Properties

Label 804.2.c.b.671.8
Level 804
Weight 2
Character 804.671
Analytic conductor 6.420
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(128\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 671.8
Character \(\chi\) = 804.671
Dual form 804.2.c.b.671.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +O(q^{10})\) \(q+(-1.39093 + 0.255554i) q^{2} +(1.65649 + 0.506011i) q^{3} +(1.86938 - 0.710916i) q^{4} +2.60371i q^{5} +(-2.43338 - 0.280506i) q^{6} +2.89039i q^{7} +(-2.41851 + 1.46656i) q^{8} +(2.48790 + 1.67640i) q^{9} +(-0.665387 - 3.62158i) q^{10} +3.13662 q^{11} +(3.45634 - 0.231693i) q^{12} +5.12990 q^{13} +(-0.738650 - 4.02034i) q^{14} +(-1.31750 + 4.31301i) q^{15} +(2.98920 - 2.65795i) q^{16} -0.537965i q^{17} +(-3.88892 - 1.69597i) q^{18} -8.08261i q^{19} +(1.85102 + 4.86733i) q^{20} +(-1.46257 + 4.78790i) q^{21} +(-4.36282 + 0.801574i) q^{22} -5.12854 q^{23} +(-4.74833 + 1.20555i) q^{24} -1.77929 q^{25} +(-7.13534 + 1.31096i) q^{26} +(3.27291 + 4.03585i) q^{27} +(2.05482 + 5.40325i) q^{28} +4.94932i q^{29} +(0.730355 - 6.33579i) q^{30} +0.241206i q^{31} +(-3.47852 + 4.46093i) q^{32} +(5.19577 + 1.58716i) q^{33} +(0.137479 + 0.748273i) q^{34} -7.52573 q^{35} +(5.84263 + 1.36515i) q^{36} -9.79271 q^{37} +(2.06554 + 11.2424i) q^{38} +(8.49762 + 2.59579i) q^{39} +(-3.81850 - 6.29709i) q^{40} +4.04845i q^{41} +(0.810771 - 7.03340i) q^{42} -3.02636i q^{43} +(5.86354 - 2.22987i) q^{44} +(-4.36486 + 6.47777i) q^{45} +(7.13345 - 1.31062i) q^{46} -11.7709 q^{47} +(6.29652 - 2.89029i) q^{48} -1.35435 q^{49} +(2.47486 - 0.454703i) q^{50} +(0.272216 - 0.891132i) q^{51} +(9.58976 - 3.64693i) q^{52} -13.6619i q^{53} +(-5.58377 - 4.77719i) q^{54} +8.16683i q^{55} +(-4.23894 - 6.99044i) q^{56} +(4.08989 - 13.3888i) q^{57} +(-1.26482 - 6.88416i) q^{58} +9.66333 q^{59} +(0.603261 + 8.99931i) q^{60} +10.5873 q^{61} +(-0.0616412 - 0.335502i) q^{62} +(-4.84546 + 7.19101i) q^{63} +(3.69838 - 7.09380i) q^{64} +13.3568i q^{65} +(-7.63257 - 0.879840i) q^{66} +1.00000i q^{67} +(-0.382448 - 1.00566i) q^{68} +(-8.49536 - 2.59510i) q^{69} +(10.4678 - 1.92323i) q^{70} +4.47112 q^{71} +(-8.47558 - 0.405728i) q^{72} -2.88507 q^{73} +(13.6210 - 2.50256i) q^{74} +(-2.94736 - 0.900339i) q^{75} +(-5.74606 - 15.1095i) q^{76} +9.06605i q^{77} +(-12.4830 - 1.43897i) q^{78} +10.8286i q^{79} +(6.92052 + 7.78299i) q^{80} +(3.37934 + 8.34147i) q^{81} +(-1.03460 - 5.63112i) q^{82} -7.05254 q^{83} +(0.669684 + 9.99018i) q^{84} +1.40070 q^{85} +(0.773396 + 4.20945i) q^{86} +(-2.50441 + 8.19848i) q^{87} +(-7.58594 + 4.60005i) q^{88} -7.16263i q^{89} +(4.41581 - 10.1256i) q^{90} +14.8274i q^{91} +(-9.58721 + 3.64596i) q^{92} +(-0.122053 + 0.399556i) q^{93} +(16.3726 - 3.00810i) q^{94} +21.0447 q^{95} +(-8.01941 + 5.62930i) q^{96} -5.26621 q^{97} +(1.88381 - 0.346110i) q^{98} +(7.80360 + 5.25824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \) \( 128q + 4q^{4} - 6q^{6} - 4q^{9} - 4q^{10} + 4q^{12} - 8q^{13} - 4q^{16} + 18q^{18} - 8q^{21} - 8q^{22} - 24q^{24} - 136q^{25} + 14q^{30} - 32q^{33} + 34q^{36} - 48q^{37} + 16q^{40} - 28q^{42} - 16q^{45} - 28q^{46} - 22q^{48} - 152q^{49} + 8q^{52} - 16q^{54} - 32q^{57} - 20q^{58} - 14q^{60} + 8q^{61} + 16q^{64} + 14q^{66} + 56q^{69} - 4q^{70} - 8q^{72} - 48q^{73} - 36q^{76} + 40q^{78} + 44q^{81} + 60q^{82} + 46q^{84} + 64q^{85} - 28q^{88} - 14q^{90} + 32q^{93} - 8q^{96} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39093 + 0.255554i −0.983538 + 0.180704i
\(3\) 1.65649 + 0.506011i 0.956374 + 0.292146i
\(4\) 1.86938 0.710916i 0.934692 0.355458i
\(5\) 2.60371i 1.16441i 0.813041 + 0.582206i \(0.197810\pi\)
−0.813041 + 0.582206i \(0.802190\pi\)
\(6\) −2.43338 0.280506i −0.993421 0.114516i
\(7\) 2.89039i 1.09246i 0.837634 + 0.546232i \(0.183938\pi\)
−0.837634 + 0.546232i \(0.816062\pi\)
\(8\) −2.41851 + 1.46656i −0.855072 + 0.518509i
\(9\) 2.48790 + 1.67640i 0.829302 + 0.558801i
\(10\) −0.665387 3.62158i −0.210414 1.14524i
\(11\) 3.13662 0.945726 0.472863 0.881136i \(-0.343221\pi\)
0.472863 + 0.881136i \(0.343221\pi\)
\(12\) 3.45634 0.231693i 0.997761 0.0668841i
\(13\) 5.12990 1.42278 0.711389 0.702798i \(-0.248066\pi\)
0.711389 + 0.702798i \(0.248066\pi\)
\(14\) −0.738650 4.02034i −0.197412 1.07448i
\(15\) −1.31750 + 4.31301i −0.340178 + 1.11361i
\(16\) 2.98920 2.65795i 0.747299 0.664487i
\(17\) 0.537965i 0.130476i −0.997870 0.0652378i \(-0.979219\pi\)
0.997870 0.0652378i \(-0.0207806\pi\)
\(18\) −3.88892 1.69597i −0.916627 0.399744i
\(19\) 8.08261i 1.85428i −0.374717 0.927139i \(-0.622260\pi\)
0.374717 0.927139i \(-0.377740\pi\)
\(20\) 1.85102 + 4.86733i 0.413900 + 1.08837i
\(21\) −1.46257 + 4.78790i −0.319159 + 1.04480i
\(22\) −4.36282 + 0.801574i −0.930157 + 0.170896i
\(23\) −5.12854 −1.06937 −0.534687 0.845050i \(-0.679571\pi\)
−0.534687 + 0.845050i \(0.679571\pi\)
\(24\) −4.74833 + 1.20555i −0.969249 + 0.246082i
\(25\) −1.77929 −0.355857
\(26\) −7.13534 + 1.31096i −1.39936 + 0.257101i
\(27\) 3.27291 + 4.03585i 0.629871 + 0.776700i
\(28\) 2.05482 + 5.40325i 0.388325 + 1.02112i
\(29\) 4.94932i 0.919065i 0.888161 + 0.459533i \(0.151983\pi\)
−0.888161 + 0.459533i \(0.848017\pi\)
\(30\) 0.730355 6.33579i 0.133344 1.15675i
\(31\) 0.241206i 0.0433220i 0.999765 + 0.0216610i \(0.00689544\pi\)
−0.999765 + 0.0216610i \(0.993105\pi\)
\(32\) −3.47852 + 4.46093i −0.614922 + 0.788588i
\(33\) 5.19577 + 1.58716i 0.904467 + 0.276290i
\(34\) 0.137479 + 0.748273i 0.0235774 + 0.128328i
\(35\) −7.52573 −1.27208
\(36\) 5.84263 + 1.36515i 0.973772 + 0.227525i
