Properties

Label 8.4.b.a.5.1
Level $8$
Weight $4$
Character 8.5
Analytic conductor $0.472$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.472015280046\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-7}) \)
Defining polynomial: \( x^{2} - x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(0.500000 + 1.32288i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.4.b.a.5.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 2.64575i) q^{2} +5.29150i q^{3} +(-6.00000 + 5.29150i) q^{4} -10.5830i q^{5} +(14.0000 - 5.29150i) q^{6} -8.00000 q^{7} +(20.0000 + 10.5830i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 - 2.64575i) q^{2} +5.29150i q^{3} +(-6.00000 + 5.29150i) q^{4} -10.5830i q^{5} +(14.0000 - 5.29150i) q^{6} -8.00000 q^{7} +(20.0000 + 10.5830i) q^{8} -1.00000 q^{9} +(-28.0000 + 10.5830i) q^{10} -15.8745i q^{11} +(-28.0000 - 31.7490i) q^{12} +52.9150i q^{13} +(8.00000 + 21.1660i) q^{14} +56.0000 q^{15} +(8.00000 - 63.4980i) q^{16} -14.0000 q^{17} +(1.00000 + 2.64575i) q^{18} -37.0405i q^{19} +(56.0000 + 63.4980i) q^{20} -42.3320i q^{21} +(-42.0000 + 15.8745i) q^{22} -152.000 q^{23} +(-56.0000 + 105.830i) q^{24} +13.0000 q^{25} +(140.000 - 52.9150i) q^{26} +137.579i q^{27} +(48.0000 - 42.3320i) q^{28} -158.745i q^{29} +(-56.0000 - 148.162i) q^{30} +224.000 q^{31} +(-176.000 + 42.3320i) q^{32} +84.0000 q^{33} +(14.0000 + 37.0405i) q^{34} +84.6640i q^{35} +(6.00000 - 5.29150i) q^{36} +243.409i q^{37} +(-98.0000 + 37.0405i) q^{38} -280.000 q^{39} +(112.000 - 211.660i) q^{40} -70.0000 q^{41} +(-112.000 + 42.3320i) q^{42} -439.195i q^{43} +(84.0000 + 95.2470i) q^{44} +10.5830i q^{45} +(152.000 + 402.154i) q^{46} +336.000 q^{47} +(336.000 + 42.3320i) q^{48} -279.000 q^{49} +(-13.0000 - 34.3948i) q^{50} -74.0810i q^{51} +(-280.000 - 317.490i) q^{52} +31.7490i q^{53} +(364.000 - 137.579i) q^{54} -168.000 q^{55} +(-160.000 - 84.6640i) q^{56} +196.000 q^{57} +(-420.000 + 158.745i) q^{58} +534.442i q^{59} +(-336.000 + 296.324i) q^{60} +95.2470i q^{61} +(-224.000 - 592.648i) q^{62} +8.00000 q^{63} +(288.000 + 423.320i) q^{64} +560.000 q^{65} +(-84.0000 - 222.243i) q^{66} +174.620i q^{67} +(84.0000 - 74.0810i) q^{68} -804.308i q^{69} +(224.000 - 84.6640i) q^{70} -72.0000 q^{71} +(-20.0000 - 10.5830i) q^{72} -294.000 q^{73} +(644.000 - 243.409i) q^{74} +68.7895i q^{75} +(196.000 + 222.243i) q^{76} +126.996i q^{77} +(280.000 + 740.810i) q^{78} -464.000 q^{79} +(-672.000 - 84.6640i) q^{80} -755.000 q^{81} +(70.0000 + 185.203i) q^{82} -545.025i q^{83} +(224.000 + 253.992i) q^{84} +148.162i q^{85} +(-1162.00 + 439.195i) q^{86} +840.000 q^{87} +(168.000 - 317.490i) q^{88} +266.000 q^{89} +(28.0000 - 10.5830i) q^{90} -423.320i q^{91} +(912.000 - 804.308i) q^{92} +1185.30i q^{93} +(-336.000 - 888.972i) q^{94} -392.000 q^{95} +(-224.000 - 931.304i) q^{96} +994.000 q^{97} +(279.000 + 738.165i) q^{98} +15.8745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 12 q^{4} + 28 q^{6} - 16 q^{7} + 40 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 12 q^{4} + 28 q^{6} - 16 q^{7} + 40 q^{8} - 2 q^{9} - 56 q^{10} - 56 q^{12} + 16 q^{14} + 112 q^{15} + 16 q^{16} - 28 q^{17} + 2 q^{18} + 112 q^{20} - 84 q^{22} - 304 q^{23} - 112 q^{24} + 26 q^{25} + 280 q^{26} + 96 q^{28} - 112 q^{30} + 448 q^{31} - 352 q^{32} + 168 q^{33} + 28 q^{34} + 12 q^{36} - 196 q^{38} - 560 q^{39} + 224 q^{40} - 140 q^{41} - 224 q^{42} + 168 q^{44} + 304 q^{46} + 672 q^{47} + 672 q^{48} - 558 q^{49} - 26 q^{50} - 560 q^{52} + 728 q^{54} - 336 q^{55} - 320 q^{56} + 392 q^{57} - 840 q^{58} - 672 q^{60} - 448 q^{62} + 16 q^{63} + 576 q^{64} + 1120 q^{65} - 168 q^{66} + 168 q^{68} + 448 q^{70} - 144 q^{71} - 40 q^{72} - 588 q^{73} + 1288 q^{74} + 392 q^{76} + 560 q^{78} - 928 q^{79} - 1344 q^{80} - 1510 q^{81} + 140 q^{82} + 448 q^{84} - 2324 q^{86} + 1680 q^{87} + 336 q^{88} + 532 q^{89} + 56 q^{90} + 1824 q^{92} - 672 q^{94} - 784 q^{95} - 448 q^{96} + 1988 q^{97} + 558 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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 2.64575i −0.353553 0.935414i
\(3\) 5.29150i 1.01835i 0.860663 + 0.509175i \(0.170049\pi\)
−0.860663 + 0.509175i \(0.829951\pi\)
\(4\) −6.00000 + 5.29150i −0.750000 + 0.661438i
\(5\) 10.5830i 0.946573i −0.880909 0.473286i \(-0.843068\pi\)
0.880909 0.473286i \(-0.156932\pi\)
\(6\) 14.0000 5.29150i 0.952579 0.360041i
\(7\) −8.00000 −0.431959 −0.215980 0.976398i \(-0.569295\pi\)
−0.215980 + 0.976398i \(0.569295\pi\)
\(8\) 20.0000 + 10.5830i 0.883883 + 0.467707i
\(9\) −1.00000 −0.0370370
\(10\) −28.0000 + 10.5830i −0.885438 + 0.334664i
\(11\) 15.8745i 0.435122i −0.976047 0.217561i \(-0.930190\pi\)
0.976047 0.217561i \(-0.0698101\pi\)
\(12\) −28.0000 31.7490i −0.673575 0.763763i
\(13\) 52.9150i 1.12892i 0.825460 + 0.564461i \(0.190916\pi\)
−0.825460 + 0.564461i \(0.809084\pi\)
\(14\) 8.00000 + 21.1660i 0.152721 + 0.404061i
\(15\) 56.0000 0.963943
\(16\) 8.00000 63.4980i 0.125000 0.992157i
\(17\) −14.0000 −0.199735 −0.0998676 0.995001i \(-0.531842\pi\)
−0.0998676 + 0.995001i \(0.531842\pi\)
\(18\) 1.00000 + 2.64575i 0.0130946 + 0.0346450i
\(19\) 37.0405i 0.447246i −0.974676 0.223623i \(-0.928212\pi\)
0.974676 0.223623i \(-0.0717885\pi\)
\(20\) 56.0000 + 63.4980i 0.626099 + 0.709930i
\(21\) 42.3320i 0.439886i
\(22\) −42.0000 + 15.8745i −0.407020 + 0.153839i
