LMFDB - Embedded newform 4026.2.a.z.1.6

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 18x^{5} - 10x^{4} + 91x^{3} + 90x^{2} - 66x - 56 $ x^7 - 18x^5 - 10x^4 + 91x^3 + 90x^2 - 66*x - 56
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.20695$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06294 q^{5} +1.00000 q^{6} +4.73255 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06294 q^{5} +1.00000 q^{6} +4.73255 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.06294 q^{10} +1.00000 q^{11} -1.00000 q^{12} -0.231429 q^{13} -4.73255 q^{14} -3.06294 q^{15} +1.00000 q^{16} -4.87703 q^{17} -1.00000 q^{18} -4.20484 q^{19} +3.06294 q^{20} -4.73255 q^{21} -1.00000 q^{22} +1.20402 q^{23} +1.00000 q^{24} +4.38158 q^{25} +0.231429 q^{26} -1.00000 q^{27} +4.73255 q^{28} +5.32668 q^{29} +3.06294 q^{30} +0.0819253 q^{31} -1.00000 q^{32} -1.00000 q^{33} +4.87703 q^{34} +14.4955 q^{35} +1.00000 q^{36} -7.00611 q^{37} +4.20484 q^{38} +0.231429 q^{39} -3.06294 q^{40} +5.37220 q^{41} +4.73255 q^{42} -9.29543 q^{43} +1.00000 q^{44} +3.06294 q^{45} -1.20402 q^{46} +1.75602 q^{47} -1.00000 q^{48} +15.3970 q^{49} -4.38158 q^{50} +4.87703 q^{51} -0.231429 q^{52} +10.9374 q^{53} +1.00000 q^{54} +3.06294 q^{55} -4.73255 q^{56} +4.20484 q^{57} -5.32668 q^{58} +5.79389 q^{59} -3.06294 q^{60} -1.00000 q^{61} -0.0819253 q^{62} +4.73255 q^{63} +1.00000 q^{64} -0.708852 q^{65} +1.00000 q^{66} +15.3970 q^{67} -4.87703 q^{68} -1.20402 q^{69} -14.4955 q^{70} +9.99200 q^{71} -1.00000 q^{72} +4.57918 q^{73} +7.00611 q^{74} -4.38158 q^{75} -4.20484 q^{76} +4.73255 q^{77} -0.231429 q^{78} +8.25495 q^{79} +3.06294 q^{80} +1.00000 q^{81} -5.37220 q^{82} +11.2416 q^{83} -4.73255 q^{84} -14.9380 q^{85} +9.29543 q^{86} -5.32668 q^{87} -1.00000 q^{88} +3.38667 q^{89} -3.06294 q^{90} -1.09525 q^{91} +1.20402 q^{92} -0.0819253 q^{93} -1.75602 q^{94} -12.8792 q^{95} +1.00000 q^{96} +0.864478 q^{97} -15.3970 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * 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
$5$	3.06294	1.36979	0.684893	−	0.728643i	$-0.259849\pi$
$5$	3.06294	1.36979	0.684893	+	0.728643i	$0.259849\pi$
$6$	1.00000	0.408248
$7$	4.73255	1.78874	0.894368	−	0.447332i	$-0.147626\pi$
$7$	4.73255	1.78874	0.894368	+	0.447332i	$0.147626\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.06294	−0.968586
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−0.231429	−0.0641869	−0.0320934	−	0.999485i	$-0.510217\pi$
$13$	−0.231429	−0.0641869	−0.0320934	+	0.999485i	$0.510217\pi$
$14$	−4.73255	−1.26483
$15$	−3.06294	−0.790847
$16$	1.00000	0.250000
$17$	−4.87703	−1.18285	−0.591426	−	0.806359i	$-0.701435\pi$
$17$	−4.87703	−1.18285	−0.591426	+	0.806359i	$0.701435\pi$
$18$	−1.00000	−0.235702
$19$	−4.20484	−0.964657	−0.482328	−	0.875990i	$-0.660209\pi$
$19$	−4.20484	−0.964657	−0.482328	+	0.875990i	$0.660209\pi$
$20$	3.06294	0.684893
$21$	−4.73255	−1.03273
$22$	−1.00000	−0.213201
$23$	1.20402	0.251056	0.125528	−	0.992090i	$-0.459937\pi$
$23$	1.20402	0.251056	0.125528	+	0.992090i	$0.459937\pi$
$24$	1.00000	0.204124
$25$	4.38158	0.876316
$26$	0.231429	0.0453870
$27$	−1.00000	−0.192450
$28$	4.73255	0.894368
$29$	5.32668	0.989139	0.494570	−	0.869138i	$-0.335326\pi$
$29$	5.32668	0.989139	0.494570	+	0.869138i	$0.335326\pi$
$30$	3.06294	0.559213
$31$	0.0819253	0.0147142	0.00735711	−	0.999973i	$-0.497658\pi$
$31$	0.0819253	0.0147142	0.00735711	+	0.999973i	$0.497658\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	4.87703	0.836403
$35$	14.4955	2.45019
$36$	1.00000	0.166667
$37$	−7.00611	−1.15180	−0.575899	−	0.817521i	$-0.695348\pi$
$37$	−7.00611	−1.15180	−0.575899	+	0.817521i	$0.695348\pi$
$38$	4.20484	0.682115
$39$	0.231429	0.0370583
$40$	−3.06294	−0.484293
$41$	5.37220	0.838996	0.419498	−	0.907756i	$-0.362206\pi$
$41$	5.37220	0.838996	0.419498	+	0.907756i	$0.362206\pi$
$42$	4.73255	0.730248
$43$	−9.29543	−1.41754	−0.708770	−	0.705440i	$-0.750750\pi$
$43$	−9.29543	−1.41754	−0.708770	+	0.705440i	$0.750750\pi$
$44$	1.00000	0.150756
$45$	3.06294	0.456596
$46$	−1.20402	−0.177524
$47$	1.75602	0.256142	0.128071	−	0.991765i	$-0.459121\pi$
$47$	1.75602	0.256142	0.128071	+	0.991765i	$0.459121\pi$
$48$	−1.00000	−0.144338
$49$	15.3970	2.19958
$50$	−4.38158	−0.619649
$51$	4.87703	0.682920
$52$	−0.231429	−0.0320934
$53$	10.9374	1.50237	0.751183	−	0.660094i	$-0.229483\pi$
$53$	10.9374	1.50237	0.751183	+	0.660094i	$0.229483\pi$
$54$	1.00000	0.136083
$55$	3.06294	0.413006
$56$	−4.73255	−0.632414
$57$	4.20484	0.556945
$58$	−5.32668	−0.699427
$59$	5.79389	0.754300	0.377150	−	0.926152i	$-0.376904\pi$
$59$	5.79389	0.754300	0.377150	+	0.926152i	$0.376904\pi$
$60$	−3.06294	−0.395423
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.0819253	−0.0104045
$63$	4.73255	0.596245
$64$	1.00000	0.125000
$65$	−0.708852	−0.0879223
$66$	1.00000	0.123091
$67$	15.3970	1.88104	0.940522	−	0.339732i	$-0.110336\pi$
$67$	15.3970	1.88104	0.940522	+	0.339732i	$0.110336\pi$
$68$	−4.87703	−0.591426
$69$	−1.20402	−0.144947
$70$	−14.4955	−1.73254
$71$	9.99200	1.18583	0.592916	−	0.805264i	$-0.297977\pi$
$71$	9.99200	1.18583	0.592916	+	0.805264i	$0.297977\pi$
$72$	−1.00000	−0.117851
$73$	4.57918	0.535952	0.267976	−	0.963426i	$-0.413645\pi$
$73$	4.57918	0.535952	0.267976	+	0.963426i	$0.413645\pi$
$74$	7.00611	0.814443
$75$	−4.38158	−0.505941
$76$	−4.20484	−0.482328
$77$	4.73255	0.539324
$78$	−0.231429	−0.0262042
$79$	8.25495	0.928755	0.464377	−	0.885637i	$-0.346278\pi$
$79$	8.25495	0.928755	0.464377	+	0.885637i	$0.346278\pi$