\(37\) −9.79271 −1.60991 −0.804956 0.593335i \(-0.797811\pi\)
−0.804956 + 0.593335i \(0.797811\pi\)
\(38\) 2.06554 + 11.2424i 0.335075 + 1.82375i
\(39\) 8.49762 + 2.59579i 1.36071 + 0.415659i
\(40\) −3.81850 6.29709i −0.603758 0.995657i
\(41\) 4.04845i 0.632262i 0.948716 + 0.316131i \(0.102384\pi\)
−0.948716 + 0.316131i \(0.897616\pi\)
\(42\) 0.810771 7.03340i 0.125105 1.08528i
\(43\) 3.02636i 0.461515i −0.973011 0.230757i \(-0.925880\pi\)
0.973011 0.230757i \(-0.0741204\pi\)
\(44\) 5.86354 2.22987i 0.883962 0.336166i
\(45\) −4.36486 + 6.47777i −0.650675 + 0.965649i
\(46\) 7.13345 1.31062i 1.05177 0.193240i
\(47\) −11.7709 −1.71697 −0.858483 0.512842i \(-0.828593\pi\)
−0.858483 + 0.512842i \(0.828593\pi\)
\(48\) 6.29652 2.89029i 0.908825 0.417178i
\(49\) −1.35435 −0.193479
\(50\) 2.47486 0.454703i 0.349999 0.0643047i
\(51\) 0.272216 0.891132i 0.0381179 0.124783i
\(52\) 9.58976 3.64693i 1.32986 0.505738i
\(53\) 13.6619i 1.87660i −0.345819 0.938301i \(-0.612399\pi\)
0.345819 0.938301i \(-0.387601\pi\)
\(54\) −5.58377 4.77719i −0.759854 0.650093i
\(55\) 8.16683i 1.10121i
\(56\) −4.23894 6.99044i −0.566452 0.934136i
\(57\) 4.08989 13.3888i 0.541720 1.77338i
\(58\) −1.26482 6.88416i −0.166078 0.903935i
\(59\) 9.66333 1.25806 0.629029 0.777382i \(-0.283453\pi\)
0.629029 + 0.777382i \(0.283453\pi\)
\(60\) 0.603261 + 8.99931i 0.0778807 + 1.16181i
\(61\) 10.5873 1.35556 0.677780 0.735265i \(-0.262942\pi\)
0.677780 + 0.735265i \(0.262942\pi\)
\(62\) −0.0616412 0.335502i −0.00782844 0.0426088i
\(63\) −4.84546 + 7.19101i −0.610471 + 0.905983i
\(64\) 3.69838 7.09380i 0.462298 0.886725i
\(65\) 13.3568i 1.65670i
\(66\) −7.63257 0.879840i −0.939504 0.108301i
\(67\) 1.00000i 0.122169i
\(68\) −0.382448 1.00566i −0.0463786 0.121955i
\(69\) −8.49536 2.59510i −1.02272 0.312413i
\(70\) 10.4678 1.92323i 1.25114 0.229870i
\(71\) 4.47112 0.530624 0.265312 0.964163i \(-0.414525\pi\)
0.265312 + 0.964163i \(0.414525\pi\)
\(72\) −8.47558 0.405728i −0.998856 0.0478155i
\(73\) −2.88507 −0.337671 −0.168836 0.985644i \(-0.554001\pi\)
−0.168836 + 0.985644i \(0.554001\pi\)
\(74\) 13.6210 2.50256i 1.58341 0.290917i
\(75\) −2.94736 0.900339i −0.340332 0.103962i
\(76\) −5.74606 15.1095i −0.659118 1.73318i
\(77\) 9.06605i 1.03317i
\(78\) −12.4830 1.43897i −1.41342 0.162931i
\(79\) 10.8286i 1.21831i 0.793050 + 0.609157i \(0.208492\pi\)
−0.793050 + 0.609157i \(0.791508\pi\)
\(80\) 6.92052 + 7.78299i 0.773738 + 0.870165i
\(81\) 3.37934 + 8.34147i 0.375482 + 0.926829i
\(82\) −1.03460 5.63112i −0.114252 0.621854i
\(83\) −7.05254 −0.774117 −0.387059 0.922055i \(-0.626509\pi\)
−0.387059 + 0.922055i \(0.626509\pi\)
\(84\) 0.669684 + 9.99018i 0.0730685 + 1.09002i
\(85\) 1.40070 0.151928
\(86\) 0.773396 + 4.20945i 0.0833975 + 0.453917i
\(87\) −2.50441 + 8.19848i −0.268501 + 0.878970i
\(88\) −7.58594 + 4.60005i −0.808664 + 0.490367i
\(89\) 7.16263i 0.759238i −0.925143 0.379619i \(-0.876055\pi\)
0.925143 0.379619i \(-0.123945\pi\)
\(90\) 4.41581 10.1256i 0.465467 1.06733i
\(91\) 14.8274i 1.55433i
\(92\) −9.58721 + 3.64596i −0.999536 + 0.380117i
\(93\) −0.122053 + 0.399556i −0.0126563 + 0.0414320i
\(94\) 16.3726 3.00810i 1.68870 0.310262i
\(95\) 21.0447 2.15915
\(96\) −8.01941 + 5.62930i −0.818478 + 0.574538i
\(97\) −5.26621 −0.534702 −0.267351 0.963599i \(-0.586148\pi\)
−0.267351 + 0.963599i \(0.586148\pi\)
\(98\) 1.88381 0.346110i 0.190294 0.0349624i
\(99\) 7.80360 + 5.25824i 0.784292 + 0.528473i
\(100\) −3.32617 + 1.26492i −0.332617 + 0.126492i
\(101\) 10.4079i 1.03562i −0.855495 0.517810i \(-0.826747\pi\)
0.855495 0.517810i \(-0.173253\pi\)
\(102\) −0.150902 + 1.30907i −0.0149416 + 0.129617i
\(103\) 0.00173282i 0.000170740i −1.00000 8.53699e-5i \(-0.999973\pi\)
1.00000 8.53699e-5i \(-2.71741e-5\pi\)
\(104\) −12.4067 + 7.52332i −1.21658 + 0.737723i
\(105\) −12.4663 3.80810i −1.21658 0.371633i
\(106\) 3.49134 + 19.0027i 0.339109 + 1.84571i
\(107\) 2.95907 0.286064 0.143032 0.989718i \(-0.454315\pi\)
0.143032 + 0.989718i \(0.454315\pi\)
\(108\) 8.98747 + 5.21780i 0.864820 + 0.502083i
\(109\) −16.3226 −1.56342 −0.781710 0.623643i \(-0.785652\pi\)
−0.781710 + 0.623643i \(0.785652\pi\)
\(110\) −2.08706 11.3595i −0.198994 1.08309i
\(111\) −16.2215 4.95522i −1.53968 0.470329i
\(112\) 7.68251 + 8.63995i 0.725929 + 0.816398i
\(113\) 15.5422i 1.46209i −0.682328 0.731046i \(-0.739033\pi\)
0.682328 0.731046i \(-0.260967\pi\)
\(114\) −2.26722 + 19.6680i −0.212345 + 1.84208i
\(115\) 13.3532i 1.24519i
\(116\) 3.51855 + 9.25218i 0.326689 + 0.859043i
\(117\) 12.7627 + 8.59978i 1.17991 + 0.795050i
\(118\) −13.4410 + 2.46950i −1.23735 + 0.227336i
\(119\) 1.55493 0.142540
\(120\) −3.13890 12.3633i −0.286541 1.12861i
\(121\) −1.16163 −0.105603
\(122\) −14.7262 + 2.70561i −1.33324 + 0.244955i
\(123\) −2.04856 + 6.70622i −0.184713 + 0.604679i
\(124\) 0.171477 + 0.450908i 0.0153991 + 0.0404927i
\(125\) 8.38579i 0.750048i
\(126\) 4.90202 11.2405i 0.436706 1.00138i
\(127\) 15.8546i 1.40687i 0.710760 + 0.703434i \(0.248351\pi\)
−0.710760 + 0.703434i \(0.751649\pi\)
\(128\) −3.33135 + 10.8121i −0.294453 + 0.955666i
\(129\) 1.53137 5.01312i 0.134830 0.441381i
\(130\) −3.41337 18.5783i −0.299372 1.62943i
\(131\) 0.830906 0.0725966 0.0362983 0.999341i \(-0.488443\pi\)
0.0362983 + 0.999341i \(0.488443\pi\)
\(132\) 10.8412 0.726733i 0.943608 0.0632540i
\(133\) 23.3619 2.02573
\(134\) −0.255554 1.39093i −0.0220765 0.120158i
\(135\) −10.5082 + 8.52168i −0.904399 + 0.733430i
\(136\) 0.788960 + 1.30107i 0.0676527 + 0.111566i
\(137\) 7.67384i 0.655621i −0.944744 0.327810i \(-0.893689\pi\)
