LMFDB - Embedded newform 6029.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57920 q^{2} -2.40579 q^{3} +4.65225 q^{4} +2.56752 q^{5} +6.20501 q^{6} -4.72770 q^{7} -6.84068 q^{8} +2.78784 q^{9} +O(q^{10})$	\(q-2.57920 q^{2} -2.40579 q^{3} +4.65225 q^{4} +2.56752 q^{5} +6.20501 q^{6} -4.72770 q^{7} -6.84068 q^{8} +2.78784 q^{9} -6.62214 q^{10} -5.78832 q^{11} -11.1924 q^{12} +6.23915 q^{13} +12.1937 q^{14} -6.17692 q^{15} +8.33896 q^{16} -0.556892 q^{17} -7.19039 q^{18} -2.88698 q^{19} +11.9447 q^{20} +11.3739 q^{21} +14.9292 q^{22} -4.38590 q^{23} +16.4573 q^{24} +1.59215 q^{25} -16.0920 q^{26} +0.510411 q^{27} -21.9945 q^{28} -1.85502 q^{29} +15.9315 q^{30} -7.68287 q^{31} -7.82644 q^{32} +13.9255 q^{33} +1.43633 q^{34} -12.1385 q^{35} +12.9697 q^{36} -4.07493 q^{37} +7.44608 q^{38} -15.0101 q^{39} -17.5636 q^{40} +10.3419 q^{41} -29.3354 q^{42} +8.43713 q^{43} -26.9288 q^{44} +7.15783 q^{45} +11.3121 q^{46} +6.13947 q^{47} -20.0618 q^{48} +15.3512 q^{49} -4.10648 q^{50} +1.33977 q^{51} +29.0261 q^{52} +8.62014 q^{53} -1.31645 q^{54} -14.8616 q^{55} +32.3407 q^{56} +6.94547 q^{57} +4.78447 q^{58} +7.70372 q^{59} -28.7366 q^{60} -15.0960 q^{61} +19.8156 q^{62} -13.1801 q^{63} +3.50801 q^{64} +16.0191 q^{65} -35.9166 q^{66} +14.4560 q^{67} -2.59080 q^{68} +10.5516 q^{69} +31.3075 q^{70} +5.25198 q^{71} -19.0707 q^{72} -13.4347 q^{73} +10.5101 q^{74} -3.83039 q^{75} -13.4310 q^{76} +27.3655 q^{77} +38.7140 q^{78} -4.78182 q^{79} +21.4104 q^{80} -9.59147 q^{81} -26.6739 q^{82} +4.98752 q^{83} +52.9141 q^{84} -1.42983 q^{85} -21.7610 q^{86} +4.46280 q^{87} +39.5961 q^{88} +4.41352 q^{89} -18.4615 q^{90} -29.4968 q^{91} -20.4043 q^{92} +18.4834 q^{93} -15.8349 q^{94} -7.41237 q^{95} +18.8288 q^{96} +5.51738 q^{97} -39.5936 q^{98} -16.1369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.57920	−1.82377	−0.911884	−	0.410449i	$-0.865372\pi$
$2$	−2.57920	−1.82377	−0.911884	+	0.410449i	$0.865372\pi$
$3$	−2.40579	−1.38899	−0.694493	−	0.719500i	$-0.744371\pi$
$3$	−2.40579	−1.38899	−0.694493	+	0.719500i	$0.744371\pi$
$4$	4.65225	2.32613
$5$	2.56752	1.14823	0.574115	−	0.818775i	$-0.305346\pi$
$5$	2.56752	1.14823	0.574115	+	0.818775i	$0.305346\pi$
$6$	6.20501	2.53319
$7$	−4.72770	−1.78690	−0.893451	−	0.449160i	$-0.851723\pi$
$7$	−4.72770	−1.78690	−0.893451	+	0.449160i	$0.851723\pi$
$8$	−6.84068	−2.41855
$9$	2.78784	0.929280
$10$	−6.62214	−2.09410
$11$	−5.78832	−1.74525	−0.872623	−	0.488395i	$-0.837583\pi$
$11$	−5.78832	−1.74525	−0.872623	+	0.488395i	$0.837583\pi$
$12$	−11.1924	−3.23096
$13$	6.23915	1.73043	0.865215	−	0.501402i	$-0.167182\pi$
$13$	6.23915	1.73043	0.865215	+	0.501402i	$0.167182\pi$
$14$	12.1937	3.25889
$15$	−6.17692	−1.59487
$16$	8.33896	2.08474
$17$	−0.556892	−0.135066	−0.0675331	−	0.997717i	$-0.521513\pi$
$17$	−0.556892	−0.135066	−0.0675331	+	0.997717i	$0.521513\pi$
$18$	−7.19039	−1.69479
$19$	−2.88698	−0.662318	−0.331159	−	0.943575i	$-0.607440\pi$
$19$	−2.88698	−0.662318	−0.331159	+	0.943575i	$0.607440\pi$
$20$	11.9447	2.67093
$21$	11.3739	2.48198
$22$	14.9292	3.18292
$23$	−4.38590	−0.914523	−0.457261	−	0.889332i	$-0.651170\pi$
$23$	−4.38590	−0.914523	−0.457261	+	0.889332i	$0.651170\pi$
$24$	16.4573	3.35933
$25$	1.59215	0.318431
$26$	−16.0920	−3.15590
$27$	0.510411	0.0982286
$28$	−21.9945	−4.15656
$29$	−1.85502	−0.344469	−0.172234	−	0.985056i	$-0.555099\pi$
$29$	−1.85502	−0.344469	−0.172234	+	0.985056i	$0.555099\pi$
$30$	15.9315	2.90868
$31$	−7.68287	−1.37988	−0.689942	−	0.723865i	$-0.742364\pi$
$31$	−7.68287	−1.37988	−0.689942	+	0.723865i	$0.742364\pi$
$32$	−7.82644	−1.38353
$33$	13.9255	2.42412
$34$	1.43633	0.246329
$35$	−12.1385	−2.05177
$36$	12.9697	2.16162
$37$	−4.07493	−0.669915	−0.334957	−	0.942233i	$-0.608722\pi$
$37$	−4.07493	−0.669915	−0.334957	+	0.942233i	$0.608722\pi$
$38$	7.44608	1.20791
$39$	−15.0101	−2.40354
$40$	−17.5636	−2.77705
$41$	10.3419	1.61514	0.807569	−	0.589773i	$-0.200783\pi$
$41$	10.3419	1.61514	0.807569	+	0.589773i	$0.200783\pi$
$42$	−29.3354	−4.52656
$43$	8.43713	1.28665	0.643325	−	0.765593i	$-0.277554\pi$
$43$	8.43713	1.28665	0.643325	+	0.765593i	$0.277554\pi$
$44$	−26.9288	−4.05966
$45$	7.15783	1.06703
$46$	11.3121	1.66788
$47$	6.13947	0.895534	0.447767	−	0.894150i	$-0.352219\pi$
$47$	6.13947	0.895534	0.447767	+	0.894150i	$0.352219\pi$
$48$	−20.0618	−2.89567
$49$	15.3512	2.19302
$50$	−4.10648	−0.580744
$51$	1.33977	0.187605
$52$	29.0261	4.02520
$53$	8.62014	1.18407	0.592034	−	0.805913i	$-0.298325\pi$
$53$	8.62014	1.18407	0.592034	+	0.805913i	$0.298325\pi$
$54$	−1.31645	−0.179146
$55$	−14.8616	−2.00394
$56$	32.3407	4.32171
$57$	6.94547	0.919950
$58$	4.78447	0.628231
$59$	7.70372	1.00294	0.501470	−	0.865175i	$-0.332793\pi$
$59$	7.70372	1.00294	0.501470	+	0.865175i	$0.332793\pi$
$60$	−28.7366	−3.70988
$61$	−15.0960	−1.93285	−0.966424	−	0.256951i	$-0.917282\pi$
$61$	−15.0960	−1.93285	−0.966424	+	0.256951i	$0.917282\pi$
$62$	19.8156	2.51659
$63$	−13.1801	−1.66053
$64$	3.50801	0.438501
$65$	16.0191	1.98693
$66$	−35.9166	−4.42103
$67$	14.4560	1.76608	0.883041	−	0.469296i	$-0.155492\pi$
$67$	14.4560	1.76608	0.883041	+	0.469296i	$0.155492\pi$
$68$	−2.59080	−0.314181
$69$	10.5516	1.27026
$70$	31.3075	3.74196
$71$	5.25198	0.623295	0.311648	−	0.950198i	$-0.399119\pi$
$71$	5.25198	0.623295	0.311648	+	0.950198i	$0.399119\pi$
$72$	−19.0707	−2.24751
$73$	−13.4347	−1.57241	−0.786204	−	0.617967i	$-0.787956\pi$
$73$	−13.4347	−1.57241	−0.786204	+	0.617967i	$0.787956\pi$
