LMFDB - Embedded newform 1280.2.s.d.1087.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(703,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.703"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1087.5
Character	$\chi$	$=$	1280.1087
Dual form			1280.2.s.d.703.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.81199 q^{3} +(0.344369 + 2.20939i) q^{5} +(-1.54814 - 1.54814i) q^{7} +0.283291 q^{9} +(2.69839 - 2.69839i) q^{11} +3.33474i q^{13} +(-0.623991 - 4.00338i) q^{15} +(-0.680078 - 0.680078i) q^{17} +(-2.79866 + 2.79866i) q^{19} +(2.80521 + 2.80521i) q^{21} +(-1.75563 + 1.75563i) q^{23} +(-4.76282 + 1.52169i) q^{25} +4.92264 q^{27} +(-3.13750 - 3.13750i) q^{29} -8.56830i q^{31} +(-4.88944 + 4.88944i) q^{33} +(2.88732 - 3.95358i) q^{35} +8.30361i q^{37} -6.04250i q^{39} -10.8252i q^{41} -2.87092i q^{43} +(0.0975564 + 0.625900i) q^{45} +(-0.985023 + 0.985023i) q^{47} -2.20651i q^{49} +(1.23229 + 1.23229i) q^{51} +13.1354 q^{53} +(6.89103 + 5.03255i) q^{55} +(5.07113 - 5.07113i) q^{57} +(-4.36188 - 4.36188i) q^{59} +(7.83616 - 7.83616i) q^{61} +(-0.438574 - 0.438574i) q^{63} +(-7.36775 + 1.14838i) q^{65} -13.0450i q^{67} +(3.18118 - 3.18118i) q^{69} -0.134408 q^{71} +(-7.36590 - 7.36590i) q^{73} +(8.63016 - 2.75728i) q^{75} -8.35497 q^{77} +7.88100 q^{79} -9.76962 q^{81} -12.0979 q^{83} +(1.26836 - 1.73676i) q^{85} +(5.68510 + 5.68510i) q^{87} +15.7833 q^{89} +(5.16265 - 5.16265i) q^{91} +15.5256i q^{93} +(-7.14711 - 5.21957i) q^{95} +(-3.00550 - 3.00550i) q^{97} +(0.764428 - 0.764428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{5} + 32 q^{9} + 8 q^{17} - 8 q^{21} - 16 q^{25} - 16 q^{29} + 56 q^{33} + 48 q^{45} - 112 q^{53} + 8 q^{57} + 8 q^{61} - 72 q^{65} + 40 q^{69} - 8 q^{73} - 144 q^{77} - 64 q^{81} - 40 q^{85}+ \cdots + 72 q^{97}+O(q^{100}) $ 32 * q + 8 * q^5 + 32 * q^9 + 8 * q^17 - 8 * q^21 - 16 * q^25 - 16 * q^29 + 56 * q^33 + 48 * q^45 - 112 * q^53 + 8 * q^57 + 8 * q^61 - 72 * q^65 + 40 * q^69 - 8 * q^73 - 144 * q^77 - 64 * q^81 - 40 * q^85 + 16 * q^89 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.81199			−1.04615			−0.523075	−	0.852287i	$-0.675215\pi$
$3$	−1.81199			−1.04615			−0.523075	+	0.852287i	$0.675215\pi$
$4$		0			0
$5$	0.344369	+	2.20939i	0.154006	+	0.988070i
$5$	0.344369	+	2.20939i	0.154006	+	0.988070i
$6$		0			0
$7$	−1.54814	−	1.54814i	−0.585143	−	0.585143i	0.351169	−	0.936312i	$-0.385784\pi$
$7$	−1.54814	−	1.54814i	−0.585143	−	0.585143i	−0.936312	+	0.351169i	$0.885784\pi$
$8$		0			0
$9$	0.283291			0.0944303
$10$		0			0
$11$	2.69839	−	2.69839i	0.813594	−	0.813594i	−0.171577	−	0.985171i	$-0.554886\pi$
$11$	2.69839	−	2.69839i	0.813594	−	0.813594i	0.985171	+	0.171577i	$0.0548862\pi$
$12$		0			0
$13$			3.33474i			0.924890i	0.886648	+	0.462445i	$0.153028\pi$
$13$			3.33474i			0.924890i	−0.886648	+	0.462445i	$0.846972\pi$
$14$		0			0
$15$	−0.623991	−	4.00338i	−0.161114	−	1.03367i
$16$		0			0
$17$	−0.680078	−	0.680078i	−0.164943	−	0.164943i	0.619809	−	0.784752i	$-0.287210\pi$
$17$	−0.680078	−	0.680078i	−0.164943	−	0.164943i	−0.784752	+	0.619809i	$0.787210\pi$
$18$		0			0
$19$	−2.79866	+	2.79866i	−0.642057	+	0.642057i	−0.951061	−	0.309004i	$-0.900004\pi$
$19$	−2.79866	+	2.79866i	−0.642057	+	0.642057i	0.309004	+	0.951061i	$0.400004\pi$
$20$		0			0
$21$	2.80521	+	2.80521i	0.612147	+	0.612147i
$22$		0			0
$23$	−1.75563	+	1.75563i	−0.366074	+	0.366074i	−0.866043	−	0.499969i	$-0.833345\pi$
$23$	−1.75563	+	1.75563i	−0.366074	+	0.366074i	0.499969	+	0.866043i	$0.333345\pi$
$24$		0			0
$25$	−4.76282	+	1.52169i	−0.952564	+	0.304338i
$26$		0			0
$27$	4.92264			0.947362
$28$		0			0
$29$	−3.13750	−	3.13750i	−0.582619	−	0.582619i	0.353003	−	0.935622i	$-0.385160\pi$
$29$	−3.13750	−	3.13750i	−0.582619	−	0.582619i	−0.935622	+	0.353003i	$0.885160\pi$
$30$		0			0
$31$		−	8.56830i		−	1.53891i	−0.638699	−	0.769456i	$-0.720527\pi$
$31$		−	8.56830i		−	1.53891i	0.638699	−	0.769456i	$-0.279473\pi$
$32$		0			0
$33$	−4.88944	+	4.88944i	−0.851141	+	0.851141i
$34$		0			0
$35$	2.88732	−	3.95358i	0.488046	−	0.668278i
$36$		0			0
$37$			8.30361i			1.36510i	0.730837	+	0.682552i	$0.239130\pi$
$37$			8.30361i			1.36510i	−0.730837	+	0.682552i	$0.760870\pi$
$38$		0			0
$39$		−	6.04250i		−	0.967574i
$40$		0			0
$41$		−	10.8252i		−	1.69061i	−0.534282	−	0.845306i	$-0.679418\pi$
$41$		−	10.8252i		−	1.69061i	0.534282	−	0.845306i	$-0.320582\pi$
$42$		0			0
$43$		−	2.87092i		−	0.437811i	−0.975746	−	0.218906i	$-0.929751\pi$
$43$		−	2.87092i		−	0.437811i	0.975746	−	0.218906i	$-0.0702487\pi$
$44$		0			0
$45$	0.0975564	+	0.625900i	0.0145429	+	0.0933037i
$46$		0			0
$47$	−0.985023	+	0.985023i	−0.143680	+	0.143680i	−0.775288	−	0.631608i	$-0.782395\pi$
$47$	−0.985023	+	0.985023i	−0.143680	+	0.143680i	0.631608	+	0.775288i	$0.282395\pi$
$48$		0			0
$49$		−	2.20651i		−	0.315216i
$50$		0			0
$51$	1.23229	+	1.23229i	0.172555	+	0.172555i
$52$		0			0
$53$	13.1354			1.80428			0.902141	−	0.431441i	$-0.141995\pi$
$53$	13.1354			1.80428			0.902141	+	0.431441i	$0.141995\pi$
$54$		0			0
$55$	6.89103	+	5.03255i	0.929186	+	0.678589i
$56$		0			0
$57$	5.07113	−	5.07113i	0.671688	−	0.671688i
$58$		0			0
$59$	−4.36188	−	4.36188i	−0.567868	−	0.567868i	0.363663	−	0.931531i	$-0.381526\pi$
$59$	−4.36188	−	4.36188i	−0.567868	−	0.567868i	−0.931531	+	0.363663i	$0.881526\pi$
$60$		0			0
$61$	7.83616	−	7.83616i	1.00332	−	1.00332i	0.00332328	−	0.999994i	$-0.498942\pi$
$61$	7.83616	−	7.83616i	1.00332	−	1.00332i	0.999994	−	0.00332328i	$-0.00105784\pi$
$62$		0			0
$63$	−0.438574	−	0.438574i	−0.0552552	−	0.0552552i
$64$		0			0
$65$	−7.36775	+	1.14838i	−0.913856	+	0.142439i
$66$		0			0
$67$		−	13.0450i		−	1.59370i	−0.604179	−	0.796849i	$-0.706499\pi$
$67$		−	13.0450i		−	1.59370i	0.604179	−	0.796849i	$-0.293501\pi$
$68$		0			0
$69$	3.18118	−	3.18118i	0.382968	−	0.382968i
$70$		0			0
$71$	−0.134408			−0.0159512			−0.00797562	−	0.999968i	$-0.502539\pi$
$71$	−0.134408			−0.0159512			−0.00797562	+	0.999968i	$0.502539\pi$
$72$		0			0
$73$	−7.36590	−	7.36590i	−0.862113	−	0.862113i	0.129470	−	0.991583i	$-0.458672\pi$
$73$	−7.36590	−	7.36590i	−0.862113	−	0.862113i	−0.991583	+	0.129470i	$0.958672\pi$
$74$		0			0
$75$	8.63016	−	2.75728i	0.996525	−	0.318383i
$76$		0			0
$77$	−8.35497			−0.952137
$78$		0			0
$79$	7.88100			0.886682			0.443341	−	0.896353i	$-0.353793\pi$
