LMFDB - Embedded newform 4033.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68964 q^{2} -0.345637 q^{3} +5.23416 q^{4} +3.86855 q^{5} +0.929638 q^{6} -2.16399 q^{7} -8.69874 q^{8} -2.88054 q^{9} +O(q^{10})$	\(q-2.68964 q^{2} -0.345637 q^{3} +5.23416 q^{4} +3.86855 q^{5} +0.929638 q^{6} -2.16399 q^{7} -8.69874 q^{8} -2.88054 q^{9} -10.4050 q^{10} -2.11365 q^{11} -1.80912 q^{12} -3.53651 q^{13} +5.82035 q^{14} -1.33711 q^{15} +12.9281 q^{16} -1.96634 q^{17} +7.74760 q^{18} -0.950502 q^{19} +20.2486 q^{20} +0.747953 q^{21} +5.68496 q^{22} +0.909001 q^{23} +3.00660 q^{24} +9.96568 q^{25} +9.51193 q^{26} +2.03253 q^{27} -11.3267 q^{28} -8.86822 q^{29} +3.59635 q^{30} -5.20464 q^{31} -17.3746 q^{32} +0.730555 q^{33} +5.28875 q^{34} -8.37149 q^{35} -15.0772 q^{36} +1.00000 q^{37} +2.55651 q^{38} +1.22235 q^{39} -33.6515 q^{40} +0.661852 q^{41} -2.01173 q^{42} +2.54695 q^{43} -11.0632 q^{44} -11.1435 q^{45} -2.44488 q^{46} +3.71734 q^{47} -4.46844 q^{48} -2.31716 q^{49} -26.8041 q^{50} +0.679640 q^{51} -18.5106 q^{52} +8.37049 q^{53} -5.46677 q^{54} -8.17677 q^{55} +18.8240 q^{56} +0.328528 q^{57} +23.8523 q^{58} -3.52961 q^{59} -6.99867 q^{60} -6.66154 q^{61} +13.9986 q^{62} +6.23344 q^{63} +20.8751 q^{64} -13.6812 q^{65} -1.96493 q^{66} +11.9472 q^{67} -10.2922 q^{68} -0.314184 q^{69} +22.5163 q^{70} +1.05772 q^{71} +25.0570 q^{72} -2.24645 q^{73} -2.68964 q^{74} -3.44451 q^{75} -4.97508 q^{76} +4.57391 q^{77} -3.28767 q^{78} +9.45818 q^{79} +50.0132 q^{80} +7.93909 q^{81} -1.78014 q^{82} +0.586152 q^{83} +3.91491 q^{84} -7.60689 q^{85} -6.85039 q^{86} +3.06518 q^{87} +18.3861 q^{88} +9.11543 q^{89} +29.9720 q^{90} +7.65295 q^{91} +4.75786 q^{92} +1.79891 q^{93} -9.99830 q^{94} -3.67706 q^{95} +6.00529 q^{96} +4.64541 q^{97} +6.23232 q^{98} +6.08845 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.68964	−1.90186	−0.950931	−	0.309402i	$-0.899871\pi$
$2$	−2.68964	−1.90186	−0.950931	+	0.309402i	$0.899871\pi$
$3$	−0.345637	−0.199553	−0.0997767	−	0.995010i	$-0.531813\pi$
$3$	−0.345637	−0.199553	−0.0997767	+	0.995010i	$0.531813\pi$
$4$	5.23416	2.61708
$5$	3.86855	1.73007	0.865034	−	0.501713i	$-0.167297\pi$
$5$	3.86855	1.73007	0.865034	+	0.501713i	$0.167297\pi$
$6$	0.929638	0.379523
$7$	−2.16399	−0.817910	−0.408955	−	0.912554i	$-0.634107\pi$
$7$	−2.16399	−0.817910	−0.408955	+	0.912554i	$0.634107\pi$
$8$	−8.69874	−3.07547
$9$	−2.88054	−0.960178
$10$	−10.4050	−3.29035
$11$	−2.11365	−0.637290	−0.318645	−	0.947874i	$-0.603228\pi$
$11$	−2.11365	−0.637290	−0.318645	+	0.947874i	$0.603228\pi$
$12$	−1.80912	−0.522248
$13$	−3.53651	−0.980850	−0.490425	−	0.871483i	$-0.663158\pi$
$13$	−3.53651	−0.980850	−0.490425	+	0.871483i	$0.663158\pi$
$14$	5.82035	1.55555
$15$	−1.33711	−0.345241
$16$	12.9281	3.23204
$17$	−1.96634	−0.476908	−0.238454	−	0.971154i	$-0.576641\pi$
$17$	−1.96634	−0.476908	−0.238454	+	0.971154i	$0.576641\pi$
$18$	7.74760	1.82613
$19$	−0.950502	−0.218060	−0.109030	−	0.994038i	$-0.534774\pi$
$19$	−0.950502	−0.218060	−0.109030	+	0.994038i	$0.534774\pi$
$20$	20.2486	4.52773
$21$	0.747953	0.163217
$22$	5.68496	1.21204
$23$	0.909001	0.189540	0.0947699	−	0.995499i	$-0.469788\pi$
$23$	0.909001	0.189540	0.0947699	+	0.995499i	$0.469788\pi$
$24$	3.00660	0.613720
$25$	9.96568	1.99314
$26$	9.51193	1.86544
$27$	2.03253	0.391160
$28$	−11.3267	−2.14054
$29$	−8.86822	−1.64679	−0.823393	−	0.567471i	$-0.807922\pi$
$29$	−8.86822	−1.64679	−0.823393	+	0.567471i	$0.807922\pi$
$30$	3.59635	0.656601
$31$	−5.20464	−0.934781	−0.467390	−	0.884051i	$-0.654806\pi$
$31$	−5.20464	−0.934781	−0.467390	+	0.884051i	$0.654806\pi$
$32$	−17.3746	−3.07142
$33$	0.730555	0.127173
$34$	5.28875	0.907014
$35$	−8.37149	−1.41504
$36$	−15.0772	−2.51287
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	2.55651	0.414720
$39$	1.22235	0.195732
$40$	−33.6515	−5.32077
$41$	0.661852	0.103364	0.0516820	−	0.998664i	$-0.483542\pi$
$41$	0.661852	0.103364	0.0516820	+	0.998664i	$0.483542\pi$
$42$	−2.01173	−0.310416
$43$	2.54695	0.388407	0.194203	−	0.980961i	$-0.437788\pi$
$43$	2.54695	0.388407	0.194203	+	0.980961i	$0.437788\pi$
$44$	−11.0632	−1.66784
$45$	−11.1435	−1.66117
$46$	−2.44488	−0.360479
$47$	3.71734	0.542230	0.271115	−	0.962547i	$-0.412608\pi$
$47$	3.71734	0.542230	0.271115	+	0.962547i	$0.412608\pi$
$48$	−4.46844	−0.644964
$49$	−2.31716	−0.331023
$50$	−26.8041	−3.79067
$51$	0.679640	0.0951686
$52$	−18.5106	−2.56697
$53$	8.37049	1.14977	0.574887	−	0.818233i	$-0.305046\pi$
$53$	8.37049	1.14977	0.574887	+	0.818233i	$0.305046\pi$
$54$	−5.46677	−0.743933
$55$	−8.17677	−1.10255
$56$	18.8240	2.51546
$57$	0.328528	0.0435146
$58$	23.8523	3.13196
$59$	−3.52961	−0.459516	−0.229758	−	0.973248i	$-0.573793\pi$
$59$	−3.52961	−0.459516	−0.229758	+	0.973248i	$0.573793\pi$
$60$	−6.99867	−0.903524
$61$	−6.66154	−0.852923	−0.426462	−	0.904506i	$-0.640240\pi$
$61$	−6.66154	−0.852923	−0.426462	+	0.904506i	$0.640240\pi$
$62$	13.9986	1.77783
$63$	6.23344	0.785340
$64$	20.8751	2.60938
$65$	−13.6812	−1.69694
$66$	−1.96493	−0.241866
$67$	11.9472	1.45958	0.729792	−	0.683670i	$-0.239617\pi$
$67$	11.9472	1.45958	0.729792	+	0.683670i	$0.239617\pi$
$68$	−10.2922	−1.24811
$69$	−0.314184	−0.0378233
$70$	22.5163	2.69121
$71$	1.05772	0.125528	0.0627641	−	0.998028i	$-0.480008\pi$
$71$	1.05772	0.125528	0.0627641	+	0.998028i	$0.480008\pi$
$72$	25.0570	2.95300
$73$	−2.24645	−0.262927	−0.131464	−	0.991321i	$-0.541968\pi$
$73$	−2.24645	−0.262927	−0.131464	+	0.991321i	$0.541968\pi$
$74$	−2.68964	−0.312664
