LMFDB - Embedded newform 8018.2.a.f.1.16

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:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} -2.52015 q^{10} +5.01379 q^{11} -0.860547 q^{12} -0.222564 q^{13} +0.0296623 q^{14} -2.16871 q^{15} +1.00000 q^{16} +3.18383 q^{17} +2.25946 q^{18} -1.00000 q^{19} +2.52015 q^{20} +0.0255258 q^{21} -5.01379 q^{22} +5.25526 q^{23} +0.860547 q^{24} +1.35115 q^{25} +0.222564 q^{26} +4.52601 q^{27} -0.0296623 q^{28} -9.76733 q^{29} +2.16871 q^{30} -1.46739 q^{31} -1.00000 q^{32} -4.31461 q^{33} -3.18383 q^{34} -0.0747534 q^{35} -2.25946 q^{36} -8.01581 q^{37} +1.00000 q^{38} +0.191526 q^{39} -2.52015 q^{40} -11.7770 q^{41} -0.0255258 q^{42} +1.24837 q^{43} +5.01379 q^{44} -5.69417 q^{45} -5.25526 q^{46} -6.14331 q^{47} -0.860547 q^{48} -6.99912 q^{49} -1.35115 q^{50} -2.73984 q^{51} -0.222564 q^{52} -1.12509 q^{53} -4.52601 q^{54} +12.6355 q^{55} +0.0296623 q^{56} +0.860547 q^{57} +9.76733 q^{58} -8.52613 q^{59} -2.16871 q^{60} +3.33339 q^{61} +1.46739 q^{62} +0.0670207 q^{63} +1.00000 q^{64} -0.560893 q^{65} +4.31461 q^{66} +0.833415 q^{67} +3.18383 q^{68} -4.52240 q^{69} +0.0747534 q^{70} +5.44844 q^{71} +2.25946 q^{72} -0.905671 q^{73} +8.01581 q^{74} -1.16273 q^{75} -1.00000 q^{76} -0.148721 q^{77} -0.191526 q^{78} -6.25659 q^{79} +2.52015 q^{80} +2.88353 q^{81} +11.7770 q^{82} -10.6237 q^{83} +0.0255258 q^{84} +8.02373 q^{85} -1.24837 q^{86} +8.40525 q^{87} -5.01379 q^{88} -12.0829 q^{89} +5.69417 q^{90} +0.00660175 q^{91} +5.25526 q^{92} +1.26276 q^{93} +6.14331 q^{94} -2.52015 q^{95} +0.860547 q^{96} -9.41167 q^{97} +6.99912 q^{98} -11.3285 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−0.860547	−0.496837	−0.248419	−	0.968653i	$-0.579911\pi$
$3$	−0.860547	−0.496837	−0.248419	+	0.968653i	$0.579911\pi$
$4$	1.00000	0.500000
$5$	2.52015	1.12704	0.563522	−	0.826101i	$-0.309446\pi$
$5$	2.52015	1.12704	0.563522	+	0.826101i	$0.309446\pi$
$6$	0.860547	0.351317
$7$	−0.0296623	−0.0112113	−0.00560565	−	0.999984i	$-0.501784\pi$
$7$	−0.0296623	−0.0112113	−0.00560565	+	0.999984i	$0.501784\pi$
$8$	−1.00000	−0.353553
$9$	−2.25946	−0.753153
$10$	−2.52015	−0.796941
$11$	5.01379	1.51172	0.755858	−	0.654736i	$-0.227220\pi$
$11$	5.01379	1.51172	0.755858	+	0.654736i	$0.227220\pi$
$12$	−0.860547	−0.248419
$13$	−0.222564	−0.0617280	−0.0308640	−	0.999524i	$-0.509826\pi$
$13$	−0.222564	−0.0617280	−0.0308640	+	0.999524i	$0.509826\pi$
$14$	0.0296623	0.00792758
$15$	−2.16871	−0.559958
$16$	1.00000	0.250000
$17$	3.18383	0.772193	0.386096	−	0.922458i	$-0.373823\pi$
$17$	3.18383	0.772193	0.386096	+	0.922458i	$0.373823\pi$
$18$	2.25946	0.532559
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.52015	0.563522
$21$	0.0255258	0.00557019
$22$	−5.01379	−1.06894
$23$	5.25526	1.09580	0.547899	−	0.836545i	$-0.315428\pi$
$23$	5.25526	1.09580	0.547899	+	0.836545i	$0.315428\pi$
$24$	0.860547	0.175659
$25$	1.35115	0.270230
$26$	0.222564	0.0436483
$27$	4.52601	0.871032
$28$	−0.0296623	−0.00560565
$29$	−9.76733	−1.81375	−0.906874	−	0.421402i	$-0.861538\pi$
$29$	−9.76733	−1.81375	−0.906874	+	0.421402i	$0.861538\pi$
$30$	2.16871	0.395950
$31$	−1.46739	−0.263550	−0.131775	−	0.991280i	$-0.542068\pi$
$31$	−1.46739	−0.263550	−0.131775	+	0.991280i	$0.542068\pi$
$32$	−1.00000	−0.176777
$33$	−4.31461	−0.751077
$34$	−3.18383	−0.546023
$35$	−0.0747534	−0.0126356
$36$	−2.25946	−0.376576
$37$	−8.01581	−1.31779	−0.658895	−	0.752235i	$-0.728976\pi$
$37$	−8.01581	−1.31779	−0.658895	+	0.752235i	$0.728976\pi$
$38$	1.00000	0.162221
$39$	0.191526	0.0306688
$40$	−2.52015	−0.398470
$41$	−11.7770	−1.83926	−0.919631	−	0.392784i	$-0.871512\pi$
$41$	−11.7770	−1.83926	−0.919631	+	0.392784i	$0.871512\pi$
$42$	−0.0255258	−0.00393872
$43$	1.24837	0.190375	0.0951874	−	0.995459i	$-0.469655\pi$
$43$	1.24837	0.190375	0.0951874	+	0.995459i	$0.469655\pi$
$44$	5.01379	0.755858
$45$	−5.69417	−0.848837
$46$	−5.25526	−0.774846
$47$	−6.14331	−0.896094	−0.448047	−	0.894010i	$-0.647880\pi$
$47$	−6.14331	−0.896094	−0.448047	+	0.894010i	$0.647880\pi$
$48$	−0.860547	−0.124209
$49$	−6.99912	−0.999874
$50$	−1.35115	−0.191081
$51$	−2.73984	−0.383654
$52$	−0.222564	−0.0308640
$53$	−1.12509	−0.154543	−0.0772716	−	0.997010i	$-0.524621\pi$
$53$	−1.12509	−0.154543	−0.0772716	+	0.997010i	$0.524621\pi$
$54$	−4.52601	−0.615912
$55$	12.6355	1.70377
$56$	0.0296623	0.00396379
$57$	0.860547	0.113982
$58$	9.76733	1.28251
$59$	−8.52613	−1.11001	−0.555004	−	0.831848i	$-0.687283\pi$
$59$	−8.52613	−1.11001	−0.555004	+	0.831848i	$0.687283\pi$
$60$	−2.16871	−0.279979
$61$	3.33339	0.426797	0.213398	−	0.976965i	$-0.431547\pi$
$61$	3.33339	0.426797	0.213398	+	0.976965i	$0.431547\pi$
$62$	1.46739	0.186358
$63$	0.0670207	0.00844382
$64$	1.00000	0.125000
$65$	−0.560893	−0.0695702
$66$	4.31461	0.531092
$67$	0.833415	0.101818	0.0509089	−	0.998703i	$-0.483788\pi$
$67$	0.833415	0.101818	0.0509089	+	0.998703i	$0.483788\pi$
$68$	3.18383	0.386096
$69$	−4.52240	−0.544433
$70$	0.0747534	0.00893474
$71$	5.44844	0.646611	0.323305	−	0.946295i	$-0.395206\pi$
$71$	5.44844	0.646611	0.323305	+	0.946295i	$0.395206\pi$
$72$	2.25946	0.266280
$73$	−0.905671	−0.106001	−0.0530004	−	0.998594i	$-0.516878\pi$
$73$	−0.905671	−0.106001	−0.0530004	+	0.998594i	$0.516878\pi$
$74$	8.01581	0.931818
$75$	−1.16273	−0.134260
$76$	−1.00000	−0.114708
$77$	−0.148721	−0.0169483
$78$	−0.191526	−0.0216861
$79$	−6.25659	−0.703922	−0.351961	−	0.936015i	$-0.614485\pi$
$79$	−6.25659	−0.703922	−0.351961	+	0.936015i	$0.614485\pi$
$80$	2.52015	0.281761
$81$	2.88353	0.320392
$82$	11.7770	1.30055
