Properties

Label 384.3.i.d.353.3
Level $384$
Weight $3$
Character 384.353
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{23} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 353.3
Root \(-1.85381 - 0.750590i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.d.161.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50491 - 2.59524i) q^{3} +(2.59897 - 2.59897i) q^{5} +7.30027i q^{7} +(-4.47050 + 7.81118i) q^{9} +O(q^{10})\) \(q+(-1.50491 - 2.59524i) q^{3} +(2.59897 - 2.59897i) q^{5} +7.30027i q^{7} +(-4.47050 + 7.81118i) q^{9} +(-11.3161 + 11.3161i) q^{11} +(0.746462 - 0.746462i) q^{13} +(-10.6561 - 2.83373i) q^{15} -6.67452i q^{17} +(-22.1936 + 22.1936i) q^{19} +(18.9459 - 10.9862i) q^{21} +21.4389 q^{23} +11.4908i q^{25} +(26.9996 - 0.153096i) q^{27} +(-1.54272 - 1.54272i) q^{29} -14.6082 q^{31} +(46.3976 + 12.3382i) q^{33} +(18.9732 + 18.9732i) q^{35} +(50.1010 + 50.1010i) q^{37} +(-3.06060 - 0.813888i) q^{39} -15.0731 q^{41} +(-26.3634 - 26.3634i) q^{43} +(8.68231 + 31.9197i) q^{45} +36.6067i q^{47} -4.29399 q^{49} +(-17.3220 + 10.0445i) q^{51} +(-50.9270 + 50.9270i) q^{53} +58.8202i q^{55} +(90.9971 + 24.1983i) q^{57} +(12.1683 - 12.1683i) q^{59} +(27.5789 - 27.5789i) q^{61} +(-57.0238 - 32.6359i) q^{63} -3.88006i q^{65} +(4.84214 - 4.84214i) q^{67} +(-32.2636 - 55.6391i) q^{69} -74.9072 q^{71} -3.47110i q^{73} +(29.8212 - 17.2925i) q^{75} +(-82.6105 - 82.6105i) q^{77} +103.463 q^{79} +(-41.0292 - 69.8399i) q^{81} +(31.7254 + 31.7254i) q^{83} +(-17.3469 - 17.3469i) q^{85} +(-1.68207 + 6.32538i) q^{87} -78.2605 q^{89} +(5.44937 + 5.44937i) q^{91} +(21.9840 + 37.9118i) q^{93} +115.361i q^{95} -61.5651 q^{97} +(-37.8034 - 138.981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{3} + O(q^{10}) \) \( 20q + 6q^{3} - 92q^{13} - 116q^{15} + 52q^{19} - 48q^{21} - 18q^{27} - 80q^{31} + 60q^{33} + 116q^{37} - 172q^{43} - 60q^{45} - 364q^{49} - 128q^{51} + 244q^{61} + 296q^{63} - 356q^{67} + 20q^{69} + 146q^{75} + 384q^{79} - 188q^{81} - 48q^{85} - 136q^{91} + 132q^{93} + 472q^{97} + 452q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
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 0
\(3\) −1.50491 2.59524i −0.501636 0.865079i
\(4\) 0 0
\(5\) 2.59897 2.59897i 0.519793 0.519793i −0.397716 0.917509i \(-0.630197\pi\)
0.917509 + 0.397716i \(0.130197\pi\)
\(6\) 0 0
\(7\) 7.30027i 1.04290i 0.853283 + 0.521448i \(0.174608\pi\)
−0.853283 + 0.521448i \(0.825392\pi\)
\(8\) 0 0
\(9\) −4.47050 + 7.81118i −0.496723 + 0.867909i
\(10\) 0 0
\(11\) −11.3161 + 11.3161i −1.02873 + 1.02873i −0.0291601 + 0.999575i \(0.509283\pi\)
−0.999575 + 0.0291601i \(0.990717\pi\)
\(12\) 0 0
\(13\) 0.746462 0.746462i 0.0574201 0.0574201i −0.677814 0.735234i \(-0.737072\pi\)
0.735234 + 0.677814i \(0.237072\pi\)
\(14\) 0 0
\(15\) −10.6561 2.83373i −0.710409 0.188915i
\(16\) 0 0
\(17\) 6.67452i 0.392619i −0.980542 0.196310i \(-0.937104\pi\)
0.980542 0.196310i \(-0.0628957\pi\)
\(18\) 0 0
\(19\) −22.1936 + 22.1936i −1.16809 + 1.16809i −0.185428 + 0.982658i \(0.559367\pi\)
−0.982658 + 0.185428i \(0.940633\pi\)
\(20\) 0 0
\(21\) 18.9459 10.9862i 0.902187 0.523154i
\(22\) 0 0
\(23\) 21.4389 0.932128 0.466064 0.884751i \(-0.345672\pi\)
0.466064 + 0.884751i \(0.345672\pi\)
\(24\) 0 0
\(25\) 11.4908i 0.459630i
\(26\) 0 0
\(27\) 26.9996 0.153096i 0.999984 0.00567024i
\(28\) 0 0
\(29\) −1.54272 1.54272i −0.0531973 0.0531973i 0.680008 0.733205i \(-0.261976\pi\)
−0.733205 + 0.680008i \(0.761976\pi\)
\(30\) 0 0
\(31\) −14.6082 −0.471233 −0.235616 0.971846i \(-0.575711\pi\)
−0.235616 + 0.971846i \(0.575711\pi\)
\(32\) 0 0
\(33\) 46.3976 + 12.3382i 1.40599 + 0.373886i
\(34\) 0 0
\(35\) 18.9732 + 18.9732i 0.542090 + 0.542090i
\(36\) 0 0
\(37\) 50.1010 + 50.1010i 1.35408 + 1.35408i 0.881041 + 0.473039i \(0.156843\pi\)
0.473039 + 0.881041i \(0.343157\pi\)
\(38\) 0 0
\(39\) −3.06060 0.813888i −0.0784769 0.0208689i
\(40\) 0 0
\(41\) −15.0731 −0.367637 −0.183819 0.982960i \(-0.558846\pi\)
−0.183819 + 0.982960i \(0.558846\pi\)
\(42\) 0 0
\(43\) −26.3634 26.3634i −0.613102 0.613102i 0.330651 0.943753i \(-0.392732\pi\)
−0.943753 + 0.330651i \(0.892732\pi\)
\(44\) 0 0
