LMFDB - Embedded newform 4015.2.a.g.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.06358 q^{2} +2.59950 q^{3} +2.25838 q^{4} -1.00000 q^{5} -5.36430 q^{6} -1.01430 q^{7} -0.533185 q^{8} +3.75743 q^{9} +O(q^{10})$	\(q-2.06358 q^{2} +2.59950 q^{3} +2.25838 q^{4} -1.00000 q^{5} -5.36430 q^{6} -1.01430 q^{7} -0.533185 q^{8} +3.75743 q^{9} +2.06358 q^{10} -1.00000 q^{11} +5.87067 q^{12} +0.591408 q^{13} +2.09310 q^{14} -2.59950 q^{15} -3.41648 q^{16} -1.74690 q^{17} -7.75376 q^{18} -3.68501 q^{19} -2.25838 q^{20} -2.63669 q^{21} +2.06358 q^{22} +2.17727 q^{23} -1.38602 q^{24} +1.00000 q^{25} -1.22042 q^{26} +1.96893 q^{27} -2.29068 q^{28} +8.50037 q^{29} +5.36430 q^{30} -2.16878 q^{31} +8.11657 q^{32} -2.59950 q^{33} +3.60488 q^{34} +1.01430 q^{35} +8.48569 q^{36} -8.65334 q^{37} +7.60432 q^{38} +1.53737 q^{39} +0.533185 q^{40} -1.23245 q^{41} +5.44103 q^{42} +12.4123 q^{43} -2.25838 q^{44} -3.75743 q^{45} -4.49298 q^{46} -10.9619 q^{47} -8.88117 q^{48} -5.97119 q^{49} -2.06358 q^{50} -4.54109 q^{51} +1.33562 q^{52} +1.57287 q^{53} -4.06305 q^{54} +1.00000 q^{55} +0.540812 q^{56} -9.57919 q^{57} -17.5412 q^{58} -6.86851 q^{59} -5.87067 q^{60} -0.278562 q^{61} +4.47545 q^{62} -3.81117 q^{63} -9.91626 q^{64} -0.591408 q^{65} +5.36430 q^{66} +5.68941 q^{67} -3.94517 q^{68} +5.65982 q^{69} -2.09310 q^{70} -9.63282 q^{71} -2.00340 q^{72} -1.00000 q^{73} +17.8569 q^{74} +2.59950 q^{75} -8.32214 q^{76} +1.01430 q^{77} -3.17249 q^{78} +6.04589 q^{79} +3.41648 q^{80} -6.15403 q^{81} +2.54327 q^{82} -9.00725 q^{83} -5.95464 q^{84} +1.74690 q^{85} -25.6139 q^{86} +22.0968 q^{87} +0.533185 q^{88} +3.21687 q^{89} +7.75376 q^{90} -0.599868 q^{91} +4.91710 q^{92} -5.63775 q^{93} +22.6208 q^{94} +3.68501 q^{95} +21.0991 q^{96} +8.99316 q^{97} +12.3220 q^{98} -3.75743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.06358	−1.45917	−0.729587	−	0.683888i	$-0.760288\pi$
$2$	−2.06358	−1.45917	−0.729587	+	0.683888i	$0.760288\pi$
$3$	2.59950	1.50082	0.750412	−	0.660970i	$-0.229855\pi$
$3$	2.59950	1.50082	0.750412	+	0.660970i	$0.229855\pi$
$4$	2.25838	1.12919
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.36430	−2.18996
$7$	−1.01430	−0.383371	−0.191685	−	0.981456i	$-0.561395\pi$
$7$	−1.01430	−0.383371	−0.191685	+	0.981456i	$0.561395\pi$
$8$	−0.533185	−0.188509
$9$	3.75743	1.25248
$10$	2.06358	0.652563
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.87067	1.69472
$13$	0.591408	0.164027	0.0820135	−	0.996631i	$-0.473865\pi$
$13$	0.591408	0.164027	0.0820135	+	0.996631i	$0.473865\pi$
$14$	2.09310	0.559405
$15$	−2.59950	−0.671189
$16$	−3.41648	−0.854121
$17$	−1.74690	−0.423686	−0.211843	−	0.977304i	$-0.567947\pi$
$17$	−1.74690	−0.423686	−0.211843	+	0.977304i	$0.567947\pi$
$18$	−7.75376	−1.82758
$19$	−3.68501	−0.845398	−0.422699	−	0.906270i	$-0.638917\pi$
$19$	−3.68501	−0.845398	−0.422699	+	0.906270i	$0.638917\pi$
$20$	−2.25838	−0.504989
$21$	−2.63669	−0.575373
$22$	2.06358	0.439958
$23$	2.17727	0.453992	0.226996	−	0.973896i	$-0.427110\pi$
$23$	2.17727	0.453992	0.226996	+	0.973896i	$0.427110\pi$
$24$	−1.38602	−0.282920
$25$	1.00000	0.200000
$26$	−1.22042	−0.239344
$27$	1.96893	0.378921
$28$	−2.29068	−0.432898
$29$	8.50037	1.57848	0.789240	−	0.614085i	$-0.210475\pi$
$29$	8.50037	1.57848	0.789240	+	0.614085i	$0.210475\pi$
$30$	5.36430	0.979382
$31$	−2.16878	−0.389524	−0.194762	−	0.980851i	$-0.562393\pi$
$31$	−2.16878	−0.389524	−0.194762	+	0.980851i	$0.562393\pi$
$32$	8.11657	1.43482
$33$	−2.59950	−0.452516
$34$	3.60488	0.618232
$35$	1.01430	0.171449
$36$	8.48569	1.41428
$37$	−8.65334	−1.42260	−0.711300	−	0.702889i	$-0.751893\pi$
$37$	−8.65334	−1.42260	−0.711300	+	0.702889i	$0.751893\pi$
$38$	7.60432	1.23358
$39$	1.53737	0.246176
$40$	0.533185	0.0843040
$41$	−1.23245	−0.192477	−0.0962384	−	0.995358i	$-0.530681\pi$
$41$	−1.23245	−0.192477	−0.0962384	+	0.995358i	$0.530681\pi$
$42$	5.44103	0.839569
$43$	12.4123	1.89287	0.946433	−	0.322902i	$-0.104658\pi$
$43$	12.4123	1.89287	0.946433	+	0.322902i	$0.104658\pi$
$44$	−2.25838	−0.340463
$45$	−3.75743	−0.560124
$46$	−4.49298	−0.662453
$47$	−10.9619	−1.59896	−0.799480	−	0.600693i	$-0.794892\pi$
$47$	−10.9619	−1.59896	−0.799480	+	0.600693i	$0.794892\pi$
$48$	−8.88117	−1.28189
$49$	−5.97119	−0.853027
$50$	−2.06358	−0.291835
$51$	−4.54109	−0.635879
$52$	1.33562	0.185218
$53$	1.57287	0.216051	0.108025	−	0.994148i	$-0.465547\pi$
$53$	1.57287	0.216051	0.108025	+	0.994148i	$0.465547\pi$
$54$	−4.06305	−0.552912
$55$	1.00000	0.134840
$56$	0.540812	0.0722690
$57$	−9.57919	−1.26879
$58$	−17.5412	−2.30328
$59$	−6.86851	−0.894204	−0.447102	−	0.894483i	$-0.647544\pi$
$59$	−6.86851	−0.894204	−0.447102	+	0.894483i	$0.647544\pi$
$60$	−5.87067	−0.757900
$61$	−0.278562	−0.0356662	−0.0178331	−	0.999841i	$-0.505677\pi$
$61$	−0.278562	−0.0356662	−0.0178331	+	0.999841i	$0.505677\pi$
$62$	4.47545	0.568383
$63$	−3.81117	−0.480163
$64$	−9.91626	−1.23953
$65$	−0.591408	−0.0733551
$66$	5.36430	0.660299
$67$	5.68941	0.695072	0.347536	−	0.937667i	$-0.387018\pi$
$67$	5.68941	0.695072	0.347536	+	0.937667i	$0.387018\pi$
$68$	−3.94517	−0.478422
$69$	5.65982	0.681362
$70$	−2.09310	−0.250174
$71$	−9.63282	−1.14321	−0.571603	−	0.820531i	$-0.693678\pi$
$71$	−9.63282	−1.14321	−0.571603	+	0.820531i	$0.693678\pi$
$72$	−2.00340	−0.236103
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	17.8569	2.07582
$75$	2.59950	0.300165
$76$	−8.32214	−0.954615
$77$	1.01430	0.115591
$78$	−3.17249	−0.359214
$79$	6.04589	0.680216	0.340108	−	0.940386i	$-0.389536\pi$
