LMFDB - Embedded newform 4029.2.a.e.1.16

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			1.16
Root			$-2.08785$ 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)

$f(q)$	$=$	$q+2.08785 q^{2} +1.00000 q^{3} +2.35911 q^{4} -3.16874 q^{5} +2.08785 q^{6} +0.308283 q^{7} +0.749773 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08785 q^{2} +1.00000 q^{3} +2.35911 q^{4} -3.16874 q^{5} +2.08785 q^{6} +0.308283 q^{7} +0.749773 q^{8} +1.00000 q^{9} -6.61585 q^{10} -5.34687 q^{11} +2.35911 q^{12} +5.25507 q^{13} +0.643649 q^{14} -3.16874 q^{15} -3.15281 q^{16} +1.00000 q^{17} +2.08785 q^{18} +2.21970 q^{19} -7.47541 q^{20} +0.308283 q^{21} -11.1635 q^{22} -1.72891 q^{23} +0.749773 q^{24} +5.04091 q^{25} +10.9718 q^{26} +1.00000 q^{27} +0.727275 q^{28} -7.33038 q^{29} -6.61585 q^{30} -3.47175 q^{31} -8.08214 q^{32} -5.34687 q^{33} +2.08785 q^{34} -0.976869 q^{35} +2.35911 q^{36} -3.75602 q^{37} +4.63441 q^{38} +5.25507 q^{39} -2.37584 q^{40} -10.5468 q^{41} +0.643649 q^{42} -0.578184 q^{43} -12.6139 q^{44} -3.16874 q^{45} -3.60971 q^{46} +10.9600 q^{47} -3.15281 q^{48} -6.90496 q^{49} +10.5247 q^{50} +1.00000 q^{51} +12.3973 q^{52} -9.54427 q^{53} +2.08785 q^{54} +16.9429 q^{55} +0.231143 q^{56} +2.21970 q^{57} -15.3047 q^{58} -8.21340 q^{59} -7.47541 q^{60} -12.8474 q^{61} -7.24850 q^{62} +0.308283 q^{63} -10.5687 q^{64} -16.6519 q^{65} -11.1635 q^{66} -0.0935160 q^{67} +2.35911 q^{68} -1.72891 q^{69} -2.03956 q^{70} +2.20566 q^{71} +0.749773 q^{72} +7.90398 q^{73} -7.84200 q^{74} +5.04091 q^{75} +5.23653 q^{76} -1.64835 q^{77} +10.9718 q^{78} -1.00000 q^{79} +9.99044 q^{80} +1.00000 q^{81} -22.0202 q^{82} +10.1620 q^{83} +0.727275 q^{84} -3.16874 q^{85} -1.20716 q^{86} -7.33038 q^{87} -4.00894 q^{88} -9.77321 q^{89} -6.61585 q^{90} +1.62005 q^{91} -4.07870 q^{92} -3.47175 q^{93} +22.8828 q^{94} -7.03366 q^{95} -8.08214 q^{96} +8.88402 q^{97} -14.4165 q^{98} -5.34687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.08785	1.47633	0.738166	−	0.674619i	$-0.235692\pi$
$2$	2.08785	1.47633	0.738166	+	0.674619i	$0.235692\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.35911	1.17956
$5$	−3.16874	−1.41710	−0.708552	−	0.705659i	$-0.750651\pi$
$5$	−3.16874	−1.41710	−0.708552	+	0.705659i	$0.750651\pi$
$6$	2.08785	0.852361
$7$	0.308283	0.116520	0.0582601	−	0.998301i	$-0.481445\pi$
$7$	0.308283	0.116520	0.0582601	+	0.998301i	$0.481445\pi$
$8$	0.749773	0.265085
$9$	1.00000	0.333333
$10$	−6.61585	−2.09211
$11$	−5.34687	−1.61214	−0.806072	−	0.591818i	$-0.798410\pi$
$11$	−5.34687	−1.61214	−0.806072	+	0.591818i	$0.798410\pi$
$12$	2.35911	0.681017
$13$	5.25507	1.45749	0.728746	−	0.684784i	$-0.240103\pi$
$13$	5.25507	1.45749	0.728746	+	0.684784i	$0.240103\pi$
$14$	0.643649	0.172022
$15$	−3.16874	−0.818165
$16$	−3.15281	−0.788203
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.08785	0.492111
$19$	2.21970	0.509235	0.254617	−	0.967042i	$-0.418050\pi$
$19$	2.21970	0.509235	0.254617	+	0.967042i	$0.418050\pi$
$20$	−7.47541	−1.67155
$21$	0.308283	0.0672729
$22$	−11.1635	−2.38006
$23$	−1.72891	−0.360503	−0.180252	−	0.983621i	$-0.557691\pi$
$23$	−1.72891	−0.360503	−0.180252	+	0.983621i	$0.557691\pi$
$24$	0.749773	0.153047
$25$	5.04091	1.00818
$26$	10.9718	2.15174
$27$	1.00000	0.192450
$28$	0.727275	0.137442
$29$	−7.33038	−1.36122	−0.680608	−	0.732648i	$-0.738284\pi$
$29$	−7.33038	−1.36122	−0.680608	+	0.732648i	$0.738284\pi$
$30$	−6.61585	−1.20788
$31$	−3.47175	−0.623545	−0.311773	−	0.950157i	$-0.600923\pi$
$31$	−3.47175	−0.623545	−0.311773	+	0.950157i	$0.600923\pi$
$32$	−8.08214	−1.42873
$33$	−5.34687	−0.930771
$34$	2.08785	0.358063
$35$	−0.976869	−0.165121
$36$	2.35911	0.393185
$37$	−3.75602	−0.617486	−0.308743	−	0.951145i	$-0.599908\pi$
$37$	−3.75602	−0.617486	−0.308743	+	0.951145i	$0.599908\pi$
$38$	4.63441	0.751800
$39$	5.25507	0.841484
$40$	−2.37584	−0.375653
$41$	−10.5468	−1.64714	−0.823569	−	0.567216i	$-0.808020\pi$
$41$	−10.5468	−1.64714	−0.823569	+	0.567216i	$0.808020\pi$
$42$	0.643649	0.0993172
$43$	−0.578184	−0.0881723	−0.0440861	−	0.999028i	$-0.514038\pi$
$43$	−0.578184	−0.0881723	−0.0440861	+	0.999028i	$0.514038\pi$
$44$	−12.6139	−1.90161
$45$	−3.16874	−0.472368
$46$	−3.60971	−0.532223
$47$	10.9600	1.59868	0.799339	−	0.600880i	$-0.205183\pi$
$47$	10.9600	1.59868	0.799339	+	0.600880i	$0.205183\pi$
$48$	−3.15281	−0.455069
$49$	−6.90496	−0.986423
$50$	10.5247	1.48841
$51$	1.00000	0.140028
$52$	12.3973	1.71920
$53$	−9.54427	−1.31101	−0.655503	−	0.755192i	$-0.727544\pi$
$53$	−9.54427	−1.31101	−0.655503	+	0.755192i	$0.727544\pi$
$54$	2.08785	0.284120
$55$	16.9429	2.28457
$56$	0.231143	0.0308877
$57$	2.21970	0.294007
$58$	−15.3047	−2.00961
$59$	−8.21340	−1.06929	−0.534647	−	0.845076i	$-0.679555\pi$
$59$	−8.21340	−1.06929	−0.534647	+	0.845076i	$0.679555\pi$
$60$	−7.47541	−0.965072
$61$	−12.8474	−1.64495	−0.822473	−	0.568805i	$-0.807406\pi$
$61$	−12.8474	−1.64495	−0.822473	+	0.568805i	$0.807406\pi$
$62$	−7.24850	−0.920560
$63$	0.308283	0.0388400
$64$	−10.5687	−1.32108
$65$	−16.6519	−2.06542
$66$	−11.1635	−1.37413
$67$	−0.0935160	−0.0114248	−0.00571240	−	0.999984i	$-0.501818\pi$
$67$	−0.0935160	−0.0114248	−0.00571240	+	0.999984i	$0.501818\pi$
$68$	2.35911	0.286084
$69$	−1.72891	−0.208137
$70$	−2.03956	−0.243774
$71$	2.20566	0.261763	0.130882	−	0.991398i	$-0.458219\pi$
$71$	2.20566	0.261763	0.130882	+	0.991398i	$0.458219\pi$
$72$	0.749773	0.0883616
$73$	7.90398	0.925091	0.462545	−	0.886596i	$-0.346936\pi$
$73$	7.90398	0.925091	0.462545	+	0.886596i	$0.346936\pi$
