Properties

Label 405.4.e.s.136.3
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.148347072.2
Defining polynomial: \( x^{6} + 29x^{4} + 223x^{2} + 243 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.3
Root \(1.13993i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.s.271.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.92514 - 3.33444i) q^{2} +(-3.41235 - 5.91036i) q^{4} +(2.50000 + 4.33013i) q^{5} +(13.1641 - 22.8009i) q^{7} +4.52526 q^{8} +O(q^{10})\) \(q+(1.92514 - 3.33444i) q^{2} +(-3.41235 - 5.91036i) q^{4} +(2.50000 + 4.33013i) q^{5} +(13.1641 - 22.8009i) q^{7} +4.52526 q^{8} +19.2514 q^{10} +(2.53997 - 4.39937i) q^{11} +(41.3605 + 71.6385i) q^{13} +(-50.6855 - 87.7899i) q^{14} +(36.0106 - 62.3721i) q^{16} +52.5976 q^{17} -29.8611 q^{19} +(17.0617 - 29.5518i) q^{20} +(-9.77963 - 16.9388i) q^{22} +(49.1340 + 85.1026i) q^{23} +(-12.5000 + 21.6506i) q^{25} +318.499 q^{26} -179.682 q^{28} +(83.9679 - 145.437i) q^{29} +(-95.3871 - 165.215i) q^{31} +(-120.550 - 208.798i) q^{32} +(101.258 - 175.384i) q^{34} +131.641 q^{35} -365.864 q^{37} +(-57.4869 + 99.5703i) q^{38} +(11.3132 + 19.5950i) q^{40} +(-55.8564 - 96.7461i) q^{41} +(201.802 - 349.531i) q^{43} -34.6691 q^{44} +378.360 q^{46} +(116.088 - 201.070i) q^{47} +(-175.087 - 303.260i) q^{49} +(48.1286 + 83.3611i) q^{50} +(282.273 - 488.911i) q^{52} +410.528 q^{53} +25.3997 q^{55} +(59.5710 - 103.180i) q^{56} +(-323.300 - 559.973i) q^{58} +(76.0067 + 131.647i) q^{59} +(-266.125 + 460.942i) q^{61} -734.535 q^{62} -352.134 q^{64} +(-206.803 + 358.193i) q^{65} +(-306.702 - 531.224i) q^{67} +(-179.481 - 310.870i) q^{68} +(253.428 - 438.950i) q^{70} +413.938 q^{71} -114.484 q^{73} +(-704.341 + 1219.95i) q^{74} +(101.897 + 176.490i) q^{76} +(-66.8730 - 115.827i) q^{77} +(-39.5526 + 68.5072i) q^{79} +360.106 q^{80} -430.126 q^{82} +(-713.664 + 1236.10i) q^{83} +(131.494 + 227.754i) q^{85} +(-776.994 - 1345.79i) q^{86} +(11.4941 - 19.9083i) q^{88} -450.084 q^{89} +2177.90 q^{91} +(335.325 - 580.799i) q^{92} +(-446.971 - 774.177i) q^{94} +(-74.6528 - 129.302i) q^{95} +(-718.438 + 1244.37i) q^{97} -1348.27 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 15 q^{5} + 25 q^{7} - 54 q^{8} - 10 q^{10} - 58 q^{11} + 47 q^{13} - 159 q^{14} + 127 q^{16} + 68 q^{17} - 10 q^{19} + 25 q^{20} - 260 q^{22} + 51 q^{23} - 75 q^{25} + 506 q^{26} + 166 q^{28} - 350 q^{29} - 638 q^{31} - 245 q^{32} + 154 q^{34} + 250 q^{35} - 828 q^{37} - 397 q^{38} - 135 q^{40} - 179 q^{41} + 836 q^{43} + 664 q^{44} + 522 q^{46} - 235 q^{47} - 892 q^{49} - 25 q^{50} + 1335 q^{52} + 1010 q^{53} - 580 q^{55} - 15 q^{56} - 1876 q^{58} - 535 q^{59} + 104 q^{61} + 696 q^{62} - 606 q^{64} - 235 q^{65} + 40 q^{67} - 830 q^{68} + 795 q^{70} + 904 q^{71} - 1420 q^{73} - 1394 q^{74} - 849 q^{76} - 2148 q^{77} + 634 q^{79} + 1270 q^{80} + 1226 q^{82} - 1734 q^{83} + 170 q^{85} - 460 q^{86} + 768 q^{88} - 1704 q^{89} - 2458 q^{91} + 1839 q^{92} - 1751 q^{94} - 25 q^{95} + 76 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92514 3.33444i 0.680641 1.17890i −0.294145 0.955761i \(-0.595035\pi\)
0.974786 0.223143i \(-0.0716318\pi\)
\(3\) 0 0
\(4\) −3.41235 5.91036i −0.426543 0.738795i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 13.1641 22.8009i 0.710795 1.23113i −0.253765 0.967266i \(-0.581669\pi\)
0.964559 0.263866i \(-0.0849978\pi\)
\(8\) 4.52526 0.199990
\(9\) 0 0
\(10\) 19.2514 0.608783
\(11\) 2.53997 4.39937i 0.0696210 0.120587i −0.829113 0.559080i \(-0.811154\pi\)
0.898735 + 0.438493i \(0.144488\pi\)
\(12\) 0 0
\(13\) 41.3605 + 71.6385i 0.882411 + 1.52838i 0.848653 + 0.528950i \(0.177414\pi\)
0.0337582 + 0.999430i \(0.489252\pi\)
\(14\) −50.6855 87.7899i −0.967591 1.67592i
\(15\) 0 0
