LMFDB - Embedded newform 8018.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.02842 q^{3} +1.00000 q^{4} +2.47134 q^{5} -2.02842 q^{6} +1.41486 q^{7} +1.00000 q^{8} +1.11447 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.02842 q^{3} +1.00000 q^{4} +2.47134 q^{5} -2.02842 q^{6} +1.41486 q^{7} +1.00000 q^{8} +1.11447 q^{9} +2.47134 q^{10} -1.90125 q^{11} -2.02842 q^{12} +3.04945 q^{13} +1.41486 q^{14} -5.01290 q^{15} +1.00000 q^{16} -0.777246 q^{17} +1.11447 q^{18} +1.00000 q^{19} +2.47134 q^{20} -2.86993 q^{21} -1.90125 q^{22} -7.98162 q^{23} -2.02842 q^{24} +1.10751 q^{25} +3.04945 q^{26} +3.82464 q^{27} +1.41486 q^{28} -5.89103 q^{29} -5.01290 q^{30} -5.52189 q^{31} +1.00000 q^{32} +3.85652 q^{33} -0.777246 q^{34} +3.49660 q^{35} +1.11447 q^{36} -3.09139 q^{37} +1.00000 q^{38} -6.18556 q^{39} +2.47134 q^{40} -6.61679 q^{41} -2.86993 q^{42} +11.4467 q^{43} -1.90125 q^{44} +2.75423 q^{45} -7.98162 q^{46} -6.04983 q^{47} -2.02842 q^{48} -4.99817 q^{49} +1.10751 q^{50} +1.57658 q^{51} +3.04945 q^{52} -3.46843 q^{53} +3.82464 q^{54} -4.69863 q^{55} +1.41486 q^{56} -2.02842 q^{57} -5.89103 q^{58} -1.73246 q^{59} -5.01290 q^{60} -11.6171 q^{61} -5.52189 q^{62} +1.57682 q^{63} +1.00000 q^{64} +7.53623 q^{65} +3.85652 q^{66} +5.11260 q^{67} -0.777246 q^{68} +16.1900 q^{69} +3.49660 q^{70} -0.661692 q^{71} +1.11447 q^{72} -11.5032 q^{73} -3.09139 q^{74} -2.24649 q^{75} +1.00000 q^{76} -2.69001 q^{77} -6.18556 q^{78} -15.7474 q^{79} +2.47134 q^{80} -11.1014 q^{81} -6.61679 q^{82} +13.7324 q^{83} -2.86993 q^{84} -1.92084 q^{85} +11.4467 q^{86} +11.9495 q^{87} -1.90125 q^{88} -5.29706 q^{89} +2.75423 q^{90} +4.31455 q^{91} -7.98162 q^{92} +11.2007 q^{93} -6.04983 q^{94} +2.47134 q^{95} -2.02842 q^{96} +11.1561 q^{97} -4.99817 q^{98} -2.11889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.02842	−1.17111	−0.585553	−	0.810634i	$-0.699123\pi$
$3$	−2.02842	−1.17111	−0.585553	+	0.810634i	$0.699123\pi$
$4$	1.00000	0.500000
$5$	2.47134	1.10522	0.552608	−	0.833441i	$-0.313633\pi$
$5$	2.47134	1.10522	0.552608	+	0.833441i	$0.313633\pi$
$6$	−2.02842	−0.828097
$7$	1.41486	0.534767	0.267384	−	0.963590i	$-0.413841\pi$
$7$	1.41486	0.534767	0.267384	+	0.963590i	$0.413841\pi$
$8$	1.00000	0.353553
$9$	1.11447	0.371490
$10$	2.47134	0.781505
$11$	−1.90125	−0.573248	−0.286624	−	0.958043i	$-0.592533\pi$
$11$	−1.90125	−0.573248	−0.286624	+	0.958043i	$0.592533\pi$
$12$	−2.02842	−0.585553
$13$	3.04945	0.845766	0.422883	−	0.906184i	$-0.361018\pi$
$13$	3.04945	0.845766	0.422883	+	0.906184i	$0.361018\pi$
$14$	1.41486	0.378138
$15$	−5.01290	−1.29432
$16$	1.00000	0.250000
$17$	−0.777246	−0.188510	−0.0942549	−	0.995548i	$-0.530047\pi$
$17$	−0.777246	−0.188510	−0.0942549	+	0.995548i	$0.530047\pi$
$18$	1.11447	0.262683
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.47134	0.552608
$21$	−2.86993	−0.626269
$22$	−1.90125	−0.405348
$23$	−7.98162	−1.66428	−0.832141	−	0.554564i	$-0.812885\pi$
$23$	−7.98162	−1.66428	−0.832141	+	0.554564i	$0.812885\pi$
$24$	−2.02842	−0.414049
$25$	1.10751	0.221502
$26$	3.04945	0.598047
$27$	3.82464	0.736052
$28$	1.41486	0.267384
$29$	−5.89103	−1.09394	−0.546969	−	0.837153i	$-0.684218\pi$
$29$	−5.89103	−1.09394	−0.546969	+	0.837153i	$0.684218\pi$
$30$	−5.01290	−0.915226
$31$	−5.52189	−0.991761	−0.495880	−	0.868391i	$-0.665155\pi$
$31$	−5.52189	−0.991761	−0.495880	+	0.868391i	$0.665155\pi$
$32$	1.00000	0.176777
$33$	3.85652	0.671335
$34$	−0.777246	−0.133297
$35$	3.49660	0.591033
$36$	1.11447	0.185745
$37$	−3.09139	−0.508221	−0.254111	−	0.967175i	$-0.581783\pi$
$37$	−3.09139	−0.508221	−0.254111	+	0.967175i	$0.581783\pi$
$38$	1.00000	0.162221
$39$	−6.18556	−0.990482
$40$	2.47134	0.390753
$41$	−6.61679	−1.03337	−0.516684	−	0.856176i	$-0.672834\pi$
$41$	−6.61679	−1.03337	−0.516684	+	0.856176i	$0.672834\pi$
$42$	−2.86993	−0.442839
$43$	11.4467	1.74560	0.872799	−	0.488080i	$-0.162303\pi$
$43$	11.4467	1.74560	0.872799	+	0.488080i	$0.162303\pi$
$44$	−1.90125	−0.286624
$45$	2.75423	0.410577
$46$	−7.98162	−1.17683
$47$	−6.04983	−0.882459	−0.441230	−	0.897394i	$-0.645458\pi$
$47$	−6.04983	−0.882459	−0.441230	+	0.897394i	$0.645458\pi$
$48$	−2.02842	−0.292777
$49$	−4.99817	−0.714024
$50$	1.10751	0.156625
$51$	1.57658	0.220765
$52$	3.04945	0.422883
$53$	−3.46843	−0.476426	−0.238213	−	0.971213i	$-0.576562\pi$
$53$	−3.46843	−0.476426	−0.238213	+	0.971213i	$0.576562\pi$
$54$	3.82464	0.520467
$55$	−4.69863	−0.633563
$56$	1.41486	0.189069
$57$	−2.02842	−0.268670
$58$	−5.89103	−0.773530
$59$	−1.73246	−0.225547	−0.112774	−	0.993621i	$-0.535974\pi$
$59$	−1.73246	−0.225547	−0.112774	+	0.993621i	$0.535974\pi$
$60$	−5.01290	−0.647162
$61$	−11.6171	−1.48742	−0.743709	−	0.668504i	$-0.766935\pi$
$61$	−11.6171	−1.48742	−0.743709	+	0.668504i	$0.766935\pi$
$62$	−5.52189	−0.701281
$63$	1.57682	0.198661
$64$	1.00000	0.125000
$65$	7.53623	0.934754
$66$	3.85652	0.474705
$67$	5.11260	0.624604	0.312302	−	0.949983i	$-0.398900\pi$
$67$	5.11260	0.624604	0.312302	+	0.949983i	$0.398900\pi$
$68$	−0.777246	−0.0942549
$69$	16.1900	1.94905
$70$	3.49660	0.417924
$71$	−0.661692	−0.0785284	−0.0392642	−	0.999229i	$-0.512501\pi$
$71$	−0.661692	−0.0785284	−0.0392642	+	0.999229i	$0.512501\pi$
$72$	1.11447	0.131342
$73$	−11.5032	−1.34635	−0.673173	−	0.739485i	$-0.735069\pi$
$73$	−11.5032	−1.34635	−0.673173	+	0.739485i	$0.735069\pi$
$74$	−3.09139	−0.359367
$75$	−2.24649	−0.259402
$76$	1.00000	0.114708
$77$	−2.69001	−0.306555
$78$	−6.18556	−0.700377
$79$	−15.7474	−1.77172	−0.885858	−	0.463956i	$-0.846429\pi$