$74$	−7.84200	−0.911614
$75$	5.04091	0.582074
$76$	5.23653	0.600671
$77$	−1.64835	−0.187847
$78$	10.9718	1.24231
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	9.99044	1.11697
$81$	1.00000	0.111111
$82$	−22.0202	−2.43172
$83$	10.1620	1.11542	0.557711	−	0.830035i	$-0.311680\pi$
$83$	10.1620	1.11542	0.557711	+	0.830035i	$0.311680\pi$
$84$	0.727275	0.0793522
$85$	−3.16874	−0.343698
$86$	−1.20716	−0.130172
$87$	−7.33038	−0.785899
$88$	−4.00894	−0.427355
$89$	−9.77321	−1.03596	−0.517979	−	0.855393i	$-0.673316\pi$
$89$	−9.77321	−1.03596	−0.517979	+	0.855393i	$0.673316\pi$
$90$	−6.61585	−0.697372
$91$	1.62005	0.169827
$92$	−4.07870	−0.425234
$93$	−3.47175	−0.360004
$94$	22.8828	2.36018
$95$	−7.03366	−0.721638
$96$	−8.08214	−0.824880
$97$	8.88402	0.902036	0.451018	−	0.892515i	$-0.351061\pi$
$97$	8.88402	0.902036	0.451018	+	0.892515i	$0.351061\pi$
$98$	−14.4165	−1.45629
$99$	−5.34687	−0.537381
$100$	11.8921	1.18921
$101$	5.36804	0.534140	0.267070	−	0.963677i	$-0.413945\pi$
$101$	5.36804	0.534140	0.267070	+	0.963677i	$0.413945\pi$
$102$	2.08785	0.206728
$103$	3.03724	0.299269	0.149634	−	0.988741i	$-0.452190\pi$
$103$	3.03724	0.299269	0.149634	+	0.988741i	$0.452190\pi$
$104$	3.94011	0.386359
$105$	−0.976869	−0.0953327
$106$	−19.9270	−1.93548
$107$	−0.132451	−0.0128045	−0.00640226	−	0.999980i	$-0.502038\pi$
$107$	−0.132451	−0.0128045	−0.00640226	+	0.999980i	$0.502038\pi$
$108$	2.35911	0.227006
$109$	−5.77497	−0.553141	−0.276571	−	0.960994i	$-0.589198\pi$
$109$	−5.77497	−0.553141	−0.276571	+	0.960994i	$0.589198\pi$
$110$	35.3741	3.37279
$111$	−3.75602	−0.356506
$112$	−0.971959	−0.0918415
$113$	−15.3154	−1.44075	−0.720373	−	0.693586i	$-0.756030\pi$
$113$	−15.3154	−1.44075	−0.720373	+	0.693586i	$0.756030\pi$
$114$	4.63441	0.434052
$115$	5.47848	0.510871
$116$	−17.2932	−1.60563
$117$	5.25507	0.485831
$118$	−17.1483	−1.57863
$119$	0.308283	0.0282603
$120$	−2.37584	−0.216883
$121$	17.5891	1.59901
$122$	−26.8235	−2.42849
$123$	−10.5468	−0.950976
$124$	−8.19026	−0.735507
$125$	−0.129624	−0.0115939
$126$	0.643649	0.0573408
$127$	−8.41023	−0.746287	−0.373143	−	0.927774i	$-0.621720\pi$
$127$	−8.41023	−0.746287	−0.373143	+	0.927774i	$0.621720\pi$
$128$	−5.90149	−0.521623
$129$	−0.578184	−0.0509063
$130$	−34.7667	−3.04924
$131$	13.4704	1.17691	0.588456	−	0.808529i	$-0.299736\pi$
$131$	13.4704	1.17691	0.588456	+	0.808529i	$0.299736\pi$
$132$	−12.6139	−1.09790
$133$	0.684298	0.0593361
$134$	−0.195247	−0.0168668
$135$	−3.16874	−0.272722
$136$	0.749773	0.0642925
$137$	−19.5101	−1.66686	−0.833429	−	0.552627i	$-0.813625\pi$
$137$	−19.5101	−1.66686	−0.833429	+	0.552627i	$0.813625\pi$
$138$	−3.60971	−0.307279
$139$	12.0358	1.02087	0.510433	−	0.859918i	$-0.329485\pi$
$139$	12.0358	1.02087	0.510433	+	0.859918i	$0.329485\pi$
$140$	−2.30455	−0.194770
$141$	10.9600	0.922998
$142$	4.60508	0.386450
$143$	−28.0982	−2.34969
$144$	−3.15281	−0.262734
$145$	23.2280	1.92898
$146$	16.5023	1.36574
$147$	−6.90496	−0.569512
$148$	−8.86088	−0.728360
$149$	13.1702	1.07895	0.539473	−	0.842003i	$-0.318623\pi$
$149$	13.1702	1.07895	0.539473	+	0.842003i	$0.318623\pi$
$150$	10.5247	0.859334
$151$	−5.27435	−0.429221	−0.214610	−	0.976700i	$-0.568848\pi$
$151$	−5.27435	−0.429221	−0.214610	+	0.976700i	$0.568848\pi$
$152$	1.66427	0.134990
$153$	1.00000	0.0808452
$154$	−3.44151	−0.277325
$155$	11.0011	0.883628
$156$	12.3973	0.992578
$157$	12.4585	0.994299	0.497149	−	0.867665i	$-0.334380\pi$
$157$	12.4585	0.994299	0.497149	+	0.867665i	$0.334380\pi$
$158$	−2.08785	−0.166100
$159$	−9.54427	−0.756910
$160$	25.6102	2.02466
$161$	−0.532995	−0.0420059
$162$	2.08785	0.164037
$163$	−13.9662	−1.09392	−0.546960	−	0.837158i	$-0.684215\pi$
$163$	−13.9662	−1.09392	−0.546960	+	0.837158i	$0.684215\pi$
$164$	−24.8812	−1.94289
$165$	16.9429	1.31900
$166$	21.2167	1.64673
$167$	−7.74870	−0.599613	−0.299806	−	0.954000i	$-0.596922\pi$
$167$	−7.74870	−0.599613	−0.299806	+	0.954000i	$0.596922\pi$
$168$	0.231143	0.0178330
$169$	14.6157	1.12429
$170$	−6.61585	−0.507412
$171$	2.21970	0.169745
$172$	−1.36400	−0.104004
$173$	3.43913	0.261472	0.130736	−	0.991417i	$-0.458266\pi$
$173$	3.43913	0.261472	0.130736	+	0.991417i	$0.458266\pi$
$174$	−15.3047	−1.16025
$175$	1.55403	0.117473
$176$	16.8577	1.27070
$177$	−8.21340	−0.617357
$178$	−20.4050	−1.52942
$179$	8.53108	0.637643	0.318821	−	0.947815i	$-0.396713\pi$
$179$	8.53108	0.637643	0.318821	+	0.947815i	$0.396713\pi$
$180$	−7.47541	−0.557184
$181$	7.48147	0.556093	0.278047	−	0.960568i	$-0.410313\pi$
$181$	7.48147	0.556093	0.278047	+	0.960568i	$0.410313\pi$
$182$	3.38242	0.250721
$183$	−12.8474	−0.949710
$184$	−1.29629	−0.0955640
$185$	11.9019	0.875041
$186$	−7.24850	−0.531486
$187$	−5.34687	−0.391002
$188$	25.8559	1.88573
$189$	0.308283	0.0224243
$190$	−14.6852	−1.06538
$191$	13.7737	0.996632	0.498316	−	0.866995i	$-0.333952\pi$
$191$	13.7737	0.996632	0.498316	+	0.866995i	$0.333952\pi$
$192$	−10.5687	−0.762728
$193$	−0.554452	−0.0399104	−0.0199552	−	0.999801i	$-0.506352\pi$
$193$	−0.554452	−0.0399104	−0.0199552	+	0.999801i	$0.506352\pi$
$194$	18.5485	1.33170
$195$	−16.6519	−1.19247
$196$	−16.2896	−1.16354
$197$	6.46919	0.460911	0.230455	−	0.973083i	$-0.425978\pi$
$197$	6.46919	0.460911	0.230455	+	0.973083i	$0.425978\pi$
$198$	−11.1635	−0.793353
$199$	6.95027	0.492692	0.246346	−	0.969182i	$-0.420770\pi$
$199$	6.95027	0.492692	0.246346	+	0.969182i	$0.420770\pi$
$200$	3.77954	0.267254
$201$	−0.0935160	−0.00659611
$202$	11.2077	0.788568
$203$	−2.25983	−0.158609
$204$	2.35911	0.165171
$205$	33.4202	2.33416
