Properties

Label 280.2.h.b.251.6
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
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 251.6
Root \(-0.470943 - 1.33350i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +O(q^{10})\) \(q+(-0.470943 + 1.33350i) q^{2} +0.528177i q^{3} +(-1.55642 - 1.25600i) q^{4} +1.00000 q^{5} +(-0.704322 - 0.248741i) q^{6} +(2.17448 - 1.50719i) q^{7} +(2.40786 - 1.48398i) q^{8} +2.72103 q^{9} +(-0.470943 + 1.33350i) q^{10} +3.04781 q^{11} +(0.663391 - 0.822067i) q^{12} -4.75069 q^{13} +(0.985772 + 3.60947i) q^{14} +0.528177i q^{15} +(0.844916 + 3.90975i) q^{16} +6.78894i q^{17} +(-1.28145 + 3.62848i) q^{18} -0.584285i q^{19} +(-1.55642 - 1.25600i) q^{20} +(0.796062 + 1.14851i) q^{21} +(-1.43535 + 4.06425i) q^{22} -5.80481i q^{23} +(0.783804 + 1.27178i) q^{24} +1.00000 q^{25} +(2.23730 - 6.33502i) q^{26} +3.02172i q^{27} +(-5.27745 - 0.385331i) q^{28} -0.185682i q^{29} +(-0.704322 - 0.248741i) q^{30} +3.12589 q^{31} +(-5.61154 - 0.714577i) q^{32} +1.60978i q^{33} +(-9.05303 - 3.19721i) q^{34} +(2.17448 - 1.50719i) q^{35} +(-4.23508 - 3.41762i) q^{36} +7.04672i q^{37} +(0.779143 + 0.275165i) q^{38} -2.50920i q^{39} +(2.40786 - 1.48398i) q^{40} -3.83583i q^{41} +(-1.90644 + 0.520662i) q^{42} -1.43554 q^{43} +(-4.74369 - 3.82806i) q^{44} +2.72103 q^{45} +(7.74069 + 2.73374i) q^{46} +2.95871 q^{47} +(-2.06504 + 0.446265i) q^{48} +(2.45676 - 6.55472i) q^{49} +(-0.470943 + 1.33350i) q^{50} -3.58576 q^{51} +(7.39409 + 5.96688i) q^{52} -0.535513i q^{53} +(-4.02945 - 1.42306i) q^{54} +3.04781 q^{55} +(2.99922 - 6.85600i) q^{56} +0.308606 q^{57} +(0.247606 + 0.0874456i) q^{58} -1.52116i q^{59} +(0.663391 - 0.822067i) q^{60} -13.2354 q^{61} +(-1.47212 + 4.16837i) q^{62} +(5.91683 - 4.10111i) q^{63} +(3.59560 - 7.14644i) q^{64} -4.75069 q^{65} +(-2.14664 - 0.758117i) q^{66} -9.13242 q^{67} +(8.52693 - 10.5665i) q^{68} +3.06597 q^{69} +(0.985772 + 3.60947i) q^{70} -9.68233i q^{71} +(6.55186 - 4.03795i) q^{72} +12.4295i q^{73} +(-9.39678 - 3.31861i) q^{74} +0.528177i q^{75} +(-0.733864 + 0.909396i) q^{76} +(6.62742 - 4.59363i) q^{77} +(3.34601 + 1.18169i) q^{78} -2.81383i q^{79} +(0.844916 + 3.90975i) q^{80} +6.56709 q^{81} +(5.11507 + 1.80646i) q^{82} -13.4535i q^{83} +(0.203523 - 2.78743i) q^{84} +6.78894i q^{85} +(0.676056 - 1.91428i) q^{86} +0.0980728 q^{87} +(7.33871 - 4.52289i) q^{88} -3.10041i q^{89} +(-1.28145 + 3.62848i) q^{90} +(-10.3303 + 7.16019i) q^{91} +(-7.29085 + 9.03475i) q^{92} +1.65102i q^{93} +(-1.39338 + 3.94543i) q^{94} -0.584285i q^{95} +(0.377423 - 2.96389i) q^{96} -13.5027i q^{97} +(7.58370 + 6.36298i) q^{98} +8.29319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.470943 + 1.33350i −0.333007 + 0.942924i
\(3\) 0.528177i 0.304943i 0.988308 + 0.152472i \(0.0487232\pi\)
−0.988308 + 0.152472i \(0.951277\pi\)
\(4\) −1.55642 1.25600i −0.778212 0.628001i
\(5\) 1.00000 0.447214
\(6\) −0.704322 0.248741i −0.287538 0.101548i
\(7\) 2.17448 1.50719i 0.821878 0.569664i
\(8\) 2.40786 1.48398i 0.851308 0.524666i
\(9\) 2.72103 0.907010
\(10\) −0.470943 + 1.33350i −0.148925 + 0.421689i
\(11\) 3.04781 0.918950 0.459475 0.888191i \(-0.348038\pi\)
0.459475 + 0.888191i \(0.348038\pi\)
\(12\) 0.663391 0.822067i 0.191505 0.237310i
\(13\) −4.75069 −1.31760 −0.658802 0.752317i \(-0.728936\pi\)
−0.658802 + 0.752317i \(0.728936\pi\)
\(14\) 0.985772 + 3.60947i 0.263459 + 0.964671i
\(15\) 0.528177i 0.136375i
\(16\) 0.844916 + 3.90975i 0.211229 + 0.977437i
\(17\) 6.78894i 1.64656i 0.567635 + 0.823280i \(0.307858\pi\)
−0.567635 + 0.823280i \(0.692142\pi\)
\(18\) −1.28145 + 3.62848i −0.302041 + 0.855242i
\(19\) 0.584285i 0.134044i −0.997751 0.0670221i \(-0.978650\pi\)
0.997751 0.0670221i \(-0.0213498\pi\)
\(20\) −1.55642 1.25600i −0.348027 0.280851i
\(21\) 0.796062 + 1.14851i 0.173715 + 0.250626i
\(22\) −1.43535 + 4.06425i −0.306017 + 0.866500i
\(23\) 5.80481i 1.21039i −0.796079 0.605193i \(-0.793096\pi\)
0.796079 0.605193i \(-0.206904\pi\)
\(24\) 0.783804 + 1.27178i 0.159993 + 0.259600i
\(25\) 1.00000 0.200000
\(26\) 2.23730 6.33502i 0.438772 1.24240i
\(27\) 3.02172i 0.581529i
\(28\) −5.27745 0.385331i −0.997345 0.0728206i
\(29\) 0.185682i 0.0344802i −0.999851 0.0172401i \(-0.994512\pi\)
0.999851 0.0172401i \(-0.00548797\pi\)
\(30\) −0.704322 0.248741i −0.128591 0.0454138i
\(31\) 3.12589 0.561427 0.280714 0.959792i \(-0.409429\pi\)
0.280714 + 0.959792i \(0.409429\pi\)
\(32\) −5.61154 0.714577i −0.991989 0.126321i
\(33\) 1.60978i 0.280227i
\(34\) −9.05303 3.19721i −1.55258 0.548317i
\(35\) 2.17448 1.50719i 0.367555 0.254761i
\(36\) −4.23508 3.41762i −0.705846 0.569603i
\(37\) 7.04672i 1.15847i 0.815159 + 0.579237i \(0.196649\pi\)
−0.815159 + 0.579237i \(0.803351\pi\)
\(38\) 0.779143 + 0.275165i 0.126394 + 0.0446377i
\(39\) 2.50920i 0.401794i
\(40\) 2.40786 1.48398i 0.380716 0.234638i
\(41\) 3.83583i 0.599056i −0.954087 0.299528i \(-0.903171\pi\)
0.954087 0.299528i \(-0.0968292\pi\)
\(42\) −1.90644 + 0.520662i −0.294170 + 0.0803399i
\(43\) −1.43554 −0.218917 −0.109459 0.993991i \(-0.534912\pi\)
−0.109459 + 0.993991i \(0.534912\pi\)
\(44\) −4.74369 3.82806i −0.715138 0.577102i
\(45\) 2.72103 0.405627
\(46\) 7.74069 + 2.73374i 1.14130 + 0.403067i
\(47\) 2.95871 0.431572 0.215786 0.976441i \(-0.430769\pi\)
0.215786 + 0.976441i \(0.430769\pi\)
\(48\) −2.06504 + 0.446265i −0.298062 + 0.0644128i
