Properties

Label 483.2.h.b.160.5
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 160.5
Root \(-1.51343i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.b.160.7

$q$-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 \(-0.532683\pi\)
−0.102496 + 0.994733i \(0.532683\pi\)
\(6\) 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 \(0.210419\pi\)
−0.789348 + 0.613946i \(0.789581\pi\)
\(14\) 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 \(-0.169900\pi\)
0.860902 + 0.508771i \(0.169900\pi\)
\(18\) −0.254102 −0.0598923
\(19\) 4.40811 1.01129 0.505644 0.862742i \(-0.331255\pi\)
0.505644 + 0.862742i \(0.331255\pi\)
\(20\) 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 \(-0.873225\pi\)
0.921732 0.387828i \(-0.126775\pi\)
\(32\) 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 \(0.0961686\pi\)
−0.954707 + 0.297547i \(0.903831\pi\)
\(42\) 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 \(0.176893\pi\)
−0.849518 + 0.527559i \(0.823107\pi\)
\(48\) 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 \(-0.823009\pi\)
0.849355 0.527822i \(-0.176991\pi\)
\(60\) 0.887158i 0.114532i
\(61\) −10.2486 −1.31220 −0.656101 0.754673i \(-0.727795\pi\)
−0.656101 + 0.754673i \(0.727795\pi\)
\(62\) 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 \(-0.864754\pi\)
0.911085 0.412218i \(-0.135246\pi\)
\(74\) 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 \(-0.587636\pi\)
−0.271851 + 0.962339i \(0.587636\pi\)
\(84\) −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 \(-0.177736\pi\)
0.848118 + 0.529807i \(0.177736\pi\)
\(90\) 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 \(-0.562830\pi\)
−0.196107 + 0.980583i \(0.562830\pi\)
\(98\) −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 \(-0.783325\pi\)
0.777130 0.629340i \(-0.216675\pi\)
\(102\) 1.80391i 0.178614i
\(103\) −7.52796 −0.741752 −0.370876 0.928682i \(-0.620942\pi\)
−0.370876 + 0.928682i \(0.620942\pi\)
\(104\) 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 \(-0.927439\pi\)
0.974130 0.225989i \(-0.0725614\pi\)
\(132\) −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 \(-0.726654\pi\)
0.653391 0.757021i \(-0.273346\pi\)
\(140\) 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 \(-0.200207\pi\)
0.808634 + 0.588312i \(0.200207\pi\)
\(158\) 1.74472i 0.138802i
\(159\) −8.35783 −0.662819
\(160\) −1.33802 −0.105779
\(161\) −9.13027 8.81125i −0.719566 0.694424i
\(162\) 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 \(-0.962424\pi\)
0.993040 0.117776i \(-0.0375763\pi\)
\(168\) −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 \(0.170454\pi\)
−0.860015 + 0.510268i \(0.829546\pi\)
\(174\) 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 \(-0.240207\pi\)
0.728524 + 0.685020i \(0.240207\pi\)
\(182\) −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 \(-0.576298\pi\)
−0.237407 + 0.971410i \(0.576298\pi\)
\(200\) 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 \(-0.887632\pi\)
0.938334 0.345729i \(-0.112368\pi\)
\(224\) 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 \(-0.195193\pi\)
0.817800 + 0.575502i \(0.195193\pi\)
\(228\) 8.53159i 0.565018i
\(229\) 8.21928 0.543146 0.271573 0.962418i \(-0.412456\pi\)
0.271573 + 0.962418i \(0.412456\pi\)
\(230\) 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 \(-0.555688\pi\)
−0.174058 + 0.984735i \(0.555688\pi\)
\(242\) 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 \(-0.709824\pi\)
−0.612471 + 0.790493i \(0.709824\pi\)
\(252\) 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 \(0.0432821\pi\)
−0.990770 + 0.135556i \(0.956718\pi\)
\(258\) 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 \(0.226266\pi\)
−0.757818 + 0.652466i \(0.773734\pi\)
\(270\) 0.116474i 0.00708841i
\(271\) 15.3267i 0.931033i −0.885039 0.465517i \(-0.845869\pi\)
0.885039 0.465517i \(-0.154131\pi\)
\(272\) 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 \(-0.480509\pi\)
0.0611956 + 0.998126i \(0.480509\pi\)
\(284\) −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 \(-0.329275\pi\)
0.511001 + 0.859580i \(0.329275\pi\)
\(294\) 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 \(0.363226\pi\)
−0.416587 + 0.909096i \(0.636774\pi\)
\(308\) 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 \(-0.975443\pi\)
0.997026 0.0770707i \(-0.0245567\pi\)
\(312\) −4.42723 −0.250642
\(313\) 21.1811 1.19722 0.598612 0.801039i \(-0.295719\pi\)
0.598612 + 0.801039i \(0.295719\pi\)
