LMFDB - Embedded newform 139.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [139,2,Mod(1,139)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(139, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("139.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	139.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:	$1.10992058810$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 11x^{5} + 8x^{4} + 35x^{3} - 10x^{2} - 32x - 8 $ x^7 - x^6 - 11x^5 + 8x^4 + 35x^3 - 10x^2 - 32*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.308806$ of defining polynomial
Character	$\chi$	$=$	139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.308806 q^{2} -1.39811 q^{3} -1.90464 q^{4} +2.83261 q^{5} +0.431745 q^{6} +4.16776 q^{7} +1.20578 q^{8} -1.04529 q^{9} +O(q^{10})$	\(q-0.308806 q^{2} -1.39811 q^{3} -1.90464 q^{4} +2.83261 q^{5} +0.431745 q^{6} +4.16776 q^{7} +1.20578 q^{8} -1.04529 q^{9} -0.874728 q^{10} +1.93164 q^{11} +2.66290 q^{12} +4.12937 q^{13} -1.28703 q^{14} -3.96031 q^{15} +3.43693 q^{16} +1.03363 q^{17} +0.322790 q^{18} -7.34157 q^{19} -5.39511 q^{20} -5.82699 q^{21} -0.596503 q^{22} -4.09697 q^{23} -1.68581 q^{24} +3.02371 q^{25} -1.27517 q^{26} +5.65576 q^{27} -7.93807 q^{28} +4.49067 q^{29} +1.22297 q^{30} -1.28386 q^{31} -3.47289 q^{32} -2.70065 q^{33} -0.319192 q^{34} +11.8056 q^{35} +1.99089 q^{36} -7.77849 q^{37} +2.26712 q^{38} -5.77331 q^{39} +3.41550 q^{40} +11.5603 q^{41} +1.79941 q^{42} -7.87867 q^{43} -3.67908 q^{44} -2.96089 q^{45} +1.26517 q^{46} -6.84669 q^{47} -4.80521 q^{48} +10.3702 q^{49} -0.933738 q^{50} -1.44513 q^{51} -7.86495 q^{52} +3.68473 q^{53} -1.74653 q^{54} +5.47160 q^{55} +5.02538 q^{56} +10.2643 q^{57} -1.38675 q^{58} +1.24534 q^{59} +7.54296 q^{60} +0.281096 q^{61} +0.396462 q^{62} -4.35649 q^{63} -5.80140 q^{64} +11.6969 q^{65} +0.833977 q^{66} -8.51902 q^{67} -1.96870 q^{68} +5.72803 q^{69} -3.64565 q^{70} -6.40133 q^{71} -1.26038 q^{72} -5.92608 q^{73} +2.40204 q^{74} -4.22748 q^{75} +13.9830 q^{76} +8.05062 q^{77} +1.78283 q^{78} -8.65375 q^{79} +9.73549 q^{80} -4.77152 q^{81} -3.56988 q^{82} +15.8366 q^{83} +11.0983 q^{84} +2.92789 q^{85} +2.43298 q^{86} -6.27846 q^{87} +2.32913 q^{88} -3.23844 q^{89} +0.914340 q^{90} +17.2102 q^{91} +7.80326 q^{92} +1.79497 q^{93} +2.11430 q^{94} -20.7958 q^{95} +4.85549 q^{96} -7.27325 q^{97} -3.20237 q^{98} -2.01912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) $ 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.308806	−0.218359	−0.109179	−	0.994022i	$-0.534822\pi$
$2$	−0.308806	−0.218359	−0.109179	+	0.994022i	$0.534822\pi$
$3$	−1.39811	−0.807200	−0.403600	−	0.914936i	$-0.632241\pi$
$3$	−1.39811	−0.807200	−0.403600	+	0.914936i	$0.632241\pi$
$4$	−1.90464	−0.952319
$5$	2.83261	1.26678	0.633392	−	0.773831i	$-0.281662\pi$
$5$	2.83261	1.26678	0.633392	+	0.773831i	$0.281662\pi$
$6$	0.431745	0.176259
$7$	4.16776	1.57526	0.787632	−	0.616146i	$-0.211307\pi$
$7$	4.16776	1.57526	0.787632	+	0.616146i	$0.211307\pi$
$8$	1.20578	0.426306
$9$	−1.04529	−0.348428
$10$	−0.874728	−0.276613
$11$	1.93164	0.582412	0.291206	−	0.956660i	$-0.405943\pi$
$11$	1.93164	0.582412	0.291206	+	0.956660i	$0.405943\pi$
$12$	2.66290	0.768712
$13$	4.12937	1.14528	0.572640	−	0.819807i	$-0.305919\pi$
$13$	4.12937	1.14528	0.572640	+	0.819807i	$0.305919\pi$
$14$	−1.28703	−0.343972
$15$	−3.96031	−1.02255
$16$	3.43693	0.859232
$17$	1.03363	0.250693	0.125347	−	0.992113i	$-0.459996\pi$
$17$	1.03363	0.250693	0.125347	+	0.992113i	$0.459996\pi$
$18$	0.322790	0.0760824
$19$	−7.34157	−1.68427	−0.842135	−	0.539266i	$-0.818702\pi$
$19$	−7.34157	−1.68427	−0.842135	+	0.539266i	$0.818702\pi$
$20$	−5.39511	−1.20638
$21$	−5.82699	−1.27155
$22$	−0.596503	−0.127175
$23$	−4.09697	−0.854278	−0.427139	−	0.904186i	$-0.640479\pi$
$23$	−4.09697	−0.854278	−0.427139	+	0.904186i	$0.640479\pi$
$24$	−1.68581	−0.344114
$25$	3.02371	0.604741
$26$	−1.27517	−0.250082
$27$	5.65576	1.08845
$28$	−7.93807	−1.50015
$29$	4.49067	0.833897	0.416948	−	0.908930i	$-0.363100\pi$
$29$	4.49067	0.833897	0.416948	+	0.908930i	$0.363100\pi$
$30$	1.22297	0.223282
$31$	−1.28386	−0.230587	−0.115294	−	0.993331i	$-0.536781\pi$
$31$	−1.28386	−0.230587	−0.115294	+	0.993331i	$0.536781\pi$
$32$	−3.47289	−0.613927
$33$	−2.70065	−0.470123
$34$	−0.319192	−0.0547410
$35$	11.8056	1.99552
$36$	1.99089	0.331815
$37$	−7.77849	−1.27878	−0.639388	−	0.768884i	$-0.720812\pi$
$37$	−7.77849	−1.27878	−0.639388	+	0.768884i	$0.720812\pi$
$38$	2.26712	0.367775
$39$	−5.77331	−0.924470
$40$	3.41550	0.540038
$41$	11.5603	1.80541	0.902706	−	0.430258i	$-0.141577\pi$
$41$	11.5603	1.80541	0.902706	+	0.430258i	$0.141577\pi$
$42$	1.79941	0.277655
$43$	−7.87867	−1.20149	−0.600743	−	0.799442i	$-0.705129\pi$
$43$	−7.87867	−1.20149	−0.600743	+	0.799442i	$0.705129\pi$
$44$	−3.67908	−0.554643
$45$	−2.96089	−0.441383
$46$	1.26517	0.186539
$47$	−6.84669	−0.998692	−0.499346	−	0.866403i	$-0.666426\pi$
$47$	−6.84669	−0.998692	−0.499346	+	0.866403i	$0.666426\pi$
$48$	−4.80521	−0.693572
$49$	10.3702	1.48145
$50$	−0.933738	−0.132051
$51$	−1.44513	−0.202359
$52$	−7.86495	−1.09067
$53$	3.68473	0.506136	0.253068	−	0.967449i	$-0.418560\pi$
$53$	3.68473	0.506136	0.253068	+	0.967449i	$0.418560\pi$
$54$	−1.74653	−0.237673
$55$	5.47160	0.737791
$56$	5.02538	0.671544
$57$	10.2643	1.35954
$58$	−1.38675	−0.182089
$59$	1.24534	0.162129	0.0810647	−	0.996709i	$-0.474168\pi$
$59$	1.24534	0.162129	0.0810647	+	0.996709i	$0.474168\pi$
$60$	7.54296	0.973792
$61$	0.281096	0.0359907	0.0179953	−	0.999838i	$-0.494272\pi$
$61$	0.281096	0.0359907	0.0179953	+	0.999838i	$0.494272\pi$
$62$	0.396462	0.0503507
$63$	−4.35649	−0.548867
$64$	−5.80140	−0.725176
$65$	11.6969	1.45082
$66$	0.833977	0.102655
$67$	−8.51902	−1.04076	−0.520382	−	0.853934i	$-0.674210\pi$
$67$	−8.51902	−1.04076	−0.520382	+	0.853934i	$0.674210\pi$
$68$	−1.96870	−0.238740
$69$	5.72803	0.689573
$70$	−3.64565	−0.435739
$71$	−6.40133	−0.759698	−0.379849	−	0.925048i	$-0.624024\pi$
