Properties

Label 384.3.i.c.161.2
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 161.2
Root \(1.85381 - 0.750590i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.2

$q$-expansion

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

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
\(3\) −2.59524 + 1.50491i −0.865079 + 0.501636i
\(4\) 0 0
\(5\) −2.59897 2.59897i −0.519793 0.519793i 0.397716 0.917509i \(-0.369803\pi\)
−0.917509 + 0.397716i \(0.869803\pi\)
\(6\) 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 −0.999575 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 \(-0.937104\pi\)
0.980542 0.196310i \(-0.0628957\pi\)
\(18\) 0 0
\(19\) 22.1936 + 22.1936i 1.16809 + 1.16809i 0.982658 + 0.185428i \(0.0593670\pi\)
0.185428 + 0.982658i \(0.440633\pi\)
\(20\) 0 0
\(21\) −10.9862 18.9459i −0.523154 0.902187i
\(22\) 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
\(27\) 0.153096 + 26.9996i 0.00567024 + 0.999984i
\(28\) 0 0
\(29\) 1.54272 1.54272i 0.0531973 0.0531973i −0.680008 0.733205i \(-0.738024\pi\)
0.733205 + 0.680008i \(0.238024\pi\)
\(30\) 0 0
\(31\) 14.6082 0.471233 0.235616 0.971846i \(-0.424289\pi\)
0.235616 + 0.971846i \(0.424289\pi\)
\(32\) 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 \(-0.441154\pi\)
0.183819 + 0.982960i \(0.441154\pi\)
\(42\) 0 0
\(43\) 26.3634 26.3634i 0.613102 0.613102i −0.330651 0.943753i \(-0.607268\pi\)
0.943753 + 0.330651i \(0.107268\pi\)
\(44\) 0 0
\(45\) −31.9197 + 8.68231i −0.709326 + 0.192940i
\(46\) 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
\(51\) 10.0445 + 17.3220i 0.196952 + 0.339646i
\(52\) 0 0
\(53\) 50.9270 + 50.9270i 0.960887 + 0.960887i 0.999263 0.0383765i \(-0.0122186\pi\)
−0.0383765 + 0.999263i \(0.512219\pi\)
\(54\) 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 0.670047 0.742318i \(-0.266274\pi\)
−0.742318 + 0.670047i \(0.766274\pi\)
\(68\) 0 0
\(69\) −55.6391 + 32.2636i −0.806364 + 0.467589i
\(70\) 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
\(75\) 17.2925 + 29.8212i 0.230567 + 0.397616i
\(76\) 0 0
\(77\) 82.6105 82.6105i 1.07286 1.07286i
\(78\) 0 0
\(79\) −103.463 −1.30966 −0.654831 0.755775i \(-0.727260\pi\)
−0.654831 + 0.755775i \(0.727260\pi\)
\(80\) 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 \(-0.355097\pi\)
0.439666 + 0.898162i \(0.355097\pi\)
\(90\) 0 0
\(91\) −5.44937 + 5.44937i −0.0598832 + 0.0598832i
\(92\) 0 0
\(93\) −37.9118 + 21.9840i −0.407653 + 0.236387i
\(94\) 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
\(99\) −138.981 + 37.8034i −1.40384 + 0.381853i
\(100\) 0 0
\(101\) −56.9675 56.9675i −0.564034 0.564034i 0.366417 0.930451i \(-0.380585\pi\)
−0.930451 + 0.366417i \(0.880585\pi\)
\(102\) 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 0.249390 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 \(0.0543352\pi\)
−0.985466 + 0.169871i \(0.945665\pi\)
\(114\) 0 0
\(115\) −55.7191 55.7191i −0.484514 0.484514i
\(116\) 0 0
\(117\) 9.16781 2.49369i 0.0783573 0.0213136i
\(118\) 0 0
\(119\) 48.7259 0.409461
\(120\) 0 0
\(121\) 135.108i 1.11659i
\(122\) 0 0
