Properties

Label 1008.2.r.m.337.4
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 337.4
Root \(0.947217 + 0.807294i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.m.673.4

$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

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

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 −0.0530397 0.998592i \(-0.516891\pi\)
0.891326 0.453362i \(-0.149776\pi\)
\(6\) 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 −0.998244 0.0592287i \(-0.981136\pi\)
0.447829 0.894119i \(-0.352197\pi\)
\(12\) 0 0
\(13\) 2.77274 4.80253i 0.769020 1.33198i −0.169076 0.985603i \(-0.554078\pi\)
0.938095 0.346378i \(-0.112588\pi\)
\(14\) 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 0.479602 + 0.877486i \(0.340781\pi\)
−0.999726 + 0.0233954i \(0.992552\pi\)
\(24\) 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 0.842331 0.538960i \(-0.181183\pi\)
−0.887919 + 0.460000i \(0.847849\pi\)
\(30\) 0 0
\(31\) −1.94722 + 3.37268i −0.349730 + 0.605751i −0.986201 0.165550i \(-0.947060\pi\)
0.636471 + 0.771301i \(0.280394\pi\)
\(32\) 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 −0.989878 0.141924i \(-0.954671\pi\)
0.617849 + 0.786297i \(0.288004\pi\)
\(42\) 0 0
\(43\) −0.801714 1.38861i −0.122260 0.211761i 0.798398 0.602130i \(-0.205681\pi\)
−0.920659 + 0.390369i \(0.872348\pi\)
\(44\) 0 0
\(45\) 9.74720 5.61092i 1.45303 0.836427i
\(46\) 0 0
\(47\) 4.81995 + 8.34840i 0.703062 + 1.21774i 0.967386 + 0.253305i \(0.0815177\pi\)
−0.264324 + 0.964434i \(0.585149\pi\)
\(48\) 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 −0.910951 0.412514i \(-0.864651\pi\)
0.812723 + 0.582650i \(0.197984\pi\)
\(60\) 0 0
\(61\) 1.04337 + 1.80717i 0.133590 + 0.231385i 0.925058 0.379826i \(-0.124016\pi\)
−0.791468 + 0.611211i \(0.790683\pi\)
\(62\) 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 −0.743154 0.669120i \(-0.766671\pi\)
0.951052 + 0.309030i \(0.100004\pi\)
\(68\) 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 0.951622 0.307271i \(-0.0994159\pi\)
−0.741916 + 0.670493i \(0.766083\pi\)
\(80\) 0 0
\(81\) 4.48003 + 7.80572i 0.497781 + 0.867303i
\(82\) 0 0
\(83\) −5.69058 9.85637i −0.624622 1.08188i −0.988614 0.150475i \(-0.951920\pi\)
0.363992 0.931402i \(-0.381414\pi\)
\(84\) 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 0.998005 + 0.0631422i \(0.0201122\pi\)
−0.444320 + 0.895868i \(0.646555\pi\)
\(98\) 0 0
\(99\) 0.0140201 10.9531i 0.00140908 1.10083i
\(100\) 0 0
\(101\) 6.40171 + 11.0881i 0.636994 + 1.10331i 0.986089 + 0.166218i \(0.0531557\pi\)
−0.349095 + 0.937087i \(0.613511\pi\)
\(102\) 0 0
\(103\) −4.76717 + 8.25698i −0.469723 + 0.813584i −0.999401 0.0346149i \(-0.988980\pi\)
0.529678 + 0.848199i \(0.322313\pi\)
\(104\) 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 −0.867565 0.497324i \(-0.834316\pi\)
0.864478 + 0.502671i \(0.167649\pi\)
\(114\) 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 −0.307668 0.951494i \(-0.599548\pi\)
0.977852 0.209299i \(-0.0671182\pi\)
\(132\) 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 0.851002 0.525162i \(-0.175995\pi\)
−0.880305 + 0.474409i \(0.842662\pi\)
\(138\) 0 0
\(139\) −10.1004 + 17.4944i −0.856702 + 1.48385i 0.0183546 + 0.999832i \(0.494157\pi\)
−0.875057 + 0.484020i \(0.839176\pi\)
\(140\) 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 −0.633259 0.773940i \(-0.718283\pi\)
