LMFDB - Embedded newform 4029.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-2.08696$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.08696 q^{2} +1.00000 q^{3} +2.35542 q^{4} -2.36854 q^{5} +2.08696 q^{6} -0.791085 q^{7} +0.741746 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08696 q^{2} +1.00000 q^{3} +2.35542 q^{4} -2.36854 q^{5} +2.08696 q^{6} -0.791085 q^{7} +0.741746 q^{8} +1.00000 q^{9} -4.94306 q^{10} +1.46076 q^{11} +2.35542 q^{12} -2.45845 q^{13} -1.65097 q^{14} -2.36854 q^{15} -3.16284 q^{16} +1.00000 q^{17} +2.08696 q^{18} -0.298072 q^{19} -5.57891 q^{20} -0.791085 q^{21} +3.04855 q^{22} -7.61554 q^{23} +0.741746 q^{24} +0.609997 q^{25} -5.13070 q^{26} +1.00000 q^{27} -1.86334 q^{28} -1.68146 q^{29} -4.94306 q^{30} -2.70893 q^{31} -8.08423 q^{32} +1.46076 q^{33} +2.08696 q^{34} +1.87372 q^{35} +2.35542 q^{36} +9.81484 q^{37} -0.622065 q^{38} -2.45845 q^{39} -1.75686 q^{40} -10.9098 q^{41} -1.65097 q^{42} -1.38681 q^{43} +3.44070 q^{44} -2.36854 q^{45} -15.8934 q^{46} -8.90941 q^{47} -3.16284 q^{48} -6.37418 q^{49} +1.27304 q^{50} +1.00000 q^{51} -5.79069 q^{52} +12.9131 q^{53} +2.08696 q^{54} -3.45987 q^{55} -0.586784 q^{56} -0.298072 q^{57} -3.50914 q^{58} -6.45957 q^{59} -5.57891 q^{60} +9.65516 q^{61} -5.65345 q^{62} -0.791085 q^{63} -10.5458 q^{64} +5.82295 q^{65} +3.04855 q^{66} -0.660667 q^{67} +2.35542 q^{68} -7.61554 q^{69} +3.91038 q^{70} -10.2409 q^{71} +0.741746 q^{72} -1.42377 q^{73} +20.4832 q^{74} +0.609997 q^{75} -0.702084 q^{76} -1.15558 q^{77} -5.13070 q^{78} -1.00000 q^{79} +7.49132 q^{80} +1.00000 q^{81} -22.7684 q^{82} -2.22307 q^{83} -1.86334 q^{84} -2.36854 q^{85} -2.89422 q^{86} -1.68146 q^{87} +1.08351 q^{88} -1.32988 q^{89} -4.94306 q^{90} +1.94484 q^{91} -17.9378 q^{92} -2.70893 q^{93} -18.5936 q^{94} +0.705996 q^{95} -8.08423 q^{96} -11.0879 q^{97} -13.3027 q^{98} +1.46076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	2.08696	1.47571	0.737853	−	0.674961i	$-0.235840\pi$
$2$	2.08696	1.47571	0.737853	+	0.674961i	$0.235840\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.35542	1.17771
$5$	−2.36854	−1.05924	−0.529622	−	0.848234i	$-0.677666\pi$
$5$	−2.36854	−1.05924	−0.529622	+	0.848234i	$0.677666\pi$
$6$	2.08696	0.851999
$7$	−0.791085	−0.299002	−0.149501	−	0.988762i	$-0.547767\pi$
$7$	−0.791085	−0.299002	−0.149501	+	0.988762i	$0.547767\pi$
$8$	0.741746	0.262247
$9$	1.00000	0.333333
$10$	−4.94306	−1.56313
$11$	1.46076	0.440435	0.220218	−	0.975451i	$-0.429323\pi$
$11$	1.46076	0.440435	0.220218	+	0.975451i	$0.429323\pi$
$12$	2.35542	0.679951
$13$	−2.45845	−0.681852	−0.340926	−	0.940090i	$-0.610741\pi$
$13$	−2.45845	−0.681852	−0.340926	+	0.940090i	$0.610741\pi$
$14$	−1.65097	−0.441239
$15$	−2.36854	−0.611555
$16$	−3.16284	−0.790710
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.08696	0.491902
$19$	−0.298072	−0.0683824	−0.0341912	−	0.999415i	$-0.510886\pi$
$19$	−0.298072	−0.0683824	−0.0341912	+	0.999415i	$0.510886\pi$
$20$	−5.57891	−1.24748
$21$	−0.791085	−0.172629
$22$	3.04855	0.649953
$23$	−7.61554	−1.58795	−0.793975	−	0.607951i	$-0.791992\pi$
$23$	−7.61554	−1.58795	−0.793975	+	0.607951i	$0.791992\pi$
$24$	0.741746	0.151408
$25$	0.609997	0.121999
$26$	−5.13070	−1.00621
$27$	1.00000	0.192450
$28$	−1.86334	−0.352137
$29$	−1.68146	−0.312239	−0.156119	−	0.987738i	$-0.549898\pi$
$29$	−1.68146	−0.312239	−0.156119	+	0.987738i	$0.549898\pi$
$30$	−4.94306	−0.902476
$31$	−2.70893	−0.486539	−0.243269	−	0.969959i	$-0.578220\pi$
$31$	−2.70893	−0.486539	−0.243269	+	0.969959i	$0.578220\pi$
$32$	−8.08423	−1.42910
$33$	1.46076	0.254285
$34$	2.08696	0.357911
$35$	1.87372	0.316716
$36$	2.35542	0.392570
$37$	9.81484	1.61355	0.806775	−	0.590859i	$-0.201211\pi$
$37$	9.81484	1.61355	0.806775	+	0.590859i	$0.201211\pi$
$38$	−0.622065	−0.100912
$39$	−2.45845	−0.393667
$40$	−1.75686	−0.277784
$41$	−10.9098	−1.70383	−0.851914	−	0.523681i	$-0.824558\pi$
$41$	−10.9098	−1.70383	−0.851914	+	0.523681i	$0.824558\pi$
$42$	−1.65097	−0.254750
$43$	−1.38681	−0.211487	−0.105743	−	0.994393i	$-0.533722\pi$
$43$	−1.38681	−0.211487	−0.105743	+	0.994393i	$0.533722\pi$
$44$	3.44070	0.518705
$45$	−2.36854	−0.353082
$46$	−15.8934	−2.34335
$47$	−8.90941	−1.29957	−0.649786	−	0.760118i	$-0.725141\pi$
$47$	−8.90941	−1.29957	−0.649786	+	0.760118i	$0.725141\pi$
$48$	−3.16284	−0.456517
$49$	−6.37418	−0.910598
$50$	1.27304	0.180035
$51$	1.00000	0.140028
$52$	−5.79069	−0.803024
$53$	12.9131	1.77376	0.886878	−	0.462004i	$-0.152869\pi$
$53$	12.9131	1.77376	0.886878	+	0.462004i	$0.152869\pi$
$54$	2.08696	0.284000
$55$	−3.45987	−0.466529
$56$	−0.586784	−0.0784124
$57$	−0.298072	−0.0394806
$58$	−3.50914	−0.460772
$59$	−6.45957	−0.840965	−0.420482	−	0.907301i	$-0.638139\pi$
$59$	−6.45957	−0.840965	−0.420482	+	0.907301i	$0.638139\pi$
$60$	−5.57891	−0.720234
$61$	9.65516	1.23622	0.618109	−	0.786093i	$-0.287899\pi$
$61$	9.65516	1.23622	0.618109	+	0.786093i	$0.287899\pi$
$62$	−5.65345	−0.717988
$63$	−0.791085	−0.0996673
$64$	−10.5458	−1.31823
$65$	5.82295	0.722248
$66$	3.04855	0.375251
$67$	−0.660667	−0.0807134	−0.0403567	−	0.999185i	$-0.512849\pi$
$67$	−0.660667	−0.0807134	−0.0403567	+	0.999185i	$0.512849\pi$
$68$	2.35542	0.285636
$69$	−7.61554	−0.916803
$70$	3.91038	0.467380
$71$	−10.2409	−1.21537	−0.607686	−	0.794177i	$-0.707902\pi$
$71$	−10.2409	−1.21537	−0.607686	+	0.794177i	$0.707902\pi$
$72$	0.741746	0.0874157
$73$	−1.42377	−0.166639	−0.0833196	−	0.996523i	$-0.526552\pi$
$73$	−1.42377	−0.166639	−0.0833196	+	0.996523i	$0.526552\pi$
$74$	20.4832	2.38113
