LMFDB - Embedded newform 4026.2.a.x.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.46101901.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 12x^{3} + 6x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 12x^3 + 6x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.371781$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.28209 q^{5} -1.00000 q^{6} -0.306395 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.28209 q^{5} -1.00000 q^{6} -0.306395 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.28209 q^{10} -1.00000 q^{11} -1.00000 q^{12} -0.0653864 q^{13} -0.306395 q^{14} -1.28209 q^{15} +1.00000 q^{16} -0.119525 q^{17} +1.00000 q^{18} -7.96238 q^{19} +1.28209 q^{20} +0.306395 q^{21} -1.00000 q^{22} -1.37465 q^{23} -1.00000 q^{24} -3.35626 q^{25} -0.0653864 q^{26} -1.00000 q^{27} -0.306395 q^{28} -7.31061 q^{29} -1.28209 q^{30} +3.09717 q^{31} +1.00000 q^{32} +1.00000 q^{33} -0.119525 q^{34} -0.392824 q^{35} +1.00000 q^{36} -4.58287 q^{37} -7.96238 q^{38} +0.0653864 q^{39} +1.28209 q^{40} -7.06969 q^{41} +0.306395 q^{42} +4.86465 q^{43} -1.00000 q^{44} +1.28209 q^{45} -1.37465 q^{46} -6.46008 q^{47} -1.00000 q^{48} -6.90612 q^{49} -3.35626 q^{50} +0.119525 q^{51} -0.0653864 q^{52} +5.11394 q^{53} -1.00000 q^{54} -1.28209 q^{55} -0.306395 q^{56} +7.96238 q^{57} -7.31061 q^{58} +11.2122 q^{59} -1.28209 q^{60} +1.00000 q^{61} +3.09717 q^{62} -0.306395 q^{63} +1.00000 q^{64} -0.0838310 q^{65} +1.00000 q^{66} -5.22547 q^{67} -0.119525 q^{68} +1.37465 q^{69} -0.392824 q^{70} +11.2202 q^{71} +1.00000 q^{72} -9.21003 q^{73} -4.58287 q^{74} +3.35626 q^{75} -7.96238 q^{76} +0.306395 q^{77} +0.0653864 q^{78} +13.9169 q^{79} +1.28209 q^{80} +1.00000 q^{81} -7.06969 q^{82} -17.0516 q^{83} +0.306395 q^{84} -0.153241 q^{85} +4.86465 q^{86} +7.31061 q^{87} -1.00000 q^{88} -5.41939 q^{89} +1.28209 q^{90} +0.0200340 q^{91} -1.37465 q^{92} -3.09717 q^{93} -6.46008 q^{94} -10.2084 q^{95} -1.00000 q^{96} -7.22689 q^{97} -6.90612 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.28209	0.573366	0.286683	−	0.958026i	$-0.407447\pi$
$5$	1.28209	0.573366	0.286683	+	0.958026i	$0.407447\pi$
$6$	−1.00000	−0.408248
$7$	−0.306395	−0.115806	−0.0579031	−	0.998322i	$-0.518441\pi$
$7$	−0.306395	−0.115806	−0.0579031	+	0.998322i	$0.518441\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.28209	0.405431
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	−0.0653864	−0.0181349	−0.00906747	−	0.999959i	$-0.502886\pi$
$13$	−0.0653864	−0.0181349	−0.00906747	+	0.999959i	$0.502886\pi$
$14$	−0.306395	−0.0818874
$15$	−1.28209	−0.331033
$16$	1.00000	0.250000
$17$	−0.119525	−0.0289890	−0.0144945	−	0.999895i	$-0.504614\pi$
$17$	−0.119525	−0.0289890	−0.0144945	+	0.999895i	$0.504614\pi$
$18$	1.00000	0.235702
$19$	−7.96238	−1.82669	−0.913347	−	0.407181i	$-0.866512\pi$
$19$	−7.96238	−1.82669	−0.913347	+	0.407181i	$0.866512\pi$
$20$	1.28209	0.286683
$21$	0.306395	0.0668608
$22$	−1.00000	−0.213201
$23$	−1.37465	−0.286635	−0.143318	−	0.989677i	$-0.545777\pi$
$23$	−1.37465	−0.286635	−0.143318	+	0.989677i	$0.545777\pi$
$24$	−1.00000	−0.204124
$25$	−3.35626	−0.671252
$26$	−0.0653864	−0.0128233
$27$	−1.00000	−0.192450
$28$	−0.306395	−0.0579031
$29$	−7.31061	−1.35755	−0.678773	−	0.734348i	$-0.737488\pi$
$29$	−7.31061	−1.35755	−0.678773	+	0.734348i	$0.737488\pi$
$30$	−1.28209	−0.234076
$31$	3.09717	0.556269	0.278134	−	0.960542i	$-0.410284\pi$
$31$	3.09717	0.556269	0.278134	+	0.960542i	$0.410284\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−0.119525	−0.0204983
$35$	−0.392824	−0.0663994
$36$	1.00000	0.166667
$37$	−4.58287	−0.753419	−0.376709	−	0.926332i	$-0.622944\pi$
$37$	−4.58287	−0.753419	−0.376709	+	0.926332i	$0.622944\pi$
$38$	−7.96238	−1.29167
$39$	0.0653864	0.0104702
$40$	1.28209	0.202715
$41$	−7.06969	−1.10410	−0.552050	−	0.833811i	$-0.686154\pi$
$41$	−7.06969	−1.10410	−0.552050	+	0.833811i	$0.686154\pi$
$42$	0.306395	0.0472777
$43$	4.86465	0.741853	0.370926	−	0.928662i	$-0.379040\pi$
$43$	4.86465	0.741853	0.370926	+	0.928662i	$0.379040\pi$
$44$	−1.00000	−0.150756
$45$	1.28209	0.191122
$46$	−1.37465	−0.202682
$47$	−6.46008	−0.942299	−0.471149	−	0.882053i	$-0.656161\pi$
$47$	−6.46008	−0.942299	−0.471149	+	0.882053i	$0.656161\pi$
$48$	−1.00000	−0.144338
$49$	−6.90612	−0.986589
$50$	−3.35626	−0.474647
$51$	0.119525	0.0167368
$52$	−0.0653864	−0.00906747
$53$	5.11394	0.702454	0.351227	−	0.936290i	$-0.385765\pi$
$53$	5.11394	0.702454	0.351227	+	0.936290i	$0.385765\pi$
$54$	−1.00000	−0.136083
$55$	−1.28209	−0.172876
$56$	−0.306395	−0.0409437
$57$	7.96238	1.05464
$58$	−7.31061	−0.959930
$59$	11.2122	1.45970	0.729849	−	0.683608i	$-0.239590\pi$
$59$	11.2122	1.45970	0.729849	+	0.683608i	$0.239590\pi$
$60$	−1.28209	−0.165516
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	3.09717	0.393341
$63$	−0.306395	−0.0386021
$64$	1.00000	0.125000
$65$	−0.0838310	−0.0103980
$66$	1.00000	0.123091
$67$	−5.22547	−0.638392	−0.319196	−	0.947689i	$-0.603413\pi$
$67$	−5.22547	−0.638392	−0.319196	+	0.947689i	$0.603413\pi$
$68$	−0.119525	−0.0144945
$69$	1.37465	0.165489
$70$	−0.392824	−0.0469514
$71$	11.2202	1.33160	0.665799	−	0.746131i	$-0.268091\pi$
$71$	11.2202	1.33160	0.665799	+	0.746131i	$0.268091\pi$
$72$	1.00000	0.117851
$73$	−9.21003	−1.07795	−0.538976	−	0.842321i	$-0.681189\pi$
$73$	−9.21003	−1.07795	−0.538976	+	0.842321i	$0.681189\pi$
$74$	−4.58287	−0.532747
$75$	3.35626	0.387547
$76$	−7.96238	−0.913347
$77$	0.306395	0.0349169
$78$	0.0653864	0.00740355
$79$	13.9169	1.56578	0.782888	−	0.622163i	$-0.213746\pi$