\(23\) −152.000 −1.37801 −0.689004 0.724757i \(-0.741952\pi\)
−0.689004 + 0.724757i \(0.741952\pi\)
\(24\) −56.0000 + 105.830i −0.476290 + 0.900103i
\(25\) 13.0000 0.104000
\(26\) 140.000 52.9150i 1.05601 0.399134i
\(27\) 137.579i 0.980633i
\(28\) 48.0000 42.3320i 0.323970 0.285714i
\(29\) 158.745i 1.01649i −0.861212 0.508245i \(-0.830294\pi\)
0.861212 0.508245i \(-0.169706\pi\)
\(30\) −56.0000 148.162i −0.340805 0.901686i
\(31\) 224.000 1.29779 0.648897 0.760877i \(-0.275231\pi\)
0.648897 + 0.760877i \(0.275231\pi\)
\(32\) −176.000 + 42.3320i −0.972272 + 0.233854i
\(33\) 84.0000 0.443107
\(34\) 14.0000 + 37.0405i 0.0706171 + 0.186835i
\(35\) 84.6640i 0.408881i
\(36\) 6.00000 5.29150i 0.0277778 0.0244977i
\(37\) 243.409i 1.08152i 0.841177 + 0.540760i \(0.181863\pi\)
−0.841177 + 0.540760i \(0.818137\pi\)
\(38\) −98.0000 + 37.0405i −0.418361 + 0.158125i
\(39\) −280.000 −1.14964
\(40\) 112.000 211.660i 0.442719 0.836660i
\(41\) −70.0000 −0.266638 −0.133319 0.991073i \(-0.542564\pi\)
−0.133319 + 0.991073i \(0.542564\pi\)
\(42\) −112.000 + 42.3320i −0.411476 + 0.155523i
\(43\) 439.195i 1.55759i −0.627276 0.778797i \(-0.715830\pi\)
0.627276 0.778797i \(-0.284170\pi\)
\(44\) 84.0000 + 95.2470i 0.287806 + 0.326342i
\(45\) 10.5830i 0.0350583i
\(46\) 152.000 + 402.154i 0.487200 + 1.28901i
\(47\) 336.000 1.04278 0.521390 0.853319i \(-0.325414\pi\)
0.521390 + 0.853319i \(0.325414\pi\)
\(48\) 336.000 + 42.3320i 1.01036 + 0.127294i
\(49\) −279.000 −0.813411
\(50\) −13.0000 34.3948i −0.0367696 0.0972831i
\(51\) 74.0810i 0.203400i
\(52\) −280.000 317.490i −0.746712 0.846692i
\(53\) 31.7490i 0.0822842i 0.999153 + 0.0411421i \(0.0130996\pi\)
−0.999153 + 0.0411421i \(0.986900\pi\)
\(54\) 364.000 137.579i 0.917299 0.346706i
\(55\) −168.000 −0.411875
\(56\) −160.000 84.6640i −0.381802 0.202031i
\(57\) 196.000 0.455453
\(58\) −420.000 + 158.745i −0.950840 + 0.359384i
\(59\) 534.442i 1.17929i 0.807661 + 0.589647i \(0.200733\pi\)
−0.807661 + 0.589647i \(0.799267\pi\)
\(60\) −336.000 + 296.324i −0.722957 + 0.637588i
\(61\) 95.2470i 0.199920i 0.994991 + 0.0999601i \(0.0318715\pi\)
−0.994991 + 0.0999601i \(0.968128\pi\)
\(62\) −224.000 592.648i −0.458839 1.21397i
\(63\) 8.00000 0.0159985
\(64\) 288.000 + 423.320i 0.562500 + 0.826797i
\(65\) 560.000 1.06861
\(66\) −84.0000 222.243i −0.156662 0.414488i
\(67\) 174.620i 0.318406i 0.987246 + 0.159203i \(0.0508924\pi\)
−0.987246 + 0.159203i \(0.949108\pi\)
\(68\) 84.0000 74.0810i 0.149801 0.132112i
\(69\) 804.308i 1.40329i
\(70\) 224.000 84.6640i 0.382473 0.144561i
\(71\) −72.0000 −0.120350 −0.0601748 0.998188i \(-0.519166\pi\)
−0.0601748 + 0.998188i \(0.519166\pi\)
\(72\) −20.0000 10.5830i −0.0327364 0.0173225i
\(73\) −294.000 −0.471371 −0.235686 0.971829i \(-0.575734\pi\)
−0.235686 + 0.971829i \(0.575734\pi\)
\(74\) 644.000 243.409i 1.01167 0.382375i
\(75\) 68.7895i 0.105908i
\(76\) 196.000 + 222.243i 0.295826 + 0.335435i
\(77\) 126.996i 0.187955i
\(78\) 280.000 + 740.810i 0.406458 + 1.07539i
\(79\) −464.000 −0.660811 −0.330406 0.943839i \(-0.607186\pi\)
−0.330406 + 0.943839i \(0.607186\pi\)
\(80\) −672.000 84.6640i −0.939149 0.118322i
\(81\) −755.000 −1.03567
\(82\) 70.0000 + 185.203i 0.0942708 + 0.249417i
\(83\) 545.025i 0.720774i −0.932803 0.360387i \(-0.882645\pi\)
0.932803 0.360387i \(-0.117355\pi\)
\(84\) 224.000 + 253.992i 0.290957 + 0.329914i
\(85\) 148.162i 0.189064i
\(86\) −1162.00 + 439.195i −1.45700 + 0.550693i
\(87\) 840.000 1.03514
\(88\) 168.000 317.490i 0.203510 0.384597i
\(89\) 266.000 0.316808 0.158404 0.987374i \(-0.449365\pi\)
0.158404 + 0.987374i \(0.449365\pi\)
\(90\) 28.0000 10.5830i 0.0327940 0.0123950i
\(91\) 423.320i 0.487649i
\(92\) 912.000 804.308i 1.03351 0.911467i
\(93\) 1185.30i 1.32161i
\(94\) −336.000 888.972i −0.368678 0.975431i
\(95\) −392.000 −0.423351
\(96\) −224.000 931.304i −0.238145 0.990113i
\(97\) 994.000 1.04047 0.520234 0.854024i \(-0.325845\pi\)
0.520234 + 0.854024i \(0.325845\pi\)
\(98\) 279.000 + 738.165i 0.287584 + 0.760876i
\(99\) 15.8745i 0.0161156i
\(100\) −78.0000 + 68.7895i −0.0780000 + 0.0687895i
\(101\) 751.393i 0.740262i 0.928980 + 0.370131i \(0.120687\pi\)
−0.928980 + 0.370131i \(0.879313\pi\)
\(102\) −196.000 + 74.0810i −0.190264 + 0.0719129i
\(103\) 1176.00 1.12500 0.562499 0.826798i \(-0.309840\pi\)
0.562499 + 0.826798i \(0.309840\pi\)
\(104\) −560.000 + 1058.30i −0.528005 + 0.997836i
\(105\) −448.000 −0.416384
\(106\) 84.0000 31.7490i 0.0769698 0.0290919i
\(107\) 269.867i 0.243822i −0.992541 0.121911i \(-0.961098\pi\)
0.992541 0.121911i \(-0.0389023\pi\)
\(108\) −728.000 825.474i −0.648628 0.735475i
\(109\) 1894.36i 1.66465i −0.554290 0.832324i \(-0.687010\pi\)
0.554290 0.832324i \(-0.312990\pi\)
\(110\) 168.000 + 444.486i 0.145620 + 0.385274i
\(111\) −1288.00 −1.10137
\(112\) −64.0000 + 507.984i −0.0539949 + 0.428571i
\(113\) −1710.00 −1.42357 −0.711784 0.702398i \(-0.752113\pi\)
−0.711784 + 0.702398i \(0.752113\pi\)
\(114\) −196.000 518.567i −0.161027 0.426037i
\(115\) 1608.62i 1.30439i
\(116\) 840.000 + 952.470i 0.672345 + 0.762368i
\(117\) 52.9150i 0.0418119i
\(118\) 1414.00 534.442i 1.10313 0.416944i
\(119\) 112.000 0.0862775
\(120\) 1120.00 + 592.648i 0.852013 + 0.450843i
\(121\) 1079.00 0.810669
\(122\) 252.000 95.2470i 0.187008 0.0706825i
\(123\) 370.405i 0.271531i
\(124\) −1344.00 + 1185.30i −0.973345 + 0.858409i
