LMFDB - Embedded newform 4026.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$7$
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} - 2x^{6} - 21x^{5} + 39x^{4} + 89x^{3} - 100x^{2} - 96x + 8 $ x^7 - 2x^6 - 21x^5 + 39x^4 + 89x^3 - 100x^2 - 96x + 8
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			1.4
Root			$0.0775196$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.0775196 q^{5} +1.00000 q^{6} +2.74128 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.0775196 q^{5} +1.00000 q^{6} +2.74128 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.0775196 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.76942 q^{13} -2.74128 q^{14} +0.0775196 q^{15} +1.00000 q^{16} +4.60781 q^{17} -1.00000 q^{18} -5.24912 q^{19} -0.0775196 q^{20} -2.74128 q^{21} +1.00000 q^{22} -9.37723 q^{23} +1.00000 q^{24} -4.99399 q^{25} -4.76942 q^{26} -1.00000 q^{27} +2.74128 q^{28} -4.01523 q^{29} -0.0775196 q^{30} +3.80272 q^{31} -1.00000 q^{32} +1.00000 q^{33} -4.60781 q^{34} -0.212503 q^{35} +1.00000 q^{36} -0.483396 q^{37} +5.24912 q^{38} -4.76942 q^{39} +0.0775196 q^{40} +1.38324 q^{41} +2.74128 q^{42} -5.58539 q^{43} -1.00000 q^{44} -0.0775196 q^{45} +9.37723 q^{46} -11.4075 q^{47} -1.00000 q^{48} +0.514595 q^{49} +4.99399 q^{50} -4.60781 q^{51} +4.76942 q^{52} -4.36082 q^{53} +1.00000 q^{54} +0.0775196 q^{55} -2.74128 q^{56} +5.24912 q^{57} +4.01523 q^{58} -4.92164 q^{59} +0.0775196 q^{60} -1.00000 q^{61} -3.80272 q^{62} +2.74128 q^{63} +1.00000 q^{64} -0.369723 q^{65} -1.00000 q^{66} -2.49939 q^{67} +4.60781 q^{68} +9.37723 q^{69} +0.212503 q^{70} +0.600594 q^{71} -1.00000 q^{72} +8.32148 q^{73} +0.483396 q^{74} +4.99399 q^{75} -5.24912 q^{76} -2.74128 q^{77} +4.76942 q^{78} -0.850463 q^{79} -0.0775196 q^{80} +1.00000 q^{81} -1.38324 q^{82} -0.613172 q^{83} -2.74128 q^{84} -0.357196 q^{85} +5.58539 q^{86} +4.01523 q^{87} +1.00000 q^{88} +0.357196 q^{89} +0.0775196 q^{90} +13.0743 q^{91} -9.37723 q^{92} -3.80272 q^{93} +11.4075 q^{94} +0.406910 q^{95} +1.00000 q^{96} +9.29450 q^{97} -0.514595 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + 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 + 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} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 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
$5$	−0.0775196	−0.0346678	−0.0173339	−	0.999850i	$-0.505518\pi$
$5$	−0.0775196	−0.0346678	−0.0173339	+	0.999850i	$0.505518\pi$
$6$	1.00000	0.408248
$7$	2.74128	1.03611	0.518053	−	0.855349i	$-0.326657\pi$
$7$	2.74128	1.03611	0.518053	+	0.855349i	$0.326657\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.0775196	0.0245138
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	4.76942	1.32280	0.661399	−	0.750034i	$-0.269963\pi$
$13$	4.76942	1.32280	0.661399	+	0.750034i	$0.269963\pi$
$14$	−2.74128	−0.732637
$15$	0.0775196	0.0200155
$16$	1.00000	0.250000
$17$	4.60781	1.11756	0.558779	−	0.829317i	$-0.311270\pi$
$17$	4.60781	1.11756	0.558779	+	0.829317i	$0.311270\pi$
$18$	−1.00000	−0.235702
$19$	−5.24912	−1.20423	−0.602116	−	0.798409i	$-0.705675\pi$
$19$	−5.24912	−1.20423	−0.602116	+	0.798409i	$0.705675\pi$
$20$	−0.0775196	−0.0173339
$21$	−2.74128	−0.598196
$22$	1.00000	0.213201
$23$	−9.37723	−1.95529	−0.977644	−	0.210269i	$-0.932566\pi$
$23$	−9.37723	−1.95529	−0.977644	+	0.210269i	$0.932566\pi$
$24$	1.00000	0.204124
$25$	−4.99399	−0.998798
$26$	−4.76942	−0.935360
$27$	−1.00000	−0.192450
$28$	2.74128	0.518053
$29$	−4.01523	−0.745609	−0.372804	−	0.927910i	$-0.621604\pi$
$29$	−4.01523	−0.745609	−0.372804	+	0.927910i	$0.621604\pi$
$30$	−0.0775196	−0.0141531
$31$	3.80272	0.682990	0.341495	−	0.939884i	$-0.389067\pi$
$31$	3.80272	0.682990	0.341495	+	0.939884i	$0.389067\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−4.60781	−0.790233
$35$	−0.212503	−0.0359195
$36$	1.00000	0.166667
$37$	−0.483396	−0.0794698	−0.0397349	−	0.999210i	$-0.512651\pi$
$37$	−0.483396	−0.0794698	−0.0397349	+	0.999210i	$0.512651\pi$
$38$	5.24912	0.851520
$39$	−4.76942	−0.763718
$40$	0.0775196	0.0122569
$41$	1.38324	0.216025	0.108013	−	0.994150i	$-0.465551\pi$
$41$	1.38324	0.216025	0.108013	+	0.994150i	$0.465551\pi$
$42$	2.74128	0.422988
$43$	−5.58539	−0.851764	−0.425882	−	0.904779i	$-0.640036\pi$
$43$	−5.58539	−0.851764	−0.425882	+	0.904779i	$0.640036\pi$
$44$	−1.00000	−0.150756
$45$	−0.0775196	−0.0115559
$46$	9.37723	1.38260
$47$	−11.4075	−1.66395	−0.831976	−	0.554812i	$-0.812790\pi$
$47$	−11.4075	−1.66395	−0.831976	+	0.554812i	$0.812790\pi$
$48$	−1.00000	−0.144338
$49$	0.514595	0.0735136
$50$	4.99399	0.706257
$51$	−4.60781	−0.645222
$52$	4.76942	0.661399
$53$	−4.36082	−0.599005	−0.299502	−	0.954096i	$-0.596821\pi$
$53$	−4.36082	−0.599005	−0.299502	+	0.954096i	$0.596821\pi$
$54$	1.00000	0.136083
$55$	0.0775196	0.0104527
$56$	−2.74128	−0.366318
$57$	5.24912	0.695263
$58$	4.01523	0.527225
$59$	−4.92164	−0.640743	−0.320371	−	0.947292i	$-0.603808\pi$
$59$	−4.92164	−0.640743	−0.320371	+	0.947292i	$0.603808\pi$
$60$	0.0775196	0.0100077
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.80272	−0.482947
$63$	2.74128	0.345368
$64$	1.00000	0.125000
$65$	−0.369723	−0.0458585
$66$	−1.00000	−0.123091
$67$	−2.49939	−0.305350	−0.152675	−	0.988276i	$-0.548789\pi$
$67$	−2.49939	−0.305350	−0.152675	+	0.988276i	$0.548789\pi$
$68$	4.60781	0.558779
$69$	9.37723	1.12889
$70$	0.212503	0.0253989
$71$	0.600594	0.0712774	0.0356387	−	0.999365i	$-0.488653\pi$
$71$	0.600594	0.0712774	0.0356387	+	0.999365i	$0.488653\pi$
$72$	−1.00000	−0.117851
$73$	8.32148	0.973955	0.486978	−	0.873414i	$-0.338099\pi$
$73$	8.32148	0.973955	0.486978	+	0.873414i	$0.338099\pi$
$74$	0.483396	0.0561937
$75$	4.99399	0.576656
$76$	−5.24912	−0.602116
$77$	−2.74128	−0.312397
$78$	4.76942	0.540030
$79$	−0.850463	−0.0956845	−0.0478423	−	0.998855i	$-0.515234\pi$
