Properties

Label 570.2.f.d.341.2
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.7278137344.1
Defining polynomial: \(x^{8} - 2 x^{7} + x^{6} + 6 x^{5} - 20 x^{4} + 18 x^{3} + 9 x^{2} - 54 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.2
Root \(1.67936 - 0.423958i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.d.341.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.67936 + 0.423958i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-1.67936 + 0.423958i) q^{6} -2.47197 q^{7} +1.00000 q^{8} +(2.64052 - 1.42396i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.67936 + 0.423958i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-1.67936 + 0.423958i) q^{6} -2.47197 q^{7} +1.00000 q^{8} +(2.64052 - 1.42396i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(-1.67936 + 0.423958i) q^{12} -1.15208i q^{13} -2.47197 q^{14} +(0.423958 + 1.67936i) q^{15} +1.00000 q^{16} -6.67861i q^{17} +(2.64052 - 1.42396i) q^{18} +(4.35873 - 0.0388432i) q^{19} -1.00000i q^{20} +(4.15133 - 1.04801i) q^{21} -2.00000i q^{22} -5.79185i q^{23} +(-1.67936 + 0.423958i) q^{24} -1.00000 q^{25} -1.15208i q^{26} +(-3.83069 + 3.51081i) q^{27} -2.47197 q^{28} -3.35873 q^{29} +(0.423958 + 1.67936i) q^{30} +4.80907i q^{31} +1.00000 q^{32} +(0.847915 + 3.35873i) q^{33} -6.67861i q^{34} +2.47197i q^{35} +(2.64052 - 1.42396i) q^{36} -11.6614i q^{37} +(4.35873 - 0.0388432i) q^{38} +(0.488435 + 1.93477i) q^{39} -1.00000i q^{40} +7.83069 q^{41} +(4.15133 - 1.04801i) q^{42} -0.978379 q^{43} -2.00000i q^{44} +(-1.42396 - 2.64052i) q^{45} -5.79185i q^{46} +3.02162i q^{47} +(-1.67936 + 0.423958i) q^{48} -0.889378 q^{49} -1.00000 q^{50} +(2.83145 + 11.2158i) q^{51} -1.15208i q^{52} +2.33710 q^{53} +(-3.83069 + 3.51081i) q^{54} -2.00000 q^{55} -2.47197 q^{56} +(-7.30341 + 1.91315i) q^{57} -3.35873 q^{58} -12.8076 q^{59} +(0.423958 + 1.67936i) q^{60} +11.9656 q^{61} +4.80907i q^{62} +(-6.52728 + 3.51998i) q^{63} +1.00000 q^{64} -1.15208 q^{65} +(0.847915 + 3.35873i) q^{66} +10.0183i q^{67} -6.67861i q^{68} +(2.45550 + 9.72662i) q^{69} +2.47197i q^{70} +7.24810 q^{71} +(2.64052 - 1.42396i) q^{72} -6.97687 q^{73} -11.6614i q^{74} +(1.67936 - 0.423958i) q^{75} +(4.35873 - 0.0388432i) q^{76} +4.94393i q^{77} +(0.488435 + 1.93477i) q^{78} -5.75301i q^{79} -1.00000i q^{80} +(4.94469 - 7.51998i) q^{81} +7.83069 q^{82} +11.1565i q^{83} +(4.15133 - 1.04801i) q^{84} -6.67861 q^{85} -0.978379 q^{86} +(5.64052 - 1.42396i) q^{87} -2.00000i q^{88} -10.8868 q^{89} +(-1.42396 - 2.64052i) q^{90} +2.84792i q^{91} -5.79185i q^{92} +(-2.03884 - 8.07618i) q^{93} +3.02162i q^{94} +(-0.0388432 - 4.35873i) q^{95} +(-1.67936 + 0.423958i) q^{96} +6.94393i q^{97} -0.889378 q^{98} +(-2.84792 - 5.28104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} - 2q^{12} + 4q^{14} + 8q^{16} + 2q^{18} + 12q^{19} - 2q^{21} - 2q^{24} - 8q^{25} + 16q^{27} + 4q^{28} - 4q^{29} + 8q^{32} + 2q^{36} + 12q^{38} - 22q^{39} + 16q^{41} - 2q^{42} - 40q^{43} - 8q^{45} - 2q^{48} + 4q^{49} - 8q^{50} + 18q^{51} + 28q^{53} + 16q^{54} - 16q^{55} + 4q^{56} - 30q^{57} - 4q^{58} - 4q^{59} + 16q^{61} - 34q^{63} + 8q^{64} - 16q^{65} - 2q^{69} + 24q^{71} + 2q^{72} - 4q^{73} + 2q^{75} + 12q^{76} - 22q^{78} + 34q^{81} + 16q^{82} - 2q^{84} - 40q^{86} + 26q^{87} - 88q^{89} - 8q^{90} - 24q^{93} - 8q^{95} - 2q^{96} + 4q^{98} - 16q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.67936 + 0.423958i −0.969581 + 0.244772i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) −1.67936 + 0.423958i −0.685597 + 0.173080i
\(7\) −2.47197 −0.934316 −0.467158 0.884174i \(-0.654722\pi\)
−0.467158 + 0.884174i \(0.654722\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.64052 1.42396i 0.880173 0.474653i
\(10\) 1.00000i 0.316228i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) −1.67936 + 0.423958i −0.484790 + 0.122386i
\(13\) 1.15208i 0.319531i −0.987155 0.159765i \(-0.948926\pi\)
0.987155 0.159765i \(-0.0510738\pi\)
\(14\) −2.47197 −0.660661
\(15\) 0.423958 + 1.67936i 0.109465 + 0.433610i
\(16\) 1.00000 0.250000
\(17\) 6.67861i 1.61980i −0.586568 0.809900i \(-0.699521\pi\)
0.586568 0.809900i \(-0.300479\pi\)
\(18\) 2.64052 1.42396i 0.622376 0.335630i
\(19\) 4.35873 0.0388432i 0.999960 0.00891124i
\(20\) 1.00000i 0.223607i
\(21\) 4.15133 1.04801i 0.905895 0.228694i
\(22\) 2.00000i 0.426401i
\(23\) 5.79185i 1.20768i −0.797104 0.603842i \(-0.793636\pi\)
0.797104 0.603842i \(-0.206364\pi\)
\(24\) −1.67936 + 0.423958i −0.342799 + 0.0865400i
\(25\) −1.00000 −0.200000
\(26\) 1.15208i 0.225942i
\(27\) −3.83069 + 3.51081i −0.737217 + 0.675656i
\(28\) −2.47197 −0.467158
\(29\) −3.35873 −0.623700 −0.311850 0.950131i \(-0.600949\pi\)
−0.311850 + 0.950131i \(0.600949\pi\)
\(30\) 0.423958 + 1.67936i 0.0774037 + 0.306608i
\(31\) 4.80907i 0.863735i 0.901937 + 0.431867i \(0.142145\pi\)
−0.901937 + 0.431867i \(0.857855\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.847915 + 3.35873i 0.147603 + 0.584679i
\(34\) 6.67861i 1.14537i
\(35\) 2.47197i 0.417839i
\(36\) 2.64052 1.42396i 0.440087 0.237326i
