Properties

Label 378.4.g.e.163.2
Level $378$
Weight $4$
Character 378.163
Analytic conductor $22.303$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.3027219822\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 163.2
Root \(-3.50329 - 6.06788i\) of defining polynomial
Character \(\chi\) \(=\) 378.163
Dual form 378.4.g.e.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.21575 + 3.83779i) q^{5} +(-11.5959 + 14.4407i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-2.21575 + 3.83779i) q^{5} +(-11.5959 + 14.4407i) q^{7} -8.00000 q^{8} +(4.43150 + 7.67558i) q^{10} +(-19.8193 - 34.3281i) q^{11} +37.4863 q^{13} +(13.4162 + 34.5255i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(57.0112 + 98.7463i) q^{17} +(67.5634 - 117.023i) q^{19} +17.7260 q^{20} -79.2774 q^{22} +(96.1989 - 166.621i) q^{23} +(52.6809 + 91.2460i) q^{25} +(37.4863 - 64.9282i) q^{26} +(73.2160 + 11.2880i) q^{28} +129.302 q^{29} +(122.291 + 211.813i) q^{31} +(16.0000 + 27.7128i) q^{32} +228.045 q^{34} +(-29.7269 - 76.4998i) q^{35} +(-136.629 + 236.649i) q^{37} +(-135.127 - 234.047i) q^{38} +(17.7260 - 30.7023i) q^{40} +365.448 q^{41} +57.2537 q^{43} +(-79.2774 + 137.312i) q^{44} +(-192.398 - 333.243i) q^{46} +(172.495 - 298.771i) q^{47} +(-74.0693 - 334.907i) q^{49} +210.724 q^{50} +(-74.9727 - 129.856i) q^{52} +(-300.911 - 521.193i) q^{53} +175.659 q^{55} +(92.7674 - 115.526i) q^{56} +(129.302 - 223.957i) q^{58} +(15.7631 + 27.3024i) q^{59} +(-431.259 + 746.963i) q^{61} +489.162 q^{62} +64.0000 q^{64} +(-83.0604 + 143.865i) q^{65} +(341.295 + 591.141i) q^{67} +(228.045 - 394.985i) q^{68} +(-162.228 - 25.0114i) q^{70} +664.860 q^{71} +(-471.122 - 816.007i) q^{73} +(273.259 + 473.298i) q^{74} -540.507 q^{76} +(725.546 + 111.860i) q^{77} +(1.66271 - 2.87990i) q^{79} +(-35.4520 - 61.4047i) q^{80} +(365.448 - 632.975i) q^{82} -54.0900 q^{83} -505.290 q^{85} +(57.2537 - 99.1664i) q^{86} +(158.555 + 274.625i) q^{88} +(142.700 - 247.163i) q^{89} +(-434.689 + 541.330i) q^{91} -769.591 q^{92} +(-344.991 - 597.542i) q^{94} +(299.407 + 518.589i) q^{95} +240.309 q^{97} +(-654.145 - 206.615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 16 q^{4} - 4 q^{5} + 25 q^{7} - 64 q^{8} + 8 q^{10} - 56 q^{11} - 18 q^{13} + 22 q^{14} - 64 q^{16} + 118 q^{17} + 37 q^{19} + 32 q^{20} - 224 q^{22} - 200 q^{23} - 104 q^{25} - 18 q^{26} - 56 q^{28} + 524 q^{29} + 276 q^{31} + 128 q^{32} + 472 q^{34} - 290 q^{35} - 185 q^{37} - 74 q^{38} + 32 q^{40} - 60 q^{41} - 1556 q^{43} - 224 q^{44} + 400 q^{46} - 30 q^{47} - 1159 q^{49} - 416 q^{50} + 36 q^{52} - 480 q^{53} + 1456 q^{55} - 200 q^{56} + 524 q^{58} + 296 q^{59} + 474 q^{61} + 1104 q^{62} + 512 q^{64} - 1542 q^{65} + 1319 q^{67} + 472 q^{68} - 32 q^{70} + 1852 q^{71} - 1423 q^{73} + 370 q^{74} - 296 q^{76} - 1228 q^{77} + 765 q^{79} - 64 q^{80} - 60 q^{82} + 1660 q^{83} - 584 q^{85} - 1556 q^{86} + 448 q^{88} + 864 q^{89} - 738 q^{91} + 1600 q^{92} + 60 q^{94} - 1766 q^{95} + 1088 q^{97} - 2704 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −2.21575 + 3.83779i −0.198183 + 0.343263i −0.947939 0.318451i \(-0.896837\pi\)
0.749756 + 0.661714i \(0.230171\pi\)
\(6\) 0 0
\(7\) −11.5959 + 14.4407i −0.626121 + 0.779726i
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 4.43150 + 7.67558i 0.140136 + 0.242723i
\(11\) −19.8193 34.3281i −0.543251 0.940938i −0.998715 0.0506835i \(-0.983860\pi\)
0.455464 0.890254i \(-0.349473\pi\)
\(12\) 0 0
\(13\) 37.4863 0.799757 0.399878 0.916568i \(-0.369052\pi\)
0.399878 + 0.916568i \(0.369052\pi\)
\(14\) 13.4162 + 34.5255i 0.256116 + 0.659094i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 57.0112 + 98.7463i 0.813367 + 1.40879i 0.910494 + 0.413521i \(0.135701\pi\)
−0.0971273 + 0.995272i \(0.530965\pi\)
\(18\) 0 0
\(19\) 67.5634 117.023i 0.815796 1.41300i −0.0929597 0.995670i \(-0.529633\pi\)
0.908755 0.417329i \(-0.137034\pi\)
\(20\) 17.7260 0.198183
\(21\) 0 0
\(22\) −79.2774 −0.768272
\(23\) 96.1989 166.621i 0.872124 1.51056i 0.0123284 0.999924i \(-0.496076\pi\)
0.859795 0.510639i \(-0.170591\pi\)
\(24\) 0 0
\(25\) 52.6809 + 91.2460i 0.421447 + 0.729968i
\(26\) 37.4863 64.9282i 0.282757 0.489749i
\(27\) 0 0
\(28\) 73.2160 + 11.2880i 0.494161 + 0.0761867i
\(29\) 129.302 0.827957 0.413978 0.910287i \(-0.364139\pi\)
0.413978 + 0.910287i \(0.364139\pi\)
\(30\) 0 0
\(31\) 122.291 + 211.813i 0.708517 + 1.22719i 0.965407 + 0.260747i \(0.0839687\pi\)
−0.256890 + 0.966441i \(0.582698\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 228.045 1.15027
\(35\) −29.7269 76.4998i −0.143564 0.369452i
\(36\) 0 0
\(37\) −136.629 + 236.649i −0.607073 + 1.05148i 0.384647 + 0.923064i \(0.374323\pi\)
−0.991720 + 0.128418i \(0.959010\pi\)
