LMFDB - Embedded newform 4030.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
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} - 3x^{6} - 8x^{5} + 24x^{4} + 18x^{3} - 48x^{2} - 9x + 4 $ x^7 - 3x^6 - 8x^5 + 24x^4 + 18x^3 - 48x^2 - 9x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.80583$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.80583 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.80583 q^{6} -2.29018 q^{7} -1.00000 q^{8} +4.87266 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.80583 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.80583 q^{6} -2.29018 q^{7} -1.00000 q^{8} +4.87266 q^{9} +1.00000 q^{10} -0.201867 q^{11} +2.80583 q^{12} -1.00000 q^{13} +2.29018 q^{14} -2.80583 q^{15} +1.00000 q^{16} -3.76999 q^{17} -4.87266 q^{18} -2.78735 q^{19} -1.00000 q^{20} -6.42585 q^{21} +0.201867 q^{22} +7.54453 q^{23} -2.80583 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.25435 q^{27} -2.29018 q^{28} -2.95377 q^{29} +2.80583 q^{30} -1.00000 q^{31} -1.00000 q^{32} -0.566405 q^{33} +3.76999 q^{34} +2.29018 q^{35} +4.87266 q^{36} -8.32009 q^{37} +2.78735 q^{38} -2.80583 q^{39} +1.00000 q^{40} +4.88556 q^{41} +6.42585 q^{42} -4.86909 q^{43} -0.201867 q^{44} -4.87266 q^{45} -7.54453 q^{46} -0.508409 q^{47} +2.80583 q^{48} -1.75506 q^{49} -1.00000 q^{50} -10.5779 q^{51} -1.00000 q^{52} +5.48198 q^{53} -5.25435 q^{54} +0.201867 q^{55} +2.29018 q^{56} -7.82081 q^{57} +2.95377 q^{58} -9.36178 q^{59} -2.80583 q^{60} -2.01070 q^{61} +1.00000 q^{62} -11.1593 q^{63} +1.00000 q^{64} +1.00000 q^{65} +0.566405 q^{66} -2.12006 q^{67} -3.76999 q^{68} +21.1686 q^{69} -2.29018 q^{70} -12.3037 q^{71} -4.87266 q^{72} -3.58247 q^{73} +8.32009 q^{74} +2.80583 q^{75} -2.78735 q^{76} +0.462313 q^{77} +2.80583 q^{78} -1.35143 q^{79} -1.00000 q^{80} +0.124812 q^{81} -4.88556 q^{82} -0.363599 q^{83} -6.42585 q^{84} +3.76999 q^{85} +4.86909 q^{86} -8.28775 q^{87} +0.201867 q^{88} -6.59269 q^{89} +4.87266 q^{90} +2.29018 q^{91} +7.54453 q^{92} -2.80583 q^{93} +0.508409 q^{94} +2.78735 q^{95} -2.80583 q^{96} +4.64195 q^{97} +1.75506 q^{98} -0.983631 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	$ 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.80583	1.61994	0.809972	−	0.586468i	$-0.199482\pi$
$3$	2.80583	1.61994	0.809972	+	0.586468i	$0.199482\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.80583	−1.14547
$7$	−2.29018	−0.865608	−0.432804	−	0.901488i	$-0.642476\pi$
$7$	−2.29018	−0.865608	−0.432804	+	0.901488i	$0.642476\pi$
$8$	−1.00000	−0.353553
$9$	4.87266	1.62422
$10$	1.00000	0.316228
$11$	−0.201867	−0.0608653	−0.0304327	−	0.999537i	$-0.509689\pi$
$11$	−0.201867	−0.0608653	−0.0304327	+	0.999537i	$0.509689\pi$
$12$	2.80583	0.809972
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.29018	0.612077
$15$	−2.80583	−0.724461
$16$	1.00000	0.250000
$17$	−3.76999	−0.914357	−0.457178	−	0.889375i	$-0.651140\pi$
$17$	−3.76999	−0.914357	−0.457178	+	0.889375i	$0.651140\pi$
$18$	−4.87266	−1.14850
$19$	−2.78735	−0.639461	−0.319731	−	0.947508i	$-0.603592\pi$
$19$	−2.78735	−0.639461	−0.319731	+	0.947508i	$0.603592\pi$
$20$	−1.00000	−0.223607
$21$	−6.42585	−1.40224
$22$	0.201867	0.0430383
$23$	7.54453	1.57314	0.786572	−	0.617499i	$-0.211854\pi$
$23$	7.54453	1.57314	0.786572	+	0.617499i	$0.211854\pi$
$24$	−2.80583	−0.572737
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	5.25435	1.01120
$28$	−2.29018	−0.432804
$29$	−2.95377	−0.548501	−0.274250	−	0.961658i	$-0.588430\pi$
$29$	−2.95377	−0.548501	−0.274250	+	0.961658i	$0.588430\pi$
$30$	2.80583	0.512271
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−0.566405	−0.0985984
$34$	3.76999	0.646548
$35$	2.29018	0.387112
$36$	4.87266	0.812109
$37$	−8.32009	−1.36782	−0.683908	−	0.729569i	$-0.739721\pi$
$37$	−8.32009	−1.36782	−0.683908	+	0.729569i	$0.739721\pi$
$38$	2.78735	0.452167
$39$	−2.80583	−0.449292
$40$	1.00000	0.158114
$41$	4.88556	0.762996	0.381498	−	0.924370i	$-0.375408\pi$
$41$	4.88556	0.762996	0.381498	+	0.924370i	$0.375408\pi$
$42$	6.42585	0.991531
$43$	−4.86909	−0.742529	−0.371265	−	0.928527i	$-0.621076\pi$
$43$	−4.86909	−0.742529	−0.371265	+	0.928527i	$0.621076\pi$
$44$	−0.201867	−0.0304327
$45$	−4.87266	−0.726373
$46$	−7.54453	−1.11238
$47$	−0.508409	−0.0741591	−0.0370795	−	0.999312i	$-0.511805\pi$
$47$	−0.508409	−0.0741591	−0.0370795	+	0.999312i	$0.511805\pi$
$48$	2.80583	0.404986
$49$	−1.75506	−0.250723
$50$	−1.00000	−0.141421
$51$	−10.5779	−1.48121
$52$	−1.00000	−0.138675
$53$	5.48198	0.753009	0.376504	−	0.926415i	$-0.377126\pi$
$53$	5.48198	0.753009	0.376504	+	0.926415i	$0.377126\pi$
$54$	−5.25435	−0.715026
$55$	0.201867	0.0272198
$56$	2.29018	0.306039
$57$	−7.82081	−1.03589
$58$	2.95377	0.387849
$59$	−9.36178	−1.21880	−0.609400	−	0.792863i	$-0.708590\pi$
$59$	−9.36178	−1.21880	−0.609400	+	0.792863i	$0.708590\pi$
$60$	−2.80583	−0.362231
$61$	−2.01070	−0.257444	−0.128722	−	0.991681i	$-0.541087\pi$
$61$	−2.01070	−0.257444	−0.128722	+	0.991681i	$0.541087\pi$
$62$	1.00000	0.127000
$63$	−11.1593	−1.40594
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	0.566405	0.0697196
$67$	−2.12006	−0.259007	−0.129503	−	0.991579i	$-0.541338\pi$
$67$	−2.12006	−0.259007	−0.129503	+	0.991579i	$0.541338\pi$
$68$	−3.76999	−0.457178
$69$	21.1686	2.54840
$70$	−2.29018	−0.273729
$71$	−12.3037	−1.46018	−0.730088	−	0.683353i	$-0.760521\pi$
$71$	−12.3037	−1.46018	−0.730088	+	0.683353i	$0.760521\pi$
$72$	−4.87266	−0.574248
$73$	−3.58247	−0.419297	−0.209648	−	0.977777i	$-0.567232\pi$
$73$	−3.58247	−0.419297	−0.209648	+	0.977777i	$0.567232\pi$
$74$	8.32009	0.967191
$75$	2.80583	0.323989
$76$	−2.78735	−0.319731
$77$	0.462313	0.0526855
$78$	2.80583	0.317697
$79$	−1.35143	−0.152048	−0.0760239	−	0.997106i	$-0.524223\pi$
$79$	−1.35143	−0.152048	−0.0760239	+	0.997106i	$0.524223\pi$
