LMFDB - Embedded newform 93.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(1,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("93.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.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:	$0.742608738798$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	93.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} +1.68133 q^{5} +0.254102 q^{6} +3.68133 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} +1.68133 q^{5} +0.254102 q^{6} +3.68133 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.427229 q^{10} -5.87086 q^{11} -1.93543 q^{12} -3.87086 q^{13} +0.935432 q^{14} +1.68133 q^{15} +3.61676 q^{16} -5.36266 q^{17} +0.254102 q^{18} +4.69774 q^{19} -3.25410 q^{20} +3.68133 q^{21} -1.49180 q^{22} -2.50820 q^{23} -1.00000 q^{24} -2.17313 q^{25} -0.983593 q^{26} +1.00000 q^{27} -7.12497 q^{28} +7.23353 q^{29} +0.427229 q^{30} -1.00000 q^{31} +2.91903 q^{32} -5.87086 q^{33} -1.36266 q^{34} +6.18953 q^{35} -1.93543 q^{36} +0.508203 q^{37} +1.19370 q^{38} -3.87086 q^{39} -1.68133 q^{40} -6.69774 q^{41} +0.935432 q^{42} +8.85446 q^{43} +11.3627 q^{44} +1.68133 q^{45} -0.637339 q^{46} +5.01641 q^{47} +3.61676 q^{48} +6.55220 q^{49} -0.552195 q^{50} -5.36266 q^{51} +7.49180 q^{52} +2.37907 q^{53} +0.254102 q^{54} -9.87086 q^{55} -3.68133 q^{56} +4.69774 q^{57} +1.83805 q^{58} +5.81047 q^{59} -3.25410 q^{60} -4.34625 q^{61} -0.254102 q^{62} +3.68133 q^{63} -6.49180 q^{64} -6.50820 q^{65} -1.49180 q^{66} +4.00000 q^{67} +10.3791 q^{68} -2.50820 q^{69} +1.57277 q^{70} -4.15672 q^{71} -1.00000 q^{72} -5.52461 q^{73} +0.129135 q^{74} -2.17313 q^{75} -9.09215 q^{76} -21.6126 q^{77} -0.983593 q^{78} +7.36266 q^{79} +6.08097 q^{80} +1.00000 q^{81} -1.70191 q^{82} +11.3627 q^{83} -7.12497 q^{84} -9.01641 q^{85} +2.24993 q^{86} +7.23353 q^{87} +5.87086 q^{88} -6.00000 q^{89} +0.427229 q^{90} -14.2499 q^{91} +4.85446 q^{92} -1.00000 q^{93} +1.27468 q^{94} +7.89845 q^{95} +2.91903 q^{96} +3.17313 q^{97} +1.66492 q^{98} -5.87086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 2 * q^4 - 2 * q^5 + 4 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} - 4 q^{16} - 2 q^{17} + 4 q^{19} - 9 q^{20} + 4 q^{21} - 6 q^{22} - 6 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} + 3 q^{27} - 5 q^{28} - 8 q^{29} - 5 q^{30} - 3 q^{31} + 4 q^{32} - 2 q^{33} + 10 q^{34} + 10 q^{35} + 2 q^{36} + 27 q^{38} + 4 q^{39} + 2 q^{40} - 10 q^{41} - 5 q^{42} + 14 q^{43} + 20 q^{44} - 2 q^{45} - 16 q^{46} + 12 q^{47} - 4 q^{48} - 3 q^{49} + 21 q^{50} - 2 q^{51} + 24 q^{52} - 10 q^{53} - 14 q^{55} - 4 q^{56} + 4 q^{57} - 4 q^{58} + 26 q^{59} - 9 q^{60} - 2 q^{61} + 4 q^{63} - 21 q^{64} - 18 q^{65} - 6 q^{66} + 12 q^{67} + 14 q^{68} - 6 q^{69} + 11 q^{70} - 10 q^{71} - 3 q^{72} - 12 q^{73} + 16 q^{74} - q^{75} - 17 q^{76} - 18 q^{77} - 6 q^{78} + 8 q^{79} + 23 q^{80} + 3 q^{81} - 27 q^{82} + 20 q^{83} - 5 q^{84} - 24 q^{85} - 26 q^{86} - 8 q^{87} + 2 q^{88} - 18 q^{89} - 5 q^{90} - 10 q^{91} + 2 q^{92} - 3 q^{93} + 32 q^{94} - 10 q^{95} + 4 q^{96} + 4 q^{97} + q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 - 2 * q^5 + 4 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 - 4 * q^16 - 2 * q^17 + 4 * q^19 - 9 * q^20 + 4 * q^21 - 6 * q^22 - 6 * q^23 - 3 * q^24 - q^25 - 6 * q^26 + 3 * q^27 - 5 * q^28 - 8 * q^29 - 5 * q^30 - 3 * q^31 + 4 * q^32 - 2 * q^33 + 10 * q^34 + 10 * q^35 + 2 * q^36 + 27 * q^38 + 4 * q^39 + 2 * q^40 - 10 * q^41 - 5 * q^42 + 14 * q^43 + 20 * q^44 - 2 * q^45 - 16 * q^46 + 12 * q^47 - 4 * q^48 - 3 * q^49 + 21 * q^50 - 2 * q^51 + 24 * q^52 - 10 * q^53 - 14 * q^55 - 4 * q^56 + 4 * q^57 - 4 * q^58 + 26 * q^59 - 9 * q^60 - 2 * q^61 + 4 * q^63 - 21 * q^64 - 18 * q^65 - 6 * q^66 + 12 * q^67 + 14 * q^68 - 6 * q^69 + 11 * q^70 - 10 * q^71 - 3 * q^72 - 12 * q^73 + 16 * q^74 - q^75 - 17 * q^76 - 18 * q^77 - 6 * q^78 + 8 * q^79 + 23 * q^80 + 3 * q^81 - 27 * q^82 + 20 * q^83 - 5 * q^84 - 24 * q^85 - 26 * q^86 - 8 * q^87 + 2 * q^88 - 18 * q^89 - 5 * q^90 - 10 * q^91 + 2 * q^92 - 3 * q^93 + 32 * q^94 - 10 * q^95 + 4 * q^96 + 4 * q^97 + q^98 - 2 * 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 $

$2$	0.254102	0.179677	0.0898385	−	0.995956i	$-0.471365\pi$
$2$	0.254102	0.179677	0.0898385	+	0.995956i	$0.471365\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.93543	−0.967716
$5$	1.68133	0.751914	0.375957	−	0.926637i	$-0.377314\pi$
$5$	1.68133	0.751914	0.375957	+	0.926637i	$0.377314\pi$
$6$	0.254102	0.103737
$7$	3.68133	1.39141	0.695706	−	0.718327i	$-0.255092\pi$
$7$	3.68133	1.39141	0.695706	+	0.718327i	$0.255092\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.427229	0.135102
$11$	−5.87086	−1.77013	−0.885066	−	0.465465i	$-0.845887\pi$
$11$	−5.87086	−1.77013	−0.885066	+	0.465465i	$0.845887\pi$
$12$	−1.93543	−0.558711
$13$	−3.87086	−1.07358	−0.536792	−	0.843714i	$-0.680364\pi$
$13$	−3.87086	−1.07358	−0.536792	+	0.843714i	$0.680364\pi$
$14$	0.935432	0.250005
$15$	1.68133	0.434118
$16$	3.61676	0.904191
$17$	−5.36266	−1.30064	−0.650318	−	0.759662i	$-0.725364\pi$
$17$	−5.36266	−1.30064	−0.650318	+	0.759662i	$0.725364\pi$
$18$	0.254102	0.0598923
$19$	4.69774	1.07773	0.538867	−	0.842391i	$-0.318852\pi$
$19$	4.69774	1.07773	0.538867	+	0.842391i	$0.318852\pi$
$20$	−3.25410	−0.727639
$21$	3.68133	0.803332
$22$	−1.49180	−0.318052
$23$	−2.50820	−0.522997	−0.261498	−	0.965204i	$-0.584217\pi$
$23$	−2.50820	−0.522997	−0.261498	+	0.965204i	$0.584217\pi$
$24$	−1.00000	−0.204124
$25$	−2.17313	−0.434625
$26$	−0.983593	−0.192899
$27$	1.00000	0.192450
$28$	−7.12497	−1.34649
$29$	7.23353	1.34323	0.671616	−	0.740899i	$-0.265600\pi$
$29$	7.23353	1.34323	0.671616	+	0.740899i	$0.265600\pi$
$30$	0.427229	0.0780010
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.91903	0.516016
$33$	−5.87086	−1.02199
$34$	−1.36266	−0.233694
$35$	6.18953	1.04622
$36$	−1.93543	−0.322572
$37$	0.508203	0.0835481	0.0417741	−	0.999127i	$-0.486699\pi$
$37$	0.508203	0.0835481	0.0417741	+	0.999127i	$0.486699\pi$
$38$	1.19370	0.193644
$39$	−3.87086	−0.619834
$40$	−1.68133	−0.265842
$41$	−6.69774	−1.04601	−0.523005	−	0.852329i	$-0.675189\pi$
$41$	−6.69774	−1.04601	−0.523005	+	0.852329i	$0.675189\pi$
