Properties

Label 441.3.j.b.275.1
Level $441$
Weight $3$
Character 441.275
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.j (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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 9)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 275.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.275
Dual form 441.3.j.b.263.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-3.00000 - 5.19615i) q^{10} +(1.50000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +(-2.00000 + 3.46410i) q^{13} -10.3923i q^{15} -11.0000 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} +(24.0000 - 13.8564i) q^{23} +(-22.5000 - 12.9904i) q^{24} +(-6.50000 + 11.2583i) q^{25} +(6.00000 + 3.46410i) q^{26} -27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} -18.0000 q^{30} -32.0000 q^{31} -15.5885i q^{32} +(4.50000 - 2.59808i) q^{33} +(13.5000 + 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 - 29.4449i) q^{37} +(-16.5000 - 9.52628i) q^{38} +(6.00000 + 10.3923i) q^{39} +(-15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(1.50000 + 0.866025i) q^{44} +(-27.0000 - 15.5885i) q^{45} +(-24.0000 - 41.5692i) q^{46} +48.4974i q^{47} +(-16.5000 + 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +46.7654i q^{51} +(-2.00000 + 3.46410i) q^{52} +46.7654i q^{54} +6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +(-39.0000 - 67.5500i) q^{58} +50.2295i q^{59} -10.3923i q^{60} -56.0000 q^{61} +55.4256i q^{62} -71.0000 q^{64} +13.8564i q^{65} +(-4.50000 - 7.79423i) q^{66} -31.0000 q^{67} +(-13.5000 + 7.79423i) q^{68} -83.1384i q^{69} -31.1769i q^{71} +(-67.5000 + 38.9711i) q^{72} +(32.5000 + 56.2917i) q^{73} +(-51.0000 - 29.4449i) q^{74} +(19.5000 + 33.7750i) q^{75} +(5.50000 - 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +38.0000 q^{79} +(-33.0000 + 19.0526i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(10.5000 - 18.1865i) q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 - 52.8275i) q^{86} -135.100i q^{87} +(7.50000 - 12.9904i) 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} +84.0000 q^{94} -38.1051i q^{95} +(-40.5000 - 23.3827i) q^{96} +(-57.5000 - 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9} + O(q^{10}) \) \( 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9} - 6 q^{10} + 3 q^{11} + 3 q^{12} - 4 q^{13} - 22 q^{16} - 27 q^{17} - 27 q^{18} + 11 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 45 q^{24} - 13 q^{25} + 12 q^{26} - 54 q^{27} + 78 q^{29} - 36 q^{30} - 64 q^{31} + 9 q^{33} + 27 q^{34} - 9 q^{36} + 34 q^{37} - 33 q^{38} + 12 q^{39} - 30 q^{40} + 21 q^{41} + 61 q^{43} + 3 q^{44} - 54 q^{45} - 48 q^{46} - 33 q^{48} + 39 q^{50} - 4 q^{52} + 12 q^{55} - 33 q^{57} - 78 q^{58} - 112 q^{61} - 142 q^{64} - 9 q^{66} - 62 q^{67} - 27 q^{68} - 135 q^{72} + 65 q^{73} - 102 q^{74} + 39 q^{75} + 11 q^{76} + 36 q^{78} + 76 q^{79} - 66 q^{80} - 81 q^{81} + 21 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} + 216 q^{89} - 54 q^{90} + 48 q^{92} - 96 q^{93} + 168 q^{94} - 81 q^{96} - 115 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 0.866025i −0.901388 0.433013i \(-0.857451\pi\)
0.901388 0.433013i \(-0.142549\pi\)
\(3\) 1.50000 2.59808i 0.500000 0.866025i
\(4\) 1.00000 0.250000
\(5\) 3.00000 1.73205i 0.600000 0.346410i −0.169042 0.985609i \(-0.554067\pi\)
0.769042 + 0.639199i \(0.220734\pi\)
\(6\) −4.50000 2.59808i −0.750000 0.433013i
\(7\) 0 0
\(8\) 8.66025i 1.08253i
\(9\) −4.50000 7.79423i −0.500000 0.866025i
\(10\) −3.00000 5.19615i −0.300000 0.519615i
\(11\) 1.50000 + 0.866025i 0.136364 + 0.0787296i 0.566630 0.823972i \(-0.308247\pi\)
−0.430266 + 0.902702i \(0.641580\pi\)
\(12\) 1.50000 2.59808i 0.125000 0.216506i
\(13\) −2.00000 + 3.46410i −0.153846 + 0.266469i −0.932638 0.360813i \(-0.882499\pi\)
0.778792 + 0.627282i \(0.215833\pi\)
\(14\) 0 0
\(15\) 10.3923i 0.692820i
\(16\) −11.0000 −0.687500
\(17\) −13.5000 + 7.79423i −0.794118 + 0.458484i −0.841410 0.540397i \(-0.818274\pi\)
0.0472925 + 0.998881i \(0.484941\pi\)
\(18\) −13.5000 + 7.79423i −0.750000 + 0.433013i
\(19\) 5.50000 9.52628i 0.289474 0.501383i −0.684211 0.729285i \(-0.739853\pi\)
0.973684 + 0.227901i \(0.0731864\pi\)
\(20\) 3.00000 1.73205i 0.150000 0.0866025i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.0681818 0.118094i
\(23\) 24.0000 13.8564i 1.04348 0.602452i 0.122662 0.992449i \(-0.460857\pi\)