$71$	−6.40133	−0.759698	−0.379849	+	0.925048i	$0.624024\pi$
$72$	−1.26038	−0.148537
$73$	−5.92608	−0.693595	−0.346798	−	0.937940i	$-0.612731\pi$
$73$	−5.92608	−0.693595	−0.346798	+	0.937940i	$0.612731\pi$
$74$	2.40204	0.279232
$75$	−4.22748	−0.488147
$76$	13.9830	1.60396
$77$	8.05062	0.917453
$78$	1.78283	0.201866
$79$	−8.65375	−0.973623	−0.486811	−	0.873507i	$-0.661840\pi$
$79$	−8.65375	−0.973623	−0.486811	+	0.873507i	$0.661840\pi$
$80$	9.73549	1.08846
$81$	−4.77152	−0.530169
$82$	−3.56988	−0.394228
$83$	15.8366	1.73829	0.869146	−	0.494555i	$-0.164669\pi$
$83$	15.8366	1.73829	0.869146	+	0.494555i	$0.164669\pi$
$84$	11.0983	1.21092
$85$	2.92789	0.317574
$86$	2.43298	0.262355
$87$	−6.27846	−0.673121
$88$	2.32913	0.248286
$89$	−3.23844	−0.343274	−0.171637	−	0.985160i	$-0.554906\pi$
$89$	−3.23844	−0.343274	−0.171637	+	0.985160i	$0.554906\pi$
$90$	0.914340	0.0963799
$91$	17.2102	1.80412
$92$	7.80326	0.813546
$93$	1.79497	0.186130
$94$	2.11430	0.218073
$95$	−20.7958	−2.13361
$96$	4.85549	0.495562
$97$	−7.27325	−0.738487	−0.369243	−	0.929333i	$-0.620383\pi$
$97$	−7.27325	−0.738487	−0.369243	+	0.929333i	$0.620383\pi$
$98$	−3.20237	−0.323489
$99$	−2.01912	−0.202929
$100$	−5.75907	−0.575907
$101$	−13.0456	−1.29809	−0.649044	−	0.760751i	$-0.724831\pi$
$101$	−13.0456	−1.29809	−0.649044	+	0.760751i	$0.724831\pi$
$102$	0.446266	0.0441869
$103$	−11.9048	−1.17302	−0.586510	−	0.809942i	$-0.699498\pi$
$103$	−11.9048	−1.17302	−0.586510	+	0.809942i	$0.699498\pi$
$104$	4.97909	0.488240
$105$	−16.5056	−1.61078
$106$	−1.13786	−0.110519
$107$	16.1058	1.55700	0.778502	−	0.627642i	$-0.215980\pi$
$107$	16.1058	1.55700	0.778502	+	0.627642i	$0.215980\pi$
$108$	−10.7722	−1.03655
$109$	13.1464	1.25919	0.629597	−	0.776922i	$-0.283220\pi$
$109$	13.1464	1.25919	0.629597	+	0.776922i	$0.283220\pi$
$110$	−1.68966	−0.161103
$111$	10.8752	1.03223
$112$	14.3243	1.35352
$113$	−14.7595	−1.38846	−0.694228	−	0.719755i	$-0.744254\pi$
$113$	−14.7595	−1.38846	−0.694228	+	0.719755i	$0.744254\pi$
$114$	−3.16968	−0.296868
$115$	−11.6052	−1.08219
$116$	−8.55311	−0.794136
$117$	−4.31636	−0.399048
$118$	−0.384568	−0.0354024
$119$	4.30793	0.394908
$120$	−4.77524	−0.435918
$121$	−7.26876	−0.660796
$122$	−0.0868042	−0.00785888
$123$	−16.1626	−1.45733
$124$	2.44528	0.219593
$125$	−5.59808	−0.500707
$126$	1.34531	0.119850
$127$	11.0142	0.977350	0.488675	−	0.872466i	$-0.337480\pi$
$127$	11.0142	0.977350	0.488675	+	0.872466i	$0.337480\pi$
$128$	8.73730	0.772275
$129$	11.0153	0.969840
$130$	−3.61207	−0.316800
$131$	−5.25402	−0.459046	−0.229523	−	0.973303i	$-0.573717\pi$
$131$	−5.25402	−0.459046	−0.229523	+	0.973303i	$0.573717\pi$
$132$	5.14377	0.447707
$133$	−30.5979	−2.65317
$134$	2.63072	0.227260
$135$	16.0206	1.37883
$136$	1.24633	0.106872
$137$	−1.68115	−0.143630	−0.0718151	−	0.997418i	$-0.522879\pi$
$137$	−1.68115	−0.143630	−0.0718151	+	0.997418i	$0.522879\pi$
$138$	−1.76885	−0.150574
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−22.4855	−1.90037
$141$	9.57243	0.806144
$142$	1.97677	0.165887
$143$	7.97646	0.667025
$144$	−3.59257	−0.299381
$145$	12.7203	1.05637
$146$	1.83001	0.151453
$147$	−14.4987	−1.19583
$148$	14.8152	1.21780
$149$	13.9257	1.14084	0.570421	−	0.821353i	$-0.306780\pi$
$149$	13.9257	1.14084	0.570421	+	0.821353i	$0.306780\pi$
$150$	1.30547	0.106591
$151$	8.63888	0.703022	0.351511	−	0.936184i	$-0.385668\pi$
$151$	8.63888	0.703022	0.351511	+	0.936184i	$0.385668\pi$
$152$	−8.85228	−0.718015
$153$	−1.08044	−0.0873486
$154$	−2.48608	−0.200334
$155$	−3.63667	−0.292104
$156$	10.9961	0.880390
$157$	10.4362	0.832900	0.416450	−	0.909159i	$-0.363274\pi$
$157$	10.4362	0.832900	0.416450	+	0.909159i	$0.363274\pi$
$158$	2.67233	0.212599
$159$	−5.15166	−0.408553
$160$	−9.83737	−0.777712
$161$	−17.0752	−1.34571
$162$	1.47347	0.115767
$163$	−3.73406	−0.292474	−0.146237	−	0.989250i	$-0.546716\pi$
$163$	−3.73406	−0.292474	−0.146237	+	0.989250i	$0.546716\pi$
$164$	−22.0182	−1.71933
$165$	−7.64991	−0.595544
$166$	−4.89043	−0.379571
$167$	−19.7503	−1.52832	−0.764161	−	0.645025i	$-0.776847\pi$
$167$	−19.7503	−1.52832	−0.764161	+	0.645025i	$0.776847\pi$
$168$	−7.02604	−0.542070
$169$	4.05166	0.311666
$170$	−0.904148	−0.0693450
$171$	7.67403	0.586848
$172$	15.0060	1.14420
$173$	−7.51428	−0.571300	−0.285650	−	0.958334i	$-0.592210\pi$
$173$	−7.51428	−0.571300	−0.285650	+	0.958334i	$0.592210\pi$
$174$	1.93882	0.146982
$175$	12.6021	0.952627
$176$	6.63892	0.500427
$177$	−1.74112	−0.130871
$178$	1.00005	0.0749568
$179$	24.2625	1.81346	0.906732	−	0.421708i	$-0.138569\pi$
$179$	24.2625	1.81346	0.906732	+	0.421708i	$0.138569\pi$
$180$	5.63943	0.420338
$181$	−3.06020	−0.227463	−0.113732	−	0.993512i	$-0.536280\pi$
$181$	−3.06020	−0.227463	−0.113732	+	0.993512i	$0.536280\pi$
$182$	−5.31461	−0.393945
$183$	−0.393004	−0.0290517
$184$	−4.94003	−0.364184
$185$	−22.0335	−1.61993
$186$	−0.554298	−0.0406431
$187$	1.99661	0.146007
$188$	13.0405	0.951074
$189$	23.5718	1.71460
$190$	6.42187	0.465892
$191$	8.83544	0.639310	0.319655	−	0.947534i	$-0.396433\pi$
$191$	8.83544	0.639310	0.319655	+	0.947534i	$0.396433\pi$
$192$	8.11101	0.585362
$193$	14.9309	1.07475	0.537374	−	0.843344i	$-0.319416\pi$
$193$	14.9309	1.07475	0.537374	+	0.843344i	$0.319416\pi$
$194$	2.24602	0.161255
$195$	−16.3536	−1.17110
$196$	−19.7515	−1.41082
$197$	−11.8981	−0.847702	−0.423851	−	0.905732i	$-0.639322\pi$
$197$	−11.8981	−0.847702	−0.423851	+	0.905732i	$0.639322\pi$
$198$	0.623515	0.0443113
$199$	−4.40723	−0.312420	−0.156210	−	0.987724i	$-0.549928\pi$
$199$	−4.40723	−0.312420	−0.156210	+	0.987724i	$0.549928\pi$
$200$	3.64591	0.257805
$201$	11.9105	0.840104
$202$	4.02857	0.283449
$203$	18.7160	1.31361
$204$	2.75246	0.192711
$205$	32.7458	2.28707
$206$	3.67629	0.256139
$207$	4.28251	0.297655
$208$	14.1923	0.984061
$209$	−14.1813	−0.980940
$210$	5.09703	0.351728
$211$	21.4218	1.47474	0.737368	−	0.675492i	$-0.236069\pi$
