Properties

Label 324.4.i.a.37.7
Level 324
Weight 4
Character 324.37
Analytic conductor 19.117
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.7
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.7

$q$-expansion

\(f(q)\) \(=\) \(q+(6.50317 - 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +O(q^{10})\) \(q+(6.50317 - 2.36696i) q^{5} +(1.34685 + 7.63837i) q^{7} +(-13.7454 - 5.00292i) q^{11} +(40.8838 + 34.3056i) q^{13} +(29.6006 - 51.2697i) q^{17} +(46.8884 + 81.2131i) q^{19} +(-4.51998 + 25.6341i) q^{23} +(-59.0669 + 49.5630i) q^{25} +(172.381 - 144.645i) q^{29} +(4.27764 - 24.2597i) q^{31} +(26.8385 + 46.4856i) q^{35} +(-38.3554 + 66.4335i) q^{37} +(305.098 + 256.008i) q^{41} +(282.678 + 102.886i) q^{43} +(3.08562 + 17.4994i) q^{47} +(265.784 - 96.7374i) q^{49} +242.682 q^{53} -101.230 q^{55} +(211.368 - 76.9317i) q^{59} +(81.1159 + 460.031i) q^{61} +(347.074 + 126.325i) q^{65} +(333.309 + 279.680i) q^{67} +(-277.317 + 480.327i) q^{71} +(-226.923 - 393.043i) q^{73} +(19.7011 - 111.731i) q^{77} +(-537.292 + 450.842i) q^{79} +(427.701 - 358.883i) q^{83} +(71.1442 - 403.479i) q^{85} +(-578.094 - 1001.29i) q^{89} +(-206.974 + 358.490i) q^{91} +(497.151 + 417.160i) q^{95} +(1388.22 + 505.270i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{9}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 6.50317 2.36696i 0.581661 0.211707i −0.0343968 0.999408i \(-0.510951\pi\)
0.616058 + 0.787701i \(0.288729\pi\)
\(6\) 0 0
\(7\) 1.34685 + 7.63837i 0.0727231 + 0.412433i 0.999337 + 0.0364180i \(0.0115948\pi\)
−0.926614 + 0.376015i \(0.877294\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −13.7454 5.00292i −0.376763 0.137131i 0.146695 0.989182i \(-0.453136\pi\)
−0.523459 + 0.852051i \(0.675359\pi\)
\(12\) 0 0
\(13\) 40.8838 + 34.3056i 0.872241 + 0.731897i 0.964569 0.263832i \(-0.0849864\pi\)
−0.0923280 + 0.995729i \(0.529431\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 29.6006 51.2697i 0.422306 0.731455i −0.573859 0.818954i \(-0.694554\pi\)
0.996165 + 0.0874994i \(0.0278876\pi\)
\(18\) 0 0
\(19\) 46.8884 + 81.2131i 0.566155 + 0.980609i 0.996941 + 0.0781550i \(0.0249029\pi\)
−0.430786 + 0.902454i \(0.641764\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.51998 + 25.6341i −0.0409774 + 0.232395i −0.998417 0.0562379i \(-0.982089\pi\)
0.957440 + 0.288633i \(0.0932006\pi\)
\(24\) 0 0
\(25\) −59.0669 + 49.5630i −0.472535 + 0.396504i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 172.381 144.645i 1.10380 0.926201i 0.106129 0.994352i \(-0.466154\pi\)
0.997675 + 0.0681509i \(0.0217099\pi\)
\(30\) 0 0
\(31\) 4.27764 24.2597i 0.0247834 0.140554i −0.969905 0.243482i \(-0.921710\pi\)
0.994689 + 0.102929i \(0.0328213\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 26.8385 + 46.4856i 0.129615 + 0.224500i
\(36\) 0 0
\(37\) −38.3554 + 66.4335i −0.170421 + 0.295178i −0.938567 0.345096i \(-0.887846\pi\)
0.768146 + 0.640275i \(0.221180\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 305.098 + 256.008i 1.16215 + 0.975164i 0.999933 0.0115905i \(-0.00368946\pi\)
0.162222 + 0.986754i \(0.448134\pi\)
\(42\) 0 0
\(43\) 282.678 + 102.886i 1.00251 + 0.364885i 0.790553 0.612394i \(-0.209793\pi\)
0.211960 + 0.977278i \(0.432016\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.08562 + 17.4994i 0.00957624 + 0.0543096i 0.989221 0.146427i \(-0.0467775\pi\)
−0.979645 + 0.200737i \(0.935666\pi\)
\(48\) 0 0
\(49\) 265.784 96.7374i 0.774880 0.282033i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 242.682 0.628960 0.314480 0.949264i \(-0.398170\pi\)
0.314480 + 0.949264i \(0.398170\pi\)
\(54\) 0 0
\(55\) −101.230 −0.248180
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 211.368 76.9317i 0.466403 0.169757i −0.0981193 0.995175i \(-0.531283\pi\)
0.564522 + 0.825418i \(0.309060\pi\)
\(60\) 0 0
