Properties

Label 1008.2.r.m.673.4
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.508277025.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 21 x^{4} + 3 x^{3} - 22 x^{2} + 3 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.4
Root \(0.947217 - 0.807294i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.m.337.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +O(q^{10})\) \(q+(1.67275 - 0.449358i) q^{3} +(1.87447 + 3.24667i) q^{5} +(0.500000 - 0.866025i) q^{7} +(2.59615 - 1.50332i) q^{9} +(-1.82552 + 3.16190i) q^{11} +(2.77274 + 4.80253i) q^{13} +(4.59442 + 4.58854i) q^{15} -7.20767 q^{17} +3.30555 q^{19} +(0.447217 - 1.67332i) q^{21} +(-2.49443 - 4.32048i) q^{23} +(-4.52724 + 7.84141i) q^{25} +(3.66717 - 3.68128i) q^{27} +(-0.245497 + 0.425213i) q^{29} +(-1.94722 - 3.37268i) q^{31} +(-1.63281 + 6.10936i) q^{33} +3.74893 q^{35} +7.89443 q^{37} +(6.79614 + 6.78745i) q^{39} +(-2.38215 - 4.12600i) q^{41} +(-0.801714 + 1.38861i) q^{43} +(9.74720 + 5.61092i) q^{45} +(4.81995 - 8.34840i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-12.0566 + 3.23883i) q^{51} -8.03647 q^{53} -13.6875 q^{55} +(5.52935 - 1.48538i) q^{57} +(-0.754503 - 1.30684i) q^{59} +(1.04337 - 1.80717i) q^{61} +(-0.00384004 - 3.00000i) q^{63} +(-10.3948 + 18.0043i) q^{65} +(1.70172 + 2.94747i) q^{67} +(-6.11398 - 6.10616i) q^{69} +10.7301 q^{71} +9.83567 q^{73} +(-4.04932 + 15.1510i) q^{75} +(1.82552 + 3.16190i) q^{77} +(1.86391 - 3.22839i) q^{79} +(4.48003 - 7.80572i) q^{81} +(-5.69058 + 9.85637i) q^{83} +(-13.5105 - 23.4009i) q^{85} +(-0.219580 + 0.821588i) q^{87} +7.14891 q^{89} +5.54548 q^{91} +(-4.77274 - 4.76663i) q^{93} +(6.19615 + 10.7320i) q^{95} +(5.45316 - 9.44516i) q^{97} +(0.0140201 + 10.9531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + 6q^{11} - 3q^{13} - 4q^{15} - 16q^{17} + 4q^{19} - q^{21} + 5q^{23} - 14q^{25} - 5q^{27} + q^{29} - 11q^{31} + 8q^{35} + 54q^{37} + 12q^{39} + 2q^{41} + 11q^{43} + 26q^{45} - 7q^{47} - 4q^{49} - 17q^{51} - 8q^{53} - 12q^{55} - 13q^{57} - 9q^{59} - 7q^{61} + 5q^{63} - 9q^{65} + 12q^{67} + 4q^{69} + 24q^{71} + 26q^{73} + 23q^{75} - 6q^{77} + 22q^{79} + 34q^{81} + 6q^{83} - 11q^{85} - 37q^{87} - 28q^{89} - 6q^{91} - 13q^{93} + 23q^{95} - q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.67275 0.449358i 0.965760 0.259437i
\(4\) 0 0
\(5\) 1.87447 + 3.24667i 0.838287 + 1.45195i 0.891326 + 0.453362i \(0.149776\pi\)
−0.0530397 + 0.998592i \(0.516891\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) 2.59615 1.50332i 0.865385 0.501108i
\(10\) 0 0
\(11\) −1.82552 + 3.16190i −0.550416 + 0.953348i 0.447829 + 0.894119i \(0.352197\pi\)
−0.998244 + 0.0592287i \(0.981136\pi\)
\(12\) 0 0
\(13\) 2.77274 + 4.80253i 0.769020 + 1.33198i 0.938095 + 0.346378i \(0.112588\pi\)
−0.169076 + 0.985603i \(0.554078\pi\)
\(14\) 0 0
\(15\) 4.59442 + 4.58854i 1.18627 + 1.18476i
\(16\) 0 0
\(17\) −7.20767 −1.74812 −0.874058 0.485821i \(-0.838521\pi\)
−0.874058 + 0.485821i \(0.838521\pi\)
\(18\) 0 0
\(19\) 3.30555 0.758346 0.379173 0.925326i \(-0.376208\pi\)
0.379173 + 0.925326i \(0.376208\pi\)
\(20\) 0 0
\(21\) 0.447217 1.67332i 0.0975907 0.365148i
\(22\) 0 0
\(23\) −2.49443 4.32048i −0.520124 0.900881i −0.999726 0.0233954i \(-0.992552\pi\)
0.479602 0.877486i \(-0.340781\pi\)
\(24\) 0 0
\(25\) −4.52724 + 7.84141i −0.905449 + 1.56828i
\(26\) 0 0
\(27\) 3.66717 3.68128i 0.705748 0.708463i
\(28\) 0 0
\(29\) −0.245497 + 0.425213i −0.0455876 + 0.0789600i −0.887919 0.460000i \(-0.847849\pi\)
0.842331 + 0.538960i \(0.181183\pi\)
\(30\) 0 0
\(31\) −1.94722 3.37268i −0.349730 0.605751i 0.636471 0.771301i \(-0.280394\pi\)
−0.986201 + 0.165550i \(0.947060\pi\)
\(32\) 0 0
\(33\) −1.63281 + 6.10936i −0.284236 + 1.06350i
\(34\) 0 0
\(35\) 3.74893 0.633685
\(36\) 0 0
\(37\) 7.89443 1.29784 0.648918 0.760858i \(-0.275222\pi\)
0.648918 + 0.760858i \(0.275222\pi\)
\(38\) 0 0
\(39\) 6.79614 + 6.78745i 1.08825 + 1.08686i
\(40\) 0 0
\(41\) −2.38215 4.12600i −0.372029 0.644373i 0.617849 0.786297i \(-0.288004\pi\)
−0.989878 + 0.141924i \(0.954671\pi\)
\(42\) 0 0
\(43\) −0.801714 + 1.38861i −0.122260 + 0.211761i −0.920659 0.390369i \(-0.872348\pi\)
0.798398 + 0.602130i \(0.205681\pi\)
\(44\) 0 0
\(45\) 9.74720 + 5.61092i 1.45303 + 0.836427i
\(46\) 0 0
