LMFDB - Embedded newform 4010.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} + \cdots - 512 $ x^15 - 7x^14 - 7x^13 + 133x^12 - 99x^11 - 941x^10 + 1290x^9 + 3031x^8 - 5452x^7 - 4098x^6 + 9986x^5 + 850x^4 - 7216x^3 + 1688x^2 + 1441x - 512
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.81559$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +1.00000 q^{10} +0.395658 q^{11} -0.876107 q^{12} -1.38994 q^{13} -4.75824 q^{14} +0.876107 q^{15} +1.00000 q^{16} +1.97628 q^{17} +2.23244 q^{18} -4.95938 q^{19} -1.00000 q^{20} -4.16872 q^{21} -0.395658 q^{22} +7.99038 q^{23} +0.876107 q^{24} +1.00000 q^{25} +1.38994 q^{26} +4.58417 q^{27} +4.75824 q^{28} -5.94547 q^{29} -0.876107 q^{30} -7.55920 q^{31} -1.00000 q^{32} -0.346639 q^{33} -1.97628 q^{34} -4.75824 q^{35} -2.23244 q^{36} -7.50357 q^{37} +4.95938 q^{38} +1.21774 q^{39} +1.00000 q^{40} -3.64477 q^{41} +4.16872 q^{42} -1.96929 q^{43} +0.395658 q^{44} +2.23244 q^{45} -7.99038 q^{46} +10.0246 q^{47} -0.876107 q^{48} +15.6408 q^{49} -1.00000 q^{50} -1.73143 q^{51} -1.38994 q^{52} -9.91023 q^{53} -4.58417 q^{54} -0.395658 q^{55} -4.75824 q^{56} +4.34494 q^{57} +5.94547 q^{58} +9.82894 q^{59} +0.876107 q^{60} -5.61187 q^{61} +7.55920 q^{62} -10.6225 q^{63} +1.00000 q^{64} +1.38994 q^{65} +0.346639 q^{66} -12.8370 q^{67} +1.97628 q^{68} -7.00043 q^{69} +4.75824 q^{70} +2.66068 q^{71} +2.23244 q^{72} -4.87744 q^{73} +7.50357 q^{74} -0.876107 q^{75} -4.95938 q^{76} +1.88263 q^{77} -1.21774 q^{78} +9.52194 q^{79} -1.00000 q^{80} +2.68108 q^{81} +3.64477 q^{82} -11.3659 q^{83} -4.16872 q^{84} -1.97628 q^{85} +1.96929 q^{86} +5.20887 q^{87} -0.395658 q^{88} +7.21172 q^{89} -2.23244 q^{90} -6.61366 q^{91} +7.99038 q^{92} +6.62267 q^{93} -10.0246 q^{94} +4.95938 q^{95} +0.876107 q^{96} -10.6902 q^{97} -15.6408 q^{98} -0.883281 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * 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
$3$	−0.876107	−0.505821	−0.252910	−	0.967490i	$-0.581388\pi$
$3$	−0.876107	−0.505821	−0.252910	+	0.967490i	$0.581388\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.876107	0.357669
$7$	4.75824	1.79844	0.899222	−	0.437493i	$-0.144133\pi$
$7$	4.75824	1.79844	0.899222	+	0.437493i	$0.144133\pi$
$8$	−1.00000	−0.353553
$9$	−2.23244	−0.744146
$10$	1.00000	0.316228
$11$	0.395658	0.119295	0.0596477	−	0.998219i	$-0.481002\pi$
$11$	0.395658	0.119295	0.0596477	+	0.998219i	$0.481002\pi$
$12$	−0.876107	−0.252910
$13$	−1.38994	−0.385500	−0.192750	−	0.981248i	$-0.561741\pi$
$13$	−1.38994	−0.385500	−0.192750	+	0.981248i	$0.561741\pi$
$14$	−4.75824	−1.27169
$15$	0.876107	0.226210
$16$	1.00000	0.250000
$17$	1.97628	0.479319	0.239659	−	0.970857i	$-0.422964\pi$
$17$	1.97628	0.479319	0.239659	+	0.970857i	$0.422964\pi$
$18$	2.23244	0.526190
$19$	−4.95938	−1.13776	−0.568879	−	0.822421i	$-0.692623\pi$
$19$	−4.95938	−1.13776	−0.568879	+	0.822421i	$0.692623\pi$
$20$	−1.00000	−0.223607
$21$	−4.16872	−0.909690
$22$	−0.395658	−0.0843546
$23$	7.99038	1.66611	0.833055	−	0.553191i	$-0.186590\pi$
$23$	7.99038	1.66611	0.833055	+	0.553191i	$0.186590\pi$
$24$	0.876107	0.178835
$25$	1.00000	0.200000
$26$	1.38994	0.272590
$27$	4.58417	0.882225
$28$	4.75824	0.899222
$29$	−5.94547	−1.10405	−0.552023	−	0.833829i	$-0.686144\pi$
$29$	−5.94547	−1.10405	−0.552023	+	0.833829i	$0.686144\pi$
$30$	−0.876107	−0.159955
$31$	−7.55920	−1.35767	−0.678836	−	0.734290i	$-0.737515\pi$
$31$	−7.55920	−1.35767	−0.678836	+	0.734290i	$0.737515\pi$
$32$	−1.00000	−0.176777
$33$	−0.346639	−0.0603420
$34$	−1.97628	−0.338929
$35$	−4.75824	−0.804289
$36$	−2.23244	−0.372073
$37$	−7.50357	−1.23358	−0.616790	−	0.787128i	$-0.711567\pi$
$37$	−7.50357	−1.23358	−0.616790	+	0.787128i	$0.711567\pi$
$38$	4.95938	0.804517
$39$	1.21774	0.194994
$40$	1.00000	0.158114
$41$	−3.64477	−0.569218	−0.284609	−	0.958644i	$-0.591864\pi$
$41$	−3.64477	−0.569218	−0.284609	+	0.958644i	$0.591864\pi$
$42$	4.16872	0.643248
$43$	−1.96929	−0.300314	−0.150157	−	0.988662i	$-0.547978\pi$
$43$	−1.96929	−0.300314	−0.150157	+	0.988662i	$0.547978\pi$
$44$	0.395658	0.0596477
$45$	2.23244	0.332792
$46$	−7.99038	−1.17812
$47$	10.0246	1.46224	0.731121	−	0.682248i	$-0.238997\pi$
$47$	10.0246	1.46224	0.731121	+	0.682248i	$0.238997\pi$
$48$	−0.876107	−0.126455
$49$	15.6408	2.23440
$50$	−1.00000	−0.141421
$51$	−1.73143	−0.242449
$52$	−1.38994	−0.192750
$53$	−9.91023	−1.36127	−0.680637	−	0.732620i	$-0.738297\pi$
$53$	−9.91023	−1.36127	−0.680637	+	0.732620i	$0.738297\pi$
$54$	−4.58417	−0.623827
$55$	−0.395658	−0.0533505
$56$	−4.75824	−0.635846
$57$	4.34494	0.575502
$58$	5.94547	0.780678
$59$	9.82894	1.27962	0.639810	−	0.768533i	$-0.279013\pi$
$59$	9.82894	1.27962	0.639810	+	0.768533i	$0.279013\pi$
$60$	0.876107	0.113105
$61$	−5.61187	−0.718527	−0.359263	−	0.933236i	$-0.616972\pi$
$61$	−5.61187	−0.718527	−0.359263	+	0.933236i	$0.616972\pi$
$62$	7.55920	0.960019
$63$	−10.6225	−1.33830
$64$	1.00000	0.125000
$65$	1.38994	0.172401
$66$	0.346639	0.0426683
$67$	−12.8370	−1.56829	−0.784144	−	0.620578i	$-0.786898\pi$
$67$	−12.8370	−1.56829	−0.784144	+	0.620578i	$0.786898\pi$
$68$	1.97628	0.239659
$69$	−7.00043	−0.842752
$70$	4.75824	0.568718
$71$	2.66068	0.315764	0.157882	−	0.987458i	$-0.449533\pi$
$71$	2.66068	0.315764	0.157882	+	0.987458i	$0.449533\pi$
$72$	2.23244	0.263095
$73$	−4.87744	−0.570861	−0.285430	−	0.958399i	$-0.592137\pi$
$73$	−4.87744	−0.570861	−0.285430	+	0.958399i	$0.592137\pi$
$74$	7.50357	0.872273
$75$	−0.876107	−0.101164
$76$	−4.95938	−0.568879
$77$	1.88263	0.214546
$78$	−1.21774	−0.137881
$79$	9.52194	1.07130	0.535651	−	0.844439i	$-0.320066\pi$
$79$	9.52194	1.07130	0.535651	+	0.844439i	$0.320066\pi$
$80$	−1.00000	−0.111803
$81$	2.68108	0.297898
$82$	3.64477	0.402498
$83$	−11.3659	−1.24757	−0.623787	−	0.781594i	$-0.714407\pi$
