LMFDB - Embedded newform 4026.2.a.bb.1.5

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 $ x^8 - 3x^7 - 22x^6 + 42x^5 + 182x^4 - 111x^3 - 538x^2 - 256*x - 32
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			1.5
Root			$-2.68569$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.94066 q^{5} +1.00000 q^{6} +4.68569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.94066 q^{5} +1.00000 q^{6} +4.68569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.94066 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.54296 q^{13} +4.68569 q^{14} +1.94066 q^{15} +1.00000 q^{16} -4.52111 q^{17} +1.00000 q^{18} -6.57912 q^{19} +1.94066 q^{20} +4.68569 q^{21} -1.00000 q^{22} +2.30849 q^{23} +1.00000 q^{24} -1.23385 q^{25} +3.54296 q^{26} +1.00000 q^{27} +4.68569 q^{28} +8.87158 q^{29} +1.94066 q^{30} -2.24915 q^{31} +1.00000 q^{32} -1.00000 q^{33} -4.52111 q^{34} +9.09332 q^{35} +1.00000 q^{36} +10.2387 q^{37} -6.57912 q^{38} +3.54296 q^{39} +1.94066 q^{40} +3.95278 q^{41} +4.68569 q^{42} -12.8057 q^{43} -1.00000 q^{44} +1.94066 q^{45} +2.30849 q^{46} -9.63852 q^{47} +1.00000 q^{48} +14.9557 q^{49} -1.23385 q^{50} -4.52111 q^{51} +3.54296 q^{52} +1.32122 q^{53} +1.00000 q^{54} -1.94066 q^{55} +4.68569 q^{56} -6.57912 q^{57} +8.87158 q^{58} -2.76033 q^{59} +1.94066 q^{60} +1.00000 q^{61} -2.24915 q^{62} +4.68569 q^{63} +1.00000 q^{64} +6.87566 q^{65} -1.00000 q^{66} -7.05220 q^{67} -4.52111 q^{68} +2.30849 q^{69} +9.09332 q^{70} -4.17995 q^{71} +1.00000 q^{72} +14.6272 q^{73} +10.2387 q^{74} -1.23385 q^{75} -6.57912 q^{76} -4.68569 q^{77} +3.54296 q^{78} +1.12670 q^{79} +1.94066 q^{80} +1.00000 q^{81} +3.95278 q^{82} +2.01082 q^{83} +4.68569 q^{84} -8.77391 q^{85} -12.8057 q^{86} +8.87158 q^{87} -1.00000 q^{88} -16.3921 q^{89} +1.94066 q^{90} +16.6012 q^{91} +2.30849 q^{92} -2.24915 q^{93} -9.63852 q^{94} -12.7678 q^{95} +1.00000 q^{96} +3.05621 q^{97} +14.9557 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * 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
$5$	1.94066	0.867888	0.433944	−	0.900940i	$-0.357122\pi$
$5$	1.94066	0.867888	0.433944	+	0.900940i	$0.357122\pi$
$6$	1.00000	0.408248
$7$	4.68569	1.77103	0.885513	−	0.464615i	$-0.153807\pi$
$7$	4.68569	1.77103	0.885513	+	0.464615i	$0.153807\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.94066	0.613689
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	3.54296	0.982640	0.491320	−	0.870979i	$-0.336515\pi$
$13$	3.54296	0.982640	0.491320	+	0.870979i	$0.336515\pi$
$14$	4.68569	1.25230
$15$	1.94066	0.501075
$16$	1.00000	0.250000
$17$	−4.52111	−1.09653	−0.548265	−	0.836305i	$-0.684711\pi$
$17$	−4.52111	−1.09653	−0.548265	+	0.836305i	$0.684711\pi$
$18$	1.00000	0.235702
$19$	−6.57912	−1.50935	−0.754677	−	0.656096i	$-0.772207\pi$
$19$	−6.57912	−1.50935	−0.754677	+	0.656096i	$0.772207\pi$
$20$	1.94066	0.433944
$21$	4.68569	1.02250
$22$	−1.00000	−0.213201
$23$	2.30849	0.481354	0.240677	−	0.970605i	$-0.422630\pi$
$23$	2.30849	0.481354	0.240677	+	0.970605i	$0.422630\pi$
$24$	1.00000	0.204124
$25$	−1.23385	−0.246771
$26$	3.54296	0.694831
$27$	1.00000	0.192450
$28$	4.68569	0.885513
$29$	8.87158	1.64741	0.823706	−	0.567018i	$-0.191903\pi$
$29$	8.87158	1.64741	0.823706	+	0.567018i	$0.191903\pi$
$30$	1.94066	0.354314
$31$	−2.24915	−0.403959	−0.201980	−	0.979390i	$-0.564737\pi$
$31$	−2.24915	−0.403959	−0.201980	+	0.979390i	$0.564737\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−4.52111	−0.775364
$35$	9.09332	1.53705
$36$	1.00000	0.166667
$37$	10.2387	1.68324	0.841619	−	0.540071i	$-0.181603\pi$
$37$	10.2387	1.68324	0.841619	+	0.540071i	$0.181603\pi$
$38$	−6.57912	−1.06727
$39$	3.54296	0.567327
$40$	1.94066	0.306845
$41$	3.95278	0.617320	0.308660	−	0.951172i	$-0.400120\pi$
$41$	3.95278	0.617320	0.308660	+	0.951172i	$0.400120\pi$
$42$	4.68569	0.723018
$43$	−12.8057	−1.95286	−0.976429	−	0.215840i	$-0.930751\pi$
$43$	−12.8057	−1.95286	−0.976429	+	0.215840i	$0.930751\pi$
$44$	−1.00000	−0.150756
$45$	1.94066	0.289296
$46$	2.30849	0.340369
$47$	−9.63852	−1.40592	−0.702961	−	0.711228i	$-0.748139\pi$
$47$	−9.63852	−1.40592	−0.702961	+	0.711228i	$0.748139\pi$
$48$	1.00000	0.144338
$49$	14.9557	2.13653
$50$	−1.23385	−0.174493
$51$	−4.52111	−0.633082
$52$	3.54296	0.491320
$53$	1.32122	0.181484	0.0907419	−	0.995874i	$-0.471076\pi$
$53$	1.32122	0.181484	0.0907419	+	0.995874i	$0.471076\pi$
$54$	1.00000	0.136083
$55$	−1.94066	−0.261678
$56$	4.68569	0.626152
$57$	−6.57912	−0.871426
$58$	8.87158	1.16490
$59$	−2.76033	−0.359365	−0.179682	−	0.983725i	$-0.557507\pi$
$59$	−2.76033	−0.359365	−0.179682	+	0.983725i	$0.557507\pi$
$60$	1.94066	0.250538
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−2.24915	−0.285642
$63$	4.68569	0.590342
$64$	1.00000	0.125000
$65$	6.87566	0.852821
$66$	−1.00000	−0.123091
$67$	−7.05220	−0.861564	−0.430782	−	0.902456i	$-0.641762\pi$
$67$	−7.05220	−0.861564	−0.430782	+	0.902456i	$0.641762\pi$
$68$	−4.52111	−0.548265
$69$	2.30849	0.277910
$70$	9.09332	1.08686
$71$	−4.17995	−0.496069	−0.248034	−	0.968751i	$-0.579785\pi$
$71$	−4.17995	−0.496069	−0.248034	+	0.968751i	$0.579785\pi$
$72$	1.00000	0.117851
$73$	14.6272	1.71198	0.855989	−	0.516993i	$-0.172949\pi$
$73$	14.6272	1.71198	0.855989	+	0.516993i	$0.172949\pi$
$74$	10.2387	1.19023
$75$	−1.23385	−0.142473
$76$	−6.57912	−0.754677
$77$	−4.68569	−0.533984
$78$	3.54296	0.401161
$79$	1.12670	0.126763	0.0633817	−	0.997989i	$-0.479811\pi$
$79$	1.12670	0.126763	0.0633817	+	0.997989i	$0.479811\pi$