$79$	−15.7474	−1.77172	−0.885858	+	0.463956i	$0.846429\pi$
$80$	2.47134	0.276304
$81$	−11.1014	−1.23349
$82$	−6.61679	−0.730702
$83$	13.7324	1.50732	0.753661	−	0.657263i	$-0.228286\pi$
$83$	13.7324	1.50732	0.753661	+	0.657263i	$0.228286\pi$
$84$	−2.86993	−0.313135
$85$	−1.92084	−0.208344
$86$	11.4467	1.23432
$87$	11.9495	1.28112
$88$	−1.90125	−0.202674
$89$	−5.29706	−0.561488	−0.280744	−	0.959783i	$-0.590581\pi$
$89$	−5.29706	−0.561488	−0.280744	+	0.959783i	$0.590581\pi$
$90$	2.75423	0.290321
$91$	4.31455	0.452288
$92$	−7.98162	−0.832141
$93$	11.2007	1.16146
$94$	−6.04983	−0.623993
$95$	2.47134	0.253554
$96$	−2.02842	−0.207024
$97$	11.1561	1.13273	0.566364	−	0.824155i	$-0.308350\pi$
$97$	11.1561	1.13273	0.566364	+	0.824155i	$0.308350\pi$
$98$	−4.99817	−0.504891
$99$	−2.11889	−0.212956
$100$	1.10751	0.110751
$101$	−2.64209	−0.262898	−0.131449	−	0.991323i	$-0.541963\pi$
$101$	−2.64209	−0.262898	−0.131449	+	0.991323i	$0.541963\pi$
$102$	1.57658	0.156104
$103$	0.481843	0.0474774	0.0237387	−	0.999718i	$-0.492443\pi$
$103$	0.481843	0.0474774	0.0237387	+	0.999718i	$0.492443\pi$
$104$	3.04945	0.299024
$105$	−7.09256	−0.692163
$106$	−3.46843	−0.336884
$107$	10.6017	1.02490	0.512451	−	0.858716i	$-0.328738\pi$
$107$	10.6017	1.02490	0.512451	+	0.858716i	$0.328738\pi$
$108$	3.82464	0.368026
$109$	−11.9045	−1.14025	−0.570124	−	0.821559i	$-0.693105\pi$
$109$	−11.9045	−1.14025	−0.570124	+	0.821559i	$0.693105\pi$
$110$	−4.69863	−0.447997
$111$	6.27062	0.595181
$112$	1.41486	0.133692
$113$	3.01625	0.283745	0.141872	−	0.989885i	$-0.454688\pi$
$113$	3.01625	0.283745	0.141872	+	0.989885i	$0.454688\pi$
$114$	−2.02842	−0.189979
$115$	−19.7253	−1.83939
$116$	−5.89103	−0.546969
$117$	3.39852	0.314194
$118$	−1.73246	−0.159486
$119$	−1.09970	−0.100809
$120$	−5.01290	−0.457613
$121$	−7.38525	−0.671386
$122$	−11.6171	−1.05176
$123$	13.4216	1.21018
$124$	−5.52189	−0.495880
$125$	−9.61966	−0.860409
$126$	1.57682	0.140474
$127$	18.1456	1.61016	0.805079	−	0.593168i	$-0.202123\pi$
$127$	18.1456	1.61016	0.805079	+	0.593168i	$0.202123\pi$
$128$	1.00000	0.0883883
$129$	−23.2186	−2.04428
$130$	7.53623	0.660971
$131$	5.03267	0.439706	0.219853	−	0.975533i	$-0.429442\pi$
$131$	5.03267	0.439706	0.219853	+	0.975533i	$0.429442\pi$
$132$	3.85652	0.335667
$133$	1.41486	0.122684
$134$	5.11260	0.441662
$135$	9.45197	0.813496
$136$	−0.777246	−0.0666483
$137$	−9.66429	−0.825676	−0.412838	−	0.910805i	$-0.635462\pi$
$137$	−9.66429	−0.825676	−0.412838	+	0.910805i	$0.635462\pi$
$138$	16.1900	1.37819
$139$	6.20866	0.526612	0.263306	−	0.964712i	$-0.415187\pi$
$139$	6.20866	0.526612	0.263306	+	0.964712i	$0.415187\pi$
$140$	3.49660	0.295517
$141$	12.2716	1.03345
$142$	−0.661692	−0.0555280
$143$	−5.79777	−0.484834
$144$	1.11447	0.0928725
$145$	−14.5587	−1.20904
$146$	−11.5032	−0.952010
$147$	10.1384	0.836198
$148$	−3.09139	−0.254111
$149$	14.0579	1.15167	0.575833	−	0.817567i	$-0.304678\pi$
$149$	14.0579	1.15167	0.575833	+	0.817567i	$0.304678\pi$
$150$	−2.24649	−0.183425
$151$	−8.58786	−0.698870	−0.349435	−	0.936961i	$-0.613626\pi$
$151$	−8.58786	−0.698870	−0.349435	+	0.936961i	$0.613626\pi$
$152$	1.00000	0.0811107
$153$	−0.866217	−0.0700295
$154$	−2.69001	−0.216767
$155$	−13.6465	−1.09611
$156$	−6.18556	−0.495241
$157$	10.2251	0.816055	0.408027	−	0.912970i	$-0.366217\pi$
$157$	10.2251	0.816055	0.408027	+	0.912970i	$0.366217\pi$
$158$	−15.7474	−1.25279
$159$	7.03542	0.557945
$160$	2.47134	0.195376
$161$	−11.2929	−0.890004
$162$	−11.1014	−0.872206
$163$	−13.0794	−1.02446	−0.512229	−	0.858849i	$-0.671180\pi$
$163$	−13.0794	−1.02446	−0.512229	+	0.858849i	$0.671180\pi$
$164$	−6.61679	−0.516684
$165$	9.53077	0.741970
$166$	13.7324	1.06584
$167$	−22.6408	−1.75200	−0.875999	−	0.482313i	$-0.839797\pi$
$167$	−22.6408	−1.75200	−0.875999	+	0.482313i	$0.839797\pi$
$168$	−2.86993	−0.221420
$169$	−3.70083	−0.284679
$170$	−1.92084	−0.147321
$171$	1.11447	0.0852257
$172$	11.4467	0.872799
$173$	12.6704	0.963316	0.481658	−	0.876359i	$-0.340035\pi$
$173$	12.6704	0.963316	0.481658	+	0.876359i	$0.340035\pi$
$174$	11.9495	0.905886
$175$	1.56697	0.118452
$176$	−1.90125	−0.143312
$177$	3.51415	0.264140
$178$	−5.29706	−0.397032
$179$	24.8335	1.85614	0.928070	−	0.372405i	$-0.121467\pi$
$179$	24.8335	1.85614	0.928070	+	0.372405i	$0.121467\pi$
$180$	2.75423	0.205288
$181$	−9.34261	−0.694431	−0.347215	−	0.937785i	$-0.612873\pi$
$181$	−9.34261	−0.694431	−0.347215	+	0.937785i	$0.612873\pi$
$182$	4.31455	0.319816
$183$	23.5643	1.74192
$184$	−7.98162	−0.588413
$185$	−7.63986	−0.561694
$186$	11.2007	0.821274
$187$	1.47774	0.108063
$188$	−6.04983	−0.441230
$189$	5.41133	0.393617
$190$	2.47134	0.179290
$191$	20.9150	1.51335	0.756677	−	0.653789i	$-0.226822\pi$
$191$	20.9150	1.51335	0.756677	+	0.653789i	$0.226822\pi$
$192$	−2.02842	−0.146388
$193$	−19.1158	−1.37599	−0.687993	−	0.725717i	$-0.741508\pi$
$193$	−19.1158	−1.37599	−0.687993	+	0.725717i	$0.741508\pi$
$194$	11.1561	0.800959
$195$	−15.2866	−1.09470
$196$	−4.99817	−0.357012
$197$	17.4473	1.24307	0.621534	−	0.783387i	$-0.286510\pi$
$197$	17.4473	1.24307	0.621534	+	0.783387i	$0.286510\pi$
$198$	−2.11889	−0.150583
$199$	−2.95613	−0.209554	−0.104777	−	0.994496i	$-0.533413\pi$
$199$	−2.95613	−0.209554	−0.104777	+	0.994496i	$0.533413\pi$
$200$	1.10751	0.0783126
$201$	−10.3705	−0.731478
$202$	−2.64209	−0.185897
$203$	−8.33499	−0.585002
$204$	1.57658	0.110383
$205$	−16.3523	−1.14209
$206$	0.481843	0.0335716
$207$	−8.89527	−0.618264
$208$	3.04945	0.211442
$209$	−1.90125	−0.131512
