Properties

Label 384.3.i.d.161.3
Level $384$
Weight $3$
Character 384.161
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 161.3
Root \(-1.85381 + 0.750590i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.d.353.3

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 0.917509 0.397716i \(-0.130197\pi\)
−0.397716 + 0.917509i \(0.630197\pi\)
\(6\) 0 0
\(7\) 7.30027i 1.04290i −0.853283 0.521448i \(-0.825392\pi\)
0.853283 0.521448i \(-0.174608\pi\)
\(8\) 0 0
\(9\) −4.47050 7.81118i −0.496723 0.867909i
\(10\) 0 0
\(11\) −11.3161 11.3161i −1.02873 1.02873i −0.999575 0.0291601i \(-0.990717\pi\)
−0.0291601 0.999575i \(-0.509283\pi\)
\(12\) 0 0
\(13\) 0.746462 + 0.746462i 0.0574201 + 0.0574201i 0.735234 0.677814i \(-0.237072\pi\)
−0.677814 + 0.735234i \(0.737072\pi\)
\(14\) 0 0
\(15\) −10.6561 + 2.83373i −0.710409 + 0.188915i
\(16\) 0 0
\(17\) 6.67452i 0.392619i 0.980542 + 0.196310i \(0.0628957\pi\)
−0.980542 + 0.196310i \(0.937104\pi\)
\(18\) 0 0
\(19\) −22.1936 22.1936i −1.16809 1.16809i −0.982658 0.185428i \(-0.940633\pi\)
−0.185428 0.982658i \(-0.559367\pi\)
\(20\) 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 −0.733205 0.680008i \(-0.761976\pi\)
0.680008 + 0.733205i \(0.261976\pi\)
\(30\) 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 0.473039 0.881041i \(-0.343157\pi\)
0.881041 0.473039i \(-0.156843\pi\)
\(38\) 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 −0.943753 0.330651i \(-0.892732\pi\)
0.330651 + 0.943753i \(0.392732\pi\)
\(44\) 0 0
\(45\) 8.68231 31.9197i 0.192940 0.709326i
\(46\) 0 0
\(47\) 36.6067i 0.778866i −0.921055 0.389433i \(-0.872671\pi\)
0.921055 0.389433i \(-0.127329\pi\)
\(48\) 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 0.0383765 0.999263i \(-0.487781\pi\)
−0.999263 + 0.0383765i \(0.987781\pi\)
\(54\) 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 0.802668 0.596426i \(-0.203413\pi\)
−0.596426 + 0.802668i \(0.703413\pi\)
\(60\) 0 0
\(61\) 27.5789 + 27.5789i 0.452113 + 0.452113i 0.896055 0.443943i \(-0.146421\pi\)
−0.443943 + 0.896055i \(0.646421\pi\)
\(62\) 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 0.742318 0.670047i \(-0.233726\pi\)
−0.670047 + 0.742318i \(0.733726\pi\)
\(68\) 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 \(0.00756843\pi\)
−0.999717 + 0.0237747i \(0.992432\pi\)
\(74\) 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 −0.489673 0.871906i \(-0.662884\pi\)
0.871906 + 0.489673i \(0.162884\pi\)
\(84\) 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 0.930451 0.366417i \(-0.119415\pi\)
−0.366417 + 0.930451i \(0.619415\pi\)
\(102\) 0 0
\(103\) 153.944i 1.49460i 0.664485 + 0.747301i \(0.268651\pi\)
−0.664485 + 0.747301i \(0.731349\pi\)
\(104\) 0 0
\(105\) 20.6870 + 77.7927i 0.197019 + 0.740883i
\(106\) 0 0
\(107\) −76.9344 76.9344i −0.719013 0.719013i 0.249390 0.968403i \(-0.419770\pi\)
−0.968403 + 0.249390i \(0.919770\pi\)
\(108\) 0 0
\(109\) −74.1271 74.1271i −0.680065 0.680065i 0.279949 0.960015i \(-0.409682\pi\)
−0.960015 + 0.279949i \(0.909682\pi\)
\(110\) 0 0
\(111\) 54.6265 + 205.421i 0.492131 + 1.85064i
\(112\) 0 0
\(113\) 38.3909i 0.339742i −0.985466 0.169871i \(-0.945665\pi\)
0.985466 0.169871i \(-0.0543352\pi\)
\(114\) 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 −0.711726 0.702457i \(-0.752086\pi\)
0.702457 + 0.711726i \(0.252086\pi\)
\(132\) 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 −0.605041 0.796195i \(-0.706843\pi\)
0.796195 + 0.605041i \(0.206843\pi\)
