LMFDB - Embedded newform 5054.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.56155 q^{5} -2.56155 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.56155 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.56155 q^{5} -2.56155 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.56155 q^{9} +1.56155 q^{10} -6.56155 q^{11} -2.56155 q^{12} +0.438447 q^{13} -1.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +3.56155 q^{18} +1.56155 q^{20} +2.56155 q^{21} -6.56155 q^{22} +3.56155 q^{23} -2.56155 q^{24} -2.56155 q^{25} +0.438447 q^{26} -1.43845 q^{27} -1.00000 q^{28} +10.2462 q^{29} -4.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} +16.8078 q^{33} +2.00000 q^{34} -1.56155 q^{35} +3.56155 q^{36} +1.12311 q^{37} -1.12311 q^{39} +1.56155 q^{40} +7.68466 q^{41} +2.56155 q^{42} -7.12311 q^{43} -6.56155 q^{44} +5.56155 q^{45} +3.56155 q^{46} -7.12311 q^{47} -2.56155 q^{48} +1.00000 q^{49} -2.56155 q^{50} -5.12311 q^{51} +0.438447 q^{52} -9.12311 q^{53} -1.43845 q^{54} -10.2462 q^{55} -1.00000 q^{56} +10.2462 q^{58} -11.0000 q^{59} -4.00000 q^{60} -10.4384 q^{61} +2.00000 q^{62} -3.56155 q^{63} +1.00000 q^{64} +0.684658 q^{65} +16.8078 q^{66} +3.68466 q^{67} +2.00000 q^{68} -9.12311 q^{69} -1.56155 q^{70} -5.80776 q^{71} +3.56155 q^{72} +4.56155 q^{73} +1.12311 q^{74} +6.56155 q^{75} +6.56155 q^{77} -1.12311 q^{78} +2.24621 q^{79} +1.56155 q^{80} -7.00000 q^{81} +7.68466 q^{82} -1.00000 q^{83} +2.56155 q^{84} +3.12311 q^{85} -7.12311 q^{86} -26.2462 q^{87} -6.56155 q^{88} -15.3693 q^{89} +5.56155 q^{90} -0.438447 q^{91} +3.56155 q^{92} -5.12311 q^{93} -7.12311 q^{94} -2.56155 q^{96} -3.43845 q^{97} +1.00000 q^{98} -23.3693 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} - q^{10} - 9 q^{11} - q^{12} + 5 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 4 q^{17} + 3 q^{18} - q^{20} + q^{21} - 9 q^{22} + 3 q^{23} - q^{24} - q^{25} + 5 q^{26} - 7 q^{27} - 2 q^{28} + 4 q^{29} - 8 q^{30} + 4 q^{31} + 2 q^{32} + 13 q^{33} + 4 q^{34} + q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{39} - q^{40} + 3 q^{41} + q^{42} - 6 q^{43} - 9 q^{44} + 7 q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 2 q^{49} - q^{50} - 2 q^{51} + 5 q^{52} - 10 q^{53} - 7 q^{54} - 4 q^{55} - 2 q^{56} + 4 q^{58} - 22 q^{59} - 8 q^{60} - 25 q^{61} + 4 q^{62} - 3 q^{63} + 2 q^{64} - 11 q^{65} + 13 q^{66} - 5 q^{67} + 4 q^{68} - 10 q^{69} + q^{70} + 9 q^{71} + 3 q^{72} + 5 q^{73} - 6 q^{74} + 9 q^{75} + 9 q^{77} + 6 q^{78} - 12 q^{79} - q^{80} - 14 q^{81} + 3 q^{82} - 2 q^{83} + q^{84} - 2 q^{85} - 6 q^{86} - 36 q^{87} - 9 q^{88} - 6 q^{89} + 7 q^{90} - 5 q^{91} + 3 q^{92} - 2 q^{93} - 6 q^{94} - q^{96} - 11 q^{97} + 2 q^{98} - 22 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 - q^10 - 9 * q^11 - q^12 + 5 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 4 * q^17 + 3 * q^18 - q^20 + q^21 - 9 * q^22 + 3 * q^23 - q^24 - q^25 + 5 * q^26 - 7 * q^27 - 2 * q^28 + 4 * q^29 - 8 * q^30 + 4 * q^31 + 2 * q^32 + 13 * q^33 + 4 * q^34 + q^35 + 3 * q^36 - 6 * q^37 + 6 * q^39 - q^40 + 3 * q^41 + q^42 - 6 * q^43 - 9 * q^44 + 7 * q^45 + 3 * q^46 - 6 * q^47 - q^48 + 2 * q^49 - q^50 - 2 * q^51 + 5 * q^52 - 10 * q^53 - 7 * q^54 - 4 * q^55 - 2 * q^56 + 4 * q^58 - 22 * q^59 - 8 * q^60 - 25 * q^61 + 4 * q^62 - 3 * q^63 + 2 * q^64 - 11 * q^65 + 13 * q^66 - 5 * q^67 + 4 * q^68 - 10 * q^69 + q^70 + 9 * q^71 + 3 * q^72 + 5 * q^73 - 6 * q^74 + 9 * q^75 + 9 * q^77 + 6 * q^78 - 12 * q^79 - q^80 - 14 * q^81 + 3 * q^82 - 2 * q^83 + q^84 - 2 * q^85 - 6 * q^86 - 36 * q^87 - 9 * q^88 - 6 * q^89 + 7 * q^90 - 5 * q^91 + 3 * q^92 - 2 * q^93 - 6 * q^94 - q^96 - 11 * q^97 + 2 * q^98 - 22 * 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
$3$	−2.56155	−1.47891	−0.739457	−	0.673204i	$-0.764917\pi$
$3$	−2.56155	−1.47891	−0.739457	+	0.673204i	$0.764917\pi$
$4$	1.00000	0.500000
$5$	1.56155	0.698348	0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155	0.698348	0.349174	+	0.937058i	$0.386462\pi$
$6$	−2.56155	−1.04575
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	3.56155	1.18718
$10$	1.56155	0.493806
$11$	−6.56155	−1.97838	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−6.56155	−1.97838	−0.989191	+	0.146631i	$0.953157\pi$
$12$	−2.56155	−0.739457
$13$	0.438447	0.121603	0.0608017	−	0.998150i	$-0.480634\pi$
$13$	0.438447	0.121603	0.0608017	+	0.998150i	$0.480634\pi$
$14$	−1.00000	−0.267261
$15$	−4.00000	−1.03280
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	3.56155	0.839466
$19$	0	0
$19$	0	0
$20$	1.56155	0.349174
$21$	2.56155	0.558977
$22$	−6.56155	−1.39893
$23$	3.56155	0.742635	0.371318	−	0.928506i	$-0.378906\pi$
$23$	3.56155	0.742635	0.371318	+	0.928506i	$0.378906\pi$
$24$	−2.56155	−0.522875
$25$	−2.56155	−0.512311
$26$	0.438447	0.0859866
$27$	−1.43845	−0.276829
$28$	−1.00000	−0.188982
$29$	10.2462	1.90267	0.951337	−	0.308153i	$-0.0997109\pi$
$29$	10.2462	1.90267	0.951337	+	0.308153i	$0.0997109\pi$
$30$	−4.00000	−0.730297
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	16.8078	2.92586
$34$	2.00000	0.342997
$35$	−1.56155	−0.263951
$36$	3.56155	0.593592
$37$	1.12311	0.184637	0.0923187	−	0.995730i	$-0.470572\pi$
$37$	1.12311	0.184637	0.0923187	+	0.995730i	$0.470572\pi$
$38$	0	0
$39$	−1.12311	−0.179841
$40$	1.56155	0.246903
$41$	7.68466	1.20014	0.600071	−	0.799947i	$-0.295139\pi$
$41$	7.68466	1.20014	0.600071	+	0.799947i	$0.295139\pi$
$42$	2.56155	0.395256
$43$	−7.12311	−1.08626	−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311	−1.08626	−0.543132	+	0.839648i	$0.682762\pi$
$44$	−6.56155	−0.989191
$45$	5.56155	0.829067
$46$	3.56155	0.525122
$47$	−7.12311	−1.03901	−0.519506	−	0.854467i	$-0.673884\pi$
$47$	−7.12311	−1.03901	−0.519506	+	0.854467i	$0.673884\pi$
$48$	−2.56155	−0.369728
$49$	1.00000	0.142857
$50$	−2.56155	−0.362258
$51$	−5.12311	−0.717378
$52$	0.438447	0.0608017
$53$	−9.12311	−1.25315	−0.626577	−	0.779359i	$-0.715545\pi$
