LMFDB - Embedded newform 2254.2.a.x.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2254,2,Mod(1,2254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2254, 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("2254.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2254 = 2 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2254.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:	$17.9982806156$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 322)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	2254.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.57641 q^{3} +1.00000 q^{4} -1.32664 q^{5} -2.57641 q^{6} +1.00000 q^{8} +3.63791 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.57641 q^{3} +1.00000 q^{4} -1.32664 q^{5} -2.57641 q^{6} +1.00000 q^{8} +3.63791 q^{9} -1.32664 q^{10} +2.09133 q^{11} -2.57641 q^{12} -3.11142 q^{13} +3.41797 q^{15} +1.00000 q^{16} +6.94919 q^{17} +3.63791 q^{18} -7.76653 q^{19} -1.32664 q^{20} +2.09133 q^{22} -1.00000 q^{23} -2.57641 q^{24} -3.24003 q^{25} -3.11142 q^{26} -1.64353 q^{27} +1.15845 q^{29} +3.41797 q^{30} +8.71388 q^{31} +1.00000 q^{32} -5.38814 q^{33} +6.94919 q^{34} +3.63791 q^{36} -3.30944 q^{37} -7.76653 q^{38} +8.01631 q^{39} -1.32664 q^{40} +4.26425 q^{41} -8.36716 q^{43} +2.09133 q^{44} -4.82619 q^{45} -1.00000 q^{46} +3.48130 q^{47} -2.57641 q^{48} -3.24003 q^{50} -17.9040 q^{51} -3.11142 q^{52} +4.24003 q^{53} -1.64353 q^{54} -2.77444 q^{55} +20.0098 q^{57} +1.15845 q^{58} -9.18450 q^{59} +3.41797 q^{60} -12.0387 q^{61} +8.71388 q^{62} +1.00000 q^{64} +4.12772 q^{65} -5.38814 q^{66} -7.26319 q^{67} +6.94919 q^{68} +2.57641 q^{69} -7.41708 q^{71} +3.63791 q^{72} +4.36805 q^{73} -3.30944 q^{74} +8.34767 q^{75} -7.76653 q^{76} +8.01631 q^{78} -0.797250 q^{79} -1.32664 q^{80} -6.67932 q^{81} +4.26425 q^{82} -10.3746 q^{83} -9.21906 q^{85} -8.36716 q^{86} -2.98464 q^{87} +2.09133 q^{88} -16.6426 q^{89} -4.82619 q^{90} -1.00000 q^{92} -22.4506 q^{93} +3.48130 q^{94} +10.3034 q^{95} -2.57641 q^{96} -6.65800 q^{97} +7.60808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9} - 7 q^{10} + 2 q^{11} - 3 q^{12} - q^{13} + 9 q^{15} + 4 q^{16} - 5 q^{17} - q^{18} - 11 q^{19} - 7 q^{20} + 2 q^{22} - 4 q^{23} - 3 q^{24} + 3 q^{25} - q^{26} - 3 q^{27} + 2 q^{29} + 9 q^{30} - 6 q^{31} + 4 q^{32} - 15 q^{33} - 5 q^{34} - q^{36} - 8 q^{37} - 11 q^{38} + 3 q^{39} - 7 q^{40} - 9 q^{41} + 4 q^{43} + 2 q^{44} - 3 q^{45} - 4 q^{46} - 11 q^{47} - 3 q^{48} + 3 q^{50} - 18 q^{51} - q^{52} + q^{53} - 3 q^{54} - 10 q^{55} + 3 q^{57} + 2 q^{58} - 12 q^{59} + 9 q^{60} - 21 q^{61} - 6 q^{62} + 4 q^{64} - 24 q^{65} - 15 q^{66} - 3 q^{67} - 5 q^{68} + 3 q^{69} + 11 q^{71} - q^{72} + 16 q^{73} - 8 q^{74} - 18 q^{75} - 11 q^{76} + 3 q^{78} - 21 q^{79} - 7 q^{80} - 8 q^{81} - 9 q^{82} - 4 q^{83} + 10 q^{85} + 4 q^{86} + 7 q^{87} + 2 q^{88} - 27 q^{89} - 3 q^{90} - 4 q^{92} - 27 q^{93} - 11 q^{94} + 5 q^{95} - 3 q^{96} - 6 q^{97} + 13 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9 - 7 * q^10 + 2 * q^11 - 3 * q^12 - q^13 + 9 * q^15 + 4 * q^16 - 5 * q^17 - q^18 - 11 * q^19 - 7 * q^20 + 2 * q^22 - 4 * q^23 - 3 * q^24 + 3 * q^25 - q^26 - 3 * q^27 + 2 * q^29 + 9 * q^30 - 6 * q^31 + 4 * q^32 - 15 * q^33 - 5 * q^34 - q^36 - 8 * q^37 - 11 * q^38 + 3 * q^39 - 7 * q^40 - 9 * q^41 + 4 * q^43 + 2 * q^44 - 3 * q^45 - 4 * q^46 - 11 * q^47 - 3 * q^48 + 3 * q^50 - 18 * q^51 - q^52 + q^53 - 3 * q^54 - 10 * q^55 + 3 * q^57 + 2 * q^58 - 12 * q^59 + 9 * q^60 - 21 * q^61 - 6 * q^62 + 4 * q^64 - 24 * q^65 - 15 * q^66 - 3 * q^67 - 5 * q^68 + 3 * q^69 + 11 * q^71 - q^72 + 16 * q^73 - 8 * q^74 - 18 * q^75 - 11 * q^76 + 3 * q^78 - 21 * q^79 - 7 * q^80 - 8 * q^81 - 9 * q^82 - 4 * q^83 + 10 * q^85 + 4 * q^86 + 7 * q^87 + 2 * q^88 - 27 * q^89 - 3 * q^90 - 4 * q^92 - 27 * q^93 - 11 * q^94 + 5 * q^95 - 3 * q^96 - 6 * q^97 + 13 * 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
$3$	−2.57641	−1.48749	−0.743747	−	0.668461i	$-0.766953\pi$
$3$	−2.57641	−1.48749	−0.743747	+	0.668461i	$0.766953\pi$
$4$	1.00000	0.500000
$5$	−1.32664	−0.593290	−0.296645	−	0.954988i	$-0.595868\pi$
$5$	−1.32664	−0.593290	−0.296645	+	0.954988i	$0.595868\pi$
$6$	−2.57641	−1.05182
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	3.63791	1.21264
$10$	−1.32664	−0.419520
$11$	2.09133	0.630560	0.315280	−	0.948999i	$-0.397902\pi$
$11$	2.09133	0.630560	0.315280	+	0.948999i	$0.397902\pi$
$12$	−2.57641	−0.743747
$13$	−3.11142	−0.862952	−0.431476	−	0.902124i	$-0.642007\pi$
$13$	−3.11142	−0.862952	−0.431476	+	0.902124i	$0.642007\pi$
$14$	0	0
$15$	3.41797	0.882516
$16$	1.00000	0.250000
$17$	6.94919	1.68543	0.842713	−	0.538363i	$-0.180957\pi$
$17$	6.94919	1.68543	0.842713	+	0.538363i	$0.180957\pi$
$18$	3.63791	0.857464
$19$	−7.76653	−1.78176	−0.890882	−	0.454235i	$-0.849913\pi$
$19$	−7.76653	−1.78176	−0.890882	+	0.454235i	$0.849913\pi$
$20$	−1.32664	−0.296645
$21$	0	0
$22$	2.09133	0.445873
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.57641	−0.525908
$25$	−3.24003	−0.648007
$26$	−3.11142	−0.610199
$27$	−1.64353	−0.316298
$28$	0	0
$29$	1.15845	0.215118	0.107559	−	0.994199i	$-0.465697\pi$
$29$	1.15845	0.215118	0.107559	+	0.994199i	$0.465697\pi$
$30$	3.41797	0.624033
$31$	8.71388	1.56506	0.782530	−	0.622613i	$-0.213929\pi$
$31$	8.71388	1.56506	0.782530	+	0.622613i	$0.213929\pi$
$32$	1.00000	0.176777
$33$	−5.38814	−0.937954
$34$	6.94919	1.19178
$35$	0	0
$36$	3.63791	0.606319
$37$	−3.30944	−0.544069	−0.272034	−	0.962288i	$-0.587696\pi$
$37$	−3.30944	−0.544069	−0.272034	+	0.962288i	$0.587696\pi$
$38$	−7.76653	−1.25990
$39$	8.01631	1.28364
$40$	−1.32664	−0.209760
$41$	4.26425	0.665964	0.332982	−	0.942933i	$-0.391945\pi$
$41$	4.26425	0.665964	0.332982	+	0.942933i	$0.391945\pi$