0.944744 0.327810i \(-0.106311\pi\)
\(138\) 12.4797 + 1.43859i 1.06234 + 0.122461i
\(139\) 5.01542i 0.425402i −0.977117 0.212701i \(-0.931774\pi\)
0.977117 0.212701i \(-0.0682261\pi\)
\(140\) −14.0685 + 5.35016i −1.18900 + 0.452171i
\(141\) −19.4984 5.95622i −1.64206 0.501605i
\(142\) −6.21902 + 1.14261i −0.521889 + 0.0958858i
\(143\) 16.0905 1.34556
\(144\) 11.8926 1.60162i 0.991053 0.133469i
\(145\) −12.8866 −1.07017
\(146\) 4.01293 0.737289i 0.332112 0.0610185i
\(147\) −2.24347 0.685318i −0.185038 0.0565241i
\(148\) −18.3063 + 6.96179i −1.50477 + 0.572256i
\(149\) 13.6112i 1.11507i −0.830154 0.557535i \(-0.811747\pi\)
0.830154 0.557535i \(-0.188253\pi\)
\(150\) 4.32967 + 0.499100i 0.353516 + 0.0407513i
\(151\) 7.06893i 0.575262i −0.957741 0.287631i \(-0.907132\pi\)
0.957741 0.287631i \(-0.0928676\pi\)
\(152\) 11.8537 + 19.5479i 0.961459 + 1.58554i
\(153\) 0.901846 1.33841i 0.0729099 0.108204i
\(154\) −2.31686 12.6103i −0.186698 1.01616i
\(155\) −0.628031 −0.0504446
\(156\) 17.7307 1.18856i 1.41959 0.0951613i
\(157\) −2.96479 −0.236616 −0.118308 0.992977i \(-0.537747\pi\)
−0.118308 + 0.992977i \(0.537747\pi\)
\(158\) −2.76729 15.0619i −0.220154 1.19826i
\(159\) 6.91306 22.6307i 0.548241 1.79473i
\(160\) −11.6149 9.05705i −0.918242 0.716023i
\(161\) 14.8235i 1.16825i
\(162\) −6.83213 10.7388i −0.536783 0.843721i
\(163\) 1.41672i 0.110966i −0.998460 0.0554830i \(-0.982330\pi\)
0.998460 0.0554830i \(-0.0176699\pi\)
\(164\) 2.87811 + 7.56812i 0.224743 + 0.590971i
\(165\) −4.13251 + 13.5283i −0.321715 + 1.05317i
\(166\) 9.80961 1.80230i 0.761373 0.139886i
\(167\) 22.3132 1.72665 0.863324 0.504651i \(-0.168379\pi\)
0.863324 + 0.504651i \(0.168379\pi\)
\(168\) −3.48451 13.7245i −0.268836 1.05887i
\(169\) 13.3159 1.02430
\(170\) −1.94828 + 0.357955i −0.149426 + 0.0274539i
\(171\) 13.5497 20.1088i 1.03617 1.53776i
\(172\) −2.15148 5.65742i −0.164049 0.431374i
\(173\) 2.80929i 0.213587i 0.994281 + 0.106793i \(0.0340583\pi\)
−0.994281 + 0.106793i \(0.965942\pi\)
\(174\) 1.38831 12.0435i 0.105248 0.913019i
\(175\) 5.14283i 0.388761i
\(176\) 9.37597 8.33697i 0.706740 0.628423i
\(177\) 16.0072 + 4.88975i 1.20317 + 0.367536i
\(178\) 1.83044 + 9.96274i 0.137197 + 0.746739i
\(179\) −2.18653 −0.163429 −0.0817144 0.996656i \(-0.526040\pi\)
−0.0817144 + 0.996656i \(0.526040\pi\)
\(180\) −3.55446 + 15.2125i −0.264933 + 1.13387i
\(181\) 8.83532 0.656724 0.328362 0.944552i \(-0.393503\pi\)
0.328362 + 0.944552i \(0.393503\pi\)
\(182\) −3.78920 20.6239i −0.280874 1.52875i
\(183\) 17.5377 + 5.35727i 1.29642 + 0.396021i
\(184\) 12.4034 7.52133i 0.914393 0.554480i
\(185\) 25.4973i 1.87460i
\(186\) 0.0676598 0.586946i 0.00496106 0.0430370i
\(187\) 1.68739i 0.123394i
\(188\) −22.0044 + 8.36814i −1.60484 + 0.610309i
\(189\) −11.6652 + 9.45997i −0.848517 + 0.688112i
\(190\) −29.2718 + 5.37806i −2.12360 + 0.390166i
\(191\) 11.3374 0.820349 0.410174 0.912007i \(-0.365468\pi\)
0.410174 + 0.912007i \(0.365468\pi\)
\(192\) 9.71587 9.87937i 0.701182 0.712982i
\(193\) −14.4765 −1.04204 −0.521019 0.853545i \(-0.674448\pi\)
−0.521019 + 0.853545i \(0.674448\pi\)
\(194\) 7.32493 1.34580i 0.525900 0.0966227i
\(195\) −6.75867 + 22.1253i −0.483998 + 1.58443i
\(196\) −2.53181 + 0.962831i −0.180843 + 0.0687736i
\(197\) 9.67681i 0.689444i 0.938705 + 0.344722i \(0.112027\pi\)
−0.938705 + 0.344722i \(0.887973\pi\)
\(198\) −12.1980 5.31961i −0.866877 0.378048i
\(199\) 18.5428i 1.31447i −0.753687 0.657233i \(-0.771727\pi\)
0.753687 0.657233i \(-0.228273\pi\)
\(200\) 4.30322 2.60943i 0.304284 0.184515i
\(201\) −0.506011 + 1.65649i −0.0356913 + 0.116840i
\(202\) 2.65977 + 14.4766i 0.187141 + 1.01857i
\(203\) −14.3055 −1.00405
\(204\) −0.124643 1.85939i −0.00872675 0.130183i
\(205\) −10.5410 −0.736214
\(206\) 0.000442828 0.00241023i 3.08533e−5 0.000167929i
\(207\) −12.7593 8.59750i −0.886834 0.597568i
\(208\) 15.3343 13.6350i 1.06324 0.945418i
\(209\) 25.3521i 1.75364i
\(210\) 18.3129 + 2.11101i 1.26371 + 0.145674i
\(211\) 26.6463i 1.83440i 0.398423 + 0.917202i \(0.369558\pi\)
−0.398423 + 0.917202i \(0.630442\pi\)
\(212\) −9.71244 25.5393i −0.667053 1.75405i
\(213\) 7.40635 + 2.26244i 0.507475 + 0.155020i
\(214\) −4.11587 + 0.756202i −0.281355 + 0.0516929i
\(215\) 7.87974 0.537394
\(216\) −13.8344 4.96082i −0.941311 0.337541i
\(217\) −0.697181 −0.0473277
\(218\) 22.7036 4.17129i 1.53768 0.282516i
\(219\) −4.77908 1.45988i −0.322940 0.0986493i
\(220\) 5.80593 + 15.2669i 0.391435 + 1.02930i
\(221\) 2.75971i 0.185638i
\(222\) 23.8293 + 2.74691i 1.59932 + 0.184361i
\(223\) 22.1167i 1.48105i −0.672031 0.740523i \(-0.734578\pi\)
0.672031 0.740523i \(-0.265422\pi\)
\(224\) −12.8938 10.0543i −0.861505 0.671780i
\(225\) −4.42669 2.98280i −0.295113 0.198853i
\(226\) 3.97188 + 21.6182i 0.264205 + 1.43802i
\(227\) −14.7383 −0.978216 −0.489108 0.872223i \(-0.662678\pi\)
−0.489108 + 0.872223i \(0.662678\pi\)
\(228\) −1.87269 27.9363i −0.124022 1.85013i
\(229\) 17.1738 1.13488 0.567438 0.823416i \(-0.307935\pi\)
0.567438 + 0.823416i \(0.307935\pi\)
\(230\) 3.41246 + 18.5734i 0.225011 + 1.22469i
\(231\) −4.58752 + 15.0178i −0.301837 + 0.988098i
\(232\) −7.25849 11.9700i −0.476543 0.785867i
\(233\) 5.34290i 0.350025i 0.984566 + 0.175013i \(0.0559966\pi\)
−0.984566 + 0.175013i \(0.944003\pi\)
\(234\) −19.9498 8.70016i −1.30416 0.568747i
\(235\) 30.6480i 1.99926i
\(236\) 18.0645 6.86981i 1.17590 0.447187i
\(237\) −5.47940 + 17.9375i −0.355925 + 1.16516i
\(238\) −2.16280 + 0.397368i −0.140193 + 0.0257575i
