Properties

Label 144.3.m.c.19.5
Level $144$
Weight $3$
Character 144.19
Analytic conductor $3.924$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.5
Root \(0.125358 - 1.99607i\) of defining polynomial
Character \(\chi\) \(=\) 144.19
Dual form 144.3.m.c.91.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +O(q^{10})\) \(q+(0.125358 + 1.99607i) q^{2} +(-3.96857 + 0.500444i) q^{4} +(-3.32679 + 3.32679i) q^{5} -4.04088 q^{7} +(-1.49641 - 7.85880i) q^{8} +(-7.05755 - 6.22347i) q^{10} +(-6.82458 - 6.82458i) q^{11} +(4.29091 + 4.29091i) q^{13} +(-0.506555 - 8.06588i) q^{14} +(15.4991 - 3.97210i) q^{16} -30.1192 q^{17} +(-19.7548 + 19.7548i) q^{19} +(11.5377 - 14.8675i) q^{20} +(12.7668 - 14.4778i) q^{22} +28.2345 q^{23} +2.86488i q^{25} +(-8.02705 + 9.10285i) q^{26} +(16.0365 - 2.02224i) q^{28} +(21.3607 + 21.3607i) q^{29} -38.0396i q^{31} +(9.87151 + 30.4393i) q^{32} +(-3.77567 - 60.1200i) q^{34} +(13.4432 - 13.4432i) q^{35} +(-42.8916 + 42.8916i) q^{37} +(-41.9084 - 36.9556i) q^{38} +(31.1229 + 21.1664i) q^{40} +48.2343i q^{41} +(32.6765 + 32.6765i) q^{43} +(30.4991 + 23.6685i) q^{44} +(3.53941 + 56.3580i) q^{46} -15.8305i q^{47} -32.6713 q^{49} +(-5.71849 + 0.359134i) q^{50} +(-19.1761 - 14.8814i) q^{52} +(0.476870 - 0.476870i) q^{53} +45.4079 q^{55} +(6.04682 + 31.7565i) q^{56} +(-39.9596 + 45.3151i) q^{58} +(-9.97719 - 9.97719i) q^{59} +(37.9455 + 37.9455i) q^{61} +(75.9296 - 4.76855i) q^{62} +(-59.5215 + 23.5200i) q^{64} -28.5500 q^{65} +(20.0705 - 20.0705i) q^{67} +(119.530 - 15.0730i) q^{68} +(28.5187 + 25.1483i) q^{70} -40.0818 q^{71} -30.8095i q^{73} +(-90.9912 - 80.2377i) q^{74} +(68.5123 - 88.2846i) q^{76} +(27.5773 + 27.5773i) q^{77} -130.125i q^{79} +(-38.3480 + 64.7767i) q^{80} +(-96.2789 + 6.04653i) q^{82} +(2.26155 - 2.26155i) q^{83} +(100.200 - 100.200i) q^{85} +(-61.1282 + 69.3207i) q^{86} +(-43.4206 + 63.8454i) q^{88} -72.2232i q^{89} +(-17.3391 - 17.3391i) q^{91} +(-112.051 + 14.1298i) q^{92} +(31.5986 - 1.98447i) q^{94} -131.441i q^{95} -112.343 q^{97} +(-4.09559 - 65.2140i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} + 12q^{8} - 56q^{10} - 32q^{11} + 44q^{14} + 32q^{16} - 32q^{19} - 80q^{20} + 32q^{22} + 128q^{23} + 100q^{26} - 120q^{28} - 32q^{29} - 160q^{32} + 96q^{34} - 96q^{35} - 96q^{37} - 168q^{38} + 48q^{40} + 160q^{43} - 88q^{44} + 136q^{46} + 112q^{49} + 236q^{50} - 48q^{52} + 160q^{53} - 256q^{55} + 224q^{56} + 144q^{58} + 128q^{59} - 32q^{61} + 276q^{62} - 408q^{64} + 32q^{65} + 320q^{67} + 448q^{68} - 384q^{70} - 512q^{71} - 348q^{74} + 72q^{76} - 224q^{77} - 552q^{80} - 40q^{82} + 160q^{83} + 160q^{85} - 528q^{86} + 480q^{88} - 480q^{91} - 496q^{92} + 312q^{94} + 440q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.125358 + 1.99607i 0.0626788 + 0.998034i
\(3\) 0 0
\(4\) −3.96857 + 0.500444i −0.992143 + 0.125111i
\(5\) −3.32679 + 3.32679i −0.665359 + 0.665359i −0.956638 0.291279i \(-0.905919\pi\)
0.291279 + 0.956638i \(0.405919\pi\)
\(6\) 0 0
\(7\) −4.04088 −0.577269 −0.288635 0.957439i \(-0.593201\pi\)
−0.288635 + 0.957439i \(0.593201\pi\)
\(8\) −1.49641 7.85880i −0.187051 0.982350i
\(9\) 0 0
\(10\) −7.05755 6.22347i −0.705755 0.622347i
\(11\) −6.82458 6.82458i −0.620416 0.620416i 0.325222 0.945638i \(-0.394561\pi\)
−0.945638 + 0.325222i \(0.894561\pi\)
\(12\) 0 0
\(13\) 4.29091 + 4.29091i 0.330070 + 0.330070i 0.852613 0.522543i \(-0.175017\pi\)
−0.522543 + 0.852613i \(0.675017\pi\)
\(14\) −0.506555 8.06588i −0.0361825 0.576134i
\(15\) 0 0
\(16\) 15.4991 3.97210i 0.968694 0.248256i
\(17\) −30.1192 −1.77172 −0.885859 0.463954i \(-0.846430\pi\)
−0.885859 + 0.463954i \(0.846430\pi\)
\(18\) 0 0
\(19\) −19.7548 + 19.7548i −1.03973 + 1.03973i −0.0405505 + 0.999177i \(0.512911\pi\)
−0.999177 + 0.0405505i \(0.987089\pi\)
\(20\) 11.5377 14.8675i 0.576887 0.743375i
\(21\) 0 0
\(22\) 12.7668 14.4778i 0.580309 0.658083i
\(23\) 28.2345 1.22759 0.613794 0.789466i \(-0.289642\pi\)
0.613794 + 0.789466i \(0.289642\pi\)
\(24\) 0 0
\(25\) 2.86488i 0.114595i
\(26\) −8.02705 + 9.10285i −0.308733 + 0.350109i
\(27\) 0 0
\(28\) 16.0365 2.02224i 0.572733 0.0722227i
\(29\) 21.3607 + 21.3607i 0.736575 + 0.736575i 0.971914 0.235338i \(-0.0756198\pi\)
−0.235338 + 0.971914i \(0.575620\pi\)
\(30\) 0 0
\(31\) 38.0396i 1.22708i −0.789662 0.613541i \(-0.789744\pi\)
0.789662 0.613541i \(-0.210256\pi\)
\(32\) 9.87151 + 30.4393i 0.308485 + 0.951229i
\(33\) 0 0
\(34\) −3.77567 60.1200i −0.111049 1.76823i
\(35\) 13.4432 13.4432i 0.384091 0.384091i
\(36\) 0 0
\(37\) −42.8916 + 42.8916i −1.15923 + 1.15923i −0.174590 + 0.984641i \(0.555860\pi\)
−0.984641 + 0.174590i \(0.944140\pi\)
\(38\) −41.9084 36.9556i −1.10285 0.972515i
\(39\) 0 0
\(40\) 31.1229 + 21.1664i 0.778072 + 0.529159i
\(41\) 48.2343i 1.17645i 0.808699 + 0.588223i \(0.200172\pi\)