\(125\) 1460.45i 1.04502i
\(126\) −8.00000 21.1660i −0.00565632 0.0149652i
\(127\) −1664.00 −1.16265 −0.581323 0.813673i \(-0.697465\pi\)
−0.581323 + 0.813673i \(0.697465\pi\)
\(128\) 832.000 1185.30i 0.574524 0.818488i
\(129\) 2324.00 1.58618
\(130\) −560.000 1481.62i −0.377810 0.999590i
\(131\) 672.021i 0.448204i −0.974566 0.224102i \(-0.928055\pi\)
0.974566 0.224102i \(-0.0719449\pi\)
\(132\) −504.000 + 444.486i −0.332330 + 0.293088i
\(133\) 296.324i 0.193192i
\(134\) 462.000 174.620i 0.297841 0.112573i
\(135\) 1456.00 0.928241
\(136\) −280.000 148.162i −0.176543 0.0934176i
\(137\) −1062.00 −0.662283 −0.331142 0.943581i \(-0.607434\pi\)
−0.331142 + 0.943581i \(0.607434\pi\)
\(138\) −2128.00 + 804.308i −1.31266 + 0.496140i
\(139\) 2693.37i 1.64352i 0.569835 + 0.821759i \(0.307007\pi\)
−0.569835 + 0.821759i \(0.692993\pi\)
\(140\) −448.000 507.984i −0.270449 0.306661i
\(141\) 1777.94i 1.06191i
\(142\) 72.0000 + 190.494i 0.0425500 + 0.112577i
\(143\) 840.000 0.491219
\(144\) −8.00000 + 63.4980i −0.00462963 + 0.0367465i
\(145\) −1680.00 −0.962182
\(146\) 294.000 + 777.851i 0.166655 + 0.440927i
\(147\) 1476.33i 0.828337i
\(148\) −1288.00 1460.45i −0.715358 0.811139i
\(149\) 793.725i 0.436406i 0.975903 + 0.218203i \(0.0700195\pi\)
−0.975903 + 0.218203i \(0.929980\pi\)
\(150\) 182.000 68.7895i 0.0990683 0.0374443i
\(151\) 744.000 0.400966 0.200483 0.979697i \(-0.435749\pi\)
0.200483 + 0.979697i \(0.435749\pi\)
\(152\) 392.000 740.810i 0.209180 0.395314i
\(153\) 14.0000 0.00739760
\(154\) 336.000 126.996i 0.175816 0.0664522i
\(155\) 2370.59i 1.22846i
\(156\) 1680.00 1481.62i 0.862229 0.760414i
\(157\) 179.911i 0.0914552i 0.998954 + 0.0457276i \(0.0145606\pi\)
−0.998954 + 0.0457276i \(0.985439\pi\)
\(158\) 464.000 + 1227.63i 0.233632 + 0.618132i
\(159\) −168.000 −0.0837941
\(160\) 448.000 + 1862.61i 0.221359 + 0.920326i
\(161\) 1216.00 0.595244
\(162\) 755.000 + 1997.54i 0.366163 + 0.968776i
\(163\) 1772.65i 0.851809i −0.904768 0.425905i \(-0.859956\pi\)
0.904768 0.425905i \(-0.140044\pi\)
\(164\) 420.000 370.405i 0.199979 0.176365i
\(165\) 888.972i 0.419433i
\(166\) −1442.00 + 545.025i −0.674222 + 0.254832i
\(167\) −1960.00 −0.908200 −0.454100 0.890951i \(-0.650039\pi\)
−0.454100 + 0.890951i \(0.650039\pi\)
\(168\) 448.000 846.640i 0.205738 0.388808i
\(169\) −603.000 −0.274465
\(170\) 392.000 148.162i 0.176853 0.0668442i
\(171\) 37.0405i 0.0165647i
\(172\) 2324.00 + 2635.17i 1.03025 + 1.16820i
\(173\) 2000.19i 0.879026i 0.898236 + 0.439513i \(0.144849\pi\)
−0.898236 + 0.439513i \(0.855151\pi\)
\(174\) −840.000 2222.43i −0.365978 0.968288i
\(175\) −104.000 −0.0449238
\(176\) −1008.00 126.996i −0.431709 0.0543903i
\(177\) −2828.00 −1.20094
\(178\) −266.000 703.770i −0.112009 0.296347i
\(179\) 3264.86i 1.36328i 0.731688 + 0.681639i \(0.238733\pi\)
−0.731688 + 0.681639i \(0.761267\pi\)
\(180\) −56.0000 63.4980i −0.0231889 0.0262937i
\(181\) 2338.84i 0.960469i −0.877140 0.480235i \(-0.840552\pi\)
0.877140 0.480235i \(-0.159448\pi\)
\(182\) −1120.00 + 423.320i −0.456153 + 0.172410i
\(183\) −504.000 −0.203589
\(184\) −3040.00 1608.62i −1.21800 0.644504i
\(185\) 2576.00 1.02374
\(186\) 3136.00 1185.30i 1.23625 0.467259i
\(187\) 222.243i 0.0869092i
\(188\) −2016.00 + 1777.94i −0.782085 + 0.689734i
\(189\) 1100.63i 0.423594i
\(190\) 392.000 + 1037.13i 0.149677 + 0.396009i
\(191\) 3904.00 1.47897 0.739486 0.673172i \(-0.235069\pi\)
0.739486 + 0.673172i \(0.235069\pi\)
\(192\) −2240.00 + 1523.95i −0.841969 + 0.572822i
\(193\) 3330.00 1.24196 0.620981 0.783826i \(-0.286734\pi\)
0.620981 + 0.783826i \(0.286734\pi\)
\(194\) −994.000 2629.88i −0.367861 0.973269i
\(195\) 2963.24i 1.08822i
\(196\) 1674.00 1476.33i 0.610058 0.538021i
\(197\) 1195.88i 0.432502i −0.976338 0.216251i \(-0.930617\pi\)
0.976338 0.216251i \(-0.0693829\pi\)
\(198\) 42.0000 15.8745i 0.0150748 0.00569774i
\(199\) −1736.00 −0.618401 −0.309200 0.950997i \(-0.600061\pi\)
−0.309200 + 0.950997i \(0.600061\pi\)
\(200\) 260.000 + 137.579i 0.0919239 + 0.0486415i
\(201\) −924.000 −0.324248
\(202\) 1988.00 751.393i 0.692451 0.261722i
\(203\) 1269.96i 0.439083i
\(204\) 392.000 + 444.486i 0.134537 + 0.152550i
\(205\) 740.810i 0.252392i
\(206\) −1176.00 3111.40i −0.397747 1.05234i
\(207\) 152.000 0.0510373
\(208\) 3360.00 + 423.320i 1.12007 + 0.141115i
\(209\) −588.000 −0.194607
\(210\) 448.000 + 1185.30i 0.147214 + 0.389492i
\(211\) 2915.62i 0.951277i −0.879641 0.475638i \(-0.842217\pi\)
0.879641 0.475638i \(-0.157783\pi\)
\(212\) −168.000 190.494i −0.0544259 0.0617132i
\(213\) 380.988i 0.122558i
\(214\) −714.000 + 269.867i −0.228075 + 0.0862042i
\(215\) −4648.00 −1.47438
\(216\) −1456.00 + 2751.58i −0.458649 + 0.866766i
\(217\) −1792.00 −0.560594
\(218\) −5012.00 + 1894.36i −1.55714 + 0.588542i
\(219\) 1555.70i 0.480021i
\(220\) 1008.00 888.972i 0.308906 0.272430i
\(221\) 740.810i 0.225486i
\(222\) 1288.00 + 3407.73i 0.389391 + 1.03023i
\(223\) 1568.00 0.470857 0.235428 0.971892i \(-0.424351\pi\)
0.235428 + 0.971892i \(0.424351\pi\)
\(224\) 1408.00 338.656i 0.419982 0.101015i
\(225\) −13.0000 −0.00385185
\(226\) 1710.00 + 4524.23i 0.503308 + 1.33163i
\(227\) 1264.67i 0.369775i −0.982760 0.184888i \(-0.940808\pi\)
0.982760 0.184888i \(-0.0591922\pi\)
\(228\) −1176.00 + 1037.13i −0.341590 + 0.301254i
\(229\) 5153.92i 1.48725i 0.668595 + 0.743626i \(0.266896\pi\)
