LMFDB - Embedded newform 6033.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08609 q^{2} +1.00000 q^{3} +2.35176 q^{4} +3.34556 q^{5} -2.08609 q^{6} -3.89610 q^{7} -0.733796 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.08609 q^{2} +1.00000 q^{3} +2.35176 q^{4} +3.34556 q^{5} -2.08609 q^{6} -3.89610 q^{7} -0.733796 q^{8} +1.00000 q^{9} -6.97912 q^{10} -3.98225 q^{11} +2.35176 q^{12} +3.25910 q^{13} +8.12761 q^{14} +3.34556 q^{15} -3.17275 q^{16} -4.20451 q^{17} -2.08609 q^{18} -4.73052 q^{19} +7.86794 q^{20} -3.89610 q^{21} +8.30731 q^{22} +3.36390 q^{23} -0.733796 q^{24} +6.19276 q^{25} -6.79876 q^{26} +1.00000 q^{27} -9.16269 q^{28} -3.53025 q^{29} -6.97912 q^{30} +5.05751 q^{31} +8.08623 q^{32} -3.98225 q^{33} +8.77097 q^{34} -13.0346 q^{35} +2.35176 q^{36} +0.737629 q^{37} +9.86827 q^{38} +3.25910 q^{39} -2.45496 q^{40} +3.87961 q^{41} +8.12761 q^{42} +5.36409 q^{43} -9.36528 q^{44} +3.34556 q^{45} -7.01739 q^{46} -5.25997 q^{47} -3.17275 q^{48} +8.17961 q^{49} -12.9186 q^{50} -4.20451 q^{51} +7.66460 q^{52} +8.24194 q^{53} -2.08609 q^{54} -13.3228 q^{55} +2.85894 q^{56} -4.73052 q^{57} +7.36442 q^{58} -4.33084 q^{59} +7.86794 q^{60} -1.48482 q^{61} -10.5504 q^{62} -3.89610 q^{63} -10.5231 q^{64} +10.9035 q^{65} +8.30731 q^{66} +4.11499 q^{67} -9.88798 q^{68} +3.36390 q^{69} +27.1914 q^{70} +3.25459 q^{71} -0.733796 q^{72} -0.206474 q^{73} -1.53876 q^{74} +6.19276 q^{75} -11.1250 q^{76} +15.5152 q^{77} -6.79876 q^{78} +4.99485 q^{79} -10.6146 q^{80} +1.00000 q^{81} -8.09319 q^{82} +6.26024 q^{83} -9.16269 q^{84} -14.0664 q^{85} -11.1900 q^{86} -3.53025 q^{87} +2.92216 q^{88} +2.77317 q^{89} -6.97912 q^{90} -12.6978 q^{91} +7.91108 q^{92} +5.05751 q^{93} +10.9727 q^{94} -15.8262 q^{95} +8.08623 q^{96} -5.52882 q^{97} -17.0634 q^{98} -3.98225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−2.08609	−1.47509	−0.737543	−	0.675300i	$-0.764014\pi$
$2$	−2.08609	−1.47509	−0.737543	+	0.675300i	$0.764014\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.35176	1.17588
$5$	3.34556	1.49618	0.748090	−	0.663598i	$-0.230971\pi$
$5$	3.34556	1.49618	0.748090	+	0.663598i	$0.230971\pi$
$6$	−2.08609	−0.851641
$7$	−3.89610	−1.47259	−0.736294	−	0.676662i	$-0.763426\pi$
$7$	−3.89610	−1.47259	−0.736294	+	0.676662i	$0.763426\pi$
$8$	−0.733796	−0.259436
$9$	1.00000	0.333333
$10$	−6.97912	−2.20699
$11$	−3.98225	−1.20069	−0.600346	−	0.799740i	$-0.704971\pi$
$11$	−3.98225	−1.20069	−0.600346	+	0.799740i	$0.704971\pi$
$12$	2.35176	0.678894
$13$	3.25910	0.903911	0.451955	−	0.892041i	$-0.350727\pi$
$13$	3.25910	0.903911	0.451955	+	0.892041i	$0.350727\pi$
$14$	8.12761	2.17219
$15$	3.34556	0.863819
$16$	−3.17275	−0.793188
$17$	−4.20451	−1.01974	−0.509871	−	0.860251i	$-0.670307\pi$
$17$	−4.20451	−1.01974	−0.509871	+	0.860251i	$0.670307\pi$
$18$	−2.08609	−0.491695
$19$	−4.73052	−1.08526	−0.542628	−	0.839973i	$-0.682570\pi$
$19$	−4.73052	−1.08526	−0.542628	+	0.839973i	$0.682570\pi$
$20$	7.86794	1.75932
$21$	−3.89610	−0.850199
$22$	8.30731	1.77112
$23$	3.36390	0.701422	0.350711	−	0.936484i	$-0.385940\pi$
$23$	3.36390	0.701422	0.350711	+	0.936484i	$0.385940\pi$
$24$	−0.733796	−0.149785
$25$	6.19276	1.23855
$26$	−6.79876	−1.33335
$27$	1.00000	0.192450
$28$	−9.16269	−1.73158
$29$	−3.53025	−0.655552	−0.327776	−	0.944755i	$-0.606299\pi$
$29$	−3.53025	−0.655552	−0.327776	+	0.944755i	$0.606299\pi$
$30$	−6.97912	−1.27421
$31$	5.05751	0.908356	0.454178	−	0.890911i	$-0.349933\pi$
$31$	5.05751	0.908356	0.454178	+	0.890911i	$0.349933\pi$
$32$	8.08623	1.42946
$33$	−3.98225	−0.693220
$34$	8.77097	1.50421
$35$	−13.0346	−2.20326
$36$	2.35176	0.391960
$37$	0.737629	0.121265	0.0606327	−	0.998160i	$-0.480688\pi$
$37$	0.737629	0.121265	0.0606327	+	0.998160i	$0.480688\pi$
$38$	9.86827	1.60084
$39$	3.25910	0.521873
$40$	−2.45496	−0.388163
$41$	3.87961	0.605893	0.302946	−	0.953008i	$-0.402030\pi$
$41$	3.87961	0.605893	0.302946	+	0.953008i	$0.402030\pi$
$42$	8.12761	1.25412
$43$	5.36409	0.818016	0.409008	−	0.912531i	$-0.365875\pi$
$43$	5.36409	0.818016	0.409008	+	0.912531i	$0.365875\pi$
$44$	−9.36528	−1.41187
$45$	3.34556	0.498726
$46$	−7.01739	−1.03466
$47$	−5.25997	−0.767245	−0.383622	−	0.923490i	$-0.625324\pi$
$47$	−5.25997	−0.767245	−0.383622	+	0.923490i	$0.625324\pi$
$48$	−3.17275	−0.457947
$49$	8.17961	1.16852
$50$	−12.9186	−1.82697
$51$	−4.20451	−0.588749
$52$	7.66460	1.06289
$53$	8.24194	1.13212	0.566059	−	0.824365i	$-0.308467\pi$
$53$	8.24194	1.13212	0.566059	+	0.824365i	$0.308467\pi$
$54$	−2.08609	−0.283880
$55$	−13.3228	−1.79645
$56$	2.85894	0.382042
$57$	−4.73052	−0.626572
$58$	7.36442	0.966995
$59$	−4.33084	−0.563827	−0.281914	−	0.959440i	$-0.590969\pi$
$59$	−4.33084	−0.563827	−0.281914	+	0.959440i	$0.590969\pi$
$60$	7.86794	1.01575
$61$	−1.48482	−0.190112	−0.0950560	−	0.995472i	$-0.530303\pi$
$61$	−1.48482	−0.190112	−0.0950560	+	0.995472i	$0.530303\pi$
$62$	−10.5504	−1.33990
$63$	−3.89610	−0.490863
$64$	−10.5231	−1.31538
$65$	10.9035	1.35241
$66$	8.30731	1.02256
$67$	4.11499	0.502726	0.251363	−	0.967893i	$-0.419121\pi$
$67$	4.11499	0.502726	0.251363	+	0.967893i	$0.419121\pi$
$68$	−9.88798	−1.19909
$69$	3.36390	0.404966
$70$	27.1914	3.24999
$71$	3.25459	0.386249	0.193124	−	0.981174i	$-0.438138\pi$
$71$	3.25459	0.386249	0.193124	+	0.981174i	$0.438138\pi$
$72$	−0.733796	−0.0864786
$73$	−0.206474	−0.0241660	−0.0120830	−	0.999927i	$-0.503846\pi$
$73$	−0.206474	−0.0241660	−0.0120830	+	0.999927i	$0.503846\pi$
$74$	−1.53876	−0.178877
$75$	6.19276	0.715078