$42$	0.935432	0.144340
$43$	8.85446	1.35029	0.675146	−	0.737684i	$-0.264081\pi$
$43$	8.85446	1.35029	0.675146	+	0.737684i	$0.264081\pi$
$44$	11.3627	1.71299
$45$	1.68133	0.250638
$46$	−0.637339	−0.0939705
$47$	5.01641	0.731718	0.365859	−	0.930670i	$-0.380775\pi$
$47$	5.01641	0.731718	0.365859	+	0.930670i	$0.380775\pi$
$48$	3.61676	0.522035
$49$	6.55220	0.936028
$50$	−0.552195	−0.0780922
$51$	−5.36266	−0.750923
$52$	7.49180	1.03893
$53$	2.37907	0.326790	0.163395	−	0.986561i	$-0.447755\pi$
$53$	2.37907	0.326790	0.163395	+	0.986561i	$0.447755\pi$
$54$	0.254102	0.0345789
$55$	−9.87086	−1.33099
$56$	−3.68133	−0.491938
$57$	4.69774	0.622231
$58$	1.83805	0.241348
$59$	5.81047	0.756458	0.378229	−	0.925712i	$-0.376533\pi$
$59$	5.81047	0.756458	0.378229	+	0.925712i	$0.376533\pi$
$60$	−3.25410	−0.420103
$61$	−4.34625	−0.556481	−0.278240	−	0.960511i	$-0.589751\pi$
$61$	−4.34625	−0.556481	−0.278240	+	0.960511i	$0.589751\pi$
$62$	−0.254102	−0.0322709
$63$	3.68133	0.463804
$64$	−6.49180	−0.811475
$65$	−6.50820	−0.807243
$66$	−1.49180	−0.183627
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	10.3791	1.25865
$69$	−2.50820	−0.301952
$70$	1.57277	0.187982
$71$	−4.15672	−0.493312	−0.246656	−	0.969103i	$-0.579332\pi$
$71$	−4.15672	−0.493312	−0.246656	+	0.969103i	$0.579332\pi$
$72$	−1.00000	−0.117851
$73$	−5.52461	−0.646607	−0.323303	−	0.946295i	$-0.604793\pi$
$73$	−5.52461	−0.646607	−0.323303	+	0.946295i	$0.604793\pi$
$74$	0.129135	0.0150117
$75$	−2.17313	−0.250931
$76$	−9.09215	−1.04294
$77$	−21.6126	−2.46298
$78$	−0.983593	−0.111370
$79$	7.36266	0.828364	0.414182	−	0.910194i	$-0.364068\pi$
$79$	7.36266	0.828364	0.414182	+	0.910194i	$0.364068\pi$
$80$	6.08097	0.679874
$81$	1.00000	0.111111
$82$	−1.70191	−0.187944
$83$	11.3627	1.24721	0.623607	−	0.781738i	$-0.285667\pi$
$83$	11.3627	1.24721	0.623607	+	0.781738i	$0.285667\pi$
$84$	−7.12497	−0.777398
$85$	−9.01641	−0.977967
$86$	2.24993	0.242616
$87$	7.23353	0.775515
$88$	5.87086	0.625836
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0.427229	0.0450339
$91$	−14.2499	−1.49380
$92$	4.85446	0.506112
$93$	−1.00000	−0.103695
$94$	1.27468	0.131473
$95$	7.89845	0.810364
$96$	2.91903	0.297922
$97$	3.17313	0.322182	0.161091	−	0.986940i	$-0.448499\pi$
$97$	3.17313	0.322182	0.161091	+	0.986940i	$0.448499\pi$
$98$	1.66492	0.168183
$99$	−5.87086	−0.590044
$100$	4.20594	0.420594
$101$	5.42306	0.539615	0.269807	−	0.962914i	$-0.413040\pi$
$101$	5.42306	0.539615	0.269807	+	0.962914i	$0.413040\pi$
$102$	−1.36266	−0.134924
$103$	−8.69774	−0.857014	−0.428507	−	0.903539i	$-0.640960\pi$
$103$	−8.69774	−0.857014	−0.428507	+	0.903539i	$0.640960\pi$
$104$	3.87086	0.379570
$105$	6.18953	0.604037
$106$	0.604525	0.0587167
$107$	−1.55220	−0.150056	−0.0750282	−	0.997181i	$-0.523905\pi$
$107$	−1.55220	−0.150056	−0.0750282	+	0.997181i	$0.523905\pi$
$108$	−1.93543	−0.186237
$109$	−11.9313	−1.14281	−0.571404	−	0.820669i	$-0.693601\pi$
$109$	−11.9313	−1.14281	−0.571404	+	0.820669i	$0.693601\pi$
$110$	−2.50820	−0.239148
$111$	0.508203	0.0482365
$112$	13.3145	1.25810
$113$	−12.0276	−1.13146	−0.565730	−	0.824591i	$-0.691406\pi$
$113$	−12.0276	−1.13146	−0.565730	+	0.824591i	$0.691406\pi$
$114$	1.19370	0.111801
$115$	−4.21712	−0.393248
$116$	−14.0000	−1.29987
$117$	−3.87086	−0.357862
$118$	1.47645	0.135918
$119$	−19.7417	−1.80972
$120$	−1.68133	−0.153484
$121$	23.4671	2.13337
$122$	−1.10439	−0.0999868
$123$	−6.69774	−0.603915
$124$	1.93543	0.173807
$125$	−12.0604	−1.07871
$126$	0.935432	0.0833349
$127$	6.88727	0.611147	0.305573	−	0.952169i	$-0.401152\pi$
$127$	6.88727	0.611147	0.305573	+	0.952169i	$0.401152\pi$
$128$	−7.48763	−0.661819
$129$	8.85446	0.779592
$130$	−1.65375	−0.145043
$131$	18.7253	1.63604	0.818020	−	0.575190i	$-0.195072\pi$
$131$	18.7253	1.63604	0.818020	+	0.575190i	$0.195072\pi$
$132$	11.3627	0.988993
$133$	17.2939	1.49957
$134$	1.01641	0.0878042
$135$	1.68133	0.144706
$136$	5.36266	0.459844
$137$	20.6290	1.76245	0.881227	−	0.472693i	$-0.156718\pi$
$137$	20.6290	1.76245	0.881227	+	0.472693i	$0.156718\pi$
$138$	−0.637339	−0.0542539
$139$	7.90368	0.670381	0.335191	−	0.942150i	$-0.391199\pi$
$139$	7.90368	0.670381	0.335191	+	0.942150i	$0.391199\pi$
$140$	−11.9794	−1.01245
$141$	5.01641	0.422458
$142$	−1.05623	−0.0886368
$143$	22.7253	1.90039
$144$	3.61676	0.301397
$145$	12.1619	1.00999
$146$	−1.40381	−0.116180
$147$	6.55220	0.540416
$148$	−0.983593	−0.0808509
$149$	−13.7417	−1.12577	−0.562883	−	0.826536i	$-0.690308\pi$
$149$	−13.7417	−1.12577	−0.562883	+	0.826536i	$0.690308\pi$
$150$	−0.552195	−0.0450866
$151$	−18.6290	−1.51601	−0.758003	−	0.652251i	$-0.773825\pi$
$151$	−18.6290	−1.51601	−0.758003	+	0.652251i	$0.773825\pi$
$152$	−4.69774	−0.381037
$153$	−5.36266	−0.433545
$154$	−5.49180	−0.442542
$155$	−1.68133	−0.135048
$156$	7.49180	0.599824
$157$	−3.17313	−0.253243	−0.126622	−	0.991951i	$-0.540413\pi$
$157$	−3.17313	−0.253243	−0.126622	+	0.991951i	$0.540413\pi$
$158$	1.87086	0.148838
$159$	2.37907	0.188672
$160$	4.90785	0.387999
$161$	−9.23353	−0.727704
$162$	0.254102	0.0199641
$163$	−4.06040	−0.318035	−0.159017	−	0.987276i	$-0.550833\pi$
$163$	−4.06040	−0.318035	−0.159017	+	0.987276i	$0.550833\pi$
$164$	12.9630	1.01224
$165$	−9.87086	−0.768446
$166$	2.88727	0.224096
$167$	2.50820	0.194091	0.0970453	−	0.995280i	$-0.469061\pi$
$167$	2.50820	0.194091	0.0970453	+	0.995280i	$0.469061\pi$
$168$	−3.68133	−0.284021
$169$	1.98359	0.152584
$170$	−2.29108	−0.175718
$171$	4.69774	0.359245
$172$	−17.1372	−1.30670
$173$	−0.725323	−0.0551453	−0.0275726	−	0.999620i	$-0.508778\pi$
$173$	−0.725323	−0.0551453	−0.0275726	+	0.999620i	$0.508778\pi$
$174$	1.83805	0.139342
$175$	−8.00000	−0.604743
$176$	−21.2335	−1.60054
$177$	5.81047	0.436741
$178$	−1.52461	−0.114274
$179$	−1.01641	−0.0759698	−0.0379849	−	0.999278i	$-0.512094\pi$
$179$	−1.01641	−0.0759698	−0.0379849	+	0.999278i	$0.512094\pi$
$180$	−3.25410	−0.242546
$181$	3.32985	0.247506	0.123753	−	0.992313i	$-0.460507\pi$
$181$	3.32985	0.247506	0.123753	+	0.992313i	$0.460507\pi$
$182$	−3.62093	−0.268401
$183$	−4.34625	−0.321284
$184$	2.50820	0.184907
$185$	0.854458	0.0628210
$186$	−0.254102	−0.0186316