\(123\) −39.1184 + 22.6837i −0.318035 + 0.184420i
\(124\) 0 0
\(125\) −94.8382 + 94.8382i −0.758706 + 0.758706i
\(126\) 0 0
\(127\) 43.3417 0.341273 0.170636 0.985334i \(-0.445418\pi\)
0.170636 + 0.985334i \(0.445418\pi\)
\(128\) 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 \(-0.164478\pi\)
0.869443 + 0.494033i \(0.164478\pi\)
\(138\) 0 0
\(139\) −26.5704 + 26.5704i −0.191154 + 0.191154i −0.796195 0.605041i \(-0.793157\pi\)
0.605041 + 0.796195i \(0.293157\pi\)
\(140\) 0 0
\(141\) 55.0897 + 95.0030i 0.390707 + 0.673780i
\(142\) 0 0
\(143\) 16.8940i 0.118140i
\(144\) 0 0
\(145\) −8.01896 −0.0553032
\(146\) 0 0
\(147\) 11.1439 6.46207i 0.0758090 0.0439596i
\(148\) 0 0
\(149\) 133.254 + 133.254i 0.894321 + 0.894321i 0.994926 0.100605i \(-0.0320779\pi\)
−0.100605 + 0.994926i \(0.532078\pi\)
\(150\) 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 0.943125 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 0.314896 0.949126i \(-0.398030\pi\)
−0.949126 + 0.314896i \(0.898030\pi\)
\(164\) 0 0
\(165\) −88.5190 152.652i −0.536479 0.925166i
\(166\) 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
\(171\) 272.575 74.1418i 1.59401 0.433578i
\(172\) 0 0
\(173\) 144.265 144.265i 0.833901 0.833901i −0.154147 0.988048i \(-0.549263\pi\)
0.988048 + 0.154147i \(0.0492630\pi\)
\(174\) 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
\(189\) −197.104 + 1.11765i −1.04288 + 0.00591347i
\(190\) 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
\(195\) 5.83913 + 10.0697i 0.0299442 + 0.0516393i
\(196\) 0 0
\(197\) 31.8524 + 31.8524i 0.161688 + 0.161688i 0.783314 0.621626i \(-0.213528\pi\)
−0.621626 + 0.783314i \(0.713528\pi\)
\(198\) 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 \(-0.164928\pi\)
−0.495262 + 0.868743i \(0.664928\pi\)
\(212\) 0 0
\(213\) 194.402 112.728i 0.912685 0.529241i
\(214\) 0 0
\(215\) −137.035 −0.637372
\(216\) 0 0
\(217\) 106.644i 0.491447i
\(218\) 0 0
\(219\) −5.22369 9.00834i −0.0238525 0.0411340i
\(220\) 0 0
\(221\) 4.98228 4.98228i 0.0225442 0.0225442i
\(222\) 0 0
\(223\) 153.748 0.689455 0.344727 0.938703i \(-0.387971\pi\)
0.344727 + 0.938703i \(0.387971\pi\)
\(224\) 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 \(-0.477796\pi\)
0.0696980 + 0.997568i \(0.477796\pi\)
\(234\) 0 0
\(235\) −95.1395 + 95.1395i −0.404849 + 0.404849i
\(236\) 0 0
\(237\) 268.512 155.703i 1.13296 0.656974i
\(238\) 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
\(243\) 211.583 + 119.506i 0.870712 + 0.491793i
\(244\) 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 \(0.233236\pi\)
−0.743350 + 0.668903i \(0.766764\pi\)
\(258\) 0 0
\(259\) 365.751 + 365.751i 1.41217 + 1.41217i
\(260\) 0 0
\(261\) −5.15374 18.9472i −0.0197461 0.0725948i
\(262\) 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
\(267\) −203.104 + 117.775i −0.760691 + 0.441104i
\(268\) 0 0
\(269\) −102.194 + 102.194i −0.379904 + 0.379904i −0.871067 0.491164i \(-0.836572\pi\)
0.491164 + 0.871067i \(0.336572\pi\)
\(270\) 0 0
\(271\) 38.5636 0.142301 0.0711505 0.997466i \(-0.477333\pi\)
0.0711505 + 0.997466i \(0.477333\pi\)
