Properties

Label 570.2.m.a.37.10
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.10
Root \(-0.498616 + 0.498616i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.a.493.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.89390 - 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 + 0.705149i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(1.89390 - 1.18875i) q^{5} +1.00000 q^{6} +(0.705149 + 0.705149i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(0.498616 - 2.17977i) q^{10} +1.32903 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.741383 - 0.741383i) q^{13} +0.997232 q^{14} +(2.17977 + 0.498616i) q^{15} -1.00000 q^{16} +(2.17373 + 2.17373i) q^{17} +(0.707107 + 0.707107i) q^{18} +(0.939768 - 4.25639i) q^{19} +(-1.18875 - 1.89390i) q^{20} +0.997232i q^{21} +(0.939768 - 0.939768i) q^{22} +(-1.08266 + 1.08266i) q^{23} -1.00000i q^{24} +(2.17373 - 4.50276i) q^{25} -1.04847 q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.705149 - 0.705149i) q^{28} -5.95089 q^{29} +(1.89390 - 1.18875i) q^{30} +5.95089i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.939768 + 0.939768i) q^{33} +3.07412 q^{34} +(2.17373 + 0.497236i) q^{35} +1.00000 q^{36} +(-1.33551 + 1.33551i) q^{37} +(-2.34520 - 3.67424i) q^{38} -1.04847i q^{39} +(-2.17977 - 0.498616i) q^{40} -0.531910i q^{41} +(0.705149 + 0.705149i) q^{42} +(1.53142 - 1.53142i) q^{43} -1.32903i q^{44} +(1.18875 + 1.89390i) q^{45} +1.53111i q^{46} +(4.13113 + 4.13113i) q^{47} +(-0.707107 - 0.707107i) q^{48} -6.00553i q^{49} +(-1.64687 - 4.72100i) q^{50} +3.07412i q^{51} +(-0.741383 + 0.741383i) q^{52} +(-5.48557 - 5.48557i) q^{53} +1.00000i q^{54} +(2.51706 - 1.57989i) q^{55} -0.997232i q^{56} +(3.67424 - 2.34520i) q^{57} +(-4.20791 + 4.20791i) q^{58} -3.53944 q^{59} +(0.498616 - 2.17977i) q^{60} +3.41030 q^{61} +(4.20791 + 4.20791i) q^{62} +(-0.705149 + 0.705149i) q^{63} +1.00000i q^{64} +(-2.28543 - 0.522786i) q^{65} +1.32903 q^{66} +(-1.99446 + 1.99446i) q^{67} +(2.17373 - 2.17373i) q^{68} -1.53111 q^{69} +(1.88866 - 1.18546i) q^{70} +8.71907i q^{71} +(0.707107 - 0.707107i) q^{72} +(-5.83628 + 5.83628i) q^{73} +1.88869i q^{74} +(4.72100 - 1.64687i) q^{75} +(-4.25639 - 0.939768i) q^{76} +(0.937166 + 0.937166i) q^{77} +(-0.741383 - 0.741383i) q^{78} +9.31319 q^{79} +(-1.89390 + 1.18875i) q^{80} -1.00000 q^{81} +(-0.376117 - 0.376117i) q^{82} +(-9.50276 + 9.50276i) q^{83} +0.997232 q^{84} +(6.70087 + 1.53281i) q^{85} -2.16575i q^{86} +(-4.20791 - 4.20791i) q^{87} +(-0.939768 - 0.939768i) q^{88} -16.7874 q^{89} +(2.17977 + 0.498616i) q^{90} -1.04557i q^{91} +(1.08266 + 1.08266i) q^{92} +(-4.20791 + 4.20791i) q^{93} +5.84230 q^{94} +(-3.27997 - 9.17833i) q^{95} -1.00000 q^{96} +(1.11691 - 1.11691i) q^{97} +(-4.24655 - 4.24655i) q^{98} +1.32903i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 1.89390 1.18875i 0.846979 0.531627i
\(6\) 1.00000 0.408248
\(7\) 0.705149 + 0.705149i 0.266521 + 0.266521i 0.827697 0.561175i \(-0.189651\pi\)
−0.561175 + 0.827697i \(0.689651\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 0.498616 2.17977i 0.157676 0.689303i
\(11\) 1.32903 0.400718 0.200359 0.979723i \(-0.435789\pi\)
0.200359 + 0.979723i \(0.435789\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −0.741383 0.741383i −0.205623 0.205623i 0.596781 0.802404i \(-0.296446\pi\)
−0.802404 + 0.596781i \(0.796446\pi\)
\(14\) 0.997232 0.266521
\(15\) 2.17977 + 0.498616i 0.562813 + 0.128742i
\(16\) −1.00000 −0.250000
\(17\) 2.17373 + 2.17373i 0.527208 + 0.527208i 0.919739 0.392531i \(-0.128400\pi\)
−0.392531 + 0.919739i \(0.628400\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) 0.939768 4.25639i 0.215597 0.976482i
\(20\) −1.18875 1.89390i −0.265813 0.423489i
\(21\) 0.997232i 0.217614i
\(22\) 0.939768 0.939768i 0.200359 0.200359i
\(23\) −1.08266 + 1.08266i −0.225749 + 0.225749i −0.810914 0.585165i \(-0.801030\pi\)
0.585165 + 0.810914i \(0.301030\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 2.17373 4.50276i 0.434746 0.900553i
\(26\) −1.04847 −0.205623
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 0.705149 0.705149i 0.133261 0.133261i
\(29\) −5.95089 −1.10505 −0.552526 0.833496i \(-0.686336\pi\)
−0.552526 + 0.833496i \(0.686336\pi\)
\(30\) 1.89390 1.18875i 0.345778 0.217036i
\(31\) 5.95089i 1.06881i 0.845228 + 0.534406i \(0.179464\pi\)
−0.845228 + 0.534406i \(0.820536\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.939768 + 0.939768i 0.163593 + 0.163593i
\(34\) 3.07412 0.527208
\(35\) 2.17373 + 0.497236i 0.367428 + 0.0840481i
\(36\) 1.00000 0.166667
\(37\) −1.33551 + 1.33551i −0.219556 + 0.219556i −0.808311 0.588755i \(-0.799618\pi\)
0.588755 + 0.808311i \(0.299618\pi\)
\(38\) −2.34520 3.67424i −0.380442 0.596040i
\(39\) 1.04847i 0.167890i
\(40\) −2.17977 0.498616i −0.344651 0.0788381i
\(41\) 0.531910i 0.0830704i −0.999137 0.0415352i \(-0.986775\pi\)
0.999137 0.0415352i \(-0.0132249\pi\)
\(42\) 0.705149 + 0.705149i 0.108807 + 0.108807i
\(43\) 1.53142 1.53142i 0.233539 0.233539i −0.580629 0.814168i \(-0.697193\pi\)
0.814168 + 0.580629i \(0.197193\pi\)
\(44\) 1.32903i 0.200359i
\(45\) 1.18875 + 1.89390i 0.177209 + 0.282326i
\(46\) 1.53111i 0.225749i
\(47\) 4.13113 + 4.13113i 0.602587 + 0.602587i 0.940998 0.338411i \(-0.109889\pi\)
−0.338411 + 0.940998i \(0.609889\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 6.00553i 0.857933i
\(50\) −1.64687 4.72100i −0.232903 0.667650i
\(51\) 3.07412i 0.430463i
\(52\) −0.741383 + 0.741383i −0.102811 + 0.102811i