$75$	0.609997	0.0704364
$76$	−0.702084	−0.0805346
$77$	−1.15558	−0.131691
$78$	−5.13070	−0.580938
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	7.49132	0.837555
$81$	1.00000	0.111111
$82$	−22.7684	−2.51435
$83$	−2.22307	−0.244014	−0.122007	−	0.992529i	$-0.538933\pi$
$83$	−2.22307	−0.244014	−0.122007	+	0.992529i	$0.538933\pi$
$84$	−1.86334	−0.203307
$85$	−2.36854	−0.256905
$86$	−2.89422	−0.312092
$87$	−1.68146	−0.180271
$88$	1.08351	0.115503
$89$	−1.32988	−0.140967	−0.0704833	−	0.997513i	$-0.522454\pi$
$89$	−1.32988	−0.140967	−0.0704833	+	0.997513i	$0.522454\pi$
$90$	−4.94306	−0.521045
$91$	1.94484	0.203875
$92$	−17.9378	−1.87014
$93$	−2.70893	−0.280903
$94$	−18.5936	−1.91779
$95$	0.705996	0.0724337
$96$	−8.08423	−0.825093
$97$	−11.0879	−1.12581	−0.562904	−	0.826522i	$-0.690316\pi$
$97$	−11.0879	−1.12581	−0.562904	+	0.826522i	$0.690316\pi$
$98$	−13.3027	−1.34378
$99$	1.46076	0.146812
$100$	1.43680	0.143680
$101$	13.7425	1.36743	0.683714	−	0.729750i	$-0.260363\pi$
$101$	13.7425	1.36743	0.683714	+	0.729750i	$0.260363\pi$
$102$	2.08696	0.206640
$103$	−3.36521	−0.331584	−0.165792	−	0.986161i	$-0.553018\pi$
$103$	−3.36521	−0.331584	−0.165792	+	0.986161i	$0.553018\pi$
$104$	−1.82355	−0.178814
$105$	1.87372	0.182856
$106$	26.9492	2.61754
$107$	10.2101	0.987045	0.493522	−	0.869733i	$-0.335709\pi$
$107$	10.2101	0.987045	0.493522	+	0.869733i	$0.335709\pi$
$108$	2.35542	0.226650
$109$	−6.12985	−0.587133	−0.293566	−	0.955939i	$-0.594842\pi$
$109$	−6.12985	−0.587133	−0.293566	+	0.955939i	$0.594842\pi$
$110$	−7.22062	−0.688459
$111$	9.81484	0.931583
$112$	2.50207	0.236424
$113$	−2.43974	−0.229511	−0.114756	−	0.993394i	$-0.536608\pi$
$113$	−2.43974	−0.229511	−0.114756	+	0.993394i	$0.536608\pi$
$114$	−0.622065	−0.0582618
$115$	18.0377	1.68203
$116$	−3.96053	−0.367726
$117$	−2.45845	−0.227284
$118$	−13.4809	−1.24102
$119$	−0.791085	−0.0725186
$120$	−1.75686	−0.160379
$121$	−8.86619	−0.806017
$122$	20.1500	1.82429
$123$	−10.9098	−0.983706
$124$	−6.38067	−0.573001
$125$	10.3979	0.930018
$126$	−1.65097	−0.147080
$127$	0.196448	0.0174319	0.00871596	−	0.999962i	$-0.497226\pi$
$127$	0.196448	0.0174319	0.00871596	+	0.999962i	$0.497226\pi$
$128$	−5.84027	−0.516212
$129$	−1.38681	−0.122102
$130$	12.1523	1.06583
$131$	−6.55286	−0.572526	−0.286263	−	0.958151i	$-0.592413\pi$
$131$	−6.55286	−0.572526	−0.286263	+	0.958151i	$0.592413\pi$
$132$	3.44070	0.299474
$133$	0.235800	0.0204465
$134$	−1.37879	−0.119109
$135$	−2.36854	−0.203852
$136$	0.741746	0.0636042
$137$	13.8136	1.18017	0.590087	−	0.807339i	$-0.299093\pi$
$137$	13.8136	1.18017	0.590087	+	0.807339i	$0.299093\pi$
$138$	−15.8934	−1.35293
$139$	−14.8602	−1.26043	−0.630214	−	0.776421i	$-0.717033\pi$
$139$	−14.8602	−1.26043	−0.630214	+	0.776421i	$0.717033\pi$
$140$	4.41339	0.373000
$141$	−8.90941	−0.750308
$142$	−21.3724	−1.79353
$143$	−3.59120	−0.300312
$144$	−3.16284	−0.263570
$145$	3.98260	0.330737
$146$	−2.97135	−0.245911
$147$	−6.37418	−0.525734
$148$	23.1181	1.90029
$149$	2.65233	0.217287	0.108644	−	0.994081i	$-0.465349\pi$
$149$	2.65233	0.217287	0.108644	+	0.994081i	$0.465349\pi$
$150$	1.27304	0.103943
$151$	23.7813	1.93530	0.967649	−	0.252302i	$-0.0811875\pi$
$151$	23.7813	1.93530	0.967649	+	0.252302i	$0.0811875\pi$
$152$	−0.221094	−0.0179331
$153$	1.00000	0.0808452
$154$	−2.41166	−0.194337
$155$	6.41623	0.515364
$156$	−5.79069	−0.463626
$157$	14.5361	1.16010	0.580052	−	0.814580i	$-0.303032\pi$
$157$	14.5361	1.16010	0.580052	+	0.814580i	$0.303032\pi$
$158$	−2.08696	−0.166030
$159$	12.9131	1.02408
$160$	19.1478	1.51377
$161$	6.02454	0.474800
$162$	2.08696	0.163967
$163$	−14.3495	−1.12394	−0.561969	−	0.827158i	$-0.689956\pi$
$163$	−14.3495	−1.12394	−0.561969	+	0.827158i	$0.689956\pi$
$164$	−25.6972	−2.00661
$165$	−3.45987	−0.269350
$166$	−4.63947	−0.360092
$167$	−15.5112	−1.20029	−0.600147	−	0.799889i	$-0.704891\pi$
$167$	−15.5112	−1.20029	−0.600147	+	0.799889i	$0.704891\pi$
$168$	−0.586784	−0.0452714
$169$	−6.95601	−0.535078
$170$	−4.94306	−0.379116
$171$	−0.298072	−0.0227941
$172$	−3.26652	−0.249070
$173$	−4.04609	−0.307619	−0.153809	−	0.988101i	$-0.549154\pi$
$173$	−4.04609	−0.307619	−0.153809	+	0.988101i	$0.549154\pi$
$174$	−3.50914	−0.266027
$175$	−0.482559	−0.0364781
$176$	−4.62014	−0.348256
$177$	−6.45957	−0.485531
$178$	−2.77540	−0.208025
$179$	5.20936	0.389366	0.194683	−	0.980866i	$-0.437632\pi$
$179$	5.20936	0.389366	0.194683	+	0.980866i	$0.437632\pi$
$180$	−5.57891	−0.415828
$181$	−13.9513	−1.03700	−0.518498	−	0.855079i	$-0.673509\pi$
$181$	−13.9513	−1.03700	−0.518498	+	0.855079i	$0.673509\pi$
$182$	4.05882	0.300860
$183$	9.65516	0.713730
$184$	−5.64880	−0.416435
$185$	−23.2469	−1.70914
$186$	−5.65345	−0.414531
$187$	1.46076	0.106821
$188$	−20.9854	−1.53052
$189$	−0.791085	−0.0575430
$190$	1.47339	0.106891
$191$	−20.8723	−1.51027	−0.755134	−	0.655570i	$-0.772428\pi$
$191$	−20.8723	−1.51027	−0.755134	+	0.655570i	$0.772428\pi$
$192$	−10.5458	−0.761078
$193$	19.3118	1.39010	0.695048	−	0.718963i	$-0.255383\pi$
$193$	19.3118	1.39010	0.695048	+	0.718963i	$0.255383\pi$
$194$	−23.1401	−1.66136
$195$	5.82295	0.416990
$196$	−15.0139	−1.07242
$197$	8.13386	0.579513	0.289757	−	0.957100i	$-0.406426\pi$
$197$	8.13386	0.579513	0.289757	+	0.957100i	$0.406426\pi$
$198$	3.04855	0.216651
$199$	23.3191	1.65305	0.826523	−	0.562903i	$-0.190315\pi$
$199$	23.3191	1.65305	0.826523	+	0.562903i	$0.190315\pi$
$200$	0.452463	0.0319940
$201$	−0.660667	−0.0465999
$202$	28.6801	2.01792
$203$	1.33017	0.0933599
$204$	2.35542	0.164912
$205$	25.8404	1.80477