\(272\) 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 \(-0.803983\pi\)
−0.816308 + 0.577617i \(0.803983\pi\)
\(282\) 0 0
\(283\) 276.746 276.746i 0.977900 0.977900i −0.0218614 0.999761i \(-0.506959\pi\)
0.999761 + 0.0218614i \(0.00695927\pi\)
\(284\) 0 0
\(285\) 173.608 + 299.389i 0.609149 + 1.05049i
\(286\) 0 0
\(287\) 110.038i 0.383408i
\(288\) 0 0
\(289\) 244.451 0.845850
\(290\) 0 0
\(291\) 159.776 92.6499i 0.549059 0.318384i
\(292\) 0 0
\(293\) −306.513 306.513i −1.04612 1.04612i −0.998884 0.0472370i \(-0.984958\pi\)
−0.0472370 0.998884i \(-0.515042\pi\)
\(294\) 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 \(-0.939211\pi\)
−0.189814 0.981820i \(-0.560789\pi\)
\(308\) 0 0
\(309\) 231.672 + 399.521i 0.749746 + 1.29295i
\(310\) 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
\(315\) −63.3832 233.022i −0.201217 0.739754i
\(316\) 0 0
\(317\) −266.382 + 266.382i −0.840322 + 0.840322i −0.988901 0.148578i \(-0.952530\pi\)
0.148578 + 0.988901i \(0.452530\pi\)
\(318\) 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 \(-0.899936\pi\)
0.309208 + 0.950995i \(0.399936\pi\)
\(332\) 0 0
\(333\) −167.371 615.325i −0.502617 1.84782i
\(334\) 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
\(339\) −57.7748 99.6335i −0.170427 0.293904i
\(340\) 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 \(0.136387\pi\)
−0.909601 + 0.415482i \(0.863613\pi\)
\(354\) 0 0
\(355\) 194.681 + 194.681i 0.548398 + 0.548398i
\(356\) 0 0
\(357\) −126.455 + 73.3279i −0.354216 + 0.205400i
\(358\) 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
\(363\) −203.324 350.636i −0.560122 0.965939i
\(364\) 0 0
\(365\) 9.02128 9.02128i 0.0247158 0.0247158i
\(366\) 0 0
\(367\) −221.149 −0.602585 −0.301292 0.953532i \(-0.597418\pi\)
−0.301292 + 0.953532i \(0.597418\pi\)
\(368\) 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 −0.193342 0.981131i \(-0.561933\pi\)
0.981131 + 0.193342i \(0.0619326\pi\)
\(380\) 0 0
\(381\) −112.482 + 65.2252i −0.295228 + 0.171195i
\(382\) 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
\(387\) −88.0716 323.787i −0.227575 0.836658i
\(388\) 0 0
\(389\) −314.075 314.075i −0.807391 0.807391i 0.176847 0.984238i \(-0.443410\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(390\) 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 \(0.108548\pi\)
−0.942416 + 0.334443i \(0.891452\pi\)
\(402\) 0 0
\(403\) 10.9045 + 10.9045i 0.0270582 + 0.0270582i
\(404\) 0 0
\(405\) −74.8780 + 288.145i −0.184884 + 0.711469i
\(406\) 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
\(411\) −618.257 + 358.510i −1.50427 + 0.872288i
\(412\) 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
\(429\) 25.4240 + 43.8440i 0.0592634 + 0.102201i
\(430\) 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
\(435\) 20.8111 12.0678i 0.0478416 0.0277421i
\(436\) 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 0.352399 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 \(-0.812878\pi\)
0.832129 0.554582i \(-0.187122\pi\)
\(450\) 0 0
\(451\) −170.569 170.569i −0.378201 0.378201i
\(452\) 0 0
