LMFDB - Embedded newform 4031.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$103$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71060 q^{2} -0.763863 q^{3} +5.34738 q^{4} +1.53299 q^{5} +2.07053 q^{6} +3.02090 q^{7} -9.07341 q^{8} -2.41651 q^{9} +O(q^{10})$	\(q-2.71060 q^{2} -0.763863 q^{3} +5.34738 q^{4} +1.53299 q^{5} +2.07053 q^{6} +3.02090 q^{7} -9.07341 q^{8} -2.41651 q^{9} -4.15533 q^{10} +5.73486 q^{11} -4.08466 q^{12} +4.36302 q^{13} -8.18847 q^{14} -1.17099 q^{15} +13.8997 q^{16} -6.39820 q^{17} +6.55021 q^{18} -7.40298 q^{19} +8.19748 q^{20} -2.30756 q^{21} -15.5449 q^{22} +2.26429 q^{23} +6.93084 q^{24} -2.64994 q^{25} -11.8264 q^{26} +4.13747 q^{27} +16.1539 q^{28} -1.00000 q^{29} +3.17410 q^{30} +7.90422 q^{31} -19.5297 q^{32} -4.38064 q^{33} +17.3430 q^{34} +4.63101 q^{35} -12.9220 q^{36} -7.18679 q^{37} +20.0665 q^{38} -3.33275 q^{39} -13.9095 q^{40} -3.79013 q^{41} +6.25487 q^{42} +4.03821 q^{43} +30.6664 q^{44} -3.70449 q^{45} -6.13760 q^{46} -1.42979 q^{47} -10.6174 q^{48} +2.12585 q^{49} +7.18294 q^{50} +4.88735 q^{51} +23.3307 q^{52} -14.2544 q^{53} -11.2151 q^{54} +8.79148 q^{55} -27.4099 q^{56} +5.65486 q^{57} +2.71060 q^{58} +7.96926 q^{59} -6.26175 q^{60} +7.24924 q^{61} -21.4252 q^{62} -7.30005 q^{63} +25.1379 q^{64} +6.68846 q^{65} +11.8742 q^{66} +8.26100 q^{67} -34.2136 q^{68} -1.72961 q^{69} -12.5528 q^{70} +11.6668 q^{71} +21.9260 q^{72} +9.81263 q^{73} +19.4806 q^{74} +2.02419 q^{75} -39.5865 q^{76} +17.3244 q^{77} +9.03376 q^{78} +3.83142 q^{79} +21.3081 q^{80} +4.08908 q^{81} +10.2736 q^{82} +1.86471 q^{83} -12.3394 q^{84} -9.80838 q^{85} -10.9460 q^{86} +0.763863 q^{87} -52.0347 q^{88} -4.65572 q^{89} +10.0414 q^{90} +13.1802 q^{91} +12.1080 q^{92} -6.03774 q^{93} +3.87559 q^{94} -11.3487 q^{95} +14.9180 q^{96} +12.9699 q^{97} -5.76233 q^{98} -13.8584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) $ 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * 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 $

$2$	−2.71060	−1.91669	−0.958343	−	0.285619i	$-0.907801\pi$
$2$	−2.71060	−1.91669	−0.958343	+	0.285619i	$0.907801\pi$
$3$	−0.763863	−0.441016	−0.220508	−	0.975385i	$-0.570772\pi$
$3$	−0.763863	−0.441016	−0.220508	+	0.975385i	$0.570772\pi$
$4$	5.34738	2.67369
$5$	1.53299	0.685574	0.342787	−	0.939413i	$-0.388629\pi$
$5$	1.53299	0.685574	0.342787	+	0.939413i	$0.388629\pi$
$6$	2.07053	0.845290
$7$	3.02090	1.14179	0.570897	−	0.821022i	$-0.306596\pi$
$7$	3.02090	1.14179	0.570897	+	0.821022i	$0.306596\pi$
$8$	−9.07341	−3.20794
$9$	−2.41651	−0.805504
$10$	−4.15533	−1.31403
$11$	5.73486	1.72912	0.864562	−	0.502526i	$-0.167596\pi$
$11$	5.73486	1.72912	0.864562	+	0.502526i	$0.167596\pi$
$12$	−4.08466	−1.17914
$13$	4.36302	1.21008	0.605042	−	0.796194i	$-0.293156\pi$
$13$	4.36302	1.21008	0.605042	+	0.796194i	$0.293156\pi$
$14$	−8.18847	−2.18846
$15$	−1.17099	−0.302350
$16$	13.8997	3.47492
$17$	−6.39820	−1.55179	−0.775896	−	0.630861i	$-0.782702\pi$
$17$	−6.39820	−1.55179	−0.775896	+	0.630861i	$0.782702\pi$
$18$	6.55021	1.54390
$19$	−7.40298	−1.69836	−0.849180	−	0.528103i	$-0.822903\pi$
$19$	−7.40298	−1.69836	−0.849180	+	0.528103i	$0.822903\pi$
$20$	8.19748	1.83301
$21$	−2.30756	−0.503550
$22$	−15.5449	−3.31419
$23$	2.26429	0.472138	0.236069	−	0.971736i	$-0.424141\pi$
$23$	2.26429	0.472138	0.236069	+	0.971736i	$0.424141\pi$
$24$	6.93084	1.41475
$25$	−2.64994	−0.529988
$26$	−11.8264	−2.31935
$27$	4.13747	0.796257
$28$	16.1539	3.05280
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.17410	0.579509
$31$	7.90422	1.41964	0.709820	−	0.704383i	$-0.248776\pi$
$31$	7.90422	1.41964	0.709820	+	0.704383i	$0.248776\pi$
$32$	−19.5297	−3.45240
$33$	−4.38064	−0.762572
$34$	17.3430	2.97430
$35$	4.63101	0.782784
$36$	−12.9220	−2.15367
$37$	−7.18679	−1.18150	−0.590751	−	0.806854i	$-0.701168\pi$
$37$	−7.18679	−1.18150	−0.590751	+	0.806854i	$0.701168\pi$
$38$	20.0665	3.25522
$39$	−3.33275	−0.533667
$40$	−13.9095	−2.19928
$41$	−3.79013	−0.591919	−0.295960	−	0.955200i	$-0.595639\pi$
$41$	−3.79013	−0.591919	−0.295960	+	0.955200i	$0.595639\pi$
$42$	6.25487	0.965147
$43$	4.03821	0.615821	0.307911	−	0.951415i	$-0.400370\pi$
$43$	4.03821	0.615821	0.307911	+	0.951415i	$0.400370\pi$
$44$	30.6664	4.62314
$45$	−3.70449	−0.552233
$46$	−6.13760	−0.904940
$47$	−1.42979	−0.208556	−0.104278	−	0.994548i	$-0.533253\pi$
$47$	−1.42979	−0.208556	−0.104278	+	0.994548i	$0.533253\pi$
$48$	−10.6174	−1.53250
$49$	2.12585	0.303693
$50$	7.18294	1.01582
$51$	4.88735	0.684366
$52$	23.3307	3.23539
$53$	−14.2544	−1.95800	−0.978998	−	0.203869i	$-0.934648\pi$
$53$	−14.2544	−1.95800	−0.978998	+	0.203869i	$0.934648\pi$
$54$	−11.2151	−1.52618
$55$	8.79148	1.18544
$56$	−27.4099	−3.66280
$57$	5.65486	0.749005
$58$	2.71060	0.355920
$59$	7.96926	1.03751	0.518754	−	0.854923i	$-0.326396\pi$
$59$	7.96926	1.03751	0.518754	+	0.854923i	$0.326396\pi$
$60$	−6.26175	−0.808388
$61$	7.24924	0.928170	0.464085	−	0.885791i	$-0.346383\pi$
$61$	7.24924	0.928170	0.464085	+	0.885791i	$0.346383\pi$
$62$	−21.4252	−2.72100
$63$	−7.30005	−0.919720
$64$	25.1379	3.14224
$65$	6.68846	0.829602
$66$	11.8742	1.46161
$67$	8.26100	1.00924	0.504621	−	0.863341i	$-0.331632\pi$
$67$	8.26100	1.00924	0.504621	+	0.863341i	$0.331632\pi$
$68$	−34.2136	−4.14901
$69$	−1.72961	−0.208220
$70$	−12.5528	−1.50035
$71$	11.6668	1.38459	0.692295	−	0.721615i	$-0.256600\pi$
$71$	11.6668	1.38459	0.692295	+	0.721615i	$0.256600\pi$
$72$	21.9260	2.58401
$73$	9.81263	1.14848	0.574241	−	0.818686i	$-0.305297\pi$
$73$	9.81263	1.14848	0.574241	+	0.818686i	$0.305297\pi$
$74$	19.4806	2.26457
$75$	2.02419	0.233733
$76$	−39.5865	−4.54088
$77$	17.3244	1.97430
$78$	9.03376	1.02287
$79$	3.83142	0.431068	0.215534	−	0.976496i	$-0.430851\pi$
$79$	3.83142	0.431068	0.215534	+	0.976496i	$0.430851\pi$