−0.668595 + 0.743626i \(0.733104\pi\)
\(230\) 4256.00 1608.62i 1.22014 0.461170i
\(231\) −672.000 −0.191404
\(232\) 1680.00 3174.90i 0.475420 0.898459i
\(233\) −838.000 −0.235619 −0.117809 0.993036i \(-0.537587\pi\)
−0.117809 + 0.993036i \(0.537587\pi\)
\(234\) −140.000 + 52.9150i −0.0391115 + 0.0147827i
\(235\) 3555.89i 0.987067i
\(236\) −2828.00 3206.65i −0.780030 0.884471i
\(237\) 2455.26i 0.672937i
\(238\) −112.000 296.324i −0.0305037 0.0807052i
\(239\) 6288.00 1.70183 0.850914 0.525305i \(-0.176049\pi\)
0.850914 + 0.525305i \(0.176049\pi\)
\(240\) 448.000 3555.89i 0.120493 0.956382i
\(241\) −2926.00 −0.782076 −0.391038 0.920375i \(-0.627884\pi\)
−0.391038 + 0.920375i \(0.627884\pi\)
\(242\) −1079.00 2854.77i −0.286615 0.758311i
\(243\) 280.450i 0.0740364i
\(244\) −504.000 571.482i −0.132235 0.149940i
\(245\) 2952.66i 0.769953i
\(246\) −980.000 + 370.405i −0.253994 + 0.0960007i
\(247\) 1960.00 0.504906
\(248\) 4480.00 + 2370.59i 1.14710 + 0.606987i
\(249\) 2884.00 0.734000
\(250\) −3864.00 + 1460.45i −0.977523 + 0.369469i
\(251\) 5444.96i 1.36925i 0.728894 + 0.684627i \(0.240035\pi\)
−0.728894 + 0.684627i \(0.759965\pi\)
\(252\) −48.0000 + 42.3320i −0.0119989 + 0.0105820i
\(253\) 2412.93i 0.599602i
\(254\) 1664.00 + 4402.53i 0.411058 + 1.08756i
\(255\) −784.000 −0.192533
\(256\) −3968.00 1015.97i −0.968750 0.248039i
\(257\) 2562.00 0.621841 0.310921 0.950436i \(-0.399363\pi\)
0.310921 + 0.950436i \(0.399363\pi\)
\(258\) −2324.00 6148.73i −0.560798 1.48373i
\(259\) 1947.27i 0.467172i
\(260\) −3360.00 + 2963.24i −0.801455 + 0.706817i
\(261\) 158.745i 0.0376478i
\(262\) −1778.00 + 672.021i −0.419257 + 0.158464i
\(263\) −5896.00 −1.38237 −0.691184 0.722679i \(-0.742911\pi\)
−0.691184 + 0.722679i \(0.742911\pi\)
\(264\) 1680.00 + 888.972i 0.391655 + 0.207244i
\(265\) 336.000 0.0778880
\(266\) 784.000 296.324i 0.180715 0.0683038i
\(267\) 1407.54i 0.322622i
\(268\) −924.000 1047.72i −0.210606 0.238804i
\(269\) 5365.58i 1.21615i −0.793878 0.608077i \(-0.791941\pi\)
0.793878 0.608077i \(-0.208059\pi\)
\(270\) −1456.00 3852.21i −0.328183 0.868290i
\(271\) −1680.00 −0.376578 −0.188289 0.982114i \(-0.560294\pi\)
−0.188289 + 0.982114i \(0.560294\pi\)
\(272\) −112.000 + 888.972i −0.0249669 + 0.198169i
\(273\) 2240.00 0.496597
\(274\) 1062.00 + 2809.79i 0.234152 + 0.619509i
\(275\) 206.369i 0.0452527i
\(276\) 4256.00 + 4825.85i 0.928192 + 1.05247i
\(277\) 1576.87i 0.342039i −0.985268 0.171019i \(-0.945294\pi\)
0.985268 0.171019i \(-0.0547061\pi\)
\(278\) 7126.00 2693.37i 1.53737 0.581072i
\(279\) −224.000 −0.0480664
\(280\) −896.000 + 1693.28i −0.191237 + 0.361403i
\(281\) −2742.00 −0.582114 −0.291057 0.956706i \(-0.594007\pi\)
−0.291057 + 0.956706i \(0.594007\pi\)
\(282\) 4704.00 1777.94i 0.993330 0.375444i
\(283\) 2989.70i 0.627983i 0.949426 + 0.313991i \(0.101666\pi\)
−0.949426 + 0.313991i \(0.898334\pi\)
\(284\) 432.000 380.988i 0.0902623 0.0796038i
\(285\) 2074.27i 0.431120i
\(286\) −840.000 2222.43i −0.173672 0.459493i
\(287\) 560.000 0.115177
\(288\) 176.000 42.3320i 0.0360101 0.00866124i
\(289\) −4717.00 −0.960106
\(290\) 1680.00 + 4444.86i 0.340183 + 0.900039i
\(291\) 5259.75i 1.05956i
\(292\) 1764.00 1555.70i 0.353528 0.311783i
\(293\) 9238.96i 1.84214i −0.389401 0.921068i \(-0.627318\pi\)
0.389401 0.921068i \(-0.372682\pi\)
\(294\) −3906.00 + 1476.33i −0.774839 + 0.292861i
\(295\) 5656.00 1.11629
\(296\) −2576.00 + 4868.18i −0.505834 + 0.955937i
\(297\) 2184.00 0.426695
\(298\) 2100.00 793.725i 0.408221 0.154293i
\(299\) 8043.08i 1.55566i
\(300\) −364.000 412.737i −0.0700518 0.0794313i
\(301\) 3513.56i 0.672818i
\(302\) −744.000 1968.44i −0.141763 0.375069i
\(303\) −3976.00 −0.753846
\(304\) −2352.00 296.324i −0.443738 0.0559058i
\(305\) 1008.00 0.189239
\(306\) −14.0000 37.0405i −0.00261545 0.00691982i
\(307\) 2587.54i 0.481039i 0.970644 + 0.240520i \(0.0773178\pi\)
−0.970644 + 0.240520i \(0.922682\pi\)
\(308\) −672.000 761.976i −0.124321 0.140966i
\(309\) 6222.81i 1.14564i
\(310\) −6272.00 + 2370.59i −1.14912 + 0.434325i
\(311\) −2744.00 −0.500315 −0.250157 0.968205i \(-0.580482\pi\)
−0.250157 + 0.968205i \(0.580482\pi\)
\(312\) −5600.00 2963.24i −1.01615 0.537694i
\(313\) 2282.00 0.412097 0.206048 0.978542i \(-0.433940\pi\)
0.206048 + 0.978542i \(0.433940\pi\)
\(314\) 476.000 179.911i 0.0855485 0.0323343i
\(315\) 84.6640i 0.0151437i
\(316\) 2784.00 2455.26i 0.495608 0.437085i
\(317\) 9577.62i 1.69695i 0.529237 + 0.848474i \(0.322478\pi\)
−0.529237 + 0.848474i \(0.677522\pi\)
\(318\) 168.000 + 444.486i 0.0296257 + 0.0783822i
\(319\) −2520.00 −0.442298
\(320\) 4480.00 3047.91i 0.782624 0.532447i
\(321\) 1428.00 0.248297
\(322\) −1216.00 3217.23i −0.210450 0.556799i
\(323\) 518.567i 0.0893308i
\(324\) 4530.00 3995.08i 0.776749 0.685028i
\(325\) 687.895i 0.117408i
\(326\) −4690.00 + 1772.65i −0.796795 + 0.301160i
\(327\) 10024.0 1.69519
\(328\) −1400.00 740.810i −0.235677 0.124709i
\(329\) −2688.00 −0.450438
\(330\) −2352.00 + 888.972i −0.392343 + 0.148292i
\(331\) 4249.08i 0.705590i −0.935701 0.352795i \(-0.885231\pi\)
0.935701 0.352795i \(-0.114769\pi\)
\(332\) 2884.00 + 3270.15i 0.476747 + 0.540580i
\(333\) 243.409i 0.0400563i
\(334\) 1960.00 + 5185.67i 0.321097 + 0.849543i
\(335\) 1848.00 0.301394
\(336\) −2688.00 338.656i −0.436436 0.0549857i
\(337\) 6130.00 0.990868 0.495434 0.868646i \(-0.335009\pi\)
