Properties

Label 882.3.s.h.863.4
Level $882$
Weight $3$
Character 882.863
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.621801639936.1
Defining polynomial: \(x^{8} - 4 x^{7} - 34 x^{6} + 116 x^{5} + 413 x^{4} - 1024 x^{3} - 1664 x^{2} + 2196 x + 4467\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.4
Root \(-1.31664 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.h.557.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(7.44983 + 4.30116i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(7.44983 + 4.30116i) q^{5} +2.82843i q^{8} +(6.08276 + 10.5357i) q^{10} +(2.44949 - 1.41421i) q^{11} +12.1655 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-22.3495 + 12.9035i) q^{17} +(12.1655 - 21.0713i) q^{19} +17.2047i q^{20} +4.00000 q^{22} +(36.7423 + 21.2132i) q^{23} +(24.5000 + 42.4352i) q^{25} +(14.8997 + 8.60233i) q^{26} +15.5563i q^{29} +(-12.1655 - 21.0713i) q^{31} +(-4.89898 + 2.82843i) q^{32} -36.4966 q^{34} +(3.00000 - 5.19615i) q^{37} +(29.7993 - 17.2047i) q^{38} +(-12.1655 + 21.0713i) q^{40} -25.8070i q^{41} -68.0000 q^{43} +(4.89898 + 2.82843i) q^{44} +(30.0000 + 51.9615i) q^{46} +(-59.5987 - 34.4093i) q^{47} +69.2965i q^{50} +(12.1655 + 21.0713i) q^{52} +(35.5176 - 20.5061i) q^{53} +24.3311 q^{55} +(-11.0000 + 19.0526i) q^{58} +(59.5987 - 34.4093i) q^{59} +(-48.6621 + 84.2852i) q^{61} -34.4093i q^{62} -8.00000 q^{64} +(90.6311 + 52.3259i) q^{65} +(52.0000 + 90.0666i) q^{67} +(-44.6990 - 25.8070i) q^{68} +70.7107i q^{71} +(-30.4138 - 52.6783i) q^{73} +(7.34847 - 4.24264i) q^{74} +48.6621 q^{76} +(10.0000 - 17.3205i) q^{79} +(-29.7993 + 17.2047i) q^{80} +(18.2483 - 31.6070i) q^{82} -222.000 q^{85} +(-83.2827 - 48.0833i) q^{86} +(4.00000 + 6.92820i) q^{88} +(81.9482 + 47.3128i) q^{89} +84.8528i q^{92} +(-48.6621 - 84.2852i) q^{94} +(181.262 - 104.652i) q^{95} -158.152 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} + O(q^{10}) \) \( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} + 196 q^{25} + 24 q^{37} - 544 q^{43} + 240 q^{46} - 88 q^{58} - 64 q^{64} + 416 q^{67} + 80 q^{79} - 1776 q^{85} + 32 q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 + 0.707107i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 7.44983 + 4.30116i 1.48997 + 0.860233i 0.999934 0.0114718i \(-0.00365166\pi\)
0.490032 + 0.871704i \(0.336985\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 6.08276 + 10.5357i 0.608276 + 1.05357i
\(11\) 2.44949 1.41421i 0.222681 0.128565i −0.384510 0.923121i \(-0.625630\pi\)
0.607191 + 0.794556i \(0.292296\pi\)
\(12\) 0 0
\(13\) 12.1655 0.935810 0.467905 0.883779i \(-0.345009\pi\)
0.467905 + 0.883779i \(0.345009\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −22.3495 + 12.9035i −1.31468 + 0.759029i −0.982867 0.184318i \(-0.940992\pi\)
−0.331810 + 0.943346i \(0.607659\pi\)
\(18\) 0 0
\(19\) 12.1655 21.0713i 0.640291 1.10902i −0.345077 0.938574i \(-0.612147\pi\)
0.985368 0.170442i \(-0.0545195\pi\)
\(20\) 17.2047i 0.860233i
\(21\) 0 0
\(22\) 4.00000 0.181818
\(23\) 36.7423 + 21.2132i 1.59749 + 0.922313i 0.991968 + 0.126487i \(0.0403702\pi\)
0.605525 + 0.795826i \(0.292963\pi\)
\(24\) 0 0
\(25\) 24.5000 + 42.4352i 0.980000 + 1.69741i
\(26\) 14.8997 + 8.60233i 0.573064 + 0.330859i
\(27\) 0 0
\(28\) 0 0
\(29\) 15.5563i 0.536426i 0.963360 + 0.268213i \(0.0864331\pi\)
−0.963360 + 0.268213i \(0.913567\pi\)
\(30\) 0 0
\(31\) −12.1655 21.0713i −0.392436 0.679720i 0.600334 0.799749i \(-0.295034\pi\)
−0.992770 + 0.120030i \(0.961701\pi\)
\(32\) −4.89898 + 2.82843i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −36.4966 −1.07343
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 5.19615i 0.0810811 0.140437i −0.822633 0.568572i \(-0.807496\pi\)
0.903715 + 0.428135i \(0.140829\pi\)
\(38\) 29.7993 17.2047i 0.784193 0.452754i
\(39\) 0 0
\(40\) −12.1655 + 21.0713i −0.304138 + 0.526783i
\(41\) 25.8070i 0.629438i −0.949185 0.314719i \(-0.898090\pi\)
0.949185 0.314719i \(-0.101910\pi\)
\(42\) 0 0
\(43\) −68.0000 −1.58140 −0.790698 0.612207i \(-0.790282\pi\)
−0.790698 + 0.612207i \(0.790282\pi\)
\(44\) 4.89898 + 2.82843i 0.111340 + 0.0642824i
\(45\) 0 0
\(46\) 30.0000 + 51.9615i 0.652174 + 1.12960i
\(47\) −59.5987 34.4093i −1.26806 0.732113i −0.293437 0.955979i \(-0.594799\pi\)