\(49\) 2.45676 6.55472i 0.350966 0.936388i
\(50\) −0.470943 + 1.33350i −0.0666014 + 0.188585i
\(51\) −3.58576 −0.502107
\(52\) 7.39409 + 5.96688i 1.02538 + 0.827457i
\(53\) 0.535513i 0.0735584i −0.999323 0.0367792i \(-0.988290\pi\)
0.999323 0.0367792i \(-0.0117098\pi\)
\(54\) −4.02945 1.42306i −0.548338 0.193653i
\(55\) 3.04781 0.410967
\(56\) 2.99922 6.85600i 0.400787 0.916171i
\(57\) 0.308606 0.0408759
\(58\) 0.247606 + 0.0874456i 0.0325123 + 0.0114822i
\(59\) 1.52116i 0.198038i −0.995086 0.0990188i \(-0.968430\pi\)
0.995086 0.0990188i \(-0.0315704\pi\)
\(60\) 0.663391 0.822067i 0.0856435 0.106128i
\(61\) −13.2354 −1.69461 −0.847307 0.531103i \(-0.821778\pi\)
−0.847307 + 0.531103i \(0.821778\pi\)
\(62\) −1.47212 + 4.16837i −0.186959 + 0.529383i
\(63\) 5.91683 4.10111i 0.745451 0.516691i
\(64\) 3.59560 7.14644i 0.449450 0.893305i
\(65\) −4.75069 −0.589250
\(66\) −2.14664 0.758117i −0.264233 0.0933177i
\(67\) −9.13242 −1.11570 −0.557851 0.829941i \(-0.688374\pi\)
−0.557851 + 0.829941i \(0.688374\pi\)
\(68\) 8.52693 10.5665i 1.03404 1.28137i
\(69\) 3.06597 0.369099
\(70\) 0.985772 + 3.60947i 0.117822 + 0.431414i
\(71\) 9.68233i 1.14908i −0.818476 0.574540i \(-0.805181\pi\)
0.818476 0.574540i \(-0.194819\pi\)
\(72\) 6.55186 4.03795i 0.772145 0.475878i
\(73\) 12.4295i 1.45476i 0.686235 + 0.727380i \(0.259262\pi\)
−0.686235 + 0.727380i \(0.740738\pi\)
\(74\) −9.39678 3.31861i −1.09235 0.385780i
\(75\) 0.528177i 0.0609886i
\(76\) −0.733864 + 0.909396i −0.0841800 + 0.104315i
\(77\) 6.62742 4.59363i 0.755264 0.523493i
\(78\) 3.34601 + 1.18169i 0.378861 + 0.133800i
\(79\) 2.81383i 0.316580i −0.987393 0.158290i \(-0.949402\pi\)
0.987393 0.158290i \(-0.0505982\pi\)
\(80\) 0.844916 + 3.90975i 0.0944645 + 0.437123i
\(81\) 6.56709 0.729676
\(82\) 5.11507 + 1.80646i 0.564865 + 0.199490i
\(83\) 13.4535i 1.47671i −0.674412 0.738355i \(-0.735603\pi\)
0.674412 0.738355i \(-0.264397\pi\)
\(84\) 0.203523 2.78743i 0.0222061 0.304133i
\(85\) 6.78894i 0.736364i
\(86\) 0.676056 1.91428i 0.0729010 0.206422i
\(87\) 0.0980728 0.0105145
\(88\) 7.33871 4.52289i 0.782309 0.482142i
\(89\) 3.10041i 0.328642i −0.986407 0.164321i \(-0.947457\pi\)
0.986407 0.164321i \(-0.0525434\pi\)
\(90\) −1.28145 + 3.62848i −0.135077 + 0.382476i
\(91\) −10.3303 + 7.16019i −1.08291 + 0.750591i
\(92\) −7.29085 + 9.03475i −0.760124 + 0.941938i
\(93\) 1.65102i 0.171203i
\(94\) −1.39338 + 3.94543i −0.143717 + 0.406940i
\(95\) 0.584285i 0.0599464i
\(96\) 0.377423 2.96389i 0.0385206 0.302500i
\(97\) 13.5027i 1.37099i −0.728077 0.685495i \(-0.759586\pi\)
0.728077 0.685495i \(-0.240414\pi\)
\(98\) 7.58370 + 6.36298i 0.766069 + 0.642758i
\(99\) 8.29319 0.833497
\(100\) −1.55642 1.25600i −0.155642 0.125600i
\(101\) −1.29842 −0.129198 −0.0645988 0.997911i \(-0.520577\pi\)
−0.0645988 + 0.997911i \(0.520577\pi\)
\(102\) 1.68869 4.78160i 0.167205 0.473449i
\(103\) −19.0846 −1.88046 −0.940232 0.340535i \(-0.889392\pi\)
−0.940232 + 0.340535i \(0.889392\pi\)
\(104\) −11.4390 + 7.04993i −1.12169 + 0.691302i
\(105\) 0.796062 + 1.14851i 0.0776877 + 0.112083i
\(106\) 0.714105 + 0.252196i 0.0693600 + 0.0244955i
\(107\) −3.81102 −0.368425 −0.184213 0.982886i \(-0.558973\pi\)
−0.184213 + 0.982886i \(0.558973\pi\)
\(108\) 3.79528 4.70307i 0.365201 0.452553i
\(109\) 15.1487i 1.45098i 0.688233 + 0.725490i \(0.258387\pi\)
−0.688233 + 0.725490i \(0.741613\pi\)
\(110\) −1.43535 + 4.06425i −0.136855 + 0.387511i
\(111\) −3.72192 −0.353269
\(112\) 7.72998 + 7.22823i 0.730415 + 0.683004i
\(113\) −16.6411 −1.56546 −0.782732 0.622359i \(-0.786175\pi\)
−0.782732 + 0.622359i \(0.786175\pi\)
\(114\) −0.145336 + 0.411525i −0.0136120 + 0.0385429i
\(115\) 5.80481i 0.541301i
\(116\) −0.233217 + 0.289000i −0.0216536 + 0.0268330i
\(117\) −12.9268 −1.19508
\(118\) 2.02846 + 0.716378i 0.186734 + 0.0659479i
\(119\) 10.2322 + 14.7624i 0.937986 + 1.35327i
\(120\) 0.783804 + 1.27178i 0.0715512 + 0.116097i
\(121\) −1.71084 −0.155531
\(122\) 6.23311 17.6493i 0.564319 1.59789i
\(123\) 2.02600 0.182678
\(124\) −4.86522 3.92613i −0.436909 0.352577i
\(125\) 1.00000 0.0894427
\(126\) 2.68232 + 9.82147i 0.238960 + 0.874966i
\(127\) 15.9073i 1.41154i 0.708440 + 0.705771i \(0.249399\pi\)
−0.708440 + 0.705771i \(0.750601\pi\)
\(128\) 7.83643 + 8.16029i 0.692649 + 0.721275i
\(129\) 0.758217i 0.0667573i
\(130\) 2.23730 6.33502i 0.196225 0.555618i
\(131\) 20.2439i 1.76872i 0.466806 + 0.884360i \(0.345405\pi\)
−0.466806 + 0.884360i \(0.654595\pi\)
\(132\) 2.02189 2.50551i 0.175983 0.218076i
\(133\) −0.880629 1.27052i −0.0763602 0.110168i
\(134\) 4.30085 12.1780i 0.371537 1.05202i
\(135\) 3.02172i 0.260068i
\(136\) 10.0747 + 16.3468i 0.863895 + 1.40173i
\(137\) 6.38933 0.545877 0.272939 0.962031i \(-0.412004\pi\)
0.272939 + 0.962031i \(0.412004\pi\)
\(138\) −1.44390 + 4.08845i −0.122913 + 0.348032i
\(139\) 21.8128i 1.85014i −0.379801 0.925068i \(-0.624008\pi\)
0.379801 0.925068i \(-0.375992\pi\)
\(140\) −5.27745 0.385331i −0.446026 0.0325664i
\(141\) 1.56272i 0.131605i
\(142\) 12.9113 + 4.55983i 1.08350 + 0.382652i
\(143\) −14.4792 −1.21081
\(144\) 2.29904 + 10.6385i 0.191587 + 0.886545i
\(145\) 0.185682i 0.0154200i
\(146\) −16.5747 5.85358i −1.37173 0.484446i
\(147\) 3.46205 + 1.29760i 0.285545 + 0.107025i
\(148\) 8.85070 10.9677i 0.727523 0.901539i
\(149\) 11.5156i 0.943396i −0.881760 0.471698i \(-0.843641\pi\)
0.881760 0.471698i \(-0.156359\pi\)