$187$	31.4835	2.30230
$188$	−9.70892	−0.708095
$189$	3.68133	0.267777
$190$	2.00701	0.145604
$191$	−17.2939	−1.25134	−0.625672	−	0.780086i	$-0.715175\pi$
$191$	−17.2939	−1.25134	−0.625672	+	0.780086i	$0.715175\pi$
$192$	−6.49180	−0.468505
$193$	−11.5522	−0.831545	−0.415773	−	0.909469i	$-0.636489\pi$
$193$	−11.5522	−0.831545	−0.415773	+	0.909469i	$0.636489\pi$
$194$	0.806297	0.0578888
$195$	−6.50820	−0.466062
$196$	−12.6813	−0.905809
$197$	2.85446	0.203372	0.101686	−	0.994817i	$-0.467576\pi$
$197$	2.85446	0.203372	0.101686	+	0.994817i	$0.467576\pi$
$198$	−1.49180	−0.106017
$199$	8.59619	0.609368	0.304684	−	0.952454i	$-0.401449\pi$
$199$	8.59619	0.609368	0.304684	+	0.952454i	$0.401449\pi$
$200$	2.17313	0.153663
$201$	4.00000	0.282138
$202$	1.37801	0.0969564
$203$	26.6290	1.86899
$204$	10.3791	0.726680
$205$	−11.2611	−0.786510
$206$	−2.21011	−0.153986
$207$	−2.50820	−0.174332
$208$	−14.0000	−0.970725
$209$	−27.5798	−1.90773
$210$	1.57277	0.108532
$211$	−17.7141	−1.21949	−0.609746	−	0.792597i	$-0.708729\pi$
$211$	−17.7141	−1.21949	−0.609746	+	0.792597i	$0.708729\pi$
$212$	−4.60453	−0.316240
$213$	−4.15672	−0.284814
$214$	−0.394415	−0.0269617
$215$	14.8873	1.01530
$216$	−1.00000	−0.0680414
$217$	−3.68133	−0.249905
$218$	−3.03175	−0.205336
$219$	−5.52461	−0.373319
$220$	19.1044	1.28802
$221$	20.7581	1.39634
$222$	0.129135	0.00866700
$223$	−5.49180	−0.367758	−0.183879	−	0.982949i	$-0.558865\pi$
$223$	−5.49180	−0.367758	−0.183879	+	0.982949i	$0.558865\pi$
$224$	10.7459	0.717991
$225$	−2.17313	−0.144875
$226$	−3.05623	−0.203297
$227$	28.7581	1.90874	0.954372	−	0.298619i	$-0.0965261\pi$
$227$	28.7581	1.90874	0.954372	+	0.298619i	$0.0965261\pi$
$228$	−9.09215	−0.602143
$229$	−17.9588	−1.18675	−0.593377	−	0.804925i	$-0.702206\pi$
$229$	−17.9588	−1.18675	−0.593377	+	0.804925i	$0.702206\pi$
$230$	−1.07158	−0.0706577
$231$	−21.6126	−1.42200
$232$	−7.23353	−0.474904
$233$	20.4067	1.33688	0.668442	−	0.743764i	$-0.266961\pi$
$233$	20.4067	1.33688	0.668442	+	0.743764i	$0.266961\pi$
$234$	−0.983593	−0.0642995
$235$	8.43424	0.550189
$236$	−11.2458	−0.732037
$237$	7.36266	0.478256
$238$	−5.01641	−0.325165
$239$	−21.1372	−1.36725	−0.683626	−	0.729832i	$-0.739598\pi$
$239$	−21.1372	−1.36725	−0.683626	+	0.729832i	$0.739598\pi$
$240$	6.08097	0.392525
$241$	17.2007	1.10800	0.553998	−	0.832518i	$-0.313102\pi$
$241$	17.2007	1.10800	0.553998	+	0.832518i	$0.313102\pi$
$242$	5.96302	0.383317
$243$	1.00000	0.0641500
$244$	8.41188	0.538516
$245$	11.0164	0.703812
$246$	−1.70191	−0.108510
$247$	−18.1843	−1.15704
$248$	1.00000	0.0635001
$249$	11.3627	0.720079
$250$	−3.06457	−0.193820
$251$	−10.8873	−0.687198	−0.343599	−	0.939116i	$-0.611646\pi$
$251$	−10.8873	−0.687198	−0.343599	+	0.939116i	$0.611646\pi$
$252$	−7.12497	−0.448831
$253$	14.7253	0.925773
$254$	1.75007	0.109809
$255$	−9.01641	−0.564629
$256$	11.0810	0.692561
$257$	8.66492	0.540503	0.270252	−	0.962790i	$-0.412893\pi$
$257$	8.66492	0.540503	0.270252	+	0.962790i	$0.412893\pi$
$258$	2.24993	0.140075
$259$	1.87086	0.116250
$260$	12.5962	0.781182
$261$	7.23353	0.447744
$262$	4.75814	0.293959
$263$	−2.98359	−0.183976	−0.0919881	−	0.995760i	$-0.529322\pi$
$263$	−2.98359	−0.183976	−0.0919881	+	0.995760i	$0.529322\pi$
$264$	5.87086	0.361327
$265$	4.00000	0.245718
$266$	4.39442	0.269439
$267$	−6.00000	−0.367194
$268$	−7.74173	−0.472901
$269$	10.8545	0.661808	0.330904	−	0.943664i	$-0.392646\pi$
$269$	10.8545	0.661808	0.330904	+	0.943664i	$0.392646\pi$
$270$	0.427229	0.0260003
$271$	2.67015	0.162200	0.0811001	−	0.996706i	$-0.474157\pi$
$271$	2.67015	0.162200	0.0811001	+	0.996706i	$0.474157\pi$
$272$	−19.3955	−1.17602
$273$	−14.2499	−0.862445
$274$	5.24186	0.316673
$275$	12.7581	0.769345
$276$	4.85446	0.292204
$277$	−6.25827	−0.376023	−0.188012	−	0.982167i	$-0.560204\pi$
$277$	−6.25827	−0.376023	−0.188012	+	0.982167i	$0.560204\pi$
$278$	2.00834	0.120452
$279$	−1.00000	−0.0598684
$280$	−6.18953	−0.369895
$281$	−3.07681	−0.183547	−0.0917734	−	0.995780i	$-0.529254\pi$
$281$	−3.07681	−0.183547	−0.0917734	+	0.995780i	$0.529254\pi$
$282$	1.27468	0.0759059
$283$	−26.2088	−1.55795	−0.778975	−	0.627055i	$-0.784260\pi$
$283$	−26.2088	−1.55795	−0.778975	+	0.627055i	$0.784260\pi$
$284$	8.04505	0.477386
$285$	7.89845	0.467864
$286$	5.77454	0.341456
$287$	−24.6566	−1.45543
$288$	2.91903	0.172005
$289$	11.7581	0.691655
$290$	3.09037	0.181473
$291$	3.17313	0.186012
$292$	10.6925	0.625732
$293$	31.7089	1.85245	0.926227	−	0.376965i	$-0.123032\pi$
$293$	31.7089	1.85245	0.926227	+	0.376965i	$0.123032\pi$
$294$	1.66492	0.0971003
$295$	9.76931	0.568791
$296$	−0.508203	−0.0295387
$297$	−5.87086	−0.340662
$298$	−3.49180	−0.202274
$299$	9.70892	0.561481
$300$	4.20594	0.242830
$301$	32.5962	1.87881
$302$	−4.73366	−0.272392
$303$	5.42306	0.311547
$304$	16.9906	0.974478
$305$	−7.30749	−0.418426
$306$	−1.36266	−0.0778982
$307$	−17.5110	−0.999408	−0.499704	−	0.866196i	$-0.666558\pi$
$307$	−17.5110	−0.999408	−0.499704	+	0.866196i	$0.666558\pi$
$308$	41.8297	2.38347
$309$	−8.69774	−0.494797
$310$	−0.427229	−0.0242650
$311$	−33.9313	−1.92407	−0.962033	−	0.272934i	$-0.912006\pi$
$311$	−33.9313	−1.92407	−0.962033	+	0.272934i	$0.912006\pi$
$312$	3.87086	0.219145
$313$	−26.8133	−1.51558	−0.757789	−	0.652500i	$-0.773720\pi$
$313$	−26.8133	−1.51558	−0.757789	+	0.652500i	$0.773720\pi$
$314$	−0.806297	−0.0455020
$315$	6.18953	0.348741
$316$	−14.2499	−0.801621
$317$	4.66492	0.262008	0.131004	−	0.991382i	$-0.458180\pi$
$317$	4.66492	0.262008	0.131004	+	0.991382i	$0.458180\pi$
$318$	0.604525	0.0339001
$319$	−42.4671	−2.37770
$320$	−10.9149	−0.610159
$321$	−1.55220	−0.0866351
$322$	−2.34625	−0.130752
$323$	−25.1924	−1.40174
$324$	−1.93543	−0.107524
$325$	8.41188	0.466607
$326$	−1.03175	−0.0571436
$327$	−11.9313	−0.659800
$328$	6.69774	0.369821
$329$	18.4671	1.01812
$330$	−2.50820	−0.138072
$331$	17.1372	0.941946	0.470973	−	0.882148i	$-0.343903\pi$
$331$	17.1372	0.941946	0.470973	+	0.882148i	$0.343903\pi$
$332$	−21.9917	−1.20695
$333$	0.508203	0.0278494
$334$	0.637339	0.0348736
$335$	6.72532	0.367444
$336$	13.3145	0.726366
$337$	0.725323	0.0395108	0.0197554	−	0.999805i	$-0.493711\pi$
$337$	0.725323	0.0395108	0.0197554	+	0.999805i	$0.493711\pi$