\(45\) 8.68231 + 31.9197i 0.192940 + 0.709326i
\(46\) 0 0
\(47\) 36.6067i 0.778866i 0.921055 + 0.389433i \(0.127329\pi\)
−0.921055 + 0.389433i \(0.872671\pi\)
\(48\) 0 0
\(49\) −4.29399 −0.0876325
\(50\) 0 0
\(51\) −17.3220 + 10.0445i −0.339646 + 0.196952i
\(52\) 0 0
\(53\) −50.9270 + 50.9270i −0.960887 + 0.960887i −0.999263 0.0383765i \(-0.987781\pi\)
0.0383765 + 0.999263i \(0.487781\pi\)
\(54\) 0 0
\(55\) 58.8202i 1.06946i
\(56\) 0 0
\(57\) 90.9971 + 24.1983i 1.59644 + 0.424532i
\(58\) 0 0
\(59\) 12.1683 12.1683i 0.206242 0.206242i −0.596426 0.802668i \(-0.703413\pi\)
0.802668 + 0.596426i \(0.203413\pi\)
\(60\) 0 0
\(61\) 27.5789 27.5789i 0.452113 0.452113i −0.443943 0.896055i \(-0.646421\pi\)
0.896055 + 0.443943i \(0.146421\pi\)
\(62\) 0 0
\(63\) −57.0238 32.6359i −0.905139 0.518030i
\(64\) 0 0
\(65\) 3.88006i 0.0596932i
\(66\) 0 0
\(67\) 4.84214 4.84214i 0.0722707 0.0722707i −0.670047 0.742318i \(-0.733726\pi\)
0.742318 + 0.670047i \(0.233726\pi\)
\(68\) 0 0
\(69\) −32.2636 55.6391i −0.467589 0.806364i
\(70\) 0 0
\(71\) −74.9072 −1.05503 −0.527515 0.849546i \(-0.676876\pi\)
−0.527515 + 0.849546i \(0.676876\pi\)
\(72\) 0 0
\(73\) 3.47110i 0.0475494i −0.999717 0.0237747i \(-0.992432\pi\)
0.999717 0.0237747i \(-0.00756843\pi\)
\(74\) 0 0
\(75\) 29.8212 17.2925i 0.397616 0.230567i
\(76\) 0 0
\(77\) −82.6105 82.6105i −1.07286 1.07286i
\(78\) 0 0
\(79\) 103.463 1.30966 0.654831 0.755775i \(-0.272740\pi\)
0.654831 + 0.755775i \(0.272740\pi\)
\(80\) 0 0
\(81\) −41.0292 69.8399i −0.506533 0.862221i
\(82\) 0 0
\(83\) 31.7254 + 31.7254i 0.382233 + 0.382233i 0.871906 0.489673i \(-0.162884\pi\)
−0.489673 + 0.871906i \(0.662884\pi\)
\(84\) 0 0
\(85\) −17.3469 17.3469i −0.204081 0.204081i
\(86\) 0 0
\(87\) −1.68207 + 6.32538i −0.0193342 + 0.0727056i
\(88\) 0 0
\(89\) −78.2605 −0.879331 −0.439666 0.898162i \(-0.644903\pi\)
−0.439666 + 0.898162i \(0.644903\pi\)
\(90\) 0 0
\(91\) 5.44937 + 5.44937i 0.0598832 + 0.0598832i
\(92\) 0 0
\(93\) 21.9840 + 37.9118i 0.236387 + 0.407653i
\(94\) 0 0
\(95\) 115.361i 1.21433i
\(96\) 0 0
\(97\) −61.5651 −0.634692 −0.317346 0.948310i \(-0.602792\pi\)
−0.317346 + 0.948310i \(0.602792\pi\)
\(98\) 0 0
\(99\) −37.8034 138.981i −0.381853 1.40384i
\(100\) 0 0
\(101\) 56.9675 56.9675i 0.564034 0.564034i −0.366417 0.930451i \(-0.619415\pi\)
0.930451 + 0.366417i \(0.119415\pi\)
\(102\) 0 0
\(103\) 153.944i 1.49460i −0.664485 0.747301i \(-0.731349\pi\)
0.664485 0.747301i \(-0.268651\pi\)
\(104\) 0 0
\(105\) 20.6870 77.7927i 0.197019 0.740883i
\(106\) 0 0
\(107\) −76.9344 + 76.9344i −0.719013 + 0.719013i −0.968403 0.249390i \(-0.919770\pi\)
0.249390 + 0.968403i \(0.419770\pi\)
\(108\) 0 0
\(109\) −74.1271 + 74.1271i −0.680065 + 0.680065i −0.960015 0.279949i \(-0.909682\pi\)
0.279949 + 0.960015i \(0.409682\pi\)
\(110\) 0 0
\(111\) 54.6265 205.421i 0.492131 1.85064i
\(112\) 0 0
\(113\) 38.3909i 0.339742i 0.985466 + 0.169871i \(0.0543352\pi\)
−0.985466 + 0.169871i \(0.945665\pi\)
\(114\) 0 0
\(115\) 55.7191 55.7191i 0.484514 0.484514i
\(116\) 0 0
\(117\) 2.49369 + 9.16781i 0.0213136 + 0.0783573i
\(118\) 0 0
\(119\) 48.7259 0.409461
\(120\) 0 0
\(121\) 135.108i 1.11659i
\(122\) 0 0
\(123\) 22.6837 + 39.1184i 0.184420 + 0.318035i
\(124\) 0 0
\(125\) 94.8382 + 94.8382i 0.758706 + 0.758706i
\(126\) 0 0
\(127\) −43.3417 −0.341273 −0.170636 0.985334i \(-0.554582\pi\)
−0.170636 + 0.985334i \(0.554582\pi\)
\(128\) 0 0
\(129\) −28.7447 + 108.094i −0.222827 + 0.837935i
\(130\) 0 0
\(131\) −1.21414 1.21414i −0.00926827 0.00926827i 0.702457 0.711726i \(-0.252086\pi\)
−0.711726 + 0.702457i \(0.752086\pi\)
\(132\) 0 0
\(133\) −162.020 162.020i −1.21819 1.21819i
\(134\) 0 0
\(135\) 69.7730 70.5688i 0.516837 0.522732i
\(136\) 0 0
\(137\) −238.227 −1.73889 −0.869443 0.494033i \(-0.835522\pi\)
−0.869443 + 0.494033i \(0.835522\pi\)
\(138\) 0 0
\(139\) 26.5704 + 26.5704i 0.191154 + 0.191154i 0.796195 0.605041i \(-0.206843\pi\)
−0.605041 + 0.796195i \(0.706843\pi\)
\(140\) 0 0
\(141\) 95.0030 55.0897i 0.673780 0.390707i
\(142\) 0 0
\(143\) 16.8940i 0.118140i
\(144\) 0 0
\(145\) −8.01896 −0.0553032
\(146\) 0 0
\(147\) 6.46207 + 11.1439i 0.0439596 + 0.0758090i