$83$	−10.6237	−1.16610	−0.583051	−	0.812436i	$-0.698141\pi$
$83$	−10.6237	−1.16610	−0.583051	+	0.812436i	$0.698141\pi$
$84$	0.0255258	0.00278510
$85$	8.02373	0.870295
$86$	−1.24837	−0.134615
$87$	8.40525	0.901137
$88$	−5.01379	−0.534472
$89$	−12.0829	−1.28079	−0.640395	−	0.768046i	$-0.721229\pi$
$89$	−12.0829	−1.28079	−0.640395	+	0.768046i	$0.721229\pi$
$90$	5.69417	0.600218
$91$	0.00660175	0.000692051 0
$92$	5.25526	0.547899
$93$	1.26276	0.130942
$94$	6.14331	0.633634
$95$	−2.52015	−0.258562
$96$	0.860547	0.0878293
$97$	−9.41167	−0.955611	−0.477805	−	0.878466i	$-0.658568\pi$
$97$	−9.41167	−0.955611	−0.477805	+	0.878466i	$0.658568\pi$
$98$	6.99912	0.707018
$99$	−11.3285	−1.13855
$100$	1.35115	0.135115
$101$	17.5243	1.74373	0.871867	−	0.489743i	$-0.162910\pi$
$101$	17.5243	1.74373	0.871867	+	0.489743i	$0.162910\pi$
$102$	2.73984	0.271284
$103$	−3.53667	−0.348478	−0.174239	−	0.984703i	$-0.555747\pi$
$103$	−3.53667	−0.348478	−0.174239	+	0.984703i	$0.555747\pi$
$104$	0.222564	0.0218241
$105$	0.0643289	0.00627785
$106$	1.12509	0.109278
$107$	−6.29343	−0.608409	−0.304205	−	0.952607i	$-0.598391\pi$
$107$	−6.29343	−0.608409	−0.304205	+	0.952607i	$0.598391\pi$
$108$	4.52601	0.435516
$109$	13.2389	1.26806	0.634029	−	0.773309i	$-0.281400\pi$
$109$	13.2389	1.26806	0.634029	+	0.773309i	$0.281400\pi$
$110$	−12.6355	−1.20475
$111$	6.89798	0.654727
$112$	−0.0296623	−0.00280282
$113$	9.17526	0.863136	0.431568	−	0.902081i	$-0.357961\pi$
$113$	9.17526	0.863136	0.431568	+	0.902081i	$0.357961\pi$
$114$	−0.860547	−0.0805976
$115$	13.2440	1.23501
$116$	−9.76733	−0.906874
$117$	0.502873	0.0464906
$118$	8.52613	0.784894
$119$	−0.0944398	−0.00865728
$120$	2.16871	0.197975
$121$	14.1381	1.28529
$122$	−3.33339	−0.301791
$123$	10.1347	0.913813
$124$	−1.46739	−0.131775
$125$	−9.19565	−0.822484
$126$	−0.0670207	−0.00597068
$127$	−4.76962	−0.423235	−0.211617	−	0.977353i	$-0.567873\pi$
$127$	−4.76962	−0.423235	−0.211617	+	0.977353i	$0.567873\pi$
$128$	−1.00000	−0.0883883
$129$	−1.07428	−0.0945853
$130$	0.560893	0.0491936
$131$	−18.0524	−1.57725	−0.788624	−	0.614876i	$-0.789206\pi$
$131$	−18.0524	−1.57725	−0.788624	+	0.614876i	$0.789206\pi$
$132$	−4.31461	−0.375538
$133$	0.0296623	0.00257205
$134$	−0.833415	−0.0719961
$135$	11.4062	0.981692
$136$	−3.18383	−0.273011
$137$	−6.30139	−0.538364	−0.269182	−	0.963089i	$-0.586753\pi$
$137$	−6.30139	−0.538364	−0.269182	+	0.963089i	$0.586753\pi$
$138$	4.52240	0.384972
$139$	−3.04750	−0.258486	−0.129243	−	0.991613i	$-0.541255\pi$
$139$	−3.04750	−0.258486	−0.129243	+	0.991613i	$0.541255\pi$
$140$	−0.0747534	−0.00631782
$141$	5.28661	0.445213
$142$	−5.44844	−0.457223
$143$	−1.11589	−0.0933152
$144$	−2.25946	−0.188288
$145$	−24.6151	−2.04417
$146$	0.905671	0.0749538
$147$	6.02307	0.496775
$148$	−8.01581	−0.658895
$149$	−11.5581	−0.946873	−0.473437	−	0.880828i	$-0.656987\pi$
$149$	−11.5581	−0.946873	−0.473437	+	0.880828i	$0.656987\pi$
$150$	1.16273	0.0949363
$151$	13.7023	1.11508	0.557539	−	0.830151i	$-0.311746\pi$
$151$	13.7023	1.11508	0.557539	+	0.830151i	$0.311746\pi$
$152$	1.00000	0.0811107
$153$	−7.19373	−0.581579
$154$	0.148721	0.0119843
$155$	−3.69803	−0.297033
$156$	0.191526	0.0153344
$157$	4.98953	0.398208	0.199104	−	0.979978i	$-0.436197\pi$
$157$	4.98953	0.398208	0.199104	+	0.979978i	$0.436197\pi$
$158$	6.25659	0.497748
$159$	0.968194	0.0767828
$160$	−2.52015	−0.199235
$161$	−0.155883	−0.0122853
$162$	−2.88353	−0.226551
$163$	2.90353	0.227422	0.113711	−	0.993514i	$-0.463726\pi$
$163$	2.90353	0.227422	0.113711	+	0.993514i	$0.463726\pi$
$164$	−11.7770	−0.919631
$165$	−10.8735	−0.846497
$166$	10.6237	0.824558
$167$	21.2988	1.64815	0.824074	−	0.566482i	$-0.191696\pi$
$167$	21.2988	1.64815	0.824074	+	0.566482i	$0.191696\pi$
$168$	−0.0255258	−0.00196936
$169$	−12.9505	−0.996190
$170$	−8.02373	−0.615392
$171$	2.25946	0.172785
$172$	1.24837	0.0951874
$173$	−19.3813	−1.47353	−0.736765	−	0.676149i	$-0.763647\pi$
$173$	−19.3813	−1.47353	−0.736765	+	0.676149i	$0.763647\pi$
$174$	−8.40525	−0.637200
$175$	−0.0400782	−0.00302963
$176$	5.01379	0.377929
$177$	7.33714	0.551493
$178$	12.0829	0.905655
$179$	−18.9865	−1.41912	−0.709561	−	0.704644i	$-0.751107\pi$
$179$	−18.9865	−1.41912	−0.709561	+	0.704644i	$0.751107\pi$
$180$	−5.69417	−0.424418
$181$	5.40224	0.401545	0.200773	−	0.979638i	$-0.435655\pi$
$181$	5.40224	0.401545	0.200773	+	0.979638i	$0.435655\pi$
$182$	−0.00660175	−0.000489354 0
$183$	−2.86854	−0.212049
$184$	−5.25526	−0.387423
$185$	−20.2010	−1.48521
$186$	−1.26276	−0.0925897
$187$	15.9631	1.16734
$188$	−6.14331	−0.448047
$189$	−0.134252	−0.00976539
$190$	2.52015	0.182831
$191$	−7.31657	−0.529408	−0.264704	−	0.964330i	$-0.585274\pi$
$191$	−7.31657	−0.529408	−0.264704	+	0.964330i	$0.585274\pi$
$192$	−0.860547	−0.0621047
$193$	−4.18426	−0.301190	−0.150595	−	0.988596i	$-0.548119\pi$
$193$	−4.18426	−0.301190	−0.150595	+	0.988596i	$0.548119\pi$
$194$	9.41167	0.675719
$195$	0.482675	0.0345651
$196$	−6.99912	−0.499937
$197$	−1.52396	−0.108577	−0.0542887	−	0.998525i	$-0.517289\pi$
$197$	−1.52396	−0.108577	−0.0542887	+	0.998525i	$0.517289\pi$
$198$	11.3285	0.805079
$199$	22.3056	1.58120	0.790600	−	0.612333i	$-0.209769\pi$
$199$	22.3056	1.58120	0.790600	+	0.612333i	$0.209769\pi$
$200$	−1.35115	−0.0955406
$201$	−0.717193	−0.0505869
$202$	−17.5243	−1.23301
$203$	0.289721	0.0203345
$204$	−2.73984	−0.191827
$205$	−29.6798	−2.07293
$206$	3.53667	0.246411
$207$	−11.8740	−0.825303
$208$	−0.222564	−0.0154320
$209$	−5.01379	−0.346811
$210$	−0.0643289	−0.00443911