$75$	−3.44451	−0.397737
$76$	−4.97508	−0.570681
$77$	4.57391	0.521246
$78$	−3.28767	−0.372255
$79$	9.45818	1.06413	0.532064	−	0.846704i	$-0.321417\pi$
$79$	9.45818	1.06413	0.532064	+	0.846704i	$0.321417\pi$
$80$	50.0132	5.59164
$81$	7.93909	0.882121
$82$	−1.78014	−0.196584
$83$	0.586152	0.0643385	0.0321693	−	0.999482i	$-0.489758\pi$
$83$	0.586152	0.0643385	0.0321693	+	0.999482i	$0.489758\pi$
$84$	3.91491	0.427152
$85$	−7.60689	−0.825083
$86$	−6.85039	−0.738696
$87$	3.06518	0.328622
$88$	18.3861	1.95996
$89$	9.11543	0.966234	0.483117	−	0.875556i	$-0.339505\pi$
$89$	9.11543	0.966234	0.483117	+	0.875556i	$0.339505\pi$
$90$	29.9720	3.15933
$91$	7.65295	0.802247
$92$	4.75786	0.496041
$93$	1.79891	0.186539
$94$	−9.99830	−1.03125
$95$	−3.67706	−0.377259
$96$	6.00529	0.612912
$97$	4.64541	0.471670	0.235835	−	0.971793i	$-0.424217\pi$
$97$	4.64541	0.471670	0.235835	+	0.971793i	$0.424217\pi$
$98$	6.23232	0.629560
$99$	6.08845	0.611912
$100$	52.1620	5.21620
$101$	16.5113	1.64294	0.821468	−	0.570254i	$-0.193155\pi$
$101$	16.5113	1.64294	0.821468	+	0.570254i	$0.193155\pi$
$102$	−1.82799	−0.180998
$103$	9.99313	0.984652	0.492326	−	0.870411i	$-0.336147\pi$
$103$	9.99313	0.984652	0.492326	+	0.870411i	$0.336147\pi$
$104$	30.7631	3.01657
$105$	2.89350	0.282376
$106$	−22.5136	−2.18671
$107$	−7.15332	−0.691538	−0.345769	−	0.938320i	$-0.612382\pi$
$107$	−7.15332	−0.691538	−0.345769	+	0.938320i	$0.612382\pi$
$108$	10.6386	1.02370
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	21.9926	2.09691
$111$	−0.345637	−0.0328064
$112$	−27.9763	−2.64351
$113$	11.1017	1.04436	0.522180	−	0.852835i	$-0.325119\pi$
$113$	11.1017	1.04436	0.522180	+	0.852835i	$0.325119\pi$
$114$	−0.883623	−0.0827589
$115$	3.51651	0.327917
$116$	−46.4177	−4.30978
$117$	10.1870	0.941791
$118$	9.49337	0.873936
$119$	4.25514	0.390068
$120$	11.6312	1.06178
$121$	−6.53248	−0.593862
$122$	17.9172	1.62214
$123$	−0.228760	−0.0206266
$124$	−27.2419	−2.44640
$125$	19.2100	1.71819
$126$	−16.7657	−1.49361
$127$	16.4682	1.46131	0.730657	−	0.682745i	$-0.239214\pi$
$127$	16.4682	1.46131	0.730657	+	0.682745i	$0.239214\pi$
$128$	−21.3973	−1.89127
$129$	−0.880320	−0.0775079
$130$	36.7974	3.22734
$131$	−4.62509	−0.404096	−0.202048	−	0.979376i	$-0.564760\pi$
$131$	−4.62509	−0.404096	−0.202048	+	0.979376i	$0.564760\pi$
$132$	3.82385	0.332823
$133$	2.05687	0.178354
$134$	−32.1337	−2.77593
$135$	7.86294	0.676734
$136$	17.1047	1.46672
$137$	4.42448	0.378009	0.189005	−	0.981976i	$-0.439474\pi$
$137$	4.42448	0.378009	0.189005	+	0.981976i	$0.439474\pi$
$138$	0.845042	0.0719347
$139$	18.0338	1.52961	0.764804	−	0.644263i	$-0.222836\pi$
$139$	18.0338	1.52961	0.764804	+	0.644263i	$0.222836\pi$
$140$	−43.8178	−3.70328
$141$	−1.28485	−0.108204
$142$	−2.84489	−0.238737
$143$	7.47494	0.625086
$144$	−37.2400	−3.10333
$145$	−34.3071	−2.84905
$146$	6.04215	0.500052
$147$	0.800895	0.0660567
$148$	5.23416	0.430246
$149$	−13.6491	−1.11818	−0.559088	−	0.829108i	$-0.688849\pi$
$149$	−13.6491	−1.11818	−0.559088	+	0.829108i	$0.688849\pi$
$150$	9.26448	0.756442
$151$	−1.80394	−0.146802	−0.0734012	−	0.997302i	$-0.523385\pi$
$151$	−1.80394	−0.146802	−0.0734012	+	0.997302i	$0.523385\pi$
$152$	8.26816	0.670637
$153$	5.66412	0.457917
$154$	−12.3022	−0.991338
$155$	−20.1344	−1.61724
$156$	6.39796	0.512247
$157$	−22.8056	−1.82008	−0.910041	−	0.414518i	$-0.863950\pi$
$157$	−22.8056	−1.82008	−0.910041	+	0.414518i	$0.863950\pi$
$158$	−25.4391	−2.02383
$159$	−2.89315	−0.229441
$160$	−67.2144	−5.31377
$161$	−1.96707	−0.155027
$162$	−21.3533	−1.67767
$163$	1.30217	0.101994	0.0509970	−	0.998699i	$-0.483760\pi$
$163$	1.30217	0.101994	0.0509970	+	0.998699i	$0.483760\pi$
$164$	3.46424	0.270512
$165$	2.82619	0.220019
$166$	−1.57654	−0.122363
$167$	14.7007	1.13757	0.568786	−	0.822486i	$-0.307413\pi$
$167$	14.7007	1.13757	0.568786	+	0.822486i	$0.307413\pi$
$168$	−6.50625	−0.501968
$169$	−0.493128	−0.0379329
$170$	20.4598	1.56920
$171$	2.73795	0.209377
$172$	13.3312	1.01649
$173$	6.25440	0.475513	0.237757	−	0.971325i	$-0.423588\pi$
$173$	6.25440	0.475513	0.237757	+	0.971325i	$0.423588\pi$
$174$	−8.24423	−0.624994
$175$	−21.5656	−1.63021
$176$	−27.3256	−2.05974
$177$	1.21996	0.0916980
$178$	−24.5172	−1.83764
$179$	24.0229	1.79556	0.897779	−	0.440446i	$-0.145180\pi$
$179$	24.0229	1.79556	0.897779	+	0.440446i	$0.145180\pi$
$180$	−58.3269	−4.34743
$181$	−6.76865	−0.503110	−0.251555	−	0.967843i	$-0.580942\pi$
$181$	−6.76865	−0.503110	−0.251555	+	0.967843i	$0.580942\pi$
$182$	−20.5837	−1.52576
$183$	2.30247	0.170204
$184$	−7.90716	−0.582923
$185$	3.86855	0.284421
$186$	−4.83843	−0.354771
$187$	4.15616	0.303929
$188$	19.4572	1.41906
$189$	−4.39837	−0.319934
$190$	9.88998	0.717494
$191$	7.10824	0.514334	0.257167	−	0.966367i	$-0.417211\pi$
$191$	7.10824	0.514334	0.257167	+	0.966367i	$0.417211\pi$
$192$	−7.21519	−0.520711
$193$	12.9026	0.928747	0.464373	−	0.885640i	$-0.346280\pi$
$193$	12.9026	0.928747	0.464373	+	0.885640i	$0.346280\pi$
$194$	−12.4945	−0.897052
$195$	4.72871	0.338630
$196$	−12.1284	−0.866314
$197$	17.3765	1.23803	0.619013	−	0.785381i	$-0.287533\pi$
$197$	17.3765	1.23803	0.619013	+	0.785381i	$0.287533\pi$
$198$	−16.3757	−1.16377
$199$	1.04875	0.0743437	0.0371718	−	0.999309i	$-0.488165\pi$
$199$	1.04875	0.0743437	0.0371718	+	0.999309i	$0.488165\pi$
$200$	−86.6888	−6.12983
$201$	−4.12939	−0.291265
$202$	−44.4095	−3.12464
$203$	19.1907	1.34692
$204$	3.55735	0.249064
$205$	2.56041	0.178827
$206$	−26.8779	−1.87267
$207$	−2.61841	−0.181992
