LMFDB - Embedded newform 6018.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1668357.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 11x^{3} + x^{2} + 17x - 2 $ x^5 - x^4 - 11x^3 + x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.24777$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.08688 q^{5} -1.00000 q^{6} -1.24777 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.08688 q^{5} -1.00000 q^{6} -1.24777 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.08688 q^{10} -1.58865 q^{11} +1.00000 q^{12} -3.49933 q^{13} +1.24777 q^{14} -1.08688 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.42776 q^{19} -1.08688 q^{20} -1.24777 q^{21} +1.58865 q^{22} +1.76754 q^{23} -1.00000 q^{24} -3.81868 q^{25} +3.49933 q^{26} +1.00000 q^{27} -1.24777 q^{28} +6.53238 q^{29} +1.08688 q^{30} +1.05627 q^{31} -1.00000 q^{32} -1.58865 q^{33} +1.00000 q^{34} +1.35618 q^{35} +1.00000 q^{36} -5.65400 q^{37} -3.42776 q^{38} -3.49933 q^{39} +1.08688 q^{40} -0.263080 q^{41} +1.24777 q^{42} +4.90177 q^{43} -1.58865 q^{44} -1.08688 q^{45} -1.76754 q^{46} -7.04190 q^{47} +1.00000 q^{48} -5.44307 q^{49} +3.81868 q^{50} -1.00000 q^{51} -3.49933 q^{52} +8.92088 q^{53} -1.00000 q^{54} +1.72667 q^{55} +1.24777 q^{56} +3.42776 q^{57} -6.53238 q^{58} -1.00000 q^{59} -1.08688 q^{60} +2.97847 q^{61} -1.05627 q^{62} -1.24777 q^{63} +1.00000 q^{64} +3.80337 q^{65} +1.58865 q^{66} +1.69459 q^{67} -1.00000 q^{68} +1.76754 q^{69} -1.35618 q^{70} -3.41002 q^{71} -1.00000 q^{72} -2.04835 q^{73} +5.65400 q^{74} -3.81868 q^{75} +3.42776 q^{76} +1.98227 q^{77} +3.49933 q^{78} -13.9437 q^{79} -1.08688 q^{80} +1.00000 q^{81} +0.263080 q^{82} -7.00506 q^{83} -1.24777 q^{84} +1.08688 q^{85} -4.90177 q^{86} +6.53238 q^{87} +1.58865 q^{88} +2.56073 q^{89} +1.08688 q^{90} +4.36637 q^{91} +1.76754 q^{92} +1.05627 q^{93} +7.04190 q^{94} -3.72558 q^{95} -1.00000 q^{96} +5.85172 q^{97} +5.44307 q^{98} -1.58865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.08688	−0.486070	−0.243035	−	0.970018i	$-0.578143\pi$
$5$	−1.08688	−0.486070	−0.243035	+	0.970018i	$0.578143\pi$
$6$	−1.00000	−0.408248
$7$	−1.24777	−0.471613	−0.235807	−	0.971800i	$-0.575773\pi$
$7$	−1.24777	−0.471613	−0.235807	+	0.971800i	$0.575773\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.08688	0.343703
$11$	−1.58865	−0.478995	−0.239497	−	0.970897i	$-0.576983\pi$
$11$	−1.58865	−0.478995	−0.239497	+	0.970897i	$0.576983\pi$
$12$	1.00000	0.288675
$13$	−3.49933	−0.970541	−0.485270	−	0.874364i	$-0.661279\pi$
$13$	−3.49933	−0.970541	−0.485270	+	0.874364i	$0.661279\pi$
$14$	1.24777	0.333481
$15$	−1.08688	−0.280632
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.42776	0.786382	0.393191	−	0.919457i	$-0.371371\pi$
$19$	3.42776	0.786382	0.393191	+	0.919457i	$0.371371\pi$
$20$	−1.08688	−0.243035
$21$	−1.24777	−0.272286
$22$	1.58865	0.338700
$23$	1.76754	0.368557	0.184279	−	0.982874i	$-0.441005\pi$
$23$	1.76754	0.368557	0.184279	+	0.982874i	$0.441005\pi$
$24$	−1.00000	−0.204124
$25$	−3.81868	−0.763736
$26$	3.49933	0.686276
$27$	1.00000	0.192450
$28$	−1.24777	−0.235807
$29$	6.53238	1.21303	0.606516	−	0.795071i	$-0.292567\pi$
$29$	6.53238	1.21303	0.606516	+	0.795071i	$0.292567\pi$
$30$	1.08688	0.198437
$31$	1.05627	0.189711	0.0948556	−	0.995491i	$-0.469761\pi$
$31$	1.05627	0.189711	0.0948556	+	0.995491i	$0.469761\pi$
$32$	−1.00000	−0.176777
$33$	−1.58865	−0.276548
$34$	1.00000	0.171499
$35$	1.35618	0.229237
$36$	1.00000	0.166667
$37$	−5.65400	−0.929512	−0.464756	−	0.885439i	$-0.653858\pi$
$37$	−5.65400	−0.929512	−0.464756	+	0.885439i	$0.653858\pi$
$38$	−3.42776	−0.556056
$39$	−3.49933	−0.560342
$40$	1.08688	0.171852
$41$	−0.263080	−0.0410861	−0.0205431	−	0.999789i	$-0.506540\pi$
$41$	−0.263080	−0.0410861	−0.0205431	+	0.999789i	$0.506540\pi$
$42$	1.24777	0.192535
$43$	4.90177	0.747513	0.373757	−	0.927527i	$-0.378069\pi$
$43$	4.90177	0.747513	0.373757	+	0.927527i	$0.378069\pi$
$44$	−1.58865	−0.239497
$45$	−1.08688	−0.162023
$46$	−1.76754	−0.260609
$47$	−7.04190	−1.02717	−0.513583	−	0.858040i	$-0.671682\pi$
$47$	−7.04190	−1.02717	−0.513583	+	0.858040i	$0.671682\pi$
$48$	1.00000	0.144338
$49$	−5.44307	−0.777581
$50$	3.81868	0.540043
$51$	−1.00000	−0.140028
$52$	−3.49933	−0.485270
$53$	8.92088	1.22538	0.612688	−	0.790325i	$-0.290088\pi$
$53$	8.92088	1.22538	0.612688	+	0.790325i	$0.290088\pi$
$54$	−1.00000	−0.136083
$55$	1.72667	0.232825
$56$	1.24777	0.166740
$57$	3.42776	0.454018
$58$	−6.53238	−0.857743
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−1.08688	−0.140316
$61$	2.97847	0.381354	0.190677	−	0.981653i	$-0.438932\pi$
$61$	2.97847	0.381354	0.190677	+	0.981653i	$0.438932\pi$
$62$	−1.05627	−0.134146
$63$	−1.24777	−0.157204
$64$	1.00000	0.125000
$65$	3.80337	0.471750
$66$	1.58865	0.195549
$67$	1.69459	0.207028	0.103514	−	0.994628i	$-0.466991\pi$
$67$	1.69459	0.207028	0.103514	+	0.994628i	$0.466991\pi$
$68$	−1.00000	−0.121268
$69$	1.76754	0.212787
$70$	−1.35618	−0.162095
$71$	−3.41002	−0.404695	−0.202348	−	0.979314i	$-0.564857\pi$
$71$	−3.41002	−0.404695	−0.202348	+	0.979314i	$0.564857\pi$
$72$	−1.00000	−0.117851
$73$	−2.04835	−0.239741	−0.119871	−	0.992790i	$-0.538248\pi$
$73$	−2.04835	−0.239741	−0.119871	+	0.992790i	$0.538248\pi$
$74$	5.65400	0.657264
$75$	−3.81868	−0.440943
$76$	3.42776	0.393191
$77$	1.98227	0.225900
$78$	3.49933	0.396222
$79$	−13.9437	−1.56879	−0.784393	−	0.620264i	$-0.787025\pi$
$79$	−13.9437	−1.56879	−0.784393	+	0.620264i	$0.787025\pi$
$80$	−1.08688	−0.121517
$81$	1.00000	0.111111
$82$	0.263080	0.0290523
$83$	−7.00506	−0.768905	−0.384453	−	0.923145i	$-0.625610\pi$
$83$	−7.00506	−0.768905	−0.384453	+	0.923145i	$0.625610\pi$
$84$	−1.24777	−0.136143
$85$	1.08688	0.117889
$86$	−4.90177	−0.528572
$87$	6.53238	0.700344