$83$	−11.3659	−1.24757	−0.623787	+	0.781594i	$0.714407\pi$
$84$	−4.16872	−0.454845
$85$	−1.97628	−0.214358
$86$	1.96929	0.212354
$87$	5.20887	0.558449
$88$	−0.395658	−0.0421773
$89$	7.21172	0.764441	0.382221	−	0.924071i	$-0.375159\pi$
$89$	7.21172	0.764441	0.382221	+	0.924071i	$0.375159\pi$
$90$	−2.23244	−0.235319
$91$	−6.61366	−0.693300
$92$	7.99038	0.833055
$93$	6.62267	0.686738
$94$	−10.0246	−1.03396
$95$	4.95938	0.508821
$96$	0.876107	0.0894173
$97$	−10.6902	−1.08542	−0.542710	−	0.839920i	$-0.682602\pi$
$97$	−10.6902	−1.08542	−0.542710	+	0.839920i	$0.682602\pi$
$98$	−15.6408	−1.57996
$99$	−0.883281	−0.0887731
$100$	1.00000	0.100000
$101$	−15.0071	−1.49327	−0.746633	−	0.665236i	$-0.768331\pi$
$101$	−15.0071	−1.49327	−0.746633	+	0.665236i	$0.768331\pi$
$102$	1.73143	0.171437
$103$	12.5325	1.23487	0.617433	−	0.786623i	$-0.288173\pi$
$103$	12.5325	1.23487	0.617433	+	0.786623i	$0.288173\pi$
$104$	1.38994	0.136295
$105$	4.16872	0.406826
$106$	9.91023	0.962567
$107$	−8.92000	−0.862329	−0.431164	−	0.902273i	$-0.641897\pi$
$107$	−8.92000	−0.862329	−0.431164	+	0.902273i	$0.641897\pi$
$108$	4.58417	0.441112
$109$	0.0344053	0.00329543	0.00164771	−	0.999999i	$-0.499476\pi$
$109$	0.0344053	0.00329543	0.00164771	+	0.999999i	$0.499476\pi$
$110$	0.395658	0.0377245
$111$	6.57393	0.623970
$112$	4.75824	0.449611
$113$	−9.62394	−0.905344	−0.452672	−	0.891677i	$-0.649529\pi$
$113$	−9.62394	−0.905344	−0.452672	+	0.891677i	$0.649529\pi$
$114$	−4.34494	−0.406941
$115$	−7.99038	−0.745107
$116$	−5.94547	−0.552023
$117$	3.10295	0.286868
$118$	−9.82894	−0.904828
$119$	9.40361	0.862027
$120$	−0.876107	−0.0799773
$121$	−10.8435	−0.985769
$122$	5.61187	0.508075
$123$	3.19321	0.287922
$124$	−7.55920	−0.678836
$125$	−1.00000	−0.0894427
$126$	10.6225	0.946324
$127$	22.1935	1.96936	0.984678	−	0.174380i	$-0.0557920\pi$
$127$	22.1935	1.96936	0.984678	+	0.174380i	$0.0557920\pi$
$128$	−1.00000	−0.0883883
$129$	1.72531	0.151905
$130$	−1.38994	−0.121906
$131$	12.4596	1.08860	0.544299	−	0.838891i	$-0.316796\pi$
$131$	12.4596	1.08860	0.544299	+	0.838891i	$0.316796\pi$
$132$	−0.346639	−0.0301710
$133$	−23.5979	−2.04620
$134$	12.8370	1.10895
$135$	−4.58417	−0.394543
$136$	−1.97628	−0.169465
$137$	14.0918	1.20395	0.601973	−	0.798516i	$-0.294381\pi$
$137$	14.0918	1.20395	0.601973	+	0.798516i	$0.294381\pi$
$138$	7.00043	0.595916
$139$	9.24434	0.784095	0.392047	−	0.919945i	$-0.371767\pi$
$139$	9.24434	0.784095	0.392047	+	0.919945i	$0.371767\pi$
$140$	−4.75824	−0.402144
$141$	−8.78264	−0.739632
$142$	−2.66068	−0.223279
$143$	−0.549941	−0.0459884
$144$	−2.23244	−0.186036
$145$	5.94547	0.493744
$146$	4.87744	0.403659
$147$	−13.7030	−1.13021
$148$	−7.50357	−0.616790
$149$	5.05203	0.413878	0.206939	−	0.978354i	$-0.433650\pi$
$149$	5.05203	0.413878	0.206939	+	0.978354i	$0.433650\pi$
$150$	0.876107	0.0715338
$151$	5.58234	0.454284	0.227142	−	0.973862i	$-0.427062\pi$
$151$	5.58234	0.454284	0.227142	+	0.973862i	$0.427062\pi$
$152$	4.95938	0.402259
$153$	−4.41192	−0.356683
$154$	−1.88263	−0.151707
$155$	7.55920	0.607169
$156$	1.21774	0.0974969
$157$	−19.9358	−1.59105	−0.795526	−	0.605919i	$-0.792806\pi$
$157$	−19.9358	−1.59105	−0.795526	+	0.605919i	$0.792806\pi$
$158$	−9.52194	−0.757525
$159$	8.68242	0.688561
$160$	1.00000	0.0790569
$161$	38.0201	2.99640
$162$	−2.68108	−0.210646
$163$	−9.29534	−0.728067	−0.364033	−	0.931386i	$-0.618601\pi$
$163$	−9.29534	−0.728067	−0.364033	+	0.931386i	$0.618601\pi$
$164$	−3.64477	−0.284609
$165$	0.346639	0.0269858
$166$	11.3659	0.882168
$167$	−10.5835	−0.818973	−0.409487	−	0.912316i	$-0.634292\pi$
$167$	−10.5835	−0.818973	−0.409487	+	0.912316i	$0.634292\pi$
$168$	4.16872	0.321624
$169$	−11.0681	−0.851390
$170$	1.97628	0.151574
$171$	11.0715	0.846658
$172$	−1.96929	−0.150157
$173$	−8.23238	−0.625897	−0.312948	−	0.949770i	$-0.601317\pi$
$173$	−8.23238	−0.625897	−0.312948	+	0.949770i	$0.601317\pi$
$174$	−5.20887	−0.394883
$175$	4.75824	0.359689
$176$	0.395658	0.0298238
$177$	−8.61120	−0.647258
$178$	−7.21172	−0.540542
$179$	13.4926	1.00848	0.504240	−	0.863563i	$-0.331773\pi$
$179$	13.4926	1.00848	0.504240	+	0.863563i	$0.331773\pi$
$180$	2.23244	0.166396
$181$	19.8239	1.47350	0.736749	−	0.676166i	$-0.236360\pi$
$181$	19.8239	1.47350	0.736749	+	0.676166i	$0.236360\pi$
$182$	6.61366	0.490237
$183$	4.91660	0.363445
$184$	−7.99038	−0.589059
$185$	7.50357	0.551674
$186$	−6.62267	−0.485597
$187$	0.781931	0.0571805
$188$	10.0246	0.731121
$189$	21.8126	1.58663
$190$	−4.95938	−0.359791
$191$	4.39707	0.318161	0.159080	−	0.987266i	$-0.449147\pi$
$191$	4.39707	0.318161	0.159080	+	0.987266i	$0.449147\pi$
$192$	−0.876107	−0.0632276
$193$	−18.8033	−1.35349	−0.676745	−	0.736218i	$-0.736610\pi$
$193$	−18.8033	−1.35349	−0.676745	+	0.736218i	$0.736610\pi$
$194$	10.6902	0.767508
$195$	−1.21774	−0.0872039
$196$	15.6408	1.11720
$197$	15.7824	1.12445	0.562223	−	0.826986i	$-0.309946\pi$
$197$	15.7824	1.12445	0.562223	+	0.826986i	$0.309946\pi$
$198$	0.883281	0.0627721
$199$	−6.39499	−0.453329	−0.226664	−	0.973973i	$-0.572782\pi$
$199$	−6.39499	−0.453329	−0.226664	+	0.973973i	$0.572782\pi$
$200$	−1.00000	−0.0707107
$201$	11.2466	0.793273
$202$	15.0071	1.05590
$203$	−28.2899	−1.98556
$204$	−1.73143	−0.121225
$205$	3.64477	0.254562
$206$	−12.5325	−0.873183
$207$	−17.8380	−1.23983
$208$	−1.38994	−0.0963750
$209$	−1.96222	−0.135729
$210$	−4.16872	−0.287669
$211$	−21.5689	−1.48487	−0.742433	−	0.669921i	$-0.766328\pi$
$211$	−21.5689	−1.48487	−0.742433	+	0.669921i	$0.766328\pi$
$212$	−9.91023	−0.680637
$213$	−2.33104	−0.159720
$214$	8.92000	0.609758
$215$	1.96929	0.134305
$216$	−4.58417	−0.311914
$217$	−35.9684	−2.44170
$218$	−0.0344053	−0.00233022
$219$	4.27315	0.288753
$220$	−0.395658	−0.0266753
$221$	−2.74691	−0.184777
$222$	−6.57393	−0.441213