$79$	7.88100			0.886682			0.443341	+	0.896353i	$0.353793\pi$
$80$		0			0
$81$	−9.76962			−1.08551
$82$		0			0
$83$	−12.0979			−1.32792			−0.663961	−	0.747768i	$-0.731126\pi$
$83$	−12.0979			−1.32792			−0.663961	+	0.747768i	$0.731126\pi$
$84$		0			0
$85$	1.26836	−	1.73676i	0.137573	−	0.188378i
$86$		0			0
$87$	5.68510	+	5.68510i	0.609507	+	0.609507i
$88$		0			0
$89$	15.7833			1.67303			0.836514	−	0.547945i	$-0.184590\pi$
$89$	15.7833			1.67303			0.836514	+	0.547945i	$0.184590\pi$
$90$		0			0
$91$	5.16265	−	5.16265i	0.541193	−	0.541193i
$92$		0			0
$93$			15.5256i			1.60993i
$94$		0			0
$95$	−7.14711	−	5.21957i	−0.733278	−	0.535516i
$96$		0			0
$97$	−3.00550	−	3.00550i	−0.305162	−	0.305162i	0.537867	−	0.843029i	$-0.319230\pi$
$97$	−3.00550	−	3.00550i	−0.305162	−	0.305162i	−0.843029	+	0.537867i	$0.819230\pi$
$98$		0			0
$99$	0.764428	−	0.764428i	0.0768279	−	0.0768279i
$100$		0			0
$101$	−6.84933	−	6.84933i	−0.681534	−	0.681534i	0.278812	−	0.960346i	$-0.410059\pi$
$101$	−6.84933	−	6.84933i	−0.681534	−	0.681534i	−0.960346	+	0.278812i	$0.910059\pi$
$102$		0			0
$103$	4.45391	−	4.45391i	0.438857	−	0.438857i	−0.452770	−	0.891627i	$-0.649564\pi$
$103$	4.45391	−	4.45391i	0.438857	−	0.438857i	0.891627	+	0.452770i	$0.149564\pi$
$104$		0			0
$105$	−5.23178	+	7.16384i	−0.510570	+	0.699119i
$106$		0			0
$107$	−14.0189			−1.35526			−0.677631	−	0.735403i	$-0.736993\pi$
$107$	−14.0189			−1.35526			−0.677631	+	0.735403i	$0.736993\pi$
$108$		0			0
$109$	7.01357	+	7.01357i	0.671778	+	0.671778i	0.958126	−	0.286348i	$-0.0924413\pi$
$109$	7.01357	+	7.01357i	0.671778	+	0.671778i	−0.286348	+	0.958126i	$0.592441\pi$
$110$		0			0
$111$		−	15.0460i		−	1.42810i
$112$		0			0
$113$	7.44675	−	7.44675i	0.700532	−	0.700532i	−0.263993	−	0.964525i	$-0.585040\pi$
$113$	7.44675	−	7.44675i	0.700532	−	0.700532i	0.964525	+	0.263993i	$0.0850395\pi$
$114$		0			0
$115$	−4.48346	−	3.27429i	−0.418084	−	0.305329i
$116$		0			0
$117$			0.944701i			0.0873376i
$118$		0			0
$119$			2.10572i			0.193031i
$120$		0			0
$121$		−	3.56257i		−	0.323870i
$122$		0			0
$123$			19.6151i			1.76863i
$124$		0			0
$125$	−5.00217	−	9.99891i	−0.447408	−	0.894330i
$126$		0			0
$127$	−2.89344	+	2.89344i	−0.256751	+	0.256751i	−0.823732	−	0.566980i	$-0.808112\pi$
$127$	−2.89344	+	2.89344i	−0.256751	+	0.256751i	0.566980	+	0.823732i	$0.308112\pi$
$128$		0			0
$129$			5.20206i			0.458016i
$130$		0			0
$131$	−0.534493	−	0.534493i	−0.0466989	−	0.0466989i	0.683372	−	0.730071i	$-0.260513\pi$
$131$	−0.534493	−	0.534493i	−0.0466989	−	0.0466989i	−0.730071	+	0.683372i	$0.760513\pi$
$132$		0			0
$133$	8.66546			0.751390
$134$		0			0
$135$	1.69520	+	10.8760i	0.145900	+	0.936060i
$136$		0			0
$137$	4.46199	−	4.46199i	0.381214	−	0.381214i	−0.490326	−	0.871539i	$-0.663122\pi$
$137$	4.46199	−	4.46199i	0.381214	−	0.381214i	0.871539	+	0.490326i	$0.163122\pi$
$138$		0			0
$139$	−13.3184	−	13.3184i	−1.12965	−	1.12965i	−0.990233	−	0.139419i	$-0.955476\pi$
$139$	−13.3184	−	13.3184i	−1.12965	−	1.12965i	−0.139419	−	0.990233i	$-0.544524\pi$
$140$		0			0
$141$	1.78485	−	1.78485i	0.150311	−	0.150311i
$142$		0			0
$143$	8.99841	+	8.99841i	0.752485	+	0.752485i
$144$		0			0
$145$	5.85150	−	8.01241i	0.485941	−	0.665395i
$146$		0			0
$147$			3.99816i			0.329763i
$148$		0			0
$149$	−10.3862	+	10.3862i	−0.850874	+	0.850874i	−0.990241	−	0.139366i	$-0.955493\pi$
$149$	−10.3862	+	10.3862i	−0.850874	+	0.850874i	0.139366	+	0.990241i	$0.455493\pi$
$150$		0			0
$151$	−6.86253			−0.558465			−0.279233	−	0.960223i	$-0.590080\pi$
$151$	−6.86253			−0.558465			−0.279233	+	0.960223i	$0.590080\pi$
$152$		0			0
$153$	−0.192660	−	0.192660i	−0.0155756	−	0.0155756i
$154$		0			0
$155$	18.9307	−	2.95065i	1.52055	−	0.237002i
$156$		0			0
$157$	−4.58973			−0.366300			−0.183150	−	0.983085i	$-0.558629\pi$
$157$	−4.58973			−0.366300			−0.183150	+	0.983085i	$0.558629\pi$
$158$		0			0
$159$	−23.8011			−1.88755
$160$		0			0
$161$	5.43593			0.428411
$162$		0			0
$163$	2.83480			0.222039			0.111019	−	0.993818i	$-0.464588\pi$
$163$	2.83480			0.222039			0.111019	+	0.993818i	$0.464588\pi$
$164$		0			0
$165$	−12.4864	−	9.11891i	−0.972068	−	0.709906i
$166$		0			0
$167$	−10.6049	−	10.6049i	−0.820629	−	0.820629i	0.165569	−	0.986198i	$-0.447054\pi$
$167$	−10.6049	−	10.6049i	−0.820629	−	0.820629i	−0.986198	+	0.165569i	$0.947054\pi$
$168$		0			0
$169$	1.87951			0.144578
$170$		0			0
$171$	−0.792835	+	0.792835i	−0.0606296	+	0.0606296i
$172$		0			0
$173$			1.19118i			0.0905636i	0.998974	+	0.0452818i	$0.0144186\pi$
$173$			1.19118i			0.0905636i	−0.998974	+	0.0452818i	$0.985581\pi$
$174$		0			0
$175$	9.72932	+	5.01773i	0.735467	+	0.379305i
$176$		0			0
$177$	7.90366	+	7.90366i	0.594075	+	0.594075i
$178$		0			0
$179$	−3.66019	+	3.66019i	−0.273575	+	0.273575i	−0.830538	−	0.556962i	$-0.811967\pi$
$179$	−3.66019	+	3.66019i	−0.273575	+	0.273575i	0.556962	+	0.830538i	$0.311967\pi$
$180$		0			0
$181$	−6.16389	−	6.16389i	−0.458158	−	0.458158i	0.439892	−	0.898050i	$-0.355017\pi$
$181$	−6.16389	−	6.16389i	−0.458158	−	0.458158i	−0.898050	+	0.439892i	$0.855017\pi$
$182$		0			0
$183$	−14.1990	+	14.1990i	−1.04962	+	1.04962i
$184$		0			0
$185$	−18.3459	+	2.85950i	−1.34882	+	0.210235i
$186$		0			0
$187$	−3.67023			−0.268393
$188$		0			0
$189$	−7.62094	−	7.62094i	−0.554342	−	0.554342i
$190$		0			0
$191$			10.5198i			0.761184i	0.924743	+	0.380592i	$0.124280\pi$
$191$			10.5198i			0.761184i	−0.924743	+	0.380592i	$0.875720\pi$
$192$		0			0
$193$	5.63558	−	5.63558i	0.405658	−	0.405658i	−0.474563	−	0.880221i	$-0.657394\pi$
$193$	5.63558	−	5.63558i	0.405658	−	0.405658i	0.880221	+	0.474563i	$0.157394\pi$
$194$		0			0
$195$	13.3502	−	2.08085i	0.956031	−	0.149013i
$196$		0			0
$197$			9.83517i			0.700727i	0.936614	+	0.350364i	$0.113942\pi$
$197$			9.83517i			0.700727i	−0.936614	+	0.350364i	$0.886058\pi$
$198$		0			0
$199$		−	26.3116i		−	1.86518i	−0.360934	−	0.932592i	$-0.617542\pi$
$199$		−	26.3116i		−	1.86518i	0.360934	−	0.932592i	$-0.382458\pi$
$200$		0			0
$201$			23.6373i			1.66725i
$202$		0			0
$203$			9.71458i			0.681830i
$204$		0			0
$205$	23.9171	−	3.72786i	1.67044	−	0.260365i
$206$		0			0
$207$	−0.497354	+	0.497354i	−0.0345685	+	0.0345685i
$208$		0			0
$209$			15.1037i			1.04475i
$210$		0			0
$211$	18.6349	+	18.6349i	1.28288	+	1.28288i	0.939023	+	0.343853i	$0.111732\pi$
