Properties

Label 240.3.c.e.209.3
Level $240$
Weight $3$
Character 240.209
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 34 x^{10} + 305 x^{8} + 616 x^{6} + 305 x^{4} + 34 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{15}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.3
Root \(-0.304307i\) of defining polynomial
Character \(\chi\) \(=\) 240.209
Dual form 240.3.c.e.209.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.49147 - 1.67109i) q^{3} +(4.19906 - 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} +O(q^{10})\) \(q+(-2.49147 - 1.67109i) q^{3} +(4.19906 - 2.71439i) q^{5} +12.7692i q^{7} +(3.41489 + 8.32698i) q^{9} -12.6296i q^{11} +7.44085i q^{13} +(-14.9978 - 0.254179i) q^{15} +14.0550 q^{17} +31.0176 q^{19} +(21.3386 - 31.8142i) q^{21} +7.50423 q^{23} +(10.2641 - 22.7958i) q^{25} +(5.40707 - 26.4530i) q^{27} +15.7298i q^{29} +20.4893 q^{31} +(-21.1053 + 31.4663i) q^{33} +(34.6607 + 53.6186i) q^{35} +12.9261i q^{37} +(12.4344 - 18.5387i) q^{39} -13.8451i q^{41} +30.0797i q^{43} +(36.9420 + 25.6961i) q^{45} +20.2570 q^{47} -114.053 q^{49} +(-35.0176 - 23.4872i) q^{51} -29.1185 q^{53} +(-34.2817 - 53.0324i) q^{55} +(-77.2795 - 51.8333i) q^{57} -47.6333i q^{59} +43.0176 q^{61} +(-106.329 + 43.6054i) q^{63} +(20.1974 + 31.2445i) q^{65} +0.630153i q^{67} +(-18.6966 - 12.5403i) q^{69} +90.4047i q^{71} -46.2193i q^{73} +(-63.6667 + 39.6427i) q^{75} +161.270 q^{77} -37.9610 q^{79} +(-57.6771 + 56.8713i) q^{81} -80.2267 q^{83} +(59.0176 - 38.1507i) q^{85} +(26.2860 - 39.1904i) q^{87} +140.923i q^{89} -95.0138 q^{91} +(-51.0486 - 34.2396i) q^{93} +(130.245 - 84.1939i) q^{95} +10.3429i q^{97} +(105.166 - 43.1286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{9} + O(q^{10}) \) \( 12 q + 8 q^{9} - 16 q^{15} + 4 q^{21} + 36 q^{25} + 48 q^{31} + 128 q^{39} - 68 q^{45} - 252 q^{49} - 48 q^{51} + 48 q^{55} + 144 q^{61} + 268 q^{69} - 304 q^{75} - 432 q^{79} - 188 q^{81} + 336 q^{85} + 560 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.49147 1.67109i −0.830491 0.557032i
\(4\) 0 0
\(5\) 4.19906 2.71439i 0.839811 0.542879i
\(6\) 0 0
\(7\) 12.7692i 1.82417i 0.409998 + 0.912086i \(0.365529\pi\)
−0.409998 + 0.912086i \(0.634471\pi\)
\(8\) 0 0
\(9\) 3.41489 + 8.32698i 0.379432 + 0.925220i
\(10\) 0 0
\(11\) 12.6296i 1.14815i −0.818804 0.574073i \(-0.805363\pi\)
0.818804 0.574073i \(-0.194637\pi\)
\(12\) 0 0
\(13\) 7.44085i 0.572373i 0.958174 + 0.286187i \(0.0923877\pi\)
−0.958174 + 0.286187i \(0.907612\pi\)
\(14\) 0 0
\(15\) −14.9978 0.254179i −0.999856 0.0169452i
\(16\) 0 0
\(17\) 14.0550 0.826763 0.413381 0.910558i \(-0.364348\pi\)
0.413381 + 0.910558i \(0.364348\pi\)
\(18\) 0 0
\(19\) 31.0176 1.63250 0.816252 0.577696i \(-0.196048\pi\)
0.816252 + 0.577696i \(0.196048\pi\)
\(20\) 0 0
\(21\) 21.3386 31.8142i 1.01612 1.51496i
\(22\) 0 0
\(23\) 7.50423 0.326271 0.163135 0.986604i \(-0.447839\pi\)
0.163135 + 0.986604i \(0.447839\pi\)
\(24\) 0 0
\(25\) 10.2641 22.7958i 0.410565 0.911831i
\(26\) 0 0
\(27\) 5.40707 26.4530i 0.200262 0.979742i
\(28\) 0 0
\(29\) 15.7298i 0.542407i 0.962522 + 0.271204i \(0.0874217\pi\)
−0.962522 + 0.271204i \(0.912578\pi\)
\(30\) 0 0
\(31\) 20.4893 0.660945 0.330473 0.943816i \(-0.392792\pi\)
0.330473 + 0.943816i \(0.392792\pi\)
\(32\) 0 0
\(33\) −21.1053 + 31.4663i −0.639553 + 0.953525i
\(34\) 0 0
\(35\) 34.6607 + 53.6186i 0.990305 + 1.53196i
\(36\) 0 0
\(37\) 12.9261i 0.349355i 0.984626 + 0.174677i \(0.0558883\pi\)
−0.984626 + 0.174677i \(0.944112\pi\)
\(38\) 0 0
\(39\) 12.4344 18.5387i 0.318830 0.475351i
\(40\) 0 0
\(41\) 13.8451i 0.337685i −0.985643 0.168843i \(-0.945997\pi\)
0.985643 0.168843i \(-0.0540029\pi\)
\(42\) 0 0
\(43\) 30.0797i 0.699528i 0.936838 + 0.349764i \(0.113738\pi\)
−0.936838 + 0.349764i \(0.886262\pi\)
\(44\) 0 0
\(45\) 36.9420 + 25.6961i 0.820933 + 0.571024i
\(46\) 0 0
\(47\) 20.2570 0.431000 0.215500 0.976504i \(-0.430862\pi\)
