LMFDB - Embedded newform 4030.2.a.c.1.4

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:	$6$
Coefficient field:	6.6.3081125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 10x - 5 $ x^6 - x^5 - 8x^4 + 6x^3 + 16x^2 - 10x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.04356$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.344929 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.344929 q^{6} +4.21970 q^{7} -1.00000 q^{8} -2.88102 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.344929 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.344929 q^{6} +4.21970 q^{7} -1.00000 q^{8} -2.88102 q^{9} +1.00000 q^{10} -2.82110 q^{11} +0.344929 q^{12} +1.00000 q^{13} -4.21970 q^{14} -0.344929 q^{15} +1.00000 q^{16} -6.07701 q^{17} +2.88102 q^{18} +0.371851 q^{19} -1.00000 q^{20} +1.45550 q^{21} +2.82110 q^{22} +3.73208 q^{23} -0.344929 q^{24} +1.00000 q^{25} -1.00000 q^{26} -2.02854 q^{27} +4.21970 q^{28} +6.00867 q^{29} +0.344929 q^{30} +1.00000 q^{31} -1.00000 q^{32} -0.973078 q^{33} +6.07701 q^{34} -4.21970 q^{35} -2.88102 q^{36} +1.34635 q^{37} -0.371851 q^{38} +0.344929 q^{39} +1.00000 q^{40} -0.473191 q^{41} -1.45550 q^{42} -2.00161 q^{43} -2.82110 q^{44} +2.88102 q^{45} -3.73208 q^{46} -4.96019 q^{47} +0.344929 q^{48} +10.8059 q^{49} -1.00000 q^{50} -2.09614 q^{51} +1.00000 q^{52} -11.7966 q^{53} +2.02854 q^{54} +2.82110 q^{55} -4.21970 q^{56} +0.128262 q^{57} -6.00867 q^{58} +0.139104 q^{59} -0.344929 q^{60} -0.378102 q^{61} -1.00000 q^{62} -12.1571 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.973078 q^{66} -3.07397 q^{67} -6.07701 q^{68} +1.28730 q^{69} +4.21970 q^{70} -0.880146 q^{71} +2.88102 q^{72} -14.0900 q^{73} -1.34635 q^{74} +0.344929 q^{75} +0.371851 q^{76} -11.9042 q^{77} -0.344929 q^{78} -6.52320 q^{79} -1.00000 q^{80} +7.94337 q^{81} +0.473191 q^{82} -7.82984 q^{83} +1.45550 q^{84} +6.07701 q^{85} +2.00161 q^{86} +2.07256 q^{87} +2.82110 q^{88} -9.55175 q^{89} -2.88102 q^{90} +4.21970 q^{91} +3.73208 q^{92} +0.344929 q^{93} +4.96019 q^{94} -0.371851 q^{95} -0.344929 q^{96} +9.65236 q^{97} -10.8059 q^{98} +8.12765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} + q^{18} + 3 q^{19} - 6 q^{20} - q^{21} + 6 q^{22} - 7 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - q^{27} + 4 q^{28} - 14 q^{29} - q^{30} + 6 q^{31} - 6 q^{32} - 2 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 14 q^{37} - 3 q^{38} - q^{39} + 6 q^{40} - 12 q^{41} + q^{42} + 3 q^{43} - 6 q^{44} + q^{45} + 7 q^{46} - 2 q^{47} - q^{48} - 6 q^{49} - 6 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + q^{54} + 6 q^{55} - 4 q^{56} + 13 q^{57} + 14 q^{58} - 17 q^{59} + q^{60} - 5 q^{61} - 6 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + 2 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 4 q^{70} - 16 q^{71} + q^{72} + 11 q^{73} - 14 q^{74} - q^{75} + 3 q^{76} - 15 q^{77} + q^{78} - 2 q^{79} - 6 q^{80} - 26 q^{81} + 12 q^{82} + 4 q^{83} - q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 6 q^{88} - 8 q^{89} - q^{90} + 4 q^{91} - 7 q^{92} - q^{93} + 2 q^{94} - 3 q^{95} + q^{96} + 5 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9 + 6 * q^10 - 6 * q^11 - q^12 + 6 * q^13 - 4 * q^14 + q^15 + 6 * q^16 - 4 * q^17 + q^18 + 3 * q^19 - 6 * q^20 - q^21 + 6 * q^22 - 7 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 14 * q^29 - q^30 + 6 * q^31 - 6 * q^32 - 2 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 14 * q^37 - 3 * q^38 - q^39 + 6 * q^40 - 12 * q^41 + q^42 + 3 * q^43 - 6 * q^44 + q^45 + 7 * q^46 - 2 * q^47 - q^48 - 6 * q^49 - 6 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + q^54 + 6 * q^55 - 4 * q^56 + 13 * q^57 + 14 * q^58 - 17 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + 2 * q^66 + 8 * q^67 - 4 * q^68 - 8 * q^69 + 4 * q^70 - 16 * q^71 + q^72 + 11 * q^73 - 14 * q^74 - q^75 + 3 * q^76 - 15 * q^77 + q^78 - 2 * q^79 - 6 * q^80 - 26 * q^81 + 12 * q^82 + 4 * q^83 - q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 6 * q^88 - 8 * q^89 - q^90 + 4 * q^91 - 7 * q^92 - q^93 + 2 * q^94 - 3 * q^95 + q^96 + 5 * q^97 + 6 * q^98 + 15 * 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
$3$	0.344929	0.199145	0.0995724	−	0.995030i	$-0.468253\pi$
$3$	0.344929	0.199145	0.0995724	+	0.995030i	$0.468253\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.344929	−0.140817
$7$	4.21970	1.59490	0.797449	−	0.603387i	$-0.206182\pi$
$7$	4.21970	1.59490	0.797449	+	0.603387i	$0.206182\pi$
$8$	−1.00000	−0.353553
$9$	−2.88102	−0.960341
$10$	1.00000	0.316228
$11$	−2.82110	−0.850593	−0.425296	−	0.905054i	$-0.639830\pi$
$11$	−2.82110	−0.850593	−0.425296	+	0.905054i	$0.639830\pi$
$12$	0.344929	0.0995724
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.21970	−1.12776
$15$	−0.344929	−0.0890603
$16$	1.00000	0.250000
$17$	−6.07701	−1.47389	−0.736945	−	0.675952i	$-0.763732\pi$
$17$	−6.07701	−1.47389	−0.736945	+	0.675952i	$0.763732\pi$
$18$	2.88102	0.679064
$19$	0.371851	0.0853085	0.0426542	−	0.999090i	$-0.486419\pi$
$19$	0.371851	0.0853085	0.0426542	+	0.999090i	$0.486419\pi$
$20$	−1.00000	−0.223607
$21$	1.45550	0.317616
$22$	2.82110	0.601460
$23$	3.73208	0.778192	0.389096	−	0.921197i	$-0.372787\pi$
$23$	3.73208	0.778192	0.389096	+	0.921197i	$0.372787\pi$
$24$	−0.344929	−0.0704083
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−2.02854	−0.390392
$28$	4.21970	0.797449
$29$	6.00867	1.11578	0.557891	−	0.829914i	$-0.311611\pi$
$29$	6.00867	1.11578	0.557891	+	0.829914i	$0.311611\pi$
$30$	0.344929	0.0629751
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−0.973078	−0.169391
$34$	6.07701	1.04220
$35$	−4.21970	−0.713260
$36$	−2.88102	−0.480171
$37$	1.34635	0.221339	0.110669	−	0.993857i	$-0.464701\pi$
$37$	1.34635	0.221339	0.110669	+	0.993857i	$0.464701\pi$
$38$	−0.371851	−0.0603222
$39$	0.344929	0.0552328
$40$	1.00000	0.158114
$41$	−0.473191	−0.0739000	−0.0369500	−	0.999317i	$-0.511764\pi$
$41$	−0.473191	−0.0739000	−0.0369500	+	0.999317i	$0.511764\pi$
$42$	−1.45550	−0.224588
$43$	−2.00161	−0.305243	−0.152622	−	0.988285i	$-0.548772\pi$
