LMFDB - Embedded newform 6022.2.a.d.1.9

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:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.46766 q^{3} +1.00000 q^{4} +0.852564 q^{5} +2.46766 q^{6} -2.40231 q^{7} -1.00000 q^{8} +3.08936 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.46766 q^{3} +1.00000 q^{4} +0.852564 q^{5} +2.46766 q^{6} -2.40231 q^{7} -1.00000 q^{8} +3.08936 q^{9} -0.852564 q^{10} +5.04656 q^{11} -2.46766 q^{12} -0.871257 q^{13} +2.40231 q^{14} -2.10384 q^{15} +1.00000 q^{16} +5.41905 q^{17} -3.08936 q^{18} +2.42242 q^{19} +0.852564 q^{20} +5.92809 q^{21} -5.04656 q^{22} -4.05743 q^{23} +2.46766 q^{24} -4.27313 q^{25} +0.871257 q^{26} -0.220499 q^{27} -2.40231 q^{28} -0.677793 q^{29} +2.10384 q^{30} -5.75887 q^{31} -1.00000 q^{32} -12.4532 q^{33} -5.41905 q^{34} -2.04812 q^{35} +3.08936 q^{36} -9.72864 q^{37} -2.42242 q^{38} +2.14997 q^{39} -0.852564 q^{40} +3.64594 q^{41} -5.92809 q^{42} -7.38927 q^{43} +5.04656 q^{44} +2.63387 q^{45} +4.05743 q^{46} +5.40574 q^{47} -2.46766 q^{48} -1.22890 q^{49} +4.27313 q^{50} -13.3724 q^{51} -0.871257 q^{52} -6.02881 q^{53} +0.220499 q^{54} +4.30251 q^{55} +2.40231 q^{56} -5.97772 q^{57} +0.677793 q^{58} +10.0899 q^{59} -2.10384 q^{60} +1.31817 q^{61} +5.75887 q^{62} -7.42159 q^{63} +1.00000 q^{64} -0.742802 q^{65} +12.4532 q^{66} +7.21292 q^{67} +5.41905 q^{68} +10.0124 q^{69} +2.04812 q^{70} +2.77901 q^{71} -3.08936 q^{72} -0.0772887 q^{73} +9.72864 q^{74} +10.5447 q^{75} +2.42242 q^{76} -12.1234 q^{77} -2.14997 q^{78} -0.216838 q^{79} +0.852564 q^{80} -8.72395 q^{81} -3.64594 q^{82} +12.1138 q^{83} +5.92809 q^{84} +4.62008 q^{85} +7.38927 q^{86} +1.67257 q^{87} -5.04656 q^{88} -0.339472 q^{89} -2.63387 q^{90} +2.09303 q^{91} -4.05743 q^{92} +14.2109 q^{93} -5.40574 q^{94} +2.06527 q^{95} +2.46766 q^{96} +0.0292133 q^{97} +1.22890 q^{98} +15.5906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * 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
$3$	−2.46766	−1.42471	−0.712353	−	0.701822i	$-0.752370\pi$
$3$	−2.46766	−1.42471	−0.712353	+	0.701822i	$0.752370\pi$
$4$	1.00000	0.500000
$5$	0.852564	0.381278	0.190639	−	0.981660i	$-0.438944\pi$
$5$	0.852564	0.381278	0.190639	+	0.981660i	$0.438944\pi$
$6$	2.46766	1.00742
$7$	−2.40231	−0.907988	−0.453994	−	0.891005i	$-0.650001\pi$
$7$	−2.40231	−0.907988	−0.453994	+	0.891005i	$0.650001\pi$
$8$	−1.00000	−0.353553
$9$	3.08936	1.02979
$10$	−0.852564	−0.269604
$11$	5.04656	1.52159	0.760797	−	0.648990i	$-0.224808\pi$
$11$	5.04656	1.52159	0.760797	+	0.648990i	$0.224808\pi$
$12$	−2.46766	−0.712353
$13$	−0.871257	−0.241643	−0.120822	−	0.992674i	$-0.538553\pi$
$13$	−0.871257	−0.241643	−0.120822	+	0.992674i	$0.538553\pi$
$14$	2.40231	0.642045
$15$	−2.10384	−0.543209
$16$	1.00000	0.250000
$17$	5.41905	1.31431	0.657156	−	0.753755i	$-0.271759\pi$
$17$	5.41905	1.31431	0.657156	+	0.753755i	$0.271759\pi$
$18$	−3.08936	−0.728168
$19$	2.42242	0.555742	0.277871	−	0.960618i	$-0.410371\pi$
$19$	2.42242	0.555742	0.277871	+	0.960618i	$0.410371\pi$
$20$	0.852564	0.190639
$21$	5.92809	1.29362
$22$	−5.04656	−1.07593
$23$	−4.05743	−0.846033	−0.423017	−	0.906122i	$-0.639029\pi$
$23$	−4.05743	−0.846033	−0.423017	+	0.906122i	$0.639029\pi$
$24$	2.46766	0.503709
$25$	−4.27313	−0.854627
$26$	0.871257	0.170868
$27$	−0.220499	−0.0424351
$28$	−2.40231	−0.453994
$29$	−0.677793	−0.125863	−0.0629315	−	0.998018i	$-0.520045\pi$
$29$	−0.677793	−0.125863	−0.0629315	+	0.998018i	$0.520045\pi$
$30$	2.10384	0.384107
$31$	−5.75887	−1.03432	−0.517162	−	0.855888i	$-0.673011\pi$
$31$	−5.75887	−1.03432	−0.517162	+	0.855888i	$0.673011\pi$
$32$	−1.00000	−0.176777
$33$	−12.4532	−2.16782
$34$	−5.41905	−0.929359
$35$	−2.04812	−0.346196
$36$	3.08936	0.514893
$37$	−9.72864	−1.59938	−0.799689	−	0.600414i	$-0.795003\pi$
$37$	−9.72864	−1.59938	−0.799689	+	0.600414i	$0.795003\pi$
$38$	−2.42242	−0.392969
$39$	2.14997	0.344270
$40$	−0.852564	−0.134802
$41$	3.64594	0.569400	0.284700	−	0.958617i	$-0.408106\pi$
$41$	3.64594	0.569400	0.284700	+	0.958617i	$0.408106\pi$
$42$	−5.92809	−0.914724
$43$	−7.38927	−1.12685	−0.563426	−	0.826166i	$-0.690517\pi$
$43$	−7.38927	−1.12685	−0.563426	+	0.826166i	$0.690517\pi$
$44$	5.04656	0.760797
$45$	2.63387	0.392635
$46$	4.05743	0.598236
$47$	5.40574	0.788508	0.394254	−	0.919002i	$-0.371003\pi$
$47$	5.40574	0.788508	0.394254	+	0.919002i	$0.371003\pi$
$48$	−2.46766	−0.356176
$49$	−1.22890	−0.175558
$50$	4.27313	0.604313
$51$	−13.3724	−1.87251
$52$	−0.871257	−0.120822
$53$	−6.02881	−0.828121	−0.414060	−	0.910249i	$-0.635890\pi$
$53$	−6.02881	−0.828121	−0.414060	+	0.910249i	$0.635890\pi$
$54$	0.220499	0.0300061
$55$	4.30251	0.580151
$56$	2.40231	0.321022
$57$	−5.97772	−0.791769
$58$	0.677793	0.0889986
$59$	10.0899	1.31359	0.656793	−	0.754071i	$-0.271912\pi$
$59$	10.0899	1.31359	0.656793	+	0.754071i	$0.271912\pi$
$60$	−2.10384	−0.271605
$61$	1.31817	0.168775	0.0843874	−	0.996433i	$-0.473107\pi$
$61$	1.31817	0.168775	0.0843874	+	0.996433i	$0.473107\pi$
$62$	5.75887	0.731377
$63$	−7.42159	−0.935033
$64$	1.00000	0.125000
$65$	−0.742802	−0.0921333
$66$	12.4532	1.53288
$67$	7.21292	0.881198	0.440599	−	0.897704i	$-0.354766\pi$
$67$	7.21292	0.881198	0.440599	+	0.897704i	$0.354766\pi$
$68$	5.41905	0.657156
$69$	10.0124	1.20535
$70$	2.04812	0.244798
$71$	2.77901	0.329808	0.164904	−	0.986310i	$-0.447269\pi$
$71$	2.77901	0.329808	0.164904	+	0.986310i	$0.447269\pi$
$72$	−3.08936	−0.364084
$73$	−0.0772887	−0.00904596	−0.00452298	−	0.999990i	$-0.501440\pi$
$73$	−0.0772887	−0.00904596	−0.00452298	+	0.999990i	$0.501440\pi$