\(47\) 4.81995 8.34840i 0.703062 1.21774i −0.264324 0.964434i \(-0.585149\pi\)
0.967386 0.253305i \(-0.0815177\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −12.0566 + 3.23883i −1.68826 + 0.453526i
\(52\) 0 0
\(53\) −8.03647 −1.10389 −0.551947 0.833879i \(-0.686115\pi\)
−0.551947 + 0.833879i \(0.686115\pi\)
\(54\) 0 0
\(55\) −13.6875 −1.84562
\(56\) 0 0
\(57\) 5.52935 1.48538i 0.732380 0.196743i
\(58\) 0 0
\(59\) −0.754503 1.30684i −0.0982280 0.170136i 0.812723 0.582650i \(-0.197984\pi\)
−0.910951 + 0.412514i \(0.864651\pi\)
\(60\) 0 0
\(61\) 1.04337 1.80717i 0.133590 0.231385i −0.791468 0.611211i \(-0.790683\pi\)
0.925058 + 0.379826i \(0.124016\pi\)
\(62\) 0 0
\(63\) −0.00384004 3.00000i −0.000483799 0.377964i
\(64\) 0 0
\(65\) −10.3948 + 18.0043i −1.28932 + 2.23316i
\(66\) 0 0
\(67\) 1.70172 + 2.94747i 0.207898 + 0.360090i 0.951052 0.309030i \(-0.100004\pi\)
−0.743154 + 0.669120i \(0.766671\pi\)
\(68\) 0 0
\(69\) −6.11398 6.10616i −0.736037 0.735096i
\(70\) 0 0
\(71\) 10.7301 1.27343 0.636715 0.771099i \(-0.280293\pi\)
0.636715 + 0.771099i \(0.280293\pi\)
\(72\) 0 0
\(73\) 9.83567 1.15118 0.575589 0.817739i \(-0.304773\pi\)
0.575589 + 0.817739i \(0.304773\pi\)
\(74\) 0 0
\(75\) −4.04932 + 15.1510i −0.467575 + 1.74949i
\(76\) 0 0
\(77\) 1.82552 + 3.16190i 0.208038 + 0.360332i
\(78\) 0 0
\(79\) 1.86391 3.22839i 0.209706 0.363222i −0.741916 0.670493i \(-0.766083\pi\)
0.951622 + 0.307271i \(0.0994159\pi\)
\(80\) 0 0
\(81\) 4.48003 7.80572i 0.497781 0.867303i
\(82\) 0 0
\(83\) −5.69058 + 9.85637i −0.624622 + 1.08188i 0.363992 + 0.931402i \(0.381414\pi\)
−0.988614 + 0.150475i \(0.951920\pi\)
\(84\) 0 0
\(85\) −13.5105 23.4009i −1.46542 2.53819i
\(86\) 0 0
\(87\) −0.219580 + 0.821588i −0.0235415 + 0.0880835i
\(88\) 0 0
\(89\) 7.14891 0.757783 0.378891 0.925441i \(-0.376305\pi\)
0.378891 + 0.925441i \(0.376305\pi\)
\(90\) 0 0
\(91\) 5.54548 0.581324
\(92\) 0 0
\(93\) −4.77274 4.76663i −0.494910 0.494277i
\(94\) 0 0
\(95\) 6.19615 + 10.7320i 0.635711 + 1.10108i
\(96\) 0 0
\(97\) 5.45316 9.44516i 0.553685 0.959011i −0.444320 0.895868i \(-0.646555\pi\)
0.998005 0.0631422i \(-0.0201122\pi\)
\(98\) 0 0
\(99\) 0.0140201 + 10.9531i 0.00140908 + 1.10083i
\(100\) 0 0
\(101\) 6.40171 11.0881i 0.636994 1.10331i −0.349095 0.937087i \(-0.613511\pi\)
0.986089 0.166218i \(-0.0531557\pi\)
\(102\) 0 0
\(103\) −4.76717 8.25698i −0.469723 0.813584i 0.529678 0.848199i \(-0.322313\pi\)
−0.999401 + 0.0346149i \(0.988980\pi\)
\(104\) 0 0
\(105\) 6.27101 1.68461i 0.611988 0.164401i
\(106\) 0 0
\(107\) −8.43223 −0.815175 −0.407587 0.913166i \(-0.633630\pi\)
−0.407587 + 0.913166i \(0.633630\pi\)
\(108\) 0 0
\(109\) 16.5574 1.58591 0.792954 0.609281i \(-0.208542\pi\)
0.792954 + 0.609281i \(0.208542\pi\)
\(110\) 0 0
\(111\) 13.2054 3.54743i 1.25340 0.336707i
\(112\) 0 0
\(113\) −0.0328150 0.0568372i −0.00308697 0.00534679i 0.864478 0.502671i \(-0.167649\pi\)
−0.867565 + 0.497324i \(0.834316\pi\)
\(114\) 0 0
\(115\) 9.35144 16.1972i 0.872026 1.51039i
\(116\) 0 0
\(117\) 14.4182 + 8.29977i 1.33296 + 0.767314i
\(118\) 0 0
\(119\) −3.60383 + 6.24202i −0.330363 + 0.572205i
\(120\) 0 0
\(121\) −1.16507 2.01795i −0.105915 0.183450i
\(122\) 0 0
\(123\) −5.83877 5.83131i −0.526465 0.525791i
\(124\) 0 0
\(125\) −15.2000 −1.35953
\(126\) 0 0
\(127\) −3.20080 −0.284025 −0.142012 0.989865i \(-0.545357\pi\)
−0.142012 + 0.989865i \(0.545357\pi\)
\(128\) 0 0
\(129\) −0.717080 + 2.68305i −0.0631354 + 0.236229i
\(130\) 0 0
\(131\) 7.67061 + 13.2859i 0.670184 + 1.16079i 0.977852 + 0.209299i \(0.0671182\pi\)
−0.307668 + 0.951494i \(0.599548\pi\)
\(132\) 0 0
\(133\) 1.65278 2.86269i 0.143314 0.248227i
\(134\) 0 0
\(135\) 18.8259 + 5.00566i 1.62028 + 0.430819i
\(136\) 0 0
\(137\) −0.342977 + 0.594054i −0.0293025 + 0.0507535i −0.880305 0.474409i \(-0.842662\pi\)
0.851002 + 0.525162i \(0.175995\pi\)
\(138\) 0 0
\(139\) −10.1004 17.4944i −0.856702 1.48385i −0.875057 0.484020i \(-0.839176\pi\)
0.0183546 0.999832i \(-0.494157\pi\)
\(140\) 0 0
\(141\) 4.31113 16.1306i 0.363062 1.35844i
\(142\) 0 0
\(143\) −20.2468 −1.69312
\(144\) 0 0
\(145\) −1.84070 −0.152862
\(146\) 0 0
\(147\) −1.22553 1.22396i −0.101080 0.100951i
\(148\) 0 0
\(149\) 4.31652 + 7.47642i 0.353623 + 0.612493i 0.986881 0.161448i \(-0.0516163\pi\)
