LMFDB - Embedded newform 4030.2.a.c.1.5

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			1.5
Root			$2.52877$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.71605 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.71605 q^{6} +1.86590 q^{7} -1.00000 q^{8} -0.0551701 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.71605 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.71605 q^{6} +1.86590 q^{7} -1.00000 q^{8} -0.0551701 q^{9} +1.00000 q^{10} -2.21376 q^{11} +1.71605 q^{12} +1.00000 q^{13} -1.86590 q^{14} -1.71605 q^{15} +1.00000 q^{16} +4.52238 q^{17} +0.0551701 q^{18} -1.08288 q^{19} -1.00000 q^{20} +3.20197 q^{21} +2.21376 q^{22} -8.23843 q^{23} -1.71605 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.24283 q^{27} +1.86590 q^{28} -4.82270 q^{29} +1.71605 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.79893 q^{33} -4.52238 q^{34} -1.86590 q^{35} -0.0551701 q^{36} -9.03414 q^{37} +1.08288 q^{38} +1.71605 q^{39} +1.00000 q^{40} +0.142228 q^{41} -3.20197 q^{42} -8.04176 q^{43} -2.21376 q^{44} +0.0551701 q^{45} +8.23843 q^{46} +6.91363 q^{47} +1.71605 q^{48} -3.51843 q^{49} -1.00000 q^{50} +7.76064 q^{51} +1.00000 q^{52} -2.28467 q^{53} +5.24283 q^{54} +2.21376 q^{55} -1.86590 q^{56} -1.85828 q^{57} +4.82270 q^{58} +3.72875 q^{59} -1.71605 q^{60} +0.177556 q^{61} -1.00000 q^{62} -0.102942 q^{63} +1.00000 q^{64} -1.00000 q^{65} +3.79893 q^{66} +1.81395 q^{67} +4.52238 q^{68} -14.1376 q^{69} +1.86590 q^{70} -5.31719 q^{71} +0.0551701 q^{72} +7.41362 q^{73} +9.03414 q^{74} +1.71605 q^{75} -1.08288 q^{76} -4.13065 q^{77} -1.71605 q^{78} +12.3734 q^{79} -1.00000 q^{80} -8.83145 q^{81} -0.142228 q^{82} -6.89883 q^{83} +3.20197 q^{84} -4.52238 q^{85} +8.04176 q^{86} -8.27599 q^{87} +2.21376 q^{88} -8.72553 q^{89} -0.0551701 q^{90} +1.86590 q^{91} -8.23843 q^{92} +1.71605 q^{93} -6.91363 q^{94} +1.08288 q^{95} -1.71605 q^{96} -3.63760 q^{97} +3.51843 q^{98} +0.122134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.71605	0.990762	0.495381	−	0.868676i	$-0.335028\pi$
$3$	1.71605	0.990762	0.495381	+	0.868676i	$0.335028\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.71605	−0.700575
$7$	1.86590	0.705242	0.352621	−	0.935766i	$-0.385290\pi$
$7$	1.86590	0.705242	0.352621	+	0.935766i	$0.385290\pi$
$8$	−1.00000	−0.353553
$9$	−0.0551701	−0.0183900
$10$	1.00000	0.316228
$11$	−2.21376	−0.667475	−0.333738	−	0.942666i	$-0.608310\pi$
$11$	−2.21376	−0.667475	−0.333738	+	0.942666i	$0.608310\pi$
$12$	1.71605	0.495381
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.86590	−0.498682
$15$	−1.71605	−0.443082
$16$	1.00000	0.250000
$17$	4.52238	1.09684	0.548419	−	0.836204i	$-0.315230\pi$
$17$	4.52238	1.09684	0.548419	+	0.836204i	$0.315230\pi$
$18$	0.0551701	0.0130037
$19$	−1.08288	−0.248430	−0.124215	−	0.992255i	$-0.539641\pi$
$19$	−1.08288	−0.248430	−0.124215	+	0.992255i	$0.539641\pi$
$20$	−1.00000	−0.223607
$21$	3.20197	0.698727
$22$	2.21376	0.471976
$23$	−8.23843	−1.71783	−0.858916	−	0.512117i	$-0.828862\pi$
$23$	−8.23843	−1.71783	−0.858916	+	0.512117i	$0.828862\pi$
$24$	−1.71605	−0.350287
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−5.24283	−1.00898
$28$	1.86590	0.352621
$29$	−4.82270	−0.895552	−0.447776	−	0.894146i	$-0.647784\pi$
$29$	−4.82270	−0.895552	−0.447776	+	0.894146i	$0.647784\pi$
$30$	1.71605	0.313307
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−3.79893	−0.661309
$34$	−4.52238	−0.775582
$35$	−1.86590	−0.315394
$36$	−0.0551701	−0.00919501
$37$	−9.03414	−1.48520	−0.742602	−	0.669733i	$-0.766409\pi$
$37$	−9.03414	−1.48520	−0.742602	+	0.669733i	$0.766409\pi$
$38$	1.08288	0.175667
$39$	1.71605	0.274788
$40$	1.00000	0.158114
$41$	0.142228	0.0222123	0.0111062	−	0.999938i	$-0.496465\pi$
$41$	0.142228	0.0222123	0.0111062	+	0.999938i	$0.496465\pi$
$42$	−3.20197	−0.494075
$43$	−8.04176	−1.22636	−0.613178	−	0.789945i	$-0.710109\pi$
$43$	−8.04176	−1.22636	−0.613178	+	0.789945i	$0.710109\pi$
$44$	−2.21376	−0.333738
$45$	0.0551701	0.00822427
$46$	8.23843	1.21469
$47$	6.91363	1.00846	0.504228	−	0.863571i	$-0.331777\pi$
$47$	6.91363	1.00846	0.504228	+	0.863571i	$0.331777\pi$
$48$	1.71605	0.247691
$49$	−3.51843	−0.502634
$50$	−1.00000	−0.141421
$51$	7.76064	1.08671
$52$	1.00000	0.138675
$53$	−2.28467	−0.313824	−0.156912	−	0.987613i	$-0.550154\pi$
$53$	−2.28467	−0.313824	−0.156912	+	0.987613i	$0.550154\pi$
$54$	5.24283	0.713458
$55$	2.21376	0.298504
$56$	−1.86590	−0.249341
$57$	−1.85828	−0.246135
$58$	4.82270	0.633251
$59$	3.72875	0.485442	0.242721	−	0.970096i	$-0.421960\pi$
$59$	3.72875	0.485442	0.242721	+	0.970096i	$0.421960\pi$
$60$	−1.71605	−0.221541
$61$	0.177556	0.0227337	0.0113668	−	0.999935i	$-0.496382\pi$
$61$	0.177556	0.0227337	0.0113668	+	0.999935i	$0.496382\pi$
$62$	−1.00000	−0.127000
$63$	−0.102942	−0.0129694
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	3.79893	0.467616
$67$	1.81395	0.221609	0.110804	−	0.993842i	$-0.464657\pi$
$67$	1.81395	0.221609	0.110804	+	0.993842i	$0.464657\pi$
$68$	4.52238	0.548419
$69$	−14.1376	−1.70196
$70$	1.86590	0.223017
$71$	−5.31719	−0.631034	−0.315517	−	0.948920i	$-0.602178\pi$
$71$	−5.31719	−0.631034	−0.315517	+	0.948920i	$0.602178\pi$
$72$	0.0551701	0.00650185
$73$	7.41362	0.867699	0.433849	−	0.900985i	$-0.357155\pi$
$73$	7.41362	0.867699	0.433849	+	0.900985i	$0.357155\pi$
$74$	9.03414	1.05020
$75$	1.71605	0.198152
$76$	−1.08288	−0.124215
$77$	−4.13065	−0.470732
$78$	−1.71605	−0.194304
$79$	12.3734	1.39212	0.696060	−	0.717983i	$-0.254935\pi$
$79$	12.3734	1.39212	0.696060	+	0.717983i	$0.254935\pi$