$223$	−8.59690	−0.575691	−0.287845	−	0.957677i	$-0.592939\pi$
$223$	−8.59690	−0.575691	−0.287845	+	0.957677i	$0.592939\pi$
$224$	−4.75824	−0.317923
$225$	−2.23244	−0.148829
$226$	9.62394	0.640175
$227$	15.3902	1.02148	0.510742	−	0.859734i	$-0.329371\pi$
$227$	15.3902	1.02148	0.510742	+	0.859734i	$0.329371\pi$
$228$	4.34494	0.287751
$229$	−27.3915	−1.81008	−0.905041	−	0.425324i	$-0.860160\pi$
$229$	−27.3915	−1.81008	−0.905041	+	0.425324i	$0.860160\pi$
$230$	7.99038	0.526870
$231$	−1.64939	−0.108522
$232$	5.94547	0.390339
$233$	7.72662	0.506188	0.253094	−	0.967442i	$-0.418552\pi$
$233$	7.72662	0.506188	0.253094	+	0.967442i	$0.418552\pi$
$234$	−3.10295	−0.202846
$235$	−10.0246	−0.653935
$236$	9.82894	0.639810
$237$	−8.34224	−0.541887
$238$	−9.40361	−0.609545
$239$	−21.0286	−1.36023	−0.680113	−	0.733107i	$-0.738069\pi$
$239$	−21.0286	−1.36023	−0.680113	+	0.733107i	$0.738069\pi$
$240$	0.876107	0.0565525
$241$	−11.6531	−0.750645	−0.375322	−	0.926894i	$-0.622468\pi$
$241$	−11.6531	−0.750645	−0.375322	+	0.926894i	$0.622468\pi$
$242$	10.8435	0.697044
$243$	−16.1014	−1.03291
$244$	−5.61187	−0.359263
$245$	−15.6408	−0.999254
$246$	−3.19321	−0.203592
$247$	6.89323	0.438606
$248$	7.55920	0.480010
$249$	9.95778	0.631049
$250$	1.00000	0.0632456
$251$	−10.6941	−0.675005	−0.337503	−	0.941325i	$-0.609582\pi$
$251$	−10.6941	−0.675005	−0.337503	+	0.941325i	$0.609582\pi$
$252$	−10.6225	−0.669152
$253$	3.16146	0.198759
$254$	−22.1935	−1.39255
$255$	1.73143	0.108427
$256$	1.00000	0.0625000
$257$	−11.0713	−0.690611	−0.345305	−	0.938490i	$-0.612225\pi$
$257$	−11.0713	−0.690611	−0.345305	+	0.938490i	$0.612225\pi$
$258$	−1.72531	−0.107413
$259$	−35.7038	−2.21852
$260$	1.38994	0.0862004
$261$	13.2729	0.821571
$262$	−12.4596	−0.769755
$263$	−10.8041	−0.666208	−0.333104	−	0.942890i	$-0.608096\pi$
$263$	−10.8041	−0.666208	−0.333104	+	0.942890i	$0.608096\pi$
$264$	0.346639	0.0213341
$265$	9.91023	0.608781
$266$	23.5979	1.44688
$267$	−6.31824	−0.386670
$268$	−12.8370	−0.784144
$269$	12.3033	0.750143	0.375072	−	0.926996i	$-0.377618\pi$
$269$	12.3033	0.750143	0.375072	+	0.926996i	$0.377618\pi$
$270$	4.58417	0.278984
$271$	−31.0283	−1.88484	−0.942418	−	0.334438i	$-0.891453\pi$
$271$	−31.0283	−1.88484	−0.942418	+	0.334438i	$0.891453\pi$
$272$	1.97628	0.119830
$273$	5.79427	0.350685
$274$	−14.0918	−0.851319
$275$	0.395658	0.0238591
$276$	−7.00043	−0.421376
$277$	−3.37527	−0.202801	−0.101400	−	0.994846i	$-0.532332\pi$
$277$	−3.37527	−0.202801	−0.101400	+	0.994846i	$0.532332\pi$
$278$	−9.24434	−0.554439
$279$	16.8754	1.01031
$280$	4.75824	0.284359
$281$	−12.5542	−0.748918	−0.374459	−	0.927243i	$-0.622172\pi$
$281$	−12.5542	−0.748918	−0.374459	+	0.927243i	$0.622172\pi$
$282$	8.78264	0.522999
$283$	27.0370	1.60718	0.803592	−	0.595180i	$-0.202919\pi$
$283$	27.0370	1.60718	0.803592	+	0.595180i	$0.202919\pi$
$284$	2.66068	0.157882
$285$	−4.34494	−0.257372
$286$	0.549941	0.0325187
$287$	−17.3427	−1.02371
$288$	2.23244	0.131548
$289$	−13.0943	−0.770254
$290$	−5.94547	−0.349130
$291$	9.36572	0.549028
$292$	−4.87744	−0.285430
$293$	6.48231	0.378700	0.189350	−	0.981910i	$-0.439362\pi$
$293$	6.48231	0.378700	0.189350	+	0.981910i	$0.439362\pi$
$294$	13.7030	0.799176
$295$	−9.82894	−0.572263
$296$	7.50357	0.436136
$297$	1.81376	0.105245
$298$	−5.05203	−0.292656
$299$	−11.1061	−0.642285
$300$	−0.876107	−0.0505821
$301$	−9.37035	−0.540098
$302$	−5.58234	−0.321228
$303$	13.1479	0.755324
$304$	−4.95938	−0.284440
$305$	5.61187	0.321335
$306$	4.41192	0.252213
$307$	7.54205	0.430448	0.215224	−	0.976565i	$-0.430952\pi$
$307$	7.54205	0.430448	0.215224	+	0.976565i	$0.430952\pi$
$308$	1.88263	0.107273
$309$	−10.9798	−0.624621
$310$	−7.55920	−0.429334
$311$	−20.5320	−1.16427	−0.582133	−	0.813094i	$-0.697782\pi$
$311$	−20.5320	−1.16427	−0.582133	+	0.813094i	$0.697782\pi$
$312$	−1.21774	−0.0689407
$313$	−33.5343	−1.89547	−0.947735	−	0.319059i	$-0.896633\pi$
$313$	−33.5343	−1.89547	−0.947735	+	0.319059i	$0.896633\pi$
$314$	19.9358	1.12504
$315$	10.6225	0.598508
$316$	9.52194	0.535651
$317$	−25.7170	−1.44441	−0.722204	−	0.691680i	$-0.756871\pi$
$317$	−25.7170	−1.44441	−0.722204	+	0.691680i	$0.756871\pi$
$318$	−8.68242	−0.486886
$319$	−2.35237	−0.131708
$320$	−1.00000	−0.0559017
$321$	7.81487	0.436183
$322$	−38.0201	−2.11878
$323$	−9.80112	−0.545349
$324$	2.68108	0.148949
$325$	−1.38994	−0.0771000
$326$	9.29534	0.514821
$327$	−0.0301427	−0.00166690
$328$	3.64477	0.201249
$329$	47.6995	2.62976
$330$	−0.346639	−0.0190818
$331$	−23.4317	−1.28792	−0.643960	−	0.765059i	$-0.722710\pi$
$331$	−23.4317	−1.28792	−0.643960	+	0.765059i	$0.722710\pi$
$332$	−11.3659	−0.623787
$333$	16.7513	0.917963
$334$	10.5835	0.579102
$335$	12.8370	0.701360
$336$	−4.16872	−0.227422
$337$	−14.8968	−0.811482	−0.405741	−	0.913988i	$-0.632986\pi$
$337$	−14.8968	−0.811482	−0.405741	+	0.913988i	$0.632986\pi$
$338$	11.0681	0.602024
$339$	8.43160	0.457942
$340$	−1.97628	−0.107179
$341$	−2.99086	−0.161964
$342$	−11.0715	−0.598678
$343$	41.1150	2.22000
$344$	1.96929	0.106177
$345$	7.00043	0.376890
$346$	8.23238	0.442576
$347$	22.8362	1.22591	0.612957	−	0.790116i	$-0.289980\pi$
$347$	22.8362	1.22591	0.612957	+	0.790116i	$0.289980\pi$
$348$	5.20887	0.279225
$349$	18.2849	0.978766	0.489383	−	0.872069i	$-0.337222\pi$
$349$	18.2849	0.978766	0.489383	+	0.872069i	$0.337222\pi$
$350$	−4.75824	−0.254338
$351$	−6.37172	−0.340098
$352$	−0.395658	−0.0210886
$353$	2.13029	0.113384	0.0566920	−	0.998392i	$-0.481945\pi$
$353$	2.13029	0.113384	0.0566920	+	0.998392i	$0.481945\pi$
$354$	8.61120	0.457680
$355$	−2.66068	−0.141214
$356$	7.21172	0.382221
$357$	−8.23857	−0.436031
$358$	−13.4926	−0.713104
$359$	−3.43071	−0.181066	−0.0905330	−	0.995893i	$-0.528857\pi$
$359$	−3.43071	−0.181066	−0.0905330	+	0.995893i	$0.528857\pi$
$360$	−2.23244	−0.117660