−0.808699 + 0.588223i \(0.799828\pi\)
\(42\) 0 0
\(43\) 32.6765 + 32.6765i 0.759918 + 0.759918i 0.976307 0.216389i \(-0.0694281\pi\)
−0.216389 + 0.976307i \(0.569428\pi\)
\(44\) 30.4991 + 23.6685i 0.693162 + 0.537921i
\(45\) 0 0
\(46\) 3.53941 + 56.3580i 0.0769437 + 1.22517i
\(47\) 15.8305i 0.336818i −0.985717 0.168409i \(-0.946137\pi\)
0.985717 0.168409i \(-0.0538630\pi\)
\(48\) 0 0
\(49\) −32.6713 −0.666760
\(50\) −5.71849 + 0.359134i −0.114370 + 0.00718268i
\(51\) 0 0
\(52\) −19.1761 14.8814i −0.368772 0.286181i
\(53\) 0.476870 0.476870i 0.00899755 0.00899755i −0.702594 0.711591i \(-0.747975\pi\)
0.711591 + 0.702594i \(0.247975\pi\)
\(54\) 0 0
\(55\) 45.4079 0.825599
\(56\) 6.04682 + 31.7565i 0.107979 + 0.567080i
\(57\) 0 0
\(58\) −39.9596 + 45.3151i −0.688959 + 0.781295i
\(59\) −9.97719 9.97719i −0.169105 0.169105i 0.617481 0.786586i \(-0.288153\pi\)
−0.786586 + 0.617481i \(0.788153\pi\)
\(60\) 0 0
\(61\) 37.9455 + 37.9455i 0.622057 + 0.622057i 0.946057 0.324000i \(-0.105028\pi\)
−0.324000 + 0.946057i \(0.605028\pi\)
\(62\) 75.9296 4.76855i 1.22467 0.0769121i
\(63\) 0 0
\(64\) −59.5215 + 23.5200i −0.930024 + 0.367500i
\(65\) −28.5500 −0.439230
\(66\) 0 0
\(67\) 20.0705 20.0705i 0.299559 0.299559i −0.541282 0.840841i \(-0.682061\pi\)
0.840841 + 0.541282i \(0.182061\pi\)
\(68\) 119.530 15.0730i 1.75780 0.221662i
\(69\) 0 0
\(70\) 28.5187 + 25.1483i 0.407410 + 0.359261i
\(71\) −40.0818 −0.564532 −0.282266 0.959336i \(-0.591086\pi\)
−0.282266 + 0.959336i \(0.591086\pi\)
\(72\) 0 0
\(73\) 30.8095i 0.422049i −0.977481 0.211024i \(-0.932320\pi\)
0.977481 0.211024i \(-0.0676799\pi\)
\(74\) −90.9912 80.2377i −1.22961 1.08429i
\(75\) 0 0
\(76\) 68.5123 88.2846i 0.901477 1.16164i
\(77\) 27.5773 + 27.5773i 0.358147 + 0.358147i
\(78\) 0 0
\(79\) 130.125i 1.64716i −0.567203 0.823578i \(-0.691975\pi\)
0.567203 0.823578i \(-0.308025\pi\)
\(80\) −38.3480 + 64.7767i −0.479350 + 0.809709i
\(81\) 0 0
\(82\) −96.2789 + 6.04653i −1.17413 + 0.0737382i
\(83\) 2.26155 2.26155i 0.0272476 0.0272476i −0.693352 0.720599i \(-0.743867\pi\)
0.720599 + 0.693352i \(0.243867\pi\)
\(84\) 0 0
\(85\) 100.200 100.200i 1.17883 1.17883i
\(86\) −61.1282 + 69.3207i −0.710793 + 0.806054i
\(87\) 0 0
\(88\) −43.4206 + 63.8454i −0.493416 + 0.725516i
\(89\) 72.2232i 0.811496i −0.913985 0.405748i \(-0.867011\pi\)
0.913985 0.405748i \(-0.132989\pi\)
\(90\) 0 0
\(91\) −17.3391 17.3391i −0.190539 0.190539i
\(92\) −112.051 + 14.1298i −1.21794 + 0.153585i
\(93\) 0 0
\(94\) 31.5986 1.98447i 0.336156 0.0211113i
\(95\) 131.441i 1.38358i
\(96\) 0 0
\(97\) −112.343 −1.15817 −0.579085 0.815267i \(-0.696590\pi\)
−0.579085 + 0.815267i \(0.696590\pi\)
\(98\) −4.09559 65.2140i −0.0417917 0.665449i
\(99\) 0 0
\(100\) −1.43371 11.3695i −0.0143371 0.113695i
\(101\) 1.61933 1.61933i 0.0160330 0.0160330i −0.699045 0.715078i \(-0.746391\pi\)
0.715078 + 0.699045i \(0.246391\pi\)
\(102\) 0 0
\(103\) 27.9974 0.271819 0.135910 0.990721i \(-0.456604\pi\)
0.135910 + 0.990721i \(0.456604\pi\)
\(104\) 27.3005 40.1424i 0.262504 0.385984i
\(105\) 0 0
\(106\) 1.01164 + 0.892086i 0.00954381 + 0.00841590i
\(107\) 40.3835 + 40.3835i 0.377416 + 0.377416i 0.870169 0.492753i \(-0.164010\pi\)
−0.492753 + 0.870169i \(0.664010\pi\)
\(108\) 0 0
\(109\) 36.8336 + 36.8336i 0.337923 + 0.337923i 0.855585 0.517662i \(-0.173198\pi\)
−0.517662 + 0.855585i \(0.673198\pi\)
\(110\) 5.69223 + 90.6373i 0.0517475 + 0.823976i
\(111\) 0 0
\(112\) −62.6301 + 16.0508i −0.559197 + 0.143311i
\(113\) 55.5952 0.491993 0.245997 0.969271i \(-0.420885\pi\)
0.245997 + 0.969271i \(0.420885\pi\)
\(114\) 0 0
\(115\) −93.9305 + 93.9305i −0.816787 + 0.816787i
\(116\) −95.4612 74.0815i −0.822941 0.638634i
\(117\) 0 0
\(118\) 18.6644 21.1659i 0.158173 0.179372i
\(119\) 121.708 1.02276
\(120\) 0 0
\(121\) 27.8503i 0.230167i
\(122\) −70.9850 + 80.4985i −0.581844 + 0.659824i
\(123\) 0 0
\(124\) 19.0367 + 150.963i 0.153522 + 1.21744i
\(125\) −92.7007 92.7007i −0.741606 0.741606i
\(126\) 0 0
\(127\) 109.927i 0.865569i 0.901497 + 0.432785i \(0.142469\pi\)
−0.901497 + 0.432785i \(0.857531\pi\)
\(128\) −54.4090 115.861i −0.425070 0.905160i
\(129\) 0 0
\(130\) −3.57895 56.9876i −0.0275304 0.438367i
\(131\) −75.6795 + 75.6795i −0.577706 + 0.577706i −0.934271 0.356565i \(-0.883948\pi\)
0.356565 + 0.934271i \(0.383948\pi\)
\(132\) 0 0
\(133\) 79.8270 79.8270i 0.600203 0.600203i
\(134\) 42.5780 + 37.5460i 0.317746 + 0.280194i
\(135\) 0 0
\(136\) 45.0707 + 236.701i 0.331402 + 1.74045i
\(137\) 2.14751i 0.0156752i −0.999969 0.00783762i \(-0.997505\pi\)
0.999969 0.00783762i \(-0.00249482\pi\)
\(138\) 0 0
\(139\) −109.246 109.246i −0.785941 0.785941i 0.194885 0.980826i \(-0.437567\pi\)
−0.980826 + 0.194885i \(0.937567\pi\)
\(140\) −46.6227 + 60.0778i −0.333019 + 0.429127i
