LMFDB - Embedded newform 6022.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$2$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.445042$ of defining polynomial
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} -0.753020 q^{5} -1.44504 q^{6} -4.35690 q^{7} +1.00000 q^{8} -0.911854 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} -0.753020 q^{5} -1.44504 q^{6} -4.35690 q^{7} +1.00000 q^{8} -0.911854 q^{9} -0.753020 q^{10} -4.44504 q^{11} -1.44504 q^{12} -2.75302 q^{13} -4.35690 q^{14} +1.08815 q^{15} +1.00000 q^{16} -4.24698 q^{17} -0.911854 q^{18} -6.63102 q^{19} -0.753020 q^{20} +6.29590 q^{21} -4.44504 q^{22} +0.0489173 q^{23} -1.44504 q^{24} -4.43296 q^{25} -2.75302 q^{26} +5.65279 q^{27} -4.35690 q^{28} -10.1588 q^{29} +1.08815 q^{30} -3.26875 q^{31} +1.00000 q^{32} +6.42327 q^{33} -4.24698 q^{34} +3.28083 q^{35} -0.911854 q^{36} -1.50604 q^{37} -6.63102 q^{38} +3.97823 q^{39} -0.753020 q^{40} +10.3937 q^{41} +6.29590 q^{42} +10.5036 q^{43} -4.44504 q^{44} +0.686645 q^{45} +0.0489173 q^{46} -5.63102 q^{47} -1.44504 q^{48} +11.9825 q^{49} -4.43296 q^{50} +6.13706 q^{51} -2.75302 q^{52} -6.67994 q^{53} +5.65279 q^{54} +3.34721 q^{55} -4.35690 q^{56} +9.58211 q^{57} -10.1588 q^{58} +8.54288 q^{59} +1.08815 q^{60} +0.185981 q^{61} -3.26875 q^{62} +3.97285 q^{63} +1.00000 q^{64} +2.07308 q^{65} +6.42327 q^{66} +4.48188 q^{67} -4.24698 q^{68} -0.0706876 q^{69} +3.28083 q^{70} -13.2838 q^{71} -0.911854 q^{72} -10.2838 q^{73} -1.50604 q^{74} +6.40581 q^{75} -6.63102 q^{76} +19.3666 q^{77} +3.97823 q^{78} +3.94869 q^{79} -0.753020 q^{80} -5.43296 q^{81} +10.3937 q^{82} +6.76809 q^{83} +6.29590 q^{84} +3.19806 q^{85} +10.5036 q^{86} +14.6799 q^{87} -4.44504 q^{88} -1.46681 q^{89} +0.686645 q^{90} +11.9946 q^{91} +0.0489173 q^{92} +4.72348 q^{93} -5.63102 q^{94} +4.99330 q^{95} -1.44504 q^{96} -5.52111 q^{97} +11.9825 q^{98} +4.05323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9} - 7 q^{10} - 13 q^{11} - 4 q^{12} - 13 q^{13} - 9 q^{14} + 7 q^{15} + 3 q^{16} - 8 q^{17} + q^{18} - 5 q^{19} - 7 q^{20} + 5 q^{21} - 13 q^{22} - 9 q^{23} - 4 q^{24} + 6 q^{25} - 13 q^{26} - q^{27} - 9 q^{28} - 22 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} + 22 q^{33} - 8 q^{34} + 21 q^{35} + q^{36} - 14 q^{37} - 5 q^{38} + 15 q^{39} - 7 q^{40} - q^{41} + 5 q^{42} - 13 q^{44} - 9 q^{46} - 2 q^{47} - 4 q^{48} + 20 q^{49} + 6 q^{50} + 13 q^{51} - 13 q^{52} + 4 q^{53} - q^{54} + 28 q^{55} - 9 q^{56} + 23 q^{57} - 22 q^{58} + 7 q^{59} + 7 q^{60} - 14 q^{61} - 2 q^{62} + 18 q^{63} + 3 q^{64} + 35 q^{65} + 22 q^{66} - 15 q^{67} - 8 q^{68} + 12 q^{69} + 21 q^{70} - 7 q^{71} + q^{72} + 2 q^{73} - 14 q^{74} + 6 q^{75} - 5 q^{76} + 32 q^{77} + 15 q^{78} - 20 q^{79} - 7 q^{80} + 3 q^{81} - q^{82} + 5 q^{84} + 14 q^{85} + 20 q^{87} - 13 q^{88} - q^{89} + 39 q^{91} - 9 q^{92} - 16 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} - q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9 - 7 * q^10 - 13 * q^11 - 4 * q^12 - 13 * q^13 - 9 * q^14 + 7 * q^15 + 3 * q^16 - 8 * q^17 + q^18 - 5 * q^19 - 7 * q^20 + 5 * q^21 - 13 * q^22 - 9 * q^23 - 4 * q^24 + 6 * q^25 - 13 * q^26 - q^27 - 9 * q^28 - 22 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 + 22 * q^33 - 8 * q^34 + 21 * q^35 + q^36 - 14 * q^37 - 5 * q^38 + 15 * q^39 - 7 * q^40 - q^41 + 5 * q^42 - 13 * q^44 - 9 * q^46 - 2 * q^47 - 4 * q^48 + 20 * q^49 + 6 * q^50 + 13 * q^51 - 13 * q^52 + 4 * q^53 - q^54 + 28 * q^55 - 9 * q^56 + 23 * q^57 - 22 * q^58 + 7 * q^59 + 7 * q^60 - 14 * q^61 - 2 * q^62 + 18 * q^63 + 3 * q^64 + 35 * q^65 + 22 * q^66 - 15 * q^67 - 8 * q^68 + 12 * q^69 + 21 * q^70 - 7 * q^71 + q^72 + 2 * q^73 - 14 * q^74 + 6 * q^75 - 5 * q^76 + 32 * q^77 + 15 * q^78 - 20 * q^79 - 7 * q^80 + 3 * q^81 - q^82 + 5 * q^84 + 14 * q^85 + 20 * q^87 - 13 * q^88 - q^89 + 39 * q^91 - 9 * q^92 - 16 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 - q^97 + 20 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.44504	−0.834295	−0.417148	−	0.908839i	$-0.636970\pi$
$3$	−1.44504	−0.834295	−0.417148	+	0.908839i	$0.636970\pi$
$4$	1.00000	0.500000
$5$	−0.753020	−0.336761	−0.168380	−	0.985722i	$-0.553854\pi$
$5$	−0.753020	−0.336761	−0.168380	+	0.985722i	$0.553854\pi$
$6$	−1.44504	−0.589936
$7$	−4.35690	−1.64675	−0.823376	−	0.567496i	$-0.807912\pi$
$7$	−4.35690	−1.64675	−0.823376	+	0.567496i	$0.807912\pi$
$8$	1.00000	0.353553
$9$	−0.911854	−0.303951
$10$	−0.753020	−0.238126
$11$	−4.44504	−1.34023	−0.670115	−	0.742257i	$-0.733755\pi$
$11$	−4.44504	−1.34023	−0.670115	+	0.742257i	$0.733755\pi$
$12$	−1.44504	−0.417148
$13$	−2.75302	−0.763550	−0.381775	−	0.924255i	$-0.624687\pi$
$13$	−2.75302	−0.763550	−0.381775	+	0.924255i	$0.624687\pi$
$14$	−4.35690	−1.16443
$15$	1.08815	0.280958
$16$	1.00000	0.250000
$17$	−4.24698	−1.03004	−0.515022	−	0.857177i	$-0.672216\pi$
$17$	−4.24698	−1.03004	−0.515022	+	0.857177i	$0.672216\pi$
$18$	−0.911854	−0.214926
$19$	−6.63102	−1.52126	−0.760630	−	0.649185i	$-0.775110\pi$
$19$	−6.63102	−1.52126	−0.760630	+	0.649185i	$0.775110\pi$
$20$	−0.753020	−0.168380
$21$	6.29590	1.37388
$22$	−4.44504	−0.947686
$23$	0.0489173	0.0102000	0.00509999	−	0.999987i	$-0.498377\pi$
$23$	0.0489173	0.0102000	0.00509999	+	0.999987i	$0.498377\pi$
$24$	−1.44504	−0.294968
$25$	−4.43296	−0.886592
$26$	−2.75302	−0.539912
$27$	5.65279	1.08788
$28$	−4.35690	−0.823376
$29$	−10.1588	−1.88645	−0.943224	−	0.332157i	$-0.892224\pi$
$29$	−10.1588	−1.88645	−0.943224	+	0.332157i	$0.892224\pi$
$30$	1.08815	0.198667
$31$	−3.26875	−0.587085	−0.293542	−	0.955946i	$-0.594834\pi$
$31$	−3.26875	−0.587085	−0.293542	+	0.955946i	$0.594834\pi$
$32$	1.00000	0.176777
$33$	6.42327	1.11815
$34$	−4.24698	−0.728351
$35$	3.28083	0.554562
$36$	−0.911854	−0.151976
$37$	−1.50604	−0.247592	−0.123796	−	0.992308i	$-0.539507\pi$
$37$	−1.50604	−0.247592	−0.123796	+	0.992308i	$0.539507\pi$
$38$	−6.63102	−1.07569
$39$	3.97823	0.637027
$40$	−0.753020	−0.119063
$41$	10.3937	1.62323	0.811614	−	0.584194i	$-0.198589\pi$
$41$	10.3937	1.62323	0.811614	+	0.584194i	$0.198589\pi$