$80$	3.06294	0.342447
$81$	1.00000	0.111111
$82$	−5.37220	−0.593260
$83$	11.2416	1.23392	0.616961	−	0.786994i	$-0.288364\pi$
$83$	11.2416	1.23392	0.616961	+	0.786994i	$0.288364\pi$
$84$	−4.73255	−0.516364
$85$	−14.9380	−1.62026
$86$	9.29543	1.00235
$87$	−5.32668	−0.571080
$88$	−1.00000	−0.106600
$89$	3.38667	0.358987	0.179493	−	0.983759i	$-0.442554\pi$
$89$	3.38667	0.358987	0.179493	+	0.983759i	$0.442554\pi$
$90$	−3.06294	−0.322862
$91$	−1.09525	−0.114813
$92$	1.20402	0.125528
$93$	−0.0819253	−0.00849525
$94$	−1.75602	−0.181120
$95$	−12.8792	−1.32137
$96$	1.00000	0.102062
$97$	0.864478	0.0877744	0.0438872	−	0.999036i	$-0.486026\pi$
$97$	0.864478	0.0877744	0.0438872	+	0.999036i	$0.486026\pi$
$98$	−15.3970	−1.55533
$99$	1.00000	0.100504
$100$	4.38158	0.438158
$101$	0.314449	0.0312888	0.0156444	−	0.999878i	$-0.495020\pi$
$101$	0.314449	0.0312888	0.0156444	+	0.999878i	$0.495020\pi$
$102$	−4.87703	−0.482898
$103$	−3.40473	−0.335478	−0.167739	−	0.985831i	$-0.553647\pi$
$103$	−3.40473	−0.335478	−0.167739	+	0.985831i	$0.553647\pi$
$104$	0.231429	0.0226935
$105$	−14.4955	−1.41462
$106$	−10.9374	−1.06233
$107$	9.08294	0.878081	0.439040	−	0.898467i	$-0.355318\pi$
$107$	9.08294	0.878081	0.439040	+	0.898467i	$0.355318\pi$
$108$	−1.00000	−0.0962250
$109$	5.77532	0.553176	0.276588	−	0.960989i	$-0.410796\pi$
$109$	5.77532	0.553176	0.276588	+	0.960989i	$0.410796\pi$
$110$	−3.06294	−0.292040
$111$	7.00611	0.664990
$112$	4.73255	0.447184
$113$	−19.2142	−1.80752	−0.903762	−	0.428036i	$-0.859206\pi$
$113$	−19.2142	−1.80752	−0.903762	+	0.428036i	$0.859206\pi$
$114$	−4.20484	−0.393820
$115$	3.68785	0.343893
$116$	5.32668	0.494570
$117$	−0.231429	−0.0213956
$118$	−5.79389	−0.533371
$119$	−23.0808	−2.11581
$120$	3.06294	0.279607
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−5.37220	−0.484395
$124$	0.0819253	0.00735711
$125$	−1.89418	−0.169421
$126$	−4.73255	−0.421609
$127$	−12.3154	−1.09282	−0.546410	−	0.837518i	$-0.684006\pi$
$127$	−12.3154	−1.09282	−0.546410	+	0.837518i	$0.684006\pi$
$128$	−1.00000	−0.0883883
$129$	9.29543	0.818417
$130$	0.708852	0.0621705
$131$	7.13278	0.623194	0.311597	−	0.950214i	$-0.399136\pi$
$131$	7.13278	0.623194	0.311597	+	0.950214i	$0.399136\pi$
$132$	−1.00000	−0.0870388
$133$	−19.8996	−1.72552
$134$	−15.3970	−1.33010
$135$	−3.06294	−0.263616
$136$	4.87703	0.418202
$137$	−5.96047	−0.509237	−0.254618	−	0.967042i	$-0.581950\pi$
$137$	−5.96047	−0.509237	−0.254618	+	0.967042i	$0.581950\pi$
$138$	1.20402	0.102493
$139$	−18.5293	−1.57163	−0.785816	−	0.618460i	$-0.787757\pi$
$139$	−18.5293	−1.57163	−0.785816	+	0.618460i	$0.787757\pi$
$140$	14.4955	1.22509
$141$	−1.75602	−0.147884
$142$	−9.99200	−0.838510
$143$	−0.231429	−0.0193531
$144$	1.00000	0.0833333
$145$	16.3153	1.35491
$146$	−4.57918	−0.378975
$147$	−15.3970	−1.26993
$148$	−7.00611	−0.575899
$149$	−3.03040	−0.248260	−0.124130	−	0.992266i	$-0.539614\pi$
$149$	−3.03040	−0.248260	−0.124130	+	0.992266i	$0.539614\pi$
$150$	4.38158	0.357754
$151$	−5.81269	−0.473030	−0.236515	−	0.971628i	$-0.576005\pi$
$151$	−5.81269	−0.473030	−0.236515	+	0.971628i	$0.576005\pi$
$152$	4.20484	0.341058
$153$	−4.87703	−0.394284
$154$	−4.73255	−0.381360
$155$	0.250932	0.0201553
$156$	0.231429	0.0185291
$157$	19.1457	1.52800	0.763998	−	0.645219i	$-0.223234\pi$
$157$	19.1457	1.52800	0.763998	+	0.645219i	$0.223234\pi$
$158$	−8.25495	−0.656729
$159$	−10.9374	−0.867392
$160$	−3.06294	−0.242146
$161$	5.69810	0.449073
$162$	−1.00000	−0.0785674
$163$	12.3047	0.963778	0.481889	−	0.876232i	$-0.339951\pi$
$163$	12.3047	0.963778	0.481889	+	0.876232i	$0.339951\pi$
$164$	5.37220	0.419498
$165$	−3.06294	−0.238449
$166$	−11.2416	−0.872514
$167$	6.76133	0.523207	0.261604	−	0.965175i	$-0.415749\pi$
$167$	6.76133	0.523207	0.261604	+	0.965175i	$0.415749\pi$
$168$	4.73255	0.365124
$169$	−12.9464	−0.995880
$170$	14.9380	1.14569
$171$	−4.20484	−0.321552
$172$	−9.29543	−0.708770
$173$	6.94964	0.528371	0.264186	−	0.964472i	$-0.414897\pi$
$173$	6.94964	0.528371	0.264186	+	0.964472i	$0.414897\pi$
$174$	5.32668	0.403814
$175$	20.7360	1.56750
$176$	1.00000	0.0753778
$177$	−5.79389	−0.435496
$178$	−3.38667	−0.253842
$179$	−0.426608	−0.0318862	−0.0159431	−	0.999873i	$-0.505075\pi$
$179$	−0.426608	−0.0318862	−0.0159431	+	0.999873i	$0.505075\pi$
$180$	3.06294	0.228298
$181$	−10.4989	−0.780376	−0.390188	−	0.920735i	$-0.627590\pi$
$181$	−10.4989	−0.780376	−0.390188	+	0.920735i	$0.627590\pi$
$182$	1.09525	0.0811853
$183$	1.00000	0.0739221
$184$	−1.20402	−0.0887618
$185$	−21.4593	−1.57772
$186$	0.0819253	0.00600705
$187$	−4.87703	−0.356643
$188$	1.75602	0.128071
$189$	−4.73255	−0.344242
$190$	12.8792	0.934353
$191$	10.4894	0.758989	0.379495	−	0.925194i	$-0.376098\pi$
$191$	10.4894	0.758989	0.379495	+	0.925194i	$0.376098\pi$
$192$	−1.00000	−0.0721688
$193$	1.55657	0.112045	0.0560223	−	0.998430i	$-0.482158\pi$
$193$	1.55657	0.112045	0.0560223	+	0.998430i	$0.482158\pi$
$194$	−0.864478	−0.0620659
$195$	0.708852	0.0507620
$196$	15.3970	1.09979
$197$	6.50848	0.463710	0.231855	−	0.972750i	$-0.425520\pi$
$197$	6.50848	0.463710	0.231855	+	0.972750i	$0.425520\pi$
$198$	−1.00000	−0.0710669
$199$	4.91653	0.348524	0.174262	−	0.984699i	$-0.444246\pi$
$199$	4.91653	0.348524	0.174262	+	0.984699i	$0.444246\pi$
$200$	−4.38158	−0.309824
$201$	−15.3970	−1.08602
$202$	−0.314449	−0.0221245
$203$	25.2088	1.76931
$204$	4.87703	0.341460
$205$	16.4547	1.14925
$206$	3.40473	0.237219
$207$	1.20402	0.0836854
$208$	−0.231429	−0.0160467
$209$	−4.20484	−0.290855
$210$	14.4955	1.00028