\(37\) 11.6614i 1.91712i −0.284891 0.958560i \(-0.591957\pi\)
0.284891 0.958560i \(-0.408043\pi\)
\(38\) 4.35873 0.0388432i 0.707079 0.00630120i
\(39\) 0.488435 + 1.93477i 0.0782122 + 0.309811i
\(40\) 1.00000i 0.158114i
\(41\) 7.83069 1.22295 0.611474 0.791264i \(-0.290577\pi\)
0.611474 + 0.791264i \(0.290577\pi\)
\(42\) 4.15133 1.04801i 0.640564 0.161711i
\(43\) −0.978379 −0.149201 −0.0746007 0.997213i \(-0.523768\pi\)
−0.0746007 + 0.997213i \(0.523768\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −1.42396 2.64052i −0.212271 0.393625i
\(46\) 5.79185i 0.853962i
\(47\) 3.02162i 0.440749i 0.975415 + 0.220374i \(0.0707279\pi\)
−0.975415 + 0.220374i \(0.929272\pi\)
\(48\) −1.67936 + 0.423958i −0.242395 + 0.0611930i
\(49\) −0.889378 −0.127054
\(50\) −1.00000 −0.141421
\(51\) 2.83145 + 11.2158i 0.396482 + 1.57053i
\(52\) 1.15208i 0.159765i
\(53\) 2.33710 0.321026 0.160513 0.987034i \(-0.448685\pi\)
0.160513 + 0.987034i \(0.448685\pi\)
\(54\) −3.83069 + 3.51081i −0.521291 + 0.477761i
\(55\) −2.00000 −0.269680
\(56\) −2.47197 −0.330331
\(57\) −7.30341 + 1.91315i −0.967361 + 0.253403i
\(58\) −3.35873 −0.441022
\(59\) −12.8076 −1.66740 −0.833701 0.552216i \(-0.813783\pi\)
−0.833701 + 0.552216i \(0.813783\pi\)
\(60\) 0.423958 + 1.67936i 0.0547327 + 0.216805i
\(61\) 11.9656 1.53203 0.766016 0.642821i \(-0.222236\pi\)
0.766016 + 0.642821i \(0.222236\pi\)
\(62\) 4.80907i 0.610753i
\(63\) −6.52728 + 3.51998i −0.822360 + 0.443475i
\(64\) 1.00000 0.125000
\(65\) −1.15208 −0.142899
\(66\) 0.847915 + 3.35873i 0.104371 + 0.413431i
\(67\) 10.0183i 1.22393i 0.790883 + 0.611967i \(0.209622\pi\)
−0.790883 + 0.611967i \(0.790378\pi\)
\(68\) 6.67861i 0.809900i
\(69\) 2.45550 + 9.72662i 0.295607 + 1.17095i
\(70\) 2.47197i 0.295457i
\(71\) 7.24810 0.860192 0.430096 0.902783i \(-0.358480\pi\)
0.430096 + 0.902783i \(0.358480\pi\)
\(72\) 2.64052 1.42396i 0.311188 0.167815i
\(73\) −6.97687 −0.816581 −0.408290 0.912852i \(-0.633875\pi\)
−0.408290 + 0.912852i \(0.633875\pi\)
\(74\) 11.6614i 1.35561i
\(75\) 1.67936 0.423958i 0.193916 0.0489544i
\(76\) 4.35873 0.0388432i 0.499980 0.00445562i
\(77\) 4.94393i 0.563414i
\(78\) 0.488435 + 1.93477i 0.0553044 + 0.219069i
\(79\) 5.75301i 0.647264i −0.946183 0.323632i \(-0.895096\pi\)
0.946183 0.323632i \(-0.104904\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 4.94469 7.51998i 0.549410 0.835553i
\(82\) 7.83069 0.864755
\(83\) 11.1565i 1.22458i 0.790632 + 0.612292i \(0.209752\pi\)
−0.790632 + 0.612292i \(0.790248\pi\)
\(84\) 4.15133 1.04801i 0.452947 0.114347i
\(85\) −6.67861 −0.724397
\(86\) −0.978379 −0.105501
\(87\) 5.64052 1.42396i 0.604727 0.152664i
\(88\) 2.00000i 0.213201i
\(89\) −10.8868 −1.15399 −0.576997 0.816746i \(-0.695776\pi\)
−0.576997 + 0.816746i \(0.695776\pi\)
\(90\) −1.42396 2.64052i −0.150098 0.278335i
\(91\) 2.84792i 0.298543i
\(92\) 5.79185i 0.603842i
\(93\) −2.03884 8.07618i −0.211418 0.837461i
\(94\) 3.02162i 0.311656i
\(95\) −0.0388432 4.35873i −0.00398523 0.447196i
\(96\) −1.67936 + 0.423958i −0.171399 + 0.0432700i
\(97\) 6.94393i 0.705050i 0.935802 + 0.352525i \(0.114677\pi\)
−0.935802 + 0.352525i \(0.885323\pi\)
\(98\) −0.889378 −0.0898407
\(99\) −2.84792 5.28104i −0.286226 0.530764i
\(100\) −1.00000 −0.100000
\(101\) 16.3356i 1.62545i 0.582646 + 0.812726i \(0.302018\pi\)
−0.582646 + 0.812726i \(0.697982\pi\)
\(102\) 2.83145 + 11.2158i 0.280355 + 1.11053i
\(103\) 4.04324i 0.398392i 0.979960 + 0.199196i \(0.0638331\pi\)
−0.979960 + 0.199196i \(0.936167\pi\)
\(104\) 1.15208i 0.112971i
\(105\) −1.04801 4.15133i −0.102275 0.405128i
\(106\) 2.33710 0.227000
\(107\) −4.03294 −0.389879 −0.194939 0.980815i \(-0.562451\pi\)
−0.194939 + 0.980815i \(0.562451\pi\)
\(108\) −3.83069 + 3.51081i −0.368609 + 0.337828i
\(109\) 7.65699i 0.733406i −0.930338 0.366703i \(-0.880486\pi\)
0.930338 0.366703i \(-0.119514\pi\)
\(110\) −2.00000 −0.190693
\(111\) 4.94393 + 19.5837i 0.469257 + 1.85880i
\(112\) −2.47197 −0.233579
\(113\) 7.08749 0.666735 0.333368 0.942797i \(-0.391815\pi\)
0.333368 + 0.942797i \(0.391815\pi\)
\(114\) −7.30341 + 1.91315i −0.684027 + 0.179183i
\(115\) −5.79185 −0.540093
\(116\) −3.35873 −0.311850
\(117\) −1.64052 3.04210i −0.151666 0.281242i
\(118\) −12.8076 −1.17903
\(119\) 16.5093i 1.51341i
\(120\) 0.423958 + 1.67936i 0.0387019 + 0.153304i
\(121\) 7.00000 0.636364
\(122\) 11.9656 1.08331
\(123\) −13.1506 + 3.31988i −1.18575 + 0.299344i
\(124\) 4.80907i 0.431867i
\(125\) 1.00000i 0.0894427i
\(126\) −6.52728 + 3.51998i −0.581496 + 0.313584i
\(127\) 8.71745i 0.773549i −0.922174 0.386774i \(-0.873589\pi\)
0.922174 0.386774i \(-0.126411\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.64305 0.414791i 0.144663 0.0365203i
\(130\) −1.15208 −0.101045
\(131\) 0.795138i 0.0694715i −0.999397 0.0347358i \(-0.988941\pi\)
0.999397 0.0347358i \(-0.0110590\pi\)
\(132\) 0.847915 + 3.35873i 0.0738016 + 0.292340i
\(133\) −10.7746 + 0.0960191i −0.934279 + 0.00832591i
\(134\) 10.0183i 0.865452i
\(135\) 3.51081 + 3.83069i 0.302162 + 0.329694i
\(136\) 6.67861i 0.572686i
