LMFDB - Embedded newform 6046.2.a.g.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, 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("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.13336 q^{3} +1.00000 q^{4} -4.20234 q^{5} +3.13336 q^{6} -4.60058 q^{7} -1.00000 q^{8} +6.81797 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.13336 q^{3} +1.00000 q^{4} -4.20234 q^{5} +3.13336 q^{6} -4.60058 q^{7} -1.00000 q^{8} +6.81797 q^{9} +4.20234 q^{10} +0.559208 q^{11} -3.13336 q^{12} +4.10409 q^{13} +4.60058 q^{14} +13.1675 q^{15} +1.00000 q^{16} +3.32993 q^{17} -6.81797 q^{18} -7.35264 q^{19} -4.20234 q^{20} +14.4153 q^{21} -0.559208 q^{22} +1.58746 q^{23} +3.13336 q^{24} +12.6597 q^{25} -4.10409 q^{26} -11.9631 q^{27} -4.60058 q^{28} -1.18014 q^{29} -13.1675 q^{30} +7.65798 q^{31} -1.00000 q^{32} -1.75220 q^{33} -3.32993 q^{34} +19.3332 q^{35} +6.81797 q^{36} +1.38144 q^{37} +7.35264 q^{38} -12.8596 q^{39} +4.20234 q^{40} +3.27131 q^{41} -14.4153 q^{42} -10.0687 q^{43} +0.559208 q^{44} -28.6514 q^{45} -1.58746 q^{46} +0.857267 q^{47} -3.13336 q^{48} +14.1653 q^{49} -12.6597 q^{50} -10.4339 q^{51} +4.10409 q^{52} +5.51635 q^{53} +11.9631 q^{54} -2.34998 q^{55} +4.60058 q^{56} +23.0385 q^{57} +1.18014 q^{58} +7.20654 q^{59} +13.1675 q^{60} -6.99081 q^{61} -7.65798 q^{62} -31.3666 q^{63} +1.00000 q^{64} -17.2468 q^{65} +1.75220 q^{66} -6.63543 q^{67} +3.32993 q^{68} -4.97409 q^{69} -19.3332 q^{70} +9.26083 q^{71} -6.81797 q^{72} +13.1192 q^{73} -1.38144 q^{74} -39.6673 q^{75} -7.35264 q^{76} -2.57268 q^{77} +12.8596 q^{78} +3.41069 q^{79} -4.20234 q^{80} +17.0308 q^{81} -3.27131 q^{82} -13.9284 q^{83} +14.4153 q^{84} -13.9935 q^{85} +10.0687 q^{86} +3.69781 q^{87} -0.559208 q^{88} -13.8487 q^{89} +28.6514 q^{90} -18.8812 q^{91} +1.58746 q^{92} -23.9952 q^{93} -0.857267 q^{94} +30.8983 q^{95} +3.13336 q^{96} -3.01918 q^{97} -14.1653 q^{98} +3.81266 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * 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
$3$	−3.13336	−1.80905	−0.904524	−	0.426422i	$-0.859774\pi$
$3$	−3.13336	−1.80905	−0.904524	+	0.426422i	$0.859774\pi$
$4$	1.00000	0.500000
$5$	−4.20234	−1.87934	−0.939672	−	0.342078i	$-0.888869\pi$
$5$	−4.20234	−1.87934	−0.939672	+	0.342078i	$0.888869\pi$
$6$	3.13336	1.27919
$7$	−4.60058	−1.73886	−0.869428	−	0.494060i	$-0.835512\pi$
$7$	−4.60058	−1.73886	−0.869428	+	0.494060i	$0.835512\pi$
$8$	−1.00000	−0.353553
$9$	6.81797	2.27266
$10$	4.20234	1.32890
$11$	0.559208	0.168607	0.0843037	−	0.996440i	$-0.473133\pi$
$11$	0.559208	0.168607	0.0843037	+	0.996440i	$0.473133\pi$
$12$	−3.13336	−0.904524
$13$	4.10409	1.13827	0.569135	−	0.822244i	$-0.307278\pi$
$13$	4.10409	1.13827	0.569135	+	0.822244i	$0.307278\pi$
$14$	4.60058	1.22956
$15$	13.1675	3.39982
$16$	1.00000	0.250000
$17$	3.32993	0.807625	0.403813	−	0.914842i	$-0.367685\pi$
$17$	3.32993	0.807625	0.403813	+	0.914842i	$0.367685\pi$
$18$	−6.81797	−1.60701
$19$	−7.35264	−1.68681	−0.843406	−	0.537276i	$-0.819453\pi$
$19$	−7.35264	−1.68681	−0.843406	+	0.537276i	$0.819453\pi$
$20$	−4.20234	−0.939672
$21$	14.4153	3.14567
$22$	−0.559208	−0.119223
$23$	1.58746	0.331008	0.165504	−	0.986209i	$-0.447075\pi$
$23$	1.58746	0.331008	0.165504	+	0.986209i	$0.447075\pi$
$24$	3.13336	0.639595
$25$	12.6597	2.53193
$26$	−4.10409	−0.804879
$27$	−11.9631	−2.30230
$28$	−4.60058	−0.869428
$29$	−1.18014	−0.219146	−0.109573	−	0.993979i	$-0.534948\pi$
$29$	−1.18014	−0.219146	−0.109573	+	0.993979i	$0.534948\pi$
$30$	−13.1675	−2.40404
$31$	7.65798	1.37541	0.687706	−	0.725989i	$-0.258618\pi$
$31$	7.65798	1.37541	0.687706	+	0.725989i	$0.258618\pi$
$32$	−1.00000	−0.176777
$33$	−1.75220	−0.305019
$34$	−3.32993	−0.571077
$35$	19.3332	3.26791
$36$	6.81797	1.13633
$37$	1.38144	0.227108	0.113554	−	0.993532i	$-0.463777\pi$
$37$	1.38144	0.227108	0.113554	+	0.993532i	$0.463777\pi$
$38$	7.35264	1.19276
$39$	−12.8596	−2.05919
$40$	4.20234	0.664448
$41$	3.27131	0.510892	0.255446	−	0.966823i	$-0.417778\pi$
$41$	3.27131	0.510892	0.255446	+	0.966823i	$0.417778\pi$
$42$	−14.4153	−2.22433
$43$	−10.0687	−1.53547	−0.767734	−	0.640769i	$-0.778616\pi$
$43$	−10.0687	−1.53547	−0.767734	+	0.640769i	$0.778616\pi$
$44$	0.559208	0.0843037
$45$	−28.6514	−4.27110
$46$	−1.58746	−0.234058
$47$	0.857267	0.125045	0.0625226	−	0.998044i	$-0.480085\pi$
$47$	0.857267	0.125045	0.0625226	+	0.998044i	$0.480085\pi$
$48$	−3.13336	−0.452262
$49$	14.1653	2.02362
$50$	−12.6597	−1.79035
$51$	−10.4339	−1.46103
$52$	4.10409	0.569135
$53$	5.51635	0.757728	0.378864	−	0.925452i	$-0.376315\pi$
$53$	5.51635	0.757728	0.378864	+	0.925452i	$0.376315\pi$
$54$	11.9631	1.62797
$55$	−2.34998	−0.316871
$56$	4.60058	0.614778
$57$	23.0385	3.05153
$58$	1.18014	0.154960
$59$	7.20654	0.938211	0.469106	−	0.883142i	$-0.344576\pi$
$59$	7.20654	0.938211	0.469106	+	0.883142i	$0.344576\pi$
$60$	13.1675	1.69991
$61$	−6.99081	−0.895081	−0.447541	−	0.894264i	$-0.647700\pi$
$61$	−6.99081	−0.895081	−0.447541	+	0.894264i	$0.647700\pi$
$62$	−7.65798	−0.972564
$63$	−31.3666	−3.95182
$64$	1.00000	0.125000
$65$	−17.2468	−2.13920
$66$	1.75220	0.215681
$67$	−6.63543	−0.810647	−0.405323	−	0.914173i	$-0.632841\pi$
$67$	−6.63543	−0.810647	−0.405323	+	0.914173i	$0.632841\pi$
$68$	3.32993	0.403813
$69$	−4.97409	−0.598810
$70$	−19.3332	−2.31076
$71$	9.26083	1.09906	0.549529	−	0.835474i	$-0.314807\pi$
$71$	9.26083	1.09906	0.549529	+	0.835474i	$0.314807\pi$
$72$	−6.81797	−0.803506
$73$	13.1192	1.53548	0.767740	−	0.640761i	$-0.221381\pi$
$73$	13.1192	1.53548	0.767740	+	0.640761i	$0.221381\pi$
$74$	−1.38144	−0.160589
$75$	−39.6673	−4.58039
$76$	−7.35264	−0.843406
$77$	−2.57268	−0.293184
$78$	12.8596	1.45607
$79$	3.41069	0.383733	0.191866	−	0.981421i	$-0.438546\pi$
$79$	3.41069	0.383733	0.191866	+	0.981421i	$0.438546\pi$