$80$	21.3081	2.38231
$81$	4.08908	0.454342
$82$	10.2736	1.13452
$83$	1.86471	0.204678	0.102339	−	0.994750i	$-0.467367\pi$
$83$	1.86471	0.204678	0.102339	+	0.994750i	$0.467367\pi$
$84$	−12.3394	−1.34633
$85$	−9.80838	−1.06387
$86$	−10.9460	−1.18034
$87$	0.763863	0.0818947
$88$	−52.0347	−5.54692
$89$	−4.65572	−0.493505	−0.246753	−	0.969079i	$-0.579364\pi$
$89$	−4.65572	−0.493505	−0.246753	+	0.969079i	$0.579364\pi$
$90$	10.0414	1.05846
$91$	13.1802	1.38167
$92$	12.1080	1.26235
$93$	−6.03774	−0.626084
$94$	3.87559	0.399736
$95$	−11.3487	−1.16435
$96$	14.9180	1.52256
$97$	12.9699	1.31690	0.658449	−	0.752626i	$-0.271213\pi$
$97$	12.9699	1.31690	0.658449	+	0.752626i	$0.271213\pi$
$98$	−5.76233	−0.582083
$99$	−13.8584	−1.39282
$100$	−14.1702	−1.41702
$101$	4.25466	0.423355	0.211677	−	0.977340i	$-0.432107\pi$
$101$	4.25466	0.423355	0.211677	+	0.977340i	$0.432107\pi$
$102$	−13.2477	−1.31171
$103$	12.0207	1.18444	0.592219	−	0.805777i	$-0.298252\pi$
$103$	12.0207	1.18444	0.592219	+	0.805777i	$0.298252\pi$
$104$	−39.5875	−3.88187
$105$	−3.53746	−0.345221
$106$	38.6381	3.75287
$107$	16.3424	1.57988	0.789942	−	0.613182i	$-0.210111\pi$
$107$	16.3424	1.57988	0.789942	+	0.613182i	$0.210111\pi$
$108$	22.1246	2.12894
$109$	13.7986	1.32167	0.660835	−	0.750531i	$-0.270202\pi$
$109$	13.7986	1.32167	0.660835	+	0.750531i	$0.270202\pi$
$110$	−23.8302	−2.27212
$111$	5.48972	0.521062
$112$	41.9896	3.96764
$113$	−13.8031	−1.29849	−0.649243	−	0.760581i	$-0.724914\pi$
$113$	−13.8031	−1.29849	−0.649243	+	0.760581i	$0.724914\pi$
$114$	−15.3281	−1.43561
$115$	3.47114	0.323685
$116$	−5.34738	−0.496491
$117$	−10.5433	−0.974728
$118$	−21.6015	−1.98858
$119$	−19.3283	−1.77183
$120$	10.6249	0.969918
$121$	21.8886	1.98987
$122$	−19.6498	−1.77901
$123$	2.89514	0.261046
$124$	42.2668	3.79567
$125$	−11.7273	−1.04892
$126$	19.7875	1.76281
$127$	−4.68652	−0.415862	−0.207931	−	0.978144i	$-0.566673\pi$
$127$	−4.68652	−0.415862	−0.207931	+	0.978144i	$0.566673\pi$
$128$	−29.0796	−2.57030
$129$	−3.08464	−0.271587
$130$	−18.1298	−1.59009
$131$	5.11657	0.447037	0.223519	−	0.974700i	$-0.428246\pi$
$131$	5.11657	0.447037	0.223519	+	0.974700i	$0.428246\pi$
$132$	−23.4250	−2.03888
$133$	−22.3637	−1.93918
$134$	−22.3923	−1.93440
$135$	6.34271	0.545893
$136$	58.0535	4.97805
$137$	4.33382	0.370263	0.185132	−	0.982714i	$-0.440729\pi$
$137$	4.33382	0.370263	0.185132	+	0.982714i	$0.440729\pi$
$138$	4.68829	0.399093
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	24.7638	2.09292
$141$	1.09216	0.0919766
$142$	−31.6240	−2.65382
$143$	25.0213	2.09238
$144$	−33.5888	−2.79906
$145$	−1.53299	−0.127308
$146$	−26.5982	−2.20128
$147$	−1.62386	−0.133933
$148$	−38.4305	−3.15897
$149$	19.4257	1.59141	0.795706	−	0.605684i	$-0.207100\pi$
$149$	19.4257	1.59141	0.795706	+	0.605684i	$0.207100\pi$
$150$	−5.48678	−0.447994
$151$	9.76249	0.794460	0.397230	−	0.917719i	$-0.369972\pi$
$151$	9.76249	0.794460	0.397230	+	0.917719i	$0.369972\pi$
$152$	67.1703	5.44823
$153$	15.4613	1.24998
$154$	−46.9597	−3.78412
$155$	12.1171	0.973268
$156$	−17.8215	−1.42686
$157$	−5.81322	−0.463946	−0.231973	−	0.972722i	$-0.574518\pi$
$157$	−5.81322	−0.463946	−0.231973	+	0.972722i	$0.574518\pi$
$158$	−10.3855	−0.826222
$159$	10.8884	0.863509
$160$	−29.9388	−2.36687
$161$	6.84021	0.539084
$162$	−11.0839	−0.870831
$163$	15.1896	1.18974	0.594872	−	0.803821i	$-0.297203\pi$
$163$	15.1896	1.18974	0.594872	+	0.803821i	$0.297203\pi$
$164$	−20.2673	−1.58261
$165$	−6.71549	−0.522800
$166$	−5.05449	−0.392304
$167$	2.81792	0.218057	0.109028	−	0.994039i	$-0.465226\pi$
$167$	2.81792	0.218057	0.109028	+	0.994039i	$0.465226\pi$
$168$	20.9374	1.61536
$169$	6.03592	0.464302
$170$	26.5866	2.03910
$171$	17.8894	1.36804
$172$	21.5938	1.64651
$173$	−7.72357	−0.587212	−0.293606	−	0.955927i	$-0.594855\pi$
$173$	−7.72357	−0.587212	−0.293606	+	0.955927i	$0.594855\pi$
$174$	−2.07053	−0.156966
$175$	−8.00521	−0.605137
$176$	79.7127	6.00857
$177$	−6.08742	−0.457559
$178$	12.6198	0.945895
$179$	−19.5076	−1.45806	−0.729032	−	0.684480i	$-0.760029\pi$
$179$	−19.5076	−1.45806	−0.729032	+	0.684480i	$0.760029\pi$
$180$	−19.8093	−1.47650
$181$	−0.313174	−0.0232780	−0.0116390	−	0.999932i	$-0.503705\pi$
$181$	−0.313174	−0.0232780	−0.0116390	+	0.999932i	$0.503705\pi$
$182$	−35.7264	−2.64822
$183$	−5.53742	−0.409338
$184$	−20.5449	−1.51459
$185$	−11.0173	−0.810007
$186$	16.3659	1.20001
$187$	−36.6928	−2.68324
$188$	−7.64561	−0.557613
$189$	12.4989	0.909161
$190$	30.7618	2.23170
$191$	−13.1474	−0.951316	−0.475658	−	0.879630i	$-0.657790\pi$
$191$	−13.1474	−0.951316	−0.475658	+	0.879630i	$0.657790\pi$
$192$	−19.2019	−1.38578
$193$	−25.0114	−1.80036	−0.900181	−	0.435517i	$-0.856566\pi$
$193$	−25.0114	−1.80036	−0.900181	+	0.435517i	$0.856566\pi$
$194$	−35.1564	−2.52408
$195$	−5.10907	−0.365868
$196$	11.3677	0.811979
$197$	4.11057	0.292866	0.146433	−	0.989221i	$-0.453221\pi$
$197$	4.11057	0.292866	0.146433	+	0.989221i	$0.453221\pi$
$198$	37.5645	2.66959
$199$	−14.5559	−1.03184	−0.515920	−	0.856637i	$-0.672550\pi$
$199$	−14.5559	−1.03184	−0.515920	+	0.856637i	$0.672550\pi$
$200$	24.0440	1.70017
$201$	−6.31027	−0.445092
$202$	−11.5327	−0.811439
$203$	−3.02090	−0.212026
$204$	26.1345	1.82978
$205$	−5.81024	−0.405805
$206$	−32.5834	−2.27020
$207$	−5.47169	−0.380309
$208$	60.6445	4.20494
$209$	−42.4550	−2.93668
$210$	9.58865	0.661680
$211$	−3.69983	−0.254707	−0.127353	−	0.991857i	$-0.540648\pi$
$211$	−3.69983	−0.254707	−0.127353	+	0.991857i	$0.540648\pi$
$212$	−76.2238	−5.23507
$213$	−8.91181	−0.610627
$214$	−44.2979	−3.02814
$215$	6.19054	0.422191
$216$	−37.5410	−2.55434
$217$	23.8779	1.62094
$218$	−37.4027	−2.53323
$219$	−7.49551	−0.506499
$220$	47.0113	3.16950
$221$	−27.9155	−1.87780
$222$	−14.8805	−0.998712