$80$	1.94066	0.216972
$81$	1.00000	0.111111
$82$	3.95278	0.436511
$83$	2.01082	0.220716	0.110358	−	0.993892i	$-0.464800\pi$
$83$	2.01082	0.220716	0.110358	+	0.993892i	$0.464800\pi$
$84$	4.68569	0.511251
$85$	−8.77391	−0.951665
$86$	−12.8057	−1.38088
$87$	8.87158	0.951133
$88$	−1.00000	−0.106600
$89$	−16.3921	−1.73756	−0.868779	−	0.495201i	$-0.835094\pi$
$89$	−16.3921	−1.73756	−0.868779	+	0.495201i	$0.835094\pi$
$90$	1.94066	0.204563
$91$	16.6012	1.74028
$92$	2.30849	0.240677
$93$	−2.24915	−0.233226
$94$	−9.63852	−0.994137
$95$	−12.7678	−1.30995
$96$	1.00000	0.102062
$97$	3.05621	0.310311	0.155156	−	0.987890i	$-0.450412\pi$
$97$	3.05621	0.310311	0.155156	+	0.987890i	$0.450412\pi$
$98$	14.9557	1.51076
$99$	−1.00000	−0.100504
$100$	−1.23385	−0.123385
$101$	−18.8931	−1.87993	−0.939966	−	0.341268i	$-0.889144\pi$
$101$	−18.8931	−1.87993	−0.939966	+	0.341268i	$0.889144\pi$
$102$	−4.52111	−0.447656
$103$	2.51786	0.248092	0.124046	−	0.992276i	$-0.460413\pi$
$103$	2.51786	0.248092	0.124046	+	0.992276i	$0.460413\pi$
$104$	3.54296	0.347416
$105$	9.09332	0.887417
$106$	1.32122	0.128328
$107$	0.804104	0.0777356	0.0388678	−	0.999244i	$-0.487625\pi$
$107$	0.804104	0.0777356	0.0388678	+	0.999244i	$0.487625\pi$
$108$	1.00000	0.0962250
$109$	−12.6101	−1.20783	−0.603913	−	0.797051i	$-0.706392\pi$
$109$	−12.6101	−1.20783	−0.603913	+	0.797051i	$0.706392\pi$
$110$	−1.94066	−0.185034
$111$	10.2387	0.971818
$112$	4.68569	0.442756
$113$	−2.76273	−0.259896	−0.129948	−	0.991521i	$-0.541481\pi$
$113$	−2.76273	−0.259896	−0.129948	+	0.991521i	$0.541481\pi$
$114$	−6.57912	−0.616191
$115$	4.47999	0.417762
$116$	8.87158	0.823706
$117$	3.54296	0.327547
$118$	−2.76033	−0.254109
$119$	−21.1845	−1.94198
$120$	1.94066	0.177157
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	3.95278	0.356410
$124$	−2.24915	−0.201980
$125$	−12.0978	−1.08206
$126$	4.68569	0.417435
$127$	−7.83021	−0.694819	−0.347409	−	0.937714i	$-0.612939\pi$
$127$	−7.83021	−0.694819	−0.347409	+	0.937714i	$0.612939\pi$
$128$	1.00000	0.0883883
$129$	−12.8057	−1.12748
$130$	6.87566	0.603035
$131$	0.294983	0.0257728	0.0128864	−	0.999917i	$-0.495898\pi$
$131$	0.294983	0.0257728	0.0128864	+	0.999917i	$0.495898\pi$
$132$	−1.00000	−0.0870388
$133$	−30.8277	−2.67310
$134$	−7.05220	−0.609217
$135$	1.94066	0.167025
$136$	−4.52111	−0.387682
$137$	−6.63420	−0.566798	−0.283399	−	0.959002i	$-0.591462\pi$
$137$	−6.63420	−0.566798	−0.283399	+	0.959002i	$0.591462\pi$
$138$	2.30849	0.196512
$139$	21.7689	1.84642	0.923209	−	0.384298i	$-0.125557\pi$
$139$	21.7689	1.84642	0.923209	+	0.384298i	$0.125557\pi$
$140$	9.09332	0.768526
$141$	−9.63852	−0.811710
$142$	−4.17995	−0.350774
$143$	−3.54296	−0.296277
$144$	1.00000	0.0833333
$145$	17.2167	1.42977
$146$	14.6272	1.21055
$147$	14.9557	1.23353
$148$	10.2387	0.841619
$149$	−15.9373	−1.30563	−0.652816	−	0.757516i	$-0.726413\pi$
$149$	−15.9373	−1.30563	−0.652816	+	0.757516i	$0.726413\pi$
$150$	−1.23385	−0.100744
$151$	−0.395019	−0.0321462	−0.0160731	−	0.999871i	$-0.505116\pi$
$151$	−0.395019	−0.0321462	−0.0160731	+	0.999871i	$0.505116\pi$
$152$	−6.57912	−0.533637
$153$	−4.52111	−0.365510
$154$	−4.68569	−0.377584
$155$	−4.36483	−0.350591
$156$	3.54296	0.283664
$157$	16.6154	1.32605	0.663026	−	0.748596i	$-0.269272\pi$
$157$	16.6154	1.32605	0.663026	+	0.748596i	$0.269272\pi$
$158$	1.12670	0.0896352
$159$	1.32122	0.104780
$160$	1.94066	0.153422
$161$	10.8169	0.852491
$162$	1.00000	0.0785674
$163$	−11.5483	−0.904532	−0.452266	−	0.891883i	$-0.649384\pi$
$163$	−11.5483	−0.904532	−0.452266	+	0.891883i	$0.649384\pi$
$164$	3.95278	0.308660
$165$	−1.94066	−0.151080
$166$	2.01082	0.156070
$167$	13.1731	1.01937	0.509684	−	0.860362i	$-0.329762\pi$
$167$	13.1731	1.01937	0.509684	+	0.860362i	$0.329762\pi$
$168$	4.68569	0.361509
$169$	−0.447449	−0.0344191
$170$	−8.77391	−0.672929
$171$	−6.57912	−0.503118
$172$	−12.8057	−0.976429
$173$	−18.9212	−1.43855	−0.719274	−	0.694726i	$-0.755526\pi$
$173$	−18.9212	−1.43855	−0.719274	+	0.694726i	$0.755526\pi$
$174$	8.87158	0.672553
$175$	−5.78146	−0.437038
$176$	−1.00000	−0.0753778
$177$	−2.76033	−0.207479
$178$	−16.3921	−1.22864
$179$	16.4768	1.23154	0.615768	−	0.787928i	$-0.288846\pi$
$179$	16.4768	1.23154	0.615768	+	0.787928i	$0.288846\pi$
$180$	1.94066	0.144648
$181$	11.2607	0.836998	0.418499	−	0.908217i	$-0.362556\pi$
$181$	11.2607	0.836998	0.418499	+	0.908217i	$0.362556\pi$
$182$	16.6012	1.23056
$183$	1.00000	0.0739221
$184$	2.30849	0.170184
$185$	19.8699	1.46086
$186$	−2.24915	−0.164916
$187$	4.52111	0.330616
$188$	−9.63852	−0.702961
$189$	4.68569	0.340834
$190$	−12.7678	−0.926275
$191$	18.5307	1.34083	0.670417	−	0.741985i	$-0.266115\pi$
$191$	18.5307	1.34083	0.670417	+	0.741985i	$0.266115\pi$
$192$	1.00000	0.0721688
$193$	1.37903	0.0992650	0.0496325	−	0.998768i	$-0.484195\pi$
$193$	1.37903	0.0992650	0.0496325	+	0.998768i	$0.484195\pi$
$194$	3.05621	0.219423
$195$	6.87566	0.492376
$196$	14.9557	1.06827
$197$	0.395172	0.0281549	0.0140774	−	0.999901i	$-0.495519\pi$
$197$	0.395172	0.0281549	0.0140774	+	0.999901i	$0.495519\pi$
$198$	−1.00000	−0.0710669
$199$	4.97157	0.352426	0.176213	−	0.984352i	$-0.443615\pi$
$199$	4.97157	0.352426	0.176213	+	0.984352i	$0.443615\pi$
$200$	−1.23385	−0.0872467
$201$	−7.05220	−0.497424
$202$	−18.8931	−1.32931
$203$	41.5695	2.91761
$204$	−4.52111	−0.316541
$205$	7.67098	0.535764
$206$	2.51786	0.175428
$207$	2.30849	0.160451
$208$	3.54296	0.245660
$209$	6.57912	0.455087
$210$	9.09332	0.627498