\(16\) 36.0106 62.3721i 0.562665 0.974564i
\(17\) 52.5976 0.750399 0.375199 0.926944i \(-0.377574\pi\)
0.375199 + 0.926944i \(0.377574\pi\)
\(18\) 0 0
\(19\) −29.8611 −0.360559 −0.180279 0.983615i \(-0.557700\pi\)
−0.180279 + 0.983615i \(0.557700\pi\)
\(20\) 17.0617 29.5518i 0.190756 0.330399i
\(21\) 0 0
\(22\) −9.77963 16.9388i −0.0947738 0.164153i
\(23\) 49.1340 + 85.1026i 0.445441 + 0.771527i 0.998083 0.0618920i \(-0.0197134\pi\)
−0.552641 + 0.833419i \(0.686380\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 318.499 2.40242
\(27\) 0 0
\(28\) −179.682 −1.21274
\(29\) 83.9679 145.437i 0.537671 0.931273i −0.461358 0.887214i \(-0.652638\pi\)
0.999029 0.0440590i \(-0.0140290\pi\)
\(30\) 0 0
\(31\) −95.3871 165.215i −0.552646 0.957211i −0.998083 0.0618974i \(-0.980285\pi\)
0.445437 0.895314i \(-0.353048\pi\)
\(32\) −120.550 208.798i −0.665950 1.15346i
\(33\) 0 0
\(34\) 101.258 175.384i 0.510752 0.884648i
\(35\) 131.641 0.635754
\(36\) 0 0
\(37\) −365.864 −1.62561 −0.812807 0.582533i \(-0.802062\pi\)
−0.812807 + 0.582533i \(0.802062\pi\)
\(38\) −57.4869 + 99.5703i −0.245411 + 0.425064i
\(39\) 0 0
\(40\) 11.3132 + 19.5950i 0.0447192 + 0.0774559i
\(41\) −55.8564 96.7461i −0.212763 0.368517i 0.739815 0.672810i \(-0.234913\pi\)
−0.952578 + 0.304293i \(0.901580\pi\)
\(42\) 0 0
\(43\) 201.802 349.531i 0.715685 1.23960i −0.247010 0.969013i \(-0.579448\pi\)
0.962695 0.270590i \(-0.0872187\pi\)
\(44\) −34.6691 −0.118786
\(45\) 0 0
\(46\) 378.360 1.21274
\(47\) 116.088 201.070i 0.360280 0.624023i −0.627727 0.778434i \(-0.716014\pi\)
0.988007 + 0.154411i \(0.0493478\pi\)
\(48\) 0 0
\(49\) −175.087 303.260i −0.510458 0.884139i
\(50\) 48.1286 + 83.3611i 0.136128 + 0.235781i
\(51\) 0 0
\(52\) 282.273 488.911i 0.752773 1.30384i
\(53\) 410.528 1.06397 0.531984 0.846754i \(-0.321447\pi\)
0.531984 + 0.846754i \(0.321447\pi\)
\(54\) 0 0
\(55\) 25.3997 0.0622709
\(56\) 59.5710 103.180i 0.142152 0.246214i
\(57\) 0 0
\(58\) −323.300 559.973i −0.731921 1.26772i
\(59\) 76.0067 + 131.647i 0.167716 + 0.290492i 0.937616 0.347672i \(-0.113028\pi\)
−0.769901 + 0.638164i \(0.779694\pi\)
\(60\) 0 0
\(61\) −266.125 + 460.942i −0.558588 + 0.967502i 0.439027 + 0.898474i \(0.355323\pi\)
−0.997615 + 0.0690283i \(0.978010\pi\)
\(62\) −734.535 −1.50461
\(63\) 0 0
\(64\) −352.134 −0.687761
\(65\) −206.803 + 358.193i −0.394626 + 0.683513i
\(66\) 0 0
\(67\) −306.702 531.224i −0.559248 0.968647i −0.997559 0.0698233i \(-0.977756\pi\)
0.438311 0.898823i \(-0.355577\pi\)
\(68\) −179.481 310.870i −0.320078 0.554391i
\(69\) 0 0
\(70\) 253.428 438.950i 0.432720 0.749493i
\(71\) 413.938 0.691908 0.345954 0.938252i \(-0.387555\pi\)
0.345954 + 0.938252i \(0.387555\pi\)
\(72\) 0 0
\(73\) −114.484 −0.183552 −0.0917761 0.995780i \(-0.529254\pi\)
−0.0917761 + 0.995780i \(0.529254\pi\)
\(74\) −704.341 + 1219.95i −1.10646 + 1.91644i
\(75\) 0 0
\(76\) 101.897 + 176.490i 0.153794 + 0.266379i
\(77\) −66.8730 115.827i −0.0989725 0.171425i
\(78\) 0 0
\(79\) −39.5526 + 68.5072i −0.0563294 + 0.0975653i −0.892815 0.450423i \(-0.851273\pi\)
0.836486 + 0.547989i \(0.184606\pi\)
\(80\) 360.106 0.503263
\(81\) 0 0
\(82\) −430.126 −0.579262
\(83\) −713.664 + 1236.10i −0.943792 + 1.63470i −0.185641 + 0.982618i \(0.559436\pi\)
−0.758151 + 0.652079i \(0.773897\pi\)
\(84\) 0 0
\(85\) 131.494 + 227.754i 0.167794 + 0.290628i
\(86\) −776.994 1345.79i −0.974249 1.68745i
\(87\) 0 0
\(88\) 11.4941 19.9083i 0.0139235 0.0241163i
\(89\) −450.084 −0.536054 −0.268027 0.963411i \(-0.586372\pi\)
−0.268027 + 0.963411i \(0.586372\pi\)
\(90\) 0 0
\(91\) 2177.90 2.50885
\(92\) 335.325 580.799i 0.380000 0.658180i
\(93\) 0 0
\(94\) −446.971 774.177i −0.490442 0.849471i
\(95\) −74.6528 129.302i −0.0806233 0.139644i