$88$	1.58865	0.169350
$89$	2.56073	0.271436	0.135718	−	0.990747i	$-0.456666\pi$
$89$	2.56073	0.271436	0.135718	+	0.990747i	$0.456666\pi$
$90$	1.08688	0.114568
$91$	4.36637	0.457720
$92$	1.76754	0.184279
$93$	1.05627	0.109530
$94$	7.04190	0.726316
$95$	−3.72558	−0.382236
$96$	−1.00000	−0.102062
$97$	5.85172	0.594153	0.297076	−	0.954854i	$-0.403988\pi$
$97$	5.85172	0.594153	0.297076	+	0.954854i	$0.403988\pi$
$98$	5.44307	0.549833
$99$	−1.58865	−0.159665
$100$	−3.81868	−0.381868
$101$	12.6294	1.25668	0.628339	−	0.777940i	$-0.283735\pi$
$101$	12.6294	1.25668	0.628339	+	0.777940i	$0.283735\pi$
$102$	1.00000	0.0990148
$103$	19.1684	1.88872	0.944360	−	0.328914i	$-0.106683\pi$
$103$	19.1684	1.88872	0.944360	+	0.328914i	$0.106683\pi$
$104$	3.49933	0.343138
$105$	1.35618	0.132350
$106$	−8.92088	−0.866472
$107$	18.4199	1.78072	0.890361	−	0.455255i	$-0.150452\pi$
$107$	18.4199	1.78072	0.890361	+	0.455255i	$0.150452\pi$
$108$	1.00000	0.0962250
$109$	0.567118	0.0543200	0.0271600	−	0.999631i	$-0.491354\pi$
$109$	0.567118	0.0543200	0.0271600	+	0.999631i	$0.491354\pi$
$110$	−1.72667	−0.164632
$111$	−5.65400	−0.536654
$112$	−1.24777	−0.117903
$113$	2.30294	0.216643	0.108321	−	0.994116i	$-0.465452\pi$
$113$	2.30294	0.216643	0.108321	+	0.994116i	$0.465452\pi$
$114$	−3.42776	−0.321039
$115$	−1.92111	−0.179144
$116$	6.53238	0.606516
$117$	−3.49933	−0.323514
$118$	1.00000	0.0920575
$119$	1.24777	0.114383
$120$	1.08688	0.0992185
$121$	−8.47621	−0.770564
$122$	−2.97847	−0.269658
$123$	−0.263080	−0.0237211
$124$	1.05627	0.0948556
$125$	9.58489	0.857299
$126$	1.24777	0.111160
$127$	−12.6195	−1.11980	−0.559899	−	0.828561i	$-0.689160\pi$
$127$	−12.6195	−1.11980	−0.559899	+	0.828561i	$0.689160\pi$
$128$	−1.00000	−0.0883883
$129$	4.90177	0.431577
$130$	−3.80337	−0.333578
$131$	11.3817	0.994422	0.497211	−	0.867630i	$-0.334358\pi$
$131$	11.3817	0.994422	0.497211	+	0.867630i	$0.334358\pi$
$132$	−1.58865	−0.138274
$133$	−4.27706	−0.370868
$134$	−1.69459	−0.146391
$135$	−1.08688	−0.0935441
$136$	1.00000	0.0857493
$137$	11.5144	0.983742	0.491871	−	0.870668i	$-0.336313\pi$
$137$	11.5144	0.983742	0.491871	+	0.870668i	$0.336313\pi$
$138$	−1.76754	−0.150463
$139$	−10.0793	−0.854918	−0.427459	−	0.904035i	$-0.640591\pi$
$139$	−10.0793	−0.854918	−0.427459	+	0.904035i	$0.640591\pi$
$140$	1.35618	0.114618
$141$	−7.04190	−0.593035
$142$	3.41002	0.286163
$143$	5.55920	0.464884
$144$	1.00000	0.0833333
$145$	−7.09994	−0.589618
$146$	2.04835	0.169523
$147$	−5.44307	−0.448937
$148$	−5.65400	−0.464756
$149$	3.14073	0.257298	0.128649	−	0.991690i	$-0.458936\pi$
$149$	3.14073	0.257298	0.128649	+	0.991690i	$0.458936\pi$
$150$	3.81868	0.311794
$151$	−2.68202	−0.218260	−0.109130	−	0.994028i	$-0.534806\pi$
$151$	−2.68202	−0.218260	−0.109130	+	0.994028i	$0.534806\pi$
$152$	−3.42776	−0.278028
$153$	−1.00000	−0.0808452
$154$	−1.98227	−0.159736
$155$	−1.14804	−0.0922128
$156$	−3.49933	−0.280171
$157$	24.7992	1.97919	0.989595	−	0.143878i	$-0.0459573\pi$
$157$	24.7992	1.97919	0.989595	+	0.143878i	$0.0459573\pi$
$158$	13.9437	1.10930
$159$	8.92088	0.707471
$160$	1.08688	0.0859258
$161$	−2.20548	−0.173816
$162$	−1.00000	−0.0785674
$163$	−1.67796	−0.131428	−0.0657138	−	0.997839i	$-0.520932\pi$
$163$	−1.67796	−0.131428	−0.0657138	+	0.997839i	$0.520932\pi$
$164$	−0.263080	−0.0205431
$165$	1.72667	0.134421
$166$	7.00506	0.543698
$167$	17.5555	1.35849	0.679244	−	0.733912i	$-0.262308\pi$
$167$	17.5555	1.35849	0.679244	+	0.733912i	$0.262308\pi$
$168$	1.24777	0.0962676
$169$	−0.754655	−0.0580504
$170$	−1.08688	−0.0833602
$171$	3.42776	0.262127
$172$	4.90177	0.373757
$173$	22.5221	1.71233	0.856163	−	0.516706i	$-0.172842\pi$
$173$	22.5221	1.71233	0.856163	+	0.516706i	$0.172842\pi$
$174$	−6.53238	−0.495218
$175$	4.76484	0.360188
$176$	−1.58865	−0.119749
$177$	−1.00000	−0.0751646
$178$	−2.56073	−0.191934
$179$	0.971809	0.0726364	0.0363182	−	0.999340i	$-0.488437\pi$
$179$	0.971809	0.0726364	0.0363182	+	0.999340i	$0.488437\pi$
$180$	−1.08688	−0.0810116
$181$	7.46723	0.555035	0.277517	−	0.960721i	$-0.410488\pi$
$181$	7.46723	0.555035	0.277517	+	0.960721i	$0.410488\pi$
$182$	−4.36637	−0.323657
$183$	2.97847	0.220175
$184$	−1.76754	−0.130305
$185$	6.14525	0.451808
$186$	−1.05627	−0.0774493
$187$	1.58865	0.116173
$188$	−7.04190	−0.513583
$189$	−1.24777	−0.0907620
$190$	3.72558	0.270282
$191$	−19.4441	−1.40693	−0.703463	−	0.710732i	$-0.748364\pi$
$191$	−19.4441	−1.40693	−0.703463	+	0.710732i	$0.748364\pi$
$192$	1.00000	0.0721688
$193$	4.96696	0.357529	0.178765	−	0.983892i	$-0.442790\pi$
$193$	4.96696	0.357529	0.178765	+	0.983892i	$0.442790\pi$
$194$	−5.85172	−0.420129
$195$	3.80337	0.272365
$196$	−5.44307	−0.388791
$197$	10.2631	0.731214	0.365607	−	0.930769i	$-0.380861\pi$
$197$	10.2631	0.731214	0.365607	+	0.930769i	$0.380861\pi$
$198$	1.58865	0.112900
$199$	11.9743	0.848835	0.424417	−	0.905467i	$-0.360479\pi$
$199$	11.9743	0.848835	0.424417	+	0.905467i	$0.360479\pi$
$200$	3.81868	0.270022
$201$	1.69459	0.119527
$202$	−12.6294	−0.888605
$203$	−8.15091	−0.572082
$204$	−1.00000	−0.0700140
$205$	0.285937	0.0199707
$206$	−19.1684	−1.33553
$207$	1.76754	0.122852
$208$	−3.49933	−0.242635
$209$	−5.44549	−0.376673
$210$	−1.35618	−0.0935855
$211$	0.298820	0.0205716	0.0102858	−	0.999947i	$-0.496726\pi$
$211$	0.298820	0.0205716	0.0102858	+	0.999947i	$0.496726\pi$
$212$	8.92088	0.612688
$213$	−3.41002	−0.233651
$214$	−18.4199	−1.25916
$215$	−5.32766	−0.363344
$216$	−1.00000	−0.0680414
$217$	−1.31798	−0.0894703
$218$	−0.567118	−0.0384101
$219$	−2.04835	−0.138415
$220$	1.72667	0.116412
$221$	3.49933	0.235391
$222$	5.65400	0.379472
$223$	22.6580	1.51729	0.758645	−	0.651504i	$-0.225862\pi$
$223$	22.6580	1.51729	0.758645	+	0.651504i	$0.225862\pi$
$224$	1.24777	0.0833702