$208$	−45.7204	−3.17014
$209$	2.00903	0.138967
$210$	−7.78246	−0.537041
$211$	−8.82102	−0.607264	−0.303632	−	0.952789i	$-0.598199\pi$
$211$	−8.82102	−0.607264	−0.303632	+	0.952789i	$0.598199\pi$
$212$	43.8125	3.00905
$213$	−0.365587	−0.0250496
$214$	19.2399	1.31521
$215$	9.85302	0.671970
$216$	−17.6804	−1.20300
$217$	11.2628	0.764567
$218$	2.68964	0.182165
$219$	0.776456	0.0524681
$220$	−42.7985	−2.88548
$221$	6.95398	0.467775
$222$	0.929638	0.0623932
$223$	−2.80122	−0.187584	−0.0937919	−	0.995592i	$-0.529899\pi$
$223$	−2.80122	−0.187584	−0.0937919	+	0.995592i	$0.529899\pi$
$224$	37.5984	2.51215
$225$	−28.7065	−1.91377
$226$	−29.8596	−1.98623
$227$	1.65494	0.109843	0.0549213	−	0.998491i	$-0.482509\pi$
$227$	1.65494	0.109843	0.0549213	+	0.998491i	$0.482509\pi$
$228$	1.71957	0.113881
$229$	−10.7610	−0.711107	−0.355554	−	0.934656i	$-0.615708\pi$
$229$	−10.7610	−0.711107	−0.355554	+	0.934656i	$0.615708\pi$
$230$	−9.45816	−0.623653
$231$	−1.58091	−0.104016
$232$	77.1423	5.06464
$233$	28.3296	1.85593	0.927967	−	0.372662i	$-0.121555\pi$
$233$	28.3296	1.85593	0.927967	+	0.372662i	$0.121555\pi$
$234$	−27.3994	−1.79116
$235$	14.3807	0.938094
$236$	−18.4745	−1.20259
$237$	−3.26909	−0.212350
$238$	−11.4448	−0.741856
$239$	−7.79201	−0.504023	−0.252011	−	0.967724i	$-0.581092\pi$
$239$	−7.79201	−0.504023	−0.252011	+	0.967724i	$0.581092\pi$
$240$	−17.2864	−1.11583
$241$	−22.8239	−1.47022	−0.735110	−	0.677948i	$-0.762869\pi$
$241$	−22.8239	−1.47022	−0.735110	+	0.677948i	$0.762869\pi$
$242$	17.5700	1.12944
$243$	−8.84163	−0.567191
$244$	−34.8676	−2.23217
$245$	−8.96405	−0.572692
$246$	0.615283	0.0392290
$247$	3.36146	0.213884
$248$	45.2738	2.87489
$249$	−0.202596	−0.0128390
$250$	−51.6680	−3.26777
$251$	10.4314	0.658425	0.329212	−	0.944256i	$-0.393217\pi$
$251$	10.4314	0.658425	0.329212	+	0.944256i	$0.393217\pi$
$252$	32.6269	2.05530
$253$	−1.92131	−0.120792
$254$	−44.2935	−2.77922
$255$	2.62922	0.164648
$256$	15.8008	0.987551
$257$	−11.7357	−0.732055	−0.366027	−	0.930604i	$-0.619282\pi$
$257$	−11.7357	−0.732055	−0.366027	+	0.930604i	$0.619282\pi$
$258$	2.36775	0.147409
$259$	−2.16399	−0.134464
$260$	−71.6094	−4.44103
$261$	25.5452	1.58121
$262$	12.4398	0.768536
$263$	−18.8468	−1.16214	−0.581072	−	0.813852i	$-0.697367\pi$
$263$	−18.8468	−1.16214	−0.581072	+	0.813852i	$0.697367\pi$
$264$	−6.35491	−0.391118
$265$	32.3816	1.98919
$266$	−5.53225	−0.339204
$267$	−3.15063	−0.192815
$268$	62.5336	3.81985
$269$	16.1673	0.985740	0.492870	−	0.870103i	$-0.335948\pi$
$269$	16.1673	0.985740	0.492870	+	0.870103i	$0.335948\pi$
$270$	−21.1485	−1.28706
$271$	17.3848	1.05605	0.528025	−	0.849229i	$-0.322933\pi$
$271$	17.3848	1.05605	0.528025	+	0.849229i	$0.322933\pi$
$272$	−25.4211	−1.54138
$273$	−2.64514	−0.160091
$274$	−11.9003	−0.718922
$275$	−21.0640	−1.27021
$276$	−1.64449	−0.0989867
$277$	−26.4921	−1.59176	−0.795879	−	0.605455i	$-0.792991\pi$
$277$	−26.4921	−1.59176	−0.795879	+	0.605455i	$0.792991\pi$
$278$	−48.5045	−2.90911
$279$	14.9921	0.897557
$280$	72.8214	4.35191
$281$	7.41753	0.442493	0.221246	−	0.975218i	$-0.428987\pi$
$281$	7.41753	0.442493	0.221246	+	0.975218i	$0.428987\pi$
$282$	3.45578	0.205789
$283$	−2.64722	−0.157361	−0.0786805	−	0.996900i	$-0.525071\pi$
$283$	−2.64722	−0.157361	−0.0786805	+	0.996900i	$0.525071\pi$
$284$	5.53628	0.328518
$285$	1.27093	0.0752833
$286$	−20.1049	−1.18883
$287$	−1.43224	−0.0845425
$288$	50.0481	2.94911
$289$	−13.1335	−0.772559
$290$	92.2739	5.41851
$291$	−1.60562	−0.0941234
$292$	−11.7583	−0.688102
$293$	0.472409	0.0275984	0.0137992	−	0.999905i	$-0.495607\pi$
$293$	0.472409	0.0275984	0.0137992	+	0.999905i	$0.495607\pi$
$294$	−2.15412	−0.125631
$295$	−13.6545	−0.794994
$296$	−8.69874	−0.505604
$297$	−4.29606	−0.249282
$298$	36.7111	2.12662
$299$	−3.21469	−0.185910
$300$	−18.0291	−1.04091
$301$	−5.51157	−0.317682
$302$	4.85194	0.279198
$303$	−5.70691	−0.327854
$304$	−12.2882	−0.704778
$305$	−25.7705	−1.47562
$306$	−15.2344	−0.870895
$307$	24.7340	1.41165	0.705823	−	0.708389i	$-0.250578\pi$
$307$	24.7340	1.41165	0.705823	+	0.708389i	$0.250578\pi$
$308$	23.9406	1.36414
$309$	−3.45399	−0.196491
$310$	54.1543	3.07576
$311$	21.0280	1.19239	0.596195	−	0.802839i	$-0.296678\pi$
$311$	21.0280	1.19239	0.596195	+	0.802839i	$0.296678\pi$
$312$	−10.6329	−0.601968
$313$	−1.89149	−0.106913	−0.0534567	−	0.998570i	$-0.517024\pi$
$313$	−1.89149	−0.106913	−0.0534567	+	0.998570i	$0.517024\pi$
$314$	61.3388	3.46155
$315$	24.1144	1.35869
$316$	49.5057	2.78491
$317$	24.1853	1.35838	0.679190	−	0.733962i	$-0.262331\pi$
$317$	24.1853	1.35838	0.679190	+	0.733962i	$0.262331\pi$
$318$	7.78152	0.436366
$319$	18.7443	1.04948
$320$	80.7562	4.51441
$321$	2.47245	0.137999
$322$	5.29070	0.294839
$323$	1.86901	0.103995
$324$	41.5545	2.30858
$325$	−35.2437	−1.95497
$326$	−3.50237	−0.193979
$327$	0.345637	0.0191138
$328$	−5.75728	−0.317893
$329$	−8.04427	−0.443495
$330$	−7.60143	−0.418445
$331$	−30.0361	−1.65093	−0.825467	−	0.564451i	$-0.809088\pi$
$331$	−30.0361	−1.65093	−0.825467	+	0.564451i	$0.809088\pi$
$332$	3.06801	0.168379
$333$	−2.88054	−0.157852
$334$	−39.5395	−2.16351
$335$	46.2184	2.52518
$336$	9.66965	0.527522
$337$	28.0745	1.52932	0.764658	−	0.644436i	$-0.222908\pi$
$337$	28.0745	1.52932	0.764658	+	0.644436i	$0.222908\pi$
$338$	1.32634	0.0721432
$339$	−3.83715	−0.208406
$340$	−39.8157	−2.15931
$341$	11.0008	0.595726
$342$	−7.36411	−0.398205
$343$	20.1622	1.08866
$344$	−22.1553	−1.19453
$345$	−1.21544	−0.0654369
$346$	−16.8221	−0.904361