$76$	−11.1250	−1.27613
$77$	15.5152	1.76813
$78$	−6.79876	−0.769808
$79$	4.99485	0.561964	0.280982	−	0.959713i	$-0.409340\pi$
$79$	4.99485	0.561964	0.280982	+	0.959713i	$0.409340\pi$
$80$	−10.6146	−1.18675
$81$	1.00000	0.111111
$82$	−8.09319	−0.893744
$83$	6.26024	0.687150	0.343575	−	0.939125i	$-0.388362\pi$
$83$	6.26024	0.687150	0.343575	+	0.939125i	$0.388362\pi$
$84$	−9.16269	−0.999731
$85$	−14.0664	−1.52572
$86$	−11.1900	−1.20664
$87$	−3.53025	−0.378483
$88$	2.92216	0.311503
$89$	2.77317	0.293955	0.146978	−	0.989140i	$-0.453045\pi$
$89$	2.77317	0.293955	0.146978	+	0.989140i	$0.453045\pi$
$90$	−6.97912	−0.735664
$91$	−12.6978	−1.33109
$92$	7.91108	0.824787
$93$	5.05751	0.524440
$94$	10.9727	1.13175
$95$	−15.8262	−1.62374
$96$	8.08623	0.825297
$97$	−5.52882	−0.561366	−0.280683	−	0.959800i	$-0.590561\pi$
$97$	−5.52882	−0.561366	−0.280683	+	0.959800i	$0.590561\pi$
$98$	−17.0634	−1.72366
$99$	−3.98225	−0.400231
$100$	14.5639	1.45639
$101$	−12.0822	−1.20222	−0.601112	−	0.799165i	$-0.705276\pi$
$101$	−12.0822	−1.20222	−0.601112	+	0.799165i	$0.705276\pi$
$102$	8.77097	0.868455
$103$	−9.92512	−0.977951	−0.488976	−	0.872297i	$-0.662629\pi$
$103$	−9.92512	−0.977951	−0.488976	+	0.872297i	$0.662629\pi$
$104$	−2.39151	−0.234507
$105$	−13.0346	−1.27205
$106$	−17.1934	−1.66997
$107$	−19.3461	−1.87026	−0.935131	−	0.354302i	$-0.884719\pi$
$107$	−19.3461	−1.87026	−0.935131	+	0.354302i	$0.884719\pi$
$108$	2.35176	0.226298
$109$	4.53071	0.433964	0.216982	−	0.976176i	$-0.430379\pi$
$109$	4.53071	0.433964	0.216982	+	0.976176i	$0.430379\pi$
$110$	27.7926	2.64992
$111$	0.737629	0.0700126
$112$	12.3614	1.16804
$113$	16.1300	1.51738	0.758690	−	0.651452i	$-0.225840\pi$
$113$	16.1300	1.51738	0.758690	+	0.651452i	$0.225840\pi$
$114$	9.86827	0.924248
$115$	11.2541	1.04945
$116$	−8.30230	−0.770849
$117$	3.25910	0.301304
$118$	9.03450	0.831694
$119$	16.3812	1.50166
$120$	−2.45496	−0.224106
$121$	4.85829	0.441663
$122$	3.09747	0.280431
$123$	3.87961	0.349812
$124$	11.8940	1.06812
$125$	3.99045	0.356916
$126$	8.12761	0.724065
$127$	−5.63731	−0.500230	−0.250115	−	0.968216i	$-0.580468\pi$
$127$	−5.63731	−0.500230	−0.250115	+	0.968216i	$0.580468\pi$
$128$	5.77957	0.510847
$129$	5.36409	0.472282
$130$	−22.7456	−1.99492
$131$	−9.39576	−0.820911	−0.410456	−	0.911881i	$-0.634630\pi$
$131$	−9.39576	−0.820911	−0.410456	+	0.911881i	$0.634630\pi$
$132$	−9.36528	−0.815143
$133$	18.4306	1.59813
$134$	−8.58422	−0.741564
$135$	3.34556	0.287940
$136$	3.08525	0.264558
$137$	−9.99417	−0.853860	−0.426930	−	0.904285i	$-0.640405\pi$
$137$	−9.99417	−0.853860	−0.426930	+	0.904285i	$0.640405\pi$
$138$	−7.01739	−0.597360
$139$	−18.6606	−1.58277	−0.791386	−	0.611317i	$-0.790640\pi$
$139$	−18.6606	−1.58277	−0.791386	+	0.611317i	$0.790640\pi$
$140$	−30.6543	−2.59076
$141$	−5.25997	−0.442969
$142$	−6.78936	−0.569750
$143$	−12.9785	−1.08532
$144$	−3.17275	−0.264396
$145$	−11.8107	−0.980823
$146$	0.430724	0.0356469
$147$	8.17961	0.674643
$148$	1.73472	0.142593
$149$	−19.9498	−1.63435	−0.817176	−	0.576388i	$-0.804462\pi$
$149$	−19.9498	−1.63435	−0.817176	+	0.576388i	$0.804462\pi$
$150$	−12.9186	−1.05480
$151$	−7.09357	−0.577267	−0.288633	−	0.957440i	$-0.593201\pi$
$151$	−7.09357	−0.577267	−0.288633	+	0.957440i	$0.593201\pi$
$152$	3.47123	0.281554
$153$	−4.20451	−0.339914
$154$	−32.3661	−2.60814
$155$	16.9202	1.35906
$156$	7.66460	0.613659
$157$	−16.4493	−1.31280	−0.656399	−	0.754414i	$-0.727921\pi$
$157$	−16.4493	−1.31280	−0.656399	+	0.754414i	$0.727921\pi$
$158$	−10.4197	−0.828945
$159$	8.24194	0.653629
$160$	27.0529	2.13872
$161$	−13.1061	−1.03291
$162$	−2.08609	−0.163898
$163$	−15.0281	−1.17709	−0.588547	−	0.808463i	$-0.700300\pi$
$163$	−15.0281	−1.17709	−0.588547	+	0.808463i	$0.700300\pi$
$164$	9.12389	0.712456
$165$	−13.3228	−1.03718
$166$	−13.0594	−1.01361
$167$	−5.49701	−0.425371	−0.212686	−	0.977121i	$-0.568221\pi$
$167$	−5.49701	−0.425371	−0.212686	+	0.977121i	$0.568221\pi$
$168$	2.85894	0.220572
$169$	−2.37829	−0.182945
$170$	29.3438	2.25056
$171$	−4.73052	−0.361752
$172$	12.6150	0.961887
$173$	−7.87902	−0.599031	−0.299515	−	0.954091i	$-0.596825\pi$
$173$	−7.87902	−0.599031	−0.299515	+	0.954091i	$0.596825\pi$
$174$	7.36442	0.558295
$175$	−24.1276	−1.82388
$176$	12.6347	0.952375
$177$	−4.33084	−0.325526
$178$	−5.78507	−0.433609
$179$	−12.3055	−0.919756	−0.459878	−	0.887982i	$-0.652107\pi$
$179$	−12.3055	−0.919756	−0.459878	+	0.887982i	$0.652107\pi$
$180$	7.86794	0.586442
$181$	10.9254	0.812077	0.406039	−	0.913856i	$-0.366910\pi$
$181$	10.9254	0.812077	0.406039	+	0.913856i	$0.366910\pi$
$182$	26.4887	1.96347
$183$	−1.48482	−0.109761
$184$	−2.46842	−0.181974
$185$	2.46778	0.181435
$186$	−10.5504	−0.773594
$187$	16.7434	1.22440
$188$	−12.3702	−0.902187
$189$	−3.89610	−0.283400
$190$	33.0149	2.39515
$191$	7.17024	0.518821	0.259410	−	0.965767i	$-0.416472\pi$
$191$	7.17024	0.518821	0.259410	+	0.965767i	$0.416472\pi$
$192$	−10.5231	−0.759437
$193$	−11.1996	−0.806163	−0.403081	−	0.915164i	$-0.632061\pi$
$193$	−11.1996	−0.806163	−0.403081	+	0.915164i	$0.632061\pi$
$194$	11.5336	0.828064
$195$	10.9035	0.780816
$196$	19.2365	1.37403
$197$	19.5016	1.38943	0.694716	−	0.719284i	$-0.255530\pi$
$197$	19.5016	1.38943	0.694716	+	0.719284i	$0.255530\pi$
$198$	8.30731	0.590375
$199$	−25.8494	−1.83242	−0.916208	−	0.400704i	$-0.868766\pi$
$199$	−25.8494	−1.83242	−0.916208	+	0.400704i	$0.868766\pi$
$200$	−4.54422	−0.321325
$201$	4.11499	0.290249
$202$	25.2045	1.77338
$203$	13.7542	0.965358
$204$	−9.88798	−0.692297