0.920817 + 0.389996i \(0.127524\pi\)
\(24\) −22.5000 12.9904i −0.937500 0.541266i
\(25\) −6.50000 + 11.2583i −0.260000 + 0.450333i
\(26\) 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 \(0.0503586\pi\)
\(30\) −18.0000 −0.600000
\(31\) −32.0000 −1.03226 −0.516129 0.856511i \(-0.672628\pi\)
−0.516129 + 0.856511i \(0.672628\pi\)
\(32\) 15.5885i 0.487139i
\(33\) 4.50000 2.59808i 0.136364 0.0787296i
\(34\) 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 −0.539473 0.842003i \(-0.681376\pi\)
0.998932 + 0.0461958i \(0.0147098\pi\)
\(38\) −16.5000 9.52628i −0.434211 0.250692i
\(39\) 6.00000 + 10.3923i 0.153846 + 0.266469i
\(40\) −15.0000 25.9808i −0.375000 0.649519i
\(41\) 10.5000 + 6.06218i 0.256098 + 0.147858i 0.622553 0.782578i \(-0.286095\pi\)
−0.366456 + 0.930436i \(0.619429\pi\)
\(42\) 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
\(45\) −27.0000 15.5885i −0.600000 0.346410i
\(46\) −24.0000 41.5692i −0.521739 0.903679i
\(47\) 48.4974i 1.03186i 0.856631 + 0.515930i \(0.172554\pi\)
−0.856631 + 0.515930i \(0.827446\pi\)
\(48\) −16.5000 + 28.5788i −0.343750 + 0.595392i
\(49\) 0 0
\(50\) 19.5000 + 11.2583i 0.390000 + 0.225167i
\(51\) 46.7654i 0.916968i
\(52\) −2.00000 + 3.46410i −0.0384615 + 0.0666173i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 46.7654i 0.866025i
\(55\) 6.00000 0.109091
\(56\) 0 0
\(57\) −16.5000 28.5788i −0.289474 0.501383i
\(58\) −39.0000 67.5500i −0.672414 1.16465i
\(59\) 50.2295i 0.851347i 0.904877 + 0.425674i \(0.139963\pi\)
−0.904877 + 0.425674i \(0.860037\pi\)
\(60\) 10.3923i 0.173205i
\(61\) −56.0000 −0.918033 −0.459016 0.888428i \(-0.651798\pi\)
−0.459016 + 0.888428i \(0.651798\pi\)
\(62\) 55.4256i 0.893962i
\(63\) 0 0
\(64\) −71.0000 −1.10938
\(65\) 13.8564i 0.213175i
\(66\) −4.50000 7.79423i −0.0681818 0.118094i
\(67\) −31.0000 −0.462687 −0.231343 0.972872i \(-0.574312\pi\)
−0.231343 + 0.972872i \(0.574312\pi\)
\(68\) −13.5000 + 7.79423i −0.198529 + 0.114621i
\(69\) 83.1384i 1.20490i
\(70\) 0 0
\(71\) 31.1769i 0.439111i −0.975600 0.219556i \(-0.929539\pi\)
0.975600 0.219556i \(-0.0704608\pi\)
\(72\) −67.5000 + 38.9711i −0.937500 + 0.541266i
\(73\) 32.5000 + 56.2917i 0.445205 + 0.771119i 0.998067 0.0621550i \(-0.0197973\pi\)
−0.552861 + 0.833273i \(0.686464\pi\)
\(74\) −51.0000 29.4449i −0.689189 0.397904i
\(75\) 19.5000 + 33.7750i 0.260000 + 0.450333i
\(76\) 5.50000 9.52628i 0.0723684 0.125346i
\(77\) 0 0
\(78\) 18.0000 10.3923i 0.230769 0.133235i
\(79\) 38.0000 0.481013 0.240506 0.970648i \(-0.422687\pi\)
0.240506 + 0.970648i \(0.422687\pi\)
\(80\) −33.0000 + 19.0526i −0.412500 + 0.238157i
\(81\) −40.5000 + 70.1481i −0.500000 + 0.866025i
\(82\) 10.5000 18.1865i 0.128049 0.221787i
\(83\) 42.0000 24.2487i 0.506024 0.292153i −0.225174 0.974319i \(-0.572295\pi\)
0.731198 + 0.682165i \(0.238962\pi\)
\(84\) 0 0
\(85\) −27.0000 + 46.7654i −0.317647 + 0.550181i
\(86\) 91.5000 52.8275i 1.06395 0.614274i
\(87\) 135.100i 1.55287i
\(88\) 7.50000 12.9904i 0.0852273 0.147618i
\(89\) 108.000 + 62.3538i 1.21348 + 0.700605i 0.963516 0.267650i \(-0.0862469\pi\)
0.249967 + 0.968254i \(0.419580\pi\)
\(90\) −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
\(94\) 84.0000 0.893617
\(95\) 38.1051i 0.401107i
\(96\) −40.5000 23.3827i −0.421875 0.243570i
\(97\) −57.5000 99.5929i −0.592784 1.02673i −0.993856 0.110685i \(-0.964696\pi\)
0.401072 0.916047i \(-0.368638\pi\)
\(98\) 0 0
\(99\) 15.5885i 0.157459i
\(100\) −6.50000 + 11.2583i −0.0650000 + 0.112583i
\(101\) 39.0000 + 22.5167i 0.386139 + 0.222937i 0.680486 0.732761i \(-0.261769\pi\)
−0.294347 + 0.955699i \(0.595102\pi\)
\(102\) 81.0000 0.794118
\(103\) −20.0000 34.6410i −0.194175 0.336321i 0.752455 0.658644i \(-0.228870\pi\)
−0.946630 + 0.322323i \(0.895536\pi\)
\(104\) 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 \(-0.105754\pi\)
0.190198 + 0.981746i \(0.439087\pi\)
\(108\) −27.0000 −0.250000
\(109\) 26.0000 + 45.0333i 0.238532 + 0.413150i 0.960293 0.278992i \(-0.0900004\pi\)
−0.721761 + 0.692142i \(0.756667\pi\)
\(110\) 10.3923i 0.0944755i
\(111\) −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 \(0.797144\pi\)
\(114\) −49.5000 + 28.5788i −0.434211 + 0.250692i
\(115\) 48.0000 83.1384i 0.417391 0.722943i
\(116\) 39.0000 22.5167i 0.336207 0.194109i
\(117\) 36.0000 0.307692
\(118\) 87.0000 0.737288
\(119\) 0 0
\(120\) −90.0000 −0.750000