$79$	6.04589	0.680216	0.340108	+	0.940386i	$0.389536\pi$
$80$	3.41648	0.381975
$81$	−6.15403	−0.683781
$82$	2.54327	0.280857
$83$	−9.00725	−0.988674	−0.494337	−	0.869270i	$-0.664589\pi$
$83$	−9.00725	−0.988674	−0.494337	+	0.869270i	$0.664589\pi$
$84$	−5.95464	−0.649705
$85$	1.74690	0.189478
$86$	−25.6139	−2.76202
$87$	22.0968	2.36902
$88$	0.533185	0.0568377
$89$	3.21687	0.340987	0.170494	−	0.985359i	$-0.445464\pi$
$89$	3.21687	0.340987	0.170494	+	0.985359i	$0.445464\pi$
$90$	7.75376	0.817318
$91$	−0.599868	−0.0628832
$92$	4.91710	0.512643
$93$	−5.63775	−0.584607
$94$	22.6208	2.33316
$95$	3.68501	0.378074
$96$	21.0991	2.15341
$97$	8.99316	0.913117	0.456559	−	0.889693i	$-0.349082\pi$
$97$	8.99316	0.913117	0.456559	+	0.889693i	$0.349082\pi$
$98$	12.3220	1.24471
$99$	−3.75743	−0.377635
$100$	2.25838	0.225838
$101$	−5.85995	−0.583087	−0.291544	−	0.956558i	$-0.594169\pi$
$101$	−5.85995	−0.583087	−0.291544	+	0.956558i	$0.594169\pi$
$102$	9.37091	0.927858
$103$	−5.79504	−0.571003	−0.285501	−	0.958378i	$-0.592160\pi$
$103$	−5.79504	−0.571003	−0.285501	+	0.958378i	$0.592160\pi$
$104$	−0.315330	−0.0309206
$105$	2.63669	0.257314
$106$	−3.24576	−0.315256
$107$	−14.2395	−1.37659	−0.688293	−	0.725432i	$-0.741640\pi$
$107$	−14.2395	−1.37659	−0.688293	+	0.725432i	$0.741640\pi$
$108$	4.44659	0.427873
$109$	2.96355	0.283857	0.141928	−	0.989877i	$-0.454670\pi$
$109$	2.96355	0.283857	0.141928	+	0.989877i	$0.454670\pi$
$110$	−2.06358	−0.196755
$111$	−22.4944	−2.13507
$112$	3.46535	0.327445
$113$	−8.75702	−0.823791	−0.411896	−	0.911231i	$-0.635133\pi$
$113$	−8.75702	−0.823791	−0.411896	+	0.911231i	$0.635133\pi$
$114$	19.7675	1.85139
$115$	−2.17727	−0.203031
$116$	19.1971	1.78240
$117$	2.22217	0.205440
$118$	14.1737	1.30480
$119$	1.77189	0.162429
$120$	1.38602	0.126525
$121$	1.00000	0.0909091
$122$	0.574836	0.0520432
$123$	−3.20377	−0.288874
$124$	−4.89792	−0.439846
$125$	−1.00000	−0.0894427
$126$	7.86467	0.700641
$127$	−0.933819	−0.0828630	−0.0414315	−	0.999141i	$-0.513192\pi$
$127$	−0.933819	−0.0828630	−0.0414315	+	0.999141i	$0.513192\pi$
$128$	4.22989	0.373873
$129$	32.2660	2.84086
$130$	1.22042	0.107038
$131$	5.45429	0.476543	0.238272	−	0.971199i	$-0.423419\pi$
$131$	5.45429	0.476543	0.238272	+	0.971199i	$0.423419\pi$
$132$	−5.87067	−0.510976
$133$	3.73772	0.324101
$134$	−11.7406	−1.01423
$135$	−1.96893	−0.169459
$136$	0.931423	0.0798689
$137$	−20.8866	−1.78446	−0.892230	−	0.451581i	$-0.850860\pi$
$137$	−20.8866	−1.78446	−0.892230	+	0.451581i	$0.850860\pi$
$138$	−11.6795	−0.994226
$139$	−0.380071	−0.0322372	−0.0161186	−	0.999870i	$-0.505131\pi$
$139$	−0.380071	−0.0322372	−0.0161186	+	0.999870i	$0.505131\pi$
$140$	2.29068	0.193598
$141$	−28.4956	−2.39976
$142$	19.8781	1.66814
$143$	−0.591408	−0.0494560
$144$	−12.8372	−1.06977
$145$	−8.50037	−0.705917
$146$	2.06358	0.170783
$147$	−15.5221	−1.28024
$148$	−19.5425	−1.60638
$149$	2.17111	0.177864	0.0889322	−	0.996038i	$-0.471655\pi$
$149$	2.17111	0.177864	0.0889322	+	0.996038i	$0.471655\pi$
$150$	−5.36430	−0.437993
$151$	−17.8530	−1.45286	−0.726428	−	0.687242i	$-0.758821\pi$
$151$	−17.8530	−1.45286	−0.726428	+	0.687242i	$0.758821\pi$
$152$	1.96479	0.159366
$153$	−6.56386	−0.530657
$154$	−2.09310	−0.168667
$155$	2.16878	0.174200
$156$	3.47196	0.277979
$157$	4.68568	0.373958	0.186979	−	0.982364i	$-0.440130\pi$
$157$	4.68568	0.373958	0.186979	+	0.982364i	$0.440130\pi$
$158$	−12.4762	−0.992553
$159$	4.08870	0.324255
$160$	−8.11657	−0.641671
$161$	−2.20841	−0.174047
$162$	12.6994	0.997756
$163$	6.40150	0.501404	0.250702	−	0.968064i	$-0.419339\pi$
$163$	6.40150	0.501404	0.250702	+	0.968064i	$0.419339\pi$
$164$	−2.78334	−0.217343
$165$	2.59950	0.202371
$166$	18.5872	1.44265
$167$	4.68674	0.362671	0.181335	−	0.983421i	$-0.441958\pi$
$167$	4.68674	0.362671	0.181335	+	0.983421i	$0.441958\pi$
$168$	1.40584	0.108463
$169$	−12.6502	−0.973095
$170$	−3.60488	−0.276482
$171$	−13.8461	−1.05884
$172$	28.0318	2.13740
$173$	−4.98798	−0.379229	−0.189614	−	0.981859i	$-0.560724\pi$
$173$	−4.98798	−0.379229	−0.189614	+	0.981859i	$0.560724\pi$
$174$	−45.5985	−3.45681
$175$	−1.01430	−0.0766742
$176$	3.41648	0.257527
$177$	−17.8547	−1.34204
$178$	−6.63827	−0.497560
$179$	−16.6157	−1.24191	−0.620957	−	0.783845i	$-0.713256\pi$
$179$	−16.6157	−1.24191	−0.620957	+	0.783845i	$0.713256\pi$
$180$	−8.48569	−0.632486
$181$	−10.3377	−0.768399	−0.384199	−	0.923250i	$-0.625522\pi$
$181$	−10.3377	−0.768399	−0.384199	+	0.923250i	$0.625522\pi$
$182$	1.23788	0.0917576
$183$	−0.724123	−0.0535287
$184$	−1.16089	−0.0855817
$185$	8.65334	0.636206
$186$	11.6340	0.853043
$187$	1.74690	0.127746
$188$	−24.7562	−1.80553
$189$	−1.99710	−0.145267
$190$	−7.60432	−0.551675
$191$	5.83922	0.422511	0.211255	−	0.977431i	$-0.432245\pi$
$191$	5.83922	0.422511	0.211255	+	0.977431i	$0.432245\pi$
$192$	−25.7774	−1.86032
$193$	−20.4737	−1.47373	−0.736865	−	0.676039i	$-0.763695\pi$
$193$	−20.4737	−1.47373	−0.736865	+	0.676039i	$0.763695\pi$
$194$	−18.5581	−1.33240
$195$	−1.53737	−0.110093
$196$	−13.4852	−0.963228
$197$	−21.8668	−1.55794	−0.778971	−	0.627060i	$-0.784258\pi$
$197$	−21.8668	−1.55794	−0.778971	+	0.627060i	$0.784258\pi$
$198$	7.75376	0.551036
$199$	15.8455	1.12326	0.561630	−	0.827388i	$-0.310174\pi$
$199$	15.8455	1.12326	0.561630	+	0.827388i	$0.310174\pi$
$200$	−0.533185	−0.0377019
$201$	14.7896	1.04318
$202$	12.0925	0.850826
$203$	−8.62196	−0.605143
$204$	−10.2555	−0.718028
$205$	1.23245	0.0860782
$206$	11.9586	0.833192
$207$	8.18092	0.568614