\(96\) 0 0
\(97\) −718.438 + 1244.37i −0.752024 + 1.30254i 0.194816 + 0.980840i \(0.437589\pi\)
−0.946840 + 0.321705i \(0.895744\pi\)
\(98\) −1348.27 −1.38975
\(99\) 0 0
\(100\) 170.617 0.170617
\(101\) −923.517 + 1599.58i −0.909835 + 1.57588i −0.0955437 + 0.995425i \(0.530459\pi\)
−0.814292 + 0.580456i \(0.802874\pi\)
\(102\) 0 0
\(103\) −23.8766 41.3554i −0.0228410 0.0395618i 0.854379 0.519650i \(-0.173938\pi\)
−0.877220 + 0.480089i \(0.840604\pi\)
\(104\) 187.167 + 324.183i 0.176474 + 0.305661i
\(105\) 0 0
\(106\) 790.324 1368.88i 0.724180 1.25432i
\(107\) 1839.39 1.66187 0.830936 0.556368i \(-0.187806\pi\)
0.830936 + 0.556368i \(0.187806\pi\)
\(108\) 0 0
\(109\) 559.158 0.491354 0.245677 0.969352i \(-0.420990\pi\)
0.245677 + 0.969352i \(0.420990\pi\)
\(110\) 48.8981 84.6941i 0.0423841 0.0734115i
\(111\) 0 0
\(112\) −948.093 1642.15i −0.799878 1.38543i
\(113\) 1182.42 + 2048.01i 0.984359 + 1.70496i 0.644751 + 0.764393i \(0.276961\pi\)
0.339609 + 0.940567i \(0.389705\pi\)
\(114\) 0 0
\(115\) −245.670 + 425.513i −0.199207 + 0.345037i
\(116\) −1146.11 −0.917360
\(117\) 0 0
\(118\) 585.295 0.456616
\(119\) 692.399 1199.27i 0.533379 0.923840i
\(120\) 0 0
\(121\) 652.597 + 1130.33i 0.490306 + 0.849235i
\(122\) 1024.66 + 1774.76i 0.760395 + 1.31704i
\(123\) 0 0
\(124\) −650.988 + 1127.54i −0.471455 + 0.816584i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −2403.43 −1.67929 −0.839646 0.543134i \(-0.817238\pi\)
−0.839646 + 0.543134i \(0.817238\pi\)
\(128\) 286.491 496.218i 0.197832 0.342655i
\(129\) 0 0
\(130\) 796.249 + 1379.14i 0.537197 + 0.930453i
\(131\) −817.404 1415.78i −0.545167 0.944257i −0.998596 0.0529648i \(-0.983133\pi\)
0.453429 0.891292i \(-0.350200\pi\)
\(132\) 0 0
\(133\) −393.095 + 680.860i −0.256283 + 0.443895i
\(134\) −2361.78 −1.52259
\(135\) 0 0
\(136\) 238.018 0.150072
\(137\) 1263.19 2187.91i 0.787749 1.36442i −0.139594 0.990209i \(-0.544580\pi\)
0.927343 0.374212i \(-0.122087\pi\)
\(138\) 0 0
\(139\) −945.422 1637.52i −0.576904 0.999227i −0.995832 0.0912078i \(-0.970927\pi\)
0.418928 0.908020i \(-0.362406\pi\)
\(140\) −449.205 778.045i −0.271177 0.469692i
\(141\) 0 0
\(142\) 796.890 1380.25i 0.470940 0.815693i
\(143\) 420.219 0.245737
\(144\) 0 0
\(145\) 839.679 0.480907
\(146\) −220.398 + 381.740i −0.124933 + 0.216391i
\(147\) 0 0
\(148\) 1248.46 + 2162.39i 0.693395 + 1.20099i
\(149\) −139.451 241.535i −0.0766727 0.132801i 0.825140 0.564929i \(-0.191096\pi\)
−0.901812 + 0.432128i \(0.857763\pi\)
\(150\) 0 0
\(151\) 215.976 374.081i 0.116396 0.201604i −0.801941 0.597404i \(-0.796199\pi\)
0.918337 + 0.395799i \(0.129532\pi\)
\(152\) −135.129 −0.0721082
\(153\) 0 0
\(154\) −514.960 −0.269459
\(155\) 476.935 826.076i 0.247151 0.428078i
\(156\) 0 0
\(157\) 222.554 + 385.474i 0.113132 + 0.195950i 0.917031 0.398815i \(-0.130578\pi\)
−0.803900 + 0.594765i \(0.797245\pi\)
\(158\) 152.289 + 263.772i 0.0766801 + 0.132814i
\(159\) 0 0
\(160\) 602.749 1043.99i 0.297822 0.515843i
\(161\) 2587.22 1.26647
\(162\) 0 0
\(163\) −2533.56 −1.21745 −0.608723 0.793382i \(-0.708318\pi\)
−0.608723 + 0.793382i \(0.708318\pi\)
\(164\) −381.203 + 660.263i −0.181506 + 0.314377i
\(165\) 0 0
\(166\) 2747.81 + 4759.34i 1.28477 + 2.22528i
\(167\) 1082.74 + 1875.37i 0.501707 + 0.868983i 0.999998 + 0.00197267i \(0.000627922\pi\)
−0.498291 + 0.867010i \(0.666039\pi\)
\(168\) 0 0
\(169\) −2322.88 + 4023.35i −1.05730 + 1.83129i
\(170\) 1012.58 0.456830
\(171\) 0 0
\(172\) −2754.47 −1.22108
\(173\) 681.847 1180.99i 0.299653 0.519013i −0.676404 0.736531i \(-0.736463\pi\)
0.976056 + 0.217517i \(0.0697959\pi\)
\(174\) 0 0
\(175\) 329.102 + 570.022i 0.142159 + 0.246226i
\(176\) −182.932 316.847i −0.0783466 0.135700i
\(177\) 0 0
