LMFDB - Embedded newform 448.3.o.b.95.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [448,3,Mod(95,448)] 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("448.95"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(448, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	448.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,6] 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:	$12.2071158433$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 34 x^{18} + 755 x^{16} - 9698 x^{14} + 89921 x^{12} - 522048 x^{10} + 2189920 x^{8} + \cdots + 7311616 $ x^20 - 34x^18 + 755x^16 - 9698x^14 + 89921x^12 - 522048x^10 + 2189920x^8 - 5640416x^6 + 10423552x^4 - 10729472*x^2 + 7311616
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.5
Root			$1.96054 - 1.13192i$ of defining polynomial
Character	$\chi$	$=$	448.95
Dual form			448.3.o.b.415.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.459807 + 0.796409i) q^{3} +(-7.80113 + 4.50398i) q^{5} +(6.78682 - 1.71436i) q^{7} +(4.07716 + 7.06184i) q^{9} +(-6.32702 + 10.9587i) q^{11} -16.1125i q^{13} -8.28385i q^{15} +(-0.984338 + 1.70492i) q^{17} +(0.216902 + 0.375684i) q^{19} +(-1.75530 + 6.19336i) q^{21} +(-34.6927 + 20.0298i) q^{23} +(28.0717 - 48.6217i) q^{25} -15.7753 q^{27} -40.7786i q^{29} +(-40.7424 - 23.5226i) q^{31} +(-5.81841 - 10.0778i) q^{33} +(-45.2234 + 43.9417i) q^{35} +(-27.5719 + 15.9186i) q^{37} +(12.8321 + 7.40863i) q^{39} -52.2116 q^{41} +14.1020 q^{43} +(-63.6128 - 36.7269i) q^{45} +(29.9037 - 17.2649i) q^{47} +(43.1219 - 23.2701i) q^{49} +(-0.905211 - 1.56787i) q^{51} +(-11.2463 - 6.49306i) q^{53} -113.987i q^{55} -0.398931 q^{57} +(-7.30775 + 12.6574i) q^{59} +(21.1429 - 12.2069i) q^{61} +(39.7775 + 40.9378i) q^{63} +(72.5704 + 125.696i) q^{65} +(-39.7900 + 68.9184i) q^{67} -36.8394i q^{69} +28.2994i q^{71} +(25.3528 - 43.9124i) q^{73} +(25.8151 + 44.7131i) q^{75} +(-24.1532 + 85.2216i) q^{77} +(-70.2147 + 40.5385i) q^{79} +(-29.4408 + 50.9930i) q^{81} +77.5181 q^{83} -17.7338i q^{85} +(32.4764 + 18.7503i) q^{87} +(-65.4595 - 113.379i) q^{89} +(-27.6226 - 109.353i) q^{91} +(37.4673 - 21.6317i) q^{93} +(-3.38415 - 1.95384i) q^{95} -7.27222 q^{97} -103.185 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) $ 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−0.459807	+	0.796409i	−0.153269	+	0.265470i	−0.932427	−	0.361357i	$-0.882313\pi$
$3$	−0.459807	+	0.796409i	−0.153269	+	0.265470i	0.779158	+	0.626827i	$0.215647\pi$
$4$		0			0
$5$	−7.80113	+	4.50398i	−1.56023	+	0.900797i	−0.562992	+	0.826462i	$0.690350\pi$
$5$	−7.80113	+	4.50398i	−1.56023	+	0.900797i	−0.997233	+	0.0743347i	$0.976317\pi$
$6$		0			0
$7$	6.78682	−	1.71436i	0.969546	−	0.244908i
$7$	6.78682	−	1.71436i	0.969546	−	0.244908i
$8$		0			0
$9$	4.07716	+	7.06184i	0.453017	+	0.784649i
$10$		0			0
$11$	−6.32702	+	10.9587i	−0.575183	+	0.996247i	0.420838	+	0.907136i	$0.361736\pi$
$11$	−6.32702	+	10.9587i	−0.575183	+	0.996247i	−0.996022	+	0.0891111i	$0.971597\pi$
$12$		0			0
$13$		−	16.1125i		−	1.23942i	−0.784830	−	0.619711i	$-0.787250\pi$
$13$		−	16.1125i		−	1.23942i	0.784830	−	0.619711i	$-0.212750\pi$
$14$		0			0
$15$		−	8.28385i		−	0.552257i
$16$		0			0
$17$	−0.984338	+	1.70492i	−0.0579023	+	0.100290i	−0.893524	−	0.449016i	$-0.851775\pi$
$17$	−0.984338	+	1.70492i	−0.0579023	+	0.100290i	0.835621	+	0.549306i	$0.185108\pi$
$18$		0			0
$19$	0.216902	+	0.375684i	0.0114159	+	0.0197729i	0.871677	−	0.490081i	$-0.163033\pi$
$19$	0.216902	+	0.375684i	0.0114159	+	0.0197729i	−0.860261	+	0.509854i	$0.829699\pi$
$20$		0			0
$21$	−1.75530	+	6.19336i	−0.0835855	+	0.294922i
$22$		0			0
$23$	−34.6927	+	20.0298i	−1.50838	+	0.870862i	−0.508425	+	0.861107i	$0.669772\pi$
$23$	−34.6927	+	20.0298i	−1.50838	+	0.870862i	−0.999952	+	0.00975527i	$0.996895\pi$
$24$		0			0
$25$	28.0717	−	48.6217i	1.12287	−	1.94487i
$26$		0			0
$27$	−15.7753			−0.584272
$28$		0			0
$29$		−	40.7786i		−	1.40616i	−0.711111	−	0.703079i	$-0.751808\pi$
$29$		−	40.7786i		−	1.40616i	0.711111	−	0.703079i	$-0.248192\pi$
$30$		0			0
$31$	−40.7424	−	23.5226i	−1.31427	−	0.758795i	−0.331470	−	0.943466i	$-0.607545\pi$
$31$	−40.7424	−	23.5226i	−1.31427	−	0.758795i	−0.982800	+	0.184671i	$0.940878\pi$
$32$		0			0
$33$	−5.81841	−	10.0778i	−0.176315	−	0.305387i
$34$		0			0
$35$	−45.2234	+	43.9417i	−1.29210	+	1.25548i
$36$		0			0
$37$	−27.5719	+	15.9186i	−0.745185	+	0.430233i	−0.823952	−	0.566660i	$-0.808235\pi$
$37$	−27.5719	+	15.9186i	−0.745185	+	0.430233i	0.0787663	+	0.996893i	$0.474902\pi$
$38$		0			0
$39$	12.8321	+	7.40863i	0.329029	+	0.189965i
$40$		0			0
$41$	−52.2116			−1.27345			−0.636727	−	0.771089i	$-0.719712\pi$
$41$	−52.2116			−1.27345			−0.636727	+	0.771089i	$0.719712\pi$
$42$		0			0
$43$	14.1020			0.327954			0.163977	−	0.986464i	$-0.447568\pi$
$43$	14.1020			0.327954			0.163977	+	0.986464i	$0.447568\pi$
$44$		0			0
$45$	−63.6128	−	36.7269i	−1.41362	−	0.816153i
$46$		0			0
$47$	29.9037	−	17.2649i	0.636249	−	0.367339i	−0.146919	−	0.989149i	$-0.546936\pi$
$47$	29.9037	−	17.2649i	0.636249	−	0.367339i	0.783168	+	0.621810i	$0.213602\pi$
$48$		0			0
$49$	43.1219	−	23.2701i	0.880040	−	0.474900i
$50$		0			0
$51$	−0.905211	−	1.56787i	−0.0177492	−	0.0307426i
$52$		0			0
$53$	−11.2463	−	6.49306i	−0.212195	−	0.122511i	0.390136	−	0.920757i	$-0.372428\pi$
$53$	−11.2463	−	6.49306i	−0.212195	−	0.122511i	−0.602331	+	0.798246i	$0.705761\pi$
$54$		0			0
$55$		−	113.987i		−	2.07249i
$56$		0			0
$57$	−0.398931			−0.00699879
$58$		0			0
$59$	−7.30775	+	12.6574i	−0.123860	+	0.214532i	−0.921287	−	0.388884i	$-0.872861\pi$
$59$	−7.30775	+	12.6574i	−0.123860	+	0.214532i	0.797427	+	0.603416i	$0.206194\pi$
$60$		0			0
$61$	21.1429	−	12.2069i	0.346605	−	0.200112i	−0.316584	−	0.948564i	$-0.602536\pi$
$61$	21.1429	−	12.2069i	0.346605	−	0.200112i	0.663189	+	0.748452i	$0.269203\pi$
$62$		0			0
$63$	39.7775	+	40.9378i	0.631388	+	0.649806i
$64$		0			0
$65$	72.5704	+	125.696i	1.11647	+	1.93378i
$66$		0			0
$67$	−39.7900	+	68.9184i	−0.593881	+	1.02863i	0.399823	+	0.916592i	$0.369072\pi$
$67$	−39.7900	+	68.9184i	−0.593881	+	1.02863i	−0.993704	+	0.112040i	$0.964262\pi$
$68$		0			0
$69$		−	36.8394i		−	0.533904i
$70$		0			0
$71$			28.2994i			0.398584i	0.979940	+	0.199292i	$0.0638642\pi$
$71$			28.2994i			0.398584i	−0.979940	+	0.199292i	$0.936136\pi$
$72$		0			0
$73$	25.3528	−	43.9124i	0.347299	−	0.601540i	−0.638469	−	0.769647i	$-0.720432\pi$
$73$	25.3528	−	43.9124i	0.347299	−	0.601540i	0.985769	+	0.168107i	$0.0537655\pi$
