LMFDB - Embedded newform 4026.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.30998405.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 8x^{3} + 16x^{2} - 13x + 2 $ x^6 - x^5 - 9x^4 + 8x^3 + 16x^2 - 13x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.70935$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89759 q^{5} +1.00000 q^{6} +3.22249 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89759 q^{5} +1.00000 q^{6} +3.22249 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.89759 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.07586 q^{13} -3.22249 q^{14} +3.89759 q^{15} +1.00000 q^{16} -1.51314 q^{17} -1.00000 q^{18} -6.85856 q^{19} -3.89759 q^{20} -3.22249 q^{21} -1.00000 q^{22} -3.58900 q^{23} +1.00000 q^{24} +10.1912 q^{25} -2.07586 q^{26} -1.00000 q^{27} +3.22249 q^{28} +5.44981 q^{29} -3.89759 q^{30} -2.54981 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.51314 q^{34} -12.5599 q^{35} +1.00000 q^{36} +1.72649 q^{37} +6.85856 q^{38} -2.07586 q^{39} +3.89759 q^{40} +1.77939 q^{41} +3.22249 q^{42} +5.70459 q^{43} +1.00000 q^{44} -3.89759 q^{45} +3.58900 q^{46} -8.69832 q^{47} -1.00000 q^{48} +3.38445 q^{49} -10.1912 q^{50} +1.51314 q^{51} +2.07586 q^{52} +0.850418 q^{53} +1.00000 q^{54} -3.89759 q^{55} -3.22249 q^{56} +6.85856 q^{57} -5.44981 q^{58} +0.453224 q^{59} +3.89759 q^{60} +1.00000 q^{61} +2.54981 q^{62} +3.22249 q^{63} +1.00000 q^{64} -8.09085 q^{65} +1.00000 q^{66} -3.84897 q^{67} -1.51314 q^{68} +3.58900 q^{69} +12.5599 q^{70} +4.50121 q^{71} -1.00000 q^{72} -3.75956 q^{73} -1.72649 q^{74} -10.1912 q^{75} -6.85856 q^{76} +3.22249 q^{77} +2.07586 q^{78} +14.8761 q^{79} -3.89759 q^{80} +1.00000 q^{81} -1.77939 q^{82} +4.65993 q^{83} -3.22249 q^{84} +5.89759 q^{85} -5.70459 q^{86} -5.44981 q^{87} -1.00000 q^{88} +2.59976 q^{89} +3.89759 q^{90} +6.68944 q^{91} -3.58900 q^{92} +2.54981 q^{93} +8.69832 q^{94} +26.7318 q^{95} +1.00000 q^{96} +14.5789 q^{97} -3.38445 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * 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
$5$	−3.89759	−1.74305	−0.871527	−	0.490348i	$-0.836870\pi$
$5$	−3.89759	−1.74305	−0.871527	+	0.490348i	$0.836870\pi$
$6$	1.00000	0.408248
$7$	3.22249	1.21799	0.608994	−	0.793175i	$-0.291574\pi$
$7$	3.22249	1.21799	0.608994	+	0.793175i	$0.291574\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.89759	1.23252
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	2.07586	0.575740	0.287870	−	0.957669i	$-0.407053\pi$
$13$	2.07586	0.575740	0.287870	+	0.957669i	$0.407053\pi$
$14$	−3.22249	−0.861247
$15$	3.89759	1.00635
$16$	1.00000	0.250000
$17$	−1.51314	−0.366990	−0.183495	−	0.983021i	$-0.558741\pi$
$17$	−1.51314	−0.366990	−0.183495	+	0.983021i	$0.558741\pi$
$18$	−1.00000	−0.235702
$19$	−6.85856	−1.57346	−0.786731	−	0.617296i	$-0.788228\pi$
$19$	−6.85856	−1.57346	−0.786731	+	0.617296i	$0.788228\pi$
$20$	−3.89759	−0.871527
$21$	−3.22249	−0.703205
$22$	−1.00000	−0.213201
$23$	−3.58900	−0.748358	−0.374179	−	0.927356i	$-0.622075\pi$
$23$	−3.58900	−0.748358	−0.374179	+	0.927356i	$0.622075\pi$
$24$	1.00000	0.204124
$25$	10.1912	2.03823
$26$	−2.07586	−0.407110
$27$	−1.00000	−0.192450
$28$	3.22249	0.608994
$29$	5.44981	1.01201	0.506003	−	0.862532i	$-0.331123\pi$
$29$	5.44981	1.01201	0.506003	+	0.862532i	$0.331123\pi$
$30$	−3.89759	−0.711599
$31$	−2.54981	−0.457960	−0.228980	−	0.973431i	$-0.573539\pi$
$31$	−2.54981	−0.457960	−0.228980	+	0.973431i	$0.573539\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	1.51314	0.259501
$35$	−12.5599	−2.12302
$36$	1.00000	0.166667
$37$	1.72649	0.283834	0.141917	−	0.989879i	$-0.454673\pi$
$37$	1.72649	0.283834	0.141917	+	0.989879i	$0.454673\pi$
$38$	6.85856	1.11261
$39$	−2.07586	−0.332404
$40$	3.89759	0.616262
$41$	1.77939	0.277894	0.138947	−	0.990300i	$-0.455628\pi$
$41$	1.77939	0.277894	0.138947	+	0.990300i	$0.455628\pi$
$42$	3.22249	0.497241
$43$	5.70459	0.869941	0.434971	−	0.900445i	$-0.356759\pi$
$43$	5.70459	0.869941	0.434971	+	0.900445i	$0.356759\pi$
$44$	1.00000	0.150756
$45$	−3.89759	−0.581018
$46$	3.58900	0.529169
$47$	−8.69832	−1.26878	−0.634390	−	0.773013i	$-0.718749\pi$
$47$	−8.69832	−1.26878	−0.634390	+	0.773013i	$0.718749\pi$
$48$	−1.00000	−0.144338
$49$	3.38445	0.483492
$50$	−10.1912	−1.44125
$51$	1.51314	0.211882
$52$	2.07586	0.287870
$53$	0.850418	0.116814	0.0584069	−	0.998293i	$-0.481398\pi$
$53$	0.850418	0.116814	0.0584069	+	0.998293i	$0.481398\pi$
$54$	1.00000	0.136083
$55$	−3.89759	−0.525550
$56$	−3.22249	−0.430623
$57$	6.85856	0.908439
$58$	−5.44981	−0.715596
$59$	0.453224	0.0590047	0.0295024	−	0.999565i	$-0.490608\pi$
$59$	0.453224	0.0590047	0.0295024	+	0.999565i	$0.490608\pi$
$60$	3.89759	0.503176
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.54981	0.323827
$63$	3.22249	0.405996
$64$	1.00000	0.125000
$65$	−8.09085	−1.00355
$66$	1.00000	0.123091
$67$	−3.84897	−0.470226	−0.235113	−	0.971968i	$-0.575546\pi$
$67$	−3.84897	−0.470226	−0.235113	+	0.971968i	$0.575546\pi$
$68$	−1.51314	−0.183495
$69$	3.58900	0.432065
$70$	12.5599	1.50120
$71$	4.50121	0.534196	0.267098	−	0.963669i	$-0.413935\pi$
$71$	4.50121	0.534196	0.267098	+	0.963669i	$0.413935\pi$
$72$	−1.00000	−0.117851
$73$	−3.75956	−0.440023	−0.220011	−	0.975497i	$-0.570609\pi$
$73$	−3.75956	−0.440023	−0.220011	+	0.975497i	$0.570609\pi$
$74$	−1.72649	−0.200701
$75$	−10.1912	−1.17678
$76$	−6.85856	−0.786731
$77$	3.22249	0.367237
$78$	2.07586	0.235045
$79$	14.8761	1.67370	0.836848	−	0.547436i	$-0.184396\pi$