\(178\) −866.476 + 1500.78i −0.364860 + 0.631957i
\(179\) 1198.29 0.500358 0.250179 0.968200i \(-0.419511\pi\)
0.250179 + 0.968200i \(0.419511\pi\)
\(180\) 0 0
\(181\) 1098.13 0.450959 0.225480 0.974248i \(-0.427605\pi\)
0.225480 + 0.974248i \(0.427605\pi\)
\(182\) 4192.76 7262.07i 1.70763 2.95770i
\(183\) 0 0
\(184\) 222.344 + 385.112i 0.0890839 + 0.154298i
\(185\) −914.661 1584.24i −0.363498 0.629597i
\(186\) 0 0
\(187\) 133.596 231.396i 0.0522435 0.0904885i
\(188\) −1584.53 −0.614700
\(189\) 0 0
\(190\) −574.869 −0.219502
\(191\) −625.013 + 1082.55i −0.236777 + 0.410110i −0.959788 0.280727i \(-0.909424\pi\)
0.723011 + 0.690837i \(0.242758\pi\)
\(192\) 0 0
\(193\) −1620.76 2807.23i −0.604480 1.04699i −0.992133 0.125185i \(-0.960048\pi\)
0.387654 0.921805i \(-0.373286\pi\)
\(194\) 2766.19 + 4791.19i 1.02372 + 1.77313i
\(195\) 0 0
\(196\) −1194.92 + 2069.65i −0.435465 + 0.754247i
\(197\) −714.141 −0.258276 −0.129138 0.991627i \(-0.541221\pi\)
−0.129138 + 0.991627i \(0.541221\pi\)
\(198\) 0 0
\(199\) −666.927 −0.237574 −0.118787 0.992920i \(-0.537901\pi\)
−0.118787 + 0.992920i \(0.537901\pi\)
\(200\) −56.5658 + 97.9748i −0.0199990 + 0.0346393i
\(201\) 0 0
\(202\) 3555.80 + 6158.83i 1.23854 + 2.14522i
\(203\) −2210.72 3829.09i −0.764347 1.32389i
\(204\) 0 0
\(205\) 279.282 483.731i 0.0951507 0.164806i
\(206\) −183.863 −0.0621862
\(207\) 0 0
\(208\) 5957.66 1.98601
\(209\) −75.8465 + 131.370i −0.0251025 + 0.0434787i
\(210\) 0 0
\(211\) 2479.61 + 4294.80i 0.809019 + 1.40126i 0.913544 + 0.406740i \(0.133335\pi\)
−0.104525 + 0.994522i \(0.533332\pi\)
\(212\) −1400.86 2426.37i −0.453829 0.786054i
\(213\) 0 0
\(214\) 3541.08 6133.33i 1.13114 1.95919i
\(215\) 2018.02 0.640128
\(216\) 0 0
\(217\) −5022.74 −1.57127
\(218\) 1076.46 1864.48i 0.334436 0.579260i
\(219\) 0 0
\(220\) −86.6728 150.122i −0.0265613 0.0460054i
\(221\) 2175.46 + 3768.01i 0.662160 + 1.14689i
\(222\) 0 0
\(223\) −561.885 + 973.213i −0.168729 + 0.292248i −0.937973 0.346707i \(-0.887300\pi\)
0.769244 + 0.638955i \(0.220633\pi\)
\(224\) −6347.72 −1.89341
\(225\) 0 0
\(226\) 9105.30 2.67998
\(227\) −612.555 + 1060.98i −0.179104 + 0.310218i −0.941574 0.336806i \(-0.890653\pi\)
0.762470 + 0.647024i \(0.223987\pi\)
\(228\) 0 0
\(229\) 1789.09 + 3098.79i 0.516272 + 0.894209i 0.999822 + 0.0188922i \(0.00601392\pi\)
−0.483550 + 0.875317i \(0.660653\pi\)
\(230\) 945.900 + 1638.35i 0.271177 + 0.469693i
\(231\) 0 0
\(232\) 379.977 658.139i 0.107529 0.186246i
\(233\) −527.061 −0.148193 −0.0740963 0.997251i \(-0.523607\pi\)
−0.0740963 + 0.997251i \(0.523607\pi\)
\(234\) 0 0
\(235\) 1160.88 0.322244
\(236\) 518.722 898.453i 0.143076 0.247815i
\(237\) 0 0
\(238\) −2665.93 4617.53i −0.726079 1.25761i
\(239\) 48.1693 + 83.4317i 0.0130369 + 0.0225805i 0.872470 0.488667i \(-0.162517\pi\)
−0.859433 + 0.511248i \(0.829183\pi\)
\(240\) 0 0
\(241\) −461.973 + 800.160i −0.123478 + 0.213871i −0.921137 0.389238i \(-0.872738\pi\)
0.797659 + 0.603109i \(0.206072\pi\)
\(242\) 5025.37 1.33489
\(243\) 0 0
\(244\) 3632.45 0.953047
\(245\) 875.435 1516.30i 0.228284 0.395399i
\(246\) 0 0
\(247\) −1235.07 2139.21i −0.318161 0.551071i
\(248\) −431.652 747.643i −0.110524 0.191433i
\(249\) 0 0
\(250\) −240.643 + 416.806i −0.0608783 + 0.105444i
\(251\) 4134.83 1.03979 0.519897 0.854229i \(-0.325970\pi\)
0.519897 + 0.854229i \(0.325970\pi\)
\(252\) 0 0
\(253\) 499.197 0.124048
\(254\) −4626.95 + 8014.11i −1.14299 + 1.97972i
\(255\) 0 0
\(256\) −2511.61 4350.23i −0.613185 1.06207i
\(257\) 893.588 + 1547.74i 0.216889 + 0.375663i 0.953855 0.300267i \(-0.0970757\pi\)
−0.736966 + 0.675930i \(0.763742\pi\)
\(258\) 0 0
\(259\) −4816.27 + 8342.03i −1.15548 + 2.00135i
\(260\) 2822.73 0.673301
\(261\) 0 0