\(150\) −0.704322 0.248741i −0.0575076 0.0203096i
\(151\) 7.70970i 0.627407i 0.949521 + 0.313703i \(0.101570\pi\)
−0.949521 + 0.313703i \(0.898430\pi\)
\(152\) −0.867068 1.40688i −0.0703285 0.114113i
\(153\) 18.4729i 1.49345i
\(154\) 3.00445 + 11.0010i 0.242105 + 0.886484i
\(155\) 3.12589 0.251078
\(156\) −3.15157 + 3.90539i −0.252327 + 0.312681i
\(157\) 4.42111 0.352843 0.176422 0.984315i \(-0.443548\pi\)
0.176422 + 0.984315i \(0.443548\pi\)
\(158\) 3.75223 + 1.32515i 0.298511 + 0.105424i
\(159\) 0.282846 0.0224311
\(160\) −5.61154 0.714577i −0.443631 0.0564923i
\(161\) −8.74895 12.6225i −0.689514 0.994790i
\(162\) −3.09273 + 8.75719i −0.242988 + 0.688030i
\(163\) 17.5475 1.37443 0.687213 0.726456i \(-0.258834\pi\)
0.687213 + 0.726456i \(0.258834\pi\)
\(164\) −4.81781 + 5.97018i −0.376208 + 0.466193i
\(165\) 1.60978i 0.125321i
\(166\) 17.9402 + 6.33582i 1.39243 + 0.491755i
\(167\) −1.57597 −0.121952 −0.0609760 0.998139i \(-0.519421\pi\)
−0.0609760 + 0.998139i \(0.519421\pi\)
\(168\) 3.62118 + 1.58412i 0.279380 + 0.122217i
\(169\) 9.56903 0.736079
\(170\) −9.05303 3.19721i −0.694336 0.245215i
\(171\) 1.58986i 0.121579i
\(172\) 2.23430 + 1.80304i 0.170364 + 0.137480i
\(173\) 0.208914 0.0158835 0.00794173 0.999968i \(-0.497472\pi\)
0.00794173 + 0.999968i \(0.497472\pi\)
\(174\) −0.0461867 + 0.130780i −0.00350141 + 0.00991439i
\(175\) 2.17448 1.50719i 0.164376 0.113933i
\(176\) 2.57514 + 11.9162i 0.194109 + 0.898215i
\(177\) 0.803439 0.0603902
\(178\) 4.13438 + 1.46012i 0.309885 + 0.109440i
\(179\) −5.84685 −0.437014 −0.218507 0.975835i \(-0.570119\pi\)
−0.218507 + 0.975835i \(0.570119\pi\)
\(180\) −4.23508 3.41762i −0.315664 0.254734i
\(181\) 8.66680 0.644198 0.322099 0.946706i \(-0.395612\pi\)
0.322099 + 0.946706i \(0.395612\pi\)
\(182\) −4.68310 17.1475i −0.347134 1.27105i
\(183\) 6.99061i 0.516761i
\(184\) −8.61422 13.9772i −0.635049 1.03041i
\(185\) 7.04672i 0.518085i
\(186\) −2.20163 0.777539i −0.161432 0.0570119i
\(187\) 20.6914i 1.51311i
\(188\) −4.60501 3.71615i −0.335855 0.271028i
\(189\) 4.55430 + 6.57067i 0.331276 + 0.477946i
\(190\) 0.779143 + 0.275165i 0.0565249 + 0.0199626i
\(191\) 12.9741i 0.938770i 0.882993 + 0.469385i \(0.155524\pi\)
−0.882993 + 0.469385i \(0.844476\pi\)
\(192\) 3.77459 + 1.89911i 0.272407 + 0.137057i
\(193\) −24.5869 −1.76980 −0.884901 0.465780i \(-0.845774\pi\)
−0.884901 + 0.465780i \(0.845774\pi\)
\(194\) 18.0058 + 6.35900i 1.29274 + 0.456550i
\(195\) 2.50920i 0.179688i
\(196\) −12.0565 + 7.11623i −0.861179 + 0.508302i
\(197\) 7.21194i 0.513829i −0.966434 0.256915i \(-0.917294\pi\)
0.966434 0.256915i \(-0.0827059\pi\)
\(198\) −3.90562 + 11.0589i −0.277560 + 0.785924i
\(199\) 6.32808 0.448585 0.224293 0.974522i \(-0.427993\pi\)
0.224293 + 0.974522i \(0.427993\pi\)
\(200\) 2.40786 1.48398i 0.170262 0.104933i
\(201\) 4.82353i 0.340226i
\(202\) 0.611482 1.73144i 0.0430237 0.121823i
\(203\) −0.279858 0.403762i −0.0196422 0.0283385i
\(204\) 5.58097 + 4.50373i 0.390746 + 0.315324i
\(205\) 3.83583i 0.267906i
\(206\) 8.98777 25.4493i 0.626208 1.77313i
\(207\) 15.7951i 1.09783i
\(208\) −4.01393 18.5740i −0.278316 1.28787i
\(209\) 1.78079i 0.123180i
\(210\) −1.90644 + 0.520662i −0.131557 + 0.0359291i
\(211\) −10.2211 −0.703650 −0.351825 0.936066i \(-0.614439\pi\)
−0.351825 + 0.936066i \(0.614439\pi\)
\(212\) −0.672606 + 0.833486i −0.0461948 + 0.0572441i
\(213\) 5.11398 0.350404
\(214\) 1.79477 5.08198i 0.122688 0.347397i
\(215\) −1.43554 −0.0979028
\(216\) 4.48417 + 7.27587i 0.305109 + 0.495061i
\(217\) 6.79721 4.71131i 0.461424 0.319825i
\(218\) −20.2007 7.13417i −1.36816 0.483187i
\(219\) −6.56496 −0.443619
\(220\) −4.74369 3.82806i −0.319820 0.258088i
\(221\) 32.2521i 2.16951i
\(222\) 1.75281 4.96316i 0.117641 0.333106i
\(223\) −2.64553 −0.177158 −0.0885790 0.996069i \(-0.528233\pi\)
−0.0885790 + 0.996069i \(0.528233\pi\)
\(224\) −13.2792 + 6.90382i −0.887254 + 0.461281i
\(225\) 2.72103 0.181402
\(226\) 7.83702 22.1909i 0.521311 1.47611i
\(227\) 16.2979i 1.08173i −0.841109 0.540866i \(-0.818097\pi\)
0.841109 0.540866i \(-0.181903\pi\)
\(228\) −0.480322 0.387610i −0.0318101 0.0256701i
\(229\) −5.51840 −0.364666 −0.182333 0.983237i \(-0.558365\pi\)
−0.182333 + 0.983237i \(0.558365\pi\)
\(230\) 7.74069 + 2.73374i 0.510406 + 0.180257i
\(231\) 2.42625 + 3.50045i 0.159635 + 0.230313i
\(232\) −0.275548 0.447096i −0.0180906 0.0293533i
\(233\) 18.6314 1.22058 0.610291 0.792177i \(-0.291053\pi\)
0.610291 + 0.792177i \(0.291053\pi\)
\(234\) 6.08777 17.2378i 0.397970 1.12687i
\(235\) 2.95871 0.193005
\(236\) −1.91057 + 2.36756i −0.124368 + 0.154115i
\(237\) 1.48620 0.0965390
\(238\) −24.5045 + 6.69235i −1.58839 + 0.433801i
\(239\) 5.77674i 0.373666i 0.982392 + 0.186833i \(0.0598223\pi\)
−0.982392 + 0.186833i \(0.940178\pi\)
\(240\) −2.06504 + 0.446265i −0.133298 + 0.0288063i
\(241\) 1.42853i 0.0920200i −0.998941 0.0460100i \(-0.985349\pi\)
0.998941 0.0460100i \(-0.0146506\pi\)
\(242\) 0.805710 2.28140i 0.0517930 0.146654i
\(243\) 12.5337i 0.804039i
\(244\) 20.5999 + 16.6237i 1.31877 + 1.06422i
\(245\) 2.45676 6.55472i 0.156957 0.418766i
\(246\) −0.954130 + 2.70166i −0.0608331 + 0.172252i
\(247\) 2.77576i 0.176617i
\(248\) 7.52672 4.63877i 0.477947 0.294562i
\(249\) 7.10581 0.450312
\(250\) −0.470943 + 1.33350i −0.0297851 + 0.0843377i
\(251\) 11.6354i 0.734419i 0.930138 + 0.367210i \(0.119687\pi\)