\(148\) 0 0
\(149\) −133.254 + 133.254i −0.894321 + 0.894321i −0.994926 0.100605i \(-0.967922\pi\)
0.100605 + 0.994926i \(0.467922\pi\)
\(150\) 0 0
\(151\) 23.3716i 0.154779i −0.997001 0.0773895i \(-0.975342\pi\)
0.997001 0.0773895i \(-0.0246585\pi\)
\(152\) 0 0
\(153\) 52.1359 + 29.8385i 0.340758 + 0.195023i
\(154\) 0 0
\(155\) −37.9662 + 37.9662i −0.244943 + 0.244943i
\(156\) 0 0
\(157\) 95.8780 95.8780i 0.610688 0.610688i −0.332438 0.943125i \(-0.607871\pi\)
0.943125 + 0.332438i \(0.107871\pi\)
\(158\) 0 0
\(159\) 208.808 + 55.5272i 1.31326 + 0.349227i
\(160\) 0 0
\(161\) 156.510i 0.972113i
\(162\) 0 0
\(163\) 103.379 103.379i 0.634230 0.634230i −0.314896 0.949126i \(-0.601970\pi\)
0.949126 + 0.314896i \(0.101970\pi\)
\(164\) 0 0
\(165\) 152.652 88.5190i 0.925166 0.536479i
\(166\) 0 0
\(167\) 113.980 0.682515 0.341258 0.939970i \(-0.389147\pi\)
0.341258 + 0.939970i \(0.389147\pi\)
\(168\) 0 0
\(169\) 167.886i 0.993406i
\(170\) 0 0
\(171\) −74.1418 272.575i −0.433578 1.59401i
\(172\) 0 0
\(173\) −144.265 144.265i −0.833901 0.833901i 0.154147 0.988048i \(-0.450737\pi\)
−0.988048 + 0.154147i \(0.950737\pi\)
\(174\) 0 0
\(175\) −83.8857 −0.479347
\(176\) 0 0
\(177\) −49.8918 13.2674i −0.281875 0.0749573i
\(178\) 0 0
\(179\) 16.8240 + 16.8240i 0.0939888 + 0.0939888i 0.752538 0.658549i \(-0.228829\pi\)
−0.658549 + 0.752538i \(0.728829\pi\)
\(180\) 0 0
\(181\) −34.2037 34.2037i −0.188971 0.188971i 0.606280 0.795251i \(-0.292661\pi\)
−0.795251 + 0.606280i \(0.792661\pi\)
\(182\) 0 0
\(183\) −113.077 30.0700i −0.617909 0.164317i
\(184\) 0 0
\(185\) 260.421 1.40768
\(186\) 0 0
\(187\) 75.5295 + 75.5295i 0.403901 + 0.403901i
\(188\) 0 0
\(189\) 1.11765 + 197.104i 0.00591347 + 1.04288i
\(190\) 0 0
\(191\) 150.160i 0.786177i −0.919501 0.393088i \(-0.871407\pi\)
0.919501 0.393088i \(-0.128593\pi\)
\(192\) 0 0
\(193\) 117.637 0.609518 0.304759 0.952429i \(-0.401424\pi\)
0.304759 + 0.952429i \(0.401424\pi\)
\(194\) 0 0
\(195\) −10.0697 + 5.83913i −0.0516393 + 0.0299442i
\(196\) 0 0
\(197\) −31.8524 + 31.8524i −0.161688 + 0.161688i −0.783314 0.621626i \(-0.786472\pi\)
0.621626 + 0.783314i \(0.286472\pi\)
\(198\) 0 0
\(199\) 128.347i 0.644959i 0.946576 + 0.322480i \(0.104516\pi\)
−0.946576 + 0.322480i \(0.895484\pi\)
\(200\) 0 0
\(201\) −19.8535 5.27952i −0.0987735 0.0262663i
\(202\) 0 0
\(203\) 11.2623 11.2623i 0.0554793 0.0554793i
\(204\) 0 0
\(205\) −39.1746 + 39.1746i −0.191095 + 0.191095i
\(206\) 0 0
\(207\) −95.8429 + 167.464i −0.463009 + 0.809003i
\(208\) 0 0
\(209\) 502.290i 2.40330i
\(210\) 0 0
\(211\) −78.8045 + 78.8045i −0.373481 + 0.373481i −0.868743 0.495262i \(-0.835072\pi\)
0.495262 + 0.868743i \(0.335072\pi\)
\(212\) 0 0
\(213\) 112.728 + 194.402i 0.529241 + 0.912685i
\(214\) 0 0
\(215\) −137.035 −0.637372
\(216\) 0 0
\(217\) 106.644i 0.491447i
\(218\) 0 0
\(219\) −9.00834 + 5.22369i −0.0411340 + 0.0238525i
\(220\) 0 0
\(221\) −4.98228 4.98228i −0.0225442 0.0225442i
\(222\) 0 0
\(223\) −153.748 −0.689455 −0.344727 0.938703i \(-0.612029\pi\)
−0.344727 + 0.938703i \(0.612029\pi\)
\(224\) 0 0
\(225\) −89.7564 51.3695i −0.398917 0.228309i
\(226\) 0 0
\(227\) 43.6518 + 43.6518i 0.192299 + 0.192299i 0.796689 0.604390i \(-0.206583\pi\)
−0.604390 + 0.796689i \(0.706583\pi\)
\(228\) 0 0
\(229\) 111.882 + 111.882i 0.488566 + 0.488566i 0.907853 0.419288i \(-0.137720\pi\)
−0.419288 + 0.907853i \(0.637720\pi\)
\(230\) 0 0
\(231\) −90.0726 + 338.715i −0.389925 + 1.46630i
\(232\) 0 0
\(233\) −32.4793 −0.139396 −0.0696980 0.997568i \(-0.522204\pi\)
−0.0696980 + 0.997568i \(0.522204\pi\)
\(234\) 0 0
\(235\) 95.1395 + 95.1395i 0.404849 + 0.404849i
\(236\) 0 0
\(237\) −155.703 268.512i −0.656974 1.13296i
\(238\) 0 0
\(239\) 133.305i 0.557762i 0.960326 + 0.278881i \(0.0899636\pi\)
−0.960326 + 0.278881i \(0.910036\pi\)
\(240\) 0 0
\(241\) 159.670 0.662532 0.331266 0.943537i \(-0.392524\pi\)
0.331266 + 0.943537i \(0.392524\pi\)
\(242\) 0 0
\(243\) −119.506 + 211.583i −0.491793 + 0.870712i
\(244\) 0 0
\(245\) −11.1599 + 11.1599i −0.0455508 + 0.0455508i
\(246\) 0 0
\(247\) 33.1334i 0.134143i
\(248\) 0 0
\(249\) 34.5911 130.079i 0.138920 0.522404i
\(250\) 0 0