\(38\) −135.127 234.047i −0.576855 0.999141i
\(39\) 0 0
\(40\) 17.7260 30.7023i 0.0700682 0.121362i
\(41\) 365.448 1.39203 0.696017 0.718025i \(-0.254954\pi\)
0.696017 + 0.718025i \(0.254954\pi\)
\(42\) 0 0
\(43\) 57.2537 0.203049 0.101525 0.994833i \(-0.467628\pi\)
0.101525 + 0.994833i \(0.467628\pi\)
\(44\) −79.2774 + 137.312i −0.271625 + 0.470469i
\(45\) 0 0
\(46\) −192.398 333.243i −0.616685 1.06813i
\(47\) 172.495 298.771i 0.535341 0.927238i −0.463805 0.885937i \(-0.653516\pi\)
0.999147 0.0413012i \(-0.0131503\pi\)
\(48\) 0 0
\(49\) −74.0693 334.907i −0.215946 0.976405i
\(50\) 210.724 0.596016
\(51\) 0 0
\(52\) −74.9727 129.856i −0.199939 0.346305i
\(53\) −300.911 521.193i −0.779874 1.35078i −0.932014 0.362422i \(-0.881950\pi\)
0.152140 0.988359i \(-0.451384\pi\)
\(54\) 0 0
\(55\) 175.659 0.430652
\(56\) 92.7674 115.526i 0.221367 0.275675i
\(57\) 0 0
\(58\) 129.302 223.957i 0.292727 0.507018i
\(59\) 15.7631 + 27.3024i 0.0347827 + 0.0602454i 0.882893 0.469575i \(-0.155593\pi\)
−0.848110 + 0.529820i \(0.822259\pi\)
\(60\) 0 0
\(61\) −431.259 + 746.963i −0.905199 + 1.56785i −0.0845483 + 0.996419i \(0.526945\pi\)
−0.820650 + 0.571431i \(0.806389\pi\)
\(62\) 489.162 1.00199
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −83.0604 + 143.865i −0.158498 + 0.274527i
\(66\) 0 0
\(67\) 341.295 + 591.141i 0.622326 + 1.07790i 0.989051 + 0.147571i \(0.0471456\pi\)
−0.366725 + 0.930329i \(0.619521\pi\)
\(68\) 228.045 394.985i 0.406684 0.704397i
\(69\) 0 0
\(70\) −162.228 25.0114i −0.277000 0.0427061i
\(71\) 664.860 1.11133 0.555665 0.831406i \(-0.312464\pi\)
0.555665 + 0.831406i \(0.312464\pi\)
\(72\) 0 0
\(73\) −471.122 816.007i −0.755351 1.30831i −0.945199 0.326494i \(-0.894133\pi\)
0.189848 0.981813i \(-0.439200\pi\)
\(74\) 273.259 + 473.298i 0.429266 + 0.743510i
\(75\) 0 0
\(76\) −540.507 −0.815796
\(77\) 725.546 + 111.860i 1.07381 + 0.165554i
\(78\) 0 0
\(79\) 1.66271 2.87990i 0.00236797 0.00410145i −0.864839 0.502049i \(-0.832580\pi\)
0.867207 + 0.497948i \(0.165913\pi\)
\(80\) −35.4520 61.4047i −0.0495457 0.0858156i
\(81\) 0 0
\(82\) 365.448 632.975i 0.492159 0.852444i
\(83\) −54.0900 −0.0715319 −0.0357660 0.999360i \(-0.511387\pi\)
−0.0357660 + 0.999360i \(0.511387\pi\)
\(84\) 0 0
\(85\) −505.290 −0.644781
\(86\) 57.2537 99.1664i 0.0717887 0.124342i
\(87\) 0 0
\(88\) 158.555 + 274.625i 0.192068 + 0.332672i
\(89\) 142.700 247.163i 0.169957 0.294374i −0.768448 0.639913i \(-0.778971\pi\)
0.938404 + 0.345539i \(0.112304\pi\)
\(90\) 0 0
\(91\) −434.689 + 541.330i −0.500744 + 0.623591i
\(92\) −769.591 −0.872124
\(93\) 0 0
\(94\) −344.991 597.542i −0.378543 0.655656i
\(95\) 299.407 + 518.589i 0.323353 + 0.560064i
\(96\) 0 0
\(97\) 240.309 0.251543 0.125771 0.992059i \(-0.459859\pi\)
0.125771 + 0.992059i \(0.459859\pi\)
\(98\) −654.145 206.615i −0.674272 0.212972i
\(99\) 0 0
\(100\) 210.724 364.984i 0.210724 0.364984i
\(101\) −222.821 385.937i −0.219520 0.380220i 0.735141 0.677914i \(-0.237116\pi\)
−0.954661 + 0.297694i \(0.903782\pi\)
\(102\) 0 0
\(103\) 423.094 732.821i 0.404745 0.701039i −0.589547 0.807734i \(-0.700694\pi\)
0.994292 + 0.106695i \(0.0340270\pi\)
\(104\) −299.891 −0.282757
\(105\) 0 0
\(106\) −1203.64 −1.10291
\(107\) −281.156 + 486.976i −0.254022 + 0.439979i −0.964629 0.263610i \(-0.915087\pi\)
0.710607 + 0.703589i \(0.248420\pi\)
\(108\) 0 0
\(109\) 557.817 + 966.168i 0.490176 + 0.849010i 0.999936 0.0113064i \(-0.00359902\pi\)
−0.509760 + 0.860317i \(0.670266\pi\)
\(110\) 175.659 304.250i 0.152258 0.263719i
\(111\) 0 0
\(112\) −107.329 276.204i −0.0905506 0.233025i
\(113\) 1518.31 1.26399 0.631995 0.774972i \(-0.282236\pi\)
0.631995 + 0.774972i \(0.282236\pi\)
\(114\) 0 0
\(115\) 426.305 + 738.382i 0.345680 + 0.598735i
\(116\) −258.604 447.915i −0.206989 0.358516i
\(117\) 0 0
\(118\) 63.0523 0.0491901
\(119\) −2087.06 321.771i −1.60774 0.247871i
\(120\) 0 0
\(121\) −120.113 + 208.041i −0.0902423 + 0.156304i
\(122\) 862.519 + 1493.93i 0.640072 + 1.10864i
\(123\) 0 0
\(124\) 489.162 847.253i 0.354258 0.613594i
\(125\) −1020.85 −0.730460
\(126\) 0 0
\(127\) −803.079 −0.561116 −0.280558 0.959837i \(-0.590519\pi\)
−0.280558 + 0.959837i \(0.590519\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 166.121 + 287.730i 0.112075 + 0.194120i
\(131\) −445.107 + 770.948i −0.296864 + 0.514183i −0.975417 0.220368i \(-0.929274\pi\)
0.678553 + 0.734552i \(0.262607\pi\)
\(132\) 0 0
\(133\) 906.442 + 2332.66i 0.590966 + 1.52081i
\(134\) 1365.18 0.880102
\(135\) 0 0
\(136\) −456.089 789.970i −0.287569 0.498084i
\(137\) −1022.28 1770.64i −0.637514 1.10421i −0.985976 0.166884i \(-0.946629\pi\)
0.348462 0.937323i \(-0.386704\pi\)
\(138\) 0 0
\(139\) 587.471 0.358479 0.179240 0.983805i \(-0.442636\pi\)