$223$	6.70249	0.448832	0.224416	−	0.974493i	$-0.427953\pi$
$223$	6.70249	0.448832	0.224416	+	0.974493i	$0.427953\pi$
$224$	−58.9973	−3.94192
$225$	6.40362	0.426908
$226$	37.4148	2.48879
$227$	−4.95436	−0.328832	−0.164416	−	0.986391i	$-0.552574\pi$
$227$	−4.95436	−0.328832	−0.164416	+	0.986391i	$0.552574\pi$
$228$	30.2387	2.00261
$229$	24.3652	1.61010	0.805050	−	0.593207i	$-0.202138\pi$
$229$	24.3652	1.61010	0.805050	+	0.593207i	$0.202138\pi$
$230$	−9.40888	−0.620403
$231$	−13.2335	−0.870700
$232$	9.07341	0.595699
$233$	−10.1557	−0.665321	−0.332661	−	0.943047i	$-0.607946\pi$
$233$	−10.1557	−0.665321	−0.332661	+	0.943047i	$0.607946\pi$
$234$	28.5787	1.86825
$235$	−2.19185	−0.142981
$236$	42.6146	2.77398
$237$	−2.92668	−0.190108
$238$	52.3915	3.39604
$239$	−20.0645	−1.29787	−0.648933	−	0.760846i	$-0.724784\pi$
$239$	−20.0645	−1.29787	−0.648933	+	0.760846i	$0.724784\pi$
$240$	−16.2764	−1.05064
$241$	15.2489	0.982269	0.491135	−	0.871084i	$-0.336582\pi$
$241$	15.2489	0.982269	0.491135	+	0.871084i	$0.336582\pi$
$242$	−59.3313	−3.81396
$243$	−15.5359	−0.996630
$244$	38.7644	2.48164
$245$	3.25890	0.208204
$246$	−7.84759	−0.500344
$247$	−32.2993	−2.05516
$248$	−71.7182	−4.55411
$249$	−1.42438	−0.0902665
$250$	31.7880	2.01045
$251$	26.9611	1.70177	0.850885	−	0.525351i	$-0.176066\pi$
$251$	26.9611	1.70177	0.850885	+	0.525351i	$0.176066\pi$
$252$	−39.0361	−2.45904
$253$	12.9854	0.816385
$254$	12.7033	0.797076
$255$	7.49226	0.469184
$256$	28.5474	1.78421
$257$	−9.36344	−0.584076	−0.292038	−	0.956407i	$-0.594333\pi$
$257$	−9.36344	−0.584076	−0.292038	+	0.956407i	$0.594333\pi$
$258$	8.36124	0.520548
$259$	−21.7106	−1.34903
$260$	35.7657	2.21810
$261$	2.41651	0.149578
$262$	−13.8690	−0.856830
$263$	14.3320	0.883748	0.441874	−	0.897077i	$-0.354314\pi$
$263$	14.3320	0.883748	0.441874	+	0.897077i	$0.354314\pi$
$264$	39.7474	2.44628
$265$	−21.8519	−1.34235
$266$	60.6191	3.71679
$267$	3.55633	0.217644
$268$	44.1746	2.69840
$269$	−12.1643	−0.741668	−0.370834	−	0.928699i	$-0.620928\pi$
$269$	−12.1643	−0.741668	−0.370834	+	0.928699i	$0.620928\pi$
$270$	−17.1926	−1.04631
$271$	29.6248	1.79958	0.899789	−	0.436326i	$-0.143721\pi$
$271$	29.6248	1.79958	0.899789	+	0.436326i	$0.143721\pi$
$272$	−88.9329	−5.39235
$273$	−10.0679	−0.609337
$274$	−11.7473	−0.709679
$275$	−15.1970	−0.916415
$276$	−9.24887	−0.556717
$277$	−1.28507	−0.0772121	−0.0386061	−	0.999255i	$-0.512292\pi$
$277$	−1.28507	−0.0772121	−0.0386061	+	0.999255i	$0.512292\pi$
$278$	−2.71060	−0.162571
$279$	−19.1006	−1.14353
$280$	−42.0191	−2.51112
$281$	13.3393	0.795757	0.397879	−	0.917438i	$-0.369746\pi$
$281$	13.3393	0.795757	0.397879	+	0.917438i	$0.369746\pi$
$282$	−2.96042	−0.176290
$283$	29.8173	1.77245	0.886227	−	0.463252i	$-0.153317\pi$
$283$	29.8173	1.77245	0.886227	+	0.463252i	$0.153317\pi$
$284$	62.3865	3.70196
$285$	8.66885	0.513498
$286$	−67.8228	−4.01045
$287$	−11.4496	−0.675850
$288$	47.1938	2.78092
$289$	23.9370	1.40806
$290$	4.15533	0.244009
$291$	−9.90725	−0.580773
$292$	52.4718	3.07068
$293$	−20.0564	−1.17171	−0.585853	−	0.810417i	$-0.699240\pi$
$293$	−20.0564	−1.17171	−0.585853	+	0.810417i	$0.699240\pi$
$294$	4.40163	0.256708
$295$	12.2168	0.711289
$296$	65.2087	3.79018
$297$	23.7278	1.37683
$298$	−52.6553	−3.05024
$299$	9.87915	0.571326
$300$	10.8241	0.624930
$301$	12.1990	0.703141
$302$	−26.4622	−1.52273
$303$	−3.24998	−0.186707
$304$	−102.899	−5.90166
$305$	11.1130	0.636329
$306$	−41.9096	−2.39581
$307$	3.61400	0.206262	0.103131	−	0.994668i	$-0.467114\pi$
$307$	3.61400	0.206262	0.103131	+	0.994668i	$0.467114\pi$
$308$	92.6403	5.27867
$309$	−9.18219	−0.522357
$310$	−32.8446	−1.86545
$311$	24.8752	1.41054	0.705272	−	0.708937i	$-0.250825\pi$
$311$	24.8752	1.41054	0.705272	+	0.708937i	$0.250825\pi$
$312$	30.2394	1.71197
$313$	−16.4459	−0.929575	−0.464788	−	0.885422i	$-0.653869\pi$
$313$	−16.4459	−0.929575	−0.464788	+	0.885422i	$0.653869\pi$
$314$	15.7574	0.889239
$315$	−11.1909	−0.630536
$316$	20.4880	1.15254
$317$	−4.37059	−0.245477	−0.122738	−	0.992439i	$-0.539168\pi$
$317$	−4.37059	−0.245477	−0.122738	+	0.992439i	$0.539168\pi$
$318$	−29.5142	−1.65508
$319$	−5.73486	−0.321090
$320$	38.5362	2.15424
$321$	−12.4834	−0.696755
$322$	−18.5411	−1.03325
$323$	47.3658	2.63550
$324$	21.8658	1.21477
$325$	−11.5617	−0.641330
$326$	−41.1731	−2.28037
$327$	−10.5403	−0.582878
$328$	34.3894	1.89884
$329$	−4.31925	−0.238128
$330$	18.2030	1.00204
$331$	−17.4414	−0.958664	−0.479332	−	0.877634i	$-0.659121\pi$
$331$	−17.4414	−0.958664	−0.479332	+	0.877634i	$0.659121\pi$
$332$	9.97130	0.547246
$333$	17.3670	0.951705
$334$	−7.63826	−0.417947
$335$	12.6640	0.691910
$336$	−32.0743	−1.74979
$337$	−13.9051	−0.757459	−0.378730	−	0.925507i	$-0.623639\pi$
$337$	−13.9051	−0.757459	−0.378730	+	0.925507i	$0.623639\pi$
$338$	−16.3610	−0.889921
$339$	10.5437	0.572654
$340$	−52.4491	−2.84445
$341$	45.3296	2.45473
$342$	−48.4911	−2.62210
$343$	−14.7243	−0.795039
$344$	−36.6404	−1.97552
$345$	−2.65147	−0.142751
$346$	20.9355	1.12550
$347$	31.5434	1.69334	0.846670	−	0.532118i	$-0.178604\pi$
$347$	31.5434	1.69334	0.846670	+	0.532118i	$0.178604\pi$
$348$	4.08466	0.218961
$349$	16.3140	0.873267	0.436633	−	0.899639i	$-0.356171\pi$
$349$	16.3140	0.873267	0.436633	+	0.899639i	$0.356171\pi$
$350$	21.6990	1.15986
$351$	18.0519	0.963538
$352$	−112.000	−5.96962
$353$	−3.36036	−0.178854	−0.0894269	−	0.995993i	$-0.528504\pi$
$353$	−3.36036	−0.178854	−0.0894269	+	0.995993i	$0.528504\pi$
$354$	16.5006	0.876996
$355$	17.8850	0.949239
$356$	−24.8959	−1.31948
$357$	14.7642	0.781404
$358$	52.8773	2.79465
$359$	9.23374	0.487338	0.243669	−	0.969858i	$-0.421649\pi$
$359$	9.23374	0.487338	0.243669	+	0.969858i	$0.421649\pi$
$360$	33.6124	1.77153
$361$	35.8041	1.88443
$362$	0.848890	0.0446167
$363$	−16.7199	−0.877566
$364$	70.4797	3.69414