$361$	5.59541	0.294495
$362$	−19.8239	−1.04192
$363$	9.50003	0.498622
$364$	−6.61366	−0.346650
$365$	4.87744	0.255297
$366$	−4.91660	−0.256995
$367$	20.1607	1.05238	0.526191	−	0.850366i	$-0.323620\pi$
$367$	20.1607	1.05238	0.526191	+	0.850366i	$0.323620\pi$
$368$	7.99038	0.416527
$369$	8.13673	0.423581
$370$	−7.50357	−0.390092
$371$	−47.1552	−2.44818
$372$	6.62267	0.343369
$373$	−7.92957	−0.410578	−0.205289	−	0.978701i	$-0.565813\pi$
$373$	−7.92957	−0.410578	−0.205289	+	0.978701i	$0.565813\pi$
$374$	−0.781931	−0.0404327
$375$	0.876107	0.0452420
$376$	−10.0246	−0.516981
$377$	8.26384	0.425610
$378$	−21.8126	−1.12192
$379$	7.50938	0.385731	0.192865	−	0.981225i	$-0.438222\pi$
$379$	7.50938	0.385731	0.192865	+	0.981225i	$0.438222\pi$
$380$	4.95938	0.254411
$381$	−19.4439	−0.996141
$382$	−4.39707	−0.224974
$383$	−33.5814	−1.71593	−0.857964	−	0.513711i	$-0.828271\pi$
$383$	−33.5814	−1.71593	−0.857964	+	0.513711i	$0.828271\pi$
$384$	0.876107	0.0447086
$385$	−1.88263	−0.0959479
$386$	18.8033	0.957061
$387$	4.39632	0.223477
$388$	−10.6902	−0.542710
$389$	−21.7398	−1.10225	−0.551125	−	0.834423i	$-0.685801\pi$
$389$	−21.7398	−1.10225	−0.551125	+	0.834423i	$0.685801\pi$
$390$	1.21774	0.0616624
$391$	15.7912	0.798597
$392$	−15.6408	−0.789980
$393$	−10.9159	−0.550635
$394$	−15.7824	−0.795103
$395$	−9.52194	−0.479101
$396$	−0.883281	−0.0443866
$397$	4.08329	0.204935	0.102467	−	0.994736i	$-0.467326\pi$
$397$	4.08329	0.204935	0.102467	+	0.994736i	$0.467326\pi$
$398$	6.39499	0.320552
$399$	20.6743	1.03501
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−11.2466	−0.560929
$403$	10.5068	0.523382
$404$	−15.0071	−0.746633
$405$	−2.68108	−0.133224
$406$	28.2899	1.40401
$407$	−2.96885	−0.147160
$408$	1.73143	0.0857187
$409$	3.59578	0.177800	0.0888999	−	0.996041i	$-0.471665\pi$
$409$	3.59578	0.177800	0.0888999	+	0.996041i	$0.471665\pi$
$410$	−3.64477	−0.180003
$411$	−12.3460	−0.608981
$412$	12.5325	0.617433
$413$	46.7684	2.30132
$414$	17.8380	0.876691
$415$	11.3659	0.557932
$416$	1.38994	0.0681474
$417$	−8.09903	−0.396611
$418$	1.96222	0.0959752
$419$	26.1714	1.27855	0.639277	−	0.768976i	$-0.279234\pi$
$419$	26.1714	1.27855	0.639277	+	0.768976i	$0.279234\pi$
$420$	4.16872	0.203413
$421$	−5.98077	−0.291485	−0.145742	−	0.989323i	$-0.546557\pi$
$421$	−5.98077	−0.291485	−0.145742	+	0.989323i	$0.546557\pi$
$422$	21.5689	1.04996
$423$	−22.3793	−1.08812
$424$	9.91023	0.481283
$425$	1.97628	0.0958637
$426$	2.33104	0.112939
$427$	−26.7026	−1.29223
$428$	−8.92000	−0.431164
$429$	0.481807	0.0232619
$430$	−1.96929	−0.0949677
$431$	−36.2323	−1.74525	−0.872624	−	0.488393i	$-0.837583\pi$
$431$	−36.2323	−1.74525	−0.872624	+	0.488393i	$0.837583\pi$
$432$	4.58417	0.220556
$433$	−27.4578	−1.31954	−0.659770	−	0.751468i	$-0.729346\pi$
$433$	−27.4578	−1.31954	−0.659770	+	0.751468i	$0.729346\pi$
$434$	35.9684	1.72654
$435$	−5.20887	−0.249746
$436$	0.0344053	0.00164771
$437$	−39.6273	−1.89563
$438$	−4.27315	−0.204179
$439$	−29.0886	−1.38833	−0.694163	−	0.719818i	$-0.744225\pi$
$439$	−29.0886	−1.38833	−0.694163	+	0.719818i	$0.744225\pi$
$440$	0.395658	0.0188623
$441$	−34.9171	−1.66272
$442$	2.74691	0.130657
$443$	35.2356	1.67409	0.837047	−	0.547131i	$-0.184280\pi$
$443$	35.2356	1.67409	0.837047	+	0.547131i	$0.184280\pi$
$444$	6.57393	0.311985
$445$	−7.21172	−0.341869
$446$	8.59690	0.407075
$447$	−4.42612	−0.209348
$448$	4.75824	0.224805
$449$	16.6369	0.785144	0.392572	−	0.919721i	$-0.371585\pi$
$449$	16.6369	0.785144	0.392572	+	0.919721i	$0.371585\pi$
$450$	2.23244	0.105238
$451$	−1.44208	−0.0679051
$452$	−9.62394	−0.452672
$453$	−4.89073	−0.229786
$454$	−15.3902	−0.722298
$455$	6.61366	0.310053
$456$	−4.34494	−0.203471
$457$	−4.95999	−0.232018	−0.116009	−	0.993248i	$-0.537010\pi$
$457$	−4.95999	−0.232018	−0.116009	+	0.993248i	$0.537010\pi$
$458$	27.3915	1.27992
$459$	9.05962	0.422867
$460$	−7.99038	−0.372553
$461$	14.9403	0.695840	0.347920	−	0.937524i	$-0.386888\pi$
$461$	14.9403	0.695840	0.347920	+	0.937524i	$0.386888\pi$
$462$	1.64939	0.0767365
$463$	−21.7295	−1.00985	−0.504927	−	0.863162i	$-0.668481\pi$
$463$	−21.7295	−1.00985	−0.504927	+	0.863162i	$0.668481\pi$
$464$	−5.94547	−0.276012
$465$	−6.62267	−0.307119
$466$	−7.72662	−0.357929
$467$	−30.1884	−1.39695	−0.698475	−	0.715634i	$-0.746138\pi$
$467$	−30.1884	−1.39695	−0.698475	+	0.715634i	$0.746138\pi$
$468$	3.10295	0.143434
$469$	−61.0815	−2.82048
$470$	10.0246	0.462402
$471$	17.4659	0.804787
$472$	−9.82894	−0.452414
$473$	−0.779166	−0.0358261
$474$	8.34224	0.383172
$475$	−4.95938	−0.227552
$476$	9.40361	0.431014
$477$	22.1240	1.01299
$478$	21.0286	0.961825
$479$	3.17305	0.144981	0.0724903	−	0.997369i	$-0.476905\pi$
$479$	3.17305	0.144981	0.0724903	+	0.997369i	$0.476905\pi$
$480$	−0.876107	−0.0399886
$481$	10.4295	0.475545
$482$	11.6531	0.530786
$483$	−33.3097	−1.51564
$484$	−10.8435	−0.492884
$485$	10.6902	0.485415
$486$	16.1014	0.730376
$487$	−27.7483	−1.25739	−0.628697	−	0.777650i	$-0.716411\pi$
$487$	−27.7483	−1.25739	−0.628697	+	0.777650i	$0.716411\pi$
$488$	5.61187	0.254037
$489$	8.14371	0.368271
$490$	15.6408	0.706579
$491$	29.5110	1.33181	0.665907	−	0.746035i	$-0.268045\pi$
$491$	29.5110	1.33181	0.665907	+	0.746035i	$0.268045\pi$
$492$	3.19321	0.143961
$493$	−11.7499	−0.529190
$494$	−6.89323	−0.310141
$495$	0.883281	0.0397005
$496$	−7.55920	−0.339418
$497$	12.6601	0.567884
$498$	−9.95778	−0.446219
$499$	−38.3533	−1.71693	−0.858464	−	0.512874i	$-0.828581\pi$
$499$	−38.3533	−1.71693	−0.858464	+	0.512874i	$0.828581\pi$
$500$	−1.00000	−0.0447214
$501$	9.27225	0.414254
$502$	10.6941	0.477301
$503$	1.67540	0.0747024	0.0373512	−	0.999302i	$-0.488108\pi$
$503$	1.67540	0.0747024	0.0373512	+	0.999302i	$0.488108\pi$
$504$	10.6225	0.473162
$505$	15.0071	0.667809
$506$	−3.16146	−0.140544
$507$	9.69681	0.430650