\(141\) 0 0
\(142\) −5.02455 80.0059i −0.0353842 0.563422i
\(143\) 58.5673i 0.409562i
\(144\) 0 0
\(145\) −142.125 −0.980174
\(146\) 61.4979 3.86221i 0.421219 0.0264535i
\(147\) 0 0
\(148\) 148.753 191.683i 1.00509 1.29516i
\(149\) −79.6950 + 79.6950i −0.534866 + 0.534866i −0.922016 0.387151i \(-0.873459\pi\)
0.387151 + 0.922016i \(0.373459\pi\)
\(150\) 0 0
\(151\) 105.546 0.698982 0.349491 0.936940i \(-0.386355\pi\)
0.349491 + 0.936940i \(0.386355\pi\)
\(152\) 184.811 + 125.688i 1.21586 + 0.826894i
\(153\) 0 0
\(154\) −51.5892 + 58.5032i −0.334995 + 0.379891i
\(155\) 126.550 + 126.550i 0.816451 + 0.816451i
\(156\) 0 0
\(157\) 190.060 + 190.060i 1.21057 + 1.21057i 0.970839 + 0.239733i \(0.0770598\pi\)
0.239733 + 0.970839i \(0.422940\pi\)
\(158\) 259.739 16.3122i 1.64392 0.103242i
\(159\) 0 0
\(160\) −134.106 68.4250i −0.838162 0.427656i
\(161\) −114.092 −0.708649
\(162\) 0 0
\(163\) −59.4130 + 59.4130i −0.364497 + 0.364497i −0.865465 0.500969i \(-0.832977\pi\)
0.500969 + 0.865465i \(0.332977\pi\)
\(164\) −24.1386 191.421i −0.147186 1.16720i
\(165\) 0 0
\(166\) 4.79772 + 4.23071i 0.0289019 + 0.0254862i
\(167\) −65.3894 −0.391553 −0.195777 0.980649i \(-0.562723\pi\)
−0.195777 + 0.980649i \(0.562723\pi\)
\(168\) 0 0
\(169\) 132.176i 0.782107i
\(170\) 212.568 + 187.446i 1.25040 + 1.10262i
\(171\) 0 0
\(172\) −146.032 113.326i −0.849021 0.658873i
\(173\) 212.939 + 212.939i 1.23086 + 1.23086i 0.963633 + 0.267228i \(0.0861077\pi\)
0.267228 + 0.963633i \(0.413892\pi\)
\(174\) 0 0
\(175\) 11.5766i 0.0661522i
\(176\) −132.883 78.6670i −0.755016 0.446972i
\(177\) 0 0
\(178\) 144.162 9.05372i 0.809901 0.0508636i
\(179\) −196.852 + 196.852i −1.09973 + 1.09973i −0.105289 + 0.994442i \(0.533577\pi\)
−0.994442 + 0.105289i \(0.966423\pi\)
\(180\) 0 0
\(181\) −27.4330 + 27.4330i −0.151564 + 0.151564i −0.778816 0.627252i \(-0.784179\pi\)
0.627252 + 0.778816i \(0.284179\pi\)
\(182\) 32.4364 36.7835i 0.178222 0.202107i
\(183\) 0 0
\(184\) −42.2505 221.890i −0.229622 1.20592i
\(185\) 285.383i 1.54261i
\(186\) 0 0
\(187\) 205.551 + 205.551i 1.09920 + 1.09920i
\(188\) 7.92226 + 62.8243i 0.0421397 + 0.334172i
\(189\) 0 0
\(190\) 262.364 16.4771i 1.38086 0.0867214i
\(191\) 244.409i 1.27963i 0.768530 + 0.639814i \(0.220989\pi\)
−0.768530 + 0.639814i \(0.779011\pi\)
\(192\) 0 0
\(193\) 255.040 1.32145 0.660726 0.750627i \(-0.270249\pi\)
0.660726 + 0.750627i \(0.270249\pi\)
\(194\) −14.0830 224.243i −0.0725927 1.15589i
\(195\) 0 0
\(196\) 129.658 16.3501i 0.661522 0.0834191i
\(197\) 194.229 194.229i 0.985936 0.985936i −0.0139666 0.999902i \(-0.504446\pi\)
0.999902 + 0.0139666i \(0.00444586\pi\)
\(198\) 0 0
\(199\) −169.797 −0.853252 −0.426626 0.904428i \(-0.640298\pi\)
−0.426626 + 0.904428i \(0.640298\pi\)
\(200\) 22.5145 4.28703i 0.112573 0.0214352i
\(201\) 0 0
\(202\) 3.43529 + 3.02930i 0.0170064 + 0.0149965i
\(203\) −86.3160 86.3160i −0.425202 0.425202i
\(204\) 0 0
\(205\) −160.466 160.466i −0.782759 0.782759i
\(206\) 3.50969 + 55.8847i 0.0170373 + 0.271285i
\(207\) 0 0
\(208\) 83.5492 + 49.4614i 0.401679 + 0.237795i
\(209\) 269.637 1.29013
\(210\) 0 0
\(211\) −132.691 + 132.691i −0.628868 + 0.628868i −0.947783 0.318915i \(-0.896681\pi\)
0.318915 + 0.947783i \(0.396681\pi\)
\(212\) −1.65385 + 2.13114i −0.00780116 + 0.0100525i
\(213\) 0 0
\(214\) −75.5458 + 85.6705i −0.353018 + 0.400330i
\(215\) −217.416 −1.01124
\(216\) 0 0
\(217\) 153.713i 0.708357i
\(218\) −68.9050 + 78.1398i −0.316078 + 0.358439i
\(219\) 0 0
\(220\) −180.205 + 22.7241i −0.819112 + 0.103292i
\(221\) −129.239 129.239i −0.584791 0.584791i
\(222\) 0 0
\(223\) 26.3436i 0.118133i 0.998254 + 0.0590664i \(0.0188124\pi\)
−0.998254 + 0.0590664i \(0.981188\pi\)
\(224\) −39.8896 123.002i −0.178079 0.549115i
\(225\) 0 0
\(226\) 6.96928 + 110.972i 0.0308375 + 0.491026i
\(227\) 70.3362 70.3362i 0.309851 0.309851i −0.535001 0.844852i \(-0.679689\pi\)
0.844852 + 0.535001i \(0.179689\pi\)
\(228\) 0 0
\(229\) −215.607 + 215.607i −0.941516 + 0.941516i −0.998382 0.0568658i \(-0.981889\pi\)
0.0568658 + 0.998382i \(0.481889\pi\)
\(230\) −199.266 175.717i −0.866376 0.763986i
\(231\) 0 0
\(232\) 135.905 199.834i 0.585797 0.861352i
\(233\) 183.853i 0.789069i 0.918881 + 0.394534i \(0.129094\pi\)
−0.918881 + 0.394534i \(0.870906\pi\)
\(234\) 0 0
\(235\) 52.6647 + 52.6647i 0.224105 + 0.224105i
\(236\) 44.5882 + 34.6021i 0.188933 + 0.146619i
\(237\) 0 0
\(238\) 15.2570 + 242.938i 0.0641052 + 1.02075i
\(239\) 315.183i 1.31876i 0.751811 + 0.659379i \(0.229181\pi\)
−0.751811 + 0.659379i \(0.770819\pi\)
\(240\) 0 0
\(241\) −327.804 −1.36018 −0.680090 0.733128i \(-0.738059\pi\)
−0.680090 + 0.733128i \(0.738059\pi\)
\(242\) 55.5910 3.49124i 0.229715 0.0144266i
\(243\) 0 0
\(244\) −169.579 131.600i −0.694996 0.539343i