$74$	10.5101	1.22177
$75$	−3.83039	−0.442296
$76$	−13.4310	−1.54064
$77$	27.3655	3.11858
$78$	38.7140	4.38350
$79$	−4.78182	−0.537997	−0.268998	−	0.963141i	$-0.586693\pi$
$79$	−4.78182	−0.537997	−0.268998	+	0.963141i	$0.586693\pi$
$80$	21.4104	2.39376
$81$	−9.59147	−1.06572
$82$	−26.6739	−2.94564
$83$	4.98752	0.547452	0.273726	−	0.961808i	$-0.411744\pi$
$83$	4.98752	0.547452	0.273726	+	0.961808i	$0.411744\pi$
$84$	52.9141	5.77340
$85$	−1.42983	−0.155087
$86$	−21.7610	−2.34655
$87$	4.46280	0.478462
$88$	39.5961	4.22096
$89$	4.41352	0.467832	0.233916	−	0.972257i	$-0.424846\pi$
$89$	4.41352	0.467832	0.233916	+	0.972257i	$0.424846\pi$
$90$	−18.4615	−1.94601
$91$	−29.4968	−3.09211
$92$	−20.4043	−2.12730
$93$	18.4834	1.91664
$94$	−15.8349	−1.63325
$95$	−7.41237	−0.760493
$96$	18.8288	1.92171
$97$	5.51738	0.560205	0.280102	−	0.959970i	$-0.409632\pi$
$97$	5.51738	0.560205	0.280102	+	0.959970i	$0.409632\pi$
$98$	−39.5936	−3.99956
$99$	−16.1369	−1.62182
$100$	7.40711	0.740711
$101$	−19.0843	−1.89896	−0.949481	−	0.313823i	$-0.898390\pi$
$101$	−19.0843	−1.89896	−0.949481	+	0.313823i	$0.898390\pi$
$102$	−3.45552	−0.342148
$103$	18.8513	1.85747	0.928736	−	0.370742i	$-0.120897\pi$
$103$	18.8513	1.85747	0.928736	+	0.370742i	$0.120897\pi$
$104$	−42.6800	−4.18512
$105$	29.2026	2.84988
$106$	−22.2330	−2.15946
$107$	−5.57237	−0.538701	−0.269350	−	0.963042i	$-0.586809\pi$
$107$	−5.57237	−0.538701	−0.269350	+	0.963042i	$0.586809\pi$
$108$	2.37456	0.228492
$109$	5.37386	0.514722	0.257361	−	0.966315i	$-0.417147\pi$
$109$	5.37386	0.514722	0.257361	+	0.966315i	$0.417147\pi$
$110$	38.3311	3.65472
$111$	9.80345	0.930502
$112$	−39.4241	−3.72523
$113$	−2.48073	−0.233367	−0.116684	−	0.993169i	$-0.537226\pi$
$113$	−2.48073	−0.233367	−0.116684	+	0.993169i	$0.537226\pi$
$114$	−17.9137	−1.67777
$115$	−11.2609	−1.05008
$116$	−8.63003	−0.801278
$117$	17.3938	1.60805
$118$	−19.8694	−1.82913
$119$	2.63282	0.241350
$120$	42.2543	3.85728
$121$	22.5047	2.04588
$122$	38.9356	3.52507
$123$	−24.8805	−2.24340
$124$	−35.7426	−3.20978
$125$	−8.74971	−0.782598
$126$	33.9940	3.02843
$127$	4.30028	0.381588	0.190794	−	0.981630i	$-0.438894\pi$
$127$	4.30028	0.381588	0.190794	+	0.981630i	$0.438894\pi$
$128$	6.60503	0.583808
$129$	−20.2980	−1.78714
$130$	−41.3165	−3.62370
$131$	7.43935	0.649979	0.324990	−	0.945718i	$-0.394639\pi$
$131$	7.43935	0.649979	0.324990	+	0.945718i	$0.394639\pi$
$132$	64.7850	5.63881
$133$	13.6488	1.18350
$134$	−37.2849	−3.22092
$135$	1.31049	0.112789
$136$	3.80952	0.326664
$137$	−12.9122	−1.10317	−0.551583	−	0.834120i	$-0.685976\pi$
$137$	−12.9122	−1.10317	−0.551583	+	0.834120i	$0.685976\pi$
$138$	−27.2145	−2.31666
$139$	−4.76470	−0.404137	−0.202068	−	0.979371i	$-0.564766\pi$
$139$	−4.76470	−0.404137	−0.202068	+	0.979371i	$0.564766\pi$
$140$	−56.4712	−4.77269
$141$	−14.7703	−1.24388
$142$	−13.5459	−1.13675
$143$	−36.1142	−3.02002
$144$	23.2477	1.93731
$145$	−4.76280	−0.395529
$146$	34.6506	2.86771
$147$	−36.9317	−3.04607
$148$	−18.9576	−1.55831
$149$	−5.56649	−0.456025	−0.228012	−	0.973658i	$-0.573223\pi$
$149$	−5.56649	−0.456025	−0.228012	+	0.973658i	$0.573223\pi$
$150$	9.87934	0.806645
$151$	13.4292	1.09285	0.546426	−	0.837507i	$-0.315988\pi$
$151$	13.4292	1.09285	0.546426	+	0.837507i	$0.315988\pi$
$152$	19.7489	1.60185
$153$	−1.55253	−0.125514
$154$	−70.5809	−5.68757
$155$	−19.7259	−1.58442
$156$	−69.8308	−5.59094
$157$	−18.8855	−1.50723	−0.753615	−	0.657316i	$-0.771692\pi$
$157$	−18.8855	−1.50723	−0.753615	+	0.657316i	$0.771692\pi$
$158$	12.3333	0.981181
$159$	−20.7383	−1.64465
$160$	−20.0945	−1.58861
$161$	20.7352	1.63416
$162$	24.7383	1.94362
$163$	1.29751	0.101629	0.0508146	−	0.998708i	$-0.483818\pi$
$163$	1.29751	0.101629	0.0508146	+	0.998708i	$0.483818\pi$
$164$	48.1133	3.75702
$165$	35.7540	2.78345
$166$	−12.8638	−0.998424
$167$	12.1209	0.937941	0.468970	−	0.883214i	$-0.344625\pi$
$167$	12.1209	0.937941	0.468970	+	0.883214i	$0.344625\pi$
$168$	−77.8050	−6.00279
$169$	25.9270	1.99438
$170$	3.68781	0.282842
$171$	−8.04843	−0.615479
$172$	39.2517	2.99291
$173$	2.69317	0.204758	0.102379	−	0.994745i	$-0.467355\pi$
$173$	2.69317	0.204758	0.102379	+	0.994745i	$0.467355\pi$
$174$	−11.5104	−0.872604
$175$	−7.52723	−0.569005
$176$	−48.2686	−3.63838
$177$	−18.5336	−1.39307
$178$	−11.3833	−0.853216
$179$	7.42195	0.554742	0.277371	−	0.960763i	$-0.410537\pi$
$179$	7.42195	0.554742	0.277371	+	0.960763i	$0.410537\pi$
$180$	33.3001	2.48204
$181$	1.40936	0.104757	0.0523786	−	0.998627i	$-0.483320\pi$
$181$	1.40936	0.104757	0.0523786	+	0.998627i	$0.483320\pi$
$182$	76.0781	5.63929
$183$	36.3179	2.68470
$184$	30.0025	2.21182
$185$	−10.4625	−0.769216
$186$	−47.6723	−3.49550
$187$	3.22347	0.235724
$188$	28.5624	2.08313
$189$	−2.41307	−0.175525
$190$	19.1180	1.38696
$191$	−4.83349	−0.349739	−0.174870	−	0.984592i	$-0.555950\pi$
$191$	−4.83349	−0.349739	−0.174870	+	0.984592i	$0.555950\pi$
$192$	−8.43954	−0.609072
$193$	−6.85312	−0.493298	−0.246649	−	0.969105i	$-0.579329\pi$
$193$	−6.85312	−0.493298	−0.246649	+	0.969105i	$0.579329\pi$
$194$	−14.2304	−1.02168
$195$	−38.5387	−2.75982
$196$	71.4174	5.10125
$197$	20.6141	1.46869	0.734346	−	0.678776i	$-0.237489\pi$
$197$	20.6141	1.46869	0.734346	+	0.678776i	$0.237489\pi$
$198$	41.6203	2.95783
$199$	−19.8549	−1.40748	−0.703740	−	0.710458i	$-0.748488\pi$
$199$	−19.8549	−1.40748	−0.703740	+	0.710458i	$0.748488\pi$
$200$	−10.8914	−0.770140
$201$	−34.7782	−2.45306
$202$	49.2223	3.46327
$203$	8.76999	0.615533