\(140\) 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 0.100605 0.994926i \(-0.467922\pi\)
−0.994926 + 0.100605i \(0.967922\pi\)
\(150\) 0 0
\(151\) 23.3716i 0.154779i 0.997001 + 0.0773895i \(0.0246585\pi\)
−0.997001 + 0.0773895i \(0.975342\pi\)
\(152\) 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 0.943125 0.332438i \(-0.107871\pi\)
−0.332438 + 0.943125i \(0.607871\pi\)
\(158\) 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 0.949126 0.314896i \(-0.101970\pi\)
−0.314896 + 0.949126i \(0.601970\pi\)
\(164\) 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 −0.988048 0.154147i \(-0.950737\pi\)
0.154147 + 0.988048i \(0.450737\pi\)
\(174\) 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 −0.658549 0.752538i \(-0.728829\pi\)
0.752538 + 0.658549i \(0.228829\pi\)
\(180\) 0 0
\(181\) −34.2037 + 34.2037i −0.188971 + 0.188971i −0.795251 0.606280i \(-0.792661\pi\)
0.606280 + 0.795251i \(0.292661\pi\)
\(182\) 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 \(0.128593\pi\)
−0.919501 + 0.393088i \(0.871407\pi\)
\(192\) 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 0.621626 0.783314i \(-0.286472\pi\)
−0.783314 + 0.621626i \(0.786472\pi\)
\(198\) 0 0
\(199\) 128.347i 0.644959i −0.946576 0.322480i \(-0.895484\pi\)
0.946576 0.322480i \(-0.104516\pi\)
\(200\) 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 0.495262 0.868743i \(-0.335072\pi\)
−0.868743 + 0.495262i \(0.835072\pi\)
\(212\) 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 −0.604390 0.796689i \(-0.706583\pi\)
0.796689 + 0.604390i \(0.206583\pi\)
\(228\) 0 0
\(229\) 111.882 111.882i 0.488566 0.488566i −0.419288 0.907853i \(-0.637720\pi\)
0.907853 + 0.419288i \(0.137720\pi\)
\(230\) 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 \(-0.910036\pi\)
0.960326 0.278881i \(-0.0899636\pi\)
\(240\) 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 0.886969 0.461828i \(-0.152806\pi\)
−0.461828 + 0.886969i \(0.652806\pi\)
\(252\) 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 \(-0.766764\pi\)
0.743350 0.668903i \(-0.233236\pi\)
\(258\) 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 −0.491164 0.871067i \(-0.663428\pi\)
0.871067 + 0.491164i \(0.163428\pi\)
\(270\) 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 0.00110593 0.999999i \(-0.499648\pi\)
0.999999 0.00110593i \(-0.000352027\pi\)
\(278\) 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 −0.999761 0.0218614i \(-0.993041\pi\)
0.0218614 + 0.999761i \(0.493041\pi\)
\(284\) 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 0.998884 + 0.0472370i \(0.0150416\pi\)
0.0472370 + 0.998884i \(0.484958\pi\)
\(294\) 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 0.981820 + 0.189814i \(0.0607886\pi\)
0.189814 + 0.981820i \(0.439211\pi\)
\(308\) 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 \(-0.821271\pi\)
0.846461 0.532450i \(-0.178729\pi\)
\(314\) 0 0
\(315\) −233.022 63.3832i −0.739754 0.201217i
\(316\) 0 0
\(317\) 266.382 266.382i 0.840322 0.840322i −0.148578 0.988901i \(-0.547470\pi\)
0.988901 + 0.148578i \(0.0474697\pi\)
\(318\) 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 −0.309208 0.950995i \(-0.600064\pi\)
0.950995 + 0.309208i \(0.100064\pi\)
\(332\) 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 0.834612 0.550839i \(-0.185692\pi\)
−0.550839 + 0.834612i \(0.685692\pi\)
\(348\) 0 0
\(349\) 337.382 + 337.382i 0.966711 + 0.966711i 0.999463 0.0327527i \(-0.0104274\pi\)
−0.0327527 + 0.999463i \(0.510427\pi\)
\(350\) 0 0
\(351\) 20.0399 + 20.2684i 0.0570936 + 0.0577448i