0.215500 + 0.976504i \(0.430862\pi\)
\(48\) 0 0
\(49\) −114.053 −2.32761
\(50\) 0 0
\(51\) −35.0176 23.4872i −0.686619 0.460533i
\(52\) 0 0
\(53\) −29.1185 −0.549406 −0.274703 0.961529i \(-0.588580\pi\)
−0.274703 + 0.961529i \(0.588580\pi\)
\(54\) 0 0
\(55\) −34.2817 53.0324i −0.623304 0.964226i
\(56\) 0 0
\(57\) −77.2795 51.8333i −1.35578 0.909356i
\(58\) 0 0
\(59\) 47.6333i 0.807344i −0.914904 0.403672i \(-0.867734\pi\)
0.914904 0.403672i \(-0.132266\pi\)
\(60\) 0 0
\(61\) 43.0176 0.705206 0.352603 0.935773i \(-0.385297\pi\)
0.352603 + 0.935773i \(0.385297\pi\)
\(62\) 0 0
\(63\) −106.329 + 43.6054i −1.68776 + 0.692149i
\(64\) 0 0
\(65\) 20.1974 + 31.2445i 0.310729 + 0.480685i
\(66\) 0 0
\(67\) 0.630153i 0.00940527i 0.999989 + 0.00470264i \(0.00149690\pi\)
−0.999989 + 0.00470264i \(0.998503\pi\)
\(68\) 0 0
\(69\) −18.6966 12.5403i −0.270965 0.181743i
\(70\) 0 0
\(71\) 90.4047i 1.27330i 0.771151 + 0.636652i \(0.219681\pi\)
−0.771151 + 0.636652i \(0.780319\pi\)
\(72\) 0 0
\(73\) 46.2193i 0.633140i −0.948569 0.316570i \(-0.897469\pi\)
0.948569 0.316570i \(-0.102531\pi\)
\(74\) 0 0
\(75\) −63.6667 + 39.6427i −0.848890 + 0.528570i
\(76\) 0 0
\(77\) 161.270 2.09442
\(78\) 0 0
\(79\) −37.9610 −0.480519 −0.240260 0.970709i \(-0.577233\pi\)
−0.240260 + 0.970709i \(0.577233\pi\)
\(80\) 0 0
\(81\) −57.6771 + 56.8713i −0.712063 + 0.702115i
\(82\) 0 0
\(83\) −80.2267 −0.966587 −0.483294 0.875458i \(-0.660560\pi\)
−0.483294 + 0.875458i \(0.660560\pi\)
\(84\) 0 0
\(85\) 59.0176 38.1507i 0.694324 0.448832i
\(86\) 0 0
\(87\) 26.2860 39.1904i 0.302138 0.450465i
\(88\) 0 0
\(89\) 140.923i 1.58341i 0.610907 + 0.791703i \(0.290805\pi\)
−0.610907 + 0.791703i \(0.709195\pi\)
\(90\) 0 0
\(91\) −95.0138 −1.04411
\(92\) 0 0
\(93\) −51.0486 34.2396i −0.548909 0.368168i
\(94\) 0 0
\(95\) 130.245 84.1939i 1.37100 0.886252i
\(96\) 0 0
\(97\) 10.3429i 0.106628i 0.998578 + 0.0533138i \(0.0169784\pi\)
−0.998578 + 0.0533138i \(0.983022\pi\)
\(98\) 0 0
\(99\) 105.166 43.1286i 1.06229 0.435643i
\(100\) 0 0
\(101\) 19.2739i 0.190830i 0.995438 + 0.0954152i \(0.0304179\pi\)
−0.995438 + 0.0954152i \(0.969582\pi\)
\(102\) 0 0
\(103\) 6.97008i 0.0676707i 0.999427 + 0.0338353i \(0.0107722\pi\)
−0.999427 + 0.0338353i \(0.989228\pi\)
\(104\) 0 0
\(105\) 3.24566 191.511i 0.0309110 1.82391i
\(106\) 0 0
\(107\) −73.7731 −0.689468 −0.344734 0.938700i \(-0.612031\pi\)
−0.344734 + 0.938700i \(0.612031\pi\)
\(108\) 0 0
\(109\) 74.0314 0.679187 0.339593 0.940572i \(-0.389711\pi\)
0.339593 + 0.940572i \(0.389711\pi\)
\(110\) 0 0
\(111\) 21.6008 32.2051i 0.194602 0.290136i
\(112\) 0 0
\(113\) −147.215 −1.30279 −0.651394 0.758739i \(-0.725816\pi\)
−0.651394 + 0.758739i \(0.725816\pi\)
\(114\) 0 0
\(115\) 31.5107 20.3694i 0.274006 0.177126i
\(116\) 0 0
\(117\) −61.9598 + 25.4096i −0.529571 + 0.217176i
\(118\) 0 0
\(119\) 179.471i 1.50816i
\(120\) 0 0
\(121\) −38.5069 −0.318239
\(122\) 0 0
\(123\) −23.1364 + 34.4947i −0.188101 + 0.280444i
\(124\) 0 0
\(125\) −18.7770 123.582i −0.150216 0.988653i
\(126\) 0 0
\(127\) 90.0171i 0.708796i −0.935095 0.354398i \(-0.884686\pi\)
0.935095 0.354398i \(-0.115314\pi\)
\(128\) 0 0
\(129\) 50.2660 74.9428i 0.389659 0.580952i
\(130\) 0 0
\(131\) 11.2911i 0.0861917i 0.999071 + 0.0430958i \(0.0137221\pi\)
−0.999071 + 0.0430958i \(0.986278\pi\)
\(132\) 0 0
\(133\) 396.070i 2.97797i
\(134\) 0 0
\(135\) −49.0994 125.755i −0.363699 0.931516i
\(136\) 0 0
\(137\) 22.4905 0.164164 0.0820822 0.996626i \(-0.473843\pi\)
0.0820822 + 0.996626i \(0.473843\pi\)
\(138\) 0 0
\(139\) −91.0955 −0.655363 −0.327682 0.944788i \(-0.606267\pi\)
−0.327682 + 0.944788i \(0.606267\pi\)
\(140\) 0 0
\(141\) −50.4698 33.8514i −0.357942 0.240081i
\(142\) 0 0
\(143\) 93.9750 0.657168
\(144\) 0 0
\(145\) 42.6969 + 66.0504i 0.294461 + 0.455520i
\(146\) 0 0
\(147\) 284.159 + 190.593i 1.93306 + 1.29655i
\(148\) 0 0
\(149\) 228.330i 1.53242i −0.642593 0.766208i \(-0.722141\pi\)