$80$	−4.20234	−0.469836
$81$	17.0308	1.89231
$82$	−3.27131	−0.361255
$83$	−13.9284	−1.52884	−0.764418	−	0.644720i	$-0.776974\pi$
$83$	−13.9284	−1.52884	−0.764418	+	0.644720i	$0.776974\pi$
$84$	14.4153	1.57284
$85$	−13.9935	−1.51781
$86$	10.0687	1.08574
$87$	3.69781	0.396446
$88$	−0.559208	−0.0596117
$89$	−13.8487	−1.46796	−0.733980	−	0.679171i	$-0.762340\pi$
$89$	−13.8487	−1.46796	−0.733980	+	0.679171i	$0.762340\pi$
$90$	28.6514	3.02013
$91$	−18.8812	−1.97929
$92$	1.58746	0.165504
$93$	−23.9952	−2.48819
$94$	−0.857267	−0.0884203
$95$	30.8983	3.17010
$96$	3.13336	0.319798
$97$	−3.01918	−0.306552	−0.153276	−	0.988183i	$-0.548982\pi$
$97$	−3.01918	−0.306552	−0.153276	+	0.988183i	$0.548982\pi$
$98$	−14.1653	−1.43091
$99$	3.81266	0.383187
$100$	12.6597	1.26597
$101$	−15.8394	−1.57608	−0.788038	−	0.615627i	$-0.788903\pi$
$101$	−15.8394	−1.57608	−0.788038	+	0.615627i	$0.788903\pi$
$102$	10.4339	1.03311
$103$	−11.6640	−1.14929	−0.574645	−	0.818403i	$-0.694860\pi$
$103$	−11.6640	−1.14929	−0.574645	+	0.818403i	$0.694860\pi$
$104$	−4.10409	−0.402439
$105$	−60.5779	−5.91180
$106$	−5.51635	−0.535795
$107$	−19.9277	−1.92649	−0.963244	−	0.268630i	$-0.913429\pi$
$107$	−19.9277	−1.92649	−0.963244	+	0.268630i	$0.913429\pi$
$108$	−11.9631	−1.15115
$109$	15.0646	1.44293	0.721464	−	0.692452i	$-0.243469\pi$
$109$	15.0646	1.44293	0.721464	+	0.692452i	$0.243469\pi$
$110$	2.34998	0.224062
$111$	−4.32856	−0.410849
$112$	−4.60058	−0.434714
$113$	2.69753	0.253762	0.126881	−	0.991918i	$-0.459503\pi$
$113$	2.69753	0.253762	0.126881	+	0.991918i	$0.459503\pi$
$114$	−23.0385	−2.15775
$115$	−6.67104	−0.622078
$116$	−1.18014	−0.109573
$117$	27.9816	2.58690
$118$	−7.20654	−0.663415
$119$	−15.3196	−1.40434
$120$	−13.1675	−1.20202
$121$	−10.6873	−0.971572
$122$	6.99081	0.632918
$123$	−10.2502	−0.924229
$124$	7.65798	0.687706
$125$	−32.1885	−2.87903
$126$	31.3666	2.79436
$127$	−5.81130	−0.515670	−0.257835	−	0.966189i	$-0.583009\pi$
$127$	−5.81130	−0.515670	−0.257835	+	0.966189i	$0.583009\pi$
$128$	−1.00000	−0.0883883
$129$	31.5490	2.77774
$130$	17.2468	1.51264
$131$	10.8163	0.945022	0.472511	−	0.881325i	$-0.343348\pi$
$131$	10.8163	0.945022	0.472511	+	0.881325i	$0.343348\pi$
$132$	−1.75220	−0.152510
$133$	33.8264	2.93312
$134$	6.63543	0.573214
$135$	50.2730	4.32681
$136$	−3.32993	−0.285539
$137$	10.0022	0.854544	0.427272	−	0.904123i	$-0.359475\pi$
$137$	10.0022	0.854544	0.427272	+	0.904123i	$0.359475\pi$
$138$	4.97409	0.423422
$139$	1.82323	0.154644	0.0773220	−	0.997006i	$-0.475363\pi$
$139$	1.82323	0.154644	0.0773220	+	0.997006i	$0.475363\pi$
$140$	19.3332	1.63395
$141$	−2.68613	−0.226213
$142$	−9.26083	−0.777152
$143$	2.29504	0.191921
$144$	6.81797	0.568164
$145$	4.95935	0.411851
$146$	−13.1192	−1.08575
$147$	−44.3851	−3.66082
$148$	1.38144	0.113554
$149$	6.41681	0.525686	0.262843	−	0.964839i	$-0.415340\pi$
$149$	6.41681	0.525686	0.262843	+	0.964839i	$0.415340\pi$
$150$	39.6673	3.23882
$151$	−14.2028	−1.15581	−0.577905	−	0.816104i	$-0.696129\pi$
$151$	−14.2028	−1.15581	−0.577905	+	0.816104i	$0.696129\pi$
$152$	7.35264	0.596378
$153$	22.7033	1.83546
$154$	2.57268	0.207312
$155$	−32.1814	−2.58487
$156$	−12.8596	−1.02959
$157$	−20.5119	−1.63703	−0.818515	−	0.574485i	$-0.805202\pi$
$157$	−20.5119	−1.63703	−0.818515	+	0.574485i	$0.805202\pi$
$158$	−3.41069	−0.271340
$159$	−17.2847	−1.37077
$160$	4.20234	0.332224
$161$	−7.30323	−0.575575
$162$	−17.0308	−1.33807
$163$	18.6074	1.45744	0.728720	−	0.684811i	$-0.240115\pi$
$163$	18.6074	1.45744	0.728720	+	0.684811i	$0.240115\pi$
$164$	3.27131	0.255446
$165$	7.36334	0.573235
$166$	13.9284	1.08105
$167$	−15.6045	−1.20751	−0.603754	−	0.797170i	$-0.706329\pi$
$167$	−15.6045	−1.20751	−0.603754	+	0.797170i	$0.706329\pi$
$168$	−14.4153	−1.11216
$169$	3.84358	0.295660
$170$	13.9935	1.07325
$171$	−50.1301	−3.83355
$172$	−10.0687	−0.767734
$173$	12.1566	0.924249	0.462124	−	0.886815i	$-0.347087\pi$
$173$	12.1566	0.924249	0.462124	+	0.886815i	$0.347087\pi$
$174$	−3.69781	−0.280330
$175$	−58.2418	−4.40266
$176$	0.559208	0.0421519
$177$	−22.5807	−1.69727
$178$	13.8487	1.03801
$179$	17.8889	1.33708	0.668540	−	0.743676i	$-0.266919\pi$
$179$	17.8889	1.33708	0.668540	+	0.743676i	$0.266919\pi$
$180$	−28.6514	−2.13555
$181$	7.45514	0.554136	0.277068	−	0.960850i	$-0.410637\pi$
$181$	7.45514	0.554136	0.277068	+	0.960850i	$0.410637\pi$
$182$	18.8812	1.39957
$183$	21.9048	1.61925
$184$	−1.58746	−0.117029
$185$	−5.80529	−0.426813
$186$	23.9952	1.75942
$187$	1.86212	0.136172
$188$	0.857267	0.0625226
$189$	55.0372	4.00336
$190$	−30.8983	−2.24160
$191$	8.06766	0.583756	0.291878	−	0.956456i	$-0.405720\pi$
$191$	8.06766	0.583756	0.291878	+	0.956456i	$0.405720\pi$
$192$	−3.13336	−0.226131
$193$	−26.3337	−1.89554	−0.947771	−	0.318952i	$-0.896669\pi$
$193$	−26.3337	−1.89554	−0.947771	+	0.318952i	$0.896669\pi$
$194$	3.01918	0.216765
$195$	54.0405	3.86992
$196$	14.1653	1.01181
$197$	11.8531	0.844499	0.422249	−	0.906480i	$-0.361241\pi$
$197$	11.8531	0.844499	0.422249	+	0.906480i	$0.361241\pi$
$198$	−3.81266	−0.270954
$199$	5.20332	0.368853	0.184427	−	0.982846i	$-0.440957\pi$
$199$	5.20332	0.368853	0.184427	+	0.982846i	$0.440957\pi$
$200$	−12.6597	−0.895173
$201$	20.7912	1.46650
$202$	15.8394	1.11445
$203$	5.42932	0.381064
$204$	−10.4339	−0.730517
$205$	−13.7471	−0.960142
$206$	11.6640	0.812670
$207$	10.8232	0.752268
$208$	4.10409	0.284568
$209$	−4.11165	−0.284409
$210$	60.5779	4.18028
$211$	27.0726	1.86376	0.931879	−	0.362770i	$-0.118169\pi$
$211$	27.0726	1.86376	0.931879	+	0.362770i	$0.118169\pi$
$212$	5.51635	0.378864
$213$	−29.0176	−1.98825
$214$	19.9277	1.36223
$215$	42.3122	2.88567
$216$	11.9631	0.813985
$217$	−35.2311	−2.39164
$218$	−15.0646	−1.02030
$219$	−41.1071	−2.77776
$220$	−2.34998	−0.158436
$221$	13.6663	0.919296