$205$	12.9794	0.906524
$206$	20.7047	1.44256
$207$	3.36390	0.233807
$208$	−10.3403	−0.716971
$209$	18.8381	1.30306
$210$	27.1914	1.87638
$211$	−26.9615	−1.85611	−0.928055	−	0.372444i	$-0.878520\pi$
$211$	−26.9615	−1.85611	−0.928055	+	0.372444i	$0.878520\pi$
$212$	19.3830	1.33123
$213$	3.25459	0.223001
$214$	40.3577	2.75880
$215$	17.9459	1.22390
$216$	−0.733796	−0.0499285
$217$	−19.7046	−1.33763
$218$	−9.45146	−0.640134
$219$	−0.206474	−0.0139522
$220$	−31.3321	−2.11241
$221$	−13.7029	−0.921756
$222$	−1.53876	−0.103275
$223$	−23.6818	−1.58585	−0.792925	−	0.609319i	$-0.791443\pi$
$223$	−23.6818	−1.58585	−0.792925	+	0.609319i	$0.791443\pi$
$224$	−31.5048	−2.10500
$225$	6.19276	0.412851
$226$	−33.6485	−2.23827
$227$	−24.5014	−1.62622	−0.813108	−	0.582113i	$-0.802226\pi$
$227$	−24.5014	−1.62622	−0.813108	+	0.582113i	$0.802226\pi$
$228$	−11.1250	−0.736773
$229$	−19.5522	−1.29204	−0.646022	−	0.763319i	$-0.723569\pi$
$229$	−19.5522	−1.29204	−0.646022	+	0.763319i	$0.723569\pi$
$230$	−23.4771	−1.54803
$231$	15.5152	1.02083
$232$	2.59049	0.170074
$233$	−8.87982	−0.581736	−0.290868	−	0.956763i	$-0.593944\pi$
$233$	−8.87982	−0.581736	−0.290868	+	0.956763i	$0.593944\pi$
$234$	−6.79876	−0.444449
$235$	−17.5975	−1.14794
$236$	−10.1851	−0.662992
$237$	4.99485	0.324450
$238$	−34.1726	−2.21508
$239$	20.6205	1.33383	0.666913	−	0.745135i	$-0.267615\pi$
$239$	20.6205	1.33383	0.666913	+	0.745135i	$0.267615\pi$
$240$	−10.6146	−0.685171
$241$	−5.87690	−0.378565	−0.189282	−	0.981923i	$-0.560616\pi$
$241$	−5.87690	−0.378565	−0.189282	+	0.981923i	$0.560616\pi$
$242$	−10.1348	−0.651491
$243$	1.00000	0.0641500
$244$	−3.49194	−0.223549
$245$	27.3654	1.74831
$246$	−8.09319	−0.516003
$247$	−15.4172	−0.980974
$248$	−3.71118	−0.235660
$249$	6.26024	0.396726
$250$	−8.32441	−0.526482
$251$	11.6372	0.734532	0.367266	−	0.930116i	$-0.380294\pi$
$251$	11.6372	0.734532	0.367266	+	0.930116i	$0.380294\pi$
$252$	−9.16269	−0.577195
$253$	−13.3959	−0.842193
$254$	11.7599	0.737882
$255$	−14.0664	−0.880874
$256$	8.98945	0.561841
$257$	−9.05047	−0.564553	−0.282276	−	0.959333i	$-0.591090\pi$
$257$	−9.05047	−0.564553	−0.282276	+	0.959333i	$0.591090\pi$
$258$	−11.1900	−0.696656
$259$	−2.87388	−0.178574
$260$	25.6424	1.59027
$261$	−3.53025	−0.218517
$262$	19.6004	1.21091
$263$	9.14306	0.563785	0.281893	−	0.959446i	$-0.409038\pi$
$263$	9.14306	0.563785	0.281893	+	0.959446i	$0.409038\pi$
$264$	2.92216	0.179846
$265$	27.5739	1.69385
$266$	−38.4478	−2.35738
$267$	2.77317	0.169715
$268$	9.67745	0.591145
$269$	24.5706	1.49809	0.749047	−	0.662517i	$-0.230512\pi$
$269$	24.5706	1.49809	0.749047	+	0.662517i	$0.230512\pi$
$270$	−6.97912	−0.424736
$271$	−19.8836	−1.20784	−0.603922	−	0.797044i	$-0.706396\pi$
$271$	−19.8836	−1.20784	−0.603922	+	0.797044i	$0.706396\pi$
$272$	13.3399	0.808848
$273$	−12.6978	−0.768504
$274$	20.8487	1.25952
$275$	−24.6611	−1.48712
$276$	7.91108	0.476191
$277$	2.79467	0.167915	0.0839576	−	0.996469i	$-0.473244\pi$
$277$	2.79467	0.167915	0.0839576	+	0.996469i	$0.473244\pi$
$278$	38.9276	2.33472
$279$	5.05751	0.302785
$280$	9.56476	0.571604
$281$	−9.61429	−0.573541	−0.286770	−	0.957999i	$-0.592582\pi$
$281$	−9.61429	−0.573541	−0.286770	+	0.957999i	$0.592582\pi$
$282$	10.9727	0.653417
$283$	9.02152	0.536274	0.268137	−	0.963381i	$-0.413592\pi$
$283$	9.02152	0.536274	0.268137	+	0.963381i	$0.413592\pi$
$284$	7.65401	0.454182
$285$	−15.8262	−0.937464
$286$	27.0743	1.60094
$287$	−15.1153	−0.892230
$288$	8.08623	0.476486
$289$	0.677880	0.0398753
$290$	24.6381	1.44680
$291$	−5.52882	−0.324105
$292$	−0.485578	−0.0284163
$293$	8.06808	0.471342	0.235671	−	0.971833i	$-0.424271\pi$
$293$	8.06808	0.471342	0.235671	+	0.971833i	$0.424271\pi$
$294$	−17.0634	−0.995156
$295$	−14.4891	−0.843586
$296$	−0.541269	−0.0314606
$297$	−3.98225	−0.231073
$298$	41.6170	2.41081
$299$	10.9633	0.634023
$300$	14.5639	0.840845
$301$	−20.8990	−1.20460
$302$	14.7978	0.851518
$303$	−12.0822	−0.694105
$304$	15.0088	0.860812
$305$	−4.96756	−0.284441
$306$	8.77097	0.501403
$307$	−2.53149	−0.144480	−0.0722400	−	0.997387i	$-0.523015\pi$
$307$	−2.53149	−0.144480	−0.0722400	+	0.997387i	$0.523015\pi$
$308$	36.4881	2.07910
$309$	−9.92512	−0.564620
$310$	−35.2970	−2.00474
$311$	20.6371	1.17022	0.585111	−	0.810953i	$-0.301051\pi$
$311$	20.6371	1.17022	0.585111	+	0.810953i	$0.301051\pi$
$312$	−2.39151	−0.135393
$313$	−5.94667	−0.336125	−0.168063	−	0.985776i	$-0.553751\pi$
$313$	−5.94667	−0.336125	−0.168063	+	0.985776i	$0.553751\pi$
$314$	34.3147	1.93649
$315$	−13.0346	−0.734419
$316$	11.7467	0.660802
$317$	27.6092	1.55069	0.775343	−	0.631540i	$-0.217577\pi$
$317$	27.6092	1.55069	0.775343	+	0.631540i	$0.217577\pi$
$318$	−17.1934	−0.964158
$319$	14.0583	0.787116
$320$	−35.2055	−1.96805
$321$	−19.3461	−1.07980
$322$	27.3405	1.52363
$323$	19.8895	1.10668
$324$	2.35176	0.130653
$325$	20.1828	1.11954
$326$	31.3500	1.73632
$327$	4.53071	0.250549
$328$	−2.84684	−0.157190
$329$	20.4934	1.12984
$330$	27.7926	1.52993
$331$	−2.52976	−0.139048	−0.0695242	−	0.997580i	$-0.522148\pi$
$331$	−2.52976	−0.139048	−0.0695242	+	0.997580i	$0.522148\pi$
$332$	14.7226	0.808005
$333$	0.737629	0.0404218
$334$	11.4672	0.627459
$335$	13.7669	0.752168
$336$	12.3614	0.674368
$337$	−33.6967	−1.83558	−0.917788	−	0.397071i	$-0.870027\pi$
$337$	−33.6967	−1.83558	−0.917788	+	0.397071i	$0.870027\pi$
$338$	4.96132	0.269860
$339$	16.1300	0.876060
$340$	−33.0808	−1.79406
$341$	−20.1403	−1.09066
$342$	9.86827	0.533615
$343$	−4.59589	−0.248155
$344$	−3.93614	−0.212223