\(251\) 106.711 106.711i 0.425141 0.425141i −0.461828 0.886969i \(-0.652806\pi\)
0.886969 + 0.461828i \(0.152806\pi\)
\(252\) 0 0
\(253\) −242.605 + 242.605i −0.958913 + 0.958913i
\(254\) 0 0
\(255\) −18.9138 + 71.1246i −0.0741717 + 0.278920i
\(256\) 0 0
\(257\) 343.816i 1.33781i 0.743350 + 0.668903i \(0.233236\pi\)
−0.743350 + 0.668903i \(0.766764\pi\)
\(258\) 0 0
\(259\) −365.751 + 365.751i −1.41217 + 1.41217i
\(260\) 0 0
\(261\) 18.9472 5.15374i 0.0725948 0.0197461i
\(262\) 0 0
\(263\) −266.255 −1.01238 −0.506188 0.862423i \(-0.668946\pi\)
−0.506188 + 0.862423i \(0.668946\pi\)
\(264\) 0 0
\(265\) 264.715i 0.998925i
\(266\) 0 0
\(267\) 117.775 + 203.104i 0.441104 + 0.760691i
\(268\) 0 0
\(269\) 102.194 + 102.194i 0.379904 + 0.379904i 0.871067 0.491164i \(-0.163428\pi\)
−0.491164 + 0.871067i \(0.663428\pi\)
\(270\) 0 0
\(271\) −38.5636 −0.142301 −0.0711505 0.997466i \(-0.522667\pi\)
−0.0711505 + 0.997466i \(0.522667\pi\)
\(272\) 0 0
\(273\) 5.94161 22.3432i 0.0217641 0.0818433i
\(274\) 0 0
\(275\) −130.030 130.030i −0.472838 0.472838i
\(276\) 0 0
\(277\) 277.306 + 277.306i 1.00111 + 1.00111i 0.999999 + 0.00110593i \(0.000352027\pi\)
0.00110593 + 0.999999i \(0.499648\pi\)
\(278\) 0 0
\(279\) 65.3061 114.107i 0.234072 0.408987i
\(280\) 0 0
\(281\) 458.765 1.63262 0.816308 0.577617i \(-0.196017\pi\)
0.816308 + 0.577617i \(0.196017\pi\)
\(282\) 0 0
\(283\) −276.746 276.746i −0.977900 0.977900i 0.0218614 0.999761i \(-0.493041\pi\)
−0.999761 + 0.0218614i \(0.993041\pi\)
\(284\) 0 0
\(285\) 299.389 173.608i 1.05049 0.609149i
\(286\) 0 0
\(287\) 110.038i 0.383408i
\(288\) 0 0
\(289\) 244.451 0.845850
\(290\) 0 0
\(291\) 92.6499 + 159.776i 0.318384 + 0.549059i
\(292\) 0 0
\(293\) 306.513 306.513i 1.04612 1.04612i 0.0472370 0.998884i \(-0.484958\pi\)
0.998884 0.0472370i \(-0.0150416\pi\)
\(294\) 0 0
\(295\) 63.2500i 0.214407i
\(296\) 0 0
\(297\) −303.797 + 307.262i −1.02289 + 1.03455i
\(298\) 0 0
\(299\) 16.0033 16.0033i 0.0535229 0.0535229i
\(300\) 0 0
\(301\) 192.460 192.460i 0.639401 0.639401i
\(302\) 0 0
\(303\) −233.575 62.1133i −0.770874 0.204994i
\(304\) 0 0
\(305\) 143.353i 0.470010i
\(306\) 0 0
\(307\) 359.692 359.692i 1.17163 1.17163i 0.189814 0.981820i \(-0.439211\pi\)
0.981820 0.189814i \(-0.0607886\pi\)
\(308\) 0 0
\(309\) −399.521 + 231.672i −1.29295 + 0.749746i
\(310\) 0 0
\(311\) 572.008 1.83925 0.919626 0.392794i \(-0.128492\pi\)
0.919626 + 0.392794i \(0.128492\pi\)
\(312\) 0 0
\(313\) 333.314i 1.06490i 0.846461 + 0.532450i \(0.178729\pi\)
−0.846461 + 0.532450i \(0.821271\pi\)
\(314\) 0 0
\(315\) −233.022 + 63.3832i −0.739754 + 0.201217i
\(316\) 0 0
\(317\) 266.382 + 266.382i 0.840322 + 0.840322i 0.988901 0.148578i \(-0.0474697\pi\)
−0.148578 + 0.988901i \(0.547470\pi\)
\(318\) 0 0
\(319\) 34.9151 0.109452
\(320\) 0 0
\(321\) 315.442 + 83.8838i 0.982686 + 0.261320i
\(322\) 0 0
\(323\) 148.132 + 148.132i 0.458613 + 0.458613i
\(324\) 0 0
\(325\) 8.57741 + 8.57741i 0.0263920 + 0.0263920i
\(326\) 0 0
\(327\) 303.932 + 80.8229i 0.929455 + 0.247165i
\(328\) 0 0
\(329\) −267.239 −0.812276
\(330\) 0 0
\(331\) 212.431 + 212.431i 0.641787 + 0.641787i 0.950995 0.309208i \(-0.100064\pi\)
−0.309208 + 0.950995i \(0.600064\pi\)
\(332\) 0 0
\(333\) −615.325 + 167.371i −1.84782 + 0.502617i
\(334\) 0 0
\(335\) 25.1691i 0.0751317i
\(336\) 0 0
\(337\) −207.477 −0.615658 −0.307829 0.951442i \(-0.599602\pi\)
−0.307829 + 0.951442i \(0.599602\pi\)
\(338\) 0 0
\(339\) 99.6335 57.7748i 0.293904 0.170427i
\(340\) 0 0
\(341\) 165.308 165.308i 0.484773 0.484773i
\(342\) 0 0
\(343\) 326.366i 0.951505i
\(344\) 0 0
\(345\) −228.456 60.7521i −0.662192 0.176093i
\(346\) 0 0
\(347\) 98.4692 98.4692i 0.283773 0.283773i −0.550839 0.834612i \(-0.685692\pi\)
0.834612 + 0.550839i \(0.185692\pi\)
\(348\) 0 0
\(349\) 337.382 337.382i 0.966711 0.966711i −0.0327527 0.999463i \(-0.510427\pi\)
0.999463 + 0.0327527i \(0.0104274\pi\)
\(350\) 0 0
\(351\) 20.0399 20.2684i 0.0570936 0.0577448i
\(352\) 0 0
\(353\) 293.330i 0.830964i 0.909601 + 0.415482i \(0.136387\pi\)
−0.909601 + 0.415482i \(0.863613\pi\)
\(354\) 0 0
\(355\) −194.681 + 194.681i −0.548398 + 0.548398i
\(356\) 0 0