$211$	23.1466	1.59348	0.796740	−	0.604322i	$-0.206556\pi$
$211$	23.1466	1.59348	0.796740	+	0.604322i	$0.206556\pi$
$212$	10.9374	0.751183
$213$	−9.99200	−0.684641
$214$	−9.08294	−0.620897
$215$	−28.4713	−1.94173
$216$	1.00000	0.0680414
$217$	0.387715	0.0263198
$218$	−5.77532	−0.391154
$219$	−4.57918	−0.309432
$220$	3.06294	0.206503
$221$	1.12869	0.0759236
$222$	−7.00611	−0.470219
$223$	4.05427	0.271494	0.135747	−	0.990744i	$-0.456657\pi$
$223$	4.05427	0.271494	0.135747	+	0.990744i	$0.456657\pi$
$224$	−4.73255	−0.316207
$225$	4.38158	0.292105
$226$	19.2142	1.27811
$227$	−11.8552	−0.786857	−0.393429	−	0.919355i	$-0.628711\pi$
$227$	−11.8552	−0.786857	−0.393429	+	0.919355i	$0.628711\pi$
$228$	4.20484	0.278472
$229$	19.5061	1.28900	0.644499	−	0.764605i	$-0.277066\pi$
$229$	19.5061	1.28900	0.644499	+	0.764605i	$0.277066\pi$
$230$	−3.68785	−0.243169
$231$	−4.73255	−0.311379
$232$	−5.32668	−0.349714
$233$	12.0667	0.790517	0.395258	−	0.918570i	$-0.370655\pi$
$233$	12.0667	0.790517	0.395258	+	0.918570i	$0.370655\pi$
$234$	0.231429	0.0151290
$235$	5.37859	0.350860
$236$	5.79389	0.377150
$237$	−8.25495	−0.536217
$238$	23.0808	1.49610
$239$	14.0086	0.906143	0.453072	−	0.891474i	$-0.350328\pi$
$239$	14.0086	0.906143	0.453072	+	0.891474i	$0.350328\pi$
$240$	−3.06294	−0.197712
$241$	−7.66981	−0.494056	−0.247028	−	0.969008i	$-0.579454\pi$
$241$	−7.66981	−0.494056	−0.247028	+	0.969008i	$0.579454\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	47.1601	3.01295
$246$	5.37220	0.342519
$247$	0.973122	0.0619183
$248$	−0.0819253	−0.00520226
$249$	−11.2416	−0.712405
$250$	1.89418	0.119799
$251$	4.02152	0.253836	0.126918	−	0.991913i	$-0.459492\pi$
$251$	4.02152	0.253836	0.126918	+	0.991913i	$0.459492\pi$
$252$	4.73255	0.298123
$253$	1.20402	0.0756963
$254$	12.3154	0.772740
$255$	14.9380	0.935455
$256$	1.00000	0.0625000
$257$	9.34424	0.582878	0.291439	−	0.956589i	$-0.405866\pi$
$257$	9.34424	0.582878	0.291439	+	0.956589i	$0.405866\pi$
$258$	−9.29543	−0.578708
$259$	−33.1568	−2.06026
$260$	−0.708852	−0.0439612
$261$	5.32668	0.329713
$262$	−7.13278	−0.440665
$263$	−13.3821	−0.825174	−0.412587	−	0.910918i	$-0.635375\pi$
$263$	−13.3821	−0.825174	−0.412587	+	0.910918i	$0.635375\pi$
$264$	1.00000	0.0615457
$265$	33.5005	2.05792
$266$	19.8996	1.22012
$267$	−3.38667	−0.207261
$268$	15.3970	0.940522
$269$	6.60537	0.402737	0.201368	−	0.979516i	$-0.435461\pi$
$269$	6.60537	0.402737	0.201368	+	0.979516i	$0.435461\pi$
$270$	3.06294	0.186404
$271$	−24.5532	−1.49150	−0.745751	−	0.666225i	$-0.767909\pi$
$271$	−24.5532	−1.49150	−0.745751	+	0.666225i	$0.767909\pi$
$272$	−4.87703	−0.295713
$273$	1.09525	0.0662875
$274$	5.96047	0.360085
$275$	4.38158	0.264219
$276$	−1.20402	−0.0724737
$277$	−28.0405	−1.68479	−0.842396	−	0.538858i	$-0.818856\pi$
$277$	−28.0405	−1.68479	−0.842396	+	0.538858i	$0.818856\pi$
$278$	18.5293	1.11131
$279$	0.0819253	0.00490474
$280$	−14.4955	−0.866272
$281$	−17.4004	−1.03802	−0.519011	−	0.854767i	$-0.673700\pi$
$281$	−17.4004	−1.03802	−0.519011	+	0.854767i	$0.673700\pi$
$282$	1.75602	0.104570
$283$	−0.671127	−0.0398944	−0.0199472	−	0.999801i	$-0.506350\pi$
$283$	−0.671127	−0.0398944	−0.0199472	+	0.999801i	$0.506350\pi$
$284$	9.99200	0.592916
$285$	12.8792	0.762896
$286$	0.231429	0.0136847
$287$	25.4242	1.50074
$288$	−1.00000	−0.0589256
$289$	6.78538	0.399140
$290$	−16.3153	−0.958066
$291$	−0.864478	−0.0506766
$292$	4.57918	0.267976
$293$	17.3834	1.01555	0.507773	−	0.861491i	$-0.330469\pi$
$293$	17.3834	1.01555	0.507773	+	0.861491i	$0.330469\pi$
$294$	15.3970	0.897973
$295$	17.7463	1.03323
$296$	7.00611	0.407222
$297$	−1.00000	−0.0580259
$298$	3.03040	0.175546
$299$	−0.278646	−0.0161145
$300$	−4.38158	−0.252971
$301$	−43.9911	−2.53560
$302$	5.81269	0.334483
$303$	−0.314449	−0.0180646
$304$	−4.20484	−0.241164
$305$	−3.06294	−0.175383
$306$	4.87703	0.278801
$307$	−14.7476	−0.841691	−0.420845	−	0.907132i	$-0.638267\pi$
$307$	−14.7476	−0.841691	−0.420845	+	0.907132i	$0.638267\pi$
$308$	4.73255	0.269662
$309$	3.40473	0.193689
$310$	−0.250932	−0.0142520
$311$	4.04166	0.229181	0.114591	−	0.993413i	$-0.463444\pi$
$311$	4.04166	0.229181	0.114591	+	0.993413i	$0.463444\pi$
$312$	−0.231429	−0.0131021
$313$	−18.1455	−1.02564	−0.512821	−	0.858495i	$-0.671400\pi$
$313$	−18.1455	−1.02564	−0.512821	+	0.858495i	$0.671400\pi$
$314$	−19.1457	−1.08046
$315$	14.4955	0.816729
$316$	8.25495	0.464377
$317$	1.21019	0.0679709	0.0339855	−	0.999422i	$-0.489180\pi$
$317$	1.21019	0.0679709	0.0339855	+	0.999422i	$0.489180\pi$
$318$	10.9374	0.613338
$319$	5.32668	0.298237
$320$	3.06294	0.171223
$321$	−9.08294	−0.506960
$322$	−5.69810	−0.317543
$323$	20.5071	1.14105
$324$	1.00000	0.0555556
$325$	−1.01402	−0.0562480
$326$	−12.3047	−0.681494
$327$	−5.77532	−0.319376
$328$	−5.37220	−0.296630
$329$	8.31046	0.458171
$330$	3.06294	0.168609
$331$	−26.9173	−1.47951	−0.739755	−	0.672877i	$-0.765059\pi$
$331$	−26.9173	−1.47951	−0.739755	+	0.672877i	$0.765059\pi$
$332$	11.2416	0.616961
$333$	−7.00611	−0.383932
$334$	−6.76133	−0.369963
$335$	47.1601	2.57663
$336$	−4.73255	−0.258182
$337$	−25.2874	−1.37749	−0.688745	−	0.725004i	$-0.741838\pi$
$337$	−25.2874	−1.37749	−0.688745	+	0.725004i	$0.741838\pi$
$338$	12.9464	0.704194
$339$	19.2142	1.04357
$340$	−14.9380	−0.810128
$341$	0.0819253	0.00443650
$342$	4.20484	0.227372
$343$	39.7393	2.14572
$344$	9.29543	0.501176
$345$	−3.68785	−0.198547
$346$	−6.94964	−0.373615
$347$	−3.58079	−0.192227	−0.0961133	−	0.995370i	$-0.530641\pi$
$347$	−3.58079	−0.192227	−0.0961133	+	0.995370i	$0.530641\pi$