$345$	11.2541	0.605902
$346$	16.4363	0.883622
$347$	15.2422	0.818244	0.409122	−	0.912480i	$-0.365835\pi$
$347$	15.2422	0.818244	0.409122	+	0.912480i	$0.365835\pi$
$348$	−8.30230	−0.445050
$349$	11.3998	0.610219	0.305110	−	0.952317i	$-0.401307\pi$
$349$	11.3998	0.610219	0.305110	+	0.952317i	$0.401307\pi$
$350$	50.3323	2.69037
$351$	3.25910	0.173958
$352$	−32.2014	−1.71634
$353$	16.1360	0.858832	0.429416	−	0.903107i	$-0.358719\pi$
$353$	16.1360	0.858832	0.429416	+	0.903107i	$0.358719\pi$
$354$	9.03450	0.480178
$355$	10.8884	0.577898
$356$	6.52182	0.345656
$357$	16.3812	0.866984
$358$	25.6703	1.35672
$359$	7.30331	0.385454	0.192727	−	0.981252i	$-0.438267\pi$
$359$	7.30331	0.385454	0.192727	+	0.981252i	$0.438267\pi$
$360$	−2.45496	−0.129388
$361$	3.37779	0.177778
$362$	−22.7913	−1.19788
$363$	4.85829	0.254994
$364$	−29.8621	−1.56520
$365$	−0.690772	−0.0361567
$366$	3.09747	0.161907
$367$	19.1983	1.00214	0.501071	−	0.865406i	$-0.332940\pi$
$367$	19.1983	1.00214	0.501071	+	0.865406i	$0.332940\pi$
$368$	−10.6728	−0.556360
$369$	3.87961	0.201964
$370$	−5.14800	−0.267632
$371$	−32.1114	−1.66714
$372$	11.8940	0.616678
$373$	−1.04727	−0.0542256	−0.0271128	−	0.999632i	$-0.508631\pi$
$373$	−1.04727	−0.0542256	−0.0271128	+	0.999632i	$0.508631\pi$
$374$	−34.9282	−1.80609
$375$	3.99045	0.206066
$376$	3.85974	0.199051
$377$	−11.5054	−0.592560
$378$	8.12761	0.418039
$379$	24.3912	1.25289	0.626446	−	0.779465i	$-0.284509\pi$
$379$	24.3912	1.25289	0.626446	+	0.779465i	$0.284509\pi$
$380$	−37.2194	−1.90932
$381$	−5.63731	−0.288808
$382$	−14.9578	−0.765305
$383$	2.96081	0.151290	0.0756451	−	0.997135i	$-0.475898\pi$
$383$	2.96081	0.151290	0.0756451	+	0.997135i	$0.475898\pi$
$384$	5.77957	0.294937
$385$	51.9071	2.64543
$386$	23.3633	1.18916
$387$	5.36409	0.272672
$388$	−13.0024	−0.660099
$389$	13.1893	0.668722	0.334361	−	0.942445i	$-0.391479\pi$
$389$	13.1893	0.668722	0.334361	+	0.942445i	$0.391479\pi$
$390$	−22.7456	−1.15177
$391$	−14.1436	−0.715270
$392$	−6.00216	−0.303155
$393$	−9.39576	−0.473953
$394$	−40.6821	−2.04953
$395$	16.7105	0.840799
$396$	−9.36528	−0.470623
$397$	−25.8558	−1.29766	−0.648832	−	0.760931i	$-0.724742\pi$
$397$	−25.8558	−1.29766	−0.648832	+	0.760931i	$0.724742\pi$
$398$	53.9241	2.70297
$399$	18.4306	0.922683
$400$	−19.6481	−0.982405
$401$	−21.7770	−1.08749	−0.543745	−	0.839250i	$-0.682994\pi$
$401$	−21.7770	−1.08749	−0.543745	+	0.839250i	$0.682994\pi$
$402$	−8.58422	−0.428142
$403$	16.4829	0.821073
$404$	−28.4144	−1.41367
$405$	3.34556	0.166242
$406$	−28.6925	−1.42399
$407$	−2.93742	−0.145602
$408$	3.08525	0.152743
$409$	32.1184	1.58815	0.794076	−	0.607818i	$-0.207955\pi$
$409$	32.1184	1.58815	0.794076	+	0.607818i	$0.207955\pi$
$410$	−27.0763	−1.33720
$411$	−9.99417	−0.492976
$412$	−23.3415	−1.14995
$413$	16.8734	0.830285
$414$	−7.01739	−0.344886
$415$	20.9440	1.02810
$416$	26.3538	1.29210
$417$	−18.6606	−0.913813
$418$	−39.2979	−1.92212
$419$	10.0656	0.491737	0.245868	−	0.969303i	$-0.420927\pi$
$419$	10.0656	0.491737	0.245868	+	0.969303i	$0.420927\pi$
$420$	−30.6543	−1.49578
$421$	−8.62674	−0.420442	−0.210221	−	0.977654i	$-0.567418\pi$
$421$	−8.62674	−0.420442	−0.210221	+	0.977654i	$0.567418\pi$
$422$	56.2441	2.73792
$423$	−5.25997	−0.255748
$424$	−6.04790	−0.293712
$425$	−26.0375	−1.26300
$426$	−6.78936	−0.328946
$427$	5.78502	0.279957
$428$	−45.4974	−2.19920
$429$	−12.9785	−0.626609
$430$	−37.4366	−1.80535
$431$	6.66210	0.320902	0.160451	−	0.987044i	$-0.448705\pi$
$431$	6.66210	0.320902	0.160451	+	0.987044i	$0.448705\pi$
$432$	−3.17275	−0.152649
$433$	−8.22183	−0.395116	−0.197558	−	0.980291i	$-0.563301\pi$
$433$	−8.22183	−0.395116	−0.197558	+	0.980291i	$0.563301\pi$
$434$	41.1055	1.97313
$435$	−11.8107	−0.566278
$436$	10.6551	0.510289
$437$	−15.9130	−0.761222
$438$	0.430724	0.0205808
$439$	−14.5645	−0.695128	−0.347564	−	0.937656i	$-0.612991\pi$
$439$	−14.5645	−0.695128	−0.347564	+	0.937656i	$0.612991\pi$
$440$	9.77624	0.466064
$441$	8.17961	0.389505
$442$	28.5854	1.35967
$443$	−2.38395	−0.113265	−0.0566323	−	0.998395i	$-0.518036\pi$
$443$	−2.38395	−0.113265	−0.0566323	+	0.998395i	$0.518036\pi$
$444$	1.73472	0.0823263
$445$	9.27780	0.439810
$446$	49.4023	2.33927
$447$	−19.9498	−0.943593
$448$	40.9989	1.93702
$449$	−20.6807	−0.975984	−0.487992	−	0.872848i	$-0.662270\pi$
$449$	−20.6807	−0.975984	−0.487992	+	0.872848i	$0.662270\pi$
$450$	−12.9186	−0.608990
$451$	−15.4496	−0.727491
$452$	37.9338	1.78425
$453$	−7.09357	−0.333285
$454$	51.1121	2.39881
$455$	−42.4811	−1.99155
$456$	3.47123	0.162555
$457$	4.87957	0.228257	0.114128	−	0.993466i	$-0.463593\pi$
$457$	4.87957	0.228257	0.114128	+	0.993466i	$0.463593\pi$
$458$	40.7875	1.90588
$459$	−4.20451	−0.196250
$460$	26.4670	1.23403
$461$	29.2604	1.36279	0.681396	−	0.731915i	$-0.261373\pi$
$461$	29.2604	1.36279	0.681396	+	0.731915i	$0.261373\pi$
$462$	−32.3661	−1.50581
$463$	13.5428	0.629389	0.314694	−	0.949193i	$-0.398098\pi$
$463$	13.5428	0.629389	0.314694	+	0.949193i	$0.398098\pi$
$464$	11.2006	0.519976
$465$	16.9202	0.784656
$466$	18.5241	0.858111
$467$	−15.1969	−0.703227	−0.351613	−	0.936145i	$-0.614367\pi$
$467$	−15.1969	−0.703227	−0.351613	+	0.936145i	$0.614367\pi$
$468$	7.66460	0.354296
$469$	−16.0324	−0.740308
$470$	36.7100	1.69330
$471$	−16.4493	−0.757945
$472$	3.17795	0.146277
$473$	−21.3611	−0.982186
$474$	−10.4197	−0.478592
$475$	−29.2950	−1.34414
$476$	38.5246	1.76577
$477$	8.24194	0.377373
$478$	−43.0161	−1.96751
$479$	1.25284	0.0572437	0.0286219	−	0.999590i	$-0.490888\pi$