$74$		0			0
$75$	25.8151	+	44.7131i	0.344202	+	0.596175i
$76$		0			0
$77$	−24.1532	+	85.2216i	−0.313678	+	1.10677i
$78$		0			0
$79$	−70.2147	+	40.5385i	−0.888793	+	0.513145i	−0.873548	−	0.486739i	$-0.838186\pi$
$79$	−70.2147	+	40.5385i	−0.888793	+	0.513145i	−0.0152457	+	0.999884i	$0.504853\pi$
$80$		0			0
$81$	−29.4408	+	50.9930i	−0.363467	+	0.629543i
$82$		0			0
$83$	77.5181			0.933953			0.466977	−	0.884270i	$-0.345343\pi$
$83$	77.5181			0.933953			0.466977	+	0.884270i	$0.345343\pi$
$84$		0			0
$85$		−	17.7338i		−	0.208633i
$86$		0			0
$87$	32.4764	+	18.7503i	0.373292	+	0.215520i
$88$		0			0
$89$	−65.4595	−	113.379i	−0.735500	−	1.27392i	−0.954504	−	0.298199i	$-0.903614\pi$
$89$	−65.4595	−	113.379i	−0.735500	−	1.27392i	0.219004	−	0.975724i	$-0.429719\pi$
$90$		0			0
$91$	−27.6226	−	109.353i	−0.303545	−	1.20168i
$92$		0			0
$93$	37.4673	−	21.6317i	0.402874	−	0.232599i
$94$		0			0
$95$	−3.38415	−	1.95384i	−0.0356227	−	0.0205668i
$96$		0			0
$97$	−7.27222			−0.0749713			−0.0374857	−	0.999297i	$-0.511935\pi$
$97$	−7.27222			−0.0749713			−0.0374857	+	0.999297i	$0.511935\pi$
$98$		0			0
$99$	−103.185			−1.04227
$100$		0			0
$101$	−11.0636	−	6.38756i	−0.109540	−	0.0632431i	0.444229	−	0.895913i	$-0.353478\pi$
$101$	−11.0636	−	6.38756i	−0.109540	−	0.0632431i	−0.553769	+	0.832670i	$0.686811\pi$
$102$		0			0
$103$	−82.0565	+	47.3753i	−0.796665	+	0.459955i	−0.842304	−	0.539003i	$-0.818801\pi$
$103$	−82.0565	+	47.3753i	−0.796665	+	0.459955i	0.0456390	+	0.998958i	$0.485468\pi$
$104$		0			0
$105$	−14.2015	−	56.2210i	−0.135252	−	0.535438i
$106$		0			0
$107$	16.9208	+	29.3076i	0.158138	+	0.273903i	0.934197	−	0.356757i	$-0.116118\pi$
$107$	16.9208	+	29.3076i	0.158138	+	0.273903i	−0.776059	+	0.630660i	$0.782784\pi$
$108$		0			0
$109$	114.203	+	65.9353i	1.04774	+	0.604911i	0.922015	−	0.387155i	$-0.126542\pi$
$109$	114.203	+	65.9353i	1.04774	+	0.604911i	0.125722	+	0.992066i	$0.459875\pi$
$110$		0			0
$111$		−	29.2780i		−	0.263765i
$112$		0			0
$113$	−43.8639			−0.388176			−0.194088	−	0.980984i	$-0.562175\pi$
$113$	−43.8639			−0.388176			−0.194088	+	0.980984i	$0.562175\pi$
$114$		0			0
$115$	180.428	−	312.510i	1.56894	−	2.71748i
$116$		0			0
$117$	113.784	−	65.6931i	0.972511	−	0.561480i
$118$		0			0
$119$	−3.75768	+	13.2585i	−0.0315771	+	0.111416i
$120$		0			0
$121$	−19.5623	−	33.8829i	−0.161672	−	0.280024i
$122$		0			0
$123$	24.0073	−	41.5818i	0.195181	−	0.338063i
$124$		0			0
$125$			280.539i			2.24432i
$126$		0			0
$127$			92.1089i			0.725267i	0.931932	+	0.362634i	$0.118122\pi$
$127$			92.1089i			0.725267i	−0.931932	+	0.362634i	$0.881878\pi$
$128$		0			0
$129$	−6.48419	+	11.2310i	−0.0502651	+	0.0870617i
$130$		0			0
$131$	−10.7488	−	18.6174i	−0.0820518	−	0.142118i	0.822079	−	0.569373i	$-0.192814\pi$
$131$	−10.7488	−	18.6174i	−0.0820518	−	0.142118i	−0.904131	+	0.427255i	$0.859481\pi$
$132$		0			0
$133$	2.11613	+	2.17786i	0.0159108	+	0.0163749i
$134$		0			0
$135$	123.065	−	71.0519i	0.911596	−	0.526310i
$136$		0			0
$137$	−32.8022	+	56.8150i	−0.239432	+	0.414708i	−0.960551	−	0.278102i	$-0.910295\pi$
$137$	−32.8022	+	56.8150i	−0.239432	+	0.414708i	0.721119	+	0.692811i	$0.243628\pi$
$138$		0			0
$139$	−213.452			−1.53563			−0.767813	−	0.640674i	$-0.778655\pi$
$139$	−213.452			−1.53563			−0.767813	+	0.640674i	$0.778655\pi$
$140$		0			0
$141$			31.7541i			0.225206i
$142$		0			0
$143$	176.572	+	101.944i	1.23477	+	0.712895i
$144$		0			0
$145$	183.666	+	318.119i	1.26666	+	2.19392i
$146$		0			0
$147$	−1.29524	+	45.0424i	−0.00881119	+	0.306411i
$148$		0			0
$149$	115.093	−	66.4490i	0.772436	−	0.445966i	−0.0613069	−	0.998119i	$-0.519527\pi$
$149$	115.093	−	66.4490i	0.772436	−	0.445966i	0.833743	+	0.552153i	$0.186194\pi$
$150$		0			0
$151$	50.1819	+	28.9725i	0.332331	+	0.191871i	0.656875	−	0.753999i	$-0.271878\pi$
$151$	50.1819	+	28.9725i	0.332331	+	0.191871i	−0.324545	+	0.945870i	$0.605211\pi$
$152$		0			0
$153$	−16.0532			−0.104923
$154$		0			0
$155$	423.782			2.73408
$156$		0			0
$157$	−83.1606	−	48.0128i	−0.529685	−	0.305814i	0.211203	−	0.977442i	$-0.432262\pi$
$157$	−83.1606	−	48.0128i	−0.529685	−	0.305814i	−0.740888	+	0.671628i	$0.765595\pi$
$158$		0			0
$159$	10.3423	−	5.97111i	0.0650457	−	0.0375541i
$160$		0			0
$161$	−201.115	+	195.415i	−1.24916	+	1.21376i
$162$		0			0
$163$	147.278	+	255.092i	0.903543	+	1.56498i	0.822861	+	0.568242i	$0.192376\pi$
$163$	147.278	+	255.092i	0.903543	+	1.56498i	0.0806819	+	0.996740i	$0.474290\pi$
$164$		0			0
$165$	90.7803	+	52.4120i	0.550184	+	0.317649i
$166$		0			0
$167$			153.695i			0.920331i	0.887833	+	0.460166i	$0.152210\pi$
$167$			153.695i			0.920331i	−0.887833	+	0.460166i	$0.847790\pi$
$168$		0			0
$169$	−90.6122			−0.536167
$170$		0			0
$171$	−1.76868	+	3.06345i	−0.0103432	+	0.0179149i
$172$		0			0
$173$	−29.3569	+	16.9492i	−0.169693	+	0.0979724i	−0.582441	−	0.812873i	$-0.697902\pi$
$173$	−29.3569	+	16.9492i	−0.169693	+	0.0979724i	0.412748	+	0.910845i	$0.364569\pi$
$174$		0			0
$175$	107.163	−	378.112i	0.612359	−	2.16064i
$176$		0			0
$177$	−6.72030	−	11.6399i	−0.0379678	−	0.0657622i
$178$		0			0
$179$	100.243	−	173.627i	0.560018	−	0.969980i	−0.437476	−	0.899230i	$-0.644127\pi$
$179$	100.243	−	173.627i	0.560018	−	0.969980i	0.997494	−	0.0707502i	$-0.0225393\pi$
$180$		0			0
$181$			162.562i			0.898132i	0.893499	+	0.449066i	$0.148243\pi$
$181$			162.562i			0.898132i	−0.893499	+	0.449066i	$0.851757\pi$
$182$		0			0
$183$			22.4512i			0.122684i
$184$		0			0
$185$	143.394	−	248.366i	0.775105	−	1.34252i
$186$		0			0
$187$	−12.4559	−	21.5742i	−0.0666088	−	0.115370i
$188$		0			0
$189$	−107.064	+	27.0446i	−0.566478	+	0.143093i
$190$		0			0
$191$	−39.8493	+	23.0070i	−0.208635	+	0.120455i	−0.600677	−	0.799492i	$-0.705102\pi$
$191$	−39.8493	+	23.0070i	−0.208635	+	0.120455i	0.392042	+	0.919947i	$0.371769\pi$
$192$		0			0
$193$	−58.2777	+	100.940i	−0.301957	+	0.523004i	−0.976579	−	0.215159i	$-0.930973\pi$
$193$	−58.2777	+	100.940i	−0.301957	+	0.523004i	0.674622	+	0.738163i	$0.264306\pi$
$194$		0			0
$195$	−133.473			−0.684479
$196$		0			0
$197$			17.7289i			0.0899943i	0.998987	+	0.0449971i	$0.0143279\pi$
$197$			17.7289i			0.0899943i	−0.998987	+	0.0449971i	$0.985672\pi$
$198$		0			0
$199$	133.182	+	76.8926i	0.669256	+	0.386395i	0.795795	−	0.605567i	$-0.207053\pi$
$199$	133.182	+	76.8926i	0.669256	+	0.386395i	−0.126539	+	0.991962i	$0.540387\pi$
$200$		0			0
$201$	−36.5914	−	63.3782i	−0.182047	−	0.315315i
$202$		0			0
