Properties

Label 483.2.h.b.160.8
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 14 x^{10} + 67 x^{8} + 141 x^{6} + 129 x^{4} + 39 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.8
Root \(0.167898i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.b.160.6

$q$-expansion

\(f(q)\) \(=\) \(q+0.254102 q^{2} +1.00000i q^{3} -1.93543 q^{4} +0.458377 q^{5} +0.254102i q^{6} +(-1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+0.254102 q^{2} +1.00000i q^{3} -1.93543 q^{4} +0.458377 q^{5} +0.254102i q^{6} +(-1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +0.116474 q^{10} +1.34554i q^{11} -1.93543i q^{12} -4.42723i q^{13} +(-0.272628 + 0.614531i) q^{14} +0.458377i q^{15} +3.61676 q^{16} -7.09918 q^{17} -0.254102 q^{18} -4.40811 q^{19} -0.887158 q^{20} +(-2.41844 - 1.07291i) q^{21} +0.341903i q^{22} +(-4.44364 + 1.80391i) q^{23} -1.00000i q^{24} -4.78989 q^{25} -1.12497i q^{26} -1.00000i q^{27} +(2.07654 - 4.68073i) q^{28} +4.18953 q^{29} +0.116474i q^{30} +4.31867i q^{31} +2.91903 q^{32} -1.34554 q^{33} -1.80391 q^{34} +(-0.491797 + 1.10856i) q^{35} +1.93543 q^{36} +8.56119i q^{37} -1.12011 q^{38} +4.42723 q^{39} -0.458377 q^{40} -3.81047i q^{41} +(-0.614531 - 0.272628i) q^{42} +7.18606i q^{43} -2.60419i q^{44} -0.458377 q^{45} +(-1.12914 + 0.458377i) q^{46} -7.23353i q^{47} +3.61676i q^{48} +(-4.69774 - 5.18953i) q^{49} -1.21712 q^{50} -7.09918i q^{51} +8.56860i q^{52} -8.35783i q^{53} -0.254102i q^{54} +0.616763i q^{55} +(1.07291 - 2.41844i) q^{56} -4.40811i q^{57} +1.06457 q^{58} +8.10856i q^{59} -0.887158i q^{60} +10.2486 q^{61} +1.09738i q^{62} +(1.07291 - 2.41844i) q^{63} -6.49180 q^{64} -2.02934i q^{65} -0.341903 q^{66} +5.84052i q^{67} +13.7400 q^{68} +(-1.80391 - 4.44364i) q^{69} +(-0.124966 + 0.281687i) q^{70} +8.42723 q^{71} +1.00000 q^{72} +7.04399i q^{73} +2.17541i q^{74} -4.78989i q^{75} +8.53159 q^{76} +(-3.25410 - 1.44364i) q^{77} +1.12497 q^{78} +6.86623i q^{79} +1.65784 q^{80} +1.00000 q^{81} -0.968246i q^{82} +4.95336 q^{83} +(4.68073 + 2.07654i) q^{84} -3.25410 q^{85} +1.82599i q^{86} +4.18953i q^{87} -1.34554i q^{88} -16.0023 q^{89} -0.116474 q^{90} +(10.7070 + 4.75001i) q^{91} +(8.60036 - 3.49135i) q^{92} -4.31867 q^{93} -1.83805i q^{94} -2.02058 q^{95} +2.91903i q^{96} +3.86285 q^{97} +(-1.19370 - 1.31867i) q^{98} -1.34554i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} + O(q^{10}) \) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} - 16q^{16} - 16q^{23} + 24q^{25} + 16q^{29} + 16q^{32} - 12q^{35} - 8q^{36} + 28q^{39} - 76q^{46} - 16q^{49} + 92q^{50} + 44q^{58} - 84q^{64} + 64q^{70} + 76q^{71} + 12q^{72} - 36q^{77} - 52q^{78} + 12q^{81} - 36q^{85} + 56q^{92} - 80q^{93} - 140q^{95} - 108q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.254102 0.179677 0.0898385 0.995956i \(-0.471365\pi\)
0.0898385 + 0.995956i \(0.471365\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.93543 −0.967716
\(5\) 0.458377 0.204993 0.102496 0.994733i \(-0.467317\pi\)
0.102496 + 0.994733i \(0.467317\pi\)
\(6\) 0.254102i 0.103737i
\(7\) −1.07291 + 2.41844i −0.405521 + 0.914086i
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) 0.116474 0.0368325
\(11\) 1.34554i 0.405694i 0.979210 + 0.202847i \(0.0650194\pi\)
−0.979210 + 0.202847i \(0.934981\pi\)
\(12\) 1.93543i 0.558711i
\(13\) 4.42723i 1.22789i −0.789348 0.613946i \(-0.789581\pi\)
0.789348 0.613946i \(-0.210419\pi\)
\(14\) −0.272628 + 0.614531i −0.0728628 + 0.164240i
\(15\) 0.458377i 0.118353i
\(16\) 3.61676 0.904191
\(17\) −7.09918 −1.72180 −0.860902 0.508771i \(-0.830100\pi\)
−0.860902 + 0.508771i \(0.830100\pi\)
\(18\) −0.254102 −0.0598923
\(19\) −4.40811 −1.01129 −0.505644 0.862742i \(-0.668745\pi\)
−0.505644 + 0.862742i \(0.668745\pi\)
\(20\) −0.887158 −0.198375
\(21\) −2.41844 1.07291i −0.527748 0.234128i
\(22\) 0.341903i 0.0728939i
\(23\) −4.44364 + 1.80391i −0.926562 + 0.376142i
\(24\) 1.00000i 0.204124i
\(25\) −4.78989 −0.957978
\(26\) 1.12497i 0.220624i
\(27\) 1.00000i 0.192450i
\(28\) 2.07654 4.68073i 0.392429 0.884576i
\(29\) 4.18953 0.777977 0.388988 0.921243i \(-0.372825\pi\)
0.388988 + 0.921243i \(0.372825\pi\)
\(30\) 0.116474i 0.0212652i
\(31\) 4.31867i 0.775656i 0.921732 + 0.387828i \(0.126775\pi\)
−0.921732 + 0.387828i \(0.873225\pi\)
\(32\) 2.91903 0.516016
\(33\) −1.34554 −0.234228
\(34\) −1.80391 −0.309369
\(35\) −0.491797 + 1.10856i −0.0831288 + 0.187381i
\(36\) 1.93543 0.322572
\(37\) 8.56119i 1.40745i 0.710472 + 0.703725i \(0.248481\pi\)
−0.710472 + 0.703725i \(0.751519\pi\)
\(38\) −1.12011 −0.181705
\(39\) 4.42723 0.708924
\(40\) −0.458377 −0.0724758
\(41\) 3.81047i 0.595095i −0.954707 0.297547i \(-0.903831\pi\)