$206$	−7.02306	−0.489320
$207$	−7.61554	−0.529316
$208$	7.77569	0.539147
$209$	−0.435411	−0.0301180
$210$	3.91038	0.269842
$211$	−3.56505	−0.245428	−0.122714	−	0.992442i	$-0.539160\pi$
$211$	−3.56505	−0.245428	−0.122714	+	0.992442i	$0.539160\pi$
$212$	30.4158	2.08897
$213$	−10.2409	−0.701696
$214$	21.3081	1.45659
$215$	3.28472	0.224016
$216$	0.741746	0.0504695
$217$	2.14300	0.145476
$218$	−12.7928	−0.866436
$219$	−1.42377	−0.0962092
$220$	−8.14944	−0.549435
$221$	−2.45845	−0.165373
$222$	20.4832	1.37474
$223$	−22.9128	−1.53435	−0.767177	−	0.641436i	$-0.778339\pi$
$223$	−22.9128	−1.53435	−0.767177	+	0.641436i	$0.778339\pi$
$224$	6.39531	0.427305
$225$	0.609997	0.0406665
$226$	−5.09164	−0.338691
$227$	9.04208	0.600144	0.300072	−	0.953917i	$-0.402989\pi$
$227$	9.04208	0.600144	0.300072	+	0.953917i	$0.402989\pi$
$228$	−0.702084	−0.0464967
$229$	16.6133	1.09784	0.548920	−	0.835875i	$-0.315039\pi$
$229$	16.6133	1.09784	0.548920	+	0.835875i	$0.315039\pi$
$230$	37.6441	2.48218
$231$	−1.15558	−0.0760318
$232$	−1.24721	−0.0818836
$233$	−25.6933	−1.68323	−0.841614	−	0.540080i	$-0.818394\pi$
$233$	−25.6933	−1.68323	−0.841614	+	0.540080i	$0.818394\pi$
$234$	−5.13070	−0.335404
$235$	21.1023	1.37656
$236$	−15.2150	−0.990412
$237$	−1.00000	−0.0649570
$238$	−1.65097	−0.107016
$239$	27.1545	1.75648	0.878238	−	0.478224i	$-0.158719\pi$
$239$	27.1545	1.75648	0.878238	+	0.478224i	$0.158719\pi$
$240$	7.49132	0.483563
$241$	15.6756	1.00975	0.504876	−	0.863192i	$-0.331538\pi$
$241$	15.6756	1.00975	0.504876	+	0.863192i	$0.331538\pi$
$242$	−18.5034	−1.18944
$243$	1.00000	0.0641500
$244$	22.7420	1.45590
$245$	15.0975	0.964546
$246$	−22.7684	−1.45166
$247$	0.732796	0.0466267
$248$	−2.00934	−0.127593
$249$	−2.22307	−0.140881
$250$	21.7001	1.37243
$251$	25.0120	1.57874	0.789372	−	0.613915i	$-0.210406\pi$
$251$	25.0120	1.57874	0.789372	+	0.613915i	$0.210406\pi$
$252$	−1.86334	−0.117379
$253$	−11.1245	−0.699389
$254$	0.409980	0.0257244
$255$	−2.36854	−0.148324
$256$	8.90318	0.556449
$257$	−9.15047	−0.570791	−0.285395	−	0.958410i	$-0.592125\pi$
$257$	−9.15047	−0.570791	−0.285395	+	0.958410i	$0.592125\pi$
$258$	−2.89422	−0.180187
$259$	−7.76437	−0.482455
$260$	13.7155	0.850598
$261$	−1.68146	−0.104080
$262$	−13.6756	−0.844881
$263$	−24.8460	−1.53207	−0.766036	−	0.642797i	$-0.777774\pi$
$263$	−24.8460	−1.53207	−0.766036	+	0.642797i	$0.777774\pi$
$264$	1.08351	0.0666856
$265$	−30.5853	−1.87884
$266$	0.492107	0.0301730
$267$	−1.32988	−0.0813871
$268$	−1.55615	−0.0950569
$269$	−5.17985	−0.315821	−0.157911	−	0.987453i	$-0.550476\pi$
$269$	−5.17985	−0.315821	−0.157911	+	0.987453i	$0.550476\pi$
$270$	−4.94306	−0.300825
$271$	16.1115	0.978702	0.489351	−	0.872087i	$-0.337234\pi$
$271$	16.1115	0.978702	0.489351	+	0.872087i	$0.337234\pi$
$272$	−3.16284	−0.191775
$273$	1.94484	0.117707
$274$	28.8285	1.74159
$275$	0.891058	0.0537328
$276$	−17.9378	−1.07973
$277$	17.2264	1.03504	0.517518	−	0.855672i	$-0.326856\pi$
$277$	17.2264	1.03504	0.517518	+	0.855672i	$0.326856\pi$
$278$	−31.0128	−1.86002
$279$	−2.70893	−0.162180
$280$	1.38982	0.0830579
$281$	2.86238	0.170755	0.0853775	−	0.996349i	$-0.472790\pi$
$281$	2.86238	0.170755	0.0853775	+	0.996349i	$0.472790\pi$
$282$	−18.5936	−1.10723
$283$	−25.6633	−1.52553	−0.762763	−	0.646678i	$-0.776158\pi$
$283$	−25.6633	−1.52553	−0.762763	+	0.646678i	$0.776158\pi$
$284$	−24.1216	−1.43136
$285$	0.705996	0.0418196
$286$	−7.49471	−0.443172
$287$	8.63060	0.509448
$288$	−8.08423	−0.476368
$289$	1.00000	0.0588235
$290$	8.31155	0.488071
$291$	−11.0879	−0.649985
$292$	−3.35357	−0.196253
$293$	−1.91018	−0.111594	−0.0557970	−	0.998442i	$-0.517770\pi$
$293$	−1.91018	−0.111594	−0.0557970	+	0.998442i	$0.517770\pi$
$294$	−13.3027	−0.775829
$295$	15.2998	0.890788
$296$	7.28012	0.423149
$297$	1.46076	0.0847618
$298$	5.53532	0.320652
$299$	18.7224	1.08275
$300$	1.43680	0.0829536
$301$	1.09709	0.0632349
$302$	49.6308	2.85593
$303$	13.7425	0.789485
$304$	0.942754	0.0540706
$305$	−22.8687	−1.30946
$306$	2.08696	0.119304
$307$	13.1981	0.753256	0.376628	−	0.926365i	$-0.377083\pi$
$307$	13.1981	0.753256	0.376628	+	0.926365i	$0.377083\pi$
$308$	−2.72188	−0.155094
$309$	−3.36521	−0.191440
$310$	13.3904	0.760525
$311$	10.7003	0.606756	0.303378	−	0.952870i	$-0.401885\pi$
$311$	10.7003	0.606756	0.303378	+	0.952870i	$0.401885\pi$
$312$	−1.82355	−0.103238
$313$	−13.6346	−0.770670	−0.385335	−	0.922777i	$-0.625914\pi$
$313$	−13.6346	−0.770670	−0.385335	+	0.922777i	$0.625914\pi$
$314$	30.3362	1.71197
$315$	1.87372	0.105572
$316$	−2.35542	−0.132503
$317$	−11.8711	−0.666745	−0.333373	−	0.942795i	$-0.608187\pi$
$317$	−11.8711	−0.666745	−0.333373	+	0.942795i	$0.608187\pi$
$318$	26.9492	1.51124
$319$	−2.45620	−0.137521
$320$	24.9782	1.39632
$321$	10.2101	0.569871
$322$	12.5730	0.700665
$323$	−0.298072	−0.0165852
$324$	2.35542	0.130857
$325$	−1.49965	−0.0831855
$326$	−29.9469	−1.65860
$327$	−6.12985	−0.338981
$328$	−8.09232	−0.446824
$329$	7.04810	0.388574
$330$	−7.22062	−0.397482
$331$	32.1386	1.76650	0.883249	−	0.468903i	$-0.155351\pi$
$331$	32.1386	1.76650	0.883249	+	0.468903i	$0.155351\pi$
$332$	−5.23626	−0.287377
$333$	9.81484	0.537850
$334$	−32.3714	−1.77128
$335$	1.56482	0.0854952
$336$	2.50207	0.136499
$337$	−14.4545	−0.787388	−0.393694	−	0.919242i	$-0.628803\pi$
$337$	−14.4545	−0.787388	−0.393694	+	0.919242i	$0.628803\pi$
$338$	−14.5169	−0.789618
$339$	−2.43974	−0.132508
$340$	−5.57891	−0.302559
$341$	−3.95710	−0.214289
$342$	−0.622065	−0.0336374
$343$	10.5801	0.571273
$344$	−1.02866	−0.0554617