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−1.12509	−0.0772716
$213$	−4.68864	−0.321260
$214$	6.29343	0.430210
$215$	3.14608	0.214561
$216$	−4.52601	−0.307956
$217$	0.0435261	0.00295474
$218$	−13.2389	−0.896652
$219$	0.779372	0.0526651
$220$	12.6355	0.851886
$221$	−0.708605	−0.0476659
$222$	−6.89798	−0.462962
$223$	−29.0976	−1.94852	−0.974258	−	0.225434i	$-0.927620\pi$
$223$	−29.0976	−1.94852	−0.974258	+	0.225434i	$0.927620\pi$
$224$	0.0296623	0.00198190
$225$	−3.05286	−0.203524
$226$	−9.17526	−0.610329
$227$	23.2960	1.54621	0.773105	−	0.634278i	$-0.218703\pi$
$227$	23.2960	1.54621	0.773105	+	0.634278i	$0.218703\pi$
$228$	0.860547	0.0569911
$229$	15.4214	1.01908	0.509539	−	0.860448i	$-0.329816\pi$
$229$	15.4214	1.01908	0.509539	+	0.860448i	$0.329816\pi$
$230$	−13.2440	−0.873286
$231$	0.127981	0.00842055
$232$	9.76733	0.641257
$233$	−3.14863	−0.206274	−0.103137	−	0.994667i	$-0.532888\pi$
$233$	−3.14863	−0.206274	−0.103137	+	0.994667i	$0.532888\pi$
$234$	−0.502873	−0.0328738
$235$	−15.4821	−1.00994
$236$	−8.52613	−0.555004
$237$	5.38409	0.349735
$238$	0.0944398	0.00612162
$239$	−12.7965	−0.827737	−0.413868	−	0.910337i	$-0.635823\pi$
$239$	−12.7965	−0.827737	−0.413868	+	0.910337i	$0.635823\pi$
$240$	−2.16871	−0.139989
$241$	0.450062	0.0289911	0.0144955	−	0.999895i	$-0.495386\pi$
$241$	0.450062	0.0289911	0.0144955	+	0.999895i	$0.495386\pi$
$242$	−14.1381	−0.908834
$243$	−16.0594	−1.03021
$244$	3.33339	0.213398
$245$	−17.6388	−1.12690
$246$	−10.1347	−0.646164
$247$	0.222564	0.0141614
$248$	1.46739	0.0931791
$249$	9.14219	0.579363
$250$	9.19565	0.581584
$251$	26.7435	1.68804	0.844019	−	0.536314i	$-0.180184\pi$
$251$	26.7435	1.68804	0.844019	+	0.536314i	$0.180184\pi$
$252$	0.0670207	0.00422191
$253$	26.3488	1.65654
$254$	4.76962	0.299272
$255$	−6.90480	−0.432395
$256$	1.00000	0.0625000
$257$	21.3320	1.33066	0.665328	−	0.746551i	$-0.268292\pi$
$257$	21.3320	1.33066	0.665328	+	0.746551i	$0.268292\pi$
$258$	1.07428	0.0668819
$259$	0.237767	0.0147741
$260$	−0.560893	−0.0347851
$261$	22.0689	1.36603
$262$	18.0524	1.11528
$263$	1.59249	0.0981972	0.0490986	−	0.998794i	$-0.484365\pi$
$263$	1.59249	0.0981972	0.0490986	+	0.998794i	$0.484365\pi$
$264$	4.31461	0.265546
$265$	−2.83540	−0.174177
$266$	−0.0296623	−0.00181871
$267$	10.3979	0.636344
$268$	0.833415	0.0509089
$269$	30.5204	1.86086	0.930430	−	0.366470i	$-0.119434\pi$
$269$	30.5204	1.86086	0.930430	+	0.366470i	$0.119434\pi$
$270$	−11.4062	−0.694161
$271$	−0.0288858	−0.00175469	−0.000877345	−	1.00000i	$-0.500279\pi$
$271$	−0.0288858	−0.00175469	−0.000877345		1.00000i	$0.500279\pi$
$272$	3.18383	0.193048
$273$	−0.00568112	−0.000343837 0
$274$	6.30139	0.380681
$275$	6.77438	0.408511
$276$	−4.52240	−0.272217
$277$	2.62360	0.157637	0.0788185	−	0.996889i	$-0.474885\pi$
$277$	2.62360	0.157637	0.0788185	+	0.996889i	$0.474885\pi$
$278$	3.04750	0.182777
$279$	3.31550	0.198494
$280$	0.0747534	0.00446737
$281$	−7.68302	−0.458330	−0.229165	−	0.973388i	$-0.573600\pi$
$281$	−7.68302	−0.458330	−0.229165	+	0.973388i	$0.573600\pi$
$282$	−5.28661	−0.314813
$283$	−6.15859	−0.366090	−0.183045	−	0.983105i	$-0.558595\pi$
$283$	−6.15859	−0.366090	−0.183045	+	0.983105i	$0.558595\pi$
$284$	5.44844	0.323305
$285$	2.16871	0.128463
$286$	1.11589	0.0659838
$287$	0.349333	0.0206205
$288$	2.25946	0.133140
$289$	−6.86322	−0.403719
$290$	24.6151	1.44545
$291$	8.09919	0.474783
$292$	−0.905671	−0.0530004
$293$	14.5946	0.852625	0.426313	−	0.904576i	$-0.359812\pi$
$293$	14.5946	0.852625	0.426313	+	0.904576i	$0.359812\pi$
$294$	−6.02307	−0.351273
$295$	−21.4871	−1.25103
$296$	8.01581	0.465909
$297$	22.6925	1.31675
$298$	11.5581	0.669541
$299$	−1.16963	−0.0676414
$300$	−1.16273	−0.0671301
$301$	−0.0370296	−0.00213435
$302$	−13.7023	−0.788479
$303$	−15.0805	−0.866352
$304$	−1.00000	−0.0573539
$305$	8.40064	0.481019
$306$	7.19373	0.411238
$307$	−32.4099	−1.84973	−0.924865	−	0.380296i	$-0.875822\pi$
$307$	−32.4099	−1.84973	−0.924865	+	0.380296i	$0.875822\pi$
$308$	−0.148721	−0.00847415
$309$	3.04347	0.173137
$310$	3.69803	0.210034
$311$	−20.5365	−1.16452	−0.582258	−	0.813004i	$-0.697831\pi$
$311$	−20.5365	−1.16452	−0.582258	+	0.813004i	$0.697831\pi$
$312$	−0.191526	−0.0108431
$313$	21.1913	1.19780	0.598902	−	0.800822i	$-0.295604\pi$
$313$	21.1913	1.19780	0.598902	+	0.800822i	$0.295604\pi$
$314$	−4.98953	−0.281576
$315$	0.168902	0.00951656
$316$	−6.25659	−0.351961
$317$	24.0002	1.34799	0.673993	−	0.738738i	$-0.264578\pi$
$317$	24.0002	1.34799	0.673993	+	0.738738i	$0.264578\pi$
$318$	−0.968194	−0.0542936
$319$	−48.9714	−2.74187
$320$	2.52015	0.140881
$321$	5.41580	0.302280
$322$	0.155883	0.00868703
$323$	−3.18383	−0.177153
$324$	2.88353	0.160196
$325$	−0.300716	−0.0166807
$326$	−2.90353	−0.160812
$327$	−11.3927	−0.630018
$328$	11.7770	0.650277
$329$	0.182225	0.0100464
$330$	10.8735	0.598564
$331$	3.63684	0.199899	0.0999494	−	0.994993i	$-0.468132\pi$
$331$	3.63684	0.199899	0.0999494	+	0.994993i	$0.468132\pi$
$332$	−10.6237	−0.583051
$333$	18.1114	0.992497
$334$	−21.2988	−1.16542
$335$	2.10033	0.114753
$336$	0.0255258	0.00139255
$337$	20.0352	1.09139	0.545693	−	0.837985i	$-0.316267\pi$
$337$	20.0352	1.09139	0.545693	+	0.837985i	$0.316267\pi$
$338$	12.9505	0.704412
$339$	−7.89574	−0.428838
$340$	8.02373	0.435148
$341$	−7.35717	−0.398413
$342$	−2.25946	−0.122178
$343$	0.415246	0.0224212
$344$	−1.24837	−0.0673077
$345$	−11.3971	−0.613600
$346$	19.3813	1.04194
$347$	−7.42937	−0.398830	−0.199415	−	0.979915i	$-0.563904\pi$
$347$	−7.42937	−0.398830	−0.199415	+	0.979915i	$0.563904\pi$
$348$	8.40525	0.450569