0.954707 0.297547i \(-0.0961686\pi\)
\(42\) −0.614531 0.272628i −0.0948241 0.0420674i
\(43\) 7.18606i 1.09586i 0.836523 + 0.547932i \(0.184585\pi\)
−0.836523 + 0.547932i \(0.815415\pi\)
\(44\) 2.60419i 0.392597i
\(45\) −0.458377 −0.0683309
\(46\) −1.12914 + 0.458377i −0.166482 + 0.0675840i
\(47\) 7.23353i 1.05512i −0.849518 0.527559i \(-0.823107\pi\)
0.849518 0.527559i \(-0.176893\pi\)
\(48\) 3.61676i 0.522035i
\(49\) −4.69774 5.18953i −0.671105 0.741362i
\(50\) −1.21712 −0.172127
\(51\) 7.09918i 0.994084i
\(52\) 8.56860i 1.18825i
\(53\) 8.35783i 1.14804i −0.818842 0.574018i \(-0.805384\pi\)
0.818842 0.574018i \(-0.194616\pi\)
\(54\) 0.254102i 0.0345789i
\(55\) 0.616763i 0.0831643i
\(56\) 1.07291 2.41844i 0.143373 0.323178i
\(57\) 4.40811i 0.583868i
\(58\) 1.06457 0.139785
\(59\) 8.10856i 1.05564i 0.849355 + 0.527822i \(0.176991\pi\)
−0.849355 + 0.527822i \(0.823009\pi\)
\(60\) 0.887158i 0.114532i
\(61\) 10.2486 1.31220 0.656101 0.754673i \(-0.272205\pi\)
0.656101 + 0.754673i \(0.272205\pi\)
\(62\) 1.09738i 0.139368i
\(63\) 1.07291 2.41844i 0.135174 0.304695i
\(64\) −6.49180 −0.811475
\(65\) 2.02934i 0.251709i
\(66\) −0.341903 −0.0420853
\(67\) 5.84052i 0.713533i 0.934194 + 0.356767i \(0.116121\pi\)
−0.934194 + 0.356767i \(0.883879\pi\)
\(68\) 13.7400 1.66622
\(69\) −1.80391 4.44364i −0.217166 0.534951i
\(70\) −0.124966 + 0.281687i −0.0149363 + 0.0336680i
\(71\) 8.42723 1.00013 0.500064 0.865988i \(-0.333310\pi\)
0.500064 + 0.865988i \(0.333310\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.04399i 0.824437i 0.911085 + 0.412218i \(0.135246\pi\)
−0.911085 + 0.412218i \(0.864754\pi\)
\(74\) 2.17541i 0.252887i
\(75\) 4.78989i 0.553089i
\(76\) 8.53159 0.978641
\(77\) −3.25410 1.44364i −0.370839 0.164518i
\(78\) 1.12497 0.127377
\(79\) 6.86623i 0.772511i 0.922392 + 0.386256i \(0.126232\pi\)
−0.922392 + 0.386256i \(0.873768\pi\)
\(80\) 1.65784 0.185352
\(81\) 1.00000 0.111111
\(82\) 0.968246i 0.106925i
\(83\) 4.95336 0.543702 0.271851 0.962339i \(-0.412364\pi\)
0.271851 + 0.962339i \(0.412364\pi\)
\(84\) 4.68073 + 2.07654i 0.510710 + 0.226569i
\(85\) −3.25410 −0.352957
\(86\) 1.82599i 0.196901i
\(87\) 4.18953i 0.449165i
\(88\) 1.34554i 0.143435i
\(89\) −16.0023 −1.69624 −0.848118 0.529807i \(-0.822264\pi\)
−0.848118 + 0.529807i \(0.822264\pi\)
\(90\) −0.116474 −0.0122775
\(91\) 10.7070 + 4.75001i 1.12240 + 0.497936i
\(92\) 8.60036 3.49135i 0.896649 0.363999i
\(93\) −4.31867 −0.447825
\(94\) 1.83805i 0.189581i
\(95\) −2.02058 −0.207307
\(96\) 2.91903i 0.297922i
\(97\) 3.86285 0.392213 0.196107 0.980583i \(-0.437170\pi\)
0.196107 + 0.980583i \(0.437170\pi\)
\(98\) −1.19370 1.31867i −0.120582 0.133206i
\(99\) 1.34554i 0.135231i
\(100\) 9.27051 0.927051
\(101\) 12.6496i 1.25868i 0.777130 + 0.629340i \(0.216675\pi\)
−0.777130 + 0.629340i \(0.783325\pi\)
\(102\) 1.80391i 0.178614i
\(103\) 7.52796 0.741752 0.370876 0.928682i \(-0.379058\pi\)
0.370876 + 0.928682i \(0.379058\pi\)
\(104\) 4.42723i 0.434126i
\(105\) −1.10856 0.491797i −0.108184 0.0479944i
\(106\) 2.12374i 0.206276i
\(107\) 20.1553i 1.94849i −0.225490 0.974246i \(-0.572398\pi\)
0.225490 0.974246i \(-0.427602\pi\)
\(108\) 1.93543i 0.186237i
\(109\) 5.06232i 0.484882i 0.970166 + 0.242441i \(0.0779481\pi\)
−0.970166 + 0.242441i \(0.922052\pi\)
\(110\) 0.156721i 0.0149427i
\(111\) −8.56119 −0.812592
\(112\) −3.88045 + 8.74694i −0.366668 + 0.826508i
\(113\) 3.38240i 0.318189i 0.987263 + 0.159095i \(0.0508575\pi\)
−0.987263 + 0.159095i \(0.949143\pi\)
\(114\) 1.12011i 0.104908i
\(115\) −2.03686 + 0.826873i −0.189938 + 0.0771063i
\(116\) −8.10856 −0.752861
\(117\) 4.42723i 0.409297i
\(118\) 2.06040i 0.189675i
\(119\) 7.61676 17.1690i 0.698228 1.57388i
\(120\) 0.458377i 0.0418439i
\(121\) 9.18953 0.835412
\(122\) 2.60419 0.235773
\(123\) 3.81047 0.343578
\(124\) 8.35849i 0.750615i
\(125\) −4.48746 −0.401371
\(126\) 0.272628 0.614531i 0.0242876 0.0547467i
\(127\) −12.2981 −1.09128 −0.545640 0.838020i \(-0.683713\pi\)
−0.545640 + 0.838020i \(0.683713\pi\)
\(128\) −7.48763 −0.661819
\(129\) −7.18606 −0.632697
\(130\) 0.515659i 0.0452263i
\(131\) 5.17313i 0.451978i 0.974130 + 0.225989i \(0.0725614\pi\)
−0.974130 + 0.225989i \(0.927439\pi\)
\(132\) 2.60419 0.226666
\(133\) 4.72949 10.6608i 0.410099 0.924405i
\(134\) 1.48409i 0.128205i
\(135\) 0.458377i 0.0394508i
\(136\) 7.09918 0.608749
\(137\) 9.10644i 0.778016i −0.921234 0.389008i \(-0.872818\pi\)
0.921234 0.389008i \(-0.127182\pi\)
\(138\) −0.458377 1.12914i −0.0390197 0.0961184i
\(139\) 17.8503i 1.51404i 0.653391 + 0.757021i \(0.273346\pi\)
−0.653391 + 0.757021i \(0.726654\pi\)