$345$	18.0377	0.971119
$346$	−8.44405	−0.453955
$347$	0.484183	0.0259923	0.0129962	−	0.999916i	$-0.495863\pi$
$347$	0.484183	0.0259923	0.0129962	+	0.999916i	$0.495863\pi$
$348$	−3.96053	−0.212307
$349$	35.5831	1.90472	0.952361	−	0.304973i	$-0.0986473\pi$
$349$	35.5831	1.90472	0.952361	+	0.304973i	$0.0986473\pi$
$350$	−1.00708	−0.0538309
$351$	−2.45845	−0.131222
$352$	−11.8091	−0.629427
$353$	−29.9196	−1.59246	−0.796230	−	0.604994i	$-0.793176\pi$
$353$	−29.9196	−1.59246	−0.796230	+	0.604994i	$0.793176\pi$
$354$	−13.4809	−0.716502
$355$	24.2560	1.28738
$356$	−3.13241	−0.166018
$357$	−0.791085	−0.0418687
$358$	10.8717	0.574590
$359$	1.68323	0.0888377	0.0444188	−	0.999013i	$-0.485856\pi$
$359$	1.68323	0.0888377	0.0444188	+	0.999013i	$0.485856\pi$
$360$	−1.75686	−0.0925946
$361$	−18.9112	−0.995324
$362$	−29.1160	−1.53030
$363$	−8.86619	−0.465354
$364$	4.58092	0.240106
$365$	3.37225	0.176512
$366$	20.1500	1.05326
$367$	−19.5619	−1.02112	−0.510560	−	0.859842i	$-0.670562\pi$
$367$	−19.5619	−1.02112	−0.510560	+	0.859842i	$0.670562\pi$
$368$	24.0867	1.25561
$369$	−10.9098	−0.567943
$370$	−48.5154	−2.52219
$371$	−10.2154	−0.530356
$372$	−6.38067	−0.330822
$373$	35.3825	1.83204	0.916019	−	0.401134i	$-0.131384\pi$
$373$	35.3825	1.83204	0.916019	+	0.401134i	$0.131384\pi$
$374$	3.04855	0.157637
$375$	10.3979	0.536946
$376$	−6.60852	−0.340809
$377$	4.13378	0.212901
$378$	−1.65097	−0.0849165
$379$	−9.40672	−0.483191	−0.241595	−	0.970377i	$-0.577671\pi$
$379$	−9.40672	−0.483191	−0.241595	+	0.970377i	$0.577671\pi$
$380$	1.66292	0.0853058
$381$	0.196448	0.0100643
$382$	−43.5598	−2.22871
$383$	−8.08970	−0.413364	−0.206682	−	0.978408i	$-0.566267\pi$
$383$	−8.08970	−0.413364	−0.206682	+	0.978408i	$0.566267\pi$
$384$	−5.84027	−0.298035
$385$	2.73705	0.139493
$386$	40.3031	2.05137
$387$	−1.38681	−0.0704956
$388$	−26.1167	−1.32587
$389$	−14.1492	−0.717392	−0.358696	−	0.933454i	$-0.616779\pi$
$389$	−14.1492	−0.717392	−0.358696	+	0.933454i	$0.616779\pi$
$390$	12.1523	0.615355
$391$	−7.61554	−0.385134
$392$	−4.72803	−0.238802
$393$	−6.55286	−0.330548
$394$	16.9751	0.855192
$395$	2.36854	0.119174
$396$	3.44070	0.172902
$397$	31.1667	1.56421	0.782105	−	0.623147i	$-0.214146\pi$
$397$	31.1667	1.56421	0.782105	+	0.623147i	$0.214146\pi$
$398$	48.6661	2.43941
$399$	0.235800	0.0118048
$400$	−1.92932	−0.0964661
$401$	−12.1169	−0.605088	−0.302544	−	0.953135i	$-0.597836\pi$
$401$	−12.1169	−0.605088	−0.302544	+	0.953135i	$0.597836\pi$
$402$	−1.37879	−0.0687678
$403$	6.65978	0.331747
$404$	32.3693	1.61043
$405$	−2.36854	−0.117694
$406$	2.77603	0.137772
$407$	14.3371	0.710664
$408$	0.741746	0.0367219
$409$	28.4820	1.40834	0.704172	−	0.710030i	$-0.251319\pi$
$409$	28.4820	1.40834	0.704172	+	0.710030i	$0.251319\pi$
$410$	53.9280	2.66331
$411$	13.8136	0.681374
$412$	−7.92647	−0.390509
$413$	5.11007	0.251450
$414$	−15.8934	−0.781116
$415$	5.26544	0.258470
$416$	19.8747	0.974437
$417$	−14.8602	−0.727709
$418$	−0.908687	−0.0444453
$419$	12.4786	0.609621	0.304811	−	0.952413i	$-0.401407\pi$
$419$	12.4786	0.609621	0.304811	+	0.952413i	$0.401407\pi$
$420$	4.41339	0.215351
$421$	−24.2274	−1.18077	−0.590386	−	0.807121i	$-0.701025\pi$
$421$	−24.2274	−1.18077	−0.590386	+	0.807121i	$0.701025\pi$
$422$	−7.44013	−0.362180
$423$	−8.90941	−0.433190
$424$	9.57827	0.465162
$425$	0.609997	0.0295892
$426$	−21.3724	−1.03550
$427$	−7.63805	−0.369631
$428$	24.0490	1.16245
$429$	−3.59120	−0.173385
$430$	6.85510	0.330582
$431$	28.1161	1.35431	0.677153	−	0.735842i	$-0.263214\pi$
$431$	28.1161	1.35431	0.677153	+	0.735842i	$0.263214\pi$
$432$	−3.16284	−0.152172
$433$	15.8127	0.759908	0.379954	−	0.925005i	$-0.375940\pi$
$433$	15.8127	0.759908	0.379954	+	0.925005i	$0.375940\pi$
$434$	4.47236	0.214680
$435$	3.98260	0.190951
$436$	−14.4384	−0.691472
$437$	2.26998	0.108588
$438$	−2.97135	−0.141977
$439$	−4.38559	−0.209313	−0.104656	−	0.994508i	$-0.533374\pi$
$439$	−4.38559	−0.209313	−0.104656	+	0.994508i	$0.533374\pi$
$440$	−2.56635	−0.122346
$441$	−6.37418	−0.303533
$442$	−5.13070	−0.244043
$443$	20.7058	0.983763	0.491882	−	0.870662i	$-0.336309\pi$
$443$	20.7058	0.983763	0.491882	+	0.870662i	$0.336309\pi$
$444$	23.1181	1.09713
$445$	3.14987	0.149318
$446$	−47.8181	−2.26425
$447$	2.65233	0.125451
$448$	8.34263	0.394152
$449$	−17.3384	−0.818250	−0.409125	−	0.912478i	$-0.634166\pi$
$449$	−17.3384	−0.818250	−0.409125	+	0.912478i	$0.634166\pi$
$450$	1.27304	0.0600117
$451$	−15.9366	−0.750426
$452$	−5.74660	−0.270297
$453$	23.7813	1.11734
$454$	18.8705	0.885636
$455$	−4.60645	−0.215954
$456$	−0.221094	−0.0103537
$457$	2.98020	0.139408	0.0697039	−	0.997568i	$-0.477795\pi$
$457$	2.98020	0.139408	0.0697039	+	0.997568i	$0.477795\pi$
$458$	34.6715	1.62009
$459$	1.00000	0.0466760
$460$	42.4864	1.98094
$461$	−19.4767	−0.907122	−0.453561	−	0.891225i	$-0.649847\pi$
$461$	−19.4767	−0.907122	−0.453561	+	0.891225i	$0.649847\pi$
$462$	−2.41166	−0.112201
$463$	21.3500	0.992218	0.496109	−	0.868260i	$-0.334762\pi$
$463$	21.3500	0.992218	0.496109	+	0.868260i	$0.334762\pi$
$464$	5.31818	0.246890
$465$	6.41623	0.297545
$466$	−53.6211	−2.48395
$467$	13.3921	0.619712	0.309856	−	0.950784i	$-0.399719\pi$
$467$	13.3921	0.619712	0.309856	+	0.950784i	$0.399719\pi$
$468$	−5.79069	−0.267675
$469$	0.522644	0.0241335
$470$	44.0398	2.03140
$471$	14.5361	0.669786
$472$	−4.79137	−0.220541
$473$	−2.02580	−0.0931462
$474$	−2.08696	−0.0958574
$475$	−0.181823	−0.00834261
$476$	−1.86334	−0.0854059
$477$	12.9131	0.591252
$478$	56.6704	2.59204
$479$	−11.2840	−0.515580	−0.257790	−	0.966201i	$-0.582994\pi$