$42$	0	0
$43$	−8.36716	−1.27598	−0.637990	−	0.770045i	$-0.720234\pi$
$43$	−8.36716	−1.27598	−0.637990	+	0.770045i	$0.720234\pi$
$44$	2.09133	0.315280
$45$	−4.82619	−0.719446
$46$	−1.00000	−0.147442
$47$	3.48130	0.507800	0.253900	−	0.967230i	$-0.418287\pi$
$47$	3.48130	0.507800	0.253900	+	0.967230i	$0.418287\pi$
$48$	−2.57641	−0.371873
$49$	0	0
$50$	−3.24003	−0.458210
$51$	−17.9040	−2.50706
$52$	−3.11142	−0.431476
$53$	4.24003	0.582413	0.291207	−	0.956660i	$-0.405943\pi$
$53$	4.24003	0.582413	0.291207	+	0.956660i	$0.405943\pi$
$54$	−1.64353	−0.223656
$55$	−2.77444	−0.374105
$56$	0	0
$57$	20.0098	2.65036
$58$	1.15845	0.152111
$59$	−9.18450	−1.19572	−0.597860	−	0.801601i	$-0.703982\pi$
$59$	−9.18450	−1.19572	−0.597860	+	0.801601i	$0.703982\pi$
$60$	3.41797	0.441258
$61$	−12.0387	−1.54140	−0.770698	−	0.637201i	$-0.780092\pi$
$61$	−12.0387	−1.54140	−0.770698	+	0.637201i	$0.780092\pi$
$62$	8.71388	1.10666
$63$	0	0
$64$	1.00000	0.125000
$65$	4.12772	0.511981
$66$	−5.38814	−0.663234
$67$	−7.26319	−0.887340	−0.443670	−	0.896190i	$-0.646324\pi$
$67$	−7.26319	−0.887340	−0.443670	+	0.896190i	$0.646324\pi$
$68$	6.94919	0.842713
$69$	2.57641	0.310164
$70$	0	0
$71$	−7.41708	−0.880245	−0.440123	−	0.897938i	$-0.645065\pi$
$71$	−7.41708	−0.880245	−0.440123	+	0.897938i	$0.645065\pi$
$72$	3.63791	0.428732
$73$	4.36805	0.511241	0.255621	−	0.966777i	$-0.417720\pi$
$73$	4.36805	0.511241	0.255621	+	0.966777i	$0.417720\pi$
$74$	−3.30944	−0.384715
$75$	8.34767	0.963906
$76$	−7.76653	−0.890882
$77$	0	0
$78$	8.01631	0.907668
$79$	−0.797250	−0.0896977	−0.0448488	−	0.998994i	$-0.514281\pi$
$79$	−0.797250	−0.0896977	−0.0448488	+	0.998994i	$0.514281\pi$
$80$	−1.32664	−0.148323
$81$	−6.67932	−0.742147
$82$	4.26425	0.470907
$83$	−10.3746	−1.13876	−0.569381	−	0.822074i	$-0.692817\pi$
$83$	−10.3746	−1.13876	−0.569381	+	0.822074i	$0.692817\pi$
$84$	0	0
$85$	−9.21906	−0.999947
$86$	−8.36716	−0.902254
$87$	−2.98464	−0.319987
$88$	2.09133	0.222937
$89$	−16.6426	−1.76412	−0.882058	−	0.471140i	$-0.843842\pi$
$89$	−16.6426	−1.76412	−0.882058	+	0.471140i	$0.843842\pi$
$90$	−4.82619	−0.508725
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−22.4506	−2.32802
$94$	3.48130	0.359069
$95$	10.3034	1.05710
$96$	−2.57641	−0.262954
$97$	−6.65800	−0.676018	−0.338009	−	0.941143i	$-0.609753\pi$
$97$	−6.65800	−0.676018	−0.338009	+	0.941143i	$0.609753\pi$
$98$	0	0
$99$	7.60808	0.764641
$100$	−3.24003	−0.324003
$101$	−9.15879	−0.911334	−0.455667	−	0.890150i	$-0.650599\pi$
$101$	−9.15879	−0.911334	−0.455667	+	0.890150i	$0.650599\pi$
$102$	−17.9040	−1.77276
$103$	−4.53211	−0.446562	−0.223281	−	0.974754i	$-0.571677\pi$
$103$	−4.53211	−0.446562	−0.223281	+	0.974754i	$0.571677\pi$
$104$	−3.11142	−0.305100
$105$	0	0
$106$	4.24003	0.411828
$107$	−12.3344	−1.19241	−0.596207	−	0.802830i	$-0.703326\pi$
$107$	−12.3344	−1.19241	−0.596207	+	0.802830i	$0.703326\pi$
$108$	−1.64353	−0.158149
$109$	−1.09984	−0.105346	−0.0526728	−	0.998612i	$-0.516774\pi$
$109$	−1.09984	−0.105346	−0.0526728	+	0.998612i	$0.516774\pi$
$110$	−2.77444	−0.264532
$111$	8.52649	0.809299
$112$	0	0
$113$	4.44278	0.417942	0.208971	−	0.977922i	$-0.432989\pi$
$113$	4.44278	0.417942	0.208971	+	0.977922i	$0.432989\pi$
$114$	20.0098	1.87409
$115$	1.32664	0.123710
$116$	1.15845	0.107559
$117$	−11.3191	−1.04645
$118$	−9.18450	−0.845501
$119$	0	0
$120$	3.41797	0.312016
$121$	−6.62633	−0.602394
$122$	−12.0387	−1.08993
$123$	−10.9865	−0.990617
$124$	8.71388	0.782530
$125$	10.9315	0.977746
$126$	0	0
$127$	2.41201	0.214031	0.107015	−	0.994257i	$-0.465871\pi$
$127$	2.41201	0.214031	0.107015	+	0.994257i	$0.465871\pi$
$128$	1.00000	0.0883883
$129$	21.5573	1.89801
$130$	4.12772	0.362025
$131$	−1.52342	−0.133102	−0.0665511	−	0.997783i	$-0.521200\pi$
$131$	−1.52342	−0.133102	−0.0665511	+	0.997783i	$0.521200\pi$
$132$	−5.38814	−0.468977
$133$	0	0
$134$	−7.26319	−0.627444
$135$	2.18037	0.187656
$136$	6.94919	0.595888
$137$	9.62668	0.822463	0.411231	−	0.911531i	$-0.365099\pi$
$137$	9.62668	0.822463	0.411231	+	0.911531i	$0.365099\pi$
$138$	2.57641	0.219319
$139$	−8.57676	−0.727471	−0.363736	−	0.931502i	$-0.618499\pi$
$139$	−8.57676	−0.727471	−0.363736	+	0.931502i	$0.618499\pi$
$140$	0	0
$141$	−8.96928	−0.755349
$142$	−7.41708	−0.622427
$143$	−6.50701	−0.544143
$144$	3.63791	0.303159
$145$	−1.53684	−0.127627
$146$	4.36805	0.361502
$147$	0	0
$148$	−3.30944	−0.272034
$149$	16.0214	1.31252	0.656261	−	0.754534i	$-0.272137\pi$
$149$	16.0214	1.31252	0.656261	+	0.754534i	$0.272137\pi$
$150$	8.34767	0.681584
$151$	−13.9358	−1.13408	−0.567039	−	0.823691i	$-0.691911\pi$
$151$	−13.9358	−1.13408	−0.567039	+	0.823691i	$0.691911\pi$
$152$	−7.76653	−0.629949
$153$	25.2806	2.04381
$154$	0	0
$155$	−11.5602	−0.928535
$156$	8.01631	0.641818
$157$	15.4227	1.23087	0.615433	−	0.788190i	$-0.288981\pi$
$157$	15.4227	1.23087	0.615433	+	0.788190i	$0.288981\pi$
$158$	−0.797250	−0.0634258
$159$	−10.9241	−0.866336
$160$	−1.32664	−0.104880
$161$	0	0
$162$	−6.67932	−0.524777
$163$	−8.61387	−0.674690	−0.337345	−	0.941381i	$-0.609529\pi$
$163$	−8.61387	−0.674690	−0.337345	+	0.941381i	$0.609529\pi$
$164$	4.26425	0.332982
$165$	7.14810	0.556479
$166$	−10.3746	−0.805226
$167$	−11.9693	−0.926211	−0.463105	−	0.886303i	$-0.653265\pi$
$167$	−11.9693	−0.926211	−0.463105	+	0.886303i	$0.653265\pi$
$168$	0	0
$169$	−3.31907	−0.255313
$170$	−9.21906	−0.707069
$171$	−28.2540	−2.16063
$172$	−8.36716	−0.637990
$173$	19.8197	1.50686	0.753431	−	0.657527i	$-0.228397\pi$
$173$	19.8197	1.50686	0.753431	+	0.657527i	$0.228397\pi$
$174$	−2.98464	−0.226265
$175$	0	0
$176$	2.09133	0.157640
$177$	23.6631	1.77863
$178$	−16.6426	−1.24742
$179$	−16.4096	−1.22651	−0.613257	−	0.789884i	$-0.710141\pi$
$179$	−16.4096	−1.22651	−0.613257	+	0.789884i	$0.710141\pi$