−0.974620 + 0.223866i \(0.928132\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 69.2965i 1.38593i
\(51\) 0 0
\(52\) 12.1655 + 21.0713i 0.233952 + 0.405217i
\(53\) 35.5176 20.5061i 0.670143 0.386907i −0.125988 0.992032i \(-0.540210\pi\)
0.796131 + 0.605124i \(0.206877\pi\)
\(54\) 0 0
\(55\) 24.3311 0.442383
\(56\) 0 0
\(57\) 0 0
\(58\) −11.0000 + 19.0526i −0.189655 + 0.328492i
\(59\) 59.5987 34.4093i 1.01015 0.583208i 0.0989121 0.995096i \(-0.468464\pi\)
0.911235 + 0.411888i \(0.135130\pi\)
\(60\) 0 0
\(61\) −48.6621 + 84.2852i −0.797739 + 1.38173i 0.123346 + 0.992364i \(0.460638\pi\)
−0.921085 + 0.389361i \(0.872696\pi\)
\(62\) 34.4093i 0.554989i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 90.6311 + 52.3259i 1.39432 + 0.805014i
\(66\) 0 0
\(67\) 52.0000 + 90.0666i 0.776119 + 1.34428i 0.934163 + 0.356846i \(0.116148\pi\)
−0.158044 + 0.987432i \(0.550519\pi\)
\(68\) −44.6990 25.8070i −0.657338 0.379514i
\(69\) 0 0
\(70\) 0 0
\(71\) 70.7107i 0.995925i 0.867199 + 0.497963i \(0.165918\pi\)
−0.867199 + 0.497963i \(0.834082\pi\)
\(72\) 0 0
\(73\) −30.4138 52.6783i −0.416628 0.721620i 0.578970 0.815349i \(-0.303455\pi\)
−0.995598 + 0.0937286i \(0.970121\pi\)
\(74\) 7.34847 4.24264i 0.0993036 0.0573330i
\(75\) 0 0
\(76\) 48.6621 0.640291
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 17.3205i 0.126582 0.219247i −0.795768 0.605602i \(-0.792933\pi\)
0.922350 + 0.386355i \(0.126266\pi\)
\(80\) −29.7993 + 17.2047i −0.372492 + 0.215058i
\(81\) 0 0
\(82\) 18.2483 31.6070i 0.222540 0.385451i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −222.000 −2.61176
\(86\) −83.2827 48.0833i −0.968403 0.559108i
\(87\) 0 0
\(88\) 4.00000 + 6.92820i 0.0454545 + 0.0787296i
\(89\) 81.9482 + 47.3128i 0.920766 + 0.531604i 0.883879 0.467715i \(-0.154923\pi\)
0.0368865 + 0.999319i \(0.488256\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 84.8528i 0.922313i
\(93\) 0 0
\(94\) −48.6621 84.2852i −0.517682 0.896651i
\(95\) 181.262 104.652i 1.90802 1.10160i
\(96\) 0 0
\(97\) −158.152 −1.63043 −0.815216 0.579158i \(-0.803382\pi\)
−0.815216 + 0.579158i \(0.803382\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −49.0000 + 84.8705i −0.490000 + 0.848705i
\(101\) −52.1488 + 30.1081i −0.516325 + 0.298100i −0.735430 0.677601i \(-0.763020\pi\)
0.219105 + 0.975701i \(0.429686\pi\)
\(102\) 0 0
\(103\) 85.1587 147.499i 0.826783 1.43203i −0.0737655 0.997276i \(-0.523502\pi\)
0.900549 0.434755i \(-0.143165\pi\)
\(104\) 34.4093i 0.330859i
\(105\) 0 0
\(106\) 58.0000 0.547170
\(107\) 17.1464 + 9.89949i 0.160247 + 0.0925186i 0.577979 0.816052i \(-0.303842\pi\)
−0.417732 + 0.908570i \(0.637175\pi\)
\(108\) 0 0
\(109\) 28.0000 + 48.4974i 0.256881 + 0.444930i 0.965405 0.260756i \(-0.0839719\pi\)
−0.708524 + 0.705687i \(0.750639\pi\)
\(110\) 29.7993 + 17.2047i 0.270903 + 0.156406i
\(111\) 0 0
\(112\) 0 0
\(113\) 159.806i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(114\) 0 0
\(115\) 182.483 + 316.070i 1.58681 + 2.74843i
\(116\) −26.9444 + 15.5563i −0.232279 + 0.134106i
\(117\) 0 0
\(118\) 97.3242 0.824781
\(119\) 0 0
\(120\) 0 0
\(121\) −56.5000 + 97.8609i −0.466942 + 0.808768i
\(122\) −119.197 + 68.8186i −0.977027 + 0.564087i
\(123\) 0 0
\(124\) 24.3311 42.1426i 0.196218 0.339860i
\(125\) 206.456i 1.65165i
\(126\) 0 0
\(127\) −76.0000 −0.598425 −0.299213 0.954186i \(-0.596724\pi\)
−0.299213 + 0.954186i \(0.596724\pi\)
\(128\) −9.79796 5.65685i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 74.0000 + 128.172i 0.569231 + 0.985937i
\(131\) 89.3980 + 51.6140i 0.682427 + 0.394000i 0.800769 0.598973i \(-0.204424\pi\)
−0.118342 + 0.992973i \(0.537758\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 147.078i 1.09760i
\(135\) 0 0
\(136\) −36.4966 63.2139i −0.268357 0.464808i
\(137\) 86.9569 50.2046i 0.634722 0.366457i −0.147857 0.989009i \(-0.547237\pi\)
0.782578 + 0.622552i \(0.213904\pi\)
\(138\) 0 0
\(139\) 145.986 1.05026 0.525131 0.851022i \(-0.324016\pi\)
0.525131 + 0.851022i \(0.324016\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −50.0000 + 86.6025i −0.352113 + 0.609877i
\(143\) 29.7993 17.2047i 0.208387 0.120312i
\(144\) 0 0
\(145\) −66.9104 + 115.892i −0.461451 + 0.799256i
\(146\) 86.0233i 0.589200i
\(147\) 0 0
\(148\) 12.0000 0.0810811
\(149\) −35.5176 20.5061i −0.238373 0.137625i 0.376056 0.926597i \(-0.377280\pi\)