$338$	0.504034	0.0274159
$339$	−12.0276	−0.653249
$340$	17.4506	0.946394
$341$	5.87086	0.317925
$342$	1.19370	0.0645481
$343$	−1.64852	−0.0890116
$344$	−8.85446	−0.477400
$345$	−4.21712	−0.227042
$346$	−0.184306	−0.00990834
$347$	19.9588	1.07145	0.535724	−	0.844393i	$-0.320039\pi$
$347$	19.9588	1.07145	0.535724	+	0.844393i	$0.320039\pi$
$348$	−14.0000	−0.750479
$349$	20.2088	1.08175	0.540876	−	0.841103i	$-0.318093\pi$
$349$	20.2088	1.08175	0.540876	+	0.841103i	$0.318093\pi$
$350$	−2.03281	−0.108658
$351$	−3.87086	−0.206611
$352$	−17.1372	−0.913416
$353$	−2.09632	−0.111576	−0.0557880	−	0.998443i	$-0.517767\pi$
$353$	−2.09632	−0.111576	−0.0557880	+	0.998443i	$0.517767\pi$
$354$	1.47645	0.0784724
$355$	−6.98882	−0.370928
$356$	11.6126	0.615466
$357$	−19.7417	−1.04484
$358$	−0.258271	−0.0136500
$359$	−6.70608	−0.353933	−0.176967	−	0.984217i	$-0.556628\pi$
$359$	−6.70608	−0.353933	−0.176967	+	0.984217i	$0.556628\pi$
$360$	−1.68133	−0.0886139
$361$	3.06874	0.161512
$362$	0.846120	0.0444711
$363$	23.4671	1.23170
$364$	27.5798	1.44557
$365$	−9.28870	−0.486193
$366$	−1.10439	−0.0577274
$367$	−21.1372	−1.10335	−0.551677	−	0.834058i	$-0.686012\pi$
$367$	−21.1372	−1.10335	−0.551677	+	0.834058i	$0.686012\pi$
$368$	−9.07158	−0.472889
$369$	−6.69774	−0.348670
$370$	0.217119	0.0112875
$371$	8.75814	0.454700
$372$	1.93543	0.100347
$373$	9.84328	0.509666	0.254833	−	0.966985i	$-0.417980\pi$
$373$	9.84328	0.509666	0.254833	+	0.966985i	$0.417980\pi$
$374$	8.00000	0.413670
$375$	−12.0604	−0.622796
$376$	−5.01641	−0.258701
$377$	−28.0000	−1.44207
$378$	0.935432	0.0481134
$379$	−22.4671	−1.15405	−0.577027	−	0.816725i	$-0.695787\pi$
$379$	−22.4671	−1.15405	−0.577027	+	0.816725i	$0.695787\pi$
$380$	−15.2869	−0.784202
$381$	6.88727	0.352846
$382$	−4.39442	−0.224838
$383$	2.34625	0.119888	0.0599440	−	0.998202i	$-0.480908\pi$
$383$	2.34625	0.119888	0.0599440	+	0.998202i	$0.480908\pi$
$384$	−7.48763	−0.382101
$385$	−36.3379	−1.85195
$386$	−2.93543	−0.149410
$387$	8.85446	0.450097
$388$	−6.14137	−0.311781
$389$	−34.0796	−1.72791	−0.863953	−	0.503572i	$-0.832019\pi$
$389$	−34.0796	−1.72791	−0.863953	+	0.503572i	$0.832019\pi$
$390$	−1.65375	−0.0837407
$391$	13.4506	0.680228
$392$	−6.55220	−0.330936
$393$	18.7253	0.944568
$394$	0.725323	0.0365412
$395$	12.3791	0.622859
$396$	11.3627	0.570995
$397$	11.4314	0.573725	0.286863	−	0.957972i	$-0.407388\pi$
$397$	11.4314	0.573725	0.286863	+	0.957972i	$0.407388\pi$
$398$	2.18431	0.109489
$399$	17.2939	0.865779
$400$	−7.85969	−0.392984
$401$	−27.9260	−1.39456	−0.697280	−	0.716799i	$-0.745606\pi$
$401$	−27.9260	−1.39456	−0.697280	+	0.716799i	$0.745606\pi$
$402$	1.01641	0.0506938
$403$	3.87086	0.192822
$404$	−10.4960	−0.522194
$405$	1.68133	0.0835460
$406$	6.76647	0.335814
$407$	−2.98359	−0.147891
$408$	5.36266	0.265491
$409$	8.12914	0.401960	0.200980	−	0.979595i	$-0.435587\pi$
$409$	8.12914	0.401960	0.200980	+	0.979595i	$0.435587\pi$
$410$	−2.86147	−0.141318
$411$	20.6290	1.01755
$412$	16.8339	0.829346
$413$	21.3902	1.05255
$414$	−0.637339	−0.0313235
$415$	19.1044	0.937798
$416$	−11.2992	−0.553987
$417$	7.90368	0.387045
$418$	−7.00807	−0.342776
$419$	−20.9805	−1.02496	−0.512482	−	0.858698i	$-0.671274\pi$
$419$	−20.9805	−1.02496	−0.512482	+	0.858698i	$0.671274\pi$
$420$	−11.9794	−0.584536
$421$	−36.0521	−1.75707	−0.878535	−	0.477678i	$-0.841479\pi$
$421$	−36.0521	−1.75707	−0.878535	+	0.477678i	$0.841479\pi$
$422$	−4.50119	−0.219115
$423$	5.01641	0.243906
$424$	−2.37907	−0.115538
$425$	11.6537	0.565290
$426$	−1.05623	−0.0511745
$427$	−16.0000	−0.774294
$428$	3.00417	0.145212
$429$	22.7253	1.09719
$430$	3.78288	0.182427
$431$	29.7745	1.43419	0.717095	−	0.696976i	$-0.245472\pi$
$431$	29.7745	1.43419	0.717095	+	0.696976i	$0.245472\pi$
$432$	3.61676	0.174012
$433$	33.9177	1.62998	0.814990	−	0.579475i	$-0.196742\pi$
$433$	33.9177	1.62998	0.814990	+	0.579475i	$0.196742\pi$
$434$	−0.935432	−0.0449022
$435$	12.1619	0.583121
$436$	23.0922	1.10591
$437$	−11.7829	−0.563652
$438$	−1.40381	−0.0670768
$439$	14.7857	0.705684	0.352842	−	0.935683i	$-0.385215\pi$
$439$	14.7857	0.705684	0.352842	+	0.935683i	$0.385215\pi$
$440$	9.87086	0.470575
$441$	6.55220	0.312009
$442$	5.27468	0.250891
$443$	−32.2775	−1.53355	−0.766776	−	0.641915i	$-0.778140\pi$
$443$	−32.2775	−1.53355	−0.766776	+	0.641915i	$0.778140\pi$
$444$	−0.983593	−0.0466793
$445$	−10.0880	−0.478216
$446$	−1.39547	−0.0660776
$447$	−13.7417	−0.649961
$448$	−23.8984	−1.12910
$449$	3.99166	0.188378	0.0941891	−	0.995554i	$-0.469974\pi$
$449$	3.99166	0.188378	0.0941891	+	0.995554i	$0.469974\pi$
$450$	−0.552195	−0.0260307
$451$	39.3215	1.85158
$452$	23.2786	1.09493
$453$	−18.6290	−0.875267
$454$	7.30749	0.342958
$455$	−23.9588	−1.12321
$456$	−4.69774	−0.219992
$457$	16.8873	0.789953	0.394977	−	0.918691i	$-0.370753\pi$
$457$	16.8873	0.789953	0.394977	+	0.918691i	$0.370753\pi$
$458$	−4.56337	−0.213232
$459$	−5.36266	−0.250308
$460$	8.16195	0.380553
$461$	−0.725323	−0.0337816	−0.0168908	−	0.999857i	$-0.505377\pi$
$461$	−0.725323	−0.0337816	−0.0168908	+	0.999857i	$0.505377\pi$
$462$	−5.49180	−0.255502
$463$	25.8297	1.20041	0.600204	−	0.799847i	$-0.295086\pi$
$463$	25.8297	1.20041	0.600204	+	0.799847i	$0.295086\pi$
$464$	26.1619	1.21454
$465$	−1.68133	−0.0779698
$466$	5.18537	0.240207
$467$	5.05233	0.233794	0.116897	−	0.993144i	$-0.462705\pi$
$467$	5.05233	0.233794	0.116897	+	0.993144i	$0.462705\pi$
$468$	7.49180	0.346308
$469$	14.7253	0.679952
$470$	2.14315	0.0988563
$471$	−3.17313	−0.146210
$472$	−5.81047	−0.267448
$473$	−51.9833	−2.39020
$474$	1.87086	0.0859317
$475$	−10.2088	−0.468411
$476$	38.2088	1.75130
$477$	2.37907	0.108930
$478$	−5.37100	−0.245664
$479$	24.9805	1.14139	0.570694	−	0.821163i	$-0.306674\pi$
$479$	24.9805	1.14139	0.570694	+	0.821163i	$0.306674\pi$
$480$	4.90785	0.224012
$481$	−1.96719	−0.0896960
$482$	4.37073	0.199081
$483$	−9.23353	−0.420140
$484$	−45.4189	−2.06450
$485$	5.33508	0.242253
$486$	0.254102	0.0115263
$487$	31.9588	1.44819	0.724097	−	0.689698i	$-0.242257\pi$
$487$	31.9588	1.44819	0.724097	+	0.689698i	$0.242257\pi$
$488$	4.34625	0.196746
$489$	−4.06040	−0.183618
$490$	2.79929	0.126459