$365$	15.0427	0.787370
$366$	15.0098	0.784573
$367$	2.75699	0.143914	0.0719570	−	0.997408i	$-0.477076\pi$
$367$	2.75699	0.143914	0.0719570	+	0.997408i	$0.477076\pi$
$368$	31.4729	1.64064
$369$	9.15891	0.476794
$370$	29.8635	1.55253
$371$	−43.0612	−2.23563
$372$	−32.2861	−1.67395
$373$	−6.60755	−0.342126	−0.171063	−	0.985260i	$-0.554720\pi$
$373$	−6.60755	−0.342126	−0.171063	+	0.985260i	$0.554720\pi$
$374$	99.4596	5.14293
$375$	8.95804	0.462591
$376$	12.9730	0.669034
$377$	−4.36302	−0.224707
$378$	−33.8796	−1.74258
$379$	−12.6479	−0.649679	−0.324840	−	0.945769i	$-0.605310\pi$
$379$	−12.6479	−0.649679	−0.324840	+	0.945769i	$0.605310\pi$
$380$	−60.6858	−3.11311
$381$	3.57986	0.183402
$382$	35.6375	1.82337
$383$	−7.02538	−0.358980	−0.179490	−	0.983760i	$-0.557445\pi$
$383$	−7.02538	−0.358980	−0.179490	+	0.983760i	$0.557445\pi$
$384$	22.2128	1.13354
$385$	26.5582	1.35353
$386$	67.7961	3.45073
$387$	−9.75839	−0.496047
$388$	69.3551	3.52097
$389$	36.9188	1.87186	0.935928	−	0.352191i	$-0.114563\pi$
$389$	36.9188	1.87186	0.935928	+	0.352191i	$0.114563\pi$
$390$	13.8487	0.701255
$391$	−14.4874	−0.732659
$392$	−19.2887	−0.974226
$393$	−3.90836	−0.197151
$394$	−11.1421	−0.561332
$395$	5.87352	0.295529
$396$	−74.1058	−3.72396
$397$	23.8733	1.19817	0.599084	−	0.800686i	$-0.295531\pi$
$397$	23.8733	1.19817	0.599084	+	0.800686i	$0.295531\pi$
$398$	39.4553	1.97771
$399$	17.0828	0.855209
$400$	−36.8333	−1.84167
$401$	3.65335	0.182440	0.0912198	−	0.995831i	$-0.470923\pi$
$401$	3.65335	0.182440	0.0912198	+	0.995831i	$0.470923\pi$
$402$	17.1046	0.853102
$403$	34.4862	1.71788
$404$	22.7513	1.13192
$405$	6.26852	0.311485
$406$	8.18847	0.406387
$407$	−41.2152	−2.04296
$408$	−44.3449	−2.19540
$409$	5.31406	0.262764	0.131382	−	0.991332i	$-0.458059\pi$
$409$	5.31406	0.262764	0.131382	+	0.991332i	$0.458059\pi$
$410$	15.7493	0.777800
$411$	−3.31045	−0.163292
$412$	64.2794	3.16682
$413$	24.0743	1.18462
$414$	14.8316	0.728933
$415$	2.85858	0.140322
$416$	−85.2084	−4.17769
$417$	−0.763863	−0.0374065
$418$	115.079	5.62869
$419$	−33.0156	−1.61292	−0.806460	−	0.591289i	$-0.798619\pi$
$419$	−33.0156	−1.61292	−0.806460	+	0.591289i	$0.798619\pi$
$420$	−18.9161	−0.923012
$421$	15.4345	0.752229	0.376115	−	0.926573i	$-0.377260\pi$
$421$	15.4345	0.752229	0.376115	+	0.926573i	$0.377260\pi$
$422$	10.0288	0.488193
$423$	3.45510	0.167993
$424$	129.336	6.28113
$425$	16.9549	0.822431
$426$	24.1564	1.17038
$427$	21.8992	1.05978
$428$	87.3892	4.22411
$429$	−19.1128	−0.922776
$430$	−16.7801	−0.809208
$431$	28.5972	1.37748	0.688740	−	0.725009i	$-0.258164\pi$
$431$	28.5972	1.37748	0.688740	+	0.725009i	$0.258164\pi$
$432$	57.5096	2.76693
$433$	−34.7525	−1.67010	−0.835050	−	0.550175i	$-0.814561\pi$
$433$	−34.7525	−1.67010	−0.835050	+	0.550175i	$0.814561\pi$
$434$	−64.7234	−3.10682
$435$	1.17099	0.0561449
$436$	73.7865	3.53373
$437$	−16.7625	−0.801860
$438$	20.3174	0.970801
$439$	−9.86646	−0.470901	−0.235450	−	0.971886i	$-0.575656\pi$
$439$	−9.86646	−0.470901	−0.235450	+	0.971886i	$0.575656\pi$
$440$	−79.7687	−3.80282
$441$	−5.13714	−0.244626
$442$	75.6678	3.59915
$443$	−6.87796	−0.326782	−0.163391	−	0.986561i	$-0.552243\pi$
$443$	−6.87796	−0.326782	−0.163391	+	0.986561i	$0.552243\pi$
$444$	29.3556	1.39316
$445$	−7.13717	−0.338334
$446$	−18.1678	−0.860270
$447$	−14.8385	−0.701839
$448$	75.9392	3.58779
$449$	22.0777	1.04191	0.520955	−	0.853584i	$-0.325576\pi$
$449$	22.0777	1.04191	0.520955	+	0.853584i	$0.325576\pi$
$450$	−17.3577	−0.818248
$451$	−21.7359	−1.02350
$452$	−73.8104	−3.47175
$453$	−7.45720	−0.350370
$454$	13.4293	0.630269
$455$	20.2052	0.947234
$456$	−51.3089	−2.40276
$457$	2.69253	0.125951	0.0629757	−	0.998015i	$-0.479941\pi$
$457$	2.69253	0.125951	0.0629757	+	0.998015i	$0.479941\pi$
$458$	−66.0445	−3.08606
$459$	−26.4724	−1.23563
$460$	18.5615	0.865434
$461$	26.4975	1.23411	0.617056	−	0.786919i	$-0.288325\pi$
$461$	26.4975	1.23411	0.617056	+	0.786919i	$0.288325\pi$
$462$	35.8708	1.66886
$463$	−38.8343	−1.80478	−0.902391	−	0.430918i	$-0.858190\pi$
$463$	−38.8343	−1.80478	−0.902391	+	0.430918i	$0.858190\pi$
$464$	−13.8997	−0.645276
$465$	−9.25580	−0.429227
$466$	27.5280	1.27521
$467$	−26.7478	−1.23774	−0.618870	−	0.785493i	$-0.712409\pi$
$467$	−26.7478	−1.23774	−0.618870	+	0.785493i	$0.712409\pi$
$468$	−56.3789	−2.60612
$469$	24.9557	1.15235
$470$	5.94124	0.274049
$471$	4.44051	0.204608
$472$	−72.3083	−3.32826
$473$	23.1586	1.06483
$474$	7.93306	0.364378
$475$	19.6175	0.900111
$476$	−103.356	−4.73731
$477$	34.4460	1.57717
$478$	54.3870	2.48760
$479$	24.6674	1.12708	0.563541	−	0.826088i	$-0.309439\pi$
$479$	24.6674	1.12708	0.563541	+	0.826088i	$0.309439\pi$
$480$	22.8692	1.04383
$481$	−31.3561	−1.42972
$482$	−41.3338	−1.88270
$483$	−5.22498	−0.237745
$484$	117.046	5.32029
$485$	19.8828	0.902831
$486$	42.1117	1.91023
$487$	8.96201	0.406107	0.203054	−	0.979168i	$-0.434913\pi$
$487$	8.96201	0.406107	0.203054	+	0.979168i	$0.434913\pi$
$488$	−65.7753	−2.97751
$489$	−11.6028	−0.524696
$490$	−8.83360	−0.399061
$491$	−14.6523	−0.661250	−0.330625	−	0.943762i	$-0.607260\pi$
$491$	−14.6523	−0.661250	−0.330625	+	0.943762i	$0.607260\pi$
$492$	15.4814	0.697956
$493$	6.39820	0.288161
$494$	87.5507	3.93909
$495$	−21.2447	−0.954880
$496$	109.866	4.93313
$497$	35.2441	1.58092
$498$	3.86094	0.173013
$499$	2.54841	0.114083	0.0570414	−	0.998372i	$-0.481833\pi$
$499$	2.54841	0.114083	0.0570414	+	0.998372i	$0.481833\pi$
$500$	−62.7102	−2.80449
$501$	−2.15250	−0.0961667
$502$	−73.0809	−3.26176
$503$	3.45181	0.153908	0.0769542	−	0.997035i	$-0.475480\pi$
$503$	3.45181	0.153908	0.0769542	+	0.997035i	$0.475480\pi$
$504$	66.2364	2.95040
$505$	6.52236	0.290241
$506$	−35.1983	−1.56475
$507$	−4.61062	−0.204765
$508$	−25.0606	−1.11188
$509$	29.1886	1.29376	0.646882	−	0.762590i	$-0.276073\pi$