\(245\) 108.691 108.691i 0.443635 0.443635i
\(246\) 0 0
\(247\) −169.532 −0.686366
\(248\) −298.945 + 56.9228i −1.20543 + 0.229528i
\(249\) 0 0
\(250\) 173.416 196.658i 0.693665 0.786631i
\(251\) −219.813 219.813i −0.875747 0.875747i 0.117344 0.993091i \(-0.462562\pi\)
−0.993091 + 0.117344i \(0.962562\pi\)
\(252\) 0 0
\(253\) −192.689 192.689i −0.761616 0.761616i
\(254\) −219.422 + 13.7802i −0.863867 + 0.0542528i
\(255\) 0 0
\(256\) 224.445 123.128i 0.876738 0.480969i
\(257\) −150.042 −0.583823 −0.291911 0.956445i \(-0.594291\pi\)
−0.291911 + 0.956445i \(0.594291\pi\)
\(258\) 0 0
\(259\) 173.320 173.320i 0.669188 0.669188i
\(260\) 113.303 14.2877i 0.435779 0.0549526i
\(261\) 0 0
\(262\) −160.548 141.574i −0.612780 0.540360i
\(263\) −14.8922 −0.0566242 −0.0283121 0.999599i \(-0.509013\pi\)
−0.0283121 + 0.999599i \(0.509013\pi\)
\(264\) 0 0
\(265\) 3.17290i 0.0119732i
\(266\) 169.347 + 149.333i 0.636643 + 0.561403i
\(267\) 0 0
\(268\) −69.6069 + 89.6952i −0.259727 + 0.334684i
\(269\) −95.4169 95.4169i −0.354710 0.354710i 0.507149 0.861858i \(-0.330699\pi\)
−0.861858 + 0.507149i \(0.830699\pi\)
\(270\) 0 0
\(271\) 46.4991i 0.171583i 0.996313 + 0.0857917i \(0.0273420\pi\)
−0.996313 + 0.0857917i \(0.972658\pi\)
\(272\) −466.821 + 119.636i −1.71625 + 0.439840i
\(273\) 0 0
\(274\) 4.28657 0.269206i 0.0156444 0.000982505i
\(275\) 19.5516 19.5516i 0.0710967 0.0710967i
\(276\) 0 0
\(277\) 30.5071 30.5071i 0.110134 0.110134i −0.649892 0.760026i \(-0.725186\pi\)
0.760026 + 0.649892i \(0.225186\pi\)
\(278\) 204.367 231.757i 0.735134 0.833657i
\(279\) 0 0
\(280\) −125.764 85.5308i −0.449157 0.305467i
\(281\) 217.239i 0.773093i 0.922270 + 0.386547i \(0.126332\pi\)
−0.922270 + 0.386547i \(0.873668\pi\)
\(282\) 0 0
\(283\) −136.055 136.055i −0.480760 0.480760i 0.424614 0.905374i \(-0.360410\pi\)
−0.905374 + 0.424614i \(0.860410\pi\)
\(284\) 159.067 20.0587i 0.560096 0.0706292i
\(285\) 0 0
\(286\) 116.904 7.34186i 0.408756 0.0256708i
\(287\) 194.909i 0.679126i
\(288\) 0 0
\(289\) 618.167 2.13898
\(290\) −17.8165 283.691i −0.0614361 0.978246i
\(291\) 0 0
\(292\) 15.4185 + 122.270i 0.0528030 + 0.418732i
\(293\) 56.8362 56.8362i 0.193980 0.193980i −0.603433 0.797414i \(-0.706201\pi\)
0.797414 + 0.603433i \(0.206201\pi\)
\(294\) 0 0
\(295\) 66.3841 0.225031
\(296\) 401.260 + 272.893i 1.35561 + 0.921935i
\(297\) 0 0
\(298\) −169.067 149.086i −0.567339 0.500289i
\(299\) 121.152 + 121.152i 0.405190 + 0.405190i
\(300\) 0 0
\(301\) −132.042 132.042i −0.438677 0.438677i
\(302\) 13.2310 + 210.677i 0.0438113 + 0.697608i
\(303\) 0 0
\(304\) −227.714 + 384.650i −0.749060 + 1.26530i
\(305\) −252.474 −0.827782
\(306\) 0 0
\(307\) 245.927 245.927i 0.801067 0.801067i −0.182196 0.983262i \(-0.558320\pi\)
0.983262 + 0.182196i \(0.0583205\pi\)
\(308\) −123.243 95.6416i −0.400141 0.310525i
\(309\) 0 0
\(310\) −236.738 + 268.466i −0.763671 + 0.866019i
\(311\) 359.964 1.15744 0.578721 0.815526i \(-0.303552\pi\)
0.578721 + 0.815526i \(0.303552\pi\)
\(312\) 0 0
\(313\) 131.023i 0.418605i 0.977851 + 0.209303i \(0.0671194\pi\)
−0.977851 + 0.209303i \(0.932881\pi\)
\(314\) −355.547 + 403.198i −1.13231 + 1.28407i
\(315\) 0 0
\(316\) 65.1205 + 516.412i 0.206077 + 1.63421i
\(317\) −89.0470 89.0470i −0.280905 0.280905i 0.552565 0.833470i \(-0.313649\pi\)
−0.833470 + 0.552565i \(0.813649\pi\)
\(318\) 0 0
\(319\) 291.555i 0.913966i
\(320\) 119.770 276.262i 0.374280 0.863319i
\(321\) 0 0
\(322\) −14.3024 227.736i −0.0444172 0.707255i
\(323\) 595.000 595.000i 1.84210 1.84210i
\(324\) 0 0
\(325\) −12.2929 + 12.2929i −0.0378244 + 0.0378244i
\(326\) −126.040 111.144i −0.386626 0.340934i
\(327\) 0 0
\(328\) 379.064 72.1783i 1.15568 0.220056i
\(329\) 63.9690i 0.194435i
\(330\) 0 0
\(331\) 95.5992 + 95.5992i 0.288819 + 0.288819i 0.836613 0.547794i \(-0.184532\pi\)
−0.547794 + 0.836613i \(0.684532\pi\)
\(332\) −7.84336 + 10.1069i −0.0236246 + 0.0304425i
\(333\) 0 0
\(334\) −8.19706 130.522i −0.0245421 0.390783i
\(335\) 133.541i 0.398629i
\(336\) 0 0
\(337\) 583.717 1.73210 0.866050 0.499958i \(-0.166651\pi\)
0.866050 + 0.499958i \(0.166651\pi\)
\(338\) 263.833 16.5693i 0.780570 0.0490215i
\(339\) 0 0
\(340\) −347.508 + 447.797i −1.02208 + 1.31705i
\(341\) −259.604 + 259.604i −0.761302 + 0.761302i
\(342\) 0 0
\(343\) 330.024 0.962169
\(344\) 207.900 305.695i 0.604362 0.888649i
\(345\) 0 0
\(346\) −398.347 + 451.734i −1.15129 + 1.30559i
\(347\) −191.655 191.655i −0.552320 0.552320i 0.374790 0.927110i \(-0.377715\pi\)
−0.927110 + 0.374790i \(0.877715\pi\)
\(348\) 0 0
\(349\) −19.4781 19.4781i −0.0558112 0.0558112i 0.678650 0.734462i \(-0.262565\pi\)
−0.734462 + 0.678650i \(0.762565\pi\)
\(350\) 23.1077 1.45122i 0.0660221 0.00414634i
\(351\) 0 0
\(352\) 140.367 275.105i 0.398769 0.781547i