−0.633259 + 0.773940i \(0.718283\pi\)
\(150\) 0 0
\(151\) −5.43836 + 9.41952i −0.442568 + 0.766550i −0.997879 0.0650926i \(-0.979266\pi\)
0.555311 + 0.831642i \(0.312599\pi\)
\(152\) 0 0
\(153\) −18.7122 + 10.8355i −1.51279 + 0.875995i
\(154\) 0 0
\(155\) 7.29998 12.6439i 0.586349 1.01559i
\(156\) 0 0
\(157\) 5.49613 + 9.51958i 0.438639 + 0.759745i 0.997585 0.0694592i \(-0.0221274\pi\)
−0.558946 + 0.829204i \(0.688794\pi\)
\(158\) 0 0
\(159\) −13.4430 + 3.61126i −1.06610 + 0.286391i
\(160\) 0 0
\(161\) −4.98886 −0.393177
\(162\) 0 0
\(163\) −4.79233 −0.375364 −0.187682 0.982230i \(-0.560098\pi\)
−0.187682 + 0.982230i \(0.560098\pi\)
\(164\) 0 0
\(165\) −22.8957 + 6.15060i −1.78243 + 0.478824i
\(166\) 0 0
\(167\) 1.46719 + 2.54124i 0.113534 + 0.196647i 0.917193 0.398444i \(-0.130450\pi\)
−0.803659 + 0.595091i \(0.797116\pi\)
\(168\) 0 0
\(169\) −8.87617 + 15.3740i −0.682782 + 1.18261i
\(170\) 0 0
\(171\) 8.58173 4.96932i 0.656261 0.380013i
\(172\) 0 0
\(173\) 5.99483 10.3834i 0.455779 0.789432i −0.542954 0.839763i \(-0.682694\pi\)
0.998733 + 0.0503306i \(0.0160275\pi\)
\(174\) 0 0
\(175\) 4.52724 + 7.84141i 0.342227 + 0.592755i
\(176\) 0 0
\(177\) −1.84933 1.84697i −0.139004 0.138826i
\(178\) 0 0
\(179\) −24.9266 −1.86310 −0.931552 0.363608i \(-0.881545\pi\)
−0.931552 + 0.363608i \(0.881545\pi\)
\(180\) 0 0
\(181\) −21.4203 −1.59216 −0.796078 0.605194i \(-0.793096\pi\)
−0.796078 + 0.605194i \(0.793096\pi\)
\(182\) 0 0
\(183\) 0.933226 3.49179i 0.0689861 0.258120i
\(184\) 0 0
\(185\) 14.7978 + 25.6306i 1.08796 + 1.88440i
\(186\) 0 0
\(187\) 13.1578 22.7899i 0.962191 1.66656i
\(188\) 0 0
\(189\) −1.35450 5.01651i −0.0985252 0.364897i
\(190\) 0 0
\(191\) 8.98003 15.5539i 0.649772 1.12544i −0.333405 0.942784i \(-0.608198\pi\)
0.983177 0.182655i \(-0.0584691\pi\)
\(192\) 0 0
\(193\) −4.68943 8.12233i −0.337553 0.584658i 0.646419 0.762983i \(-0.276266\pi\)
−0.983972 + 0.178324i \(0.942932\pi\)
\(194\) 0 0
\(195\) −9.29747 + 34.7877i −0.665806 + 2.49120i
\(196\) 0 0
\(197\) −0.206917 −0.0147422 −0.00737110 0.999973i \(-0.502346\pi\)
−0.00737110 + 0.999973i \(0.502346\pi\)
\(198\) 0 0
\(199\) −12.6169 −0.894386 −0.447193 0.894438i \(-0.647576\pi\)
−0.447193 + 0.894438i \(0.647576\pi\)
\(200\) 0 0
\(201\) 4.17101 + 4.16568i 0.294201 + 0.293824i
\(202\) 0 0
\(203\) 0.245497 + 0.425213i 0.0172305 + 0.0298441i
\(204\) 0 0
\(205\) 8.93050 15.4681i 0.623733 1.08034i
\(206\) 0 0
\(207\) −12.9710 7.46669i −0.901547 0.518971i
\(208\) 0 0
\(209\) −6.03436 + 10.4518i −0.417406 + 0.722968i
\(210\) 0 0
\(211\) −2.96505 5.13561i −0.204122 0.353550i 0.745730 0.666248i \(-0.232101\pi\)
−0.949853 + 0.312698i \(0.898767\pi\)
\(212\) 0 0
\(213\) 17.9487 4.82166i 1.22983 0.330375i
\(214\) 0 0
\(215\) −6.01114 −0.409957
\(216\) 0 0
\(217\) −3.89443 −0.264371
\(218\) 0 0
\(219\) 16.4526 4.41974i 1.11176 0.298659i
\(220\) 0 0
\(221\) −19.9850 34.6150i −1.34434 2.32846i
\(222\) 0 0
\(223\) −1.80500 + 3.12634i −0.120871 + 0.209355i −0.920112 0.391656i \(-0.871902\pi\)
0.799240 + 0.601012i \(0.205236\pi\)
\(224\) 0 0
\(225\) 0.0347696 + 27.1634i 0.00231797 + 1.81090i
\(226\) 0 0
\(227\) −9.30710 + 16.1204i −0.617734 + 1.06995i 0.372164 + 0.928167i \(0.378616\pi\)
−0.989898 + 0.141780i \(0.954717\pi\)
\(228\) 0 0
\(229\) −11.4965 19.9126i −0.759712 1.31586i −0.942997 0.332801i \(-0.892006\pi\)
0.183285 0.983060i \(-0.441327\pi\)
\(230\) 0 0
\(231\) 4.47446 + 4.46874i 0.294398 + 0.294021i
\(232\) 0 0
\(233\) −4.07066 −0.266678 −0.133339 0.991071i \(-0.542570\pi\)
−0.133339 + 0.991071i \(0.542570\pi\)
\(234\) 0 0
\(235\) 36.1393 2.35747
\(236\) 0 0
\(237\) 1.66714 6.23783i 0.108293 0.405191i
\(238\) 0 0
\(239\) 2.50000 + 4.33013i 0.161712 + 0.280093i 0.935483 0.353373i \(-0.114965\pi\)
−0.773771 + 0.633465i \(0.781632\pi\)
\(240\) 0 0
\(241\) −7.30843 + 12.6586i −0.470777 + 0.815410i −0.999441 0.0334208i \(-0.989360\pi\)
0.528664 + 0.848831i \(0.322693\pi\)
\(242\) 0 0
\(243\) 3.98639 15.0701i 0.255727 0.966749i
\(244\) 0 0
\(245\) 1.87447 3.24667i 0.119755 0.207422i
\(246\) 0 0
\(247\) 9.16544 + 15.8750i 0.583183 + 1.01010i
\(248\) 0 0
\(249\) −5.08984 + 19.0443i −0.322556 + 1.20688i
\(250\) 0 0
\(251\) −8.74206 −0.551794 −0.275897 0.961187i \(-0.588975\pi\)
−0.275897 + 0.961187i \(0.588975\pi\)