−0.930138 + 0.367210i \(0.880313\pi\)
\(252\) −14.3601 1.04850i −0.904602 0.0660490i
\(253\) 17.6920i 1.11228i
\(254\) −21.2123 7.49142i −1.33098 0.470054i
\(255\) −3.58576 −0.224549
\(256\) −14.5722 + 6.60681i −0.910765 + 0.412926i
\(257\) 12.0011i 0.748611i −0.927305 0.374306i \(-0.877881\pi\)
0.927305 0.374306i \(-0.122119\pi\)
\(258\) 1.01108 + 0.357077i 0.0629471 + 0.0222307i
\(259\) 10.6207 + 15.3230i 0.659941 + 0.952124i
\(260\) 7.39409 + 5.96688i 0.458562 + 0.370050i
\(261\) 0.505246i 0.0312739i
\(262\) −26.9952 9.53374i −1.66777 0.588996i
\(263\) 26.7775i 1.65117i 0.564277 + 0.825585i \(0.309155\pi\)
−0.564277 + 0.825585i \(0.690845\pi\)
\(264\) 2.38889 + 3.87614i 0.147026 + 0.238560i
\(265\) 0.535513i 0.0328963i
\(266\) 2.10896 0.575973i 0.129309 0.0353151i
\(267\) 1.63756 0.100217
\(268\) 14.2139 + 11.4703i 0.868253 + 0.700662i
\(269\) 19.0365 1.16067 0.580337 0.814376i \(-0.302921\pi\)
0.580337 + 0.814376i \(0.302921\pi\)
\(270\) −4.02945 1.42306i −0.245224 0.0866045i
\(271\) 2.47835 0.150549 0.0752745 0.997163i \(-0.476017\pi\)
0.0752745 + 0.997163i \(0.476017\pi\)
\(272\) −26.5430 + 5.73608i −1.60941 + 0.347801i
\(273\) −3.78184 5.45622i −0.228888 0.330226i
\(274\) −3.00901 + 8.52015i −0.181781 + 0.514721i
\(275\) 3.04781 0.183790
\(276\) −4.77194 3.85086i −0.287237 0.231795i
\(277\) 16.0967i 0.967159i −0.875301 0.483579i \(-0.839336\pi\)
0.875301 0.483579i \(-0.160664\pi\)
\(278\) 29.0873 + 10.2726i 1.74454 + 0.616109i
\(279\) 8.50565 0.509220
\(280\) 2.99922 6.85600i 0.179238 0.409724i
\(281\) 17.4111 1.03866 0.519328 0.854575i \(-0.326182\pi\)
0.519328 + 0.854575i \(0.326182\pi\)
\(282\) −2.08388 0.735954i −0.124093 0.0438254i
\(283\) 29.4211i 1.74890i −0.485114 0.874451i \(-0.661222\pi\)
0.485114 0.874451i \(-0.338778\pi\)
\(284\) −12.1610 + 15.0698i −0.721624 + 0.894229i
\(285\) 0.308606 0.0182802
\(286\) 6.81888 19.3080i 0.403209 1.14170i
\(287\) −5.78132 8.34095i −0.341261 0.492351i
\(288\) −15.2692 1.94439i −0.899744 0.114574i
\(289\) −29.0897 −1.71116
\(290\) 0.247606 + 0.0874456i 0.0145399 + 0.00513498i
\(291\) 7.13181 0.418074
\(292\) 15.6115 19.3456i 0.913591 1.13211i
\(293\) 23.7367 1.38671 0.693357 0.720594i \(-0.256131\pi\)
0.693357 + 0.720594i \(0.256131\pi\)
\(294\) −3.36078 + 4.00553i −0.196005 + 0.233607i
\(295\) 1.52116i 0.0885651i
\(296\) 10.4572 + 16.9675i 0.607812 + 0.986218i
\(297\) 9.20962i 0.534396i
\(298\) 15.3560 + 5.42320i 0.889551 + 0.314158i
\(299\) 27.5768i 1.59481i
\(300\) 0.663391 0.822067i 0.0383009 0.0474621i
\(301\) −3.12155 + 2.16362i −0.179923 + 0.124709i
\(302\) −10.2809 3.63083i −0.591597 0.208931i
\(303\) 0.685795i 0.0393979i
\(304\) 2.28441 0.493672i 0.131020 0.0283140i
\(305\) −13.2354 −0.757855
\(306\) −24.6336 8.69969i −1.40821 0.497328i
\(307\) 3.27590i 0.186965i −0.995621 0.0934827i \(-0.970200\pi\)
0.995621 0.0934827i \(-0.0298000\pi\)
\(308\) −16.0847 1.17442i −0.916510 0.0669185i
\(309\) 10.0801i 0.573434i
\(310\) −1.47212 + 4.16837i −0.0836107 + 0.236747i
\(311\) −20.9116 −1.18579 −0.592893 0.805282i \(-0.702014\pi\)
−0.592893 + 0.805282i \(0.702014\pi\)
\(312\) −3.72361 6.04182i −0.210808 0.342050i
\(313\) 13.8819i 0.784650i 0.919827 + 0.392325i \(0.128329\pi\)
−0.919827 + 0.392325i \(0.871671\pi\)
\(314\) −2.08209 + 5.89554i −0.117499 + 0.332704i
\(315\) 5.91683 4.10111i 0.333376 0.231071i
\(316\) −3.53418 + 4.37951i −0.198813 + 0.246367i
\(317\) 5.93227i 0.333190i −0.986025 0.166595i \(-0.946723\pi\)
0.986025 0.166595i \(-0.0532772\pi\)
\(318\) −0.133204 + 0.377174i −0.00746973 + 0.0211509i
\(319\) 0.565923i 0.0316856i
\(320\) 3.59560 7.14644i 0.201000 0.399498i
\(321\) 2.01289i 0.112349i
\(322\) 20.9523 5.72222i 1.16762 0.318887i
\(323\) 3.96668 0.220712
\(324\) −10.2212 8.24828i −0.567843 0.458238i
\(325\) −4.75069 −0.263521
\(326\) −8.26388 + 23.3995i −0.457694 + 1.29598i
\(327\) −8.00118 −0.442466
\(328\) −5.69230 9.23615i −0.314305 0.509981i
\(329\) 6.43367 4.45934i 0.354700 0.245851i
\(330\) −2.14664 0.758117i −0.118169 0.0417330i
\(331\) −7.33151 −0.402976 −0.201488 0.979491i \(-0.564578\pi\)
−0.201488 + 0.979491i \(0.564578\pi\)
\(332\) −16.8976 + 20.9393i −0.927376 + 1.14919i
\(333\) 19.1743i 1.05075i
\(334\) 0.742192 2.10155i 0.0406109 0.114992i
\(335\) −9.13242 −0.498957
\(336\) −3.81779 + 4.08280i −0.208277 + 0.222735i
\(337\) −16.5861 −0.903505 −0.451752 0.892143i \(-0.649201\pi\)
−0.451752 + 0.892143i \(0.649201\pi\)
\(338\) −4.50647 + 12.7603i −0.245120 + 0.694067i
\(339\) 8.78945i 0.477378i
\(340\) 8.52693 10.5665i 0.462438 0.573048i
\(341\) 9.52714 0.515923
\(342\) 2.12007 + 0.748733i 0.114640 + 0.0404868i
\(343\) −4.53701 17.9559i −0.244976 0.969529i
\(344\) −3.45657 + 2.13031i −0.186366 + 0.114859i
\(345\) 3.06597 0.165066
\(346\) −0.0983868 + 0.278586i −0.00528931 + 0.0149769i
\(347\) 28.9802 1.55574 0.777870 0.628425i \(-0.216300\pi\)
0.777870 + 0.628425i \(0.216300\pi\)
\(348\) −0.152643 0.123180i −0.00818252 0.00660313i
\(349\) 10.2706 0.549772 0.274886 0.961477i \(-0.411360\pi\)
0.274886 + 0.961477i \(0.411360\pi\)
\(350\) 0.985772 + 3.60947i 0.0526918 + 0.192934i
\(351\) 14.3552i 0.766225i
\(352\) −17.1029 2.17790i −0.911589 0.116082i
\(353\) 24.6097i 1.30984i 0.755697 + 0.654921i \(0.227298\pi\)
−0.755697 + 0.654921i \(0.772702\pi\)
\(354\) −0.378374 + 1.07138i −0.0201104 + 0.0569434i
\(355\) 9.68233i 0.513885i