$79$	14.8761	1.67370	0.836848	+	0.547436i	$0.184396\pi$
$80$	−3.89759	−0.435763
$81$	1.00000	0.111111
$82$	−1.77939	−0.196501
$83$	4.65993	0.511494	0.255747	−	0.966744i	$-0.417679\pi$
$83$	4.65993	0.511494	0.255747	+	0.966744i	$0.417679\pi$
$84$	−3.22249	−0.351603
$85$	5.89759	0.639683
$86$	−5.70459	−0.615142
$87$	−5.44981	−0.584281
$88$	−1.00000	−0.106600
$89$	2.59976	0.275574	0.137787	−	0.990462i	$-0.456001\pi$
$89$	2.59976	0.275574	0.137787	+	0.990462i	$0.456001\pi$
$90$	3.89759	0.410842
$91$	6.68944	0.701244
$92$	−3.58900	−0.374179
$93$	2.54981	0.264403
$94$	8.69832	0.897163
$95$	26.7318	2.74263
$96$	1.00000	0.102062
$97$	14.5789	1.48027	0.740133	−	0.672460i	$-0.234762\pi$
$97$	14.5789	1.48027	0.740133	+	0.672460i	$0.234762\pi$
$98$	−3.38445	−0.341881
$99$	1.00000	0.100504
$100$	10.1912	1.01912
$101$	−14.7350	−1.46619	−0.733093	−	0.680128i	$-0.761924\pi$
$101$	−14.7350	−1.46619	−0.733093	+	0.680128i	$0.761924\pi$
$102$	−1.51314	−0.149823
$103$	4.69654	0.462764	0.231382	−	0.972863i	$-0.425675\pi$
$103$	4.69654	0.462764	0.231382	+	0.972863i	$0.425675\pi$
$104$	−2.07586	−0.203555
$105$	12.5599	1.22572
$106$	−0.850418	−0.0825999
$107$	−13.3128	−1.28700	−0.643501	−	0.765445i	$-0.722519\pi$
$107$	−13.3128	−1.28700	−0.643501	+	0.765445i	$0.722519\pi$
$108$	−1.00000	−0.0962250
$109$	−11.9625	−1.14580	−0.572900	−	0.819625i	$-0.694182\pi$
$109$	−11.9625	−1.14580	−0.572900	+	0.819625i	$0.694182\pi$
$110$	3.89759	0.371620
$111$	−1.72649	−0.163871
$112$	3.22249	0.304497
$113$	10.0074	0.941420	0.470710	−	0.882288i	$-0.343998\pi$
$113$	10.0074	0.941420	0.470710	+	0.882288i	$0.343998\pi$
$114$	−6.85856	−0.642363
$115$	13.9884	1.30443
$116$	5.44981	0.506003
$117$	2.07586	0.191913
$118$	−0.453224	−0.0417227
$119$	−4.87607	−0.446989
$120$	−3.89759	−0.355799
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	−1.77939	−0.160442
$124$	−2.54981	−0.228980
$125$	−20.2330	−1.80970
$126$	−3.22249	−0.287082
$127$	3.35056	0.297314	0.148657	−	0.988889i	$-0.452505\pi$
$127$	3.35056	0.297314	0.148657	+	0.988889i	$0.452505\pi$
$128$	−1.00000	−0.0883883
$129$	−5.70459	−0.502261
$130$	8.09085	0.709614
$131$	−13.3096	−1.16286	−0.581431	−	0.813596i	$-0.697507\pi$
$131$	−13.3096	−1.16286	−0.581431	+	0.813596i	$0.697507\pi$
$132$	−1.00000	−0.0870388
$133$	−22.1017	−1.91646
$134$	3.84897	0.332500
$135$	3.89759	0.335451
$136$	1.51314	0.129751
$137$	11.7086	1.00033	0.500167	−	0.865929i	$-0.333272\pi$
$137$	11.7086	1.00033	0.500167	+	0.865929i	$0.333272\pi$
$138$	−3.58900	−0.305516
$139$	6.18105	0.524270	0.262135	−	0.965031i	$-0.415573\pi$
$139$	6.18105	0.524270	0.262135	+	0.965031i	$0.415573\pi$
$140$	−12.5599	−1.06151
$141$	8.69832	0.732531
$142$	−4.50121	−0.377733
$143$	2.07586	0.173592
$144$	1.00000	0.0833333
$145$	−21.2411	−1.76398
$146$	3.75956	0.311143
$147$	−3.38445	−0.279145
$148$	1.72649	0.141917
$149$	−0.590452	−0.0483717	−0.0241859	−	0.999707i	$-0.507699\pi$
$149$	−0.590452	−0.0483717	−0.0241859	+	0.999707i	$0.507699\pi$
$150$	10.1912	0.832106
$151$	20.4142	1.66128	0.830642	−	0.556808i	$-0.187974\pi$
$151$	20.4142	1.66128	0.830642	+	0.556808i	$0.187974\pi$
$152$	6.85856	0.556303
$153$	−1.51314	−0.122330
$154$	−3.22249	−0.259676
$155$	9.93812	0.798249
$156$	−2.07586	−0.166202
$157$	2.28784	0.182589	0.0912947	−	0.995824i	$-0.470899\pi$
$157$	2.28784	0.182589	0.0912947	+	0.995824i	$0.470899\pi$
$158$	−14.8761	−1.18348
$159$	−0.850418	−0.0674425
$160$	3.89759	0.308131
$161$	−11.5655	−0.911491
$162$	−1.00000	−0.0785674
$163$	−0.460681	−0.0360833	−0.0180417	−	0.999837i	$-0.505743\pi$
$163$	−0.460681	−0.0360833	−0.0180417	+	0.999837i	$0.505743\pi$
$164$	1.77939	0.138947
$165$	3.89759	0.303427
$166$	−4.65993	−0.361681
$167$	−21.6773	−1.67744	−0.838720	−	0.544563i	$-0.816696\pi$
$167$	−21.6773	−1.67744	−0.838720	+	0.544563i	$0.816696\pi$
$168$	3.22249	0.248621
$169$	−8.69080	−0.668523
$170$	−5.89759	−0.452324
$171$	−6.85856	−0.524487
$172$	5.70459	0.434971
$173$	−15.0723	−1.14592	−0.572962	−	0.819582i	$-0.694206\pi$
$173$	−15.0723	−1.14592	−0.572962	+	0.819582i	$0.694206\pi$
$174$	5.44981	0.413149
$175$	32.8410	2.48254
$176$	1.00000	0.0753778
$177$	−0.453224	−0.0340664
$178$	−2.59976	−0.194860
$179$	−15.6795	−1.17194	−0.585969	−	0.810333i	$-0.699286\pi$
$179$	−15.6795	−1.17194	−0.585969	+	0.810333i	$0.699286\pi$
$180$	−3.89759	−0.290509
$181$	−9.65321	−0.717518	−0.358759	−	0.933430i	$-0.616800\pi$
$181$	−9.65321	−0.717518	−0.358759	+	0.933430i	$0.616800\pi$
$182$	−6.68944	−0.495855
$183$	−1.00000	−0.0739221
$184$	3.58900	0.264585
$185$	−6.72915	−0.494737
$186$	−2.54981	−0.186961
$187$	−1.51314	−0.110652
$188$	−8.69832	−0.634390
$189$	−3.22249	−0.234402
$190$	−26.7318	−1.93933
$191$	−5.07692	−0.367353	−0.183677	−	0.982987i	$-0.558800\pi$
$191$	−5.07692	−0.367353	−0.183677	+	0.982987i	$0.558800\pi$
$192$	−1.00000	−0.0721688
$193$	−11.0707	−0.796888	−0.398444	−	0.917193i	$-0.630450\pi$
$193$	−11.0707	−0.796888	−0.398444	+	0.917193i	$0.630450\pi$
$194$	−14.5789	−1.04671
$195$	8.09085	0.579398
$196$	3.38445	0.241746
$197$	−1.77134	−0.126203	−0.0631013	−	0.998007i	$-0.520099\pi$
$197$	−1.77134	−0.126203	−0.0631013	+	0.998007i	$0.520099\pi$
$198$	−1.00000	−0.0710669
$199$	−21.3944	−1.51661	−0.758304	−	0.651901i	$-0.773972\pi$
$199$	−21.3944	−1.51661	−0.758304	+	0.651901i	$0.773972\pi$
$200$	−10.1912	−0.720625
$201$	3.84897	0.271485
$202$	14.7350	1.03675
$203$	17.5620	1.23261
$204$	1.51314	0.105941
$205$	−6.93532	−0.484384
$206$	−4.69654	−0.327223
$207$	−3.58900	−0.249453