$42$	6.29590	0.971478
$43$	10.5036	1.60179	0.800896	−	0.598804i	$-0.204357\pi$
$43$	10.5036	1.60179	0.800896	+	0.598804i	$0.204357\pi$
$44$	−4.44504	−0.670115
$45$	0.686645	0.102359
$46$	0.0489173	0.00721247
$47$	−5.63102	−0.821369	−0.410685	−	0.911778i	$-0.634710\pi$
$47$	−5.63102	−0.821369	−0.410685	+	0.911778i	$0.634710\pi$
$48$	−1.44504	−0.208574
$49$	11.9825	1.71179
$50$	−4.43296	−0.626915
$51$	6.13706	0.859361
$52$	−2.75302	−0.381775
$53$	−6.67994	−0.917560	−0.458780	−	0.888550i	$-0.651713\pi$
$53$	−6.67994	−0.917560	−0.458780	+	0.888550i	$0.651713\pi$
$54$	5.65279	0.769248
$55$	3.34721	0.451337
$56$	−4.35690	−0.582215
$57$	9.58211	1.26918
$58$	−10.1588	−1.33392
$59$	8.54288	1.11219	0.556094	−	0.831119i	$-0.312299\pi$
$59$	8.54288	1.11219	0.556094	+	0.831119i	$0.312299\pi$
$60$	1.08815	0.140479
$61$	0.185981	0.0238124	0.0119062	−	0.999929i	$-0.496210\pi$
$61$	0.185981	0.0238124	0.0119062	+	0.999929i	$0.496210\pi$
$62$	−3.26875	−0.415132
$63$	3.97285	0.500532
$64$	1.00000	0.125000
$65$	2.07308	0.257134
$66$	6.42327	0.790650
$67$	4.48188	0.547548	0.273774	−	0.961794i	$-0.411728\pi$
$67$	4.48188	0.547548	0.273774	+	0.961794i	$0.411728\pi$
$68$	−4.24698	−0.515022
$69$	−0.0706876	−0.00850979
$70$	3.28083	0.392134
$71$	−13.2838	−1.57650	−0.788249	−	0.615356i	$-0.789012\pi$
$71$	−13.2838	−1.57650	−0.788249	+	0.615356i	$0.789012\pi$
$72$	−0.911854	−0.107463
$73$	−10.2838	−1.20363	−0.601815	−	0.798636i	$-0.705555\pi$
$73$	−10.2838	−1.20363	−0.601815	+	0.798636i	$0.705555\pi$
$74$	−1.50604	−0.175074
$75$	6.40581	0.739680
$76$	−6.63102	−0.760630
$77$	19.3666	2.20703
$78$	3.97823	0.450446
$79$	3.94869	0.444262	0.222131	−	0.975017i	$-0.428699\pi$
$79$	3.94869	0.444262	0.222131	+	0.975017i	$0.428699\pi$
$80$	−0.753020	−0.0841902
$81$	−5.43296	−0.603662
$82$	10.3937	1.14780
$83$	6.76809	0.742894	0.371447	−	0.928454i	$-0.378862\pi$
$83$	6.76809	0.742894	0.371447	+	0.928454i	$0.378862\pi$
$84$	6.29590	0.686939
$85$	3.19806	0.346879
$86$	10.5036	1.13264
$87$	14.6799	1.57385
$88$	−4.44504	−0.473843
$89$	−1.46681	−0.155482	−0.0777409	−	0.996974i	$-0.524771\pi$
$89$	−1.46681	−0.155482	−0.0777409	+	0.996974i	$0.524771\pi$
$90$	0.686645	0.0723787
$91$	11.9946	1.25738
$92$	0.0489173	0.00509999
$93$	4.72348	0.489802
$94$	−5.63102	−0.580796
$95$	4.99330	0.512301
$96$	−1.44504	−0.147484
$97$	−5.52111	−0.560583	−0.280292	−	0.959915i	$-0.590431\pi$
$97$	−5.52111	−0.560583	−0.280292	+	0.959915i	$0.590431\pi$
$98$	11.9825	1.21042
$99$	4.05323	0.407365
$100$	−4.43296	−0.443296
$101$	−9.43296	−0.938615	−0.469307	−	0.883035i	$-0.655496\pi$
$101$	−9.43296	−0.938615	−0.469307	+	0.883035i	$0.655496\pi$
$102$	6.13706	0.607660
$103$	−18.2174	−1.79502	−0.897509	−	0.440996i	$-0.854625\pi$
$103$	−18.2174	−1.79502	−0.897509	+	0.440996i	$0.854625\pi$
$104$	−2.75302	−0.269956
$105$	−4.74094	−0.462668
$106$	−6.67994	−0.648813
$107$	−7.31767	−0.707426	−0.353713	−	0.935354i	$-0.615081\pi$
$107$	−7.31767	−0.707426	−0.353713	+	0.935354i	$0.615081\pi$
$108$	5.65279	0.543940
$109$	−6.48427	−0.621080	−0.310540	−	0.950560i	$-0.600510\pi$
$109$	−6.48427	−0.621080	−0.310540	+	0.950560i	$0.600510\pi$
$110$	3.34721	0.319144
$111$	2.17629	0.206564
$112$	−4.35690	−0.411688
$113$	16.7114	1.57208	0.786038	−	0.618178i	$-0.212129\pi$
$113$	16.7114	1.57208	0.786038	+	0.618178i	$0.212129\pi$
$114$	9.58211	0.897446
$115$	−0.0368358	−0.00343495
$116$	−10.1588	−0.943224
$117$	2.51035	0.232082
$118$	8.54288	0.786436
$119$	18.5036	1.69623
$120$	1.08815	0.0993337
$121$	8.75840	0.796218
$122$	0.185981	0.0168379
$123$	−15.0194	−1.35425
$124$	−3.26875	−0.293542
$125$	7.10321	0.635331
$126$	3.97285	0.353930
$127$	−4.32304	−0.383608	−0.191804	−	0.981433i	$-0.561434\pi$
$127$	−4.32304	−0.383608	−0.191804	+	0.981433i	$0.561434\pi$
$128$	1.00000	0.0883883
$129$	−15.1782	−1.33637
$130$	2.07308	0.181821
$131$	21.3110	1.86195	0.930974	−	0.365086i	$-0.118960\pi$
$131$	21.3110	1.86195	0.930974	+	0.365086i	$0.118960\pi$
$132$	6.42327	0.559074
$133$	28.8907	2.50514
$134$	4.48188	0.387175
$135$	−4.25667	−0.366356
$136$	−4.24698	−0.364175
$137$	−22.5013	−1.92241	−0.961206	−	0.275832i	$-0.911047\pi$
$137$	−22.5013	−1.92241	−0.961206	+	0.275832i	$0.911047\pi$
$138$	−0.0706876	−0.00601733
$139$	−15.1250	−1.28288	−0.641442	−	0.767171i	$-0.721664\pi$
$139$	−15.1250	−1.28288	−0.641442	+	0.767171i	$0.721664\pi$
$140$	3.28083	0.277281
$141$	8.13706	0.685264
$142$	−13.2838	−1.11475
$143$	12.2373	1.02333
$144$	−0.911854	−0.0759878
$145$	7.64981	0.635282
$146$	−10.2838	−0.851095
$147$	−17.3153	−1.42814
$148$	−1.50604	−0.123796
$149$	−7.14244	−0.585131	−0.292566	−	0.956245i	$-0.594509\pi$
$149$	−7.14244	−0.585131	−0.292566	+	0.956245i	$0.594509\pi$
$150$	6.40581	0.523032
$151$	15.4644	1.25848	0.629238	−	0.777212i	$-0.283367\pi$
$151$	15.4644	1.25848	0.629238	+	0.777212i	$0.283367\pi$
$152$	−6.63102	−0.537847
$153$	3.87263	0.313083
$154$	19.3666	1.56060
$155$	2.46144	0.197707
$156$	3.97823	0.318513
$157$	−18.6799	−1.49082	−0.745411	−	0.666605i	$-0.767747\pi$
$157$	−18.6799	−1.49082	−0.745411	+	0.666605i	$0.767747\pi$
$158$	3.94869	0.314141
$159$	9.65279	0.765516
$160$	−0.753020	−0.0595315
$161$	−0.213128	−0.0167968
$162$	−5.43296	−0.426854
$163$	0.219833	0.0172186	0.00860931	−	0.999963i	$-0.497260\pi$
$163$	0.219833	0.0172186	0.00860931	+	0.999963i	$0.497260\pi$
$164$	10.3937	0.811614
$165$	−4.83685	−0.376549
$166$	6.76809	0.525305
$167$	−24.7821	−1.91770	−0.958848	−	0.283921i	$-0.908365\pi$
$167$	−24.7821	−1.91770	−0.958848	+	0.283921i	$0.908365\pi$
$168$	6.29590	0.485739
$169$	−5.42088	−0.416991
$170$	3.19806	0.245280
$171$	6.04652	0.462389
$172$	10.5036	0.800896
$173$	2.05429	0.156185	0.0780925	−	0.996946i	$-0.475117\pi$
$173$	2.05429	0.156185	0.0780925	+	0.996946i	$0.475117\pi$
$174$	14.6799	1.11288
$175$	19.3139	1.46000
$176$	−4.44504	−0.335058
$177$	−12.3448	−0.927893
$178$	−1.46681	−0.109942
$179$	−4.93362	−0.368756	−0.184378	−	0.982855i	$-0.559027\pi$
$179$	−4.93362	−0.368756	−0.184378	+	0.982855i	$0.559027\pi$
$180$	0.686645	0.0511795