$211$	18.6349	+	18.6349i	1.28288	+	1.28288i	0.343853	+	0.939023i	$0.388268\pi$
$212$		0			0
$213$	0.243545			0.0166874
$214$		0			0
$215$	6.34298	−	0.988654i	0.432588	−	0.0674257i
$216$		0			0
$217$	−13.2650	+	13.2650i	−0.900484	+	0.900484i
$218$		0			0
$219$	13.3469	+	13.3469i	0.901900	+	0.901900i
$220$		0			0
$221$	2.26788	−	2.26788i	0.152554	−	0.152554i
$222$		0			0
$223$	18.4764	+	18.4764i	1.23727	+	1.23727i	0.961113	+	0.276157i	$0.0890610\pi$
$223$	18.4764	+	18.4764i	1.23727	+	1.23727i	0.276157	+	0.961113i	$0.410939\pi$
$224$		0			0
$225$	−1.34926	+	0.431081i	−0.0899509	+	0.0287387i
$226$		0			0
$227$			23.4080i			1.55364i	0.629721	+	0.776821i	$0.283169\pi$
$227$			23.4080i			1.55364i	−0.629721	+	0.776821i	$0.716831\pi$
$228$		0			0
$229$	−1.09387	+	1.09387i	−0.0722850	+	0.0722850i	−0.742325	−	0.670040i	$-0.766277\pi$
$229$	−1.09387	+	1.09387i	−0.0722850	+	0.0722850i	0.670040	+	0.742325i	$0.266277\pi$
$230$		0			0
$231$	15.1391			0.996079
$232$		0			0
$233$	−3.14271	−	3.14271i	−0.205886	−	0.205886i	0.596630	−	0.802516i	$-0.296506\pi$
$233$	−3.14271	−	3.14271i	−0.205886	−	0.205886i	−0.802516	+	0.596630i	$0.796506\pi$
$234$		0			0
$235$	−2.51551	−	1.83709i	−0.164094	−	0.119839i
$236$		0			0
$237$	−14.2803			−0.927603
$238$		0			0
$239$	9.46338			0.612135			0.306068	−	0.952010i	$-0.400987\pi$
$239$	9.46338			0.612135			0.306068	+	0.952010i	$0.400987\pi$
$240$		0			0
$241$	5.06898			0.326522			0.163261	−	0.986583i	$-0.447799\pi$
$241$	5.06898			0.326522			0.163261	+	0.986583i	$0.447799\pi$
$242$		0			0
$243$	2.93449			0.188248
$244$		0			0
$245$	4.87504	−	0.759853i	0.311455	−	0.0485452i
$246$		0			0
$247$	−9.33281	−	9.33281i	−0.593832	−	0.593832i
$248$		0			0
$249$	21.9213			1.38921
$250$		0			0
$251$	−7.15197	+	7.15197i	−0.451428	+	0.451428i	−0.895828	−	0.444400i	$-0.853417\pi$
$251$	−7.15197	+	7.15197i	−0.451428	+	0.451428i	0.444400	+	0.895828i	$0.353417\pi$
$252$		0			0
$253$			9.47473i			0.595671i
$254$		0			0
$255$	−2.29825	+	3.14698i	−0.143922	+	0.197071i
$256$		0			0
$257$	4.88244	+	4.88244i	0.304558	+	0.304558i	0.842794	−	0.538236i	$-0.180909\pi$
$257$	4.88244	+	4.88244i	0.304558	+	0.304558i	−0.538236	+	0.842794i	$0.680909\pi$
$258$		0			0
$259$	12.8552	−	12.8552i	0.798781	−	0.798781i
$260$		0			0
$261$	−0.888824	−	0.888824i	−0.0550168	−	0.0550168i
$262$		0			0
$263$	−11.9619	+	11.9619i	−0.737605	+	0.737605i	−0.972114	−	0.234509i	$-0.924652\pi$
$263$	−11.9619	+	11.9619i	−0.737605	+	0.737605i	0.234509	+	0.972114i	$0.424652\pi$
$264$		0			0
$265$	4.52341	+	29.0212i	0.277871	+	1.78276i
$266$		0			0
$267$	−28.5991			−1.75024
$268$		0			0
$269$	−12.6832	−	12.6832i	−0.773309	−	0.773309i	0.205375	−	0.978683i	$-0.434159\pi$
$269$	−12.6832	−	12.6832i	−0.773309	−	0.773309i	−0.978683	+	0.205375i	$0.934159\pi$
$270$		0			0
$271$			8.14653i			0.494867i	0.968905	+	0.247433i	$0.0795871\pi$
$271$			8.14653i			0.494867i	−0.968905	+	0.247433i	$0.920413\pi$
$272$		0			0
$273$	−9.35465	+	9.35465i	−0.566169	+	0.566169i
$274$		0			0
$275$	−8.74582	+	16.9580i	−0.527393	+	1.02261i
$276$		0			0
$277$		−	13.5277i		−	0.812800i	−0.913695	−	0.406400i	$-0.866784\pi$
$277$		−	13.5277i		−	0.812800i	0.913695	−	0.406400i	$-0.133216\pi$
$278$		0			0
$279$		−	2.42732i		−	0.145320i
$280$		0			0
$281$			28.4048i			1.69449i	0.531202	+	0.847245i	$0.321741\pi$
$281$			28.4048i			1.69449i	−0.531202	+	0.847245i	$0.678259\pi$
$282$		0			0
$283$			22.7335i			1.35136i	0.737193	+	0.675682i	$0.236151\pi$
$283$			22.7335i			1.35136i	−0.737193	+	0.675682i	$0.763849\pi$
$284$		0			0
$285$	12.9505	+	9.45778i	0.767119	+	0.560231i
$286$		0			0
$287$	−16.7590	+	16.7590i	−0.989250	+	0.989250i
$288$		0			0
$289$		−	16.0750i		−	0.945588i
$290$		0			0
$291$	5.44592	+	5.44592i	0.319245	+	0.319245i
$292$		0			0
$293$	−5.40978			−0.316043			−0.158021	−	0.987436i	$-0.550511\pi$
$293$	−5.40978			−0.316043			−0.158021	+	0.987436i	$0.550511\pi$
$294$		0			0
$295$	8.13500	−	11.1392i	0.473638	−	0.648549i
$296$		0			0
$297$	13.2832	−	13.2832i	0.770768	−	0.770768i
$298$		0			0
$299$	−5.85457	−	5.85457i	−0.338578	−	0.338578i
$300$		0			0
$301$	−4.44459	+	4.44459i	−0.256182	+	0.256182i
$302$		0			0
$303$	12.4109	+	12.4109i	0.712987	+	0.712987i
$304$		0			0
$305$	20.0117	+	14.6146i	1.14587	+	0.836831i
$306$		0			0
$307$		−	18.6048i		−	1.06183i	−0.847424	−	0.530917i	$-0.821848\pi$
$307$		−	18.6048i		−	1.06183i	0.847424	−	0.530917i	$-0.178152\pi$
$308$		0			0
$309$	−8.07043	+	8.07043i	−0.459111	+	0.459111i
$310$		0			0
$311$	11.2873			0.640042			0.320021	−	0.947410i	$-0.396310\pi$
$311$	11.2873			0.640042			0.320021	+	0.947410i	$0.396310\pi$
$312$		0			0
$313$	−23.2411	−	23.2411i	−1.31366	−	1.31366i	−0.918694	−	0.394971i	$-0.870755\pi$
$313$	−23.2411	−	23.2411i	−1.31366	−	1.31366i	−0.394971	−	0.918694i	$-0.629245\pi$
$314$		0			0
$315$	0.817951	−	1.12001i	0.0460863	−	0.0631056i
$316$		0			0
$317$	3.16629			0.177837			0.0889184	−	0.996039i	$-0.471659\pi$
$317$	3.16629			0.177837			0.0889184	+	0.996039i	$0.471659\pi$
$318$		0			0
$319$	−16.9324			−0.948030
$320$		0			0
$321$	25.4021			1.41781
$322$		0			0
$323$	3.80662			0.211806
$324$		0			0
$325$	−5.07444	−	15.8828i	−0.281479	−	0.881017i
$326$		0			0
$327$	−12.7085	−	12.7085i	−0.702781	−	0.702781i
$328$		0			0
$329$	3.04991			0.168147
$330$		0			0
$331$	5.20766	−	5.20766i	0.286239	−	0.286239i	−0.549352	−	0.835591i	$-0.685125\pi$
$331$	5.20766	−	5.20766i	0.286239	−	0.286239i	0.835591	+	0.549352i	$0.185125\pi$
$332$		0			0
$333$			2.35234i			0.128907i
$334$		0			0
$335$	28.8215	−	4.49228i	1.57468	−	0.245440i
$336$		0			0
$337$	−20.1503	−	20.1503i	−1.09765	−	1.09765i	−0.994684	−	0.102970i	$-0.967165\pi$
$337$	−20.1503	−	20.1503i	−1.09765	−	1.09765i	−0.102970	−	0.994684i	$-0.532835\pi$
$338$		0			0
$339$	−13.4934	+	13.4934i	−0.732861	+	0.732861i
$340$		0			0
$341$	−23.1206	−	23.1206i	−1.25205	−	1.25205i
$342$		0			0
$343$	−14.2530	+	14.2530i	−0.769589	+	0.769589i
$344$		0			0
$345$	8.12396	+	5.93296i	0.437379	+	0.319420i
$346$		0			0
$347$	12.9438			0.694861			0.347430	−	0.937706i	$-0.387054\pi$
$347$	12.9438			0.694861			0.347430	+	0.937706i	$0.387054\pi$
$348$		0			0
$349$	0.0888151	+	0.0888151i	0.00475416	+	0.00475416i	0.709480	−	0.704726i	$-0.248930\pi$