$222$	4.32856	0.290514
$223$	−19.9333	−1.33483	−0.667416	−	0.744685i	$-0.732600\pi$
$223$	−19.9333	−1.33483	−0.667416	+	0.744685i	$0.732600\pi$
$224$	4.60058	0.307389
$225$	86.3132	5.75421
$226$	−2.69753	−0.179437
$227$	4.49492	0.298338	0.149169	−	0.988812i	$-0.452340\pi$
$227$	4.49492	0.298338	0.149169	+	0.988812i	$0.452340\pi$
$228$	23.0385	1.52576
$229$	−21.4489	−1.41738	−0.708691	−	0.705519i	$-0.750714\pi$
$229$	−21.4489	−1.41738	−0.708691	+	0.705519i	$0.750714\pi$
$230$	6.67104	0.439875
$231$	8.06114	0.530384
$232$	1.18014	0.0774799
$233$	11.4466	0.749893	0.374947	−	0.927046i	$-0.377661\pi$
$233$	11.4466	0.749893	0.374947	+	0.927046i	$0.377661\pi$
$234$	−27.9816	−1.82921
$235$	−3.60253	−0.235003
$236$	7.20654	0.469106
$237$	−10.6869	−0.694191
$238$	15.3196	0.993021
$239$	24.6005	1.59127	0.795637	−	0.605774i	$-0.207136\pi$
$239$	24.6005	1.59127	0.795637	+	0.605774i	$0.207136\pi$
$240$	13.1675	0.849956
$241$	19.2746	1.24159	0.620793	−	0.783975i	$-0.286811\pi$
$241$	19.2746	1.24159	0.620793	+	0.783975i	$0.286811\pi$
$242$	10.6873	0.687005
$243$	−17.4745	−1.12099
$244$	−6.99081	−0.447541
$245$	−59.5275	−3.80307
$246$	10.2502	0.653529
$247$	−30.1759	−1.92005
$248$	−7.65798	−0.486282
$249$	43.6426	2.76574
$250$	32.1885	2.03578
$251$	3.19310	0.201547	0.100773	−	0.994909i	$-0.467868\pi$
$251$	3.19310	0.201547	0.100773	+	0.994909i	$0.467868\pi$
$252$	−31.3666	−1.97591
$253$	0.887719	0.0558104
$254$	5.81130	0.364634
$255$	43.8467	2.74578
$256$	1.00000	0.0625000
$257$	11.0271	0.687854	0.343927	−	0.938996i	$-0.388243\pi$
$257$	11.0271	0.687854	0.343927	+	0.938996i	$0.388243\pi$
$258$	−31.5490	−1.96416
$259$	−6.35544	−0.394908
$260$	−17.2468	−1.06960
$261$	−8.04616	−0.498044
$262$	−10.8163	−0.668232
$263$	−6.98610	−0.430782	−0.215391	−	0.976528i	$-0.569103\pi$
$263$	−6.98610	−0.430782	−0.215391	+	0.976528i	$0.569103\pi$
$264$	1.75220	0.107841
$265$	−23.1816	−1.42403
$266$	−33.8264	−2.07403
$267$	43.3931	2.65561
$268$	−6.63543	−0.405323
$269$	2.10641	0.128430	0.0642150	−	0.997936i	$-0.479546\pi$
$269$	2.10641	0.128430	0.0642150	+	0.997936i	$0.479546\pi$
$270$	−50.2730	−3.05952
$271$	−9.25324	−0.562094	−0.281047	−	0.959694i	$-0.590682\pi$
$271$	−9.25324	−0.562094	−0.281047	+	0.959694i	$0.590682\pi$
$272$	3.32993	0.201906
$273$	59.1617	3.58063
$274$	−10.0022	−0.604254
$275$	7.07938	0.426902
$276$	−4.97409	−0.299405
$277$	−17.1780	−1.03212	−0.516062	−	0.856551i	$-0.672603\pi$
$277$	−17.1780	−1.03212	−0.516062	+	0.856551i	$0.672603\pi$
$278$	−1.82323	−0.109350
$279$	52.2119	3.12584
$280$	−19.3332	−1.15538
$281$	17.4514	1.04106	0.520531	−	0.853843i	$-0.325734\pi$
$281$	17.4514	1.04106	0.520531	+	0.853843i	$0.325734\pi$
$282$	2.68613	0.159957
$283$	3.00962	0.178903	0.0894517	−	0.995991i	$-0.471489\pi$
$283$	3.00962	0.178903	0.0894517	+	0.995991i	$0.471489\pi$
$284$	9.26083	0.549529
$285$	−96.8157	−5.73486
$286$	−2.29504	−0.135709
$287$	−15.0499	−0.888368
$288$	−6.81797	−0.401753
$289$	−5.91160	−0.347741
$290$	−4.95935	−0.291223
$291$	9.46020	0.554567
$292$	13.1192	0.767740
$293$	8.59337	0.502030	0.251015	−	0.967983i	$-0.419236\pi$
$293$	8.59337	0.502030	0.251015	+	0.967983i	$0.419236\pi$
$294$	44.3851	2.58859
$295$	−30.2843	−1.76322
$296$	−1.38144	−0.0802947
$297$	−6.68985	−0.388185
$298$	−6.41681	−0.371716
$299$	6.51508	0.376777
$300$	−39.6673	−2.29019
$301$	46.3220	2.66996
$302$	14.2028	0.817281
$303$	49.6305	2.85120
$304$	−7.35264	−0.421703
$305$	29.3778	1.68217
$306$	−22.7033	−1.29786
$307$	−20.7432	−1.18387	−0.591937	−	0.805984i	$-0.701637\pi$
$307$	−20.7432	−1.18387	−0.591937	+	0.805984i	$0.701637\pi$
$308$	−2.57268	−0.146592
$309$	36.5476	2.07912
$310$	32.1814	1.82778
$311$	19.3692	1.09833	0.549163	−	0.835715i	$-0.314947\pi$
$311$	19.3692	1.09833	0.549163	+	0.835715i	$0.314947\pi$
$312$	12.8596	0.728033
$313$	−4.37855	−0.247490	−0.123745	−	0.992314i	$-0.539490\pi$
$313$	−4.37855	−0.247490	−0.123745	+	0.992314i	$0.539490\pi$
$314$	20.5119	1.15755
$315$	131.813	7.42683
$316$	3.41069	0.191866
$317$	−18.5624	−1.04257	−0.521285	−	0.853383i	$-0.674547\pi$
$317$	−18.5624	−1.04257	−0.521285	+	0.853383i	$0.674547\pi$
$318$	17.2847	0.969279
$319$	−0.659943	−0.0369497
$320$	−4.20234	−0.234918
$321$	62.4409	3.48511
$322$	7.30323	0.406993
$323$	−24.4838	−1.36231
$324$	17.0308	0.946157
$325$	51.9564	2.88202
$326$	−18.6074	−1.03057
$327$	−47.2029	−2.61033
$328$	−3.27131	−0.180628
$329$	−3.94392	−0.217436
$330$	−7.36334	−0.405339
$331$	27.8021	1.52814	0.764072	−	0.645131i	$-0.223197\pi$
$331$	27.8021	1.52814	0.764072	+	0.645131i	$0.223197\pi$
$332$	−13.9284	−0.764418
$333$	9.41863	0.516138
$334$	15.6045	0.853838
$335$	27.8843	1.52348
$336$	14.4153	0.786419
$337$	−0.0898006	−0.00489175	−0.00244588	−	0.999997i	$-0.500779\pi$
$337$	−0.0898006	−0.00489175	−0.00244588	+	0.999997i	$0.500779\pi$
$338$	−3.84358	−0.209063
$339$	−8.45234	−0.459068
$340$	−13.9935	−0.758903
$341$	4.28240	0.231905
$342$	50.1301	2.71073
$343$	−32.9647	−1.77992
$344$	10.0687	0.542870
$345$	20.9028	1.12537
$346$	−12.1566	−0.653542
$347$	−10.1679	−0.545843	−0.272922	−	0.962036i	$-0.587990\pi$
$347$	−10.1679	−0.545843	−0.272922	+	0.962036i	$0.587990\pi$
$348$	3.69781	0.198223
$349$	−20.4857	−1.09657	−0.548286	−	0.836291i	$-0.684719\pi$
$349$	−20.4857	−1.09657	−0.548286	+	0.836291i	$0.684719\pi$
$350$	58.2418	3.11315
$351$	−49.0977	−2.62064
$352$	−0.559208	−0.0298059
$353$	−15.4912	−0.824515	−0.412258	−	0.911067i	$-0.635260\pi$
$353$	−15.4912	−0.824515	−0.412258	+	0.911067i	$0.635260\pi$
$354$	22.5807	1.20015
$355$	−38.9172	−2.06551
$356$	−13.8487	−0.733980
$357$	48.0018	2.54053
$358$	−17.8889	−0.945459
$359$	29.6852	1.56673	0.783363	−	0.621565i	$-0.213503\pi$
$359$	29.6852	1.56673	0.783363	+	0.621565i	$0.213503\pi$
$360$	28.6514	1.51006
$361$	35.0614	1.84534