$181$	−18.2838	−1.35903	−0.679513	−	0.733664i	$-0.737809\pi$
$181$	−18.2838	−1.35903	−0.679513	+	0.733664i	$0.737809\pi$
$182$	11.9946	0.889101
$183$	−0.268750	−0.0198666
$184$	0.0489173	0.00360623
$185$	1.13408	0.0833792
$186$	4.72348	0.346342
$187$	18.8780	1.38050
$188$	−5.63102	−0.410685
$189$	−24.6286	−1.79147
$190$	4.99330	0.362252
$191$	15.6504	1.13242	0.566212	−	0.824260i	$-0.308409\pi$
$191$	15.6504	1.13242	0.566212	+	0.824260i	$0.308409\pi$
$192$	−1.44504	−0.104287
$193$	21.8853	1.57534	0.787669	−	0.616099i	$-0.211288\pi$
$193$	21.8853	1.57534	0.787669	+	0.616099i	$0.211288\pi$
$194$	−5.52111	−0.396392
$195$	−2.99569	−0.214526
$196$	11.9825	0.855896
$197$	−0.350191	−0.0249501	−0.0124750	−	0.999922i	$-0.503971\pi$
$197$	−0.350191	−0.0249501	−0.0124750	+	0.999922i	$0.503971\pi$
$198$	4.05323	0.288050
$199$	6.99462	0.495836	0.247918	−	0.968781i	$-0.420254\pi$
$199$	6.99462	0.495836	0.247918	+	0.968781i	$0.420254\pi$
$200$	−4.43296	−0.313458
$201$	−6.47650	−0.456817
$202$	−9.43296	−0.663701
$203$	44.2610	3.10651
$204$	6.13706	0.429680
$205$	−7.82669	−0.546640
$206$	−18.2174	−1.26927
$207$	−0.0446055	−0.00310029
$208$	−2.75302	−0.190888
$209$	29.4752	2.03884
$210$	−4.74094	−0.327156
$211$	−7.02715	−0.483769	−0.241884	−	0.970305i	$-0.577765\pi$
$211$	−7.02715	−0.483769	−0.241884	+	0.970305i	$0.577765\pi$
$212$	−6.67994	−0.458780
$213$	19.1957	1.31527
$214$	−7.31767	−0.500225
$215$	−7.90946	−0.539421
$216$	5.65279	0.384624
$217$	14.2416	0.966783
$218$	−6.48427	−0.439170
$219$	14.8605	1.00418
$220$	3.34721	0.225669
$221$	11.6920	0.786490
$222$	2.17629	0.146063
$223$	10.5211	0.704545	0.352273	−	0.935897i	$-0.385409\pi$
$223$	10.5211	0.704545	0.352273	+	0.935897i	$0.385409\pi$
$224$	−4.35690	−0.291107
$225$	4.04221	0.269481
$226$	16.7114	1.11163
$227$	21.5254	1.42869	0.714346	−	0.699793i	$-0.246724\pi$
$227$	21.5254	1.42869	0.714346	+	0.699793i	$0.246724\pi$
$228$	9.58211	0.634590
$229$	6.88338	0.454866	0.227433	−	0.973794i	$-0.426967\pi$
$229$	6.88338	0.454866	0.227433	+	0.973794i	$0.426967\pi$
$230$	−0.0368358	−0.00242888
$231$	−27.9855	−1.84131
$232$	−10.1588	−0.666960
$233$	−19.3793	−1.26958	−0.634789	−	0.772686i	$-0.718913\pi$
$233$	−19.3793	−1.26958	−0.634789	+	0.772686i	$0.718913\pi$
$234$	2.51035	0.164107
$235$	4.24027	0.276605
$236$	8.54288	0.556094
$237$	−5.70602	−0.370646
$238$	18.5036	1.19941
$239$	−26.4198	−1.70896	−0.854478	−	0.519488i	$-0.826123\pi$
$239$	−26.4198	−1.70896	−0.854478	+	0.519488i	$0.826123\pi$
$240$	1.08815	0.0702395
$241$	10.4916	0.675821	0.337911	−	0.941178i	$-0.390280\pi$
$241$	10.4916	0.675821	0.337911	+	0.941178i	$0.390280\pi$
$242$	8.75840	0.563011
$243$	−9.10752	−0.584248
$244$	0.185981	0.0119062
$245$	−9.02310	−0.576465
$246$	−15.0194	−0.957601
$247$	18.2553	1.16156
$248$	−3.26875	−0.207566
$249$	−9.78017	−0.619793
$250$	7.10321	0.449247
$251$	−28.1957	−1.77969	−0.889847	−	0.456258i	$-0.849189\pi$
$251$	−28.1957	−1.77969	−0.889847	+	0.456258i	$0.849189\pi$
$252$	3.97285	0.250266
$253$	−0.217440	−0.0136703
$254$	−4.32304	−0.271252
$255$	−4.62133	−0.289399
$256$	1.00000	0.0625000
$257$	12.2325	0.763043	0.381521	−	0.924360i	$-0.375400\pi$
$257$	12.2325	0.763043	0.381521	+	0.924360i	$0.375400\pi$
$258$	−15.1782	−0.944954
$259$	6.56166	0.407722
$260$	2.07308	0.128567
$261$	9.26337	0.573388
$262$	21.3110	1.31660
$263$	4.53856	0.279860	0.139930	−	0.990161i	$-0.455312\pi$
$263$	4.53856	0.279860	0.139930	+	0.990161i	$0.455312\pi$
$264$	6.42327	0.395325
$265$	5.03013	0.308998
$266$	28.8907	1.77140
$267$	2.11960	0.129718
$268$	4.48188	0.273774
$269$	−9.69740	−0.591261	−0.295630	−	0.955302i	$-0.595530\pi$
$269$	−9.69740	−0.591261	−0.295630	+	0.955302i	$0.595530\pi$
$270$	−4.25667	−0.259053
$271$	28.2989	1.71903	0.859517	−	0.511107i	$-0.170764\pi$
$271$	28.2989	1.71903	0.859517	+	0.511107i	$0.170764\pi$
$272$	−4.24698	−0.257511
$273$	−17.3327	−1.04902
$274$	−22.5013	−1.35935
$275$	19.7047	1.18824
$276$	−0.0706876	−0.00425489
$277$	−21.4155	−1.28673	−0.643366	−	0.765558i	$-0.722463\pi$
$277$	−21.4155	−1.28673	−0.643366	+	0.765558i	$0.722463\pi$
$278$	−15.1250	−0.907136
$279$	2.98062	0.178445
$280$	3.28083	0.196067
$281$	−3.39373	−0.202453	−0.101227	−	0.994863i	$-0.532277\pi$
$281$	−3.39373	−0.202453	−0.101227	+	0.994863i	$0.532277\pi$
$282$	8.13706	0.484555
$283$	−18.2905	−1.08726	−0.543629	−	0.839325i	$-0.682950\pi$
$283$	−18.2905	−1.08726	−0.543629	+	0.839325i	$0.682950\pi$
$284$	−13.2838	−0.788249
$285$	−7.21552	−0.427411
$286$	12.2373	0.723606
$287$	−45.2844	−2.67305
$288$	−0.911854	−0.0537315
$289$	1.03684	0.0609903
$290$	7.64981	0.449212
$291$	7.97823	0.467692
$292$	−10.2838	−0.601815
$293$	−29.3274	−1.71332	−0.856661	−	0.515879i	$-0.827465\pi$
$293$	−29.3274	−1.71332	−0.856661	+	0.515879i	$0.827465\pi$
$294$	−17.3153	−1.00985
$295$	−6.43296	−0.374541
$296$	−1.50604	−0.0875368
$297$	−25.1269	−1.45801
$298$	−7.14244	−0.413750
$299$	−0.134670	−0.00778819
$300$	6.40581	0.369840
$301$	−45.7633	−2.63775
$302$	15.4644	0.889877
$303$	13.6310	0.783082
$304$	−6.63102	−0.380315
$305$	−0.140047	−0.00801908
$306$	3.87263	0.221383
$307$	15.2717	0.871604	0.435802	−	0.900043i	$-0.356465\pi$
$307$	15.2717	0.871604	0.435802	+	0.900043i	$0.356465\pi$
$308$	19.3666	1.10351
$309$	26.3250	1.49757
$310$	2.46144	0.139800
$311$	−27.4795	−1.55822	−0.779109	−	0.626888i	$-0.784328\pi$
$311$	−27.4795	−1.55822	−0.779109	+	0.626888i	$0.784328\pi$
$312$	3.97823	0.225223
$313$	4.44265	0.251113	0.125557	−	0.992086i	$-0.459928\pi$
$313$	4.44265	0.251113	0.125557	+	0.992086i	$0.459928\pi$
$314$	−18.6799	−1.05417
$315$	−2.99164	−0.168560
$316$	3.94869	0.222131
$317$	−6.92825	−0.389129	−0.194565	−	0.980890i	$-0.562329\pi$
$317$	−6.92825	−0.389129	−0.194565	+	0.980890i	$0.562329\pi$
$318$	9.65279	0.541302
$319$	45.1564	2.52828
$320$	−0.753020	−0.0420951
$321$	10.5743	0.590202
$322$	−0.213128	−0.0118771
$323$	28.1618	1.56697
$324$	−5.43296	−0.301831
$325$	12.2040	0.676958
$326$	0.219833	0.0121754
$327$	9.37004	0.518165
$328$	10.3937	0.573898
$329$	24.5338	1.35259
$330$	−4.83685	−0.266260