$211$	7.02591	0.483684	0.241842	−	0.970316i	$-0.422248\pi$
$211$	7.02591	0.483684	0.241842	+	0.970316i	$0.422248\pi$
$212$	1.32122	0.0907419
$213$	−4.17995	−0.286406
$214$	0.804104	0.0549674
$215$	−24.8515	−1.69486
$216$	1.00000	0.0680414
$217$	−10.5388	−0.715422
$218$	−12.6101	−0.854061
$219$	14.6272	0.988411
$220$	−1.94066	−0.130839
$221$	−16.0181	−1.07749
$222$	10.2387	0.687179
$223$	−21.0936	−1.41253	−0.706265	−	0.707948i	$-0.749621\pi$
$223$	−21.0936	−1.41253	−0.706265	+	0.707948i	$0.749621\pi$
$224$	4.68569	0.313076
$225$	−1.23385	−0.0822570
$226$	−2.76273	−0.183774
$227$	4.60697	0.305776	0.152888	−	0.988244i	$-0.451143\pi$
$227$	4.60697	0.305776	0.152888	+	0.988244i	$0.451143\pi$
$228$	−6.57912	−0.435713
$229$	7.72279	0.510337	0.255168	−	0.966897i	$-0.417869\pi$
$229$	7.72279	0.510337	0.255168	+	0.966897i	$0.417869\pi$
$230$	4.47999	0.295402
$231$	−4.68569	−0.308296
$232$	8.87158	0.582448
$233$	17.7056	1.15993	0.579965	−	0.814641i	$-0.303066\pi$
$233$	17.7056	1.15993	0.579965	+	0.814641i	$0.303066\pi$
$234$	3.54296	0.231610
$235$	−18.7051	−1.22018
$236$	−2.76033	−0.179682
$237$	1.12670	0.0731869
$238$	−21.1845	−1.37319
$239$	−19.8454	−1.28369	−0.641845	−	0.766834i	$-0.721831\pi$
$239$	−19.8454	−1.28369	−0.641845	+	0.766834i	$0.721831\pi$
$240$	1.94066	0.125269
$241$	24.1295	1.55431	0.777157	−	0.629306i	$-0.216661\pi$
$241$	24.1295	1.55431	0.777157	+	0.629306i	$0.216661\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	29.0239	1.85427
$246$	3.95278	0.252020
$247$	−23.3096	−1.48315
$248$	−2.24915	−0.142821
$249$	2.01082	0.127431
$250$	−12.0978	−0.765130
$251$	7.32052	0.462067	0.231034	−	0.972946i	$-0.425789\pi$
$251$	7.32052	0.462067	0.231034	+	0.972946i	$0.425789\pi$
$252$	4.68569	0.295171
$253$	−2.30849	−0.145134
$254$	−7.83021	−0.491311
$255$	−8.77391	−0.549444
$256$	1.00000	0.0625000
$257$	−20.8803	−1.30248	−0.651238	−	0.758873i	$-0.725750\pi$
$257$	−20.8803	−1.30248	−0.651238	+	0.758873i	$0.725750\pi$
$258$	−12.8057	−0.797251
$259$	47.9756	2.98106
$260$	6.87566	0.426410
$261$	8.87158	0.549137
$262$	0.294983	0.0182241
$263$	−6.51652	−0.401826	−0.200913	−	0.979609i	$-0.564391\pi$
$263$	−6.51652	−0.401826	−0.200913	+	0.979609i	$0.564391\pi$
$264$	−1.00000	−0.0615457
$265$	2.56404	0.157508
$266$	−30.8277	−1.89017
$267$	−16.3921	−1.00318
$268$	−7.05220	−0.430782
$269$	17.3097	1.05539	0.527695	−	0.849434i	$-0.323056\pi$
$269$	17.3097	1.05539	0.527695	+	0.849434i	$0.323056\pi$
$270$	1.94066	0.118105
$271$	3.52912	0.214379	0.107189	−	0.994239i	$-0.465815\pi$
$271$	3.52912	0.214379	0.107189	+	0.994239i	$0.465815\pi$
$272$	−4.52111	−0.274132
$273$	16.6012	1.00475
$274$	−6.63420	−0.400787
$275$	1.23385	0.0744042
$276$	2.30849	0.138955
$277$	10.9000	0.654920	0.327460	−	0.944865i	$-0.393807\pi$
$277$	10.9000	0.654920	0.327460	+	0.944865i	$0.393807\pi$
$278$	21.7689	1.30561
$279$	−2.24915	−0.134653
$280$	9.09332	0.543430
$281$	10.8840	0.649282	0.324641	−	0.945837i	$-0.394757\pi$
$281$	10.8840	0.649282	0.324641	+	0.945837i	$0.394757\pi$
$282$	−9.63852	−0.573966
$283$	−12.7121	−0.755658	−0.377829	−	0.925875i	$-0.623329\pi$
$283$	−12.7121	−0.755658	−0.377829	+	0.925875i	$0.623329\pi$
$284$	−4.17995	−0.248034
$285$	−12.7678	−0.756300
$286$	−3.54296	−0.209499
$287$	18.5215	1.09329
$288$	1.00000	0.0589256
$289$	3.44042	0.202377
$290$	17.2167	1.01100
$291$	3.05621	0.179158
$292$	14.6272	0.855989
$293$	11.2244	0.655737	0.327869	−	0.944723i	$-0.393670\pi$
$293$	11.2244	0.655737	0.327869	+	0.944723i	$0.393670\pi$
$294$	14.9557	0.872235
$295$	−5.35686	−0.311888
$296$	10.2387	0.595115
$297$	−1.00000	−0.0580259
$298$	−15.9373	−0.923221
$299$	8.17890	0.472998
$300$	−1.23385	−0.0712366
$301$	−60.0038	−3.45856
$302$	−0.395019	−0.0227308
$303$	−18.8931	−1.08538
$304$	−6.57912	−0.377339
$305$	1.94066	0.111122
$306$	−4.52111	−0.258455
$307$	1.14250	0.0652058	0.0326029	−	0.999468i	$-0.489620\pi$
$307$	1.14250	0.0652058	0.0326029	+	0.999468i	$0.489620\pi$
$308$	−4.68569	−0.266992
$309$	2.51786	0.143236
$310$	−4.36483	−0.247906
$311$	−27.3801	−1.55258	−0.776292	−	0.630373i	$-0.782902\pi$
$311$	−27.3801	−1.55258	−0.776292	+	0.630373i	$0.782902\pi$
$312$	3.54296	0.200580
$313$	3.89382	0.220092	0.110046	−	0.993927i	$-0.464900\pi$
$313$	3.89382	0.220092	0.110046	+	0.993927i	$0.464900\pi$
$314$	16.6154	0.937660
$315$	9.09332	0.512350
$316$	1.12670	0.0633817
$317$	−19.0542	−1.07019	−0.535094	−	0.844793i	$-0.679724\pi$
$317$	−19.0542	−1.07019	−0.535094	+	0.844793i	$0.679724\pi$
$318$	1.32122	0.0740905
$319$	−8.87158	−0.496713
$320$	1.94066	0.108486
$321$	0.804104	0.0448807
$322$	10.8169	0.602802
$323$	29.7449	1.65505
$324$	1.00000	0.0555556
$325$	−4.37150	−0.242487
$326$	−11.5483	−0.639601
$327$	−12.6101	−0.697338
$328$	3.95278	0.218255
$329$	−45.1631	−2.48992
$330$	−1.94066	−0.106830
$331$	−16.5174	−0.907878	−0.453939	−	0.891033i	$-0.649982\pi$
$331$	−16.5174	−0.907878	−0.453939	+	0.891033i	$0.649982\pi$
$332$	2.01082	0.110358
$333$	10.2387	0.561079
$334$	13.1731	0.720802
$335$	−13.6859	−0.747740
$336$	4.68569	0.255625
$337$	−23.4235	−1.27596	−0.637981	−	0.770052i	$-0.720230\pi$
$337$	−23.4235	−1.27596	−0.637981	+	0.770052i	$0.720230\pi$
$338$	−0.447449	−0.0243380
$339$	−2.76273	−0.150051
$340$	−8.77391	−0.475832
$341$	2.24915	0.121798
$342$	−6.57912	−0.355758
$343$	37.2780	2.01282
$344$	−12.8057	−0.690439
$345$	4.47999	0.241195
$346$	−18.9212	−1.01721
$347$	−17.5562	−0.942466	−0.471233	−	0.882009i	$-0.656191\pi$
