LMFDB - Embedded newform 250.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(1,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} +1.23607 q^{6} -0.618034 q^{7} +1.00000 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} +1.23607 q^{6} -0.618034 q^{7} +1.00000 q^{8} -1.47214 q^{9} +5.61803 q^{11} +1.23607 q^{12} +0.381966 q^{13} -0.618034 q^{14} +1.00000 q^{16} -6.47214 q^{17} -1.47214 q^{18} -1.38197 q^{19} -0.763932 q^{21} +5.61803 q^{22} -6.85410 q^{23} +1.23607 q^{24} +0.381966 q^{26} -5.52786 q^{27} -0.618034 q^{28} +7.23607 q^{29} -0.763932 q^{31} +1.00000 q^{32} +6.94427 q^{33} -6.47214 q^{34} -1.47214 q^{36} +6.61803 q^{37} -1.38197 q^{38} +0.472136 q^{39} -8.32624 q^{41} -0.763932 q^{42} -10.4721 q^{43} +5.61803 q^{44} -6.85410 q^{46} +4.38197 q^{47} +1.23607 q^{48} -6.61803 q^{49} -8.00000 q^{51} +0.381966 q^{52} +11.5623 q^{53} -5.52786 q^{54} -0.618034 q^{56} -1.70820 q^{57} +7.23607 q^{58} +7.56231 q^{59} -3.52786 q^{61} -0.763932 q^{62} +0.909830 q^{63} +1.00000 q^{64} +6.94427 q^{66} -4.76393 q^{67} -6.47214 q^{68} -8.47214 q^{69} +0.291796 q^{71} -1.47214 q^{72} +2.29180 q^{73} +6.61803 q^{74} -1.38197 q^{76} -3.47214 q^{77} +0.472136 q^{78} -4.47214 q^{79} -2.41641 q^{81} -8.32624 q^{82} +4.00000 q^{83} -0.763932 q^{84} -10.4721 q^{86} +8.94427 q^{87} +5.61803 q^{88} +8.09017 q^{89} -0.236068 q^{91} -6.85410 q^{92} -0.944272 q^{93} +4.38197 q^{94} +1.23607 q^{96} +14.1803 q^{97} -6.61803 q^{98} -8.27051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + q^7 + 2 * q^8 + 6 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + 2 q^{8} + 6 q^{9} + 9 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} + 2 q^{16} - 4 q^{17} + 6 q^{18} - 5 q^{19} - 6 q^{21} + 9 q^{22} - 7 q^{23} - 2 q^{24} + 3 q^{26} - 20 q^{27} + q^{28} + 10 q^{29} - 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{36} + 11 q^{37} - 5 q^{38} - 8 q^{39} - q^{41} - 6 q^{42} - 12 q^{43} + 9 q^{44} - 7 q^{46} + 11 q^{47} - 2 q^{48} - 11 q^{49} - 16 q^{51} + 3 q^{52} + 3 q^{53} - 20 q^{54} + q^{56} + 10 q^{57} + 10 q^{58} - 5 q^{59} - 16 q^{61} - 6 q^{62} + 13 q^{63} + 2 q^{64} - 4 q^{66} - 14 q^{67} - 4 q^{68} - 8 q^{69} + 14 q^{71} + 6 q^{72} + 18 q^{73} + 11 q^{74} - 5 q^{76} + 2 q^{77} - 8 q^{78} + 22 q^{81} - q^{82} + 8 q^{83} - 6 q^{84} - 12 q^{86} + 9 q^{88} + 5 q^{89} + 4 q^{91} - 7 q^{92} + 16 q^{93} + 11 q^{94} - 2 q^{96} + 6 q^{97} - 11 q^{98} + 17 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + q^7 + 2 * q^8 + 6 * q^9 + 9 * q^11 - 2 * q^12 + 3 * q^13 + q^14 + 2 * q^16 - 4 * q^17 + 6 * q^18 - 5 * q^19 - 6 * q^21 + 9 * q^22 - 7 * q^23 - 2 * q^24 + 3 * q^26 - 20 * q^27 + q^28 + 10 * q^29 - 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^36 + 11 * q^37 - 5 * q^38 - 8 * q^39 - q^41 - 6 * q^42 - 12 * q^43 + 9 * q^44 - 7 * q^46 + 11 * q^47 - 2 * q^48 - 11 * q^49 - 16 * q^51 + 3 * q^52 + 3 * q^53 - 20 * q^54 + q^56 + 10 * q^57 + 10 * q^58 - 5 * q^59 - 16 * q^61 - 6 * q^62 + 13 * q^63 + 2 * q^64 - 4 * q^66 - 14 * q^67 - 4 * q^68 - 8 * q^69 + 14 * q^71 + 6 * q^72 + 18 * q^73 + 11 * q^74 - 5 * q^76 + 2 * q^77 - 8 * q^78 + 22 * q^81 - q^82 + 8 * q^83 - 6 * q^84 - 12 * q^86 + 9 * q^88 + 5 * q^89 + 4 * q^91 - 7 * q^92 + 16 * q^93 + 11 * q^94 - 2 * q^96 + 6 * q^97 - 11 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.23607	0.504623
$7$	−0.618034	−0.233595	−0.116797	−	0.993156i	$-0.537263\pi$
$7$	−0.618034	−0.233595	−0.116797	+	0.993156i	$0.537263\pi$
$8$	1.00000	0.353553
$9$	−1.47214	−0.490712
$10$	0	0
$11$	5.61803	1.69390	0.846950	−	0.531672i	$-0.178436\pi$
$11$	5.61803	1.69390	0.846950	+	0.531672i	$0.178436\pi$
$12$	1.23607	0.356822
$13$	0.381966	0.105938	0.0529692	−	0.998596i	$-0.483131\pi$
$13$	0.381966	0.105938	0.0529692	+	0.998596i	$0.483131\pi$
$14$	−0.618034	−0.165177
$15$	0	0
$16$	1.00000	0.250000
$17$	−6.47214	−1.56972	−0.784862	−	0.619671i	$-0.787266\pi$
$17$	−6.47214	−1.56972	−0.784862	+	0.619671i	$0.787266\pi$
$18$	−1.47214	−0.346986
$19$	−1.38197	−0.317045	−0.158522	−	0.987355i	$-0.550673\pi$
$19$	−1.38197	−0.317045	−0.158522	+	0.987355i	$0.550673\pi$
$20$	0	0
$21$	−0.763932	−0.166704
$22$	5.61803	1.19777
$23$	−6.85410	−1.42918	−0.714590	−	0.699544i	$-0.753386\pi$
$23$	−6.85410	−1.42918	−0.714590	+	0.699544i	$0.753386\pi$
$24$	1.23607	0.252311
$25$	0	0
$26$	0.381966	0.0749097
$27$	−5.52786	−1.06384
$28$	−0.618034	−0.116797
$29$	7.23607	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$29$	7.23607	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$30$	0	0
$31$	−0.763932	−0.137206	−0.0686031	−	0.997644i	$-0.521854\pi$
$31$	−0.763932	−0.137206	−0.0686031	+	0.997644i	$0.521854\pi$
$32$	1.00000	0.176777
$33$	6.94427	1.20884
$34$	−6.47214	−1.10996
$35$	0	0
$36$	−1.47214	−0.245356
$37$	6.61803	1.08800	0.543999	−	0.839086i	$-0.316910\pi$
$37$	6.61803	1.08800	0.543999	+	0.839086i	$0.316910\pi$
$38$	−1.38197	−0.224184
$39$	0.472136	0.0756023
$40$	0	0
$41$	−8.32624	−1.30034	−0.650170	−	0.759789i	$-0.725302\pi$
$41$	−8.32624	−1.30034	−0.650170	+	0.759789i	$0.725302\pi$
$42$	−0.763932	−0.117877
$43$	−10.4721	−1.59699	−0.798493	−	0.602004i	$-0.794369\pi$
$43$	−10.4721	−1.59699	−0.798493	+	0.602004i	$0.794369\pi$
$44$	5.61803	0.846950
$45$	0	0
$46$	−6.85410	−1.01058
$47$	4.38197	0.639175	0.319588	−	0.947557i	$-0.396456\pi$
$47$	4.38197	0.639175	0.319588	+	0.947557i	$0.396456\pi$
$48$	1.23607	0.178411
$49$	−6.61803	−0.945433
$50$	0	0
$51$	−8.00000	−1.12022
$52$	0.381966	0.0529692
$53$	11.5623	1.58820	0.794102	−	0.607784i	$-0.207941\pi$
$53$	11.5623	1.58820	0.794102	+	0.607784i	$0.207941\pi$
