13.1044	−0.539043
$592$	5.95184	0.244619
$593$	33.0081	1.35548	0.677739	−	0.735302i	$-0.262960\pi$
$593$	33.0081	1.35548	0.677739	+	0.735302i	$0.262960\pi$
$594$	35.9588	1.47541
$595$	−16.3072	−0.668531
$596$	−3.35148	−0.137282
$597$	−28.1208	−1.15091
$598$	−13.6977	−0.560142
$599$	9.65659	0.394557	0.197279	−	0.980347i	$-0.436790\pi$
$599$	9.65659	0.394557	0.197279	+	0.980347i	$0.436790\pi$
$600$	−15.1854	−0.619940
$601$	−21.2294	−0.865964	−0.432982	−	0.901403i	$-0.642539\pi$
$601$	−21.2294	−0.865964	−0.432982	+	0.901403i	$0.642539\pi$
$602$	17.1924	0.700709
$603$	76.0273	3.09607
$604$	−14.2130	−0.578317
$605$	34.8133	1.41536
$606$	−37.2130	−1.51167
$607$	−29.7006	−1.20551	−0.602755	−	0.797927i	$-0.705930\pi$
$607$	−29.7006	−1.20551	−0.602755	+	0.797927i	$0.705930\pi$
$608$	−1.25410	−0.0508605
$609$	51.5592	2.08928
$610$	−3.18953	−0.129140
$611$	22.4671	0.908920
$612$	−8.37907	−0.338704
$613$	32.0880	1.29602	0.648011	−	0.761631i	$-0.275601\pi$
$613$	32.0880	1.29602	0.648011	+	0.761631i	$0.275601\pi$
$614$	−3.91486	−0.157991
$615$	43.3788	1.74920
$616$	−16.0440	−0.646431
$617$	−21.7969	−0.877510	−0.438755	−	0.898607i	$-0.644580\pi$
$617$	−21.7969	−0.877510	−0.438755	+	0.898607i	$0.644580\pi$
$618$	15.3627	0.617977
$619$	8.36372	0.336166	0.168083	−	0.985773i	$-0.446242\pi$
$619$	8.36372	0.336166	0.168083	+	0.985773i	$0.446242\pi$
$620$	−26.4671	−1.06294
$621$	−39.2405	−1.57467
$622$	−3.77348	−0.151303
$623$	9.89534	0.396448
$624$	7.87086	0.315087
$625$	−24.1044	−0.964176
$626$	8.72532	0.348734
$627$	−17.2335	−0.688241
$628$	−6.74590	−0.269191
$629$	−8.87893	−0.354026
$630$	61.3983	2.44617
$631$	−3.81463	−0.151858	−0.0759291	−	0.997113i	$-0.524192\pi$
$631$	−3.81463	−0.151858	−0.0759291	+	0.997113i	$0.524192\pi$
$632$	9.56860	0.380619
$633$	−19.1044	−0.759331
$634$	−14.1208	−0.560809
$635$	39.0716	1.55051
$636$	41.2130	1.63420
$637$	−12.7253	−0.504196
$638$	23.9917	0.949839
$639$	46.2692	1.83038
$640$	3.18953	0.126077
$641$	3.93649	0.155482	0.0777410	−	0.996974i	$-0.475229\pi$
$641$	3.93649	0.155482	0.0777410	+	0.996974i	$0.475229\pi$
$642$	1.07681	0.0424981
$643$	37.8709	1.49348	0.746741	−	0.665115i	$-0.231618\pi$
$643$	37.8709	1.49348	0.746741	+	0.665115i	$0.231618\pi$
$644$	17.5082	0.689920
$645$	−46.9669	−1.84932
$646$	1.87086	0.0736082
$647$	−33.5910	−1.32060	−0.660298	−	0.751003i	$-0.729570\pi$
$647$	−33.5910	−1.32060	−0.660298	+	0.751003i	$0.729570\pi$
$648$	5.69774	0.223828
$649$	22.5194	0.883963
$650$	−13.8709	−0.544060
$651$	83.4821	3.27192
$652$	7.95184	0.311418
$653$	24.8255	0.971499	0.485749	−	0.874098i	$-0.338547\pi$