$348$	−5.32668	−0.285540
$349$	26.7319	1.43093	0.715463	−	0.698651i	$-0.246216\pi$
$349$	26.7319	1.43093	0.715463	+	0.698651i	$0.246216\pi$
$350$	−20.7360	−1.10839
$351$	0.231429	0.0123528
$352$	−1.00000	−0.0533002
$353$	−33.6272	−1.78980	−0.894899	−	0.446269i	$-0.852752\pi$
$353$	−33.6272	−1.78980	−0.894899	+	0.446269i	$0.852752\pi$
$354$	5.79389	0.307942
$355$	30.6049	1.62434
$356$	3.38667	0.179493
$357$	23.0808	1.22156
$358$	0.426608	0.0225469
$359$	1.93143	0.101937	0.0509685	−	0.998700i	$-0.483769\pi$
$359$	1.93143	0.101937	0.0509685	+	0.998700i	$0.483769\pi$
$360$	−3.06294	−0.161431
$361$	−1.31930	−0.0694370
$362$	10.4989	0.551809
$363$	−1.00000	−0.0524864
$364$	−1.09525	−0.0574067
$365$	14.0257	0.734140
$366$	−1.00000	−0.0522708
$367$	19.2126	1.00289	0.501446	−	0.865189i	$-0.332802\pi$
$367$	19.2126	1.00289	0.501446	+	0.865189i	$0.332802\pi$
$368$	1.20402	0.0627640
$369$	5.37220	0.279665
$370$	21.4593	1.11561
$371$	51.7618	2.68734
$372$	−0.0819253	−0.00424763
$373$	−26.7346	−1.38427	−0.692134	−	0.721769i	$-0.743329\pi$
$373$	−26.7346	−1.38427	−0.692134	+	0.721769i	$0.743329\pi$
$374$	4.87703	0.252185
$375$	1.89418	0.0978151
$376$	−1.75602	−0.0905600
$377$	−1.23275	−0.0634897
$378$	4.73255	0.243416
$379$	18.0946	0.929457	0.464728	−	0.885453i	$-0.346152\pi$
$379$	18.0946	0.929457	0.464728	+	0.885453i	$0.346152\pi$
$380$	−12.8792	−0.660687
$381$	12.3154	0.630940
$382$	−10.4894	−0.536686
$383$	21.6196	1.10471	0.552356	−	0.833609i	$-0.313729\pi$
$383$	21.6196	1.10471	0.552356	+	0.833609i	$0.313729\pi$
$384$	1.00000	0.0510310
$385$	14.4955	0.738759
$386$	−1.55657	−0.0792276
$387$	−9.29543	−0.472513
$388$	0.864478	0.0438872
$389$	−25.1663	−1.27598	−0.637992	−	0.770043i	$-0.720235\pi$
$389$	−25.1663	−1.27598	−0.637992	+	0.770043i	$0.720235\pi$
$390$	−0.708852	−0.0358941
$391$	−5.87205	−0.296962
$392$	−15.3970	−0.777667
$393$	−7.13278	−0.359801
$394$	−6.50848	−0.327893
$395$	25.2844	1.27220
$396$	1.00000	0.0502519
$397$	−12.3807	−0.621372	−0.310686	−	0.950513i	$-0.600559\pi$
$397$	−12.3807	−0.621372	−0.310686	+	0.950513i	$0.600559\pi$
$398$	−4.91653	−0.246444
$399$	19.8996	0.996227
$400$	4.38158	0.219079
$401$	7.34649	0.366866	0.183433	−	0.983032i	$-0.441279\pi$
$401$	7.34649	0.366866	0.183433	+	0.983032i	$0.441279\pi$
$402$	15.3970	0.767933
$403$	−0.0189599	−0.000944459 0
$404$	0.314449	0.0156444
$405$	3.06294	0.152199
$406$	−25.2088	−1.25109
$407$	−7.00611	−0.347280
$408$	−4.87703	−0.241449
$409$	−5.30255	−0.262194	−0.131097	−	0.991370i	$-0.541850\pi$
$409$	−5.30255	−0.262194	−0.131097	+	0.991370i	$0.541850\pi$
$410$	−16.4547	−0.812640
$411$	5.96047	0.294008
$412$	−3.40473	−0.167739
$413$	27.4199	1.34924
$414$	−1.20402	−0.0591745
$415$	34.4322	1.69021
$416$	0.231429	0.0113467
$417$	18.5293	0.907382
$418$	4.20484	0.205666
$419$	14.5810	0.712329	0.356165	−	0.934423i	$-0.384084\pi$
$419$	14.5810	0.712329	0.356165	+	0.934423i	$0.384084\pi$
$420$	−14.4955	−0.707308
$421$	−27.4752	−1.33906	−0.669529	−	0.742786i	$-0.733504\pi$
$421$	−27.4752	−1.33906	−0.669529	+	0.742786i	$0.733504\pi$
$422$	−23.1466	−1.12676
$423$	1.75602	0.0853807
$424$	−10.9374	−0.531167
$425$	−21.3691	−1.03655
$426$	9.99200	0.484114
$427$	−4.73255	−0.229024
$428$	9.08294	0.439040
$429$	0.231429	0.0111735
$430$	28.4713	1.37301
$431$	−4.07682	−0.196373	−0.0981867	−	0.995168i	$-0.531304\pi$
$431$	−4.07682	−0.196373	−0.0981867	+	0.995168i	$0.531304\pi$
$432$	−1.00000	−0.0481125
$433$	34.9492	1.67955	0.839775	−	0.542934i	$-0.182687\pi$
$433$	34.9492	1.67955	0.839775	+	0.542934i	$0.182687\pi$
$434$	−0.387715	−0.0186109
$435$	−16.3153	−0.782258
$436$	5.77532	0.276588
$437$	−5.06273	−0.242183
$438$	4.57918	0.218802
$439$	1.14999	0.0548860	0.0274430	−	0.999623i	$-0.491264\pi$
$439$	1.14999	0.0548860	0.0274430	+	0.999623i	$0.491264\pi$
$440$	−3.06294	−0.146020
$441$	15.3970	0.733192
$442$	−1.12869	−0.0536861
$443$	−6.90102	−0.327877	−0.163939	−	0.986471i	$-0.552420\pi$
$443$	−6.90102	−0.327877	−0.163939	+	0.986471i	$0.552420\pi$
$444$	7.00611	0.332495
$445$	10.3732	0.491735
$446$	−4.05427	−0.191975
$447$	3.03040	0.143333
$448$	4.73255	0.223592
$449$	9.92865	0.468562	0.234281	−	0.972169i	$-0.424726\pi$
$449$	9.92865	0.468562	0.234281	+	0.972169i	$0.424726\pi$
$450$	−4.38158	−0.206550
$451$	5.37220	0.252967
$452$	−19.2142	−0.903762
$453$	5.81269	0.273104
$454$	11.8552	0.556392
$455$	−3.35468	−0.157270
$456$	−4.20484	−0.196910
$457$	−31.9253	−1.49340	−0.746701	−	0.665160i	$-0.768363\pi$
$457$	−31.9253	−1.49340	−0.746701	+	0.665160i	$0.768363\pi$
$458$	−19.5061	−0.911460
$459$	4.87703	0.227640
$460$	3.68785	0.171947
$461$	24.4378	1.13818	0.569091	−	0.822275i	$-0.307295\pi$
$461$	24.4378	1.13818	0.569091	+	0.822275i	$0.307295\pi$
$462$	4.73255	0.220178
$463$	−15.9097	−0.739386	−0.369693	−	0.929154i	$-0.620537\pi$
$463$	−15.9097	−0.739386	−0.369693	+	0.929154i	$0.620537\pi$
$464$	5.32668	0.247285
$465$	−0.250932	−0.0116367
$466$	−12.0667	−0.558980
$467$	−9.01702	−0.417258	−0.208629	−	0.977995i	$-0.566900\pi$
$467$	−9.01702	−0.417258	−0.208629	+	0.977995i	$0.566900\pi$
$468$	−0.231429	−0.0106978
$469$	72.8671	3.36469
$470$	−5.37859	−0.248096
$471$	−19.1457	−0.882188
$472$	−5.79389	−0.266685
$473$	−9.29543	−0.427404
$474$	8.25495	0.379163
$475$	−18.4239	−0.845344
$476$	−23.0808	−1.05791
$477$	10.9374	0.500789
$478$	−14.0086	−0.640740
$479$	−10.5048	−0.479975	−0.239988	−	0.970776i	$-0.577143\pi$
$479$	−10.5048	−0.479975	−0.239988	+	0.970776i	$0.577143\pi$
$480$	3.06294	0.139803