$479$	1.25284	0.0572437	0.0286219	+	0.999590i	$0.490888\pi$
$480$	27.0529	1.23479
$481$	2.40400	0.109613
$482$	12.2597	0.558415
$483$	−13.1061	−0.596349
$484$	11.4255	0.519342
$485$	−18.4970	−0.839905
$486$	−2.08609	−0.0946268
$487$	−14.5782	−0.660599	−0.330300	−	0.943876i	$-0.607150\pi$
$487$	−14.5782	−0.660599	−0.330300	+	0.943876i	$0.607150\pi$
$488$	1.08956	0.0493219
$489$	−15.0281	−0.679596
$490$	−57.0865	−2.57891
$491$	−32.1252	−1.44979	−0.724895	−	0.688860i	$-0.758112\pi$
$491$	−32.1252	−1.44979	−0.724895	+	0.688860i	$0.758112\pi$
$492$	9.12389	0.411337
$493$	14.8430	0.668494
$494$	32.1616	1.44702
$495$	−13.3228	−0.598817
$496$	−16.0462	−0.720498
$497$	−12.6802	−0.568786
$498$	−13.0594	−0.585206
$499$	6.10474	0.273286	0.136643	−	0.990620i	$-0.456369\pi$
$499$	6.10474	0.273286	0.136643	+	0.990620i	$0.456369\pi$
$500$	9.38456	0.419690
$501$	−5.49701	−0.245588
$502$	−24.2761	−1.08350
$503$	−20.7070	−0.923281	−0.461640	−	0.887067i	$-0.652739\pi$
$503$	−20.7070	−0.923281	−0.461640	+	0.887067i	$0.652739\pi$
$504$	2.85894	0.127347
$505$	−40.4217	−1.79874
$506$	27.9450	1.24231
$507$	−2.37829	−0.105624
$508$	−13.2576	−0.588210
$509$	36.0077	1.59601	0.798007	−	0.602648i	$-0.205888\pi$
$509$	36.0077	1.59601	0.798007	+	0.602648i	$0.205888\pi$
$510$	29.3438	1.29936
$511$	0.804445	0.0355866
$512$	−30.3119	−1.33961
$513$	−4.73052	−0.208857
$514$	18.8801	0.832764
$515$	−33.2051	−1.46319
$516$	12.6150	0.555346
$517$	20.9465	0.921225
$518$	5.99516	0.263412
$519$	−7.87902	−0.345851
$520$	−8.00094	−0.350864
$521$	20.0339	0.877700	0.438850	−	0.898560i	$-0.355386\pi$
$521$	20.0339	0.877700	0.438850	+	0.898560i	$0.355386\pi$
$522$	7.36442	0.322332
$523$	−38.4838	−1.68278	−0.841390	−	0.540428i	$-0.818262\pi$
$523$	−38.4838	−1.68278	−0.841390	+	0.540428i	$0.818262\pi$
$524$	−22.0965	−0.965292
$525$	−24.1276	−1.05302
$526$	−19.0732	−0.831632
$527$	−21.2644	−0.926290
$528$	12.6347	0.549854
$529$	−11.6842	−0.508007
$530$	−57.5215	−2.49858
$531$	−4.33084	−0.187942
$532$	43.3442	1.87921
$533$	12.6440	0.547673
$534$	−5.78507	−0.250344
$535$	−64.7237	−2.79825
$536$	−3.01956	−0.130425
$537$	−12.3055	−0.531021
$538$	−51.2563	−2.20982
$539$	−32.5732	−1.40303
$540$	7.86794	0.338582
$541$	−5.26893	−0.226529	−0.113265	−	0.993565i	$-0.536131\pi$
$541$	−5.26893	−0.226529	−0.113265	+	0.993565i	$0.536131\pi$
$542$	41.4789	1.78167
$543$	10.9254	0.468853
$544$	−33.9986	−1.45768
$545$	15.1578	0.649287
$546$	26.4887	1.13361
$547$	40.9388	1.75042	0.875209	−	0.483745i	$-0.160724\pi$
$547$	40.9388	1.75042	0.875209	+	0.483745i	$0.160724\pi$
$548$	−23.5039	−1.00404
$549$	−1.48482	−0.0633706
$550$	51.4452	2.19363
$551$	16.6999	0.711441
$552$	−2.46842	−0.105063
$553$	−19.4604	−0.827542
$554$	−5.82992	−0.247689
$555$	2.46778	0.104751
$556$	−43.8852	−1.86115
$557$	−23.6112	−1.00044	−0.500219	−	0.865899i	$-0.666747\pi$
$557$	−23.6112	−1.00044	−0.500219	+	0.865899i	$0.666747\pi$
$558$	−10.5504	−0.446635
$559$	17.4821	0.739413
$560$	41.3557	1.74760
$561$	16.7434	0.706906
$562$	20.0563	0.846022
$563$	14.9086	0.628322	0.314161	−	0.949370i	$-0.398277\pi$
$563$	14.9086	0.628322	0.314161	+	0.949370i	$0.398277\pi$
$564$	−12.3702	−0.520878
$565$	53.9638	2.27027
$566$	−18.8197	−0.791050
$567$	−3.89610	−0.163621
$568$	−2.38821	−0.100207
$569$	31.9154	1.33796	0.668981	−	0.743280i	$-0.266731\pi$
$569$	31.9154	1.33796	0.668981	+	0.743280i	$0.266731\pi$
$570$	33.0149	1.38284
$571$	−3.52240	−0.147408	−0.0737038	−	0.997280i	$-0.523482\pi$
$571$	−3.52240	−0.147408	−0.0737038	+	0.997280i	$0.523482\pi$
$572$	−30.5223	−1.27620
$573$	7.17024	0.299541
$574$	31.5319	1.31612
$575$	20.8318	0.868748
$576$	−10.5231	−0.438461
$577$	34.5372	1.43780	0.718901	−	0.695113i	$-0.244646\pi$
$577$	34.5372	1.43780	0.718901	+	0.695113i	$0.244646\pi$
$578$	−1.41412	−0.0588195
$579$	−11.1996	−0.465438
$580$	−27.7758	−1.15333
$581$	−24.3905	−1.01189
$582$	11.5336	0.478083
$583$	−32.8215	−1.35933
$584$	0.151510	0.00626953
$585$	10.9035	0.450804
$586$	−16.8307	−0.695270
$587$	−37.8857	−1.56371	−0.781856	−	0.623459i	$-0.785727\pi$
$587$	−37.8857	−1.56371	−0.781856	+	0.623459i	$0.785727\pi$
$588$	19.2365	0.793298
$589$	−23.9247	−0.985798
$590$	30.2255	1.24436
$591$	19.5016	0.802189
$592$	−2.34031	−0.0961863
$593$	−18.4057	−0.755831	−0.377915	−	0.925840i	$-0.623359\pi$
$593$	−18.4057	−0.755831	−0.377915	+	0.925840i	$0.623359\pi$
$594$	8.30731	0.340853
$595$	54.8042	2.24675
$596$	−46.9171	−1.92180
$597$	−25.8494	−1.05795
$598$	−22.8704	−0.935239
$599$	−45.4078	−1.85531	−0.927657	−	0.373433i	$-0.878181\pi$
$599$	−45.4078	−1.85531	−0.927657	+	0.373433i	$0.878181\pi$
$600$	−4.54422	−0.185517
$601$	−21.6467	−0.882987	−0.441493	−	0.897264i	$-0.645551\pi$
$601$	−21.6467	−0.882987	−0.441493	+	0.897264i	$0.645551\pi$
$602$	43.5972	1.77689
$603$	4.11499	0.167575
$604$	−16.6824	−0.678795
$605$	16.2537	0.660807
$606$	25.2045	1.02386
$607$	31.7109	1.28710	0.643552	−	0.765402i	$-0.277460\pi$
$607$	31.7109	1.28710	0.643552	+	0.765402i	$0.277460\pi$
$608$	−38.2520	−1.55133
$609$	13.7542	0.557350
$610$	10.3628	0.419576
$611$	−17.1427	−0.693521
$612$	−9.88798	−0.399698
$613$	45.7870	1.84932	0.924659	−	0.380795i	$-0.124350\pi$
$613$	45.7870	1.84932	0.924659	+	0.380795i	$0.124350\pi$
$614$	5.28091	0.213120
$615$	12.9794	0.523382
$616$	−11.3850	−0.458715
$617$	29.9230	1.20466	0.602328	−	0.798249i	$-0.294240\pi$
$617$	29.9230	1.20466	0.602328	+	0.798249i	$0.294240\pi$
$618$	20.7047	0.832864
$619$	12.9962	0.522363	0.261182	−	0.965290i	$-0.415888\pi$