$211$	21.4218	1.47474	0.737368	+	0.675492i	$0.236069\pi$
$212$	−7.01807	−0.482003
$213$	8.94977	0.613228
$214$	−4.97356	−0.339985
$215$	−22.3173	−1.52202
$216$	6.81957	0.464013
$217$	−5.35079	−0.363236
$218$	−4.05968	−0.274956
$219$	8.28532	0.559870
$220$	−10.4214	−0.702612
$221$	4.26825	0.287114
$222$	−3.35833	−0.225396
$223$	−7.93581	−0.531421	−0.265711	−	0.964053i	$-0.585607\pi$
$223$	−7.93581	−0.531421	−0.265711	+	0.964053i	$0.585607\pi$
$224$	−14.4742	−0.967096
$225$	−3.16064	−0.210709
$226$	4.55782	0.303181
$227$	15.9354	1.05767	0.528836	−	0.848724i	$-0.322629\pi$
$227$	15.9354	1.05767	0.528836	+	0.848724i	$0.322629\pi$
$228$	−19.5498	−1.29472
$229$	13.4712	0.890203	0.445102	−	0.895480i	$-0.353168\pi$
$229$	13.4712	0.890203	0.445102	+	0.895480i	$0.353168\pi$
$230$	3.58374	0.236305
$231$	−11.2557	−0.740568
$232$	5.41474	0.355495
$233$	18.4315	1.20749	0.603745	−	0.797177i	$-0.293674\pi$
$233$	18.4315	1.20749	0.603745	+	0.797177i	$0.293674\pi$
$234$	1.33292	0.0871356
$235$	−19.3940	−1.26513
$236$	−2.37192	−0.154399
$237$	12.0989	0.785908
$238$	−1.33031	−0.0862315
$239$	0.889441	0.0575331	0.0287666	−	0.999586i	$-0.490842\pi$
$239$	0.889441	0.0575331	0.0287666	+	0.999586i	$0.490842\pi$
$240$	−13.6113	−0.878606
$241$	−11.7554	−0.757233	−0.378616	−	0.925554i	$-0.623600\pi$
$241$	−11.7554	−0.757233	−0.378616	+	0.925554i	$0.623600\pi$
$242$	2.24463	0.144291
$243$	−10.2962	−0.660499
$244$	−0.535387	−0.0342746
$245$	29.3747	1.87668
$246$	4.99109	0.318220
$247$	−30.3160	−1.92896
$248$	−1.54804	−0.0983007
$249$	−22.1413	−1.40315
$250$	1.72872	0.109334
$251$	−14.4551	−0.912397	−0.456199	−	0.889878i	$-0.650789\pi$
$251$	−14.4551	−0.912397	−0.456199	+	0.889878i	$0.650789\pi$
$252$	8.29755	0.522696
$253$	−7.91389	−0.497542
$254$	−3.40124	−0.213413
$255$	−4.09351	−0.256346
$256$	8.90468	0.556543
$257$	17.2989	1.07907	0.539537	−	0.841962i	$-0.318599\pi$
$257$	17.2989	1.07907	0.539537	+	0.841962i	$0.318599\pi$
$258$	−3.40158	−0.211773
$259$	−32.4189	−2.01441
$260$	−22.2784	−1.38165
$261$	−4.69403	−0.290553
$262$	1.62247	0.100237
$263$	4.00876	0.247191	0.123595	−	0.992333i	$-0.460558\pi$
$263$	4.00876	0.247191	0.123595	+	0.992333i	$0.460558\pi$
$264$	−3.25638	−0.200416
$265$	10.4374	0.641165
$266$	9.44880	0.579343
$267$	4.52770	0.277091
$268$	16.2257	0.991140
$269$	28.0301	1.70902	0.854511	−	0.519433i	$-0.173857\pi$
$269$	28.0301	1.70902	0.854511	+	0.519433i	$0.173857\pi$
$270$	−4.94725	−0.301080
$271$	16.3058	0.990507	0.495253	−	0.868749i	$-0.335075\pi$
$271$	16.3058	0.990507	0.495253	+	0.868749i	$0.335075\pi$
$272$	3.55252	0.215403
$273$	−24.0617	−1.45628
$274$	0.519149	0.0313629
$275$	5.84072	0.352209
$276$	−10.9098	−0.656694
$277$	−26.3241	−1.58166	−0.790831	−	0.612035i	$-0.790351\pi$
$277$	−26.3241	−1.58166	−0.790831	+	0.612035i	$0.790351\pi$
$278$	−0.308806	−0.0185209
$279$	1.34199	0.0803431
$280$	14.2350	0.850701
$281$	−7.58167	−0.452285	−0.226142	−	0.974094i	$-0.572611\pi$
$281$	−7.58167	−0.452285	−0.226142	+	0.974094i	$0.572611\pi$
$282$	−2.95602	−0.176029
$283$	−14.2221	−0.845417	−0.422709	−	0.906266i	$-0.638921\pi$
$283$	−14.2221	−0.845417	−0.422709	+	0.906266i	$0.638921\pi$
$284$	12.1922	0.723475
$285$	29.0749	1.72225
$286$	−2.46318	−0.145651
$287$	48.1804	2.84400
$288$	3.63016	0.213910
$289$	−15.9316	−0.937153
$290$	−3.92812	−0.230667
$291$	10.1688	0.596107
$292$	11.2870	0.660524
$293$	−4.68983	−0.273983	−0.136991	−	0.990572i	$-0.543743\pi$
$293$	−4.68983	−0.273983	−0.136991	+	0.990572i	$0.543743\pi$
$294$	4.47727	0.261120
$295$	3.52757	0.205383
$296$	−9.37912	−0.545150
$297$	10.9249	0.633927
$298$	−4.30035	−0.249113
$299$	−16.9179	−0.978388
$300$	8.05182	0.464872
$301$	−32.8364	−1.89266
$302$	−2.66774	−0.153511
$303$	18.2392	1.04782
$304$	−25.2324	−1.44718
$305$	0.796238	0.0455924
$306$	0.333647	0.0190733
$307$	10.6916	0.610199	0.305100	−	0.952320i	$-0.401310\pi$
$307$	10.6916	0.610199	0.305100	+	0.952320i	$0.401310\pi$
$308$	−15.3335	−0.873708
$309$	16.6443	0.946861
$310$	1.12302	0.0637835
$311$	−21.0455	−1.19338	−0.596690	−	0.802472i	$-0.703518\pi$
$311$	−21.0455	−1.19338	−0.596690	+	0.802472i	$0.703518\pi$
$312$	−6.96132	−0.394107
$313$	−14.2033	−0.802819	−0.401409	−	0.915899i	$-0.631480\pi$
$313$	−14.2033	−0.802819	−0.401409	+	0.915899i	$0.631480\pi$
$314$	−3.22276	−0.181871
$315$	−12.3403	−0.695295
$316$	16.4823	0.927200
$317$	2.85738	0.160487	0.0802433	−	0.996775i	$-0.474430\pi$
$317$	2.85738	0.160487	0.0802433	+	0.996775i	$0.474430\pi$
$318$	1.59086	0.0892111
$319$	8.67437	0.485672
$320$	−16.4331	−0.918641
$321$	−22.5177	−1.25681
$322$	5.27292	0.293848
$323$	−7.58849	−0.422235
$324$	9.08803	0.504890
$325$	12.4860	0.692598
$326$	1.15310	0.0638642
$327$	−18.3801	−1.01642
$328$	13.9391	0.769658
$329$	−28.5353	−1.57320
$330$	2.36234	0.130042
$331$	12.1172	0.666019	0.333010	−	0.942923i	$-0.391936\pi$
$331$	12.1172	0.666019	0.333010	+	0.942923i	$0.391936\pi$
$332$	−30.1630	−1.65541
$333$	8.13074	0.445562
$334$	6.09900	0.333722
$335$	−24.1311	−1.31842
$336$	−20.0269	−1.09256
$337$	−12.4929	−0.680532	−0.340266	−	0.940329i	$-0.610517\pi$
$337$	−12.4929	−0.680532	−0.340266	+	0.940329i	$0.610517\pi$
$338$	−1.25117	−0.0680549
$339$	20.6354	1.12076
$340$	−5.57657	−0.302432
$341$	−2.47995	−0.134297
$342$	−2.36979	−0.128143
$343$	14.0461	0.758418
$344$	−9.49991	−0.512201
$345$	16.2253	0.873540
$346$	2.32045	0.124748
$347$	−11.1030	−0.596039	−0.298020	−	0.954560i	$-0.596326\pi$
$347$	−11.1030	−0.596039	−0.298020	+	0.954560i	$0.596326\pi$
$348$	11.9582	0.641026
$349$	16.3372	0.874509	0.437254	−	0.899338i	$-0.355951\pi$
$349$	16.3372	0.874509	0.437254	+	0.899338i	$0.355951\pi$
$350$	−3.89159	−0.208014
$351$	23.3547	1.24658
$352$	−6.70839	−0.357558
$353$	−26.2175	−1.39542	−0.697709	−	0.716382i	$-0.745797\pi$
$353$	−26.2175	−1.39542	−0.697709	+	0.716382i	$0.745797\pi$
$354$	0.537669	0.0285768
$355$	−18.1325	−0.962373
$356$	6.16806	0.326906
$357$	−6.02297	−0.318769
$358$	−7.49240	−0.395986