$481$	1.62142	0.0739302
$482$	7.66981	0.349350
$483$	−5.69810	−0.259273
$484$	1.00000	0.0454545
$485$	2.64784	0.120232
$486$	1.00000	0.0453609
$487$	24.1537	1.09451	0.547254	−	0.836967i	$-0.315673\pi$
$487$	24.1537	1.09451	0.547254	+	0.836967i	$0.315673\pi$
$488$	1.00000	0.0452679
$489$	−12.3047	−0.556437
$490$	−47.1601	−2.13048
$491$	−20.5679	−0.928216	−0.464108	−	0.885779i	$-0.653625\pi$
$491$	−20.5679	−0.928216	−0.464108	+	0.885779i	$0.653625\pi$
$492$	−5.37220	−0.242197
$493$	−25.9783	−1.17001
$494$	−0.973122	−0.0437828
$495$	3.06294	0.137669
$496$	0.0819253	0.00367855
$497$	47.2876	2.12114
$498$	11.2416	0.503746
$499$	−13.4642	−0.602742	−0.301371	−	0.953507i	$-0.597444\pi$
$499$	−13.4642	−0.602742	−0.301371	+	0.953507i	$0.597444\pi$
$500$	−1.89418	−0.0847104
$501$	−6.76133	−0.302074
$502$	−4.02152	−0.179489
$503$	−18.8158	−0.838953	−0.419477	−	0.907766i	$-0.637786\pi$
$503$	−18.8158	−0.838953	−0.419477	+	0.907766i	$0.637786\pi$
$504$	−4.73255	−0.210805
$505$	0.963136	0.0428590
$506$	−1.20402	−0.0535254
$507$	12.9464	0.574972
$508$	−12.3154	−0.546410
$509$	2.04632	0.0907017	0.0453508	−	0.998971i	$-0.485559\pi$
$509$	2.04632	0.0907017	0.0453508	+	0.998971i	$0.485559\pi$
$510$	−14.9380	−0.661467
$511$	21.6712	0.958677
$512$	−1.00000	−0.0441942
$513$	4.20484	0.185648
$514$	−9.34424	−0.412157
$515$	−10.4285	−0.459534
$516$	9.29543	0.409209
$517$	1.75602	0.0772298
$518$	33.1568	1.45682
$519$	−6.94964	−0.305055
$520$	0.708852	0.0310852
$521$	−18.0925	−0.792645	−0.396323	−	0.918111i	$-0.629714\pi$
$521$	−18.0925	−0.792645	−0.396323	+	0.918111i	$0.629714\pi$
$522$	−5.32668	−0.233142
$523$	34.4158	1.50490	0.752449	−	0.658650i	$-0.228872\pi$
$523$	34.4158	1.50490	0.752449	+	0.658650i	$0.228872\pi$
$524$	7.13278	0.311597
$525$	−20.7360	−0.904995
$526$	13.3821	0.583486
$527$	−0.399552	−0.0174047
$528$	−1.00000	−0.0435194
$529$	−21.5503	−0.936971
$530$	−33.5005	−1.45517
$531$	5.79389	0.251433
$532$	−19.8996	−0.862758
$533$	−1.24328	−0.0538525
$534$	3.38667	0.146556
$535$	27.8205	1.20278
$536$	−15.3970	−0.665050
$537$	0.426608	0.0184095
$538$	−6.60537	−0.284778
$539$	15.3970	0.663197
$540$	−3.06294	−0.131808
$541$	−24.1414	−1.03792	−0.518960	−	0.854799i	$-0.673681\pi$
$541$	−24.1414	−1.03792	−0.518960	+	0.854799i	$0.673681\pi$
$542$	24.5532	1.05465
$543$	10.4989	0.450550
$544$	4.87703	0.209101
$545$	17.6894	0.757733
$546$	−1.09525	−0.0468723
$547$	19.0617	0.815021	0.407511	−	0.913200i	$-0.366397\pi$
$547$	19.0617	0.815021	0.407511	+	0.913200i	$0.366397\pi$
$548$	−5.96047	−0.254618
$549$	−1.00000	−0.0426790
$550$	−4.38158	−0.186831
$551$	−22.3978	−0.954180
$552$	1.20402	0.0512466
$553$	39.0670	1.66130
$554$	28.0405	1.19133
$555$	21.4593	0.910895
$556$	−18.5293	−0.785816
$557$	−3.22229	−0.136533	−0.0682663	−	0.997667i	$-0.521747\pi$
$557$	−3.22229	−0.136533	−0.0682663	+	0.997667i	$0.521747\pi$
$558$	−0.0819253	−0.00346817
$559$	2.15123	0.0909874
$560$	14.4955	0.612547
$561$	4.87703	0.205908
$562$	17.4004	0.733993
$563$	−7.59530	−0.320104	−0.160052	−	0.987109i	$-0.551166\pi$
$563$	−7.59530	−0.320104	−0.160052	+	0.987109i	$0.551166\pi$
$564$	−1.75602	−0.0739419
$565$	−58.8520	−2.47592
$566$	0.671127	0.0282096
$567$	4.73255	0.198748
$568$	−9.99200	−0.419255
$569$	19.5973	0.821562	0.410781	−	0.911734i	$-0.365256\pi$
$569$	19.5973	0.821562	0.410781	+	0.911734i	$0.365256\pi$
$570$	−12.8792	−0.539449
$571$	−36.2306	−1.51620	−0.758102	−	0.652136i	$-0.773873\pi$
$571$	−36.2306	−1.51620	−0.758102	+	0.652136i	$0.773873\pi$
$572$	−0.231429	−0.00967653
$573$	−10.4894	−0.438203
$574$	−25.4242	−1.06119
$575$	5.27552	0.220005
$576$	1.00000	0.0416667
$577$	−18.8091	−0.783034	−0.391517	−	0.920171i	$-0.628050\pi$
$577$	−18.8091	−0.783034	−0.391517	+	0.920171i	$0.628050\pi$
$578$	−6.78538	−0.282235
$579$	−1.55657	−0.0646890
$580$	16.3153	0.677455
$581$	53.2012	2.20716
$582$	0.864478	0.0358338
$583$	10.9374	0.452980
$584$	−4.57918	−0.189488
$585$	−0.708852	−0.0293074
$586$	−17.3834	−0.718100
$587$	−14.5854	−0.602002	−0.301001	−	0.953624i	$-0.597321\pi$
$587$	−14.5854	−0.602002	−0.301001	+	0.953624i	$0.597321\pi$
$588$	−15.3970	−0.634963
$589$	−0.344483	−0.0141942
$590$	−17.7463	−0.730605
$591$	−6.50848	−0.267723
$592$	−7.00611	−0.287949
$593$	−24.2341	−0.995175	−0.497588	−	0.867414i	$-0.665781\pi$
$593$	−24.2341	−0.995175	−0.497588	+	0.867414i	$0.665781\pi$
$594$	1.00000	0.0410305
$595$	−70.6949	−2.89821
$596$	−3.03040	−0.124130
$597$	−4.91653	−0.201220
$598$	0.278646	0.0113947
$599$	20.5826	0.840981	0.420490	−	0.907297i	$-0.361858\pi$
$599$	20.5826	0.840981	0.420490	+	0.907297i	$0.361858\pi$
$600$	4.38158	0.178877
$601$	−4.45636	−0.181779	−0.0908895	−	0.995861i	$-0.528971\pi$
$601$	−4.45636	−0.181779	−0.0908895	+	0.995861i	$0.528971\pi$
$602$	43.9911	1.79294
$603$	15.3970	0.627015
$604$	−5.81269	−0.236515
$605$	3.06294	0.124526
$606$	0.314449	0.0127736
$607$	−20.5723	−0.835005	−0.417503	−	0.908676i	$-0.637095\pi$
$607$	−20.5723	−0.835005	−0.417503	+	0.908676i	$0.637095\pi$
$608$	4.20484	0.170529
$609$	−25.2088	−1.02151
$610$	3.06294	0.124015
$611$	−0.406395	−0.0164410
$612$	−4.87703	−0.197142
$613$	−17.3703	−0.701580	−0.350790	−	0.936454i	$-0.614087\pi$
$613$	−17.3703	−0.701580	−0.350790	+	0.936454i	$0.614087\pi$
$614$	14.7476	0.595165
$615$	−16.4547	−0.663517
$616$	−4.73255	−0.190680
$617$	−25.1167	−1.01116	−0.505580	−	0.862780i	$-0.668721\pi$
$617$	−25.1167	−1.01116	−0.505580	+	0.862780i	$0.668721\pi$
$618$	−3.40473	−0.136958
$619$	23.5863	0.948013	0.474006	−	0.880521i	$-0.342807\pi$