$80$	−1.00000	−0.111803
$81$	−8.83145	−0.981272
$82$	−0.142228	−0.0157065
$83$	−6.89883	−0.757245	−0.378622	−	0.925551i	$-0.623602\pi$
$83$	−6.89883	−0.757245	−0.378622	+	0.925551i	$0.623602\pi$
$84$	3.20197	0.349364
$85$	−4.52238	−0.490521
$86$	8.04176	0.867165
$87$	−8.27599	−0.887279
$88$	2.21376	0.235988
$89$	−8.72553	−0.924904	−0.462452	−	0.886644i	$-0.653030\pi$
$89$	−8.72553	−0.924904	−0.462452	+	0.886644i	$0.653030\pi$
$90$	−0.0551701	−0.00581543
$91$	1.86590	0.195599
$92$	−8.23843	−0.858916
$93$	1.71605	0.177946
$94$	−6.91363	−0.713086
$95$	1.08288	0.111101
$96$	−1.71605	−0.175144
$97$	−3.63760	−0.369342	−0.184671	−	0.982800i	$-0.559122\pi$
$97$	−3.63760	−0.369342	−0.184671	+	0.982800i	$0.559122\pi$
$98$	3.51843	0.355416
$99$	0.122134	0.0122749
$100$	1.00000	0.100000
$101$	−3.72275	−0.370427	−0.185214	−	0.982698i	$-0.559298\pi$
$101$	−3.72275	−0.370427	−0.185214	+	0.982698i	$0.559298\pi$
$102$	−7.76064	−0.768417
$103$	1.00260	0.0987887	0.0493943	−	0.998779i	$-0.484271\pi$
$103$	1.00260	0.0987887	0.0493943	+	0.998779i	$0.484271\pi$
$104$	−1.00000	−0.0980581
$105$	−3.20197	−0.312480
$106$	2.28467	0.221907
$107$	−1.54724	−0.149578	−0.0747889	−	0.997199i	$-0.523828\pi$
$107$	−1.54724	−0.149578	−0.0747889	+	0.997199i	$0.523828\pi$
$108$	−5.24283	−0.504491
$109$	14.3241	1.37200	0.686000	−	0.727601i	$-0.259365\pi$
$109$	14.3241	1.37200	0.686000	+	0.727601i	$0.259365\pi$
$110$	−2.21376	−0.211074
$111$	−15.5030	−1.47148
$112$	1.86590	0.176311
$113$	−18.2715	−1.71883	−0.859417	−	0.511275i	$-0.829173\pi$
$113$	−18.2715	−1.71883	−0.859417	+	0.511275i	$0.829173\pi$
$114$	1.85828	0.174044
$115$	8.23843	0.768238
$116$	−4.82270	−0.447776
$117$	−0.0551701	−0.00510047
$118$	−3.72875	−0.343259
$119$	8.43829	0.773537
$120$	1.71605	0.156653
$121$	−6.09925	−0.554477
$122$	−0.177556	−0.0160752
$123$	0.244071	0.0220072
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	0.102942	0.00917076
$127$	−11.2308	−0.996573	−0.498286	−	0.867013i	$-0.666037\pi$
$127$	−11.2308	−0.996573	−0.498286	+	0.867013i	$0.666037\pi$
$128$	−1.00000	−0.0883883
$129$	−13.8001	−1.21503
$130$	1.00000	0.0877058
$131$	1.08409	0.0947173	0.0473587	−	0.998878i	$-0.484920\pi$
$131$	1.08409	0.0947173	0.0473587	+	0.998878i	$0.484920\pi$
$132$	−3.79893	−0.330655
$133$	−2.02054	−0.175203
$134$	−1.81395	−0.156701
$135$	5.24283	0.451231
$136$	−4.52238	−0.387791
$137$	−15.4492	−1.31992	−0.659958	−	0.751302i	$-0.729426\pi$
$137$	−15.4492	−1.31992	−0.659958	+	0.751302i	$0.729426\pi$
$138$	14.1376	1.20347
$139$	−1.77892	−0.150886	−0.0754432	−	0.997150i	$-0.524037\pi$
$139$	−1.77892	−0.150886	−0.0754432	+	0.997150i	$0.524037\pi$
$140$	−1.86590	−0.157697
$141$	11.8641	0.999140
$142$	5.31719	0.446209
$143$	−2.21376	−0.185124
$144$	−0.0551701	−0.00459751
$145$	4.82270	0.400503
$146$	−7.41362	−0.613556
$147$	−6.03781	−0.497990
$148$	−9.03414	−0.742602
$149$	6.42843	0.526638	0.263319	−	0.964709i	$-0.415183\pi$
$149$	6.42843	0.526638	0.263319	+	0.964709i	$0.415183\pi$
$150$	−1.71605	−0.140115
$151$	2.85898	0.232660	0.116330	−	0.993211i	$-0.462887\pi$
$151$	2.85898	0.232660	0.116330	+	0.993211i	$0.462887\pi$
$152$	1.08288	0.0878333
$153$	−0.249500	−0.0201709
$154$	4.13065	0.332857
$155$	−1.00000	−0.0803219
$156$	1.71605	0.137394
$157$	15.6113	1.24592	0.622958	−	0.782255i	$-0.285931\pi$
$157$	15.6113	1.24592	0.622958	+	0.782255i	$0.285931\pi$
$158$	−12.3734	−0.984378
$159$	−3.92062	−0.310925
$160$	1.00000	0.0790569
$161$	−15.3721	−1.21149
$162$	8.83145	0.693864
$163$	24.0089	1.88053	0.940263	−	0.340450i	$-0.110579\pi$
$163$	24.0089	1.88053	0.940263	+	0.340450i	$0.110579\pi$
$164$	0.142228	0.0111062
$165$	3.79893	0.295746
$166$	6.89883	0.535453
$167$	−16.4415	−1.27228	−0.636142	−	0.771572i	$-0.719471\pi$
$167$	−16.4415	−1.27228	−0.636142	+	0.771572i	$0.719471\pi$
$168$	−3.20197	−0.247037
$169$	1.00000	0.0769231
$170$	4.52238	0.346851
$171$	0.0597426	0.00456863
$172$	−8.04176	−0.613178
$173$	−8.02459	−0.610098	−0.305049	−	0.952337i	$-0.598673\pi$
$173$	−8.02459	−0.610098	−0.305049	+	0.952337i	$0.598673\pi$
$174$	8.27599	0.627401
$175$	1.86590	0.141048
$176$	−2.21376	−0.166869
$177$	6.39872	0.480957
$178$	8.72553	0.654006
$179$	6.42601	0.480303	0.240151	−	0.970735i	$-0.422803\pi$
$179$	6.42601	0.480303	0.240151	+	0.970735i	$0.422803\pi$
$180$	0.0551701	0.00411213
$181$	−7.51174	−0.558343	−0.279171	−	0.960241i	$-0.590060\pi$
$181$	−7.51174	−0.558343	−0.279171	+	0.960241i	$0.590060\pi$
$182$	−1.86590	−0.138309
$183$	0.304695	0.0225237
$184$	8.23843	0.607345
$185$	9.03414	0.664203
$186$	−1.71605	−0.125827
$187$	−10.0115	−0.732112
$188$	6.91363	0.504228
$189$	−9.78257	−0.711577
$190$	−1.08288	−0.0785605
$191$	−25.1923	−1.82285	−0.911425	−	0.411467i	$-0.865016\pi$
$191$	−25.1923	−1.82285	−0.911425	+	0.411467i	$0.865016\pi$
$192$	1.71605	0.123845
$193$	2.67153	0.192301	0.0961503	−	0.995367i	$-0.469347\pi$
$193$	2.67153	0.192301	0.0961503	+	0.995367i	$0.469347\pi$
$194$	3.63760	0.261164
$195$	−1.71605	−0.122889
$196$	−3.51843	−0.251317
$197$	10.1549	0.723505	0.361752	−	0.932274i	$-0.382179\pi$
$197$	10.1549	0.723505	0.361752	+	0.932274i	$0.382179\pi$
$198$	−0.122134	−0.00867965
$199$	1.45983	0.103484	0.0517421	−	0.998660i	$-0.483523\pi$
$199$	1.45983	0.103484	0.0517421	+	0.998660i	$0.483523\pi$
$200$	−1.00000	−0.0707107
$201$	3.11282	0.219562
$202$	3.72275	0.261932
$203$	−8.99865	−0.631581
$204$	7.76064	0.543353
$205$	−0.142228	−0.00993366
$206$	−1.00260	−0.0698541
$207$	0.454515	0.0315910
$208$	1.00000	0.0693375
$209$	2.39724	0.165821
$210$	3.20197	0.220957