$54$	−5.52786	−0.752247
$55$	0	0
$56$	−0.618034	−0.0825883
$57$	−1.70820	−0.226257
$58$	7.23607	0.950142
$59$	7.56231	0.984528	0.492264	−	0.870446i	$-0.336169\pi$
$59$	7.56231	0.984528	0.492264	+	0.870446i	$0.336169\pi$
$60$	0	0
$61$	−3.52786	−0.451697	−0.225848	−	0.974162i	$-0.572515\pi$
$61$	−3.52786	−0.451697	−0.225848	+	0.974162i	$0.572515\pi$
$62$	−0.763932	−0.0970195
$63$	0.909830	0.114628
$64$	1.00000	0.125000
$65$	0	0
$66$	6.94427	0.854781
$67$	−4.76393	−0.582007	−0.291003	−	0.956722i	$-0.593989\pi$
$67$	−4.76393	−0.582007	−0.291003	+	0.956722i	$0.593989\pi$
$68$	−6.47214	−0.784862
$69$	−8.47214	−1.01993
$70$	0	0
$71$	0.291796	0.0346298	0.0173149	−	0.999850i	$-0.494488\pi$
$71$	0.291796	0.0346298	0.0173149	+	0.999850i	$0.494488\pi$
$72$	−1.47214	−0.173493
$73$	2.29180	0.268234	0.134117	−	0.990965i	$-0.457180\pi$
$73$	2.29180	0.268234	0.134117	+	0.990965i	$0.457180\pi$
$74$	6.61803	0.769331
$75$	0	0
$76$	−1.38197	−0.158522
$77$	−3.47214	−0.395687
$78$	0.472136	0.0534589
$79$	−4.47214	−0.503155	−0.251577	−	0.967837i	$-0.580949\pi$
$79$	−4.47214	−0.503155	−0.251577	+	0.967837i	$0.580949\pi$
$80$	0	0
$81$	−2.41641	−0.268490
$82$	−8.32624	−0.919479
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−0.763932	−0.0833518
$85$	0	0
$86$	−10.4721	−1.12924
$87$	8.94427	0.958927
$88$	5.61803	0.598884
$89$	8.09017	0.857556	0.428778	−	0.903410i	$-0.358944\pi$
$89$	8.09017	0.857556	0.428778	+	0.903410i	$0.358944\pi$
$90$	0	0
$91$	−0.236068	−0.0247466
$92$	−6.85410	−0.714590
$93$	−0.944272	−0.0979164
$94$	4.38197	0.451965
$95$	0	0
$96$	1.23607	0.126156
$97$	14.1803	1.43980	0.719898	−	0.694080i	$-0.244189\pi$
$97$	14.1803	1.43980	0.719898	+	0.694080i	$0.244189\pi$
$98$	−6.61803	−0.668522
$99$	−8.27051	−0.831218
$100$	0	0
$101$	10.9443	1.08900	0.544498	−	0.838762i	$-0.316720\pi$
$101$	10.9443	1.08900	0.544498	+	0.838762i	$0.316720\pi$
$102$	−8.00000	−0.792118
$103$	−14.0902	−1.38835	−0.694173	−	0.719808i	$-0.744230\pi$
$103$	−14.0902	−1.38835	−0.694173	+	0.719808i	$0.744230\pi$
$104$	0.381966	0.0374548
$105$	0	0
$106$	11.5623	1.12303
$107$	5.23607	0.506190	0.253095	−	0.967441i	$-0.418552\pi$
$107$	5.23607	0.506190	0.253095	+	0.967441i	$0.418552\pi$
$108$	−5.52786	−0.531919
$109$	8.94427	0.856706	0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427	0.856706	0.428353	+	0.903612i	$0.359094\pi$
$110$	0	0
$111$	8.18034	0.776444
$112$	−0.618034	−0.0583987
$113$	1.23607	0.116279	0.0581397	−	0.998308i	$-0.481483\pi$
$113$	1.23607	0.116279	0.0581397	+	0.998308i	$0.481483\pi$
$114$	−1.70820	−0.159988
$115$	0	0
$116$	7.23607	0.671852
$117$	−0.562306	−0.0519852
$118$	7.56231	0.696167
$119$	4.00000	0.366679
$120$	0	0
$121$	20.5623	1.86930
$122$	−3.52786	−0.319398
$123$	−10.2918	−0.927980
$124$	−0.763932	−0.0686031
$125$	0	0
$126$	0.909830	0.0810541
$127$	11.4164	1.01304	0.506521	−	0.862228i	$-0.330931\pi$
$127$	11.4164	1.01304	0.506521	+	0.862228i	$0.330931\pi$
$128$	1.00000	0.0883883
$129$	−12.9443	−1.13968
$130$	0	0
$131$	−3.32624	−0.290615	−0.145307	−	0.989387i	$-0.546417\pi$
$131$	−3.32624	−0.290615	−0.145307	+	0.989387i	$0.546417\pi$
$132$	6.94427	0.604421
$133$	0.854102	0.0740600
$134$	−4.76393	−0.411541
$135$	0	0
$136$	−6.47214	−0.554981
$137$	2.47214	0.211209	0.105604	−	0.994408i	$-0.466322\pi$
$137$	2.47214	0.211209	0.105604	+	0.994408i	$0.466322\pi$
$138$	−8.47214	−0.721196
$139$	−9.79837	−0.831087	−0.415544	−	0.909573i	$-0.636409\pi$
$139$	−9.79837	−0.831087	−0.415544	+	0.909573i	$0.636409\pi$
$140$	0	0
$141$	5.41641	0.456144
$142$	0.291796	0.0244870
$143$	2.14590	0.179449
$144$	−1.47214	−0.122678
$145$	0	0
$146$	2.29180	0.189670
$147$	−8.18034	−0.674703
$148$	6.61803	0.543999
$149$	16.1803	1.32555	0.662773	−	0.748821i	$-0.269380\pi$
$149$	16.1803	1.32555	0.662773	+	0.748821i	$0.269380\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−1.38197	−0.112092
$153$	9.52786	0.770282
$154$	−3.47214	−0.279793
$155$	0	0
$156$	0.472136	0.0378011
$157$	−7.52786	−0.600789	−0.300394	−	0.953815i	$-0.597118\pi$
$157$	−7.52786	−0.600789	−0.300394	+	0.953815i	$0.597118\pi$
$158$	−4.47214	−0.355784
$159$	14.2918	1.13341
$160$	0	0
$161$	4.23607	0.333849
$162$	−2.41641	−0.189851
$163$	−6.00000	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$164$	−8.32624	−0.650170
$165$	0	0
$166$	4.00000	0.310460
$167$	14.5066	1.12255	0.561276	−	0.827628i	$-0.310310\pi$
$167$	14.5066	1.12255	0.561276	+	0.827628i	$0.310310\pi$
$168$	−0.763932	−0.0589386
$169$	−12.8541	−0.988777
$170$	0	0
$171$	2.03444	0.155578
$172$	−10.4721	−0.798493
$173$	17.0902	1.29934	0.649671	−	0.760216i	$-0.274907\pi$
$173$	17.0902	1.29934	0.649671	+	0.760216i	$0.274907\pi$
$174$	8.94427	0.678064
$175$	0	0
$176$	5.61803	0.423475
$177$	9.34752	0.702603
$178$	8.09017	0.606384
$179$	15.8541	1.18499	0.592496	−	0.805574i	$-0.298143\pi$
$179$	15.8541	1.18499	0.592496	+	0.805574i	$0.298143\pi$
$180$	0	0
$181$	−10.7639	−0.800077	−0.400038	−	0.916498i	$-0.631003\pi$
$181$	−10.7639	−0.800077	−0.400038	+	0.916498i	$0.631003\pi$
$182$	−0.236068	−0.0174985
$183$	−4.36068	−0.322351
$184$	−6.85410	−0.505291
$185$	0	0
$186$	−0.944272	−0.0692374
$187$	−36.3607	−2.65896
$188$	4.38197	0.319588
$189$	3.41641	0.248507
$190$	0	0
$191$	−15.8885	−1.14965	−0.574827	−	0.818275i	$-0.694931\pi$
$191$	−15.8885	−1.14965	−0.574827	+	0.818275i	$0.694931\pi$
$192$	1.23607	0.0892055
$193$	10.1803	0.732797	0.366398	−	0.930458i	$-0.380591\pi$
$193$	10.1803	0.732797	0.366398	+	0.930458i	$0.380591\pi$
$194$	14.1803	1.01809
$195$	0	0
$196$	−6.61803	−0.472717
$197$	−10.9443	−0.779747	−0.389874	−	0.920868i	$-0.627481\pi$