$53$	−9.12311	−1.25315	−0.626577	+	0.779359i	$0.715545\pi$
$54$	−1.43845	−0.195748
$55$	−10.2462	−1.38160
$56$	−1.00000	−0.133631
$57$	0	0
$58$	10.2462	1.34539
$59$	−11.0000	−1.43208	−0.716039	−	0.698060i	$-0.754047\pi$
$59$	−11.0000	−1.43208	−0.716039	+	0.698060i	$0.754047\pi$
$60$	−4.00000	−0.516398
$61$	−10.4384	−1.33651	−0.668253	−	0.743934i	$-0.732958\pi$
$61$	−10.4384	−1.33651	−0.668253	+	0.743934i	$0.732958\pi$
$62$	2.00000	0.254000
$63$	−3.56155	−0.448713
$64$	1.00000	0.125000
$65$	0.684658	0.0849214
$66$	16.8078	2.06889
$67$	3.68466	0.450153	0.225076	−	0.974341i	$-0.427737\pi$
$67$	3.68466	0.450153	0.225076	+	0.974341i	$0.427737\pi$
$68$	2.00000	0.242536
$69$	−9.12311	−1.09829
$70$	−1.56155	−0.186641
$71$	−5.80776	−0.689255	−0.344627	−	0.938740i	$-0.611995\pi$
$71$	−5.80776	−0.689255	−0.344627	+	0.938740i	$0.611995\pi$
$72$	3.56155	0.419733
$73$	4.56155	0.533889	0.266945	−	0.963712i	$-0.413986\pi$
$73$	4.56155	0.533889	0.266945	+	0.963712i	$0.413986\pi$
$74$	1.12311	0.130558
$75$	6.56155	0.757663
$76$	0	0
$77$	6.56155	0.747758
$78$	−1.12311	−0.127167
$79$	2.24621	0.252719	0.126359	−	0.991985i	$-0.459671\pi$
$79$	2.24621	0.252719	0.126359	+	0.991985i	$0.459671\pi$
$80$	1.56155	0.174587
$81$	−7.00000	−0.777778
$82$	7.68466	0.848629
$83$	−1.00000	−0.109764	−0.0548821	−	0.998493i	$-0.517478\pi$
$83$	−1.00000	−0.109764	−0.0548821	+	0.998493i	$0.517478\pi$
$84$	2.56155	0.279488
$85$	3.12311	0.338748
$86$	−7.12311	−0.768104
$87$	−26.2462	−2.81389
$88$	−6.56155	−0.699464
$89$	−15.3693	−1.62914	−0.814572	−	0.580062i	$-0.803028\pi$
$89$	−15.3693	−1.62914	−0.814572	+	0.580062i	$0.803028\pi$
$90$	5.56155	0.586239
$91$	−0.438447	−0.0459618
$92$	3.56155	0.371318
$93$	−5.12311	−0.531241
$94$	−7.12311	−0.734692
$95$	0	0
$96$	−2.56155	−0.261437
$97$	−3.43845	−0.349121	−0.174561	−	0.984646i	$-0.555851\pi$
$97$	−3.43845	−0.349121	−0.174561	+	0.984646i	$0.555851\pi$
$98$	1.00000	0.101015
$99$	−23.3693	−2.34870
$100$	−2.56155	−0.256155
$101$	−13.3693	−1.33030	−0.665148	−	0.746711i	$-0.731632\pi$
$101$	−13.3693	−1.33030	−0.665148	+	0.746711i	$0.731632\pi$
$102$	−5.12311	−0.507263
$103$	2.87689	0.283469	0.141734	−	0.989905i	$-0.454732\pi$
$103$	2.87689	0.283469	0.141734	+	0.989905i	$0.454732\pi$
$104$	0.438447	0.0429933
$105$	4.00000	0.390360
$106$	−9.12311	−0.886114
$107$	3.12311	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$107$	3.12311	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$108$	−1.43845	−0.138415
$109$	6.24621	0.598279	0.299139	−	0.954209i	$-0.403300\pi$
$109$	6.24621	0.598279	0.299139	+	0.954209i	$0.403300\pi$
$110$	−10.2462	−0.976938
$111$	−2.87689	−0.273063
$112$	−1.00000	−0.0944911
$113$	17.0000	1.59923	0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000	1.59923	0.799613	+	0.600516i	$0.205038\pi$
$114$	0	0
$115$	5.56155	0.518617
$116$	10.2462	0.951337
$117$	1.56155	0.144366
$118$	−11.0000	−1.01263
$119$	−2.00000	−0.183340
$120$	−4.00000	−0.365148
$121$	32.0540	2.91400
$122$	−10.4384	−0.945053
$123$	−19.6847	−1.77491
$124$	2.00000	0.179605
$125$	−11.8078	−1.05612
$126$	−3.56155	−0.317288
$127$	−1.31534	−0.116718	−0.0583588	−	0.998296i	$-0.518587\pi$
$127$	−1.31534	−0.116718	−0.0583588	+	0.998296i	$0.518587\pi$
$128$	1.00000	0.0883883
$129$	18.2462	1.60649
$130$	0.684658	0.0600485
$131$	11.2462	0.982586	0.491293	−	0.870994i	$-0.336524\pi$
$131$	11.2462	0.982586	0.491293	+	0.870994i	$0.336524\pi$
$132$	16.8078	1.46293
$133$	0	0
$134$	3.68466	0.318306
$135$	−2.24621	−0.193323
$136$	2.00000	0.171499
$137$	−8.36932	−0.715039	−0.357519	−	0.933906i	$-0.616377\pi$
$137$	−8.36932	−0.715039	−0.357519	+	0.933906i	$0.616377\pi$
$138$	−9.12311	−0.776610
$139$	−14.5616	−1.23509	−0.617547	−	0.786534i	$-0.711874\pi$
$139$	−14.5616	−1.23509	−0.617547	+	0.786534i	$0.711874\pi$
$140$	−1.56155	−0.131975
$141$	18.2462	1.53661
$142$	−5.80776	−0.487377
$143$	−2.87689	−0.240578
$144$	3.56155	0.296796
$145$	16.0000	1.32873
$146$	4.56155	0.377517
$147$	−2.56155	−0.211273
$148$	1.12311	0.0923187
$149$	15.3693	1.25910	0.629552	−	0.776959i	$-0.283239\pi$
$149$	15.3693	1.25910	0.629552	+	0.776959i	$0.283239\pi$
$150$	6.56155	0.535749
$151$	3.56155	0.289835	0.144918	−	0.989444i	$-0.453708\pi$
$151$	3.56155	0.289835	0.144918	+	0.989444i	$0.453708\pi$
$152$	0	0
$153$	7.12311	0.575869
$154$	6.56155	0.528745
$155$	3.12311	0.250854
$156$	−1.12311	−0.0899204
$157$	−7.31534	−0.583828	−0.291914	−	0.956445i	$-0.594292\pi$
$157$	−7.31534	−0.583828	−0.291914	+	0.956445i	$0.594292\pi$
$158$	2.24621	0.178699
$159$	23.3693	1.85331
$160$	1.56155	0.123452
$161$	−3.56155	−0.280690
$162$	−7.00000	−0.549972
$163$	−6.31534	−0.494656	−0.247328	−	0.968932i	$-0.579552\pi$
$163$	−6.31534	−0.494656	−0.247328	+	0.968932i	$0.579552\pi$
$164$	7.68466	0.600071
$165$	26.2462	2.04326
$166$	−1.00000	−0.0776151
$167$	−12.8769	−0.996444	−0.498222	−	0.867050i	$-0.666014\pi$
$167$	−12.8769	−0.996444	−0.498222	+	0.867050i	$0.666014\pi$
$168$	2.56155	0.197628
$169$	−12.8078	−0.985213
$170$	3.12311	0.239531
$171$	0	0
$172$	−7.12311	−0.543132
$173$	−5.31534	−0.404118	−0.202059	−	0.979373i	$-0.564763\pi$
$173$	−5.31534	−0.404118	−0.202059	+	0.979373i	$0.564763\pi$
$174$	−26.2462	−1.98972
$175$	2.56155	0.193635
$176$	−6.56155	−0.494596
$177$	28.1771	2.11792
$178$	−15.3693	−1.15198
$179$	−19.9309	−1.48970	−0.744852	−	0.667230i	$-0.767480\pi$
$179$	−19.9309	−1.48970	−0.744852	+	0.667230i	$0.767480\pi$
$180$	5.56155	0.414534
$181$	−17.8078	−1.32364	−0.661820	−	0.749662i	$-0.730216\pi$
$181$	−17.8078	−1.32364	−0.661820	+	0.749662i	$0.730216\pi$
$182$	−0.438447	−0.0324999
$183$	26.7386	1.97658
$184$	3.56155	0.262561
$185$	1.75379	0.128941
$186$	−5.12311	−0.375644
$187$	−13.1231	−0.959657
$188$	−7.12311	−0.519506
$189$	1.43845	0.104632
$190$	0	0
$191$	0.192236	0.0139097	0.00695485	−	0.999976i	$-0.497786\pi$
$191$	0.192236	0.0139097	0.00695485	+	0.999976i	$0.497786\pi$