$359$	18.6480	0.984204	0.492102	−	0.870537i	$-0.336229\pi$
$359$	18.6480	0.984204	0.492102	+	0.870537i	$0.336229\pi$
$360$	−3.57017	−0.188164
$361$	34.8986	1.83677
$362$	0.945009	0.0496686
$363$	10.1625	0.533394
$364$	−32.7792	−1.71810
$365$	−16.7863	−0.878636
$366$	0.121362	0.00634369
$367$	−3.92562	−0.204916	−0.102458	−	0.994737i	$-0.532671\pi$
$367$	−3.92562	−0.204916	−0.102458	+	0.994737i	$0.532671\pi$
$368$	−14.0810	−0.734023
$369$	−12.0838	−0.629057
$370$	6.80407	0.353727
$371$	15.3570	0.797297
$372$	−3.41877	−0.177255
$373$	14.3279	0.741870	0.370935	−	0.928659i	$-0.379037\pi$
$373$	14.3279	0.741870	0.370935	+	0.928659i	$0.379037\pi$
$374$	−0.616565	−0.0318818
$375$	7.82673	0.404171
$376$	−8.25557	−0.425749
$377$	18.5436	0.955045
$378$	−7.27912	−0.374397
$379$	5.65835	0.290650	0.145325	−	0.989384i	$-0.453577\pi$
$379$	5.65835	0.290650	0.145325	+	0.989384i	$0.453577\pi$
$380$	39.6085	2.03188
$381$	−15.3990	−0.788917
$382$	−2.72844	−0.139599
$383$	4.23323	0.216308	0.108154	−	0.994134i	$-0.465506\pi$
$383$	4.23323	0.216308	0.108154	+	0.994134i	$0.465506\pi$
$384$	−12.2157	−0.623380
$385$	22.8043	1.16221
$386$	−4.61074	−0.234681
$387$	8.23546	0.418632
$388$	13.8529	0.703275
$389$	−5.21409	−0.264365	−0.132182	−	0.991225i	$-0.542198\pi$
$389$	−5.21409	−0.264365	−0.132182	+	0.991225i	$0.542198\pi$
$390$	5.05008	0.255721
$391$	−4.23477	−0.214162
$392$	12.5041	0.631553
$393$	7.34570	0.370542
$394$	3.67419	0.185103
$395$	−24.5127	−1.23337
$396$	3.84569	0.193253
$397$	9.63263	0.483448	0.241724	−	0.970345i	$-0.422287\pi$
$397$	9.63263	0.483448	0.241724	+	0.970345i	$0.422287\pi$
$398$	1.36098	0.0682196
$399$	42.7792	2.14164
$400$	10.3923	0.519613
$401$	24.8722	1.24206	0.621030	−	0.783787i	$-0.286714\pi$
$401$	24.8722	1.24206	0.621030	+	0.783787i	$0.286714\pi$
$402$	−3.67804	−0.183444
$403$	−5.30151	−0.264087
$404$	24.8472	1.23619
$405$	−13.5159	−0.671610
$406$	−5.77962	−0.286837
$407$	−15.0253	−0.744775
$408$	−1.74251	−0.0862670
$409$	−28.4449	−1.40651	−0.703255	−	0.710938i	$-0.748271\pi$
$409$	−28.4449	−1.40651	−0.703255	+	0.710938i	$0.748271\pi$
$410$	−10.1121	−0.499401
$411$	2.35043	0.115938
$412$	22.6744	1.11709
$413$	5.19027	0.255397
$414$	−1.32246	−0.0649955
$415$	44.8590	2.20204
$416$	−14.3408	−0.703118
$417$	−1.39811	−0.0684658
$418$	4.37926	0.214197
$419$	−4.59075	−0.224273	−0.112136	−	0.993693i	$-0.535769\pi$
$419$	−4.59075	−0.224273	−0.112136	+	0.993693i	$0.535769\pi$
$420$	31.4372	1.53398
$421$	20.9586	1.02146	0.510729	−	0.859742i	$-0.329375\pi$
$421$	20.9586	1.02146	0.510729	+	0.859742i	$0.329375\pi$
$422$	−6.61517	−0.322021
$423$	7.15674	0.347973
$424$	4.44295	0.215769
$425$	3.12541	0.151604
$426$	−2.76374	−0.133904
$427$	1.17154	0.0566948
$428$	−30.6757	−1.48276
$429$	−11.1520	−0.538423
$430$	6.89170	0.332347
$431$	14.1727	0.682676	0.341338	−	0.939941i	$-0.389120\pi$
$431$	14.1727	0.682676	0.341338	+	0.939941i	$0.389120\pi$
$432$	19.4384	0.935232
$433$	7.32714	0.352120	0.176060	−	0.984379i	$-0.443665\pi$
$433$	7.32714	0.352120	0.176060	+	0.984379i	$0.443665\pi$
$434$	1.65236	0.0793157
$435$	−17.7844	−0.852699
$436$	−25.0391	−1.19916
$437$	30.0782	1.43884
$438$	−2.55856	−0.122253
$439$	3.07088	0.146565	0.0732825	−	0.997311i	$-0.476653\pi$
$439$	3.07088	0.146565	0.0732825	+	0.997311i	$0.476653\pi$
$440$	6.59752	0.314525
$441$	−10.8398	−0.516181
$442$	−1.31806	−0.0626938
$443$	14.9982	0.712586	0.356293	−	0.934374i	$-0.384040\pi$
$443$	14.9982	0.712586	0.356293	+	0.934374i	$0.384040\pi$
$444$	−20.7133	−0.983011
$445$	−9.17325	−0.434854
$446$	2.45063	0.116041
$447$	−19.4697	−0.920887
$448$	−24.1788	−1.14234
$449$	−22.4064	−1.05742	−0.528711	−	0.848802i	$-0.677324\pi$
$449$	−22.4064	−1.05742	−0.528711	+	0.848802i	$0.677324\pi$
$450$	0.976023	0.0460102
$451$	22.3303	1.05149
$452$	28.1115	1.32225
$453$	−12.0781	−0.567479
$454$	−4.92096	−0.230952
$455$	48.7498	2.28543
$456$	12.3765	0.579581
$457$	−12.9317	−0.604919	−0.302460	−	0.953162i	$-0.597808\pi$
$457$	−12.9317	−0.604919	−0.302460	+	0.953162i	$0.597808\pi$
$458$	−4.15999	−0.194384
$459$	5.84598	0.272867
$460$	22.1036	1.03059
$461$	−39.7115	−1.84955	−0.924774	−	0.380517i	$-0.875746\pi$
$461$	−39.7115	−1.84955	−0.924774	+	0.380517i	$0.875746\pi$
$462$	3.47581	0.161709
$463$	21.4987	0.999130	0.499565	−	0.866276i	$-0.333493\pi$
$463$	21.4987	0.999130	0.499565	+	0.866276i	$0.333493\pi$
$464$	15.4341	0.716510
$465$	5.08447	0.235786
$466$	−5.69177	−0.263666
$467$	−19.2688	−0.891655	−0.445827	−	0.895119i	$-0.647090\pi$
$467$	−19.2688	−0.891655	−0.445827	+	0.895119i	$0.647090\pi$
$468$	8.22112	0.380021
$469$	−35.5052	−1.63948
$470$	5.98899	0.276252
$471$	−14.5910	−0.672317
$472$	1.50160	0.0691168
$473$	−15.2188	−0.699761
$474$	−3.73621	−0.171610
$475$	−22.1987	−1.01855
$476$	−8.20506	−0.376078
$477$	−3.85159	−0.176352
$478$	−0.274665	−0.0125629
$479$	−23.7465	−1.08500	−0.542502	−	0.840055i	$-0.682523\pi$
$479$	−23.7465	−1.08500	−0.542502	+	0.840055i	$0.682523\pi$
$480$	13.7537	0.627769
$481$	−32.1202	−1.46456
$482$	3.63014	0.165348
$483$	23.8730	1.08626
$484$	13.8444	0.629289
$485$	−20.6023	−0.935503
$486$	3.17951	0.144226
$487$	−27.3504	−1.23937	−0.619683	−	0.784852i	$-0.712739\pi$
$487$	−27.3504	−1.23937	−0.619683	+	0.784852i	$0.712739\pi$
$488$	0.338939	0.0153430
$489$	5.22062	0.236085
$490$	−9.07109	−0.409790
$491$	−29.0333	−1.31025	−0.655126	−	0.755519i	$-0.727385\pi$
$491$	−29.0333	−1.31025	−0.655126	+	0.755519i	$0.727385\pi$
$492$	30.7838	1.38784
$493$	4.64171	0.209052
$494$	9.36176	0.421206
$495$	−5.71938	−0.257067
$496$	−4.41252	−0.198128
$497$	−26.6792	−1.19672
$498$	6.83737	0.306390
$499$	26.6880	1.19472	0.597359	−	0.801974i	$-0.296217\pi$
$499$	26.6880	1.19472	0.597359	+	0.801974i	$0.296217\pi$
$500$	10.6623	0.476833
$501$	27.6131	1.23366
$502$	4.46382	0.199230
$503$	7.41588	0.330658	0.165329	−	0.986238i	$-0.447131\pi$
$503$	7.41588	0.330658	0.165329	+	0.986238i	$0.447131\pi$
$504$	−5.25295	−0.233985