$80$	−1.00000	−0.111803
$81$	0.124812	0.0138680
$82$	−4.88556	−0.539520
$83$	−0.363599	−0.0399102	−0.0199551	−	0.999801i	$-0.506352\pi$
$83$	−0.363599	−0.0399102	−0.0199551	+	0.999801i	$0.506352\pi$
$84$	−6.42585	−0.701118
$85$	3.76999	0.408913
$86$	4.86909	0.525048
$87$	−8.28775	−0.888540
$88$	0.201867	0.0215191
$89$	−6.59269	−0.698824	−0.349412	−	0.936969i	$-0.613619\pi$
$89$	−6.59269	−0.698824	−0.349412	+	0.936969i	$0.613619\pi$
$90$	4.87266	0.513623
$91$	2.29018	0.240076
$92$	7.54453	0.786572
$93$	−2.80583	−0.290951
$94$	0.508409	0.0524384
$95$	2.78735	0.285976
$96$	−2.80583	−0.286368
$97$	4.64195	0.471318	0.235659	−	0.971836i	$-0.424275\pi$
$97$	4.64195	0.471318	0.235659	+	0.971836i	$0.424275\pi$
$98$	1.75506	0.177288
$99$	−0.983631	−0.0988586
$100$	1.00000	0.100000
$101$	−7.30718	−0.727091	−0.363546	−	0.931576i	$-0.618434\pi$
$101$	−7.30718	−0.727091	−0.363546	+	0.931576i	$0.618434\pi$
$102$	10.5779	1.04737
$103$	18.4644	1.81936	0.909678	−	0.415315i	$-0.136329\pi$
$103$	18.4644	1.81936	0.909678	+	0.415315i	$0.136329\pi$
$104$	1.00000	0.0980581
$105$	6.42585	0.627099
$106$	−5.48198	−0.532457
$107$	−16.3834	−1.58384	−0.791920	−	0.610625i	$-0.790918\pi$
$107$	−16.3834	−1.58384	−0.791920	+	0.610625i	$0.790918\pi$
$108$	5.25435	0.505600
$109$	12.0736	1.15644	0.578221	−	0.815880i	$-0.303747\pi$
$109$	12.0736	1.15644	0.578221	+	0.815880i	$0.303747\pi$
$110$	−0.201867	−0.0192473
$111$	−23.3447	−2.21578
$112$	−2.29018	−0.216402
$113$	1.42734	0.134273	0.0671363	−	0.997744i	$-0.478614\pi$
$113$	1.42734	0.134273	0.0671363	+	0.997744i	$0.478614\pi$
$114$	7.82081	0.732486
$115$	−7.54453	−0.703531
$116$	−2.95377	−0.274250
$117$	−4.87266	−0.450477
$118$	9.36178	0.861822
$119$	8.63397	0.791474
$120$	2.80583	0.256136
$121$	−10.9592	−0.996295
$122$	2.01070	0.182040
$123$	13.7080	1.23601
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	11.1593	0.994147
$127$	10.9809	0.974400	0.487200	−	0.873290i	$-0.338018\pi$
$127$	10.9809	0.974400	0.487200	+	0.873290i	$0.338018\pi$
$128$	−1.00000	−0.0883883
$129$	−13.6618	−1.20286
$130$	−1.00000	−0.0877058
$131$	−4.97497	−0.434666	−0.217333	−	0.976098i	$-0.569736\pi$
$131$	−4.97497	−0.434666	−0.217333	+	0.976098i	$0.569736\pi$
$132$	−0.566405	−0.0492992
$133$	6.38353	0.553523
$134$	2.12006	0.183145
$135$	−5.25435	−0.452222
$136$	3.76999	0.323274
$137$	−12.2209	−1.04410	−0.522051	−	0.852914i	$-0.674833\pi$
$137$	−12.2209	−1.04410	−0.522051	+	0.852914i	$0.674833\pi$
$138$	−21.1686	−1.80199
$139$	−15.5499	−1.31892	−0.659462	−	0.751738i	$-0.729216\pi$
$139$	−15.5499	−1.31892	−0.659462	+	0.751738i	$0.729216\pi$
$140$	2.29018	0.193556
$141$	−1.42651	−0.120134
$142$	12.3037	1.03250
$143$	0.201867	0.0168810
$144$	4.87266	0.406055
$145$	2.95377	0.245297
$146$	3.58247	0.296488
$147$	−4.92440	−0.406158
$148$	−8.32009	−0.683908
$149$	−3.72549	−0.305204	−0.152602	−	0.988288i	$-0.548765\pi$
$149$	−3.72549	−0.305204	−0.152602	+	0.988288i	$0.548765\pi$
$150$	−2.80583	−0.229095
$151$	−8.18954	−0.666455	−0.333228	−	0.942846i	$-0.608138\pi$
$151$	−8.18954	−0.666455	−0.333228	+	0.942846i	$0.608138\pi$
$152$	2.78735	0.226084
$153$	−18.3699	−1.48512
$154$	−0.462313	−0.0372543
$155$	1.00000	0.0803219
$156$	−2.80583	−0.224646
$157$	10.3700	0.827614	0.413807	−	0.910365i	$-0.364199\pi$
$157$	10.3700	0.827614	0.413807	+	0.910365i	$0.364199\pi$
$158$	1.35143	0.107514
$159$	15.3815	1.21983
$160$	1.00000	0.0790569
$161$	−17.2784	−1.36172
$162$	−0.124812	−0.00980619
$163$	9.56398	0.749109	0.374554	−	0.927205i	$-0.377796\pi$
$163$	9.56398	0.749109	0.374554	+	0.927205i	$0.377796\pi$
$164$	4.88556	0.381498
$165$	0.566405	0.0440946
$166$	0.363599	0.0282208
$167$	−23.9248	−1.85136	−0.925678	−	0.378313i	$-0.876504\pi$
$167$	−23.9248	−1.85136	−0.925678	+	0.378313i	$0.876504\pi$
$168$	6.42585	0.495765
$169$	1.00000	0.0769231
$170$	−3.76999	−0.289145
$171$	−13.5818	−1.03863
$172$	−4.86909	−0.371265
$173$	7.29299	0.554476	0.277238	−	0.960801i	$-0.410581\pi$
$173$	7.29299	0.554476	0.277238	+	0.960801i	$0.410581\pi$
$174$	8.28775	0.628293
$175$	−2.29018	−0.173122
$176$	−0.201867	−0.0152163
$177$	−26.2675	−1.97439
$178$	6.59269	0.494143
$179$	−12.9403	−0.967204	−0.483602	−	0.875288i	$-0.660672\pi$
$179$	−12.9403	−0.967204	−0.483602	+	0.875288i	$0.660672\pi$
$180$	−4.87266	−0.363186
$181$	−5.56297	−0.413492	−0.206746	−	0.978395i	$-0.566287\pi$
$181$	−5.56297	−0.413492	−0.206746	+	0.978395i	$0.566287\pi$
$182$	−2.29018	−0.169760
$183$	−5.64167	−0.417044
$184$	−7.54453	−0.556190
$185$	8.32009	0.611705
$186$	2.80583	0.205733
$187$	0.761038	0.0556526
$188$	−0.508409	−0.0370795
$189$	−12.0334	−0.875302
$190$	−2.78735	−0.202215
$191$	−20.1067	−1.45487	−0.727435	−	0.686177i	$-0.759288\pi$
$191$	−20.1067	−1.45487	−0.727435	+	0.686177i	$0.759288\pi$
$192$	2.80583	0.202493
$193$	−1.16762	−0.0840469	−0.0420235	−	0.999117i	$-0.513380\pi$
$193$	−1.16762	−0.0840469	−0.0420235	+	0.999117i	$0.513380\pi$
$194$	−4.64195	−0.333272
$195$	2.80583	0.200929
$196$	−1.75506	−0.125362
$197$	−7.08555	−0.504825	−0.252412	−	0.967620i	$-0.581224\pi$
$197$	−7.08555	−0.504825	−0.252412	+	0.967620i	$0.581224\pi$
$198$	0.983631	0.0699036
$199$	−3.97615	−0.281862	−0.140931	−	0.990019i	$-0.545010\pi$
$199$	−3.97615	−0.281862	−0.140931	+	0.990019i	$0.545010\pi$
$200$	−1.00000	−0.0707107
$201$	−5.94852	−0.419576
$202$	7.30718	0.514131
$203$	6.76466	0.474786
$204$	−10.5779	−0.740604
$205$	−4.88556	−0.341222
$206$	−18.4644	−1.28648
$207$	36.7619	2.55513
$208$	−1.00000	−0.0693375
$209$	0.562675	0.0389210
$210$	−6.42585	−0.443426
$211$	10.8435	0.746499	0.373249	−	0.927731i	$-0.378244\pi$
$211$	10.8435	0.746499	0.373249	+	0.927731i	$0.378244\pi$
$212$	5.48198	0.376504
$213$	−34.5219	−2.36540
$214$	16.3834	1.11994
$215$	4.86909	0.332069
$216$	−5.25435	−0.357513
$217$	2.29018	0.155468
