Properties

Label 637.2.c.g.246.16
Level $637$
Weight $2$
Character 637.246
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 121 x^{12} + 296 x^{10} + 3468 x^{8} - 1748 x^{6} + 40192 x^{4} - 65056 x^{2} + 228484\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 246.16
Root \(-1.41421 + 2.73420i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.g.246.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.73420i q^{2} +1.15595 q^{3} -5.47586 q^{4} +1.87727i q^{5} +3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} +O(q^{10})\) \(q+2.73420i q^{2} +1.15595 q^{3} -5.47586 q^{4} +1.87727i q^{5} +3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} -5.13283 q^{10} +2.29974i q^{11} -6.32982 q^{12} +(-0.574228 + 3.55953i) q^{13} +2.17003i q^{15} +15.0333 q^{16} -6.07156 q^{17} -4.54911i q^{18} -5.15008i q^{19} -10.2797i q^{20} -6.28794 q^{22} -4.41782 q^{23} -10.9858i q^{24} +1.47586 q^{25} +(-9.73248 - 1.57006i) q^{26} -5.39110 q^{27} +7.50488 q^{29} -5.93330 q^{30} +4.33173i q^{31} +22.0967i q^{32} +2.65838i q^{33} -16.6009i q^{34} +9.11062 q^{36} -3.16867i q^{37} +14.0814 q^{38} +(-0.663779 + 4.11464i) q^{39} +17.8410 q^{40} +2.45446i q^{41} -2.17732 q^{43} -12.5930i q^{44} -3.12336i q^{45} -12.0792i q^{46} +8.90462i q^{47} +17.3778 q^{48} +4.03530i q^{50} -7.01842 q^{51} +(3.14439 - 19.4915i) q^{52} +8.10002 q^{53} -14.7403i q^{54} -4.31722 q^{55} -5.95323i q^{57} +20.5199i q^{58} +7.13955i q^{59} -11.8828i q^{60} -8.00979 q^{61} -11.8438 q^{62} -30.3503 q^{64} +(-6.68220 - 1.07798i) q^{65} -7.26855 q^{66} +1.15732i q^{67} +33.2470 q^{68} -5.10678 q^{69} +5.11328i q^{71} +15.8121i q^{72} +1.96898i q^{73} +8.66378 q^{74} +1.70602 q^{75} +28.2011i q^{76} +(-11.2503 - 1.81491i) q^{78} +3.81208 q^{79} +28.2216i q^{80} -1.24050 q^{81} -6.71098 q^{82} +2.49170i q^{83} -11.3980i q^{85} -5.95323i q^{86} +8.67527 q^{87} +21.8560 q^{88} +10.4291i q^{89} +8.53990 q^{90} +24.1914 q^{92} +5.00726i q^{93} -24.3470 q^{94} +9.66808 q^{95} +25.5427i q^{96} -2.51219i q^{97} -3.82625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 20 q^{4} + 16 q^{9} + O(q^{10}) \) \( 16 q - 20 q^{4} + 16 q^{9} + 28 q^{16} - 8 q^{22} - 36 q^{23} - 44 q^{25} + 36 q^{29} + 52 q^{36} + 32 q^{39} - 36 q^{43} - 72 q^{51} + 12 q^{53} - 164 q^{64} - 24 q^{65} + 96 q^{74} + 24 q^{78} + 36 q^{79} + 16 q^{81} + 136 q^{88} + 24 q^{92} - 84 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73420i 1.93337i 0.255964 + 0.966686i \(0.417607\pi\)
−0.255964 + 0.966686i \(0.582393\pi\)
\(3\) 1.15595 0.667388 0.333694 0.942681i \(-0.391705\pi\)
0.333694 + 0.942681i \(0.391705\pi\)
\(4\) −5.47586 −2.73793
\(5\) 1.87727i 0.839540i 0.907630 + 0.419770i \(0.137889\pi\)
−0.907630 + 0.419770i \(0.862111\pi\)
\(6\) 3.16060i 1.29031i
\(7\) 0 0
\(8\) 9.50370i 3.36007i
\(9\) −1.66378 −0.554593
\(10\) −5.13283 −1.62314
\(11\) 2.29974i 0.693396i 0.937977 + 0.346698i \(0.112697\pi\)
−0.937977 + 0.346698i \(0.887303\pi\)
\(12\) −6.32982 −1.82726
\(13\) −0.574228 + 3.55953i −0.159262 + 0.987236i
\(14\) 0 0
\(15\) 2.17003i 0.560299i
\(16\) 15.0333 3.75833
\(17\) −6.07156 −1.47257 −0.736285 0.676672i \(-0.763422\pi\)
−0.736285 + 0.676672i \(0.763422\pi\)
\(18\) 4.54911i 1.07223i
\(19\) 5.15008i 1.18151i −0.806851 0.590754i \(-0.798830\pi\)
0.806851 0.590754i \(-0.201170\pi\)
\(20\) 10.2797i 2.29860i
\(21\) 0 0
\(22\) −6.28794 −1.34059
\(23\) −4.41782 −0.921180 −0.460590 0.887613i \(-0.652362\pi\)
−0.460590 + 0.887613i \(0.652362\pi\)
\(24\) 10.9858i 2.24247i
\(25\) 1.47586 0.295172
\(26\) −9.73248 1.57006i −1.90870 0.307913i
\(27\) −5.39110 −1.03752
\(28\) 0 0
\(29\) 7.50488 1.39362 0.696810 0.717255i \(-0.254602\pi\)
0.696810 + 0.717255i \(0.254602\pi\)
\(30\) −5.93330 −1.08327
\(31\) 4.33173i 0.778001i 0.921238 + 0.389001i \(0.127180\pi\)
−0.921238 + 0.389001i \(0.872820\pi\)
\(32\) 22.0967i 3.90619i
\(33\) 2.65838i 0.462765i
\(34\) 16.6009i 2.84703i
\(35\) 0 0
\(36\) 9.11062 1.51844
\(37\) 3.16867i 0.520926i −0.965484 0.260463i \(-0.916125\pi\)
0.965484 0.260463i \(-0.0838752\pi\)
\(38\) 14.0814 2.28430
\(39\) −0.663779 + 4.11464i −0.106290 + 0.658870i