\(61\) 81.1159 + 460.031i 0.170259 + 0.965589i 0.943475 + 0.331445i \(0.107536\pi\)
−0.773215 + 0.634144i \(0.781353\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 347.074 + 126.325i 0.662296 + 0.241056i
\(66\) 0 0
\(67\) 333.309 + 279.680i 0.607764 + 0.509975i 0.893931 0.448205i \(-0.147937\pi\)
−0.286166 + 0.958180i \(0.592381\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −277.317 + 480.327i −0.463541 + 0.802877i −0.999134 0.0415991i \(-0.986755\pi\)
0.535593 + 0.844476i \(0.320088\pi\)
\(72\) 0 0
\(73\) −226.923 393.043i −0.363827 0.630166i 0.624760 0.780817i \(-0.285197\pi\)
−0.988587 + 0.150650i \(0.951863\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 19.7011 111.731i 0.0291578 0.165362i
\(78\) 0 0
\(79\) −537.292 + 450.842i −0.765191 + 0.642072i −0.939473 0.342624i \(-0.888684\pi\)
0.174281 + 0.984696i \(0.444240\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 427.701 358.883i 0.565617 0.474609i −0.314571 0.949234i \(-0.601861\pi\)
0.880188 + 0.474625i \(0.157416\pi\)
\(84\) 0 0
\(85\) 71.1442 403.479i 0.0907844 0.514864i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −578.094 1001.29i −0.688515 1.19254i −0.972318 0.233660i \(-0.924930\pi\)
0.283804 0.958882i \(-0.408404\pi\)
\(90\) 0 0
\(91\) −206.974 + 358.490i −0.238426 + 0.412967i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 497.151 + 417.160i 0.536912 + 0.450523i
\(96\) 0 0
\(97\) 1388.22 + 505.270i 1.45312 + 0.528891i 0.943460 0.331488i \(-0.107551\pi\)
0.509656 + 0.860378i \(0.329773\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −285.927 1621.57i −0.281691 1.59755i −0.716870 0.697207i \(-0.754426\pi\)
0.435178 0.900344i \(-0.356685\pi\)
\(102\) 0 0
\(103\) 495.107 180.204i 0.473634 0.172389i −0.0941639 0.995557i \(-0.530018\pi\)
0.567798 + 0.823168i \(0.307796\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1997.93 −1.80512 −0.902559 0.430566i \(-0.858314\pi\)
−0.902559 + 0.430566i \(0.858314\pi\)
\(108\) 0 0
\(109\) −1268.88 −1.11502 −0.557509 0.830171i \(-0.688243\pi\)
−0.557509 + 0.830171i \(0.688243\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −216.017 + 78.6237i −0.179833 + 0.0654539i −0.430367 0.902654i \(-0.641616\pi\)
0.250534 + 0.968108i \(0.419394\pi\)
\(114\) 0 0
\(115\) 31.2806 + 177.401i 0.0253647 + 0.143850i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 431.484 + 157.047i 0.332387 + 0.120979i
\(120\) 0 0
\(121\) −855.698 718.016i −0.642899 0.539456i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −699.341 + 1211.29i −0.500408 + 0.866732i
\(126\) 0 0
\(127\) −923.845 1600.15i −0.645496 1.11803i −0.984187 0.177134i \(-0.943317\pi\)
0.338691 0.940898i \(-0.390016\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −462.901 + 2625.24i −0.308732 + 1.75091i 0.296665 + 0.954981i \(0.404125\pi\)
−0.605397 + 0.795924i \(0.706986\pi\)
\(132\) 0 0
\(133\) −557.184 + 467.533i −0.363263 + 0.304814i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 150.629 126.392i 0.0939348 0.0788206i −0.594611 0.804014i \(-0.702694\pi\)
0.688546 + 0.725193i \(0.258249\pi\)
\(138\) 0 0
\(139\) 236.445 1340.95i 0.144281 0.818257i −0.823661 0.567082i \(-0.808072\pi\)
0.967942 0.251174i \(-0.0808168\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −390.337 676.083i −0.228263 0.395363i
\(144\) 0 0
\(145\) 778.653 1348.67i 0.445956 0.772419i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 582.798 + 489.026i 0.320434 + 0.268876i 0.788789 0.614664i \(-0.210709\pi\)
−0.468355 + 0.883541i \(0.655153\pi\)
\(150\) 0 0
\(151\) −2128.86 774.842i −1.14731 0.417588i −0.302764 0.953066i \(-0.597909\pi\)
−0.844549 + 0.535478i \(0.820132\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −29.6035 167.890i −0.0153407 0.0870016i
\(156\) 0 0
\(157\) 3067.14 1116.35i 1.55914 0.567480i 0.588599 0.808425i \(-0.299680\pi\)