\(356\) −3.89412 + 4.82555i −0.206388 + 0.255754i
\(357\) −7.79718 + 5.40442i −0.412671 + 0.286032i
\(358\) 2.75354 7.79676i 0.145529 0.412072i
\(359\) 5.06081i 0.267099i 0.991042 + 0.133550i \(0.0426375\pi\)
−0.991042 + 0.133550i \(0.957362\pi\)
\(360\) 6.55186 4.03795i 0.345314 0.212819i
\(361\) 18.6586 0.982032
\(362\) −4.08157 + 11.5571i −0.214523 + 0.607430i
\(363\) 0.903627i 0.0474281i
\(364\) 25.0715 + 1.83059i 1.31411 + 0.0959487i
\(365\) 12.4295i 0.650589i
\(366\) 9.32196 + 3.29218i 0.487266 + 0.172085i
\(367\) −12.8106 −0.668708 −0.334354 0.942447i \(-0.608518\pi\)
−0.334354 + 0.942447i \(0.608518\pi\)
\(368\) 22.6953 4.90458i 1.18308 0.255669i
\(369\) 10.4374i 0.543350i
\(370\) −9.39678 3.31861i −0.488515 0.172526i
\(371\) −0.807120 1.16447i −0.0419036 0.0604560i
\(372\) 2.07369 2.56970i 0.107516 0.133232i
\(373\) 12.4155i 0.642849i 0.946935 + 0.321425i \(0.104162\pi\)
−0.946935 + 0.321425i \(0.895838\pi\)
\(374\) −27.5919 9.74449i −1.42674 0.503875i
\(375\) 0.528177i 0.0272749i
\(376\) 7.12417 4.39067i 0.367401 0.226431i
\(377\) 0.882116i 0.0454313i
\(378\) −10.9068 + 2.97872i −0.560984 + 0.153209i
\(379\) 9.41586 0.483660 0.241830 0.970319i \(-0.422252\pi\)
0.241830 + 0.970319i \(0.422252\pi\)
\(380\) −0.733864 + 0.909396i −0.0376464 + 0.0466511i
\(381\) −8.40185 −0.430440
\(382\) −17.3009 6.11005i −0.885189 0.312617i
\(383\) 28.8384 1.47358 0.736788 0.676124i \(-0.236342\pi\)
0.736788 + 0.676124i \(0.236342\pi\)
\(384\) −4.31008 + 4.13902i −0.219948 + 0.211218i
\(385\) 6.62742 4.59363i 0.337765 0.234113i
\(386\) 11.5790 32.7865i 0.589357 1.66879i
\(387\) −3.90614 −0.198560
\(388\) −16.9594 + 21.0159i −0.860984 + 1.06692i
\(389\) 4.35382i 0.220747i −0.993890 0.110374i \(-0.964795\pi\)
0.993890 0.110374i \(-0.0352048\pi\)
\(390\) 3.34601 + 1.18169i 0.169432 + 0.0598373i
\(391\) 39.4085 1.99297
\(392\) −3.81153 19.4286i −0.192511 0.981295i
\(393\) −10.6924 −0.539359
\(394\) 9.61709 + 3.39641i 0.484502 + 0.171109i
\(395\) 2.81383i 0.141579i
\(396\) −12.9077 10.4163i −0.648637 0.523437i
\(397\) −16.9988 −0.853148 −0.426574 0.904453i \(-0.640280\pi\)
−0.426574 + 0.904453i \(0.640280\pi\)
\(398\) −2.98017 + 8.43847i −0.149382 + 0.422982i
\(399\) 0.671059 0.465128i 0.0335950 0.0232855i
\(400\) 0.844916 + 3.90975i 0.0422458 + 0.195487i
\(401\) 10.4337 0.521035 0.260518 0.965469i \(-0.416107\pi\)
0.260518 + 0.965469i \(0.416107\pi\)
\(402\) 6.43216 + 2.27161i 0.320807 + 0.113298i
\(403\) −14.8501 −0.739738
\(404\) 2.02089 + 1.63082i 0.100543 + 0.0811362i
\(405\) 6.56709 0.326321
\(406\) 0.670212 0.183040i 0.0332621 0.00908412i
\(407\) 21.4771i 1.06458i
\(408\) −8.63402 + 5.32120i −0.427448 + 0.263439i
\(409\) 27.7527i 1.37228i 0.727469 + 0.686141i \(0.240697\pi\)
−0.727469 + 0.686141i \(0.759303\pi\)
\(410\) 5.11507 + 1.80646i 0.252615 + 0.0892147i
\(411\) 3.37470i 0.166461i
\(412\) 29.7038 + 23.9703i 1.46340 + 1.18093i
\(413\) −2.29267 3.30773i −0.112815 0.162763i
\(414\) 21.0626 + 7.43858i 1.03517 + 0.365586i
\(415\) 13.4535i 0.660405i
\(416\) 26.6587 + 3.39473i 1.30705 + 0.166440i
\(417\) 11.5210 0.564186
\(418\) 2.37468 + 0.838652i 0.116149 + 0.0410198i
\(419\) 30.1125i 1.47109i 0.677476 + 0.735545i \(0.263074\pi\)
−0.677476 + 0.735545i \(0.736926\pi\)
\(420\) 0.203523 2.78743i 0.00993089 0.136013i
\(421\) 27.1321i 1.32234i 0.750236 + 0.661170i \(0.229940\pi\)
−0.750236 + 0.661170i \(0.770060\pi\)
\(422\) 4.81356 13.6298i 0.234321 0.663489i
\(423\) 8.05074 0.391440
\(424\) −0.794691 1.28944i −0.0385936 0.0626209i
\(425\) 6.78894i 0.329312i
\(426\) −2.40840 + 6.81948i −0.116687 + 0.330405i
\(427\) −28.7801 + 19.9482i −1.39277 + 0.965361i
\(428\) 5.93156 + 4.78665i 0.286713 + 0.231371i
\(429\) 7.64758i 0.369229i
\(430\) 0.676056 1.91428i 0.0326023 0.0923149i
\(431\) 3.80266i 0.183167i 0.995797 + 0.0915837i \(0.0291929\pi\)
−0.995797 + 0.0915837i \(0.970807\pi\)
\(432\) −11.8141 + 2.55309i −0.568408 + 0.122836i
\(433\) 6.04283i 0.290400i −0.989402 0.145200i \(-0.953617\pi\)
0.989402 0.145200i \(-0.0463825\pi\)
\(434\) 3.08142 + 11.2828i 0.147913 + 0.541592i
\(435\) 0.0980728 0.00470223
\(436\) 19.0268 23.5778i 0.911217 1.12917i
\(437\) −3.39167 −0.162245
\(438\) 3.09173 8.75435i 0.147728 0.418299i
\(439\) −20.7511 −0.990398 −0.495199 0.868780i \(-0.664905\pi\)
−0.495199 + 0.868780i \(0.664905\pi\)
\(440\) 7.33871 4.52289i 0.349859 0.215621i
\(441\) 6.68492 17.8356i 0.318329 0.849313i
\(442\) 43.0081 + 15.1889i 2.04569 + 0.722464i
\(443\) 40.9174 1.94404 0.972022 0.234891i \(-0.0754733\pi\)
0.972022 + 0.234891i \(0.0754733\pi\)
\(444\) 5.79288 + 4.67474i 0.274918 + 0.221853i
\(445\) 3.10041i 0.146973i
\(446\) 1.24590 3.52781i 0.0589949 0.167047i
\(447\) 6.08228 0.287682
\(448\) −2.95246 20.9591i −0.139491 0.990223i
\(449\) 9.64737 0.455288 0.227644 0.973744i \(-0.426898\pi\)
0.227644 + 0.973744i \(0.426898\pi\)
\(450\) −1.28145 + 3.62848i −0.0604082 + 0.171048i
\(451\) 11.6909i 0.550503i
\(452\) 25.9006 + 20.9013i 1.21826 + 0.983114i
\(453\) −4.07209 −0.191323
\(454\) 21.7332 + 7.67540i 1.01999 + 0.360224i
\(455\) −10.3303 + 7.16019i −0.484292 + 0.335675i
\(456\) 0.743081 0.457965i 0.0347980 0.0214462i
\(457\) 8.31667 0.389037 0.194519 0.980899i \(-0.437686\pi\)
0.194519 + 0.980899i \(0.437686\pi\)
\(458\) 2.59886 7.35877i 0.121437 0.343853i
\(459\) −20.5142 −0.957523
\(460\) −7.29085 + 9.03475i −0.339938 + 0.421247i