\(53\) −5.48557 5.48557i −0.753501 0.753501i 0.221630 0.975131i \(-0.428862\pi\)
−0.975131 + 0.221630i \(0.928862\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 2.51706 1.57989i 0.339400 0.213032i
\(56\) 0.997232i 0.133261i
\(57\) 3.67424 2.34520i 0.486665 0.310630i
\(58\) −4.20791 + 4.20791i −0.552526 + 0.552526i
\(59\) −3.53944 −0.460796 −0.230398 0.973096i \(-0.574003\pi\)
−0.230398 + 0.973096i \(0.574003\pi\)
\(60\) 0.498616 2.17977i 0.0643710 0.281407i
\(61\) 3.41030 0.436644 0.218322 0.975877i \(-0.429942\pi\)
0.218322 + 0.975877i \(0.429942\pi\)
\(62\) 4.20791 + 4.20791i 0.534406 + 0.534406i
\(63\) −0.705149 + 0.705149i −0.0888405 + 0.0888405i
\(64\) 1.00000i 0.125000i
\(65\) −2.28543 0.522786i −0.283473 0.0648436i
\(66\) 1.32903 0.163593
\(67\) −1.99446 + 1.99446i −0.243662 + 0.243662i −0.818363 0.574701i \(-0.805118\pi\)
0.574701 + 0.818363i \(0.305118\pi\)
\(68\) 2.17373 2.17373i 0.263604 0.263604i
\(69\) −1.53111 −0.184323
\(70\) 1.88866 1.18546i 0.225738 0.141690i
\(71\) 8.71907i 1.03476i 0.855755 + 0.517381i \(0.173093\pi\)
−0.855755 + 0.517381i \(0.826907\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) −5.83628 + 5.83628i −0.683085 + 0.683085i −0.960694 0.277609i \(-0.910458\pi\)
0.277609 + 0.960694i \(0.410458\pi\)
\(74\) 1.88869i 0.219556i
\(75\) 4.72100 1.64687i 0.545134 0.190165i
\(76\) −4.25639 0.939768i −0.488241 0.107799i
\(77\) 0.937166 + 0.937166i 0.106800 + 0.106800i
\(78\) −0.741383 0.741383i −0.0839451 0.0839451i
\(79\) 9.31319 1.04782 0.523908 0.851775i \(-0.324474\pi\)
0.523908 + 0.851775i \(0.324474\pi\)
\(80\) −1.89390 + 1.18875i −0.211745 + 0.132907i
\(81\) −1.00000 −0.111111
\(82\) −0.376117 0.376117i −0.0415352 0.0415352i
\(83\) −9.50276 + 9.50276i −1.04306 + 1.04306i −0.0440339 + 0.999030i \(0.514021\pi\)
−0.999030 + 0.0440339i \(0.985979\pi\)
\(84\) 0.997232 0.108807
\(85\) 6.70087 + 1.53281i 0.726811 + 0.166256i
\(86\) 2.16575i 0.233539i
\(87\) −4.20791 4.20791i −0.451136 0.451136i
\(88\) −0.939768 0.939768i −0.100180 0.100180i
\(89\) −16.7874 −1.77946 −0.889729 0.456490i \(-0.849106\pi\)
−0.889729 + 0.456490i \(0.849106\pi\)
\(90\) 2.17977 + 0.498616i 0.229768 + 0.0525587i
\(91\) 1.04557i 0.109606i
\(92\) 1.08266 + 1.08266i 0.112875 + 0.112875i
\(93\) −4.20791 + 4.20791i −0.436340 + 0.436340i
\(94\) 5.84230 0.602587
\(95\) −3.27997 9.17833i −0.336517 0.941677i
\(96\) −1.00000 −0.102062
\(97\) 1.11691 1.11691i 0.113405 0.113405i −0.648127 0.761532i \(-0.724447\pi\)
0.761532 + 0.648127i \(0.224447\pi\)
\(98\) −4.24655 4.24655i −0.428966 0.428966i
\(99\) 1.32903i 0.133573i
\(100\) −4.50276 2.17373i −0.450276 0.217373i
\(101\) −15.7109 −1.56329 −0.781645 0.623723i \(-0.785619\pi\)
−0.781645 + 0.623723i \(0.785619\pi\)
\(102\) 2.17373 + 2.17373i 0.215232 + 0.215232i
\(103\) 10.7950 + 10.7950i 1.06367 + 1.06367i 0.997831 + 0.0658345i \(0.0209710\pi\)
0.0658345 + 0.997831i \(0.479029\pi\)
\(104\) 1.04847i 0.102811i
\(105\) 1.18546 + 1.88866i 0.115689 + 0.184314i
\(106\) −7.75776 −0.753501
\(107\) −2.65129 + 2.65129i −0.256309 + 0.256309i −0.823551 0.567242i \(-0.808010\pi\)
0.567242 + 0.823551i \(0.308010\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −5.83596 −0.558984 −0.279492 0.960148i \(-0.590166\pi\)
−0.279492 + 0.960148i \(0.590166\pi\)
\(110\) 0.662676 2.89698i 0.0631837 0.276216i
\(111\) −1.88869 −0.179267
\(112\) −0.705149 0.705149i −0.0666303 0.0666303i
\(113\) −0.463357 0.463357i −0.0435890 0.0435890i 0.684976 0.728565i \(-0.259813\pi\)
−0.728565 + 0.684976i \(0.759813\pi\)
\(114\) 0.939768 4.25639i 0.0880173 0.398647i
\(115\) −0.763434 + 3.33745i −0.0711906 + 0.311219i
\(116\) 5.95089i 0.552526i
\(117\) 0.741383 0.741383i 0.0685409 0.0685409i
\(118\) −2.50276 + 2.50276i −0.230398 + 0.230398i
\(119\) 3.06561i 0.281024i
\(120\) −1.18875 1.89390i −0.108518 0.172889i
\(121\) −9.23367 −0.839425
\(122\) 2.41145 2.41145i 0.218322 0.218322i
\(123\) 0.376117 0.376117i 0.0339133 0.0339133i
\(124\) 5.95089 0.534406
\(125\) −1.23584 11.1118i −0.110537 0.993872i
\(126\) 0.997232i 0.0888405i
\(127\) 7.75499 7.75499i 0.688144 0.688144i −0.273678 0.961821i \(-0.588240\pi\)
0.961821 + 0.273678i \(0.0882402\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 2.16575 0.190684
\(130\) −1.98571 + 1.24638i −0.174158 + 0.109314i
\(131\) −13.2521 −1.15784 −0.578921 0.815384i \(-0.696526\pi\)
−0.578921 + 0.815384i \(0.696526\pi\)
\(132\) 0.939768 0.939768i 0.0817963 0.0817963i
\(133\) 3.66407 2.33871i 0.317715 0.202792i
\(134\) 2.82060i 0.243662i
\(135\) −0.498616 + 2.17977i −0.0429140 + 0.187604i
\(136\) 3.07412i 0.263604i
\(137\) 4.42031 + 4.42031i 0.377653 + 0.377653i 0.870255 0.492602i \(-0.163954\pi\)
−0.492602 + 0.870255i \(0.663954\pi\)
\(138\) −1.08266 + 1.08266i −0.0921617 + 0.0921617i
\(139\) 2.68665i 0.227879i −0.993488 0.113939i \(-0.963653\pi\)
0.993488 0.113939i \(-0.0363469\pi\)
\(140\) 0.497236 2.17373i 0.0420241 0.183714i
\(141\) 5.84230i 0.492010i
\(142\) 6.16531 + 6.16531i 0.517381 + 0.517381i
\(143\) −0.985322 0.985322i −0.0823968 0.0823968i
\(144\) 1.00000i 0.0833333i
\(145\) −11.2704 + 7.07414i −0.935956 + 0.587475i
\(146\) 8.25374i 0.683085i
\(147\) 4.24655 4.24655i 0.350250 0.350250i
\(148\) 1.33551 + 1.33551i 0.109778 + 0.109778i
\(149\) 14.1380i 1.15823i 0.815244 + 0.579117i \(0.196603\pi\)
−0.815244 + 0.579117i \(0.803397\pi\)
\(150\) 2.17373 4.50276i 0.177485 0.367649i
\(151\) 9.45030i 0.769054i −0.923114 0.384527i \(-0.874365\pi\)