$218$	−12.0736	−0.817728
$219$	−10.0518	−0.679237
$220$	0.201867	0.0136099
$221$	3.76999	0.253597
$222$	23.3447	1.56680
$223$	12.4769	0.835512	0.417756	−	0.908559i	$-0.362817\pi$
$223$	12.4769	0.835512	0.417756	+	0.908559i	$0.362817\pi$
$224$	2.29018	0.153019
$225$	4.87266	0.324844
$226$	−1.42734	−0.0949451
$227$	0.0801578	0.00532026	0.00266013	−	0.999996i	$-0.499153\pi$
$227$	0.0801578	0.00532026	0.00266013	+	0.999996i	$0.499153\pi$
$228$	−7.82081	−0.517946
$229$	19.4014	1.28208	0.641040	−	0.767508i	$-0.278503\pi$
$229$	19.4014	1.28208	0.641040	+	0.767508i	$0.278503\pi$
$230$	7.54453	0.497472
$231$	1.29717	0.0853475
$232$	2.95377	0.193924
$233$	−21.4817	−1.40731	−0.703657	−	0.710540i	$-0.748451\pi$
$233$	−21.4817	−1.40731	−0.703657	+	0.710540i	$0.748451\pi$
$234$	4.87266	0.318536
$235$	0.508409	0.0331649
$236$	−9.36178	−0.609400
$237$	−3.79188	−0.246309
$238$	−8.63397	−0.559657
$239$	27.5372	1.78123	0.890616	−	0.454757i	$-0.150274\pi$
$239$	27.5372	1.78123	0.890616	+	0.454757i	$0.150274\pi$
$240$	−2.80583	−0.181115
$241$	−9.81973	−0.632544	−0.316272	−	0.948669i	$-0.602431\pi$
$241$	−9.81973	−0.632544	−0.316272	+	0.948669i	$0.602431\pi$
$242$	10.9592	0.704487
$243$	−15.4128	−0.988734
$244$	−2.01070	−0.128722
$245$	1.75506	0.112127
$246$	−13.7080	−0.873992
$247$	2.78735	0.177355
$248$	1.00000	0.0635001
$249$	−1.02020	−0.0646523
$250$	1.00000	0.0632456
$251$	19.3647	1.22229	0.611146	−	0.791518i	$-0.290709\pi$
$251$	19.3647	1.22229	0.611146	+	0.791518i	$0.290709\pi$
$252$	−11.1593	−0.702968
$253$	−1.52299	−0.0957499
$254$	−10.9809	−0.689005
$255$	10.5779	0.662416
$256$	1.00000	0.0625000
$257$	−19.8231	−1.23653	−0.618264	−	0.785970i	$-0.712164\pi$
$257$	−19.8231	−1.23653	−0.618264	+	0.785970i	$0.712164\pi$
$258$	13.6618	0.850548
$259$	19.0545	1.18399
$260$	1.00000	0.0620174
$261$	−14.3927	−0.890885
$262$	4.97497	0.307355
$263$	−2.78719	−0.171866	−0.0859328	−	0.996301i	$-0.527387\pi$
$263$	−2.78719	−0.171866	−0.0859328	+	0.996301i	$0.527387\pi$
$264$	0.566405	0.0348598
$265$	−5.48198	−0.336756
$266$	−6.38353	−0.391400
$267$	−18.4979	−1.13206
$268$	−2.12006	−0.129503
$269$	14.2157	0.866745	0.433373	−	0.901215i	$-0.357323\pi$
$269$	14.2157	0.866745	0.433373	+	0.901215i	$0.357323\pi$
$270$	5.25435	0.319769
$271$	−2.39103	−0.145245	−0.0726225	−	0.997360i	$-0.523137\pi$
$271$	−2.39103	−0.145245	−0.0726225	+	0.997360i	$0.523137\pi$
$272$	−3.76999	−0.228589
$273$	6.42585	0.388910
$274$	12.2209	0.738292
$275$	−0.201867	−0.0121731
$276$	21.1686	1.27420
$277$	11.7564	0.706372	0.353186	−	0.935553i	$-0.385098\pi$
$277$	11.7564	0.706372	0.353186	+	0.935553i	$0.385098\pi$
$278$	15.5499	0.932620
$279$	−4.87266	−0.291718
$280$	−2.29018	−0.136865
$281$	14.4263	0.860598	0.430299	−	0.902686i	$-0.358408\pi$
$281$	14.4263	0.860598	0.430299	+	0.902686i	$0.358408\pi$
$282$	1.42651	0.0849472
$283$	18.7054	1.11192	0.555962	−	0.831208i	$-0.312350\pi$
$283$	18.7054	1.11192	0.555962	+	0.831208i	$0.312350\pi$
$284$	−12.3037	−0.730088
$285$	7.82081	0.463265
$286$	−0.201867	−0.0119367
$287$	−11.1888	−0.660456
$288$	−4.87266	−0.287124
$289$	−2.78717	−0.163951
$290$	−2.95377	−0.173451
$291$	13.0245	0.763509
$292$	−3.58247	−0.209648
$293$	−4.31376	−0.252012	−0.126006	−	0.992029i	$-0.540216\pi$
$293$	−4.31376	−0.252012	−0.126006	+	0.992029i	$0.540216\pi$
$294$	4.92440	0.287197
$295$	9.36178	0.545064
$296$	8.32009	0.483596
$297$	−1.06068	−0.0615470
$298$	3.72549	0.215812
$299$	−7.54453	−0.436311
$300$	2.80583	0.161994
$301$	11.1511	0.642739
$302$	8.18954	0.471255
$303$	−20.5027	−1.17785
$304$	−2.78735	−0.159865
$305$	2.01070	0.115132
$306$	18.3699	1.05014
$307$	0.225323	0.0128598	0.00642992	−	0.999979i	$-0.497953\pi$
$307$	0.225323	0.0128598	0.00642992	+	0.999979i	$0.497953\pi$
$308$	0.462313	0.0263427
$309$	51.8080	2.94725
$310$	−1.00000	−0.0567962
$311$	23.7904	1.34903	0.674514	−	0.738262i	$-0.264353\pi$
$311$	23.7904	1.34903	0.674514	+	0.738262i	$0.264353\pi$
$312$	2.80583	0.158849
$313$	−19.5955	−1.10761	−0.553803	−	0.832648i	$-0.686824\pi$
$313$	−19.5955	−1.10761	−0.553803	+	0.832648i	$0.686824\pi$
$314$	−10.3700	−0.585212
$315$	11.1593	0.628754
$316$	−1.35143	−0.0760239
$317$	14.6381	0.822156	0.411078	−	0.911600i	$-0.365152\pi$
$317$	14.6381	0.822156	0.411078	+	0.911600i	$0.365152\pi$
$318$	−15.3815	−0.862551
$319$	0.596269	0.0333847
$320$	−1.00000	−0.0559017
$321$	−45.9688	−2.56573
$322$	17.2784	0.962885
$323$	10.5083	0.584696
$324$	0.124812	0.00693402
$325$	−1.00000	−0.0554700
$326$	−9.56398	−0.529700
$327$	33.8765	1.87337
$328$	−4.88556	−0.269760
$329$	1.16435	0.0641927
$330$	−0.566405	−0.0311796
$331$	19.1391	1.05198	0.525990	−	0.850491i	$-0.323695\pi$
$331$	19.1391	1.05198	0.525990	+	0.850491i	$0.323695\pi$
$332$	−0.363599	−0.0199551
$333$	−40.5410	−2.22163
$334$	23.9248	1.30911
$335$	2.12006	0.115831
$336$	−6.42585	−0.350559
$337$	25.3486	1.38082	0.690412	−	0.723417i	$-0.257429\pi$
$337$	25.3486	1.38082	0.690412	+	0.723417i	$0.257429\pi$
$338$	−1.00000	−0.0543928
$339$	4.00486	0.217514
$340$	3.76999	0.204456
$341$	0.201867	0.0109317
$342$	13.5818	0.734419
$343$	20.0507	1.08264
$344$	4.86909	0.262524
$345$	−21.1686	−1.13968
$346$	−7.29299	−0.392073
$347$	22.7897	1.22342	0.611709	−	0.791083i	$-0.290482\pi$
$347$	22.7897	1.22342	0.611709	+	0.791083i	$0.290482\pi$
$348$	−8.28775	−0.444270
$349$	−6.83428	−0.365831	−0.182915	−	0.983129i	$-0.558553\pi$
$349$	−6.83428	−0.365831	−0.182915	+	0.983129i	$0.558553\pi$
$350$	2.29018	0.122415
$351$	−5.25435	−0.280456
$352$	0.201867	0.0107596
$353$	−7.85275	−0.417960	−0.208980	−	0.977920i	$-0.567014\pi$
$353$	−7.85275	−0.417960	−0.208980	+	0.977920i	$0.567014\pi$
$354$	26.2675	1.39610
$355$	12.3037	0.653011
$356$	−6.59269	−0.349412
$357$	24.2254	1.28214
$358$	12.9403	0.683917
$359$	−3.19031	−0.168378	−0.0841892	−	0.996450i	$-0.526830\pi$