\(262\) −6294.47 −1.48425
\(263\) −2674.07 + 4631.63i −0.626960 + 1.08593i 0.361199 + 0.932489i \(0.382368\pi\)
−0.988158 + 0.153437i \(0.950966\pi\)
\(264\) 0 0
\(265\) 1026.32 + 1777.64i 0.237911 + 0.412073i
\(266\) 1513.53 + 2621.51i 0.348873 + 0.604266i
\(267\) 0 0
\(268\) −2093.15 + 3625.44i −0.477087 + 0.826340i
\(269\) −8266.59 −1.87369 −0.936846 0.349743i \(-0.886269\pi\)
−0.936846 + 0.349743i \(0.886269\pi\)
\(270\) 0 0
\(271\) −7114.58 −1.59476 −0.797380 0.603478i \(-0.793781\pi\)
−0.797380 + 0.603478i \(0.793781\pi\)
\(272\) 1894.07 3280.62i 0.422223 0.731312i
\(273\) 0 0
\(274\) −4863.64 8424.07i −1.07235 1.85736i
\(275\) 63.4994 + 109.984i 0.0139242 + 0.0241174i
\(276\) 0 0
\(277\) 1948.74 3375.32i 0.422702 0.732141i −0.573501 0.819205i \(-0.694415\pi\)
0.996203 + 0.0870636i \(0.0277483\pi\)
\(278\) −7280.29 −1.57066
\(279\) 0 0
\(280\) 595.710 0.127145
\(281\) −2647.47 + 4585.55i −0.562045 + 0.973490i 0.435273 + 0.900299i \(0.356652\pi\)
−0.997318 + 0.0731918i \(0.976681\pi\)
\(282\) 0 0
\(283\) 2321.50 + 4020.95i 0.487628 + 0.844596i 0.999899 0.0142281i \(-0.00452909\pi\)
−0.512271 + 0.858824i \(0.671196\pi\)
\(284\) −1412.50 2446.52i −0.295129 0.511178i
\(285\) 0 0
\(286\) 808.981 1401.20i 0.167259 0.289701i
\(287\) −2941.20 −0.604924
\(288\) 0 0
\(289\) −2146.50 −0.436902
\(290\) 1616.50 2799.86i 0.327325 0.566944i
\(291\) 0 0
\(292\) 390.658 + 676.640i 0.0782930 + 0.135607i
\(293\) −1957.53 3390.55i −0.390309 0.676034i 0.602182 0.798359i \(-0.294298\pi\)
−0.992490 + 0.122325i \(0.960965\pi\)
\(294\) 0 0
\(295\) −380.033 + 658.237i −0.0750047 + 0.129912i
\(296\) −1655.63 −0.325107
\(297\) 0 0
\(298\) −1073.85 −0.208746
\(299\) −4064.42 + 7039.78i −0.786125 + 1.36161i
\(300\) 0 0
\(301\) −5313.07 9202.51i −1.01741 1.76221i
\(302\) −831.568 1440.32i −0.158448 0.274440i
\(303\) 0 0
\(304\) −1075.32 + 1862.50i −0.202874 + 0.351387i
\(305\) −2661.25 −0.499616
\(306\) 0 0
\(307\) 6637.24 1.23390 0.616950 0.787002i \(-0.288368\pi\)
0.616950 + 0.787002i \(0.288368\pi\)
\(308\) −456.387 + 790.486i −0.0844321 + 0.146241i
\(309\) 0 0
\(310\) −1836.34 3180.63i −0.336442 0.582734i
\(311\) −1118.61 1937.49i −0.203957 0.353263i 0.745843 0.666122i \(-0.232047\pi\)
−0.949800 + 0.312858i \(0.898713\pi\)
\(312\) 0 0
\(313\) −657.096 + 1138.12i −0.118662 + 0.205529i −0.919238 0.393703i \(-0.871194\pi\)
0.800576 + 0.599232i \(0.204527\pi\)
\(314\) 1713.79 0.308009
\(315\) 0 0
\(316\) 539.869 0.0961077
\(317\) 470.230 814.462i 0.0833147 0.144305i −0.821357 0.570414i \(-0.806783\pi\)
0.904672 + 0.426109i \(0.140116\pi\)
\(318\) 0 0
\(319\) −426.553 738.811i −0.0748664 0.129672i
\(320\) −880.334 1524.78i −0.153788 0.266369i
\(321\) 0 0
\(322\) 4980.77 8626.94i 0.862010 1.49305i
\(323\) −1570.62 −0.270563
\(324\) 0 0
\(325\) −2068.03 −0.352964
\(326\) −4877.47 + 8448.02i −0.828644 + 1.43525i
\(327\) 0 0
\(328\) −252.765 437.802i −0.0425506 0.0736999i
\(329\) −3056.38 5293.81i −0.512170 0.887105i
\(330\) 0 0
\(331\) 1121.23 1942.03i 0.186188 0.322487i −0.757788 0.652501i \(-0.773720\pi\)
0.943976 + 0.330013i \(0.107053\pi\)
\(332\) 9741.07 1.61027
\(333\) 0 0
\(334\) 8337.73 1.36593
\(335\) 1533.51 2656.12i 0.250103 0.433192i
\(336\) 0 0
\(337\) 1561.83 + 2705.16i 0.252457 + 0.437269i 0.964202 0.265170i \(-0.0854279\pi\)
−0.711744 + 0.702438i \(0.752095\pi\)
\(338\) 8943.76 + 15491.1i 1.43928 + 2.49291i
\(339\) 0 0
\(340\) 897.405 1554.35i 0.143143 0.247931i
\(341\) −969.123 −0.153903
\(342\) 0 0
\(343\) −188.878 −0.0297332
\(344\) 913.206 1581.72i 0.143130 0.247909i
\(345\) 0 0
\(346\) −2625.31 4547.16i −0.407911 0.706523i
\(347\) −5361.13 9285.75i −0.829397 1.43656i −0.898512 0.438948i \(-0.855351\pi\)
0.0691157 0.997609i \(-0.477982\pi\)