$204$	6.23293	0.436393
$205$	26.5531	1.85455
$206$	−48.6211	−3.38760
$207$	−12.2272	−0.849848
$208$	52.0280	3.60749
$209$	16.7108	1.15591
$210$	−75.3193	−5.19753
$211$	−12.9995	−0.894920	−0.447460	−	0.894304i	$-0.647671\pi$
$211$	−12.9995	−0.894920	−0.447460	+	0.894304i	$0.647671\pi$
$212$	40.1031	2.75429
$213$	−12.6352	−0.865748
$214$	14.3722	0.982465
$215$	21.6625	1.47737
$216$	−3.49156	−0.237571
$217$	36.3223	2.46572
$218$	−13.8602	−0.938734
$219$	32.3210	2.18405
$220$	−69.1401	−4.66142
$221$	−3.47453	−0.233722
$222$	−25.2850	−1.69702
$223$	−20.3788	−1.36466	−0.682332	−	0.731043i	$-0.739034\pi$
$223$	−20.3788	−1.36466	−0.682332	+	0.731043i	$0.739034\pi$
$224$	37.0011	2.47224
$225$	4.43867	0.295912
$226$	6.39828	0.425607
$227$	6.42395	0.426373	0.213186	−	0.977012i	$-0.431616\pi$
$227$	6.42395	0.426373	0.213186	+	0.977012i	$0.431616\pi$
$228$	32.3121	2.13992
$229$	27.8098	1.83772	0.918860	−	0.394583i	$-0.129111\pi$
$229$	27.8098	1.83772	0.918860	+	0.394583i	$0.129111\pi$
$230$	29.0440	1.91510
$231$	−65.8356	−4.33167
$232$	12.6896	0.833114
$233$	20.6035	1.34978	0.674889	−	0.737919i	$-0.264191\pi$
$233$	20.6035	1.34978	0.674889	+	0.737919i	$0.264191\pi$
$234$	−44.8619	−2.93272
$235$	15.7632	1.02828
$236$	35.8397	2.33296
$237$	11.5041	0.747270
$238$	−6.79055	−0.440166
$239$	−23.5481	−1.52320	−0.761599	−	0.648049i	$-0.775585\pi$
$239$	−23.5481	−1.52320	−0.761599	+	0.648049i	$0.775585\pi$
$240$	−51.5091	−3.32490
$241$	12.7278	0.819869	0.409935	−	0.912115i	$-0.365551\pi$
$241$	12.7278	0.819869	0.409935	+	0.912115i	$0.365551\pi$
$242$	−58.0440	−3.73121
$243$	21.5439	1.38204
$244$	−70.2306	−4.49605
$245$	39.4144	2.51809
$246$	64.1718	4.09145
$247$	−18.0123	−1.14609
$248$	52.5561	3.33731
$249$	−11.9989	−0.760402
$250$	22.5672	1.42728
$251$	23.8639	1.50628	0.753140	−	0.657861i	$-0.228538\pi$
$251$	23.8639	1.50628	0.753140	+	0.657861i	$0.228538\pi$
$252$	−61.3171	−3.86261
$253$	25.3870	1.59607
$254$	−11.0913	−0.695928
$255$	3.43988	0.215413
$256$	−24.0517	−1.50323
$257$	−7.44015	−0.464104	−0.232052	−	0.972703i	$-0.574544\pi$
$257$	−7.44015	−0.464104	−0.232052	+	0.972703i	$0.574544\pi$
$258$	52.3525	3.25932
$259$	19.2651	1.19707
$260$	74.5251	4.62185
$261$	−5.17151	−0.320108
$262$	−19.1876	−1.18541
$263$	13.9505	0.860227	0.430114	−	0.902775i	$-0.358473\pi$
$263$	13.9505	0.860227	0.430114	+	0.902775i	$0.358473\pi$
$264$	−95.2600	−5.86285
$265$	22.1324	1.35958
$266$	−35.2028	−2.15843
$267$	−10.6180	−0.649811
$268$	67.2530	4.10813
$269$	8.43062	0.514024	0.257012	−	0.966408i	$-0.417262\pi$
$269$	8.43062	0.514024	0.257012	+	0.966408i	$0.417262\pi$
$270$	−3.38001	−0.205701
$271$	−5.04065	−0.306198	−0.153099	−	0.988211i	$-0.548925\pi$
$271$	−5.04065	−0.306198	−0.153099	+	0.988211i	$0.548925\pi$
$272$	−4.64390	−0.281578
$273$	70.9633	4.29489
$274$	33.3032	2.01192
$275$	−9.21591	−0.555740
$276$	49.0885	2.95478
$277$	13.1693	0.791266	0.395633	−	0.918409i	$-0.370525\pi$
$277$	13.1693	0.791266	0.395633	+	0.918409i	$0.370525\pi$
$278$	12.2891	0.737052
$279$	−21.4186	−1.28230
$280$	83.0354	4.96231
$281$	−27.7271	−1.65406	−0.827029	−	0.562159i	$-0.809971\pi$
$281$	−27.7271	−1.65406	−0.827029	+	0.562159i	$0.809971\pi$
$282$	38.0955	2.26855
$283$	−9.76259	−0.580325	−0.290163	−	0.956977i	$-0.593709\pi$
$283$	−9.76259	−0.580325	−0.290163	+	0.956977i	$0.593709\pi$
$284$	24.4335	1.44986
$285$	17.8326	1.05631
$286$	93.1457	5.50782
$287$	−48.8936	−2.88610
$288$	−21.8189	−1.28569
$289$	−16.6899	−0.981757
$290$	12.2842	0.721354
$291$	−13.2737	−0.778117
$292$	−62.5014	−3.65762
$293$	6.14734	0.359131	0.179566	−	0.983746i	$-0.442531\pi$
$293$	6.14734	0.359131	0.179566	+	0.983746i	$0.442531\pi$
$294$	95.2541	5.55533
$295$	19.7795	1.15160
$296$	27.8753	1.62022
$297$	−2.95442	−0.171433
$298$	14.3571	0.831683
$299$	−27.3643	−1.58252
$300$	−17.8200	−1.02884
$301$	−39.8882	−2.29912
$302$	−34.6365	−1.99311
$303$	45.9130	2.63763
$304$	−24.0744	−1.38076
$305$	−38.7594	−2.21935
$306$	4.00427	0.228909
$307$	10.8290	0.618045	0.309022	−	0.951055i	$-0.399998\pi$
$307$	10.8290	0.618045	0.309022	+	0.951055i	$0.399998\pi$
$308$	127.311	7.25422
$309$	−45.3523	−2.58000
$310$	50.8770	2.88962
$311$	17.8056	1.00966	0.504830	−	0.863219i	$-0.331555\pi$
$311$	17.8056	1.00966	0.504830	+	0.863219i	$0.331555\pi$
$312$	102.679	5.81307
$313$	−29.4567	−1.66499	−0.832496	−	0.554032i	$-0.813089\pi$
$313$	−29.4567	−1.66499	−0.832496	+	0.554032i	$0.813089\pi$
$314$	48.7095	2.74884
$315$	−33.8401	−1.90667
$316$	−22.2462	−1.25145
$317$	6.26843	0.352070	0.176035	−	0.984384i	$-0.443673\pi$
$317$	6.26843	0.352070	0.176035	+	0.984384i	$0.443673\pi$
$318$	53.4881	2.99946
$319$	10.7375	0.601183
$320$	9.00688	0.503500
$321$	13.4060	0.748248
$322$	−53.4802	−2.98033
$323$	1.60773	0.0894567
$324$	−44.6219	−2.47900
$325$	9.93369	0.551022
$326$	−3.34654	−0.185348
$327$	−12.9284	−0.714942
$328$	−70.7459	−3.90629
$329$	−29.0256	−1.60023
$330$	−92.2166	−5.07636
$331$	−8.40186	−0.461808	−0.230904	−	0.972977i	$-0.574168\pi$
$331$	−8.40186	−0.461808	−0.230904	+	0.972977i	$0.574168\pi$
$332$	23.2032	1.27344
$333$	−11.3603	−0.622539
$334$	−31.2621	−1.71059
$335$	37.1161	2.02787
$336$	94.8462	5.17428
$337$	5.64169	0.307322	0.153661	−	0.988124i	$-0.450894\pi$
$337$	5.64169	0.307322	0.153661	+	0.988124i	$0.450894\pi$
$338$	−66.8708	−3.63729
$339$	5.96811	0.324143
$340$	−6.65193	−0.360752
$341$	44.4709	2.40824
$342$	20.7585	1.12249
$343$	−39.4817	−2.13181
$344$	−57.7157	−3.11182