−0.614429 + 0.788972i \(0.710613\pi\)
\(150\) 0 0
\(151\) −80.0000 138.564i −0.529801 0.917643i −0.999396 0.0347605i \(-0.988933\pi\)
0.469594 0.882882i \(-0.344400\pi\)
\(152\) 59.5987 + 34.4093i 0.392096 + 0.226377i
\(153\) 0 0
\(154\) 0 0
\(155\) 209.304i 1.35035i
\(156\) 0 0
\(157\) −97.3242 168.570i −0.619899 1.07370i −0.989504 0.144508i \(-0.953840\pi\)
0.369604 0.929189i \(-0.379493\pi\)
\(158\) 24.4949 14.1421i 0.155031 0.0895072i
\(159\) 0 0
\(160\) −48.6621 −0.304138
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(164\) 44.6990 25.8070i 0.272555 0.157360i
\(165\) 0 0
\(166\) 0 0
\(167\) 172.047i 1.03022i −0.857125 0.515109i \(-0.827751\pi\)
0.857125 0.515109i \(-0.172249\pi\)
\(168\) 0 0
\(169\) −21.0000 −0.124260
\(170\) −271.893 156.978i −1.59937 0.923398i
\(171\) 0 0
\(172\) −68.0000 117.779i −0.395349 0.684764i
\(173\) −7.44983 4.30116i −0.0430626 0.0248622i 0.478314 0.878189i \(-0.341248\pi\)
−0.521377 + 0.853327i \(0.674581\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 11.3137i 0.0642824i
\(177\) 0 0
\(178\) 66.9104 + 115.892i 0.375901 + 0.651080i
\(179\) 124.924 72.1249i 0.697899 0.402932i −0.108665 0.994078i \(-0.534658\pi\)
0.806565 + 0.591146i \(0.201324\pi\)
\(180\) 0 0
\(181\) −12.1655 −0.0672128 −0.0336064 0.999435i \(-0.510699\pi\)
−0.0336064 + 0.999435i \(0.510699\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −60.0000 + 103.923i −0.326087 + 0.564799i
\(185\) 44.6990 25.8070i 0.241616 0.139497i
\(186\) 0 0
\(187\) −36.4966 + 63.2139i −0.195169 + 0.338042i
\(188\) 137.637i 0.732113i
\(189\) 0 0
\(190\) 296.000 1.55789
\(191\) 227.803 + 131.522i 1.19268 + 0.688596i 0.958914 0.283696i \(-0.0915606\pi\)
0.233769 + 0.972292i \(0.424894\pi\)
\(192\) 0 0
\(193\) −19.0000 32.9090i −0.0984456 0.170513i 0.812596 0.582828i \(-0.198054\pi\)
−0.911041 + 0.412315i \(0.864720\pi\)
\(194\) −193.696 111.830i −0.998431 0.576444i
\(195\) 0 0
\(196\) 0 0
\(197\) 165.463i 0.839914i −0.907544 0.419957i \(-0.862045\pi\)
0.907544 0.419957i \(-0.137955\pi\)
\(198\) 0 0
\(199\) −121.655 210.713i −0.611333 1.05886i −0.991016 0.133743i \(-0.957300\pi\)
0.379683 0.925117i \(-0.376033\pi\)
\(200\) −120.025 + 69.2965i −0.600125 + 0.346482i
\(201\) 0 0
\(202\) −85.1587 −0.421578
\(203\) 0 0
\(204\) 0 0
\(205\) 111.000 192.258i 0.541463 0.937842i
\(206\) 208.595 120.433i 1.01260 0.584624i
\(207\) 0 0
\(208\) −24.3311 + 42.1426i −0.116976 + 0.202609i
\(209\) 68.8186i 0.329276i
\(210\) 0 0
\(211\) 44.0000 0.208531 0.104265 0.994550i \(-0.466751\pi\)
0.104265 + 0.994550i \(0.466751\pi\)
\(212\) 71.0352 + 41.0122i 0.335072 + 0.193454i
\(213\) 0 0
\(214\) 14.0000 + 24.2487i 0.0654206 + 0.113312i
\(215\) −506.589 292.479i −2.35623 1.36037i
\(216\) 0 0
\(217\) 0 0
\(218\) 79.1960i 0.363284i
\(219\) 0 0
\(220\) 24.3311 + 42.1426i 0.110596 + 0.191557i
\(221\) −271.893 + 156.978i −1.23029 + 0.710306i
\(222\) 0 0
\(223\) −194.648 −0.872863 −0.436431 0.899738i \(-0.643758\pi\)
−0.436431 + 0.899738i \(0.643758\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 113.000 195.722i 0.500000 0.866025i
\(227\) 29.7993 17.2047i 0.131275 0.0757914i −0.432925 0.901430i \(-0.642518\pi\)
0.564199 + 0.825639i \(0.309185\pi\)
\(228\) 0 0
\(229\) −6.08276 + 10.5357i −0.0265623 + 0.0460072i −0.879001 0.476820i \(-0.841789\pi\)
0.852439 + 0.522827i \(0.175123\pi\)
\(230\) 516.140i 2.24408i
\(231\) 0 0
\(232\) −44.0000 −0.189655
\(233\) −233.926 135.057i −1.00398 0.579645i −0.0945533 0.995520i \(-0.530142\pi\)
−0.909422 + 0.415874i \(0.863476\pi\)
\(234\) 0 0
\(235\) −296.000 512.687i −1.25957 2.18165i
\(236\) 119.197 + 68.8186i 0.505073 + 0.291604i
\(237\) 0 0
\(238\) 0 0
\(239\) 76.3675i 0.319529i −0.987155 0.159765i \(-0.948926\pi\)
0.987155 0.159765i \(-0.0510736\pi\)
\(240\) 0 0
\(241\) −66.9104 115.892i −0.277636 0.480880i 0.693160 0.720783i \(-0.256218\pi\)
−0.970797 + 0.239903i \(0.922884\pi\)
\(242\) −138.396 + 79.9031i −0.571885 + 0.330178i
\(243\) 0 0
\(244\) −194.648 −0.797739
\(245\) 0 0
\(246\) 0 0
\(247\) 148.000 256.344i 0.599190 1.03783i
\(248\) 59.5987 34.4093i 0.240317 0.138747i
\(249\) 0 0
\(250\) −145.986 + 252.856i −0.583945 + 1.01142i
\(251\) 137.637i 0.548355i −0.961679 0.274178i \(-0.911594\pi\)
0.961679 0.274178i \(-0.0884056\pi\)
\(252\) 0 0
\(253\) 120.000 0.474308