$180$	−4.82619	−0.359723
$181$	11.2306	0.834766	0.417383	−	0.908731i	$-0.362947\pi$
$181$	11.2306	0.834766	0.417383	+	0.908731i	$0.362947\pi$
$182$	0	0
$183$	31.0167	2.29282
$184$	−1.00000	−0.0737210
$185$	4.39043	0.322791
$186$	−22.4506	−1.64616
$187$	14.5331	1.06276
$188$	3.48130	0.253900
$189$	0	0
$190$	10.3034	0.747485
$191$	6.36805	0.460776	0.230388	−	0.973099i	$-0.426000\pi$
$191$	6.36805	0.460776	0.230388	+	0.973099i	$0.426000\pi$
$192$	−2.57641	−0.185937
$193$	−14.0550	−1.01170	−0.505850	−	0.862621i	$-0.668821\pi$
$193$	−14.0550	−1.01170	−0.505850	+	0.862621i	$0.668821\pi$
$194$	−6.65800	−0.478017
$195$	−10.6347	−0.761569
$196$	0	0
$197$	−6.95570	−0.495573	−0.247786	−	0.968815i	$-0.579703\pi$
$197$	−6.95570	−0.495573	−0.247786	+	0.968815i	$0.579703\pi$
$198$	7.60808	0.540683
$199$	−21.0897	−1.49501	−0.747506	−	0.664255i	$-0.768749\pi$
$199$	−21.0897	−1.49501	−0.747506	+	0.664255i	$0.768749\pi$
$200$	−3.24003	−0.229105
$201$	18.7130	1.31991
$202$	−9.15879	−0.644410
$203$	0	0
$204$	−17.9040	−1.25353
$205$	−5.65711	−0.395110
$206$	−4.53211	−0.315767
$207$	−3.63791	−0.252852
$208$	−3.11142	−0.215738
$209$	−16.2424	−1.12351
$210$	0	0
$211$	26.5036	1.82458	0.912290	−	0.409544i	$-0.134312\pi$
$211$	26.5036	1.82458	0.912290	+	0.409544i	$0.134312\pi$
$212$	4.24003	0.291207
$213$	19.1095	1.30936
$214$	−12.3344	−0.843165
$215$	11.1002	0.757026
$216$	−1.64353	−0.111828
$217$	0	0
$218$	−1.09984	−0.0744906
$219$	−11.2539	−0.760468
$220$	−2.77444	−0.187053
$221$	−21.6218	−1.45444
$222$	8.52649	0.572261
$223$	9.80109	0.656329	0.328165	−	0.944621i	$-0.393570\pi$
$223$	9.80109	0.656329	0.328165	+	0.944621i	$0.393570\pi$
$224$	0	0
$225$	−11.7870	−0.785797
$226$	4.44278	0.295530
$227$	28.4962	1.89136	0.945679	−	0.325103i	$-0.105399\pi$
$227$	28.4962	1.89136	0.945679	+	0.325103i	$0.105399\pi$
$228$	20.0098	1.32518
$229$	25.1914	1.66469	0.832347	−	0.554254i	$-0.186996\pi$
$229$	25.1914	1.66469	0.832347	+	0.554254i	$0.186996\pi$
$230$	1.32664	0.0874759
$231$	0	0
$232$	1.15845	0.0760557
$233$	−13.1625	−0.862302	−0.431151	−	0.902280i	$-0.641892\pi$
$233$	−13.1625	−0.862302	−0.431151	+	0.902280i	$0.641892\pi$
$234$	−11.3191	−0.739951
$235$	−4.61843	−0.301273
$236$	−9.18450	−0.597860
$237$	2.05405	0.133425
$238$	0	0
$239$	−8.78283	−0.568114	−0.284057	−	0.958807i	$-0.591681\pi$
$239$	−8.78283	−0.568114	−0.284057	+	0.958807i	$0.591681\pi$
$240$	3.41797	0.220629
$241$	−1.52755	−0.0983983	−0.0491992	−	0.998789i	$-0.515667\pi$
$241$	−1.52755	−0.0983983	−0.0491992	+	0.998789i	$0.515667\pi$
$242$	−6.62633	−0.425957
$243$	22.1393	1.42024
$244$	−12.0387	−0.770698
$245$	0	0
$246$	−10.9865	−0.700472
$247$	24.1649	1.53758
$248$	8.71388	0.553332
$249$	26.7293	1.69390
$250$	10.9315	0.691371
$251$	−1.04230	−0.0657895	−0.0328947	−	0.999459i	$-0.510473\pi$
$251$	−1.04230	−0.0657895	−0.0328947	+	0.999459i	$0.510473\pi$
$252$	0	0
$253$	−2.09133	−0.131481
$254$	2.41201	0.151343
$255$	23.7521	1.48741
$256$	1.00000	0.0625000
$257$	6.77409	0.422556	0.211278	−	0.977426i	$-0.432237\pi$
$257$	6.77409	0.422556	0.211278	+	0.977426i	$0.432237\pi$
$258$	21.5573	1.34210
$259$	0	0
$260$	4.12772	0.255991
$261$	4.21433	0.260860
$262$	−1.52342	−0.0941175
$263$	0.457086	0.0281852	0.0140926	−	0.999901i	$-0.495514\pi$
$263$	0.457086	0.0281852	0.0140926	+	0.999901i	$0.495514\pi$
$264$	−5.38814	−0.331617
$265$	−5.62499	−0.345540
$266$	0	0
$267$	42.8783	2.62411
$268$	−7.26319	−0.443670
$269$	−18.5535	−1.13123	−0.565613	−	0.824671i	$-0.691360\pi$
$269$	−18.5535	−1.13123	−0.565613	+	0.824671i	$0.691360\pi$
$270$	2.18037	0.132693
$271$	−18.2909	−1.11109	−0.555546	−	0.831485i	$-0.687491\pi$
$271$	−18.2909	−1.11109	−0.555546	+	0.831485i	$0.687491\pi$
$272$	6.94919	0.421357
$273$	0	0
$274$	9.62668	0.581569
$275$	−6.77598	−0.408607
$276$	2.57641	0.155082
$277$	20.1567	1.21110	0.605548	−	0.795809i	$-0.292954\pi$
$277$	20.1567	1.21110	0.605548	+	0.795809i	$0.292954\pi$
$278$	−8.57676	−0.514400
$279$	31.7004	1.89785
$280$	0	0
$281$	−7.27365	−0.433909	−0.216955	−	0.976182i	$-0.569612\pi$
$281$	−7.27365	−0.433909	−0.216955	+	0.976182i	$0.569612\pi$
$282$	−8.96928	−0.534113
$283$	2.76240	0.164208	0.0821038	−	0.996624i	$-0.473836\pi$
$283$	2.76240	0.164208	0.0821038	+	0.996624i	$0.473836\pi$
$284$	−7.41708	−0.440123
$285$	−26.5457	−1.57243
$286$	−6.50701	−0.384767
$287$	0	0
$288$	3.63791	0.214366
$289$	31.2912	1.84066
$290$	−1.53684	−0.0902463
$291$	17.1538	1.00557
$292$	4.36805	0.255621
$293$	−25.3756	−1.48246	−0.741228	−	0.671253i	$-0.765756\pi$
$293$	−25.3756	−1.48246	−0.741228	+	0.671253i	$0.765756\pi$
$294$	0	0
$295$	12.1845	0.709409
$296$	−3.30944	−0.192357
$297$	−3.43717	−0.199445
$298$	16.0214	0.928094
$299$	3.11142	0.179938
$300$	8.34767	0.481953
$301$	0	0
$302$	−13.9358	−0.801914
$303$	23.5968	1.35560
$304$	−7.76653	−0.445441
$305$	15.9710	0.914495
$306$	25.2806	1.44519
$307$	29.2469	1.66921	0.834606	−	0.550848i	$-0.185696\pi$
$307$	29.2469	1.66921	0.834606	+	0.550848i	$0.185696\pi$
$308$	0	0
$309$	11.6766	0.664259
$310$	−11.5602	−0.656573
$311$	−27.2828	−1.54707	−0.773534	−	0.633755i	$-0.781513\pi$
$311$	−27.2828	−1.54707	−0.773534	+	0.633755i	$0.781513\pi$
$312$	8.01631	0.453834
$313$	−2.57676	−0.145647	−0.0728236	−	0.997345i	$-0.523201\pi$
$313$	−2.57676	−0.145647	−0.0728236	+	0.997345i	$0.523201\pi$
$314$	15.4227	0.870353
$315$	0	0
$316$	−0.797250	−0.0448488
$317$	−12.5065	−0.702433	−0.351216	−	0.936294i	$-0.614232\pi$
$317$	−12.5065	−0.702433	−0.351216	+	0.936294i	$0.614232\pi$
$318$	−10.9241	−0.612592
$319$	2.42270	0.135645
$320$	−1.32664	−0.0741613
$321$	31.7786	1.77371
$322$	0	0
$323$	−53.9711	−3.00303
$324$	−6.67932	−0.371074
$325$	10.0811	0.559199
$326$	−8.61387	−0.477078
$327$	2.83364	0.156701
$328$	4.26425	0.235454