$79$	13.9169	1.56578	0.782888	+	0.622163i	$0.213746\pi$
$80$	1.28209	0.143341
$81$	1.00000	0.111111
$82$	−7.06969	−0.780717
$83$	−17.0516	−1.87165	−0.935827	−	0.352460i	$-0.885345\pi$
$83$	−17.0516	−1.87165	−0.935827	+	0.352460i	$0.885345\pi$
$84$	0.306395	0.0334304
$85$	−0.153241	−0.0166213
$86$	4.86465	0.524569
$87$	7.31061	0.783779
$88$	−1.00000	−0.106600
$89$	−5.41939	−0.574454	−0.287227	−	0.957862i	$-0.592733\pi$
$89$	−5.41939	−0.574454	−0.287227	+	0.957862i	$0.592733\pi$
$90$	1.28209	0.135144
$91$	0.0200340	0.00210014
$92$	−1.37465	−0.143318
$93$	−3.09717	−0.321162
$94$	−6.46008	−0.666306
$95$	−10.2084	−1.04736
$96$	−1.00000	−0.102062
$97$	−7.22689	−0.733780	−0.366890	−	0.930264i	$-0.619577\pi$
$97$	−7.22689	−0.733780	−0.366890	+	0.930264i	$0.619577\pi$
$98$	−6.90612	−0.697624
$99$	−1.00000	−0.100504
$100$	−3.35626	−0.335626
$101$	−3.15901	−0.314333	−0.157167	−	0.987572i	$-0.550236\pi$
$101$	−3.15901	−0.314333	−0.157167	+	0.987572i	$0.550236\pi$
$102$	0.119525	0.0118347
$103$	−1.53431	−0.151180	−0.0755901	−	0.997139i	$-0.524084\pi$
$103$	−1.53431	−0.151180	−0.0755901	+	0.997139i	$0.524084\pi$
$104$	−0.0653864	−0.00641167
$105$	0.392824	0.0383357
$106$	5.11394	0.496710
$107$	18.3917	1.77800	0.888998	−	0.457911i	$-0.151402\pi$
$107$	18.3917	1.77800	0.888998	+	0.457911i	$0.151402\pi$
$108$	−1.00000	−0.0962250
$109$	−12.6183	−1.20862	−0.604308	−	0.796751i	$-0.706550\pi$
$109$	−12.6183	−1.20862	−0.604308	+	0.796751i	$0.706550\pi$
$110$	−1.28209	−0.122242
$111$	4.58287	0.434986
$112$	−0.306395	−0.0289516
$113$	4.40410	0.414303	0.207152	−	0.978309i	$-0.433581\pi$
$113$	4.40410	0.414303	0.207152	+	0.978309i	$0.433581\pi$
$114$	7.96238	0.745745
$115$	−1.76242	−0.164347
$116$	−7.31061	−0.678773
$117$	−0.0653864	−0.00604498
$118$	11.2122	1.03216
$119$	0.0366218	0.00335711
$120$	−1.28209	−0.117038
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	7.06969	0.637453
$124$	3.09717	0.278134
$125$	−10.7134	−0.958239
$126$	−0.306395	−0.0272958
$127$	3.99965	0.354912	0.177456	−	0.984129i	$-0.443213\pi$
$127$	3.99965	0.354912	0.177456	+	0.984129i	$0.443213\pi$
$128$	1.00000	0.0883883
$129$	−4.86465	−0.428309
$130$	−0.0838310	−0.00735246
$131$	3.12817	0.273310	0.136655	−	0.990619i	$-0.456365\pi$
$131$	3.12817	0.273310	0.136655	+	0.990619i	$0.456365\pi$
$132$	1.00000	0.0870388
$133$	2.43963	0.211543
$134$	−5.22547	−0.451412
$135$	−1.28209	−0.110344
$136$	−0.119525	−0.0102492
$137$	−10.1055	−0.863375	−0.431688	−	0.902023i	$-0.642082\pi$
$137$	−10.1055	−0.863375	−0.431688	+	0.902023i	$0.642082\pi$
$138$	1.37465	0.117018
$139$	−3.14296	−0.266582	−0.133291	−	0.991077i	$-0.542555\pi$
$139$	−3.14296	−0.266582	−0.133291	+	0.991077i	$0.542555\pi$
$140$	−0.392824	−0.0331997
$141$	6.46008	0.544036
$142$	11.2202	0.941582
$143$	0.0653864	0.00546789
$144$	1.00000	0.0833333
$145$	−9.37282	−0.778370
$146$	−9.21003	−0.762227
$147$	6.90612	0.569607
$148$	−4.58287	−0.376709
$149$	−6.05865	−0.496344	−0.248172	−	0.968716i	$-0.579830\pi$
$149$	−6.05865	−0.496344	−0.248172	+	0.968716i	$0.579830\pi$
$150$	3.35626	0.274037
$151$	−4.68404	−0.381182	−0.190591	−	0.981670i	$-0.561040\pi$
$151$	−4.68404	−0.381182	−0.190591	+	0.981670i	$0.561040\pi$
$152$	−7.96238	−0.645834
$153$	−0.119525	−0.00966301
$154$	0.306395	0.0246900
$155$	3.97084	0.318946
$156$	0.0653864	0.00523510
$157$	16.8353	1.34360	0.671801	−	0.740731i	$-0.265521\pi$
$157$	16.8353	1.34360	0.671801	+	0.740731i	$0.265521\pi$
$158$	13.9169	1.10717
$159$	−5.11394	−0.405562
$160$	1.28209	0.101358
$161$	0.421187	0.0331942
$162$	1.00000	0.0785674
$163$	7.64538	0.598832	0.299416	−	0.954123i	$-0.403208\pi$
$163$	7.64538	0.598832	0.299416	+	0.954123i	$0.403208\pi$
$164$	−7.06969	−0.552050
$165$	1.28209	0.0998102
$166$	−17.0516	−1.32346
$167$	−10.1273	−0.783672	−0.391836	−	0.920035i	$-0.628160\pi$
$167$	−10.1273	−0.783672	−0.391836	+	0.920035i	$0.628160\pi$
$168$	0.306395	0.0236389
$169$	−12.9957	−0.999671
$170$	−0.153241	−0.0117531
$171$	−7.96238	−0.608898
$172$	4.86465	0.370926
$173$	−9.26217	−0.704190	−0.352095	−	0.935964i	$-0.614531\pi$
$173$	−9.26217	−0.704190	−0.352095	+	0.935964i	$0.614531\pi$
$174$	7.31061	0.554216
$175$	1.02834	0.0777351
$176$	−1.00000	−0.0753778
$177$	−11.2122	−0.842757
$178$	−5.41939	−0.406201
$179$	−16.3528	−1.22227	−0.611135	−	0.791527i	$-0.709287\pi$
$179$	−16.3528	−1.22227	−0.611135	+	0.791527i	$0.709287\pi$
$180$	1.28209	0.0955610
$181$	16.9939	1.26315	0.631574	−	0.775316i	$-0.282409\pi$
$181$	16.9939	1.26315	0.631574	+	0.775316i	$0.282409\pi$
$182$	0.0200340	0.00148502
$183$	−1.00000	−0.0739221
$184$	−1.37465	−0.101341
$185$	−5.87563	−0.431985
$186$	−3.09717	−0.227096
$187$	0.119525	0.00874052
$188$	−6.46008	−0.471149
$189$	0.306395	0.0222869
$190$	−10.2084	−0.740599
$191$	−7.84349	−0.567535	−0.283768	−	0.958893i	$-0.591584\pi$
$191$	−7.84349	−0.567535	−0.283768	+	0.958893i	$0.591584\pi$
$192$	−1.00000	−0.0721688
$193$	3.14963	0.226716	0.113358	−	0.993554i	$-0.463839\pi$
$193$	3.14963	0.226716	0.113358	+	0.993554i	$0.463839\pi$
$194$	−7.22689	−0.518860
$195$	0.0838310	0.00600326
$196$	−6.90612	−0.493294
$197$	−7.72185	−0.550159	−0.275079	−	0.961421i	$-0.588704\pi$
$197$	−7.72185	−0.550159	−0.275079	+	0.961421i	$0.588704\pi$
$198$	−1.00000	−0.0710669
$199$	25.9363	1.83858	0.919288	−	0.393585i	$-0.128765\pi$
$199$	25.9363	1.83858	0.919288	+	0.393585i	$0.128765\pi$
$200$	−3.35626	−0.237323
$201$	5.22547	0.368576
$202$	−3.15901	−0.222267
$203$	2.23993	0.157212
$204$	0.119525	0.00836841
$205$	−9.06395	−0.633053
$206$	−1.53431	−0.106901
$207$	−1.37465	−0.0955451
$208$	−0.0653864	−0.00453373