$509$	29.1886	1.29376	0.646882	+	0.762590i	$0.276073\pi$
$510$	−20.3086	−0.899278
$511$	29.6430	1.31133
$512$	−19.2216	−0.849481
$513$	−30.6296	−1.35233
$514$	25.3806	1.11949
$515$	18.4277	0.812020
$516$	−16.4947	−0.726140
$517$	−8.19963	−0.360619
$518$	58.8488	2.58567
$519$	5.89975	0.258970
$520$	−60.6872	−2.66131
$521$	−27.1377	−1.18892	−0.594462	−	0.804123i	$-0.702635\pi$
$521$	−27.1377	−1.18892	−0.594462	+	0.804123i	$0.702635\pi$
$522$	−6.55021	−0.286695
$523$	15.3830	0.672653	0.336327	−	0.941745i	$-0.390815\pi$
$523$	15.3830	0.672653	0.336327	+	0.941745i	$0.390815\pi$
$524$	27.3602	1.19524
$525$	6.11488	0.266875
$526$	−38.8483	−1.69387
$527$	−50.5728	−2.20298
$528$	−60.8895	−2.64988
$529$	−17.8730	−0.777086
$530$	59.2319	2.57287
$531$	−19.2578	−0.835718
$532$	−119.587	−5.18475
$533$	−16.5364	−0.716272
$534$	−9.63981	−0.417155
$535$	25.0528	1.08313
$536$	−74.9554	−3.23758
$537$	14.9011	0.643030
$538$	32.9725	1.42154
$539$	12.1914	0.525122
$540$	33.9168	1.45955
$541$	17.0471	0.732911	0.366455	−	0.930436i	$-0.380571\pi$
$541$	17.0471	0.732911	0.366455	+	0.930436i	$0.380571\pi$
$542$	−80.3011	−3.44923
$543$	0.239222	0.0102660
$544$	124.955	5.35740
$545$	21.1532	0.906103
$546$	27.2901	1.16791
$547$	−21.1273	−0.903339	−0.451670	−	0.892185i	$-0.649171\pi$
$547$	−21.1273	−0.903339	−0.451670	+	0.892185i	$0.649171\pi$
$548$	23.1746	0.989968
$549$	−17.5179	−0.747645
$550$	41.1931	1.75648
$551$	7.40298	0.315378
$552$	15.6935	0.667958
$553$	11.5743	0.492191
$554$	3.48330	0.147991
$555$	8.41570	0.357226
$556$	5.34738	0.226779
$557$	12.4895	0.529198	0.264599	−	0.964359i	$-0.414760\pi$
$557$	12.4895	0.529198	0.264599	+	0.964359i	$0.414760\pi$
$558$	51.7743	2.19178
$559$	17.6188	0.745195
$560$	64.3696	2.72011
$561$	28.0282	1.18335
$562$	−36.1576	−1.52522
$563$	25.6710	1.08190	0.540952	−	0.841053i	$-0.318064\pi$
$563$	25.6710	1.08190	0.540952	+	0.841053i	$0.318064\pi$
$564$	5.84020	0.245917
$565$	−21.1600	−0.890209
$566$	−80.8229	−3.39724
$567$	12.3527	0.518765
$568$	−105.857	−4.44167
$569$	−21.2595	−0.891246	−0.445623	−	0.895221i	$-0.647018\pi$
$569$	−21.2595	−0.891246	−0.445623	+	0.895221i	$0.647018\pi$
$570$	−23.4978	−0.984215
$571$	31.5714	1.32122	0.660611	−	0.750728i	$-0.270297\pi$
$571$	31.5714	1.32122	0.660611	+	0.750728i	$0.270297\pi$
$572$	133.798	5.59438
$573$	10.0428	0.419546
$574$	31.0354	1.29539
$575$	−6.00024	−0.250227
$576$	−60.7462	−2.53109
$577$	−12.6227	−0.525489	−0.262744	−	0.964865i	$-0.584628\pi$
$577$	−12.6227	−0.525489	−0.262744	+	0.964865i	$0.584628\pi$
$578$	−64.8837	−2.69881
$579$	19.1053	0.793989
$580$	−8.19748	−0.340382
$581$	5.63310	0.233700
$582$	26.8546	1.11316
$583$	−81.7471	−3.38562
$584$	−89.0341	−3.68426
$585$	−16.1628	−0.668248
$586$	54.3649	2.24579
$587$	−13.8082	−0.569924	−0.284962	−	0.958539i	$-0.591981\pi$
$587$	−13.8082	−0.569924	−0.284962	+	0.958539i	$0.591981\pi$
$588$	−8.68337	−0.358096
$589$	−58.5148	−2.41106
$590$	−33.1149	−1.36332
$591$	−3.13991	−0.129159
$592$	−99.8941	−4.10562
$593$	−23.2434	−0.954493	−0.477246	−	0.878769i	$-0.658365\pi$
$593$	−23.2434	−0.954493	−0.477246	+	0.878769i	$0.658365\pi$
$594$	−64.3167	−2.63895
$595$	−29.6302	−1.21472
$596$	103.876	4.25494
$597$	11.1187	0.455059
$598$	−26.7785	−1.09505
$599$	−13.9210	−0.568797	−0.284399	−	0.958706i	$-0.591794\pi$
$599$	−13.9210	−0.568797	−0.284399	+	0.958706i	$0.591794\pi$
$600$	−18.3663	−0.749802
$601$	−25.6073	−1.04454	−0.522272	−	0.852779i	$-0.674915\pi$
$601$	−25.6073	−1.04454	−0.522272	+	0.852779i	$0.674915\pi$
$602$	−33.0668	−1.34770
$603$	−19.9628	−0.812948
$604$	52.2037	2.12414
$605$	33.5550	1.36420
$606$	8.80941	0.357858
$607$	23.0937	0.937343	0.468671	−	0.883373i	$-0.344733\pi$
$607$	23.0937	0.937343	0.468671	+	0.883373i	$0.344733\pi$
$608$	144.578	5.86341
$609$	2.30756	0.0935068
$610$	−30.1230	−1.21964
$611$	−6.23819	−0.252370
$612$	82.6776	3.34204
$613$	−29.6804	−1.19878	−0.599390	−	0.800457i	$-0.704590\pi$
$613$	−29.6804	−1.19878	−0.599390	+	0.800457i	$0.704590\pi$
$614$	−9.79614	−0.395340
$615$	4.43823	0.178967
$616$	−157.192	−6.33344
$617$	11.1390	0.448439	0.224220	−	0.974539i	$-0.428017\pi$
$617$	11.1390	0.448439	0.224220	+	0.974539i	$0.428017\pi$
$618$	24.8893	1.00119
$619$	−13.1835	−0.529888	−0.264944	−	0.964264i	$-0.585354\pi$
$619$	−13.1835	−0.529888	−0.264944	+	0.964264i	$0.585354\pi$
$620$	64.7946	2.60222
$621$	9.36845	0.375943
$622$	−67.4269	−2.70357
$623$	−14.0645	−0.563481
$624$	−46.3241	−1.85445
$625$	−4.72811	−0.189125
$626$	44.5782	1.78170
$627$	32.4298	1.29512
$628$	−31.0855	−1.24045
$629$	45.9825	1.83344
$630$	30.3341	1.20854
$631$	40.6042	1.61643	0.808214	−	0.588889i	$-0.200434\pi$
$631$	40.6042	1.61643	0.808214	+	0.588889i	$0.200434\pi$
$632$	−34.7640	−1.38284
$633$	2.82617	0.112330
$634$	11.8469	0.470502
$635$	−7.18439	−0.285104
$636$	58.2245	2.30875
$637$	9.27511	0.367493
$638$	15.5449	0.615430
$639$	−28.1929	−1.11529
$640$	−44.5787	−1.76213
$641$	−24.8399	−0.981116	−0.490558	−	0.871409i	$-0.663207\pi$
$641$	−24.8399	−0.981116	−0.490558	+	0.871409i	$0.663207\pi$
$642$	33.8375	1.33546
$643$	−14.9999	−0.591540	−0.295770	−	0.955259i	$-0.595576\pi$
$643$	−14.9999	−0.591540	−0.295770	+	0.955259i	$0.595576\pi$
$644$	36.5771	1.44134
$645$	−4.72872	−0.186193
$646$	−128.390	−5.05143
$647$	44.0100	1.73021	0.865106	−	0.501589i	$-0.167251\pi$
$647$	44.0100	1.73021	0.865106	+	0.501589i	$0.167251\pi$
$648$	−37.1019	−1.45750
$649$	45.7025	1.79398
$650$	31.3393	1.22923
$651$	−18.2394	−0.714859
$652$	81.2246	3.18100
$653$	−29.6152	−1.15893	−0.579465	−	0.814997i	$-0.696739\pi$
$653$	−29.6152	−1.15893	−0.579465	+	0.814997i	$0.696739\pi$
$654$	28.5705	1.11720
$655$	7.84366	0.306477
$656$	−52.6816	−2.05687
$657$	−23.7124	−0.925107
$658$	11.7078	0.456416