\(254\) −93.0806 53.7401i −0.366459 0.211575i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 216.045 + 124.734i 0.840643 + 0.485345i 0.857483 0.514513i \(-0.172027\pi\)
−0.0168400 + 0.999858i \(0.505361\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 209.304i 0.805014i
\(261\) 0 0
\(262\) 72.9932 + 126.428i 0.278600 + 0.482549i
\(263\) −203.308 + 117.380i −0.773033 + 0.446311i −0.833955 0.551832i \(-0.813929\pi\)
0.0609226 + 0.998142i \(0.480596\pi\)
\(264\) 0 0
\(265\) 352.800 1.33132
\(266\) 0 0
\(267\) 0 0
\(268\) −104.000 + 180.133i −0.388060 + 0.672139i
\(269\) −186.246 + 107.529i −0.692364 + 0.399736i −0.804497 0.593957i \(-0.797565\pi\)
0.112133 + 0.993693i \(0.464232\pi\)
\(270\) 0 0
\(271\) 158.152 273.927i 0.583586 1.01080i −0.411464 0.911426i \(-0.634982\pi\)
0.995050 0.0993747i \(-0.0316843\pi\)
\(272\) 103.228i 0.379514i
\(273\) 0 0
\(274\) 142.000 0.518248
\(275\) 120.025 + 69.2965i 0.436455 + 0.251987i
\(276\) 0 0
\(277\) −32.0000 55.4256i −0.115523 0.200093i 0.802465 0.596699i \(-0.203521\pi\)
−0.917989 + 0.396606i \(0.870188\pi\)
\(278\) 178.796 + 103.228i 0.643151 + 0.371323i
\(279\) 0 0
\(280\) 0 0
\(281\) 462.448i 1.64572i −0.568243 0.822861i \(-0.692377\pi\)
0.568243 0.822861i \(-0.307623\pi\)
\(282\) 0 0
\(283\) −12.1655 21.0713i −0.0429877 0.0744569i 0.843731 0.536766i \(-0.180354\pi\)
−0.886719 + 0.462309i \(0.847021\pi\)
\(284\) −122.474 + 70.7107i −0.431248 + 0.248981i
\(285\) 0 0
\(286\) 48.6621 0.170147
\(287\) 0 0
\(288\) 0 0
\(289\) 188.500 326.492i 0.652249 1.12973i
\(290\) −163.896 + 94.6256i −0.565160 + 0.326295i
\(291\) 0 0
\(292\) 60.8276 105.357i 0.208314 0.360810i
\(293\) 283.877i 0.968863i −0.874829 0.484431i \(-0.839027\pi\)
0.874829 0.484431i \(-0.160973\pi\)
\(294\) 0 0
\(295\) 592.000 2.00678
\(296\) 14.6969 + 8.48528i 0.0496518 + 0.0286665i
\(297\) 0 0
\(298\) −29.0000 50.2295i −0.0973154 0.168555i
\(299\) 446.990 + 258.070i 1.49495 + 0.863110i
\(300\) 0 0
\(301\) 0 0
\(302\) 226.274i 0.749252i
\(303\) 0 0
\(304\) 48.6621 + 84.2852i 0.160073 + 0.277254i
\(305\) −725.049 + 418.607i −2.37721 + 1.37248i
\(306\) 0 0
\(307\) 316.304 1.03031 0.515153 0.857099i \(-0.327735\pi\)
0.515153 + 0.857099i \(0.327735\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 148.000 256.344i 0.477419 0.826915i
\(311\) −238.395 + 137.637i −0.766542 + 0.442563i −0.831640 0.555316i \(-0.812597\pi\)
0.0650975 + 0.997879i \(0.479264\pi\)
\(312\) 0 0
\(313\) 145.986 252.856i 0.466410 0.807846i −0.532854 0.846207i \(-0.678881\pi\)
0.999264 + 0.0383615i \(0.0122139\pi\)
\(314\) 275.274i 0.876670i
\(315\) 0 0
\(316\) 40.0000 0.126582
\(317\) 290.265 + 167.584i 0.915661 + 0.528657i 0.882248 0.470785i \(-0.156029\pi\)
0.0334128 + 0.999442i \(0.489362\pi\)
\(318\) 0 0
\(319\) 22.0000 + 38.1051i 0.0689655 + 0.119452i
\(320\) −59.5987 34.4093i −0.186246 0.107529i
\(321\) 0 0
\(322\) 0 0
\(323\) 627.911i 1.94400i
\(324\) 0 0
\(325\) 298.055 + 516.247i 0.917093 + 1.58845i
\(326\) 0 0
\(327\) 0 0
\(328\) 72.9932 0.222540
\(329\) 0 0
\(330\) 0 0
\(331\) 194.000 336.018i 0.586103 1.01516i −0.408634 0.912698i \(-0.633995\pi\)
0.994737 0.102461i \(-0.0326718\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 121.655 210.713i 0.364237 0.630877i
\(335\) 894.642i 2.67057i
\(336\) 0 0
\(337\) −208.000 −0.617211 −0.308605 0.951190i \(-0.599862\pi\)
−0.308605 + 0.951190i \(0.599862\pi\)
\(338\) −25.7196 14.8492i −0.0760936 0.0439327i
\(339\) 0 0
\(340\) −222.000 384.515i −0.652941 1.13093i
\(341\) −59.5987 34.4093i −0.174776 0.100907i
\(342\) 0 0
\(343\) 0 0
\(344\) 192.333i 0.559108i
\(345\) 0 0
\(346\) −6.08276 10.5357i −0.0175802 0.0304499i
\(347\) 315.984 182.434i 0.910617 0.525745i 0.0299875 0.999550i \(-0.490453\pi\)
0.880630 + 0.473805i \(0.157120\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.00000 + 13.8564i −0.0227273 + 0.0393648i
\(353\) 22.3495 12.9035i 0.0633130 0.0365538i −0.468009 0.883724i \(-0.655029\pi\)
0.531322 + 0.847170i \(0.321695\pi\)
\(354\) 0 0
\(355\) −304.138 + 526.783i −0.856727 + 1.48389i
\(356\) 189.251i 0.531604i
\(357\) 0 0
\(358\) 204.000 0.569832
\(359\) −262.095 151.321i −0.730071 0.421507i 0.0883773 0.996087i \(-0.471832\pi\)
−0.818448 + 0.574581i \(0.805165\pi\)
\(360\) 0 0
\(361\) −115.500 200.052i −0.319945 0.554160i