$208$	2.07586	0.143935
$209$	−6.85856	−0.474417
$210$	−12.5599	−0.866718
$211$	−24.7909	−1.70668	−0.853339	−	0.521357i	$-0.825426\pi$
$211$	−24.7909	−1.70668	−0.853339	+	0.521357i	$0.825426\pi$
$212$	0.850418	0.0584069
$213$	−4.50121	−0.308418
$214$	13.3128	0.910047
$215$	−22.2341	−1.51635
$216$	1.00000	0.0680414
$217$	−8.21675	−0.557789
$218$	11.9625	0.810204
$219$	3.75956	0.254047
$220$	−3.89759	−0.262775
$221$	−3.14107	−0.211291
$222$	1.72649	0.115875
$223$	−9.40166	−0.629582	−0.314791	−	0.949161i	$-0.601934\pi$
$223$	−9.40166	−0.629582	−0.314791	+	0.949161i	$0.601934\pi$
$224$	−3.22249	−0.215312
$225$	10.1912	0.679412
$226$	−10.0074	−0.665684
$227$	22.4913	1.49280	0.746400	−	0.665497i	$-0.231780\pi$
$227$	22.4913	1.49280	0.746400	+	0.665497i	$0.231780\pi$
$228$	6.85856	0.454219
$229$	−7.94879	−0.525271	−0.262635	−	0.964895i	$-0.584592\pi$
$229$	−7.94879	−0.525271	−0.262635	+	0.964895i	$0.584592\pi$
$230$	−13.9884	−0.922370
$231$	−3.22249	−0.212024
$232$	−5.44981	−0.357798
$233$	−16.5993	−1.08746	−0.543728	−	0.839262i	$-0.682988\pi$
$233$	−16.5993	−1.08746	−0.543728	+	0.839262i	$0.682988\pi$
$234$	−2.07586	−0.135703
$235$	33.9025	2.21155
$236$	0.453224	0.0295024
$237$	−14.8761	−0.966308
$238$	4.87607	0.316069
$239$	17.7454	1.14786	0.573929	−	0.818905i	$-0.305419\pi$
$239$	17.7454	1.14786	0.573929	+	0.818905i	$0.305419\pi$
$240$	3.89759	0.251588
$241$	−17.6386	−1.13621	−0.568103	−	0.822958i	$-0.692322\pi$
$241$	−17.6386	−1.13621	−0.568103	+	0.822958i	$0.692322\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−13.1912	−0.842753
$246$	1.77939	0.113450
$247$	−14.2374	−0.905906
$248$	2.54981	0.161913
$249$	−4.65993	−0.295311
$250$	20.2330	1.27965
$251$	−12.3727	−0.780958	−0.390479	−	0.920612i	$-0.627691\pi$
$251$	−12.3727	−0.780958	−0.390479	+	0.920612i	$0.627691\pi$
$252$	3.22249	0.202998
$253$	−3.58900	−0.225638
$254$	−3.35056	−0.210233
$255$	−5.89759	−0.369321
$256$	1.00000	0.0625000
$257$	−1.72146	−0.107382	−0.0536910	−	0.998558i	$-0.517099\pi$
$257$	−1.72146	−0.107382	−0.0536910	+	0.998558i	$0.517099\pi$
$258$	5.70459	0.355152
$259$	5.56360	0.345706
$260$	−8.09085	−0.501773
$261$	5.44981	0.337335
$262$	13.3096	0.822268
$263$	−14.2931	−0.881352	−0.440676	−	0.897666i	$-0.645261\pi$
$263$	−14.2931	−0.881352	−0.440676	+	0.897666i	$0.645261\pi$
$264$	1.00000	0.0615457
$265$	−3.31458	−0.203613
$266$	22.1017	1.35514
$267$	−2.59976	−0.159103
$268$	−3.84897	−0.235113
$269$	14.3323	0.873857	0.436929	−	0.899496i	$-0.356066\pi$
$269$	14.3323	0.873857	0.436929	+	0.899496i	$0.356066\pi$
$270$	−3.89759	−0.237200
$271$	−6.20274	−0.376790	−0.188395	−	0.982093i	$-0.560328\pi$
$271$	−6.20274	−0.376790	−0.188395	+	0.982093i	$0.560328\pi$
$272$	−1.51314	−0.0917475
$273$	−6.68944	−0.404864
$274$	−11.7086	−0.707344
$275$	10.1912	0.614551
$276$	3.58900	0.216032
$277$	−21.3349	−1.28189	−0.640944	−	0.767588i	$-0.721457\pi$
$277$	−21.3349	−1.28189	−0.640944	+	0.767588i	$0.721457\pi$
$278$	−6.18105	−0.370715
$279$	−2.54981	−0.152653
$280$	12.5599	0.750600
$281$	19.9031	1.18732	0.593660	−	0.804716i	$-0.297682\pi$
$281$	19.9031	1.18732	0.593660	+	0.804716i	$0.297682\pi$
$282$	−8.69832	−0.517978
$283$	−16.6261	−0.988317	−0.494158	−	0.869372i	$-0.664524\pi$
$283$	−16.6261	−0.988317	−0.494158	+	0.869372i	$0.664524\pi$
$284$	4.50121	0.267098
$285$	−26.7318	−1.58346
$286$	−2.07586	−0.122748
$287$	5.73406	0.338471
$288$	−1.00000	−0.0589256
$289$	−14.7104	−0.865318
$290$	21.2411	1.24732
$291$	−14.5789	−0.854632
$292$	−3.75956	−0.220011
$293$	−2.14124	−0.125093	−0.0625464	−	0.998042i	$-0.519922\pi$
$293$	−2.14124	−0.125093	−0.0625464	+	0.998042i	$0.519922\pi$
$294$	3.38445	0.197385
$295$	−1.76648	−0.102848
$296$	−1.72649	−0.100350
$297$	−1.00000	−0.0580259
$298$	0.590452	0.0342040
$299$	−7.45027	−0.430860
$300$	−10.1912	−0.588388
$301$	18.3830	1.05958
$302$	−20.4142	−1.17470
$303$	14.7350	0.846503
$304$	−6.85856	−0.393366
$305$	−3.89759	−0.223175
$306$	1.51314	0.0865004
$307$	4.30296	0.245583	0.122791	−	0.992433i	$-0.460815\pi$
$307$	4.30296	0.245583	0.122791	+	0.992433i	$0.460815\pi$
$308$	3.22249	0.183618
$309$	−4.69654	−0.267177
$310$	−9.93812	−0.564447
$311$	28.9086	1.63926	0.819629	−	0.572894i	$-0.194179\pi$
$311$	28.9086	1.63926	0.819629	+	0.572894i	$0.194179\pi$
$312$	2.07586	0.117523
$313$	−1.72907	−0.0977329	−0.0488665	−	0.998805i	$-0.515561\pi$
$313$	−1.72907	−0.0977329	−0.0488665	+	0.998805i	$0.515561\pi$
$314$	−2.28784	−0.129110
$315$	−12.5599	−0.707672
$316$	14.8761	0.836848
$317$	7.18518	0.403560	0.201780	−	0.979431i	$-0.435327\pi$
$317$	7.18518	0.403560	0.201780	+	0.979431i	$0.435327\pi$
$318$	0.850418	0.0476891
$319$	5.44981	0.305131
$320$	−3.89759	−0.217882
$321$	13.3128	0.743051
$322$	11.5655	0.644521
$323$	10.3780	0.577445
$324$	1.00000	0.0555556
$325$	21.1555	1.17349
$326$	0.460681	0.0255148
$327$	11.9625	0.661528
$328$	−1.77939	−0.0982503
$329$	−28.0303	−1.54536
$330$	−3.89759	−0.214555
$331$	−12.7264	−0.699507	−0.349754	−	0.936842i	$-0.613735\pi$
$331$	−12.7264	−0.699507	−0.349754	+	0.936842i	$0.613735\pi$
$332$	4.65993	0.255747
$333$	1.72649	0.0946112
$334$	21.6773	1.18613
$335$	15.0017	0.819629
$336$	−3.22249	−0.175801
$337$	−4.66583	−0.254164	−0.127082	−	0.991892i	$-0.540561\pi$
$337$	−4.66583	−0.254164	−0.127082	+	0.991892i	$0.540561\pi$
$338$	8.69080	0.472717
$339$	−10.0074	−0.543529
$340$	5.89759	0.319841
$341$	−2.54981	−0.138080
$342$	6.85856	0.370869
$343$	−11.6511	−0.629099
$344$	−5.70459	−0.307571
$345$	−13.9884	−0.753112
$346$	15.0723	0.810290