$203$	−69.9092	−	276.757i	−0.344380	−	1.36334i
$204$		0			0
$205$	407.310	−	235.160i	1.98688	−	1.14712i
$206$		0			0
$207$	−282.895	−	163.329i	−1.36664	−	0.789031i
$208$		0			0
$209$	−5.48936			−0.0262649
$210$		0			0
$211$	−182.410			−0.864502			−0.432251	−	0.901753i	$-0.642281\pi$
$211$	−182.410			−0.864502			−0.432251	+	0.901753i	$0.642281\pi$
$212$		0			0
$213$	−22.5379	−	13.0123i	−0.105812	−	0.0610905i
$214$		0			0
$215$	−110.012	+	63.5152i	−0.511682	+	0.295419i
$216$		0			0
$217$	−316.838	−	89.7968i	−1.46008	−	0.413810i
$218$		0			0
$219$	23.3148	+	40.3825i	0.106460	+	0.184395i
$220$		0			0
$221$	27.4706	+	15.8601i	0.124301	+	0.0717653i
$222$		0			0
$223$			316.251i			1.41817i	0.705124	+	0.709084i	$0.250891\pi$
$223$			316.251i			1.41817i	−0.705124	+	0.709084i	$0.749109\pi$
$224$		0			0
$225$	457.811			2.03472
$226$		0			0
$227$	131.749	−	228.195i	0.580391	−	1.00527i	−0.415042	−	0.909802i	$-0.636233\pi$
$227$	131.749	−	228.195i	0.580391	−	1.00527i	0.995433	−	0.0954639i	$-0.0304334\pi$
$228$		0			0
$229$	−225.621	+	130.262i	−0.985246	+	0.568832i	−0.903850	−	0.427850i	$-0.859271\pi$
$229$	−225.621	+	130.262i	−0.985246	+	0.568832i	−0.0813959	+	0.996682i	$0.525938\pi$
$230$		0			0
$231$	−56.7655	−	58.4213i	−0.245738	−	0.252906i
$232$		0			0
$233$	−139.311	−	241.294i	−0.597902	−	1.03560i	−0.993130	−	0.117014i	$-0.962668\pi$
$233$	−139.311	−	241.294i	−0.597902	−	1.03560i	0.395228	−	0.918583i	$-0.370666\pi$
$234$		0			0
$235$	−155.522	+	269.372i	−0.661795	+	1.14626i
$236$		0			0
$237$		−	74.5594i		−	0.314597i
$238$		0			0
$239$			139.808i			0.584970i	0.956270	+	0.292485i	$0.0944821\pi$
$239$			139.808i			0.584970i	−0.956270	+	0.292485i	$0.905518\pi$
$240$		0			0
$241$	49.5884	−	85.8896i	0.205761	−	0.356388i	−0.744614	−	0.667495i	$-0.767366\pi$
$241$	49.5884	−	85.8896i	0.205761	−	0.356388i	0.950375	+	0.311107i	$0.100700\pi$
$242$		0			0
$243$	−98.0632	−	169.850i	−0.403552	−	0.698973i
$244$		0			0
$245$	−231.592	+	375.754i	−0.945272	+	1.53369i
$246$		0			0
$247$	6.05321	−	3.49482i	0.0245069	−	0.0141491i
$248$		0			0
$249$	−35.6433	+	61.7361i	−0.143146	+	0.247936i
$250$		0			0
$251$	−232.634			−0.926829			−0.463414	−	0.886142i	$-0.653376\pi$
$251$	−232.634			−0.926829			−0.463414	+	0.886142i	$0.653376\pi$
$252$		0			0
$253$		−	506.916i		−	2.00362i
$254$		0			0
$255$	14.1233	+	8.15411i	0.0553856	+	0.0319769i
$256$		0			0
$257$	−77.0149	−	133.394i	−0.299669	−	0.519042i	0.676391	−	0.736543i	$-0.263543\pi$
$257$	−77.0149	−	133.394i	−0.299669	−	0.519042i	−0.976060	+	0.217501i	$0.930210\pi$
$258$		0			0
$259$	−159.835	+	155.305i	−0.617124	+	0.599633i
$260$		0			0
$261$	287.972	−	166.261i	1.10334	−	0.637014i
$262$		0			0
$263$	−331.143	−	191.185i	−1.25910	−	0.726941i	−0.286199	−	0.958170i	$-0.592392\pi$
$263$	−331.143	−	191.185i	−1.25910	−	0.726941i	−0.972899	+	0.231230i	$0.925725\pi$
$264$		0			0
$265$	116.979			0.441429
$266$		0			0
$267$	120.395			0.450917
$268$		0			0
$269$	−301.543	−	174.096i	−1.12098	−	0.647197i	−0.179328	−	0.983789i	$-0.557392\pi$
$269$	−301.543	−	174.096i	−1.12098	−	0.647197i	−0.941651	+	0.336592i	$0.890726\pi$
$270$		0			0
$271$	153.069	−	88.3745i	0.564831	−	0.326105i	−0.190251	−	0.981735i	$-0.560930\pi$
$271$	153.069	−	88.3745i	0.564831	−	0.326105i	0.755082	+	0.655630i	$0.227597\pi$
$272$		0			0
$273$	99.7904	+	28.2822i	0.365533	+	0.103598i
$274$		0			0
$275$	355.221	+	615.260i	1.29171	+	2.23731i
$276$		0			0
$277$	−276.470	−	159.620i	−0.998088	−	0.576247i	−0.0904063	−	0.995905i	$-0.528817\pi$
$277$	−276.470	−	159.620i	−0.998088	−	0.576247i	−0.907682	+	0.419658i	$0.862150\pi$
$278$		0			0
$279$		−	383.622i		−	1.37499i
$280$		0			0
$281$	216.962			0.772107			0.386053	−	0.922476i	$-0.373838\pi$
$281$	216.962			0.772107			0.386053	+	0.922476i	$0.373838\pi$
$282$		0			0
$283$	−107.240	+	185.745i	−0.378940	+	0.656344i	−0.990908	−	0.134539i	$-0.957045\pi$
$283$	−107.240	+	185.745i	−0.378940	+	0.656344i	0.611968	+	0.790883i	$0.290378\pi$
$284$		0			0
$285$	3.11211	−	1.79678i	0.0109197	−	0.00630449i
$286$		0			0
$287$	−354.351	+	89.5095i	−1.23467	+	0.311880i
$288$		0			0
$289$	142.562	+	246.925i	0.493295	+	0.854411i
$290$		0			0
$291$	3.34381	−	5.79166i	0.0114908	−	0.0199026i
$292$		0			0
$293$			397.846i			1.35784i	0.734214	+	0.678918i	$0.237551\pi$
$293$			397.846i			1.35784i	−0.734214	+	0.678918i	$0.762449\pi$
$294$		0			0
$295$		−	131.656i		−	0.446291i
$296$		0			0
$297$	99.8108	−	172.877i	0.336063	−	0.582079i
$298$		0			0
$299$	322.730	+	558.985i	1.07937	+	1.86952i
$300$		0			0
$301$	95.7078	−	24.1759i	0.317966	−	0.0803186i
$302$		0			0
$303$	10.1742	−	5.87408i	0.0335782	−	0.0193864i
$304$		0			0
$305$	−109.959	+	190.455i	−0.360521	+	0.624441i
$306$		0			0
$307$	−369.153			−1.20245			−0.601227	−	0.799078i	$-0.705321\pi$
$307$	−369.153			−1.20245			−0.601227	+	0.799078i	$0.705321\pi$
$308$		0			0
$309$		−	87.1340i		−	0.281987i
$310$		0			0
$311$	399.700	+	230.767i	1.28521	+	0.742015i	0.977796	−	0.209561i	$-0.0672035\pi$
$311$	399.700	+	230.767i	1.28521	+	0.742015i	0.307412	+	0.951576i	$0.400537\pi$
$312$		0			0
$313$	134.221	+	232.478i	0.428822	+	0.742741i	0.996769	−	0.0803240i	$-0.0255955\pi$
$313$	134.221	+	232.478i	0.428822	+	0.742741i	−0.567947	+	0.823065i	$0.692262\pi$
$314$		0			0
$315$	−494.692	−	140.204i	−1.57045	−	0.445091i
$316$		0			0
$317$	−327.713	+	189.205i	−1.03379	+	0.596861i	−0.918069	−	0.396420i	$-0.870252\pi$
$317$	−327.713	+	189.205i	−1.03379	+	0.596861i	−0.115725	+	0.993281i	$0.536919\pi$
$318$		0			0
$319$	446.881	+	258.007i	1.40088	+	0.808799i
$320$		0			0
$321$	−31.1211			−0.0969506
$322$		0			0
$323$	−0.854018			−0.00264402
$324$		0			0
$325$	−783.416	−	452.305i	−2.41051	−	1.39171i
$326$		0			0
$327$	−105.023	+	60.6350i	−0.321171	+	0.185428i
$328$		0			0
$329$	173.353	−	168.440i	0.526909	−	0.511974i
$330$		0			0
$331$	−151.150	−	261.799i	−0.456646	−	0.790934i	0.542135	−	0.840291i	$-0.317616\pi$
$331$	−151.150	−	261.799i	−0.456646	−	0.790934i	−0.998781	+	0.0493573i	$0.984283\pi$
$332$		0			0
$333$	−224.829	−	129.805i	−0.675164	−	0.389806i
$334$		0			0
$335$		−	716.855i		−	2.13986i
$336$		0			0
$337$	−171.204			−0.508025			−0.254013	−	0.967201i	$-0.581750\pi$
$337$	−171.204			−0.508025			−0.254013	+	0.967201i	$0.581750\pi$
$338$		0			0
$339$	20.1689	−	34.9336i	0.0594954	−	0.103049i
$340$		0			0
$341$	515.556	−	297.656i	1.51189	−	0.872892i
$342$		0			0
$343$	252.768	−	231.857i	0.736932	−	0.675967i
$344$		0			0