$74$	9.72864	1.13093
$75$	10.5447	1.21759
$76$	2.42242	0.277871
$77$	−12.1234	−1.38159
$78$	−2.14997	−0.243436
$79$	−0.216838	−0.0243961	−0.0121981	−	0.999926i	$-0.503883\pi$
$79$	−0.216838	−0.0243961	−0.0121981	+	0.999926i	$0.503883\pi$
$80$	0.852564	0.0953195
$81$	−8.72395	−0.969328
$82$	−3.64594	−0.402626
$83$	12.1138	1.32966	0.664830	−	0.746995i	$-0.268504\pi$
$83$	12.1138	1.32966	0.664830	+	0.746995i	$0.268504\pi$
$84$	5.92809	0.646808
$85$	4.62008	0.501118
$86$	7.38927	0.796805
$87$	1.67257	0.179318
$88$	−5.04656	−0.537965
$89$	−0.339472	−0.0359839	−0.0179920	−	0.999838i	$-0.505727\pi$
$89$	−0.339472	−0.0359839	−0.0179920	+	0.999838i	$0.505727\pi$
$90$	−2.63387	−0.277635
$91$	2.09303	0.219409
$92$	−4.05743	−0.423017
$93$	14.2109	1.47361
$94$	−5.40574	−0.557559
$95$	2.06527	0.211892
$96$	2.46766	0.251855
$97$	0.0292133	0.00296616	0.00148308	−	0.999999i	$-0.499528\pi$
$97$	0.0292133	0.00296616	0.00148308	+	0.999999i	$0.499528\pi$
$98$	1.22890	0.124138
$99$	15.5906	1.56692
$100$	−4.27313	−0.427313
$101$	−7.63981	−0.760190	−0.380095	−	0.924948i	$-0.624109\pi$
$101$	−7.63981	−0.760190	−0.380095	+	0.924948i	$0.624109\pi$
$102$	13.3724	1.32406
$103$	−7.44511	−0.733588	−0.366794	−	0.930302i	$-0.619545\pi$
$103$	−7.44511	−0.733588	−0.366794	+	0.930302i	$0.619545\pi$
$104$	0.871257	0.0854338
$105$	5.05408	0.493227
$106$	6.02881	0.585570
$107$	3.24685	0.313885	0.156942	−	0.987608i	$-0.449836\pi$
$107$	3.24685	0.313885	0.156942	+	0.987608i	$0.449836\pi$
$108$	−0.220499	−0.0212175
$109$	−13.7559	−1.31758	−0.658789	−	0.752328i	$-0.728931\pi$
$109$	−13.7559	−1.31758	−0.658789	+	0.752328i	$0.728931\pi$
$110$	−4.30251	−0.410229
$111$	24.0070	2.27864
$112$	−2.40231	−0.226997
$113$	0.681001	0.0640632	0.0320316	−	0.999487i	$-0.489802\pi$
$113$	0.681001	0.0640632	0.0320316	+	0.999487i	$0.489802\pi$
$114$	5.97772	0.559865
$115$	−3.45922	−0.322574
$116$	−0.677793	−0.0629315
$117$	−2.69162	−0.248841
$118$	−10.0899	−0.928846
$119$	−13.0182	−1.19338
$120$	2.10384	0.192053
$121$	14.4677	1.31525
$122$	−1.31817	−0.119342
$123$	−8.99694	−0.811227
$124$	−5.75887	−0.517162
$125$	−7.90594	−0.707129
$126$	7.42159	0.661168
$127$	15.0754	1.33773	0.668865	−	0.743384i	$-0.266780\pi$
$127$	15.0754	1.33773	0.668865	+	0.743384i	$0.266780\pi$
$128$	−1.00000	−0.0883883
$129$	18.2342	1.60543
$130$	0.742802	0.0651481
$131$	17.0957	1.49366	0.746828	−	0.665017i	$-0.231576\pi$
$131$	17.0957	1.49366	0.746828	+	0.665017i	$0.231576\pi$
$132$	−12.4532	−1.08391
$133$	−5.81941	−0.504607
$134$	−7.21292	−0.623101
$135$	−0.187990	−0.0161796
$136$	−5.41905	−0.464679
$137$	−5.24767	−0.448339	−0.224169	−	0.974550i	$-0.571967\pi$
$137$	−5.24767	−0.448339	−0.224169	+	0.974550i	$0.571967\pi$
$138$	−10.0124	−0.852310
$139$	−16.3465	−1.38649	−0.693247	−	0.720700i	$-0.743820\pi$
$139$	−16.3465	−1.38649	−0.693247	+	0.720700i	$0.743820\pi$
$140$	−2.04812	−0.173098
$141$	−13.3395	−1.12339
$142$	−2.77901	−0.233209
$143$	−4.39685	−0.367683
$144$	3.08936	0.257446
$145$	−0.577862	−0.0479888
$146$	0.0772887	0.00639646
$147$	3.03252	0.250118
$148$	−9.72864	−0.799689
$149$	9.49750	0.778065	0.389033	−	0.921224i	$-0.372809\pi$
$149$	9.49750	0.778065	0.389033	+	0.921224i	$0.372809\pi$
$150$	−10.5447	−0.860967
$151$	13.1457	1.06978	0.534890	−	0.844922i	$-0.320353\pi$
$151$	13.1457	1.06978	0.534890	+	0.844922i	$0.320353\pi$
$152$	−2.42242	−0.196485
$153$	16.7414	1.35346
$154$	12.1234	0.976931
$155$	−4.90980	−0.394365
$156$	2.14997	0.172135
$157$	−7.28450	−0.581366	−0.290683	−	0.956819i	$-0.593883\pi$
$157$	−7.28450	−0.581366	−0.290683	+	0.956819i	$0.593883\pi$
$158$	0.216838	0.0172507
$159$	14.8771	1.17983
$160$	−0.852564	−0.0674011
$161$	9.74722	0.768188
$162$	8.72395	0.685418
$163$	−17.3929	−1.36232	−0.681158	−	0.732136i	$-0.738523\pi$
$163$	−17.3929	−1.36232	−0.681158	+	0.732136i	$0.738523\pi$
$164$	3.64594	0.284700
$165$	−10.6171	−0.826544
$166$	−12.1138	−0.940212
$167$	−2.59913	−0.201127	−0.100563	−	0.994931i	$-0.532065\pi$
$167$	−2.59913	−0.201127	−0.100563	+	0.994931i	$0.532065\pi$
$168$	−5.92809	−0.457362
$169$	−12.2409	−0.941609
$170$	−4.62008	−0.354344
$171$	7.48373	0.572295
$172$	−7.38927	−0.563426
$173$	−4.68515	−0.356206	−0.178103	−	0.984012i	$-0.556996\pi$
$173$	−4.68515	−0.356206	−0.178103	+	0.984012i	$0.556996\pi$
$174$	−1.67257	−0.126797
$175$	10.2654	0.775991
$176$	5.04656	0.380399
$177$	−24.8983	−1.87147
$178$	0.339472	0.0254445
$179$	13.4316	1.00393	0.501963	−	0.864889i	$-0.332611\pi$
$179$	13.4316	1.00393	0.501963	+	0.864889i	$0.332611\pi$
$180$	2.63387	0.196317
$181$	9.97416	0.741374	0.370687	−	0.928758i	$-0.379122\pi$
$181$	9.97416	0.741374	0.370687	+	0.928758i	$0.379122\pi$
$182$	−2.09303	−0.155146
$183$	−3.25280	−0.240454
$184$	4.05743	0.299118
$185$	−8.29429	−0.609808
$186$	−14.2109	−1.04200
$187$	27.3475	1.99985
$188$	5.40574	0.394254
$189$	0.529707	0.0385305
$190$	−2.06527	−0.149831
$191$	−8.85766	−0.640917	−0.320459	−	0.947262i	$-0.603837\pi$
$191$	−8.85766	−0.640917	−0.320459	+	0.947262i	$0.603837\pi$
$192$	−2.46766	−0.178088
$193$	−21.6075	−1.55535	−0.777673	−	0.628669i	$-0.783600\pi$
$193$	−21.6075	−1.55535	−0.777673	+	0.628669i	$0.783600\pi$
$194$	−0.0292133	−0.00209739
$195$	1.83298	0.131263
$196$	−1.22890	−0.0877788
$197$	6.73644	0.479951	0.239976	−	0.970779i	$-0.422861\pi$
$197$	6.73644	0.479951	0.239976	+	0.970779i	$0.422861\pi$
$198$	−15.5906	−1.10798
$199$	4.27583	0.303105	0.151553	−	0.988449i	$-0.451573\pi$
$199$	4.27583	0.303105	0.151553	+	0.988449i	$0.451573\pi$
$200$	4.27313	0.302156
$201$	−17.7990	−1.25545