$206$	6.34131	0.441820
$207$	−1.72891	−0.120168
$208$	−16.5682	−1.14880
$209$	−11.8685	−0.820960
$210$	−2.03956	−0.140743
$211$	10.4063	0.716400	0.358200	−	0.933645i	$-0.383391\pi$
$211$	10.4063	0.716400	0.358200	+	0.933645i	$0.383391\pi$
$212$	−22.5160	−1.54641
$213$	2.20566	0.151129
$214$	−0.276538	−0.0189037
$215$	1.83212	0.124949
$216$	0.749773	0.0510156
$217$	−1.07028	−0.0726556
$218$	−12.0573	−0.816620
$219$	7.90398	0.534101
$220$	39.9701	2.69478
$221$	5.25507	0.353494
$222$	−7.84200	−0.526321
$223$	23.9069	1.60093	0.800464	−	0.599381i	$-0.204587\pi$
$223$	23.9069	1.60093	0.800464	+	0.599381i	$0.204587\pi$
$224$	−2.49159	−0.166476
$225$	5.04091	0.336060
$226$	−31.9761	−2.12702
$227$	−13.4343	−0.891665	−0.445833	−	0.895116i	$-0.647092\pi$
$227$	−13.4343	−0.891665	−0.445833	+	0.895116i	$0.647092\pi$
$228$	5.23653	0.346798
$229$	−11.5992	−0.766497	−0.383248	−	0.923645i	$-0.625195\pi$
$229$	−11.5992	−0.766497	−0.383248	+	0.923645i	$0.625195\pi$
$230$	11.4382	0.754215
$231$	−1.64835	−0.108454
$232$	−5.49612	−0.360838
$233$	17.9607	1.17664	0.588322	−	0.808627i	$-0.299789\pi$
$233$	17.9607	1.17664	0.588322	+	0.808627i	$0.299789\pi$
$234$	10.9718	0.717248
$235$	−34.7293	−2.26549
$236$	−19.3763	−1.26129
$237$	−1.00000	−0.0649570
$238$	0.643649	0.0417216
$239$	−16.9208	−1.09451	−0.547257	−	0.836965i	$-0.684328\pi$
$239$	−16.9208	−1.09451	−0.547257	+	0.836965i	$0.684328\pi$
$240$	9.99044	0.644880
$241$	30.1609	1.94283	0.971416	−	0.237383i	$-0.0762897\pi$
$241$	30.1609	1.94283	0.971416	+	0.237383i	$0.0762897\pi$
$242$	36.7233	2.36066
$243$	1.00000	0.0641500
$244$	−30.3085	−1.94031
$245$	21.8800	1.39786
$246$	−22.0202	−1.40396
$247$	11.6647	0.742206
$248$	−2.60303	−0.165292
$249$	10.1620	0.643989
$250$	−0.270634	−0.0171164
$251$	−16.6899	−1.05346	−0.526728	−	0.850034i	$-0.676581\pi$
$251$	−16.6899	−1.05346	−0.526728	+	0.850034i	$0.676581\pi$
$252$	0.727275	0.0458140
$253$	9.24428	0.581183
$254$	−17.5593	−1.10177
$255$	−3.16874	−0.198434
$256$	8.81590	0.550994
$257$	−26.9572	−1.68155	−0.840773	−	0.541387i	$-0.817899\pi$
$257$	−26.9572	−1.68155	−0.840773	+	0.541387i	$0.817899\pi$
$258$	−1.20716	−0.0751546
$259$	−1.15792	−0.0719496
$260$	−39.2838	−2.43628
$261$	−7.33038	−0.453739
$262$	28.1241	1.73751
$263$	13.0255	0.803188	0.401594	−	0.915818i	$-0.368456\pi$
$263$	13.0255	0.803188	0.401594	+	0.915818i	$0.368456\pi$
$264$	−4.00894	−0.246733
$265$	30.2433	1.85783
$266$	1.42871	0.0875998
$267$	−9.77321	−0.598111
$268$	−0.220615	−0.0134762
$269$	8.34355	0.508715	0.254357	−	0.967110i	$-0.418136\pi$
$269$	8.34355	0.508715	0.254357	+	0.967110i	$0.418136\pi$
$270$	−6.61585	−0.402628
$271$	−15.4470	−0.938336	−0.469168	−	0.883109i	$-0.655446\pi$
$271$	−15.4470	−0.938336	−0.469168	+	0.883109i	$0.655446\pi$
$272$	−3.15281	−0.191167
$273$	1.62005	0.0980498
$274$	−40.7341	−2.46084
$275$	−26.9531	−1.62533
$276$	−4.07870	−0.245509
$277$	−21.4257	−1.28735	−0.643673	−	0.765301i	$-0.722590\pi$
$277$	−21.4257	−1.28735	−0.643673	+	0.765301i	$0.722590\pi$
$278$	25.1290	1.50714
$279$	−3.47175	−0.207848
$280$	−0.732431	−0.0437711
$281$	31.9309	1.90484	0.952418	−	0.304794i	$-0.0985875\pi$
$281$	31.9309	1.90484	0.952418	+	0.304794i	$0.0985875\pi$
$282$	22.8828	1.36265
$283$	12.4069	0.737511	0.368756	−	0.929526i	$-0.379784\pi$
$283$	12.4069	0.737511	0.368756	+	0.929526i	$0.379784\pi$
$284$	5.20339	0.308765
$285$	−7.03366	−0.416638
$286$	−58.6647	−3.46892
$287$	−3.25141	−0.191925
$288$	−8.08214	−0.476245
$289$	1.00000	0.0588235
$290$	48.4967	2.84782
$291$	8.88402	0.520791
$292$	18.6464	1.09120
$293$	−8.93736	−0.522126	−0.261063	−	0.965322i	$-0.584073\pi$
$293$	−8.93736	−0.522126	−0.261063	+	0.965322i	$0.584073\pi$
$294$	−14.4165	−0.840788
$295$	26.0261	1.51530
$296$	−2.81616	−0.163686
$297$	−5.34687	−0.310257
$298$	27.4974	1.59288
$299$	−9.08555	−0.525431
$300$	11.8921	0.686589
$301$	−0.178245	−0.0102738
$302$	−11.0121	−0.633673
$303$	5.36804	0.308386
$304$	−6.99831	−0.401380
$305$	40.7102	2.33106
$306$	2.08785	0.119354
$307$	−16.2459	−0.927201	−0.463601	−	0.886044i	$-0.653443\pi$
$307$	−16.2459	−0.927201	−0.463601	+	0.886044i	$0.653443\pi$
$308$	−3.88865	−0.221576
$309$	3.03724	0.172783
$310$	22.9686	1.30453
$311$	15.9725	0.905717	0.452859	−	0.891582i	$-0.350404\pi$
$311$	15.9725	0.905717	0.452859	+	0.891582i	$0.350404\pi$
$312$	3.94011	0.223065
$313$	−3.97242	−0.224534	−0.112267	−	0.993678i	$-0.535811\pi$
$313$	−3.97242	−0.224534	−0.112267	+	0.993678i	$0.535811\pi$
$314$	26.0115	1.46792
$315$	−0.976869	−0.0550404
$316$	−2.35911	−0.132710
$317$	25.8367	1.45113	0.725566	−	0.688153i	$-0.241578\pi$
$317$	25.8367	1.45113	0.725566	+	0.688153i	$0.241578\pi$
$318$	−19.9270	−1.11745
$319$	39.1946	2.19448
$320$	33.4893	1.87211
$321$	−0.132451	−0.00739270
$322$	−1.11281	−0.0620147
$323$	2.21970	0.123508
$324$	2.35911	0.131062
$325$	26.4903	1.46942
$326$	−29.1594	−1.61499
$327$	−5.77497	−0.319356
$328$	−7.90773	−0.436631
$329$	3.37878	0.186278
$330$	35.3741	1.94728
$331$	−2.11168	−0.116069	−0.0580343	−	0.998315i	$-0.518483\pi$
$331$	−2.11168	−0.116069	−0.0580343	+	0.998315i	$0.518483\pi$
$332$	23.9732	1.31570
$333$	−3.75602	−0.205829
$334$	−16.1781	−0.885227
$335$	0.296328	0.0161901
$336$	−0.971959	−0.0530247
$337$	16.1789	0.881319	0.440660	−	0.897674i	$-0.354745\pi$
$337$	16.1789	0.881319	0.440660	+	0.897674i	$0.354745\pi$
$338$	30.5154	1.65982
$339$	−15.3154	−0.831816
$340$	−7.47541	−0.405411
$341$	18.5630	1.00524
$342$	4.63441	0.250600
$343$	−4.28667	−0.231458
$344$	−0.433507	−0.0233731
$345$	5.47848	0.294951
