LMFDB - Embedded newform 6031.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30236 q^{2} +0.992330 q^{3} +3.30086 q^{4} +2.64832 q^{5} -2.28470 q^{6} -0.416453 q^{7} -2.99506 q^{8} -2.01528 q^{9} +O(q^{10})$	\(q-2.30236 q^{2} +0.992330 q^{3} +3.30086 q^{4} +2.64832 q^{5} -2.28470 q^{6} -0.416453 q^{7} -2.99506 q^{8} -2.01528 q^{9} -6.09738 q^{10} +3.13151 q^{11} +3.27555 q^{12} -4.50915 q^{13} +0.958824 q^{14} +2.62801 q^{15} +0.293975 q^{16} -1.30393 q^{17} +4.63990 q^{18} +0.862312 q^{19} +8.74174 q^{20} -0.413259 q^{21} -7.20987 q^{22} +6.29683 q^{23} -2.97209 q^{24} +2.01359 q^{25} +10.3817 q^{26} -4.97682 q^{27} -1.37465 q^{28} -7.07285 q^{29} -6.05062 q^{30} -6.76747 q^{31} +5.31328 q^{32} +3.10749 q^{33} +3.00213 q^{34} -1.10290 q^{35} -6.65217 q^{36} +1.00000 q^{37} -1.98535 q^{38} -4.47457 q^{39} -7.93187 q^{40} +3.26837 q^{41} +0.951471 q^{42} -8.75016 q^{43} +10.3367 q^{44} -5.33710 q^{45} -14.4976 q^{46} +10.2251 q^{47} +0.291721 q^{48} -6.82657 q^{49} -4.63602 q^{50} -1.29393 q^{51} -14.8841 q^{52} +4.61900 q^{53} +11.4584 q^{54} +8.29324 q^{55} +1.24730 q^{56} +0.855699 q^{57} +16.2843 q^{58} +0.827669 q^{59} +8.67470 q^{60} +8.08190 q^{61} +15.5812 q^{62} +0.839269 q^{63} -12.8210 q^{64} -11.9417 q^{65} -7.15457 q^{66} -0.269965 q^{67} -4.30411 q^{68} +6.24854 q^{69} +2.53927 q^{70} -7.11715 q^{71} +6.03588 q^{72} -6.71969 q^{73} -2.30236 q^{74} +1.99815 q^{75} +2.84638 q^{76} -1.30413 q^{77} +10.3021 q^{78} +15.2973 q^{79} +0.778540 q^{80} +1.10720 q^{81} -7.52496 q^{82} -9.44992 q^{83} -1.36411 q^{84} -3.45323 q^{85} +20.1460 q^{86} -7.01861 q^{87} -9.37906 q^{88} +10.2824 q^{89} +12.2879 q^{90} +1.87785 q^{91} +20.7850 q^{92} -6.71556 q^{93} -23.5418 q^{94} +2.28368 q^{95} +5.27253 q^{96} +2.14588 q^{97} +15.7172 q^{98} -6.31087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.30236	−1.62801	−0.814007	−	0.580855i	$-0.802719\pi$
$2$	−2.30236	−1.62801	−0.814007	+	0.580855i	$0.802719\pi$
$3$	0.992330	0.572922	0.286461	−	0.958092i	$-0.407521\pi$
$3$	0.992330	0.572922	0.286461	+	0.958092i	$0.407521\pi$
$4$	3.30086	1.65043
$5$	2.64832	1.18436	0.592182	−	0.805804i	$-0.298267\pi$
$5$	2.64832	1.18436	0.592182	+	0.805804i	$0.298267\pi$
$6$	−2.28470	−0.932726
$7$	−0.416453	−0.157404	−0.0787022	−	0.996898i	$-0.525078\pi$
$7$	−0.416453	−0.157404	−0.0787022	+	0.996898i	$0.525078\pi$
$8$	−2.99506	−1.05891
$9$	−2.01528	−0.671760
$10$	−6.09738	−1.92816
$11$	3.13151	0.944186	0.472093	−	0.881549i	$-0.343499\pi$
$11$	3.13151	0.944186	0.472093	+	0.881549i	$0.343499\pi$
$12$	3.27555	0.945569
$13$	−4.50915	−1.25061	−0.625307	−	0.780379i	$-0.715026\pi$
$13$	−4.50915	−1.25061	−0.625307	+	0.780379i	$0.715026\pi$
$14$	0.958824	0.256257
$15$	2.62801	0.678549
$16$	0.293975	0.0734938
$17$	−1.30393	−0.316250	−0.158125	−	0.987419i	$-0.550545\pi$
$17$	−1.30393	−0.316250	−0.158125	+	0.987419i	$0.550545\pi$
$18$	4.63990	1.09364
$19$	0.862312	0.197828	0.0989140	−	0.995096i	$-0.468463\pi$
$19$	0.862312	0.197828	0.0989140	+	0.995096i	$0.468463\pi$
$20$	8.74174	1.95471
$21$	−0.413259	−0.0901805
$22$	−7.20987	−1.53715
$23$	6.29683	1.31298	0.656490	−	0.754335i	$-0.272040\pi$
$23$	6.29683	1.31298	0.656490	+	0.754335i	$0.272040\pi$
$24$	−2.97209	−0.606675
$25$	2.01359	0.402719
$26$	10.3817	2.03602
$27$	−4.97682	−0.957789
$28$	−1.37465	−0.259785
$29$	−7.07285	−1.31340	−0.656698	−	0.754154i	$-0.728047\pi$
$29$	−7.07285	−1.31340	−0.656698	+	0.754154i	$0.728047\pi$
$30$	−6.05062	−1.10469
$31$	−6.76747	−1.21547	−0.607737	−	0.794139i	$-0.707922\pi$
$31$	−6.76747	−1.21547	−0.607737	+	0.794139i	$0.707922\pi$
$32$	5.31328	0.939264
$33$	3.10749	0.540945
$34$	3.00213	0.514860
$35$	−1.10290	−0.186424
$36$	−6.65217	−1.10869
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−1.98535	−0.322067
$39$	−4.47457	−0.716505
$40$	−7.93187	−1.25414
$41$	3.26837	0.510433	0.255217	−	0.966884i	$-0.417853\pi$
$41$	3.26837	0.510433	0.255217	+	0.966884i	$0.417853\pi$
$42$	0.951471	0.146815
$43$	−8.75016	−1.33439	−0.667194	−	0.744884i	$-0.732505\pi$
$43$	−8.75016	−1.33439	−0.667194	+	0.744884i	$0.732505\pi$
$44$	10.3367	1.55832
$45$	−5.33710	−0.795609
$46$	−14.4976	−2.13755
$47$	10.2251	1.49148	0.745738	−	0.666239i	$-0.232097\pi$
$47$	10.2251	1.49148	0.745738	+	0.666239i	$0.232097\pi$
$48$	0.291721	0.0421062
$49$	−6.82657	−0.975224
$50$	−4.63602	−0.655632
$51$	−1.29393	−0.181187
$52$	−14.8841	−2.06405
$53$	4.61900	0.634468	0.317234	−	0.948347i	$-0.397246\pi$
$53$	4.61900	0.634468	0.317234	+	0.948347i	$0.397246\pi$
$54$	11.4584	1.55929
$55$	8.29324	1.11826
$56$	1.24730	0.166678
$57$	0.855699	0.113340
$58$	16.2843	2.13823
$59$	0.827669	0.107753	0.0538766	−	0.998548i	$-0.482842\pi$
$59$	0.827669	0.107753	0.0538766	+	0.998548i	$0.482842\pi$
$60$	8.67470	1.11990
$61$	8.08190	1.03478	0.517391	−	0.855749i	$-0.326903\pi$
$61$	8.08190	1.03478	0.517391	+	0.855749i	$0.326903\pi$
$62$	15.5812	1.97881
$63$	0.839269	0.105738
$64$	−12.8210	−1.60263
$65$	−11.9417	−1.48118
$66$	−7.15457	−0.880667
$67$	−0.269965	−0.0329814	−0.0164907	−	0.999864i	$-0.505249\pi$
$67$	−0.269965	−0.0329814	−0.0164907	+	0.999864i	$0.505249\pi$
$68$	−4.30411	−0.521950
$69$	6.24854	0.752235
$70$	2.53927	0.303501
$71$	−7.11715	−0.844650	−0.422325	−	0.906444i	$-0.638786\pi$
$71$	−7.11715	−0.844650	−0.422325	+	0.906444i	$0.638786\pi$
$72$	6.03588	0.711335
$73$	−6.71969	−0.786480	−0.393240	−	0.919436i	$-0.628646\pi$
$73$	−6.71969	−0.786480	−0.393240	+	0.919436i	$0.628646\pi$
$74$	−2.30236	−0.267644
$75$	1.99815	0.230726