0.986881 + 0.161448i \(0.0516163\pi\)
\(150\) 0 0
\(151\) −5.43836 9.41952i −0.442568 0.766550i 0.555311 0.831642i \(-0.312599\pi\)
−0.997879 + 0.0650926i \(0.979266\pi\)
\(152\) 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 −0.558946 0.829204i \(-0.688794\pi\)
0.997585 + 0.0694592i \(0.0221274\pi\)
\(158\) 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 −0.803659 0.595091i \(-0.797116\pi\)
0.917193 + 0.398444i \(0.130450\pi\)
\(168\) 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 0.998733 0.0503306i \(-0.0160275\pi\)
−0.542954 + 0.839763i \(0.682694\pi\)
\(174\) 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 0.983177 + 0.182655i \(0.0584691\pi\)
−0.333405 + 0.942784i \(0.608198\pi\)
\(192\) 0 0
\(193\) −4.68943 + 8.12233i −0.337553 + 0.584658i −0.983972 0.178324i \(-0.942932\pi\)
0.646419 + 0.762983i \(0.276266\pi\)
\(194\) 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 −0.949853 0.312698i \(-0.898767\pi\)
0.745730 + 0.666248i \(0.232101\pi\)
\(212\) 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 0.799240 0.601012i \(-0.205236\pi\)
−0.920112 + 0.391656i \(0.871902\pi\)
\(224\) 0 0
\(225\) 0.0347696 27.1634i 0.00231797 1.81090i
\(226\) 0 0
\(227\) −9.30710 16.1204i −0.617734 1.06995i −0.989898 0.141780i \(-0.954717\pi\)
0.372164 0.928167i \(-0.378616\pi\)
\(228\) 0 0
\(229\) −11.4965 + 19.9126i −0.759712 + 1.31586i 0.183285 + 0.983060i \(0.441327\pi\)
−0.942997 + 0.332801i \(0.892006\pi\)
\(230\) 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 −0.773771 0.633465i \(-0.781632\pi\)
0.935483 + 0.353373i \(0.114965\pi\)
\(240\) 0 0
\(241\) −7.30843 12.6586i −0.470777 0.815410i 0.528664 0.848831i \(-0.322693\pi\)
−0.999441 + 0.0334208i \(0.989360\pi\)
\(242\) 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 0.315938 + 0.948780i \(0.397681\pi\)
−0.979636 + 0.200780i \(0.935652\pi\)
\(258\) 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 0.995901 0.0904446i \(-0.0288288\pi\)
−0.576278 + 0.817254i \(0.695495\pi\)
\(264\) 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 0.846283 0.532733i \(-0.178835\pi\)
−0.884502 + 0.466536i \(0.845502\pi\)
\(278\) 0 0
\(279\) −10.1255 + 5.82869i −0.606198 + 0.348955i
\(280\) 0 0
\(281\) 4.66891 + 8.08678i 0.278524 + 0.482417i 0.971018 0.239006i \(-0.0768216\pi\)
−0.692494 + 0.721423i \(0.743488\pi\)
\(282\) 0 0
\(283\) 4.88983 8.46943i 0.290670 0.503455i −0.683298 0.730139i \(-0.739455\pi\)
0.973968 + 0.226684i \(0.0727885\pi\)
\(284\) 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 −0.261729 0.965141i \(-0.584293\pi\)
0.966702 0.255906i \(-0.0823738\pi\)
\(294\) 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 −0.617523 0.786553i \(-0.711864\pi\)
0.989936 + 0.141514i \(0.0451970\pi\)
\(312\) 0 0
\(313\) −6.29311 10.9000i −0.355708 0.616104i 0.631531 0.775351i \(-0.282427\pi\)
−0.987239 + 0.159247i \(0.949093\pi\)
\(314\) 0 0
\(315\) 9.73280 + 5.63586i 0.548381 + 0.317545i
\(316\) 0 0
\(317\) 5.36679 + 9.29555i 0.301429 + 0.522090i 0.976460 0.215699i \(-0.0692031\pi\)
−0.675031 + 0.737789i \(0.735870\pi\)
\(318\) 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 0.669254 0.743034i \(-0.266614\pi\)
−0.978113 + 0.208074i \(0.933280\pi\)
\(332\) 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 −0.900558 0.434737i \(-0.856841\pi\)