$192$	−2.56155	−0.184864
$193$	−1.31534	−0.0946804	−0.0473402	−	0.998879i	$-0.515074\pi$
$193$	−1.31534	−0.0946804	−0.0473402	+	0.998879i	$0.515074\pi$
$194$	−3.43845	−0.246866
$195$	−1.75379	−0.125591
$196$	1.00000	0.0714286
$197$	−25.6155	−1.82503	−0.912515	−	0.409042i	$-0.865863\pi$
$197$	−25.6155	−1.82503	−0.912515	+	0.409042i	$0.865863\pi$
$198$	−23.3693	−1.66079
$199$	−10.0000	−0.708881	−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000	−0.708881	−0.354441	+	0.935079i	$0.615329\pi$
$200$	−2.56155	−0.181129
$201$	−9.43845	−0.665737
$202$	−13.3693	−0.940662
$203$	−10.2462	−0.719143
$204$	−5.12311	−0.358689
$205$	12.0000	0.838116
$206$	2.87689	0.200443
$207$	12.6847	0.881645
$208$	0.438447	0.0304008
$209$	0	0
$210$	4.00000	0.276026
$211$	16.4924	1.13539	0.567693	−	0.823241i	$-0.307836\pi$
$211$	16.4924	1.13539	0.567693	+	0.823241i	$0.307836\pi$
$212$	−9.12311	−0.626577
$213$	14.8769	1.01935
$214$	3.12311	0.213491
$215$	−11.1231	−0.758590
$216$	−1.43845	−0.0978739
$217$	−2.00000	−0.135769
$218$	6.24621	0.423047
$219$	−11.6847	−0.789576
$220$	−10.2462	−0.690799
$221$	0.876894	0.0589863
$222$	−2.87689	−0.193085
$223$	−22.4924	−1.50620	−0.753102	−	0.657904i	$-0.771443\pi$
$223$	−22.4924	−1.50620	−0.753102	+	0.657904i	$0.771443\pi$
$224$	−1.00000	−0.0668153
$225$	−9.12311	−0.608207
$226$	17.0000	1.13082
$227$	−25.7386	−1.70833	−0.854167	−	0.520000i	$-0.825932\pi$
$227$	−25.7386	−1.70833	−0.854167	+	0.520000i	$0.825932\pi$
$228$	0	0
$229$	−3.80776	−0.251624	−0.125812	−	0.992054i	$-0.540154\pi$
$229$	−3.80776	−0.251624	−0.125812	+	0.992054i	$0.540154\pi$
$230$	5.56155	0.366718
$231$	−16.8078	−1.10587
$232$	10.2462	0.672697
$233$	−24.1231	−1.58036	−0.790179	−	0.612877i	$-0.790012\pi$
$233$	−24.1231	−1.58036	−0.790179	+	0.612877i	$0.790012\pi$
$234$	1.56155	0.102082
$235$	−11.1231	−0.725591
$236$	−11.0000	−0.716039
$237$	−5.75379	−0.373749
$238$	−2.00000	−0.129641
$239$	23.8078	1.54000	0.769998	−	0.638046i	$-0.220257\pi$
$239$	23.8078	1.54000	0.769998	+	0.638046i	$0.220257\pi$
$240$	−4.00000	−0.258199
$241$	−3.93087	−0.253210	−0.126605	−	0.991953i	$-0.540408\pi$
$241$	−3.93087	−0.253210	−0.126605	+	0.991953i	$0.540408\pi$
$242$	32.0540	2.06051
$243$	22.2462	1.42710
$244$	−10.4384	−0.668253
$245$	1.56155	0.0997639
$246$	−19.6847	−1.25505
$247$	0	0
$248$	2.00000	0.127000
$249$	2.56155	0.162332
$250$	−11.8078	−0.746789
$251$	18.3693	1.15946	0.579731	−	0.814808i	$-0.303158\pi$
$251$	18.3693	1.15946	0.579731	+	0.814808i	$0.303158\pi$
$252$	−3.56155	−0.224357
$253$	−23.3693	−1.46922
$254$	−1.31534	−0.0825319
$255$	−8.00000	−0.500979
$256$	1.00000	0.0625000
$257$	2.56155	0.159785	0.0798926	−	0.996803i	$-0.474542\pi$
$257$	2.56155	0.159785	0.0798926	+	0.996803i	$0.474542\pi$
$258$	18.2462	1.13596
$259$	−1.12311	−0.0697864
$260$	0.684658	0.0424607
$261$	36.4924	2.25882
$262$	11.2462	0.694793
$263$	−10.0540	−0.619955	−0.309977	−	0.950744i	$-0.600321\pi$
$263$	−10.0540	−0.619955	−0.309977	+	0.950744i	$0.600321\pi$
$264$	16.8078	1.03445
$265$	−14.2462	−0.875138
$266$	0	0
$267$	39.3693	2.40936
$268$	3.68466	0.225076
$269$	−15.1231	−0.922072	−0.461036	−	0.887381i	$-0.652522\pi$
$269$	−15.1231	−0.922072	−0.461036	+	0.887381i	$0.652522\pi$
$270$	−2.24621	−0.136700
$271$	−2.63068	−0.159803	−0.0799013	−	0.996803i	$-0.525461\pi$
$271$	−2.63068	−0.159803	−0.0799013	+	0.996803i	$0.525461\pi$
$272$	2.00000	0.121268
$273$	1.12311	0.0679734
$274$	−8.36932	−0.505609
$275$	16.8078	1.01355
$276$	−9.12311	−0.549146
$277$	7.12311	0.427986	0.213993	−	0.976835i	$-0.431353\pi$
$277$	7.12311	0.427986	0.213993	+	0.976835i	$0.431353\pi$
$278$	−14.5616	−0.873344
$279$	7.12311	0.426449
$280$	−1.56155	−0.0933206
$281$	13.6847	0.816358	0.408179	−	0.912902i	$-0.366164\pi$
$281$	13.6847	0.816358	0.408179	+	0.912902i	$0.366164\pi$
$282$	18.2462	1.08655
$283$	−2.12311	−0.126206	−0.0631028	−	0.998007i	$-0.520100\pi$
$283$	−2.12311	−0.126206	−0.0631028	+	0.998007i	$0.520100\pi$
$284$	−5.80776	−0.344627
$285$	0	0
$286$	−2.87689	−0.170114
$287$	−7.68466	−0.453611
$288$	3.56155	0.209867
$289$	−13.0000	−0.764706
$290$	16.0000	0.939552
$291$	8.80776	0.516320
$292$	4.56155	0.266945
$293$	2.93087	0.171223	0.0856116	−	0.996329i	$-0.472716\pi$
$293$	2.93087	0.171223	0.0856116	+	0.996329i	$0.472716\pi$
$294$	−2.56155	−0.149393
$295$	−17.1771	−1.00009
$296$	1.12311	0.0652792
$297$	9.43845	0.547674
$298$	15.3693	0.890321
$299$	1.56155	0.0903069
$300$	6.56155	0.378831
$301$	7.12311	0.410569
$302$	3.56155	0.204944
$303$	34.2462	1.96739
$304$	0	0
$305$	−16.3002	−0.933346
$306$	7.12311	0.407201
$307$	3.00000	0.171219	0.0856095	−	0.996329i	$-0.472716\pi$
$307$	3.00000	0.171219	0.0856095	+	0.996329i	$0.472716\pi$
$308$	6.56155	0.373879
$309$	−7.36932	−0.419226
$310$	3.12311	0.177380
$311$	−22.4924	−1.27543	−0.637714	−	0.770273i	$-0.720120\pi$
$311$	−22.4924	−1.27543	−0.637714	+	0.770273i	$0.720120\pi$
$312$	−1.12311	−0.0635833
$313$	−32.1771	−1.81876	−0.909378	−	0.415971i	$-0.863442\pi$
$313$	−32.1771	−1.81876	−0.909378	+	0.415971i	$0.863442\pi$
$314$	−7.31534	−0.412829
$315$	−5.56155	−0.313358
$316$	2.24621	0.126359
$317$	14.4924	0.813976	0.406988	−	0.913434i	$-0.366579\pi$
$317$	14.4924	0.813976	0.406988	+	0.913434i	$0.366579\pi$
$318$	23.3693	1.31049
$319$	−67.2311	−3.76422
$320$	1.56155	0.0872935
$321$	−8.00000	−0.446516
$322$	−3.56155	−0.198478
$323$	0	0
$324$	−7.00000	−0.388889
$325$	−1.12311	−0.0622987
$326$	−6.31534	−0.349774
$327$	−16.0000	−0.884802
$328$	7.68466	0.424314
$329$	7.12311	0.392710
$330$	26.2462	1.44481
$331$	−4.80776	−0.264259	−0.132129	−	0.991232i	$-0.542181\pi$
$331$	−4.80776	−0.264259	−0.132129	+	0.991232i	$0.542181\pi$
$332$	−1.00000	−0.0548821
$333$	4.00000	0.219199
$334$	−12.8769	−0.704592
$335$	5.75379	0.314363
$336$	2.56155	0.139744
$337$	−10.6155	−0.578265	−0.289132	−	0.957289i	$-0.593367\pi$
$337$	−10.6155	−0.578265	−0.289132	+	0.957289i	$0.593367\pi$