\(137\) 14.1480i 1.20874i 0.796703 + 0.604371i \(0.206575\pi\)
−0.796703 + 0.604371i \(0.793425\pi\)
\(138\) 2.45550 + 9.72662i 0.209026 + 0.827985i
\(139\) −5.39166 −0.457315 −0.228657 0.973507i \(-0.573434\pi\)
−0.228657 + 0.973507i \(0.573434\pi\)
\(140\) 2.47197i 0.208919i
\(141\) −1.28104 5.07440i −0.107883 0.427341i
\(142\) 7.24810 0.608247
\(143\) −2.30417 −0.192684
\(144\) 2.64052 1.42396i 0.220043 0.118663i
\(145\) 3.35873i 0.278927i
\(146\) −6.97687 −0.577410
\(147\) 1.49359 0.377059i 0.123189 0.0310993i
\(148\) 11.6614i 0.958560i
\(149\) 11.0530i 0.905501i 0.891637 + 0.452750i \(0.149557\pi\)
−0.891637 + 0.452750i \(0.850443\pi\)
\(150\) 1.67936 0.423958i 0.137119 0.0346160i
\(151\) 20.8837i 1.69949i −0.527190 0.849747i \(-0.676754\pi\)
0.527190 0.849747i \(-0.323246\pi\)
\(152\) 4.35873 0.0388432i 0.353539 0.00315060i
\(153\) −9.51006 17.6350i −0.768842 1.42571i
\(154\) 4.94393i 0.398394i
\(155\) 4.80907 0.386274
\(156\) 0.488435 + 1.93477i 0.0391061 + 0.154905i
\(157\) −1.90838 −0.152305 −0.0761526 0.997096i \(-0.524264\pi\)
−0.0761526 + 0.997096i \(0.524264\pi\)
\(158\) 5.75301i 0.457685i
\(159\) −3.92485 + 0.990834i −0.311261 + 0.0785782i
\(160\) 1.00000i 0.0790569i
\(161\) 14.3173i 1.12836i
\(162\) 4.94469 7.51998i 0.388491 0.590825i
\(163\) 14.0747 1.10241 0.551207 0.834369i \(-0.314168\pi\)
0.551207 + 0.834369i \(0.314168\pi\)
\(164\) 7.83069 0.611474
\(165\) 3.35873 0.847915i 0.261476 0.0660101i
\(166\) 11.1565i 0.865911i
\(167\) −1.92231 −0.148753 −0.0743765 0.997230i \(-0.523697\pi\)
−0.0743765 + 0.997230i \(0.523697\pi\)
\(168\) 4.15133 1.04801i 0.320282 0.0808557i
\(169\) 11.6727 0.897900
\(170\) −6.67861 −0.512226
\(171\) 11.4540 6.30921i 0.875909 0.482477i
\(172\) −0.978379 −0.0746007
\(173\) 18.2235 1.38550 0.692752 0.721176i \(-0.256398\pi\)
0.692752 + 0.721176i \(0.256398\pi\)
\(174\) 5.64052 1.42396i 0.427607 0.107950i
\(175\) 2.47197 0.186863
\(176\) 2.00000i 0.150756i
\(177\) 21.5085 5.42987i 1.61668 0.408134i
\(178\) −10.8868 −0.815997
\(179\) 4.42722 0.330906 0.165453 0.986218i \(-0.447091\pi\)
0.165453 + 0.986218i \(0.447091\pi\)
\(180\) −1.42396 2.64052i −0.106136 0.196813i
\(181\) 7.68190i 0.570991i −0.958380 0.285495i \(-0.907842\pi\)
0.958380 0.285495i \(-0.0921581\pi\)
\(182\) 2.84792i 0.211102i
\(183\) −20.0945 + 5.07289i −1.48543 + 0.374999i
\(184\) 5.79185i 0.426981i
\(185\) −11.6614 −0.857362
\(186\) −2.03884 8.07618i −0.149495 0.592174i
\(187\) −13.3572 −0.976776
\(188\) 3.02162i 0.220374i
\(189\) 9.46935 8.67861i 0.688794 0.631276i
\(190\) −0.0388432 4.35873i −0.00281798 0.316215i
\(191\) 24.0153i 1.73769i −0.495087 0.868844i \(-0.664864\pi\)
0.495087 0.868844i \(-0.335136\pi\)
\(192\) −1.67936 + 0.423958i −0.121198 + 0.0305965i
\(193\) 21.2018i 1.52614i −0.646315 0.763071i \(-0.723691\pi\)
0.646315 0.763071i \(-0.276309\pi\)
\(194\) 6.94393i 0.498545i
\(195\) 1.93477 0.488435i 0.138552 0.0349776i
\(196\) −0.889378 −0.0635270
\(197\) 6.53065i 0.465290i −0.972562 0.232645i \(-0.925262\pi\)
0.972562 0.232645i \(-0.0747380\pi\)
\(198\) −2.84792 5.28104i −0.202393 0.375307i
\(199\) 13.4020 0.950040 0.475020 0.879975i \(-0.342441\pi\)
0.475020 + 0.879975i \(0.342441\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.24735 16.8244i −0.299585 1.18670i
\(202\) 16.3356i 1.14937i
\(203\) 8.30266 0.582733
\(204\) 2.83145 + 11.2158i 0.198241 + 0.785264i
\(205\) 7.83069i 0.546919i
\(206\) 4.04324i 0.281706i
\(207\) −8.24735 15.2935i −0.573230 1.06297i
\(208\) 1.15208i 0.0798827i
\(209\) −0.0776864 8.71745i −0.00537368 0.602999i
\(210\) −1.04801 4.15133i −0.0723195 0.286469i
\(211\) 25.9010i 1.78310i 0.452926 + 0.891548i \(0.350380\pi\)
−0.452926 + 0.891548i \(0.649620\pi\)
\(212\) 2.33710 0.160513
\(213\) −12.1722 + 3.07289i −0.834025 + 0.210551i
\(214\) −4.03294 −0.275686
\(215\) 0.978379i 0.0667249i
\(216\) −3.83069 + 3.51081i −0.260646 + 0.238880i
\(217\) 11.8879i 0.807001i
\(218\) 7.65699i 0.518597i
\(219\) 11.7167 2.95790i 0.791741 0.199876i
\(220\) −2.00000 −0.134840
\(221\) −7.69432 −0.517576
\(222\) 4.94393 + 19.5837i 0.331815 + 1.31437i
\(223\) 8.18680i 0.548229i 0.961697 + 0.274114i \(0.0883847\pi\)
−0.961697 + 0.274114i \(0.911615\pi\)
\(224\) −2.47197 −0.165165
\(225\) −2.64052 + 1.42396i −0.176035 + 0.0949305i
\(226\) 7.08749 0.471453
\(227\) 11.6943 0.776179 0.388090 0.921622i \(-0.373135\pi\)
0.388090 + 0.921622i \(0.373135\pi\)
\(228\) −7.30341 + 1.91315i −0.483680 + 0.126701i
\(229\) 12.5621 0.830126 0.415063 0.909793i \(-0.363760\pi\)
0.415063 + 0.909793i \(0.363760\pi\)
\(230\) −5.79185 −0.381903
\(231\) −2.09602 8.30266i −0.137908 0.546275i
\(232\) −3.35873 −0.220511
\(233\) 13.0077i 0.852162i 0.904685 + 0.426081i \(0.140106\pi\)
−0.904685 + 0.426081i \(0.859894\pi\)
\(234\) −1.64052 3.04210i −0.107244 0.198868i
\(235\) 3.02162 0.197109
\(236\) −12.8076 −0.833701
\(237\) 2.43903 + 9.66139i 0.158432 + 0.627574i
\(238\) 16.5093i 1.07014i
\(239\) 27.0780i 1.75153i −0.482740 0.875764i \(-0.660358\pi\)
0.482740 0.875764i \(-0.339642\pi\)
\(240\) 0.423958 + 1.67936i 0.0273664 + 0.108402i