$347$	−9.92619	−0.532866	−0.266433	−	0.963853i	$-0.585845\pi$
$347$	−9.92619	−0.532866	−0.266433	+	0.963853i	$0.585845\pi$
$348$	−5.44981	−0.292141
$349$	11.7514	0.629038	0.314519	−	0.949251i	$-0.398157\pi$
$349$	11.7514	0.629038	0.314519	+	0.949251i	$0.398157\pi$
$350$	−32.8410	−1.75542
$351$	−2.07586	−0.110801
$352$	−1.00000	−0.0533002
$353$	−5.29458	−0.281802	−0.140901	−	0.990024i	$-0.545000\pi$
$353$	−5.29458	−0.281802	−0.140901	+	0.990024i	$0.545000\pi$
$354$	0.453224	0.0240886
$355$	−17.5439	−0.931131
$356$	2.59976	0.137787
$357$	4.87607	0.258069
$358$	15.6795	0.828686
$359$	−12.0185	−0.634315	−0.317157	−	0.948373i	$-0.602728\pi$
$359$	−12.0185	−0.634315	−0.317157	+	0.948373i	$0.602728\pi$
$360$	3.89759	0.205421
$361$	28.0399	1.47578
$362$	9.65321	0.507362
$363$	−1.00000	−0.0524864
$364$	6.68944	0.350622
$365$	14.6532	0.766983
$366$	1.00000	0.0522708
$367$	10.3670	0.541155	0.270577	−	0.962698i	$-0.412785\pi$
$367$	10.3670	0.541155	0.270577	+	0.962698i	$0.412785\pi$
$368$	−3.58900	−0.187090
$369$	1.77939	0.0926313
$370$	6.72915	0.349832
$371$	2.74046	0.142278
$372$	2.54981	0.132202
$373$	−21.3809	−1.10706	−0.553531	−	0.832828i	$-0.686720\pi$
$373$	−21.3809	−1.10706	−0.553531	+	0.832828i	$0.686720\pi$
$374$	1.51314	0.0782425
$375$	20.2330	1.04483
$376$	8.69832	0.448582
$377$	11.3131	0.582652
$378$	3.22249	0.165747
$379$	7.09080	0.364230	0.182115	−	0.983277i	$-0.441706\pi$
$379$	7.09080	0.364230	0.182115	+	0.983277i	$0.441706\pi$
$380$	26.7318	1.37131
$381$	−3.35056	−0.171654
$382$	5.07692	0.259758
$383$	11.8909	0.607598	0.303799	−	0.952736i	$-0.401745\pi$
$383$	11.8909	0.607598	0.303799	+	0.952736i	$0.401745\pi$
$384$	1.00000	0.0510310
$385$	−12.5599	−0.640113
$386$	11.0707	0.563485
$387$	5.70459	0.289980
$388$	14.5789	0.740133
$389$	−17.7582	−0.900376	−0.450188	−	0.892934i	$-0.648643\pi$
$389$	−17.7582	−0.900376	−0.450188	+	0.892934i	$0.648643\pi$
$390$	−8.09085	−0.409696
$391$	5.43065	0.274640
$392$	−3.38445	−0.170940
$393$	13.3096	0.671379
$394$	1.77134	0.0892387
$395$	−57.9810	−2.91734
$396$	1.00000	0.0502519
$397$	−18.2520	−0.916044	−0.458022	−	0.888941i	$-0.651442\pi$
$397$	−18.2520	−0.916044	−0.458022	+	0.888941i	$0.651442\pi$
$398$	21.3944	1.07240
$399$	22.1017	1.10647
$400$	10.1912	0.509559
$401$	16.6878	0.833351	0.416676	−	0.909055i	$-0.363195\pi$
$401$	16.6878	0.833351	0.416676	+	0.909055i	$0.363195\pi$
$402$	−3.84897	−0.191969
$403$	−5.29306	−0.263666
$404$	−14.7350	−0.733093
$405$	−3.89759	−0.193673
$406$	−17.5620	−0.871586
$407$	1.72649	0.0855790
$408$	−1.51314	−0.0749115
$409$	−33.8658	−1.67456	−0.837279	−	0.546776i	$-0.815855\pi$
$409$	−33.8658	−1.67456	−0.837279	+	0.546776i	$0.815855\pi$
$410$	6.93532	0.342511
$411$	−11.7086	−0.577544
$412$	4.69654	0.231382
$413$	1.46051	0.0718670
$414$	3.58900	0.176390
$415$	−18.1625	−0.891561
$416$	−2.07586	−0.101777
$417$	−6.18105	−0.302687
$418$	6.85856	0.335463
$419$	−1.35092	−0.0659967	−0.0329984	−	0.999455i	$-0.510506\pi$
$419$	−1.35092	−0.0659967	−0.0329984	+	0.999455i	$0.510506\pi$
$420$	12.5599	0.612862
$421$	−1.33509	−0.0650682	−0.0325341	−	0.999471i	$-0.510358\pi$
$421$	−1.33509	−0.0650682	−0.0325341	+	0.999471i	$0.510358\pi$
$422$	24.7909	1.20680
$423$	−8.69832	−0.422927
$424$	−0.850418	−0.0412999
$425$	−15.4207	−0.748012
$426$	4.50121	0.218084
$427$	3.22249	0.155947
$428$	−13.3128	−0.643501
$429$	−2.07586	−0.100224
$430$	22.2341	1.07222
$431$	−34.0690	−1.64105	−0.820524	−	0.571612i	$-0.806318\pi$
$431$	−34.0690	−1.64105	−0.820524	+	0.571612i	$0.806318\pi$
$432$	−1.00000	−0.0481125
$433$	−34.6591	−1.66561	−0.832805	−	0.553567i	$-0.813266\pi$
$433$	−34.6591	−1.66561	−0.832805	+	0.553567i	$0.813266\pi$
$434$	8.21675	0.394417
$435$	21.2411	1.01843
$436$	−11.9625	−0.572900
$437$	24.6154	1.17751
$438$	−3.75956	−0.179639
$439$	−26.9234	−1.28498	−0.642491	−	0.766293i	$-0.722099\pi$
$439$	−26.9234	−1.28498	−0.642491	+	0.766293i	$0.722099\pi$
$440$	3.89759	0.185810
$441$	3.38445	0.161164
$442$	3.14107	0.149405
$443$	−3.59603	−0.170853	−0.0854263	−	0.996344i	$-0.527225\pi$
$443$	−3.59603	−0.170853	−0.0854263	+	0.996344i	$0.527225\pi$
$444$	−1.72649	−0.0819357
$445$	−10.1328	−0.480340
$446$	9.40166	0.445182
$447$	0.590452	0.0279274
$448$	3.22249	0.152248
$449$	32.7485	1.54550	0.772749	−	0.634712i	$-0.218881\pi$
$449$	32.7485	1.54550	0.772749	+	0.634712i	$0.218881\pi$
$450$	−10.1912	−0.480416
$451$	1.77939	0.0837882
$452$	10.0074	0.470710
$453$	−20.4142	−0.959142
$454$	−22.4913	−1.05557
$455$	−26.0727	−1.22231
$456$	−6.85856	−0.321182
$457$	19.1457	0.895599	0.447800	−	0.894134i	$-0.352208\pi$
$457$	19.1457	0.895599	0.447800	+	0.894134i	$0.352208\pi$
$458$	7.94879	0.371423
$459$	1.51314	0.0706272
$460$	13.9884	0.652214
$461$	15.6385	0.728356	0.364178	−	0.931329i	$-0.381350\pi$
$461$	15.6385	0.728356	0.364178	+	0.931329i	$0.381350\pi$
$462$	3.22249	0.149924
$463$	−5.46714	−0.254080	−0.127040	−	0.991898i	$-0.540548\pi$
$463$	−5.46714	−0.254080	−0.127040	+	0.991898i	$0.540548\pi$
$464$	5.44981	0.253001
$465$	−9.93812	−0.460869
$466$	16.5993	0.768947
$467$	−21.1830	−0.980235	−0.490117	−	0.871656i	$-0.663046\pi$
$467$	−21.1830	−0.980235	−0.490117	+	0.871656i	$0.663046\pi$
$468$	2.07586	0.0959567
$469$	−12.4033	−0.572729
$470$	−33.9025	−1.56380
$471$	−2.28784	−0.105418
$472$	−0.453224	−0.0208613
$473$	5.70459	0.262297
$474$	14.8761	0.683283
$475$	−69.8968	−3.20709
$476$	−4.87607	−0.223494
$477$	0.850418	0.0389380
$478$	−17.7454	−0.811658
$479$	−20.7740	−0.949189	−0.474595	−	0.880204i	$-0.657405\pi$