$659$	−13.7296	−0.534831	−0.267416	−	0.963581i	$-0.586170\pi$
$659$	−13.7296	−0.534831	−0.267416	+	0.963581i	$0.586170\pi$
$660$	−35.9102	−1.39780
$661$	9.41225	0.366094	0.183047	−	0.983104i	$-0.441404\pi$
$661$	9.41225	0.366094	0.183047	+	0.983104i	$0.441404\pi$
$662$	47.2766	1.83746
$663$	21.3236	0.828140
$664$	−16.9193	−0.656595
$665$	−34.2833	−1.32945
$666$	−47.0750	−1.82412
$667$	−2.26429	−0.0876738
$668$	15.0685	0.583016
$669$	−5.11978	−0.197942
$670$	−34.3272	−1.32617
$671$	41.5733	1.60492
$672$	45.0659	1.73845
$673$	−41.2686	−1.59079	−0.795393	−	0.606094i	$-0.792736\pi$
$673$	−41.2686	−1.59079	−0.795393	+	0.606094i	$0.792736\pi$
$674$	37.6912	1.45181
$675$	−10.9641	−0.422007
$676$	32.2764	1.24140
$677$	9.18625	0.353056	0.176528	−	0.984296i	$-0.443513\pi$
$677$	9.18625	0.353056	0.176528	+	0.984296i	$0.443513\pi$
$678$	−28.5797	−1.09760
$679$	39.1809	1.50362
$680$	88.9955	3.41282
$681$	3.78445	0.145021
$682$	−122.870	−4.70495
$683$	22.6201	0.865535	0.432767	−	0.901506i	$-0.357537\pi$
$683$	22.6201	0.865535	0.432767	+	0.901506i	$0.357537\pi$
$684$	95.6613	3.65770
$685$	6.64371	0.253843
$686$	39.9118	1.52384
$687$	−18.6117	−0.710081
$688$	56.1298	2.13993
$689$	−62.1923	−2.36934
$690$	7.18710	0.273608
$691$	−17.7920	−0.676838	−0.338419	−	0.940995i	$-0.609892\pi$
$691$	−17.7920	−0.676838	−0.338419	+	0.940995i	$0.609892\pi$
$692$	−41.3008	−1.57002
$693$	−41.8647	−1.59031
$694$	−85.5018	−3.24560
$695$	1.53299	0.0581496
$696$	−6.93084	−0.262713
$697$	24.2500	0.918536
$698$	−44.2207	−1.67378
$699$	7.75755	0.293418
$700$	−42.8069	−1.61795
$701$	−28.1174	−1.06198	−0.530990	−	0.847378i	$-0.678180\pi$
$701$	−28.1174	−1.06198	−0.530990	+	0.847378i	$0.678180\pi$
$702$	−48.9315	−1.84680
$703$	53.2037	2.00661
$704$	144.162	5.43333
$705$	1.67427	0.0630568
$706$	9.10860	0.342807
$707$	12.8529	0.483384
$708$	−32.5517	−1.22337
$709$	17.2041	0.646112	0.323056	−	0.946380i	$-0.395290\pi$
$709$	17.2041	0.646112	0.323056	+	0.946380i	$0.395290\pi$
$710$	−48.4792	−1.81939
$711$	−9.25867	−0.347227
$712$	42.2433	1.58313
$713$	17.8975	0.670265
$714$	−40.0199	−1.49771
$715$	38.3574	1.43448
$716$	−104.314	−3.89841
$717$	15.3265	0.572380
$718$	−25.0290	−0.934075
$719$	27.2786	1.01732	0.508660	−	0.860968i	$-0.330141\pi$
$719$	27.2786	1.01732	0.508660	+	0.860968i	$0.330141\pi$
$720$	−51.4912	−1.91897
$721$	36.3134	1.35238
$722$	−97.0508	−3.61186
$723$	−11.6481	−0.433197
$724$	−1.67466	−0.0622381
$725$	2.64994	0.0984163
$726$	45.3210	1.68202
$727$	12.3948	0.459697	0.229849	−	0.973226i	$-0.426177\pi$
$727$	12.3948	0.459697	0.229849	+	0.973226i	$0.426177\pi$
$728$	−119.590	−4.43229
$729$	−0.399919	−0.0148118
$730$	−40.7747	−1.50914
$731$	−25.8373	−0.955627
$732$	−29.6107	−1.09444
$733$	−6.94996	−0.256703	−0.128351	−	0.991729i	$-0.540969\pi$
$733$	−6.94996	−0.256703	−0.128351	+	0.991729i	$0.540969\pi$
$734$	−7.47312	−0.275838
$735$	−2.48936	−0.0918213
$736$	−44.2210	−1.63001
$737$	47.3756	1.74510
$738$	−24.8262	−0.913864
$739$	6.16212	0.226677	0.113339	−	0.993556i	$-0.463846\pi$
$739$	6.16212	0.226677	0.113339	+	0.993556i	$0.463846\pi$
$740$	−58.9136	−2.16571
$741$	24.6723	0.906358
$742$	116.722	4.28500
$743$	−38.7449	−1.42141	−0.710706	−	0.703489i	$-0.751625\pi$
$743$	−38.7449	−1.42141	−0.710706	+	0.703489i	$0.751625\pi$
$744$	54.7829	2.00844
$745$	29.7793	1.09103
$746$	17.9105	0.655749
$747$	−4.50609	−0.164869
$748$	−196.210	−7.17415
$749$	49.3689	1.80390
$750$	−24.2817	−0.886642
$751$	18.4232	0.672271	0.336135	−	0.941814i	$-0.390880\pi$
$751$	18.4232	0.672271	0.336135	+	0.941814i	$0.390880\pi$
$752$	−19.8736	−0.724715
$753$	−20.5946	−0.750509
$754$	11.8264	0.430693
$755$	14.9658	0.544661
$756$	66.8363	2.43081
$757$	43.6097	1.58502	0.792511	−	0.609857i	$-0.208773\pi$
$757$	43.6097	1.58502	0.792511	+	0.609857i	$0.208773\pi$
$758$	34.2835	1.24523
$759$	−9.91906	−0.360039
$760$	102.971	3.73517
$761$	26.3850	0.956456	0.478228	−	0.878236i	$-0.341279\pi$
$761$	26.3850	0.956456	0.478228	+	0.878236i	$0.341279\pi$
$762$	−9.70359	−0.351524
$763$	41.6843	1.50907
$764$	−70.3043	−2.54352
$765$	23.7021	0.856951
$766$	19.0430	0.688052
$767$	34.7700	1.25547
$768$	−21.8063	−0.786868
$769$	−21.1451	−0.762511	−0.381255	−	0.924470i	$-0.624508\pi$
$769$	−21.1451	−0.762511	−0.381255	+	0.924470i	$0.624508\pi$
$770$	−71.9888	−2.59430
$771$	7.15239	0.257587
$772$	−133.745	−4.81360
$773$	52.6854	1.89496	0.947480	−	0.319814i	$-0.103620\pi$
$773$	52.6854	1.89496	0.947480	+	0.319814i	$0.103620\pi$
$774$	26.4511	0.950767
$775$	−20.9457	−0.752392
$776$	−117.682	−4.22452
$777$	16.5839	0.594945
$778$	−100.072	−3.58776
$779$	28.0583	1.00529
$780$	−27.3201	−0.978217
$781$	66.9072	2.39413
$782$	39.2696	1.40428
$783$	−4.13747	−0.147861
$784$	29.5486	1.05531
$785$	−8.91162	−0.318069
$786$	10.5940	0.377876
$787$	−26.3741	−0.940136	−0.470068	−	0.882630i	$-0.655771\pi$
$787$	−26.3741	−0.940136	−0.470068	+	0.882630i	$0.655771\pi$
$788$	21.9808	0.783032
$789$	−10.9477	−0.389748
$790$	−15.9208	−0.566437
$791$	−41.6978	−1.48260
$792$	125.743	4.46807
$793$	31.6286	1.12316
$794$	−64.7112	−2.29651
$795$	16.6919	0.591999
$796$	−77.8359	−2.75882
$797$	−14.7117	−0.521115	−0.260558	−	0.965458i	$-0.583906\pi$
$797$	−14.7117	−0.521115	−0.260558	+	0.965458i	$0.583906\pi$
$798$	−46.3047	−1.63917
$799$	9.14807	0.323635
$800$	51.7525	1.82973
$801$	11.2506	0.397521
$802$	−9.90279	−0.349680
$803$	56.2740	1.98587
$804$	−33.7434	−1.19004
$805$	10.4860	0.369582
$806$	−93.4786	−3.29264
$807$	9.29183	0.327088
$808$	−38.6043	−1.35810
$809$	−4.50086	−0.158242	−0.0791210	−	0.996865i	$-0.525211\pi$
$809$	−4.50086	−0.158242	−0.0791210	+	0.996865i	$0.525211\pi$
$810$	−16.9915	−0.597019
$811$	−51.9106	−1.82283	−0.911414	−	0.411490i	$-0.865009\pi$
$811$	−51.9106	−1.82283	−0.911414	+	0.411490i	$0.865009\pi$
$812$	−16.1539	−0.566891