0.923114 0.384527i \(-0.125635\pi\)
\(152\) −3.67424 + 2.34520i −0.298020 + 0.190221i
\(153\) −2.17373 + 2.17373i −0.175736 + 0.175736i
\(154\) 1.32535 0.106800
\(155\) 7.07414 + 11.2704i 0.568208 + 0.905260i
\(156\) −1.04847 −0.0839451
\(157\) 13.7650 + 13.7650i 1.09857 + 1.09857i 0.994578 + 0.103990i \(0.0331610\pi\)
0.103990 + 0.994578i \(0.466839\pi\)
\(158\) 6.58542 6.58542i 0.523908 0.523908i
\(159\) 7.75776i 0.615231i
\(160\) −0.498616 + 2.17977i −0.0394190 + 0.172326i
\(161\) −1.52687 −0.120334
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 0.792086 0.792086i 0.0620410 0.0620410i −0.675406 0.737447i \(-0.736031\pi\)
0.737447 + 0.675406i \(0.236031\pi\)
\(164\) −0.531910 −0.0415352
\(165\) 2.89698 + 0.662676i 0.225530 + 0.0515893i
\(166\) 13.4389i 1.04306i
\(167\) 11.1325 11.1325i 0.861457 0.861457i −0.130051 0.991507i \(-0.541514\pi\)
0.991507 + 0.130051i \(0.0415140\pi\)
\(168\) 0.705149 0.705149i 0.0544035 0.0544035i
\(169\) 11.9007i 0.915439i
\(170\) 5.82209 3.65437i 0.446534 0.280278i
\(171\) 4.25639 + 0.939768i 0.325494 + 0.0718658i
\(172\) −1.53142 1.53142i −0.116769 0.116769i
\(173\) 5.42532 + 5.42532i 0.412479 + 0.412479i 0.882601 0.470122i \(-0.155790\pi\)
−0.470122 + 0.882601i \(0.655790\pi\)
\(174\) −5.95089 −0.451136
\(175\) 4.70793 1.64232i 0.355886 0.124147i
\(176\) −1.32903 −0.100180
\(177\) −2.50276 2.50276i −0.188119 0.188119i
\(178\) −11.8705 + 11.8705i −0.889729 + 0.889729i
\(179\) −0.963050 −0.0719817 −0.0359909 0.999352i \(-0.511459\pi\)
−0.0359909 + 0.999352i \(0.511459\pi\)
\(180\) 1.89390 1.18875i 0.141163 0.0886044i
\(181\) 20.4214i 1.51791i −0.651141 0.758956i \(-0.725710\pi\)
0.651141 0.758956i \(-0.274290\pi\)
\(182\) −0.739331 0.739331i −0.0548028 0.0548028i
\(183\) 2.41145 + 2.41145i 0.178259 + 0.178259i
\(184\) 1.53111 0.112875
\(185\) −0.941732 + 4.11691i −0.0692375 + 0.302681i
\(186\) 5.95089i 0.436340i
\(187\) 2.88896 + 2.88896i 0.211262 + 0.211262i
\(188\) 4.13113 4.13113i 0.301294 0.301294i
\(189\) −0.997232 −0.0725379
\(190\) −8.80935 4.17078i −0.639097 0.302580i
\(191\) −7.34773 −0.531663 −0.265832 0.964019i \(-0.585647\pi\)
−0.265832 + 0.964019i \(0.585647\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) 9.32428 + 9.32428i 0.671176 + 0.671176i 0.957987 0.286811i \(-0.0925952\pi\)
−0.286811 + 0.957987i \(0.592595\pi\)
\(194\) 1.57955i 0.113405i
\(195\) −1.24638 1.98571i −0.0892549 0.142199i
\(196\) −6.00553 −0.428966
\(197\) 5.43012 + 5.43012i 0.386880 + 0.386880i 0.873573 0.486693i \(-0.161797\pi\)
−0.486693 + 0.873573i \(0.661797\pi\)
\(198\) 0.939768 + 0.939768i 0.0667864 + 0.0667864i
\(199\) 23.4987i 1.66578i 0.553440 + 0.832889i \(0.313315\pi\)
−0.553440 + 0.832889i \(0.686685\pi\)
\(200\) −4.72100 + 1.64687i −0.333825 + 0.116452i
\(201\) −2.82060 −0.198950
\(202\) −11.1093 + 11.1093i −0.781645 + 0.781645i
\(203\) −4.19627 4.19627i −0.294520 0.294520i
\(204\) 3.07412 0.215232
\(205\) −0.632310 1.00739i −0.0441624 0.0703589i
\(206\) 15.2665 1.06367
\(207\) −1.08266 1.08266i −0.0752498 0.0752498i
\(208\) 0.741383 + 0.741383i 0.0514057 + 0.0514057i
\(209\) 1.24898 5.65688i 0.0863938 0.391294i
\(210\) 2.17373 + 0.497236i 0.150002 + 0.0343125i
\(211\) 8.16488i 0.562094i −0.959694 0.281047i \(-0.909318\pi\)
0.959694 0.281047i \(-0.0906816\pi\)
\(212\) −5.48557 + 5.48557i −0.376750 + 0.376750i
\(213\) −6.16531 + 6.16531i −0.422440 + 0.422440i
\(214\) 3.74948i 0.256309i
\(215\) 1.07988 4.72083i 0.0736470 0.321958i
\(216\) 1.00000 0.0680414
\(217\) −4.19627 + 4.19627i −0.284861 + 0.284861i
\(218\) −4.12665 + 4.12665i −0.279492 + 0.279492i
\(219\) −8.25374 −0.557736
\(220\) −1.57989 2.51706i −0.106516 0.169700i
\(221\) 3.22314i 0.216812i
\(222\) −1.33551 + 1.33551i −0.0896334 + 0.0896334i
\(223\) 0.212542 + 0.212542i 0.0142329 + 0.0142329i 0.714187 0.699955i \(-0.246796\pi\)
−0.699955 + 0.714187i \(0.746796\pi\)
\(224\) −0.997232 −0.0666303
\(225\) 4.50276 + 2.17373i 0.300184 + 0.144915i
\(226\) −0.655286 −0.0435890
\(227\) 16.9240 16.9240i 1.12328 1.12328i 0.132040 0.991244i \(-0.457847\pi\)
0.991244 0.132040i \(-0.0421528\pi\)
\(228\) −2.34520 3.67424i −0.155315 0.243332i
\(229\) 7.59523i 0.501907i −0.967999 0.250953i \(-0.919256\pi\)
0.967999 0.250953i \(-0.0807441\pi\)
\(230\) 1.82011 + 2.89977i 0.120014 + 0.191205i
\(231\) 1.32535i 0.0872018i
\(232\) 4.20791 + 4.20791i 0.276263 + 0.276263i
\(233\) 0.816115 0.816115i 0.0534655 0.0534655i −0.679869 0.733334i \(-0.737963\pi\)
0.733334 + 0.679869i \(0.237963\pi\)
\(234\) 1.04847i 0.0685409i
\(235\) 12.7348 + 2.91306i 0.830730 + 0.190027i
\(236\) 3.53944i 0.230398i
\(237\) 6.58542 + 6.58542i 0.427769 + 0.427769i
\(238\) 2.16771 + 2.16771i 0.140512 + 0.140512i
\(239\) 4.21103i 0.272389i −0.990682 0.136195i \(-0.956513\pi\)
0.990682 0.136195i \(-0.0434872\pi\)
\(240\) −2.17977 0.498616i −0.140703 0.0321855i
\(241\) 24.8896i 1.60328i −0.597809 0.801638i \(-0.703962\pi\)
0.597809 0.801638i \(-0.296038\pi\)
\(242\) −6.52919 + 6.52919i −0.419712 + 0.419712i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 3.41030i 0.218322i
\(245\) −7.13909 11.3739i −0.456100 0.726651i
\(246\) 0.531910i 0.0339133i
\(247\) −3.85234 + 2.45889i −0.245119 + 0.156455i
\(248\) 4.20791 4.20791i 0.267203 0.267203i
\(249\) −13.4389 −0.851658
\(250\) −8.73112 6.98338i −0.552204 0.441668i
\(251\) −0.952848 −0.0601432 −0.0300716 0.999548i \(-0.509574\pi\)
−0.0300716 + 0.999548i \(0.509574\pi\)
\(252\) 0.705149 + 0.705149i 0.0444202 + 0.0444202i