$479$	−11.2840	−0.515580	−0.257790	+	0.966201i	$0.582994\pi$
$480$	19.1478	0.873975
$481$	−24.1293	−1.10020
$482$	32.7143	1.49010
$483$	6.02454	0.274126
$484$	−20.8836	−0.949254
$485$	26.2622	1.19251
$486$	2.08696	0.0946666
$487$	−9.23745	−0.418589	−0.209294	−	0.977853i	$-0.567117\pi$
$487$	−9.23745	−0.418589	−0.209294	+	0.977853i	$0.567117\pi$
$488$	7.16168	0.324194
$489$	−14.3495	−0.648906
$490$	31.5080	1.42339
$491$	−22.9558	−1.03598	−0.517989	−	0.855387i	$-0.673319\pi$
$491$	−22.9558	−1.03598	−0.517989	+	0.855387i	$0.673319\pi$
$492$	−25.6972	−1.15852
$493$	−1.68146	−0.0757290
$494$	1.52932	0.0688073
$495$	−3.45987	−0.155510
$496$	8.56792	0.384711
$497$	8.10143	0.363399
$498$	−4.63947	−0.207899
$499$	−17.2191	−0.770834	−0.385417	−	0.922743i	$-0.625942\pi$
$499$	−17.2191	−0.770834	−0.385417	+	0.922743i	$0.625942\pi$
$500$	24.4914	1.09529
$501$	−15.5112	−0.692991
$502$	52.1992	2.32976
$503$	0.674712	0.0300839	0.0150420	−	0.999887i	$-0.495212\pi$
$503$	0.674712	0.0300839	0.0150420	+	0.999887i	$0.495212\pi$
$504$	−0.586784	−0.0261375
$505$	−32.5497	−1.44844
$506$	−23.2163	−1.03209
$507$	−6.95601	−0.308927
$508$	0.462717	0.0205297
$509$	−42.9309	−1.90288	−0.951439	−	0.307836i	$-0.900395\pi$
$509$	−42.9309	−1.90288	−0.951439	+	0.307836i	$0.900395\pi$
$510$	−4.94306	−0.218883
$511$	1.12632	0.0498255
$512$	30.2612	1.33737
$513$	−0.298072	−0.0131602
$514$	−19.0967	−0.842320
$515$	7.97063	0.351228
$516$	−3.26652	−0.143801
$517$	−13.0145	−0.572377
$518$	−16.2040	−0.711961
$519$	−4.04609	−0.177604
$520$	4.31915	0.189407
$521$	1.95565	0.0856787	0.0428394	−	0.999082i	$-0.486360\pi$
$521$	1.95565	0.0856787	0.0428394	+	0.999082i	$0.486360\pi$
$522$	−3.50914	−0.153591
$523$	−15.5184	−0.678573	−0.339286	−	0.940683i	$-0.610186\pi$
$523$	−15.5184	−0.678573	−0.339286	+	0.940683i	$0.610186\pi$
$524$	−15.4347	−0.674269
$525$	−0.482559	−0.0210606
$526$	−51.8528	−2.26089
$527$	−2.70893	−0.118003
$528$	−4.62014	−0.201066
$529$	34.9964	1.52158
$530$	−63.8305	−2.77262
$531$	−6.45957	−0.280322
$532$	0.555408	0.0240800
$533$	26.8213	1.16176
$534$	−2.77540	−0.120103
$535$	−24.1830	−1.04552
$536$	−0.490048	−0.0211668
$537$	5.20936	0.224800
$538$	−10.8102	−0.466059
$539$	−9.31114	−0.401059
$540$	−5.57891	−0.240078
$541$	11.3788	0.489212	0.244606	−	0.969623i	$-0.421341\pi$
$541$	11.3788	0.489212	0.244606	+	0.969623i	$0.421341\pi$
$542$	33.6240	1.44428
$543$	−13.9513	−0.598710
$544$	−8.08423	−0.346608
$545$	14.5188	0.621917
$546$	4.05882	0.173701
$547$	−15.0424	−0.643169	−0.321584	−	0.946881i	$-0.604215\pi$
$547$	−15.0424	−0.643169	−0.321584	+	0.946881i	$0.604215\pi$
$548$	32.5368	1.38990
$549$	9.65516	0.412072
$550$	1.85961	0.0792939
$551$	0.501195	0.0213516
$552$	−5.64880	−0.240429
$553$	0.791085	0.0336403
$554$	35.9510	1.52741
$555$	−23.2469	−0.986775
$556$	−35.0021	−1.48442
$557$	17.0115	0.720802	0.360401	−	0.932797i	$-0.382640\pi$
$557$	17.0115	0.720802	0.360401	+	0.932797i	$0.382640\pi$
$558$	−5.65345	−0.239329
$559$	3.40941	0.144203
$560$	−5.92627	−0.250431
$561$	1.46076	0.0616733
$562$	5.97368	0.251984
$563$	−15.2990	−0.644778	−0.322389	−	0.946607i	$-0.604486\pi$
$563$	−15.2990	−0.644778	−0.322389	+	0.946607i	$0.604486\pi$
$564$	−20.9854	−0.883644
$565$	5.77862	0.243108
$566$	−53.5584	−2.25123
$567$	−0.791085	−0.0332224
$568$	−7.59616	−0.318728
$569$	−14.6202	−0.612910	−0.306455	−	0.951885i	$-0.599143\pi$
$569$	−14.6202	−0.612910	−0.306455	+	0.951885i	$0.599143\pi$
$570$	1.47339	0.0617135
$571$	−14.7159	−0.615840	−0.307920	−	0.951412i	$-0.599633\pi$
$571$	−14.7159	−0.615840	−0.307920	+	0.951412i	$0.599633\pi$
$572$	−8.45879	−0.353680
$573$	−20.8723	−0.871954
$574$	18.0117	0.751796
$575$	−4.64545	−0.193729
$576$	−10.5458	−0.439409
$577$	37.4608	1.55952	0.779758	−	0.626082i	$-0.215342\pi$
$577$	37.4608	1.55952	0.779758	+	0.626082i	$0.215342\pi$
$578$	2.08696	0.0868063
$579$	19.3118	0.802573
$580$	9.38069	0.389512
$581$	1.75864	0.0729605
$582$	−23.1401	−0.959188
$583$	18.8630	0.781224
$584$	−1.05607	−0.0437006
$585$	5.82295	0.240749
$586$	−3.98648	−0.164680
$587$	−16.8800	−0.696714	−0.348357	−	0.937362i	$-0.613260\pi$
$587$	−16.8800	−0.696714	−0.348357	+	0.937362i	$0.613260\pi$
$588$	−15.0139	−0.619162
$589$	0.807457	0.0332707
$590$	31.9301	1.31454
$591$	8.13386	0.334582
$592$	−31.0428	−1.27585
$593$	−27.9753	−1.14881	−0.574403	−	0.818573i	$-0.694766\pi$
$593$	−27.9753	−1.14881	−0.574403	+	0.818573i	$0.694766\pi$
$594$	3.04855	0.125084
$595$	1.87372	0.0768150
$596$	6.24735	0.255901
$597$	23.3191	0.954387
$598$	39.0730	1.59782
$599$	−28.4390	−1.16199	−0.580993	−	0.813909i	$-0.697336\pi$
$599$	−28.4390	−1.16199	−0.580993	+	0.813909i	$0.697336\pi$
$600$	0.452463	0.0184717
$601$	8.44692	0.344557	0.172279	−	0.985048i	$-0.444887\pi$
$601$	8.44692	0.344557	0.172279	+	0.985048i	$0.444887\pi$
$602$	2.28958	0.0933162
$603$	−0.660667	−0.0269045
$604$	56.0150	2.27922
$605$	20.9999	0.853769
$606$	28.6801	1.16505
$607$	−23.6580	−0.960248	−0.480124	−	0.877201i	$-0.659408\pi$
$607$	−23.6580	−0.960248	−0.480124	+	0.877201i	$0.659408\pi$
$608$	2.40968	0.0977255
$609$	1.33017	0.0539014
$610$	−47.7261	−1.93237
$611$	21.9034	0.886115
$612$	2.35542	0.0952122
$613$	−28.2776	−1.14212	−0.571061	−	0.820908i	$-0.693468\pi$
$613$	−28.2776	−1.14212	−0.571061	+	0.820908i	$0.693468\pi$
$614$	27.5440	1.11159
$615$	25.8404	1.04199
$616$	−0.857150	−0.0345356
$617$	−42.6145	−1.71559	−0.857797	−	0.513989i	$-0.828167\pi$
$617$	−42.6145	−1.71559	−0.857797	+	0.513989i	$0.828167\pi$
$618$	−7.02306	−0.282509