\(348\) 0 0
\(349\) 3050.82 5284.18i 0.467928 0.810475i −0.531400 0.847121i \(-0.678334\pi\)
0.999328 + 0.0366457i \(0.0116673\pi\)
\(350\) 2534.28 0.387037
\(351\) 0 0
\(352\) −1224.77 −0.185456
\(353\) −5164.28 + 8944.79i −0.778659 + 1.34868i 0.154056 + 0.988062i \(0.450766\pi\)
−0.932715 + 0.360615i \(0.882567\pi\)
\(354\) 0 0
\(355\) 1034.85 + 1792.41i 0.154715 + 0.267975i
\(356\) 1535.84 + 2660.16i 0.228650 + 0.396034i
\(357\) 0 0
\(358\) 2306.87 3995.62i 0.340564 0.589874i
\(359\) −1122.33 −0.164998 −0.0824992 0.996591i \(-0.526290\pi\)
−0.0824992 + 0.996591i \(0.526290\pi\)
\(360\) 0 0
\(361\) −5967.31 −0.869998
\(362\) 2114.06 3661.67i 0.306941 0.531638i
\(363\) 0 0
\(364\) −7431.73 12872.1i −1.07013 1.85353i
\(365\) −286.209 495.729i −0.0410435 0.0710895i
\(366\) 0 0
\(367\) 1821.44 3154.82i 0.259069 0.448720i −0.706924 0.707290i \(-0.749918\pi\)
0.965993 + 0.258569i \(0.0832510\pi\)
\(368\) 7077.37 1.00254
\(369\) 0 0
\(370\) −7043.41 −0.989647
\(371\) 5404.23 9360.40i 0.756263 1.30989i
\(372\) 0 0
\(373\) −4767.16 8256.97i −0.661755 1.14619i −0.980154 0.198236i \(-0.936479\pi\)
0.318400 0.947957i \(-0.396855\pi\)
\(374\) −514.384 890.940i −0.0711181 0.123180i
\(375\) 0 0
\(376\) 525.328 909.895i 0.0720525 0.124799i
\(377\) 13891.8 1.89779
\(378\) 0 0
\(379\) 10826.9 1.46738 0.733691 0.679483i \(-0.237796\pi\)
0.733691 + 0.679483i \(0.237796\pi\)
\(380\) −509.483 + 882.450i −0.0687787 + 0.119128i
\(381\) 0 0
\(382\) 2406.48 + 4168.14i 0.322320 + 0.558274i
\(383\) −3336.87 5779.63i −0.445185 0.771084i 0.552880 0.833261i \(-0.313529\pi\)
−0.998065 + 0.0621773i \(0.980196\pi\)
\(384\) 0 0
\(385\) 334.365 579.137i 0.0442618 0.0766638i
\(386\) −12480.7 −1.64573
\(387\) 0 0
\(388\) 9806.24 1.28308
\(389\) −631.501 + 1093.79i −0.0823094 + 0.142564i −0.904242 0.427021i \(-0.859563\pi\)
0.821932 + 0.569585i \(0.192896\pi\)
\(390\) 0 0
\(391\) 2584.33 + 4476.19i 0.334259 + 0.578953i
\(392\) −792.315 1372.33i −0.102087 0.176819i
\(393\) 0 0
\(394\) −1374.82 + 2381.26i −0.175793 + 0.304483i
\(395\) −395.526 −0.0503825
\(396\) 0 0
\(397\) −888.172 −0.112282 −0.0561411 0.998423i \(-0.517880\pi\)
−0.0561411 + 0.998423i \(0.517880\pi\)
\(398\) −1283.93 + 2223.83i −0.161703 + 0.280077i
\(399\) 0 0
\(400\) 900.264 + 1559.30i 0.112533 + 0.194913i
\(401\) −6186.20 10714.8i −0.770385 1.33435i −0.937352 0.348383i \(-0.886731\pi\)
0.166968 0.985962i \(-0.446602\pi\)
\(402\) 0 0
\(403\) 7890.52 13666.8i 0.975322 1.68931i
\(404\) 12605.4 1.55234
\(405\) 0 0
\(406\) −17023.8 −2.08098
\(407\) −929.286 + 1609.57i −0.113177 + 0.196028i
\(408\) 0 0
\(409\) 6323.64 + 10952.9i 0.764508 + 1.32417i 0.940506 + 0.339776i \(0.110351\pi\)
−0.175999 + 0.984390i \(0.556315\pi\)
\(410\) −1075.32 1862.50i −0.129527 0.224347i
\(411\) 0 0
\(412\) −162.950 + 282.238i −0.0194854 + 0.0337497i
\(413\) 4002.24 0.476846
\(414\) 0 0
\(415\) −7136.64 −0.844154
\(416\) 9972.01 17272.0i 1.17528 2.03565i
\(417\) 0 0
\(418\) 292.031 + 505.812i 0.0341715 + 0.0591868i
\(419\) 7126.00 + 12342.6i 0.830855 + 1.43908i 0.897361 + 0.441296i \(0.145481\pi\)
−0.0665067 + 0.997786i \(0.521185\pi\)
\(420\) 0 0
\(421\) −1272.84 + 2204.63i −0.147351 + 0.255219i −0.930247 0.366933i \(-0.880408\pi\)
0.782897 + 0.622151i \(0.213741\pi\)
\(422\) 19094.4 2.20261
\(423\) 0 0
\(424\) 1857.75 0.212783
\(425\) −657.469 + 1138.77i −0.0750399 + 0.129973i
\(426\) 0 0
\(427\) 7006.60 + 12135.8i 0.794082 + 1.37539i
\(428\) −6276.63 10871.4i −0.708860 1.22778i
\(429\) 0 0
\(430\) 3884.97 6728.96i 0.435697 0.754650i
\(431\) −3068.41 −0.342923 −0.171462 0.985191i \(-0.554849\pi\)
−0.171462 + 0.985191i \(0.554849\pi\)
\(432\) 0 0
\(433\) −13982.0 −1.55180 −0.775900 0.630856i \(-0.782704\pi\)