$349$	24.7756	1.32621	0.663104	−	0.748527i	$-0.269239\pi$
$349$	24.7756	1.32621	0.663104	+	0.748527i	$0.269239\pi$
$350$	0.0400782	0.00214227
$351$	−1.00733	−0.0537671
$352$	−5.01379	−0.267236
$353$	−1.77080	−0.0942504	−0.0471252	−	0.998889i	$-0.515006\pi$
$353$	−1.77080	−0.0942504	−0.0471252	+	0.998889i	$0.515006\pi$
$354$	−7.33714	−0.389964
$355$	13.7309	0.728759
$356$	−12.0829	−0.640395
$357$	0.0812699	0.00430126
$358$	18.9865	1.00347
$359$	−35.7298	−1.88575	−0.942873	−	0.333151i	$-0.891888\pi$
$359$	−35.7298	−1.88575	−0.942873	+	0.333151i	$0.891888\pi$
$360$	5.69417	0.300109
$361$	1.00000	0.0526316
$362$	−5.40224	−0.283935
$363$	−12.1665	−0.638578
$364$	0.00660175	0.000346026 0
$365$	−2.28242	−0.119468
$366$	2.86854	0.149941
$367$	0.959187	0.0500691	0.0250346	−	0.999687i	$-0.492030\pi$
$367$	0.959187	0.0500691	0.0250346	+	0.999687i	$0.492030\pi$
$368$	5.25526	0.273949
$369$	26.6097	1.38524
$370$	20.2010	1.05020
$371$	0.0333728	0.00173263
$372$	1.26276	0.0654708
$373$	−20.1033	−1.04091	−0.520456	−	0.853889i	$-0.674238\pi$
$373$	−20.1033	−1.04091	−0.520456	+	0.853889i	$0.674238\pi$
$374$	−15.9631	−0.825431
$375$	7.91329	0.408641
$376$	6.14331	0.316817
$377$	2.17385	0.111959
$378$	0.134252	0.00690518
$379$	0.895330	0.0459900	0.0229950	−	0.999736i	$-0.492680\pi$
$379$	0.895330	0.0459900	0.0229950	+	0.999736i	$0.492680\pi$
$380$	−2.52015	−0.129281
$381$	4.10448	0.210279
$382$	7.31657	0.374348
$383$	−5.71870	−0.292212	−0.146106	−	0.989269i	$-0.546674\pi$
$383$	−5.71870	−0.292212	−0.146106	+	0.989269i	$0.546674\pi$
$384$	0.860547	0.0439146
$385$	−0.374798	−0.0191015
$386$	4.18426	0.212973
$387$	−2.82064	−0.143381
$388$	−9.41167	−0.477805
$389$	−24.0148	−1.21760	−0.608800	−	0.793323i	$-0.708349\pi$
$389$	−24.0148	−1.21760	−0.608800	+	0.793323i	$0.708349\pi$
$390$	−0.482675	−0.0244412
$391$	16.7319	0.846167
$392$	6.99912	0.353509
$393$	15.5350	0.783636
$394$	1.52396	0.0767758
$395$	−15.7675	−0.793351
$396$	−11.3285	−0.569277
$397$	−12.1982	−0.612209	−0.306105	−	0.951998i	$-0.599026\pi$
$397$	−12.1982	−0.612209	−0.306105	+	0.951998i	$0.599026\pi$
$398$	−22.3056	−1.11808
$399$	−0.0255258	−0.00127789
$400$	1.35115	0.0675574
$401$	−6.57122	−0.328151	−0.164075	−	0.986448i	$-0.552464\pi$
$401$	−6.57122	−0.328151	−0.164075	+	0.986448i	$0.552464\pi$
$402$	0.717193	0.0357704
$403$	0.326587	0.0162684
$404$	17.5243	0.871867
$405$	7.26691	0.361096
$406$	−0.289721	−0.0143786
$407$	−40.1896	−1.99212
$408$	2.73984	0.135642
$409$	19.8248	0.980272	0.490136	−	0.871646i	$-0.336947\pi$
$409$	19.8248	0.980272	0.490136	+	0.871646i	$0.336947\pi$
$410$	29.6798	1.46578
$411$	5.42265	0.267479
$412$	−3.53667	−0.174239
$413$	0.252905	0.0124446
$414$	11.8740	0.583577
$415$	−26.7733	−1.31425
$416$	0.222564	0.0109121
$417$	2.62252	0.128425
$418$	5.01379	0.245233
$419$	−18.9986	−0.928142	−0.464071	−	0.885798i	$-0.653612\pi$
$419$	−18.9986	−0.928142	−0.464071	+	0.885798i	$0.653612\pi$
$420$	0.0643289	0.00313893
$421$	−20.7075	−1.00922	−0.504610	−	0.863347i	$-0.668364\pi$
$421$	−20.7075	−1.00922	−0.504610	+	0.863347i	$0.668364\pi$
$422$	1.00000	0.0486792
$423$	13.8806	0.674896
$424$	1.12509	0.0546392
$425$	4.30183	0.208669
$426$	4.68864	0.227165
$427$	−0.0988760	−0.00478495
$428$	−6.29343	−0.304205
$429$	0.960274	0.0463625
$430$	−3.14608	−0.151718
$431$	4.31233	0.207718	0.103859	−	0.994592i	$-0.466881\pi$
$431$	4.31233	0.207718	0.103859	+	0.994592i	$0.466881\pi$
$432$	4.52601	0.217758
$433$	−19.5928	−0.941572	−0.470786	−	0.882248i	$-0.656030\pi$
$433$	−19.5928	−0.941572	−0.470786	+	0.882248i	$0.656030\pi$
$434$	−0.0435261	−0.00208932
$435$	21.1825	1.01562
$436$	13.2389	0.634029
$437$	−5.25526	−0.251393
$438$	−0.779372	−0.0372399
$439$	15.0337	0.717520	0.358760	−	0.933430i	$-0.383200\pi$
$439$	15.0337	0.717520	0.358760	+	0.933430i	$0.383200\pi$
$440$	−12.6355	−0.602374
$441$	15.8142	0.753058
$442$	0.708605	0.0337049
$443$	−21.1704	−1.00584	−0.502918	−	0.864334i	$-0.667740\pi$
$443$	−21.1704	−1.00584	−0.502918	+	0.864334i	$0.667740\pi$
$444$	6.89798	0.327364
$445$	−30.4508	−1.44351
$446$	29.0976	1.37781
$447$	9.94626	0.470442
$448$	−0.0296623	−0.00140141
$449$	40.7663	1.92388	0.961941	−	0.273258i	$-0.0881013\pi$
$449$	40.7663	1.92388	0.961941	+	0.273258i	$0.0881013\pi$
$450$	3.05286	0.143913
$451$	−59.0476	−2.78044
$452$	9.17526	0.431568
$453$	−11.7915	−0.554012
$454$	−23.2960	−1.09334
$455$	0.0166374	0.000779973 0
$456$	−0.860547	−0.0402988
$457$	8.18021	0.382654	0.191327	−	0.981526i	$-0.438721\pi$
$457$	8.18021	0.382654	0.191327	+	0.981526i	$0.438721\pi$
$458$	−15.4214	−0.720596
$459$	14.4101	0.672604
$460$	13.2440	0.617507
$461$	−9.09547	−0.423618	−0.211809	−	0.977311i	$-0.567936\pi$
$461$	−9.09547	−0.423618	−0.211809	+	0.977311i	$0.567936\pi$
$462$	−0.127981	−0.00595422
$463$	−4.16675	−0.193646	−0.0968228	−	0.995302i	$-0.530868\pi$
$463$	−4.16675	−0.193646	−0.0968228	+	0.995302i	$0.530868\pi$
$464$	−9.76733	−0.453437
$465$	3.18233	0.147577
$466$	3.14863	0.145857
$467$	16.1212	0.746001	0.373000	−	0.927831i	$-0.378329\pi$
$467$	16.1212	0.746001	0.373000	+	0.927831i	$0.378329\pi$
$468$	0.502873	0.0232453
$469$	−0.0247210	−0.00114151
$470$	15.4821	0.714134
$471$	−4.29373	−0.197845
$472$	8.52613	0.392447
$473$	6.25908	0.287793
$474$	−5.38409	−0.247300
$475$	−1.35115	−0.0619950
$476$	−0.0944398	−0.00432864
$477$	2.54210	0.116395
$478$	12.7965	0.585298
$479$	20.4401	0.933933	0.466966	−	0.884275i	$-0.345347\pi$
$479$	20.4401	0.933933	0.466966	+	0.884275i	$0.345347\pi$
$480$	2.16871	0.0989875
$481$	1.78403	0.0813446
$482$	−0.450062	−0.0204998