$349$	0.0888151	+	0.0888151i	0.00475416	+	0.00475416i	−0.704726	+	0.709480i	$0.748930\pi$
$350$		0			0
$351$			16.4157i			0.876206i
$352$		0			0
$353$	6.22306	−	6.22306i	0.331220	−	0.331220i	−0.521830	−	0.853050i	$-0.674750\pi$
$353$	6.22306	−	6.22306i	0.331220	−	0.331220i	0.853050	+	0.521830i	$0.174750\pi$
$354$		0			0
$355$	−0.0462857	−	0.296959i	−0.00245659	−	0.0157609i
$356$		0			0
$357$		−	3.81553i		−	0.201939i
$358$		0			0
$359$			22.4574i			1.18525i	0.805477	+	0.592627i	$0.201909\pi$
$359$			22.4574i			1.18525i	−0.805477	+	0.592627i	$0.798091\pi$
$360$		0			0
$361$			3.33498i			0.175525i
$362$		0			0
$363$			6.45533i			0.338817i
$364$		0			0
$365$	13.7376	−	18.8107i	0.719057	−	0.984599i
$366$		0			0
$367$	−12.7444	+	12.7444i	−0.665252	+	0.665252i	−0.956613	−	0.291361i	$-0.905892\pi$
$367$	−12.7444	+	12.7444i	−0.665252	+	0.665252i	0.291361	+	0.956613i	$0.405892\pi$
$368$		0			0
$369$		−	3.06668i		−	0.159645i
$370$		0			0
$371$	−20.3354	−	20.3354i	−1.05576	−	1.05576i
$372$		0			0
$373$	−24.3812			−1.26241			−0.631205	−	0.775616i	$-0.717439\pi$
$373$	−24.3812			−1.26241			−0.631205	+	0.775616i	$0.717439\pi$
$374$		0			0
$375$	9.06387	+	18.1179i	0.468056	+	0.935603i
$376$		0			0
$377$	10.4627	−	10.4627i	0.538858	−	0.538858i
$378$		0			0
$379$	−20.9815	−	20.9815i	−1.07775	−	1.07775i	−0.996711	−	0.0810340i	$-0.974178\pi$
$379$	−20.9815	−	20.9815i	−1.07775	−	1.07775i	−0.0810340	−	0.996711i	$-0.525822\pi$
$380$		0			0
$381$	5.24287	−	5.24287i	0.268601	−	0.268601i
$382$		0			0
$383$	−13.4514	−	13.4514i	−0.687333	−	0.687333i	0.274309	−	0.961642i	$-0.411551\pi$
$383$	−13.4514	−	13.4514i	−0.687333	−	0.687333i	−0.961642	+	0.274309i	$0.911551\pi$
$384$		0			0
$385$	−2.87719	−	18.4594i	−0.146635	−	0.940778i
$386$		0			0
$387$		−	0.813305i		−	0.0413426i
$388$		0			0
$389$	7.64401	−	7.64401i	0.387567	−	0.387567i	−0.486252	−	0.873819i	$-0.661636\pi$
$389$	7.64401	−	7.64401i	0.387567	−	0.387567i	0.873819	+	0.486252i	$0.161636\pi$
$390$		0			0
$391$	2.38793			0.120763
$392$		0			0
$393$	0.968494	+	0.968494i	0.0488541	+	0.0488541i
$394$		0			0
$395$	2.71397	+	17.4122i	0.136555	+	0.876104i
$396$		0			0
$397$	0.575578			0.0288874			0.0144437	−	0.999896i	$-0.495402\pi$
$397$	0.575578			0.0288874			0.0144437	+	0.999896i	$0.495402\pi$
$398$		0			0
$399$	−15.7017			−0.786067
$400$		0			0
$401$	−16.7178			−0.834845			−0.417422	−	0.908713i	$-0.637066\pi$
$401$	−16.7178			−0.834845			−0.417422	+	0.908713i	$0.637066\pi$
$402$		0			0
$403$	28.5731			1.42333
$404$		0			0
$405$	−3.36435	−	21.5849i	−0.167176	−	1.07256i
$406$		0			0
$407$	22.4063	+	22.4063i	1.11064	+	1.11064i
$408$		0			0
$409$	−14.4690			−0.715448			−0.357724	−	0.933827i	$-0.616447\pi$
$409$	−14.4690			−0.715448			−0.357724	+	0.933827i	$0.616447\pi$
$410$		0			0
$411$	−8.08507	+	8.08507i	−0.398807	+	0.398807i
$412$		0			0
$413$			13.5056i			0.664568i
$414$		0			0
$415$	−4.16615	−	26.7291i	−0.204508	−	1.31208i
$416$		0			0
$417$	24.1328	+	24.1328i	1.18179	+	1.18179i
$418$		0			0
$419$	24.5270	−	24.5270i	1.19822	−	1.19822i	0.223527	−	0.974698i	$-0.428243\pi$
$419$	24.5270	−	24.5270i	1.19822	−	1.19822i	0.974698	−	0.223527i	$-0.0717570\pi$
$420$		0			0
$421$	10.6240	+	10.6240i	0.517783	+	0.517783i	0.916900	−	0.399117i	$-0.130683\pi$
$421$	10.6240	+	10.6240i	0.517783	+	0.517783i	−0.399117	+	0.916900i	$0.630683\pi$
$422$		0			0
$423$	−0.279048	+	0.279048i	−0.0135678	+	0.0135678i
$424$		0			0
$425$	4.27396	+	2.20422i	0.207317	+	0.106920i
$426$		0			0
$427$	−24.2630			−1.17417
$428$		0			0
$429$	−16.3050	−	16.3050i	−0.787213	−	0.787213i
$430$		0			0
$431$		−	2.25550i		−	0.108644i	−0.998523	−	0.0543219i	$-0.982700\pi$
$431$		−	2.25550i		−	0.108644i	0.998523	−	0.0543219i	$-0.0172997\pi$
$432$		0			0
$433$	19.9639	−	19.9639i	0.959404	−	0.959404i	−0.0398034	−	0.999208i	$-0.512673\pi$
$433$	19.9639	−	19.9639i	0.959404	−	0.959404i	0.999208	+	0.0398034i	$0.0126732\pi$
$434$		0			0
$435$	−10.6028	+	14.5184i	−0.508367	+	0.696103i
$436$		0			0
$437$		−	9.82683i		−	0.470081i
$438$		0			0
$439$		−	21.0582i		−	1.00505i	−0.864561	−	0.502527i	$-0.832404\pi$
$439$		−	21.0582i		−	1.00505i	0.864561	−	0.502527i	$-0.167596\pi$
$440$		0			0
$441$		−	0.625084i		−	0.0297659i
$442$		0			0
$443$			19.4033i			0.921877i	0.887432	+	0.460938i	$0.152487\pi$
$443$			19.4033i			0.921877i	−0.887432	+	0.460938i	$0.847513\pi$
$444$		0			0
$445$	5.43528	+	34.8715i	0.257657	+	1.65307i
$446$		0			0
$447$	18.8197	−	18.8197i	0.890142	−	0.890142i
$448$		0			0
$449$		−	11.7669i		−	0.555313i	−0.960680	−	0.277656i	$-0.910442\pi$
$449$		−	11.7669i		−	0.555313i	0.960680	−	0.277656i	$-0.0895577\pi$
$450$		0			0
$451$	−29.2106	−	29.2106i	−1.37547	−	1.37547i
$452$		0			0
$453$	12.4348			0.584238
$454$		0			0
$455$	13.1842	+	9.62846i	0.618084	+	0.451389i
$456$		0			0
$457$	16.1247	−	16.1247i	0.754280	−	0.754280i	−0.220995	−	0.975275i	$-0.570930\pi$
$457$	16.1247	−	16.1247i	0.754280	−	0.754280i	0.975275	+	0.220995i	$0.0709305\pi$
$458$		0			0
$459$	−3.34778	−	3.34778i	−0.156261	−	0.156261i
$460$		0			0
$461$	−2.87775	+	2.87775i	−0.134030	+	0.134030i	−0.770939	−	0.636909i	$-0.780213\pi$
$461$	−2.87775	+	2.87775i	−0.134030	+	0.134030i	0.636909	+	0.770939i	$0.280213\pi$
$462$		0			0
$463$	−9.81984	−	9.81984i	−0.456367	−	0.456367i	0.441094	−	0.897461i	$-0.354590\pi$
$463$	−9.81984	−	9.81984i	−0.456367	−	0.456367i	−0.897461	+	0.441094i	$0.854590\pi$
$464$		0			0
$465$	−34.3022	+	5.34654i	−1.59073	+	0.247940i
$466$		0			0
$467$			21.7864i			1.00816i	0.863658	+	0.504078i	$0.168168\pi$
$467$			21.7864i			1.00816i	−0.863658	+	0.504078i	$0.831832\pi$
$468$		0			0
$469$	−20.1955	+	20.1955i	−0.932541	+	0.932541i
$470$		0			0
$471$	8.31652			0.383205
$472$		0			0
$473$	−7.74685	−	7.74685i	−0.356200	−	0.356200i
$474$		0			0
$475$	9.07083	−	17.5882i	0.416198	−	0.807003i
$476$		0			0
$477$	3.72113			0.170379
$478$		0			0
$479$	9.22756			0.421618			0.210809	−	0.977527i	$-0.432390\pi$
$479$	9.22756			0.421618			0.210809	+	0.977527i	$0.432390\pi$
$480$		0			0
$481$	−27.6904			−1.26257
$482$		0			0
$483$	−9.84982			−0.448183
$484$		0			0
$485$	5.60532	−	7.67532i	0.254525	−	0.348518i
$486$		0			0
$487$	−25.1713	−	25.1713i	−1.14062	−	1.14062i	−0.988337	−	0.152284i	$-0.951337\pi$
$487$	−25.1713	−	25.1713i	−1.14062	−	1.14062i	−0.152284	−	0.988337i	$-0.548663\pi$
$488$		0			0