\(362\) −14.8997 8.60233i −0.0411593 0.0237633i
\(363\) 0 0
\(364\) 0 0
\(365\) 523.259i 1.43359i
\(366\) 0 0
\(367\) −194.648 337.141i −0.530377 0.918640i −0.999372 0.0354391i \(-0.988717\pi\)
0.468995 0.883201i \(-0.344616\pi\)
\(368\) −146.969 + 84.8528i −0.399373 + 0.230578i
\(369\) 0 0
\(370\) 72.9932 0.197279
\(371\) 0 0
\(372\) 0 0
\(373\) −353.000 + 611.414i −0.946381 + 1.63918i −0.193418 + 0.981116i \(0.561957\pi\)
−0.752963 + 0.658063i \(0.771376\pi\)
\(374\) −89.3980 + 51.6140i −0.239032 + 0.138005i
\(375\) 0 0
\(376\) 97.3242 168.570i 0.258841 0.448326i
\(377\) 189.251i 0.501992i
\(378\) 0 0
\(379\) 708.000 1.86807 0.934037 0.357176i \(-0.116261\pi\)
0.934037 + 0.357176i \(0.116261\pi\)
\(380\) 362.524 + 209.304i 0.954012 + 0.550799i
\(381\) 0 0
\(382\) 186.000 + 322.161i 0.486911 + 0.843355i
\(383\) 268.194 + 154.842i 0.700245 + 0.404287i 0.807439 0.589951i \(-0.200853\pi\)
−0.107193 + 0.994238i \(0.534186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 53.7401i 0.139223i
\(387\) 0 0
\(388\) −158.152 273.927i −0.407608 0.705997i
\(389\) −113.901 + 65.7609i −0.292805 + 0.169051i −0.639206 0.769035i \(-0.720737\pi\)
0.346401 + 0.938087i \(0.387404\pi\)
\(390\) 0 0
\(391\) −1094.90 −2.80025
\(392\) 0 0
\(393\) 0 0
\(394\) 117.000 202.650i 0.296954 0.514340i
\(395\) 148.997 86.0233i 0.377207 0.217780i
\(396\) 0 0
\(397\) 48.6621 84.2852i 0.122575 0.212305i −0.798208 0.602382i \(-0.794218\pi\)
0.920782 + 0.390077i \(0.127552\pi\)
\(398\) 344.093i 0.864555i
\(399\) 0 0
\(400\) −196.000 −0.490000
\(401\) −77.1589 44.5477i −0.192416 0.111092i 0.400697 0.916211i \(-0.368768\pi\)
−0.593113 + 0.805119i \(0.702101\pi\)
\(402\) 0 0
\(403\) −148.000 256.344i −0.367246 0.636088i
\(404\) −104.298 60.2163i −0.258163 0.149050i
\(405\) 0 0
\(406\) 0 0
\(407\) 16.9706i 0.0416967i
\(408\) 0 0
\(409\) 273.724 + 474.104i 0.669253 + 1.15918i 0.978113 + 0.208072i \(0.0667189\pi\)
−0.308861 + 0.951107i \(0.599948\pi\)
\(410\) 271.893 156.978i 0.663155 0.382872i
\(411\) 0 0
\(412\) 340.635 0.826783
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −59.5987 + 34.4093i −0.143266 + 0.0827147i
\(417\) 0 0
\(418\) 48.6621 84.2852i 0.116417 0.201639i
\(419\) 653.777i 1.56033i −0.625576 0.780163i \(-0.715136\pi\)
0.625576 0.780163i \(-0.284864\pi\)
\(420\) 0 0
\(421\) 240.000 0.570071 0.285036 0.958517i \(-0.407995\pi\)
0.285036 + 0.958517i \(0.407995\pi\)
\(422\) 53.8888 + 31.1127i 0.127699 + 0.0737268i
\(423\) 0 0
\(424\) 58.0000 + 100.459i 0.136792 + 0.236931i
\(425\) −1095.13 632.271i −2.57677 1.48770i
\(426\) 0 0
\(427\) 0 0
\(428\) 39.5980i 0.0925186i
\(429\) 0 0
\(430\) −413.628 716.424i −0.961925 1.66610i
\(431\) 12.2474 7.07107i 0.0284164 0.0164062i −0.485725 0.874112i \(-0.661444\pi\)
0.514141 + 0.857706i \(0.328111\pi\)
\(432\) 0 0
\(433\) −389.297 −0.899069 −0.449534 0.893263i \(-0.648410\pi\)
−0.449534 + 0.893263i \(0.648410\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −56.0000 + 96.9948i −0.128440 + 0.222465i
\(437\) 893.980 516.140i 2.04572 1.18110i
\(438\) 0 0
\(439\) −145.986 + 252.856i −0.332543 + 0.575981i −0.983010 0.183554i \(-0.941240\pi\)
0.650467 + 0.759535i \(0.274573\pi\)
\(440\) 68.8186i 0.156406i
\(441\) 0 0
\(442\) −444.000 −1.00452
\(443\) 22.0454 + 12.7279i 0.0497639 + 0.0287312i 0.524676 0.851302i \(-0.324187\pi\)
−0.474912 + 0.880033i \(0.657520\pi\)
\(444\) 0 0
\(445\) 407.000 + 704.945i 0.914607 + 1.58415i
\(446\) −238.395 137.637i −0.534517 0.308604i
\(447\) 0 0
\(448\) 0 0
\(449\) 733.977i 1.63469i 0.576147 + 0.817346i \(0.304556\pi\)
−0.576147 + 0.817346i \(0.695444\pi\)
\(450\) 0 0
\(451\) −36.4966 63.2139i −0.0809237 0.140164i
\(452\) 276.792 159.806i 0.612372 0.353553i
\(453\) 0 0
\(454\) 48.6621 0.107185
\(455\) 0 0
\(456\) 0 0
\(457\) −136.000 + 235.559i −0.297593 + 0.515446i −0.975585 0.219623i \(-0.929517\pi\)
0.677992 + 0.735070i \(0.262851\pi\)
\(458\) −14.8997 + 8.60233i −0.0325320 + 0.0187824i
\(459\) 0 0
\(460\) −364.966 + 632.139i −0.793404 + 1.37422i
\(461\) 490.333i 1.06363i −0.846861 0.531814i \(-0.821511\pi\)
0.846861 0.531814i \(-0.178489\pi\)
\(462\) 0 0
\(463\) −436.000 −0.941685 −0.470842 0.882217i \(-0.656050\pi\)
−0.470842 + 0.882217i \(0.656050\pi\)
\(464\) −53.8888 31.1127i −0.116140 0.0670532i
\(465\) 0 0
\(466\) −191.000 330.822i −0.409871 0.709918i