$359$	−3.19031	−0.168378	−0.0841892	+	0.996450i	$0.526830\pi$
$360$	4.87266	0.256812
$361$	−11.2307	−0.591089
$362$	5.56297	0.292383
$363$	−30.7497	−1.61394
$364$	2.29018	0.120038
$365$	3.58247	0.187515
$366$	5.64167	0.294895
$367$	29.7441	1.55263	0.776314	−	0.630346i	$-0.217087\pi$
$367$	29.7441	1.55263	0.776314	+	0.630346i	$0.217087\pi$
$368$	7.54453	0.393286
$369$	23.8057	1.23927
$370$	−8.32009	−0.432541
$371$	−12.5547	−0.651810
$372$	−2.80583	−0.145475
$373$	21.1975	1.09756	0.548782	−	0.835965i	$-0.315092\pi$
$373$	21.1975	1.09756	0.548782	+	0.835965i	$0.315092\pi$
$374$	−0.761038	−0.0393524
$375$	−2.80583	−0.144892
$376$	0.508409	0.0262192
$377$	2.95377	0.152127
$378$	12.0334	0.618932
$379$	−18.0543	−0.927388	−0.463694	−	0.885995i	$-0.653476\pi$
$379$	−18.0543	−0.927388	−0.463694	+	0.885995i	$0.653476\pi$
$380$	2.78735	0.142988
$381$	30.8106	1.57847
$382$	20.1067	1.02875
$383$	−8.17974	−0.417965	−0.208983	−	0.977919i	$-0.567015\pi$
$383$	−8.17974	−0.417965	−0.208983	+	0.977919i	$0.567015\pi$
$384$	−2.80583	−0.143184
$385$	−0.462313	−0.0235617
$386$	1.16762	0.0594301
$387$	−23.7254	−1.20603
$388$	4.64195	0.235659
$389$	31.5320	1.59874	0.799368	−	0.600842i	$-0.205168\pi$
$389$	31.5320	1.59874	0.799368	+	0.600842i	$0.205168\pi$
$390$	−2.80583	−0.142078
$391$	−28.4428	−1.43841
$392$	1.75506	0.0886441
$393$	−13.9589	−0.704134
$394$	7.08555	0.356965
$395$	1.35143	0.0679978
$396$	−0.983631	−0.0494293
$397$	0.447717	0.0224703	0.0112351	−	0.999937i	$-0.496424\pi$
$397$	0.447717	0.0224703	0.0112351	+	0.999937i	$0.496424\pi$
$398$	3.97615	0.199307
$399$	17.9111	0.896676
$400$	1.00000	0.0500000
$401$	28.2694	1.41171	0.705854	−	0.708358i	$-0.250564\pi$
$401$	28.2694	1.41171	0.705854	+	0.708358i	$0.250564\pi$
$402$	5.94852	0.296685
$403$	1.00000	0.0498135
$404$	−7.30718	−0.363546
$405$	−0.124812	−0.00620198
$406$	−6.76466	−0.335725
$407$	1.67956	0.0832525
$408$	10.5779	0.523686
$409$	−24.5781	−1.21531	−0.607654	−	0.794202i	$-0.707889\pi$
$409$	−24.5781	−1.21531	−0.607654	+	0.794202i	$0.707889\pi$
$410$	4.88556	0.241281
$411$	−34.2897	−1.69139
$412$	18.4644	0.909678
$413$	21.4402	1.05500
$414$	−36.7619	−1.80675
$415$	0.363599	0.0178484
$416$	1.00000	0.0490290
$417$	−43.6303	−2.13658
$418$	−0.562675	−0.0275213
$419$	−3.09415	−0.151159	−0.0755797	−	0.997140i	$-0.524081\pi$
$419$	−3.09415	−0.151159	−0.0755797	+	0.997140i	$0.524081\pi$
$420$	6.42585	0.313550
$421$	2.05940	0.100369	0.0501846	−	0.998740i	$-0.484019\pi$
$421$	2.05940	0.100369	0.0501846	+	0.998740i	$0.484019\pi$
$422$	−10.8435	−0.527854
$423$	−2.47730	−0.120451
$424$	−5.48198	−0.266229
$425$	−3.76999	−0.182871
$426$	34.5219	1.67259
$427$	4.60487	0.222845
$428$	−16.3834	−0.791920
$429$	0.566405	0.0273463
$430$	−4.86909	−0.234808
$431$	−6.21975	−0.299595	−0.149797	−	0.988717i	$-0.547862\pi$
$431$	−6.21975	−0.299595	−0.149797	+	0.988717i	$0.547862\pi$
$432$	5.25435	0.252800
$433$	17.6960	0.850416	0.425208	−	0.905096i	$-0.360201\pi$
$433$	17.6960	0.850416	0.425208	+	0.905096i	$0.360201\pi$
$434$	−2.29018	−0.109932
$435$	8.28775	0.397367
$436$	12.0736	0.578221
$437$	−21.0292	−1.00596
$438$	10.0518	0.480293
$439$	−35.4405	−1.69148	−0.845742	−	0.533592i	$-0.820842\pi$
$439$	−35.4405	−1.69148	−0.845742	+	0.533592i	$0.820842\pi$
$440$	−0.201867	−0.00962365
$441$	−8.55182	−0.407230
$442$	−3.76999	−0.179320
$443$	23.0913	1.09710	0.548550	−	0.836118i	$-0.315180\pi$
$443$	23.0913	1.09710	0.548550	+	0.836118i	$0.315180\pi$
$444$	−23.3447	−1.10789
$445$	6.59269	0.312524
$446$	−12.4769	−0.590797
$447$	−10.4531	−0.494413
$448$	−2.29018	−0.108201
$449$	−19.4000	−0.915541	−0.457770	−	0.889070i	$-0.651352\pi$
$449$	−19.4000	−0.915541	−0.457770	+	0.889070i	$0.651352\pi$
$450$	−4.87266	−0.229699
$451$	−0.986236	−0.0464400
$452$	1.42734	0.0671363
$453$	−22.9784	−1.07962
$454$	−0.0801578	−0.00376199
$455$	−2.29018	−0.107365
$456$	7.82081	0.366243
$457$	−4.64875	−0.217459	−0.108730	−	0.994071i	$-0.534678\pi$
$457$	−4.64875	−0.217459	−0.108730	+	0.994071i	$0.534678\pi$
$458$	−19.4014	−0.906567
$459$	−19.8088	−0.924597
$460$	−7.54453	−0.351766
$461$	14.8003	0.689320	0.344660	−	0.938728i	$-0.387994\pi$
$461$	14.8003	0.689320	0.344660	+	0.938728i	$0.387994\pi$
$462$	−1.29717	−0.0603498
$463$	−34.2934	−1.59375	−0.796874	−	0.604146i	$-0.793514\pi$
$463$	−34.2934	−1.59375	−0.796874	+	0.604146i	$0.793514\pi$
$464$	−2.95377	−0.137125
$465$	2.80583	0.130117
$466$	21.4817	0.995121
$467$	−10.8650	−0.502774	−0.251387	−	0.967887i	$-0.580887\pi$
$467$	−10.8650	−0.502774	−0.251387	+	0.967887i	$0.580887\pi$
$468$	−4.87266	−0.225239
$469$	4.85532	0.224198
$470$	−0.508409	−0.0234512
$471$	29.0963	1.34069
$472$	9.36178	0.430911
$473$	0.982911	0.0451943
$474$	3.79188	0.174167
$475$	−2.78735	−0.127892
$476$	8.63397	0.395737
$477$	26.7118	1.22305
$478$	−27.5372	−1.25952
$479$	−18.8288	−0.860308	−0.430154	−	0.902755i	$-0.641541\pi$
$479$	−18.8288	−0.860308	−0.430154	+	0.902755i	$0.641541\pi$
$480$	2.80583	0.128068
$481$	8.32009	0.379364
$482$	9.81973	0.447276
$483$	−48.4800	−2.20592
$484$	−10.9592	−0.498148
$485$	−4.64195	−0.210780
$486$	15.4128	0.699141
$487$	−29.2019	−1.32327	−0.661633	−	0.749828i	$-0.730136\pi$
$487$	−29.2019	−1.32327	−0.661633	+	0.749828i	$0.730136\pi$
$488$	2.01070	0.0910201
$489$	26.8349	1.21351
$490$	−1.75506	−0.0792857
$491$	−43.5102	−1.96359	−0.981794	−	0.189947i	$-0.939168\pi$
$491$	−43.5102	−1.96359	−0.981794	+	0.189947i	$0.939168\pi$
$492$	13.7080	0.618006
$493$	11.1357	0.501525
$494$	−2.78735	−0.125409
$495$	0.983631	0.0442109
$496$	−1.00000	−0.0449013
$497$	28.1776	1.26394
$498$	1.02020	0.0457161
$499$	36.4427	1.63140	0.815699	−	0.578477i	$-0.196353\pi$
$499$	36.4427	1.63140	0.815699	+	0.578477i	$0.196353\pi$
$500$	−1.00000	−0.0447214
$501$	−67.1288	−2.99909
$502$	−19.3647	−0.864290