\(121\) −59.0000 102.191i −0.487603 0.844554i
\(122\) 96.9948i 0.795040i
\(123\) 31.5000 18.1865i 0.256098 0.147858i
\(124\) −32.0000 −0.258065
\(125\) 131.636i 1.05309i
\(126\) 0 0
\(127\) −16.0000 −0.125984 −0.0629921 0.998014i \(-0.520064\pi\)
−0.0629921 + 0.998014i \(0.520064\pi\)
\(128\) 60.6218i 0.473608i
\(129\) 183.000 1.41860
\(130\) 24.0000 0.184615
\(131\) 138.000 79.6743i 1.05344 0.608201i 0.129826 0.991537i \(-0.458558\pi\)
0.923609 + 0.383336i \(0.125225\pi\)
\(132\) 4.50000 2.59808i 0.0340909 0.0196824i
\(133\) 0 0
\(134\) 53.6936i 0.400698i
\(135\) −81.0000 + 46.7654i −0.600000 + 0.346410i
\(136\) 67.5000 + 116.913i 0.496324 + 0.859658i
\(137\) 163.500 + 94.3968i 1.19343 + 0.689028i 0.959083 0.283125i \(-0.0913712\pi\)
0.234348 + 0.972153i \(0.424705\pi\)
\(138\) −144.000 −1.04348
\(139\) 2.50000 4.33013i 0.0179856 0.0311520i −0.856893 0.515495i \(-0.827608\pi\)
0.874878 + 0.484343i \(0.160941\pi\)
\(140\) 0 0
\(141\) 126.000 + 72.7461i 0.893617 + 0.515930i
\(142\) −54.0000 −0.380282
\(143\) −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
\(149\) 132.000 76.2102i 0.885906 0.511478i 0.0133049 0.999911i \(-0.495765\pi\)
0.872601 + 0.488433i \(0.162431\pi\)
\(150\) 58.5000 33.7750i 0.390000 0.225167i
\(151\) −10.0000 + 17.3205i −0.0662252 + 0.114705i −0.897237 0.441550i \(-0.854429\pi\)
0.831012 + 0.556255i \(0.187762\pi\)
\(152\) −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
\(156\) 6.00000 + 10.3923i 0.0384615 + 0.0666173i
\(157\) 40.0000 0.254777 0.127389 0.991853i \(-0.459340\pi\)
0.127389 + 0.991853i \(0.459340\pi\)
\(158\) 65.8179i 0.416569i
\(159\) 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 −0.656390 0.754422i \(-0.727917\pi\)
0.981543 + 0.191240i \(0.0612507\pi\)
\(164\) 10.5000 + 6.06218i 0.0640244 + 0.0369645i
\(165\) 9.00000 15.5885i 0.0545455 0.0944755i
\(166\) −42.0000 72.7461i −0.253012 0.438230i
\(167\) −165.000 95.2628i −0.988024 0.570436i −0.0833409 0.996521i \(-0.526559\pi\)
−0.904683 + 0.426085i \(0.859892\pi\)
\(168\) 0 0
\(169\) 76.5000 + 132.502i 0.452663 + 0.784035i
\(170\) 81.0000 + 46.7654i 0.476471 + 0.275090i
\(171\) −99.0000 −0.578947
\(172\) 30.5000 + 52.8275i 0.177326 + 0.307137i
\(173\) 232.095i 1.34159i −0.741644 0.670794i \(-0.765953\pi\)
0.741644 0.670794i \(-0.234047\pi\)
\(174\) −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
\(178\) 108.000 187.061i 0.606742 1.05091i
\(179\) 54.0000 31.1769i 0.301676 0.174173i −0.341520 0.939875i \(-0.610942\pi\)
0.643196 + 0.765702i \(0.277608\pi\)
\(180\) −27.0000 15.5885i −0.150000 0.0866025i
\(181\) 232.000 1.28177 0.640884 0.767638i \(-0.278568\pi\)
0.640884 + 0.767638i \(0.278568\pi\)
\(182\) 0 0
\(183\) −84.0000 + 145.492i −0.459016 + 0.795040i
\(184\) −120.000 207.846i −0.652174 1.12960i
\(185\) 117.779i 0.636646i
\(186\) 144.000 + 83.1384i 0.774194 + 0.446981i
\(187\) −27.0000 −0.144385
\(188\) 48.4974i 0.257965i
\(189\) 0 0
\(190\) −66.0000 −0.347368
\(191\) 232.095i 1.21516i 0.794260 + 0.607578i \(0.207859\pi\)
−0.794260 + 0.607578i \(0.792141\pi\)
\(192\) −106.500 + 184.463i −0.554688 + 0.960747i
\(193\) −265.000 −1.37306 −0.686528 0.727103i \(-0.740866\pi\)
−0.686528 + 0.727103i \(0.740866\pi\)
\(194\) −172.500 + 99.5929i −0.889175 + 0.513366i
\(195\) 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 \(0.897487\pi\)
\(198\) −27.0000 −0.136364
\(199\) 145.000 + 251.147i 0.728643 + 1.26205i 0.957457 + 0.288577i \(0.0931821\pi\)
−0.228814 + 0.973470i \(0.573485\pi\)
\(200\) 97.5000 + 56.2917i 0.487500 + 0.281458i
\(201\) −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
\(205\) 42.0000 0.204878
\(206\) −60.0000 + 34.6410i −0.291262 + 0.168160i
\(207\) −216.000 124.708i −1.04348 0.602452i
\(208\) 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
\(213\) −81.0000 46.7654i −0.380282 0.219556i
\(214\) 121.500 210.444i 0.567757 0.983384i
\(215\) 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
\(219\) 195.000 0.890411
\(220\) 6.00000 0.0272727
\(221\) 62.3538i 0.282144i
\(222\) −153.000 + 88.3346i −0.689189 + 0.397904i
\(223\) −26.0000 45.0333i −0.116592 0.201943i 0.801823 0.597562i \(-0.203864\pi\)
−0.918415 + 0.395618i \(0.870530\pi\)
\(224\) 0 0
\(225\) 117.000 0.520000
\(226\) −78.0000 + 135.100i −0.345133 + 0.597787i
\(227\) −163.500 94.3968i −0.720264 0.415845i 0.0945856 0.995517i \(-0.469847\pi\)
−0.814850 + 0.579672i \(0.803181\pi\)