$208$	−2.02054	−0.140099
$209$	3.68501	0.254897
$210$	−5.44103	−0.375467
$211$	18.7134	1.28828	0.644142	−	0.764906i	$-0.277215\pi$
$211$	18.7134	1.28828	0.644142	+	0.764906i	$0.277215\pi$
$212$	3.55215	0.243962
$213$	−25.0406	−1.71575
$214$	29.3845	2.00868
$215$	−12.4123	−0.846515
$216$	−1.04980	−0.0714302
$217$	2.19980	0.149332
$218$	−6.11554	−0.414196
$219$	−2.59950	−0.175658
$220$	2.25838	0.152260
$221$	−1.03313	−0.0694961
$222$	46.4191	3.11544
$223$	27.9281	1.87021	0.935103	−	0.354376i	$-0.115307\pi$
$223$	27.9281	1.87021	0.935103	+	0.354376i	$0.115307\pi$
$224$	−8.23267	−0.550069
$225$	3.75743	0.250495
$226$	18.0709	1.20206
$227$	−9.51027	−0.631219	−0.315609	−	0.948889i	$-0.602209\pi$
$227$	−9.51027	−0.631219	−0.315609	+	0.948889i	$0.602209\pi$
$228$	−21.6334	−1.43271
$229$	−3.21542	−0.212481	−0.106241	−	0.994340i	$-0.533881\pi$
$229$	−3.21542	−0.212481	−0.106241	+	0.994340i	$0.533881\pi$
$230$	4.49298	0.296258
$231$	2.63669	0.173481
$232$	−4.53227	−0.297558
$233$	−3.13672	−0.205493	−0.102747	−	0.994708i	$-0.532763\pi$
$233$	−3.13672	−0.205493	−0.102747	+	0.994708i	$0.532763\pi$
$234$	−4.58564	−0.299773
$235$	10.9619	0.715077
$236$	−15.5117	−1.00973
$237$	15.7163	1.02088
$238$	−3.65645	−0.237012
$239$	−8.96475	−0.579882	−0.289941	−	0.957045i	$-0.593636\pi$
$239$	−8.96475	−0.579882	−0.289941	+	0.957045i	$0.593636\pi$
$240$	8.88117	0.573277
$241$	20.4163	1.31513	0.657564	−	0.753399i	$-0.271587\pi$
$241$	20.4163	1.31513	0.657564	+	0.753399i	$0.271587\pi$
$242$	−2.06358	−0.132652
$243$	−21.9042	−1.40516
$244$	−0.629098	−0.0402739
$245$	5.97119	0.381485
$246$	6.61124	0.421517
$247$	−2.17934	−0.138668
$248$	1.15636	0.0734289
$249$	−23.4144	−1.48383
$250$	2.06358	0.130513
$251$	−21.8472	−1.37898	−0.689491	−	0.724295i	$-0.742166\pi$
$251$	−21.8472	−1.37898	−0.689491	+	0.724295i	$0.742166\pi$
$252$	−8.60707	−0.542194
$253$	−2.17727	−0.136884
$254$	1.92701	0.120912
$255$	4.54109	0.284374
$256$	11.1038	0.693987
$257$	24.3656	1.51988	0.759942	−	0.649990i	$-0.225227\pi$
$257$	24.3656	1.51988	0.759942	+	0.649990i	$0.225227\pi$
$258$	−66.5835	−4.14531
$259$	8.77711	0.545383
$260$	−1.33562	−0.0828318
$261$	31.9395	1.97701
$262$	−11.2554	−0.695360
$263$	−4.71621	−0.290814	−0.145407	−	0.989372i	$-0.546449\pi$
$263$	−4.71621	−0.290814	−0.145407	+	0.989372i	$0.546449\pi$
$264$	1.38602	0.0853035
$265$	−1.57287	−0.0966209
$266$	−7.71309	−0.472920
$267$	8.36226	0.511762
$268$	12.8488	0.784868
$269$	0.957420	0.0583750	0.0291875	−	0.999574i	$-0.490708\pi$
$269$	0.957420	0.0583750	0.0291875	+	0.999574i	$0.490708\pi$
$270$	4.06305	0.247270
$271$	11.8315	0.718714	0.359357	−	0.933200i	$-0.382996\pi$
$271$	11.8315	0.718714	0.359357	+	0.933200i	$0.382996\pi$
$272$	5.96827	0.361880
$273$	−1.55936	−0.0943767
$274$	43.1012	2.60384
$275$	−1.00000	−0.0603023
$276$	12.7820	0.769387
$277$	−1.12012	−0.0673017	−0.0336508	−	0.999434i	$-0.510713\pi$
$277$	−1.12012	−0.0673017	−0.0336508	+	0.999434i	$0.510713\pi$
$278$	0.784308	0.0470397
$279$	−8.14902	−0.487869
$280$	−0.540812	−0.0323197
$281$	4.92451	0.293772	0.146886	−	0.989153i	$-0.453075\pi$
$281$	4.92451	0.293772	0.146886	+	0.989153i	$0.453075\pi$
$282$	58.8030	3.50167
$283$	−2.19985	−0.130767	−0.0653837	−	0.997860i	$-0.520827\pi$
$283$	−2.19985	−0.130767	−0.0653837	+	0.997860i	$0.520827\pi$
$284$	−21.7545	−1.29089
$285$	9.57919	0.567422
$286$	1.22042	0.0721650
$287$	1.25008	0.0737900
$288$	30.4974	1.79708
$289$	−13.9483	−0.820490
$290$	17.5412	1.03006
$291$	23.3778	1.37043
$292$	−2.25838	−0.132162
$293$	−20.4562	−1.19506	−0.597531	−	0.801846i	$-0.703852\pi$
$293$	−20.4562	−1.19506	−0.597531	+	0.801846i	$0.703852\pi$
$294$	32.0312	1.86810
$295$	6.86851	0.399900
$296$	4.61383	0.268173
$297$	−1.96893	−0.114249
$298$	−4.48027	−0.259535
$299$	1.28765	0.0744670
$300$	5.87067	0.338943
$301$	−12.5899	−0.725670
$302$	36.8412	2.11997
$303$	−15.2330	−0.875112
$304$	12.5898	0.722072
$305$	0.278562	0.0159504
$306$	13.5451	0.774321
$307$	−3.82941	−0.218556	−0.109278	−	0.994011i	$-0.534854\pi$
$307$	−3.82941	−0.218556	−0.109278	+	0.994011i	$0.534854\pi$
$308$	2.29068	0.130524
$309$	−15.0642	−0.856975
$310$	−4.47545	−0.254189
$311$	22.3665	1.26829	0.634145	−	0.773214i	$-0.281352\pi$
$311$	22.3665	1.26829	0.634145	+	0.773214i	$0.281352\pi$
$312$	−0.819702	−0.0464065
$313$	−6.52651	−0.368900	−0.184450	−	0.982842i	$-0.559050\pi$
$313$	−6.52651	−0.368900	−0.184450	+	0.982842i	$0.559050\pi$
$314$	−9.66929	−0.545670
$315$	3.81117	0.214735
$316$	13.6539	0.768092
$317$	−32.9706	−1.85181	−0.925906	−	0.377754i	$-0.876696\pi$
$317$	−32.9706	−1.85181	−0.925906	+	0.377754i	$0.876696\pi$
$318$	−8.43737	−0.473144
$319$	−8.50037	−0.475929
$320$	9.91626	0.554336
$321$	−37.0157	−2.06602
$322$	4.55725	0.253965
$323$	6.43735	0.358184
$324$	−13.8981	−0.772118
$325$	0.591408	0.0328054
$326$	−13.2100	−0.731636
$327$	7.70377	0.426019
$328$	0.657125	0.0362837
$329$	11.1187	0.612995
$330$	−5.36430	−0.295295
$331$	3.89765	0.214234	0.107117	−	0.994246i	$-0.465838\pi$
$331$	3.89765	0.214234	0.107117	+	0.994246i	$0.465838\pi$
$332$	−20.3418	−1.11640
$333$	−32.5143	−1.78177
$334$	−9.67148	−0.529200
$335$	−5.68941	−0.310846
$336$	9.00821	0.491438
$337$	9.75879	0.531595	0.265798	−	0.964029i	$-0.414365\pi$
$337$	9.75879	0.531595	0.265798	+	0.964029i	$0.414365\pi$
$338$	26.1048	1.41992
$339$	−22.7639	−1.23637
$340$	3.94517	0.213957
$341$	2.16878	0.117446
$342$	28.5727	1.54503
$343$	13.1567	0.710397
$344$	−6.61808	−0.356823
$345$	−5.65982	−0.304714
$346$	10.2931	0.553361