\(467\) 417.191 + 240.865i 0.893342 + 0.515771i 0.875034 0.484061i \(-0.160839\pi\)
0.0183077 + 0.999832i \(0.494172\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 837.214i 1.78131i
\(471\) 0 0
\(472\) 97.3242 + 168.570i 0.206195 + 0.357141i
\(473\) −166.565 + 96.1665i −0.352147 + 0.203312i
\(474\) 0 0
\(475\) 1192.22 2.50994
\(476\) 0 0
\(477\) 0 0
\(478\) 54.0000 93.5307i 0.112971 0.195671i
\(479\) 89.3980 51.6140i 0.186635 0.107754i −0.403772 0.914860i \(-0.632301\pi\)
0.590406 + 0.807106i \(0.298968\pi\)
\(480\) 0 0
\(481\) 36.4966 63.2139i 0.0758765 0.131422i
\(482\) 189.251i 0.392637i
\(483\) 0 0
\(484\) −226.000 −0.466942
\(485\) −1178.20 680.237i −2.42929 1.40255i
\(486\) 0 0
\(487\) −116.000 200.918i −0.238193 0.412562i 0.722003 0.691890i \(-0.243222\pi\)
−0.960196 + 0.279328i \(0.909888\pi\)
\(488\) −238.395 137.637i −0.488514 0.282043i
\(489\) 0 0
\(490\) 0 0
\(491\) 449.720i 0.915927i 0.888971 + 0.457963i \(0.151421\pi\)
−0.888971 + 0.457963i \(0.848579\pi\)
\(492\) 0 0
\(493\) −200.731 347.677i −0.407163 0.705226i
\(494\) 362.524 209.304i 0.733855 0.423692i
\(495\) 0 0
\(496\) 97.3242 0.196218
\(497\) 0 0
\(498\) 0 0
\(499\) −378.000 + 654.715i −0.757515 + 1.31205i 0.186599 + 0.982436i \(0.440253\pi\)
−0.944114 + 0.329618i \(0.893080\pi\)
\(500\) −357.592 + 206.456i −0.715184 + 0.412912i
\(501\) 0 0
\(502\) 97.3242 168.570i 0.193873 0.335798i
\(503\) 550.549i 1.09453i 0.836959 + 0.547265i \(0.184331\pi\)
−0.836959 + 0.547265i \(0.815669\pi\)
\(504\) 0 0
\(505\) −518.000 −1.02574
\(506\) 146.969 + 84.8528i 0.290453 + 0.167693i
\(507\) 0 0
\(508\) −76.0000 131.636i −0.149606 0.259126i
\(509\) −7.44983 4.30116i −0.0146362 0.00845022i 0.492664 0.870220i \(-0.336023\pi\)
−0.507300 + 0.861769i \(0.669356\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 176.400 + 305.534i 0.343191 + 0.594424i
\(515\) 1268.84 732.563i 2.46376 1.42245i
\(516\) 0 0
\(517\) −194.648 −0.376496
\(518\) 0 0
\(519\) 0 0
\(520\) −148.000 + 256.344i −0.284615 + 0.492968i
\(521\) −81.9482 + 47.3128i −0.157290 + 0.0908115i −0.576579 0.817041i \(-0.695613\pi\)
0.419289 + 0.907853i \(0.362279\pi\)
\(522\) 0 0
\(523\) −462.290 + 800.710i −0.883920 + 1.53099i −0.0369726 + 0.999316i \(0.511771\pi\)
−0.846947 + 0.531677i \(0.821562\pi\)
\(524\) 206.456i 0.394000i
\(525\) 0 0
\(526\) −332.000 −0.631179
\(527\) 543.787 + 313.955i 1.03185 + 0.595741i
\(528\) 0 0
\(529\) 635.500 + 1100.72i 1.20132 + 2.08075i
\(530\) 432.090 + 249.467i 0.815265 + 0.470693i
\(531\) 0 0
\(532\) 0 0
\(533\) 313.955i 0.589035i
\(534\) 0 0
\(535\) 85.1587 + 147.499i 0.159175 + 0.275699i
\(536\) −254.747 + 147.078i −0.475274 + 0.274400i
\(537\) 0 0
\(538\) −304.138 −0.565313
\(539\) 0 0
\(540\) 0 0
\(541\) −296.000 + 512.687i −0.547135 + 0.947666i 0.451334 + 0.892355i \(0.350948\pi\)
−0.998469 + 0.0553105i \(0.982385\pi\)
\(542\) 387.391 223.660i 0.714744 0.412658i
\(543\) 0 0
\(544\) 72.9932 126.428i 0.134179 0.232404i
\(545\) 481.730i 0.883909i
\(546\) 0 0
\(547\) −416.000 −0.760512 −0.380256 0.924881i \(-0.624164\pi\)
−0.380256 + 0.924881i \(0.624164\pi\)
\(548\) 173.914 + 100.409i 0.317361 + 0.183228i
\(549\) 0 0
\(550\) 98.0000 + 169.741i 0.178182 + 0.308620i
\(551\) 327.793 + 189.251i 0.594905 + 0.343469i
\(552\) 0 0
\(553\) 0 0
\(554\) 90.5097i 0.163375i
\(555\) 0 0
\(556\) 145.986 + 252.856i 0.262565 + 0.454776i
\(557\) −268.219 + 154.856i −0.481542 + 0.278019i −0.721059 0.692874i \(-0.756344\pi\)
0.239517 + 0.970892i \(0.423011\pi\)
\(558\) 0 0
\(559\) −827.256 −1.47988
\(560\) 0 0
\(561\) 0 0
\(562\) 327.000 566.381i 0.581851 1.00779i
\(563\) −774.783 + 447.321i −1.37617 + 0.794531i −0.991696 0.128606i \(-0.958950\pi\)
−0.384472 + 0.923137i \(0.625617\pi\)
\(564\) 0 0
\(565\) 687.352 1190.53i 1.21655 2.10713i
\(566\) 34.4093i 0.0607938i
\(567\) 0 0
\(568\) −200.000 −0.352113
\(569\) −635.643 366.988i −1.11712 0.644971i −0.176458 0.984308i \(-0.556464\pi\)
−0.940665 + 0.339337i \(0.889797\pi\)
\(570\) 0 0
\(571\) −156.000 270.200i −0.273205 0.473205i 0.696476 0.717580i \(-0.254750\pi\)
−0.969681 + 0.244376i \(0.921417\pi\)
\(572\) 59.5987 + 34.4093i 0.104193 + 0.0601561i
\(573\) 0 0
\(574\) 0 0
\(575\) 2078.89i 3.61547i
\(576\) 0 0
\(577\) 97.3242 + 168.570i 0.168673 + 0.292150i 0.937953 0.346761i \(-0.112719\pi\)