\(40\) 17.8410 2.82091
\(41\) 2.45446i 0.383322i 0.981461 + 0.191661i \(0.0613874\pi\)
−0.981461 + 0.191661i \(0.938613\pi\)
\(42\) 0 0
\(43\) −2.17732 −0.332038 −0.166019 0.986123i \(-0.553091\pi\)
−0.166019 + 0.986123i \(0.553091\pi\)
\(44\) 12.5930i 1.89847i
\(45\) 3.12336i 0.465603i
\(46\) 12.0792i 1.78098i
\(47\) 8.90462i 1.29887i 0.760416 + 0.649436i \(0.224995\pi\)
−0.760416 + 0.649436i \(0.775005\pi\)
\(48\) 17.3778 2.50827
\(49\) 0 0
\(50\) 4.03530i 0.570677i
\(51\) −7.01842 −0.982775
\(52\) 3.14439 19.4915i 0.436049 2.70298i
\(53\) 8.10002 1.11262 0.556312 0.830974i \(-0.312216\pi\)
0.556312 + 0.830974i \(0.312216\pi\)
\(54\) 14.7403i 2.00591i
\(55\) −4.31722 −0.582134
\(56\) 0 0
\(57\) 5.95323i 0.788525i
\(58\) 20.5199i 2.69439i
\(59\) 7.13955i 0.929491i 0.885444 + 0.464745i \(0.153854\pi\)
−0.885444 + 0.464745i \(0.846146\pi\)
\(60\) 11.8828i 1.53406i
\(61\) −8.00979 −1.02555 −0.512774 0.858523i \(-0.671382\pi\)
−0.512774 + 0.858523i \(0.671382\pi\)
\(62\) −11.8438 −1.50417
\(63\) 0 0
\(64\) −30.3503 −3.79379
\(65\) −6.68220 1.07798i −0.828825 0.133707i
\(66\) −7.26855 −0.894696
\(67\) 1.15732i 0.141389i 0.997498 + 0.0706947i \(0.0225216\pi\)
−0.997498 + 0.0706947i \(0.977478\pi\)
\(68\) 33.2470 4.03179
\(69\) −5.10678 −0.614785
\(70\) 0 0
\(71\) 5.11328i 0.606835i 0.952858 + 0.303417i \(0.0981276\pi\)
−0.952858 + 0.303417i \(0.901872\pi\)
\(72\) 15.8121i 1.86347i
\(73\) 1.96898i 0.230452i 0.993339 + 0.115226i \(0.0367593\pi\)
−0.993339 + 0.115226i \(0.963241\pi\)
\(74\) 8.66378 1.00714
\(75\) 1.70602 0.196994
\(76\) 28.2011i 3.23489i
\(77\) 0 0
\(78\) −11.2503 1.81491i −1.27384 0.205498i
\(79\) 3.81208 0.428893 0.214446 0.976736i \(-0.431205\pi\)
0.214446 + 0.976736i \(0.431205\pi\)
\(80\) 28.2216i 3.15527i
\(81\) −1.24050 −0.137834
\(82\) −6.71098 −0.741104
\(83\) 2.49170i 0.273499i 0.990606 + 0.136750i \(0.0436656\pi\)
−0.990606 + 0.136750i \(0.956334\pi\)
\(84\) 0 0
\(85\) 11.3980i 1.23628i
\(86\) 5.95323i 0.641954i
\(87\) 8.67527 0.930086
\(88\) 21.8560 2.32986
\(89\) 10.4291i 1.10548i 0.833353 + 0.552742i \(0.186418\pi\)
−0.833353 + 0.552742i \(0.813582\pi\)
\(90\) 8.53990 0.900185
\(91\) 0 0
\(92\) 24.1914 2.52213
\(93\) 5.00726i 0.519229i
\(94\) −24.3470 −2.51120
\(95\) 9.66808 0.991924
\(96\) 25.5427i 2.60694i
\(97\) 2.51219i 0.255074i −0.991834 0.127537i \(-0.959293\pi\)
0.991834 0.127537i \(-0.0407072\pi\)
\(98\) 0 0
\(99\) 3.82625i 0.384553i
\(100\) −8.08160 −0.808160
\(101\) 10.6804 1.06274 0.531368 0.847141i \(-0.321678\pi\)
0.531368 + 0.847141i \(0.321678\pi\)
\(102\) 19.1898i 1.90007i
\(103\) −11.8030 −1.16298 −0.581492 0.813552i \(-0.697531\pi\)
−0.581492 + 0.813552i \(0.697531\pi\)
\(104\) 33.8287 + 5.45729i 3.31718 + 0.535131i
\(105\) 0 0
\(106\) 22.1471i 2.15112i
\(107\) −4.27734 −0.413506 −0.206753 0.978393i \(-0.566290\pi\)
−0.206753 + 0.978393i \(0.566290\pi\)
\(108\) 29.5209 2.84065
\(109\) 2.01135i 0.192652i 0.995350 + 0.0963260i \(0.0307091\pi\)
−0.995350 + 0.0963260i \(0.969291\pi\)
\(110\) 11.8042i 1.12548i
\(111\) 3.66282i 0.347660i
\(112\) 0 0
\(113\) −4.16866 −0.392154 −0.196077 0.980588i \(-0.562820\pi\)
−0.196077 + 0.980588i \(0.562820\pi\)
\(114\) 16.2773 1.52451
\(115\) 8.29344i 0.773368i
\(116\) −41.0957 −3.81564
\(117\) 0.955388 5.92227i 0.0883257 0.547514i
\(118\) −19.5210 −1.79705
\(119\) 0 0
\(120\) 20.6233 1.88264
\(121\) 5.71122 0.519202
\(122\) 21.9004i 1.98277i
\(123\) 2.83723i 0.255824i
\(124\) 23.7199i 2.13011i
\(125\) 12.1569i 1.08735i
\(126\) 0 0
\(127\) 15.1922 1.34809 0.674046 0.738689i \(-0.264555\pi\)
0.674046 + 0.738689i \(0.264555\pi\)
\(128\) 38.7903i 3.42861i
\(129\) −2.51687 −0.221598
\(130\) 2.94742 18.2705i 0.258506 1.60243i
\(131\) 0.950977 0.0830872 0.0415436 0.999137i \(-0.486772\pi\)
0.0415436 + 0.999137i \(0.486772\pi\)
\(132\) 14.5569i 1.26702i
\(133\) 0 0
\(134\) −3.16435 −0.273359
\(135\) 10.1205i 0.871037i
\(136\) 57.7023i 4.94793i
\(137\) 12.2379i 1.04555i 0.852469 + 0.522777i \(0.175104\pi\)
−0.852469 + 0.522777i \(0.824896\pi\)
\(138\) 13.9630i 1.18861i
\(139\) −5.24824 −0.445150 −0.222575 0.974916i \(-0.571446\pi\)