$347$	−32.0287	−1.71939	−0.859696	−	0.510807i	$-0.829347\pi$
$347$	−32.0287	−1.71939	−0.859696	+	0.510807i	$0.829347\pi$
$348$	16.0437	0.860031
$349$	−27.4101	−1.46723	−0.733614	−	0.679566i	$-0.762168\pi$
$349$	−27.4101	−1.46723	−0.733614	+	0.679566i	$0.762168\pi$
$350$	58.0037	3.10043
$351$	−7.18805	−0.383670
$352$	36.7238	1.95738
$353$	−13.0182	−0.692889	−0.346445	−	0.938070i	$-0.612611\pi$
$353$	−13.0182	−0.692889	−0.346445	+	0.938070i	$0.612611\pi$
$354$	−3.28126	−0.174397
$355$	4.09184	0.217172
$356$	47.7117	2.52871
$357$	−1.47073	−0.0778394
$358$	−64.6130	−3.41490
$359$	23.8608	1.25932	0.629662	−	0.776869i	$-0.283193\pi$
$359$	23.8608	1.25932	0.629662	+	0.776869i	$0.283193\pi$
$360$	96.9343	5.10889
$361$	−18.0965	−0.952450
$362$	18.2052	0.956846
$363$	2.25786	0.118507
$364$	40.0568	2.09955
$365$	−8.69051	−0.454882
$366$	−6.19283	−0.323704
$367$	12.3113	0.642645	0.321323	−	0.946970i	$-0.395873\pi$
$367$	12.3113	0.642645	0.321323	+	0.946970i	$0.395873\pi$
$368$	11.7517	0.612599
$369$	−1.90649	−0.0992478
$370$	−10.4050	−0.540931
$371$	−18.1136	−0.940412
$372$	9.41581	0.488187
$373$	−23.7004	−1.22716	−0.613580	−	0.789633i	$-0.710271\pi$
$373$	−23.7004	−1.22716	−0.613580	+	0.789633i	$0.710271\pi$
$374$	−11.1786	−0.578030
$375$	−6.63968	−0.342872
$376$	−32.3361	−1.66761
$377$	31.3625	1.61525
$378$	11.8300	0.608471
$379$	−18.9519	−0.973496	−0.486748	−	0.873542i	$-0.661817\pi$
$379$	−18.9519	−0.973496	−0.486748	+	0.873542i	$0.661817\pi$
$380$	−19.2464	−0.987317
$381$	−5.69201	−0.291610
$382$	−19.1186	−0.978193
$383$	4.69227	0.239764	0.119882	−	0.992788i	$-0.461748\pi$
$383$	4.69227	0.239764	0.119882	+	0.992788i	$0.461748\pi$
$384$	7.39568	0.377409
$385$	17.6944	0.901791
$386$	−34.7032	−1.76635
$387$	−7.33659	−0.372940
$388$	24.3148	1.23440
$389$	−8.92481	−0.452506	−0.226253	−	0.974069i	$-0.572648\pi$
$389$	−8.92481	−0.452506	−0.226253	+	0.974069i	$0.572648\pi$
$390$	−12.7185	−0.644027
$391$	−1.78741	−0.0903930
$392$	20.1564	1.01805
$393$	1.59860	0.0806388
$394$	−46.7366	−2.35456
$395$	36.5894	1.84101
$396$	31.8679	1.60142
$397$	−11.7872	−0.591581	−0.295791	−	0.955253i	$-0.595583\pi$
$397$	−11.7872	−0.591581	−0.295791	+	0.955253i	$0.595583\pi$
$398$	−2.82075	−0.141391
$399$	−0.710931	−0.0355911
$400$	128.838	6.44189
$401$	1.28910	0.0643748	0.0321874	−	0.999482i	$-0.489753\pi$
$401$	1.28910	0.0643748	0.0321874	+	0.999482i	$0.489753\pi$
$402$	11.1066	0.553946
$403$	18.4062	0.916880
$404$	86.4229	4.29970
$405$	30.7128	1.52613
$406$	−51.6161	−2.56166
$407$	−2.11365	−0.104770
$408$	−5.91201	−0.292688
$409$	23.1148	1.14296	0.571478	−	0.820618i	$-0.306370\pi$
$409$	23.1148	1.14296	0.571478	+	0.820618i	$0.306370\pi$
$410$	−6.88658	−0.340104
$411$	−1.52926	−0.0754330
$412$	52.3057	2.57691
$413$	7.63803	0.375843
$414$	7.04258	0.346124
$415$	2.26756	0.111310
$416$	61.4453	3.01260
$417$	−6.23315	−0.305239
$418$	−5.40357	−0.264297
$419$	−11.3461	−0.554293	−0.277146	−	0.960828i	$-0.589389\pi$
$419$	−11.3461	−0.554293	−0.277146	+	0.960828i	$0.589389\pi$
$420$	15.1450	0.739002
$421$	6.08285	0.296460	0.148230	−	0.988953i	$-0.452642\pi$
$421$	6.08285	0.296460	0.148230	+	0.988953i	$0.452642\pi$
$422$	23.7254	1.15493
$423$	−10.7079	−0.520637
$424$	−72.8126	−3.53609
$425$	−19.5959	−0.950543
$426$	0.983297	0.0476409
$427$	14.4155	0.697615
$428$	−37.4417	−1.80981
$429$	−2.58361	−0.124738
$430$	−26.5011	−1.27799
$431$	−15.7949	−0.760813	−0.380406	−	0.924819i	$-0.624216\pi$
$431$	−15.7949	−0.760813	−0.380406	+	0.924819i	$0.624216\pi$
$432$	26.2768	1.26424
$433$	16.0145	0.769610	0.384805	−	0.922998i	$-0.374269\pi$
$433$	16.0145	0.769610	0.384805	+	0.922998i	$0.374269\pi$
$434$	−30.2928	−1.45410
$435$	11.8578	0.568538
$436$	−5.23416	−0.250671
$437$	−0.864007	−0.0413310
$438$	−2.08839	−0.0997870
$439$	31.3650	1.49697	0.748485	−	0.663151i	$-0.230781\pi$
$439$	31.3650	1.49697	0.748485	+	0.663151i	$0.230781\pi$
$440$	71.1275	3.39087
$441$	6.67466	0.317841
$442$	−18.7037	−0.889644
$443$	16.3845	0.778451	0.389226	−	0.921142i	$-0.372743\pi$
$443$	16.3845	0.778451	0.389226	+	0.921142i	$0.372743\pi$
$444$	−1.80912	−0.0858570
$445$	35.2635	1.67165
$446$	7.53428	0.356759
$447$	4.71762	0.223136
$448$	−45.1734	−2.13424
$449$	7.43781	0.351012	0.175506	−	0.984478i	$-0.443844\pi$
$449$	7.43781	0.351012	0.175506	+	0.984478i	$0.443844\pi$
$450$	77.2102	3.63972
$451$	−1.39892	−0.0658728
$452$	58.1081	2.73318
$453$	0.623507	0.0292949
$454$	−4.45121	−0.208905
$455$	29.6058	1.38794
$456$	−2.85778	−0.133828
$457$	−37.8000	−1.76821	−0.884104	−	0.467290i	$-0.845231\pi$
$457$	−37.8000	−1.76821	−0.884104	+	0.467290i	$0.845231\pi$
$458$	28.9432	1.35243
$459$	−3.99665	−0.186548
$460$	18.4060	0.858185
$461$	13.0769	0.609051	0.304526	−	0.952504i	$-0.401502\pi$
$461$	13.0769	0.609051	0.304526	+	0.952504i	$0.401502\pi$
$462$	4.25209	0.197825
$463$	5.67804	0.263881	0.131940	−	0.991258i	$-0.457879\pi$
$463$	5.67804	0.263881	0.131940	+	0.991258i	$0.457879\pi$
$464$	−114.650	−5.32247
$465$	6.95919	0.322725
$466$	−76.1964	−3.52973
$467$	−15.5874	−0.721301	−0.360651	−	0.932701i	$-0.617445\pi$
$467$	−15.5874	−0.721301	−0.360651	+	0.932701i	$0.617445\pi$
$468$	53.3206	2.46474
$469$	−25.8536	−1.19381
$470$	−38.6789	−1.78413
$471$	7.88244	0.363204
$472$	30.7031	1.41323
$473$	−5.38337	−0.247528
$474$	8.79269	0.403861
$475$	−9.47240	−0.434623
$476$	22.2721	1.02084
$477$	−24.1115	−1.10399
$478$	20.9577	0.958582
$479$	13.5956	0.621200	0.310600	−	0.950541i	$-0.399470\pi$