\(453\) 35.1721 + 60.6549i 0.0776427 + 0.133896i
\(454\) 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
\(459\) 180.209 1.02185i 0.392613 0.00222624i
\(460\) 0 0
\(461\) 389.251 389.251i 0.844362 0.844362i −0.145061 0.989423i \(-0.546338\pi\)
0.989423 + 0.145061i \(0.0463378\pi\)
\(462\) 0 0
\(463\) −500.857 −1.08177 −0.540883 0.841098i \(-0.681910\pi\)
−0.540883 + 0.841098i \(0.681910\pi\)
\(464\) 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
\(477\) 625.470 170.131i 1.31126 0.356668i
\(478\) 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
\(483\) −235.533 406.181i −0.487647 0.840954i
\(484\) 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 0.966774 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 0.307582 0.951522i \(-0.400480\pi\)
−0.951522 + 0.307582i \(0.900480\pi\)
\(500\) 0 0
\(501\) −295.805 + 171.530i −0.590430 + 0.342374i
\(502\) 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
\(507\) 252.652 + 435.703i 0.498328 + 0.859374i
\(508\) 0 0
\(509\) −452.448 + 452.448i −0.888897 + 0.888897i −0.994417 0.105520i \(-0.966349\pi\)
0.105520 + 0.994417i \(0.466349\pi\)
\(510\) 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 \(-0.640447\pi\)
−0.427050 + 0.904228i \(0.640447\pi\)
\(522\) 0 0
\(523\) 399.942 399.942i 0.764707 0.764707i −0.212462 0.977169i \(-0.568148\pi\)
0.977169 + 0.212462i \(0.0681483\pi\)
\(524\) 0 0
\(525\) −217.703 + 126.240i −0.414673 + 0.240458i
\(526\) 0 0
\(527\) 97.5029i 0.185015i
\(528\) 0 0
\(529\) −69.3715 −0.131137
\(530\) 0 0
\(531\) 149.447 40.6504i 0.281445 0.0765544i
\(532\) 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 0.781084 0.624427i \(-0.214667\pi\)
−0.624427 + 0.781084i \(0.714667\pi\)
\(548\) 0 0
\(549\) 338.715 92.1322i 0.616968 0.167818i
\(550\) 0 0
\(551\) 68.4772 0.124278
\(552\) 0 0
\(553\) 755.311i 1.36584i
\(554\) 0 0
\(555\) 675.855 391.910i 1.21776 0.706145i
\(556\) 0 0
\(557\) −104.194 + 104.194i −0.187062 + 0.187062i −0.794425 0.607363i \(-0.792228\pi\)
0.607363 + 0.794425i \(0.292228\pi\)
\(558\) 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 \(-0.368599\pi\)
0.401183 + 0.915998i \(0.368599\pi\)
\(570\) 0 0
\(571\) −475.108 + 475.108i −0.832062 + 0.832062i −0.987799 0.155736i \(-0.950225\pi\)
0.155736 + 0.987799i \(0.450225\pi\)
\(572\) 0 0
\(573\) −225.977 389.700i −0.394375 0.680105i
\(574\) 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
\(579\) −305.296 + 177.033i −0.527281 + 0.305756i
\(580\) 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 \(0.262500\pi\)
−0.678801 + 0.734322i \(0.737500\pi\)
\(594\) 0 0
\(595\) −126.637 126.637i −0.212835 0.212835i
\(596\) 0 0
\(597\) −193.150 333.090i −0.323535 0.557940i
\(598\) 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
\(603\) −59.4697 + 16.1760i −0.0986230 + 0.0268259i
\(604\) 0 0
\(605\) 351.140 351.140i 0.580396 0.580396i
\(606\) 0 0
\(607\) 620.755 1.02266 0.511330 0.859384i \(-0.329153\pi\)
0.511330 + 0.859384i \(0.329153\pi\)
\(608\) 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 \(-0.456039\pi\)
0.137669 + 0.990478i \(0.456039\pi\)
\(618\) 0 0