$43$	−2.00161	−0.305243	−0.152622	+	0.988285i	$0.548772\pi$
$44$	−2.82110	−0.425296
$45$	2.88102	0.429478
$46$	−3.73208	−0.550265
$47$	−4.96019	−0.723518	−0.361759	−	0.932272i	$-0.617824\pi$
$47$	−4.96019	−0.723518	−0.361759	+	0.932272i	$0.617824\pi$
$48$	0.344929	0.0497862
$49$	10.8059	1.54370
$50$	−1.00000	−0.141421
$51$	−2.09614	−0.293518
$52$	1.00000	0.138675
$53$	−11.7966	−1.62039	−0.810193	−	0.586163i	$-0.800638\pi$
$53$	−11.7966	−1.62039	−0.810193	+	0.586163i	$0.800638\pi$
$54$	2.02854	0.276049
$55$	2.82110	0.380397
$56$	−4.21970	−0.563881
$57$	0.128262	0.0169887
$58$	−6.00867	−0.788977
$59$	0.139104	0.0181098	0.00905488	−	0.999959i	$-0.497118\pi$
$59$	0.139104	0.0181098	0.00905488	+	0.999959i	$0.497118\pi$
$60$	−0.344929	−0.0445301
$61$	−0.378102	−0.0484111	−0.0242055	−	0.999707i	$-0.507706\pi$
$61$	−0.378102	−0.0484111	−0.0242055	+	0.999707i	$0.507706\pi$
$62$	−1.00000	−0.127000
$63$	−12.1571	−1.53165
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	0.973078	0.119778
$67$	−3.07397	−0.375545	−0.187773	−	0.982213i	$-0.560127\pi$
$67$	−3.07397	−0.375545	−0.187773	+	0.982213i	$0.560127\pi$
$68$	−6.07701	−0.736945
$69$	1.28730	0.154973
$70$	4.21970	0.504351
$71$	−0.880146	−0.104454	−0.0522270	−	0.998635i	$-0.516632\pi$
$71$	−0.880146	−0.104454	−0.0522270	+	0.998635i	$0.516632\pi$
$72$	2.88102	0.339532
$73$	−14.0900	−1.64911	−0.824554	−	0.565784i	$-0.808574\pi$
$73$	−14.0900	−1.64911	−0.824554	+	0.565784i	$0.808574\pi$
$74$	−1.34635	−0.156510
$75$	0.344929	0.0398290
$76$	0.371851	0.0426542
$77$	−11.9042	−1.35661
$78$	−0.344929	−0.0390555
$79$	−6.52320	−0.733918	−0.366959	−	0.930237i	$-0.619601\pi$
$79$	−6.52320	−0.733918	−0.366959	+	0.930237i	$0.619601\pi$
$80$	−1.00000	−0.111803
$81$	7.94337	0.882597
$82$	0.473191	0.0522552
$83$	−7.82984	−0.859437	−0.429718	−	0.902963i	$-0.641387\pi$
$83$	−7.82984	−0.859437	−0.429718	+	0.902963i	$0.641387\pi$
$84$	1.45550	0.158808
$85$	6.07701	0.659144
$86$	2.00161	0.215840
$87$	2.07256	0.222202
$88$	2.82110	0.300730
$89$	−9.55175	−1.01248	−0.506242	−	0.862392i	$-0.668966\pi$
$89$	−9.55175	−1.01248	−0.506242	+	0.862392i	$0.668966\pi$
$90$	−2.88102	−0.303687
$91$	4.21970	0.442345
$92$	3.73208	0.389096
$93$	0.344929	0.0357675
$94$	4.96019	0.511604
$95$	−0.371851	−0.0381511
$96$	−0.344929	−0.0352042
$97$	9.65236	0.980048	0.490024	−	0.871709i	$-0.336988\pi$
$97$	9.65236	0.980048	0.490024	+	0.871709i	$0.336988\pi$
$98$	−10.8059	−1.09156
$99$	8.12765	0.816859
$100$	1.00000	0.100000
$101$	−2.30495	−0.229351	−0.114676	−	0.993403i	$-0.536583\pi$
$101$	−2.30495	−0.229351	−0.114676	+	0.993403i	$0.536583\pi$
$102$	2.09614	0.207548
$103$	4.26856	0.420594	0.210297	−	0.977638i	$-0.432557\pi$
$103$	4.26856	0.420594	0.210297	+	0.977638i	$0.432557\pi$
$104$	−1.00000	−0.0980581
$105$	−1.45550	−0.142042
$106$	11.7966	1.14579
$107$	5.21167	0.503831	0.251916	−	0.967749i	$-0.418939\pi$
$107$	5.21167	0.503831	0.251916	+	0.967749i	$0.418939\pi$
$108$	−2.02854	−0.195196
$109$	−13.3113	−1.27500	−0.637498	−	0.770452i	$-0.720030\pi$
$109$	−13.3113	−1.27500	−0.637498	+	0.770452i	$0.720030\pi$
$110$	−2.82110	−0.268981
$111$	0.464395	0.0440784
$112$	4.21970	0.398724
$113$	10.2500	0.964237	0.482119	−	0.876106i	$-0.339867\pi$
$113$	10.2500	0.964237	0.482119	+	0.876106i	$0.339867\pi$
$114$	−0.128262	−0.0120129
$115$	−3.73208	−0.348018
$116$	6.00867	0.557891
$117$	−2.88102	−0.266351
$118$	−0.139104	−0.0128055
$119$	−25.6432	−2.35070
$120$	0.344929	0.0314876
$121$	−3.04141	−0.276492
$122$	0.378102	0.0342318
$123$	−0.163217	−0.0147168
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	12.1571	1.08304
$127$	−11.3742	−1.00929	−0.504647	−	0.863326i	$-0.668377\pi$
$127$	−11.3742	−1.00929	−0.504647	+	0.863326i	$0.668377\pi$
$128$	−1.00000	−0.0883883
$129$	−0.690414	−0.0607876
$130$	1.00000	0.0877058
$131$	−9.32834	−0.815021	−0.407510	−	0.913201i	$-0.633603\pi$
$131$	−9.32834	−0.815021	−0.407510	+	0.913201i	$0.633603\pi$
$132$	−0.973078	−0.0846956
$133$	1.56910	0.136058
$134$	3.07397	0.265551
$135$	2.02854	0.174589
$136$	6.07701	0.521099
$137$	2.88511	0.246491	0.123246	−	0.992376i	$-0.460670\pi$
$137$	2.88511	0.246491	0.123246	+	0.992376i	$0.460670\pi$
$138$	−1.28730	−0.109582
$139$	7.55412	0.640732	0.320366	−	0.947294i	$-0.396194\pi$
$139$	7.55412	0.640732	0.320366	+	0.947294i	$0.396194\pi$
$140$	−4.21970	−0.356630
$141$	−1.71091	−0.144085
$142$	0.880146	0.0738602
$143$	−2.82110	−0.235912
$144$	−2.88102	−0.240085
$145$	−6.00867	−0.498993
$146$	14.0900	1.16610
$147$	3.72726	0.307419
$148$	1.34635	0.110669
$149$	3.07077	0.251567	0.125784	−	0.992058i	$-0.459856\pi$
$149$	3.07077	0.251567	0.125784	+	0.992058i	$0.459856\pi$
$150$	−0.344929	−0.0281633
$151$	−5.48330	−0.446224	−0.223112	−	0.974793i	$-0.571622\pi$
$151$	−5.48330	−0.446224	−0.223112	+	0.974793i	$0.571622\pi$
$152$	−0.371851	−0.0301611
$153$	17.5080	1.41544
$154$	11.9042	0.959267
$155$	−1.00000	−0.0803219
$156$	0.344929	0.0276164
$157$	15.8819	1.26751	0.633755	−	0.773534i	$-0.281513\pi$
$157$	15.8819	1.26751	0.633755	+	0.773534i	$0.281513\pi$
$158$	6.52320	0.518958
$159$	−4.06899	−0.322692
$160$	1.00000	0.0790569
$161$	15.7483	1.24114
$162$	−7.94337	−0.624090
$163$	2.40864	0.188659	0.0943296	−	0.995541i	$-0.469929\pi$
$163$	2.40864	0.188659	0.0943296	+	0.995541i	$0.469929\pi$
$164$	−0.473191	−0.0369500
$165$	0.973078	0.0757540
$166$	7.82984	0.607713
$167$	−8.89497	−0.688314	−0.344157	−	0.938912i	$-0.611835\pi$
$167$	−8.89497	−0.688314	−0.344157	+	0.938912i	$0.611835\pi$
$168$	−1.45550	−0.112294
$169$	1.00000	0.0769231
$170$	−6.07701	−0.466085
$171$	−1.07131	−0.0819253
$172$	−2.00161	−0.152622
$173$	5.87935	0.446999	0.223499	−	0.974704i	$-0.428252\pi$
$173$	5.87935	0.446999	0.223499	+	0.974704i	$0.428252\pi$
$174$	−2.07256	−0.157121
$175$	4.21970	0.318979
$176$	−2.82110	−0.212648
$177$	0.0479809	0.00360646
$178$	9.55175	0.715934
$179$	−12.9107	−0.964994	−0.482497	−	0.875898i	$-0.660270\pi$
$179$	−12.9107	−0.964994	−0.482497	+	0.875898i	$0.660270\pi$
$180$	2.88102	0.214739
$181$	6.76590	0.502906	0.251453	−	0.967870i	$-0.419092\pi$