$479$	13.5956	0.621200	0.310600	+	0.950541i	$0.399470\pi$
$480$	23.2318	1.06038
$481$	−3.53651	−0.161251
$482$	61.3882	2.79616
$483$	0.679890	0.0309361
$484$	−34.1921	−1.55418
$485$	17.9710	0.816022
$486$	23.7808	1.07872
$487$	−13.8809	−0.629005	−0.314502	−	0.949257i	$-0.601838\pi$
$487$	−13.8809	−0.629005	−0.314502	+	0.949257i	$0.601838\pi$
$488$	57.9470	2.62314
$489$	−0.450079	−0.0203533
$490$	24.1101	1.08918
$491$	−6.06555	−0.273734	−0.136867	−	0.990589i	$-0.543703\pi$
$491$	−6.06555	−0.273734	−0.136867	+	0.990589i	$0.543703\pi$
$492$	−1.19737	−0.0539816
$493$	17.4379	0.785366
$494$	−9.04110	−0.406778
$495$	23.5535	1.05865
$496$	−67.2863	−3.02124
$497$	−2.28889	−0.102671
$498$	0.544909	0.0244180
$499$	−10.4959	−0.469859	−0.234929	−	0.972012i	$-0.575486\pi$
$499$	−10.4959	−0.469859	−0.234929	+	0.972012i	$0.575486\pi$
$500$	100.548	4.49665
$501$	−5.08109	−0.227006
$502$	−28.0567	−1.25223
$503$	−14.9886	−0.668310	−0.334155	−	0.942518i	$-0.608451\pi$
$503$	−14.9886	−0.668310	−0.334155	+	0.942518i	$0.608451\pi$
$504$	−54.2231	−2.41529
$505$	63.8748	2.84239
$506$	5.16763	0.229729
$507$	0.170443	0.00756964
$508$	86.1971	3.82438
$509$	−31.3789	−1.39085	−0.695423	−	0.718600i	$-0.744783\pi$
$509$	−31.3789	−1.39085	−0.695423	+	0.718600i	$0.744783\pi$
$510$	−7.07166	−0.313138
$511$	4.86129	0.215051
$512$	0.296039	0.0130832
$513$	−1.93192	−0.0852965
$514$	31.5649	1.39227
$515$	38.6589	1.70352
$516$	−4.60774	−0.202845
$517$	−7.85716	−0.345557
$518$	5.82035	0.255731
$519$	−2.16175	−0.0948903
$520$	119.009	5.21888
$521$	−7.70180	−0.337422	−0.168711	−	0.985666i	$-0.553960\pi$
$521$	−7.70180	−0.337422	−0.168711	+	0.985666i	$0.553960\pi$
$522$	−68.7074	−3.00724
$523$	20.3564	0.890122	0.445061	−	0.895500i	$-0.353182\pi$
$523$	20.3564	0.890122	0.445061	+	0.895500i	$0.353182\pi$
$524$	−24.2085	−1.05755
$525$	7.45387	0.325313
$526$	50.6911	2.21024
$527$	10.2341	0.445805
$528$	9.44472	0.411029
$529$	−22.1737	−0.964075
$530$	−87.0950	−3.78316
$531$	10.1672	0.441217
$532$	10.7660	0.466766
$533$	−2.34064	−0.101385
$534$	8.47406	0.366708
$535$	−27.6730	−1.19641
$536$	−103.926	−4.48890
$537$	−8.30321	−0.358310
$538$	−43.4843	−1.87474
$539$	4.89767	0.210957
$540$	41.1559	1.77107
$541$	37.7833	1.62443	0.812216	−	0.583357i	$-0.198261\pi$
$541$	37.7833	1.62443	0.812216	+	0.583357i	$0.198261\pi$
$542$	−46.7588	−2.00846
$543$	2.33949	0.100397
$544$	34.1644	1.46478
$545$	−3.86855	−0.165710
$546$	7.11448	0.304472
$547$	−38.8381	−1.66060	−0.830299	−	0.557318i	$-0.811830\pi$
$547$	−38.8381	−1.66060	−0.830299	+	0.557318i	$0.811830\pi$
$548$	23.1585	0.989281
$549$	19.1888	0.818958
$550$	56.6545	2.41576
$551$	8.42926	0.359098
$552$	2.73300	0.116324
$553$	−20.4674	−0.870362
$554$	71.2543	3.02731
$555$	−1.33711	−0.0567573
$556$	94.3920	4.00311
$557$	29.7144	1.25904	0.629519	−	0.776985i	$-0.283252\pi$
$557$	29.7144	1.25904	0.629519	+	0.776985i	$0.283252\pi$
$558$	−40.3235	−1.70703
$559$	−9.00731	−0.380969
$560$	−108.228	−4.57346
$561$	−1.43652	−0.0606500
$562$	−19.9505	−0.841561
$563$	12.0044	0.505924	0.252962	−	0.967476i	$-0.418595\pi$
$563$	12.0044	0.505924	0.252962	+	0.967476i	$0.418595\pi$
$564$	−6.72511	−0.283178
$565$	42.9475	1.80681
$566$	7.12007	0.299279
$567$	−17.1801	−0.721496
$568$	−9.20082	−0.386058
$569$	4.82179	0.202140	0.101070	−	0.994879i	$-0.467773\pi$
$569$	4.82179	0.202140	0.101070	+	0.994879i	$0.467773\pi$
$570$	−3.41834	−0.143179
$571$	17.7041	0.740892	0.370446	−	0.928854i	$-0.379205\pi$
$571$	17.7041	0.740892	0.370446	+	0.928854i	$0.379205\pi$
$572$	39.1251	1.63590
$573$	−2.45687	−0.102637
$574$	3.85221	0.160788
$575$	9.05881	0.377779
$576$	−60.1314	−2.50547
$577$	−30.7159	−1.27872	−0.639359	−	0.768908i	$-0.720800\pi$
$577$	−30.7159	−1.27872	−0.639359	+	0.768908i	$0.720800\pi$
$578$	35.3244	1.46930
$579$	−4.45960	−0.185335
$580$	−179.569	−7.45621
$581$	−1.26843	−0.0526231
$582$	4.31855	0.179010
$583$	−17.6923	−0.732740
$584$	19.5413	0.808624
$585$	39.4090	1.62936
$586$	−1.27061	−0.0524884
$587$	27.1975	1.12256	0.561281	−	0.827625i	$-0.310309\pi$
$587$	27.1975	1.12256	0.561281	+	0.827625i	$0.310309\pi$
$588$	4.19202	0.172876
$589$	4.94702	0.203838
$590$	36.7256	1.51197
$591$	−6.00597	−0.247052
$592$	12.9281	0.531343
$593$	−25.5638	−1.04978	−0.524889	−	0.851171i	$-0.675893\pi$
$593$	−25.5638	−1.04978	−0.524889	+	0.851171i	$0.675893\pi$
$594$	11.5548	0.474101
$595$	16.4612	0.674844
$596$	−71.4415	−2.92636
$597$	−0.362485	−0.0148355
$598$	8.64635	0.353575
$599$	24.3202	0.993696	0.496848	−	0.867838i	$-0.334491\pi$
$599$	24.3202	0.993696	0.496848	+	0.867838i	$0.334491\pi$
$600$	29.9628	1.22323
$601$	−15.9277	−0.649705	−0.324853	−	0.945765i	$-0.605315\pi$
$601$	−15.9277	−0.649705	−0.324853	+	0.945765i	$0.605315\pi$
$602$	14.8242	0.604187
$603$	−34.4143	−1.40146
$604$	−9.44210	−0.384194
$605$	−25.2712	−1.02742
$606$	15.3495	0.623533
$607$	−22.7920	−0.925097	−0.462548	−	0.886594i	$-0.653065\pi$
$607$	−22.7920	−0.925097	−0.462548	+	0.886594i	$0.653065\pi$
$608$	16.5146	0.669754
$609$	−6.63301	−0.268783
$610$	69.3134	2.80642
$611$	−13.1464	−0.531846
$612$	29.6469	1.19841
$613$	23.7478	0.959163	0.479581	−	0.877497i	$-0.340789\pi$
$613$	23.7478	0.959163	0.479581	+	0.877497i	$0.340789\pi$
$614$	−66.5256	−2.68476
$615$	−0.884971	−0.0356855
$616$	−39.7873	−1.60307
$617$	27.1045	1.09119	0.545594	−	0.838050i	$-0.316304\pi$
$617$	27.1045	1.09119	0.545594	+	0.838050i	$0.316304\pi$
$618$	9.28999	0.373698
$619$	−44.0418	−1.77019	−0.885094	−	0.465413i	$-0.845906\pi$