$346$	7.18038	0.386019
$347$	−27.2693	−1.46389	−0.731947	−	0.681362i	$-0.761388\pi$
$347$	−27.2693	−1.46389	−0.731947	+	0.681362i	$0.761388\pi$
$348$	−17.2932	−0.927012
$349$	−9.36661	−0.501383	−0.250692	−	0.968067i	$-0.580658\pi$
$349$	−9.36661	−0.501383	−0.250692	+	0.968067i	$0.580658\pi$
$350$	3.24457	0.173430
$351$	5.25507	0.280495
$352$	43.2142	2.30332
$353$	−8.08102	−0.430109	−0.215055	−	0.976602i	$-0.568993\pi$
$353$	−8.08102	−0.430109	−0.215055	+	0.976602i	$0.568993\pi$
$354$	−17.1483	−0.911424
$355$	−6.98915	−0.370946
$356$	−23.0561	−1.22197
$357$	0.308283	0.0163161
$358$	17.8116	0.941373
$359$	−19.3470	−1.02109	−0.510547	−	0.859850i	$-0.670557\pi$
$359$	−19.3470	−1.02109	−0.510547	+	0.859850i	$0.670557\pi$
$360$	−2.37584	−0.125218
$361$	−14.0729	−0.740680
$362$	15.6202	0.820978
$363$	17.5891	0.923187
$364$	3.82188	0.200321
$365$	−25.0456	−1.31095
$366$	−26.8235	−1.40209
$367$	2.83699	0.148090	0.0740448	−	0.997255i	$-0.476409\pi$
$367$	2.83699	0.148090	0.0740448	+	0.997255i	$0.476409\pi$
$368$	5.45094	0.284150
$369$	−10.5468	−0.549046
$370$	24.8493	1.29185
$371$	−2.94234	−0.152759
$372$	−8.19026	−0.424645
$373$	−37.4706	−1.94016	−0.970078	−	0.242795i	$-0.921936\pi$
$373$	−37.4706	−1.94016	−0.970078	+	0.242795i	$0.921936\pi$
$374$	−11.1635	−0.577249
$375$	−0.129624	−0.00669373
$376$	8.21751	0.423786
$377$	−38.5216	−1.98396
$378$	0.643649	0.0331057
$379$	−27.8339	−1.42973	−0.714865	−	0.699263i	$-0.753512\pi$
$379$	−27.8339	−1.42973	−0.714865	+	0.699263i	$0.753512\pi$
$380$	−16.5932	−0.851213
$381$	−8.41023	−0.430869
$382$	28.7575	1.47136
$383$	−14.2678	−0.729049	−0.364525	−	0.931194i	$-0.618769\pi$
$383$	−14.2678	−0.729049	−0.364525	+	0.931194i	$0.618769\pi$
$384$	−5.90149	−0.301159
$385$	5.22320	0.266199
$386$	−1.15761	−0.0589209
$387$	−0.578184	−0.0293908
$388$	20.9584	1.06400
$389$	−31.7110	−1.60781	−0.803907	−	0.594755i	$-0.797249\pi$
$389$	−31.7110	−1.60781	−0.803907	+	0.594755i	$0.797249\pi$
$390$	−34.7667	−1.76048
$391$	−1.72891	−0.0874349
$392$	−5.17716	−0.261486
$393$	13.4704	0.679491
$394$	13.5067	0.680457
$395$	3.16874	0.159437
$396$	−12.6139	−0.633871
$397$	−18.9810	−0.952627	−0.476314	−	0.879275i	$-0.658027\pi$
$397$	−18.9810	−0.952627	−0.476314	+	0.879275i	$0.658027\pi$
$398$	14.5111	0.727377
$399$	0.684298	0.0342577
$400$	−15.8930	−0.794652
$401$	6.51746	0.325467	0.162733	−	0.986670i	$-0.447969\pi$
$401$	6.51746	0.325467	0.162733	+	0.986670i	$0.447969\pi$
$402$	−0.195247	−0.00973804
$403$	−18.2443	−0.908813
$404$	12.6638	0.630048
$405$	−3.16874	−0.157456
$406$	−4.71819	−0.234160
$407$	20.0830	0.995476
$408$	0.749773	0.0371193
$409$	19.8549	0.981759	0.490880	−	0.871227i	$-0.336675\pi$
$409$	19.8549	0.981759	0.490880	+	0.871227i	$0.336675\pi$
$410$	69.7762	3.44600
$411$	−19.5101	−0.962361
$412$	7.16520	0.353004
$413$	−2.53205	−0.124594
$414$	−3.60971	−0.177408
$415$	−32.2006	−1.58067
$416$	−42.4722	−2.08237
$417$	12.0358	0.589397
$418$	−24.7796	−1.21201
$419$	−16.4201	−0.802172	−0.401086	−	0.916040i	$-0.631367\pi$
$419$	−16.4201	−0.802172	−0.401086	+	0.916040i	$0.631367\pi$
$420$	−2.30455	−0.112450
$421$	−30.2988	−1.47667	−0.738336	−	0.674433i	$-0.764388\pi$
$421$	−30.2988	−1.47667	−0.738336	+	0.674433i	$0.764388\pi$
$422$	21.7268	1.05764
$423$	10.9600	0.532893
$424$	−7.15604	−0.347528
$425$	5.04091	0.244520
$426$	4.60508	0.223117
$427$	−3.96065	−0.191669
$428$	−0.312467	−0.0151037
$429$	−28.0982	−1.35659
$430$	3.82518	0.184467
$431$	12.1969	0.587505	0.293752	−	0.955882i	$-0.405096\pi$
$431$	12.1969	0.587505	0.293752	+	0.955882i	$0.405096\pi$
$432$	−3.15281	−0.151690
$433$	18.6915	0.898257	0.449128	−	0.893467i	$-0.351735\pi$
$433$	18.6915	0.898257	0.449128	+	0.893467i	$0.351735\pi$
$434$	−2.23459	−0.107264
$435$	23.2280	1.11370
$436$	−13.6238	−0.652462
$437$	−3.83768	−0.183581
$438$	16.5023	0.788511
$439$	−10.9395	−0.522114	−0.261057	−	0.965323i	$-0.584071\pi$
$439$	−10.9395	−0.522114	−0.261057	+	0.965323i	$0.584071\pi$
$440$	12.7033	0.605606
$441$	−6.90496	−0.328808
$442$	10.9718	0.521874
$443$	18.8099	0.893684	0.446842	−	0.894613i	$-0.352549\pi$
$443$	18.8099	0.893684	0.446842	+	0.894613i	$0.352549\pi$
$444$	−8.86088	−0.420519
$445$	30.9688	1.46806
$446$	49.9141	2.36350
$447$	13.1702	0.622930
$448$	−3.25814	−0.153933
$449$	15.5344	0.733114	0.366557	−	0.930396i	$-0.380536\pi$
$449$	15.5344	0.733114	0.366557	+	0.930396i	$0.380536\pi$
$450$	10.5247	0.496137
$451$	56.3926	2.65542
$452$	−36.1306	−1.69944
$453$	−5.27435	−0.247811
$454$	−28.0488	−1.31639
$455$	−5.13351	−0.240663
$456$	1.66427	0.0779368
$457$	31.9149	1.49292	0.746459	−	0.665431i	$-0.231752\pi$
$457$	31.9149	1.49292	0.746459	+	0.665431i	$0.231752\pi$
$458$	−24.2174	−1.13160
$459$	1.00000	0.0466760
$460$	12.9243	0.602601
$461$	29.5788	1.37762	0.688811	−	0.724941i	$-0.258133\pi$
$461$	29.5788	1.37762	0.688811	+	0.724941i	$0.258133\pi$
$462$	−3.44151	−0.160114
$463$	−36.6726	−1.70432	−0.852161	−	0.523279i	$-0.824708\pi$
$463$	−36.6726	−1.70432	−0.852161	+	0.523279i	$0.824708\pi$
$464$	23.1113	1.07292
$465$	11.0011	0.510163
$466$	37.4992	1.73712
$467$	−28.1287	−1.30164	−0.650820	−	0.759232i	$-0.725575\pi$
$467$	−28.1287	−1.30164	−0.650820	+	0.759232i	$0.725575\pi$
$468$	12.3973	0.573065
$469$	−0.0288294	−0.00133122
$470$	−72.5096	−3.34462
$471$	12.4585	0.574059
$472$	−6.15819	−0.283454
$473$	3.09148	0.142146
$474$	−2.08785	−0.0958981
$475$	11.1893	0.513401
$476$	0.727275	0.0333346
$477$	−9.54427	−0.437002
$478$	−35.3280	−1.61586
$479$	8.92320	0.407712	0.203856	−	0.979001i	$-0.434653\pi$