0.970539 + 0.240946i \(0.0774576\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −201.890 −0.0988272
\(162\) 0 0
\(163\) −3101.93 −1.49057 −0.745283 0.666749i \(-0.767685\pi\)
−0.745283 + 0.666749i \(0.767685\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −875.969 + 318.826i −0.405895 + 0.147734i −0.536896 0.843649i \(-0.680403\pi\)
0.131001 + 0.991382i \(0.458181\pi\)
\(168\) 0 0
\(169\) 113.107 + 641.464i 0.0514827 + 0.291973i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2953.58 1075.01i −1.29801 0.472439i −0.401665 0.915787i \(-0.631568\pi\)
−0.896349 + 0.443348i \(0.853790\pi\)
\(174\) 0 0
\(175\) −458.134 384.420i −0.197895 0.166054i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1491.37 + 2583.12i −0.622737 + 1.07861i 0.366237 + 0.930522i \(0.380646\pi\)
−0.988974 + 0.148090i \(0.952687\pi\)
\(180\) 0 0
\(181\) −475.603 823.768i −0.195311 0.338289i 0.751691 0.659515i \(-0.229238\pi\)
−0.947002 + 0.321226i \(0.895905\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −92.1862 + 522.814i −0.0366360 + 0.207773i
\(186\) 0 0
\(187\) −663.370 + 556.634i −0.259414 + 0.217674i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2073.86 1740.18i 0.785651 0.659240i −0.159014 0.987276i \(-0.550831\pi\)
0.944665 + 0.328037i \(0.106387\pi\)
\(192\) 0 0
\(193\) 742.402 4210.37i 0.276887 1.57031i −0.456015 0.889972i \(-0.650724\pi\)
0.732903 0.680334i \(-0.238165\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2280.07 3949.20i −0.824610 1.42827i −0.902217 0.431282i \(-0.858061\pi\)
0.0776069 0.996984i \(-0.475272\pi\)
\(198\) 0 0
\(199\) −1556.41 + 2695.78i −0.554428 + 0.960297i 0.443520 + 0.896264i \(0.353730\pi\)
−0.997948 + 0.0640327i \(0.979604\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1337.02 + 1121.89i 0.462268 + 0.387889i
\(204\) 0 0
\(205\) 2590.07 + 942.707i 0.882429 + 0.321178i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −238.198 1350.89i −0.0788349 0.447095i
\(210\) 0 0
\(211\) −1845.57 + 671.733i −0.602153 + 0.219166i −0.625066 0.780572i \(-0.714928\pi\)
0.0229132 + 0.999737i \(0.492706\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2081.83 0.660371
\(216\) 0 0
\(217\) 191.066 0.0597714
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2969.02 1080.64i 0.903702 0.328920i
\(222\) 0 0
\(223\) 737.919 + 4184.95i 0.221591 + 1.25670i 0.869096 + 0.494643i \(0.164701\pi\)
−0.647506 + 0.762061i \(0.724188\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1470.13 + 535.082i 0.429849 + 0.156452i 0.547879 0.836558i \(-0.315436\pi\)
−0.118030 + 0.993010i \(0.537658\pi\)
\(228\) 0 0
\(229\) 3409.84 + 2861.19i 0.983967 + 0.825647i 0.984683 0.174353i \(-0.0557834\pi\)
−0.000715825 1.00000i \(0.500228\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1513.22 + 2620.97i −0.425469 + 0.736934i −0.996464 0.0840197i \(-0.973224\pi\)
0.570995 + 0.820953i \(0.306557\pi\)
\(234\) 0 0
\(235\) 61.4866 + 106.498i 0.0170679 + 0.0295624i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −352.245 + 1997.68i −0.0953340 + 0.540666i 0.899311 + 0.437311i \(0.144069\pi\)
−0.994645 + 0.103355i \(0.967042\pi\)
\(240\) 0 0
\(241\) 1684.85 1413.75i 0.450334 0.377875i −0.389226 0.921142i \(-0.627257\pi\)
0.839560 + 0.543267i \(0.182813\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1499.46 1258.20i 0.391009 0.328096i
\(246\) 0 0
\(247\) −869.087 + 4928.84i −0.223881 + 1.26969i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1848.46 3201.63i −0.464836 0.805119i 0.534359 0.845258i \(-0.320553\pi\)
−0.999194 + 0.0401391i \(0.987220\pi\)
\(252\) 0 0
\(253\) 190.374 329.738i 0.0473072 0.0819385i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2233.86 1874.44i −0.542197 0.454957i 0.330091 0.943949i \(-0.392920\pi\)
−0.872289 + 0.488992i \(0.837365\pi\)
\(258\) 0 0