$76$	2.84638	0.326502
$77$	−1.30413	−0.148619
$78$	10.3021	1.16648
$79$	15.2973	1.72108	0.860538	−	0.509386i	$-0.170127\pi$
$79$	15.2973	1.72108	0.860538	+	0.509386i	$0.170127\pi$
$80$	0.778540	0.0870434
$81$	1.10720	0.123022
$82$	−7.52496	−0.830993
$83$	−9.44992	−1.03726	−0.518632	−	0.854998i	$-0.673559\pi$
$83$	−9.44992	−1.03726	−0.518632	+	0.854998i	$0.673559\pi$
$84$	−1.36411	−0.148837
$85$	−3.45323	−0.374556
$86$	20.1460	2.17240
$87$	−7.01861	−0.752474
$88$	−9.37906	−0.999811
$89$	10.2824	1.08993	0.544965	−	0.838459i	$-0.316543\pi$
$89$	10.2824	1.08993	0.544965	+	0.838459i	$0.316543\pi$
$90$	12.2879	1.29526
$91$	1.87785	0.196852
$92$	20.7850	2.16698
$93$	−6.71556	−0.696372
$94$	−23.5418	−2.42815
$95$	2.28368	0.234300
$96$	5.27253	0.538125
$97$	2.14588	0.217881	0.108941	−	0.994048i	$-0.465254\pi$
$97$	2.14588	0.217881	0.108941	+	0.994048i	$0.465254\pi$
$98$	15.7172	1.58768
$99$	−6.31087	−0.634267
$100$	6.64660	0.664660
$101$	−1.85823	−0.184900	−0.0924502	−	0.995717i	$-0.529470\pi$
$101$	−1.85823	−0.184900	−0.0924502	+	0.995717i	$0.529470\pi$
$102$	2.97910	0.294975
$103$	−18.0753	−1.78102	−0.890508	−	0.454968i	$-0.849651\pi$
$103$	−18.0753	−1.78102	−0.890508	+	0.454968i	$0.849651\pi$
$104$	13.5052	1.32429
$105$	−1.09444	−0.106807
$106$	−10.6346	−1.03292
$107$	−15.7549	−1.52308	−0.761540	−	0.648118i	$-0.775556\pi$
$107$	−15.7549	−1.52308	−0.761540	+	0.648118i	$0.775556\pi$
$108$	−16.4278	−1.58076
$109$	−8.38875	−0.803496	−0.401748	−	0.915750i	$-0.631597\pi$
$109$	−8.38875	−0.803496	−0.401748	+	0.915750i	$0.631597\pi$
$110$	−19.0940	−1.82054
$111$	0.992330	0.0941878
$112$	−0.122427	−0.0115682
$113$	18.7329	1.76224	0.881121	−	0.472890i	$-0.156789\pi$
$113$	18.7329	1.76224	0.881121	+	0.472890i	$0.156789\pi$
$114$	−1.97013	−0.184519
$115$	16.6760	1.55505
$116$	−23.3465	−2.16767
$117$	9.08721	0.840113
$118$	−1.90559	−0.175424
$119$	0.543027	0.0497792
$120$	−7.87103	−0.718524
$121$	−1.19364	−0.108512
$122$	−18.6075	−1.68464
$123$	3.24330	0.292439
$124$	−22.3385	−2.00606
$125$	−7.90896	−0.707399
$126$	−1.93230	−0.172143
$127$	−12.5022	−1.10939	−0.554696	−	0.832053i	$-0.687165\pi$
$127$	−12.5022	−1.10939	−0.554696	+	0.832053i	$0.687165\pi$
$128$	18.8921	1.66984
$129$	−8.68305	−0.764500
$130$	27.4941	2.41139
$131$	−21.2056	−1.85274	−0.926369	−	0.376617i	$-0.877087\pi$
$131$	−21.2056	−1.85274	−0.926369	+	0.376617i	$0.877087\pi$
$132$	10.2574	0.892793
$133$	−0.359112	−0.0311390
$134$	0.621556	0.0536942
$135$	−13.1802	−1.13437
$136$	3.90536	0.334882
$137$	−5.53119	−0.472562	−0.236281	−	0.971685i	$-0.575929\pi$
$137$	−5.53119	−0.472562	−0.236281	+	0.971685i	$0.575929\pi$
$138$	−14.3864	−1.22465
$139$	9.50998	0.806626	0.403313	−	0.915062i	$-0.367859\pi$
$139$	9.50998	0.806626	0.403313	+	0.915062i	$0.367859\pi$
$140$	−3.64052	−0.307680
$141$	10.1466	0.854500
$142$	16.3862	1.37510
$143$	−14.1205	−1.18081
$144$	−0.592442	−0.0493702
$145$	−18.7312	−1.55554
$146$	15.4711	1.28040
$147$	−6.77421	−0.558727
$148$	3.30086	0.271329
$149$	8.58013	0.702912	0.351456	−	0.936204i	$-0.385687\pi$
$149$	8.58013	0.702912	0.351456	+	0.936204i	$0.385687\pi$
$150$	−4.60046	−0.375626
$151$	−18.7964	−1.52963	−0.764815	−	0.644250i	$-0.777170\pi$
$151$	−18.7964	−1.52963	−0.764815	+	0.644250i	$0.777170\pi$
$152$	−2.58267	−0.209483
$153$	2.62779	0.212444
$154$	3.00257	0.241954
$155$	−17.9224	−1.43956
$156$	−14.7700	−1.18254
$157$	−14.1898	−1.13247	−0.566233	−	0.824245i	$-0.691600\pi$
$157$	−14.1898	−1.13247	−0.566233	+	0.824245i	$0.691600\pi$
$158$	−35.2198	−2.80194
$159$	4.58357	0.363501
$160$	14.0713	1.11243
$161$	−2.62233	−0.206669
$162$	−2.54916	−0.200281
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	10.7884	0.842435
$165$	8.22964	0.640676
$166$	21.7571	1.68868
$167$	−0.535603	−0.0414462	−0.0207231	−	0.999785i	$-0.506597\pi$
$167$	−0.535603	−0.0414462	−0.0207231	+	0.999785i	$0.506597\pi$
$168$	1.23773	0.0954933
$169$	7.33248	0.564037
$170$	7.95059	0.609782
$171$	−1.73780	−0.132893
$172$	−28.8831	−2.20232
$173$	−3.93319	−0.299035	−0.149517	−	0.988759i	$-0.547772\pi$
$173$	−3.93319	−0.299035	−0.149517	+	0.988759i	$0.547772\pi$
$174$	16.1594	1.22504
$175$	−0.838566	−0.0633896
$176$	0.920587	0.0693918
$177$	0.821321	0.0617343
$178$	−23.6737	−1.77442
$179$	−6.64936	−0.496997	−0.248498	−	0.968632i	$-0.579937\pi$
$179$	−6.64936	−0.496997	−0.248498	+	0.968632i	$0.579937\pi$
$180$	−17.6171	−1.31310
$181$	23.7349	1.76420	0.882100	−	0.471062i	$-0.156129\pi$
$181$	23.7349	1.76420	0.882100	+	0.471062i	$0.156129\pi$
$182$	−4.32349	−0.320478
$183$	8.01992	0.592849
$184$	−18.8594	−1.39033
$185$	2.64832	0.194708
$186$	15.4617	1.13370
$187$	−4.08328	−0.298599
$188$	33.7515	2.46158
$189$	2.07261	0.150760
$190$	−5.25785	−0.381444
$191$	−18.6836	−1.35190	−0.675950	−	0.736947i	$-0.736267\pi$
$191$	−18.6836	−1.35190	−0.675950	+	0.736947i	$0.736267\pi$
$192$	−12.7227	−0.918182
$193$	−23.7557	−1.70997	−0.854985	−	0.518653i	$-0.826434\pi$
$193$	−23.7557	−1.70997	−0.854985	+	0.518653i	$0.826434\pi$
$194$	−4.94059	−0.354714
$195$	−11.8501	−0.848603
$196$	−22.5336	−1.60954
$197$	−21.2938	−1.51712	−0.758562	−	0.651601i	$-0.774098\pi$
$197$	−21.2938	−1.51712	−0.758562	+	0.651601i	$0.774098\pi$
$198$	14.5299	1.03260
$199$	3.92639	0.278335	0.139167	−	0.990269i	$-0.455557\pi$
$199$	3.92639	0.278335	0.139167	+	0.990269i	$0.455557\pi$
$200$	−6.03083	−0.426444
$201$	−0.267894	−0.0188958
$202$	4.27831	0.301021
$203$	2.94551	0.206734
$204$	−4.27110	−0.299037
$205$	8.65568	0.604539
$206$	41.6159	2.89952
