Properties

Label 882.3.s.h.863.2
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 863.2
Root \(2.31664 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.863
Dual form 882.3.s.h.557.2

$q$-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 −0.607191 0.794556i \(-0.707704\pi\)
0.384510 + 0.923121i \(0.374370\pi\)
\(12\) 0 0
\(13\) −12.1655 −0.935810 −0.467905 0.883779i \(-0.654991\pi\)
−0.467905 + 0.883779i \(0.654991\pi\)
\(14\) 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 \(0.387853\pi\)
−0.985368 + 0.170442i \(0.945481\pi\)
\(20\) 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 \(-0.959630\pi\)
−0.605525 0.795826i \(-0.707037\pi\)
\(24\) 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 \(-0.913567\pi\)
0.963360 0.268213i \(-0.0864331\pi\)
\(30\) 0 0
\(31\) 12.1655 + 21.0713i 0.392436 + 0.679720i 0.992770 0.120030i \(-0.0382990\pi\)
−0.600334 + 0.799749i \(0.704966\pi\)
\(32\) 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 −0.796131 0.605124i \(-0.793123\pi\)
0.125988 + 0.992032i \(0.459790\pi\)
\(54\) 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 \(-0.539362\pi\)
0.921085 0.389361i \(-0.127304\pi\)
\(62\) 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 \(-0.834082\pi\)
0.867199 0.497963i \(-0.165918\pi\)
\(72\) 0 0
\(73\) 30.4138 + 52.6783i 0.416628 + 0.721620i 0.995598 0.0937286i \(-0.0298786\pi\)
−0.578970 + 0.815349i \(0.696545\pi\)
\(74\) −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 \(-0.196618\pi\)
0.815216 + 0.579158i \(0.196618\pi\)
\(98\) 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 \(0.476498\pi\)
−0.900549 + 0.434755i \(0.856835\pi\)
\(104\) 34.4093i 0.330859i
\(105\) 0 0
\(106\) 58.0000 0.547170
\(107\) −17.1464 9.89949i −0.160247 0.0925186i 0.417732 0.908570i \(-0.362825\pi\)
−0.577979 + 0.816052i \(0.696158\pi\)
\(108\) 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 \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 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 −0.782578 0.622552i \(-0.786096\pi\)
0.147857 + 0.989009i \(0.452763\pi\)
\(138\) 0 0
\(139\) −145.986 −1.05026 −0.525131 0.851022i \(-0.675984\pi\)
−0.525131 + 0.851022i \(0.675984\pi\)
\(140\) 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 0.614429 0.788972i \(-0.289387\pi\)
−0.376056 + 0.926597i \(0.622720\pi\)
\(150\) 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 \(0.0461599\pi\)
−0.369604 + 0.929189i \(0.620507\pi\)
\(158\) −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 −0.806565 0.591146i \(-0.798676\pi\)
0.108665 + 0.994078i \(0.465342\pi\)
\(180\) 0 0
\(181\) 12.1655 0.0672128 0.0336064 0.999435i \(-0.489301\pi\)
0.0336064 + 0.999435i \(0.489301\pi\)
\(182\) 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 −0.233769 0.972292i \(-0.575106\pi\)
−0.958914 + 0.283696i \(0.908439\pi\)
\(192\) 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 \(0.137955\pi\)
−0.907544 + 0.419957i \(0.862045\pi\)
\(198\) 0 0
\(199\) 121.655 + 210.713i 0.611333 + 1.05886i 0.991016 + 0.133743i \(0.0426997\pi\)
−0.379683 + 0.925117i \(0.623967\pi\)
\(200\) 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 \(-0.356242\pi\)
0.436431 + 0.899738i \(0.356242\pi\)
\(224\) 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 −0.852439 0.522827i \(-0.824877\pi\)
0.879001 + 0.476820i \(0.158211\pi\)
\(230\) 516.140i 2.24408i
\(231\) 0 0
\(232\) −44.0000 −0.189655
\(233\) 233.926 + 135.057i 1.00398 + 0.579645i 0.909422 0.415874i \(-0.136524\pi\)
0.0945533 + 0.995520i \(0.469858\pi\)
\(234\) 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 \(0.0510736\pi\)
−0.987155 + 0.159765i \(0.948926\pi\)
\(240\) 0 0
\(241\) 66.9104 + 115.892i 0.277636 + 0.480880i 0.970797 0.239903i \(-0.0771156\pi\)
−0.693160 + 0.720783i \(0.743782\pi\)
\(242\) 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 −0.0609226 0.998142i \(-0.519404\pi\)
0.833955 + 0.551832i \(0.186071\pi\)
\(264\) 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 \(0.365018\pi\)
−0.995050 + 0.0993747i \(0.968316\pi\)
\(272\) 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 \(0.307623\pi\)
−0.568243 + 0.822861i \(0.692377\pi\)
\(282\) 0 0
\(283\) 12.1655 + 21.0713i 0.0429877 + 0.0744569i 0.886719 0.462309i \(-0.152979\pi\)
−0.843731 + 0.536766i \(0.819646\pi\)
\(284\) 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 \(-0.672265\pi\)
−0.515153 + 0.857099i \(0.672265\pi\)
\(308\) 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 −0.999264 0.0383615i \(-0.987786\pi\)
0.532854 + 0.846207i \(0.321119\pi\)
\(314\) 275.274i 0.876670i
\(315\) 0 0
\(316\) 40.0000 0.126582
\(317\) −290.265 167.584i −0.915661 0.528657i −0.0334128 0.999442i \(-0.510638\pi\)