\(140\) 0.951839 2.14554i 0.0804451 0.181331i
\(141\) 7.23353 0.609173
\(142\) 2.14137 0.179700
\(143\) 5.95699 0.498149
\(144\) −3.61676 −0.301397
\(145\) 1.92039 0.159479
\(146\) 1.78989i 0.148132i
\(147\) 5.18953 4.69774i 0.428026 0.387463i
\(148\) 16.5696i 1.36201i
\(149\) 20.1849i 1.65362i 0.562485 + 0.826808i \(0.309845\pi\)
−0.562485 + 0.826808i \(0.690155\pi\)
\(150\) 1.21712i 0.0993774i
\(151\) −11.5798 −0.942349 −0.471175 0.882040i \(-0.656170\pi\)
−0.471175 + 0.882040i \(0.656170\pi\)
\(152\) 4.40811 0.357545
\(153\) 7.09918 0.573934
\(154\) −0.826873 0.366830i −0.0666313 0.0295600i
\(155\) 1.97958i 0.159004i
\(156\) −8.56860 −0.686037
\(157\) −20.2643 −1.61727 −0.808634 0.588312i \(-0.799793\pi\)
−0.808634 + 0.588312i \(0.799793\pi\)
\(158\) 1.74472i 0.138802i
\(159\) 8.35783 0.662819
\(160\) 1.33802 0.105779
\(161\) 0.404950 12.6821i 0.0319146 0.999491i
\(162\) 0.254102 0.0199641
\(163\) 7.97942 0.624997 0.312498 0.949918i \(-0.398834\pi\)
0.312498 + 0.949918i \(0.398834\pi\)
\(164\) 7.37490i 0.575883i
\(165\) −0.616763 −0.0480149
\(166\) 1.25866 0.0976908
\(167\) 3.04399i 0.235551i 0.993040 + 0.117776i \(0.0375763\pi\)
−0.993040 + 0.117776i \(0.962424\pi\)
\(168\) 2.41844 + 1.07291i 0.186587 + 0.0827766i
\(169\) −6.60036 −0.507720
\(170\) −0.826873 −0.0634182
\(171\) 4.40811 0.337096
\(172\) 13.9081i 1.06048i
\(173\) 13.4231i 1.02054i −0.860015 0.510268i \(-0.829546\pi\)
0.860015 0.510268i \(-0.170454\pi\)
\(174\) 1.06457i 0.0807047i
\(175\) 5.13911 11.5841i 0.388480 0.875674i
\(176\) 4.86648i 0.366825i
\(177\) −8.10856 −0.609477
\(178\) −4.06620 −0.304775
\(179\) 14.2294 1.06355 0.531776 0.846885i \(-0.321525\pi\)
0.531776 + 0.846885i \(0.321525\pi\)
\(180\) 0.887158 0.0661249
\(181\) −19.6026 −1.45705 −0.728524 0.685020i \(-0.759793\pi\)
−0.728524 + 0.685020i \(0.759793\pi\)
\(182\) 2.72067 + 1.20699i 0.201669 + 0.0894677i
\(183\) 10.2486i 0.757600i
\(184\) 4.44364 1.80391i 0.327589 0.132986i
\(185\) 3.92425i 0.288517i
\(186\) −1.09738 −0.0804639
\(187\) 9.55220i 0.698526i
\(188\) 14.0000i 1.02105i
\(189\) 2.41844 + 1.07291i 0.175916 + 0.0780426i
\(190\) −0.513432 −0.0372483
\(191\) 21.1811i 1.53261i −0.642478 0.766304i \(-0.722094\pi\)
0.642478 0.766304i \(-0.277906\pi\)
\(192\) 6.49180i 0.468505i
\(193\) 10.0328 0.722178 0.361089 0.932531i \(-0.382405\pi\)
0.361089 + 0.932531i \(0.382405\pi\)
\(194\) 0.981557 0.0704717
\(195\) 2.02934 0.145324
\(196\) 9.09215 + 10.0440i 0.649439 + 0.717428i
\(197\) 5.53996 0.394706 0.197353 0.980333i \(-0.436766\pi\)
0.197353 + 0.980333i \(0.436766\pi\)
\(198\) 0.341903i 0.0242980i
\(199\) 6.69808 0.474814 0.237407 0.971410i \(-0.423702\pi\)
0.237407 + 0.971410i \(0.423702\pi\)
\(200\) 4.78989 0.338696
\(201\) −5.84052 −0.411958
\(202\) 3.21428i 0.226156i
\(203\) −4.49498 + 10.1322i −0.315486 + 0.711138i
\(204\) 13.7400i 0.961991i
\(205\) 1.74663i 0.121990i
\(206\) 1.91287 0.133276
\(207\) 4.44364 1.80391i 0.308854 0.125381i
\(208\) 16.0122i 1.11025i
\(209\) 5.93126i 0.410274i
\(210\) −0.281687 0.124966i −0.0194382 0.00862350i
\(211\) −9.33508 −0.642653 −0.321327 0.946968i \(-0.604129\pi\)
−0.321327 + 0.946968i \(0.604129\pi\)
\(212\) 16.1760i 1.11097i
\(213\) 8.42723i 0.577424i
\(214\) 5.12151i 0.350099i
\(215\) 3.29392i 0.224644i
\(216\) 1.00000i 0.0680414i
\(217\) −10.4445 4.63353i −0.709016 0.314545i
\(218\) 1.28634i 0.0871221i
\(219\) −7.04399 −0.475989
\(220\) 1.19370i 0.0804794i
\(221\) 31.4297i 2.11419i
\(222\) −2.17541 −0.146004
\(223\) 10.3257i 0.691459i 0.938334 + 0.345729i \(0.112368\pi\)
−0.938334 + 0.345729i \(0.887632\pi\)
\(224\) −3.13185 + 7.05950i −0.209255 + 0.471683i
\(225\) 4.78989 0.319326
\(226\) 0.859473i 0.0571713i
\(227\) −24.6428 −1.63560 −0.817800 0.575502i \(-0.804807\pi\)
−0.817800 + 0.575502i \(0.804807\pi\)
\(228\) 8.53159i 0.565018i
\(229\) −8.21928 −0.543146 −0.271573 0.962418i \(-0.587544\pi\)
−0.271573 + 0.962418i \(0.587544\pi\)
\(230\) −0.517570 + 0.210110i −0.0341276 + 0.0138542i
\(231\) 1.44364 3.25410i 0.0949843 0.214104i
\(232\) −4.18953 −0.275056
\(233\) −11.3749 −0.745194 −0.372597 0.927993i \(-0.621533\pi\)
−0.372597 + 0.927993i \(0.621533\pi\)
\(234\) 1.12497i 0.0735414i
\(235\) 3.31568i 0.216291i
\(236\) 15.6936i 1.02156i
\(237\) −6.86623 −0.446009
\(238\) 1.93543 4.36266i 0.125455 0.282789i
\(239\) −26.9547 −1.74355 −0.871777 0.489904i \(-0.837032\pi\)
−0.871777 + 0.489904i \(0.837032\pi\)
\(240\) 1.65784i 0.107013i
\(241\) 5.40422 0.348116 0.174058 0.984735i \(-0.444312\pi\)
0.174058 + 0.984735i \(0.444312\pi\)
\(242\) 2.33508 0.150104
\(243\) 1.00000i 0.0641500i
\(244\) −19.8355 −1.26984