−0.222575 + 0.974916i \(0.571446\pi\)
\(140\) 0 0
\(141\) 10.2933i 0.866852i
\(142\) −13.9807 −1.17324
\(143\) −8.18598 1.32057i −0.684546 0.110432i
\(144\) −25.0121 −2.08434
\(145\) 14.0887i 1.17000i
\(146\) −5.38360 −0.445550
\(147\) 0 0
\(148\) 17.3512i 1.42626i
\(149\) 2.38138i 0.195090i 0.995231 + 0.0975451i \(0.0310990\pi\)
−0.995231 + 0.0975451i \(0.968901\pi\)
\(150\) 4.66460i 0.380863i
\(151\) 20.3085i 1.65268i 0.563170 + 0.826341i \(0.309582\pi\)
−0.563170 + 0.826341i \(0.690418\pi\)
\(152\) −48.9448 −3.96995
\(153\) 10.1017 0.816677
\(154\) 0 0
\(155\) −8.13182 −0.653163
\(156\) 3.63476 22.5312i 0.291014 1.80394i
\(157\) −11.0405 −0.881124 −0.440562 0.897722i \(-0.645221\pi\)
−0.440562 + 0.897722i \(0.645221\pi\)
\(158\) 10.4230i 0.829209i
\(159\) 9.36322 0.742552
\(160\) −41.4815 −3.27940
\(161\) 0 0
\(162\) 3.39178i 0.266484i
\(163\) 18.9784i 1.48651i −0.669011 0.743253i \(-0.733282\pi\)
0.669011 0.743253i \(-0.266718\pi\)
\(164\) 13.4403i 1.04951i
\(165\) −4.99049 −0.388509
\(166\) −6.81280 −0.528776
\(167\) 21.7305i 1.68155i −0.541382 0.840776i \(-0.682099\pi\)
0.541382 0.840776i \(-0.317901\pi\)
\(168\) 0 0
\(169\) −12.3405 4.08796i −0.949271 0.314459i
\(170\) 31.1643 2.39019
\(171\) 8.56859i 0.655256i
\(172\) 11.9227 0.909097
\(173\) 2.90301 0.220712 0.110356 0.993892i \(-0.464801\pi\)
0.110356 + 0.993892i \(0.464801\pi\)
\(174\) 23.7199i 1.79820i
\(175\) 0 0
\(176\) 34.5727i 2.60601i
\(177\) 8.25297i 0.620331i
\(178\) −28.5153 −2.13731
\(179\) −19.3503 −1.44631 −0.723154 0.690687i \(-0.757308\pi\)
−0.723154 + 0.690687i \(0.757308\pi\)
\(180\) 17.1031i 1.27479i
\(181\) 9.98016 0.741820 0.370910 0.928669i \(-0.379046\pi\)
0.370910 + 0.928669i \(0.379046\pi\)
\(182\) 0 0
\(183\) −9.25892 −0.684439
\(184\) 41.9857i 3.09523i
\(185\) 5.94844 0.437338
\(186\) −13.6909 −1.00386
\(187\) 13.9630i 1.02107i
\(188\) 48.7604i 3.55622i
\(189\) 0 0
\(190\) 26.4345i 1.91776i
\(191\) 5.40486 0.391082 0.195541 0.980696i \(-0.437354\pi\)
0.195541 + 0.980696i \(0.437354\pi\)
\(192\) −35.0834 −2.53193
\(193\) 14.5666i 1.04853i −0.851556 0.524264i \(-0.824340\pi\)
0.851556 0.524264i \(-0.175660\pi\)
\(194\) 6.86883 0.493153
\(195\) −7.72429 1.24609i −0.553148 0.0892345i
\(196\) 0 0
\(197\) 15.9055i 1.13322i −0.823987 0.566609i \(-0.808255\pi\)
0.823987 0.566609i \(-0.191745\pi\)
\(198\) 10.4617 0.743484
\(199\) −0.373666 −0.0264885 −0.0132442 0.999912i \(-0.504216\pi\)
−0.0132442 + 0.999912i \(0.504216\pi\)
\(200\) 14.0261i 0.991797i
\(201\) 1.33781i 0.0943617i
\(202\) 29.2023i 2.05467i
\(203\) 0 0
\(204\) 38.4319 2.69077
\(205\) −4.60768 −0.321814
\(206\) 32.2718i 2.24848i
\(207\) 7.35028 0.510880
\(208\) −8.63255 + 53.5116i −0.598560 + 3.71036i
\(209\) 11.8438 0.819254
\(210\) 0 0
\(211\) 6.05258 0.416677 0.208339 0.978057i \(-0.433194\pi\)
0.208339 + 0.978057i \(0.433194\pi\)
\(212\) −44.3546 −3.04629
\(213\) 5.91070i 0.404994i
\(214\) 11.6951i 0.799462i
\(215\) 4.08742i 0.278760i
\(216\) 51.2354i 3.48613i
\(217\) 0 0
\(218\) −5.49943 −0.372468
\(219\) 2.27605i 0.153801i
\(220\) 23.6405 1.59384
\(221\) 3.48646 21.6119i 0.234525 1.45377i
\(222\) 10.0149 0.672156
\(223\) 7.30624i 0.489262i −0.969616 0.244631i \(-0.921333\pi\)
0.969616 0.244631i \(-0.0786668\pi\)
\(224\) 0 0
\(225\) −2.45550 −0.163700
\(226\) 11.3980i 0.758180i
\(227\) 15.6914i 1.04147i 0.853717 + 0.520737i \(0.174343\pi\)
−0.853717 + 0.520737i \(0.825657\pi\)
\(228\) 32.5991i 2.15893i
\(229\) 25.5632i 1.68926i 0.535347 + 0.844632i \(0.320181\pi\)
−0.535347 + 0.844632i \(0.679819\pi\)
\(230\) 22.6759 1.49521
\(231\) 0 0
\(232\) 71.3241i 4.68266i
\(233\) 16.3405 1.07050 0.535252 0.844693i \(-0.320217\pi\)
0.535252 + 0.844693i \(0.320217\pi\)
\(234\) 16.1927 + 2.61222i 1.05855 + 0.170766i
\(235\) −16.7164 −1.09046
\(236\) 39.0952i 2.54488i
\(237\) 4.40658 0.286238
\(238\) 0 0
\(239\) 17.2505i 1.11584i −0.829895 0.557920i \(-0.811600\pi\)
0.829895 0.557920i \(-0.188400\pi\)
\(240\) 32.6228i 2.10579i
\(241\) 10.1130i 0.651434i 0.945467 + 0.325717i \(0.105606\pi\)
−0.945467 + 0.325717i \(0.894394\pi\)
\(242\) 15.6156i 1.00381i
\(243\) 14.7393 0.945528