$345$	165.924	+	287.389i	0.480939	+	0.833011i
$346$		0			0
$347$	−163.843	+	283.785i	−0.472170	+	0.817823i	−0.999493	−	0.0318422i	$-0.989863\pi$
$347$	−163.843	+	283.785i	−0.472170	+	0.817823i	0.527323	+	0.849665i	$0.323196\pi$
$348$		0			0
$349$		−	26.2785i		−	0.0752964i	−0.999291	−	0.0376482i	$-0.988013\pi$
$349$		−	26.2785i		−	0.0752964i	0.999291	−	0.0376482i	$-0.0119866\pi$
$350$		0			0
$351$			254.180i			0.724159i
$352$		0			0
$353$	112.342	−	194.583i	0.318250	−	0.551225i	−0.661873	−	0.749616i	$-0.730238\pi$
$353$	112.342	−	194.583i	0.318250	−	0.551225i	0.980123	+	0.198391i	$0.0635715\pi$
$354$		0			0
$355$	−127.460	−	220.768i	−0.359043	−	0.621881i
$356$		0			0
$357$	−8.83140	−	9.08901i	−0.0247378	−	0.0254594i
$358$		0			0
$359$	−585.508	+	338.043i	−1.63094	+	0.941624i	−0.647137	+	0.762374i	$0.724034\pi$
$359$	−585.508	+	338.043i	−1.63094	+	0.941624i	−0.983804	+	0.179250i	$0.942633\pi$
$360$		0			0
$361$	180.406	−	312.472i	0.499739	−	0.865574i
$362$		0			0
$363$	35.9795			0.0991170
$364$		0			0
$365$			456.755i			1.25138i
$366$		0			0
$367$	−412.555	−	238.189i	−1.12413	−	0.649015i	−0.181676	−	0.983358i	$-0.558152\pi$
$367$	−412.555	−	238.189i	−1.12413	−	0.649015i	−0.942451	+	0.334343i	$0.891486\pi$
$368$		0			0
$369$	−212.875	−	368.710i	−0.576897	−	0.999215i
$370$		0			0
$371$	−87.4582	−	24.7870i	−0.235736	−	0.0668114i
$372$		0			0
$373$	206.693	−	119.334i	0.554138	−	0.319932i	−0.196652	−	0.980473i	$-0.563007\pi$
$373$	206.693	−	119.334i	0.554138	−	0.319932i	0.750789	+	0.660542i	$0.229673\pi$
$374$		0			0
$375$	−223.424	−	128.994i	−0.595797	−	0.343984i
$376$		0			0
$377$	−657.045			−1.74282
$378$		0			0
$379$	361.641			0.954198			0.477099	−	0.878850i	$-0.341688\pi$
$379$	361.641			0.954198			0.477099	+	0.878850i	$0.341688\pi$
$380$		0			0
$381$	−73.3564	−	42.3523i	−0.192536	−	0.111161i
$382$		0			0
$383$	−30.9081	+	17.8448i	−0.0807000	+	0.0465921i	−0.539807	−	0.841789i	$-0.681503\pi$
$383$	−30.9081	+	17.8448i	−0.0807000	+	0.0465921i	0.459107	+	0.888381i	$0.348169\pi$
$384$		0			0
$385$	−195.415	−	773.610i	−0.507571	−	2.00938i
$386$		0			0
$387$	57.4961	+	99.5861i	0.148569	+	0.257328i
$388$		0			0
$389$	415.411	+	239.838i	1.06789	+	0.616549i	0.927605	−	0.373562i	$-0.121864\pi$
$389$	415.411	+	239.838i	1.06789	+	0.616549i	0.140289	+	0.990111i	$0.455197\pi$
$390$		0			0
$391$		−	78.8645i		−	0.201699i
$392$		0			0
$393$	19.7695			0.0503040
$394$		0			0
$395$	365.169	−	632.491i	0.924479	−	1.60124i
$396$		0			0
$397$	−97.0586	+	56.0368i	−0.244480	+	0.141151i	−0.617234	−	0.786780i	$-0.711747\pi$
$397$	−97.0586	+	56.0368i	−0.244480	+	0.141151i	0.372754	+	0.927930i	$0.378414\pi$
$398$		0			0
$399$	−2.70747	+	0.683911i	−0.00678565	+	0.00171406i
$400$		0			0
$401$	38.7177	+	67.0610i	0.0965528	+	0.167234i	0.910256	−	0.414047i	$-0.135885\pi$
$401$	38.7177	+	67.0610i	0.0965528	+	0.167234i	−0.813703	+	0.581281i	$0.802552\pi$
$402$		0			0
$403$	−379.008	+	656.461i	−0.940467	+	1.62894i
$404$		0			0
$405$		−	530.403i		−	1.30964i
$406$		0			0
$407$		−	402.869i		−	0.989851i
$408$		0			0
$409$	−146.009	+	252.895i	−0.356990	+	0.618325i	−0.987456	−	0.157892i	$-0.949530\pi$
$409$	−146.009	+	252.895i	−0.356990	+	0.618325i	0.630466	+	0.776217i	$0.282864\pi$
$410$		0			0
$411$	−30.1653	−	52.2479i	−0.0733949	−	0.127124i
$412$		0			0
$413$	−27.8971	+	98.4316i	−0.0675474	+	0.238333i
$414$		0			0
$415$	−604.729	+	349.140i	−1.45718	+	0.841302i
$416$		0			0
$417$	98.1467	−	169.995i	0.235364	−	0.407662i
$418$		0			0
$419$	274.205			0.654427			0.327214	−	0.944950i	$-0.393890\pi$
$419$	274.205			0.654427			0.327214	+	0.944950i	$0.393890\pi$
$420$		0			0
$421$		−	588.325i		−	1.39745i	−0.715392	−	0.698724i	$-0.753752\pi$
$421$		−	588.325i		−	1.39745i	0.715392	−	0.698724i	$-0.246248\pi$
$422$		0			0
$423$	243.844	+	140.783i	0.576464	+	0.332821i
$424$		0			0
$425$	55.2642	+	95.7204i	0.130033	+	0.225224i
$426$		0			0
$427$	122.566	−	119.092i	0.287040	−	0.278905i
$428$		0			0
$429$	−162.378	+	93.7490i	−0.378504	+	0.218529i
$430$		0			0
$431$	411.785	+	237.744i	0.955418	+	0.551611i	0.894760	−	0.446547i	$-0.147347\pi$
$431$	411.785	+	237.744i	0.955418	+	0.551611i	0.0606585	+	0.998159i	$0.480680\pi$
$432$		0			0
$433$	26.3299			0.0608081			0.0304041	−	0.999538i	$-0.490321\pi$
$433$	26.3299			0.0608081			0.0304041	+	0.999538i	$0.490321\pi$
$434$		0			0
$435$	−337.804			−0.776560
$436$		0			0
$437$	−15.0498	−	8.68900i	−0.0344389	−	0.0198833i
$438$		0			0
$439$	−307.812	+	177.715i	−0.701165	+	0.404818i	−0.807781	−	0.589482i	$-0.799332\pi$
$439$	−307.812	+	177.715i	−0.701165	+	0.404818i	0.106616	+	0.994300i	$0.465998\pi$
$440$		0			0
$441$	340.145	+	209.644i	0.771303	+	0.475384i
$442$		0			0
$443$	−19.6235	−	33.9889i	−0.0442969	−	0.0767244i	0.843027	−	0.537871i	$-0.180771\pi$
$443$	−19.6235	−	33.9889i	−0.0442969	−	0.0767244i	−0.887324	+	0.461147i	$0.847438\pi$
$444$		0			0
$445$	1021.32	+	589.657i	2.29509	+	1.32507i
$446$		0			0
$447$			122.215i			0.273411i
$448$		0			0
$449$	−298.951			−0.665814			−0.332907	−	0.942960i	$-0.608030\pi$
$449$	−298.951			−0.665814			−0.332907	+	0.942960i	$0.608030\pi$
$450$		0			0
$451$	330.344	−	572.173i	0.732470	−	1.26868i
$452$		0			0
$453$	−46.1480	+	26.6435i	−0.101872	+	0.0588158i
$454$		0			0
$455$	708.010	+	728.662i	1.55607	+	1.60145i
$456$		0			0
$457$	417.480	+	723.096i	0.913523	+	1.58227i	0.809050	+	0.587740i	$0.199982\pi$
$457$	417.480	+	723.096i	0.913523	+	1.58227i	0.104473	+	0.994528i	$0.466684\pi$
$458$		0			0
$459$	15.5283	−	26.8957i	0.0338306	−	0.0585964i
$460$		0			0
$461$			365.921i			0.793755i	0.917872	+	0.396877i	$0.129906\pi$
$461$			365.921i			0.793755i	−0.917872	+	0.396877i	$0.870094\pi$
$462$		0			0
$463$		−	528.067i		−	1.14053i	−0.821460	−	0.570266i	$-0.806840\pi$
$463$		−	528.067i		−	1.14053i	0.821460	−	0.570266i	$-0.193160\pi$
$464$		0			0
$465$	−194.858	+	337.504i	−0.419049	+	0.725815i
$466$		0			0
$467$	436.603	+	756.218i	0.934910	+	1.61931i	0.774795	+	0.632213i	$0.217853\pi$
$467$	436.603	+	756.218i	0.934910	+	1.61931i	0.160115	+	0.987098i	$0.448813\pi$
$468$		0			0
$469$	−151.897	+	535.951i	−0.323874	+	1.14275i
$470$		0			0
$471$	76.4756	−	44.1532i	0.162369	−	0.0937435i
$472$		0			0
$473$	−89.2236	+	154.540i	−0.188633	+	0.326723i
$474$		0			0
$475$	24.3552			0.0512741
$476$		0			0
$477$		−	105.893i		−	0.221998i
$478$		0			0
$479$	223.400	+	128.980i	0.466388	+	0.269269i	0.714727	−	0.699404i	$-0.246551\pi$
$479$	223.400	+	128.980i	0.466388	+	0.269269i	−0.248338	+	0.968673i	$0.579884\pi$