\(461\) −14.8017 −0.689385 −0.344693 0.938716i \(-0.612017\pi\)
−0.344693 + 0.938716i \(0.612017\pi\)
\(462\) −5.81046 + 1.58688i −0.270327 + 0.0738284i
\(463\) 10.2328i 0.475556i −0.971319 0.237778i \(-0.923581\pi\)
0.971319 0.237778i \(-0.0764191\pi\)
\(464\) 0.725969 0.156885i 0.0337023 0.00728323i
\(465\) 1.65102i 0.0765644i
\(466\) −8.77432 + 24.8449i −0.406463 + 1.15092i
\(467\) 1.49149i 0.0690179i −0.999404 0.0345090i \(-0.989013\pi\)
0.999404 0.0345090i \(-0.0109867\pi\)
\(468\) 20.1195 + 16.2360i 0.930026 + 0.750511i
\(469\) −19.8583 + 13.7643i −0.916971 + 0.635575i
\(470\) −1.39338 + 3.94543i −0.0642721 + 0.181989i
\(471\) 2.33513i 0.107597i
\(472\) −2.25737 3.66273i −0.103904 0.168591i
\(473\) −4.37524 −0.201174
\(474\) −0.699916 + 1.98184i −0.0321482 + 0.0910290i
\(475\) 0.584285i 0.0268089i
\(476\) 2.61599 35.8283i 0.119904 1.64219i
\(477\) 1.45715i 0.0667182i
\(478\) −7.70326 2.72052i −0.352339 0.124434i
\(479\) −33.0698 −1.51100 −0.755499 0.655150i \(-0.772605\pi\)
−0.755499 + 0.655150i \(0.772605\pi\)
\(480\) 0.377423 2.96389i 0.0172269 0.135282i
\(481\) 33.4768i 1.52641i
\(482\) 1.90494 + 0.672759i 0.0867679 + 0.0306433i
\(483\) 6.66689 4.62099i 0.303354 0.210262i
\(484\) 2.66280 + 2.14882i 0.121036 + 0.0976737i
\(485\) 13.5027i 0.613126i
\(486\) −16.7137 5.90268i −0.758148 0.267751i
\(487\) 30.3143i 1.37367i −0.726811 0.686837i \(-0.758999\pi\)
0.726811 0.686837i \(-0.241001\pi\)
\(488\) −31.8689 + 19.6410i −1.44264 + 0.889107i
\(489\) 9.26819i 0.419122i
\(490\) 7.58370 + 6.36298i 0.342596 + 0.287450i
\(491\) −24.0080 −1.08347 −0.541733 0.840551i \(-0.682232\pi\)
−0.541733 + 0.840551i \(0.682232\pi\)
\(492\) −3.15331 2.54466i −0.142162 0.114722i
\(493\) 1.26058 0.0567738
\(494\) −3.70146 1.30722i −0.166537 0.0588148i
\(495\) 8.29319 0.372751
\(496\) 2.64112 + 12.2215i 0.118590 + 0.548759i
\(497\) −14.5931 21.0541i −0.654590 0.944404i
\(498\) −3.34643 + 9.47557i −0.149957 + 0.424611i
\(499\) −36.6238 −1.63951 −0.819754 0.572716i \(-0.805890\pi\)
−0.819754 + 0.572716i \(0.805890\pi\)
\(500\) −1.55642 1.25600i −0.0696054 0.0561701i
\(501\) 0.832390i 0.0371884i
\(502\) −15.5157 5.47961i −0.692502 0.244567i
\(503\) −0.225539 −0.0100563 −0.00502815 0.999987i \(-0.501601\pi\)
−0.00502815 + 0.999987i \(0.501601\pi\)
\(504\) 8.16096 18.6554i 0.363518 0.830976i
\(505\) −1.29842 −0.0577789
\(506\) 23.5922 + 8.33191i 1.04880 + 0.370399i
\(507\) 5.05414i 0.224462i
\(508\) 19.9796 24.7585i 0.886450 1.09848i
\(509\) 11.4130 0.505871 0.252935 0.967483i \(-0.418604\pi\)
0.252935 + 0.967483i \(0.418604\pi\)
\(510\) 1.68869 4.78160i 0.0747765 0.211733i
\(511\) 18.7336 + 27.0277i 0.828725 + 1.19564i
\(512\) −1.94746 22.5435i −0.0860665 0.996289i
\(513\) 1.76554 0.0779507
\(514\) 16.0035 + 5.65186i 0.705884 + 0.249293i
\(515\) −19.0846 −0.840969
\(516\) −0.952322 + 1.18011i −0.0419237 + 0.0519513i
\(517\) 9.01759 0.396593
\(518\) −25.4349 + 6.94647i −1.11755 + 0.305210i
\(519\) 0.110344i 0.00484355i
\(520\) −11.4390 + 7.04993i −0.501633 + 0.309160i
\(521\) 18.6069i 0.815183i 0.913164 + 0.407591i \(0.133631\pi\)
−0.913164 + 0.407591i \(0.866369\pi\)
\(522\) 0.673743 + 0.237942i 0.0294889 + 0.0104144i
\(523\) 35.5417i 1.55413i −0.629420 0.777065i \(-0.716708\pi\)
0.629420 0.777065i \(-0.283292\pi\)
\(524\) 25.4264 31.5081i 1.11076 1.37644i
\(525\) 0.796062 + 1.14851i 0.0347430 + 0.0501252i
\(526\) −35.7077 12.6107i −1.55693 0.549852i
\(527\) 21.2215i 0.924424i
\(528\) −6.29385 + 1.36013i −0.273904 + 0.0591921i
\(529\) −10.6958 −0.465035
\(530\) 0.714105 + 0.252196i 0.0310187 + 0.0109547i
\(531\) 4.13911i 0.179622i
\(532\) −0.225143 + 3.08354i −0.00976119 + 0.133688i
\(533\) 18.2228i 0.789319i
\(534\) −0.771199 + 2.18368i −0.0333731 + 0.0944972i
\(535\) −3.81102 −0.164765
\(536\) −21.9896 + 13.5523i −0.949806 + 0.585371i
\(537\) 3.08817i 0.133265i
\(538\) −8.96510 + 25.3851i −0.386513 + 1.09443i
\(539\) 7.48775 19.9775i 0.322520 0.860494i
\(540\) 3.79528 4.70307i 0.163323 0.202388i
\(541\) 40.2046i 1.72853i 0.503035 + 0.864266i \(0.332216\pi\)
−0.503035 + 0.864266i \(0.667784\pi\)
\(542\) −1.16716 + 3.30487i −0.0501339 + 0.141956i
\(543\) 4.57760i 0.196444i
\(544\) 4.85122 38.0964i 0.207994 1.63337i
\(545\) 15.1487i 0.648898i
\(546\) 9.05689 2.47350i 0.387599 0.105856i
\(547\) −6.38283 −0.272910 −0.136455 0.990646i \(-0.543571\pi\)
−0.136455 + 0.990646i \(0.543571\pi\)
\(548\) −9.94451 8.02501i −0.424808 0.342812i
\(549\) −36.0138 −1.53703
\(550\) −1.43535 + 4.06425i −0.0612034 + 0.173300i
\(551\) −0.108491 −0.00462188
\(552\) 7.38242 4.54983i 0.314217 0.193654i
\(553\) −4.24097 6.11863i −0.180344 0.260190i
\(554\) 21.4649 + 7.58065i 0.911957 + 0.322071i
\(555\) −3.72192 −0.157987
\(556\) −27.3969 + 33.9500i −1.16189 + 1.43980i
\(557\) 33.9096i 1.43680i 0.695631 + 0.718399i \(0.255125\pi\)
−0.695631 + 0.718399i \(0.744875\pi\)
\(558\) −4.00568 + 11.3422i −0.169574 + 0.480156i
\(559\) 6.81978 0.288446
\(560\) 7.72998 + 7.22823i 0.326651 + 0.305449i
\(561\) −10.9287 −0.461411
\(562\) −8.19962 + 23.2176i −0.345880 + 0.979375i
\(563\) 13.9112i 0.586288i −0.956068 0.293144i \(-0.905298\pi\)
0.956068 0.293144i \(-0.0947016\pi\)
\(564\) 1.96278 2.43226i 0.0826481 0.102417i
\(565\) −16.6411 −0.700097
\(566\) 39.2329 + 13.8557i 1.64908 + 0.582397i
\(567\) 14.2800 9.89784i 0.599705 0.415670i
\(568\) −14.3684 23.3137i −0.602884 0.978222i