$653$	24.8255	0.971499	0.485749	+	0.874098i	$0.338547\pi$
$654$	−7.87086	−0.307775
$655$	−62.9669	−2.46032
$656$	−4.63317	−0.180895
$657$	61.5139	2.39989
$658$	−28.7170	−1.11950
$659$	−12.9682	−0.505171	−0.252586	−	0.967575i	$-0.581281\pi$
$659$	−12.9682	−0.505171	−0.252586	+	0.967575i	$0.581281\pi$
$660$	43.8297	1.70607
$661$	1.70191	0.0661965	0.0330982	−	0.999452i	$-0.489463\pi$
$661$	1.70191	0.0661965	0.0330982	+	0.999452i	$0.489463\pi$
$662$	−27.1484	−1.05515
$663$	−11.7417	−0.456011
$664$	5.47122	0.212325
$665$	−13.7089	−0.531609
$666$	33.4301	1.29539
$667$	−26.1812	−1.01374
$668$	8.54102	0.330462
$669$	15.3298	0.592686
$670$	43.1729	1.66791
$671$	4.68133	0.180721
$672$	−10.0604	−0.388088
$673$	−28.0245	−1.08026	−0.540132	−	0.841580i	$-0.681626\pi$
$673$	−28.0245	−1.08026	−0.540132	+	0.841580i	$0.681626\pi$
$674$	−4.46705	−0.172064
$675$	−39.7365	−1.52946
$676$	−5.81047	−0.223479
$677$	15.7969	0.607124	0.303562	−	0.952812i	$-0.401824\pi$
$677$	15.7969	0.607124	0.303562	+	0.952812i	$0.401824\pi$
$678$	−14.4395	−0.554544
$679$	1.46421	0.0561913
$680$	−4.75814	−0.182466
$681$	−20.6290	−0.790505
$682$	38.8461	1.48749
$683$	−8.90785	−0.340849	−0.170425	−	0.985371i	$-0.554514\pi$
$683$	−8.90785	−0.340849	−0.170425	+	0.985371i	$0.554514\pi$
$684$	−7.04399	−0.269334
$685$	−15.6014	−0.596099
$686$	−7.72532	−0.294954
$687$	−61.0632	−2.32971
$688$	5.01641	0.191249
$689$	37.6454	1.43418
$690$	−47.8297	−1.82085
$691$	−28.2018	−1.07285	−0.536423	−	0.843949i	$-0.680225\pi$
$691$	−28.2018	−1.07285	−0.536423	+	0.843949i	$0.680225\pi$
$692$	3.63317	0.138112
$693$	−90.1153	−3.42320
$694$	31.4835	1.19510
$695$	12.8984	0.489266
$696$	15.0440	0.570241
$697$	6.91175	0.261801
$698$	−32.8789	−1.24449
$699$	−19.6454	−0.743058
$700$	17.7295	0.670112
$701$	19.2182	0.725861	0.362930	−	0.931816i	$-0.381776\pi$
$701$	19.2182	0.725861	0.362930	+	0.931816i	$0.381776\pi$
$702$	20.5962	0.777353
$703$	−7.46421	−0.281518
$704$	−4.68133	−0.176434
$705$	78.4504	2.95461
$706$	−31.1278	−1.17151
$707$	43.4475	1.63401
$708$	14.1208	0.530692
$709$	−25.1596	−0.944887	−0.472444	−	0.881361i	$-0.656628\pi$
$709$	−25.1596	−0.944887	−0.472444	+	0.881361i	$0.656628\pi$
$710$	26.2744	0.986061
$711$	53.7446	2.01558
$712$	2.88727	0.108205
$713$	−42.3913	−1.58757
$714$	15.0081	0.561663
$715$	40.0357	1.49725
$716$	−17.6608	−0.660013
$717$	−82.1676	−3.06861
$718$	2.20488	0.0822854
$719$	2.31344	0.0862768	0.0431384	−	0.999069i	$-0.486264\pi$
$719$	2.31344	0.0862768	0.0431384	+	0.999069i	$0.486264\pi$
$720$	17.9149	0.667647