$329$	0	0
$330$	7.14810	0.393490
$331$	2.73397	0.150273	0.0751363	−	0.997173i	$-0.476061\pi$
$331$	2.73397	0.150273	0.0751363	+	0.997173i	$0.476061\pi$
$332$	−10.3746	−0.569381
$333$	−12.0395	−0.659759
$334$	−11.9693	−0.654930
$335$	9.63562	0.526450
$336$	0	0
$337$	12.4355	0.677405	0.338703	−	0.940893i	$-0.390012\pi$
$337$	12.4355	0.677405	0.338703	+	0.940893i	$0.390012\pi$
$338$	−3.31907	−0.180534
$339$	−11.4465	−0.621686
$340$	−9.21906	−0.499973
$341$	18.2236	0.986864
$342$	−28.2540	−1.52780
$343$	0	0
$344$	−8.36716	−0.451127
$345$	−3.41797	−0.184017
$346$	19.8197	1.06551
$347$	2.20748	0.118504	0.0592518	−	0.998243i	$-0.481129\pi$
$347$	2.20748	0.118504	0.0592518	+	0.998243i	$0.481129\pi$
$348$	−2.98464	−0.159993
$349$	−10.7710	−0.576558	−0.288279	−	0.957546i	$-0.593083\pi$
$349$	−10.7710	−0.576558	−0.288279	+	0.957546i	$0.593083\pi$
$350$	0	0
$351$	5.11371	0.272950
$352$	2.09133	0.111468
$353$	13.8970	0.739661	0.369831	−	0.929099i	$-0.379416\pi$
$353$	13.8970	0.739661	0.369831	+	0.929099i	$0.379416\pi$
$354$	23.6631	1.25768
$355$	9.83977	0.522241
$356$	−16.6426	−0.882058
$357$	0	0
$358$	−16.4096	−0.867276
$359$	−19.4670	−1.02743	−0.513714	−	0.857961i	$-0.671731\pi$
$359$	−19.4670	−1.02743	−0.513714	+	0.857961i	$0.671731\pi$
$360$	−4.82619	−0.254363
$361$	41.3190	2.17468
$362$	11.2306	0.590269
$363$	17.0722	0.896057
$364$	0	0
$365$	−5.79482	−0.303315
$366$	31.0167	1.62127
$367$	−17.1874	−0.897174	−0.448587	−	0.893739i	$-0.648073\pi$
$367$	−17.1874	−0.897174	−0.448587	+	0.893739i	$0.648073\pi$
$368$	−1.00000	−0.0521286
$369$	15.5130	0.807573
$370$	4.39043	0.228248
$371$	0	0
$372$	−22.4506	−1.16401
$373$	−9.43657	−0.488607	−0.244303	−	0.969699i	$-0.578559\pi$
$373$	−9.43657	−0.488607	−0.244303	+	0.969699i	$0.578559\pi$
$374$	14.5331	0.751486
$375$	−28.1642	−1.45439
$376$	3.48130	0.179534
$377$	−3.60441	−0.185637
$378$	0	0
$379$	6.99131	0.359120	0.179560	−	0.983747i	$-0.442533\pi$
$379$	6.99131	0.359120	0.179560	+	0.983747i	$0.442533\pi$
$380$	10.3034	0.528552
$381$	−6.21433	−0.318370
$382$	6.36805	0.325818
$383$	−27.5410	−1.40728	−0.703640	−	0.710556i	$-0.748443\pi$
$383$	−27.5410	−1.40728	−0.703640	+	0.710556i	$0.748443\pi$
$384$	−2.57641	−0.131477
$385$	0	0
$386$	−14.0550	−0.715380
$387$	−30.4390	−1.54730
$388$	−6.65800	−0.338009
$389$	6.70443	0.339928	0.169964	−	0.985450i	$-0.445635\pi$
$389$	6.70443	0.339928	0.169964	+	0.985450i	$0.445635\pi$
$390$	−10.6347	−0.538511
$391$	−6.94919	−0.351436
$392$	0	0
$393$	3.92497	0.197989
$394$	−6.95570	−0.350423
$395$	1.05766	0.0532168
$396$	7.60808	0.382320
$397$	−22.6052	−1.13452	−0.567262	−	0.823537i	$-0.691997\pi$
$397$	−22.6052	−1.13452	−0.567262	+	0.823537i	$0.691997\pi$
$398$	−21.0897	−1.05713
$399$	0	0
$400$	−3.24003	−0.162002
$401$	−9.70827	−0.484808	−0.242404	−	0.970175i	$-0.577936\pi$
$401$	−9.70827	−0.484808	−0.242404	+	0.970175i	$0.577936\pi$
$402$	18.7130	0.933319
$403$	−27.1125	−1.35057
$404$	−9.15879	−0.455667
$405$	8.86104	0.440309
$406$	0	0
$407$	−6.92114	−0.343068
$408$	−17.9040	−0.886380
$409$	36.3360	1.79670	0.898350	−	0.439281i	$-0.144767\pi$
$409$	36.3360	1.79670	0.898350	+	0.439281i	$0.144767\pi$
$410$	−5.65711	−0.279385
$411$	−24.8023	−1.22341
$412$	−4.53211	−0.223281
$413$	0	0
$414$	−3.63791	−0.178794
$415$	13.7633	0.675616
$416$	−3.11142	−0.152550
$417$	22.0973	1.08211
$418$	−16.2424	−0.794441
$419$	−9.98642	−0.487868	−0.243934	−	0.969792i	$-0.578438\pi$
$419$	−9.98642	−0.487868	−0.243934	+	0.969792i	$0.578438\pi$
$420$	0	0
$421$	14.1053	0.687448	0.343724	−	0.939071i	$-0.388312\pi$
$421$	14.1053	0.687448	0.343724	+	0.939071i	$0.388312\pi$
$422$	26.5036	1.29017
$423$	12.6647	0.615778
$424$	4.24003	0.205914
$425$	−22.5156	−1.09217
$426$	19.1095	0.925857
$427$	0	0
$428$	−12.3344	−0.596207
$429$	16.7647	0.809410
$430$	11.1002	0.535298
$431$	−3.54369	−0.170694	−0.0853468	−	0.996351i	$-0.527200\pi$
$431$	−3.54369	−0.170694	−0.0853468	+	0.996351i	$0.527200\pi$
$432$	−1.64353	−0.0790744
$433$	16.2680	0.781792	0.390896	−	0.920435i	$-0.372165\pi$
$433$	16.2680	0.781792	0.390896	+	0.920435i	$0.372165\pi$
$434$	0	0
$435$	3.95953	0.189845
$436$	−1.09984	−0.0526728
$437$	7.76653	0.371523
$438$	−11.2539	−0.537732
$439$	−1.17003	−0.0558423	−0.0279211	−	0.999610i	$-0.508889\pi$
$439$	−1.17003	−0.0558423	−0.0279211	+	0.999610i	$0.508889\pi$
$440$	−2.77444	−0.132266
$441$	0	0
$442$	−21.6218	−1.02845
$443$	39.0073	1.85329	0.926647	−	0.375934i	$-0.122678\pi$
$443$	39.0073	1.85329	0.926647	+	0.375934i	$0.122678\pi$
$444$	8.52649	0.404650
$445$	22.0787	1.04663
$446$	9.80109	0.464095
$447$	−41.2777	−1.95237
$448$	0	0
$449$	32.1714	1.51826	0.759130	−	0.650939i	$-0.225624\pi$
$449$	32.1714	1.51826	0.759130	+	0.650939i	$0.225624\pi$
$450$	−11.7870	−0.555643
$451$	8.91796	0.419930
$452$	4.44278	0.208971
$453$	35.9043	1.68693
$454$	28.4962	1.33739
$455$	0	0
$456$	20.0098	0.937045
$457$	−34.3548	−1.60705	−0.803524	−	0.595273i	$-0.797044\pi$
$457$	−34.3548	−1.60705	−0.803524	+	0.595273i	$0.797044\pi$
$458$	25.1914	1.17712
$459$	−11.4212	−0.533096
$460$	1.32664	0.0618548
$461$	−10.5155	−0.489756	−0.244878	−	0.969554i	$-0.578748\pi$
$461$	−10.5155	−0.489756	−0.244878	+	0.969554i	$0.578748\pi$
$462$	0	0
$463$	−19.9943	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$463$	−19.9943	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$464$	1.15845	0.0537795
$465$	29.7838	1.38119
$466$	−13.1625	−0.609739
$467$	27.4643	1.27090	0.635448	−	0.772144i	$-0.280816\pi$
$467$	27.4643	1.27090	0.635448	+	0.772144i	$0.280816\pi$
$468$	−11.3191	−0.523224
$469$	0	0
$470$	−4.61843	−0.213032
$471$	−39.7353	−1.83090
$472$	−9.18450	−0.422751
$473$	−17.4985	−0.804582
$474$	2.05405	0.0943455
$475$	25.1638	1.15459
$476$	0	0
$477$	15.4249	0.706257