$181$	6.76590	0.502906	0.251453	+	0.967870i	$0.419092\pi$
$182$	−4.21970	−0.312785
$183$	−0.130418	−0.00964081
$184$	−3.73208	−0.275132
$185$	−1.34635	−0.0989856
$186$	−0.344929	−0.0252914
$187$	17.1438	1.25368
$188$	−4.96019	−0.361759
$189$	−8.55981	−0.622635
$190$	0.371851	0.0269769
$191$	−24.0162	−1.73775	−0.868876	−	0.495030i	$-0.835157\pi$
$191$	−24.0162	−1.73775	−0.868876	+	0.495030i	$0.835157\pi$
$192$	0.344929	0.0248931
$193$	2.15280	0.154962	0.0774810	−	0.996994i	$-0.475312\pi$
$193$	2.15280	0.154962	0.0774810	+	0.996994i	$0.475312\pi$
$194$	−9.65236	−0.692999
$195$	−0.344929	−0.0247009
$196$	10.8059	0.771849
$197$	0.319274	0.0227473	0.0113736	−	0.999935i	$-0.496380\pi$
$197$	0.319274	0.0227473	0.0113736	+	0.999935i	$0.496380\pi$
$198$	−8.12765	−0.577607
$199$	−22.0172	−1.56076	−0.780380	−	0.625305i	$-0.784974\pi$
$199$	−22.0172	−1.56076	−0.780380	+	0.625305i	$0.784974\pi$
$200$	−1.00000	−0.0707107
$201$	−1.06030	−0.0747879
$202$	2.30495	0.162176
$203$	25.3548	1.77956
$204$	−2.09614	−0.146759
$205$	0.473191	0.0330491
$206$	−4.26856	−0.297405
$207$	−10.7522	−0.747330
$208$	1.00000	0.0693375
$209$	−1.04903	−0.0725628
$210$	1.45550	0.100439
$211$	−17.6058	−1.21203	−0.606017	−	0.795451i	$-0.707234\pi$
$211$	−17.6058	−1.21203	−0.606017	+	0.795451i	$0.707234\pi$
$212$	−11.7966	−0.810193
$213$	−0.303588	−0.0208015
$214$	−5.21167	−0.356262
$215$	2.00161	0.136509
$216$	2.02854	0.138024
$217$	4.21970	0.286452
$218$	13.3113	0.901558
$219$	−4.86004	−0.328411
$220$	2.82110	0.190198
$221$	−6.07701	−0.408784
$222$	−0.464395	−0.0311682
$223$	−9.83104	−0.658335	−0.329167	−	0.944272i	$-0.606768\pi$
$223$	−9.83104	−0.658335	−0.329167	+	0.944272i	$0.606768\pi$
$224$	−4.21970	−0.281941
$225$	−2.88102	−0.192068
$226$	−10.2500	−0.681819
$227$	−0.244900	−0.0162546	−0.00812729	−	0.999967i	$-0.502587\pi$
$227$	−0.244900	−0.0162546	−0.00812729	+	0.999967i	$0.502587\pi$
$228$	0.128262	0.00849437
$229$	25.8196	1.70621	0.853103	−	0.521742i	$-0.174718\pi$
$229$	25.8196	1.70621	0.853103	+	0.521742i	$0.174718\pi$
$230$	3.73208	0.246086
$231$	−4.10610	−0.270161
$232$	−6.00867	−0.394489
$233$	−16.7428	−1.09685	−0.548427	−	0.836198i	$-0.684773\pi$
$233$	−16.7428	−1.09685	−0.548427	+	0.836198i	$0.684773\pi$
$234$	2.88102	0.188338
$235$	4.96019	0.323567
$236$	0.139104	0.00905488
$237$	−2.25004	−0.146156
$238$	25.6432	1.66220
$239$	−9.37679	−0.606534	−0.303267	−	0.952906i	$-0.598077\pi$
$239$	−9.37679	−0.606534	−0.303267	+	0.952906i	$0.598077\pi$
$240$	−0.344929	−0.0222651
$241$	−6.37825	−0.410859	−0.205430	−	0.978672i	$-0.565859\pi$
$241$	−6.37825	−0.410859	−0.205430	+	0.978672i	$0.565859\pi$
$242$	3.04141	0.195509
$243$	8.82551	0.566156
$244$	−0.378102	−0.0242055
$245$	−10.8059	−0.690362
$246$	0.163217	0.0104064
$247$	0.371851	0.0236603
$248$	−1.00000	−0.0635001
$249$	−2.70074	−0.171152
$250$	1.00000	0.0632456
$251$	−19.4538	−1.22791	−0.613957	−	0.789340i	$-0.710423\pi$
$251$	−19.4538	−1.22791	−0.613957	+	0.789340i	$0.710423\pi$
$252$	−12.1571	−0.765823
$253$	−10.5286	−0.661924
$254$	11.3742	0.713679
$255$	2.09614	0.131265
$256$	1.00000	0.0625000
$257$	−6.85857	−0.427826	−0.213913	−	0.976853i	$-0.568621\pi$
$257$	−6.85857	−0.427826	−0.213913	+	0.976853i	$0.568621\pi$
$258$	0.690414	0.0429833
$259$	5.68120	0.353012
$260$	−1.00000	−0.0620174
$261$	−17.3111	−1.07153
$262$	9.32834	0.576307
$263$	−6.30941	−0.389055	−0.194527	−	0.980897i	$-0.562317\pi$
$263$	−6.30941	−0.389055	−0.194527	+	0.980897i	$0.562317\pi$
$264$	0.973078	0.0598888
$265$	11.7966	0.724659
$266$	−1.56910	−0.0962077
$267$	−3.29468	−0.201631
$268$	−3.07397	−0.187773
$269$	−18.8613	−1.14999	−0.574997	−	0.818155i	$-0.694997\pi$
$269$	−18.8613	−1.14999	−0.574997	+	0.818155i	$0.694997\pi$
$270$	−2.02854	−0.123453
$271$	8.79116	0.534025	0.267012	−	0.963693i	$-0.413964\pi$
$271$	8.79116	0.534025	0.267012	+	0.963693i	$0.413964\pi$
$272$	−6.07701	−0.368473
$273$	1.45550	0.0880907
$274$	−2.88511	−0.174296
$275$	−2.82110	−0.170119
$276$	1.28730	0.0774865
$277$	−15.2749	−0.917779	−0.458890	−	0.888493i	$-0.651753\pi$
$277$	−15.2749	−0.917779	−0.458890	+	0.888493i	$0.651753\pi$
$278$	−7.55412	−0.453066
$279$	−2.88102	−0.172482
$280$	4.21970	0.252175
$281$	17.7079	1.05637	0.528183	−	0.849130i	$-0.322873\pi$
$281$	17.7079	1.05637	0.528183	+	0.849130i	$0.322873\pi$
$282$	1.71091	0.101883
$283$	−7.98019	−0.474373	−0.237187	−	0.971464i	$-0.576225\pi$
$283$	−7.98019	−0.474373	−0.237187	+	0.971464i	$0.576225\pi$
$284$	−0.880146	−0.0522270
$285$	−0.128262	−0.00759760
$286$	2.82110	0.166815
$287$	−1.99673	−0.117863
$288$	2.88102	0.169766
$289$	19.9300	1.17235
$290$	6.00867	0.352841
$291$	3.32938	0.195172
$292$	−14.0900	−0.824554
$293$	−10.2118	−0.596580	−0.298290	−	0.954475i	$-0.596416\pi$
$293$	−10.2118	−0.596580	−0.298290	+	0.954475i	$0.596416\pi$
$294$	−3.72726	−0.217378
$295$	−0.139104	−0.00809893
$296$	−1.34635	−0.0782550
$297$	5.72269	0.332064
$298$	−3.07077	−0.177885
$299$	3.73208	0.215832
$300$	0.344929	0.0199145
$301$	−8.44621	−0.486832
$302$	5.48330	0.315528
$303$	−0.795044	−0.0456741
$304$	0.371851	0.0213271
$305$	0.378102	0.0216501
$306$	−17.5080	−1.00087
$307$	17.8483	1.01866	0.509329	−	0.860572i	$-0.329894\pi$
$307$	17.8483	1.01866	0.509329	+	0.860572i	$0.329894\pi$
$308$	−11.9042	−0.678304
$309$	1.47235	0.0837591
$310$	1.00000	0.0567962
$311$	−6.35494	−0.360356	−0.180178	−	0.983634i	$-0.557667\pi$
$311$	−6.35494	−0.360356	−0.180178	+	0.983634i	$0.557667\pi$
$312$	−0.344929	−0.0195278
$313$	−12.3934	−0.700519	−0.350260	−	0.936653i	$-0.613907\pi$
$313$	−12.3934	−0.700519	−0.350260	+	0.936653i	$0.613907\pi$
$314$	−15.8819	−0.896265
$315$	12.1571	0.684973
$316$	−6.52320	−0.366959
$317$	14.0273	0.787849	0.393925	−	0.919143i	$-0.371117\pi$
$317$	14.0273	0.787849	0.393925	+	0.919143i	$0.371117\pi$
$318$	4.06899	0.228177
$319$	−16.9510	−0.949076
$320$	−1.00000	−0.0559017
$321$	1.79766	0.100335
$322$	−15.7483	−0.877616
$323$	−2.25974	−0.125735
$324$	7.94337	0.441298
$325$	1.00000	0.0554700
$326$	−2.40864	−0.133402
$327$	−4.59147	−0.253909
$328$	0.473191	0.0261276
$329$	−20.9305	−1.15394
$330$	−0.973078	−0.0535662