$619$	−44.0418	−1.77019	−0.885094	+	0.465413i	$0.845906\pi$
$620$	−105.387	−4.23244
$621$	1.84757	0.0741404
$622$	−56.5579	−2.26776
$623$	−19.7257	−0.790293
$624$	15.8027	0.632613
$625$	24.4864	0.979457
$626$	5.08743	0.203335
$627$	−0.694394	−0.0277314
$628$	−119.368	−4.76330
$629$	−1.96634	−0.0784032
$630$	−64.8590	−2.58404
$631$	−20.6647	−0.822648	−0.411324	−	0.911489i	$-0.634933\pi$
$631$	−20.6647	−0.822648	−0.411324	+	0.911489i	$0.634933\pi$
$632$	−82.2742	−3.27269
$633$	3.04887	0.121182
$634$	−65.0497	−2.58345
$635$	63.7080	2.52817
$636$	−15.1432	−0.600467
$637$	8.19465	0.324684
$638$	−50.4155	−1.99597
$639$	−3.04680	−0.120530
$640$	−82.7764	−3.27202
$641$	12.7501	0.503598	0.251799	−	0.967780i	$-0.418978\pi$
$641$	12.7501	0.503598	0.251799	+	0.967780i	$0.418978\pi$
$642$	−6.65000	−0.262455
$643$	36.9270	1.45626	0.728128	−	0.685441i	$-0.240390\pi$
$643$	36.9270	1.45626	0.728128	+	0.685441i	$0.240390\pi$
$644$	−10.2959	−0.405717
$645$	−3.40556	−0.134094
$646$	−5.02697	−0.197783
$647$	38.0762	1.49693	0.748465	−	0.663174i	$-0.230791\pi$
$647$	38.0762	1.49693	0.748465	+	0.663174i	$0.230791\pi$
$648$	−69.0600	−2.71293
$649$	7.46036	0.292845
$650$	94.7928	3.71808
$651$	−3.89283	−0.152572
$652$	6.81578	0.266927
$653$	−0.00788604	−0.000308605 0	−0.000154302	−	1.00000i	$-0.500049\pi$
$653$	−0.00788604	−0.000308605 0	−0.000154302		1.00000i	$0.500049\pi$
$654$	−0.929638	−0.0363517
$655$	−17.8924	−0.699114
$656$	8.55652	0.334076
$657$	6.47098	0.252457
$658$	21.6362	0.843467
$659$	−50.6543	−1.97321	−0.986606	−	0.163123i	$-0.947843\pi$
$659$	−50.6543	−1.97321	−0.986606	+	0.163123i	$0.947843\pi$
$660$	14.7927	0.575807
$661$	16.1565	0.628416	0.314208	−	0.949354i	$-0.398261\pi$
$661$	16.1565	0.628416	0.314208	+	0.949354i	$0.398261\pi$
$662$	80.7863	3.13985
$663$	−2.40355	−0.0933462
$664$	−5.09878	−0.197871
$665$	7.95712	0.308564
$666$	7.74760	0.300214
$667$	−8.06122	−0.312132
$668$	76.9457	2.97712
$669$	0.968206	0.0374330
$670$	−124.311	−4.80254
$671$	14.0802	0.543559
$672$	−12.9954	−0.501307
$673$	−0.534697	−0.0206111	−0.0103055	−	0.999947i	$-0.503280\pi$
$673$	−0.534697	−0.0206111	−0.0103055	+	0.999947i	$0.503280\pi$
$674$	−75.5104	−2.90855
$675$	20.2555	0.779636
$676$	−2.58111	−0.0992735
$677$	12.1931	0.468617	0.234309	−	0.972162i	$-0.424717\pi$
$677$	12.1931	0.468617	0.234309	+	0.972162i	$0.424717\pi$
$678$	10.3206	0.396359
$679$	−10.0526	−0.385784
$680$	66.1704	2.53752
$681$	−0.572010	−0.0219195
$682$	−29.5882	−1.13299
$683$	−42.0787	−1.61009	−0.805047	−	0.593210i	$-0.797860\pi$
$683$	−42.0787	−1.61009	−0.805047	+	0.593210i	$0.797860\pi$
$684$	14.3309	0.547956
$685$	17.1163	0.653982
$686$	−54.2291	−2.07048
$687$	3.71940	0.141904
$688$	32.9274	1.25534
$689$	−29.6023	−1.12776
$690$	3.26909	0.124452
$691$	31.3963	1.19437	0.597187	−	0.802102i	$-0.296285\pi$
$691$	31.3963	1.19437	0.597187	+	0.802102i	$0.296285\pi$
$692$	32.7365	1.24446
$693$	−13.1753	−0.500489
$694$	86.1457	3.27005
$695$	69.7647	2.64633
$696$	−26.6632	−1.01067
$697$	−1.30143	−0.0492951
$698$	73.7233	2.79047
$699$	−9.79175	−0.370358
$700$	−112.878	−4.26638
$701$	36.8293	1.39102	0.695511	−	0.718515i	$-0.255178\pi$
$701$	36.8293	1.39102	0.695511	+	0.718515i	$0.255178\pi$
$702$	19.3333	0.729687
$703$	−0.950502	−0.0358489
$704$	−44.1226	−1.66293
$705$	−4.97050	−0.187200
$706$	35.0143	1.31778
$707$	−35.7303	−1.34377
$708$	6.38548	0.239981
$709$	−14.0304	−0.526922	−0.263461	−	0.964670i	$-0.584864\pi$
$709$	−14.0304	−0.526922	−0.263461	+	0.964670i	$0.584864\pi$
$710$	−11.0056	−0.413032
$711$	−27.2446	−1.02175
$712$	−79.2927	−2.97162
$713$	−4.73102	−0.177178
$714$	3.95574	0.148040
$715$	28.9172	1.08144
$716$	125.740	4.69912
$717$	2.69320	0.100580
$718$	−64.1769	−2.39506
$719$	16.2660	0.606620	0.303310	−	0.952892i	$-0.401908\pi$
$719$	16.2660	0.606620	0.303310	+	0.952892i	$0.401908\pi$
$720$	−144.065	−5.36897
$721$	−21.6250	−0.805357
$722$	48.6732	1.81143
$723$	7.88879	0.293387
$724$	−35.4282	−1.31668
$725$	−88.3778	−3.28227
$726$	−6.07284	−0.225384
$727$	−24.5893	−0.911965	−0.455982	−	0.889989i	$-0.650712\pi$
$727$	−24.5893	−0.911965	−0.455982	+	0.889989i	$0.650712\pi$
$728$	−66.5710	−2.46729
$729$	−20.7613	−0.768936
$730$	23.3743	0.865123
$731$	−5.00818	−0.185234
$732$	12.0515	0.445437
$733$	−5.04851	−0.186471	−0.0932355	−	0.995644i	$-0.529721\pi$
$733$	−5.04851	−0.186471	−0.0932355	+	0.995644i	$0.529721\pi$
$734$	−33.1130	−1.22222
$735$	3.09830	0.114283
$736$	−15.7935	−0.582156
$737$	−25.2522	−0.930178
$738$	5.12777	0.188756
$739$	25.2991	0.930643	0.465322	−	0.885142i	$-0.345939\pi$
$739$	25.2991	0.930643	0.465322	+	0.885142i	$0.345939\pi$
$740$	20.2486	0.744354
$741$	−1.16184	−0.0426813
$742$	48.7191	1.78854
$743$	14.3827	0.527651	0.263825	−	0.964570i	$-0.415016\pi$
$743$	14.3827	0.527651	0.263825	+	0.964570i	$0.415016\pi$
$744$	−15.6483	−0.573694
$745$	−52.8022	−1.93452
$746$	63.7455	2.33389
$747$	−1.68843	−0.0617765
$748$	21.7540	0.795406
$749$	15.4797	0.565616
$750$	17.8583	0.652095
$751$	22.8332	0.833195	0.416597	−	0.909091i	$-0.363223\pi$
$751$	22.8332	0.833195	0.416597	+	0.909091i	$0.363223\pi$
$752$	48.0583	1.75250
$753$	−3.60548	−0.131391
$754$	−84.3538	−3.07199
$755$	−6.97862	−0.253978
$756$	−23.0218	−0.837294
$757$	−36.8537	−1.33947	−0.669735	−	0.742601i	$-0.733592\pi$
$757$	−36.8537	−1.33947	−0.669735	+	0.742601i	$0.733592\pi$
$758$	50.9739	1.85146
$759$	0.664075	0.0241044
$760$	31.9858	1.16025
$761$	4.39081	0.159167	0.0795834	−	0.996828i	$-0.474641\pi$