$202$	7.63981	0.537535
$203$	1.62827	0.114282
$204$	−13.3724	−0.936254
$205$	3.10839	0.217100
$206$	7.44511	0.518725
$207$	−12.5349	−0.871233
$208$	−0.871257	−0.0604108
$209$	12.2249	0.845614
$210$	−5.05408	−0.348764
$211$	18.1540	1.24977	0.624887	−	0.780715i	$-0.285145\pi$
$211$	18.1540	1.24977	0.624887	+	0.780715i	$0.285145\pi$
$212$	−6.02881	−0.414060
$213$	−6.85766	−0.469879
$214$	−3.24685	−0.221950
$215$	−6.29982	−0.429644
$216$	0.220499	0.0150031
$217$	13.8346	0.939153
$218$	13.7559	0.931668
$219$	0.190722	0.0128878
$220$	4.30251	0.290075
$221$	−4.72138	−0.317594
$222$	−24.0070	−1.61124
$223$	−12.2064	−0.817400	−0.408700	−	0.912669i	$-0.634018\pi$
$223$	−12.2064	−0.817400	−0.408700	+	0.912669i	$0.634018\pi$
$224$	2.40231	0.160511
$225$	−13.2012	−0.880082
$226$	−0.681001	−0.0452995
$227$	10.3671	0.688091	0.344045	−	0.938953i	$-0.388203\pi$
$227$	10.3671	0.688091	0.344045	+	0.938953i	$0.388203\pi$
$228$	−5.97772	−0.395884
$229$	8.11927	0.536537	0.268268	−	0.963344i	$-0.413549\pi$
$229$	8.11927	0.536537	0.268268	+	0.963344i	$0.413549\pi$
$230$	3.45922	0.228094
$231$	29.9165	1.96836
$232$	0.677793	0.0444993
$233$	25.4298	1.66596	0.832981	−	0.553302i	$-0.186632\pi$
$233$	25.4298	1.66596	0.832981	+	0.553302i	$0.186632\pi$
$234$	2.69162	0.175957
$235$	4.60874	0.300641
$236$	10.0899	0.656793
$237$	0.535082	0.0347573
$238$	13.0182	0.843847
$239$	−2.41598	−0.156277	−0.0781384	−	0.996943i	$-0.524898\pi$
$239$	−2.41598	−0.156277	−0.0781384	+	0.996943i	$0.524898\pi$
$240$	−2.10384	−0.135802
$241$	10.6378	0.685239	0.342619	−	0.939474i	$-0.388686\pi$
$241$	10.6378	0.685239	0.342619	+	0.939474i	$0.388686\pi$
$242$	−14.4677	−0.930022
$243$	22.1893	1.42344
$244$	1.31817	0.0843874
$245$	−1.04772	−0.0669363
$246$	8.99694	0.573624
$247$	−2.11055	−0.134291
$248$	5.75887	0.365689
$249$	−29.8927	−1.89437
$250$	7.90594	0.500016
$251$	−14.5567	−0.918808	−0.459404	−	0.888227i	$-0.651937\pi$
$251$	−14.5567	−0.918808	−0.459404	+	0.888227i	$0.651937\pi$
$252$	−7.42159	−0.467516
$253$	−20.4761	−1.28732
$254$	−15.0754	−0.945918
$255$	−11.4008	−0.713946
$256$	1.00000	0.0625000
$257$	−24.9555	−1.55668	−0.778341	−	0.627841i	$-0.783939\pi$
$257$	−24.9555	−1.55668	−0.778341	+	0.627841i	$0.783939\pi$
$258$	−18.2342	−1.13521
$259$	23.3712	1.45222
$260$	−0.742802	−0.0460666
$261$	−2.09394	−0.129612
$262$	−17.0957	−1.05617
$263$	−21.5103	−1.32638	−0.663190	−	0.748451i	$-0.730798\pi$
$263$	−21.5103	−1.32638	−0.663190	+	0.748451i	$0.730798\pi$
$264$	12.4532	0.766441
$265$	−5.13995	−0.315744
$266$	5.81941	0.356811
$267$	0.837701	0.0512665
$268$	7.21292	0.440599
$269$	29.7788	1.81564	0.907822	−	0.419357i	$-0.137744\pi$
$269$	29.7788	1.81564	0.907822	+	0.419357i	$0.137744\pi$
$270$	0.187990	0.0114407
$271$	7.30997	0.444049	0.222025	−	0.975041i	$-0.428733\pi$
$271$	7.30997	0.444049	0.222025	+	0.975041i	$0.428733\pi$
$272$	5.41905	0.328578
$273$	−5.16489	−0.312593
$274$	5.24767	0.317023
$275$	−21.5646	−1.30040
$276$	10.0124	0.602674
$277$	−8.60985	−0.517316	−0.258658	−	0.965969i	$-0.583280\pi$
$277$	−8.60985	−0.517316	−0.258658	+	0.965969i	$0.583280\pi$
$278$	16.3465	0.980399
$279$	−17.7912	−1.06513
$280$	2.04812	0.122399
$281$	−15.5284	−0.926348	−0.463174	−	0.886267i	$-0.653290\pi$
$281$	−15.5284	−0.926348	−0.463174	+	0.886267i	$0.653290\pi$
$282$	13.3395	0.794358
$283$	−22.3925	−1.33110	−0.665548	−	0.746355i	$-0.731802\pi$
$283$	−22.3925	−1.33110	−0.665548	+	0.746355i	$0.731802\pi$
$284$	2.77901	0.164904
$285$	−5.09639	−0.301884
$286$	4.39685	0.259991
$287$	−8.75867	−0.517008
$288$	−3.08936	−0.182042
$289$	12.3661	0.727416
$290$	0.577862	0.0339332
$291$	−0.0720885	−0.00422590
$292$	−0.0772887	−0.00452298
$293$	−3.88336	−0.226869	−0.113434	−	0.993546i	$-0.536185\pi$
$293$	−3.88336	−0.226869	−0.113434	+	0.993546i	$0.536185\pi$
$294$	−3.03252	−0.176860
$295$	8.60224	0.500842
$296$	9.72864	0.565466
$297$	−1.11276	−0.0645689
$298$	−9.49750	−0.550175
$299$	3.53507	0.204438
$300$	10.5447	0.608796
$301$	17.7513	1.02317
$302$	−13.1457	−0.756449
$303$	18.8525	1.08305
$304$	2.42242	0.138936
$305$	1.12383	0.0643501
$306$	−16.7414	−0.957040
$307$	4.42927	0.252792	0.126396	−	0.991980i	$-0.459659\pi$
$307$	4.42927	0.252792	0.126396	+	0.991980i	$0.459659\pi$
$308$	−12.1234	−0.690795
$309$	18.3720	1.04515
$310$	4.90980	0.278858
$311$	−1.46451	−0.0830449	−0.0415225	−	0.999138i	$-0.513221\pi$
$311$	−1.46451	−0.0830449	−0.0415225	+	0.999138i	$0.513221\pi$
$312$	−2.14997	−0.121718
$313$	−11.5136	−0.650788	−0.325394	−	0.945579i	$-0.605497\pi$
$313$	−11.5136	−0.650788	−0.325394	+	0.945579i	$0.605497\pi$
$314$	7.28450	0.411088
$315$	−6.32738	−0.356508
$316$	−0.216838	−0.0121981
$317$	4.55810	0.256008	0.128004	−	0.991774i	$-0.459143\pi$
$317$	4.55810	0.256008	0.128004	+	0.991774i	$0.459143\pi$
$318$	−14.8771	−0.834265
$319$	−3.42052	−0.191513
$320$	0.852564	0.0476598
$321$	−8.01212	−0.447193
$322$	−9.74722	−0.543191
$323$	13.1272	0.730418
$324$	−8.72395	−0.484664
$325$	3.72300	0.206515
$326$	17.3929	0.963303
$327$	33.9450	1.87716
$328$	−3.64594	−0.201313
$329$	−12.9863	−0.715956
$330$	10.6171	0.584455
$331$	5.40676	0.297182	0.148591	−	0.988899i	$-0.452526\pi$
$331$	5.40676	0.297182	0.148591	+	0.988899i	$0.452526\pi$
$332$	12.1138	0.664830
$333$	−30.0552	−1.64702
$334$	2.59913	0.142218
$335$	6.14947	0.335982
$336$	5.92809	0.323404
$337$	−2.71437	−0.147861	−0.0739306	−	0.997263i	$-0.523554\pi$
$337$	−2.71437	−0.147861	−0.0739306	+	0.997263i	$0.523554\pi$
$338$	12.2409	0.665818
$339$	−1.68048	−0.0912712
$340$	4.62008	0.250559
$341$	−29.0625	−1.57382
$342$	−7.48373	−0.404674