$331$	7.88514	0.433407	0.216703	−	0.976238i	$-0.430470\pi$
$331$	7.88514	0.433407	0.216703	+	0.976238i	$0.430470\pi$
$332$	−7.82984	−0.429718
$333$	−3.87887	−0.212561
$334$	8.89497	0.486711
$335$	3.07397	0.167949
$336$	1.45550	0.0794039
$337$	17.1297	0.933112	0.466556	−	0.884492i	$-0.345495\pi$
$337$	17.1297	0.933112	0.466556	+	0.884492i	$0.345495\pi$
$338$	−1.00000	−0.0543928
$339$	3.53551	0.192023
$340$	6.07701	0.329572
$341$	−2.82110	−0.152771
$342$	1.07131	0.0579299
$343$	16.0597	0.867141
$344$	2.00161	0.107920
$345$	−1.28730	−0.0693060
$346$	−5.87935	−0.316076
$347$	27.9190	1.49877	0.749385	−	0.662134i	$-0.230349\pi$
$347$	27.9190	1.49877	0.749385	+	0.662134i	$0.230349\pi$
$348$	2.07256	0.111101
$349$	−13.1905	−0.706072	−0.353036	−	0.935610i	$-0.614851\pi$
$349$	−13.1905	−0.706072	−0.353036	+	0.935610i	$0.614851\pi$
$350$	−4.21970	−0.225553
$351$	−2.02854	−0.108275
$352$	2.82110	0.150365
$353$	5.94603	0.316475	0.158238	−	0.987401i	$-0.449419\pi$
$353$	5.94603	0.316475	0.158238	+	0.987401i	$0.449419\pi$
$354$	−0.0479809	−0.00255016
$355$	0.880146	0.0467133
$356$	−9.55175	−0.506242
$357$	−8.84507	−0.468131
$358$	12.9107	0.682354
$359$	18.7523	0.989708	0.494854	−	0.868976i	$-0.335222\pi$
$359$	18.7523	0.989708	0.494854	+	0.868976i	$0.335222\pi$
$360$	−2.88102	−0.151843
$361$	−18.8617	−0.992722
$362$	−6.76590	−0.355608
$363$	−1.04907	−0.0550620
$364$	4.21970	0.221172
$365$	14.0900	0.737503
$366$	0.130418	0.00681708
$367$	32.1646	1.67898	0.839488	−	0.543377i	$-0.182855\pi$
$367$	32.1646	1.67898	0.839488	+	0.543377i	$0.182855\pi$
$368$	3.73208	0.194548
$369$	1.36327	0.0709693
$370$	1.34635	0.0699934
$371$	−49.7781	−2.58435
$372$	0.344929	0.0178837
$373$	−35.0936	−1.81708	−0.908539	−	0.417800i	$-0.862801\pi$
$373$	−35.0936	−1.81708	−0.908539	+	0.417800i	$0.862801\pi$
$374$	−17.1438	−0.886486
$375$	−0.344929	−0.0178121
$376$	4.96019	0.255802
$377$	6.00867	0.309462
$378$	8.55981	0.440269
$379$	−25.4831	−1.30898	−0.654489	−	0.756072i	$-0.727116\pi$
$379$	−25.4831	−1.30898	−0.654489	+	0.756072i	$0.727116\pi$
$380$	−0.371851	−0.0190756
$381$	−3.92328	−0.200996
$382$	24.0162	1.22878
$383$	−19.2072	−0.981440	−0.490720	−	0.871317i	$-0.663266\pi$
$383$	−19.2072	−0.981440	−0.490720	+	0.871317i	$0.663266\pi$
$384$	−0.344929	−0.0176021
$385$	11.9042	0.606694
$386$	−2.15280	−0.109575
$387$	5.76670	0.293138
$388$	9.65236	0.490024
$389$	−21.0242	−1.06597	−0.532985	−	0.846125i	$-0.678930\pi$
$389$	−21.0242	−1.06597	−0.532985	+	0.846125i	$0.678930\pi$
$390$	0.344929	0.0174662
$391$	−22.6799	−1.14697
$392$	−10.8059	−0.545779
$393$	−3.21761	−0.162307
$394$	−0.319274	−0.0160848
$395$	6.52320	0.328218
$396$	8.12765	0.408430
$397$	−15.6573	−0.785816	−0.392908	−	0.919578i	$-0.628531\pi$
$397$	−15.6573	−0.785816	−0.392908	+	0.919578i	$0.628531\pi$
$398$	22.0172	1.10362
$399$	0.541228	0.0270953
$400$	1.00000	0.0500000
$401$	20.2722	1.01234	0.506172	−	0.862432i	$-0.331060\pi$
$401$	20.2722	1.01234	0.506172	+	0.862432i	$0.331060\pi$
$402$	1.06030	0.0528831
$403$	1.00000	0.0498135
$404$	−2.30495	−0.114676
$405$	−7.94337	−0.394709
$406$	−25.3548	−1.25834
$407$	−3.79818	−0.188269
$408$	2.09614	0.103774
$409$	37.2489	1.84184	0.920920	−	0.389751i	$-0.127439\pi$
$409$	37.2489	1.84184	0.920920	+	0.389751i	$0.127439\pi$
$410$	−0.473191	−0.0233692
$411$	0.995156	0.0490874
$412$	4.26856	0.210297
$413$	0.586976	0.0288832
$414$	10.7522	0.528442
$415$	7.82984	0.384352
$416$	−1.00000	−0.0490290
$417$	2.60564	0.127599
$418$	1.04903	0.0513096
$419$	3.32321	0.162350	0.0811748	−	0.996700i	$-0.474133\pi$
$419$	3.32321	0.162350	0.0811748	+	0.996700i	$0.474133\pi$
$420$	−1.45550	−0.0710210
$421$	−29.9514	−1.45974	−0.729870	−	0.683586i	$-0.760420\pi$
$421$	−29.9514	−1.45974	−0.729870	+	0.683586i	$0.760420\pi$
$422$	17.6058	0.857038
$423$	14.2904	0.694824
$424$	11.7966	0.572893
$425$	−6.07701	−0.294778
$426$	0.303588	0.0147089
$427$	−1.59548	−0.0772107
$428$	5.21167	0.251916
$429$	−0.973078	−0.0469806
$430$	−2.00161	−0.0965264
$431$	−9.52967	−0.459028	−0.229514	−	0.973305i	$-0.573714\pi$
$431$	−9.52967	−0.459028	−0.229514	+	0.973305i	$0.573714\pi$
$432$	−2.02854	−0.0975980
$433$	8.91362	0.428361	0.214181	−	0.976794i	$-0.431292\pi$
$433$	8.91362	0.428361	0.214181	+	0.976794i	$0.431292\pi$
$434$	−4.21970	−0.202552
$435$	−2.07256	−0.0993719
$436$	−13.3113	−0.637498
$437$	1.38778	0.0663864
$438$	4.86004	0.232222
$439$	−19.0360	−0.908541	−0.454270	−	0.890864i	$-0.650100\pi$
$439$	−19.0360	−0.908541	−0.454270	+	0.890864i	$0.650100\pi$
$440$	−2.82110	−0.134491
$441$	−31.1320	−1.48248
$442$	6.07701	0.289054
$443$	3.32231	0.157847	0.0789237	−	0.996881i	$-0.474852\pi$
$443$	3.32231	0.157847	0.0789237	+	0.996881i	$0.474852\pi$
$444$	0.464395	0.0220392
$445$	9.55175	0.452797
$446$	9.83104	0.465513
$447$	1.05920	0.0500983
$448$	4.21970	0.199362
$449$	−38.9603	−1.83865	−0.919325	−	0.393500i	$-0.871264\pi$
$449$	−38.9603	−1.83865	−0.919325	+	0.393500i	$0.871264\pi$
$450$	2.88102	0.135813
$451$	1.33492	0.0628588
$452$	10.2500	0.482119
$453$	−1.89135	−0.0888633
$454$	0.244900	0.0114937
$455$	−4.21970	−0.197823
$456$	−0.128262	−0.00600643
$457$	−10.9132	−0.510497	−0.255248	−	0.966876i	$-0.582157\pi$
$457$	−10.9132	−0.510497	−0.255248	+	0.966876i	$0.582157\pi$
$458$	−25.8196	−1.20647
$459$	12.3274	0.575395
$460$	−3.73208	−0.174009
$461$	22.6730	1.05599	0.527993	−	0.849249i	$-0.322945\pi$
$461$	22.6730	1.05599	0.527993	+	0.849249i	$0.322945\pi$
$462$	4.10610	0.191033
$463$	−19.7656	−0.918585	−0.459293	−	0.888285i	$-0.651897\pi$
$463$	−19.7656	−0.918585	−0.459293	+	0.888285i	$0.651897\pi$
$464$	6.00867	0.278946
$465$	−0.344929	−0.0159957
$466$	16.7428	0.775593
$467$	15.5159	0.717990	0.358995	−	0.933340i	$-0.383120\pi$
$467$	15.5159	0.717990	0.358995	+	0.933340i	$0.383120\pi$
$468$	−2.88102	−0.133175
$469$	−12.9712	−0.598956
$470$	−4.96019	−0.228796
$471$	5.47811	0.252418
$472$	−0.139104	−0.00640277
$473$	5.64675	0.259638
$474$	2.25004	0.103348
$475$	0.371851	0.0170617
$476$	−25.6432	−1.17535
$477$	33.9863	1.55612
$478$	9.37679	0.428884