\(357\) −73.3279 126.455i −0.205400 0.354216i
\(358\) 0 0
\(359\) 305.954 0.852239 0.426119 0.904667i \(-0.359880\pi\)
0.426119 + 0.904667i \(0.359880\pi\)
\(360\) 0 0
\(361\) 624.114i 1.72885i
\(362\) 0 0
\(363\) −350.636 + 203.324i −0.965939 + 0.560122i
\(364\) 0 0
\(365\) −9.02128 9.02128i −0.0247158 0.0247158i
\(366\) 0 0
\(367\) 221.149 0.602585 0.301292 0.953532i \(-0.402582\pi\)
0.301292 + 0.953532i \(0.402582\pi\)
\(368\) 0 0
\(369\) 67.3845 117.739i 0.182614 0.319076i
\(370\) 0 0
\(371\) −371.781 371.781i −1.00211 1.00211i
\(372\) 0 0
\(373\) −147.216 147.216i −0.394682 0.394682i 0.481671 0.876352i \(-0.340030\pi\)
−0.876352 + 0.481671i \(0.840030\pi\)
\(374\) 0 0
\(375\) 103.405 388.850i 0.275746 1.03693i
\(376\) 0 0
\(377\) −2.30317 −0.00610919
\(378\) 0 0
\(379\) −298.572 298.572i −0.787790 0.787790i 0.193342 0.981131i \(-0.438067\pi\)
−0.981131 + 0.193342i \(0.938067\pi\)
\(380\) 0 0
\(381\) 65.2252 + 112.482i 0.171195 + 0.295228i
\(382\) 0 0
\(383\) 427.326i 1.11573i −0.829931 0.557866i \(-0.811620\pi\)
0.829931 0.557866i \(-0.188380\pi\)
\(384\) 0 0
\(385\) −429.404 −1.11533
\(386\) 0 0
\(387\) 323.787 88.0716i 0.836658 0.227575i
\(388\) 0 0
\(389\) 314.075 314.075i 0.807391 0.807391i −0.176847 0.984238i \(-0.556590\pi\)
0.984238 + 0.176847i \(0.0565899\pi\)
\(390\) 0 0
\(391\) 143.095i 0.365971i
\(392\) 0 0
\(393\) −1.32382 + 4.97816i −0.00336849 + 0.0126671i
\(394\) 0 0
\(395\) 268.898 268.898i 0.680753 0.680753i
\(396\) 0 0
\(397\) −189.839 + 189.839i −0.478185 + 0.478185i −0.904551 0.426366i \(-0.859794\pi\)
0.426366 + 0.904551i \(0.359794\pi\)
\(398\) 0 0
\(399\) −176.655 + 664.304i −0.442743 + 1.66492i
\(400\) 0 0
\(401\) 268.223i 0.668886i 0.942416 + 0.334443i \(0.108548\pi\)
−0.942416 + 0.334443i \(0.891452\pi\)
\(402\) 0 0
\(403\) −10.9045 + 10.9045i −0.0270582 + 0.0270582i
\(404\) 0 0
\(405\) −288.145 74.8780i −0.711469 0.184884i
\(406\) 0 0
\(407\) −1133.89 −2.78598
\(408\) 0 0
\(409\) 25.8478i 0.0631976i −0.999501 0.0315988i \(-0.989940\pi\)
0.999501 0.0315988i \(-0.0100599\pi\)
\(410\) 0 0
\(411\) 358.510 + 618.257i 0.872288 + 1.50427i
\(412\) 0 0
\(413\) 88.8319 + 88.8319i 0.215089 + 0.215089i
\(414\) 0 0
\(415\) 164.906 0.397365
\(416\) 0 0
\(417\) 28.9705 108.942i 0.0694735 0.261253i
\(418\) 0 0
\(419\) −243.361 243.361i −0.580813 0.580813i 0.354313 0.935127i \(-0.384715\pi\)
−0.935127 + 0.354313i \(0.884715\pi\)
\(420\) 0 0
\(421\) −115.847 115.847i −0.275171 0.275171i 0.556007 0.831178i \(-0.312333\pi\)
−0.831178 + 0.556007i \(0.812333\pi\)
\(422\) 0 0
\(423\) −285.942 163.650i −0.675985 0.386880i
\(424\) 0 0
\(425\) 76.6953 0.180460
\(426\) 0 0
\(427\) 201.333 + 201.333i 0.471507 + 0.471507i
\(428\) 0 0
\(429\) 43.8440 25.4240i 0.102201 0.0592634i
\(430\) 0 0
\(431\) 568.037i 1.31795i −0.752165 0.658975i \(-0.770990\pi\)
0.752165 0.658975i \(-0.229010\pi\)
\(432\) 0 0
\(433\) −647.222 −1.49474 −0.747370 0.664408i \(-0.768684\pi\)
−0.747370 + 0.664408i \(0.768684\pi\)
\(434\) 0 0
\(435\) 12.0678 + 20.8111i 0.0277421 + 0.0478416i
\(436\) 0 0
\(437\) −475.808 + 475.808i −1.08881 + 1.08881i
\(438\) 0 0
\(439\) 486.389i 1.10795i −0.832534 0.553973i \(-0.813111\pi\)
0.832534 0.553973i \(-0.186889\pi\)
\(440\) 0 0
\(441\) 19.1963 33.5412i 0.0435291 0.0760571i
\(442\) 0 0
\(443\) −258.469 + 258.469i −0.583451 + 0.583451i −0.935850 0.352399i \(-0.885366\pi\)
0.352399 + 0.935850i \(0.385366\pi\)
\(444\) 0 0
\(445\) −203.396 + 203.396i −0.457070 + 0.457070i
\(446\) 0 0
\(447\) 546.360 + 145.290i 1.22228 + 0.325035i
\(448\) 0 0
\(449\) 498.015i 1.10916i −0.832129 0.554582i \(-0.812878\pi\)
0.832129 0.554582i \(-0.187122\pi\)
\(450\) 0 0
\(451\) 170.569 170.569i 0.378201 0.378201i
\(452\) 0 0
\(453\) −60.6549 + 35.1721i −0.133896 + 0.0776427i
\(454\) 0 0
\(455\) 28.3255 0.0622538
\(456\) 0 0
\(457\) 466.468i 1.02072i −0.859961 0.510359i \(-0.829513\pi\)
0.859961 0.510359i \(-0.170487\pi\)
\(458\) 0 0
\(459\) −1.02185 180.209i −0.00222624 0.392613i
\(460\) 0 0
\(461\) −389.251 389.251i −0.844362 0.844362i 0.145061 0.989423i \(-0.453662\pi\)
−0.989423 + 0.145061i \(0.953662\pi\)
\(462\) 0 0