\(252\) 0 0
\(253\) 18.2145 1.14514
\(254\) 0 0
\(255\) −33.1151 33.0727i −2.07375 2.07109i
\(256\) 0 0
\(257\) −10.6399 18.4288i −0.663699 1.14956i −0.979636 0.200780i \(-0.935652\pi\)
0.315938 0.948780i \(-0.397681\pi\)
\(258\) 0 0
\(259\) 3.94722 6.83678i 0.245268 0.424817i
\(260\) 0 0
\(261\) 0.00188543 + 1.47298i 0.000116705 + 0.0911751i
\(262\) 0 0
\(263\) 6.80515 11.7869i 0.419623 0.726809i −0.576278 0.817254i \(-0.695495\pi\)
0.995901 + 0.0904446i \(0.0288288\pi\)
\(264\) 0 0
\(265\) −15.0641 26.0918i −0.925380 1.60280i
\(266\) 0 0
\(267\) 11.9583 3.21242i 0.731836 0.196597i
\(268\) 0 0
\(269\) −18.9343 −1.15445 −0.577223 0.816587i \(-0.695864\pi\)
−0.577223 + 0.816587i \(0.695864\pi\)
\(270\) 0 0
\(271\) −14.1669 −0.860579 −0.430290 0.902691i \(-0.641589\pi\)
−0.430290 + 0.902691i \(0.641589\pi\)
\(272\) 0 0
\(273\) 9.27617 2.49191i 0.561420 0.150817i
\(274\) 0 0
\(275\) −16.5292 28.6294i −0.996746 1.72642i
\(276\) 0 0
\(277\) −0.636090 + 1.10174i −0.0382190 + 0.0661972i −0.884502 0.466536i \(-0.845502\pi\)
0.846283 + 0.532733i \(0.178835\pi\)
\(278\) 0 0
\(279\) −10.1255 5.82869i −0.606198 0.348955i
\(280\) 0 0
\(281\) 4.66891 8.08678i 0.278524 0.482417i −0.692494 0.721423i \(-0.743488\pi\)
0.971018 + 0.239006i \(0.0768216\pi\)
\(282\) 0 0
\(283\) 4.88983 + 8.46943i 0.290670 + 0.503455i 0.973968 0.226684i \(-0.0727885\pi\)
−0.683298 + 0.730139i \(0.739455\pi\)
\(284\) 0 0
\(285\) 15.1871 + 15.1677i 0.899607 + 0.898456i
\(286\) 0 0
\(287\) −4.76429 −0.281227
\(288\) 0 0
\(289\) 34.9505 2.05591
\(290\) 0 0
\(291\) 4.87749 18.2498i 0.285924 1.06982i
\(292\) 0 0
\(293\) 12.0672 + 20.9010i 0.704972 + 1.22105i 0.966702 + 0.255906i \(0.0823738\pi\)
−0.261729 + 0.965141i \(0.584293\pi\)
\(294\) 0 0
\(295\) 2.82858 4.89925i 0.164686 0.285245i
\(296\) 0 0
\(297\) 4.94533 + 18.3155i 0.286957 + 1.06277i
\(298\) 0 0
\(299\) 13.8328 23.9591i 0.799971 1.38559i
\(300\) 0 0
\(301\) 0.801714 + 1.38861i 0.0462100 + 0.0800382i
\(302\) 0 0
\(303\) 5.72590 21.4242i 0.328945 1.23079i
\(304\) 0 0
\(305\) 7.82305 0.447947
\(306\) 0 0
\(307\) −20.0425 −1.14389 −0.571944 0.820293i \(-0.693810\pi\)
−0.571944 + 0.820293i \(0.693810\pi\)
\(308\) 0 0
\(309\) −11.6846 11.6697i −0.664714 0.663863i
\(310\) 0 0
\(311\) 6.56758 + 11.3754i 0.372414 + 0.645039i 0.989936 0.141514i \(-0.0451970\pi\)
−0.617523 + 0.786553i \(0.711864\pi\)
\(312\) 0 0
\(313\) −6.29311 + 10.9000i −0.355708 + 0.616104i −0.987239 0.159247i \(-0.949093\pi\)
0.631531 + 0.775351i \(0.282427\pi\)
\(314\) 0 0
\(315\) 9.73280 5.63586i 0.548381 0.317545i
\(316\) 0 0
\(317\) 5.36679 9.29555i 0.301429 0.522090i −0.675031 0.737789i \(-0.735870\pi\)
0.976460 + 0.215699i \(0.0692031\pi\)
\(318\) 0 0
\(319\) −0.896319 1.55247i −0.0501842 0.0869217i
\(320\) 0 0
\(321\) −14.1050 + 3.78909i −0.787263 + 0.211487i
\(322\) 0 0
\(323\) −23.8253 −1.32568
\(324\) 0 0
\(325\) −50.2115 −2.78523
\(326\) 0 0
\(327\) 27.6963 7.44020i 1.53161 0.411444i
\(328\) 0 0
\(329\) −4.81995 8.34840i −0.265732 0.460262i
\(330\) 0 0
\(331\) −5.61919 + 9.73273i −0.308859 + 0.534959i −0.978113 0.208074i \(-0.933280\pi\)
0.669254 + 0.743034i \(0.266614\pi\)
\(332\) 0 0
\(333\) 20.4952 11.8679i 1.12313 0.650357i
\(334\) 0 0
\(335\) −6.37963 + 11.0498i −0.348557 + 0.603718i
\(336\) 0 0
\(337\) −1.35453 2.34611i −0.0737858 0.127801i 0.826772 0.562537i \(-0.190175\pi\)
−0.900558 + 0.434737i \(0.856841\pi\)
\(338\) 0 0
\(339\) −0.0804313 0.0803284i −0.00436843 0.00436284i
\(340\) 0 0
\(341\) 14.2188 0.769989
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 8.36424 31.2959i 0.450316 1.68491i
\(346\) 0 0
\(347\) −4.77314 8.26733i −0.256236 0.443813i 0.708995 0.705214i \(-0.249149\pi\)
−0.965230 + 0.261400i \(0.915816\pi\)
\(348\) 0 0
\(349\) 1.01114 1.75135i 0.0541253 0.0937478i −0.837693 0.546141i \(-0.816096\pi\)
0.891819 + 0.452393i \(0.149430\pi\)
\(350\) 0 0
\(351\) 27.8476 + 7.40446i 1.48639 + 0.395221i
\(352\) 0 0
\(353\) −5.93836 + 10.2855i −0.316067 + 0.547444i −0.979664 0.200646i \(-0.935696\pi\)
0.663597 + 0.748091i \(0.269029\pi\)
\(354\) 0 0
\(355\) 20.1132 + 34.8371i 1.06750 + 1.84896i
\(356\) 0 0
\(357\) −3.22339 + 12.0607i −0.170600 + 0.638321i
\(358\) 0 0
\(359\) 13.9796 0.737817 0.368909 0.929466i \(-0.379732\pi\)
0.368909 + 0.929466i \(0.379732\pi\)