$79$	−0.850463	−0.0956845	−0.0478423	+	0.998855i	$0.515234\pi$
$80$	−0.0775196	−0.00866695
$81$	1.00000	0.111111
$82$	−1.38324	−0.152753
$83$	−0.613172	−0.0673044	−0.0336522	−	0.999434i	$-0.510714\pi$
$83$	−0.613172	−0.0673044	−0.0336522	+	0.999434i	$0.510714\pi$
$84$	−2.74128	−0.299098
$85$	−0.357196	−0.0387433
$86$	5.58539	0.602288
$87$	4.01523	0.430478
$88$	1.00000	0.106600
$89$	0.357196	0.0378626	0.0189313	−	0.999821i	$-0.493974\pi$
$89$	0.357196	0.0378626	0.0189313	+	0.999821i	$0.493974\pi$
$90$	0.0775196	0.00817128
$91$	13.0743	1.37056
$92$	−9.37723	−0.977644
$93$	−3.80272	−0.394324
$94$	11.4075	1.17659
$95$	0.406910	0.0417481
$96$	1.00000	0.102062
$97$	9.29450	0.943714	0.471857	−	0.881675i	$-0.343584\pi$
$97$	9.29450	0.943714	0.471857	+	0.881675i	$0.343584\pi$
$98$	−0.514595	−0.0519820
$99$	−1.00000	−0.100504
$100$	−4.99399	−0.499399
$101$	5.00003	0.497521	0.248761	−	0.968565i	$-0.419977\pi$
$101$	5.00003	0.497521	0.248761	+	0.968565i	$0.419977\pi$
$102$	4.60781	0.456241
$103$	−11.3902	−1.12231	−0.561157	−	0.827709i	$-0.689644\pi$
$103$	−11.3902	−1.12231	−0.561157	+	0.827709i	$0.689644\pi$
$104$	−4.76942	−0.467680
$105$	0.212503	0.0207381
$106$	4.36082	0.423560
$107$	−4.08474	−0.394886	−0.197443	−	0.980314i	$-0.563264\pi$
$107$	−4.08474	−0.394886	−0.197443	+	0.980314i	$0.563264\pi$
$108$	−1.00000	−0.0962250
$109$	7.28009	0.697306	0.348653	−	0.937252i	$-0.386639\pi$
$109$	7.28009	0.697306	0.348653	+	0.937252i	$0.386639\pi$
$110$	−0.0775196	−0.00739120
$111$	0.483396	0.0458819
$112$	2.74128	0.259026
$113$	−10.6170	−0.998766	−0.499383	−	0.866381i	$-0.666440\pi$
$113$	−10.6170	−0.998766	−0.499383	+	0.866381i	$0.666440\pi$
$114$	−5.24912	−0.491625
$115$	0.726919	0.0677855
$116$	−4.01523	−0.372804
$117$	4.76942	0.440933
$118$	4.92164	0.453073
$119$	12.6313	1.15791
$120$	−0.0775196	−0.00707654
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−1.38324	−0.124722
$124$	3.80272	0.341495
$125$	0.774730	0.0692940
$126$	−2.74128	−0.244212
$127$	7.39369	0.656084	0.328042	−	0.944663i	$-0.393611\pi$
$127$	7.39369	0.656084	0.328042	+	0.944663i	$0.393611\pi$
$128$	−1.00000	−0.0883883
$129$	5.58539	0.491766
$130$	0.369723	0.0324269
$131$	4.96575	0.433860	0.216930	−	0.976187i	$-0.430396\pi$
$131$	4.96575	0.433860	0.216930	+	0.976187i	$0.430396\pi$
$132$	1.00000	0.0870388
$133$	−14.3893	−1.24771
$134$	2.49939	0.215915
$135$	0.0775196	0.00667182
$136$	−4.60781	−0.395116
$137$	−18.5188	−1.58217	−0.791086	−	0.611705i	$-0.790484\pi$
$137$	−18.5188	−1.58217	−0.791086	+	0.611705i	$0.790484\pi$
$138$	−9.37723	−0.798243
$139$	−8.43590	−0.715524	−0.357762	−	0.933813i	$-0.616460\pi$
$139$	−8.43590	−0.715524	−0.357762	+	0.933813i	$0.616460\pi$
$140$	−0.212503	−0.0179597
$141$	11.4075	0.960683
$142$	−0.600594	−0.0504008
$143$	−4.76942	−0.398839
$144$	1.00000	0.0833333
$145$	0.311259	0.0258486
$146$	−8.32148	−0.688690
$147$	−0.514595	−0.0424431
$148$	−0.483396	−0.0397349
$149$	−4.05746	−0.332400	−0.166200	−	0.986092i	$-0.553150\pi$
$149$	−4.05746	−0.332400	−0.166200	+	0.986092i	$0.553150\pi$
$150$	−4.99399	−0.407758
$151$	−9.51639	−0.774433	−0.387217	−	0.921989i	$-0.626563\pi$
$151$	−9.51639	−0.774433	−0.387217	+	0.921989i	$0.626563\pi$
$152$	5.24912	0.425760
$153$	4.60781	0.372519
$154$	2.74128	0.220898
$155$	−0.294786	−0.0236778
$156$	−4.76942	−0.381859
$157$	10.8786	0.868207	0.434104	−	0.900863i	$-0.357065\pi$
$157$	10.8786	0.868207	0.434104	+	0.900863i	$0.357065\pi$
$158$	0.850463	0.0676592
$159$	4.36082	0.345836
$160$	0.0775196	0.00612846
$161$	−25.7056	−2.02588
$162$	−1.00000	−0.0785674
$163$	−18.7055	−1.46513	−0.732566	−	0.680696i	$-0.761677\pi$
$163$	−18.7055	−1.46513	−0.732566	+	0.680696i	$0.761677\pi$
$164$	1.38324	0.108013
$165$	−0.0775196	−0.00603489
$166$	0.613172	0.0475914
$167$	25.4986	1.97314	0.986570	−	0.163340i	$-0.0522266\pi$
$167$	25.4986	1.97314	0.986570	+	0.163340i	$0.0522266\pi$
$168$	2.74128	0.211494
$169$	9.74735	0.749796
$170$	0.357196	0.0273956
$171$	−5.24912	−0.401411
$172$	−5.58539	−0.425882
$173$	−16.4451	−1.25030	−0.625150	−	0.780505i	$-0.714962\pi$
$173$	−16.4451	−1.25030	−0.625150	+	0.780505i	$0.714962\pi$
$174$	−4.01523	−0.304394
$175$	−13.6899	−1.03486
$176$	−1.00000	−0.0753778
$177$	4.92164	0.369933
$178$	−0.357196	−0.0267729
$179$	−13.5728	−1.01448	−0.507240	−	0.861805i	$-0.669334\pi$
$179$	−13.5728	−1.01448	−0.507240	+	0.861805i	$0.669334\pi$
$180$	−0.0775196	−0.00577797
$181$	21.3301	1.58546	0.792728	−	0.609576i	$-0.208660\pi$
$181$	21.3301	1.58546	0.792728	+	0.609576i	$0.208660\pi$
$182$	−13.0743	−0.969131
$183$	1.00000	0.0739221
$184$	9.37723	0.691298
$185$	0.0374727	0.00275505
$186$	3.80272	0.278829
$187$	−4.60781	−0.336956
$188$	−11.4075	−0.831976
$189$	−2.74128	−0.199399
$190$	−0.406910	−0.0295203
$191$	9.45958	0.684471	0.342236	−	0.939614i	$-0.388816\pi$
$191$	9.45958	0.684471	0.342236	+	0.939614i	$0.388816\pi$
$192$	−1.00000	−0.0721688
$193$	−19.5557	−1.40765	−0.703824	−	0.710374i	$-0.748526\pi$
$193$	−19.5557	−1.40765	−0.703824	+	0.710374i	$0.748526\pi$
$194$	−9.29450	−0.667306
$195$	0.369723	0.0264764
$196$	0.514595	0.0367568
$197$	−7.92644	−0.564736	−0.282368	−	0.959306i	$-0.591120\pi$
$197$	−7.92644	−0.564736	−0.282368	+	0.959306i	$0.591120\pi$
$198$	1.00000	0.0710669
$199$	13.9521	0.989040	0.494520	−	0.869166i	$-0.335344\pi$
$199$	13.9521	0.989040	0.494520	+	0.869166i	$0.335344\pi$
$200$	4.99399	0.353128
$201$	2.49939	0.176294
$202$	−5.00003	−0.351801
$203$	−11.0068	−0.772529
$204$	−4.60781	−0.322611
$205$	−0.107228	−0.00748912
$206$	11.3902	0.793596
$207$	−9.37723	−0.651762
$208$	4.76942	0.330700
$209$	5.24912	0.363089
$210$	−0.212503	−0.0146641
$211$	8.91983	0.614066	0.307033	−	0.951699i	$-0.400664\pi$
$211$	8.91983	0.614066	0.307033	+	0.951699i	$0.400664\pi$
$212$	−4.36082	−0.299502
$213$	−0.600594	−0.0411521
$214$	4.08474	0.279227
$215$	0.432977	0.0295288