\(463\) 500.857 1.08177 0.540883 0.841098i \(-0.318090\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(464\) 0 0
\(465\) 155.667 + 41.3957i 0.334768 + 0.0890229i
\(466\) 0 0
\(467\) 188.836 + 188.836i 0.404359 + 0.404359i 0.879766 0.475407i \(-0.157699\pi\)
−0.475407 + 0.879766i \(0.657699\pi\)
\(468\) 0 0
\(469\) 35.3489 + 35.3489i 0.0753709 + 0.0753709i
\(470\) 0 0
\(471\) −393.113 104.538i −0.834636 0.221950i
\(472\) 0 0
\(473\) 596.660 1.26144
\(474\) 0 0
\(475\) −255.022 255.022i −0.536888 0.536888i
\(476\) 0 0
\(477\) −170.131 625.470i −0.356668 1.31126i
\(478\) 0 0
\(479\) 326.344i 0.681303i 0.940190 + 0.340652i \(0.110648\pi\)
−0.940190 + 0.340652i \(0.889352\pi\)
\(480\) 0 0
\(481\) 74.7969 0.155503
\(482\) 0 0
\(483\) 406.181 235.533i 0.840954 0.487647i
\(484\) 0 0
\(485\) −160.006 + 160.006i −0.329909 + 0.329909i
\(486\) 0 0
\(487\) 196.238i 0.402952i 0.979493 + 0.201476i \(0.0645739\pi\)
−0.979493 + 0.201476i \(0.935426\pi\)
\(488\) 0 0
\(489\) −423.871 112.718i −0.866812 0.230506i
\(490\) 0 0
\(491\) 349.172 349.172i 0.711144 0.711144i −0.255631 0.966774i \(-0.582283\pi\)
0.966774 + 0.255631i \(0.0822831\pi\)
\(492\) 0 0
\(493\) −10.2969 + 10.2969i −0.0208863 + 0.0208863i
\(494\) 0 0
\(495\) −459.456 262.956i −0.928193 0.531224i
\(496\) 0 0
\(497\) 546.843i 1.10029i
\(498\) 0 0
\(499\) 321.326 321.326i 0.643940 0.643940i −0.307582 0.951522i \(-0.599520\pi\)
0.951522 + 0.307582i \(0.0995198\pi\)
\(500\) 0 0
\(501\) −171.530 295.805i −0.342374 0.590430i
\(502\) 0 0
\(503\) 623.698 1.23996 0.619978 0.784619i \(-0.287142\pi\)
0.619978 + 0.784619i \(0.287142\pi\)
\(504\) 0 0
\(505\) 296.113i 0.586362i
\(506\) 0 0
\(507\) 435.703 252.652i 0.859374 0.498328i
\(508\) 0 0
\(509\) 452.448 + 452.448i 0.888897 + 0.888897i 0.994417 0.105520i \(-0.0336508\pi\)
−0.105520 + 0.994417i \(0.533651\pi\)
\(510\) 0 0
\(511\) 25.3400 0.0495891
\(512\) 0 0
\(513\) −595.821 + 602.616i −1.16144 + 1.17469i
\(514\) 0 0
\(515\) −400.095 400.095i −0.776884 0.776884i
\(516\) 0 0
\(517\) −414.244 414.244i −0.801247 0.801247i
\(518\) 0 0
\(519\) −157.296 + 591.506i −0.303075 + 1.13970i
\(520\) 0 0
\(521\) 444.986 0.854100 0.427050 0.904228i \(-0.359553\pi\)
0.427050 + 0.904228i \(0.359553\pi\)
\(522\) 0 0
\(523\) −399.942 399.942i −0.764707 0.764707i 0.212462 0.977169i \(-0.431852\pi\)
−0.977169 + 0.212462i \(0.931852\pi\)
\(524\) 0 0
\(525\) 126.240 + 217.703i 0.240458 + 0.414673i
\(526\) 0 0
\(527\) 97.5029i 0.185015i
\(528\) 0 0
\(529\) −69.3715 −0.131137
\(530\) 0 0
\(531\) 40.6504 + 149.447i 0.0765544 + 0.281445i
\(532\) 0 0
\(533\) −11.2515 + 11.2515i −0.0211098 + 0.0211098i
\(534\) 0 0
\(535\) 399.900i 0.747476i
\(536\) 0 0
\(537\) 18.3437 68.9808i 0.0341595 0.128456i
\(538\) 0 0
\(539\) 48.5912 48.5912i 0.0901506 0.0901506i
\(540\) 0 0
\(541\) 116.940 116.940i 0.216155 0.216155i −0.590721 0.806876i \(-0.701156\pi\)
0.806876 + 0.590721i \(0.201156\pi\)
\(542\) 0 0
\(543\) −37.2932 + 140.240i −0.0686800 + 0.258269i
\(544\) 0 0
\(545\) 385.308i 0.706987i
\(546\) 0 0
\(547\) −85.6914 + 85.6914i −0.156657 + 0.156657i −0.781084 0.624427i \(-0.785333\pi\)
0.624427 + 0.781084i \(0.285333\pi\)
\(548\) 0 0
\(549\) 92.1322 + 338.715i 0.167818 + 0.616968i
\(550\) 0 0
\(551\) 68.4772 0.124278
\(552\) 0 0
\(553\) 755.311i 1.36584i
\(554\) 0 0
\(555\) −391.910 675.855i −0.706145 1.21776i
\(556\) 0 0
\(557\) 104.194 + 104.194i 0.187062 + 0.187062i 0.794425 0.607363i \(-0.207772\pi\)
−0.607363 + 0.794425i \(0.707772\pi\)
\(558\) 0 0
\(559\) −39.3585 −0.0704087
\(560\) 0 0
\(561\) 82.3519 309.682i 0.146795 0.552017i
\(562\) 0 0
\(563\) 776.673 + 776.673i 1.37953 + 1.37953i 0.845414 + 0.534111i \(0.179354\pi\)
0.534111 + 0.845414i \(0.320646\pi\)
\(564\) 0 0
\(565\) 99.7766 + 99.7766i 0.176596 + 0.176596i
\(566\) 0 0
\(567\) 509.850 299.524i 0.899207 0.528261i
\(568\) 0 0
\(569\) −456.546 −0.802366 −0.401183 0.915998i \(-0.631401\pi\)
−0.401183 + 0.915998i \(0.631401\pi\)
\(570\) 0 0
\(571\) 475.108 + 475.108i 0.832062 + 0.832062i 0.987799 0.155736i \(-0.0497750\pi\)
−0.155736 + 0.987799i \(0.549775\pi\)
\(572\) 0 0
\(573\) −389.700 + 225.977i −0.680105 + 0.394375i
\(574\) 0 0
\(575\) 246.350i 0.428434i