0.642593 0.766208i \(-0.277859\pi\)
\(150\) 0 0
\(151\) 74.0390 0.490324 0.245162 0.969482i \(-0.421159\pi\)
0.245162 + 0.969482i \(0.421159\pi\)
\(152\) 0 0
\(153\) 47.9961 + 117.035i 0.313700 + 0.764937i
\(154\) 0 0
\(155\) 86.0358 55.6161i 0.555069 0.358813i
\(156\) 0 0
\(157\) 245.742i 1.56523i −0.622504 0.782616i \(-0.713885\pi\)
0.622504 0.782616i \(-0.286115\pi\)
\(158\) 0 0
\(159\) 72.5481 + 48.6598i 0.456277 + 0.306037i
\(160\) 0 0
\(161\) 95.8231i 0.595175i
\(162\) 0 0
\(163\) 60.1570i 0.369061i 0.982827 + 0.184531i \(0.0590765\pi\)
−0.982827 + 0.184531i \(0.940924\pi\)
\(164\) 0 0
\(165\) −3.21017 + 189.417i −0.0194556 + 1.14798i
\(166\) 0 0
\(167\) −81.5664 −0.488421 −0.244211 0.969722i \(-0.578529\pi\)
−0.244211 + 0.969722i \(0.578529\pi\)
\(168\) 0 0
\(169\) 113.634 0.672389
\(170\) 0 0
\(171\) 105.921 + 258.283i 0.619424 + 1.51043i
\(172\) 0 0
\(173\) −167.064 −0.965687 −0.482843 0.875707i \(-0.660396\pi\)
−0.482843 + 0.875707i \(0.660396\pi\)
\(174\) 0 0
\(175\) 291.084 + 131.065i 1.66334 + 0.748942i
\(176\) 0 0
\(177\) −79.5997 + 118.677i −0.449716 + 0.670492i
\(178\) 0 0
\(179\) 270.104i 1.50896i −0.656322 0.754481i \(-0.727889\pi\)
0.656322 0.754481i \(-0.272111\pi\)
\(180\) 0 0
\(181\) 86.9786 0.480545 0.240272 0.970705i \(-0.422763\pi\)
0.240272 + 0.970705i \(0.422763\pi\)
\(182\) 0 0
\(183\) −107.177 71.8865i −0.585668 0.392822i
\(184\) 0 0
\(185\) 35.0866 + 54.2776i 0.189657 + 0.293392i
\(186\) 0 0
\(187\) 177.509i 0.949244i
\(188\) 0 0
\(189\) 337.785 + 69.0440i 1.78722 + 0.365312i
\(190\) 0 0
\(191\) 302.223i 1.58232i −0.611610 0.791159i \(-0.709478\pi\)
0.611610 0.791159i \(-0.290522\pi\)
\(192\) 0 0
\(193\) 306.780i 1.58953i −0.606916 0.794766i \(-0.707593\pi\)
0.606916 0.794766i \(-0.292407\pi\)
\(194\) 0 0
\(195\) 1.89130 111.597i 0.00969900 0.572291i
\(196\) 0 0
\(197\) 289.956 1.47186 0.735930 0.677058i \(-0.236745\pi\)
0.735930 + 0.677058i \(0.236745\pi\)
\(198\) 0 0
\(199\) −382.595 −1.92259 −0.961293 0.275527i \(-0.911148\pi\)
−0.961293 + 0.275527i \(0.911148\pi\)
\(200\) 0 0
\(201\) 1.05305 1.57001i 0.00523903 0.00781100i
\(202\) 0 0
\(203\) −200.857 −0.989445
\(204\) 0 0
\(205\) −37.5810 58.1363i −0.183322 0.283592i
\(206\) 0 0
\(207\) 25.6261 + 62.4876i 0.123798 + 0.301872i
\(208\) 0 0
\(209\) 391.740i 1.87435i
\(210\) 0 0
\(211\) 321.115 1.52187 0.760937 0.648826i \(-0.224740\pi\)
0.760937 + 0.648826i \(0.224740\pi\)
\(212\) 0 0
\(213\) 151.075 225.241i 0.709271 1.05747i
\(214\) 0 0
\(215\) 81.6482 + 126.306i 0.379759 + 0.587471i
\(216\) 0 0
\(217\) 261.632i 1.20568i
\(218\) 0 0
\(219\) −77.2368 + 115.154i −0.352679 + 0.525818i
\(220\) 0 0
\(221\) 104.581i 0.473217i
\(222\) 0 0
\(223\) 292.432i 1.31135i 0.755042 + 0.655676i \(0.227616\pi\)
−0.755042 + 0.655676i \(0.772384\pi\)
\(224\) 0 0
\(225\) 224.871 + 7.62426i 0.999426 + 0.0338856i
\(226\) 0 0
\(227\) −370.155 −1.63064 −0.815319 0.579013i \(-0.803438\pi\)
−0.815319 + 0.579013i \(0.803438\pi\)
\(228\) 0 0
\(229\) −381.985 −1.66806 −0.834028 0.551722i \(-0.813971\pi\)
−0.834028 + 0.551722i \(0.813971\pi\)
\(230\) 0 0
\(231\) −401.800 269.498i −1.73939 1.16666i
\(232\) 0 0
\(233\) 144.262 0.619150 0.309575 0.950875i \(-0.399813\pi\)
0.309575 + 0.950875i \(0.399813\pi\)
\(234\) 0 0
\(235\) 85.0603 54.9855i 0.361959 0.233981i
\(236\) 0 0
\(237\) 94.5789 + 63.4365i 0.399067 + 0.267665i
\(238\) 0 0
\(239\) 249.478i 1.04384i 0.852994 + 0.521921i \(0.174784\pi\)
−0.852994 + 0.521921i \(0.825216\pi\)
\(240\) 0 0
\(241\) 30.4541 0.126366 0.0631829 0.998002i \(-0.479875\pi\)
0.0631829 + 0.998002i \(0.479875\pi\)
\(242\) 0 0
\(243\) 238.738 45.3095i 0.982463 0.186459i
\(244\) 0 0
\(245\) −478.914 + 309.584i −1.95475 + 1.26361i
\(246\) 0 0
\(247\) 230.797i 0.934401i
\(248\) 0 0
\(249\) 199.883 + 134.066i 0.802742 + 0.538420i
\(250\) 0 0
\(251\) 68.9183i 0.274575i 0.990531 + 0.137287i \(0.0438384\pi\)
−0.990531 + 0.137287i \(0.956162\pi\)