$479$	−3.44545	−0.157427	−0.0787133	−	0.996897i	$-0.525081\pi$
$479$	−3.44545	−0.157427	−0.0787133	+	0.996897i	$0.525081\pi$
$480$	0.344929	0.0157438
$481$	1.34635	0.0613883
$482$	6.37825	0.290521
$483$	5.43203	0.247166
$484$	−3.04141	−0.138246
$485$	−9.65236	−0.438291
$486$	−8.82551	−0.400333
$487$	27.2384	1.23429	0.617145	−	0.786850i	$-0.288289\pi$
$487$	27.2384	1.23429	0.617145	+	0.786850i	$0.288289\pi$
$488$	0.378102	0.0171159
$489$	0.830809	0.0375705
$490$	10.8059	0.488160
$491$	−0.908547	−0.0410022	−0.0205011	−	0.999790i	$-0.506526\pi$
$491$	−0.908547	−0.0410022	−0.0205011	+	0.999790i	$0.506526\pi$
$492$	−0.163217	−0.00735840
$493$	−36.5147	−1.64454
$494$	−0.371851	−0.0167304
$495$	−8.12765	−0.365311
$496$	1.00000	0.0449013
$497$	−3.71395	−0.166593
$498$	2.70074	0.121023
$499$	40.0823	1.79433	0.897165	−	0.441696i	$-0.145623\pi$
$499$	40.0823	1.79433	0.897165	+	0.441696i	$0.145623\pi$
$500$	−1.00000	−0.0447214
$501$	−3.06813	−0.137074
$502$	19.4538	0.868266
$503$	10.6342	0.474157	0.237079	−	0.971490i	$-0.423810\pi$
$503$	10.6342	0.474157	0.237079	+	0.971490i	$0.423810\pi$
$504$	12.1571	0.541519
$505$	2.30495	0.102569
$506$	10.5286	0.468051
$507$	0.344929	0.0153188
$508$	−11.3742	−0.504647
$509$	4.51155	0.199971	0.0999856	−	0.994989i	$-0.468120\pi$
$509$	4.51155	0.199971	0.0999856	+	0.994989i	$0.468120\pi$
$510$	−2.09614	−0.0928184
$511$	−59.4555	−2.63016
$512$	−1.00000	−0.0441942
$513$	−0.754313	−0.0333037
$514$	6.85857	0.302519
$515$	−4.26856	−0.188095
$516$	−0.690414	−0.0303938
$517$	13.9932	0.615419
$518$	−5.68120	−0.249617
$519$	2.02796	0.0890175
$520$	1.00000	0.0438529
$521$	0.519511	0.0227602	0.0113801	−	0.999935i	$-0.496378\pi$
$521$	0.519511	0.0227602	0.0113801	+	0.999935i	$0.496378\pi$
$522$	17.3111	0.757687
$523$	−4.96291	−0.217013	−0.108506	−	0.994096i	$-0.534607\pi$
$523$	−4.96291	−0.217013	−0.108506	+	0.994096i	$0.534607\pi$
$524$	−9.32834	−0.407510
$525$	1.45550	0.0635231
$526$	6.30941	0.275103
$527$	−6.07701	−0.264719
$528$	−0.973078	−0.0423478
$529$	−9.07160	−0.394417
$530$	−11.7966	−0.512411
$531$	−0.400761	−0.0173915
$532$	1.56910	0.0680291
$533$	−0.473191	−0.0204962
$534$	3.29468	0.142575
$535$	−5.21167	−0.225320
$536$	3.07397	0.132775
$537$	−4.45329	−0.192174
$538$	18.8613	0.813169
$539$	−30.4844	−1.31306
$540$	2.02854	0.0872943
$541$	40.0816	1.72324	0.861622	−	0.507550i	$-0.169449\pi$
$541$	40.0816	1.72324	0.861622	+	0.507550i	$0.169449\pi$
$542$	−8.79116	−0.377613
$543$	2.33376	0.100151
$544$	6.07701	0.260550
$545$	13.3113	0.570195
$546$	−1.45550	−0.0622895
$547$	28.0897	1.20103	0.600515	−	0.799613i	$-0.294962\pi$
$547$	28.0897	1.20103	0.600515	+	0.799613i	$0.294962\pi$
$548$	2.88511	0.123246
$549$	1.08932	0.0464911
$550$	2.82110	0.120292
$551$	2.23433	0.0951857
$552$	−1.28730	−0.0547912
$553$	−27.5260	−1.17052
$554$	15.2749	0.648968
$555$	−0.464395	−0.0197125
$556$	7.55412	0.320366
$557$	22.4423	0.950913	0.475456	−	0.879739i	$-0.342283\pi$
$557$	22.4423	0.950913	0.475456	+	0.879739i	$0.342283\pi$
$558$	2.88102	0.121963
$559$	−2.00161	−0.0846592
$560$	−4.21970	−0.178315
$561$	5.91340	0.249664
$562$	−17.7079	−0.746964
$563$	4.59502	0.193657	0.0968286	−	0.995301i	$-0.469130\pi$
$563$	4.59502	0.193657	0.0968286	+	0.995301i	$0.469130\pi$
$564$	−1.71091	−0.0720424
$565$	−10.2500	−0.431220
$566$	7.98019	0.335433
$567$	33.5187	1.40765
$568$	0.880146	0.0369301
$569$	−36.7633	−1.54120	−0.770598	−	0.637321i	$-0.780042\pi$
$569$	−36.7633	−1.54120	−0.770598	+	0.637321i	$0.780042\pi$
$570$	0.128262	0.00537231
$571$	−36.8794	−1.54336	−0.771678	−	0.636013i	$-0.780582\pi$
$571$	−36.8794	−1.54336	−0.771678	+	0.636013i	$0.780582\pi$
$572$	−2.82110	−0.117956
$573$	−8.28388	−0.346064
$574$	1.99673	0.0833417
$575$	3.73208	0.155638
$576$	−2.88102	−0.120043
$577$	−14.9657	−0.623030	−0.311515	−	0.950241i	$-0.600836\pi$
$577$	−14.9657	−0.623030	−0.311515	+	0.950241i	$0.600836\pi$
$578$	−19.9300	−0.828979
$579$	0.742564	0.0308599
$580$	−6.00867	−0.249497
$581$	−33.0396	−1.37071
$582$	−3.32938	−0.138007
$583$	33.2793	1.37829
$584$	14.0900	0.583048
$585$	2.88102	0.119116
$586$	10.2118	0.421846
$587$	12.0449	0.497147	0.248573	−	0.968613i	$-0.420038\pi$
$587$	12.0449	0.497147	0.248573	+	0.968613i	$0.420038\pi$
$588$	3.72726	0.153710
$589$	0.371851	0.0153219
$590$	0.139104	0.00572681
$591$	0.110127	0.00453001
$592$	1.34635	0.0553347
$593$	−7.56551	−0.310678	−0.155339	−	0.987861i	$-0.549647\pi$
$593$	−7.56551	−0.310678	−0.155339	+	0.987861i	$0.549647\pi$
$594$	−5.72269	−0.234805
$595$	25.6432	1.05127
$596$	3.07077	0.125784
$597$	−7.59438	−0.310817
$598$	−3.73208	−0.152616
$599$	39.9616	1.63279	0.816394	−	0.577495i	$-0.195970\pi$
$599$	39.9616	1.63279	0.816394	+	0.577495i	$0.195970\pi$
$600$	−0.344929	−0.0140817
$601$	−8.75249	−0.357022	−0.178511	−	0.983938i	$-0.557128\pi$
$601$	−8.75249	−0.357022	−0.178511	+	0.983938i	$0.557128\pi$
$602$	8.44621	0.344242
$603$	8.85619	0.360652
$604$	−5.48330	−0.223112
$605$	3.04141	0.123651
$606$	0.795044	0.0322965
$607$	−18.0976	−0.734561	−0.367280	−	0.930110i	$-0.619711\pi$
$607$	−18.0976	−0.734561	−0.367280	+	0.930110i	$0.619711\pi$
$608$	−0.371851	−0.0150805
$609$	8.74560	0.354390
$610$	−0.378102	−0.0153089
$611$	−4.96019	−0.200668
$612$	17.5080	0.707719
$613$	−20.1112	−0.812285	−0.406143	−	0.913810i	$-0.633126\pi$
$613$	−20.1112	−0.812285	−0.406143	+	0.913810i	$0.633126\pi$
$614$	−17.8483	−0.720299
$615$	0.163217	0.00658156
$616$	11.9042	0.479633
$617$	40.3369	1.62390	0.811950	−	0.583726i	$-0.198406\pi$
$617$	40.3369	1.62390	0.811950	+	0.583726i	$0.198406\pi$
$618$	−1.47235	−0.0592266
$619$	12.1217	0.487214	0.243607	−	0.969874i	$-0.421669\pi$
$619$	12.1217	0.487214	0.243607	+	0.969874i	$0.421669\pi$
$620$	−1.00000	−0.0401610
$621$	−7.57065	−0.303800
$622$	6.35494	0.254810
$623$	−40.3055	−1.61481
$624$	0.344929	0.0138082
$625$	1.00000	0.0400000
$626$	12.3934	0.495342
$627$	−0.361840	−0.0144505
$628$	15.8819	0.633755
$629$	−8.18178	−0.326229
$630$	−12.1571	−0.484349
$631$	−36.8826	−1.46827	−0.734136	−	0.679003i	$-0.762412\pi$
$631$	−36.8826	−1.46827	−0.734136	+	0.679003i	$0.762412\pi$