0.179240 + 0.983805i \(0.442636\pi\)
\(140\) −205.549 + 255.976i −0.124086 + 0.154528i
\(141\) 0 0
\(142\) 664.860 1151.57i 0.392914 0.680547i
\(143\) −742.955 1286.84i −0.434468 0.752521i
\(144\) 0 0
\(145\) −286.501 + 496.233i −0.164087 + 0.284207i
\(146\) −1884.49 −1.06823
\(147\) 0 0
\(148\) 1093.03 0.607073
\(149\) −1356.66 + 2349.80i −0.745918 + 1.29197i 0.203847 + 0.979003i \(0.434655\pi\)
−0.949765 + 0.312964i \(0.898678\pi\)
\(150\) 0 0
\(151\) 83.2159 + 144.134i 0.0448478 + 0.0776786i 0.887578 0.460658i \(-0.152386\pi\)
−0.842730 + 0.538336i \(0.819053\pi\)
\(152\) −540.507 + 936.186i −0.288427 + 0.499571i
\(153\) 0 0
\(154\) 919.294 1144.82i 0.481031 0.599042i
\(155\) −1083.86 −0.561663
\(156\) 0 0
\(157\) 267.786 + 463.819i 0.136125 + 0.235776i 0.926027 0.377458i \(-0.123202\pi\)
−0.789901 + 0.613234i \(0.789868\pi\)
\(158\) −3.32542 5.75980i −0.00167441 0.00290016i
\(159\) 0 0
\(160\) −141.808 −0.0700682
\(161\) 1290.62 + 3321.31i 0.631770 + 1.62581i
\(162\) 0 0
\(163\) −601.378 + 1041.62i −0.288979 + 0.500526i −0.973566 0.228404i \(-0.926649\pi\)
0.684587 + 0.728931i \(0.259982\pi\)
\(164\) −730.896 1265.95i −0.348009 0.602769i
\(165\) 0 0
\(166\) −54.0900 + 93.6866i −0.0252903 + 0.0438042i
\(167\) 3467.14 1.60656 0.803279 0.595604i \(-0.203087\pi\)
0.803279 + 0.595604i \(0.203087\pi\)
\(168\) 0 0
\(169\) −791.774 −0.360389
\(170\) −505.290 + 875.188i −0.227965 + 0.394846i
\(171\) 0 0
\(172\) −114.507 198.333i −0.0507623 0.0879229i
\(173\) −208.096 + 360.433i −0.0914524 + 0.158400i −0.908122 0.418705i \(-0.862484\pi\)
0.816670 + 0.577105i \(0.195818\pi\)
\(174\) 0 0
\(175\) −1928.54 297.331i −0.833052 0.128435i
\(176\) 634.219 0.271625
\(177\) 0 0
\(178\) −285.400 494.327i −0.120178 0.208154i
\(179\) −187.817 325.309i −0.0784251 0.135836i 0.824145 0.566378i \(-0.191656\pi\)
−0.902571 + 0.430542i \(0.858322\pi\)
\(180\) 0 0
\(181\) 2201.29 0.903981 0.451990 0.892023i \(-0.350714\pi\)
0.451990 + 0.892023i \(0.350714\pi\)
\(182\) 502.923 + 1294.23i 0.204830 + 0.527115i
\(183\) 0 0
\(184\) −769.591 + 1332.97i −0.308342 + 0.534065i
\(185\) −605.473 1048.71i −0.240623 0.416771i
\(186\) 0 0
\(187\) 2259.85 3914.17i 0.883724 1.53066i
\(188\) −1379.96 −0.535341
\(189\) 0 0
\(190\) 1197.63 0.457290
\(191\) −2176.64 + 3770.05i −0.824587 + 1.42823i 0.0776467 + 0.996981i \(0.475259\pi\)
−0.902234 + 0.431246i \(0.858074\pi\)
\(192\) 0 0
\(193\) 1113.21 + 1928.14i 0.415184 + 0.719121i 0.995448 0.0953083i \(-0.0303837\pi\)
−0.580263 + 0.814429i \(0.697050\pi\)
\(194\) 240.309 416.227i 0.0889339 0.154038i
\(195\) 0 0
\(196\) −1012.01 + 926.398i −0.368810 + 0.337609i
\(197\) −3746.39 −1.35492 −0.677460 0.735559i \(-0.736919\pi\)
−0.677460 + 0.735559i \(0.736919\pi\)
\(198\) 0 0
\(199\) 1432.02 + 2480.33i 0.510116 + 0.883547i 0.999931 + 0.0117211i \(0.00373101\pi\)
−0.489815 + 0.871826i \(0.662936\pi\)
\(200\) −421.447 729.968i −0.149004 0.258083i
\(201\) 0 0
\(202\) −891.284 −0.310448
\(203\) −1499.37 + 1867.21i −0.518401 + 0.645579i
\(204\) 0 0
\(205\) −809.742 + 1402.51i −0.275877 + 0.477833i
\(206\) −846.189 1465.64i −0.286198 0.495709i
\(207\) 0 0
\(208\) −299.891 + 519.426i −0.0999696 + 0.173152i
\(209\) −5356.25 −1.77273
\(210\) 0 0
\(211\) 3729.13 1.21670 0.608350 0.793669i \(-0.291832\pi\)
0.608350 + 0.793669i \(0.291832\pi\)
\(212\) −1203.64 + 2084.77i −0.389937 + 0.675391i
\(213\) 0 0
\(214\) 562.311 + 973.952i 0.179621 + 0.311112i
\(215\) −126.860 + 219.728i −0.0402408 + 0.0696992i
\(216\) 0 0
\(217\) −4476.81 690.207i −1.40049 0.215918i
\(218\) 2231.27 0.693214
\(219\) 0 0
\(220\) −351.318 608.500i −0.107663 0.186478i
\(221\) 2137.14 + 3701.64i 0.650496 + 1.12669i
\(222\) 0 0
\(223\) 152.890 0.0459115 0.0229557 0.999736i \(-0.492692\pi\)
0.0229557 + 0.999736i \(0.492692\pi\)
\(224\) −585.728 90.3039i −0.174712 0.0269361i
\(225\) 0 0
\(226\) 1518.31 2629.80i 0.446888 0.774033i
\(227\) −1693.04 2932.43i −0.495027 0.857411i 0.504957 0.863144i \(-0.331508\pi\)
−0.999984 + 0.00573340i \(0.998175\pi\)
\(228\) 0 0
\(229\) 386.178 668.880i 0.111438 0.193017i −0.804912 0.593394i \(-0.797788\pi\)
0.916350 + 0.400377i \(0.131121\pi\)
\(230\) 1705.22 0.488865
\(231\) 0 0
\(232\) −1034.41 −0.292727
\(233\) 1781.93 3086.39i 0.501021 0.867794i −0.498978 0.866614i \(-0.666291\pi\)
0.999999 0.00117935i \(-0.000375398\pi\)
\(234\) 0 0
\(235\) 764.413 + 1324.00i 0.212191 + 0.367525i
\(236\) 63.0523 109.210i 0.0173913 0.0301227i
\(237\) 0 0
\(238\) −2644.39 + 3293.13i −0.720211 + 0.896899i
\(239\) 5832.92 1.57866 0.789331 0.613968i \(-0.210428\pi\)
0.789331 + 0.613968i \(0.210428\pi\)
\(240\) 0 0
\(241\) −1846.61 3198.42i −0.493570 0.854889i 0.506402 0.862297i \(-0.330975\pi\)
−0.999973 + 0.00740841i \(0.997642\pi\)