\(253\) −1.43888 + 1.43888i −0.0904619 + 0.0904619i
\(254\) 10.9672i 0.688144i
\(255\) 3.65437 + 5.82209i 0.228846 + 0.364593i
\(256\) 1.00000 0.0625000
\(257\) 12.4298 12.4298i 0.775349 0.775349i −0.203687 0.979036i \(-0.565292\pi\)
0.979036 + 0.203687i \(0.0652924\pi\)
\(258\) 1.53142 1.53142i 0.0953419 0.0953419i
\(259\) −1.88346 −0.117033
\(260\) −0.522786 + 2.28543i −0.0324218 + 0.141736i
\(261\) 5.95089i 0.368351i
\(262\) −9.37065 + 9.37065i −0.578921 + 0.578921i
\(263\) 3.37612 3.37612i 0.208180 0.208180i −0.595313 0.803494i \(-0.702972\pi\)
0.803494 + 0.595313i \(0.202972\pi\)
\(264\) 1.32903i 0.0817963i
\(265\) −16.9101 3.86814i −1.03878 0.237618i
\(266\) 0.937166 4.24460i 0.0574613 0.260253i
\(267\) −11.8705 11.8705i −0.726460 0.726460i
\(268\) 1.99446 + 1.99446i 0.121831 + 0.121831i
\(269\) 1.10025 0.0670834 0.0335417 0.999437i \(-0.489321\pi\)
0.0335417 + 0.999437i \(0.489321\pi\)
\(270\) 1.18875 + 1.89390i 0.0723452 + 0.115259i
\(271\) 18.3193 1.11282 0.556409 0.830909i \(-0.312179\pi\)
0.556409 + 0.830909i \(0.312179\pi\)
\(272\) −2.17373 2.17373i −0.131802 0.131802i
\(273\) 0.739331 0.739331i 0.0447463 0.0447463i
\(274\) 6.25126 0.377653
\(275\) 2.88896 5.98432i 0.174211 0.360868i
\(276\) 1.53111i 0.0921617i
\(277\) −6.48039 6.48039i −0.389369 0.389369i 0.485093 0.874462i \(-0.338786\pi\)
−0.874462 + 0.485093i \(0.838786\pi\)
\(278\) −1.89975 1.89975i −0.113939 0.113939i
\(279\) −5.95089 −0.356270
\(280\) −1.18546 1.88866i −0.0708449 0.112869i
\(281\) 12.6675i 0.755678i −0.925871 0.377839i \(-0.876667\pi\)
0.925871 0.377839i \(-0.123333\pi\)
\(282\) 4.13113 + 4.13113i 0.246005 + 0.246005i
\(283\) 11.2107 11.2107i 0.666406 0.666406i −0.290476 0.956882i \(-0.593814\pi\)
0.956882 + 0.290476i \(0.0938136\pi\)
\(284\) 8.71907 0.517381
\(285\) 4.17078 8.80935i 0.247055 0.521821i
\(286\) −1.39346 −0.0823968
\(287\) 0.375076 0.375076i 0.0221400 0.0221400i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 7.54978i 0.444104i
\(290\) −2.96721 + 12.9715i −0.174240 + 0.761716i
\(291\) 1.57955 0.0925948
\(292\) 5.83628 + 5.83628i 0.341542 + 0.341542i
\(293\) 0.128802 + 0.128802i 0.00752471 + 0.00752471i 0.710859 0.703334i \(-0.248306\pi\)
−0.703334 + 0.710859i \(0.748306\pi\)
\(294\) 6.00553i 0.350250i
\(295\) −6.70336 + 4.20752i −0.390285 + 0.244972i
\(296\) 1.88869 0.109778
\(297\) −0.939768 + 0.939768i −0.0545308 + 0.0545308i
\(298\) 9.99711 + 9.99711i 0.579117 + 0.579117i
\(299\) 1.60532 0.0928383
\(300\) −1.64687 4.72100i −0.0950823 0.272567i
\(301\) 2.15976 0.124486
\(302\) −6.68237 6.68237i −0.384527 0.384527i
\(303\) −11.1093 11.1093i −0.638211 0.638211i
\(304\) −0.939768 + 4.25639i −0.0538994 + 0.244121i
\(305\) 6.45877 4.05400i 0.369828 0.232132i
\(306\) 3.07412i 0.175736i
\(307\) 15.7940 15.7940i 0.901413 0.901413i −0.0941458 0.995558i \(-0.530012\pi\)
0.995558 + 0.0941458i \(0.0300120\pi\)
\(308\) 0.937166 0.937166i 0.0534000 0.0534000i
\(309\) 15.2665i 0.868479i
\(310\) 12.9715 + 2.96721i 0.736734 + 0.168526i
\(311\) 14.6924 0.833132 0.416566 0.909105i \(-0.363233\pi\)
0.416566 + 0.909105i \(0.363233\pi\)
\(312\) −0.741383 + 0.741383i −0.0419726 + 0.0419726i
\(313\) −1.77069 + 1.77069i −0.100086 + 0.100086i −0.755377 0.655291i \(-0.772546\pi\)
0.655291 + 0.755377i \(0.272546\pi\)
\(314\) 19.4667 1.09857
\(315\) −0.497236 + 2.17373i −0.0280160 + 0.122476i
\(316\) 9.31319i 0.523908i
\(317\) −4.63384 + 4.63384i −0.260262 + 0.260262i −0.825161 0.564898i \(-0.808915\pi\)
0.564898 + 0.825161i \(0.308915\pi\)
\(318\) −5.48557 5.48557i −0.307615 0.307615i
\(319\) −7.90892 −0.442815
\(320\) 1.18875 + 1.89390i 0.0664533 + 0.105872i
\(321\) −3.74948 −0.209276
\(322\) −1.07966 + 1.07966i −0.0601670 + 0.0601670i
\(323\) 11.2951 7.20944i 0.628473 0.401144i
\(324\) 1.00000i 0.0555556i
\(325\) −4.94984 + 1.72670i −0.274568 + 0.0957804i
\(326\) 1.12018i 0.0620410i
\(327\) −4.12665 4.12665i −0.228204 0.228204i
\(328\) −0.376117 + 0.376117i −0.0207676 + 0.0207676i
\(329\) 5.82613i 0.321205i
\(330\) 2.51706 1.57989i 0.138559 0.0869701i
\(331\) 10.5075i 0.577544i −0.957398 0.288772i \(-0.906753\pi\)
0.957398 0.288772i \(-0.0932470\pi\)
\(332\) 9.50276 + 9.50276i 0.521532 + 0.521532i
\(333\) −1.33551 1.33551i −0.0731853 0.0731853i
\(334\) 15.7437i 0.861457i
\(335\) −1.40639 + 6.14824i −0.0768395 + 0.335914i
\(336\) 0.997232i 0.0544035i
\(337\) −18.8126 + 18.8126i −1.02479 + 1.02479i −0.0251053 + 0.999685i \(0.507992\pi\)
−0.999685 + 0.0251053i \(0.992008\pi\)
\(338\) −8.41507 8.41507i −0.457719 0.457719i
\(339\) 0.655286i 0.0355903i
\(340\) 1.53281 6.70087i 0.0831281 0.363406i
\(341\) 7.90892i 0.428292i
\(342\) 3.67424 2.34520i 0.198680 0.126814i
\(343\) 9.17084 9.17084i 0.495179 0.495179i
\(344\) −2.16575 −0.116769
\(345\) −2.89977 + 1.82011i −0.156118 + 0.0979913i
\(346\) 7.67256 0.412479
\(347\) 16.9775 + 16.9775i 0.911399 + 0.911399i 0.996382 0.0849832i \(-0.0270836\pi\)
−0.0849832 + 0.996382i \(0.527084\pi\)
\(348\) −4.20791 + 4.20791i −0.225568 + 0.225568i
\(349\) 16.3106i 0.873086i −0.899683 0.436543i \(-0.856203\pi\)
0.899683 0.436543i \(-0.143797\pi\)
\(350\) 2.16771 4.49030i 0.115869 0.240017i
\(351\) 1.04847 0.0559634
\(352\) −0.939768 + 0.939768i −0.0500898 + 0.0500898i
\(353\) 7.93890 7.93890i 0.422545 0.422545i −0.463534 0.886079i \(-0.653419\pi\)
0.886079 + 0.463534i \(0.153419\pi\)
\(354\) −3.53944 −0.188119
\(355\) 10.3648 + 16.5131i 0.550107 + 0.876422i
\(356\) 16.7874i 0.889729i