$209$	7.96238	0.550769
$210$	0.392824	0.0271074
$211$	−16.9053	−1.16381	−0.581903	−	0.813258i	$-0.697692\pi$
$211$	−16.9053	−1.16381	−0.581903	+	0.813258i	$0.697692\pi$
$212$	5.11394	0.351227
$213$	−11.2202	−0.768799
$214$	18.3917	1.25723
$215$	6.23690	0.425353
$216$	−1.00000	−0.0680414
$217$	−0.948957	−0.0644194
$218$	−12.6183	−0.854621
$219$	9.21003	0.622356
$220$	−1.28209	−0.0864382
$221$	0.00781530	0.000525714 0
$222$	4.58287	0.307582
$223$	0.267385	0.0179054	0.00895272	−	0.999960i	$-0.497150\pi$
$223$	0.267385	0.0179054	0.00895272	+	0.999960i	$0.497150\pi$
$224$	−0.306395	−0.0204718
$225$	−3.35626	−0.223751
$226$	4.40410	0.292956
$227$	28.4651	1.88929	0.944647	−	0.328089i	$-0.106405\pi$
$227$	28.4651	1.88929	0.944647	+	0.328089i	$0.106405\pi$
$228$	7.96238	0.527321
$229$	2.76382	0.182638	0.0913191	−	0.995822i	$-0.470892\pi$
$229$	2.76382	0.182638	0.0913191	+	0.995822i	$0.470892\pi$
$230$	−1.76242	−0.116211
$231$	−0.306395	−0.0201593
$232$	−7.31061	−0.479965
$233$	−16.1770	−1.05979	−0.529895	−	0.848063i	$-0.677769\pi$
$233$	−16.1770	−1.05979	−0.529895	+	0.848063i	$0.677769\pi$
$234$	−0.0653864	−0.00427444
$235$	−8.28237	−0.540282
$236$	11.2122	0.729849
$237$	−13.9169	−0.904001
$238$	0.0366218	0.00237384
$239$	−7.43602	−0.480996	−0.240498	−	0.970650i	$-0.577311\pi$
$239$	−7.43602	−0.480996	−0.240498	+	0.970650i	$0.577311\pi$
$240$	−1.28209	−0.0827582
$241$	−10.3334	−0.665636	−0.332818	−	0.942991i	$-0.607999\pi$
$241$	−10.3334	−0.665636	−0.332818	+	0.942991i	$0.607999\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−8.85424	−0.565676
$246$	7.06969	0.450747
$247$	0.520631	0.0331270
$248$	3.09717	0.196671
$249$	17.0516	1.08060
$250$	−10.7134	−0.677577
$251$	21.9097	1.38293	0.691466	−	0.722409i	$-0.256965\pi$
$251$	21.9097	1.38293	0.691466	+	0.722409i	$0.256965\pi$
$252$	−0.306395	−0.0193010
$253$	1.37465	0.0864238
$254$	3.99965	0.250961
$255$	0.153241	0.00959633
$256$	1.00000	0.0625000
$257$	−23.1488	−1.44398	−0.721992	−	0.691901i	$-0.756773\pi$
$257$	−23.1488	−1.44398	−0.721992	+	0.691901i	$0.756773\pi$
$258$	−4.86465	−0.302860
$259$	1.40417	0.0872506
$260$	−0.0838310	−0.00519898
$261$	−7.31061	−0.452515
$262$	3.12817	0.193259
$263$	−0.600263	−0.0370138	−0.0185069	−	0.999829i	$-0.505891\pi$
$263$	−0.600263	−0.0370138	−0.0185069	+	0.999829i	$0.505891\pi$
$264$	1.00000	0.0615457
$265$	6.55651	0.402763
$266$	2.43963	0.149583
$267$	5.41939	0.331661
$268$	−5.22547	−0.319196
$269$	−8.21551	−0.500908	−0.250454	−	0.968128i	$-0.580580\pi$
$269$	−8.21551	−0.500908	−0.250454	+	0.968128i	$0.580580\pi$
$270$	−1.28209	−0.0780252
$271$	−16.6008	−1.00843	−0.504213	−	0.863579i	$-0.668217\pi$
$271$	−16.6008	−1.00843	−0.504213	+	0.863579i	$0.668217\pi$
$272$	−0.119525	−0.00724726
$273$	−0.0200340	−0.00121252
$274$	−10.1055	−0.610498
$275$	3.35626	0.202390
$276$	1.37465	0.0827445
$277$	−4.56378	−0.274211	−0.137106	−	0.990556i	$-0.543780\pi$
$277$	−4.56378	−0.274211	−0.137106	+	0.990556i	$0.543780\pi$
$278$	−3.14296	−0.188502
$279$	3.09717	0.185423
$280$	−0.392824	−0.0234757
$281$	13.5122	0.806068	0.403034	−	0.915185i	$-0.367956\pi$
$281$	13.5122	0.806068	0.403034	+	0.915185i	$0.367956\pi$
$282$	6.46008	0.384692
$283$	−2.53926	−0.150943	−0.0754717	−	0.997148i	$-0.524046\pi$
$283$	−2.53926	−0.150943	−0.0754717	+	0.997148i	$0.524046\pi$
$284$	11.2202	0.665799
$285$	10.2084	0.604696
$286$	0.0653864	0.00386638
$287$	2.16612	0.127862
$288$	1.00000	0.0589256
$289$	−16.9857	−0.999160
$290$	−9.37282	−0.550391
$291$	7.22689	0.423648
$292$	−9.21003	−0.538976
$293$	7.11041	0.415394	0.207697	−	0.978193i	$-0.433403\pi$
$293$	7.11041	0.415394	0.207697	+	0.978193i	$0.433403\pi$
$294$	6.90612	0.402773
$295$	14.3749	0.836941
$296$	−4.58287	−0.266374
$297$	1.00000	0.0580259
$298$	−6.05865	−0.350968
$299$	0.0898838	0.00519811
$300$	3.35626	0.193774
$301$	−1.49050	−0.0859112
$302$	−4.68404	−0.269536
$303$	3.15901	0.181481
$304$	−7.96238	−0.456674
$305$	1.28209	0.0734120
$306$	−0.119525	−0.00683278
$307$	−9.14513	−0.521940	−0.260970	−	0.965347i	$-0.584042\pi$
$307$	−9.14513	−0.521940	−0.260970	+	0.965347i	$0.584042\pi$
$308$	0.306395	0.0174585
$309$	1.53431	0.0872839
$310$	3.97084	0.225529
$311$	7.24589	0.410877	0.205438	−	0.978670i	$-0.434138\pi$
$311$	7.24589	0.410877	0.205438	+	0.978670i	$0.434138\pi$
$312$	0.0653864	0.00370178
$313$	−12.1899	−0.689012	−0.344506	−	0.938784i	$-0.611954\pi$
$313$	−12.1899	−0.689012	−0.344506	+	0.938784i	$0.611954\pi$
$314$	16.8353	0.950071
$315$	−0.392824	−0.0221331
$316$	13.9169	0.782888
$317$	30.3849	1.70658	0.853292	−	0.521433i	$-0.174602\pi$
$317$	30.3849	1.70658	0.853292	+	0.521433i	$0.174602\pi$
$318$	−5.11394	−0.286776
$319$	7.31061	0.409315
$320$	1.28209	0.0716707
$321$	−18.3917	−1.02653
$322$	0.421187	0.0234718
$323$	0.951702	0.0529541
$324$	1.00000	0.0555556
$325$	0.219454	0.0121731
$326$	7.64538	0.423438
$327$	12.6183	0.697795
$328$	−7.06969	−0.390358
$329$	1.97933	0.109124
$330$	1.28209	0.0705765
$331$	−4.37349	−0.240389	−0.120194	−	0.992750i	$-0.538352\pi$
$331$	−4.37349	−0.240389	−0.120194	+	0.992750i	$0.538352\pi$
$332$	−17.0516	−0.935827
$333$	−4.58287	−0.251140
$334$	−10.1273	−0.554140
$335$	−6.69949	−0.366032
$336$	0.306395	0.0167152
$337$	−2.13253	−0.116166	−0.0580831	−	0.998312i	$-0.518499\pi$
$337$	−2.13253	−0.116166	−0.0580831	+	0.998312i	$0.518499\pi$
$338$	−12.9957	−0.706874
$339$	−4.40410	−0.239198
$340$	−0.153241	−0.00831066
$341$	−3.09717	−0.167721
$342$	−7.96238	−0.430556
$343$	4.26076	0.230059
$344$	4.86465	0.262284
$345$	1.76242	0.0948857
$346$	−9.26217	−0.497938