$480$		0			0
$481$	256.488	+	444.251i	0.533240	+	0.923599i
$482$		0			0
$483$	−63.1559	−	250.022i	−0.130758	−	0.517645i
$484$		0			0
$485$	56.7315	−	32.7539i	0.116972	−	0.0675339i
$486$		0			0
$487$	403.470	+	232.944i	0.828481	+	0.478324i	0.853332	−	0.521367i	$-0.174578\pi$
$487$	403.470	+	232.944i	0.828481	+	0.478324i	−0.0248512	+	0.999691i	$0.507911\pi$
$488$		0			0
$489$	−270.877			−0.553940
$490$		0			0
$491$	265.442			0.540615			0.270307	−	0.962774i	$-0.412875\pi$
$491$	265.442			0.540615			0.270307	+	0.962774i	$0.412875\pi$
$492$		0			0
$493$	69.5244	+	40.1399i	0.141023	+	0.0814198i
$494$		0			0
$495$	804.959	−	464.743i	1.62618	−	0.938875i
$496$		0			0
$497$	48.5154	+	192.063i	0.0976165	+	0.386445i
$498$		0			0
$499$	−349.630	−	605.578i	−0.700662	−	1.21358i	−0.968234	−	0.250044i	$-0.919555\pi$
$499$	−349.630	−	605.578i	−0.700662	−	1.21358i	0.267572	−	0.963538i	$-0.413779\pi$
$500$		0			0
$501$	−122.404	−	70.6701i	−0.244320	−	0.141058i
$502$		0			0
$503$			155.162i			0.308473i	0.988034	+	0.154237i	$0.0492918\pi$
$503$			155.162i			0.308473i	−0.988034	+	0.154237i	$0.950708\pi$
$504$		0			0
$505$	115.078			0.227877
$506$		0			0
$507$	41.6641	−	72.1643i	0.0821777	−	0.142336i
$508$		0			0
$509$	−111.931	+	64.6236i	−0.219904	+	0.126962i	−0.605906	−	0.795536i	$-0.707189\pi$
$509$	−111.931	+	64.6236i	−0.219904	+	0.126962i	0.386002	+	0.922498i	$0.373856\pi$
$510$		0			0
$511$	96.7836	−	341.490i	0.189400	−	0.668277i
$512$		0			0
$513$	−3.42169	−	5.92655i	−0.00666997	−	0.0115527i
$514$		0			0
$515$	426.755	−	739.162i	0.828651	−	1.43527i
$516$		0			0
$517$			436.942i			0.845148i
$518$		0			0
$519$		−	31.1735i		−	0.0600645i
$520$		0			0
$521$	−211.232	+	365.865i	−0.405436	+	0.702236i	−0.994372	−	0.105944i	$-0.966214\pi$
$521$	−211.232	+	365.865i	−0.405436	+	0.702236i	0.588936	+	0.808179i	$0.299547\pi$
$522$		0			0
$523$	−253.739	−	439.488i	−0.485160	−	0.840321i	0.514695	−	0.857373i	$-0.327905\pi$
$523$	−253.739	−	439.488i	−0.485160	−	0.840321i	−0.999855	+	0.0170520i	$0.994572\pi$
$524$		0			0
$525$	251.857	+	259.204i	0.479728	+	0.493722i
$526$		0			0
$527$	80.2086	−	46.3085i	0.152198	−	0.0878718i
$528$		0			0
$529$	537.888	−	931.649i	1.01680	−	1.76115i
$530$		0			0
$531$	−119.179			−0.224443
$532$		0			0
$533$			841.259i			1.57835i
$534$		0			0
$535$	−264.002	−	152.422i	−0.493462	−	0.284900i
$536$		0			0
$537$	92.1851	+	159.669i	0.171667	+	0.297336i
$538$		0			0
$539$	−17.8228	+	619.791i	−0.0330664	+	1.14989i
$540$		0			0
$541$	296.986	−	171.465i	0.548958	−	0.316941i	−0.199744	−	0.979848i	$-0.564011\pi$
$541$	296.986	−	171.465i	0.548958	−	0.316941i	0.748701	+	0.662907i	$0.230678\pi$
$542$		0			0
$543$	−129.466	−	74.7470i	−0.238427	−	0.137656i
$544$		0			0
$545$	−1187.89			−2.17961
$546$		0			0
$547$	936.416			1.71191			0.855956	−	0.517049i	$-0.172970\pi$
$547$	936.416			1.71191			0.855956	+	0.517049i	$0.172970\pi$
$548$		0			0
$549$	172.406	+	99.5385i	0.314036	+	0.181309i
$550$		0			0
$551$	15.3199	−	8.84494i	0.0278038	−	0.0160525i
$552$		0			0
$553$	−407.037	+	395.501i	−0.736053	+	0.715191i
$554$		0			0
$555$	131.867	+	228.401i	0.237599	+	0.411533i
$556$		0			0
$557$	−526.381	−	303.906i	−0.945029	−	0.545613i	−0.0534960	−	0.998568i	$-0.517036\pi$
$557$	−526.381	−	303.906i	−0.945029	−	0.545613i	−0.891533	+	0.452955i	$0.850370\pi$
$558$		0			0
$559$		−	227.218i		−	0.406473i
$560$		0			0
$561$	22.9091			0.0408362
$562$		0			0
$563$	−133.544	+	231.305i	−0.237200	+	0.410843i	−0.959910	−	0.280309i	$-0.909563\pi$
$563$	−133.544	+	231.305i	−0.237200	+	0.410843i	0.722710	+	0.691152i	$0.242896\pi$
$564$		0			0
$565$	342.188	−	197.562i	0.605643	−	0.349668i
$566$		0			0
$567$	−112.389	+	396.552i	−0.198217	+	0.699387i
$568$		0			0
$569$	8.55667	+	14.8206i	0.0150381	+	0.0260467i	0.873447	−	0.486920i	$-0.161880\pi$
$569$	8.55667	+	14.8206i	0.0150381	+	0.0260467i	−0.858408	+	0.512967i	$0.828546\pi$
$570$		0			0
$571$	396.662	−	687.038i	0.694679	−	1.20322i	−0.275610	−	0.961270i	$-0.588880\pi$
$571$	396.662	−	687.038i	0.694679	−	1.20322i	0.970289	−	0.241950i	$-0.0777868\pi$
$572$		0			0
$573$		−	42.3151i		−	0.0738483i
$574$		0			0
$575$			2249.09i			3.91146i
$576$		0			0
$577$	475.169	−	823.017i	0.823517	−	1.42637i	−0.0795304	−	0.996832i	$-0.525342\pi$
$577$	475.169	−	823.017i	0.823517	−	1.42637i	0.903047	−	0.429541i	$-0.141325\pi$
$578$		0			0
$579$	−53.5929	−	92.8256i	−0.0925612	−	0.160321i
$580$		0			0
$581$	526.102	−	132.894i	0.905511	−	0.228733i
$582$		0			0
$583$	142.311	−	82.1634i	0.244102	−	0.140932i
$584$		0			0
$585$	−591.761	+	1024.96i	−1.01156	+	1.75207i
$586$		0			0
$587$	189.969			0.323626			0.161813	−	0.986821i	$-0.448266\pi$
$587$	189.969			0.323626			0.161813	+	0.986821i	$0.448266\pi$
$588$		0			0
$589$		−	20.4084i		−	0.0346492i
$590$		0			0
$591$	−14.1194	−	8.15185i	−0.0238907	−	0.0137933i
$592$		0			0
$593$	−401.904	−	696.117i	−0.677746	−	1.17389i	−0.975658	−	0.219298i	$-0.929623\pi$
$593$	−401.904	−	696.117i	−0.677746	−	1.17389i	0.297912	−	0.954593i	$-0.403710\pi$
$594$		0			0
$595$	−30.4021	−	120.356i	−0.0510959	−	0.202279i
$596$		0			0
$597$	−122.476	+	70.7115i	−0.205152	+	0.118445i
$598$		0			0
$599$	−575.459	−	332.241i	−0.960699	−	0.554660i	−0.0643112	−	0.997930i	$-0.520485\pi$
$599$	−575.459	−	332.241i	−0.960699	−	0.554660i	−0.896388	+	0.443270i	$0.853818\pi$
$600$		0			0
$601$	809.705			1.34726			0.673632	−	0.739067i	$-0.264733\pi$
$601$	809.705			1.34726			0.673632	+	0.739067i	$0.264733\pi$
$602$		0			0
$603$	−648.921			−1.07615
$604$		0			0
$605$	305.216	+	176.216i	0.504489	+	0.291267i
$606$		0			0
$607$	−206.564	+	119.260i	−0.340304	+	0.196474i	−0.660406	−	0.750909i	$-0.729616\pi$
$607$	−206.564	+	119.260i	−0.340304	+	0.196474i	0.320103	+	0.947383i	$0.396283\pi$
$608$		0			0
$609$	252.556	+	71.5785i	0.414707	+	0.117535i
$610$		0			0
$611$	−278.181	−	481.823i	−0.455287	−	0.788581i
$612$		0			0
$613$	634.610	+	366.392i	1.03525	+	0.597703i	0.918485	−	0.395456i	$-0.129413\pi$
$613$	634.610	+	366.392i	1.03525	+	0.597703i	0.116768	+	0.993159i	$0.462747\pi$
$614$		0			0
$615$			432.513i			0.703274i
$616$		0			0
$617$	367.893			0.596261			0.298130	−	0.954525i	$-0.403637\pi$
$617$	367.893			0.596261			0.298130	+	0.954525i	$0.403637\pi$
$618$		0			0
$619$	−84.9132	+	147.074i	−0.137178	+	0.237599i	−0.926427	−	0.376474i	$-0.877137\pi$
$619$	−84.9132	+	147.074i	−0.137178	+	0.237599i	0.789249	+	0.614073i	$0.210470\pi$
$620$		0			0