$619$	41.6717	1.67493	0.837463	−	0.546494i	$-0.184038\pi$
$619$	41.6717	1.67493	0.837463	+	0.546494i	$0.184038\pi$
$620$	15.1129	0.606949
$621$	−7.61554	−0.305601
$622$	22.3311	0.895394
$623$	1.05204	0.0421493
$624$	7.77569	0.311277
$625$	−27.6779	−1.10712
$626$	−28.4548	−1.13728
$627$	−0.435411	−0.0173886
$628$	34.2385	1.36626
$629$	9.81484	0.391343
$630$	3.91038	0.155793
$631$	36.2489	1.44305	0.721523	−	0.692391i	$-0.243443\pi$
$631$	36.2489	1.44305	0.721523	+	0.692391i	$0.243443\pi$
$632$	−0.741746	−0.0295051
$633$	−3.56505	−0.141698
$634$	−24.7745	−0.983920
$635$	−0.465295	−0.0184647
$636$	30.4158	1.20607
$637$	15.6706	0.620893
$638$	−5.12600	−0.202940
$639$	−10.2409	−0.405124
$640$	13.8329	0.546795
$641$	41.8329	1.65230	0.826151	−	0.563449i	$-0.190526\pi$
$641$	41.8329	1.65230	0.826151	+	0.563449i	$0.190526\pi$
$642$	21.3081	0.840962
$643$	−21.2290	−0.837190	−0.418595	−	0.908173i	$-0.637477\pi$
$643$	−21.2290	−0.837190	−0.418595	+	0.908173i	$0.637477\pi$
$644$	14.1903	0.559176
$645$	3.28472	0.129336
$646$	−0.622065	−0.0244748
$647$	−20.1428	−0.791896	−0.395948	−	0.918273i	$-0.629584\pi$
$647$	−20.1428	−0.791896	−0.395948	+	0.918273i	$0.629584\pi$
$648$	0.741746	0.0291386
$649$	−9.43588	−0.370391
$650$	−3.12971	−0.122757
$651$	2.14300	0.0839906
$652$	−33.7991	−1.32367
$653$	15.2392	0.596357	0.298179	−	0.954510i	$-0.403621\pi$
$653$	15.2392	0.596357	0.298179	+	0.954510i	$0.403621\pi$
$654$	−12.7928	−0.500237
$655$	15.5207	0.606445
$656$	34.5060	1.34723
$657$	−1.42377	−0.0555464
$658$	14.7091	0.573422
$659$	−11.1548	−0.434528	−0.217264	−	0.976113i	$-0.569713\pi$
$659$	−11.1548	−0.434528	−0.217264	+	0.976113i	$0.569713\pi$
$660$	−8.14944	−0.317217
$661$	15.8954	0.618261	0.309130	−	0.951020i	$-0.399962\pi$
$661$	15.8954	0.618261	0.309130	+	0.951020i	$0.399962\pi$
$662$	67.0722	2.60683
$663$	−2.45845	−0.0954784
$664$	−1.64895	−0.0639918
$665$	−0.558503	−0.0216578
$666$	20.4832	0.793709
$667$	12.8052	0.495819
$668$	−36.5354	−1.41360
$669$	−22.9128	−0.885859
$670$	3.26572	0.126166
$671$	14.1039	0.544473
$672$	6.39531	0.246704
$673$	−9.92443	−0.382559	−0.191279	−	0.981536i	$-0.561264\pi$
$673$	−9.92443	−0.382559	−0.191279	+	0.981536i	$0.561264\pi$
$674$	−30.1661	−1.16195
$675$	0.609997	0.0234788
$676$	−16.3843	−0.630166
$677$	−27.5371	−1.05834	−0.529168	−	0.848517i	$-0.677496\pi$
$677$	−27.5371	−1.05834	−0.529168	+	0.848517i	$0.677496\pi$
$678$	−5.09164	−0.195543
$679$	8.77149	0.336619
$680$	−1.75686	−0.0673724
$681$	9.04208	0.346493
$682$	−8.25832	−0.316227
$683$	7.47563	0.286047	0.143024	−	0.989719i	$-0.454318\pi$
$683$	7.47563	0.286047	0.143024	+	0.989719i	$0.454318\pi$
$684$	−0.702084	−0.0268449
$685$	−32.7181	−1.25009
$686$	22.0803	0.843031
$687$	16.6133	0.633839
$688$	4.38626	0.167225
$689$	−31.7463	−1.20944
$690$	37.6441	1.43309
$691$	−51.5024	−1.95924	−0.979622	−	0.200851i	$-0.935629\pi$
$691$	−51.5024	−1.95924	−0.979622	+	0.200851i	$0.935629\pi$
$692$	−9.53025	−0.362286
$693$	−1.15558	−0.0438970
$694$	1.01047	0.0383570
$695$	35.1971	1.33510
$696$	−1.24721	−0.0472755
$697$	−10.9098	−0.413239
$698$	74.2608	2.81081
$699$	−25.6933	−0.971812
$700$	−1.13663	−0.0429605
$701$	11.4859	0.433815	0.216907	−	0.976192i	$-0.430403\pi$
$701$	11.4859	0.433815	0.216907	+	0.976192i	$0.430403\pi$
$702$	−5.13070	−0.193646
$703$	−2.92553	−0.110338
$704$	−15.4049	−0.580593
$705$	21.1023	0.794759
$706$	−62.4412	−2.35000
$707$	−10.8715	−0.408864
$708$	−15.2150	−0.571815
$709$	−4.27749	−0.160645	−0.0803223	−	0.996769i	$-0.525595\pi$
$709$	−4.27749	−0.160645	−0.0803223	+	0.996769i	$0.525595\pi$
$710$	50.6215	1.89979
$711$	−1.00000	−0.0375029
$712$	−0.986430	−0.0369680
$713$	20.6300	0.772599
$714$	−1.65097	−0.0617858
$715$	8.50592	0.318103
$716$	12.2702	0.458560
$717$	27.1545	1.01410
$718$	3.51285	0.131098
$719$	28.1922	1.05139	0.525695	−	0.850673i	$-0.323805\pi$
$719$	28.1922	1.05139	0.525695	+	0.850673i	$0.323805\pi$
$720$	7.49132	0.279185
$721$	2.66216	0.0991441
$722$	−39.4669	−1.46881
$723$	15.6756	0.582980
$724$	−32.8613	−1.22128
$725$	−1.02568	−0.0380929
$726$	−18.5034	−0.686726
$727$	−27.7245	−1.02824	−0.514122	−	0.857717i	$-0.671882\pi$
$727$	−27.7245	−1.02824	−0.514122	+	0.857717i	$0.671882\pi$
$728$	1.44258	0.0534656
$729$	1.00000	0.0370370
$730$	7.03777	0.260480
$731$	−1.38681	−0.0512931
$732$	22.7420	0.840567
$733$	7.72906	0.285479	0.142740	−	0.989760i	$-0.454409\pi$
$733$	7.72906	0.285479	0.142740	+	0.989760i	$0.454409\pi$
$734$	−40.8249	−1.50687
$735$	15.0975	0.556881
$736$	61.5657	2.26934
$737$	−0.965075	−0.0355490
$738$	−22.7684	−0.838117
$739$	−36.6742	−1.34908	−0.674540	−	0.738238i	$-0.735658\pi$
$739$	−36.6742	−1.34908	−0.674540	+	0.738238i	$0.735658\pi$
$740$	−54.7561	−2.01288
$741$	0.732796	0.0269199
$742$	−21.3191	−0.782650
$743$	15.5789	0.571534	0.285767	−	0.958299i	$-0.407752\pi$
$743$	15.5789	0.571534	0.285767	+	0.958299i	$0.407752\pi$
$744$	−2.00934	−0.0736660
$745$	−6.28216	−0.230160
$746$	73.8421	2.70355
$747$	−2.22307	−0.0813378
$748$	3.44070	0.125804
$749$	−8.07703	−0.295128
$750$	21.7001	0.792374
$751$	−24.2110	−0.883474	−0.441737	−	0.897145i	$-0.645638\pi$
$751$	−24.2110	−0.883474	−0.441737	+	0.897145i	$0.645638\pi$
$752$	28.1790	1.02758
$753$	25.0120	0.911489
$754$	8.62705	0.314179
$755$	−56.3271	−2.04995
$756$	−1.86334	−0.0677689
$757$	14.9775	0.544365	0.272182	−	0.962246i	$-0.412255\pi$
$757$	14.9775	0.544365	0.272182	+	0.962246i	$0.412255\pi$
$758$	−19.6315	−0.713047
$759$	−11.1245	−0.403792
$760$	0.523670	0.0189955