$207$	−12.6899	−0.882007
$208$	−1.32558	−0.0919124
$209$	2.70034	0.186786
$210$	2.51980	0.173883
$211$	4.47251	0.307901	0.153950	−	0.988079i	$-0.450800\pi$
$211$	4.47251	0.307901	0.153950	+	0.988079i	$0.450800\pi$
$212$	15.2467	1.04715
$213$	−7.06257	−0.483919
$214$	36.2734	2.47960
$215$	−23.1732	−1.58040
$216$	14.9059	1.01421
$217$	2.81833	0.191321
$218$	19.3139	1.30810
$219$	−6.66815	−0.450592
$220$	27.3749	1.84561
$221$	5.87964	0.395507
$222$	−2.28470	−0.153339
$223$	5.76910	0.386328	0.193164	−	0.981167i	$-0.438125\pi$
$223$	5.76910	0.386328	0.193164	+	0.981167i	$0.438125\pi$
$224$	−2.21273	−0.147844
$225$	−4.05795	−0.270530
$226$	−43.1299	−2.86896
$227$	5.63786	0.374198	0.187099	−	0.982341i	$-0.440091\pi$
$227$	5.63786	0.374198	0.187099	+	0.982341i	$0.440091\pi$
$228$	2.82454	0.187060
$229$	−22.9035	−1.51351	−0.756754	−	0.653700i	$-0.773216\pi$
$229$	−22.9035	−1.51351	−0.756754	+	0.653700i	$0.773216\pi$
$230$	−38.3942	−2.53164
$231$	−1.29412	−0.0851472
$232$	21.1836	1.39077
$233$	24.2262	1.58711	0.793555	−	0.608499i	$-0.208228\pi$
$233$	24.2262	1.58711	0.793555	+	0.608499i	$0.208228\pi$
$234$	−20.9220	−1.36772
$235$	27.0792	1.76645
$236$	2.73202	0.177839
$237$	15.1799	0.986043
$238$	−1.25024	−0.0810413
$239$	1.27086	0.0822052	0.0411026	−	0.999155i	$-0.486913\pi$
$239$	1.27086	0.0822052	0.0411026	+	0.999155i	$0.486913\pi$
$240$	0.772569	0.0498691
$241$	0.0203602	0.00131152	0.000655758	−	1.00000i	$-0.499791\pi$
$241$	0.0203602	0.00131152	0.000655758		1.00000i	$0.499791\pi$
$242$	2.74818	0.176660
$243$	16.0291	1.02827
$244$	26.6773	1.70784
$245$	−18.0789	−1.15502
$246$	−7.46725	−0.476094
$247$	−3.88830	−0.247407
$248$	20.2690	1.28708
$249$	−9.37745	−0.594272
$250$	18.2093	1.15166
$251$	5.60461	0.353760	0.176880	−	0.984232i	$-0.443400\pi$
$251$	5.60461	0.353760	0.176880	+	0.984232i	$0.443400\pi$
$252$	2.77031	0.174513
$253$	19.7186	1.23970
$254$	28.7846	1.80611
$255$	−3.42675	−0.214591
$256$	−17.8543	−1.11590
$257$	18.8438	1.17545	0.587723	−	0.809062i	$-0.300024\pi$
$257$	18.8438	1.17545	0.587723	+	0.809062i	$0.300024\pi$
$258$	19.9915	1.24462
$259$	−0.416453	−0.0258771
$260$	−39.4179	−2.44459
$261$	14.2538	0.882287
$262$	48.8228	3.01628
$263$	−11.3766	−0.701514	−0.350757	−	0.936467i	$-0.614076\pi$
$263$	−11.3766	−0.701514	−0.350757	+	0.936467i	$0.614076\pi$
$264$	−9.30713	−0.572814
$265$	12.2326	0.751441
$266$	0.826806	0.0506947
$267$	10.2035	0.624445
$268$	−0.891116	−0.0544336
$269$	−20.2278	−1.23331	−0.616656	−	0.787232i	$-0.711513\pi$
$269$	−20.2278	−1.23331	−0.616656	+	0.787232i	$0.711513\pi$
$270$	30.3456	1.84677
$271$	−14.2967	−0.868464	−0.434232	−	0.900801i	$-0.642980\pi$
$271$	−14.2967	−0.868464	−0.434232	+	0.900801i	$0.642980\pi$
$272$	−0.383324	−0.0232424
$273$	1.86345	0.112781
$274$	12.7348	0.769337
$275$	6.30559	0.380241
$276$	20.6256	1.24151
$277$	−9.36614	−0.562757	−0.281378	−	0.959597i	$-0.590792\pi$
$277$	−9.36614	−0.562757	−0.281378	+	0.959597i	$0.590792\pi$
$278$	−21.8954	−1.31320
$279$	13.6383	0.816506
$280$	3.30325	0.197407
$281$	−23.3083	−1.39046	−0.695228	−	0.718789i	$-0.744697\pi$
$281$	−23.3083	−1.39046	−0.695228	+	0.718789i	$0.744697\pi$
$282$	−23.3612	−1.39114
$283$	5.07182	0.301488	0.150744	−	0.988573i	$-0.451833\pi$
$283$	5.07182	0.301488	0.150744	+	0.988573i	$0.451833\pi$
$284$	−23.4927	−1.39404
$285$	2.26616	0.134236
$286$	32.5104	1.92238
$287$	−1.36112	−0.0803444
$288$	−10.7077	−0.630960
$289$	−15.2998	−0.899986
$290$	43.1259	2.53244
$291$	2.12942	0.124829
$292$	−22.1808	−1.29803
$293$	−15.7436	−0.919751	−0.459876	−	0.887983i	$-0.652106\pi$
$293$	−15.7436	−0.919751	−0.459876	+	0.887983i	$0.652106\pi$
$294$	15.5967	0.909617
$295$	2.19193	0.127619
$296$	−2.99506	−0.174084
$297$	−15.5850	−0.904331
$298$	−19.7546	−1.14435
$299$	−28.3934	−1.64203
$300$	6.59562	0.380798
$301$	3.64403	0.210038
$302$	43.2761	2.49026
$303$	−1.84398	−0.105934
$304$	0.253498	0.0145391
$305$	21.4035	1.22556
$306$	−6.05013	−0.345863
$307$	24.3434	1.38935	0.694675	−	0.719324i	$-0.255548\pi$
$307$	24.3434	1.38935	0.694675	+	0.719324i	$0.255548\pi$
$308$	−4.30474	−0.245286
$309$	−17.9367	−1.02038
$310$	41.2639	2.34363
$311$	−11.2859	−0.639965	−0.319983	−	0.947423i	$-0.603677\pi$
$311$	−11.2859	−0.639965	−0.319983	+	0.947423i	$0.603677\pi$
$312$	13.4016	0.758716
$313$	8.51744	0.481434	0.240717	−	0.970595i	$-0.422617\pi$
$313$	8.51744	0.481434	0.240717	+	0.970595i	$0.422617\pi$
$314$	32.6700	1.84367
$315$	2.22265	0.125232
$316$	50.4942	2.84052
$317$	20.9549	1.17694	0.588472	−	0.808517i	$-0.299730\pi$
$317$	20.9549	1.17694	0.588472	+	0.808517i	$0.299730\pi$
$318$	−10.5530	−0.591785
$319$	−22.1487	−1.24009
$320$	−33.9542	−1.89810
$321$	−15.6340	−0.872606
$322$	6.03755	0.336460
$323$	−1.12440	−0.0625632
$324$	3.65470	0.203039
$325$	−9.07960	−0.503646
$326$	−2.30236	−0.127516
$327$	−8.32441	−0.460341
$328$	−9.78895	−0.540504
$329$	−4.25825	−0.234765
$330$	−18.9476	−1.04303
$331$	−17.0855	−0.939103	−0.469551	−	0.882905i	$-0.655584\pi$
$331$	−17.0855	−0.939103	−0.469551	+	0.882905i	$0.655584\pi$
$332$	−31.1929	−1.71193
$333$	−2.01528	−0.110437
$334$	1.23315	0.0674751
$335$	−0.714952	−0.0390620
$336$	−0.121488	−0.00662770
$337$	28.3580	1.54476	0.772379	−	0.635162i	$-0.219067\pi$
$337$	28.3580	1.54476	0.772379	+	0.635162i	$0.219067\pi$
$338$	−16.8820	−0.918260
$339$	18.5892	1.00963
$340$	−11.3987	−0.618179
$341$	−21.1924	−1.14763
$342$	4.00104	0.216352
$343$	5.75811	0.310909
$344$	26.2072	1.41300
$345$	16.5481	0.890921
$346$	9.05561	0.486833