$347$	−21.9589	−1.17882	−0.589409	−	0.807835i	$-0.700639\pi$
$347$	−21.9589	−1.17882	−0.589409	+	0.807835i	$0.700639\pi$
$348$	7.31061	0.391890
$349$	0.784481	0.0419923	0.0209961	−	0.999780i	$-0.493316\pi$
$349$	0.784481	0.0419923	0.0209961	+	0.999780i	$0.493316\pi$
$350$	1.02834	0.0549670
$351$	0.0653864	0.00349007
$352$	−1.00000	−0.0533002
$353$	−21.6533	−1.15249	−0.576244	−	0.817278i	$-0.695482\pi$
$353$	−21.6533	−1.15249	−0.576244	+	0.817278i	$0.695482\pi$
$354$	−11.2122	−0.595919
$355$	14.3853	0.763493
$356$	−5.41939	−0.287227
$357$	−0.0366218	−0.00193823
$358$	−16.3528	−0.864275
$359$	18.2171	0.961464	0.480732	−	0.876868i	$-0.340371\pi$
$359$	18.2171	0.961464	0.480732	+	0.876868i	$0.340371\pi$
$360$	1.28209	0.0675718
$361$	44.3995	2.33681
$362$	16.9939	0.893181
$363$	−1.00000	−0.0524864
$364$	0.0200340	0.00105007
$365$	−11.8080	−0.618061
$366$	−1.00000	−0.0522708
$367$	−31.6511	−1.65217	−0.826086	−	0.563544i	$-0.809438\pi$
$367$	−31.6511	−1.65217	−0.826086	+	0.563544i	$0.809438\pi$
$368$	−1.37465	−0.0716588
$369$	−7.06969	−0.368033
$370$	−5.87563	−0.305459
$371$	−1.56688	−0.0813486
$372$	−3.09717	−0.160581
$373$	−13.7580	−0.712363	−0.356181	−	0.934417i	$-0.615921\pi$
$373$	−13.7580	−0.712363	−0.356181	+	0.934417i	$0.615921\pi$
$374$	0.119525	0.00618048
$375$	10.7134	0.553239
$376$	−6.46008	−0.333153
$377$	0.478014	0.0246190
$378$	0.306395	0.0157592
$379$	37.3474	1.91840	0.959202	−	0.282720i	$-0.0912368\pi$
$379$	37.3474	1.91840	0.959202	+	0.282720i	$0.0912368\pi$
$380$	−10.2084	−0.523682
$381$	−3.99965	−0.204909
$382$	−7.84349	−0.401308
$383$	−14.7499	−0.753683	−0.376842	−	0.926278i	$-0.622990\pi$
$383$	−14.7499	−0.753683	−0.376842	+	0.926278i	$0.622990\pi$
$384$	−1.00000	−0.0510310
$385$	0.392824	0.0200202
$386$	3.14963	0.160312
$387$	4.86465	0.247284
$388$	−7.22689	−0.366890
$389$	−6.37543	−0.323247	−0.161624	−	0.986852i	$-0.551673\pi$
$389$	−6.37543	−0.323247	−0.161624	+	0.986852i	$0.551673\pi$
$390$	0.0838310	0.00424495
$391$	0.164305	0.00830928
$392$	−6.90612	−0.348812
$393$	−3.12817	−0.157796
$394$	−7.72185	−0.389021
$395$	17.8427	0.897762
$396$	−1.00000	−0.0502519
$397$	35.6189	1.78766	0.893831	−	0.448403i	$-0.148007\pi$
$397$	35.6189	1.78766	0.893831	+	0.448403i	$0.148007\pi$
$398$	25.9363	1.30007
$399$	−2.43963	−0.122134
$400$	−3.35626	−0.167813
$401$	6.93779	0.346457	0.173228	−	0.984882i	$-0.444580\pi$
$401$	6.93779	0.346457	0.173228	+	0.984882i	$0.444580\pi$
$402$	5.22547	0.260623
$403$	−0.202513	−0.0100879
$404$	−3.15901	−0.157167
$405$	1.28209	0.0637073
$406$	2.23993	0.111166
$407$	4.58287	0.227164
$408$	0.119525	0.00591736
$409$	35.3571	1.74829	0.874147	−	0.485661i	$-0.161421\pi$
$409$	35.3571	1.74829	0.874147	+	0.485661i	$0.161421\pi$
$410$	−9.06395	−0.447636
$411$	10.1055	0.498470
$412$	−1.53431	−0.0755901
$413$	−3.43534	−0.169042
$414$	−1.37465	−0.0675606
$415$	−21.8616	−1.07314
$416$	−0.0653864	−0.00320583
$417$	3.14296	0.153911
$418$	7.96238	0.389453
$419$	−20.0147	−0.977784	−0.488892	−	0.872344i	$-0.662599\pi$
$419$	−20.0147	−0.977784	−0.488892	+	0.872344i	$0.662599\pi$
$420$	0.392824	0.0191678
$421$	20.4627	0.997289	0.498645	−	0.866807i	$-0.333831\pi$
$421$	20.4627	0.997289	0.498645	+	0.866807i	$0.333831\pi$
$422$	−16.9053	−0.822935
$423$	−6.46008	−0.314100
$424$	5.11394	0.248355
$425$	0.401156	0.0194589
$426$	−11.2202	−0.543623
$427$	−0.306395	−0.0148275
$428$	18.3917	0.888998
$429$	−0.0653864	−0.00315689
$430$	6.23690	0.300770
$431$	−1.31266	−0.0632285	−0.0316143	−	0.999500i	$-0.510065\pi$
$431$	−1.31266	−0.0632285	−0.0316143	+	0.999500i	$0.510065\pi$
$432$	−1.00000	−0.0481125
$433$	28.5477	1.37192	0.685958	−	0.727641i	$-0.259383\pi$
$433$	28.5477	1.37192	0.685958	+	0.727641i	$0.259383\pi$
$434$	−0.948957	−0.0455514
$435$	9.37282	0.449392
$436$	−12.6183	−0.604308
$437$	10.9455	0.523595
$438$	9.21003	0.440072
$439$	13.9298	0.664832	0.332416	−	0.943133i	$-0.392136\pi$
$439$	13.9298	0.664832	0.332416	+	0.943133i	$0.392136\pi$
$440$	−1.28209	−0.0611210
$441$	−6.90612	−0.328863
$442$	0.00781530	0.000371736 0
$443$	−26.2396	−1.24668	−0.623340	−	0.781951i	$-0.714225\pi$
$443$	−26.2396	−1.24668	−0.623340	+	0.781951i	$0.714225\pi$
$444$	4.58287	0.217493
$445$	−6.94812	−0.329373
$446$	0.267385	0.0126611
$447$	6.05865	0.286564
$448$	−0.306395	−0.0144758
$449$	−14.8301	−0.699875	−0.349938	−	0.936773i	$-0.613797\pi$
$449$	−14.8301	−0.699875	−0.349938	+	0.936773i	$0.613797\pi$
$450$	−3.35626	−0.158216
$451$	7.06969	0.332899
$452$	4.40410	0.207152
$453$	4.68404	0.220075
$454$	28.4651	1.33593
$455$	0.0256854	0.00120415
$456$	7.96238	0.372872
$457$	14.1383	0.661362	0.330681	−	0.943743i	$-0.392722\pi$
$457$	14.1383	0.661362	0.330681	+	0.943743i	$0.392722\pi$
$458$	2.76382	0.129145
$459$	0.119525	0.00557894
$460$	−1.76242	−0.0821735
$461$	18.2378	0.849421	0.424710	−	0.905329i	$-0.360376\pi$
$461$	18.2378	0.849421	0.424710	+	0.905329i	$0.360376\pi$
$462$	−0.306395	−0.0142548
$463$	34.3144	1.59472	0.797362	−	0.603501i	$-0.206228\pi$
$463$	34.3144	1.59472	0.797362	+	0.603501i	$0.206228\pi$
$464$	−7.31061	−0.339386
$465$	−3.97084	−0.184143
$466$	−16.1770	−0.749384
$467$	−36.1926	−1.67479	−0.837397	−	0.546596i	$-0.815924\pi$
$467$	−36.1926	−1.67479	−0.837397	+	0.546596i	$0.815924\pi$
$468$	−0.0653864	−0.00302249
$469$	1.60105	0.0739298
$470$	−8.28237	−0.382037
$471$	−16.8353	−0.775729
$472$	11.2122	0.516081
$473$	−4.86465	−0.223677
$474$	−13.9169	−0.639225
$475$	26.7238	1.22617
$476$	0.0366218	0.00167856
$477$	5.11394	0.234151
$478$	−7.43602	−0.340116
$479$	−18.7943	−0.858734	−0.429367	−	0.903130i	$-0.641263\pi$