$483$	0.134145	0.00610380
$484$	14.1381	0.642643
$485$	−23.7188	−1.07702
$486$	16.0594	0.728471
$487$	7.56813	0.342945	0.171472	−	0.985189i	$-0.445148\pi$
$487$	7.56813	0.342945	0.171472	+	0.985189i	$0.445148\pi$
$488$	−3.33339	−0.150895
$489$	−2.49863	−0.112992
$490$	17.6388	0.796841
$491$	3.59508	0.162244	0.0811219	−	0.996704i	$-0.474150\pi$
$491$	3.59508	0.162244	0.0811219	+	0.996704i	$0.474150\pi$
$492$	10.1347	0.456907
$493$	−31.0975	−1.40056
$494$	−0.222564	−0.0100136
$495$	−28.5494	−1.28320
$496$	−1.46739	−0.0658876
$497$	−0.161613	−0.00724935
$498$	−9.14219	−0.409671
$499$	−4.44310	−0.198901	−0.0994503	−	0.995043i	$-0.531708\pi$
$499$	−4.44310	−0.198901	−0.0994503	+	0.995043i	$0.531708\pi$
$500$	−9.19565	−0.411242
$501$	−18.3286	−0.818861
$502$	−26.7435	−1.19362
$503$	15.2203	0.678640	0.339320	−	0.940671i	$-0.389803\pi$
$503$	15.2203	0.678640	0.339320	+	0.940671i	$0.389803\pi$
$504$	−0.0670207	−0.00298534
$505$	44.1638	1.96527
$506$	−26.3488	−1.17135
$507$	11.1445	0.494944
$508$	−4.76962	−0.211617
$509$	−0.520118	−0.0230538	−0.0115269	−	0.999934i	$-0.503669\pi$
$509$	−0.520118	−0.0230538	−0.0115269	+	0.999934i	$0.503669\pi$
$510$	6.90480	0.305750
$511$	0.0268643	0.00118841
$512$	−1.00000	−0.0441942
$513$	−4.52601	−0.199828
$514$	−21.3320	−0.940916
$515$	−8.91293	−0.392751
$516$	−1.07428	−0.0472927
$517$	−30.8013	−1.35464
$518$	−0.237767	−0.0104469
$519$	16.6785	0.732104
$520$	0.560893	0.0245968
$521$	11.1839	0.489976	0.244988	−	0.969526i	$-0.421216\pi$
$521$	11.1839	0.489976	0.244988	+	0.969526i	$0.421216\pi$
$522$	−22.0689	−0.965928
$523$	12.5800	0.550086	0.275043	−	0.961432i	$-0.411308\pi$
$523$	12.5800	0.550086	0.275043	+	0.961432i	$0.411308\pi$
$524$	−18.0524	−0.788624
$525$	0.0344892	0.00150523
$526$	−1.59249	−0.0694359
$527$	−4.67191	−0.203512
$528$	−4.31461	−0.187769
$529$	4.61777	0.200773
$530$	2.83540	0.123162
$531$	19.2644	0.836005
$532$	0.0296623	0.00128602
$533$	2.62113	0.113534
$534$	−10.3979	−0.449963
$535$	−15.8604	−0.685704
$536$	−0.833415	−0.0359981
$537$	16.3388	0.705072
$538$	−30.5204	−1.31583
$539$	−35.0922	−1.51153
$540$	11.4062	0.490846
$541$	−2.39105	−0.102799	−0.0513997	−	0.998678i	$-0.516368\pi$
$541$	−2.39105	−0.102799	−0.0513997	+	0.998678i	$0.516368\pi$
$542$	0.0288858	0.00124075
$543$	−4.64888	−0.199503
$544$	−3.18383	−0.136506
$545$	33.3640	1.42916
$546$	0.00568112	0.000243129 0
$547$	−42.2702	−1.80735	−0.903673	−	0.428224i	$-0.859139\pi$
$547$	−42.2702	−1.80735	−0.903673	+	0.428224i	$0.859139\pi$
$548$	−6.30139	−0.269182
$549$	−7.53166	−0.321443
$550$	−6.77438	−0.288861
$551$	9.76733	0.416102
$552$	4.52240	0.192486
$553$	0.185585	0.00789187
$554$	−2.62360	−0.111466
$555$	17.3839	0.737907
$556$	−3.04750	−0.129243
$557$	−23.8100	−1.00886	−0.504431	−	0.863452i	$-0.668298\pi$
$557$	−23.8100	−1.00886	−0.504431	+	0.863452i	$0.668298\pi$
$558$	−3.31550	−0.140356
$559$	−0.277842	−0.0117515
$560$	−0.0747534	−0.00315891
$561$	−13.7370	−0.579976
$562$	7.68302	0.324089
$563$	−3.06108	−0.129009	−0.0645046	−	0.997917i	$-0.520547\pi$
$563$	−3.06108	−0.129009	−0.0645046	+	0.997917i	$0.520547\pi$
$564$	5.28661	0.222606
$565$	23.1230	0.972792
$566$	6.15859	0.258865
$567$	−0.0855320	−0.00359201
$568$	−5.44844	−0.228611
$569$	9.86924	0.413740	0.206870	−	0.978368i	$-0.433672\pi$
$569$	9.86924	0.413740	0.206870	+	0.978368i	$0.433672\pi$
$570$	−2.16871	−0.0908372
$571$	30.6161	1.28124	0.640621	−	0.767857i	$-0.278677\pi$
$571$	30.6161	1.28124	0.640621	+	0.767857i	$0.278677\pi$
$572$	−1.11589	−0.0466576
$573$	6.29625	0.263030
$574$	−0.349333	−0.0145809
$575$	7.10064	0.296117
$576$	−2.25946	−0.0941441
$577$	−19.3481	−0.805473	−0.402737	−	0.915316i	$-0.631941\pi$
$577$	−19.3481	−0.805473	−0.402737	+	0.915316i	$0.631941\pi$
$578$	6.86322	0.285472
$579$	3.60075	0.149642
$580$	−24.6151	−1.02209
$581$	0.315123	0.0130735
$582$	−8.09919	−0.335722
$583$	−5.64097	−0.233625
$584$	0.905671	0.0374769
$585$	1.26731	0.0523970
$586$	−14.5946	−0.602897
$587$	8.82453	0.364227	0.182114	−	0.983277i	$-0.441706\pi$
$587$	8.82453	0.364227	0.182114	+	0.983277i	$0.441706\pi$
$588$	6.02307	0.248387
$589$	1.46739	0.0604626
$590$	21.4871	0.884610
$591$	1.31144	0.0539453
$592$	−8.01581	−0.329448
$593$	−25.6885	−1.05490	−0.527449	−	0.849586i	$-0.676852\pi$
$593$	−25.6885	−1.05490	−0.527449	+	0.849586i	$0.676852\pi$
$594$	−22.6925	−0.931085
$595$	−0.238002	−0.00975714
$596$	−11.5581	−0.473437
$597$	−19.1950	−0.785599
$598$	1.16963	0.0478297
$599$	28.7061	1.17290	0.586451	−	0.809985i	$-0.300525\pi$
$599$	28.7061	1.17290	0.586451	+	0.809985i	$0.300525\pi$
$600$	1.16273	0.0474682
$601$	−2.31156	−0.0942904	−0.0471452	−	0.998888i	$-0.515012\pi$
$601$	−2.31156	−0.0942904	−0.0471452	+	0.998888i	$0.515012\pi$
$602$	0.0370296	0.00150921
$603$	−1.88307	−0.0766844
$604$	13.7023	0.557539
$605$	35.6302	1.44857
$606$	15.0805	0.612603
$607$	−28.6107	−1.16127	−0.580637	−	0.814163i	$-0.697196\pi$
$607$	−28.6107	−1.16127	−0.580637	+	0.814163i	$0.697196\pi$
$608$	1.00000	0.0405554
$609$	−0.249319	−0.0101029
$610$	−8.40064	−0.340132
$611$	1.36728	0.0553141
$612$	−7.19373	−0.290789
$613$	−7.31330	−0.295381	−0.147691	−	0.989034i	$-0.547184\pi$
$613$	−7.31330	−0.295381	−0.147691	+	0.989034i	$0.547184\pi$
$614$	32.4099	1.30796
$615$	25.5409	1.02991
$616$	0.148721	0.00599213
$617$	1.53020	0.0616034	0.0308017	−	0.999526i	$-0.490194\pi$
$617$	1.53020	0.0616034	0.0308017	+	0.999526i	$0.490194\pi$
$618$	−3.04347	−0.122426
$619$	−0.281979	−0.0113337	−0.00566685	−	0.999984i	$-0.501804\pi$
$619$	−0.281979	−0.0113337	−0.00566685	+	0.999984i	$0.501804\pi$