\(245\) −2.15334 2.37876i −0.137572 0.151974i
\(246\) 0.968246 0.0617331
\(247\) 19.5157i 1.24175i
\(248\) 4.31867i 0.274236i
\(249\) 4.95336i 0.313907i
\(250\) −1.14027 −0.0721171
\(251\) 19.4067 1.22494 0.612471 0.790493i \(-0.290176\pi\)
0.612471 + 0.790493i \(0.290176\pi\)
\(252\) −2.07654 + 4.68073i −0.130810 + 0.294859i
\(253\) −2.42723 5.97907i −0.152599 0.375901i
\(254\) −3.12497 −0.196078
\(255\) 3.25410i 0.203780i
\(256\) 11.0810 0.692561
\(257\) 4.34625i 0.271112i −0.990770 0.135556i \(-0.956718\pi\)
0.990770 0.135556i \(-0.0432821\pi\)
\(258\) −1.82599 −0.113681
\(259\) −20.7047 9.18537i −1.28653 0.570751i
\(260\) 3.92765i 0.243583i
\(261\) −4.18953 −0.259326
\(262\) 1.31450i 0.0812101i
\(263\) 1.57848i 0.0973335i 0.998815 + 0.0486668i \(0.0154972\pi\)
−0.998815 + 0.0486668i \(0.984503\pi\)
\(264\) 1.34554 0.0828120
\(265\) 3.83104i 0.235339i
\(266\) 1.20177 2.70892i 0.0736854 0.166094i
\(267\) 16.0023i 0.979323i
\(268\) 11.3039i 0.690497i
\(269\) 21.4025i 1.30493i −0.757818 0.652466i \(-0.773734\pi\)
0.757818 0.652466i \(-0.226266\pi\)
\(270\) 0.116474i 0.00708841i
\(271\) 15.3267i 0.931033i 0.885039 + 0.465517i \(0.154131\pi\)
−0.885039 + 0.465517i \(0.845869\pi\)
\(272\) −25.6760 −1.55684
\(273\) −4.75001 + 10.7070i −0.287484 + 0.648017i
\(274\) 2.31396i 0.139792i
\(275\) 6.44497i 0.388646i
\(276\) 3.49135 + 8.60036i 0.210155 + 0.517681i
\(277\) 10.5152 0.631798 0.315899 0.948793i \(-0.397694\pi\)
0.315899 + 0.948793i \(0.397694\pi\)
\(278\) 4.53579i 0.272039i
\(279\) 4.31867i 0.258552i
\(280\) 0.491797 1.10856i 0.0293905 0.0662491i
\(281\) 5.30278i 0.316338i −0.987412 0.158169i \(-0.949441\pi\)
0.987412 0.158169i \(-0.0505590\pi\)
\(282\) 1.83805 0.109454
\(283\) −2.05894 −0.122391 −0.0611956 0.998126i \(-0.519491\pi\)
−0.0611956 + 0.998126i \(0.519491\pi\)
\(284\) −16.3103 −0.967840
\(285\) 2.02058i 0.119689i
\(286\) 1.51368 0.0895059
\(287\) 9.21540 + 4.08828i 0.543968 + 0.241323i
\(288\) −2.91903 −0.172005
\(289\) 33.3983 1.96461
\(290\) 0.487974 0.0286548
\(291\) 3.86285i 0.226444i
\(292\) 13.6332i 0.797821i
\(293\) −17.4939 −1.02200 −0.511001 0.859580i \(-0.670725\pi\)
−0.511001 + 0.859580i \(0.670725\pi\)
\(294\) 1.31867 1.19370i 0.0769064 0.0696182i
\(295\) 3.71678i 0.216399i
\(296\) 8.56119i 0.497609i
\(297\) 1.34554 0.0780759
\(298\) 5.12903i 0.297117i
\(299\) 7.98634 + 19.6730i 0.461862 + 1.13772i
\(300\) 9.27051i 0.535233i
\(301\) −17.3791 7.70998i −1.00171 0.444396i
\(302\) −2.94244 −0.169318
\(303\) −12.6496 −0.726699
\(304\) −15.9431 −0.914398
\(305\) 4.69774 0.268992
\(306\) 1.80391 0.103123
\(307\) 31.8573i 1.81819i −0.416587 0.909096i \(-0.636774\pi\)
0.416587 0.909096i \(-0.363226\pi\)
\(308\) 6.29809 + 2.79406i 0.358867 + 0.159206i
\(309\) 7.52796i 0.428251i
\(310\) 0.503015i 0.0285693i
\(311\) 2.71831i 0.154141i 0.997026 + 0.0770707i \(0.0245567\pi\)
−0.997026 + 0.0770707i \(0.975443\pi\)
\(312\) −4.42723 −0.250642
\(313\) −21.1811 −1.19722 −0.598612 0.801039i \(-0.704281\pi\)
−0.598612 + 0.801039i \(0.704281\pi\)
\(314\) −5.14919 −0.290586
\(315\) 0.491797 1.10856i 0.0277096 0.0624603i
\(316\) 13.2891i 0.747571i
\(317\) −11.2541 −0.632093 −0.316047 0.948744i \(-0.602356\pi\)
−0.316047 + 0.948744i \(0.602356\pi\)
\(318\) 2.12374 0.119093
\(319\) 5.63717i 0.315621i
\(320\) −2.97569 −0.166346
\(321\) 20.1553 1.12496
\(322\) 0.102899 3.22255i 0.00573431 0.179585i
\(323\) 31.2939 1.74124
\(324\) −1.93543 −0.107524
\(325\) 21.2059i 1.17629i
\(326\) 2.02759 0.112298
\(327\) −5.06232 −0.279947
\(328\) 3.81047i 0.210398i
\(329\) 17.4939 + 7.76091i 0.964468 + 0.427873i
\(330\) −0.156721 −0.00862718
\(331\) 8.54102 0.469457 0.234728 0.972061i \(-0.424580\pi\)
0.234728 + 0.972061i \(0.424580\pi\)
\(332\) −9.58690 −0.526149
\(333\) 8.56119i 0.469150i
\(334\) 0.773483i 0.0423231i
\(335\) 2.67716i 0.146269i
\(336\) −8.74694 3.88045i −0.477185 0.211696i
\(337\) 8.24136i 0.448935i 0.974482 + 0.224468i \(0.0720643\pi\)
−0.974482 + 0.224468i \(0.927936\pi\)
\(338\) −1.67716 −0.0912256
\(339\) −3.38240 −0.183707
\(340\) 6.29809 0.341562
\(341\) −5.81092 −0.314679
\(342\) 1.12011 0.0605685
\(343\) 17.5908 5.79332i 0.949816 0.312810i
\(344\) 7.18606i 0.387446i
\(345\) −0.826873 2.03686i −0.0445173 0.109661i
\(346\) 3.41082i 0.183367i
\(347\) −10.6649 −0.572523 −0.286262 0.958152i \(-0.592413\pi\)
−0.286262 + 0.958152i \(0.592413\pi\)
\(348\) 8.10856i 0.434664i
\(349\) 1.00417i 0.0537519i 0.999639 + 0.0268760i \(0.00855592\pi\)
−0.999639 + 0.0268760i \(0.991444\pi\)
\(350\) 1.30586 2.94353i 0.0698010 0.157339i
\(351\) −4.42723 −0.236308
\(352\) 3.92765i 0.209345i
\(353\) 35.7693i 1.90381i 0.306396 + 0.951904i \(0.400877\pi\)