$619$	12.9962	0.522363	0.261182	+	0.965290i	$0.415888\pi$
$620$	39.7922	1.59809
$621$	3.36390	0.134989
$622$	−43.0507	−1.72618
$623$	−10.8045	−0.432875
$624$	−10.3403	−0.413944
$625$	−17.6135	−0.704541
$626$	12.4053	0.495814
$627$	18.8381	0.752321
$628$	−38.6848	−1.54369
$629$	−3.10137	−0.123660
$630$	27.1914	1.08333
$631$	−13.3750	−0.532451	−0.266226	−	0.963911i	$-0.585777\pi$
$631$	−13.3750	−0.532451	−0.266226	+	0.963911i	$0.585777\pi$
$632$	−3.66520	−0.145794
$633$	−26.9615	−1.07163
$634$	−57.5951	−2.28740
$635$	−18.8599	−0.748434
$636$	19.3830	0.768588
$637$	26.6581	1.05623
$638$	−29.3269	−1.16106
$639$	3.25459	0.128750
$640$	19.3359	0.764318
$641$	−43.4926	−1.71785	−0.858926	−	0.512099i	$-0.828868\pi$
$641$	−43.4926	−1.71785	−0.858926	+	0.512099i	$0.828868\pi$
$642$	40.3577	1.59279
$643$	−29.8781	−1.17828	−0.589139	−	0.808031i	$-0.700533\pi$
$643$	−29.8781	−1.17828	−0.589139	+	0.808031i	$0.700533\pi$
$644$	−30.8224	−1.21457
$645$	17.9459	0.706618
$646$	−41.4912	−1.63245
$647$	−1.96512	−0.0772568	−0.0386284	−	0.999254i	$-0.512299\pi$
$647$	−1.96512	−0.0772568	−0.0386284	+	0.999254i	$0.512299\pi$
$648$	−0.733796	−0.0288262
$649$	17.2465	0.676983
$650$	−42.1031	−1.65142
$651$	−19.7046	−0.772284
$652$	−35.3425	−1.38412
$653$	−23.4215	−0.916554	−0.458277	−	0.888810i	$-0.651533\pi$
$653$	−23.4215	−0.916554	−0.458277	+	0.888810i	$0.651533\pi$
$654$	−9.45146	−0.369581
$655$	−31.4341	−1.22823
$656$	−12.3090	−0.480587
$657$	−0.206474	−0.00805533
$658$	−42.7509	−1.66660
$659$	−7.39118	−0.287919	−0.143960	−	0.989584i	$-0.545984\pi$
$659$	−7.39118	−0.287919	−0.143960	+	0.989584i	$0.545984\pi$
$660$	−31.3321	−1.21960
$661$	28.3496	1.10267	0.551335	−	0.834284i	$-0.314119\pi$
$661$	28.3496	1.10267	0.551335	+	0.834284i	$0.314119\pi$
$662$	5.27730	0.205108
$663$	−13.7029	−0.532176
$664$	−4.59373	−0.178271
$665$	61.6606	2.39109
$666$	−1.53876	−0.0596256
$667$	−11.8754	−0.459819
$668$	−12.9276	−0.500185
$669$	−23.6818	−0.915591
$670$	−28.7190	−1.10951
$671$	5.91293	0.228266
$672$	−31.5048	−1.21532
$673$	−1.37760	−0.0531027	−0.0265514	−	0.999647i	$-0.508453\pi$
$673$	−1.37760	−0.0531027	−0.0265514	+	0.999647i	$0.508453\pi$
$674$	70.2942	2.70763
$675$	6.19276	0.238359
$676$	−5.59316	−0.215121
$677$	−5.34398	−0.205386	−0.102693	−	0.994713i	$-0.532746\pi$
$677$	−5.34398	−0.205386	−0.102693	+	0.994713i	$0.532746\pi$
$678$	−33.6485	−1.29226
$679$	21.5408	0.826661
$680$	10.3219	0.395826
$681$	−24.5014	−0.938896
$682$	42.0144	1.60881
$683$	−19.4950	−0.745957	−0.372979	−	0.927840i	$-0.621663\pi$
$683$	−19.4950	−0.745957	−0.372979	+	0.927840i	$0.621663\pi$
$684$	−11.1250	−0.425376
$685$	−33.4361	−1.27753
$686$	9.58742	0.366049
$687$	−19.5522	−0.745962
$688$	−17.0189	−0.648840
$689$	26.8613	1.02333
$690$	−23.4771	−0.893758
$691$	−36.9138	−1.40427	−0.702133	−	0.712046i	$-0.747769\pi$
$691$	−36.9138	−1.40427	−0.702133	+	0.712046i	$0.747769\pi$
$692$	−18.5295	−0.704388
$693$	15.5152	0.589375
$694$	−31.7965	−1.20698
$695$	−62.4301	−2.36811
$696$	2.59049	0.0981921
$697$	−16.3118	−0.617855
$698$	−23.7810	−0.900125
$699$	−8.87982	−0.335866
$700$	−56.7423	−2.14466
$701$	39.4631	1.49050	0.745250	−	0.666785i	$-0.232330\pi$
$701$	39.4631	1.49050	0.745250	+	0.666785i	$0.232330\pi$
$702$	−6.79876	−0.256603
$703$	−3.48936	−0.131604
$704$	41.9055	1.57937
$705$	−17.5975	−0.662761
$706$	−33.6611	−1.26685
$707$	47.0735	1.77038
$708$	−10.1851	−0.382779
$709$	8.74156	0.328296	0.164148	−	0.986436i	$-0.447513\pi$
$709$	8.74156	0.328296	0.164148	+	0.986436i	$0.447513\pi$
$710$	−22.7142	−0.852449
$711$	4.99485	0.187321
$712$	−2.03494	−0.0762626
$713$	17.0130	0.637141
$714$	−34.1726	−1.27888
$715$	−43.4204	−1.62383
$716$	−28.9395	−1.08152
$717$	20.6205	0.770085
$718$	−15.2353	−0.568578
$719$	18.3708	0.685115	0.342557	−	0.939497i	$-0.388707\pi$
$719$	18.3708	0.685115	0.342557	+	0.939497i	$0.388707\pi$
$720$	−10.6146	−0.395584
$721$	38.6693	1.44012
$722$	−7.04636	−0.262239
$723$	−5.87690	−0.218564
$724$	25.6939	0.954904
$725$	−21.8620	−0.811935
$726$	−10.1348	−0.376138
$727$	2.23736	0.0829789	0.0414895	−	0.999139i	$-0.486790\pi$
$727$	2.23736	0.0829789	0.0414895	+	0.999139i	$0.486790\pi$
$728$	9.31757	0.345332
$729$	1.00000	0.0370370
$730$	1.44101	0.0533342
$731$	−22.5533	−0.834166
$732$	−3.49194	−0.129066
$733$	20.4169	0.754117	0.377059	−	0.926189i	$-0.376936\pi$
$733$	20.4169	0.754117	0.377059	+	0.926189i	$0.376936\pi$
$734$	−40.0493	−1.47825
$735$	27.3654	1.00939
$736$	27.2013	1.00265
$737$	−16.3869	−0.603619
$738$	−8.09319	−0.297915
$739$	25.7182	0.946059	0.473029	−	0.881047i	$-0.343160\pi$
$739$	25.7182	0.946059	0.473029	+	0.881047i	$0.343160\pi$
$740$	5.80362	0.213345
$741$	−15.4172	−0.566365
$742$	66.9873	2.45918
$743$	−37.8069	−1.38700	−0.693500	−	0.720456i	$-0.743932\pi$
$743$	−37.8069	−1.38700	−0.693500	+	0.720456i	$0.743932\pi$
$744$	−3.71118	−0.136059
$745$	−66.7432	−2.44528
$746$	2.18470	0.0799874
$747$	6.26024	0.229050
$748$	39.3764	1.43974
$749$	75.3746	2.75413
$750$	−8.32441	−0.303965
$751$	9.92736	0.362254	0.181127	−	0.983460i	$-0.442025\pi$
$751$	9.92736	0.362254	0.181127	+	0.983460i	$0.442025\pi$
$752$	16.6886	0.608570
$753$	11.6372	0.424082
$754$	24.0013	0.874078
$755$	−23.7320	−0.863694
$756$	−9.16269	−0.333244
$757$	14.6611	0.532867	0.266433	−	0.963853i	$-0.414155\pi$
$757$	14.6611	0.532867	0.266433	+	0.963853i	$0.414155\pi$
$758$	−50.8821	−1.84812
$759$	−13.3959	−0.486240
$760$	11.6132	0.421255
$761$	37.0182	1.34191	0.670954	−	0.741499i	$-0.265885\pi$