−0.775900 + 0.630856i \(0.782704\pi\)
\(434\) −9669.49 + 16748.0i −1.06947 + 1.85238i
\(435\) 0 0
\(436\) −1908.04 3304.82i −0.209584 0.363010i
\(437\) −1467.20 2541.26i −0.160608 0.278181i
\(438\) 0 0
\(439\) −3846.22 + 6661.85i −0.418155 + 0.724266i −0.995754 0.0920549i \(-0.970656\pi\)
0.577599 + 0.816321i \(0.303990\pi\)
\(440\) 114.941 0.0124536
\(441\) 0 0
\(442\) 16752.3 1.80277
\(443\) 17.9124 31.0252i 0.00192109 0.00332743i −0.865063 0.501663i \(-0.832722\pi\)
0.866984 + 0.498335i \(0.166055\pi\)
\(444\) 0 0
\(445\) −1125.21 1948.92i −0.119865 0.207613i
\(446\) 2163.42 + 3747.15i 0.229688 + 0.397831i
\(447\) 0 0
\(448\) −4635.52 + 8028.96i −0.488857 + 0.846725i
\(449\) −2602.16 −0.273505 −0.136752 0.990605i \(-0.543666\pi\)
−0.136752 + 0.990605i \(0.543666\pi\)
\(450\) 0 0
\(451\) −567.495 −0.0592512
\(452\) 8069.64 13977.0i 0.839744 1.45448i
\(453\) 0 0
\(454\) 2358.51 + 4085.06i 0.243811 + 0.422294i
\(455\) 5444.74 + 9430.56i 0.560996 + 0.971674i
\(456\) 0 0
\(457\) −4075.83 + 7059.55i −0.417198 + 0.722608i −0.995656 0.0931041i \(-0.970321\pi\)
0.578459 + 0.815712i \(0.303654\pi\)
\(458\) 13777.0 1.40558
\(459\) 0 0
\(460\) 3353.25 0.339882
\(461\) 3373.66 5843.34i 0.340839 0.590351i −0.643750 0.765236i \(-0.722622\pi\)
0.984589 + 0.174886i \(0.0559555\pi\)
\(462\) 0 0
\(463\) −419.278 726.210i −0.0420853 0.0728939i 0.844215 0.536004i \(-0.180067\pi\)
−0.886301 + 0.463110i \(0.846733\pi\)
\(464\) −6047.46 10474.5i −0.605057 1.04799i
\(465\) 0 0
\(466\) −1014.67 + 1757.45i −0.100866 + 0.174705i
\(467\) 7253.46 0.718737 0.359369 0.933196i \(-0.382992\pi\)
0.359369 + 0.933196i \(0.382992\pi\)
\(468\) 0 0
\(469\) −16149.8 −1.59004
\(470\) 2234.86 3870.89i 0.219332 0.379895i
\(471\) 0 0
\(472\) 343.950 + 595.739i 0.0335415 + 0.0580956i
\(473\) −1025.14 1775.60i −0.0996535 0.172605i
\(474\) 0 0
\(475\) 373.264 646.512i 0.0360559 0.0624506i
\(476\) −9450.83 −0.910038
\(477\) 0 0
\(478\) 370.931 0.0354937
\(479\) 5175.92 8964.95i 0.493724 0.855154i −0.506250 0.862387i \(-0.668969\pi\)
0.999974 + 0.00723223i \(0.00230211\pi\)
\(480\) 0 0
\(481\) −15132.3 26210.0i −1.43446 2.48456i
\(482\) 1778.73 + 3080.85i 0.168089 + 0.291138i
\(483\) 0 0
\(484\) 4453.78 7714.16i 0.418273 0.724471i
\(485\) −7184.38 −0.672631
\(486\) 0 0
\(487\) 5202.70 0.484100 0.242050 0.970264i \(-0.422180\pi\)
0.242050 + 0.970264i \(0.422180\pi\)
\(488\) −1204.29 + 2085.89i −0.111712 + 0.193491i
\(489\) 0 0
\(490\) −3370.67 5838.18i −0.310758 0.538249i
\(491\) 1230.26 + 2130.87i 0.113077 + 0.195855i 0.917009 0.398866i \(-0.130596\pi\)
−0.803932 + 0.594721i \(0.797263\pi\)
\(492\) 0 0
\(493\) 4416.51 7649.61i 0.403467 0.698826i
\(494\) −9510.75 −0.866213
\(495\) 0 0
\(496\) −13739.8 −1.24382
\(497\) 5449.12 9438.16i 0.491804 0.851830i
\(498\) 0 0
\(499\) 6428.16 + 11133.9i 0.576681 + 0.998842i 0.995857 + 0.0909363i \(0.0289860\pi\)
−0.419175 + 0.907905i \(0.637681\pi\)
\(500\) 426.543 + 738.795i 0.0381512 + 0.0660798i
\(501\) 0 0
\(502\) 7960.14 13787.4i 0.707726 1.22582i
\(503\) −21744.3 −1.92750 −0.963749 0.266810i \(-0.914030\pi\)
−0.963749 + 0.266810i \(0.914030\pi\)
\(504\) 0 0
\(505\) −9235.17 −0.813782
\(506\) 961.025 1664.54i 0.0844323 0.146241i
\(507\) 0 0
\(508\) 8201.34 + 14205.1i 0.716291 + 1.24065i
\(509\) 4871.91 + 8438.40i 0.424251 + 0.734824i 0.996350 0.0853605i \(-0.0272042\pi\)
−0.572099 + 0.820184i \(0.693871\pi\)
\(510\) 0 0
\(511\) −1507.08 + 2610.33i −0.130468 + 0.225977i
\(512\) −14756.9 −1.27377
\(513\) 0 0
\(514\) 6881.13 0.590494
\(515\) 119.383 206.777i 0.0102148 0.0176926i
\(516\) 0 0
\(517\) −589.721 1021.43i −0.0501661 0.0868903i
\(518\) 18544.0 + 32119.2i 1.57293 + 2.72439i
\(519\) 0 0
\(520\) −935.836 + 1620.92i −0.0789214 + 0.136696i