\(569\) −23.6948 −0.993336 −0.496668 0.867940i \(-0.665443\pi\)
−0.496668 + 0.867940i \(0.665443\pi\)
\(570\) −0.145336 + 0.411525i −0.00608745 + 0.0172369i
\(571\) 20.9646 0.877340 0.438670 0.898648i \(-0.355450\pi\)
0.438670 + 0.898648i \(0.355450\pi\)
\(572\) 22.5358 + 18.1859i 0.942269 + 0.760391i
\(573\) −6.85260 −0.286271
\(574\) 13.8453 3.78126i 0.577892 0.157827i
\(575\) 5.80481i 0.242077i
\(576\) 9.78374 19.4457i 0.407656 0.810237i
\(577\) 11.5447i 0.480614i −0.970697 0.240307i \(-0.922752\pi\)
0.970697 0.240307i \(-0.0772481\pi\)
\(578\) 13.6996 38.7911i 0.569829 1.61350i
\(579\) 12.9862i 0.539689i
\(580\) −0.233217 + 0.289000i −0.00968380 + 0.0120001i
\(581\) −20.2769 29.2544i −0.841229 1.21368i
\(582\) −3.35868 + 9.51024i −0.139222 + 0.394212i
\(583\) 1.63214i 0.0675965i
\(584\) 18.4451 + 29.9285i 0.763264 + 1.23845i
\(585\) −12.9268 −0.534456
\(586\) −11.1786 + 31.6528i −0.461786 + 1.30757i
\(587\) 8.38593i 0.346124i −0.984911 0.173062i \(-0.944634\pi\)
0.984911 0.173062i \(-0.0553661\pi\)
\(588\) −3.75863 6.36797i −0.155003 0.262611i
\(589\) 1.82641i 0.0752561i
\(590\) 2.02846 + 0.716378i 0.0835102 + 0.0294928i
\(591\) 3.80918 0.156689
\(592\) −27.5509 + 5.95389i −1.13234 + 0.244703i
\(593\) 26.8713i 1.10347i −0.834018 0.551737i \(-0.813965\pi\)
0.834018 0.551737i \(-0.186035\pi\)
\(594\) −12.2810 4.33721i −0.503895 0.177958i
\(595\) 10.2322 + 14.7624i 0.419480 + 0.605201i
\(596\) −14.4636 + 17.9232i −0.592454 + 0.734162i
\(597\) 3.34234i 0.136793i
\(598\) −36.7736 12.9871i −1.50378 0.531083i
\(599\) 34.0473i 1.39113i −0.718462 0.695566i \(-0.755153\pi\)
0.718462 0.695566i \(-0.244847\pi\)
\(600\) 0.783804 + 1.27178i 0.0319987 + 0.0519201i
\(601\) 24.5067i 0.999649i 0.866127 + 0.499825i \(0.166602\pi\)
−0.866127 + 0.499825i \(0.833398\pi\)
\(602\) −1.41511 5.18152i −0.0576757 0.211183i
\(603\) −24.8496 −1.01195
\(604\) 9.68340 11.9996i 0.394012 0.488256i
\(605\) −1.71084 −0.0695556
\(606\) 0.914505 + 0.322970i 0.0371492 + 0.0131198i
\(607\) 36.7082 1.48994 0.744971 0.667097i \(-0.232463\pi\)
0.744971 + 0.667097i \(0.232463\pi\)
\(608\) −0.417517 + 3.27874i −0.0169326 + 0.132971i
\(609\) 0.213258 0.147814i 0.00864164 0.00598974i
\(610\) 6.23311 17.6493i 0.252371 0.714600i
\(611\) −14.0559 −0.568641
\(612\) 23.2020 28.7517i 0.937886 1.16222i
\(613\) 41.6702i 1.68304i 0.540224 + 0.841521i \(0.318339\pi\)
−0.540224 + 0.841521i \(0.681661\pi\)
\(614\) 4.36840 + 1.54276i 0.176294 + 0.0622608i
\(615\) 2.02600 0.0816961
\(616\) 9.14106 20.8958i 0.368304 0.841915i
\(617\) 18.6715 0.751688 0.375844 0.926683i \(-0.377353\pi\)
0.375844 + 0.926683i \(0.377353\pi\)
\(618\) 13.4417 + 4.74713i 0.540705 + 0.190958i
\(619\) 19.0302i 0.764888i −0.923979 0.382444i \(-0.875083\pi\)
0.923979 0.382444i \(-0.124917\pi\)
\(620\) −4.86522 3.92613i −0.195392 0.157677i
\(621\) 17.5405 0.703875
\(622\) 9.84816 27.8855i 0.394875 1.11811i
\(623\) −4.67290 6.74178i −0.187216 0.270104i
\(624\) 9.81035 2.12007i 0.392728 0.0848705i
\(625\) 1.00000 0.0400000
\(626\) −18.5114 6.53758i −0.739866 0.261294i
\(627\) 0.940573 0.0375629
\(628\) −6.88113 5.55293i −0.274587 0.221586i
\(629\) −47.8398 −1.90750
\(630\) 2.68232 + 9.82147i 0.106866 + 0.391297i
\(631\) 28.1199i 1.11944i −0.828683 0.559718i \(-0.810910\pi\)
0.828683 0.559718i \(-0.189090\pi\)
\(632\) −4.17567 6.77531i −0.166099 0.269507i
\(633\) 5.39855i 0.214573i
\(634\) 7.91067 + 2.79377i 0.314173 + 0.110955i
\(635\) 15.9073i 0.631261i
\(636\) −0.440228 0.355255i −0.0174562 0.0140868i
\(637\) −11.6713 + 31.1394i −0.462434 + 1.23379i
\(638\) 0.754657 + 0.266518i 0.0298771 + 0.0105515i
\(639\) 26.3459i 1.04223i
\(640\) 7.83643 + 8.16029i 0.309762 + 0.322564i
\(641\) −7.40297 −0.292400 −0.146200 0.989255i \(-0.546704\pi\)
−0.146200 + 0.989255i \(0.546704\pi\)
\(642\) 2.68418 + 0.947958i 0.105936 + 0.0374129i
\(643\) 10.9752i 0.432819i −0.976303 0.216409i \(-0.930565\pi\)
0.976303 0.216409i \(-0.0694346\pi\)
\(644\) −2.23677 + 30.6346i −0.0881411 + 1.20717i
\(645\) 0.758217i 0.0298548i
\(646\) −1.86808 + 5.28955i −0.0734987 + 0.208115i
\(647\) 37.3313 1.46765 0.733823 0.679340i \(-0.237734\pi\)
0.733823 + 0.679340i \(0.237734\pi\)
\(648\) 15.8126 9.74543i 0.621179 0.382837i
\(649\) 4.63620i 0.181987i
\(650\) 2.23730 6.33502i 0.0877543 0.248480i
\(651\) 2.48841 + 3.59013i 0.0975283 + 0.140708i
\(652\) −27.3114 22.0397i −1.06960 0.863142i
\(653\) 27.0398i 1.05815i −0.848575 0.529074i \(-0.822539\pi\)
0.848575 0.529074i \(-0.177461\pi\)
\(654\) 3.76810 10.6695i 0.147344 0.417212i
\(655\) 20.2439i 0.790995i
\(656\) 14.9971 3.24095i 0.585539 0.126538i
\(657\) 33.8210i 1.31948i
\(658\) 2.91662 + 10.6794i 0.113701 + 0.416325i
\(659\) 16.0036 0.623410 0.311705 0.950179i \(-0.399100\pi\)
0.311705 + 0.950179i \(0.399100\pi\)
\(660\) 2.02189 2.50551i 0.0787020 0.0975267i
\(661\) 28.7776 1.11932 0.559659 0.828723i \(-0.310932\pi\)
0.559659 + 0.828723i \(0.310932\pi\)
\(662\) 3.45273 9.77654i 0.134194 0.379976i
\(663\) 17.0348 0.661578
\(664\) −19.9647 32.3941i −0.774780 1.25714i
\(665\) −0.880629 1.27052i −0.0341493 0.0492686i
\(666\) −25.5689 9.03003i −0.990775 0.349907i
\(667\) −1.07785 −0.0417344
\(668\) 2.45288 + 1.97942i 0.0949046 + 0.0765861i
\(669\) 1.39731i 0.0540231i
\(670\) 4.30085 12.1780i 0.166156 0.470479i
\(671\) −40.3389 −1.55727
\(672\) −3.64644 7.01377i −0.140664 0.270562i