$621$	547.288	−	315.977i	0.881302	−	0.508820i
$622$		0			0
$623$	−638.634	−	657.263i	−1.02510	−	1.05500i
$624$		0			0
$625$	−561.752	−	972.982i	−0.898803	−	1.55677i
$626$		0			0
$627$	2.52404	−	4.37177i	0.00402559	−	0.00697252i
$628$		0			0
$629$		−	62.6772i		−	0.0996458i
$630$		0			0
$631$		−	1128.49i		−	1.78841i	−0.447654	−	0.894207i	$-0.647740\pi$
$631$		−	1128.49i		−	1.78841i	0.447654	−	0.894207i	$-0.352260\pi$
$632$		0			0
$633$	83.8733	−	145.273i	0.132501	−	0.229499i
$634$		0			0
$635$	−414.857	−	718.554i	−0.653318	−	1.13158i
$636$		0			0
$637$	−374.939	−	694.802i	−0.588602	−	1.09074i
$638$		0			0
$639$	−199.846	+	115.381i	−0.312748	+	0.180565i
$640$		0			0
$641$	−454.911	+	787.929i	−0.709690	+	1.22922i	0.255282	+	0.966867i	$0.417832\pi$
$641$	−454.911	+	787.929i	−0.709690	+	1.22922i	−0.964972	+	0.262352i	$0.915502\pi$
$642$		0			0
$643$	426.353			0.663068			0.331534	−	0.943443i	$-0.392434\pi$
$643$	426.353			0.663068			0.331534	+	0.943443i	$0.392434\pi$
$644$		0			0
$645$		−	116.819i		−	0.181114i
$646$		0			0
$647$	89.3712	+	51.5985i	0.138132	+	0.0797503i	0.567473	−	0.823392i	$-0.307921\pi$
$647$	89.3712	+	51.5985i	0.138132	+	0.0797503i	−0.429342	+	0.903142i	$0.641254\pi$
$648$		0			0
$649$	−92.4725	−	160.167i	−0.142485	−	0.246791i
$650$		0			0
$651$	217.199	−	211.043i	0.333639	−	0.324183i
$652$		0			0
$653$	353.462	−	204.071i	0.541289	−	0.312513i	−0.204312	−	0.978906i	$-0.565496\pi$
$653$	353.462	−	204.071i	0.541289	−	0.312513i	0.745601	+	0.666392i	$0.232162\pi$
$654$		0			0
$655$	167.705	+	96.8247i	0.256039	+	0.147824i
$656$		0			0
$657$	413.470			0.629330
$658$		0			0
$659$	484.221			0.734781			0.367391	−	0.930067i	$-0.380251\pi$
$659$	484.221			0.734781			0.367391	+	0.930067i	$0.380251\pi$
$660$		0			0
$661$	1023.59	+	590.970i	1.54855	+	0.894054i	0.998253	+	0.0590827i	$0.0188176\pi$
$661$	1023.59	+	590.970i	1.54855	+	0.894054i	0.550294	+	0.834971i	$0.314516\pi$
$662$		0			0
$663$	−25.2623	+	14.5852i	−0.0381030	+	0.0219988i
$664$		0			0
$665$	−26.3172	−	7.45872i	−0.0395748	−	0.0112161i
$666$		0			0
$667$	816.788	+	1414.72i	1.22457	+	2.12102i
$668$		0			0
$669$	−251.865	−	145.414i	−0.376480	−	0.217361i
$670$		0			0
$671$			308.932i			0.460405i
$672$		0			0
$673$	−557.182			−0.827908			−0.413954	−	0.910298i	$-0.635853\pi$
$673$	−557.182			−0.827908			−0.413954	+	0.910298i	$0.635853\pi$
$674$		0			0
$675$	−442.841	+	767.023i	−0.656061	+	1.13633i
$676$		0			0
$677$	−1053.55	+	608.266i	−1.55620	+	0.898473i	−0.558586	+	0.829447i	$0.688656\pi$
$677$	−1053.55	+	608.266i	−1.55620	+	0.898473i	−0.997615	+	0.0690260i	$0.978011\pi$
$678$		0			0
$679$	−49.3553	+	12.4672i	−0.0726881	+	0.0183611i
$680$		0			0
$681$	121.158	+	209.852i	0.177912	+	0.308152i
$682$		0			0
$683$	119.229	−	206.511i	0.174567	−	0.302359i	−0.765444	−	0.643502i	$-0.777481\pi$
$683$	119.229	−	206.511i	0.174567	−	0.302359i	0.940011	+	0.341143i	$0.110814\pi$
$684$		0			0
$685$		−	590.962i		−	0.862718i
$686$		0			0
$687$		−	239.582i		−	0.348737i
$688$		0			0
$689$	−104.619	+	181.206i	−0.151842	+	0.262999i
$690$		0			0
$691$	−229.499	−	397.504i	−0.332126	−	0.575259i	0.650803	−	0.759247i	$-0.274433\pi$
$691$	−229.499	−	397.504i	−0.332126	−	0.575259i	−0.982928	+	0.183988i	$0.941099\pi$
$692$		0			0
$693$	−700.298	+	176.896i	−1.01053	+	0.255261i
$694$		0			0
$695$	1665.17	−	961.385i	2.39592	−	1.38329i
$696$		0			0
$697$	51.3939	−	89.0169i	0.0737359	−	0.127714i
$698$		0			0
$699$	256.225			0.366559
$700$		0			0
$701$		−	854.640i		−	1.21917i	−0.792720	−	0.609586i	$-0.791336\pi$
$701$		−	854.640i		−	1.21917i	0.792720	−	0.609586i	$-0.208664\pi$
$702$		0			0
$703$	−11.9608	−	6.90554i	−0.0170139	−	0.00982297i
$704$		0			0
$705$	−143.020	−	247.718i	−0.202865	−	0.351373i
$706$		0			0
$707$	−86.0371	−	24.3843i	−0.121693	−	0.0344898i
$708$		0			0
$709$	−715.777	+	413.254i	−1.00956	+	0.582869i	−0.911062	−	0.412269i	$-0.864736\pi$
$709$	−715.777	+	413.254i	−1.00956	+	0.582869i	−0.0984958	+	0.995137i	$0.531403\pi$
$710$		0			0
$711$	−572.552	−	330.563i	−0.805277	−	0.464927i
$712$		0			0
$713$	1884.62			2.64322
$714$		0			0
$715$	−1836.62			−2.56869
$716$		0			0
$717$	−111.344	−	64.2846i	−0.155292	−	0.0896577i
$718$		0			0
$719$	633.214	−	365.586i	0.880687	−	0.508465i	0.00980210	−	0.999952i	$-0.496880\pi$
$719$	633.214	−	365.586i	0.880687	−	0.508465i	0.870885	+	0.491487i	$0.163547\pi$
$720$		0			0
$721$	−475.684	+	462.202i	−0.659756	+	0.641057i
$722$		0			0
$723$	45.6022	+	78.9853i	0.0630735	+	0.109247i
$724$		0			0
$725$	−1982.72	−	1144.73i	−2.73479	−	1.57893i
$726$		0			0
$727$			96.7088i			0.133024i	0.997786	+	0.0665122i	$0.0211871\pi$
$727$			96.7088i			0.133024i	−0.997786	+	0.0665122i	$0.978813\pi$
$728$		0			0
$729$	−349.574			−0.479525
$730$		0			0
$731$	−13.8811	+	24.0428i	−0.0189892	+	0.0328903i
$732$		0			0
$733$	−954.726	+	551.211i	−1.30249	+	0.751993i	−0.980831	−	0.194862i	$-0.937574\pi$
$733$	−954.726	+	551.211i	−1.30249	+	0.751993i	−0.321660	+	0.946855i	$0.604241\pi$
$734$		0			0
$735$	−192.766	−	357.216i	−0.262267	−	0.486008i
$736$		0			0
$737$	−503.504	−	872.095i	−0.683181	−	1.18330i
$738$		0			0
$739$	−734.977	+	1273.02i	−0.994556	+	1.72262i	−0.407034	+	0.913413i	$0.633437\pi$
$739$	−734.977	+	1273.02i	−0.994556	+	1.72262i	−0.587522	+	0.809208i	$0.699896\pi$
$740$		0			0
$741$			6.42777i			0.00867445i
$742$		0			0
$743$			143.647i			0.193333i	0.995317	+	0.0966666i	$0.0308181\pi$
$743$			143.647i			0.193333i	−0.995317	+	0.0966666i	$0.969182\pi$
$744$		0			0
$745$	−598.570	+	1036.75i	−0.803450	+	1.39162i
$746$		0			0
$747$	316.053	+	547.421i	0.423097	+	0.732825i
$748$		0			0
$749$	165.082	+	169.897i	0.220403	+	0.226832i
$750$		0			0
$751$	906.936	−	523.619i	1.20764	−	0.697230i	0.245395	−	0.969423i	$-0.421082\pi$
$751$	906.936	−	523.619i	1.20764	−	0.697230i	0.962243	+	0.272194i	$0.0877491\pi$
$752$		0			0
$753$	106.967	−	185.272i	0.142054	−	0.246045i
$754$		0			0
$755$	−521.967			−0.691348
$756$		0			0
$757$			673.016i			0.889057i	0.895765	+	0.444529i	$0.146629\pi$
$757$			673.016i			0.889057i	−0.895765	+	0.444529i	$0.853371\pi$
$758$		0			0
$759$	403.712	+	233.083i	0.531900	+	0.307093i
$760$		0			0
$761$	409.427	+	709.148i	0.538011	+	0.931863i	0.999011	+	0.0444627i	$0.0141576\pi$
$761$	409.427	+	709.148i	0.538011	+	0.931863i	−0.461000	+	0.887400i	$0.652509\pi$
$762$		0			0
$763$	888.114	+	251.706i	1.16398	+	0.329890i
$764$		0			0
$765$	125.233	−	72.3034i	0.163703	−	0.0945142i
$766$		0			0