$479$	−18.7943	−0.858734	−0.429367	+	0.903130i	$0.641263\pi$
$480$	−1.28209	−0.0585189
$481$	0.299657	0.0136632
$482$	−10.3334	−0.470675
$483$	−0.421187	−0.0191647
$484$	1.00000	0.0454545
$485$	−9.26549	−0.420724
$486$	−1.00000	−0.0453609
$487$	2.57917	0.116873	0.0584366	−	0.998291i	$-0.481388\pi$
$487$	2.57917	0.116873	0.0584366	+	0.998291i	$0.481388\pi$
$488$	1.00000	0.0452679
$489$	−7.64538	−0.345736
$490$	−8.85424	−0.399994
$491$	14.7250	0.664529	0.332264	−	0.943186i	$-0.392187\pi$
$491$	14.7250	0.664529	0.332264	+	0.943186i	$0.392187\pi$
$492$	7.06969	0.318726
$493$	0.873799	0.0393539
$494$	0.520631	0.0234243
$495$	−1.28209	−0.0576254
$496$	3.09717	0.139067
$497$	−3.43782	−0.154207
$498$	17.0516	0.764099
$499$	−19.4585	−0.871081	−0.435540	−	0.900169i	$-0.643443\pi$
$499$	−19.4585	−0.871081	−0.435540	+	0.900169i	$0.643443\pi$
$500$	−10.7134	−0.479119
$501$	10.1273	0.452453
$502$	21.9097	0.977880
$503$	−8.05445	−0.359130	−0.179565	−	0.983746i	$-0.557469\pi$
$503$	−8.05445	−0.359130	−0.179565	+	0.983746i	$0.557469\pi$
$504$	−0.306395	−0.0136479
$505$	−4.05012	−0.180228
$506$	1.37465	0.0611109
$507$	12.9957	0.577160
$508$	3.99965	0.177456
$509$	6.91751	0.306613	0.153307	−	0.988179i	$-0.451008\pi$
$509$	6.91751	0.306613	0.153307	+	0.988179i	$0.451008\pi$
$510$	0.153241	0.00678563
$511$	2.82190	0.124834
$512$	1.00000	0.0441942
$513$	7.96238	0.351548
$514$	−23.1488	−1.02105
$515$	−1.96712	−0.0866816
$516$	−4.86465	−0.214154
$517$	6.46008	0.284114
$518$	1.40417	0.0616955
$519$	9.26217	0.406564
$520$	−0.0838310	−0.00367623
$521$	−10.3277	−0.452465	−0.226233	−	0.974073i	$-0.572641\pi$
$521$	−10.3277	−0.452465	−0.226233	+	0.974073i	$0.572641\pi$
$522$	−7.31061	−0.319977
$523$	4.11796	0.180066	0.0900329	−	0.995939i	$-0.471303\pi$
$523$	4.11796	0.180066	0.0900329	+	0.995939i	$0.471303\pi$
$524$	3.12817	0.136655
$525$	−1.02834	−0.0448804
$526$	−0.600263	−0.0261727
$527$	−0.370189	−0.0161257
$528$	1.00000	0.0435194
$529$	−21.1103	−0.917840
$530$	6.55651	0.284797
$531$	11.2122	0.486566
$532$	2.43963	0.105771
$533$	0.462262	0.0200228
$534$	5.41939	0.234520
$535$	23.5798	1.01944
$536$	−5.22547	−0.225706
$537$	16.3528	0.705677
$538$	−8.21551	−0.354196
$539$	6.90612	0.297468
$540$	−1.28209	−0.0551722
$541$	−29.1316	−1.25246	−0.626232	−	0.779637i	$-0.715404\pi$
$541$	−29.1316	−1.25246	−0.626232	+	0.779637i	$0.715404\pi$
$542$	−16.6008	−0.713065
$543$	−16.9939	−0.729279
$544$	−0.119525	−0.00512459
$545$	−16.1778	−0.692979
$546$	−0.0200340	−0.000857378 0
$547$	8.34064	0.356620	0.178310	−	0.983974i	$-0.442937\pi$
$547$	8.34064	0.356620	0.178310	+	0.983974i	$0.442937\pi$
$548$	−10.1055	−0.431688
$549$	1.00000	0.0426790
$550$	3.35626	0.143111
$551$	58.2098	2.47982
$552$	1.37465	0.0585092
$553$	−4.26407	−0.181327
$554$	−4.56378	−0.193897
$555$	5.87563	0.249406
$556$	−3.14296	−0.133291
$557$	24.7130	1.04712	0.523561	−	0.851988i	$-0.324603\pi$
$557$	24.7130	1.04712	0.523561	+	0.851988i	$0.324603\pi$
$558$	3.09717	0.131114
$559$	−0.318082	−0.0134534
$560$	−0.392824	−0.0165998
$561$	−0.119525	−0.00504634
$562$	13.5122	0.569976
$563$	18.9234	0.797528	0.398764	−	0.917054i	$-0.369439\pi$
$563$	18.9234	0.797528	0.398764	+	0.917054i	$0.369439\pi$
$564$	6.46008	0.272018
$565$	5.64643	0.237547
$566$	−2.53926	−0.106733
$567$	−0.306395	−0.0128674
$568$	11.2202	0.470791
$569$	−16.5197	−0.692543	−0.346271	−	0.938134i	$-0.612552\pi$
$569$	−16.5197	−0.692543	−0.346271	+	0.938134i	$0.612552\pi$
$570$	10.2084	0.427585
$571$	−14.4786	−0.605912	−0.302956	−	0.953005i	$-0.597973\pi$
$571$	−14.4786	−0.605912	−0.302956	+	0.953005i	$0.597973\pi$
$572$	0.0653864	0.00273394
$573$	7.84349	0.327667
$574$	2.16612	0.0904119
$575$	4.61370	0.192404
$576$	1.00000	0.0416667
$577$	2.89042	0.120330	0.0601648	−	0.998188i	$-0.480837\pi$
$577$	2.89042	0.120330	0.0601648	+	0.998188i	$0.480837\pi$
$578$	−16.9857	−0.706513
$579$	−3.14963	−0.130894
$580$	−9.37282	−0.389185
$581$	5.22451	0.216749
$582$	7.22689	0.299564
$583$	−5.11394	−0.211798
$584$	−9.21003	−0.381114
$585$	−0.0838310	−0.00346598
$586$	7.11041	0.293728
$587$	23.8514	0.984454	0.492227	−	0.870467i	$-0.336183\pi$
$587$	23.8514	0.984454	0.492227	+	0.870467i	$0.336183\pi$
$588$	6.90612	0.284804
$589$	−24.6609	−1.01613
$590$	14.3749	0.591807
$591$	7.72185	0.317634
$592$	−4.58287	−0.188355
$593$	28.8539	1.18489	0.592443	−	0.805612i	$-0.298163\pi$
$593$	28.8539	1.18489	0.592443	+	0.805612i	$0.298163\pi$
$594$	1.00000	0.0410305
$595$	0.0469522	0.00192485
$596$	−6.05865	−0.248172
$597$	−25.9363	−1.06150
$598$	0.0898838	0.00367562
$599$	−17.9666	−0.734094	−0.367047	−	0.930202i	$-0.619631\pi$
$599$	−17.9666	−0.734094	−0.367047	+	0.930202i	$0.619631\pi$
$600$	3.35626	0.137019
$601$	10.4697	0.427069	0.213534	−	0.976936i	$-0.431502\pi$
$601$	10.4697	0.427069	0.213534	+	0.976936i	$0.431502\pi$
$602$	−1.49050	−0.0607484
$603$	−5.22547	−0.212797
$604$	−4.68404	−0.190591
$605$	1.28209	0.0521242
$606$	3.15901	0.128326
$607$	−35.9096	−1.45753	−0.728763	−	0.684766i	$-0.759904\pi$
$607$	−35.9096	−1.45753	−0.728763	+	0.684766i	$0.759904\pi$
$608$	−7.96238	−0.322917
$609$	−2.23993	−0.0907666
$610$	1.28209	0.0519101
$611$	0.422401	0.0170885
$612$	−0.119525	−0.00483151
$613$	43.7423	1.76674	0.883368	−	0.468680i	$-0.155270\pi$
$613$	43.7423	1.76674	0.883368	+	0.468680i	$0.155270\pi$
$614$	−9.14513	−0.369067
$615$	9.06395	0.365494
$616$	0.306395	0.0123450
$617$	−18.5492	−0.746763	−0.373382	−	0.927678i	$-0.621802\pi$
$617$	−18.5492	−0.746763	−0.373382	+	0.927678i	$0.621802\pi$
$618$	1.53431	0.0617191