$478$	−8.78283	−0.401717
$479$	8.44551	0.385885	0.192943	−	0.981210i	$-0.438197\pi$
$479$	8.44551	0.385885	0.192943	+	0.981210i	$0.438197\pi$
$480$	3.41797	0.156008
$481$	10.2971	0.469505
$482$	−1.52755	−0.0695781
$483$	0	0
$484$	−6.62633	−0.301197
$485$	8.83275	0.401075
$486$	22.1393	1.00426
$487$	33.2791	1.50802	0.754009	−	0.656864i	$-0.228117\pi$
$487$	33.2791	1.50802	0.754009	+	0.656864i	$0.228117\pi$
$488$	−12.0387	−0.544966
$489$	22.1929	1.00360
$490$	0	0
$491$	15.8532	0.715444	0.357722	−	0.933828i	$-0.383553\pi$
$491$	15.8532	0.715444	0.357722	+	0.933828i	$0.383553\pi$
$492$	−10.9865	−0.495308
$493$	8.05027	0.362566
$494$	24.1649	1.08723
$495$	−10.0932	−0.453654
$496$	8.71388	0.391265
$497$	0	0
$498$	26.7293	1.19777
$499$	−19.3323	−0.865433	−0.432717	−	0.901530i	$-0.642445\pi$
$499$	−19.3323	−0.865433	−0.432717	+	0.901530i	$0.642445\pi$
$500$	10.9315	0.488873
$501$	30.8378	1.37773
$502$	−1.04230	−0.0465202
$503$	−40.9220	−1.82462	−0.912310	−	0.409500i	$-0.865703\pi$
$503$	−40.9220	−1.82462	−0.912310	+	0.409500i	$0.865703\pi$
$504$	0	0
$505$	12.1504	0.540686
$506$	−2.09133	−0.0929710
$507$	8.55131	0.379777
$508$	2.41201	0.107015
$509$	−0.521823	−0.0231294	−0.0115647	−	0.999933i	$-0.503681\pi$
$509$	−0.521823	−0.0231294	−0.0115647	+	0.999933i	$0.503681\pi$
$510$	23.7521	1.05176
$511$	0	0
$512$	1.00000	0.0441942
$513$	12.7645	0.563568
$514$	6.77409	0.298792
$515$	6.01247	0.264941
$516$	21.5573	0.949006
$517$	7.28055	0.320198
$518$	0	0
$519$	−51.0637	−2.24145
$520$	4.12772	0.181013
$521$	−12.2977	−0.538774	−0.269387	−	0.963032i	$-0.586821\pi$
$521$	−12.2977	−0.538774	−0.269387	+	0.963032i	$0.586821\pi$
$522$	4.21433	0.184456
$523$	−31.3781	−1.37207	−0.686034	−	0.727569i	$-0.740650\pi$
$523$	−31.3781	−1.37207	−0.686034	+	0.727569i	$0.740650\pi$
$524$	−1.52342	−0.0665511
$525$	0	0
$526$	0.457086	0.0199299
$527$	60.5544	2.63779
$528$	−5.38814	−0.234489
$529$	1.00000	0.0434783
$530$	−5.62499	−0.244334
$531$	−33.4124	−1.44997
$532$	0	0
$533$	−13.2679	−0.574695
$534$	42.8783	1.85553
$535$	16.3633	0.707448
$536$	−7.26319	−0.313722
$537$	42.2780	1.82443
$538$	−18.5535	−0.799898
$539$	0	0
$540$	2.18037	0.0938281
$541$	0.751971	0.0323298	0.0161649	−	0.999869i	$-0.494854\pi$
$541$	0.751971	0.0323298	0.0161649	+	0.999869i	$0.494854\pi$
$542$	−18.2909	−0.785661
$543$	−28.9348	−1.24171
$544$	6.94919	0.297944
$545$	1.45909	0.0625005
$546$	0	0
$547$	−27.3113	−1.16775	−0.583874	−	0.811844i	$-0.698464\pi$
$547$	−27.3113	−1.16775	−0.583874	+	0.811844i	$0.698464\pi$
$548$	9.62668	0.411231
$549$	−43.7957	−1.86916
$550$	−6.77598	−0.288929
$551$	−8.99711	−0.383290
$552$	2.57641	0.109660
$553$	0	0
$554$	20.1567	0.856375
$555$	−11.3116	−0.480149
$556$	−8.57676	−0.363736
$557$	29.2485	1.23930	0.619650	−	0.784878i	$-0.287274\pi$
$557$	29.2485	1.23930	0.619650	+	0.784878i	$0.287274\pi$
$558$	31.7004	1.34198
$559$	26.0337	1.10111
$560$	0	0
$561$	−37.4432	−1.58085
$562$	−7.27365	−0.306820
$563$	−0.514516	−0.0216843	−0.0108421	−	0.999941i	$-0.503451\pi$
$563$	−0.514516	−0.0216843	−0.0108421	+	0.999941i	$0.503451\pi$
$564$	−8.96928	−0.377675
$565$	−5.89396	−0.247961
$566$	2.76240	0.116112
$567$	0	0
$568$	−7.41708	−0.311214
$569$	33.8004	1.41699	0.708493	−	0.705718i	$-0.249375\pi$
$569$	33.8004	1.41699	0.708493	+	0.705718i	$0.249375\pi$
$570$	−26.5457	−1.11188
$571$	−13.3829	−0.560055	−0.280028	−	0.959992i	$-0.590344\pi$
$571$	−13.3829	−0.560055	−0.280028	+	0.959992i	$0.590344\pi$
$572$	−6.50701	−0.272072
$573$	−16.4067	−0.685401
$574$	0	0
$575$	3.24003	0.135119
$576$	3.63791	0.151580
$577$	36.6482	1.52568	0.762842	−	0.646585i	$-0.223804\pi$
$577$	36.6482	1.52568	0.762842	+	0.646585i	$0.223804\pi$
$578$	31.2912	1.30154
$579$	36.2115	1.50490
$580$	−1.53684	−0.0638137
$581$	0	0
$582$	17.1538	0.711047
$583$	8.86731	0.367247
$584$	4.36805	0.180751
$585$	15.0163	0.620848
$586$	−25.3756	−1.04825
$587$	10.8300	0.447003	0.223502	−	0.974704i	$-0.428251\pi$
$587$	10.8300	0.447003	0.223502	+	0.974704i	$0.428251\pi$
$588$	0	0
$589$	−67.6766	−2.78857
$590$	12.1845	0.501628
$591$	17.9208	0.737162
$592$	−3.30944	−0.136017
$593$	7.80794	0.320634	0.160317	−	0.987066i	$-0.448748\pi$
$593$	7.80794	0.320634	0.160317	+	0.987066i	$0.448748\pi$
$594$	−3.43717	−0.141029
$595$	0	0
$596$	16.0214	0.656261
$597$	54.3359	2.22382
$598$	3.11142	0.127235
$599$	−34.7398	−1.41943	−0.709715	−	0.704489i	$-0.751176\pi$
$599$	−34.7398	−1.41943	−0.709715	+	0.704489i	$0.751176\pi$
$600$	8.34767	0.340792
$601$	33.4939	1.36625	0.683123	−	0.730303i	$-0.260621\pi$
$601$	33.4939	1.36625	0.683123	+	0.730303i	$0.260621\pi$
$602$	0	0
$603$	−26.4229	−1.07602
$604$	−13.9358	−0.567039
$605$	8.79074	0.357395
$606$	23.5968	0.958556
$607$	33.0399	1.34105	0.670523	−	0.741888i	$-0.266070\pi$
$607$	33.0399	1.34105	0.670523	+	0.741888i	$0.266070\pi$
$608$	−7.76653	−0.314974
$609$	0	0
$610$	15.9710	0.646646
$611$	−10.8318	−0.438207
$612$	25.2806	1.02191
$613$	0.344610	0.0139187	0.00695934	−	0.999976i	$-0.497785\pi$
$613$	0.344610	0.0139187	0.00695934	+	0.999976i	$0.497785\pi$
$614$	29.2469	1.18031
$615$	14.5751	0.587723
$616$	0	0
$617$	18.8997	0.760872	0.380436	−	0.924807i	$-0.375774\pi$
$617$	18.8997	0.760872	0.380436	+	0.924807i	$0.375774\pi$
$618$	11.6766	0.469702
$619$	−22.4272	−0.901424	−0.450712	−	0.892669i	$-0.648830\pi$
$619$	−22.4272	−0.901424	−0.450712	+	0.892669i	$0.648830\pi$
$620$	−11.5602	−0.464267
$621$	1.64353	0.0659526
$622$	−27.2828	−1.09394
$623$	0	0
$624$	8.01631	0.320909
$625$	1.69798	0.0679193
$626$	−2.57676	−0.102988
$627$	41.8471	1.67121
$628$	15.4227	0.615433
$629$	−22.9979	−0.916988
$630$	0	0
$631$	45.9749	1.83023	0.915117	−	0.403189i	$-0.132098\pi$
$631$	45.9749	1.83023	0.915117	+	0.403189i	$0.132098\pi$
$632$	−0.797250	−0.0317129