\(228\) −16.5000 28.5788i −0.0723684 0.125346i
\(229\) 133.000 + 230.363i 0.580786 + 1.00595i 0.995386 + 0.0959473i \(0.0305880\pi\)
−0.414600 + 0.910004i \(0.636079\pi\)
\(230\) −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 \(-0.476539\pi\)
−0.826856 + 0.562414i \(0.809873\pi\)
\(234\) 62.3538i 0.266469i
\(235\) 84.0000 + 145.492i 0.357447 + 0.619116i
\(236\) 50.2295i 0.212837i
\(237\) 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 \(0.984500\pi\)
\(240\) 114.315i 0.476314i
\(241\) 59.5000 103.057i 0.246888 0.427623i −0.715773 0.698333i \(-0.753925\pi\)
0.962661 + 0.270711i \(0.0872587\pi\)
\(242\) −177.000 + 102.191i −0.731405 + 0.422277i
\(243\) 121.500 + 210.444i 0.500000 + 0.866025i
\(244\) −56.0000 −0.229508
\(245\) 0 0
\(246\) −31.5000 54.5596i −0.128049 0.221787i
\(247\) 22.0000 + 38.1051i 0.0890688 + 0.154272i
\(248\) 277.128i 1.11745i
\(249\) 145.492i 0.584306i
\(250\) 228.000 0.912000
\(251\) 389.711i 1.55264i 0.630342 + 0.776318i \(0.282915\pi\)
−0.630342 + 0.776318i \(0.717085\pi\)
\(252\) 0 0
\(253\) 48.0000 0.189723
\(254\) 27.7128i 0.109106i
\(255\) 81.0000 + 140.296i 0.317647 + 0.550181i
\(256\) −179.000 −0.699219
\(257\) 151.500 87.4686i 0.589494 0.340345i −0.175403 0.984497i \(-0.556123\pi\)
0.764897 + 0.644152i \(0.222790\pi\)
\(258\) 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
\(263\) −39.0000 22.5167i −0.148289 0.0856147i 0.424020 0.905653i \(-0.360619\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(264\) −22.5000 38.9711i −0.0852273 0.147618i
\(265\) 0 0
\(266\) 0 0
\(267\) 324.000 187.061i 1.21348 0.700605i
\(268\) −31.0000 −0.115672
\(269\) 162.000 93.5307i 0.602230 0.347698i −0.167688 0.985840i \(-0.553630\pi\)
0.769919 + 0.638142i \(0.220297\pi\)
\(270\) 81.0000 + 140.296i 0.300000 + 0.519615i
\(271\) −134.000 + 232.095i −0.494465 + 0.856438i −0.999980 0.00637958i \(-0.997969\pi\)
0.505515 + 0.862818i \(0.331303\pi\)
\(272\) 148.500 85.7365i 0.545956 0.315208i
\(273\) 0 0
\(274\) 163.500 283.190i 0.596715 1.03354i
\(275\) −19.5000 + 11.2583i −0.0709091 + 0.0409394i
\(276\) 83.1384i 0.301226i
\(277\) −28.0000 + 48.4974i −0.101083 + 0.175081i −0.912131 0.409899i \(-0.865564\pi\)
0.811048 + 0.584979i \(0.198897\pi\)
\(278\) −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
\(283\) −374.000 −1.32155 −0.660777 0.750582i \(-0.729773\pi\)
−0.660777 + 0.750582i \(0.729773\pi\)
\(284\) 31.1769i 0.109778i
\(285\) −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
\(290\) −234.000 135.100i −0.806897 0.465862i
\(291\) −345.000 −1.18557
\(292\) 32.5000 + 56.2917i 0.111301 + 0.192780i
\(293\) −219.000 126.440i −0.747440 0.431535i 0.0773280 0.997006i \(-0.475361\pi\)
−0.824768 + 0.565471i \(0.808694\pi\)
\(294\) 0 0
\(295\) 87.0000 + 150.688i 0.294915 + 0.510808i
\(296\) −255.000 147.224i −0.861486 0.497379i
\(297\) −40.5000 23.3827i −0.136364 0.0787296i
\(298\) −132.000 228.631i −0.442953 0.767217i
\(299\) 110.851i 0.370740i
\(300\) 19.5000 + 33.7750i 0.0650000 + 0.112583i
\(301\) 0 0
\(302\) 30.0000 + 17.3205i 0.0993377 + 0.0573527i
\(303\) 117.000 67.5500i 0.386139 0.222937i
\(304\) −60.5000 + 104.789i −0.199013 + 0.344701i
\(305\) −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 \(-0.834645\pi\)
−0.868078 + 0.496428i \(0.834645\pi\)
\(308\) 0 0
\(309\) −120.000 −0.388350
\(310\) 96.0000 + 166.277i 0.309677 + 0.536377i
\(311\) 245.951i 0.790840i −0.918500 0.395420i \(-0.870599\pi\)
0.918500 0.395420i \(-0.129401\pi\)
\(312\) 90.0000 51.9615i 0.288462 0.166543i
\(313\) −155.000 −0.495208 −0.247604 0.968861i \(-0.579643\pi\)
−0.247604 + 0.968861i \(0.579643\pi\)
\(314\) 69.2820i 0.220643i
\(315\) 0 0
\(316\) 38.0000 0.120253
\(317\) 48.4974i 0.152989i −0.997070 0.0764944i \(-0.975627\pi\)
0.997070 0.0764944i \(-0.0243727\pi\)
\(318\) 0 0
\(319\) 78.0000 0.244514
\(320\) −213.000 + 122.976i −0.665625 + 0.384299i
\(321\) 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
\(326\) −159.000 91.7987i −0.487730 0.281591i
\(327\) 156.000 0.477064
\(328\) 52.5000 90.9327i 0.160061 0.277234i
\(329\) 0 0
\(330\) −27.0000 15.5885i −0.0818182 0.0472377i
\(331\) 2.00000 0.00604230 0.00302115 0.999995i \(-0.499038\pi\)
0.00302115 + 0.999995i \(0.499038\pi\)
\(332\) 42.0000 24.2487i 0.126506 0.0730383i
\(333\) −306.000 −0.918919
\(334\) −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 \(0.203111\pi\)