$331$	4.53856	0.249462	0.124731	−	0.992191i	$-0.460193\pi$
$331$	4.53856	0.249462	0.124731	+	0.992191i	$0.460193\pi$
$332$	6.76809	0.371447
$333$	1.37329	0.0752558
$334$	−24.7821	−1.35602
$335$	−3.37495	−0.184393
$336$	6.29590	0.343469
$337$	−21.0804	−1.14832	−0.574161	−	0.818743i	$-0.694672\pi$
$337$	−21.0804	−1.14832	−0.574161	+	0.818743i	$0.694672\pi$
$338$	−5.42088	−0.294857
$339$	−24.1487	−1.31158
$340$	3.19806	0.173439
$341$	14.5297	0.786829
$342$	6.04652	0.326959
$343$	−21.7084	−1.17214
$344$	10.5036	0.566319
$345$	0.0532292	0.00286576
$346$	2.05429	0.110440
$347$	21.0610	1.13061	0.565307	−	0.824881i	$-0.308758\pi$
$347$	21.0610	1.13061	0.565307	+	0.824881i	$0.308758\pi$
$348$	14.6799	0.786927
$349$	−4.14138	−0.221683	−0.110841	−	0.993838i	$-0.535355\pi$
$349$	−4.14138	−0.221683	−0.110841	+	0.993838i	$0.535355\pi$
$350$	19.3139	1.03237
$351$	−15.5623	−0.830652
$352$	−4.44504	−0.236922
$353$	−11.2567	−0.599132	−0.299566	−	0.954076i	$-0.596842\pi$
$353$	−11.2567	−0.599132	−0.299566	+	0.954076i	$0.596842\pi$
$354$	−12.3448	−0.656119
$355$	10.0030	0.530903
$356$	−1.46681	−0.0777409
$357$	−26.7385	−1.41515
$358$	−4.93362	−0.260750
$359$	11.4752	0.605636	0.302818	−	0.953048i	$-0.402072\pi$
$359$	11.4752	0.605636	0.302818	+	0.953048i	$0.402072\pi$
$360$	0.686645	0.0361894
$361$	24.9705	1.31423
$362$	−18.2838	−0.960976
$363$	−12.6563	−0.664281
$364$	11.9946	0.628689
$365$	7.74392	0.405335
$366$	−0.268750	−0.0140478
$367$	8.14244	0.425032	0.212516	−	0.977158i	$-0.431834\pi$
$367$	8.14244	0.425032	0.212516	+	0.977158i	$0.431834\pi$
$368$	0.0489173	0.00254999
$369$	−9.47757	−0.493382
$370$	1.13408	0.0589580
$371$	29.1038	1.51099
$372$	4.72348	0.244901
$373$	−8.25236	−0.427291	−0.213645	−	0.976911i	$-0.568534\pi$
$373$	−8.25236	−0.427291	−0.213645	+	0.976911i	$0.568534\pi$
$374$	18.8780	0.976158
$375$	−10.2644	−0.530053
$376$	−5.63102	−0.290398
$377$	27.9675	1.44040
$378$	−24.6286	−1.26676
$379$	0.291585	0.0149777	0.00748886	−	0.999972i	$-0.497616\pi$
$379$	0.291585	0.0149777	0.00748886	+	0.999972i	$0.497616\pi$
$380$	4.99330	0.256151
$381$	6.24698	0.320042
$382$	15.6504	0.800744
$383$	21.2218	1.08438	0.542190	−	0.840256i	$-0.317595\pi$
$383$	21.2218	1.08438	0.542190	+	0.840256i	$0.317595\pi$
$384$	−1.44504	−0.0737420
$385$	−14.5834	−0.743241
$386$	21.8853	1.11393
$387$	−9.57779	−0.486867
$388$	−5.52111	−0.280292
$389$	−15.3491	−0.778232	−0.389116	−	0.921189i	$-0.627219\pi$
$389$	−15.3491	−0.778232	−0.389116	+	0.921189i	$0.627219\pi$
$390$	−2.99569	−0.151693
$391$	−0.207751	−0.0105064
$392$	11.9825	0.605210
$393$	−30.7952	−1.55341
$394$	−0.350191	−0.0176424
$395$	−2.97344	−0.149610
$396$	4.05323	0.203682
$397$	23.4239	1.17561	0.587805	−	0.809003i	$-0.299992\pi$
$397$	23.4239	1.17561	0.587805	+	0.809003i	$0.299992\pi$
$398$	6.99462	0.350609
$399$	−41.7482	−2.09003
$400$	−4.43296	−0.221648
$401$	20.4892	1.02318	0.511590	−	0.859230i	$-0.329057\pi$
$401$	20.4892	1.02318	0.511590	+	0.859230i	$0.329057\pi$
$402$	−6.47650	−0.323019
$403$	8.99894	0.448269
$404$	−9.43296	−0.469307
$405$	4.09113	0.203290
$406$	44.2610	2.19664
$407$	6.69441	0.331830
$408$	6.13706	0.303830
$409$	22.5429	1.11467	0.557337	−	0.830287i	$-0.311823\pi$
$409$	22.5429	1.11467	0.557337	+	0.830287i	$0.311823\pi$
$410$	−7.82669	−0.386533
$411$	32.5153	1.60386
$412$	−18.2174	−0.897509
$413$	−37.2204	−1.83150
$414$	−0.0446055	−0.00219224
$415$	−5.09651	−0.250178
$416$	−2.75302	−0.134978
$417$	21.8562	1.07030
$418$	29.4752	1.44168
$419$	−33.5217	−1.63764	−0.818821	−	0.574049i	$-0.805372\pi$
$419$	−33.5217	−1.63764	−0.818821	+	0.574049i	$0.805372\pi$
$420$	−4.74094	−0.231334
$421$	−33.8920	−1.65180	−0.825898	−	0.563820i	$-0.809331\pi$
$421$	−33.8920	−1.65180	−0.825898	+	0.563820i	$0.809331\pi$
$422$	−7.02715	−0.342076
$423$	5.13467	0.249656
$424$	−6.67994	−0.324407
$425$	18.8267	0.913229
$426$	19.1957	0.930033
$427$	−0.810298	−0.0392131
$428$	−7.31767	−0.353713
$429$	−17.6834	−0.853762
$430$	−7.90946	−0.381428
$431$	−15.1860	−0.731483	−0.365741	−	0.930716i	$-0.619185\pi$
$431$	−15.1860	−0.731483	−0.365741	+	0.930716i	$0.619185\pi$
$432$	5.65279	0.271970
$433$	−7.01938	−0.337330	−0.168665	−	0.985673i	$-0.553946\pi$
$433$	−7.01938	−0.337330	−0.168665	+	0.985673i	$0.553946\pi$
$434$	14.2416	0.683619
$435$	−11.0543	−0.530013
$436$	−6.48427	−0.310540
$437$	−0.324372	−0.0155168
$438$	14.8605	0.710064
$439$	−12.8465	−0.613132	−0.306566	−	0.951849i	$-0.599180\pi$
$439$	−12.8465	−0.613132	−0.306566	+	0.951849i	$0.599180\pi$
$440$	3.34721	0.159572
$441$	−10.9263	−0.520301
$442$	11.6920	0.556133
$443$	−20.1709	−0.958349	−0.479175	−	0.877720i	$-0.659064\pi$
$443$	−20.1709	−0.958349	−0.479175	+	0.877720i	$0.659064\pi$
$444$	2.17629	0.103282
$445$	1.10454	0.0523602
$446$	10.5211	0.498189
$447$	10.3211	0.488172
$448$	−4.35690	−0.205844
$449$	−17.4571	−0.823853	−0.411926	−	0.911217i	$-0.635144\pi$
$449$	−17.4571	−0.823853	−0.411926	+	0.911217i	$0.635144\pi$
$450$	4.04221	0.190552
$451$	−46.2006	−2.17550
$452$	16.7114	0.786038
$453$	−22.3467	−1.04994
$454$	21.5254	1.01024
$455$	−9.03220	−0.423436
$456$	9.58211	0.448723
$457$	11.3080	0.528965	0.264482	−	0.964390i	$-0.414799\pi$
$457$	11.3080	0.528965	0.264482	+	0.964390i	$0.414799\pi$
$458$	6.88338	0.321639
$459$	−24.0073	−1.12056
$460$	−0.0368358	−0.00171748
$461$	−4.81700	−0.224350	−0.112175	−	0.993688i	$-0.535782\pi$
$461$	−4.81700	−0.224350	−0.112175	+	0.993688i	$0.535782\pi$
$462$	−27.9855	−1.30200
$463$	21.5690	1.00239	0.501197	−	0.865333i	$-0.332893\pi$
$463$	21.5690	1.00239	0.501197	+	0.865333i	$0.332893\pi$
$464$	−10.1588	−0.471612
$465$	−3.55688	−0.164946
$466$	−19.3793	−0.897727
$467$	12.6069	0.583376	0.291688	−	0.956514i	$-0.405783\pi$
$467$	12.6069	0.583376	0.291688	+	0.956514i	$0.405783\pi$
$468$	2.51035	0.116041
$469$	−19.5271	−0.901677
$470$	4.24027	0.195589
$471$	26.9933	1.24379
$472$	8.54288	0.393218
$473$	−46.6892	−2.14677
$474$	−5.70602	−0.262086
$475$	29.3951	1.34874
$476$	18.5036	0.848113
$477$	6.09113	0.278894
$478$	−26.4198	−1.20841
$479$	12.5265	0.572350	0.286175	−	0.958177i	$-0.407616\pi$