$211$	−6.53939	−0.450190	−0.225095	−	0.974337i	$-0.572269\pi$
$211$	−6.53939	−0.450190	−0.225095	+	0.974337i	$0.572269\pi$
$212$	−2.28467	−0.156912
$213$	−9.12457	−0.625205
$214$	1.54724	0.105767
$215$	8.04176	0.548443
$216$	5.24283	0.356729
$217$	1.86590	0.126665
$218$	−14.3241	−0.970151
$219$	12.7222	0.859683
$220$	2.21376	0.149252
$221$	4.52238	0.304208
$222$	15.5030	1.04050
$223$	−4.03096	−0.269933	−0.134966	−	0.990850i	$-0.543093\pi$
$223$	−4.03096	−0.269933	−0.134966	+	0.990850i	$0.543093\pi$
$224$	−1.86590	−0.124670
$225$	−0.0551701	−0.00367800
$226$	18.2715	1.21540
$227$	12.7892	0.848851	0.424425	−	0.905463i	$-0.360476\pi$
$227$	12.7892	0.848851	0.424425	+	0.905463i	$0.360476\pi$
$228$	−1.85828	−0.123068
$229$	−11.5998	−0.766535	−0.383268	−	0.923637i	$-0.625201\pi$
$229$	−11.5998	−0.766535	−0.383268	+	0.923637i	$0.625201\pi$
$230$	−8.23843	−0.543226
$231$	−7.08841	−0.466383
$232$	4.82270	0.316626
$233$	−12.8825	−0.843963	−0.421982	−	0.906604i	$-0.638665\pi$
$233$	−12.8825	−0.843963	−0.421982	+	0.906604i	$0.638665\pi$
$234$	0.0551701	0.00360658
$235$	−6.91363	−0.450995
$236$	3.72875	0.242721
$237$	21.2334	1.37926
$238$	−8.43829	−0.546973
$239$	−13.0007	−0.840945	−0.420472	−	0.907305i	$-0.638136\pi$
$239$	−13.0007	−0.840945	−0.420472	+	0.907305i	$0.638136\pi$
$240$	−1.71605	−0.110771
$241$	−10.7505	−0.692503	−0.346251	−	0.938142i	$-0.612546\pi$
$241$	−10.7505	−0.692503	−0.346251	+	0.938142i	$0.612546\pi$
$242$	6.09925	0.392074
$243$	0.573271	0.0367753
$244$	0.177556	0.0113668
$245$	3.51843	0.224785
$246$	−0.244071	−0.0155614
$247$	−1.08288	−0.0689021
$248$	−1.00000	−0.0635001
$249$	−11.8387	−0.750250
$250$	1.00000	0.0632456
$251$	−27.3344	−1.72533	−0.862667	−	0.505772i	$-0.831208\pi$
$251$	−27.3344	−1.72533	−0.862667	+	0.505772i	$0.831208\pi$
$252$	−0.102942	−0.00648471
$253$	18.2379	1.14661
$254$	11.2308	0.704683
$255$	−7.76064	−0.485990
$256$	1.00000	0.0625000
$257$	−4.25161	−0.265208	−0.132604	−	0.991169i	$-0.542334\pi$
$257$	−4.25161	−0.265208	−0.132604	+	0.991169i	$0.542334\pi$
$258$	13.8001	0.859155
$259$	−16.8568	−1.04743
$260$	−1.00000	−0.0620174
$261$	0.266068	0.0164692
$262$	−1.08409	−0.0669752
$263$	9.73588	0.600340	0.300170	−	0.953886i	$-0.402957\pi$
$263$	9.73588	0.600340	0.300170	+	0.953886i	$0.402957\pi$
$264$	3.79893	0.233808
$265$	2.28467	0.140346
$266$	2.02054	0.123887
$267$	−14.9734	−0.916360
$268$	1.81395	0.110804
$269$	−6.91774	−0.421782	−0.210891	−	0.977510i	$-0.567636\pi$
$269$	−6.91774	−0.421782	−0.210891	+	0.977510i	$0.567636\pi$
$270$	−5.24283	−0.319068
$271$	−20.5152	−1.24621	−0.623106	−	0.782137i	$-0.714129\pi$
$271$	−20.5152	−1.24621	−0.623106	+	0.782137i	$0.714129\pi$
$272$	4.52238	0.274210
$273$	3.20197	0.193792
$274$	15.4492	0.933322
$275$	−2.21376	−0.133495
$276$	−14.1376	−0.850982
$277$	12.6959	0.762821	0.381411	−	0.924406i	$-0.375438\pi$
$277$	12.6959	0.762821	0.381411	+	0.924406i	$0.375438\pi$
$278$	1.77892	0.106693
$279$	−0.0551701	−0.00330295
$280$	1.86590	0.111509
$281$	12.0905	0.721258	0.360629	−	0.932709i	$-0.382562\pi$
$281$	12.0905	0.721258	0.360629	+	0.932709i	$0.382562\pi$
$282$	−11.8641	−0.706499
$283$	10.4139	0.619042	0.309521	−	0.950893i	$-0.399831\pi$
$283$	10.4139	0.619042	0.309521	+	0.950893i	$0.399831\pi$
$284$	−5.31719	−0.315517
$285$	1.85828	0.110075
$286$	2.21376	0.130903
$287$	0.265383	0.0156651
$288$	0.0551701	0.00325093
$289$	3.45193	0.203055
$290$	−4.82270	−0.283198
$291$	−6.24230	−0.365930
$292$	7.41362	0.433849
$293$	17.1130	0.999754	0.499877	−	0.866096i	$-0.333378\pi$
$293$	17.1130	0.999754	0.499877	+	0.866096i	$0.333378\pi$
$294$	6.03781	0.352132
$295$	−3.72875	−0.217096
$296$	9.03414	0.525099
$297$	11.6064	0.673471
$298$	−6.42843	−0.372389
$299$	−8.23843	−0.476441
$300$	1.71605	0.0990762
$301$	−15.0051	−0.864878
$302$	−2.85898	−0.164516
$303$	−6.38843	−0.367005
$304$	−1.08288	−0.0621075
$305$	−0.177556	−0.0101668
$306$	0.249500	0.0142630
$307$	24.6348	1.40598	0.702992	−	0.711198i	$-0.251847\pi$
$307$	24.6348	1.40598	0.702992	+	0.711198i	$0.251847\pi$
$308$	−4.13065	−0.235366
$309$	1.72050	0.0978761
$310$	1.00000	0.0567962
$311$	−10.7470	−0.609404	−0.304702	−	0.952448i	$-0.598557\pi$
$311$	−10.7470	−0.609404	−0.304702	+	0.952448i	$0.598557\pi$
$312$	−1.71605	−0.0971522
$313$	3.27273	0.184986	0.0924928	−	0.995713i	$-0.470516\pi$
$313$	3.27273	0.184986	0.0924928	+	0.995713i	$0.470516\pi$
$314$	−15.6113	−0.880996
$315$	0.102942	0.00580010
$316$	12.3734	0.696060
$317$	8.42722	0.473320	0.236660	−	0.971593i	$-0.423947\pi$
$317$	8.42722	0.473320	0.236660	+	0.971593i	$0.423947\pi$
$318$	3.92062	0.219857
$319$	10.6763	0.597759
$320$	−1.00000	−0.0559017
$321$	−2.65515	−0.148196
$322$	15.3721	0.856651
$323$	−4.89720	−0.272488
$324$	−8.83145	−0.490636
$325$	1.00000	0.0554700
$326$	−24.0089	−1.32973
$327$	24.5809	1.35933
$328$	−0.142228	−0.00785325
$329$	12.9001	0.711206
$330$	−3.79893	−0.209124
$331$	−7.33557	−0.403199	−0.201600	−	0.979468i	$-0.564614\pi$
$331$	−7.33557	−0.403199	−0.201600	+	0.979468i	$0.564614\pi$
$332$	−6.89883	−0.378622
$333$	0.498414	0.0273129
$334$	16.4415	0.899640
$335$	−1.81395	−0.0991065
$336$	3.20197	0.174682
$337$	−8.04576	−0.438281	−0.219140	−	0.975693i	$-0.570325\pi$
$337$	−8.04576	−0.438281	−0.219140	+	0.975693i	$0.570325\pi$
$338$	−1.00000	−0.0543928
$339$	−31.3547	−1.70296
$340$	−4.52238	−0.245261
$341$	−2.21376	−0.119882
$342$	−0.0597426	−0.00323051
$343$	−19.6263	−1.05972
$344$	8.04176	0.433583
$345$	14.1376	0.761141
$346$	8.02459	0.431405
$347$	2.06162	0.110674	0.0553368	−	0.998468i	$-0.482377\pi$
