Properties

Label 441.3.n.b.410.1
Level $441$
Weight $3$
Character 441.410
Analytic conductor $12.016$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0163796583\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 9)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 410.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.410
Dual form 441.3.n.b.128.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(4.50000 + 2.59808i) q^{6} -8.66025i q^{8} +9.00000 q^{9} +(3.00000 - 5.19615i) q^{10} -1.73205i q^{11} +(-1.50000 - 2.59808i) q^{12} +(2.00000 - 3.46410i) q^{13} -10.3923i q^{15} +(5.50000 - 9.52628i) q^{16} +(-13.5000 - 7.79423i) q^{17} +(13.5000 + 7.79423i) q^{18} +(-5.50000 - 9.52628i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +27.7128i q^{23} -25.9808i q^{24} +13.0000 q^{25} +(6.00000 - 3.46410i) q^{26} +27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} +(9.00000 - 15.5885i) q^{30} +(-16.0000 - 27.7128i) q^{31} +(-13.5000 + 7.79423i) q^{32} -5.19615i q^{33} +(-13.5000 - 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 + 29.4449i) q^{37} -19.0526i q^{38} +(6.00000 - 10.3923i) q^{39} -30.0000 q^{40} +(-10.5000 - 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(-1.50000 + 0.866025i) q^{44} -31.1769i q^{45} +(-24.0000 + 41.5692i) q^{46} +(42.0000 + 24.2487i) q^{47} +(16.5000 - 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +(-40.5000 - 23.3827i) q^{51} -4.00000 q^{52} +(40.5000 + 23.3827i) q^{54} -6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +78.0000 q^{58} +(-43.5000 + 25.1147i) q^{59} +(-9.00000 + 5.19615i) q^{60} +(-28.0000 + 48.4974i) q^{61} -55.4256i q^{62} -71.0000 q^{64} +(-12.0000 - 6.92820i) q^{65} +(4.50000 - 7.79423i) q^{66} +(15.5000 + 26.8468i) q^{67} +15.5885i q^{68} +83.1384i q^{69} -31.1769i q^{71} -77.9423i q^{72} +(-32.5000 + 56.2917i) q^{73} +58.8897i q^{74} +39.0000 q^{75} +(-5.50000 + 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +(-19.0000 + 32.9090i) q^{79} +(-33.0000 - 19.0526i) q^{80} +81.0000 q^{81} +(-10.5000 - 18.1865i) q^{82} +(-42.0000 + 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +105.655i q^{86} +(117.000 - 67.5500i) q^{87} -15.0000 q^{88} +(108.000 - 62.3538i) q^{89} +(27.0000 - 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 - 83.1384i) q^{93} +(42.0000 + 72.7461i) q^{94} +(-33.0000 + 19.0526i) q^{95} +(-40.5000 + 23.3827i) q^{96} +(57.5000 + 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + O(q^{10}) \) \( 2q + 3q^{2} + 6q^{3} - q^{4} + 9q^{6} + 18q^{9} + 6q^{10} - 3q^{12} + 4q^{13} + 11q^{16} - 27q^{17} + 27q^{18} - 11q^{19} - 6q^{20} + 3q^{22} + 26q^{25} + 12q^{26} + 54q^{27} + 78q^{29} + 18q^{30} - 32q^{31} - 27q^{32} - 27q^{34} - 9q^{36} + 34q^{37} + 12q^{39} - 60q^{40} - 21q^{41} + 61q^{43} - 3q^{44} - 48q^{46} + 84q^{47} + 33q^{48} + 39q^{50} - 81q^{51} - 8q^{52} + 81q^{54} - 12q^{55} - 33q^{57} + 156q^{58} - 87q^{59} - 18q^{60} - 56q^{61} - 142q^{64} - 24q^{65} + 9q^{66} + 31q^{67} - 65q^{73} + 78q^{75} - 11q^{76} + 36q^{78} - 38q^{79} - 66q^{80} + 162q^{81} - 21q^{82} - 84q^{83} - 54q^{85} + 234q^{87} - 30q^{88} + 216q^{89} + 54q^{90} + 48q^{92} - 96q^{93} + 84q^{94} - 66q^{95} - 81q^{96} + 115q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 0.866025i 0.750000 + 0.433013i 0.825694 0.564118i \(-0.190784\pi\)
−0.0756939 + 0.997131i \(0.524117\pi\)
\(3\) 3.00000 1.00000
\(4\) −0.500000 0.866025i −0.125000 0.216506i
\(5\) 3.46410i 0.692820i −0.938083 0.346410i \(-0.887401\pi\)
0.938083 0.346410i \(-0.112599\pi\)
\(6\) 4.50000 + 2.59808i 0.750000 + 0.433013i
\(7\) 0 0
\(8\) 8.66025i 1.08253i
\(9\) 9.00000 1.00000
\(10\) 3.00000 5.19615i 0.300000 0.519615i
\(11\) 1.73205i 0.157459i −0.996896 0.0787296i \(-0.974914\pi\)
0.996896 0.0787296i \(-0.0250864\pi\)
\(12\) −1.50000 2.59808i −0.125000 0.216506i
\(13\) 2.00000 3.46410i 0.153846 0.266469i −0.778792 0.627282i \(-0.784167\pi\)
0.932638 + 0.360813i \(0.117501\pi\)
\(14\) 0 0
\(15\) 10.3923i 0.692820i
\(16\) 5.50000 9.52628i 0.343750 0.595392i
\(17\) −13.5000 7.79423i −0.794118 0.458484i 0.0472925 0.998881i \(-0.484941\pi\)
−0.841410 + 0.540397i \(0.818274\pi\)
\(18\) 13.5000 + 7.79423i 0.750000 + 0.433013i
\(19\) −5.50000 9.52628i −0.289474 0.501383i 0.684211 0.729285i \(-0.260147\pi\)
−0.973684 + 0.227901i \(0.926814\pi\)
\(20\) −3.00000 + 1.73205i −0.150000 + 0.0866025i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.0681818 0.118094i
\(23\) 27.7128i 1.20490i 0.798155 + 0.602452i \(0.205810\pi\)
−0.798155 + 0.602452i \(0.794190\pi\)
\(24\) 25.9808i 1.08253i
\(25\) 13.0000 0.520000
\(26\) 6.00000 3.46410i 0.230769 0.133235i
\(27\) 27.0000 1.00000
\(28\) 0 0
\(29\) 39.0000 22.5167i 1.34483 0.776437i 0.357316 0.933984i \(-0.383692\pi\)
0.987511 + 0.157547i \(0.0503586\pi\)
\(30\) 9.00000 15.5885i 0.300000 0.519615i
\(31\) −16.0000 27.7128i −0.516129 0.893962i −0.999825 0.0187254i \(-0.994039\pi\)
0.483696 0.875236i \(-0.339294\pi\)
\(32\) −13.5000 + 7.79423i −0.421875 + 0.243570i
\(33\) 5.19615i 0.157459i
\(34\) −13.5000 23.3827i −0.397059 0.687726i
\(35\) 0 0
\(36\) −4.50000 7.79423i −0.125000 0.216506i