$761$	4.39081	0.159167	0.0795834	+	0.996828i	$0.474641\pi$
$762$	15.3094	0.554603
$763$	2.16399	0.0783416
$764$	37.2057	1.34606
$765$	21.9119	0.792227
$766$	−12.6205	−0.455998
$767$	12.4825	0.450716
$768$	−5.46134	−0.197069
$769$	−20.7518	−0.748329	−0.374165	−	0.927362i	$-0.622071\pi$
$769$	−20.7518	−0.748329	−0.374165	+	0.927362i	$0.622071\pi$
$770$	−47.5916	−1.71508
$771$	4.05630	0.146084
$772$	67.5341	2.43061
$773$	2.51774	0.0905567	0.0452784	−	0.998974i	$-0.485583\pi$
$773$	2.51774	0.0905567	0.0452784	+	0.998974i	$0.485583\pi$
$774$	19.7328	0.709280
$775$	−51.8678	−1.86315
$776$	−40.4092	−1.45061
$777$	0.747953	0.0268327
$778$	24.0045	0.860604
$779$	−0.629092	−0.0225396
$780$	24.7508	0.886222
$781$	−2.23565	−0.0799979
$782$	4.80748	0.171915
$783$	−18.0249	−0.644158
$784$	−29.9566	−1.06988
$785$	−88.2245	−3.14887
$786$	−4.29966	−0.153364
$787$	−0.718531	−0.0256128	−0.0128064	−	0.999918i	$-0.504077\pi$
$787$	−0.718531	−0.0256128	−0.0128064	+	0.999918i	$0.504077\pi$
$788$	90.9516	3.24002
$789$	6.51415	0.231910
$790$	−98.4124	−3.50136
$791$	−24.0239	−0.854193
$792$	−52.9618	−1.88192
$793$	23.5586	0.836590
$794$	31.7033	1.12511
$795$	−11.1923	−0.396949
$796$	5.48931	0.194564
$797$	−9.08434	−0.321784	−0.160892	−	0.986972i	$-0.551437\pi$
$797$	−9.08434	−0.321784	−0.160892	+	0.986972i	$0.551437\pi$
$798$	1.91215	0.0676893
$799$	−7.30956	−0.258594
$800$	−173.149	−6.12176
$801$	−26.2573	−0.927757
$802$	−3.46723	−0.122432
$803$	4.74822	0.167561
$804$	−21.6139	−0.762264
$805$	−7.60969	−0.268206
$806$	−49.5062	−1.74378
$807$	−5.58803	−0.196708
$808$	−143.627	−5.05280
$809$	−1.93279	−0.0679533	−0.0339767	−	0.999423i	$-0.510817\pi$
$809$	−1.93279	−0.0679533	−0.0339767	+	0.999423i	$0.510817\pi$
$810$	−82.6063	−2.90249
$811$	54.6206	1.91799	0.958995	−	0.283423i	$-0.0914699\pi$
$811$	54.6206	1.91799	0.958995	+	0.283423i	$0.0914699\pi$
$812$	100.447	3.52501
$813$	−6.00881	−0.210738
$814$	5.68496	0.199258
$815$	5.03752	0.176457
$816$	8.78648	0.307588
$817$	−2.42088	−0.0846960
$818$	−62.1706	−2.17374
$819$	−22.0446	−0.770301
$820$	13.4016	0.468004
$821$	−14.3807	−0.501891	−0.250945	−	0.968001i	$-0.580741\pi$
$821$	−14.3807	−0.501891	−0.250945	+	0.968001i	$0.580741\pi$
$822$	4.11317	0.143463
$823$	33.5316	1.16884	0.584418	−	0.811452i	$-0.301323\pi$
$823$	33.5316	1.16884	0.584418	+	0.811452i	$0.301323\pi$
$824$	−86.9276	−3.02827
$825$	7.28048	0.253474
$826$	−20.5435	−0.714801
$827$	55.6060	1.93361	0.966805	−	0.255514i	$-0.0822446\pi$
$827$	55.6060	1.93361	0.966805	+	0.255514i	$0.0822446\pi$
$828$	−13.7052	−0.476288
$829$	19.9074	0.691411	0.345706	−	0.938343i	$-0.387640\pi$
$829$	19.9074	0.691411	0.345706	+	0.938343i	$0.387640\pi$
$830$	−6.09891	−0.211696
$831$	9.15666	0.317641
$832$	−73.8248	−2.55941
$833$	4.55633	0.157867
$834$	16.7649	0.580522
$835$	56.8703	1.96808
$836$	10.5156	0.363689
$837$	−10.5786	−0.365649
$838$	30.5169	1.05419
$839$	47.4290	1.63743	0.818716	−	0.574198i	$-0.194686\pi$
$839$	47.4290	1.63743	0.818716	+	0.574198i	$0.194686\pi$
$840$	−25.1698	−0.868439
$841$	49.6453	1.71191
$842$	−16.3607	−0.563826
$843$	−2.56377	−0.0883010
$844$	−46.1707	−1.58926
$845$	−1.90769	−0.0656265
$846$	28.8005	0.990180
$847$	14.1362	0.485726
$848$	108.215	3.71611
$849$	0.914977	0.0314019
$850$	52.7060	1.80780
$851$	0.909001	0.0311601
$852$	−1.91354	−0.0655568
$853$	−14.5863	−0.499427	−0.249713	−	0.968320i	$-0.580336\pi$
$853$	−14.5863	−0.499427	−0.249713	+	0.968320i	$0.580336\pi$
$854$	−38.7725	−1.32677
$855$	10.5919	0.362236
$856$	62.2249	2.12680
$857$	16.1067	0.550194	0.275097	−	0.961416i	$-0.411290\pi$
$857$	16.1067	0.550194	0.275097	+	0.961416i	$0.411290\pi$
$858$	6.94899	0.237235
$859$	−6.26434	−0.213737	−0.106868	−	0.994273i	$-0.534082\pi$
$859$	−6.26434	−0.213737	−0.106868	+	0.994273i	$0.534082\pi$
$860$	51.5723	1.75860
$861$	0.495035	0.0168707
$862$	42.4826	1.44696
$863$	−10.2778	−0.349859	−0.174930	−	0.984581i	$-0.555970\pi$
$863$	−10.2778	−0.349859	−0.174930	+	0.984581i	$0.555970\pi$
$864$	−35.3143	−1.20142
$865$	24.1955	0.822670
$866$	−43.0733	−1.46369
$867$	4.53942	0.154167
$868$	58.9512	2.00093
$869$	−19.9913	−0.678158
$870$	−31.8932	−1.08128
$871$	−42.2514	−1.43163
$872$	8.69874	0.294576
$873$	−13.3813	−0.452887
$874$	2.32387	0.0786060
$875$	−41.5702	−1.40533
$876$	4.06410	0.137313
$877$	22.5972	0.763054	0.381527	−	0.924358i	$-0.375398\pi$
$877$	22.5972	0.763054	0.381527	+	0.924358i	$0.375398\pi$
$878$	−84.3606	−2.84703
$879$	−0.163282	−0.00550736
$880$	−105.710	−3.56350
$881$	24.1769	0.814541	0.407270	−	0.913308i	$-0.366481\pi$
$881$	24.1769	0.814541	0.407270	+	0.913308i	$0.366481\pi$
$882$	−17.9524	−0.604490
$883$	22.8981	0.770583	0.385292	−	0.922795i	$-0.374101\pi$
$883$	22.8981	0.770583	0.385292	+	0.922795i	$0.374101\pi$
$884$	36.3983	1.22421
$885$	4.71948	0.158644
$886$	−44.0684	−1.48051
$887$	42.6153	1.43088	0.715440	−	0.698674i	$-0.246226\pi$
$887$	42.6153	1.43088	0.715440	+	0.698674i	$0.246226\pi$
$888$	3.00660	0.100895
$889$	−35.6369	−1.19522
$890$	−94.8462	−3.17925
$891$	−16.7805	−0.562167
$892$	−14.6621	−0.490922
$893$	−3.53334	−0.118239
$894$	−12.6887	−0.424374
$895$	92.9339	3.10644
$896$	46.3034	1.54689
$897$	1.11111	0.0370990
$898$	−20.0050	−0.667577
$899$	46.1559	1.53938
$900$	−150.255	−5.00848
$901$	−16.4592	−0.548337
$902$	3.76260	0.125281
$903$	1.90500	0.0633945
$904$	−96.5707	−3.21190
$905$	−26.1849	−0.870414
$906$	−1.67701	−0.0557149
$907$	8.16789	0.271210	0.135605	−	0.990763i	$-0.456702\pi$
$907$	8.16789	0.271210	0.135605	+	0.990763i	$0.456702\pi$