$343$	19.7684	1.06739
$344$	7.38927	0.398403
$345$	8.53619	0.459573
$346$	4.68515	0.251875
$347$	−14.7370	−0.791126	−0.395563	−	0.918439i	$-0.629451\pi$
$347$	−14.7370	−0.791126	−0.395563	+	0.918439i	$0.629451\pi$
$348$	1.67257	0.0896589
$349$	1.53134	0.0819707	0.0409854	−	0.999160i	$-0.486950\pi$
$349$	1.53134	0.0819707	0.0409854	+	0.999160i	$0.486950\pi$
$350$	−10.2654	−0.548709
$351$	0.192111	0.0102541
$352$	−5.04656	−0.268982
$353$	−25.4747	−1.35588	−0.677941	−	0.735117i	$-0.737127\pi$
$353$	−25.4747	−1.35588	−0.677941	+	0.735117i	$0.737127\pi$
$354$	24.8983	1.32333
$355$	2.36928	0.125749
$356$	−0.339472	−0.0179920
$357$	32.1246	1.70021
$358$	−13.4316	−0.709883
$359$	−24.4639	−1.29116	−0.645578	−	0.763695i	$-0.723383\pi$
$359$	−24.4639	−1.29116	−0.645578	+	0.763695i	$0.723383\pi$
$360$	−2.63387	−0.138817
$361$	−13.1319	−0.691151
$362$	−9.97416	−0.524230
$363$	−35.7015	−1.87384
$364$	2.09303	0.109705
$365$	−0.0658935	−0.00344903
$366$	3.25280	0.170027
$367$	−33.7511	−1.76179	−0.880896	−	0.473309i	$-0.843059\pi$
$367$	−33.7511	−1.76179	−0.880896	+	0.473309i	$0.843059\pi$
$368$	−4.05743	−0.211508
$369$	11.2636	0.586359
$370$	8.29429	0.431200
$371$	14.4831	0.751924
$372$	14.2109	0.736803
$373$	31.0145	1.60587	0.802935	−	0.596067i	$-0.203271\pi$
$373$	31.0145	1.60587	0.802935	+	0.596067i	$0.203271\pi$
$374$	−27.3475	−1.41411
$375$	19.5092	1.00745
$376$	−5.40574	−0.278780
$377$	0.590532	0.0304140
$378$	−0.529707	−0.0272452
$379$	−14.2420	−0.731564	−0.365782	−	0.930701i	$-0.619198\pi$
$379$	−14.2420	−0.731564	−0.365782	+	0.930701i	$0.619198\pi$
$380$	2.06527	0.105946
$381$	−37.2011	−1.90587
$382$	8.85766	0.453197
$383$	−15.3028	−0.781934	−0.390967	−	0.920405i	$-0.627859\pi$
$383$	−15.3028	−0.781934	−0.390967	+	0.920405i	$0.627859\pi$
$384$	2.46766	0.125927
$385$	−10.3360	−0.526770
$386$	21.6075	1.09980
$387$	−22.8281	−1.16042
$388$	0.0292133	0.00148308
$389$	−9.01684	−0.457172	−0.228586	−	0.973524i	$-0.573410\pi$
$389$	−9.01684	−0.457172	−0.228586	+	0.973524i	$0.573410\pi$
$390$	−1.83298	−0.0928168
$391$	−21.9874	−1.11195
$392$	1.22890	0.0620690
$393$	−42.1863	−2.12802
$394$	−6.73644	−0.339377
$395$	−0.184868	−0.00930172
$396$	15.5906	0.783458
$397$	8.52777	0.427996	0.213998	−	0.976834i	$-0.431351\pi$
$397$	8.52777	0.427996	0.213998	+	0.976834i	$0.431351\pi$
$398$	−4.27583	−0.214328
$399$	14.3603	0.718917
$400$	−4.27313	−0.213657
$401$	5.83712	0.291492	0.145746	−	0.989322i	$-0.453442\pi$
$401$	5.83712	0.291492	0.145746	+	0.989322i	$0.453442\pi$
$402$	17.7990	0.887736
$403$	5.01745	0.249937
$404$	−7.63981	−0.380095
$405$	−7.43772	−0.369584
$406$	−1.62827	−0.0808097
$407$	−49.0962	−2.43361
$408$	13.3724	0.662031
$409$	−6.82106	−0.337280	−0.168640	−	0.985678i	$-0.553938\pi$
$409$	−6.82106	−0.337280	−0.168640	+	0.985678i	$0.553938\pi$
$410$	−3.10839	−0.153513
$411$	12.9495	0.638751
$412$	−7.44511	−0.366794
$413$	−24.2390	−1.19272
$414$	12.5349	0.616055
$415$	10.3278	0.506970
$416$	0.871257	0.0427169
$417$	40.3377	1.97534
$418$	−12.2249	−0.597940
$419$	−19.1246	−0.934300	−0.467150	−	0.884178i	$-0.654719\pi$
$419$	−19.1246	−0.934300	−0.467150	+	0.884178i	$0.654719\pi$
$420$	5.05408	0.246614
$421$	−31.1428	−1.51781	−0.758904	−	0.651203i	$-0.774265\pi$
$421$	−31.1428	−1.51781	−0.758904	+	0.651203i	$0.774265\pi$
$422$	−18.1540	−0.883724
$423$	16.7002	0.811994
$424$	6.02881	0.292785
$425$	−23.1563	−1.12325
$426$	6.85766	0.332255
$427$	−3.16666	−0.153245
$428$	3.24685	0.156942
$429$	10.8499	0.523840
$430$	6.29982	0.303804
$431$	−20.9830	−1.01072	−0.505358	−	0.862910i	$-0.668639\pi$
$431$	−20.9830	−1.01072	−0.505358	+	0.862910i	$0.668639\pi$
$432$	−0.220499	−0.0106088
$433$	−33.2280	−1.59684	−0.798419	−	0.602102i	$-0.794330\pi$
$433$	−33.2280	−1.59684	−0.798419	+	0.602102i	$0.794330\pi$
$434$	−13.8346	−0.664082
$435$	1.42597	0.0683700
$436$	−13.7559	−0.658789
$437$	−9.82882	−0.470176
$438$	−0.190722	−0.00911307
$439$	−0.843872	−0.0402758	−0.0201379	−	0.999797i	$-0.506411\pi$
$439$	−0.843872	−0.0402758	−0.0201379	+	0.999797i	$0.506411\pi$
$440$	−4.30251	−0.205114
$441$	−3.79652	−0.180787
$442$	4.72138	0.224573
$443$	37.4738	1.78043	0.890216	−	0.455538i	$-0.150553\pi$
$443$	37.4738	1.78043	0.890216	+	0.455538i	$0.150553\pi$
$444$	24.0070	1.13932
$445$	−0.289421	−0.0137199
$446$	12.2064	0.577989
$447$	−23.4366	−1.10851
$448$	−2.40231	−0.113499
$449$	14.3286	0.676207	0.338103	−	0.941109i	$-0.390215\pi$
$449$	14.3286	0.676207	0.338103	+	0.941109i	$0.390215\pi$
$450$	13.2012	0.622312
$451$	18.3994	0.866395
$452$	0.681001	0.0320316
$453$	−32.4391	−1.52412
$454$	−10.3671	−0.486553
$455$	1.78444	0.0836559
$456$	5.97772	0.279933
$457$	−18.8795	−0.883146	−0.441573	−	0.897225i	$-0.645579\pi$
$457$	−18.8795	−0.883146	−0.441573	+	0.897225i	$0.645579\pi$
$458$	−8.11927	−0.379389
$459$	−1.19489	−0.0557729
$460$	−3.45922	−0.161287
$461$	24.7280	1.15170	0.575849	−	0.817556i	$-0.304671\pi$
$461$	24.7280	1.15170	0.575849	+	0.817556i	$0.304671\pi$
$462$	−29.9165	−1.39184
$463$	−30.1377	−1.40062	−0.700309	−	0.713840i	$-0.746954\pi$
$463$	−30.1377	−1.40062	−0.700309	+	0.713840i	$0.746954\pi$
$464$	−0.677793	−0.0314658
$465$	12.1157	0.561854
$466$	−25.4298	−1.17801
$467$	−26.9818	−1.24857	−0.624284	−	0.781197i	$-0.714609\pi$
$467$	−26.9818	−1.24857	−0.624284	+	0.781197i	$0.714609\pi$
$468$	−2.69162	−0.124420
$469$	−17.3277	−0.800118
$470$	−4.60874	−0.212585
$471$	17.9757	0.828276
$472$	−10.0899	−0.464423
$473$	−37.2904	−1.71461
$474$	−0.535082	−0.0245771
$475$	−10.3513	−0.474952
$476$	−13.0182	−0.596690
$477$	−18.6251	−0.852787