\(244\) 43.8605 2.80788
\(245\) 0 0
\(246\) −7.75756 −0.494604
\(247\) 18.3319 + 2.95732i 1.16643 + 0.188170i
\(248\) 41.1674 2.61414
\(249\) 2.88028i 0.182530i
\(250\) −33.2395 −2.10225
\(251\) 20.8184 1.31404 0.657022 0.753871i \(-0.271816\pi\)
0.657022 + 0.753871i \(0.271816\pi\)
\(252\) 0 0
\(253\) 10.1598i 0.638743i
\(254\) 41.5386i 2.60636i
\(255\) 13.1755i 0.825080i
\(256\) 45.3600 2.83500
\(257\) 28.2296 1.76091 0.880456 0.474127i \(-0.157236\pi\)
0.880456 + 0.474127i \(0.157236\pi\)
\(258\) 6.88164i 0.428432i
\(259\) 0 0
\(260\) 36.5908 + 5.90287i 2.26926 + 0.366080i
\(261\) −12.4865 −0.772892
\(262\) 2.60016i 0.160639i
\(263\) 6.10868 0.376678 0.188339 0.982104i \(-0.439690\pi\)
0.188339 + 0.982104i \(0.439690\pi\)
\(264\) 25.2645 1.55492
\(265\) 15.2059i 0.934092i
\(266\) 0 0
\(267\) 12.0555i 0.737787i
\(268\) 6.33734i 0.387114i
\(269\) 4.84124 0.295176 0.147588 0.989049i \(-0.452849\pi\)
0.147588 + 0.989049i \(0.452849\pi\)
\(270\) 27.6716 1.68404
\(271\) 0.298894i 0.0181565i 0.999959 + 0.00907826i \(0.00288974\pi\)
−0.999959 + 0.00907826i \(0.997110\pi\)
\(272\) −91.2757 −5.53440
\(273\) 0 0
\(274\) −33.4609 −2.02145
\(275\) 3.39409i 0.204671i
\(276\) 27.9640 1.68324
\(277\) −8.72696 −0.524352 −0.262176 0.965020i \(-0.584440\pi\)
−0.262176 + 0.965020i \(0.584440\pi\)
\(278\) 14.3497i 0.860640i
\(279\) 7.20704i 0.431474i
\(280\) 0 0
\(281\) 24.7012i 1.47355i 0.676137 + 0.736776i \(0.263653\pi\)
−0.676137 + 0.736776i \(0.736347\pi\)
\(282\) −28.1439 −1.67595
\(283\) −12.2524 −0.728332 −0.364166 0.931334i \(-0.618646\pi\)
−0.364166 + 0.931334i \(0.618646\pi\)
\(284\) 27.9996i 1.66147i
\(285\) 11.1758 0.661999
\(286\) 3.61071 22.3821i 0.213506 1.32348i
\(287\) 0 0
\(288\) 36.7641i 2.16634i
\(289\) 19.8638 1.16846
\(290\) −38.5213 −2.26205
\(291\) 2.90397i 0.170233i
\(292\) 10.7819i 0.630962i
\(293\) 14.6524i 0.856001i 0.903779 + 0.428000i \(0.140782\pi\)
−0.903779 + 0.428000i \(0.859218\pi\)
\(294\) 0 0
\(295\) −13.4029 −0.780345
\(296\) −30.1141 −1.75035
\(297\) 12.3981i 0.719410i
\(298\) −6.51117 −0.377182
\(299\) 2.53684 15.7254i 0.146709 0.909422i
\(300\) −9.34193 −0.539357
\(301\) 0 0
\(302\) −55.5275 −3.19525
\(303\) 12.3460 0.709258
\(304\) 77.4228i 4.44050i
\(305\) 15.0365i 0.860990i
\(306\) 27.6202i 1.57894i
\(307\) 18.8687i 1.07690i −0.842659 0.538448i \(-0.819011\pi\)
0.842659 0.538448i \(-0.180989\pi\)
\(308\) 0 0
\(309\) −13.6437 −0.776162
\(310\) 22.2340i 1.26281i
\(311\) 5.70539 0.323523 0.161761 0.986830i \(-0.448283\pi\)
0.161761 + 0.986830i \(0.448283\pi\)
\(312\) 39.1043 + 6.30836i 2.21385 + 0.357140i
\(313\) −3.94334 −0.222891 −0.111445 0.993771i \(-0.535548\pi\)
−0.111445 + 0.993771i \(0.535548\pi\)
\(314\) 30.1868i 1.70354i
\(315\) 0 0
\(316\) −20.8744 −1.17428
\(317\) 3.84116i 0.215741i −0.994165 0.107871i \(-0.965597\pi\)
0.994165 0.107871i \(-0.0344032\pi\)
\(318\) 25.6009i 1.43563i
\(319\) 17.2592i 0.966332i
\(320\) 56.9757i 3.18504i
\(321\) −4.94439 −0.275969
\(322\) 0 0
\(323\) 31.2690i 1.73985i
\(324\) 6.79282 0.377379
\(325\) −0.847480 + 5.25337i −0.0470097 + 0.291405i
\(326\) 51.8908 2.87397
\(327\) 2.32502i 0.128574i
\(328\) 23.3264 1.28799
\(329\) 0 0
\(330\) 13.6450i 0.751134i
\(331\) 6.12599i 0.336715i −0.985726 0.168357i \(-0.946154\pi\)
0.985726 0.168357i \(-0.0538463\pi\)
\(332\) 13.6442i 0.748822i
\(333\) 5.27196i 0.288902i
\(334\) 59.4154 3.25107
\(335\) −2.17261 −0.118702
\(336\) 0 0
\(337\) 20.8026 1.13319 0.566594 0.823997i \(-0.308261\pi\)
0.566594 + 0.823997i \(0.308261\pi\)
\(338\) 11.1773 33.7415i 0.607966 1.83529i
\(339\) −4.81876 −0.261719
\(340\) 62.4136i 3.38485i
\(341\) −9.96183 −0.539463
\(342\) −23.4283 −1.26686
\(343\) 0 0
\(344\) 20.6926i 1.11567i
\(345\) 9.58681i 0.516136i
\(346\) 7.93741i 0.426718i
\(347\) 17.7508 0.952915 0.476457 0.879198i \(-0.341921\pi\)
0.476457 + 0.879198i \(0.341921\pi\)
\(348\) −47.5045 −2.54651
\(349\) 1.00552i 0.0538245i 0.999638 + 0.0269122i \(0.00856746\pi\)
−0.999638 + 0.0269122i \(0.991433\pi\)
\(350\) 0 0
\(351\) 3.09572 19.1898i 0.165237 1.02427i
\(352\) −50.8166 −2.70854