$479$	8.92320	0.407712	0.203856	+	0.979001i	$0.434653\pi$
$480$	25.6102	1.16894
$481$	−19.7381	−0.899981
$482$	62.9713	2.86827
$483$	−0.532995	−0.0242521
$484$	41.4946	1.88612
$485$	−28.1512	−1.27828
$486$	2.08785	0.0947067
$487$	−0.824143	−0.0373455	−0.0186727	−	0.999826i	$-0.505944\pi$
$487$	−0.824143	−0.0373455	−0.0186727	+	0.999826i	$0.505944\pi$
$488$	−9.63266	−0.436050
$489$	−13.9662	−0.631575
$490$	45.6822	2.06371
$491$	15.0113	0.677449	0.338724	−	0.940886i	$-0.390005\pi$
$491$	15.0113	0.677449	0.338724	+	0.940886i	$0.390005\pi$
$492$	−24.8812	−1.12173
$493$	−7.33038	−0.330144
$494$	24.3541	1.09574
$495$	16.9429	0.761524
$496$	10.9458	0.491480
$497$	0.679967	0.0305007
$498$	21.2167	0.950741
$499$	38.1260	1.70676	0.853378	−	0.521293i	$-0.174550\pi$
$499$	38.1260	1.70676	0.853378	+	0.521293i	$0.174550\pi$
$500$	−0.305797	−0.0136756
$501$	−7.74870	−0.346186
$502$	−34.8460	−1.55525
$503$	25.5047	1.13720	0.568599	−	0.822615i	$-0.307486\pi$
$503$	25.5047	1.13720	0.568599	+	0.822615i	$0.307486\pi$
$504$	0.231143	0.0102959
$505$	−17.0099	−0.756931
$506$	19.3007	0.858019
$507$	14.6157	0.649106
$508$	−19.8407	−0.880287
$509$	33.3250	1.47710	0.738552	−	0.674196i	$-0.235510\pi$
$509$	33.3250	1.47710	0.738552	+	0.674196i	$0.235510\pi$
$510$	−6.61585	−0.292955
$511$	2.43666	0.107792
$512$	30.2093	1.33507
$513$	2.21970	0.0980023
$514$	−56.2827	−2.48252
$515$	−9.62423	−0.424094
$516$	−1.36400	−0.0600469
$517$	−58.6017	−2.57730
$518$	−2.41756	−0.106221
$519$	3.43913	0.150961
$520$	−12.4852	−0.547511
$521$	−29.7631	−1.30395	−0.651973	−	0.758242i	$-0.726059\pi$
$521$	−29.7631	−1.30395	−0.651973	+	0.758242i	$0.726059\pi$
$522$	−15.3047	−0.669869
$523$	−38.4941	−1.68323	−0.841614	−	0.540080i	$-0.818394\pi$
$523$	−38.4941	−1.68323	−0.841614	+	0.540080i	$0.818394\pi$
$524$	31.7781	1.38823
$525$	1.55403	0.0678233
$526$	27.1953	1.18577
$527$	−3.47175	−0.151232
$528$	16.8577	0.733637
$529$	−20.0109	−0.870037
$530$	63.1435	2.74278
$531$	−8.21340	−0.356431
$532$	1.61434	0.0699903
$533$	−55.4243	−2.40069
$534$	−20.4050	−0.883010
$535$	0.419703	0.0181453
$536$	−0.0701158	−0.00302854
$537$	8.53108	0.368143
$538$	17.4201	0.751032
$539$	36.9200	1.59026
$540$	−7.47541	−0.321691
$541$	37.9677	1.63236	0.816180	−	0.577798i	$-0.196088\pi$
$541$	37.9677	1.63236	0.816180	+	0.577798i	$0.196088\pi$
$542$	−32.2509	−1.38530
$543$	7.48147	0.321060
$544$	−8.08214	−0.346519
$545$	18.2994	0.783858
$546$	3.38242	0.144754
$547$	18.0532	0.771901	0.385950	−	0.922519i	$-0.373874\pi$
$547$	18.0532	0.771901	0.385950	+	0.922519i	$0.373874\pi$
$548$	−46.0265	−1.96615
$549$	−12.8474	−0.548315
$550$	−56.2740	−2.39953
$551$	−16.2713	−0.693179
$552$	−1.29629	−0.0551739
$553$	−0.308283	−0.0131095
$554$	−44.7336	−1.90055
$555$	11.9019	0.505205
$556$	28.3939	1.20417
$557$	0.790017	0.0334741	0.0167370	−	0.999860i	$-0.494672\pi$
$557$	0.790017	0.0334741	0.0167370	+	0.999860i	$0.494672\pi$
$558$	−7.24850	−0.306853
$559$	−3.03840	−0.128510
$560$	3.07989	0.130149
$561$	−5.34687	−0.225745
$562$	66.6669	2.81217
$563$	−18.4634	−0.778142	−0.389071	−	0.921208i	$-0.627204\pi$
$563$	−18.4634	−0.778142	−0.389071	+	0.921208i	$0.627204\pi$
$564$	25.8559	1.08873
$565$	48.5303	2.04169
$566$	25.9037	1.08881
$567$	0.308283	0.0129467
$568$	1.65374	0.0693895
$569$	−23.6849	−0.992923	−0.496462	−	0.868059i	$-0.665368\pi$
$569$	−23.6849	−0.992923	−0.496462	+	0.868059i	$0.665368\pi$
$570$	−14.6852	−0.615096
$571$	−43.8584	−1.83541	−0.917707	−	0.397257i	$-0.869962\pi$
$571$	−43.8584	−1.83541	−0.917707	+	0.397257i	$0.869962\pi$
$572$	−66.2868	−2.77159
$573$	13.7737	0.575406
$574$	−6.78846	−0.283345
$575$	−8.71529	−0.363453
$576$	−10.5687	−0.440361
$577$	35.9643	1.49721	0.748606	−	0.663015i	$-0.230723\pi$
$577$	35.9643	1.49721	0.748606	+	0.663015i	$0.230723\pi$
$578$	2.08785	0.0868431
$579$	−0.554452	−0.0230423
$580$	54.7976	2.27535
$581$	3.13277	0.129969
$582$	18.5485	0.768860
$583$	51.0320	2.11353
$584$	5.92619	0.245228
$585$	−16.6519	−0.688473
$586$	−18.6599	−0.770831
$587$	−9.34714	−0.385798	−0.192899	−	0.981219i	$-0.561789\pi$
$587$	−9.34714	−0.385798	−0.192899	+	0.981219i	$0.561789\pi$
$588$	−16.2896	−0.671771
$589$	−7.70626	−0.317531
$590$	54.3386	2.23709
$591$	6.46919	0.266107
$592$	11.8420	0.486704
$593$	−4.75769	−0.195375	−0.0976874	−	0.995217i	$-0.531145\pi$
$593$	−4.75769	−0.195375	−0.0976874	+	0.995217i	$0.531145\pi$
$594$	−11.1635	−0.458043
$595$	−0.976869	−0.0400477
$596$	31.0700	1.27268
$597$	6.95027	0.284456
$598$	−18.9693	−0.775711
$599$	−1.45808	−0.0595753	−0.0297877	−	0.999556i	$-0.509483\pi$
$599$	−1.45808	−0.0595753	−0.0297877	+	0.999556i	$0.509483\pi$
$600$	3.77954	0.154299
$601$	−2.33261	−0.0951492	−0.0475746	−	0.998868i	$-0.515149\pi$
$601$	−2.33261	−0.0951492	−0.0475746	+	0.998868i	$0.515149\pi$
$602$	−0.372148	−0.0151676
$603$	−0.0935160	−0.00380826
$604$	−12.4428	−0.506290
$605$	−55.7352	−2.26596
$606$	11.2077	0.455280
$607$	−27.1914	−1.10366	−0.551832	−	0.833955i	$-0.686071\pi$
$607$	−27.1914	−1.10366	−0.551832	+	0.833955i	$0.686071\pi$
$608$	−17.9400	−0.727561
$609$	−2.25983	−0.0915730
$610$	84.9967	3.44141
$611$	57.5955	2.33006
$612$	2.35911	0.0953615
$613$	−24.2688	−0.980208	−0.490104	−	0.871664i	$-0.663041\pi$
$613$	−24.2688	−0.980208	−0.490104	+	0.871664i	$0.663041\pi$
$614$	−33.9189	−1.36886
$615$	33.4202	1.34763
$616$	−1.23589	−0.0497955
$617$	25.1059	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$617$	25.1059	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$618$	6.34131	0.255085