$633$	−68.2842	−2.71405
$634$	−12.5065	−0.496695
$635$	−3.19986	−0.126982
$636$	−10.9241	−0.433168
$637$	0	0
$638$	2.42270	0.0959154
$639$	−26.9827	−1.06742
$640$	−1.32664	−0.0524399
$641$	−11.8457	−0.467876	−0.233938	−	0.972251i	$-0.575161\pi$
$641$	−11.8457	−0.467876	−0.233938	+	0.972251i	$0.575161\pi$
$642$	31.7786	1.25420
$643$	−40.7199	−1.60584	−0.802918	−	0.596089i	$-0.796720\pi$
$643$	−40.7199	−1.60584	−0.802918	+	0.596089i	$0.796720\pi$
$644$	0	0
$645$	−28.5987	−1.12607
$646$	−53.9711	−2.12346
$647$	−0.721680	−0.0283722	−0.0141861	−	0.999899i	$-0.504516\pi$
$647$	−0.721680	−0.0283722	−0.0141861	+	0.999899i	$0.504516\pi$
$648$	−6.67932	−0.262389
$649$	−19.2078	−0.753973
$650$	10.0811	0.395413
$651$	0	0
$652$	−8.61387	−0.337345
$653$	−0.746263	−0.0292035	−0.0146018	−	0.999893i	$-0.504648\pi$
$653$	−0.746263	−0.0292035	−0.0146018	+	0.999893i	$0.504648\pi$
$654$	2.83364	0.110804
$655$	2.02103	0.0789683
$656$	4.26425	0.166491
$657$	15.8906	0.619951
$658$	0	0
$659$	6.85325	0.266965	0.133482	−	0.991051i	$-0.457384\pi$
$659$	6.85325	0.266965	0.133482	+	0.991051i	$0.457384\pi$
$660$	7.14810	0.278240
$661$	−33.7836	−1.31403	−0.657016	−	0.753877i	$-0.728181\pi$
$661$	−33.7836	−1.31403	−0.657016	+	0.753877i	$0.728181\pi$
$662$	2.73397	0.106259
$663$	55.7068	2.16347
$664$	−10.3746	−0.402613
$665$	0	0
$666$	−12.0395	−0.466520
$667$	−1.15845	−0.0448552
$668$	−11.9693	−0.463105
$669$	−25.2517	−0.976286
$670$	9.63562	0.372257
$671$	−25.1769	−0.971943
$672$	0	0
$673$	32.6054	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$673$	32.6054	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$674$	12.4355	0.478998
$675$	5.32509	0.204963
$676$	−3.31907	−0.127657
$677$	−25.1527	−0.966697	−0.483349	−	0.875428i	$-0.660580\pi$
$677$	−25.1527	−0.966697	−0.483349	+	0.875428i	$0.660580\pi$
$678$	−11.4465	−0.439598
$679$	0	0
$680$	−9.21906	−0.353535
$681$	−73.4180	−2.81338
$682$	18.2236	0.697818
$683$	−33.7015	−1.28955	−0.644776	−	0.764372i	$-0.723049\pi$
$683$	−33.7015	−1.28955	−0.644776	+	0.764372i	$0.723049\pi$
$684$	−28.2540	−1.08032
$685$	−12.7711	−0.487959
$686$	0	0
$687$	−64.9035	−2.47622
$688$	−8.36716	−0.318995
$689$	−13.1925	−0.502595
$690$	−3.41797	−0.130120
$691$	−25.1004	−0.954863	−0.477431	−	0.878669i	$-0.658432\pi$
$691$	−25.1004	−0.954863	−0.477431	+	0.878669i	$0.658432\pi$
$692$	19.8197	0.753431
$693$	0	0
$694$	2.20748	0.0837947
$695$	11.3783	0.431602
$696$	−2.98464	−0.113132
$697$	29.6331	1.12243
$698$	−10.7710	−0.407688
$699$	33.9120	1.28267
$700$	0	0
$701$	−32.8099	−1.23921	−0.619607	−	0.784912i	$-0.712708\pi$
$701$	−32.8099	−1.23921	−0.619607	+	0.784912i	$0.712708\pi$
$702$	5.11371	0.193005
$703$	25.7029	0.969402
$704$	2.09133	0.0788200
$705$	11.8990	0.448141
$706$	13.8970	0.523020
$707$	0	0
$708$	23.6631	0.889313
$709$	−19.0921	−0.717019	−0.358510	−	0.933526i	$-0.616715\pi$
$709$	−19.0921	−0.717019	−0.358510	+	0.933526i	$0.616715\pi$
$710$	9.83977	0.369280
$711$	−2.90033	−0.108771
$712$	−16.6426	−0.623709
$713$	−8.71388	−0.326338
$714$	0	0
$715$	8.63244	0.322835
$716$	−16.4096	−0.613257
$717$	22.6282	0.845067
$718$	−19.4670	−0.726502
$719$	−21.0449	−0.784842	−0.392421	−	0.919786i	$-0.628362\pi$
$719$	−21.0449	−0.784842	−0.392421	+	0.919786i	$0.628362\pi$
$720$	−4.82619	−0.179862
$721$	0	0
$722$	41.3190	1.53773
$723$	3.93561	0.146367
$724$	11.2306	0.417383
$725$	−3.75341	−0.139398
$726$	17.0722	0.633608
$727$	−11.6826	−0.433282	−0.216641	−	0.976251i	$-0.569510\pi$
$727$	−11.6826	−0.433282	−0.216641	+	0.976251i	$0.569510\pi$
$728$	0	0
$729$	−37.0021	−1.37045
$730$	−5.79482	−0.214476
$731$	−58.1450	−2.15057
$732$	31.0167	1.14641
$733$	24.2475	0.895603	0.447802	−	0.894133i	$-0.352207\pi$
$733$	24.2475	0.895603	0.447802	+	0.894133i	$0.352207\pi$
$734$	−17.1874	−0.634398
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−15.1897	−0.559521
$738$	15.5130	0.571040
$739$	−27.1189	−0.997586	−0.498793	−	0.866721i	$-0.666223\pi$
$739$	−27.1189	−0.997586	−0.498793	+	0.866721i	$0.666223\pi$
$740$	4.39043	0.161395
$741$	−62.2589	−2.28714
$742$	0	0
$743$	−10.3281	−0.378902	−0.189451	−	0.981890i	$-0.560671\pi$
$743$	−10.3281	−0.378902	−0.189451	+	0.981890i	$0.560671\pi$
$744$	−22.4506	−0.823078
$745$	−21.2546	−0.778707
$746$	−9.43657	−0.345497
$747$	−37.7419	−1.38091
$748$	14.5331	0.531381
$749$	0	0
$750$	−28.1642	−1.02841
$751$	−10.3067	−0.376095	−0.188048	−	0.982160i	$-0.560216\pi$
$751$	−10.3067	−0.376095	−0.188048	+	0.982160i	$0.560216\pi$
$752$	3.48130	0.126950
$753$	2.68540	0.0978614
$754$	−3.60441	−0.131265
$755$	18.4877	0.672837
$756$	0	0
$757$	−39.6243	−1.44017	−0.720084	−	0.693887i	$-0.755897\pi$
$757$	−39.6243	−1.44017	−0.720084	+	0.693887i	$0.755897\pi$
$758$	6.99131	0.253936
$759$	5.38814	0.195577
$760$	10.3034	0.373742
$761$	53.4638	1.93806	0.969031	−	0.246941i	$-0.0794254\pi$
$761$	53.4638	1.93806	0.969031	+	0.246941i	$0.0794254\pi$
$762$	−6.21433	−0.225121
$763$	0	0
$764$	6.36805	0.230388
$765$	−33.5381	−1.21257
$766$	−27.5410	−0.995098
$767$	28.5768	1.03185
$768$	−2.57641	−0.0929684
$769$	−8.56383	−0.308820	−0.154410	−	0.988007i	$-0.549348\pi$
$769$	−8.56383	−0.308820	−0.154410	+	0.988007i	$0.549348\pi$
$770$	0	0
$771$	−17.4529	−0.628550
$772$	−14.0550	−0.505850
$773$	31.7891	1.14338	0.571688	−	0.820471i	$-0.306289\pi$
$773$	31.7891	1.14338	0.571688	+	0.820471i	$0.306289\pi$
$774$	−30.4390	−1.09411
$775$	−28.2333	−1.01417
$776$	−6.65800	−0.239008
$777$	0	0
$778$	6.70443	0.240365
$779$	−33.1184	−1.18659
$780$	−10.6347	−0.380784
$781$	−15.5116	−0.555047
$782$	−6.94919	−0.248503
$783$	−1.90394	−0.0680413
$784$	0	0
$785$	−20.4603	−0.730260
$786$	3.92497	0.139999
$787$	−10.4395	−0.372130	−0.186065	−	0.982537i	$-0.559573\pi$
$787$	−10.4395	−0.372130	−0.186065	+	0.982537i	$0.559573\pi$