$225$	−3.81868	−0.254579
$226$	−2.30294	−0.153189
$227$	−21.7085	−1.44085	−0.720424	−	0.693534i	$-0.756053\pi$
$227$	−21.7085	−1.44085	−0.720424	+	0.693534i	$0.756053\pi$
$228$	3.42776	0.227009
$229$	2.56949	0.169796	0.0848982	−	0.996390i	$-0.472943\pi$
$229$	2.56949	0.169796	0.0848982	+	0.996390i	$0.472943\pi$
$230$	1.92111	0.126674
$231$	1.98227	0.130423
$232$	−6.53238	−0.428872
$233$	−5.23889	−0.343211	−0.171606	−	0.985166i	$-0.554895\pi$
$233$	−5.23889	−0.343211	−0.171606	+	0.985166i	$0.554895\pi$
$234$	3.49933	0.228759
$235$	7.65373	0.499274
$236$	−1.00000	−0.0650945
$237$	−13.9437	−0.905739
$238$	−1.24777	−0.0808810
$239$	−7.38807	−0.477894	−0.238947	−	0.971033i	$-0.576802\pi$
$239$	−7.38807	−0.477894	−0.238947	+	0.971033i	$0.576802\pi$
$240$	−1.08688	−0.0701581
$241$	−23.1478	−1.49108	−0.745541	−	0.666460i	$-0.767809\pi$
$241$	−23.1478	−1.49108	−0.745541	+	0.666460i	$0.767809\pi$
$242$	8.47621	0.544871
$243$	1.00000	0.0641500
$244$	2.97847	0.190677
$245$	5.91599	0.377959
$246$	0.263080	0.0167733
$247$	−11.9949	−0.763216
$248$	−1.05627	−0.0670730
$249$	−7.00506	−0.443928
$250$	−9.58489	−0.606202
$251$	19.9514	1.25932	0.629662	−	0.776870i	$-0.283194\pi$
$251$	19.9514	1.25932	0.629662	+	0.776870i	$0.283194\pi$
$252$	−1.24777	−0.0786022
$253$	−2.80799	−0.176537
$254$	12.6195	0.791816
$255$	1.08688	0.0680634
$256$	1.00000	0.0625000
$257$	21.6923	1.35313	0.676564	−	0.736384i	$-0.263468\pi$
$257$	21.6923	1.35313	0.676564	+	0.736384i	$0.263468\pi$
$258$	−4.90177	−0.305171
$259$	7.05490	0.438370
$260$	3.80337	0.235875
$261$	6.53238	0.404344
$262$	−11.3817	−0.703162
$263$	23.4791	1.44778	0.723892	−	0.689913i	$-0.242351\pi$
$263$	23.4791	1.44778	0.723892	+	0.689913i	$0.242351\pi$
$264$	1.58865	0.0977744
$265$	−9.69596	−0.595618
$266$	4.27706	0.262243
$267$	2.56073	0.156714
$268$	1.69459	0.103514
$269$	−18.4264	−1.12348	−0.561740	−	0.827314i	$-0.689868\pi$
$269$	−18.4264	−1.12348	−0.561740	+	0.827314i	$0.689868\pi$
$270$	1.08688	0.0661457
$271$	4.78257	0.290521	0.145260	−	0.989393i	$-0.453598\pi$
$271$	4.78257	0.290521	0.145260	+	0.989393i	$0.453598\pi$
$272$	−1.00000	−0.0606339
$273$	4.36637	0.264265
$274$	−11.5144	−0.695611
$275$	6.06653	0.365826
$276$	1.76754	0.106393
$277$	11.4444	0.687627	0.343814	−	0.939038i	$-0.388281\pi$
$277$	11.4444	0.687627	0.343814	+	0.939038i	$0.388281\pi$
$278$	10.0793	0.604518
$279$	1.05627	0.0632371
$280$	−1.35618	−0.0810474
$281$	24.7173	1.47451	0.737254	−	0.675615i	$-0.236122\pi$
$281$	24.7173	1.47451	0.737254	+	0.675615i	$0.236122\pi$
$282$	7.04190	0.419339
$283$	11.3884	0.676972	0.338486	−	0.940971i	$-0.390085\pi$
$283$	11.3884	0.676972	0.338486	+	0.940971i	$0.390085\pi$
$284$	−3.41002	−0.202348
$285$	−3.72558	−0.220684
$286$	−5.55920	−0.328723
$287$	0.328263	0.0193768
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	7.09994	0.416923
$291$	5.85172	0.343034
$292$	−2.04835	−0.119871
$293$	4.39572	0.256800	0.128400	−	0.991722i	$-0.459016\pi$
$293$	4.39572	0.256800	0.128400	+	0.991722i	$0.459016\pi$
$294$	5.44307	0.317446
$295$	1.08688	0.0632809
$296$	5.65400	0.328632
$297$	−1.58865	−0.0921826
$298$	−3.14073	−0.181937
$299$	−6.18521	−0.357700
$300$	−3.81868	−0.220472
$301$	−6.11629	−0.352537
$302$	2.68202	0.154333
$303$	12.6294	0.725543
$304$	3.42776	0.196595
$305$	−3.23726	−0.185365
$306$	1.00000	0.0571662
$307$	−2.47798	−0.141426	−0.0707129	−	0.997497i	$-0.522527\pi$
$307$	−2.47798	−0.141426	−0.0707129	+	0.997497i	$0.522527\pi$
$308$	1.98227	0.112950
$309$	19.1684	1.09045
$310$	1.14804	0.0652043
$311$	4.05650	0.230023	0.115012	−	0.993364i	$-0.463309\pi$
$311$	4.05650	0.230023	0.115012	+	0.993364i	$0.463309\pi$
$312$	3.49933	0.198111
$313$	6.30146	0.356179	0.178090	−	0.984014i	$-0.443008\pi$
$313$	6.30146	0.356179	0.178090	+	0.984014i	$0.443008\pi$
$314$	−24.7992	−1.39950
$315$	1.35618	0.0764123
$316$	−13.9437	−0.784393
$317$	17.0586	0.958108	0.479054	−	0.877785i	$-0.340980\pi$
$317$	17.0586	0.958108	0.479054	+	0.877785i	$0.340980\pi$
$318$	−8.92088	−0.500258
$319$	−10.3776	−0.581036
$320$	−1.08688	−0.0607587
$321$	18.4199	1.02810
$322$	2.20548	0.122907
$323$	−3.42776	−0.190726
$324$	1.00000	0.0555556
$325$	13.3628	0.741237
$326$	1.67796	0.0929334
$327$	0.567118	0.0313617
$328$	0.263080	0.0145261
$329$	8.78668	0.484425
$330$	−1.72667	−0.0950503
$331$	5.78371	0.317901	0.158951	−	0.987287i	$-0.449189\pi$
$331$	5.78371	0.317901	0.158951	+	0.987287i	$0.449189\pi$
$332$	−7.00506	−0.384453
$333$	−5.65400	−0.309837
$334$	−17.5555	−0.960596
$335$	−1.84183	−0.100630
$336$	−1.24777	−0.0680715
$337$	−15.2489	−0.830659	−0.415329	−	0.909671i	$-0.636334\pi$
$337$	−15.2489	−0.830659	−0.415329	+	0.909671i	$0.636334\pi$
$338$	0.754655	0.0410478
$339$	2.30294	0.125079
$340$	1.08688	0.0589446
$341$	−1.67803	−0.0908706
$342$	−3.42776	−0.185352
$343$	15.5261	0.838331
$344$	−4.90177	−0.264286
$345$	−1.92111	−0.103429
$346$	−22.5221	−1.21080
$347$	15.3513	0.824103	0.412051	−	0.911161i	$-0.364812\pi$
$347$	15.3513	0.824103	0.412051	+	0.911161i	$0.364812\pi$
$348$	6.53238	0.350172
$349$	19.4089	1.03893	0.519467	−	0.854490i	$-0.326130\pi$
$349$	19.4089	1.03893	0.519467	+	0.854490i	$0.326130\pi$
$350$	−4.76484	−0.254691
$351$	−3.49933	−0.186781
$352$	1.58865	0.0846751
$353$	−8.51189	−0.453042	−0.226521	−	0.974006i	$-0.572735\pi$
$353$	−8.51189	−0.453042	−0.226521	+	0.974006i	$0.572735\pi$
$354$	1.00000	0.0531494
$355$	3.70630	0.196710
$356$	2.56073	0.135718
$357$	1.24777	0.0660390
$358$	−0.971809	−0.0513617
$359$	6.28008	0.331450	0.165725	−	0.986172i	$-0.447004\pi$
$359$	6.28008	0.331450	0.165725	+	0.986172i	$0.447004\pi$
$360$	1.08688	0.0572838
$361$	−7.25047	−0.381604
$362$	−7.46723	−0.392469
$363$	−8.47621	−0.444885
$364$	4.36637	0.228860
$365$	2.22632	0.116531