−0.882248 + 0.470785i \(0.843971\pi\)
\(318\) 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 −0.880630 0.473805i \(-0.842880\pi\)
−0.0299875 + 0.999550i \(0.509547\pi\)
\(348\) 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 0.818448 0.574581i \(-0.194835\pi\)
−0.0883773 + 0.996087i \(0.528168\pi\)
\(360\) 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 \(0.0112830\pi\)
−0.468995 + 0.883201i \(0.655384\pi\)
\(368\) 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 −0.346401 0.938087i \(-0.612596\pi\)
0.639206 + 0.769035i \(0.279263\pi\)
\(390\) 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 −0.920782 0.390077i \(-0.872448\pi\)
0.798208 + 0.602382i \(0.205782\pi\)
\(398\) 344.093i 0.864555i
\(399\) 0 0
\(400\) −196.000 −0.490000
\(401\) 77.1589 + 44.5477i 0.192416 + 0.111092i 0.593113 0.805119i \(-0.297899\pi\)
−0.400697 + 0.916211i \(0.631232\pi\)
\(402\) 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 \(-0.933281\pi\)
0.308861 0.951107i \(-0.400052\pi\)
\(410\) −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 −0.514141 0.857706i \(-0.671889\pi\)
0.485725 + 0.874112i \(0.338556\pi\)
\(432\) 0 0
\(433\) 389.297 0.899069 0.449534 0.893263i \(-0.351590\pi\)
0.449534 + 0.893263i \(0.351590\pi\)
\(434\) 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 −0.650467 0.759535i \(-0.725427\pi\)
0.983010 + 0.183554i \(0.0587601\pi\)
\(440\) 68.8186i 0.156406i
\(441\) 0 0
\(442\) −444.000 −1.00452
\(443\) −22.0454 12.7279i −0.0497639 0.0287312i 0.474912 0.880033i \(-0.342480\pi\)
−0.524676 + 0.851302i \(0.675813\pi\)
\(444\) 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 \(-0.695444\pi\)
0.576147 0.817346i \(-0.304556\pi\)
\(450\) 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 \(-0.848579\pi\)
0.888971 0.457963i \(-0.151421\pi\)
\(492\) 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 \(-0.488229\pi\)
0.846947 0.531677i \(-0.178438\pi\)
\(524\) 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 −0.239517 0.970892i \(-0.576989\pi\)
0.721059 + 0.692874i \(0.243656\pi\)
\(558\) 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 0.940665 0.339337i \(-0.110203\pi\)
0.176458 + 0.984308i \(0.443536\pi\)
\(570\) 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 0.769281 0.638911i \(-0.220615\pi\)
−0.937953 + 0.346761i \(0.887281\pi\)
\(578\) −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 −0.906378 0.422468i \(-0.861164\pi\)
−0.0873214 + 0.996180i \(0.527831\pi\)
\(600\) 0 0
\(601\) −1070.57 −1.78131 −0.890654 0.454682i \(-0.849753\pi\)
−0.890654 + 0.454682i \(0.849753\pi\)
\(602\) 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 \(0.372002\pi\)
−0.992630 + 0.121182i \(0.961332\pi\)
\(608\) 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 \(0.0524022\pi\)
−0.986480 + 0.163884i \(0.947598\pi\)
\(618\) 0 0
\(619\) 340.635 + 589.997i 0.550298 + 0.953145i 0.998253 + 0.0590883i \(0.0188194\pi\)
−0.447954 + 0.894056i \(0.647847\pi\)
\(620\) −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 −0.551623 0.834094i \(-0.685991\pi\)
0.446535 + 0.894766i \(0.352658\pi\)
\(642\) 0 0
\(643\) −510.952 −0.794638 −0.397319 0.917681i \(-0.630059\pi\)
−0.397319 + 0.917681i \(0.630059\pi\)
\(644\) 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 0.0133783 0.999911i \(-0.495741\pi\)
−0.859259 + 0.511541i \(0.829075\pi\)
\(654\) 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 \(-0.951311\pi\)
0.988324 0.152366i \(-0.0486892\pi\)
\(660\) 0 0
\(661\) −48.6621 84.2852i −0.0736189 0.127512i 0.826866 0.562399i \(-0.190122\pi\)
−0.900485 + 0.434887i \(0.856788\pi\)
\(662\) −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 −0.303799 0.952736i \(-0.598255\pi\)
0.673195 + 0.739465i \(0.264922\pi\)
\(684\) 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 −0.604764 0.796405i \(-0.706732\pi\)
0.992089 + 0.125538i \(0.0400658\pi\)
\(692\) 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 \(-0.732240\pi\)
0.666575 0.745438i \(-0.267760\pi\)
\(702\) 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 \(-0.287476\pi\)
0.619153 + 0.785270i \(0.287476\pi\)
\(728\) 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 \(-0.544268\pi\)
0.926976 0.375122i \(-0.122399\pi\)
\(734\) 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 \(-0.830310\pi\)
0.861237 0.508203i \(-0.169690\pi\)
\(744\) 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 \(-0.353929\pi\)
0.442958 + 0.896542i \(0.353929\pi\)
\(770\) 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 0.797545 0.603259i \(-0.206131\pi\)
−0.921210 + 0.389065i \(0.872798\pi\)
\(788\) −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 +