\(239\) −18.4034 −1.19042 −0.595209 0.803571i \(-0.702931\pi\)
−0.595209 + 0.803571i \(0.702931\pi\)
\(240\) 7.52547 + 16.3943i 0.485767 + 1.05825i
\(241\) −1.10051 −0.0708901 −0.0354451 0.999372i \(-0.511285\pi\)
−0.0354451 + 0.999372i \(0.511285\pi\)
\(242\) 1.61575 0.296860i 0.103865 0.0190829i
\(243\) 1.37696 + 15.5275i 0.0883322 + 0.996091i
\(244\) 19.7917 7.52665i 1.26703 0.481844i
\(245\) 3.52634i 0.225289i
\(246\) 1.13562 9.85141i 0.0724042 0.628103i
\(247\) 41.4630i 2.63823i
\(248\) −0.353745 0.583360i −0.0224628 0.0370434i
\(249\) −11.6825 3.56867i −0.740345 0.226155i
\(250\) −2.14302 11.6641i −0.135537 0.737701i
\(251\) −2.45480 −0.154945 −0.0774727 0.996994i \(-0.524685\pi\)
−0.0774727 + 0.996994i \(0.524685\pi\)
\(252\) −3.94582 + 16.8875i −0.248563 + 1.06381i
\(253\) −16.0863 −1.01133
\(254\) −4.05170 22.0527i −0.254226 1.38371i
\(255\) 2.32025 + 0.708771i 0.145299 + 0.0443850i
\(256\) 1.87061 15.8903i 0.116913 0.993142i
\(257\) 19.2402i 1.20017i −0.799935 0.600087i \(-0.795133\pi\)
0.799935 0.600087i \(-0.204867\pi\)
\(258\) −0.848910 + 7.36426i −0.0528509 + 0.458479i
\(259\) 28.3048i 1.75877i
\(260\) 9.49552 + 24.9689i 0.588887 + 1.54851i
\(261\) −8.29705 + 12.3134i −0.513575 + 0.762182i
\(262\) −1.15573 + 0.212341i −0.0714015 + 0.0131185i
\(263\) −1.53590 −0.0947078 −0.0473539 0.998878i \(-0.515079\pi\)
−0.0473539 + 0.998878i \(0.515079\pi\)
\(264\) −14.8937 + 3.78135i −0.916644 + 0.232726i
\(265\) 35.5715 2.18514
\(266\) −32.4948 + 5.97022i −1.99239 + 0.366058i
\(267\) 3.62437 11.8648i 0.221808 0.726115i
\(268\) 0.710916 + 1.86938i 0.0434261 + 0.114191i
\(269\) 1.08351i 0.0660627i 0.999454 + 0.0330314i \(0.0105161\pi\)
−0.999454 + 0.0330314i \(0.989484\pi\)
\(270\) 12.4384 14.5385i 0.756977 0.884784i
\(271\) 31.2660i 1.89927i 0.313352 + 0.949637i \(0.398548\pi\)
−0.313352 + 0.949637i \(0.601452\pi\)
\(272\) −1.42988 1.60808i −0.0866994 0.0975044i
\(273\) −7.50284 + 24.5614i −0.454092 + 1.48653i
\(274\) 1.96108 + 10.6738i 0.118473 + 0.644828i
\(275\) −5.58094 −0.336543
\(276\) −17.7260 + 1.18825i −1.06698 + 0.0715242i
\(277\) 16.3666 0.983375 0.491687 0.870772i \(-0.336380\pi\)
0.491687 + 0.870772i \(0.336380\pi\)
\(278\) 1.28171 + 6.97611i 0.0768718 + 0.418399i
\(279\) −0.404359 + 0.600099i −0.0242084 + 0.0359270i
\(280\) 18.2010 11.0370i 1.08772 0.659584i
\(281\) 14.2167i 0.848100i 0.905639 + 0.424050i \(0.139392\pi\)
−0.905639 + 0.424050i \(0.860608\pi\)
\(282\) 28.6431 + 3.30182i 1.70567 + 0.196620i
\(283\) 0.188096i 0.0111811i −0.999984 0.00559057i \(-0.998220\pi\)
0.999984 0.00559057i \(-0.00177954\pi\)
\(284\) 8.35824 3.17859i 0.495970 0.188615i
\(285\) 34.8604 + 10.6489i 2.06495 + 0.630785i
\(286\) −22.3808 + 4.11199i −1.32341 + 0.243147i
\(287\) −11.7016 −0.690724
\(288\) −16.1325 + 5.26696i −0.950620 + 0.310358i
\(289\) 16.7106 0.982976
\(290\) 17.9243 3.29321i 1.05255 0.193384i
\(291\) −8.72341 2.66476i −0.511375 0.156211i
\(292\) −5.39330 + 2.05104i −0.315619 + 0.120028i
\(293\) 1.17556i 0.0686772i −0.999410 0.0343386i \(-0.989068\pi\)
0.999410 0.0343386i \(-0.0109325\pi\)
\(294\) 3.29565 + 0.379904i 0.192206 + 0.0221564i
\(295\) 25.1605i 1.46490i
\(296\) 23.6838 14.3616i 1.37659 0.834753i
\(297\) 10.2659 + 12.6589i 0.595685 + 0.734545i
\(298\) 3.47838 + 18.9322i 0.201497 + 1.09671i
\(299\) −26.3089 −1.52148
\(300\) −6.14982 + 0.412249i −0.355060 + 0.0238012i
\(301\) 8.74735 0.504189
\(302\) 1.80649 + 9.83241i 0.103952 + 0.565791i
\(303\) 5.26649 17.2405i 0.302552 0.990440i
\(304\) −21.4832 24.1605i −1.23214 1.38570i
\(305\) 27.5661i 1.57843i
\(306\) −0.912372 + 2.09210i −0.0521569 + 0.119597i
\(307\) 5.47903i 0.312705i −0.987701 0.156352i \(-0.950026\pi\)
0.987701 0.156352i \(-0.0499736\pi\)
\(308\) 6.44519 + 16.9479i 0.367249 + 0.965698i
\(309\) 0.000876826 0.00287039i 4.98809e−5 0.000163291i
\(310\) 0.873548 0.160496i 0.0496142 0.00911554i
\(311\) −9.27227 −0.525782 −0.262891 0.964826i \(-0.584676\pi\)
−0.262891 + 0.964826i \(0.584676\pi\)
\(312\) −24.3585 + 6.18436i −1.37903 + 0.350120i
\(313\) 22.7364 1.28514 0.642569 0.766228i \(-0.277869\pi\)
0.642569 + 0.766228i \(0.277869\pi\)
\(314\) 4.12381 0.757662i 0.232720 0.0427573i
\(315\) −18.7233 12.6162i −1.05494 0.710840i
\(316\) 7.69823 + 20.2428i 0.433059 + 1.13875i
\(317\) 5.56216i 0.312402i 0.987725 + 0.156201i \(0.0499247\pi\)
−0.987725 + 0.156201i \(0.950075\pi\)
\(318\) −3.83224 + 33.2445i −0.214901 + 1.86426i
\(319\) 15.5241i 0.869183i
\(320\) 18.4702 + 9.62950i 1.03251 + 0.538305i
\(321\) 4.90167 + 1.49732i 0.273584 + 0.0835725i
\(322\) 3.78819 + 20.6185i 0.211108 + 1.14902i
\(323\) −4.34816 −0.241938
\(324\) 12.2474 + 13.1910i 0.680409 + 0.732832i
\(325\) −9.12755 −0.506306
\(326\) 0.362048 + 1.97056i 0.0200520 + 0.109139i
\(327\) −27.0381 8.25941i −1.49521 0.456746i
\(328\) −5.93732 9.79123i −0.327833 0.540630i
\(329\) 34.0226i 1.87573i
\(330\) 2.29084 19.8730i 0.126107 1.09397i
\(331\) 8.35781i 0.459387i −0.973263 0.229693i \(-0.926228\pi\)
0.973263 0.229693i \(-0.0737723\pi\)
\(332\) −13.1839 + 5.01376i −0.723561 + 0.275166i
\(333\) −24.3633 16.4165i −1.33510 0.899621i
\(334\) −31.0361 + 5.70222i −1.69822 + 0.312012i
\(335\) −2.60371 −0.142256
\(336\) 8.35407 + 18.1994i 0.455752 + 0.992859i
\(337\) 8.67869 0.472759 0.236379 0.971661i \(-0.424039\pi\)
0.236379 + 0.971661i \(0.424039\pi\)
\(338\) −18.5215 + 3.40292i −1.00744 + 0.185094i
\(339\) 7.86455 25.7455i 0.427144 1.39831i
\(340\) 2.61845 0.995781i 0.142005 0.0540038i
\(341\) 0.756572i 0.0409707i
\(342\) −13.7079 + 31.4326i −0.741237 + 1.69968i