\(360\) 0 0
\(361\) −8.07331 −0.424911
\(362\) 0 0
\(363\) −2.85564 2.85199i −0.149882 0.149691i
\(364\) 0 0
\(365\) 18.4366 + 31.9332i 0.965017 + 1.67146i
\(366\) 0 0
\(367\) −1.14299 + 1.97972i −0.0596635 + 0.103340i −0.894314 0.447439i \(-0.852336\pi\)
0.834651 + 0.550779i \(0.185669\pi\)
\(368\) 0 0
\(369\) −12.3871 7.13059i −0.644848 0.371204i
\(370\) 0 0
\(371\) −4.01824 + 6.95979i −0.208616 + 0.361334i
\(372\) 0 0
\(373\) 17.0527 + 29.5362i 0.882957 + 1.52933i 0.848038 + 0.529936i \(0.177784\pi\)
0.0349186 + 0.999390i \(0.488883\pi\)
\(374\) 0 0
\(375\) −25.4257 + 6.83024i −1.31298 + 0.352712i
\(376\) 0 0
\(377\) −2.72279 −0.140231
\(378\) 0 0
\(379\) 6.50473 0.334126 0.167063 0.985946i \(-0.446572\pi\)
0.167063 + 0.985946i \(0.446572\pi\)
\(380\) 0 0
\(381\) −5.35412 + 1.43831i −0.274300 + 0.0736866i
\(382\) 0 0
\(383\) 11.2348 + 19.4592i 0.574069 + 0.994317i 0.996142 + 0.0877552i \(0.0279693\pi\)
−0.422073 + 0.906562i \(0.638697\pi\)
\(384\) 0 0
\(385\) −6.84376 + 11.8537i −0.348790 + 0.604122i
\(386\) 0 0
\(387\) 0.00615723 + 4.81028i 0.000312989 + 0.244520i
\(388\) 0 0
\(389\) 2.57316 4.45684i 0.130464 0.225971i −0.793391 0.608712i \(-0.791687\pi\)
0.923856 + 0.382741i \(0.125020\pi\)
\(390\) 0 0
\(391\) 17.9790 + 31.1406i 0.909238 + 1.57485i
\(392\) 0 0
\(393\) 18.8011 + 18.7770i 0.948390 + 0.947177i
\(394\) 0 0
\(395\) 13.9753 0.703176
\(396\) 0 0
\(397\) −21.0214 −1.05503 −0.527517 0.849544i \(-0.676877\pi\)
−0.527517 + 0.849544i \(0.676877\pi\)
\(398\) 0 0
\(399\) 1.47830 5.53125i 0.0740076 0.276909i
\(400\) 0 0
\(401\) 0.803852 + 1.39231i 0.0401424 + 0.0695288i 0.885399 0.464833i \(-0.153885\pi\)
−0.845256 + 0.534361i \(0.820552\pi\)
\(402\) 0 0
\(403\) 10.7983 18.7031i 0.537899 0.931669i
\(404\) 0 0
\(405\) 33.7403 0.0863761i 1.67657 0.00429207i
\(406\) 0 0
\(407\) −14.4115 + 24.9614i −0.714350 + 1.23729i
\(408\) 0 0
\(409\) −10.7055 18.5425i −0.529354 0.916869i −0.999414 0.0342340i \(-0.989101\pi\)
0.470059 0.882635i \(-0.344232\pi\)
\(410\) 0 0
\(411\) −0.306771 + 1.14782i −0.0151319 + 0.0566178i
\(412\) 0 0
\(413\) −1.50901 −0.0742534
\(414\) 0 0
\(415\) −42.6672 −2.09445
\(416\) 0 0
\(417\) −24.7566 24.7249i −1.21234 1.21078i
\(418\) 0 0
\(419\) −17.3497 30.0505i −0.847587 1.46806i −0.883355 0.468704i \(-0.844721\pi\)
0.0357681 0.999360i \(-0.488612\pi\)
\(420\) 0 0
\(421\) 11.6234 20.1323i 0.566488 0.981186i −0.430421 0.902628i \(-0.641635\pi\)
0.996910 0.0785583i \(-0.0250317\pi\)
\(422\) 0 0
\(423\) −0.0370176 28.9197i −0.00179986 1.40612i
\(424\) 0 0
\(425\) 32.6309 56.5183i 1.58283 2.74154i
\(426\) 0 0
\(427\) −1.04337 1.80717i −0.0504923 0.0874552i
\(428\) 0 0
\(429\) −33.8677 + 9.09807i −1.63515 + 0.439259i
\(430\) 0 0
\(431\) −10.5201 −0.506735 −0.253368 0.967370i \(-0.581538\pi\)
−0.253368 + 0.967370i \(0.581538\pi\)
\(432\) 0 0
\(433\) −29.8296 −1.43352 −0.716758 0.697322i \(-0.754375\pi\)
−0.716758 + 0.697322i \(0.754375\pi\)
\(434\) 0 0
\(435\) −3.07902 + 0.827134i −0.147628 + 0.0396580i
\(436\) 0 0
\(437\) −8.24547 14.2816i −0.394434 0.683180i
\(438\) 0 0
\(439\) 2.28462 3.95708i 0.109039 0.188861i −0.806342 0.591449i \(-0.798556\pi\)
0.915381 + 0.402588i \(0.131889\pi\)
\(440\) 0 0
\(441\) −2.59999 1.49667i −0.123809 0.0712702i
\(442\) 0 0
\(443\) −5.01455 + 8.68545i −0.238248 + 0.412658i −0.960212 0.279273i \(-0.909907\pi\)
0.721963 + 0.691931i \(0.243240\pi\)
\(444\) 0 0
\(445\) 13.4004 + 23.2101i 0.635239 + 1.10027i
\(446\) 0 0
\(447\) 10.5800 + 10.5665i 0.500418 + 0.499778i
\(448\) 0 0
\(449\) −18.1908 −0.858476 −0.429238 0.903192i \(-0.641218\pi\)
−0.429238 + 0.903192i \(0.641218\pi\)
\(450\) 0 0
\(451\) 17.3946 0.819082
\(452\) 0 0
\(453\) −4.86426 + 18.2002i −0.228543 + 0.855122i
\(454\) 0 0
\(455\) 10.3948 + 18.0043i 0.487316 + 0.844056i
\(456\) 0 0
\(457\) 2.62708 4.55024i 0.122890 0.212851i −0.798016 0.602636i \(-0.794117\pi\)
0.920906 + 0.389784i \(0.127451\pi\)
\(458\) 0 0
\(459\) −26.4318 + 26.5335i −1.23373 + 1.23848i
\(460\) 0 0
\(461\) −4.32763 + 7.49568i −0.201558 + 0.349108i −0.949031 0.315184i \(-0.897934\pi\)
0.747473 + 0.664293i \(0.231267\pi\)
\(462\) 0 0
\(463\) −0.509788 0.882979i −0.0236919 0.0410355i 0.853936 0.520377i \(-0.174209\pi\)
−0.877628 + 0.479342i \(0.840875\pi\)