$721$	−17.9365	−0.667990
$722$	−17.4272	−0.648574
$723$	−64.2692	−2.39020
$724$	−1.03698	−0.0385392
$725$	−26.5121	−0.984635
$726$	−32.0398	−1.18911
$727$	11.7417	0.435477	0.217738	−	0.976007i	$-0.430132\pi$
$727$	11.7417	0.435477	0.217738	+	0.976007i	$0.430132\pi$
$728$	−9.18953	−0.340587
$729$	−35.6412	−1.32005
$730$	34.9313	1.29286
$731$	−7.48346	−0.276786
$732$	2.93543	0.108497
$733$	−26.0133	−0.960823	−0.480412	−	0.877043i	$-0.659513\pi$
$733$	−26.0133	−0.960823	−0.480412	+	0.877043i	$0.659513\pi$
$734$	−8.72532	−0.322058
$735$	−44.4342	−1.63898
$736$	5.10856	0.188304
$737$	−63.3655	−2.33410
$738$	−26.0234	−0.957935
$739$	25.6566	0.943793	0.471896	−	0.881654i	$-0.343570\pi$
$739$	25.6566	0.943793	0.471896	+	0.881654i	$0.343570\pi$
$740$	18.9836	0.697851
$741$	−9.87086	−0.362615
$742$	−48.1177	−1.76646
$743$	−13.7183	−0.503276	−0.251638	−	0.967821i	$-0.580969\pi$
$743$	−13.7183	−0.503276	−0.251638	+	0.967821i	$0.580969\pi$
$744$	24.3585	0.893026
$745$	−10.6897	−0.391639
$746$	31.0562	1.13705
$747$	30.7306	1.12437
$748$	6.98359	0.255345
$749$	−1.25721	−0.0459375
$750$	−1.62093	−0.0591881
$751$	−12.3874	−0.452023	−0.226011	−	0.974125i	$-0.572569\pi$
$751$	−12.3874	−0.452023	−0.226011	+	0.974125i	$0.572569\pi$
$752$	−8.37907	−0.305553
$753$	−80.2004	−2.92267
$754$	13.7417	0.500444
$755$	−45.3327	−1.64983
$756$	−26.3257	−0.957456
$757$	−4.77765	−0.173647	−0.0868234	−	0.996224i	$-0.527672\pi$
$757$	−4.77765	−0.173647	−0.0868234	+	0.996224i	$0.527672\pi$
$758$	12.3913	0.450072
$759$	70.2004	2.54811
$760$	−4.00000	−0.145095
$761$	−33.9588	−1.23101	−0.615504	−	0.788134i	$-0.711047\pi$
$761$	−33.9588	−1.23101	−0.615504	+	0.788134i	$0.711047\pi$
$762$	−35.9588	−1.30265
$763$	9.18953	0.332683
$764$	−3.74590	−0.135522
$765$	−26.7253	−0.966256
$766$	−20.3145	−0.733993
$767$	12.8984	0.465736
$768$	−2.93543	−0.105923
$769$	44.5962	1.60818	0.804090	−	0.594508i	$-0.202653\pi$
$769$	44.5962	1.60818	0.804090	+	0.594508i	$0.202653\pi$
$770$	−51.1729	−1.84414
$771$	2.66492	0.0959749
$772$	−4.97526	−0.179063
$773$	−14.2416	−0.512235	−0.256117	−	0.966646i	$-0.582443\pi$
$773$	−14.2416	−0.512235	−0.256117	+	0.966646i	$0.582443\pi$
$774$	28.1760	1.01276
$775$	−42.9271	−1.54199
$776$	0.427229	0.0153366
$777$	−59.8779	−2.14811
$778$	7.09215	0.254266
$779$	5.81047	0.208182
$780$	25.1044	0.898881
$781$	−38.5634	−1.37991
$782$	−7.62093	−0.272524
$783$	39.3666	1.40685
$784$	4.74590	0.169496
$785$	−21.5163	−0.767949
$786$	57.9505	2.06703
$787$	18.6597	0.665146	0.332573	−	0.943077i	$-0.392083\pi$
$787$	18.6597	0.665146	0.332573	+	0.943077i	$0.392083\pi$