$508$	22.1935	0.984678
$509$	6.72849	0.298235	0.149118	−	0.988819i	$-0.452357\pi$
$509$	6.72849	0.298235	0.149118	+	0.988819i	$0.452357\pi$
$510$	−1.73143	−0.0766692
$511$	−23.2080	−1.02666
$512$	−1.00000	−0.0441942
$513$	−22.7346	−1.00376
$514$	11.0713	0.488336
$515$	−12.5325	−0.552249
$516$	1.72531	0.0759525
$517$	3.96632	0.174439
$518$	35.7038	1.56873
$519$	7.21245	0.316591
$520$	−1.38994	−0.0609529
$521$	17.0764	0.748129	0.374064	−	0.927403i	$-0.377964\pi$
$521$	17.0764	0.748129	0.374064	+	0.927403i	$0.377964\pi$
$522$	−13.2729	−0.580938
$523$	−8.47342	−0.370517	−0.185258	−	0.982690i	$-0.559312\pi$
$523$	−8.47342	−0.370517	−0.185258	+	0.982690i	$0.559312\pi$
$524$	12.4596	0.544299
$525$	−4.16872	−0.181938
$526$	10.8041	0.471080
$527$	−14.9391	−0.650757
$528$	−0.346639	−0.0150855
$529$	40.8462	1.77592
$530$	−9.91023	−0.430473
$531$	−21.9425	−0.952223
$532$	−23.5979	−1.02310
$533$	5.06602	0.219434
$534$	6.31824	0.273417
$535$	8.92000	0.385645
$536$	12.8370	0.554474
$537$	−11.8209	−0.510110
$538$	−12.3033	−0.530431
$539$	6.18841	0.266554
$540$	−4.58417	−0.197271
$541$	−40.1909	−1.72794	−0.863970	−	0.503543i	$-0.832029\pi$
$541$	−40.1909	−1.72794	−0.863970	+	0.503543i	$0.832029\pi$
$542$	31.0283	1.33278
$543$	−17.3678	−0.745325
$544$	−1.97628	−0.0847323
$545$	−0.0344053	−0.00147376
$546$	−5.79427	−0.247972
$547$	39.5768	1.69218	0.846090	−	0.533040i	$-0.178950\pi$
$547$	39.5768	1.69218	0.846090	+	0.533040i	$0.178950\pi$
$548$	14.0918	0.601973
$549$	12.5281	0.534688
$550$	−0.395658	−0.0168709
$551$	29.4858	1.25614
$552$	7.00043	0.297958
$553$	45.3077	1.92668
$554$	3.37527	0.143402
$555$	−6.57393	−0.279048
$556$	9.24434	0.392047
$557$	−15.7255	−0.666309	−0.333155	−	0.942872i	$-0.608113\pi$
$557$	−15.7255	−0.666309	−0.333155	+	0.942872i	$0.608113\pi$
$558$	−16.8754	−0.714394
$559$	2.73720	0.115771
$560$	−4.75824	−0.201072
$561$	−0.685055	−0.0289231
$562$	12.5542	0.529565
$563$	−30.4925	−1.28510	−0.642552	−	0.766242i	$-0.722124\pi$
$563$	−30.4925	−1.28510	−0.642552	+	0.766242i	$0.722124\pi$
$564$	−8.78264	−0.369816
$565$	9.62394	0.404882
$566$	−27.0370	−1.13645
$567$	12.7572	0.535753
$568$	−2.66068	−0.111639
$569$	21.6186	0.906300	0.453150	−	0.891434i	$-0.350300\pi$
$569$	21.6186	0.906300	0.453150	+	0.891434i	$0.350300\pi$
$570$	4.34494	0.181990
$571$	38.3294	1.60404	0.802018	−	0.597300i	$-0.203760\pi$
$571$	38.3294	1.60404	0.802018	+	0.597300i	$0.203760\pi$
$572$	−0.549941	−0.0229942
$573$	−3.85230	−0.160932
$574$	17.3427	0.723870
$575$	7.99038	0.333222
$576$	−2.23244	−0.0930182
$577$	19.4816	0.811028	0.405514	−	0.914089i	$-0.367093\pi$
$577$	19.4816	0.811028	0.405514	+	0.914089i	$0.367093\pi$
$578$	13.0943	0.544652
$579$	16.4737	0.684623
$580$	5.94547	0.246872
$581$	−54.0818	−2.24369
$582$	−9.36572	−0.388222
$583$	−3.92106	−0.162394
$584$	4.87744	0.201830
$585$	−3.10295	−0.128291
$586$	−6.48231	−0.267782
$587$	−21.2556	−0.877313	−0.438656	−	0.898655i	$-0.644545\pi$
$587$	−21.2556	−0.877313	−0.438656	+	0.898655i	$0.644545\pi$
$588$	−13.7030	−0.565103
$589$	37.4889	1.54470
$590$	9.82894	0.404651
$591$	−13.8270	−0.568768
$592$	−7.50357	−0.308395
$593$	43.6717	1.79338	0.896691	−	0.442657i	$-0.145964\pi$
$593$	43.6717	1.79338	0.896691	+	0.442657i	$0.145964\pi$
$594$	−1.81376	−0.0744197
$595$	−9.40361	−0.385510
$596$	5.05203	0.206939
$597$	5.60269	0.229303
$598$	11.1061	0.454164
$599$	7.61091	0.310973	0.155487	−	0.987838i	$-0.450305\pi$
$599$	7.61091	0.310973	0.155487	+	0.987838i	$0.450305\pi$
$600$	0.876107	0.0357669
$601$	29.9971	1.22361	0.611804	−	0.791010i	$-0.290444\pi$
$601$	29.9971	1.22361	0.611804	+	0.791010i	$0.290444\pi$
$602$	9.37035	0.381907
$603$	28.6578	1.16704
$604$	5.58234	0.227142
$605$	10.8435	0.440849
$606$	−13.1479	−0.534095
$607$	24.4068	0.990643	0.495321	−	0.868710i	$-0.335050\pi$
$607$	24.4068	0.990643	0.495321	+	0.868710i	$0.335050\pi$
$608$	4.95938	0.201129
$609$	24.7850	1.00434
$610$	−5.61187	−0.227218
$611$	−13.9336	−0.563694
$612$	−4.41192	−0.178341
$613$	−10.3544	−0.418209	−0.209105	−	0.977893i	$-0.567055\pi$
$613$	−10.3544	−0.418209	−0.209105	+	0.977893i	$0.567055\pi$
$614$	−7.54205	−0.304372
$615$	−3.19321	−0.128763
$616$	−1.88263	−0.0758535
$617$	−18.9377	−0.762404	−0.381202	−	0.924492i	$-0.624490\pi$
$617$	−18.9377	−0.762404	−0.381202	+	0.924492i	$0.624490\pi$
$618$	10.9798	0.441674
$619$	28.8582	1.15991	0.579954	−	0.814649i	$-0.303070\pi$
$619$	28.8582	1.15991	0.579954	+	0.814649i	$0.303070\pi$
$620$	7.55920	0.303585
$621$	36.6293	1.46988
$622$	20.5320	0.823260
$623$	34.3151	1.37480
$624$	1.21774	0.0487484
$625$	1.00000	0.0400000
$626$	33.5343	1.34030
$627$	1.71911	0.0686547
$628$	−19.9358	−0.795526
$629$	−14.8292	−0.591278
$630$	−10.6225	−0.423209
$631$	−20.1714	−0.803010	−0.401505	−	0.915857i	$-0.631513\pi$
$631$	−20.1714	−0.803010	−0.401505	+	0.915857i	$0.631513\pi$
$632$	−9.52194	−0.378763
$633$	18.8967	0.751075
$634$	25.7170	1.02135
$635$	−22.1935	−0.880723
$636$	8.68242	0.344280
$637$	−21.7398	−0.861361
$638$	2.35237	0.0931313
$639$	−5.93979	−0.234974
$640$	1.00000	0.0395285
$641$	40.6758	1.60660	0.803300	−	0.595575i	$-0.203076\pi$
$641$	40.6758	1.60660	0.803300	+	0.595575i	$0.203076\pi$
$642$	−7.81487	−0.308428
$643$	−12.3398	−0.486636	−0.243318	−	0.969947i	$-0.578236\pi$
$643$	−12.3398	−0.486636	−0.243318	+	0.969947i	$0.578236\pi$
$644$	38.0201	1.49820
$645$	−1.72531	−0.0679340
$646$	9.80112	0.385620
$647$	−25.7692	−1.01309	−0.506545	−	0.862214i	$-0.669078\pi$
$647$	−25.7692	−1.01309	−0.506545	+	0.862214i	$0.669078\pi$
$648$	−2.68108	−0.105323
$649$	3.88890	0.152653
$650$	1.38994	0.0545179
$651$	31.5122	1.23506
$652$	−9.29534	−0.364033
$653$	31.4621	1.23121	0.615603	−	0.788057i	$-0.288913\pi$
$653$	31.4621	1.23121	0.615603	+	0.788057i	$0.288913\pi$
$654$	0.0301427	0.00117867