\(343\) 16.3181i 0.881096i
\(344\) 4.43834 + 7.31927i 0.239299 + 0.394629i
\(345\) 6.75688 22.1194i 0.363778 1.19087i
\(346\) −0.717925 3.90754i −0.0385959 0.210070i
\(347\) 19.5109 1.04740 0.523699 0.851904i \(-0.324552\pi\)
0.523699 + 0.851904i \(0.324552\pi\)
\(348\) 1.14672 + 17.1065i 0.0614709 + 0.917007i
\(349\) −4.07790 −0.218285 −0.109142 0.994026i \(-0.534810\pi\)
−0.109142 + 0.994026i \(0.534810\pi\)
\(350\) 1.31427 + 7.15332i 0.0702506 + 0.382361i
\(351\) 16.7897 + 20.7035i 0.896167 + 1.10507i
\(352\) −10.9108 + 13.9922i −0.581547 + 0.745788i
\(353\) 1.47353i 0.0784281i 0.999231 + 0.0392141i \(0.0124854\pi\)
−0.999231 + 0.0392141i \(0.987515\pi\)
\(354\) −23.5145 2.71062i −1.24978 0.144068i
\(355\) 11.6415i 0.617866i
\(356\) −5.09203 13.3897i −0.269877 0.709654i
\(357\) 2.57572 + 0.786811i 0.136322 + 0.0416425i
\(358\) 3.04131 0.558775i 0.160738 0.0295322i
\(359\) 18.8230 0.993441 0.496720 0.867911i \(-0.334537\pi\)
0.496720 + 0.867911i \(0.334537\pi\)
\(360\) 1.05640 22.0679i 0.0556770 1.16308i
\(361\) −46.3286 −2.43835
\(362\) −12.2893 + 2.25790i −0.645913 + 0.118672i
\(363\) −1.92423 0.587800i −0.100996 0.0308515i
\(364\) 10.5410 + 27.7181i 0.552501 + 1.45282i
\(365\) 7.51186i 0.393189i
\(366\) −25.7628 2.96979i −1.34664 0.155233i
\(367\) 4.83690i 0.252484i 0.991999 + 0.126242i \(0.0402916\pi\)
−0.991999 + 0.126242i \(0.959708\pi\)
\(368\) −15.3302 + 13.6314i −0.799143 + 0.710586i
\(369\) −6.78684 + 10.0722i −0.353309 + 0.524336i
\(370\) 6.51594 + 35.4651i 0.338748 + 1.84374i
\(371\) 39.4881 2.05012
\(372\) 0.0558859 + 0.833693i 0.00289755 + 0.0432250i
\(373\) 4.48557 0.232254 0.116127 0.993234i \(-0.462952\pi\)
0.116127 + 0.993234i \(0.462952\pi\)
\(374\) 0.431219 + 2.34704i 0.0222978 + 0.121363i
\(375\) −4.24331 + 13.8910i −0.219123 + 0.717327i
\(376\) 28.4681 17.2628i 1.46813 0.890262i
\(377\) 25.3895i 1.30763i
\(378\) 13.8079 16.1393i 0.710204 0.830114i
\(379\) 0.465906i 0.0239320i −0.999928 0.0119660i \(-0.996191\pi\)
0.999928 0.0119660i \(-0.00380899\pi\)
\(380\) 39.3407 14.9610i 2.01814 0.767485i
\(381\) −8.02261 + 26.2630i −0.411011 + 1.34549i
\(382\) −15.7696 + 2.89733i −0.806844 + 0.148240i
\(383\) 1.39234 0.0711454 0.0355727 0.999367i \(-0.488674\pi\)
0.0355727 + 0.999367i \(0.488674\pi\)
\(384\) −10.9894 + 16.2245i −0.560801 + 0.827951i
\(385\) −23.6053 −1.20304
\(386\) 20.1358 3.69951i 1.02488 0.188300i
\(387\) 5.07339 7.52928i 0.257895 0.382735i
\(388\) −9.84456 + 3.74383i −0.499782 + 0.190064i
\(389\) 24.3328i 1.23372i −0.787072 0.616862i \(-0.788404\pi\)
0.787072 0.616862i \(-0.211596\pi\)
\(390\) 3.74665 32.5020i 0.189719 1.64580i
\(391\) 2.75897i 0.139527i
\(392\) 3.27552 1.98624i 0.165439 0.100320i
\(393\) 1.37639 + 0.420448i 0.0694295 + 0.0212088i
\(394\) −2.47294 13.4598i −0.124585 0.678094i
\(395\) −28.1945 −1.41862
\(396\) 18.3261 + 4.28196i 0.920921 + 0.215177i
\(397\) 13.2159 0.663285 0.331643 0.943405i \(-0.392397\pi\)
0.331643 + 0.943405i \(0.392397\pi\)
\(398\) 4.73869 + 25.7918i 0.237529 + 1.29283i
\(399\) 38.6987 + 11.8214i 1.93736 + 0.591810i
\(400\) −5.31864 + 4.72925i −0.265932 + 0.236463i
\(401\) 1.22666i 0.0612565i 0.999531 + 0.0306283i \(0.00975080\pi\)
−0.999531 + 0.0306283i \(0.990249\pi\)
\(402\) 0.280506 2.43338i 0.0139904 0.121366i
\(403\) 1.23737i 0.0616375i
\(404\) −7.39911 19.4563i −0.368119 0.967987i
\(405\) −21.7187 + 8.79881i −1.07921 + 0.437217i
\(406\) 19.8979 3.65581i 0.987517 0.181435i
\(407\) −30.7160 −1.52253
\(408\) 0.648544 + 2.55444i 0.0321077 + 0.126463i
\(409\) 15.7033 0.776481 0.388240 0.921558i \(-0.373083\pi\)
0.388240 + 0.921558i \(0.373083\pi\)
\(410\) 14.6618 2.69379i 0.724094 0.133037i
\(411\) 3.88305 12.7116i 0.191537 0.627018i
\(412\) −0.00123189 0.00323931i −6.06908e−5 0.000159589i
\(413\) 27.9308i 1.37438i
\(414\) 19.9445 + 8.69785i 0.980217 + 0.427476i
\(415\) 18.3628i 0.901392i
\(416\) −17.8445 + 22.8841i −0.874897 + 1.12199i
\(417\) 2.53786 8.30798i 0.124279 0.406844i
\(418\) 6.47881 + 35.2630i 0.316889 + 1.72477i
\(419\) −15.0320 −0.734361 −0.367180 0.930150i \(-0.619677\pi\)
−0.367180 + 0.930150i \(0.619677\pi\)
\(420\) −26.0115 + 1.74366i −1.26923 + 0.0850819i
\(421\) −9.76119 −0.475731 −0.237866 0.971298i \(-0.576448\pi\)
−0.237866 + 0.971298i \(0.576448\pi\)
\(422\) −6.80955 37.0631i −0.331484 1.80421i
\(423\) −29.2850 19.7328i −1.42388 0.959443i
\(424\) 20.0360 + 33.0414i 0.973034 + 1.60463i
\(425\) 0.957193i 0.0464307i
\(426\) −10.8799 1.25418i −0.527133 0.0607650i
\(427\) 30.6013i 1.48090i
\(428\) 5.53164 2.10365i 0.267382 0.101684i
\(429\) 26.6538 + 8.14199i 1.28686 + 0.393099i
\(430\) −10.9602 + 2.01370i −0.528547 + 0.0971091i
\(431\) 20.9130 1.00734 0.503672 0.863895i \(-0.331982\pi\)
0.503672 + 0.863895i \(0.331982\pi\)
\(432\) 20.5104 + 3.36474i 0.986809 + 0.161886i
\(433\) −21.7276 −1.04416 −0.522081 0.852896i \(-0.674844\pi\)
−0.522081 + 0.852896i \(0.674844\pi\)
\(434\) 0.969731 0.178167i 0.0465486 0.00855229i
\(435\) −21.3464 6.52075i −1.02348 0.312646i
\(436\) −30.5132 + 11.6040i −1.46132 + 0.555730i
\(437\) 41.4520i 1.98292i
\(438\) 7.02045 + 0.809278i 0.335450 + 0.0386688i
\(439\) 28.9489i 1.38166i −0.723019 0.690828i \(-0.757246\pi\)
0.723019 0.690828i \(-0.242754\pi\)
\(440\) −11.9772 19.7516i −0.570989 0.941619i
\(441\) −3.36950 2.27044i −0.160452 0.108116i
\(442\) 0.705253 + 3.83856i 0.0335455 + 0.182582i
\(443\) 20.9377 0.994782 0.497391 0.867526i \(-0.334291\pi\)
0.497391 + 0.867526i \(0.334291\pi\)
\(444\) −33.8470 + 2.26891i −1.60631 + 0.107678i