$505$	−36.9532	−1.64440
$506$	2.44386	0.108643
$507$	−5.66466	−0.251577
$508$	−20.9780	−0.930749
$509$	36.1455	1.60212	0.801060	−	0.598583i	$-0.204270\pi$
$509$	36.1455	1.60212	0.801060	+	0.598583i	$0.204270\pi$
$510$	1.26410	0.0559753
$511$	−24.6985	−1.09260
$512$	−20.2244	−0.893801
$513$	−41.5221	−1.83325
$514$	−5.34199	−0.235625
$515$	−33.7219	−1.48596
$516$	−20.9801	−0.923597
$517$	−13.2254	−0.581651
$518$	10.0111	0.439864
$519$	10.5058	0.461153
$520$	14.1038	0.618494
$521$	33.9636	1.48797	0.743986	−	0.668196i	$-0.232933\pi$
$521$	33.9636	1.48797	0.743986	+	0.668196i	$0.232933\pi$
$522$	1.44954	0.0634448
$523$	−11.7578	−0.514134	−0.257067	−	0.966394i	$-0.582756\pi$
$523$	−11.7578	−0.514134	−0.257067	+	0.966394i	$0.582756\pi$
$524$	10.0070	0.437158
$525$	−17.6191	−0.768960
$526$	−1.23793	−0.0539762
$527$	−1.32704	−0.0578066
$528$	−9.28194	−0.403945
$529$	−6.21480	−0.270209
$530$	−3.22313	−0.140004
$531$	−1.30174	−0.0564905
$532$	58.2779	2.52667
$533$	47.7366	2.06770
$534$	−1.39818	−0.0605051
$535$	45.6214	1.97239
$536$	−10.2720	−0.443684
$537$	−33.9217	−1.46383
$538$	−8.65585	−0.373180
$539$	20.0315	0.862818
$540$	−30.5134	−1.31309
$541$	0.804094	0.0345707	0.0172854	−	0.999851i	$-0.494498\pi$
$541$	0.804094	0.0345707	0.0172854	+	0.999851i	$0.494498\pi$
$542$	−5.03533	−0.216286
$543$	4.27851	0.183608
$544$	−3.58970	−0.153907
$545$	37.2386	1.59513
$546$	7.43041	0.317992
$547$	−4.34094	−0.185605	−0.0928027	−	0.995685i	$-0.529583\pi$
$547$	−4.34094	−0.185605	−0.0928027	+	0.995685i	$0.529583\pi$
$548$	3.20198	0.136782
$549$	−0.293826	−0.0125402
$550$	−1.80365	−0.0769079
$551$	−32.9686	−1.40451
$552$	6.90671	0.293969
$553$	−36.0667	−1.53371
$554$	8.12904	0.345370
$555$	30.8053	1.30761
$556$	−1.90464	−0.0807747
$557$	−29.2321	−1.23861	−0.619303	−	0.785152i	$-0.712585\pi$
$557$	−29.2321	−1.23861	−0.619303	+	0.785152i	$0.712585\pi$
$558$	−0.414416	−0.0175436
$559$	−32.5339	−1.37604
$560$	40.5751	1.71461
$561$	−2.79148	−0.117857
$562$	2.34126	0.0987603
$563$	27.9325	1.17721	0.588606	−	0.808420i	$-0.299677\pi$
$563$	27.9325	1.17721	0.588606	+	0.808420i	$0.299677\pi$
$564$	−18.2320	−0.767707
$565$	−41.8079	−1.75887
$566$	4.39187	0.184604
$567$	−19.8865	−0.835156
$568$	−7.71857	−0.323864
$569$	21.5023	0.901424	0.450712	−	0.892669i	$-0.351170\pi$
$569$	21.5023	0.901424	0.450712	+	0.892669i	$0.351170\pi$
$570$	−8.97849	−0.376068
$571$	19.6384	0.821843	0.410922	−	0.911671i	$-0.365207\pi$
$571$	19.6384	0.821843	0.410922	+	0.911671i	$0.365207\pi$
$572$	−15.1923	−0.635221
$573$	−12.3529	−0.516051
$574$	−14.8784	−0.621012
$575$	−12.3881	−0.516617
$576$	6.06412	0.252672
$577$	14.7632	0.614599	0.307299	−	0.951613i	$-0.400575\pi$
$577$	14.7632	0.614599	0.307299	+	0.951613i	$0.400575\pi$
$578$	4.91977	0.204636
$579$	−20.8750	−0.867536
$580$	−24.2277	−1.00600
$581$	66.0031	2.73827
$582$	−3.14019	−0.130165
$583$	7.11757	0.294780
$584$	−7.14552	−0.295684
$585$	−12.2266	−0.505508
$586$	1.44825	0.0598265
$587$	−6.27328	−0.258926	−0.129463	−	0.991584i	$-0.541325\pi$
$587$	−6.27328	−0.258926	−0.129463	+	0.991584i	$0.541325\pi$
$588$	27.6147	1.13881
$589$	9.42551	0.388371
$590$	−1.08933	−0.0448472
$591$	16.6348	0.684265
$592$	−26.7341	−1.09877
$593$	40.8082	1.67579	0.837895	−	0.545831i	$-0.183786\pi$
$593$	40.8082	1.67579	0.837895	+	0.545831i	$0.183786\pi$
$594$	−3.37368	−0.138424
$595$	12.2027	0.500263
$596$	−26.5235	−1.08645
$597$	6.16179	0.252185
$598$	5.22435	0.213639
$599$	−10.3330	−0.422193	−0.211096	−	0.977465i	$-0.567703\pi$
$599$	−10.3330	−0.422193	−0.211096	+	0.977465i	$0.567703\pi$
$600$	−5.09739	−0.208100
$601$	15.7883	0.644019	0.322009	−	0.946737i	$-0.395642\pi$
$601$	15.7883	0.644019	0.322009	+	0.946737i	$0.395642\pi$
$602$	10.1401	0.413278
$603$	8.90480	0.362632
$604$	−16.4539	−0.669502
$605$	−20.5896	−0.837086
$606$	−5.63238	−0.228800
$607$	12.8843	0.522958	0.261479	−	0.965209i	$-0.415790\pi$
$607$	12.8843	0.522958	0.261479	+	0.965209i	$0.415790\pi$
$608$	25.4965	1.03402
$609$	−26.1671	−1.06034
$610$	−0.245883	−0.00995551
$611$	−28.2725	−1.14378
$612$	2.05785	0.0831837
$613$	6.99917	0.282694	0.141347	−	0.989960i	$-0.454857\pi$
$613$	6.99917	0.282694	0.141347	+	0.989960i	$0.454857\pi$
$614$	−3.30162	−0.133242
$615$	−45.7823	−1.84612
$616$	9.70723	0.391116
$617$	−8.16208	−0.328593	−0.164297	−	0.986411i	$-0.552535\pi$
$617$	−8.16208	−0.328593	−0.164297	+	0.986411i	$0.552535\pi$
$618$	−5.13986	−0.206755
$619$	−12.6031	−0.506559	−0.253280	−	0.967393i	$-0.581509\pi$
$619$	−12.6031	−0.506559	−0.253280	+	0.967393i	$0.581509\pi$
$620$	6.92654	0.278176
$621$	−23.1715	−0.929840
$622$	6.49897	0.260585
$623$	−13.4970	−0.540747
$624$	−19.8425	−0.794334
$625$	−30.9757	−1.23903
$626$	4.38607	0.175303
$627$	19.8270	0.791815
$628$	−19.8772	−0.793187
$629$	−8.04011	−0.320580
$630$	3.81075	0.151824
$631$	45.4769	1.81041	0.905203	−	0.424980i	$-0.139719\pi$
$631$	45.4769	1.81041	0.905203	+	0.424980i	$0.139719\pi$
$632$	−10.4345	−0.415061
$633$	−29.9500	−1.19041
$634$	−0.882377	−0.0350437
$635$	31.1989	1.23809
$636$	9.81204	0.389073
$637$	42.8223	1.69668
$638$	−2.67870	−0.106051
$639$	6.69122	0.264700
$640$	24.7494	0.978306
$641$	12.1865	0.481339	0.240669	−	0.970607i	$-0.422633\pi$
$641$	12.1865	0.481339	0.240669	+	0.970607i	$0.422633\pi$
$642$	6.95358	0.274436
$643$	29.7340	1.17259	0.586296	−	0.810097i	$-0.300585\pi$
$643$	29.7340	1.17259	0.586296	+	0.810097i	$0.300585\pi$
$644$	32.5221	1.28155
$645$	31.2020	1.22858
$646$	2.34337	0.0921987
$647$	−32.8228	−1.29040	−0.645199	−	0.764015i	$-0.723226\pi$
$647$	−32.8228	−1.29040	−0.645199	+	0.764015i	$0.723226\pi$
$648$	−5.75339	−0.226014
$649$	2.40555	0.0944262
$650$	−3.85575	−0.151235
$651$	7.48100	0.293204
$652$	7.11203	0.278529
$653$	10.3258	0.404078	0.202039	−	0.979377i	$-0.435243\pi$
$653$	10.3258	0.404078	0.202039	+	0.979377i	$0.435243\pi$
$654$	5.67588	0.221944
$655$	−14.8826	−0.581512
$656$	39.7318	1.55127
$657$	6.19445	0.241668
$658$	8.81188	0.343523