\(259\) −559.102 203.497i −0.134135 0.0488211i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 270.803 + 1535.80i 0.0634920 + 0.360081i 0.999957 + 0.00931899i \(0.00296637\pi\)
−0.936465 + 0.350762i \(0.885923\pi\)
\(264\) 0 0
\(265\) 1578.20 574.417i 0.365841 0.133155i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7131.45 1.61640 0.808201 0.588906i \(-0.200441\pi\)
0.808201 + 0.588906i \(0.200441\pi\)
\(270\) 0 0
\(271\) 5551.33 1.24435 0.622175 0.782878i \(-0.286249\pi\)
0.622175 + 0.782878i \(0.286249\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1059.86 385.757i 0.232407 0.0845891i
\(276\) 0 0
\(277\) 680.783 + 3860.91i 0.147669 + 0.837471i 0.965185 + 0.261567i \(0.0842391\pi\)
−0.817517 + 0.575905i \(0.804650\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5176.79 + 1884.20i 1.09901 + 0.400006i 0.826950 0.562275i \(-0.190074\pi\)
0.272057 + 0.962281i \(0.412296\pi\)
\(282\) 0 0
\(283\) −962.891 807.961i −0.202254 0.169711i 0.536035 0.844196i \(-0.319922\pi\)
−0.738289 + 0.674484i \(0.764366\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1544.56 + 2675.26i −0.317674 + 0.550228i
\(288\) 0 0
\(289\) 704.111 + 1219.56i 0.143316 + 0.248230i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1207.87 6850.17i 0.240834 1.36584i −0.589137 0.808033i \(-0.700532\pi\)
0.829971 0.557806i \(-0.188357\pi\)
\(294\) 0 0
\(295\) 1192.47 1000.60i 0.235350 0.197482i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1064.19 + 892.959i −0.205831 + 0.172713i
\(300\) 0 0
\(301\) −405.159 + 2297.77i −0.0775847 + 0.440005i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1616.38 + 2799.66i 0.303455 + 0.525600i
\(306\) 0 0
\(307\) 1319.29 2285.08i 0.245263 0.424808i −0.716942 0.697132i \(-0.754459\pi\)
0.962206 + 0.272324i \(0.0877923\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4431.20 + 3718.22i 0.807943 + 0.677945i 0.950116 0.311897i \(-0.100964\pi\)
−0.142173 + 0.989842i \(0.545409\pi\)
\(312\) 0 0
\(313\) −1731.49 630.210i −0.312682 0.113807i 0.180912 0.983499i \(-0.442095\pi\)
−0.493594 + 0.869692i \(0.664317\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 71.8687 + 407.588i 0.0127336 + 0.0722158i 0.990512 0.137424i \(-0.0438821\pi\)
−0.977779 + 0.209639i \(0.932771\pi\)
\(318\) 0 0
\(319\) −3093.09 + 1125.79i −0.542883 + 0.197593i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5551.70 0.956361
\(324\) 0 0
\(325\) −4115.17 −0.702364
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −129.511 + 47.1381i −0.0217026 + 0.00789912i
\(330\) 0 0
\(331\) −1439.06 8161.32i −0.238967 1.35525i −0.834097 0.551618i \(-0.814011\pi\)
0.595131 0.803629i \(-0.297100\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2829.56 + 1029.87i 0.461478 + 0.167964i
\(336\) 0 0
\(337\) −992.442 832.758i −0.160421 0.134609i 0.559044 0.829138i \(-0.311168\pi\)
−0.719465 + 0.694529i \(0.755613\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −180.167 + 312.059i −0.0286117 + 0.0495570i
\(342\) 0 0
\(343\) 2427.08 + 4203.82i 0.382069 + 0.661763i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −229.552 + 1301.85i −0.0355129 + 0.201404i −0.997402 0.0720360i \(-0.977050\pi\)
0.961889 + 0.273440i \(0.0881615\pi\)
\(348\) 0 0
\(349\) 1971.21 1654.04i 0.302339 0.253693i −0.478978 0.877827i \(-0.658993\pi\)
0.781317 + 0.624134i \(0.214548\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7466.29 + 6264.96i −1.12575 + 0.944618i −0.998881 0.0473007i \(-0.984938\pi\)
−0.126872 + 0.991919i \(0.540494\pi\)
\(354\) 0 0
\(355\) −666.523 + 3780.04i −0.0996490 + 0.565137i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5633.32 9757.19i −0.828176 1.43444i −0.899468 0.436987i \(-0.856046\pi\)
0.0712921 0.997455i \(-0.477288\pi\)
\(360\) 0 0
\(361\) −967.548 + 1675.84i −0.141063 + 0.244328i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2406.04 2018.90i −0.345035 0.289518i