$347$	10.6082	0.569480	0.284740	−	0.958605i	$-0.408093\pi$
$347$	10.6082	0.569480	0.284740	+	0.958605i	$0.408093\pi$
$348$	49.9028	2.67507
$349$	34.6640	1.85552	0.927761	−	0.373176i	$-0.121731\pi$
$349$	34.6640	1.85552	0.927761	+	0.373176i	$0.121731\pi$
$350$	2.09310	0.111881
$351$	1.16444	0.0621533
$352$	−8.11657	−0.432615
$353$	−16.6520	−0.886298	−0.443149	−	0.896448i	$-0.646139\pi$
$353$	−16.6520	−0.886298	−0.443149	+	0.896448i	$0.646139\pi$
$354$	36.8447	1.95827
$355$	9.63282	0.511257
$356$	7.26490	0.385039
$357$	4.60604	0.243778
$358$	34.2878	1.81217
$359$	9.44750	0.498620	0.249310	−	0.968424i	$-0.419796\pi$
$359$	9.44750	0.498620	0.249310	+	0.968424i	$0.419796\pi$
$360$	2.00340	0.105589
$361$	−5.42073	−0.285302
$362$	21.3328	1.12123
$363$	2.59950	0.136439
$364$	−1.35473	−0.0710071
$365$	1.00000	0.0523424
$366$	1.49429	0.0781077
$367$	−15.1901	−0.792917	−0.396458	−	0.918053i	$-0.629761\pi$
$367$	−15.1901	−0.792917	−0.396458	+	0.918053i	$0.629761\pi$
$368$	−7.43860	−0.387764
$369$	−4.63085	−0.241072
$370$	−17.8569	−0.928335
$371$	−1.59537	−0.0828277
$372$	−12.7322	−0.660132
$373$	−18.1519	−0.939870	−0.469935	−	0.882701i	$-0.655723\pi$
$373$	−18.1519	−0.939870	−0.469935	+	0.882701i	$0.655723\pi$
$374$	−3.60488	−0.186404
$375$	−2.59950	−0.134238
$376$	5.84473	0.301419
$377$	5.02719	0.258913
$378$	4.12117	0.211970
$379$	4.18695	0.215069	0.107535	−	0.994201i	$-0.465704\pi$
$379$	4.18695	0.215069	0.107535	+	0.994201i	$0.465704\pi$
$380$	8.32214	0.426917
$381$	−2.42747	−0.124363
$382$	−12.0497	−0.616517
$383$	24.8293	1.26872	0.634359	−	0.773038i	$-0.281264\pi$
$383$	24.8293	1.26872	0.634359	+	0.773038i	$0.281264\pi$
$384$	10.9956	0.561117
$385$	−1.01430	−0.0516937
$386$	42.2492	2.15043
$387$	46.6385	2.37077
$388$	20.3100	1.03108
$389$	14.7080	0.745725	0.372863	−	0.927887i	$-0.378376\pi$
$389$	14.7080	0.745725	0.372863	+	0.927887i	$0.378376\pi$
$390$	3.17249	0.160645
$391$	−3.80348	−0.192350
$392$	3.18375	0.160804
$393$	14.1785	0.715208
$394$	45.1239	2.27331
$395$	−6.04589	−0.304202
$396$	−8.48569	−0.426422
$397$	−1.87502	−0.0941047	−0.0470523	−	0.998892i	$-0.514983\pi$
$397$	−1.87502	−0.0941047	−0.0470523	+	0.998892i	$0.514983\pi$
$398$	−32.6986	−1.63903
$399$	9.71621	0.486419
$400$	−3.41648	−0.170824
$401$	−4.72693	−0.236052	−0.118026	−	0.993011i	$-0.537657\pi$
$401$	−4.72693	−0.236052	−0.118026	+	0.993011i	$0.537657\pi$
$402$	−30.5197	−1.52218
$403$	−1.28263	−0.0638925
$404$	−13.2340	−0.658416
$405$	6.15403	0.305796
$406$	17.7921	0.883009
$407$	8.65334	0.428930
$408$	2.42124	0.119869
$409$	−8.98089	−0.444077	−0.222038	−	0.975038i	$-0.571271\pi$
$409$	−8.98089	−0.444077	−0.222038	+	0.975038i	$0.571271\pi$
$410$	−2.54327	−0.125603
$411$	−54.2947	−2.67816
$412$	−13.0874	−0.644770
$413$	6.96676	0.342812
$414$	−16.8820	−0.829706
$415$	9.00725	0.442149
$416$	4.80021	0.235349
$417$	−0.987996	−0.0483824
$418$	−7.60432	−0.371939
$419$	−36.2922	−1.77299	−0.886496	−	0.462737i	$-0.846867\pi$
$419$	−36.2922	−1.77299	−0.886496	+	0.462737i	$0.846867\pi$
$420$	5.95464	0.290557
$421$	15.6733	0.763869	0.381934	−	0.924189i	$-0.375258\pi$
$421$	15.6733	0.763869	0.381934	+	0.924189i	$0.375258\pi$
$422$	−38.6167	−1.87983
$423$	−41.1886	−2.00266
$424$	−0.838633	−0.0407276
$425$	−1.74690	−0.0847373
$426$	51.6733	2.50358
$427$	0.282546	0.0136734
$428$	−32.1582	−1.55443
$429$	−1.53737	−0.0742248
$430$	25.6139	1.23521
$431$	2.62390	0.126389	0.0631943	−	0.998001i	$-0.479871\pi$
$431$	2.62390	0.126389	0.0631943	+	0.998001i	$0.479871\pi$
$432$	−6.72682	−0.323644
$433$	−20.6523	−0.992485	−0.496243	−	0.868184i	$-0.665287\pi$
$433$	−20.6523	−0.992485	−0.496243	+	0.868184i	$0.665287\pi$
$434$	−4.53947	−0.217902
$435$	−22.0968	−1.05946
$436$	6.69282	0.320528
$437$	−8.02325	−0.383804
$438$	5.36430	0.256316
$439$	−25.3568	−1.21021	−0.605107	−	0.796144i	$-0.706870\pi$
$439$	−25.3568	−1.21021	−0.605107	+	0.796144i	$0.706870\pi$
$440$	−0.533185	−0.0254186
$441$	−22.4363	−1.06839
$442$	2.13196	0.101407
$443$	−20.5390	−0.975839	−0.487920	−	0.872889i	$-0.662244\pi$
$443$	−20.5390	−0.975839	−0.487920	+	0.872889i	$0.662244\pi$
$444$	−50.8008	−2.41090
$445$	−3.21687	−0.152494
$446$	−57.6320	−2.72896
$447$	5.64381	0.266943
$448$	10.0581	0.475201
$449$	36.7320	1.73349	0.866744	−	0.498753i	$-0.166208\pi$
$449$	36.7320	1.73349	0.866744	+	0.498753i	$0.166208\pi$
$450$	−7.75376	−0.365516
$451$	1.23245	0.0580339
$452$	−19.7767	−0.930216
$453$	−46.4090	−2.18048
$454$	19.6252	0.921058
$455$	0.599868	0.0281222
$456$	5.10748	0.239180
$457$	−20.2635	−0.947885	−0.473943	−	0.880556i	$-0.657170\pi$
$457$	−20.2635	−0.947885	−0.473943	+	0.880556i	$0.657170\pi$
$458$	6.63529	0.310047
$459$	−3.43953	−0.160544
$460$	−4.91710	−0.229261
$461$	−6.52931	−0.304100	−0.152050	−	0.988373i	$-0.548588\pi$
$461$	−6.52931	−0.304100	−0.152050	+	0.988373i	$0.548588\pi$
$462$	−5.44103	−0.253140
$463$	−8.61104	−0.400189	−0.200094	−	0.979777i	$-0.564125\pi$
$463$	−8.61104	−0.400189	−0.200094	+	0.979777i	$0.564125\pi$
$464$	−29.0414	−1.34821
$465$	5.63775	0.261444
$466$	6.47289	0.299851
$467$	−7.39862	−0.342367	−0.171184	−	0.985239i	$-0.554759\pi$
$467$	−7.39862	−0.342367	−0.171184	+	0.985239i	$0.554759\pi$
$468$	5.01850	0.231980
$469$	−5.77079	−0.266470
$470$	−22.6208	−1.04342
$471$	12.1804	0.561245
$472$	3.66219	0.168566
$473$	−12.4123	−0.570720
$474$	−32.4319	−1.48965
$475$	−3.68501	−0.169080
$476$	4.00160	0.183413
$477$	5.90996	0.270598
$478$	18.4995	0.846148
$479$	29.9809	1.36986	0.684932	−	0.728607i	$-0.259832\pi$