$761$	−27.1665	−0.984784	−0.492392	−	0.870374i	$-0.663877\pi$
$761$	−27.1665	−0.984784	−0.492392	+	0.870374i	$0.663877\pi$
$762$	0.409980	0.0148520
$763$	4.84923	0.175554
$764$	−49.1631	−1.77866
$765$	−2.36854	−0.0856349
$766$	−16.8829	−0.610004
$767$	15.8806	0.573414
$768$	8.90318	0.321266
$769$	10.3161	0.372008	0.186004	−	0.982549i	$-0.440446\pi$
$769$	10.3161	0.372008	0.186004	+	0.982549i	$0.440446\pi$
$770$	5.71212	0.205851
$771$	−9.15047	−0.329546
$772$	45.4875	1.63713
$773$	−0.655461	−0.0235753	−0.0117876	−	0.999931i	$-0.503752\pi$
$773$	−0.655461	−0.0235753	−0.0117876	+	0.999931i	$0.503752\pi$
$774$	−2.89422	−0.104031
$775$	−1.65244	−0.0593574
$776$	−8.22443	−0.295240
$777$	−7.76437	−0.278545
$778$	−29.5288	−1.05866
$779$	3.25191	0.116512
$780$	13.7155	0.491093
$781$	−14.9595	−0.535293
$782$	−15.8934	−0.568345
$783$	−1.68146	−0.0600903
$784$	20.1605	0.720019
$785$	−34.4293	−1.22883
$786$	−13.6756	−0.487792
$787$	21.1081	0.752424	0.376212	−	0.926534i	$-0.377226\pi$
$787$	21.1081	0.752424	0.376212	+	0.926534i	$0.377226\pi$
$788$	19.1586	0.682498
$789$	−24.8460	−0.884543
$790$	4.94306	0.175866
$791$	1.93004	0.0686243
$792$	1.08351	0.0385009
$793$	−23.7368	−0.842917
$794$	65.0437	2.30831
$795$	−30.5853	−1.08475
$796$	54.9262	1.94681
$797$	−53.6510	−1.90042	−0.950208	−	0.311616i	$-0.899130\pi$
$797$	−53.6510	−1.90042	−0.950208	+	0.311616i	$0.899130\pi$
$798$	0.492107	0.0174204
$799$	−8.90941	−0.315192
$800$	−4.93135	−0.174350
$801$	−1.32988	−0.0469888
$802$	−25.2875	−0.892932
$803$	−2.07978	−0.0733938
$804$	−1.55615	−0.0548811
$805$	−14.2694	−0.502929
$806$	13.8987	0.489562
$807$	−5.17985	−0.182339
$808$	10.1934	0.358604
$809$	−18.0979	−0.636288	−0.318144	−	0.948042i	$-0.603060\pi$
$809$	−18.0979	−0.636288	−0.318144	+	0.948042i	$0.603060\pi$
$810$	−4.94306	−0.173682
$811$	−26.6849	−0.937033	−0.468517	−	0.883455i	$-0.655211\pi$
$811$	−26.6849	−0.937033	−0.468517	+	0.883455i	$0.655211\pi$
$812$	3.13312	0.109951
$813$	16.1115	0.565054
$814$	29.9210	1.04873
$815$	33.9874	1.19053
$816$	−3.16284	−0.110722
$817$	0.413369	0.0144620
$818$	59.4409	2.07830
$819$	1.94484	0.0679584
$820$	60.8649	2.12550
$821$	−34.4785	−1.20331	−0.601653	−	0.798757i	$-0.705491\pi$
$821$	−34.4785	−1.20331	−0.601653	+	0.798757i	$0.705491\pi$
$822$	28.8285	1.00551
$823$	1.97244	0.0687548	0.0343774	−	0.999409i	$-0.489055\pi$
$823$	1.97244	0.0687548	0.0343774	+	0.999409i	$0.489055\pi$
$824$	−2.49613	−0.0869568
$825$	0.891058	0.0310227
$826$	10.6645	0.371067
$827$	−53.9464	−1.87590	−0.937949	−	0.346772i	$-0.887278\pi$
$827$	−53.9464	−1.87590	−0.937949	+	0.346772i	$0.887278\pi$
$828$	−17.9378	−0.623381
$829$	−22.8291	−0.792887	−0.396443	−	0.918059i	$-0.629756\pi$
$829$	−22.8291	−0.792887	−0.396443	+	0.918059i	$0.629756\pi$
$830$	10.9888	0.381426
$831$	17.2264	0.597578
$832$	25.9264	0.898835
$833$	−6.37418	−0.220852
$834$	−31.0128	−1.07388
$835$	36.7390	1.27141
$836$	−1.02558	−0.0354703
$837$	−2.70893	−0.0936344
$838$	26.0425	0.899622
$839$	−14.7541	−0.509367	−0.254684	−	0.967024i	$-0.581971\pi$
$839$	−14.7541	−0.509367	−0.254684	+	0.967024i	$0.581971\pi$
$840$	1.38982	0.0479535
$841$	−26.1727	−0.902507
$842$	−50.5618	−1.74247
$843$	2.86238	0.0985855
$844$	−8.39719	−0.289043
$845$	16.4756	0.566778
$846$	−18.5936	−0.639262
$847$	7.01391	0.241001
$848$	−40.8422	−1.40253
$849$	−25.6633	−0.880763
$850$	1.27304	0.0436650
$851$	−74.7453	−2.56223
$852$	−24.1216	−0.826394
$853$	−37.7541	−1.29268	−0.646338	−	0.763051i	$-0.723700\pi$
$853$	−37.7541	−1.29268	−0.646338	+	0.763051i	$0.723700\pi$
$854$	−15.9403	−0.545467
$855$	0.705996	0.0241446
$856$	7.57328	0.258850
$857$	−55.8875	−1.90908	−0.954540	−	0.298083i	$-0.903653\pi$
$857$	−55.8875	−1.90908	−0.954540	+	0.298083i	$0.903653\pi$
$858$	−7.49471	−0.255865
$859$	−51.6721	−1.76303	−0.881515	−	0.472155i	$-0.843476\pi$
$859$	−51.6721	−1.76303	−0.881515	+	0.472155i	$0.843476\pi$
$860$	7.73690	0.263826
$861$	8.63060	0.294130
$862$	58.6773	1.99856
$863$	−19.9506	−0.679125	−0.339563	−	0.940583i	$-0.610279\pi$
$863$	−19.9506	−0.679125	−0.339563	+	0.940583i	$0.610279\pi$
$864$	−8.08423	−0.275031
$865$	9.58335	0.325844
$866$	33.0005	1.12140
$867$	1.00000	0.0339618
$868$	5.04765	0.171329
$869$	−1.46076	−0.0495528
$870$	8.31155	0.281788
$871$	1.62422	0.0550346
$872$	−4.54679	−0.153974
$873$	−11.0879	−0.375269
$874$	4.73736	0.160244
$875$	−8.22563	−0.278077
$876$	−3.35357	−0.113307
$877$	47.3994	1.60056	0.800282	−	0.599624i	$-0.204683\pi$
$877$	47.3994	1.60056	0.800282	+	0.599624i	$0.204683\pi$
$878$	−9.15256	−0.308884
$879$	−1.91018	−0.0644288
$880$	10.9430	0.368889
$881$	35.8102	1.20648	0.603238	−	0.797562i	$-0.293877\pi$
$881$	35.8102	1.20648	0.603238	+	0.797562i	$0.293877\pi$
$882$	−13.3027	−0.447925
$883$	−9.33694	−0.314213	−0.157107	−	0.987582i	$-0.550217\pi$
$883$	−9.33694	−0.314213	−0.157107	+	0.987582i	$0.550217\pi$
$884$	−5.79069	−0.194762
$885$	15.2998	0.514297
$886$	43.2123	1.45175
$887$	−19.8906	−0.667860	−0.333930	−	0.942598i	$-0.608375\pi$
$887$	−19.8906	−0.667860	−0.333930	+	0.942598i	$0.608375\pi$
$888$	7.28012	0.244305
$889$	−0.155407	−0.00521218
$890$	6.57366	0.220350
$891$	1.46076	0.0489372
$892$	−53.9692	−1.80702
$893$	2.65565	0.0888678
$894$	5.53532	0.185129
$895$	−12.3386	−0.412434
$896$	4.62015	0.154348
$897$	18.7224	0.625124
$898$	−36.1846	−1.20750
$899$	4.55495	0.151916
$900$	1.43680	0.0478933
$901$	12.9131	0.430199
$902$	−33.2591	−1.10741
$903$	1.09709	0.0365087
$904$	−1.80967	−0.0601886
$905$	33.0444	1.09843
$906$	49.6308	1.64887
$907$	30.4485	1.01103	0.505514	−	0.862819i	$-0.331303\pi$