−0.306396 + 0.951904i \(0.599123\pi\)
\(354\) −2.06040 −0.109509
\(355\) 3.86285 0.205019
\(356\) 30.9713 1.64148
\(357\) 17.1690 + 7.61676i 0.908678 + 0.403122i
\(358\) 3.61570 0.191096
\(359\) 20.6433i 1.08951i 0.838594 + 0.544756i \(0.183378\pi\)
−0.838594 + 0.544756i \(0.816622\pi\)
\(360\) 0.458377 0.0241586
\(361\) 0.431398 0.0227052
\(362\) −4.98105 −0.261798
\(363\) 9.18953i 0.482325i
\(364\) −20.7227 9.19332i −1.08616 0.481861i
\(365\) 3.22881i 0.169003i
\(366\) 2.60419i 0.136123i
\(367\) 25.7352 1.34337 0.671684 0.740838i \(-0.265571\pi\)
0.671684 + 0.740838i \(0.265571\pi\)
\(368\) −16.0716 + 6.52433i −0.837789 + 0.340104i
\(369\) 3.81047i 0.198365i
\(370\) 0.997160i 0.0518399i
\(371\) 20.2130 + 8.96719i 1.04940 + 0.465553i
\(372\) 8.35849 0.433368
\(373\) 16.6786i 0.863583i −0.901974 0.431791i \(-0.857882\pi\)
0.901974 0.431791i \(-0.142118\pi\)
\(374\) 2.42723i 0.125509i
\(375\) 4.48746i 0.231732i
\(376\) 7.23353i 0.373041i
\(377\) 18.5480i 0.955272i
\(378\) 0.614531 + 0.272628i 0.0316080 + 0.0140225i
\(379\) 30.9492i 1.58976i −0.606770 0.794878i \(-0.707535\pi\)
0.606770 0.794878i \(-0.292465\pi\)
\(380\) 3.91069 0.200614
\(381\) 12.2981i 0.630050i
\(382\) 5.38214i 0.275374i
\(383\) 18.6858 0.954801 0.477400 0.878686i \(-0.341579\pi\)
0.477400 + 0.878686i \(0.341579\pi\)
\(384\) 7.48763i 0.382101i
\(385\) −1.49161 0.661730i −0.0760193 0.0337249i
\(386\) 2.54935 0.129759
\(387\) 7.18606i 0.365288i
\(388\) −7.47629 −0.379551
\(389\) 26.5059i 1.34390i −0.740595 0.671952i \(-0.765456\pi\)
0.740595 0.671952i \(-0.234544\pi\)
\(390\) 0.515659 0.0261114
\(391\) 31.5462 12.8063i 1.59536 0.647642i
\(392\) 4.69774 + 5.18953i 0.237272 + 0.262111i
\(393\) −5.17313 −0.260950
\(394\) 1.40771 0.0709195
\(395\) 3.14732i 0.158359i
\(396\) 2.60419i 0.130866i
\(397\) 8.63734i 0.433496i −0.976228 0.216748i \(-0.930455\pi\)
0.976228 0.216748i \(-0.0695449\pi\)
\(398\) 1.70199 0.0853132
\(399\) 10.6608 + 4.72949i 0.533705 + 0.236771i
\(400\) −17.3239 −0.866195
\(401\) 12.9322i 0.645802i 0.946433 + 0.322901i \(0.104658\pi\)
−0.946433 + 0.322901i \(0.895342\pi\)
\(402\) −1.48409 −0.0740195
\(403\) 19.1197 0.952422
\(404\) 24.4824i 1.21804i
\(405\) 0.458377 0.0227770
\(406\) −1.14218 + 2.57460i −0.0566856 + 0.127775i
\(407\) −11.5194 −0.570995
\(408\) 7.09918i 0.351462i
\(409\) 4.40665i 0.217895i 0.994048 + 0.108947i \(0.0347480\pi\)
−0.994048 + 0.108947i \(0.965252\pi\)
\(410\) 0.443822i 0.0219188i
\(411\) 9.10644 0.449188
\(412\) −14.5699 −0.717805
\(413\) −19.6101 8.69974i −0.964950 0.428086i
\(414\) 1.12914 0.458377i 0.0554940 0.0225280i
\(415\) 2.27051 0.111455
\(416\) 12.9232i 0.633612i
\(417\) −17.8503 −0.874132
\(418\) 1.50714i 0.0737168i
\(419\) 5.91988 0.289205 0.144602 0.989490i \(-0.453810\pi\)
0.144602 + 0.989490i \(0.453810\pi\)
\(420\) 2.14554 + 0.951839i 0.104692 + 0.0464450i
\(421\) 10.4816i 0.510841i −0.966830 0.255420i \(-0.917786\pi\)
0.966830 0.255420i \(-0.0822139\pi\)
\(422\) −2.37206 −0.115470
\(423\) 7.23353i 0.351706i
\(424\) 8.35783i 0.405892i
\(425\) 34.0043 1.64945
\(426\) 2.14137i 0.103750i
\(427\) −10.9958 + 24.7857i −0.532126 + 1.19947i
\(428\) 39.0093i 1.88559i
\(429\) 5.95699i 0.287606i
\(430\) 0.836992i 0.0403633i
\(431\) 21.0129i 1.01216i −0.862488 0.506078i \(-0.831095\pi\)
0.862488 0.506078i \(-0.168905\pi\)
\(432\) 3.61676i 0.174012i
\(433\) 7.21565 0.346762 0.173381 0.984855i \(-0.444531\pi\)
0.173381 + 0.984855i \(0.444531\pi\)
\(434\) −2.65395 1.17739i −0.127394 0.0565165i
\(435\) 1.92039i 0.0920755i
\(436\) 9.79777i 0.469228i
\(437\) 19.5880 7.95184i 0.937022 0.380388i
\(438\) −1.78989 −0.0855243
\(439\) 37.1565i 1.77338i 0.462364 + 0.886690i \(0.347001\pi\)
−0.462364 + 0.886690i \(0.652999\pi\)
\(440\) 0.616763i 0.0294030i
\(441\) 4.69774 + 5.18953i 0.223702 + 0.247121i
\(442\) 7.98634i 0.379871i
\(443\) −16.8461 −0.800383 −0.400192 0.916431i \(-0.631056\pi\)
−0.400192 + 0.916431i \(0.631056\pi\)
\(444\) 16.5696 0.786358
\(445\) −7.33508 −0.347716
\(446\) 2.62377i 0.124239i
\(447\) −20.1849 −0.954715
\(448\) 6.96510 15.7000i 0.329070 0.741757i
\(449\) 0.583949 0.0275583 0.0137791 0.999905i \(-0.495614\pi\)
0.0137791 + 0.999905i \(0.495614\pi\)
\(450\) 1.21712 0.0573755
\(451\) 5.12712 0.241427
\(452\) 6.54640i 0.307917i
\(453\) 11.5798i 0.544066i
\(454\) −6.26178 −0.293880
\(455\) 4.90785 + 2.17730i 0.230083 + 0.102073i
\(456\) 4.40811i 0.206428i
\(457\) 16.8617i 0.788759i 0.918948 + 0.394379i \(0.129040\pi\)
−0.918948 + 0.394379i \(0.870960\pi\)
\(458\) −2.08853 −0.0975908
\(459\) 7.09918i 0.331361i
\(460\) 3.94221 1.60036i 0.183806 0.0746170i