$479$	29.9809	1.36986	0.684932	+	0.728607i	$0.259832\pi$
$480$	−21.0991	−0.963036
$481$	−5.11765	−0.233345
$482$	−42.1307	−1.91900
$483$	−5.74078	−0.261215
$484$	2.25838	0.102654
$485$	−8.99316	−0.408359
$486$	45.2012	2.05037
$487$	14.4603	0.655261	0.327630	−	0.944806i	$-0.393750\pi$
$487$	14.4603	0.655261	0.327630	+	0.944806i	$0.393750\pi$
$488$	0.148525	0.00672341
$489$	16.6407	0.752520
$490$	−12.3220	−0.556653
$491$	26.5702	1.19910	0.599548	−	0.800339i	$-0.295347\pi$
$491$	26.5702	1.19910	0.599548	+	0.800339i	$0.295347\pi$
$492$	−7.23532	−0.326193
$493$	−14.8493	−0.668780
$494$	4.49726	0.202341
$495$	3.75743	0.168884
$496$	7.40959	0.332701
$497$	9.77061	0.438272
$498$	48.3176	2.16516
$499$	−24.9178	−1.11547	−0.557736	−	0.830018i	$-0.688330\pi$
$499$	−24.9178	−1.11547	−0.557736	+	0.830018i	$0.688330\pi$
$500$	−2.25838	−0.100998
$501$	12.1832	0.544305
$502$	45.0835	2.01217
$503$	−4.38368	−0.195459	−0.0977293	−	0.995213i	$-0.531158\pi$
$503$	−4.38368	−0.195459	−0.0977293	+	0.995213i	$0.531158\pi$
$504$	2.03206	0.0905152
$505$	5.85995	0.260765
$506$	4.49298	0.199737
$507$	−32.8844	−1.46045
$508$	−2.10892	−0.0935680
$509$	−9.19837	−0.407710	−0.203855	−	0.979001i	$-0.565347\pi$
$509$	−9.19837	−0.407710	−0.203855	+	0.979001i	$0.565347\pi$
$510$	−9.37091	−0.414951
$511$	1.01430	0.0448702
$512$	−31.3734	−1.38652
$513$	−7.25552	−0.320339
$514$	−50.2805	−2.21778
$515$	5.79504	0.255360
$516$	72.8687	3.20787
$517$	10.9619	0.482105
$518$	−18.1123	−0.795809
$519$	−12.9663	−0.569156
$520$	0.315330	0.0138281
$521$	21.8486	0.957203	0.478601	−	0.878032i	$-0.341144\pi$
$521$	21.8486	0.957203	0.478601	+	0.878032i	$0.341144\pi$
$522$	−65.9098	−2.88480
$523$	−32.3460	−1.41439	−0.707196	−	0.707017i	$-0.750040\pi$
$523$	−32.3460	−1.41439	−0.707196	+	0.707017i	$0.750040\pi$
$524$	12.3178	0.538108
$525$	−2.63669	−0.115075
$526$	9.73229	0.424348
$527$	3.78865	0.165036
$528$	8.88117	0.386503
$529$	−18.2595	−0.793891
$530$	3.24576	0.140987
$531$	−25.8079	−1.11997
$532$	8.44118	0.365972
$533$	−0.728883	−0.0315714
$534$	−17.2562	−0.746750
$535$	14.2395	0.615628
$536$	−3.03351	−0.131028
$537$	−43.1925	−1.86389
$538$	−1.97572	−0.0851792
$539$	5.97119	0.257197
$540$	−4.44659	−0.191351
$541$	17.0230	0.731878	0.365939	−	0.930639i	$-0.380748\pi$
$541$	17.0230	0.731878	0.365939	+	0.930639i	$0.380748\pi$
$542$	−24.4154	−1.04873
$543$	−26.8730	−1.15323
$544$	−14.1789	−0.607914
$545$	−2.96355	−0.126945
$546$	3.21787	0.137712
$547$	11.1176	0.475356	0.237678	−	0.971344i	$-0.423614\pi$
$547$	11.1176	0.475356	0.237678	+	0.971344i	$0.423614\pi$
$548$	−47.1698	−2.01499
$549$	−1.04668	−0.0446710
$550$	2.06358	0.0879915
$551$	−31.3239	−1.33444
$552$	−3.01773	−0.128443
$553$	−6.13237	−0.260775
$554$	2.31147	0.0982049
$555$	22.4944	0.954834
$556$	−0.858343	−0.0364019
$557$	−12.0301	−0.509732	−0.254866	−	0.966976i	$-0.582031\pi$
$557$	−12.0301	−0.509732	−0.254866	+	0.966976i	$0.582031\pi$
$558$	16.8162	0.711886
$559$	7.34076	0.310481
$560$	−3.46535	−0.146438
$561$	4.54109	0.191725
$562$	−10.1621	−0.428664
$563$	−15.5272	−0.654395	−0.327198	−	0.944956i	$-0.606104\pi$
$563$	−15.5272	−0.654395	−0.327198	+	0.944956i	$0.606104\pi$
$564$	−64.3537	−2.70978
$565$	8.75702	0.368411
$566$	4.53957	0.190812
$567$	6.24206	0.262142
$568$	5.13608	0.215505
$569$	−40.5772	−1.70108	−0.850541	−	0.525908i	$-0.823726\pi$
$569$	−40.5772	−1.70108	−0.850541	+	0.525908i	$0.823726\pi$
$570$	−19.7675	−0.827968
$571$	26.7939	1.12129	0.560644	−	0.828057i	$-0.310553\pi$
$571$	26.7939	1.12129	0.560644	+	0.828057i	$0.310553\pi$
$572$	−1.33562	−0.0558452
$573$	15.1791	0.634115
$574$	−2.57965	−0.107672
$575$	2.17727	0.0907984
$576$	−37.2596	−1.55248
$577$	35.3833	1.47303	0.736513	−	0.676423i	$-0.236471\pi$
$577$	35.3833	1.47303	0.736513	+	0.676423i	$0.236471\pi$
$578$	28.7835	1.19724
$579$	−53.2215	−2.21181
$580$	−19.1971	−0.797114
$581$	9.13609	0.379029
$582$	−48.2420	−1.99969
$583$	−1.57287	−0.0651418
$584$	0.533185	0.0220634
$585$	−2.22217	−0.0918755
$586$	42.2130	1.74380
$587$	−26.1622	−1.07983	−0.539915	−	0.841719i	$-0.681544\pi$
$587$	−26.1622	−1.07983	−0.539915	+	0.841719i	$0.681544\pi$
$588$	−35.0548	−1.44564
$589$	7.99196	0.329303
$590$	−14.1737	−0.583524
$591$	−56.8428	−2.33820
$592$	29.5640	1.21507
$593$	26.8080	1.10087	0.550436	−	0.834877i	$-0.314461\pi$
$593$	26.8080	1.10087	0.550436	+	0.834877i	$0.314461\pi$
$594$	4.06305	0.166709
$595$	−1.77189	−0.0726405
$596$	4.90319	0.200843
$597$	41.1906	1.68582
$598$	−2.65718	−0.108660
$599$	−9.92184	−0.405395	−0.202698	−	0.979241i	$-0.564971\pi$
$599$	−9.92184	−0.405395	−0.202698	+	0.979241i	$0.564971\pi$
$600$	−1.38602	−0.0565839
$601$	−37.7850	−1.54128	−0.770641	−	0.637270i	$-0.780064\pi$
$601$	−37.7850	−1.54128	−0.770641	+	0.637270i	$0.780064\pi$
$602$	25.9803	1.05888
$603$	21.3775	0.870560
$604$	−40.3188	−1.64055
$605$	−1.00000	−0.0406558
$606$	31.4345	1.27694
$607$	−34.7162	−1.40909	−0.704544	−	0.709660i	$-0.748849\pi$
$607$	−34.7162	−1.40909	−0.704544	+	0.709660i	$0.748849\pi$
$608$	−29.9096	−1.21300
$609$	−22.4128	−0.908214
$610$	−0.574836	−0.0232744
$611$	−6.48297	−0.262273
$612$	−14.8237	−0.599212
$613$	15.4623	0.624516	0.312258	−	0.949997i	$-0.398915\pi$
$613$	15.4623	0.624516	0.312258	+	0.949997i	$0.398915\pi$
$614$	7.90231	0.318911
$615$	3.20377	0.129188
$616$	−0.540812	−0.0217899
$617$	−32.2819	−1.29962	−0.649811	−	0.760096i	$-0.725152\pi$
$617$	−32.2819	−1.29962	−0.649811	+	0.760096i	$0.725152\pi$
$618$	31.0863	1.25048