\(338\) 229.500 132.502i 0.678994 0.392017i
\(339\) −234.000 + 135.100i −0.690265 + 0.398525i
\(340\) −27.0000 + 46.7654i −0.0794118 + 0.137545i
\(341\) −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
\(345\) −144.000 249.415i −0.417391 0.722943i
\(346\) −402.000 −1.16185
\(347\) 112.583i 0.324448i −0.986754 0.162224i \(-0.948133\pi\)
0.986754 0.162224i \(-0.0518666\pi\)
\(348\) 135.100i 0.388218i
\(349\) 208.000 + 360.267i 0.595989 + 1.03228i 0.993407 + 0.114645i \(0.0365730\pi\)
−0.397418 + 0.917638i \(0.630094\pi\)
\(350\) 0 0
\(351\) 54.0000 93.5307i 0.153846 0.266469i
\(352\) 13.5000 23.3827i 0.0383523 0.0664281i
\(353\) −1.50000 0.866025i −0.00424929 0.00245333i 0.497874 0.867249i \(-0.334114\pi\)
−0.502123 + 0.864796i \(0.667448\pi\)
\(354\) 130.500 226.033i 0.368644 0.638510i
\(355\) −54.0000 93.5307i −0.152113 0.263467i
\(356\) 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 \(-0.642167\pi\)
−0.997039 + 0.0768913i \(0.975501\pi\)
\(360\) −135.000 + 233.827i −0.375000 + 0.649519i
\(361\) 120.000 + 207.846i 0.332410 + 0.575751i
\(362\) 401.836i 1.11004i
\(363\) −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
\(367\) −179.000 + 310.037i −0.487738 + 0.844788i −0.999901 0.0141011i \(-0.995511\pi\)
0.512162 + 0.858889i \(0.328845\pi\)
\(368\) −264.000 + 152.420i −0.717391 + 0.414186i
\(369\) 109.119i 0.295716i
\(370\) −204.000 −0.551351
\(371\) 0 0
\(372\) −48.0000 + 83.1384i −0.129032 + 0.223490i
\(373\) 290.000 + 502.295i 0.777480 + 1.34663i 0.933390 + 0.358863i \(0.116836\pi\)
−0.155910 + 0.987771i \(0.549831\pi\)
\(374\) 46.7654i 0.125041i
\(375\) 342.000 + 197.454i 0.912000 + 0.526543i
\(376\) 420.000 1.11702
\(377\) 180.133i 0.477807i
\(378\) 0 0
\(379\) 83.0000 0.218997 0.109499 0.993987i \(-0.465075\pi\)
0.109499 + 0.993987i \(0.465075\pi\)
\(380\) 38.1051i 0.100277i
\(381\) −24.0000 + 41.5692i −0.0629921 + 0.109106i
\(382\) 402.000 1.05236
\(383\) −483.000 + 278.860i −1.26110 + 0.728094i −0.973287 0.229593i \(-0.926260\pi\)
−0.287810 + 0.957688i \(0.592927\pi\)
\(384\) 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
\(389\) 447.000 + 258.076i 1.14910 + 0.663433i 0.948668 0.316274i \(-0.102432\pi\)
0.200432 + 0.979708i \(0.435765\pi\)
\(390\) 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
\(394\) 216.000 0.548223
\(395\) 114.000 65.8179i 0.288608 0.166628i
\(396\) 15.5885i 0.0393648i
\(397\) 181.000 313.501i 0.455919 0.789676i −0.542821 0.839848i \(-0.682644\pi\)
0.998741 + 0.0501728i \(0.0159772\pi\)
\(398\) 435.000 251.147i 1.09296 0.631024i
\(399\) 0 0
\(400\) 71.5000 123.842i 0.178750 0.309604i
\(401\) −340.500 + 196.588i −0.849127 + 0.490244i −0.860356 0.509693i \(-0.829759\pi\)
0.0112291 + 0.999937i \(0.496426\pi\)
\(402\) 139.500 + 80.5404i 0.347015 + 0.200349i
\(403\) 64.0000 110.851i 0.158809 0.275065i
\(404\) 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
\(408\) 405.000 0.992647
\(409\) −221.000 −0.540342 −0.270171 0.962812i \(-0.587080\pi\)
−0.270171 + 0.962812i \(0.587080\pi\)
\(410\) 72.7461i 0.177430i
\(411\) 490.500 283.190i 1.19343 0.689028i
\(412\) −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
\(416\) 54.0000 + 31.1769i 0.129808 + 0.0749445i
\(417\) −7.50000 12.9904i −0.0179856 0.0311520i
\(418\) −16.5000 28.5788i −0.0394737 0.0683704i
\(419\) −678.000 391.443i −1.61814 0.934233i −0.987401 0.158236i \(-0.949419\pi\)
−0.630737 0.775997i \(-0.717247\pi\)
\(420\) 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
\(425\) 202.650i 0.476823i
\(426\) −81.0000 + 140.296i −0.190141 + 0.329334i
\(427\) 0 0
\(428\) 121.500 + 70.1481i 0.283879 + 0.163897i
\(429\) 20.7846i 0.0484490i
\(430\) 183.000 316.965i 0.425581 0.737129i
\(431\) −243.000 + 140.296i −0.563805 + 0.325513i −0.754671 0.656103i \(-0.772204\pi\)
0.190866 + 0.981616i \(0.438870\pi\)
\(432\) 297.000 0.687500
\(433\) 295.000 0.681293 0.340647 0.940191i \(-0.389354\pi\)
0.340647 + 0.940191i \(0.389354\pi\)
\(434\) 0 0
\(435\) −234.000 405.300i −0.537931 0.931724i
\(436\) 26.0000 + 45.0333i 0.0596330 + 0.103287i
\(437\) 304.841i 0.697577i
\(438\) 337.750i 0.771119i
\(439\) −812.000 −1.84966 −0.924829 0.380383i \(-0.875792\pi\)
−0.924829 + 0.380383i \(0.875792\pi\)
\(440\) 51.9615i 0.118094i
\(441\) 0 0
\(442\) −108.000 −0.244344
\(443\) 91.7987i 0.207221i 0.994618 + 0.103610i \(0.0330395\pi\)
−0.994618 + 0.103610i \(0.966961\pi\)