$503$	−36.7508	−1.63864	−0.819320	−	0.573337i	$-0.805649\pi$
$503$	−36.7508	−1.63864	−0.819320	+	0.573337i	$0.805649\pi$
$504$	11.1593	0.497074
$505$	7.30718	0.325165
$506$	1.52299	0.0677054
$507$	2.80583	0.124611
$508$	10.9809	0.487200
$509$	1.54449	0.0684585	0.0342293	−	0.999414i	$-0.489102\pi$
$509$	1.54449	0.0684585	0.0342293	+	0.999414i	$0.489102\pi$
$510$	−10.5779	−0.468399
$511$	8.20452	0.362947
$512$	−1.00000	−0.0441942
$513$	−14.6457	−0.646623
$514$	19.8231	0.874358
$515$	−18.4644	−0.813640
$516$	−13.6618	−0.601428
$517$	0.102631	0.00451371
$518$	−19.0545	−0.837208
$519$	20.4629	0.898220
$520$	−1.00000	−0.0438529
$521$	23.4066	1.02546	0.512731	−	0.858549i	$-0.328634\pi$
$521$	23.4066	1.02546	0.512731	+	0.858549i	$0.328634\pi$
$522$	14.3927	0.629951
$523$	−18.2033	−0.795975	−0.397987	−	0.917391i	$-0.630291\pi$
$523$	−18.2033	−0.795975	−0.397987	+	0.917391i	$0.630291\pi$
$524$	−4.97497	−0.217333
$525$	−6.42585	−0.280447
$526$	2.78719	0.121527
$527$	3.76999	0.164223
$528$	−0.566405	−0.0246496
$529$	33.9199	1.47478
$530$	5.48198	0.238122
$531$	−45.6167	−1.97960
$532$	6.38353	0.276761
$533$	−4.88556	−0.211617
$534$	18.4979	0.800485
$535$	16.3834	0.708314
$536$	2.12006	0.0915726
$537$	−36.3083	−1.56682
$538$	−14.2157	−0.612882
$539$	0.354290	0.0152604
$540$	−5.25435	−0.226111
$541$	−28.0903	−1.20770	−0.603848	−	0.797099i	$-0.706367\pi$
$541$	−28.0903	−1.20770	−0.603848	+	0.797099i	$0.706367\pi$
$542$	2.39103	0.102704
$543$	−15.6087	−0.669834
$544$	3.76999	0.161637
$545$	−12.0736	−0.517177
$546$	−6.42585	−0.275001
$547$	2.60420	0.111347	0.0556737	−	0.998449i	$-0.482269\pi$
$547$	2.60420	0.111347	0.0556737	+	0.998449i	$0.482269\pi$
$548$	−12.2209	−0.522051
$549$	−9.79745	−0.418145
$550$	0.201867	0.00860766
$551$	8.23317	0.350745
$552$	−21.1686	−0.900997
$553$	3.09502	0.131614
$554$	−11.7564	−0.499480
$555$	23.3447	0.990929
$556$	−15.5499	−0.659462
$557$	−6.36646	−0.269755	−0.134878	−	0.990862i	$-0.543064\pi$
$557$	−6.36646	−0.269755	−0.134878	+	0.990862i	$0.543064\pi$
$558$	4.87266	0.206276
$559$	4.86909	0.205941
$560$	2.29018	0.0967779
$561$	2.13534	0.0901541
$562$	−14.4263	−0.608535
$563$	−25.3389	−1.06791	−0.533953	−	0.845514i	$-0.679294\pi$
$563$	−25.3389	−1.06791	−0.533953	+	0.845514i	$0.679294\pi$
$564$	−1.42651	−0.0600668
$565$	−1.42734	−0.0600486
$566$	−18.7054	−0.786249
$567$	−0.285843	−0.0120043
$568$	12.3037	0.516250
$569$	−28.0851	−1.17739	−0.588695	−	0.808355i	$-0.700358\pi$
$569$	−28.0851	−1.17739	−0.588695	+	0.808355i	$0.700358\pi$
$570$	−7.82081	−0.327578
$571$	−21.4886	−0.899268	−0.449634	−	0.893213i	$-0.648446\pi$
$571$	−21.4886	−0.899268	−0.449634	+	0.893213i	$0.648446\pi$
$572$	0.201867	0.00844050
$573$	−56.4159	−2.35681
$574$	11.1888	0.467013
$575$	7.54453	0.314629
$576$	4.87266	0.203027
$577$	27.3293	1.13773	0.568867	−	0.822429i	$-0.307382\pi$
$577$	27.3293	1.13773	0.568867	+	0.822429i	$0.307382\pi$
$578$	2.78717	0.115931
$579$	−3.27613	−0.136151
$580$	2.95377	0.122648
$581$	0.832709	0.0345466
$582$	−13.0245	−0.539882
$583$	−1.10663	−0.0458321
$584$	3.58247	0.148244
$585$	4.87266	0.201460
$586$	4.31376	0.178200
$587$	14.1534	0.584175	0.292088	−	0.956392i	$-0.405650\pi$
$587$	14.1534	0.584175	0.292088	+	0.956392i	$0.405650\pi$
$588$	−4.92440	−0.203079
$589$	2.78735	0.114851
$590$	−9.36178	−0.385418
$591$	−19.8808	−0.817788
$592$	−8.32009	−0.341954
$593$	18.5852	0.763203	0.381601	−	0.924327i	$-0.375373\pi$
$593$	18.5852	0.763203	0.381601	+	0.924327i	$0.375373\pi$
$594$	1.06068	0.0435203
$595$	−8.63397	−0.353958
$596$	−3.72549	−0.152602
$597$	−11.1564	−0.456601
$598$	7.54453	0.308519
$599$	−25.0758	−1.02457	−0.512285	−	0.858816i	$-0.671201\pi$
$599$	−25.0758	−1.02457	−0.512285	+	0.858816i	$0.671201\pi$
$600$	−2.80583	−0.114547
$601$	−29.5474	−1.20526	−0.602632	−	0.798019i	$-0.705881\pi$
$601$	−29.5474	−1.20526	−0.602632	+	0.798019i	$0.705881\pi$
$602$	−11.1511	−0.454485
$603$	−10.3303	−0.420683
$604$	−8.18954	−0.333228
$605$	10.9592	0.445557
$606$	20.5027	0.832864
$607$	43.2899	1.75708	0.878542	−	0.477665i	$-0.158517\pi$
$607$	43.2899	1.75708	0.878542	+	0.477665i	$0.158517\pi$
$608$	2.78735	0.113042
$609$	18.9805	0.769127
$610$	−2.01070	−0.0814108
$611$	0.508409	0.0205680
$612$	−18.3699	−0.742558
$613$	5.62376	0.227141	0.113571	−	0.993530i	$-0.463771\pi$
$613$	5.62376	0.227141	0.113571	+	0.993530i	$0.463771\pi$
$614$	−0.225323	−0.00909328
$615$	−13.7080	−0.552761
$616$	−0.462313	−0.0186271
$617$	12.0206	0.483932	0.241966	−	0.970285i	$-0.422208\pi$
$617$	12.0206	0.483932	0.241966	+	0.970285i	$0.422208\pi$
$618$	−51.8080	−2.08402
$619$	25.4878	1.02444	0.512220	−	0.858854i	$-0.328823\pi$
$619$	25.4878	1.02444	0.512220	+	0.858854i	$0.328823\pi$
$620$	1.00000	0.0401610
$621$	39.6416	1.59076
$622$	−23.7904	−0.953906
$623$	15.0985	0.604908
$624$	−2.80583	−0.112323
$625$	1.00000	0.0400000
$626$	19.5955	0.783195
$627$	1.57877	0.0630499
$628$	10.3700	0.413807
$629$	31.3667	1.25067
$630$	−11.1593	−0.444596
$631$	2.39857	0.0954855	0.0477428	−	0.998860i	$-0.484797\pi$
$631$	2.39857	0.0954855	0.0477428	+	0.998860i	$0.484797\pi$
$632$	1.35143	0.0537570
$633$	30.4250	1.20929
$634$	−14.6381	−0.581352
$635$	−10.9809	−0.435765
$636$	15.3815	0.609916
$637$	1.75506	0.0695382
$638$	−0.596269	−0.0236065
$639$	−59.9515	−2.37165
$640$	1.00000	0.0395285
$641$	19.3402	0.763892	0.381946	−	0.924185i	$-0.375254\pi$
$641$	19.3402	0.763892	0.381946	+	0.924185i	$0.375254\pi$
$642$	45.9688	1.81425
$643$	4.59843	0.181345	0.0906723	−	0.995881i	$-0.471098\pi$
$643$	4.59843	0.181345	0.0906723	+	0.995881i	$0.471098\pi$
$644$	−17.2784	−0.680862
$645$	13.6618	0.537934
$646$	−10.5083	−0.413442
$647$	42.6194	1.67554	0.837771	−	0.546022i	$-0.183858\pi$
$647$	42.6194	1.67554	0.837771	+	0.546022i	$0.183858\pi$
$648$	−0.124812	−0.00490310
$649$	1.88984	0.0741826
$650$	1.00000	0.0392232