$619$	23.5863	0.948013	0.474006	+	0.880521i	$0.342807\pi$
$620$	0.250932	0.0100777
$621$	−1.20402	−0.0483158
$622$	−4.04166	−0.162056
$623$	16.0276	0.642132
$624$	0.231429	0.00926457
$625$	−27.7097	−1.10839
$626$	18.1455	0.725239
$627$	4.20484	0.167925
$628$	19.1457	0.763998
$629$	34.1690	1.36241
$630$	−14.4955	−0.577515
$631$	33.8980	1.34946	0.674729	−	0.738066i	$-0.264261\pi$
$631$	33.8980	1.34946	0.674729	+	0.738066i	$0.264261\pi$
$632$	−8.25495	−0.328364
$633$	−23.1466	−0.919997
$634$	−1.21019	−0.0480627
$635$	−37.7214	−1.49693
$636$	−10.9374	−0.433696
$637$	−3.56332	−0.141184
$638$	−5.32668	−0.210885
$639$	9.99200	0.395278
$640$	−3.06294	−0.121073
$641$	−24.7119	−0.976060	−0.488030	−	0.872827i	$-0.662284\pi$
$641$	−24.7119	−0.976060	−0.488030	+	0.872827i	$0.662284\pi$
$642$	9.08294	0.358475
$643$	−9.58077	−0.377829	−0.188914	−	0.981994i	$-0.560497\pi$
$643$	−9.58077	−0.377829	−0.188914	+	0.981994i	$0.560497\pi$
$644$	5.69810	0.224537
$645$	28.4713	1.12106
$646$	−20.5071	−0.806842
$647$	−21.1905	−0.833083	−0.416541	−	0.909117i	$-0.636758\pi$
$647$	−21.1905	−0.833083	−0.416541	+	0.909117i	$0.636758\pi$
$648$	−1.00000	−0.0392837
$649$	5.79389	0.227430
$650$	1.01402	0.0397733
$651$	−0.387715	−0.0151958
$652$	12.3047	0.481889
$653$	25.1070	0.982511	0.491256	−	0.871016i	$-0.336538\pi$
$653$	25.1070	0.982511	0.491256	+	0.871016i	$0.336538\pi$
$654$	5.77532	0.225833
$655$	21.8473	0.853643
$656$	5.37220	0.209749
$657$	4.57918	0.178651
$658$	−8.31046	−0.323976
$659$	−38.2742	−1.49095	−0.745475	−	0.666533i	$-0.767777\pi$
$659$	−38.2742	−1.49095	−0.745475	+	0.666533i	$0.767777\pi$
$660$	−3.06294	−0.119225
$661$	31.6862	1.23245	0.616225	−	0.787570i	$-0.288661\pi$
$661$	31.6862	1.23245	0.616225	+	0.787570i	$0.288661\pi$
$662$	26.9173	1.04617
$663$	−1.12869	−0.0438345
$664$	−11.2416	−0.436257
$665$	−60.9513	−2.36359
$666$	7.00611	0.271481
$667$	6.41344	0.248330
$668$	6.76133	0.261604
$669$	−4.05427	−0.156747
$670$	−47.1601	−1.82195
$671$	−1.00000	−0.0386046
$672$	4.73255	0.182562
$673$	−16.4325	−0.633428	−0.316714	−	0.948521i	$-0.602579\pi$
$673$	−16.4325	−0.633428	−0.316714	+	0.948521i	$0.602579\pi$
$674$	25.2874	0.974032
$675$	−4.38158	−0.168647
$676$	−12.9464	−0.497940
$677$	−25.7777	−0.990719	−0.495359	−	0.868688i	$-0.664964\pi$
$677$	−25.7777	−0.990719	−0.495359	+	0.868688i	$0.664964\pi$
$678$	−19.2142	−0.737918
$679$	4.09118	0.157005
$680$	14.9380	0.572847
$681$	11.8552	0.454292
$682$	−0.0819253	−0.00313708
$683$	24.4607	0.935963	0.467982	−	0.883738i	$-0.344981\pi$
$683$	24.4607	0.935963	0.467982	+	0.883738i	$0.344981\pi$
$684$	−4.20484	−0.160776
$685$	−18.2565	−0.697546
$686$	−39.7393	−1.51726
$687$	−19.5061	−0.744204
$688$	−9.29543	−0.354385
$689$	−2.53123	−0.0964322
$690$	3.68785	0.140394
$691$	19.1727	0.729364	0.364682	−	0.931132i	$-0.381178\pi$
$691$	19.1727	0.729364	0.364682	+	0.931132i	$0.381178\pi$
$692$	6.94964	0.264186
$693$	4.73255	0.179775
$694$	3.58079	0.135925
$695$	−56.7540	−2.15280
$696$	5.32668	0.201907
$697$	−26.2003	−0.992409
$698$	−26.7319	−1.01182
$699$	−12.0667	−0.456405
$700$	20.7360	0.783749
$701$	−50.8424	−1.92029	−0.960146	−	0.279500i	$-0.909831\pi$
$701$	−50.8424	−1.92029	−0.960146	+	0.279500i	$0.909831\pi$
$702$	−0.231429	−0.00873472
$703$	29.4596	1.11109
$704$	1.00000	0.0376889
$705$	−5.37859	−0.202569
$706$	33.6272	1.26558
$707$	1.48814	0.0559674
$708$	−5.79389	−0.217748
$709$	−37.1393	−1.39480	−0.697399	−	0.716683i	$-0.745659\pi$
$709$	−37.1393	−1.39480	−0.697399	+	0.716683i	$0.745659\pi$
$710$	−30.6049	−1.14858
$711$	8.25495	0.309585
$712$	−3.38667	−0.126921
$713$	0.0986399	0.00369409
$714$	−23.0808	−0.863776
$715$	−0.708852	−0.0265096
$716$	−0.426608	−0.0159431
$717$	−14.0086	−0.523162
$718$	−1.93143	−0.0720804
$719$	42.5821	1.58805	0.794023	−	0.607888i	$-0.207983\pi$
$719$	42.5821	1.58805	0.794023	+	0.607888i	$0.207983\pi$
$720$	3.06294	0.114149
$721$	−16.1131	−0.600082
$722$	1.31930	0.0490994
$723$	7.66981	0.285243
$724$	−10.4989	−0.390188
$725$	23.3393	0.866799
$726$	1.00000	0.0371135
$727$	−51.6846	−1.91687	−0.958437	−	0.285303i	$-0.907906\pi$
$727$	−51.6846	−1.91687	−0.958437	+	0.285303i	$0.907906\pi$
$728$	1.09525	0.0405926
$729$	1.00000	0.0370370
$730$	−14.0257	−0.519115
$731$	45.3341	1.67674
$732$	1.00000	0.0369611
$733$	−45.0147	−1.66266	−0.831328	−	0.555782i	$-0.812419\pi$
$733$	−45.0147	−1.66266	−0.831328	+	0.555782i	$0.812419\pi$
$734$	−19.2126	−0.709151
$735$	−47.1601	−1.73953
$736$	−1.20402	−0.0443809
$737$	15.3970	0.567156
$738$	−5.37220	−0.197753
$739$	36.0444	1.32591	0.662957	−	0.748657i	$-0.269301\pi$
$739$	36.0444	1.32591	0.662957	+	0.748657i	$0.269301\pi$
$740$	−21.4593	−0.788858
$741$	−0.973122	−0.0357485
$742$	−51.7618	−1.90023
$743$	26.6750	0.978610	0.489305	−	0.872113i	$-0.337250\pi$
$743$	26.6750	0.978610	0.489305	+	0.872113i	$0.337250\pi$
$744$	0.0819253	0.00300353
$745$	−9.28192	−0.340063
$746$	26.7346	0.978825
$747$	11.2416	0.411307
$748$	−4.87703	−0.178322
$749$	42.9855	1.57065
$750$	−1.89418	−0.0691658
$751$	46.8892	1.71101	0.855506	−	0.517793i	$-0.173246\pi$
$751$	46.8892	1.71101	0.855506	+	0.517793i	$0.173246\pi$
$752$	1.75602	0.0640356
$753$	−4.02152	−0.146552
$754$	1.23275	0.0448940
$755$	−17.8039	−0.647950
$756$	−4.73255	−0.172121
$757$	−31.2749	−1.13670	−0.568352	−	0.822785i	$-0.692419\pi$
$757$	−31.2749	−1.13670	−0.568352	+	0.822785i	$0.692419\pi$
$758$	−18.0946	−0.657225
$759$	−1.20402	−0.0437033
$760$	12.8792	0.467176
$761$	−5.14270	−0.186423	−0.0932113	−	0.995646i	$-0.529713\pi$