$813$	−22.6293	−0.793643
$814$	111.718	3.91572
$815$	23.2856	0.815657
$816$	67.9326	2.37812
$817$	−29.8948	−1.04589
$818$	−14.4043	−0.503635
$819$	−31.8502	−1.11294
$820$	−31.0695	−1.08500
$821$	−25.4242	−0.887309	−0.443655	−	0.896198i	$-0.646318\pi$
$821$	−25.4242	−0.887309	−0.443655	+	0.896198i	$0.646318\pi$
$822$	8.97331	0.312980
$823$	−1.32556	−0.0462062	−0.0231031	−	0.999733i	$-0.507355\pi$
$823$	−1.32556	−0.0462062	−0.0231031	+	0.999733i	$0.507355\pi$
$824$	−109.069	−3.79960
$825$	11.6084	0.404154
$826$	−65.2560	−2.27055
$827$	46.7784	1.62664	0.813322	−	0.581814i	$-0.197657\pi$
$827$	46.7784	1.62664	0.813322	+	0.581814i	$0.197657\pi$
$828$	−29.2592	−1.01683
$829$	−38.6976	−1.34402	−0.672012	−	0.740541i	$-0.734570\pi$
$829$	−38.6976	−1.34402	−0.672012	+	0.740541i	$0.734570\pi$
$830$	−7.74848	−0.268954
$831$	0.981614	0.0340518
$832$	109.677	3.80238
$833$	−13.6016	−0.471268
$834$	2.07053	0.0716966
$835$	4.31984	0.149494
$836$	−227.023	−7.85175
$837$	32.7035	1.13040
$838$	89.4923	3.09146
$839$	0.996560	0.0344051	0.0172025	−	0.999852i	$-0.494524\pi$
$839$	0.996560	0.0344051	0.0172025	+	0.999852i	$0.494524\pi$
$840$	32.0968	1.10745
$841$	1.00000	0.0344828
$842$	−41.8367	−1.44179
$843$	−10.1894	−0.350942
$844$	−19.7844	−0.681007
$845$	9.25301	0.318313
$846$	−9.36541	−0.321989
$847$	66.1233	2.27202
$848$	−198.132	−6.80388
$849$	−22.7763	−0.781681
$850$	−45.9579	−1.57634
$851$	−16.2730	−0.557831
$852$	−47.6548	−1.63263
$853$	19.8139	0.678414	0.339207	−	0.940712i	$-0.389841\pi$
$853$	19.8139	0.678414	0.339207	+	0.940712i	$0.389841\pi$
$854$	−59.3602	−2.03126
$855$	27.4243	0.937891
$856$	−148.282	−5.06816
$857$	−16.5483	−0.565281	−0.282640	−	0.959226i	$-0.591210\pi$
$857$	−16.5483	−0.565281	−0.282640	+	0.959226i	$0.591210\pi$
$858$	51.8073	1.76867
$859$	6.28251	0.214356	0.107178	−	0.994240i	$-0.465818\pi$
$859$	6.28251	0.214356	0.107178	+	0.994240i	$0.465818\pi$
$860$	33.1031	1.12881
$861$	8.74594	0.298061
$862$	−77.5157	−2.64020
$863$	18.2047	0.619695	0.309848	−	0.950786i	$-0.399722\pi$
$863$	18.2047	0.619695	0.309848	+	0.950786i	$0.399722\pi$
$864$	−80.8036	−2.74900
$865$	−11.8402	−0.402577
$866$	94.2003	3.20106
$867$	−18.2846	−0.620977
$868$	127.684	4.33387
$869$	21.9726	0.745370
$870$	−3.17410	−0.107612
$871$	36.0429	1.22127
$872$	−125.201	−4.23983
$873$	−31.3420	−1.06077
$874$	45.4365	1.53691
$875$	−35.4270	−1.19765
$876$	−40.0813	−1.35422
$877$	−24.8580	−0.839395	−0.419698	−	0.907664i	$-0.637864\pi$
$877$	−24.8580	−0.839395	−0.419698	+	0.907664i	$0.637864\pi$
$878$	26.7441	0.902569
$879$	15.3203	0.516742
$880$	122.199	4.11932
$881$	−27.0209	−0.910356	−0.455178	−	0.890400i	$-0.650424\pi$
$881$	−27.0209	−0.910356	−0.455178	+	0.890400i	$0.650424\pi$
$882$	13.9248	0.468871
$883$	−32.3201	−1.08766	−0.543830	−	0.839196i	$-0.683026\pi$
$883$	−32.3201	−1.08766	−0.543830	+	0.839196i	$0.683026\pi$
$884$	−149.274	−5.02064
$885$	−9.33196	−0.313690
$886$	18.6434	0.626339
$887$	−29.3684	−0.986094	−0.493047	−	0.870003i	$-0.664117\pi$
$887$	−29.3684	−0.986094	−0.493047	+	0.870003i	$0.664117\pi$
$888$	−49.8105	−1.67153
$889$	−14.1575	−0.474828
$890$	19.3461	0.648481
$891$	23.4503	0.785614
$892$	35.8407	1.20004
$893$	10.5847	0.354203
$894$	40.2214	1.34520
$895$	−29.9049	−0.999610
$896$	−87.8466	−2.93475
$897$	−7.54632	−0.251964
$898$	−59.8438	−1.99701
$899$	−7.90422	−0.263620
$900$	34.2425	1.14142
$901$	91.2027	3.03840
$902$	58.9174	1.96173
$903$	−9.31839	−0.310097
$904$	125.241	4.16546
$905$	−0.480092	−0.0159588
$906$	20.2135	0.671549
$907$	−14.1978	−0.471429	−0.235714	−	0.971822i	$-0.575743\pi$
$907$	−14.1978	−0.471429	−0.235714	+	0.971822i	$0.575743\pi$
$908$	−26.4928	−0.879195
$909$	−10.2815	−0.341014
$910$	−54.7683	−1.81555
$911$	−30.4161	−1.00773	−0.503865	−	0.863783i	$-0.668089\pi$
$911$	−30.4161	−1.00773	−0.503865	+	0.863783i	$0.668089\pi$
$912$	78.6008	2.60273
$913$	10.6938	0.353914
$914$	−7.29839	−0.241409
$915$	−8.48882	−0.280632
$916$	130.290	4.30491
$917$	15.4567	0.510424
$918$	71.7562	2.36831
$919$	−9.17184	−0.302551	−0.151276	−	0.988492i	$-0.548338\pi$
$919$	−9.17184	−0.302551	−0.151276	+	0.988492i	$0.548338\pi$
$920$	−31.4951	−1.03836
$921$	−2.76060	−0.0909650
$922$	−71.8243	−2.36541
$923$	50.9023	1.67547
$924$	−70.7645	−2.32798
$925$	19.0446	0.626182
$926$	105.264	3.45920
$927$	−29.0483	−0.954070
$928$	19.5297	0.641094
$929$	19.0631	0.625441	0.312720	−	0.949845i	$-0.398760\pi$
$929$	19.0631	0.625441	0.312720	+	0.949845i	$0.398760\pi$
$930$	25.0888	0.822694
$931$	−15.7376	−0.515779
$932$	−54.3063	−1.77886
$933$	−19.0013	−0.622073
$934$	72.5027	2.37236
$935$	−56.2497	−1.83956
$936$	95.6636	3.12686
$937$	−4.62819	−0.151196	−0.0755981	−	0.997138i	$-0.524087\pi$
$937$	−4.62819	−0.151196	−0.0755981	+	0.997138i	$0.524087\pi$
$938$	−67.6449	−2.20868
$939$	12.5624	0.409958
$940$	−11.7206	−0.382285
$941$	23.5743	0.768500	0.384250	−	0.923229i	$-0.374460\pi$
$941$	23.5743	0.768500	0.384250	+	0.923229i	$0.374460\pi$
$942$	−12.0365	−0.392169
$943$	−8.58197	−0.279467
$944$	110.770	3.60526
$945$	19.1607	0.623298
$946$	−62.7737	−2.04095
$947$	−1.43259	−0.0465529	−0.0232765	−	0.999729i	$-0.507410\pi$
$947$	−1.43259	−0.0465529	−0.0232765	+	0.999729i	$0.507410\pi$
$948$	−15.6500	−0.508290
$949$	42.8127	1.38976
$950$	−53.1752	−1.72523
$951$	3.33853	0.108259
$952$	175.374	5.68390
$953$	−38.7909	−1.25656	−0.628281	−	0.777987i	$-0.716241\pi$
$953$	−38.7909	−1.25656	−0.628281	+	0.777987i	$0.716241\pi$
$954$	−93.3695	−3.02295
$955$	−20.1549	−0.652197
$956$	−107.292	−3.47009
$957$	4.38064	0.141606
$958$	−66.8635	−2.16026
$959$	13.0920	0.422764
$960$	−29.4364	−0.950055
$961$	31.4767	1.01538
$962$	84.9940	2.74032
$963$	−39.4917	−1.27260
$964$	81.5417	2.62628
$965$	−38.3423	−1.23428
$966$	14.1629	0.455682