$489$	−5.13662			−0.232286
$490$		0			0
$491$	20.1548	−	20.1548i	0.909574	−	0.909574i	−0.0866633	−	0.996238i	$-0.527620\pi$
$491$	20.1548	−	20.1548i	0.909574	−	0.909574i	0.996238	+	0.0866633i	$0.0276204\pi$
$492$		0			0
$493$			4.26749i			0.192198i
$494$		0			0
$495$	1.95217	+	1.42568i	0.0877433	+	0.0640793i
$496$		0			0
$497$	0.208082	+	0.208082i	0.00933376	+	0.00933376i
$498$		0			0
$499$	3.44858	−	3.44858i	0.154380	−	0.154380i	−0.625691	−	0.780071i	$-0.715183\pi$
$499$	3.44858	−	3.44858i	0.154380	−	0.154380i	0.780071	+	0.625691i	$0.215183\pi$
$500$		0			0
$501$	19.2159	+	19.2159i	0.858501	+	0.858501i
$502$		0			0
$503$	−14.8039	+	14.8039i	−0.660074	+	0.660074i	−0.955397	−	0.295323i	$-0.904573\pi$
$503$	−14.8039	+	14.8039i	−0.660074	+	0.660074i	0.295323	+	0.955397i	$0.404573\pi$
$504$		0			0
$505$	12.7742	−	17.4916i	0.568443	−	0.778364i
$506$		0			0
$507$	−3.40564			−0.151250
$508$		0			0
$509$	−14.7467	−	14.7467i	−0.653635	−	0.653635i	0.300232	−	0.953866i	$-0.402936\pi$
$509$	−14.7467	−	14.7467i	−0.653635	−	0.653635i	−0.953866	+	0.300232i	$0.902936\pi$
$510$		0			0
$511$			22.8069i			1.00892i
$512$		0			0
$513$	−13.7768	+	13.7768i	−0.608261	+	0.608261i
$514$		0			0
$515$	11.3742	+	8.30665i	0.501208	+	0.366035i
$516$		0			0
$517$			5.31594i			0.233795i
$518$		0			0
$519$		−	2.15840i		−	0.0947431i
$520$		0			0
$521$			15.2957i			0.670118i	0.942197	+	0.335059i	$0.108756\pi$
$521$			15.2957i			0.670118i	−0.942197	+	0.335059i	$0.891244\pi$
$522$		0			0
$523$			0.856013i			0.0374308i	0.999825	+	0.0187154i	$0.00595765\pi$
$523$			0.856013i			0.0374308i	−0.999825	+	0.0187154i	$0.994042\pi$
$524$		0			0
$525$	−17.6294	−	9.09206i	−0.769409	−	0.396810i
$526$		0			0
$527$	−5.82712	+	5.82712i	−0.253833	+	0.253833i
$528$		0			0
$529$			16.8355i			0.731980i
$530$		0			0
$531$	−1.23568	−	1.23568i	−0.0536239	−	0.0536239i
$532$		0			0
$533$	36.0992			1.56363
$534$		0			0
$535$	−4.82768	−	30.9733i	−0.208719	−	1.33909i
$536$		0			0
$537$	6.63221	−	6.63221i	0.286201	−	0.286201i
$538$		0			0
$539$	−5.95402	−	5.95402i	−0.256458	−	0.256458i
$540$		0			0
$541$	3.59516	−	3.59516i	0.154568	−	0.154568i	−0.625587	−	0.780155i	$-0.715140\pi$
$541$	3.59516	−	3.59516i	0.154568	−	0.154568i	0.780155	+	0.625587i	$0.215140\pi$
$542$		0			0
$543$	11.1689	+	11.1689i	0.479302	+	0.479302i
$544$		0			0
$545$	−13.0805	+	17.9110i	−0.560306	+	0.767222i
$546$		0			0
$547$		−	2.45850i		−	0.105118i	−0.998618	−	0.0525589i	$-0.983262\pi$
$547$		−	2.45850i		−	0.105118i	0.998618	−	0.0525589i	$-0.0167377\pi$
$548$		0			0
$549$	2.21991	−	2.21991i	0.0947436	−	0.0947436i
$550$		0			0
$551$	17.5616			0.748149
$552$		0			0
$553$	−12.2009	−	12.2009i	−0.518836	−	0.518836i
$554$		0			0
$555$	33.2425	−	5.18137i	1.41107	−	0.219937i
$556$		0			0
$557$	13.9664			0.591774			0.295887	−	0.955223i	$-0.404385\pi$
$557$	13.9664			0.591774			0.295887	+	0.955223i	$0.404385\pi$
$558$		0			0
$559$	9.57377			0.404927
$560$		0			0
$561$	6.65039			0.280780
$562$		0			0
$563$	−3.68729			−0.155401			−0.0777004	−	0.996977i	$-0.524758\pi$
$563$	−3.68729			−0.155401			−0.0777004	+	0.996977i	$0.524758\pi$
$564$		0			0
$565$	19.0172	+	13.8884i	0.800061	+	0.584288i
$566$		0			0
$567$	15.1248	+	15.1248i	0.635180	+	0.635180i
$568$		0			0
$569$	−2.38759			−0.100093			−0.0500466	−	0.998747i	$-0.515937\pi$
$569$	−2.38759			−0.100093			−0.0500466	+	0.998747i	$0.515937\pi$
$570$		0			0
$571$	12.9632	−	12.9632i	0.542491	−	0.542491i	−0.381767	−	0.924258i	$-0.624684\pi$
$571$	12.9632	−	12.9632i	0.542491	−	0.542491i	0.924258	+	0.381767i	$0.124684\pi$
$572$		0			0
$573$		−	19.0617i		−	0.796313i
$574$		0			0
$575$	5.69023	−	11.0333i	0.237299	−	0.460119i
$576$		0			0
$577$	4.15876	+	4.15876i	0.173131	+	0.173131i	0.788354	−	0.615222i	$-0.210934\pi$
$577$	4.15876	+	4.15876i	0.173131	+	0.173131i	−0.615222	+	0.788354i	$0.710934\pi$
$578$		0			0
$579$	−10.2116	+	10.2116i	−0.424379	+	0.424379i
$580$		0			0
$581$	18.7293	+	18.7293i	0.777024	+	0.777024i
$582$		0			0
$583$	35.4443	−	35.4443i	1.46795	−	1.46795i
$584$		0			0
$585$	−2.08721	+	0.325325i	−0.0862957	+	0.0134505i
$586$		0			0
$587$	33.0229			1.36300			0.681500	−	0.731818i	$-0.261328\pi$
$587$	33.0229			1.36300			0.681500	+	0.731818i	$0.261328\pi$
$588$		0			0
$589$	23.9798	+	23.9798i	0.988070	+	0.988070i
$590$		0			0
$591$		−	17.8212i		−	0.733066i
$592$		0			0
$593$	−11.3559	+	11.3559i	−0.466330	+	0.466330i	−0.900723	−	0.434394i	$-0.856963\pi$
$593$	−11.3559	+	11.3559i	−0.466330	+	0.466330i	0.434394	+	0.900723i	$0.356963\pi$
$594$		0			0
$595$	−4.65235	+	0.725142i	−0.190728	+	0.0297279i
$596$		0			0
$597$			47.6763i			1.95126i
$598$		0			0
$599$			15.5317i			0.634607i	0.948324	+	0.317304i	$0.102777\pi$
$599$			15.5317i			0.634607i	−0.948324	+	0.317304i	$0.897223\pi$
$600$		0			0
$601$			23.2823i			0.949705i	0.880065	+	0.474853i	$0.157499\pi$
$601$			23.2823i			0.949705i	−0.880065	+	0.474853i	$0.842501\pi$
$602$		0			0
$603$		−	3.69552i		−	0.150493i
$604$		0			0
$605$	7.87111	−	1.22684i	0.320006	−	0.0498780i
$606$		0			0
$607$	23.0138	−	23.0138i	0.934099	−	0.934099i	−0.0638595	−	0.997959i	$-0.520341\pi$
$607$	23.0138	−	23.0138i	0.934099	−	0.934099i	0.997959	+	0.0638595i	$0.0203410\pi$
$608$		0			0
$609$		−	17.6027i		−	0.713297i
$610$		0			0
$611$	−3.28480	−	3.28480i	−0.132889	−	0.132889i
$612$		0			0
$613$	23.8396			0.962874			0.481437	−	0.876481i	$-0.340115\pi$
$613$	23.8396			0.962874			0.481437	+	0.876481i	$0.340115\pi$
$614$		0			0
$615$	−43.3375	+	6.75483i	−1.74753	+	0.272381i
$616$		0			0
$617$	7.51162	−	7.51162i	0.302406	−	0.302406i	−0.539548	−	0.841955i	$-0.681405\pi$
$617$	7.51162	−	7.51162i	0.302406	−	0.302406i	0.841955	+	0.539548i	$0.181405\pi$
$618$		0			0
$619$	−3.21702	−	3.21702i	−0.129303	−	0.129303i	0.639494	−	0.768796i	$-0.279144\pi$
$619$	−3.21702	−	3.21702i	−0.129303	−	0.129303i	−0.768796	+	0.639494i	$0.779144\pi$
$620$		0			0
$621$	−8.64233	+	8.64233i	−0.346805	+	0.346805i
$622$		0			0
$623$	−24.4348	−	24.4348i	−0.978961	−	0.978961i
$624$		0			0
$625$	20.3689	−	14.4951i	0.814757	−	0.579803i
$626$		0			0
$627$		−	27.3678i		−	1.09296i
$628$		0			0
$629$	5.64710	−	5.64710i	0.225165	−	0.225165i
$630$		0			0
$631$	−17.5142			−0.697231			−0.348616	−	0.937266i	$-0.613348\pi$
$631$	−17.5142			−0.697231			−0.348616	+	0.937266i	$0.613348\pi$