$210$	−7.09256	−0.489433
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.46843	−0.238213
$213$	1.34219	0.0919651
$214$	10.6017	0.724716
$215$	28.2885	1.92926
$216$	3.82464	0.260234
$217$	−7.81271	−0.530361
$218$	−11.9045	−0.806277
$219$	23.3332	1.57671
$220$	−4.69863	−0.316782
$221$	−2.37018	−0.159435
$222$	6.27062	0.420857
$223$	−1.94987	−0.130573	−0.0652866	−	0.997867i	$-0.520796\pi$
$223$	−1.94987	−0.130573	−0.0652866	+	0.997867i	$0.520796\pi$
$224$	1.41486	0.0945344
$225$	1.23428	0.0822856
$226$	3.01625	0.200638
$227$	10.1743	0.675295	0.337647	−	0.941273i	$-0.390369\pi$
$227$	10.1743	0.675295	0.337647	+	0.941273i	$0.390369\pi$
$228$	−2.02842	−0.134335
$229$	−15.9728	−1.05551	−0.527756	−	0.849396i	$-0.676966\pi$
$229$	−15.9728	−1.05551	−0.527756	+	0.849396i	$0.676966\pi$
$230$	−19.7253	−1.30065
$231$	5.45645	0.359008
$232$	−5.89103	−0.386765
$233$	1.97470	0.129367	0.0646835	−	0.997906i	$-0.479396\pi$
$233$	1.97470	0.129367	0.0646835	+	0.997906i	$0.479396\pi$
$234$	3.39852	0.222168
$235$	−14.9512	−0.975308
$236$	−1.73246	−0.112774
$237$	31.9422	2.07487
$238$	−1.09970	−0.0712827
$239$	4.17581	0.270110	0.135055	−	0.990838i	$-0.456879\pi$
$239$	4.17581	0.270110	0.135055	+	0.990838i	$0.456879\pi$
$240$	−5.01290	−0.323581
$241$	−9.50085	−0.612003	−0.306002	−	0.952031i	$-0.598991\pi$
$241$	−9.50085	−0.612003	−0.306002	+	0.952031i	$0.598991\pi$
$242$	−7.38525	−0.474742
$243$	11.0443	0.708490
$244$	−11.6171	−0.743709
$245$	−12.3522	−0.789150
$246$	13.4216	0.855729
$247$	3.04945	0.194032
$248$	−5.52189	−0.350640
$249$	−27.8549	−1.76524
$250$	−9.61966	−0.608401
$251$	−2.77413	−0.175101	−0.0875507	−	0.996160i	$-0.527904\pi$
$251$	−2.77413	−0.175101	−0.0875507	+	0.996160i	$0.527904\pi$
$252$	1.57682	0.0993304
$253$	15.1750	0.954047
$254$	18.1456	1.13855
$255$	3.89626	0.243993
$256$	1.00000	0.0625000
$257$	13.3757	0.834350	0.417175	−	0.908826i	$-0.363020\pi$
$257$	13.3757	0.834350	0.417175	+	0.908826i	$0.363020\pi$
$258$	−23.2186	−1.44552
$259$	−4.37389	−0.271780
$260$	7.53623	0.467377
$261$	−6.56538	−0.406387
$262$	5.03267	0.310919
$263$	5.46318	0.336874	0.168437	−	0.985712i	$-0.446128\pi$
$263$	5.46318	0.336874	0.168437	+	0.985712i	$0.446128\pi$
$264$	3.85652	0.237353
$265$	−8.57167	−0.526553
$266$	1.41486	0.0867507
$267$	10.7446	0.657562
$268$	5.11260	0.312302
$269$	−5.59912	−0.341385	−0.170692	−	0.985324i	$-0.554600\pi$
$269$	−5.59912	−0.341385	−0.170692	+	0.985324i	$0.554600\pi$
$270$	9.45197	0.575229
$271$	−6.95593	−0.422543	−0.211271	−	0.977427i	$-0.567760\pi$
$271$	−6.95593	−0.422543	−0.211271	+	0.977427i	$0.567760\pi$
$272$	−0.777246	−0.0471275
$273$	−8.75171	−0.529678
$274$	−9.66429	−0.583841
$275$	−2.10565	−0.126975
$276$	16.1900	0.974526
$277$	16.3010	0.979430	0.489715	−	0.871882i	$-0.337101\pi$
$277$	16.3010	0.979430	0.489715	+	0.871882i	$0.337101\pi$
$278$	6.20866	0.372371
$279$	−6.15398	−0.368429
$280$	3.49660	0.208962
$281$	25.7357	1.53526	0.767632	−	0.640891i	$-0.221435\pi$
$281$	25.7357	1.53526	0.767632	+	0.640891i	$0.221435\pi$
$282$	12.2716	0.730762
$283$	0.131593	0.00782241	0.00391121	−	0.999992i	$-0.498755\pi$
$283$	0.131593	0.00782241	0.00391121	+	0.999992i	$0.498755\pi$
$284$	−0.661692	−0.0392642
$285$	−5.01290	−0.296939
$286$	−5.79777	−0.342829
$287$	−9.36183	−0.552612
$288$	1.11447	0.0656708
$289$	−16.3959	−0.964464
$290$	−14.5587	−0.854918
$291$	−22.6291	−1.32654
$292$	−11.5032	−0.673173
$293$	3.62743	0.211917	0.105958	−	0.994371i	$-0.466209\pi$
$293$	3.62743	0.211917	0.105958	+	0.994371i	$0.466209\pi$
$294$	10.1384	0.591281
$295$	−4.28150	−0.249278
$296$	−3.09139	−0.179683
$297$	−7.27159	−0.421941
$298$	14.0579	0.814351
$299$	−24.3396	−1.40759
$300$	−2.24649	−0.129701
$301$	16.1954	0.933489
$302$	−8.58786	−0.494176
$303$	5.35925	0.307881
$304$	1.00000	0.0573539
$305$	−28.7098	−1.64392
$306$	−0.866217	−0.0495183
$307$	0.382256	0.0218165	0.0109082	−	0.999941i	$-0.496528\pi$
$307$	0.382256	0.0218165	0.0109082	+	0.999941i	$0.496528\pi$
$308$	−2.69001	−0.153277
$309$	−0.977378	−0.0556011
$310$	−13.6465	−0.775067
$311$	14.8067	0.839613	0.419807	−	0.907614i	$-0.362098\pi$
$311$	14.8067	0.839613	0.419807	+	0.907614i	$0.362098\pi$
$312$	−6.18556	−0.350188
$313$	−18.6361	−1.05337	−0.526686	−	0.850060i	$-0.676566\pi$
$313$	−18.6361	−1.05337	−0.526686	+	0.850060i	$0.676566\pi$
$314$	10.2251	0.577038
$315$	3.89686	0.219563
$316$	−15.7474	−0.885858
$317$	0.143542	0.00806212	0.00403106	−	0.999992i	$-0.498717\pi$
$317$	0.143542	0.00806212	0.00403106	+	0.999992i	$0.498717\pi$
$318$	7.03542	0.394527
$319$	11.2003	0.627098
$320$	2.47134	0.138152
$321$	−21.5046	−1.20027
$322$	−11.2929	−0.629328
$323$	−0.777246	−0.0432471
$324$	−11.1014	−0.616743
$325$	3.37729	0.187339
$326$	−13.0794	−0.724401
$327$	24.1474	1.33535
$328$	−6.61679	−0.365351
$329$	−8.55968	−0.471910
$330$	9.53077	0.524652
$331$	−26.5807	−1.46101	−0.730505	−	0.682908i	$-0.760715\pi$
$331$	−26.5807	−1.46101	−0.730505	+	0.682908i	$0.760715\pi$
$332$	13.7324	0.753661
$333$	−3.44526	−0.188799
$334$	−22.6408	−1.23885
$335$	12.6350	0.690322
$336$	−2.86993	−0.156567
$337$	−8.74594	−0.476422	−0.238211	−	0.971213i	$-0.576561\pi$
$337$	−8.74594	−0.476422	−0.238211	+	0.971213i	$0.576561\pi$
$338$	−3.70083	−0.201299
$339$	−6.11820	−0.332295
$340$	−1.92084	−0.104172
$341$	10.4985	0.568525
$342$	1.11447	0.0602636
$343$	−16.9757	−0.916604
$344$	11.4467	0.617162
$345$	40.0110	2.15412
$346$	12.6704	0.681167
$347$	−13.8668	−0.744408	−0.372204	−	0.928151i	$-0.621398\pi$