0.826772 + 0.562537i \(0.190175\pi\)
\(338\) 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 −0.965230 0.261400i \(-0.915816\pi\)
0.708995 + 0.705214i \(0.249149\pi\)
\(348\) 0 0
\(349\) 1.01114 + 1.75135i 0.0541253 + 0.0937478i 0.891819 0.452393i \(-0.149430\pi\)
−0.837693 + 0.546141i \(0.816096\pi\)
\(350\) 0 0
\(351\) 27.8476 7.40446i 1.48639 0.395221i
\(352\) 0 0
\(353\) −5.93836 10.2855i −0.316067 0.547444i 0.663597 0.748091i \(-0.269029\pi\)
−0.979664 + 0.200646i \(0.935696\pi\)
\(354\) 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 0.834651 0.550779i \(-0.185669\pi\)
−0.894314 + 0.447439i \(0.852336\pi\)
\(368\) 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 0.0349186 0.999390i \(-0.488883\pi\)
0.848038 0.529936i \(-0.177784\pi\)
\(374\) 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 −0.422073 0.906562i \(-0.638697\pi\)
0.996142 0.0877552i \(-0.0279693\pi\)
\(384\) 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 0.923856 0.382741i \(-0.125020\pi\)
−0.793391 + 0.608712i \(0.791687\pi\)
\(390\) 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 −0.845256 0.534361i \(-0.820552\pi\)
0.885399 + 0.464833i \(0.153885\pi\)
\(402\) 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 0.470059 + 0.882635i \(0.344232\pi\)
−0.999414 + 0.0342340i \(0.989101\pi\)
\(410\) 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 0.0357681 + 0.999360i \(0.488612\pi\)
−0.883355 + 0.468704i \(0.844721\pi\)
\(420\) 0 0
\(421\) 11.6234 + 20.1323i 0.566488 + 0.981186i 0.996910 + 0.0785583i \(0.0250317\pi\)
−0.430421 + 0.902628i \(0.641635\pi\)
\(422\) 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 0.915381 0.402588i \(-0.131889\pi\)
−0.806342 + 0.591449i \(0.798556\pi\)
\(440\) 0 0
\(441\) −2.59999 + 1.49667i −0.123809 + 0.0712702i
\(442\) 0 0
\(443\) −5.01455 8.68545i −0.238248 0.412658i 0.721963 0.691931i \(-0.243240\pi\)
−0.960212 + 0.279273i \(0.909907\pi\)
\(444\) 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 0.920906 0.389784i \(-0.127451\pi\)
−0.798016 + 0.602636i \(0.794117\pi\)
\(458\) 0 0
\(459\) −26.4318 26.5335i −1.23373 1.23848i
\(460\) 0 0
\(461\) −4.32763 7.49568i −0.201558 0.349108i 0.747473 0.664293i \(-0.231267\pi\)
−0.949031 + 0.315184i \(0.897934\pi\)
\(462\) 0 0
\(463\) −0.509788 + 0.882979i −0.0236919 + 0.0410355i −0.877628 0.479342i \(-0.840875\pi\)
0.853936 + 0.520377i \(0.174209\pi\)
\(464\) 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 −0.892133 0.451773i \(-0.850792\pi\)
0.0548199 0.998496i \(-0.482542\pi\)
\(480\) 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 −0.582079 0.813133i \(-0.697760\pi\)
0.995233 + 0.0975285i \(0.0310937\pi\)
\(492\) 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 −0.448610 0.893728i \(-0.648081\pi\)
0.998296 0.0583561i \(-0.0185859\pi\)
\(500\) 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 −0.538806 0.842430i \(-0.681124\pi\)
0.998969 + 0.0454049i \(0.0144578\pi\)
\(510\) 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 0.717455 0.696605i \(-0.245307\pi\)
−0.962005 + 0.273031i \(0.911974\pi\)
\(548\) 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 −0.214884 0.976640i \(-0.568937\pi\)
0.953237 0.302225i \(-0.0977293\pi\)
\(564\) 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 0.777203 0.629250i \(-0.216638\pi\)
−0.933548 + 0.358453i \(0.883304\pi\)