\(353\) 12.6219i 0.671797i −0.941898 0.335898i \(-0.890960\pi\)
0.941898 0.335898i \(-0.109040\pi\)
\(354\) −22.5653 −1.19933
\(355\) −9.59900 −0.509462
\(356\) 57.1083i 3.02674i
\(357\) 0 0
\(358\) 52.9076i 2.79625i
\(359\) 11.4750i 0.605627i −0.953050 0.302813i \(-0.902074\pi\)
0.953050 0.302813i \(-0.0979259\pi\)
\(360\) −29.6835 −1.56446
\(361\) −7.52330 −0.395963
\(362\) 27.2878i 1.43421i
\(363\) 6.60188 0.346509
\(364\) 0 0
\(365\) −3.69631 −0.193474
\(366\) 25.3158i 1.32328i
\(367\) 28.9114 1.50917 0.754583 0.656205i \(-0.227839\pi\)
0.754583 + 0.656205i \(0.227839\pi\)
\(368\) −66.4146 −3.46210
\(369\) 4.08367i 0.212588i
\(370\) 16.2642i 0.845538i
\(371\) 0 0
\(372\) 27.4191i 1.42161i
\(373\) 23.4888 1.21621 0.608103 0.793858i \(-0.291931\pi\)
0.608103 + 0.793858i \(0.291931\pi\)
\(374\) 38.1776 1.97412
\(375\) 14.0528i 0.725684i
\(376\) 84.6268 4.36430
\(377\) −4.30951 + 26.7138i −0.221951 + 1.37583i
\(378\) 0 0
\(379\) 37.6063i 1.93171i 0.259088 + 0.965854i \(0.416578\pi\)
−0.259088 + 0.965854i \(0.583422\pi\)
\(380\) −52.9411 −2.71582
\(381\) 17.5615 0.899701
\(382\) 14.7780i 0.756107i
\(383\) 25.3183i 1.29371i −0.762615 0.646853i \(-0.776085\pi\)
0.762615 0.646853i \(-0.223915\pi\)
\(384\) 44.8397i 2.28822i
\(385\) 0 0
\(386\) 39.8281 2.02720
\(387\) 3.62258 0.184146
\(388\) 13.7564i 0.698375i
\(389\) 1.31889 0.0668706 0.0334353 0.999441i \(-0.489355\pi\)
0.0334353 + 0.999441i \(0.489355\pi\)
\(390\) 3.40707 21.1198i 0.172524 1.06944i
\(391\) 26.8231 1.35650
\(392\) 0 0
\(393\) 1.09928 0.0554514
\(394\) 43.4888 2.19093
\(395\) 7.15630i 0.360073i
\(396\) 20.9520i 1.05288i
\(397\) 37.3506i 1.87457i −0.348558 0.937287i \(-0.613329\pi\)
0.348558 0.937287i \(-0.386671\pi\)
\(398\) 1.02168i 0.0512121i
\(399\) 0 0
\(400\) 22.1871 1.10935
\(401\) 27.3183i 1.36421i 0.731253 + 0.682106i \(0.238936\pi\)
−0.731253 + 0.682106i \(0.761064\pi\)
\(402\) −3.65784 −0.182436
\(403\) −15.4189 2.48740i −0.768071 0.123906i
\(404\) −58.4842 −2.90970
\(405\) 2.32876i 0.115717i
\(406\) 0 0
\(407\) 7.28710 0.361208
\(408\) 66.7010i 3.30219i
\(409\) 23.9071i 1.18213i −0.806624 0.591065i \(-0.798708\pi\)
0.806624 0.591065i \(-0.201292\pi\)
\(410\) 12.5983i 0.622187i
\(411\) 14.1464i 0.697791i
\(412\) 64.6315 3.18417
\(413\) 0 0
\(414\) 20.0972i 0.987721i
\(415\) −4.67759 −0.229614
\(416\) −78.6540 12.6886i −3.85633 0.622108i
\(417\) −6.06670 −0.297088
\(418\) 32.3834i 1.58392i
\(419\) 16.4726 0.804739 0.402369 0.915477i \(-0.368187\pi\)
0.402369 + 0.915477i \(0.368187\pi\)
\(420\) 0 0
\(421\) 23.9857i 1.16899i −0.811397 0.584495i \(-0.801292\pi\)
0.811397 0.584495i \(-0.198708\pi\)
\(422\) 16.5490i 0.805592i
\(423\) 14.8153i 0.720345i
\(424\) 76.9802i 3.73849i
\(425\) −8.96077 −0.434661
\(426\) −16.1610 −0.783005
\(427\) 0 0
\(428\) 23.4221 1.13215
\(429\) −9.46259 1.52652i −0.456858 0.0737009i
\(430\) 11.1758 0.538946
\(431\) 22.6899i 1.09293i −0.837481 0.546467i \(-0.815973\pi\)
0.837481 0.546467i \(-0.184027\pi\)
\(432\) −81.0461 −3.89933
\(433\) −17.0937 −0.821470 −0.410735 0.911755i \(-0.634728\pi\)
−0.410735 + 0.911755i \(0.634728\pi\)
\(434\) 0 0
\(435\) 16.2858i 0.780845i
\(436\) 11.0138i 0.527468i
\(437\) 22.7521i 1.08838i
\(438\) −6.22318 −0.297355
\(439\) −35.4013 −1.68961 −0.844805 0.535074i \(-0.820284\pi\)
−0.844805 + 0.535074i \(0.820284\pi\)
\(440\) 41.0296i 1.95601i
\(441\) 0 0
\(442\) 59.0913 + 9.53268i 2.81069 + 0.453423i
\(443\) −16.2632 −0.772689 −0.386345 0.922355i \(-0.626262\pi\)
−0.386345 + 0.922355i \(0.626262\pi\)
\(444\) 20.0571i 0.951868i
\(445\) −19.5782 −0.928098
\(446\) 19.9767 0.945925
\(447\) 2.75276i 0.130201i
\(448\) 0 0
\(449\) 15.1472i 0.714839i −0.933944 0.357419i \(-0.883657\pi\)
0.933944 0.357419i \(-0.116343\pi\)
\(450\) 6.71385i 0.316494i
\(451\) −5.64460 −0.265794
\(452\) 22.8270 1.07369
\(453\) 23.4756i 1.10298i
\(454\) −42.9034 −2.01356
\(455\) 0 0
\(456\) −56.5778 −2.64950
\(457\) 39.4983i 1.84765i 0.382813 + 0.923826i \(0.374955\pi\)
−0.382813 + 0.923826i \(0.625045\pi\)
\(458\) −69.8950 −3.26598
\(459\) 32.7324 1.52782
\(460\) 45.4137i 2.11743i
\(461\) 19.0149i 0.885614i 0.896617 + 0.442807i \(0.146017\pi\)