\(37\) 17.0000 + 29.4449i 0.459459 + 0.795807i 0.998932 0.0461958i \(-0.0147098\pi\)
−0.539473 + 0.842003i \(0.681376\pi\)
\(38\) 19.0526i 0.501383i
\(39\) 6.00000 10.3923i 0.153846 0.266469i
\(40\) −30.0000 −0.750000
\(41\) −10.5000 6.06218i −0.256098 0.147858i 0.366456 0.930436i \(-0.380571\pi\)
−0.622553 + 0.782578i \(0.713905\pi\)
\(42\) 0 0
\(43\) 30.5000 + 52.8275i 0.709302 + 1.22855i 0.965116 + 0.261822i \(0.0843232\pi\)
−0.255814 + 0.966726i \(0.582343\pi\)
\(44\) −1.50000 + 0.866025i −0.0340909 + 0.0196824i
\(45\) 31.1769i 0.692820i
\(46\) −24.0000 + 41.5692i −0.521739 + 0.903679i
\(47\) 42.0000 + 24.2487i 0.893617 + 0.515930i 0.875124 0.483899i \(-0.160780\pi\)
0.0184931 + 0.999829i \(0.494113\pi\)
\(48\) 16.5000 28.5788i 0.343750 0.595392i
\(49\) 0 0
\(50\) 19.5000 + 11.2583i 0.390000 + 0.225167i
\(51\) −40.5000 23.3827i −0.794118 0.458484i
\(52\) −4.00000 −0.0769231
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 40.5000 + 23.3827i 0.750000 + 0.433013i
\(55\) −6.00000 −0.109091
\(56\) 0 0
\(57\) −16.5000 28.5788i −0.289474 0.501383i
\(58\) 78.0000 1.34483
\(59\) −43.5000 + 25.1147i −0.737288 + 0.425674i −0.821082 0.570810i \(-0.806629\pi\)
0.0837943 + 0.996483i \(0.473296\pi\)
\(60\) −9.00000 + 5.19615i −0.150000 + 0.0866025i
\(61\) −28.0000 + 48.4974i −0.459016 + 0.795040i −0.998909 0.0466940i \(-0.985131\pi\)
0.539893 + 0.841734i \(0.318465\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 0 0
\(64\) −71.0000 −1.10938
\(65\) −12.0000 6.92820i −0.184615 0.106588i
\(66\) 4.50000 7.79423i 0.0681818 0.118094i
\(67\) 15.5000 + 26.8468i 0.231343 + 0.400698i 0.958204 0.286087i \(-0.0923546\pi\)
−0.726860 + 0.686785i \(0.759021\pi\)
\(68\) 15.5885i 0.229242i
\(69\) 83.1384i 1.20490i
\(70\) 0 0
\(71\) 31.1769i 0.439111i −0.975600 0.219556i \(-0.929539\pi\)
0.975600 0.219556i \(-0.0704608\pi\)
\(72\) 77.9423i 1.08253i
\(73\) −32.5000 + 56.2917i −0.445205 + 0.771119i −0.998067 0.0621550i \(-0.980203\pi\)
0.552861 + 0.833273i \(0.313536\pi\)
\(74\) 58.8897i 0.795807i
\(75\) 39.0000 0.520000
\(76\) −5.50000 + 9.52628i −0.0723684 + 0.125346i
\(77\) 0 0
\(78\) 18.0000 10.3923i 0.230769 0.133235i
\(79\) −19.0000 + 32.9090i −0.240506 + 0.416569i −0.960859 0.277039i \(-0.910647\pi\)
0.720352 + 0.693608i \(0.243980\pi\)
\(80\) −33.0000 19.0526i −0.412500 0.238157i
\(81\) 81.0000 1.00000
\(82\) −10.5000 18.1865i −0.128049 0.221787i
\(83\) −42.0000 + 24.2487i −0.506024 + 0.292153i −0.731198 0.682165i \(-0.761038\pi\)
0.225174 + 0.974319i \(0.427705\pi\)
\(84\) 0 0
\(85\) −27.0000 + 46.7654i −0.317647 + 0.550181i
\(86\) 105.655i 1.22855i
\(87\) 117.000 67.5500i 1.34483 0.776437i
\(88\) −15.0000 −0.170455
\(89\) 108.000 62.3538i 1.21348 0.700605i 0.249967 0.968254i \(-0.419580\pi\)
0.963516 + 0.267650i \(0.0862469\pi\)
\(90\) 27.0000 46.7654i 0.300000 0.519615i
\(91\) 0 0
\(92\) 24.0000 13.8564i 0.260870 0.150613i
\(93\) −48.0000 83.1384i −0.516129 0.893962i
\(94\) 42.0000 + 72.7461i 0.446809 + 0.773895i
\(95\) −33.0000 + 19.0526i −0.347368 + 0.200553i
\(96\) −40.5000 + 23.3827i −0.421875 + 0.243570i
\(97\) 57.5000 + 99.5929i 0.592784 + 1.02673i 0.993856 + 0.110685i \(0.0353044\pi\)
−0.401072 + 0.916047i \(0.631362\pi\)
\(98\) 0 0
\(99\) 15.5885i 0.157459i
\(100\) −6.50000 11.2583i −0.0650000 0.112583i
\(101\) 45.0333i 0.445874i 0.974833 + 0.222937i \(0.0715645\pi\)
−0.974833 + 0.222937i \(0.928436\pi\)
\(102\) −40.5000 70.1481i −0.397059 0.687726i
\(103\) −40.0000 −0.388350 −0.194175 0.980967i \(-0.562203\pi\)
−0.194175 + 0.980967i \(0.562203\pi\)
\(104\) −30.0000 17.3205i −0.288462 0.166543i
\(105\) 0 0
\(106\) 0 0
\(107\) −121.500 + 70.1481i −1.13551 + 0.655589i −0.945316 0.326156i \(-0.894246\pi\)
−0.190198 + 0.981746i \(0.560913\pi\)
\(108\) −13.5000 23.3827i −0.125000 0.216506i
\(109\) 26.0000 45.0333i 0.238532 0.413150i −0.721761 0.692142i \(-0.756667\pi\)
0.960293 + 0.278992i \(0.0900004\pi\)
\(110\) −9.00000 5.19615i −0.0818182 0.0472377i
\(111\) 51.0000 + 88.3346i 0.459459 + 0.795807i
\(112\) 0 0
\(113\) −78.0000 45.0333i −0.690265 0.398525i 0.113446 0.993544i \(-0.463811\pi\)
−0.803711 + 0.595019i \(0.797144\pi\)
\(114\) 57.1577i 0.501383i
\(115\) 96.0000 0.834783
\(116\) −39.0000 22.5167i −0.336207 0.194109i
\(117\) 18.0000 31.1769i 0.153846 0.266469i
\(118\) −87.0000 −0.737288
\(119\) 0 0
\(120\) −90.0000 −0.750000
\(121\) 118.000 0.975207
\(122\) −84.0000 + 48.4974i −0.688525 + 0.397520i
\(123\) −31.5000 18.1865i −0.256098 0.147858i
\(124\) −16.0000 + 27.7128i −0.129032 + 0.223490i
\(125\) 131.636i 1.05309i
\(126\) 0 0
\(127\) −16.0000 −0.125984 −0.0629921 0.998014i \(-0.520064\pi\)
−0.0629921 + 0.998014i \(0.520064\pi\)
\(128\) −52.5000 30.3109i −0.410156 0.236804i
\(129\) 91.5000 + 158.483i 0.709302 + 1.22855i
\(130\) −12.0000 20.7846i −0.0923077 0.159882i
\(131\) 159.349i 1.21640i −0.793783 0.608201i \(-0.791891\pi\)
0.793783 0.608201i \(-0.208109\pi\)
\(132\) −4.50000 + 2.59808i −0.0340909 + 0.0196824i
\(133\) 0 0
\(134\) 53.6936i 0.400698i
\(135\) 93.5307i 0.692820i
\(136\) −67.5000 + 116.913i −0.496324 + 0.859658i
\(137\) 188.794i 1.37806i −0.724735 0.689028i \(-0.758038\pi\)
0.724735 0.689028i \(-0.241962\pi\)