$491$	−15.4590	−0.697654	−0.348827	−	0.937187i	$-0.613420\pi$
$491$	−15.4590	−0.697654	−0.348827	+	0.937187i	$0.613420\pi$
$492$	12.9630	0.584418
$493$	−38.7909	−1.74706
$494$	−4.62066	−0.207893
$495$	−9.87086	−0.443662
$496$	−3.61676	−0.162397
$497$	−15.3023	−0.686400
$498$	2.88727	0.129382
$499$	19.7969	0.886231	0.443115	−	0.896465i	$-0.353873\pi$
$499$	19.7969	0.886231	0.443115	+	0.896465i	$0.353873\pi$
$500$	23.3421	1.04389
$501$	2.50820	0.112058
$502$	−2.76647	−0.123474
$503$	20.2775	0.904130	0.452065	−	0.891985i	$-0.350688\pi$
$503$	20.2775	0.904130	0.452065	+	0.891985i	$0.350688\pi$
$504$	−3.68133	−0.163979
$505$	9.11796	0.405744
$506$	3.74173	0.166340
$507$	1.98359	0.0880945
$508$	−13.3298	−0.591416
$509$	21.9588	0.973309	0.486654	−	0.873595i	$-0.338217\pi$
$509$	21.9588	0.973309	0.486654	+	0.873595i	$0.338217\pi$
$510$	−2.29108	−0.101451
$511$	−20.3379	−0.899696
$512$	17.7909	0.786256
$513$	4.69774	0.207410
$514$	2.20177	0.0971160
$515$	−14.6238	−0.644400
$516$	−17.1372	−0.754423
$517$	−29.4506	−1.29524
$518$	0.475390	0.0208874
$519$	−0.725323	−0.0318381
$520$	6.50820	0.285404
$521$	28.4671	1.24716	0.623582	−	0.781758i	$-0.285677\pi$
$521$	28.4671	1.24716	0.623582	+	0.781758i	$0.285677\pi$
$522$	1.83805	0.0804493
$523$	32.2171	1.40876	0.704378	−	0.709825i	$-0.251226\pi$
$523$	32.2171	1.40876	0.704378	+	0.709825i	$0.251226\pi$
$524$	−36.2416	−1.58322
$525$	−8.00000	−0.349149
$526$	−0.758136	−0.0330563
$527$	5.36266	0.233601
$528$	−21.2335	−0.924071
$529$	−16.7089	−0.726475
$530$	1.01641	0.0441499
$531$	5.81047	0.252153
$532$	−33.4712	−1.45116
$533$	25.9260	1.12298
$534$	−1.52461	−0.0659763
$535$	−2.60975	−0.112829
$536$	−4.00000	−0.172774
$537$	−1.01641	−0.0438612
$538$	2.75814	0.118912
$539$	−38.4671	−1.65689
$540$	−3.25410	−0.140034
$541$	18.7941	0.808020	0.404010	−	0.914755i	$-0.367616\pi$
$541$	18.7941	0.808020	0.404010	+	0.914755i	$0.367616\pi$
$542$	0.678490	0.0291436
$543$	3.32985	0.142897
$544$	−15.6537	−0.671149
$545$	−20.0604	−0.859293
$546$	−3.62093	−0.154962
$547$	39.1648	1.67457	0.837283	−	0.546770i	$-0.184143\pi$
$547$	39.1648	1.67457	0.837283	+	0.546770i	$0.184143\pi$
$548$	−39.9260	−1.70556
$549$	−4.34625	−0.185494
$550$	3.24186	0.138234
$551$	33.9812	1.44765
$552$	2.50820	0.106756
$553$	27.1044	1.15260
$554$	−1.59024	−0.0675627
$555$	0.854458	0.0362697
$556$	−15.2970	−0.648739
$557$	−14.8545	−0.629404	−0.314702	−	0.949191i	$-0.601905\pi$
$557$	−14.8545	−0.629404	−0.314702	+	0.949191i	$0.601905\pi$
$558$	−0.254102	−0.0107570
$559$	−34.2744	−1.44965
$560$	22.3861	0.945984
$561$	31.4835	1.32923
$562$	−0.781821	−0.0329791
$563$	−9.67299	−0.407668	−0.203834	−	0.979005i	$-0.565340\pi$
$563$	−9.67299	−0.407668	−0.203834	+	0.979005i	$0.565340\pi$
$564$	−9.70892	−0.408819
$565$	−20.2223	−0.850761
$566$	−6.65970	−0.279928
$567$	3.68133	0.154601
$568$	4.15672	0.174412
$569$	−10.8956	−0.456768	−0.228384	−	0.973571i	$-0.573344\pi$
$569$	−10.8956	−0.456768	−0.228384	+	0.973571i	$0.573344\pi$
$570$	2.00701	0.0840644
$571$	19.0081	0.795463	0.397731	−	0.917502i	$-0.369798\pi$
$571$	19.0081	0.795463	0.397731	+	0.917502i	$0.369798\pi$
$572$	−43.9833	−1.83904
$573$	−17.2939	−0.722464
$574$	−6.26528	−0.261508
$575$	5.45065	0.227308
$576$	−6.49180	−0.270492
$577$	−8.98359	−0.373992	−0.186996	−	0.982361i	$-0.559875\pi$
$577$	−8.98359	−0.373992	−0.186996	+	0.982361i	$0.559875\pi$
$578$	2.98776	0.124275
$579$	−11.5522	−0.480093
$580$	−23.5386	−0.977388
$581$	41.8297	1.73539
$582$	0.806297	0.0334221
$583$	−13.9672	−0.578462
$584$	5.52461	0.228610
$585$	−6.50820	−0.269081
$586$	8.05729	0.332844
$587$	−1.77454	−0.0732432	−0.0366216	−	0.999329i	$-0.511660\pi$
$587$	−1.77454	−0.0732432	−0.0366216	+	0.999329i	$0.511660\pi$
$588$	−12.6813	−0.522969
$589$	−4.69774	−0.193567
$590$	2.48240	0.102199
$591$	2.85446	0.117417
$592$	1.83805	0.0755434
$593$	16.0276	0.658174	0.329087	−	0.944300i	$-0.393259\pi$
$593$	16.0276	0.658174	0.329087	+	0.944300i	$0.393259\pi$
$594$	−1.49180	−0.0612092
$595$	−33.1924	−1.36075
$596$	26.5962	1.08942
$597$	8.59619	0.351819
$598$	2.46705	0.100885
$599$	6.70608	0.274003	0.137001	−	0.990571i	$-0.456254\pi$
$599$	6.70608	0.274003	0.137001	+	0.990571i	$0.456254\pi$
$600$	2.17313	0.0887175
$601$	−14.2827	−0.582605	−0.291303	−	0.956631i	$-0.594089\pi$
$601$	−14.2827	−0.582605	−0.291303	+	0.956631i	$0.594089\pi$
$602$	8.28275	0.337580
$603$	4.00000	0.162893
$604$	36.0552	1.46706
$605$	39.4559	1.60411
$606$	1.37801	0.0559778
$607$	−44.1760	−1.79305	−0.896524	−	0.442996i	$-0.853916\pi$
$607$	−44.1760	−1.79305	−0.896524	+	0.442996i	$0.853916\pi$
$608$	13.7128	0.556128
$609$	26.6290	1.07906
$610$	−1.85685	−0.0751815
$611$	−19.4178	−0.785561
$612$	10.3791	0.419549
$613$	41.9833	1.69569	0.847845	−	0.530244i	$-0.177900\pi$
$613$	41.9833	1.69569	0.847845	+	0.530244i	$0.177900\pi$
$614$	−4.44959	−0.179571
$615$	−11.2611	−0.454092
$616$	21.6126	0.870796
$617$	13.7417	0.553221	0.276611	−	0.960982i	$-0.410789\pi$
$617$	13.7417	0.553221	0.276611	+	0.960982i	$0.410789\pi$
$618$	−2.21011	−0.0889037
$619$	−37.3132	−1.49974	−0.749872	−	0.661584i	$-0.769885\pi$
$619$	−37.3132	−1.49974	−0.749872	+	0.661584i	$0.769885\pi$
$620$	3.25410	0.130688
$621$	−2.50820	−0.100651
$622$	−8.62199	−0.345710
$623$	−22.0880	−0.884936
$624$	−14.0000	−0.560449
$625$	−9.41188	−0.376475
$626$	−6.81331	−0.272314
$627$	−27.5798	−1.10143
$628$	6.14137	0.245067
$629$	−2.72532	−0.108666
$630$	1.57277	0.0626607
$631$	36.3791	1.44823	0.724114	−	0.689680i	$-0.242249\pi$
$631$	36.3791	1.44823	0.724114	+	0.689680i	$0.242249\pi$
$632$	−7.36266	−0.292871
$633$	−17.7141	−0.704074
$634$	1.18537	0.0470769
$635$	11.5798	0.459530
$636$	−4.60453	−0.182581
$637$	−25.3627	−1.00491
$638$	−10.7909	−0.427218
$639$	−4.15672	−0.164437
$640$	−12.5892	−0.497631
$641$	−48.9117	−1.93190	−0.965949	−	0.258733i	$-0.916695\pi$
$641$	−48.9117	−1.93190	−0.965949	+	0.258733i	$0.916695\pi$
$642$	−0.394415	−0.0155663
$643$	12.6373	0.498368	0.249184	−	0.968456i	$-0.419838\pi$
$643$	12.6373	0.498368	0.249184	+	0.968456i	$0.419838\pi$
$644$	17.8709	0.704211
$645$	14.8873	0.586186
$646$	−6.40142	−0.251861
$647$	−1.23353	−0.0484949	−0.0242475	−	0.999706i	$-0.507719\pi$