$347$	−17.5562	−0.942466	−0.471233	+	0.882009i	$0.656191\pi$
$348$	8.87158	0.475567
$349$	22.5290	1.20595	0.602976	−	0.797759i	$-0.293982\pi$
$349$	22.5290	1.20595	0.602976	+	0.797759i	$0.293982\pi$
$350$	−5.78146	−0.309032
$351$	3.54296	0.189109
$352$	−1.00000	−0.0533002
$353$	8.20436	0.436674	0.218337	−	0.975873i	$-0.429937\pi$
$353$	8.20436	0.436674	0.218337	+	0.975873i	$0.429937\pi$
$354$	−2.76033	−0.146710
$355$	−8.11185	−0.430532
$356$	−16.3921	−0.868779
$357$	−21.1845	−1.12120
$358$	16.4768	0.870827
$359$	−11.9885	−0.632729	−0.316365	−	0.948638i	$-0.602462\pi$
$359$	−11.9885	−0.632729	−0.316365	+	0.948638i	$0.602462\pi$
$360$	1.94066	0.102282
$361$	24.2849	1.27815
$362$	11.2607	0.591847
$363$	1.00000	0.0524864
$364$	16.6012	0.870140
$365$	28.3863	1.48581
$366$	1.00000	0.0522708
$367$	15.0644	0.786355	0.393178	−	0.919463i	$-0.371376\pi$
$367$	15.0644	0.786355	0.393178	+	0.919463i	$0.371376\pi$
$368$	2.30849	0.120339
$369$	3.95278	0.205773
$370$	19.8699	1.03299
$371$	6.19084	0.321413
$372$	−2.24915	−0.116613
$373$	17.8052	0.921917	0.460958	−	0.887422i	$-0.347506\pi$
$373$	17.8052	0.921917	0.460958	+	0.887422i	$0.347506\pi$
$374$	4.52111	0.233781
$375$	−12.0978	−0.624726
$376$	−9.63852	−0.497069
$377$	31.4316	1.61881
$378$	4.68569	0.241006
$379$	0.435287	0.0223592	0.0111796	−	0.999938i	$-0.496441\pi$
$379$	0.435287	0.0223592	0.0111796	+	0.999938i	$0.496441\pi$
$380$	−12.7678	−0.654975
$381$	−7.83021	−0.401154
$382$	18.5307	0.948112
$383$	−11.9463	−0.610428	−0.305214	−	0.952284i	$-0.598728\pi$
$383$	−11.9463	−0.610428	−0.305214	+	0.952284i	$0.598728\pi$
$384$	1.00000	0.0510310
$385$	−9.09332	−0.463438
$386$	1.37903	0.0701909
$387$	−12.8057	−0.650953
$388$	3.05621	0.155156
$389$	23.6560	1.19940	0.599702	−	0.800223i	$-0.295286\pi$
$389$	23.6560	1.19940	0.599702	+	0.800223i	$0.295286\pi$
$390$	6.87566	0.348163
$391$	−10.4370	−0.527819
$392$	14.9557	0.755378
$393$	0.294983	0.0148799
$394$	0.395172	0.0199085
$395$	2.18653	0.110016
$396$	−1.00000	−0.0502519
$397$	9.23778	0.463631	0.231815	−	0.972760i	$-0.425533\pi$
$397$	9.23778	0.463631	0.231815	+	0.972760i	$0.425533\pi$
$398$	4.97157	0.249203
$399$	−30.8277	−1.54332
$400$	−1.23385	−0.0616927
$401$	−18.6248	−0.930077	−0.465039	−	0.885290i	$-0.653960\pi$
$401$	−18.6248	−0.930077	−0.465039	+	0.885290i	$0.653960\pi$
$402$	−7.05220	−0.351732
$403$	−7.96865	−0.396947
$404$	−18.8931	−0.939966
$405$	1.94066	0.0964320
$406$	41.5695	2.06306
$407$	−10.2387	−0.507516
$408$	−4.52111	−0.223828
$409$	22.9387	1.13425	0.567124	−	0.823633i	$-0.308056\pi$
$409$	22.9387	1.13425	0.567124	+	0.823633i	$0.308056\pi$
$410$	7.67098	0.378843
$411$	−6.63420	−0.327241
$412$	2.51786	0.124046
$413$	−12.9341	−0.636444
$414$	2.30849	0.113456
$415$	3.90231	0.191557
$416$	3.54296	0.173708
$417$	21.7689	1.06603
$418$	6.57912	0.321795
$419$	−19.8711	−0.970767	−0.485384	−	0.874301i	$-0.661320\pi$
$419$	−19.8711	−0.970767	−0.485384	+	0.874301i	$0.661320\pi$
$420$	9.09332	0.443708
$421$	−32.9028	−1.60358	−0.801792	−	0.597603i	$-0.796120\pi$
$421$	−32.9028	−1.60358	−0.801792	+	0.597603i	$0.796120\pi$
$422$	7.02591	0.342016
$423$	−9.63852	−0.468641
$424$	1.32122	0.0641642
$425$	5.57839	0.270592
$426$	−4.17995	−0.202519
$427$	4.68569	0.226757
$428$	0.804104	0.0388678
$429$	−3.54296	−0.171056
$430$	−24.8515	−1.19845
$431$	−28.0055	−1.34898	−0.674490	−	0.738284i	$-0.735636\pi$
$431$	−28.0055	−1.34898	−0.674490	+	0.738284i	$0.735636\pi$
$432$	1.00000	0.0481125
$433$	19.7345	0.948382	0.474191	−	0.880422i	$-0.342741\pi$
$433$	19.7345	0.948382	0.474191	+	0.880422i	$0.342741\pi$
$434$	−10.5388	−0.505880
$435$	17.2167	0.825477
$436$	−12.6101	−0.603913
$437$	−15.1879	−0.726534
$438$	14.6272	0.698912
$439$	34.1613	1.63043	0.815215	−	0.579159i	$-0.196619\pi$
$439$	34.1613	1.63043	0.815215	+	0.579159i	$0.196619\pi$
$440$	−1.94066	−0.0925171
$441$	14.9557	0.712177
$442$	−16.0181	−0.761903
$443$	2.73228	0.129814	0.0649072	−	0.997891i	$-0.479325\pi$
$443$	2.73228	0.129814	0.0649072	+	0.997891i	$0.479325\pi$
$444$	10.2387	0.485909
$445$	−31.8114	−1.50800
$446$	−21.0936	−0.998809
$447$	−15.9373	−0.753807
$448$	4.68569	0.221378
$449$	−4.69807	−0.221716	−0.110858	−	0.993836i	$-0.535360\pi$
$449$	−4.69807	−0.221716	−0.110858	+	0.993836i	$0.535360\pi$
$450$	−1.23385	−0.0581645
$451$	−3.95278	−0.186129
$452$	−2.76273	−0.129948
$453$	−0.395019	−0.0185596
$454$	4.60697	0.216216
$455$	32.2172	1.51037
$456$	−6.57912	−0.308096
$457$	−15.4353	−0.722032	−0.361016	−	0.932560i	$-0.617570\pi$
$457$	−15.4353	−0.722032	−0.361016	+	0.932560i	$0.617570\pi$
$458$	7.72279	0.360862
$459$	−4.52111	−0.211027
$460$	4.47999	0.208881
$461$	32.2504	1.50205	0.751025	−	0.660274i	$-0.229560\pi$
$461$	32.2504	1.50205	0.751025	+	0.660274i	$0.229560\pi$
$462$	−4.68569	−0.217998
$463$	15.1119	0.702311	0.351155	−	0.936317i	$-0.385789\pi$
$463$	15.1119	0.702311	0.351155	+	0.936317i	$0.385789\pi$
$464$	8.87158	0.411853
$465$	−4.36483	−0.202414
$466$	17.7056	0.820194
$467$	22.3900	1.03608	0.518042	−	0.855355i	$-0.326661\pi$
$467$	22.3900	1.03608	0.518042	+	0.855355i	$0.326661\pi$
$468$	3.54296	0.163773
$469$	−33.0445	−1.52585
$470$	−18.7051	−0.862800
$471$	16.6154	0.765596
$472$	−2.76033	−0.127055
$473$	12.8057	0.588809
$474$	1.12670	0.0517509
$475$	8.11768	0.372465
$476$	−21.1845	−0.970991
$477$	1.32122	0.0604946
$478$	−19.8454	−0.907706
$479$	−17.9121	−0.818427	−0.409213	−	0.912439i	$-0.634197\pi$
$479$	−17.9121	−0.818427	−0.409213	+	0.912439i	$0.634197\pi$