\(673\) 19.6820 0.758685 0.379342 0.925256i \(-0.376150\pi\)
0.379342 + 0.925256i \(0.376150\pi\)
\(674\) 7.81113 22.1176i 0.300874 0.851937i
\(675\) 3.02172i 0.116306i
\(676\) −14.8935 12.0187i −0.572826 0.462259i
\(677\) 41.7128 1.60315 0.801576 0.597893i \(-0.203995\pi\)
0.801576 + 0.597893i \(0.203995\pi\)
\(678\) 11.7207 + 4.13933i 0.450131 + 0.158970i
\(679\) −20.3511 29.3614i −0.781004 1.12679i
\(680\) 10.0747 + 16.3468i 0.386346 + 0.626873i
\(681\) 8.60819 0.329866
\(682\) −4.48674 + 12.7044i −0.171806 + 0.486477i
\(683\) −22.1942 −0.849237 −0.424618 0.905372i \(-0.639592\pi\)
−0.424618 + 0.905372i \(0.639592\pi\)
\(684\) −1.99687 + 2.47449i −0.0763521 + 0.0946146i
\(685\) 6.38933 0.244124
\(686\) 26.0808 + 2.40614i 0.995771 + 0.0918668i
\(687\) 2.91469i 0.111202i
\(688\) −1.21291 5.61258i −0.0462417 0.213978i
\(689\) 2.54406i 0.0969208i
\(690\) −1.44390 + 4.08845i −0.0549682 + 0.155645i
\(691\) 7.35566i 0.279822i 0.990164 + 0.139911i \(0.0446817\pi\)
−0.990164 + 0.139911i \(0.955318\pi\)
\(692\) −0.325159 0.262397i −0.0123607 0.00997483i
\(693\) 18.0334 12.4994i 0.685032 0.474813i
\(694\) −13.6481 + 38.6450i −0.518073 + 1.46695i
\(695\) 21.8128i 0.827406i
\(696\) 0.236146 0.145538i 0.00895109 0.00551661i
\(697\) 26.0412 0.986382
\(698\) −4.83687 + 13.6958i −0.183078 + 0.518393i
\(699\) 9.84066i 0.372208i
\(700\) −5.27745 0.385331i −0.199469 0.0145641i
\(701\) 10.2820i 0.388346i −0.980967 0.194173i \(-0.937798\pi\)
0.980967 0.194173i \(-0.0622024\pi\)
\(702\) 19.1426 + 6.76050i 0.722492 + 0.255159i
\(703\) 4.11730 0.155287
\(704\) 10.9587 21.7810i 0.413022 0.820903i
\(705\) 1.56272i 0.0588555i
\(706\) −32.8169 11.5898i −1.23508 0.436187i
\(707\) −2.82339 + 1.95696i −0.106185 + 0.0735992i
\(708\) −1.25049 1.00912i −0.0469964 0.0379251i
\(709\) 10.8180i 0.406277i −0.979150 0.203139i \(-0.934886\pi\)
0.979150 0.203139i \(-0.0651142\pi\)
\(710\) 12.9113 + 4.55983i 0.484554 + 0.171127i
\(711\) 7.65651i 0.287142i
\(712\) −4.60094 7.46535i −0.172428 0.279776i
\(713\) 18.1452i 0.679544i
\(714\) −3.53475 12.9427i −0.132285 0.484368i
\(715\) −14.4792 −0.541491
\(716\) 9.10019 + 7.34366i 0.340090 + 0.274446i
\(717\) −3.05114 −0.113947
\(718\) −6.74857 2.38335i −0.251854 0.0889459i
\(719\) 29.4274 1.09746 0.548729 0.836000i \(-0.315112\pi\)
0.548729 + 0.836000i \(0.315112\pi\)
\(720\) 2.29904 + 10.6385i 0.0856802 + 0.396475i
\(721\) −41.4992 + 28.7641i −1.54551 + 1.07123i
\(722\) −8.78715 + 24.8812i −0.327024 + 0.925982i
\(723\) 0.754518 0.0280608
\(724\) −13.4892 10.8855i −0.501323 0.404557i
\(725\) 0.185682i 0.00689605i
\(726\) 1.20498 + 0.425557i 0.0447211 + 0.0157939i
\(727\) −31.0932 −1.15318 −0.576591 0.817033i \(-0.695617\pi\)
−0.576591 + 0.817033i \(0.695617\pi\)
\(728\) −14.2484 + 32.5707i −0.528079 + 1.20715i
\(729\) 13.0812 0.484490
\(730\) −16.5747 5.85358i −0.613456 0.216651i
\(731\) 9.74577i 0.360460i
\(732\) −8.78023 + 10.8804i −0.324527 + 0.402150i
\(733\) −10.0076 −0.369639 −0.184820 0.982772i \(-0.559170\pi\)
−0.184820 + 0.982772i \(0.559170\pi\)
\(734\) 6.03307 17.0829i 0.222685 0.630541i
\(735\) 3.46205 + 1.29760i 0.127700 + 0.0478629i
\(736\) −4.14798 + 32.5739i −0.152897 + 1.20069i
\(737\) −27.8339 −1.02527
\(738\) 13.9182 + 4.91543i 0.512338 + 0.180939i
\(739\) 40.1592 1.47728 0.738641 0.674099i \(-0.235468\pi\)
0.738641 + 0.674099i \(0.235468\pi\)
\(740\) 8.85070 10.9677i 0.325358 0.403180i
\(741\) −1.46609 −0.0538582
\(742\) 1.93292 0.527894i 0.0709596 0.0193796i
\(743\) 41.3554i 1.51718i 0.651567 + 0.758591i \(0.274112\pi\)
−0.651567 + 0.758591i \(0.725888\pi\)
\(744\) 2.45009 + 3.97544i 0.0898246 + 0.145747i
\(745\) 11.5156i 0.421899i
\(746\) −16.5560 5.84699i −0.606158 0.214073i
\(747\) 36.6073i 1.33939i
\(748\) 25.9885 32.2046i 0.950233 1.17752i
\(749\) −8.28700 + 5.74393i −0.302800 + 0.209878i
\(750\) −0.704322 0.248741i −0.0257182 0.00908275i
\(751\) 10.4171i 0.380126i −0.981772 0.190063i \(-0.939131\pi\)
0.981772 0.190063i \(-0.0608693\pi\)
\(752\) 2.49986 + 11.5678i 0.0911605 + 0.421835i
\(753\) −6.14554 −0.223956
\(754\) −1.17630 0.415427i −0.0428383 0.0151290i
\(755\) 7.70970i 0.280585i
\(756\) 1.16436 15.9470i 0.0423473 0.579985i
\(757\) 31.7145i 1.15268i −0.817209 0.576341i \(-0.804480\pi\)
0.817209 0.576341i \(-0.195520\pi\)
\(758\) −4.43434 + 12.5560i −0.161062 + 0.456055i
\(759\) 9.34449 0.339183
\(760\) −0.867068 1.40688i −0.0314519 0.0510329i
\(761\) 11.9199i 0.432095i 0.976383 + 0.216047i \(0.0693166\pi\)
−0.976383 + 0.216047i \(0.930683\pi\)
\(762\) 3.95680 11.2038i 0.143340 0.405872i
\(763\) 22.8319 + 32.9406i 0.826571 + 1.19253i
\(764\) 16.2955 20.1932i 0.589549 0.730563i
\(765\) 18.4729i 0.667890i
\(766\) −13.5813 + 38.4560i −0.490711 + 1.38947i
\(767\) 7.22653i 0.260935i
\(768\) −3.48957 7.69672i −0.125919 0.277731i
\(769\) 9.56458i 0.344908i 0.985018 + 0.172454i \(0.0551695\pi\)
−0.985018 + 0.172454i \(0.944830\pi\)
\(770\) 3.00445 + 11.0010i 0.108273 + 0.396448i
\(771\) 6.33873 0.228284
\(772\) 38.2676 + 30.8812i 1.37728 + 1.11144i
\(773\) 30.6270 1.10158 0.550788 0.834645i \(-0.314327\pi\)
0.550788 + 0.834645i \(0.314327\pi\)
\(774\) 1.83957 5.20882i 0.0661219 0.187227i
\(775\) 3.12589 0.112285
\(776\) −20.0377 32.5126i −0.719313 1.16714i
\(777\) −8.09325 + 5.60963i −0.290344 + 0.201244i
\(778\) 5.80580 + 2.05040i 0.208148 + 0.0735105i
\(779\) −2.24122 −0.0803001