$761$	−5.14270	−0.186423	−0.0932113	+	0.995646i	$0.529713\pi$
$762$	−12.3154	−0.446142
$763$	27.3320	0.989485
$764$	10.4894	0.379495
$765$	−14.9380	−0.540085
$766$	−21.6196	−0.781149
$767$	−1.34087	−0.0484162
$768$	−1.00000	−0.0360844
$769$	−10.4551	−0.377019	−0.188509	−	0.982071i	$-0.560366\pi$
$769$	−10.4551	−0.377019	−0.188509	+	0.982071i	$0.560366\pi$
$770$	−14.4955	−0.522382
$771$	−9.34424	−0.336525
$772$	1.55657	0.0560223
$773$	−15.7808	−0.567596	−0.283798	−	0.958884i	$-0.591594\pi$
$773$	−15.7808	−0.567596	−0.283798	+	0.958884i	$0.591594\pi$
$774$	9.29543	0.334117
$775$	0.358962	0.0128943
$776$	−0.864478	−0.0310329
$777$	33.1568	1.18949
$778$	25.1663	0.902257
$779$	−22.5892	−0.809344
$780$	0.708852	0.0253810
$781$	9.99200	0.357542
$782$	5.87205	0.209984
$783$	−5.32668	−0.190360
$784$	15.3970	0.549894
$785$	58.6421	2.09303
$786$	7.13278	0.254418
$787$	−4.17921	−0.148973	−0.0744864	−	0.997222i	$-0.523732\pi$
$787$	−4.17921	−0.148973	−0.0744864	+	0.997222i	$0.523732\pi$
$788$	6.50848	0.231855
$789$	13.3821	0.476415
$790$	−25.2844	−0.899579
$791$	−90.9323	−3.23318
$792$	−1.00000	−0.0355335
$793$	0.231429	0.00821828
$794$	12.3807	0.439376
$795$	−33.5005	−1.18814
$796$	4.91653	0.174262
$797$	9.41247	0.333407	0.166703	−	0.986007i	$-0.446688\pi$
$797$	9.41247	0.333407	0.166703	+	0.986007i	$0.446688\pi$
$798$	−19.8996	−0.704439
$799$	−8.56417	−0.302979
$800$	−4.38158	−0.154912
$801$	3.38667	0.119662
$802$	−7.34649	−0.259414
$803$	4.57918	0.161596
$804$	−15.3970	−0.543011
$805$	17.4529	0.615135
$806$	0.0189599	0.000667833 0
$807$	−6.60537	−0.232520
$808$	−0.314449	−0.0110623
$809$	−25.2621	−0.888167	−0.444083	−	0.895986i	$-0.646471\pi$
$809$	−25.2621	−0.888167	−0.444083	+	0.895986i	$0.646471\pi$
$810$	−3.06294	−0.107621
$811$	−37.1278	−1.30373	−0.651866	−	0.758334i	$-0.726014\pi$
$811$	−37.1278	−1.30373	−0.651866	+	0.758334i	$0.726014\pi$
$812$	25.2088	0.884654
$813$	24.5532	0.861119
$814$	7.00611	0.245564
$815$	37.6885	1.32017
$816$	4.87703	0.170730
$817$	39.0858	1.36744
$818$	5.30255	0.185399
$819$	−1.09525	−0.0382711
$820$	16.4547	0.574623
$821$	15.2581	0.532513	0.266256	−	0.963902i	$-0.414213\pi$
$821$	15.2581	0.532513	0.266256	+	0.963902i	$0.414213\pi$
$822$	−5.96047	−0.207895
$823$	−19.0347	−0.663508	−0.331754	−	0.943366i	$-0.607640\pi$
$823$	−19.0347	−0.663508	−0.331754	+	0.943366i	$0.607640\pi$
$824$	3.40473	0.118610
$825$	−4.38158	−0.152547
$826$	−27.4199	−0.954060
$827$	2.83479	0.0985752	0.0492876	−	0.998785i	$-0.484305\pi$
$827$	2.83479	0.0985752	0.0492876	+	0.998785i	$0.484305\pi$
$828$	1.20402	0.0418427
$829$	18.4404	0.640463	0.320232	−	0.947339i	$-0.396239\pi$
$829$	18.4404	0.640463	0.320232	+	0.947339i	$0.396239\pi$
$830$	−34.4322	−1.19516
$831$	28.0405	0.972716
$832$	−0.231429	−0.00802336
$833$	−75.0917	−2.60177
$834$	−18.5293	−0.641616
$835$	20.7095	0.716682
$836$	−4.20484	−0.145428
$837$	−0.0819253	−0.00283175
$838$	−14.5810	−0.503693
$839$	49.1894	1.69821	0.849104	−	0.528226i	$-0.177143\pi$
$839$	49.1894	1.69821	0.849104	+	0.528226i	$0.177143\pi$
$840$	14.4955	0.500142
$841$	−0.626498	−0.0216034
$842$	27.4752	0.946857
$843$	17.4004	0.599302
$844$	23.1466	0.796740
$845$	−39.6541	−1.36414
$846$	−1.75602	−0.0603733
$847$	4.73255	0.162612
$848$	10.9374	0.375592
$849$	0.671127	0.0230330
$850$	21.3691	0.732953
$851$	−8.43552	−0.289166
$852$	−9.99200	−0.342320
$853$	−4.76285	−0.163077	−0.0815384	−	0.996670i	$-0.525983\pi$
$853$	−4.76285	−0.163077	−0.0815384	+	0.996670i	$0.525983\pi$
$854$	4.73255	0.161945
$855$	−12.8792	−0.440458
$856$	−9.08294	−0.310449
$857$	26.4620	0.903926	0.451963	−	0.892037i	$-0.350724\pi$
$857$	26.4620	0.903926	0.451963	+	0.892037i	$0.350724\pi$
$858$	−0.231429	−0.00790086
$859$	−49.6272	−1.69326	−0.846629	−	0.532183i	$-0.821372\pi$
$859$	−49.6272	−1.69326	−0.846629	+	0.532183i	$0.821372\pi$
$860$	−28.4713	−0.970864
$861$	−25.4242	−0.866454
$862$	4.07682	0.138857
$863$	−0.470725	−0.0160237	−0.00801184	−	0.999968i	$-0.502550\pi$
$863$	−0.470725	−0.0160237	−0.00801184	+	0.999968i	$0.502550\pi$
$864$	1.00000	0.0340207
$865$	21.2863	0.723756
$866$	−34.9492	−1.18762
$867$	−6.78538	−0.230444
$868$	0.387715	0.0131599
$869$	8.25495	0.280030
$870$	16.3153	0.553140
$871$	−3.56332	−0.120738
$872$	−5.77532	−0.195577
$873$	0.864478	0.0292581
$874$	5.06273	0.171249
$875$	−8.96431	−0.303049
$876$	−4.57918	−0.154716
$877$	37.6367	1.27090	0.635451	−	0.772142i	$-0.280814\pi$
$877$	37.6367	1.27090	0.635451	+	0.772142i	$0.280814\pi$
$878$	−1.14999	−0.0388103
$879$	−17.3834	−0.586326
$880$	3.06294	0.103252
$881$	26.6545	0.898015	0.449007	−	0.893528i	$-0.351778\pi$
$881$	26.6545	0.898015	0.449007	+	0.893528i	$0.351778\pi$
$882$	−15.3970	−0.518445
$883$	41.9501	1.41173	0.705867	−	0.708345i	$-0.250558\pi$
$883$	41.9501	1.41173	0.705867	+	0.708345i	$0.250558\pi$
$884$	1.12869	0.0379618
$885$	−17.7463	−0.596536
$886$	6.90102	0.231844
$887$	1.12548	0.0377900	0.0188950	−	0.999821i	$-0.493985\pi$
$887$	1.12548	0.0377900	0.0188950	+	0.999821i	$0.493985\pi$
$888$	−7.00611	−0.235110
$889$	−58.2835	−1.95477
$890$	−10.3732	−0.347709
$891$	1.00000	0.0335013
$892$	4.05427	0.135747
$893$	−7.38380	−0.247089
$894$	−3.03040	−0.101352
$895$	−1.30667	−0.0436773
$896$	−4.73255	−0.158103
$897$	0.278646	0.00930372
$898$	−9.92865	−0.331323
$899$	0.436389	0.0145544
$900$	4.38158	0.146053
$901$	−53.3419	−1.77708
$902$	−5.37220	−0.178875
$903$	43.9911	1.46393
$904$	19.2142	0.639056
$905$	−32.1574	−1.06895
$906$	−5.81269	−0.193114
$907$	13.2877	0.441210	0.220605	−	0.975363i	$-0.429197\pi$