$480$	1.94066	0.0885784
$481$	36.2754	1.65402
$482$	24.1295	1.09907
$483$	10.8169	0.492186
$484$	1.00000	0.0454545
$485$	5.93105	0.269315
$486$	1.00000	0.0453609
$487$	22.6522	1.02647	0.513235	−	0.858248i	$-0.328447\pi$
$487$	22.6522	1.02647	0.513235	+	0.858248i	$0.328447\pi$
$488$	1.00000	0.0452679
$489$	−11.5483	−0.522232
$490$	29.0239	1.31117
$491$	−25.4936	−1.15051	−0.575254	−	0.817975i	$-0.695097\pi$
$491$	−25.4936	−1.15051	−0.575254	+	0.817975i	$0.695097\pi$
$492$	3.95278	0.178205
$493$	−40.1094	−1.80644
$494$	−23.3096	−1.04875
$495$	−1.94066	−0.0872260
$496$	−2.24915	−0.100990
$497$	−19.5860	−0.878551
$498$	2.01082	0.0901071
$499$	−2.80077	−0.125380	−0.0626899	−	0.998033i	$-0.519968\pi$
$499$	−2.80077	−0.125380	−0.0626899	+	0.998033i	$0.519968\pi$
$500$	−12.0978	−0.541029
$501$	13.1731	0.588532
$502$	7.32052	0.326731
$503$	31.8978	1.42225	0.711127	−	0.703064i	$-0.248185\pi$
$503$	31.8978	1.42225	0.711127	+	0.703064i	$0.248185\pi$
$504$	4.68569	0.208717
$505$	−36.6650	−1.63157
$506$	−2.30849	−0.102625
$507$	−0.447449	−0.0198719
$508$	−7.83021	−0.347409
$509$	−41.3679	−1.83360	−0.916799	−	0.399349i	$-0.869236\pi$
$509$	−41.3679	−1.83360	−0.916799	+	0.399349i	$0.869236\pi$
$510$	−8.77391	−0.388515
$511$	68.5383	3.03196
$512$	1.00000	0.0441942
$513$	−6.57912	−0.290475
$514$	−20.8803	−0.920990
$515$	4.88630	0.215316
$516$	−12.8057	−0.563741
$517$	9.63852	0.423902
$518$	47.9756	2.10793
$519$	−18.9212	−0.830547
$520$	6.87566	0.301518
$521$	−3.79183	−0.166123	−0.0830615	−	0.996544i	$-0.526470\pi$
$521$	−3.79183	−0.166123	−0.0830615	+	0.996544i	$0.526470\pi$
$522$	8.87158	0.388299
$523$	−6.15004	−0.268922	−0.134461	−	0.990919i	$-0.542930\pi$
$523$	−6.15004	−0.268922	−0.134461	+	0.990919i	$0.542930\pi$
$524$	0.294983	0.0128864
$525$	−5.78146	−0.252324
$526$	−6.51652	−0.284134
$527$	10.1687	0.442953
$528$	−1.00000	−0.0435194
$529$	−17.6709	−0.768298
$530$	2.56404	0.111375
$531$	−2.76033	−0.119788
$532$	−30.8277	−1.33655
$533$	14.0045	0.606603
$534$	−16.3921	−0.709355
$535$	1.56049	0.0674658
$536$	−7.05220	−0.304609
$537$	16.4768	0.711027
$538$	17.3097	0.746274
$539$	−14.9557	−0.644188
$540$	1.94066	0.0835125
$541$	−36.5498	−1.57140	−0.785700	−	0.618608i	$-0.787697\pi$
$541$	−36.5498	−1.57140	−0.785700	+	0.618608i	$0.787697\pi$
$542$	3.52912	0.151589
$543$	11.2607	0.483241
$544$	−4.52111	−0.193841
$545$	−24.4718	−1.04826
$546$	16.6012	0.710466
$547$	13.9550	0.596671	0.298335	−	0.954461i	$-0.403569\pi$
$547$	13.9550	0.596671	0.298335	+	0.954461i	$0.403569\pi$
$548$	−6.63420	−0.283399
$549$	1.00000	0.0426790
$550$	1.23385	0.0526117
$551$	−58.3672	−2.48653
$552$	2.30849	0.0982561
$553$	5.27936	0.224501
$554$	10.9000	0.463099
$555$	19.8699	0.843429
$556$	21.7689	0.923209
$557$	15.2605	0.646608	0.323304	−	0.946295i	$-0.395206\pi$
$557$	15.2605	0.646608	0.323304	+	0.946295i	$0.395206\pi$
$558$	−2.24915	−0.0952141
$559$	−45.3702	−1.91896
$560$	9.09332	0.384263
$561$	4.52111	0.190881
$562$	10.8840	0.459112
$563$	13.0591	0.550375	0.275188	−	0.961391i	$-0.411260\pi$
$563$	13.0591	0.550375	0.275188	+	0.961391i	$0.411260\pi$
$564$	−9.63852	−0.405855
$565$	−5.36152	−0.225561
$566$	−12.7121	−0.534331
$567$	4.68569	0.196781
$568$	−4.17995	−0.175387
$569$	−0.493809	−0.0207015	−0.0103508	−	0.999946i	$-0.503295\pi$
$569$	−0.493809	−0.0207015	−0.0103508	+	0.999946i	$0.503295\pi$
$570$	−12.7678	−0.534785
$571$	−43.3189	−1.81284	−0.906420	−	0.422377i	$-0.861196\pi$
$571$	−43.3189	−1.81284	−0.906420	+	0.422377i	$0.861196\pi$
$572$	−3.54296	−0.148139
$573$	18.5307	0.774130
$574$	18.5215	0.773072
$575$	−2.84835	−0.118784
$576$	1.00000	0.0416667
$577$	−26.5623	−1.10580	−0.552902	−	0.833246i	$-0.686480\pi$
$577$	−26.5623	−1.10580	−0.552902	+	0.833246i	$0.686480\pi$
$578$	3.44042	0.143102
$579$	1.37903	0.0573107
$580$	17.2167	0.714884
$581$	9.42210	0.390894
$582$	3.05621	0.126684
$583$	−1.32122	−0.0547194
$584$	14.6272	0.605276
$585$	6.87566	0.284274
$586$	11.2244	0.463676
$587$	−14.0625	−0.580422	−0.290211	−	0.956963i	$-0.593726\pi$
$587$	−14.0625	−0.580422	−0.290211	+	0.956963i	$0.593726\pi$
$588$	14.9557	0.616763
$589$	14.7974	0.609718
$590$	−5.35686	−0.220538
$591$	0.395172	0.0162552
$592$	10.2387	0.420810
$593$	9.91252	0.407058	0.203529	−	0.979069i	$-0.434759\pi$
$593$	9.91252	0.407058	0.203529	+	0.979069i	$0.434759\pi$
$594$	−1.00000	−0.0410305
$595$	−41.1119	−1.68542
$596$	−15.9373	−0.652816
$597$	4.97157	0.203473
$598$	8.17890	0.334460
$599$	−25.7820	−1.05342	−0.526712	−	0.850044i	$-0.676576\pi$
$599$	−25.7820	−1.05342	−0.526712	+	0.850044i	$0.676576\pi$
$600$	−1.23385	−0.0503719
$601$	−21.7545	−0.887384	−0.443692	−	0.896179i	$-0.646332\pi$
$601$	−21.7545	−0.887384	−0.443692	+	0.896179i	$0.646332\pi$
$602$	−60.0038	−2.44557
$603$	−7.05220	−0.287188
$604$	−0.395019	−0.0160731
$605$	1.94066	0.0788989
$606$	−18.8931	−0.767479
$607$	−35.2839	−1.43213	−0.716065	−	0.698034i	$-0.754058\pi$
$607$	−35.2839	−1.43213	−0.716065	+	0.698034i	$0.754058\pi$
$608$	−6.57912	−0.266819
$609$	41.5695	1.68448
$610$	1.94066	0.0785749
$611$	−34.1489	−1.38152
$612$	−4.52111	−0.182755
$613$	−11.1593	−0.450718	−0.225359	−	0.974276i	$-0.572356\pi$
$613$	−11.1593	−0.450718	−0.225359	+	0.974276i	$0.572356\pi$
$614$	1.14250	0.0461075
$615$	7.67098	0.309324
$616$	−4.68569	−0.188792
$617$	27.2684	1.09779	0.548893	−	0.835893i	$-0.315050\pi$
$617$	27.2684	1.09779	0.548893	+	0.835893i	$0.315050\pi$
$618$	2.51786	0.101283
$619$	18.3387	0.737095	0.368548	−	0.929609i	$-0.379855\pi$