$788$	4.46421	0.159031
$789$	13.7745	0.490387
$790$	30.5194	1.08583
$791$	16.8586	0.599424
$792$	−26.2939	−0.934314
$793$	2.68133	0.0952168
$794$	30.1637	1.07047
$795$	131.450	4.66205
$796$	9.57978	0.339546
$797$	31.1072	1.10187	0.550937	−	0.834547i	$-0.314270\pi$
$797$	31.1072	1.10187	0.550937	+	0.834547i	$0.314270\pi$
$798$	12.6168	0.446629
$799$	12.4999	0.442213
$800$	5.17313	0.182898
$801$	16.2171	0.573004
$802$	−6.88727	−0.243198
$803$	−51.2692	−1.80925
$804$	−39.7334	−1.40129
$805$	55.8430	1.96821
$806$	22.2499	0.783720
$807$	−34.2088	−1.20421
$808$	12.6772	0.445981
$809$	47.8615	1.68272	0.841360	−	0.540475i	$-0.181756\pi$
$809$	47.8615	1.68272	0.841360	+	0.540475i	$0.181756\pi$
$810$	18.1731	0.638539
$811$	19.3843	0.680675	0.340337	−	0.940303i	$-0.389459\pi$
$811$	19.3843	0.680675	0.340337	+	0.940303i	$0.389459\pi$
$812$	−17.5644	−0.616391
$813$	57.8542	2.02903
$814$	−27.8625	−0.976581
$815$	25.3627	0.888415
$816$	4.37907	0.153298
$817$	−6.29108	−0.220097
$818$	−10.4342	−0.364825
$819$	−51.6154	−1.80359
$820$	−14.7777	−0.516058
$821$	31.9383	1.11465	0.557327	−	0.830293i	$-0.311827\pi$
$821$	31.9383	1.11465	0.557327	+	0.830293i	$0.311827\pi$
$822$	14.3585	0.500810
$823$	45.7128	1.59345	0.796724	−	0.604343i	$-0.206564\pi$
$823$	45.7128	1.59345	0.796724	+	0.604343i	$0.206564\pi$
$824$	−5.23353	−0.182319
$825$	71.0877	2.47496
$826$	−16.4866	−0.573641
$827$	−2.33091	−0.0810536	−0.0405268	−	0.999178i	$-0.512904\pi$
$827$	−2.33091	−0.0810536	−0.0405268	+	0.999178i	$0.512904\pi$
$828$	28.6936	0.997170
$829$	−41.1156	−1.42800	−0.714001	−	0.700144i	$-0.753119\pi$
$829$	−41.1156	−1.42800	−0.714001	+	0.700144i	$0.753119\pi$
$830$	17.4506	0.605721
$831$	15.0440	0.521870
$832$	−2.68133	−0.0929584
$833$	−7.07992	−0.245305
$834$	−11.8709	−0.411054
$835$	27.2419	0.942744
$836$	5.87086	0.203048
$837$	63.7404	2.20319
$838$	29.0409	1.00320
$839$	−27.4095	−0.946281	−0.473140	−	0.880987i	$-0.656880\pi$
$839$	−27.4095	−0.946281	−0.473140	+	0.880987i	$0.656880\pi$
$840$	−32.0880	−1.10714
$841$	−2.73472	−0.0943007
$842$	−14.9630	−0.515660
$843$	−32.2416	−1.11046
$844$	6.50820	0.224022
$845$	−18.5327	−0.637544
$846$	−47.0632	−1.61807
$847$	37.4077	1.28534
$848$	−14.0398	−0.482129
$849$	−3.88310	−0.133268
$850$	−7.71725	−0.264700
$851$	30.4053	1.04228
$852$	−24.1812	−0.828434
$853$	−46.2856	−1.58479	−0.792394	−	0.610009i	$-0.791166\pi$
$853$	−46.2856	−1.58479	−0.792394	+	0.610009i	$0.791166\pi$
$854$	−3.42723	−0.117277
$855$	−22.4671	−0.768357
$856$	−0.366830	−0.0125380
$857$	55.0867	1.88172	0.940862	−	0.338790i	$-0.110017\pi$