$347$	2.06162	0.110674	0.0553368	+	0.998468i	$0.482377\pi$
$348$	−8.27599	−0.443640
$349$	31.2845	1.67462	0.837311	−	0.546727i	$-0.184127\pi$
$349$	31.2845	1.67462	0.837311	+	0.546727i	$0.184127\pi$
$350$	−1.86590	−0.0997363
$351$	−5.24283	−0.279841
$352$	2.21376	0.117994
$353$	−14.5857	−0.776316	−0.388158	−	0.921593i	$-0.626888\pi$
$353$	−14.5857	−0.776316	−0.388158	+	0.921593i	$0.626888\pi$
$354$	−6.39872	−0.340088
$355$	5.31719	0.282207
$356$	−8.72553	−0.462452
$357$	14.4805	0.766391
$358$	−6.42601	−0.339625
$359$	34.0342	1.79626	0.898128	−	0.439734i	$-0.144927\pi$
$359$	34.0342	1.79626	0.898128	+	0.439734i	$0.144927\pi$
$360$	−0.0551701	−0.00290772
$361$	−17.8274	−0.938283
$362$	7.51174	0.394808
$363$	−10.4666	−0.549355
$364$	1.86590	0.0977995
$365$	−7.41362	−0.388047
$366$	−0.304695	−0.0159267
$367$	−8.23211	−0.429713	−0.214856	−	0.976646i	$-0.568928\pi$
$367$	−8.23211	−0.429713	−0.214856	+	0.976646i	$0.568928\pi$
$368$	−8.23843	−0.429458
$369$	−0.00784675	−0.000408485 0
$370$	−9.03414	−0.469663
$371$	−4.26296	−0.221322
$372$	1.71605	0.0889731
$373$	25.3277	1.31142	0.655709	−	0.755014i	$-0.272370\pi$
$373$	25.3277	1.31142	0.655709	+	0.755014i	$0.272370\pi$
$374$	10.0115	0.517682
$375$	−1.71605	−0.0886165
$376$	−6.91363	−0.356543
$377$	−4.82270	−0.248382
$378$	9.78257	0.503161
$379$	−3.99921	−0.205426	−0.102713	−	0.994711i	$-0.532752\pi$
$379$	−3.99921	−0.205426	−0.102713	+	0.994711i	$0.532752\pi$
$380$	1.08288	0.0555506
$381$	−19.2726	−0.987367
$382$	25.1923	1.28895
$383$	−24.8734	−1.27097	−0.635485	−	0.772113i	$-0.719200\pi$
$383$	−24.8734	−1.27097	−0.635485	+	0.772113i	$0.719200\pi$
$384$	−1.71605	−0.0875718
$385$	4.13065	0.210518
$386$	−2.67153	−0.135977
$387$	0.443664	0.0225527
$388$	−3.63760	−0.184671
$389$	−6.27952	−0.318384	−0.159192	−	0.987248i	$-0.550889\pi$
$389$	−6.27952	−0.318384	−0.159192	+	0.987248i	$0.550889\pi$
$390$	1.71605	0.0868956
$391$	−37.2573	−1.88418
$392$	3.51843	0.177708
$393$	1.86035	0.0938423
$394$	−10.1549	−0.511595
$395$	−12.3734	−0.622575
$396$	0.122134	0.00613744
$397$	−14.9080	−0.748211	−0.374106	−	0.927386i	$-0.622050\pi$
$397$	−14.9080	−0.748211	−0.374106	+	0.927386i	$0.622050\pi$
$398$	−1.45983	−0.0731744
$399$	−3.46735	−0.173585
$400$	1.00000	0.0500000
$401$	15.6267	0.780358	0.390179	−	0.920739i	$-0.372413\pi$
$401$	15.6267	0.780358	0.390179	+	0.920739i	$0.372413\pi$
$402$	−3.11282	−0.155254
$403$	1.00000	0.0498135
$404$	−3.72275	−0.185214
$405$	8.83145	0.438838
$406$	8.99865	0.446595
$407$	19.9995	0.991337
$408$	−7.76064	−0.384209
$409$	−15.2310	−0.753122	−0.376561	−	0.926392i	$-0.622894\pi$
$409$	−15.2310	−0.753122	−0.376561	+	0.926392i	$0.622894\pi$
$410$	0.142228	0.00702416
$411$	−26.5117	−1.30772
$412$	1.00260	0.0493943
$413$	6.95745	0.342354
$414$	−0.454515	−0.0223382
$415$	6.89883	0.338650
$416$	−1.00000	−0.0490290
$417$	−3.05272	−0.149493
$418$	−2.39724	−0.117253
$419$	18.2163	0.889923	0.444962	−	0.895550i	$-0.353217\pi$
$419$	18.2163	0.889923	0.444962	+	0.895550i	$0.353217\pi$
$420$	−3.20197	−0.156240
$421$	35.3304	1.72190	0.860950	−	0.508690i	$-0.169870\pi$
$421$	35.3304	1.72190	0.860950	+	0.508690i	$0.169870\pi$
$422$	6.53939	0.318332
$423$	−0.381425	−0.0185455
$424$	2.28467	0.110954
$425$	4.52238	0.219368
$426$	9.12457	0.442087
$427$	0.331301	0.0160328
$428$	−1.54724	−0.0747889
$429$	−3.79893	−0.183414
$430$	−8.04176	−0.387808
$431$	−1.49798	−0.0721552	−0.0360776	−	0.999349i	$-0.511486\pi$
$431$	−1.49798	−0.0721552	−0.0360776	+	0.999349i	$0.511486\pi$
$432$	−5.24283	−0.252246
$433$	−24.2383	−1.16482	−0.582408	−	0.812897i	$-0.697889\pi$
$433$	−24.2383	−1.16482	−0.582408	+	0.812897i	$0.697889\pi$
$434$	−1.86590	−0.0895658
$435$	8.27599	0.396803
$436$	14.3241	0.686000
$437$	8.92124	0.426761
$438$	−12.7222	−0.607888
$439$	−29.9128	−1.42766	−0.713831	−	0.700318i	$-0.753042\pi$
$439$	−29.9128	−1.42766	−0.713831	+	0.700318i	$0.753042\pi$
$440$	−2.21376	−0.105537
$441$	0.194112	0.00924344
$442$	−4.52238	−0.215108
$443$	−13.7469	−0.653136	−0.326568	−	0.945174i	$-0.605892\pi$
$443$	−13.7469	−0.653136	−0.326568	+	0.945174i	$0.605892\pi$
$444$	−15.5030	−0.735742
$445$	8.72553	0.413630
$446$	4.03096	0.190871
$447$	11.0315	0.521773
$448$	1.86590	0.0881553
$449$	25.2426	1.19127	0.595636	−	0.803254i	$-0.296900\pi$
$449$	25.2426	1.19127	0.595636	+	0.803254i	$0.296900\pi$
$450$	0.0551701	0.00260074
$451$	−0.314860	−0.0148262
$452$	−18.2715	−0.859417
$453$	4.90615	0.230511
$454$	−12.7892	−0.600228
$455$	−1.86590	−0.0874745
$456$	1.85828	0.0870219
$457$	21.2788	0.995382	0.497691	−	0.867354i	$-0.334181\pi$
$457$	21.2788	0.995382	0.497691	+	0.867354i	$0.334181\pi$
$458$	11.5998	0.542022
$459$	−23.7101	−1.10669
$460$	8.23843	0.384119
$461$	−24.8737	−1.15849	−0.579243	−	0.815155i	$-0.696652\pi$
$461$	−24.8737	−1.15849	−0.579243	+	0.815155i	$0.696652\pi$
$462$	7.08841	0.329783
$463$	33.0174	1.53445	0.767225	−	0.641378i	$-0.221637\pi$
$463$	33.0174	1.53445	0.767225	+	0.641378i	$0.221637\pi$
$464$	−4.82270	−0.223888
$465$	−1.71605	−0.0795799
$466$	12.8825	0.596772
$467$	22.7294	1.05179	0.525896	−	0.850549i	$-0.323730\pi$
$467$	22.7294	1.05179	0.525896	+	0.850549i	$0.323730\pi$
$468$	−0.0551701	−0.00255024
$469$	3.38463	0.156288
$470$	6.91363	0.318902
$471$	26.7898	1.23441
$472$	−3.72875	−0.171629
$473$	17.8026	0.818563
$474$	−21.2334	−0.975285
$475$	−1.08288	−0.0496860
$476$	8.43829	0.386768
$477$	0.126046	0.00577123
$478$	13.0007	0.594638
$479$	21.3305	0.974618	0.487309	−	0.873230i	$-0.337979\pi$
$479$	21.3305	0.974618	0.487309	+	0.873230i	$0.337979\pi$