\(444\) −51.0000 88.3346i −0.114865 0.198952i
\(445\) 432.000 0.970787
\(446\) −78.0000 + 45.0333i −0.174888 + 0.100972i
\(447\) 457.261i 1.02296i
\(448\) 0 0
\(449\) 639.127i 1.42344i −0.702461 0.711722i \(-0.747915\pi\)
0.702461 0.711722i \(-0.252085\pi\)
\(450\) 202.650i 0.450333i
\(451\) 10.5000 + 18.1865i 0.0232816 + 0.0403249i
\(452\) −78.0000 45.0333i −0.172566 0.0996312i
\(453\) 30.0000 + 51.9615i 0.0662252 + 0.114705i
\(454\) −163.500 + 283.190i −0.360132 + 0.623767i
\(455\) 0 0
\(456\) −247.500 + 142.894i −0.542763 + 0.313364i
\(457\) 65.0000 0.142232 0.0711160 0.997468i \(-0.477344\pi\)
0.0711160 + 0.997468i \(0.477344\pi\)
\(458\) 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 0.496753 0.867892i \(-0.334525\pi\)
0.999993 + 0.00374501i \(0.00119208\pi\)
\(462\) 0 0
\(463\) −367.000 + 635.663i −0.792657 + 1.37292i 0.131660 + 0.991295i \(0.457969\pi\)
−0.924317 + 0.381627i \(0.875364\pi\)
\(464\) −429.000 + 247.683i −0.924569 + 0.533800i
\(465\) 332.554i 0.715169i
\(466\) −175.500 + 303.975i −0.376609 + 0.652307i
\(467\) −175.500 101.325i −0.375803 0.216970i 0.300188 0.953880i \(-0.402951\pi\)
−0.675991 + 0.736910i \(0.736284\pi\)
\(468\) 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
\(472\) 435.000 0.921610
\(473\) 105.655i 0.223372i
\(474\) −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
\(479\) 525.000 + 303.109i 1.09603 + 0.632795i 0.935176 0.354183i \(-0.115241\pi\)
0.160857 + 0.986978i \(0.448574\pi\)
\(480\) −162.000 −0.337500
\(481\) 68.0000 + 117.779i 0.141372 + 0.244864i
\(482\) −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 0.915296 0.402781i \(-0.131956\pi\)
−0.806467 + 0.591279i \(0.798623\pi\)
\(488\) 484.974i 0.993800i
\(489\) −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 \(0.742040\pi\)
\(492\) 31.5000 18.1865i 0.0640244 0.0369645i
\(493\) −351.000 + 607.950i −0.711968 + 1.23316i
\(494\) 66.0000 38.1051i 0.133603 0.0771359i
\(495\) −27.0000 46.7654i −0.0545455 0.0944755i
\(496\) 352.000 0.709677
\(497\) 0 0
\(498\) −252.000 −0.506024
\(499\) 393.500 + 681.562i 0.788577 + 1.36586i 0.926839 + 0.375460i \(0.122515\pi\)
−0.138261 + 0.990396i \(0.544151\pi\)
\(500\) 131.636i 0.263272i
\(501\) −495.000 + 285.788i −0.988024 + 0.570436i
\(502\) 675.000 1.34462
\(503\) 623.538i 1.23964i −0.784745 0.619819i \(-0.787206\pi\)
0.784745 0.619819i \(-0.212794\pi\)
\(504\) 0 0
\(505\) 156.000 0.308911
\(506\) 83.1384i 0.164305i
\(507\) 459.000 0.905325
\(508\) −16.0000 −0.0314961
\(509\) −186.000 + 107.387i −0.365422 + 0.210977i −0.671457 0.741044i \(-0.734331\pi\)
0.306034 + 0.952020i \(0.400998\pi\)
\(510\) 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
\(515\) −120.000 69.2820i −0.233010 0.134528i
\(516\) 183.000 0.354651
\(517\) −42.0000 + 72.7461i −0.0812379 + 0.140708i
\(518\) 0 0
\(519\) −603.000 348.142i −1.16185 0.670794i
\(520\) 120.000 0.230769
\(521\) 175.500 101.325i 0.336852 0.194482i −0.322027 0.946730i \(-0.604364\pi\)
0.658879 + 0.752249i \(0.271031\pi\)
\(522\) −351.000 + 607.950i −0.672414 + 1.16465i
\(523\) −125.000 + 216.506i −0.239006 + 0.413970i −0.960429 0.278524i \(-0.910155\pi\)
0.721424 + 0.692494i \(0.243488\pi\)
\(524\) 138.000 79.6743i 0.263359 0.152050i
\(525\) 0 0
\(526\) −39.0000 + 67.5500i −0.0741445 + 0.128422i
\(527\) 432.000 249.415i 0.819734 0.473274i
\(528\) −49.5000 + 28.5788i −0.0937500 + 0.0541266i
\(529\) 119.500 206.980i 0.225898 0.391267i
\(530\) 0 0
\(531\) 391.500 226.033i 0.737288 0.425674i
\(532\) 0 0
\(533\) −42.0000 + 24.2487i −0.0787992 + 0.0454948i
\(534\) −324.000 561.184i −0.606742 1.05091i
\(535\) 486.000 0.908411
\(536\) 268.468i 0.500873i
\(537\) 187.061i 0.348345i
\(538\) −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 0.391970 + 0.919978i \(0.371794\pi\)
−0.992709 + 0.120533i \(0.961540\pi\)
\(542\) 402.000 + 232.095i 0.741697 + 0.428219i
\(543\) 348.000 602.754i 0.640884 1.11004i
\(544\) 121.500 + 210.444i 0.223346 + 0.386846i
\(545\) 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
\(551\) 495.367i 0.899032i
\(552\) −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
\(556\) 2.50000 4.33013i 0.00449640 0.00778800i
\(557\) 459.000 265.004i 0.824057 0.475770i −0.0277562 0.999615i \(-0.508836\pi\)
0.851814 + 0.523845i \(0.175503\pi\)
\(558\) 432.000 249.415i 0.774194 0.446981i
\(559\) −244.000 −0.436494
\(560\) 0 0