$857$	55.0867	1.88172	0.940862	+	0.338790i	$0.110017\pi$
$858$	−36.8461	−1.25791
$859$	0.726651	0.0247930	0.0123965	−	0.999923i	$-0.496054\pi$
$859$	0.726651	0.0247930	0.0123965	+	0.999923i	$0.496054\pi$
$860$	16.0000	0.545595
$861$	46.6115	1.58852
$862$	−14.9753	−0.510059
$863$	−30.8461	−1.05001	−0.525007	−	0.851098i	$-0.675937\pi$
$863$	−30.8461	−1.05001	−0.525007	+	0.851098i	$0.675937\pi$
$864$	−7.68133	−0.261324
$865$	11.5881	0.394008
$866$	23.3215	0.792497
$867$	43.3697	1.47291
$868$	−28.4395	−0.965298
$869$	−44.7938	−1.51953
$870$	47.9833	1.62679
$871$	−36.2939	−1.22977
$872$	2.68133	0.0908013
$873$	2.39964	0.0812156
$874$	−6.40665	−0.216708
$875$	1.89250	0.0639782
$876$	−32.1484	−1.08619
$877$	−36.0039	−1.21577	−0.607883	−	0.794027i	$-0.707981\pi$
$877$	−36.0039	−1.21577	−0.607883	+	0.794027i	$0.707981\pi$
$878$	−16.1208	−0.544051
$879$	−20.5962	−0.694692
$880$	−14.9313	−0.503333
$881$	−33.9188	−1.14275	−0.571376	−	0.820688i	$-0.693590\pi$
$881$	−33.9188	−1.14275	−0.571376	+	0.820688i	$0.693590\pi$
$882$	26.6566	0.897574
$883$	−56.4699	−1.90036	−0.950182	−	0.311697i	$-0.899103\pi$
$883$	−56.4699	−1.90036	−0.950182	+	0.311697i	$0.899103\pi$
$884$	4.00000	0.134535
$885$	45.0388	1.51396
$886$	−39.4436	−1.32513
$887$	31.2419	1.04900	0.524500	−	0.851411i	$-0.324252\pi$
$887$	31.2419	1.04900	0.524500	+	0.851411i	$0.324252\pi$
$888$	−17.4712	−0.586296
$889$	41.9833	1.40808
$890$	9.20905	0.308688
$891$	−26.6730	−0.893579
$892$	−5.22235	−0.174857
$893$	10.5082	0.351644
$894$	9.83805	0.329034
$895$	−56.3296	−1.88289
$896$	3.42723	0.114496
$897$	40.2088	1.34253
$898$	20.1250	0.671579
$899$	42.5275	1.41837
$900$	29.0562	0.968541
$901$	20.9446	0.697764
$902$	21.6894	0.722178
$903$	−50.4671	−1.67944
$904$	4.91903	0.163604
$905$	−3.30749	−0.109945
$906$	41.7212	1.38609
$907$	32.0552	1.06437	0.532187	−	0.846627i	$-0.321370\pi$
$907$	32.0552	1.06437	0.532187	+	0.846627i	$0.321370\pi$
$908$	7.02759	0.233219
$909$	71.2046	2.36171
$910$	−29.3103	−0.971628
$911$	8.00834	0.265328	0.132664	−	0.991161i	$-0.457647\pi$
$911$	8.00834	0.265328	0.132664	+	0.991161i	$0.457647\pi$
$912$	3.68133	0.121901
$913$	−25.6126	−0.847653
$914$	−14.9836	−0.495613
$915$	9.36266	0.309520
$916$	20.8021	0.687322
$917$	−67.6594	−2.23431
$918$	11.4590	0.378203
$919$	8.59619	0.283562	0.141781	−	0.989898i	$-0.454717\pi$
$919$	8.59619	0.283562	0.141781	+	0.989898i	$0.454717\pi$
$920$	16.2939	0.537195
$921$	11.4918	0.378668
$922$	−29.5798	−0.974158
$923$	−22.0880	−0.727035
$924$	47.0961	1.54935
$925$	30.7896	1.01236