$216$	1.00000	0.0680414
$217$	10.4243	0.707649
$218$	−7.28009	−0.493070
$219$	−8.32148	−0.562313
$220$	0.0775196	0.00522637
$221$	21.9766	1.47830
$222$	−0.483396	−0.0324434
$223$	4.65318	0.311600	0.155800	−	0.987789i	$-0.450205\pi$
$223$	4.65318	0.311600	0.155800	+	0.987789i	$0.450205\pi$
$224$	−2.74128	−0.183159
$225$	−4.99399	−0.332933
$226$	10.6170	0.706234
$227$	12.3447	0.819345	0.409673	−	0.912233i	$-0.365643\pi$
$227$	12.3447	0.819345	0.409673	+	0.912233i	$0.365643\pi$
$228$	5.24912	0.347632
$229$	−18.8764	−1.24738	−0.623692	−	0.781670i	$-0.714368\pi$
$229$	−18.8764	−1.24738	−0.623692	+	0.781670i	$0.714368\pi$
$230$	−0.726919	−0.0479316
$231$	2.74128	0.180363
$232$	4.01523	0.263613
$233$	25.5410	1.67325	0.836623	−	0.547779i	$-0.184526\pi$
$233$	25.5410	1.67325	0.836623	+	0.547779i	$0.184526\pi$
$234$	−4.76942	−0.311787
$235$	0.884303	0.0576856
$236$	−4.92164	−0.320371
$237$	0.850463	0.0552435
$238$	−12.6313	−0.818764
$239$	−8.90122	−0.575772	−0.287886	−	0.957665i	$-0.592952\pi$
$239$	−8.90122	−0.575772	−0.287886	+	0.957665i	$0.592952\pi$
$240$	0.0775196	0.00500387
$241$	−1.33706	−0.0861278	−0.0430639	−	0.999072i	$-0.513712\pi$
$241$	−1.33706	−0.0861278	−0.0430639	+	0.999072i	$0.513712\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	−0.0398912	−0.00254856
$246$	1.38324	0.0881920
$247$	−25.0353	−1.59296
$248$	−3.80272	−0.241473
$249$	0.613172	0.0388582
$250$	−0.774730	−0.0489982
$251$	−11.2198	−0.708188	−0.354094	−	0.935210i	$-0.615211\pi$
$251$	−11.2198	−0.708188	−0.354094	+	0.935210i	$0.615211\pi$
$252$	2.74128	0.172684
$253$	9.37723	0.589541
$254$	−7.39369	−0.463922
$255$	0.357196	0.0223685
$256$	1.00000	0.0625000
$257$	4.34093	0.270780	0.135390	−	0.990792i	$-0.456771\pi$
$257$	4.34093	0.270780	0.135390	+	0.990792i	$0.456771\pi$
$258$	−5.58539	−0.347731
$259$	−1.32512	−0.0823391
$260$	−0.369723	−0.0229293
$261$	−4.01523	−0.248536
$262$	−4.96575	−0.306785
$263$	7.88279	0.486074	0.243037	−	0.970017i	$-0.421856\pi$
$263$	7.88279	0.486074	0.243037	+	0.970017i	$0.421856\pi$
$264$	−1.00000	−0.0615457
$265$	0.338049	0.0207662
$266$	14.3893	0.882264
$267$	−0.357196	−0.0218600
$268$	−2.49939	−0.152675
$269$	−22.3610	−1.36338	−0.681688	−	0.731643i	$-0.738754\pi$
$269$	−22.3610	−1.36338	−0.681688	+	0.731643i	$0.738754\pi$
$270$	−0.0775196	−0.00471769
$271$	−0.541334	−0.0328837	−0.0164418	−	0.999865i	$-0.505234\pi$
$271$	−0.541334	−0.0328837	−0.0164418	+	0.999865i	$0.505234\pi$
$272$	4.60781	0.279390
$273$	−13.0743	−0.791292
$274$	18.5188	1.11876
$275$	4.99399	0.301149
$276$	9.37723	0.564443
$277$	−14.0662	−0.845158	−0.422579	−	0.906326i	$-0.638875\pi$
$277$	−14.0662	−0.845158	−0.422579	+	0.906326i	$0.638875\pi$
$278$	8.43590	0.505952
$279$	3.80272	0.227663
$280$	0.212503	0.0126995
$281$	5.12802	0.305912	0.152956	−	0.988233i	$-0.451121\pi$
$281$	5.12802	0.305912	0.152956	+	0.988233i	$0.451121\pi$
$282$	−11.4075	−0.679305
$283$	18.3589	1.09133	0.545663	−	0.838005i	$-0.316278\pi$
$283$	18.3589	1.09133	0.545663	+	0.838005i	$0.316278\pi$
$284$	0.600594	0.0356387
$285$	−0.406910	−0.0241033
$286$	4.76942	0.282022
$287$	3.79183	0.223825
$288$	−1.00000	−0.0589256
$289$	4.23191	0.248936
$290$	−0.311259	−0.0182777
$291$	−9.29450	−0.544853
$292$	8.32148	0.486978
$293$	10.8946	0.636471	0.318236	−	0.948012i	$-0.396910\pi$
$293$	10.8946	0.636471	0.318236	+	0.948012i	$0.396910\pi$
$294$	0.514595	0.0300118
$295$	0.381523	0.0222131
$296$	0.483396	0.0280968
$297$	1.00000	0.0580259
$298$	4.05746	0.235043
$299$	−44.7239	−2.58645
$300$	4.99399	0.288328
$301$	−15.3111	−0.882517
$302$	9.51639	0.547607
$303$	−5.00003	−0.287244
$304$	−5.24912	−0.301058
$305$	0.0775196	0.00443876
$306$	−4.60781	−0.263411
$307$	6.37298	0.363725	0.181863	−	0.983324i	$-0.441787\pi$
$307$	6.37298	0.363725	0.181863	+	0.983324i	$0.441787\pi$
$308$	−2.74128	−0.156199
$309$	11.3902	0.647968
$310$	0.294786	0.0167427
$311$	−22.1220	−1.25442	−0.627212	−	0.778848i	$-0.715804\pi$
$311$	−22.1220	−1.25442	−0.627212	+	0.778848i	$0.715804\pi$
$312$	4.76942	0.270015
$313$	11.0920	0.626959	0.313479	−	0.949595i	$-0.398505\pi$
$313$	11.0920	0.626959	0.313479	+	0.949595i	$0.398505\pi$
$314$	−10.8786	−0.613915
$315$	−0.212503	−0.0119732
$316$	−0.850463	−0.0478423
$317$	−29.1084	−1.63489	−0.817445	−	0.576006i	$-0.804610\pi$
$317$	−29.1084	−1.63489	−0.817445	+	0.576006i	$0.804610\pi$
$318$	−4.36082	−0.244543
$319$	4.01523	0.224810
$320$	−0.0775196	−0.00433348
$321$	4.08474	0.227988
$322$	25.7056	1.43252
$323$	−24.1870	−1.34580
$324$	1.00000	0.0555556
$325$	−23.8184	−1.32121
$326$	18.7055	1.03600
$327$	−7.28009	−0.402590
$328$	−1.38324	−0.0763765
$329$	−31.2710	−1.72403
$330$	0.0775196	0.00426731
$331$	−9.60210	−0.527779	−0.263890	−	0.964553i	$-0.585005\pi$
$331$	−9.60210	−0.527779	−0.263890	+	0.964553i	$0.585005\pi$
$332$	−0.613172	−0.0336522
$333$	−0.483396	−0.0264899
$334$	−25.4986	−1.39522
$335$	0.193752	0.0105858
$336$	−2.74128	−0.149549
$337$	−8.79480	−0.479084	−0.239542	−	0.970886i	$-0.576997\pi$
$337$	−8.79480	−0.479084	−0.239542	+	0.970886i	$0.576997\pi$
$338$	−9.74735	−0.530186
$339$	10.6170	0.576638
$340$	−0.357196	−0.0193716
$341$	−3.80272	−0.205929
$342$	5.24912	0.283840
$343$	−17.7783	−0.959937
$344$	5.58539	0.301144
$345$	−0.726919	−0.0391360
$346$	16.4451	0.884095
$347$	−21.7116	−1.16554	−0.582769	−	0.812638i	$-0.698031\pi$
$347$	−21.7116	−1.16554	−0.582769	+	0.812638i	$0.698031\pi$
$348$	4.01523	0.215239
$349$	−33.2445	−1.77954	−0.889768	−	0.456414i	$-0.849134\pi$
$349$	−33.2445	−1.77954	−0.889768	+	0.456414i	$0.849134\pi$
$350$	13.6899	0.731756
$351$	−4.76942	−0.254573
$352$	1.00000	0.0533002
$353$	35.7212	1.90125	0.950625	−	0.310343i	$-0.100444\pi$
$353$	35.7212	1.90125	0.950625	+	0.310343i	$0.100444\pi$
$354$	−4.92164	−0.261582
$355$	−0.0465578	−0.00247103
$356$	0.357196	0.0189313
$357$	−12.6313	−0.668518