0.495434 + 0.868646i \(0.335009\pi\)
\(338\) 603.000 + 1595.39i 0.0970381 + 0.256739i
\(339\) 9048.47i 1.44969i
\(340\) −784.000 888.972i −0.125054 0.141798i
\(341\) 3555.89i 0.564699i
\(342\) 98.0000 37.0405i 0.0154948 0.00585650i
\(343\) 4976.00 0.783320
\(344\) 4648.00 8783.89i 0.728498 1.37673i
\(345\) −8512.00 −1.32832
\(346\) 5292.00 2000.19i 0.822253 0.310783i
\(347\) 2481.71i 0.383935i 0.981401 + 0.191967i \(0.0614868\pi\)
−0.981401 + 0.191967i \(0.938513\pi\)
\(348\) −5040.00 + 4444.86i −0.776357 + 0.684683i
\(349\) 328.073i 0.0503191i −0.999683 0.0251595i \(-0.991991\pi\)
0.999683 0.0251595i \(-0.00800937\pi\)
\(350\) 104.000 + 275.158i 0.0158830 + 0.0420223i
\(351\) −7280.00 −1.10706
\(352\) 672.000 + 2793.91i 0.101755 + 0.423057i
\(353\) −10206.0 −1.53884 −0.769420 0.638743i \(-0.779455\pi\)
−0.769420 + 0.638743i \(0.779455\pi\)
\(354\) 2828.00 + 7482.18i 0.424595 + 1.12337i
\(355\) 761.976i 0.113920i
\(356\) −1596.00 + 1407.54i −0.237606 + 0.209549i
\(357\) 592.648i 0.0878607i
\(358\) 8638.00 3264.86i 1.27523 0.481992i
\(359\) −3176.00 −0.466916 −0.233458 0.972367i \(-0.575004\pi\)
−0.233458 + 0.972367i \(0.575004\pi\)
\(360\) −112.000 + 211.660i −0.0163970 + 0.0309874i
\(361\) 5487.00 0.799971
\(362\) −6188.00 + 2338.84i −0.898437 + 0.339577i
\(363\) 5709.53i 0.825545i
\(364\) 2240.00 + 2539.92i 0.322549 + 0.365736i
\(365\) 3111.40i 0.446187i
\(366\) 504.000 + 1333.46i 0.0719795 + 0.190440i
\(367\) −11760.0 −1.67266 −0.836331 0.548225i \(-0.815304\pi\)
−0.836331 + 0.548225i \(0.815304\pi\)
\(368\) −1216.00 + 9651.70i −0.172251 + 1.36720i
\(369\) 70.0000 0.00987549
\(370\) −2576.00 6815.46i −0.361946 0.957618i
\(371\) 253.992i 0.0355434i
\(372\) −6272.00 7111.78i −0.874161 0.991206i
\(373\) 10974.6i 1.52344i −0.647908 0.761719i \(-0.724356\pi\)
0.647908 0.761719i \(-0.275644\pi\)
\(374\) 588.000 222.243i 0.0812961 0.0307271i
\(375\) 7728.00 1.06419
\(376\) 6720.00 + 3555.89i 0.921696 + 0.487715i
\(377\) 8400.00 1.14754
\(378\) −2912.00 + 1100.63i −0.396236 + 0.149763i
\(379\) 3074.36i 0.416674i 0.978057 + 0.208337i \(0.0668051\pi\)
−0.978057 + 0.208337i \(0.933195\pi\)
\(380\) 2352.00 2074.27i 0.317513 0.280020i
\(381\) 8805.06i 1.18398i
\(382\) −3904.00 10329.0i −0.522895 1.38345i
\(383\) 2688.00 0.358617 0.179309 0.983793i \(-0.442614\pi\)
0.179309 + 0.983793i \(0.442614\pi\)
\(384\) 6272.00 + 4402.53i 0.833507 + 0.585067i
\(385\) 1344.00 0.177913
\(386\) −3330.00 8810.35i −0.439100 1.16175i
\(387\) 439.195i 0.0576887i
\(388\) −5964.00 + 5259.75i −0.780351 + 0.688205i
\(389\) 10487.8i 1.36697i 0.729966 + 0.683484i \(0.239536\pi\)
−0.729966 + 0.683484i \(0.760464\pi\)
\(390\) 7840.00 2963.24i 1.01793 0.384742i
\(391\) 2128.00 0.275237
\(392\) −5580.00 2952.66i −0.718961 0.380438i
\(393\) 3556.00 0.456429
\(394\) −3164.00 + 1195.88i −0.404569 + 0.152913i
\(395\) 4910.51i 0.625506i
\(396\) −84.0000 95.2470i −0.0106595 0.0120867i
\(397\) 5704.24i 0.721127i −0.932735 0.360564i \(-0.882584\pi\)
0.932735 0.360564i \(-0.117416\pi\)
\(398\) 1736.00 + 4593.02i 0.218638 + 0.578461i
\(399\) −1568.00 −0.196737
\(400\) 104.000 825.474i 0.0130000 0.103184i
\(401\) 12402.0 1.54445 0.772227 0.635346i \(-0.219143\pi\)
0.772227 + 0.635346i \(0.219143\pi\)
\(402\) 924.000 + 2444.67i 0.114639 + 0.303307i
\(403\) 11853.0i 1.46511i
\(404\) −3976.00 4508.36i −0.489637 0.555196i
\(405\) 7990.17i 0.980333i
\(406\) 3360.00 1269.96i 0.410724 0.155239i
\(407\) 3864.00 0.470593
\(408\) 784.000 1481.62i 0.0951318 0.179782i
\(409\) −12278.0 −1.48437 −0.742186 0.670194i \(-0.766211\pi\)
−0.742186 + 0.670194i \(0.766211\pi\)
\(410\) 1960.00 740.810i 0.236091 0.0892342i
\(411\) 5619.58i 0.674436i
\(412\) −7056.00 + 6222.81i −0.843748 + 0.744116i
\(413\) 4275.53i 0.509407i
\(414\) −152.000 402.154i −0.0180444 0.0477411i
\(415\) −5768.00 −0.682265
\(416\) −2240.00 9313.04i −0.264002 1.09762i
\(417\) −14252.0 −1.67368
\(418\) 588.000 + 1555.70i 0.0688039 + 0.182038i
\(419\) 8207.12i 0.956907i −0.878113 0.478454i \(-0.841198\pi\)
0.878113 0.478454i \(-0.158802\pi\)
\(420\) 2688.00 2370.59i 0.312288 0.275412i
\(421\) 1449.87i 0.167844i −0.996472 0.0839221i \(-0.973255\pi\)
0.996472 0.0839221i \(-0.0267447\pi\)
\(422\) −7714.00 + 2915.62i −0.889838 + 0.336327i
\(423\) −336.000 −0.0386215
\(424\) −336.000 + 634.980i −0.0384849 + 0.0727296i
\(425\) −182.000 −0.0207725
\(426\) −1008.00 + 380.988i −0.114643 + 0.0433308i
\(427\) 761.976i 0.0863574i
\(428\) 1428.00 + 1619.20i 0.161273 + 0.182867i
\(429\) 4444.86i 0.500233i
\(430\) 4648.00 + 12297.5i 0.521271 + 1.37915i
\(431\) 7632.00 0.852948 0.426474 0.904500i \(-0.359756\pi\)
0.426474 + 0.904500i \(0.359756\pi\)
\(432\) 8736.00 + 1100.63i 0.972942 + 0.122579i
\(433\) 3794.00 0.421081 0.210540 0.977585i \(-0.432478\pi\)
0.210540 + 0.977585i \(0.432478\pi\)
\(434\) 1792.00 + 4741.19i 0.198200 + 0.524388i
\(435\) 8889.72i 0.979838i
\(436\) 10024.0 + 11366.1i 1.10106 + 1.24849i
\(437\) 5630.16i 0.616309i
\(438\) −4116.00 + 1555.70i −0.449018 + 0.169713i
\(439\) −1848.00 −0.200912 −0.100456 0.994942i \(-0.532030\pi\)
−0.100456 + 0.994942i \(0.532030\pi\)
\(440\) −3360.00 1777.94i −0.364049 0.192637i
\(441\) 279.000 0.0301263
\(442\) −1960.00 + 740.810i −0.210922 + 0.0797212i
\(443\) 12334.5i 1.32287i −0.750004 0.661433i \(-0.769949\pi\)
0.750004 0.661433i \(-0.230051\pi\)