$197$	−10.9443	−0.779747	−0.389874	+	0.920868i	$0.627481\pi$
$198$	−8.27051	−0.587760
$199$	−12.7639	−0.904811	−0.452406	−	0.891812i	$-0.649434\pi$
$199$	−12.7639	−0.904811	−0.452406	+	0.891812i	$0.649434\pi$
$200$	0	0
$201$	−5.88854	−0.415346
$202$	10.9443	0.770036
$203$	−4.47214	−0.313882
$204$	−8.00000	−0.560112
$205$	0	0
$206$	−14.0902	−0.981709
$207$	10.0902	0.701315
$208$	0.381966	0.0264846
$209$	−7.76393	−0.537042
$210$	0	0
$211$	−1.09017	−0.0750504	−0.0375252	−	0.999296i	$-0.511947\pi$
$211$	−1.09017	−0.0750504	−0.0375252	+	0.999296i	$0.511947\pi$
$212$	11.5623	0.794102
$213$	0.360680	0.0247134
$214$	5.23607	0.357930
$215$	0	0
$216$	−5.52786	−0.376124
$217$	0.472136	0.0320507
$218$	8.94427	0.605783
$219$	2.83282	0.191424
$220$	0	0
$221$	−2.47214	−0.166294
$222$	8.18034	0.549028
$223$	12.9443	0.866813	0.433406	−	0.901199i	$-0.357312\pi$
$223$	12.9443	0.866813	0.433406	+	0.901199i	$0.357312\pi$
$224$	−0.618034	−0.0412941
$225$	0	0
$226$	1.23607	0.0822220
$227$	−12.6525	−0.839774	−0.419887	−	0.907576i	$-0.637930\pi$
$227$	−12.6525	−0.839774	−0.419887	+	0.907576i	$0.637930\pi$
$228$	−1.70820	−0.113129
$229$	8.29180	0.547937	0.273969	−	0.961739i	$-0.411664\pi$
$229$	8.29180	0.547937	0.273969	+	0.961739i	$0.411664\pi$
$230$	0	0
$231$	−4.29180	−0.282379
$232$	7.23607	0.475071
$233$	−20.4721	−1.34117	−0.670587	−	0.741831i	$-0.733958\pi$
$233$	−20.4721	−1.34117	−0.670587	+	0.741831i	$0.733958\pi$
$234$	−0.562306	−0.0367591
$235$	0	0
$236$	7.56231	0.492264
$237$	−5.52786	−0.359073
$238$	4.00000	0.259281
$239$	−20.6525	−1.33590	−0.667949	−	0.744207i	$-0.732827\pi$
$239$	−20.6525	−1.33590	−0.667949	+	0.744207i	$0.732827\pi$
$240$	0	0
$241$	−16.0902	−1.03646	−0.518229	−	0.855242i	$-0.673409\pi$
$241$	−16.0902	−1.03646	−0.518229	+	0.855242i	$0.673409\pi$
$242$	20.5623	1.32180
$243$	13.5967	0.872232
$244$	−3.52786	−0.225848
$245$	0	0
$246$	−10.2918	−0.656181
$247$	−0.527864	−0.0335872
$248$	−0.763932	−0.0485097
$249$	4.94427	0.313331
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	0.909830	0.0573139
$253$	−38.5066	−2.42089
$254$	11.4164	0.716329
$255$	0	0
$256$	1.00000	0.0625000
$257$	−0.291796	−0.0182017	−0.00910087	−	0.999959i	$-0.502897\pi$
$257$	−0.291796	−0.0182017	−0.00910087	+	0.999959i	$0.502897\pi$
$258$	−12.9443	−0.805875
$259$	−4.09017	−0.254151
$260$	0	0
$261$	−10.6525	−0.659372
$262$	−3.32624	−0.205496
$263$	9.85410	0.607630	0.303815	−	0.952731i	$-0.401740\pi$
$263$	9.85410	0.607630	0.303815	+	0.952731i	$0.401740\pi$
$264$	6.94427	0.427390
$265$	0	0
$266$	0.854102	0.0523684
$267$	10.0000	0.611990
$268$	−4.76393	−0.291003
$269$	−19.5967	−1.19483	−0.597417	−	0.801930i	$-0.703806\pi$
$269$	−19.5967	−1.19483	−0.597417	+	0.801930i	$0.703806\pi$
$270$	0	0
$271$	−27.5967	−1.67638	−0.838192	−	0.545376i	$-0.816387\pi$
$271$	−27.5967	−1.67638	−0.838192	+	0.545376i	$0.816387\pi$
$272$	−6.47214	−0.392431
$273$	−0.291796	−0.0176603
$274$	2.47214	0.149347
$275$	0	0
$276$	−8.47214	−0.509963
$277$	0.562306	0.0337857	0.0168928	−	0.999857i	$-0.494623\pi$
$277$	0.562306	0.0337857	0.0168928	+	0.999857i	$0.494623\pi$
$278$	−9.79837	−0.587667
$279$	1.12461	0.0673287
$280$	0	0
$281$	0.0901699	0.00537909	0.00268954	−	0.999996i	$-0.499144\pi$
$281$	0.0901699	0.00537909	0.00268954	+	0.999996i	$0.499144\pi$
$282$	5.41641	0.322542
$283$	−7.05573	−0.419419	−0.209710	−	0.977764i	$-0.567252\pi$
$283$	−7.05573	−0.419419	−0.209710	+	0.977764i	$0.567252\pi$
$284$	0.291796	0.0173149
$285$	0	0
$286$	2.14590	0.126890
$287$	5.14590	0.303753
$288$	−1.47214	−0.0867464
$289$	24.8885	1.46403
$290$	0	0
$291$	17.5279	1.02750
$292$	2.29180	0.134117
$293$	5.90983	0.345256	0.172628	−	0.984987i	$-0.444774\pi$
$293$	5.90983	0.345256	0.172628	+	0.984987i	$0.444774\pi$
$294$	−8.18034	−0.477087
$295$	0	0
$296$	6.61803	0.384665
$297$	−31.0557	−1.80204
$298$	16.1803	0.937302
$299$	−2.61803	−0.151405
$300$	0	0
$301$	6.47214	0.373048
$302$	2.00000	0.115087
$303$	13.5279	0.777155
$304$	−1.38197	−0.0792612
$305$	0	0
$306$	9.52786	0.544672
$307$	−28.1803	−1.60834	−0.804168	−	0.594401i	$-0.797389\pi$
$307$	−28.1803	−1.60834	−0.804168	+	0.594401i	$0.797389\pi$
$308$	−3.47214	−0.197843
$309$	−17.4164	−0.990785
$310$	0	0
$311$	31.5967	1.79169	0.895844	−	0.444370i	$-0.146572\pi$
$311$	31.5967	1.79169	0.895844	+	0.444370i	$0.146572\pi$
$312$	0.472136	0.0267294
$313$	−22.8328	−1.29059	−0.645294	−	0.763935i	$-0.723265\pi$
$313$	−22.8328	−1.29059	−0.645294	+	0.763935i	$0.723265\pi$
$314$	−7.52786	−0.424822
$315$	0	0
$316$	−4.47214	−0.251577
$317$	17.1459	0.963010	0.481505	−	0.876443i	$-0.340090\pi$
$317$	17.1459	0.963010	0.481505	+	0.876443i	$0.340090\pi$
$318$	14.2918	0.801444
$319$	40.6525	2.27610
$320$	0	0
$321$	6.47214	0.361239
$322$	4.23607	0.236067
$323$	8.94427	0.497673
$324$	−2.41641	−0.134245
$325$	0	0
$326$	−6.00000	−0.332309
$327$	11.0557	0.611383
$328$	−8.32624	−0.459740
$329$	−2.70820	−0.149308
$330$	0	0
$331$	29.8885	1.64282	0.821411	−	0.570336i	$-0.193187\pi$
$331$	29.8885	1.64282	0.821411	+	0.570336i	$0.193187\pi$
$332$	4.00000	0.219529
$333$	−9.74265	−0.533894
$334$	14.5066	0.793765
$335$	0	0
$336$	−0.763932	−0.0416759
$337$	−14.3607	−0.782276	−0.391138	−	0.920332i	$-0.627918\pi$
$337$	−14.3607	−0.782276	−0.391138	+	0.920332i	$0.627918\pi$
$338$	−12.8541	−0.699171
$339$	1.52786	0.0829822
$340$	0	0
$341$	−4.29180	−0.232414
$342$	2.03444	0.110010
$343$	8.41641	0.454443
$344$	−10.4721	−0.564620
$345$	0	0
$346$	17.0902	0.918773
$347$	−25.4164	−1.36442	−0.682212	−	0.731154i	$-0.738982\pi$
$347$	−25.4164	−1.36442	−0.682212	+	0.731154i	$0.738982\pi$
$348$	8.94427	0.479463