\(314\) 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
\(322\) −2.32002 2.23895i −0.129290 0.124772i
\(323\) 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 \(-0.991444\pi\)
0.999639 0.0268760i \(-0.00855592\pi\)
\(350\) −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 \(-0.599123\pi\)
0.306396 0.951904i \(-0.400877\pi\)
\(354\) −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 \(-0.734429\pi\)
−0.671684 + 0.740838i \(0.734429\pi\)
\(368\) −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 \(-0.658421\pi\)
−0.477400 + 0.878686i \(0.658421\pi\)
\(384\) 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 \(0.0695449\pi\)
−0.976228 + 0.216748i \(0.930455\pi\)
\(398\) −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 \(-0.965252\pi\)
0.994048 0.108947i \(-0.0347480\pi\)
\(410\) 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 \(-0.546190\pi\)
−0.144602 + 0.989490i \(0.546190\pi\)
\(420\) 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 \(-0.555469\pi\)
−0.173381 + 0.984855i \(0.555469\pi\)
\(434\) 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 \(-0.652999\pi\)
0.462364 0.886690i \(-0.347001\pi\)
\(440\) 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 \(-0.959088\pi\)
0.991752 0.128174i \(-0.0409117\pi\)
\(462\) 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 \(-0.426551\pi\)
0.228703 + 0.973496i \(0.426551\pi\)
\(468\) 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 \(-0.493493\pi\)
0.0204395 + 0.999791i \(0.493493\pi\)
\(480\) 1.33802i 0.0610718i
\(481\) −37.9023 −1.72820
\(482\) −1.37322 −0.0625485
\(483\) −8.81125 + 9.13027i −0.400926 + 0.415442i
\(484\) −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 \(-0.491644\pi\)
0.0262486 + 0.999655i \(0.491644\pi\)
\(504\) 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 \(-0.941472\pi\)
0.983143 0.182836i \(-0.0585277\pi\)
\(510\) 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 \(-0.691058\pi\)
−0.564831 + 0.825207i \(0.691058\pi\)
\(522\) −1.06457 −0.0465949
\(523\) 26.9939 1.18036 0.590180 0.807272i \(-0.299057\pi\)
0.590180 + 0.807272i \(0.299057\pi\)
\(524\) 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 \(-0.780771\pi\)
−0.772055 + 0.635555i \(0.780771\pi\)
\(564\) −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 \(0.136436\pi\)
−0.909537 + 0.415622i \(0.863564\pi\)
\(578\) 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 \(-0.851054\pi\)
0.892505 0.451037i \(-0.148946\pi\)
\(588\) −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 \(-0.726229\pi\)
0.652380 0.757892i \(-0.273771\pi\)
\(594\) −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 \(0.167674\pi\)
−0.864438 + 0.502739i \(0.832326\pi\)
\(602\) −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 \(-0.841763\pi\)
0.878961 0.476894i \(-0.158237\pi\)
\(608\) 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 \(-0.769202\pi\)
−0.748452 + 0.663189i \(0.769202\pi\)
\(620\) 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 \(-0.122074\pi\)
0.927358 + 0.374176i \(0.122074\pi\)
\(644\) 17.6710 + 17.0536i 0.696336 + 0.672005i
\(645\) −3.29392 −0.129698
\(646\) 7.95184 0.312861
\(647\) 29.5592i 1.16209i 0.813871 + 0.581046i \(0.197356\pi\)
−0.813871 + 0.581046i \(0.802644\pi\)
\(648\) −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 \(-0.425431\pi\)
0.232130 + 0.972685i \(0.425431\pi\)
\(662\) 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 \(-0.0880943\pi\)
0.961947 + 0.273237i \(0.0880943\pi\)
\(678\) 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 \(-0.943709\pi\)
0.984404 0.175922i \(-0.0562906\pi\)
\(692\) 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 \(-0.703104\pi\)
0.595646 0.803247i \(-0.296896\pi\)
\(720\) 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 \(-0.295290\pi\)
0.599692 + 0.800231i \(0.295290\pi\)
\(728\) 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 \(-0.272458\pi\)
0.655500 + 0.755195i \(0.272458\pi\)
\(734\) −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 \(-0.725318\pi\)
0.650206 0.759758i \(-0.274682\pi\)
\(762\) 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 \(-0.557422\pi\)
−0.179419 + 0.983773i \(0.557422\pi\)
\(770\) 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 \(-0.345537\pi\)
0.466439 + 0.884554i \(0.345537\pi\)
\(774\) 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 \(-0.473271\pi\)
0.0838728 + 0.996476i \(0.473271\pi\)
\(788\) −10.7222 −0.381963
\(789\) 1.57848