$907$	13.2877	0.441210	0.220605	+	0.975363i	$0.429197\pi$
$908$	−11.8552	−0.393429
$909$	0.314449	0.0104296
$910$	3.35468	0.111207
$911$	54.2777	1.79830	0.899151	−	0.437639i	$-0.144185\pi$
$911$	54.2777	1.79830	0.899151	+	0.437639i	$0.144185\pi$
$912$	4.20484	0.139236
$913$	11.2416	0.372041
$914$	31.9253	1.05599
$915$	3.06294	0.101258
$916$	19.5061	0.644499
$917$	33.7563	1.11473
$918$	−4.87703	−0.160966
$919$	46.8470	1.54534	0.772670	−	0.634808i	$-0.218921\pi$
$919$	46.8470	1.54534	0.772670	+	0.634808i	$0.218921\pi$
$920$	−3.68785	−0.121585
$921$	14.7476	0.485950
$922$	−24.4378	−0.804816
$923$	−2.31244	−0.0761149
$924$	−4.73255	−0.155689
$925$	−30.6978	−1.00934
$926$	15.9097	0.522825
$927$	−3.40473	−0.111826
$928$	−5.32668	−0.174857
$929$	−13.7051	−0.449651	−0.224826	−	0.974399i	$-0.572181\pi$
$929$	−13.7051	−0.449651	−0.224826	+	0.974399i	$0.572181\pi$
$930$	0.250932	0.00822838
$931$	−64.7421	−2.12184
$932$	12.0667	0.395258
$933$	−4.04166	−0.132318
$934$	9.01702	0.295046
$935$	−14.9380	−0.488526
$936$	0.231429	0.00756449
$937$	−25.5752	−0.835505	−0.417753	−	0.908561i	$-0.637182\pi$
$937$	−25.5752	−0.835505	−0.417753	+	0.908561i	$0.637182\pi$
$938$	−72.8671	−2.37920
$939$	18.1455	0.592155
$940$	5.37859	0.175430
$941$	−12.0459	−0.392684	−0.196342	−	0.980535i	$-0.562906\pi$
$941$	−12.0459	−0.392684	−0.196342	+	0.980535i	$0.562906\pi$
$942$	19.1457	0.623801
$943$	6.46825	0.210635
$944$	5.79389	0.188575
$945$	−14.4955	−0.471539
$946$	9.29543	0.302221
$947$	−0.0477269	−0.00155092	−0.000775458	−	1.00000i	$-0.500247\pi$
$947$	−0.0477269	−0.00155092	−0.000775458		1.00000i	$0.500247\pi$
$948$	−8.25495	−0.268108
$949$	−1.05975	−0.0344011
$950$	18.4239	0.597749
$951$	−1.21019	−0.0392430
$952$	23.0808	0.748052
$953$	−58.6533	−1.89997	−0.949984	−	0.312298i	$-0.898901\pi$
$953$	−58.6533	−1.89997	−0.949984	+	0.312298i	$0.898901\pi$
$954$	−10.9374	−0.354111
$955$	32.1285	1.03965
$956$	14.0086	0.453072
$957$	−5.32668	−0.172187
$958$	10.5048	0.339394
$959$	−28.2082	−0.910890
$960$	−3.06294	−0.0988558
$961$	−30.9933	−0.999783
$962$	−1.62142	−0.0522766
$963$	9.08294	0.292694
$964$	−7.66981	−0.247028
$965$	4.76769	0.153477
$966$	5.69810	0.183333
$967$	52.6030	1.69160	0.845799	−	0.533502i	$-0.179124\pi$
$967$	52.6030	1.69160	0.845799	+	0.533502i	$0.179124\pi$
$968$	−1.00000	−0.0321412
$969$	−20.5071	−0.658784
$970$	−2.64784	−0.0850170
$971$	−40.7266	−1.30698	−0.653490	−	0.756935i	$-0.726696\pi$
$971$	−40.7266	−1.30698	−0.653490	+	0.756935i	$0.726696\pi$
$972$	−1.00000	−0.0320750
$973$	−87.6907	−2.81124
$974$	−24.1537	−0.773934
$975$	1.01402	0.0324748
$976$	−1.00000	−0.0320092
$977$	−54.5706	−1.74587	−0.872934	−	0.487837i	$-0.837786\pi$
$977$	−54.5706	−1.74587	−0.872934	+	0.487837i	$0.837786\pi$
$978$	12.3047	0.393461
$979$	3.38667	0.108239
$980$	47.1601	1.50647
$981$	5.77532	0.184392
$982$	20.5679	0.656348
$983$	−47.1376	−1.50345	−0.751727	−	0.659474i	$-0.770779\pi$
$983$	−47.1376	−1.50345	−0.751727	+	0.659474i	$0.770779\pi$
$984$	5.37220	0.171259
$985$	19.9351	0.635184
$986$	25.9783	0.827319
$987$	−8.31046	−0.264525
$988$	0.973122	0.0309591
$989$	−11.1919	−0.355882
$990$	−3.06294	−0.0973465
$991$	−20.0405	−0.636608	−0.318304	−	0.947989i	$-0.603113\pi$
$991$	−20.0405	−0.636608	−0.318304	+	0.947989i	$0.603113\pi$
$992$	−0.0819253	−0.00260113
$993$	26.9173	0.854195
$994$	−47.2876	−1.49987
$995$	15.0590	0.477403
$996$	−11.2416	−0.356202
$997$	51.1343	1.61944	0.809720	−	0.586816i	$-0.199619\pi$
$997$	51.1343	1.61944	0.809720	+	0.586816i	$0.199619\pi$
$998$	13.4642	0.426203
$999$	7.00611	0.221663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.z.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.z.1.6	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06294 q^{5} +1.00000 q^{6} +4.73255 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.06294 q^{5} +1.00000 q^{6} +4.73255 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.06294 q^{10} +1.00000 q^{11} -1.00000 q^{12} -0.231429 q^{13} -4.73255 q^{14} -3.06294 q^{15} +1.00000 q^{16} -4.87703 q^{17} -1.00000 q^{18} -4.20484 q^{19} +3.06294 q^{20} -4.73255 q^{21} -1.00000 q^{22} +1.20402 q^{23} +1.00000 q^{24} +4.38158 q^{25} +0.231429 q^{26} -1.00000 q^{27} +4.73255 q^{28} +5.32668 q^{29} +3.06294 q^{30} +0.0819253 q^{31} -1.00000 q^{32} -1.00000 q^{33} +4.87703 q^{34} +14.4955 q^{35} +1.00000 q^{36} -7.00611 q^{37} +4.20484 q^{38} +0.231429 q^{39} -3.06294 q^{40} +5.37220 q^{41} +4.73255 q^{42} -9.29543 q^{43} +1.00000 q^{44} +3.06294 q^{45} -1.20402 q^{46} +1.75602 q^{47} -1.00000 q^{48} +15.3970 q^{49} -4.38158 q^{50} +4.87703 q^{51} -0.231429 q^{52} +10.9374 q^{53} +1.00000 q^{54} +3.06294 q^{55} -4.73255 q^{56} +4.20484 q^{57} -5.32668 q^{58} +5.79389 q^{59} -3.06294 q^{60} -1.00000 q^{61} -0.0819253 q^{62} +4.73255 q^{63} +1.00000 q^{64} -0.708852 q^{65} +1.00000 q^{66} +15.3970 q^{67} -4.87703 q^{68} -1.20402 q^{69} -14.4955 q^{70} +9.99200 q^{71} -1.00000 q^{72} +4.57918 q^{73} +7.00611 q^{74} -4.38158 q^{75} -4.20484 q^{76} +4.73255 q^{77} -0.231429 q^{78} +8.25495 q^{79} +3.06294 q^{80} +1.00000 q^{81} -5.37220 q^{82} +11.2416 q^{83} -4.73255 q^{84} -14.9380 q^{85} +9.29543 q^{86} -5.32668 q^{87} -1.00000 q^{88} +3.38667 q^{89} -3.06294 q^{90} -1.09525 q^{91} +1.20402 q^{92} -0.0819253 q^{93} -1.75602 q^{94} -12.8792 q^{95} +1.00000 q^{96} +0.864478 q^{97} -15.3970 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * q^99

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