$651$	6.42585	0.251849
$652$	9.56398	0.374554
$653$	9.90828	0.387741	0.193870	−	0.981027i	$-0.437896\pi$
$653$	9.90828	0.387741	0.193870	+	0.981027i	$0.437896\pi$
$654$	−33.8765	−1.32467
$655$	4.97497	0.194388
$656$	4.88556	0.190749
$657$	−17.4562	−0.681030
$658$	−1.16435	−0.0453911
$659$	−18.8055	−0.732558	−0.366279	−	0.930505i	$-0.619368\pi$
$659$	−18.8055	−0.732558	−0.366279	+	0.930505i	$0.619368\pi$
$660$	0.566405	0.0220473
$661$	8.84834	0.344161	0.172080	−	0.985083i	$-0.444951\pi$
$661$	8.84834	0.344161	0.172080	+	0.985083i	$0.444951\pi$
$662$	−19.1391	−0.743862
$663$	10.5779	0.410813
$664$	0.363599	0.0141104
$665$	−6.38353	−0.247543
$666$	40.5410	1.57093
$667$	−22.2848	−0.862870
$668$	−23.9248	−0.925678
$669$	35.0079	1.35348
$670$	−2.12006	−0.0819051
$671$	0.405895	0.0156694
$672$	6.42585	0.247883
$673$	10.7596	0.414754	0.207377	−	0.978261i	$-0.433507\pi$
$673$	10.7596	0.414754	0.207377	+	0.978261i	$0.433507\pi$
$674$	−25.3486	−0.976390
$675$	5.25435	0.202240
$676$	1.00000	0.0384615
$677$	−0.105190	−0.00404279	−0.00202140	−	0.999998i	$-0.500643\pi$
$677$	−0.105190	−0.00404279	−0.00202140	+	0.999998i	$0.500643\pi$
$678$	−4.00486	−0.153806
$679$	−10.6309	−0.407977
$680$	−3.76999	−0.144573
$681$	0.224909	0.00861852
$682$	−0.201867	−0.00772990
$683$	−13.2945	−0.508701	−0.254350	−	0.967112i	$-0.581862\pi$
$683$	−13.2945	−0.508701	−0.254350	+	0.967112i	$0.581862\pi$
$684$	−13.5818	−0.519313
$685$	12.2209	0.466937
$686$	−20.0507	−0.765539
$687$	54.4369	2.07690
$688$	−4.86909	−0.185632
$689$	−5.48198	−0.208847
$690$	21.1686	0.805876
$691$	36.9324	1.40498	0.702488	−	0.711696i	$-0.252073\pi$
$691$	36.9324	1.40498	0.702488	+	0.711696i	$0.252073\pi$
$692$	7.29299	0.277238
$693$	2.25269	0.0855728
$694$	−22.7897	−0.865087
$695$	15.5499	0.589841
$696$	8.28775	0.314146
$697$	−18.4185	−0.697651
$698$	6.83428	0.258681
$699$	−60.2739	−2.27977
$700$	−2.29018	−0.0865608
$701$	−13.2247	−0.499489	−0.249744	−	0.968312i	$-0.580347\pi$
$701$	−13.2247	−0.499489	−0.249744	+	0.968312i	$0.580347\pi$
$702$	5.25435	0.198313
$703$	23.1910	0.874665
$704$	−0.201867	−0.00760816
$705$	1.42651	0.0537254
$706$	7.85275	0.295542
$707$	16.7348	0.629376
$708$	−26.2675	−0.987194
$709$	13.5778	0.509925	0.254963	−	0.966951i	$-0.417937\pi$
$709$	13.5778	0.509925	0.254963	+	0.966951i	$0.417937\pi$
$710$	−12.3037	−0.461748
$711$	−6.58505	−0.246959
$712$	6.59269	0.247072
$713$	−7.54453	−0.282545
$714$	−24.2254	−0.906613
$715$	−0.201867	−0.00754941
$716$	−12.9403	−0.483602
$717$	77.2645	2.88550
$718$	3.19031	0.119061
$719$	−39.0380	−1.45587	−0.727936	−	0.685645i	$-0.759520\pi$
$719$	−39.0380	−1.45587	−0.727936	+	0.685645i	$0.759520\pi$
$720$	−4.87266	−0.181593
$721$	−42.2869	−1.57485
$722$	11.2307	0.417963
$723$	−27.5524	−1.02469
$724$	−5.56297	−0.206746
$725$	−2.95377	−0.109700
$726$	30.7497	1.14123
$727$	−10.1581	−0.376744	−0.188372	−	0.982098i	$-0.560321\pi$
$727$	−10.1581	−0.376744	−0.188372	+	0.982098i	$0.560321\pi$
$728$	−2.29018	−0.0848798
$729$	−43.6202	−1.61556
$730$	−3.58247	−0.132593
$731$	18.3564	0.678937
$732$	−5.64167	−0.208522
$733$	38.2218	1.41175	0.705877	−	0.708334i	$-0.250553\pi$
$733$	38.2218	1.41175	0.705877	+	0.708334i	$0.250553\pi$
$734$	−29.7441	−1.09787
$735$	4.92440	0.181639
$736$	−7.54453	−0.278095
$737$	0.427971	0.0157645
$738$	−23.8057	−0.876298
$739$	2.09143	0.0769343	0.0384672	−	0.999260i	$-0.487752\pi$
$739$	2.09143	0.0769343	0.0384672	+	0.999260i	$0.487752\pi$
$740$	8.32009	0.305853
$741$	7.82081	0.287305
$742$	12.5547	0.460899
$743$	−37.1737	−1.36377	−0.681885	−	0.731459i	$-0.738840\pi$
$743$	−37.1737	−1.36377	−0.681885	+	0.731459i	$0.738840\pi$
$744$	2.80583	0.102867
$745$	3.72549	0.136491
$746$	−21.1975	−0.776096
$747$	−1.77169	−0.0648229
$748$	0.761038	0.0278263
$749$	37.5209	1.37098
$750$	2.80583	0.102454
$751$	37.8798	1.38225	0.691127	−	0.722733i	$-0.257114\pi$
$751$	37.8798	1.38225	0.691127	+	0.722733i	$0.257114\pi$
$752$	−0.508409	−0.0185398
$753$	54.3341	1.98004
$754$	−2.95377	−0.107570
$755$	8.18954	0.298048
$756$	−12.0334	−0.437651
$757$	−25.4694	−0.925701	−0.462851	−	0.886436i	$-0.653173\pi$
$757$	−25.4694	−0.925701	−0.462851	+	0.886436i	$0.653173\pi$
$758$	18.0543	0.655762
$759$	−4.27326	−0.155109
$760$	−2.78735	−0.101108
$761$	9.57415	0.347063	0.173531	−	0.984828i	$-0.444482\pi$
$761$	9.57415	0.347063	0.173531	+	0.984828i	$0.444482\pi$
$762$	−30.8106	−1.11615
$763$	−27.6508	−1.00103
$764$	−20.1067	−0.727435
$765$	18.3699	0.664164
$766$	8.17974	0.295546
$767$	9.36178	0.338034
$768$	2.80583	0.101247
$769$	−1.63499	−0.0589592	−0.0294796	−	0.999565i	$-0.509385\pi$
$769$	−1.63499	−0.0589592	−0.0294796	+	0.999565i	$0.509385\pi$
$770$	0.462313	0.0166606
$771$	−55.6200	−2.00311
$772$	−1.16762	−0.0420235
$773$	17.9795	0.646677	0.323338	−	0.946283i	$-0.395195\pi$
$773$	17.9795	0.646677	0.323338	+	0.946283i	$0.395195\pi$
$774$	23.7254	0.852792
$775$	−1.00000	−0.0359211
$776$	−4.64195	−0.166636
$777$	53.4637	1.91800
$778$	−31.5320	−1.13048
$779$	−13.6178	−0.487907
$780$	2.80583	0.100465
$781$	2.48371	0.0888741
$782$	28.4428	1.01711
$783$	−15.5201	−0.554644
$784$	−1.75506	−0.0626808
$785$	−10.3700	−0.370120
$786$	13.9589	0.497898
$787$	35.3310	1.25941	0.629707	−	0.776833i	$-0.283175\pi$
$787$	35.3310	1.25941	0.629707	+	0.776833i	$0.283175\pi$
$788$	−7.08555	−0.252412
$789$	−7.82038	−0.278413
$790$	−1.35143	−0.0480817
$791$	−3.26887	−0.116227
$792$	0.983631	0.0349518
$793$	2.01070	0.0714020
$794$	−0.447717	−0.0158889
$795$	−15.3815	−0.545525
$796$	−3.97615	−0.140931
$797$	−15.6015	−0.552633	−0.276317	−	0.961067i	$-0.589114\pi$
$797$	−15.6015	−0.552633	−0.276317	+	0.961067i	$0.589114\pi$
$798$	−17.9111	−0.634045
$799$	1.91670	0.0678079
$800$	−1.00000	−0.0353553
$801$	−32.1239	−1.13504
$802$	−28.2694	−0.998228
$803$	0.723185	0.0255206