$619$	17.6340	0.708772	0.354386	−	0.935099i	$-0.384690\pi$
$619$	17.6340	0.708772	0.354386	+	0.935099i	$0.384690\pi$
$620$	3.97084	0.159473
$621$	1.37465	0.0551630
$622$	7.24589	0.290534
$623$	1.66047	0.0665254
$624$	0.0653864	0.00261755
$625$	3.04575	0.121830
$626$	−12.1899	−0.487205
$627$	−7.96238	−0.317987
$628$	16.8353	0.671801
$629$	0.547766	0.0218409
$630$	−0.392824	−0.0156505
$631$	9.73802	0.387664	0.193832	−	0.981035i	$-0.437908\pi$
$631$	9.73802	0.387664	0.193832	+	0.981035i	$0.437908\pi$
$632$	13.9169	0.553585
$633$	16.9053	0.671924
$634$	30.3849	1.20674
$635$	5.12790	0.203494
$636$	−5.11394	−0.202781
$637$	0.451567	0.0178917
$638$	7.31061	0.289430
$639$	11.2202	0.443866
$640$	1.28209	0.0506789
$641$	5.51350	0.217770	0.108885	−	0.994054i	$-0.465272\pi$
$641$	5.51350	0.217770	0.108885	+	0.994054i	$0.465272\pi$
$642$	−18.3917	−0.725864
$643$	5.85656	0.230960	0.115480	−	0.993310i	$-0.463159\pi$
$643$	5.85656	0.230960	0.115480	+	0.993310i	$0.463159\pi$
$644$	0.421187	0.0165971
$645$	−6.23690	−0.245578
$646$	0.951702	0.0374442
$647$	−43.8029	−1.72207	−0.861036	−	0.508545i	$-0.830184\pi$
$647$	−43.8029	−1.72207	−0.861036	+	0.508545i	$0.830184\pi$
$648$	1.00000	0.0392837
$649$	−11.2122	−0.440116
$650$	0.219454	0.00860768
$651$	0.948957	0.0371926
$652$	7.64538	0.299416
$653$	24.0831	0.942446	0.471223	−	0.882014i	$-0.343813\pi$
$653$	24.0831	0.942446	0.471223	+	0.882014i	$0.343813\pi$
$654$	12.6183	0.493415
$655$	4.01059	0.156707
$656$	−7.06969	−0.276025
$657$	−9.21003	−0.359317
$658$	1.97933	0.0771624
$659$	−36.9725	−1.44025	−0.720123	−	0.693847i	$-0.755915\pi$
$659$	−36.9725	−1.44025	−0.720123	+	0.693847i	$0.755915\pi$
$660$	1.28209	0.0499051
$661$	0.445845	0.0173414	0.00867068	−	0.999962i	$-0.497240\pi$
$661$	0.445845	0.0173414	0.00867068	+	0.999962i	$0.497240\pi$
$662$	−4.37349	−0.169981
$663$	−0.00781530	−0.000303521 0
$664$	−17.0516	−0.661729
$665$	3.12781	0.121291
$666$	−4.58287	−0.177582
$667$	10.0496	0.389121
$668$	−10.1273	−0.391836
$669$	−0.267385	−0.0103377
$670$	−6.69949	−0.258824
$671$	−1.00000	−0.0386046
$672$	0.306395	0.0118194
$673$	29.0043	1.11803	0.559016	−	0.829157i	$-0.311179\pi$
$673$	29.0043	1.11803	0.559016	+	0.829157i	$0.311179\pi$
$674$	−2.13253	−0.0821419
$675$	3.35626	0.129182
$676$	−12.9957	−0.499836
$677$	0.189783	0.00729395	0.00364697	−	0.999993i	$-0.498839\pi$
$677$	0.189783	0.00729395	0.00364697	+	0.999993i	$0.498839\pi$
$678$	−4.40410	−0.169139
$679$	2.21428	0.0849763
$680$	−0.153241	−0.00587653
$681$	−28.4651	−1.09078
$682$	−3.09717	−0.118597
$683$	34.4956	1.31994	0.659968	−	0.751293i	$-0.270570\pi$
$683$	34.4956	1.31994	0.659968	+	0.751293i	$0.270570\pi$
$684$	−7.96238	−0.304449
$685$	−12.9562	−0.495030
$686$	4.26076	0.162677
$687$	−2.76382	−0.105446
$688$	4.86465	0.185463
$689$	−0.334382	−0.0127390
$690$	1.76242	0.0670944
$691$	15.7111	0.597678	0.298839	−	0.954304i	$-0.403401\pi$
$691$	15.7111	0.597678	0.298839	+	0.954304i	$0.403401\pi$
$692$	−9.26217	−0.352095
$693$	0.306395	0.0116390
$694$	−21.9589	−0.833550
$695$	−4.02954	−0.152849
$696$	7.31061	0.277108
$697$	0.845004	0.0320068
$698$	0.784481	0.0296930
$699$	16.1770	0.611870
$700$	1.02834	0.0388676
$701$	−42.4449	−1.60312	−0.801562	−	0.597912i	$-0.795997\pi$
$701$	−42.4449	−1.60312	−0.801562	+	0.597912i	$0.795997\pi$
$702$	0.0653864	0.00246785
$703$	36.4905	1.37627
$704$	−1.00000	−0.0376889
$705$	8.28237	0.311932
$706$	−21.6533	−0.814932
$707$	0.967904	0.0364018
$708$	−11.2122	−0.421379
$709$	14.5801	0.547568	0.273784	−	0.961791i	$-0.411725\pi$
$709$	14.5801	0.547568	0.273784	+	0.961791i	$0.411725\pi$
$710$	14.3853	0.539871
$711$	13.9169	0.521925
$712$	−5.41939	−0.203100
$713$	−4.25754	−0.159446
$714$	−0.0366218	−0.00137054
$715$	0.0838310	0.00313510
$716$	−16.3528	−0.611135
$717$	7.43602	0.277703
$718$	18.2171	0.679858
$719$	3.03099	0.113037	0.0565185	−	0.998402i	$-0.482000\pi$
$719$	3.03099	0.113037	0.0565185	+	0.998402i	$0.482000\pi$
$720$	1.28209	0.0477805
$721$	0.470105	0.0175076
$722$	44.3995	1.65238
$723$	10.3334	0.384305
$724$	16.9939	0.631574
$725$	24.5363	0.911254
$726$	−1.00000	−0.0371135
$727$	−15.0100	−0.556690	−0.278345	−	0.960481i	$-0.589786\pi$
$727$	−15.0100	−0.556690	−0.278345	+	0.960481i	$0.589786\pi$
$728$	0.0200340	0.000742511 0
$729$	1.00000	0.0370370
$730$	−11.8080	−0.437035
$731$	−0.581447	−0.0215056
$732$	−1.00000	−0.0369611
$733$	37.6448	1.39044	0.695222	−	0.718795i	$-0.255306\pi$
$733$	37.6448	1.39044	0.695222	+	0.718795i	$0.255306\pi$
$734$	−31.6511	−1.16826
$735$	8.85424	0.326593
$736$	−1.37465	−0.0506704
$737$	5.22547	0.192483
$738$	−7.06969	−0.260239
$739$	−8.92791	−0.328418	−0.164209	−	0.986426i	$-0.552507\pi$
$739$	−8.92791	−0.328418	−0.164209	+	0.986426i	$0.552507\pi$
$740$	−5.87563	−0.215992
$741$	−0.520631	−0.0191259
$742$	−1.56688	−0.0575221
$743$	−5.15973	−0.189292	−0.0946462	−	0.995511i	$-0.530172\pi$
$743$	−5.15973	−0.189292	−0.0946462	+	0.995511i	$0.530172\pi$
$744$	−3.09717	−0.113548
$745$	−7.76770	−0.284587
$746$	−13.7580	−0.503717
$747$	−17.0516	−0.623885
$748$	0.119525	0.00437026
$749$	−5.63513	−0.205903
$750$	10.7134	0.391199
$751$	51.1613	1.86690	0.933451	−	0.358706i	$-0.116782\pi$
$751$	51.1613	1.86690	0.933451	+	0.358706i	$0.116782\pi$
$752$	−6.46008	−0.235575
$753$	−21.9097	−0.798436
$754$	0.478014	0.0174083
$755$	−6.00534	−0.218557
$756$	0.306395	0.0111435
$757$	42.5085	1.54500	0.772499	−	0.635016i	$-0.219007\pi$
$757$	42.5085	1.54500	0.772499	+	0.635016i	$0.219007\pi$
$758$	37.3474	1.35652
$759$	−1.37465	−0.0498968
$760$	−10.2084	−0.370299