$479$	−20.7740	−0.949189	−0.474595	+	0.880204i	$0.657405\pi$
$480$	−3.89759	−0.177900
$481$	3.58396	0.163414
$482$	17.6386	0.803418
$483$	11.5655	0.526249
$484$	1.00000	0.0454545
$485$	−56.8226	−2.58018
$486$	1.00000	0.0453609
$487$	−5.57242	−0.252510	−0.126255	−	0.991998i	$-0.540296\pi$
$487$	−5.57242	−0.252510	−0.126255	+	0.991998i	$0.540296\pi$
$488$	−1.00000	−0.0452679
$489$	0.460681	0.0208327
$490$	13.1912	0.595916
$491$	−39.0277	−1.76130	−0.880649	−	0.473770i	$-0.842893\pi$
$491$	−39.0277	−1.76130	−0.880649	+	0.473770i	$0.842893\pi$
$492$	−1.77939	−0.0802211
$493$	−8.24632	−0.371396
$494$	14.2374	0.640572
$495$	−3.89759	−0.175183
$496$	−2.54981	−0.114490
$497$	14.5051	0.650643
$498$	4.65993	0.208816
$499$	−2.10287	−0.0941374	−0.0470687	−	0.998892i	$-0.514988\pi$
$499$	−2.10287	−0.0941374	−0.0470687	+	0.998892i	$0.514988\pi$
$500$	−20.2330	−0.904849
$501$	21.6773	0.968470
$502$	12.3727	0.552220
$503$	28.5044	1.27095	0.635475	−	0.772122i	$-0.280804\pi$
$503$	28.5044	1.27095	0.635475	+	0.772122i	$0.280804\pi$
$504$	−3.22249	−0.143541
$505$	57.4309	2.55564
$506$	3.58900	0.159550
$507$	8.69080	0.385972
$508$	3.35056	0.148657
$509$	−17.3635	−0.769622	−0.384811	−	0.922995i	$-0.625733\pi$
$509$	−17.3635	−0.769622	−0.384811	+	0.922995i	$0.625733\pi$
$510$	5.89759	0.261149
$511$	−12.1151	−0.535942
$512$	−1.00000	−0.0441942
$513$	6.85856	0.302813
$514$	1.72146	0.0759305
$515$	−18.3052	−0.806622
$516$	−5.70459	−0.251130
$517$	−8.69832	−0.382552
$518$	−5.56360	−0.244451
$519$	15.0723	0.661599
$520$	8.09085	0.354807
$521$	34.8832	1.52826	0.764130	−	0.645062i	$-0.223169\pi$
$521$	34.8832	1.52826	0.764130	+	0.645062i	$0.223169\pi$
$522$	−5.44981	−0.238532
$523$	7.50083	0.327989	0.163994	−	0.986461i	$-0.447562\pi$
$523$	7.50083	0.327989	0.163994	+	0.986461i	$0.447562\pi$
$524$	−13.3096	−0.581431
$525$	−32.8410	−1.43330
$526$	14.2931	0.623210
$527$	3.85822	0.168067
$528$	−1.00000	−0.0435194
$529$	−10.1191	−0.439960
$530$	3.31458	0.143976
$531$	0.453224	0.0196682
$532$	−22.1017	−0.958228
$533$	3.69376	0.159995
$534$	2.59976	0.112503
$535$	51.8880	2.24331
$536$	3.84897	0.166250
$537$	15.6795	0.676619
$538$	−14.3323	−0.617910
$539$	3.38445	0.145778
$540$	3.89759	0.167725
$541$	25.2027	1.08355	0.541775	−	0.840524i	$-0.317753\pi$
$541$	25.2027	1.08355	0.541775	+	0.840524i	$0.317753\pi$
$542$	6.20274	0.266430
$543$	9.65321	0.414259
$544$	1.51314	0.0648753
$545$	46.6249	1.99719
$546$	6.68944	0.286282
$547$	15.3158	0.654858	0.327429	−	0.944876i	$-0.393818\pi$
$547$	15.3158	0.654858	0.327429	+	0.944876i	$0.393818\pi$
$548$	11.7086	0.500167
$549$	1.00000	0.0426790
$550$	−10.1912	−0.434553
$551$	−37.3779	−1.59235
$552$	−3.58900	−0.152758
$553$	47.9382	2.03854
$554$	21.3349	0.906432
$555$	6.72915	0.285636
$556$	6.18105	0.262135
$557$	2.40602	0.101946	0.0509731	−	0.998700i	$-0.483768\pi$
$557$	2.40602	0.101946	0.0509731	+	0.998700i	$0.483768\pi$
$558$	2.54981	0.107942
$559$	11.8419	0.500860
$560$	−12.5599	−0.530754
$561$	1.51314	0.0638847
$562$	−19.9031	−0.839562
$563$	−18.8863	−0.795961	−0.397980	−	0.917394i	$-0.630289\pi$
$563$	−18.8863	−0.795961	−0.397980	+	0.917394i	$0.630289\pi$
$564$	8.69832	0.366265
$565$	−39.0048	−1.64094
$566$	16.6261	0.698845
$567$	3.22249	0.135332
$568$	−4.50121	−0.188867
$569$	9.61033	0.402886	0.201443	−	0.979500i	$-0.435437\pi$
$569$	9.61033	0.402886	0.201443	+	0.979500i	$0.435437\pi$
$570$	26.7318	1.11967
$571$	−5.33709	−0.223350	−0.111675	−	0.993745i	$-0.535622\pi$
$571$	−5.33709	−0.223350	−0.111675	+	0.993745i	$0.535622\pi$
$572$	2.07586	0.0867961
$573$	5.07692	0.212092
$574$	−5.73406	−0.239335
$575$	−36.5761	−1.52533
$576$	1.00000	0.0416667
$577$	−31.1669	−1.29750	−0.648748	−	0.761003i	$-0.724707\pi$
$577$	−31.1669	−1.29750	−0.648748	+	0.761003i	$0.724707\pi$
$578$	14.7104	0.611873
$579$	11.0707	0.460084
$580$	−21.2411	−0.881989
$581$	15.0166	0.622993
$582$	14.5789	0.604316
$583$	0.850418	0.0352207
$584$	3.75956	0.155572
$585$	−8.09085	−0.334515
$586$	2.14124	0.0884540
$587$	36.8738	1.52195	0.760973	−	0.648783i	$-0.224722\pi$
$587$	36.8738	1.52195	0.760973	+	0.648783i	$0.224722\pi$
$588$	−3.38445	−0.139572
$589$	17.4881	0.720583
$590$	1.76648	0.0727248
$591$	1.77134	0.0728631
$592$	1.72649	0.0709584
$593$	39.2908	1.61348	0.806741	−	0.590905i	$-0.201229\pi$
$593$	39.2908	1.61348	0.806741	+	0.590905i	$0.201229\pi$
$594$	1.00000	0.0410305
$595$	19.0049	0.779126
$596$	−0.590452	−0.0241859
$597$	21.3944	0.875614
$598$	7.45027	0.304664
$599$	8.87858	0.362769	0.181385	−	0.983412i	$-0.441942\pi$
$599$	8.87858	0.362769	0.181385	+	0.983412i	$0.441942\pi$
$600$	10.1912	0.416053
$601$	−1.23828	−0.0505104	−0.0252552	−	0.999681i	$-0.508040\pi$
$601$	−1.23828	−0.0505104	−0.0252552	+	0.999681i	$0.508040\pi$
$602$	−18.3830	−0.749234
$603$	−3.84897	−0.156742
$604$	20.4142	0.830642
$605$	−3.89759	−0.158459
$606$	−14.7350	−0.598568
$607$	14.8047	0.600905	0.300453	−	0.953797i	$-0.402862\pi$
$607$	14.8047	0.600905	0.300453	+	0.953797i	$0.402862\pi$
$608$	6.85856	0.278151
$609$	−17.5620	−0.711647
$610$	3.89759	0.157809
$611$	−18.0565	−0.730488
$612$	−1.51314	−0.0611650
$613$	−6.07336	−0.245301	−0.122650	−	0.992450i	$-0.539139\pi$
$613$	−6.07336	−0.245301	−0.122650	+	0.992450i	$0.539139\pi$
$614$	−4.30296	−0.173653
$615$	6.93532	0.279659
$616$	−3.22249	−0.129838
$617$	48.1683	1.93918	0.969591	−	0.244730i	$-0.0786994\pi$
$617$	48.1683	1.93918	0.969591	+	0.244730i	$0.0786994\pi$
$618$	4.69654	0.188922