$347$	−13.8668	−0.744408	−0.372204	+	0.928151i	$0.621398\pi$
$348$	11.9495	0.640558
$349$	7.60207	0.406930	0.203465	−	0.979082i	$-0.434780\pi$
$349$	7.60207	0.406930	0.203465	+	0.979082i	$0.434780\pi$
$350$	1.56697	0.0837581
$351$	11.6631	0.622528
$352$	−1.90125	−0.101337
$353$	5.74221	0.305627	0.152813	−	0.988255i	$-0.451167\pi$
$353$	5.74221	0.305627	0.152813	+	0.988255i	$0.451167\pi$
$354$	3.51415	0.186775
$355$	−1.63526	−0.0867908
$356$	−5.29706	−0.280744
$357$	2.23064	0.118058
$358$	24.8335	1.31249
$359$	−12.4080	−0.654869	−0.327434	−	0.944874i	$-0.606184\pi$
$359$	−12.4080	−0.654869	−0.327434	+	0.944874i	$0.606184\pi$
$360$	2.75423	0.145161
$361$	1.00000	0.0526316
$362$	−9.34261	−0.491037
$363$	14.9804	0.786265
$364$	4.31455	0.226144
$365$	−28.4282	−1.48800
$366$	23.5643	1.23173
$367$	−3.66093	−0.191099	−0.0955495	−	0.995425i	$-0.530461\pi$
$367$	−3.66093	−0.191099	−0.0955495	+	0.995425i	$0.530461\pi$
$368$	−7.98162	−0.416071
$369$	−7.37421	−0.383886
$370$	−7.63986	−0.397178
$371$	−4.90735	−0.254777
$372$	11.2007	0.580729
$373$	−35.5897	−1.84276	−0.921382	−	0.388658i	$-0.872939\pi$
$373$	−35.5897	−1.84276	−0.921382	+	0.388658i	$0.872939\pi$
$374$	1.47774	0.0764120
$375$	19.5127	1.00763
$376$	−6.04983	−0.311996
$377$	−17.9644	−0.925215
$378$	5.41133	0.278329
$379$	33.7772	1.73502	0.867508	−	0.497423i	$-0.165720\pi$
$379$	33.7772	1.73502	0.867508	+	0.497423i	$0.165720\pi$
$380$	2.47134	0.126777
$381$	−36.8067	−1.88567
$382$	20.9150	1.07010
$383$	25.0970	1.28240	0.641199	−	0.767375i	$-0.278437\pi$
$383$	25.0970	1.28240	0.641199	+	0.767375i	$0.278437\pi$
$384$	−2.02842	−0.103512
$385$	−6.64791	−0.338809
$386$	−19.1158	−0.972969
$387$	12.7569	0.648472
$388$	11.1561	0.566364
$389$	14.8264	0.751730	0.375865	−	0.926674i	$-0.377346\pi$
$389$	14.8264	0.751730	0.375865	+	0.926674i	$0.377346\pi$
$390$	−15.2866	−0.774067
$391$	6.20368	0.313734
$392$	−4.99817	−0.252446
$393$	−10.2083	−0.514943
$394$	17.4473	0.878981
$395$	−38.9170	−1.95813
$396$	−2.11889	−0.106478
$397$	−17.7690	−0.891801	−0.445900	−	0.895083i	$-0.647116\pi$
$397$	−17.7690	−0.891801	−0.445900	+	0.895083i	$0.647116\pi$
$398$	−2.95613	−0.148177
$399$	−2.86993	−0.143676
$400$	1.10751	0.0553754
$401$	−8.78872	−0.438888	−0.219444	−	0.975625i	$-0.570424\pi$
$401$	−8.78872	−0.438888	−0.219444	+	0.975625i	$0.570424\pi$
$402$	−10.3705	−0.517233
$403$	−16.8388	−0.838798
$404$	−2.64209	−0.131449
$405$	−27.4352	−1.36327
$406$	−8.33499	−0.413659
$407$	5.87750	0.291337
$408$	1.57658	0.0780522
$409$	3.01022	0.148846	0.0744229	−	0.997227i	$-0.476289\pi$
$409$	3.01022	0.148846	0.0744229	+	0.997227i	$0.476289\pi$
$410$	−16.3523	−0.807583
$411$	19.6032	0.966954
$412$	0.481843	0.0237387
$413$	−2.45119	−0.120615
$414$	−8.89527	−0.437179
$415$	33.9373	1.66592
$416$	3.04945	0.149512
$417$	−12.5937	−0.616719
$418$	−1.90125	−0.0929932
$419$	−16.5426	−0.808157	−0.404079	−	0.914724i	$-0.632408\pi$
$419$	−16.5426	−0.808157	−0.404079	+	0.914724i	$0.632408\pi$
$420$	−7.09256	−0.346081
$421$	0.785599	0.0382877	0.0191439	−	0.999817i	$-0.493906\pi$
$421$	0.785599	0.0382877	0.0191439	+	0.999817i	$0.493906\pi$
$422$	−1.00000	−0.0486792
$423$	−6.74236	−0.327825
$424$	−3.46843	−0.168442
$425$	−0.860806	−0.0417552
$426$	1.34219	0.0650292
$427$	−16.4366	−0.795422
$428$	10.6017	0.512451
$429$	11.7603	0.567792
$430$	28.2885	1.36419
$431$	12.1340	0.584473	0.292237	−	0.956346i	$-0.405601\pi$
$431$	12.1340	0.584473	0.292237	+	0.956346i	$0.405601\pi$
$432$	3.82464	0.184013
$433$	−18.7692	−0.901990	−0.450995	−	0.892527i	$-0.648931\pi$
$433$	−18.7692	−0.901990	−0.450995	+	0.892527i	$0.648931\pi$
$434$	−7.81271	−0.375022
$435$	29.5311	1.41591
$436$	−11.9045	−0.570124
$437$	−7.98162	−0.381812
$438$	23.3332	1.11490
$439$	−36.7958	−1.75617	−0.878084	−	0.478506i	$-0.841179\pi$
$439$	−36.7958	−1.75617	−0.878084	+	0.478506i	$0.841179\pi$
$440$	−4.69863	−0.223998
$441$	−5.57031	−0.265253
$442$	−2.37018	−0.112738
$443$	−25.3134	−1.20267	−0.601337	−	0.798995i	$-0.705365\pi$
$443$	−25.3134	−1.20267	−0.601337	+	0.798995i	$0.705365\pi$
$444$	6.27062	0.297590
$445$	−13.0908	−0.620565
$446$	−1.94987	−0.0923292
$447$	−28.5152	−1.34872
$448$	1.41486	0.0668459
$449$	−7.49329	−0.353630	−0.176815	−	0.984244i	$-0.556579\pi$
$449$	−7.49329	−0.353630	−0.176815	+	0.984244i	$0.556579\pi$
$450$	1.23428	0.0581847
$451$	12.5802	0.592377
$452$	3.01625	0.141872
$453$	17.4198	0.818451
$454$	10.1743	0.477505
$455$	10.6627	0.499876
$456$	−2.02842	−0.0949893
$457$	10.7570	0.503193	0.251596	−	0.967832i	$-0.419044\pi$
$457$	10.7570	0.503193	0.251596	+	0.967832i	$0.419044\pi$
$458$	−15.9728	−0.746359
$459$	−2.97268	−0.138753
$460$	−19.7253	−0.919695
$461$	−17.7218	−0.825386	−0.412693	−	0.910870i	$-0.635412\pi$
$461$	−17.7218	−0.825386	−0.412693	+	0.910870i	$0.635412\pi$
$462$	5.45645	0.253857
$463$	18.3631	0.853404	0.426702	−	0.904392i	$-0.359675\pi$
$463$	18.3631	0.853404	0.426702	+	0.904392i	$0.359675\pi$
$464$	−5.89103	−0.273484
$465$	27.6807	1.28366
$466$	1.97470	0.0914763
$467$	−3.64293	−0.168575	−0.0842874	−	0.996441i	$-0.526861\pi$
$467$	−3.64293	−0.168575	−0.0842874	+	0.996441i	$0.526861\pi$
$468$	3.39852	0.157097
$469$	7.23363	0.334018
$470$	−14.9512	−0.689647
$471$	−20.7408	−0.955687
$472$	−1.73246	−0.0797430
$473$	−21.7629	−1.00066
$474$	31.9422	1.46715
$475$	1.10751	0.0508159
$476$	−1.09970	−0.0504045
$477$	−3.86546	−0.176987
$478$	4.17581	0.190997
$479$	10.6715	0.487592	0.243796	−	0.969827i	$-0.421607\pi$
$479$	10.6715	0.487592	0.243796	+	0.969827i	$0.421607\pi$