$345$	27.0913	1.45855
$346$	−6.94621	−0.373431
$347$	16.1896	0.869101	0.434551	−	0.900647i	$-0.356907\pi$
$347$	16.1896	0.869101	0.434551	+	0.900647i	$0.356907\pi$
$348$	20.7621	1.11296
$349$	20.4982	1.09724	0.548621	−	0.836071i	$-0.315153\pi$
$349$	20.4982	1.09724	0.548621	+	0.836071i	$0.315153\pi$
$350$	19.4142	1.03773
$351$	3.18453	0.169978
$352$	45.3020	2.41460
$353$	4.09495	0.217952	0.108976	−	0.994044i	$-0.465243\pi$
$353$	4.09495	0.217952	0.108976	+	0.994044i	$0.465243\pi$
$354$	47.8017	2.54063
$355$	13.4846	0.715686
$356$	20.5328	1.08824
$357$	−6.33401	−0.335232
$358$	−19.1427	−1.01172
$359$	−17.1731	−0.906363	−0.453182	−	0.891418i	$-0.649711\pi$
$359$	−17.1731	−0.906363	−0.453182	+	0.891418i	$0.649711\pi$
$360$	−48.9645	−2.58065
$361$	−10.6654	−0.561335
$362$	−3.63502	−0.191053
$363$	−54.1417	−2.84170
$364$	−137.227	−7.19264
$365$	−34.4937	−1.80549
$366$	−93.6711	−4.89627
$367$	−3.21091	−0.167608	−0.0838040	−	0.996482i	$-0.526707\pi$
$367$	−3.21091	−0.167608	−0.0838040	+	0.996482i	$0.526707\pi$
$368$	−36.5738	−1.90654
$369$	28.8317	1.50092
$370$	26.9848	1.40287
$371$	−40.7534	−2.11581
$372$	85.9894	4.45834
$373$	−4.04825	−0.209611	−0.104805	−	0.994493i	$-0.533422\pi$
$373$	−4.04825	−0.209611	−0.104805	+	0.994493i	$0.533422\pi$
$374$	−8.31396	−0.429905
$375$	21.0500	1.08702
$376$	−41.9982	−2.16589
$377$	−11.5738	−0.596079
$378$	6.22378	0.320117
$379$	−27.7735	−1.42663	−0.713314	−	0.700845i	$-0.752807\pi$
$379$	−27.7735	−1.42663	−0.713314	+	0.700845i	$0.752807\pi$
$380$	−34.4842	−1.76900
$381$	−10.3456	−0.530021
$382$	12.4665	0.637843
$383$	15.2091	0.777147	0.388573	−	0.921418i	$-0.372968\pi$
$383$	15.2091	0.777147	0.388573	+	0.921418i	$0.372968\pi$
$384$	−15.8903	−0.810901
$385$	70.2614	3.58085
$386$	17.6755	0.899661
$387$	23.5214	1.19566
$388$	25.6682	1.30311
$389$	29.9618	1.51912	0.759562	−	0.650434i	$-0.225413\pi$
$389$	29.9618	1.51912	0.759562	+	0.650434i	$0.225413\pi$
$390$	99.3990	5.03326
$391$	2.44247	0.123521
$392$	−105.012	−5.30392
$393$	−17.8975	−0.902812
$394$	−53.1677	−2.67855
$395$	−12.2774	−0.617744
$396$	−75.0731	−3.77256
$397$	14.7805	0.741814	0.370907	−	0.928670i	$-0.379047\pi$
$397$	14.7805	0.741814	0.370907	+	0.928670i	$0.379047\pi$
$398$	51.2098	2.56692
$399$	−32.8361	−1.64386
$400$	13.2769	0.663845
$401$	20.2007	1.00878	0.504388	−	0.863477i	$-0.331718\pi$
$401$	20.2007	1.00878	0.504388	+	0.863477i	$0.331718\pi$
$402$	89.6997	4.47381
$403$	−47.9346	−2.38779
$404$	−88.7852	−4.41723
$405$	−24.6263	−1.22369
$406$	−22.6195	−1.12259
$407$	23.5870	1.16917
$408$	−9.16492	−0.453731
$409$	−9.28632	−0.459179	−0.229589	−	0.973288i	$-0.573738\pi$
$409$	−9.28632	−0.459179	−0.229589	+	0.973288i	$0.573738\pi$
$410$	−68.4857	−3.38227
$411$	31.0641	1.53228
$412$	87.7009	4.32071
$413$	−36.4209	−1.79215
$414$	31.5363	1.54992
$415$	12.8056	0.628600
$416$	−48.8303	−2.39410
$417$	11.4629	0.561340
$418$	−43.1003	−2.10811
$419$	21.8182	1.06589	0.532945	−	0.846150i	$-0.321085\pi$
$419$	21.8182	1.06589	0.532945	+	0.846150i	$0.321085\pi$
$420$	135.858	6.62919
$421$	12.4374	0.606162	0.303081	−	0.952965i	$-0.401985\pi$
$421$	12.4374	0.606162	0.303081	+	0.952965i	$0.401985\pi$
$422$	33.5282	1.63212
$423$	17.1159	0.832202
$424$	−58.9676	−2.86372
$425$	−0.886658	−0.0430092
$426$	32.5886	1.57892
$427$	71.3695	3.45381
$428$	−25.9241	−1.25309
$429$	86.8834	4.19477
$430$	−55.8718	−2.69438
$431$	−29.3130	−1.41196	−0.705978	−	0.708234i	$-0.749492\pi$
$431$	−29.3130	−1.41196	−0.705978	+	0.708234i	$0.749492\pi$
$432$	4.25629	0.204781
$433$	0.0501689	0.00241096	0.00120548	−	0.999999i	$-0.499616\pi$
$433$	0.0501689	0.00241096	0.00120548	+	0.999999i	$0.499616\pi$
$434$	−93.6823	−4.49690
$435$	11.4583	0.549385
$436$	25.0006	1.19731
$437$	12.6620	0.605705
$438$	−83.3622	−3.98320
$439$	27.1006	1.29344	0.646720	−	0.762728i	$-0.276140\pi$
$439$	27.1006	1.29344	0.646720	+	0.762728i	$0.276140\pi$
$440$	101.664	4.84663
$441$	42.7966	2.03793
$442$	8.96150	0.426255
$443$	16.4223	0.780249	0.390125	−	0.920762i	$-0.372432\pi$
$443$	16.4223	0.780249	0.390125	+	0.920762i	$0.372432\pi$
$444$	45.6081	2.16447
$445$	11.3318	0.537178
$446$	52.5609	2.48883
$447$	13.3918	0.633411
$448$	−16.5848	−0.783559
$449$	21.9065	1.03383	0.516915	−	0.856037i	$-0.327080\pi$
$449$	21.9065	1.03383	0.516915	+	0.856037i	$0.327080\pi$
$450$	−11.4482	−0.539674
$451$	−59.8625	−2.81881
$452$	−11.5410	−0.542841
$453$	−32.3079	−1.51796
$454$	−16.5686	−0.777605
$455$	−75.7337	−3.55045
$456$	−47.5118	−2.22494
$457$	−35.3890	−1.65543	−0.827715	−	0.561149i	$-0.810359\pi$
$457$	−35.3890	−1.65543	−0.827715	+	0.561149i	$0.810359\pi$
$458$	−71.7268	−3.35157
$459$	−0.284244	−0.0132674
$460$	−52.3884	−2.44262
$461$	24.7892	1.15455	0.577273	−	0.816551i	$-0.304117\pi$
$461$	24.7892	1.15455	0.577273	+	0.816551i	$0.304117\pi$
$462$	169.803	7.89995
$463$	−33.6062	−1.56181	−0.780905	−	0.624650i	$-0.785242\pi$
$463$	−33.6062	−1.56181	−0.780905	+	0.624650i	$0.785242\pi$
$464$	−15.4689	−0.718128
$465$	47.4565	2.20074
$466$	−53.1404	−2.46168
$467$	0.652499	0.0301940	0.0150970	−	0.999886i	$-0.495194\pi$
$467$	0.652499	0.0301940	0.0150970	+	0.999886i	$0.495194\pi$
$468$	80.9202	3.74054
$469$	−68.3437	−3.15582
$470$	−40.6564	−1.87534
$471$	45.4347	2.09352
$472$	−52.6987	−2.42565
$473$	−48.8368	−2.24552
$474$	−29.6713	−1.36285
$475$	−4.59652	−0.210903
$476$	12.2485	0.561411
$477$	24.0316	1.10033
$478$	60.7351	2.77796
$479$	−12.4196	−0.567465	−0.283732	−	0.958903i	$-0.591573\pi$