$632$		0			0
$633$	−33.7661	−	33.7661i	−1.34208	−	1.34208i
$634$		0			0
$635$	−7.38916	−	5.39634i	−0.293230	−	0.214147i
$636$		0			0
$637$	7.35814			0.291540
$638$		0			0
$639$	−0.0380764			−0.00150628
$640$		0			0
$641$	−4.81236			−0.190077			−0.0950383	−	0.995474i	$-0.530297\pi$
$641$	−4.81236			−0.190077			−0.0950383	+	0.995474i	$0.530297\pi$
$642$		0			0
$643$	0.379678			0.0149730			0.00748652	−	0.999972i	$-0.497617\pi$
$643$	0.379678			0.0149730			0.00748652	+	0.999972i	$0.497617\pi$
$644$		0			0
$645$	−11.4934	+	1.79143i	−0.452552	+	0.0705374i
$646$		0			0
$647$	−10.4814	−	10.4814i	−0.412066	−	0.412066i	0.470392	−	0.882458i	$-0.344113\pi$
$647$	−10.4814	−	10.4814i	−0.412066	−	0.412066i	−0.882458	+	0.470392i	$0.844113\pi$
$648$		0			0
$649$	−23.5401			−0.924028
$650$		0			0
$651$	24.0359	−	24.0359i	0.942041	−	0.942041i
$652$		0			0
$653$		−	3.39325i		−	0.132788i	−0.997793	−	0.0663941i	$-0.978851\pi$
$653$		−	3.39325i		−	0.132788i	0.997793	−	0.0663941i	$-0.0211495\pi$
$654$		0			0
$655$	0.996843	−	1.36497i	0.0389499	−	0.0533337i
$656$		0			0
$657$	−2.08669	−	2.08669i	−0.0814096	−	0.0814096i
$658$		0			0
$659$	−3.63069	+	3.63069i	−0.141431	+	0.141431i	−0.774278	−	0.632846i	$-0.781887\pi$
$659$	−3.63069	+	3.63069i	−0.141431	+	0.141431i	0.632846	+	0.774278i	$0.281887\pi$
$660$		0			0
$661$	7.92705	+	7.92705i	0.308327	+	0.308327i	0.844260	−	0.535934i	$-0.180040\pi$
$661$	7.92705	+	7.92705i	0.308327	+	0.308327i	−0.535934	+	0.844260i	$0.680040\pi$
$662$		0			0
$663$	−4.10937	+	4.10937i	−0.159595	+	0.159595i
$664$		0			0
$665$	2.98411	+	19.1454i	0.115719	+	0.742426i
$666$		0			0
$667$	11.0166			0.426563
$668$		0			0
$669$	−33.4789	−	33.4789i	−1.29437	−	1.29437i
$670$		0			0
$671$		−	42.2900i		−	1.63259i
$672$		0			0
$673$	−6.74727	+	6.74727i	−0.260088	+	0.260088i	−0.825090	−	0.565002i	$-0.808876\pi$
$673$	−6.74727	+	6.74727i	−0.260088	+	0.260088i	0.565002	+	0.825090i	$0.308876\pi$
$674$		0			0
$675$	−23.4456	+	7.49073i	−0.902423	+	0.288318i
$676$		0			0
$677$			21.3785i			0.821641i	0.911716	+	0.410821i	$0.134758\pi$
$677$			21.3785i			0.821641i	−0.911716	+	0.410821i	$0.865242\pi$
$678$		0			0
$679$			9.30588i			0.357127i
$680$		0			0
$681$		−	42.4149i		−	1.62534i
$682$		0			0
$683$		−	14.6001i		−	0.558658i	−0.960195	−	0.279329i	$-0.909888\pi$
$683$		−	14.6001i		−	0.558658i	0.960195	−	0.279329i	$-0.0901120\pi$
$684$		0			0
$685$	11.3949	+	8.32172i	0.435375	+	0.317957i
$686$		0			0
$687$	1.98208	−	1.98208i	0.0756210	−	0.0756210i
$688$		0			0
$689$			43.8031i			1.66876i
$690$		0			0
$691$	21.0583	+	21.0583i	0.801097	+	0.801097i	0.983267	−	0.182170i	$-0.0583121\pi$
$691$	21.0583	+	21.0583i	0.801097	+	0.801097i	−0.182170	+	0.983267i	$0.558312\pi$
$692$		0			0
$693$	−2.36689			−0.0899106
$694$		0			0
$695$	24.8391	−	34.0120i	0.942202	−	1.29015i
$696$		0			0
$697$	−7.36198	+	7.36198i	−0.278855	+	0.278855i
$698$		0			0
$699$	5.69455	+	5.69455i	0.215388	+	0.215388i
$700$		0			0
$701$	−27.3282	+	27.3282i	−1.03217	+	1.03217i	−0.0327069	+	0.999465i	$0.510413\pi$
$701$	−27.3282	+	27.3282i	−1.03217	+	1.03217i	−0.999465	+	0.0327069i	$0.989587\pi$
$702$		0			0
$703$	−23.2390	−	23.2390i	−0.876475	−	0.876475i
$704$		0			0
$705$	4.55807	+	3.32878i	0.171667	+	0.125369i
$706$		0			0
$707$			21.2075i			0.797590i
$708$		0			0
$709$	−28.3895	+	28.3895i	−1.06619	+	1.06619i	−0.0685403	+	0.997648i	$0.521834\pi$
$709$	−28.3895	+	28.3895i	−1.06619	+	1.06619i	−0.997648	+	0.0685403i	$0.978166\pi$
$710$		0			0
$711$	2.23262			0.0837296
$712$		0			0
$713$	15.0428	+	15.0428i	0.563356	+	0.563356i
$714$		0			0
$715$	−16.7822	+	22.9798i	−0.627621	+	0.859395i
$716$		0			0
$717$	−17.1475			−0.640385
$718$		0			0
$719$	−22.2952			−0.831471			−0.415736	−	0.909486i	$-0.636476\pi$
$719$	−22.2952			−0.831471			−0.415736	+	0.909486i	$0.636476\pi$
$720$		0			0
$721$	−13.7906			−0.513588
$722$		0			0
$723$	−9.18491			−0.341591
$724$		0			0
$725$	19.7176	+	10.1690i	0.732295	+	0.377669i
$726$		0			0
$727$	−20.3177	−	20.3177i	−0.753543	−	0.753543i	0.221596	−	0.975139i	$-0.428873\pi$
$727$	−20.3177	−	20.3177i	−0.753543	−	0.753543i	−0.975139	+	0.221596i	$0.928873\pi$
$728$		0			0
$729$	23.9916			0.888578
$730$		0			0
$731$	−1.95245	+	1.95245i	−0.0722139	+	0.0722139i
$732$		0			0
$733$			1.80400i			0.0666323i	0.999445	+	0.0333162i	$0.0106068\pi$
$733$			1.80400i			0.0666323i	−0.999445	+	0.0333162i	$0.989393\pi$
$734$		0			0
$735$	−8.83351	+	1.37684i	−0.325829	+	0.0507856i
$736$		0			0
$737$	−35.2004	−	35.2004i	−1.29662	−	1.29662i
$738$		0			0
$739$	0.240927	−	0.240927i	0.00886264	−	0.00886264i	−0.702662	−	0.711524i	$-0.748005\pi$
$739$	0.240927	−	0.240927i	0.00886264	−	0.00886264i	0.711524	+	0.702662i	$0.248005\pi$
$740$		0			0
$741$	16.9109	+	16.9109i	0.621238	+	0.621238i
$742$		0			0
$743$	−35.9128	+	35.9128i	−1.31751	+	1.31751i	−0.401775	+	0.915738i	$0.631607\pi$
$743$	−35.9128	+	35.9128i	−1.31751	+	1.31751i	−0.915738	+	0.401775i	$0.868393\pi$
$744$		0			0
$745$	−26.5240	−	19.3706i	−0.971763	−	0.709683i
$746$		0			0
$747$	−3.42723			−0.125396
$748$		0			0
$749$	21.7033	+	21.7033i	0.793021	+	0.793021i
$750$		0			0
$751$		−	22.2372i		−	0.811448i	−0.913996	−	0.405724i	$-0.867019\pi$
$751$		−	22.2372i		−	0.811448i	0.913996	−	0.405724i	$-0.132981\pi$
$752$		0			0
$753$	12.9593	−	12.9593i	0.472262	−	0.472262i
$754$		0			0
$755$	−2.36324	−	15.1620i	−0.0860072	−	0.551803i
$756$		0			0
$757$		−	8.65429i		−	0.314545i	−0.987555	−	0.157273i	$-0.949730\pi$
$757$		−	8.65429i		−	0.314545i	0.987555	−	0.157273i	$-0.0502702\pi$
$758$		0			0
$759$		−	17.1681i		−	0.623162i
$760$		0			0
$761$		−	51.2052i		−	1.85619i	−0.372345	−	0.928094i	$-0.621446\pi$
$761$		−	51.2052i		−	1.85619i	0.372345	−	0.928094i	$-0.378554\pi$
$762$		0			0
$763$		−	21.7160i		−	0.786172i
$764$		0			0
$765$	0.359315	−	0.492007i	0.0129911	−	0.0177885i
$766$		0			0
$767$	14.5457	−	14.5457i	0.525216	−	0.525216i
$768$		0			0
$769$		−	6.33900i		−	0.228590i	−0.993447	−	0.114295i	$-0.963539\pi$
$769$		−	6.33900i		−	0.228590i	0.993447	−	0.114295i	$-0.0364610\pi$
$770$		0			0
$771$	−8.84691	−	8.84691i	−0.318614	−	0.318614i
$772$		0			0
$773$	−49.9518			−1.79664			−0.898321	−	0.439341i	$-0.855212\pi$
$773$	−49.9518			−1.79664			−0.898321	+	0.439341i	$0.855212\pi$
$774$		0			0