$655$	−12.4596	−0.486836
$656$	−3.64477	−0.142305
$657$	10.8886	0.424803
$658$	−47.6995	−1.85952
$659$	−26.1508	−1.01869	−0.509345	−	0.860562i	$-0.670112\pi$
$659$	−26.1508	−1.01869	−0.509345	+	0.860562i	$0.670112\pi$
$660$	0.346639	0.0134929
$661$	−7.68461	−0.298897	−0.149448	−	0.988770i	$-0.547750\pi$
$661$	−7.68461	−0.298897	−0.149448	+	0.988770i	$0.547750\pi$
$662$	23.4317	0.910698
$663$	2.40659	0.0934641
$664$	11.3659	0.441084
$665$	23.5979	0.915086
$666$	−16.7513	−0.649098
$667$	−47.5066	−1.83946
$668$	−10.5835	−0.409487
$669$	7.53180	0.291196
$670$	−12.8370	−0.495937
$671$	−2.22038	−0.0857169
$672$	4.16872	0.160812
$673$	−29.5730	−1.13995	−0.569977	−	0.821660i	$-0.693048\pi$
$673$	−29.5730	−1.13995	−0.569977	+	0.821660i	$0.693048\pi$
$674$	14.8968	0.573804
$675$	4.58417	0.176445
$676$	−11.0681	−0.425695
$677$	−11.6055	−0.446036	−0.223018	−	0.974814i	$-0.571591\pi$
$677$	−11.6055	−0.446036	−0.223018	+	0.974814i	$0.571591\pi$
$678$	−8.43160	−0.323814
$679$	−50.8663	−1.95207
$680$	1.97628	0.0757869
$681$	−13.4835	−0.516687
$682$	2.99086	0.114526
$683$	36.7503	1.40621	0.703105	−	0.711086i	$-0.251796\pi$
$683$	36.7503	1.40621	0.703105	+	0.711086i	$0.251796\pi$
$684$	11.0715	0.423329
$685$	−14.0918	−0.538421
$686$	−41.1150	−1.56978
$687$	23.9979	0.915577
$688$	−1.96929	−0.0750785
$689$	13.7746	0.524771
$690$	−7.00043	−0.266502
$691$	24.4972	0.931917	0.465959	−	0.884806i	$-0.345710\pi$
$691$	24.4972	0.931917	0.465959	+	0.884806i	$0.345710\pi$
$692$	−8.23238	−0.312948
$693$	−4.20286	−0.159653
$694$	−22.8362	−0.866852
$695$	−9.24434	−0.350658
$696$	−5.20887	−0.197442
$697$	−7.20310	−0.272837
$698$	−18.2849	−0.692092
$699$	−6.76934	−0.256040
$700$	4.75824	0.179844
$701$	15.2021	0.574174	0.287087	−	0.957905i	$-0.407313\pi$
$701$	15.2021	0.574174	0.287087	+	0.957905i	$0.407313\pi$
$702$	6.37172	0.240485
$703$	37.2130	1.40352
$704$	0.395658	0.0149119
$705$	8.78264	0.330774
$706$	−2.13029	−0.0801746
$707$	−71.4075	−2.68555
$708$	−8.61120	−0.323629
$709$	25.5679	0.960224	0.480112	−	0.877207i	$-0.340596\pi$
$709$	25.5679	0.960224	0.480112	+	0.877207i	$0.340596\pi$
$710$	2.66068	0.0998534
$711$	−21.2571	−0.797205
$712$	−7.21172	−0.270271
$713$	−60.4009	−2.26203
$714$	8.23857	0.308321
$715$	0.549941	0.0205666
$716$	13.4926	0.504240
$717$	18.4233	0.688030
$718$	3.43071	0.128033
$719$	19.1720	0.714997	0.357498	−	0.933914i	$-0.383630\pi$
$719$	19.1720	0.714997	0.357498	+	0.933914i	$0.383630\pi$
$720$	2.23244	0.0831980
$721$	59.6327	2.22084
$722$	−5.59541	−0.208240
$723$	10.2094	0.379691
$724$	19.8239	0.736749
$725$	−5.94547	−0.220809
$726$	−9.50003	−0.352579
$727$	47.0498	1.74498	0.872491	−	0.488630i	$-0.162503\pi$
$727$	47.0498	1.74498	0.872491	+	0.488630i	$0.162503\pi$
$728$	6.61366	0.245119
$729$	6.06333	0.224568
$730$	−4.87744	−0.180522
$731$	−3.89187	−0.143946
$732$	4.91660	0.181723
$733$	−39.6927	−1.46608	−0.733041	−	0.680185i	$-0.761900\pi$
$733$	−39.6927	−1.46608	−0.733041	+	0.680185i	$0.761900\pi$
$734$	−20.1607	−0.744146
$735$	13.7030	0.505443
$736$	−7.99038	−0.294529
$737$	−5.07906	−0.187090
$738$	−8.13673	−0.299517
$739$	20.5005	0.754122	0.377061	−	0.926188i	$-0.376935\pi$
$739$	20.5005	0.754122	0.377061	+	0.926188i	$0.376935\pi$
$740$	7.50357	0.275837
$741$	−6.03921	−0.221856
$742$	47.1552	1.73112
$743$	−25.8088	−0.946833	−0.473417	−	0.880839i	$-0.656980\pi$
$743$	−25.8088	−0.946833	−0.473417	+	0.880839i	$0.656980\pi$
$744$	−6.62267	−0.242799
$745$	−5.05203	−0.185092
$746$	7.92957	0.290322
$747$	25.3737	0.928377
$748$	0.781931	0.0285902
$749$	−42.4434	−1.55085
$750$	−0.876107	−0.0319909
$751$	−7.09348	−0.258845	−0.129422	−	0.991590i	$-0.541312\pi$
$751$	−7.09348	−0.258845	−0.129422	+	0.991590i	$0.541312\pi$
$752$	10.0246	0.365561
$753$	9.36917	0.341432
$754$	−8.26384	−0.300951
$755$	−5.58234	−0.203162
$756$	21.8126	0.793316
$757$	20.5508	0.746933	0.373466	−	0.927644i	$-0.378169\pi$
$757$	20.5508	0.746933	0.373466	+	0.927644i	$0.378169\pi$
$758$	−7.50938	−0.272753
$759$	−2.76977	−0.100536
$760$	−4.95938	−0.179895
$761$	−40.4347	−1.46576	−0.732878	−	0.680360i	$-0.761824\pi$
$761$	−40.4347	−1.46576	−0.732878	+	0.680360i	$0.761824\pi$
$762$	19.4439	0.704378
$763$	0.163708	0.00592664
$764$	4.39707	0.159080
$765$	4.41192	0.159513
$766$	33.5814	1.21334
$767$	−13.6616	−0.493293
$768$	−0.876107	−0.0316138
$769$	−6.15961	−0.222121	−0.111061	−	0.993814i	$-0.535425\pi$
$769$	−6.15961	−0.222121	−0.111061	+	0.993814i	$0.535425\pi$
$770$	1.88263	0.0678454
$771$	9.69967	0.349325
$772$	−18.8033	−0.676745
$773$	22.1383	0.796259	0.398129	−	0.917329i	$-0.369659\pi$
$773$	22.1383	0.796259	0.398129	+	0.917329i	$0.369659\pi$
$774$	−4.39632	−0.158022
$775$	−7.55920	−0.271534
$776$	10.6902	0.383754
$777$	31.2803	1.12218
$778$	21.7398	0.779408
$779$	18.0758	0.647633
$780$	−1.21774	−0.0436019
$781$	1.05272	0.0376692
$782$	−15.7912	−0.564693
$783$	−27.2551	−0.974017
$784$	15.6408	0.558600
$785$	19.9358	0.711540
$786$	10.9159	0.389358
$787$	−14.8875	−0.530682	−0.265341	−	0.964155i	$-0.585484\pi$
$787$	−14.8875	−0.530682	−0.265341	+	0.964155i	$0.585484\pi$
$788$	15.7824	0.562223
$789$	9.46553	0.336982
$790$	9.52194	0.338776
$791$	−45.7930	−1.62821
$792$	0.883281	0.0313860
$793$	7.80016	0.276992
$794$	−4.08329	−0.144911
$795$	−8.68242	−0.307934
$796$	−6.39499	−0.226664
$797$	−43.5372	−1.54217	−0.771083	−	0.636734i	$-0.780285\pi$
$797$	−43.5372	−1.54217	−0.771083	+	0.636734i	$0.780285\pi$
$798$	−20.6743	−0.731861
$799$	19.8115	0.700880
$800$	−1.00000	−0.0353553
$801$	−16.0997	−0.568856
$802$	1.00000	0.0353112
$803$	−1.92980	−0.0681010
$804$	11.2466	0.396636
$805$	−38.0201	−1.34003
$806$	−10.5068	−0.370087
$807$	−10.7790	−0.379438
$808$	15.0071	0.527949
$809$	0.564011	0.0198296	0.00991479	−	0.999951i	$-0.496844\pi$