$479$	−12.4196	−0.567465	−0.283732	+	0.958903i	$0.591573\pi$
$480$	48.3433	2.20656
$481$	−25.4241	−1.15924
$482$	−32.8275	−1.49525
$483$	−49.8846	−2.26983
$484$	104.698	4.75898
$485$	14.1660	0.643244
$486$	−55.5658	−2.52052
$487$	21.7727	0.986614	0.493307	−	0.869855i	$-0.335788\pi$
$487$	21.7727	0.986614	0.493307	+	0.869855i	$0.335788\pi$
$488$	103.267	4.67468
$489$	−3.12155	−0.141161
$490$	−101.657	−4.59241
$491$	−40.1119	−1.81023	−0.905113	−	0.425171i	$-0.860214\pi$
$491$	−40.1119	−1.81023	−0.905113	+	0.425171i	$0.860214\pi$
$492$	−115.751	−5.21844
$493$	1.03305	0.0465261
$494$	46.4572	2.09021
$495$	−41.4319	−1.86222
$496$	−64.0671	−2.87670
$497$	−24.8298	−1.11377
$498$	30.9476	1.38680
$499$	4.90870	0.219744	0.109872	−	0.993946i	$-0.464956\pi$
$499$	4.90870	0.219744	0.109872	+	0.993946i	$0.464956\pi$
$500$	−40.7059	−1.82042
$501$	−29.1603	−1.30279
$502$	−61.5498	−2.74710
$503$	0.0395248	0.00176232	0.000881162	−	1.00000i	$-0.499720\pi$
$503$	0.0395248	0.00176232	0.000881162		1.00000i	$0.499720\pi$
$504$	90.1607	4.01608
$505$	−48.9994	−2.18045
$506$	−65.4780	−2.91085
$507$	−62.3750	−2.77017
$508$	20.0060	0.887623
$509$	−21.1512	−0.937509	−0.468755	−	0.883328i	$-0.655297\pi$
$509$	−21.1512	−0.937509	−0.468755	+	0.883328i	$0.655297\pi$
$510$	−8.87212	−0.392864
$511$	63.5150	2.80974
$512$	48.8240	2.15774
$513$	−1.47355	−0.0650586
$514$	19.1896	0.846417
$515$	48.4010	2.13280
$516$	−94.4314	−4.15711
$517$	−35.5373	−1.56293
$518$	−49.6884	−2.18318
$519$	−6.47921	−0.284406
$520$	−109.582	−4.80548
$521$	−2.11118	−0.0924923	−0.0462462	−	0.998930i	$-0.514726\pi$
$521$	−2.11118	−0.0924923	−0.0462462	+	0.998930i	$0.514726\pi$
$522$	13.3383	0.583803
$523$	−43.6512	−1.90873	−0.954366	−	0.298640i	$-0.903467\pi$
$523$	−43.6512	−1.90873	−0.954366	+	0.298640i	$0.903467\pi$
$524$	34.6098	1.51193
$525$	18.1090	0.790340
$526$	−35.9812	−1.56885
$527$	4.27853	0.186376
$528$	116.124	5.05366
$529$	−3.76391	−0.163648
$530$	−57.0837	−2.47956
$531$	21.4768	0.932012
$532$	63.4975	2.75297
$533$	64.5249	2.79488
$534$	27.3859	1.18510
$535$	−14.3072	−0.618552
$536$	−98.8889	−4.27135
$537$	−17.8557	−0.770529
$538$	−21.7442	−0.937460
$539$	−88.8574	−3.82736
$540$	6.09673	0.262362
$541$	−0.540551	−0.0232401	−0.0116201	−	0.999932i	$-0.503699\pi$
$541$	−0.540551	−0.0232401	−0.0116201	+	0.999932i	$0.503699\pi$
$542$	13.0008	0.558434
$543$	−3.39064	−0.145506
$544$	4.35848	0.186868
$545$	13.7975	0.591020
$546$	−183.028	−7.83289
$547$	1.18342	0.0505995	0.0252998	−	0.999680i	$-0.491946\pi$
$547$	1.18342	0.0505995	0.0252998	+	0.999680i	$0.491946\pi$
$548$	−60.0709	−2.56610
$549$	−42.0853	−1.79616
$550$	23.7696	1.01354
$551$	5.35541	0.228148
$552$	−72.1799	−3.07218
$553$	22.6070	0.961348
$554$	−33.9662	−1.44309
$555$	25.1705	1.06843
$556$	−22.1666	−0.940074
$557$	−2.51856	−0.106715	−0.0533573	−	0.998575i	$-0.516992\pi$
$557$	−2.51856	−0.106715	−0.0533573	+	0.998575i	$0.516992\pi$
$558$	55.2428	2.33861
$559$	52.6405	2.22646
$560$	−101.222	−4.27741
$561$	−7.75500	−0.327416
$562$	71.5135	3.01662
$563$	20.8115	0.877101	0.438551	−	0.898707i	$-0.355492\pi$
$563$	20.8115	0.877101	0.438551	+	0.898707i	$0.355492\pi$
$564$	−68.7152	−2.89343
$565$	−6.36931	−0.267959
$566$	25.1796	1.05838
$567$	45.3456	1.90434
$568$	−35.9271	−1.50747
$569$	−35.6203	−1.49328	−0.746640	−	0.665229i	$-0.768334\pi$
$569$	−35.6203	−1.49328	−0.746640	+	0.665229i	$0.768334\pi$
$570$	−45.9939	−1.92647
$571$	−24.5571	−1.02768	−0.513841	−	0.857886i	$-0.671778\pi$
$571$	−24.5571	−1.02768	−0.513841	+	0.857886i	$0.671778\pi$
$572$	−168.013	−7.02496
$573$	11.6284	0.485783
$574$	126.106	5.26357
$575$	−6.98303	−0.291212
$576$	9.77977	0.407490
$577$	−18.7161	−0.779161	−0.389580	−	0.920992i	$-0.627380\pi$
$577$	−18.7161	−0.779161	−0.389580	+	0.920992i	$0.627380\pi$
$578$	43.0465	1.79050
$579$	16.4872	0.685184
$580$	−22.1578	−0.920052
$581$	−23.5795	−0.978243
$582$	34.2354	1.41910
$583$	−49.8962	−2.06649
$584$	91.9022	3.80294
$585$	44.6588	1.84641
$586$	−15.8552	−0.654972
$587$	−19.3334	−0.797973	−0.398986	−	0.916957i	$-0.630638\pi$
$587$	−19.3334	−0.797973	−0.398986	+	0.916957i	$0.630638\pi$
$588$	−171.816	−7.08556
$589$	22.1803	0.913922
$590$	−51.0151	−2.10026
$591$	−49.5932	−2.03999
$592$	−33.9807	−1.39660
$593$	−26.1405	−1.07346	−0.536730	−	0.843754i	$-0.680341\pi$
$593$	−26.1405	−1.07346	−0.536730	+	0.843754i	$0.680341\pi$
$594$	7.62004	0.312654
$595$	6.75981	0.277125
$596$	−25.8967	−1.06077
$597$	47.7669	1.95497
$598$	70.5778	2.88614
$599$	−10.8290	−0.442460	−0.221230	−	0.975222i	$-0.571007\pi$
$599$	−10.8290	−0.442460	−0.221230	+	0.975222i	$0.571007\pi$
$600$	26.2025	1.06971
$601$	6.53243	0.266464	0.133232	−	0.991085i	$-0.457465\pi$
$601$	6.53243	0.266464	0.133232	+	0.991085i	$0.457465\pi$
$602$	102.880	4.19306
$603$	40.3010	1.64119
$604$	62.4760	2.54211
$605$	57.7812	2.34914
$606$	−118.419	−4.81043
$607$	32.8694	1.33413	0.667065	−	0.745000i	$-0.267551\pi$
$607$	32.8694	1.33413	0.667065	+	0.745000i	$0.267551\pi$
$608$	22.5948	0.916338
$609$	−21.0988	−0.854966
$610$	99.9680	4.04759
$611$	38.3051	1.54966
$612$	−7.22274	−0.291962
$613$	−24.3500	−0.983489	−0.491744	−	0.870740i	$-0.663641\pi$
$613$	−24.3500	−0.983489	−0.491744	+	0.870740i	$0.663641\pi$
$614$	−27.9302	−1.12717
$615$	−63.8813	−2.57594
$616$	−187.198	−7.54244
$617$	27.2576	1.09735	0.548675	−	0.836036i	$-0.315133\pi$
$617$	27.2576	1.09735	0.548675	+	0.836036i	$0.315133\pi$
$618$	116.972	4.70532