\(445\) 18.6494 0.884066
\(446\) 5.65201 + 30.7629i 0.267631 + 1.45666i
\(447\) 6.88740 22.5467i 0.325763 1.06642i
\(448\) 20.5038 + 10.6898i 0.968715 + 0.505044i
\(449\) 19.0209i 0.897654i 0.893619 + 0.448827i \(0.148158\pi\)
−0.893619 + 0.448827i \(0.851842\pi\)
\(450\) 6.91949 + 3.01761i 0.326188 + 0.142252i
\(451\) 12.6984i 0.597947i
\(452\) −11.0492 29.0544i −0.519712 1.36661i
\(453\) 3.57696 11.7096i 0.168060 0.550165i
\(454\) 20.5000 3.76643i 0.962112 0.176767i
\(455\) −38.6062 −1.80989
\(456\) 9.74401 + 38.3789i 0.456305 + 1.79726i
\(457\) −8.99556 −0.420795 −0.210397 0.977616i \(-0.567476\pi\)
−0.210397 + 0.977616i \(0.567476\pi\)
\(458\) −23.8876 + 4.38882i −1.11619 + 0.205076i
\(459\) 2.17115 1.76071i 0.101340 0.0821828i
\(460\) −9.49301 24.9623i −0.442614 1.16387i
\(461\) 29.0327i 1.35219i −0.736816 0.676094i \(-0.763671\pi\)
0.736816 0.676094i \(-0.236329\pi\)
\(462\) 2.54308 22.0611i 0.118315 1.02637i
\(463\) 3.45414i 0.160528i 0.996774 + 0.0802638i \(0.0255763\pi\)
−0.996774 + 0.0802638i \(0.974424\pi\)
\(464\) 13.1550 + 14.7945i 0.610707 + 0.686817i
\(465\) −1.04033 0.317791i −0.0482439 0.0147372i
\(466\) −1.36540 7.43162i −0.0632509 0.344263i
\(467\) 19.7530 0.914062 0.457031 0.889451i \(-0.348913\pi\)
0.457031 + 0.889451i \(0.348913\pi\)
\(468\) 29.9721 + 7.00310i 1.38546 + 0.323718i
\(469\) −2.89039 −0.133466
\(470\) 7.83222 + 42.6293i 0.361273 + 1.96635i
\(471\) −4.91113 1.50021i −0.226293 0.0691263i
\(472\) −23.3709 + 14.1719i −1.07573 + 0.652314i
\(473\) 9.49252i 0.436466i
\(474\) 3.03749 26.3501i 0.139517 1.21030i
\(475\) 14.3813i 0.659858i
\(476\) 2.90676 1.10542i 0.133231 0.0506670i
\(477\) 22.9028 33.9894i 1.04865 1.55627i
\(478\) 25.5979 4.70306i 1.17082 0.215113i
\(479\) 21.6257 0.988102 0.494051 0.869433i \(-0.335516\pi\)
0.494051 + 0.869433i \(0.335516\pi\)
\(480\) −14.6570 20.8802i −0.669000 0.953046i
\(481\) −50.2356 −2.29055
\(482\) 1.53074 0.281240i 0.0697231 0.0128101i
\(483\) 7.50085 24.5549i 0.341300 1.11729i
\(484\) −2.17154 + 0.825824i −0.0987064 + 0.0375375i
\(485\) 13.7117i 0.622614i
\(486\) −5.88338 21.2458i −0.266875 0.963731i
\(487\) 40.3439i 1.82816i −0.405538 0.914078i \(-0.632916\pi\)
0.405538 0.914078i \(-0.367084\pi\)
\(488\) −25.6054 + 15.5269i −1.15910 + 0.702869i
\(489\) 0.716877 2.34678i 0.0324183 0.106125i
\(490\) 0.901168 + 4.90489i 0.0407106 + 0.221581i
\(491\) −2.10393 −0.0949492 −0.0474746 0.998872i \(-0.515117\pi\)
−0.0474746 + 0.998872i \(0.515117\pi\)
\(492\) 0.938000 + 13.9929i 0.0422883 + 0.630846i
\(493\) 2.66256 0.119916
\(494\) 10.5960 + 57.6722i 0.476738 + 2.59480i
\(495\) −13.6909 + 20.3183i −0.615360 + 0.913239i
\(496\) 0.641115 + 0.721014i 0.0287869 + 0.0323745i
\(497\) 12.9233i 0.579688i
\(498\) 17.1615 + 1.97828i 0.769025 + 0.0886489i
\(499\) 3.96304i 0.177410i −0.996058 0.0887049i \(-0.971727\pi\)
0.996058 0.0887049i \(-0.0282728\pi\)
\(500\) 5.96159 + 15.6763i 0.266611 + 0.701064i
\(501\) 36.9615 + 11.2907i 1.65132 + 0.504433i
\(502\) 3.41446 0.627333i 0.152395 0.0279992i
\(503\) −6.23728 −0.278106 −0.139053 0.990285i \(-0.544406\pi\)
−0.139053 + 0.990285i \(0.544406\pi\)
\(504\) 1.17271 24.4977i 0.0522368 1.09122i
\(505\) 27.0990 1.20589
\(506\) 22.3749 4.11090i 0.994686 0.182752i
\(507\) 22.0576 + 6.73798i 0.979612 + 0.299244i
\(508\) 11.2713 + 29.6384i 0.500082 + 1.31499i
\(509\) 36.3220i 1.60995i 0.593312 + 0.804973i \(0.297820\pi\)
−0.593312 + 0.804973i \(0.702180\pi\)
\(510\) −3.40843 0.392905i −0.150928 0.0173981i
\(511\) 8.33896i 0.368894i
\(512\) 1.45893 + 22.5803i 0.0644762 + 0.997919i
\(513\) 32.6202 26.4536i 1.44022 1.16796i
\(514\) 4.91692 + 26.7619i 0.216876 + 1.18042i
\(515\) 0.00451175 0.000198812
\(516\) −0.701186 10.4601i −0.0308680 0.460481i
\(517\) −36.9209 −1.62378
\(518\) 7.23338 + 39.3700i 0.317817 + 1.72982i
\(519\) −1.42153 + 4.65356i −0.0623984 + 0.204269i
\(520\) −19.5885 32.3034i −0.859014 1.41660i
\(521\) 26.1623i 1.14619i −0.819488 0.573096i \(-0.805742\pi\)
0.819488 0.573096i \(-0.194258\pi\)
\(522\) 8.39389 19.2475i 0.367391 0.842440i
\(523\) 16.4105i 0.717582i 0.933418 + 0.358791i \(0.116811\pi\)
−0.933418 + 0.358791i \(0.883189\pi\)
\(524\) 1.55328 0.590704i 0.0678555 0.0258050i
\(525\) 2.60233 8.51903i 0.113575 0.371801i
\(526\) 2.13634 0.392505i 0.0931487 0.0171141i
\(527\) 0.129761 0.00565246
\(528\) 19.7498 9.06574i 0.859499 0.394536i
\(529\) 3.30191 0.143561
\(530\) −49.4775 + 9.09043i −2.14917 + 0.394863i
\(531\) 24.0414 + 16.1996i 1.04331 + 0.703005i
\(532\) 43.6724 16.6083i 1.89344 0.720063i
\(533\) 20.7682i 0.899569i
\(534\) −2.00916 + 17.4294i −0.0869449 + 0.754243i
\(535\) 7.70455i 0.333097i
\(536\) −1.46656 2.41851i −0.0633459 0.104464i
\(537\) −3.62196 1.10641i −0.156299 0.0477450i
\(538\) −0.276895 1.50709i −0.0119378 0.0649751i
\(539\) −4.24809 −0.182978
\(540\) −13.5856 + 23.4007i −0.584632 + 1.00701i
\(541\) −30.0867 −1.29353 −0.646764 0.762690i \(-0.723878\pi\)
−0.646764 + 0.762690i \(0.723878\pi\)
\(542\) −7.99014 43.4889i −0.343206 1.86801i
\(543\) 14.6356 + 4.47077i 0.628073 + 0.191859i
\(544\) 2.39982 + 1.87132i 0.102892 + 0.0802323i
\(545\) 42.4992i 1.82047i
\(546\) 4.15918 36.0807i 0.177996 1.54411i
\(547\) 13.6119i 0.582001i 0.956723 + 0.291001i \(0.0939882\pi\)
−0.956723 + 0.291001i \(0.906012\pi\)
\(548\) −5.45546 14.3454i −0.233046 0.612804i
\(549\) 26.3401 + 17.7485i 1.12417 + 0.757488i
\(550\) 7.76270 1.42623i 0.331003 0.0608146i
\(551\) 40.0034 1.70420
\(552\) 24.3520 6.18272i 1.03649 0.263154i
\(553\) −31.2989 −1.33097