$366$	−2.97847	−0.155687
$367$	−6.36236	−0.332113	−0.166056	−	0.986116i	$-0.553103\pi$
$367$	−6.36236	−0.332113	−0.166056	+	0.986116i	$0.553103\pi$
$368$	1.76754	0.0921393
$369$	−0.263080	−0.0136954
$370$	−6.14525	−0.319476
$371$	−11.1312	−0.577904
$372$	1.05627	0.0547649
$373$	−8.37898	−0.433847	−0.216924	−	0.976189i	$-0.569602\pi$
$373$	−8.37898	−0.433847	−0.216924	+	0.976189i	$0.569602\pi$
$374$	−1.58865	−0.0821469
$375$	9.58489	0.494962
$376$	7.04190	0.363158
$377$	−22.8590	−1.17730
$378$	1.24777	0.0641784
$379$	16.4736	0.846192	0.423096	−	0.906085i	$-0.360943\pi$
$379$	16.4736	0.846192	0.423096	+	0.906085i	$0.360943\pi$
$380$	−3.72558	−0.191118
$381$	−12.6195	−0.646515
$382$	19.4441	0.994847
$383$	29.4135	1.50296	0.751479	−	0.659757i	$-0.229341\pi$
$383$	29.4135	1.50296	0.751479	+	0.659757i	$0.229341\pi$
$384$	−1.00000	−0.0510310
$385$	−2.15449	−0.109803
$386$	−4.96696	−0.252811
$387$	4.90177	0.249171
$388$	5.85172	0.297076
$389$	−11.0075	−0.558104	−0.279052	−	0.960276i	$-0.590020\pi$
$389$	−11.0075	−0.558104	−0.279052	+	0.960276i	$0.590020\pi$
$390$	−3.80337	−0.192591
$391$	−1.76754	−0.0893882
$392$	5.44307	0.274916
$393$	11.3817	0.574130
$394$	−10.2631	−0.517046
$395$	15.1552	0.762539
$396$	−1.58865	−0.0798324
$397$	−10.9319	−0.548659	−0.274329	−	0.961636i	$-0.588456\pi$
$397$	−10.9319	−0.548659	−0.274329	+	0.961636i	$0.588456\pi$
$398$	−11.9743	−0.600217
$399$	−4.27706	−0.214121
$400$	−3.81868	−0.190934
$401$	−16.0447	−0.801234	−0.400617	−	0.916246i	$-0.631204\pi$
$401$	−16.0447	−0.801234	−0.400617	+	0.916246i	$0.631204\pi$
$402$	−1.69459	−0.0845187
$403$	−3.69623	−0.184122
$404$	12.6294	0.628339
$405$	−1.08688	−0.0540077
$406$	8.15091	0.404523
$407$	8.98220	0.445231
$408$	1.00000	0.0495074
$409$	−34.4158	−1.70175	−0.850876	−	0.525367i	$-0.823928\pi$
$409$	−34.4158	−1.70175	−0.850876	+	0.525367i	$0.823928\pi$
$410$	−0.285937	−0.0141214
$411$	11.5144	0.567964
$412$	19.1684	0.944360
$413$	1.24777	0.0613988
$414$	−1.76754	−0.0868697
$415$	7.61369	0.373742
$416$	3.49933	0.171569
$417$	−10.0793	−0.493587
$418$	5.44549	0.266348
$419$	−30.4667	−1.48840	−0.744198	−	0.667959i	$-0.767168\pi$
$419$	−30.4667	−1.48840	−0.744198	+	0.667959i	$0.767168\pi$
$420$	1.35618	0.0661750
$421$	−35.3614	−1.72341	−0.861704	−	0.507411i	$-0.830603\pi$
$421$	−35.3614	−1.72341	−0.861704	+	0.507411i	$0.830603\pi$
$422$	−0.298820	−0.0145463
$423$	−7.04190	−0.342389
$424$	−8.92088	−0.433236
$425$	3.81868	0.185233
$426$	3.41002	0.165216
$427$	−3.71645	−0.179852
$428$	18.4199	0.890361
$429$	5.55920	0.268401
$430$	5.32766	0.256923
$431$	37.8294	1.82218	0.911089	−	0.412210i	$-0.135243\pi$
$431$	37.8294	1.82218	0.911089	+	0.412210i	$0.135243\pi$
$432$	1.00000	0.0481125
$433$	23.4830	1.12852	0.564262	−	0.825596i	$-0.309161\pi$
$433$	23.4830	1.12852	0.564262	+	0.825596i	$0.309161\pi$
$434$	1.31798	0.0632651
$435$	−7.09994	−0.340416
$436$	0.567118	0.0271600
$437$	6.05869	0.289827
$438$	2.04835	0.0978740
$439$	−11.4651	−0.547201	−0.273601	−	0.961843i	$-0.588215\pi$
$439$	−11.4651	−0.547201	−0.273601	+	0.961843i	$0.588215\pi$
$440$	−1.72667	−0.0823160
$441$	−5.44307	−0.259194
$442$	−3.49933	−0.166446
$443$	−3.17547	−0.150871	−0.0754355	−	0.997151i	$-0.524035\pi$
$443$	−3.17547	−0.150871	−0.0754355	+	0.997151i	$0.524035\pi$
$444$	−5.65400	−0.268327
$445$	−2.78321	−0.131937
$446$	−22.6580	−1.07289
$447$	3.14073	0.148551
$448$	−1.24777	−0.0589516
$449$	−1.50463	−0.0710080	−0.0355040	−	0.999370i	$-0.511304\pi$
$449$	−1.50463	−0.0710080	−0.0355040	+	0.999370i	$0.511304\pi$
$450$	3.81868	0.180014
$451$	0.417940	0.0196800
$452$	2.30294	0.108321
$453$	−2.68202	−0.126012
$454$	21.7085	1.01883
$455$	−4.74574	−0.222484
$456$	−3.42776	−0.160520
$457$	4.28245	0.200325	0.100162	−	0.994971i	$-0.468064\pi$
$457$	4.28245	0.200325	0.100162	+	0.994971i	$0.468064\pi$
$458$	−2.56949	−0.120064
$459$	−1.00000	−0.0466760
$460$	−1.92111	−0.0895722
$461$	−25.6090	−1.19273	−0.596365	−	0.802713i	$-0.703389\pi$
$461$	−25.6090	−1.19273	−0.596365	+	0.802713i	$0.703389\pi$
$462$	−1.98227	−0.0922233
$463$	−22.8439	−1.06165	−0.530823	−	0.847483i	$-0.678117\pi$
$463$	−22.8439	−1.06165	−0.530823	+	0.847483i	$0.678117\pi$
$464$	6.53238	0.303258
$465$	−1.14804	−0.0532391
$466$	5.23889	0.242687
$467$	15.5653	0.720278	0.360139	−	0.932899i	$-0.382729\pi$
$467$	15.5653	0.720278	0.360139	+	0.932899i	$0.382729\pi$
$468$	−3.49933	−0.161757
$469$	−2.11447	−0.0976370
$470$	−7.65373	−0.353040
$471$	24.7992	1.14269
$472$	1.00000	0.0460287
$473$	−7.78718	−0.358055
$474$	13.9437	0.640454
$475$	−13.0895	−0.600588
$476$	1.24777	0.0571915
$477$	8.92088	0.408459
$478$	7.38807	0.337922
$479$	−20.7173	−0.946596	−0.473298	−	0.880902i	$-0.656937\pi$
$479$	−20.7173	−0.946596	−0.473298	+	0.880902i	$0.656937\pi$
$480$	1.08688	0.0496093
$481$	19.7852	0.902130
$482$	23.1478	1.05435
$483$	−2.20548	−0.100353
$484$	−8.47621	−0.385282
$485$	−6.36015	−0.288800
$486$	−1.00000	−0.0453609
$487$	15.5679	0.705448	0.352724	−	0.935727i	$-0.385255\pi$
$487$	15.5679	0.705448	0.352724	+	0.935727i	$0.385255\pi$
$488$	−2.97847	−0.134829
$489$	−1.67796	−0.0758798
$490$	−5.91599	−0.267257
$491$	31.4196	1.41795	0.708973	−	0.705235i	$-0.249159\pi$
$491$	31.4196	1.41795	0.708973	+	0.705235i	$0.249159\pi$
$492$	−0.263080	−0.0118605
$493$	−6.53238	−0.294204
$494$	11.9949	0.539675
$495$	1.72667	0.0776082
$496$	1.05627	0.0474278
$497$	4.25493	0.190860
$498$	7.00506	0.313904
$499$	21.7979	0.975806	0.487903	−	0.872898i	$-0.337762\pi$
$499$	21.7979	0.975806	0.487903	+	0.872898i	$0.337762\pi$
$500$	9.58489	0.428649
$501$	17.5555	0.784324
$502$	−19.9514	−0.890476
$503$	−23.4545	−1.04579	−0.522893	−	0.852398i	$-0.675147\pi$
$503$	−23.4545	−1.04579	−0.522893	+	0.852398i	$0.675147\pi$
$504$	1.24777	0.0555801