$479$	12.5265	0.572350	0.286175	+	0.958177i	$0.407616\pi$
$480$	1.08815	0.0496668
$481$	4.14616	0.189049
$482$	10.4916	0.477878
$483$	0.307979	0.0140135
$484$	8.75840	0.398109
$485$	4.15751	0.188783
$486$	−9.10752	−0.413126
$487$	−34.6625	−1.57071	−0.785353	−	0.619048i	$-0.787519\pi$
$487$	−34.6625	−1.57071	−0.785353	+	0.619048i	$0.787519\pi$
$488$	0.185981	0.00841895
$489$	−0.317667	−0.0143654
$490$	−9.02310	−0.407622
$491$	35.8474	1.61777	0.808885	−	0.587967i	$-0.200071\pi$
$491$	35.8474	1.61777	0.808885	+	0.587967i	$0.200071\pi$
$492$	−15.0194	−0.677126
$493$	43.1444	1.94312
$494$	18.2553	0.821347
$495$	−3.05216	−0.137185
$496$	−3.26875	−0.146771
$497$	57.8762	2.59610
$498$	−9.78017	−0.438260
$499$	−0.170915	−0.00765121	−0.00382561	−	0.999993i	$-0.501218\pi$
$499$	−0.170915	−0.00765121	−0.00382561	+	0.999993i	$0.501218\pi$
$500$	7.10321	0.317665
$501$	35.8112	1.59992
$502$	−28.1957	−1.25843
$503$	29.7918	1.32835	0.664175	−	0.747577i	$-0.268783\pi$
$503$	29.7918	1.32835	0.664175	+	0.747577i	$0.268783\pi$
$504$	3.97285	0.176965
$505$	7.10321	0.316089
$506$	−0.217440	−0.00966637
$507$	7.83340	0.347893
$508$	−4.32304	−0.191804
$509$	30.2717	1.34177	0.670886	−	0.741561i	$-0.265914\pi$
$509$	30.2717	1.34177	0.670886	+	0.741561i	$0.265914\pi$
$510$	−4.62133	−0.204636
$511$	44.8055	1.98208
$512$	1.00000	0.0441942
$513$	−37.4838	−1.65495
$514$	12.2325	0.539553
$515$	13.7181	0.604492
$516$	−15.1782	−0.668183
$517$	25.0301	1.10082
$518$	6.56166	0.288303
$519$	−2.96854	−0.130304
$520$	2.07308	0.0909106
$521$	−19.8418	−0.869283	−0.434642	−	0.900604i	$-0.643125\pi$
$521$	−19.8418	−0.869283	−0.434642	+	0.900604i	$0.643125\pi$
$522$	9.26337	0.405447
$523$	12.6987	0.555277	0.277638	−	0.960686i	$-0.410448\pi$
$523$	12.6987	0.555277	0.277638	+	0.960686i	$0.410448\pi$
$524$	21.3110	0.930974
$525$	−27.9095	−1.21807
$526$	4.53856	0.197891
$527$	13.8823	0.604723
$528$	6.42327	0.279537
$529$	−22.9976	−0.999896
$530$	5.03013	0.218495
$531$	−7.78986	−0.338051
$532$	28.8907	1.25257
$533$	−28.6142	−1.23942
$534$	2.11960	0.0917243
$535$	5.51035	0.238233
$536$	4.48188	0.193588
$537$	7.12929	0.307652
$538$	−9.69740	−0.418085
$539$	−53.2629	−2.29420
$540$	−4.25667	−0.183178
$541$	−27.6364	−1.18818	−0.594091	−	0.804398i	$-0.702488\pi$
$541$	−27.6364	−1.18818	−0.594091	+	0.804398i	$0.702488\pi$
$542$	28.2989	1.21554
$543$	26.4209	1.13383
$544$	−4.24698	−0.182088
$545$	4.88279	0.209156
$546$	−17.3327	−0.741772
$547$	−13.7235	−0.586774	−0.293387	−	0.955994i	$-0.594782\pi$
$547$	−13.7235	−0.586774	−0.293387	+	0.955994i	$0.594782\pi$
$548$	−22.5013	−0.961206
$549$	−0.169587	−0.00723781
$550$	19.7047	0.840211
$551$	67.3635	2.86978
$552$	−0.0706876	−0.00300866
$553$	−17.2040	−0.731590
$554$	−21.4155	−0.909857
$555$	−1.63879	−0.0695629
$556$	−15.1250	−0.641442
$557$	20.6614	0.875452	0.437726	−	0.899108i	$-0.355784\pi$
$557$	20.6614	0.875452	0.437726	+	0.899108i	$0.355784\pi$
$558$	2.98062	0.126180
$559$	−28.9168	−1.22305
$560$	3.28083	0.138640
$561$	−27.2795	−1.15174
$562$	−3.39373	−0.143156
$563$	−26.4892	−1.11639	−0.558193	−	0.829711i	$-0.688505\pi$
$563$	−26.4892	−1.11639	−0.558193	+	0.829711i	$0.688505\pi$
$564$	8.13706	0.342632
$565$	−12.5840	−0.529414
$566$	−18.2905	−0.768808
$567$	23.6708	0.994082
$568$	−13.2838	−0.557377
$569$	−36.7222	−1.53947	−0.769736	−	0.638362i	$-0.779612\pi$
$569$	−36.7222	−1.53947	−0.769736	+	0.638362i	$0.779612\pi$
$570$	−7.21552	−0.302225
$571$	2.19328	0.0917858	0.0458929	−	0.998946i	$-0.485387\pi$
$571$	2.19328	0.0917858	0.0458929	+	0.998946i	$0.485387\pi$
$572$	12.2373	0.511667
$573$	−22.6155	−0.944775
$574$	−45.2844	−1.89013
$575$	−0.216849	−0.00904321
$576$	−0.911854	−0.0379939
$577$	−20.3217	−0.846004	−0.423002	−	0.906129i	$-0.639024\pi$
$577$	−20.3217	−0.846004	−0.423002	+	0.906129i	$0.639024\pi$
$578$	1.03684	0.0431267
$579$	−31.6252	−1.31430
$580$	7.64981	0.317641
$581$	−29.4878	−1.22336
$582$	7.97823	0.330708
$583$	29.6926	1.22974
$584$	−10.2838	−0.425547
$585$	−1.89035	−0.0781562
$586$	−29.3274	−1.21150
$587$	20.6582	0.852654	0.426327	−	0.904569i	$-0.359807\pi$
$587$	20.6582	0.852654	0.426327	+	0.904569i	$0.359807\pi$
$588$	−17.3153	−0.714070
$589$	21.6752	0.893109
$590$	−6.43296	−0.264841
$591$	0.506041	0.0208157
$592$	−1.50604	−0.0618979
$593$	35.6461	1.46381	0.731905	−	0.681407i	$-0.238632\pi$
$593$	35.6461	1.46381	0.731905	+	0.681407i	$0.238632\pi$
$594$	−25.1269	−1.03097
$595$	−13.9336	−0.571223
$596$	−7.14244	−0.292566
$597$	−10.1075	−0.413673
$598$	−0.134670	−0.00550708
$599$	21.9081	0.895142	0.447571	−	0.894248i	$-0.352289\pi$
$599$	21.9081	0.895142	0.447571	+	0.894248i	$0.352289\pi$
$600$	6.40581	0.261516
$601$	35.9396	1.46601	0.733003	−	0.680225i	$-0.238118\pi$
$601$	35.9396	1.46601	0.733003	+	0.680225i	$0.238118\pi$
$602$	−45.7633	−1.86517
$603$	−4.08682	−0.166428
$604$	15.4644	0.629238
$605$	−6.59525	−0.268135
$606$	13.6310	0.553722
$607$	−25.1444	−1.02058	−0.510289	−	0.860003i	$-0.670462\pi$
$607$	−25.1444	−1.02058	−0.510289	+	0.860003i	$0.670462\pi$
$608$	−6.63102	−0.268923
$609$	−63.9590	−2.59175
$610$	−0.140047	−0.00567035
$611$	15.5023	0.627157
$612$	3.87263	0.156542
$613$	−34.5036	−1.39359	−0.696795	−	0.717271i	$-0.745391\pi$
$613$	−34.5036	−1.39359	−0.696795	+	0.717271i	$0.745391\pi$
$614$	15.2717	0.616317
$615$	11.3099	0.456059
$616$	19.3666	0.780302
$617$	9.36419	0.376988	0.188494	−	0.982074i	$-0.439639\pi$
$617$	9.36419	0.376988	0.188494	+	0.982074i	$0.439639\pi$
$618$	26.3250	1.05895
$619$	4.30559	0.173056	0.0865280	−	0.996249i	$-0.472423\pi$
$619$	4.30559	0.173056	0.0865280	+	0.996249i	$0.472423\pi$
$620$	2.46144	0.0988536
$621$	0.276520	0.0110963
$622$	−27.4795	−1.10183
$623$	6.39075	0.256040
$624$	3.97823	0.159257
$625$	16.8159	0.672638
$626$	4.44265	0.177564
$627$	−42.5929	−1.70099
$628$	−18.6799	−0.745411
$629$	6.39612	0.255030
$630$	−2.99164	−0.119190
$631$	−20.5714	−0.818933	−0.409466	−	0.912325i	$-0.634285\pi$
$631$	−20.5714	−0.818933	−0.409466	+	0.912325i	$0.634285\pi$
$632$	3.94869	0.157070
$633$	10.1545	0.403606
$634$	−6.92825	−0.275156