\(576\) 0 0
\(577\) 1127.70 1.95443 0.977213 0.212262i \(-0.0680832\pi\)
0.977213 + 0.212262i \(0.0680832\pi\)
\(578\) 0 0
\(579\) −177.033 305.296i −0.305756 0.527281i
\(580\) 0 0
\(581\) −231.604 + 231.604i −0.398630 + 0.398630i
\(582\) 0 0
\(583\) 1152.59i 1.97700i
\(584\) 0 0
\(585\) 30.3078 + 17.3458i 0.0518082 + 0.0296509i
\(586\) 0 0
\(587\) −584.236 + 584.236i −0.995292 + 0.995292i −0.999989 0.00469688i \(-0.998505\pi\)
0.00469688 + 0.999989i \(0.498505\pi\)
\(588\) 0 0
\(589\) 324.209 324.209i 0.550440 0.550440i
\(590\) 0 0
\(591\) 130.600 + 34.7296i 0.220981 + 0.0587642i
\(592\) 0 0
\(593\) 870.906i 1.46864i 0.678801 + 0.734322i \(0.262500\pi\)
−0.678801 + 0.734322i \(0.737500\pi\)
\(594\) 0 0
\(595\) 126.637 126.637i 0.212835 0.212835i
\(596\) 0 0
\(597\) 333.090 193.150i 0.557940 0.323535i
\(598\) 0 0
\(599\) −224.305 −0.374466 −0.187233 0.982316i \(-0.559952\pi\)
−0.187233 + 0.982316i \(0.559952\pi\)
\(600\) 0 0
\(601\) 234.358i 0.389946i 0.980809 + 0.194973i \(0.0624620\pi\)
−0.980809 + 0.194973i \(0.937538\pi\)
\(602\) 0 0
\(603\) 16.1760 + 59.4697i 0.0268259 + 0.0986230i
\(604\) 0 0
\(605\) −351.140 351.140i −0.580396 0.580396i
\(606\) 0 0
\(607\) −620.755 −1.02266 −0.511330 0.859384i \(-0.670847\pi\)
−0.511330 + 0.859384i \(0.670847\pi\)
\(608\) 0 0
\(609\) −46.1770 12.2796i −0.0758244 0.0201635i
\(610\) 0 0
\(611\) 27.3255 + 27.3255i 0.0447226 + 0.0447226i
\(612\) 0 0
\(613\) 645.945 + 645.945i 1.05374 + 1.05374i 0.998471 + 0.0552724i \(0.0176027\pi\)
0.0552724 + 0.998471i \(0.482397\pi\)
\(614\) 0 0
\(615\) 160.621 + 42.7131i 0.261173 + 0.0694523i
\(616\) 0 0
\(617\) −169.883 −0.275337 −0.137669 0.990478i \(-0.543961\pi\)
−0.137669 + 0.990478i \(0.543961\pi\)
\(618\) 0 0
\(619\) 647.603 + 647.603i 1.04621 + 1.04621i 0.998879 + 0.0473286i \(0.0150708\pi\)
0.0473286 + 0.998879i \(0.484929\pi\)
\(620\) 0 0
\(621\) 578.842 3.28222i 0.932113 0.00528539i
\(622\) 0 0
\(623\) 571.323i 0.917051i
\(624\) 0 0
\(625\) 205.694 0.329110
\(626\) 0 0
\(627\) −1303.56 + 755.900i −2.07904 + 1.20558i
\(628\) 0 0
\(629\) 334.400 334.400i 0.531638 0.531638i
\(630\) 0 0
\(631\) 975.374i 1.54576i 0.634553 + 0.772880i \(0.281184\pi\)
−0.634553 + 0.772880i \(0.718816\pi\)
\(632\) 0 0
\(633\) 323.110 + 85.9228i 0.510442 + 0.135739i
\(634\) 0 0
\(635\) −112.643 + 112.643i −0.177391 + 0.177391i
\(636\) 0 0
\(637\) −3.20530 + 3.20530i −0.00503187 + 0.00503187i
\(638\) 0 0
\(639\) 334.873 585.114i 0.524058 0.915671i
\(640\) 0 0
\(641\) 771.555i 1.20367i −0.798619 0.601837i \(-0.794436\pi\)
0.798619 0.601837i \(-0.205564\pi\)
\(642\) 0 0
\(643\) −319.214 + 319.214i −0.496445 + 0.496445i −0.910330 0.413884i \(-0.864172\pi\)
0.413884 + 0.910330i \(0.364172\pi\)
\(644\) 0 0
\(645\) 206.225 + 355.638i 0.319729 + 0.551377i
\(646\) 0 0
\(647\) 360.720 0.557527 0.278764 0.960360i \(-0.410075\pi\)
0.278764 + 0.960360i \(0.410075\pi\)
\(648\) 0 0
\(649\) 275.395i 0.424338i
\(650\) 0 0
\(651\) −276.766 + 160.489i −0.425140 + 0.246527i
\(652\) 0 0
\(653\) 415.043 + 415.043i 0.635595 + 0.635595i 0.949466 0.313871i \(-0.101626\pi\)
−0.313871 + 0.949466i \(0.601626\pi\)
\(654\) 0 0
\(655\) −6.31104 −0.00963517
\(656\) 0 0
\(657\) 27.1134 + 15.5176i 0.0412685 + 0.0236189i
\(658\) 0 0
\(659\) −363.535 363.535i −0.551646 0.551646i 0.375269 0.926916i \(-0.377550\pi\)
−0.926916 + 0.375269i \(0.877550\pi\)
\(660\) 0 0
\(661\) 151.997 + 151.997i 0.229951 + 0.229951i 0.812672 0.582721i \(-0.198012\pi\)
−0.582721 + 0.812672i \(0.698012\pi\)
\(662\) 0 0
\(663\) −5.43232 + 20.4280i −0.00819354 + 0.0308115i
\(664\) 0 0
\(665\) −842.166 −1.26642
\(666\) 0 0
\(667\) −33.0743 33.0743i −0.0495867 0.0495867i
\(668\) 0 0
\(669\) 231.377 + 399.013i 0.345855 + 0.596433i
\(670\) 0 0
\(671\) 624.170i 0.930208i
\(672\) 0 0
\(673\) −271.149 −0.402896 −0.201448 0.979499i \(-0.564565\pi\)
−0.201448 + 0.979499i \(0.564565\pi\)
\(674\) 0 0
\(675\) 1.75919 + 310.245i 0.00260621 + 0.459623i
\(676\) 0 0
\(677\) 639.750 639.750i 0.944978 0.944978i −0.0535849 0.998563i \(-0.517065\pi\)
0.998563 + 0.0535849i \(0.0170648\pi\)
\(678\) 0 0
\(679\) 449.442i 0.661918i
\(680\) 0 0
\(681\) 47.5948 178.979i 0.0698895 0.262817i