$347$	−3.38206	−0.181559	−0.0907794	−	0.995871i	$-0.528936\pi$
$347$	−3.38206	−0.181559	−0.0907794	+	0.995871i	$0.528936\pi$
$348$	−23.1675	−1.24191
$349$	−4.06257	−0.217464	−0.108732	−	0.994071i	$-0.534679\pi$
$349$	−4.06257	−0.217464	−0.108732	+	0.994071i	$0.534679\pi$
$350$	1.93068	0.103199
$351$	22.4412	1.19782
$352$	16.6386	0.886840
$353$	−3.61031	−0.192157	−0.0960786	−	0.995374i	$-0.530630\pi$
$353$	−3.61031	−0.192157	−0.0960786	+	0.995374i	$0.530630\pi$
$354$	−1.89098	−0.100504
$355$	−18.8485	−1.00037
$356$	33.9407	1.79885
$357$	0.538862	0.0285196
$358$	15.3092	0.809118
$359$	−1.21583	−0.0641690	−0.0320845	−	0.999485i	$-0.510215\pi$
$359$	−1.21583	−0.0641690	−0.0320845	+	0.999485i	$0.510215\pi$
$360$	15.9849	0.842480
$361$	−18.2564	−0.960864
$362$	−54.6463	−2.87214
$363$	−1.18448	−0.0621691
$364$	6.19853	0.324891
$365$	−17.7959	−0.931478
$366$	−18.4647	−0.965167
$367$	5.46520	0.285281	0.142641	−	0.989775i	$-0.454441\pi$
$367$	5.46520	0.285281	0.142641	+	0.989775i	$0.454441\pi$
$368$	1.85111	0.0964959
$369$	−6.58668	−0.342889
$370$	−6.09738	−0.316988
$371$	−1.92359	−0.0998681
$372$	−22.1672	−1.14931
$373$	24.7840	1.28326	0.641632	−	0.767012i	$-0.278257\pi$
$373$	24.7840	1.28326	0.641632	+	0.767012i	$0.278257\pi$
$374$	9.40119	0.486124
$375$	−7.84830	−0.405285
$376$	−30.6246	−1.57934
$377$	31.8926	1.64255
$378$	−4.77189	−0.245440
$379$	6.38786	0.328123	0.164061	−	0.986450i	$-0.447541\pi$
$379$	6.38786	0.328123	0.164061	+	0.986450i	$0.447541\pi$
$380$	7.53811	0.386697
$381$	−12.4063	−0.635595
$382$	43.0165	2.20091
$383$	20.9784	1.07195	0.535974	−	0.844234i	$-0.319944\pi$
$383$	20.9784	1.07195	0.535974	+	0.844234i	$0.319944\pi$
$384$	18.7472	0.956689
$385$	−3.45374	−0.176019
$386$	54.6941	2.78386
$387$	17.6340	0.896388
$388$	7.08326	0.359598
$389$	34.7212	1.76043	0.880216	−	0.474572i	$-0.157397\pi$
$389$	34.7212	1.76043	0.880216	+	0.474572i	$0.157397\pi$
$390$	27.2832	1.38154
$391$	−8.21065	−0.415230
$392$	20.4460	1.03268
$393$	−21.0429	−1.06147
$394$	49.0261	2.46990
$395$	40.5120	2.03838
$396$	−20.8313	−1.04681
$397$	−17.0560	−0.856017	−0.428008	−	0.903775i	$-0.640785\pi$
$397$	−17.0560	−0.856017	−0.428008	+	0.903775i	$0.640785\pi$
$398$	−9.03998	−0.453133
$399$	−0.356358	−0.0178402
$400$	0.591946	0.0295973
$401$	−6.09141	−0.304191	−0.152095	−	0.988366i	$-0.548602\pi$
$401$	−6.09141	−0.304191	−0.152095	+	0.988366i	$0.548602\pi$
$402$	0.616789	0.0307626
$403$	30.5156	1.52009
$404$	−6.13375	−0.305166
$405$	2.93221	0.145702
$406$	−6.78162	−0.336566
$407$	3.13151	0.155223
$408$	3.87541	0.191861
$409$	5.07564	0.250974	0.125487	−	0.992095i	$-0.459951\pi$
$409$	5.07564	0.250974	0.125487	+	0.992095i	$0.459951\pi$
$410$	−19.9285	−0.984198
$411$	−5.48877	−0.270741
$412$	−59.6642	−2.93945
$413$	−0.344685	−0.0169608
$414$	29.2167	1.43592
$415$	−25.0264	−1.22850
$416$	−23.9584	−1.17466
$417$	9.43704	0.462134
$418$	−6.21716	−0.304091
$419$	35.1874	1.71902	0.859508	−	0.511122i	$-0.170770\pi$
$419$	35.1874	1.71902	0.859508	+	0.511122i	$0.170770\pi$
$420$	−3.61260	−0.176277
$421$	16.1000	0.784664	0.392332	−	0.919824i	$-0.371668\pi$
$421$	16.1000	0.784664	0.392332	+	0.919824i	$0.371668\pi$
$422$	−10.2973	−0.501267
$423$	−20.6063	−1.00191
$424$	−13.8342	−0.671847
$425$	−2.62559	−0.127360
$426$	16.2606	0.787827
$427$	−3.36573	−0.162879
$428$	−52.0046	−2.51374
$429$	−14.0122	−0.676514
$430$	53.3531	2.57292
$431$	8.30003	0.399798	0.199899	−	0.979816i	$-0.435939\pi$
$431$	8.30003	0.399798	0.199899	+	0.979816i	$0.435939\pi$
$432$	−1.46306	−0.0703915
$433$	1.72178	0.0827433	0.0413717	−	0.999144i	$-0.486827\pi$
$433$	1.72178	0.0827433	0.0413717	+	0.999144i	$0.486827\pi$
$434$	−6.48881	−0.311473
$435$	−18.5875	−0.891203
$436$	−27.6901	−1.32612
$437$	5.42983	0.259744
$438$	15.3525	0.733570
$439$	−2.59604	−0.123902	−0.0619512	−	0.998079i	$-0.519732\pi$
$439$	−2.59604	−0.123902	−0.0619512	+	0.998079i	$0.519732\pi$
$440$	−24.8387	−1.18414
$441$	13.7574	0.655116
$442$	−13.5371	−0.643892
$443$	−24.9559	−1.18569	−0.592845	−	0.805317i	$-0.701995\pi$
$443$	−24.9559	−1.18569	−0.592845	+	0.805317i	$0.701995\pi$
$444$	3.27555	0.155451
$445$	27.2310	1.29087
$446$	−13.2826	−0.628947
$447$	8.51433	0.402714
$448$	5.33936	0.252261
$449$	−21.9609	−1.03640	−0.518200	−	0.855259i	$-0.673398\pi$
$449$	−21.9609	−1.03640	−0.518200	+	0.855259i	$0.673398\pi$
$450$	9.34287	0.440427
$451$	10.2349	0.481944
$452$	61.8347	2.90846
$453$	−18.6522	−0.876359
$454$	−12.9804	−0.609200
$455$	4.97315	0.233145
$456$	−2.56287	−0.120017
$457$	39.8555	1.86436	0.932180	−	0.361996i	$-0.117904\pi$
$457$	39.8555	1.86436	0.932180	+	0.361996i	$0.117904\pi$
$458$	52.7322	2.46401
$459$	6.48944	0.302901
$460$	55.0453	2.56650
$461$	−2.93915	−0.136890	−0.0684449	−	0.997655i	$-0.521804\pi$
$461$	−2.93915	−0.136890	−0.0684449	+	0.997655i	$0.521804\pi$
$462$	2.97954	0.138621
$463$	8.15189	0.378850	0.189425	−	0.981895i	$-0.439338\pi$
$463$	8.15189	0.378850	0.189425	+	0.981895i	$0.439338\pi$
$464$	−2.07924	−0.0965265
$465$	−17.7850	−0.824758
$466$	−55.7774	−2.58384
$467$	2.68470	0.124233	0.0621165	−	0.998069i	$-0.480215\pi$
$467$	2.68470	0.124233	0.0621165	+	0.998069i	$0.480215\pi$
$468$	29.9956	1.38655
$469$	0.112427	0.00519142
$470$	−62.3461	−2.87581
$471$	−14.0809	−0.648815
$472$	−2.47892	−0.114101
$473$	−27.4012	−1.25991
$474$	−34.9497	−1.60529
$475$	1.73635	0.0796690
$476$	1.79246	0.0821572
$477$	−9.30858	−0.426210
$478$	−2.92598	−0.133831
$479$	−31.2203	−1.42649	−0.713247	−	0.700913i	$-0.752776\pi$