\(138\) −72.0000 + 124.708i −0.521739 + 0.903679i
\(139\) −2.50000 + 4.33013i −0.0179856 + 0.0311520i −0.874878 0.484343i \(-0.839059\pi\)
0.856893 + 0.515495i \(0.172392\pi\)
\(140\) 0 0
\(141\) 126.000 + 72.7461i 0.893617 + 0.515930i
\(142\) 27.0000 46.7654i 0.190141 0.329334i
\(143\) −6.00000 3.46410i −0.0419580 0.0242245i
\(144\) 49.5000 85.7365i 0.343750 0.595392i
\(145\) −78.0000 135.100i −0.537931 0.931724i
\(146\) −97.5000 + 56.2917i −0.667808 + 0.385559i
\(147\) 0 0
\(148\) 17.0000 29.4449i 0.114865 0.198952i
\(149\) 152.420i 1.02296i 0.859296 + 0.511478i \(0.170902\pi\)
−0.859296 + 0.511478i \(0.829098\pi\)
\(150\) 58.5000 + 33.7750i 0.390000 + 0.225167i
\(151\) 20.0000 0.132450 0.0662252 0.997805i \(-0.478904\pi\)
0.0662252 + 0.997805i \(0.478904\pi\)
\(152\) −82.5000 + 47.6314i −0.542763 + 0.313364i
\(153\) −121.500 70.1481i −0.794118 0.458484i
\(154\) 0 0
\(155\) −96.0000 + 55.4256i −0.619355 + 0.357585i
\(156\) −12.0000 −0.0769231
\(157\) 20.0000 + 34.6410i 0.127389 + 0.220643i 0.922664 0.385605i \(-0.126007\pi\)
−0.795276 + 0.606248i \(0.792674\pi\)
\(158\) −57.0000 + 32.9090i −0.360759 + 0.208285i
\(159\) 0 0
\(160\) 27.0000 + 46.7654i 0.168750 + 0.292284i
\(161\) 0 0
\(162\) 121.500 + 70.1481i 0.750000 + 0.433013i
\(163\) 53.0000 + 91.7987i 0.325153 + 0.563182i 0.981543 0.191240i \(-0.0612507\pi\)
−0.656390 + 0.754422i \(0.727917\pi\)
\(164\) 12.1244i 0.0739290i
\(165\) −18.0000 −0.109091
\(166\) −84.0000 −0.506024
\(167\) 165.000 + 95.2628i 0.988024 + 0.570436i 0.904683 0.426085i \(-0.140108\pi\)
0.0833409 + 0.996521i \(0.473441\pi\)
\(168\) 0 0
\(169\) 76.5000 + 132.502i 0.452663 + 0.784035i
\(170\) −81.0000 + 46.7654i −0.476471 + 0.275090i
\(171\) −49.5000 85.7365i −0.289474 0.501383i
\(172\) 30.5000 52.8275i 0.177326 0.307137i
\(173\) −201.000 116.047i −1.16185 0.670794i −0.210103 0.977679i \(-0.567380\pi\)
−0.951747 + 0.306885i \(0.900713\pi\)
\(174\) 234.000 1.34483
\(175\) 0 0
\(176\) −16.5000 9.52628i −0.0937500 0.0541266i
\(177\) −130.500 + 75.3442i −0.737288 + 0.425674i
\(178\) 216.000 1.21348
\(179\) −54.0000 31.1769i −0.301676 0.174173i 0.341520 0.939875i \(-0.389058\pi\)
−0.643196 + 0.765702i \(0.722392\pi\)
\(180\) −27.0000 + 15.5885i −0.150000 + 0.0866025i
\(181\) −232.000 −1.28177 −0.640884 0.767638i \(-0.721432\pi\)
−0.640884 + 0.767638i \(0.721432\pi\)
\(182\) 0 0
\(183\) −84.0000 + 145.492i −0.459016 + 0.795040i
\(184\) 240.000 1.30435
\(185\) 102.000 58.8897i 0.551351 0.318323i
\(186\) 166.277i 0.893962i
\(187\) −13.5000 + 23.3827i −0.0721925 + 0.125041i
\(188\) 48.4974i 0.257965i
\(189\) 0 0
\(190\) −66.0000 −0.347368
\(191\) −201.000 116.047i −1.05236 0.607578i −0.129048 0.991638i \(-0.541192\pi\)
−0.923308 + 0.384060i \(0.874525\pi\)
\(192\) −213.000 −1.10938
\(193\) 132.500 + 229.497i 0.686528 + 1.18910i 0.972954 + 0.231000i \(0.0741996\pi\)
−0.286425 + 0.958103i \(0.592467\pi\)
\(194\) 199.186i 1.02673i
\(195\) −36.0000 20.7846i −0.184615 0.106588i
\(196\) 0 0
\(197\) 124.708i 0.633034i 0.948587 + 0.316517i \(0.102513\pi\)
−0.948587 + 0.316517i \(0.897487\pi\)
\(198\) 13.5000 23.3827i 0.0681818 0.118094i
\(199\) −145.000 + 251.147i −0.728643 + 1.26205i 0.228814 + 0.973470i \(0.426515\pi\)
−0.957457 + 0.288577i \(0.906818\pi\)
\(200\) 112.583i 0.562917i
\(201\) 46.5000 + 80.5404i 0.231343 + 0.400698i
\(202\) −39.0000 + 67.5500i −0.193069 + 0.334406i
\(203\) 0 0
\(204\) 46.7654i 0.229242i
\(205\) −21.0000 + 36.3731i −0.102439 + 0.177430i
\(206\) −60.0000 34.6410i −0.291262 0.168160i
\(207\) 249.415i 1.20490i
\(208\) −22.0000 38.1051i −0.105769 0.183198i
\(209\) −16.5000 + 9.52628i −0.0789474 + 0.0455803i
\(210\) 0 0
\(211\) 47.0000 81.4064i 0.222749 0.385812i −0.732893 0.680344i \(-0.761830\pi\)
0.955642 + 0.294532i \(0.0951637\pi\)
\(212\) 0 0
\(213\) 93.5307i 0.439111i
\(214\) −243.000 −1.13551
\(215\) 183.000 105.655i 0.851163 0.491419i
\(216\) 233.827i 1.08253i
\(217\) 0 0
\(218\) 78.0000 45.0333i 0.357798 0.206575i
\(219\) −97.5000 + 168.875i −0.445205 + 0.771119i
\(220\) 3.00000 + 5.19615i 0.0136364 + 0.0236189i
\(221\) −54.0000 + 31.1769i −0.244344 + 0.141072i
\(222\) 176.669i 0.795807i
\(223\) 26.0000 + 45.0333i 0.116592 + 0.201943i 0.918415 0.395618i \(-0.129470\pi\)
−0.801823 + 0.597562i \(0.796136\pi\)
\(224\) 0 0
\(225\) 117.000 0.520000
\(226\) −78.0000 135.100i −0.345133 0.597787i
\(227\) 188.794i 0.831690i −0.909436 0.415845i \(-0.863486\pi\)
0.909436 0.415845i \(-0.136514\pi\)
\(228\) −16.5000 + 28.5788i −0.0723684 + 0.125346i
\(229\) 266.000 1.16157 0.580786 0.814056i \(-0.302745\pi\)
0.580786 + 0.814056i \(0.302745\pi\)
\(230\) 144.000 + 83.1384i 0.626087 + 0.361471i
\(231\) 0 0
\(232\) −195.000 337.750i −0.840517 1.45582i
\(233\) 175.500 101.325i 0.753219 0.434871i −0.0736369 0.997285i \(-0.523461\pi\)
0.826856 + 0.562414i \(0.190127\pi\)
\(234\) 54.0000 31.1769i 0.230769 0.133235i
\(235\) 84.0000 145.492i 0.357447 0.619116i
\(236\) 43.5000 + 25.1147i 0.184322 + 0.106418i
\(237\) −57.0000 + 98.7269i −0.240506 + 0.416569i
\(238\) 0 0
\(239\) −348.000 200.918i −1.45607 0.840661i −0.457252 0.889337i \(-0.651166\pi\)
−0.998815 + 0.0486764i \(0.984500\pi\)