$478$	2.41598	0.110504
$479$	11.4451	0.522940	0.261470	−	0.965212i	$-0.415793\pi$
$479$	11.4451	0.522940	0.261470	+	0.965212i	$0.415793\pi$
$480$	2.10384	0.0960267
$481$	8.47615	0.386479
$482$	−10.6378	−0.484537
$483$	−24.0528	−1.09444
$484$	14.4677	0.657625
$485$	0.0249062	0.00113093
$486$	−22.1893	−1.00653
$487$	16.1772	0.733057	0.366528	−	0.930407i	$-0.380546\pi$
$487$	16.1772	0.733057	0.366528	+	0.930407i	$0.380546\pi$
$488$	−1.31817	−0.0596709
$489$	42.9198	1.94090
$490$	1.04772	0.0473311
$491$	20.8819	0.942385	0.471193	−	0.882030i	$-0.343824\pi$
$491$	20.8819	0.942385	0.471193	+	0.882030i	$0.343824\pi$
$492$	−8.99694	−0.405613
$493$	−3.67299	−0.165423
$494$	2.11055	0.0949583
$495$	13.2920	0.597431
$496$	−5.75887	−0.258581
$497$	−6.67604	−0.299462
$498$	29.8927	1.33952
$499$	−9.55075	−0.427550	−0.213775	−	0.976883i	$-0.568576\pi$
$499$	−9.55075	−0.427550	−0.213775	+	0.976883i	$0.568576\pi$
$500$	−7.90594	−0.353564
$501$	6.41378	0.286547
$502$	14.5567	0.649695
$503$	−26.9386	−1.20113	−0.600567	−	0.799574i	$-0.705058\pi$
$503$	−26.9386	−1.20113	−0.600567	+	0.799574i	$0.705058\pi$
$504$	7.42159	0.330584
$505$	−6.51343	−0.289844
$506$	20.4761	0.910273
$507$	30.2064	1.34151
$508$	15.0754	0.668865
$509$	−17.3799	−0.770349	−0.385175	−	0.922844i	$-0.625859\pi$
$509$	−17.3799	−0.770349	−0.385175	+	0.922844i	$0.625859\pi$
$510$	11.4008	0.504836
$511$	0.185671	0.00821362
$512$	−1.00000	−0.0441942
$513$	−0.534142	−0.0235829
$514$	24.9555	1.10074
$515$	−6.34743	−0.279701
$516$	18.2342	0.802716
$517$	27.2804	1.19979
$518$	−23.3712	−1.02687
$519$	11.5614	0.507488
$520$	0.742802	0.0325740
$521$	19.2765	0.844520	0.422260	−	0.906475i	$-0.361237\pi$
$521$	19.2765	0.844520	0.422260	+	0.906475i	$0.361237\pi$
$522$	2.09394	0.0916495
$523$	30.0480	1.31391	0.656954	−	0.753931i	$-0.271845\pi$
$523$	30.0480	1.31391	0.656954	+	0.753931i	$0.271845\pi$
$524$	17.0957	0.746828
$525$	−25.3315	−1.10556
$526$	21.5103	0.937892
$527$	−31.2076	−1.35942
$528$	−12.4532	−0.541956
$529$	−6.53723	−0.284227
$530$	5.13995	0.223265
$531$	31.1711	1.35271
$532$	−5.81941	−0.252304
$533$	−3.17655	−0.137592
$534$	−0.837701	−0.0362509
$535$	2.76815	0.119677
$536$	−7.21292	−0.311551
$537$	−33.1447	−1.43030
$538$	−29.7788	−1.28385
$539$	−6.20173	−0.267127
$540$	−0.187990	−0.00808978
$541$	−42.8632	−1.84283	−0.921417	−	0.388576i	$-0.872967\pi$
$541$	−42.8632	−1.84283	−0.921417	+	0.388576i	$0.872967\pi$
$542$	−7.30997	−0.313990
$543$	−24.6129	−1.05624
$544$	−5.41905	−0.232340
$545$	−11.7278	−0.502364
$546$	5.16489	0.221037
$547$	−7.53521	−0.322182	−0.161091	−	0.986940i	$-0.551501\pi$
$547$	−7.53521	−0.322182	−0.161091	+	0.986940i	$0.551501\pi$
$548$	−5.24767	−0.224169
$549$	4.07230	0.173802
$550$	21.5646	0.919519
$551$	−1.64190	−0.0699474
$552$	−10.0124	−0.426155
$553$	0.520911	0.0221514
$554$	8.60985	0.365797
$555$	20.4675	0.868797
$556$	−16.3465	−0.693247
$557$	4.82581	0.204476	0.102238	−	0.994760i	$-0.467400\pi$
$557$	4.82581	0.204476	0.102238	+	0.994760i	$0.467400\pi$
$558$	17.7912	0.753161
$559$	6.43795	0.272296
$560$	−2.04812	−0.0865490
$561$	−67.4845	−2.84920
$562$	15.5284	0.655027
$563$	23.5734	0.993501	0.496750	−	0.867893i	$-0.334526\pi$
$563$	23.5734	0.993501	0.496750	+	0.867893i	$0.334526\pi$
$564$	−13.3395	−0.561696
$565$	0.580597	0.0244259
$566$	22.3925	0.941227
$567$	20.9576	0.880138
$568$	−2.77901	−0.116605
$569$	16.5757	0.694888	0.347444	−	0.937701i	$-0.387050\pi$
$569$	16.5757	0.694888	0.347444	+	0.937701i	$0.387050\pi$
$570$	5.09639	0.213464
$571$	11.1343	0.465954	0.232977	−	0.972482i	$-0.425153\pi$
$571$	11.1343	0.465954	0.232977	+	0.972482i	$0.425153\pi$
$572$	−4.39685	−0.183841
$573$	21.8577	0.913118
$574$	8.75867	0.365580
$575$	17.3380	0.723043
$576$	3.08936	0.128723
$577$	42.6982	1.77755	0.888774	−	0.458345i	$-0.151558\pi$
$577$	42.6982	1.77755	0.888774	+	0.458345i	$0.151558\pi$
$578$	−12.3661	−0.514361
$579$	53.3201	2.21591
$580$	−0.577862	−0.0239944
$581$	−29.1011	−1.20732
$582$	0.0720885	0.00298816
$583$	−30.4247	−1.26006
$584$	0.0772887	0.00319823
$585$	−2.29478	−0.0948775
$586$	3.88336	0.160420
$587$	−5.11475	−0.211108	−0.105554	−	0.994414i	$-0.533662\pi$
$587$	−5.11475	−0.211108	−0.105554	+	0.994414i	$0.533662\pi$
$588$	3.03252	0.125059
$589$	−13.9504	−0.574817
$590$	−8.60224	−0.354149
$591$	−16.6233	−0.683789
$592$	−9.72864	−0.399845
$593$	−24.0002	−0.985569	−0.492784	−	0.870151i	$-0.664021\pi$
$593$	−24.0002	−0.985569	−0.492784	+	0.870151i	$0.664021\pi$
$594$	1.11276	0.0456571
$595$	−11.0989	−0.455010
$596$	9.49750	0.389033
$597$	−10.5513	−0.431836
$598$	−3.53507	−0.144560
$599$	−11.4511	−0.467878	−0.233939	−	0.972251i	$-0.575162\pi$
$599$	−11.4511	−0.467878	−0.233939	+	0.972251i	$0.575162\pi$
$600$	−10.5447	−0.430484
$601$	−13.7582	−0.561210	−0.280605	−	0.959823i	$-0.590535\pi$
$601$	−13.7582	−0.561210	−0.280605	+	0.959823i	$0.590535\pi$
$602$	−17.7513	−0.723490
$603$	22.2833	0.907445
$604$	13.1457	0.534890
$605$	12.3347	0.501476
$606$	−18.8525	−0.765829
$607$	12.1472	0.493040	0.246520	−	0.969138i	$-0.420713\pi$
$607$	12.1472	0.493040	0.246520	+	0.969138i	$0.420713\pi$
$608$	−2.42242	−0.0982423
$609$	−4.01802	−0.162818
$610$	−1.12383	−0.0455024
$611$	−4.70979	−0.190538
$612$	16.7414	0.676729
$613$	−20.9908	−0.847812	−0.423906	−	0.905706i	$-0.639341\pi$
$613$	−20.9908	−0.847812	−0.423906	+	0.905706i	$0.639341\pi$
$614$	−4.42927	−0.178751
$615$	−7.67047	−0.309303
$616$	12.1234	0.488466
$617$	39.0818	1.57337	0.786686	−	0.617353i	$-0.211795\pi$
$617$	39.0818	1.57337	0.786686	+	0.617353i	$0.211795\pi$