$505$	−13.7268	−0.610832
$506$	2.80799	0.124830
$507$	−0.754655	−0.0335154
$508$	−12.6195	−0.559899
$509$	−25.4825	−1.12949	−0.564746	−	0.825265i	$-0.691026\pi$
$509$	−25.4825	−1.12949	−0.564746	+	0.825265i	$0.691026\pi$
$510$	−1.08688	−0.0481281
$511$	2.55587	0.113065
$512$	−1.00000	−0.0441942
$513$	3.42776	0.151339
$514$	−21.6923	−0.956806
$515$	−20.8339	−0.918049
$516$	4.90177	0.215789
$517$	11.1871	0.492007
$518$	−7.05490	−0.309975
$519$	22.5221	0.988612
$520$	−3.80337	−0.166789
$521$	14.4675	0.633831	0.316916	−	0.948454i	$-0.397353\pi$
$521$	14.4675	0.633831	0.316916	+	0.948454i	$0.397353\pi$
$522$	−6.53238	−0.285914
$523$	−25.9563	−1.13499	−0.567495	−	0.823377i	$-0.692087\pi$
$523$	−25.9563	−1.13499	−0.567495	+	0.823377i	$0.692087\pi$
$524$	11.3817	0.497211
$525$	4.76484	0.207955
$526$	−23.4791	−1.02374
$527$	−1.05627	−0.0460117
$528$	−1.58865	−0.0691369
$529$	−19.8758	−0.864166
$530$	9.69596	0.421166
$531$	−1.00000	−0.0433963
$532$	−4.27706	−0.185434
$533$	0.920604	0.0398758
$534$	−2.56073	−0.110813
$535$	−20.0203	−0.865555
$536$	−1.69459	−0.0731953
$537$	0.971809	0.0419366
$538$	18.4264	0.794420
$539$	8.64710	0.372457
$540$	−1.08688	−0.0467721
$541$	38.0841	1.63736	0.818681	−	0.574249i	$-0.194706\pi$
$541$	38.0841	1.63736	0.818681	+	0.574249i	$0.194706\pi$
$542$	−4.78257	−0.205429
$543$	7.46723	0.320450
$544$	1.00000	0.0428746
$545$	−0.616392	−0.0264033
$546$	−4.36637	−0.186863
$547$	−22.6929	−0.970277	−0.485139	−	0.874437i	$-0.661231\pi$
$547$	−22.6929	−0.970277	−0.485139	+	0.874437i	$0.661231\pi$
$548$	11.5144	0.491871
$549$	2.97847	0.127118
$550$	−6.06653	−0.258678
$551$	22.3914	0.953906
$552$	−1.76754	−0.0752314
$553$	17.3985	0.739860
$554$	−11.4444	−0.486226
$555$	6.14525	0.260851
$556$	−10.0793	−0.427459
$557$	−19.3892	−0.821545	−0.410773	−	0.911738i	$-0.634741\pi$
$557$	−19.3892	−0.821545	−0.410773	+	0.911738i	$0.634741\pi$
$558$	−1.05627	−0.0447154
$559$	−17.1529	−0.725492
$560$	1.35618	0.0573092
$561$	1.58865	0.0670727
$562$	−24.7173	−1.04264
$563$	27.4649	1.15751	0.578753	−	0.815503i	$-0.303540\pi$
$563$	27.4649	1.15751	0.578753	+	0.815503i	$0.303540\pi$
$564$	−7.04190	−0.296517
$565$	−2.50303	−0.105303
$566$	−11.3884	−0.478692
$567$	−1.24777	−0.0524015
$568$	3.41002	0.143081
$569$	−30.6953	−1.28682	−0.643408	−	0.765524i	$-0.722480\pi$
$569$	−30.6953	−1.28682	−0.643408	+	0.765524i	$0.722480\pi$
$570$	3.72558	0.156047
$571$	7.37235	0.308523	0.154262	−	0.988030i	$-0.450700\pi$
$571$	7.37235	0.308523	0.154262	+	0.988030i	$0.450700\pi$
$572$	5.55920	0.232442
$573$	−19.4441	−0.812289
$574$	−0.328263	−0.0137014
$575$	−6.74966	−0.281480
$576$	1.00000	0.0416667
$577$	4.25420	0.177105	0.0885523	−	0.996072i	$-0.471776\pi$
$577$	4.25420	0.177105	0.0885523	+	0.996072i	$0.471776\pi$
$578$	−1.00000	−0.0415945
$579$	4.96696	0.206420
$580$	−7.09994	−0.294809
$581$	8.74071	0.362626
$582$	−5.85172	−0.242562
$583$	−14.1721	−0.586949
$584$	2.04835	0.0847614
$585$	3.80337	0.157250
$586$	−4.39572	−0.181585
$587$	−6.17387	−0.254823	−0.127411	−	0.991850i	$-0.540667\pi$
$587$	−6.17387	−0.254823	−0.127411	+	0.991850i	$0.540667\pi$
$588$	−5.44307	−0.224468
$589$	3.62063	0.149185
$590$	−1.08688	−0.0447463
$591$	10.2631	0.422167
$592$	−5.65400	−0.232378
$593$	31.2741	1.28427	0.642136	−	0.766590i	$-0.278048\pi$
$593$	31.2741	1.28427	0.642136	+	0.766590i	$0.278048\pi$
$594$	1.58865	0.0651829
$595$	−1.35618	−0.0555981
$596$	3.14073	0.128649
$597$	11.9743	0.490075
$598$	6.18521	0.252932
$599$	24.1012	0.984748	0.492374	−	0.870384i	$-0.336129\pi$
$599$	24.1012	0.984748	0.492374	+	0.870384i	$0.336129\pi$
$600$	3.81868	0.155897
$601$	−8.87445	−0.361996	−0.180998	−	0.983483i	$-0.557933\pi$
$601$	−8.87445	−0.361996	−0.180998	+	0.983483i	$0.557933\pi$
$602$	6.11629	0.249281
$603$	1.69459	0.0690092
$604$	−2.68202	−0.109130
$605$	9.21266	0.374548
$606$	−12.6294	−0.513036
$607$	7.30188	0.296374	0.148187	−	0.988959i	$-0.452656\pi$
$607$	7.30188	0.296374	0.148187	+	0.988959i	$0.452656\pi$
$608$	−3.42776	−0.139014
$609$	−8.15091	−0.330292
$610$	3.23726	0.131073
$611$	24.6420	0.996907
$612$	−1.00000	−0.0404226
$613$	24.3518	0.983561	0.491781	−	0.870719i	$-0.336346\pi$
$613$	24.3518	0.983561	0.491781	+	0.870719i	$0.336346\pi$
$614$	2.47798	0.100003
$615$	0.285937	0.0115301
$616$	−1.98227	−0.0798678
$617$	34.1199	1.37362	0.686808	−	0.726839i	$-0.259011\pi$
$617$	34.1199	1.37362	0.686808	+	0.726839i	$0.259011\pi$
$618$	−19.1684	−0.771067
$619$	−40.6829	−1.63518	−0.817592	−	0.575798i	$-0.804691\pi$
$619$	−40.6829	−1.63518	−0.817592	+	0.575798i	$0.804691\pi$
$620$	−1.14804	−0.0461064
$621$	1.76754	0.0709288
$622$	−4.05650	−0.162651
$623$	−3.19520	−0.128013
$624$	−3.49933	−0.140086
$625$	8.67574	0.347030
$626$	−6.30146	−0.251857
$627$	−5.44549	−0.217472
$628$	24.7992	0.989595
$629$	5.65400	0.225440
$630$	−1.35618	−0.0540316
$631$	33.9858	1.35295	0.676477	−	0.736464i	$-0.263506\pi$
$631$	33.9858	1.35295	0.676477	+	0.736464i	$0.263506\pi$
$632$	13.9437	0.554649
$633$	0.298820	0.0118770
$634$	−17.0586	−0.677485
$635$	13.7159	0.544299
$636$	8.92088	0.353736
$637$	19.0471	0.754674
$638$	10.3776	0.410854
$639$	−3.41002	−0.134898
$640$	1.08688	0.0429629
$641$	49.3913	1.95084	0.975420	−	0.220353i	$-0.0707209\pi$
$641$	49.3913	1.95084	0.975420	+	0.220353i	$0.0707209\pi$
$642$	−18.4199	−0.726977
$643$	−37.4159	−1.47554	−0.737769	−	0.675054i	$-0.764120\pi$
$643$	−37.4159	−1.47554	−0.737769	+	0.675054i	$0.764120\pi$
$644$	−2.20548	−0.0869082
$645$	−5.32766	−0.209776
$646$	3.42776	0.134863
$647$	−43.5462	−1.71198	−0.855989	−	0.516994i	$-0.827051\pi$
$647$	−43.5462	−1.71198	−0.855989	+	0.516994i	$0.827051\pi$
$648$	−1.00000	−0.0392837
$649$	1.58865	0.0623598
$650$	−13.3628	−0.524134
$651$	−1.31798	−0.0516557