$775$	13.0383	+	40.8093i	0.468350	+	1.46591i
$776$		0			0
$777$	−23.2934	+	23.2934i	−0.835645	+	0.835645i
$778$		0			0
$779$	30.2961	+	30.2961i	1.08547	+	1.08547i
$780$		0			0
$781$	−0.362683	+	0.362683i	−0.0129778	+	0.0129778i
$782$		0			0
$783$	−15.4448	−	15.4448i	−0.551951	−	0.551951i
$784$		0			0
$785$	−1.58056	−	10.1405i	−0.0564126	−	0.361930i
$786$		0			0
$787$		−	41.6365i		−	1.48418i	−0.670300	−	0.742090i	$-0.733835\pi$
$787$		−	41.6365i		−	1.48418i	0.670300	−	0.742090i	$-0.266165\pi$
$788$		0			0
$789$	21.6749	−	21.6749i	0.771645	−	0.771645i
$790$		0			0
$791$	−23.0573			−0.819822
$792$		0			0
$793$	26.1316	+	26.1316i	0.927959	+	0.927959i
$794$		0			0
$795$	−8.19635	−	52.5860i	−0.290695	−	1.86503i
$796$		0			0
$797$	−29.3268			−1.03881			−0.519405	−	0.854528i	$-0.673846\pi$
$797$	−29.3268			−1.03881			−0.519405	+	0.854528i	$0.673846\pi$
$798$		0			0
$799$	1.33978			0.0473982
$800$		0			0
$801$	4.47127			0.157984
$802$		0			0
$803$	−39.7521			−1.40282
$804$		0			0
$805$	1.87196	+	12.0101i	0.0659780	+	0.423300i
$806$		0			0
$807$	22.9818	+	22.9818i	0.808997	+	0.808997i
$808$		0			0
$809$	6.43307			0.226175			0.113087	−	0.993585i	$-0.463926\pi$
$809$	6.43307			0.226175			0.113087	+	0.993585i	$0.463926\pi$
$810$		0			0
$811$	−14.4038	+	14.4038i	−0.505786	+	0.505786i	−0.913230	−	0.407444i	$-0.866420\pi$
$811$	−14.4038	+	14.4038i	−0.505786	+	0.505786i	0.407444	+	0.913230i	$0.366420\pi$
$812$		0			0
$813$		−	14.7614i		−	0.517705i
$814$		0			0
$815$	0.976217	+	6.26319i	0.0341954	+	0.219390i
$816$		0			0
$817$	8.03473	+	8.03473i	0.281100	+	0.281100i
$818$		0			0
$819$	1.46253	−	1.46253i	0.0511050	−	0.0511050i
$820$		0			0
$821$	−20.5284	−	20.5284i	−0.716446	−	0.716446i	0.251429	−	0.967876i	$-0.419099\pi$
$821$	−20.5284	−	20.5284i	−0.716446	−	0.716446i	−0.967876	+	0.251429i	$0.919099\pi$
$822$		0			0
$823$	13.8988	−	13.8988i	0.484481	−	0.484481i	−0.422078	−	0.906559i	$-0.638699\pi$
$823$	13.8988	−	13.8988i	0.484481	−	0.484481i	0.906559	+	0.422078i	$0.138699\pi$
$824$		0			0
$825$	15.8473	−	30.7277i	0.551732	−	1.06980i
$826$		0			0
$827$	29.3843			1.02179			0.510897	−	0.859642i	$-0.329313\pi$
$827$	29.3843			1.02179			0.510897	+	0.859642i	$0.329313\pi$
$828$		0			0
$829$	34.7193	+	34.7193i	1.20585	+	1.20585i	0.972359	+	0.233492i	$0.0750154\pi$
$829$	34.7193	+	34.7193i	1.20585	+	1.20585i	0.233492	+	0.972359i	$0.424985\pi$
$830$		0			0
$831$			24.5120i			0.850310i
$832$		0			0
$833$	−1.50060	+	1.50060i	−0.0519927	+	0.0519927i
$834$		0			0
$835$	19.7783	−	27.0823i	0.684457	−	0.937220i
$836$		0			0
$837$		−	42.1787i		−	1.45791i
$838$		0			0
$839$			4.78293i			0.165125i	0.996586	+	0.0825626i	$0.0263104\pi$
$839$			4.78293i			0.165125i	−0.996586	+	0.0825626i	$0.973690\pi$
$840$		0			0
$841$		−	9.31222i		−	0.321111i
$842$		0			0
$843$		−	51.4692i		−	1.77269i
$844$		0			0
$845$	0.647244	+	4.15257i	0.0222659	+	0.142853i
$846$		0			0
$847$	−5.51537	+	5.51537i	−0.189510	+	0.189510i
$848$		0			0
$849$		−	41.1927i		−	1.41373i
$850$		0			0
$851$	−14.5781	−	14.5781i	−0.499729	−	0.499729i
$852$		0			0
$853$	45.2839			1.55049			0.775246	−	0.631659i	$-0.217626\pi$
$853$	45.2839			1.55049			0.775246	+	0.631659i	$0.217626\pi$
$854$		0			0
$855$	−2.02471	−	1.47866i	−0.0692436	−	0.0505690i
$856$		0			0
$857$	−2.73476	+	2.73476i	−0.0934175	+	0.0934175i	−0.752271	−	0.658854i	$-0.771042\pi$
$857$	−2.73476	+	2.73476i	−0.0934175	+	0.0934175i	0.658854	+	0.752271i	$0.271042\pi$
$858$		0			0
$859$	−5.94695	−	5.94695i	−0.202907	−	0.202907i	0.598337	−	0.801244i	$-0.295828\pi$
$859$	−5.94695	−	5.94695i	−0.202907	−	0.202907i	−0.801244	+	0.598337i	$0.795828\pi$
$860$		0			0
$861$	30.3670	−	30.3670i	1.03490	−	1.03490i
$862$		0			0
$863$	34.3328	+	34.3328i	1.16870	+	1.16870i	0.982514	+	0.186187i	$0.0596130\pi$
$863$	34.3328	+	34.3328i	1.16870	+	1.16870i	0.186187	+	0.982514i	$0.440387\pi$
$864$		0			0
$865$	−2.63178	+	0.410204i	−0.0894832	+	0.0139474i
$866$		0			0
$867$			29.1276i			0.989227i
$868$		0			0
$869$	21.2660	−	21.2660i	0.721399	−	0.721399i
$870$		0			0
$871$	43.5016			1.47400
$872$		0			0
$873$	−0.851430	−	0.851430i	−0.0288165	−	0.0288165i
$874$		0			0
$875$	−7.73566	+	23.2238i	−0.261513	+	0.785108i
$876$		0			0
$877$	3.27398			0.110555			0.0552773	−	0.998471i	$-0.482396\pi$
$877$	3.27398			0.110555			0.0552773	+	0.998471i	$0.482396\pi$
$878$		0			0
$879$	9.80244			0.330628
$880$		0			0
$881$	39.5807			1.33351			0.666753	−	0.745279i	$-0.267684\pi$
$881$	39.5807			1.33351			0.666753	+	0.745279i	$0.267684\pi$
$882$		0			0
$883$	17.8181			0.599628			0.299814	−	0.953998i	$-0.403075\pi$
$883$	17.8181			0.599628			0.299814	+	0.953998i	$0.403075\pi$
$884$		0			0
$885$	−14.7405	+	20.1841i	−0.495497	+	0.678479i
$886$		0			0
$887$	20.2924	+	20.2924i	0.681352	+	0.681352i	0.960305	−	0.278953i	$-0.0899872\pi$
$887$	20.2924	+	20.2924i	0.681352	+	0.681352i	−0.278953	+	0.960305i	$0.589987\pi$
$888$		0			0
$889$	8.95892			0.300473
$890$		0			0
$891$	−26.3622	+	26.3622i	−0.883167	+	0.883167i
$892$		0			0
$893$		−	5.51349i		−	0.184502i
$894$		0			0
$895$	−9.34724	−	6.82633i	−0.312444	−	0.228179i
$896$		0			0
$897$	10.6084	+	10.6084i	0.354204	+	0.354204i
$898$		0			0
$899$	−26.8830	+	26.8830i	−0.896599	+	0.896599i
$900$		0			0
$901$	−8.93308	−	8.93308i	−0.297604	−	0.297604i
$902$		0			0
$903$	8.05354	−	8.05354i	0.268005	−	0.268005i
$904$		0			0
$905$	11.4958	−	15.7411i	0.382133	−	0.523251i
$906$		0			0
$907$	−31.2744			−1.03845			−0.519225	−	0.854638i	$-0.673779\pi$
$907$	−31.2744			−1.03845			−0.519225	+	0.854638i	$0.673779\pi$
$908$		0			0
$909$	−1.94035	−	1.94035i	−0.0643574	−	0.0643574i
$910$		0			0
$911$		−	16.8051i		−	0.556777i	−0.960469	−	0.278388i	$-0.910200\pi$
$911$		−	16.8051i		−	0.556777i	0.960469	−	0.278388i	$-0.0898002\pi$
$912$		0			0
$913$	−32.6449	+	32.6449i	−1.08039	+	1.08039i
$914$		0			0
$915$	−36.2609	−	26.4815i	−1.19875	−	0.875451i
$916$		0			0
$917$			1.65494i			0.0546511i
$918$		0			0
$919$		−	6.78337i		−	0.223763i	−0.993722	−	0.111881i	$-0.964312\pi$
$919$		−	6.78337i		−	0.223763i	0.993722	−	0.111881i	$-0.0356876\pi$
$920$		0			0
$921$			33.7117i			1.11084i
$922$		0			0
$923$		−	0.448214i		−	0.0147532i
$924$		0			0
$925$	−12.6355	−	39.5486i	−0.415453	−	1.30035i
$926$		0			0
$927$	1.26175	−	1.26175i	0.0414414	−	0.0414414i
$928$		0			0