\(242\) 240.225 + 416.082i 0.0638110 + 0.110524i
\(243\) 0 0
\(244\) 3450.08 0.905199
\(245\) 1449.42 + 457.808i 0.377960 + 0.119381i
\(246\) 0 0
\(247\) 2532.71 4386.78i 0.652438 1.13006i
\(248\) −978.324 1694.51i −0.250499 0.433876i
\(249\) 0 0
\(250\) −1020.85 + 1768.16i −0.258257 + 0.447313i
\(251\) −1571.78 −0.395259 −0.197630 0.980277i \(-0.563324\pi\)
−0.197630 + 0.980277i \(0.563324\pi\)
\(252\) 0 0
\(253\) −7626.39 −1.89513
\(254\) −803.079 + 1390.97i −0.198384 + 0.343612i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1826.14 3162.97i 0.443236 0.767707i −0.554692 0.832056i \(-0.687164\pi\)
0.997927 + 0.0643490i \(0.0204971\pi\)
\(258\) 0 0
\(259\) −1833.04 4717.19i −0.439767 1.13171i
\(260\) 664.483 0.158498
\(261\) 0 0
\(262\) 890.214 + 1541.90i 0.209914 + 0.363582i
\(263\) −355.268 615.342i −0.0832956 0.144272i 0.821368 0.570399i \(-0.193211\pi\)
−0.904664 + 0.426126i \(0.859878\pi\)
\(264\) 0 0
\(265\) 2666.98 0.618230
\(266\) 4946.72 + 762.655i 1.14024 + 0.175795i
\(267\) 0 0
\(268\) 1365.18 2364.56i 0.311163 0.538950i
\(269\) 4.13321 + 7.15894i 0.000936827 + 0.00162263i 0.866493 0.499188i \(-0.166368\pi\)
−0.865557 + 0.500811i \(0.833035\pi\)
\(270\) 0 0
\(271\) 1361.85 2358.79i 0.305264 0.528732i −0.672056 0.740500i \(-0.734589\pi\)
0.977320 + 0.211768i \(0.0679221\pi\)
\(272\) −1824.36 −0.406684
\(273\) 0 0
\(274\) −4089.13 −0.901581
\(275\) 2088.20 3616.87i 0.457903 0.793111i
\(276\) 0 0
\(277\) −620.284 1074.36i −0.134546 0.233041i 0.790878 0.611974i \(-0.209624\pi\)
−0.925424 + 0.378933i \(0.876291\pi\)
\(278\) 587.471 1017.53i 0.126742 0.219523i
\(279\) 0 0
\(280\) 237.815 + 611.998i 0.0507577 + 0.130621i
\(281\) 7346.62 1.55965 0.779826 0.625996i \(-0.215307\pi\)
0.779826 + 0.625996i \(0.215307\pi\)
\(282\) 0 0
\(283\) −2058.87 3566.06i −0.432462 0.749047i 0.564622 0.825349i \(-0.309022\pi\)
−0.997085 + 0.0763025i \(0.975689\pi\)
\(284\) −1329.72 2303.14i −0.277832 0.481220i
\(285\) 0 0
\(286\) −2971.82 −0.614431
\(287\) −4237.71 + 5277.34i −0.871582 + 1.08541i
\(288\) 0 0
\(289\) −4044.05 + 7004.50i −0.823132 + 1.42571i
\(290\) 573.001 + 992.467i 0.116027 + 0.200964i
\(291\) 0 0
\(292\) −1884.49 + 3264.03i −0.377676 + 0.654154i
\(293\) −2410.10 −0.480545 −0.240273 0.970705i \(-0.577237\pi\)
−0.240273 + 0.970705i \(0.577237\pi\)
\(294\) 0 0
\(295\) −139.708 −0.0275733
\(296\) 1093.03 1893.19i 0.214633 0.371755i
\(297\) 0 0
\(298\) 2713.32 + 4699.60i 0.527443 + 0.913559i
\(299\) 3606.14 6246.02i 0.697487 1.20808i
\(300\) 0 0
\(301\) −663.910 + 826.786i −0.127133 + 0.158323i
\(302\) 332.864 0.0634244
\(303\) 0 0
\(304\) 1081.01 + 1872.37i 0.203949 + 0.353250i
\(305\) −1911.13 3310.17i −0.358789 0.621442i
\(306\) 0 0
\(307\) −5172.84 −0.961661 −0.480830 0.876814i \(-0.659665\pi\)
−0.480830 + 0.876814i \(0.659665\pi\)
\(308\) −1063.60 2737.09i −0.196767 0.506364i
\(309\) 0 0
\(310\) −1083.86 + 1877.30i −0.198578 + 0.343947i
\(311\) −1714.23 2969.14i −0.312557 0.541365i 0.666358 0.745632i \(-0.267852\pi\)
−0.978915 + 0.204267i \(0.934519\pi\)
\(312\) 0 0
\(313\) 2292.03 3969.91i 0.413908 0.716909i −0.581406 0.813614i \(-0.697497\pi\)
0.995313 + 0.0967050i \(0.0308303\pi\)
\(314\) 1071.14 0.192510
\(315\) 0 0
\(316\) −13.3017 −0.00236797
\(317\) −74.0671 + 128.288i −0.0131231 + 0.0227299i −0.872512 0.488592i \(-0.837511\pi\)
0.859389 + 0.511322i \(0.170844\pi\)
\(318\) 0 0
\(319\) −2562.68 4438.69i −0.449788 0.779055i
\(320\) −141.808 + 245.619i −0.0247728 + 0.0429078i
\(321\) 0 0
\(322\) 7043.29 + 1085.89i 1.21897 + 0.187933i
\(323\) 15407.5 2.65417
\(324\) 0 0
\(325\) 1974.81 + 3420.48i 0.337055 + 0.583797i
\(326\) 1202.76 + 2083.24i 0.204339 + 0.353926i
\(327\) 0 0
\(328\) −2923.59 −0.492159
\(329\) 2314.23 + 5955.48i 0.387804 + 0.997983i
\(330\) 0 0
\(331\) 3893.30 6743.40i 0.646512 1.11979i −0.337438 0.941348i \(-0.609560\pi\)
0.983950 0.178444i \(-0.0571062\pi\)
\(332\) 108.180 + 187.373i 0.0178830 + 0.0309742i
\(333\) 0 0
\(334\) 3467.14 6005.26i 0.568004 0.983811i
\(335\) −3024.90 −0.493337
\(336\) 0 0
\(337\) 906.591 0.146544 0.0732718 0.997312i \(-0.476656\pi\)
0.0732718 + 0.997312i \(0.476656\pi\)
\(338\) −791.774 + 1371.39i −0.127417 + 0.220692i
\(339\) 0 0
\(340\) 1010.58 + 1750.38i 0.161195 + 0.279199i
\(341\) 4847.43 8396.00i 0.769804 1.33334i
\(342\) 0 0
\(343\) 5695.20 + 2813.94i 0.896537 + 0.442969i
\(344\) −458.030 −0.0717887
\(345\) 0 0
\(346\) 416.192 + 720.866i 0.0646666 + 0.112006i
\(347\) −2098.16 3634.12i −0.324597 0.562219i 0.656834 0.754036i \(-0.271895\pi\)
−0.981431 + 0.191817i \(0.938562\pi\)
\(348\) 0 0
\(349\) −5970.17 −0.915690 −0.457845 0.889032i \(-0.651379\pi\)
−0.457845 + 0.889032i \(0.651379\pi\)