\(353\) 82.9610 0.235017 0.117509 0.993072i \(-0.462509\pi\)
0.117509 + 0.993072i \(0.462509\pi\)
\(354\) 0 0
\(355\) 133.344 133.344i 0.375616 0.375616i
\(356\) 36.1437 + 286.623i 0.101527 + 0.805120i
\(357\) 0 0
\(358\) −417.606 368.253i −1.16650 1.02864i
\(359\) −357.792 −0.996634 −0.498317 0.866995i \(-0.666048\pi\)
−0.498317 + 0.866995i \(0.666048\pi\)
\(360\) 0 0
\(361\) 419.507i 1.16207i
\(362\) −58.1971 51.3193i −0.160766 0.141766i
\(363\) 0 0
\(364\) 77.4886 + 60.1341i 0.212881 + 0.165204i
\(365\) 102.497 + 102.497i 0.280814 + 0.280814i
\(366\) 0 0
\(367\) 651.729i 1.77583i 0.460010 + 0.887914i \(0.347846\pi\)
−0.460010 + 0.887914i \(0.652154\pi\)
\(368\) 437.610 112.150i 1.18916 0.304756i
\(369\) 0 0
\(370\) 569.643 35.7749i 1.53958 0.0966889i
\(371\) −1.92698 + 1.92698i −0.00519401 + 0.00519401i
\(372\) 0 0
\(373\) 199.720 199.720i 0.535442 0.535442i −0.386745 0.922187i \(-0.626401\pi\)
0.922187 + 0.386745i \(0.126401\pi\)
\(374\) −384.526 + 436.061i −1.02814 + 1.16594i
\(375\) 0 0
\(376\) −124.408 + 23.6889i −0.330873 + 0.0630023i
\(377\) 183.314i 0.486243i
\(378\) 0 0
\(379\) −330.204 330.204i −0.871251 0.871251i 0.121358 0.992609i \(-0.461275\pi\)
−0.992609 + 0.121358i \(0.961275\pi\)
\(380\) 65.7787 + 521.631i 0.173102 + 1.37271i
\(381\) 0 0
\(382\) −487.857 + 30.6385i −1.27711 + 0.0802055i
\(383\) 174.284i 0.455049i −0.973772 0.227524i \(-0.926937\pi\)
0.973772 0.227524i \(-0.0730631\pi\)
\(384\) 0 0
\(385\) −183.488 −0.476593
\(386\) 31.9712 + 509.077i 0.0828270 + 1.31885i
\(387\) 0 0
\(388\) 445.839 56.2212i 1.14907 0.144900i
\(389\) −207.835 + 207.835i −0.534279 + 0.534279i −0.921843 0.387564i \(-0.873317\pi\)
0.387564 + 0.921843i \(0.373317\pi\)
\(390\) 0 0
\(391\) −850.402 −2.17494
\(392\) 48.8896 + 256.757i 0.124718 + 0.654992i
\(393\) 0 0
\(394\) 412.043 + 363.347i 1.04579 + 0.922200i
\(395\) 432.900 + 432.900i 1.09595 + 1.09595i
\(396\) 0 0
\(397\) −37.2994 37.2994i −0.0939533 0.0939533i 0.658568 0.752521i \(-0.271162\pi\)
−0.752521 + 0.658568i \(0.771162\pi\)
\(398\) −21.2854 338.927i −0.0534808 0.851574i
\(399\) 0 0
\(400\) 11.3796 + 44.4031i 0.0284489 + 0.111008i
\(401\) 524.704 1.30849 0.654244 0.756284i \(-0.272987\pi\)
0.654244 + 0.756284i \(0.272987\pi\)
\(402\) 0 0
\(403\) 163.224 163.224i 0.405023 0.405023i
\(404\) −5.61605 + 7.23682i −0.0139011 + 0.0179129i
\(405\) 0 0
\(406\) 161.472 183.113i 0.397715 0.451017i
\(407\) 585.434 1.43841
\(408\) 0 0
\(409\) 787.357i 1.92508i 0.271141 + 0.962540i \(0.412599\pi\)
−0.271141 + 0.962540i \(0.587401\pi\)
\(410\) 300.184 340.416i 0.732157 0.830282i
\(411\) 0 0
\(412\) −111.110 + 14.0111i −0.269684 + 0.0340076i
\(413\) 40.3166 + 40.3166i 0.0976190 + 0.0976190i
\(414\) 0 0
\(415\) 15.0475i 0.0362589i
\(416\) −88.2548 + 172.970i −0.212151 + 0.415794i
\(417\) 0 0
\(418\) 33.8010 + 538.213i 0.0808637 + 1.28759i
\(419\) −30.1767 + 30.1767i −0.0720209 + 0.0720209i −0.742200 0.670179i \(-0.766217\pi\)
0.670179 + 0.742200i \(0.266217\pi\)
\(420\) 0 0
\(421\) −261.021 + 261.021i −0.620003 + 0.620003i −0.945532 0.325529i \(-0.894458\pi\)
0.325529 + 0.945532i \(0.394458\pi\)
\(422\) −281.494 248.227i −0.667048 0.588215i
\(423\) 0 0
\(424\) −4.46122 3.03403i −0.0105217 0.00715574i
\(425\) 86.2878i 0.203030i
\(426\) 0 0
\(427\) −153.333 153.333i −0.359094 0.359094i
\(428\) −180.474 140.055i −0.421669 0.327231i
\(429\) 0 0
\(430\) −27.2547 433.977i −0.0633830 1.00925i
\(431\) 459.989i 1.06726i −0.845718 0.533630i \(-0.820828\pi\)
0.845718 0.533630i \(-0.179172\pi\)
\(432\) 0 0
\(433\) −445.246 −1.02828 −0.514140 0.857706i \(-0.671889\pi\)
−0.514140 + 0.857706i \(0.671889\pi\)
\(434\) −306.822 + 19.2691i −0.706964 + 0.0443989i
\(435\) 0 0
\(436\) −164.610 127.744i −0.377546 0.292990i
\(437\) −557.768 + 557.768i −1.27636 + 1.27636i
\(438\) 0 0
\(439\) 356.467 0.811998 0.405999 0.913874i \(-0.366924\pi\)
0.405999 + 0.913874i \(0.366924\pi\)
\(440\) −67.9489 356.852i −0.154429 0.811027i
\(441\) 0 0
\(442\) 241.768 274.171i 0.546987 0.620295i
\(443\) −358.752 358.752i −0.809824 0.809824i 0.174783 0.984607i \(-0.444078\pi\)
−0.984607 + 0.174783i \(0.944078\pi\)
\(444\) 0 0
\(445\) 240.272 + 240.272i 0.539936 + 0.539936i
\(446\) −52.5837 + 3.30237i −0.117901 + 0.00740442i
\(447\) 0 0
\(448\) 240.519 95.0415i 0.536874 0.212146i
\(449\) 44.6564 0.0994576 0.0497288 0.998763i \(-0.484164\pi\)
0.0497288 + 0.998763i \(0.484164\pi\)
\(450\) 0 0
\(451\) 329.179 329.179i 0.729886 0.729886i
\(452\) −220.634 + 27.8223i −0.488128 + 0.0615538i
\(453\) 0 0
\(454\) 149.213 + 131.579i 0.328663 + 0.289821i
\(455\) 115.367 0.253554
\(456\) 0 0
\(457\) 84.2332i 0.184318i 0.995744 + 0.0921589i \(0.0293768\pi\)
−0.995744 + 0.0921589i \(0.970623\pi\)
\(458\) −457.394 403.338i −0.998678 0.880652i
\(459\) 0 0
\(460\) 325.763 419.777i 0.708180 0.912558i