$619$	−0.450820	−0.0181200	−0.00905999	−	0.999959i	$-0.502884\pi$
$619$	−0.450820	−0.0181200	−0.00905999	+	0.999959i	$0.502884\pi$
$620$	25.9528	1.04229
$621$	−1.72891	−0.0693789
$622$	33.3482	1.33714
$623$	−3.01292	−0.120710
$624$	−16.5682	−0.663260
$625$	−24.7938	−0.991752
$626$	−8.29380	−0.331487
$627$	−11.8685	−0.473981
$628$	29.3911	1.17283
$629$	−3.75602	−0.149762
$630$	−2.03956	−0.0812578
$631$	25.5971	1.01901	0.509503	−	0.860469i	$-0.329829\pi$
$631$	25.5971	1.01901	0.509503	+	0.860469i	$0.329829\pi$
$632$	−0.749773	−0.0298244
$633$	10.4063	0.413614
$634$	53.9431	2.14235
$635$	26.6498	1.05757
$636$	−22.5160	−0.892818
$637$	−36.2860	−1.43770
$638$	81.8324	3.23978
$639$	2.20566	0.0872545
$640$	18.7003	0.739194
$641$	12.1786	0.481026	0.240513	−	0.970646i	$-0.422684\pi$
$641$	12.1786	0.481026	0.240513	+	0.970646i	$0.422684\pi$
$642$	−0.276538	−0.0109141
$643$	−25.3453	−0.999521	−0.499761	−	0.866164i	$-0.666579\pi$
$643$	−25.3453	−0.999521	−0.499761	+	0.866164i	$0.666579\pi$
$644$	−1.25740	−0.0495483
$645$	1.83212	0.0721395
$646$	4.63441	0.182338
$647$	31.9687	1.25682	0.628410	−	0.777882i	$-0.283706\pi$
$647$	31.9687	1.25682	0.628410	+	0.777882i	$0.283706\pi$
$648$	0.749773	0.0294539
$649$	43.9160	1.72385
$650$	55.3077	2.16935
$651$	−1.07028	−0.0419477
$652$	−32.9480	−1.29034
$653$	11.1016	0.434441	0.217220	−	0.976123i	$-0.430301\pi$
$653$	11.1016	0.434441	0.217220	+	0.976123i	$0.430301\pi$
$654$	−12.0573	−0.471476
$655$	−42.6841	−1.66781
$656$	33.2522	1.29828
$657$	7.90398	0.308364
$658$	7.05439	0.275009
$659$	−7.79127	−0.303505	−0.151752	−	0.988419i	$-0.548492\pi$
$659$	−7.79127	−0.303505	−0.151752	+	0.988419i	$0.548492\pi$
$660$	39.9701	1.55583
$661$	−3.39776	−0.132158	−0.0660788	−	0.997814i	$-0.521049\pi$
$661$	−3.39776	−0.132158	−0.0660788	+	0.997814i	$0.521049\pi$
$662$	−4.40887	−0.171356
$663$	5.25507	0.204090
$664$	7.61918	0.295681
$665$	−2.16836	−0.0840854
$666$	−7.84200	−0.303871
$667$	12.6736	0.490723
$668$	−18.2801	−0.707277
$669$	23.9069	0.924296
$670$	0.618687	0.0239020
$671$	68.6936	2.65189
$672$	−2.49159	−0.0961152
$673$	−34.9791	−1.34835	−0.674173	−	0.738574i	$-0.735500\pi$
$673$	−34.9791	−1.34835	−0.674173	+	0.738574i	$0.735500\pi$
$674$	33.7790	1.30112
$675$	5.04091	0.194025
$676$	34.4801	1.32616
$677$	16.9430	0.651172	0.325586	−	0.945512i	$-0.394438\pi$
$677$	16.9430	0.651172	0.325586	+	0.945512i	$0.394438\pi$
$678$	−31.9761	−1.22804
$679$	2.73880	0.105105
$680$	−2.37584	−0.0911092
$681$	−13.4343	−0.514803
$682$	38.7568	1.48407
$683$	−10.3479	−0.395952	−0.197976	−	0.980207i	$-0.563437\pi$
$683$	−10.3479	−0.395952	−0.197976	+	0.980207i	$0.563437\pi$
$684$	5.23653	0.200224
$685$	61.8223	2.36211
$686$	−8.94991	−0.341709
$687$	−11.5992	−0.442537
$688$	1.82291	0.0694977
$689$	−50.1558	−1.91078
$690$	11.4382	0.435446
$691$	−28.5343	−1.08550	−0.542749	−	0.839895i	$-0.682616\pi$
$691$	−28.5343	−1.08550	−0.542749	+	0.839895i	$0.682616\pi$
$692$	8.11329	0.308421
$693$	−1.64835	−0.0626157
$694$	−56.9342	−2.16119
$695$	−38.1384	−1.44667
$696$	−5.49612	−0.208330
$697$	−10.5468	−0.399490
$698$	−19.5561	−0.740208
$699$	17.9607	0.679335
$700$	3.66613	0.138567
$701$	−6.72105	−0.253851	−0.126925	−	0.991912i	$-0.540511\pi$
$701$	−6.72105	−0.253851	−0.126925	+	0.991912i	$0.540511\pi$
$702$	10.9718	0.414103
$703$	−8.33725	−0.314445
$704$	56.5093	2.12978
$705$	−34.7293	−1.30798
$706$	−16.8719	−0.634984
$707$	1.65488	0.0622380
$708$	−19.3763	−0.728207
$709$	−10.5819	−0.397410	−0.198705	−	0.980059i	$-0.563674\pi$
$709$	−10.5819	−0.397410	−0.198705	+	0.980059i	$0.563674\pi$
$710$	−14.5923	−0.547639
$711$	−1.00000	−0.0375029
$712$	−7.32769	−0.274617
$713$	6.00236	0.224790
$714$	0.643649	0.0240880
$715$	89.0358	3.32975
$716$	20.1258	0.752136
$717$	−16.9208	−0.631917
$718$	−40.3936	−1.50747
$719$	6.85070	0.255488	0.127744	−	0.991807i	$-0.459226\pi$
$719$	6.85070	0.255488	0.127744	+	0.991807i	$0.459226\pi$
$720$	9.99044	0.372322
$721$	0.936332	0.0348708
$722$	−29.3821	−1.09349
$723$	30.1609	1.12169
$724$	17.6496	0.655943
$725$	−36.9517	−1.37235
$726$	36.7233	1.36293
$727$	−50.0076	−1.85468	−0.927339	−	0.374221i	$-0.877910\pi$
$727$	−50.0076	−1.85468	−0.927339	+	0.374221i	$0.877910\pi$
$728$	1.21467	0.0450186
$729$	1.00000	0.0370370
$730$	−52.2915	−1.93540
$731$	−0.578184	−0.0213849
$732$	−30.3085	−1.12024
$733$	−9.17816	−0.339003	−0.169501	−	0.985530i	$-0.554216\pi$
$733$	−9.17816	−0.339003	−0.169501	+	0.985530i	$0.554216\pi$
$734$	5.92321	0.218630
$735$	21.8800	0.807057
$736$	13.9733	0.515064
$737$	0.500018	0.0184184
$738$	−22.0202	−0.810574
$739$	14.3685	0.528553	0.264277	−	0.964447i	$-0.414867\pi$
$739$	14.3685	0.528553	0.264277	+	0.964447i	$0.414867\pi$
$740$	28.0778	1.03216
$741$	11.6647	0.428513
$742$	−6.14316	−0.225523
$743$	19.8897	0.729683	0.364842	−	0.931070i	$-0.381123\pi$
$743$	19.8897	0.729683	0.364842	+	0.931070i	$0.381123\pi$
$744$	−2.60303	−0.0954317
$745$	−41.7330	−1.52898
$746$	−78.2330	−2.86431
$747$	10.1620	0.371807
$748$	−12.6139	−0.461209
$749$	−0.0408324	−0.00149199
$750$	−0.270634	−0.00988217
$751$	−22.8744	−0.834701	−0.417350	−	0.908746i	$-0.637041\pi$
$751$	−22.8744	−0.834701	−0.417350	+	0.908746i	$0.637041\pi$
$752$	−34.5548	−1.26008
$753$	−16.6899	−0.608213
$754$	−80.4273	−2.92899
$755$	16.7131	0.608250
$756$	0.727275	0.0264507
$757$	−19.0876	−0.693751	−0.346876	−	0.937911i	$-0.612757\pi$
$757$	−19.0876	−0.693751	−0.346876	+	0.937911i	$0.612757\pi$
$758$	−58.1129	−2.11076
$759$	9.24428	0.335546
$760$	−5.27365	−0.191295
$761$	−12.2883	−0.445449	−0.222725	−	0.974881i	$-0.571495\pi$