$929$			43.0476i			1.41235i	0.708039	+	0.706173i	$0.249580\pi$
$929$			43.0476i			1.41235i	−0.708039	+	0.706173i	$0.750420\pi$
$930$		0			0
$931$	6.17528	+	6.17528i	0.202387	+	0.202387i
$932$		0			0
$933$	−20.4524			−0.669580
$934$		0			0
$935$	−1.26391	−	8.10896i	−0.0413343	−	0.265192i
$936$		0			0
$937$	11.1198	−	11.1198i	0.363268	−	0.363268i	−0.501747	−	0.865015i	$-0.667309\pi$
$937$	11.1198	−	11.1198i	0.363268	−	0.363268i	0.865015	+	0.501747i	$0.167309\pi$
$938$		0			0
$939$	42.1125	+	42.1125i	1.37429	+	1.37429i
$940$		0			0
$941$	2.76429	−	2.76429i	0.0901131	−	0.0901131i	−0.660613	−	0.750726i	$-0.729704\pi$
$941$	2.76429	−	2.76429i	0.0901131	−	0.0901131i	0.750726	+	0.660613i	$0.229704\pi$
$942$		0			0
$943$	19.0050	+	19.0050i	0.618889	+	0.618889i
$944$		0			0
$945$	14.2132	−	19.4621i	0.462357	−	0.633101i
$946$		0			0
$947$		−	6.77325i		−	0.220101i	−0.993926	−	0.110051i	$-0.964899\pi$
$947$		−	6.77325i		−	0.220101i	0.993926	−	0.110051i	$-0.0351013\pi$
$948$		0			0
$949$	24.5634	−	24.5634i	0.797360	−	0.797360i
$950$		0			0
$951$	−5.73728			−0.186044
$952$		0			0
$953$	28.6073	+	28.6073i	0.926682	+	0.926682i	0.997490	−	0.0708083i	$-0.0225579\pi$
$953$	28.6073	+	28.6073i	0.926682	+	0.926682i	−0.0708083	+	0.997490i	$0.522558\pi$
$954$		0			0
$955$	−23.2423	+	3.62268i	−0.752103	+	0.117227i
$956$		0			0
$957$	30.6812			0.991782
$958$		0			0
$959$	−13.8156			−0.446129
$960$		0			0
$961$	−42.4158			−1.36825
$962$		0			0
$963$	−3.97143			−0.127978
$964$		0			0
$965$	14.3919	+	10.5105i	0.463292	+	0.338344i
$966$		0			0
$967$	18.3434	+	18.3434i	0.589882	+	0.589882i	0.937600	−	0.347717i	$-0.113043\pi$
$967$	18.3434	+	18.3434i	0.589882	+	0.589882i	−0.347717	+	0.937600i	$0.613043\pi$
$968$		0			0
$969$	−6.89753			−0.221581
$970$		0			0
$971$	−9.66321	+	9.66321i	−0.310107	+	0.310107i	−0.844951	−	0.534844i	$-0.820370\pi$
$971$	−9.66321	+	9.66321i	−0.310107	+	0.310107i	0.534844	+	0.844951i	$0.320370\pi$
$972$		0			0
$973$			41.2376i			1.32202i
$974$		0			0
$975$	9.19481	+	28.7793i	0.294470	+	0.921677i
$976$		0			0
$977$	−40.1076	−	40.1076i	−1.28316	−	1.28316i	−0.938862	−	0.344293i	$-0.888119\pi$
$977$	−40.1076	−	40.1076i	−1.28316	−	1.28316i	−0.344293	−	0.938862i	$-0.611881\pi$
$978$		0			0
$979$	42.5895	−	42.5895i	1.36117	−	1.36117i
$980$		0			0
$981$	1.98688	+	1.98688i	0.0634362	+	0.0634362i
$982$		0			0
$983$	39.6507	−	39.6507i	1.26466	−	1.26466i	0.315854	−	0.948808i	$-0.397709\pi$
$983$	39.6507	−	39.6507i	1.26466	−	1.26466i	0.948808	−	0.315854i	$-0.102291\pi$
$984$		0			0
$985$	−21.7297	+	3.38692i	−0.692367	+	0.107916i
$986$		0			0
$987$	−5.52640			−0.175907
$988$		0			0
$989$	5.04027	+	5.04027i	0.160271	+	0.160271i
$990$		0			0
$991$		−	5.77959i		−	0.183595i	−0.995778	−	0.0917974i	$-0.970739\pi$
$991$		−	5.77959i		−	0.183595i	0.995778	−	0.0917974i	$-0.0292612\pi$
$992$		0			0
$993$	−9.43621	+	9.43621i	−0.299449	+	0.299449i
$994$		0			0
$995$	58.1327	−	9.06090i	1.84293	−	0.287250i
$996$		0			0
$997$		−	28.8109i		−	0.912449i	−0.889865	−	0.456225i	$-0.849201\pi$
$997$		−	28.8109i		−	0.912449i	0.889865	−	0.456225i	$-0.150799\pi$
$998$		0			0
$999$			40.8756i			1.29325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.s.d.1087.5	yes	32
4.3	odd	2	inner	1280.2.s.d.1087.12	yes	32
5.3	odd	4		1280.2.j.c.63.5	✓	32
8.3	odd	2		1280.2.s.c.1087.5	yes	32
8.5	even	2		1280.2.s.c.1087.12	yes	32
16.3	odd	4		1280.2.j.c.447.12	yes	32
16.5	even	4		1280.2.j.d.447.12	yes	32
16.11	odd	4		1280.2.j.d.447.5	yes	32
16.13	even	4		1280.2.j.c.447.5	yes	32
20.3	even	4		1280.2.j.c.63.12	yes	32
40.3	even	4		1280.2.j.d.63.5	yes	32
40.13	odd	4		1280.2.j.d.63.12	yes	32
80.3	even	4	inner	1280.2.s.d.703.5	yes	32
80.13	odd	4	inner	1280.2.s.d.703.12	yes	32
80.43	even	4		1280.2.s.c.703.12	yes	32
80.53	odd	4		1280.2.s.c.703.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.5	✓	32	5.3	odd	4
1280.2.j.c.63.12	yes	32	20.3	even	4
1280.2.j.c.447.5	yes	32	16.13	even	4
1280.2.j.c.447.12	yes	32	16.3	odd	4
1280.2.j.d.63.5	yes	32	40.3	even	4
1280.2.j.d.63.12	yes	32	40.13	odd	4
1280.2.j.d.447.5	yes	32	16.11	odd	4
1280.2.j.d.447.12	yes	32	16.5	even	4
1280.2.s.c.703.5	yes	32	80.53	odd	4
1280.2.s.c.703.12	yes	32	80.43	even	4
1280.2.s.c.1087.5	yes	32	8.3	odd	2
1280.2.s.c.1087.12	yes	32	8.5	even	2
1280.2.s.d.703.5	yes	32	80.3	even	4	inner
1280.2.s.d.703.12	yes	32	80.13	odd	4	inner
1280.2.s.d.1087.5	yes	32	1.1	even	1	trivial
1280.2.s.d.1087.12	yes	32	4.3	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.81199 q^{3} +(0.344369 + 2.20939i) q^{5} +(-1.54814 - 1.54814i) q^{7} +0.283291 q^{9} +(2.69839 - 2.69839i) q^{11} +3.33474i q^{13} +(-0.623991 - 4.00338i) q^{15} +(-0.680078 - 0.680078i) q^{17} +(-2.79866 + 2.79866i) q^{19} +(2.80521 + 2.80521i) q^{21} +(-1.75563 + 1.75563i) q^{23} +(-4.76282 + 1.52169i) q^{25} +4.92264 q^{27} +(-3.13750 - 3.13750i) q^{29} -8.56830i q^{31} +(-4.88944 + 4.88944i) q^{33} +(2.88732 - 3.95358i) q^{35} +8.30361i q^{37} -6.04250i q^{39} -10.8252i q^{41} -2.87092i q^{43} +(0.0975564 + 0.625900i) q^{45} +(-0.985023 + 0.985023i) q^{47} -2.20651i q^{49} +(1.23229 + 1.23229i) q^{51} +13.1354 q^{53} +(6.89103 + 5.03255i) q^{55} +(5.07113 - 5.07113i) q^{57} +(-4.36188 - 4.36188i) q^{59} +(7.83616 - 7.83616i) q^{61} +(-0.438574 - 0.438574i) q^{63} +(-7.36775 + 1.14838i) q^{65} -13.0450i q^{67} +(3.18118 - 3.18118i) q^{69} -0.134408 q^{71} +(-7.36590 - 7.36590i) q^{73} +(8.63016 - 2.75728i) q^{75} -8.35497 q^{77} +7.88100 q^{79} -9.76962 q^{81} -12.0979 q^{83} +(1.26836 - 1.73676i) q^{85} +(5.68510 + 5.68510i) q^{87} +15.7833 q^{89} +(5.16265 - 5.16265i) q^{91} +15.5256i q^{93} +(-7.14711 - 5.21957i) q^{95} +(-3.00550 - 3.00550i) q^{97} +(0.764428 - 0.764428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{5} + 32 q^{9} + 8 q^{17} - 8 q^{21} - 16 q^{25} - 16 q^{29} + 56 q^{33} + 48 q^{45} - 112 q^{53} + 8 q^{57} + 8 q^{61} - 72 q^{65} + 40 q^{69} - 8 q^{73} - 144 q^{77} - 64 q^{81} - 40 q^{85}+ \cdots + 72 q^{97}+O(q^{100}) \) 32 * q + 8 * q^5 + 32 * q^9 + 8 * q^17 - 8 * q^21 - 16 * q^25 - 16 * q^29 + 56 * q^33 + 48 * q^45 - 112 * q^53 + 8 * q^57 + 8 * q^61 - 72 * q^65 + 40 * q^69 - 8 * q^73 - 144 * q^77 - 64 * q^81 - 40 * q^85 + 16 * q^89 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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