$788$	−6.95570	−0.247786
$789$	−1.17764	−0.0419253
$790$	1.05766	0.0376299
$791$	0	0
$792$	7.60808	0.270341
$793$	37.4574	1.33015
$794$	−22.6052	−0.802230
$795$	14.4923	0.513989
$796$	−21.0897	−0.747506
$797$	−2.70514	−0.0958211	−0.0479105	−	0.998852i	$-0.515256\pi$
$797$	−2.70514	−0.0958211	−0.0479105	+	0.998852i	$0.515256\pi$
$798$	0	0
$799$	24.1922	0.855860
$800$	−3.24003	−0.114552
$801$	−60.5445	−2.13923
$802$	−9.70827	−0.342811
$803$	9.13503	0.322368
$804$	18.7130	0.659956
$805$	0	0
$806$	−27.1125	−0.954999
$807$	47.8015	1.68269
$808$	−9.15879	−0.322205
$809$	22.3936	0.787318	0.393659	−	0.919257i	$-0.371209\pi$
$809$	22.3936	0.787318	0.393659	+	0.919257i	$0.371209\pi$
$810$	8.86104	0.311345
$811$	23.7712	0.834719	0.417359	−	0.908742i	$-0.362956\pi$
$811$	23.7712	0.834719	0.417359	+	0.908742i	$0.362956\pi$
$812$	0	0
$813$	47.1249	1.65274
$814$	−6.92114	−0.242586
$815$	11.4275	0.400287
$816$	−17.9040	−0.626765
$817$	64.9838	2.27349
$818$	36.3360	1.27046
$819$	0	0
$820$	−5.65711	−0.197555
$821$	−21.8755	−0.763459	−0.381729	−	0.924274i	$-0.624671\pi$
$821$	−21.8755	−0.763459	−0.381729	+	0.924274i	$0.624671\pi$
$822$	−24.8023	−0.865080
$823$	−27.6968	−0.965449	−0.482724	−	0.875772i	$-0.660353\pi$
$823$	−27.6968	−0.965449	−0.482724	+	0.875772i	$0.660353\pi$
$824$	−4.53211	−0.157884
$825$	17.4577	0.607801
$826$	0	0
$827$	44.6016	1.55095	0.775475	−	0.631378i	$-0.217510\pi$
$827$	44.6016	1.55095	0.775475	+	0.631378i	$0.217510\pi$
$828$	−3.63791	−0.126426
$829$	36.3293	1.26177	0.630884	−	0.775877i	$-0.282692\pi$
$829$	36.3293	1.26177	0.630884	+	0.775877i	$0.282692\pi$
$830$	13.7633	0.477733
$831$	−51.9319	−1.80150
$832$	−3.11142	−0.107869
$833$	0	0
$834$	22.0973	0.765167
$835$	15.8789	0.549512
$836$	−16.2424	−0.561754
$837$	−14.3215	−0.495025
$838$	−9.98642	−0.344975
$839$	−51.3975	−1.77444	−0.887219	−	0.461348i	$-0.847366\pi$
$839$	−51.3975	−1.77444	−0.887219	+	0.461348i	$0.847366\pi$
$840$	0	0
$841$	−27.6580	−0.953724
$842$	14.1053	0.486099
$843$	18.7399	0.645438
$844$	26.5036	0.912290
$845$	4.40321	0.151475
$846$	12.6647	0.435421
$847$	0	0
$848$	4.24003	0.145603
$849$	−7.11709	−0.244258
$850$	−22.5156	−0.772279
$851$	3.30944	0.113446
$852$	19.1095	0.654680
$853$	36.8505	1.26174	0.630868	−	0.775890i	$-0.282699\pi$
$853$	36.8505	1.26174	0.630868	+	0.775890i	$0.282699\pi$
$854$	0	0
$855$	37.4828	1.28188
$856$	−12.3344	−0.421582
$857$	15.7872	0.539282	0.269641	−	0.962961i	$-0.413095\pi$
$857$	15.7872	0.539282	0.269641	+	0.962961i	$0.413095\pi$
$858$	16.7647	0.572339
$859$	−30.2068	−1.03064	−0.515322	−	0.856997i	$-0.672328\pi$
$859$	−30.2068	−1.03064	−0.515322	+	0.856997i	$0.672328\pi$
$860$	11.1002	0.378513
$861$	0	0
$862$	−3.54369	−0.120699
$863$	51.9316	1.76777	0.883886	−	0.467702i	$-0.154918\pi$
$863$	51.9316	1.76777	0.883886	+	0.467702i	$0.154918\pi$
$864$	−1.64353	−0.0559140
$865$	−26.2935	−0.894007
$866$	16.2680	0.552810
$867$	−80.6192	−2.73797
$868$	0	0
$869$	−1.66731	−0.0565598
$870$	3.95953	0.134241
$871$	22.5988	0.765732
$872$	−1.09984	−0.0372453
$873$	−24.2212	−0.819765
$874$	7.76653	0.262707
$875$	0	0
$876$	−11.2539	−0.380234
$877$	−11.3012	−0.381615	−0.190807	−	0.981627i	$-0.561111\pi$
$877$	−11.3012	−0.381615	−0.190807	+	0.981627i	$0.561111\pi$
$878$	−1.17003	−0.0394864
$879$	65.3780	2.20514
$880$	−2.77444	−0.0935263
$881$	−17.4345	−0.587384	−0.293692	−	0.955900i	$-0.594884\pi$
$881$	−17.4345	−0.587384	−0.293692	+	0.955900i	$0.594884\pi$
$882$	0	0
$883$	48.0567	1.61724	0.808618	−	0.588333i	$-0.200216\pi$
$883$	48.0567	1.61724	0.808618	+	0.588333i	$0.200216\pi$
$884$	−21.6218	−0.727221
$885$	−31.3923	−1.05524
$886$	39.0073	1.31048
$887$	2.19433	0.0736783	0.0368391	−	0.999321i	$-0.488271\pi$
$887$	2.19433	0.0736783	0.0368391	+	0.999321i	$0.488271\pi$
$888$	8.52649	0.286130
$889$	0	0
$890$	22.0787	0.740081
$891$	−13.9687	−0.467968
$892$	9.80109	0.328165
$893$	−27.0376	−0.904780
$894$	−41.2777	−1.38053
$895$	21.7696	0.727678
$896$	0	0
$897$	−8.01631	−0.267657
$898$	32.1714	1.07357
$899$	10.0946	0.336673
$900$	−11.7870	−0.392899
$901$	29.4648	0.981615
$902$	8.91796	0.296935
$903$	0	0
$904$	4.44278	0.147765
$905$	−14.8990	−0.495259
$906$	35.9043	1.19284
$907$	−30.3570	−1.00799	−0.503993	−	0.863708i	$-0.668136\pi$
$907$	−30.3570	−1.00799	−0.503993	+	0.863708i	$0.668136\pi$
$908$	28.4962	0.945679
$909$	−33.3189	−1.10512
$910$	0	0
$911$	−1.09959	−0.0364309	−0.0182155	−	0.999834i	$-0.505798\pi$
$911$	−1.09959	−0.0364309	−0.0182155	+	0.999834i	$0.505798\pi$
$912$	20.0098	0.662591
$913$	−21.6967	−0.718057
$914$	−34.3548	−1.13635
$915$	−41.1478	−1.36031
$916$	25.1914	0.832347
$917$	0	0
$918$	−11.4212	−0.376956
$919$	−9.67342	−0.319097	−0.159548	−	0.987190i	$-0.551004\pi$
$919$	−9.67342	−0.319097	−0.159548	+	0.987190i	$0.551004\pi$
$920$	1.32664	0.0437379
$921$	−75.3523	−2.48294
$922$	−10.5155	−0.346310
$923$	23.0776	0.759610
$924$	0	0
$925$	10.7227	0.352560
$926$	−19.9943	−0.657052
$927$	−16.4874	−0.541518
$928$	1.15845	0.0380279
$929$	−11.3437	−0.372175	−0.186088	−	0.982533i	$-0.559581\pi$
$929$	−11.3437	−0.372175	−0.186088	+	0.982533i	$0.559581\pi$
$930$	29.7838	0.976649
$931$	0	0
$932$	−13.1625	−0.431151
$933$	70.2919	2.30125
$934$	27.4643	0.898658
$935$	−19.2801	−0.630527
$936$	−11.3191	−0.369975
$937$	1.06500	0.0347921	0.0173960	−	0.999849i	$-0.494462\pi$
$937$	1.06500	0.0347921	0.0173960	+	0.999849i	$0.494462\pi$
$938$	0	0
$939$	6.63880	0.216649
$940$	−4.61843	−0.150636
$941$	−46.7079	−1.52263	−0.761317	−	0.648379i	$-0.775447\pi$
$941$	−46.7079	−1.52263	−0.761317	+	0.648379i	$0.775447\pi$
$942$	−39.7353	−1.29464
$943$	−4.26425	−0.138863
$944$	−9.18450	−0.298930
$945$	0	0
$946$	−17.4985	−0.568925
$947$	46.8692	1.52305	0.761523	−	0.648138i	$-0.224452\pi$