$480$	−5.01290	−0.228806
$481$	−9.42705	−0.429836
$482$	−9.50085	−0.432752
$483$	22.9067	1.04229
$484$	−7.38525	−0.335693
$485$	27.5704	1.25191
$486$	11.0443	0.500978
$487$	13.0919	0.593249	0.296624	−	0.954994i	$-0.404139\pi$
$487$	13.0919	0.593249	0.296624	+	0.954994i	$0.404139\pi$
$488$	−11.6171	−0.525882
$489$	26.5305	1.19975
$490$	−12.3522	−0.558014
$491$	−13.4801	−0.608350	−0.304175	−	0.952616i	$-0.598381\pi$
$491$	−13.4801	−0.608350	−0.304175	+	0.952616i	$0.598381\pi$
$492$	13.4216	0.605092
$493$	4.57878	0.206218
$494$	3.04945	0.137201
$495$	−5.23648	−0.235362
$496$	−5.52189	−0.247940
$497$	−0.936203	−0.0419944
$498$	−27.8549	−1.24821
$499$	−29.7634	−1.33239	−0.666197	−	0.745776i	$-0.732079\pi$
$499$	−29.7634	−1.33239	−0.666197	+	0.745776i	$0.732079\pi$
$500$	−9.61966	−0.430204
$501$	45.9250	2.05178
$502$	−2.77413	−0.123815
$503$	−23.4365	−1.04498	−0.522492	−	0.852644i	$-0.674997\pi$
$503$	−23.4365	−1.04498	−0.522492	+	0.852644i	$0.674997\pi$
$504$	1.57682	0.0702372
$505$	−6.52949	−0.290559
$506$	15.1750	0.674613
$507$	7.50683	0.333390
$508$	18.1456	0.805079
$509$	20.1337	0.892412	0.446206	−	0.894930i	$-0.352775\pi$
$509$	20.1337	0.892412	0.446206	+	0.894930i	$0.352775\pi$
$510$	3.89626	0.172529
$511$	−16.2754	−0.719982
$512$	1.00000	0.0441942
$513$	3.82464	0.168862
$514$	13.3757	0.589975
$515$	1.19080	0.0524728
$516$	−23.2186	−1.02214
$517$	11.5022	0.505868
$518$	−4.37389	−0.192178
$519$	−25.7009	−1.12814
$520$	7.53623	0.330485
$521$	9.00411	0.394477	0.197239	−	0.980356i	$-0.436803\pi$
$521$	9.00411	0.394477	0.197239	+	0.980356i	$0.436803\pi$
$522$	−6.56538	−0.287359
$523$	10.0738	0.440495	0.220247	−	0.975444i	$-0.429314\pi$
$523$	10.0738	0.440495	0.220247	+	0.975444i	$0.429314\pi$
$524$	5.03267	0.219853
$525$	−3.17847	−0.138720
$526$	5.46318	0.238206
$527$	4.29187	0.186957
$528$	3.85652	0.167834
$529$	40.7062	1.76983
$530$	−8.57167	−0.372329
$531$	−1.93078	−0.0837886
$532$	1.41486	0.0613420
$533$	−20.1776	−0.873988
$534$	10.7446	0.464966
$535$	26.2003	1.13274
$536$	5.11260	0.220831
$537$	−50.3726	−2.17374
$538$	−5.59912	−0.241395
$539$	9.50276	0.409313
$540$	9.45197	0.406748
$541$	3.52908	0.151727	0.0758635	−	0.997118i	$-0.475829\pi$
$541$	3.52908	0.151727	0.0758635	+	0.997118i	$0.475829\pi$
$542$	−6.95593	−0.298783
$543$	18.9507	0.813252
$544$	−0.777246	−0.0333241
$545$	−29.4201	−1.26022
$546$	−8.75171	−0.374539
$547$	−3.83335	−0.163902	−0.0819512	−	0.996636i	$-0.526115\pi$
$547$	−3.83335	−0.163902	−0.0819512	+	0.996636i	$0.526115\pi$
$548$	−9.66429	−0.412838
$549$	−12.9469	−0.552561
$550$	−2.10565	−0.0897852
$551$	−5.89103	−0.250966
$552$	16.1900	0.689094
$553$	−22.2803	−0.947456
$554$	16.3010	0.692562
$555$	15.4968	0.657803
$556$	6.20866	0.263306
$557$	−0.553697	−0.0234609	−0.0117304	−	0.999931i	$-0.503734\pi$
$557$	−0.553697	−0.0234609	−0.0117304	+	0.999931i	$0.503734\pi$
$558$	−6.15398	−0.260519
$559$	34.9060	1.47637
$560$	3.49660	0.147758
$561$	−2.99747	−0.126553
$562$	25.7357	1.08559
$563$	8.85702	0.373279	0.186640	−	0.982428i	$-0.440240\pi$
$563$	8.85702	0.373279	0.186640	+	0.982428i	$0.440240\pi$
$564$	12.2716	0.516727
$565$	7.45416	0.313599
$566$	0.131593	0.00553128
$567$	−15.7069	−0.659628
$568$	−0.661692	−0.0277640
$569$	8.30103	0.347997	0.173999	−	0.984746i	$-0.444331\pi$
$569$	8.30103	0.347997	0.173999	+	0.984746i	$0.444331\pi$
$570$	−5.01290	−0.209967
$571$	−17.5829	−0.735823	−0.367912	−	0.929861i	$-0.619927\pi$
$571$	−17.5829	−0.735823	−0.367912	+	0.929861i	$0.619927\pi$
$572$	−5.79777	−0.242417
$573$	−42.4242	−1.77230
$574$	−9.36183	−0.390755
$575$	−8.83970	−0.368641
$576$	1.11447	0.0464362
$577$	−18.3546	−0.764111	−0.382056	−	0.924139i	$-0.624784\pi$
$577$	−18.3546	−0.764111	−0.382056	+	0.924139i	$0.624784\pi$
$578$	−16.3959	−0.681979
$579$	38.7748	1.61143
$580$	−14.5587	−0.604518
$581$	19.4294	0.806067
$582$	−22.6291	−0.938008
$583$	6.59436	0.273110
$584$	−11.5032	−0.476005
$585$	8.39890	0.347252
$586$	3.62743	0.149848
$587$	15.9962	0.660233	0.330116	−	0.943940i	$-0.392912\pi$
$587$	15.9962	0.660233	0.330116	+	0.943940i	$0.392912\pi$
$588$	10.1384	0.418099
$589$	−5.52189	−0.227526
$590$	−4.28150	−0.176266
$591$	−35.3903	−1.45576
$592$	−3.09139	−0.127055
$593$	−28.0311	−1.15110	−0.575550	−	0.817767i	$-0.695212\pi$
$593$	−28.0311	−1.15110	−0.575550	+	0.817767i	$0.695212\pi$
$594$	−7.27159	−0.298357
$595$	−2.71772	−0.111416
$596$	14.0579	0.575833
$597$	5.99625	0.245410
$598$	−24.3396	−0.995319
$599$	8.11967	0.331761	0.165880	−	0.986146i	$-0.446953\pi$
$599$	8.11967	0.331761	0.165880	+	0.986146i	$0.446953\pi$
$600$	−2.24649	−0.0917124
$601$	−3.79839	−0.154940	−0.0774698	−	0.996995i	$-0.524684\pi$
$601$	−3.79839	−0.154940	−0.0774698	+	0.996995i	$0.524684\pi$
$602$	16.1954	0.660076
$603$	5.69784	0.232034
$604$	−8.58786	−0.349435
$605$	−18.2514	−0.742027
$606$	5.35925	0.217705
$607$	−3.64245	−0.147842	−0.0739212	−	0.997264i	$-0.523551\pi$
$607$	−3.64245	−0.147842	−0.0739212	+	0.997264i	$0.523551\pi$
$608$	1.00000	0.0405554
$609$	16.9068	0.685099
$610$	−28.7098	−1.16242
$611$	−18.4487	−0.746354
$612$	−0.866217	−0.0350148
$613$	−44.5363	−1.79881	−0.899403	−	0.437120i	$-0.855998\pi$
$613$	−44.5363	−1.79881	−0.899403	+	0.437120i	$0.855998\pi$
$614$	0.382256	0.0154266
$615$	33.1693	1.33751
$616$	−2.69001	−0.108383
$617$	−36.8606	−1.48395	−0.741976	−	0.670426i	$-0.766111\pi$
$617$	−36.8606	−1.48395	−0.741976	+	0.670426i	$0.766111\pi$
$618$	−0.977378	−0.0393159
$619$	−44.3504	−1.78259	−0.891296	−	0.453421i	$-0.850203\pi$