$804$	−5.94852	−0.209788
$805$	17.2784	0.608982
$806$	−1.00000	−0.0352235
$807$	39.8867	1.40408
$808$	7.30718	0.257066
$809$	−31.4067	−1.10420	−0.552101	−	0.833777i	$-0.686174\pi$
$809$	−31.4067	−1.10420	−0.552101	+	0.833777i	$0.686174\pi$
$810$	0.124812	0.00438546
$811$	36.1269	1.26859	0.634293	−	0.773093i	$-0.281291\pi$
$811$	36.1269	1.26859	0.634293	+	0.773093i	$0.281291\pi$
$812$	6.76466	0.237393
$813$	−6.70882	−0.235289
$814$	−1.67956	−0.0588684
$815$	−9.56398	−0.335012
$816$	−10.5779	−0.370302
$817$	13.5718	0.474819
$818$	24.5781	0.859353
$819$	11.1593	0.389937
$820$	−4.88556	−0.170611
$821$	−15.1762	−0.529655	−0.264827	−	0.964296i	$-0.585315\pi$
$821$	−15.1762	−0.529655	−0.264827	+	0.964296i	$0.585315\pi$
$822$	34.2897	1.19599
$823$	17.7858	0.619973	0.309987	−	0.950741i	$-0.399675\pi$
$823$	17.7858	0.619973	0.309987	+	0.950741i	$0.399675\pi$
$824$	−18.4644	−0.643239
$825$	−0.566405	−0.0197197
$826$	−21.4402	−0.745999
$827$	−2.10838	−0.0733156	−0.0366578	−	0.999328i	$-0.511671\pi$
$827$	−2.10838	−0.0733156	−0.0366578	+	0.999328i	$0.511671\pi$
$828$	36.7619	1.27756
$829$	−1.53122	−0.0531816	−0.0265908	−	0.999646i	$-0.508465\pi$
$829$	−1.53122	−0.0531816	−0.0265908	+	0.999646i	$0.508465\pi$
$830$	−0.363599	−0.0126207
$831$	32.9863	1.14428
$832$	−1.00000	−0.0346688
$833$	6.61657	0.229251
$834$	43.6303	1.51079
$835$	23.9248	0.827951
$836$	0.562675	0.0194605
$837$	−5.25435	−0.181617
$838$	3.09415	0.106886
$839$	−34.6053	−1.19471	−0.597354	−	0.801978i	$-0.703781\pi$
$839$	−34.6053	−1.19471	−0.597354	+	0.801978i	$0.703781\pi$
$840$	−6.42585	−0.221713
$841$	−20.2753	−0.699147
$842$	−2.05940	−0.0709717
$843$	40.4776	1.39412
$844$	10.8435	0.373249
$845$	−1.00000	−0.0344010
$846$	2.47730	0.0851714
$847$	25.0987	0.862401
$848$	5.48198	0.188252
$849$	52.4842	1.80125
$850$	3.76999	0.129310
$851$	−62.7712	−2.15177
$852$	−34.5219	−1.18270
$853$	−11.6403	−0.398555	−0.199277	−	0.979943i	$-0.563859\pi$
$853$	−11.6403	−0.398555	−0.199277	+	0.979943i	$0.563859\pi$
$854$	−4.60487	−0.157575
$855$	13.5818	0.464487
$856$	16.3834	0.559972
$857$	42.0283	1.43566	0.717830	−	0.696219i	$-0.245136\pi$
$857$	42.0283	1.43566	0.717830	+	0.696219i	$0.245136\pi$
$858$	−0.566405	−0.0193367
$859$	−5.44079	−0.185637	−0.0928186	−	0.995683i	$-0.529588\pi$
$859$	−5.44079	−0.185637	−0.0928186	+	0.995683i	$0.529588\pi$
$860$	4.86909	0.166035
$861$	−31.3939	−1.06990
$862$	6.21975	0.211845
$863$	32.7299	1.11414	0.557069	−	0.830466i	$-0.311926\pi$
$863$	32.7299	1.11414	0.557069	+	0.830466i	$0.311926\pi$
$864$	−5.25435	−0.178757
$865$	−7.29299	−0.247969
$866$	−17.6960	−0.601335
$867$	−7.82032	−0.265592
$868$	2.29018	0.0777339
$869$	0.272810	0.00925443
$870$	−8.28775	−0.280981
$871$	2.12006	0.0718355
$872$	−12.0736	−0.408864
$873$	22.6186	0.765524
$874$	21.0292	0.711324
$875$	2.29018	0.0774223
$876$	−10.0518	−0.339619
$877$	−41.5221	−1.40210	−0.701051	−	0.713111i	$-0.747285\pi$
$877$	−41.5221	−1.40210	−0.701051	+	0.713111i	$0.747285\pi$
$878$	35.4405	1.19606
$879$	−12.1036	−0.408246
$880$	0.201867	0.00680495
$881$	−45.4431	−1.53102	−0.765509	−	0.643425i	$-0.777513\pi$
$881$	−45.4431	−1.53102	−0.765509	+	0.643425i	$0.777513\pi$
$882$	8.55182	0.287955
$883$	36.1264	1.21575	0.607876	−	0.794032i	$-0.292022\pi$
$883$	36.1264	1.21575	0.607876	+	0.794032i	$0.292022\pi$
$884$	3.76999	0.126798
$885$	26.2675	0.882973
$886$	−23.0913	−0.775767
$887$	−6.13459	−0.205980	−0.102990	−	0.994682i	$-0.532841\pi$
$887$	−6.13459	−0.205980	−0.102990	+	0.994682i	$0.532841\pi$
$888$	23.3447	0.783398
$889$	−25.1483	−0.843448
$890$	−6.59269	−0.220988
$891$	−0.0251956	−0.000844083 0
$892$	12.4769	0.417756
$893$	1.41711	0.0474219
$894$	10.4531	0.349603
$895$	12.9403	0.432547
$896$	2.29018	0.0765096
$897$	−21.1686	−0.706800
$898$	19.4000	0.647385
$899$	2.95377	0.0985136
$900$	4.87266	0.162422
$901$	−20.6670	−0.688519
$902$	0.986236	0.0328381
$903$	31.2881	1.04120
$904$	−1.42734	−0.0474726
$905$	5.56297	0.184919
$906$	22.9784	0.763407
$907$	13.8731	0.460650	0.230325	−	0.973114i	$-0.426021\pi$
$907$	13.8731	0.460650	0.230325	+	0.973114i	$0.426021\pi$
$908$	0.0801578	0.00266013
$909$	−35.6054	−1.18096
$910$	2.29018	0.0759188
$911$	11.9716	0.396638	0.198319	−	0.980138i	$-0.436452\pi$
$911$	11.9716	0.396638	0.198319	+	0.980138i	$0.436452\pi$
$912$	−7.82081	−0.258973
$913$	0.0733989	0.00242915
$914$	4.64875	0.153767
$915$	5.64167	0.186508
$916$	19.4014	0.641040
$917$	11.3936	0.376250
$918$	19.8088	0.653789
$919$	−3.01328	−0.0993990	−0.0496995	−	0.998764i	$-0.515826\pi$
$919$	−3.01328	−0.0993990	−0.0496995	+	0.998764i	$0.515826\pi$
$920$	7.54453	0.248736
$921$	0.632216	0.0208322
$922$	−14.8003	−0.487423
$923$	12.3037	0.404980
$924$	1.29717	0.0426738
$925$	−8.32009	−0.273563
$926$	34.2934	1.12695
$927$	89.9709	2.95503
$928$	2.95377	0.0969621
$929$	−14.6749	−0.481469	−0.240735	−	0.970591i	$-0.577388\pi$
$929$	−14.6749	−0.481469	−0.240735	+	0.970591i	$0.577388\pi$
$930$	−2.80583	−0.0920066
$931$	4.89197	0.160328
$932$	−21.4817	−0.703657
$933$	66.7516	2.18535
$934$	10.8650	0.355515
$935$	−0.761038	−0.0248886
$936$	4.87266	0.159268
$937$	29.6388	0.968256	0.484128	−	0.874997i	$-0.339137\pi$
$937$	29.6388	0.968256	0.484128	+	0.874997i	$0.339137\pi$
$938$	−4.85532	−0.158532
$939$	−54.9817	−1.79426
$940$	0.508409	0.0165825
$941$	−20.7391	−0.676074	−0.338037	−	0.941133i	$-0.609763\pi$
$941$	−20.7391	−0.676074	−0.338037	+	0.941133i	$0.609763\pi$
$942$	−29.0963	−0.948010
$943$	36.8593	1.20030
$944$	−9.36178	−0.304700
$945$	12.0334	0.391447
$946$	−0.982911	−0.0319572
$947$	21.5746	0.701080	0.350540	−	0.936548i	$-0.385998\pi$
$947$	21.5746	0.701080	0.350540	+	0.936548i	$0.385998\pi$
$948$	−3.79188	−0.123154
$949$	3.58247	0.116292
$950$	2.78735	0.0904335
$951$	41.0719	1.33185
$952$	−8.63397	−0.279828
$953$	16.4596	0.533180	0.266590	−	0.963810i	$-0.414103\pi$