$362$	−7.45514	−0.391833
$363$	33.4872	1.75762
$364$	−18.8812	−0.989644
$365$	−55.1311	−2.88570
$366$	−21.9048	−1.14498
$367$	−7.58658	−0.396016	−0.198008	−	0.980200i	$-0.563447\pi$
$367$	−7.58658	−0.396016	−0.198008	+	0.980200i	$0.563447\pi$
$368$	1.58746	0.0827520
$369$	22.3037	1.16108
$370$	5.80529	0.301803
$371$	−25.3784	−1.31758
$372$	−23.9952	−1.24409
$373$	6.15969	0.318937	0.159468	−	0.987203i	$-0.449022\pi$
$373$	6.15969	0.318937	0.159468	+	0.987203i	$0.449022\pi$
$374$	−1.86212	−0.0962879
$375$	100.858	5.20830
$376$	−0.857267	−0.0442102
$377$	−4.84340	−0.249448
$378$	−55.0372	−2.83081
$379$	−21.1727	−1.08757	−0.543785	−	0.839224i	$-0.683009\pi$
$379$	−21.1727	−1.08757	−0.543785	+	0.839224i	$0.683009\pi$
$380$	30.8983	1.58505
$381$	18.2089	0.932872
$382$	−8.06766	−0.412777
$383$	−32.6476	−1.66821	−0.834107	−	0.551602i	$-0.814017\pi$
$383$	−32.6476	−1.66821	−0.834107	+	0.551602i	$0.814017\pi$
$384$	3.13336	0.159899
$385$	10.8113	0.550993
$386$	26.3337	1.34035
$387$	−68.6483	−3.48959
$388$	−3.01918	−0.153276
$389$	2.53376	0.128467	0.0642333	−	0.997935i	$-0.479540\pi$
$389$	2.53376	0.128467	0.0642333	+	0.997935i	$0.479540\pi$
$390$	−54.0405	−2.73645
$391$	5.28612	0.267330
$392$	−14.1653	−0.715457
$393$	−33.8913	−1.70959
$394$	−11.8531	−0.597151
$395$	−14.3329	−0.721166
$396$	3.81266	0.191593
$397$	−20.2832	−1.01798	−0.508992	−	0.860771i	$-0.669982\pi$
$397$	−20.2832	−1.01798	−0.508992	+	0.860771i	$0.669982\pi$
$398$	−5.20332	−0.260819
$399$	−105.991	−5.30616
$400$	12.6597	0.632983
$401$	−26.0298	−1.29986	−0.649932	−	0.759992i	$-0.725203\pi$
$401$	−26.0298	−1.29986	−0.649932	+	0.759992i	$0.725203\pi$
$402$	−20.7912	−1.03697
$403$	31.4290	1.56559
$404$	−15.8394	−0.788038
$405$	−71.5693	−3.55631
$406$	−5.42932	−0.269453
$407$	0.772513	0.0382920
$408$	10.4339	0.516553
$409$	−16.4721	−0.814493	−0.407247	−	0.913318i	$-0.633511\pi$
$409$	−16.4721	−0.814493	−0.407247	+	0.913318i	$0.633511\pi$
$410$	13.7471	0.678923
$411$	−31.3405	−1.54591
$412$	−11.6640	−0.574645
$413$	−33.1542	−1.63141
$414$	−10.8232	−0.531934
$415$	58.5317	2.87321
$416$	−4.10409	−0.201220
$417$	−5.71283	−0.279758
$418$	4.11165	0.201108
$419$	35.0125	1.71047	0.855236	−	0.518238i	$-0.173412\pi$
$419$	35.0125	1.71047	0.855236	+	0.518238i	$0.173412\pi$
$420$	−60.5779	−2.95590
$421$	−14.7780	−0.720236	−0.360118	−	0.932907i	$-0.617263\pi$
$421$	−14.7780	−0.720236	−0.360118	+	0.932907i	$0.617263\pi$
$422$	−27.0726	−1.31788
$423$	5.84482	0.284185
$424$	−5.51635	−0.267897
$425$	42.1557	2.04485
$426$	29.0176	1.40591
$427$	32.1618	1.55642
$428$	−19.9277	−0.963244
$429$	−7.19120	−0.347194
$430$	−42.3122	−2.04048
$431$	−1.22176	−0.0588501	−0.0294250	−	0.999567i	$-0.509368\pi$
$431$	−1.22176	−0.0588501	−0.0294250	+	0.999567i	$0.509368\pi$
$432$	−11.9631	−0.575575
$433$	38.1533	1.83353	0.916766	−	0.399425i	$-0.130790\pi$
$433$	38.1533	1.83353	0.916766	+	0.399425i	$0.130790\pi$
$434$	35.2311	1.69115
$435$	−15.5394	−0.745059
$436$	15.0646	0.721464
$437$	−11.6720	−0.558348
$438$	41.1071	1.96417
$439$	−31.9428	−1.52455	−0.762274	−	0.647254i	$-0.775917\pi$
$439$	−31.9428	−1.52455	−0.762274	+	0.647254i	$0.775917\pi$
$440$	2.34998	0.112031
$441$	96.5788	4.59899
$442$	−13.6663	−0.650041
$443$	3.01246	0.143126	0.0715632	−	0.997436i	$-0.477201\pi$
$443$	3.01246	0.143126	0.0715632	+	0.997436i	$0.477201\pi$
$444$	−4.32856	−0.205424
$445$	58.1970	2.75880
$446$	19.9333	0.943869
$447$	−20.1062	−0.950991
$448$	−4.60058	−0.217357
$449$	−13.2468	−0.625155	−0.312578	−	0.949892i	$-0.601192\pi$
$449$	−13.2468	−0.625155	−0.312578	+	0.949892i	$0.601192\pi$
$450$	−86.3132	−4.06884
$451$	1.82934	0.0861402
$452$	2.69753	0.126881
$453$	44.5026	2.09092
$454$	−4.49492	−0.210957
$455$	79.3452	3.71976
$456$	−23.0385	−1.07888
$457$	5.73373	0.268212	0.134106	−	0.990967i	$-0.457184\pi$
$457$	5.73373	0.268212	0.134106	+	0.990967i	$0.457184\pi$
$458$	21.4489	1.00224
$459$	−39.8362	−1.85939
$460$	−6.67104	−0.311039
$461$	−30.1914	−1.40616	−0.703078	−	0.711113i	$-0.748191\pi$
$461$	−30.1914	−1.40616	−0.703078	+	0.711113i	$0.748191\pi$
$462$	−8.06114	−0.375038
$463$	−2.04586	−0.0950794	−0.0475397	−	0.998869i	$-0.515138\pi$
$463$	−2.04586	−0.0950794	−0.0475397	+	0.998869i	$0.515138\pi$
$464$	−1.18014	−0.0547866
$465$	100.836	4.67616
$466$	−11.4466	−0.530254
$467$	14.5304	0.672387	0.336193	−	0.941793i	$-0.390860\pi$
$467$	14.5304	0.672387	0.336193	+	0.941793i	$0.390860\pi$
$468$	27.9816	1.29345
$469$	30.5268	1.40960
$470$	3.60253	0.166172
$471$	64.2713	2.96147
$472$	−7.20654	−0.331708
$473$	−5.63051	−0.258891
$474$	10.6869	0.490867
$475$	−93.0820	−4.27089
$476$	−15.3196	−0.702172
$477$	37.6103	1.72206
$478$	−24.6005	−1.12520
$479$	−15.7746	−0.720762	−0.360381	−	0.932805i	$-0.617353\pi$
$479$	−15.7746	−0.720762	−0.360381	+	0.932805i	$0.617353\pi$
$480$	−13.1675	−0.601010
$481$	5.66957	0.258510
$482$	−19.2746	−0.877934
$483$	22.8837	1.04124
$484$	−10.6873	−0.485786
$485$	12.6876	0.576116
$486$	17.4745	0.792658
$487$	−24.6357	−1.11635	−0.558175	−	0.829723i	$-0.688498\pi$
$487$	−24.6357	−1.11635	−0.558175	+	0.829723i	$0.688498\pi$
$488$	6.99081	0.316459
$489$	−58.3036	−2.63658
$490$	59.5275	2.68918
$491$	−17.0093	−0.767619	−0.383809	−	0.923412i	$-0.625388\pi$
$491$	−17.0093	−0.767619	−0.383809	+	0.923412i	$0.625388\pi$
$492$	−10.2502	−0.462115
$493$	−3.92978	−0.176988
$494$	30.1759	1.35768
$495$	−16.0221	−0.720140
$496$	7.65798	0.343853
$497$	−42.6052	−1.91110
$498$	−43.6426	−1.95567
$499$	20.1742	0.903122	0.451561	−	0.892240i	$-0.350867\pi$
$499$	20.1742	0.903122	0.451561	+	0.892240i	$0.350867\pi$
$500$	−32.1885	−1.43951
$501$	48.8944	2.18444
$502$	−3.19310	−0.142515
$503$	20.0340	0.893271	0.446636	−	0.894716i	$-0.352622\pi$
$503$	20.0340	0.893271	0.446636	+	0.894716i	$0.352622\pi$