\(444\) 7728.00 6815.46i 0.826024 0.728485i
\(445\) 2815.08i 0.299882i
\(446\) −1568.00 4148.54i −0.166473 0.440446i
\(447\) −4200.00 −0.444414
\(448\) −2304.00 3386.56i −0.242977 0.357143i
\(449\) −3582.00 −0.376492 −0.188246 0.982122i \(-0.560280\pi\)
−0.188246 + 0.982122i \(0.560280\pi\)
\(450\) 13.0000 + 34.3948i 0.00136184 + 0.00360308i
\(451\) 1111.22i 0.116020i
\(452\) 10260.0 9048.47i 1.06768 0.941602i
\(453\) 3936.88i 0.408324i
\(454\) −3346.00 + 1264.67i −0.345893 + 0.130735i
\(455\) −4480.00 −0.461595
\(456\) 3920.00 + 2074.27i 0.402568 + 0.213019i
\(457\) 2714.00 0.277802 0.138901 0.990306i \(-0.455643\pi\)
0.138901 + 0.990306i \(0.455643\pi\)
\(458\) 13636.0 5153.92i 1.39120 0.525823i
\(459\) 1926.11i 0.195867i
\(460\) −8512.00 9651.70i −0.862770 0.978289i
\(461\) 8349.99i 0.843596i 0.906690 + 0.421798i \(0.138601\pi\)
−0.906690 + 0.421798i \(0.861399\pi\)
\(462\) 672.000 + 1777.94i 0.0676716 + 0.179042i
\(463\) 2224.00 0.223236 0.111618 0.993751i \(-0.464397\pi\)
0.111618 + 0.993751i \(0.464397\pi\)
\(464\) −10080.0 1269.96i −1.00852 0.127061i
\(465\) 12544.0 1.25100
\(466\) 838.000 + 2217.14i 0.0833039 + 0.220401i
\(467\) 10292.0i 1.01982i 0.860228 + 0.509910i \(0.170321\pi\)
−0.860228 + 0.509910i \(0.829679\pi\)
\(468\) 280.000 + 317.490i 0.0276560 + 0.0313589i
\(469\) 1396.96i 0.137538i
\(470\) −9408.00 + 3555.89i −0.923316 + 0.348981i
\(471\) −952.000 −0.0931334
\(472\) −5656.00 + 10688.8i −0.551565 + 1.04236i
\(473\) −6972.00 −0.677744
\(474\) −6496.00 + 2455.26i −0.629475 + 0.237919i
\(475\) 481.527i 0.0465136i
\(476\) −672.000 + 592.648i −0.0647081 + 0.0570672i
\(477\) 31.7490i 0.00304756i
\(478\) −6288.00 16636.5i −0.601687 1.59191i
\(479\) 17696.0 1.68800 0.843999 0.536345i \(-0.180195\pi\)
0.843999 + 0.536345i \(0.180195\pi\)
\(480\) −9856.00 + 2370.59i −0.937214 + 0.225421i
\(481\) −12880.0 −1.22095
\(482\) 2926.00 + 7741.47i 0.276505 + 0.731565i
\(483\) 6434.47i 0.606166i
\(484\) −6474.00 + 5709.53i −0.608002 + 0.536207i
\(485\) 10519.5i 0.984879i
\(486\) −742.000 + 280.450i −0.0692547 + 0.0261758i
\(487\) 1304.00 0.121334 0.0606672 0.998158i \(-0.480677\pi\)
0.0606672 + 0.998158i \(0.480677\pi\)
\(488\) −1008.00 + 1904.94i −0.0935041 + 0.176706i
\(489\) 9380.00 0.867440
\(490\) 7812.00 2952.66i 0.720225 0.272219i
\(491\) 16662.9i 1.53154i 0.643112 + 0.765772i \(0.277643\pi\)
−0.643112 + 0.765772i \(0.722357\pi\)
\(492\) 1960.00 + 2222.43i 0.179601 + 0.203648i
\(493\) 2222.43i 0.203029i
\(494\) −1960.00 5185.67i −0.178511 0.472296i
\(495\) 168.000 0.0152546
\(496\) 1792.00 14223.6i 0.162224 1.28761i
\(497\) 576.000 0.0519862
\(498\) −2884.00 7630.35i −0.259508 0.686594i
\(499\) 3095.53i 0.277705i 0.990313 + 0.138853i \(0.0443414\pi\)
−0.990313 + 0.138853i \(0.955659\pi\)
\(500\) 7728.00 + 8762.73i 0.691213 + 0.783762i
\(501\) 10371.3i 0.924865i
\(502\) 14406.0 5444.96i 1.28082 0.484104i
\(503\) −19320.0 −1.71260 −0.856298 0.516481i \(-0.827242\pi\)
−0.856298 + 0.516481i \(0.827242\pi\)
\(504\) 160.000 + 84.6640i 0.0141408 + 0.00748261i
\(505\) 7952.00 0.700712
\(506\) 6384.00 2412.93i 0.560876 0.211991i
\(507\) 3190.78i 0.279502i
\(508\) 9984.00 8805.06i 0.871985 0.769018i
\(509\) 4476.61i 0.389828i −0.980820 0.194914i \(-0.937557\pi\)
0.980820 0.194914i \(-0.0624427\pi\)
\(510\) 784.000 + 2074.27i 0.0680708 + 0.180098i
\(511\) 2352.00 0.203613
\(512\) 1280.00 + 11514.3i 0.110485 + 0.993878i
\(513\) 5096.00 0.438585
\(514\) −2562.00 6778.41i −0.219854 0.581679i
\(515\) 12445.6i 1.06489i
\(516\) −13944.0 + 12297.5i −1.18963 + 1.04916i
\(517\) 5333.83i 0.453737i
\(518\) −5152.00 + 1947.27i −0.437000 + 0.165170i
\(519\) −10584.0 −0.895156
\(520\) 11200.0 + 5926.48i 0.944524 + 0.499795i
\(521\) −2982.00 −0.250756 −0.125378 0.992109i \(-0.540014\pi\)
−0.125378 + 0.992109i \(0.540014\pi\)
\(522\) 420.000 158.745i 0.0352163 0.0133105i
\(523\) 2016.06i 0.168559i 0.996442 + 0.0842794i \(0.0268588\pi\)
−0.996442 + 0.0842794i \(0.973141\pi\)
\(524\) 3556.00 + 4032.12i 0.296459 + 0.336153i
\(525\) 550.316i 0.0457481i
\(526\) 5896.00 + 15599.3i 0.488741 + 1.29309i
\(527\) −3136.00 −0.259215
\(528\) 672.000 5333.83i 0.0553883 0.439631i
\(529\) 10937.0 0.898907
\(530\) −336.000 888.972i −0.0275376 0.0728575i
\(531\) 534.442i 0.0436776i
\(532\) −1568.00 1777.94i −0.127785 0.144894i
\(533\) 3704.05i 0.301014i
\(534\) 3724.00 1407.54i 0.301785 0.114064i
\(535\) −2856.00 −0.230796
\(536\) −1848.00 + 3492.39i −0.148921 + 0.281433i
\(537\) −17276.0 −1.38830
\(538\) −14196.0 + 5365.58i −1.13761 + 0.429975i
\(539\) 4428.99i 0.353933i
\(540\) −8736.00 + 7704.43i −0.696181 + 0.613974i
\(541\) 15419.4i 1.22539i 0.790321 + 0.612693i \(0.209914\pi\)
−0.790321 + 0.612693i \(0.790086\pi\)
\(542\) 1680.00 + 4444.86i 0.133141 + 0.352257i
\(543\) 12376.0 0.978094
\(544\) 2464.00 592.648i 0.194197 0.0467088i
\(545\) −20048.0 −1.57571
\(546\) −2240.00 5926.48i −0.175574 0.464524i
\(547\) 12609.7i 0.985649i −0.870129 0.492824i \(-0.835965\pi\)
0.870129 0.492824i \(-0.164035\pi\)
\(548\) 6372.00 5619.58i 0.496712 0.438059i
\(549\) 95.2470i 0.00740445i
\(550\) −546.000 + 206.369i −0.0423300 + 0.0159992i
\(551\) −5880.00 −0.454621
\(552\) 8512.00 16086.2i 0.656331 1.24035i
\(553\) 3712.00 0.285444
\(554\) −4172.00 + 1576.87i −0.319948 + 0.120929i
\(555\) 13630.9i 1.04252i
\(556\) −14252.0 16160.2i −1.08709 1.23264i