$358$	13.5728	0.717346
$359$	−10.4153	−0.549697	−0.274848	−	0.961488i	$-0.588628\pi$
$359$	−10.4153	−0.549697	−0.274848	+	0.961488i	$0.588628\pi$
$360$	0.0775196	0.00408564
$361$	8.55330	0.450174
$362$	−21.3301	−1.12109
$363$	−1.00000	−0.0524864
$364$	13.0743	0.685279
$365$	−0.645078	−0.0337649
$366$	−1.00000	−0.0522708
$367$	−7.81416	−0.407896	−0.203948	−	0.978982i	$-0.565377\pi$
$367$	−7.81416	−0.407896	−0.203948	+	0.978982i	$0.565377\pi$
$368$	−9.37723	−0.488822
$369$	1.38324	0.0720084
$370$	−0.0374727	−0.00194811
$371$	−11.9542	−0.620632
$372$	−3.80272	−0.197162
$373$	−15.8856	−0.822527	−0.411263	−	0.911517i	$-0.634912\pi$
$373$	−15.8856	−0.822527	−0.411263	+	0.911517i	$0.634912\pi$
$374$	4.60781	0.238264
$375$	−0.774730	−0.0400069
$376$	11.4075	0.588296
$377$	−19.1503	−0.986290
$378$	2.74128	0.140996
$379$	3.93473	0.202114	0.101057	−	0.994881i	$-0.467778\pi$
$379$	3.93473	0.202114	0.101057	+	0.994881i	$0.467778\pi$
$380$	0.406910	0.0208740
$381$	−7.39369	−0.378790
$382$	−9.45958	−0.483994
$383$	23.9054	1.22151	0.610755	−	0.791819i	$-0.290866\pi$
$383$	23.9054	1.22151	0.610755	+	0.791819i	$0.290866\pi$
$384$	1.00000	0.0510310
$385$	0.212503	0.0108301
$386$	19.5557	0.995357
$387$	−5.58539	−0.283921
$388$	9.29450	0.471857
$389$	−5.11812	−0.259499	−0.129749	−	0.991547i	$-0.541417\pi$
$389$	−5.11812	−0.259499	−0.129749	+	0.991547i	$0.541417\pi$
$390$	−0.369723	−0.0187217
$391$	−43.2085	−2.18515
$392$	−0.514595	−0.0259910
$393$	−4.96575	−0.250489
$394$	7.92644	0.399328
$395$	0.0659275	0.00331717
$396$	−1.00000	−0.0502519
$397$	−11.2940	−0.566832	−0.283416	−	0.958997i	$-0.591468\pi$
$397$	−11.2940	−0.566832	−0.283416	+	0.958997i	$0.591468\pi$
$398$	−13.9521	−0.699357
$399$	14.3893	0.720366
$400$	−4.99399	−0.249700
$401$	−10.4147	−0.520086	−0.260043	−	0.965597i	$-0.583737\pi$
$401$	−10.4147	−0.520086	−0.260043	+	0.965597i	$0.583737\pi$
$402$	−2.49939	−0.124658
$403$	18.1368	0.903457
$404$	5.00003	0.248761
$405$	−0.0775196	−0.00385198
$406$	11.0068	0.546261
$407$	0.483396	0.0239611
$408$	4.60781	0.228121
$409$	−18.9313	−0.936092	−0.468046	−	0.883704i	$-0.655042\pi$
$409$	−18.9313	−0.936092	−0.468046	+	0.883704i	$0.655042\pi$
$410$	0.107228	0.00529561
$411$	18.5188	0.913467
$412$	−11.3902	−0.561157
$413$	−13.4916	−0.663877
$414$	9.37723	0.460866
$415$	0.0475329	0.00233330
$416$	−4.76942	−0.233840
$417$	8.43590	0.413108
$418$	−5.24912	−0.256743
$419$	−8.19804	−0.400500	−0.200250	−	0.979745i	$-0.564176\pi$
$419$	−8.19804	−0.400500	−0.200250	+	0.979745i	$0.564176\pi$
$420$	0.212503	0.0103691
$421$	12.1723	0.593241	0.296621	−	0.954995i	$-0.404140\pi$
$421$	12.1723	0.593241	0.296621	+	0.954995i	$0.404140\pi$
$422$	−8.91983	−0.434210
$423$	−11.4075	−0.554651
$424$	4.36082	0.211780
$425$	−23.0114	−1.11621
$426$	0.600594	0.0290989
$427$	−2.74128	−0.132660
$428$	−4.08474	−0.197443
$429$	4.76942	0.230270
$430$	−0.432977	−0.0208800
$431$	−31.8012	−1.53181	−0.765904	−	0.642955i	$-0.777708\pi$
$431$	−31.8012	−1.53181	−0.765904	+	0.642955i	$0.777708\pi$
$432$	−1.00000	−0.0481125
$433$	14.7405	0.708385	0.354192	−	0.935173i	$-0.384756\pi$
$433$	14.7405	0.708385	0.354192	+	0.935173i	$0.384756\pi$
$434$	−10.4243	−0.500383
$435$	−0.311259	−0.0149237
$436$	7.28009	0.348653
$437$	49.2222	2.35462
$438$	8.32148	0.397616
$439$	−8.58307	−0.409648	−0.204824	−	0.978799i	$-0.565662\pi$
$439$	−8.58307	−0.409648	−0.204824	+	0.978799i	$0.565662\pi$
$440$	−0.0775196	−0.00369560
$441$	0.514595	0.0245045
$442$	−21.9766	−1.04532
$443$	18.1526	0.862454	0.431227	−	0.902243i	$-0.358081\pi$
$443$	18.1526	0.862454	0.431227	+	0.902243i	$0.358081\pi$
$444$	0.483396	0.0229410
$445$	−0.0276896	−0.00131262
$446$	−4.65318	−0.220334
$447$	4.05746	0.191911
$448$	2.74128	0.129513
$449$	−17.2605	−0.814576	−0.407288	−	0.913300i	$-0.633525\pi$
$449$	−17.2605	−0.814576	−0.407288	+	0.913300i	$0.633525\pi$
$450$	4.99399	0.235419
$451$	−1.38324	−0.0651341
$452$	−10.6170	−0.499383
$453$	9.51639	0.447119
$454$	−12.3447	−0.579364
$455$	−1.01351	−0.0475143
$456$	−5.24912	−0.245813
$457$	−22.3016	−1.04323	−0.521613	−	0.853182i	$-0.674670\pi$
$457$	−22.3016	−1.04323	−0.521613	+	0.853182i	$0.674670\pi$
$458$	18.8764	0.882034
$459$	−4.60781	−0.215074
$460$	0.726919	0.0338928
$461$	15.8413	0.737803	0.368902	−	0.929468i	$-0.379734\pi$
$461$	15.8413	0.737803	0.368902	+	0.929468i	$0.379734\pi$
$462$	−2.74128	−0.127536
$463$	−30.8242	−1.43252	−0.716261	−	0.697832i	$-0.754148\pi$
$463$	−30.8242	−1.43252	−0.716261	+	0.697832i	$0.754148\pi$
$464$	−4.01523	−0.186402
$465$	0.294786	0.0136704
$466$	−25.5410	−1.18316
$467$	11.5959	0.536593	0.268297	−	0.963336i	$-0.413539\pi$
$467$	11.5959	0.536593	0.268297	+	0.963336i	$0.413539\pi$
$468$	4.76942	0.220466
$469$	−6.85153	−0.316374
$470$	−0.884303	−0.0407899
$471$	−10.8786	−0.501260
$472$	4.92164	0.226537
$473$	5.58539	0.256817
$474$	−0.850463	−0.0390630
$475$	26.2141	1.20278
$476$	12.6313	0.578954
$477$	−4.36082	−0.199668
$478$	8.90122	0.407132
$479$	14.2601	0.651562	0.325781	−	0.945445i	$-0.394373\pi$
$479$	14.2601	0.651562	0.325781	+	0.945445i	$0.394373\pi$
$480$	−0.0775196	−0.00353827
$481$	−2.30552	−0.105123
$482$	1.33706	0.0609016
$483$	25.7056	1.16964
$484$	1.00000	0.0454545
$485$	−0.720506	−0.0327165
$486$	1.00000	0.0453609
$487$	35.1649	1.59347	0.796737	−	0.604326i	$-0.206558\pi$
$487$	35.1649	1.59347	0.796737	+	0.604326i	$0.206558\pi$
$488$	1.00000	0.0452679
$489$	18.7055	0.845894
$490$	0.0398912	0.00180210
$491$	21.6380	0.976510	0.488255	−	0.872701i	$-0.337634\pi$
$491$	21.6380	0.976510	0.488255	+	0.872701i	$0.337634\pi$
$492$	−1.38324	−0.0623611
$493$	−18.5014	−0.833261
$494$	25.0353	1.12639
$495$	0.0775196	0.00348425
$496$	3.80272	0.170747
$497$	1.64640	0.0738509
$498$	−0.613172	−0.0274769
$499$	−6.11790	−0.273875	−0.136937	−	0.990580i	$-0.543726\pi$