$647$	−1.23353	−0.0484949	−0.0242475	+	0.999706i	$0.507719\pi$
$648$	−1.00000	−0.0392837
$649$	−34.1125	−1.33903
$650$	2.13747	0.0838386
$651$	−3.68133	−0.144283
$652$	7.85863	0.307768
$653$	9.30749	0.364230	0.182115	−	0.983277i	$-0.441706\pi$
$653$	9.30749	0.364230	0.182115	+	0.983277i	$0.441706\pi$
$654$	−3.03175	−0.118551
$655$	31.4835	1.23016
$656$	−24.2241	−0.945793
$657$	−5.52461	−0.215536
$658$	4.69251	0.182933
$659$	33.7938	1.31642	0.658210	−	0.752835i	$-0.271314\pi$
$659$	33.7938	1.31642	0.658210	+	0.752835i	$0.271314\pi$
$660$	19.1044	0.743637
$661$	7.29392	0.283701	0.141850	−	0.989888i	$-0.454695\pi$
$661$	7.29392	0.283701	0.141850	+	0.989888i	$0.454695\pi$
$662$	4.35459	0.169246
$663$	20.7581	0.806179
$664$	−11.3627	−0.440957
$665$	29.0768	1.12755
$666$	0.129135	0.00500389
$667$	−18.1432	−0.702506
$668$	−4.85446	−0.187825
$669$	−5.49180	−0.212325
$670$	1.70892	0.0660212
$671$	25.5163	0.985045
$672$	10.7459	0.414532
$673$	0.00833797	0.000321405 0	0.000160703	−	1.00000i	$-0.499949\pi$
$673$	0.00833797	0.000321405 0	0.000160703		1.00000i	$0.499949\pi$
$674$	0.184306	0.00709919
$675$	−2.17313	−0.0836437
$676$	−3.83911	−0.147658
$677$	−18.9096	−0.726756	−0.363378	−	0.931642i	$-0.618377\pi$
$677$	−18.9096	−0.726756	−0.363378	+	0.931642i	$0.618377\pi$
$678$	−3.05623	−0.117374
$679$	11.6813	0.448288
$680$	9.01641	0.345763
$681$	28.7581	1.10201
$682$	1.49180	0.0571238
$683$	24.3983	0.933576	0.466788	−	0.884369i	$-0.345411\pi$
$683$	24.3983	0.933576	0.466788	+	0.884369i	$0.345411\pi$
$684$	−9.09215	−0.347647
$685$	34.6842	1.32521
$686$	−0.418891	−0.0159933
$687$	−17.9588	−0.685173
$688$	32.0245	1.22092
$689$	−9.20905	−0.350837
$690$	−1.07158	−0.0407942
$691$	18.2692	0.694992	0.347496	−	0.937681i	$-0.387032\pi$
$691$	18.2692	0.694992	0.347496	+	0.937681i	$0.387032\pi$
$692$	1.40381	0.0533650
$693$	−21.6126	−0.820995
$694$	5.07158	0.192514
$695$	13.2887	0.504069
$696$	−7.23353	−0.274186
$697$	35.9177	1.36048
$698$	5.13509	0.194366
$699$	20.4067	0.771851
$700$	15.4835	0.585220
$701$	−2.37384	−0.0896587	−0.0448293	−	0.998995i	$-0.514274\pi$
$701$	−2.37384	−0.0896587	−0.0448293	+	0.998995i	$0.514274\pi$
$702$	−0.983593	−0.0371233
$703$	2.38741	0.0900427
$704$	38.1125	1.43642
$705$	8.43424	0.317652
$706$	−0.532679	−0.0200476
$707$	19.9641	0.750826
$708$	−11.2458	−0.422642
$709$	−38.3791	−1.44136	−0.720678	−	0.693270i	$-0.756169\pi$
$709$	−38.3791	−1.44136	−0.720678	+	0.693270i	$0.756169\pi$
$710$	−1.77587	−0.0666473
$711$	7.36266	0.276121
$712$	6.00000	0.224860
$713$	2.50820	0.0939330
$714$	−5.01641	−0.187734
$715$	38.2088	1.42893
$716$	1.96719	0.0735172
$717$	−21.1372	−0.789383
$718$	−1.70403	−0.0635937
$719$	2.67015	0.0995799	0.0497899	−	0.998760i	$-0.484145\pi$
$719$	2.67015	0.0995799	0.0497899	+	0.998760i	$0.484145\pi$
$720$	6.08097	0.226625
$721$	−32.0192	−1.19246
$722$	0.779771	0.0290201
$723$	17.2007	0.639701
$724$	−6.44470	−0.239515
$725$	−15.7194	−0.583803
$726$	5.96302	0.221308
$727$	22.0276	0.816958	0.408479	−	0.912768i	$-0.366059\pi$
$727$	22.0276	0.816958	0.408479	+	0.912768i	$0.366059\pi$
$728$	14.2499	0.528138
$729$	1.00000	0.0370370
$730$	−2.36027	−0.0873576
$731$	−47.4835	−1.75624
$732$	8.41188	0.310912
$733$	16.4478	0.607514	0.303757	−	0.952750i	$-0.401759\pi$
$733$	16.4478	0.607514	0.303757	+	0.952750i	$0.401759\pi$
$734$	−5.37100	−0.198247
$735$	11.0164	0.406346
$736$	−7.32151	−0.269874
$737$	−23.4835	−0.865024
$738$	−1.70191	−0.0626480
$739$	28.4035	1.04484	0.522421	−	0.852688i	$-0.325029\pi$
$739$	28.4035	1.04484	0.522421	+	0.852688i	$0.325029\pi$
$740$	−1.65375	−0.0607929
$741$	−18.1843	−0.668017
$742$	2.22546	0.0816991
$743$	−1.43663	−0.0527047	−0.0263524	−	0.999653i	$-0.508389\pi$
$743$	−1.43663	−0.0527047	−0.0263524	+	0.999653i	$0.508389\pi$
$744$	1.00000	0.0366618
$745$	−23.1044	−0.846479
$746$	2.50119	0.0915752
$747$	11.3627	0.415738
$748$	−60.9341	−2.22797
$749$	−5.71414	−0.208790
$750$	−3.06457	−0.111902
$751$	−36.4395	−1.32970	−0.664848	−	0.746979i	$-0.731503\pi$
$751$	−36.4395	−1.32970	−0.664848	+	0.746979i	$0.731503\pi$
$752$	18.1432	0.661613
$753$	−10.8873	−0.396754
$754$	−7.11485	−0.259107
$755$	−31.3215	−1.13991
$756$	−7.12497	−0.259133
$757$	−41.2007	−1.49747	−0.748733	−	0.662872i	$-0.769337\pi$
$757$	−41.2007	−1.49747	−0.748733	+	0.662872i	$0.769337\pi$
$758$	−5.70892	−0.207357
$759$	14.7253	0.534495
$760$	−7.89845	−0.286507
$761$	5.78288	0.209629	0.104815	−	0.994492i	$-0.466575\pi$
$761$	5.78288	0.209629	0.104815	+	0.994492i	$0.466575\pi$
$762$	1.75007	0.0633982
$763$	−43.9229	−1.59012
$764$	33.4712	1.21095
$765$	−9.01641	−0.325989
$766$	0.596187	0.0215411
$767$	−22.4915	−0.812122
$768$	11.0810	0.399850
$769$	31.6730	1.14216	0.571079	−	0.820895i	$-0.306525\pi$
$769$	31.6730	1.14216	0.571079	+	0.820895i	$0.306525\pi$
$770$	−9.23353	−0.332753
$771$	8.66492	0.312060
$772$	22.3585	0.804700
$773$	−10.4754	−0.376774	−0.188387	−	0.982095i	$-0.560326\pi$
$773$	−10.4754	−0.376774	−0.188387	+	0.982095i	$0.560326\pi$
$774$	2.24993	0.0808722
$775$	2.17313	0.0780610
$776$	−3.17313	−0.113909
$777$	1.87086	0.0671169
$778$	−8.65970	−0.310465
$779$	−31.4642	−1.12732
$780$	12.5962	0.451016
$781$	24.4035	0.873227
$782$	3.41783	0.122221
$783$	7.23353	0.258505
$784$	23.6977	0.846348
$785$	−5.33508	−0.190417
$786$	4.75814	0.169717
$787$	5.07158	0.180782	0.0903911	−	0.995906i	$-0.471188\pi$
$787$	5.07158	0.180782	0.0903911	+	0.995906i	$0.471188\pi$
$788$	−5.52461	−0.196806
$789$	−2.98359	−0.106219
$790$	3.14554	0.111913
$791$	−44.2775	−1.57433
$792$	5.87086	0.208612
$793$	16.8238	0.597429
$794$	2.90474	0.103085
$795$	4.00000	0.141865
$796$	−16.6373	−0.589695
$797$	29.7969	1.05546	0.527730	−	0.849412i	$-0.323043\pi$
$797$	29.7969	1.05546	0.527730	+	0.849412i	$0.323043\pi$
$798$	4.39442	0.155561
$799$	−26.9013	−0.951699
$800$	−6.34341	−0.224274
$801$	−6.00000	−0.212000
$802$	−7.09605	−0.250570
$803$	32.4342	1.14458
$804$	−7.74173	−0.273030
$805$	−15.5246	−0.547171
$806$	0.983593	0.0346456
$807$	10.8545	0.382095
$808$	−5.42306	−0.190783
$809$	−23.5470	−0.827867	−0.413934	−	0.910307i	$-0.635845\pi$
$809$	−23.5470	−0.827867	−0.413934	+	0.910307i	$0.635845\pi$