$349$	−7.88854	−0.422264	−0.211132	−	0.977458i	$-0.567715\pi$
$349$	−7.88854	−0.422264	−0.211132	+	0.977458i	$0.567715\pi$
$350$	0	0
$351$	−2.11146	−0.112701
$352$	5.61803	0.299442
$353$	8.47214	0.450926	0.225463	−	0.974252i	$-0.427610\pi$
$353$	8.47214	0.450926	0.225463	+	0.974252i	$0.427610\pi$
$354$	9.34752	0.496815
$355$	0	0
$356$	8.09017	0.428778
$357$	4.94427	0.261679
$358$	15.8541	0.837915
$359$	−12.7639	−0.673655	−0.336827	−	0.941566i	$-0.609354\pi$
$359$	−12.7639	−0.673655	−0.336827	+	0.941566i	$0.609354\pi$
$360$	0	0
$361$	−17.0902	−0.899483
$362$	−10.7639	−0.565740
$363$	25.4164	1.33402
$364$	−0.236068	−0.0123733
$365$	0	0
$366$	−4.36068	−0.227936
$367$	13.5279	0.706149	0.353074	−	0.935595i	$-0.385136\pi$
$367$	13.5279	0.706149	0.353074	+	0.935595i	$0.385136\pi$
$368$	−6.85410	−0.357295
$369$	12.2574	0.638092
$370$	0	0
$371$	−7.14590	−0.370997
$372$	−0.944272	−0.0489582
$373$	10.9098	0.564890	0.282445	−	0.959284i	$-0.408855\pi$
$373$	10.9098	0.564890	0.282445	+	0.959284i	$0.408855\pi$
$374$	−36.3607	−1.88017
$375$	0	0
$376$	4.38197	0.225983
$377$	2.76393	0.142350
$378$	3.41641	0.175721
$379$	−4.67376	−0.240075	−0.120038	−	0.992769i	$-0.538301\pi$
$379$	−4.67376	−0.240075	−0.120038	+	0.992769i	$0.538301\pi$
$380$	0	0
$381$	14.1115	0.722952
$382$	−15.8885	−0.812929
$383$	−7.38197	−0.377201	−0.188600	−	0.982054i	$-0.560395\pi$
$383$	−7.38197	−0.377201	−0.188600	+	0.982054i	$0.560395\pi$
$384$	1.23607	0.0630778
$385$	0	0
$386$	10.1803	0.518166
$387$	15.4164	0.783660
$388$	14.1803	0.719898
$389$	14.4721	0.733766	0.366883	−	0.930267i	$-0.380425\pi$
$389$	14.4721	0.733766	0.366883	+	0.930267i	$0.380425\pi$
$390$	0	0
$391$	44.3607	2.24342
$392$	−6.61803	−0.334261
$393$	−4.11146	−0.207396
$394$	−10.9443	−0.551364
$395$	0	0
$396$	−8.27051	−0.415609
$397$	30.0344	1.50739	0.753693	−	0.657227i	$-0.228271\pi$
$397$	30.0344	1.50739	0.753693	+	0.657227i	$0.228271\pi$
$398$	−12.7639	−0.639798
$399$	1.05573	0.0528525
$400$	0	0
$401$	24.6869	1.23281	0.616403	−	0.787431i	$-0.288589\pi$
$401$	24.6869	1.23281	0.616403	+	0.787431i	$0.288589\pi$
$402$	−5.88854	−0.293694
$403$	−0.291796	−0.0145354
$404$	10.9443	0.544498
$405$	0	0
$406$	−4.47214	−0.221948
$407$	37.1803	1.84296
$408$	−8.00000	−0.396059
$409$	−12.0344	−0.595065	−0.297532	−	0.954712i	$-0.596164\pi$
$409$	−12.0344	−0.595065	−0.297532	+	0.954712i	$0.596164\pi$
$410$	0	0
$411$	3.05573	0.150728
$412$	−14.0902	−0.694173
$413$	−4.67376	−0.229981
$414$	10.0902	0.495905
$415$	0	0
$416$	0.381966	0.0187274
$417$	−12.1115	−0.593101
$418$	−7.76393	−0.379746
$419$	−17.8885	−0.873913	−0.436956	−	0.899483i	$-0.643944\pi$
$419$	−17.8885	−0.873913	−0.436956	+	0.899483i	$0.643944\pi$
$420$	0	0
$421$	8.18034	0.398685	0.199343	−	0.979930i	$-0.436119\pi$
$421$	8.18034	0.398685	0.199343	+	0.979930i	$0.436119\pi$
$422$	−1.09017	−0.0530686
$423$	−6.45085	−0.313651
$424$	11.5623	0.561515
$425$	0	0
$426$	0.360680	0.0174750
$427$	2.18034	0.105514
$428$	5.23607	0.253095
$429$	2.65248	0.128063
$430$	0	0
$431$	2.00000	0.0963366	0.0481683	−	0.998839i	$-0.484662\pi$
$431$	2.00000	0.0963366	0.0481683	+	0.998839i	$0.484662\pi$
$432$	−5.52786	−0.265959
$433$	5.70820	0.274319	0.137159	−	0.990549i	$-0.456203\pi$
$433$	5.70820	0.274319	0.137159	+	0.990549i	$0.456203\pi$
$434$	0.472136	0.0226633
$435$	0	0
$436$	8.94427	0.428353
$437$	9.47214	0.453114
$438$	2.83282	0.135357
$439$	−2.76393	−0.131915	−0.0659576	−	0.997822i	$-0.521010\pi$
$439$	−2.76393	−0.131915	−0.0659576	+	0.997822i	$0.521010\pi$
$440$	0	0
$441$	9.74265	0.463936
$442$	−2.47214	−0.117588
$443$	28.4721	1.35275	0.676376	−	0.736557i	$-0.263549\pi$
$443$	28.4721	1.35275	0.676376	+	0.736557i	$0.263549\pi$
$444$	8.18034	0.388222
$445$	0	0
$446$	12.9443	0.612929
$447$	20.0000	0.945968
$448$	−0.618034	−0.0291994
$449$	14.7984	0.698378	0.349189	−	0.937052i	$-0.386457\pi$
$449$	14.7984	0.698378	0.349189	+	0.937052i	$0.386457\pi$
$450$	0	0
$451$	−46.7771	−2.20265
$452$	1.23607	0.0581397
$453$	2.47214	0.116151
$454$	−12.6525	−0.593810
$455$	0	0
$456$	−1.70820	−0.0799940
$457$	24.1803	1.13111	0.565554	−	0.824711i	$-0.308662\pi$
$457$	24.1803	1.13111	0.565554	+	0.824711i	$0.308662\pi$
$458$	8.29180	0.387450
$459$	35.7771	1.66993
$460$	0	0
$461$	−40.3607	−1.87978	−0.939892	−	0.341471i	$-0.889075\pi$
$461$	−40.3607	−1.87978	−0.939892	+	0.341471i	$0.889075\pi$
$462$	−4.29180	−0.199672
$463$	−13.8885	−0.645455	−0.322728	−	0.946492i	$-0.604600\pi$
$463$	−13.8885	−0.645455	−0.322728	+	0.946492i	$0.604600\pi$
$464$	7.23607	0.335926
$465$	0	0
$466$	−20.4721	−0.948353
$467$	−37.1246	−1.71792	−0.858961	−	0.512041i	$-0.828890\pi$
$467$	−37.1246	−1.71792	−0.858961	+	0.512041i	$0.828890\pi$
$468$	−0.562306	−0.0259926
$469$	2.94427	0.135954
$470$	0	0
$471$	−9.30495	−0.428750
$472$	7.56231	0.348083
$473$	−58.8328	−2.70514
$474$	−5.52786	−0.253903
$475$	0	0
$476$	4.00000	0.183340
$477$	−17.0213	−0.779351
$478$	−20.6525	−0.944622
$479$	−42.3607	−1.93551	−0.967754	−	0.251896i	$-0.918946\pi$
$479$	−42.3607	−1.93551	−0.967754	+	0.251896i	$0.918946\pi$
$480$	0	0
$481$	2.52786	0.115261
$482$	−16.0902	−0.732887
$483$	5.23607	0.238249
$484$	20.5623	0.934650
$485$	0	0
$486$	13.5967	0.616761
$487$	−0.742646	−0.0336525	−0.0168262	−	0.999858i	$-0.505356\pi$
$487$	−0.742646	−0.0336525	−0.0168262	+	0.999858i	$0.505356\pi$
$488$	−3.52786	−0.159699
$489$	−7.41641	−0.335382
$490$	0	0
$491$	−3.85410	−0.173933	−0.0869666	−	0.996211i	$-0.527717\pi$
$491$	−3.85410	−0.173933	−0.0869666	+	0.996211i	$0.527717\pi$
$492$	−10.2918	−0.463990
$493$	−46.8328	−2.10924
$494$	−0.527864	−0.0237497