$504$	31.3666	1.39718
$505$	66.5624	2.96199
$506$	−0.887719	−0.0394639
$507$	−12.0433	−0.534863
$508$	−5.81130	−0.257835
$509$	14.5652	0.645589	0.322795	−	0.946469i	$-0.395378\pi$
$509$	14.5652	0.645589	0.322795	+	0.946469i	$0.395378\pi$
$510$	−43.8467	−1.94156
$511$	−60.3557	−2.66998
$512$	−1.00000	−0.0441942
$513$	87.9604	3.88355
$514$	−11.0271	−0.486386
$515$	49.0161	2.15991
$516$	31.5490	1.38887
$517$	0.479390	0.0210836
$518$	6.35544	0.279242
$519$	−38.0910	−1.67201
$520$	17.2468	0.756322
$521$	−14.4484	−0.632995	−0.316497	−	0.948593i	$-0.602507\pi$
$521$	−14.4484	−0.632995	−0.316497	+	0.948593i	$0.602507\pi$
$522$	8.04616	0.352171
$523$	5.98580	0.261741	0.130870	−	0.991399i	$-0.458223\pi$
$523$	5.98580	0.261741	0.130870	+	0.991399i	$0.458223\pi$
$524$	10.8163	0.472511
$525$	182.493	7.96463
$526$	6.98610	0.304609
$527$	25.5005	1.11082
$528$	−1.75220	−0.0762548
$529$	−20.4800	−0.890434
$530$	23.1816	1.00694
$531$	49.1340	2.13223
$532$	33.8264	1.46656
$533$	13.4257	0.581534
$534$	−43.3931	−1.87780
$535$	83.7431	3.62053
$536$	6.63543	0.286607
$537$	−56.0525	−2.41884
$538$	−2.10641	−0.0908137
$539$	7.92136	0.341197
$540$	50.2730	2.16340
$541$	7.42817	0.319362	0.159681	−	0.987169i	$-0.448953\pi$
$541$	7.42817	0.319362	0.159681	+	0.987169i	$0.448953\pi$
$542$	9.25324	0.397461
$543$	−23.3597	−1.00246
$544$	−3.32993	−0.142769
$545$	−63.3066	−2.71176
$546$	−59.1617	−2.53189
$547$	13.7673	0.588649	0.294325	−	0.955706i	$-0.404905\pi$
$547$	13.7673	0.588649	0.294325	+	0.955706i	$0.404905\pi$
$548$	10.0022	0.427272
$549$	−47.6631	−2.03421
$550$	−7.07938	−0.301866
$551$	8.67714	0.369659
$552$	4.97409	0.211711
$553$	−15.6912	−0.667256
$554$	17.1780	0.729822
$555$	18.1901	0.772126
$556$	1.82323	0.0773220
$557$	1.50359	0.0637093	0.0318547	−	0.999493i	$-0.489859\pi$
$557$	1.50359	0.0637093	0.0318547	+	0.999493i	$0.489859\pi$
$558$	−52.2119	−2.21030
$559$	−41.3230	−1.74778
$560$	19.3332	0.816977
$561$	−5.83470	−0.246341
$562$	−17.4514	−0.736142
$563$	9.10192	0.383600	0.191800	−	0.981434i	$-0.438567\pi$
$563$	9.10192	0.383600	0.191800	+	0.981434i	$0.438567\pi$
$564$	−2.68613	−0.113106
$565$	−11.3359	−0.476906
$566$	−3.00962	−0.126504
$567$	−78.3516	−3.29046
$568$	−9.26083	−0.388576
$569$	−18.1526	−0.760996	−0.380498	−	0.924782i	$-0.624247\pi$
$569$	−18.1526	−0.760996	−0.380498	+	0.924782i	$0.624247\pi$
$570$	96.8157	4.05516
$571$	−17.9951	−0.753072	−0.376536	−	0.926402i	$-0.622885\pi$
$571$	−17.9951	−0.753072	−0.376536	+	0.926402i	$0.622885\pi$
$572$	2.29504	0.0959604
$573$	−25.2789	−1.05604
$574$	15.0499	0.628171
$575$	20.0967	0.838090
$576$	6.81797	0.284082
$577$	−44.4198	−1.84922	−0.924611	−	0.380912i	$-0.875610\pi$
$577$	−44.4198	−1.84922	−0.924611	+	0.380912i	$0.875610\pi$
$578$	5.91160	0.245890
$579$	82.5131	3.42913
$580$	4.95935	0.205926
$581$	64.0786	2.65843
$582$	−9.46020	−0.392138
$583$	3.08478	0.127759
$584$	−13.1192	−0.542874
$585$	−117.588	−4.86167
$586$	−8.59337	−0.354989
$587$	18.0342	0.744351	0.372175	−	0.928162i	$-0.378612\pi$
$587$	18.0342	0.744351	0.372175	+	0.928162i	$0.378612\pi$
$588$	−44.3851	−1.83041
$589$	−56.3064	−2.32006
$590$	30.2843	1.24679
$591$	−37.1401	−1.52774
$592$	1.38144	0.0567769
$593$	−10.9658	−0.450313	−0.225157	−	0.974323i	$-0.572289\pi$
$593$	−10.9658	−0.450313	−0.225157	+	0.974323i	$0.572289\pi$
$594$	6.68985	0.274488
$595$	64.3781	2.63924
$596$	6.41681	0.262843
$597$	−16.3039	−0.667274
$598$	−6.51508	−0.266421
$599$	20.1764	0.824385	0.412192	−	0.911097i	$-0.364763\pi$
$599$	20.1764	0.824385	0.412192	+	0.911097i	$0.364763\pi$
$600$	39.6673	1.61941
$601$	−28.5432	−1.16430	−0.582150	−	0.813081i	$-0.697788\pi$
$601$	−28.5432	−1.16430	−0.582150	+	0.813081i	$0.697788\pi$
$602$	−46.3220	−1.88794
$603$	−45.2402	−1.84232
$604$	−14.2028	−0.577905
$605$	44.9116	1.82592
$606$	−49.6305	−2.01610
$607$	30.3983	1.23383	0.616915	−	0.787030i	$-0.288382\pi$
$607$	30.3983	1.23383	0.616915	+	0.787030i	$0.288382\pi$
$608$	7.35264	0.298189
$609$	−17.0120	−0.689363
$610$	−29.3778	−1.18947
$611$	3.51830	0.142335
$612$	22.7033	0.917728
$613$	27.5675	1.11344	0.556721	−	0.830700i	$-0.312059\pi$
$613$	27.5675	1.11344	0.556721	+	0.830700i	$0.312059\pi$
$614$	20.7432	0.837125
$615$	43.0748	1.73694
$616$	2.57268	0.103656
$617$	5.30336	0.213505	0.106753	−	0.994286i	$-0.465955\pi$
$617$	5.30336	0.213505	0.106753	+	0.994286i	$0.465955\pi$
$618$	−36.5476	−1.47016
$619$	−1.66344	−0.0668591	−0.0334295	−	0.999441i	$-0.510643\pi$
$619$	−1.66344	−0.0668591	−0.0334295	+	0.999441i	$0.510643\pi$
$620$	−32.1814	−1.29244
$621$	−18.9909	−0.762079
$622$	−19.3692	−0.776634
$623$	63.7121	2.55257
$624$	−12.8596	−0.514797
$625$	71.9686	2.87875
$626$	4.37855	0.175002
$627$	12.8833	0.514510
$628$	−20.5119	−0.818515
$629$	4.60010	0.183418
$630$	−131.813	−5.25156
$631$	−22.7991	−0.907620	−0.453810	−	0.891099i	$-0.649935\pi$
$631$	−22.7991	−0.907620	−0.453810	+	0.891099i	$0.649935\pi$
$632$	−3.41069	−0.135670
$633$	−84.8284	−3.37163
$634$	18.5624	0.737208
$635$	24.4211	0.969121
$636$	−17.2847	−0.685384
$637$	58.1358	2.30343
$638$	0.659943	0.0261274
$639$	63.1401	2.49778
$640$	4.20234	0.166112
$641$	46.8008	1.84852	0.924260	−	0.381764i	$-0.124683\pi$
$641$	46.8008	1.84852	0.924260	+	0.381764i	$0.124683\pi$
$642$	−62.4409	−2.46434
$643$	−23.8787	−0.941686	−0.470843	−	0.882217i	$-0.656050\pi$
$643$	−23.8787	−0.941686	−0.470843	+	0.882217i	$0.656050\pi$
$644$	−7.30323	−0.287788
$645$	−132.580	−5.22032
$646$	24.4838	0.963301
$647$	8.36619	0.328909	0.164454	−	0.986385i	$-0.447414\pi$
$647$	8.36619	0.328909	0.164454	+	0.986385i	$0.447414\pi$
$648$	−17.0308	−0.669034
$649$	4.02995	0.158189
$650$	−51.9564	−2.03790
$651$	110.392	4.32660
$652$	18.6074	0.728720
$653$	36.8803	1.44324	0.721619	−	0.692290i	$-0.243398\pi$