$659$	25.8076	1.00532	0.502661	−	0.864484i	$-0.332354\pi$
$659$	25.8076	1.00532	0.502661	+	0.864484i	$0.332354\pi$
$660$	14.5703	0.567149
$661$	−13.3955	−0.521025	−0.260513	−	0.965470i	$-0.583892\pi$
$661$	−13.3955	−0.521025	−0.260513	+	0.965470i	$0.583892\pi$
$662$	−3.74185	−0.145431
$663$	−5.96749	−0.231758
$664$	19.0954	0.741044
$665$	−86.6719	−3.36099
$666$	−2.51082	−0.0972924
$667$	−18.3982	−0.712380
$668$	37.6171	1.45545
$669$	11.0952	0.428963
$670$	7.45182	0.287889
$671$	0.542978	0.0209614
$672$	20.2365	0.780640
$673$	−6.82079	−0.262922	−0.131461	−	0.991321i	$-0.541967\pi$
$673$	−6.82079	−0.262922	−0.131461	+	0.991321i	$0.541967\pi$
$674$	3.85788	0.148600
$675$	17.1014	0.658232
$676$	−7.71694	−0.296805
$677$	10.5869	0.406888	0.203444	−	0.979087i	$-0.434787\pi$
$677$	10.5869	0.406888	0.203444	+	0.979087i	$0.434787\pi$
$678$	−6.37233	−0.244728
$679$	−30.3131	−1.16331
$680$	3.53037	0.135384
$681$	−22.2795	−0.853753
$682$	0.765823	0.0293249
$683$	43.3107	1.65724	0.828620	−	0.559812i	$-0.189127\pi$
$683$	43.3107	1.65724	0.828620	+	0.559812i	$0.189127\pi$
$684$	−14.6163	−0.558867
$685$	−4.76205	−0.181948
$686$	−4.33752	−0.165607
$687$	−18.8343	−0.718572
$688$	−27.0784	−1.03236
$689$	15.2156	0.579667
$690$	−5.01047	−0.190745
$691$	−27.5238	−1.04706	−0.523528	−	0.852009i	$-0.675384\pi$
$691$	−27.5238	−1.04706	−0.523528	+	0.852009i	$0.675384\pi$
$692$	14.3120	0.544060
$693$	−8.41519	−0.319667
$694$	3.42867	0.130150
$695$	2.83261	0.107447
$696$	−7.57041	−0.286956
$697$	11.9491	0.452604
$698$	−5.04501	−0.190957
$699$	−25.7694	−0.974686
$700$	−24.0024	−0.907205
$701$	51.4490	1.94320	0.971601	−	0.236625i	$-0.0760413\pi$
$701$	51.4490	1.94320	0.971601	+	0.236625i	$0.0760413\pi$
$702$	−7.21207	−0.272202
$703$	57.1063	2.15381
$704$	−11.2062	−0.422351
$705$	27.1150	1.02121
$706$	8.09612	0.304702
$707$	−54.3710	−2.04483
$708$	3.31621	0.124631
$709$	16.8255	0.631894	0.315947	−	0.948777i	$-0.397678\pi$
$709$	16.8255	0.631894	0.315947	+	0.948777i	$0.397678\pi$
$710$	5.59942	0.210143
$711$	9.04563	0.339238
$712$	−3.90483	−0.146340
$713$	5.25992	0.196986
$714$	1.85993	0.0696061
$715$	22.5942	0.844977
$716$	−46.2113	−1.72700
$717$	−1.24354	−0.0464407
$718$	−5.75862	−0.214910
$719$	26.2933	0.980574	0.490287	−	0.871561i	$-0.336892\pi$
$719$	26.2933	0.980574	0.490287	+	0.871561i	$0.336892\pi$
$720$	−10.1764	−0.379251
$721$	−49.6165	−1.84781
$722$	−10.7769	−0.401074
$723$	16.4354	0.611238
$724$	5.82858	0.216618
$725$	13.5785	0.504292
$726$	−3.13825	−0.116471
$727$	23.5378	0.872967	0.436484	−	0.899712i	$-0.356224\pi$
$727$	23.5378	0.872967	0.436484	+	0.899712i	$0.356224\pi$
$728$	20.7516	0.769106
$729$	28.7097	1.06332
$730$	5.18371	0.191858
$731$	−8.14366	−0.301204
$732$	0.748531	0.0276665
$733$	−10.0422	−0.370919	−0.185459	−	0.982652i	$-0.559377\pi$
$733$	−10.0422	−0.370919	−0.185459	+	0.982652i	$0.559377\pi$
$734$	1.21225	0.0447451
$735$	−41.0691	−1.51486
$736$	14.2284	0.524464
$737$	−16.4557	−0.606154
$738$	3.73154	0.137360
$739$	8.15975	0.300161	0.150081	−	0.988674i	$-0.452047\pi$
$739$	8.15975	0.300161	0.150081	+	0.988674i	$0.452047\pi$
$740$	41.9658	1.54269
$741$	42.3851	1.55706
$742$	−4.74234	−0.174097
$743$	7.78206	0.285496	0.142748	−	0.989759i	$-0.454406\pi$
$743$	7.78206	0.285496	0.142748	+	0.989759i	$0.454406\pi$
$744$	2.16433	0.0793483
$745$	39.4463	1.44520
$746$	−4.42454	−0.161994
$747$	−16.5538	−0.605670
$748$	−3.80282	−0.139045
$749$	67.1249	2.45269
$750$	−2.41694	−0.0882542
$751$	−8.30887	−0.303195	−0.151598	−	0.988442i	$-0.548442\pi$
$751$	−8.30887	−0.303195	−0.151598	+	0.988442i	$0.548442\pi$
$752$	−23.5316	−0.858108
$753$	20.2098	0.736487
$754$	−5.72638	−0.208542
$755$	24.4706	0.890577
$756$	−44.8958	−1.63284
$757$	−38.8376	−1.41158	−0.705788	−	0.708424i	$-0.749407\pi$
$757$	−38.8376	−1.41158	−0.705788	+	0.708424i	$0.749407\pi$
$758$	−1.74733	−0.0634659
$759$	11.0645	0.401616
$760$	−25.0751	−0.909569
$761$	−25.3906	−0.920408	−0.460204	−	0.887813i	$-0.652224\pi$
$761$	−25.3906	−0.920408	−0.460204	+	0.887813i	$0.652224\pi$
$762$	4.75531	0.172267
$763$	54.7909	1.98356
$764$	−16.8283	−0.608827
$765$	−3.06048	−0.110652
$766$	−1.30725	−0.0472327
$767$	5.14246	0.185684
$768$	−12.4497	−0.449241
$769$	39.8098	1.43558	0.717788	−	0.696261i	$-0.245155\pi$
$769$	39.8098	1.43558	0.717788	+	0.696261i	$0.245155\pi$
$770$	−7.04210	−0.253780
$771$	−24.1857	−0.871028
$772$	−28.4379	−1.02350
$773$	9.95735	0.358141	0.179070	−	0.983836i	$-0.442691\pi$
$773$	9.95735	0.358141	0.179070	+	0.983836i	$0.442691\pi$
$774$	−2.54316	−0.0914120
$775$	−3.88200	−0.139446
$776$	−8.76991	−0.314821
$777$	45.3252	1.62603
$778$	1.61014	0.0577263
$779$	−84.8706	−3.04080
$780$	31.1476	1.11526
$781$	−12.3651	−0.442458
$782$	1.30772	0.0467641
$783$	25.3981	0.907656
$784$	35.6416	1.27291
$785$	29.5618	1.05510
$786$	−2.26839	−0.0809110
$787$	30.2211	1.07727	0.538633	−	0.842541i	$-0.318941\pi$
$787$	30.2211	1.07727	0.538633	+	0.842541i	$0.318941\pi$
$788$	22.6615	0.807283
$789$	−5.60469	−0.199532
$790$	7.56968	0.269317
$791$	−61.5139	−2.18718
$792$	−2.43460	−0.0865098
$793$	1.16075	0.0412194
$794$	−2.97461	−0.105565
$795$	−14.5927	−0.517548
$796$	8.39417	0.297524
$797$	−10.6318	−0.376597	−0.188298	−	0.982112i	$-0.560297\pi$
$797$	−10.6318	−0.376597	−0.188298	+	0.982112i	$0.560297\pi$
$798$	−13.2105	−0.467645
$799$	−7.07697	−0.250365
$800$	−10.5010	−0.371267
$801$	3.38509	0.119606
$802$	−7.68069	−0.271215
$803$	−11.4471	−0.403959
$804$	−22.6853	−0.800048
$805$	−48.3674	−1.70473
$806$	1.63714	0.0576657
$807$	−39.1891	−1.37952
$808$	−15.7301	−0.553383
$809$	−15.9047	−0.559178	−0.279589	−	0.960120i	$-0.590198\pi$
$809$	−15.9047	−0.559178	−0.279589	+	0.960120i	$0.590198\pi$
$810$	4.17379	0.146652
$811$	53.3099	1.87196	0.935981	−	0.352049i	$-0.114515\pi$
$811$	53.3099	1.87196	0.935981	+	0.352049i	$0.114515\pi$
$812$	−35.6473	−1.25097
$813$	−22.7973	−0.799537
$814$	4.63989	0.162628
$815$	−10.5771	−0.370501