$953$	16.4596	0.533180	0.266590	+	0.963810i	$0.414103\pi$
$954$	−26.7118	−0.864827
$955$	20.1067	0.650637
$956$	27.5372	0.890616
$957$	1.67303	0.0540813
$958$	18.8288	0.608330
$959$	27.9881	0.903783
$960$	−2.80583	−0.0905576
$961$	1.00000	0.0322581
$962$	−8.32009	−0.268251
$963$	−79.8305	−2.57250
$964$	−9.81973	−0.316272
$965$	1.16762	0.0375869
$966$	48.4800	1.55982
$967$	48.1447	1.54823	0.774115	−	0.633045i	$-0.218195\pi$
$967$	48.1447	1.54823	0.774115	+	0.633045i	$0.218195\pi$
$968$	10.9592	0.352244
$969$	29.4844	0.947175
$970$	4.64195	0.149044
$971$	−24.9675	−0.801245	−0.400622	−	0.916243i	$-0.631206\pi$
$971$	−24.9675	−0.801245	−0.400622	+	0.916243i	$0.631206\pi$
$972$	−15.4128	−0.494367
$973$	35.6121	1.14167
$974$	29.2019	0.935690
$975$	−2.80583	−0.0898583
$976$	−2.01070	−0.0643609
$977$	7.85961	0.251451	0.125726	−	0.992065i	$-0.459874\pi$
$977$	7.85961	0.251451	0.125726	+	0.992065i	$0.459874\pi$
$978$	−26.8349	−0.858084
$979$	1.33085	0.0425342
$980$	1.75506	0.0560634
$981$	58.8306	1.87832
$982$	43.5102	1.38847
$983$	−43.6591	−1.39251	−0.696254	−	0.717795i	$-0.745151\pi$
$983$	−43.6591	−1.39251	−0.696254	+	0.717795i	$0.745151\pi$
$984$	−13.7080	−0.436996
$985$	7.08555	0.225764
$986$	−11.1357	−0.354632
$987$	3.26696	0.103989
$988$	2.78735	0.0886773
$989$	−36.7350	−1.16811
$990$	−0.983631	−0.0312618
$991$	10.4493	0.331934	0.165967	−	0.986131i	$-0.446925\pi$
$991$	10.4493	0.331934	0.165967	+	0.986131i	$0.446925\pi$
$992$	1.00000	0.0317500
$993$	53.7010	1.70415
$994$	−28.1776	−0.893740
$995$	3.97615	0.126053
$996$	−1.02020	−0.0323262
$997$	6.88381	0.218013	0.109006	−	0.994041i	$-0.465233\pi$
$997$	6.88381	0.218013	0.109006	+	0.994041i	$0.465233\pi$
$998$	−36.4427	−1.15357
$999$	−43.7167	−1.38313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.i.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.i.1.7	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.80583 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.80583 q^{6} -2.29018 q^{7} -1.00000 q^{8} +4.87266 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.80583 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.80583 q^{6} -2.29018 q^{7} -1.00000 q^{8} +4.87266 q^{9} +1.00000 q^{10} -0.201867 q^{11} +2.80583 q^{12} -1.00000 q^{13} +2.29018 q^{14} -2.80583 q^{15} +1.00000 q^{16} -3.76999 q^{17} -4.87266 q^{18} -2.78735 q^{19} -1.00000 q^{20} -6.42585 q^{21} +0.201867 q^{22} +7.54453 q^{23} -2.80583 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.25435 q^{27} -2.29018 q^{28} -2.95377 q^{29} +2.80583 q^{30} -1.00000 q^{31} -1.00000 q^{32} -0.566405 q^{33} +3.76999 q^{34} +2.29018 q^{35} +4.87266 q^{36} -8.32009 q^{37} +2.78735 q^{38} -2.80583 q^{39} +1.00000 q^{40} +4.88556 q^{41} +6.42585 q^{42} -4.86909 q^{43} -0.201867 q^{44} -4.87266 q^{45} -7.54453 q^{46} -0.508409 q^{47} +2.80583 q^{48} -1.75506 q^{49} -1.00000 q^{50} -10.5779 q^{51} -1.00000 q^{52} +5.48198 q^{53} -5.25435 q^{54} +0.201867 q^{55} +2.29018 q^{56} -7.82081 q^{57} +2.95377 q^{58} -9.36178 q^{59} -2.80583 q^{60} -2.01070 q^{61} +1.00000 q^{62} -11.1593 q^{63} +1.00000 q^{64} +1.00000 q^{65} +0.566405 q^{66} -2.12006 q^{67} -3.76999 q^{68} +21.1686 q^{69} -2.29018 q^{70} -12.3037 q^{71} -4.87266 q^{72} -3.58247 q^{73} +8.32009 q^{74} +2.80583 q^{75} -2.78735 q^{76} +0.462313 q^{77} +2.80583 q^{78} -1.35143 q^{79} -1.00000 q^{80} +0.124812 q^{81} -4.88556 q^{82} -0.363599 q^{83} -6.42585 q^{84} +3.76999 q^{85} +4.86909 q^{86} -8.28775 q^{87} +0.201867 q^{88} -6.59269 q^{89} +4.87266 q^{90} +2.29018 q^{91} +7.54453 q^{92} -2.80583 q^{93} +0.508409 q^{94} +2.78735 q^{95} -2.80583 q^{96} +4.64195 q^{97} +1.75506 q^{98} -0.983631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 2 q^{7} - 7 q^{8} + 4 q^{9} + 7 q^{10} - 6 q^{11} + 3 q^{12} - 7 q^{13} - 2 q^{14} - 3 q^{15} + 7 q^{16} - 4 q^{18} - 9 q^{19} - 7 q^{20} + q^{21} + 6 q^{22} + 7 q^{23} - 3 q^{24} + 7 q^{25} + 7 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} + 3 q^{30} - 7 q^{31} - 7 q^{32} - 2 q^{35} + 4 q^{36} + 2 q^{37} + 9 q^{38} - 3 q^{39} + 7 q^{40} - 14 q^{41} - q^{42} + 9 q^{43} - 6 q^{44} - 4 q^{45} - 7 q^{46} - 8 q^{47} + 3 q^{48} - q^{49} - 7 q^{50} - 7 q^{51} - 7 q^{52} - 6 q^{53} - 9 q^{54} + 6 q^{55} - 2 q^{56} - 11 q^{57} + 4 q^{58} - 15 q^{59} - 3 q^{60} + q^{61} + 7 q^{62} - 17 q^{63} + 7 q^{64} + 7 q^{65} + 14 q^{67} - 14 q^{69} + 2 q^{70} - 16 q^{71} - 4 q^{72} - 13 q^{73} - 2 q^{74} + 3 q^{75} - 9 q^{76} - 5 q^{77} + 3 q^{78} - 14 q^{79} - 7 q^{80} - 25 q^{81} + 14 q^{82} - 10 q^{83} + q^{84} - 9 q^{86} - 9 q^{87} + 6 q^{88} - 26 q^{89} + 4 q^{90} - 2 q^{91} + 7 q^{92} - 3 q^{93} + 8 q^{94} + 9 q^{95} - 3 q^{96} - 5 q^{97} + q^{98} - 37 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 2 * q^7 - 7 * q^8 + 4 * q^9 + 7 * q^10 - 6 * q^11 + 3 * q^12 - 7 * q^13 - 2 * q^14 - 3 * q^15 + 7 * q^16 - 4 * q^18 - 9 * q^19 - 7 * q^20 + q^21 + 6 * q^22 + 7 * q^23 - 3 * q^24 + 7 * q^25 + 7 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 + 3 * q^30 - 7 * q^31 - 7 * q^32 - 2 * q^35 + 4 * q^36 + 2 * q^37 + 9 * q^38 - 3 * q^39 + 7 * q^40 - 14 * q^41 - q^42 + 9 * q^43 - 6 * q^44 - 4 * q^45 - 7 * q^46 - 8 * q^47 + 3 * q^48 - q^49 - 7 * q^50 - 7 * q^51 - 7 * q^52 - 6 * q^53 - 9 * q^54 + 6 * q^55 - 2 * q^56 - 11 * q^57 + 4 * q^58 - 15 * q^59 - 3 * q^60 + q^61 + 7 * q^62 - 17 * q^63 + 7 * q^64 + 7 * q^65 + 14 * q^67 - 14 * q^69 + 2 * q^70 - 16 * q^71 - 4 * q^72 - 13 * q^73 - 2 * q^74 + 3 * q^75 - 9 * q^76 - 5 * q^77 + 3 * q^78 - 14 * q^79 - 7 * q^80 - 25 * q^81 + 14 * q^82 - 10 * q^83 + q^84 - 9 * q^86 - 9 * q^87 + 6 * q^88 - 26 * q^89 + 4 * q^90 - 2 * q^91 + 7 * q^92 - 3 * q^93 + 8 * q^94 + 9 * q^95 - 3 * q^96 - 5 * q^97 + q^98 - 37 * q^99

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