\(464\) 0 0
\(465\) 6.52935 24.4304i 0.302791 1.13293i
\(466\) 0 0
\(467\) −18.7167 −0.866104 −0.433052 0.901369i \(-0.642563\pi\)
−0.433052 + 0.901369i \(0.642563\pi\)
\(468\) 0 0
\(469\) 3.40344 0.157156
\(470\) 0 0
\(471\) 13.4713 + 13.4541i 0.620726 + 0.619932i
\(472\) 0 0
\(473\) −2.92710 5.06988i −0.134588 0.233113i
\(474\) 0 0
\(475\) −14.9650 + 25.9202i −0.686643 + 1.18930i
\(476\) 0 0
\(477\) −20.8639 + 12.0814i −0.955293 + 0.553170i
\(478\) 0 0
\(479\) −18.3255 + 31.7407i −0.837313 + 1.45027i 0.0548199 + 0.998496i \(0.482542\pi\)
−0.892133 + 0.451773i \(0.850792\pi\)
\(480\) 0 0
\(481\) 21.8892 + 37.9132i 0.998062 + 1.72869i
\(482\) 0 0
\(483\) −8.34509 + 2.24178i −0.379715 + 0.102005i
\(484\) 0 0
\(485\) 40.8871 1.85659
\(486\) 0 0
\(487\) 35.1877 1.59451 0.797253 0.603646i \(-0.206286\pi\)
0.797253 + 0.603646i \(0.206286\pi\)
\(488\) 0 0
\(489\) −8.01635 + 2.15347i −0.362512 + 0.0973835i
\(490\) 0 0
\(491\) 9.15489 + 15.8567i 0.413154 + 0.715604i 0.995233 0.0975285i \(-0.0310937\pi\)
−0.582079 + 0.813133i \(0.697760\pi\)
\(492\) 0 0
\(493\) 1.76946 3.06479i 0.0796924 0.138031i
\(494\) 0 0
\(495\) −35.5349 + 20.5768i −1.59718 + 0.924857i
\(496\) 0 0
\(497\) 5.36505 9.29255i 0.240656 0.416828i
\(498\) 0 0
\(499\) 12.2791 + 21.2679i 0.549686 + 0.952084i 0.998296 + 0.0583561i \(0.0185859\pi\)
−0.448610 + 0.893728i \(0.648081\pi\)
\(500\) 0 0
\(501\) 3.59615 + 3.59155i 0.160664 + 0.160459i
\(502\) 0 0
\(503\) 17.0176 0.758779 0.379390 0.925237i \(-0.376134\pi\)
0.379390 + 0.925237i \(0.376134\pi\)
\(504\) 0 0
\(505\) 47.9991 2.13593
\(506\) 0 0
\(507\) −7.93914 + 29.7053i −0.352590 + 1.31926i
\(508\) 0 0
\(509\) 10.3817 + 17.9817i 0.460163 + 0.797025i 0.998969 0.0454049i \(-0.0144578\pi\)
−0.538806 + 0.842430i \(0.681124\pi\)
\(510\) 0 0
\(511\) 4.91784 8.51794i 0.217552 0.376812i
\(512\) 0 0
\(513\) 12.1220 12.1687i 0.535201 0.537260i
\(514\) 0 0
\(515\) 17.8718 30.9548i 0.787525 1.36403i
\(516\) 0 0
\(517\) 17.5979 + 30.4804i 0.773953 + 1.34053i
\(518\) 0 0
\(519\) 5.36198 20.0625i 0.235365 0.880648i
\(520\) 0 0
\(521\) 29.9915 1.31395 0.656977 0.753911i \(-0.271835\pi\)
0.656977 + 0.753911i \(0.271835\pi\)
\(522\) 0 0
\(523\) −2.57036 −0.112394 −0.0561970 0.998420i \(-0.517898\pi\)
−0.0561970 + 0.998420i \(0.517898\pi\)
\(524\) 0 0
\(525\) 11.0965 + 11.0823i 0.484292 + 0.483673i
\(526\) 0 0
\(527\) 14.0349 + 24.3091i 0.611370 + 1.05892i
\(528\) 0 0
\(529\) −0.944341 + 1.63565i −0.0410583 + 0.0711151i
\(530\) 0 0
\(531\) −3.92341 2.25849i −0.170261 0.0980101i
\(532\) 0 0
\(533\) 13.2101 22.8806i 0.572195 0.991070i
\(534\) 0 0
\(535\) −15.8059 27.3767i −0.683350 1.18360i
\(536\) 0 0
\(537\) −41.6959 + 11.2010i −1.79931 + 0.483358i
\(538\) 0 0
\(539\) 3.65105 0.157262
\(540\) 0 0
\(541\) 24.7962 1.06607 0.533036 0.846093i \(-0.321051\pi\)
0.533036 + 0.846093i \(0.321051\pi\)
\(542\) 0 0
\(543\) −35.8307 + 9.62538i −1.53764 + 0.413065i
\(544\) 0 0
\(545\) 31.0362 + 53.7563i 1.32945 + 2.30267i
\(546\) 0 0
\(547\) −5.71955 + 9.90655i −0.244550 + 0.423574i −0.962005 0.273031i \(-0.911974\pi\)
0.717455 + 0.696605i \(0.245307\pi\)
\(548\) 0 0
\(549\) −0.00801317 6.26022i −0.000341994 0.267180i
\(550\) 0 0
\(551\) −0.811502 + 1.40556i −0.0345712 + 0.0598790i
\(552\) 0 0
\(553\) −1.86391 3.22839i −0.0792615 0.137285i
\(554\) 0 0
\(555\) 36.2704 + 36.2240i 1.53959 + 1.53762i
\(556\) 0 0
\(557\) 13.8445 0.586609 0.293305 0.956019i \(-0.405245\pi\)
0.293305 + 0.956019i \(0.405245\pi\)
\(558\) 0 0
\(559\) −8.89178 −0.376082
\(560\) 0 0
\(561\) 11.7687 44.0343i 0.496877 1.85913i
\(562\) 0 0
\(563\) 17.5194 + 30.3444i 0.738353 + 1.27886i 0.953237 + 0.302225i \(0.0977293\pi\)
−0.214884 + 0.976640i \(0.568937\pi\)
\(564\) 0 0
\(565\) 0.123021 0.213079i 0.00517553 0.00896429i
\(566\) 0 0
\(567\) −4.51994 7.78268i −0.189820 0.326842i
\(568\) 0 0
\(569\) −3.72940 + 6.45951i −0.156344 + 0.270797i −0.933548 0.358453i \(-0.883304\pi\)
0.777203 + 0.629250i \(0.216638\pi\)
\(570\) 0 0
\(571\) 21.4174 + 37.0961i 0.896292 + 1.55242i 0.832197 + 0.554480i \(0.187083\pi\)
0.0640949 + 0.997944i \(0.479584\pi\)
\(572\) 0 0
\(573\) 8.03204 30.0529i 0.335543 1.25548i
\(574\) 0 0
\(575\) 45.1715 1.88378
\(576\) 0 0
\(577\) −16.1386 −0.671860 −0.335930 0.941887i \(-0.609051\pi\)