\(241\) 16.2697i 1.04803i −0.851711 0.524013i \(-0.824434\pi\)
0.851711 0.524013i \(-0.175566\pi\)
\(242\) 7.00000 0.449977
\(243\) −5.11578 + 14.7251i −0.328177 + 0.944616i
\(244\) 11.9656 0.766016
\(245\) 0.889378i 0.0568203i
\(246\) −13.1506 + 3.31988i −0.838450 + 0.211668i
\(247\) −0.0447507 5.02162i −0.00284742 0.319518i
\(248\) 4.80907i 0.305376i
\(249\) −4.72988 18.7358i −0.299744 1.18733i
\(250\) 1.00000i 0.0632456i
\(251\) 18.0088i 1.13671i 0.822785 + 0.568353i \(0.192419\pi\)
−0.822785 + 0.568353i \(0.807581\pi\)
\(252\) −6.52728 + 3.51998i −0.411180 + 0.221738i
\(253\) −11.5837 −0.728261
\(254\) 8.71745i 0.546982i
\(255\) 11.2158 2.83145i 0.702361 0.177312i
\(256\) 1.00000 0.0625000
\(257\) 0.639765 0.0399075 0.0199537 0.999801i \(-0.493648\pi\)
0.0199537 + 0.999801i \(0.493648\pi\)
\(258\) 1.64305 0.414791i 0.102292 0.0258238i
\(259\) 28.8266i 1.79120i
\(260\) −1.15208 −0.0714493
\(261\) −8.86878 + 4.78268i −0.548964 + 0.296041i
\(262\) 0.795138i 0.0491238i
\(263\) 0.186800i 0.0115186i 0.999983 + 0.00575928i \(0.00183325\pi\)
−0.999983 + 0.00575928i \(0.998167\pi\)
\(264\) 0.847915 + 3.35873i 0.0521856 + 0.206715i
\(265\) 2.33710i 0.143567i
\(266\) −10.7746 + 0.0960191i −0.660635 + 0.00588731i
\(267\) 18.2828 4.61553i 1.11889 0.282466i
\(268\) 10.0183i 0.611967i
\(269\) −2.87282 −0.175159 −0.0875796 0.996158i \(-0.527913\pi\)
−0.0875796 + 0.996158i \(0.527913\pi\)
\(270\) 3.51081 + 3.83069i 0.213661 + 0.233129i
\(271\) −15.3557 −0.932793 −0.466396 0.884576i \(-0.654448\pi\)
−0.466396 + 0.884576i \(0.654448\pi\)
\(272\) 6.67861i 0.404950i
\(273\) −1.20740 4.78268i −0.0730749 0.289461i
\(274\) 14.1480i 0.854709i
\(275\) 2.00000i 0.120605i
\(276\) 2.45550 + 9.72662i 0.147804 + 0.585474i
\(277\) 4.65370 0.279614 0.139807 0.990179i \(-0.455352\pi\)
0.139807 + 0.990179i \(0.455352\pi\)
\(278\) −5.39166 −0.323370
\(279\) 6.84792 + 12.6985i 0.409974 + 0.760236i
\(280\) 2.47197i 0.147728i
\(281\) 15.6753 0.935111 0.467556 0.883964i \(-0.345135\pi\)
0.467556 + 0.883964i \(0.345135\pi\)
\(282\) −1.28104 5.07440i −0.0762848 0.302176i
\(283\) 12.4447 0.739761 0.369881 0.929079i \(-0.379399\pi\)
0.369881 + 0.929079i \(0.379399\pi\)
\(284\) 7.24810 0.430096
\(285\) 1.91315 + 7.30341i 0.113325 + 0.432617i
\(286\) −2.30417 −0.136248
\(287\) −19.3572 −1.14262
\(288\) 2.64052 1.42396i 0.155594 0.0839075i
\(289\) −27.6038 −1.62375
\(290\) 3.35873i 0.197231i
\(291\) −2.94393 11.6614i −0.172576 0.683603i
\(292\) −6.97687 −0.408290
\(293\) −3.84312 −0.224517 −0.112259 0.993679i \(-0.535809\pi\)
−0.112259 + 0.993679i \(0.535809\pi\)
\(294\) 1.49359 0.377059i 0.0871078 0.0219905i
\(295\) 12.8076i 0.745685i
\(296\) 11.6614i 0.677804i
\(297\) 7.02162 + 7.66139i 0.407436 + 0.444559i
\(298\) 11.0530i 0.640286i
\(299\) −6.67270 −0.385892
\(300\) 1.67936 0.423958i 0.0969581 0.0244772i
\(301\) 2.41852 0.139401
\(302\) 20.8837i 1.20172i
\(303\) −6.92560 27.4334i −0.397865 1.57601i
\(304\) 4.35873 0.0388432i 0.249990 0.00222781i
\(305\) 11.9656i 0.685146i
\(306\) −9.51006 17.6350i −0.543654 1.00813i
\(307\) 4.19204i 0.239252i 0.992819 + 0.119626i \(0.0381696\pi\)
−0.992819 + 0.119626i \(0.961830\pi\)
\(308\) 4.94393i 0.281707i
\(309\) −1.71416 6.79007i −0.0975154 0.386274i
\(310\) 4.80907 0.273137
\(311\) 14.8912i 0.844400i −0.906503 0.422200i \(-0.861258\pi\)
0.906503 0.422200i \(-0.138742\pi\)
\(312\) 0.488435 + 1.93477i 0.0276522 + 0.109535i
\(313\) 6.42003 0.362882 0.181441 0.983402i \(-0.441924\pi\)
0.181441 + 0.983402i \(0.441924\pi\)
\(314\) −1.90838 −0.107696
\(315\) 3.51998 + 6.52728i 0.198328 + 0.367770i
\(316\) 5.75301i 0.323632i
\(317\) −18.0417 −1.01332 −0.506662 0.862145i \(-0.669121\pi\)
−0.506662 + 0.862145i \(0.669121\pi\)
\(318\) −3.92485 + 0.990834i −0.220095 + 0.0555632i
\(319\) 6.71745i 0.376105i
\(320\) 1.00000i 0.0559017i
\(321\) 6.77276 1.70979i 0.378019 0.0954314i
\(322\) 14.3173i 0.797870i
\(323\) −0.259419 29.1102i −0.0144344 1.61974i
\(324\) 4.94469 7.51998i 0.274705 0.417776i
\(325\) 1.15208i 0.0639062i
\(326\) 14.0747 0.779524
\(327\) 3.24624 + 12.8589i 0.179517 + 0.711097i
\(328\) 7.83069 0.432378
\(329\) 7.46935i 0.411798i
\(330\) 3.35873 0.847915i 0.184892 0.0466762i
\(331\) 23.1176i 1.27066i 0.772241 + 0.635330i \(0.219136\pi\)
−0.772241 + 0.635330i \(0.780864\pi\)
\(332\) 11.1565i 0.612292i
\(333\) −16.6053 30.7921i −0.909966 1.68740i
\(334\) −1.92231 −0.105184
\(335\) 10.0183 0.547360
\(336\) 4.15133 1.04801i 0.226474 0.0571736i
\(337\) 19.6584i 1.07086i 0.844580 + 0.535430i \(0.179850\pi\)
−0.844580 + 0.535430i \(0.820150\pi\)
\(338\) 11.6727 0.634911
\(339\) −11.9025 + 3.00480i −0.646454 + 0.163198i
\(340\) −6.67861 −0.362198
\(341\) 9.61814 0.520852
\(342\) 11.4540 6.30921i 0.619361 0.341163i
\(343\) 19.5023 1.05302
\(344\) −0.978379 −0.0527507
\(345\) 9.72662 2.45550i 0.523664 0.132200i
\(346\) 18.2235 0.979700
\(347\) 6.62583i 0.355693i 0.984058 + 0.177847i \(0.0569131\pi\)
−0.984058 + 0.177847i \(0.943087\pi\)
\(348\) 5.64052 1.42396i 0.302364 0.0763321i