\(366\) 0 0
\(367\) −721.883 262.744i −0.102676 0.0373709i 0.290171 0.956975i \(-0.406288\pi\)
−0.392847 + 0.919604i \(0.628510\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 326.856 + 1853.69i 0.0457399 + 0.259404i
\(372\) 0 0
\(373\) −3384.75 + 1231.95i −0.469854 + 0.171013i −0.566086 0.824346i \(-0.691543\pi\)
0.0962323 + 0.995359i \(0.469321\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12009.7 1.64067
\(378\) 0 0
\(379\) 11322.2 1.53451 0.767257 0.641340i \(-0.221621\pi\)
0.767257 + 0.641340i \(0.221621\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6956.61 + 2532.00i −0.928110 + 0.337805i −0.761460 0.648212i \(-0.775517\pi\)
−0.166650 + 0.986016i \(0.553295\pi\)
\(384\) 0 0
\(385\) −136.342 773.235i −0.0180484 0.102358i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6863.75 2498.20i −0.894617 0.325614i −0.146523 0.989207i \(-0.546808\pi\)
−0.748094 + 0.663593i \(0.769031\pi\)
\(390\) 0 0
\(391\) 1180.46 + 990.522i 0.152681 + 0.128115i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2426.98 + 4203.65i −0.309151 + 0.535465i
\(396\) 0 0
\(397\) 4660.31 + 8071.90i 0.589155 + 1.02045i 0.994343 + 0.106213i \(0.0338725\pi\)
−0.405189 + 0.914233i \(0.632794\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1648.21 9347.46i 0.205256 1.16406i −0.691781 0.722108i \(-0.743173\pi\)
0.897037 0.441956i \(-0.145715\pi\)
\(402\) 0 0
\(403\) 1007.13 845.082i 0.124488 0.104458i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 859.572 721.267i 0.104687 0.0878424i
\(408\) 0 0
\(409\) 727.417 4125.39i 0.0879424 0.498746i −0.908740 0.417362i \(-0.862955\pi\)
0.996683 0.0813844i \(-0.0259341\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 872.313 + 1510.89i 0.103932 + 0.180015i
\(414\) 0 0
\(415\) 1931.95 3346.23i 0.228519 0.395807i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12673.7 10634.5i −1.47769 1.23993i −0.908611 0.417643i \(-0.862856\pi\)
−0.569077 0.822284i \(-0.692699\pi\)
\(420\) 0 0
\(421\) −6440.45 2344.13i −0.745578 0.271368i −0.0588342 0.998268i \(-0.518738\pi\)
−0.686744 + 0.726900i \(0.740961\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 792.666 + 4495.43i 0.0904705 + 0.513084i
\(426\) 0 0
\(427\) −3404.63 + 1239.19i −0.385859 + 0.140441i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16248.1 1.81588 0.907938 0.419104i \(-0.137656\pi\)
0.907938 + 0.419104i \(0.137656\pi\)
\(432\) 0 0
\(433\) −6251.26 −0.693803 −0.346901 0.937902i \(-0.612766\pi\)
−0.346901 + 0.937902i \(0.612766\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2293.76 + 834.860i −0.251088 + 0.0913885i
\(438\) 0 0
\(439\) −2321.71 13167.1i −0.252412 1.43150i −0.802629 0.596479i \(-0.796566\pi\)
0.550216 0.835022i \(-0.314545\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13255.0 4824.43i −1.42159 0.517417i −0.487081 0.873357i \(-0.661939\pi\)
−0.934509 + 0.355940i \(0.884161\pi\)
\(444\) 0 0
\(445\) −6129.45 5143.22i −0.652952 0.547892i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6125.14 + 10609.0i −0.643793 + 1.11508i 0.340786 + 0.940141i \(0.389307\pi\)
−0.984579 + 0.174941i \(0.944026\pi\)
\(450\) 0 0
\(451\) −2912.91 5045.32i −0.304133 0.526773i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −497.457 + 2821.22i −0.0512553 + 0.290683i
\(456\) 0 0
\(457\) −3161.89 + 2653.14i −0.323648 + 0.271573i −0.790106 0.612971i \(-0.789974\pi\)
0.466458 + 0.884544i \(0.345530\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11312.5 + 9492.29i −1.14289 + 0.959002i −0.999530 0.0306683i \(-0.990236\pi\)
−0.143364 + 0.989670i \(0.545792\pi\)
\(462\) 0 0
\(463\) −1803.16 + 10226.2i −0.180993 + 1.02646i 0.750003 + 0.661434i \(0.230052\pi\)