$653$	36.8803	1.44324	0.721619	+	0.692290i	$0.243398\pi$
$654$	47.2029	1.84578
$655$	−45.4537	−1.77602
$656$	3.27131	0.127723
$657$	89.4460	3.48962
$658$	3.94392	0.153750
$659$	−24.3403	−0.948164	−0.474082	−	0.880481i	$-0.657220\pi$
$659$	−24.3403	−0.948164	−0.474082	+	0.880481i	$0.657220\pi$
$660$	7.36334	0.286618
$661$	−15.5367	−0.604309	−0.302155	−	0.953259i	$-0.597706\pi$
$661$	−15.5367	−0.604309	−0.302155	+	0.953259i	$0.597706\pi$
$662$	−27.8021	−1.08056
$663$	−42.8216	−1.66305
$664$	13.9284	0.540525
$665$	−142.150	−5.51235
$666$	−9.41863	−0.364965
$667$	−1.87342	−0.0725392
$668$	−15.6045	−0.603754
$669$	62.4583	2.41478
$670$	−27.8843	−1.07727
$671$	−3.90931	−0.150917
$672$	−14.4153	−0.556082
$673$	−12.0788	−0.465602	−0.232801	−	0.972524i	$-0.574789\pi$
$673$	−12.0788	−0.465602	−0.232801	+	0.972524i	$0.574789\pi$
$674$	0.0898006	0.00345899
$675$	−151.449	−5.82926
$676$	3.84358	0.147830
$677$	28.0645	1.07861	0.539304	−	0.842111i	$-0.318687\pi$
$677$	28.0645	1.07861	0.539304	+	0.842111i	$0.318687\pi$
$678$	8.45234	0.324610
$679$	13.8900	0.533049
$680$	13.9935	0.536625
$681$	−14.0842	−0.539709
$682$	−4.28240	−0.163981
$683$	10.7490	0.411299	0.205650	−	0.978626i	$-0.434069\pi$
$683$	10.7490	0.411299	0.205650	+	0.978626i	$0.434069\pi$
$684$	−50.1301	−1.91677
$685$	−42.0326	−1.60598
$686$	32.9647	1.25860
$687$	67.2072	2.56411
$688$	−10.0687	−0.383867
$689$	22.6396	0.862500
$690$	−20.9028	−0.795756
$691$	−35.8150	−1.36247	−0.681233	−	0.732067i	$-0.738556\pi$
$691$	−35.8150	−1.36247	−0.681233	+	0.732067i	$0.738556\pi$
$692$	12.1566	0.462124
$693$	−17.5404	−0.666307
$694$	10.1679	0.385970
$695$	−7.66181	−0.290629
$696$	−3.69781	−0.140165
$697$	10.8932	0.412610
$698$	20.4857	0.775394
$699$	−35.8664	−1.35659
$700$	−58.2418	−2.20133
$701$	−33.8927	−1.28011	−0.640055	−	0.768329i	$-0.721088\pi$
$701$	−33.8927	−1.28011	−0.640055	+	0.768329i	$0.721088\pi$
$702$	49.0977	1.85307
$703$	−10.1573	−0.383088
$704$	0.559208	0.0210759
$705$	11.2880	0.425132
$706$	15.4912	0.583020
$707$	72.8703	2.74057
$708$	−22.5807	−0.848635
$709$	6.33859	0.238051	0.119025	−	0.992891i	$-0.462023\pi$
$709$	6.33859	0.238051	0.119025	+	0.992891i	$0.462023\pi$
$710$	38.9172	1.46054
$711$	23.2540	0.872093
$712$	13.8487	0.519003
$713$	12.1567	0.455273
$714$	−48.0018	−1.79642
$715$	−9.64454	−0.360685
$716$	17.8889	0.668540
$717$	−77.0823	−2.87869
$718$	−29.6852	−1.10784
$719$	34.4568	1.28502	0.642511	−	0.766277i	$-0.277893\pi$
$719$	34.4568	1.28502	0.642511	+	0.766277i	$0.277893\pi$
$720$	−28.6514	−1.06778
$721$	53.6612	1.99845
$722$	−35.0614	−1.30485
$723$	−60.3943	−2.24609
$724$	7.45514	0.277068
$725$	−14.9402	−0.554864
$726$	−33.4872	−1.24283
$727$	35.5316	1.31779	0.658897	−	0.752233i	$-0.271023\pi$
$727$	35.5316	1.31779	0.658897	+	0.752233i	$0.271023\pi$
$728$	18.8812	0.699784
$729$	3.66143	0.135609
$730$	55.1311	2.04050
$731$	−33.5281	−1.24008
$732$	21.9048	0.809623
$733$	4.86050	0.179527	0.0897634	−	0.995963i	$-0.471389\pi$
$733$	4.86050	0.179527	0.0897634	+	0.995963i	$0.471389\pi$
$734$	7.58658	0.280026
$735$	186.521	6.87994
$736$	−1.58746	−0.0585145
$737$	−3.71058	−0.136681
$738$	−22.3037	−0.821010
$739$	18.2447	0.671143	0.335572	−	0.942015i	$-0.391071\pi$
$739$	18.2447	0.671143	0.335572	+	0.942015i	$0.391071\pi$
$740$	−5.80529	−0.213407
$741$	94.5522	3.47346
$742$	25.3784	0.931670
$743$	−39.4898	−1.44874	−0.724369	−	0.689412i	$-0.757869\pi$
$743$	−39.4898	−1.44874	−0.724369	+	0.689412i	$0.757869\pi$
$744$	23.9952	0.879708
$745$	−26.9656	−0.987944
$746$	−6.15969	−0.225522
$747$	−94.9632	−3.47452
$748$	1.86212	0.0680858
$749$	91.6791	3.34988
$750$	−100.858	−3.68282
$751$	−2.37876	−0.0868021	−0.0434011	−	0.999058i	$-0.513819\pi$
$751$	−2.37876	−0.0868021	−0.0434011	+	0.999058i	$0.513819\pi$
$752$	0.857267	0.0312613
$753$	−10.0052	−0.364608
$754$	4.84340	0.176386
$755$	59.6851	2.17216
$756$	55.0372	2.00168
$757$	−14.6154	−0.531207	−0.265603	−	0.964082i	$-0.585571\pi$
$757$	−14.6154	−0.531207	−0.265603	+	0.964082i	$0.585571\pi$
$758$	21.1727	0.769029
$759$	−2.78155	−0.100964
$760$	−30.8983	−1.12080
$761$	27.6511	1.00235	0.501175	−	0.865346i	$-0.332901\pi$
$761$	27.6511	1.00235	0.501175	+	0.865346i	$0.332901\pi$
$762$	−18.2089	−0.659640
$763$	−69.3060	−2.50904
$764$	8.06766	0.291878
$765$	−95.4071	−3.44945
$766$	32.6476	1.17961
$767$	29.5763	1.06794
$768$	−3.13336	−0.113066
$769$	−36.4125	−1.31307	−0.656535	−	0.754296i	$-0.727978\pi$
$769$	−36.4125	−1.31307	−0.656535	+	0.754296i	$0.727978\pi$
$770$	−10.8113	−0.389611
$771$	−34.5520	−1.24436
$772$	−26.3337	−0.947771
$773$	−29.7957	−1.07168	−0.535838	−	0.844321i	$-0.680004\pi$
$773$	−29.7957	−1.07168	−0.535838	+	0.844321i	$0.680004\pi$
$774$	68.6483	2.46751
$775$	96.9473	3.48245
$776$	3.01918	0.108382
$777$	19.9139	0.714407
$778$	−2.53376	−0.0908396
$779$	−24.0528	−0.861780
$780$	54.0405	1.93496
$781$	5.17873	0.185309
$782$	−5.28612	−0.189031
$783$	14.1181	0.504540
$784$	14.1653	0.505905
$785$	86.1981	3.07654
$786$	33.8913	1.20886
$787$	23.6747	0.843911	0.421955	−	0.906617i	$-0.361344\pi$
$787$	23.6747	0.843911	0.421955	+	0.906617i	$0.361344\pi$
$788$	11.8531	0.422249
$789$	21.8900	0.779305
$790$	14.3329	0.509941
$791$	−12.4102	−0.441256
$792$	−3.81266	−0.135477
$793$	−28.6909	−1.01884
$794$	20.2832	0.719824
$795$	72.6363	2.57614
$796$	5.20332	0.184427
$797$	−11.2514	−0.398543	−0.199272	−	0.979944i	$-0.563858\pi$
$797$	−11.2514	−0.398543	−0.199272	+	0.979944i	$0.563858\pi$
$798$	105.991	3.75202
$799$	2.85464	0.100990
$800$	−12.6597	−0.447586
$801$	−94.4201	−3.33617
$802$	26.0298	0.919142
$803$	7.33633	0.258893
$804$	20.7912	0.733250
$805$	30.6906	1.08170
$806$	−31.4290	−1.10704
$807$	−6.60014	−0.232336
$808$	15.8394	0.557227
$809$	17.1917	0.604428	0.302214	−	0.953240i	$-0.402274\pi$
$809$	17.1917	0.604428	0.302214	+	0.953240i	$0.402274\pi$