\(682\) 0 0
\(683\) −93.1730 + 93.1730i −0.136417 + 0.136417i −0.772018 0.635601i \(-0.780752\pi\)
0.635601 + 0.772018i \(0.280752\pi\)
\(684\) 0 0
\(685\) −619.145 + 619.145i −0.903861 + 0.903861i
\(686\) 0 0
\(687\) 121.988 458.731i 0.177566 0.667730i
\(688\) 0 0
\(689\) 76.0301i 0.110348i
\(690\) 0 0
\(691\) −303.844 + 303.844i −0.439716 + 0.439716i −0.891916 0.452200i \(-0.850639\pi\)
0.452200 + 0.891916i \(0.350639\pi\)
\(692\) 0 0
\(693\) 1014.60 275.975i 1.46406 0.398233i
\(694\) 0 0
\(695\) 138.111 0.198721
\(696\) 0 0
\(697\) 100.606i 0.144341i
\(698\) 0 0
\(699\) 48.8783 + 84.2914i 0.0699261 + 0.120589i
\(700\) 0 0
\(701\) −797.170 797.170i −1.13719 1.13719i −0.988952 0.148238i \(-0.952640\pi\)
−0.148238 0.988952i \(-0.547360\pi\)
\(702\) 0 0
\(703\) −2223.85 −3.16336
\(704\) 0 0
\(705\) 103.733 390.086i 0.147140 0.553313i
\(706\) 0 0
\(707\) 415.878 + 415.878i 0.588229 + 0.588229i
\(708\) 0 0
\(709\) −592.848 592.848i −0.836176 0.836176i 0.152178 0.988353i \(-0.451371\pi\)
−0.988353 + 0.152178i \(0.951371\pi\)
\(710\) 0 0
\(711\) −462.533 + 808.171i −0.650539 + 1.13667i
\(712\) 0 0
\(713\) −313.185 −0.439249
\(714\) 0 0
\(715\) 43.9070 + 43.9070i 0.0614084 + 0.0614084i
\(716\) 0 0
\(717\) 345.959 200.612i 0.482508 0.279794i
\(718\) 0 0
\(719\) 1252.89i 1.74255i 0.490799 + 0.871273i \(0.336705\pi\)
−0.490799 + 0.871273i \(0.663295\pi\)
\(720\) 0 0
\(721\) 1123.83 1.55872
\(722\) 0 0
\(723\) −240.289 414.382i −0.332350 0.573142i
\(724\) 0 0
\(725\) 17.7270 17.7270i 0.0244511 0.0244511i
\(726\) 0 0
\(727\) 1182.91i 1.62711i 0.581490 + 0.813553i \(0.302470\pi\)
−0.581490 + 0.813553i \(0.697530\pi\)
\(728\) 0 0
\(729\) 728.953 8.26707i 0.999936 0.0113403i
\(730\) 0 0
\(731\) −175.963 + 175.963i −0.240715 + 0.240715i
\(732\) 0 0
\(733\) −679.023 + 679.023i −0.926361 + 0.926361i −0.997469 0.0711072i \(-0.977347\pi\)
0.0711072 + 0.997469i \(0.477347\pi\)
\(734\) 0 0
\(735\) 45.7574 + 12.1680i 0.0622549 + 0.0165551i
\(736\) 0 0
\(737\) 109.588i 0.148695i
\(738\) 0 0
\(739\) −408.587 + 408.587i −0.552892 + 0.552892i −0.927274 0.374383i \(-0.877855\pi\)
0.374383 + 0.927274i \(0.377855\pi\)
\(740\) 0 0
\(741\) 85.9889 49.8627i 0.116044 0.0672911i
\(742\) 0 0
\(743\) −228.202 −0.307137 −0.153568 0.988138i \(-0.549077\pi\)
−0.153568 + 0.988138i \(0.549077\pi\)
\(744\) 0 0
\(745\) 692.644i 0.929724i
\(746\) 0 0
\(747\) −389.641 + 105.984i −0.521608 + 0.141880i
\(748\) 0 0
\(749\) −561.642 561.642i −0.749856 0.749856i
\(750\) 0 0
\(751\) 835.943 1.11311 0.556553 0.830812i \(-0.312124\pi\)
0.556553 + 0.830812i \(0.312124\pi\)
\(752\) 0 0
\(753\) −437.528 116.350i −0.581047 0.154515i
\(754\) 0 0
\(755\) −60.7421 60.7421i −0.0804530 0.0804530i
\(756\) 0 0
\(757\) −144.017 144.017i −0.190247 0.190247i 0.605556 0.795803i \(-0.292951\pi\)
−0.795803 + 0.605556i \(0.792951\pi\)
\(758\) 0 0
\(759\) 994.715 + 264.519i 1.31056 + 0.348510i
\(760\) 0 0
\(761\) −1238.49 −1.62745 −0.813727 0.581247i \(-0.802565\pi\)
−0.813727 + 0.581247i \(0.802565\pi\)
\(762\) 0 0
\(763\) −541.148 541.148i −0.709238 0.709238i
\(764\) 0 0
\(765\) 213.049 57.9503i 0.278495 0.0757520i
\(766\) 0 0
\(767\) 18.1663i 0.0236849i
\(768\) 0 0
\(769\) −906.729 −1.17910 −0.589551 0.807732i \(-0.700695\pi\)
−0.589551 + 0.807732i \(0.700695\pi\)
\(770\) 0 0
\(771\) 892.284 517.411i 1.15731 0.671091i
\(772\) 0 0
\(773\) −989.152 + 989.152i −1.27963 + 1.27963i −0.338752 + 0.940876i \(0.610005\pi\)
−0.940876 + 0.338752i \(0.889995\pi\)
\(774\) 0 0
\(775\) 167.859i 0.216593i
\(776\) 0 0
\(777\) 1499.63 + 398.789i 1.93003 + 0.513241i
\(778\) 0 0
\(779\) 334.528 334.528i 0.429432 0.429432i
\(780\) 0 0
\(781\) 847.656 847.656i 1.08535 1.08535i
\(782\) 0 0
\(783\) −41.8890 41.4166i −0.0534981 0.0528948i
\(784\) 0 0
\(785\) 498.367i 0.634862i
\(786\) 0 0
\(787\) −100.012 + 100.012i −0.127080 + 0.127080i −0.767786 0.640706i \(-0.778642\pi\)
0.640706 + 0.767786i \(0.278642\pi\)
\(788\) 0 0
\(789\) 400.689 + 690.994i 0.507844 + 0.875785i
\(790\) 0 0
\(791\) −280.264 −0.354316
\(792\) 0 0
\(793\) 41.1731i 0.0519207i
\(794\) 0 0
\(795\) 686.998 398.372i 0.864149 0.501097i
\(796\) 0