−0.930996 + 0.365029i \(0.881059\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9089.22 15743.0i −0.900640 1.55995i −0.826665 0.562694i \(-0.809765\pi\)
−0.0739745 0.997260i \(-0.523568\pi\)
\(468\) 0 0
\(469\) −1687.38 + 2922.63i −0.166132 + 0.287749i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3370.80 2828.43i −0.327673 0.274950i
\(474\) 0 0
\(475\) −6794.72 2473.07i −0.656343 0.238889i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 878.825 + 4984.07i 0.0838300 + 0.475423i 0.997603 + 0.0691981i \(0.0220441\pi\)
−0.913773 + 0.406225i \(0.866845\pi\)
\(480\) 0 0
\(481\) −3847.16 + 1400.25i −0.364689 + 0.132736i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 10223.8 0.957191
\(486\) 0 0
\(487\) 16549.8 1.53993 0.769963 0.638089i \(-0.220275\pi\)
0.769963 + 0.638089i \(0.220275\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1518.20 + 552.579i −0.139542 + 0.0507893i −0.410847 0.911704i \(-0.634767\pi\)
0.271305 + 0.962493i \(0.412545\pi\)
\(492\) 0 0
\(493\) −2313.32 13119.5i −0.211332 1.19852i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4042.41 1471.32i −0.364843 0.132792i
\(498\) 0 0
\(499\) −4436.72 3722.85i −0.398026 0.333983i 0.421704 0.906733i \(-0.361432\pi\)
−0.819730 + 0.572750i \(0.805876\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2966.70 + 5138.47i −0.262979 + 0.455493i −0.967032 0.254654i \(-0.918038\pi\)
0.704053 + 0.710147i \(0.251372\pi\)
\(504\) 0 0
\(505\) −5697.64 9868.59i −0.502062 0.869597i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1327.68 7529.66i 0.115616 0.655690i −0.870828 0.491589i \(-0.836416\pi\)
0.986443 0.164102i \(-0.0524725\pi\)
\(510\) 0 0
\(511\) 2696.57 2262.69i 0.233443 0.195882i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2793.23 2343.79i 0.238998 0.200544i
\(516\) 0 0
\(517\) 45.1350 255.974i 0.00383953 0.0217751i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −294.488 510.068i −0.0247635 0.0428916i 0.853378 0.521292i \(-0.174550\pi\)
−0.878142 + 0.478401i \(0.841217\pi\)
\(522\) 0 0
\(523\) 4872.57 8439.54i 0.407386 0.705613i −0.587210 0.809434i \(-0.699774\pi\)
0.994596 + 0.103822i \(0.0331071\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1117.17 937.415i −0.0923426 0.0774847i
\(528\) 0 0
\(529\) 10796.6 + 3929.63i 0.887365 + 0.322974i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3691.08 + 20933.2i 0.299960 + 1.70115i
\(534\) 0 0
\(535\) −12992.9 + 4729.03i −1.04997 + 0.382157i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4137.28 −0.330622
\(540\) 0 0
\(541\) −4636.36 −0.368452 −0.184226 0.982884i \(-0.558978\pi\)
−0.184226 + 0.982884i \(0.558978\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8251.77 + 3003.40i −0.648563 + 0.236058i
\(546\) 0 0
\(547\) −3576.84 20285.3i −0.279588 1.58562i −0.723999 0.689801i \(-0.757698\pi\)
0.444411 0.895823i \(-0.353413\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 19829.7 + 7217.42i 1.53317 + 0.558027i
\(552\) 0 0
\(553\) −4167.35 3496.82i −0.320459 0.268897i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2376.10 + 4115.53i −0.180752 + 0.313071i −0.942137 0.335229i \(-0.891186\pi\)
0.761385 + 0.648300i \(0.224520\pi\)
\(558\) 0 0
\(559\) 8027.38 + 13903.8i 0.607374 + 1.05200i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1868.80 + 10598.5i −0.139894 + 0.793379i 0.831432 + 0.555627i \(0.187522\pi\)
−0.971326 + 0.237752i \(0.923589\pi\)
\(564\) 0 0
\(565\) −1218.69 + 1022.61i −0.0907449 + 0.0761440i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2744.52 + 2302.93i −0.202208 + 0.169673i −0.738269 0.674507i \(-0.764356\pi\)
0.536061 + 0.844180i \(0.319912\pi\)
\(570\) 0 0
\(571\) 588.801 3339.25i 0.0431533 0.244735i −0.955599 0.294670i \(-0.904790\pi\)
0.998752 + 0.0499351i \(0.0159015\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1003.52 1738.15i −0.0727821 0.126062i
\(576\) 0 0