\(561\) −40.5000 + 70.1481i −0.0721925 + 0.125041i
\(562\) 42.0000 + 72.7461i 0.0747331 + 0.129442i
\(563\) 112.583i 0.199970i 0.994989 + 0.0999852i \(0.0318795\pi\)
−0.994989 + 0.0999852i \(0.968120\pi\)
\(564\) 126.000 + 72.7461i 0.223404 + 0.128983i
\(565\) −312.000 −0.552212
\(566\) 647.787i 1.14450i
\(567\) 0 0
\(568\) −270.000 −0.475352
\(569\) 652.983i 1.14760i 0.818996 + 0.573799i \(0.194531\pi\)
−0.818996 + 0.573799i \(0.805469\pi\)
\(570\) −99.0000 + 171.473i −0.173684 + 0.300830i
\(571\) 545.000 0.954466 0.477233 0.878777i \(-0.341640\pi\)
0.477233 + 0.878777i \(0.341640\pi\)
\(572\) −6.00000 + 3.46410i −0.0104895 + 0.00605612i
\(573\) 603.000 + 348.142i 1.05236 + 0.607578i
\(574\) 0 0
\(575\) 360.267i 0.626551i
\(576\) 319.500 + 553.390i 0.554688 + 0.960747i
\(577\) −435.500 754.308i −0.754766 1.30729i −0.945491 0.325650i \(-0.894417\pi\)
0.190725 0.981644i \(-0.438916\pi\)
\(578\) 69.0000 + 39.8372i 0.119377 + 0.0689224i
\(579\) −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 −0.498722 0.866762i \(-0.666197\pi\)
0.501277 + 0.865287i \(0.332864\pi\)
\(588\) 0 0
\(589\) −176.000 + 304.841i −0.298812 + 0.517557i
\(590\) 261.000 150.688i 0.442373 0.255404i
\(591\) 324.000 + 187.061i 0.548223 + 0.316517i
\(592\) −187.000 + 323.894i −0.315878 + 0.547117i
\(593\) 162.000 + 93.5307i 0.273187 + 0.157725i 0.630335 0.776323i \(-0.282917\pi\)
−0.357148 + 0.934048i \(0.616251\pi\)
\(594\) −40.5000 + 70.1481i −0.0681818 + 0.118094i
\(595\) 0 0
\(596\) 132.000 76.2102i 0.221477 0.127870i
\(597\) 870.000 1.45729
\(598\) 192.000 0.321070
\(599\) 564.649i 0.942652i −0.881959 0.471326i \(-0.843776\pi\)
0.881959 0.471326i \(-0.156224\pi\)
\(600\) 292.500 168.875i 0.487500 0.281458i
\(601\) 230.500 + 399.238i 0.383527 + 0.664289i 0.991564 0.129620i \(-0.0413758\pi\)
−0.608036 + 0.793909i \(0.708042\pi\)
\(602\) 0 0
\(603\) 139.500 + 241.621i 0.231343 + 0.400698i
\(604\) −10.0000 + 17.3205i −0.0165563 + 0.0286763i
\(605\) −354.000 204.382i −0.585124 0.337821i
\(606\) −117.000 202.650i −0.193069 0.334406i
\(607\) −56.0000 96.9948i −0.0922570 0.159794i 0.816204 0.577765i \(-0.196075\pi\)
−0.908461 + 0.417971i \(0.862741\pi\)
\(608\) −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
\(612\) 121.500 + 70.1481i 0.198529 + 0.114621i
\(613\) −451.000 781.155i −0.735726 1.27431i −0.954404 0.298518i \(-0.903508\pi\)
0.218678 0.975797i \(-0.429826\pi\)
\(614\) 923.183i 1.50356i
\(615\) 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 \(0.759570\pi\)
\(618\) 207.846i 0.336321i
\(619\) −399.500 + 691.954i −0.645396 + 1.11786i 0.338814 + 0.940853i \(0.389974\pi\)
−0.984210 + 0.177005i \(0.943359\pi\)
\(620\) −96.0000 + 55.4256i −0.154839 + 0.0893962i
\(621\) −648.000 + 374.123i −1.04348 + 0.602452i
\(622\) −426.000 −0.684887
\(623\) 0 0
\(624\) −66.0000 114.315i −0.105769 0.183198i
\(625\) 65.5000 + 113.449i 0.104800 + 0.181519i
\(626\) 268.468i 0.428862i
\(627\) 57.1577i 0.0911606i
\(628\) 40.0000 0.0636943
\(629\) 530.008i 0.842619i
\(630\) 0 0
\(631\) 830.000 1.31537 0.657686 0.753292i \(-0.271535\pi\)
0.657686 + 0.753292i \(0.271535\pi\)
\(632\) 329.090i 0.520711i
\(633\) −141.000 244.219i −0.222749 0.385812i
\(634\) −84.0000 −0.132492
\(635\) −48.0000 + 27.7128i −0.0755906 + 0.0436422i
\(636\) 0 0
\(637\) 0 0
\(638\) 135.100i 0.211755i
\(639\) −243.000 + 140.296i −0.380282 + 0.219556i
\(640\) 105.000 + 181.865i 0.164062 + 0.284165i
\(641\) 325.500 + 187.928i 0.507800 + 0.293179i 0.731929 0.681381i \(-0.238620\pi\)
−0.224129 + 0.974560i \(0.571954\pi\)
\(642\) −364.500 631.333i −0.567757 0.983384i
\(643\) −6.50000 + 11.2583i −0.0101089 + 0.0175091i −0.871036 0.491220i \(-0.836551\pi\)
0.860927 + 0.508729i \(0.169884\pi\)
\(644\) 0 0
\(645\) 549.000 316.965i 0.851163 0.491419i
\(646\) 297.000 0.459752
\(647\) −405.000 + 233.827i −0.625966 + 0.361402i −0.779188 0.626790i \(-0.784368\pi\)
0.153222 + 0.988192i \(0.451035\pi\)
\(648\) 607.500 + 350.740i 0.937500 + 0.541266i
\(649\) −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
\(653\) −327.000 + 188.794i −0.500766 + 0.289117i −0.729030 0.684482i \(-0.760028\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(654\) 270.200i 0.413150i
\(655\) 276.000 478.046i 0.421374 0.729841i
\(656\) −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
\(661\) 382.000 0.577912 0.288956 0.957342i \(-0.406692\pi\)