\(570\) 0 0
\(571\) 21.4174 37.0961i 0.896292 1.55242i 0.0640949 0.997944i \(-0.479584\pi\)
0.832197 0.554480i \(-0.187083\pi\)
\(572\) 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 0.754605 + 0.656179i \(0.227829\pi\)
0.190965 + 0.981597i \(0.438838\pi\)
\(588\) 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 −0.853033 0.521857i \(-0.825240\pi\)
0.878458 + 0.477820i \(0.158573\pi\)
\(600\) 0 0
\(601\) 18.9011 + 32.7377i 0.770993 + 1.33540i 0.937019 + 0.349277i \(0.113573\pi\)
−0.166027 + 0.986121i \(0.553094\pi\)
\(602\) 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 −0.717817 0.696232i \(-0.754858\pi\)
0.961863 + 0.273531i \(0.0881917\pi\)
\(608\) 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 −0.711803 0.702379i \(-0.752121\pi\)
0.964180 + 0.265250i \(0.0854546\pi\)
\(618\) 0 0
\(619\) −15.2153 26.3537i −0.611555 1.05924i −0.990978 0.134022i \(-0.957211\pi\)
0.379423 0.925223i \(-0.376122\pi\)
\(620\) 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 0.950810 0.309775i \(-0.100254\pi\)
−0.743678 + 0.668538i \(0.766920\pi\)
\(642\) 0 0
\(643\) −20.2056 + 34.9971i −0.796830 + 1.38015i 0.124841 + 0.992177i \(0.460158\pi\)
−0.921671 + 0.387972i \(0.873176\pi\)
\(644\) 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 −0.201707 0.979446i \(-0.564649\pi\)
0.949079 0.315040i \(-0.102018\pi\)
\(654\) 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 0.993480 + 0.114006i \(0.0363684\pi\)
−0.398008 + 0.917382i \(0.630298\pi\)
\(660\) 0 0
\(661\) −12.0894 + 20.9395i −0.470223 + 0.814451i −0.999420 0.0340482i \(-0.989160\pi\)
0.529197 + 0.848499i \(0.322493\pi\)
\(662\) 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 −0.999665 0.0258933i \(-0.991757\pi\)
0.477408 0.878682i \(-0.341576\pi\)
\(674\) 0 0
\(675\) 12.2643 45.4219i 0.472052 1.74829i
\(676\) 0 0
\(677\) −6.72453 11.6472i −0.258445 0.447640i 0.707381 0.706833i \(-0.249877\pi\)
−0.965825 + 0.259193i \(0.916543\pi\)
\(678\) 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 0.971792 + 0.235840i \(0.0757840\pi\)
−0.281653 + 0.959516i \(0.590883\pi\)
\(692\) 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 0.958399 0.285432i \(-0.0921370\pi\)
−0.726391 + 0.687282i \(0.758804\pi\)
\(710\) 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 0.645479 0.763778i \(-0.276658\pi\)
−0.984191 + 0.177112i \(0.943324\pi\)
\(728\) 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 0.0689673 0.997619i \(-0.478030\pi\)
0.829480 0.558537i \(-0.188637\pi\)
\(734\) 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 −0.754453 0.656354i \(-0.772098\pi\)
0.945646 + 0.325198i \(0.105431\pi\)
\(744\) 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 −0.757753 0.652542i \(-0.773703\pi\)
0.943994 + 0.329962i \(0.107036\pi\)
\(752\) 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 0.411555 + 0.911385i \(0.364986\pi\)
−0.995060 + 0.0992757i \(0.968347\pi\)
\(762\) 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 −0.752441 0.658660i \(-0.771124\pi\)
0.946636 + 0.322303i \(0.104457\pi\)
\(770\) 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 −0.928503 0.371325i \(-0.878903\pi\)
0.785829 + 0.618444i \(0.212237\pi\)
\(788\) 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 −0.996318 0.0857334i \(-0.972677\pi\)
0.572406 + 0.819970i \(0.306010\pi\)
\(798\) 0