$495$	0	0
$496$	−0.763932	−0.0343016
$497$	−0.180340	−0.00808935
$498$	4.94427	0.221558
$499$	2.96556	0.132757	0.0663783	−	0.997795i	$-0.478856\pi$
$499$	2.96556	0.132757	0.0663783	+	0.997795i	$0.478856\pi$
$500$	0	0
$501$	17.9311	0.801103
$502$	−8.00000	−0.357057
$503$	27.6180	1.23143	0.615714	−	0.787970i	$-0.288868\pi$
$503$	27.6180	1.23143	0.615714	+	0.787970i	$0.288868\pi$
$504$	0.909830	0.0405271
$505$	0	0
$506$	−38.5066	−1.71183
$507$	−15.8885	−0.705635
$508$	11.4164	0.506521
$509$	−30.6525	−1.35865	−0.679324	−	0.733839i	$-0.737727\pi$
$509$	−30.6525	−1.35865	−0.679324	+	0.733839i	$0.737727\pi$
$510$	0	0
$511$	−1.41641	−0.0626582
$512$	1.00000	0.0441942
$513$	7.63932	0.337284
$514$	−0.291796	−0.0128706
$515$	0	0
$516$	−12.9443	−0.569840
$517$	24.6180	1.08270
$518$	−4.09017	−0.179712
$519$	21.1246	0.927268
$520$	0	0
$521$	−19.9098	−0.872265	−0.436133	−	0.899882i	$-0.643652\pi$
$521$	−19.9098	−0.872265	−0.436133	+	0.899882i	$0.643652\pi$
$522$	−10.6525	−0.466246
$523$	25.7082	1.12414	0.562071	−	0.827089i	$-0.310005\pi$
$523$	25.7082	1.12414	0.562071	+	0.827089i	$0.310005\pi$
$524$	−3.32624	−0.145307
$525$	0	0
$526$	9.85410	0.429659
$527$	4.94427	0.215376
$528$	6.94427	0.302211
$529$	23.9787	1.04255
$530$	0	0
$531$	−11.1327	−0.483120
$532$	0.854102	0.0370300
$533$	−3.18034	−0.137756
$534$	10.0000	0.432742
$535$	0	0
$536$	−4.76393	−0.205771
$537$	19.5967	0.845662
$538$	−19.5967	−0.844876
$539$	−37.1803	−1.60147
$540$	0	0
$541$	−15.8885	−0.683102	−0.341551	−	0.939863i	$-0.610952\pi$
$541$	−15.8885	−0.683102	−0.341551	+	0.939863i	$0.610952\pi$
$542$	−27.5967	−1.18538
$543$	−13.3050	−0.570970
$544$	−6.47214	−0.277491
$545$	0	0
$546$	−0.291796	−0.0124877
$547$	12.0689	0.516028	0.258014	−	0.966141i	$-0.416932\pi$
$547$	12.0689	0.516028	0.258014	+	0.966141i	$0.416932\pi$
$548$	2.47214	0.105604
$549$	5.19350	0.221653
$550$	0	0
$551$	−10.0000	−0.426014
$552$	−8.47214	−0.360598
$553$	2.76393	0.117534
$554$	0.562306	0.0238901
$555$	0	0
$556$	−9.79837	−0.415544
$557$	−21.1459	−0.895980	−0.447990	−	0.894038i	$-0.647860\pi$
$557$	−21.1459	−0.895980	−0.447990	+	0.894038i	$0.647860\pi$
$558$	1.12461	0.0476086
$559$	−4.00000	−0.169182
$560$	0	0
$561$	−44.9443	−1.89755
$562$	0.0901699	0.00380359
$563$	−14.2918	−0.602327	−0.301164	−	0.953572i	$-0.597375\pi$
$563$	−14.2918	−0.602327	−0.301164	+	0.953572i	$0.597375\pi$
$564$	5.41641	0.228072
$565$	0	0
$566$	−7.05573	−0.296574
$567$	1.49342	0.0627178
$568$	0.291796	0.0122435
$569$	−17.4377	−0.731026	−0.365513	−	0.930806i	$-0.619106\pi$
$569$	−17.4377	−0.731026	−0.365513	+	0.930806i	$0.619106\pi$
$570$	0	0
$571$	−1.09017	−0.0456222	−0.0228111	−	0.999740i	$-0.507262\pi$
$571$	−1.09017	−0.0456222	−0.0228111	+	0.999740i	$0.507262\pi$
$572$	2.14590	0.0897245
$573$	−19.6393	−0.820444
$574$	5.14590	0.214786
$575$	0	0
$576$	−1.47214	−0.0613390
$577$	15.8885	0.661449	0.330724	−	0.943727i	$-0.392707\pi$
$577$	15.8885	0.661449	0.330724	+	0.943727i	$0.392707\pi$
$578$	24.8885	1.03523
$579$	12.5836	0.522956
$580$	0	0
$581$	−2.47214	−0.102561
$582$	17.5279	0.726553
$583$	64.9574	2.69026
$584$	2.29180	0.0948352
$585$	0	0
$586$	5.90983	0.244133
$587$	31.4164	1.29669	0.648347	−	0.761345i	$-0.275461\pi$
$587$	31.4164	1.29669	0.648347	+	0.761345i	$0.275461\pi$
$588$	−8.18034	−0.337352
$589$	1.05573	0.0435005
$590$	0	0
$591$	−13.5279	−0.556462
$592$	6.61803	0.272000
$593$	8.47214	0.347909	0.173954	−	0.984754i	$-0.444345\pi$
$593$	8.47214	0.347909	0.173954	+	0.984754i	$0.444345\pi$
$594$	−31.0557	−1.27423
$595$	0	0
$596$	16.1803	0.662773
$597$	−15.7771	−0.645713
$598$	−2.61803	−0.107059
$599$	35.1246	1.43515	0.717576	−	0.696480i	$-0.245251\pi$
$599$	35.1246	1.43515	0.717576	+	0.696480i	$0.245251\pi$
$600$	0	0
$601$	25.6180	1.04498	0.522491	−	0.852645i	$-0.325003\pi$
$601$	25.6180	1.04498	0.522491	+	0.852645i	$0.325003\pi$
$602$	6.47214	0.263785
$603$	7.01316	0.285598
$604$	2.00000	0.0813788
$605$	0	0
$606$	13.5279	0.549532
$607$	−9.56231	−0.388122	−0.194061	−	0.980989i	$-0.562166\pi$
$607$	−9.56231	−0.388122	−0.194061	+	0.980989i	$0.562166\pi$
$608$	−1.38197	−0.0560461
$609$	−5.52786	−0.224000
$610$	0	0
$611$	1.67376	0.0677132
$612$	9.52786	0.385141
$613$	33.1459	1.33875	0.669375	−	0.742925i	$-0.266562\pi$
$613$	33.1459	1.33875	0.669375	+	0.742925i	$0.266562\pi$
$614$	−28.1803	−1.13727
$615$	0	0
$616$	−3.47214	−0.139896
$617$	−25.8197	−1.03946	−0.519730	−	0.854330i	$-0.673968\pi$
$617$	−25.8197	−1.03946	−0.519730	+	0.854330i	$0.673968\pi$
$618$	−17.4164	−0.700591
$619$	24.2705	0.975514	0.487757	−	0.872979i	$-0.337815\pi$
$619$	24.2705	0.975514	0.487757	+	0.872979i	$0.337815\pi$
$620$	0	0
$621$	37.8885	1.52041
$622$	31.5967	1.26691
$623$	−5.00000	−0.200321
$624$	0.472136	0.0189006
$625$	0	0
$626$	−22.8328	−0.912583
$627$	−9.59675	−0.383257
$628$	−7.52786	−0.300394
$629$	−42.8328	−1.70786
$630$	0	0
$631$	−43.1246	−1.71676	−0.858382	−	0.513011i	$-0.828530\pi$
$631$	−43.1246	−1.71676	−0.858382	+	0.513011i	$0.828530\pi$
$632$	−4.47214	−0.177892
$633$	−1.34752	−0.0535593
$634$	17.1459	0.680951
$635$	0	0
$636$	14.2918	0.566707
$637$	−2.52786	−0.100158
$638$	40.6525	1.60945
$639$	−0.429563	−0.0169933
$640$	0	0
$641$	27.4508	1.08424	0.542122	−	0.840300i	$-0.317621\pi$
$641$	27.4508	1.08424	0.542122	+	0.840300i	$0.317621\pi$
$642$	6.47214	0.255435
$643$	−36.6525	−1.44543	−0.722716	−	0.691145i	$-0.757107\pi$
$643$	−36.6525	−1.44543	−0.722716	+	0.691145i	$0.757107\pi$
$644$	4.23607	0.166924
$645$	0	0
$646$	8.94427	0.351908
$647$	31.7426	1.24793	0.623966	−	0.781451i	$-0.285520\pi$
$647$	31.7426	1.24793	0.623966	+	0.781451i	$0.285520\pi$