0.288956 + 0.957342i \(0.406692\pi\)
\(662\) 3.46410i 0.00523278i
\(663\) −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
\(668\) −165.000 95.2628i −0.247006 0.142609i
\(669\) −156.000 −0.233184
\(670\) 93.0000 + 161.081i 0.138806 + 0.240419i
\(671\) −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
\(675\) 175.500 303.975i 0.260000 0.450333i
\(676\) 76.5000 + 132.502i 0.113166 + 0.196009i
\(677\) 699.749i 1.03360i −0.856106 0.516801i \(-0.827123\pi\)
0.856106 0.516801i \(-0.172877\pi\)
\(678\) 234.000 + 405.300i 0.345133 + 0.597787i
\(679\) 0 0
\(680\) 405.000 + 233.827i 0.595588 + 0.343863i
\(681\) −490.500 + 283.190i −0.720264 + 0.415845i
\(682\) −48.0000 + 83.1384i −0.0703812 + 0.121904i
\(683\) −904.500 + 522.213i −1.32430 + 0.764588i −0.984412 0.175877i \(-0.943724\pi\)
−0.339892 + 0.940464i \(0.610391\pi\)
\(684\) −99.0000 −0.144737
\(685\) 654.000 0.954745
\(686\) 0 0
\(687\) 798.000 1.16157
\(688\) −335.500 581.103i −0.487645 0.844627i
\(689\) 0 0
\(690\) −432.000 + 249.415i −0.626087 + 0.361471i
\(691\) −182.000 −0.263386 −0.131693 0.991291i \(-0.542041\pi\)
−0.131693 + 0.991291i \(0.542041\pi\)
\(692\) 232.095i 0.335397i
\(693\) 0 0
\(694\) −195.000 −0.280980
\(695\) 17.3205i 0.0249216i
\(696\) −1170.00 −1.68103
\(697\) −189.000 −0.271162
\(698\) 624.000 360.267i 0.893983 0.516141i
\(699\) −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
\(704\) −106.500 61.4878i −0.151278 0.0873406i
\(705\) 504.000 0.714894
\(706\) −1.50000 + 2.59808i −0.00212465 + 0.00367999i
\(707\) 0 0
\(708\) 130.500 + 75.3442i 0.184322 + 0.106418i
\(709\) −700.000 −0.987306 −0.493653 0.869659i \(-0.664339\pi\)
−0.493653 + 0.869659i \(0.664339\pi\)
\(710\) −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
\(716\) 54.0000 31.1769i 0.0754190 0.0435432i
\(717\) −1044.00 + 602.754i −1.45607 + 0.840661i
\(718\) −513.000 + 888.542i −0.714485 + 1.23752i
\(719\) −513.000 296.181i −0.713491 0.411934i 0.0988613 0.995101i \(-0.468480\pi\)
−0.812352 + 0.583167i \(0.801813\pi\)
\(720\) 297.000 + 171.473i 0.412500 + 0.238157i
\(721\) 0 0
\(722\) 360.000 207.846i 0.498615 0.287875i
\(723\) −178.500 309.171i −0.246888 0.427623i
\(724\) 232.000 0.320442
\(725\) 585.433i 0.807494i
\(726\) 613.146i 0.844554i
\(727\) −332.000 575.041i −0.456671 0.790978i 0.542111 0.840307i \(-0.317625\pi\)
−0.998783 + 0.0493289i \(0.984292\pi\)
\(728\) 0 0
\(729\) 729.000 1.00000
\(730\) 195.000 337.750i 0.267123 0.462671i
\(731\) −823.500 475.448i −1.12654 0.650408i
\(732\) −84.0000 + 145.492i −0.114754 + 0.198760i
\(733\) −335.000 580.237i −0.457026 0.791592i 0.541776 0.840523i \(-0.317752\pi\)
−0.998802 + 0.0489306i \(0.984419\pi\)
\(734\) 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
\(738\) −189.000 −0.256098
\(739\) −158.500 274.530i −0.214479 0.371489i 0.738632 0.674109i \(-0.235472\pi\)
−0.953111 + 0.302620i \(0.902139\pi\)
\(740\) 117.779i 0.159161i
\(741\) 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
\(745\) 264.000 457.261i 0.354362 0.613774i
\(746\) 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
\(751\) −655.000 1134.49i −0.872170 1.51064i −0.859747 0.510721i \(-0.829379\pi\)
−0.0124237 0.999923i \(-0.503955\pi\)
\(752\) 533.472i 0.709404i
\(753\) 1012.50 + 584.567i 1.34462 + 0.776318i
\(754\) 312.000 0.413793
\(755\) 69.2820i 0.0917643i
\(756\) 0 0
\(757\) 218.000 0.287979 0.143989 0.989579i \(-0.454007\pi\)
0.143989 + 0.989579i \(0.454007\pi\)
\(758\) 143.760i 0.189657i
\(759\) 72.0000 124.708i 0.0948617 0.164305i
\(760\) −330.000 −0.434211
\(761\) 570.000 329.090i 0.749014 0.432444i −0.0763232 0.997083i \(-0.524318\pi\)
0.825338 + 0.564639i \(0.190985\pi\)
\(762\) 72.0000 + 41.5692i 0.0944882 + 0.0545528i
\(763\) 0 0
\(764\) 232.095i 0.303789i
\(765\) 486.000 0.635294
\(766\) 483.000 + 836.581i 0.630548 + 1.09214i
\(767\) −174.000 100.459i −0.226858 0.130976i
\(768\) −268.500 + 465.056i −0.349609 + 0.605541i
\(769\) 511.000 885.078i 0.664499 1.15095i −0.314921 0.949118i \(-0.601978\pi\)
0.979421 0.201829i \(-0.0646885\pi\)
\(770\) 0 0
\(771\) 524.811i 0.680689i
\(772\) −265.000 −0.343264
\(773\) −1026.00 + 592.361i −1.32730 + 0.766315i −0.984881 0.173234i \(-0.944578\pi\)
−0.342416 + 0.939549i \(0.611245\pi\)
\(774\) −823.500 475.448i −1.06395 0.614274i
\(775\) 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
\(779\) 115.500 66.6840i 0.148267 0.0856020i
\(780\)