$810$	0.427229	0.0150113
$811$	−2.72532	−0.0956990	−0.0478495	−	0.998855i	$-0.515237\pi$
$811$	−2.72532	−0.0956990	−0.0478495	+	0.998855i	$0.515237\pi$
$812$	−51.5386	−1.80865
$813$	2.67015	0.0936463
$814$	−0.758136	−0.0265727
$815$	−6.82687	−0.239135
$816$	−19.3955	−0.678977
$817$	41.5959	1.45526
$818$	2.06563	0.0722230
$819$	−14.2499	−0.497933
$820$	21.7951	0.761119
$821$	−38.4999	−1.34365	−0.671827	−	0.740708i	$-0.734490\pi$
$821$	−38.4999	−1.34365	−0.671827	+	0.740708i	$0.734490\pi$
$822$	5.24186	0.182831
$823$	−49.6266	−1.72987	−0.864937	−	0.501880i	$-0.832642\pi$
$823$	−49.6266	−1.72987	−0.864937	+	0.501880i	$0.832642\pi$
$824$	8.69774	0.303000
$825$	12.7581	0.444181
$826$	5.43530	0.189118
$827$	2.44258	0.0849367	0.0424684	−	0.999098i	$-0.486478\pi$
$827$	2.44258	0.0849367	0.0424684	+	0.999098i	$0.486478\pi$
$828$	4.85446	0.168704
$829$	−37.7417	−1.31082	−0.655412	−	0.755271i	$-0.727505\pi$
$829$	−37.7417	−1.31082	−0.655412	+	0.755271i	$0.727505\pi$
$830$	4.85446	0.168501
$831$	−6.25827	−0.217097
$832$	25.1289	0.871187
$833$	−35.1372	−1.21743
$834$	2.00834	0.0695431
$835$	4.21712	0.145939
$836$	53.3788	1.84614
$837$	−1.00000	−0.0345651
$838$	−5.33118	−0.184162
$839$	25.5163	0.880920	0.440460	−	0.897772i	$-0.354815\pi$
$839$	25.5163	0.880920	0.440460	+	0.897772i	$0.354815\pi$
$840$	−6.18953	−0.213559
$841$	23.3239	0.804272
$842$	−9.16089	−0.315705
$843$	−3.07681	−0.105971
$844$	34.2845	1.18012
$845$	3.33508	0.114730
$846$	1.27468	0.0438243
$847$	86.3900	2.96839
$848$	8.60453	0.295481
$849$	−26.2088	−0.899483
$850$	2.96124	0.101570
$851$	−1.27468	−0.0436954
$852$	8.04505	0.275619
$853$	25.9833	0.889652	0.444826	−	0.895617i	$-0.353266\pi$
$853$	25.9833	0.889652	0.444826	+	0.895617i	$0.353266\pi$
$854$	−4.06563	−0.139123
$855$	7.89845	0.270121
$856$	1.55220	0.0530529
$857$	−5.04922	−0.172478	−0.0862390	−	0.996274i	$-0.527485\pi$
$857$	−5.04922	−0.172478	−0.0862390	+	0.996274i	$0.527485\pi$
$858$	5.77454	0.197140
$859$	15.2663	0.520881	0.260440	−	0.965490i	$-0.416132\pi$
$859$	15.2663	0.520881	0.260440	+	0.965490i	$0.416132\pi$
$860$	−28.8133	−0.982526
$861$	−24.6566	−0.840294
$862$	7.56576	0.257691
$863$	−18.6702	−0.635539	−0.317770	−	0.948168i	$-0.602934\pi$
$863$	−18.6702	−0.635539	−0.317770	+	0.948168i	$0.602934\pi$
$864$	2.91903	0.0993073
$865$	−1.21951	−0.0414645
$866$	8.61854	0.292870
$867$	11.7581	0.399327
$868$	7.12497	0.241837
$869$	−43.2252	−1.46631
$870$	3.09037	0.104773
$871$	−15.4835	−0.524637
$872$	11.9313	0.404044
$873$	3.17313	0.107394
$874$	−2.99405	−0.101275
$875$	−44.3983	−1.50094
$876$	10.6925	0.361266
$877$	−39.0357	−1.31814	−0.659070	−	0.752081i	$-0.729050\pi$
$877$	−39.0357	−1.31814	−0.659070	+	0.752081i	$0.729050\pi$
$878$	3.75708	0.126795
$879$	31.7089	1.06952
$880$	−35.7006	−1.20347
$881$	−22.8789	−0.770811	−0.385405	−	0.922747i	$-0.625938\pi$
$881$	−22.8789	−0.770811	−0.385405	+	0.922747i	$0.625938\pi$
$882$	1.66492	0.0560609
$883$	−19.4835	−0.655671	−0.327835	−	0.944735i	$-0.606319\pi$
$883$	−19.4835	−0.655671	−0.327835	+	0.944735i	$0.606319\pi$
$884$	−40.1760	−1.35126
$885$	9.76931	0.328392
$886$	−8.20177	−0.275544
$887$	−26.4863	−0.889323	−0.444661	−	0.895699i	$-0.646676\pi$
$887$	−26.4863	−0.889323	−0.444661	+	0.895699i	$0.646676\pi$
$888$	−0.508203	−0.0170542
$889$	25.3543	0.850357
$890$	−2.56337	−0.0859245
$891$	−5.87086	−0.196681
$892$	10.6290	0.355885
$893$	23.5658	0.788598
$894$	−3.49180	−0.116783
$895$	−1.70892	−0.0571228
$896$	−27.5644	−0.920863
$897$	9.70892	0.324171
$898$	1.01429	0.0338472
$899$	−7.23353	−0.241252
$900$	4.20594	0.140198
$901$	−12.7581	−0.425035
$902$	9.99166	0.332686
$903$	32.5962	1.08473
$904$	12.0276	0.400032
$905$	5.59858	0.186103
$906$	−4.73366	−0.157265
$907$	10.0276	0.332961	0.166480	−	0.986045i	$-0.446760\pi$
$907$	10.0276	0.332961	0.166480	+	0.986045i	$0.446760\pi$
$908$	−55.6594	−1.84712
$909$	5.42306	0.179872
$910$	−6.08798	−0.201815
$911$	16.5962	0.549856	0.274928	−	0.961465i	$-0.411346\pi$
$911$	16.5962	0.549856	0.274928	+	0.961465i	$0.411346\pi$
$912$	16.9906	0.562615
$913$	−66.7086	−2.20773
$914$	4.29108	0.141936
$915$	−7.30749	−0.241578
$916$	34.7581	1.14844
$917$	68.9341	2.27640
$918$	−1.36266	−0.0449745
$919$	3.93437	0.129783	0.0648915	−	0.997892i	$-0.479330\pi$
$919$	3.93437	0.129783	0.0648915	+	0.997892i	$0.479330\pi$
$920$	4.21712	0.139034
$921$	−17.5110	−0.577009
$922$	−0.184306	−0.00606978
$923$	16.0901	0.529612
$924$	41.8297	1.37610
$925$	−1.10439	−0.0363121
$926$	6.56337	0.215686
$927$	−8.69774	−0.285671
$928$	21.1148	0.693129
$929$	−22.1619	−0.727110	−0.363555	−	0.931573i	$-0.618437\pi$
$929$	−22.1619	−0.727110	−0.363555	+	0.931573i	$0.618437\pi$
$930$	−0.427229	−0.0140094
$931$	30.7805	1.00879
$932$	−39.4957	−1.29372
$933$	−33.9313	−1.11086
$934$	1.28381	0.0420074
$935$	52.9341	1.73113
$936$	3.87086	0.126523
$937$	−24.7909	−0.809885	−0.404943	−	0.914342i	$-0.632708\pi$
$937$	−24.7909	−0.809885	−0.404943	+	0.914342i	$0.632708\pi$
$938$	3.74173	0.122172
$939$	−26.8133	−0.875019
$940$	−16.3239	−0.532427
$941$	18.6925	0.609358	0.304679	−	0.952455i	$-0.401451\pi$
$941$	18.6925	0.609358	0.304679	+	0.952455i	$0.401451\pi$
$942$	−0.806297	−0.0262706
$943$	16.7993	0.547060
$944$	21.0151	0.683983
$945$	6.18953	0.201346
$946$	−13.2091	−0.429463
$947$	−3.21117	−0.104349	−0.0521745	−	0.998638i	$-0.516615\pi$
$947$	−3.21117	−0.104349	−0.0521745	+	0.998638i	$0.516615\pi$
$948$	−14.2499	−0.462816
$949$	21.3850	0.694187
$950$	−2.59407	−0.0841627
$951$	4.66492	0.151271
$952$	19.7417	0.639833
$953$	40.5222	1.31264	0.656322	−	0.754481i	$-0.272111\pi$
$953$	40.5222	1.31264	0.656322	+	0.754481i	$0.272111\pi$
$954$	0.604525	0.0195722
$955$	−29.0768	−0.940903
$956$	40.9096	1.32311
$957$	−42.4671	−1.37276
$958$	6.34758	0.205081
$959$	75.9422	2.45230
$960$	−10.9149	−0.352275
$961$	1.00000	0.0322581
$962$	−0.499865	−0.0161163
$963$	−1.55220	−0.0500188
$964$	−33.2908	−1.07222
$965$	−19.4231	−0.625250
$966$	−2.34625	−0.0754895
$967$	−7.52461	−0.241975	−0.120988	−	0.992654i	$-0.538606\pi$
$967$	−7.52461	−0.241975	−0.120988	+	0.992654i	$0.538606\pi$
$968$	−23.4671	−0.754260
$969$	−25.1924	−0.809296
$970$	1.35565	0.0435274