$619$	−44.3504	−1.78259	−0.891296	+	0.453421i	$0.850203\pi$
$620$	−13.6465	−0.548055
$621$	−30.5268	−1.22500
$622$	14.8067	0.593696
$623$	−7.49461	−0.300265
$624$	−6.18556	−0.247621
$625$	−29.3110	−1.17244
$626$	−18.6361	−0.744847
$627$	3.85652	0.154015
$628$	10.2251	0.408027
$629$	2.40277	0.0958047
$630$	3.89686	0.155254
$631$	−25.8963	−1.03092	−0.515458	−	0.856915i	$-0.672378\pi$
$631$	−25.8963	−1.03092	−0.515458	+	0.856915i	$0.672378\pi$
$632$	−15.7474	−0.626396
$633$	2.02842	0.0806223
$634$	0.143542	0.00570078
$635$	44.8438	1.77957
$636$	7.03542	0.278973
$637$	−15.2417	−0.603897
$638$	11.2003	0.443425
$639$	−0.737436	−0.0291725
$640$	2.47134	0.0976882
$641$	14.8972	0.588404	0.294202	−	0.955743i	$-0.404946\pi$
$641$	14.8972	0.588404	0.294202	+	0.955743i	$0.404946\pi$
$642$	−21.5046	−0.848719
$643$	10.8458	0.427717	0.213858	−	0.976865i	$-0.431397\pi$
$643$	10.8458	0.427717	0.213858	+	0.976865i	$0.431397\pi$
$644$	−11.2929	−0.445002
$645$	−57.3809	−2.25937
$646$	−0.777246	−0.0305803
$647$	−33.6114	−1.32140	−0.660700	−	0.750650i	$-0.729741\pi$
$647$	−33.6114	−1.32140	−0.660700	+	0.750650i	$0.729741\pi$
$648$	−11.1014	−0.436103
$649$	3.29384	0.129295
$650$	3.37729	0.132468
$651$	15.8474	0.621110
$652$	−13.0794	−0.512229
$653$	−9.13589	−0.357515	−0.178757	−	0.983893i	$-0.557208\pi$
$653$	−9.13589	−0.357515	−0.178757	+	0.983893i	$0.557208\pi$
$654$	24.1474	0.944236
$655$	12.4374	0.485970
$656$	−6.61679	−0.258342
$657$	−12.8199	−0.500154
$658$	−8.55968	−0.333691
$659$	−6.11303	−0.238130	−0.119065	−	0.992886i	$-0.537990\pi$
$659$	−6.11303	−0.238130	−0.119065	+	0.992886i	$0.537990\pi$
$660$	9.53077	0.370985
$661$	33.6797	1.30999	0.654994	−	0.755634i	$-0.272671\pi$
$661$	33.6797	1.30999	0.654994	+	0.755634i	$0.272671\pi$
$662$	−26.5807	−1.03309
$663$	4.80770	0.186716
$664$	13.7324	0.532919
$665$	3.49660	0.135592
$666$	−3.44526	−0.133501
$667$	47.0200	1.82062
$668$	−22.6408	−0.875999
$669$	3.95516	0.152915
$670$	12.6350	0.488131
$671$	22.0870	0.852660
$672$	−2.86993	−0.110710
$673$	20.3592	0.784790	0.392395	−	0.919797i	$-0.371647\pi$
$673$	20.3592	0.784790	0.392395	+	0.919797i	$0.371647\pi$
$674$	−8.74594	−0.336881
$675$	4.23582	0.163037
$676$	−3.70083	−0.142340
$677$	7.62176	0.292928	0.146464	−	0.989216i	$-0.453211\pi$
$677$	7.62176	0.292928	0.146464	+	0.989216i	$0.453211\pi$
$678$	−6.11820	−0.234968
$679$	15.7843	0.605746
$680$	−1.92084	−0.0736607
$681$	−20.6378	−0.790842
$682$	10.4985	0.402008
$683$	26.5582	1.01622	0.508111	−	0.861292i	$-0.330344\pi$
$683$	26.5582	1.01622	0.508111	+	0.861292i	$0.330344\pi$
$684$	1.11447	0.0426128
$685$	−23.8837	−0.912550
$686$	−16.9757	−0.648137
$687$	32.3995	1.23612
$688$	11.4467	0.436399
$689$	−10.5768	−0.402945
$690$	40.0110	1.52319
$691$	−40.5853	−1.54394	−0.771969	−	0.635660i	$-0.780728\pi$
$691$	−40.5853	−1.54394	−0.771969	+	0.635660i	$0.780728\pi$
$692$	12.6704	0.481658
$693$	−2.99793	−0.113882
$694$	−13.8668	−0.526376
$695$	15.3437	0.582020
$696$	11.9495	0.452943
$697$	5.14287	0.194800
$698$	7.60207	0.287743
$699$	−4.00552	−0.151503
$700$	1.56697	0.0592259
$701$	27.6768	1.04534	0.522670	−	0.852535i	$-0.324936\pi$
$701$	27.6768	1.04534	0.522670	+	0.852535i	$0.324936\pi$
$702$	11.6631	0.440194
$703$	−3.09139	−0.116594
$704$	−1.90125	−0.0716560
$705$	30.3272	1.14219
$706$	5.74221	0.216111
$707$	−3.73819	−0.140589
$708$	3.51415	0.132070
$709$	13.7299	0.515639	0.257820	−	0.966193i	$-0.416996\pi$
$709$	13.7299	0.515639	0.257820	+	0.966193i	$0.416996\pi$
$710$	−1.63526	−0.0613704
$711$	−17.5500	−0.658175
$712$	−5.29706	−0.198516
$713$	44.0736	1.65057
$714$	2.23064	0.0834796
$715$	−14.3283	−0.535846
$716$	24.8335	0.928070
$717$	−8.47027	−0.316328
$718$	−12.4080	−0.463062
$719$	11.3179	0.422088	0.211044	−	0.977477i	$-0.432314\pi$
$719$	11.3179	0.422088	0.211044	+	0.977477i	$0.432314\pi$
$720$	2.75423	0.102644
$721$	0.681741	0.0253894
$722$	1.00000	0.0372161
$723$	19.2717	0.716721
$724$	−9.34261	−0.347215
$725$	−6.52436	−0.242309
$726$	14.9804	0.555973
$727$	11.8370	0.439010	0.219505	−	0.975611i	$-0.429556\pi$
$727$	11.8370	0.439010	0.219505	+	0.975611i	$0.429556\pi$
$728$	4.31455	0.159908
$729$	10.9017	0.403768
$730$	−28.4282	−1.05218
$731$	−8.89686	−0.329062
$732$	23.5643	0.870962
$733$	27.3043	1.00851	0.504254	−	0.863555i	$-0.331768\pi$
$733$	27.3043	1.00851	0.504254	+	0.863555i	$0.331768\pi$
$734$	−3.66093	−0.135127
$735$	25.0553	0.924179
$736$	−7.98162	−0.294206
$737$	−9.72034	−0.358053
$738$	−7.37421	−0.271448
$739$	35.4056	1.30242	0.651208	−	0.758899i	$-0.274262\pi$
$739$	35.4056	1.30242	0.651208	+	0.758899i	$0.274262\pi$
$740$	−7.63986	−0.280847
$741$	−6.18556	−0.227232
$742$	−4.90735	−0.180155
$743$	−7.81352	−0.286650	−0.143325	−	0.989676i	$-0.545779\pi$
$743$	−7.81352	−0.286650	−0.143325	+	0.989676i	$0.545779\pi$
$744$	11.2007	0.410637
$745$	34.7418	1.27284
$746$	−35.5897	−1.30303
$747$	15.3043	0.559955
$748$	1.47774	0.0540315
$749$	14.9999	0.548084
$750$	19.5127	0.712502
$751$	−28.6632	−1.04593	−0.522967	−	0.852353i	$-0.675175\pi$
$751$	−28.6632	−1.04593	−0.522967	+	0.852353i	$0.675175\pi$
$752$	−6.04983	−0.220615
$753$	5.62709	0.205062
$754$	−17.9644	−0.654226
$755$	−21.2235	−0.772402
$756$	5.41133	0.196808
$757$	38.3471	1.39375	0.696875	−	0.717192i	$-0.254573\pi$
$757$	38.3471	1.39375	0.696875	+	0.717192i	$0.254573\pi$
$758$	33.7772	1.22684
$759$	−30.7813	−1.11729
$760$	2.47134	0.0896448
$761$	12.5038	0.453264	0.226632	−	0.973980i	$-0.427228\pi$
$761$	12.5038	0.453264	0.226632	+	0.973980i	$0.427228\pi$
$762$	−36.8067	−1.33337