$810$	71.5693	2.51469
$811$	−30.8923	−1.08478	−0.542388	−	0.840128i	$-0.682480\pi$
$811$	−30.8923	−1.08478	−0.542388	+	0.840128i	$0.682480\pi$
$812$	5.42932	0.190532
$813$	28.9938	1.01686
$814$	−0.772513	−0.0270766
$815$	−78.1944	−2.73903
$816$	−10.4339	−0.365258
$817$	74.0318	2.59005
$818$	16.4721	0.575934
$819$	−128.732	−4.49824
$820$	−13.7471	−0.480071
$821$	−21.8277	−0.761791	−0.380896	−	0.924618i	$-0.624384\pi$
$821$	−21.8277	−0.761791	−0.380896	+	0.924618i	$0.624384\pi$
$822$	31.3405	1.09312
$823$	19.4553	0.678170	0.339085	−	0.940756i	$-0.389883\pi$
$823$	19.4553	0.678170	0.339085	+	0.940756i	$0.389883\pi$
$824$	11.6640	0.406335
$825$	−22.1823	−0.772287
$826$	33.1542	1.15358
$827$	−29.3922	−1.02207	−0.511033	−	0.859561i	$-0.670737\pi$
$827$	−29.3922	−1.02207	−0.511033	+	0.859561i	$0.670737\pi$
$828$	10.8232	0.376134
$829$	42.0806	1.46152	0.730759	−	0.682635i	$-0.239166\pi$
$829$	42.0806	1.46152	0.730759	+	0.682635i	$0.239166\pi$
$830$	−58.5317	−2.03167
$831$	53.8249	1.86716
$832$	4.10409	0.142284
$833$	47.1695	1.63433
$834$	5.71283	0.197819
$835$	65.5752	2.26932
$836$	−4.11165	−0.142205
$837$	−91.6131	−3.16661
$838$	−35.0125	−1.20949
$839$	−0.172907	−0.00596940	−0.00298470	−	0.999996i	$-0.500950\pi$
$839$	−0.172907	−0.00596940	−0.00298470	+	0.999996i	$0.500950\pi$
$840$	60.5779	2.09014
$841$	−27.6073	−0.951975
$842$	14.7780	0.509283
$843$	−54.6815	−1.88333
$844$	27.0726	0.931879
$845$	−16.1520	−0.555647
$846$	−5.84482	−0.200949
$847$	49.1677	1.68942
$848$	5.51635	0.189432
$849$	−9.43024	−0.323645
$850$	−42.1557	−1.44593
$851$	2.19298	0.0751745
$852$	−29.0176	−0.994125
$853$	3.18335	0.108996	0.0544979	−	0.998514i	$-0.482644\pi$
$853$	3.18335	0.108996	0.0544979	+	0.998514i	$0.482644\pi$
$854$	−32.1618	−1.10055
$855$	210.664	7.20455
$856$	19.9277	0.681116
$857$	9.48940	0.324152	0.162076	−	0.986778i	$-0.448181\pi$
$857$	9.48940	0.324152	0.162076	+	0.986778i	$0.448181\pi$
$858$	7.19120	0.245503
$859$	41.3867	1.41210	0.706049	−	0.708163i	$-0.250476\pi$
$859$	41.3867	1.41210	0.706049	+	0.708163i	$0.250476\pi$
$860$	42.3122	1.44284
$861$	47.1568	1.60710
$862$	1.22176	0.0416133
$863$	37.5229	1.27729	0.638646	−	0.769500i	$-0.279495\pi$
$863$	37.5229	1.27729	0.638646	+	0.769500i	$0.279495\pi$
$864$	11.9631	0.406993
$865$	−51.0861	−1.73698
$866$	−38.1533	−1.29650
$867$	18.5232	0.629081
$868$	−35.2311	−1.19582
$869$	1.90728	0.0647002
$870$	15.5394	0.526836
$871$	−27.2324	−0.922735
$872$	−15.0646	−0.510152
$873$	−20.5847	−0.696687
$874$	11.6720	0.394812
$875$	148.086	5.00621
$876$	−41.1071	−1.38888
$877$	29.0222	0.980010	0.490005	−	0.871720i	$-0.336995\pi$
$877$	29.0222	0.980010	0.490005	+	0.871720i	$0.336995\pi$
$878$	31.9428	1.07802
$879$	−26.9261	−0.908196
$880$	−2.34998	−0.0792178
$881$	36.1160	1.21678	0.608389	−	0.793639i	$-0.291816\pi$
$881$	36.1160	1.21678	0.608389	+	0.793639i	$0.291816\pi$
$882$	−96.5788	−3.25198
$883$	25.4519	0.856526	0.428263	−	0.903654i	$-0.359126\pi$
$883$	25.4519	0.856526	0.428263	+	0.903654i	$0.359126\pi$
$884$	13.6663	0.459648
$885$	94.8918	3.18975
$886$	−3.01246	−0.101206
$887$	−40.4617	−1.35857	−0.679285	−	0.733874i	$-0.737710\pi$
$887$	−40.4617	−1.35857	−0.679285	+	0.733874i	$0.737710\pi$
$888$	4.32856	0.145257
$889$	26.7354	0.896675
$890$	−58.1970	−1.95077
$891$	9.52376	0.319058
$892$	−19.9333	−0.667416
$893$	−6.30318	−0.210928
$894$	20.1062	0.672452
$895$	−75.1753	−2.51283
$896$	4.60058	0.153695
$897$	−20.4141	−0.681607
$898$	13.2468	0.442051
$899$	−9.03748	−0.301417
$900$	86.3132	2.87711
$901$	18.3690	0.611961
$902$	−1.82934	−0.0609103
$903$	−145.144	−4.83008
$904$	−2.69753	−0.0897185
$905$	−31.3290	−1.04141
$906$	−44.5026	−1.47850
$907$	−0.838773	−0.0278510	−0.0139255	−	0.999903i	$-0.504433\pi$
$907$	−0.838773	−0.0278510	−0.0139255	+	0.999903i	$0.504433\pi$
$908$	4.49492	0.149169
$909$	−107.992	−3.58188
$910$	−79.3452	−2.63027
$911$	−46.6550	−1.54575	−0.772875	−	0.634559i	$-0.781182\pi$
$911$	−46.6550	−1.54575	−0.772875	+	0.634559i	$0.781182\pi$
$912$	23.0385	0.762881
$913$	−7.78885	−0.257773
$914$	−5.73373	−0.189655
$915$	−92.0512	−3.04312
$916$	−21.4489	−0.708691
$917$	−49.7611	−1.64326
$918$	39.8362	1.31479
$919$	−51.1224	−1.68637	−0.843186	−	0.537622i	$-0.819323\pi$
$919$	−51.1224	−1.68637	−0.843186	+	0.537622i	$0.819323\pi$
$920$	6.67104	0.219938
$921$	64.9958	2.14169
$922$	30.1914	0.994302
$923$	38.0073	1.25103
$924$	8.06114	0.265192
$925$	17.4886	0.575021
$926$	2.04586	0.0672313
$927$	−79.5249	−2.61194
$928$	1.18014	0.0387400
$929$	−0.437059	−0.0143394	−0.00716972	−	0.999974i	$-0.502282\pi$
$929$	−0.437059	−0.0143394	−0.00716972	+	0.999974i	$0.502282\pi$
$930$	−100.836	−3.30655
$931$	−104.153	−3.41346
$932$	11.4466	0.374947
$933$	−60.6907	−1.98693
$934$	−14.5304	−0.475449
$935$	−7.82526	−0.255913
$936$	−27.9816	−0.914607
$937$	56.7534	1.85405	0.927026	−	0.374997i	$-0.122356\pi$
$937$	56.7534	1.85405	0.927026	+	0.374997i	$0.122356\pi$
$938$	−30.5268	−0.996736
$939$	13.7196	0.447722
$940$	−3.60253	−0.117501
$941$	−27.9589	−0.911433	−0.455717	−	0.890125i	$-0.650617\pi$
$941$	−27.9589	−0.911433	−0.455717	+	0.890125i	$0.650617\pi$
$942$	−64.2713	−2.09407
$943$	5.19306	0.169109
$944$	7.20654	0.234553
$945$	−231.285	−7.52370
$946$	5.63051	0.183064
$947$	−0.312396	−0.0101515	−0.00507575	−	0.999987i	$-0.501616\pi$
$947$	−0.312396	−0.0101515	−0.00507575	+	0.999987i	$0.501616\pi$
$948$	−10.6869	−0.347096
$949$	53.8422	1.74779
$950$	93.0820	3.01998
$951$	58.1628	1.88606
$952$	15.3196	0.496511
$953$	4.27274	0.138408	0.0692039	−	0.997603i	$-0.477954\pi$
$953$	4.27274	0.138408	0.0692039	+	0.997603i	$0.477954\pi$
$954$	−37.6103	−1.21768
$955$	−33.9031	−1.09708
$956$	24.6005	0.795637
$957$	2.06784	0.0668438
$958$	15.7746	0.509656
$959$	−46.0158	−1.48593