\(350\) −2443.53 + 3043.00i −0.373178 + 0.464729i
\(351\) 0 0
\(352\) 634.219 1098.50i 0.0960340 0.166336i
\(353\) −5523.89 9567.65i −0.832880 1.44259i −0.895745 0.444569i \(-0.853357\pi\)
0.0628644 0.998022i \(-0.479976\pi\)
\(354\) 0 0
\(355\) −1473.16 + 2551.60i −0.220246 + 0.381478i
\(356\) −1141.60 −0.169957
\(357\) 0 0
\(358\) −751.268 −0.110910
\(359\) −3781.82 + 6550.31i −0.555980 + 0.962986i 0.441846 + 0.897091i \(0.354324\pi\)
−0.997827 + 0.0658953i \(0.979010\pi\)
\(360\) 0 0
\(361\) −5700.14 9872.93i −0.831045 1.43941i
\(362\) 2201.29 3812.74i 0.319605 0.553573i
\(363\) 0 0
\(364\) 2744.60 + 423.145i 0.395209 + 0.0609309i
\(365\) 4175.55 0.598790
\(366\) 0 0
\(367\) 1716.04 + 2972.26i 0.244077 + 0.422754i 0.961872 0.273501i \(-0.0881816\pi\)
−0.717794 + 0.696255i \(0.754848\pi\)
\(368\) 1539.18 + 2665.94i 0.218031 + 0.377641i
\(369\) 0 0
\(370\) −2421.89 −0.340292
\(371\) 11015.8 + 1698.34i 1.54153 + 0.237664i
\(372\) 0 0
\(373\) 2636.84 4567.15i 0.366034 0.633989i −0.622908 0.782295i \(-0.714049\pi\)
0.988941 + 0.148306i \(0.0473822\pi\)
\(374\) −4519.70 7828.34i −0.624887 1.08234i
\(375\) 0 0
\(376\) −1379.96 + 2390.17i −0.189272 + 0.327828i
\(377\) 4847.05 0.662164
\(378\) 0 0
\(379\) 8856.92 1.20039 0.600197 0.799852i \(-0.295089\pi\)
0.600197 + 0.799852i \(0.295089\pi\)
\(380\) 1197.63 2074.36i 0.161677 0.280032i
\(381\) 0 0
\(382\) 4353.28 + 7540.10i 0.583071 + 1.00991i
\(383\) −520.852 + 902.142i −0.0694890 + 0.120358i −0.898676 0.438612i \(-0.855470\pi\)
0.829187 + 0.558971i \(0.188804\pi\)
\(384\) 0 0
\(385\) −2036.93 + 2536.64i −0.269640 + 0.335790i
\(386\) 4452.84 0.587160
\(387\) 0 0
\(388\) −480.618 832.454i −0.0628857 0.108921i
\(389\) 4666.34 + 8082.33i 0.608207 + 1.05345i 0.991536 + 0.129834i \(0.0414445\pi\)
−0.383328 + 0.923612i \(0.625222\pi\)
\(390\) 0 0
\(391\) 21937.6 2.83743
\(392\) 592.555 + 2679.26i 0.0763483 + 0.345211i
\(393\) 0 0
\(394\) −3746.39 + 6488.94i −0.479037 + 0.829716i
\(395\) 7.36831 + 12.7623i 0.000938582 + 0.00162567i
\(396\) 0 0
\(397\) −3411.16 + 5908.31i −0.431238 + 0.746926i −0.996980 0.0776562i \(-0.975256\pi\)
0.565742 + 0.824582i \(0.308590\pi\)
\(398\) 5728.08 0.721414
\(399\) 0 0
\(400\) −1685.79 −0.210724
\(401\) −4054.97 + 7023.42i −0.504977 + 0.874646i 0.495007 + 0.868889i \(0.335166\pi\)
−0.999983 + 0.00575638i \(0.998168\pi\)
\(402\) 0 0
\(403\) 4584.22 + 7940.11i 0.566641 + 0.981452i
\(404\) −891.284 + 1543.75i −0.109760 + 0.190110i
\(405\) 0 0
\(406\) 1734.73 + 4464.20i 0.212053 + 0.545701i
\(407\) 10831.6 1.31917
\(408\) 0 0
\(409\) −2216.52 3839.13i −0.267970 0.464138i 0.700367 0.713783i \(-0.253020\pi\)
−0.968338 + 0.249644i \(0.919686\pi\)
\(410\) 1619.48 + 2805.03i 0.195075 + 0.337879i
\(411\) 0 0
\(412\) −3384.76 −0.404745
\(413\) −577.055 88.9667i −0.0687530 0.0105999i
\(414\) 0 0
\(415\) 119.850 207.586i 0.0141764 0.0245542i
\(416\) 599.781 + 1038.85i 0.0706892 + 0.122437i
\(417\) 0 0
\(418\) −5356.25 + 9277.30i −0.626753 + 1.08557i
\(419\) −6782.36 −0.790787 −0.395394 0.918512i \(-0.629392\pi\)
−0.395394 + 0.918512i \(0.629392\pi\)
\(420\) 0 0
\(421\) −4798.62 −0.555512 −0.277756 0.960652i \(-0.589591\pi\)
−0.277756 + 0.960652i \(0.589591\pi\)
\(422\) 3729.13 6459.04i 0.430168 0.745073i
\(423\) 0 0
\(424\) 2407.29 + 4169.55i 0.275727 + 0.477573i
\(425\) −6006.80 + 10404.1i −0.685583 + 1.18746i
\(426\) 0 0
\(427\) −5785.85 14889.4i −0.655730 1.68747i
\(428\) 2249.25 0.254022
\(429\) 0 0
\(430\) 253.720 + 439.456i 0.0284546 + 0.0492848i
\(431\) −6474.64 11214.4i −0.723602 1.25332i −0.959547 0.281549i \(-0.909152\pi\)
0.235945 0.971766i \(-0.424182\pi\)
\(432\) 0 0
\(433\) 937.240 0.104020 0.0520102 0.998647i \(-0.483437\pi\)
0.0520102 + 0.998647i \(0.483437\pi\)
\(434\) −5672.28 + 7063.86i −0.627369 + 0.781281i
\(435\) 0 0
\(436\) 2231.27 3864.67i 0.245088 0.424505i
\(437\) −12999.1 22515.0i −1.42295 2.46462i
\(438\) 0 0
\(439\) 6800.15 11778.2i 0.739302 1.28051i −0.213509 0.976941i \(-0.568489\pi\)
0.952810 0.303567i \(-0.0981775\pi\)
\(440\) −1405.27 −0.152258
\(441\) 0 0
\(442\) 8548.56 0.919940
\(443\) −2316.24 + 4011.84i −0.248415 + 0.430267i −0.963086 0.269193i \(-0.913243\pi\)
0.714671 + 0.699460i \(0.246576\pi\)
\(444\) 0 0
\(445\) 632.374 + 1095.30i 0.0673650 + 0.116680i
\(446\) 152.890 264.813i 0.0162322 0.0281149i
\(447\) 0 0
\(448\) −742.139 + 924.207i −0.0782651 + 0.0974658i
\(449\) −254.426 −0.0267419 −0.0133709 0.999911i \(-0.504256\pi\)
−0.0133709 + 0.999911i \(0.504256\pi\)
\(450\) 0 0
\(451\) −7242.94 12545.1i −0.756224 1.30982i
\(452\) −3036.63 5259.59i −0.315998 0.547324i
\(453\) 0 0
\(454\) −6772.16 −0.700073
\(455\) −1114.35 2867.70i −0.114817 0.295472i
\(456\) 0 0