$619$	−31.2889	−1.25761	−0.628805	−	0.777563i	$-0.716455\pi$
$619$	−31.2889	−1.25761	−0.628805	+	0.777563i	$0.716455\pi$
$620$	4.89792	0.196705
$621$	4.28689	0.172027
$622$	−46.1552	−1.85066
$623$	−3.26288	−0.130725
$624$	−5.25239	−0.210264
$625$	1.00000	0.0400000
$626$	13.4680	0.538289
$627$	9.57919	0.382556
$628$	10.5820	0.422269
$629$	15.1165	0.602736
$630$	−7.86467	−0.313336
$631$	4.55677	0.181402	0.0907010	−	0.995878i	$-0.471089\pi$
$631$	4.55677	0.181402	0.0907010	+	0.995878i	$0.471089\pi$
$632$	−3.22358	−0.128227
$633$	48.6456	1.93349
$634$	68.0375	2.70212
$635$	0.933819	0.0370575
$636$	9.23382	0.366145
$637$	−3.53141	−0.139919
$638$	17.5412	0.694464
$639$	−36.1946	−1.43184
$640$	−4.22989	−0.167201
$641$	49.1794	1.94247	0.971234	−	0.238127i	$-0.0765334\pi$
$641$	49.1794	1.94247	0.971234	+	0.238127i	$0.0765334\pi$
$642$	76.3850	3.01468
$643$	−21.5406	−0.849479	−0.424739	−	0.905316i	$-0.639634\pi$
$643$	−21.5406	−0.849479	−0.424739	+	0.905316i	$0.639634\pi$
$644$	−4.98743	−0.196532
$645$	−32.2660	−1.27047
$646$	−13.2840	−0.522653
$647$	27.4887	1.08069	0.540346	−	0.841443i	$-0.318293\pi$
$647$	27.4887	1.08069	0.540346	+	0.841443i	$0.318293\pi$
$648$	3.28124	0.128899
$649$	6.86851	0.269613
$650$	−1.22042	−0.0478688
$651$	5.71839	0.224121
$652$	14.4570	0.566180
$653$	2.69055	0.105289	0.0526446	−	0.998613i	$-0.483235\pi$
$653$	2.69055	0.105289	0.0526446	+	0.998613i	$0.483235\pi$
$654$	−15.8974	−0.621636
$655$	−5.45429	−0.213117
$656$	4.21066	0.164398
$657$	−3.75743	−0.146591
$658$	−22.9444	−0.894466
$659$	11.4604	0.446433	0.223216	−	0.974769i	$-0.428344\pi$
$659$	11.4604	0.446433	0.223216	+	0.974769i	$0.428344\pi$
$660$	5.87067	0.228515
$661$	−28.1541	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$661$	−28.1541	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$662$	−8.04314	−0.312605
$663$	−2.68563	−0.104301
$664$	4.80253	0.186374
$665$	−3.73772	−0.144942
$666$	67.0959	2.59991
$667$	18.5076	0.716617
$668$	10.5844	0.409524
$669$	72.5993	2.80685
$670$	11.7406	0.453578
$671$	0.278562	0.0107538
$672$	−21.4009	−0.825557
$673$	34.1595	1.31675	0.658376	−	0.752689i	$-0.271244\pi$
$673$	34.1595	1.31675	0.658376	+	0.752689i	$0.271244\pi$
$674$	−20.1381	−0.775690
$675$	1.96893	0.0757842
$676$	−28.5690	−1.09881
$677$	−27.0278	−1.03876	−0.519381	−	0.854543i	$-0.673837\pi$
$677$	−27.0278	−1.03876	−0.519381	+	0.854543i	$0.673837\pi$
$678$	46.9753	1.80407
$679$	−9.12180	−0.350063
$680$	−0.931423	−0.0357184
$681$	−24.7220	−0.947349
$682$	−4.47545	−0.171374
$683$	−21.3331	−0.816287	−0.408144	−	0.912918i	$-0.633824\pi$
$683$	−21.3331	−0.816287	−0.408144	+	0.912918i	$0.633824\pi$
$684$	−31.2698	−1.19563
$685$	20.8866	0.798035
$686$	−27.1500	−1.03659
$687$	−8.35851	−0.318897
$688$	−42.4066	−1.61674
$689$	0.930211	0.0354382
$690$	11.6795	0.444632
$691$	48.6239	1.84974	0.924870	−	0.380285i	$-0.124174\pi$
$691$	48.6239	1.84974	0.924870	+	0.380285i	$0.124174\pi$
$692$	−11.2647	−0.428221
$693$	3.81117	0.144774
$694$	−21.8910	−0.830970
$695$	0.380071	0.0144169
$696$	−11.7817	−0.446583
$697$	2.15298	0.0815498
$698$	−71.5321	−2.70753
$699$	−8.15392	−0.308410
$700$	−2.29068	−0.0865797
$701$	11.6161	0.438733	0.219366	−	0.975643i	$-0.429601\pi$
$701$	11.6161	0.438733	0.219366	+	0.975643i	$0.429601\pi$
$702$	−2.40292	−0.0906925
$703$	31.8876	1.20266
$704$	9.91626	0.373733
$705$	28.4956	1.07320
$706$	34.3628	1.29326
$707$	5.94378	0.223539
$708$	−40.3227	−1.51542
$709$	15.6876	0.589162	0.294581	−	0.955627i	$-0.404820\pi$
$709$	15.6876	0.589162	0.294581	+	0.955627i	$0.404820\pi$
$710$	−19.8781	−0.746013
$711$	22.7170	0.851953
$712$	−1.71518	−0.0642793
$713$	−4.72201	−0.176841
$714$	−9.50495	−0.355714
$715$	0.591408	0.0221174
$716$	−37.5245	−1.40236
$717$	−23.3039	−0.870301
$718$	−19.4957	−0.727573
$719$	51.0977	1.90562	0.952812	−	0.303561i	$-0.0981756\pi$
$719$	51.0977	1.90562	0.952812	+	0.303561i	$0.0981756\pi$
$720$	12.8372	0.478414
$721$	5.87794	0.218906
$722$	11.1861	0.416305
$723$	53.0722	1.97378
$724$	−23.3465	−0.867668
$725$	8.50037	0.315696
$726$	−5.36430	−0.199088
$727$	23.9440	0.888033	0.444016	−	0.896019i	$-0.353553\pi$
$727$	23.9440	0.888033	0.444016	+	0.896019i	$0.353553\pi$
$728$	0.319841	0.0118541
$729$	−38.4780	−1.42511
$730$	−2.06358	−0.0763767
$731$	−21.6832	−0.801981
$732$	−1.63534	−0.0604440
$733$	−18.8554	−0.696441	−0.348220	−	0.937413i	$-0.613214\pi$
$733$	−18.8554	−0.696441	−0.348220	+	0.937413i	$0.613214\pi$
$734$	31.3461	1.15700
$735$	15.5221	0.572542
$736$	17.6720	0.651397
$737$	−5.68941	−0.209572
$738$	9.55615	0.351767
$739$	22.8075	0.838987	0.419494	−	0.907758i	$-0.362208\pi$
$739$	22.8075	0.838987	0.419494	+	0.907758i	$0.362208\pi$
$740$	19.5425	0.718397
$741$	−5.66521	−0.208117
$742$	3.29219	0.120860
$743$	−14.5136	−0.532453	−0.266226	−	0.963911i	$-0.585777\pi$
$743$	−14.5136	−0.532453	−0.266226	+	0.963911i	$0.585777\pi$
$744$	3.00596	0.110204
$745$	−2.17111	−0.0795434
$746$	37.4580	1.37143
$747$	−33.8441	−1.23829
$748$	3.94517	0.144250
$749$	14.4432	0.527743
$750$	5.36430	0.195876
$751$	−1.75345	−0.0639843	−0.0319921	−	0.999488i	$-0.510185\pi$
$751$	−1.75345	−0.0639843	−0.0319921	+	0.999488i	$0.510185\pi$
$752$	37.4512	1.36571
$753$	−56.7918	−2.06961
$754$	−10.3740	−0.377800
$755$	17.8530	0.649737
$756$	−4.51020	−0.164034
$757$	−19.9238	−0.724143	−0.362071	−	0.932150i	$-0.617930\pi$
$757$	−19.9238	−0.724143	−0.362071	+	0.932150i	$0.617930\pi$
$758$	−8.64013	−0.313824
$759$	−5.65982	−0.205438
$760$	−1.96479	−0.0712704