$635$	3.25534	0.129184
$636$	9.65279	0.382758
$637$	−32.9882	−1.30704
$638$	45.1564	1.78776
$639$	12.1129	0.479179
$640$	−0.753020	−0.0297657
$641$	−5.07547	−0.200469	−0.100235	−	0.994964i	$-0.531959\pi$
$641$	−5.07547	−0.200469	−0.100235	+	0.994964i	$0.531959\pi$
$642$	10.5743	0.417336
$643$	31.0183	1.22324	0.611621	−	0.791151i	$-0.290518\pi$
$643$	31.0183	1.22324	0.611621	+	0.791151i	$0.290518\pi$
$644$	−0.213128	−0.00839841
$645$	11.4295	0.450036
$646$	28.1618	1.10801
$647$	−16.0616	−0.631446	−0.315723	−	0.948851i	$-0.602247\pi$
$647$	−16.0616	−0.631446	−0.315723	+	0.948851i	$0.602247\pi$
$648$	−5.43296	−0.213427
$649$	−37.9734	−1.49059
$650$	12.2040	0.478681
$651$	−20.5797	−0.806583
$652$	0.219833	0.00860931
$653$	−10.6334	−0.416118	−0.208059	−	0.978116i	$-0.566715\pi$
$653$	−10.6334	−0.416118	−0.208059	+	0.978116i	$0.566715\pi$
$654$	9.37004	0.366398
$655$	−16.0476	−0.627031
$656$	10.3937	0.405807
$657$	9.37734	0.365845
$658$	24.5338	0.956426
$659$	−13.4045	−0.522165	−0.261082	−	0.965317i	$-0.584079\pi$
$659$	−13.4045	−0.522165	−0.261082	+	0.965317i	$0.584079\pi$
$660$	−4.83685	−0.188274
$661$	−22.8278	−0.887897	−0.443948	−	0.896052i	$-0.646423\pi$
$661$	−22.8278	−0.887897	−0.443948	+	0.896052i	$0.646423\pi$
$662$	4.53856	0.176396
$663$	−16.8955	−0.656165
$664$	6.76809	0.262653
$665$	−21.7553	−0.843633
$666$	1.37329	0.0532139
$667$	−0.496943	−0.0192417
$668$	−24.7821	−0.958848
$669$	−15.2034	−0.587799
$670$	−3.37495	−0.130386
$671$	−0.826692	−0.0319141
$672$	6.29590	0.242869
$673$	−23.7764	−0.916515	−0.458257	−	0.888820i	$-0.651526\pi$
$673$	−23.7764	−0.916515	−0.458257	+	0.888820i	$0.651526\pi$
$674$	−21.0804	−0.811986
$675$	−25.0586	−0.964506
$676$	−5.42088	−0.208495
$677$	27.3612	1.05158	0.525788	−	0.850615i	$-0.323770\pi$
$677$	27.3612	1.05158	0.525788	+	0.850615i	$0.323770\pi$
$678$	−24.1487	−0.927424
$679$	24.0549	0.923142
$680$	3.19806	0.122640
$681$	−31.1051	−1.19195
$682$	14.5297	0.556372
$683$	−12.3241	−0.471569	−0.235784	−	0.971805i	$-0.575766\pi$
$683$	−12.3241	−0.471569	−0.235784	+	0.971805i	$0.575766\pi$
$684$	6.04652	0.231195
$685$	16.9439	0.647393
$686$	−21.7084	−0.828831
$687$	−9.94677	−0.379493
$688$	10.5036	0.400448
$689$	18.3900	0.700604
$690$	0.0532292	0.00202640
$691$	28.0508	1.06710	0.533552	−	0.845767i	$-0.320857\pi$
$691$	28.0508	1.06710	0.533552	+	0.845767i	$0.320857\pi$
$692$	2.05429	0.0780925
$693$	−17.6595	−0.670829
$694$	21.0610	0.799465
$695$	11.3894	0.432025
$696$	14.6799	0.556442
$697$	−44.1420	−1.67200
$698$	−4.14138	−0.156753
$699$	28.0038	1.05920
$700$	19.3139	0.729999
$701$	20.3545	0.768779	0.384389	−	0.923171i	$-0.374412\pi$
$701$	20.3545	0.768779	0.384389	+	0.923171i	$0.374412\pi$
$702$	−15.5623	−0.587359
$703$	9.98659	0.376651
$704$	−4.44504	−0.167529
$705$	−6.12737	−0.230770
$706$	−11.2567	−0.423650
$707$	41.0984	1.54567
$708$	−12.3448	−0.463947
$709$	−2.60388	−0.0977906	−0.0488953	−	0.998804i	$-0.515570\pi$
$709$	−2.60388	−0.0977906	−0.0488953	+	0.998804i	$0.515570\pi$
$710$	10.0030	0.375405
$711$	−3.60063	−0.135034
$712$	−1.46681	−0.0549711
$713$	−0.159899	−0.00598825
$714$	−26.7385	−1.00066
$715$	−9.21493	−0.344619
$716$	−4.93362	−0.184378
$717$	38.1777	1.42577
$718$	11.4752	0.428250
$719$	28.6515	1.06852	0.534260	−	0.845320i	$-0.320590\pi$
$719$	28.6515	1.06852	0.534260	+	0.845320i	$0.320590\pi$
$720$	0.686645	0.0255897
$721$	79.3715	2.95595
$722$	24.9705	0.929304
$723$	−15.1608	−0.563834
$724$	−18.2838	−0.679513
$725$	45.0337	1.67251
$726$	−12.6563	−0.469718
$727$	47.9995	1.78020	0.890102	−	0.455761i	$-0.150633\pi$
$727$	47.9995	1.78020	0.890102	+	0.455761i	$0.150633\pi$
$728$	11.9946	0.444550
$729$	29.4596	1.09110
$730$	7.74392	0.286615
$731$	−44.6088	−1.64992
$732$	−0.268750	−0.00993328
$733$	−2.95885	−0.109288	−0.0546439	−	0.998506i	$-0.517402\pi$
$733$	−2.95885	−0.109288	−0.0546439	+	0.998506i	$0.517402\pi$
$734$	8.14244	0.300543
$735$	13.0388	0.480942
$736$	0.0489173	0.00180312
$737$	−19.9221	−0.733841
$738$	−9.47757	−0.348874
$739$	−11.1304	−0.409437	−0.204718	−	0.978821i	$-0.565628\pi$
$739$	−11.1304	−0.409437	−0.204718	+	0.978821i	$0.565628\pi$
$740$	1.13408	0.0416896
$741$	−26.3797	−0.969084
$742$	29.1038	1.06843
$743$	−9.80864	−0.359844	−0.179922	−	0.983681i	$-0.557585\pi$
$743$	−9.80864	−0.359844	−0.179922	+	0.983681i	$0.557585\pi$
$744$	4.72348	0.173171
$745$	5.37840	0.197049
$746$	−8.25236	−0.302140
$747$	−6.17151	−0.225804
$748$	18.8780	0.690248
$749$	31.8823	1.16495
$750$	−10.2644	−0.374804
$751$	−5.59073	−0.204009	−0.102004	−	0.994784i	$-0.532526\pi$
$751$	−5.59073	−0.204009	−0.102004	+	0.994784i	$0.532526\pi$
$752$	−5.63102	−0.205342
$753$	40.7439	1.48479
$754$	27.9675	1.01852
$755$	−11.6450	−0.423806
$756$	−24.6286	−0.895735
$757$	16.7028	0.607073	0.303536	−	0.952820i	$-0.401833\pi$
$757$	16.7028	0.607073	0.303536	+	0.952820i	$0.401833\pi$
$758$	0.291585	0.0105908
$759$	0.314209	0.0114051
$760$	4.99330	0.181126
$761$	−20.5972	−0.746647	−0.373323	−	0.927701i	$-0.621782\pi$
$761$	−20.5972	−0.746647	−0.373323	+	0.927701i	$0.621782\pi$
$762$	6.24698	0.226304
$763$	28.2513	1.02277
$764$	15.6504	0.566212
$765$	−2.91617	−0.105434
$766$	21.2218	0.766773
$767$	−23.5187	−0.849212
$768$	−1.44504	−0.0521435
$769$	−26.5133	−0.956095	−0.478048	−	0.878334i	$-0.658655\pi$
$769$	−26.5133	−0.956095	−0.478048	+	0.878334i	$0.658655\pi$
$770$	−14.5834	−0.525550
$771$	−17.6765	−0.636603
$772$	21.8853	0.787669
$773$	−6.28083	−0.225906	−0.112953	−	0.993600i	$-0.536031\pi$
$773$	−6.28083	−0.225906	−0.112953	+	0.993600i	$0.536031\pi$
$774$	−9.57779	−0.344267
$775$	14.4902	0.520505
$776$	−5.52111	−0.198196
$777$	−9.48188	−0.340160
$778$	−15.3491	−0.550293
$779$	−68.9211	−2.46935
$780$	−2.99569	−0.107263
$781$	59.0471	2.11287
$782$	−0.207751	−0.00742916
$783$	−57.4258	−2.05223
$784$	11.9825	0.427948
$785$	14.0664	0.502050
$786$	−30.7952	−1.09843
$787$	−53.4258	−1.90442	−0.952212	−	0.305439i	$-0.901197\pi$
$787$	−53.4258	−1.90442	−0.952212	+	0.305439i	$0.901197\pi$
$788$	−0.350191	−0.0124750
$789$	−6.55842	−0.233486
$790$	−2.97344	−0.105790