$338$	−12.8078	−0.696651
$339$	−43.5464	−2.36512
$340$	3.12311	0.169374
$341$	−13.1231	−0.710656
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−7.12311	−0.384052
$345$	−14.2462	−0.766990
$346$	−5.31534	−0.285755
$347$	2.31534	0.124294	0.0621470	−	0.998067i	$-0.480205\pi$
$347$	2.31534	0.124294	0.0621470	+	0.998067i	$0.480205\pi$
$348$	−26.2462	−1.40694
$349$	5.36932	0.287413	0.143706	−	0.989620i	$-0.454098\pi$
$349$	5.36932	0.287413	0.143706	+	0.989620i	$0.454098\pi$
$350$	2.56155	0.136921
$351$	−0.630683	−0.0336634
$352$	−6.56155	−0.349732
$353$	11.6847	0.621912	0.310956	−	0.950424i	$-0.399351\pi$
$353$	11.6847	0.621912	0.310956	+	0.950424i	$0.399351\pi$
$354$	28.1771	1.49759
$355$	−9.06913	−0.481339
$356$	−15.3693	−0.814572
$357$	5.12311	0.271144
$358$	−19.9309	−1.05338
$359$	15.3693	0.811162	0.405581	−	0.914059i	$-0.367069\pi$
$359$	15.3693	0.811162	0.405581	+	0.914059i	$0.367069\pi$
$360$	5.56155	0.293120
$361$	0	0
$362$	−17.8078	−0.935955
$363$	−82.1080	−4.30955
$364$	−0.438447	−0.0229809
$365$	7.12311	0.372840
$366$	26.7386	1.39765
$367$	23.3693	1.21987	0.609934	−	0.792452i	$-0.291196\pi$
$367$	23.3693	1.21987	0.609934	+	0.792452i	$0.291196\pi$
$368$	3.56155	0.185659
$369$	27.3693	1.42479
$370$	1.75379	0.0911751
$371$	9.12311	0.473648
$372$	−5.12311	−0.265621
$373$	24.8769	1.28808	0.644038	−	0.764993i	$-0.277258\pi$
$373$	24.8769	1.28808	0.644038	+	0.764993i	$0.277258\pi$
$374$	−13.1231	−0.678580
$375$	30.2462	1.56191
$376$	−7.12311	−0.367346
$377$	4.49242	0.231372
$378$	1.43845	0.0739857
$379$	−29.3693	−1.50860	−0.754300	−	0.656530i	$-0.772024\pi$
$379$	−29.3693	−1.50860	−0.754300	+	0.656530i	$0.772024\pi$
$380$	0	0
$381$	3.36932	0.172615
$382$	0.192236	0.00983565
$383$	32.0000	1.63512	0.817562	−	0.575841i	$-0.195325\pi$
$383$	32.0000	1.63512	0.817562	+	0.575841i	$0.195325\pi$
$384$	−2.56155	−0.130719
$385$	10.2462	0.522195
$386$	−1.31534	−0.0669491
$387$	−25.3693	−1.28959
$388$	−3.43845	−0.174561
$389$	−22.7386	−1.15289	−0.576447	−	0.817134i	$-0.695561\pi$
$389$	−22.7386	−1.15289	−0.576447	+	0.817134i	$0.695561\pi$
$390$	−1.75379	−0.0888065
$391$	7.12311	0.360231
$392$	1.00000	0.0505076
$393$	−28.8078	−1.45316
$394$	−25.6155	−1.29049
$395$	3.50758	0.176485
$396$	−23.3693	−1.17435
$397$	12.7386	0.639334	0.319667	−	0.947530i	$-0.396429\pi$
$397$	12.7386	0.639334	0.319667	+	0.947530i	$0.396429\pi$
$398$	−10.0000	−0.501255
$399$	0	0
$400$	−2.56155	−0.128078
$401$	−6.36932	−0.318069	−0.159034	−	0.987273i	$-0.550838\pi$
$401$	−6.36932	−0.318069	−0.159034	+	0.987273i	$0.550838\pi$
$402$	−9.43845	−0.470747
$403$	0.876894	0.0436812
$404$	−13.3693	−0.665148
$405$	−10.9309	−0.543159
$406$	−10.2462	−0.508511
$407$	−7.36932	−0.365283
$408$	−5.12311	−0.253632
$409$	3.68466	0.182195	0.0910973	−	0.995842i	$-0.470963\pi$
$409$	3.68466	0.182195	0.0910973	+	0.995842i	$0.470963\pi$
$410$	12.0000	0.592638
$411$	21.4384	1.05748
$412$	2.87689	0.141734
$413$	11.0000	0.541275
$414$	12.6847	0.623417
$415$	−1.56155	−0.0766536
$416$	0.438447	0.0214966
$417$	37.3002	1.82660
$418$	0	0
$419$	32.4924	1.58736	0.793679	−	0.608336i	$-0.208163\pi$
$419$	32.4924	1.58736	0.793679	+	0.608336i	$0.208163\pi$
$420$	4.00000	0.195180
$421$	4.63068	0.225686	0.112843	−	0.993613i	$-0.464004\pi$
$421$	4.63068	0.225686	0.112843	+	0.993613i	$0.464004\pi$
$422$	16.4924	0.802839
$423$	−25.3693	−1.23350
$424$	−9.12311	−0.443057
$425$	−5.12311	−0.248507
$426$	14.8769	0.720788
$427$	10.4384	0.505152
$428$	3.12311	0.150961
$429$	7.36932	0.355794
$430$	−11.1231	−0.536404
$431$	31.3693	1.51101	0.755503	−	0.655145i	$-0.227392\pi$
$431$	31.3693	1.51101	0.755503	+	0.655145i	$0.227392\pi$
$432$	−1.43845	−0.0692073
$433$	29.6155	1.42323	0.711616	−	0.702569i	$-0.247964\pi$
$433$	29.6155	1.42323	0.711616	+	0.702569i	$0.247964\pi$
$434$	−2.00000	−0.0960031
$435$	−40.9848	−1.96507
$436$	6.24621	0.299139
$437$	0	0
$438$	−11.6847	−0.558315
$439$	−28.7386	−1.37162	−0.685810	−	0.727781i	$-0.740552\pi$
$439$	−28.7386	−1.37162	−0.685810	+	0.727781i	$0.740552\pi$
$440$	−10.2462	−0.488469
$441$	3.56155	0.169598
$442$	0.876894	0.0417096
$443$	−21.0540	−1.00030	−0.500152	−	0.865937i	$-0.666723\pi$
$443$	−21.0540	−1.00030	−0.500152	+	0.865937i	$0.666723\pi$
$444$	−2.87689	−0.136531
$445$	−24.0000	−1.13771
$446$	−22.4924	−1.06505
$447$	−39.3693	−1.86210
$448$	−1.00000	−0.0472456
$449$	−27.7386	−1.30907	−0.654534	−	0.756033i	$-0.727135\pi$
$449$	−27.7386	−1.30907	−0.654534	+	0.756033i	$0.727135\pi$
$450$	−9.12311	−0.430067
$451$	−50.4233	−2.37434
$452$	17.0000	0.799613
$453$	−9.12311	−0.428641
$454$	−25.7386	−1.20797
$455$	−0.684658	−0.0320973
$456$	0	0
$457$	27.2462	1.27452	0.637262	−	0.770647i	$-0.280067\pi$
$457$	27.2462	1.27452	0.637262	+	0.770647i	$0.280067\pi$
$458$	−3.80776	−0.177925
$459$	−2.87689	−0.134282
$460$	5.56155	0.259309
$461$	33.8078	1.57458	0.787292	−	0.616580i	$-0.211482\pi$
$461$	33.8078	1.57458	0.787292	+	0.616580i	$0.211482\pi$
$462$	−16.8078	−0.781968
$463$	16.4384	0.763959	0.381980	−	0.924171i	$-0.375242\pi$
$463$	16.4384	0.763959	0.381980	+	0.924171i	$0.375242\pi$
$464$	10.2462	0.475668
$465$	−8.00000	−0.370991
$466$	−24.1231	−1.11748
$467$	12.8078	0.592673	0.296336	−	0.955084i	$-0.404235\pi$
$467$	12.8078	0.592673	0.296336	+	0.955084i	$0.404235\pi$
$468$	1.56155	0.0721828
$469$	−3.68466	−0.170142
$470$	−11.1231	−0.513071
$471$	18.7386	0.863431
$472$	−11.0000	−0.506316
$473$	46.7386	2.14904
$474$	−5.75379	−0.264280
$475$	0	0
$476$	−2.00000	−0.0916698
$477$	−32.4924	−1.48773
$478$	23.8078	1.08894
$479$	−16.8769	−0.771125	−0.385562	−	0.922682i	$-0.625993\pi$
$479$	−16.8769	−0.771125	−0.385562	+	0.922682i	$0.625993\pi$
$480$	−4.00000	−0.182574
$481$	0.492423	0.0224525
$482$	−3.93087	−0.179046
$483$	9.12311	0.415116
$484$	32.0540	1.45700
$485$	−5.36932	−0.243808
$486$	22.2462	1.00911
$487$	39.8617	1.80631	0.903154	−	0.429317i	$-0.141246\pi$