$809$	0.564011	0.0198296	0.00991479	+	0.999951i	$0.496844\pi$
$810$	2.68108	0.0942037
$811$	26.4569	0.929027	0.464514	−	0.885566i	$-0.346229\pi$
$811$	26.4569	0.929027	0.464514	+	0.885566i	$0.346229\pi$
$812$	−28.2899	−0.992782
$813$	27.1841	0.953388
$814$	2.96885	0.104058
$815$	9.29534	0.325601
$816$	−1.73143	−0.0606123
$817$	9.76646	0.341685
$818$	−3.59578	−0.125723
$819$	14.7646	0.515916
$820$	3.64477	0.127281
$821$	6.42811	0.224342	0.112171	−	0.993689i	$-0.464219\pi$
$821$	6.42811	0.224342	0.112171	+	0.993689i	$0.464219\pi$
$822$	12.3460	0.430615
$823$	−44.0461	−1.53535	−0.767676	−	0.640838i	$-0.778587\pi$
$823$	−44.0461	−1.53535	−0.767676	+	0.640838i	$0.778587\pi$
$824$	−12.5325	−0.436591
$825$	−0.346639	−0.0120684
$826$	−46.7684	−1.62728
$827$	10.6766	0.371263	0.185632	−	0.982619i	$-0.440567\pi$
$827$	10.6766	0.371263	0.185632	+	0.982619i	$0.440567\pi$
$828$	−17.8380	−0.619914
$829$	45.6828	1.58663	0.793314	−	0.608813i	$-0.208354\pi$
$829$	45.6828	1.58663	0.793314	+	0.608813i	$0.208354\pi$
$830$	−11.3659	−0.394518
$831$	2.95710	0.102581
$832$	−1.38994	−0.0481875
$833$	30.9106	1.07099
$834$	8.09903	0.280446
$835$	10.5835	0.366256
$836$	−1.96222	−0.0678647
$837$	−34.6527	−1.19777
$838$	−26.1714	−0.904075
$839$	14.4341	0.498319	0.249159	−	0.968462i	$-0.419846\pi$
$839$	14.4341	0.498319	0.249159	+	0.968462i	$0.419846\pi$
$840$	−4.16872	−0.143835
$841$	6.34861	0.218918
$842$	5.98077	0.206111
$843$	10.9988	0.378818
$844$	−21.5689	−0.742433
$845$	11.0681	0.380753
$846$	22.3793	0.769418
$847$	−51.5957	−1.77285
$848$	−9.91023	−0.340319
$849$	−23.6873	−0.812947
$850$	−1.97628	−0.0677859
$851$	−59.9564	−2.05528
$852$	−2.33104	−0.0798600
$853$	33.8632	1.15945	0.579726	−	0.814811i	$-0.303159\pi$
$853$	33.8632	1.15945	0.579726	+	0.814811i	$0.303159\pi$
$854$	26.7026	0.913744
$855$	−11.0715	−0.378637
$856$	8.92000	0.304879
$857$	27.9423	0.954492	0.477246	−	0.878770i	$-0.341635\pi$
$857$	27.9423	0.954492	0.477246	+	0.878770i	$0.341635\pi$
$858$	−0.481807	−0.0164486
$859$	35.0800	1.19692	0.598458	−	0.801154i	$-0.295780\pi$
$859$	35.0800	1.19692	0.598458	+	0.801154i	$0.295780\pi$
$860$	1.96929	0.0671523
$861$	15.1941	0.517812
$862$	36.2323	1.23408
$863$	1.82264	0.0620434	0.0310217	−	0.999519i	$-0.490124\pi$
$863$	1.82264	0.0620434	0.0310217	+	0.999519i	$0.490124\pi$
$864$	−4.58417	−0.155957
$865$	8.23238	0.279909
$866$	27.4578	0.933055
$867$	11.4720	0.389610
$868$	−35.9684	−1.22085
$869$	3.76743	0.127801
$870$	5.20887	0.176597
$871$	17.8427	0.604575
$872$	−0.0344053	−0.00116511
$873$	23.8651	0.807711
$874$	39.6273	1.34041
$875$	−4.75824	−0.160858
$876$	4.27315	0.144377
$877$	−31.9023	−1.07727	−0.538633	−	0.842541i	$-0.681059\pi$
$877$	−31.9023	−1.07727	−0.538633	+	0.842541i	$0.681059\pi$
$878$	29.0886	0.981694
$879$	−5.67919	−0.191554
$880$	−0.395658	−0.0133376
$881$	−7.37640	−0.248517	−0.124259	−	0.992250i	$-0.539655\pi$
$881$	−7.37640	−0.248517	−0.124259	+	0.992250i	$0.539655\pi$
$882$	34.9171	1.17572
$883$	2.59396	0.0872937	0.0436469	−	0.999047i	$-0.486102\pi$
$883$	2.59396	0.0872937	0.0436469	+	0.999047i	$0.486102\pi$
$884$	−2.74691	−0.0923886
$885$	8.61120	0.289462
$886$	−35.2356	−1.18376
$887$	−8.88122	−0.298202	−0.149101	−	0.988822i	$-0.547638\pi$
$887$	−8.88122	−0.298202	−0.149101	+	0.988822i	$0.547638\pi$
$888$	−6.57393	−0.220607
$889$	105.602	3.54178
$890$	7.21172	0.241738
$891$	1.06079	0.0355379
$892$	−8.59690	−0.287845
$893$	−49.7159	−1.66368
$894$	4.42612	0.148032
$895$	−13.4926	−0.451006
$896$	−4.75824	−0.158961
$897$	9.73017	0.324881
$898$	−16.6369	−0.555181
$899$	44.9430	1.49893
$900$	−2.23244	−0.0744146
$901$	−19.5854	−0.652484
$902$	1.44208	0.0480161
$903$	8.20943	0.273193
$904$	9.62394	0.320088
$905$	−19.8239	−0.658968
$906$	4.89073	0.162483
$907$	7.35532	0.244229	0.122115	−	0.992516i	$-0.461032\pi$
$907$	7.35532	0.244229	0.122115	+	0.992516i	$0.461032\pi$
$908$	15.3902	0.510742
$909$	33.5025	1.11121
$910$	−6.61366	−0.219241
$911$	−44.0558	−1.45963	−0.729817	−	0.683643i	$-0.760395\pi$
$911$	−44.0558	−1.45963	−0.729817	+	0.683643i	$0.760395\pi$
$912$	4.34494	0.143875
$913$	−4.49702	−0.148830
$914$	4.95999	0.164062
$915$	−4.91660	−0.162538
$916$	−27.3915	−0.905041
$917$	59.2856	1.95778
$918$	−9.05962	−0.299012
$919$	−25.1336	−0.829082	−0.414541	−	0.910031i	$-0.636058\pi$
$919$	−25.1336	−0.829082	−0.414541	+	0.910031i	$0.636058\pi$
$920$	7.99038	0.263435
$921$	−6.60764	−0.217729
$922$	−14.9403	−0.492034
$923$	−3.69818	−0.121727
$924$	−1.64939	−0.0542609
$925$	−7.50357	−0.246716
$926$	21.7295	0.714075
$927$	−27.9781	−0.918920
$928$	5.94547	0.195170
$929$	−7.27655	−0.238736	−0.119368	−	0.992850i	$-0.538087\pi$
$929$	−7.27655	−0.238736	−0.119368	+	0.992850i	$0.538087\pi$
$930$	6.62267	0.217166
$931$	−77.5686	−2.54221
$932$	7.72662	0.253094
$933$	17.9883	0.588910
$934$	30.1884	0.987793
$935$	−0.781931	−0.0255719
$936$	−3.10295	−0.101423
$937$	45.4287	1.48409	0.742046	−	0.670349i	$-0.233856\pi$
$937$	45.4287	1.48409	0.742046	+	0.670349i	$0.233856\pi$
$938$	61.0815	1.99438
$939$	29.3796	0.958767
$940$	−10.0246	−0.326967
$941$	41.6926	1.35914	0.679570	−	0.733611i	$-0.262167\pi$
$941$	41.6926	1.35914	0.679570	+	0.733611i	$0.262167\pi$
$942$	−17.4659	−0.569070
$943$	−29.1231	−0.948380
$944$	9.82894	0.319905
$945$	−21.8126	−0.709563
$946$	0.779166	0.0253329
$947$	−4.07217	−0.132328	−0.0661639	−	0.997809i	$-0.521076\pi$
$947$	−4.07217	−0.132328	−0.0661639	+	0.997809i	$0.521076\pi$
$948$	−8.34224	−0.270943
$949$	6.77934	0.220067
$950$	4.95938	0.160903
$951$	22.5308	0.730611
$952$	−9.40361	−0.304773
$953$	25.7356	0.833656	0.416828	−	0.908985i	$-0.363142\pi$
$953$	25.7356	0.833656	0.416828	+	0.908985i	$0.363142\pi$
$954$	−22.1240	−0.716290
$955$	−4.39707	−0.142286
$956$	−21.0286	−0.680113
$957$	2.06093	0.0666204
$958$	−3.17305	−0.102517