\(457\) −8205.25 + 14211.9i −0.839881 + 1.45472i 0.0501133 + 0.998744i \(0.484042\pi\)
−0.889994 + 0.455972i \(0.849292\pi\)
\(458\) −772.356 1337.76i −0.0787988 0.136483i
\(459\) 0 0
\(460\) 1705.22 2953.53i 0.172840 0.299367i
\(461\) 5842.56 0.590272 0.295136 0.955455i \(-0.404635\pi\)
0.295136 + 0.955455i \(0.404635\pi\)
\(462\) 0 0
\(463\) 6699.12 0.672429 0.336215 0.941785i \(-0.390853\pi\)
0.336215 + 0.941785i \(0.390853\pi\)
\(464\) −1034.41 + 1791.66i −0.103495 + 0.179258i
\(465\) 0 0
\(466\) −3563.85 6172.77i −0.354275 0.613623i
\(467\) −912.817 + 1581.05i −0.0904500 + 0.156664i −0.907701 0.419619i \(-0.862164\pi\)
0.817251 + 0.576282i \(0.195497\pi\)
\(468\) 0 0
\(469\) −12494.1 1926.27i −1.23012 0.189652i
\(470\) 3057.65 0.300083
\(471\) 0 0
\(472\) −126.105 218.420i −0.0122975 0.0212999i
\(473\) −1134.73 1965.41i −0.110307 0.191057i
\(474\) 0 0
\(475\) 14237.2 1.37526
\(476\) 3059.48 + 7873.35i 0.294603 + 0.758139i
\(477\) 0 0
\(478\) 5832.92 10102.9i 0.558141 0.966729i
\(479\) 5518.07 + 9557.58i 0.526362 + 0.911685i 0.999528 + 0.0307121i \(0.00977749\pi\)
−0.473167 + 0.880973i \(0.656889\pi\)
\(480\) 0 0
\(481\) −5121.73 + 8871.10i −0.485511 + 0.840930i
\(482\) −7386.43 −0.698014
\(483\) 0 0
\(484\) 960.900 0.0902423
\(485\) −532.464 + 922.255i −0.0498515 + 0.0863453i
\(486\) 0 0
\(487\) −4092.78 7088.90i −0.380824 0.659607i 0.610356 0.792127i \(-0.291026\pi\)
−0.991180 + 0.132520i \(0.957693\pi\)
\(488\) 3450.08 5975.71i 0.320036 0.554319i
\(489\) 0 0
\(490\) 2242.37 2052.67i 0.206735 0.189245i
\(491\) −19006.2 −1.74692 −0.873459 0.486897i \(-0.838129\pi\)
−0.873459 + 0.486897i \(0.838129\pi\)
\(492\) 0 0
\(493\) 7371.65 + 12768.1i 0.673433 + 1.16642i
\(494\) −5065.41 8773.55i −0.461343 0.799070i
\(495\) 0 0
\(496\) −3913.30 −0.354258
\(497\) −7709.66 + 9601.07i −0.695826 + 0.866533i
\(498\) 0 0
\(499\) −8246.79 + 14283.9i −0.739834 + 1.28143i 0.212736 + 0.977110i \(0.431763\pi\)
−0.952570 + 0.304320i \(0.901571\pi\)
\(500\) 2041.70 + 3536.32i 0.182615 + 0.316298i
\(501\) 0 0
\(502\) −1571.78 + 2722.41i −0.139745 + 0.242046i
\(503\) −10368.0 −0.919059 −0.459530 0.888162i \(-0.651982\pi\)
−0.459530 + 0.888162i \(0.651982\pi\)
\(504\) 0 0
\(505\) 1974.86 0.174020
\(506\) −7626.39 + 13209.3i −0.670029 + 1.16052i
\(507\) 0 0
\(508\) 1606.16 + 2781.95i 0.140279 + 0.242970i
\(509\) 3254.37 5636.74i 0.283394 0.490853i −0.688825 0.724928i \(-0.741873\pi\)
0.972218 + 0.234075i \(0.0752063\pi\)
\(510\) 0 0
\(511\) 17246.8 + 2659.01i 1.49306 + 0.230191i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −3652.28 6325.94i −0.313415 0.542851i
\(515\) 1874.94 + 3247.50i 0.160427 + 0.277868i
\(516\) 0 0
\(517\) −13675.0 −1.16330
\(518\) −10003.4 1542.27i −0.848506 0.130817i
\(519\) 0 0
\(520\) 664.483 1150.92i 0.0560375 0.0970598i
\(521\) 6759.54 + 11707.9i 0.568409 + 0.984513i 0.996724 + 0.0808831i \(0.0257741\pi\)
−0.428315 + 0.903630i \(0.640893\pi\)
\(522\) 0 0
\(523\) −929.020 + 1609.11i −0.0776734 + 0.134534i −0.902246 0.431222i \(-0.858082\pi\)
0.824572 + 0.565757i \(0.191416\pi\)
\(524\) 3560.85 0.296864
\(525\) 0 0
\(526\) −1421.07 −0.117798
\(527\) −13943.9 + 24151.5i −1.15257 + 1.99631i
\(528\) 0 0
\(529\) −12424.9 21520.6i −1.02120 1.76877i
\(530\) 2666.98 4619.34i 0.218577 0.378587i
\(531\) 0 0
\(532\) 6267.68 7805.32i 0.510787 0.636097i
\(533\) 13699.3 1.11329
\(534\) 0 0
\(535\) −1245.94 2158.03i −0.100686 0.174392i
\(536\) −2730.36 4729.13i −0.220026 0.381095i
\(537\) 0 0
\(538\) 16.5329 0.00132487
\(539\) −10028.7 + 9180.30i −0.801424 + 0.733624i
\(540\) 0 0
\(541\) −6846.27 + 11858.1i −0.544075 + 0.942365i 0.454590 + 0.890701i \(0.349786\pi\)
−0.998665 + 0.0516640i \(0.983548\pi\)
\(542\) −2723.70 4717.58i −0.215854 0.373870i
\(543\) 0 0
\(544\) −1824.36 + 3159.88i −0.143784 + 0.249042i
\(545\) −4943.94 −0.388578
\(546\) 0 0
\(547\) −9054.00 −0.707717 −0.353858 0.935299i \(-0.615131\pi\)
−0.353858 + 0.935299i \(0.615131\pi\)
\(548\) −4089.13 + 7082.58i −0.318757 + 0.552104i
\(549\) 0 0
\(550\) −4176.40 7233.74i −0.323786 0.560814i
\(551\) 8736.07 15131.3i 0.675443 1.16990i
\(552\) 0 0
\(553\) 22.3072 + 57.4059i 0.00171537 + 0.00441437i
\(554\) −2481.14 −0.190277
\(555\) 0 0
\(556\) −1174.94 2035.06i −0.0896198 0.155226i
\(557\) 4717.22 + 8170.46i 0.358842 + 0.621533i 0.987768 0.155933i \(-0.0498383\pi\)
−0.628926 + 0.777465i \(0.716505\pi\)
\(558\) 0 0
\(559\) 2146.23 0.162390
\(560\) 1297.83 + 200.091i 0.0979343 + 0.0150989i
\(561\) 0 0
\(562\) 7346.62 12724.7i 0.551421 0.955088i
\(563\) −3205.10 5551.39i −0.239927 0.415565i 0.720766 0.693178i \(-0.243790\pi\)
−0.960693 + 0.277613i \(0.910457\pi\)
\(564\) 0 0
\(565\) −3364.20 + 5826.97i −0.250501 + 0.433880i
\(566\) −8235.46 −0.611594
\(567\) 0 0
\(568\) −5318.88 −0.392914