$648$	−2.41641	−0.0949255
$649$	42.4853	1.66769
$650$	0	0
$651$	0.583592	0.0228728
$652$	−6.00000	−0.234978
$653$	−7.25735	−0.284002	−0.142001	−	0.989866i	$-0.545354\pi$
$653$	−7.25735	−0.284002	−0.142001	+	0.989866i	$0.545354\pi$
$654$	11.0557	0.432313
$655$	0	0
$656$	−8.32624	−0.325085
$657$	−3.37384	−0.131626
$658$	−2.70820	−0.105577
$659$	4.67376	0.182064	0.0910320	−	0.995848i	$-0.470983\pi$
$659$	4.67376	0.182064	0.0910320	+	0.995848i	$0.470983\pi$
$660$	0	0
$661$	25.4164	0.988584	0.494292	−	0.869296i	$-0.335427\pi$
$661$	25.4164	0.988584	0.494292	+	0.869296i	$0.335427\pi$
$662$	29.8885	1.16165
$663$	−3.05573	−0.118675
$664$	4.00000	0.155230
$665$	0	0
$666$	−9.74265	−0.377520
$667$	−49.5967	−1.92039
$668$	14.5066	0.561276
$669$	16.0000	0.618596
$670$	0	0
$671$	−19.8197	−0.765129
$672$	−0.763932	−0.0294693
$673$	17.8197	0.686897	0.343449	−	0.939171i	$-0.388405\pi$
$673$	17.8197	0.686897	0.343449	+	0.939171i	$0.388405\pi$
$674$	−14.3607	−0.553153
$675$	0	0
$676$	−12.8541	−0.494389
$677$	−34.0344	−1.30805	−0.654025	−	0.756473i	$-0.726921\pi$
$677$	−34.0344	−1.30805	−0.654025	+	0.756473i	$0.726921\pi$
$678$	1.52786	0.0586773
$679$	−8.76393	−0.336329
$680$	0	0
$681$	−15.6393	−0.599300
$682$	−4.29180	−0.164341
$683$	2.94427	0.112659	0.0563297	−	0.998412i	$-0.482060\pi$
$683$	2.94427	0.112659	0.0563297	+	0.998412i	$0.482060\pi$
$684$	2.03444	0.0777888
$685$	0	0
$686$	8.41641	0.321340
$687$	10.2492	0.391032
$688$	−10.4721	−0.399246
$689$	4.41641	0.168252
$690$	0	0
$691$	24.3607	0.926724	0.463362	−	0.886169i	$-0.346643\pi$
$691$	24.3607	0.926724	0.463362	+	0.886169i	$0.346643\pi$
$692$	17.0902	0.649671
$693$	5.11146	0.194168
$694$	−25.4164	−0.964794
$695$	0	0
$696$	8.94427	0.339032
$697$	53.8885	2.04117
$698$	−7.88854	−0.298586
$699$	−25.3050	−0.957121
$700$	0	0
$701$	13.7082	0.517752	0.258876	−	0.965911i	$-0.416648\pi$
$701$	13.7082	0.517752	0.258876	+	0.965911i	$0.416648\pi$
$702$	−2.11146	−0.0796918
$703$	−9.14590	−0.344944
$704$	5.61803	0.211738
$705$	0	0
$706$	8.47214	0.318853
$707$	−6.76393	−0.254384
$708$	9.34752	0.351301
$709$	−0.652476	−0.0245042	−0.0122521	−	0.999925i	$-0.503900\pi$
$709$	−0.652476	−0.0245042	−0.0122521	+	0.999925i	$0.503900\pi$
$710$	0	0
$711$	6.58359	0.246904
$712$	8.09017	0.303192
$713$	5.23607	0.196092
$714$	4.94427	0.185035
$715$	0	0
$716$	15.8541	0.592496
$717$	−25.5279	−0.953356
$718$	−12.7639	−0.476346
$719$	26.1803	0.976362	0.488181	−	0.872742i	$-0.337661\pi$
$719$	26.1803	0.976362	0.488181	+	0.872742i	$0.337661\pi$
$720$	0	0
$721$	8.70820	0.324310
$722$	−17.0902	−0.636030
$723$	−19.8885	−0.739663
$724$	−10.7639	−0.400038
$725$	0	0
$726$	25.4164	0.943291
$727$	−32.9787	−1.22311	−0.611556	−	0.791201i	$-0.709456\pi$
$727$	−32.9787	−1.22311	−0.611556	+	0.791201i	$0.709456\pi$
$728$	−0.236068	−0.00874926
$729$	24.0557	0.890953
$730$	0	0
$731$	67.7771	2.50683
$732$	−4.36068	−0.161175
$733$	33.1459	1.22427	0.612136	−	0.790753i	$-0.290311\pi$
$733$	33.1459	1.22427	0.612136	+	0.790753i	$0.290311\pi$
$734$	13.5279	0.499323
$735$	0	0
$736$	−6.85410	−0.252646
$737$	−26.7639	−0.985862
$738$	12.2574	0.451199
$739$	−24.1459	−0.888221	−0.444111	−	0.895972i	$-0.646480\pi$
$739$	−24.1459	−0.888221	−0.444111	+	0.895972i	$0.646480\pi$
$740$	0	0
$741$	−0.652476	−0.0239693
$742$	−7.14590	−0.262334
$743$	−42.6312	−1.56399	−0.781993	−	0.623287i	$-0.785797\pi$
$743$	−42.6312	−1.56399	−0.781993	+	0.623287i	$0.785797\pi$
$744$	−0.944272	−0.0346187
$745$	0	0
$746$	10.9098	0.399437
$747$	−5.88854	−0.215451
$748$	−36.3607	−1.32948
$749$	−3.23607	−0.118243
$750$	0	0
$751$	43.3050	1.58022	0.790110	−	0.612965i	$-0.210023\pi$
$751$	43.3050	1.58022	0.790110	+	0.612965i	$0.210023\pi$
$752$	4.38197	0.159794
$753$	−9.88854	−0.360359
$754$	2.76393	0.100656
$755$	0	0
$756$	3.41641	0.124254
$757$	−8.38197	−0.304648	−0.152324	−	0.988331i	$-0.548676\pi$
$757$	−8.38197	−0.304648	−0.152324	+	0.988331i	$0.548676\pi$
$758$	−4.67376	−0.169759
$759$	−47.5967	−1.72765
$760$	0	0
$761$	14.4377	0.523366	0.261683	−	0.965154i	$-0.415723\pi$
$761$	14.4377	0.523366	0.261683	+	0.965154i	$0.415723\pi$
$762$	14.1115	0.511204
$763$	−5.52786	−0.200122
$764$	−15.8885	−0.574827
$765$	0	0
$766$	−7.38197	−0.266721
$767$	2.88854	0.104299
$768$	1.23607	0.0446028
$769$	−34.9230	−1.25936	−0.629678	−	0.776857i	$-0.716813\pi$
$769$	−34.9230	−1.25936	−0.629678	+	0.776857i	$0.716813\pi$
$770$	0	0
$771$	−0.360680	−0.0129896
$772$	10.1803	0.366398
$773$	6.36068	0.228778	0.114389	−	0.993436i	$-0.463509\pi$
$773$	6.36068	0.228778	0.114389	+	0.993436i	$0.463509\pi$
$774$	15.4164	0.554131
$775$	0	0
$776$	14.1803	0.509045
$777$	−5.05573	−0.181373
$778$	14.4721	0.518851
$779$	11.5066	0.412266
$780$	0	0
$781$	1.63932	0.0586595
$782$	44.3607	1.58633
$783$	−40.0000	−1.42948
$784$	−6.61803	−0.236358
$785$	0	0
$786$	−4.11146	−0.146651
$787$	−13.7082	−0.488645	−0.244322	−	0.969694i	$-0.578566\pi$
$787$	−13.7082	−0.488645	−0.244322	+	0.969694i	$0.578566\pi$
$788$	−10.9443	−0.389874
$789$	12.1803	0.433632
$790$	0	0
$791$	−0.763932	−0.0271623
$792$	−8.27051	−0.293880
$793$	−1.34752	−0.0478520
$794$	30.0344	1.06588
$795$	0	0
$796$	−12.7639	−0.452406
$797$	−25.7426	−0.911851	−0.455926	−	0.890018i	$-0.650692\pi$
$797$	−25.7426	−0.911851	−0.455926	+	0.890018i	$0.650692\pi$
$798$	1.05573	0.0373724
$799$	−28.3607	−1.00333
$800$	0	0
$801$	−11.9098	−0.420813
$802$	24.6869	0.871725
$803$	12.8754	0.454363
$804$	−5.88854	−0.207673
$805$	0	0
$806$	−0.291796	−0.0102781
$807$	−24.2229	−0.852687
$808$	10.9443	0.385018
$809$	29.7984	1.04766	0.523828	−	0.851824i	$-0.324504\pi$