$763$	−16.8433	−0.609768
$764$	20.9150	0.756677
$765$	−2.14072	−0.0773977
$766$	25.0970	0.906792
$767$	−5.28306	−0.190760
$768$	−2.02842	−0.0731941
$769$	−42.3418	−1.52688	−0.763442	−	0.645877i	$-0.776492\pi$
$769$	−42.3418	−1.52688	−0.763442	+	0.645877i	$0.776492\pi$
$770$	−6.64791	−0.239574
$771$	−27.1314	−0.977113
$772$	−19.1158	−0.687993
$773$	21.5922	0.776619	0.388310	−	0.921529i	$-0.373059\pi$
$773$	21.5922	0.776619	0.388310	+	0.921529i	$0.373059\pi$
$774$	12.7569	0.458539
$775$	−6.11554	−0.219677
$776$	11.1561	0.400480
$777$	8.87206	0.318283
$778$	14.8264	0.531553
$779$	−6.61679	−0.237071
$780$	−15.2866	−0.547348
$781$	1.25804	0.0450163
$782$	6.20368	0.221843
$783$	−22.5311	−0.805195
$784$	−4.99817	−0.178506
$785$	25.2698	0.901916
$786$	−10.2083	−0.364119
$787$	−15.4220	−0.549734	−0.274867	−	0.961482i	$-0.588634\pi$
$787$	−15.4220	−0.549734	−0.274867	+	0.961482i	$0.588634\pi$
$788$	17.4473	0.621534
$789$	−11.0816	−0.394516
$790$	−38.9170	−1.38461
$791$	4.26757	0.151737
$792$	−2.11889	−0.0752913
$793$	−35.4258	−1.25801
$794$	−17.7690	−0.630598
$795$	17.3869	0.616650
$796$	−2.95613	−0.104777
$797$	30.0978	1.06612	0.533060	−	0.846078i	$-0.321042\pi$
$797$	30.0978	1.06612	0.533060	+	0.846078i	$0.321042\pi$
$798$	−2.86993	−0.101594
$799$	4.70221	0.166352
$800$	1.10751	0.0391563
$801$	−5.90342	−0.208587
$802$	−8.78872	−0.310341
$803$	21.8704	0.771790
$804$	−10.3705	−0.365739
$805$	−27.9085	−0.983646
$806$	−16.8388	−0.593120
$807$	11.3573	0.399798
$808$	−2.64209	−0.0929483
$809$	−13.4974	−0.474542	−0.237271	−	0.971443i	$-0.576253\pi$
$809$	−13.4974	−0.474542	−0.237271	+	0.971443i	$0.576253\pi$
$810$	−27.4352	−0.963975
$811$	30.4280	1.06847	0.534236	−	0.845335i	$-0.320599\pi$
$811$	30.4280	1.06847	0.534236	+	0.845335i	$0.320599\pi$
$812$	−8.33499	−0.292501
$813$	14.1095	0.494843
$814$	5.87750	0.206006
$815$	−32.3236	−1.13225
$816$	1.57658	0.0551913
$817$	11.4467	0.400468
$818$	3.01022	0.105250
$819$	4.80844	0.168021
$820$	−16.3523	−0.571047
$821$	41.4936	1.44814	0.724069	−	0.689728i	$-0.242270\pi$
$821$	41.4936	1.44814	0.724069	+	0.689728i	$0.242270\pi$
$822$	19.6032	0.683740
$823$	25.7677	0.898205	0.449103	−	0.893480i	$-0.351744\pi$
$823$	25.7677	0.898205	0.449103	+	0.893480i	$0.351744\pi$
$824$	0.481843	0.0167858
$825$	4.27113	0.148702
$826$	−2.45119	−0.0852879
$827$	−42.4322	−1.47551	−0.737756	−	0.675068i	$-0.764114\pi$
$827$	−42.4322	−1.47551	−0.737756	+	0.675068i	$0.764114\pi$
$828$	−8.89527	−0.309132
$829$	−14.3266	−0.497583	−0.248792	−	0.968557i	$-0.580033\pi$
$829$	−14.3266	−0.497583	−0.248792	+	0.968557i	$0.580033\pi$
$830$	33.9373	1.17798
$831$	−33.0651	−1.14702
$832$	3.04945	0.105721
$833$	3.88480	0.134601
$834$	−12.5937	−0.436086
$835$	−55.9531	−1.93634
$836$	−1.90125	−0.0657561
$837$	−21.1192	−0.729988
$838$	−16.5426	−0.571454
$839$	5.05886	0.174651	0.0873257	−	0.996180i	$-0.472168\pi$
$839$	5.05886	0.174651	0.0873257	+	0.996180i	$0.472168\pi$
$840$	−7.09256	−0.244717
$841$	5.70425	0.196698
$842$	0.785599	0.0270735
$843$	−52.2027	−1.79796
$844$	−1.00000	−0.0344214
$845$	−9.14601	−0.314632
$846$	−6.74236	−0.231807
$847$	−10.4491	−0.359036
$848$	−3.46843	−0.119106
$849$	−0.266926	−0.00916087
$850$	−0.860806	−0.0295254
$851$	24.6743	0.845823
$852$	1.34219	0.0459826
$853$	15.5422	0.532156	0.266078	−	0.963951i	$-0.414272\pi$
$853$	15.5422	0.532156	0.266078	+	0.963951i	$0.414272\pi$
$854$	−16.4366	−0.562449
$855$	2.75423	0.0941927
$856$	10.6017	0.362358
$857$	−0.110482	−0.00377400	−0.00188700	−	0.999998i	$-0.500601\pi$
$857$	−0.110482	−0.00377400	−0.00188700	+	0.999998i	$0.500601\pi$
$858$	11.7603	0.401490
$859$	−43.3466	−1.47897	−0.739484	−	0.673174i	$-0.764930\pi$
$859$	−43.3466	−1.47897	−0.739484	+	0.673174i	$0.764930\pi$
$860$	28.2885	0.964631
$861$	18.9897	0.647167
$862$	12.1340	0.413285
$863$	0.477080	0.0162400	0.00811999	−	0.999967i	$-0.497415\pi$
$863$	0.477080	0.0162400	0.00811999	+	0.999967i	$0.497415\pi$
$864$	3.82464	0.130117
$865$	31.3129	1.06467
$866$	−18.7692	−0.637803
$867$	33.2577	1.12949
$868$	−7.81271	−0.265181
$869$	29.9397	1.01563
$870$	29.5311	1.00120
$871$	15.5906	0.528269
$872$	−11.9045	−0.403139
$873$	12.4331	0.420797
$874$	−7.98162	−0.269982
$875$	−13.6105	−0.460118
$876$	23.3332	0.788357
$877$	16.5224	0.557922	0.278961	−	0.960302i	$-0.410010\pi$
$877$	16.5224	0.557922	0.278961	+	0.960302i	$0.410010\pi$
$878$	−36.7958	−1.24180
$879$	−7.35794	−0.248177
$880$	−4.69863	−0.158391
$881$	−20.8866	−0.703688	−0.351844	−	0.936059i	$-0.614445\pi$
$881$	−20.8866	−0.703688	−0.351844	+	0.936059i	$0.614445\pi$
$882$	−5.57031	−0.187562
$883$	−19.5105	−0.656580	−0.328290	−	0.944577i	$-0.606472\pi$
$883$	−19.5105	−0.656580	−0.328290	+	0.944577i	$0.606472\pi$
$884$	−2.37018	−0.0797176
$885$	8.68466	0.291932
$886$	−25.3134	−0.850420
$887$	18.4635	0.619944	0.309972	−	0.950746i	$-0.399680\pi$
$887$	18.4635	0.619944	0.309972	+	0.950746i	$0.399680\pi$
$888$	6.27062	0.210428
$889$	25.6735	0.861060
$890$	−13.0908	−0.438806
$891$	21.1065	0.707093
$892$	−1.94987	−0.0652866
$893$	−6.04983	−0.202450
$894$	−28.5152	−0.953692
$895$	61.3719	2.05144
$896$	1.41486	0.0472672
$897$	49.3708	1.64844
$898$	−7.49329	−0.250054
$899$	32.5296	1.08492
$900$	1.23428	0.0411428
$901$	2.69582	0.0898109
$902$	12.5802	0.418874
$903$	−32.8511	−1.09321
$904$	3.01625	0.100319
$905$	−23.0887	−0.767496
$906$	17.4198	0.578732
$907$	59.4568	1.97423	0.987115	−	0.160014i	$-0.0511540\pi$
$907$	59.4568	1.97423	0.987115	+	0.160014i	$0.0511540\pi$
$908$	10.1743	0.337647