$618$	−18.3720	−0.739030
$619$	1.87724	0.0754527	0.0377263	−	0.999288i	$-0.487988\pi$
$619$	1.87724	0.0754527	0.0377263	+	0.999288i	$0.487988\pi$
$620$	−4.90980	−0.197182
$621$	0.894660	0.0359015
$622$	1.46451	0.0587216
$623$	0.815516	0.0326730
$624$	2.14997	0.0860676
$625$	14.6254	0.585014
$626$	11.5136	0.460177
$627$	−30.1669	−1.20475
$628$	−7.28450	−0.290683
$629$	−52.7200	−2.10208
$630$	6.32738	0.252089
$631$	−30.4850	−1.21359	−0.606794	−	0.794859i	$-0.707545\pi$
$631$	−30.4850	−1.21359	−0.606794	+	0.794859i	$0.707545\pi$
$632$	0.216838	0.00862534
$633$	−44.7980	−1.78056
$634$	−4.55810	−0.181025
$635$	12.8528	0.510047
$636$	14.8771	0.589914
$637$	1.07069	0.0424223
$638$	3.42052	0.135420
$639$	8.58535	0.339631
$640$	−0.852564	−0.0337005
$641$	11.3531	0.448422	0.224211	−	0.974541i	$-0.428020\pi$
$641$	11.3531	0.448422	0.224211	+	0.974541i	$0.428020\pi$
$642$	8.01212	0.316213
$643$	25.7403	1.01510	0.507549	−	0.861623i	$-0.330552\pi$
$643$	25.7403	1.01510	0.507549	+	0.861623i	$0.330552\pi$
$644$	9.74722	0.384094
$645$	15.5458	0.612117
$646$	−13.1272	−0.516484
$647$	−7.14234	−0.280795	−0.140397	−	0.990095i	$-0.544838\pi$
$647$	−7.14234	−0.280795	−0.140397	+	0.990095i	$0.544838\pi$
$648$	8.72395	0.342709
$649$	50.9190	1.99875
$650$	−3.72300	−0.146028
$651$	−34.1391	−1.33802
$652$	−17.3929	−0.681158
$653$	−11.5935	−0.453689	−0.226844	−	0.973931i	$-0.572841\pi$
$653$	−11.5935	−0.453689	−0.226844	+	0.973931i	$0.572841\pi$
$654$	−33.9450	−1.32735
$655$	14.5752	0.569498
$656$	3.64594	0.142350
$657$	−0.238772	−0.00931539
$658$	12.9863	0.506257
$659$	0.100863	0.00392907	0.00196453	−	0.999998i	$-0.499375\pi$
$659$	0.100863	0.00392907	0.00196453	+	0.999998i	$0.499375\pi$
$660$	−10.6171	−0.413272
$661$	−14.3224	−0.557078	−0.278539	−	0.960425i	$-0.589850\pi$
$661$	−14.3224	−0.557078	−0.278539	+	0.960425i	$0.589850\pi$
$662$	−5.40676	−0.210140
$663$	11.6508	0.452479
$664$	−12.1138	−0.470106
$665$	−4.96142	−0.192396
$666$	30.0552	1.16462
$667$	2.75010	0.106484
$668$	−2.59913	−0.100563
$669$	30.1212	1.16455
$670$	−6.14947	−0.237575
$671$	6.65224	0.256807
$672$	−5.92809	−0.228681
$673$	4.86790	0.187644	0.0938218	−	0.995589i	$-0.470092\pi$
$673$	4.86790	0.187644	0.0938218	+	0.995589i	$0.470092\pi$
$674$	2.71437	0.104554
$675$	0.942222	0.0362661
$676$	−12.2409	−0.470804
$677$	−10.2554	−0.394148	−0.197074	−	0.980389i	$-0.563144\pi$
$677$	−10.2554	−0.394148	−0.197074	+	0.980389i	$0.563144\pi$
$678$	1.68048	0.0645385
$679$	−0.0701793	−0.00269324
$680$	−4.62008	−0.177172
$681$	−25.5826	−0.980326
$682$	29.0625	1.11286
$683$	−46.3982	−1.77538	−0.887689	−	0.460444i	$-0.847690\pi$
$683$	−46.3982	−1.77538	−0.887689	+	0.460444i	$0.847690\pi$
$684$	7.48373	0.286147
$685$	−4.47397	−0.170942
$686$	−19.7684	−0.754760
$687$	−20.0356	−0.764407
$688$	−7.38927	−0.281713
$689$	5.25264	0.200110
$690$	−8.53619	−0.324967
$691$	−40.4547	−1.53897	−0.769484	−	0.638666i	$-0.779487\pi$
$691$	−40.4547	−1.53897	−0.769484	+	0.638666i	$0.779487\pi$
$692$	−4.68515	−0.178103
$693$	−37.4535	−1.42274
$694$	14.7370	0.559411
$695$	−13.9365	−0.528640
$696$	−1.67257	−0.0633984
$697$	19.7575	0.748369
$698$	−1.53134	−0.0579621
$699$	−62.7521	−2.37350
$700$	10.2654	0.387996
$701$	−38.3447	−1.44826	−0.724129	−	0.689664i	$-0.757758\pi$
$701$	−38.3447	−1.44826	−0.724129	+	0.689664i	$0.757758\pi$
$702$	−0.192111	−0.00725077
$703$	−23.5669	−0.888842
$704$	5.04656	0.190199
$705$	−11.3728	−0.428325
$706$	25.4747	0.958753
$707$	18.3532	0.690243
$708$	−24.8983	−0.935737
$709$	−44.8064	−1.68274	−0.841370	−	0.540459i	$-0.818250\pi$
$709$	−44.8064	−1.68274	−0.841370	+	0.540459i	$0.818250\pi$
$710$	−2.36928	−0.0889176
$711$	−0.669888	−0.0251228
$712$	0.339472	0.0127222
$713$	23.3662	0.875072
$714$	−32.1246	−1.20223
$715$	−3.74859	−0.140189
$716$	13.4316	0.501963
$717$	5.96182	0.222648
$718$	24.4639	0.912984
$719$	−24.7087	−0.921480	−0.460740	−	0.887535i	$-0.652416\pi$
$719$	−24.7087	−0.921480	−0.460740	+	0.887535i	$0.652416\pi$
$720$	2.63387	0.0981587
$721$	17.8855	0.666089
$722$	13.1319	0.488717
$723$	−26.2504	−0.976263
$724$	9.97416	0.370687
$725$	2.89630	0.107566
$726$	35.7015	1.32501
$727$	41.3313	1.53289	0.766446	−	0.642308i	$-0.222023\pi$
$727$	41.3313	1.53289	0.766446	+	0.642308i	$0.222023\pi$
$728$	−2.09303	−0.0775728
$729$	−28.5837	−1.05866
$730$	0.0658935	0.00243883
$731$	−40.0428	−1.48104
$732$	−3.25280	−0.120227
$733$	−26.2163	−0.968323	−0.484161	−	0.874979i	$-0.660875\pi$
$733$	−26.2163	−0.968323	−0.484161	+	0.874979i	$0.660875\pi$
$734$	33.7511	1.24578
$735$	2.58541	0.0953644
$736$	4.05743	0.149559
$737$	36.4004	1.34083
$738$	−11.2636	−0.414619
$739$	−35.6000	−1.30957	−0.654783	−	0.755817i	$-0.727240\pi$
$739$	−35.6000	−1.30957	−0.654783	+	0.755817i	$0.727240\pi$
$740$	−8.29429	−0.304904
$741$	5.20813	0.191325
$742$	−14.4831	−0.531691
$743$	32.1518	1.17954	0.589768	−	0.807572i	$-0.299219\pi$
$743$	32.1518	1.17954	0.589768	+	0.807572i	$0.299219\pi$
$744$	−14.2109	−0.520998
$745$	8.09722	0.296659
$746$	−31.0145	−1.13552
$747$	37.4238	1.36926
$748$	27.3475	0.999925
$749$	−7.79994	−0.285003
$750$	−19.5092	−0.712375
$751$	52.1855	1.90428	0.952139	−	0.305667i	$-0.0988793\pi$
$751$	52.1855	1.90428	0.952139	+	0.305667i	$0.0988793\pi$
$752$	5.40574	0.197127
$753$	35.9209	1.30903
$754$	−0.590532	−0.0215059
$755$	11.2075	0.407884
$756$	0.529707	0.0192653
$757$	−27.7309	−1.00790	−0.503949	−	0.863733i	$-0.668120\pi$
$757$	−27.7309	−1.00790	−0.503949	+	0.863733i	$0.668120\pi$
$758$	14.2420	0.517294
$759$	50.5280	1.83405
$760$	−2.06527	−0.0749153