\(569\) −2432.99 + 4214.06i −0.179255 + 0.310479i −0.941626 0.336662i \(-0.890702\pi\)
0.762370 + 0.647141i \(0.224035\pi\)
\(570\) 0 0
\(571\) −9349.38 16193.6i −0.685218 1.18683i −0.973368 0.229247i \(-0.926374\pi\)
0.288150 0.957585i \(-0.406960\pi\)
\(572\) −2971.82 + 5147.34i −0.217234 + 0.376261i
\(573\) 0 0
\(574\) 4902.91 + 12617.3i 0.356522 + 0.917482i
\(575\) 20271.4 1.47022
\(576\) 0 0
\(577\) 9174.11 + 15890.0i 0.661912 + 1.14647i 0.980113 + 0.198442i \(0.0635882\pi\)
−0.318200 + 0.948023i \(0.603079\pi\)
\(578\) 8088.10 + 14009.0i 0.582042 + 1.00813i
\(579\) 0 0
\(580\) 2292.00 0.164087
\(581\) 627.223 781.099i 0.0447876 0.0557753i
\(582\) 0 0
\(583\) −11927.7 + 20659.4i −0.847334 + 1.46763i
\(584\) 3768.98 + 6528.06i 0.267057 + 0.462556i
\(585\) 0 0
\(586\) −2410.10 + 4174.42i −0.169898 + 0.294273i
\(587\) −17246.6 −1.21268 −0.606340 0.795206i \(-0.707363\pi\)
−0.606340 + 0.795206i \(0.707363\pi\)
\(588\) 0 0
\(589\) 33049.5 2.31202
\(590\) −139.708 + 241.982i −0.00974863 + 0.0168851i
\(591\) 0 0
\(592\) −2186.07 3786.38i −0.151768 0.262870i
\(593\) −8806.40 + 15253.1i −0.609841 + 1.05628i 0.381426 + 0.924400i \(0.375433\pi\)
−0.991266 + 0.131875i \(0.957900\pi\)
\(594\) 0 0
\(595\) 5859.30 7296.76i 0.403711 0.502753i
\(596\) 10853.3 0.745918
\(597\) 0 0
\(598\) −7212.29 12492.0i −0.493198 0.854244i
\(599\) −6533.22 11315.9i −0.445643 0.771876i 0.552454 0.833544i \(-0.313692\pi\)
−0.998097 + 0.0616672i \(0.980358\pi\)
\(600\) 0 0
\(601\) −10232.8 −0.694516 −0.347258 0.937770i \(-0.612887\pi\)
−0.347258 + 0.937770i \(0.612887\pi\)
\(602\) 768.125 + 1976.71i 0.0520041 + 0.133828i
\(603\) 0 0
\(604\) 332.864 576.537i 0.0224239 0.0388393i
\(605\) −532.279 921.934i −0.0357689 0.0619536i
\(606\) 0 0
\(607\) 5116.84 8862.63i 0.342152 0.592625i −0.642680 0.766135i \(-0.722178\pi\)
0.984832 + 0.173510i \(0.0555109\pi\)
\(608\) 4324.06 0.288427
\(609\) 0 0
\(610\) −7644.51 −0.507405
\(611\) 6466.22 11199.8i 0.428143 0.741565i
\(612\) 0 0
\(613\) 1435.08 + 2485.63i 0.0945550 + 0.163774i 0.909423 0.415873i \(-0.136524\pi\)
−0.814868 + 0.579647i \(0.803191\pi\)
\(614\) −5172.84 + 8959.63i −0.339998 + 0.588894i
\(615\) 0 0
\(616\) −5804.37 894.882i −0.379651 0.0585322i
\(617\) 743.774 0.0485304 0.0242652 0.999706i \(-0.492275\pi\)
0.0242652 + 0.999706i \(0.492275\pi\)
\(618\) 0 0
\(619\) 11435.6 + 19807.0i 0.742543 + 1.28612i 0.951334 + 0.308162i \(0.0997140\pi\)
−0.208790 + 0.977960i \(0.566953\pi\)
\(620\) 2167.72 + 3754.60i 0.140416 + 0.243207i
\(621\) 0 0
\(622\) −6856.94 −0.442023
\(623\) 1914.48 + 4926.78i 0.123117 + 0.316833i
\(624\) 0 0
\(625\) −4323.17 + 7487.95i −0.276683 + 0.479228i
\(626\) −4584.06 7939.82i −0.292677 0.506931i
\(627\) 0 0
\(628\) 1071.14 1855.28i 0.0680626 0.117888i
\(629\) −31157.6 −1.97509
\(630\) 0 0
\(631\) −16861.8 −1.06380 −0.531901 0.846807i \(-0.678522\pi\)
−0.531901 + 0.846807i \(0.678522\pi\)
\(632\) −13.3017 + 23.0392i −0.000837204 + 0.00145008i
\(633\) 0 0
\(634\) 148.134 + 256.576i 0.00927943 + 0.0160724i
\(635\) 1779.42 3082.05i 0.111203 0.192610i
\(636\) 0 0
\(637\) −2776.59 12554.4i −0.172704 0.780887i
\(638\) −10250.7 −0.636096
\(639\) 0 0
\(640\) 283.616 + 491.237i 0.0175170 + 0.0303404i
\(641\) −4259.46 7377.61i −0.262463 0.454599i 0.704433 0.709771i \(-0.251201\pi\)
−0.966896 + 0.255172i \(0.917868\pi\)
\(642\) 0 0
\(643\) −12045.2 −0.738748 −0.369374 0.929281i \(-0.620428\pi\)
−0.369374 + 0.929281i \(0.620428\pi\)
\(644\) 8924.11 11113.5i 0.546055 0.680018i
\(645\) 0 0
\(646\) 15407.5 26686.5i 0.938389 1.62534i
\(647\) −2078.82 3600.63i −0.126317 0.218787i 0.795930 0.605389i \(-0.206982\pi\)
−0.922247 + 0.386601i \(0.873649\pi\)
\(648\) 0 0
\(649\) 624.828 1082.23i 0.0377914 0.0654566i
\(650\) 7899.26 0.476668
\(651\) 0 0
\(652\) 4811.03 0.288979
\(653\) −15174.8 + 26283.5i −0.909394 + 1.57512i −0.0944872 + 0.995526i \(0.530121\pi\)
−0.814907 + 0.579591i \(0.803212\pi\)
\(654\) 0 0
\(655\) −1972.49 3416.45i −0.117667 0.203804i
\(656\) −2923.59 + 5063.80i −0.174004 + 0.301384i
\(657\) 0 0
\(658\) 12629.4 + 1947.13i 0.748246 + 0.115360i
\(659\) −14482.7 −0.856093 −0.428046 0.903757i \(-0.640798\pi\)
−0.428046 + 0.903757i \(0.640798\pi\)
\(660\) 0 0
\(661\) 3262.70 + 5651.16i 0.191988 + 0.332533i 0.945909 0.324432i \(-0.105173\pi\)
−0.753921 + 0.656965i \(0.771840\pi\)
\(662\) −7786.61 13486.8i −0.457153 0.791812i
\(663\) 0 0
\(664\) 432.720 0.0252903
\(665\) −10960.7 1689.85i −0.639155 0.0985409i
\(666\) 0 0
\(667\) 12438.7 21544.4i 0.722081 1.25068i
\(668\) −6934.27 12010.5i −0.401639 0.695660i
\(669\) 0 0
\(670\) −3024.90 + 5239.28i −0.174421 + 0.302106i
\(671\) 34189.1 1.96700
\(672\) 0 0
\(673\) 1453.70 0.0832629 0.0416314 0.999133i \(-0.486744\pi\)