$926$	−10.4119	−0.342156
$927$	−29.3955	−0.965474
$928$	−5.12497	−0.168235
$929$	−27.3327	−0.896756	−0.448378	−	0.893844i	$-0.647998\pi$
$929$	−27.3327	−0.896756	−0.448378	+	0.893844i	$0.647998\pi$
$930$	77.6922	2.54763
$931$	−5.95184	−0.195064
$932$	6.69251	0.219220
$933$	11.0768	0.362638
$934$	−22.8656	−0.748186
$935$	22.2744	0.728451
$936$	−15.0604	−0.492265
$937$	51.4985	1.68238	0.841192	−	0.540737i	$-0.181854\pi$
$937$	51.4985	1.68238	0.841192	+	0.540737i	$0.181854\pi$
$938$	46.3902	1.51470
$939$	−25.6126	−0.835835
$940$	−26.7253	−0.871684
$941$	44.4671	1.44958	0.724792	−	0.688968i	$-0.241936\pi$
$941$	44.4671	1.44958	0.724792	+	0.688968i	$0.241936\pi$
$942$	19.8021	0.645188
$943$	−23.6688	−0.770763
$944$	−4.81047	−0.156567
$945$	−83.9666	−2.73144
$946$	−23.4835	−0.763513
$947$	−30.2528	−0.983083	−0.491542	−	0.870854i	$-0.663566\pi$
$947$	−30.2528	−0.983083	−0.491542	+	0.870854i	$0.663566\pi$
$948$	−28.0880	−0.912255
$949$	−29.3655	−0.953245
$950$	−6.48763	−0.210486
$951$	41.4506	1.34413
$952$	−5.11273	−0.165704
$953$	−9.36266	−0.303286	−0.151643	−	0.988435i	$-0.548456\pi$
$953$	−9.36266	−0.303286	−0.151643	+	0.988435i	$0.548456\pi$
$954$	−78.8584	−2.55313
$955$	−11.9477	−0.386618
$956$	27.9917	0.905315
$957$	−70.4259	−2.27655
$958$	−11.2747	−0.364268
$959$	−16.7641	−0.541341
$960$	−9.36266	−0.302179
$961$	37.8584	1.22124
$962$	−15.9588	−0.514534
$963$	−2.06040	−0.0663954
$964$	21.8943	0.705167
$965$	−15.8687	−0.510833
$966$	−51.3941	−1.65358
$967$	59.5303	1.91437	0.957183	−	0.289485i	$-0.0934840\pi$
$967$	59.5303	1.91437	0.957183	+	0.289485i	$0.0934840\pi$
$968$	10.9149	0.350817
$969$	−5.49180	−0.176422
$970$	1.36266	0.0437524
$971$	45.0479	1.44566	0.722828	−	0.691028i	$-0.242842\pi$
$971$	45.0479	1.44566	0.722828	+	0.691028i	$0.242842\pi$
$972$	6.31867	0.202671
$973$	13.8597	0.444321
$974$	−27.7969	−0.890670
$975$	40.7170	1.30399
$976$	−1.00000	−0.0320092
$977$	−8.26528	−0.264430	−0.132215	−	0.991221i	$-0.542209\pi$
$977$	−8.26528	−0.264430	−0.132215	+	0.991221i	$0.542209\pi$
$978$	−23.3421	−0.746398
$979$	−13.5163	−0.431982
$980$	15.1372	0.483540
$981$	15.0604	0.480842
$982$	−38.2294	−1.21995
$983$	14.0070	0.446754	0.223377	−	0.974732i	$-0.428292\pi$
$983$	14.0070	0.446754	0.223377	+	0.974732i	$0.428292\pi$
$984$	13.6004	0.433564
$985$	14.2388	0.453684
$986$	7.64541	0.243479
$987$	84.2968	2.68320
$988$	3.36266	0.106981
$989$	25.6266	0.814879
$990$	−83.8654	−2.66542
$991$	−43.3460	−1.37693	−0.688465	−	0.725269i	$-0.741715\pi$
$991$	−43.3460	−1.37693	−0.688465	+	0.725269i	$0.741715\pi$
$992$	−8.29809	−0.263465