−0.896617 + 0.442807i \(0.853983\pi\)
\(462\) 0 0
\(463\) 2.48740i 0.115599i 0.998328 + 0.0577996i \(0.0184084\pi\)
−0.998328 + 0.0577996i \(0.981592\pi\)
\(464\) 112.823 5.23769
\(465\) −9.39998 −0.435913
\(466\) 44.6783i 2.06968i
\(467\) 14.8786 0.688501 0.344250 0.938878i \(-0.388133\pi\)
0.344250 + 0.938878i \(0.388133\pi\)
\(468\) −5.23157 + 32.4295i −0.241830 + 1.49906i
\(469\) 0 0
\(470\) 45.7059i 2.10826i
\(471\) −12.7622 −0.588052
\(472\) 67.8522 3.12315
\(473\) 5.00726i 0.230234i
\(474\) 12.0485i 0.553404i
\(475\) 7.60079i 0.348748i
\(476\) 0 0
\(477\) −13.4766 −0.617053
\(478\) 47.1662 2.15733
\(479\) 16.8798i 0.771256i −0.922654 0.385628i \(-0.873985\pi\)
0.922654 0.385628i \(-0.126015\pi\)
\(480\) −47.9506 −2.18863
\(481\) 11.2790 + 1.81954i 0.514277 + 0.0829638i
\(482\) −27.6509 −1.25947
\(483\) 0 0
\(484\) −31.2738 −1.42154
\(485\) 4.71606 0.214145
\(486\) 40.3003i 1.82806i
\(487\) 4.44539i 0.201440i −0.994915 0.100720i \(-0.967885\pi\)
0.994915 0.100720i \(-0.0321146\pi\)
\(488\) 76.1227i 3.44591i
\(489\) 21.9381i 0.992076i
\(490\) 0 0
\(491\) −16.9816 −0.766368 −0.383184 0.923672i \(-0.625172\pi\)
−0.383184 + 0.923672i \(0.625172\pi\)
\(492\) 15.5363i 0.700430i
\(493\) −45.5663 −2.05220
\(494\) −8.08591 + 50.1230i −0.363802 + 2.25514i
\(495\) 7.18290 0.322848
\(496\) 65.1202i 2.92399i
\(497\) 0 0
\(498\) −7.87526 −0.352899
\(499\) 41.0011i 1.83546i −0.397203 0.917731i \(-0.630019\pi\)
0.397203 0.917731i \(-0.369981\pi\)
\(500\) 66.5697i 2.97709i
\(501\) 25.1193i 1.12225i
\(502\) 56.9217i 2.54054i
\(503\) −37.2910 −1.66272 −0.831361 0.555732i \(-0.812438\pi\)
−0.831361 + 0.555732i \(0.812438\pi\)
\(504\) 0 0
\(505\) 20.0499i 0.892210i
\(506\) 27.7790 1.23493
\(507\) −14.2650 4.72548i −0.633532 0.209866i
\(508\) −83.1905 −3.69098
\(509\) 8.21571i 0.364155i −0.983284 0.182077i \(-0.941718\pi\)
0.983284 0.182077i \(-0.0582821\pi\)
\(510\) 36.0244 1.59519
\(511\) 0 0
\(512\) 46.4428i 2.05250i
\(513\) 27.7646i 1.22584i
\(514\) 77.1854i 3.40450i
\(515\) 22.1574i 0.976372i
\(516\) 13.7821 0.606721
\(517\) −20.4783 −0.900633
\(518\) 0 0
\(519\) 3.35573 0.147300
\(520\) −10.2448 + 63.5056i −0.449264 + 2.78491i
\(521\) 33.9993 1.48954 0.744768 0.667323i \(-0.232560\pi\)
0.744768 + 0.667323i \(0.232560\pi\)
\(522\) 34.1405i 1.49429i
\(523\) −22.8782 −1.00039 −0.500197 0.865912i \(-0.666739\pi\)
−0.500197 + 0.865912i \(0.666739\pi\)
\(524\) −5.20742 −0.227487
\(525\) 0 0
\(526\) 16.7024i 0.728258i
\(527\) 26.3003i 1.14566i
\(528\) 39.9643i 1.73922i
\(529\) −3.48284 −0.151428
\(530\) −41.5761 −1.80595
\(531\) 11.8786i 0.515489i
\(532\) 0 0
\(533\) −8.73672 1.40942i −0.378429 0.0610487i
\(534\) −32.9623 −1.42642
\(535\) 8.02972i 0.347155i
\(536\) 10.9989 0.475078
\(537\) −22.3680 −0.965249
\(538\) 13.2369i 0.570685i
\(539\) 0 0
\(540\) 55.4187i 2.38484i
\(541\) 39.4983i 1.69816i 0.528261 + 0.849082i \(0.322844\pi\)
−0.528261 + 0.849082i \(0.677156\pi\)
\(542\) −0.817236 −0.0351033
\(543\) 11.5366 0.495082
\(544\) 134.162i 5.75213i
\(545\) −3.77584 −0.161739
\(546\) 0 0
\(547\) 37.0129 1.58256 0.791279 0.611455i \(-0.209416\pi\)
0.791279 + 0.611455i \(0.209416\pi\)
\(548\) 67.0131i 2.86266i
\(549\) 13.3265 0.568762
\(550\) −9.28012 −0.395706
\(551\) 38.6507i 1.64658i
\(552\) 48.5334i 2.06572i
\(553\) 0 0
\(554\) 23.8613i 1.01377i
\(555\) 6.87611 0.291874
\(556\) 28.7386 1.21879
\(557\) 24.0867i 1.02059i 0.860001 + 0.510293i \(0.170463\pi\)
−0.860001 + 0.510293i \(0.829537\pi\)
\(558\) 19.7055 0.834200
\(559\) 1.25028 7.75024i 0.0528811 0.327800i
\(560\) 0 0
\(561\) 16.1405i 0.681453i
\(562\) −67.5381 −2.84892
\(563\) −6.49397 −0.273688 −0.136844 0.990593i \(-0.543696\pi\)
−0.136844 + 0.990593i \(0.543696\pi\)
\(564\) 56.3646i 2.37338i
\(565\) 7.82569i 0.329229i
\(566\) 33.5006i 1.40814i
\(567\) 0 0
\(568\) 48.5951 2.03900
\(569\) −28.7638 −1.20584 −0.602921 0.797801i \(-0.705996\pi\)
−0.602921 + 0.797801i \(0.705996\pi\)
\(570\) 30.5570i 1.27989i
\(571\) 2.48615 0.104042 0.0520211 0.998646i \(-0.483434\pi\)
0.0520211 + 0.998646i \(0.483434\pi\)
\(572\) 44.8253 + 7.23127i 1.87424 + 0.302355i