\(461\) 5.50403i 0.256348i 0.991752 + 0.128174i \(0.0409117\pi\)
−0.991752 + 0.128174i \(0.959088\pi\)
\(462\) 0.366830 0.826873i 0.0170665 0.0384696i
\(463\) 14.3103 0.665058 0.332529 0.943093i \(-0.392098\pi\)
0.332529 + 0.943093i \(0.392098\pi\)
\(464\) 15.1526 0.703440
\(465\) −1.97958 −0.0918008
\(466\) −2.89038 −0.133894
\(467\) −9.88465 −0.457407 −0.228703 0.973496i \(-0.573449\pi\)
−0.228703 + 0.973496i \(0.573449\pi\)
\(468\) 8.56860i 0.396084i
\(469\) −14.1250 6.26634i −0.652230 0.289353i
\(470\) 0.842521i 0.0388626i
\(471\) 20.2643i 0.933730i
\(472\) 8.10856i 0.373227i
\(473\) −9.66909 −0.444585
\(474\) −1.74472 −0.0801377
\(475\) 21.1143 0.968793
\(476\) −14.7417 + 33.2294i −0.675686 + 1.52307i
\(477\) 8.35783i 0.382679i
\(478\) −6.84923 −0.313276
\(479\) −0.894679 −0.0408789 −0.0204395 0.999791i \(-0.506507\pi\)
−0.0204395 + 0.999791i \(0.506507\pi\)
\(480\) 1.33802i 0.0610718i
\(481\) 37.9023 1.72820
\(482\) 1.37322 0.0625485
\(483\) 12.6821 + 0.404950i 0.577056 + 0.0184259i
\(484\) −17.7857 −0.808442
\(485\) 1.77064 0.0804008
\(486\) 0.254102i 0.0115263i
\(487\) 4.41499 0.200062 0.100031 0.994984i \(-0.468106\pi\)
0.100031 + 0.994984i \(0.468106\pi\)
\(488\) −10.2486 −0.463933
\(489\) 7.97942i 0.360842i
\(490\) −0.547166 0.604448i −0.0247185 0.0273062i
\(491\) 26.5480 1.19810 0.599048 0.800713i \(-0.295546\pi\)
0.599048 + 0.800713i \(0.295546\pi\)
\(492\) −7.37490 −0.332486
\(493\) −29.7422 −1.33952
\(494\) 4.95897i 0.223115i
\(495\) 0.616763i 0.0277214i
\(496\) 15.6196i 0.701341i
\(497\) −9.04164 + 20.3808i −0.405573 + 0.914203i
\(498\) 1.25866i 0.0564018i
\(499\) 20.0206 0.896244 0.448122 0.893972i \(-0.352093\pi\)
0.448122 + 0.893972i \(0.352093\pi\)
\(500\) 8.68518 0.388413
\(501\) −3.04399 −0.135996
\(502\) 4.93129 0.220094
\(503\) −1.17739 −0.0524972 −0.0262486 0.999655i \(-0.508356\pi\)
−0.0262486 + 0.999655i \(0.508356\pi\)
\(504\) −1.07291 + 2.41844i −0.0477911 + 0.107726i
\(505\) 5.79828i 0.258020i
\(506\) −0.616763 1.51929i −0.0274185 0.0675408i
\(507\) 6.60036i 0.293132i
\(508\) 23.8021 1.05605
\(509\) 8.24993i 0.365672i 0.983143 + 0.182836i \(0.0585277\pi\)
−0.983143 + 0.182836i \(0.941472\pi\)
\(510\) 0.826873i 0.0366145i
\(511\) −17.0355 7.55755i −0.753606 0.334327i
\(512\) 17.7909 0.786256
\(513\) 4.40811i 0.194623i
\(514\) 1.10439i 0.0487126i
\(515\) 3.45065 0.152054
\(516\) 13.9081 0.612271
\(517\) 9.73297 0.428055
\(518\) −5.26111 2.33402i −0.231160 0.102551i
\(519\) 13.4231 0.589207
\(520\) 2.02934i 0.0889925i
\(521\) 25.7850 1.12966 0.564831 0.825207i \(-0.308942\pi\)
0.564831 + 0.825207i \(0.308942\pi\)
\(522\) −1.06457 −0.0465949
\(523\) −26.9939 −1.18036 −0.590180 0.807272i \(-0.700943\pi\)
−0.590180 + 0.807272i \(0.700943\pi\)
\(524\) 10.0122i 0.437387i
\(525\) 11.5841 + 5.13911i 0.505571 + 0.224289i
\(526\) 0.401096i 0.0174886i
\(527\) 30.6590i 1.33553i
\(528\) −4.86648 −0.211786
\(529\) 16.4918 16.0319i 0.717035 0.697038i
\(530\) 0.973474i 0.0422850i
\(531\) 8.10856i 0.351882i
\(532\) −9.15361 + 20.6332i −0.396859 + 0.894561i
\(533\) −16.8698 −0.730712
\(534\) 4.06620i 0.175962i
\(535\) 9.23875i 0.399426i
\(536\) 5.84052i 0.252272i
\(537\) 14.2294i 0.614042i
\(538\) 5.43841i 0.234466i
\(539\) 6.98270 6.32097i 0.300766 0.272264i
\(540\) 0.887158i 0.0381772i
\(541\) −12.6373 −0.543322 −0.271661 0.962393i \(-0.587573\pi\)
−0.271661 + 0.962393i \(0.587573\pi\)
\(542\) 3.89455i 0.167285i
\(543\) 19.6026i 0.841227i
\(544\) −20.7227 −0.888478
\(545\) 2.32045i 0.0993972i
\(546\) −1.20699 + 2.72067i −0.0516542 + 0.116434i
\(547\) 2.52878 0.108123 0.0540614 0.998538i \(-0.482783\pi\)
0.0540614 + 0.998538i \(0.482783\pi\)
\(548\) 17.6249i 0.752899i
\(549\) −10.2486 −0.437401
\(550\) 1.63768i 0.0698308i
\(551\) −18.4679 −0.786759
\(552\) 1.80391 + 4.44364i 0.0767796 + 0.189134i
\(553\) −16.6056 7.36683i −0.706141 0.313269i
\(554\) 2.67193 0.113520
\(555\) −3.92425 −0.166575
\(556\) 34.5480i 1.46516i
\(557\) 30.2654i 1.28239i 0.767379 + 0.641194i \(0.221560\pi\)
−0.767379 + 0.641194i \(0.778440\pi\)
\(558\) 1.09738i 0.0464558i
\(559\) 31.8143 1.34560
\(560\) −1.77871 + 4.00940i −0.0751643 + 0.169428i
\(561\) 9.55220 0.403294
\(562\) 1.34745i 0.0568386i
\(563\) 36.6381 1.54411 0.772055 0.635555i \(-0.219229\pi\)
0.772055 + 0.635555i \(0.219229\pi\)
\(564\) −14.0000 −0.589506
\(565\) 1.55041i 0.0652264i
\(566\) −0.523180 −0.0219909
\(567\) −1.07291 + 2.41844i −0.0450579 + 0.101565i
\(568\) −8.42723 −0.353599
\(569\) 27.1085i 1.13645i −0.822875 0.568223i \(-0.807631\pi\)
0.822875 0.568223i \(-0.192369\pi\)
\(570\) 0.513432i 0.0215053i
\(571\) 7.95674i 0.332979i 0.986043 + 0.166490i \(0.0532432\pi\)