\(349\) −7.09931 −0.380017 −0.190009 0.981782i \(-0.560852\pi\)
−0.190009 + 0.981782i \(0.560852\pi\)
\(350\) 2.47197 0.132132
\(351\) 4.04475 + 4.41328i 0.215893 + 0.235564i
\(352\) 2.00000i 0.106600i
\(353\) 8.98278i 0.478105i −0.971007 0.239053i \(-0.923163\pi\)
0.971007 0.239053i \(-0.0768368\pi\)
\(354\) 21.5085 5.42987i 1.14317 0.288594i
\(355\) 7.24810i 0.384689i
\(356\) −10.8868 −0.576997
\(357\) −6.99925 27.7251i −0.370439 1.46737i
\(358\) 4.42722 0.233986
\(359\) 3.28907i 0.173590i 0.996226 + 0.0867951i \(0.0276626\pi\)
−0.996226 + 0.0867951i \(0.972337\pi\)
\(360\) −1.42396 2.64052i −0.0750492 0.139168i
\(361\) 18.9970 0.338614i 0.999841 0.0178218i
\(362\) 7.68190i 0.403752i
\(363\) −11.7555 + 2.96770i −0.617006 + 0.155764i
\(364\) 2.84792i 0.149271i
\(365\) 6.97687i 0.365186i
\(366\) −20.0945 + 5.07289i −1.05036 + 0.265164i
\(367\) 24.1977 1.26311 0.631555 0.775331i \(-0.282417\pi\)
0.631555 + 0.775331i \(0.282417\pi\)
\(368\) 5.79185i 0.301921i
\(369\) 20.6771 11.1506i 1.07641 0.580476i
\(370\) −11.6614 −0.606247
\(371\) −5.77725 −0.299940
\(372\) −2.03884 8.07618i −0.105709 0.418730i
\(373\) 9.22977i 0.477899i 0.971032 + 0.238950i \(0.0768031\pi\)
−0.971032 + 0.238950i \(0.923197\pi\)
\(374\) −13.3572 −0.690685
\(375\) −0.423958 1.67936i −0.0218931 0.0867219i
\(376\) 3.02162i 0.155828i
\(377\) 3.86954i 0.199291i
\(378\) 9.46935 8.67861i 0.487051 0.446379i
\(379\) 14.8567i 0.763138i −0.924340 0.381569i \(-0.875384\pi\)
0.924340 0.381569i \(-0.124616\pi\)
\(380\) −0.0388432 4.35873i −0.00199261 0.223598i
\(381\) 3.69583 + 14.6398i 0.189343 + 0.750018i
\(382\) 24.0153i 1.22873i
\(383\) −36.7079 −1.87568 −0.937842 0.347063i \(-0.887179\pi\)
−0.937842 + 0.347063i \(0.887179\pi\)
\(384\) −1.67936 + 0.423958i −0.0856996 + 0.0216350i
\(385\) 4.94393 0.251966
\(386\) 21.2018i 1.07915i
\(387\) −2.58343 + 1.39317i −0.131323 + 0.0708188i
\(388\) 6.94393i 0.352525i
\(389\) 35.0500i 1.77711i 0.458773 + 0.888554i \(0.348289\pi\)
−0.458773 + 0.888554i \(0.651711\pi\)
\(390\) 1.93477 0.488435i 0.0979708 0.0247329i
\(391\) −38.6815 −1.95621
\(392\) −0.889378 −0.0449204
\(393\) 0.337105 + 1.33533i 0.0170047 + 0.0673583i
\(394\) 6.53065i 0.329009i
\(395\) −5.75301 −0.289465
\(396\) −2.84792 5.28104i −0.143113 0.265382i
\(397\) −38.0197 −1.90815 −0.954077 0.299560i \(-0.903160\pi\)
−0.954077 + 0.299560i \(0.903160\pi\)
\(398\) 13.4020 0.671780
\(399\) 18.0538 4.72924i 0.903821 0.236758i
\(400\) −1.00000 −0.0500000
\(401\) 38.5451 1.92485 0.962426 0.271544i \(-0.0875344\pi\)
0.962426 + 0.271544i \(0.0875344\pi\)
\(402\) −4.24735 16.8244i −0.211839 0.839126i
\(403\) 5.54046 0.275990
\(404\) 16.3356i 0.812726i
\(405\) −7.51998 4.94469i −0.373671 0.245704i
\(406\) 8.30266 0.412054
\(407\) −23.3228 −1.15607
\(408\) 2.83145 + 11.2158i 0.140178 + 0.555265i
\(409\) 7.99698i 0.395425i −0.980260 0.197713i \(-0.936649\pi\)
0.980260 0.197713i \(-0.0633513\pi\)
\(410\) 7.83069i 0.386730i
\(411\) −5.99814 23.7596i −0.295866 1.17197i
\(412\) 4.04324i 0.199196i
\(413\) 31.6599 1.55788
\(414\) −8.24735 15.2935i −0.405335 0.751634i
\(415\) 11.1565 0.547650
\(416\) 1.15208i 0.0564856i
\(417\) 9.05456 2.28584i 0.443404 0.111938i
\(418\) −0.0776864 8.71745i −0.00379977 0.426385i
\(419\) 24.7144i 1.20738i −0.797219 0.603690i \(-0.793697\pi\)
0.797219 0.603690i \(-0.206303\pi\)
\(420\) −1.04801 4.15133i −0.0511376 0.202564i
\(421\) 24.1449i 1.17675i 0.808587 + 0.588376i \(0.200233\pi\)
−0.808587 + 0.588376i \(0.799767\pi\)
\(422\) 25.9010i 1.26084i
\(423\) 4.30266 + 7.97865i 0.209203 + 0.387935i
\(424\) 2.33710 0.113500
\(425\) 6.67861i 0.323960i
\(426\) −12.1722 + 3.07289i −0.589745 + 0.148882i
\(427\) −29.5785 −1.43140
\(428\) −4.03294 −0.194939
\(429\) 3.86954 0.976870i 0.186823 0.0471637i
\(430\) 0.978379i 0.0471816i
\(431\) 34.6748 1.67022 0.835112 0.550080i \(-0.185403\pi\)
0.835112 + 0.550080i \(0.185403\pi\)
\(432\) −3.83069 + 3.51081i −0.184304 + 0.168914i
\(433\) 1.77653i 0.0853748i 0.999088 + 0.0426874i \(0.0135920\pi\)
−0.999088 + 0.0426874i \(0.986408\pi\)
\(434\) 11.8879i 0.570636i
\(435\) −1.42396 5.64052i −0.0682735 0.270442i
\(436\) 7.65699i 0.366703i
\(437\) −0.224974 25.2451i −0.0107620 1.20764i
\(438\) 11.7167 2.95790i 0.559845 0.141334i
\(439\) 11.1997i 0.534534i 0.963623 + 0.267267i \(0.0861205\pi\)
−0.963623 + 0.267267i \(0.913879\pi\)
\(440\) −2.00000 −0.0953463
\(441\) −2.34842 + 1.26644i −0.111830 + 0.0603065i
\(442\) −7.69432 −0.365982
\(443\) 0.969683i 0.0460711i 0.999735 + 0.0230355i \(0.00733308\pi\)
−0.999735 + 0.0230355i \(0.992667\pi\)
\(444\) 4.94393 + 19.5837i 0.234629 + 0.929401i
\(445\) 10.8868i 0.516082i
\(446\) 8.18680i 0.387656i
\(447\) −4.68602 18.5621i −0.221641 0.877956i
\(448\) −2.47197 −0.116789
\(449\) −19.1168 −0.902178 −0.451089 0.892479i \(-0.648964\pi\)
−0.451089 + 0.892479i \(0.648964\pi\)
\(450\) −2.64052 + 1.42396i −0.124475 + 0.0671260i
\(451\) 15.6614i 0.737466i
\(452\) 7.08749 0.333368
\(453\) 8.85382 + 35.0714i 0.415989 + 1.64780i
\(454\) 11.6943 0.548842
\(455\) 2.84792 0.133512