\(557\) 7143.53i 0.543413i −0.962380 0.271706i \(-0.912412\pi\)
0.962380 0.271706i \(-0.0875880\pi\)
\(558\) 224.000 + 592.648i 0.0169940 + 0.0449620i
\(559\) 23240.0 1.75840
\(560\) 5376.00 + 677.312i 0.405674 + 0.0511101i
\(561\) −1176.00 −0.0885040
\(562\) 2742.00 + 7254.65i 0.205808 + 0.544518i
\(563\) 7572.14i 0.566834i −0.958997 0.283417i \(-0.908532\pi\)
0.958997 0.283417i \(-0.0914681\pi\)
\(564\) −9408.00 10667.7i −0.702391 0.796436i
\(565\) 18096.9i 1.34751i
\(566\) 7910.00 2989.70i 0.587424 0.222025i
\(567\) 6040.00 0.447365
\(568\) −1440.00 761.976i −0.106375 0.0562884i
\(569\) 15594.0 1.14892 0.574459 0.818533i \(-0.305212\pi\)
0.574459 + 0.818533i \(0.305212\pi\)
\(570\) −5488.00 + 2074.27i −0.403275 + 0.152424i
\(571\) 16737.0i 1.22666i −0.789827 0.613330i \(-0.789830\pi\)
0.789827 0.613330i \(-0.210170\pi\)
\(572\) −5040.00 + 4444.86i −0.368414 + 0.324911i
\(573\) 20658.0i 1.50611i
\(574\) −560.000 1481.62i −0.0407212 0.107738i
\(575\) −1976.00 −0.143313
\(576\) −288.000 423.320i −0.0208333 0.0306221i
\(577\) 6594.00 0.475757 0.237879 0.971295i \(-0.423548\pi\)
0.237879 + 0.971295i \(0.423548\pi\)
\(578\) 4717.00 + 12480.0i 0.339449 + 0.898097i
\(579\) 17620.7i 1.26475i
\(580\) 10080.0 8889.72i 0.721637 0.636424i
\(581\) 4360.20i 0.311345i
\(582\) 13916.0 5259.75i 0.991128 0.374611i
\(583\) 504.000 0.0358037
\(584\) −5880.00 3111.40i −0.416637 0.220464i
\(585\) −560.000 −0.0395780
\(586\) −24444.0 + 9238.96i −1.72316 + 0.651294i
\(587\) 23213.8i 1.63226i −0.577868 0.816130i \(-0.696115\pi\)
0.577868 0.816130i \(-0.303885\pi\)
\(588\) 7812.00 + 8857.98i 0.547894 + 0.621253i
\(589\) 8297.08i 0.580433i
\(590\) −5656.00 14964.4i −0.394668 1.04419i
\(591\) 6328.00 0.440438
\(592\) 15456.0 + 1947.27i 1.07304 + 0.135190i
\(593\) 14322.0 0.991794 0.495897 0.868381i \(-0.334839\pi\)
0.495897 + 0.868381i \(0.334839\pi\)
\(594\) −2184.00 5778.32i −0.150860 0.399137i
\(595\) 1185.30i 0.0816679i
\(596\) −4200.00 4762.35i −0.288656 0.327305i
\(597\) 9186.05i 0.629749i
\(598\) −21280.0 + 8043.08i −1.45519 + 0.550010i
\(599\) −16088.0 −1.09739 −0.548696 0.836022i \(-0.684876\pi\)
−0.548696 + 0.836022i \(0.684876\pi\)
\(600\) −728.000 + 1375.79i −0.0495341 + 0.0936107i
\(601\) −21238.0 −1.44146 −0.720729 0.693217i \(-0.756193\pi\)
−0.720729 + 0.693217i \(0.756193\pi\)
\(602\) 9296.00 3513.56i 0.629363 0.237877i
\(603\) 174.620i 0.0117928i
\(604\) −4464.00 + 3936.88i −0.300724 + 0.265214i
\(605\) 11419.1i 0.767357i
\(606\) 3976.00 + 10519.5i 0.266525 + 0.705158i
\(607\) −13664.0 −0.913681 −0.456841 0.889549i \(-0.651019\pi\)
−0.456841 + 0.889549i \(0.651019\pi\)
\(608\) 1568.00 + 6519.13i 0.104590 + 0.434845i
\(609\) −6720.00 −0.447140
\(610\) −1008.00 2666.92i −0.0669061 0.177017i
\(611\) 17779.4i 1.17722i
\(612\) −84.0000 + 74.0810i −0.00554820 + 0.00489305i
\(613\) 20393.5i 1.34369i 0.740690 + 0.671846i \(0.234499\pi\)
−0.740690 + 0.671846i \(0.765501\pi\)
\(614\) 6846.00 2587.54i 0.449971 0.170073i
\(615\) −3920.00 −0.257024
\(616\) −1344.00 + 2539.92i −0.0879080 + 0.166130i
\(617\) −3782.00 −0.246771 −0.123385 0.992359i \(-0.539375\pi\)
−0.123385 + 0.992359i \(0.539375\pi\)
\(618\) 16464.0 6222.81i 1.07165 0.405045i
\(619\) 5825.94i 0.378295i 0.981949 + 0.189147i \(0.0605724\pi\)
−0.981949 + 0.189147i \(0.939428\pi\)
\(620\) 12544.0 + 14223.6i 0.812547 + 0.921342i
\(621\) 20912.0i 1.35132i
\(622\) 2744.00 + 7259.94i 0.176888 + 0.468002i
\(623\) −2128.00 −0.136848
\(624\) −2240.00 + 17779.4i −0.143705 + 1.14062i
\(625\) −13831.0 −0.885184
\(626\) −2282.00 6037.60i −0.145698 0.385481i
\(627\) 3111.40i 0.198178i
\(628\) −952.000 1079.47i −0.0604919 0.0685914i
\(629\) 3407.73i 0.216017i
\(630\) −224.000 + 84.6640i −0.0141657 + 0.00535412i
\(631\) 2056.00 0.129712 0.0648558 0.997895i \(-0.479341\pi\)
0.0648558 + 0.997895i \(0.479341\pi\)
\(632\) −9280.00 4910.51i −0.584080 0.309066i
\(633\) 15428.0 0.968733
\(634\) 25340.0 9577.62i 1.58735 0.599962i
\(635\) 17610.1i 1.10053i
\(636\) 1008.00 888.972i 0.0628456 0.0554246i
\(637\) 14763.3i 0.918278i
\(638\) 2520.00 + 6667.29i 0.156376 + 0.413731i
\(639\) 72.0000 0.00445740
\(640\) −12544.0 8805.06i −0.774758 0.543829i
\(641\) 11842.0 0.729689 0.364845 0.931068i \(-0.381122\pi\)
0.364845 + 0.931068i \(0.381122\pi\)
\(642\) −1428.00 3778.13i −0.0877861 0.232260i
\(643\) 16250.2i 0.996649i −0.866991 0.498325i \(-0.833949\pi\)
0.866991 0.498325i \(-0.166051\pi\)
\(644\) −7296.00 + 6434.47i −0.446433 + 0.393717i
\(645\) 24594.9i 1.50143i
\(646\) 1372.00 518.567i 0.0835613 0.0315832i
\(647\) 19320.0 1.17395 0.586976 0.809604i \(-0.300318\pi\)
0.586976 + 0.809604i \(0.300318\pi\)
\(648\) −15100.0 7990.17i −0.915407 0.484388i
\(649\) 8484.00 0.513137
\(650\) 1820.00 687.895i 0.109825 0.0415100i
\(651\) 9482.37i 0.570881i
\(652\) 9380.00 + 10635.9i 0.563419 + 0.638857i
\(653\) 2317.68i 0.138894i −0.997586 0.0694470i \(-0.977877\pi\)
0.997586 0.0694470i \(-0.0221235\pi\)
\(654\) −10024.0 26521.0i −0.599342 1.58571i
\(655\) −7112.00 −0.424258
\(656\) −560.000 + 4444.86i −0.0333298 + 0.264547i
\(657\) 294.000 0.0174582
\(658\) 2688.00 + 7111.78i 0.159254 + 0.421347i
\(659\) 27732.8i 1.63932i 0.572847 + 0.819662i \(0.305839\pi\)
−0.572847 + 0.819662i \(0.694161\pi\)
\(660\) 4704.00 + 5333.83i 0.277429 + 0.314575i
\(661\) 22467.7i 1.32208i 0.750352 + 0.661039i \(0.229884\pi\)