$947$	46.8692	1.52305	0.761523	+	0.648138i	$0.224452\pi$
$948$	2.05405	0.0667124
$949$	−13.5908	−0.441177
$950$	25.1638	0.816422
$951$	32.2218	1.04486
$952$	0	0
$953$	−42.2926	−1.36999	−0.684996	−	0.728547i	$-0.740196\pi$
$953$	−42.2926	−1.36999	−0.684996	+	0.728547i	$0.740196\pi$
$954$	15.4249	0.499399
$955$	−8.44809	−0.273374
$956$	−8.78283	−0.284057
$957$	−6.24187	−0.201771
$958$	8.44551	0.272862
$959$	0	0
$960$	3.41797	0.110314
$961$	44.9318	1.44941
$962$	10.2971	0.331991
$963$	−44.8716	−1.44597
$964$	−1.52755	−0.0491992
$965$	18.6459	0.600232
$966$	0	0
$967$	42.5007	1.36673	0.683366	−	0.730076i	$-0.260515\pi$
$967$	42.5007	1.36673	0.683366	+	0.730076i	$0.260515\pi$
$968$	−6.62633	−0.212978
$969$	139.052	4.46699
$970$	8.83275	0.283603
$971$	−1.03232	−0.0331289	−0.0165644	−	0.999863i	$-0.505273\pi$
$971$	−1.03232	−0.0331289	−0.0165644	+	0.999863i	$0.505273\pi$
$972$	22.1393	0.710118
$973$	0	0
$974$	33.2791	1.06633
$975$	−25.9731	−0.831805
$976$	−12.0387	−0.385349
$977$	0.852420	0.0272713	0.0136357	−	0.999907i	$-0.495659\pi$
$977$	0.852420	0.0272713	0.0136357	+	0.999907i	$0.495659\pi$
$978$	22.1929	0.709650
$979$	−34.8053	−1.11238
$980$	0	0
$981$	−4.00112	−0.127746
$982$	15.8532	0.505896
$983$	6.92136	0.220757	0.110379	−	0.993890i	$-0.464794\pi$
$983$	6.92136	0.220757	0.110379	+	0.993890i	$0.464794\pi$
$984$	−10.9865	−0.350236
$985$	9.22769	0.294019
$986$	8.05027	0.256373
$987$	0	0
$988$	24.1649	0.768789
$989$	8.36716	0.266060
$990$	−10.0932	−0.320782
$991$	−1.34596	−0.0427558	−0.0213779	−	0.999771i	$-0.506805\pi$
$991$	−1.34596	−0.0427558	−0.0213779	+	0.999771i	$0.506805\pi$
$992$	8.71388	0.276666
$993$	−7.04384	−0.223530
$994$	0	0
$995$	27.9784	0.886976
$996$	26.7293	0.846950
$997$	−4.84179	−0.153341	−0.0766705	−	0.997056i	$-0.524429\pi$
$997$	−4.84179	−0.153341	−0.0766705	+	0.997056i	$0.524429\pi$
$998$	−19.3323	−0.611954
$999$	5.43917	0.172088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2254.2.a.x.1.1		4
7.3	odd	6		322.2.e.a.93.1	✓	8
7.5	odd	6		322.2.e.a.277.1	yes	8
7.6	odd	2		2254.2.a.z.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.a.93.1	✓	8	7.3	odd	6
322.2.e.a.277.1	yes	8	7.5	odd	6
2254.2.a.x.1.1		4	1.1	even	1	trivial
2254.2.a.z.1.4		4	7.6	odd	2

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:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2254.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.57641 q^{3} +1.00000 q^{4} -1.32664 q^{5} -2.57641 q^{6} +1.00000 q^{8} +3.63791 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.57641 q^{3} +1.00000 q^{4} -1.32664 q^{5} -2.57641 q^{6} +1.00000 q^{8} +3.63791 q^{9} -1.32664 q^{10} +2.09133 q^{11} -2.57641 q^{12} -3.11142 q^{13} +3.41797 q^{15} +1.00000 q^{16} +6.94919 q^{17} +3.63791 q^{18} -7.76653 q^{19} -1.32664 q^{20} +2.09133 q^{22} -1.00000 q^{23} -2.57641 q^{24} -3.24003 q^{25} -3.11142 q^{26} -1.64353 q^{27} +1.15845 q^{29} +3.41797 q^{30} +8.71388 q^{31} +1.00000 q^{32} -5.38814 q^{33} +6.94919 q^{34} +3.63791 q^{36} -3.30944 q^{37} -7.76653 q^{38} +8.01631 q^{39} -1.32664 q^{40} +4.26425 q^{41} -8.36716 q^{43} +2.09133 q^{44} -4.82619 q^{45} -1.00000 q^{46} +3.48130 q^{47} -2.57641 q^{48} -3.24003 q^{50} -17.9040 q^{51} -3.11142 q^{52} +4.24003 q^{53} -1.64353 q^{54} -2.77444 q^{55} +20.0098 q^{57} +1.15845 q^{58} -9.18450 q^{59} +3.41797 q^{60} -12.0387 q^{61} +8.71388 q^{62} +1.00000 q^{64} +4.12772 q^{65} -5.38814 q^{66} -7.26319 q^{67} +6.94919 q^{68} +2.57641 q^{69} -7.41708 q^{71} +3.63791 q^{72} +4.36805 q^{73} -3.30944 q^{74} +8.34767 q^{75} -7.76653 q^{76} +8.01631 q^{78} -0.797250 q^{79} -1.32664 q^{80} -6.67932 q^{81} +4.26425 q^{82} -10.3746 q^{83} -9.21906 q^{85} -8.36716 q^{86} -2.98464 q^{87} +2.09133 q^{88} -16.6426 q^{89} -4.82619 q^{90} -1.00000 q^{92} -22.4506 q^{93} +3.48130 q^{94} +10.3034 q^{95} -2.57641 q^{96} -6.65800 q^{97} +7.60808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{8} - q^{9} - 7 q^{10} + 2 q^{11} - 3 q^{12} - q^{13} + 9 q^{15} + 4 q^{16} - 5 q^{17} - q^{18} - 11 q^{19} - 7 q^{20} + 2 q^{22} - 4 q^{23} - 3 q^{24} + 3 q^{25} - q^{26} - 3 q^{27} + 2 q^{29} + 9 q^{30} - 6 q^{31} + 4 q^{32} - 15 q^{33} - 5 q^{34} - q^{36} - 8 q^{37} - 11 q^{38} + 3 q^{39} - 7 q^{40} - 9 q^{41} + 4 q^{43} + 2 q^{44} - 3 q^{45} - 4 q^{46} - 11 q^{47} - 3 q^{48} + 3 q^{50} - 18 q^{51} - q^{52} + q^{53} - 3 q^{54} - 10 q^{55} + 3 q^{57} + 2 q^{58} - 12 q^{59} + 9 q^{60} - 21 q^{61} - 6 q^{62} + 4 q^{64} - 24 q^{65} - 15 q^{66} - 3 q^{67} - 5 q^{68} + 3 q^{69} + 11 q^{71} - q^{72} + 16 q^{73} - 8 q^{74} - 18 q^{75} - 11 q^{76} + 3 q^{78} - 21 q^{79} - 7 q^{80} - 8 q^{81} - 9 q^{82} - 4 q^{83} + 10 q^{85} + 4 q^{86} + 7 q^{87} + 2 q^{88} - 27 q^{89} - 3 q^{90} - 4 q^{92} - 27 q^{93} - 11 q^{94} + 5 q^{95} - 3 q^{96} - 6 q^{97} + 13 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^8 - q^9 - 7 * q^10 + 2 * q^11 - 3 * q^12 - q^13 + 9 * q^15 + 4 * q^16 - 5 * q^17 - q^18 - 11 * q^19 - 7 * q^20 + 2 * q^22 - 4 * q^23 - 3 * q^24 + 3 * q^25 - q^26 - 3 * q^27 + 2 * q^29 + 9 * q^30 - 6 * q^31 + 4 * q^32 - 15 * q^33 - 5 * q^34 - q^36 - 8 * q^37 - 11 * q^38 + 3 * q^39 - 7 * q^40 - 9 * q^41 + 4 * q^43 + 2 * q^44 - 3 * q^45 - 4 * q^46 - 11 * q^47 - 3 * q^48 + 3 * q^50 - 18 * q^51 - q^52 + q^53 - 3 * q^54 - 10 * q^55 + 3 * q^57 + 2 * q^58 - 12 * q^59 + 9 * q^60 - 21 * q^61 - 6 * q^62 + 4 * q^64 - 24 * q^65 - 15 * q^66 - 3 * q^67 - 5 * q^68 + 3 * q^69 + 11 * q^71 - q^72 + 16 * q^73 - 8 * q^74 - 18 * q^75 - 11 * q^76 + 3 * q^78 - 21 * q^79 - 7 * q^80 - 8 * q^81 - 9 * q^82 - 4 * q^83 + 10 * q^85 + 4 * q^86 + 7 * q^87 + 2 * q^88 - 27 * q^89 - 3 * q^90 - 4 * q^92 - 27 * q^93 - 11 * q^94 + 5 * q^95 - 3 * q^96 - 6 * q^97 + 13 * q^99

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