0.0416314 + 0.999133i \(0.486744\pi\)
\(674\) 906.591 1570.26i 0.0518110 0.0897392i
\(675\) 0 0
\(676\) 1583.55 + 2742.79i 0.0900972 + 0.156053i
\(677\) 7385.35 12791.8i 0.419265 0.726187i −0.576601 0.817026i \(-0.695621\pi\)
0.995866 + 0.0908383i \(0.0289546\pi\)
\(678\) 0 0
\(679\) −2786.60 + 3470.23i −0.157496 + 0.196135i
\(680\) 4042.32 0.227965
\(681\) 0 0
\(682\) −9694.87 16792.0i −0.544334 0.942814i
\(683\) 4539.15 + 7862.04i 0.254298 + 0.440457i 0.964705 0.263334i \(-0.0848222\pi\)
−0.710406 + 0.703792i \(0.751489\pi\)
\(684\) 0 0
\(685\) 9060.49 0.505377
\(686\) 10569.1 7050.44i 0.588236 0.392401i
\(687\) 0 0
\(688\) −458.030 + 793.331i −0.0253811 + 0.0439614i
\(689\) −11280.1 19537.6i −0.623710 1.08030i
\(690\) 0 0
\(691\) −2234.84 + 3870.86i −0.123035 + 0.213104i −0.920963 0.389649i \(-0.872596\pi\)
0.797928 + 0.602753i \(0.205930\pi\)
\(692\) 1664.77 0.0914524
\(693\) 0 0
\(694\) −8392.65 −0.459050
\(695\) −1301.69 + 2254.59i −0.0710444 + 0.123053i
\(696\) 0 0
\(697\) 20834.6 + 36086.6i 1.13224 + 1.96109i
\(698\) −5970.17 + 10340.6i −0.323745 + 0.560743i
\(699\) 0 0
\(700\) 2827.10 + 7275.33i 0.152649 + 0.392831i
\(701\) 29024.1 1.56380 0.781901 0.623403i \(-0.214250\pi\)
0.781901 + 0.623403i \(0.214250\pi\)
\(702\) 0 0
\(703\) 18462.3 + 31977.6i 0.990496 + 1.71559i
\(704\) −1268.44 2197.00i −0.0679063 0.117617i
\(705\) 0 0
\(706\) −22095.5 −1.17787
\(707\) 8157.03 + 1257.60i 0.433913 + 0.0668980i
\(708\) 0 0
\(709\) 33.0540 57.2511i 0.00175087 0.00303260i −0.865149 0.501516i \(-0.832776\pi\)
0.866900 + 0.498483i \(0.166109\pi\)
\(710\) 2946.33 + 5103.19i 0.155738 + 0.269746i
\(711\) 0 0
\(712\) −1141.60 + 1977.31i −0.0600888 + 0.104077i
\(713\) 47056.8 2.47166
\(714\) 0 0
\(715\) 6584.81 0.344417
\(716\) −751.268 + 1301.23i −0.0392126 + 0.0679182i
\(717\) 0 0
\(718\) 7563.64 + 13100.6i 0.393137 + 0.680934i
\(719\) 14833.0 25691.4i 0.769368 1.33259i −0.168537 0.985695i \(-0.553904\pi\)
0.937906 0.346890i \(-0.112762\pi\)
\(720\) 0 0
\(721\) 5676.30 + 14607.5i 0.293199 + 0.754525i
\(722\) −22800.5 −1.17527
\(723\) 0 0
\(724\) −4402.58 7625.49i −0.225995 0.391435i
\(725\) 6811.74 + 11798.3i 0.348940 + 0.604382i
\(726\) 0 0
\(727\) 23619.7 1.20496 0.602481 0.798133i \(-0.294179\pi\)
0.602481 + 0.798133i \(0.294179\pi\)
\(728\) 3477.51 4330.64i 0.177040 0.220473i
\(729\) 0 0
\(730\) 4175.55 7232.27i 0.211704 0.366683i
\(731\) 3264.10 + 5653.59i 0.165154 + 0.286054i
\(732\) 0 0
\(733\) −10767.9 + 18650.5i −0.542593 + 0.939798i 0.456161 + 0.889897i \(0.349224\pi\)
−0.998754 + 0.0499012i \(0.984109\pi\)
\(734\) 6864.15 0.345177
\(735\) 0 0
\(736\) 6156.73 0.308342
\(737\) 13528.5 23432.0i 0.676158 1.17114i
\(738\) 0 0
\(739\) −5373.78 9307.66i −0.267494 0.463312i 0.700720 0.713436i \(-0.252862\pi\)
−0.968214 + 0.250124i \(0.919529\pi\)
\(740\) −2421.89 + 4194.84i −0.120311 + 0.208386i
\(741\) 0 0
\(742\) 13957.4 17381.5i 0.690554 0.859966i
\(743\) −19106.9 −0.943426 −0.471713 0.881752i \(-0.656364\pi\)
−0.471713 + 0.881752i \(0.656364\pi\)
\(744\) 0 0
\(745\) −6012.03 10413.1i −0.295656 0.512091i
\(746\) −5273.69 9134.29i −0.258825 0.448298i
\(747\) 0 0
\(748\) −18078.8 −0.883724
\(749\) −3772.03 9707.03i −0.184015 0.473547i
\(750\) 0 0
\(751\) 2371.18 4107.00i 0.115214 0.199556i −0.802651 0.596448i \(-0.796578\pi\)
0.917865 + 0.396892i \(0.129911\pi\)
\(752\) 2759.93 + 4780.33i 0.133835 + 0.231810i
\(753\) 0 0
\(754\) 4847.05 8395.34i 0.234110 0.405491i
\(755\) −737.543 −0.0355522
\(756\) 0 0
\(757\) −3717.28 −0.178476 −0.0892382 0.996010i \(-0.528443\pi\)
−0.0892382 + 0.996010i \(0.528443\pi\)
\(758\) 8856.92 15340.6i 0.424403 0.735088i
\(759\) 0 0
\(760\) −2395.26 4148.71i −0.114323 0.198013i
\(761\) 2047.43 3546.26i 0.0975288 0.168925i −0.813132 0.582079i \(-0.802240\pi\)
0.910661 + 0.413154i \(0.135573\pi\)
\(762\) 0 0
\(763\) −20420.6 3148.32i −0.968905 0.149380i
\(764\) 17413.1 0.824587
\(765\) 0 0
\(766\) 1041.70 + 1804.28i 0.0491361 + 0.0851063i
\(767\) 590.900 + 1023.47i 0.0278177 + 0.0481816i
\(768\) 0 0
\(769\) 16871.2 0.791145 0.395573 0.918435i \(-0.370546\pi\)
0.395573 + 0.918435i \(0.370546\pi\)
\(770\) 2356.67 + 6064.70i 0.110297 + 0.283840i
\(771\) 0 0
\(772\) 4452.84 7712.54i 0.207592 0.359560i
\(773\) 14015.1 + 24274.9i 0.652121 + 1.12951i 0.982607 + 0.185696i \(0.0594538\pi\)
−0.330487 + 0.943811i \(0.607213\pi\)
\(774\) 0 0
\(775\) −12884.7 + 22317.0i −0.597205 + 1.03439i
\(776\) −1922.47 −0.0889339
\(777\) 0 0
\(778\) 18665.4 0.860135
\(779\) 24690.9 42766.0i 1.13562 1.96694i
\(780\) 0 0
\(781\) −13177.1 22823.4i −0.603730 1.04569i
\(782\) 21937.6 37997.1i 1.00318 1.73756i
\(783\) 0 0
\(784\) 5233.16 + 1652.92i 0.238391 + 0.0752971i