\(573\) 6.24775 0.261003
\(574\) 0 0
\(575\) −6.52009 −0.271906
\(576\) 50.4962 2.10401
\(577\) 14.5747i 0.606755i 0.952871 + 0.303377i \(0.0981142\pi\)
−0.952871 + 0.303377i \(0.901886\pi\)
\(578\) 54.3117i 2.25907i
\(579\) 16.8383i 0.699775i
\(580\) 77.1476i 3.20338i
\(581\) 0 0
\(582\) 7.94003 0.329125
\(583\) 18.6279i 0.771489i
\(584\) 18.7126 0.774335
\(585\) 11.1177 + 1.79352i 0.459660 + 0.0741530i
\(586\) −40.0625 −1.65497
\(587\) 8.69744i 0.358982i 0.983760 + 0.179491i \(0.0574450\pi\)
−0.983760 + 0.179491i \(0.942555\pi\)
\(588\) 0 0
\(589\) 22.3087 0.919215
\(590\) 36.6461i 1.50870i
\(591\) 18.3859i 0.756296i
\(592\) 47.6356i 1.95781i
\(593\) 18.0299i 0.740399i 0.928952 + 0.370200i \(0.120711\pi\)
−0.928952 + 0.370200i \(0.879289\pi\)
\(594\) 33.8989 1.39089
\(595\) 0 0
\(596\) 13.0401i 0.534143i
\(597\) −0.431939 −0.0176781
\(598\) 42.9964 + 6.93623i 1.75825 + 0.283643i
\(599\) 0.0141162 0.000576774 0.000288387 1.00000i \(-0.499908\pi\)
0.000288387 1.00000i \(0.499908\pi\)
\(600\) 16.2135i 0.661914i
\(601\) −13.7533 −0.561007 −0.280504 0.959853i \(-0.590501\pi\)
−0.280504 + 0.959853i \(0.590501\pi\)
\(602\) 0 0
\(603\) 1.92553i 0.0784136i
\(604\) 111.207i 4.52493i
\(605\) 10.7215i 0.435891i
\(606\) 33.7564i 1.37126i
\(607\) −23.7484 −0.963918 −0.481959 0.876194i \(-0.660075\pi\)
−0.481959 + 0.876194i \(0.660075\pi\)
\(608\) 113.800 4.61519
\(609\) 0 0
\(610\) 41.1129 1.66461
\(611\) −31.6963 5.11328i −1.28229 0.206861i
\(612\) −55.3157 −2.23600
\(613\) 2.18410i 0.0882149i −0.999027 0.0441075i \(-0.985956\pi\)
0.999027 0.0441075i \(-0.0140444\pi\)
\(614\) 51.5910 2.08204
\(615\) −5.32625 −0.214775
\(616\) 0 0
\(617\) 14.6673i 0.590485i 0.955422 + 0.295243i \(0.0954005\pi\)
−0.955422 + 0.295243i \(0.904600\pi\)
\(618\) 37.3046i 1.50061i
\(619\) 21.2649i 0.854708i −0.904084 0.427354i \(-0.859446\pi\)
0.904084 0.427354i \(-0.140554\pi\)
\(620\) 44.5287 1.78832
\(621\) 23.8169 0.955740
\(622\) 15.5997i 0.625490i
\(623\) 0 0
\(624\) −9.97880 + 61.8567i −0.399472 + 2.47625i
\(625\) −15.4425 −0.617702
\(626\) 10.7819i 0.430931i
\(627\) 13.6909 0.546760
\(628\) 60.4560 2.41246
\(629\) 19.2388i 0.767099i
\(630\) 0 0
\(631\) 34.4910i 1.37307i −0.727099 0.686533i \(-0.759132\pi\)
0.727099 0.686533i \(-0.240868\pi\)
\(632\) 36.2289i 1.44111i
\(633\) 6.99649 0.278085
\(634\) 10.5025 0.417108
\(635\) 28.5199i 1.13178i
\(636\) −51.2717 −2.03305
\(637\) 0 0
\(638\) −47.1902 −1.86828
\(639\) 8.50737i 0.336546i
\(640\) 72.8199 2.87846
\(641\) −21.7944 −0.860829 −0.430414 0.902631i \(-0.641633\pi\)
−0.430414 + 0.902631i \(0.641633\pi\)
\(642\) 13.5190i 0.533551i
\(643\) 5.81898i 0.229478i −0.993396 0.114739i \(-0.963397\pi\)
0.993396 0.114739i \(-0.0366032\pi\)
\(644\) 0 0
\(645\) 4.72485i 0.186041i
\(646\) −85.4957 −3.36379
\(647\) −33.0708 −1.30015 −0.650074 0.759871i \(-0.725262\pi\)
−0.650074 + 0.759871i \(0.725262\pi\)
\(648\) 11.7894i 0.463130i
\(649\) −16.4191 −0.644505
\(650\) −14.3638 2.31718i −0.563394 0.0908873i
\(651\) 0 0
\(652\) 103.923i 4.06995i
\(653\) −1.73993 −0.0680886 −0.0340443 0.999420i \(-0.510839\pi\)
−0.0340443 + 0.999420i \(0.510839\pi\)
\(654\) −6.35706 −0.248581
\(655\) 1.78524i 0.0697551i
\(656\) 36.8986i 1.44065i
\(657\) 3.27596i 0.127807i
\(658\) 0 0
\(659\) 27.9823 1.09003 0.545017 0.838425i \(-0.316523\pi\)
0.545017 + 0.838425i \(0.316523\pi\)
\(660\) 27.3273 1.06371
\(661\) 20.8334i 0.810325i −0.914245 0.405163i \(-0.867215\pi\)
0.914245 0.405163i \(-0.132785\pi\)
\(662\) 16.7497 0.650995
\(663\) 4.03017 24.9823i 0.156519 0.970232i
\(664\) 23.6804 0.918976
\(665\) 0 0
\(666\) −14.4146 −0.558555
\(667\) −33.1552 −1.28378
\(668\) 118.993i 4.60397i
\(669\) 8.44565i 0.326528i
\(670\) 5.94034i 0.229496i
\(671\) 18.4204i 0.711112i
\(672\) 0 0
\(673\) −7.06203 −0.272221 −0.136111 0.990694i \(-0.543460\pi\)
−0.136111 + 0.990694i \(0.543460\pi\)
\(674\) 56.8784i 2.19088i
\(675\) −7.95650 −0.306246
\(676\) 67.5750 + 22.3851i 2.59904 + 0.860966i
\(677\) −5.22990 −0.201001 −0.100501 0.994937i \(-0.532044\pi\)
−0.100501 + 0.994937i \(0.532044\pi\)
\(678\) 13.1755i 0.506001i
\(679\) 0 0