$480$	1.71605	0.0783266
$481$	−9.03414	−0.411921
$482$	10.7505	0.489673
$483$	−26.3792	−1.20030
$484$	−6.09925	−0.277239
$485$	3.63760	0.165175
$486$	−0.573271	−0.0260041
$487$	−2.95002	−0.133678	−0.0668391	−	0.997764i	$-0.521291\pi$
$487$	−2.95002	−0.133678	−0.0668391	+	0.997764i	$0.521291\pi$
$488$	−0.177556	−0.00803758
$489$	41.2006	1.86315
$490$	−3.51843	−0.158947
$491$	13.5803	0.612871	0.306435	−	0.951891i	$-0.400864\pi$
$491$	13.5803	0.612871	0.306435	+	0.951891i	$0.400864\pi$
$492$	0.244071	0.0110036
$493$	−21.8101	−0.982276
$494$	1.08288	0.0487211
$495$	−0.122134	−0.00548949
$496$	1.00000	0.0449013
$497$	−9.92132	−0.445032
$498$	11.8387	0.530507
$499$	−30.1819	−1.35113	−0.675564	−	0.737301i	$-0.736100\pi$
$499$	−30.1819	−1.35113	−0.675564	+	0.737301i	$0.736100\pi$
$500$	−1.00000	−0.0447214
$501$	−28.2145	−1.26053
$502$	27.3344	1.22000
$503$	−20.5894	−0.918036	−0.459018	−	0.888427i	$-0.651799\pi$
$503$	−20.5894	−0.918036	−0.459018	+	0.888427i	$0.651799\pi$
$504$	0.102942	0.00458538
$505$	3.72275	0.165660
$506$	−18.2379	−0.810776
$507$	1.71605	0.0762125
$508$	−11.2308	−0.498286
$509$	−41.4780	−1.83848	−0.919239	−	0.393700i	$-0.871195\pi$
$509$	−41.4780	−1.83848	−0.919239	+	0.393700i	$0.871195\pi$
$510$	7.76064	0.343647
$511$	13.8330	0.611938
$512$	−1.00000	−0.0441942
$513$	5.67736	0.250662
$514$	4.25161	0.187531
$515$	−1.00260	−0.0441796
$516$	−13.8001	−0.607514
$517$	−15.3051	−0.673119
$518$	16.8568	0.740644
$519$	−13.7706	−0.604463
$520$	1.00000	0.0438529
$521$	10.0329	0.439548	0.219774	−	0.975551i	$-0.429468\pi$
$521$	10.0329	0.439548	0.219774	+	0.975551i	$0.429468\pi$
$522$	−0.266068	−0.0116455
$523$	5.62983	0.246175	0.123088	−	0.992396i	$-0.460720\pi$
$523$	5.62983	0.246175	0.123088	+	0.992396i	$0.460720\pi$
$524$	1.08409	0.0473587
$525$	3.20197	0.139745
$526$	−9.73588	−0.424504
$527$	4.52238	0.196998
$528$	−3.79893	−0.165327
$529$	44.8718	1.95095
$530$	−2.28467	−0.0992399
$531$	−0.205715	−0.00892728
$532$	−2.02054	−0.0876017
$533$	0.142228	0.00616060
$534$	14.9734	0.647964
$535$	1.54724	0.0668932
$536$	−1.81395	−0.0783506
$537$	11.0274	0.475866
$538$	6.91774	0.298245
$539$	7.78899	0.335495
$540$	5.24283	0.225615
$541$	6.61110	0.284233	0.142117	−	0.989850i	$-0.454609\pi$
$541$	6.61110	0.284233	0.142117	+	0.989850i	$0.454609\pi$
$542$	20.5152	0.881205
$543$	−12.8905	−0.553185
$544$	−4.52238	−0.193895
$545$	−14.3241	−0.613577
$546$	−3.20197	−0.137032
$547$	−6.85720	−0.293193	−0.146596	−	0.989196i	$-0.546832\pi$
$547$	−6.85720	−0.293193	−0.146596	+	0.989196i	$0.546832\pi$
$548$	−15.4492	−0.659958
$549$	−0.00979577	−0.000418073 0
$550$	2.21376	0.0943952
$551$	5.22241	0.222482
$552$	14.1376	0.601735
$553$	23.0875	0.981782
$554$	−12.6959	−0.539396
$555$	15.5030	0.658068
$556$	−1.77892	−0.0754432
$557$	−16.5163	−0.699816	−0.349908	−	0.936784i	$-0.613787\pi$
$557$	−16.5163	−0.699816	−0.349908	+	0.936784i	$0.613787\pi$
$558$	0.0551701	0.00233553
$559$	−8.04176	−0.340130
$560$	−1.86590	−0.0788485
$561$	−17.1802	−0.725349
$562$	−12.0905	−0.510006
$563$	4.75292	0.200312	0.100156	−	0.994972i	$-0.468066\pi$
$563$	4.75292	0.200312	0.100156	+	0.994972i	$0.468066\pi$
$564$	11.8641	0.499570
$565$	18.2715	0.768686
$566$	−10.4139	−0.437729
$567$	−16.4786	−0.692034
$568$	5.31719	0.223104
$569$	−4.98704	−0.209068	−0.104534	−	0.994521i	$-0.533335\pi$
$569$	−4.98704	−0.209068	−0.104534	+	0.994521i	$0.533335\pi$
$570$	−1.85828	−0.0778347
$571$	−12.2277	−0.511715	−0.255858	−	0.966714i	$-0.582358\pi$
$571$	−12.2277	−0.511715	−0.255858	+	0.966714i	$0.582358\pi$
$572$	−2.21376	−0.0925621
$573$	−43.2312	−1.80601
$574$	−0.265383	−0.0110769
$575$	−8.23843	−0.343566
$576$	−0.0551701	−0.00229875
$577$	−30.2183	−1.25801	−0.629003	−	0.777403i	$-0.716537\pi$
$577$	−30.2183	−1.25801	−0.629003	+	0.777403i	$0.716537\pi$
$578$	−3.45193	−0.143581
$579$	4.58447	0.190524
$580$	4.82270	0.200252
$581$	−12.8725	−0.534041
$582$	6.24230	0.258752
$583$	5.05773	0.209470
$584$	−7.41362	−0.306778
$585$	0.0551701	0.00228100
$586$	−17.1130	−0.706933
$587$	23.2875	0.961180	0.480590	−	0.876946i	$-0.340423\pi$
$587$	23.2875	0.961180	0.480590	+	0.876946i	$0.340423\pi$
$588$	−6.03781	−0.248995
$589$	−1.08288	−0.0446193
$590$	3.72875	0.153510
$591$	17.4263	0.716821
$592$	−9.03414	−0.371301
$593$	0.680073	0.0279272	0.0139636	−	0.999903i	$-0.495555\pi$
$593$	0.680073	0.0279272	0.0139636	+	0.999903i	$0.495555\pi$
$594$	−11.6064	−0.476216
$595$	−8.43829	−0.345936
$596$	6.42843	0.263319
$597$	2.50513	0.102528
$598$	8.23843	0.336895
$599$	−24.9434	−1.01916	−0.509579	−	0.860424i	$-0.670199\pi$
$599$	−24.9434	−1.01916	−0.509579	+	0.860424i	$0.670199\pi$
$600$	−1.71605	−0.0700575
$601$	13.6852	0.558231	0.279116	−	0.960257i	$-0.409959\pi$
$601$	13.6852	0.558231	0.279116	+	0.960257i	$0.409959\pi$
$602$	15.0051	0.611561
$603$	−0.100076	−0.00407539
$604$	2.85898	0.116330
$605$	6.09925	0.247970
$606$	6.38843	0.259512
$607$	33.1578	1.34583	0.672917	−	0.739718i	$-0.265041\pi$
$607$	33.1578	1.34583	0.672917	+	0.739718i	$0.265041\pi$
$608$	1.08288	0.0439166
$609$	−15.4421	−0.625747
$610$	0.177556	0.00718903
$611$	6.91363	0.279695
$612$	−0.249500	−0.0100854
$613$	−28.7517	−1.16127	−0.580635	−	0.814164i	$-0.697196\pi$
$613$	−28.7517	−1.16127	−0.580635	+	0.814164i	$0.697196\pi$
$614$	−24.6348	−0.994181
$615$	−0.244071	−0.00984190
$616$	4.13065	0.166429
$617$	−9.01465	−0.362916	−0.181458	−	0.983399i	$-0.558082\pi$
$617$	−9.01465	−0.362916	−0.181458	+	0.983399i	$0.558082\pi$
$618$	−1.72050	−0.0692089
$619$	13.0051	0.522717	0.261359	−	0.965242i	$-0.415829\pi$