$761$	−32.7806	−1.18830	−0.594148	−	0.804355i	$-0.702511\pi$
$761$	−32.7806	−1.18830	−0.594148	+	0.804355i	$0.702511\pi$
$762$	37.2011	1.34765
$763$	33.0460	1.19635
$764$	−8.85766	−0.320459
$765$	14.2731	0.516044
$766$	15.3028	0.552911
$767$	−8.79085	−0.317419
$768$	−2.46766	−0.0890441
$769$	40.0727	1.44506	0.722530	−	0.691340i	$-0.242979\pi$
$769$	40.0727	1.44506	0.722530	+	0.691340i	$0.242979\pi$
$770$	10.3360	0.372483
$771$	61.5818	2.21781
$772$	−21.6075	−0.777673
$773$	−8.86195	−0.318742	−0.159371	−	0.987219i	$-0.550947\pi$
$773$	−8.86195	−0.318742	−0.159371	+	0.987219i	$0.550947\pi$
$774$	22.8281	0.820538
$775$	24.6084	0.883961
$776$	−0.0292133	−0.00104870
$777$	−57.6723	−2.06898
$778$	9.01684	0.323269
$779$	8.83200	0.316439
$780$	1.83298	0.0656314
$781$	14.0244	0.501834
$782$	21.9874	0.786269
$783$	0.149453	0.00534101
$784$	−1.22890	−0.0438894
$785$	−6.21050	−0.221662
$786$	42.1863	1.50474
$787$	−38.0343	−1.35578	−0.677888	−	0.735165i	$-0.737104\pi$
$787$	−38.0343	−1.35578	−0.677888	+	0.735165i	$0.737104\pi$
$788$	6.73644	0.239976
$789$	53.0801	1.88970
$790$	0.184868	0.00657731
$791$	−1.63598	−0.0581686
$792$	−15.5906	−0.553988
$793$	−1.14847	−0.0407833
$794$	−8.52777	−0.302639
$795$	12.6837	0.449843
$796$	4.27583	0.151553
$797$	−5.50030	−0.194830	−0.0974152	−	0.995244i	$-0.531057\pi$
$797$	−5.50030	−0.194830	−0.0974152	+	0.995244i	$0.531057\pi$
$798$	−14.3603	−0.508351
$799$	29.2939	1.03635
$800$	4.27313	0.151078
$801$	−1.04875	−0.0370557
$802$	−5.83712	−0.206116
$803$	−0.390042	−0.0137643
$804$	−17.7990	−0.627724
$805$	8.31013	0.292893
$806$	−5.01745	−0.176732
$807$	−73.4839	−2.58676
$808$	7.63981	0.268768
$809$	35.0527	1.23239	0.616194	−	0.787594i	$-0.288674\pi$
$809$	35.0527	1.23239	0.616194	+	0.787594i	$0.288674\pi$
$810$	7.43772	0.261335
$811$	−38.8208	−1.36318	−0.681591	−	0.731734i	$-0.738712\pi$
$811$	−38.8208	−1.36318	−0.681591	+	0.731734i	$0.738712\pi$
$812$	1.62827	0.0571411
$813$	−18.0385	−0.632639
$814$	49.0962	1.72082
$815$	−14.8285	−0.519421
$816$	−13.3724	−0.468127
$817$	−17.8999	−0.626239
$818$	6.82106	0.238493
$819$	6.46611	0.225944
$820$	3.10839	0.108550
$821$	−45.0018	−1.57057	−0.785287	−	0.619132i	$-0.787485\pi$
$821$	−45.0018	−1.57057	−0.785287	+	0.619132i	$0.787485\pi$
$822$	−12.9495	−0.451665
$823$	−23.1858	−0.808205	−0.404102	−	0.914714i	$-0.632416\pi$
$823$	−23.1858	−0.808205	−0.404102	+	0.914714i	$0.632416\pi$
$824$	7.44511	0.259363
$825$	53.2142	1.85268
$826$	24.2390	0.843381
$827$	−25.7437	−0.895196	−0.447598	−	0.894235i	$-0.647720\pi$
$827$	−25.7437	−0.895196	−0.447598	+	0.894235i	$0.647720\pi$
$828$	−12.5349	−0.435616
$829$	41.0397	1.42537	0.712684	−	0.701486i	$-0.247480\pi$
$829$	41.0397	1.42537	0.712684	+	0.701486i	$0.247480\pi$
$830$	−10.3278	−0.358482
$831$	21.2462	0.737022
$832$	−0.871257	−0.0302054
$833$	−6.65948	−0.230737
$834$	−40.3377	−1.39678
$835$	−2.21593	−0.0766853
$836$	12.2249	0.422807
$837$	1.26982	0.0438916
$838$	19.1246	0.660650
$839$	−22.1777	−0.765659	−0.382830	−	0.923819i	$-0.625050\pi$
$839$	−22.1777	−0.765659	−0.382830	+	0.923819i	$0.625050\pi$
$840$	−5.05408	−0.174382
$841$	−28.5406	−0.984158
$842$	31.1428	1.07325
$843$	38.3189	1.31977
$844$	18.1540	0.624887
$845$	−10.4362	−0.359015
$846$	−16.7002	−0.574166
$847$	−34.7560	−1.19423
$848$	−6.02881	−0.207030
$849$	55.2571	1.89642
$850$	23.1563	0.794255
$851$	39.4733	1.35313
$852$	−6.85766	−0.234939
$853$	−12.3930	−0.424328	−0.212164	−	0.977234i	$-0.568051\pi$
$853$	−12.3930	−0.424328	−0.212164	+	0.977234i	$0.568051\pi$
$854$	3.16666	0.108361
$855$	6.38036	0.218204
$856$	−3.24685	−0.110975
$857$	−11.9048	−0.406660	−0.203330	−	0.979110i	$-0.565176\pi$
$857$	−11.9048	−0.406660	−0.203330	+	0.979110i	$0.565176\pi$
$858$	−10.8499	−0.370411
$859$	−25.0573	−0.854943	−0.427471	−	0.904029i	$-0.640596\pi$
$859$	−25.0573	−0.854943	−0.427471	+	0.904029i	$0.640596\pi$
$860$	−6.29982	−0.214822
$861$	21.6134	0.736584
$862$	20.9830	0.714684
$863$	7.60643	0.258926	0.129463	−	0.991584i	$-0.458675\pi$
$863$	7.60643	0.258926	0.129463	+	0.991584i	$0.458675\pi$
$864$	0.220499	0.00750153
$865$	−3.99439	−0.135813
$866$	33.2280	1.12913
$867$	−30.5153	−1.03635
$868$	13.8346	0.469577
$869$	−1.09428	−0.0371210
$870$	−1.42597	−0.0483449
$871$	−6.28430	−0.212936
$872$	13.7559	0.465834
$873$	0.0902502	0.00305451
$874$	9.82882	0.332465
$875$	18.9925	0.642065
$876$	0.190722	0.00644391
$877$	−26.7163	−0.902145	−0.451072	−	0.892487i	$-0.648958\pi$
$877$	−26.7163	−0.902145	−0.451072	+	0.892487i	$0.648958\pi$
$878$	0.843872	0.0284793
$879$	9.58283	0.323221
$880$	4.30251	0.145038
$881$	6.31351	0.212708	0.106354	−	0.994328i	$-0.466082\pi$
$881$	6.31351	0.212708	0.106354	+	0.994328i	$0.466082\pi$
$882$	3.79652	0.127835
$883$	11.8048	0.397262	0.198631	−	0.980074i	$-0.436350\pi$
$883$	11.8048	0.397262	0.198631	+	0.980074i	$0.436350\pi$
$884$	−4.72138	−0.158797
$885$	−21.2274	−0.713552
$886$	−37.4738	−1.25896
$887$	−6.70279	−0.225058	−0.112529	−	0.993648i	$-0.535895\pi$
$887$	−6.70279	−0.225058	−0.112529	+	0.993648i	$0.535895\pi$
$888$	−24.0070	−0.805622
$889$	−36.2159	−1.21464
$890$	0.289421	0.00970142
$891$	−44.0259	−1.47492
$892$	−12.2064	−0.408700
$893$	13.0950	0.438207
$894$	23.4366	0.783838
$895$	11.4513	0.382775
$896$	2.40231	0.0802556
$897$	−8.72335	−0.291264
$898$	−14.3286	−0.478150
$899$	3.90332	0.130183
$900$	−13.2012	−0.440041
$901$	−32.6704	−1.08841
$902$	−18.3994	−0.612634
$903$	−43.8042	−1.45771
$904$	−0.681001	−0.0226498
$905$	8.50361	0.282670
$906$	32.4391	1.07772
$907$	14.7410	0.489466	0.244733	−	0.969590i	$-0.421300\pi$