$993$	79.6922	2.52896
$994$	28.2325	0.895479
$995$	30.5550	0.968660
$996$	−16.0604	−0.508893
$997$	50.1278	1.58756	0.793782	−	0.608203i	$-0.208109\pi$
$997$	50.1278	1.58756	0.793782	+	0.608203i	$0.208109\pi$
$998$	38.0768	1.20530
$999$	−45.7180	−1.44645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.a.c.1.1	✓	3
3.2	odd	2		1098.2.a.p.1.1		3
4.3	odd	2		976.2.a.g.1.3		3
5.2	odd	4		3050.2.b.k.1099.6		6
5.3	odd	4		3050.2.b.k.1099.1		6
5.4	even	2		3050.2.a.t.1.3		3
7.6	odd	2		5978.2.a.q.1.3		3
8.3	odd	2		3904.2.a.t.1.1		3
8.5	even	2		3904.2.a.u.1.3		3
12.11	even	2		8784.2.a.bm.1.1		3
61.60	even	2		7442.2.a.j.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.a.c.1.1	✓	3	1.1	even	1	trivial
976.2.a.g.1.3		3	4.3	odd	2
1098.2.a.p.1.1		3	3.2	odd	2
3050.2.a.t.1.3		3	5.4	even	2
3050.2.b.k.1099.1		6	5.3	odd	4
3050.2.b.k.1099.6		6	5.2	odd	4
3904.2.a.t.1.1		3	8.3	odd	2
3904.2.a.u.1.3		3	8.5	even	2
5978.2.a.q.1.3		3	7.6	odd	2
7442.2.a.j.1.1		3	61.60	even	2
8784.2.a.bm.1.1		3	12.11	even	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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.93543 q^{3} +1.00000 q^{4} +3.18953 q^{5} -2.93543 q^{6} +3.42723 q^{7} +1.00000 q^{8} +5.61676 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.93543 q^{3} +1.00000 q^{4} +3.18953 q^{5} -2.93543 q^{6} +3.42723 q^{7} +1.00000 q^{8} +5.61676 q^{9} +3.18953 q^{10} -4.68133 q^{11} -2.93543 q^{12} -2.68133 q^{13} +3.42723 q^{14} -9.36266 q^{15} +1.00000 q^{16} -1.49180 q^{17} +5.61676 q^{18} -1.25410 q^{19} +3.18953 q^{20} -10.0604 q^{21} -4.68133 q^{22} +5.10856 q^{23} -2.93543 q^{24} +5.17313 q^{25} -2.68133 q^{26} -7.68133 q^{27} +3.42723 q^{28} -5.12497 q^{29} -9.36266 q^{30} -8.29809 q^{31} +1.00000 q^{32} +13.7417 q^{33} -1.49180 q^{34} +10.9313 q^{35} +5.61676 q^{36} +5.95184 q^{37} -1.25410 q^{38} +7.87086 q^{39} +3.18953 q^{40} -4.63317 q^{41} -10.0604 q^{42} +5.01641 q^{43} -4.68133 q^{44} +17.9149 q^{45} +5.10856 q^{46} -8.37907 q^{47} -2.93543 q^{48} +4.74590 q^{49} +5.17313 q^{50} +4.37907 q^{51} -2.68133 q^{52} -14.0398 q^{53} -7.68133 q^{54} -14.9313 q^{55} +3.42723 q^{56} +3.68133 q^{57} -5.12497 q^{58} -4.81047 q^{59} -9.36266 q^{60} -1.00000 q^{61} -8.29809 q^{62} +19.2499 q^{63} +1.00000 q^{64} -8.55220 q^{65} +13.7417 q^{66} +13.5358 q^{67} -1.49180 q^{68} -14.9958 q^{69} +10.9313 q^{70} +8.23769 q^{71} +5.61676 q^{72} +10.9518 q^{73} +5.95184 q^{74} -15.1854 q^{75} -1.25410 q^{76} -16.0440 q^{77} +7.87086 q^{78} +9.56860 q^{79} +3.18953 q^{80} +5.69774 q^{81} -4.63317 q^{82} +5.47122 q^{83} -10.0604 