$632$	6.52320	0.259479
$633$	−6.07276	−0.241370
$634$	−14.0273	−0.557094
$635$	11.3742	0.451370
$636$	−4.06899	−0.161346
$637$	10.8059	0.428145
$638$	16.9510	0.671098
$639$	2.53572	0.100312
$640$	1.00000	0.0395285
$641$	−12.2616	−0.484305	−0.242152	−	0.970238i	$-0.577853\pi$
$641$	−12.2616	−0.484305	−0.242152	+	0.970238i	$0.577853\pi$
$642$	−1.79766	−0.0709478
$643$	−10.8165	−0.426562	−0.213281	−	0.976991i	$-0.568415\pi$
$643$	−10.8165	−0.426562	−0.213281	+	0.976991i	$0.568415\pi$
$644$	15.7483	0.620568
$645$	0.690414	0.0271850
$646$	2.25974	0.0889083
$647$	−50.0501	−1.96767	−0.983835	−	0.179075i	$-0.942690\pi$
$647$	−50.0501	−1.96767	−0.983835	+	0.179075i	$0.942690\pi$
$648$	−7.94337	−0.312045
$649$	−0.392425	−0.0154040
$650$	−1.00000	−0.0392232
$651$	1.45550	0.0570454
$652$	2.40864	0.0943296
$653$	30.2311	1.18304	0.591518	−	0.806292i	$-0.298529\pi$
$653$	30.2311	1.18304	0.591518	+	0.806292i	$0.298529\pi$
$654$	4.59147	0.179541
$655$	9.32834	0.364488
$656$	−0.473191	−0.0184750
$657$	40.5936	1.58371
$658$	20.9305	0.815956
$659$	28.2110	1.09895	0.549473	−	0.835511i	$-0.314829\pi$
$659$	28.2110	1.09895	0.549473	+	0.835511i	$0.314829\pi$
$660$	0.973078	0.0378770
$661$	−3.53307	−0.137421	−0.0687103	−	0.997637i	$-0.521888\pi$
$661$	−3.53307	−0.137421	−0.0687103	+	0.997637i	$0.521888\pi$
$662$	−7.88514	−0.306465
$663$	−2.09614	−0.0814072
$664$	7.82984	0.303857
$665$	−1.56910	−0.0608471
$666$	3.87887	0.150303
$667$	22.4248	0.868293
$668$	−8.89497	−0.344157
$669$	−3.39101	−0.131104
$670$	−3.07397	−0.118758
$671$	1.06666	0.0411781
$672$	−1.45550	−0.0561470
$673$	−46.0259	−1.77417	−0.887084	−	0.461607i	$-0.847273\pi$
$673$	−46.0259	−1.77417	−0.887084	+	0.461607i	$0.847273\pi$
$674$	−17.1297	−0.659810
$675$	−2.02854	−0.0780784
$676$	1.00000	0.0384615
$677$	10.4098	0.400082	0.200041	−	0.979788i	$-0.435893\pi$
$677$	10.4098	0.400082	0.200041	+	0.979788i	$0.435893\pi$
$678$	−3.53551	−0.135781
$679$	40.7301	1.56308
$680$	−6.07701	−0.233043
$681$	−0.0844731	−0.00323702
$682$	2.82110	0.108025
$683$	24.0234	0.919230	0.459615	−	0.888118i	$-0.347987\pi$
$683$	24.0234	0.919230	0.459615	+	0.888118i	$0.347987\pi$
$684$	−1.07131	−0.0409626
$685$	−2.88511	−0.110234
$686$	−16.0597	−0.613162
$687$	8.90592	0.339782
$688$	−2.00161	−0.0763108
$689$	−11.7966	−0.449414
$690$	1.28730	0.0490067
$691$	−14.1601	−0.538674	−0.269337	−	0.963046i	$-0.586805\pi$
$691$	−14.1601	−0.538674	−0.269337	+	0.963046i	$0.586805\pi$
$692$	5.87935	0.223499
$693$	34.2962	1.30281
$694$	−27.9190	−1.05979
$695$	−7.55412	−0.286544
$696$	−2.07256	−0.0785604
$697$	2.87559	0.108921
$698$	13.1905	0.499268
$699$	−5.77506	−0.218433
$700$	4.21970	0.159490
$701$	−29.0243	−1.09623	−0.548117	−	0.836402i	$-0.684655\pi$
$701$	−29.0243	−1.09623	−0.548117	+	0.836402i	$0.684655\pi$
$702$	2.02854	0.0765621
$703$	0.500642	0.0188821
$704$	−2.82110	−0.106324
$705$	1.71091	0.0644367
$706$	−5.94603	−0.223782
$707$	−9.72621	−0.365792
$708$	0.0479809	0.00180323
$709$	3.61798	0.135876	0.0679380	−	0.997690i	$-0.478358\pi$
$709$	3.61798	0.135876	0.0679380	+	0.997690i	$0.478358\pi$
$710$	−0.880146	−0.0330313
$711$	18.7935	0.704812
$712$	9.55175	0.357967
$713$	3.73208	0.139767
$714$	8.84507	0.331018
$715$	2.82110	0.105503
$716$	−12.9107	−0.482497
$717$	−3.23433	−0.120788
$718$	−18.7523	−0.699829
$719$	39.3609	1.46791	0.733957	−	0.679196i	$-0.237671\pi$
$719$	39.3609	1.46791	0.733957	+	0.679196i	$0.237671\pi$
$720$	2.88102	0.107369
$721$	18.0121	0.670804
$722$	18.8617	0.701961
$723$	−2.20004	−0.0818205
$724$	6.76590	0.251453
$725$	6.00867	0.223156
$726$	1.04907	0.0389347
$727$	40.3181	1.49532	0.747659	−	0.664083i	$-0.231178\pi$
$727$	40.3181	1.49532	0.747659	+	0.664083i	$0.231178\pi$
$728$	−4.21970	−0.156393
$729$	−20.7859	−0.769850
$730$	−14.0900	−0.521494
$731$	12.1638	0.449895
$732$	−0.130418	−0.00482041
$733$	10.5032	0.387944	0.193972	−	0.981007i	$-0.437863\pi$
$733$	10.5032	0.387944	0.193972	+	0.981007i	$0.437863\pi$
$734$	−32.1646	−1.18722
$735$	−3.72726	−0.137482
$736$	−3.73208	−0.137566
$737$	8.67197	0.319436
$738$	−1.36327	−0.0501828
$739$	18.0757	0.664925	0.332463	−	0.943116i	$-0.392120\pi$
$739$	18.0757	0.664925	0.332463	+	0.943116i	$0.392120\pi$
$740$	−1.34635	−0.0494928
$741$	0.128262	0.00471183
$742$	49.7781	1.82741
$743$	−13.5271	−0.496261	−0.248131	−	0.968727i	$-0.579816\pi$
$743$	−13.5271	−0.496261	−0.248131	+	0.968727i	$0.579816\pi$
$744$	−0.344929	−0.0126457
$745$	−3.07077	−0.112504
$746$	35.0936	1.28487
$747$	22.5580	0.825352
$748$	17.1438	0.626840
$749$	21.9917	0.803559
$750$	0.344929	0.0125950
$751$	−21.5119	−0.784980	−0.392490	−	0.919756i	$-0.628386\pi$
$751$	−21.5119	−0.784980	−0.392490	+	0.919756i	$0.628386\pi$
$752$	−4.96019	−0.180879
$753$	−6.71018	−0.244533
$754$	−6.00867	−0.218823
$755$	5.48330	0.199558
$756$	−8.55981	−0.311317
$757$	−17.6136	−0.640178	−0.320089	−	0.947387i	$-0.603713\pi$
$757$	−17.6136	−0.640178	−0.320089	+	0.947387i	$0.603713\pi$
$758$	25.4831	0.925587
$759$	−3.63160	−0.131819
$760$	0.371851	0.0134885
$761$	41.1624	1.49214	0.746069	−	0.665869i	$-0.231939\pi$
$761$	41.1624	1.49214	0.746069	+	0.665869i	$0.231939\pi$
$762$	3.92328	0.142126
$763$	−56.1699	−2.03349
$764$	−24.0162	−0.868876
$765$	−17.5080	−0.633003
$766$	19.2072	0.693983
$767$	0.139104	0.00502274
$768$	0.344929	0.0124466
$769$	11.9165	0.429721	0.214860	−	0.976645i	$-0.431070\pi$
$769$	11.9165	0.429721	0.214860	+	0.976645i	$0.431070\pi$
$770$	−11.9042	−0.428997
$771$	−2.36572	−0.0851993
$772$	2.15280	0.0774810
$773$	−30.1003	−1.08263	−0.541317	−	0.840819i	$-0.682074\pi$
$773$	−30.1003	−1.08263	−0.541317	+	0.840819i	$0.682074\pi$
$774$	−5.76670	−0.207280
$775$	1.00000	0.0359211
$776$	−9.65236	−0.346499
$777$	1.95961	0.0703006
$778$	21.0242	0.753754
$779$	−0.175957	−0.00630430
$780$	−0.344929	−0.0123504
$781$	2.48298	0.0888479
$782$	22.6799	0.811030
$783$	−12.1888	−0.435592
$784$	10.8059	0.385924
$785$	−15.8819	−0.566848
$786$	3.21761	0.114769
$787$	−7.79882	−0.277998	−0.138999	−	0.990293i	$-0.544388\pi$
$787$	−7.79882	−0.277998	−0.138999	+	0.990293i	$0.544388\pi$
$788$	0.319274	0.0113736