$487$	39.8617	1.80631	0.903154	+	0.429317i	$0.141246\pi$
$488$	−10.4384	−0.472526
$489$	16.1771	0.731553
$490$	1.56155	0.0705438
$491$	−10.7386	−0.484628	−0.242314	−	0.970198i	$-0.577906\pi$
$491$	−10.7386	−0.484628	−0.242314	+	0.970198i	$0.577906\pi$
$492$	−19.6847	−0.887453
$493$	20.4924	0.922932
$494$	0	0
$495$	−36.4924	−1.64021
$496$	2.00000	0.0898027
$497$	5.80776	0.260514
$498$	2.56155	0.114786
$499$	−18.1771	−0.813718	−0.406859	−	0.913491i	$-0.633376\pi$
$499$	−18.1771	−0.813718	−0.406859	+	0.913491i	$0.633376\pi$
$500$	−11.8078	−0.528059
$501$	32.9848	1.47365
$502$	18.3693	0.819863
$503$	−7.75379	−0.345724	−0.172862	−	0.984946i	$-0.555302\pi$
$503$	−7.75379	−0.345724	−0.172862	+	0.984946i	$0.555302\pi$
$504$	−3.56155	−0.158644
$505$	−20.8769	−0.929010
$506$	−23.3693	−1.03889
$507$	32.8078	1.45704
$508$	−1.31534	−0.0583588
$509$	−16.6847	−0.739534	−0.369767	−	0.929124i	$-0.620563\pi$
$509$	−16.6847	−0.739534	−0.369767	+	0.929124i	$0.620563\pi$
$510$	−8.00000	−0.354246
$511$	−4.56155	−0.201791
$512$	1.00000	0.0441942
$513$	0	0
$514$	2.56155	0.112985
$515$	4.49242	0.197960
$516$	18.2462	0.803245
$517$	46.7386	2.05556
$518$	−1.12311	−0.0493464
$519$	13.6155	0.597655
$520$	0.684658	0.0300243
$521$	−7.93087	−0.347458	−0.173729	−	0.984794i	$-0.555582\pi$
$521$	−7.93087	−0.347458	−0.173729	+	0.984794i	$0.555582\pi$
$522$	36.4924	1.59723
$523$	−18.2462	−0.797851	−0.398926	−	0.916983i	$-0.630617\pi$
$523$	−18.2462	−0.797851	−0.398926	+	0.916983i	$0.630617\pi$
$524$	11.2462	0.491293
$525$	−6.56155	−0.286370
$526$	−10.0540	−0.438374
$527$	4.00000	0.174243
$528$	16.8078	0.731464
$529$	−10.3153	−0.448493
$530$	−14.2462	−0.618816
$531$	−39.1771	−1.70014
$532$	0	0
$533$	3.36932	0.145941
$534$	39.3693	1.70368
$535$	4.87689	0.210847
$536$	3.68466	0.159153
$537$	51.0540	2.20314
$538$	−15.1231	−0.652003
$539$	−6.56155	−0.282626
$540$	−2.24621	−0.0966615
$541$	−13.7538	−0.591322	−0.295661	−	0.955293i	$-0.595540\pi$
$541$	−13.7538	−0.591322	−0.295661	+	0.955293i	$0.595540\pi$
$542$	−2.63068	−0.112998
$543$	45.6155	1.95755
$544$	2.00000	0.0857493
$545$	9.75379	0.417806
$546$	1.12311	0.0480645
$547$	−40.1080	−1.71489	−0.857446	−	0.514574i	$-0.827950\pi$
$547$	−40.1080	−1.71489	−0.857446	+	0.514574i	$0.827950\pi$
$548$	−8.36932	−0.357519
$549$	−37.1771	−1.58668
$550$	16.8078	0.716685
$551$	0	0
$552$	−9.12311	−0.388305
$553$	−2.24621	−0.0955186
$554$	7.12311	0.302632
$555$	−4.49242	−0.190693
$556$	−14.5616	−0.617547
$557$	43.1231	1.82718	0.913592	−	0.406631i	$-0.133297\pi$
$557$	43.1231	1.82718	0.913592	+	0.406631i	$0.133297\pi$
$558$	7.12311	0.301545
$559$	−3.12311	−0.132093
$560$	−1.56155	−0.0659877
$561$	33.6155	1.41925
$562$	13.6847	0.577252
$563$	−31.0000	−1.30649	−0.653247	−	0.757145i	$-0.726594\pi$
$563$	−31.0000	−1.30649	−0.653247	+	0.757145i	$0.726594\pi$
$564$	18.2462	0.768304
$565$	26.5464	1.11682
$566$	−2.12311	−0.0892408
$567$	7.00000	0.293972
$568$	−5.80776	−0.243688
$569$	27.5616	1.15544	0.577720	−	0.816235i	$-0.303942\pi$
$569$	27.5616	1.15544	0.577720	+	0.816235i	$0.303942\pi$
$570$	0	0
$571$	−11.3002	−0.472898	−0.236449	−	0.971644i	$-0.575984\pi$
$571$	−11.3002	−0.472898	−0.236449	+	0.971644i	$0.575984\pi$
$572$	−2.87689	−0.120289
$573$	−0.492423	−0.0205712
$574$	−7.68466	−0.320751
$575$	−9.12311	−0.380460
$576$	3.56155	0.148398
$577$	−39.0540	−1.62584	−0.812919	−	0.582377i	$-0.802123\pi$
$577$	−39.0540	−1.62584	−0.812919	+	0.582377i	$0.802123\pi$
$578$	−13.0000	−0.540729
$579$	3.36932	0.140024
$580$	16.0000	0.664364
$581$	1.00000	0.0414870
$582$	8.80776	0.365094
$583$	59.8617	2.47922
$584$	4.56155	0.188758
$585$	2.43845	0.100817
$586$	2.93087	0.121073
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−2.56155	−0.105637
$589$	0	0
$590$	−17.1771	−0.707169
$591$	65.6155	2.69906
$592$	1.12311	0.0461594
$593$	17.9309	0.736333	0.368166	−	0.929760i	$-0.379986\pi$
$593$	17.9309	0.736333	0.368166	+	0.929760i	$0.379986\pi$
$594$	9.43845	0.387264
$595$	−3.12311	−0.128035
$596$	15.3693	0.629552
$597$	25.6155	1.04837
$598$	1.56155	0.0638566
$599$	−5.31534	−0.217179	−0.108589	−	0.994087i	$-0.534633\pi$
$599$	−5.31534	−0.217179	−0.108589	+	0.994087i	$0.534633\pi$
$600$	6.56155	0.267874
$601$	2.94602	0.120171	0.0600854	−	0.998193i	$-0.480863\pi$
$601$	2.94602	0.120171	0.0600854	+	0.998193i	$0.480863\pi$
$602$	7.12311	0.290316
$603$	13.1231	0.534414
$604$	3.56155	0.144918
$605$	50.0540	2.03498
$606$	34.2462	1.39116
$607$	18.7386	0.760578	0.380289	−	0.924868i	$-0.375825\pi$
$607$	18.7386	0.760578	0.380289	+	0.924868i	$0.375825\pi$
$608$	0	0
$609$	26.2462	1.06355
$610$	−16.3002	−0.659975
$611$	−3.12311	−0.126347
$612$	7.12311	0.287934
$613$	−2.49242	−0.100668	−0.0503340	−	0.998732i	$-0.516029\pi$
$613$	−2.49242	−0.100668	−0.0503340	+	0.998732i	$0.516029\pi$
$614$	3.00000	0.121070
$615$	−30.7386	−1.23950
$616$	6.56155	0.264372
$617$	−38.3693	−1.54469	−0.772345	−	0.635203i	$-0.780916\pi$
$617$	−38.3693	−1.54469	−0.772345	+	0.635203i	$0.780916\pi$
$618$	−7.36932	−0.296437
$619$	0.192236	0.00772661	0.00386331	−	0.999993i	$-0.498770\pi$
$619$	0.192236	0.00772661	0.00386331	+	0.999993i	$0.498770\pi$
$620$	3.12311	0.125427
$621$	−5.12311	−0.205583
$622$	−22.4924	−0.901864
$623$	15.3693	0.615759
$624$	−1.12311	−0.0449602
$625$	−5.63068	−0.225227
$626$	−32.1771	−1.28605
$627$	0	0
$628$	−7.31534	−0.291914
$629$	2.24621	0.0895623
$630$	−5.56155	−0.221578
$631$	−36.4924	−1.45274	−0.726370	−	0.687304i	$-0.758794\pi$
$631$	−36.4924	−1.45274	−0.726370	+	0.687304i	$0.758794\pi$
$632$	2.24621	0.0893495
$633$	−42.2462	−1.67914
$634$	14.4924	0.575568
$635$	−2.05398	−0.0815095
$636$	23.3693	0.926654
$637$	0.438447	0.0173719
$638$	−67.2311	−2.66170
$639$	−20.6847	−0.818272
$640$	1.56155	0.0617258
$641$	34.1231	1.34778	0.673891	−	0.738831i	$-0.264622\pi$
$641$	34.1231	1.34778	0.673891	+	0.738831i	$0.264622\pi$
$642$	−8.00000	−0.315735