−0.986043 + 0.166490i \(0.946757\pi\)
\(572\) −11.5294 −0.482067
\(573\) 21.1811 0.884851
\(574\) 2.34165 + 1.03884i 0.0977385 + 0.0433603i
\(575\) 21.2845 8.64054i 0.887626 0.360336i
\(576\) 6.49180 0.270492
\(577\) 19.9672i 0.831245i −0.909537 0.415622i \(-0.863564\pi\)
0.909537 0.415622i \(-0.136436\pi\)
\(578\) 8.48657 0.352995
\(579\) 10.0328i 0.416950i
\(580\) −3.71678 −0.154331
\(581\) −5.31450 + 11.9794i −0.220483 + 0.496990i
\(582\) 0.981557i 0.0406868i
\(583\) 11.2458 0.465752
\(584\) 7.04399i 0.291482i
\(585\) 2.02934i 0.0839029i
\(586\) −4.44522 −0.183630
\(587\) 21.8555i 0.902074i 0.892505 + 0.451037i \(0.148946\pi\)
−0.892505 + 0.451037i \(0.851054\pi\)
\(588\) −10.0440 + 9.09215i −0.414207 + 0.374954i
\(589\) 19.0372i 0.784412i
\(590\) 0.944440i 0.0388820i
\(591\) 5.53996i 0.227883i
\(592\) 30.9638i 1.27260i
\(593\) 36.9117i 1.51578i 0.652380 + 0.757892i \(0.273771\pi\)
−0.652380 + 0.757892i \(0.726229\pi\)
\(594\) 0.341903 0.0140284
\(595\) 3.49135 7.86986i 0.143131 0.322633i
\(596\) 39.0666i 1.60023i
\(597\) 6.69808i 0.274134i
\(598\) 2.02934 + 4.99894i 0.0829859 + 0.204422i
\(599\) −32.2898 −1.31932 −0.659662 0.751563i \(-0.729300\pi\)
−0.659662 + 0.751563i \(0.729300\pi\)
\(600\) 4.78989i 0.195546i
\(601\) 24.6496i 1.00548i −0.864438 0.502739i \(-0.832326\pi\)
0.864438 0.502739i \(-0.167674\pi\)
\(602\) −4.41605 1.95912i −0.179985 0.0798477i
\(603\) 5.84052i 0.237844i
\(604\) 22.4119 0.911927
\(605\) 4.21227 0.171253
\(606\) −3.21428 −0.130571
\(607\) 23.4988i 0.953787i 0.878961 + 0.476894i \(0.158237\pi\)
−0.878961 + 0.476894i \(0.841763\pi\)
\(608\) −12.8674 −0.521841
\(609\) −10.1322 4.49498i −0.410575 0.182146i
\(610\) 1.19370 0.0483316
\(611\) −32.0245 −1.29557
\(612\) −13.7400 −0.555406
\(613\) 1.34554i 0.0543457i −0.999631 0.0271728i \(-0.991350\pi\)
0.999631 0.0271728i \(-0.00865045\pi\)
\(614\) 8.09499i 0.326687i
\(615\) 1.74663 0.0704310
\(616\) 3.25410 + 1.44364i 0.131111 + 0.0581657i
\(617\) 20.2347i 0.814619i 0.913290 + 0.407309i \(0.133533\pi\)
−0.913290 + 0.407309i \(0.866467\pi\)
\(618\) 1.91287i 0.0769468i
\(619\) 37.2425 1.49690 0.748452 0.663189i \(-0.230798\pi\)
0.748452 + 0.663189i \(0.230798\pi\)
\(620\) 3.83134i 0.153870i
\(621\) 1.80391 + 4.44364i 0.0723885 + 0.178317i
\(622\) 0.690728i 0.0276957i
\(623\) 17.1690 38.7006i 0.687860 1.55051i
\(624\) 16.0122 0.641003
\(625\) 21.8925 0.875700
\(626\) −5.38214 −0.215114
\(627\) 5.93126 0.236872
\(628\) 39.2202 1.56506
\(629\) 60.7774i 2.42335i
\(630\) 0.124966 0.281687i 0.00497878 0.0112227i
\(631\) 39.5546i 1.57464i 0.616543 + 0.787321i \(0.288533\pi\)
−0.616543 + 0.787321i \(0.711467\pi\)
\(632\) 6.86623i 0.273124i
\(633\) 9.33508i 0.371036i
\(634\) −2.85969 −0.113573
\(635\) −5.63717 −0.223704
\(636\) −16.1760 −0.641421
\(637\) −22.9753 + 20.7980i −0.910313 + 0.824045i
\(638\) 1.43241i 0.0567098i
\(639\) −8.42723 −0.333376
\(640\) −3.43216 −0.135668
\(641\) 19.8430i 0.783753i −0.920018 0.391877i \(-0.871826\pi\)
0.920018 0.391877i \(-0.128174\pi\)
\(642\) 5.12151 0.202130
\(643\) −47.0309 −1.85472 −0.927358 0.374176i \(-0.877926\pi\)
−0.927358 + 0.374176i \(0.877926\pi\)
\(644\) −0.783754 + 24.5454i −0.0308842 + 0.967223i
\(645\) −3.29392 −0.129698
\(646\) 7.95184 0.312861
\(647\) 29.5592i 1.16209i −0.813871 0.581046i \(-0.802644\pi\)
0.813871 0.581046i \(-0.197356\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −10.9104 −0.428269
\(650\) 5.38847i 0.211353i
\(651\) 4.63353 10.4445i 0.181603 0.409351i
\(652\) −15.4436 −0.604819
\(653\) 31.9466 1.25017 0.625084 0.780558i \(-0.285065\pi\)
0.625084 + 0.780558i \(0.285065\pi\)
\(654\) −1.28634 −0.0503000
\(655\) 2.37124i 0.0926522i
\(656\) 13.7816i 0.538079i
\(657\) 7.04399i 0.274812i
\(658\) 4.44522 + 1.97206i 0.173293 + 0.0768789i
\(659\) 32.7104i 1.27422i −0.770774 0.637108i \(-0.780130\pi\)
0.770774 0.637108i \(-0.219870\pi\)
\(660\) 1.19370 0.0464648
\(661\) −11.9361 −0.464259 −0.232130 0.972685i \(-0.574569\pi\)
−0.232130 + 0.972685i \(0.574569\pi\)
\(662\) 2.17029 0.0843506
\(663\) −31.4297 −1.22063
\(664\) −4.95336 −0.192228
\(665\) 2.16789 4.88665i 0.0840672 0.189496i
\(666\) 2.17541i 0.0842955i
\(667\) −18.6168 + 7.55755i −0.720844 + 0.292630i
\(668\) 5.89144i 0.227947i
\(669\) −10.3257 −0.399214
\(670\) 0.680271i 0.0262812i
\(671\) 13.7899i 0.532353i
\(672\) −7.05950 3.13185i −0.272326 0.120814i
\(673\) −18.0521 −0.695856 −0.347928 0.937521i \(-0.613115\pi\)
−0.347928 + 0.937521i \(0.613115\pi\)
\(674\) 2.09414i 0.0806634i
\(675\) 4.78989i 0.184363i
\(676\) 12.7745 0.491329
\(677\) −50.0582 −1.92389 −0.961947 0.273237i \(-0.911906\pi\)