$619$	−42.6627	−1.71476	−0.857379	−	0.514685i	$-0.827909\pi$
$619$	−42.6627	−1.71476	−0.857379	+	0.514685i	$0.827909\pi$
$620$	9.93812	0.399124
$621$	3.58900	0.144022
$622$	−28.9086	−1.15913
$623$	8.37770	0.335645
$624$	−2.07586	−0.0831010
$625$	27.9041	1.11617
$626$	1.72907	0.0691076
$627$	6.85856	0.273905
$628$	2.28784	0.0912947
$629$	−2.61242	−0.104164
$630$	12.5599	0.500400
$631$	19.0610	0.758806	0.379403	−	0.925231i	$-0.376129\pi$
$631$	19.0610	0.758806	0.379403	+	0.925231i	$0.376129\pi$
$632$	−14.8761	−0.591741
$633$	24.7909	0.985351
$634$	−7.18518	−0.285360
$635$	−13.0591	−0.518235
$636$	−0.850418	−0.0337213
$637$	7.02564	0.278366
$638$	−5.44981	−0.215760
$639$	4.50121	0.178065
$640$	3.89759	0.154066
$641$	−15.9727	−0.630884	−0.315442	−	0.948945i	$-0.602153\pi$
$641$	−15.9727	−0.630884	−0.315442	+	0.948945i	$0.602153\pi$
$642$	−13.3128	−0.525416
$643$	−3.81730	−0.150539	−0.0752697	−	0.997163i	$-0.523982\pi$
$643$	−3.81730	−0.150539	−0.0752697	+	0.997163i	$0.523982\pi$
$644$	−11.5655	−0.455745
$645$	22.2341	0.875468
$646$	−10.3780	−0.408315
$647$	34.9045	1.37224	0.686118	−	0.727490i	$-0.259313\pi$
$647$	34.9045	1.37224	0.686118	+	0.727490i	$0.259313\pi$
$648$	−1.00000	−0.0392837
$649$	0.453224	0.0177906
$650$	−21.1555	−0.829785
$651$	8.21675	0.322040
$652$	−0.460681	−0.0180417
$653$	−35.2453	−1.37926	−0.689628	−	0.724164i	$-0.742226\pi$
$653$	−35.2453	−1.37926	−0.689628	+	0.724164i	$0.742226\pi$
$654$	−11.9625	−0.467771
$655$	51.8752	2.02693
$656$	1.77939	0.0694735
$657$	−3.75956	−0.146674
$658$	28.0303	1.09273
$659$	−33.0638	−1.28798	−0.643992	−	0.765032i	$-0.722723\pi$
$659$	−33.0638	−1.28798	−0.643992	+	0.765032i	$0.722723\pi$
$660$	3.89759	0.151713
$661$	10.3884	0.404061	0.202030	−	0.979379i	$-0.435246\pi$
$661$	10.3884	0.404061	0.202030	+	0.979379i	$0.435246\pi$
$662$	12.7264	0.494626
$663$	3.14107	0.121989
$664$	−4.65993	−0.180840
$665$	86.1431	3.34049
$666$	−1.72649	−0.0669002
$667$	−19.5594	−0.757342
$668$	−21.6773	−0.838720
$669$	9.40166	0.363489
$670$	−15.0017	−0.579565
$671$	1.00000	0.0386046
$672$	3.22249	0.124310
$673$	11.7662	0.453555	0.226778	−	0.973947i	$-0.427181\pi$
$673$	11.7662	0.453555	0.226778	+	0.973947i	$0.427181\pi$
$674$	4.66583	0.179721
$675$	−10.1912	−0.392258
$676$	−8.69080	−0.334262
$677$	−12.7267	−0.489127	−0.244564	−	0.969633i	$-0.578645\pi$
$677$	−12.7267	−0.489127	−0.244564	+	0.969633i	$0.578645\pi$
$678$	10.0074	0.384333
$679$	46.9805	1.80295
$680$	−5.89759	−0.226162
$681$	−22.4913	−0.861869
$682$	2.54981	0.0976374
$683$	−3.53977	−0.135446	−0.0677228	−	0.997704i	$-0.521573\pi$
$683$	−3.53977	−0.135446	−0.0677228	+	0.997704i	$0.521573\pi$
$684$	−6.85856	−0.262244
$685$	−45.6353	−1.74364
$686$	11.6511	0.444841
$687$	7.94879	0.303265
$688$	5.70459	0.217485
$689$	1.76535	0.0672545
$690$	13.9884	0.532531
$691$	9.38436	0.356998	0.178499	−	0.983940i	$-0.442876\pi$
$691$	9.38436	0.356998	0.178499	+	0.983940i	$0.442876\pi$
$692$	−15.0723	−0.572962
$693$	3.22249	0.122412
$694$	9.92619	0.376793
$695$	−24.0912	−0.913830
$696$	5.44981	0.206575
$697$	−2.69246	−0.101984
$698$	−11.7514	−0.444797
$699$	16.5993	0.627843
$700$	32.8410	1.24127
$701$	−29.1090	−1.09943	−0.549715	−	0.835352i	$-0.685264\pi$
$701$	−29.1090	−1.09943	−0.549715	+	0.835352i	$0.685264\pi$
$702$	2.07586	0.0783483
$703$	−11.8413	−0.446601
$704$	1.00000	0.0376889
$705$	−33.9025	−1.27684
$706$	5.29458	0.199264
$707$	−47.4834	−1.78580
$708$	−0.453224	−0.0170332
$709$	23.5909	0.885976	0.442988	−	0.896527i	$-0.353918\pi$
$709$	23.5909	0.885976	0.442988	+	0.896527i	$0.353918\pi$
$710$	17.5439	0.658409
$711$	14.8761	0.557898
$712$	−2.59976	−0.0974300
$713$	9.15128	0.342718
$714$	−4.87607	−0.182482
$715$	−8.09085	−0.302581
$716$	−15.6795	−0.585969
$717$	−17.7454	−0.662716
$718$	12.0185	0.448528
$719$	−38.8017	−1.44706	−0.723530	−	0.690293i	$-0.757482\pi$
$719$	−38.8017	−1.44706	−0.723530	+	0.690293i	$0.757482\pi$
$720$	−3.89759	−0.145254
$721$	15.1346	0.563640
$722$	−28.0399	−1.04354
$723$	17.6386	0.655988
$724$	−9.65321	−0.358759
$725$	55.5400	2.06270
$726$	1.00000	0.0371135
$727$	−43.1096	−1.59885	−0.799424	−	0.600768i	$-0.794862\pi$
$727$	−43.1096	−1.59885	−0.799424	+	0.600768i	$0.794862\pi$
$728$	−6.68944	−0.247927
$729$	1.00000	0.0370370
$730$	−14.6532	−0.542339
$731$	−8.63183	−0.319260
$732$	−1.00000	−0.0369611
$733$	5.73545	0.211844	0.105922	−	0.994374i	$-0.466221\pi$
$733$	5.73545	0.211844	0.105922	+	0.994374i	$0.466221\pi$
$734$	−10.3670	−0.382654
$735$	13.1912	0.486564
$736$	3.58900	0.132292
$737$	−3.84897	−0.141778
$738$	−1.77939	−0.0655002
$739$	−25.3818	−0.933686	−0.466843	−	0.884340i	$-0.654609\pi$
$739$	−25.3818	−0.933686	−0.466843	+	0.884340i	$0.654609\pi$
$740$	−6.72915	−0.247368
$741$	14.2374	0.523025
$742$	−2.74046	−0.100606
$743$	13.2309	0.485395	0.242698	−	0.970102i	$-0.421968\pi$
$743$	13.2309	0.485395	0.242698	+	0.970102i	$0.421968\pi$
$744$	−2.54981	−0.0934807
$745$	2.30134	0.0843145
$746$	21.3809	0.782811
$747$	4.65993	0.170498
$748$	−1.51314	−0.0553258
$749$	−42.9005	−1.56755
$750$	−20.2330	−0.738806
$751$	−50.4199	−1.83985	−0.919925	−	0.392096i	$-0.871750\pi$
$751$	−50.4199	−1.83985	−0.919925	+	0.392096i	$0.871750\pi$
$752$	−8.69832	−0.317195
$753$	12.3727	0.450886
$754$	−11.3131	−0.411997
$755$	−79.5660	−2.89570
$756$	−3.22249	−0.117201
$757$	24.3579	0.885302	0.442651	−	0.896694i	$-0.354038\pi$
$757$	24.3579	0.885302	0.442651	+	0.896694i	$0.354038\pi$
$758$	−7.09080	−0.257549
$759$	3.58900	0.130272
$760$	−26.7318	−0.969666