\(619\) −647.603 + 647.603i −1.04621 + 1.04621i −0.0473286 + 0.998879i \(0.515071\pi\)
−0.998879 + 0.0473286i \(0.984929\pi\)
\(620\) 0 0
\(621\) 3.28222 + 578.842i 0.00528539 + 0.932113i
\(622\) 0 0
\(623\) 571.323i 0.917051i
\(624\) 0 0
\(625\) 205.694 0.329110
\(626\) 0 0
\(627\) 755.900 + 1303.56i 1.20558 + 2.07904i
\(628\) 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 \(-0.135828\pi\)
−0.413884 + 0.910330i \(0.635828\pi\)
\(644\) 0 0
\(645\) 355.638 206.225i 0.551377 0.319729i
\(646\) 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
\(651\) −160.489 276.766i −0.246527 0.425140i
\(652\) 0 0
\(653\) −415.043 + 415.043i −0.635595 + 0.635595i −0.949466 0.313871i \(-0.898374\pi\)
0.313871 + 0.949466i \(0.398374\pi\)
\(654\) 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
\(669\) −399.013 + 231.377i −0.596433 + 0.345855i
\(670\) 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
\(675\) 310.245 1.75919i 0.459623 0.00260621i
\(676\) 0 0
\(677\) −639.750 639.750i −0.944978 0.944978i 0.0535849 0.998563i \(-0.482935\pi\)
−0.998563 + 0.0535849i \(0.982935\pi\)
\(678\) 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 0.891916 0.452200i \(-0.149361\pi\)
−0.452200 + 0.891916i \(0.649361\pi\)
\(692\) 0 0
\(693\) −275.975 1014.60i −0.398233 1.46406i
\(694\) 0 0
\(695\) 138.111 0.198721
\(696\) 0 0
\(697\) 100.606i 0.144341i
\(698\) 0 0
\(699\) −84.2914 + 48.8783i −0.120589 + 0.0699261i
\(700\) 0 0
\(701\) 797.170 797.170i 1.13719 1.13719i 0.148238 0.988952i \(-0.452640\pi\)
0.988952 0.148238i \(-0.0473601\pi\)
\(702\) 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
\(717\) 200.612 + 345.959i 0.279794 + 0.482508i
\(718\) 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
\(723\) −414.382 + 240.289i −0.573142 + 0.332350i
\(724\) 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 0.0711072 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 0.927274 0.374383i \(-0.122145\pi\)
−0.374383 + 0.927274i \(0.622145\pi\)
\(740\) 0 0
\(741\) −49.8627 85.9889i −0.0672911 0.116044i
\(742\) 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
\(747\) −105.984 389.641i −0.141880 0.521608i
\(748\) 0 0
\(749\) 561.642 561.642i 0.749856 0.749856i
\(750\) 0 0
\(751\) −835.943 −1.11311 −0.556553 0.830812i \(-0.687876\pi\)
−0.556553 + 0.830812i \(0.687876\pi\)
\(752\) 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 \(-0.197435\pi\)
0.813727 + 0.581247i \(0.197435\pi\)
\(762\) 0 0
\(763\) 541.148 541.148i 0.709238 0.709238i
\(764\) 0 0
\(765\) 57.9503 + 213.049i 0.0757520 + 0.278495i
\(766\) 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
\(771\) −517.411 892.284i −0.671091 1.15731i
\(772\) 0 0
\(773\) 989.152 + 989.152i 1.27963 + 1.27963i 0.940876 + 0.338752i \(0.110005\pi\)
0.338752 + 0.940876i \(0.389995\pi\)
\(774\) 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 \(-0.221358\pi\)
−0.640706 + 0.767786i \(0.721358\pi\)
\(788\) 0 0
\(789\) 690.994 400.689i 0.875785 0.507844i
\(790\) 0 0
\(791\) −280.264 −0.354316
\(792\) 0 0
\(793\) 41.1731i 0.0519207i
\(794\) 0 0
\(795\) 398.372 + 686.998i 0.501097