$619$	13.0051	0.522717	0.261359	+	0.965242i	$0.415829\pi$
$620$	−1.00000	−0.0401610
$621$	43.1927	1.73326
$622$	10.7470	0.430914
$623$	−16.2809	−0.652281
$624$	1.71605	0.0686970
$625$	1.00000	0.0400000
$626$	−3.27273	−0.130805
$627$	4.11379	0.164289
$628$	15.6113	0.622958
$629$	−40.8558	−1.62903
$630$	−0.102942	−0.00410129
$631$	−10.6898	−0.425556	−0.212778	−	0.977101i	$-0.568251\pi$
$631$	−10.6898	−0.425556	−0.212778	+	0.977101i	$0.568251\pi$
$632$	−12.3734	−0.492189
$633$	−11.2219	−0.446031
$634$	−8.42722	−0.334688
$635$	11.2308	0.445681
$636$	−3.92062	−0.155463
$637$	−3.51843	−0.139405
$638$	−10.6763	−0.422679
$639$	0.293350	0.0116047
$640$	1.00000	0.0395285
$641$	−49.2387	−1.94481	−0.972405	−	0.233298i	$-0.925048\pi$
$641$	−49.2387	−1.94481	−0.972405	+	0.233298i	$0.925048\pi$
$642$	2.65515	0.104790
$643$	−26.9828	−1.06410	−0.532048	−	0.846714i	$-0.678577\pi$
$643$	−26.9828	−1.06410	−0.532048	+	0.846714i	$0.678577\pi$
$644$	−15.3721	−0.605744
$645$	13.8001	0.543377
$646$	4.89720	0.192678
$647$	46.7471	1.83782	0.918910	−	0.394468i	$-0.129071\pi$
$647$	46.7471	1.83782	0.918910	+	0.394468i	$0.129071\pi$
$648$	8.83145	0.346932
$649$	−8.25457	−0.324020
$650$	−1.00000	−0.0392232
$651$	3.20197	0.125495
$652$	24.0089	0.940263
$653$	−14.3071	−0.559879	−0.279940	−	0.960018i	$-0.590314\pi$
$653$	−14.3071	−0.559879	−0.279940	+	0.960018i	$0.590314\pi$
$654$	−24.5809	−0.961189
$655$	−1.08409	−0.0423589
$656$	0.142228	0.00555309
$657$	−0.409010	−0.0159570
$658$	−12.9001	−0.502898
$659$	−24.9169	−0.970623	−0.485311	−	0.874341i	$-0.661294\pi$
$659$	−24.9169	−0.970623	−0.485311	+	0.874341i	$0.661294\pi$
$660$	3.79893	0.147873
$661$	−22.1977	−0.863392	−0.431696	−	0.902019i	$-0.642085\pi$
$661$	−22.1977	−0.863392	−0.431696	+	0.902019i	$0.642085\pi$
$662$	7.33557	0.285105
$663$	7.76064	0.301398
$664$	6.89883	0.267727
$665$	2.02054	0.0783533
$666$	−0.498414	−0.0193132
$667$	39.7315	1.53841
$668$	−16.4415	−0.636142
$669$	−6.91733	−0.267439
$670$	1.81395	0.0700789
$671$	−0.393067	−0.0151742
$672$	−3.20197	−0.123519
$673$	24.3941	0.940323	0.470161	−	0.882580i	$-0.344196\pi$
$673$	24.3941	0.940323	0.470161	+	0.882580i	$0.344196\pi$
$674$	8.04576	0.309911
$675$	−5.24283	−0.201796
$676$	1.00000	0.0384615
$677$	6.81517	0.261928	0.130964	−	0.991387i	$-0.458193\pi$
$677$	6.81517	0.261928	0.130964	+	0.991387i	$0.458193\pi$
$678$	31.3547	1.20417
$679$	−6.78738	−0.260476
$680$	4.52238	0.173425
$681$	21.9470	0.841009
$682$	2.21376	0.0847694
$683$	−6.76822	−0.258979	−0.129489	−	0.991581i	$-0.541334\pi$
$683$	−6.76822	−0.258979	−0.129489	+	0.991581i	$0.541334\pi$
$684$	0.0597426	0.00228432
$685$	15.4492	0.590285
$686$	19.6263	0.749336
$687$	−19.9058	−0.759454
$688$	−8.04176	−0.306589
$689$	−2.28467	−0.0870392
$690$	−14.1376	−0.538208
$691$	−18.7747	−0.714225	−0.357112	−	0.934061i	$-0.616239\pi$
$691$	−18.7747	−0.714225	−0.357112	+	0.934061i	$0.616239\pi$
$692$	−8.02459	−0.305049
$693$	0.227888	0.00865676
$694$	−2.06162	−0.0782580
$695$	1.77892	0.0674784
$696$	8.27599	0.313701
$697$	0.643211	0.0243634
$698$	−31.2845	−1.18414
$699$	−22.1071	−0.836167
$700$	1.86590	0.0705242
$701$	34.8737	1.31716	0.658582	−	0.752509i	$-0.271157\pi$
$701$	34.8737	1.31716	0.658582	+	0.752509i	$0.271157\pi$
$702$	5.24283	0.197878
$703$	9.78290	0.368969
$704$	−2.21376	−0.0834344
$705$	−11.8641	−0.446829
$706$	14.5857	0.548938
$707$	−6.94626	−0.261241
$708$	6.39872	0.240479
$709$	−8.34588	−0.313436	−0.156718	−	0.987643i	$-0.550091\pi$
$709$	−8.34588	−0.313436	−0.156718	+	0.987643i	$0.550091\pi$
$710$	−5.31719	−0.199551
$711$	−0.682643	−0.0256011
$712$	8.72553	0.327003
$713$	−8.23843	−0.308532
$714$	−14.4805	−0.541920
$715$	2.21376	0.0827901
$716$	6.42601	0.240151
$717$	−22.3098	−0.833176
$718$	−34.0342	−1.27014
$719$	12.6791	0.472850	0.236425	−	0.971650i	$-0.424024\pi$
$719$	12.6791	0.472850	0.236425	+	0.971650i	$0.424024\pi$
$720$	0.0551701	0.00205607
$721$	1.87074	0.0696699
$722$	17.8274	0.663466
$723$	−18.4485	−0.686106
$724$	−7.51174	−0.279171
$725$	−4.82270	−0.179110
$726$	10.4666	0.388453
$727$	5.04986	0.187289	0.0936445	−	0.995606i	$-0.470148\pi$
$727$	5.04986	0.187289	0.0936445	+	0.995606i	$0.470148\pi$
$728$	−1.86590	−0.0691547
$729$	27.4781	1.01771
$730$	7.41362	0.274390
$731$	−36.3679	−1.34512
$732$	0.304695	0.0112618
$733$	−5.04888	−0.186485	−0.0932423	−	0.995643i	$-0.529723\pi$
$733$	−5.04888	−0.186485	−0.0932423	+	0.995643i	$0.529723\pi$
$734$	8.23211	0.303853
$735$	6.03781	0.222708
$736$	8.23843	0.303673
$737$	−4.01565	−0.147918
$738$	0.00784675	0.000288843 0
$739$	42.2356	1.55366	0.776831	−	0.629709i	$-0.216826\pi$
$739$	42.2356	1.55366	0.776831	+	0.629709i	$0.216826\pi$
$740$	9.03414	0.332102
$741$	−1.85828	−0.0682656
$742$	4.26296	0.156498
$743$	23.8136	0.873638	0.436819	−	0.899549i	$-0.356105\pi$
$743$	23.8136	0.873638	0.436819	+	0.899549i	$0.356105\pi$
$744$	−1.71605	−0.0629135
$745$	−6.42843	−0.235520
$746$	−25.3277	−0.927313
$747$	0.380609	0.0139257
$748$	−10.0115	−0.366056
$749$	−2.88700	−0.105489
$750$	1.71605	0.0626613
$751$	−38.6542	−1.41051	−0.705255	−	0.708954i	$-0.749168\pi$
$751$	−38.6542	−1.41051	−0.705255	+	0.708954i	$0.749168\pi$
$752$	6.91363	0.252114
$753$	−46.9073	−1.70940
$754$	4.82270	0.175632
$755$	−2.85898	−0.104049
$756$	−9.78257	−0.355788
$757$	29.2162	1.06188	0.530941	−	0.847409i	$-0.321839\pi$
$757$	29.2162	1.06188	0.530941	+	0.847409i	$0.321839\pi$
$758$	3.99921	0.145258
$759$	31.2972	1.13602
$760$	−1.08288	−0.0392802
$761$	−43.2345	−1.56725	−0.783624	−	0.621235i	$-0.786631\pi$