$620$	−3.69803	−0.148517
$621$	23.7854	0.954474
$622$	20.5365	0.823437
$623$	0.358408	0.0143593
$624$	0.191526	0.00766719
$625$	−29.9301	−1.19721
$626$	−21.1913	−0.846976
$627$	4.31461	0.172309
$628$	4.98953	0.199104
$629$	−25.5210	−1.01759
$630$	−0.168902	−0.00672922
$631$	30.5588	1.21653	0.608264	−	0.793735i	$-0.291866\pi$
$631$	30.5588	1.21653	0.608264	+	0.793735i	$0.291866\pi$
$632$	6.25659	0.248874
$633$	0.860547	0.0342037
$634$	−24.0002	−0.953170
$635$	−12.0201	−0.477005
$636$	0.968194	0.0383914
$637$	1.55775	0.0617203
$638$	48.9714	1.93880
$639$	−12.3105	−0.486997
$640$	−2.52015	−0.0996176
$641$	−12.1246	−0.478892	−0.239446	−	0.970910i	$-0.576966\pi$
$641$	−12.1246	−0.478892	−0.239446	+	0.970910i	$0.576966\pi$
$642$	−5.41580	−0.213745
$643$	−19.1273	−0.754307	−0.377154	−	0.926151i	$-0.623097\pi$
$643$	−19.1273	−0.754307	−0.377154	+	0.926151i	$0.623097\pi$
$644$	−0.155883	−0.00614266
$645$	−2.70735	−0.106602
$646$	3.18383	0.125266
$647$	−29.1395	−1.14559	−0.572796	−	0.819698i	$-0.694141\pi$
$647$	−29.1395	−1.14559	−0.572796	+	0.819698i	$0.694141\pi$
$648$	−2.88353	−0.113276
$649$	−42.7483	−1.67802
$650$	0.300716	0.0117951
$651$	−0.0374562	−0.00146803
$652$	2.90353	0.113711
$653$	1.81037	0.0708451	0.0354225	−	0.999372i	$-0.488722\pi$
$653$	1.81037	0.0708451	0.0354225	+	0.999372i	$0.488722\pi$
$654$	11.3927	0.445490
$655$	−45.4948	−1.77763
$656$	−11.7770	−0.459815
$657$	2.04632	0.0798347
$658$	−0.182225	−0.00710386
$659$	−4.06468	−0.158337	−0.0791687	−	0.996861i	$-0.525227\pi$
$659$	−4.06468	−0.158337	−0.0791687	+	0.996861i	$0.525227\pi$
$660$	−10.8735	−0.423249
$661$	45.5246	1.77070	0.885352	−	0.464922i	$-0.153918\pi$
$661$	45.5246	1.77070	0.885352	+	0.464922i	$0.153918\pi$
$662$	−3.63684	−0.141350
$663$	0.609788	0.0236822
$664$	10.6237	0.412279
$665$	0.0747534	0.00289881
$666$	−18.1114	−0.701802
$667$	−51.3299	−1.98750
$668$	21.2988	0.824074
$669$	25.0398	0.968096
$670$	−2.10033	−0.0811428
$671$	16.7129	0.645196
$672$	−0.0255258	−0.000984680 0
$673$	23.7554	0.915704	0.457852	−	0.889028i	$-0.348619\pi$
$673$	23.7554	0.915704	0.457852	+	0.889028i	$0.348619\pi$
$674$	−20.0352	−0.771726
$675$	6.11532	0.235379
$676$	−12.9505	−0.498095
$677$	−12.2946	−0.472521	−0.236261	−	0.971690i	$-0.575922\pi$
$677$	−12.2946	−0.472521	−0.236261	+	0.971690i	$0.575922\pi$
$678$	7.89574	0.303234
$679$	0.279172	0.0107136
$680$	−8.02373	−0.307696
$681$	−20.0473	−0.768215
$682$	7.35717	0.281721
$683$	−1.56366	−0.0598318	−0.0299159	−	0.999552i	$-0.509524\pi$
$683$	−1.56366	−0.0598318	−0.0299159	+	0.999552i	$0.509524\pi$
$684$	2.25946	0.0863925
$685$	−15.8804	−0.606760
$686$	−0.415246	−0.0158542
$687$	−13.2709	−0.506316
$688$	1.24837	0.0475937
$689$	0.250404	0.00953964
$690$	11.3971	0.433881
$691$	−37.5952	−1.43019	−0.715094	−	0.699029i	$-0.753616\pi$
$691$	−37.5952	−1.43019	−0.715094	+	0.699029i	$0.753616\pi$
$692$	−19.3813	−0.736765
$693$	0.336028	0.0127647
$694$	7.42937	0.282015
$695$	−7.68016	−0.291325
$696$	−8.40525	−0.318600
$697$	−37.4960	−1.42026
$698$	−24.7756	−0.937771
$699$	2.70954	0.102484
$700$	−0.0400782	−0.00151481
$701$	24.9060	0.940686	0.470343	−	0.882484i	$-0.344130\pi$
$701$	24.9060	0.940686	0.470343	+	0.882484i	$0.344130\pi$
$702$	1.00733	0.0380190
$703$	8.01581	0.302322
$704$	5.01379	0.188965
$705$	13.3230	0.501775
$706$	1.77080	0.0666451
$707$	−0.519811	−0.0195495
$708$	7.33714	0.275746
$709$	−27.7247	−1.04122	−0.520612	−	0.853793i	$-0.674296\pi$
$709$	−27.7247	−1.04122	−0.520612	+	0.853793i	$0.674296\pi$
$710$	−13.7309	−0.515311
$711$	14.1365	0.530161
$712$	12.0829	0.452827
$713$	−7.71150	−0.288798
$714$	−0.0812699	−0.00304145
$715$	−2.81220	−0.105170
$716$	−18.9865	−0.709561
$717$	11.0120	0.411251
$718$	35.7298	1.33342
$719$	−15.4129	−0.574805	−0.287402	−	0.957810i	$-0.592792\pi$
$719$	−15.4129	−0.574805	−0.287402	+	0.957810i	$0.592792\pi$
$720$	−5.69417	−0.212209
$721$	0.104906	0.00390689
$722$	−1.00000	−0.0372161
$723$	−0.387300	−0.0144038
$724$	5.40224	0.200773
$725$	−13.1971	−0.490129
$726$	12.1665	0.451543
$727$	−23.7326	−0.880194	−0.440097	−	0.897950i	$-0.645056\pi$
$727$	−23.7326	−0.880194	−0.440097	+	0.897950i	$0.645056\pi$
$728$	−0.00660175	−0.000244677 0
$729$	5.16934	0.191457
$730$	2.28242	0.0844763
$731$	3.97460	0.147006
$732$	−2.86854	−0.106024
$733$	−41.4373	−1.53052	−0.765261	−	0.643720i	$-0.777390\pi$
$733$	−41.4373	−1.53052	−0.765261	+	0.643720i	$0.777390\pi$
$734$	−0.959187	−0.0354042
$735$	15.1790	0.559887
$736$	−5.25526	−0.193711
$737$	4.17857	0.153920
$738$	−26.6097	−0.979516
$739$	7.16667	0.263630	0.131815	−	0.991274i	$-0.457919\pi$
$739$	7.16667	0.263630	0.131815	+	0.991274i	$0.457919\pi$
$740$	−20.2010	−0.742604
$741$	−0.191526	−0.00703590
$742$	−0.0333728	−0.00122515
$743$	10.2019	0.374273	0.187136	−	0.982334i	$-0.440079\pi$
$743$	10.2019	0.374273	0.187136	+	0.982334i	$0.440079\pi$
$744$	−1.26276	−0.0462949
$745$	−29.1280	−1.06717
$746$	20.1033	0.736036
$747$	24.0038	0.878253
$748$	15.9631	0.583668
$749$	0.186678	0.00682106
$750$	−7.91329	−0.288953
$751$	−29.8760	−1.09019	−0.545095	−	0.838374i	$-0.683506\pi$
$751$	−29.8760	−1.09019	−0.545095	+	0.838374i	$0.683506\pi$
$752$	−6.14331	−0.224023
$753$	−23.0141	−0.838680
$754$	−2.17385	−0.0791670
$755$	34.5318	1.25674
$756$	−0.134252	−0.00488270
$757$	10.1738	0.369773	0.184887	−	0.982760i	$-0.440808\pi$
$757$	10.1738	0.369773	0.184887	+	0.982760i	$0.440808\pi$
$758$	−0.895330	−0.0325198
$759$	−22.6744	−0.823028
$760$	2.52015	0.0914154
$761$	7.25106	0.262851	0.131425	−	0.991326i	$-0.458045\pi$