−0.750352 + 0.661039i \(0.770116\pi\)
\(662\) −11242.0 + 4249.08i −0.660019 + 0.249464i
\(663\) 3920.00 0.229623
\(664\) 5768.00 10900.5i 0.337111 0.637080i
\(665\) 3136.00 0.182870
\(666\) −644.000 + 243.409i −0.0374692 + 0.0141620i
\(667\) 24129.3i 1.40073i
\(668\) 11760.0 10371.3i 0.681150 0.600718i
\(669\) 8297.08i 0.479497i
\(670\) −1848.00 4889.35i −0.106559 0.281928i
\(671\) 1512.00 0.0869897
\(672\) 1792.00 + 7450.44i 0.102869 + 0.427689i
\(673\) −10078.0 −0.577234 −0.288617 0.957445i \(-0.593195\pi\)
−0.288617 + 0.957445i \(0.593195\pi\)
\(674\) −6130.00 16218.5i −0.350325 0.926872i
\(675\) 1788.53i 0.101986i
\(676\) 3618.00 3190.78i 0.205849 0.181542i
\(677\) 16160.2i 0.917413i 0.888588 + 0.458707i \(0.151687\pi\)
−0.888588 + 0.458707i \(0.848313\pi\)
\(678\) −23940.0 + 9048.47i −1.35606 + 0.512543i
\(679\) −7952.00 −0.449440
\(680\) −1568.00 + 2963.24i −0.0884266 + 0.167110i
\(681\) 6692.00 0.376561
\(682\) −9408.00 + 3555.89i −0.528227 + 0.199651i
\(683\) 16356.0i 0.916320i −0.888870 0.458160i \(-0.848509\pi\)
0.888870 0.458160i \(-0.151491\pi\)
\(684\) −196.000 222.243i −0.0109565 0.0124235i
\(685\) 11239.2i 0.626899i
\(686\) −4976.00 13165.3i −0.276945 0.732729i
\(687\) −27272.0 −1.51454
\(688\) −27888.0 3513.56i −1.54538 0.194699i
\(689\) −1680.00 −0.0928925
\(690\) 8512.00 + 22520.6i 0.469632 + 1.24253i
\(691\) 29246.1i 1.61009i −0.593211 0.805047i \(-0.702140\pi\)
0.593211 0.805047i \(-0.297860\pi\)
\(692\) −10584.0 12001.1i −0.581421 0.659269i
\(693\) 126.996i 0.00696130i
\(694\) 6566.00 2481.71i 0.359138 0.135742i
\(695\) 28504.0 1.55571
\(696\) 16800.0 + 8889.72i 0.914946 + 0.484144i
\(697\) 980.000 0.0532570
\(698\) −868.000 + 328.073i −0.0470692 + 0.0177905i
\(699\) 4434.28i 0.239943i
\(700\) 624.000 550.316i 0.0336928 0.0297143i
\(701\) 2465.84i 0.132858i 0.997791 + 0.0664290i \(0.0211606\pi\)
−0.997791 + 0.0664290i \(0.978839\pi\)
\(702\) 7280.00 + 19261.1i 0.391404 + 1.03556i
\(703\) 9016.00 0.483705
\(704\) 6720.00 4571.86i 0.359758 0.244756i
\(705\) 18816.0 1.00518
\(706\) 10206.0 + 27002.5i 0.544062 + 1.43945i
\(707\) 6011.15i 0.319763i
\(708\) 16968.0 14964.4i 0.900701 0.794344i
\(709\) 31674.9i 1.67782i −0.544267 0.838912i \(-0.683192\pi\)
0.544267 0.838912i \(-0.316808\pi\)
\(710\) 2016.00 761.976i 0.106562 0.0402767i
\(711\) 464.000 0.0244745
\(712\) 5320.00 + 2815.08i 0.280022 + 0.148174i
\(713\) −34048.0 −1.78837
\(714\) 1568.00 592.648i 0.0821862 0.0310635i
\(715\) 8889.72i 0.464975i
\(716\) −17276.0 19589.1i −0.901724 1.02246i
\(717\) 33273.0i 1.73306i
\(718\) 3176.00 + 8402.91i 0.165080 + 0.436760i
\(719\) −9296.00 −0.482173 −0.241086 0.970504i \(-0.577504\pi\)
−0.241086 + 0.970504i \(0.577504\pi\)
\(720\) 672.000 + 84.6640i 0.0347833 + 0.00438228i
\(721\) −9408.00 −0.485953
\(722\) −5487.00 14517.2i −0.282832 0.748304i
\(723\) 15482.9i 0.796427i
\(724\) 12376.0 + 14033.1i 0.635291 + 0.720352i
\(725\) 2063.69i 0.105715i
\(726\) 15106.0 5709.53i 0.772226 0.291874i
\(727\) 21672.0 1.10560 0.552799 0.833315i \(-0.313560\pi\)
0.552799 + 0.833315i \(0.313560\pi\)
\(728\) 4480.00 8466.40i 0.228077 0.431024i
\(729\) −18901.0 −0.960270
\(730\) 8232.00 3111.40i 0.417370 0.157751i
\(731\) 6148.73i 0.311106i
\(732\) 3024.00 2666.92i 0.152692 0.134661i
\(733\) 9471.79i 0.477283i −0.971108 0.238642i \(-0.923298\pi\)
0.971108 0.238642i \(-0.0767021\pi\)
\(734\) 11760.0 + 31114.0i 0.591375 + 1.56463i
\(735\) −15624.0 −0.784082
\(736\) 26752.0 6434.47i 1.33980 0.322252i
\(737\) 2772.00 0.138545
\(738\) −70.0000 185.203i −0.00349151 0.00923767i
\(739\) 6863.08i 0.341627i 0.985303 + 0.170814i \(0.0546396\pi\)
−0.985303 + 0.170814i \(0.945360\pi\)
\(740\) −15456.0 + 13630.9i −0.767803 + 0.677138i
\(741\) 10371.3i 0.514171i
\(742\) −672.000 + 253.992i −0.0332478 + 0.0125665i
\(743\) 17432.0 0.860724 0.430362 0.902656i \(-0.358386\pi\)
0.430362 + 0.902656i \(0.358386\pi\)
\(744\) −12544.0 + 23705.9i −0.618125 + 1.16815i
\(745\) 8400.00 0.413090
\(746\) −29036.0 + 10974.6i −1.42504 + 0.538616i
\(747\) 545.025i 0.0266953i
\(748\) −1176.00 1333.46i −0.0574851 0.0651819i
\(749\) 2158.93i 0.105321i
\(750\) −7728.00 20446.4i −0.376249 0.995461i
\(751\) −11632.0 −0.565190 −0.282595 0.959239i \(-0.591195\pi\)
−0.282595 + 0.959239i \(0.591195\pi\)
\(752\) 2688.00 21335.3i 0.130347 1.03460i
\(753\) −28812.0 −1.39438
\(754\) −8400.00 22224.3i −0.405716 1.07342i
\(755\) 7873.76i 0.379543i
\(756\) 5824.00 + 6603.80i 0.280181 + 0.317695i
\(757\) 16731.7i 0.803336i −0.915785 0.401668i \(-0.868431\pi\)
0.915785 0.401668i \(-0.131569\pi\)
\(758\) 8134.00 3074.36i 0.389763 0.147316i
\(759\) −12768.0 −0.610605
\(760\) −7840.00 4148.54i −0.374193 0.198004i
\(761\) 39466.0 1.87995 0.939975 0.341244i \(-0.110848\pi\)
0.939975 + 0.341244i \(0.110848\pi\)
\(762\) −23296.0 + 8805.06i −1.10751 + 0.418601i
\(763\) 15154.9i 0.719060i
\(764\) −23424.0 + 20658.0i −1.10923 + 0.978248i
\(765\) 148.162i 0.00700237i
\(766\) −2688.00 7111.78i −0.126790 0.335456i
\(767\) −28280.0 −1.33133
\(768\) 5376.00 20996.7i 0.252591 0.986527i
\(769\) 35266.0 1.65374 0.826869 0.562395i \(-0.190120\pi\)
0.826869 + 0.562395i \(0.190120\pi\)
\(770\) −1344.00 3555.89i −0.0629018 0.166423i
\(771\) 13556.8i 0.633252i
\(772\) −19980.0 + 17620.7i −0.931471 + 0.821481i
\(773\) 16244.9i 0.755872i 0.925832 + 0.377936i \(0.123366\pi\)