\(357\) −2.16771 + 2.16771i −0.114728 + 0.114728i
\(358\) −0.680979 + 0.680979i −0.0359909 + 0.0359909i
\(359\) 26.2304i 1.38439i −0.721712 0.692193i \(-0.756645\pi\)
0.721712 0.692193i \(-0.243355\pi\)
\(360\) 0.498616 2.17977i 0.0262794 0.114884i
\(361\) −17.2337 8.00003i −0.907035 0.421054i
\(362\) −14.4401 14.4401i −0.758956 0.758956i
\(363\) −6.52919 6.52919i −0.342694 0.342694i
\(364\) −1.04557 −0.0548028
\(365\) −4.11545 + 17.9912i −0.215412 + 0.941704i
\(366\) 3.41030 0.178259
\(367\) −1.62269 1.62269i −0.0847040 0.0847040i 0.663485 0.748189i \(-0.269077\pi\)
−0.748189 + 0.663485i \(0.769077\pi\)
\(368\) 1.08266 1.08266i 0.0564373 0.0564373i
\(369\) 0.531910 0.0276901
\(370\) 2.24519 + 3.57700i 0.116722 + 0.185959i
\(371\) 7.73629i 0.401648i
\(372\) 4.20791 + 4.20791i 0.218170 + 0.218170i
\(373\) 9.00900 + 9.00900i 0.466468 + 0.466468i 0.900768 0.434300i \(-0.143004\pi\)
−0.434300 + 0.900768i \(0.643004\pi\)
\(374\) 4.08561 0.211262
\(375\) 6.98338 8.73112i 0.360620 0.450873i
\(376\) 5.84230i 0.301294i
\(377\) 4.41189 + 4.41189i 0.227224 + 0.227224i
\(378\) −0.705149 + 0.705149i −0.0362690 + 0.0362690i
\(379\) 4.49635 0.230962 0.115481 0.993310i \(-0.463159\pi\)
0.115481 + 0.993310i \(0.463159\pi\)
\(380\) −9.17833 + 3.27997i −0.470839 + 0.168259i
\(381\) 10.9672 0.561867
\(382\) −5.19563 + 5.19563i −0.265832 + 0.265832i
\(383\) 22.5064 + 22.5064i 1.15003 + 1.15003i 0.986547 + 0.163478i \(0.0522713\pi\)
0.163478 + 0.986547i \(0.447729\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 2.88896 + 0.660842i 0.147235 + 0.0336796i
\(386\) 13.1865 0.671176
\(387\) 1.53142 + 1.53142i 0.0778463 + 0.0778463i
\(388\) −1.11691 1.11691i −0.0567025 0.0567025i
\(389\) 26.1672i 1.32673i 0.748297 + 0.663364i \(0.230872\pi\)
−0.748297 + 0.663364i \(0.769128\pi\)
\(390\) −2.28543 0.522786i −0.115727 0.0264723i
\(391\) −4.70681 −0.238033
\(392\) −4.24655 + 4.24655i −0.214483 + 0.214483i
\(393\) −9.37065 9.37065i −0.472687 0.472687i
\(394\) 7.67935 0.386880
\(395\) 17.6383 11.0711i 0.887478 0.557047i
\(396\) 1.32903 0.0667864
\(397\) −15.5911 15.5911i −0.782497 0.782497i 0.197754 0.980252i \(-0.436635\pi\)
−0.980252 + 0.197754i \(0.936635\pi\)
\(398\) 16.6161 + 16.6161i 0.832889 + 0.832889i
\(399\) 4.24460 + 0.937166i 0.212496 + 0.0469170i
\(400\) −2.17373 + 4.50276i −0.108687 + 0.225138i
\(401\) 13.8440i 0.691337i 0.938357 + 0.345668i \(0.112348\pi\)
−0.938357 + 0.345668i \(0.887652\pi\)
\(402\) −1.99446 + 1.99446i −0.0994748 + 0.0994748i
\(403\) 4.41189 4.41189i 0.219772 0.219772i
\(404\) 15.7109i 0.781645i
\(405\) −1.89390 + 1.18875i −0.0941088 + 0.0590696i
\(406\) −5.93441 −0.294520
\(407\) −1.77493 + 1.77493i −0.0879801 + 0.0879801i
\(408\) 2.17373 2.17373i 0.107616 0.107616i
\(409\) −9.17657 −0.453752 −0.226876 0.973924i \(-0.572851\pi\)
−0.226876 + 0.973924i \(0.572851\pi\)
\(410\) −1.15944 0.265219i −0.0572606 0.0130982i
\(411\) 6.25126i 0.308352i
\(412\) 10.7950 10.7950i 0.531833 0.531833i
\(413\) −2.49584 2.49584i −0.122812 0.122812i
\(414\) −1.53111 −0.0752498
\(415\) −6.70087 + 29.2937i −0.328933 + 1.43797i
\(416\) 1.04847 0.0514057
\(417\) 1.89975 1.89975i 0.0930311 0.0930311i
\(418\) −3.11685 4.88318i −0.152450 0.238844i
\(419\) 21.8535i 1.06762i −0.845606 0.533808i \(-0.820761\pi\)
0.845606 0.533808i \(-0.179239\pi\)
\(420\) 1.88866 1.18546i 0.0921571 0.0578446i
\(421\) 29.4223i 1.43396i −0.697095 0.716978i \(-0.745525\pi\)
0.697095 0.716978i \(-0.254475\pi\)
\(422\) −5.77344 5.77344i −0.281047 0.281047i
\(423\) −4.13113 + 4.13113i −0.200862 + 0.200862i
\(424\) 7.75776i 0.376750i
\(425\) 14.5129 5.06269i 0.703980 0.245577i
\(426\) 8.71907i 0.422440i
\(427\) 2.40477 + 2.40477i 0.116375 + 0.116375i
\(428\) 2.65129 + 2.65129i 0.128155 + 0.128155i
\(429\) 1.39346i 0.0672767i
\(430\) −2.57454 4.10172i −0.124155 0.197803i
\(431\) 36.4149i 1.75404i 0.480452 + 0.877021i \(0.340473\pi\)
−0.480452 + 0.877021i \(0.659527\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 16.4903 + 16.4903i 0.792475 + 0.792475i 0.981896 0.189421i \(-0.0606610\pi\)
−0.189421 + 0.981896i \(0.560661\pi\)
\(434\) 5.93441i 0.284861i
\(435\) −12.9715 2.96721i −0.621938 0.142267i
\(436\) 5.83596i 0.279492i
\(437\) 3.59076 + 5.62565i 0.171769 + 0.269111i
\(438\) −5.83628 + 5.83628i −0.278868 + 0.278868i
\(439\) 13.3446 0.636903 0.318452 0.947939i \(-0.396837\pi\)
0.318452 + 0.947939i \(0.396837\pi\)
\(440\) −2.89698 0.662676i −0.138108 0.0315919i
\(441\) 6.00553 0.285978
\(442\) −2.27910 2.27910i −0.108406 0.108406i
\(443\) −17.4215 + 17.4215i −0.827720 + 0.827720i −0.987201 0.159481i \(-0.949018\pi\)
0.159481 + 0.987201i \(0.449018\pi\)
\(444\) 1.88869i 0.0896334i
\(445\) −31.7936 + 19.9560i −1.50716 + 0.946007i
\(446\) 0.300580 0.0142329
\(447\) −9.99711 + 9.99711i −0.472847 + 0.472847i
\(448\) −0.705149 + 0.705149i −0.0333152 + 0.0333152i
\(449\) 39.0761 1.84412 0.922058 0.387051i \(-0.126506\pi\)
0.922058 + 0.387051i \(0.126506\pi\)
\(450\) 4.72100 1.64687i 0.222550 0.0776344i
\(451\) 0.706926i 0.0332878i
\(452\) −0.463357 + 0.463357i −0.0217945 + 0.0217945i
\(453\) 6.68237 6.68237i 0.313965 0.313965i
\(454\) 23.9341i 1.12328i
\(455\) −1.24293 1.98021i −0.0582693 0.0928337i
\(456\) −4.25639 0.939768i −0.199324 0.0440087i
\(457\) −25.9258 25.9258i −1.21276 1.21276i −0.970116 0.242643i \(-0.921986\pi\)
−0.242643 0.970116i \(-0.578014\pi\)
\(458\) −5.37064 5.37064i −0.250953 0.250953i
\(459\) −3.07412 −0.143488
\(460\) 3.33745 + 0.763434i 0.155610 + 0.0355953i