$479$	−31.2203	−1.42649	−0.713247	+	0.700913i	$0.752776\pi$
$480$	13.9633	0.637336
$481$	−4.50915	−0.205600
$482$	−0.0468765	−0.00213517
$483$	−2.60222	−0.118405
$484$	−3.94003	−0.179092
$485$	5.68297	0.258050
$486$	−36.9049	−1.67404
$487$	−27.7254	−1.25636	−0.628179	−	0.778069i	$-0.716199\pi$
$487$	−27.7254	−1.25636	−0.628179	+	0.778069i	$0.716199\pi$
$488$	−24.2058	−1.09574
$489$	0.992330	0.0448747
$490$	41.6242	1.88039
$491$	−40.1209	−1.81063	−0.905315	−	0.424740i	$-0.860366\pi$
$491$	−40.1209	−1.81063	−0.905315	+	0.424740i	$0.860366\pi$
$492$	10.7057	0.482650
$493$	9.22253	0.415362
$494$	8.95227	0.402782
$495$	−16.7132	−0.751203
$496$	−1.98947	−0.0893297
$497$	2.96396	0.132952
$498$	21.5903	0.967483
$499$	−25.8077	−1.15531	−0.577656	−	0.816280i	$-0.696032\pi$
$499$	−25.8077	−1.15531	−0.577656	+	0.816280i	$0.696032\pi$
$500$	−26.1064	−1.16751
$501$	−0.531495	−0.0237455
$502$	−12.9038	−0.575926
$503$	−19.4862	−0.868848	−0.434424	−	0.900708i	$-0.643048\pi$
$503$	−19.4862	−0.868848	−0.434424	+	0.900708i	$0.643048\pi$
$504$	−2.51366	−0.111967
$505$	−4.92118	−0.218990
$506$	−45.3993	−2.01825
$507$	7.27624	0.323149
$508$	−41.2681	−1.83098
$509$	33.1019	1.46721	0.733607	−	0.679574i	$-0.237835\pi$
$509$	33.1019	1.46721	0.733607	+	0.679574i	$0.237835\pi$
$510$	7.88961	0.349358
$511$	2.79843	0.123795
$512$	3.32292	0.146854
$513$	−4.29157	−0.189477
$514$	−43.3853	−1.91364
$515$	−47.8692	−2.10937
$516$	−28.6616	−1.26176
$517$	32.0199	1.40823
$518$	0.958824	0.0421283
$519$	−3.90302	−0.171324
$520$	35.7660	1.56844
$521$	3.34883	0.146715	0.0733574	−	0.997306i	$-0.476629\pi$
$521$	3.34883	0.146715	0.0733574	+	0.997306i	$0.476629\pi$
$522$	−32.8173	−1.43638
$523$	39.1620	1.71243	0.856216	−	0.516618i	$-0.172809\pi$
$523$	39.1620	1.71243	0.856216	+	0.516618i	$0.172809\pi$
$524$	−69.9967	−3.05782
$525$	−0.832135	−0.0363173
$526$	26.1931	1.14207
$527$	8.82433	0.384394
$528$	0.913526	0.0397561
$529$	16.6501	0.723916
$530$	−28.1638	−1.22336
$531$	−1.66798	−0.0723844
$532$	−1.18538	−0.0513928
$533$	−14.7376	−0.638355
$534$	−23.4922	−1.01661
$535$	−41.7239	−1.80388
$536$	0.808559	0.0349244
$537$	−6.59837	−0.284741
$538$	46.5718	2.00785
$539$	−21.3775	−0.920793
$540$	−43.5060	−1.87220
$541$	−26.6809	−1.14710	−0.573551	−	0.819170i	$-0.694435\pi$
$541$	−26.6809	−1.14710	−0.573551	+	0.819170i	$0.694435\pi$
$542$	32.9162	1.41387
$543$	23.5528	1.01075
$544$	−6.92817	−0.297043
$545$	−22.2161	−0.951632
$546$	−4.29033	−0.183609
$547$	12.8920	0.551220	0.275610	−	0.961269i	$-0.411120\pi$
$547$	12.8920	0.551220	0.275610	+	0.961269i	$0.411120\pi$
$548$	−18.2577	−0.779931
$549$	−16.2873	−0.695125
$550$	−14.5177	−0.619038
$551$	−6.09901	−0.259826
$552$	−18.7147	−0.796552
$553$	−6.37059	−0.270905
$554$	21.5642	0.916176
$555$	2.62801	0.111553
$556$	31.3911	1.33128
$557$	0.582353	0.0246751	0.0123375	−	0.999924i	$-0.496073\pi$
$557$	0.582353	0.0246751	0.0123375	+	0.999924i	$0.496073\pi$
$558$	−31.4004	−1.32928
$559$	39.4558	1.66880
$560$	−0.324225	−0.0137010
$561$	−4.05197	−0.171074
$562$	53.6641	2.26368
$563$	37.2513	1.56995	0.784977	−	0.619525i	$-0.212675\pi$
$563$	37.2513	1.56995	0.784977	+	0.619525i	$0.212675\pi$
$564$	33.4926	1.41029
$565$	49.6107	2.08714
$566$	−11.6772	−0.490828
$567$	−0.461094	−0.0193641
$568$	21.3163	0.894411
$569$	−11.4504	−0.480026	−0.240013	−	0.970770i	$-0.577152\pi$
$569$	−11.4504	−0.480026	−0.240013	+	0.970770i	$0.577152\pi$
$570$	−5.21752	−0.218538
$571$	20.6967	0.866131	0.433065	−	0.901363i	$-0.357432\pi$
$571$	20.6967	0.866131	0.433065	+	0.901363i	$0.357432\pi$
$572$	−46.6098	−1.94885
$573$	−18.5403	−0.774534
$574$	3.13379	0.130802
$575$	12.6792	0.528761
$576$	25.8380	1.07658
$577$	−41.3809	−1.72271	−0.861354	−	0.508005i	$-0.830383\pi$
$577$	−41.3809	−1.72271	−0.861354	+	0.508005i	$0.830383\pi$
$578$	35.2256	1.46519
$579$	−23.5735	−0.979680
$580$	−61.8290	−2.56731
$581$	3.93545	0.163270
$582$	−4.90270	−0.203223
$583$	14.4644	0.599056
$584$	20.1258	0.832814
$585$	24.0658	0.995000
$586$	36.2475	1.49737
$587$	−29.3539	−1.21157	−0.605783	−	0.795630i	$-0.707140\pi$
$587$	−29.3539	−1.21157	−0.605783	+	0.795630i	$0.707140\pi$
$588$	−22.3607	−0.922142
$589$	−5.83567	−0.240455
$590$	−5.04661	−0.207766
$591$	−21.1305	−0.869194
$592$	0.293975	0.0120823
$593$	26.9943	1.10852	0.554261	−	0.832343i	$-0.313001\pi$
$593$	26.9943	1.10852	0.554261	+	0.832343i	$0.313001\pi$
$594$	35.8822	1.47226
$595$	1.43811	0.0589567
$596$	28.3219	1.16011
$597$	3.89628	0.159464
$598$	65.3718	2.67325
$599$	−6.48166	−0.264833	−0.132417	−	0.991194i	$-0.542274\pi$
$599$	−6.48166	−0.264833	−0.132417	+	0.991194i	$0.542274\pi$
$600$	−5.98457	−0.244319
$601$	−27.0876	−1.10493	−0.552464	−	0.833537i	$-0.686312\pi$
$601$	−27.0876	−1.10493	−0.552464	+	0.833537i	$0.686312\pi$
$602$	−8.38987	−0.341946
$603$	0.544054	0.0221556
$604$	−62.0444	−2.52455
$605$	−3.16113	−0.128518
$606$	4.24550	0.172461
$607$	26.0982	1.05929	0.529647	−	0.848218i	$-0.322324\pi$
$607$	26.0982	1.05929	0.529647	+	0.848218i	$0.322324\pi$
$608$	4.58171	0.185813
$609$	2.92292	0.118443
$610$	−49.2785	−1.99523
$611$	−46.1063	−1.86526
$612$	8.67399	0.350625
$613$	−21.0031	−0.848309	−0.424154	−	0.905590i	$-0.639429\pi$
$613$	−21.0031	−0.848309	−0.424154	+	0.905590i	$0.639429\pi$
$614$	−56.0472	−2.26188
$615$	8.58929	0.346354
$616$	3.90593	0.157375
$617$	−37.9312	−1.52705	−0.763525	−	0.645778i	$-0.776533\pi$
$617$	−37.9312	−1.52705	−0.763525	+	0.645778i	$0.776533\pi$
$618$	41.2968	1.66120
$619$	48.2058	1.93756	0.968778	−	0.247929i	$-0.0797499\pi$