$761$	−15.4547	−0.560233	−0.280117	−	0.959966i	$-0.590373\pi$
$761$	−15.4547	−0.560233	−0.280117	+	0.959966i	$0.590373\pi$
$762$	−3.99965	−0.144892
$763$	3.86619	0.139965
$764$	−7.84349	−0.283768
$765$	−0.153241	−0.00554044
$766$	−14.7499	−0.532935
$767$	−0.733123	−0.0264715
$768$	−1.00000	−0.0360844
$769$	−14.4220	−0.520071	−0.260035	−	0.965599i	$-0.583734\pi$
$769$	−14.4220	−0.520071	−0.260035	+	0.965599i	$0.583734\pi$
$770$	0.392824	0.0141564
$771$	23.1488	0.833685
$772$	3.14963	0.113358
$773$	32.7388	1.17753	0.588766	−	0.808303i	$-0.299614\pi$
$773$	32.7388	1.17753	0.588766	+	0.808303i	$0.299614\pi$
$774$	4.86465	0.174856
$775$	−10.3949	−0.373396
$776$	−7.22689	−0.259430
$777$	−1.40417	−0.0503742
$778$	−6.37543	−0.228570
$779$	56.2916	2.01685
$780$	0.0838310	0.00300163
$781$	−11.2202	−0.401492
$782$	0.164305	0.00587555
$783$	7.31061	0.261260
$784$	−6.90612	−0.246647
$785$	21.5843	0.770376
$786$	−3.12817	−0.111578
$787$	23.3024	0.830641	0.415321	−	0.909675i	$-0.363669\pi$
$787$	23.3024	0.830641	0.415321	+	0.909675i	$0.363669\pi$
$788$	−7.72185	−0.275079
$789$	0.600263	0.0213699
$790$	17.8427	0.634814
$791$	−1.34939	−0.0479789
$792$	−1.00000	−0.0355335
$793$	−0.0653864	−0.00232194
$794$	35.6189	1.26407
$795$	−6.55651	−0.232535
$796$	25.9363	0.919288
$797$	6.77046	0.239822	0.119911	−	0.992785i	$-0.461739\pi$
$797$	6.77046	0.239822	0.119911	+	0.992785i	$0.461739\pi$
$798$	−2.43963	−0.0863619
$799$	0.772140	0.0273163
$800$	−3.35626	−0.118662
$801$	−5.41939	−0.191485
$802$	6.93779	0.244982
$803$	9.21003	0.325015
$804$	5.22547	0.184288
$805$	0.539997	0.0190324
$806$	−0.202513	−0.00713322
$807$	8.21551	0.289200
$808$	−3.15901	−0.111134
$809$	−14.1875	−0.498807	−0.249403	−	0.968400i	$-0.580235\pi$
$809$	−14.1875	−0.498807	−0.249403	+	0.968400i	$0.580235\pi$
$810$	1.28209	0.0450479
$811$	−33.9762	−1.19307	−0.596533	−	0.802589i	$-0.703455\pi$
$811$	−33.9762	−1.19307	−0.596533	+	0.802589i	$0.703455\pi$
$812$	2.23993	0.0786061
$813$	16.6008	0.582215
$814$	4.58287	0.160629
$815$	9.80203	0.343350
$816$	0.119525	0.00418421
$817$	−38.7342	−1.35514
$818$	35.3571	1.23623
$819$	0.0200340	0.000700046 0
$820$	−9.06395	−0.316527
$821$	−30.3187	−1.05813	−0.529064	−	0.848582i	$-0.677457\pi$
$821$	−30.3187	−1.05813	−0.529064	+	0.848582i	$0.677457\pi$
$822$	10.1055	0.352471
$823$	48.8581	1.70309	0.851543	−	0.524284i	$-0.175667\pi$
$823$	48.8581	1.70309	0.851543	+	0.524284i	$0.175667\pi$
$824$	−1.53431	−0.0534503
$825$	−3.35626	−0.116850
$826$	−3.43534	−0.119531
$827$	12.0183	0.417916	0.208958	−	0.977925i	$-0.432993\pi$
$827$	12.0183	0.417916	0.208958	+	0.977925i	$0.432993\pi$
$828$	−1.37465	−0.0477726
$829$	−20.4394	−0.709890	−0.354945	−	0.934887i	$-0.615500\pi$
$829$	−20.4394	−0.709890	−0.354945	+	0.934887i	$0.615500\pi$
$830$	−21.8616	−0.758826
$831$	4.56378	0.158316
$832$	−0.0653864	−0.00226687
$833$	0.825453	0.0286003
$834$	3.14296	0.108832
$835$	−12.9840	−0.449331
$836$	7.96238	0.275385
$837$	−3.09717	−0.107054
$838$	−20.0147	−0.691398
$839$	−41.7377	−1.44095	−0.720473	−	0.693483i	$-0.756075\pi$
$839$	−41.7377	−1.44095	−0.720473	+	0.693483i	$0.756075\pi$
$840$	0.392824	0.0135537
$841$	24.4450	0.842930
$842$	20.4627	0.705190
$843$	−13.5122	−0.465384
$844$	−16.9053	−0.581903
$845$	−16.6616	−0.573177
$846$	−6.46008	−0.222102
$847$	−0.306395	−0.0105278
$848$	5.11394	0.175613
$849$	2.53926	0.0871472
$850$	0.401156	0.0137595
$851$	6.29986	0.215956
$852$	−11.2202	−0.384399
$853$	−24.6230	−0.843075	−0.421537	−	0.906811i	$-0.638509\pi$
$853$	−24.6230	−0.843075	−0.421537	+	0.906811i	$0.638509\pi$
$854$	−0.306395	−0.0104846
$855$	−10.2084	−0.349121
$856$	18.3917	0.628617
$857$	−40.1222	−1.37055	−0.685273	−	0.728286i	$-0.740317\pi$
$857$	−40.1222	−1.37055	−0.685273	+	0.728286i	$0.740317\pi$
$858$	−0.0653864	−0.00223226
$859$	50.2579	1.71478	0.857389	−	0.514669i	$-0.172085\pi$
$859$	50.2579	1.71478	0.857389	+	0.514669i	$0.172085\pi$
$860$	6.23690	0.212676
$861$	−2.16612	−0.0738210
$862$	−1.31266	−0.0447093
$863$	25.8537	0.880070	0.440035	−	0.897981i	$-0.354966\pi$
$863$	25.8537	0.880070	0.440035	+	0.897981i	$0.354966\pi$
$864$	−1.00000	−0.0340207
$865$	−11.8749	−0.403759
$866$	28.5477	0.970091
$867$	16.9857	0.576865
$868$	−0.948957	−0.0322097
$869$	−13.9169	−0.472099
$870$	9.37282	0.317768
$871$	0.341675	0.0115772
$872$	−12.6183	−0.427310
$873$	−7.22689	−0.244593
$874$	10.9455	0.370238
$875$	3.28254	0.110970
$876$	9.21003	0.311178
$877$	35.3771	1.19460	0.597301	−	0.802017i	$-0.296240\pi$
$877$	35.3771	1.19460	0.597301	+	0.802017i	$0.296240\pi$
$878$	13.9298	0.470107
$879$	−7.11041	−0.239828
$880$	−1.28209	−0.0432191
$881$	14.7908	0.498316	0.249158	−	0.968463i	$-0.419846\pi$
$881$	14.7908	0.498316	0.249158	+	0.968463i	$0.419846\pi$
$882$	−6.90612	−0.232541
$883$	23.7314	0.798625	0.399313	−	0.916815i	$-0.369249\pi$
$883$	23.7314	0.798625	0.399313	+	0.916815i	$0.369249\pi$
$884$	0.00781530	0.000262857 0
$885$	−14.3749	−0.483208
$886$	−26.2396	−0.881536
$887$	20.3397	0.682939	0.341470	−	0.939893i	$-0.389075\pi$
$887$	20.3397	0.682939	0.341470	+	0.939893i	$0.389075\pi$
$888$	4.58287	0.153791
$889$	−1.22547	−0.0411010
$890$	−6.94812	−0.232902
$891$	−1.00000	−0.0335013
$892$	0.267385	0.00895272
$893$	51.4376	1.72129
$894$	6.05865	0.202632
$895$	−20.9657	−0.700807
$896$	−0.306395	−0.0102359
$897$	−0.0898838	−0.00300113
$898$	−14.8301	−0.494886
$899$	−22.6422	−0.755160
$900$	−3.35626	−0.111875
$901$	−0.611243	−0.0203635
$902$	7.06969	0.235395
$903$	1.49050	0.0496008
$904$	4.40410	0.146478
$905$	21.7877	0.724246
$906$	4.68404	0.155617
$907$	−24.9980	−0.830044	−0.415022	−	0.909811i	$-0.636226\pi$