\(456\) −7.30341 + 1.91315i −0.342014 + 0.0895913i
\(457\) 11.1292 0.520603 0.260302 0.965527i \(-0.416178\pi\)
0.260302 + 0.965527i \(0.416178\pi\)
\(458\) 12.5621 0.586987
\(459\) 23.4473 + 25.5837i 1.09443 + 1.19414i
\(460\) −5.79185 −0.270046
\(461\) 21.2861i 0.991393i 0.868496 + 0.495696i \(0.165087\pi\)
−0.868496 + 0.495696i \(0.834913\pi\)
\(462\) −2.09602 8.30266i −0.0975156 0.386275i
\(463\) 14.2060 0.660208 0.330104 0.943945i \(-0.392916\pi\)
0.330104 + 0.943945i \(0.392916\pi\)
\(464\) −3.35873 −0.155925
\(465\) −8.07618 + 2.03884i −0.374524 + 0.0945491i
\(466\) 13.0077i 0.602569i
\(467\) 9.15124i 0.423469i −0.977327 0.211735i \(-0.932089\pi\)
0.977327 0.211735i \(-0.0679112\pi\)
\(468\) −1.64052 3.04210i −0.0758331 0.140621i
\(469\) 24.7650i 1.14354i
\(470\) 3.02162 0.139377
\(471\) 3.20486 0.809072i 0.147672 0.0372801i
\(472\) −12.8076 −0.589516
\(473\) 1.95676i 0.0899718i
\(474\) 2.43903 + 9.66139i 0.112028 + 0.443762i
\(475\) −4.35873 + 0.0388432i −0.199992 + 0.00178225i
\(476\) 16.5093i 0.756703i
\(477\) 6.17117 3.32794i 0.282559 0.152376i
\(478\) 27.0780i 1.23852i
\(479\) 1.58672i 0.0724990i 0.999343 + 0.0362495i \(0.0115411\pi\)
−0.999343 + 0.0362495i \(0.988459\pi\)
\(480\) 0.423958 + 1.67936i 0.0193509 + 0.0766521i
\(481\) −13.4349 −0.612579
\(482\) 16.2697i 0.741066i
\(483\) −6.06991 24.0439i −0.276191 1.09403i
\(484\) 7.00000 0.318182
\(485\) 6.94393 0.315308
\(486\) −5.11578 + 14.7251i −0.232056 + 0.667945i
\(487\) 16.6398i 0.754020i −0.926209 0.377010i \(-0.876952\pi\)
0.926209 0.377010i \(-0.123048\pi\)
\(488\) 11.9656 0.541655
\(489\) −23.6365 + 5.96706i −1.06888 + 0.269840i
\(490\) 0.889378i 0.0401780i
\(491\) 7.42611i 0.335135i −0.985861 0.167568i \(-0.946409\pi\)
0.985861 0.167568i \(-0.0535913\pi\)
\(492\) −13.1506 + 3.31988i −0.592874 + 0.149672i
\(493\) 22.4316i 1.01027i
\(494\) −0.0447507 5.02162i −0.00201343 0.225933i
\(495\) −5.28104 + 2.84792i −0.237365 + 0.128004i
\(496\) 4.80907i 0.215934i
\(497\) −17.9171 −0.803691
\(498\) −4.72988 18.7358i −0.211951 0.839571i
\(499\) 13.5178 0.605141 0.302571 0.953127i \(-0.402155\pi\)
0.302571 + 0.953127i \(0.402155\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) 3.22826 0.814980i 0.144228 0.0364106i
\(502\) 18.0088i 0.803772i
\(503\) 24.4696i 1.09105i 0.838096 + 0.545523i \(0.183669\pi\)
−0.838096 + 0.545523i \(0.816331\pi\)
\(504\) −6.52728 + 3.51998i −0.290748 + 0.156792i
\(505\) 16.3356 0.726924
\(506\) −11.5837 −0.514958
\(507\) −19.6027 + 4.94873i −0.870587 + 0.219781i
\(508\) 8.71745i 0.386774i
\(509\) −24.0249 −1.06488 −0.532441 0.846467i \(-0.678725\pi\)
−0.532441 + 0.846467i \(0.678725\pi\)
\(510\) 11.2158 2.83145i 0.496644 0.125379i
\(511\) 17.2466 0.762944
\(512\) 1.00000 0.0441942
\(513\) −16.5606 + 15.4515i −0.731167 + 0.682198i
\(514\) 0.639765 0.0282188
\(515\) 4.04324 0.178167
\(516\) 1.64305 0.414791i 0.0723314 0.0182602i
\(517\) 6.04324 0.265781
\(518\) 28.8266i 1.26657i
\(519\) −30.6038 + 7.72598i −1.34336 + 0.339133i
\(520\) −1.15208 −0.0505223
\(521\) 26.4016 1.15667 0.578337 0.815798i \(-0.303702\pi\)
0.578337 + 0.815798i \(0.303702\pi\)
\(522\) −8.86878 + 4.78268i −0.388176 + 0.209332i
\(523\) 3.26120i 0.142602i −0.997455 0.0713011i \(-0.977285\pi\)
0.997455 0.0713011i \(-0.0227151\pi\)
\(524\) 0.795138i 0.0347358i
\(525\) −4.15133 + 1.04801i −0.181179 + 0.0457389i
\(526\) 0.186800i 0.00814486i
\(527\) 32.1179 1.39908
\(528\) 0.847915 + 3.35873i 0.0369008 + 0.146170i
\(529\) −10.5455 −0.458501
\(530\) 2.33710i 0.101517i
\(531\) −33.8186 + 18.2374i −1.46760 + 0.791437i
\(532\) −10.7746 + 0.0960191i −0.467139 + 0.00416296i
\(533\) 9.02162i 0.390770i
\(534\) 18.2828 4.61553i 0.791175 0.199733i
\(535\) 4.03294i 0.174359i
\(536\) 10.0183i 0.432726i
\(537\) −7.43490 + 1.87695i −0.320840 + 0.0809965i
\(538\) −2.87282 −0.123856
\(539\) 1.77876i 0.0766164i
\(540\) 3.51081 + 3.83069i 0.151081 + 0.164847i
\(541\) −39.2677 −1.68825 −0.844125 0.536146i \(-0.819880\pi\)
−0.844125 + 0.536146i \(0.819880\pi\)
\(542\) −15.3557 −0.659584
\(543\) 3.25680 + 12.9007i 0.139763 + 0.553622i
\(544\) 6.67861i 0.286343i
\(545\) −7.65699 −0.327989
\(546\) −1.20740 4.78268i −0.0516718 0.204680i
\(547\) 40.5656i 1.73446i 0.497907 + 0.867231i \(0.334102\pi\)
−0.497907 + 0.867231i \(0.665898\pi\)
\(548\) 14.1480i 0.604371i
\(549\) 31.5953 17.0384i 1.34845 0.727183i
\(550\) 2.00000i 0.0852803i
\(551\) −14.6398 + 0.130464i −0.623675 + 0.00555794i
\(552\) 2.45550 + 9.72662i 0.104513 + 0.413992i
\(553\) 14.2212i 0.604749i
\(554\) 4.65370 0.197717
\(555\) 19.5837 4.94393i 0.831282 0.209858i
\(556\) −5.39166 −0.228657
\(557\) 28.4844i 1.20692i 0.797392 + 0.603461i \(0.206212\pi\)
−0.797392 + 0.603461i \(0.793788\pi\)
\(558\) 6.84792 + 12.6985i 0.289895 + 0.537568i
\(559\) 1.12718i 0.0476744i
\(560\) 2.47197i 0.104460i
\(561\) 22.4316 5.66290i 0.947064 0.239088i
\(562\) 15.6753 0.661223
\(563\) 13.8600 0.584129 0.292065 0.956399i \(-0.405658\pi\)
0.292065 + 0.956399i \(0.405658\pi\)
\(564\) −1.28104 5.07440i −0.0539415 0.213671i
\(565\) 7.08749i 0.298173i