$816$	−4.96682	−0.173874
$817$	57.8418	2.02363
$818$	8.78395	0.307124
$819$	−17.9895	−0.628606
$820$	−62.3690	−2.17802
$821$	−16.7614	−0.584975	−0.292488	−	0.956269i	$-0.594483\pi$
$821$	−16.7614	−0.584975	−0.292488	+	0.956269i	$0.594483\pi$
$822$	−0.725827	−0.0253161
$823$	38.0271	1.32554	0.662770	−	0.748823i	$-0.269381\pi$
$823$	38.0271	1.32554	0.662770	+	0.748823i	$0.269381\pi$
$824$	−14.3546	−0.500065
$825$	−8.16598	−0.284303
$826$	−1.60279	−0.0557681
$827$	40.6301	1.41285	0.706424	−	0.707789i	$-0.250307\pi$
$827$	40.6301	1.41285	0.706424	+	0.707789i	$0.250307\pi$
$828$	−8.15663	−0.283462
$829$	−48.8098	−1.69523	−0.847617	−	0.530608i	$-0.821964\pi$
$829$	−48.8098	−1.69523	−0.847617	+	0.530608i	$0.821964\pi$
$830$	−13.8527	−0.480835
$831$	36.8040	1.27672
$832$	−23.9561	−0.830529
$833$	10.7190	0.371390
$834$	0.431745	0.0149501
$835$	−55.9449	−1.93605
$836$	27.0102	0.934168
$837$	−7.26117	−0.250983
$838$	1.41765	0.0489719
$839$	−13.9510	−0.481641	−0.240821	−	0.970570i	$-0.577417\pi$
$839$	−13.9510	−0.481641	−0.240821	+	0.970570i	$0.577417\pi$
$840$	−19.9021	−0.686686
$841$	−8.83388	−0.304617
$842$	−6.47213	−0.223044
$843$	10.6000	0.365084
$844$	−40.8007	−1.40442
$845$	11.4768	0.394813
$846$	−2.21004	−0.0759829
$847$	−30.2944	−1.04093
$848$	12.6641	0.434888
$849$	19.8841	0.682421
$850$	−0.965144	−0.0331042
$851$	31.8683	1.09243
$852$	−17.0461	−0.583989
$853$	−48.3304	−1.65480	−0.827401	−	0.561612i	$-0.810181\pi$
$853$	−48.3304	−1.65480	−0.827401	+	0.561612i	$0.810181\pi$
$854$	−0.361779	−0.0123798
$855$	21.7376	0.743409
$856$	19.4199	0.663760
$857$	−47.8068	−1.63305	−0.816525	−	0.577310i	$-0.804103\pi$
$857$	−47.8068	−1.63305	−0.816525	+	0.577310i	$0.804103\pi$
$858$	3.44380	0.117569
$859$	57.7110	1.96907	0.984537	−	0.175179i	$-0.0560503\pi$
$859$	57.7110	1.96907	0.984537	+	0.175179i	$0.0560503\pi$
$860$	42.5063	1.44945
$861$	−67.3616	−2.29568
$862$	−4.37662	−0.149068
$863$	22.5913	0.769018	0.384509	−	0.923121i	$-0.374371\pi$
$863$	22.5913	0.769018	0.384509	+	0.923121i	$0.374371\pi$
$864$	−19.6418	−0.668229
$865$	−21.2851	−0.723714
$866$	−2.26266	−0.0768884
$867$	22.2741	0.756470
$868$	10.1913	0.345916
$869$	−16.7160	−0.567050
$870$	5.49194	0.186194
$871$	−35.1781	−1.19197
$872$	15.8516	0.536802
$873$	7.60262	0.257310
$874$	−9.28833	−0.314182
$875$	−23.3314	−0.788746
$876$	−15.7805	−0.533175
$877$	8.20763	0.277152	0.138576	−	0.990352i	$-0.455748\pi$
$877$	8.20763	0.277152	0.138576	+	0.990352i	$0.455748\pi$
$878$	−0.948305	−0.0320037
$879$	6.55690	0.221159
$880$	18.8055	0.633933
$881$	54.9341	1.85078	0.925388	−	0.379020i	$-0.123739\pi$
$881$	54.9341	1.85078	0.925388	+	0.379020i	$0.123739\pi$
$882$	3.34739	0.112713
$883$	−42.9747	−1.44621	−0.723107	−	0.690736i	$-0.757286\pi$
$883$	−42.9747	−1.44621	−0.723107	+	0.690736i	$0.757286\pi$
$884$	−8.12948	−0.273424
$885$	−4.93193	−0.165785
$886$	−4.63153	−0.155599
$887$	−16.0125	−0.537647	−0.268824	−	0.963189i	$-0.586635\pi$
$887$	−16.0125	−0.537647	−0.268824	+	0.963189i	$0.586635\pi$
$888$	13.1130	0.440045
$889$	45.9044	1.53958
$890$	2.83275	0.0949541
$891$	−9.21688	−0.308777
$892$	15.1149	0.506083
$893$	50.2654	1.68207
$894$	6.01237	0.201084
$895$	68.7263	2.29727
$896$	36.4149	1.21654
$897$	23.6531	0.789754
$898$	6.91921	0.230897
$899$	−5.76537	−0.192286
$900$	6.01987	0.200662
$901$	3.80866	0.126885
$902$	−6.89574	−0.229603
$903$	45.9089	1.52775
$904$	−17.7966	−0.591907
$905$	−8.66838	−0.288147
$906$	3.72979	0.123914
$907$	17.4683	0.580026	0.290013	−	0.957023i	$-0.406340\pi$
$907$	17.4683	0.580026	0.290013	+	0.957023i	$0.406340\pi$
$908$	−30.3513	−1.00724
$909$	13.6364	0.452291
$910$	−15.0542	−0.499043
$911$	16.6656	0.552157	0.276078	−	0.961135i	$-0.410965\pi$
$911$	16.6656	0.552157	0.276078	+	0.961135i	$0.410965\pi$
$912$	35.2777	1.16816
$913$	30.5907	1.01240
$914$	3.99338	0.132089
$915$	−1.11323	−0.0368022
$916$	−25.6578	−0.847758
$917$	−21.8975	−0.723118
$918$	−1.80527	−0.0595829
$919$	18.5901	0.613230	0.306615	−	0.951834i	$-0.400804\pi$
$919$	18.5901	0.613230	0.306615	+	0.951834i	$0.400804\pi$
$920$	−13.9932	−0.461342
$921$	−14.9480	−0.492553
$922$	12.2631	0.403865
$923$	−26.4334	−0.870067
$924$	21.4380	0.705257
$925$	−23.5199	−0.773329
$926$	−6.63893	−0.218169
$927$	12.4440	0.408713
$928$	−15.5956	−0.511951
$929$	6.08296	0.199576	0.0997878	−	0.995009i	$-0.468184\pi$
$929$	6.08296	0.199576	0.0997878	+	0.995009i	$0.468184\pi$
$930$	−1.57011	−0.0514860
$931$	−76.1334	−2.49517
$932$	−35.1054	−1.14992
$933$	29.4239	0.963296
$934$	5.95033	0.194701
$935$	5.65563	0.184959
$936$	−5.20457	−0.170117
$937$	−50.4851	−1.64928	−0.824639	−	0.565660i	$-0.808622\pi$
$937$	−50.4851	−1.64928	−0.824639	+	0.565660i	$0.808622\pi$
$938$	10.9642	0.357994
$939$	19.8578	0.648035
$940$	36.9386	1.20481
$941$	−26.6303	−0.868123	−0.434061	−	0.900883i	$-0.642920\pi$
$941$	−26.6303	−0.868123	−0.434061	+	0.900883i	$0.642920\pi$
$942$	4.50578	0.146806
$943$	−47.3622	−1.54232
$944$	4.28014	0.139307
$945$	66.7699	2.17202
$946$	4.69965	0.152799
$947$	−41.7464	−1.35658	−0.678289	−	0.734796i	$-0.737278\pi$
$947$	−41.7464	−1.35658	−0.678289	+	0.734796i	$0.737278\pi$
$948$	−23.0440	−0.748436
$949$	−24.4710	−0.794361
$950$	6.85510	0.222409
$951$	−3.99494	−0.129545
$952$	5.19440	0.168351
$953$	−45.7416	−1.48172	−0.740858	−	0.671662i	$-0.765581\pi$
$953$	−45.7416	−1.48172	−0.740858	+	0.671662i	$0.765581\pi$
$954$	1.18939	0.0385080
$955$	25.0274	0.809867
$956$	−1.69406	−0.0547899
$957$	−12.1277	−0.392034
$958$	7.33305	0.236920
$959$	−7.00662	−0.226255
$960$	22.9754	0.741527
$961$	−29.3517	−0.946830
$962$	9.91892	0.319799
$963$	−16.8351	−0.542504
$964$	22.3898	0.721128
$965$	42.2934	1.36147
$966$	−7.37213	−0.237194
$967$	29.9836	0.964207	0.482104	−	0.876114i	$-0.339873\pi$
$967$	29.9836	0.964207	0.482104	+	0.876114i	$0.339873\pi$
$968$	−8.76449	−0.281701
$969$	10.6096	0.340828
$970$	6.36212	0.204275
$971$	−32.2248	−1.03414	−0.517071	−	0.855942i	$-0.672978\pi$