$967$	−28.2091	−0.907144	−0.453572	−	0.891220i	$-0.649850\pi$
$967$	−28.2091	−0.907144	−0.453572	+	0.891220i	$0.649850\pi$
$968$	−198.604	−6.38338
$969$	−36.1810	−1.16230
$970$	−53.8944	−1.73044
$971$	1.63699	0.0525334	0.0262667	−	0.999655i	$-0.491638\pi$
$971$	1.63699	0.0525334	0.0262667	+	0.999655i	$0.491638\pi$
$972$	−83.0764	−2.66468
$973$	3.02090	0.0968457
$974$	−24.2925	−0.778381
$975$	8.83158	0.282837
$976$	100.762	3.22531
$977$	−36.5158	−1.16824	−0.584122	−	0.811666i	$-0.698561\pi$
$977$	−36.5158	−1.16824	−0.584122	+	0.811666i	$0.698561\pi$
$978$	31.4506	1.00568
$979$	−26.6999	−0.853332
$980$	17.4266	0.556672
$981$	−33.3446	−1.06461
$982$	39.7166	1.26741
$983$	58.0049	1.85007	0.925034	−	0.379883i	$-0.124036\pi$
$983$	58.0049	1.85007	0.925034	+	0.379883i	$0.124036\pi$
$984$	−26.2688	−0.837419
$985$	6.30146	0.200781
$986$	−17.3430	−0.552313
$987$	3.29931	0.105018
$988$	−172.717	−5.49485
$989$	9.14369	0.290752
$990$	57.5861	1.83021
$991$	1.31022	0.0416204	0.0208102	−	0.999783i	$-0.493375\pi$
$991$	1.31022	0.0416204	0.0208102	+	0.999783i	$0.493375\pi$
$992$	−154.367	−4.90116
$993$	13.3228	0.422787
$994$	−95.5329	−3.03012
$995$	−22.3141	−0.707403
$996$	−7.61671	−0.241345
$997$	−17.0781	−0.540870	−0.270435	−	0.962738i	$-0.587167\pi$
$997$	−17.0781	−0.540870	−0.270435	+	0.962738i	$0.587167\pi$
$998$	−6.90774	−0.218661
$999$	−29.7352	−0.940779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.e.1.4	✓	103

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.e.1.4	✓	103	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71060 q^{2} -0.763863 q^{3} +5.34738 q^{4} +1.53299 q^{5} +2.07053 q^{6} +3.02090 q^{7} -9.07341 q^{8} -2.41651 q^{9} +O(q^{10})\)	\(q-2.71060 q^{2} -0.763863 q^{3} +5.34738 q^{4} +1.53299 q^{5} +2.07053 q^{6} +3.02090 q^{7} -9.07341 q^{8} -2.41651 q^{9} -4.15533 q^{10} +5.73486 q^{11} -4.08466 q^{12} +4.36302 q^{13} -8.18847 q^{14} -1.17099 q^{15} +13.8997 q^{16} -6.39820 q^{17} +6.55021 q^{18} -7.40298 q^{19} +8.19748 q^{20} -2.30756 q^{21} -15.5449 q^{22} +2.26429 q^{23} +6.93084 q^{24} -2.64994 q^{25} -11.8264 q^{26} +4.13747 q^{27} +16.1539 q^{28} -1.00000 q^{29} +3.17410 q^{30} +7.90422 q^{31} -19.5297 q^{32} -4.38064 q^{33} +17.3430 q^{34} +4.63101 q^{35} -12.9220 q^{36} -7.18679 q^{37} +20.0665 q^{38} -3.33275 q^{39} -13.9095 q^{40} -3.79013 q^{41} +6.25487 q^{42} +4.03821 q^{43} +30.6664 q^{44} -3.70449 q^{45} -6.13760 q^{46} -1.42979 q^{47} -10.6174 q^{48} +2.12585 q^{49} +7.18294 q^{50} +4.88735 q^{51} +23.3307 q^{52} -14.2544 q^{53} -11.2151 q^{54} +8.79148 q^{55} -27.4099 q^{56} +5.65486 q^{57} +2.71060 q^{58} +7.96926 q^{59} -6.26175 q^{60} +7.24924 q^{61} -21.4252 q^{62} -7.30005 q^{63} +25.1379 q^{64} +6.68846 q^{65} +11.8742 q^{66} +8.26100 q^{67} -34.2136 q^{68} -1.72961 q^{69} -12.5528 q^{70} +11.6668 q^{71} +21.9260 q^{72} +9.81263 q^{73} +19.4806 q^{74} +2.02419 q^{75} -39.5865 q^{76} +17.3244 q^{77} +9.03376 q^{78} +3.83142 q^{79} +21.3081 q^{80} +4.08908 q^{81} +10.2736 q^{82} +1.86471 q^{83} -12.3394 q^{84} -9.80838 q^{85} -10.9460 q^{86} +0.763863 q^{87} -52.0347 q^{88} -4.65572 q^{89} +10.0414 q^{90} +13.1802 q^{91} +12.1080 q^{92} -6.03774 q^{93} +3.87559 q^{94} -11.3487 q^{95} +14.9180 q^{96} +12.9699 q^{97} -5.76233 q^{98} -13.8584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9}+O(q^{10}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9	\( 103 q + q^{2} + 2 q^{3} + 127 q^{4} + 9 q^{5} + 19 q^{6} + 18 q^{7} + 149 q^{9} + 20 q^{10} + 9 q^{11} + 36 q^{13} - 10 q^{14} + 16 q^{15} + 179 q^{16} + 21 q^{17} + 7 q^{18} + 42 q^{19} + 24 q^{20} + 28 q^{21} + 32 q^{22} + 25 q^{23} + 68 q^{24} + 194 q^{25} - 5 q^{26} + 14 q^{27} + 59 q^{28} - 103 q^{29} + 84 q^{30} + 34 q^{31} + 11 q^{32} + 42 q^{33} + 54 q^{34} + 35 q^{35} + 214 q^{36} + 34 q^{37} + 9 q^{38} + 23 q^{39} + 46 q^{40} + 16 q^{41} + 13 q^{42} + 68 q^{43} - 6 q^{44} + 25 q^{45} + 60 q^{46} + 6 q^{47} + 5 q^{48} + 257 q^{49} - 51 q^{50} + 68 q^{51} + 37 q^{52} + 35 q^{53} + 30 q^{54} + 66 q^{55} - 54 q^{56} + 78 q^{57} - q^{58} + 10 q^{59} - 24 q^{60} + 70 q^{61} + 29 q^{62} + 26 q^{63} + 276 q^{64} + 95 q^{65} + 77 q^{66} + 71 q^{67} - 21 q^{68} - 20 q^{69} + 48 q^{70} + 32 q^{71} + 32 q^{72} + 94 q^{73} + 35 q^{74} + 7 q^{75} + 134 q^{76} + 17 q^{77} + 58 q^{78} + 110 q^{79} + 78 q^{80} + 267 q^{81} - 71 q^{82} + 35 q^{83} + 96 q^{84} + 71 q^{85} + 33 q^{86} - 2 q^{87} + 100 q^{88} + 22 q^{89} - 134 q^{90} + 108 q^{91} - 11 q^{92} + 78 q^{93} + 90 q^{94} + 12 q^{95} + 177 q^{96} + 44 q^{97} - 18 q^{98} + 83 q^{99}+O(q^{100}) \) 103 * q + q^2 + 2 * q^3 + 127 * q^4 + 9 * q^5 + 19 * q^6 + 18 * q^7 + 149 * q^9 + 20 * q^10 + 9 * q^11 + 36 * q^13 - 10 * q^14 + 16 * q^15 + 179 * q^16 + 21 * q^17 + 7 * q^18 + 42 * q^19 + 24 * q^20 + 28 * q^21 + 32 * q^22 + 25 * q^23 + 68 * q^24 + 194 * q^25 - 5 * q^26 + 14 * q^27 + 59 * q^28 - 103 * q^29 + 84 * q^30 + 34 * q^31 + 11 * q^32 + 42 * q^33 + 54 * q^34 + 35 * q^35 + 214 * q^36 + 34 * q^37 + 9 * q^38 + 23 * q^39 + 46 * q^40 + 16 * q^41 + 13 * q^42 + 68 * q^43 - 6 * q^44 + 25 * q^45 + 60 * q^46 + 6 * q^47 + 5 * q^48 + 257 * q^49 - 51 * q^50 + 68 * q^51 + 37 * q^52 + 35 * q^53 + 30 * q^54 + 66 * q^55 - 54 * q^56 + 78 * q^57 - q^58 + 10 * q^59 - 24 * q^60 + 70 * q^61 + 29 * q^62 + 26 * q^63 + 276 * q^64 + 95 * q^65 + 77 * q^66 + 71 * q^67 - 21 * q^68 - 20 * q^69 + 48 * q^70 + 32 * q^71 + 32 * q^72 + 94 * q^73 + 35 * q^74 + 7 * q^75 + 134 * q^76 + 17 * q^77 + 58 * q^78 + 110 * q^79 + 78 * q^80 + 267 * q^81 - 71 * q^82 + 35 * q^83 + 96 * q^84 + 71 * q^85 + 33 * q^86 - 2 * q^87 + 100 * q^88 + 22 * q^89 - 134 * q^90 + 108 * q^91 - 11 * q^92 + 78 * q^93 + 90 * q^94 + 12 * q^95 + 177 * q^96 + 44 * q^97 - 18 * q^98 + 83 * q^99

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