\(240\) −99.0000 57.1577i −0.412500 0.238157i
\(241\) 119.000 0.493776 0.246888 0.969044i \(-0.420592\pi\)
0.246888 + 0.969044i \(0.420592\pi\)
\(242\) 177.000 + 102.191i 0.731405 + 0.422277i
\(243\) 243.000 1.00000
\(244\) 56.0000 0.229508
\(245\) 0 0
\(246\) −31.5000 54.5596i −0.128049 0.221787i
\(247\) −44.0000 −0.178138
\(248\) −240.000 + 138.564i −0.967742 + 0.558726i
\(249\) −126.000 + 72.7461i −0.506024 + 0.292153i
\(250\) 114.000 197.454i 0.456000 0.789815i
\(251\) 389.711i 1.55264i −0.630342 0.776318i \(-0.717085\pi\)
0.630342 0.776318i \(-0.282915\pi\)
\(252\) 0 0
\(253\) 48.0000 0.189723
\(254\) −24.0000 13.8564i −0.0944882 0.0545528i
\(255\) −81.0000 + 140.296i −0.317647 + 0.550181i
\(256\) 89.5000 + 155.019i 0.349609 + 0.605541i
\(257\) 174.937i 0.680689i −0.940301 0.340345i \(-0.889456\pi\)
0.940301 0.340345i \(-0.110544\pi\)
\(258\) 316.965i 1.22855i
\(259\) 0 0
\(260\) 13.8564i 0.0532939i
\(261\) 351.000 202.650i 1.34483 0.776437i
\(262\) 138.000 239.023i 0.526718 0.912302i
\(263\) 45.0333i 0.171229i 0.996328 + 0.0856147i \(0.0272854\pi\)
−0.996328 + 0.0856147i \(0.972715\pi\)
\(264\) −45.0000 −0.170455
\(265\) 0 0
\(266\) 0 0
\(267\) 324.000 187.061i 1.21348 0.700605i
\(268\) 15.5000 26.8468i 0.0578358 0.100175i
\(269\) 162.000 + 93.5307i 0.602230 + 0.347698i 0.769919 0.638142i \(-0.220297\pi\)
−0.167688 + 0.985840i \(0.553630\pi\)
\(270\) 81.0000 140.296i 0.300000 0.519615i
\(271\) 134.000 + 232.095i 0.494465 + 0.856438i 0.999980 0.00637958i \(-0.00203070\pi\)
−0.505515 + 0.862818i \(0.668697\pi\)
\(272\) −148.500 + 85.7365i −0.545956 + 0.315208i
\(273\) 0 0
\(274\) 163.500 283.190i 0.596715 1.03354i
\(275\) 22.5167i 0.0818788i
\(276\) 72.0000 41.5692i 0.260870 0.150613i
\(277\) 56.0000 0.202166 0.101083 0.994878i \(-0.467769\pi\)
0.101083 + 0.994878i \(0.467769\pi\)
\(278\) −7.50000 + 4.33013i −0.0269784 + 0.0155760i
\(279\) −144.000 249.415i −0.516129 0.893962i
\(280\) 0 0
\(281\) −42.0000 + 24.2487i −0.149466 + 0.0862943i −0.572868 0.819648i \(-0.694169\pi\)
0.423402 + 0.905942i \(0.360836\pi\)
\(282\) 126.000 + 218.238i 0.446809 + 0.773895i
\(283\) −187.000 323.894i −0.660777 1.14450i −0.980412 0.196959i \(-0.936893\pi\)
0.319634 0.947541i \(-0.396440\pi\)
\(284\) −27.0000 + 15.5885i −0.0950704 + 0.0548889i
\(285\) −99.0000 + 57.1577i −0.347368 + 0.200553i
\(286\) −6.00000 10.3923i −0.0209790 0.0363367i
\(287\) 0 0
\(288\) −121.500 + 70.1481i −0.421875 + 0.243570i
\(289\) −23.0000 39.8372i −0.0795848 0.137845i
\(290\) 270.200i 0.931724i
\(291\) 172.500 + 298.779i 0.592784 + 1.02673i
\(292\) 65.0000 0.222603
\(293\) 219.000 + 126.440i 0.747440 + 0.431535i 0.824768 0.565471i \(-0.191306\pi\)
−0.0773280 + 0.997006i \(0.524639\pi\)
\(294\) 0 0
\(295\) 87.0000 + 150.688i 0.294915 + 0.510808i
\(296\) 255.000 147.224i 0.861486 0.497379i
\(297\) 46.7654i 0.157459i
\(298\) −132.000 + 228.631i −0.442953 + 0.767217i
\(299\) 96.0000 + 55.4256i 0.321070 + 0.185370i
\(300\) −19.5000 33.7750i −0.0650000 0.112583i
\(301\) 0 0
\(302\) 30.0000 + 17.3205i 0.0993377 + 0.0573527i
\(303\) 135.100i 0.445874i
\(304\) −121.000 −0.398026
\(305\) 168.000 + 96.9948i 0.550820 + 0.318016i
\(306\) −121.500 210.444i −0.397059 0.687726i
\(307\) 533.000 1.73616 0.868078 0.496428i \(-0.165355\pi\)
0.868078 + 0.496428i \(0.165355\pi\)
\(308\) 0 0
\(309\) −120.000 −0.388350
\(310\) −192.000 −0.619355
\(311\) 213.000 122.976i 0.684887 0.395420i −0.116806 0.993155i \(-0.537266\pi\)
0.801694 + 0.597735i \(0.203932\pi\)
\(312\) −90.0000 51.9615i −0.288462 0.166543i
\(313\) −77.5000 + 134.234i −0.247604 + 0.428862i −0.962860 0.269999i \(-0.912976\pi\)
0.715257 + 0.698862i \(0.246310\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) 42.0000 + 24.2487i 0.132492 + 0.0764944i 0.564781 0.825241i \(-0.308961\pi\)
−0.432289 + 0.901735i \(0.642294\pi\)
\(318\) 0 0
\(319\) −39.0000 67.5500i −0.122257 0.211755i
\(320\) 245.951i 0.768598i
\(321\) −364.500 + 210.444i −1.13551 + 0.655589i
\(322\) 0 0
\(323\) 171.473i 0.530876i
\(324\) −40.5000 70.1481i −0.125000 0.216506i
\(325\) 26.0000 45.0333i 0.0800000 0.138564i
\(326\) 183.597i 0.563182i
\(327\) 78.0000 135.100i 0.238532 0.413150i
\(328\) −52.5000 + 90.9327i −0.160061 + 0.277234i
\(329\) 0 0
\(330\) −27.0000 15.5885i −0.0818182 0.0472377i
\(331\) −1.00000 + 1.73205i −0.00302115 + 0.00523278i −0.867532 0.497381i \(-0.834295\pi\)
0.864511 + 0.502614i \(0.167628\pi\)
\(332\) 42.0000 + 24.2487i 0.126506 + 0.0730383i
\(333\) 153.000 + 265.004i 0.459459 + 0.795807i
\(334\) 165.000 + 285.788i 0.494012 + 0.855654i
\(335\) 93.0000 53.6936i 0.277612 0.160279i
\(336\) 0 0
\(337\) −38.5000 + 66.6840i −0.114243 + 0.197875i −0.917477 0.397789i \(-0.869778\pi\)
0.803234 + 0.595664i \(0.203111\pi\)
\(338\) 265.004i 0.784035i
\(339\) −234.000 135.100i −0.690265 0.398525i
\(340\) 54.0000 0.158824
\(341\) −48.0000 + 27.7128i −0.140762 + 0.0812692i
\(342\) 171.473i 0.501383i
\(343\) 0 0
\(344\) 457.500 264.138i 1.32994 0.767842i
\(345\) 288.000 0.834783
\(346\) −201.000 348.142i −0.580925 1.00619i
\(347\) −97.5000 + 56.2917i −0.280980 + 0.162224i −0.633867 0.773442i \(-0.718533\pi\)
0.352887 + 0.935666i \(0.385200\pi\)