$499$	−6.11790	−0.273875	−0.136937	+	0.990580i	$0.543726\pi$
$500$	0.774730	0.0346470
$501$	−25.4986	−1.13919
$502$	11.2198	0.500764
$503$	−33.2178	−1.48111	−0.740554	−	0.671997i	$-0.765437\pi$
$503$	−33.2178	−1.48111	−0.740554	+	0.671997i	$0.765437\pi$
$504$	−2.74128	−0.122106
$505$	−0.387600	−0.0172480
$506$	−9.37723	−0.416869
$507$	−9.74735	−0.432895
$508$	7.39369	0.328042
$509$	−31.8401	−1.41129	−0.705643	−	0.708567i	$-0.749342\pi$
$509$	−31.8401	−1.41129	−0.705643	+	0.708567i	$0.749342\pi$
$510$	−0.357196	−0.0158169
$511$	22.8115	1.00912
$512$	−1.00000	−0.0441942
$513$	5.24912	0.231754
$514$	−4.34093	−0.191470
$515$	0.882967	0.0389082
$516$	5.58539	0.245883
$517$	11.4075	0.501700
$518$	1.32512	0.0582225
$519$	16.4451	0.721861
$520$	0.369723	0.0162134
$521$	32.3863	1.41887	0.709434	−	0.704771i	$-0.248950\pi$
$521$	32.3863	1.41887	0.709434	+	0.704771i	$0.248950\pi$
$522$	4.01523	0.175742
$523$	12.0657	0.527595	0.263797	−	0.964578i	$-0.415025\pi$
$523$	12.0657	0.527595	0.263797	+	0.964578i	$0.415025\pi$
$524$	4.96575	0.216930
$525$	13.6899	0.597477
$526$	−7.88279	−0.343706
$527$	17.5222	0.763280
$528$	1.00000	0.0435194
$529$	64.9324	2.82315
$530$	−0.338049	−0.0146839
$531$	−4.92164	−0.213581
$532$	−14.3893	−0.623855
$533$	6.59723	0.285758
$534$	0.357196	0.0154574
$535$	0.316647	0.0136898
$536$	2.49939	0.107957
$537$	13.5728	0.585710
$538$	22.3610	0.964053
$539$	−0.514595	−0.0221652
$540$	0.0775196	0.00333591
$541$	32.6741	1.40477	0.702385	−	0.711797i	$-0.252118\pi$
$541$	32.6741	1.40477	0.702385	+	0.711797i	$0.252118\pi$
$542$	0.541334	0.0232523
$543$	−21.3301	−0.915363
$544$	−4.60781	−0.197558
$545$	−0.564349	−0.0241741
$546$	13.0743	0.559528
$547$	10.2391	0.437793	0.218897	−	0.975748i	$-0.429754\pi$
$547$	10.2391	0.437793	0.218897	+	0.975748i	$0.429754\pi$
$548$	−18.5188	−0.791086
$549$	−1.00000	−0.0426790
$550$	−4.99399	−0.212944
$551$	21.0764	0.897886
$552$	−9.37723	−0.399121
$553$	−2.33135	−0.0991392
$554$	14.0662	0.597617
$555$	−0.0374727	−0.00159063
$556$	−8.43590	−0.357762
$557$	−24.5653	−1.04087	−0.520434	−	0.853902i	$-0.674230\pi$
$557$	−24.5653	−1.04087	−0.520434	+	0.853902i	$0.674230\pi$
$558$	−3.80272	−0.160982
$559$	−26.6391	−1.12671
$560$	−0.212503	−0.00897987
$561$	4.60781	0.194542
$562$	−5.12802	−0.216313
$563$	6.62862	0.279363	0.139682	−	0.990196i	$-0.455392\pi$
$563$	6.62862	0.279363	0.139682	+	0.990196i	$0.455392\pi$
$564$	11.4075	0.480341
$565$	0.823028	0.0346250
$566$	−18.3589	−0.771683
$567$	2.74128	0.115123
$568$	−0.600594	−0.0252004
$569$	−32.8938	−1.37898	−0.689490	−	0.724295i	$-0.742165\pi$
$569$	−32.8938	−1.37898	−0.689490	+	0.724295i	$0.742165\pi$
$570$	0.406910	0.0170436
$571$	−7.85150	−0.328575	−0.164287	−	0.986413i	$-0.552532\pi$
$571$	−7.85150	−0.328575	−0.164287	+	0.986413i	$0.552532\pi$
$572$	−4.76942	−0.199419
$573$	−9.45958	−0.395180
$574$	−3.79183	−0.158268
$575$	46.8298	1.95294
$576$	1.00000	0.0416667
$577$	3.82808	0.159365	0.0796826	−	0.996820i	$-0.474609\pi$
$577$	3.82808	0.159365	0.0796826	+	0.996820i	$0.474609\pi$
$578$	−4.23191	−0.176024
$579$	19.5557	0.812706
$580$	0.311259	0.0129243
$581$	−1.68087	−0.0697344
$582$	9.29450	0.385269
$583$	4.36082	0.180607
$584$	−8.32148	−0.344345
$585$	−0.369723	−0.0152862
$586$	−10.8946	−0.450053
$587$	−19.5528	−0.807028	−0.403514	−	0.914973i	$-0.632211\pi$
$587$	−19.5528	−0.807028	−0.403514	+	0.914973i	$0.632211\pi$
$588$	−0.514595	−0.0212215
$589$	−19.9610	−0.822478
$590$	−0.381523	−0.0157071
$591$	7.92644	0.326050
$592$	−0.483396	−0.0198675
$593$	−12.0892	−0.496446	−0.248223	−	0.968703i	$-0.579847\pi$
$593$	−12.0892	−0.496446	−0.248223	+	0.968703i	$0.579847\pi$
$594$	−1.00000	−0.0410305
$595$	−0.979172	−0.0401421
$596$	−4.05746	−0.166200
$597$	−13.9521	−0.571022
$598$	44.7239	1.82890
$599$	−6.83842	−0.279410	−0.139705	−	0.990193i	$-0.544615\pi$
$599$	−6.83842	−0.279410	−0.139705	+	0.990193i	$0.544615\pi$
$600$	−4.99399	−0.203879
$601$	−0.389900	−0.0159044	−0.00795218	−	0.999968i	$-0.502531\pi$
$601$	−0.389900	−0.0159044	−0.00795218	+	0.999968i	$0.502531\pi$
$602$	15.3111	0.624034
$603$	−2.49939	−0.101783
$604$	−9.51639	−0.387217
$605$	−0.0775196	−0.00315162
$606$	5.00003	0.203112
$607$	27.5580	1.11854	0.559272	−	0.828984i	$-0.311081\pi$
$607$	27.5580	1.11854	0.559272	+	0.828984i	$0.311081\pi$
$608$	5.24912	0.212880
$609$	11.0068	0.446020
$610$	−0.0775196	−0.00313868
$611$	−54.4070	−2.20107
$612$	4.60781	0.186260
$613$	−13.1423	−0.530812	−0.265406	−	0.964137i	$-0.585506\pi$
$613$	−13.1423	−0.530812	−0.265406	+	0.964137i	$0.585506\pi$
$614$	−6.37298	−0.257193
$615$	0.107228	0.00432385
$616$	2.74128	0.110449
$617$	18.3561	0.738991	0.369495	−	0.929233i	$-0.379531\pi$
$617$	18.3561	0.738991	0.369495	+	0.929233i	$0.379531\pi$
$618$	−11.3902	−0.458183
$619$	32.5723	1.30919	0.654597	−	0.755978i	$-0.272838\pi$
$619$	32.5723	1.30919	0.654597	+	0.755978i	$0.272838\pi$
$620$	−0.294786	−0.0118389
$621$	9.37723	0.376295
$622$	22.1220	0.887012
$623$	0.979172	0.0392297
$624$	−4.76942	−0.190930
$625$	24.9099	0.996396
$626$	−11.0920	−0.443327
$627$	−5.24912	−0.209630
$628$	10.8786	0.434104
$629$	−2.22740	−0.0888122
$630$	0.212503	0.00846631
$631$	−38.0605	−1.51516	−0.757582	−	0.652740i	$-0.773620\pi$
$631$	−38.0605	−1.51516	−0.757582	+	0.652740i	$0.773620\pi$
$632$	0.850463	0.0338296
$633$	−8.91983	−0.354531
$634$	29.1084	1.15604
$635$	−0.573156	−0.0227450
$636$	4.36082	0.172918
$637$	2.45432	0.0972437
$638$	−4.01523	−0.158964
$639$	0.600594	0.0237591
$640$	0.0775196	0.00306423
$641$	−4.00229	−0.158081	−0.0790405	−	0.996871i	$-0.525186\pi$
$641$	−4.00229	−0.158081	−0.0790405	+	0.996871i	$0.525186\pi$
$642$	−4.08474	−0.161212
$643$	28.0224	1.10510	0.552548	−	0.833481i	$-0.313655\pi$
$643$	28.0224	1.10510	0.552548	+	0.833481i	$0.313655\pi$
$644$	−25.7056	−1.01294
$645$	−0.432977	−0.0170485
$646$	24.1870	0.951623