\(461\) −16.3202 −0.760108 −0.380054 0.924964i \(-0.624095\pi\)
−0.380054 + 0.924964i \(0.624095\pi\)
\(462\) 0.937166 + 0.937166i 0.0436009 + 0.0436009i
\(463\) −4.26074 + 4.26074i −0.198013 + 0.198013i −0.799148 0.601135i \(-0.794716\pi\)
0.601135 + 0.799148i \(0.294716\pi\)
\(464\) 5.95089 0.276263
\(465\) −2.96721 + 12.9715i −0.137601 + 0.601541i
\(466\) 1.15416i 0.0534655i
\(467\) −24.0643 24.0643i −1.11356 1.11356i −0.992665 0.120897i \(-0.961423\pi\)
−0.120897 0.992665i \(-0.538577\pi\)
\(468\) −0.741383 0.741383i −0.0342704 0.0342704i
\(469\) −2.81279 −0.129883
\(470\) 11.0647 6.94505i 0.510379 0.320351i
\(471\) 19.4667i 0.896977i
\(472\) 2.50276 + 2.50276i 0.115199 + 0.115199i
\(473\) 2.03530 2.03530i 0.0935833 0.0935833i
\(474\) 9.31319 0.427769
\(475\) −17.1227 13.4838i −0.785644 0.618679i
\(476\) 3.06561 0.140512
\(477\) 5.48557 5.48557i 0.251167 0.251167i
\(478\) −2.97765 2.97765i −0.136195 0.136195i
\(479\) 19.7176i 0.900920i 0.892797 + 0.450460i \(0.148740\pi\)
−0.892797 + 0.450460i \(0.851260\pi\)
\(480\) −1.89390 + 1.18875i −0.0864444 + 0.0542589i
\(481\) 1.98024 0.0902914
\(482\) −17.5996 17.5996i −0.801638 0.801638i
\(483\) −1.07966 1.07966i −0.0491262 0.0491262i
\(484\) 9.23367i 0.419712i
\(485\) 0.787588 3.44305i 0.0357625 0.156341i
\(486\) −1.00000 −0.0453609
\(487\) −23.8855 + 23.8855i −1.08236 + 1.08236i −0.0860674 + 0.996289i \(0.527430\pi\)
−0.996289 + 0.0860674i \(0.972570\pi\)
\(488\) −2.41145 2.41145i −0.109161 0.109161i
\(489\) 1.12018 0.0506563
\(490\) −13.0907 2.99445i −0.591375 0.135276i
\(491\) 21.2521 0.959094 0.479547 0.877516i \(-0.340801\pi\)
0.479547 + 0.877516i \(0.340801\pi\)
\(492\) −0.376117 0.376117i −0.0169567 0.0169567i
\(493\) −12.9356 12.9356i −0.582592 0.582592i
\(494\) −0.985322 + 4.46271i −0.0443317 + 0.200787i
\(495\) 1.57989 + 2.51706i 0.0710108 + 0.113133i
\(496\) 5.95089i 0.267203i
\(497\) −6.14824 + 6.14824i −0.275786 + 0.275786i
\(498\) −9.50276 + 9.50276i −0.425829 + 0.425829i
\(499\) 39.2906i 1.75889i 0.476002 + 0.879444i \(0.342085\pi\)
−0.476002 + 0.879444i \(0.657915\pi\)
\(500\) −11.1118 + 1.23584i −0.496936 + 0.0552684i
\(501\) 15.7437 0.703377
\(502\) −0.673765 + 0.673765i −0.0300716 + 0.0300716i
\(503\) 7.92010 7.92010i 0.353140 0.353140i −0.508137 0.861276i \(-0.669666\pi\)
0.861276 + 0.508137i \(0.169666\pi\)
\(504\) 0.997232 0.0444202
\(505\) −29.7549 + 18.6764i −1.32407 + 0.831087i
\(506\) 2.03489i 0.0904619i
\(507\) 8.41507 8.41507i 0.373726 0.373726i
\(508\) −7.75499 7.75499i −0.344072 0.344072i
\(509\) 19.7948 0.877389 0.438695 0.898636i \(-0.355441\pi\)
0.438695 + 0.898636i \(0.355441\pi\)
\(510\) 6.70087 + 1.53281i 0.296719 + 0.0678738i
\(511\) −8.23090 −0.364113
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 2.34520 + 3.67424i 0.103543 + 0.162222i
\(514\) 17.5784i 0.775349i
\(515\) 33.2773 + 7.61210i 1.46637 + 0.335429i
\(516\) 2.16575i 0.0953419i
\(517\) 5.49040 + 5.49040i 0.241468 + 0.241468i
\(518\) −1.33181 + 1.33181i −0.0585164 + 0.0585164i
\(519\) 7.67256i 0.336788i
\(520\) 1.24638 + 1.98571i 0.0546572 + 0.0870790i
\(521\) 32.9001i 1.44138i −0.693257 0.720691i \(-0.743825\pi\)
0.693257 0.720691i \(-0.256175\pi\)
\(522\) −4.20791 4.20791i −0.184175 0.184175i
\(523\) −5.26214 5.26214i −0.230098 0.230098i 0.582636 0.812733i \(-0.302021\pi\)
−0.812733 + 0.582636i \(0.802021\pi\)
\(524\) 13.2521i 0.578921i
\(525\) 4.49030 + 2.16771i 0.195973 + 0.0946068i
\(526\) 4.77455i 0.208180i
\(527\) −12.9356 + 12.9356i −0.563485 + 0.563485i
\(528\) −0.939768 0.939768i −0.0408981 0.0408981i
\(529\) 20.6557i 0.898075i
\(530\) −14.6924 + 9.22206i −0.638199 + 0.400581i
\(531\) 3.53944i 0.153599i
\(532\) −2.33871 3.66407i −0.101396 0.158857i
\(533\) −0.394349 + 0.394349i −0.0170812 + 0.0170812i
\(534\) −16.7874 −0.726460
\(535\) −1.86955 + 8.17300i −0.0808278 + 0.353350i
\(536\) 2.82060 0.121831
\(537\) −0.680979 0.680979i −0.0293864 0.0293864i
\(538\) 0.777994 0.777994i 0.0335417 0.0335417i
\(539\) 7.98154i 0.343789i
\(540\) 2.17977 + 0.498616i 0.0938022 + 0.0214570i
\(541\) −3.97998 −0.171113 −0.0855563 0.996333i \(-0.527267\pi\)
−0.0855563 + 0.996333i \(0.527267\pi\)
\(542\) 12.9537 12.9537i 0.556409 0.556409i
\(543\) 14.4401 14.4401i 0.619685 0.619685i
\(544\) −3.07412 −0.131802
\(545\) −11.0527 + 6.93752i −0.473447 + 0.297171i
\(546\) 1.04557i 0.0447463i
\(547\) 17.5769 17.5769i 0.751533 0.751533i −0.223232 0.974765i \(-0.571661\pi\)
0.974765 + 0.223232i \(0.0716608\pi\)
\(548\) 4.42031 4.42031i 0.188826 0.188826i
\(549\) 3.41030i 0.145548i
\(550\) −2.18875 6.27436i −0.0933286 0.267539i
\(551\) −5.59245 + 25.3293i −0.238246 + 1.07906i
\(552\) 1.08266 + 1.08266i 0.0460809 + 0.0460809i
\(553\) 6.56719 + 6.56719i 0.279265 + 0.279265i
\(554\) −9.16466 −0.389369
\(555\) −3.57700 + 2.24519i −0.151835 + 0.0953029i
\(556\) −2.68665 −0.113939
\(557\) 10.5795 + 10.5795i 0.448267 + 0.448267i 0.894778 0.446511i \(-0.147334\pi\)
−0.446511 + 0.894778i \(0.647334\pi\)
\(558\) −4.20791 + 4.20791i −0.178135 + 0.178135i
\(559\) −2.27073 −0.0960418
\(560\) −2.17373 0.497236i −0.0918570 0.0210120i
\(561\) 4.08561i 0.172494i
\(562\) −8.95726 8.95726i −0.377839 0.377839i
\(563\) −1.06530 1.06530i −0.0448971 0.0448971i 0.684302 0.729199i \(-0.260107\pi\)
−0.729199 + 0.684302i \(0.760107\pi\)
\(564\) 5.84230 0.246005
\(565\) −1.42837 0.326736i −0.0600920 0.0137459i
\(566\) 15.8543i 0.666406i
\(567\) −0.705149 0.705149i −0.0296135 0.0296135i
\(568\) 6.16531 6.16531i 0.258691 0.258691i