\(348\) −117.000 67.5500i −0.336207 0.194109i
\(349\) −208.000 360.267i −0.595989 1.03228i −0.993407 0.114645i \(-0.963427\pi\)
0.397418 0.917638i \(-0.369906\pi\)
\(350\) 0 0
\(351\) 54.0000 93.5307i 0.153846 0.266469i
\(352\) 13.5000 + 23.3827i 0.0383523 + 0.0664281i
\(353\) 1.73205i 0.00490666i −0.999997 0.00245333i \(-0.999219\pi\)
0.999997 0.00245333i \(-0.000780920\pi\)
\(354\) −261.000 −0.737288
\(355\) −108.000 −0.304225
\(356\) −108.000 62.3538i −0.303371 0.175151i
\(357\) 0 0
\(358\) −54.0000 93.5307i −0.150838 0.261259i
\(359\) 513.000 296.181i 1.42897 0.825016i 0.431930 0.901907i \(-0.357833\pi\)
0.997039 + 0.0768913i \(0.0244995\pi\)
\(360\) −270.000 −0.750000
\(361\) 120.000 207.846i 0.332410 0.575751i
\(362\) −348.000 200.918i −0.961326 0.555022i
\(363\) 354.000 0.975207
\(364\) 0 0
\(365\) 195.000 + 112.583i 0.534247 + 0.308447i
\(366\) −252.000 + 145.492i −0.688525 + 0.397520i
\(367\) −358.000 −0.975477 −0.487738 0.872990i \(-0.662178\pi\)
−0.487738 + 0.872990i \(0.662178\pi\)
\(368\) 264.000 + 152.420i 0.717391 + 0.414186i
\(369\) −94.5000 54.5596i −0.256098 0.147858i
\(370\) 204.000 0.551351
\(371\) 0 0
\(372\) −48.0000 + 83.1384i −0.129032 + 0.223490i
\(373\) −580.000 −1.55496 −0.777480 0.628908i \(-0.783502\pi\)
−0.777480 + 0.628908i \(0.783502\pi\)
\(374\) −40.5000 + 23.3827i −0.108289 + 0.0625206i
\(375\) 394.908i 1.05309i
\(376\) 210.000 363.731i 0.558511 0.967369i
\(377\) 180.133i 0.477807i
\(378\) 0 0
\(379\) 83.0000 0.218997 0.109499 0.993987i \(-0.465075\pi\)
0.109499 + 0.993987i \(0.465075\pi\)
\(380\) 33.0000 + 19.0526i 0.0868421 + 0.0501383i
\(381\) −48.0000 −0.125984
\(382\) −201.000 348.142i −0.526178 0.911367i
\(383\) 557.720i 1.45619i 0.685477 + 0.728094i \(0.259594\pi\)
−0.685477 + 0.728094i \(0.740406\pi\)
\(384\) −157.500 90.9327i −0.410156 0.236804i
\(385\) 0 0
\(386\) 458.993i 1.18910i
\(387\) 274.500 + 475.448i 0.709302 + 1.22855i
\(388\) 57.5000 99.5929i 0.148196 0.256683i
\(389\) 516.151i 1.32687i −0.748235 0.663433i \(-0.769099\pi\)
0.748235 0.663433i \(-0.230901\pi\)
\(390\) −36.0000 62.3538i −0.0923077 0.159882i
\(391\) 216.000 374.123i 0.552430 0.956836i
\(392\) 0 0
\(393\) 478.046i 1.21640i
\(394\) −108.000 + 187.061i −0.274112 + 0.474775i
\(395\) 114.000 + 65.8179i 0.288608 + 0.166628i
\(396\) −13.5000 + 7.79423i −0.0340909 + 0.0196824i
\(397\) −181.000 313.501i −0.455919 0.789676i 0.542821 0.839848i \(-0.317356\pi\)
−0.998741 + 0.0501728i \(0.984023\pi\)
\(398\) −435.000 + 251.147i −1.09296 + 0.631024i
\(399\) 0 0
\(400\) 71.5000 123.842i 0.178750 0.309604i
\(401\) 393.176i 0.980488i −0.871585 0.490244i \(-0.836908\pi\)
0.871585 0.490244i \(-0.163092\pi\)
\(402\) 161.081i 0.400698i
\(403\) −128.000 −0.317618
\(404\) 39.0000 22.5167i 0.0965347 0.0557343i
\(405\) 280.592i 0.692820i
\(406\) 0 0
\(407\) 51.0000 29.4449i 0.125307 0.0723461i
\(408\) −202.500 + 350.740i −0.496324 + 0.859658i
\(409\) −110.500 191.392i −0.270171 0.467950i 0.698734 0.715381i \(-0.253747\pi\)
−0.968905 + 0.247431i \(0.920414\pi\)
\(410\) −63.0000 + 36.3731i −0.153659 + 0.0887148i
\(411\) 566.381i 1.37806i
\(412\) 20.0000 + 34.6410i 0.0485437 + 0.0840801i
\(413\) 0 0
\(414\) −216.000 + 374.123i −0.521739 + 0.903679i
\(415\) 84.0000 + 145.492i 0.202410 + 0.350584i
\(416\) 62.3538i 0.149889i
\(417\) −7.50000 + 12.9904i −0.0179856 + 0.0311520i
\(418\) −33.0000 −0.0789474
\(419\) 678.000 + 391.443i 1.61814 + 0.934233i 0.987401 + 0.158236i \(0.0505807\pi\)
0.630737 + 0.775997i \(0.282753\pi\)
\(420\) 0 0
\(421\) 341.000 + 590.629i 0.809976 + 1.40292i 0.912880 + 0.408229i \(0.133853\pi\)
−0.102903 + 0.994691i \(0.532813\pi\)
\(422\) 141.000 81.4064i 0.334123 0.192906i
\(423\) 378.000 + 218.238i 0.893617 + 0.515930i
\(424\) 0 0
\(425\) −175.500 101.325i −0.412941 0.238412i
\(426\) 81.0000 140.296i 0.190141 0.329334i
\(427\) 0 0
\(428\) 121.500 + 70.1481i 0.283879 + 0.163897i
\(429\) −18.0000 10.3923i −0.0419580 0.0242245i
\(430\) 366.000 0.851163
\(431\) 243.000 + 140.296i 0.563805 + 0.325513i 0.754671 0.656103i \(-0.227796\pi\)
−0.190866 + 0.981616i \(0.561130\pi\)
\(432\) 148.500 257.210i 0.343750 0.595392i
\(433\) −295.000 −0.681293 −0.340647 0.940191i \(-0.610646\pi\)
−0.340647 + 0.940191i \(0.610646\pi\)
\(434\) 0 0
\(435\) −234.000 405.300i −0.537931 0.931724i
\(436\) −52.0000 −0.119266
\(437\) 264.000 152.420i 0.604119 0.348788i
\(438\) −292.500 + 168.875i −0.667808 + 0.385559i
\(439\) −406.000 + 703.213i −0.924829 + 1.60185i −0.132993 + 0.991117i \(0.542459\pi\)
−0.791836 + 0.610734i \(0.790874\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 0 0
\(442\) −108.000 −0.244344
\(443\) −79.5000 45.8993i −0.179458 0.103610i 0.407580 0.913170i \(-0.366373\pi\)
−0.587038 + 0.809559i \(0.699706\pi\)
\(444\) 51.0000 88.3346i 0.114865 0.198952i
\(445\) −216.000 374.123i −0.485393 0.840726i
\(446\) 90.0666i 0.201943i
\(447\) 457.261i 1.02296i
\(448\) 0 0
\(449\) 639.127i 1.42344i −0.702461 0.711722i \(-0.747915\pi\)
0.702461 0.711722i \(-0.252085\pi\)
\(450\) 175.500 + 101.325i 0.390000 + 0.225167i
\(451\) −10.5000 + 18.1865i −0.0232816 + 0.0403249i
\(452\) 90.0666i 0.199262i
\(453\) 60.0000 0.132450