\(577\) −1802.55 + 3122.12i −0.130054 + 0.225261i −0.923697 0.383123i \(-0.874848\pi\)
0.793643 + 0.608384i \(0.208182\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3317.33 + 2783.57i 0.236878 + 0.198764i
\(582\) 0 0
\(583\) −3335.76 1214.12i −0.236969 0.0862497i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3392.97 19242.5i −0.238574 1.35302i −0.834955 0.550318i \(-0.814506\pi\)
0.596381 0.802702i \(-0.296605\pi\)
\(588\) 0 0
\(589\) 2170.78 790.099i 0.151860 0.0552724i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9718.65 0.673013 0.336507 0.941681i \(-0.390755\pi\)
0.336507 + 0.941681i \(0.390755\pi\)
\(594\) 0 0
\(595\) 3177.74 0.218949
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 23413.0 8521.62i 1.59704 0.581275i 0.618222 0.786003i \(-0.287853\pi\)
0.978819 + 0.204728i \(0.0656309\pi\)
\(600\) 0 0
\(601\) 4759.65 + 26993.3i 0.323045 + 1.83208i 0.523069 + 0.852290i \(0.324787\pi\)
−0.200024 + 0.979791i \(0.564102\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7264.26 2643.98i −0.488156 0.177674i
\(606\) 0 0
\(607\) 19958.2 + 16746.9i 1.33456 + 1.11983i 0.982988 + 0.183671i \(0.0587979\pi\)
0.351574 + 0.936160i \(0.385646\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −474.175 + 821.296i −0.0313962 + 0.0543798i
\(612\) 0 0
\(613\) −694.965 1203.72i −0.0457902 0.0793109i 0.842222 0.539131i \(-0.181247\pi\)
−0.888012 + 0.459820i \(0.847914\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1604.15 9097.57i 0.104669 0.593605i −0.886684 0.462377i \(-0.846997\pi\)
0.991352 0.131228i \(-0.0418921\pi\)
\(618\) 0 0
\(619\) 5940.36 4984.55i 0.385724 0.323661i −0.429221 0.903200i \(-0.641212\pi\)
0.814945 + 0.579539i \(0.196767\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6869.59 5764.27i 0.441773 0.370691i
\(624\) 0 0
\(625\) −7.17646 + 40.6997i −0.000459293 + 0.00260478i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2270.68 + 3932.94i 0.143940 + 0.249311i
\(630\) 0 0
\(631\) −1569.14 + 2717.83i −0.0989958 + 0.171466i −0.911269 0.411811i \(-0.864896\pi\)
0.812273 + 0.583277i \(0.198230\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9795.40 8219.32i −0.612155 0.513659i
\(636\) 0 0
\(637\) 14184.9 + 5162.88i 0.882301 + 0.321131i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1044.51 5923.70i −0.0643613 0.365011i −0.999930 0.0118653i \(-0.996223\pi\)
0.935568 0.353146i \(-0.114888\pi\)
\(642\) 0 0
\(643\) −3903.59 + 1420.79i −0.239413 + 0.0871393i −0.458940 0.888467i \(-0.651771\pi\)
0.219527 + 0.975606i \(0.429549\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3878.14 0.235650 0.117825 0.993034i \(-0.462408\pi\)
0.117825 + 0.993034i \(0.462408\pi\)
\(648\) 0 0
\(649\) −3290.22 −0.199002
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3094.96 + 1126.48i −0.185475 + 0.0675075i −0.433088 0.901352i \(-0.642576\pi\)
0.247613 + 0.968859i \(0.420354\pi\)
\(654\) 0 0
\(655\) 3203.52 + 18168.1i 0.191102 + 1.08379i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14236.8 + 5181.76i 0.841556 + 0.306301i 0.726593 0.687068i \(-0.241103\pi\)
0.114963 + 0.993370i \(0.463325\pi\)
\(660\) 0 0
\(661\) 3706.41 + 3110.04i 0.218098 + 0.183006i 0.745290 0.666740i \(-0.232311\pi\)
−0.527193 + 0.849746i \(0.676755\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2516.83 + 4359.28i −0.146765 + 0.254204i
\(666\) 0 0
\(667\) 2928.68 + 5072.62i 0.170013 + 0.294471i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1186.53 6729.13i 0.0682643 0.387146i
\(672\) 0 0
\(673\) −15159.9 + 12720.6i −0.868305 + 0.728595i −0.963741 0.266841i \(-0.914020\pi\)
0.0954352 + 0.995436i \(0.469576\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6219.26 + 5218.58i −0.353066 + 0.296257i −0.802020 0.597298i \(-0.796241\pi\)
0.448954 + 0.893555i \(0.351797\pi\)
\(678\) 0 0