$652$	−1.67796	−0.0657138
$653$	12.4268	0.486299	0.243150	−	0.969989i	$-0.421819\pi$
$653$	12.4268	0.486299	0.243150	+	0.969989i	$0.421819\pi$
$654$	−0.567118	−0.0221761
$655$	−12.3706	−0.483358
$656$	−0.263080	−0.0102715
$657$	−2.04835	−0.0799138
$658$	−8.78668	−0.342540
$659$	16.8280	0.655525	0.327763	−	0.944760i	$-0.393705\pi$
$659$	16.8280	0.655525	0.327763	+	0.944760i	$0.393705\pi$
$660$	1.72667	0.0672107
$661$	−0.718490	−0.0279460	−0.0139730	−	0.999902i	$-0.504448\pi$
$661$	−0.718490	−0.0279460	−0.0139730	+	0.999902i	$0.504448\pi$
$662$	−5.78371	−0.224790
$663$	3.49933	0.135903
$664$	7.00506	0.271849
$665$	4.64867	0.180268
$666$	5.65400	0.219088
$667$	11.5462	0.447072
$668$	17.5555	0.679244
$669$	22.6580	0.876008
$670$	1.84183	0.0711560
$671$	−4.73174	−0.182667
$672$	1.24777	0.0481338
$673$	24.2378	0.934297	0.467148	−	0.884179i	$-0.345281\pi$
$673$	24.2378	0.934297	0.467148	+	0.884179i	$0.345281\pi$
$674$	15.2489	0.587364
$675$	−3.81868	−0.146981
$676$	−0.754655	−0.0290252
$677$	14.3196	0.550346	0.275173	−	0.961395i	$-0.411265\pi$
$677$	14.3196	0.550346	0.275173	+	0.961395i	$0.411265\pi$
$678$	−2.30294	−0.0884440
$679$	−7.30161	−0.280210
$680$	−1.08688	−0.0416801
$681$	−21.7085	−0.831873
$682$	1.67803	0.0642553
$683$	20.3479	0.778590	0.389295	−	0.921113i	$-0.372719\pi$
$683$	20.3479	0.778590	0.389295	+	0.921113i	$0.372719\pi$
$684$	3.42776	0.131064
$685$	−12.5148	−0.478167
$686$	−15.5261	−0.592789
$687$	2.56949	0.0980320
$688$	4.90177	0.186878
$689$	−31.2171	−1.18928
$690$	1.92111	0.0731354
$691$	−22.5023	−0.856028	−0.428014	−	0.903772i	$-0.640787\pi$
$691$	−22.5023	−0.856028	−0.428014	+	0.903772i	$0.640787\pi$
$692$	22.5221	0.856163
$693$	1.98227	0.0753000
$694$	−15.3513	−0.582729
$695$	10.9551	0.415550
$696$	−6.53238	−0.247609
$697$	0.263080	0.00996485
$698$	−19.4089	−0.734638
$699$	−5.23889	−0.198153
$700$	4.76484	0.180094
$701$	−19.9927	−0.755113	−0.377556	−	0.925987i	$-0.623236\pi$
$701$	−19.9927	−0.755113	−0.377556	+	0.925987i	$0.623236\pi$
$702$	3.49933	0.132074
$703$	−19.3806	−0.730952
$704$	−1.58865	−0.0598743
$705$	7.65373	0.288256
$706$	8.51189	0.320349
$707$	−15.7587	−0.592665
$708$	−1.00000	−0.0375823
$709$	12.3461	0.463666	0.231833	−	0.972756i	$-0.425528\pi$
$709$	12.3461	0.463666	0.231833	+	0.972756i	$0.425528\pi$
$710$	−3.70630	−0.139095
$711$	−13.9437	−0.522929
$712$	−2.56073	−0.0959672
$713$	1.86699	0.0699194
$714$	−1.24777	−0.0466967
$715$	−6.04221	−0.225966
$716$	0.971809	0.0363182
$717$	−7.38807	−0.275913
$718$	−6.28008	−0.234371
$719$	11.1568	0.416079	0.208040	−	0.978120i	$-0.433292\pi$
$719$	11.1568	0.416079	0.208040	+	0.978120i	$0.433292\pi$
$720$	−1.08688	−0.0405058
$721$	−23.9178	−0.890745
$722$	7.25047	0.269834
$723$	−23.1478	−0.860877
$724$	7.46723	0.277517
$725$	−24.9451	−0.926437
$726$	8.47621	0.314582
$727$	39.2816	1.45687	0.728436	−	0.685114i	$-0.240247\pi$
$727$	39.2816	1.45687	0.728436	+	0.685114i	$0.240247\pi$
$728$	−4.36637	−0.161828
$729$	1.00000	0.0370370
$730$	−2.22632	−0.0823999
$731$	−4.90177	−0.181299
$732$	2.97847	0.110088
$733$	−25.5761	−0.944674	−0.472337	−	0.881418i	$-0.656589\pi$
$733$	−25.5761	−0.944674	−0.472337	+	0.881418i	$0.656589\pi$
$734$	6.36236	0.234839
$735$	5.91599	0.218214
$736$	−1.76754	−0.0651523
$737$	−2.69211	−0.0991651
$738$	0.263080	0.00968409
$739$	26.8591	0.988027	0.494014	−	0.869454i	$-0.335529\pi$
$739$	26.8591	0.988027	0.494014	+	0.869454i	$0.335529\pi$
$740$	6.14525	0.225904
$741$	−11.9949	−0.440643
$742$	11.1312	0.408640
$743$	41.3809	1.51812	0.759059	−	0.651022i	$-0.225659\pi$
$743$	41.3809	1.51812	0.759059	+	0.651022i	$0.225659\pi$
$744$	−1.05627	−0.0387246
$745$	−3.41361	−0.125065
$746$	8.37898	0.306776
$747$	−7.00506	−0.256302
$748$	1.58865	0.0580866
$749$	−22.9839	−0.839812
$750$	−9.58489	−0.349991
$751$	45.8273	1.67226	0.836130	−	0.548531i	$-0.184813\pi$
$751$	45.8273	1.67226	0.836130	+	0.548531i	$0.184813\pi$
$752$	−7.04190	−0.256792
$753$	19.9514	0.727071
$754$	22.8590	0.832475
$755$	2.91505	0.106089
$756$	−1.24777	−0.0453810
$757$	−29.7711	−1.08205	−0.541025	−	0.841006i	$-0.681964\pi$
$757$	−29.7711	−1.08205	−0.541025	+	0.841006i	$0.681964\pi$
$758$	−16.4736	−0.598348
$759$	−2.80799	−0.101924
$760$	3.72558	0.135141
$761$	1.65420	0.0599645	0.0299823	−	0.999550i	$-0.490455\pi$
$761$	1.65420	0.0599645	0.0299823	+	0.999550i	$0.490455\pi$
$762$	12.6195	0.457155
$763$	−0.707633	−0.0256180
$764$	−19.4441	−0.703463
$765$	1.08688	0.0392964
$766$	−29.4135	−1.06275
$767$	3.49933	0.126354
$768$	1.00000	0.0360844
$769$	−3.49990	−0.126210	−0.0631048	−	0.998007i	$-0.520100\pi$
$769$	−3.49990	−0.126210	−0.0631048	+	0.998007i	$0.520100\pi$
$770$	2.15449	0.0776426
$771$	21.6923	0.781229
$772$	4.96696	0.178765
$773$	−42.4792	−1.52787	−0.763936	−	0.645292i	$-0.776736\pi$
$773$	−42.4792	−1.52787	−0.763936	+	0.645292i	$0.776736\pi$
$774$	−4.90177	−0.176191
$775$	−4.03355	−0.144889
$776$	−5.85172	−0.210065
$777$	7.05490	0.253093
$778$	11.0075	0.394639
$779$	−0.901773	−0.0323094
$780$	3.80337	0.136183
$781$	5.41732	0.193847
$782$	1.76754	0.0632070
$783$	6.53238	0.233448
$784$	−5.44307	−0.194395
$785$	−26.9539	−0.962024
$786$	−11.3817	−0.405971
$787$	−11.2027	−0.399333	−0.199666	−	0.979864i	$-0.563986\pi$
$787$	−11.2027	−0.399333	−0.199666	+	0.979864i	$0.563986\pi$
$788$	10.2631	0.365607
$789$	23.4791	0.835879
$790$	−15.1552	−0.539196
$791$	−2.87354	−0.102171
$792$	1.58865	0.0564501
$793$	−10.4227	−0.370120
$794$	10.9319	0.387960
$795$	−9.69596	−0.343880
$796$	11.9743	0.424417
$797$	42.4937	1.50520	0.752601	−	0.658476i	$-0.228799\pi$
$797$	42.4937	1.50520	0.752601	+	0.658476i	$0.228799\pi$
$798$	4.27706	0.151406
$799$	7.04190	0.249124
$800$	3.81868	0.135011
$801$	2.56073	0.0904788
$802$	16.0447	0.566558
$803$	3.25410	0.114835