−0.961947 + 0.273237i \(0.911906\pi\)
\(678\) −0.859473 −0.0330079
\(679\) −4.14448 + 9.34209i −0.159051 + 0.358516i
\(680\) 3.25410 0.124789
\(681\) 24.6428i 0.944315i
\(682\) −1.47657 −0.0565406
\(683\) 3.61782 0.138432 0.0692161 0.997602i \(-0.477950\pi\)
0.0692161 + 0.997602i \(0.477950\pi\)
\(684\) −8.53159 −0.326214
\(685\) 4.17419i 0.159487i
\(686\) 4.46986 1.47209i 0.170660 0.0562048i
\(687\) 8.21928i 0.313585i
\(688\) 25.9903i 0.990869i
\(689\) −37.0020 −1.40967
\(690\) −0.210110 0.517570i −0.00799874 0.0197036i
\(691\) 9.24887i 0.351844i 0.984404 + 0.175922i \(0.0562906\pi\)
−0.984404 + 0.175922i \(0.943709\pi\)
\(692\) 25.9794i 0.987590i
\(693\) 3.25410 + 1.44364i 0.123613 + 0.0548392i
\(694\) −2.70998 −0.102869
\(695\) 8.18217i 0.310367i
\(696\) 4.18953i 0.158804i
\(697\) 27.0512i 1.02464i
\(698\) 0.255161i 0.00965799i
\(699\) 11.3749i 0.430238i
\(700\) −9.94640 + 22.4202i −0.375939 + 0.847404i
\(701\) 26.8478i 1.01403i 0.861938 + 0.507014i \(0.169251\pi\)
−0.861938 + 0.507014i \(0.830749\pi\)
\(702\) −1.12497 −0.0424591
\(703\) 37.7386i 1.42334i
\(704\) 8.73494i 0.329211i
\(705\) 3.31568 0.124876
\(706\) 9.08904i 0.342071i
\(707\) −30.5923 13.5718i −1.15054 0.510421i
\(708\) 15.6936 0.589800
\(709\) 23.7632i 0.892445i 0.894922 + 0.446222i \(0.147231\pi\)
−0.894922 + 0.446222i \(0.852769\pi\)
\(710\) 0.981557 0.0368372
\(711\) 6.86623i 0.257504i
\(712\) 16.0023 0.599710
\(713\) −7.79050 19.1906i −0.291757 0.718693i
\(714\) 4.36266 + 1.93543i 0.163268 + 0.0724317i
\(715\) 2.73055 0.102117
\(716\) −27.5400 −1.02922
\(717\) 26.9547i 1.00664i
\(718\) 5.24550i 0.195760i
\(719\) 43.0768i 1.60649i 0.595646 + 0.803247i \(0.296896\pi\)
−0.595646 + 0.803247i \(0.703104\pi\)
\(720\) −1.65784 −0.0617841
\(721\) −8.07681 + 18.2059i −0.300796 + 0.678025i
\(722\) 0.109619 0.00407959
\(723\) 5.40422i 0.200985i
\(724\) 37.9395 1.41001
\(725\) −20.0674 −0.745285
\(726\) 2.33508i 0.0866628i
\(727\) −32.3389 −1.19938 −0.599692 0.800231i \(-0.704710\pi\)
−0.599692 + 0.800231i \(0.704710\pi\)
\(728\) −10.7070 4.75001i −0.396828 0.176047i
\(729\) −1.00000 −0.0370370
\(730\) 0.820445i 0.0303660i
\(731\) 51.0151i 1.88686i
\(732\) 19.8355i 0.733142i
\(733\) −35.4940 −1.31100 −0.655500 0.755195i \(-0.727542\pi\)
−0.655500 + 0.755195i \(0.727542\pi\)
\(734\) 6.53937 0.241372
\(735\) 2.37876 2.15334i 0.0877421 0.0794270i
\(736\) −12.9711 + 5.26567i −0.478121 + 0.194095i
\(737\) −7.85863 −0.289476
\(738\) 0.968246i 0.0356416i
\(739\) −19.9641 −0.734390 −0.367195 0.930144i \(-0.619682\pi\)
−0.367195 + 0.930144i \(0.619682\pi\)
\(740\) 7.59513i 0.279202i
\(741\) −19.5157 −0.716927
\(742\) 5.13614 + 2.27858i 0.188554 + 0.0836492i
\(743\) 1.29577i 0.0475373i −0.999717 0.0237687i \(-0.992433\pi\)
0.999717 0.0237687i \(-0.00756652\pi\)
\(744\) 4.31867 0.158330
\(745\) 9.25232i 0.338979i
\(746\) 4.23805i 0.155166i
\(747\) −4.95336 −0.181234
\(748\) 18.4876i 0.675975i
\(749\) 48.7446 + 21.6248i 1.78109 + 0.790154i
\(750\) 1.14027i 0.0416368i
\(751\) 45.7445i 1.66924i 0.550825 + 0.834620i \(0.314313\pi\)
−0.550825 + 0.834620i \(0.685687\pi\)
\(752\) 26.1619i 0.954028i
\(753\) 19.4067i 0.707221i
\(754\) 4.71308i 0.171640i
\(755\) −5.30791 −0.193175
\(756\) −4.68073 2.07654i −0.170237 0.0755231i
\(757\) 20.4601i 0.743636i 0.928306 + 0.371818i \(0.121265\pi\)
−0.928306 + 0.371818i \(0.878735\pi\)
\(758\) 7.86425i 0.285642i
\(759\) 5.97907 2.42723i 0.217026 0.0881028i
\(760\) 2.02058 0.0732940
\(761\) 41.9177i 1.51952i 0.650206 + 0.759758i \(0.274682\pi\)
−0.650206 + 0.759758i \(0.725318\pi\)
\(762\) 3.12497i 0.113206i
\(763\) −12.2429 5.43140i −0.443224 0.196630i
\(764\) 40.9945i 1.48313i
\(765\) 3.25410 0.117652
\(766\) 4.74810 0.171556
\(767\) 35.8984 1.29622
\(768\) 11.0810i 0.399850i
\(769\) 9.95087 0.358838 0.179419 0.983773i \(-0.442578\pi\)
0.179419 + 0.983773i \(0.442578\pi\)
\(770\) −0.379020 0.168147i −0.0136589 0.00605959i
\(771\) 4.34625 0.156527
\(772\) −19.4178 −0.698863
\(773\) −25.9367 −0.932877 −0.466439 0.884554i \(-0.654463\pi\)
−0.466439 + 0.884554i \(0.654463\pi\)
\(774\) 1.82599i 0.0656338i
\(775\) 20.6860i 0.743061i
\(776\) −3.86285 −0.138668
\(777\) 9.18537 20.7047i 0.329523 0.742779i
\(778\) 6.73520i 0.241469i
\(779\) 16.7969i 0.601813i
\(780\) −3.92765 −0.140633
\(781\) 11.3391i 0.405746i
\(782\) 8.01593 3.25410i 0.286649 0.116366i
\(783\) 4.18953i 0.149722i
\(784\) −16.9906 18.7693i −0.606807 0.670333i
\(785\) −9.28870 −0.331528
\(786\) −1.31450 −0.0468867
\(787\) −4.70586 −0.167746 −0.0838728 0.996476i \(-0.526729\pi\)
−0.0838728 + 0.996476i \(0.526729\pi\)
\(788\) −10.7222 −0.381963
\(789\) −1.57848