\(252\) 0 0
\(253\) 94.7755i 0.374607i
\(254\) 0 0
\(255\) −210.794 3.57247i −0.826644 0.0140097i
\(256\) 0 0
\(257\) −362.374 −1.41002 −0.705009 0.709199i \(-0.749057\pi\)
−0.705009 + 0.709199i \(0.749057\pi\)
\(258\) 0 0
\(259\) −165.057 −0.637284
\(260\) 0 0
\(261\) −130.982 + 53.7155i −0.501846 + 0.205807i
\(262\) 0 0
\(263\) −23.4485 −0.0891580 −0.0445790 0.999006i \(-0.514195\pi\)
−0.0445790 + 0.999006i \(0.514195\pi\)
\(264\) 0 0
\(265\) −122.270 + 79.0391i −0.461397 + 0.298261i
\(266\) 0 0
\(267\) 235.496 351.106i 0.882007 1.31500i
\(268\) 0 0
\(269\) 396.738i 1.47486i 0.675421 + 0.737432i \(0.263962\pi\)
−0.675421 + 0.737432i \(0.736038\pi\)
\(270\) 0 0
\(271\) 143.926 0.531092 0.265546 0.964098i \(-0.414448\pi\)
0.265546 + 0.964098i \(0.414448\pi\)
\(272\) 0 0
\(273\) 236.724 + 158.777i 0.867122 + 0.581601i
\(274\) 0 0
\(275\) −287.902 129.632i −1.04692 0.471389i
\(276\) 0 0
\(277\) 360.884i 1.30283i −0.758722 0.651415i \(-0.774176\pi\)
0.758722 0.651415i \(-0.225824\pi\)
\(278\) 0 0
\(279\) 69.9686 + 170.614i 0.250784 + 0.611520i
\(280\) 0 0
\(281\) 531.655i 1.89201i −0.324149 0.946006i \(-0.605078\pi\)
0.324149 0.946006i \(-0.394922\pi\)
\(282\) 0 0
\(283\) 257.400i 0.909541i −0.890609 0.454770i \(-0.849721\pi\)
0.890609 0.454770i \(-0.150279\pi\)
\(284\) 0 0
\(285\) −465.197 7.88400i −1.63227 0.0276632i
\(286\) 0 0
\(287\) 176.791 0.615996
\(288\) 0 0
\(289\) −91.4579 −0.316463
\(290\) 0 0
\(291\) 17.2839 25.7690i 0.0593949 0.0885533i
\(292\) 0 0
\(293\) −310.456 −1.05958 −0.529789 0.848130i \(-0.677729\pi\)
−0.529789 + 0.848130i \(0.677729\pi\)
\(294\) 0 0
\(295\) −129.295 200.015i −0.438290 0.678016i
\(296\) 0 0
\(297\) −334.091 68.2892i −1.12489 0.229930i
\(298\) 0 0
\(299\) 55.8379i 0.186749i
\(300\) 0 0
\(301\) −384.094 −1.27606
\(302\) 0 0
\(303\) 32.2085 48.0204i 0.106299 0.158483i
\(304\) 0 0
\(305\) 180.633 116.767i 0.592240 0.382841i
\(306\) 0 0
\(307\) 266.169i 0.866999i 0.901154 + 0.433499i \(0.142721\pi\)
−0.901154 + 0.433499i \(0.857279\pi\)
\(308\) 0 0
\(309\) 11.6477 17.3658i 0.0376947 0.0561999i
\(310\) 0 0
\(311\) 186.580i 0.599934i 0.953950 + 0.299967i \(0.0969757\pi\)
−0.953950 + 0.299967i \(0.903024\pi\)
\(312\) 0 0
\(313\) 20.5021i 0.0655019i −0.999464 0.0327510i \(-0.989573\pi\)
0.999464 0.0327510i \(-0.0104268\pi\)
\(314\) 0 0
\(315\) −328.119 + 471.720i −1.04165 + 1.49752i
\(316\) 0 0
\(317\) −18.9792 −0.0598711 −0.0299356 0.999552i \(-0.509530\pi\)
−0.0299356 + 0.999552i \(0.509530\pi\)
\(318\) 0 0
\(319\) 198.661 0.622763
\(320\) 0 0
\(321\) 183.804 + 123.282i 0.572597 + 0.384055i
\(322\) 0 0
\(323\) 435.951 1.34969
\(324\) 0 0
\(325\) 169.620 + 76.3739i 0.521908 + 0.234997i
\(326\) 0 0
\(327\) −184.447 123.713i −0.564059 0.378328i
\(328\) 0 0
\(329\) 258.666i 0.786219i
\(330\) 0 0
\(331\) −413.193 −1.24832 −0.624159 0.781297i \(-0.714558\pi\)
−0.624159 + 0.781297i \(0.714558\pi\)
\(332\) 0 0
\(333\) −107.636 + 44.1413i −0.323230 + 0.132556i
\(334\) 0 0
\(335\) 1.71048 + 2.64605i 0.00510592 + 0.00789865i
\(336\) 0 0
\(337\) 484.733i 1.43838i 0.694816 + 0.719188i \(0.255486\pi\)
−0.694816 + 0.719188i \(0.744514\pi\)
\(338\) 0 0
\(339\) 366.783 + 246.010i 1.08195 + 0.725694i
\(340\) 0 0
\(341\) 258.772i 0.758862i
\(342\) 0 0
\(343\) 830.672i 2.42178i
\(344\) 0 0
\(345\) −112.547 1.90741i −0.326224 0.00552874i
\(346\) 0 0
\(347\) −336.214 −0.968915 −0.484457 0.874815i \(-0.660983\pi\)
−0.484457 + 0.874815i \(0.660983\pi\)
\(348\) 0 0
\(349\) −428.261 −1.22711 −0.613555 0.789652i \(-0.710261\pi\)
−0.613555 + 0.789652i \(0.710261\pi\)
\(350\) 0 0
\(351\) 196.833 + 40.2332i 0.560778 + 0.114625i
\(352\) 0 0
\(353\) 558.817 1.58305 0.791525 0.611137i \(-0.209287\pi\)
0.791525 + 0.611137i \(0.209287\pi\)
\(354\) 0 0
\(355\) 245.394 + 379.614i 0.691250 + 1.06934i
\(356\) 0 0
\(357\) 299.913 447.147i 0.840092 1.25251i
\(358\) 0 0
\(359\) 206.915i 0.576365i −0.957576 0.288182i \(-0.906949\pi\)