$619$	18.3387	0.737095	0.368548	+	0.929609i	$0.379855\pi$
$620$	−4.36483	−0.175296
$621$	2.30849	0.0926367
$622$	−27.3801	−1.09784
$623$	−76.8082	−3.07726
$624$	3.54296	0.141832
$625$	−17.3083	−0.692333
$626$	3.89382	0.155628
$627$	6.57912	0.262745
$628$	16.6154	0.663026
$629$	−46.2904	−1.84572
$630$	9.09332	0.362286
$631$	46.4935	1.85088	0.925439	−	0.378897i	$-0.123696\pi$
$631$	46.4935	1.85088	0.925439	+	0.378897i	$0.123696\pi$
$632$	1.12670	0.0448176
$633$	7.02591	0.279255
$634$	−19.0542	−0.756737
$635$	−15.1957	−0.603025
$636$	1.32122	0.0523899
$637$	52.9875	2.09944
$638$	−8.87158	−0.351229
$639$	−4.17995	−0.165356
$640$	1.94066	0.0767112
$641$	−34.5917	−1.36629	−0.683145	−	0.730283i	$-0.739388\pi$
$641$	−34.5917	−1.36629	−0.683145	+	0.730283i	$0.739388\pi$
$642$	0.804104	0.0317354
$643$	16.0110	0.631411	0.315706	−	0.948857i	$-0.397759\pi$
$643$	16.0110	0.631411	0.315706	+	0.948857i	$0.397759\pi$
$644$	10.8169	0.426245
$645$	−24.8515	−0.978529
$646$	29.7449	1.17030
$647$	27.6401	1.08664	0.543322	−	0.839524i	$-0.317166\pi$
$647$	27.6401	1.08664	0.543322	+	0.839524i	$0.317166\pi$
$648$	1.00000	0.0392837
$649$	2.76033	0.108353
$650$	−4.37150	−0.171464
$651$	−10.5388	−0.413049
$652$	−11.5483	−0.452266
$653$	13.4487	0.526288	0.263144	−	0.964757i	$-0.415241\pi$
$653$	13.4487	0.526288	0.263144	+	0.964757i	$0.415241\pi$
$654$	−12.6101	−0.493092
$655$	0.572461	0.0223679
$656$	3.95278	0.154330
$657$	14.6272	0.570660
$658$	−45.1631	−1.76064
$659$	25.0126	0.974351	0.487176	−	0.873304i	$-0.338027\pi$
$659$	25.0126	0.974351	0.487176	+	0.873304i	$0.338027\pi$
$660$	−1.94066	−0.0755399
$661$	−5.04968	−0.196410	−0.0982048	−	0.995166i	$-0.531310\pi$
$661$	−5.04968	−0.196410	−0.0982048	+	0.995166i	$0.531310\pi$
$662$	−16.5174	−0.641966
$663$	−16.0181	−0.622091
$664$	2.01082	0.0780350
$665$	−59.8261	−2.31995
$666$	10.2387	0.396743
$667$	20.4800	0.792989
$668$	13.1731	0.509684
$669$	−21.0936	−0.815524
$670$	−13.6859	−0.528732
$671$	−1.00000	−0.0386046
$672$	4.68569	0.180755
$673$	9.40282	0.362452	0.181226	−	0.983441i	$-0.441993\pi$
$673$	9.40282	0.362452	0.181226	+	0.983441i	$0.441993\pi$
$674$	−23.4235	−0.902241
$675$	−1.23385	−0.0474911
$676$	−0.447449	−0.0172096
$677$	−25.3988	−0.976157	−0.488078	−	0.872800i	$-0.662302\pi$
$677$	−25.3988	−0.976157	−0.488078	+	0.872800i	$0.662302\pi$
$678$	−2.76273	−0.106102
$679$	14.3205	0.549569
$680$	−8.77391	−0.336464
$681$	4.60697	0.176540
$682$	2.24915	0.0861244
$683$	−12.8173	−0.490439	−0.245220	−	0.969468i	$-0.578860\pi$
$683$	−12.8173	−0.490439	−0.245220	+	0.969468i	$0.578860\pi$
$684$	−6.57912	−0.251559
$685$	−12.8747	−0.491917
$686$	37.2780	1.42328
$687$	7.72279	0.294643
$688$	−12.8057	−0.488214
$689$	4.68104	0.178333
$690$	4.47999	0.170550
$691$	−36.6610	−1.39465	−0.697326	−	0.716754i	$-0.745627\pi$
$691$	−36.6610	−1.39465	−0.697326	+	0.716754i	$0.745627\pi$
$692$	−18.9212	−0.719274
$693$	−4.68569	−0.177995
$694$	−17.5562	−0.666424
$695$	42.2460	1.60248
$696$	8.87158	0.336276
$697$	−17.8709	−0.676909
$698$	22.5290	0.852737
$699$	17.7056	0.669686
$700$	−5.78146	−0.218519
$701$	30.5068	1.15223	0.576113	−	0.817370i	$-0.304569\pi$
$701$	30.5068	1.15223	0.576113	+	0.817370i	$0.304569\pi$
$702$	3.54296	0.133720
$703$	−67.3619	−2.54060
$704$	−1.00000	−0.0376889
$705$	−18.7051	−0.704473
$706$	8.20436	0.308775
$707$	−88.5272	−3.32941
$708$	−2.76033	−0.103740
$709$	−10.0246	−0.376482	−0.188241	−	0.982123i	$-0.560279\pi$
$709$	−10.0246	−0.376482	−0.188241	+	0.982123i	$0.560279\pi$
$710$	−8.11185	−0.304432
$711$	1.12670	0.0422545
$712$	−16.3921	−0.614319
$713$	−5.19215	−0.194448
$714$	−21.1845	−0.792811
$715$	−6.87566	−0.257135
$716$	16.4768	0.615768
$717$	−19.8454	−0.741139
$718$	−11.9885	−0.447407
$719$	−32.9021	−1.22704	−0.613520	−	0.789679i	$-0.710247\pi$
$719$	−32.9021	−1.22704	−0.613520	+	0.789679i	$0.710247\pi$
$720$	1.94066	0.0723240
$721$	11.7979	0.439377
$722$	24.2849	0.903789
$723$	24.1295	0.897384
$724$	11.2607	0.418499
$725$	−10.9462	−0.406533
$726$	1.00000	0.0371135
$727$	47.1188	1.74754	0.873770	−	0.486339i	$-0.161668\pi$
$727$	47.1188	1.74754	0.873770	+	0.486339i	$0.161668\pi$
$728$	16.6012	0.615282
$729$	1.00000	0.0370370
$730$	28.3863	1.05062
$731$	57.8962	2.14137
$732$	1.00000	0.0369611
$733$	40.1029	1.48123	0.740617	−	0.671928i	$-0.234533\pi$
$733$	40.1029	1.48123	0.740617	+	0.671928i	$0.234533\pi$
$734$	15.0644	0.556037
$735$	29.0239	1.07056
$736$	2.30849	0.0850922
$737$	7.05220	0.259771
$738$	3.95278	0.145504
$739$	9.05667	0.333155	0.166577	−	0.986028i	$-0.446728\pi$
$739$	9.05667	0.333155	0.166577	+	0.986028i	$0.446728\pi$
$740$	19.8699	0.730431
$741$	−23.3096	−0.856298
$742$	6.19084	0.227273
$743$	−22.4504	−0.823624	−0.411812	−	0.911269i	$-0.635104\pi$
$743$	−22.4504	−0.823624	−0.411812	+	0.911269i	$0.635104\pi$
$744$	−2.24915	−0.0824579
$745$	−30.9288	−1.13314
$746$	17.8052	0.651894
$747$	2.01082	0.0735721
$748$	4.52111	0.165308
$749$	3.76778	0.137672
$750$	−12.0978	−0.441748
$751$	25.8709	0.944041	0.472020	−	0.881588i	$-0.343525\pi$
$751$	25.8709	0.944041	0.472020	+	0.881588i	$0.343525\pi$
$752$	−9.63852	−0.351481
$753$	7.32052	0.266775
$754$	31.4316	1.14467
$755$	−0.766597	−0.0278993
$756$	4.68569	0.170417
$757$	48.0925	1.74795	0.873976	−	0.485970i	$-0.161533\pi$
$757$	48.0925	1.74795	0.873976	+	0.485970i	$0.161533\pi$
$758$	0.435287	0.0158103
$759$	−2.30849	−0.0837930
$760$	−12.7678	−0.463137
$761$	−22.4777	−0.814817	−0.407409	−	0.913246i	$-0.633568\pi$