$761$	−43.2345	−1.56725	−0.783624	+	0.621235i	$0.786631\pi$
$762$	19.2726	0.698174
$763$	26.7273	0.967592
$764$	−25.1923	−0.911425
$765$	0.249500	0.00902069
$766$	24.8734	0.898712
$767$	3.72875	0.134637
$768$	1.71605	0.0619226
$769$	−16.9986	−0.612984	−0.306492	−	0.951873i	$-0.599155\pi$
$769$	−16.9986	−0.612984	−0.306492	+	0.951873i	$0.599155\pi$
$770$	−4.13065	−0.148858
$771$	−7.29598	−0.262758
$772$	2.67153	0.0961503
$773$	44.4183	1.59762	0.798808	−	0.601587i	$-0.205465\pi$
$773$	44.4183	1.59762	0.798808	+	0.601587i	$0.205465\pi$
$774$	−0.443664	−0.0159472
$775$	1.00000	0.0359211
$776$	3.63760	0.130582
$777$	−28.9271	−1.03775
$778$	6.27952	0.225132
$779$	−0.154016	−0.00551821
$780$	−1.71605	−0.0614445
$781$	11.7710	0.421200
$782$	37.2573	1.33232
$783$	25.2846	0.903597
$784$	−3.51843	−0.125658
$785$	−15.6113	−0.557191
$786$	−1.86035	−0.0663566
$787$	31.2353	1.11342	0.556709	−	0.830708i	$-0.312064\pi$
$787$	31.2353	1.11342	0.556709	+	0.830708i	$0.312064\pi$
$788$	10.1549	0.361752
$789$	16.7073	0.594794
$790$	12.3734	0.440227
$791$	−34.0926	−1.21219
$792$	−0.122134	−0.00433983
$793$	0.177556	0.00630519
$794$	14.9080	0.529065
$795$	3.92062	0.139050
$796$	1.45983	0.0517421
$797$	8.01013	0.283733	0.141867	−	0.989886i	$-0.454690\pi$
$797$	8.01013	0.283733	0.141867	+	0.989886i	$0.454690\pi$
$798$	3.46735	0.122743
$799$	31.2661	1.10611
$800$	−1.00000	−0.0353553
$801$	0.481388	0.0170090
$802$	−15.6267	−0.551797
$803$	−16.4120	−0.579167
$804$	3.11282	0.109781
$805$	15.3721	0.541794
$806$	−1.00000	−0.0352235
$807$	−11.8712	−0.417886
$808$	3.72275	0.130966
$809$	41.4090	1.45586	0.727932	−	0.685649i	$-0.240482\pi$
$809$	41.4090	1.45586	0.727932	+	0.685649i	$0.240482\pi$
$810$	−8.83145	−0.310305
$811$	16.9144	0.593945	0.296973	−	0.954886i	$-0.404023\pi$
$811$	16.9144	0.593945	0.296973	+	0.954886i	$0.404023\pi$
$812$	−8.99865	−0.315791
$813$	−35.2052	−1.23470
$814$	−19.9995	−0.700981
$815$	−24.0089	−0.840996
$816$	7.76064	0.271677
$817$	8.70827	0.304664
$818$	15.2310	0.532538
$819$	−0.102942	−0.00359707
$820$	−0.142228	−0.00496683
$821$	−40.7336	−1.42161	−0.710807	−	0.703388i	$-0.751670\pi$
$821$	−40.7336	−1.42161	−0.710807	+	0.703388i	$0.751670\pi$
$822$	26.5117	0.924700
$823$	14.3978	0.501875	0.250937	−	0.968003i	$-0.419261\pi$
$823$	14.3978	0.501875	0.250937	+	0.968003i	$0.419261\pi$
$824$	−1.00260	−0.0349271
$825$	−3.79893	−0.132262
$826$	−6.95745	−0.242081
$827$	22.1843	0.771425	0.385712	−	0.922619i	$-0.373956\pi$
$827$	22.1843	0.771425	0.385712	+	0.922619i	$0.373956\pi$
$828$	0.454515	0.0157955
$829$	43.3407	1.50528	0.752642	−	0.658430i	$-0.228779\pi$
$829$	43.3407	1.50528	0.752642	+	0.658430i	$0.228779\pi$
$830$	−6.89883	−0.239462
$831$	21.7868	0.755775
$832$	1.00000	0.0346688
$833$	−15.9117	−0.551308
$834$	3.05272	0.105707
$835$	16.4415	0.568982
$836$	2.39724	0.0829104
$837$	−5.24283	−0.181219
$838$	−18.2163	−0.629271
$839$	17.6374	0.608912	0.304456	−	0.952526i	$-0.401525\pi$
$839$	17.6374	0.608912	0.304456	+	0.952526i	$0.401525\pi$
$840$	3.20197	0.110478
$841$	−5.74160	−0.197986
$842$	−35.3304	−1.21757
$843$	20.7479	0.714595
$844$	−6.53939	−0.225095
$845$	−1.00000	−0.0344010
$846$	0.381425	0.0131137
$847$	−11.3806	−0.391041
$848$	−2.28467	−0.0784560
$849$	17.8708	0.613324
$850$	−4.52238	−0.155116
$851$	74.4272	2.55133
$852$	−9.12457	−0.312602
$853$	−7.91413	−0.270975	−0.135487	−	0.990779i	$-0.543260\pi$
$853$	−7.91413	−0.270975	−0.135487	+	0.990779i	$0.543260\pi$
$854$	−0.331301	−0.0113369
$855$	−0.0597426	−0.00204315
$856$	1.54724	0.0528837
$857$	−20.7054	−0.707284	−0.353642	−	0.935381i	$-0.615057\pi$
$857$	−20.7054	−0.707284	−0.353642	+	0.935381i	$0.615057\pi$
$858$	3.79893	0.129693
$859$	7.78139	0.265498	0.132749	−	0.991150i	$-0.457620\pi$
$859$	7.78139	0.265498	0.132749	+	0.991150i	$0.457620\pi$
$860$	8.04176	0.274222
$861$	0.455411	0.0155204
$862$	1.49798	0.0510214
$863$	53.9161	1.83533	0.917663	−	0.397359i	$-0.130073\pi$
$863$	53.9161	1.83533	0.917663	+	0.397359i	$0.130073\pi$
$864$	5.24283	0.178365
$865$	8.02459	0.272844
$866$	24.2383	0.823649
$867$	5.92369	0.201179
$868$	1.86590	0.0633326
$869$	−27.3919	−0.929206
$870$	−8.27599	−0.280582
$871$	1.81395	0.0614632
$872$	−14.3241	−0.485075
$873$	0.200687	0.00679221
$874$	−8.92124	−0.301766
$875$	−1.86590	−0.0630788
$876$	12.7222	0.429842
$877$	48.0085	1.62113	0.810567	−	0.585647i	$-0.199159\pi$
$877$	48.0085	1.62113	0.810567	+	0.585647i	$0.199159\pi$
$878$	29.9128	1.00951
$879$	29.3668	0.990519
$880$	2.21376	0.0746260
$881$	−16.6495	−0.560937	−0.280469	−	0.959863i	$-0.590490\pi$
$881$	−16.6495	−0.560937	−0.280469	+	0.959863i	$0.590490\pi$
$882$	−0.194112	−0.00653610
$883$	−39.3725	−1.32499	−0.662495	−	0.749067i	$-0.730502\pi$
$883$	−39.3725	−1.32499	−0.662495	+	0.749067i	$0.730502\pi$
$884$	4.52238	0.152104
$885$	−6.39872	−0.215091
$886$	13.7469	0.461837
$887$	4.68582	0.157334	0.0786672	−	0.996901i	$-0.474934\pi$
$887$	4.68582	0.157334	0.0786672	+	0.996901i	$0.474934\pi$
$888$	15.5030	0.520248
$889$	−20.9555	−0.702825
$890$	−8.72553	−0.292480
$891$	19.5507	0.654974
$892$	−4.03096	−0.134966
$893$	−7.48664	−0.250531
$894$	−11.0315	−0.368949
$895$	−6.42601	−0.214798
$896$	−1.86590	−0.0623352
$897$	−14.1376	−0.472040
$898$	−25.2426	−0.842357
$899$	−4.82270	−0.160846
$900$	−0.0551701	−0.00183900
$901$	−10.3322	−0.344214
$902$	0.314860	0.0104837
$903$	−25.7495	−0.856889
$904$	18.2715	0.607700
$905$	7.51174	0.249699
$906$	−4.90615	−0.162996
$907$	53.9282	1.79066	0.895328	−	0.445407i	$-0.146941\pi$
$907$	53.9282	1.79066	0.895328	+	0.445407i	$0.146941\pi$