$619$	48.2058	1.93756	0.968778	+	0.247929i	$0.0797499\pi$
$620$	−59.1594	−2.37590
$621$	−31.3382	−1.25756
$622$	25.9842	1.04187
$623$	−4.28212	−0.171560
$624$	−1.31541	−0.0526587
$625$	−31.0134	−1.24054
$626$	−19.6102	−0.783782
$627$	2.67963	0.107014
$628$	−46.8385	−1.86906
$629$	−1.30393	−0.0519913
$630$	−5.11735	−0.203880
$631$	−1.99282	−0.0793330	−0.0396665	−	0.999213i	$-0.512630\pi$
$631$	−1.99282	−0.0793330	−0.0396665	+	0.999213i	$0.512630\pi$
$632$	−45.8162	−1.82247
$633$	4.43821	0.176403
$634$	−48.2457	−1.91608
$635$	−33.1098	−1.31392
$636$	15.1298	0.599934
$637$	30.7820	1.21963
$638$	50.9943	2.01889
$639$	14.3431	0.567402
$640$	50.0323	1.97770
$641$	−26.8824	−1.06179	−0.530896	−	0.847437i	$-0.678145\pi$
$641$	−26.8824	−1.06179	−0.530896	+	0.847437i	$0.678145\pi$
$642$	35.9952	1.42062
$643$	−16.3657	−0.645401	−0.322700	−	0.946501i	$-0.604591\pi$
$643$	−16.3657	−0.645401	−0.322700	+	0.946501i	$0.604591\pi$
$644$	−8.65596	−0.341093
$645$	−22.9955	−0.905447
$646$	2.58877	0.101854
$647$	3.48771	0.137116	0.0685579	−	0.997647i	$-0.478160\pi$
$647$	3.48771	0.137116	0.0685579	+	0.997647i	$0.478160\pi$
$648$	−3.31611	−0.130269
$649$	2.59185	0.101739
$650$	20.9045	0.819943
$651$	2.79672	0.109612
$652$	3.30086	0.129272
$653$	38.1388	1.49249	0.746243	−	0.665674i	$-0.231856\pi$
$653$	38.1388	1.49249	0.746243	+	0.665674i	$0.231856\pi$
$654$	19.1658	0.749442
$655$	−56.1591	−2.19432
$656$	0.960819	0.0375137
$657$	13.5420	0.528326
$658$	9.80403	0.382201
$659$	−45.2418	−1.76237	−0.881186	−	0.472770i	$-0.843254\pi$
$659$	−45.2418	−1.76237	−0.881186	+	0.472770i	$0.843254\pi$
$660$	27.1649	1.05739
$661$	3.03927	0.118214	0.0591070	−	0.998252i	$-0.481175\pi$
$661$	3.03927	0.118214	0.0591070	+	0.998252i	$0.481175\pi$
$662$	39.3369	1.52887
$663$	5.83455	0.226595
$664$	28.3031	1.09837
$665$	−0.951044	−0.0368799
$666$	4.63990	0.179793
$667$	−44.5366	−1.72446
$668$	−1.76795	−0.0684042
$669$	5.72486	0.221336
$670$	1.64608	0.0635935
$671$	25.3086	0.977026
$672$	−2.19576	−0.0847033
$673$	−12.0153	−0.463158	−0.231579	−	0.972816i	$-0.574389\pi$
$673$	−12.0153	−0.463158	−0.231579	+	0.972816i	$0.574389\pi$
$674$	−65.2903	−2.51489
$675$	−10.0213	−0.385719
$676$	24.2035	0.930904
$677$	29.5319	1.13500	0.567501	−	0.823373i	$-0.307910\pi$
$677$	29.5319	1.13500	0.567501	+	0.823373i	$0.307910\pi$
$678$	−42.7991	−1.64369
$679$	−0.893657	−0.0342954
$680$	10.3426	0.396622
$681$	5.59462	0.214386
$682$	48.7926	1.86836
$683$	28.2925	1.08258	0.541292	−	0.840835i	$-0.317935\pi$
$683$	28.2925	1.08258	0.541292	+	0.840835i	$0.317935\pi$
$684$	−5.73624	−0.219331
$685$	−14.6484	−0.559685
$686$	−13.2573	−0.506164
$687$	−22.7279	−0.867122
$688$	−2.57233	−0.0980692
$689$	−20.8278	−0.793475
$690$	−38.0997	−1.45043
$691$	−25.4812	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$691$	−25.4812	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$692$	−12.9829	−0.493536
$693$	2.62818	0.0998363
$694$	7.78673	0.295580
$695$	25.1855	0.955339
$696$	21.0211	0.796804
$697$	−4.26173	−0.161425
$698$	9.35350	0.354035
$699$	24.0404	0.909290
$700$	−2.76799	−0.104620
$701$	1.70851	0.0645296	0.0322648	−	0.999479i	$-0.489728\pi$
$701$	1.70851	0.0645296	0.0322648	+	0.999479i	$0.489728\pi$
$702$	−51.6678	−1.95008
$703$	0.862312	0.0325227
$704$	−40.1492	−1.51318
$705$	26.8715	1.01204
$706$	8.31223	0.312835
$707$	0.773864	0.0291041
$708$	2.71107	0.101888
$709$	−18.8090	−0.706387	−0.353194	−	0.935550i	$-0.614904\pi$
$709$	−18.8090	−0.706387	−0.353194	+	0.935550i	$0.614904\pi$
$710$	43.3960	1.62862
$711$	−30.8283	−1.15615
$712$	−30.7963	−1.15414
$713$	−42.6136	−1.59589
$714$	−1.24066	−0.0464303
$715$	−37.3955	−1.39851
$716$	−21.9486	−0.820259
$717$	1.26111	0.0470972
$718$	2.79927	0.104468
$719$	−24.5183	−0.914380	−0.457190	−	0.889369i	$-0.651144\pi$
$719$	−24.5183	−0.914380	−0.457190	+	0.889369i	$0.651144\pi$
$720$	−1.56898	−0.0584723
$721$	7.52752	0.280340
$722$	42.0329	1.56430
$723$	0.0202041	0.000751397 0
$724$	78.3456	2.91169
$725$	−14.2418	−0.528929
$726$	2.72710	0.101212
$727$	2.28071	0.0845870	0.0422935	−	0.999105i	$-0.486534\pi$
$727$	2.28071	0.0845870	0.0422935	+	0.999105i	$0.486534\pi$
$728$	−5.62427	−0.208449
$729$	12.5846	0.466097
$730$	40.9725	1.51646
$731$	11.4096	0.422001
$732$	26.4727	0.978457
$733$	−39.0733	−1.44320	−0.721602	−	0.692308i	$-0.756594\pi$
$733$	−39.0733	−1.44320	−0.721602	+	0.692308i	$0.756594\pi$
$734$	−12.5829	−0.464442
$735$	−17.9403	−0.661737
$736$	33.4568	1.23323
$737$	−0.845397	−0.0311406
$738$	15.1649	0.558228
$739$	−36.4645	−1.34137	−0.670684	−	0.741743i	$-0.734000\pi$
$739$	−36.4645	−1.34137	−0.670684	+	0.741743i	$0.734000\pi$
$740$	8.74174	0.321353
$741$	−3.85848	−0.141745
$742$	4.42881	0.162587
$743$	0.644866	0.0236579	0.0118289	−	0.999930i	$-0.496235\pi$
$743$	0.644866	0.0236579	0.0118289	+	0.999930i	$0.496235\pi$
$744$	20.1135	0.737397
$745$	22.7229	0.832504
$746$	−57.0616	−2.08917
$747$	19.0442	0.696793
$748$	−13.4784	−0.492818
$749$	6.56115	0.239739
$750$	18.0696	0.659809
$751$	−39.4685	−1.44023	−0.720113	−	0.693857i	$-0.755910\pi$
$751$	−39.4685	−1.44023	−0.720113	+	0.693857i	$0.755910\pi$
$752$	3.00591	0.109614
$753$	5.56163	0.202677
$754$	−73.4282	−2.67410
$755$	−49.7789	−1.81164
$756$	6.84140	0.248819
$757$	−17.0759	−0.620636	−0.310318	−	0.950633i	$-0.600436\pi$
$757$	−17.0759	−0.620636	−0.310318	+	0.950633i	$0.600436\pi$
$758$	−14.7072	−0.534188
$759$	19.5674	0.710250
$760$	−6.83975	−0.248104
$761$	33.1113	1.20028	0.600142	−	0.799893i	$-0.295111\pi$