\(454\) 163.500 283.190i 0.360132 0.623767i
\(455\) 0 0
\(456\) −247.500 + 142.894i −0.542763 + 0.313364i
\(457\) −32.5000 + 56.2917i −0.0711160 + 0.123176i −0.899391 0.437146i \(-0.855989\pi\)
0.828275 + 0.560322i \(0.189323\pi\)
\(458\) 399.000 + 230.363i 0.871179 + 0.502975i
\(459\) −364.500 210.444i −0.794118 0.458484i
\(460\) −48.0000 83.1384i −0.104348 0.180736i
\(461\) −690.000 + 398.372i −1.49675 + 0.864147i −0.999993 0.00374501i \(-0.998808\pi\)
−0.496753 + 0.867892i \(0.665475\pi\)
\(462\) 0 0
\(463\) −367.000 + 635.663i −0.792657 + 1.37292i 0.131660 + 0.991295i \(0.457969\pi\)
−0.924317 + 0.381627i \(0.875364\pi\)
\(464\) 495.367i 1.06760i
\(465\) −288.000 + 166.277i −0.619355 + 0.357585i
\(466\) 351.000 0.753219
\(467\) −175.500 + 101.325i −0.375803 + 0.216970i −0.675991 0.736910i \(-0.736284\pi\)
0.300188 + 0.953880i \(0.402951\pi\)
\(468\) −36.0000 −0.0769231
\(469\) 0 0
\(470\) 252.000 145.492i 0.536170 0.309558i
\(471\) 60.0000 + 103.923i 0.127389 + 0.220643i
\(472\) 217.500 + 376.721i 0.460805 + 0.798138i
\(473\) 91.5000 52.8275i 0.193446 0.111686i
\(474\) −171.000 + 98.7269i −0.360759 + 0.208285i
\(475\) −71.5000 123.842i −0.150526 0.260719i
\(476\) 0 0
\(477\) 0 0
\(478\) −348.000 602.754i −0.728033 1.26099i
\(479\) 606.218i 1.26559i 0.774319 + 0.632795i \(0.218092\pi\)
−0.774319 + 0.632795i \(0.781908\pi\)
\(480\) 81.0000 + 140.296i 0.168750 + 0.292284i
\(481\) 136.000 0.282744
\(482\) 178.500 + 103.057i 0.370332 + 0.213811i
\(483\) 0 0
\(484\) −59.0000 102.191i −0.121901 0.211138i
\(485\) 345.000 199.186i 0.711340 0.410692i
\(486\) 364.500 + 210.444i 0.750000 + 0.433013i
\(487\) 53.0000 91.7987i 0.108830 0.188498i −0.806467 0.591279i \(-0.798623\pi\)
0.915296 + 0.402781i \(0.131956\pi\)
\(488\) 420.000 + 242.487i 0.860656 + 0.496900i
\(489\) 159.000 + 275.396i 0.325153 + 0.563182i
\(490\) 0 0
\(491\) −199.500 115.181i −0.406314 0.234585i 0.282891 0.959152i \(-0.408707\pi\)
−0.689205 + 0.724567i \(0.742040\pi\)
\(492\) 36.3731i 0.0739290i
\(493\) −702.000 −1.42394
\(494\) −66.0000 38.1051i −0.133603 0.0771359i
\(495\) −54.0000 −0.109091
\(496\) −352.000 −0.709677
\(497\) 0 0
\(498\) −252.000 −0.506024
\(499\) −787.000 −1.57715 −0.788577 0.614936i \(-0.789182\pi\)
−0.788577 + 0.614936i \(0.789182\pi\)
\(500\) −114.000 + 65.8179i −0.228000 + 0.131636i
\(501\) 495.000 + 285.788i 0.988024 + 0.570436i
\(502\) 337.500 584.567i 0.672311 1.16448i
\(503\) 623.538i 1.23964i 0.784745 + 0.619819i \(0.212794\pi\)
−0.784745 + 0.619819i \(0.787206\pi\)
\(504\) 0 0
\(505\) 156.000 0.308911
\(506\) 72.0000 + 41.5692i 0.142292 + 0.0821526i
\(507\) 229.500 + 397.506i 0.452663 + 0.784035i
\(508\) 8.00000 + 13.8564i 0.0157480 + 0.0272764i
\(509\) 214.774i 0.421953i 0.977491 + 0.210977i \(0.0676644\pi\)
−0.977491 + 0.210977i \(0.932336\pi\)
\(510\) −243.000 + 140.296i −0.476471 + 0.275090i
\(511\) 0 0
\(512\) 552.524i 1.07915i
\(513\) −148.500 257.210i −0.289474 0.501383i
\(514\) 151.500 262.406i 0.294747 0.510517i
\(515\) 138.564i 0.269056i
\(516\) 91.5000 158.483i 0.177326 0.307137i
\(517\) 42.0000 72.7461i 0.0812379 0.140708i
\(518\) 0 0
\(519\) −603.000 348.142i −1.16185 0.670794i
\(520\) −60.0000 + 103.923i −0.115385 + 0.199852i
\(521\) 175.500 + 101.325i 0.336852 + 0.194482i 0.658879 0.752249i \(-0.271031\pi\)
−0.322027 + 0.946730i \(0.604364\pi\)
\(522\) 702.000 1.34483
\(523\) 125.000 + 216.506i 0.239006 + 0.413970i 0.960429 0.278524i \(-0.0898452\pi\)
−0.721424 + 0.692494i \(0.756512\pi\)
\(524\) −138.000 + 79.6743i −0.263359 + 0.152050i
\(525\) 0 0
\(526\) −39.0000 + 67.5500i −0.0741445 + 0.128422i
\(527\) 498.831i 0.946548i
\(528\) −49.5000 28.5788i −0.0937500 0.0541266i
\(529\) −239.000 −0.451796
\(530\) 0 0
\(531\) −391.500 + 226.033i −0.737288 + 0.425674i
\(532\) 0 0
\(533\) −42.0000 + 24.2487i −0.0787992 + 0.0454948i
\(534\) 648.000 1.21348
\(535\) 243.000 + 420.888i 0.454206 + 0.786707i
\(536\) 232.500 134.234i 0.433769 0.250436i
\(537\) −162.000 93.5307i −0.301676 0.174173i
\(538\) 162.000 + 280.592i 0.301115 + 0.521547i
\(539\) 0 0
\(540\) −81.0000 + 46.7654i −0.150000 + 0.0866025i
\(541\) −325.000 562.917i −0.600739 1.04051i −0.992709 0.120533i \(-0.961540\pi\)
0.391970 0.919978i \(-0.371794\pi\)
\(542\) 464.190i 0.856438i
\(543\) −696.000 −1.28177
\(544\) 243.000 0.446691
\(545\) −156.000 90.0666i −0.286239 0.165260i
\(546\) 0 0
\(547\) −311.500 539.534i −0.569470 0.986351i −0.996618 0.0821692i \(-0.973815\pi\)
0.427149 0.904181i \(-0.359518\pi\)
\(548\) −163.500 + 94.3968i −0.298358 + 0.172257i
\(549\) −252.000 + 436.477i −0.459016 + 0.795040i
\(550\) 19.5000 33.7750i 0.0354545 0.0614091i
\(551\) −429.000 247.683i −0.778584 0.449516i
\(552\) 720.000 1.30435
\(553\) 0 0
\(554\) 84.0000 + 48.4974i 0.151625 + 0.0875405i
\(555\) 306.000 176.669i 0.551351 0.318323i
\(556\) 5.00000 0.00899281
\(557\) −459.000 265.004i −0.824057 0.475770i 0.0277562 0.999615i \(-0.491164\pi\)
−0.851814 + 0.523845i \(0.824497\pi\)
\(558\) 498.831i 0.893962i
\(559\) 244.000 0.436494
\(560\) 0 0
\(561\) −40.5000 + 70.1481i −0.0721925 + 0.125041i
\(562\) −84.0000 −0.149466