\(680\) −108.323 −4.15399
\(681\) 18.1385i 0.695068i
\(682\) 27.2376i 1.04298i
\(683\) 27.9416i 1.06916i −0.845119 0.534579i \(-0.820470\pi\)
0.845119 0.534579i \(-0.179530\pi\)
\(684\) 46.9204i 1.79405i
\(685\) −22.9738 −0.877785
\(686\) 0 0
\(687\) 29.5498i 1.12740i
\(688\) −32.7324 −1.24791
\(689\) −4.65126 + 28.8323i −0.177199 + 1.09842i
\(690\) 26.2123 0.997884
\(691\) 25.4515i 0.968220i 0.875007 + 0.484110i \(0.160857\pi\)
−0.875007 + 0.484110i \(0.839143\pi\)
\(692\) −15.8965 −0.604293
\(693\) 0 0
\(694\) 48.5344i 1.84234i
\(695\) 9.85235i 0.373721i
\(696\) 82.4472i 3.12515i
\(697\) 14.9024i 0.564468i
\(698\) −2.74931 −0.104063
\(699\) 18.8888 0.714441
\(700\) 0 0
\(701\) −17.9541 −0.678117 −0.339058 0.940765i \(-0.610108\pi\)
−0.339058 + 0.940765i \(0.610108\pi\)
\(702\) 52.4687 + 8.46432i 1.98030 + 0.319465i
\(703\) −16.3189 −0.615478
\(704\) 69.7976i 2.63060i
\(705\) −19.3233 −0.727757
\(706\) 34.5109 1.29883
\(707\) 0 0
\(708\) 45.1921i 1.69842i
\(709\) 29.2191i 1.09734i 0.836037 + 0.548672i \(0.184867\pi\)
−0.836037 + 0.548672i \(0.815133\pi\)
\(710\) 26.2456i 0.984980i
\(711\) −6.34246 −0.237861
\(712\) 99.1152 3.71450
\(713\) 19.1368i 0.716679i
\(714\) 0 0
\(715\) 2.47907 15.3673i 0.0927120 0.574704i
\(716\) 105.959 3.95989
\(717\) 19.9407i 0.744698i
\(718\) 31.3749 1.17090
\(719\) 38.7200 1.44401 0.722005 0.691887i \(-0.243221\pi\)
0.722005 + 0.691887i \(0.243221\pi\)
\(720\) 46.9545i 1.74989i
\(721\) 0 0
\(722\) 20.5702i 0.765544i
\(723\) 11.6901i 0.434760i
\(724\) −54.6500 −2.03105
\(725\) 11.0761 0.411358
\(726\) 18.0509i 0.669931i
\(727\) −27.9441 −1.03639 −0.518194 0.855263i \(-0.673396\pi\)
−0.518194 + 0.855263i \(0.673396\pi\)
\(728\) 0 0
\(729\) 20.7594 0.768868
\(730\) 10.1065i 0.374057i
\(731\) 13.2197 0.488949
\(732\) 50.7006 1.87395
\(733\) 43.7436i 1.61571i −0.589382 0.807854i \(-0.700629\pi\)
0.589382 0.807854i \(-0.299371\pi\)
\(734\) 79.0497i 2.91778i
\(735\) 0 0
\(736\) 97.6195i 3.59830i
\(737\) −2.66154 −0.0980389
\(738\) 11.1656 0.411011
\(739\) 7.24471i 0.266501i −0.991082 0.133251i \(-0.957459\pi\)
0.991082 0.133251i \(-0.0425415\pi\)
\(740\) −32.5728 −1.19740
\(741\) 21.1907 + 3.41851i 0.778461 + 0.125582i
\(742\) 0 0
\(743\) 33.9142i 1.24419i 0.782941 + 0.622096i \(0.213719\pi\)
−0.782941 + 0.622096i \(0.786281\pi\)
\(744\) 47.5875 1.74464
\(745\) −4.47049 −0.163786
\(746\) 64.2232i 2.35138i
\(747\) 4.14563i 0.151681i
\(748\) 76.4593i 2.79563i
\(749\) 0 0
\(750\) −38.4232 −1.40302
\(751\) −38.4973 −1.40479 −0.702393 0.711789i \(-0.747885\pi\)
−0.702393 + 0.711789i \(0.747885\pi\)
\(752\) 133.866i 4.88159i
\(753\) 24.0650 0.876978
\(754\) −73.0411 11.7831i −2.66000 0.429114i
\(755\) −38.1245 −1.38749
\(756\) 0 0
\(757\) 8.18792 0.297595 0.148797 0.988868i \(-0.452460\pi\)
0.148797 + 0.988868i \(0.452460\pi\)
\(758\) −102.823 −3.73471
\(759\) 11.7443i 0.426289i
\(760\) 91.8826i 3.33293i
\(761\) 10.0596i 0.364660i 0.983237 + 0.182330i \(0.0583639\pi\)
−0.983237 + 0.182330i \(0.941636\pi\)
\(762\) 48.0166i 1.73946i
\(763\) 0 0
\(764\) −29.5962 −1.07075
\(765\) 18.9637i 0.685633i
\(766\) 69.2254 2.50121
\(767\) −25.4135 4.09973i −0.917627 0.148033i
\(768\) 52.4339 1.89205
\(769\) 2.53594i 0.0914482i 0.998954 + 0.0457241i \(0.0145595\pi\)
−0.998954 + 0.0457241i \(0.985440\pi\)
\(770\) 0 0
\(771\) 32.6320 1.17521
\(772\) 79.7648i 2.87080i
\(773\) 29.2195i 1.05095i 0.850808 + 0.525477i \(0.176113\pi\)
−0.850808 + 0.525477i \(0.823887\pi\)
\(774\) 9.90486i 0.356023i
\(775\) 6.39302i 0.229644i
\(776\) −23.8751 −0.857066
\(777\) 0 0
\(778\) 3.60612i 0.129286i
\(779\) 12.6406 0.452898
\(780\) 42.2971 + 6.82342i 1.51448 + 0.244318i
\(781\) −11.7592 −0.420777
\(782\) 73.3397i 2.62262i
\(783\) −40.4595 −1.44591
\(784\) 0 0
\(785\) 20.7259i 0.739739i
\(786\) 3.00566i 0.107208i
\(787\) 0.149447i 0.00532721i 0.999996 + 0.00266360i \(0.000847853\pi\)
−0.999996 + 0.00266360i \(0.999152\pi\)
\(788\) 87.0961i 3.10267i
\(789\) 7.06134 0.251390
\(790\) −19.5668 −0.696155
\(791\) 0 0
\(792\) −36.3636 −1.29212
\(793\) 4.59945 28.5111i 0.163331 1.01246i
\(794\) 102.124 3.62425
\(795\) 17.5773i <