$789$	−2.17630	−0.0774782
$790$	−6.52320	−0.232085
$791$	43.2519	1.53786
$792$	−8.12765	−0.288803
$793$	−0.378102	−0.0134268
$794$	15.6573	0.555656
$795$	4.06899	0.144312
$796$	−22.0172	−0.780380
$797$	50.9167	1.80356	0.901780	−	0.432195i	$-0.142261\pi$
$797$	50.9167	1.80356	0.901780	+	0.432195i	$0.142261\pi$
$798$	−0.541228	−0.0191593
$799$	30.1431	1.06639
$800$	−1.00000	−0.0353553
$801$	27.5188	0.972330
$802$	−20.2722	−0.715836
$803$	39.7492	1.40272
$804$	−1.06030	−0.0373940
$805$	−15.7483	−0.555053
$806$	−1.00000	−0.0352235
$807$	−6.50581	−0.229015
$808$	2.30495	0.0810879
$809$	−5.48099	−0.192701	−0.0963507	−	0.995347i	$-0.530717\pi$
$809$	−5.48099	−0.192701	−0.0963507	+	0.995347i	$0.530717\pi$
$810$	7.94337	0.279102
$811$	−28.1345	−0.987934	−0.493967	−	0.869481i	$-0.664454\pi$
$811$	−28.1345	−0.987934	−0.493967	+	0.869481i	$0.664454\pi$
$812$	25.3548	0.889779
$813$	3.03233	0.106348
$814$	3.79818	0.133126
$815$	−2.40864	−0.0843710
$816$	−2.09614	−0.0733794
$817$	−0.744302	−0.0260398
$818$	−37.2489	−1.30238
$819$	−12.1571	−0.424802
$820$	0.473191	0.0165246
$821$	3.27347	0.114245	0.0571224	−	0.998367i	$-0.481807\pi$
$821$	3.27347	0.114245	0.0571224	+	0.998367i	$0.481807\pi$
$822$	−0.995156	−0.0347101
$823$	−26.2754	−0.915902	−0.457951	−	0.888978i	$-0.651416\pi$
$823$	−26.2754	−0.915902	−0.457951	+	0.888978i	$0.651416\pi$
$824$	−4.26856	−0.148702
$825$	−0.973078	−0.0338782
$826$	−0.586976	−0.0204235
$827$	26.7288	0.929453	0.464726	−	0.885454i	$-0.346153\pi$
$827$	26.7288	0.929453	0.464726	+	0.885454i	$0.346153\pi$
$828$	−10.7522	−0.373665
$829$	−20.9527	−0.727716	−0.363858	−	0.931454i	$-0.618541\pi$
$829$	−20.9527	−0.727716	−0.363858	+	0.931454i	$0.618541\pi$
$830$	−7.82984	−0.271778
$831$	−5.26875	−0.182771
$832$	1.00000	0.0346688
$833$	−65.6674	−2.27524
$834$	−2.60564	−0.0902258
$835$	8.89497	0.307823
$836$	−1.04903	−0.0362814
$837$	−2.02854	−0.0701164
$838$	−3.32321	−0.114798
$839$	11.3851	0.393056	0.196528	−	0.980498i	$-0.437033\pi$
$839$	11.3851	0.393056	0.196528	+	0.980498i	$0.437033\pi$
$840$	1.45550	0.0502194
$841$	7.10413	0.244970
$842$	29.9514	1.03219
$843$	6.10798	0.210370
$844$	−17.6058	−0.606017
$845$	−1.00000	−0.0344010
$846$	−14.2904	−0.491315
$847$	−12.8339	−0.440976
$848$	−11.7966	−0.405097
$849$	−2.75260	−0.0944690
$850$	6.07701	0.208440
$851$	5.02468	0.172244
$852$	−0.303588	−0.0104007
$853$	−3.12812	−0.107105	−0.0535524	−	0.998565i	$-0.517054\pi$
$853$	−3.12812	−0.107105	−0.0535524	+	0.998565i	$0.517054\pi$
$854$	1.59548	0.0545962
$855$	1.07131	0.0366381
$856$	−5.21167	−0.178131
$857$	19.4657	0.664936	0.332468	−	0.943115i	$-0.392119\pi$
$857$	19.4657	0.664936	0.332468	+	0.943115i	$0.392119\pi$
$858$	0.973078	0.0332203
$859$	21.4291	0.731151	0.365576	−	0.930782i	$-0.380872\pi$
$859$	21.4291	0.731151	0.365576	+	0.930782i	$0.380872\pi$
$860$	2.00161	0.0682544
$861$	−0.688728	−0.0234718
$862$	9.52967	0.324582
$863$	40.0524	1.36340	0.681700	−	0.731632i	$-0.261241\pi$
$863$	40.0524	1.36340	0.681700	+	0.731632i	$0.261241\pi$
$864$	2.02854	0.0690122
$865$	−5.87935	−0.199904
$866$	−8.91362	−0.302897
$867$	6.87444	0.233468
$868$	4.21970	0.143226
$869$	18.4026	0.624265
$870$	2.07256	0.0702665
$871$	−3.07397	−0.104158
$872$	13.3113	0.450779
$873$	−27.8087	−0.941181
$874$	−1.38778	−0.0469423
$875$	−4.21970	−0.142652
$876$	−4.86004	−0.164206
$877$	−39.4104	−1.33079	−0.665397	−	0.746490i	$-0.731738\pi$
$877$	−39.4104	−1.33079	−0.665397	+	0.746490i	$0.731738\pi$
$878$	19.0360	0.642435
$879$	−3.52235	−0.118806
$880$	2.82110	0.0950992
$881$	−34.3896	−1.15862	−0.579308	−	0.815109i	$-0.696677\pi$
$881$	−34.3896	−1.15862	−0.579308	+	0.815109i	$0.696677\pi$
$882$	31.1320	1.04827
$883$	15.8480	0.533327	0.266663	−	0.963790i	$-0.414079\pi$
$883$	15.8480	0.533327	0.266663	+	0.963790i	$0.414079\pi$
$884$	−6.07701	−0.204392
$885$	−0.0479809	−0.00161286
$886$	−3.32231	−0.111615
$887$	−10.6959	−0.359134	−0.179567	−	0.983746i	$-0.557470\pi$
$887$	−10.6959	−0.359134	−0.179567	+	0.983746i	$0.557470\pi$
$888$	−0.464395	−0.0155841
$889$	−47.9956	−1.60972
$890$	−9.55175	−0.320175
$891$	−22.4090	−0.750730
$892$	−9.83104	−0.329167
$893$	−1.84445	−0.0617222
$894$	−1.05920	−0.0354248
$895$	12.9107	0.431558
$896$	−4.21970	−0.140970
$897$	1.28730	0.0429817
$898$	38.9603	1.30012
$899$	6.00867	0.200400
$900$	−2.88102	−0.0960341
$901$	71.6880	2.38827
$902$	−1.33492	−0.0444479
$903$	−2.91334	−0.0969500
$904$	−10.2500	−0.340909
$905$	−6.76590	−0.224906
$906$	1.89135	0.0628358
$907$	1.94357	0.0645351	0.0322675	−	0.999479i	$-0.489727\pi$
$907$	1.94357	0.0645351	0.0322675	+	0.999479i	$0.489727\pi$
$908$	−0.244900	−0.00812729
$909$	6.64062	0.220255
$910$	4.21970	0.139882
$911$	31.1846	1.03319	0.516596	−	0.856229i	$-0.327199\pi$
$911$	31.1846	1.03319	0.516596	+	0.856229i	$0.327199\pi$
$912$	0.128262	0.00424719
$913$	22.0887	0.731030
$914$	10.9132	0.360976
$915$	0.130418	0.00431150
$916$	25.8196	0.853103
$917$	−39.3628	−1.29987
$918$	−12.3274	−0.406866
$919$	−15.6921	−0.517633	−0.258817	−	0.965926i	$-0.583333\pi$
$919$	−15.6921	−0.517633	−0.258817	+	0.965926i	$0.583333\pi$
$920$	3.73208	0.123043
$921$	6.15640	0.202860
$922$	−22.6730	−0.746694
$923$	−0.880146	−0.0289703
$924$	−4.10610	−0.135081
$925$	1.34635	0.0442677
$926$	19.7656	0.649538
$927$	−12.2978	−0.403914
$928$	−6.00867	−0.197244
$929$	41.0454	1.34666	0.673328	−	0.739344i	$-0.264864\pi$
$929$	41.0454	1.34666	0.673328	+	0.739344i	$0.264864\pi$
$930$	0.344929	0.0113107
$931$	4.01818	0.131690
$932$	−16.7428	−0.548427
$933$	−2.19200	−0.0717629
$934$	−15.5159	−0.507695
$935$	−17.1438	−0.560663
$936$	2.88102	0.0941692
$937$	44.5698	1.45603	0.728016	−	0.685561i	$-0.240443\pi$
$937$	44.5698	1.45603	0.728016	+	0.685561i	$0.240443\pi$
$938$	12.9712	0.423526
$939$	−4.27486	−0.139505
$940$	4.96019	0.161783
$941$	0.423841	0.0138168	0.00690842	−	0.999976i	$-0.497801\pi$
$941$	0.423841	0.0138168	0.00690842	+	0.999976i	$0.497801\pi$
$942$	−5.47811	−0.178487
$943$	−1.76599	−0.0575084
$944$	0.139104	0.00452744
$945$	8.55981	0.278451
$946$	−5.64675	−0.183592
$947$	6.98332	0.226928	0.113464	−	0.993542i	$-0.463805\pi$