\(461\) −205.347 205.347i −0.445438 0.445438i 0.448397 0.893835i \(-0.351995\pi\)
−0.893835 + 0.448397i \(0.851995\pi\)
\(462\) 0 0
\(463\) 270.647i 0.584550i 0.956334 + 0.292275i \(0.0944123\pi\)
−0.956334 + 0.292275i \(0.905588\pi\)
\(464\) 415.918 + 246.225i 0.896376 + 0.530657i
\(465\) 0 0
\(466\) −366.983 + 23.0474i −0.787517 + 0.0494579i
\(467\) −230.389 + 230.389i −0.493338 + 0.493338i −0.909356 0.416018i \(-0.863425\pi\)
0.416018 + 0.909356i \(0.363425\pi\)
\(468\) 0 0
\(469\) −81.1024 + 81.1024i −0.172926 + 0.172926i
\(470\) −98.5203 + 111.724i −0.209618 + 0.237711i
\(471\) 0 0
\(472\) −63.4788 + 93.3387i −0.134489 + 0.197751i
\(473\) 446.006i 0.942931i
\(474\) 0 0
\(475\) −56.5952 56.5952i −0.119148 0.119148i
\(476\) −483.008 + 60.9082i −1.01472 + 0.127958i
\(477\) 0 0
\(478\) −629.127 + 39.5106i −1.31616 + 0.0826581i
\(479\) 575.911i 1.20232i −0.799129 0.601159i \(-0.794706\pi\)
0.799129 0.601159i \(-0.205294\pi\)
\(480\) 0 0
\(481\) −368.088 −0.765255
\(482\) −41.0926 654.318i −0.0852545 1.35751i
\(483\) 0 0
\(484\) 13.9375 + 110.526i 0.0287965 + 0.228359i
\(485\) 373.740 373.740i 0.770599 0.770599i
\(486\) 0 0
\(487\) 600.355 1.23276 0.616381 0.787448i \(-0.288598\pi\)
0.616381 + 0.787448i \(0.288598\pi\)
\(488\) 241.424 354.988i 0.494721 0.727434i
\(489\) 0 0
\(490\) 230.579 + 203.329i 0.470569 + 0.414956i
\(491\) −79.7182 79.7182i −0.162359 0.162359i 0.621252 0.783611i \(-0.286624\pi\)
−0.783611 + 0.621252i \(0.786624\pi\)
\(492\) 0 0
\(493\) −643.367 643.367i −1.30500 1.30500i
\(494\) −21.2522 338.398i −0.0430206 0.685017i
\(495\) 0 0
\(496\) −151.097 589.580i −0.304631 1.18867i
\(497\) 161.966 0.325887
\(498\) 0 0
\(499\) −13.4912 + 13.4912i −0.0270365 + 0.0270365i −0.720496 0.693459i \(-0.756086\pi\)
0.693459 + 0.720496i \(0.256086\pi\)
\(500\) 414.281 + 321.498i 0.828562 + 0.642996i
\(501\) 0 0
\(502\) 411.205 466.316i 0.819134 0.928916i
\(503\) −892.196 −1.77375 −0.886875 0.462009i \(-0.847129\pi\)
−0.886875 + 0.462009i \(0.847129\pi\)
\(504\) 0 0
\(505\) 10.7744i 0.0213354i
\(506\) 360.465 408.775i 0.712381 0.807855i
\(507\) 0 0
\(508\) −55.0125 436.254i −0.108292 0.858768i
\(509\) 44.9128 + 44.9128i 0.0882374 + 0.0882374i 0.749848 0.661610i \(-0.230127\pi\)
−0.661610 + 0.749848i \(0.730127\pi\)
\(510\) 0 0
\(511\) 124.498i 0.243636i
\(512\) 273.908 + 432.572i 0.534976 + 0.844867i
\(513\) 0 0
\(514\) −18.8090 299.495i −0.0365933 0.582675i
\(515\) −93.1416 + 93.1416i −0.180857 + 0.180857i
\(516\) 0 0
\(517\) −108.036 + 108.036i −0.208967 + 0.208967i
\(518\) 367.685 + 324.231i 0.709816 + 0.625929i
\(519\) 0 0
\(520\) 42.7225 + 224.368i 0.0821586 + 0.431478i
\(521\) 866.038i 1.66226i 0.556078 + 0.831130i \(0.312306\pi\)
−0.556078 + 0.831130i \(0.687694\pi\)
\(522\) 0 0
\(523\) 359.579 + 359.579i 0.687531 + 0.687531i 0.961686 0.274155i \(-0.0883981\pi\)
−0.274155 + 0.961686i \(0.588398\pi\)
\(524\) 262.466 338.213i 0.500889 0.645444i
\(525\) 0 0
\(526\) −1.86684 29.7257i −0.00354913 0.0565128i
\(527\) 1145.72i 2.17405i
\(528\) 0 0
\(529\) 268.189 0.506973
\(530\) −6.33332 + 0.397747i −0.0119497 + 0.000750466i
\(531\) 0 0
\(532\) −276.850 + 356.748i −0.520395 + 0.670579i
\(533\) −206.969 + 206.969i −0.388310 + 0.388310i
\(534\) 0 0
\(535\) −268.695 −0.502234
\(536\) −187.764 127.696i −0.350305 0.238239i
\(537\) 0 0
\(538\) 178.497 202.420i 0.331779 0.376245i
\(539\) 222.968 + 222.968i 0.413669 + 0.413669i
\(540\) 0 0
\(541\) −9.41176 9.41176i −0.0173970 0.0173970i 0.698355 0.715752i \(-0.253916\pi\)
−0.715752 + 0.698355i \(0.753916\pi\)
\(542\) −92.8154 + 5.82902i −0.171246 + 0.0107546i
\(543\) 0 0
\(544\) −297.322 916.809i −0.546548 1.68531i
\(545\) −245.076 −0.449680
\(546\) 0 0
\(547\) −37.6377 + 37.6377i −0.0688075 + 0.0688075i −0.740673 0.671866i \(-0.765493\pi\)
0.671866 + 0.740673i \(0.265493\pi\)
\(548\) 1.07471 + 8.52253i 0.00196115 + 0.0155521i
\(549\) 0 0
\(550\) 41.4772 + 36.5753i 0.0754131 + 0.0665006i
\(551\) −843.953 −1.53168
\(552\) 0 0
\(553\) 525.821i 0.950852i
\(554\) 64.7186 + 57.0700i 0.116821 + 0.103014i
\(555\) 0 0
\(556\) 488.221 + 378.878i 0.878096 + 0.681436i
\(557\) −369.172 369.172i −0.662786 0.662786i 0.293250 0.956036i \(-0.405263\pi\)
−0.956036 + 0.293250i \(0.905263\pi\)
\(558\) 0 0
\(559\) 280.424i 0.501652i
\(560\) 154.960 261.755i 0.276714 0.467420i
\(561\) 0 0
\(562\) −433.624 + 27.2326i −0.771573 + 0.0484565i
\(563\) 141.210 141.210i 0.250817 0.250817i −0.570489 0.821306i \(-0.693246\pi\)
0.821306 + 0.570489i \(0.193246\pi\)
\(564\) 0 0
\(565\) −184.954 + 184.954i −0.327352 + 0.327352i
\(566\) 254.520 288.631i 0.449682 0.509949i
\(567\) 0 0
\(568\) 59.9788 + 314.995i 0.105596 + 0.554568i
\(569\) 134.928i 0.237131i −0.992946 0.118566i \(-0.962170\pi\)
0.992946 0.118566i \(-0.0378296\pi\)