$908$	12.7892	0.424425
$909$	0.205384	0.00681217
$910$	1.86590	0.0618538
$911$	22.6254	0.749612	0.374806	−	0.927103i	$-0.377709\pi$
$911$	22.6254	0.749612	0.374806	+	0.927103i	$0.377709\pi$
$912$	−1.85828	−0.0615338
$913$	15.2724	0.505442
$914$	−21.2788	−0.703841
$915$	−0.304695	−0.0100729
$916$	−11.5998	−0.383268
$917$	2.02280	0.0667986
$918$	23.7101	0.782549
$919$	6.43773	0.212361	0.106181	−	0.994347i	$-0.466138\pi$
$919$	6.43773	0.212361	0.106181	+	0.994347i	$0.466138\pi$
$920$	−8.23843	−0.271613
$921$	42.2746	1.39300
$922$	24.8737	0.819173
$923$	−5.31719	−0.175017
$924$	−7.08841	−0.233192
$925$	−9.03414	−0.297041
$926$	−33.0174	−1.08502
$927$	−0.0553133	−0.00181673
$928$	4.82270	0.158313
$929$	1.48181	0.0486165	0.0243083	−	0.999705i	$-0.492262\pi$
$929$	1.48181	0.0486165	0.0243083	+	0.999705i	$0.492262\pi$
$930$	1.71605	0.0562715
$931$	3.81005	0.124869
$932$	−12.8825	−0.421982
$933$	−18.4423	−0.603775
$934$	−22.7294	−0.743730
$935$	10.0115	0.327411
$936$	0.0551701	0.00180329
$937$	−12.3602	−0.403791	−0.201895	−	0.979407i	$-0.564710\pi$
$937$	−12.3602	−0.403791	−0.201895	+	0.979407i	$0.564710\pi$
$938$	−3.38463	−0.110512
$939$	5.61617	0.183277
$940$	−6.91363	−0.225498
$941$	20.8850	0.680831	0.340416	−	0.940275i	$-0.389432\pi$
$941$	20.8850	0.680831	0.340416	+	0.940275i	$0.389432\pi$
$942$	−26.7898	−0.872857
$943$	−1.17174	−0.0381571
$944$	3.72875	0.121360
$945$	9.78257	0.318227
$946$	−17.8026	−0.578811
$947$	11.0535	0.359189	0.179595	−	0.983741i	$-0.442521\pi$
$947$	11.0535	0.359189	0.179595	+	0.983741i	$0.442521\pi$
$948$	21.2334	0.689630
$949$	7.41362	0.240656
$950$	1.08288	0.0351333
$951$	14.4615	0.468948
$952$	−8.43829	−0.273487
$953$	25.8753	0.838183	0.419091	−	0.907944i	$-0.362349\pi$
$953$	25.8753	0.838183	0.419091	+	0.907944i	$0.362349\pi$
$954$	−0.126046	−0.00408088
$955$	25.1923	0.815203
$956$	−13.0007	−0.420472
$957$	18.3211	0.592237
$958$	−21.3305	−0.689159
$959$	−28.8266	−0.930861
$960$	−1.71605	−0.0553853
$961$	1.00000	0.0322581
$962$	9.03414	0.291272
$963$	0.0853616	0.00275074
$964$	−10.7505	−0.346251
$965$	−2.67153	−0.0859994
$966$	26.3792	0.848737
$967$	46.0027	1.47935	0.739673	−	0.672966i	$-0.234980\pi$
$967$	46.0027	1.47935	0.739673	+	0.672966i	$0.234980\pi$
$968$	6.09925	0.196037
$969$	−8.40385	−0.269970
$970$	−3.63760	−0.116796
$971$	−18.8398	−0.604597	−0.302298	−	0.953213i	$-0.597754\pi$
$971$	−18.8398	−0.604597	−0.302298	+	0.953213i	$0.597754\pi$
$972$	0.573271	0.0183877
$973$	−3.31929	−0.106411
$974$	2.95002	0.0945247
$975$	1.71605	0.0549576
$976$	0.177556	0.00568342
$977$	−34.4141	−1.10100	−0.550502	−	0.834834i	$-0.685564\pi$
$977$	−34.4141	−1.10100	−0.550502	+	0.834834i	$0.685564\pi$
$978$	−41.2006	−1.31745
$979$	19.3163	0.617350
$980$	3.51843	0.112392
$981$	−0.790262	−0.0252311
$982$	−13.5803	−0.433365
$983$	20.8946	0.666435	0.333217	−	0.942850i	$-0.391866\pi$
$983$	20.8946	0.666435	0.333217	+	0.942850i	$0.391866\pi$
$984$	−0.244071	−0.00778070
$985$	−10.1549	−0.323561
$986$	21.8101	0.694574
$987$	22.1372	0.704636
$988$	−1.08288	−0.0344510
$989$	66.2515	2.10667
$990$	0.122134	0.00388166
$991$	−29.9339	−0.950881	−0.475440	−	0.879748i	$-0.657711\pi$
$991$	−29.9339	−0.950881	−0.475440	+	0.879748i	$0.657711\pi$
$992$	−1.00000	−0.0317500
$993$	−12.5882	−0.399475
$994$	9.92132	0.314685
$995$	−1.45983	−0.0462796
$996$	−11.8387	−0.375125
$997$	10.1717	0.322140	0.161070	−	0.986943i	$-0.448506\pi$
$997$	10.1717	0.322140	0.161070	+	0.986943i	$0.448506\pi$
$998$	30.1819	0.955392
$999$	47.3644	1.49854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.c.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.71605 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.71605 q^{6} +1.86590 q^{7} -1.00000 q^{8} -0.0551701 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.71605 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.71605 q^{6} +1.86590 q^{7} -1.00000 q^{8} -0.0551701 q^{9} +1.00000 q^{10} -2.21376 q^{11} +1.71605 q^{12} +1.00000 q^{13} -1.86590 q^{14} -1.71605 q^{15} +1.00000 q^{16} +4.52238 q^{17} +0.0551701 q^{18} -1.08288 q^{19} -1.00000 q^{20} +3.20197 q^{21} +2.21376 q^{22} -8.23843 q^{23} -1.71605 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.24283 q^{27} +1.86590 q^{28} -4.82270 q^{29} +1.71605 q^{30} +1.00000 q^{31} -1.00000 q^{32} -3.79893 q^{33} -4.52238 q^{34} -1.86590 q^{35} -0.0551701 q^{36} -9.03414 q^{37} +1.08288 q^{38} +1.71605 q^{39} +1.00000 q^{40} +0.142228 q^{41} -3.20197 q^{42} -8.04176 q^{43} -2.21376 q^{44} +0.0551701 q^{45} +8.23843 q^{46} +6.91363 q^{47} +1.71605 q^{48} -3.51843 q^{49} -1.00000 q^{50} +7.76064 q^{51} +1.00000 q^{52} -2.28467 q^{53} +5.24283 q^{54} +2.21376 q^{55} -1.86590 q^{56} -1.85828 q^{57} +4.82270 q^{58} +3.72875 q^{59} -1.71605 q^{60} +0.177556 q^{61} -1.00000 q^{62} -0.102942 q^{63} +1.00000 q^{64} -1.00000 q^{65} +3.79893 q^{66} +1.81395 q^{67} +4.52238 q^{68} -14.1376 q^{69} +1.86590 q^{70} -5.31719 q^{71} +0.0551701 q^{72} +7.41362 q^{73} +9.03414 q^{74} +1.71605 q^{75} -1.08288 q^{76} -4.13065 q^{77} -1.71605 q^{78} +12.3734 q^{79} -1.00000 q^{80} -8.83145 q^{81} -0.142228 q^{82} -6.89883 q^{83} +3.20197 q^{84} -4.52238 q^{85} +8.04176 q^{86} -8.27599 q^{87} +2.21376 q^{88} -8.72553 q^{89} -0.0551701 q^{90} +1.86590 q^{91} -8.23843 q^{92} +1.71605 q^{93} -6.91363 q^{94} +1.08288 q^{95} -1.71605 q^{96} -3.63760 q^{97} +3.51843 q^{98} +0.122134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 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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