$960$	13.1675	0.424978
$961$	27.6446	0.891761
$962$	−5.66957	−0.182794
$963$	−135.867	−4.37824
$964$	19.2746	0.620793
$965$	110.663	3.56237
$966$	−22.8837	−0.736270
$967$	−11.8493	−0.381048	−0.190524	−	0.981683i	$-0.561019\pi$
$967$	−11.8493	−0.381048	−0.190524	+	0.981683i	$0.561019\pi$
$968$	10.6873	0.343502
$969$	76.7165	2.46449
$970$	−12.6876	−0.407375
$971$	−20.8264	−0.668351	−0.334175	−	0.942511i	$-0.608458\pi$
$971$	−20.8264	−0.668351	−0.334175	+	0.942511i	$0.608458\pi$
$972$	−17.4745	−0.560494
$973$	−8.38789	−0.268903
$974$	24.6357	0.789379
$975$	−162.798	−5.21372
$976$	−6.99081	−0.223770
$977$	21.7995	0.697427	0.348714	−	0.937229i	$-0.386619\pi$
$977$	21.7995	0.697427	0.348714	+	0.937229i	$0.386619\pi$
$978$	58.3036	1.86434
$979$	−7.74431	−0.247509
$980$	−59.5275	−1.90154
$981$	102.710	3.27928
$982$	17.0093	0.542788
$983$	19.7360	0.629482	0.314741	−	0.949178i	$-0.398082\pi$
$983$	19.7360	0.629482	0.314741	+	0.949178i	$0.398082\pi$
$984$	10.2502	0.326764
$985$	−49.8108	−1.58710
$986$	3.92978	0.125150
$987$	12.3578	0.393352
$988$	−30.1759	−0.960024
$989$	−15.9837	−0.508252
$990$	16.0221	0.509216
$991$	−0.454103	−0.0144251	−0.00721253	−	0.999974i	$-0.502296\pi$
$991$	−0.454103	−0.0144251	−0.00721253	+	0.999974i	$0.502296\pi$
$992$	−7.65798	−0.243141
$993$	−87.1142	−2.76449
$994$	42.6052	1.35135
$995$	−21.8661	−0.693202
$996$	43.6426	1.38287
$997$	−23.7426	−0.751936	−0.375968	−	0.926633i	$-0.622690\pi$
$997$	−23.7426	−0.751936	−0.375968	+	0.926633i	$0.622690\pi$
$998$	−20.1742	−0.638604
$999$	−16.5263	−0.522870

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.g.1.7	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.g.1.7	✓	69	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.13336 q^{3} +1.00000 q^{4} -4.20234 q^{5} +3.13336 q^{6} -4.60058 q^{7} -1.00000 q^{8} +6.81797 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.13336 q^{3} +1.00000 q^{4} -4.20234 q^{5} +3.13336 q^{6} -4.60058 q^{7} -1.00000 q^{8} +6.81797 q^{9} +4.20234 q^{10} +0.559208 q^{11} -3.13336 q^{12} +4.10409 q^{13} +4.60058 q^{14} +13.1675 q^{15} +1.00000 q^{16} +3.32993 q^{17} -6.81797 q^{18} -7.35264 q^{19} -4.20234 q^{20} +14.4153 q^{21} -0.559208 q^{22} +1.58746 q^{23} +3.13336 q^{24} +12.6597 q^{25} -4.10409 q^{26} -11.9631 q^{27} -4.60058 q^{28} -1.18014 q^{29} -13.1675 q^{30} +7.65798 q^{31} -1.00000 q^{32} -1.75220 q^{33} -3.32993 q^{34} +19.3332 q^{35} +6.81797 q^{36} +1.38144 q^{37} +7.35264 q^{38} -12.8596 q^{39} +4.20234 q^{40} +3.27131 q^{41} -14.4153 q^{42} -10.0687 q^{43} +0.559208 q^{44} -28.6514 q^{45} -1.58746 q^{46} +0.857267 q^{47} -3.13336 q^{48} +14.1653 q^{49} -12.6597 q^{50} -10.4339 q^{51} +4.10409 q^{52} +5.51635 q^{53} +11.9631 q^{54} -2.34998 q^{55} +4.60058 q^{56} +23.0385 q^{57} +1.18014 q^{58} +7.20654 q^{59} +13.1675 q^{60} -6.99081 q^{61} -7.65798 q^{62} -31.3666 q^{63} +1.00000 q^{64} -17.2468 q^{65} +1.75220 q^{66} -6.63543 q^{67} +3.32993 q^{68} -4.97409 q^{69} -19.3332 q^{70} +9.26083 q^{71} -6.81797 q^{72} +13.1192 q^{73} -1.38144 q^{74} -39.6673 q^{75} -7.35264 q^{76} -2.57268 q^{77} +12.8596 q^{78} +3.41069 q^{79} -4.20234 q^{80} +17.0308 q^{81} -3.27131 q^{82} -13.9284 q^{83} +14.4153 q^{84} -13.9935 q^{85} +10.0687 q^{86} +3.69781 q^{87} -0.559208 q^{88} -13.8487 q^{89} +28.6514 q^{90} -18.8812 q^{91} +1.58746 q^{92} -23.9952 q^{93} -0.857267 q^{94} +30.8983 q^{95} +3.13336 q^{96} -3.01918 q^{97} -14.1653 q^{98} +3.81266 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9	\( 69 q - 69 q^{2} + 69 q^{4} + 13 q^{5} - 27 q^{7} - 69 q^{8} + 99 q^{9} - 13 q^{10} + 42 q^{11} - 5 q^{13} + 27 q^{14} + 18 q^{15} + 69 q^{16} + 24 q^{17} - 99 q^{18} + q^{19} + 13 q^{20} + 7 q^{21} - 42 q^{22} + 25 q^{23} + 100 q^{25} + 5 q^{26} + 15 q^{27} - 27 q^{28} + 87 q^{29} - 18 q^{30} + 5 q^{31} - 69 q^{32} + 28 q^{33} - 24 q^{34} + 33 q^{35} + 99 q^{36} - 5 q^{37} - q^{38} + 22 q^{39} - 13 q^{40} + 47 q^{41} - 7 q^{42} - 23 q^{43} + 42 q^{44} + 14 q^{45} - 25 q^{46} + 13 q^{47} + 106 q^{49} - 100 q^{50} + 2 q^{51} - 5 q^{52} + 51 q^{53} - 15 q^{54} - 11 q^{55} + 27 q^{56} + 52 q^{57} - 87 q^{58} + 73 q^{59} + 18 q^{60} + 4 q^{61} - 5 q^{62} - 86 q^{63} + 69 q^{64} + 70 q^{65} - 28 q^{66} - 24 q^{67} + 24 q^{68} + 56 q^{69} - 33 q^{70} + 84 q^{71} - 99 q^{72} + 27 q^{73} + 5 q^{74} + 27 q^{75} + q^{76} + 45 q^{77} - 22 q^{78} + 42 q^{79} + 13 q^{80} + 205 q^{81} - 47 q^{82} + q^{83} + 7 q^{84} - 18 q^{85} + 23 q^{86} - q^{87} - 42 q^{88} + 94 q^{89} - 14 q^{90} + 6 q^{91} + 25 q^{92} - 13 q^{93} - 13 q^{94} + 86 q^{95} + 35 q^{97} - 106 q^{98} + 83 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 69 * q^4 + 13 * q^5 - 27 * q^7 - 69 * q^8 + 99 * q^9 - 13 * q^10 + 42 * q^11 - 5 * q^13 + 27 * q^14 + 18 * q^15 + 69 * q^16 + 24 * q^17 - 99 * q^18 + q^19 + 13 * q^20 + 7 * q^21 - 42 * q^22 + 25 * q^23 + 100 * q^25 + 5 * q^26 + 15 * q^27 - 27 * q^28 + 87 * q^29 - 18 * q^30 + 5 * q^31 - 69 * q^32 + 28 * q^33 - 24 * q^34 + 33 * q^35 + 99 * q^36 - 5 * q^37 - q^38 + 22 * q^39 - 13 * q^40 + 47 * q^41 - 7 * q^42 - 23 * q^43 + 42 * q^44 + 14 * q^45 - 25 * q^46 + 13 * q^47 + 106 * q^49 - 100 * q^50 + 2 * q^51 - 5 * q^52 + 51 * q^53 - 15 * q^54 - 11 * q^55 + 27 * q^56 + 52 * q^57 - 87 * q^58 + 73 * q^59 + 18 * q^60 + 4 * q^61 - 5 * q^62 - 86 * q^63 + 69 * q^64 + 70 * q^65 - 28 * q^66 - 24 * q^67 + 24 * q^68 + 56 * q^69 - 33 * q^70 + 84 * q^71 - 99 * q^72 + 27 * q^73 + 5 * q^74 + 27 * q^75 + q^76 + 45 * q^77 - 22 * q^78 + 42 * q^79 + 13 * q^80 + 205 * q^81 - 47 * q^82 + q^83 + 7 * q^84 - 18 * q^85 + 23 * q^86 - q^87 - 42 * q^88 + 94 * q^89 - 14 * q^90 + 6 * q^91 + 25 * q^92 - 13 * q^93 - 13 * q^94 + 86 * q^95 + 35 * q^97 - 106 * q^98 + 83 * q^99

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