$761$	−12.2883	−0.445449	−0.222725	+	0.974881i	$0.571495\pi$
$762$	−17.5593	−0.636106
$763$	−1.78033	−0.0644521
$764$	32.4938	1.17558
$765$	−3.16874	−0.114566
$766$	−29.7890	−1.07632
$767$	−43.1620	−1.55849
$768$	8.81590	0.318117
$769$	0.819743	0.0295607	0.0147803	−	0.999891i	$-0.495295\pi$
$769$	0.819743	0.0295607	0.0147803	+	0.999891i	$0.495295\pi$
$770$	10.9052	0.392998
$771$	−26.9572	−0.970842
$772$	−1.30802	−0.0470765
$773$	5.92106	0.212966	0.106483	−	0.994315i	$-0.466041\pi$
$773$	5.92106	0.212966	0.106483	+	0.994315i	$0.466041\pi$
$774$	−1.20716	−0.0433905
$775$	−17.5008	−0.628647
$776$	6.66100	0.239116
$777$	−1.15792	−0.0415401
$778$	−66.2079	−2.37367
$779$	−23.4108	−0.838780
$780$	−39.2838	−1.40659
$781$	−11.7934	−0.422000
$782$	−3.60971	−0.129083
$783$	−7.33038	−0.261966
$784$	21.7700	0.777502
$785$	−39.4778	−1.40902
$786$	28.1241	1.00315
$787$	−27.1446	−0.967601	−0.483801	−	0.875178i	$-0.660744\pi$
$787$	−27.1446	−0.967601	−0.483801	+	0.875178i	$0.660744\pi$
$788$	15.2615	0.543670
$789$	13.0255	0.463721
$790$	6.61585	0.235381
$791$	−4.72147	−0.167876
$792$	−4.00894	−0.142452
$793$	−67.5141	−2.39750
$794$	−39.6294	−1.40639
$795$	30.2433	1.07262
$796$	16.3965	0.581158
$797$	49.8854	1.76703	0.883516	−	0.468401i	$-0.155170\pi$
$797$	49.8854	1.76703	0.883516	+	0.468401i	$0.155170\pi$
$798$	1.42871	0.0505758
$799$	10.9600	0.387737
$800$	−40.7413	−1.44042
$801$	−9.77321	−0.345319
$802$	13.6075	0.480497
$803$	−42.2616	−1.49138
$804$	−0.220615	−0.00778048
$805$	1.68892	0.0595267
$806$	−38.0913	−1.34171
$807$	8.34355	0.293707
$808$	4.02481	0.141592
$809$	50.9398	1.79095	0.895474	−	0.445114i	$-0.146837\pi$
$809$	50.9398	1.79095	0.895474	+	0.445114i	$0.146837\pi$
$810$	−6.61585	−0.232457
$811$	−56.1661	−1.97226	−0.986129	−	0.165978i	$-0.946922\pi$
$811$	−56.1661	−1.97226	−0.986129	+	0.165978i	$0.946922\pi$
$812$	−5.33120	−0.187088
$813$	−15.4470	−0.541749
$814$	41.9302	1.46965
$815$	44.2554	1.55020
$816$	−3.15281	−0.110371
$817$	−1.28340	−0.0449004
$818$	41.4539	1.44940
$819$	1.62005	0.0566091
$820$	78.8419	2.75328
$821$	−4.63705	−0.161834	−0.0809170	−	0.996721i	$-0.525785\pi$
$821$	−4.63705	−0.161834	−0.0809170	+	0.996721i	$0.525785\pi$
$822$	−40.7341	−1.42076
$823$	−32.8170	−1.14393	−0.571965	−	0.820278i	$-0.693819\pi$
$823$	−32.8170	−1.14393	−0.571965	+	0.820278i	$0.693819\pi$
$824$	2.27724	0.0793316
$825$	−26.9531	−0.938386
$826$	−5.28655	−0.183942
$827$	−13.1613	−0.457664	−0.228832	−	0.973466i	$-0.573491\pi$
$827$	−13.1613	−0.457664	−0.228832	+	0.973466i	$0.573491\pi$
$828$	−4.07870	−0.141745
$829$	−25.8599	−0.898151	−0.449076	−	0.893494i	$-0.648247\pi$
$829$	−25.8599	−0.898151	−0.449076	+	0.893494i	$0.648247\pi$
$830$	−67.2301	−2.33359
$831$	−21.4257	−0.743250
$832$	−55.5390	−1.92547
$833$	−6.90496	−0.239243
$834$	25.1290	0.870145
$835$	24.5536	0.849713
$836$	−27.9991	−0.968368
$837$	−3.47175	−0.120001
$838$	−34.2826	−1.18427
$839$	30.8570	1.06530	0.532650	−	0.846335i	$-0.321196\pi$
$839$	30.8570	1.06530	0.532650	+	0.846335i	$0.321196\pi$
$840$	−0.732431	−0.0252713
$841$	24.7344	0.852910
$842$	−63.2593	−2.18006
$843$	31.9309	1.09976
$844$	24.5497	0.845035
$845$	−46.3134	−1.59323
$846$	22.8828	0.786727
$847$	5.42242	0.186316
$848$	30.0913	1.03334
$849$	12.4069	0.425802
$850$	10.5247	0.360993
$851$	6.49384	0.222606
$852$	5.20339	0.178265
$853$	44.2276	1.51432	0.757161	−	0.653228i	$-0.226586\pi$
$853$	44.2276	1.51432	0.757161	+	0.653228i	$0.226586\pi$
$854$	−8.26924	−0.282967
$855$	−7.03366	−0.240546
$856$	−0.0993083	−0.00339429
$857$	−42.9089	−1.46574	−0.732869	−	0.680369i	$-0.761819\pi$
$857$	−42.9089	−1.46574	−0.732869	+	0.680369i	$0.761819\pi$
$858$	−58.6647	−2.00278
$859$	−16.1946	−0.552552	−0.276276	−	0.961078i	$-0.589100\pi$
$859$	−16.1946	−0.552552	−0.276276	+	0.961078i	$0.589100\pi$
$860$	4.32217	0.147385
$861$	−3.25141	−0.110808
$862$	25.4653	0.867352
$863$	9.93319	0.338130	0.169065	−	0.985605i	$-0.445925\pi$
$863$	9.93319	0.338130	0.169065	+	0.985605i	$0.445925\pi$
$864$	−8.08214	−0.274960
$865$	−10.8977	−0.370533
$866$	39.0251	1.32613
$867$	1.00000	0.0339618
$868$	−2.52492	−0.0857014
$869$	5.34687	0.181380
$870$	48.4967	1.64419
$871$	−0.491432	−0.0166516
$872$	−4.32992	−0.146629
$873$	8.88402	0.300679
$874$	−8.01249	−0.271026
$875$	−0.0399608	−0.00135092
$876$	18.6464	0.630003
$877$	−16.6289	−0.561518	−0.280759	−	0.959778i	$-0.590586\pi$
$877$	−16.6289	−0.561518	−0.280759	+	0.959778i	$0.590586\pi$
$878$	−22.8400	−0.770813
$879$	−8.93736	−0.301450
$880$	−53.4176	−1.80071
$881$	−44.0366	−1.48363	−0.741815	−	0.670605i	$-0.766035\pi$
$881$	−44.0366	−1.48363	−0.741815	+	0.670605i	$0.766035\pi$
$882$	−14.4165	−0.485429
$883$	44.8808	1.51036	0.755179	−	0.655519i	$-0.227550\pi$
$883$	44.8808	1.51036	0.755179	+	0.655519i	$0.227550\pi$
$884$	12.3973	0.416966
$885$	26.0261	0.874859
$886$	39.2722	1.31937
$887$	−21.8883	−0.734936	−0.367468	−	0.930036i	$-0.619775\pi$
$887$	−21.8883	−0.734936	−0.367468	+	0.930036i	$0.619775\pi$
$888$	−2.81616	−0.0945043
$889$	−2.59273	−0.0869574
$890$	64.6581	2.16734
$891$	−5.34687	−0.179127
$892$	56.3992	1.88838
$893$	24.3279	0.814103
$894$	27.4974	0.919652
$895$	−27.0328	−0.903606
$896$	−1.81933	−0.0607796
$897$	−9.08555	−0.303358
$898$	32.4335	1.08232
$899$	25.4493	0.848780
$900$	11.8921	0.396402
$901$	−9.54427	−0.317966
$902$	117.739	3.92029
$903$	−0.178245	−0.00593161
$904$	−11.4830	−0.381920
$905$	−23.7068	−0.788041
$906$	−11.0121	−0.365851
$907$	49.4435	1.64174	0.820872	−	0.571112i	$-0.193488\pi$