$643$	−0.753789	−0.0297265	−0.0148633	−	0.999890i	$-0.504731\pi$
$643$	−0.753789	−0.0297265	−0.0148633	+	0.999890i	$0.504731\pi$
$644$	−3.56155	−0.140345
$645$	28.4924	1.12189
$646$	0	0
$647$	36.7386	1.44434	0.722172	−	0.691713i	$-0.243144\pi$
$647$	36.7386	1.44434	0.722172	+	0.691713i	$0.243144\pi$
$648$	−7.00000	−0.274986
$649$	72.1771	2.83320
$650$	−1.12311	−0.0440518
$651$	5.12311	0.200790
$652$	−6.31534	−0.247328
$653$	−10.6307	−0.416011	−0.208005	−	0.978128i	$-0.566697\pi$
$653$	−10.6307	−0.416011	−0.208005	+	0.978128i	$0.566697\pi$
$654$	−16.0000	−0.625650
$655$	17.5616	0.686187
$656$	7.68466	0.300036
$657$	16.2462	0.633825
$658$	7.12311	0.277688
$659$	−8.87689	−0.345795	−0.172897	−	0.984940i	$-0.555313\pi$
$659$	−8.87689	−0.345795	−0.172897	+	0.984940i	$0.555313\pi$
$660$	26.2462	1.02163
$661$	−31.8078	−1.23718	−0.618589	−	0.785714i	$-0.712296\pi$
$661$	−31.8078	−1.23718	−0.618589	+	0.785714i	$0.712296\pi$
$662$	−4.80776	−0.186859
$663$	−2.24621	−0.0872356
$664$	−1.00000	−0.0388075
$665$	0	0
$666$	4.00000	0.154997
$667$	36.4924	1.41299
$668$	−12.8769	−0.498222
$669$	57.6155	2.22755
$670$	5.75379	0.222288
$671$	68.4924	2.64412
$672$	2.56155	0.0988140
$673$	−6.68466	−0.257675	−0.128837	−	0.991666i	$-0.541125\pi$
$673$	−6.68466	−0.257675	−0.128837	+	0.991666i	$0.541125\pi$
$674$	−10.6155	−0.408895
$675$	3.68466	0.141823
$676$	−12.8078	−0.492606
$677$	−1.50758	−0.0579409	−0.0289705	−	0.999580i	$-0.509223\pi$
$677$	−1.50758	−0.0579409	−0.0289705	+	0.999580i	$0.509223\pi$
$678$	−43.5464	−1.67239
$679$	3.43845	0.131955
$680$	3.12311	0.119766
$681$	65.9309	2.52648
$682$	−13.1231	−0.502510
$683$	0.492423	0.0188420	0.00942101	−	0.999956i	$-0.497001\pi$
$683$	0.492423	0.0188420	0.00942101	+	0.999956i	$0.497001\pi$
$684$	0	0
$685$	−13.0691	−0.499346
$686$	−1.00000	−0.0381802
$687$	9.75379	0.372130
$688$	−7.12311	−0.271566
$689$	−4.00000	−0.152388
$690$	−14.2462	−0.542344
$691$	−14.0540	−0.534638	−0.267319	−	0.963608i	$-0.586138\pi$
$691$	−14.0540	−0.534638	−0.267319	+	0.963608i	$0.586138\pi$
$692$	−5.31534	−0.202059
$693$	23.3693	0.887727
$694$	2.31534	0.0878892
$695$	−22.7386	−0.862526
$696$	−26.2462	−0.994860
$697$	15.3693	0.582154
$698$	5.36932	0.203232
$699$	61.7926	2.33721
$700$	2.56155	0.0968176
$701$	−24.8769	−0.939587	−0.469794	−	0.882776i	$-0.655672\pi$
$701$	−24.8769	−0.939587	−0.469794	+	0.882776i	$0.655672\pi$
$702$	−0.630683	−0.0238036
$703$	0	0
$704$	−6.56155	−0.247298
$705$	28.4924	1.07309
$706$	11.6847	0.439758
$707$	13.3693	0.502805
$708$	28.1771	1.05896
$709$	−15.3693	−0.577207	−0.288603	−	0.957449i	$-0.593191\pi$
$709$	−15.3693	−0.577207	−0.288603	+	0.957449i	$0.593191\pi$
$710$	−9.06913	−0.340358
$711$	8.00000	0.300023
$712$	−15.3693	−0.575990
$713$	7.12311	0.266762
$714$	5.12311	0.191727
$715$	−4.49242	−0.168007
$716$	−19.9309	−0.744852
$717$	−60.9848	−2.27752
$718$	15.3693	0.573578
$719$	12.2462	0.456707	0.228353	−	0.973578i	$-0.426666\pi$
$719$	12.2462	0.456707	0.228353	+	0.973578i	$0.426666\pi$
$720$	5.56155	0.207267
$721$	−2.87689	−0.107141
$722$	0	0
$723$	10.0691	0.374475
$724$	−17.8078	−0.661820
$725$	−26.2462	−0.974760
$726$	−82.1080	−3.04731
$727$	−48.9848	−1.81675	−0.908374	−	0.418159i	$-0.862675\pi$
$727$	−48.9848	−1.81675	−0.908374	+	0.418159i	$0.862675\pi$
$728$	−0.438447	−0.0162499
$729$	−35.9848	−1.33277
$730$	7.12311	0.263638
$731$	−14.2462	−0.526915
$732$	26.7386	0.988288
$733$	−28.0540	−1.03620	−0.518099	−	0.855321i	$-0.673360\pi$
$733$	−28.0540	−1.03620	−0.518099	+	0.855321i	$0.673360\pi$
$734$	23.3693	0.862577
$735$	−4.00000	−0.147542
$736$	3.56155	0.131281
$737$	−24.1771	−0.890574
$738$	27.3693	1.00748
$739$	18.4233	0.677712	0.338856	−	0.940838i	$-0.389960\pi$
$739$	18.4233	0.677712	0.338856	+	0.940838i	$0.389960\pi$
$740$	1.75379	0.0644706
$741$	0	0
$742$	9.12311	0.334920
$743$	9.42329	0.345707	0.172854	−	0.984948i	$-0.444701\pi$
$743$	9.42329	0.345707	0.172854	+	0.984948i	$0.444701\pi$
$744$	−5.12311	−0.187822
$745$	24.0000	0.879292
$746$	24.8769	0.910808
$747$	−3.56155	−0.130310
$748$	−13.1231	−0.479828
$749$	−3.12311	−0.114116
$750$	30.2462	1.10444
$751$	41.6155	1.51857	0.759286	−	0.650757i	$-0.225548\pi$
$751$	41.6155	1.51857	0.759286	+	0.650757i	$0.225548\pi$
$752$	−7.12311	−0.259753
$753$	−47.0540	−1.71474
$754$	4.49242	0.163604
$755$	5.56155	0.202406
$756$	1.43845	0.0523158
$757$	29.2311	1.06242	0.531210	−	0.847240i	$-0.321737\pi$
$757$	29.2311	1.06242	0.531210	+	0.847240i	$0.321737\pi$
$758$	−29.3693	−1.06674
$759$	59.8617	2.17284
$760$	0	0
$761$	−25.4384	−0.922143	−0.461071	−	0.887363i	$-0.652535\pi$
$761$	−25.4384	−0.922143	−0.461071	+	0.887363i	$0.652535\pi$
$762$	3.36932	0.122057
$763$	−6.24621	−0.226128
$764$	0.192236	0.00695485
$765$	11.1231	0.402157
$766$	32.0000	1.15621
$767$	−4.82292	−0.174146
$768$	−2.56155	−0.0924321
$769$	14.4924	0.522610	0.261305	−	0.965256i	$-0.415847\pi$
$769$	14.4924	0.522610	0.261305	+	0.965256i	$0.415847\pi$
$770$	10.2462	0.369248
$771$	−6.56155	−0.236309
$772$	−1.31534	−0.0473402
$773$	−48.7926	−1.75495	−0.877474	−	0.479624i	$-0.840773\pi$
$773$	−48.7926	−1.75495	−0.877474	+	0.479624i	$0.840773\pi$
$774$	−25.3693	−0.911881
$775$	−5.12311	−0.184027
$776$	−3.43845	−0.123433
$777$	2.87689	0.103208
$778$	−22.7386	−0.815220
$779$	0	0
$780$	−1.75379	−0.0627957
$781$	38.1080	1.36361
$782$	7.12311	0.254722
$783$	−14.7386	−0.526716
$784$	1.00000	0.0357143
$785$	−11.4233	−0.407715
$786$	−28.8078	−1.02754
$787$	36.3693	1.29643	0.648213	−	0.761459i	$-0.275517\pi$
$787$	36.3693	1.29643	0.648213	+	0.761459i	$0.275517\pi$
$788$	−25.6155	−0.912515
$789$	25.7538	0.916859
$790$	3.50758	0.124794
$791$	−17.0000	−0.604450
$792$	−23.3693	−0.830393
$793$	−4.57671	−0.162524
$794$	12.7386	0.452077
$795$	36.4924	1.29425
$796$	−10.0000	−0.354441
$797$	−52.0540	−1.84385	−0.921923	−	0.387373i	$-0.873383\pi$
$797$	−52.0540	−1.84385	−0.921923	+	0.387373i	$0.873383\pi$