$791$	−72.8098	−2.58882
$792$	4.05323	0.144025
$793$	−0.512009	−0.0181820
$794$	23.4239	0.831282
$795$	−7.26875	−0.257796
$796$	6.99462	0.247918
$797$	30.7482	1.08916	0.544579	−	0.838709i	$-0.316689\pi$
$797$	30.7482	1.08916	0.544579	+	0.838709i	$0.316689\pi$
$798$	−41.7482	−1.47787
$799$	23.9148	0.846046
$800$	−4.43296	−0.156729
$801$	1.33752	0.0472589
$802$	20.4892	0.723498
$803$	45.7120	1.61314
$804$	−6.47650	−0.228409
$805$	0.160490	0.00565651
$806$	8.99894	0.316974
$807$	14.0131	0.493286
$808$	−9.43296	−0.331850
$809$	−29.8183	−1.04836	−0.524178	−	0.851609i	$-0.675627\pi$
$809$	−29.8183	−1.04836	−0.524178	+	0.851609i	$0.675627\pi$
$810$	4.09113	0.143748
$811$	−43.4403	−1.52539	−0.762697	−	0.646756i	$-0.776125\pi$
$811$	−43.4403	−1.52539	−0.762697	+	0.646756i	$0.776125\pi$
$812$	44.2610	1.55326
$813$	−40.8931	−1.43418
$814$	6.69441	0.234639
$815$	−0.165538	−0.00579856
$816$	6.13706	0.214840
$817$	−69.6499	−2.43674
$818$	22.5429	0.788193
$819$	−10.9373	−0.382182
$820$	−7.82669	−0.273320
$821$	−26.3773	−0.920575	−0.460288	−	0.887770i	$-0.652254\pi$
$821$	−26.3773	−0.920575	−0.460288	+	0.887770i	$0.652254\pi$
$822$	32.5153	1.13410
$823$	40.1094	1.39813	0.699064	−	0.715059i	$-0.253600\pi$
$823$	40.1094	1.39813	0.699064	+	0.715059i	$0.253600\pi$
$824$	−18.2174	−0.634635
$825$	−28.4741	−0.991341
$826$	−37.2204	−1.29506
$827$	−48.9691	−1.70282	−0.851412	−	0.524498i	$-0.824253\pi$
$827$	−48.9691	−1.70282	−0.851412	+	0.524498i	$0.824253\pi$
$828$	−0.0446055	−0.00155015
$829$	6.58509	0.228710	0.114355	−	0.993440i	$-0.463520\pi$
$829$	6.58509	0.228710	0.114355	+	0.993440i	$0.463520\pi$
$830$	−5.09651	−0.176902
$831$	30.9463	1.07352
$832$	−2.75302	−0.0954438
$833$	−50.8896	−1.76322
$834$	21.8562	0.756819
$835$	18.6614	0.645805
$836$	29.4752	1.01942
$837$	−18.4776	−0.638678
$838$	−33.5217	−1.15799
$839$	−6.98493	−0.241147	−0.120573	−	0.992704i	$-0.538473\pi$
$839$	−6.98493	−0.241147	−0.120573	+	0.992704i	$0.538473\pi$
$840$	−4.74094	−0.163578
$841$	74.2019	2.55869
$842$	−33.8920	−1.16800
$843$	4.90408	0.168906
$844$	−7.02715	−0.241884
$845$	4.08203	0.140426
$846$	5.13467	0.176534
$847$	−38.1594	−1.31117
$848$	−6.67994	−0.229390
$849$	26.4306	0.907095
$850$	18.8267	0.645750
$851$	−0.0736715	−0.00252543
$852$	19.1957	0.657633
$853$	12.9191	0.442343	0.221172	−	0.975235i	$-0.429012\pi$
$853$	12.9191	0.442343	0.221172	+	0.975235i	$0.429012\pi$
$854$	−0.810298	−0.0277278
$855$	−4.55316	−0.155715
$856$	−7.31767	−0.250113
$857$	21.2435	0.725665	0.362832	−	0.931854i	$-0.381810\pi$
$857$	21.2435	0.725665	0.362832	+	0.931854i	$0.381810\pi$
$858$	−17.6834	−0.603701
$859$	10.8750	0.371051	0.185525	−	0.982639i	$-0.440601\pi$
$859$	10.8750	0.371051	0.185525	+	0.982639i	$0.440601\pi$
$860$	−7.90946	−0.269710
$861$	65.4379	2.23012
$862$	−15.1860	−0.517237
$863$	18.4692	0.628699	0.314350	−	0.949307i	$-0.398214\pi$
$863$	18.4692	0.628699	0.314350	+	0.949307i	$0.398214\pi$
$864$	5.65279	0.192312
$865$	−1.54693	−0.0525970
$866$	−7.01938	−0.238528
$867$	−1.49827	−0.0508840
$868$	14.2416	0.483391
$869$	−17.5521	−0.595414
$870$	−11.0543	−0.374776
$871$	−12.3387	−0.418081
$872$	−6.48427	−0.219585
$873$	5.03444	0.170390
$874$	−0.324372	−0.0109720
$875$	−30.9480	−1.04623
$876$	14.8605	0.502091
$877$	7.88710	0.266328	0.133164	−	0.991094i	$-0.457486\pi$
$877$	7.88710	0.266328	0.133164	+	0.991094i	$0.457486\pi$
$878$	−12.8465	−0.433550
$879$	42.3793	1.42942
$880$	3.34721	0.112834
$881$	−23.8103	−0.802189	−0.401095	−	0.916037i	$-0.631370\pi$
$881$	−23.8103	−0.802189	−0.401095	+	0.916037i	$0.631370\pi$
$882$	−10.9263	−0.367909
$883$	−19.5714	−0.658628	−0.329314	−	0.944220i	$-0.606818\pi$
$883$	−19.5714	−0.658628	−0.329314	+	0.944220i	$0.606818\pi$
$884$	11.6920	0.393245
$885$	9.29590	0.312478
$886$	−20.1709	−0.677655
$887$	−52.9915	−1.77928	−0.889640	−	0.456662i	$-0.849045\pi$
$887$	−52.9915	−1.77928	−0.889640	+	0.456662i	$0.849045\pi$
$888$	2.17629	0.0730316
$889$	18.8351	0.631707
$890$	1.10454	0.0370242
$891$	24.1497	0.809047
$892$	10.5211	0.352273
$893$	37.3394	1.24952
$894$	10.3211	0.345190
$895$	3.71512	0.124183
$896$	−4.35690	−0.145554
$897$	0.194604	0.00649765
$898$	−17.4571	−0.582552
$899$	33.2067	1.10750
$900$	4.04221	0.134740
$901$	28.3696	0.945127
$902$	−46.2006	−1.53831
$903$	66.1299	2.20066
$904$	16.7114	0.555813
$905$	13.7681	0.457667
$906$	−22.3467	−0.742420
$907$	−26.7638	−0.888677	−0.444338	−	0.895859i	$-0.646561\pi$
$907$	−26.7638	−0.888677	−0.444338	+	0.895859i	$0.646561\pi$
$908$	21.5254	0.714346
$909$	8.60148	0.285293
$910$	−9.03220	−0.299414
$911$	−32.9560	−1.09188	−0.545940	−	0.837824i	$-0.683827\pi$
$911$	−32.9560	−1.09188	−0.545940	+	0.837824i	$0.683827\pi$
$912$	9.58211	0.317295
$913$	−30.0844	−0.995649
$914$	11.3080	0.374035
$915$	0.202374	0.00669028
$916$	6.88338	0.227433
$917$	−92.8496	−3.06617
$918$	−24.0073	−0.792359
$919$	1.18492	0.0390868	0.0195434	−	0.999809i	$-0.493779\pi$
$919$	1.18492	0.0390868	0.0195434	+	0.999809i	$0.493779\pi$
$920$	−0.0368358	−0.00121444
$921$	−22.0683	−0.727175
$922$	−4.81700	−0.158640
$923$	36.5706	1.20374
$924$	−27.9855	−0.920656
$925$	6.67622	0.219513
$926$	21.5690	0.708800
$927$	16.6116	0.545598
$928$	−10.1588	−0.333480
$929$	−11.5623	−0.379345	−0.189673	−	0.981847i	$-0.560743\pi$
$929$	−11.5623	−0.379345	−0.189673	+	0.981847i	$0.560743\pi$
$930$	−3.55688	−0.116635
$931$	−79.4565	−2.60408
$932$	−19.3793	−0.634789
$933$	39.7090	1.30001
$934$	12.6069	0.412509
$935$	−14.2155	−0.464897
$936$	2.51035	0.0820534
$937$	−28.3351	−0.925668	−0.462834	−	0.886445i	$-0.653167\pi$
$937$	−28.3351	−0.925668	−0.462834	+	0.886445i	$0.653167\pi$
$938$	−19.5271	−0.637582
$939$	−6.41981	−0.209503
$940$	4.24027	0.138303
$941$	−46.7348	−1.52351	−0.761756	−	0.647864i	$-0.775662\pi$
$941$	−46.7348	−1.52351	−0.761756	+	0.647864i	$0.775662\pi$
$942$	26.9933	0.879489
$943$	0.508434	0.0165569
$944$	8.54288	0.278047
$945$	18.5459	0.603297
$946$	−46.6892	−1.51800
$947$	34.3290	1.11554	0.557771	−	0.829995i	$-0.311657\pi$
$947$	34.3290	1.11554	0.557771	+	0.829995i	$0.311657\pi$