0.957576 0.288182i \(-0.0930509\pi\)
\(360\) 0 0
\(361\) 601.090 1.66507
\(362\) 0 0
\(363\) 95.9389 + 64.3487i 0.264295 + 0.177269i
\(364\) 0 0
\(365\) −125.457 194.077i −0.343718 0.531718i
\(366\) 0 0
\(367\) 185.425i 0.505246i −0.967565 0.252623i \(-0.918707\pi\)
0.967565 0.252623i \(-0.0812932\pi\)
\(368\) 0 0
\(369\) 115.288 47.2794i 0.312433 0.128128i
\(370\) 0 0
\(371\) 371.821i 1.00221i
\(372\) 0 0
\(373\) 427.345i 1.14570i −0.819661 0.572848i \(-0.805838\pi\)
0.819661 0.572848i \(-0.194162\pi\)
\(374\) 0 0
\(375\) −159.734 + 339.279i −0.425958 + 0.904743i
\(376\) 0 0
\(377\) −117.043 −0.310459
\(378\) 0 0
\(379\) −117.727 −0.310626 −0.155313 0.987865i \(-0.549639\pi\)
−0.155313 + 0.987865i \(0.549639\pi\)
\(380\) 0 0
\(381\) −150.427 + 224.275i −0.394822 + 0.588649i
\(382\) 0 0
\(383\) 470.016 1.22720 0.613598 0.789619i \(-0.289722\pi\)
0.613598 + 0.789619i \(0.289722\pi\)
\(384\) 0 0
\(385\) 677.182 437.750i 1.75891 1.13701i
\(386\) 0 0
\(387\) −250.473 + 102.719i −0.647217 + 0.265423i
\(388\) 0 0
\(389\) 128.160i 0.329461i 0.986339 + 0.164730i \(0.0526754\pi\)
−0.986339 + 0.164730i \(0.947325\pi\)
\(390\) 0 0
\(391\) 105.472 0.269749
\(392\) 0 0
\(393\) 18.8685 28.1315i 0.0480115 0.0715814i
\(394\) 0 0
\(395\) −159.401 + 103.041i −0.403546 + 0.260864i
\(396\) 0 0
\(397\) 276.316i 0.696011i 0.937493 + 0.348005i \(0.113141\pi\)
−0.937493 + 0.348005i \(0.886859\pi\)
\(398\) 0 0
\(399\) 661.871 986.798i 1.65882 2.47318i
\(400\) 0 0
\(401\) 549.912i 1.37135i 0.727907 + 0.685675i \(0.240493\pi\)
−0.727907 + 0.685675i \(0.759507\pi\)
\(402\) 0 0
\(403\) 152.458i 0.378307i
\(404\) 0 0
\(405\) −87.8182 + 395.364i −0.216835 + 0.976208i
\(406\) 0 0
\(407\) 163.252 0.401110
\(408\) 0 0
\(409\) −219.166 −0.535858 −0.267929 0.963439i \(-0.586339\pi\)
−0.267929 + 0.963439i \(0.586339\pi\)
\(410\) 0 0
\(411\) −56.0346 37.5838i −0.136337 0.0914448i
\(412\) 0 0
\(413\) 608.240 1.47273
\(414\) 0 0
\(415\) −336.877 + 217.767i −0.811751 + 0.524740i
\(416\) 0 0
\(417\) 226.962 + 152.229i 0.544274 + 0.365058i
\(418\) 0 0
\(419\) 204.522i 0.488119i −0.969760 0.244060i \(-0.921521\pi\)
0.969760 0.244060i \(-0.0784792\pi\)
\(420\) 0 0
\(421\) 577.186 1.37099 0.685494 0.728078i \(-0.259586\pi\)
0.685494 + 0.728078i \(0.259586\pi\)
\(422\) 0 0
\(423\) 69.1754 + 168.680i 0.163535 + 0.398770i
\(424\) 0 0
\(425\) 144.262 320.394i 0.339440 0.753868i
\(426\) 0 0
\(427\) 549.301i 1.28642i
\(428\) 0 0
\(429\) −234.136 157.041i −0.545772 0.366063i
\(430\) 0 0
\(431\) 663.363i 1.53913i 0.638571 + 0.769563i \(0.279526\pi\)
−0.638571 + 0.769563i \(0.720474\pi\)
\(432\) 0 0
\(433\) 226.876i 0.523964i 0.965073 + 0.261982i \(0.0843760\pi\)
−0.965073 + 0.261982i \(0.915624\pi\)
\(434\) 0 0
\(435\) 3.99818 235.913i 0.00919122 0.542329i
\(436\) 0 0
\(437\) 232.763 0.532639
\(438\) 0 0
\(439\) −282.524 −0.643564 −0.321782 0.946814i \(-0.604282\pi\)
−0.321782 + 0.946814i \(0.604282\pi\)
\(440\) 0 0
\(441\) −389.477 949.715i −0.883168 2.15355i
\(442\) 0 0
\(443\) −455.605 −1.02845 −0.514227 0.857654i \(-0.671921\pi\)
−0.514227 + 0.857654i \(0.671921\pi\)
\(444\) 0 0
\(445\) 382.521 + 591.744i 0.859597 + 1.32976i
\(446\) 0 0
\(447\) −381.561 + 568.878i −0.853604 + 1.27266i
\(448\) 0 0
\(449\) 157.206i 0.350124i −0.984557 0.175062i \(-0.943987\pi\)
0.984557 0.175062i \(-0.0560127\pi\)
\(450\) 0 0
\(451\) −174.858 −0.387712
\(452\) 0 0
\(453\) −184.466 123.726i −0.407210 0.273126i
\(454\) 0 0
\(455\) −398.968 + 257.905i −0.876853 + 0.566824i
\(456\) 0 0
\(457\) 397.152i 0.869041i 0.900662 + 0.434520i \(0.143082\pi\)
−0.900662 + 0.434520i \(0.856918\pi\)
\(458\) 0 0
\(459\) 75.9962 371.797i 0.165569 0.810014i
\(460\) 0 0
\(461\) 350.730i 0.760803i 0.924821 + 0.380401i \(0.124214\pi\)
−0.924821 + 0.380401i \(0.875786\pi\)
\(462\) 0 0
\(463\) 308.385i 0.666058i 0.942917 + 0.333029i \(0.108071\pi\)
−0.942917 + 0.333029i \(0.891929\pi\)