$761$	−10.9716	−0.397722	−0.198861	−	0.980028i	$-0.563724\pi$
$761$	−10.9716	−0.397722	−0.198861	+	0.980028i	$0.563724\pi$
$762$	5.00928	0.181467
$763$	−3.00594	−0.108822
$764$	13.1872	0.477095
$765$	6.56386	0.237317
$766$	−51.2374	−1.85128
$767$	−4.06209	−0.146674
$768$	28.8644	1.04155
$769$	22.6433	0.816537	0.408268	−	0.912862i	$-0.366133\pi$
$769$	22.6433	0.816537	0.408268	+	0.912862i	$0.366133\pi$
$770$	2.09310	0.0754302
$771$	63.3385	2.28108
$772$	−46.2374	−1.66412
$773$	−29.3699	−1.05636	−0.528181	−	0.849132i	$-0.677126\pi$
$773$	−29.3699	−1.05636	−0.528181	+	0.849132i	$0.677126\pi$
$774$	−96.2424	−3.45936
$775$	−2.16878	−0.0779048
$776$	−4.79502	−0.172131
$777$	22.8162	0.818525
$778$	−30.3512	−1.08814
$779$	4.54160	0.162720
$780$	−3.47196	−0.124316
$781$	9.63282	0.344689
$782$	7.84880	0.280672
$783$	16.7366	0.598119
$784$	20.4005	0.728588
$785$	−4.68568	−0.167239
$786$	−29.2584	−1.04361
$787$	−7.84090	−0.279498	−0.139749	−	0.990187i	$-0.544630\pi$
$787$	−7.84090	−0.279498	−0.139749	+	0.990187i	$0.544630\pi$
$788$	−49.3834	−1.75921
$789$	−12.2598	−0.436461
$790$	12.4762	0.443883
$791$	8.88229	0.315818
$792$	2.00340	0.0711878
$793$	−0.164744	−0.00585022
$794$	3.86927	0.137315
$795$	−4.08870	−0.145011
$796$	35.7852	1.26837
$797$	17.7890	0.630117	0.315059	−	0.949072i	$-0.397976\pi$
$797$	17.7890	0.630117	0.315059	+	0.949072i	$0.397976\pi$
$798$	−20.0502	−0.709770
$799$	19.1494	0.677458
$800$	8.11657	0.286964
$801$	12.0871	0.427078
$802$	9.75442	0.344441
$803$	1.00000	0.0352892
$804$	33.4006	1.17795
$805$	2.20841	0.0778363
$806$	2.64682	0.0932302
$807$	2.48882	0.0876106
$808$	3.12444	0.109917
$809$	−17.3374	−0.609551	−0.304775	−	0.952424i	$-0.598581\pi$
$809$	−17.3374	−0.609551	−0.304775	+	0.952424i	$0.598581\pi$
$810$	−12.6994	−0.446210
$811$	5.86356	0.205897	0.102949	−	0.994687i	$-0.467172\pi$
$811$	5.86356	0.205897	0.102949	+	0.994687i	$0.467172\pi$
$812$	−19.4716	−0.683321
$813$	30.7561	1.07866
$814$	−17.8569	−0.625883
$815$	−6.40150	−0.224235
$816$	15.5145	0.543118
$817$	−45.7396	−1.60022
$818$	18.5328	0.647985
$819$	−2.25396	−0.0787597
$820$	2.78334	0.0971986
$821$	35.5607	1.24108	0.620538	−	0.784177i	$-0.286914\pi$
$821$	35.5607	1.24108	0.620538	+	0.784177i	$0.286914\pi$
$822$	112.042	3.90790
$823$	13.3646	0.465859	0.232930	−	0.972494i	$-0.425169\pi$
$823$	13.3646	0.465859	0.232930	+	0.972494i	$0.425169\pi$
$824$	3.08983	0.107639
$825$	−2.59950	−0.0905031
$826$	−14.3765	−0.500222
$827$	33.5427	1.16639	0.583196	−	0.812331i	$-0.301802\pi$
$827$	33.5427	1.16639	0.583196	+	0.812331i	$0.301802\pi$
$828$	18.4756	0.642072
$829$	43.2808	1.50320	0.751602	−	0.659617i	$-0.229282\pi$
$829$	43.2808	1.50320	0.751602	+	0.659617i	$0.229282\pi$
$830$	−18.5872	−0.645172
$831$	−2.91177	−0.101008
$832$	−5.86456	−0.203317
$833$	10.4311	0.361416
$834$	2.03881	0.0705983
$835$	−4.68674	−0.162191
$836$	8.32214	0.287827
$837$	−4.27017	−0.147599
$838$	74.8921	2.58710
$839$	52.4398	1.81042	0.905212	−	0.424961i	$-0.139712\pi$
$839$	52.4398	1.81042	0.905212	+	0.424961i	$0.139712\pi$
$840$	−1.40584	−0.0485062
$841$	43.2563	1.49160
$842$	−32.3431	−1.11462
$843$	12.8013	0.440900
$844$	42.2620	1.45472
$845$	12.6502	0.435181
$846$	84.9961	2.92223
$847$	−1.01430	−0.0348519
$848$	−5.37370	−0.184534
$849$	−5.71852	−0.196259
$850$	3.60488	0.123646
$851$	−18.8406	−0.645849
$852$	−56.5511	−1.93741
$853$	−40.7768	−1.39617	−0.698086	−	0.716014i	$-0.745965\pi$
$853$	−40.7768	−1.39617	−0.698086	+	0.716014i	$0.745965\pi$
$854$	−0.583058	−0.0199518
$855$	13.8461	0.473528
$856$	7.59230	0.259500
$857$	−32.6309	−1.11465	−0.557325	−	0.830295i	$-0.688172\pi$
$857$	−32.6309	−1.11465	−0.557325	+	0.830295i	$0.688172\pi$
$858$	3.17249	0.108307
$859$	−46.4603	−1.58520	−0.792602	−	0.609739i	$-0.791274\pi$
$859$	−46.4603	−1.58520	−0.792602	+	0.609739i	$0.791274\pi$
$860$	−28.0318	−0.955875
$861$	3.24959	0.110746
$862$	−5.41463	−0.184423
$863$	−21.3662	−0.727313	−0.363657	−	0.931533i	$-0.618472\pi$
$863$	−21.3662	−0.727313	−0.363657	+	0.931533i	$0.618472\pi$
$864$	15.9810	0.543684
$865$	4.98798	0.169596
$866$	42.6177	1.44821
$867$	−36.2587	−1.23141
$868$	4.96798	0.168624
$869$	−6.04589	−0.205093
$870$	45.5985	1.54593
$871$	3.36476	0.114011
$872$	−1.58012	−0.0535097
$873$	33.7911	1.14366
$874$	16.5566	0.560037
$875$	1.01430	0.0342897
$876$	−5.87067	−0.198351
$877$	−5.53022	−0.186742	−0.0933712	−	0.995631i	$-0.529764\pi$
$877$	−5.53022	−0.186742	−0.0933712	+	0.995631i	$0.529764\pi$
$878$	52.3259	1.76591
$879$	−53.1759	−1.79358
$880$	−3.41648	−0.115170
$881$	−24.8015	−0.835584	−0.417792	−	0.908543i	$-0.637196\pi$
$881$	−24.8015	−0.835584	−0.417792	+	0.908543i	$0.637196\pi$
$882$	46.2992	1.55897
$883$	32.9734	1.10964	0.554821	−	0.831970i	$-0.312787\pi$
$883$	32.9734	1.10964	0.554821	+	0.831970i	$0.312787\pi$
$884$	−2.33321	−0.0784742
$885$	17.8547	0.600180
$886$	42.3840	1.42392
$887$	−39.7906	−1.33604	−0.668018	−	0.744145i	$-0.732857\pi$
$887$	−39.7906	−1.33604	−0.668018	+	0.744145i	$0.732857\pi$
$888$	11.9937	0.402481
$889$	0.947176	0.0317673
$890$	6.63827	0.222515
$891$	6.15403	0.206168
$892$	63.0723	2.11182
$893$	40.3947	1.35176
$894$	−11.6465	−0.389517
$895$	16.6157	0.555401
$896$	−4.29039	−0.143332
$897$	3.34726	0.111762
$898$	−75.7995	−2.52946
$899$	−18.4354	−0.614855
$900$	8.48569	0.282856
$901$	−2.74766	−0.0915379
$902$	−2.54327	−0.0846816
$903$	−32.7275	−1.08910
$904$	4.66911	0.155292
$905$	10.3377	0.343638
$906$	95.7688	3.18171
$907$	−2.20221	−0.0731231	−0.0365615	−	0.999331i	$-0.511640\pi$