$761$	33.1113	1.20028	0.600142	+	0.799893i	$0.295111\pi$
$762$	28.5638	1.03476
$763$	3.49352	0.126474
$764$	−61.6721	−2.23122
$765$	6.95923	0.251612
$766$	−48.2999	−1.74515
$767$	−3.73209	−0.134758
$768$	−17.7174	−0.639321
$769$	20.4347	0.736895	0.368447	−	0.929649i	$-0.379889\pi$
$769$	20.4347	0.736895	0.368447	+	0.929649i	$0.379889\pi$
$770$	7.95176	0.286562
$771$	18.6993	0.673440
$772$	−78.4142	−2.82219
$773$	−25.4036	−0.913704	−0.456852	−	0.889543i	$-0.651023\pi$
$773$	−25.4036	−0.913704	−0.456852	+	0.889543i	$0.651023\pi$
$774$	−40.5999	−1.45933
$775$	−13.6269	−0.489494
$776$	−6.42703	−0.230717
$777$	−0.413259	−0.0148256
$778$	−79.9406	−2.86601
$779$	2.81835	0.100978
$780$	−39.1155	−1.40056
$781$	−22.2874	−0.797507
$782$	18.9039	0.676001
$783$	35.2003	1.25796
$784$	−2.00684	−0.0716729
$785$	−37.5790	−1.34125
$786$	48.4484	1.72810
$787$	−11.6584	−0.415578	−0.207789	−	0.978174i	$-0.566627\pi$
$787$	−11.6584	−0.415578	−0.207789	+	0.978174i	$0.566627\pi$
$788$	−70.2881	−2.50391
$789$	−11.2894	−0.401913
$790$	−93.2733	−3.31851
$791$	−7.80137	−0.277385
$792$	18.9014	0.671633
$793$	−36.4425	−1.29411
$794$	39.2691	1.39361
$795$	12.1388	0.430518
$796$	12.9605	0.459373
$797$	−33.8379	−1.19860	−0.599300	−	0.800524i	$-0.704554\pi$
$797$	−33.8379	−1.19860	−0.599300	+	0.800524i	$0.704554\pi$
$798$	0.820465	0.0290441
$799$	−13.3328	−0.471680
$800$	10.6988	0.378259
$801$	−20.7219	−0.732171
$802$	14.0246	0.495227
$803$	−21.0428	−0.742583
$804$	−0.884282	−0.0311862
$805$	−6.94477	−0.244771
$806$	−70.2578	−2.47473
$807$	−20.0727	−0.706592
$808$	5.56550	0.195794
$809$	−5.13761	−0.180629	−0.0903143	−	0.995913i	$-0.528787\pi$
$809$	−5.13761	−0.180629	−0.0903143	+	0.995913i	$0.528787\pi$
$810$	−6.75099	−0.237206
$811$	36.9119	1.29615	0.648077	−	0.761575i	$-0.275574\pi$
$811$	36.9119	1.29615	0.648077	+	0.761575i	$0.275574\pi$
$812$	9.72273	0.341201
$813$	−14.1871	−0.497563
$814$	−7.20987	−0.252706
$815$	2.64832	0.0927666
$816$	−0.380384	−0.0133161
$817$	−7.54537	−0.263979
$818$	−11.6859	−0.408589
$819$	−3.78439	−0.132237
$820$	28.5712	0.997750
$821$	19.0303	0.664163	0.332082	−	0.943251i	$-0.392249\pi$
$821$	19.0303	0.664163	0.332082	+	0.943251i	$0.392249\pi$
$822$	12.6371	0.440770
$823$	−0.968377	−0.0337555	−0.0168777	−	0.999858i	$-0.505373\pi$
$823$	−0.968377	−0.0337555	−0.0168777	+	0.999858i	$0.505373\pi$
$824$	54.1367	1.88594
$825$	6.25723	0.217849
$826$	0.793589	0.0276125
$827$	−4.60852	−0.160254	−0.0801270	−	0.996785i	$-0.525533\pi$
$827$	−4.60852	−0.160254	−0.0801270	+	0.996785i	$0.525533\pi$
$828$	−41.8876	−1.45569
$829$	45.4756	1.57943	0.789717	−	0.613472i	$-0.210228\pi$
$829$	45.4756	1.57943	0.789717	+	0.613472i	$0.210228\pi$
$830$	57.6198	2.00001
$831$	−9.29430	−0.322416
$832$	57.8120	2.00427
$833$	8.90139	0.308415
$834$	−21.7275	−0.752361
$835$	−1.41845	−0.0490874
$836$	8.91346	0.308278
$837$	33.6804	1.16417
$838$	−81.0140	−2.79858
$839$	38.0516	1.31369	0.656844	−	0.754027i	$-0.271891\pi$
$839$	38.0516	1.31369	0.656844	+	0.754027i	$0.271891\pi$
$840$	3.27791	0.113099
$841$	21.0253	0.725009
$842$	−37.0679	−1.27744
$843$	−23.1295	−0.796624
$844$	14.7632	0.508169
$845$	19.4187	0.668025
$846$	47.4432	1.63113
$847$	0.497093	0.0170803
$848$	1.35787	0.0466295
$849$	5.03292	0.172729
$850$	6.04506	0.207344
$851$	6.29683	0.215853
$852$	−23.3126	−0.798675
$853$	33.9311	1.16178	0.580889	−	0.813983i	$-0.302705\pi$
$853$	33.9311	1.16178	0.580889	+	0.813983i	$0.302705\pi$
$854$	7.74912	0.265170
$855$	−4.60225	−0.157394
$856$	47.1867	1.61281
$857$	−26.4128	−0.902244	−0.451122	−	0.892462i	$-0.648976\pi$
$857$	−26.4128	−0.902244	−0.451122	+	0.892462i	$0.648976\pi$
$858$	32.2611	1.10137
$859$	26.2026	0.894020	0.447010	−	0.894529i	$-0.352489\pi$
$859$	26.2026	0.894020	0.447010	+	0.894529i	$0.352489\pi$
$860$	−76.4917	−2.60834
$861$	−1.35068	−0.0460311
$862$	−19.1097	−0.650877
$863$	44.3878	1.51098	0.755489	−	0.655162i	$-0.227399\pi$
$863$	44.3878	1.51098	0.755489	+	0.655162i	$0.227399\pi$
$864$	−26.4432	−0.899616
$865$	−10.4163	−0.354166
$866$	−3.96415	−0.134707
$867$	−15.1824	−0.515622
$868$	9.30293	0.315762
$869$	47.9035	1.62502
$870$	42.7952	1.45089
$871$	1.21731	0.0412470
$872$	25.1248	0.850833
$873$	−4.32455	−0.146364
$874$	−12.5014	−0.422867
$875$	3.29371	0.111348
$876$	−22.0107	−0.743671
$877$	14.2031	0.479604	0.239802	−	0.970822i	$-0.422918\pi$
$877$	14.2031	0.479604	0.239802	+	0.970822i	$0.422918\pi$
$878$	5.97703	0.201715
$879$	−15.6229	−0.526946
$880$	2.43801	0.0821852
$881$	−5.25936	−0.177192	−0.0885961	−	0.996068i	$-0.528238\pi$
$881$	−5.25936	−0.177192	−0.0885961	+	0.996068i	$0.528238\pi$
$882$	−31.6746	−1.06654
$883$	58.3060	1.96215	0.981076	−	0.193621i	$-0.0620232\pi$
$883$	58.3060	1.96215	0.981076	+	0.193621i	$0.0620232\pi$
$884$	19.4079	0.652758
$885$	2.17512	0.0731158
$886$	57.4574	1.93032
$887$	−48.3361	−1.62297	−0.811484	−	0.584375i	$-0.801340\pi$
$887$	−48.3361	−1.62297	−0.811484	+	0.584375i	$0.801340\pi$
$888$	−2.97209	−0.0997367
$889$	5.20658	0.174623
$890$	−62.6956	−2.10156
$891$	3.46719	0.116155
$892$	19.0430	0.637608
$893$	8.81719	0.295056
$894$	−19.6031	−0.655624
$895$	−17.6096	−0.588625
$896$	−7.86766	−0.262840
$897$	−28.1756	−0.940756
$898$	50.5620	1.68727
$899$	47.8653	1.59640
$900$	−13.3948	−0.446492
$901$	−6.02287	−0.200651
$902$	−23.5645	−0.784612
$903$	3.61608	0.120336
$904$	−56.1061	−1.86606
$905$	62.8575	2.08946
$906$	42.9442	1.42673
$907$	−47.3432	−1.57200	−0.786002	−	0.618224i	$-0.787852\pi$
$907$	−47.3432	−1.57200	−0.786002	+	0.618224i	$0.787852\pi$