$761$	7.25106	0.262851	0.131425	+	0.991326i	$0.458045\pi$
$762$	−4.10448	−0.148690
$763$	−0.392697	−0.0142166
$764$	−7.31657	−0.264704
$765$	−18.1293	−0.655465
$766$	5.71870	0.206625
$767$	1.89761	0.0685185
$768$	−0.860547	−0.0310523
$769$	−16.1672	−0.583004	−0.291502	−	0.956570i	$-0.594155\pi$
$769$	−16.1672	−0.583004	−0.291502	+	0.956570i	$0.594155\pi$
$770$	0.374798	0.0135068
$771$	−18.3572	−0.661119
$772$	−4.18426	−0.150595
$773$	12.1919	0.438510	0.219255	−	0.975668i	$-0.429637\pi$
$773$	12.1919	0.438510	0.219255	+	0.975668i	$0.429637\pi$
$774$	2.82064	0.101386
$775$	−1.98266	−0.0712191
$776$	9.41167	0.337859
$777$	−0.204610	−0.00734034
$778$	24.0148	0.860974
$779$	11.7770	0.421955
$780$	0.482675	0.0172825
$781$	27.3174	0.977492
$782$	−16.7319	−0.598330
$783$	−44.2071	−1.57983
$784$	−6.99912	−0.249969
$785$	12.5744	0.448798
$786$	−15.5350	−0.554114
$787$	−2.85992	−0.101945	−0.0509726	−	0.998700i	$-0.516232\pi$
$787$	−2.85992	−0.101945	−0.0509726	+	0.998700i	$0.516232\pi$
$788$	−1.52396	−0.0542887
$789$	−1.37041	−0.0487880
$790$	15.7675	0.560984
$791$	−0.272159	−0.00967687
$792$	11.3285	0.402539
$793$	−0.741891	−0.0263453
$794$	12.1982	0.432897
$795$	2.43999	0.0865376
$796$	22.3056	0.790600
$797$	−16.2058	−0.574038	−0.287019	−	0.957925i	$-0.592664\pi$
$797$	−16.2058	−0.574038	−0.287019	+	0.957925i	$0.592664\pi$
$798$	0.0255258	0.000903604 0
$799$	−19.5593	−0.691957
$800$	−1.35115	−0.0477703
$801$	27.3009	0.964630
$802$	6.57122	0.232038
$803$	−4.54085	−0.160243
$804$	−0.717193	−0.0252935
$805$	−0.392849	−0.0138461
$806$	−0.326587	−0.0115035
$807$	−26.2642	−0.924544
$808$	−17.5243	−0.616503
$809$	−3.65111	−0.128366	−0.0641831	−	0.997938i	$-0.520444\pi$
$809$	−3.65111	−0.128366	−0.0641831	+	0.997938i	$0.520444\pi$
$810$	−7.26691	−0.255333
$811$	11.2751	0.395922	0.197961	−	0.980210i	$-0.436568\pi$
$811$	11.2751	0.395922	0.197961	+	0.980210i	$0.436568\pi$
$812$	0.289721	0.0101672
$813$	0.0248576	0.000871795 0
$814$	40.1896	1.40864
$815$	7.31734	0.256315
$816$	−2.73984	−0.0959135
$817$	−1.24837	−0.0436750
$818$	−19.8248	−0.693157
$819$	−0.0149164	−0.000521220 0
$820$	−29.6798	−1.03646
$821$	45.2771	1.58018	0.790091	−	0.612990i	$-0.210033\pi$
$821$	45.2771	1.58018	0.790091	+	0.612990i	$0.210033\pi$
$822$	−5.42265	−0.189136
$823$	3.63808	0.126816	0.0634078	−	0.997988i	$-0.479803\pi$
$823$	3.63808	0.126816	0.0634078	+	0.997988i	$0.479803\pi$
$824$	3.53667	0.123206
$825$	−5.82968	−0.202963
$826$	−0.252905	−0.00879968
$827$	7.14954	0.248614	0.124307	−	0.992244i	$-0.460329\pi$
$827$	7.14954	0.248614	0.124307	+	0.992244i	$0.460329\pi$
$828$	−11.8740	−0.412652
$829$	−37.8847	−1.31579	−0.657895	−	0.753110i	$-0.728553\pi$
$829$	−37.8847	−1.31579	−0.657895	+	0.753110i	$0.728553\pi$
$830$	26.7733	0.929314
$831$	−2.25773	−0.0783199
$832$	−0.222564	−0.00771600
$833$	−22.2840	−0.772095
$834$	−2.62252	−0.0908105
$835$	53.6760	1.85754
$836$	−5.01379	−0.173406
$837$	−6.64141	−0.229561
$838$	18.9986	0.656296
$839$	−45.9912	−1.58779	−0.793896	−	0.608053i	$-0.791951\pi$
$839$	−45.9912	−1.58779	−0.793896	+	0.608053i	$0.791951\pi$
$840$	−0.0643289	−0.00221956
$841$	66.4007	2.28968
$842$	20.7075	0.713626
$843$	6.61160	0.227716
$844$	−1.00000	−0.0344214
$845$	−32.6371	−1.12275
$846$	−13.8806	−0.477223
$847$	−0.419370	−0.0144097
$848$	−1.12509	−0.0386358
$849$	5.29976	0.181887
$850$	−4.30183	−0.147552
$851$	−42.1251	−1.44403
$852$	−4.68864	−0.160630
$853$	−55.7213	−1.90786	−0.953930	−	0.300028i	$-0.903004\pi$
$853$	−55.7213	−1.90786	−0.953930	+	0.300028i	$0.903004\pi$
$854$	0.0988760	0.00338347
$855$	5.69417	0.194737
$856$	6.29343	0.215105
$857$	30.2926	1.03478	0.517388	−	0.855751i	$-0.326905\pi$
$857$	30.2926	1.03478	0.517388	+	0.855751i	$0.326905\pi$
$858$	−0.960274	−0.0327832
$859$	−6.49878	−0.221736	−0.110868	−	0.993835i	$-0.535363\pi$
$859$	−6.49878	−0.221736	−0.110868	+	0.993835i	$0.535363\pi$
$860$	3.14608	0.107281
$861$	−0.300618	−0.0102450
$862$	−4.31233	−0.146879
$863$	−12.5898	−0.428563	−0.214282	−	0.976772i	$-0.568741\pi$
$863$	−12.5898	−0.428563	−0.214282	+	0.976772i	$0.568741\pi$
$864$	−4.52601	−0.153978
$865$	−48.8436	−1.66073
$866$	19.5928	0.665792
$867$	5.90612	0.200582
$868$	0.0435261	0.00147737
$869$	−31.3693	−1.06413
$870$	−21.1825	−0.718153
$871$	−0.185488	−0.00628502
$872$	−13.2389	−0.448326
$873$	21.2653	0.719721
$874$	5.25526	0.177762
$875$	0.272764	0.00922111
$876$	0.779372	0.0263326
$877$	15.4915	0.523109	0.261555	−	0.965189i	$-0.415765\pi$
$877$	15.4915	0.523109	0.261555	+	0.965189i	$0.415765\pi$
$878$	−15.0337	−0.507364
$879$	−12.5593	−0.423616
$880$	12.6355	0.425943
$881$	25.8977	0.872517	0.436258	−	0.899821i	$-0.356303\pi$
$881$	25.8977	0.872517	0.436258	+	0.899821i	$0.356303\pi$
$882$	−15.8142	−0.532492
$883$	3.91482	0.131744	0.0658721	−	0.997828i	$-0.479017\pi$
$883$	3.91482	0.131744	0.0658721	+	0.997828i	$0.479017\pi$
$884$	−0.708605	−0.0238330
$885$	18.4907	0.621557
$886$	21.1704	0.711233
$887$	−28.8607	−0.969047	−0.484524	−	0.874778i	$-0.661007\pi$
$887$	−28.8607	−0.969047	−0.484524	+	0.874778i	$0.661007\pi$
$888$	−6.89798	−0.231481
$889$	0.141478	0.00474501
$890$	30.4508	1.02071
$891$	14.4574	0.484341
$892$	−29.0976	−0.974258
$893$	6.14331	0.205578
$894$	−9.94626	−0.332653
$895$	−47.8489	−1.59941
$896$	0.0296623	0.000990948 0
$897$	1.00652	0.0336068
$898$	−40.7663	−1.36039
$899$	14.3324	0.478014
$900$	−3.05286	−0.101762
$901$	−3.58210	−0.119337
$902$	59.0476	1.96607
$903$	0.0318657	0.00106042
$904$	−9.17526	−0.305165
$905$	13.6144	0.452559
$906$	11.7915	0.391746