$619$	−24.7946	−0.996578	−0.498289	−	0.867011i	$-0.666038\pi$
$619$	−24.7946	−0.996578	−0.498289	+	0.867011i	$0.666038\pi$
$620$	−91.7699	−3.68557
$621$	−2.23861	−0.0898323
$622$	−45.9240	−1.84139
$623$	−20.8658	−0.835970
$624$	−125.169	−5.01075
$625$	−30.4258	−1.21703
$626$	75.9746	3.03656
$627$	−40.2026	−1.60554
$628$	−87.8603	−3.50601
$629$	2.26930	0.0904828
$630$	87.2803	3.47733
$631$	30.8386	1.22767	0.613833	−	0.789436i	$-0.289627\pi$
$631$	30.8386	1.22767	0.613833	+	0.789436i	$0.289627\pi$
$632$	32.7109	1.30117
$633$	31.2740	1.24303
$634$	−16.1675	−0.642094
$635$	11.0411	0.438151
$636$	−96.4797	−3.82567
$637$	95.7781	3.79487
$638$	−27.6940	−1.09642
$639$	14.6417	0.579216
$640$	16.9585	0.670345
$641$	14.7832	0.583900	0.291950	−	0.956434i	$-0.405696\pi$
$641$	14.7832	0.583900	0.291950	+	0.956434i	$0.405696\pi$
$642$	−34.5766	−1.36463
$643$	−10.2608	−0.404646	−0.202323	−	0.979319i	$-0.564849\pi$
$643$	−10.2608	−0.404646	−0.202323	+	0.979319i	$0.564849\pi$
$644$	96.4654	3.80127
$645$	−52.1155	−2.05204
$646$	−4.14666	−0.163148
$647$	−11.3332	−0.445554	−0.222777	−	0.974869i	$-0.571512\pi$
$647$	−11.3332	−0.445554	−0.222777	+	0.974869i	$0.571512\pi$
$648$	65.6122	2.57749
$649$	−44.5916	−1.75038
$650$	−25.6209	−1.00494
$651$	−87.3839	−3.42485
$652$	6.03636	0.236402
$653$	−10.9118	−0.427011	−0.213506	−	0.976942i	$-0.568488\pi$
$653$	−10.9118	−0.427011	−0.213506	+	0.976942i	$0.568488\pi$
$654$	33.3449	1.30389
$655$	19.1007	0.746326
$656$	86.2409	3.36714
$657$	−37.4537	−1.46121
$658$	74.8627	2.91845
$659$	−6.84186	−0.266521	−0.133261	−	0.991081i	$-0.542545\pi$
$659$	−6.84186	−0.266521	−0.133261	+	0.991081i	$0.542545\pi$
$660$	166.337	6.47465
$661$	3.65219	0.142054	0.0710268	−	0.997474i	$-0.477372\pi$
$661$	3.65219	0.142054	0.0710268	+	0.997474i	$0.477372\pi$
$662$	21.6700	0.842230
$663$	8.35901	0.324637
$664$	−34.1180	−1.32404
$665$	35.0435	1.35893
$666$	29.3004	1.13537
$667$	8.13593	0.315025
$668$	56.3893	2.18177
$669$	49.0271	1.89550
$670$	−95.7296	−3.69836
$671$	87.3807	3.37330
$672$	−89.0169	−3.43390
$673$	−21.8535	−0.842391	−0.421196	−	0.906970i	$-0.638389\pi$
$673$	−21.8535	−0.842391	−0.421196	+	0.906970i	$0.638389\pi$
$674$	−14.5510	−0.560484
$675$	0.812653	0.0312790
$676$	120.619	4.63919
$677$	2.19554	0.0843814	0.0421907	−	0.999110i	$-0.486566\pi$
$677$	2.19554	0.0843814	0.0421907	+	0.999110i	$0.486566\pi$
$678$	−15.3929	−0.591162
$679$	−26.0845	−1.00103
$680$	9.78102	0.375085
$681$	−15.4547	−0.592226
$682$	−114.699	−4.39206
$683$	−2.98136	−0.114079	−0.0570394	−	0.998372i	$-0.518166\pi$
$683$	−2.98136	−0.114079	−0.0570394	+	0.998372i	$0.518166\pi$
$684$	−37.4434	−1.43168
$685$	−33.1524	−1.26669
$686$	101.831	3.88793
$687$	−66.9045	−2.55257
$688$	70.3568	2.68233
$689$	53.7823	2.04894
$690$	−69.8739	−2.66005
$691$	−7.94681	−0.302311	−0.151155	−	0.988510i	$-0.548299\pi$
$691$	−7.94681	−0.302311	−0.151155	+	0.988510i	$0.548299\pi$
$692$	12.5293	0.476293
$693$	76.2906	2.89804
$694$	−41.7561	−1.58504
$695$	−12.2335	−0.464042
$696$	−30.5286	−1.15718
$697$	−5.75934	−0.218150
$698$	−52.8688	−2.00111
$699$	−49.5677	−1.87482
$700$	−35.0186	−1.32358
$701$	3.97224	0.150029	0.0750146	−	0.997182i	$-0.476100\pi$
$701$	3.97224	0.150029	0.0750146	+	0.997182i	$0.476100\pi$
$702$	−8.21353	−0.310000
$703$	11.7642	0.443697
$704$	−20.3055	−0.765292
$705$	−37.9230	−1.42826
$706$	−10.5617	−0.397494
$707$	90.2250	3.39326
$708$	−86.2228	−3.24045
$709$	−42.6199	−1.60062	−0.800312	−	0.599584i	$-0.795333\pi$
$709$	−42.6199	−1.60062	−0.800312	+	0.599584i	$0.795333\pi$
$710$	−34.7793	−1.30524
$711$	−13.3310	−0.499950
$712$	−30.1915	−1.13147
$713$	33.6963	1.26193
$714$	16.3367	0.611384
$715$	−92.7240	−3.46768
$716$	34.5288	1.29040
$717$	56.6518	2.11570
$718$	44.2929	1.65300
$719$	4.03996	0.150665	0.0753325	−	0.997158i	$-0.475998\pi$
$719$	4.03996	0.150665	0.0753325	+	0.997158i	$0.475998\pi$
$720$	59.6889	2.22447
$721$	−89.1232	−3.31912
$722$	27.5081	1.02374
$723$	−30.6204	−1.13879
$724$	6.55672	0.243678
$725$	−2.95348	−0.109690
$726$	139.642	5.18260
$727$	−13.2059	−0.489780	−0.244890	−	0.969551i	$-0.578752\pi$
$727$	−13.2059	−0.489780	−0.244890	+	0.969551i	$0.578752\pi$
$728$	201.778	7.47841
$729$	−23.0557	−0.853913
$730$	88.9661	3.29278
$731$	−4.69857	−0.173783
$732$	168.960	6.24495
$733$	−4.97259	−0.183667	−0.0918334	−	0.995774i	$-0.529273\pi$
$733$	−4.97259	−0.183667	−0.0918334	+	0.995774i	$0.529273\pi$
$734$	8.28156	0.305678
$735$	−94.8228	−3.49759
$736$	34.3259	1.26527
$737$	−83.6761	−3.08225
$738$	−74.3625	−2.73732
$739$	4.38991	0.161486	0.0807428	−	0.996735i	$-0.474271\pi$
$739$	4.38991	0.161486	0.0807428	+	0.996735i	$0.474271\pi$
$740$	−48.6741	−1.78929
$741$	43.3338	1.59191
$742$	105.111	3.85875
$743$	−53.3742	−1.95811	−0.979055	−	0.203597i	$-0.934737\pi$
$743$	−53.3742	−1.95811	−0.979055	+	0.203597i	$0.934737\pi$
$744$	−126.439	−4.63548
$745$	−14.2921	−0.523621
$746$	10.4412	0.382281
$747$	13.9044	0.508736
$748$	14.9964	0.548323
$749$	26.3445	0.962606
$750$	−54.2921	−1.98247
$751$	−24.5804	−0.896951	−0.448476	−	0.893795i	$-0.648033\pi$
$751$	−24.5804	−0.896951	−0.448476	+	0.893795i	$0.648033\pi$
$752$	51.1968	1.86695
$753$	−57.4117	−2.09220
$754$	29.8510	1.08711
$755$	34.4797	1.25485
$756$	−11.2262	−0.408293
$757$	−9.80375	−0.356323	−0.178162	−	0.984001i	$-0.557015\pi$
$757$	−9.80375	−0.356323	−0.178162	+	0.984001i	$0.557015\pi$
$758$	71.6333	2.60184
$759$	−61.0759	−2.21691
$760$	50.7057	1.83929
$761$	−30.7056	−1.11308	−0.556538	−	0.830822i	$-0.687871\pi$