$804$	1.69459	0.0597637
$805$	2.39710	0.0844868
$806$	3.69623	0.130194
$807$	−18.4264	−0.648641
$808$	−12.6294	−0.444302
$809$	−38.1848	−1.34251	−0.671253	−	0.741228i	$-0.734244\pi$
$809$	−38.1848	−1.34251	−0.671253	+	0.741228i	$0.734244\pi$
$810$	1.08688	0.0381892
$811$	−25.3406	−0.889829	−0.444915	−	0.895573i	$-0.646766\pi$
$811$	−25.3406	−0.889829	−0.444915	+	0.895573i	$0.646766\pi$
$812$	−8.15091	−0.286041
$813$	4.78257	0.167732
$814$	−8.98220	−0.314826
$815$	1.82374	0.0638830
$816$	−1.00000	−0.0350070
$817$	16.8021	0.587831
$818$	34.4158	1.20332
$819$	4.36637	0.152573
$820$	0.285937	0.00998536
$821$	−29.7403	−1.03795	−0.518973	−	0.854791i	$-0.673685\pi$
$821$	−29.7403	−1.03795	−0.518973	+	0.854791i	$0.673685\pi$
$822$	−11.5144	−0.401611
$823$	14.7604	0.514517	0.257258	−	0.966343i	$-0.417181\pi$
$823$	14.7604	0.514517	0.257258	+	0.966343i	$0.417181\pi$
$824$	−19.1684	−0.667763
$825$	6.06653	0.211210
$826$	−1.24777	−0.0434155
$827$	19.1358	0.665416	0.332708	−	0.943030i	$-0.392038\pi$
$827$	19.1358	0.665416	0.332708	+	0.943030i	$0.392038\pi$
$828$	1.76754	0.0614262
$829$	43.0528	1.49529	0.747643	−	0.664100i	$-0.231185\pi$
$829$	43.0528	1.49529	0.747643	+	0.664100i	$0.231185\pi$
$830$	−7.61369	−0.264275
$831$	11.4444	0.397002
$832$	−3.49933	−0.121318
$833$	5.44307	0.188591
$834$	10.0793	0.349019
$835$	−19.0808	−0.660320
$836$	−5.44549	−0.188336
$837$	1.05627	0.0365099
$838$	30.4667	1.05246
$839$	26.3976	0.911347	0.455674	−	0.890147i	$-0.349398\pi$
$839$	26.3976	0.911347	0.455674	+	0.890147i	$0.349398\pi$
$840$	−1.35618	−0.0467928
$841$	13.6720	0.471447
$842$	35.3614	1.21863
$843$	24.7173	0.851308
$844$	0.298820	0.0102858
$845$	0.820223	0.0282165
$846$	7.04190	0.242105
$847$	10.5764	0.363408
$848$	8.92088	0.306344
$849$	11.3884	0.390850
$850$	−3.81868	−0.130980
$851$	−9.99366	−0.342578
$852$	−3.41002	−0.116826
$853$	21.8260	0.747308	0.373654	−	0.927568i	$-0.378105\pi$
$853$	21.8260	0.747308	0.373654	+	0.927568i	$0.378105\pi$
$854$	3.71645	0.127174
$855$	−3.72558	−0.127412
$856$	−18.4199	−0.629581
$857$	19.6925	0.672683	0.336341	−	0.941740i	$-0.390810\pi$
$857$	19.6925	0.672683	0.336341	+	0.941740i	$0.390810\pi$
$858$	−5.55920	−0.189788
$859$	−17.9205	−0.611438	−0.305719	−	0.952122i	$-0.598897\pi$
$859$	−17.9205	−0.611438	−0.305719	+	0.952122i	$0.598897\pi$
$860$	−5.32766	−0.181672
$861$	0.328263	0.0111872
$862$	−37.8294	−1.28847
$863$	29.5703	1.00658	0.503292	−	0.864116i	$-0.332122\pi$
$863$	29.5703	1.00658	0.503292	+	0.864116i	$0.332122\pi$
$864$	−1.00000	−0.0340207
$865$	−24.4790	−0.832310
$866$	−23.4830	−0.797986
$867$	1.00000	0.0339618
$868$	−1.31798	−0.0447351
$869$	22.1515	0.751440
$870$	7.09994	0.240711
$871$	−5.92995	−0.200929
$872$	−0.567118	−0.0192050
$873$	5.85172	0.198051
$874$	−6.05869	−0.204938
$875$	−11.9597	−0.404313
$876$	−2.04835	−0.0692074
$877$	−25.8551	−0.873064	−0.436532	−	0.899689i	$-0.643793\pi$
$877$	−25.8551	−0.873064	−0.436532	+	0.899689i	$0.643793\pi$
$878$	11.4651	0.386930
$879$	4.39572	0.148264
$880$	1.72667	0.0582062
$881$	29.0764	0.979608	0.489804	−	0.871833i	$-0.337068\pi$
$881$	29.0764	0.979608	0.489804	+	0.871833i	$0.337068\pi$
$882$	5.44307	0.183278
$883$	−22.2971	−0.750356	−0.375178	−	0.926953i	$-0.622418\pi$
$883$	−22.2971	−0.750356	−0.375178	+	0.926953i	$0.622418\pi$
$884$	3.49933	0.117695
$885$	1.08688	0.0365352
$886$	3.17547	0.106682
$887$	−53.7133	−1.80352	−0.901758	−	0.432242i	$-0.857723\pi$
$887$	−53.7133	−1.80352	−0.901758	+	0.432242i	$0.857723\pi$
$888$	5.65400	0.189736
$889$	15.7462	0.528111
$890$	2.78321	0.0932935
$891$	−1.58865	−0.0532216
$892$	22.6580	0.758645
$893$	−24.1379	−0.807745
$894$	−3.14073	−0.105042
$895$	−1.05624	−0.0353063
$896$	1.24777	0.0416851
$897$	−6.18521	−0.206518
$898$	1.50463	0.0502102
$899$	6.89994	0.230126
$900$	−3.81868	−0.127289
$901$	−8.92088	−0.297197
$902$	−0.417940	−0.0139159
$903$	−6.11629	−0.203537
$904$	−2.30294	−0.0765947
$905$	−8.11602	−0.269786
$906$	2.68202	0.0891042
$907$	27.1098	0.900165	0.450083	−	0.892987i	$-0.351395\pi$
$907$	27.1098	0.900165	0.450083	+	0.892987i	$0.351395\pi$
$908$	−21.7085	−0.720424
$909$	12.6294	0.418892
$910$	4.74574	0.157320
$911$	−27.5099	−0.911445	−0.455722	−	0.890122i	$-0.650619\pi$
$911$	−27.5099	−0.911445	−0.455722	+	0.890122i	$0.650619\pi$
$912$	3.42776	0.113504
$913$	11.1286	0.368302
$914$	−4.28245	−0.141651
$915$	−3.23726	−0.107020
$916$	2.56949	0.0848982
$917$	−14.2017	−0.468982
$918$	1.00000	0.0330049
$919$	−20.4183	−0.673537	−0.336769	−	0.941587i	$-0.609334\pi$
$919$	−20.4183	−0.673537	−0.336769	+	0.941587i	$0.609334\pi$
$920$	1.92111	0.0633371
$921$	−2.47798	−0.0816523
$922$	25.6090	0.843388
$923$	11.9328	0.392773
$924$	1.98227	0.0652117
$925$	21.5908	0.709902
$926$	22.8439	0.750697
$927$	19.1684	0.629573
$928$	−6.53238	−0.214436
$929$	16.5047	0.541501	0.270751	−	0.962650i	$-0.412728\pi$
$929$	16.5047	0.541501	0.270751	+	0.962650i	$0.412728\pi$
$930$	1.14804	0.0376457
$931$	−18.6575	−0.611476
$932$	−5.23889	−0.171606
$933$	4.05650	0.132804
$934$	−15.5653	−0.509314
$935$	−1.72667	−0.0564683
$936$	3.49933	0.114379
$937$	49.2423	1.60868	0.804338	−	0.594171i	$-0.202520\pi$
$937$	49.2423	1.60868	0.804338	+	0.594171i	$0.202520\pi$
$938$	2.11447	0.0690398
$939$	6.30146	0.205640
$940$	7.65373	0.249637
$941$	53.6543	1.74908	0.874540	−	0.484953i	$-0.161163\pi$
$941$	53.6543	1.74908	0.874540	+	0.484953i	$0.161163\pi$
$942$	−24.7992	−0.808001
$943$	−0.465003	−0.0151426
$944$	−1.00000	−0.0325472
$945$	1.35618	0.0441166
$946$	7.78718	0.253183
$947$	−50.0273	−1.62567	−0.812834	−	0.582495i	$-0.802076\pi$
$947$	−50.0273	−1.62567	−0.812834	+	0.582495i	$0.802076\pi$
$948$	−13.9437	−0.452869
$949$	7.16787	0.232679
$950$	13.0895	0.424680
$951$	17.0586	0.553164