−0.335930 + 0.941887i \(0.609051\pi\)
\(578\) 0 0
\(579\) −11.4941 11.4794i −0.477677 0.477066i
\(580\) 0 0
\(581\) 5.69058 + 9.85637i 0.236085 + 0.408911i
\(582\) 0 0
\(583\) 14.6708 25.4105i 0.607601 1.05240i
\(584\) 0 0
\(585\) 0.0798329 + 62.3688i 0.00330068 + 2.57863i
\(586\) 0 0
\(587\) 22.9094 39.6802i 0.945570 1.63778i 0.190965 0.981597i \(-0.438838\pi\)
0.754605 0.656179i \(-0.227829\pi\)
\(588\) 0 0
\(589\) −6.43663 11.1486i −0.265217 0.459369i
\(590\) 0 0
\(591\) −0.346119 + 0.0929797i −0.0142374 + 0.00382467i
\(592\) 0 0
\(593\) −22.4176 −0.920579 −0.460290 0.887769i \(-0.652254\pi\)
−0.460290 + 0.887769i \(0.652254\pi\)
\(594\) 0 0
\(595\) −27.0211 −1.10776
\(596\) 0 0
\(597\) −21.1048 + 5.66949i −0.863762 + 0.232037i
\(598\) 0 0
\(599\) 0.622253 + 1.07777i 0.0254246 + 0.0440366i 0.878458 0.477820i \(-0.158573\pi\)
−0.853033 + 0.521857i \(0.825240\pi\)
\(600\) 0 0
\(601\) 18.9011 32.7377i 0.770993 1.33540i −0.166027 0.986121i \(-0.553094\pi\)
0.937019 0.349277i \(-0.113573\pi\)
\(602\) 0 0
\(603\) 8.84893 + 5.09384i 0.360356 + 0.207437i
\(604\) 0 0
\(605\) 4.36775 7.56516i 0.177574 0.307568i
\(606\) 0 0
\(607\) 6.01266 + 10.4142i 0.244047 + 0.422701i 0.961863 0.273531i \(-0.0881917\pi\)
−0.717817 + 0.696232i \(0.754858\pi\)
\(608\) 0 0
\(609\) 0.601726 + 0.600956i 0.0243832 + 0.0243520i
\(610\) 0 0
\(611\) 53.4579 2.16267
\(612\) 0 0
\(613\) −29.5048 −1.19169 −0.595843 0.803101i \(-0.703182\pi\)
−0.595843 + 0.803101i \(0.703182\pi\)
\(614\) 0 0
\(615\) 7.98774 29.8872i 0.322097 1.20517i
\(616\) 0 0
\(617\) 6.26890 + 10.8581i 0.252376 + 0.437129i 0.964180 0.265250i \(-0.0854546\pi\)
−0.711803 + 0.702379i \(0.752121\pi\)
\(618\) 0 0
\(619\) −15.2153 + 26.3537i −0.611555 + 1.05924i 0.379423 + 0.925223i \(0.376122\pi\)
−0.990978 + 0.134022i \(0.957211\pi\)
\(620\) 0 0
\(621\) −25.0524 6.66124i −1.00532 0.267306i
\(622\) 0 0
\(623\) 3.57445 6.19114i 0.143207 0.248043i
\(624\) 0 0
\(625\) −5.85564 10.1423i −0.234226 0.405691i
\(626\) 0 0
\(627\) −5.39734 + 20.1948i −0.215549 + 0.806504i
\(628\) 0 0
\(629\) −56.9005 −2.26877
\(630\) 0 0
\(631\) 20.6901 0.823660 0.411830 0.911261i \(-0.364890\pi\)
0.411830 + 0.911261i \(0.364890\pi\)
\(632\) 0 0
\(633\) −7.26750 7.25820i −0.288857 0.288488i
\(634\) 0 0
\(635\) −5.99979 10.3919i −0.238094 0.412391i
\(636\) 0 0
\(637\) 2.77274 4.80253i 0.109860 0.190283i
\(638\) 0 0
\(639\) 27.8570 16.1308i 1.10201 0.638126i
\(640\) 0 0
\(641\) 5.24417 9.08317i 0.207132 0.358764i −0.743678 0.668538i \(-0.766920\pi\)
0.950810 + 0.309775i \(0.100254\pi\)
\(642\) 0 0
\(643\) −20.2056 34.9971i −0.796830 1.38015i −0.921671 0.387972i \(-0.873176\pi\)
0.124841 0.992177i \(-0.460158\pi\)
\(644\) 0 0
\(645\) −10.0551 + 2.70116i −0.395920 + 0.106358i
\(646\) 0 0
\(647\) 16.8906 0.664038 0.332019 0.943273i \(-0.392270\pi\)
0.332019 + 0.943273i \(0.392270\pi\)
\(648\) 0 0
\(649\) 5.50945 0.216265
\(650\) 0 0
\(651\) −6.51440 + 1.75000i −0.255319 + 0.0685878i
\(652\) 0 0
\(653\) 19.0982 + 33.0791i 0.747372 + 1.29449i 0.949079 + 0.315040i \(0.102018\pi\)
−0.201707 + 0.979446i \(0.564649\pi\)
\(654\) 0 0
\(655\) −28.7566 + 49.8079i −1.12361 + 1.94615i
\(656\) 0 0
\(657\) 25.5349 14.7862i 0.996212 0.576865i
\(658\) 0 0
\(659\) 15.2864 26.4768i 0.595472 1.03139i −0.398008 0.917382i \(-0.630298\pi\)
0.993480 0.114006i \(-0.0363684\pi\)
\(660\) 0 0
\(661\) −12.0894 20.9395i −0.470223 0.814451i 0.529197 0.848499i \(-0.322493\pi\)
−0.999420 + 0.0340482i \(0.989160\pi\)
\(662\) 0 0
\(663\) −48.9843 48.9217i −1.90239 1.89996i
\(664\) 0 0
\(665\) 12.3923 0.480553
\(666\) 0 0
\(667\) 2.44949 0.0948448
\(668\) 0 0
\(669\) −1.61445 + 6.04067i −0.0624182 + 0.233546i
\(670\) 0 0
\(671\) 3.80939 + 6.59806i 0.147060 + 0.254715i
\(672\) 0 0
\(673\) −13.5485 + 23.4667i −0.522257 + 0.904575i 0.477408 + 0.878682i \(0.341576\pi\)
−0.999665 + 0.0258933i \(0.991757\pi\)
\(674\) 0 0
\(675\) 12.2643 + 45.4219i 0.472052 + 1.74829i
\(676\) 0 0
\(677\) −6.72453 + 11.6472i −0.258445 + 0.447640i −0.965825 0.259193i \(-0.916543\pi\)
0.707381 + 0.706833i \(0.249877\pi\)
\(678\) 0 0
\(679\) −5.45316 9.44516i −0.209273 0.362472i
\(680\) 0 0
\(681\) −8.32459 + 31.1475i −0.318999 + 1.19358i
\(682\) 0 0
\(683\) −11.4449 −0.437925 −0.218963 0.975733i \(-0.570267\pi\)