$761$	−22.4777	−0.814817	−0.407409	+	0.913246i	$0.633568\pi$
$762$	−7.83021	−0.283659
$763$	−59.0869	−2.13909
$764$	18.5307	0.670417
$765$	−8.77391	−0.317222
$766$	−11.9463	−0.431638
$767$	−9.77974	−0.353126
$768$	1.00000	0.0360844
$769$	41.2006	1.48573	0.742866	−	0.669440i	$-0.233466\pi$
$769$	41.2006	1.48573	0.742866	+	0.669440i	$0.233466\pi$
$770$	−9.09332	−0.327700
$771$	−20.8803	−0.751985
$772$	1.37903	0.0496325
$773$	−17.5906	−0.632689	−0.316345	−	0.948644i	$-0.602456\pi$
$773$	−17.5906	−0.632689	−0.316345	+	0.948644i	$0.602456\pi$
$774$	−12.8057	−0.460293
$775$	2.77512	0.0996854
$776$	3.05621	0.109712
$777$	47.9756	1.72111
$778$	23.6560	0.848107
$779$	−26.0058	−0.931754
$780$	6.87566	0.246188
$781$	4.17995	0.149570
$782$	−10.4370	−0.373225
$783$	8.87158	0.317044
$784$	14.9557	0.534133
$785$	32.2447	1.15086
$786$	0.294983	0.0105217
$787$	3.68134	0.131226	0.0656128	−	0.997845i	$-0.479100\pi$
$787$	3.68134	0.131226	0.0656128	+	0.997845i	$0.479100\pi$
$788$	0.395172	0.0140774
$789$	−6.51652	−0.231994
$790$	2.18653	0.0777933
$791$	−12.9453	−0.460283
$792$	−1.00000	−0.0355335
$793$	3.54296	0.125814
$794$	9.23778	0.327836
$795$	2.56404	0.0909371
$796$	4.97157	0.176213
$797$	9.81203	0.347560	0.173780	−	0.984785i	$-0.444402\pi$
$797$	9.81203	0.347560	0.173780	+	0.984785i	$0.444402\pi$
$798$	−30.8277	−1.09129
$799$	43.5768	1.54164
$800$	−1.23385	−0.0436233
$801$	−16.3921	−0.579186
$802$	−18.6248	−0.657664
$803$	−14.6272	−0.516181
$804$	−7.05220	−0.248712
$805$	20.9919	0.739866
$806$	−7.96865	−0.280684
$807$	17.3097	0.609330
$808$	−18.8931	−0.664656
$809$	−23.3940	−0.822489	−0.411245	−	0.911525i	$-0.634906\pi$
$809$	−23.3940	−0.822489	−0.411245	+	0.911525i	$0.634906\pi$
$810$	1.94066	0.0681877
$811$	−2.24057	−0.0786771	−0.0393385	−	0.999226i	$-0.512525\pi$
$811$	−2.24057	−0.0786771	−0.0393385	+	0.999226i	$0.512525\pi$
$812$	41.5695	1.45880
$813$	3.52912	0.123772
$814$	−10.2387	−0.358868
$815$	−22.4113	−0.785032
$816$	−4.52111	−0.158270
$817$	84.2506	2.94755
$818$	22.9387	0.802034
$819$	16.6012	0.580093
$820$	7.67098	0.267882
$821$	−4.20978	−0.146922	−0.0734612	−	0.997298i	$-0.523405\pi$
$821$	−4.20978	−0.146922	−0.0734612	+	0.997298i	$0.523405\pi$
$822$	−6.63420	−0.231394
$823$	6.24729	0.217767	0.108883	−	0.994055i	$-0.465272\pi$
$823$	6.24729	0.217767	0.108883	+	0.994055i	$0.465272\pi$
$824$	2.51786	0.0877138
$825$	1.23385	0.0429573
$826$	−12.9341	−0.450034
$827$	30.7905	1.07069	0.535346	−	0.844633i	$-0.320181\pi$
$827$	30.7905	1.07069	0.535346	+	0.844633i	$0.320181\pi$
$828$	2.30849	0.0802257
$829$	−35.2703	−1.22499	−0.612494	−	0.790475i	$-0.709834\pi$
$829$	−35.2703	−1.22499	−0.612494	+	0.790475i	$0.709834\pi$
$830$	3.90231	0.135451
$831$	10.9000	0.378118
$832$	3.54296	0.122830
$833$	−67.6164	−2.34277
$834$	21.7689	0.753797
$835$	25.5645	0.884696
$836$	6.57912	0.227544
$837$	−2.24915	−0.0777420
$838$	−19.8711	−0.686436
$839$	−32.4869	−1.12157	−0.560786	−	0.827961i	$-0.689501\pi$
$839$	−32.4869	−1.12157	−0.560786	+	0.827961i	$0.689501\pi$
$840$	9.09332	0.313749
$841$	49.7049	1.71396
$842$	−32.9028	−1.13391
$843$	10.8840	0.374863
$844$	7.02591	0.241842
$845$	−0.868344	−0.0298719
$846$	−9.63852	−0.331379
$847$	4.68569	0.161002
$848$	1.32122	0.0453710
$849$	−12.7121	−0.436279
$850$	5.57839	0.191337
$851$	23.6361	0.810234
$852$	−4.17995	−0.143203
$853$	13.9865	0.478888	0.239444	−	0.970910i	$-0.423035\pi$
$853$	13.9865	0.478888	0.239444	+	0.970910i	$0.423035\pi$
$854$	4.68569	0.160341
$855$	−12.7678	−0.436650
$856$	0.804104	0.0274837
$857$	18.0088	0.615170	0.307585	−	0.951521i	$-0.400479\pi$
$857$	18.0088	0.615170	0.307585	+	0.951521i	$0.400479\pi$
$858$	−3.54296	−0.120955
$859$	−5.44862	−0.185905	−0.0929523	−	0.995671i	$-0.529630\pi$
$859$	−5.44862	−0.185905	−0.0929523	+	0.995671i	$0.529630\pi$
$860$	−24.8515	−0.847431
$861$	18.5215	0.631211
$862$	−28.0055	−0.953873
$863$	42.6014	1.45017	0.725084	−	0.688660i	$-0.241801\pi$
$863$	42.6014	1.45017	0.725084	+	0.688660i	$0.241801\pi$
$864$	1.00000	0.0340207
$865$	−36.7195	−1.24850
$866$	19.7345	0.670607
$867$	3.44042	0.116843
$868$	−10.5388	−0.357711
$869$	−1.12670	−0.0382206
$870$	17.2167	0.583700
$871$	−24.9857	−0.846607
$872$	−12.6101	−0.427031
$873$	3.05621	0.103437
$874$	−15.1879	−0.513737
$875$	−56.6864	−1.91635
$876$	14.6272	0.494206
$877$	19.5835	0.661288	0.330644	−	0.943755i	$-0.392734\pi$
$877$	19.5835	0.661288	0.330644	+	0.943755i	$0.392734\pi$
$878$	34.1613	1.15289
$879$	11.2244	0.378590
$880$	−1.94066	−0.0654195
$881$	34.9248	1.17665	0.588323	−	0.808626i	$-0.299788\pi$
$881$	34.9248	1.17665	0.588323	+	0.808626i	$0.299788\pi$
$882$	14.9557	0.503585
$883$	−0.782444	−0.0263313	−0.0131657	−	0.999913i	$-0.504191\pi$
$883$	−0.782444	−0.0263313	−0.0131657	+	0.999913i	$0.504191\pi$
$884$	−16.0181	−0.538747
$885$	−5.35686	−0.180069
$886$	2.73228	0.0917926
$887$	31.0312	1.04193	0.520963	−	0.853579i	$-0.325573\pi$
$887$	31.0312	1.04193	0.520963	+	0.853579i	$0.325573\pi$
$888$	10.2387	0.343590
$889$	−36.6900	−1.23054
$890$	−31.8114	−1.06632
$891$	−1.00000	−0.0335013
$892$	−21.0936	−0.706265
$893$	63.4130	2.12204
$894$	−15.9373	−0.533022
$895$	31.9758	1.06883
$896$	4.68569	0.156538
$897$	8.17890	0.273086
$898$	−4.69807	−0.156777
$899$	−19.9535	−0.665487
$900$	−1.23385	−0.0411285
$901$	−5.97339	−0.199002
$902$	−3.95278	−0.131613
$903$	−60.0038	−1.99680
$904$	−2.76273	−0.0918872
$905$	21.8531	0.726421
$906$	−0.395019	−0.0131236
$907$	−32.8869	−1.09199	−0.545995	−	0.837788i	$-0.683848\pi$