$647$	21.4600	0.843679	0.421840	−	0.906670i	$-0.361385\pi$
$647$	21.4600	0.843679	0.421840	+	0.906670i	$0.361385\pi$
$648$	−1.00000	−0.0392837
$649$	4.92164	0.193191
$650$	23.8184	0.934236
$651$	−10.4243	−0.408561
$652$	−18.7055	−0.732566
$653$	−21.4016	−0.837509	−0.418754	−	0.908100i	$-0.637533\pi$
$653$	−21.4016	−0.837509	−0.418754	+	0.908100i	$0.637533\pi$
$654$	7.28009	0.284674
$655$	−0.384943	−0.0150410
$656$	1.38324	0.0540063
$657$	8.32148	0.324652
$658$	31.2710	1.21907
$659$	−40.4292	−1.57490	−0.787448	−	0.616381i	$-0.788598\pi$
$659$	−40.4292	−1.57490	−0.787448	+	0.616381i	$0.788598\pi$
$660$	−0.0775196	−0.00301745
$661$	11.1312	0.432952	0.216476	−	0.976288i	$-0.430544\pi$
$661$	11.1312	0.432952	0.216476	+	0.976288i	$0.430544\pi$
$662$	9.60210	0.373196
$663$	−21.9766	−0.853499
$664$	0.613172	0.0237957
$665$	1.11545	0.0432554
$666$	0.483396	0.0187312
$667$	37.6517	1.45788
$668$	25.4986	0.986570
$669$	−4.65318	−0.179902
$670$	−0.193752	−0.00748529
$671$	1.00000	0.0386046
$672$	2.74128	0.105747
$673$	36.9687	1.42504	0.712519	−	0.701653i	$-0.247554\pi$
$673$	36.9687	1.42504	0.712519	+	0.701653i	$0.247554\pi$
$674$	8.79480	0.338763
$675$	4.99399	0.192219
$676$	9.74735	0.374898
$677$	16.7340	0.643139	0.321569	−	0.946886i	$-0.395790\pi$
$677$	16.7340	0.643139	0.321569	+	0.946886i	$0.395790\pi$
$678$	−10.6170	−0.407745
$679$	25.4788	0.977786
$680$	0.357196	0.0136978
$681$	−12.3447	−0.473049
$682$	3.80272	0.145614
$683$	−27.3086	−1.04494	−0.522468	−	0.852659i	$-0.674989\pi$
$683$	−27.3086	−1.04494	−0.522468	+	0.852659i	$0.674989\pi$
$684$	−5.24912	−0.200705
$685$	1.43557	0.0548504
$686$	17.7783	0.678778
$687$	18.8764	0.720178
$688$	−5.58539	−0.212941
$689$	−20.7986	−0.792363
$690$	0.726919	0.0276733
$691$	−35.1496	−1.33715	−0.668576	−	0.743644i	$-0.733096\pi$
$691$	−35.1496	−1.33715	−0.668576	+	0.743644i	$0.733096\pi$
$692$	−16.4451	−0.625150
$693$	−2.74128	−0.104132
$694$	21.7116	0.824160
$695$	0.653948	0.0248057
$696$	−4.01523	−0.152197
$697$	6.37369	0.241421
$698$	33.2445	1.25832
$699$	−25.5410	−0.966049
$700$	−13.6899	−0.517430
$701$	7.48900	0.282855	0.141428	−	0.989949i	$-0.454831\pi$
$701$	7.48900	0.282855	0.141428	+	0.989949i	$0.454831\pi$
$702$	4.76942	0.180010
$703$	2.53741	0.0957001
$704$	−1.00000	−0.0376889
$705$	−0.884303	−0.0333048
$706$	−35.7212	−1.34439
$707$	13.7065	0.515484
$708$	4.92164	0.184966
$709$	5.28193	0.198367	0.0991835	−	0.995069i	$-0.468377\pi$
$709$	5.28193	0.198367	0.0991835	+	0.995069i	$0.468377\pi$
$710$	0.0465578	0.00174728
$711$	−0.850463	−0.0318948
$712$	−0.357196	−0.0133865
$713$	−35.6590	−1.33544
$714$	12.6313	0.472714
$715$	0.369723	0.0138269
$716$	−13.5728	−0.507240
$717$	8.90122	0.332422
$718$	10.4153	0.388694
$719$	22.5182	0.839787	0.419894	−	0.907573i	$-0.362067\pi$
$719$	22.5182	0.839787	0.419894	+	0.907573i	$0.362067\pi$
$720$	−0.0775196	−0.00288898
$721$	−31.2238	−1.16283
$722$	−8.55330	−0.318321
$723$	1.33706	0.0497259
$724$	21.3301	0.792728
$725$	20.0520	0.744713
$726$	1.00000	0.0371135
$727$	−11.0979	−0.411598	−0.205799	−	0.978594i	$-0.565979\pi$
$727$	−11.0979	−0.411598	−0.205799	+	0.978594i	$0.565979\pi$
$728$	−13.0743	−0.484565
$729$	1.00000	0.0370370
$730$	0.645078	0.0238754
$731$	−25.7364	−0.951896
$732$	1.00000	0.0369611
$733$	22.9547	0.847851	0.423926	−	0.905697i	$-0.360652\pi$
$733$	22.9547	0.847851	0.423926	+	0.905697i	$0.360652\pi$
$734$	7.81416	0.288426
$735$	0.0398912	0.00147141
$736$	9.37723	0.345649
$737$	2.49939	0.0920664
$738$	−1.38324	−0.0509177
$739$	−20.3642	−0.749110	−0.374555	−	0.927205i	$-0.622205\pi$
$739$	−20.3642	−0.749110	−0.374555	+	0.927205i	$0.622205\pi$
$740$	0.0374727	0.00137752
$741$	25.0353	0.919693
$742$	11.9542	0.438853
$743$	−24.5873	−0.902020	−0.451010	−	0.892519i	$-0.648936\pi$
$743$	−24.5873	−0.902020	−0.451010	+	0.892519i	$0.648936\pi$
$744$	3.80272	0.139415
$745$	0.314533	0.0115236
$746$	15.8856	0.581614
$747$	−0.613172	−0.0224348
$748$	−4.60781	−0.168478
$749$	−11.1974	−0.409144
$750$	0.774730	0.0282891
$751$	49.2923	1.79870	0.899351	−	0.437227i	$-0.144039\pi$
$751$	49.2923	1.79870	0.899351	+	0.437227i	$0.144039\pi$
$752$	−11.4075	−0.415988
$753$	11.2198	0.408872
$754$	19.1503	0.697413
$755$	0.737707	0.0268479
$756$	−2.74128	−0.0996993
$757$	−43.9053	−1.59577	−0.797883	−	0.602812i	$-0.794047\pi$
$757$	−43.9053	−1.59577	−0.797883	+	0.602812i	$0.794047\pi$
$758$	−3.93473	−0.142916
$759$	−9.37723	−0.340372
$760$	−0.406910	−0.0147602
$761$	−17.5560	−0.636405	−0.318203	−	0.948023i	$-0.603079\pi$
$761$	−17.5560	−0.636405	−0.318203	+	0.948023i	$0.603079\pi$
$762$	7.39369	0.267845
$763$	19.9567	0.722482
$764$	9.45958	0.342236
$765$	−0.357196	−0.0129144
$766$	−23.9054	−0.863738
$767$	−23.4733	−0.847573
$768$	−1.00000	−0.0360844
$769$	33.2122	1.19766	0.598831	−	0.800875i	$-0.295632\pi$
$769$	33.2122	1.19766	0.598831	+	0.800875i	$0.295632\pi$
$770$	−0.212503	−0.00765806
$771$	−4.34093	−0.156335
$772$	−19.5557	−0.703824
$773$	37.7865	1.35909	0.679544	−	0.733635i	$-0.262178\pi$
$773$	37.7865	1.35909	0.679544	+	0.733635i	$0.262178\pi$
$774$	5.58539	0.200763
$775$	−18.9908	−0.682169
$776$	−9.29450	−0.333653
$777$	1.32512	0.0475385
$778$	5.11812	0.183493
$779$	−7.26078	−0.260144
$780$	0.369723	0.0132382
$781$	−0.600594	−0.0214910
$782$	43.2085	1.54513
$783$	4.01523	0.143493
$784$	0.514595	0.0183784
$785$	−0.843305	−0.0300988
$786$	4.96575	0.177122
$787$	−11.7841	−0.420059	−0.210030	−	0.977695i	$-0.567356\pi$
$787$	−11.7841	−0.420059	−0.210030	+	0.977695i	$0.567356\pi$
$788$	−7.92644	−0.282368
$789$	−7.88279	−0.280635
$790$	−0.0659275	−0.00234560
$791$	−29.1042	−1.03483
$792$	1.00000	0.0355335
$793$	−4.76942	−0.169367
$794$	11.2940	0.400811
$795$	−0.338049	−0.0119894
$796$	13.9521	0.494520
$797$	33.9136	1.20128	0.600641	−	0.799519i	$-0.294912\pi$
$797$	33.9136	1.20128	0.600641	+	0.799519i	$0.294912\pi$