$907$	−2.20221	−0.0731231	−0.0365615	+	0.999331i	$0.511640\pi$
$908$	−21.4778	−0.712766
$909$	−22.0183	−0.730302
$910$	−1.23788	−0.0410352
$911$	−46.6391	−1.54522	−0.772612	−	0.634879i	$-0.781050\pi$
$911$	−46.6391	−1.54522	−0.772612	+	0.634879i	$0.781050\pi$
$912$	32.7272	1.08370
$913$	9.00725	0.298097
$914$	41.8154	1.38313
$915$	0.724123	0.0239388
$916$	−7.26164	−0.239931
$917$	−5.53231	−0.182693
$918$	7.09777	0.234261
$919$	9.29923	0.306753	0.153377	−	0.988168i	$-0.450985\pi$
$919$	9.29923	0.306753	0.153377	+	0.988168i	$0.450985\pi$
$920$	1.16089	0.0382733
$921$	−9.95457	−0.328014
$922$	13.4738	0.443735
$923$	−5.69693	−0.187517
$924$	5.95464	0.195893
$925$	−8.65334	−0.284520
$926$	17.7696	0.583945
$927$	−21.7744	−0.715167
$928$	68.9939	2.26483
$929$	17.2704	0.566622	0.283311	−	0.959028i	$-0.408567\pi$
$929$	17.2704	0.566622	0.283311	+	0.959028i	$0.408567\pi$
$930$	−11.6340	−0.381493
$931$	22.0039	0.721147
$932$	−7.08390	−0.232041
$933$	58.1419	1.90348
$934$	15.2677	0.499573
$935$	−1.74690	−0.0571299
$936$	−1.18483	−0.0387273
$937$	−5.29388	−0.172943	−0.0864717	−	0.996254i	$-0.527559\pi$
$937$	−5.29388	−0.172943	−0.0864717	+	0.996254i	$0.527559\pi$
$938$	11.9085	0.388827
$939$	−16.9657	−0.553654
$940$	24.7562	0.807457
$941$	22.7071	0.740229	0.370114	−	0.928986i	$-0.379318\pi$
$941$	22.7071	0.740229	0.370114	+	0.928986i	$0.379318\pi$
$942$	−25.1354	−0.818955
$943$	−2.68338	−0.0873829
$944$	23.4662	0.763758
$945$	1.99710	0.0649655
$946$	25.6139	0.832780
$947$	−11.3735	−0.369590	−0.184795	−	0.982777i	$-0.559162\pi$
$947$	−11.3735	−0.369590	−0.184795	+	0.982777i	$0.559162\pi$
$948$	35.4934	1.15277
$949$	−0.591408	−0.0191979
$950$	7.60432	0.246717
$951$	−85.7072	−2.77925
$952$	−0.944746	−0.0306194
$953$	37.2098	1.20534	0.602672	−	0.797989i	$-0.294103\pi$
$953$	37.2098	1.20534	0.602672	+	0.797989i	$0.294103\pi$
$954$	−12.1957	−0.394850
$955$	−5.83922	−0.188953
$956$	−20.2458	−0.654796
$957$	−22.0968	−0.714287
$958$	−61.8682	−1.99887
$959$	21.1853	0.684110
$960$	25.7774	0.831961
$961$	−26.2964	−0.848271
$962$	10.5607	0.340491
$963$	−53.5040	−1.72414
$964$	46.1077	1.48503
$965$	20.4737	0.659073
$966$	11.8466	0.381157
$967$	−8.22289	−0.264430	−0.132215	−	0.991221i	$-0.542209\pi$
$967$	−8.22289	−0.264430	−0.132215	+	0.991221i	$0.542209\pi$
$968$	−0.533185	−0.0171372
$969$	16.7339	0.537571
$970$	18.5581	0.595866
$971$	−22.6311	−0.726267	−0.363133	−	0.931737i	$-0.618293\pi$
$971$	−22.6311	−0.726267	−0.363133	+	0.931737i	$0.618293\pi$
$972$	−49.4680	−1.58669
$973$	0.385507	0.0123588
$974$	−29.8401	−0.956140
$975$	1.53737	0.0492352
$976$	0.951702	0.0304632
$977$	−11.4149	−0.365194	−0.182597	−	0.983188i	$-0.558450\pi$
$977$	−11.4149	−0.365194	−0.182597	+	0.983188i	$0.558450\pi$
$978$	−34.3395	−1.09806
$979$	−3.21687	−0.102811
$980$	13.4852	0.430769
$981$	11.1353	0.355524
$982$	−54.8298	−1.74969
$983$	40.1280	1.27988	0.639942	−	0.768424i	$-0.278959\pi$
$983$	40.1280	1.27988	0.639942	+	0.768424i	$0.278959\pi$
$984$	1.70820	0.0544555
$985$	21.8668	0.696733
$986$	30.6428	0.975867
$987$	28.9032	0.919998
$988$	−4.92178	−0.156583
$989$	27.0250	0.859345
$990$	−7.75376	−0.246431
$991$	6.91127	0.219544	0.109772	−	0.993957i	$-0.464988\pi$
$991$	6.91127	0.219544	0.109772	+	0.993957i	$0.464988\pi$
$992$	−17.6030	−0.558897
$993$	10.1320	0.321528
$994$	−20.1625	−0.639515
$995$	−15.8455	−0.502337
$996$	−52.8786	−1.67552
$997$	44.6804	1.41504	0.707522	−	0.706691i	$-0.249813\pi$
$997$	44.6804	1.41504	0.707522	+	0.706691i	$0.249813\pi$
$998$	51.4199	1.62767
$999$	−17.0378	−0.539053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.6	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.06358 q^{2} +2.59950 q^{3} +2.25838 q^{4} -1.00000 q^{5} -5.36430 q^{6} -1.01430 q^{7} -0.533185 q^{8} +3.75743 q^{9} +O(q^{10})\)	\(q-2.06358 q^{2} +2.59950 q^{3} +2.25838 q^{4} -1.00000 q^{5} -5.36430 q^{6} -1.01430 q^{7} -0.533185 q^{8} +3.75743 q^{9} +2.06358 q^{10} -1.00000 q^{11} +5.87067 q^{12} +0.591408 q^{13} +2.09310 q^{14} -2.59950 q^{15} -3.41648 q^{16} -1.74690 q^{17} -7.75376 q^{18} -3.68501 q^{19} -2.25838 q^{20} -2.63669 q^{21} +2.06358 q^{22} +2.17727 q^{23} -1.38602 q^{24} +1.00000 q^{25} -1.22042 q^{26} +1.96893 q^{27} -2.29068 q^{28} +8.50037 q^{29} +5.36430 q^{30} -2.16878 q^{31} +8.11657 q^{32} -2.59950 q^{33} +3.60488 q^{34} +1.01430 q^{35} +8.48569 q^{36} -8.65334 q^{37} +7.60432 q^{38} +1.53737 q^{39} +0.533185 q^{40} -1.23245 q^{41} +5.44103 q^{42} +12.4123 q^{43} -2.25838 q^{44} -3.75743 q^{45} -4.49298 q^{46} -10.9619 q^{47} -8.88117 q^{48} -5.97119 q^{49} -2.06358 q^{50} -4.54109 q^{51} +1.33562 q^{52} +1.57287 q^{53} -4.06305 q^{54} +1.00000 q^{55} +0.540812 q^{56} -9.57919 q^{57} -17.5412 q^{58} -6.86851 q^{59} -5.87067 q^{60} -0.278562 q^{61} +4.47545 q^{62} -3.81117 q^{63} -9.91626 q^{64} -0.591408 q^{65} +5.36430 q^{66} +5.68941 q^{67} -3.94517 q^{68} +5.65982 q^{69} -2.09310 q^{70} -9.63282 q^{71} -2.00340 q^{72} -1.00000 q^{73} +17.8569 q^{74} +2.59950 q^{75} -8.32214 q^{76} +1.01430 q^{77} -3.17249 q^{78} +6.04589 q^{79} +3.41648 q^{80} -6.15403 q^{81} +2.54327 q^{82} -9.00725 q^{83} -5.95464 q^{84} +1.74690 q^{85} -25.6139 q^{86} +22.0968 q^{87} +0.533185 q^{88} +3.21687 q^{89} +7.75376 q^{90} -0.599868 q^{91} +4.91710 q^{92} -5.63775 q^{93} +22.6208 q^{94} +3.68501 q^{95} +21.0991 q^{96} +8.99316 q^{97} +12.3220 q^{98} -3.75743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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