$907$	14.7410	0.489466	0.244733	+	0.969590i	$0.421300\pi$
$908$	10.3671	0.344045
$909$	−23.6021	−0.782832
$910$	−1.78444	−0.0591537
$911$	34.6077	1.14660	0.573302	−	0.819344i	$-0.305662\pi$
$911$	34.6077	1.14660	0.573302	+	0.819344i	$0.305662\pi$
$912$	−5.97772	−0.197942
$913$	61.1329	2.02320
$914$	18.8795	0.624478
$915$	−2.77322	−0.0916800
$916$	8.11927	0.268268
$917$	−41.0691	−1.35622
$918$	1.19489	0.0394374
$919$	45.8242	1.51160	0.755800	−	0.654802i	$-0.227248\pi$
$919$	45.8242	1.51160	0.755800	+	0.654802i	$0.227248\pi$
$920$	3.45922	0.114047
$921$	−10.9299	−0.360154
$922$	−24.7280	−0.814374
$923$	−2.42123	−0.0796958
$924$	29.9165	0.984179
$925$	41.5718	1.36687
$926$	30.1377	0.990386
$927$	−23.0006	−0.755438
$928$	0.677793	0.0222497
$929$	−20.4017	−0.669357	−0.334679	−	0.942332i	$-0.608628\pi$
$929$	−20.4017	−0.669357	−0.334679	+	0.942332i	$0.608628\pi$
$930$	−12.1157	−0.397291
$931$	−2.97692	−0.0975647
$932$	25.4298	0.832981
$933$	3.61392	0.118315
$934$	26.9818	0.882871
$935$	23.3155	0.762499
$936$	2.69162	0.0879784
$937$	26.6820	0.871664	0.435832	−	0.900028i	$-0.356454\pi$
$937$	26.6820	0.871664	0.435832	+	0.900028i	$0.356454\pi$
$938$	17.3277	0.565769
$939$	28.4117	0.927181
$940$	4.60874	0.150320
$941$	−47.9649	−1.56361	−0.781805	−	0.623523i	$-0.785701\pi$
$941$	−47.9649	−1.56361	−0.781805	+	0.623523i	$0.785701\pi$
$942$	−17.9757	−0.585679
$943$	−14.7931	−0.481731
$944$	10.0899	0.328397
$945$	0.451609	0.0146908
$946$	37.2904	1.21241
$947$	23.0957	0.750508	0.375254	−	0.926922i	$-0.377555\pi$
$947$	23.0957	0.750508	0.375254	+	0.926922i	$0.377555\pi$
$948$	0.535082	0.0173787
$949$	0.0673383	0.00218589
$950$	10.3513	0.335842
$951$	−11.2479	−0.364737
$952$	13.0182	0.421923
$953$	18.7721	0.608087	0.304043	−	0.952658i	$-0.401663\pi$
$953$	18.7721	0.608087	0.304043	+	0.952658i	$0.401663\pi$
$954$	18.6251	0.603011
$955$	−7.55172	−0.244368
$956$	−2.41598	−0.0781384
$957$	8.44070	0.272849
$958$	−11.4451	−0.369774
$959$	12.6065	0.407086
$960$	−2.10384	−0.0679011
$961$	2.16457	0.0698247
$962$	−8.47615	−0.273282
$963$	10.0307	0.323234
$964$	10.6378	0.342619
$965$	−18.4218	−0.593019
$966$	24.0528	0.773887
$967$	5.77527	0.185720	0.0928601	−	0.995679i	$-0.470399\pi$
$967$	5.77527	0.185720	0.0928601	+	0.995679i	$0.470399\pi$
$968$	−14.4677	−0.465011
$969$	−32.3936	−1.04063
$970$	−0.0249062	−0.000799689 0
$971$	−4.60619	−0.147820	−0.0739099	−	0.997265i	$-0.523548\pi$
$971$	−4.60619	−0.147820	−0.0739099	+	0.997265i	$0.523548\pi$
$972$	22.1893	0.711721
$973$	39.2694	1.25892
$974$	−16.1772	−0.518349
$975$	−9.18710	−0.294223
$976$	1.31817	0.0421937
$977$	−36.8019	−1.17740	−0.588698	−	0.808353i	$-0.700359\pi$
$977$	−36.8019	−1.17740	−0.588698	+	0.808353i	$0.700359\pi$
$978$	−42.9198	−1.37242
$979$	−1.71316	−0.0547529
$980$	−1.04772	−0.0334681
$981$	−42.4969	−1.35682
$982$	−20.8819	−0.666367
$983$	30.0805	0.959420	0.479710	−	0.877427i	$-0.340742\pi$
$983$	30.0805	0.959420	0.479710	+	0.877427i	$0.340742\pi$
$984$	8.99694	0.286812
$985$	5.74324	0.182995
$986$	3.67299	0.116972
$987$	32.0457	1.02003
$988$	−2.11055	−0.0671456
$989$	29.9815	0.953355
$990$	−13.2920	−0.422447
$991$	−28.2106	−0.896139	−0.448070	−	0.893999i	$-0.647888\pi$
$991$	−28.2106	−0.896139	−0.448070	+	0.893999i	$0.647888\pi$
$992$	5.75887	0.182844
$993$	−13.3421	−0.423397
$994$	6.67604	0.211751
$995$	3.64542	0.115567
$996$	−29.8927	−0.947187
$997$	15.3767	0.486984	0.243492	−	0.969903i	$-0.421707\pi$
$997$	15.3767	0.486984	0.243492	+	0.969903i	$0.421707\pi$
$998$	9.55075	0.302324
$999$	2.14516	0.0678697

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.9	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.9	✓	64	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.46766 q^{3} +1.00000 q^{4} +0.852564 q^{5} +2.46766 q^{6} -2.40231 q^{7} -1.00000 q^{8} +3.08936 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.46766 q^{3} +1.00000 q^{4} +0.852564 q^{5} +2.46766 q^{6} -2.40231 q^{7} -1.00000 q^{8} +3.08936 q^{9} -0.852564 q^{10} +5.04656 q^{11} -2.46766 q^{12} -0.871257 q^{13} +2.40231 q^{14} -2.10384 q^{15} +1.00000 q^{16} +5.41905 q^{17} -3.08936 q^{18} +2.42242 q^{19} +0.852564 q^{20} +5.92809 q^{21} -5.04656 q^{22} -4.05743 q^{23} +2.46766 q^{24} -4.27313 q^{25} +0.871257 q^{26} -0.220499 q^{27} -2.40231 q^{28} -0.677793 q^{29} +2.10384 q^{30} -5.75887 q^{31} -1.00000 q^{32} -12.4532 q^{33} -5.41905 q^{34} -2.04812 q^{35} +3.08936 q^{36} -9.72864 q^{37} -2.42242 q^{38} +2.14997 q^{39} -0.852564 q^{40} +3.64594 q^{41} -5.92809 q^{42} -7.38927 q^{43} +5.04656 q^{44} +2.63387 q^{45} +4.05743 q^{46} +5.40574 q^{47} -2.46766 q^{48} -1.22890 q^{49} +4.27313 q^{50} -13.3724 q^{51} -0.871257 q^{52} -6.02881 q^{53} +0.220499 q^{54} +4.30251 q^{55} +2.40231 q^{56} -5.97772 q^{57} +0.677793 q^{58} +10.0899 q^{59} -2.10384 q^{60} +1.31817 q^{61} +5.75887 q^{62} -7.42159 q^{63} +1.00000 q^{64} -0.742802 q^{65} +12.4532 q^{66} +7.21292 q^{67} +5.41905 q^{68} +10.0124 q^{69} +2.04812 q^{70} +2.77901 q^{71} -3.08936 q^{72} -0.0772887 q^{73} +9.72864 q^{74} +10.5447 q^{75} +2.42242 q^{76} -12.1234 q^{77} -2.14997 q^{78} -0.216838 q^{79} +0.852564 q^{80} -8.72395 q^{81} -3.64594 q^{82} +12.1138 q^{83} +5.92809 q^{84} +4.62008 q^{85} +7.38927 q^{86} +1.67257 q^{87} -5.04656 q^{88} -0.339472 q^{89} -2.63387 q^{90} +2.09303 q^{91} -4.05743 q^{92} +14.2109 q^{93} -5.40574 q^{94} +2.06527 q^{95} +2.46766 q^{96} +0.0292133 q^{97} +1.22890 q^{98} +15.5906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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