$908$	8.66225	0.287467
$909$	−47.5614	−1.57751
$910$	−79.6290	−2.63968
$911$	22.9932	0.761800	0.380900	−	0.924616i	$-0.375614\pi$
$911$	22.9932	0.761800	0.380900	+	0.924616i	$0.375614\pi$
$912$	4.24726	0.140641
$913$	−1.23892	−0.0410023
$914$	101.668	3.36289
$915$	8.90724	0.294464
$916$	−56.3248	−1.86103
$917$	10.0086	0.330515
$918$	10.7495	0.354788
$919$	−8.88718	−0.293161	−0.146580	−	0.989199i	$-0.546827\pi$
$919$	−8.88718	−0.293161	−0.146580	+	0.989199i	$0.546827\pi$
$920$	−30.5892	−1.00850
$921$	−8.54899	−0.281699
$922$	−35.1721	−1.15833
$923$	−3.74063	−0.123124
$924$	−8.27475	−0.272219
$925$	9.96568	0.327670
$926$	−15.2719	−0.501865
$927$	−28.7856	−0.945442
$928$	154.081	5.05797
$929$	40.2339	1.32003	0.660015	−	0.751252i	$-0.270550\pi$
$929$	40.2339	1.32003	0.660015	+	0.751252i	$0.270550\pi$
$930$	−18.7177	−0.613778
$931$	2.20246	0.0721828
$932$	148.282	4.85713
$933$	−7.26806	−0.237946
$934$	41.9246	1.37182
$935$	16.0783	0.525817
$936$	−88.6143	−2.89645
$937$	12.7307	0.415895	0.207947	−	0.978140i	$-0.433322\pi$
$937$	12.7307	0.415895	0.207947	+	0.978140i	$0.433322\pi$
$938$	69.5369	2.27046
$939$	0.653768	0.0213349
$940$	75.2710	2.45507
$941$	40.1734	1.30961	0.654807	−	0.755796i	$-0.272750\pi$
$941$	40.1734	1.30961	0.654807	+	0.755796i	$0.272750\pi$
$942$	−21.2009	−0.690764
$943$	0.601624	0.0195916
$944$	−45.6313	−1.48517
$945$	−17.0153	−0.553508
$946$	14.4793	0.470764
$947$	−23.2868	−0.756718	−0.378359	−	0.925659i	$-0.623511\pi$
$947$	−23.2868	−0.756718	−0.378359	+	0.925659i	$0.623511\pi$
$948$	−17.1110	−0.555739
$949$	7.94459	0.257892
$950$	25.4773	0.826594
$951$	−8.35932	−0.271069
$952$	−37.0143	−1.19964
$953$	39.9622	1.29450	0.647251	−	0.762277i	$-0.275919\pi$
$953$	39.9622	1.29450	0.647251	+	0.762277i	$0.275919\pi$
$954$	64.8512	2.09963
$955$	27.4986	0.889834
$956$	−40.7846	−1.31907
$957$	−6.47872	−0.209427
$958$	−36.5673	−1.18144
$959$	−9.57453	−0.309178
$960$	−27.9123	−0.900866
$961$	−3.91172	−0.126185
$962$	9.51193	0.306677
$963$	20.6054	0.664000
$964$	−119.464	−3.84768
$965$	49.9142	1.60680
$966$	−1.82866	−0.0588362
$967$	−54.5352	−1.75373	−0.876867	−	0.480733i	$-0.840370\pi$
$967$	−54.5352	−1.75373	−0.876867	+	0.480733i	$0.840370\pi$
$968$	56.8243	1.82640
$969$	−0.645999	−0.0207525
$970$	−48.3355	−1.55196
$971$	19.7653	0.634298	0.317149	−	0.948376i	$-0.397275\pi$
$971$	19.7653	0.634298	0.317149	+	0.948376i	$0.397275\pi$
$972$	−46.2785	−1.48438
$973$	−39.0250	−1.25108
$974$	37.3347	1.19628
$975$	12.1815	0.390121
$976$	−86.1214	−2.75668
$977$	−16.9922	−0.543629	−0.271815	−	0.962350i	$-0.587624\pi$
$977$	−16.9922	−0.543629	−0.271815	+	0.962350i	$0.587624\pi$
$978$	1.21055	0.0387091
$979$	−19.2668	−0.615771
$980$	−46.9193	−1.49878
$981$	2.88054	0.0919684
$982$	16.3141	0.520605
$983$	−22.0993	−0.704857	−0.352428	−	0.935839i	$-0.614644\pi$
$983$	−22.0993	−0.704857	−0.352428	+	0.935839i	$0.614644\pi$
$984$	1.98993	0.0634365
$985$	67.2220	2.14187
$986$	−46.9018	−1.49366
$987$	2.78040	0.0885010
$988$	17.5944	0.559753
$989$	2.31518	0.0736185
$990$	−63.3503	−2.01341
$991$	10.9833	0.348895	0.174447	−	0.984667i	$-0.444186\pi$
$991$	10.9833	0.348895	0.174447	+	0.984667i	$0.444186\pi$
$992$	90.4284	2.87110
$993$	10.3816	0.329449
$994$	6.15630	0.195266
$995$	4.05713	0.128620
$996$	−1.06042	−0.0336006
$997$	−49.1972	−1.55809	−0.779046	−	0.626967i	$-0.784296\pi$
$997$	−49.1972	−1.55809	−0.779046	+	0.626967i	$0.784296\pi$
$998$	28.2301	0.893607
$999$	2.03253	0.0643064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.2	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.2	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68964 q^{2} -0.345637 q^{3} +5.23416 q^{4} +3.86855 q^{5} +0.929638 q^{6} -2.16399 q^{7} -8.69874 q^{8} -2.88054 q^{9} +O(q^{10})\)	\(q-2.68964 q^{2} -0.345637 q^{3} +5.23416 q^{4} +3.86855 q^{5} +0.929638 q^{6} -2.16399 q^{7} -8.69874 q^{8} -2.88054 q^{9} -10.4050 q^{10} -2.11365 q^{11} -1.80912 q^{12} -3.53651 q^{13} +5.82035 q^{14} -1.33711 q^{15} +12.9281 q^{16} -1.96634 q^{17} +7.74760 q^{18} -0.950502 q^{19} +20.2486 q^{20} +0.747953 q^{21} +5.68496 q^{22} +0.909001 q^{23} +3.00660 q^{24} +9.96568 q^{25} +9.51193 q^{26} +2.03253 q^{27} -11.3267 q^{28} -8.86822 q^{29} +3.59635 q^{30} -5.20464 q^{31} -17.3746 q^{32} +0.730555 q^{33} +5.28875 q^{34} -8.37149 q^{35} -15.0772 q^{36} +1.00000 q^{37} +2.55651 q^{38} +1.22235 q^{39} -33.6515 q^{40} +0.661852 q^{41} -2.01173 q^{42} +2.54695 q^{43} -11.0632 q^{44} -11.1435 q^{45} -2.44488 q^{46} +3.71734 q^{47} -4.46844 q^{48} -2.31716 q^{49} -26.8041 q^{50} +0.679640 q^{51} -18.5106 q^{52} +8.37049 q^{53} -5.46677 q^{54} -8.17677 q^{55} +18.8240 q^{56} +0.328528 q^{57} +23.8523 q^{58} -3.52961 q^{59} -6.99867 q^{60} -6.66154 q^{61} +13.9986 q^{62} +6.23344 q^{63} +20.8751 q^{64} -13.6812 q^{65} -1.96493 q^{66} +11.9472 q^{67} -10.2922 q^{68} -0.314184 q^{69} +22.5163 q^{70} +1.05772 q^{71} +25.0570 q^{72} -2.24645 q^{73} -2.68964 q^{74} -3.44451 q^{75} -4.97508 q^{76} +4.57391 q^{77} -3.28767 q^{78} +9.45818 q^{79} +50.0132 q^{80} +7.93909 q^{81} -1.78014 q^{82} +0.586152 q^{83} +3.91491 q^{84} -7.60689 q^{85} -6.85039 q^{86} +3.06518 q^{87} +18.3861 q^{88} +9.11543 q^{89} +29.9720 q^{90} +7.65295 q^{91} +4.75786 q^{92} +1.79891 q^{93} -9.99830 q^{94} -3.67706 q^{95} +6.00529 q^{96} +4.64541 q^{97} +6.23232 q^{98} +6.08845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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