$761$	37.0182	1.34191	0.670954	+	0.741499i	$0.265885\pi$
$762$	11.7599	0.426017
$763$	−17.6521	−0.639050
$764$	16.8627	0.610070
$765$	−14.0664	−0.508573
$766$	−6.17650	−0.223166
$767$	−14.1146	−0.509649
$768$	8.98945	0.324379
$769$	−38.5783	−1.39117	−0.695585	−	0.718444i	$-0.744855\pi$
$769$	−38.5783	−1.39117	−0.695585	+	0.718444i	$0.744855\pi$
$770$	−108.283	−3.90224
$771$	−9.05047	−0.325945
$772$	−26.3387	−0.947949
$773$	−15.2090	−0.547029	−0.273515	−	0.961868i	$-0.588186\pi$
$773$	−15.2090	−0.547029	−0.273515	+	0.961868i	$0.588186\pi$
$774$	−11.1900	−0.402215
$775$	31.3200	1.12505
$776$	4.05702	0.145639
$777$	−2.87388	−0.103100
$778$	−27.5140	−0.986423
$779$	−18.3525	−0.657548
$780$	25.6424	0.918144
$781$	−12.9606	−0.463766
$782$	29.5047	1.05509
$783$	−3.53025	−0.126161
$784$	−25.9519	−0.926853
$785$	−55.0322	−1.96418
$786$	19.6004	0.699122
$787$	16.0025	0.570428	0.285214	−	0.958464i	$-0.407935\pi$
$787$	16.0025	0.570428	0.285214	+	0.958464i	$0.407935\pi$
$788$	45.8631	1.63380
$789$	9.14306	0.325502
$790$	−34.8597	−1.24025
$791$	−62.8440	−2.23448
$792$	2.92216	0.103834
$793$	−4.83918	−0.171844
$794$	53.9374	1.91417
$795$	27.5739	0.977945
$796$	−60.7915	−2.15470
$797$	−21.1440	−0.748960	−0.374480	−	0.927235i	$-0.622179\pi$
$797$	−21.1440	−0.748960	−0.374480	+	0.927235i	$0.622179\pi$
$798$	−38.4478	−1.36104
$799$	22.1156	0.782392
$800$	50.0761	1.77046
$801$	2.77317	0.0979851
$802$	45.4287	1.60414
$803$	0.822232	0.0290159
$804$	9.67745	0.341297
$805$	−43.8473	−1.54541
$806$	−34.3848	−1.21115
$807$	24.5706	0.864925
$808$	8.86587	0.311900
$809$	−23.3602	−0.821300	−0.410650	−	0.911793i	$-0.634698\pi$
$809$	−23.3602	−0.821300	−0.410650	+	0.911793i	$0.634698\pi$
$810$	−6.97912	−0.245221
$811$	13.7622	0.483256	0.241628	−	0.970369i	$-0.422319\pi$
$811$	13.7622	0.483256	0.241628	+	0.970369i	$0.422319\pi$
$812$	32.3466	1.13514
$813$	−19.8836	−0.697349
$814$	6.12771	0.214776
$815$	−50.2775	−1.76114
$816$	13.3399	0.466989
$817$	−25.3749	−0.887756
$818$	−67.0017	−2.34266
$819$	−12.6978	−0.443696
$820$	30.5245	1.06596
$821$	46.1920	1.61211	0.806055	−	0.591840i	$-0.201598\pi$
$821$	46.1920	1.61211	0.806055	+	0.591840i	$0.201598\pi$
$822$	20.8487	0.727182
$823$	6.36416	0.221841	0.110920	−	0.993829i	$-0.464620\pi$
$823$	6.36416	0.221841	0.110920	+	0.993829i	$0.464620\pi$
$824$	7.28301	0.253716
$825$	−24.6611	−0.858589
$826$	−35.1994	−1.22474
$827$	−4.80521	−0.167093	−0.0835467	−	0.996504i	$-0.526625\pi$
$827$	−4.80521	−0.167093	−0.0835467	+	0.996504i	$0.526625\pi$
$828$	7.91108	0.274929
$829$	28.6509	0.995088	0.497544	−	0.867439i	$-0.334235\pi$
$829$	28.6509	0.995088	0.497544	+	0.867439i	$0.334235\pi$
$830$	−43.6910	−1.51654
$831$	2.79467	0.0969459
$832$	−34.2957	−1.18899
$833$	−34.3912	−1.19159
$834$	38.9276	1.34795
$835$	−18.3906	−0.636431
$836$	44.3026	1.53224
$837$	5.05751	0.174813
$838$	−20.9977	−0.725354
$839$	−2.27673	−0.0786014	−0.0393007	−	0.999227i	$-0.512513\pi$
$839$	−2.27673	−0.0786014	−0.0393007	+	0.999227i	$0.512513\pi$
$840$	9.56476	0.330016
$841$	−16.5373	−0.570252
$842$	17.9961	0.620188
$843$	−9.61429	−0.331134
$844$	−63.4070	−2.18256
$845$	−7.95671	−0.273719
$846$	10.9727	0.377251
$847$	−18.9284	−0.650388
$848$	−26.1496	−0.897982
$849$	9.02152	0.309618
$850$	54.3165	1.86304
$851$	2.48131	0.0850583
$852$	7.65401	0.262222
$853$	−6.17311	−0.211363	−0.105682	−	0.994400i	$-0.533702\pi$
$853$	−6.17311	−0.211363	−0.105682	+	0.994400i	$0.533702\pi$
$854$	−12.0680	−0.412960
$855$	−15.8262	−0.541245
$856$	14.1961	0.485213
$857$	33.7533	1.15299	0.576495	−	0.817100i	$-0.304420\pi$
$857$	33.7533	1.15299	0.576495	+	0.817100i	$0.304420\pi$
$858$	27.0743	0.924303
$859$	42.6797	1.45621	0.728106	−	0.685464i	$-0.240401\pi$
$859$	42.6797	1.45621	0.728106	+	0.685464i	$0.240401\pi$
$860$	42.2043	1.43916
$861$	−15.1153	−0.515129
$862$	−13.8977	−0.473358
$863$	28.0345	0.954304	0.477152	−	0.878821i	$-0.341669\pi$
$863$	28.0345	0.954304	0.477152	+	0.878821i	$0.341669\pi$
$864$	8.08623	0.275099
$865$	−26.3597	−0.896258
$866$	17.1514	0.582830
$867$	0.677880	0.0230220
$868$	−46.3404	−1.57290
$869$	−19.8907	−0.674746
$870$	24.6381	0.835309
$871$	13.4111	0.454419
$872$	−3.32462	−0.112586
$873$	−5.52882	−0.187122
$874$	33.1959	1.12287
$875$	−15.5472	−0.525591
$876$	−0.485578	−0.0164061
$877$	−17.9090	−0.604743	−0.302371	−	0.953190i	$-0.597778\pi$
$877$	−17.9090	−0.604743	−0.302371	+	0.953190i	$0.597778\pi$
$878$	30.3829	1.02537
$879$	8.06808	0.272130
$880$	42.2701	1.42492
$881$	43.5571	1.46748	0.733738	−	0.679432i	$-0.237774\pi$
$881$	43.5571	1.46748	0.733738	+	0.679432i	$0.237774\pi$
$882$	−17.0634	−0.574554
$883$	−31.3029	−1.05343	−0.526713	−	0.850043i	$-0.676576\pi$
$883$	−31.3029	−1.05343	−0.526713	+	0.850043i	$0.676576\pi$
$884$	−32.2259	−1.08387
$885$	−14.4891	−0.487045
$886$	4.97312	0.167075
$887$	2.97189	0.0997863	0.0498932	−	0.998755i	$-0.484112\pi$
$887$	2.97189	0.0997863	0.0498932	+	0.998755i	$0.484112\pi$
$888$	−0.541269	−0.0181638
$889$	21.9635	0.736633
$890$	−19.3543	−0.648757
$891$	−3.98225	−0.133410
$892$	−55.6938	−1.86477
$893$	24.8824	0.832656
$894$	41.6170	1.39188
$895$	−41.1687	−1.37612
$896$	−22.5178	−0.752267
$897$	10.9633	0.366053
$898$	43.1418	1.43966
$899$	−17.8543	−0.595475
$900$	14.5639	0.485462
$901$	−34.6533	−1.15447
$902$	32.2291	1.07311
$903$	−20.8990	−0.695476
$904$	−11.8361	−0.393663
$905$	36.5515	1.21501
$906$	14.7978	0.491624
$907$	−36.4762	−1.21117	−0.605586	−	0.795780i	$-0.707061\pi$
$907$	−36.4762	−1.21117	−0.605586	+	0.795780i	$0.707061\pi$