$907$	−24.9980	−0.830044	−0.415022	+	0.909811i	$0.636226\pi$
$908$	28.4651	0.944647
$909$	−3.15901	−0.104778
$910$	0.0256854	0.000851461 0
$911$	10.4892	0.347522	0.173761	−	0.984788i	$-0.444408\pi$
$911$	10.4892	0.347522	0.173761	+	0.984788i	$0.444408\pi$
$912$	7.96238	0.263661
$913$	17.0516	0.564325
$914$	14.1383	0.467653
$915$	−1.28209	−0.0423844
$916$	2.76382	0.0913191
$917$	−0.958456	−0.0316510
$918$	0.119525	0.00394491
$919$	41.1186	1.35638	0.678188	−	0.734888i	$-0.262765\pi$
$919$	41.1186	1.35638	0.678188	+	0.734888i	$0.262765\pi$
$920$	−1.76242	−0.0581054
$921$	9.14513	0.301342
$922$	18.2378	0.600631
$923$	−0.733652	−0.0241484
$924$	−0.306395	−0.0100796
$925$	15.3813	0.505733
$926$	34.3144	1.12764
$927$	−1.53431	−0.0503934
$928$	−7.31061	−0.239982
$929$	−1.59679	−0.0523889	−0.0261944	−	0.999657i	$-0.508339\pi$
$929$	−1.59679	−0.0523889	−0.0261944	+	0.999657i	$0.508339\pi$
$930$	−3.97084	−0.130209
$931$	54.9892	1.80220
$932$	−16.1770	−0.529895
$933$	−7.24589	−0.237220
$934$	−36.1926	−1.18426
$935$	0.153241	0.00501152
$936$	−0.0653864	−0.00213722
$937$	−43.9010	−1.43418	−0.717092	−	0.696979i	$-0.754527\pi$
$937$	−43.9010	−1.43418	−0.717092	+	0.696979i	$0.754527\pi$
$938$	1.60105	0.0522763
$939$	12.1899	0.397801
$940$	−8.28237	−0.270141
$941$	−54.9043	−1.78983	−0.894915	−	0.446237i	$-0.852764\pi$
$941$	−54.9043	−1.78983	−0.894915	+	0.446237i	$0.852764\pi$
$942$	−16.8353	−0.548523
$943$	9.71839	0.316474
$944$	11.2122	0.364925
$945$	0.392824	0.0127786
$946$	−4.86465	−0.158164
$947$	−28.0045	−0.910024	−0.455012	−	0.890485i	$-0.650365\pi$
$947$	−28.0045	−0.910024	−0.455012	+	0.890485i	$0.650365\pi$
$948$	−13.9169	−0.452000
$949$	0.602211	0.0195486
$950$	26.7238	0.867034
$951$	−30.3849	−0.985297
$952$	0.0366218	0.00118692
$953$	−31.8098	−1.03042	−0.515210	−	0.857064i	$-0.672286\pi$
$953$	−31.8098	−1.03042	−0.515210	+	0.857064i	$0.672286\pi$
$954$	5.11394	0.165570
$955$	−10.0560	−0.325405
$956$	−7.43602	−0.240498
$957$	−7.31061	−0.236318
$958$	−18.7943	−0.607216
$959$	3.09629	0.0999843
$960$	−1.28209	−0.0413791
$961$	−21.4075	−0.690565
$962$	0.299657	0.00966134
$963$	18.3917	0.592665
$964$	−10.3334	−0.332818
$965$	4.03810	0.129991
$966$	−0.421187	−0.0135515
$967$	49.3150	1.58586	0.792932	−	0.609310i	$-0.208554\pi$
$967$	49.3150	1.58586	0.792932	+	0.609310i	$0.208554\pi$
$968$	1.00000	0.0321412
$969$	−0.951702	−0.0305731
$970$	−9.26549	−0.297497
$971$	10.2967	0.330438	0.165219	−	0.986257i	$-0.447167\pi$
$971$	10.2967	0.330438	0.165219	+	0.986257i	$0.447167\pi$
$972$	−1.00000	−0.0320750
$973$	0.962986	0.0308719
$974$	2.57917	0.0826418
$975$	−0.219454	−0.00702814
$976$	1.00000	0.0320092
$977$	4.22367	0.135127	0.0675635	−	0.997715i	$-0.478477\pi$
$977$	4.22367	0.135127	0.0675635	+	0.997715i	$0.478477\pi$
$978$	−7.64538	−0.244472
$979$	5.41939	0.173204
$980$	−8.85424	−0.282838
$981$	−12.6183	−0.402872
$982$	14.7250	0.469893
$983$	−16.0307	−0.511301	−0.255651	−	0.966769i	$-0.582290\pi$
$983$	−16.0307	−0.511301	−0.255651	+	0.966769i	$0.582290\pi$
$984$	7.06969	0.225374
$985$	−9.90007	−0.315442
$986$	0.873799	0.0278274
$987$	−1.97933	−0.0630028
$988$	0.520631	0.0165635
$989$	−6.68722	−0.212641
$990$	−1.28209	−0.0407473
$991$	46.9768	1.49227	0.746134	−	0.665796i	$-0.231908\pi$
$991$	46.9768	1.49227	0.746134	+	0.665796i	$0.231908\pi$
$992$	3.09717	0.0983354
$993$	4.37349	0.138789
$994$	−3.43782	−0.109041
$995$	33.2526	1.05418
$996$	17.0516	0.540300
$997$	−17.9666	−0.569007	−0.284503	−	0.958675i	$-0.591829\pi$
$997$	−17.9666	−0.569007	−0.284503	+	0.958675i	$0.591829\pi$
$998$	−19.4585	−0.615947
$999$	4.58287	0.144995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.x.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.x.1.5	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.28209 q^{5} -1.00000 q^{6} -0.306395 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.28209 q^{5} -1.00000 q^{6} -0.306395 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.28209 q^{10} -1.00000 q^{11} -1.00000 q^{12} -0.0653864 q^{13} -0.306395 q^{14} -1.28209 q^{15} +1.00000 q^{16} -0.119525 q^{17} +1.00000 q^{18} -7.96238 q^{19} +1.28209 q^{20} +0.306395 q^{21} -1.00000 q^{22} -1.37465 q^{23} -1.00000 q^{24} -3.35626 q^{25} -0.0653864 q^{26} -1.00000 q^{27} -0.306395 q^{28} -7.31061 q^{29} -1.28209 q^{30} +3.09717 q^{31} +1.00000 q^{32} +1.00000 q^{33} -0.119525 q^{34} -0.392824 q^{35} +1.00000 q^{36} -4.58287 q^{37} -7.96238 q^{38} +0.0653864 q^{39} +1.28209 q^{40} -7.06969 q^{41} +0.306395 q^{42} +4.86465 q^{43} -1.00000 q^{44} +1.28209 q^{45} -1.37465 q^{46} -6.46008 q^{47} -1.00000 q^{48} -6.90612 q^{49} -3.35626 q^{50} +0.119525 q^{51} -0.0653864 q^{52} +5.11394 q^{53} -1.00000 q^{54} -1.28209 q^{55} -0.306395 q^{56} +7.96238 q^{57} -7.31061 q^{58} +11.2122 q^{59} -1.28209 q^{60} +1.00000 q^{61} +3.09717 q^{62} -0.306395 q^{63} +1.00000 q^{64} -0.0838310 q^{65} +1.00000 q^{66} -5.22547 q^{67} -0.119525 q^{68} +1.37465 q^{69} -0.392824 q^{70} +11.2202 q^{71} +1.00000 q^{72} -9.21003 q^{73} -4.58287 q^{74} +3.35626 q^{75} -7.96238 q^{76} +0.306395 q^{77} +0.0653864 q^{78} +13.9169 q^{79} +1.28209 q^{80} +1.00000 q^{81} -7.06969 q^{82} -17.0516 q^{83} +0.306395 q^{84} -0.153241 q^{85} +4.86465 q^{86} +7.31061 q^{87} -1.00000 q^{88} -5.41939 q^{89} +1.28209 q^{90} +0.0200340 q^{91} -1.37465 q^{92} -3.09717 q^{93} -6.46008 q^{94} -10.2084 q^{95} -1.00000 q^{96} -7.22689 q^{97} -6.90612 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * q^99

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