$907$	−32.8869	−1.09199	−0.545995	+	0.837788i	$0.683848\pi$
$908$	4.60697	0.152888
$909$	−18.8931	−0.626644
$910$	32.2172	1.06799
$911$	8.50095	0.281649	0.140825	−	0.990035i	$-0.455025\pi$
$911$	8.50095	0.281649	0.140825	+	0.990035i	$0.455025\pi$
$912$	−6.57912	−0.217857
$913$	−2.01082	−0.0665485
$914$	−15.4353	−0.510554
$915$	1.94066	0.0641561
$916$	7.72279	0.255168
$917$	1.38220	0.0456443
$918$	−4.52111	−0.149219
$919$	8.11405	0.267658	0.133829	−	0.991004i	$-0.457273\pi$
$919$	8.11405	0.267658	0.133829	+	0.991004i	$0.457273\pi$
$920$	4.47999	0.147701
$921$	1.14250	0.0376466
$922$	32.2504	1.06211
$923$	−14.8094	−0.487457
$924$	−4.68569	−0.154148
$925$	−12.6331	−0.415374
$926$	15.1119	0.496609
$927$	2.51786	0.0826974
$928$	8.87158	0.291224
$929$	45.4901	1.49248	0.746241	−	0.665676i	$-0.231857\pi$
$929$	45.4901	1.49248	0.746241	+	0.665676i	$0.231857\pi$
$930$	−4.36483	−0.143128
$931$	−98.3955	−3.22478
$932$	17.7056	0.579965
$933$	−27.3801	−0.896385
$934$	22.3900	0.732622
$935$	8.77391	0.286938
$936$	3.54296	0.115805
$937$	35.1925	1.14969	0.574844	−	0.818263i	$-0.305063\pi$
$937$	35.1925	1.14969	0.574844	+	0.818263i	$0.305063\pi$
$938$	−33.0445	−1.07894
$939$	3.89382	0.127070
$940$	−18.7051	−0.610092
$941$	10.6839	0.348285	0.174143	−	0.984720i	$-0.444285\pi$
$941$	10.6839	0.348285	0.174143	+	0.984720i	$0.444285\pi$
$942$	16.6154	0.541358
$943$	9.12496	0.297150
$944$	−2.76033	−0.0898412
$945$	9.09332	0.295806
$946$	12.8057	0.416351
$947$	−39.6950	−1.28991	−0.644956	−	0.764219i	$-0.723124\pi$
$947$	−39.6950	−1.28991	−0.644956	+	0.764219i	$0.723124\pi$
$948$	1.12670	0.0365934
$949$	51.8234	1.68226
$950$	8.11768	0.263372
$951$	−19.0542	−0.617873
$952$	−21.1845	−0.686594
$953$	34.5087	1.11785	0.558923	−	0.829220i	$-0.311215\pi$
$953$	34.5087	1.11785	0.558923	+	0.829220i	$0.311215\pi$
$954$	1.32122	0.0427762
$955$	35.9617	1.16369
$956$	−19.8454	−0.641845
$957$	−8.87158	−0.286777
$958$	−17.9121	−0.578715
$959$	−31.0858	−1.00381
$960$	1.94066	0.0626344
$961$	−25.9413	−0.836817
$962$	36.2754	1.16957
$963$	0.804104	0.0259119
$964$	24.1295	0.777157
$965$	2.67623	0.0861508
$966$	10.8169	0.348028
$967$	−19.8974	−0.639856	−0.319928	−	0.947442i	$-0.603659\pi$
$967$	−19.8974	−0.639856	−0.319928	+	0.947442i	$0.603659\pi$
$968$	1.00000	0.0321412
$969$	29.7449	0.955545
$970$	5.93105	0.190435
$971$	−9.96197	−0.319695	−0.159847	−	0.987142i	$-0.551100\pi$
$971$	−9.96197	−0.319695	−0.159847	+	0.987142i	$0.551100\pi$
$972$	1.00000	0.0320750
$973$	102.003	3.27005
$974$	22.6522	0.725824
$975$	−4.37150	−0.140000
$976$	1.00000	0.0320092
$977$	−22.1448	−0.708474	−0.354237	−	0.935156i	$-0.615259\pi$
$977$	−22.1448	−0.708474	−0.354237	+	0.935156i	$0.615259\pi$
$978$	−11.5483	−0.369274
$979$	16.3921	0.523893
$980$	29.0239	0.927134
$981$	−12.6101	−0.402608
$982$	−25.4936	−0.813532
$983$	−45.9669	−1.46612	−0.733058	−	0.680166i	$-0.761908\pi$
$983$	−45.9669	−1.46612	−0.733058	+	0.680166i	$0.761908\pi$
$984$	3.95278	0.126010
$985$	0.766893	0.0244353
$986$	−40.1094	−1.27734
$987$	−45.1631	−1.43756
$988$	−23.3096	−0.741576
$989$	−29.5620	−0.940017
$990$	−1.94066	−0.0616781
$991$	−25.3095	−0.803984	−0.401992	−	0.915643i	$-0.631682\pi$
$991$	−25.3095	−0.803984	−0.401992	+	0.915643i	$0.631682\pi$
$992$	−2.24915	−0.0714106
$993$	−16.5174	−0.524163
$994$	−19.5860	−0.621229
$995$	9.64812	0.305866
$996$	2.01082	0.0637154
$997$	−19.1672	−0.607031	−0.303516	−	0.952826i	$-0.598160\pi$
$997$	−19.1672	−0.607031	−0.303516	+	0.952826i	$0.598160\pi$
$998$	−2.80077	−0.0886569
$999$	10.2387	0.323939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bb.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bb.1.5	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.94066 q^{5} +1.00000 q^{6} +4.68569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.94066 q^{5} +1.00000 q^{6} +4.68569 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.94066 q^{10} -1.00000 q^{11} +1.00000 q^{12} +3.54296 q^{13} +4.68569 q^{14} +1.94066 q^{15} +1.00000 q^{16} -4.52111 q^{17} +1.00000 q^{18} -6.57912 q^{19} +1.94066 q^{20} +4.68569 q^{21} -1.00000 q^{22} +2.30849 q^{23} +1.00000 q^{24} -1.23385 q^{25} +3.54296 q^{26} +1.00000 q^{27} +4.68569 q^{28} +8.87158 q^{29} +1.94066 q^{30} -2.24915 q^{31} +1.00000 q^{32} -1.00000 q^{33} -4.52111 q^{34} +9.09332 q^{35} +1.00000 q^{36} +10.2387 q^{37} -6.57912 q^{38} +3.54296 q^{39} +1.94066 q^{40} +3.95278 q^{41} +4.68569 q^{42} -12.8057 q^{43} -1.00000 q^{44} +1.94066 q^{45} +2.30849 q^{46} -9.63852 q^{47} +1.00000 q^{48} +14.9557 q^{49} -1.23385 q^{50} -4.52111 q^{51} +3.54296 q^{52} +1.32122 q^{53} +1.00000 q^{54} -1.94066 q^{55} +4.68569 q^{56} -6.57912 q^{57} +8.87158 q^{58} -2.76033 q^{59} +1.94066 q^{60} +1.00000 q^{61} -2.24915 q^{62} +4.68569 q^{63} +1.00000 q^{64} +6.87566 q^{65} -1.00000 q^{66} -7.05220 q^{67} -4.52111 q^{68} +2.30849 q^{69} +9.09332 q^{70} -4.17995 q^{71} +1.00000 q^{72} +14.6272 q^{73} +10.2387 q^{74} -1.23385 q^{75} -6.57912 q^{76} -4.68569 q^{77} +3.54296 q^{78} +1.12670 q^{79} +1.94066 q^{80} +1.00000 q^{81} +3.95278 q^{82} +2.01082 q^{83} +4.68569 q^{84} -8.77391 q^{85} -12.8057 q^{86} +8.87158 q^{87} -1.00000 q^{88} -16.3921 q^{89} +1.94066 q^{90} +16.6012 q^{91} +2.30849 q^{92} -2.24915 q^{93} -9.63852 q^{94} -12.7678 q^{95} +1.00000 q^{96} +3.05621 q^{97} +14.9557 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * q^99

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