q^{84} -4.75814 q^{85} +5.01641 q^{86} +15.0440 q^{87} -4.68133 q^{88} +2.88727 q^{89} +17.9149 q^{90} -9.18953 q^{91} +5.10856 q^{92} +24.3585 q^{93} -8.37907 q^{94} -4.00000 q^{95} -2.93543 q^{96} +0.427229 q^{97} +4.74590 q^{98} -26.2939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + q^5 - q^6 + 4 * q^7 + 3 * q^8 + 2 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + q^{5} - q^{6} + 4 q^{7} + 3 q^{8} + 2 q^{9} + q^{10} - 7 q^{11} - q^{12} - q^{13} + 4 q^{14} - 14 q^{15} + 3 q^{16} - 6 q^{17} + 2 q^{18} - 3 q^{19} + q^{20} - 6 q^{21} - 7 q^{22} + 2 q^{23} - q^{24} + 10 q^{25} - q^{26} - 16 q^{27} + 4 q^{28} + q^{29} - 14 q^{30} - 3 q^{31} + 3 q^{32} + 10 q^{33} - 6 q^{34} - 7 q^{35} + 2 q^{36} + 7 q^{37} - 3 q^{38} + 8 q^{39} + q^{40} + 4 q^{41} - 6 q^{42} + 12 q^{43} - 7 q^{44} + 17 q^{45} + 2 q^{46} - 8 q^{47} - q^{48} + 15 q^{49} + 10 q^{50} - 4 q^{51} - q^{52} + 11 q^{53} - 16 q^{54} - 5 q^{55} + 4 q^{56} + 4 q^{57} + q^{58} - 23 q^{59} - 14 q^{60} - 3 q^{61} - 3 q^{62} + 25 q^{63} + 3 q^{64} - 3 q^{65} + 10 q^{66} + 21 q^{67} - 6 q^{68} - 13 q^{69} - 7 q^{70} + 27 q^{71} + 2 q^{72} + 22 q^{73} + 7 q^{74} - 5 q^{75} - 3 q^{76} - 27 q^{77} + 8 q^{78} + 3 q^{79} + q^{80} + 7 q^{81} + 4 q^{82} - 11 q^{83} - 6 q^{84} + 20 q^{85} + 12 q^{86} + 24 q^{87} - 7 q^{88} - 10 q^{89} + 17 q^{90} - 19 q^{91} + 2 q^{92} + 27 q^{93} - 8 q^{94} - 12 q^{95} - q^{96} - 5 q^{97} + 15 q^{98} - 25 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + q^5 - q^6 + 4 * q^7 + 3 * q^8 + 2 * q^9 + q^10 - 7 * q^11 - q^12 - q^13 + 4 * q^14 - 14 * q^15 + 3 * q^16 - 6 * q^17 + 2 * q^18 - 3 * q^19 + q^20 - 6 * q^21 - 7 * q^22 + 2 * q^23 - q^24 + 10 * q^25 - q^26 - 16 * q^27 + 4 * q^28 + q^29 - 14 * q^30 - 3 * q^31 + 3 * q^32 + 10 * q^33 - 6 * q^34 - 7 * q^35 + 2 * q^36 + 7 * q^37 - 3 * q^38 + 8 * q^39 + q^40 + 4 * q^41 - 6 * q^42 + 12 * q^43 - 7 * q^44 + 17 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 15 * q^49 + 10 * q^50 - 4 * q^51 - q^52 + 11 * q^53 - 16 * q^54 - 5 * q^55 + 4 * q^56 + 4 * q^57 + q^58 - 23 * q^59 - 14 * q^60 - 3 * q^61 - 3 * q^62 + 25 * q^63 + 3 * q^64 - 3 * q^65 + 10 * q^66 + 21 * q^67 - 6 * q^68 - 13 * q^69 - 7 * q^70 + 27 * q^71 + 2 * q^72 + 22 * q^73 + 7 * q^74 - 5 * q^75 - 3 * q^76 - 27 * q^77 + 8 * q^78 + 3 * q^79 + q^80 + 7 * q^81 + 4 * q^82 - 11 * q^83 - 6 * q^84 + 20 * q^85 + 12 * q^86 + 24 * q^87 - 7 * q^88 - 10 * q^89 + 17 * q^90 - 19 * q^91 + 2 * q^92 + 27 * q^93 - 8 * q^94 - 12 * q^95 - q^96 - 5 * q^97 + 15 * q^98 - 25 * q^99

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