−0.769281 + 0.638911i \(0.779385\pi\)
\(578\) 461.729 266.579i 0.798839 0.461210i
\(579\) 0 0
\(580\) −267.642 −0.461451
\(581\) 0 0
\(582\) 0 0
\(583\) 58.0000 100.459i 0.0994854 0.172314i
\(584\) 148.997 86.0233i 0.255131 0.147300i
\(585\) 0 0
\(586\) 200.731 347.677i 0.342545 0.593305i
\(587\) 447.321i 0.762046i −0.924566 0.381023i \(-0.875572\pi\)
0.924566 0.381023i \(-0.124428\pi\)
\(588\) 0 0
\(589\) −592.000 −1.00509
\(590\) 725.049 + 418.607i 1.22890 + 0.709504i
\(591\) 0 0
\(592\) 12.0000 + 20.7846i 0.0202703 + 0.0351091i
\(593\) 558.737 + 322.587i 0.942222 + 0.543992i 0.890656 0.454678i \(-0.150246\pi\)
0.0515656 + 0.998670i \(0.483579\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 82.0244i 0.137625i
\(597\) 0 0
\(598\) 364.966 + 632.139i 0.610311 + 1.05709i
\(599\) 595.226 343.654i 0.993700 0.573713i 0.0873214 0.996180i \(-0.472169\pi\)
0.906378 + 0.422468i \(0.138836\pi\)
\(600\) 0 0
\(601\) 1070.57 1.78131 0.890654 0.454682i \(-0.150247\pi\)
0.890654 + 0.454682i \(0.150247\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 160.000 277.128i 0.264901 0.458821i
\(605\) −841.831 + 486.031i −1.39146 + 0.803358i
\(606\) 0 0
\(607\) 364.966 632.139i 0.601262 1.04142i −0.391369 0.920234i \(-0.627998\pi\)
0.992630 0.121182i \(-0.0386683\pi\)
\(608\) 137.637i 0.226377i
\(609\) 0 0
\(610\) −1184.00 −1.94098
\(611\) −725.049 418.607i −1.18666 0.685118i
\(612\) 0 0
\(613\) 257.000 + 445.137i 0.419250 + 0.726162i 0.995864 0.0908547i \(-0.0289599\pi\)
−0.576615 + 0.817016i \(0.695627\pi\)
\(614\) 387.391 + 223.660i 0.630930 + 0.364268i
\(615\) 0 0
\(616\) 0 0
\(617\) 202.233i 0.327767i −0.986480 0.163884i \(-0.947598\pi\)
0.986480 0.163884i \(-0.0524022\pi\)
\(618\) 0 0
\(619\) −340.635 589.997i −0.550298 0.953145i −0.998253 0.0590883i \(-0.981181\pi\)
0.447954 0.894056i \(-0.352153\pi\)
\(620\) 362.524 209.304i 0.584717 0.337586i
\(621\) 0 0
\(622\) −389.297 −0.625879
\(623\) 0 0
\(624\) 0 0
\(625\) −275.500 + 477.180i −0.440800 + 0.763488i
\(626\) 357.592 206.456i 0.571233 0.329802i
\(627\) 0 0
\(628\) 194.648 337.141i 0.309950 0.536849i
\(629\) 154.842i 0.246171i
\(630\) 0 0
\(631\) 636.000 1.00792 0.503962 0.863726i \(-0.331875\pi\)
0.503962 + 0.863726i \(0.331875\pi\)
\(632\) 48.9898 + 28.2843i 0.0775155 + 0.0447536i
\(633\) 0 0
\(634\) 237.000 + 410.496i 0.373817 + 0.647470i
\(635\) −566.187 326.888i −0.891633 0.514785i
\(636\) 0 0
\(637\) 0 0
\(638\) 62.2254i 0.0975320i
\(639\) 0 0
\(640\) −48.6621 84.2852i −0.0760345 0.131696i
\(641\) 67.3610 38.8909i 0.105087 0.0606722i −0.446535 0.894766i \(-0.647342\pi\)
0.551623 + 0.834094i \(0.314009\pi\)
\(642\) 0 0
\(643\) 510.952 0.794638 0.397319 0.917681i \(-0.369941\pi\)
0.397319 + 0.917681i \(0.369941\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −444.000 + 769.031i −0.687307 + 1.19045i
\(647\) −804.582 + 464.526i −1.24356 + 0.717968i −0.969817 0.243835i \(-0.921594\pi\)
−0.273741 + 0.961803i \(0.588261\pi\)
\(648\) 0 0
\(649\) 97.3242 168.570i 0.149960 0.259739i
\(650\) 843.028i 1.29697i
\(651\) 0 0
\(652\) 0 0
\(653\) 552.360 + 318.905i 0.845880 + 0.488369i 0.859259 0.511541i \(-0.170925\pi\)
−0.0133783 + 0.999911i \(0.504259\pi\)
\(654\) 0 0
\(655\) 444.000 + 769.031i 0.677863 + 1.17409i
\(656\) 89.3980 + 51.6140i 0.136277 + 0.0786798i
\(657\) 0 0
\(658\) 0 0
\(659\) 200.818i 0.304732i 0.988324 + 0.152366i \(0.0486892\pi\)
−0.988324 + 0.152366i \(0.951311\pi\)
\(660\) 0 0
\(661\) 48.6621 + 84.2852i 0.0736189 + 0.127512i 0.900485 0.434887i \(-0.143212\pi\)
−0.826866 + 0.562399i \(0.809878\pi\)
\(662\) 475.201 274.357i 0.717826 0.414437i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −330.000 + 571.577i −0.494753 + 0.856937i
\(668\) 297.993 172.047i 0.446098 0.257555i
\(669\) 0 0
\(670\) −632.607 + 1095.71i −0.944190 + 1.63539i
\(671\) 275.274i 0.410245i
\(672\) 0 0
\(673\) −250.000 −0.371471 −0.185736 0.982600i \(-0.559467\pi\)
−0.185736 + 0.982600i \(0.559467\pi\)
\(674\) −254.747 147.078i −0.377963 0.218217i
\(675\) 0 0
\(676\) −21.0000 36.3731i −0.0310651 0.0538063i
\(677\) 290.543 + 167.745i 0.429163 + 0.247777i 0.698990 0.715131i \(-0.253633\pi\)
−0.269827 + 0.962909i \(0.586966\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 627.911i 0.923398i
\(681\) 0 0
\(682\) −48.6621 84.2852i −0.0713521 0.123585i