$907$	−12.8810	−0.427705	−0.213853	−	0.976866i	$-0.568601\pi$
$907$	−12.8810	−0.427705	−0.213853	+	0.976866i	$0.568601\pi$
$908$	23.2960	0.773105
$909$	−39.5954	−1.31330
$910$	−0.0166374	−0.000551524 0
$911$	0.560899	0.0185834	0.00929171	−	0.999957i	$-0.497042\pi$
$911$	0.560899	0.0185834	0.00929171	+	0.999957i	$0.497042\pi$
$912$	0.860547	0.0284956
$913$	−53.2650	−1.76281
$914$	−8.18021	−0.270577
$915$	−7.22915	−0.238988
$916$	15.4214	0.509539
$917$	0.535477	0.0176830
$918$	−14.4101	−0.475603
$919$	−1.10702	−0.0365172	−0.0182586	−	0.999833i	$-0.505812\pi$
$919$	−1.10702	−0.0365172	−0.0182586	+	0.999833i	$0.505812\pi$
$920$	−13.2440	−0.436643
$921$	27.8902	0.919014
$922$	9.09547	0.299543
$923$	−1.21262	−0.0399140
$924$	0.127981	0.00421027
$925$	−10.8305	−0.356106
$926$	4.16675	0.136928
$927$	7.99096	0.262457
$928$	9.76733	0.320628
$929$	18.9780	0.622646	0.311323	−	0.950304i	$-0.399228\pi$
$929$	18.9780	0.622646	0.311323	+	0.950304i	$0.399228\pi$
$930$	−3.18233	−0.104353
$931$	6.99912	0.229387
$932$	−3.14863	−0.103137
$933$	17.6726	0.578575
$934$	−16.1212	−0.527502
$935$	40.2293	1.31564
$936$	−0.502873	−0.0164369
$937$	−48.9810	−1.60014	−0.800071	−	0.599906i	$-0.795205\pi$
$937$	−48.9810	−1.60014	−0.800071	+	0.599906i	$0.795205\pi$
$938$	0.0247210	0.000807170 0
$939$	−18.2361	−0.595114
$940$	−15.4821	−0.504969
$941$	40.8895	1.33296	0.666479	−	0.745524i	$-0.267801\pi$
$941$	40.8895	1.33296	0.666479	+	0.745524i	$0.267801\pi$
$942$	4.29373	0.139897
$943$	−61.8913	−2.01546
$944$	−8.52613	−0.277502
$945$	−0.338335	−0.0110060
$946$	−6.25908	−0.203500
$947$	14.6355	0.475591	0.237796	−	0.971315i	$-0.423575\pi$
$947$	14.6355	0.475591	0.237796	+	0.971315i	$0.423575\pi$
$948$	5.38409	0.174867
$949$	0.201569	0.00654321
$950$	1.35115	0.0438371
$951$	−20.6533	−0.669730
$952$	0.0944398	0.00306081
$953$	−5.02387	−0.162739	−0.0813696	−	0.996684i	$-0.525929\pi$
$953$	−5.02387	−0.162739	−0.0813696	+	0.996684i	$0.525929\pi$
$954$	−2.54210	−0.0823034
$955$	−18.4388	−0.596667
$956$	−12.7965	−0.413868
$957$	42.1422	1.36226
$958$	−20.4401	−0.660390
$959$	0.186914	0.00603576
$960$	−2.16871	−0.0699947
$961$	−28.8468	−0.930541
$962$	−1.78403	−0.0575193
$963$	14.2198	0.458225
$964$	0.450062	0.0144955
$965$	−10.5450	−0.339454
$966$	−0.134145	−0.00431604
$967$	−1.83231	−0.0589230	−0.0294615	−	0.999566i	$-0.509379\pi$
$967$	−1.83231	−0.0589230	−0.0294615	+	0.999566i	$0.509379\pi$
$968$	−14.1381	−0.454417
$969$	2.73984	0.0880163
$970$	23.7188	0.761565
$971$	2.42613	0.0778581	0.0389291	−	0.999242i	$-0.487605\pi$
$971$	2.42613	0.0778581	0.0389291	+	0.999242i	$0.487605\pi$
$972$	−16.0594	−0.515107
$973$	0.0903960	0.00289796
$974$	−7.56813	−0.242499
$975$	0.258781	0.00828762
$976$	3.33339	0.106699
$977$	32.7403	1.04745	0.523727	−	0.851886i	$-0.324541\pi$
$977$	32.7403	1.04745	0.523727	+	0.851886i	$0.324541\pi$
$978$	2.49863	0.0798973
$979$	−60.5814	−1.93619
$980$	−17.6388	−0.563452
$981$	−29.9128	−0.955041
$982$	−3.59508	−0.114724
$983$	39.5703	1.26210	0.631048	−	0.775744i	$-0.282625\pi$
$983$	39.5703	1.26210	0.631048	+	0.775744i	$0.282625\pi$
$984$	−10.1347	−0.323082
$985$	−3.84060	−0.122372
$986$	31.0975	0.990347
$987$	−0.156813	−0.00499141
$988$	0.222564	0.00708069
$989$	6.56052	0.208612
$990$	28.5494	0.907360
$991$	−50.9884	−1.61970	−0.809849	−	0.586638i	$-0.800451\pi$
$991$	−50.9884	−1.61970	−0.809849	+	0.586638i	$0.800451\pi$
$992$	1.46739	0.0465896
$993$	−3.12967	−0.0993172
$994$	0.161613	0.00512606
$995$	56.2134	1.78208
$996$	9.14219	0.289681
$997$	−30.8110	−0.975795	−0.487898	−	0.872901i	$-0.662236\pi$
$997$	−30.8110	−0.975795	−0.487898	+	0.872901i	$0.662236\pi$
$998$	4.44310	0.140644
$999$	−36.2796	−1.14784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.16	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.16	✓	34	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.860547 q^{3} +1.00000 q^{4} +2.52015 q^{5} +0.860547 q^{6} -0.0296623 q^{7} -1.00000 q^{8} -2.25946 q^{9} -2.52015 q^{10} +5.01379 q^{11} -0.860547 q^{12} -0.222564 q^{13} +0.0296623 q^{14} -2.16871 q^{15} +1.00000 q^{16} +3.18383 q^{17} +2.25946 q^{18} -1.00000 q^{19} +2.52015 q^{20} +0.0255258 q^{21} -5.01379 q^{22} +5.25526 q^{23} +0.860547 q^{24} +1.35115 q^{25} +0.222564 q^{26} +4.52601 q^{27} -0.0296623 q^{28} -9.76733 q^{29} +2.16871 q^{30} -1.46739 q^{31} -1.00000 q^{32} -4.31461 q^{33} -3.18383 q^{34} -0.0747534 q^{35} -2.25946 q^{36} -8.01581 q^{37} +1.00000 q^{38} +0.191526 q^{39} -2.52015 q^{40} -11.7770 q^{41} -0.0255258 q^{42} +1.24837 q^{43} +5.01379 q^{44} -5.69417 q^{45} -5.25526 q^{46} -6.14331 q^{47} -0.860547 q^{48} -6.99912 q^{49} -1.35115 q^{50} -2.73984 q^{51} -0.222564 q^{52} -1.12509 q^{53} -4.52601 q^{54} +12.6355 q^{55} +0.0296623 q^{56} +0.860547 q^{57} +9.76733 q^{58} -8.52613 q^{59} -2.16871 q^{60} +3.33339 q^{61} +1.46739 q^{62} +0.0670207 q^{63} +1.00000 q^{64} -0.560893 q^{65} +4.31461 q^{66} +0.833415 q^{67} +3.18383 q^{68} -4.52240 q^{69} +0.0747534 q^{70} +5.44844 q^{71} +2.25946 q^{72} -0.905671 q^{73} +8.01581 q^{74} -1.16273 q^{75} -1.00000 q^{76} -0.148721 q^{77} -0.191526 q^{78} -6.25659 q^{79} +2.52015 q^{80} +2.88353 q^{81} +11.7770 q^{82} -10.6237 q^{83} +0.0255258 q^{84} +8.02373 q^{85} -1.24837 q^{86} +8.40525 q^{87} -5.01379 q^{88} -12.0829 q^{89} +5.69417 q^{90} +0.00660175 q^{91} +5.25526 q^{92} +1.26276 q^{93} +6.14331 q^{94} -2.52015 q^{95} +0.860547 q^{96} -9.41167 q^{97} +6.99912 q^{98} -11.3285 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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