\(563\) −97.5000 + 56.2917i −0.173179 + 0.0999852i −0.584084 0.811693i \(-0.698546\pi\)
0.410905 + 0.911678i \(0.365213\pi\)
\(564\) 145.492i 0.257965i
\(565\) −156.000 + 270.200i −0.276106 + 0.478230i
\(566\) 647.787i 1.14450i
\(567\) 0 0
\(568\) −270.000 −0.475352
\(569\) −565.500 326.492i −0.993849 0.573799i −0.0874263 0.996171i \(-0.527864\pi\)
−0.906423 + 0.422372i \(0.861198\pi\)
\(570\) −198.000 −0.347368
\(571\) −272.500 471.984i −0.477233 0.826592i 0.522427 0.852684i \(-0.325027\pi\)
−0.999660 + 0.0260926i \(0.991694\pi\)
\(572\) 6.92820i 0.0121122i
\(573\) −603.000 348.142i −1.05236 0.607578i
\(574\) 0 0
\(575\) 360.267i 0.626551i
\(576\) −639.000 −1.10938
\(577\) 435.500 754.308i 0.754766 1.30729i −0.190725 0.981644i \(-0.561084\pi\)
0.945491 0.325650i \(-0.105583\pi\)
\(578\) 79.6743i 0.137845i
\(579\) 397.500 + 688.490i 0.686528 + 1.18910i
\(580\) −78.0000 + 135.100i −0.134483 + 0.232931i
\(581\) 0 0
\(582\) 597.558i 1.02673i
\(583\) 0 0
\(584\) 487.500 + 281.458i 0.834760 + 0.481949i
\(585\) −108.000 62.3538i −0.184615 0.106588i
\(586\) 219.000 + 379.319i 0.373720 + 0.647302i
\(587\) −1.50000 + 0.866025i −0.00255537 + 0.00147534i −0.501277 0.865287i \(-0.667136\pi\)
0.498722 + 0.866762i \(0.333803\pi\)
\(588\) 0 0
\(589\) −176.000 + 304.841i −0.298812 + 0.517557i
\(590\) 301.377i 0.510808i
\(591\) 374.123i 0.633034i
\(592\) 374.000 0.631757
\(593\) 162.000 93.5307i 0.273187 0.157725i −0.357148 0.934048i \(-0.616251\pi\)
0.630335 + 0.776323i \(0.282917\pi\)
\(594\) 40.5000 70.1481i 0.0681818 0.118094i
\(595\) 0 0
\(596\) 132.000 76.2102i 0.221477 0.127870i
\(597\) −435.000 + 753.442i −0.728643 + 1.26205i
\(598\) 96.0000 + 166.277i 0.160535 + 0.278055i
\(599\) −489.000 + 282.324i −0.816361 + 0.471326i −0.849160 0.528136i \(-0.822891\pi\)
0.0327992 + 0.999462i \(0.489558\pi\)
\(600\) 337.750i 0.562917i
\(601\) −230.500 399.238i −0.383527 0.664289i 0.608036 0.793909i \(-0.291958\pi\)
−0.991564 + 0.129620i \(0.958624\pi\)
\(602\) 0 0
\(603\) 139.500 + 241.621i 0.231343 + 0.400698i
\(604\) −10.0000 17.3205i −0.0165563 0.0286763i
\(605\) 408.764i 0.675643i
\(606\) −117.000 + 202.650i −0.193069 + 0.334406i
\(607\) −112.000 −0.184514 −0.0922570 0.995735i \(-0.529408\pi\)
−0.0922570 + 0.995735i \(0.529408\pi\)
\(608\) 148.500 + 85.7365i 0.244243 + 0.141014i
\(609\) 0 0
\(610\) 168.000 + 290.985i 0.275410 + 0.477024i
\(611\) 168.000 96.9948i 0.274959 0.158748i
\(612\) 140.296i 0.229242i
\(613\) −451.000 + 781.155i −0.735726 + 1.27431i 0.218678 + 0.975797i \(0.429826\pi\)
−0.954404 + 0.298518i \(0.903508\pi\)
\(614\) 799.500 + 461.592i 1.30212 + 0.751778i
\(615\) −63.0000 + 109.119i −0.102439 + 0.177430i
\(616\) 0 0
\(617\) −307.500 177.535i −0.498379 0.287739i 0.229665 0.973270i \(-0.426237\pi\)
−0.728044 + 0.685530i \(0.759570\pi\)
\(618\) −180.000 103.923i −0.291262 0.168160i
\(619\) −799.000 −1.29079 −0.645396 0.763848i \(-0.723308\pi\)
−0.645396 + 0.763848i \(0.723308\pi\)
\(620\) 96.0000 + 55.4256i 0.154839 + 0.0893962i
\(621\) 748.246i 1.20490i
\(622\) 426.000 0.684887
\(623\) 0 0
\(624\) −66.0000 114.315i −0.105769 0.183198i
\(625\) −131.000 −0.209600
\(626\) −232.500 + 134.234i −0.371406 + 0.214431i
\(627\) −49.5000 + 28.5788i −0.0789474 + 0.0455803i
\(628\) 20.0000 34.6410i 0.0318471 0.0551609i
\(629\) 530.008i 0.842619i
\(630\) 0 0
\(631\) 830.000 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(632\) 285.000 + 164.545i 0.450949 + 0.260356i
\(633\) 141.000 244.219i 0.222749 0.385812i
\(634\) 42.0000 + 72.7461i 0.0662461 + 0.114742i
\(635\) 55.4256i 0.0872845i
\(636\) 0 0
\(637\) 0 0
\(638\) 135.100i 0.211755i
\(639\) 280.592i 0.439111i
\(640\) −105.000 + 181.865i −0.164062 + 0.284165i
\(641\) 375.855i 0.586357i −0.956058 0.293179i \(-0.905287\pi\)
0.956058 0.293179i \(-0.0947131\pi\)
\(642\) −729.000 −1.13551
\(643\) 6.50000 11.2583i 0.0101089 0.0175091i −0.860927 0.508729i \(-0.830116\pi\)
0.871036 + 0.491220i \(0.163449\pi\)
\(644\) 0 0
\(645\) 549.000 316.965i 0.851163 0.491419i
\(646\) −148.500 + 257.210i −0.229876 + 0.398157i
\(647\) −405.000 233.827i −0.625966 0.361402i 0.153222 0.988192i \(-0.451035\pi\)
−0.779188 + 0.626790i \(0.784368\pi\)
\(648\) 701.481i 1.08253i
\(649\) 43.5000 + 75.3442i 0.0670262 + 0.116093i
\(650\) 78.0000 45.0333i 0.120000 0.0692820i
\(651\) 0 0
\(652\) 53.0000 91.7987i 0.0812883 0.140796i
\(653\) 377.587i 0.578234i −0.957294 0.289117i \(-0.906638\pi\)
0.957294 0.289117i \(-0.0933617\pi\)
\(654\) 234.000 135.100i 0.357798 0.206575i
\(655\) −552.000 −0.842748
\(656\) −115.500 + 66.6840i −0.176067 + 0.101652i
\(657\) −292.500 + 506.625i −0.445205 + 0.771119i
\(658\) 0 0
\(659\) −852.000 + 491.902i −1.29287 + 0.746438i −0.979162 0.203082i \(-0.934904\pi\)
−0.313706 + 0.949520i \(0.601571\pi\)
\(660\) 9.00000 + 15.5885i 0.0136364 + 0.0236189i
\(661\) 191.000 + 330.822i 0.288956 + 0.500487i 0.973561 0.228428i \(-0.0733585\pi\)
−0.684605 + 0.728915i \(0.740025\pi\)
\(662\) −3.00000 + 1.73205i −0.00453172 + 0.00261639i
\(663\) −162.000 + 93.5307i −0.244344 + 0.141072i
\(664\) 210.000 + 363.731i 0.316265 + 0.547787i
\(665\) 0 0
\(666\) 530.008i 0.795807i
\(667\) 624.000 + 1080.80i 0.935532 + 1.62039i