\(464\) 0 0
\(465\) −307.296 5.20794i −0.660851 0.0111999i
\(466\) 0 0
\(467\) 800.129 1.71334 0.856669 0.515866i \(-0.172530\pi\)
0.856669 + 0.515866i \(0.172530\pi\)
\(468\) 0 0
\(469\) −8.04656 −0.0171568
\(470\) 0 0
\(471\) −410.657 + 612.259i −0.871884 + 1.29991i
\(472\) 0 0
\(473\) 379.895 0.803160
\(474\) 0 0
\(475\) 318.369 707.070i 0.670250 1.48857i
\(476\) 0 0
\(477\) −99.4364 242.469i −0.208462 0.508321i
\(478\) 0 0
\(479\) 630.135i 1.31552i −0.753227 0.657761i \(-0.771504\pi\)
0.753227 0.657761i \(-0.228496\pi\)
\(480\) 0 0
\(481\) −96.1814 −0.199961
\(482\) 0 0
\(483\) 160.130 238.741i 0.331531 0.494287i
\(484\) 0 0
\(485\) 28.0746 + 43.4303i 0.0578858 + 0.0895470i
\(486\) 0 0
\(487\) 103.952i 0.213454i −0.994288 0.106727i \(-0.965963\pi\)
0.994288 0.106727i \(-0.0340372\pi\)
\(488\) 0 0
\(489\) 100.528 149.879i 0.205579 0.306502i
\(490\) 0 0
\(491\) 286.049i 0.582585i −0.956634 0.291292i \(-0.905915\pi\)
0.956634 0.291292i \(-0.0940853\pi\)
\(492\) 0 0
\(493\) 221.082i 0.448442i
\(494\) 0 0
\(495\) 324.532 466.563i 0.655619 0.942551i
\(496\) 0 0
\(497\) −1154.40 −2.32273
\(498\) 0 0
\(499\) 528.285 1.05869 0.529344 0.848407i \(-0.322438\pi\)
0.529344 + 0.848407i \(0.322438\pi\)
\(500\) 0 0
\(501\) 203.220 + 136.305i 0.405630 + 0.272066i
\(502\) 0 0
\(503\) 733.418 1.45809 0.729044 0.684467i \(-0.239965\pi\)
0.729044 + 0.684467i \(0.239965\pi\)
\(504\) 0 0
\(505\) 52.3169 + 80.9321i 0.103598 + 0.160262i
\(506\) 0 0
\(507\) −283.116 189.893i −0.558413 0.374542i
\(508\) 0 0
\(509\) 312.619i 0.614183i −0.951680 0.307092i \(-0.900644\pi\)
0.951680 0.307092i \(-0.0993558\pi\)
\(510\) 0 0
\(511\) 590.183 1.15496
\(512\) 0 0
\(513\) 167.714 820.509i 0.326928 1.59943i
\(514\) 0 0
\(515\) 18.9195 + 29.2677i 0.0367370 + 0.0568306i
\(516\) 0 0
\(517\) 255.838i 0.494851i
\(518\) 0 0
\(519\) 416.235 + 279.179i 0.801995 + 0.537918i
\(520\) 0 0
\(521\) 715.719i 1.37374i 0.726780 + 0.686870i \(0.241016\pi\)
−0.726780 + 0.686870i \(0.758984\pi\)
\(522\) 0 0
\(523\) 109.080i 0.208567i −0.994548 0.104283i \(-0.966745\pi\)
0.994548 0.104283i \(-0.0332549\pi\)
\(524\) 0 0
\(525\) −506.207 812.974i −0.964203 1.54852i
\(526\) 0 0
\(527\) 287.977 0.546445
\(528\) 0 0
\(529\) −472.686 −0.893547
\(530\) 0 0
\(531\) 396.641 162.662i 0.746971 0.306332i
\(532\) 0 0
\(533\) 103.019 0.193282
\(534\) 0 0
\(535\) −309.777 + 200.249i −0.579023 + 0.374297i
\(536\) 0 0
\(537\) −451.370 + 672.958i −0.840540 + 1.25318i
\(538\) 0 0
\(539\) 1440.44i 2.67243i
\(540\) 0 0
\(541\) −14.9710 −0.0276729 −0.0138364 0.999904i \(-0.504404\pi\)
−0.0138364 + 0.999904i \(0.504404\pi\)
\(542\) 0 0
\(543\) −216.705 145.350i −0.399088 0.267679i
\(544\) 0 0
\(545\) 310.862 200.950i 0.570389 0.368716i
\(546\) 0 0
\(547\) 842.765i 1.54070i −0.637618 0.770352i \(-0.720080\pi\)
0.637618 0.770352i \(-0.279920\pi\)
\(548\) 0 0
\(549\) 146.900 + 358.206i 0.267578 + 0.652471i
\(550\) 0 0
\(551\) 487.901i 0.885482i
\(552\) 0 0
\(553\) 484.733i 0.876551i
\(554\) 0 0
\(555\) 3.28555 193.864i 0.00591990 0.349305i
\(556\) 0 0
\(557\) 845.989 1.51883 0.759415 0.650606i \(-0.225485\pi\)
0.759415 + 0.650606i \(0.225485\pi\)
\(558\) 0 0
\(559\) −223.819 −0.400391
\(560\) 0 0
\(561\) −296.634 + 442.258i −0.528759 + 0.788339i
\(562\) 0 0
\(563\) 336.509 0.597707 0.298853 0.954299i \(-0.403396\pi\)
0.298853 + 0.954299i \(0.403396\pi\)
\(564\) 0 0
\(565\) −618.164 + 399.600i −1.09410 + 0.707256i
\(566\) 0 0
\(567\) −726.202 736.491i −1.28078 1.29893i
\(568\) 0 0
\(569\) 552.736i 0.971416i 0.874121 + 0.485708i \(0.161438\pi\)
−0.874121 + 0.485708i \(0.838562\pi\)
\(570\) 0 0
\(571\) −772.222 −1.35240 −0.676202 0.736717i \(-0.736375\pi\)
−0.676202 + 0.736717i \(0.736375\pi\)
\(572\) 0 0
\(573\) −505.043 + 752.980i −0.881401 + 1.31410i
\(574\) 0 0
\(575\) 77.0245 171.065i 0.133956 0.297504i
\(576\) 0 0
\(577\) 848.557i 1.47064i −0.677722 0.735318i \(-0.737033\pi\)