$809$	29.7984	1.04766	0.523828	+	0.851824i	$0.324504\pi$
$810$	0	0
$811$	−18.2016	−0.639146	−0.319573	−	0.947562i	$-0.603539\pi$
$811$	−18.2016	−0.639146	−0.319573	+	0.947562i	$0.603539\pi$
$812$	−4.47214	−0.156941
$813$	−34.1115	−1.19634
$814$	37.1803	1.30317
$815$	0	0
$816$	−8.00000	−0.280056
$817$	14.4721	0.506316
$818$	−12.0344	−0.420774
$819$	0.347524	0.0121435
$820$	0	0
$821$	−6.94427	−0.242357	−0.121178	−	0.992631i	$-0.538667\pi$
$821$	−6.94427	−0.242357	−0.121178	+	0.992631i	$0.538667\pi$
$822$	3.05573	0.106581
$823$	22.2148	0.774359	0.387179	−	0.922004i	$-0.373449\pi$
$823$	22.2148	0.774359	0.387179	+	0.922004i	$0.373449\pi$
$824$	−14.0902	−0.490854
$825$	0	0
$826$	−4.67376	−0.162621
$827$	10.7639	0.374299	0.187149	−	0.982331i	$-0.440075\pi$
$827$	10.7639	0.374299	0.187149	+	0.982331i	$0.440075\pi$
$828$	10.0902	0.350658
$829$	−25.5279	−0.886619	−0.443310	−	0.896369i	$-0.646196\pi$
$829$	−25.5279	−0.886619	−0.443310	+	0.896369i	$0.646196\pi$
$830$	0	0
$831$	0.695048	0.0241110
$832$	0.381966	0.0132423
$833$	42.8328	1.48407
$834$	−12.1115	−0.419385
$835$	0	0
$836$	−7.76393	−0.268521
$837$	4.22291	0.145965
$838$	−17.8885	−0.617949
$839$	47.8885	1.65330	0.826648	−	0.562719i	$-0.190245\pi$
$839$	47.8885	1.65330	0.826648	+	0.562719i	$0.190245\pi$
$840$	0	0
$841$	23.3607	0.805541
$842$	8.18034	0.281913
$843$	0.111456	0.00383875
$844$	−1.09017	−0.0375252
$845$	0	0
$846$	−6.45085	−0.221785
$847$	−12.7082	−0.436659
$848$	11.5623	0.397051
$849$	−8.72136	−0.299316
$850$	0	0
$851$	−45.3607	−1.55494
$852$	0.360680	0.0123567
$853$	20.5066	0.702132	0.351066	−	0.936351i	$-0.385819\pi$
$853$	20.5066	0.702132	0.351066	+	0.936351i	$0.385819\pi$
$854$	2.18034	0.0746097
$855$	0	0
$856$	5.23607	0.178965
$857$	9.05573	0.309338	0.154669	−	0.987966i	$-0.450569\pi$
$857$	9.05573	0.309338	0.154669	+	0.987966i	$0.450569\pi$
$858$	2.65248	0.0905540
$859$	30.3262	1.03472	0.517359	−	0.855768i	$-0.326915\pi$
$859$	30.3262	1.03472	0.517359	+	0.855768i	$0.326915\pi$
$860$	0	0
$861$	6.36068	0.216771
$862$	2.00000	0.0681203
$863$	−7.38197	−0.251285	−0.125643	−	0.992076i	$-0.540099\pi$
$863$	−7.38197	−0.251285	−0.125643	+	0.992076i	$0.540099\pi$
$864$	−5.52786	−0.188062
$865$	0	0
$866$	5.70820	0.193973
$867$	30.7639	1.04480
$868$	0.472136	0.0160253
$869$	−25.1246	−0.852294
$870$	0	0
$871$	−1.81966	−0.0616568
$872$	8.94427	0.302891
$873$	−20.8754	−0.706525
$874$	9.47214	0.320400
$875$	0	0
$876$	2.83282	0.0957120
$877$	42.2705	1.42737	0.713687	−	0.700465i	$-0.247024\pi$
$877$	42.2705	1.42737	0.713687	+	0.700465i	$0.247024\pi$
$878$	−2.76393	−0.0932782
$879$	7.30495	0.246390
$880$	0	0
$881$	28.9098	0.973997	0.486998	−	0.873403i	$-0.338092\pi$
$881$	28.9098	0.973997	0.486998	+	0.873403i	$0.338092\pi$
$882$	9.74265	0.328052
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	−2.47214	−0.0831469
$885$	0	0
$886$	28.4721	0.956540
$887$	17.2705	0.579887	0.289943	−	0.957044i	$-0.406363\pi$
$887$	17.2705	0.579887	0.289943	+	0.957044i	$0.406363\pi$
$888$	8.18034	0.274514
$889$	−7.05573	−0.236642
$890$	0	0
$891$	−13.5755	−0.454795
$892$	12.9443	0.433406
$893$	−6.05573	−0.202647
$894$	20.0000	0.668900
$895$	0	0
$896$	−0.618034	−0.0206471
$897$	−3.23607	−0.108049
$898$	14.7984	0.493828
$899$	−5.52786	−0.184365
$900$	0	0
$901$	−74.8328	−2.49304
$902$	−46.7771	−1.55751
$903$	8.00000	0.266223
$904$	1.23607	0.0411110
$905$	0	0
$906$	2.47214	0.0821312
$907$	−7.12461	−0.236569	−0.118284	−	0.992980i	$-0.537739\pi$
$907$	−7.12461	−0.236569	−0.118284	+	0.992980i	$0.537739\pi$
$908$	−12.6525	−0.419887
$909$	−16.1115	−0.534383
$910$	0	0
$911$	15.8197	0.524129	0.262064	−	0.965050i	$-0.415597\pi$
$911$	15.8197	0.524129	0.262064	+	0.965050i	$0.415597\pi$
$912$	−1.70820	−0.0565643
$913$	22.4721	0.743719
$914$	24.1803	0.799815
$915$	0	0
$916$	8.29180	0.273969
$917$	2.05573	0.0678861
$918$	35.7771	1.18082
$919$	−0.403252	−0.0133021	−0.00665103	−	0.999978i	$-0.502117\pi$
$919$	−0.403252	−0.0133021	−0.00665103	+	0.999978i	$0.502117\pi$
$920$	0	0
$921$	−34.8328	−1.14778
$922$	−40.3607	−1.32921
$923$	0.111456	0.00366862
$924$	−4.29180	−0.141190
$925$	0	0
$926$	−13.8885	−0.456406
$927$	20.7426	0.681278
$928$	7.23607	0.237536
$929$	8.09017	0.265430	0.132715	−	0.991154i	$-0.457631\pi$
$929$	8.09017	0.265430	0.132715	+	0.991154i	$0.457631\pi$
$930$	0	0
$931$	9.14590	0.299745
$932$	−20.4721	−0.670587
$933$	39.0557	1.27863
$934$	−37.1246	−1.21475
$935$	0	0
$936$	−0.562306	−0.0183795
$937$	−44.3607	−1.44920	−0.724600	−	0.689170i	$-0.757976\pi$
$937$	−44.3607	−1.44920	−0.724600	+	0.689170i	$0.757976\pi$
$938$	2.94427	0.0961339
$939$	−28.2229	−0.921020
$940$	0	0
$941$	−26.9443	−0.878358	−0.439179	−	0.898400i	$-0.644731\pi$
$941$	−26.9443	−0.878358	−0.439179	+	0.898400i	$0.644731\pi$
$942$	−9.30495	−0.303172
$943$	57.0689	1.85842
$944$	7.56231	0.246132
$945$	0	0
$946$	−58.8328	−1.91282
$947$	20.3607	0.661633	0.330817	−	0.943695i	$-0.392676\pi$
$947$	20.3607	0.661633	0.330817	+	0.943695i	$0.392676\pi$
$948$	−5.52786	−0.179537
$949$	0.875388	0.0284163
$950$	0	0
$951$	21.1935	0.687246
$952$	4.00000	0.129641
$953$	−10.4721	−0.339226	−0.169613	−	0.985511i	$-0.554252\pi$
$953$	−10.4721	−0.339226	−0.169613	+	0.985511i	$0.554252\pi$
$954$	−17.0213	−0.551084
$955$	0	0
$956$	−20.6525	−0.667949
$957$	50.2492	1.62433
$958$	−42.3607	−1.36861
$959$	−1.52786	−0.0493373
$960$	0	0
$961$	−30.4164	−0.981174
$962$	2.52786	0.0815016
$963$	−7.70820	−0.248393
$964$	−16.0902	−0.518229
$965$	0	0
$966$	5.23607	0.168468
$967$	−42.4508	−1.36513	−0.682564	−	0.730826i	$-0.739135\pi$
$967$	−42.4508	−1.36513	−0.682564	+	0.730826i	$0.739135\pi$