$908$	18.6098	0.617588
$909$	3.74485	0.124209
$910$	−11.4500	−0.379563
$911$	28.5781	0.946835	0.473417	−	0.880838i	$-0.343020\pi$
$911$	28.5781	0.946835	0.473417	+	0.880838i	$0.343020\pi$
$912$	0.251554	0.00832979
$913$	−29.5925	−0.979370
$914$	−91.7616	−3.03520
$915$	21.2393	0.702149
$916$	−75.6014	−2.49794
$917$	8.83111	0.291629
$918$	−14.9410	−0.493127
$919$	−29.0166	−0.957171	−0.478585	−	0.878041i	$-0.658850\pi$
$919$	−29.0166	−0.957171	−0.478585	+	0.878041i	$0.658850\pi$
$920$	−49.9456	−1.64666
$921$	24.1567	0.795990
$922$	6.76698	0.222859
$923$	32.0923	1.05633
$924$	−4.27173	−0.140530
$925$	2.01359	0.0662065
$926$	−18.7686	−0.616774
$927$	36.4269	1.19642
$928$	−37.5800	−1.23363
$929$	−34.2707	−1.12439	−0.562193	−	0.827006i	$-0.690042\pi$
$929$	−34.2707	−1.12439	−0.562193	+	0.827006i	$0.690042\pi$
$930$	40.9474	1.34272
$931$	−5.88663	−0.192927
$932$	79.9673	2.61942
$933$	−11.1994	−0.366650
$934$	−6.18114	−0.202253
$935$	−10.8138	−0.353650
$936$	−27.2167	−0.889606
$937$	−48.4246	−1.58196	−0.790981	−	0.611841i	$-0.790429\pi$
$937$	−48.4246	−1.58196	−0.790981	+	0.611841i	$0.790429\pi$
$938$	−0.258849	−0.00845171
$939$	8.45211	0.275824
$940$	89.3847	2.91541
$941$	−58.0906	−1.89370	−0.946850	−	0.321675i	$-0.895754\pi$
$941$	−58.0906	−1.89370	−0.946850	+	0.321675i	$0.895754\pi$
$942$	32.4194	1.05628
$943$	20.5804	0.670188
$944$	0.243314	0.00791920
$945$	5.48893	0.178555
$946$	63.0875	2.05115
$947$	25.1023	0.815716	0.407858	−	0.913045i	$-0.366276\pi$
$947$	25.1023	0.815716	0.407858	+	0.913045i	$0.366276\pi$
$948$	50.1069	1.62740
$949$	30.3001	0.983583
$950$	−3.99769	−0.129702
$951$	20.7942	0.674298
$952$	−1.62640	−0.0527118
$953$	−0.700924	−0.0227052	−0.0113526	−	0.999936i	$-0.503614\pi$
$953$	−0.700924	−0.0227052	−0.0113526	+	0.999936i	$0.503614\pi$
$954$	21.4317	0.693877
$955$	−49.4802	−1.60114
$956$	4.19494	0.135674
$957$	−21.9789	−0.710475
$958$	71.8805	2.32235
$959$	2.30348	0.0743832
$960$	−33.6938	−1.08746
$961$	14.7986	0.477375
$962$	10.3817	0.334719
$963$	31.7504	1.02314
$964$	0.0672063	0.00216457
$965$	−62.9126	−2.02523
$966$	5.99125	0.192765
$967$	−49.4310	−1.58960	−0.794798	−	0.606875i	$-0.792423\pi$
$967$	−49.4310	−1.58960	−0.794798	+	0.606875i	$0.792423\pi$
$968$	3.57501	0.114905
$969$	−1.11577	−0.0358438
$970$	−13.0843	−0.420110
$971$	15.2208	0.488458	0.244229	−	0.969718i	$-0.421465\pi$
$971$	15.2208	0.488458	0.244229	+	0.969718i	$0.421465\pi$
$972$	52.9100	1.69709
$973$	−3.96046	−0.126966
$974$	63.8339	2.04537
$975$	−9.00996	−0.288550
$976$	2.37588	0.0760500
$977$	29.9541	0.958316	0.479158	−	0.877729i	$-0.340942\pi$
$977$	29.9541	0.958316	0.479158	+	0.877729i	$0.340942\pi$
$978$	−2.28470	−0.0730567
$979$	32.1994	1.02910
$980$	−59.6761	−1.90628
$981$	16.9057	0.539757
$982$	92.3728	2.94773
$983$	36.6918	1.17029	0.585143	−	0.810930i	$-0.301038\pi$
$983$	36.6918	1.17029	0.585143	+	0.810930i	$0.301038\pi$
$984$	−9.71387	−0.309667
$985$	−56.3929	−1.79683
$986$	−21.2336	−0.676216
$987$	−4.22559	−0.134502
$988$	−12.8347	−0.408328
$989$	−55.0983	−1.75202
$990$	38.4798	1.22297
$991$	49.2037	1.56301	0.781503	−	0.623902i	$-0.214453\pi$
$991$	49.2037	1.56301	0.781503	+	0.623902i	$0.214453\pi$
$992$	−35.9574	−1.14165
$993$	−16.9544	−0.538033
$994$	−6.82410	−0.216447
$995$	10.3983	0.329650
$996$	−30.9537	−0.980805
$997$	−3.02009	−0.0956471	−0.0478235	−	0.998856i	$-0.515229\pi$
$997$	−3.02009	−0.0956471	−0.0478235	+	0.998856i	$0.515229\pi$
$998$	59.4187	1.88086
$999$	−4.97682	−0.157459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.14	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.14	✓	109	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30236 q^{2} +0.992330 q^{3} +3.30086 q^{4} +2.64832 q^{5} -2.28470 q^{6} -0.416453 q^{7} -2.99506 q^{8} -2.01528 q^{9} +O(q^{10})\)	\(q-2.30236 q^{2} +0.992330 q^{3} +3.30086 q^{4} +2.64832 q^{5} -2.28470 q^{6} -0.416453 q^{7} -2.99506 q^{8} -2.01528 q^{9} -6.09738 q^{10} +3.13151 q^{11} +3.27555 q^{12} -4.50915 q^{13} +0.958824 q^{14} +2.62801 q^{15} +0.293975 q^{16} -1.30393 q^{17} +4.63990 q^{18} +0.862312 q^{19} +8.74174 q^{20} -0.413259 q^{21} -7.20987 q^{22} +6.29683 q^{23} -2.97209 q^{24} +2.01359 q^{25} +10.3817 q^{26} -4.97682 q^{27} -1.37465 q^{28} -7.07285 q^{29} -6.05062 q^{30} -6.76747 q^{31} +5.31328 q^{32} +3.10749 q^{33} +3.00213 q^{34} -1.10290 q^{35} -6.65217 q^{36} +1.00000 q^{37} -1.98535 q^{38} -4.47457 q^{39} -7.93187 q^{40} +3.26837 q^{41} +0.951471 q^{42} -8.75016 q^{43} +10.3367 q^{44} -5.33710 q^{45} -14.4976 q^{46} +10.2251 q^{47} +0.291721 q^{48} -6.82657 q^{49} -4.63602 q^{50} -1.29393 q^{51} -14.8841 q^{52} +4.61900 q^{53} +11.4584 q^{54} +8.29324 q^{55} +1.24730 q^{56} +0.855699 q^{57} +16.2843 q^{58} +0.827669 q^{59} +8.67470 q^{60} +8.08190 q^{61} +15.5812 q^{62} +0.839269 q^{63} -12.8210 q^{64} -11.9417 q^{65} -7.15457 q^{66} -0.269965 q^{67} -4.30411 q^{68} +6.24854 q^{69} +2.53927 q^{70} -7.11715 q^{71} +6.03588 q^{72} -6.71969 q^{73} -2.30236 q^{74} +1.99815 q^{75} +2.84638 q^{76} -1.30413 q^{77} +10.3021 q^{78} +15.2973 q^{79} +0.778540 q^{80} +1.10720 q^{81} -7.52496 q^{82} -9.44992 q^{83} -1.36411 q^{84} -3.45323 q^{85} +20.1460 q^{86} -7.01861 q^{87} -9.37906 q^{88} +10.2824 q^{89} +12.2879 q^{90} +1.87785 q^{91} +20.7850 q^{92} -6.71556 q^{93} -23.5418 q^{94} +2.28368 q^{95} +5.27253 q^{96} +2.14588 q^{97} +15.7172 q^{98} -6.31087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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