$798$	−14.3893	−0.509376
$799$	−52.5635	−1.85956
$800$	4.99399	0.176564
$801$	0.357196	0.0126209
$802$	10.4147	0.367756
$803$	−8.32148	−0.293659
$804$	2.49939	0.0881468
$805$	1.99269	0.0702329
$806$	−18.1368	−0.638841
$807$	22.3610	0.787146
$808$	−5.00003	−0.175900
$809$	31.4458	1.10558	0.552788	−	0.833322i	$-0.313564\pi$
$809$	31.4458	1.10558	0.552788	+	0.833322i	$0.313564\pi$
$810$	0.0775196	0.00272376
$811$	0.322544	0.0113261	0.00566303	−	0.999984i	$-0.498197\pi$
$811$	0.322544	0.0113261	0.00566303	+	0.999984i	$0.498197\pi$
$812$	−11.0068	−0.386265
$813$	0.541334	0.0189854
$814$	−0.483396	−0.0169430
$815$	1.45005	0.0507929
$816$	−4.60781	−0.161306
$817$	29.3184	1.02572
$818$	18.9313	0.661917
$819$	13.0743	0.456853
$820$	−0.107228	−0.00374456
$821$	36.7590	1.28290	0.641449	−	0.767166i	$-0.278334\pi$
$821$	36.7590	1.28290	0.641449	+	0.767166i	$0.278334\pi$
$822$	−18.5188	−0.645919
$823$	18.8113	0.655721	0.327860	−	0.944726i	$-0.393672\pi$
$823$	18.8113	0.655721	0.327860	+	0.944726i	$0.393672\pi$
$824$	11.3902	0.396798
$825$	−4.99399	−0.173868
$826$	13.4916	0.469432
$827$	17.9524	0.624268	0.312134	−	0.950038i	$-0.398956\pi$
$827$	17.9524	0.624268	0.312134	+	0.950038i	$0.398956\pi$
$828$	−9.37723	−0.325881
$829$	2.69793	0.0937030	0.0468515	−	0.998902i	$-0.485081\pi$
$829$	2.69793	0.0937030	0.0468515	+	0.998902i	$0.485081\pi$
$830$	−0.0475329	−0.00164989
$831$	14.0662	0.487952
$832$	4.76942	0.165350
$833$	2.37116	0.0821557
$834$	−8.43590	−0.292111
$835$	−1.97664	−0.0684044
$836$	5.24912	0.181545
$837$	−3.80272	−0.131441
$838$	8.19804	0.283197
$839$	37.7635	1.30374	0.651871	−	0.758330i	$-0.273984\pi$
$839$	37.7635	1.30374	0.651871	+	0.758330i	$0.273984\pi$
$840$	−0.212503	−0.00733204
$841$	−12.8779	−0.444067
$842$	−12.1723	−0.419485
$843$	−5.12802	−0.176619
$844$	8.91983	0.307033
$845$	−0.755610	−0.0259938
$846$	11.4075	0.392197
$847$	2.74128	0.0941914
$848$	−4.36082	−0.149751
$849$	−18.3589	−0.630077
$850$	23.0114	0.789283
$851$	4.53292	0.155386
$852$	−0.600594	−0.0205760
$853$	−9.13913	−0.312918	−0.156459	−	0.987684i	$-0.550008\pi$
$853$	−9.13913	−0.312918	−0.156459	+	0.987684i	$0.550008\pi$
$854$	2.74128	0.0938045
$855$	0.406910	0.0139160
$856$	4.08474	0.139613
$857$	29.4718	1.00674	0.503369	−	0.864071i	$-0.332094\pi$
$857$	29.4718	1.00674	0.503369	+	0.864071i	$0.332094\pi$
$858$	−4.76942	−0.162825
$859$	−13.9033	−0.474376	−0.237188	−	0.971464i	$-0.576226\pi$
$859$	−13.9033	−0.474376	−0.237188	+	0.971464i	$0.576226\pi$
$860$	0.432977	0.0147644
$861$	−3.79183	−0.129225
$862$	31.8012	1.08315
$863$	−27.4500	−0.934409	−0.467205	−	0.884149i	$-0.654739\pi$
$863$	−27.4500	−0.934409	−0.467205	+	0.884149i	$0.654739\pi$
$864$	1.00000	0.0340207
$865$	1.27482	0.0433451
$866$	−14.7405	−0.500904
$867$	−4.23191	−0.143723
$868$	10.4243	0.353824
$869$	0.850463	0.0288500
$870$	0.311259	0.0105527
$871$	−11.9207	−0.403916
$872$	−7.28009	−0.246535
$873$	9.29450	0.314571
$874$	−49.2222	−1.66497
$875$	2.12375	0.0717958
$876$	−8.32148	−0.281157
$877$	−26.4321	−0.892549	−0.446275	−	0.894896i	$-0.647250\pi$
$877$	−26.4321	−0.892549	−0.446275	+	0.894896i	$0.647250\pi$
$878$	8.58307	0.289665
$879$	−10.8946	−0.367467
$880$	0.0775196	0.00261318
$881$	32.7546	1.10353	0.551766	−	0.833999i	$-0.313954\pi$
$881$	32.7546	1.10353	0.551766	+	0.833999i	$0.313954\pi$
$882$	−0.514595	−0.0173273
$883$	26.0660	0.877191	0.438595	−	0.898685i	$-0.355476\pi$
$883$	26.0660	0.877191	0.438595	+	0.898685i	$0.355476\pi$
$884$	21.9766	0.739152
$885$	−0.381523	−0.0128248
$886$	−18.1526	−0.609847
$887$	−33.6286	−1.12914	−0.564569	−	0.825386i	$-0.690957\pi$
$887$	−33.6286	−1.12914	−0.564569	+	0.825386i	$0.690957\pi$
$888$	−0.483396	−0.0162217
$889$	20.2682	0.679772
$890$	0.0276896	0.000928159 0
$891$	−1.00000	−0.0335013
$892$	4.65318	0.155800
$893$	59.8793	2.00378
$894$	−4.05746	−0.135702
$895$	1.05216	0.0351698
$896$	−2.74128	−0.0915796
$897$	44.7239	1.49329
$898$	17.2605	0.575992
$899$	−15.2688	−0.509243
$900$	−4.99399	−0.166466
$901$	−20.0938	−0.669423
$902$	1.38324	0.0460568
$903$	15.3111	0.509522
$904$	10.6170	0.353117
$905$	−1.65350	−0.0549643
$906$	−9.51639	−0.316161
$907$	27.6123	0.916850	0.458425	−	0.888733i	$-0.348414\pi$
$907$	27.6123	0.916850	0.458425	+	0.888733i	$0.348414\pi$
$908$	12.3447	0.409673
$909$	5.00003	0.165840
$910$	1.01351	0.0335976
$911$	23.3274	0.772872	0.386436	−	0.922316i	$-0.373706\pi$
$911$	23.3274	0.772872	0.386436	+	0.922316i	$0.373706\pi$
$912$	5.24912	0.173816
$913$	0.613172	0.0202930
$914$	22.3016	0.737672
$915$	−0.0775196	−0.00256272
$916$	−18.8764	−0.623692
$917$	13.6125	0.449524
$918$	4.60781	0.152080
$919$	−21.7867	−0.718677	−0.359339	−	0.933207i	$-0.616998\pi$
$919$	−21.7867	−0.718677	−0.359339	+	0.933207i	$0.616998\pi$
$920$	−0.726919	−0.0239658
$921$	−6.37298	−0.209997
$922$	−15.8413	−0.521706
$923$	2.86449	0.0942857
$924$	2.74128	0.0901814
$925$	2.41408	0.0793743
$926$	30.8242	1.01295
$927$	−11.3902	−0.374105
$928$	4.01523	0.131806
$929$	2.38461	0.0782367	0.0391183	−	0.999235i	$-0.487545\pi$
$929$	2.38461	0.0782367	0.0391183	+	0.999235i	$0.487545\pi$
$930$	−0.294786	−0.00966640
$931$	−2.70117	−0.0885274
$932$	25.5410	0.836623
$933$	22.1220	0.724242
$934$	−11.5959	−0.379429
$935$	0.357196	0.0116815
$936$	−4.76942	−0.155893
$937$	47.1407	1.54002	0.770010	−	0.638032i	$-0.220251\pi$
$937$	47.1407	1.54002	0.770010	+	0.638032i	$0.220251\pi$
$938$	6.85153	0.223710
$939$	−11.0920	−0.361975
$940$	0.884303	0.0288428
$941$	−1.90026	−0.0619468	−0.0309734	−	0.999520i	$-0.509861\pi$
$941$	−1.90026	−0.0619468	−0.0309734	+	0.999520i	$0.509861\pi$
$942$	10.8786	0.354444
$943$	−12.9709	−0.422392
$944$	−4.92164	−0.160186
$945$	0.212503	0.00691271
$946$	−5.58539	−0.181597
$947$	−45.9291	−1.49249	−0.746247	−	0.665669i	$-0.768146\pi$
$947$	−45.9291	−1.49249	−0.746247	+	0.665669i	$0.768146\pi$