$798$	0	0
$799$	−14.2462	−0.503995
$800$	−2.56155	−0.0905646
$801$	−54.7386	−1.93409
$802$	−6.36932	−0.224908
$803$	−29.9309	−1.05624
$804$	−9.43845	−0.332868
$805$	−5.56155	−0.196019
$806$	0.876894	0.0308873
$807$	38.7386	1.36366
$808$	−13.3693	−0.470331
$809$	−35.9848	−1.26516	−0.632580	−	0.774495i	$-0.718004\pi$
$809$	−35.9848	−1.26516	−0.632580	+	0.774495i	$0.718004\pi$
$810$	−10.9309	−0.384072
$811$	−26.7386	−0.938920	−0.469460	−	0.882954i	$-0.655551\pi$
$811$	−26.7386	−0.938920	−0.469460	+	0.882954i	$0.655551\pi$
$812$	−10.2462	−0.359572
$813$	6.73863	0.236334
$814$	−7.36932	−0.258294
$815$	−9.86174	−0.345442
$816$	−5.12311	−0.179345
$817$	0	0
$818$	3.68466	0.128831
$819$	−1.56155	−0.0545651
$820$	12.0000	0.419058
$821$	29.1231	1.01640	0.508202	−	0.861238i	$-0.330310\pi$
$821$	29.1231	1.01640	0.508202	+	0.861238i	$0.330310\pi$
$822$	21.4384	0.747752
$823$	−8.93087	−0.311311	−0.155655	−	0.987811i	$-0.549749\pi$
$823$	−8.93087	−0.311311	−0.155655	+	0.987811i	$0.549749\pi$
$824$	2.87689	0.100221
$825$	−43.0540	−1.49895
$826$	11.0000	0.382739
$827$	11.6847	0.406315	0.203158	−	0.979146i	$-0.434880\pi$
$827$	11.6847	0.406315	0.203158	+	0.979146i	$0.434880\pi$
$828$	12.6847	0.440822
$829$	38.4384	1.33502	0.667511	−	0.744600i	$-0.267360\pi$
$829$	38.4384	1.33502	0.667511	+	0.744600i	$0.267360\pi$
$830$	−1.56155	−0.0542023
$831$	−18.2462	−0.632954
$832$	0.438447	0.0152004
$833$	2.00000	0.0692959
$834$	37.3002	1.29160
$835$	−20.1080	−0.695864
$836$	0	0
$837$	−2.87689	−0.0994400
$838$	32.4924	1.12243
$839$	−4.87689	−0.168369	−0.0841845	−	0.996450i	$-0.526829\pi$
$839$	−4.87689	−0.168369	−0.0841845	+	0.996450i	$0.526829\pi$
$840$	4.00000	0.138013
$841$	75.9848	2.62017
$842$	4.63068	0.159584
$843$	−35.0540	−1.20732
$844$	16.4924	0.567693
$845$	−20.0000	−0.688021
$846$	−25.3693	−0.872215
$847$	−32.0540	−1.10139
$848$	−9.12311	−0.313289
$849$	5.43845	0.186647
$850$	−5.12311	−0.175721
$851$	4.00000	0.137118
$852$	14.8769	0.509674
$853$	33.2311	1.13781	0.568905	−	0.822403i	$-0.307367\pi$
$853$	33.2311	1.13781	0.568905	+	0.822403i	$0.307367\pi$
$854$	10.4384	0.357196
$855$	0	0
$856$	3.12311	0.106746
$857$	30.8078	1.05237	0.526187	−	0.850369i	$-0.323621\pi$
$857$	30.8078	1.05237	0.526187	+	0.850369i	$0.323621\pi$
$858$	7.36932	0.251584
$859$	−35.1922	−1.20074	−0.600372	−	0.799721i	$-0.704981\pi$
$859$	−35.1922	−1.20074	−0.600372	+	0.799721i	$0.704981\pi$
$860$	−11.1231	−0.379295
$861$	19.6847	0.670851
$862$	31.3693	1.06844
$863$	14.8769	0.506415	0.253208	−	0.967412i	$-0.418514\pi$
$863$	14.8769	0.506415	0.253208	+	0.967412i	$0.418514\pi$
$864$	−1.43845	−0.0489370
$865$	−8.30019	−0.282215
$866$	29.6155	1.00638
$867$	33.3002	1.13093
$868$	−2.00000	−0.0678844
$869$	−14.7386	−0.499974
$870$	−40.9848	−1.38952
$871$	1.61553	0.0547401
$872$	6.24621	0.211523
$873$	−12.2462	−0.414471
$874$	0	0
$875$	11.8078	0.399175
$876$	−11.6847	−0.394788
$877$	18.7386	0.632759	0.316379	−	0.948633i	$-0.397533\pi$
$877$	18.7386	0.632759	0.316379	+	0.948633i	$0.397533\pi$
$878$	−28.7386	−0.969882
$879$	−7.50758	−0.253224
$880$	−10.2462	−0.345400
$881$	28.5616	0.962263	0.481132	−	0.876648i	$-0.340226\pi$
$881$	28.5616	0.962263	0.481132	+	0.876648i	$0.340226\pi$
$882$	3.56155	0.119924
$883$	29.1922	0.982397	0.491198	−	0.871048i	$-0.336559\pi$
$883$	29.1922	0.982397	0.491198	+	0.871048i	$0.336559\pi$
$884$	0.876894	0.0294931
$885$	44.0000	1.47904
$886$	−21.0540	−0.707322
$887$	−6.63068	−0.222637	−0.111318	−	0.993785i	$-0.535507\pi$
$887$	−6.63068	−0.222637	−0.111318	+	0.993785i	$0.535507\pi$
$888$	−2.87689	−0.0965423
$889$	1.31534	0.0441151
$890$	−24.0000	−0.804482
$891$	45.9309	1.53874
$892$	−22.4924	−0.753102
$893$	0	0
$894$	−39.3693	−1.31671
$895$	−31.1231	−1.04033
$896$	−1.00000	−0.0334077
$897$	−4.00000	−0.133556
$898$	−27.7386	−0.925650
$899$	20.4924	0.683461
$900$	−9.12311	−0.304104
$901$	−18.2462	−0.607869
$902$	−50.4233	−1.67891
$903$	−18.2462	−0.607196
$904$	17.0000	0.565412
$905$	−27.8078	−0.924361
$906$	−9.12311	−0.303095
$907$	−4.69981	−0.156055	−0.0780274	−	0.996951i	$-0.524862\pi$
$907$	−4.69981	−0.156055	−0.0780274	+	0.996951i	$0.524862\pi$
$908$	−25.7386	−0.854167
$909$	−47.6155	−1.57931
$910$	−0.684658	−0.0226962
$911$	−17.3153	−0.573683	−0.286841	−	0.957978i	$-0.592605\pi$
$911$	−17.3153	−0.573683	−0.286841	+	0.957978i	$0.592605\pi$
$912$	0	0
$913$	6.56155	0.217156
$914$	27.2462	0.901225
$915$	41.7538	1.38034
$916$	−3.80776	−0.125812
$917$	−11.2462	−0.371383
$918$	−2.87689	−0.0949517
$919$	4.93087	0.162654	0.0813272	−	0.996687i	$-0.474084\pi$
$919$	4.93087	0.162654	0.0813272	+	0.996687i	$0.474084\pi$
$920$	5.56155	0.183359
$921$	−7.68466	−0.253218
$922$	33.8078	1.11340
$923$	−2.54640	−0.0838157
$924$	−16.8078	−0.552935
$925$	−2.87689	−0.0945917
$926$	16.4384	0.540201
$927$	10.2462	0.336530
$928$	10.2462	0.336348
$929$	−45.4384	−1.49079	−0.745394	−	0.666625i	$-0.767738\pi$
$929$	−45.4384	−1.49079	−0.745394	+	0.666625i	$0.767738\pi$
$930$	−8.00000	−0.262330
$931$	0	0
$932$	−24.1231	−0.790179
$933$	57.6155	1.88625
$934$	12.8078	0.419083
$935$	−20.4924	−0.670174
$936$	1.56155	0.0510410
$937$	11.3002	0.369161	0.184581	−	0.982817i	$-0.440907\pi$
$937$	11.3002	0.369161	0.184581	+	0.982817i	$0.440907\pi$
$938$	−3.68466	−0.120308
$939$	82.4233	2.68978
$940$	−11.1231	−0.362796
$941$	−43.1771	−1.40753	−0.703766	−	0.710432i	$-0.748500\pi$
$941$	−43.1771	−1.40753	−0.703766	+	0.710432i	$0.748500\pi$
$942$	18.7386	0.610538
$943$	27.3693	0.891268
$944$	−11.0000	−0.358020
$945$	2.24621	0.0730693
$946$	46.7386	1.51960
$947$	7.12311	0.231470	0.115735	−	0.993280i	$-0.463078\pi$
$947$	7.12311	0.231470	0.115735	+	0.993280i	$0.463078\pi$
$948$	−5.75379	−0.186874
$949$	2.00000	0.0649227
$950$	0	0
$951$	−37.1231	−1.20380
$952$	−2.00000	−0.0648204
$953$	44.5616	1.44349	0.721745	−	0.692159i	$-0.243340\pi$
$953$	44.5616	1.44349	0.721745	+	0.692159i	$0.243340\pi$