$907$	49.4435	1.64174	0.820872	+	0.571112i	$0.193488\pi$
$908$	−31.6930	−1.05177
$909$	5.36804	0.178047
$910$	−10.7180	−0.355298
$911$	16.0758	0.532614	0.266307	−	0.963888i	$-0.414196\pi$
$911$	16.0758	0.532614	0.266307	+	0.963888i	$0.414196\pi$
$912$	−6.99831	−0.231737
$913$	−54.3348	−1.79822
$914$	66.6336	2.20404
$915$	40.7102	1.34584
$916$	−27.3638	−0.904126
$917$	4.15269	0.137134
$918$	2.08785	0.0689093
$919$	19.2596	0.635316	0.317658	−	0.948205i	$-0.397104\pi$
$919$	19.2596	0.635316	0.317658	+	0.948205i	$0.397104\pi$
$920$	4.10762	0.135424
$921$	−16.2459	−0.535320
$922$	61.7561	2.03383
$923$	11.5909	0.381518
$924$	−3.88865	−0.127927
$925$	−18.9338	−0.622538
$926$	−76.5669	−2.51615
$927$	3.03724	0.0997562
$928$	59.2451	1.94482
$929$	13.2207	0.433756	0.216878	−	0.976199i	$-0.430413\pi$
$929$	13.2207	0.433756	0.216878	+	0.976199i	$0.430413\pi$
$930$	22.9686	0.753170
$931$	−15.3270	−0.502321
$932$	42.3713	1.38792
$933$	15.9725	0.522916
$934$	−58.7285	−1.92165
$935$	16.9429	0.554090
$936$	3.94011	0.128786
$937$	−11.8573	−0.387363	−0.193681	−	0.981064i	$-0.562043\pi$
$937$	−11.8573	−0.387363	−0.193681	+	0.981064i	$0.562043\pi$
$938$	−0.0601915	−0.00196532
$939$	−3.97242	−0.129635
$940$	−81.9305	−2.67228
$941$	−46.5666	−1.51803	−0.759014	−	0.651074i	$-0.774319\pi$
$941$	−46.5666	−1.51803	−0.759014	+	0.651074i	$0.774319\pi$
$942$	26.0115	0.847501
$943$	18.2346	0.593799
$944$	25.8953	0.842821
$945$	−0.976869	−0.0317776
$946$	6.45454	0.209855
$947$	−25.9885	−0.844513	−0.422257	−	0.906476i	$-0.638762\pi$
$947$	−25.9885	−0.844513	−0.422257	+	0.906476i	$0.638762\pi$
$948$	−2.35911	−0.0766204
$949$	41.5359	1.34831
$950$	23.3616	0.757951
$951$	25.8367	0.837811
$952$	0.231143	0.00749138
$953$	−42.2465	−1.36850	−0.684249	−	0.729248i	$-0.739870\pi$
$953$	−42.2465	−1.36850	−0.684249	+	0.729248i	$0.739870\pi$
$954$	−19.9270	−0.645161
$955$	−43.6454	−1.41233
$956$	−39.9180	−1.29104
$957$	39.1946	1.26698
$958$	18.6303	0.601918
$959$	−6.01463	−0.194222
$960$	33.4893	1.08086
$961$	−18.9469	−0.611191
$962$	−41.2102	−1.32867
$963$	−0.132451	−0.00426818
$964$	71.1529	2.29168
$965$	1.75692	0.0565571
$966$	−1.11281	−0.0358042
$967$	61.7908	1.98706	0.993530	−	0.113574i	$-0.0362298\pi$
$967$	61.7908	1.98706	0.993530	+	0.113574i	$0.0362298\pi$
$968$	13.1878	0.423872
$969$	2.21970	0.0713071
$970$	−58.7753	−1.88716
$971$	−32.7127	−1.04980	−0.524900	−	0.851164i	$-0.675897\pi$
$971$	−32.7127	−1.04980	−0.524900	+	0.851164i	$0.675897\pi$
$972$	2.35911	0.0756686
$973$	3.71044	0.118951
$974$	−1.72069	−0.0551343
$975$	26.4903	0.848368
$976$	40.5055	1.29655
$977$	−30.0507	−0.961406	−0.480703	−	0.876883i	$-0.659619\pi$
$977$	−30.0507	−0.961406	−0.480703	+	0.876883i	$0.659619\pi$
$978$	−29.1594	−0.932415
$979$	52.2561	1.67011
$980$	51.6174	1.64886
$981$	−5.77497	−0.184380
$982$	31.3412	1.00014
$983$	−24.9772	−0.796650	−0.398325	−	0.917244i	$-0.630408\pi$
$983$	−24.9772	−0.796650	−0.398325	+	0.917244i	$0.630408\pi$
$984$	−7.90773	−0.252089
$985$	−20.4992	−0.653158
$986$	−15.3047	−0.487401
$987$	3.37878	0.107548
$988$	27.5183	0.875474
$989$	0.999631	0.0317864
$990$	35.3741	1.12426
$991$	−19.8856	−0.631685	−0.315843	−	0.948812i	$-0.602287\pi$
$991$	−19.8856	−0.631685	−0.315843	+	0.948812i	$0.602287\pi$
$992$	28.0592	0.890881
$993$	−2.11168	−0.0670122
$994$	1.41967	0.0450292
$995$	−22.0236	−0.698195
$996$	23.9732	0.759621
$997$	25.0359	0.792894	0.396447	−	0.918058i	$-0.370243\pi$
$997$	25.0359	0.792894	0.396447	+	0.918058i	$0.370243\pi$
$998$	79.6014	2.51974
$999$	−3.75602	−0.118835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.16	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+2.08785 q^{2} +1.00000 q^{3} +2.35911 q^{4} -3.16874 q^{5} +2.08785 q^{6} +0.308283 q^{7} +0.749773 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08785 q^{2} +1.00000 q^{3} +2.35911 q^{4} -3.16874 q^{5} +2.08785 q^{6} +0.308283 q^{7} +0.749773 q^{8} +1.00000 q^{9} -6.61585 q^{10} -5.34687 q^{11} +2.35911 q^{12} +5.25507 q^{13} +0.643649 q^{14} -3.16874 q^{15} -3.15281 q^{16} +1.00000 q^{17} +2.08785 q^{18} +2.21970 q^{19} -7.47541 q^{20} +0.308283 q^{21} -11.1635 q^{22} -1.72891 q^{23} +0.749773 q^{24} +5.04091 q^{25} +10.9718 q^{26} +1.00000 q^{27} +0.727275 q^{28} -7.33038 q^{29} -6.61585 q^{30} -3.47175 q^{31} -8.08214 q^{32} -5.34687 q^{33} +2.08785 q^{34} -0.976869 q^{35} +2.35911 q^{36} -3.75602 q^{37} +4.63441 q^{38} +5.25507 q^{39} -2.37584 q^{40} -10.5468 q^{41} +0.643649 q^{42} -0.578184 q^{43} -12.6139 q^{44} -3.16874 q^{45} -3.60971 q^{46} +10.9600 q^{47} -3.15281 q^{48} -6.90496 q^{49} +10.5247 q^{50} +1.00000 q^{51} +12.3973 q^{52} -9.54427 q^{53} +2.08785 q^{54} +16.9429 q^{55} +0.231143 q^{56} +2.21970 q^{57} -15.3047 q^{58} -8.21340 q^{59} -7.47541 q^{60} -12.8474 q^{61} -7.24850 q^{62} +0.308283 q^{63} -10.5687 q^{64} -16.6519 q^{65} -11.1635 q^{66} -0.0935160 q^{67} +2.35911 q^{68} -1.72891 q^{69} -2.03956 q^{70} +2.20566 q^{71} +0.749773 q^{72} +7.90398 q^{73} -7.84200 q^{74} +5.04091 q^{75} +5.23653 q^{76} -1.64835 q^{77} +10.9718 q^{78} -1.00000 q^{79} +9.99044 q^{80} +1.00000 q^{81} -22.0202 q^{82} +10.1620 q^{83} +0.727275 q^{84} -3.16874 q^{85} -1.20716 q^{86} -7.33038 q^{87} -4.00894 q^{88} -9.77321 q^{89} -6.61585 q^{90} +1.62005 q^{91} -4.07870 q^{92} -3.47175 q^{93} +22.8828 q^{94} -7.03366 q^{95} -8.08214 q^{96} +8.88402 q^{97} -14.4165 q^{98} -5.34687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 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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