$908$	−57.6214	−1.91223
$909$	−12.0822	−0.400742
$910$	88.6193	2.93770
$911$	−0.0141254	−0.000467996 0	−0.000233998	−	1.00000i	$-0.500074\pi$
$911$	−0.0141254	−0.000467996 0	−0.000233998		1.00000i	$0.500074\pi$
$912$	15.0088	0.496990
$913$	−24.9298	−0.825056
$914$	−10.1792	−0.336698
$915$	−4.96756	−0.164222
$916$	−45.9820	−1.51929
$917$	36.6068	1.20886
$918$	8.77097	0.289485
$919$	9.44916	0.311699	0.155850	−	0.987781i	$-0.450188\pi$
$919$	9.44916	0.311699	0.155850	+	0.987781i	$0.450188\pi$
$920$	−8.25823	−0.272266
$921$	−2.53149	−0.0834155
$922$	−61.0397	−2.01024
$923$	10.6070	0.349135
$924$	36.4881	1.20037
$925$	4.56796	0.150193
$926$	−28.2515	−0.928402
$927$	−9.92512	−0.325984
$928$	−28.5464	−0.937083
$929$	16.6477	0.546193	0.273096	−	0.961987i	$-0.411952\pi$
$929$	16.6477	0.546193	0.273096	+	0.961987i	$0.411952\pi$
$930$	−35.2970	−1.15743
$931$	−38.6938	−1.26814
$932$	−20.8832	−0.684051
$933$	20.6371	0.675628
$934$	31.7020	1.03732
$935$	56.0160	1.83192
$936$	−2.39151	−0.0781690
$937$	−16.1354	−0.527119	−0.263560	−	0.964643i	$-0.584897\pi$
$937$	−16.1354	−0.527119	−0.263560	+	0.964643i	$0.584897\pi$
$938$	33.4450	1.09202
$939$	−5.94667	−0.194062
$940$	−41.3851	−1.34983
$941$	40.0666	1.30613	0.653067	−	0.757300i	$-0.273482\pi$
$941$	40.0666	1.30613	0.653067	+	0.757300i	$0.273482\pi$
$942$	34.3147	1.11803
$943$	13.0506	0.424987
$944$	13.7407	0.447221
$945$	−13.0346	−0.424017
$946$	44.5612	1.44881
$947$	−24.0956	−0.783003	−0.391502	−	0.920177i	$-0.628044\pi$
$947$	−24.0956	−0.783003	−0.391502	+	0.920177i	$0.628044\pi$
$948$	11.7467	0.381514
$949$	−0.672920	−0.0218439
$950$	61.1118	1.98273
$951$	27.6092	0.895289
$952$	−12.0204	−0.389585
$953$	−52.7310	−1.70812	−0.854062	−	0.520171i	$-0.825868\pi$
$953$	−52.7310	−1.70812	−0.854062	+	0.520171i	$0.825868\pi$
$954$	−17.1934	−0.556657
$955$	23.9885	0.776249
$956$	48.4943	1.56842
$957$	14.0583	0.454442
$958$	−2.61353	−0.0844394
$959$	38.9383	1.25738
$960$	−35.2055	−1.13625
$961$	−5.42155	−0.174889
$962$	−5.01496	−0.161689
$963$	−19.3461	−0.623421
$964$	−13.8211	−0.445146
$965$	−37.4688	−1.20616
$966$	27.3405	0.879666
$967$	19.4016	0.623912	0.311956	−	0.950097i	$-0.399016\pi$
$967$	19.4016	0.623912	0.311956	+	0.950097i	$0.399016\pi$
$968$	−3.56499	−0.114583
$969$	19.8895	0.638943
$970$	38.5863	1.23893
$971$	24.6723	0.791773	0.395886	−	0.918299i	$-0.370437\pi$
$971$	24.6723	0.791773	0.395886	+	0.918299i	$0.370437\pi$
$972$	2.35176	0.0754326
$973$	72.7036	2.33077
$974$	30.4113	0.974441
$975$	20.1828	0.646367
$976$	4.71097	0.150795
$977$	25.1480	0.804557	0.402278	−	0.915517i	$-0.368218\pi$
$977$	25.1480	0.804557	0.402278	+	0.915517i	$0.368218\pi$
$978$	31.3500	1.00246
$979$	−11.0434	−0.352950
$980$	64.3567	2.05580
$981$	4.53071	0.144655
$982$	67.0159	2.13856
$983$	−49.1521	−1.56771	−0.783854	−	0.620945i	$-0.786749\pi$
$983$	−49.1521	−1.56771	−0.783854	+	0.620945i	$0.786749\pi$
$984$	−2.84684	−0.0907539
$985$	65.2438	2.07884
$986$	−30.9637	−0.986087
$987$	20.4934	0.652311
$988$	−36.2575	−1.15351
$989$	18.0443	0.573775
$990$	27.7926	0.883307
$991$	0.813235	0.0258333	0.0129166	−	0.999917i	$-0.495888\pi$
$991$	0.813235	0.0258333	0.0129166	+	0.999917i	$0.495888\pi$
$992$	40.8962	1.29846
$993$	−2.52976	−0.0802796
$994$	26.4520	0.839008
$995$	−86.4807	−2.74162
$996$	14.7226	0.466502
$997$	34.8821	1.10473	0.552363	−	0.833603i	$-0.313726\pi$
$997$	34.8821	1.10473	0.552363	+	0.833603i	$0.313726\pi$
$998$	−12.7350	−0.403120
$999$	0.737629	0.0233375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.13	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.13	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08609 q^{2} +1.00000 q^{3} +2.35176 q^{4} +3.34556 q^{5} -2.08609 q^{6} -3.89610 q^{7} -0.733796 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.08609 q^{2} +1.00000 q^{3} +2.35176 q^{4} +3.34556 q^{5} -2.08609 q^{6} -3.89610 q^{7} -0.733796 q^{8} +1.00000 q^{9} -6.97912 q^{10} -3.98225 q^{11} +2.35176 q^{12} +3.25910 q^{13} +8.12761 q^{14} +3.34556 q^{15} -3.17275 q^{16} -4.20451 q^{17} -2.08609 q^{18} -4.73052 q^{19} +7.86794 q^{20} -3.89610 q^{21} +8.30731 q^{22} +3.36390 q^{23} -0.733796 q^{24} +6.19276 q^{25} -6.79876 q^{26} +1.00000 q^{27} -9.16269 q^{28} -3.53025 q^{29} -6.97912 q^{30} +5.05751 q^{31} +8.08623 q^{32} -3.98225 q^{33} +8.77097 q^{34} -13.0346 q^{35} +2.35176 q^{36} +0.737629 q^{37} +9.86827 q^{38} +3.25910 q^{39} -2.45496 q^{40} +3.87961 q^{41} +8.12761 q^{42} +5.36409 q^{43} -9.36528 q^{44} +3.34556 q^{45} -7.01739 q^{46} -5.25997 q^{47} -3.17275 q^{48} +8.17961 q^{49} -12.9186 q^{50} -4.20451 q^{51} +7.66460 q^{52} +8.24194 q^{53} -2.08609 q^{54} -13.3228 q^{55} +2.85894 q^{56} -4.73052 q^{57} +7.36442 q^{58} -4.33084 q^{59} +7.86794 q^{60} -1.48482 q^{61} -10.5504 q^{62} -3.89610 q^{63} -10.5231 q^{64} +10.9035 q^{65} +8.30731 q^{66} +4.11499 q^{67} -9.88798 q^{68} +3.36390 q^{69} +27.1914 q^{70} +3.25459 q^{71} -0.733796 q^{72} -0.206474 q^{73} -1.53876 q^{74} +6.19276 q^{75} -11.1250 q^{76} +15.5152 q^{77} -6.79876 q^{78} +4.99485 q^{79} -10.6146 q^{80} +1.00000 q^{81} -8.09319 q^{82} +6.26024 q^{83} -9.16269 q^{84} -14.0664 q^{85} -11.1900 q^{86} -3.53025 q^{87} +2.92216 q^{88} +2.77317 q^{89} -6.97912 q^{90} -12.6978 q^{91} +7.91108 q^{92} +5.05751 q^{93} +10.9727 q^{94} -15.8262 q^{95} +8.08623 q^{96} -5.52882 q^{97} -17.0634 q^{98} -3.98225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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