$954$	−32.4924	−1.05198
$955$	0.300187	0.00971381
$956$	23.8078	0.769998
$957$	172.216	5.56695
$958$	−16.8769	−0.545268
$959$	8.36932	0.270259
$960$	−4.00000	−0.129099
$961$	−27.0000	−0.870968
$962$	0.492423	0.0158763
$963$	11.1231	0.358437
$964$	−3.93087	−0.126605
$965$	−2.05398	−0.0661198
$966$	9.12311	0.293531
$967$	14.6847	0.472227	0.236113	−	0.971726i	$-0.424126\pi$
$967$	14.6847	0.472227	0.236113	+	0.971726i	$0.424126\pi$
$968$	32.0540	1.03025
$969$	0	0
$970$	−5.36932	−0.172398
$971$	−4.50758	−0.144655	−0.0723275	−	0.997381i	$-0.523043\pi$
$971$	−4.50758	−0.144655	−0.0723275	+	0.997381i	$0.523043\pi$
$972$	22.2462	0.713548
$973$	14.5616	0.466822
$974$	39.8617	1.27725
$975$	2.87689	0.0921344
$976$	−10.4384	−0.334127
$977$	30.6155	0.979478	0.489739	−	0.871869i	$-0.337092\pi$
$977$	30.6155	0.979478	0.489739	+	0.871869i	$0.337092\pi$
$978$	16.1771	0.517286
$979$	100.847	3.22307
$980$	1.56155	0.0498820
$981$	22.2462	0.710267
$982$	−10.7386	−0.342684
$983$	−22.6307	−0.721807	−0.360903	−	0.932603i	$-0.617532\pi$
$983$	−22.6307	−0.721807	−0.360903	+	0.932603i	$0.617532\pi$
$984$	−19.6847	−0.627524
$985$	−40.0000	−1.27451
$986$	20.4924	0.652612
$987$	−18.2462	−0.580783
$988$	0	0
$989$	−25.3693	−0.806697
$990$	−36.4924	−1.15981
$991$	16.3002	0.517792	0.258896	−	0.965905i	$-0.416641\pi$
$991$	16.3002	0.517792	0.258896	+	0.965905i	$0.416641\pi$
$992$	2.00000	0.0635001
$993$	12.3153	0.390816
$994$	5.80776	0.184211
$995$	−15.6155	−0.495046
$996$	2.56155	0.0811659
$997$	17.0691	0.540585	0.270292	−	0.962778i	$-0.412880\pi$
$997$	17.0691	0.540585	0.270292	+	0.962778i	$0.412880\pi$
$998$	−18.1771	−0.575385
$999$	−1.61553	−0.0511130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.m.1.1		2
19.8	odd	6		266.2.f.b.197.1	✓	4
19.12	odd	6		266.2.f.b.239.1	yes	4
19.18	odd	2		5054.2.a.h.1.2		2
57.8	even	6		2394.2.o.l.1261.2		4
57.50	even	6		2394.2.o.l.505.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.b.197.1	✓	4	19.8	odd	6
266.2.f.b.239.1	yes	4	19.12	odd	6
2394.2.o.l.505.2		4	57.50	even	6
2394.2.o.l.1261.2		4	57.8	even	6
5054.2.a.h.1.2		2	19.18	odd	2
5054.2.a.m.1.1		2	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.56155 q^{5} -2.56155 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.56155 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.56155 q^{5} -2.56155 q^{6} -1.00000 q^{7} +1.00000 q^{8} +3.56155 q^{9} +1.56155 q^{10} -6.56155 q^{11} -2.56155 q^{12} +0.438447 q^{13} -1.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +3.56155 q^{18} +1.56155 q^{20} +2.56155 q^{21} -6.56155 q^{22} +3.56155 q^{23} -2.56155 q^{24} -2.56155 q^{25} +0.438447 q^{26} -1.43845 q^{27} -1.00000 q^{28} +10.2462 q^{29} -4.00000 q^{30} +2.00000 q^{31} +1.00000 q^{32} +16.8078 q^{33} +2.00000 q^{34} -1.56155 q^{35} +3.56155 q^{36} +1.12311 q^{37} -1.12311 q^{39} +1.56155 q^{40} +7.68466 q^{41} +2.56155 q^{42} -7.12311 q^{43} -6.56155 q^{44} +5.56155 q^{45} +3.56155 q^{46} -7.12311 q^{47} -2.56155 q^{48} +1.00000 q^{49} -2.56155 q^{50} -5.12311 q^{51} +0.438447 q^{52} -9.12311 q^{53} -1.43845 q^{54} -10.2462 q^{55} -1.00000 q^{56} +10.2462 q^{58} -11.0000 q^{59} -4.00000 q^{60} -10.4384 q^{61} +2.00000 q^{62} -3.56155 q^{63} +1.00000 q^{64} +0.684658 q^{65} +16.8078 q^{66} +3.68466 q^{67} +2.00000 q^{68} -9.12311 q^{69} -1.56155 q^{70} -5.80776 q^{71} +3.56155 q^{72} +4.56155 q^{73} +1.12311 q^{74} +6.56155 q^{75} +6.56155 q^{77} -1.12311 q^{78} +2.24621 q^{79} +1.56155 q^{80} -7.00000 q^{81} +7.68466 q^{82} -1.00000 q^{83} +2.56155 q^{84} +3.12311 q^{85} -7.12311 q^{86} -26.2462 q^{87} -6.56155 q^{88} -15.3693 q^{89} +5.56155 q^{90} -0.438447 q^{91} +3.56155 q^{92} -5.12311 q^{93} -7.12311 q^{94} -2.56155 q^{96} -3.43845 q^{97} +1.00000 q^{98} -23.3693 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} - q^{10} - 9 q^{11} - q^{12} + 5 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 4 q^{17} + 3 q^{18} - q^{20} + q^{21} - 9 q^{22} + 3 q^{23} - q^{24} - q^{25} + 5 q^{26} - 7 q^{27} - 2 q^{28} + 4 q^{29} - 8 q^{30} + 4 q^{31} + 2 q^{32} + 13 q^{33} + 4 q^{34} + q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{39} - q^{40} + 3 q^{41} + q^{42} - 6 q^{43} - 9 q^{44} + 7 q^{45} + 3 q^{46} - 6 q^{47} - q^{48} + 2 q^{49} - q^{50} - 2 q^{51} + 5 q^{52} - 10 q^{53} - 7 q^{54} - 4 q^{55} - 2 q^{56} + 4 q^{58} - 22 q^{59} - 8 q^{60} - 25 q^{61} + 4 q^{62} - 3 q^{63} + 2 q^{64} - 11 q^{65} + 13 q^{66} - 5 q^{67} + 4 q^{68} - 10 q^{69} + q^{70} + 9 q^{71} + 3 q^{72} + 5 q^{73} - 6 q^{74} + 9 q^{75} + 9 q^{77} + 6 q^{78} - 12 q^{79} - q^{80} - 14 q^{81} + 3 q^{82} - 2 q^{83} + q^{84} - 2 q^{85} - 6 q^{86} - 36 q^{87} - 9 q^{88} - 6 q^{89} + 7 q^{90} - 5 q^{91} + 3 q^{92} - 2 q^{93} - 6 q^{94} - q^{96} - 11 q^{97} + 2 q^{98} - 22 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 2 * q^7 + 2 * q^8 + 3 * q^9 - q^10 - 9 * q^11 - q^12 + 5 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 4 * q^17 + 3 * q^18 - q^20 + q^21 - 9 * q^22 + 3 * q^23 - q^24 - q^25 + 5 * q^26 - 7 * q^27 - 2 * q^28 + 4 * q^29 - 8 * q^30 + 4 * q^31 + 2 * q^32 + 13 * q^33 + 4 * q^34 + q^35 + 3 * q^36 - 6 * q^37 + 6 * q^39 - q^40 + 3 * q^41 + q^42 - 6 * q^43 - 9 * q^44 + 7 * q^45 + 3 * q^46 - 6 * q^47 - q^48 + 2 * q^49 - q^50 - 2 * q^51 + 5 * q^52 - 10 * q^53 - 7 * q^54 - 4 * q^55 - 2 * q^56 + 4 * q^58 - 22 * q^59 - 8 * q^60 - 25 * q^61 + 4 * q^62 - 3 * q^63 + 2 * q^64 - 11 * q^65 + 13 * q^66 - 5 * q^67 + 4 * q^68 - 10 * q^69 + q^70 + 9 * q^71 + 3 * q^72 + 5 * q^73 - 6 * q^74 + 9 * q^75 + 9 * q^77 + 6 * q^78 - 12 * q^79 - q^80 - 14 * q^81 + 3 * q^82 - 2 * q^83 + q^84 - 2 * q^85 - 6 * q^86 - 36 * q^87 - 9 * q^88 - 6 * q^89 + 7 * q^90 - 5 * q^91 + 3 * q^92 - 2 * q^93 - 6 * q^94 - q^96 - 11 * q^97 + 2 * q^98 - 22 * q^99

Introduction

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Database

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