\(679\) −1989.72 + 11284.2i −0.112457 + 0.637775i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9569.27 16574.5i −0.536102 0.928557i −0.999109 0.0422019i \(-0.986563\pi\)
0.463007 0.886355i \(-0.346771\pi\)
\(684\) 0 0
\(685\) 680.397 1178.48i 0.0379513 0.0657336i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9921.75 + 8325.33i 0.548604 + 0.460334i
\(690\) 0 0
\(691\) 101.637 + 36.9930i 0.00559547 + 0.00203658i 0.344816 0.938670i \(-0.387941\pi\)
−0.339221 + 0.940707i \(0.610163\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1636.33 9280.06i −0.0893085 0.506493i
\(696\) 0 0
\(697\) 22156.5 8064.32i 1.20407 0.438247i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 27394.8 1.47601 0.738007 0.674793i \(-0.235767\pi\)
0.738007 + 0.674793i \(0.235767\pi\)
\(702\) 0 0
\(703\) −7193.70 −0.385939
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12001.1 4368.04i 0.638398 0.232358i
\(708\) 0 0
\(709\) 2265.35 + 12847.4i 0.119996 + 0.680529i 0.984155 + 0.177310i \(0.0567397\pi\)
−0.864159 + 0.503218i \(0.832149\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 602.540 + 219.307i 0.0316484 + 0.0115191i
\(714\) 0 0
\(715\) −4138.69 3472.77i −0.216473 0.181642i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7365.93 12758.2i 0.382063 0.661752i −0.609294 0.792944i \(-0.708547\pi\)
0.991357 + 0.131192i \(0.0418805\pi\)
\(720\) 0 0
\(721\) 2043.30 + 3539.10i 0.105543 + 0.182806i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3012.97 + 17087.4i −0.154343 + 0.875325i
\(726\) 0 0
\(727\) 616.890 517.632i 0.0314707 0.0264070i −0.626917 0.779086i \(-0.715683\pi\)
0.658387 + 0.752679i \(0.271239\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 13642.4 11447.3i 0.690263 0.579200i
\(732\) 0 0
\(733\) 314.266 1782.29i 0.0158358 0.0898095i −0.975866 0.218372i \(-0.929925\pi\)
0.991701 + 0.128563i \(0.0410364\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3182.26 5511.83i −0.159050 0.275483i
\(738\) 0 0
\(739\) −2005.53 + 3473.68i −0.0998303 + 0.172911i −0.911614 0.411047i \(-0.865163\pi\)
0.811784 + 0.583958i \(0.198497\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 20551.0 + 17244.3i 1.01473 + 0.851456i 0.988956 0.148211i \(-0.0473516\pi\)
0.0257705 + 0.999668i \(0.491796\pi\)
\(744\) 0 0
\(745\) 4947.54 + 1800.76i 0.243307 + 0.0885566i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2690.92 15261.0i −0.131274 0.744490i
\(750\) 0 0
\(751\) 33872.2 12328.5i 1.64582 0.599031i 0.657780 0.753210i \(-0.271496\pi\)
0.988043 + 0.154179i \(0.0492734\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −15678.4 −0.755754
\(756\) 0 0
\(757\) −20176.1 −0.968708 −0.484354 0.874872i \(-0.660945\pi\)
−0.484354 + 0.874872i \(0.660945\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3112.67 1132.92i 0.148271 0.0539662i −0.266819 0.963747i \(-0.585972\pi\)
0.415090 + 0.909781i \(0.363750\pi\)
\(762\) 0 0
\(763\) −1709.00 9692.20i −0.0810876 0.459871i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11280.7 + 4105.84i 0.531060 + 0.193290i
\(768\) 0 0
\(769\) −872.027 731.718i −0.0408922 0.0343126i 0.622113 0.782928i \(-0.286275\pi\)
−0.663005 + 0.748615i \(0.730719\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −20299.3 + 35159.4i −0.944521 + 1.63596i −0.187814 + 0.982205i \(0.560140\pi\)
−0.756707 + 0.653754i \(0.773193\pi\)
\(774\) 0 0
\(775\) 949.716 + 1644.96i 0.0440191 + 0.0762434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6485.62 + 36781.8i −0.298295 + 1.69171i
\(780\) 0 0
\(781\) 6214.87 5214.89i 0.284744 0.238929i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17303.8 14519.6i 0.786750 0.660161i
\(786\) 0 0
\(787\) 4660.94 26433.5i 0.211111 1.19727i −0.676418 0.736518i \(-0.736469\pi\)
0.887529 0.460752i \(-0.152420\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −891.499 1544.12i