$767$	203.942	+	117.746i	0.265896	+	0.153515i
$768$		0			0
$769$	1510.85			1.96470			0.982350	−	0.187051i	$-0.0598931\pi$
$769$	1510.85			1.96470			0.982350	+	0.187051i	$0.0598931\pi$
$770$		0			0
$771$	141.648			0.183720
$772$		0			0
$773$	227.670	+	131.445i	0.294528	+	0.170046i	0.639982	−	0.768390i	$-0.278942\pi$
$773$	227.670	+	131.445i	0.294528	+	0.170046i	−0.345454	+	0.938436i	$0.612275\pi$
$774$		0			0
$775$	−2287.42	+	1320.64i	−2.95151	+	1.70405i
$776$		0			0
$777$	−50.1929	−	198.704i	−0.0645984	−	0.255733i
$778$		0			0
$779$	−11.3248	−	19.6151i	−0.0145376	−	0.0251798i
$780$		0			0
$781$	−310.125	−	179.051i	−0.397088	−	0.229259i
$782$		0			0
$783$			643.296i			0.821579i
$784$		0			0
$785$	864.995			1.10190
$786$		0			0
$787$	−645.623	+	1118.25i	−0.820360	+	1.42091i	0.0850545	+	0.996376i	$0.472894\pi$
$787$	−645.623	+	1118.25i	−0.820360	+	1.42091i	−0.905414	+	0.424529i	$0.860440\pi$
$788$		0			0
$789$	304.523	−	175.817i	0.385961	−	0.222835i
$790$		0			0
$791$	−297.697	+	75.1985i	−0.376355	+	0.0950677i
$792$		0			0
$793$	−196.683	−	340.665i	−0.248024	−	0.429590i
$794$		0			0
$795$	−53.7875	+	93.1628i	−0.0676573	+	0.117186i
$796$		0			0
$797$			806.212i			1.01156i	0.862663	+	0.505779i	$0.168795\pi$
$797$			806.212i			1.01156i	−0.862663	+	0.505779i	$0.831205\pi$
$798$		0			0
$799$			67.9781i			0.0850789i
$800$		0			0
$801$	533.777	−	924.528i	0.666388	−	1.15422i
$802$		0			0
$803$	320.816	+	555.669i	0.399522	+	0.691992i
$804$		0			0
$805$	688.778	−	2430.27i	0.855624	−	3.01897i
$806$		0			0
$807$	277.303	−	160.101i	0.343622	−	0.198390i
$808$		0			0
$809$	411.773	−	713.212i	0.508990	−	0.881597i	−0.490956	−	0.871185i	$-0.663352\pi$
$809$	411.773	−	713.212i	0.508990	−	0.881597i	0.999946	−	0.0104122i	$-0.00331437\pi$
$810$		0			0
$811$	−750.028			−0.924818			−0.462409	−	0.886667i	$-0.653015\pi$
$811$	−750.028			−0.924818			−0.462409	+	0.886667i	$0.653015\pi$
$812$		0			0
$813$			162.541i			0.199927i
$814$		0			0
$815$	−2297.86	−	1326.67i	−2.81946	−	1.62782i
$816$		0			0
$817$	3.05875	+	5.29790i	0.00374387	+	0.00648458i
$818$		0			0
$819$	659.609	−	640.914i	0.805383	−	0.782557i
$820$		0			0
$821$	−133.081	+	76.8345i	−0.162097	+	0.0935865i	−0.578854	−	0.815431i	$-0.696500\pi$
$821$	−133.081	+	76.8345i	−0.162097	+	0.0935865i	0.416757	+	0.909018i	$0.363166\pi$
$822$		0			0
$823$	−110.552	−	63.8271i	−0.134328	−	0.0775542i	0.431330	−	0.902194i	$-0.358044\pi$
$823$	−110.552	−	63.8271i	−0.134328	−	0.0775542i	−0.565658	+	0.824640i	$0.691378\pi$
$824$		0			0
$825$	−653.332			−0.791917
$826$		0			0
$827$	−1284.48			−1.55319			−0.776593	−	0.630003i	$-0.783054\pi$
$827$	−1284.48			−1.55319			−0.776593	+	0.630003i	$0.783054\pi$
$828$		0			0
$829$	−455.604	−	263.043i	−0.549582	−	0.317302i	0.199371	−	0.979924i	$-0.436110\pi$
$829$	−455.604	−	263.043i	−0.549582	−	0.317302i	−0.748954	+	0.662622i	$0.769443\pi$
$830$		0			0
$831$	254.246	−	146.789i	0.305952	−	0.176641i
$832$		0			0
$833$	−2.77281	+	96.4253i	−0.00332871	+	0.115757i
$834$		0			0
$835$	−692.241	−	1199.00i	−0.829031	−	1.43592i
$836$		0			0
$837$	642.725	+	371.077i	0.767891	+	0.443342i
$838$		0			0
$839$		−	840.139i		−	1.00136i	−0.865633	−	0.500679i	$-0.833084\pi$
$839$		−	840.139i		−	1.00136i	0.865633	−	0.500679i	$-0.166916\pi$
$840$		0			0
$841$	−821.894			−0.977282
$842$		0			0
$843$	−99.7606	+	172.790i	−0.118340	+	0.204971i
$844$		0			0
$845$	706.877	−	408.116i	0.836541	−	0.482977i
$846$		0			0
$847$	−190.853	−	196.420i	−0.225328	−	0.231901i
$848$		0			0
$849$	−98.6195	−	170.814i	−0.116160	−	0.201194i
$850$		0			0
$851$	637.694	−	1104.52i	0.749347	−	1.29791i
$852$		0			0
$853$		−	1105.89i		−	1.29648i	−0.761438	−	0.648238i	$-0.775506\pi$
$853$		−	1105.89i		−	1.29648i	0.761438	−	0.648238i	$-0.224494\pi$
$854$		0			0
$855$		−	31.8645i		−	0.0372684i
$856$		0			0
$857$	714.946	−	1238.32i	0.834242	−	1.44495i	−0.0604036	−	0.998174i	$-0.519239\pi$
$857$	714.946	−	1238.32i	0.834242	−	1.44495i	0.894646	−	0.446776i	$-0.147428\pi$
$858$		0			0
$859$	−217.390	−	376.531i	−0.253073	−	0.438336i	0.711297	−	0.702892i	$-0.248108\pi$
$859$	−217.390	−	376.531i	−0.253073	−	0.438336i	−0.964370	+	0.264556i	$0.914775\pi$
$860$		0			0
$861$	91.6469	−	323.365i	0.106442	−	0.375570i
$862$		0			0
$863$	−494.623	+	285.571i	−0.573144	+	0.330905i	−0.758404	−	0.651785i	$-0.774021\pi$
$863$	−494.623	+	285.571i	−0.573144	+	0.330905i	0.185260	+	0.982690i	$0.440687\pi$
$864$		0			0
$865$	152.678	−	264.446i	0.176506	−	0.305718i
$866$		0			0
$867$	−262.204			−0.302427
$868$		0			0
$869$		−	1025.95i		−	1.18061i
$870$		0			0
$871$	1110.45	+	641.116i	1.27491	+	0.736069i
$872$		0			0
$873$	−29.6500	−	51.3552i	−0.0339633	−	0.0588262i
$874$		0			0
$875$	480.945	+	1903.97i	0.549652	+	2.17597i
$876$		0			0
$877$	−1331.28	+	768.617i	−1.51800	+	0.876417i	−0.518222	+	0.855246i	$0.673406\pi$
$877$	−1331.28	+	768.617i	−1.51800	+	0.876417i	−0.999776	+	0.0211705i	$0.993261\pi$
$878$		0			0
$879$	−316.848	−	182.932i	−0.360464	−	0.208114i
$880$		0			0
$881$	−197.073			−0.223692			−0.111846	−	0.993726i	$-0.535676\pi$
$881$	−197.073			−0.223692			−0.111846	+	0.993726i	$0.535676\pi$
$882$		0			0
$883$	866.299			0.981086			0.490543	−	0.871417i	$-0.336798\pi$
$883$	866.299			0.981086			0.490543	+	0.871417i	$0.336798\pi$
$884$		0			0
$885$	104.852	+	60.5363i	0.118477	+	0.0684026i
$886$		0			0
$887$	−687.583	+	396.976i	−0.775178	+	0.447549i	−0.834719	−	0.550677i	$-0.814370\pi$
$887$	−687.583	+	396.976i	−0.775178	+	0.447549i	0.0595407	+	0.998226i	$0.481036\pi$
$888$		0			0
$889$	157.908	+	625.127i	0.177624	+	0.703180i
$890$		0			0
$891$	−372.545	−	645.267i	−0.418120	−	0.724205i
$892$		0			0
$893$	12.9723	+	7.48957i	0.0145267	+	0.00838698i
$894$		0			0
$895$			1805.98i			2.01785i
$896$		0			0
$897$	−593.574			−0.661732
$898$		0			0
$899$	−959.220	+	1661.42i	−1.06699	+	1.84807i
$900$		0			0
$901$	22.1404	−	12.7827i	0.0245731	−	0.0141873i
$902$		0			0
$903$	−24.7532	+	87.3387i	−0.0274122	+	0.0967206i
$904$		0			0
$905$	−732.176	−	1268.17i	−0.809034	−	1.40129i
$906$		0			0
$907$	−25.7540	+	44.6072i	−0.0283947	+	0.0491811i	−0.879874	−	0.475208i	$-0.842373\pi$
$907$	−25.7540	+	44.6072i	−0.0283947	+	0.0491811i	0.851479	+	0.524389i	$0.175706\pi$
$908$		0			0
$909$		−	104.172i		−	0.114601i
$910$		0			0
$911$		−	720.775i		−	0.791191i	−0.918425	−	0.395595i	$-0.870538\pi$
$911$		−	720.775i		−	0.791191i	0.918425	−	0.395595i	$-0.129462\pi$
$912$		0			0
$913$	−490.458	+	849.499i	−0.537194	+	0.930448i