\(554\) −22.7649 + 4.18255i −0.967186 + 0.177699i
\(555\) 12.9019 42.2360i 0.547657 1.79282i
\(556\) −3.56554 9.37575i −0.151213 0.397620i
\(557\) 15.9410i 0.675443i 0.941246 + 0.337722i \(0.109656\pi\)
−0.941246 + 0.337722i \(0.890344\pi\)
\(558\) 0.409079 0.938032i 0.0173177 0.0397101i
\(559\) 15.5249i 0.656633i
\(560\) −22.4959 + 20.0030i −0.950624 + 0.845281i
\(561\) 0.853838 2.79514i 0.0360491 0.118011i
\(562\) −3.63314 19.7745i −0.153255 0.834138i
\(563\) 19.7107 0.830706 0.415353 0.909660i \(-0.363658\pi\)
0.415353 + 0.909660i \(0.363658\pi\)
\(564\) −40.6844 + 2.72725i −1.71312 + 0.114838i
\(565\) 40.4674 1.70248
\(566\) 0.0480686 + 0.261629i 0.00202047 + 0.0109971i
\(567\) −24.1101 + 9.76762i −1.01253 + 0.410201i
\(568\) −10.8134 + 6.55718i −0.453722 + 0.275133i
\(569\) 32.0631i 1.34416i −0.740480 0.672078i \(-0.765402\pi\)
0.740480 0.672078i \(-0.234598\pi\)
\(570\) −51.2098 5.90318i −2.14494 0.247257i
\(571\) 14.4930i 0.606515i 0.952909 + 0.303257i \(0.0980742\pi\)
−0.952909 + 0.303257i \(0.901926\pi\)
\(572\) 30.0794 11.4390i 1.25768 0.478289i
\(573\) 18.7803 + 5.73688i 0.784560 + 0.239661i
\(574\) 16.2761 2.99039i 0.679353 0.124816i
\(575\) 9.12513 0.380544
\(576\) 21.0933 11.4487i 0.878887 0.477030i
\(577\) 7.34117 0.305617 0.152808 0.988256i \(-0.451168\pi\)
0.152808 + 0.988256i \(0.451168\pi\)
\(578\) −23.2433 + 4.27045i −0.966794 + 0.177627i
\(579\) −23.9801 7.32525i −0.996578 0.304427i
\(580\) −24.0899 + 9.16126i −1.00028 + 0.380401i
\(581\) 20.3846i 0.845696i
\(582\) 12.8147 + 1.47720i 0.531185 + 0.0612320i
\(583\) 42.8521i 1.77475i
\(584\) 6.97756 4.23113i 0.288733 0.175085i
\(585\) −22.3913 + 33.2303i −0.925767 + 1.37390i
\(586\) 0.300420 + 1.63513i 0.0124102 + 0.0675466i
\(587\) −21.6138 −0.892099 −0.446049 0.895008i \(-0.647169\pi\)
−0.446049 + 0.895008i \(0.647169\pi\)
\(588\) −4.68111 + 0.313795i −0.193046 + 0.0129407i
\(589\) 1.94958 0.0803310
\(590\) −6.42985 34.9965i −0.264713 1.44078i
\(591\) −4.89658 + 16.0295i −0.201418 + 0.659366i
\(592\) −29.2724 + 26.0285i −1.20309 + 1.06977i
\(593\) 28.7481i 1.18054i 0.807205 + 0.590271i \(0.200979\pi\)
−0.807205 + 0.590271i \(0.799021\pi\)
\(594\) −17.5141 14.9842i −0.718614 0.614810i
\(595\) 4.04858i 0.165975i
\(596\) −9.67638 25.4445i −0.396360 1.04225i
\(597\) 9.38289 30.7160i 0.384016 1.25712i
\(598\) 36.5939 6.72333i 1.49644 0.274938i
\(599\) 8.35373 0.341324 0.170662 0.985330i \(-0.445409\pi\)
0.170662 + 0.985330i \(0.445409\pi\)
\(600\) 8.44863 2.14502i 0.344914 0.0875701i
\(601\) −45.3779 −1.85100 −0.925501 0.378744i \(-0.876356\pi\)
−0.925501 + 0.378744i \(0.876356\pi\)
\(602\) −12.1670 + 2.23542i −0.495888 + 0.0911088i
\(603\) −1.67640 + 2.48790i −0.0682684 + 0.101315i
\(604\) −5.02542 13.2146i −0.204481 0.537693i
\(605\) 3.02456i 0.122966i
\(606\) −2.91947 + 25.3262i −0.118595 + 1.02881i
\(607\) 28.3073i 1.14896i −0.818520 0.574478i \(-0.805205\pi\)
0.818520 0.574478i \(-0.194795\pi\)
\(608\) 36.0560 + 28.1156i 1.46226 + 1.14024i
\(609\) −23.6968 7.23872i −0.960243 0.293328i
\(610\) −7.04462 38.3426i −0.285228 1.55245i
\(611\) −60.3837 −2.44286
\(612\) 0.734404 3.14313i 0.0296865 0.127054i
\(613\) −8.18630 −0.330642 −0.165321 0.986240i \(-0.552866\pi\)
−0.165321 + 0.986240i \(0.552866\pi\)
\(614\) 1.40019 + 7.62096i 0.0565069 + 0.307557i
\(615\) −17.4610 5.33386i −0.704096 0.215082i
\(616\) −13.2959 21.9263i −0.535708 0.883437i
\(617\) 2.70557i 0.108922i −0.998516 0.0544611i \(-0.982656\pi\)
0.998516 0.0544611i \(-0.0173441\pi\)
\(618\) −0.000486066 0.00421660i −1.95524e−5 0.000169617i
\(619\) 18.3004i 0.735557i 0.929913 + 0.367779i \(0.119882\pi\)
−0.929913 + 0.367779i \(0.880118\pi\)
\(620\) −1.17403 + 0.446477i −0.0471502 + 0.0179309i
\(621\) −16.7852 20.6980i −0.673568 0.830583i
\(622\) 12.8971 2.36956i 0.517126 0.0950108i
\(623\) 20.7028 0.829440
\(624\) 32.3005 14.8269i 1.29306 0.593552i
\(625\) −30.7306 −1.22922
\(626\) −31.6248 + 5.81037i −1.26398 + 0.232229i
\(627\) 12.8284 41.9954i 0.512318 1.67713i
\(628\) −5.54232 + 2.10771i −0.221163 + 0.0841069i
\(629\) 5.26813i 0.210054i
\(630\) 29.2669 + 12.7634i 1.16602 + 0.508506i
\(631\) 20.1278i 0.801275i 0.916237 + 0.400638i \(0.131211\pi\)
−0.916237 + 0.400638i \(0.868789\pi\)
\(632\) −15.8808 26.1891i −0.631706 1.04175i
\(633\) −13.4833 + 44.1392i −0.535913 + 1.75438i
\(634\) −1.42143 7.73658i −0.0564522 0.307259i
\(635\) −41.2807 −1.63818
\(636\) −3.16536 47.2201i −0.125515 1.87240i
\(637\) −6.94769 −0.275278
\(638\) −3.96724 21.5930i −0.157065 0.854874i
\(639\) 11.1237 + 7.49540i 0.440048 + 0.296513i
\(640\) −28.1516 8.67386i −1.11279 0.342865i
\(641\) 46.1614i 1.82326i −0.411007 0.911632i \(-0.634823\pi\)
0.411007 0.911632i \(-0.365177\pi\)
\(642\) −7.20053 0.830037i −0.284182 0.0327589i
\(643\) 45.4882i 1.79388i 0.442151 + 0.896941i \(0.354216\pi\)
−0.442151 + 0.896941i \(0.645784\pi\)
\(644\) −10.5382 27.7108i −0.415265 1.09196i
\(645\) 13.0527 + 3.98724i 0.513949 + 0.156997i
\(646\) 6.04800 1.11119i 0.237955 0.0437191i
\(647\) −33.6238 −1.32189 −0.660943 0.750436i \(-0.729844\pi\)
−0.660943 + 0.750436i \(0.729844\pi\)
\(648\) −20.4063 15.2179i −0.801634 0.597816i
\(649\) 30.3102 1.18978
\(650\) 12.6958 2.33258i 0.497971 0.0914913i
\(651\) −1.15487 0.352781i −0.0452630 0.0138266i
\(652\) −1.00717 2.64839i −0.0394438 0.103719i
\(653\) 9.90614i 0.387657i 0.981035 + 0.193829i \(0.0620906\pi\)
−0.981035 + 0.193829i \(0.937909\pi\)
\(654\) 39.7190 + 4.57858i 1.55313 + 0.179037i
\(655\) 2.16344i 0.0845324i
\(656\) 10.7606 + 12.1016i 0.420130 + 0.472489i