$761$	−30.7056	−1.11308	−0.556538	+	0.830822i	$0.687871\pi$
$762$	26.6833	0.966634
$763$	−25.4060	−0.919759
$764$	−22.4866	−0.813538
$765$	−3.98614	−0.144119
$766$	−39.2272	−1.41733
$767$	48.0647	1.73552
$768$	57.8634	2.08797
$769$	−25.3528	−0.914244	−0.457122	−	0.889404i	$-0.651120\pi$
$769$	−25.3528	−0.914244	−0.457122	+	0.889404i	$0.651120\pi$
$770$	−181.218	−6.53064
$771$	17.8995	0.644633
$772$	−31.8824	−1.14747
$773$	−17.2901	−0.621881	−0.310940	−	0.950429i	$-0.600644\pi$
$773$	−17.2901	−0.621881	−0.310940	+	0.950429i	$0.600644\pi$
$774$	−60.6662	−2.18060
$775$	−12.2323	−0.439398
$776$	−37.7426	−1.35488
$777$	−46.3478	−1.66272
$778$	−77.2774	−2.77053
$779$	−29.8569	−1.06974
$780$	−179.292	−6.41968
$781$	−30.4002	−1.08780
$782$	−6.29961	−0.225274
$783$	−0.946824	−0.0338367
$784$	128.013	4.57188
$785$	−48.4890	−1.73065
$786$	46.1613	1.64652
$787$	48.5331	1.73002	0.865009	−	0.501757i	$-0.167313\pi$
$787$	48.5331	1.73002	0.865009	+	0.501757i	$0.167313\pi$
$788$	95.9018	3.41636
$789$	−33.5621	−1.19484
$790$	31.6659	1.12662
$791$	11.7281	0.417004
$792$	110.388	3.92245
$793$	−94.1864	−3.34466
$794$	−38.1219	−1.35290
$795$	−53.2459	−1.88844
$796$	−92.3702	−3.27398
$797$	20.3603	0.721198	0.360599	−	0.932721i	$-0.382572\pi$
$797$	20.3603	0.721198	0.360599	+	0.932721i	$0.382572\pi$
$798$	84.6908	2.99802
$799$	−3.41902	−0.120956
$800$	−12.4609	−0.440559
$801$	12.3042	0.434747
$802$	−52.1017	−1.83977
$803$	77.7642	2.74424
$804$	−161.797	−5.70613
$805$	53.2380	1.87639
$806$	123.633	4.35477
$807$	−20.2823	−0.713972
$808$	130.550	4.59273
$809$	33.6037	1.18144	0.590721	−	0.806876i	$-0.298843\pi$
$809$	33.6037	1.18144	0.590721	+	0.806876i	$0.298843\pi$
$810$	63.5160	2.23172
$811$	27.2298	0.956167	0.478084	−	0.878314i	$-0.341332\pi$
$811$	27.2298	0.956167	0.478084	+	0.878314i	$0.341332\pi$
$812$	40.8002	1.43181
$813$	12.1268	0.425304
$814$	−60.8356	−2.13229
$815$	3.33139	0.116694
$816$	11.1723	0.391107
$817$	−24.3578	−0.852172
$818$	23.9512	0.837435
$819$	−82.2325	−2.87344
$820$	123.532	4.31392
$821$	−28.4283	−0.992155	−0.496077	−	0.868278i	$-0.665227\pi$
$821$	−28.4283	−0.992155	−0.496077	+	0.868278i	$0.665227\pi$
$822$	−80.1205	−2.79452
$823$	−21.1946	−0.738796	−0.369398	−	0.929271i	$-0.620436\pi$
$823$	−21.1946	−0.738796	−0.369398	+	0.929271i	$0.620436\pi$
$824$	−128.956	−4.49238
$825$	22.1716	0.771915
$826$	93.9366	3.26847
$827$	39.5116	1.37395	0.686976	−	0.726680i	$-0.258938\pi$
$827$	39.5116	1.37395	0.686976	+	0.726680i	$0.258938\pi$
$828$	−56.8839	−1.97685
$829$	−38.8018	−1.34764	−0.673821	−	0.738895i	$-0.735348\pi$
$829$	−38.8018	−1.34764	−0.673821	+	0.738895i	$0.735348\pi$
$830$	−33.0280	−1.14642
$831$	−31.6826	−1.09906
$832$	21.8870	0.758795
$833$	−8.54893	−0.296203
$834$	−29.5650	−1.02375
$835$	31.1205	1.07697
$836$	77.7427	2.68879
$837$	−3.92142	−0.135544
$838$	−56.2735	−1.94394
$839$	−38.6502	−1.33435	−0.667177	−	0.744899i	$-0.732497\pi$
$839$	−38.6502	−1.33435	−0.667177	+	0.744899i	$0.732497\pi$
$840$	−199.766	−6.89258
$841$	−25.5589	−0.881341
$842$	−32.0785	−1.10550
$843$	66.7056	2.29746
$844$	−60.4768	−2.08170
$845$	66.5681	2.29001
$846$	−44.1452	−1.51774
$847$	−106.395	−3.65579
$848$	71.8830	2.46847
$849$	23.4868	0.806064
$850$	2.28686	0.0784388
$851$	17.8722	0.612652
$852$	−58.7820	−2.01384
$853$	42.4460	1.45332	0.726662	−	0.686995i	$-0.241071\pi$
$853$	42.4460	1.45332	0.726662	+	0.686995i	$0.241071\pi$
$854$	−184.076	−6.29895
$855$	−20.6645	−0.706711
$856$	38.1188	1.30287
$857$	−36.4790	−1.24610	−0.623049	−	0.782183i	$-0.714106\pi$
$857$	−36.4790	−1.24610	−0.623049	+	0.782183i	$0.714106\pi$
$858$	−224.089	−7.65028
$859$	−13.0297	−0.444569	−0.222284	−	0.974982i	$-0.571351\pi$
$859$	−13.0297	−0.444569	−0.222284	+	0.974982i	$0.571351\pi$
$860$	100.779	3.43655
$861$	117.628	4.00874
$862$	75.6039	2.57508
$863$	−8.55621	−0.291257	−0.145628	−	0.989339i	$-0.546520\pi$
$863$	−8.55621	−0.291257	−0.145628	+	0.989339i	$0.546520\pi$
$864$	−3.99470	−0.135902
$865$	6.91476	0.235109
$866$	−0.129395	−0.00439703
$867$	40.1524	1.36365
$868$	168.981	5.73557
$869$	27.6787	0.938937
$870$	−29.5533	−1.00195
$871$	90.1932	3.05608
$872$	−36.7609	−1.24488
$873$	15.3816	0.520587
$874$	−32.6577	−1.10466
$875$	41.3660	1.39843
$876$	150.366	5.08038
$877$	−10.4382	−0.352471	−0.176236	−	0.984348i	$-0.556392\pi$
$877$	−10.4382	−0.352471	−0.176236	+	0.984348i	$0.556392\pi$
$878$	−69.8977	−2.35893
$879$	−14.7892	−0.498828
$880$	−123.930	−4.17770
$881$	33.8291	1.13973	0.569866	−	0.821738i	$-0.306995\pi$
$881$	33.8291	1.13973	0.569866	+	0.821738i	$0.306995\pi$
$882$	−110.381	−3.71671
$883$	−33.1993	−1.11724	−0.558622	−	0.829422i	$-0.688670\pi$
$883$	−33.1993	−1.11724	−0.558622	+	0.829422i	$0.688670\pi$
$884$	−16.1644	−0.543668
$885$	−47.5853	−1.59956
$886$	−42.3565	−1.42299
$887$	−48.3323	−1.62284	−0.811419	−	0.584464i	$-0.801305\pi$
$887$	−48.3323	−1.62284	−0.811419	+	0.584464i	$0.801305\pi$
$888$	−67.0623	−2.25046
$889$	−20.3305	−0.681861
$890$	−29.2269	−0.979688
$891$	55.5185	1.85994
$892$	−94.8072	−3.17438
$893$	−17.7245	−0.593129
$894$	−34.5401	−1.15520
$895$	19.0560	0.636972
$896$	−31.2266	−1.04321
$897$	65.8328	2.19809
$898$	−56.5011	−1.88547
$899$	14.2519	0.475327
$900$	20.6498	0.688328
$901$	−4.80049	−0.159927
$902$	154.397	5.14086
$903$	95.9628	3.19344
$904$	16.9699	0.564409
$905$	3.61857	0.120285
$906$	83.3284	2.76840
$907$	−29.1330	−0.967346	−0.483673	−	0.875249i	$-0.660698\pi$