$948$	−5.70602	−0.185323
$949$	28.3116	0.919032
$950$	29.3951	0.953702
$951$	10.0116	0.324649
$952$	18.5036	0.599707
$953$	39.6082	1.28304	0.641518	−	0.767108i	$-0.278305\pi$
$953$	39.6082	1.28304	0.641518	+	0.767108i	$0.278305\pi$
$954$	6.09113	0.197208
$955$	−11.7851	−0.381356
$956$	−26.4198	−0.854478
$957$	−65.2529	−2.10933
$958$	12.5265	0.404712
$959$	98.0356	3.16574
$960$	1.08815	0.0351198
$961$	−20.3153	−0.655331
$962$	4.14616	0.133678
$963$	6.67264	0.215023
$964$	10.4916	0.337911
$965$	−16.4801	−0.530512
$966$	0.307979	0.00990905
$967$	−51.9120	−1.66938	−0.834688	−	0.550723i	$-0.814352\pi$
$967$	−51.9120	−1.66938	−0.834688	+	0.550723i	$0.814352\pi$
$968$	8.75840	0.281506
$969$	−40.6950	−1.30731
$970$	4.15751	0.133489
$971$	3.31634	0.106426	0.0532132	−	0.998583i	$-0.483054\pi$
$971$	3.31634	0.106426	0.0532132	+	0.998583i	$0.483054\pi$
$972$	−9.10752	−0.292124
$973$	65.8980	2.11259
$974$	−34.6625	−1.11066
$975$	−17.6353	−0.564783
$976$	0.185981	0.00595310
$977$	19.9734	0.639007	0.319504	−	0.947585i	$-0.396484\pi$
$977$	19.9734	0.639007	0.319504	+	0.947585i	$0.396484\pi$
$978$	−0.317667	−0.0101579
$979$	6.52004	0.208381
$980$	−9.02310	−0.288232
$981$	5.91271	0.188778
$982$	35.8474	1.14394
$983$	−8.77910	−0.280010	−0.140005	−	0.990151i	$-0.544712\pi$
$983$	−8.77910	−0.280010	−0.140005	+	0.990151i	$0.544712\pi$
$984$	−15.0194	−0.478800
$985$	0.263701	0.00840221
$986$	43.1444	1.37400
$987$	−35.4523	−1.12846
$988$	18.2553	0.580780
$989$	0.513811	0.0163382
$990$	−3.05216	−0.0970041
$991$	−49.8641	−1.58399	−0.791993	−	0.610530i	$-0.790956\pi$
$991$	−49.8641	−1.58399	−0.791993	+	0.610530i	$0.790956\pi$
$992$	−3.26875	−0.103783
$993$	−6.55842	−0.208125
$994$	57.8762	1.83572
$995$	−5.26709	−0.166978
$996$	−9.78017	−0.309896
$997$	−6.48725	−0.205453	−0.102727	−	0.994710i	$-0.532757\pi$
$997$	−6.48725	−0.205453	−0.102727	+	0.994710i	$0.532757\pi$
$998$	−0.170915	−0.00541023
$999$	−8.51334	−0.269350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.a.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.a.1.2	✓	3	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} -0.753020 q^{5} -1.44504 q^{6} -4.35690 q^{7} +1.00000 q^{8} -0.911854 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.44504 q^{3} +1.00000 q^{4} -0.753020 q^{5} -1.44504 q^{6} -4.35690 q^{7} +1.00000 q^{8} -0.911854 q^{9} -0.753020 q^{10} -4.44504 q^{11} -1.44504 q^{12} -2.75302 q^{13} -4.35690 q^{14} +1.08815 q^{15} +1.00000 q^{16} -4.24698 q^{17} -0.911854 q^{18} -6.63102 q^{19} -0.753020 q^{20} +6.29590 q^{21} -4.44504 q^{22} +0.0489173 q^{23} -1.44504 q^{24} -4.43296 q^{25} -2.75302 q^{26} +5.65279 q^{27} -4.35690 q^{28} -10.1588 q^{29} +1.08815 q^{30} -3.26875 q^{31} +1.00000 q^{32} +6.42327 q^{33} -4.24698 q^{34} +3.28083 q^{35} -0.911854 q^{36} -1.50604 q^{37} -6.63102 q^{38} +3.97823 q^{39} -0.753020 q^{40} +10.3937 q^{41} +6.29590 q^{42} +10.5036 q^{43} -4.44504 q^{44} +0.686645 q^{45} +0.0489173 q^{46} -5.63102 q^{47} -1.44504 q^{48} +11.9825 q^{49} -4.43296 q^{50} +6.13706 q^{51} -2.75302 q^{52} -6.67994 q^{53} +5.65279 q^{54} +3.34721 q^{55} -4.35690 q^{56} +9.58211 q^{57} -10.1588 q^{58} +8.54288 q^{59} +1.08815 q^{60} +0.185981 q^{61} -3.26875 q^{62} +3.97285 q^{63} +1.00000 q^{64} +2.07308 q^{65} +6.42327 q^{66} +4.48188 q^{67} -4.24698 q^{68} -0.0706876 q^{69} +3.28083 q^{70} -13.2838 q^{71} -0.911854 q^{72} -10.2838 q^{73} -1.50604 q^{74} +6.40581 q^{75} -6.63102 q^{76} +19.3666 q^{77} +3.97823 q^{78} +3.94869 q^{79} -0.753020 q^{80} -5.43296 q^{81} +10.3937 q^{82} +6.76809 q^{83} +6.29590 q^{84} +3.19806 q^{85} +10.5036 q^{86} +14.6799 q^{87} -4.44504 q^{88} -1.46681 q^{89} +0.686645 q^{90} +11.9946 q^{91} +0.0489173 q^{92} +4.72348 q^{93} -5.63102 q^{94} +4.99330 q^{95} -1.44504 q^{96} -5.52111 q^{97} +11.9825 q^{98} +4.05323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9	\( 3 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 7 q^{5} - 4 q^{6} - 9 q^{7} + 3 q^{8} + q^{9} - 7 q^{10} - 13 q^{11} - 4 q^{12} - 13 q^{13} - 9 q^{14} + 7 q^{15} + 3 q^{16} - 8 q^{17} + q^{18} - 5 q^{19} - 7 q^{20} + 5 q^{21} - 13 q^{22} - 9 q^{23} - 4 q^{24} + 6 q^{25} - 13 q^{26} - q^{27} - 9 q^{28} - 22 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} + 22 q^{33} - 8 q^{34} + 21 q^{35} + q^{36} - 14 q^{37} - 5 q^{38} + 15 q^{39} - 7 q^{40} - q^{41} + 5 q^{42} - 13 q^{44} - 9 q^{46} - 2 q^{47} - 4 q^{48} + 20 q^{49} + 6 q^{50} + 13 q^{51} - 13 q^{52} + 4 q^{53} - q^{54} + 28 q^{55} - 9 q^{56} + 23 q^{57} - 22 q^{58} + 7 q^{59} + 7 q^{60} - 14 q^{61} - 2 q^{62} + 18 q^{63} + 3 q^{64} + 35 q^{65} + 22 q^{66} - 15 q^{67} - 8 q^{68} + 12 q^{69} + 21 q^{70} - 7 q^{71} + q^{72} + 2 q^{73} - 14 q^{74} + 6 q^{75} - 5 q^{76} + 32 q^{77} + 15 q^{78} - 20 q^{79} - 7 q^{80} + 3 q^{81} - q^{82} + 5 q^{84} + 14 q^{85} + 20 q^{87} - 13 q^{88} - q^{89} + 39 q^{91} - 9 q^{92} - 16 q^{93} - 2 q^{94} - 7 q^{95} - 4 q^{96} - q^{97} + 20 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 7 * q^5 - 4 * q^6 - 9 * q^7 + 3 * q^8 + q^9 - 7 * q^10 - 13 * q^11 - 4 * q^12 - 13 * q^13 - 9 * q^14 + 7 * q^15 + 3 * q^16 - 8 * q^17 + q^18 - 5 * q^19 - 7 * q^20 + 5 * q^21 - 13 * q^22 - 9 * q^23 - 4 * q^24 + 6 * q^25 - 13 * q^26 - q^27 - 9 * q^28 - 22 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 + 22 * q^33 - 8 * q^34 + 21 * q^35 + q^36 - 14 * q^37 - 5 * q^38 + 15 * q^39 - 7 * q^40 - q^41 + 5 * q^42 - 13 * q^44 - 9 * q^46 - 2 * q^47 - 4 * q^48 + 20 * q^49 + 6 * q^50 + 13 * q^51 - 13 * q^52 + 4 * q^53 - q^54 + 28 * q^55 - 9 * q^56 + 23 * q^57 - 22 * q^58 + 7 * q^59 + 7 * q^60 - 14 * q^61 - 2 * q^62 + 18 * q^63 + 3 * q^64 + 35 * q^65 + 22 * q^66 - 15 * q^67 - 8 * q^68 + 12 * q^69 + 21 * q^70 - 7 * q^71 + q^72 + 2 * q^73 - 14 * q^74 + 6 * q^75 - 5 * q^76 + 32 * q^77 + 15 * q^78 - 20 * q^79 - 7 * q^80 + 3 * q^81 - q^82 + 5 * q^84 + 14 * q^85 + 20 * q^87 - 13 * q^88 - q^89 + 39 * q^91 - 9 * q^92 - 16 * q^93 - 2 * q^94 - 7 * q^95 - 4 * q^96 - q^97 + 20 * q^98 - 16 * q^99

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