\(566\) 12.4447 0.523090
\(567\) −12.2231 + 18.5891i −0.513322 + 0.780670i
\(568\) 7.24810 0.304124
\(569\) −33.5750 −1.40754 −0.703769 0.710429i \(-0.748501\pi\)
−0.703769 + 0.710429i \(0.748501\pi\)
\(570\) 1.91315 + 7.30341i 0.0801329 + 0.305906i
\(571\) −36.9527 −1.54642 −0.773212 0.634148i \(-0.781351\pi\)
−0.773212 + 0.634148i \(0.781351\pi\)
\(572\) −2.30417 −0.0963422
\(573\) 10.1815 + 40.3304i 0.425337 + 1.68483i
\(574\) −19.3572 −0.807955
\(575\) 5.79185i 0.241537i
\(576\) 2.64052 1.42396i 0.110022 0.0593316i
\(577\) 44.3839 1.84773 0.923863 0.382723i \(-0.125014\pi\)
0.923863 + 0.382723i \(0.125014\pi\)
\(578\) −27.6038 −1.14817
\(579\) 8.98869 + 35.6056i 0.373557 + 1.47972i
\(580\) 3.35873i 0.139464i
\(581\) 27.5785i 1.14415i
\(582\) −2.94393 11.6614i −0.122030 0.483380i
\(583\) 4.67421i 0.193586i
\(584\) −6.97687 −0.288705
\(585\) −3.04210 + 1.64052i −0.125775 + 0.0678271i
\(586\) −3.84312 −0.158758
\(587\) 17.5003i 0.722316i 0.932505 + 0.361158i \(0.117619\pi\)
−0.932505 + 0.361158i \(0.882381\pi\)
\(588\) 1.49359 0.377059i 0.0615945 0.0155496i
\(589\) 0.186800 + 20.9614i 0.00769695 + 0.863701i
\(590\) 12.8076i 0.527279i
\(591\) 2.76872 + 10.9673i 0.113890 + 0.451136i
\(592\) 11.6614i 0.479280i
\(593\) 16.9212i 0.694871i 0.937704 + 0.347435i \(0.112947\pi\)
−0.937704 + 0.347435i \(0.887053\pi\)
\(594\) 7.02162 + 7.66139i 0.288101 + 0.314350i
\(595\) 16.5093 0.676815
\(596\) 11.0530i 0.452750i
\(597\) −22.5068 + 5.68187i −0.921141 + 0.232543i
\(598\) −6.67270 −0.272867
\(599\) 29.6928 1.21322 0.606608 0.795001i \(-0.292530\pi\)
0.606608 + 0.795001i \(0.292530\pi\)
\(600\) 1.67936 0.423958i 0.0685597 0.0173080i
\(601\) 33.0304i 1.34734i 0.739033 + 0.673669i \(0.235283\pi\)
−0.739033 + 0.673669i \(0.764717\pi\)
\(602\) 2.41852 0.0985716
\(603\) 14.2657 + 26.4536i 0.580943 + 1.07727i
\(604\) 20.8837i 0.849747i
\(605\) 7.00000i 0.284590i
\(606\) −6.92560 27.4334i −0.281333 1.11441i
\(607\) 4.60310i 0.186834i −0.995627 0.0934170i \(-0.970221\pi\)
0.995627 0.0934170i \(-0.0297790\pi\)
\(608\) 4.35873 0.0388432i 0.176770 0.00157530i
\(609\) −13.9432 + 3.51998i −0.565006 + 0.142637i
\(610\) 11.9656i 0.484471i
\(611\) 3.48116 0.140833
\(612\) −9.51006 17.6350i −0.384421 0.712853i
\(613\) 20.0293 0.808976 0.404488 0.914543i \(-0.367450\pi\)
0.404488 + 0.914543i \(0.367450\pi\)
\(614\) 4.19204i 0.169177i
\(615\) 3.31988 + 13.1506i 0.133871 + 0.530282i
\(616\) 4.94393i 0.199197i
\(617\) 25.3918i 1.02223i 0.859511 + 0.511117i \(0.170768\pi\)
−0.859511 + 0.511117i \(0.829232\pi\)
\(618\) −1.71416 6.79007i −0.0689538 0.273137i
\(619\) −12.8662 −0.517138 −0.258569 0.965993i \(-0.583251\pi\)
−0.258569 + 0.965993i \(0.583251\pi\)
\(620\) 4.80907 0.193137
\(621\) 20.3341 + 22.1868i 0.815979 + 0.890326i
\(622\) 14.8912i 0.597081i
\(623\) 26.9117 1.07819
\(624\) 0.488435 + 1.93477i 0.0195531 + 0.0774527i
\(625\) 1.00000 0.0400000
\(626\) 6.42003 0.256596
\(627\) 3.82629 + 14.6068i 0.152807 + 0.583341i
\(628\) −1.90838 −0.0761526
\(629\) −77.8818 −3.10535
\(630\) 3.51998 + 6.52728i 0.140239 + 0.260053i
\(631\) −18.8977 −0.752305 −0.376152 0.926558i \(-0.622753\pi\)
−0.376152 + 0.926558i \(0.622753\pi\)
\(632\) 5.75301i 0.228842i
\(633\) −10.9809 43.4971i −0.436452 1.72886i
\(634\) −18.0417 −0.716529
\(635\) −8.71745 −0.345942
\(636\) −3.92485 + 0.990834i −0.155630 + 0.0392891i
\(637\) 1.02464i 0.0405977i
\(638\) 6.71745i 0.265946i
\(639\) 19.1388 10.3210i 0.757118 0.408292i
\(640\) 1.00000i 0.0395285i
\(641\) −27.2430 −1.07603 −0.538016 0.842934i \(-0.680826\pi\)
−0.538016 + 0.842934i \(0.680826\pi\)
\(642\) 6.77276 1.70979i 0.267300 0.0674802i
\(643\) 16.5342 0.652046 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(644\) 14.3173i 0.564179i
\(645\) −0.414791 1.64305i −0.0163324 0.0646952i
\(646\) −0.259419 29.1102i −0.0102067 1.14533i
\(647\) 47.6797i 1.87448i −0.348681 0.937242i \(-0.613370\pi\)
0.348681 0.937242i \(-0.386630\pi\)
\(648\) 4.94469 7.51998i 0.194246 0.295413i
\(649\) 25.6151i 1.00548i
\(650\) 1.15208i 0.0451885i
\(651\) 5.03995 + 19.9640i 0.197531 + 0.782453i
\(652\) 14.0747 0.551207
\(653\) 19.5374i 0.764559i −0.924047 0.382280i \(-0.875139\pi\)
0.924047 0.382280i \(-0.124861\pi\)
\(654\) 3.24624 + 12.8589i 0.126938 + 0.502821i
\(655\) −0.795138 −0.0310686
\(656\) 7.83069 0.305737
\(657\) −18.4226 + 9.93477i −0.718733 + 0.387592i
\(658\) 7.46935i 0.291186i
\(659\) −25.0743 −0.976755 −0.488377 0.872632i \(-0.662411\pi\)
−0.488377 + 0.872632i \(0.662411\pi\)
\(660\) 3.35873 0.847915i 0.130738 0.0330051i
\(661\) 23.2407i 0.903958i 0.892029 + 0.451979i \(0.149282\pi\)
−0.892029 + 0.451979i \(0.850718\pi\)
\(662\) 23.1176i 0.898493i
\(663\) 12.9216 3.26207i 0.501832 0.126688i
\(664\) 11.1565i 0.432956i
\(665\) 0.0960191 + 10.7746i 0.00372346 + 0.417822i
\(666\) −16.6053 30.7921i −0.643443 1.19317i
\(667\) 19.4532i 0.753232i
\(668\) −1.92231 −0.0743765
\(669\) −3.47086 13.7486i −0.134191 0.531552i
\(670\) 10.0183 0.387042
\(671\) 23.9311i 0.923850i
\(672\) 4.15133 1.04801i 0.160141 0.0404278i