0.677722 0.735318i \(-0.262967\pi\)
\(578\) 0 0
\(579\) −512.658 + 764.334i −0.885420 + 1.32009i
\(580\) 0 0
\(581\) 1024.43i 1.76322i
\(582\) 0 0
\(583\) 367.755i 0.630798i
\(584\) 0 0
\(585\) −191.201 + 274.880i −0.326839 + 0.469880i
\(586\) 0 0
\(587\) 575.536 0.980470 0.490235 0.871590i \(-0.336911\pi\)
0.490235 + 0.871590i \(0.336911\pi\)
\(588\) 0 0
\(589\) 635.529 1.07900
\(590\) 0 0
\(591\) −722.419 484.544i −1.22237 0.819872i
\(592\) 0 0
\(593\) −156.935 −0.264646 −0.132323 0.991207i \(-0.542244\pi\)
−0.132323 + 0.991207i \(0.542244\pi\)
\(594\) 0 0
\(595\) 487.154 + 753.608i 0.818747 + 1.26657i
\(596\) 0 0
\(597\) 953.225 + 639.352i 1.59669 + 1.07094i
\(598\) 0 0
\(599\) 517.564i 0.864047i −0.901862 0.432024i \(-0.857800\pi\)
0.901862 0.432024i \(-0.142200\pi\)
\(600\) 0 0
\(601\) −883.588 −1.47020 −0.735098 0.677961i \(-0.762864\pi\)
−0.735098 + 0.677961i \(0.762864\pi\)
\(602\) 0 0
\(603\) −5.24727 + 2.15190i −0.00870194 + 0.00356866i
\(604\) 0 0
\(605\) −161.693 + 104.523i −0.267260 + 0.172765i
\(606\) 0 0
\(607\) 242.929i 0.400212i −0.979774 0.200106i \(-0.935871\pi\)
0.979774 0.200106i \(-0.0641287\pi\)
\(608\) 0 0
\(609\) 500.431 + 335.652i 0.821725 + 0.551152i
\(610\) 0 0
\(611\) 150.729i 0.246693i
\(612\) 0 0
\(613\) 157.263i 0.256546i −0.991739 0.128273i \(-0.959057\pi\)
0.991739 0.128273i \(-0.0409434\pi\)
\(614\) 0 0
\(615\) −3.51912 + 207.646i −0.00572215 + 0.337637i
\(616\) 0 0
\(617\) −471.040 −0.763436 −0.381718 0.924279i \(-0.624667\pi\)
−0.381718 + 0.924279i \(0.624667\pi\)
\(618\) 0 0
\(619\) −550.320 −0.889047 −0.444524 0.895767i \(-0.646627\pi\)
−0.444524 + 0.895767i \(0.646627\pi\)
\(620\) 0 0
\(621\) 40.5759 198.510i 0.0653396 0.319662i
\(622\) 0 0
\(623\) −1799.48 −2.88841
\(624\) 0 0
\(625\) −414.295 467.958i −0.662872 0.748733i
\(626\) 0 0
\(627\) −654.634 + 976.009i −1.04407 + 1.55663i
\(628\) 0 0
\(629\) 181.676i 0.288834i
\(630\) 0 0
\(631\) 347.362 0.550495 0.275248 0.961373i \(-0.411240\pi\)
0.275248 + 0.961373i \(0.411240\pi\)
\(632\) 0 0
\(633\) −800.051 536.614i −1.26390 0.847732i
\(634\) 0 0
\(635\) −244.342 377.987i −0.384790 0.595255i
\(636\) 0 0
\(637\) 848.649i 1.33226i
\(638\) 0 0
\(639\) −752.798 + 308.721i −1.17809 + 0.483132i
\(640\) 0 0
\(641\) 333.802i 0.520752i −0.965507 0.260376i \(-0.916153\pi\)
0.965507 0.260376i \(-0.0838465\pi\)
\(642\) 0 0
\(643\) 495.512i 0.770625i −0.922786 0.385313i \(-0.874094\pi\)
0.922786 0.385313i \(-0.125906\pi\)
\(644\) 0 0
\(645\) 7.64561 451.131i 0.0118537 0.699428i
\(646\) 0 0
\(647\) −149.493 −0.231056 −0.115528 0.993304i \(-0.536856\pi\)
−0.115528 + 0.993304i \(0.536856\pi\)
\(648\) 0 0
\(649\) −601.590 −0.926948
\(650\) 0 0
\(651\) 437.212 651.850i 0.671601 1.00131i
\(652\) 0 0
\(653\) −261.846 −0.400990 −0.200495 0.979695i \(-0.564255\pi\)
−0.200495 + 0.979695i \(0.564255\pi\)
\(654\) 0 0
\(655\) 30.6485 + 47.4120i 0.0467916 + 0.0723847i
\(656\) 0 0
\(657\) 384.867 157.833i 0.585794 0.240234i
\(658\) 0 0
\(659\) 148.718i 0.225672i −0.993614 0.112836i \(-0.964006\pi\)
0.993614 0.112836i \(-0.0359935\pi\)
\(660\) 0 0
\(661\) −535.548 −0.810209 −0.405104 0.914270i \(-0.632765\pi\)
−0.405104 + 0.914270i \(0.632765\pi\)
\(662\) 0 0
\(663\) 174.765 260.561i 0.263597 0.393002i
\(664\) 0 0
\(665\) 1075.09 + 1663.12i 1.61668 + 2.50093i
\(666\) 0 0
\(667\) 118.040i 0.176972i
\(668\) 0 0
\(669\) 488.681 728.586i 0.730465 1.08907i
\(670\) 0 0
\(671\) 543.295i 0.809680i
\(672\) 0 0
\(673\) 678.388i 1.00801i 0.863702 + 0.504003i \(0.168140\pi\)
−0.863702 + 0.504003i \(0.831860\pi\)
\(674\) 0 0
\(675\) −547.519 394.776i −0.811139 0.584853i
\(676\) 0 0
\(677\) −809.743 −1.19608 −0.598038 0.801468i \(-0.704053\pi\)
−0.598038 + 0.801468i \(0.704053\pi\)
\(678\) 0 0
\(679\) −132.070 −0.194507
\(680\) 0 0
\(681\) 922.231 + 618.563i 1.35423 + 0.908316i
\(682\) 0 0
\(683\) −150.099 −0.219764 −0.109882 0.993945i \(-0.535047\pi\)
−0.109882 + 0.993945i \(0.535047\pi\)