−0.218963 + 0.975733i \(0.570267\pi\)
\(684\) 0 0
\(685\) −2.57160 −0.0982557
\(686\) 0 0
\(687\) −28.1787 28.1426i −1.07508 1.07371i
\(688\) 0 0
\(689\) −22.2830 38.5954i −0.848916 1.47037i
\(690\) 0 0
\(691\) 18.1416 31.4222i 0.690139 1.19536i −0.281653 0.959516i \(-0.590883\pi\)
0.971792 0.235840i \(-0.0757840\pi\)
\(692\) 0 0
\(693\) 9.49270 + 5.46442i 0.360598 + 0.207576i
\(694\) 0 0
\(695\) 37.8656 65.5851i 1.43632 2.48779i
\(696\) 0 0
\(697\) 17.1697 + 29.7388i 0.650349 + 1.12644i
\(698\) 0 0
\(699\) −6.80917 + 1.82918i −0.257547 + 0.0691861i
\(700\) 0 0
\(701\) 4.80688 0.181553 0.0907767 0.995871i \(-0.471065\pi\)
0.0907767 + 0.995871i \(0.471065\pi\)
\(702\) 0 0
\(703\) 26.0955 0.984210
\(704\) 0 0
\(705\) 60.4519 16.2395i 2.27675 0.611615i
\(706\) 0 0
\(707\) −6.40171 11.0881i −0.240761 0.417010i
\(708\) 0 0
\(709\) 6.17770 10.7001i 0.232008 0.401850i −0.726391 0.687282i \(-0.758804\pi\)
0.958399 + 0.285432i \(0.0921370\pi\)
\(710\) 0 0
\(711\) −0.0143150 11.1834i −0.000536853 0.419412i
\(712\) 0 0
\(713\) −9.71438 + 16.8258i −0.363807 + 0.630131i
\(714\) 0 0
\(715\) −37.9519 65.7347i −1.41932 2.45834i
\(716\) 0 0
\(717\) 6.12764 + 6.11980i 0.228841 + 0.228548i
\(718\) 0 0
\(719\) 10.4488 0.389673 0.194837 0.980836i \(-0.437582\pi\)
0.194837 + 0.980836i \(0.437582\pi\)
\(720\) 0 0
\(721\) −9.53433 −0.355077
\(722\) 0 0
\(723\) −6.53691 + 24.4587i −0.243110 + 0.909628i
\(724\) 0 0
\(725\) −2.22285 3.85008i −0.0825544 0.142988i
\(726\) 0 0
\(727\) −9.13266 + 15.8182i −0.338711 + 0.586665i −0.984191 0.177112i \(-0.943324\pi\)
0.645479 + 0.763778i \(0.276658\pi\)
\(728\) 0 0
\(729\) −0.103681 26.9998i −0.00384003 0.999993i
\(730\) 0 0
\(731\) 5.77849 10.0086i 0.213725 0.370183i
\(732\) 0 0
\(733\) 24.3245 + 42.1313i 0.898447 + 1.55616i 0.829480 + 0.558537i \(0.188637\pi\)
0.0689673 + 0.997619i \(0.478030\pi\)
\(734\) 0 0
\(735\) 1.67659 6.27316i 0.0618418 0.231389i
\(736\) 0 0
\(737\) −12.4261 −0.457722
\(738\) 0 0
\(739\) −52.2935 −1.92365 −0.961823 0.273671i \(-0.911762\pi\)
−0.961823 + 0.273671i \(0.911762\pi\)
\(740\) 0 0
\(741\) 22.4650 + 22.4363i 0.825273 + 0.824217i
\(742\) 0 0
\(743\) 5.21154 + 9.02665i 0.191193 + 0.331156i 0.945646 0.325198i \(-0.105431\pi\)
−0.754453 + 0.656354i \(0.772098\pi\)
\(744\) 0 0
\(745\) −16.1823 + 28.0286i −0.592874 + 1.02689i
\(746\) 0 0
\(747\) 0.0437040 + 34.1434i 0.00159905 + 1.24924i
\(748\) 0 0
\(749\) −4.21612 + 7.30253i −0.154054 + 0.266829i
\(750\) 0 0
\(751\) 5.10383 + 8.84010i 0.186242 + 0.322580i 0.943994 0.329962i \(-0.107036\pi\)
−0.757753 + 0.652542i \(0.773703\pi\)
\(752\) 0 0
\(753\) −14.6232 + 3.92832i −0.532901 + 0.143156i
\(754\) 0 0
\(755\) −40.7761 −1.48399
\(756\) 0 0
\(757\) −6.13207 −0.222874 −0.111437 0.993772i \(-0.535545\pi\)
−0.111437 + 0.993772i \(0.535545\pi\)
\(758\) 0 0
\(759\) 30.4683 8.18486i 1.10593 0.297091i
\(760\) 0 0
\(761\) −16.0967 27.8803i −0.583505 1.01066i −0.995060 0.0992757i \(-0.968347\pi\)
0.411555 0.911385i \(-0.364986\pi\)
\(762\) 0 0
\(763\) 8.27869 14.3391i 0.299709 0.519111i
\(764\) 0 0
\(765\) −70.2546 40.4417i −2.54006 1.46217i
\(766\) 0 0
\(767\) 4.18408 7.24704i 0.151078 0.261676i
\(768\) 0 0
\(769\) 5.38520 + 9.32745i 0.194195 + 0.336356i 0.946636 0.322303i \(-0.104457\pi\)
−0.752441 + 0.658660i \(0.771124\pi\)
\(770\) 0 0
\(771\) −26.0790 26.0456i −0.939212 0.938011i
\(772\) 0 0
\(773\) −26.6154 −0.957289 −0.478644 0.878009i \(-0.658872\pi\)
−0.478644 + 0.878009i \(0.658872\pi\)
\(774\) 0 0
\(775\) 35.2621 1.26665
\(776\) 0 0
\(777\) 3.53052 13.2099i 0.126657 0.473903i
\(778\) 0 0
\(779\) −7.87431 13.6387i −0.282127 0.488657i
\(780\) 0 0
\(781\) −19.5881 + 33.9275i −0.700916 + 1.21402i
\(782\) 0 0
\(783\) 0.665049 + 2.46307i 0.0237669 + 0.0880230i
\(784\) 0 0
\(785\) −20.6046 + 35.6882i −0.735410 + 1.27377i
\(786\) 0 0
\(787\) −4.00251 6.93256i −0.142674 0.247119i 0.785829 0.618444i \(-0.212237\pi\)
−0.928503 + 0.371325i \(0.878903\pi\)
\(788\) 0 0
\(789\) 6.08676 22.7744i 0.216694 0.810789i
\(790\) 0 0
\(791\) −0.0656299 −0.00233353
\(792\) 0 0
\(793\) 11.5720 0.410933
\(794\) 0 0
\(795\) −36.9229 36.8757i −1.30952 1.30785i
\(796\) 0 0
\(797\) −11.9675 20.7284i −0.423912 0.734237i 0.572406 0.819970i \(-0.306010\pi\)
−0.996318 + 0.0857334i \(0.972677\pi\)
\(798\)