\(673\) 14.2491i 0.549263i 0.961550 + 0.274631i \(0.0885558\pi\)
−0.961550 + 0.274631i \(0.911444\pi\)
\(674\) 19.6584i 0.757212i
\(675\) 3.83069 3.51081i 0.147443 0.135131i
\(676\) 11.6727 0.448950
\(677\) 14.9372 0.574083 0.287041 0.957918i \(-0.407328\pi\)
0.287041 + 0.957918i \(0.407328\pi\)
\(678\) −11.9025 + 3.00480i −0.457112 + 0.115399i
\(679\) 17.1652i 0.658739i
\(680\) −6.67861 −0.256113
\(681\) −19.6390 + 4.95790i −0.752569 + 0.189987i
\(682\) 9.61814 0.368298
\(683\) −31.9940 −1.22422 −0.612108 0.790775i \(-0.709678\pi\)
−0.612108 + 0.790775i \(0.709678\pi\)
\(684\) 11.4540 6.30921i 0.437954 0.241239i
\(685\) 14.1480 0.540566
\(686\) 19.5023 0.744601
\(687\) −21.0963 + 5.32579i −0.804874 + 0.203192i
\(688\) −0.978379 −0.0373004
\(689\) 2.69254i 0.102578i
\(690\) 9.72662 2.45550i 0.370286 0.0934793i
\(691\) −25.8879 −0.984821 −0.492410 0.870363i \(-0.663884\pi\)
−0.492410 + 0.870363i \(0.663884\pi\)
\(692\) 18.2235 0.692752
\(693\) 7.03995 + 13.0546i 0.267426 + 0.495902i
\(694\) 6.62583i 0.251513i
\(695\) 5.39166i 0.204517i
\(696\) 5.64052 1.42396i 0.213803 0.0539750i
\(697\) 52.2981i 1.98093i
\(698\) −7.09931 −0.268713
\(699\) −5.51471 21.8446i −0.208585 0.826240i
\(700\) 2.47197 0.0934316
\(701\) 35.2765i 1.33238i −0.745784 0.666188i \(-0.767925\pi\)
0.745784 0.666188i \(-0.232075\pi\)
\(702\) 4.04475 + 4.41328i 0.152659 + 0.166569i
\(703\) −0.452966 50.8288i −0.0170839 1.91704i
\(704\) 2.00000i 0.0753778i
\(705\) −5.07440 + 1.28104i −0.191113 + 0.0482467i
\(706\) 8.98278i 0.338071i
\(707\) 40.3811i 1.51869i
\(708\) 21.5085 5.42987i 0.808341 0.204067i
\(709\) −25.1425 −0.944248 −0.472124 0.881532i \(-0.656513\pi\)
−0.472124 + 0.881532i \(0.656513\pi\)
\(710\) 7.24810i 0.272016i
\(711\) −8.19204 15.1909i −0.307225 0.569704i
\(712\) −10.8868 −0.407999
\(713\) 27.8534 1.04312
\(714\) −6.99925 27.7251i −0.261940 1.03759i
\(715\) 2.30417i 0.0861710i
\(716\) 4.42722 0.165453
\(717\) 11.4799 + 45.4737i 0.428725 + 1.69825i
\(718\) 3.28907i 0.122747i
\(719\) 2.66769i 0.0994881i −0.998762 0.0497441i \(-0.984159\pi\)
0.998762 0.0497441i \(-0.0158406\pi\)
\(720\) −1.42396 2.64052i −0.0530678 0.0984064i
\(721\) 9.99476i 0.372224i
\(722\) 18.9970 0.338614i 0.706994 0.0126019i
\(723\) 6.89768 + 27.3228i 0.256527 + 1.01614i
\(724\) 7.68190i 0.285495i
\(725\) 3.35873 0.124740
\(726\) −11.7555 + 2.96770i −0.436289 + 0.110142i
\(727\) −27.8554 −1.03310 −0.516549 0.856257i \(-0.672784\pi\)
−0.516549 + 0.856257i \(0.672784\pi\)
\(728\) 2.84792i 0.105551i
\(729\) 2.34842 26.8977i 0.0869785 0.996210i
\(730\) 6.97687i 0.258226i
\(731\) 6.53421i 0.241677i
\(732\) −20.0945 + 5.07289i −0.742714 + 0.187499i
\(733\) 51.5235 1.90306 0.951532 0.307550i \(-0.0995090\pi\)
0.951532 + 0.307550i \(0.0995090\pi\)
\(734\) 24.1977 0.893154
\(735\) −0.377059 1.49359i −0.0139080 0.0550918i
\(736\) 5.79185i 0.213490i
\(737\) 20.0367 0.738060
\(738\) 20.6771 11.1506i 0.761135 0.410458i
\(739\) 10.0036 0.367987 0.183993 0.982927i \(-0.441097\pi\)
0.183993 + 0.982927i \(0.441097\pi\)
\(740\) −11.6614 −0.428681
\(741\) 2.20411 + 8.41415i 0.0809699 + 0.309102i
\(742\) −5.77725 −0.212089
\(743\) 9.92533 0.364125 0.182063 0.983287i \(-0.441723\pi\)
0.182063 + 0.983287i \(0.441723\pi\)
\(744\) −2.03884 8.07618i −0.0747476 0.296087i
\(745\) 11.0530 0.404952
\(746\) 9.22977i 0.337926i
\(747\) 15.8864 + 29.4589i 0.581252 + 1.07785i
\(748\) −13.3572 −0.488388
\(749\) 9.96929 0.364270
\(750\) −0.423958 1.67936i −0.0154807 0.0613217i
\(751\) 52.5936i 1.91917i −0.281422 0.959584i \(-0.590806\pi\)
0.281422 0.959584i \(-0.409194\pi\)
\(752\) 3.02162i 0.110187i
\(753\) −7.63497 30.2433i −0.278234 1.10213i
\(754\) 3.86954i 0.140920i
\(755\) −20.8837 −0.760037
\(756\) 9.46935 8.67861i 0.344397 0.315638i
\(757\) −7.97949 −0.290019 −0.145010 0.989430i \(-0.546321\pi\)
−0.145010 + 0.989430i \(0.546321\pi\)
\(758\) 14.8567i 0.539620i
\(759\) 19.4532 4.91100i 0.706108 0.178258i
\(760\) −0.0388432 4.35873i −0.00140899 0.158108i
\(761\) 18.8069i 0.681749i 0.940109 + 0.340875i \(0.110723\pi\)
−0.940109 + 0.340875i \(0.889277\pi\)
\(762\) 3.69583 + 14.6398i 0.133886 + 0.530343i
\(763\) 18.9278i 0.685233i
\(764\) 24.0153i 0.868844i
\(765\) −17.6350 + 9.51006i −0.637595 + 0.343837i
\(766\) −36.7079 −1.32631
\(767\) 14.7554i 0.532786i
\(768\) −1.67936 + 0.423958i −0.0605988 + 0.0152983i
\(769\) −1.17193 −0.0422607 −0.0211304 0.999777i \(-0.506727\pi\)
−0.0211304 + 0.999777i \(0.506727\pi\)
\(770\) 4.94393 0.178167
\(771\) −1.07440 + 0.271233i −0.0386935 + 0.00976823i
\(772\) 21.2018i 0.763071i
\(773\) 47.4582 1.70695 0.853477 0.521130i \(-0.174489\pi\)
0.853477 + 0.521130i \(0.174489\pi\)
\(774\) −2.58343 + 1.39317i −0.0928594 + 0.0500765i
\(775\) 4.80907i 0.172747i
\(776\) 6.94393i 0.249273i
\(777\) −12.2212 48.4103i −0.438435 1.73671i
\(778\) 35.0500i 1.25660i
\(779\) 34.1318 0.304169i 1.22290 0.0108980i
\(780\) 1.93477 0.488435i 0.0692758 0.0174888i
\(781\) 14.4962i 0.518715i
\(782\) −38.6815 −1.38325
\(783\) 12.8662 11.7918i 0.459802 0.421406i
\(784\) −0.889378 −0.0317635