$947$	6.98332	0.226928	0.113464	+	0.993542i	$0.463805\pi$
$948$	−2.25004	−0.0730780
$949$	−14.0900	−0.457380
$950$	−0.371851	−0.0120644
$951$	4.83841	0.156896
$952$	25.6432	0.831099
$953$	23.3513	0.756422	0.378211	−	0.925719i	$-0.376539\pi$
$953$	23.3513	0.756422	0.378211	+	0.925719i	$0.376539\pi$
$954$	−33.9863	−1.10035
$955$	24.0162	0.777146
$956$	−9.37679	−0.303267
$957$	−5.84691	−0.189004
$958$	3.44545	0.111317
$959$	12.1743	0.393128
$960$	−0.344929	−0.0111325
$961$	1.00000	0.0322581
$962$	−1.34635	−0.0434081
$963$	−15.0149	−0.483850
$964$	−6.37825	−0.205430
$965$	−2.15280	−0.0693011
$966$	−5.43203	−0.174773
$967$	31.1968	1.00322	0.501611	−	0.865093i	$-0.332741\pi$
$967$	31.1968	1.00322	0.501611	+	0.865093i	$0.332741\pi$
$968$	3.04141	0.0977547
$969$	−0.779450	−0.0250395
$970$	9.65236	0.309919
$971$	0.162332	0.00520948	0.00260474	−	0.999997i	$-0.499171\pi$
$971$	0.162332	0.00520948	0.00260474	+	0.999997i	$0.499171\pi$
$972$	8.82551	0.283078
$973$	31.8762	1.02190
$974$	−27.2384	−0.872774
$975$	0.344929	0.0110466
$976$	−0.378102	−0.0121028
$977$	−42.6650	−1.36497	−0.682487	−	0.730898i	$-0.739102\pi$
$977$	−42.6650	−1.36497	−0.682487	+	0.730898i	$0.739102\pi$
$978$	−0.830809	−0.0265664
$979$	26.9464	0.861211
$980$	−10.8059	−0.345181
$981$	38.3503	1.22443
$982$	0.908547	0.0289929
$983$	25.7699	0.821931	0.410965	−	0.911651i	$-0.365192\pi$
$983$	25.7699	0.821931	0.410965	+	0.911651i	$0.365192\pi$
$984$	0.163217	0.00520318
$985$	−0.319274	−0.0101729
$986$	36.5147	1.16287
$987$	−7.21954	−0.229800
$988$	0.371851	0.0118302
$989$	−7.47018	−0.237538
$990$	8.12765	0.258314
$991$	−45.7739	−1.45406	−0.727028	−	0.686608i	$-0.759099\pi$
$991$	−45.7739	−1.45406	−0.727028	+	0.686608i	$0.759099\pi$
$992$	−1.00000	−0.0317500
$993$	2.71981	0.0863107
$994$	3.71395	0.117799
$995$	22.0172	0.697993
$996$	−2.70074	−0.0855762
$997$	−2.25138	−0.0713019	−0.0356509	−	0.999364i	$-0.511350\pi$
$997$	−2.25138	−0.0713019	−0.0356509	+	0.999364i	$0.511350\pi$
$998$	−40.0823	−1.26878
$999$	−2.73112	−0.0864088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.c.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.c.1.4	✓	6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.344929 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.344929 q^{6} +4.21970 q^{7} -1.00000 q^{8} -2.88102 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.344929 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.344929 q^{6} +4.21970 q^{7} -1.00000 q^{8} -2.88102 q^{9} +1.00000 q^{10} -2.82110 q^{11} +0.344929 q^{12} +1.00000 q^{13} -4.21970 q^{14} -0.344929 q^{15} +1.00000 q^{16} -6.07701 q^{17} +2.88102 q^{18} +0.371851 q^{19} -1.00000 q^{20} +1.45550 q^{21} +2.82110 q^{22} +3.73208 q^{23} -0.344929 q^{24} +1.00000 q^{25} -1.00000 q^{26} -2.02854 q^{27} +4.21970 q^{28} +6.00867 q^{29} +0.344929 q^{30} +1.00000 q^{31} -1.00000 q^{32} -0.973078 q^{33} +6.07701 q^{34} -4.21970 q^{35} -2.88102 q^{36} +1.34635 q^{37} -0.371851 q^{38} +0.344929 q^{39} +1.00000 q^{40} -0.473191 q^{41} -1.45550 q^{42} -2.00161 q^{43} -2.82110 q^{44} +2.88102 q^{45} -3.73208 q^{46} -4.96019 q^{47} +0.344929 q^{48} +10.8059 q^{49} -1.00000 q^{50} -2.09614 q^{51} +1.00000 q^{52} -11.7966 q^{53} +2.02854 q^{54} +2.82110 q^{55} -4.21970 q^{56} +0.128262 q^{57} -6.00867 q^{58} +0.139104 q^{59} -0.344929 q^{60} -0.378102 q^{61} -1.00000 q^{62} -12.1571 q^{63} +1.00000 q^{64} -1.00000 q^{65} +0.973078 q^{66} -3.07397 q^{67} -6.07701 q^{68} +1.28730 q^{69} +4.21970 q^{70} -0.880146 q^{71} +2.88102 q^{72} -14.0900 q^{73} -1.34635 q^{74} +0.344929 q^{75} +0.371851 q^{76} -11.9042 q^{77} -0.344929 q^{78} -6.52320 q^{79} -1.00000 q^{80} +7.94337 q^{81} +0.473191 q^{82} -7.82984 q^{83} +1.45550 q^{84} +6.07701 q^{85} +2.00161 q^{86} +2.07256 q^{87} +2.82110 q^{88} -9.55175 q^{89} -2.88102 q^{90} +4.21970 q^{91} +3.73208 q^{92} +0.344929 q^{93} +4.96019 q^{94} -0.371851 q^{95} -0.344929 q^{96} +9.65236 q^{97} -10.8059 q^{98} +8.12765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} + q^{18} + 3 q^{19} - 6 q^{20} - q^{21} + 6 q^{22} - 7 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - q^{27} + 4 q^{28} - 14 q^{29} - q^{30} + 6 q^{31} - 6 q^{32} - 2 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 14 q^{37} - 3 q^{38} - q^{39} + 6 q^{40} - 12 q^{41} + q^{42} + 3 q^{43} - 6 q^{44} + q^{45} + 7 q^{46} - 2 q^{47} - q^{48} - 6 q^{49} - 6 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + q^{54} + 6 q^{55} - 4 q^{56} + 13 q^{57} + 14 q^{58} - 17 q^{59} + q^{60} - 5 q^{61} - 6 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + 2 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 4 q^{70} - 16 q^{71} + q^{72} + 11 q^{73} - 14 q^{74} - q^{75} + 3 q^{76} - 15 q^{77} + q^{78} - 2 q^{79} - 6 q^{80} - 26 q^{81} + 12 q^{82} + 4 q^{83} - q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 6 q^{88} - 8 q^{89} - q^{90} + 4 q^{91} - 7 q^{92} - q^{93} + 2 q^{94} - 3 q^{95} + q^{96} + 5 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 + 4 * q^7 - 6 * q^8 - q^9 + 6 * q^10 - 6 * q^11 - q^12 + 6 * q^13 - 4 * q^14 + q^15 + 6 * q^16 - 4 * q^17 + q^18 + 3 * q^19 - 6 * q^20 - q^21 + 6 * q^22 - 7 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - q^27 + 4 * q^28 - 14 * q^29 - q^30 + 6 * q^31 - 6 * q^32 - 2 * q^33 + 4 * q^34 - 4 * q^35 - q^36 + 14 * q^37 - 3 * q^38 - q^39 + 6 * q^40 - 12 * q^41 + q^42 + 3 * q^43 - 6 * q^44 + q^45 + 7 * q^46 - 2 * q^47 - q^48 - 6 * q^49 - 6 * q^50 - 7 * q^51 + 6 * q^52 - 4 * q^53 + q^54 + 6 * q^55 - 4 * q^56 + 13 * q^57 + 14 * q^58 - 17 * q^59 + q^60 - 5 * q^61 - 6 * q^62 - q^63 + 6 * q^64 - 6 * q^65 + 2 * q^66 + 8 * q^67 - 4 * q^68 - 8 * q^69 + 4 * q^70 - 16 * q^71 + q^72 + 11 * q^73 - 14 * q^74 - q^75 + 3 * q^76 - 15 * q^77 + q^78 - 2 * q^79 - 6 * q^80 - 26 * q^81 + 12 * q^82 + 4 * q^83 - q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 6 * q^88 - 8 * q^89 - q^90 + 4 * q^91 - 7 * q^92 - q^93 + 2 * q^94 - 3 * q^95 + q^96 + 5 * q^97 + 6 * q^98 + 15 * q^99

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