\(352\) 0 0
\(353\) 293.330i 0.830964i −0.909601 0.415482i \(-0.863613\pi\)
0.909601 0.415482i \(-0.136387\pi\)
\(354\) 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 −0.876352 0.481671i \(-0.840030\pi\)
0.481671 + 0.876352i \(0.340030\pi\)
\(374\) 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 −0.981131 0.193342i \(-0.938067\pi\)
0.193342 + 0.981131i \(0.438067\pi\)
\(380\) 0 0
\(381\) 65.2252 112.482i 0.171195 0.295228i
\(382\) 0 0
\(383\) 427.326i 1.11573i 0.829931 + 0.557866i \(0.188380\pi\)
−0.829931 + 0.557866i \(0.811620\pi\)
\(384\) 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 0.984238 0.176847i \(-0.0565899\pi\)
−0.176847 + 0.984238i \(0.556590\pi\)
\(390\) 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 0.426366 0.904551i \(-0.359794\pi\)
−0.904551 + 0.426366i \(0.859794\pi\)
\(398\) 0 0
\(399\) −176.655 664.304i −0.442743 1.66492i
\(400\) 0 0
\(401\) 268.223i 0.668886i −0.942416 0.334443i \(-0.891452\pi\)
0.942416 0.334443i \(-0.108548\pi\)
\(402\) 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 \(0.0100599\pi\)
−0.999501 + 0.0315988i \(0.989940\pi\)
\(410\) 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 −0.935127 0.354313i \(-0.884715\pi\)
0.354313 + 0.935127i \(0.384715\pi\)
\(420\) 0 0
\(421\) −115.847 + 115.847i −0.275171 + 0.275171i −0.831178 0.556007i \(-0.812333\pi\)
0.556007 + 0.831178i \(0.312333\pi\)
\(422\) 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 \(0.229010\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(432\) 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 \(0.186889\pi\)
−0.832534 + 0.553973i \(0.813111\pi\)
\(440\) 0 0
\(441\) 19.1963 + 33.5412i 0.0435291 + 0.0760571i
\(442\) 0 0
\(443\) −258.469 258.469i −0.583451 0.583451i 0.352399 0.935850i \(-0.385366\pi\)
−0.935850 + 0.352399i \(0.885366\pi\)
\(444\) 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 \(0.187122\pi\)
−0.832129 + 0.554582i \(0.812878\pi\)
\(450\) 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 \(0.170487\pi\)
−0.859961 + 0.510359i \(0.829513\pi\)
\(458\) 0 0
\(459\) −1.02185 + 180.209i −0.00222624 + 0.392613i
\(460\) 0 0
\(461\) −389.251 + 389.251i −0.844362 + 0.844362i −0.989423 0.145061i \(-0.953662\pi\)
0.145061 + 0.989423i \(0.453662\pi\)
\(462\) 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 −0.475407 0.879766i \(-0.657699\pi\)
0.879766 + 0.475407i \(0.157699\pi\)
\(468\) 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 \(-0.889352\pi\)
0.940190 0.340652i \(-0.110648\pi\)
\(480\) 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 \(-0.935426\pi\)
0.979493 0.201476i \(-0.0645739\pi\)
\(488\) 0 0
\(489\) −423.871 + 112.718i −0.866812 + 0.230506i
\(490\) 0 0
\(491\) 349.172 + 349.172i 0.711144 + 0.711144i 0.966774 0.255631i \(-0.0822831\pi\)
−0.255631 + 0.966774i \(0.582283\pi\)
\(492\) 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 0.951522 0.307582i \(-0.0995198\pi\)
−0.307582 + 0.951522i \(0.599520\pi\)
\(500\) 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 −0.105520 0.994417i \(-0.533651\pi\)
0.994417 + 0.105520i \(0.0336508\pi\)
\(510\) 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 −0.977169 0.212462i \(-0.931852\pi\)
0.212462 + 0.977169i \(0.431852\pi\)
\(524\) 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 0.806876 0.590721i \(-0.201156\pi\)
−0.590721 + 0.806876i \(0.701156\pi\)
\(542\) 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 0.624427 0.781084i \(-0.285333\pi\)
−0.781084 + 0.624427i \(0.785333\pi\)