$971$	−32.2248	−1.03414	−0.517071	+	0.855942i	$0.672978\pi$
$972$	19.6105	0.629006
$973$	4.16776	0.133612
$974$	8.44597	0.270626
$975$	−17.4568	−0.559065
$976$	0.966108	0.0309244
$977$	−1.45628	−0.0465907	−0.0232953	−	0.999729i	$-0.507416\pi$
$977$	−1.45628	−0.0465907	−0.0232953	+	0.999729i	$0.507416\pi$
$978$	−1.61216	−0.0515512
$979$	−6.25551	−0.199927
$980$	−55.9483	−1.78720
$981$	−13.7417	−0.438739
$982$	8.96564	0.286105
$983$	−35.1255	−1.12033	−0.560164	−	0.828382i	$-0.689262\pi$
$983$	−35.1255	−1.12033	−0.560164	+	0.828382i	$0.689262\pi$
$984$	−19.4884	−0.621268
$985$	−33.7026	−1.07385
$986$	−1.43339	−0.0456483
$987$	39.8956	1.26989
$988$	57.7410	1.83699
$989$	32.2787	1.02640
$990$	1.76618	0.0561329
$991$	−9.58149	−0.304366	−0.152183	−	0.988352i	$-0.548630\pi$
$991$	−9.58149	−0.304366	−0.152183	+	0.988352i	$0.548630\pi$
$992$	4.45869	0.141564
$993$	−16.9411	−0.537611
$994$	8.23869	0.261315
$995$	−12.4840	−0.395769
$996$	42.1712	1.33625
$997$	−16.5332	−0.523613	−0.261807	−	0.965120i	$-0.584318\pi$
$997$	−16.5332	−0.523613	−0.261807	+	0.965120i	$0.584318\pi$
$998$	−8.24140	−0.260877
$999$	−43.9933	−1.39189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	139.2.a.c.1.4	✓	7
3.2	odd	2		1251.2.a.k.1.4		7
4.3	odd	2		2224.2.a.o.1.5		7
5.4	even	2		3475.2.a.e.1.4		7
7.6	odd	2		6811.2.a.p.1.4		7
8.3	odd	2		8896.2.a.bd.1.3		7
8.5	even	2		8896.2.a.be.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
139.2.a.c.1.4	✓	7	1.1	even	1	trivial
1251.2.a.k.1.4		7	3.2	odd	2
2224.2.a.o.1.5		7	4.3	odd	2
3475.2.a.e.1.4		7	5.4	even	2
6811.2.a.p.1.4		7	7.6	odd	2
8896.2.a.bd.1.3		7	8.3	odd	2
8896.2.a.be.1.5		7	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	139.a (trivial)

\(f(q)\)	\(=\)	\(q-0.308806 q^{2} -1.39811 q^{3} -1.90464 q^{4} +2.83261 q^{5} +0.431745 q^{6} +4.16776 q^{7} +1.20578 q^{8} -1.04529 q^{9} +O(q^{10})\)	\(q-0.308806 q^{2} -1.39811 q^{3} -1.90464 q^{4} +2.83261 q^{5} +0.431745 q^{6} +4.16776 q^{7} +1.20578 q^{8} -1.04529 q^{9} -0.874728 q^{10} +1.93164 q^{11} +2.66290 q^{12} +4.12937 q^{13} -1.28703 q^{14} -3.96031 q^{15} +3.43693 q^{16} +1.03363 q^{17} +0.322790 q^{18} -7.34157 q^{19} -5.39511 q^{20} -5.82699 q^{21} -0.596503 q^{22} -4.09697 q^{23} -1.68581 q^{24} +3.02371 q^{25} -1.27517 q^{26} +5.65576 q^{27} -7.93807 q^{28} +4.49067 q^{29} +1.22297 q^{30} -1.28386 q^{31} -3.47289 q^{32} -2.70065 q^{33} -0.319192 q^{34} +11.8056 q^{35} +1.99089 q^{36} -7.77849 q^{37} +2.26712 q^{38} -5.77331 q^{39} +3.41550 q^{40} +11.5603 q^{41} +1.79941 q^{42} -7.87867 q^{43} -3.67908 q^{44} -2.96089 q^{45} +1.26517 q^{46} -6.84669 q^{47} -4.80521 q^{48} +10.3702 q^{49} -0.933738 q^{50} -1.44513 q^{51} -7.86495 q^{52} +3.68473 q^{53} -1.74653 q^{54} +5.47160 q^{55} +5.02538 q^{56} +10.2643 q^{57} -1.38675 q^{58} +1.24534 q^{59} +7.54296 q^{60} +0.281096 q^{61} +0.396462 q^{62} -4.35649 q^{63} -5.80140 q^{64} +11.6969 q^{65} +0.833977 q^{66} -8.51902 q^{67} -1.96870 q^{68} +5.72803 q^{69} -3.64565 q^{70} -6.40133 q^{71} -1.26038 q^{72} -5.92608 q^{73} +2.40204 q^{74} -4.22748 q^{75} +13.9830 q^{76} +8.05062 q^{77} +1.78283 q^{78} -8.65375 q^{79} +9.73549 q^{80} -4.77152 q^{81} -3.56988 q^{82} +15.8366 q^{83} +11.0983 q^{84} +2.92789 q^{85} +2.43298 q^{86} -6.27846 q^{87} +2.32913 q^{88} -3.23844 q^{89} +0.914340 q^{90} +17.2102 q^{91} +7.80326 q^{92} +1.79497 q^{93} +2.11430 q^{94} -20.7958 q^{95} +4.85549 q^{96} -7.27325 q^{97} -3.20237 q^{98} -2.01912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9}+O(q^{10}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9	\( 7 q + q^{2} - 2 q^{3} + 9 q^{4} + 11 q^{5} - 7 q^{6} - 5 q^{7} + 6 q^{8} + 13 q^{9} - 4 q^{10} + 2 q^{11} - 8 q^{12} + 6 q^{13} + 7 q^{14} - 3 q^{15} + 5 q^{16} + 5 q^{17} - 10 q^{18} - 10 q^{19} + 12 q^{20} - 5 q^{21} - 18 q^{22} - q^{23} - 21 q^{24} + 14 q^{25} - 8 q^{26} - 11 q^{27} - 28 q^{28} + 30 q^{29} - 41 q^{30} - 20 q^{31} - 12 q^{32} - 20 q^{33} - 17 q^{34} - 7 q^{35} + 2 q^{36} + 6 q^{37} + 6 q^{38} + 11 q^{39} - 22 q^{40} + 19 q^{41} + 6 q^{42} - 12 q^{43} + 25 q^{44} + 27 q^{45} + 22 q^{46} - 3 q^{47} + 15 q^{48} - 8 q^{49} + 12 q^{50} + 23 q^{51} - 8 q^{52} + 38 q^{53} - 7 q^{54} + 7 q^{55} + 21 q^{56} - 19 q^{57} - 21 q^{58} - 14 q^{59} - 8 q^{60} + 4 q^{61} - q^{62} - 18 q^{63} - 16 q^{64} + 10 q^{65} + 18 q^{66} + 9 q^{67} - 25 q^{68} + 9 q^{69} + 20 q^{70} + 24 q^{71} + 41 q^{72} - 5 q^{73} + 9 q^{74} - 21 q^{75} + 3 q^{76} - 13 q^{77} + 20 q^{78} + 8 q^{79} + 11 q^{80} + 39 q^{81} + 56 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 39 q^{86} - 25 q^{87} - 29 q^{88} + 10 q^{89} + 72 q^{90} + 7 q^{91} + 29 q^{92} - 15 q^{93} - 36 q^{94} - 21 q^{95} - 11 q^{96} - 5 q^{97} - 49 q^{98} - 31 q^{99}+O(q^{100}) \) 7 * q + q^2 - 2 * q^3 + 9 * q^4 + 11 * q^5 - 7 * q^6 - 5 * q^7 + 6 * q^8 + 13 * q^9 - 4 * q^10 + 2 * q^11 - 8 * q^12 + 6 * q^13 + 7 * q^14 - 3 * q^15 + 5 * q^16 + 5 * q^17 - 10 * q^18 - 10 * q^19 + 12 * q^20 - 5 * q^21 - 18 * q^22 - q^23 - 21 * q^24 + 14 * q^25 - 8 * q^26 - 11 * q^27 - 28 * q^28 + 30 * q^29 - 41 * q^30 - 20 * q^31 - 12 * q^32 - 20 * q^33 - 17 * q^34 - 7 * q^35 + 2 * q^36 + 6 * q^37 + 6 * q^38 + 11 * q^39 - 22 * q^40 + 19 * q^41 + 6 * q^42 - 12 * q^43 + 25 * q^44 + 27 * q^45 + 22 * q^46 - 3 * q^47 + 15 * q^48 - 8 * q^49 + 12 * q^50 + 23 * q^51 - 8 * q^52 + 38 * q^53 - 7 * q^54 + 7 * q^55 + 21 * q^56 - 19 * q^57 - 21 * q^58 - 14 * q^59 - 8 * q^60 + 4 * q^61 - q^62 - 18 * q^63 - 16 * q^64 + 10 * q^65 + 18 * q^66 + 9 * q^67 - 25 * q^68 + 9 * q^69 + 20 * q^70 + 24 * q^71 + 41 * q^72 - 5 * q^73 + 9 * q^74 - 21 * q^75 + 3 * q^76 - 13 * q^77 + 20 * q^78 + 8 * q^79 + 11 * q^80 + 39 * q^81 + 56 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 39 * q^86 - 25 * q^87 - 29 * q^88 + 10 * q^89 + 72 * q^90 + 7 * q^91 + 29 * q^92 - 15 * q^93 - 36 * q^94 - 21 * q^95 - 11 * q^96 - 5 * q^97 - 49 * q^98 - 31 * q^99

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