$761$	−26.6485	−0.966008	−0.483004	−	0.875618i	$-0.660454\pi$
$761$	−26.6485	−0.966008	−0.483004	+	0.875618i	$0.660454\pi$
$762$	3.35056	0.121378
$763$	−38.5491	−1.39557
$764$	−5.07692	−0.183677
$765$	5.89759	0.213228
$766$	−11.8909	−0.429637
$767$	0.940830	0.0339714
$768$	−1.00000	−0.0360844
$769$	18.1640	0.655010	0.327505	−	0.944850i	$-0.393792\pi$
$769$	18.1640	0.655010	0.327505	+	0.944850i	$0.393792\pi$
$770$	12.5599	0.452629
$771$	1.72146	0.0619970
$772$	−11.0707	−0.398444
$773$	−21.3774	−0.768891	−0.384445	−	0.923148i	$-0.625607\pi$
$773$	−21.3774	−0.768891	−0.384445	+	0.923148i	$0.625607\pi$
$774$	−5.70459	−0.205047
$775$	−25.9856	−0.933430
$776$	−14.5789	−0.523353
$777$	−5.56360	−0.199593
$778$	17.7582	0.636662
$779$	−12.2041	−0.437256
$780$	8.09085	0.289699
$781$	4.50121	0.161066
$782$	−5.43065	−0.194200
$783$	−5.44981	−0.194760
$784$	3.38445	0.120873
$785$	−8.91705	−0.318263
$786$	−13.3096	−0.474737
$787$	13.4549	0.479616	0.239808	−	0.970820i	$-0.422916\pi$
$787$	13.4549	0.479616	0.239808	+	0.970820i	$0.422916\pi$
$788$	−1.77134	−0.0631013
$789$	14.2931	0.508849
$790$	57.9810	2.06287
$791$	32.2488	1.14664
$792$	−1.00000	−0.0355335
$793$	2.07586	0.0737160
$794$	18.2520	0.647741
$795$	3.31458	0.117556
$796$	−21.3944	−0.758304
$797$	29.7655	1.05435	0.527174	−	0.849757i	$-0.323252\pi$
$797$	29.7655	1.05435	0.527174	+	0.849757i	$0.323252\pi$
$798$	−22.1017	−0.782390
$799$	13.1618	0.465630
$800$	−10.1912	−0.360312
$801$	2.59976	0.0918579
$802$	−16.6878	−0.589268
$803$	−3.75956	−0.132672
$804$	3.84897	0.135743
$805$	45.0776	1.58878
$806$	5.29306	0.186440
$807$	−14.3323	−0.504522
$808$	14.7350	0.518375
$809$	−36.7455	−1.29190	−0.645951	−	0.763379i	$-0.723539\pi$
$809$	−36.7455	−1.29190	−0.645951	+	0.763379i	$0.723539\pi$
$810$	3.89759	0.136947
$811$	4.08944	0.143600	0.0717998	−	0.997419i	$-0.477126\pi$
$811$	4.08944	0.143600	0.0717998	+	0.997419i	$0.477126\pi$
$812$	17.5620	0.616305
$813$	6.20274	0.217540
$814$	−1.72649	−0.0605135
$815$	1.79554	0.0628951
$816$	1.51314	0.0529704
$817$	−39.1253	−1.36882
$818$	33.8658	1.18409
$819$	6.68944	0.233748
$820$	−6.93532	−0.242192
$821$	20.9394	0.730791	0.365395	−	0.930852i	$-0.380934\pi$
$821$	20.9394	0.730791	0.365395	+	0.930852i	$0.380934\pi$
$822$	11.7086	0.408385
$823$	−40.2885	−1.40437	−0.702185	−	0.711995i	$-0.747792\pi$
$823$	−40.2885	−1.40437	−0.702185	+	0.711995i	$0.747792\pi$
$824$	−4.69654	−0.163612
$825$	−10.1912	−0.354811
$826$	−1.46051	−0.0508176
$827$	34.9663	1.21590	0.607949	−	0.793976i	$-0.291992\pi$
$827$	34.9663	1.21590	0.607949	+	0.793976i	$0.291992\pi$
$828$	−3.58900	−0.124726
$829$	5.13468	0.178335	0.0891674	−	0.996017i	$-0.471579\pi$
$829$	5.13468	0.178335	0.0891674	+	0.996017i	$0.471579\pi$
$830$	18.1625	0.630429
$831$	21.3349	0.740098
$832$	2.07586	0.0719675
$833$	−5.12114	−0.177437
$834$	6.18105	0.214032
$835$	84.4891	2.92387
$836$	−6.85856	−0.237208
$837$	2.54981	0.0881344
$838$	1.35092	0.0466667
$839$	−51.9876	−1.79481	−0.897406	−	0.441205i	$-0.854551\pi$
$839$	−51.9876	−1.79481	−0.897406	+	0.441205i	$0.854551\pi$
$840$	−12.5599	−0.433359
$841$	0.700476	0.0241544
$842$	1.33509	0.0460102
$843$	−19.9031	−0.685500
$844$	−24.7909	−0.853339
$845$	33.8731	1.16527
$846$	8.69832	0.299054
$847$	3.22249	0.110726
$848$	0.850418	0.0292035
$849$	16.6261	0.570605
$850$	15.4207	0.528924
$851$	−6.19638	−0.212409
$852$	−4.50121	−0.154209
$853$	−14.6916	−0.503031	−0.251515	−	0.967853i	$-0.580929\pi$
$853$	−14.6916	−0.503031	−0.251515	+	0.967853i	$0.580929\pi$
$854$	−3.22249	−0.110271
$855$	26.7318	0.914209
$856$	13.3128	0.455024
$857$	25.2305	0.861859	0.430930	−	0.902386i	$-0.358186\pi$
$857$	25.2305	0.861859	0.430930	+	0.902386i	$0.358186\pi$
$858$	2.07586	0.0708687
$859$	25.2166	0.860380	0.430190	−	0.902738i	$-0.358446\pi$
$859$	25.2166	0.860380	0.430190	+	0.902738i	$0.358446\pi$
$860$	−22.2341	−0.758177
$861$	−5.73406	−0.195416
$862$	34.0690	1.16040
$863$	25.7307	0.875883	0.437941	−	0.899003i	$-0.355708\pi$
$863$	25.7307	0.875883	0.437941	+	0.899003i	$0.355708\pi$
$864$	1.00000	0.0340207
$865$	58.7455	1.99741
$866$	34.6591	1.17776
$867$	14.7104	0.499592
$868$	−8.21675	−0.278895
$869$	14.8761	0.504638
$870$	−21.2411	−0.720141
$871$	−7.98992	−0.270728
$872$	11.9625	0.405102
$873$	14.5789	0.493422
$874$	−24.6154	−0.832628
$875$	−65.2008	−2.20419
$876$	3.75956	0.127024
$877$	8.65072	0.292114	0.146057	−	0.989276i	$-0.453342\pi$
$877$	8.65072	0.292114	0.146057	+	0.989276i	$0.453342\pi$
$878$	26.9234	0.908620
$879$	2.14124	0.0722224
$880$	−3.89759	−0.131388
$881$	−17.5540	−0.591410	−0.295705	−	0.955279i	$-0.595555\pi$
$881$	−17.5540	−0.591410	−0.295705	+	0.955279i	$0.595555\pi$
$882$	−3.38445	−0.113960
$883$	−0.713625	−0.0240154	−0.0120077	−	0.999928i	$-0.503822\pi$
$883$	−0.713625	−0.0240154	−0.0120077	+	0.999928i	$0.503822\pi$
$884$	−3.14107	−0.105645
$885$	1.76648	0.0593796
$886$	3.59603	0.120811
$887$	45.5702	1.53010	0.765049	−	0.643972i	$-0.222715\pi$
$887$	45.5702	1.53010	0.765049	+	0.643972i	$0.222715\pi$
$888$	1.72649	0.0579373
$889$	10.7972	0.362125
$890$	10.1328	0.339652
$891$	1.00000	0.0335013
$892$	−9.40166	−0.314791
$893$	59.6580	1.99638
$894$	−0.590452	−0.0197477
$895$	61.1121	2.04275
$896$	−3.22249	−0.107656
$897$	7.45027	0.248757
$898$	−32.7485	−1.09283
$899$	−13.8960	−0.463458
$900$	10.1912	0.339706
$901$	−1.28680	−0.0428695
$902$	−1.77939	−0.0592472
$903$	−18.3830	−0.611747
$904$	−10.0074	−0.332842
$905$	37.6242	1.25067
$906$	20.4142	0.678216
$907$	−16.7796	−0.557156	−0.278578	−	0.960414i	$-0.589863\pi$