$948$	0.850463	0.0276217
$949$	39.6886	1.28835
$950$	−26.2141	−0.850497
$951$	29.1084	0.943905
$952$	−12.6313	−0.409382
$953$	29.7253	0.962895	0.481448	−	0.876475i	$-0.340111\pi$
$953$	29.7253	0.962895	0.481448	+	0.876475i	$0.340111\pi$
$954$	4.36082	0.141187
$955$	−0.733303	−0.0237291
$956$	−8.90122	−0.287886
$957$	−4.01523	−0.129794
$958$	−14.2601	−0.460724
$959$	−50.7653	−1.63930
$960$	0.0775196	0.00250193
$961$	−16.5393	−0.533525
$962$	2.30552	0.0743329
$963$	−4.08474	−0.131629
$964$	−1.33706	−0.0430639
$965$	1.51595	0.0488001
$966$	−25.7056	−0.827063
$967$	−59.4747	−1.91258	−0.956288	−	0.292425i	$-0.905538\pi$
$967$	−59.4747	−1.91258	−0.956288	+	0.292425i	$0.905538\pi$
$968$	−1.00000	−0.0321412
$969$	24.1870	0.776997
$970$	0.720506	0.0231340
$971$	29.0322	0.931689	0.465844	−	0.884867i	$-0.345751\pi$
$971$	29.0322	0.931689	0.465844	+	0.884867i	$0.345751\pi$
$972$	−1.00000	−0.0320750
$973$	−23.1251	−0.741358
$974$	−35.1649	−1.12676
$975$	23.8184	0.762800
$976$	−1.00000	−0.0320092
$977$	31.0002	0.991786	0.495893	−	0.868384i	$-0.334841\pi$
$977$	31.0002	0.991786	0.495893	+	0.868384i	$0.334841\pi$
$978$	−18.7055	−0.598137
$979$	−0.357196	−0.0114160
$980$	−0.0398912	−0.00127428
$981$	7.28009	0.232435
$982$	−21.6380	−0.690497
$983$	46.9310	1.49686	0.748432	−	0.663211i	$-0.230807\pi$
$983$	46.9310	1.49686	0.748432	+	0.663211i	$0.230807\pi$
$984$	1.38324	0.0440960
$985$	0.614454	0.0195781
$986$	18.5014	0.589205
$987$	31.2710	0.995368
$988$	−25.0353	−0.796478
$989$	52.3755	1.66544
$990$	−0.0775196	−0.00246373
$991$	−34.4297	−1.09370	−0.546848	−	0.837232i	$-0.684173\pi$
$991$	−34.4297	−1.09370	−0.546848	+	0.837232i	$0.684173\pi$
$992$	−3.80272	−0.120737
$993$	9.60210	0.304714
$994$	−1.64640	−0.0522205
$995$	−1.08156	−0.0342878
$996$	0.613172	0.0194291
$997$	−9.43778	−0.298898	−0.149449	−	0.988769i	$-0.547750\pi$
$997$	−9.43778	−0.298898	−0.149449	+	0.988769i	$0.547750\pi$
$998$	6.11790	0.193659
$999$	0.483396	0.0152940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.y.1.4	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.y.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.0775196 q^{5} +1.00000 q^{6} +2.74128 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.0775196 q^{5} +1.00000 q^{6} +2.74128 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.0775196 q^{10} -1.00000 q^{11} -1.00000 q^{12} +4.76942 q^{13} -2.74128 q^{14} +0.0775196 q^{15} +1.00000 q^{16} +4.60781 q^{17} -1.00000 q^{18} -5.24912 q^{19} -0.0775196 q^{20} -2.74128 q^{21} +1.00000 q^{22} -9.37723 q^{23} +1.00000 q^{24} -4.99399 q^{25} -4.76942 q^{26} -1.00000 q^{27} +2.74128 q^{28} -4.01523 q^{29} -0.0775196 q^{30} +3.80272 q^{31} -1.00000 q^{32} +1.00000 q^{33} -4.60781 q^{34} -0.212503 q^{35} +1.00000 q^{36} -0.483396 q^{37} +5.24912 q^{38} -4.76942 q^{39} +0.0775196 q^{40} +1.38324 q^{41} +2.74128 q^{42} -5.58539 q^{43} -1.00000 q^{44} -0.0775196 q^{45} +9.37723 q^{46} -11.4075 q^{47} -1.00000 q^{48} +0.514595 q^{49} +4.99399 q^{50} -4.60781 q^{51} +4.76942 q^{52} -4.36082 q^{53} +1.00000 q^{54} +0.0775196 q^{55} -2.74128 q^{56} +5.24912 q^{57} +4.01523 q^{58} -4.92164 q^{59} +0.0775196 q^{60} -1.00000 q^{61} -3.80272 q^{62} +2.74128 q^{63} +1.00000 q^{64} -0.369723 q^{65} -1.00000 q^{66} -2.49939 q^{67} +4.60781 q^{68} +9.37723 q^{69} +0.212503 q^{70} +0.600594 q^{71} -1.00000 q^{72} +8.32148 q^{73} +0.483396 q^{74} +4.99399 q^{75} -5.24912 q^{76} -2.74128 q^{77} +4.76942 q^{78} -0.850463 q^{79} -0.0775196 q^{80} +1.00000 q^{81} -1.38324 q^{82} -0.613172 q^{83} -2.74128 q^{84} -0.357196 q^{85} +5.58539 q^{86} +4.01523 q^{87} +1.00000 q^{88} +0.357196 q^{89} +0.0775196 q^{90} +13.0743 q^{91} -9.37723 q^{92} -3.80272 q^{93} +11.4075 q^{94} +0.406910 q^{95} +1.00000 q^{96} +9.29450 q^{97} -0.514595 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} - 2 q^{5} + 7 q^{6} + q^{7} - 7 q^{8} + 7 q^{9} + 2 q^{10} - 7 q^{11} - 7 q^{12} - q^{14} + 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 5 q^{19} - 2 q^{20} - q^{21} + 7 q^{22} - 3 q^{23} + 7 q^{24} + 11 q^{25} - 7 q^{27} + q^{28} - 14 q^{29} - 2 q^{30} + 5 q^{31} - 7 q^{32} + 7 q^{33} - 3 q^{34} - 9 q^{35} + 7 q^{36} + 14 q^{37} + 5 q^{38} + 2 q^{40} - 7 q^{41} + q^{42} + q^{43} - 7 q^{44} - 2 q^{45} + 3 q^{46} - 7 q^{48} - 11 q^{50} - 3 q^{51} - 3 q^{53} + 7 q^{54} + 2 q^{55} - q^{56} + 5 q^{57} + 14 q^{58} - 14 q^{59} + 2 q^{60} - 7 q^{61} - 5 q^{62} + q^{63} + 7 q^{64} - 10 q^{65} - 7 q^{66} + 3 q^{68} + 3 q^{69} + 9 q^{70} - 22 q^{71} - 7 q^{72} + q^{73} - 14 q^{74} - 11 q^{75} - 5 q^{76} - q^{77} + 10 q^{79} - 2 q^{80} + 7 q^{81} + 7 q^{82} - 17 q^{83} - q^{84} + 18 q^{85} - q^{86} + 14 q^{87} + 7 q^{88} - 18 q^{89} + 2 q^{90} + 21 q^{91} - 3 q^{92} - 5 q^{93} - 41 q^{95} + 7 q^{96} + 25 q^{97} - 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 - 2 * q^5 + 7 * q^6 + q^7 - 7 * q^8 + 7 * q^9 + 2 * q^10 - 7 * q^11 - 7 * q^12 - q^14 + 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 5 * q^19 - 2 * q^20 - q^21 + 7 * q^22 - 3 * q^23 + 7 * q^24 + 11 * q^25 - 7 * q^27 + q^28 - 14 * q^29 - 2 * q^30 + 5 * q^31 - 7 * q^32 + 7 * q^33 - 3 * q^34 - 9 * q^35 + 7 * q^36 + 14 * q^37 + 5 * q^38 + 2 * q^40 - 7 * q^41 + q^42 + q^43 - 7 * q^44 - 2 * q^45 + 3 * q^46 - 7 * q^48 - 11 * q^50 - 3 * q^51 - 3 * q^53 + 7 * q^54 + 2 * q^55 - q^56 + 5 * q^57 + 14 * q^58 - 14 * q^59 + 2 * q^60 - 7 * q^61 - 5 * q^62 + q^63 + 7 * q^64 - 10 * q^65 - 7 * q^66 + 3 * q^68 + 3 * q^69 + 9 * q^70 - 22 * q^71 - 7 * q^72 + q^73 - 14 * q^74 - 11 * q^75 - 5 * q^76 - q^77 + 10 * q^79 - 2 * q^80 + 7 * q^81 + 7 * q^82 - 17 * q^83 - q^84 + 18 * q^85 - q^86 + 14 * q^87 + 7 * q^88 - 18 * q^89 + 2 * q^90 + 21 * q^91 - 3 * q^92 - 5 * q^93 - 41 * q^95 + 7 * q^96 + 25 * q^97 - 7 * q^99

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