\(570\) 0 0
\(571\) −486.485 486.485i −0.851988 0.851988i 0.138390 0.990378i \(-0.455807\pi\)
−0.990378 + 0.138390i \(0.955807\pi\)
\(572\) 29.3097 + 232.429i 0.0512407 + 0.406344i
\(573\) 0 0
\(574\) 389.052 24.4333i 0.677790 0.0425668i
\(575\) 80.8885i 0.140676i
\(576\) 0 0
\(577\) −310.050 −0.537349 −0.268674 0.963231i \(-0.586586\pi\)
−0.268674 + 0.963231i \(0.586586\pi\)
\(578\) 77.4919 + 1233.90i 0.134069 + 2.13478i
\(579\) 0 0
\(580\) 564.034 71.1257i 0.972472 0.122631i
\(581\) −9.13868 + 9.13868i −0.0157292 + 0.0157292i
\(582\) 0 0
\(583\) −6.50888 −0.0111645
\(584\) −242.126 + 46.1037i −0.414599 + 0.0789448i
\(585\) 0 0
\(586\) 120.574 + 106.324i 0.205757 + 0.181440i
\(587\) 301.021 + 301.021i 0.512812 + 0.512812i 0.915387 0.402575i \(-0.131885\pi\)
−0.402575 + 0.915387i \(0.631885\pi\)
\(588\) 0 0
\(589\) 751.465 + 751.465i 1.27583 + 1.27583i
\(590\) 8.32175 + 132.507i 0.0141047 + 0.224588i
\(591\) 0 0
\(592\) −494.412 + 835.150i −0.835155 + 1.41073i
\(593\) −6.08782 −0.0102661 −0.00513307 0.999987i \(-0.501634\pi\)
−0.00513307 + 0.999987i \(0.501634\pi\)
\(594\) 0 0
\(595\) −404.898 + 404.898i −0.680501 + 0.680501i
\(596\) 276.392 356.158i 0.463746 0.597581i
\(597\) 0 0
\(598\) −226.640 + 257.015i −0.378997 + 0.429790i
\(599\) 756.472 1.26289 0.631446 0.775420i \(-0.282462\pi\)
0.631446 + 0.775420i \(0.282462\pi\)
\(600\) 0 0
\(601\) 753.072i 1.25303i −0.779409 0.626516i \(-0.784480\pi\)
0.779409 0.626516i \(-0.215520\pi\)
\(602\) 247.012 280.117i 0.410319 0.465310i
\(603\) 0 0
\(604\) −418.868 + 52.8200i −0.693490 + 0.0874504i
\(605\) 92.6521 + 92.6521i 0.153144 + 0.153144i
\(606\) 0 0
\(607\) 47.1200i 0.0776277i 0.999246 + 0.0388139i \(0.0123579\pi\)
−0.999246 + 0.0388139i \(0.987642\pi\)
\(608\) −796.334 406.314i −1.30976 0.668280i
\(609\) 0 0
\(610\) −31.6495 503.954i −0.0518844 0.826155i
\(611\) 67.9271 67.9271i 0.111174 0.111174i
\(612\) 0 0
\(613\) 637.192 637.192i 1.03947 1.03947i 0.0402769 0.999189i \(-0.487176\pi\)
0.999189 0.0402769i \(-0.0128240\pi\)
\(614\) 521.717 + 460.059i 0.849701 + 0.749282i
\(615\) 0 0
\(616\) 175.458 257.992i 0.284834 0.418818i
\(617\) 514.635i 0.834092i −0.908885 0.417046i \(-0.863065\pi\)
0.908885 0.417046i \(-0.136935\pi\)
\(618\) 0 0
\(619\) 313.704 + 313.704i 0.506791 + 0.506791i 0.913540 0.406749i \(-0.133338\pi\)
−0.406749 + 0.913540i \(0.633338\pi\)
\(620\) −565.553 438.891i −0.912182 0.707888i
\(621\) 0 0
\(622\) 45.1243 + 718.513i 0.0725471 + 1.15517i
\(623\) 291.845i 0.468452i
\(624\) 0 0
\(625\) 545.171 0.872273
\(626\) −261.532 + 16.4248i −0.417782 + 0.0262377i
\(627\) 0 0
\(628\) −849.380 659.151i −1.35252 1.04960i
\(629\) 1291.86 1291.86i 2.05383 2.05383i
\(630\) 0 0
\(631\) −1226.20 −1.94326 −0.971631 0.236502i \(-0.923999\pi\)
−0.971631 + 0.236502i \(0.923999\pi\)
\(632\) −1022.63 + 194.721i −1.61808 + 0.308103i
\(633\) 0 0
\(634\) 166.581 188.906i 0.262746 0.297960i
\(635\) −365.706 365.706i −0.575914 0.575914i
\(636\) 0 0
\(637\) −140.189 140.189i −0.220078 0.220078i
\(638\) 581.964 36.5487i 0.912169 0.0572863i
\(639\) 0 0
\(640\) 566.452 + 204.437i 0.885081 + 0.319432i
\(641\) −241.218 −0.376314 −0.188157 0.982139i \(-0.560251\pi\)
−0.188157 + 0.982139i \(0.560251\pi\)
\(642\) 0 0
\(643\) −736.141 + 736.141i −1.14485 + 1.14485i −0.157304 + 0.987550i \(0.550280\pi\)
−0.987550 + 0.157304i \(0.949720\pi\)
\(644\) 452.784 57.0969i 0.703081 0.0886598i
\(645\) 0 0
\(646\) 1262.25 + 1113.07i 1.95394 + 1.72302i
\(647\) 680.082 1.05113 0.525565 0.850753i \(-0.323854\pi\)
0.525565 + 0.850753i \(0.323854\pi\)
\(648\) 0 0
\(649\) 136.180i 0.209831i
\(650\) −26.0785 22.9965i −0.0401208 0.0353793i
\(651\) 0 0
\(652\) 206.052 265.518i 0.316030 0.407235i
\(653\) 716.929 + 716.929i 1.09790 + 1.09790i 0.994656 + 0.103244i \(0.0329224\pi\)
0.103244 + 0.994656i \(0.467078\pi\)
\(654\) 0 0
\(655\) 503.540i 0.768763i
\(656\) 191.591 + 747.589i 0.292060 + 1.13962i
\(657\) 0 0
\(658\) −127.686 + 8.01900i −0.194052 + 0.0121869i
\(659\) −276.868 + 276.868i −0.420133 + 0.420133i −0.885250 0.465116i \(-0.846012\pi\)
0.465116 + 0.885250i \(0.346012\pi\)
\(660\) 0 0
\(661\) 251.780 251.780i 0.380907 0.380907i −0.490522 0.871429i \(-0.663194\pi\)
0.871429 + 0.490522i \(0.163194\pi\)
\(662\) −178.838 + 202.807i −0.270149 + 0.306354i
\(663\) 0 0
\(664\) −21.1573 14.3889i −0.0318634 0.0216700i
\(665\) 531.136i 0.798700i
\(666\) 0 0
\(667\) 603.109 + 603.109i 0.904211 + 0.904211i
\(668\) 259.502 32.7238i 0.388477 0.0489877i
\(669\) 0 0
\(670\) −266.556 + 16.7403i −0.397845 + 0.0249856i
\(671\) 517.924i 0.771869i
\(672\) 0 0
\(673\) 674.332 1.00198 0.500990 0.865453i \(-0.332969\pi\)
0.500990 + 0.865453i \(0.332969\pi\)
\(674\) 73.1734 + 1165.14i 0.108566 + 1.72869i
\(675\) 0 0