$952$	−1.24777	−0.0404405
$953$	−17.4501	−0.565265	−0.282633	−	0.959228i	$-0.591208\pi$
$953$	−17.4501	−0.565265	−0.282633	+	0.959228i	$0.591208\pi$
$954$	−8.92088	−0.288824
$955$	21.1335	0.683864
$956$	−7.38807	−0.238947
$957$	−10.3776	−0.335461
$958$	20.7173	0.669345
$959$	−14.3673	−0.463946
$960$	−1.08688	−0.0350790
$961$	−29.8843	−0.964010
$962$	−19.7852	−0.637902
$963$	18.4199	0.593574
$964$	−23.1478	−0.745541
$965$	−5.39851	−0.173784
$966$	2.20548	0.0709602
$967$	41.7301	1.34195	0.670975	−	0.741480i	$-0.265876\pi$
$967$	41.7301	1.34195	0.670975	+	0.741480i	$0.265876\pi$
$968$	8.47621	0.272436
$969$	−3.42776	−0.110115
$970$	6.36015	0.204212
$971$	17.9956	0.577507	0.288754	−	0.957403i	$-0.406759\pi$
$971$	17.9956	0.577507	0.288754	+	0.957403i	$0.406759\pi$
$972$	1.00000	0.0320750
$973$	12.5767	0.403191
$974$	−15.5679	−0.498827
$975$	13.3628	0.427954
$976$	2.97847	0.0953386
$977$	−29.7319	−0.951208	−0.475604	−	0.879660i	$-0.657770\pi$
$977$	−29.7319	−0.951208	−0.475604	+	0.879660i	$0.657770\pi$
$978$	1.67796	0.0536551
$979$	−4.06808	−0.130017
$980$	5.91599	0.188979
$981$	0.567118	0.0181067
$982$	−31.4196	−1.00264
$983$	−29.0181	−0.925534	−0.462767	−	0.886480i	$-0.653143\pi$
$983$	−29.0181	−0.925534	−0.462767	+	0.886480i	$0.653143\pi$
$984$	0.263080	0.00838667
$985$	−11.1548	−0.355421
$986$	6.53238	0.208033
$987$	8.78668	0.279683
$988$	−11.9949	−0.381608
$989$	8.66407	0.275501
$990$	−1.72667	−0.0548773
$991$	36.5247	1.16025	0.580123	−	0.814529i	$-0.303005\pi$
$991$	36.5247	1.16025	0.580123	+	0.814529i	$0.303005\pi$
$992$	−1.05627	−0.0335365
$993$	5.78371	0.183540
$994$	−4.25493	−0.134958
$995$	−13.0147	−0.412593
$996$	−7.00506	−0.221964
$997$	33.3766	1.05705	0.528524	−	0.848918i	$-0.322746\pi$
$997$	33.3766	1.05705	0.528524	+	0.848918i	$0.322746\pi$
$998$	−21.7979	−0.689999
$999$	−5.65400	−0.178885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.p.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.p.1.3	✓	5	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.08688 q^{5} -1.00000 q^{6} -1.24777 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.08688 q^{5} -1.00000 q^{6} -1.24777 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.08688 q^{10} -1.58865 q^{11} +1.00000 q^{12} -3.49933 q^{13} +1.24777 q^{14} -1.08688 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.42776 q^{19} -1.08688 q^{20} -1.24777 q^{21} +1.58865 q^{22} +1.76754 q^{23} -1.00000 q^{24} -3.81868 q^{25} +3.49933 q^{26} +1.00000 q^{27} -1.24777 q^{28} +6.53238 q^{29} +1.08688 q^{30} +1.05627 q^{31} -1.00000 q^{32} -1.58865 q^{33} +1.00000 q^{34} +1.35618 q^{35} +1.00000 q^{36} -5.65400 q^{37} -3.42776 q^{38} -3.49933 q^{39} +1.08688 q^{40} -0.263080 q^{41} +1.24777 q^{42} +4.90177 q^{43} -1.58865 q^{44} -1.08688 q^{45} -1.76754 q^{46} -7.04190 q^{47} +1.00000 q^{48} -5.44307 q^{49} +3.81868 q^{50} -1.00000 q^{51} -3.49933 q^{52} +8.92088 q^{53} -1.00000 q^{54} +1.72667 q^{55} +1.24777 q^{56} +3.42776 q^{57} -6.53238 q^{58} -1.00000 q^{59} -1.08688 q^{60} +2.97847 q^{61} -1.05627 q^{62} -1.24777 q^{63} +1.00000 q^{64} +3.80337 q^{65} +1.58865 q^{66} +1.69459 q^{67} -1.00000 q^{68} +1.76754 q^{69} -1.35618 q^{70} -3.41002 q^{71} -1.00000 q^{72} -2.04835 q^{73} +5.65400 q^{74} -3.81868 q^{75} +3.42776 q^{76} +1.98227 q^{77} +3.49933 q^{78} -13.9437 q^{79} -1.08688 q^{80} +1.00000 q^{81} +0.263080 q^{82} -7.00506 q^{83} -1.24777 q^{84} +1.08688 q^{85} -4.90177 q^{86} +6.53238 q^{87} +1.58865 q^{88} +2.56073 q^{89} +1.08688 q^{90} +4.36637 q^{91} +1.76754 q^{92} +1.05627 q^{93} +7.04190 q^{94} -3.72558 q^{95} -1.00000 q^{96} +5.85172 q^{97} +5.44307 q^{98} -1.58865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} + q^{10} + 6 q^{11} + 5 q^{12} - 2 q^{13} + q^{14} - q^{15} + 5 q^{16} - 5 q^{17} - 5 q^{18} + 4 q^{19} - q^{20} - q^{21} - 6 q^{22} + 12 q^{23} - 5 q^{24} + 4 q^{25} + 2 q^{26} + 5 q^{27} - q^{28} + 19 q^{29} + q^{30} + 5 q^{31} - 5 q^{32} + 6 q^{33} + 5 q^{34} - 4 q^{35} + 5 q^{36} - 11 q^{37} - 4 q^{38} - 2 q^{39} + q^{40} + 6 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} - q^{45} - 12 q^{46} + 22 q^{47} + 5 q^{48} - 12 q^{49} - 4 q^{50} - 5 q^{51} - 2 q^{52} + 15 q^{53} - 5 q^{54} - 36 q^{55} + q^{56} + 4 q^{57} - 19 q^{58} - 5 q^{59} - q^{60} + 16 q^{61} - 5 q^{62} - q^{63} + 5 q^{64} - 2 q^{65} - 6 q^{66} + 25 q^{67} - 5 q^{68} + 12 q^{69} + 4 q^{70} - 5 q^{72} - 10 q^{73} + 11 q^{74} + 4 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 10 q^{79} - q^{80} + 5 q^{81} - 6 q^{82} + 19 q^{83} - q^{84} + q^{85} - 2 q^{86} + 19 q^{87} - 6 q^{88} + 23 q^{89} + q^{90} - 17 q^{91} + 12 q^{92} + 5 q^{93} - 22 q^{94} + q^{95} - 5 q^{96} + 8 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 + q^10 + 6 * q^11 + 5 * q^12 - 2 * q^13 + q^14 - q^15 + 5 * q^16 - 5 * q^17 - 5 * q^18 + 4 * q^19 - q^20 - q^21 - 6 * q^22 + 12 * q^23 - 5 * q^24 + 4 * q^25 + 2 * q^26 + 5 * q^27 - q^28 + 19 * q^29 + q^30 + 5 * q^31 - 5 * q^32 + 6 * q^33 + 5 * q^34 - 4 * q^35 + 5 * q^36 - 11 * q^37 - 4 * q^38 - 2 * q^39 + q^40 + 6 * q^41 + q^42 + 2 * q^43 + 6 * q^44 - q^45 - 12 * q^46 + 22 * q^47 + 5 * q^48 - 12 * q^49 - 4 * q^50 - 5 * q^51 - 2 * q^52 + 15 * q^53 - 5 * q^54 - 36 * q^55 + q^56 + 4 * q^57 - 19 * q^58 - 5 * q^59 - q^60 + 16 * q^61 - 5 * q^62 - q^63 + 5 * q^64 - 2 * q^65 - 6 * q^66 + 25 * q^67 - 5 * q^68 + 12 * q^69 + 4 * q^70 - 5 * q^72 - 10 * q^73 + 11 * q^74 + 4 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 10 * q^79 - q^80 + 5 * q^81 - 6 * q^82 + 19 * q^83 - q^84 + q^85 - 2 * q^86 + 19 * q^87 - 6 * q^88 + 23 * q^89 + q^90 - 17 * q^91 + 12 * q^92 + 5 * q^93 - 22 * q^94 + q^95 - 5 * q^96 + 8 * q^97 + 12 * q^98 + 6 * q^99

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