\(683\) −252.297 + 145.664i −0.369396 + 0.213271i −0.673195 0.739465i \(-0.735078\pi\)
0.303799 + 0.952736i \(0.401745\pi\)
\(684\) 0 0
\(685\) 863.752 1.26095
\(686\) 0 0
\(687\) 0 0
\(688\) 136.000 235.559i 0.197674 0.342382i
\(689\) 432.090 249.467i 0.627127 0.362072i
\(690\) 0 0
\(691\) −267.642 + 463.569i −0.387325 + 0.670867i −0.992089 0.125538i \(-0.959934\pi\)
0.604764 + 0.796405i \(0.293268\pi\)
\(692\) 17.2047i 0.0248622i
\(693\) 0 0
\(694\) 516.000 0.743516
\(695\) 1087.57 + 627.911i 1.56485 + 0.903469i
\(696\) 0 0
\(697\) 333.000 + 576.773i 0.477762 + 0.827508i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1045.10i 1.49088i 0.666575 + 0.745438i \(0.267760\pi\)
−0.666575 + 0.745438i \(0.732240\pi\)
\(702\) 0 0
\(703\) −72.9932 126.428i −0.103831 0.179840i
\(704\) −19.5959 + 11.3137i −0.0278351 + 0.0160706i
\(705\) 0 0
\(706\) 36.4966 0.0516949
\(707\) 0 0
\(708\) 0 0
\(709\) 244.000 422.620i 0.344147 0.596080i −0.641052 0.767498i \(-0.721502\pi\)
0.985198 + 0.171418i \(0.0548349\pi\)
\(710\) −744.983 + 430.116i −1.04927 + 0.605798i
\(711\) 0 0
\(712\) −133.821 + 231.784i −0.187951 + 0.325540i
\(713\) 1032.28i 1.44780i
\(714\) 0 0
\(715\) 296.000 0.413986
\(716\) 249.848 + 144.250i 0.348950 + 0.201466i
\(717\) 0 0
\(718\) −214.000 370.659i −0.298050 0.516238i
\(719\) −804.582 464.526i −1.11903 0.646072i −0.177876 0.984053i \(-0.556923\pi\)
−0.941153 + 0.337981i \(0.890256\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 326.683i 0.452470i
\(723\) 0 0
\(724\) −12.1655 21.0713i −0.0168032 0.0291040i
\(725\) −660.137 + 381.131i −0.910534 + 0.525697i
\(726\) 0 0
\(727\) −900.249 −1.23831 −0.619153 0.785270i \(-0.712524\pi\)
−0.619153 + 0.785270i \(0.712524\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 370.000 640.859i 0.506849 0.877889i
\(731\) 1519.77 877.437i 2.07902 1.20032i
\(732\) 0 0
\(733\) −577.862 + 1000.89i −0.788353 + 1.36547i 0.138623 + 0.990345i \(0.455732\pi\)
−0.926976 + 0.375122i \(0.877601\pi\)
\(734\) 550.549i 0.750067i
\(735\) 0 0
\(736\) −240.000 −0.326087
\(737\) 254.747 + 147.078i 0.345654 + 0.199563i
\(738\) 0 0
\(739\) 460.000 + 796.743i 0.622463 + 1.07814i 0.989026 + 0.147744i \(0.0472011\pi\)
−0.366563 + 0.930393i \(0.619466\pi\)
\(740\) 89.3980 + 51.6140i 0.120808 + 0.0697486i
\(741\) 0 0
\(742\) 0 0
\(743\) 755.190i 1.01641i 0.861237 + 0.508203i \(0.169690\pi\)
−0.861237 + 0.508203i \(0.830310\pi\)
\(744\) 0 0
\(745\) −176.400 305.534i −0.236779 0.410113i
\(746\) −864.670 + 499.217i −1.15907 + 0.669192i
\(747\) 0 0
\(748\) −145.986 −0.195169
\(749\) 0 0
\(750\) 0 0
\(751\) 60.0000 103.923i 0.0798935 0.138380i −0.823310 0.567591i \(-0.807875\pi\)
0.903204 + 0.429212i \(0.141209\pi\)
\(752\) 238.395 137.637i 0.317014 0.183028i
\(753\) 0 0
\(754\) −133.821 + 231.784i −0.177481 + 0.307406i
\(755\) 1376.37i 1.82301i
\(756\) 0 0
\(757\) −1016.00 −1.34214 −0.671070 0.741394i \(-0.734165\pi\)
−0.671070 + 0.741394i \(0.734165\pi\)
\(758\) 867.119 + 500.632i 1.14396 + 0.660464i
\(759\) 0 0
\(760\) 296.000 + 512.687i 0.389474 + 0.674588i
\(761\) −37.2492 21.5058i −0.0489476 0.0282599i 0.475326 0.879809i \(-0.342330\pi\)
−0.524274 + 0.851550i \(0.675663\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 526.087i 0.688596i
\(765\) 0 0
\(766\) 218.979 + 379.284i 0.285874 + 0.495148i
\(767\) 725.049 418.607i 0.945305 0.545772i
\(768\) 0 0
\(769\) −681.269 −0.885916 −0.442958 0.896542i \(-0.646071\pi\)
−0.442958 + 0.896542i \(0.646071\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 38.0000 65.8179i 0.0492228 0.0852564i
\(773\) 1005.73 580.657i 1.30107 0.751173i 0.320483 0.947254i \(-0.396155\pi\)
0.980588 + 0.196081i \(0.0628216\pi\)
\(774\) 0 0
\(775\) 596.111 1032.49i 0.769175 1.33225i
\(776\) 447.321i 0.576444i
\(777\) 0 0
\(778\) −186.000 −0.239075
\(779\) −543.787 313.955i −0.698057 0.403024i
\(780\) 0 0
\(781\) 100.000 + 173.205i 0.128041 + 0.221773i
\(782\) −1340.97 774.209i −1.71480 0.990037i
\(783\) 0 0
\(784\) 0 0
\(785\) 1674.43i 2.13303i
\(786\) 0 0
\(787\) 97.3242 + 168.570i 0.123665 + 0.214194i 0.921210 0.389065i \(-0.127202\pi\)
−0.797545 + 0.603259i \(0.793869\pi\)
\(788\) 286.590 165.463i 0.363693 0.209978i
\(789\) 0 0
\(790\) 243.311 0.307988
\(791\) 0 0
\(792\) 0 0
\(793\) −592.000 + 1025.37i −0.746532