\(657\) −7.17777 4.83653i −0.280031 0.188691i
\(658\) 8.69459 + 47.3231i 0.338951 + 1.84485i
\(659\) −27.0741 −1.05466 −0.527328 0.849662i \(-0.676806\pi\)
−0.527328 + 0.849662i \(0.676806\pi\)
\(660\) 1.89220 + 28.2274i 0.0736538 + 1.09875i
\(661\) 15.6830 0.609997 0.304999 0.952353i \(-0.401344\pi\)
0.304999 + 0.952353i \(0.401344\pi\)
\(662\) 2.13587 + 11.6251i 0.0830129 + 0.451824i
\(663\) 1.39644 4.57142i 0.0542333 0.177539i
\(664\) 17.0566 10.3430i 0.661926 0.401386i
\(665\) 60.8275i 2.35879i
\(666\) 38.0831 + 16.6081i 1.47569 + 0.643553i
\(667\) 25.3828i 0.982825i
\(668\) 41.7119 15.8628i 1.61388 0.613750i
\(669\) 11.1913 36.6361i 0.432681 1.41643i
\(670\) 3.62158 0.665387i 0.139914 0.0257061i
\(671\) 33.2082 1.28199
\(672\) −16.2709 23.1792i −0.627663 0.894158i
\(673\) 36.2637 1.39786 0.698931 0.715189i \(-0.253659\pi\)
0.698931 + 0.715189i \(0.253659\pi\)
\(674\) −12.0715 + 2.21787i −0.464976 + 0.0854292i
\(675\) −5.82343 7.18093i −0.224144 0.276394i
\(676\) 24.8925 9.46646i 0.957403 0.364095i
\(677\) 32.9930i 1.26802i 0.773323 + 0.634012i \(0.218593\pi\)
−0.773323 + 0.634012i \(0.781407\pi\)
\(678\) −4.35969 + 37.8201i −0.167433 + 1.45247i
\(679\) 15.2214i 0.584143i
\(680\) −3.38761 + 2.05422i −0.129909 + 0.0787757i
\(681\) −24.4138 7.45775i −0.935540 0.285782i
\(682\) −0.193345 1.05234i −0.00740356 0.0402962i
\(683\) −4.62379 −0.176924 −0.0884622 0.996080i \(-0.528195\pi\)
−0.0884622 + 0.996080i \(0.528195\pi\)
\(684\) 11.0340 47.2237i 0.421896 1.80564i
\(685\) 19.9804 0.763413
\(686\) −4.17016 22.6974i −0.159217 0.866591i
\(687\) 28.4482 + 8.69013i 1.08537 + 0.331549i
\(688\) −8.04390 9.04637i −0.306671 0.344890i
\(689\) 70.0840i 2.66999i
\(690\) −3.74565 + 32.4934i −0.142595 + 1.23700i
\(691\) 36.7601i 1.39842i 0.714916 + 0.699211i \(0.246465\pi\)
−0.714916 + 0.699211i \(0.753535\pi\)
\(692\) 1.99717 + 5.25165i 0.0759210 + 0.199638i
\(693\) −15.1984 + 22.5555i −0.577338 + 0.856811i
\(694\) −27.1383 + 4.98607i −1.03015 + 0.189269i
\(695\) 13.0587 0.495344
\(696\) −5.96666 23.5010i −0.226165 0.890803i
\(697\) 2.17793 0.0824948
\(698\) 5.67208 1.04212i 0.214691 0.0394449i
\(699\) −2.70357 + 8.85046i −0.102258 + 0.334755i
\(700\) −3.65612 9.61392i −0.138188 0.363372i
\(701\) 38.7119i 1.46213i 0.682308 + 0.731065i \(0.260976\pi\)
−0.682308 + 0.731065i \(0.739024\pi\)
\(702\) −28.6442 24.5065i −1.08110 0.924939i
\(703\) 79.1507i 2.98523i
\(704\) 11.6004 22.2505i 0.437207 0.838598i
\(705\) 15.5083 50.7681i 0.584075 1.91204i
\(706\) −0.376566 2.04958i −0.0141723 0.0771370i
\(707\) 30.0828 1.13138
\(708\) 33.3998 2.23893i 1.25524 0.0841441i
\(709\) 18.4442 0.692687 0.346343 0.938108i \(-0.387423\pi\)
0.346343 + 0.938108i \(0.387423\pi\)
\(710\) −2.97502 16.1925i −0.111651 0.607694i
\(711\) −18.1531 + 26.9406i −0.680795 + 1.01035i
\(712\) 10.5045 + 17.3229i 0.393671 + 0.649203i
\(713\) 1.23704i 0.0463274i
\(714\) −3.78372 0.436167i −0.141602 0.0163231i
\(715\) 41.8950i 1.56678i
\(716\) −4.08746 + 1.55444i −0.152756 + 0.0580920i
\(717\) −30.4850 9.31234i −1.13848 0.347776i
\(718\) −26.1815 + 4.81029i −0.977086 + 0.179518i
\(719\) −31.4138 −1.17154 −0.585768 0.810479i \(-0.699207\pi\)
−0.585768 + 0.810479i \(0.699207\pi\)
\(720\) 4.17016 + 30.9649i 0.155413 + 1.15399i
\(721\) 0.00500852 0.000186527
\(722\) 64.4400 11.8395i 2.39821 0.440619i
\(723\) −1.82298 0.556871i −0.0677974 0.0207102i
\(724\) 16.5166 6.28116i 0.613835 0.233438i
\(725\) 8.80625i 0.327056i
\(726\) 2.82669 + 0.325845i 0.104908 + 0.0120933i
\(727\) 14.1225i 0.523774i −0.965099 0.261887i \(-0.915655\pi\)
0.965099 0.261887i \(-0.0843448\pi\)
\(728\) −21.7453 35.8602i −0.805936 1.32907i
\(729\) −5.57618 + 26.4179i −0.206525 + 0.978441i
\(730\) 1.91968 + 10.4485i 0.0710507 + 0.386716i
\(731\) −1.62807 −0.0602164
\(732\) 36.5932 2.45300i 1.35252 0.0906654i
\(733\) 17.6493 0.651893 0.325947 0.945388i \(-0.394317\pi\)
0.325947 + 0.945388i \(0.394317\pi\)
\(734\) −1.23609 6.72780i −0.0456249 0.248328i
\(735\) 1.78437 5.84133i 0.0658173 0.215461i
\(736\) 17.8397 22.8780i 0.657582 0.843296i
\(737\) 3.13662i 0.115539i
\(738\) 6.86606 15.7441i 0.252743 0.579549i
\(739\) 0.103030i 0.00379003i 0.999998 + 0.00189502i \(0.000603202\pi\)
−0.999998 + 0.00189502i \(0.999397\pi\)
\(740\) −18.1265 47.6643i −0.666342 1.75218i
\(741\) 20.9807 68.6830i 0.770747 2.52313i
\(742\) −54.9253 + 10.0913i −2.01637 + 0.370465i
\(743\) −22.7858 −0.835929 −0.417965 0.908463i \(-0.637256\pi\)
−0.417965 + 0.908463i \(0.637256\pi\)
\(744\) −0.290787 1.14533i −0.0106608 0.0419898i
\(745\) 35.4395 1.29840
\(746\) −6.23913 + 1.14630i −0.228431 + 0.0419692i
\(747\) −17.5461 11.8229i −0.641977 0.432578i
\(748\) −1.19959 3.15438i −0.0438614 0.115336i
\(749\) 8.55287i 0.312515i
\(750\) 2.35227 20.4058i 0.0858926 0.745114i
\(751\) 3.39755i 0.123978i −0.998077 0.0619892i \(-0.980256\pi\)
0.998077 0.0619892i \(-0.0197444\pi\)
\(752\) −35.1856 + 31.2865i −1.28309 + 1.14090i
\(753\) −4.06634 1.24216i −0.148186 0.0452667i
\(754\) −6.48838 35.3151i −0.236293 1.28610i
\(755\) 18.4054 0.669842
\(756\) −15.0815 + 25.9773i −0.548508 + 0.944785i
\(757\) −18.0423 −0.655759 −0.327880 0.944719i \(-0.606334\pi\)
−0.327880 + 0.944719i \(0.606334\pi\)
\(758\) 0.119064 + 0.648044i 0.00432460 + 0.0235380i
\(759\) −26.6467 8.13983i −0.967214 0.295457i
\(760\) −50.8969 + 30.8635i −1.84623 + 1.11954i
\(761\) 47.3690i 1.71713i 0.512708 + 0.858563i \(0.328642\pi\)
−0.512708 + 0.858563i \(0.671358\pi\)
\(762\) 4.44731 38.5802i 0.161109 1.39761i
\(763\) 47.1786i 1.70798i