\(569\) −17.2827 −0.724528 −0.362264 0.932076i \(-0.617996\pi\)
−0.362264 + 0.932076i \(0.617996\pi\)
\(570\) −3.27997 9.17833i −0.137383 0.384438i
\(571\) 10.3420 0.432798 0.216399 0.976305i \(-0.430569\pi\)
0.216399 + 0.976305i \(0.430569\pi\)
\(572\) −0.985322 + 0.985322i −0.0411984 + 0.0411984i
\(573\) −5.19563 5.19563i −0.217051 0.217051i
\(574\) 0.530438i 0.0221400i
\(575\) 2.52154 + 7.22835i 0.105155 + 0.301443i
\(576\) −1.00000 −0.0416667
\(577\) −25.5328 25.5328i −1.06294 1.06294i −0.997881 0.0650631i \(-0.979275\pi\)
−0.0650631 0.997881i \(-0.520725\pi\)
\(578\) −5.33850 5.33850i −0.222052 0.222052i
\(579\) 13.1865i 0.548013i
\(580\) 7.07414 + 11.2704i 0.293738 + 0.467978i
\(581\) −13.4017 −0.555998
\(582\) 1.11691 1.11691i 0.0462974 0.0462974i
\(583\) −7.29049 7.29049i −0.301941 0.301941i
\(584\) 8.25374 0.341542
\(585\) 0.522786 2.28543i 0.0216145 0.0944908i
\(586\) 0.182154 0.00752471
\(587\) −25.3120 25.3120i −1.04474 1.04474i −0.998951 0.0457889i \(-0.985420\pi\)
−0.0457889 0.998951i \(-0.514580\pi\)
\(588\) −4.24655 4.24655i −0.175125 0.175125i
\(589\) 25.3293 + 5.59245i 1.04368 + 0.230433i
\(590\) −1.76482 + 7.71516i −0.0726566 + 0.317628i
\(591\) 7.67935i 0.315886i
\(592\) 1.33551 1.33551i 0.0548890 0.0548890i
\(593\) −9.66808 + 9.66808i −0.397020 + 0.397020i −0.877181 0.480160i \(-0.840578\pi\)
0.480160 + 0.877181i \(0.340578\pi\)
\(594\) 1.32903i 0.0545308i
\(595\) 3.64426 + 5.80597i 0.149400 + 0.238022i
\(596\) 14.1380 0.579117
\(597\) −16.6161 + 16.6161i −0.680051 + 0.680051i
\(598\) 1.13514 1.13514i 0.0464192 0.0464192i
\(599\) −28.5298 −1.16569 −0.582847 0.812582i \(-0.698061\pi\)
−0.582847 + 0.812582i \(0.698061\pi\)
\(600\) −4.50276 2.17373i −0.183825 0.0887423i
\(601\) 24.3760i 0.994317i −0.867660 0.497159i \(-0.834377\pi\)
0.867660 0.497159i \(-0.165623\pi\)
\(602\) 1.52718 1.52718i 0.0622431 0.0622431i
\(603\) −1.99446 1.99446i −0.0812208 0.0812208i
\(604\) −9.45030 −0.384527
\(605\) −17.4877 + 10.9766i −0.710975 + 0.446261i
\(606\) −15.7109 −0.638211
\(607\) −27.0140 + 27.0140i −1.09647 + 1.09647i −0.101646 + 0.994821i \(0.532411\pi\)
−0.994821 + 0.101646i \(0.967589\pi\)
\(608\) 2.34520 + 3.67424i 0.0951106 + 0.149010i
\(609\) 5.93441i 0.240475i
\(610\) 1.70043 7.43365i 0.0688484 0.300980i
\(611\) 6.12550i 0.247811i
\(612\) 2.17373 + 2.17373i 0.0878679 + 0.0878679i
\(613\) 17.2695 17.2695i 0.697508 0.697508i −0.266364 0.963872i \(-0.585822\pi\)
0.963872 + 0.266364i \(0.0858224\pi\)
\(614\) 22.3361i 0.901413i
\(615\) 0.265219 1.15944i 0.0106947 0.0467531i
\(616\) 1.32535i 0.0534000i
\(617\) 34.2253 + 34.2253i 1.37786 + 1.37786i 0.848232 + 0.529625i \(0.177667\pi\)
0.529625 + 0.848232i \(0.322333\pi\)
\(618\) 10.7950 + 10.7950i 0.434239 + 0.434239i
\(619\) 34.9000i 1.40275i 0.712792 + 0.701375i \(0.247430\pi\)
−0.712792 + 0.701375i \(0.752570\pi\)
\(620\) 11.2704 7.07414i 0.452630 0.284104i
\(621\) 1.53111i 0.0614412i
\(622\) 10.3891 10.3891i 0.416566 0.416566i
\(623\) −11.8376 11.8376i −0.474263 0.474263i
\(624\) 1.04847i 0.0419726i
\(625\) −15.5498 19.5756i −0.621991 0.783024i
\(626\) 2.50414i 0.100086i
\(627\) 4.88318 3.11685i 0.195015 0.124475i
\(628\) 13.7650 13.7650i 0.549284 0.549284i
\(629\) −5.80607 −0.231503
\(630\) 1.18546 + 1.88866i 0.0472299 + 0.0752460i
\(631\) 33.8489 1.34750 0.673752 0.738957i \(-0.264682\pi\)
0.673752 + 0.738957i \(0.264682\pi\)
\(632\) −6.58542 6.58542i −0.261954 0.261954i
\(633\) 5.77344 5.77344i 0.229474 0.229474i
\(634\) 6.55324i 0.260262i
\(635\) 5.46842 23.9060i 0.217008 0.948679i
\(636\) −7.75776 −0.307615
\(637\) −4.45240 + 4.45240i −0.176410 + 0.176410i
\(638\) −5.59245 + 5.59245i −0.221407 + 0.221407i
\(639\) −8.71907 −0.344921
\(640\) 2.17977 + 0.498616i 0.0861628 + 0.0197095i
\(641\) 38.3389i 1.51429i 0.653245 + 0.757147i \(0.273407\pi\)
−0.653245 + 0.757147i \(0.726593\pi\)
\(642\) −2.65129 + 2.65129i −0.104638 + 0.104638i
\(643\) −21.8777 + 21.8777i −0.862773 + 0.862773i −0.991659 0.128886i \(-0.958860\pi\)
0.128886 + 0.991659i \(0.458860\pi\)
\(644\) 1.52687i 0.0601670i
\(645\) 4.10172 2.57454i 0.161505 0.101373i
\(646\) 2.88896 13.0847i 0.113665 0.514809i
\(647\) −11.5954 11.5954i −0.455863 0.455863i 0.441432 0.897295i \(-0.354471\pi\)
−0.897295 + 0.441432i \(0.854471\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −4.70403 −0.184649
\(650\) −2.27910 + 4.72103i −0.0893937 + 0.185174i
\(651\) −5.93441 −0.232588
\(652\) −0.792086 0.792086i −0.0310205 0.0310205i
\(653\) −11.6996 + 11.6996i −0.457842 + 0.457842i −0.897946 0.440105i \(-0.854941\pi\)
0.440105 + 0.897946i \(0.354941\pi\)
\(654\) −5.83596 −0.228204
\(655\) −25.0982 + 15.7535i −0.980668 + 0.615539i
\(656\) 0.531910i 0.0207676i
\(657\) −5.83628 5.83628i −0.227695 0.227695i
\(658\) 4.11969 + 4.11969i 0.160602 + 0.160602i
\(659\) −44.6662 −1.73995 −0.869974 0.493097i \(-0.835865\pi\)
−0.869974 + 0.493097i \(0.835865\pi\)
\(660\) 0.662676 2.89698i 0.0257946 0.112765i
\(661\) 46.5099i 1.80902i 0.426447 + 0.904512i \(0.359765\pi\)
−0.426447 + 0.904512i \(0.640235\pi\)
\(662\) −7.42992 7.42992i −0.288772 0.288772i
\(663\) 2.27910 2.27910i 0.0885130 0.0885130i
\(664\) 13.4389 0.521532
\(665\) 4.15923 8.78496i 0.161288 0.340666i
\(666\) −1.88869 −0.0731853
\(667\) 6.44276 6.44276i 0.249465 0.249465i
\(668\) −11.1325 11.1325i −0.430728 0.430728i
\(669\) 0.300580i 0.0116211i
\(670\) 3.35299 + 5.34194i 0.129537 + 0.206377i
\(671\) 4.53240 0.174971