$909$	−2.94453	−0.0976638
$910$	10.6627	0.353466
$911$	−37.6820	−1.24846	−0.624230	−	0.781241i	$-0.714587\pi$
$911$	−37.6820	−1.24846	−0.624230	+	0.781241i	$0.714587\pi$
$912$	−2.02842	−0.0671676
$913$	−26.1087	−0.864070
$914$	10.7570	0.355811
$915$	58.2354	1.92520
$916$	−15.9728	−0.527756
$917$	7.12053	0.235140
$918$	−2.97268	−0.0981132
$919$	−41.5015	−1.36901	−0.684505	−	0.729008i	$-0.739981\pi$
$919$	−41.5015	−1.36901	−0.684505	+	0.729008i	$0.739981\pi$
$920$	−19.7253	−0.650323
$921$	−0.775374	−0.0255494
$922$	−17.7218	−0.583636
$923$	−2.01780	−0.0664167
$924$	5.45645	0.179504
$925$	−3.42374	−0.112572
$926$	18.3631	0.603448
$927$	0.537000	0.0176374
$928$	−5.89103	−0.193383
$929$	26.0963	0.856190	0.428095	−	0.903734i	$-0.359185\pi$
$929$	26.0963	0.856190	0.428095	+	0.903734i	$0.359185\pi$
$930$	27.6807	0.907685
$931$	−4.99817	−0.163808
$932$	1.97470	0.0646835
$933$	−30.0342	−0.983277
$934$	−3.64293	−0.119200
$935$	3.65199	0.119433
$936$	3.39852	0.111084
$937$	−12.4921	−0.408099	−0.204049	−	0.978961i	$-0.565410\pi$
$937$	−12.4921	−0.408099	−0.204049	+	0.978961i	$0.565410\pi$
$938$	7.23363	0.236186
$939$	37.8017	1.23361
$940$	−14.9512	−0.487654
$941$	−8.05821	−0.262690	−0.131345	−	0.991337i	$-0.541930\pi$
$941$	−8.05821	−0.262690	−0.131345	+	0.991337i	$0.541930\pi$
$942$	−20.7408	−0.675773
$943$	52.8126	1.71982
$944$	−1.73246	−0.0563868
$945$	13.3732	0.435031
$946$	−21.7629	−0.707574
$947$	−24.0892	−0.782793	−0.391397	−	0.920222i	$-0.628008\pi$
$947$	−24.0892	−0.782793	−0.391397	+	0.920222i	$0.628008\pi$
$948$	31.9422	1.03743
$949$	−35.0784	−1.13869
$950$	1.10751	0.0359323
$951$	−0.291163	−0.00944160
$952$	−1.09970	−0.0356413
$953$	43.3397	1.40391	0.701956	−	0.712221i	$-0.252310\pi$
$953$	43.3397	1.40391	0.701956	+	0.712221i	$0.252310\pi$
$954$	−3.86546	−0.125149
$955$	51.6879	1.67258
$956$	4.17581	0.135055
$957$	−22.7189	−0.734398
$958$	10.6715	0.344779
$959$	−13.6736	−0.441544
$960$	−5.01290	−0.161791
$961$	−0.508718	−0.0164103
$962$	−9.42705	−0.303940
$963$	11.8152	0.380741
$964$	−9.50085	−0.306002
$965$	−47.2416	−1.52076
$966$	22.9067	0.737010
$967$	21.8390	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$967$	21.8390	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$968$	−7.38525	−0.237371
$969$	1.57658	0.0506470
$970$	27.5704	0.885233
$971$	−29.3389	−0.941530	−0.470765	−	0.882259i	$-0.656022\pi$
$971$	−29.3389	−0.941530	−0.470765	+	0.882259i	$0.656022\pi$
$972$	11.0443	0.354245
$973$	8.78440	0.281615
$974$	13.0919	0.419490
$975$	−6.85055	−0.219393
$976$	−11.6171	−0.371854
$977$	5.51365	0.176397	0.0881987	−	0.996103i	$-0.471889\pi$
$977$	5.51365	0.176397	0.0881987	+	0.996103i	$0.471889\pi$
$978$	26.5305	0.848351
$979$	10.0710	0.321872
$980$	−12.3522	−0.394575
$981$	−13.2673	−0.423591
$982$	−13.4801	−0.430168
$983$	−36.3953	−1.16083	−0.580416	−	0.814320i	$-0.697110\pi$
$983$	−36.3953	−1.16083	−0.580416	+	0.814320i	$0.697110\pi$
$984$	13.4216	0.427865
$985$	43.1181	1.37386
$986$	4.57878	0.145818
$987$	17.3626	0.552657
$988$	3.04945	0.0970160
$989$	−91.3628	−2.90517
$990$	−5.23648	−0.166426
$991$	5.69743	0.180985	0.0904924	−	0.995897i	$-0.471156\pi$
$991$	5.69743	0.180985	0.0904924	+	0.995897i	$0.471156\pi$
$992$	−5.52189	−0.175320
$993$	53.9168	1.71100
$994$	−0.936203	−0.0296945
$995$	−7.30558	−0.231603
$996$	−27.8549	−0.882618
$997$	−1.79005	−0.0566916	−0.0283458	−	0.999598i	$-0.509024\pi$
$997$	−1.79005	−0.0566916	−0.0283458	+	0.999598i	$0.509024\pi$
$998$	−29.7634	−0.942145
$999$	−11.8234	−0.374077

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.8	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.8	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.02842 q^{3} +1.00000 q^{4} +2.47134 q^{5} -2.02842 q^{6} +1.41486 q^{7} +1.00000 q^{8} +1.11447 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.02842 q^{3} +1.00000 q^{4} +2.47134 q^{5} -2.02842 q^{6} +1.41486 q^{7} +1.00000 q^{8} +1.11447 q^{9} +2.47134 q^{10} -1.90125 q^{11} -2.02842 q^{12} +3.04945 q^{13} +1.41486 q^{14} -5.01290 q^{15} +1.00000 q^{16} -0.777246 q^{17} +1.11447 q^{18} +1.00000 q^{19} +2.47134 q^{20} -2.86993 q^{21} -1.90125 q^{22} -7.98162 q^{23} -2.02842 q^{24} +1.10751 q^{25} +3.04945 q^{26} +3.82464 q^{27} +1.41486 q^{28} -5.89103 q^{29} -5.01290 q^{30} -5.52189 q^{31} +1.00000 q^{32} +3.85652 q^{33} -0.777246 q^{34} +3.49660 q^{35} +1.11447 q^{36} -3.09139 q^{37} +1.00000 q^{38} -6.18556 q^{39} +2.47134 q^{40} -6.61679 q^{41} -2.86993 q^{42} +11.4467 q^{43} -1.90125 q^{44} +2.75423 q^{45} -7.98162 q^{46} -6.04983 q^{47} -2.02842 q^{48} -4.99817 q^{49} +1.10751 q^{50} +1.57658 q^{51} +3.04945 q^{52} -3.46843 q^{53} +3.82464 q^{54} -4.69863 q^{55} +1.41486 q^{56} -2.02842 q^{57} -5.89103 q^{58} -1.73246 q^{59} -5.01290 q^{60} -11.6171 q^{61} -5.52189 q^{62} +1.57682 q^{63} +1.00000 q^{64} +7.53623 q^{65} +3.85652 q^{66} +5.11260 q^{67} -0.777246 q^{68} +16.1900 q^{69} +3.49660 q^{70} -0.661692 q^{71} +1.11447 q^{72} -11.5032 q^{73} -3.09139 q^{74} -2.24649 q^{75} +1.00000 q^{76} -2.69001 q^{77} -6.18556 q^{78} -15.7474 q^{79} +2.47134 q^{80} -11.1014 q^{81} -6.61679 q^{82} +13.7324 q^{83} -2.86993 q^{84} -1.92084 q^{85} +11.4467 q^{86} +11.9495 q^{87} -1.90125 q^{88} -5.29706 q^{89} +2.75423 q^{90} +4.31455 q^{91} -7.98162 q^{92} +11.2007 q^{93} -6.04983 q^{94} +2.47134 q^{95} -2.02842 q^{96} +11.1561 q^{97} -4.99817 q^{98} -2.11889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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