\(684\) 0 0
\(685\) 94.4390 61.0481i 0.137867 0.0891214i
\(686\) 0 0
\(687\) 951.705 + 638.333i 1.38531 + 0.929160i
\(688\) 0 0
\(689\) 216.667i 0.314465i
\(690\) 0 0
\(691\) 334.001 0.483359 0.241679 0.970356i \(-0.422302\pi\)
0.241679 + 0.970356i \(0.422302\pi\)
\(692\) 0 0
\(693\) 550.719 + 1342.89i 0.794688 + 1.93780i
\(694\) 0 0
\(695\) −382.515 + 247.269i −0.550381 + 0.355783i
\(696\) 0 0
\(697\) 194.592i 0.279185i
\(698\) 0 0
\(699\) −359.425 241.076i −0.514199 0.344886i
\(700\) 0 0
\(701\) 924.471i 1.31879i 0.751797 + 0.659394i \(0.229187\pi\)
−0.751797 + 0.659394i \(0.770813\pi\)
\(702\) 0 0
\(703\) 400.937i 0.570324i
\(704\) 0 0
\(705\) −303.812 5.14890i −0.430938 0.00730340i
\(706\) 0 0
\(707\) −246.112 −0.348108
\(708\) 0 0
\(709\) 797.459 1.12477 0.562383 0.826877i \(-0.309885\pi\)
0.562383 + 0.826877i \(0.309885\pi\)
\(710\) 0 0
\(711\) −129.633 316.101i −0.182324 0.444586i
\(712\) 0 0
\(713\) 153.757 0.215647
\(714\) 0 0
\(715\) 394.606 255.085i 0.551897 0.356762i
\(716\) 0 0
\(717\) 416.902 621.568i 0.581453 0.866902i
\(718\) 0 0
\(719\) 907.966i 1.26282i 0.775450 + 0.631409i \(0.217523\pi\)
−0.775450 + 0.631409i \(0.782477\pi\)
\(720\) 0 0
\(721\) −89.0024 −0.123443
\(722\) 0 0
\(723\) −75.8757 50.8918i −0.104946 0.0703897i
\(724\) 0 0
\(725\) 358.573 + 161.453i 0.494584 + 0.222694i
\(726\) 0 0
\(727\) 1038.16i 1.42801i 0.700140 + 0.714005i \(0.253121\pi\)
−0.700140 + 0.714005i \(0.746879\pi\)
\(728\) 0 0
\(729\) −670.527 286.067i −0.919790 0.392410i
\(730\) 0 0
\(731\) 422.769i 0.578344i
\(732\) 0 0
\(733\) 399.107i 0.544485i 0.962229 + 0.272242i \(0.0877652\pi\)
−0.962229 + 0.272242i \(0.912235\pi\)
\(734\) 0 0
\(735\) 1710.55 + 28.9898i 2.32727 + 0.0394418i
\(736\) 0 0
\(737\) 7.95858 0.0107986
\(738\) 0 0
\(739\) −452.504 −0.612319 −0.306159 0.951980i \(-0.599044\pi\)
−0.306159 + 0.951980i \(0.599044\pi\)
\(740\) 0 0
\(741\) 385.684 575.025i 0.520491 0.776012i
\(742\) 0 0
\(743\) 486.909 0.655328 0.327664 0.944794i \(-0.393739\pi\)
0.327664 + 0.944794i \(0.393739\pi\)
\(744\) 0 0
\(745\) −619.777 958.770i −0.831916 1.28694i
\(746\) 0 0
\(747\) −273.965 668.046i −0.366754 0.894306i
\(748\) 0 0
\(749\) 942.024i 1.25771i
\(750\) 0 0
\(751\) 470.899 0.627029 0.313515 0.949583i \(-0.398494\pi\)
0.313515 + 0.949583i \(0.398494\pi\)
\(752\) 0 0
\(753\) 115.169 171.708i 0.152947 0.228032i
\(754\) 0 0
\(755\) 310.894 200.971i 0.411780 0.266187i
\(756\) 0 0
\(757\) 886.264i 1.17076i 0.810760 + 0.585379i \(0.199054\pi\)
−0.810760 + 0.585379i \(0.800946\pi\)
\(758\) 0 0
\(759\) −158.379 + 236.131i −0.208668 + 0.311108i
\(760\) 0 0
\(761\) 1022.30i 1.34336i −0.740841 0.671680i \(-0.765573\pi\)
0.740841 0.671680i \(-0.234427\pi\)
\(762\) 0 0
\(763\) 945.322i 1.23895i
\(764\) 0 0
\(765\) 519.218 + 361.158i 0.678717 + 0.472102i
\(766\) 0 0
\(767\) 354.432 0.462102
\(768\) 0 0
\(769\) 1051.96 1.36796 0.683982 0.729499i \(-0.260247\pi\)
0.683982 + 0.729499i \(0.260247\pi\)
\(770\) 0 0
\(771\) 902.847 + 605.562i 1.17101 + 0.785424i
\(772\) 0 0
\(773\) −983.554 −1.27238 −0.636192 0.771530i \(-0.719492\pi\)
−0.636192 + 0.771530i \(0.719492\pi\)
\(774\) 0 0
\(775\) 210.305 467.070i 0.271361 0.602671i
\(776\) 0 0
\(777\) 411.234 + 275.825i 0.529259 + 0.354987i
\(778\) 0 0
\(779\) 429.441i 0.551272i
\(780\) 0 0
\(781\) 1141.77 1.46194
\(782\) 0 0
\(783\) 416.101 + 85.0522i 0.531419 + 0.108624i
\(784\) 0 0
\(785\) −667.039 1031.88i −0.849731 1.31450i
\(786\) 0 0
\(787\) 984.726i 1.25124i −0.780128 0.625620i \(-0.784846\pi\)
0.780128 0.625620i \(-0.215154\pi\)
\(788\) 0 0
\(789\) 58.4214 + 39.1847i 0.0740449 + 0.0496638i
\(790\) 0 0
\(791\) 1879.82i 2.37651i
\(792\) 0 0
\(793\) 320.087i 0.403641i
\(794\) 0 0
\(795\) 436.715 + 7.40130i 0.549327 + 0.00930982i
\(796\) 0 0
\(797\) 359.710 0.451330 0.225665 0.974205i \(-0.427544\pi\)
0.225665 + 0.974205i \(0.427544\pi\)
\(798\) 0 0
\(799\) 284.712 0.356335