\(672\) −0.705149 0.705149i −0.0272017 0.0272017i
\(673\) 17.8598 + 17.8598i 0.688446 + 0.688446i 0.961888 0.273443i \(-0.0881624\pi\)
−0.273443 + 0.961888i \(0.588162\pi\)
\(674\) 26.6051i 1.02479i
\(675\) 1.64687 + 4.72100i 0.0633882 + 0.181711i
\(676\) −11.9007 −0.457719
\(677\) 20.6616 20.6616i 0.794092 0.794092i −0.188065 0.982157i \(-0.560222\pi\)
0.982157 + 0.188065i \(0.0602215\pi\)
\(678\) −0.463357 0.463357i −0.0177951 0.0177951i
\(679\) 1.57518 0.0604497
\(680\) −3.65437 5.82209i −0.140139 0.223267i
\(681\) 23.9341 0.917158
\(682\) 5.59245 + 5.59245i 0.214146 + 0.214146i
\(683\) −23.8243 23.8243i −0.911610 0.911610i 0.0847893 0.996399i \(-0.472978\pi\)
−0.996399 + 0.0847893i \(0.972978\pi\)
\(684\) 0.939768 4.25639i 0.0359329 0.162747i
\(685\) 13.6263 + 3.11698i 0.520634 + 0.119094i
\(686\) 12.9695i 0.495179i
\(687\) 5.37064 5.37064i 0.204903 0.204903i
\(688\) −1.53142 + 1.53142i −0.0583847 + 0.0583847i
\(689\) 8.13381i 0.309874i
\(690\) −0.763434 + 3.33745i −0.0290634 + 0.127055i
\(691\) −4.34746 −0.165385 −0.0826927 0.996575i \(-0.526352\pi\)
−0.0826927 + 0.996575i \(0.526352\pi\)
\(692\) 5.42532 5.42532i 0.206240 0.206240i
\(693\) −0.937166 + 0.937166i −0.0356000 + 0.0356000i
\(694\) 24.0098 0.911399
\(695\) −3.19376 5.08825i −0.121146 0.193008i
\(696\) 5.95089i 0.225568i
\(697\) 1.15623 1.15623i 0.0437953 0.0437953i
\(698\) −11.5333 11.5333i −0.436543 0.436543i
\(699\) 1.15416 0.0436544
\(700\) −1.64232 4.70793i −0.0620737 0.177943i
\(701\) −1.61462 −0.0609832 −0.0304916 0.999535i \(-0.509707\pi\)
−0.0304916 + 0.999535i \(0.509707\pi\)
\(702\) 0.741383 0.741383i 0.0279817 0.0279817i
\(703\) 4.42937 + 6.93950i 0.167057 + 0.261728i
\(704\) 1.32903i 0.0500898i
\(705\) 6.94505 + 11.0647i 0.261566 + 0.416722i
\(706\) 11.2273i 0.422545i
\(707\) −11.0785 11.0785i −0.416650 0.416650i
\(708\) −2.50276 + 2.50276i −0.0940596 + 0.0940596i
\(709\) 45.1909i 1.69718i −0.529052 0.848589i \(-0.677452\pi\)
0.529052 0.848589i \(-0.322548\pi\)
\(710\) 19.0055 + 4.34746i 0.713265 + 0.163157i
\(711\) 9.31319i 0.349272i
\(712\) 11.8705 + 11.8705i 0.444864 + 0.444864i
\(713\) −6.44276 6.44276i −0.241283 0.241283i
\(714\) 3.06561i 0.114728i
\(715\) −3.03741 0.694799i −0.113593 0.0259840i
\(716\) 0.963050i 0.0359909i
\(717\) 2.97765 2.97765i 0.111202 0.111202i
\(718\) −18.5477 18.5477i −0.692193 0.692193i
\(719\) 8.72035i 0.325214i −0.986691 0.162607i \(-0.948010\pi\)
0.986691 0.162607i \(-0.0519903\pi\)
\(720\) −1.18875 1.89390i −0.0443022 0.0705816i
\(721\) 15.2242i 0.566979i
\(722\) −17.8429 + 6.52917i −0.664045 + 0.242991i
\(723\) 17.5996 17.5996i 0.654535 0.654535i
\(724\) −20.4214 −0.758956
\(725\) −12.9356 + 26.7955i −0.480418 + 0.995158i
\(726\) −9.23367 −0.342694
\(727\) 16.9674 + 16.9674i 0.629286 + 0.629286i 0.947889 0.318602i \(-0.103213\pi\)
−0.318602 + 0.947889i \(0.603213\pi\)
\(728\) −0.739331 + 0.739331i −0.0274014 + 0.0274014i
\(729\) 1.00000i 0.0370370i
\(730\) 9.81166 + 15.6318i 0.363146 + 0.578558i
\(731\) 6.65778 0.246247
\(732\) 2.41145 2.41145i 0.0891296 0.0891296i
\(733\) 25.1664 25.1664i 0.929541 0.929541i −0.0681355 0.997676i \(-0.521705\pi\)
0.997676 + 0.0681355i \(0.0217050\pi\)
\(734\) −2.29484 −0.0847040
\(735\) 2.99445 13.0907i 0.110452 0.482856i
\(736\) 1.53111i 0.0564373i
\(737\) −2.65071 + 2.65071i −0.0976400 + 0.0976400i
\(738\) 0.376117 0.376117i 0.0138451 0.0138451i
\(739\) 14.7543i 0.542747i 0.962474 + 0.271373i \(0.0874778\pi\)
−0.962474 + 0.271373i \(0.912522\pi\)
\(740\) 4.11691 + 0.941732i 0.151341 + 0.0346188i
\(741\) −4.46271 0.985322i −0.163942 0.0361967i
\(742\) −5.47038 5.47038i −0.200824 0.200824i
\(743\) −8.61240 8.61240i −0.315958 0.315958i 0.531254 0.847213i \(-0.321721\pi\)
−0.847213 + 0.531254i \(0.821721\pi\)
\(744\) 5.95089 0.218170
\(745\) 16.8066 + 26.7761i 0.615748 + 0.981000i
\(746\) 12.7407 0.466468
\(747\) −9.50276 9.50276i −0.347688 0.347688i
\(748\) 2.88896 2.88896i 0.105631 0.105631i
\(749\) −3.73910 −0.136624
\(750\) −1.23584 11.1118i −0.0451264 0.405747i
\(751\) 44.6100i 1.62784i 0.580974 + 0.813922i \(0.302672\pi\)
−0.580974 + 0.813922i \(0.697328\pi\)
\(752\) −4.13113 4.13113i −0.150647 0.150647i
\(753\) −0.673765 0.673765i −0.0245534 0.0245534i
\(754\) 6.23935 0.227224
\(755\) −11.2341 17.8979i −0.408850 0.651373i
\(756\) 0.997232i 0.0362690i
\(757\) 2.38067 + 2.38067i 0.0865268 + 0.0865268i 0.749045 0.662519i \(-0.230512\pi\)
−0.662519 + 0.749045i \(0.730512\pi\)
\(758\) 3.17940 3.17940i 0.115481 0.115481i
\(759\) −2.03489 −0.0738618
\(760\) −4.17078 + 8.80935i −0.151290 + 0.319549i
\(761\) 4.25052 0.154081 0.0770406 0.997028i \(-0.475453\pi\)
0.0770406 + 0.997028i \(0.475453\pi\)
\(762\) 7.75499 7.75499i 0.280934 0.280934i
\(763\) −4.11522 4.11522i −0.148981 0.148981i
\(764\) 7.34773i 0.265832i
\(765\) −1.53281 + 6.70087i −0.0554187 + 0.242270i
\(766\) 31.8289 1.15003
\(767\) 2.62408 + 2.62408i 0.0947502 + 0.0947502i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 3.40202i 0.122680i 0.998117 + 0.0613400i \(0.0195374\pi\)
−0.998117 + 0.0613400i \(0.980463\pi\)
\(770\) 2.51009 1.57552i 0.0904573 0.0567777i
\(771\) 17.5784 0.633070
\(772\) 9.32428 9.32428i 0.335588 0.335588i
\(773\) 21.7310 + 21.7310i 0.781611 + 0.781611i 0.980103 0.198491i \(-0.0636042\pi\)
−0.198491 + 0.980103i \(0.563604\pi\)
\(774\) 2.16575 0.0778463
\(775\) 26.7955 + 12.9356i 0.962521 + 0.464662i
\(776\) −1.57955 −0.0567025
\(777\) −1.33181 1.33181i −0.0477784 0.0477784i
\(778\) 18.5030 + 18.5030i 0.663364