$914$		0			0
$915$	−101.120	−	175.145i	−0.110513	−	0.191415i
$916$		0			0
$917$	−104.867	−	107.926i	−0.114359	−	0.117695i
$918$		0			0
$919$	−550.058	+	317.576i	−0.598539	+	0.345567i	−0.768467	−	0.639890i	$-0.778980\pi$
$919$	−550.058	+	317.576i	−0.598539	+	0.345567i	0.169927	+	0.985457i	$0.445647\pi$
$920$		0			0
$921$	169.739	−	293.997i	0.184299	−	0.319215i
$922$		0			0
$923$	455.974			0.494013
$924$		0			0
$925$			1787.45i			1.93238i
$926$		0			0
$927$	−669.114	−	386.313i	−0.721806	−	0.416735i
$928$		0			0
$929$	378.206	+	655.072i	0.407111	+	0.705137i	0.994565	−	0.104121i	$-0.0332029\pi$
$929$	378.206	+	655.072i	0.407111	+	0.705137i	−0.587454	+	0.809258i	$0.699870\pi$
$930$		0			0
$931$	18.0954	+	11.1529i	0.0194366	+	0.0119795i
$932$		0			0
$933$	−367.569	+	212.216i	−0.393965	+	0.227456i
$934$		0			0
$935$	194.339	+	112.202i	0.207850	+	0.120002i
$936$		0			0
$937$	−671.863			−0.717036			−0.358518	−	0.933523i	$-0.616718\pi$
$937$	−671.863			−0.717036			−0.358518	+	0.933523i	$0.616718\pi$
$938$		0			0
$939$	−246.863			−0.262900
$940$		0			0
$941$	799.260	+	461.453i	0.849373	+	0.490386i	0.860439	−	0.509553i	$-0.170189\pi$
$941$	799.260	+	461.453i	0.849373	+	0.490386i	−0.0110660	+	0.999939i	$0.503522\pi$
$942$		0			0
$943$	1811.36	−	1045.79i	1.92085	−	1.10900i
$944$		0			0
$945$	713.415	−	693.195i	0.754936	−	0.733539i
$946$		0			0
$947$	−378.533	−	655.639i	−0.399718	−	0.692332i	0.593973	−	0.804485i	$-0.297559\pi$
$947$	−378.533	−	655.639i	−0.399718	−	0.692332i	−0.993691	+	0.112153i	$0.964225\pi$
$948$		0			0
$949$	−707.538	−	408.497i	−0.745562	−	0.430450i
$950$		0			0
$951$		−	347.991i		−	0.365921i
$952$		0			0
$953$	394.200			0.413641			0.206821	−	0.978379i	$-0.433688\pi$
$953$	394.200			0.413641			0.206821	+	0.978379i	$0.433688\pi$
$954$		0			0
$955$	207.246	−	358.961i	0.217012	−	0.375875i
$956$		0			0
$957$	−410.958	+	237.267i	−0.429423	+	0.247927i
$958$		0			0
$959$	−125.221	+	441.828i	−0.130575	+	0.460718i
$960$		0			0
$961$	626.129	+	1084.49i	0.651539	+	1.12850i
$962$		0			0
$963$	−137.977	+	238.984i	−0.143279	+	0.248166i
$964$		0			0
$965$		−	1049.93i		−	1.08801i
$966$		0			0
$967$		−	1194.61i		−	1.23538i	−0.786423	−	0.617689i	$-0.788069\pi$
$967$		−	1194.61i		−	1.23538i	0.786423	−	0.617689i	$-0.211931\pi$
$968$		0			0
$969$	0.392683	−	0.680147i	0.000405246	−	0.000701906i
$970$		0			0
$971$	−414.714	−	718.305i	−0.427099	−	0.739758i	0.569514	−	0.821981i	$-0.307131\pi$
$971$	−414.714	−	718.305i	−0.427099	−	0.739758i	−0.996614	+	0.0822233i	$0.973798\pi$
$972$		0			0
$973$	−1448.66	+	365.934i	−1.48886	+	0.376088i
$974$		0			0
$975$	720.440	−	415.946i	0.738913	−	0.426611i
$976$		0			0
$977$	−58.5535	+	101.418i	−0.0599319	+	0.103805i	−0.894435	−	0.447199i	$-0.852422\pi$
$977$	−58.5535	+	101.418i	−0.0599319	+	0.103805i	0.834503	+	0.551004i	$0.185755\pi$
$978$		0			0
$979$	1656.65			1.69219
$980$		0			0
$981$			1075.31i			1.09614i
$982$		0			0
$983$	−251.017	−	144.925i	−0.255358	−	0.147431i	0.366857	−	0.930277i	$-0.380434\pi$
$983$	−251.017	−	144.925i	−0.255358	−	0.147431i	−0.622215	+	0.782846i	$0.713767\pi$
$984$		0			0
$985$	−79.8505	−	138.305i	−0.0810665	−	0.140411i
$986$		0			0
$987$	54.4379	+	215.509i	0.0551549	+	0.218348i
$988$		0			0
$989$	−489.236	+	282.461i	−0.494678	+	0.285602i
$990$		0			0
$991$	467.933	+	270.161i	0.472182	+	0.272615i	0.717153	−	0.696916i	$-0.245445\pi$
$991$	467.933	+	270.161i	0.472182	+	0.272615i	−0.244970	+	0.969531i	$0.578778\pi$
$992$		0			0
$993$	277.999			0.279958
$994$		0			0
$995$	−1385.29			−1.39225
$996$		0			0
$997$	665.146	+	384.022i	0.667148	+	0.385178i	0.794995	−	0.606616i	$-0.207473\pi$
$997$	665.146	+	384.022i	0.667148	+	0.385178i	−0.127847	+	0.991794i	$0.540807\pi$
$998$		0			0
$999$	434.955	−	251.122i	0.435391	−	0.251373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.3.o.b.95.5	yes	20
4.3	odd	2	inner	448.3.o.b.95.6	yes	20
7.2	even	3		448.3.o.a.415.5	yes	20
8.3	odd	2		448.3.o.a.95.5	✓	20
8.5	even	2		448.3.o.a.95.6	yes	20
28.23	odd	6		448.3.o.a.415.6	yes	20
56.37	even	6	inner	448.3.o.b.415.6	yes	20
56.51	odd	6	inner	448.3.o.b.415.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.3.o.a.95.5	✓	20	8.3	odd	2
448.3.o.a.95.6	yes	20	8.5	even	2
448.3.o.a.415.5	yes	20	7.2	even	3
448.3.o.a.415.6	yes	20	28.23	odd	6
448.3.o.b.95.5	yes	20	1.1	even	1	trivial
448.3.o.b.95.6	yes	20	4.3	odd	2	inner
448.3.o.b.415.5	yes	20	56.51	odd	6	inner
448.3.o.b.415.6	yes	20	56.37	even	6	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.459807 + 0.796409i) q^{3} +(-7.80113 + 4.50398i) q^{5} +(6.78682 - 1.71436i) q^{7} +(4.07716 + 7.06184i) q^{9} +(-6.32702 + 10.9587i) q^{11} -16.1125i q^{13} -8.28385i q^{15} +(-0.984338 + 1.70492i) q^{17} +(0.216902 + 0.375684i) q^{19} +(-1.75530 + 6.19336i) q^{21} +(-34.6927 + 20.0298i) q^{23} +(28.0717 - 48.6217i) q^{25} -15.7753 q^{27} -40.7786i q^{29} +(-40.7424 - 23.5226i) q^{31} +(-5.81841 - 10.0778i) q^{33} +(-45.2234 + 43.9417i) q^{35} +(-27.5719 + 15.9186i) q^{37} +(12.8321 + 7.40863i) q^{39} -52.2116 q^{41} +14.1020 q^{43} +(-63.6128 - 36.7269i) q^{45} +(29.9037 - 17.2649i) q^{47} +(43.1219 - 23.2701i) q^{49} +(-0.905211 - 1.56787i) q^{51} +(-11.2463 - 6.49306i) q^{53} -113.987i q^{55} -0.398931 q^{57} +(-7.30775 + 12.6574i) q^{59} +(21.1429 - 12.2069i) q^{61} +(39.7775 + 40.9378i) q^{63} +(72.5704 + 125.696i) q^{65} +(-39.7900 + 68.9184i) q^{67} -36.8394i q^{69} +28.2994i q^{71} +(25.3528 - 43.9124i) q^{73} +(25.8151 + 44.7131i) q^{75} +(-24.1532 + 85.2216i) q^{77} +(-70.2147 + 40.5385i) q^{79} +(-29.4408 + 50.9930i) q^{81} +77.5181 q^{83} -17.7338i q^{85} +(32.4764 + 18.7503i) q^{87} +(-65.4595 - 113.379i) q^{89} +(-27.6226 - 109.353i) q^{91} +(37.4673 - 21.6317i) q^{93} +(-3.38415 - 1.95384i) q^{95} -7.27222 q^{97} -103.185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5} - 28 q^{9} + 46 q^{17} - 114 q^{21} + 36 q^{25} + 94 q^{33} + 114 q^{37} - 160 q^{41} - 708 q^{45} - 92 q^{49} - 6 q^{53} + 308 q^{57} + 90 q^{61} + 212 q^{65} + 314 q^{73} - 198 q^{77} - 322 q^{81}+ \cdots - 224 q^{97}+O(q^{100}) \) 20 * q + 6 * q^5 - 28 * q^9 + 46 * q^17 - 114 * q^21 + 36 * q^25 + 94 * q^33 + 114 * q^37 - 160 * q^41 - 708 * q^45 - 92 * q^49 - 6 * q^53 + 308 * q^57 + 90 * q^61 + 212 * q^65 + 314 * q^73 - 198 * q^77 - 322 * q^81 - 206 * q^89 + 1530 * q^93 - 224 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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