$907$	30.4485	1.01103	0.505514	+	0.862819i	$0.331303\pi$
$908$	21.2979	0.706795
$909$	13.7425	0.455810
$910$	−9.61349	−0.318684
$911$	−1.61350	−0.0534576	−0.0267288	−	0.999643i	$-0.508509\pi$
$911$	−1.61350	−0.0534576	−0.0267288	+	0.999643i	$0.508509\pi$
$912$	0.942754	0.0312177
$913$	−3.24737	−0.107472
$914$	6.21957	0.205725
$915$	−22.8687	−0.756015
$916$	39.1314	1.29294
$917$	5.18387	0.171186
$918$	2.08696	0.0688801
$919$	50.3699	1.66155	0.830775	−	0.556608i	$-0.187898\pi$
$919$	50.3699	1.66155	0.830775	+	0.556608i	$0.187898\pi$
$920$	13.3794	0.441106
$921$	13.1981	0.434893
$922$	−40.6472	−1.33865
$923$	25.1768	0.828704
$924$	−2.72188	−0.0895434
$925$	5.98702	0.196852
$926$	44.5567	1.46422
$927$	−3.36521	−0.110528
$928$	13.5933	0.446221
$929$	−11.8461	−0.388659	−0.194330	−	0.980936i	$-0.562253\pi$
$929$	−11.8461	−0.388659	−0.194330	+	0.980936i	$0.562253\pi$
$930$	13.3904	0.439090
$931$	1.89997	0.0622689
$932$	−60.5186	−1.98235
$933$	10.7003	0.350311
$934$	27.9488	0.914512
$935$	−3.45987	−0.113150
$936$	−1.82355	−0.0596045
$937$	21.2198	0.693221	0.346610	−	0.938009i	$-0.387333\pi$
$937$	21.2198	0.693221	0.346610	+	0.938009i	$0.387333\pi$
$938$	1.09074	0.0356139
$939$	−13.6346	−0.444947
$940$	49.7048	1.62119
$941$	−48.8182	−1.59143	−0.795713	−	0.605673i	$-0.792904\pi$
$941$	−48.8182	−1.59143	−0.795713	+	0.605673i	$0.792904\pi$
$942$	30.3362	0.988408
$943$	83.0842	2.70559
$944$	20.4306	0.664959
$945$	1.87372	0.0609521
$946$	−4.22776	−0.137456
$947$	−19.3498	−0.628784	−0.314392	−	0.949293i	$-0.601801\pi$
$947$	−19.3498	−0.628784	−0.314392	+	0.949293i	$0.601801\pi$
$948$	−2.35542	−0.0765004
$949$	3.50026	0.113623
$950$	−0.379458	−0.0123112
$951$	−11.8711	−0.384945
$952$	−0.586784	−0.0190178
$953$	15.2455	0.493849	0.246924	−	0.969035i	$-0.420580\pi$
$953$	15.2455	0.493849	0.246924	+	0.969035i	$0.420580\pi$
$954$	26.9492	0.872514
$955$	49.4370	1.59974
$956$	63.9601	2.06862
$957$	−2.45620	−0.0793977
$958$	−23.5493	−0.760845
$959$	−10.9277	−0.352875
$960$	24.9782	0.806168
$961$	−23.6617	−0.763280
$962$	−50.3570	−1.62358
$963$	10.2101	0.329015
$964$	36.9225	1.18919
$965$	−45.7409	−1.47245
$966$	12.5730	0.404529
$967$	55.9781	1.80013	0.900067	−	0.435751i	$-0.143517\pi$
$967$	55.9781	1.80013	0.900067	+	0.435751i	$0.143517\pi$
$968$	−6.57646	−0.211375
$969$	−0.298072	−0.00957545
$970$	54.8083	1.75979
$971$	43.7254	1.40321	0.701607	−	0.712564i	$-0.252466\pi$
$971$	43.7254	1.40321	0.701607	+	0.712564i	$0.252466\pi$
$972$	2.35542	0.0755501
$973$	11.7557	0.376871
$974$	−19.2782	−0.617714
$975$	−1.49965	−0.0480272
$976$	−30.5377	−0.977489
$977$	48.0968	1.53875	0.769376	−	0.638796i	$-0.220567\pi$
$977$	48.0968	1.53875	0.769376	+	0.638796i	$0.220567\pi$
$978$	−29.9469	−0.957595
$979$	−1.94263	−0.0620866
$980$	35.5610	1.13595
$981$	−6.12985	−0.195711
$982$	−47.9078	−1.52880
$983$	−53.1953	−1.69667	−0.848334	−	0.529462i	$-0.822394\pi$
$983$	−53.1953	−1.69667	−0.848334	+	0.529462i	$0.822394\pi$
$984$	−8.09232	−0.257974
$985$	−19.2654	−0.613847
$986$	−3.50914	−0.111754
$987$	7.04810	0.224343
$988$	1.72604	0.0549127
$989$	10.5613	0.335830
$990$	−7.22062	−0.229486
$991$	−29.0263	−0.922051	−0.461026	−	0.887387i	$-0.652518\pi$
$991$	−29.0263	−0.922051	−0.461026	+	0.887387i	$0.652518\pi$
$992$	21.8996	0.695314
$993$	32.1386	1.01989
$994$	16.9074	0.536270
$995$	−55.2323	−1.75098
$996$	−5.23626	−0.165917
$997$	−34.6395	−1.09704	−0.548522	−	0.836136i	$-0.684809\pi$
$997$	−34.6395	−1.09704	−0.548522	+	0.836136i	$0.684809\pi$
$998$	−35.9357	−1.13752
$999$	9.81484	0.310528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.15	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.08696 q^{2} +1.00000 q^{3} +2.35542 q^{4} -2.36854 q^{5} +2.08696 q^{6} -0.791085 q^{7} +0.741746 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08696 q^{2} +1.00000 q^{3} +2.35542 q^{4} -2.36854 q^{5} +2.08696 q^{6} -0.791085 q^{7} +0.741746 q^{8} +1.00000 q^{9} -4.94306 q^{10} +1.46076 q^{11} +2.35542 q^{12} -2.45845 q^{13} -1.65097 q^{14} -2.36854 q^{15} -3.16284 q^{16} +1.00000 q^{17} +2.08696 q^{18} -0.298072 q^{19} -5.57891 q^{20} -0.791085 q^{21} +3.04855 q^{22} -7.61554 q^{23} +0.741746 q^{24} +0.609997 q^{25} -5.13070 q^{26} +1.00000 q^{27} -1.86334 q^{28} -1.68146 q^{29} -4.94306 q^{30} -2.70893 q^{31} -8.08423 q^{32} +1.46076 q^{33} +2.08696 q^{34} +1.87372 q^{35} +2.35542 q^{36} +9.81484 q^{37} -0.622065 q^{38} -2.45845 q^{39} -1.75686 q^{40} -10.9098 q^{41} -1.65097 q^{42} -1.38681 q^{43} +3.44070 q^{44} -2.36854 q^{45} -15.8934 q^{46} -8.90941 q^{47} -3.16284 q^{48} -6.37418 q^{49} +1.27304 q^{50} +1.00000 q^{51} -5.79069 q^{52} +12.9131 q^{53} +2.08696 q^{54} -3.45987 q^{55} -0.586784 q^{56} -0.298072 q^{57} -3.50914 q^{58} -6.45957 q^{59} -5.57891 q^{60} +9.65516 q^{61} -5.65345 q^{62} -0.791085 q^{63} -10.5458 q^{64} +5.82295 q^{65} +3.04855 q^{66} -0.660667 q^{67} +2.35542 q^{68} -7.61554 q^{69} +3.91038 q^{70} -10.2409 q^{71} +0.741746 q^{72} -1.42377 q^{73} +20.4832 q^{74} +0.609997 q^{75} -0.702084 q^{76} -1.15558 q^{77} -5.13070 q^{78} -1.00000 q^{79} +7.49132 q^{80} +1.00000 q^{81} -22.7684 q^{82} -2.22307 q^{83} -1.86334 q^{84} -2.36854 q^{85} -2.89422 q^{86} -1.68146 q^{87} +1.08351 q^{88} -1.32988 q^{89} -4.94306 q^{90} +1.94484 q^{91} -17.9378 q^{92} -2.70893 q^{93} -18.5936 q^{94} +0.705996 q^{95} -8.08423 q^{96} -11.0879 q^{97} -13.3027 q^{98} +1.46076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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