\(668\) 190.526i 0.285218i
\(669\) 78.0000 + 135.100i 0.116592 + 0.201943i
\(670\) 186.000 0.277612
\(671\) 84.0000 + 48.4974i 0.125186 + 0.0722763i
\(672\) 0 0
\(673\) −289.000 500.563i −0.429421 0.743778i 0.567401 0.823441i \(-0.307949\pi\)
−0.996822 + 0.0796633i \(0.974615\pi\)
\(674\) −115.500 + 66.6840i −0.171365 + 0.0989376i
\(675\) 351.000 0.520000
\(676\) 76.5000 132.502i 0.113166 0.196009i
\(677\) −606.000 349.874i −0.895126 0.516801i −0.0195100 0.999810i \(-0.506211\pi\)
−0.875616 + 0.483009i \(0.839544\pi\)
\(678\) −234.000 405.300i −0.345133 0.597787i
\(679\) 0 0
\(680\) 405.000 + 233.827i 0.595588 + 0.343863i
\(681\) 566.381i 0.831690i
\(682\) −96.0000 −0.140762
\(683\) 904.500 + 522.213i 1.32430 + 0.764588i 0.984412 0.175877i \(-0.0562760\pi\)
0.339892 + 0.940464i \(0.389609\pi\)
\(684\) −49.5000 + 85.7365i −0.0723684 + 0.125346i
\(685\) −654.000 −0.954745
\(686\) 0 0
\(687\) 798.000 1.16157
\(688\) 671.000 0.975291
\(689\) 0 0
\(690\) 432.000 + 249.415i 0.626087 + 0.361471i
\(691\) −91.0000 + 157.617i −0.131693 + 0.228099i −0.924329 0.381596i \(-0.875375\pi\)
0.792636 + 0.609695i \(0.208708\pi\)
\(692\) 232.095i 0.335397i
\(693\) 0 0
\(694\) −195.000 −0.280980
\(695\) 15.0000 + 8.66025i 0.0215827 + 0.0124608i
\(696\) −585.000 1013.25i −0.840517 1.45582i
\(697\) 94.5000 + 163.679i 0.135581 + 0.234833i
\(698\) 720.533i 1.03228i
\(699\) 526.500 303.975i 0.753219 0.434871i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 162.000 93.5307i 0.230769 0.133235i
\(703\) 187.000 323.894i 0.266003 0.460730i
\(704\) 122.976i 0.174681i
\(705\) 252.000 436.477i 0.357447 0.619116i
\(706\) 1.50000 2.59808i 0.00212465 0.00367999i
\(707\) 0 0
\(708\) 130.500 + 75.3442i 0.184322 + 0.106418i
\(709\) 350.000 606.218i 0.493653 0.855032i −0.506320 0.862346i \(-0.668995\pi\)
0.999973 + 0.00731341i \(0.00232795\pi\)
\(710\) −162.000 93.5307i −0.228169 0.131733i
\(711\) −171.000 + 296.181i −0.240506 + 0.416569i
\(712\) −540.000 935.307i −0.758427 1.31363i
\(713\) 768.000 443.405i 1.07714 0.621886i
\(714\) 0 0
\(715\) −12.0000 + 20.7846i −0.0167832 + 0.0290694i
\(716\) 62.3538i 0.0870864i
\(717\) −1044.00 602.754i −1.45607 0.840661i
\(718\) 1026.00 1.42897
\(719\) −513.000 + 296.181i −0.713491 + 0.411934i −0.812352 0.583167i \(-0.801813\pi\)
0.0988613 + 0.995101i \(0.468480\pi\)
\(720\) −297.000 171.473i −0.412500 0.238157i
\(721\) 0 0
\(722\) 360.000 207.846i 0.498615 0.287875i
\(723\) 357.000 0.493776
\(724\) 116.000 + 200.918i 0.160221 + 0.277511i
\(725\) 507.000 292.717i 0.699310 0.403747i
\(726\) 531.000 + 306.573i 0.731405 + 0.422277i
\(727\) 332.000 + 575.041i 0.456671 + 0.790978i 0.998783 0.0493289i \(-0.0157082\pi\)
−0.542111 + 0.840307i \(0.682375\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 195.000 + 337.750i 0.267123 + 0.462671i
\(731\) 950.896i 1.30082i
\(732\) 168.000 0.229508
\(733\) −670.000 −0.914052 −0.457026 0.889453i \(-0.651085\pi\)
−0.457026 + 0.889453i \(0.651085\pi\)
\(734\) −537.000 310.037i −0.731608 0.422394i
\(735\) 0 0
\(736\) −216.000 374.123i −0.293478 0.508319i
\(737\) 46.5000 26.8468i 0.0630936 0.0364271i
\(738\) −94.5000 163.679i −0.128049 0.221787i
\(739\) −158.500 + 274.530i −0.214479 + 0.371489i −0.953111 0.302620i \(-0.902139\pi\)
0.738632 + 0.674109i \(0.235472\pi\)
\(740\) −102.000 58.8897i −0.137838 0.0795807i
\(741\) −132.000 −0.178138
\(742\) 0 0
\(743\) −537.000 310.037i −0.722746 0.417277i 0.0930168 0.995665i \(-0.470349\pi\)
−0.815762 + 0.578387i \(0.803682\pi\)
\(744\) −720.000 + 415.692i −0.967742 + 0.558726i
\(745\) 528.000 0.708725
\(746\) −870.000 502.295i −1.16622 0.673317i
\(747\) −378.000 + 218.238i −0.506024 + 0.292153i
\(748\) 27.0000 0.0360963
\(749\) 0 0
\(750\) 342.000 592.361i 0.456000 0.789815i
\(751\) 1310.00 1.74434 0.872170 0.489202i \(-0.162712\pi\)
0.872170 + 0.489202i \(0.162712\pi\)
\(752\) 462.000 266.736i 0.614362 0.354702i
\(753\) 1169.13i 1.55264i
\(754\) 156.000 270.200i 0.206897 0.358355i
\(755\) 69.2820i 0.0917643i
\(756\) 0 0
\(757\) 218.000 0.287979 0.143989 0.989579i \(-0.454007\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(758\) 124.500 + 71.8801i 0.164248 + 0.0948286i
\(759\) 144.000 0.189723
\(760\) 165.000 + 285.788i 0.217105 + 0.376037i
\(761\) 658.179i 0.864887i −0.901661 0.432444i \(-0.857651\pi\)
0.901661 0.432444i \(-0.142349\pi\)
\(762\) −72.0000 41.5692i −0.0944882 0.0545528i
\(763\) 0 0
\(764\) 232.095i 0.303789i
\(765\) −243.000 + 420.888i −0.317647 + 0.550181i
\(766\) −483.000 + 836.581i −0.630548 + 1.09214i
\(767\) 200.918i 0.261953i
\(768\) 268.500 + 465.056i 0.349609 + 0.605541i
\(769\) −511.000 + 885.078i −0.664499 + 1.15095i 0.314921 + 0.949118i \(0.398022\pi\)
−0.979421 + 0.201829i \(0.935312\pi\)
\(770\) 0 0
\(771\) 524.811i 0.680689i
\(772\) 132.500 229.497i 0.171632 0.297276i
\(773\) −1026.00 592.361i −1.32730 0.766315i −0.342416 0.939549i \(-0.611245\pi\)
−0.984881 + 0.173234i \(0.944578\pi\)
\(774\) 950.896i 1.22855i
\(775\) −208.000 360.267i −0.268387 0.464860i
\(776\) 862.500 497.965i 1.11147 0.641707i
\(777\) 0 0
\(778\) 447.000 774.227i 0.574550 0.995150i
\(779\) 133.368i 0.171204i
\(780\) 41.5692i