$971$	−2.72532	−0.0874598	−0.0437299	−	0.999043i	$-0.513924\pi$
$971$	−2.72532	−0.0874598	−0.0437299	+	0.999043i	$0.513924\pi$
$972$	−1.93543	−0.0620790
$973$	29.0961	0.932777
$974$	8.12080	0.260207
$975$	8.41188	0.269396
$976$	−15.7194	−0.503165
$977$	56.4618	1.80637	0.903187	−	0.429248i	$-0.141221\pi$
$977$	56.4618	1.80637	0.903187	+	0.429248i	$0.141221\pi$
$978$	−1.03175	−0.0329919
$979$	35.2252	1.12580
$980$	−21.3215	−0.681091
$981$	−11.9313	−0.380936
$982$	−3.92815	−0.125352
$983$	−8.35459	−0.266470	−0.133235	−	0.991084i	$-0.542537\pi$
$983$	−8.35459	−0.266470	−0.133235	+	0.991084i	$0.542537\pi$
$984$	6.69774	0.213516
$985$	4.79929	0.152918
$986$	−9.85685	−0.313906
$987$	18.4671	0.587813
$988$	35.1945	1.11969
$989$	−22.2088	−0.706198
$990$	−2.50820	−0.0797159
$991$	−14.7253	−0.467765	−0.233883	−	0.972265i	$-0.575143\pi$
$991$	−14.7253	−0.467765	−0.233883	+	0.972265i	$0.575143\pi$
$992$	−2.91903	−0.0926792
$993$	17.1372	0.543833
$994$	−3.88833	−0.123330
$995$	14.4530	0.458192
$996$	−21.9917	−0.696832
$997$	−10.8492	−0.343599	−0.171799	−	0.985132i	$-0.554958\pi$
$997$	−10.8492	−0.343599	−0.171799	+	0.985132i	$0.554958\pi$
$998$	5.03043	0.159235
$999$	0.508203	0.0160788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.a.b.1.2	✓	3
3.2	odd	2		279.2.a.c.1.2		3
4.3	odd	2		1488.2.a.t.1.3		3
5.2	odd	4		2325.2.c.n.1024.4		6
5.3	odd	4		2325.2.c.n.1024.3		6
5.4	even	2		2325.2.a.s.1.2		3
7.6	odd	2		4557.2.a.v.1.2		3
8.3	odd	2		5952.2.a.cf.1.1		3
8.5	even	2		5952.2.a.bz.1.1		3
12.11	even	2		4464.2.a.bq.1.1		3
15.14	odd	2		6975.2.a.bb.1.2		3
31.30	odd	2		2883.2.a.f.1.2		3
93.92	even	2		8649.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.a.b.1.2	✓	3	1.1	even	1	trivial
279.2.a.c.1.2		3	3.2	odd	2
1488.2.a.t.1.3		3	4.3	odd	2
2325.2.a.s.1.2		3	5.4	even	2
2325.2.c.n.1024.3		6	5.3	odd	4
2325.2.c.n.1024.4		6	5.2	odd	4
2883.2.a.f.1.2		3	31.30	odd	2
4464.2.a.bq.1.1		3	12.11	even	2
4557.2.a.v.1.2		3	7.6	odd	2
5952.2.a.bz.1.1		3	8.5	even	2
5952.2.a.cf.1.1		3	8.3	odd	2
6975.2.a.bb.1.2		3	15.14	odd	2
8649.2.a.p.1.2		3	93.92	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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.a (trivial)

\(f(q)\)	\(=\)	\(q+0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} +1.68133 q^{5} +0.254102 q^{6} +3.68133 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} +1.68133 q^{5} +0.254102 q^{6} +3.68133 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.427229 q^{10} -5.87086 q^{11} -1.93543 q^{12} -3.87086 q^{13} +0.935432 q^{14} +1.68133 q^{15} +3.61676 q^{16} -5.36266 q^{17} +0.254102 q^{18} +4.69774 q^{19} -3.25410 q^{20} +3.68133 q^{21} -1.49180 q^{22} -2.50820 q^{23} -1.00000 q^{24} -2.17313 q^{25} -0.983593 q^{26} +1.00000 q^{27} -7.12497 q^{28} +7.23353 q^{29} +0.427229 q^{30} -1.00000 q^{31} +2.91903 q^{32} -5.87086 q^{33} -1.36266 q^{34} +6.18953 q^{35} -1.93543 q^{36} +0.508203 q^{37} +1.19370 q^{38} -3.87086 q^{39} -1.68133 q^{40} -6.69774 q^{41} +0.935432 q^{42} +8.85446 q^{43} +11.3627 q^{44} +1.68133 q^{45} -0.637339 q^{46} +5.01641 q^{47} +3.61676 q^{48} +6.55220 q^{49} -0.552195 q^{50} -5.36266 q^{51} +7.49180 q^{52} +2.37907 q^{53} +0.254102 q^{54} -9.87086 q^{55} -3.68133 q^{56} +4.69774 q^{57} +1.83805 q^{58} +5.81047 q^{59} -3.25410 q^{60} -4.34625 q^{61} -0.254102 q^{62} +3.68133 q^{63} -6.49180 q^{64} -6.50820 q^{65} -1.49180 q^{66} +4.00000 q^{67} +10.3791 q^{68} -2.50820 q^{69} +1.57277 q^{70} -4.15672 q^{71} -1.00000 q^{72} -5.52461 q^{73} +0.129135 q^{74} -2.17313 q^{75} -9.09215 q^{76} -21.6126 q^{77} -0.983593 q^{78} +7.36266 q^{79} +6.08097 q^{80} +1.00000 q^{81} -1.70191 q^{82} +11.3627 q^{83} -7.12497 q^{84} -9.01641 q^{85} +2.24993 q^{86} +7.23353 q^{87} +5.87086 q^{88} -6.00000 q^{89} +0.427229 q^{90} -14.2499 q^{91} +4.85446 q^{92} -1.00000 q^{93} +1.27468 q^{94} +7.89845 q^{95} +2.91903 q^{96} +3.17313 q^{97} +1.66492 q^{98} -5.87086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 2 * q^4 - 2 * q^5 + 4 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} - 2 q^{5} + 4 q^{7} - 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 5 q^{14} - 2 q^{15} - 4 q^{16} - 2 q^{17} + 4 q^{19} - 9 q^{20} + 4 q^{21} - 6 q^{22} - 6 q^{23} - 3 q^{24} - q^{25} - 6 q^{26} + 3 q^{27} - 5 q^{28} - 8 q^{29} - 5 q^{30} - 3 q^{31} + 4 q^{32} - 2 q^{33} + 10 q^{34} + 10 q^{35} + 2 q^{36} + 27 q^{38} + 4 q^{39} + 2 q^{40} - 10 q^{41} - 5 q^{42} + 14 q^{43} + 20 q^{44} - 2 q^{45} - 16 q^{46} + 12 q^{47} - 4 q^{48} - 3 q^{49} + 21 q^{50} - 2 q^{51} + 24 q^{52} - 10 q^{53} - 14 q^{55} - 4 q^{56} + 4 q^{57} - 4 q^{58} + 26 q^{59} - 9 q^{60} - 2 q^{61} + 4 q^{63} - 21 q^{64} - 18 q^{65} - 6 q^{66} + 12 q^{67} + 14 q^{68} - 6 q^{69} + 11 q^{70} - 10 q^{71} - 3 q^{72} - 12 q^{73} + 16 q^{74} - q^{75} - 17 q^{76} - 18 q^{77} - 6 q^{78} + 8 q^{79} + 23 q^{80} + 3 q^{81} - 27 q^{82} + 20 q^{83} - 5 q^{84} - 24 q^{85} - 26 q^{86} - 8 q^{87} + 2 q^{88} - 18 q^{89} - 5 q^{90} - 10 q^{91} + 2 q^{92} - 3 q^{93} + 32 q^{94} - 10 q^{95} + 4 q^{96} + 4 q^{97} + q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 - 2 * q^5 + 4 * q^7 - 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 + 4 * q^13 - 5 * q^14 - 2 * q^15 - 4 * q^16 - 2 * q^17 + 4 * q^19 - 9 * q^20 + 4 * q^21 - 6 * q^22 - 6 * q^23 - 3 * q^24 - q^25 - 6 * q^26 + 3 * q^27 - 5 * q^28 - 8 * q^29 - 5 * q^30 - 3 * q^31 + 4 * q^32 - 2 * q^33 + 10 * q^34 + 10 * q^35 + 2 * q^36 + 27 * q^38 + 4 * q^39 + 2 * q^40 - 10 * q^41 - 5 * q^42 + 14 * q^43 + 20 * q^44 - 2 * q^45 - 16 * q^46 + 12 * q^47 - 4 * q^48 - 3 * q^49 + 21 * q^50 - 2 * q^51 + 24 * q^52 - 10 * q^53 - 14 * q^55 - 4 * q^56 + 4 * q^57 - 4 * q^58 + 26 * q^59 - 9 * q^60 - 2 * q^61 + 4 * q^63 - 21 * q^64 - 18 * q^65 - 6 * q^66 + 12 * q^67 + 14 * q^68 - 6 * q^69 + 11 * q^70 - 10 * q^71 - 3 * q^72 - 12 * q^73 + 16 * q^74 - q^75 - 17 * q^76 - 18 * q^77 - 6 * q^78 + 8 * q^79 + 23 * q^80 + 3 * q^81 - 27 * q^82 + 20 * q^83 - 5 * q^84 - 24 * q^85 - 26 * q^86 - 8 * q^87 + 2 * q^88 - 18 * q^89 - 5 * q^90 - 10 * q^91 + 2 * q^92 - 3 * q^93 + 32 * q^94 - 10 * q^95 + 4 * q^96 + 4 * q^97 + q^98 - 2 * q^99

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