\(548\) 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 −0.607363 0.794425i \(-0.707772\pi\)
0.794425 + 0.607363i \(0.207772\pi\)
\(558\) 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 0.534111 0.845414i \(-0.320646\pi\)
0.845414 0.534111i \(-0.179354\pi\)
\(564\) 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 −0.155736 0.987799i \(-0.549775\pi\)
0.987799 + 0.155736i \(0.0497750\pi\)
\(572\) 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 0.00469688 0.999989i \(-0.498505\pi\)
−0.999989 + 0.00469688i \(0.998505\pi\)
\(588\) 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 \(-0.737500\pi\)
0.678801 0.734322i \(-0.262500\pi\)
\(594\) 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 \(-0.937538\pi\)
0.980809 0.194973i \(-0.0624620\pi\)
\(602\) 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 0.0552724 0.998471i \(-0.482397\pi\)
0.998471 0.0552724i \(-0.0176027\pi\)
\(614\) 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 0.0473286 0.998879i \(-0.484929\pi\)
0.998879 0.0473286i \(-0.0150708\pi\)
\(620\) 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 \(-0.718816\pi\)
0.634553 0.772880i \(-0.281184\pi\)
\(632\) 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 \(0.205564\pi\)
−0.798619 + 0.601837i \(0.794436\pi\)
\(642\) 0 0
\(643\) −319.214 319.214i −0.496445 0.496445i 0.413884 0.910330i \(-0.364172\pi\)
−0.910330 + 0.413884i \(0.864172\pi\)
\(644\) 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 −0.313871 0.949466i \(-0.601626\pi\)
0.949466 + 0.313871i \(0.101626\pi\)
\(654\) 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 −0.926916 0.375269i \(-0.877550\pi\)
0.375269 + 0.926916i \(0.377550\pi\)
\(660\) 0 0
\(661\) 151.997 151.997i 0.229951 0.229951i −0.582721 0.812672i \(-0.698012\pi\)
0.812672 + 0.582721i \(0.198012\pi\)
\(662\) 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 0.998563 0.0535849i \(-0.0170648\pi\)
−0.0535849 + 0.998563i \(0.517065\pi\)
\(678\) 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 0.635601 0.772018i \(-0.280752\pi\)
−0.772018 + 0.635601i \(0.780752\pi\)
\(684\) 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 0.452200 0.891916i \(-0.350639\pi\)
−0.891916 + 0.452200i \(0.850639\pi\)
\(692\) 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 −0.148238 + 0.988952i \(0.547360\pi\)
−0.988952 + 0.148238i \(0.952640\pi\)
\(702\) 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 −0.988353 0.152178i \(-0.951371\pi\)
0.152178 + 0.988353i \(0.451371\pi\)
\(710\) 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 \(-0.663295\pi\)
0.490799 0.871273i \(-0.336705\pi\)
\(720\) 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 \(-0.697530\pi\)
0.581490 0.813553i \(-0.302470\pi\)
\(728\) 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 0.0711072 0.997469i \(-0.477347\pi\)
−0.997469 + 0.0711072i \(0.977347\pi\)
\(734\) 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 0.374383 0.927274i \(-0.377855\pi\)
−0.927274 + 0.374383i \(0.877855\pi\)
\(740\) 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 −0.795803 0.605556i \(-0.792951\pi\)
0.605556 + 0.795803i \(0.292951\pi\)
\(758\) 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 −0.940876 0.338752i \(-0.889995\pi\)
−0.338752 0.940876i \(-0.610005\pi\)
\(774\) 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 0.640706 0.767786i \(-0.278642\pi\)
−0.767786 + 0.640706i \(0.778642\pi\)
\(788\) 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
\(796\)