\(676\) 66.1468 + 524.550i 0.0978503 + 0.775962i
\(677\) −109.048 + 109.048i −0.161075 + 0.161075i −0.783043 0.621968i \(-0.786334\pi\)
0.621968 + 0.783043i \(0.286334\pi\)
\(678\) 0 0
\(679\) 453.963 0.668576
\(680\) −937.396 637.514i −1.37852 0.937521i
\(681\) 0 0
\(682\) −550.731 485.644i −0.807523 0.712088i
\(683\) 784.278 + 784.278i 1.14828 + 1.14828i 0.986890 + 0.161394i \(0.0515990\pi\)
0.161394 + 0.986890i \(0.448401\pi\)
\(684\) 0 0
\(685\) 7.14432 + 7.14432i 0.0104297 + 0.0104297i
\(686\) 41.3710 + 658.750i 0.0603076 + 0.960277i
\(687\) 0 0
\(688\) 636.250 + 376.662i 0.924782 + 0.547474i
\(689\) 4.09241 0.00593964
\(690\) 0 0
\(691\) −99.4915 + 99.4915i −0.143982 + 0.143982i −0.775423 0.631442i \(-0.782464\pi\)
0.631442 + 0.775423i \(0.282464\pi\)
\(692\) −951.628 738.500i −1.37518 1.06720i
\(693\) 0 0
\(694\) 358.531 406.582i 0.516615 0.585853i
\(695\) 726.877 1.04587
\(696\) 0 0
\(697\) 1452.78i 2.08433i
\(698\) 36.4379 41.3213i 0.0522032 0.0591996i
\(699\) 0 0
\(700\) 5.79346 + 45.9427i 0.00827637 + 0.0656324i
\(701\) −177.909 177.909i −0.253794 0.253794i 0.568730 0.822524i \(-0.307435\pi\)
−0.822524 + 0.568730i \(0.807435\pi\)
\(702\) 0 0
\(703\) 1694.63i 2.41057i
\(704\) 566.723 + 245.695i 0.805005 + 0.348999i
\(705\) 0 0
\(706\) 10.3998 + 165.596i 0.0147306 + 0.234555i
\(707\) −6.54353 + 6.54353i −0.00925535 + 0.00925535i
\(708\) 0 0
\(709\) −208.080 + 208.080i −0.293484 + 0.293484i −0.838455 0.544971i \(-0.816541\pi\)
0.544971 + 0.838455i \(0.316541\pi\)
\(710\) 282.879 + 249.448i 0.398421 + 0.351335i
\(711\) 0 0
\(712\) −567.587 + 108.076i −0.797173 + 0.151791i
\(713\) 1074.03i 1.50635i
\(714\) 0 0
\(715\) 194.841 + 194.841i 0.272506 + 0.272506i
\(716\) 682.707 879.734i 0.953501 1.22868i
\(717\) 0 0
\(718\) −44.8519 714.176i −0.0624678 0.994674i
\(719\) 1013.84i 1.41007i 0.709171 + 0.705036i \(0.249069\pi\)
−0.709171 + 0.705036i \(0.750931\pi\)
\(720\) 0 0
\(721\) −113.134 −0.156913
\(722\) 837.364 52.5883i 1.15978 0.0728370i
\(723\) 0 0
\(724\) 95.1413 122.599i 0.131411 0.169335i
\(725\) −61.1957 + 61.1957i −0.0844079 + 0.0844079i
\(726\) 0 0
\(727\) 697.156 0.958949 0.479474 0.877556i \(-0.340827\pi\)
0.479474 + 0.877556i \(0.340827\pi\)
\(728\) −110.318 + 162.211i −0.151536 + 0.222817i
\(729\) 0 0
\(730\) −191.742 + 217.440i −0.262661 + 0.297863i
\(731\) −984.189 984.189i −1.34636 1.34636i
\(732\) 0 0
\(733\) −39.9608 39.9608i −0.0545168 0.0545168i 0.679323 0.733840i \(-0.262274\pi\)
−0.733840 + 0.679323i \(0.762274\pi\)
\(734\) −1300.89 + 81.6991i −1.77234 + 0.111307i
\(735\) 0 0
\(736\) 278.717 + 859.441i 0.378692 + 1.16772i
\(737\) −273.945 −0.371703
\(738\) 0 0
\(739\) −236.377 + 236.377i −0.319860 + 0.319860i −0.848713 0.528853i \(-0.822622\pi\)
0.528853 + 0.848713i \(0.322622\pi\)
\(740\) 142.818 + 1132.56i 0.192998 + 1.53049i
\(741\) 0 0
\(742\) −4.08794 3.60481i −0.00550935 0.00485824i
\(743\) −804.248 −1.08243 −0.541217 0.840883i \(-0.682036\pi\)
−0.541217 + 0.840883i \(0.682036\pi\)
\(744\) 0 0
\(745\) 530.258i 0.711755i
\(746\) 423.691 + 373.618i 0.567950 + 0.500828i
\(747\) 0 0
\(748\) −918.610 712.877i −1.22809 0.953043i
\(749\) −163.185 163.185i −0.217870 0.217870i
\(750\) 0 0
\(751\) 607.492i 0.808911i −0.914558 0.404456i \(-0.867461\pi\)
0.914558 0.404456i \(-0.132539\pi\)
\(752\) −62.8801 245.358i −0.0836171 0.326274i
\(753\) 0 0
\(754\) −365.906 + 22.9797i −0.485287 + 0.0304771i
\(755\) −351.131 + 351.131i −0.465074 + 0.465074i
\(756\) 0 0
\(757\) −11.6797 + 11.6797i −0.0154289 + 0.0154289i −0.714779 0.699350i \(-0.753473\pi\)
0.699350 + 0.714779i \(0.253473\pi\)
\(758\) 617.716 700.503i 0.814929 0.924147i
\(759\) 0 0
\(760\) −1032.96 + 196.689i −1.35916 + 0.258801i
\(761\) 659.125i 0.866130i −0.901363 0.433065i \(-0.857432\pi\)
0.901363 0.433065i \(-0.142568\pi\)
\(762\) 0 0
\(763\) −148.840 148.840i −0.195073 0.195073i
\(764\) −122.313 969.954i −0.160096 1.26957i
\(765\) 0 0
\(766\) 347.882 21.8478i 0.454154 0.0285219i
\(767\) 85.6224i 0.111633i
\(768\) 0 0
\(769\) −178.802 −0.232512 −0.116256 0.993219i \(-0.537089\pi\)
−0.116256 + 0.993219i \(0.537089\pi\)
\(770\) −23.0016 366.255i −0.0298722 0.475656i
\(771\) 0 0
\(772\) −1012.15 + 127.633i −1.31107 + 0.165328i
\(773\) 91.8171 91.8171i 0.118780 0.118780i −0.645218 0.763998i \(-0.723234\pi\)
0.763998 + 0.645218i \(0.223234\pi\)
\(774\) 0 0
\(775\) 108.979 0.140618
\(776\) 168.111 + 882.877i 0.216637 + 1.13773i
\(777\) 0 0
\(778\) −440.906 388.798i −0.566717 0.499741i
\(779\) −952.860 952.860i −1.22318 1.22318i
\(780\) 0 0
\(781\) 273.541 + 273.541i 0.350245 + 0.350245i
\(782\) −106.604 1697.46i −0.136323 2.17066i
\(783\) 0 0
\(784\) −506.376 + 129.773i −0.645887 + 0.165527i
\(785\) −1264.58 −1.61093
\(786\) 0 0
\(787\) 214.856 214.856i 0.273006 0.273006i −0.557303