$907$	−29.1330	−0.967346	−0.483673	+	0.875249i	$0.660698\pi$
$908$	29.8859	0.991797
$909$	−53.2041	−1.76467
$910$	195.332	6.47519
$911$	1.50117	0.0497360	0.0248680	−	0.999691i	$-0.492083\pi$
$911$	1.50117	0.0497360	0.0248680	+	0.999691i	$0.492083\pi$
$912$	57.9180	1.91786
$913$	−28.8694	−0.955437
$914$	91.2753	3.01912
$915$	93.2470	3.08265
$916$	129.378	4.27477
$917$	−35.1710	−1.16145
$918$	0.733120	0.0241966
$919$	−15.0304	−0.495807	−0.247903	−	0.968785i	$-0.579742\pi$
$919$	−15.0304	−0.495807	−0.247903	+	0.968785i	$0.579742\pi$
$920$	77.0321	2.53967
$921$	−26.0524	−0.858455
$922$	−63.9361	−2.10562
$923$	32.7679	1.07857
$924$	−306.284	−10.0760
$925$	−6.48792	−0.213322
$926$	86.6769	2.84838
$927$	52.5544	1.72611
$928$	14.5182	0.476584
$929$	40.1387	1.31691	0.658454	−	0.752621i	$-0.271211\pi$
$929$	40.1387	1.31691	0.658454	+	0.752621i	$0.271211\pi$
$930$	−122.400	−4.01364
$931$	−44.3184	−1.45248
$932$	95.8526	3.13976
$933$	−42.8365	−1.40240
$934$	−1.68292	−0.0550669
$935$	8.27632	0.270665
$936$	−118.985	−3.88915
$937$	−36.3383	−1.18712	−0.593560	−	0.804790i	$-0.702278\pi$
$937$	−36.3383	−1.18712	−0.593560	+	0.804790i	$0.702278\pi$
$938$	176.272	5.75548
$939$	70.8667	2.31265
$940$	73.3345	2.39191
$941$	35.5298	1.15824	0.579118	−	0.815243i	$-0.303397\pi$
$941$	35.5298	1.15824	0.579118	+	0.815243i	$0.303397\pi$
$942$	−117.185	−3.81809
$943$	−45.3586	−1.47708
$944$	64.2410	2.09087
$945$	−6.19560	−0.201543
$946$	125.960	4.09531
$947$	−11.0171	−0.358007	−0.179004	−	0.983848i	$-0.557287\pi$
$947$	−11.0171	−0.358007	−0.179004	+	0.983848i	$0.557287\pi$
$948$	53.5199	1.73824
$949$	−83.8209	−2.72094
$950$	11.8553	0.384637
$951$	−15.0805	−0.489020
$952$	−18.0103	−0.583716
$953$	27.6282	0.894966	0.447483	−	0.894292i	$-0.352320\pi$
$953$	27.6282	0.894966	0.447483	+	0.894292i	$0.352320\pi$
$954$	−61.9822	−2.00675
$955$	−12.4101	−0.401581
$956$	−109.552	−3.54315
$957$	−25.8321	−0.835034
$958$	32.0325	1.03492
$959$	61.0451	1.97125
$960$	−21.6687	−0.699354
$961$	28.0265	0.904079
$962$	65.5738	2.11418
$963$	−15.5349	−0.500604
$964$	59.2129	1.90712
$965$	−17.5955	−0.566419
$966$	128.662	4.13964
$967$	−13.9563	−0.448803	−0.224402	−	0.974497i	$-0.572043\pi$
$967$	−13.9563	−0.448803	−0.224402	+	0.974497i	$0.572043\pi$
$968$	−153.947	−4.94806
$969$	−3.86788	−0.124254
$970$	−36.5368	−1.17313
$971$	−19.2858	−0.618910	−0.309455	−	0.950914i	$-0.600147\pi$
$971$	−19.2858	−0.618910	−0.309455	+	0.950914i	$0.600147\pi$
$972$	100.227	3.21480
$973$	22.5261	0.722153
$974$	−56.1560	−1.79935
$975$	−23.8984	−0.765362
$976$	−125.885	−4.02949
$977$	3.97563	0.127192	0.0635959	−	0.997976i	$-0.479743\pi$
$977$	3.97563	0.127192	0.0635959	+	0.997976i	$0.479743\pi$
$978$	8.05109	0.257445
$979$	−25.5469	−0.816481
$980$	183.366	5.85740
$981$	14.9815	0.478321
$982$	103.457	3.30143
$983$	20.8569	0.665232	0.332616	−	0.943062i	$-0.392069\pi$
$983$	20.8569	0.665232	0.332616	+	0.943062i	$0.392069\pi$
$984$	170.200	5.42578
$985$	52.9270	1.68639
$986$	−2.66443	−0.0848527
$987$	69.8296	2.22270
$988$	−83.7977	−2.66596
$989$	−37.0044	−1.17667
$990$	106.861	3.39626
$991$	13.1418	0.417463	0.208731	−	0.977973i	$-0.433067\pi$
$991$	13.1418	0.417463	0.208731	+	0.977973i	$0.433067\pi$
$992$	60.1295	1.90911
$993$	20.2131	0.641444
$994$	64.0409	2.03125
$995$	−50.9780	−1.61611
$996$	−55.8221	−1.76879
$997$	50.5623	1.60132	0.800662	−	0.599117i	$-0.204481\pi$
$997$	50.5623	1.60132	0.800662	+	0.599117i	$0.204481\pi$
$998$	−12.6605	−0.400762
$999$	−2.07989	−0.0658048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.12	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.12	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57920 q^{2} -2.40579 q^{3} +4.65225 q^{4} +2.56752 q^{5} +6.20501 q^{6} -4.72770 q^{7} -6.84068 q^{8} +2.78784 q^{9} +O(q^{10})\)	\(q-2.57920 q^{2} -2.40579 q^{3} +4.65225 q^{4} +2.56752 q^{5} +6.20501 q^{6} -4.72770 q^{7} -6.84068 q^{8} +2.78784 q^{9} -6.62214 q^{10} -5.78832 q^{11} -11.1924 q^{12} +6.23915 q^{13} +12.1937 q^{14} -6.17692 q^{15} +8.33896 q^{16} -0.556892 q^{17} -7.19039 q^{18} -2.88698 q^{19} +11.9447 q^{20} +11.3739 q^{21} +14.9292 q^{22} -4.38590 q^{23} +16.4573 q^{24} +1.59215 q^{25} -16.0920 q^{26} +0.510411 q^{27} -21.9945 q^{28} -1.85502 q^{29} +15.9315 q^{30} -7.68287 q^{31} -7.82644 q^{32} +13.9255 q^{33} +1.43633 q^{34} -12.1385 q^{35} +12.9697 q^{36} -4.07493 q^{37} +7.44608 q^{38} -15.0101 q^{39} -17.5636 q^{40} +10.3419 q^{41} -29.3354 q^{42} +8.43713 q^{43} -26.9288 q^{44} +7.15783 q^{45} +11.3121 q^{46} +6.13947 q^{47} -20.0618 q^{48} +15.3512 q^{49} -4.10648 q^{50} +1.33977 q^{51} +29.0261 q^{52} +8.62014 q^{53} -1.31645 q^{54} -14.8616 q^{55} +32.3407 q^{56} +6.94547 q^{57} +4.78447 q^{58} +7.70372 q^{59} -28.7366 q^{60} -15.0960 q^{61} +19.8156 q^{62} -13.1801 q^{63} +3.50801 q^{64} +16.0191 q^{65} -35.9166 q^{66} +14.4560 q^{67} -2.59080 q^{68} +10.5516 q^{69} +31.3075 q^{70} +5.25198 q^{71} -19.0707 q^{72} -13.4347 q^{73} +10.5101 q^{74} -3.83039 q^{75} -13.4310 q^{76} +27.3655 q^{77} +38.7140 q^{78} -4.78182 q^{79} +21.4104 q^{80} -9.59147 q^{81} -26.6739 q^{82} +4.98752 q^{83} +52.9141 q^{84} -1.42983 q^{85} -21.7610 q^{86} +4.46280 q^{87} +39.5961 q^{88} +4.41352 q^{89} -18.4615 q^{90} -29.4968 q^{91} -20.4043 q^{92} +18.4834 q^{93} -15.8349 q^{94} -7.41237 q^{95} +18.8288 q^{96} +5.51738 q^{97} -39.5936 q^{98} -16.1369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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