$907$	−16.7796	−0.557156	−0.278578	+	0.960414i	$0.589863\pi$
$908$	22.4913	0.746400
$909$	−14.7350	−0.488729
$910$	26.0727	0.864301
$911$	−21.2862	−0.705244	−0.352622	−	0.935766i	$-0.614710\pi$
$911$	−21.2862	−0.705244	−0.352622	+	0.935766i	$0.614710\pi$
$912$	6.85856	0.227110
$913$	4.65993	0.154221
$914$	−19.1457	−0.633284
$915$	3.89759	0.128850
$916$	−7.94879	−0.262635
$917$	−42.8900	−1.41635
$918$	−1.51314	−0.0499410
$919$	−49.8181	−1.64335	−0.821674	−	0.569958i	$-0.806959\pi$
$919$	−49.8181	−1.64335	−0.821674	+	0.569958i	$0.806959\pi$
$920$	−13.9884	−0.461185
$921$	−4.30296	−0.141787
$922$	−15.6385	−0.515026
$923$	9.34389	0.307558
$924$	−3.22249	−0.106012
$925$	17.5950	0.578519
$926$	5.46714	0.179662
$927$	4.69654	0.154255
$928$	−5.44981	−0.178899
$929$	−47.4351	−1.55629	−0.778147	−	0.628082i	$-0.783840\pi$
$929$	−47.4351	−1.55629	−0.778147	+	0.628082i	$0.783840\pi$
$930$	9.93812	0.325884
$931$	−23.2124	−0.760757
$932$	−16.5993	−0.543728
$933$	−28.9086	−0.946427
$934$	21.1830	0.693131
$935$	5.89759	0.192872
$936$	−2.07586	−0.0678517
$937$	58.2545	1.90309	0.951547	−	0.307505i	$-0.0994940\pi$
$937$	58.2545	1.90309	0.951547	+	0.307505i	$0.0994940\pi$
$938$	12.4033	0.404981
$939$	1.72907	0.0564261
$940$	33.9025	1.10578
$941$	31.2520	1.01879	0.509393	−	0.860534i	$-0.329870\pi$
$941$	31.2520	1.01879	0.509393	+	0.860534i	$0.329870\pi$
$942$	2.28784	0.0745418
$943$	−6.38623	−0.207964
$944$	0.453224	0.0147512
$945$	12.5599	0.408575
$946$	−5.70459	−0.185472
$947$	−2.25148	−0.0731633	−0.0365817	−	0.999331i	$-0.511647\pi$
$947$	−2.25148	−0.0731633	−0.0365817	+	0.999331i	$0.511647\pi$
$948$	−14.8761	−0.483154
$949$	−7.80432	−0.253339
$950$	69.8968	2.26775
$951$	−7.18518	−0.232996
$952$	4.87607	0.158034
$953$	12.5395	0.406193	0.203097	−	0.979159i	$-0.434899\pi$
$953$	12.5395	0.406193	0.203097	+	0.979159i	$0.434899\pi$
$954$	−0.850418	−0.0275333
$955$	19.7877	0.640316
$956$	17.7454	0.573929
$957$	−5.44981	−0.176167
$958$	20.7740	0.671178
$959$	37.7309	1.21839
$960$	3.89759	0.125794
$961$	−24.4985	−0.790273
$962$	−3.58396	−0.115551
$963$	−13.3128	−0.429000
$964$	−17.6386	−0.568103
$965$	43.1491	1.38902
$966$	−11.5655	−0.372114
$967$	−7.81418	−0.251287	−0.125643	−	0.992075i	$-0.540100\pi$
$967$	−7.81418	−0.251287	−0.125643	+	0.992075i	$0.540100\pi$
$968$	−1.00000	−0.0321412
$969$	−10.3780	−0.333388
$970$	56.8226	1.82446
$971$	−55.0844	−1.76774	−0.883872	−	0.467729i	$-0.845072\pi$
$971$	−55.0844	−1.76774	−0.883872	+	0.467729i	$0.845072\pi$
$972$	−1.00000	−0.0320750
$973$	19.9184	0.638554
$974$	5.57242	0.178552
$975$	−21.1555	−0.677517
$976$	1.00000	0.0320092
$977$	32.4028	1.03666	0.518328	−	0.855182i	$-0.326555\pi$
$977$	32.4028	1.03666	0.518328	+	0.855182i	$0.326555\pi$
$978$	−0.460681	−0.0147310
$979$	2.59976	0.0830886
$980$	−13.1912	−0.421377
$981$	−11.9625	−0.381934
$982$	39.0277	1.24543
$983$	5.25985	0.167763	0.0838816	−	0.996476i	$-0.473268\pi$
$983$	5.25985	0.167763	0.0838816	+	0.996476i	$0.473268\pi$
$984$	1.77939	0.0567249
$985$	6.90394	0.219978
$986$	8.24632	0.262616
$987$	28.0303	0.892213
$988$	−14.2374	−0.452953
$989$	−20.4738	−0.651028
$990$	3.89759	0.123873
$991$	38.0331	1.20816	0.604081	−	0.796923i	$-0.293540\pi$
$991$	38.0331	1.20816	0.604081	+	0.796923i	$0.293540\pi$
$992$	2.54981	0.0809567
$993$	12.7264	0.403861
$994$	−14.5051	−0.460074
$995$	83.3865	2.64353
$996$	−4.65993	−0.147656
$997$	49.5468	1.56916	0.784581	−	0.620026i	$-0.212878\pi$
$997$	49.5468	1.56916	0.784581	+	0.620026i	$0.212878\pi$
$998$	2.10287	0.0665652
$999$	−1.72649	−0.0546238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.w.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.w.1.1	✓	6	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89759 q^{5} +1.00000 q^{6} +3.22249 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.89759 q^{5} +1.00000 q^{6} +3.22249 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.89759 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.07586 q^{13} -3.22249 q^{14} +3.89759 q^{15} +1.00000 q^{16} -1.51314 q^{17} -1.00000 q^{18} -6.85856 q^{19} -3.89759 q^{20} -3.22249 q^{21} -1.00000 q^{22} -3.58900 q^{23} +1.00000 q^{24} +10.1912 q^{25} -2.07586 q^{26} -1.00000 q^{27} +3.22249 q^{28} +5.44981 q^{29} -3.89759 q^{30} -2.54981 q^{31} -1.00000 q^{32} -1.00000 q^{33} +1.51314 q^{34} -12.5599 q^{35} +1.00000 q^{36} +1.72649 q^{37} +6.85856 q^{38} -2.07586 q^{39} +3.89759 q^{40} +1.77939 q^{41} +3.22249 q^{42} +5.70459 q^{43} +1.00000 q^{44} -3.89759 q^{45} +3.58900 q^{46} -8.69832 q^{47} -1.00000 q^{48} +3.38445 q^{49} -10.1912 q^{50} +1.51314 q^{51} +2.07586 q^{52} +0.850418 q^{53} +1.00000 q^{54} -3.89759 q^{55} -3.22249 q^{56} +6.85856 q^{57} -5.44981 q^{58} +0.453224 q^{59} +3.89759 q^{60} +1.00000 q^{61} +2.54981 q^{62} +3.22249 q^{63} +1.00000 q^{64} -8.09085 q^{65} +1.00000 q^{66} -3.84897 q^{67} -1.51314 q^{68} +3.58900 q^{69} +12.5599 q^{70} +4.50121 q^{71} -1.00000 q^{72} -3.75956 q^{73} -1.72649 q^{74} -10.1912 q^{75} -6.85856 q^{76} +3.22249 q^{77} +2.07586 q^{78} +14.8761 q^{79} -3.89759 q^{80} +1.00000 q^{81} -1.77939 q^{82} +4.65993 q^{83} -3.22249 q^{84} +5.89759 q^{85} -5.70459 q^{86} -5.44981 q^{87} -1.00000 q^{88} +2.59976 q^{89} +3.89759 q^{90} +6.68944 q^{91} -3.58900 q^{92} +2.54981 q^{93} +8.69832 q^{94} +26.7318 q^{95} +1.00000 q^{96} +14.5789 q^{97} -3.38445 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * q^98 + 6 * q^99

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