$959$	67.0523	2.16523
$960$	0.876107	0.0282762
$961$	26.1415	0.843273
$962$	−10.4295	−0.336261
$963$	19.9133	0.641698
$964$	−11.6531	−0.375322
$965$	18.8033	0.605299
$966$	33.3097	1.07172
$967$	42.7571	1.37498	0.687488	−	0.726196i	$-0.258713\pi$
$967$	42.7571	1.37498	0.687488	+	0.726196i	$0.258713\pi$
$968$	10.8435	0.348522
$969$	8.58683	0.275849
$970$	−10.6902	−0.343240
$971$	−27.5600	−0.884443	−0.442222	−	0.896906i	$-0.645810\pi$
$971$	−27.5600	−0.884443	−0.442222	+	0.896906i	$0.645810\pi$
$972$	−16.1014	−0.516454
$973$	43.9867	1.41015
$974$	27.7483	0.889112
$975$	1.21774	0.0389988
$976$	−5.61187	−0.179632
$977$	−4.71904	−0.150975	−0.0754877	−	0.997147i	$-0.524051\pi$
$977$	−4.71904	−0.150975	−0.0754877	+	0.997147i	$0.524051\pi$
$978$	−8.14371	−0.260407
$979$	2.85338	0.0911943
$980$	−15.6408	−0.499627
$981$	−0.0768076	−0.00245228
$982$	−29.5110	−0.941735
$983$	−39.5987	−1.26300	−0.631502	−	0.775374i	$-0.717561\pi$
$983$	−39.5987	−1.26300	−0.631502	+	0.775374i	$0.717561\pi$
$984$	−3.19321	−0.101796
$985$	−15.7824	−0.502868
$986$	11.7499	0.374194
$987$	−41.7899	−1.33019
$988$	6.89323	0.219303
$989$	−15.7354	−0.500356
$990$	−0.883281	−0.0280725
$991$	27.7183	0.880499	0.440250	−	0.897875i	$-0.354890\pi$
$991$	27.7183	0.880499	0.440250	+	0.897875i	$0.354890\pi$
$992$	7.55920	0.240005
$993$	20.5286	0.651457
$994$	−12.6601	−0.401555
$995$	6.39499	0.202735
$996$	9.95778	0.315524
$997$	8.22414	0.260461	0.130231	−	0.991484i	$-0.458428\pi$
$997$	8.22414	0.260461	0.130231	+	0.991484i	$0.458428\pi$
$998$	38.3533	1.21405
$999$	−34.3977	−1.08829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.k.1.8	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.k.1.8	✓	15	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.876107 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.876107 q^{6} +4.75824 q^{7} -1.00000 q^{8} -2.23244 q^{9} +1.00000 q^{10} +0.395658 q^{11} -0.876107 q^{12} -1.38994 q^{13} -4.75824 q^{14} +0.876107 q^{15} +1.00000 q^{16} +1.97628 q^{17} +2.23244 q^{18} -4.95938 q^{19} -1.00000 q^{20} -4.16872 q^{21} -0.395658 q^{22} +7.99038 q^{23} +0.876107 q^{24} +1.00000 q^{25} +1.38994 q^{26} +4.58417 q^{27} +4.75824 q^{28} -5.94547 q^{29} -0.876107 q^{30} -7.55920 q^{31} -1.00000 q^{32} -0.346639 q^{33} -1.97628 q^{34} -4.75824 q^{35} -2.23244 q^{36} -7.50357 q^{37} +4.95938 q^{38} +1.21774 q^{39} +1.00000 q^{40} -3.64477 q^{41} +4.16872 q^{42} -1.96929 q^{43} +0.395658 q^{44} +2.23244 q^{45} -7.99038 q^{46} +10.0246 q^{47} -0.876107 q^{48} +15.6408 q^{49} -1.00000 q^{50} -1.73143 q^{51} -1.38994 q^{52} -9.91023 q^{53} -4.58417 q^{54} -0.395658 q^{55} -4.75824 q^{56} +4.34494 q^{57} +5.94547 q^{58} +9.82894 q^{59} +0.876107 q^{60} -5.61187 q^{61} +7.55920 q^{62} -10.6225 q^{63} +1.00000 q^{64} +1.38994 q^{65} +0.346639 q^{66} -12.8370 q^{67} +1.97628 q^{68} -7.00043 q^{69} +4.75824 q^{70} +2.66068 q^{71} +2.23244 q^{72} -4.87744 q^{73} +7.50357 q^{74} -0.876107 q^{75} -4.95938 q^{76} +1.88263 q^{77} -1.21774 q^{78} +9.52194 q^{79} -1.00000 q^{80} +2.68108 q^{81} +3.64477 q^{82} -11.3659 q^{83} -4.16872 q^{84} -1.97628 q^{85} +1.96929 q^{86} +5.20887 q^{87} -0.395658 q^{88} +7.21172 q^{89} -2.23244 q^{90} -6.61366 q^{91} +7.99038 q^{92} +6.62267 q^{93} -10.0246 q^{94} +4.95938 q^{95} +0.876107 q^{96} -10.6902 q^{97} -15.6408 q^{98} -0.883281 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9	\( 15 q - 15 q^{2} - 6 q^{3} + 15 q^{4} - 15 q^{5} + 6 q^{6} - 5 q^{7} - 15 q^{8} + 19 q^{9} + 15 q^{10} - 2 q^{11} - 6 q^{12} - 13 q^{13} + 5 q^{14} + 6 q^{15} + 15 q^{16} + 11 q^{17} - 19 q^{18} - 15 q^{19} - 15 q^{20} - 2 q^{21} + 2 q^{22} - 3 q^{23} + 6 q^{24} + 15 q^{25} + 13 q^{26} - 12 q^{27} - 5 q^{28} + 28 q^{29} - 6 q^{30} - 12 q^{31} - 15 q^{32} - 22 q^{33} - 11 q^{34} + 5 q^{35} + 19 q^{36} - 23 q^{37} + 15 q^{38} - 2 q^{39} + 15 q^{40} + 24 q^{41} + 2 q^{42} - 24 q^{43} - 2 q^{44} - 19 q^{45} + 3 q^{46} - 3 q^{47} - 6 q^{48} + 20 q^{49} - 15 q^{50} - 5 q^{51} - 13 q^{52} + 10 q^{53} + 12 q^{54} + 2 q^{55} + 5 q^{56} - 11 q^{57} - 28 q^{58} + 2 q^{59} + 6 q^{60} + 15 q^{61} + 12 q^{62} - 2 q^{63} + 15 q^{64} + 13 q^{65} + 22 q^{66} - 48 q^{67} + 11 q^{68} + 21 q^{69} - 5 q^{70} + 15 q^{71} - 19 q^{72} - 47 q^{73} + 23 q^{74} - 6 q^{75} - 15 q^{76} + 7 q^{77} + 2 q^{78} - 34 q^{79} - 15 q^{80} + 43 q^{81} - 24 q^{82} - 32 q^{83} - 2 q^{84} - 11 q^{85} + 24 q^{86} + 14 q^{87} + 2 q^{88} + 25 q^{89} + 19 q^{90} - 32 q^{91} - 3 q^{92} - 42 q^{93} + 3 q^{94} + 15 q^{95} + 6 q^{96} - 34 q^{97} - 20 q^{98} + 4 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 6 * q^3 + 15 * q^4 - 15 * q^5 + 6 * q^6 - 5 * q^7 - 15 * q^8 + 19 * q^9 + 15 * q^10 - 2 * q^11 - 6 * q^12 - 13 * q^13 + 5 * q^14 + 6 * q^15 + 15 * q^16 + 11 * q^17 - 19 * q^18 - 15 * q^19 - 15 * q^20 - 2 * q^21 + 2 * q^22 - 3 * q^23 + 6 * q^24 + 15 * q^25 + 13 * q^26 - 12 * q^27 - 5 * q^28 + 28 * q^29 - 6 * q^30 - 12 * q^31 - 15 * q^32 - 22 * q^33 - 11 * q^34 + 5 * q^35 + 19 * q^36 - 23 * q^37 + 15 * q^38 - 2 * q^39 + 15 * q^40 + 24 * q^41 + 2 * q^42 - 24 * q^43 - 2 * q^44 - 19 * q^45 + 3 * q^46 - 3 * q^47 - 6 * q^48 + 20 * q^49 - 15 * q^50 - 5 * q^51 - 13 * q^52 + 10 * q^53 + 12 * q^54 + 2 * q^55 + 5 * q^56 - 11 * q^57 - 28 * q^58 + 2 * q^59 + 6 * q^60 + 15 * q^61 + 12 * q^62 - 2 * q^63 + 15 * q^64 + 13 * q^65 + 22 * q^66 - 48 * q^67 + 11 * q^68 + 21 * q^69 - 5 * q^70 + 15 * q^71 - 19 * q^72 - 47 * q^73 + 23 * q^74 - 6 * q^75 - 15 * q^76 + 7 * q^77 + 2 * q^78 - 34 * q^79 - 15 * q^80 + 43 * q^81 - 24 * q^82 - 32 * q^83 - 2 * q^84 - 11 * q^85 + 24 * q^86 + 14 * q^87 + 2 * q^88 + 25 * q^89 + 19 * q^90 - 32 * q^91 - 3 * q^92 - 42 * q^93 + 3 * q^94 + 15 * q^95 + 6 * q^96 - 34 * q^97 - 20 * q^98 + 4 * q^99

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