$968$	20.5623	0.660898
$969$	11.0557	0.355161
$970$	0	0
$971$	−3.72949	−0.119685	−0.0598425	−	0.998208i	$-0.519060\pi$
$971$	−3.72949	−0.119685	−0.0598425	+	0.998208i	$0.519060\pi$
$972$	13.5967	0.436116
$973$	6.05573	0.194138
$974$	−0.742646	−0.0237959
$975$	0	0
$976$	−3.52786	−0.112924
$977$	0.111456	0.00356580	0.00178290	−	0.999998i	$-0.499432\pi$
$977$	0.111456	0.00356580	0.00178290	+	0.999998i	$0.499432\pi$
$978$	−7.41641	−0.237151
$979$	45.4508	1.45262
$980$	0	0
$981$	−13.1672	−0.420396
$982$	−3.85410	−0.122989
$983$	−53.2837	−1.69948	−0.849742	−	0.527198i	$-0.823243\pi$
$983$	−53.2837	−1.69948	−0.849742	+	0.527198i	$0.823243\pi$
$984$	−10.2918	−0.328090
$985$	0	0
$986$	−46.8328	−1.49146
$987$	−3.34752	−0.106553
$988$	−0.527864	−0.0167936
$989$	71.7771	2.28238
$990$	0	0
$991$	−18.0000	−0.571789	−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000	−0.571789	−0.285894	+	0.958261i	$0.592291\pi$
$992$	−0.763932	−0.0242549
$993$	36.9443	1.17239
$994$	−0.180340	−0.00572003
$995$	0	0
$996$	4.94427	0.156665
$997$	−8.50658	−0.269406	−0.134703	−	0.990886i	$-0.543008\pi$
$997$	−8.50658	−0.269406	−0.134703	+	0.990886i	$0.543008\pi$
$998$	2.96556	0.0938731
$999$	−36.5836	−1.15745

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.a.c.1.2	yes	2
3.2	odd	2		2250.2.a.d.1.1		2
4.3	odd	2		2000.2.a.j.1.1		2
5.2	odd	4		250.2.b.a.249.3		4
5.3	odd	4		250.2.b.a.249.2		4
5.4	even	2		250.2.a.b.1.1	✓	2
8.3	odd	2		8000.2.a.f.1.2		2
8.5	even	2		8000.2.a.s.1.1		2
15.2	even	4		2250.2.c.a.1999.1		4
15.8	even	4		2250.2.c.a.1999.4		4
15.14	odd	2		2250.2.a.k.1.2		2
20.3	even	4		2000.2.c.b.1249.2		4
20.7	even	4		2000.2.c.b.1249.3		4
20.19	odd	2		2000.2.a.c.1.2		2
40.19	odd	2		8000.2.a.t.1.1		2
40.29	even	2		8000.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.a.b.1.1	✓	2	5.4	even	2
250.2.a.c.1.2	yes	2	1.1	even	1	trivial
250.2.b.a.249.2		4	5.3	odd	4
250.2.b.a.249.3		4	5.2	odd	4
2000.2.a.c.1.2		2	20.19	odd	2
2000.2.a.j.1.1		2	4.3	odd	2
2000.2.c.b.1249.2		4	20.3	even	4
2000.2.c.b.1249.3		4	20.7	even	4
2250.2.a.d.1.1		2	3.2	odd	2
2250.2.a.k.1.2		2	15.14	odd	2
2250.2.c.a.1999.1		4	15.2	even	4
2250.2.c.a.1999.4		4	15.8	even	4
8000.2.a.e.1.2		2	40.29	even	2
8000.2.a.f.1.2		2	8.3	odd	2
8000.2.a.s.1.1		2	8.5	even	2
8000.2.a.t.1.1		2	40.19	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} +1.23607 q^{6} -0.618034 q^{7} +1.00000 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.23607 q^{3} +1.00000 q^{4} +1.23607 q^{6} -0.618034 q^{7} +1.00000 q^{8} -1.47214 q^{9} +5.61803 q^{11} +1.23607 q^{12} +0.381966 q^{13} -0.618034 q^{14} +1.00000 q^{16} -6.47214 q^{17} -1.47214 q^{18} -1.38197 q^{19} -0.763932 q^{21} +5.61803 q^{22} -6.85410 q^{23} +1.23607 q^{24} +0.381966 q^{26} -5.52786 q^{27} -0.618034 q^{28} +7.23607 q^{29} -0.763932 q^{31} +1.00000 q^{32} +6.94427 q^{33} -6.47214 q^{34} -1.47214 q^{36} +6.61803 q^{37} -1.38197 q^{38} +0.472136 q^{39} -8.32624 q^{41} -0.763932 q^{42} -10.4721 q^{43} +5.61803 q^{44} -6.85410 q^{46} +4.38197 q^{47} +1.23607 q^{48} -6.61803 q^{49} -8.00000 q^{51} +0.381966 q^{52} +11.5623 q^{53} -5.52786 q^{54} -0.618034 q^{56} -1.70820 q^{57} +7.23607 q^{58} +7.56231 q^{59} -3.52786 q^{61} -0.763932 q^{62} +0.909830 q^{63} +1.00000 q^{64} +6.94427 q^{66} -4.76393 q^{67} -6.47214 q^{68} -8.47214 q^{69} +0.291796 q^{71} -1.47214 q^{72} +2.29180 q^{73} +6.61803 q^{74} -1.38197 q^{76} -3.47214 q^{77} +0.472136 q^{78} -4.47214 q^{79} -2.41641 q^{81} -8.32624 q^{82} +4.00000 q^{83} -0.763932 q^{84} -10.4721 q^{86} +8.94427 q^{87} +5.61803 q^{88} +8.09017 q^{89} -0.236068 q^{91} -6.85410 q^{92} -0.944272 q^{93} +4.38197 q^{94} +1.23607 q^{96} +14.1803 q^{97} -6.61803 q^{98} -8.27051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + q^7 + 2 * q^8 + 6 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + 2 q^{8} + 6 q^{9} + 9 q^{11} - 2 q^{12} + 3 q^{13} + q^{14} + 2 q^{16} - 4 q^{17} + 6 q^{18} - 5 q^{19} - 6 q^{21} + 9 q^{22} - 7 q^{23} - 2 q^{24} + 3 q^{26} - 20 q^{27} + q^{28} + 10 q^{29} - 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{36} + 11 q^{37} - 5 q^{38} - 8 q^{39} - q^{41} - 6 q^{42} - 12 q^{43} + 9 q^{44} - 7 q^{46} + 11 q^{47} - 2 q^{48} - 11 q^{49} - 16 q^{51} + 3 q^{52} + 3 q^{53} - 20 q^{54} + q^{56} + 10 q^{57} + 10 q^{58} - 5 q^{59} - 16 q^{61} - 6 q^{62} + 13 q^{63} + 2 q^{64} - 4 q^{66} - 14 q^{67} - 4 q^{68} - 8 q^{69} + 14 q^{71} + 6 q^{72} + 18 q^{73} + 11 q^{74} - 5 q^{76} + 2 q^{77} - 8 q^{78} + 22 q^{81} - q^{82} + 8 q^{83} - 6 q^{84} - 12 q^{86} + 9 q^{88} + 5 q^{89} + 4 q^{91} - 7 q^{92} + 16 q^{93} + 11 q^{94} - 2 q^{96} + 6 q^{97} - 11 q^{98} + 17 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^6 + q^7 + 2 * q^8 + 6 * q^9 + 9 * q^11 - 2 * q^12 + 3 * q^13 + q^14 + 2 * q^16 - 4 * q^17 + 6 * q^18 - 5 * q^19 - 6 * q^21 + 9 * q^22 - 7 * q^23 - 2 * q^24 + 3 * q^26 - 20 * q^27 + q^28 + 10 * q^29 - 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^36 + 11 * q^37 - 5 * q^38 - 8 * q^39 - q^41 - 6 * q^42 - 12 * q^43 + 9 * q^44 - 7 * q^46 + 11 * q^47 - 2 * q^48 - 11 * q^49 - 16 * q^51 + 3 * q^52 + 3 * q^53 - 20 * q^54 + q^56 + 10 * q^57 + 10 * q^58 - 5 * q^59 - 16 * q^61 - 6 * q^62 + 13 * q^63 + 2 * q^64 - 4 * q^66 - 14 * q^67 - 4 * q^68 - 8 * q^69 + 14 * q^71 + 6 * q^72 + 18 * q^73 + 11 * q^74 - 5 * q^76 + 2 * q^77 - 8 * q^78 + 22 * q^81 - q^82 + 8 * q^83 - 6 * q^84 - 12 * q^86 + 9 * q^88 + 5 * q^89 + 4 * q^91 - 7 * q^92 + 16 * q^93 + 11 * q^94 - 2 * q^96 + 6 * q^97 - 11 * q^98 + 17 * q^99

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