\(521\) −17889.5 −1.50432 −0.752161 0.658980i \(-0.770988\pi\)
−0.752161 + 0.658980i \(0.770988\pi\)
\(522\) 0 0
\(523\) 5012.48 0.419083 0.209542 0.977800i \(-0.432803\pi\)
0.209542 + 0.977800i \(0.432803\pi\)
\(524\) −5578.53 + 9662.30i −0.465075 + 0.805533i
\(525\) 0 0
\(526\) 10295.9 + 17833.1i 0.853468 + 1.47825i
\(527\) −5017.13 8689.92i −0.414705 0.718290i
\(528\) 0 0
\(529\) 1255.20 2174.06i 0.103164 0.178685i
\(530\) 7903.24 0.647726
\(531\) 0 0
\(532\) 5365.50 0.437263
\(533\) 4620.50 8002.94i 0.375490 0.650367i
\(534\) 0 0
\(535\) 4598.47 + 7964.78i 0.371606 + 0.643640i
\(536\) −1387.91 2403.93i −0.111844 0.193720i
\(537\) 0 0
\(538\) −15914.4 + 27564.5i −1.27531 + 2.20890i
\(539\) −1778.87 −0.142154
\(540\) 0 0
\(541\) 12629.5 1.00367 0.501834 0.864964i \(-0.332659\pi\)
0.501834 + 0.864964i \(0.332659\pi\)
\(542\) −13696.6 + 23723.2i −1.08546 + 1.88007i
\(543\) 0 0
\(544\) −6340.63 10982.3i −0.499728 0.865554i
\(545\) 1397.89 + 2421.22i 0.109870 + 0.190301i
\(546\) 0 0
\(547\) −3665.93 + 6349.57i −0.286552 + 0.496322i −0.972984 0.230871i \(-0.925842\pi\)
0.686433 + 0.727193i \(0.259176\pi\)
\(548\) −17241.8 −1.34404
\(549\) 0 0
\(550\) 488.981 0.0379095
\(551\) −2507.38 + 4342.90i −0.193862 + 0.335778i
\(552\) 0 0
\(553\) 1041.35 + 1803.67i 0.0800772 + 0.138698i
\(554\) −7503.21 12995.9i −0.575416 0.996650i
\(555\) 0 0
\(556\) −6452.22 + 11175.6i −0.492149 + 0.852428i
\(557\) 11389.0 0.866371 0.433185 0.901305i \(-0.357390\pi\)
0.433185 + 0.901305i \(0.357390\pi\)
\(558\) 0 0
\(559\) 33386.5 2.52611
\(560\) 4740.46 8210.73i 0.357716 0.619583i
\(561\) 0 0
\(562\) 10193.5 + 17655.7i 0.765101 + 1.32519i
\(563\) −6610.55 11449.8i −0.494852 0.857109i 0.505130 0.863043i \(-0.331444\pi\)
−0.999982 + 0.00593423i \(0.998111\pi\)
\(564\) 0 0
\(565\) −5912.09 + 10240.0i −0.440219 + 0.762481i
\(566\) 17876.8 1.32760
\(567\) 0 0
\(568\) 1873.18 0.138375
\(569\) 4170.89 7224.20i 0.307299 0.532257i −0.670472 0.741935i \(-0.733908\pi\)
0.977770 + 0.209678i \(0.0672416\pi\)
\(570\) 0 0
\(571\) −10801.2 18708.3i −0.791625 1.37114i −0.924960 0.380064i \(-0.875902\pi\)
0.133335 0.991071i \(-0.457431\pi\)
\(572\) −1433.93 2483.64i −0.104818 0.181549i
\(573\) 0 0
\(574\) −5662.22 + 9807.26i −0.411736 + 0.713148i
\(575\) −2456.70 −0.178177
\(576\) 0 0
\(577\) −696.389 −0.0502444 −0.0251222 0.999684i \(-0.507997\pi\)
−0.0251222 + 0.999684i \(0.507997\pi\)
\(578\) −4132.31 + 7157.38i −0.297373 + 0.515065i
\(579\) 0 0
\(580\) −2865.28 4962.80i −0.205128 0.355292i
\(581\) 18789.5 + 32544.3i 1.34169 + 2.32387i
\(582\) 0 0
\(583\) 1042.73 1806.06i 0.0740746 0.128301i
\(584\) −518.069 −0.0367087
\(585\) 0 0
\(586\) −15074.1 −1.06264
\(587\) −11962.1 + 20719.0i −0.841105 + 1.45684i 0.0478566 + 0.998854i \(0.484761\pi\)
−0.888961 + 0.457982i \(0.848572\pi\)
\(588\) 0 0
\(589\) 2848.37 + 4933.51i 0.199261 + 0.345131i
\(590\) 1463.24 + 2534.40i 0.102103 + 0.176847i
\(591\) 0 0
\(592\) −13175.0 + 22819.7i −0.914676 + 1.58426i
\(593\) 11887.8 0.823226 0.411613 0.911359i \(-0.364966\pi\)
0.411613 + 0.911359i \(0.364966\pi\)
\(594\) 0 0
\(595\) 6923.99 0.477069
\(596\) −951.707 + 1648.41i −0.0654085 + 0.113291i
\(597\) 0 0
\(598\) 15649.2 + 27105.1i 1.07014 + 1.85353i
\(599\) 2453.71 + 4249.95i 0.167372 + 0.289897i 0.937495 0.347998i \(-0.113139\pi\)
−0.770123 + 0.637895i \(0.779805\pi\)
\(600\) 0 0
\(601\) −5632.34 + 9755.49i −0.382276 + 0.662121i −0.991387 0.130964i \(-0.958193\pi\)
0.609111 + 0.793085i \(0.291526\pi\)
\(602\) −40913.7 −2.76996
\(603\) 0 0
\(604\) −2947.94 −0.198592
\(605\) −3262.99 + 5651.66i −0.219271 + 0.379789i
\(606\) 0 0
\(607\) −2511.33 4349.75i −0.167927 0.290858i 0.769764 0.638329i \(-0.220374\pi\)
−0.937691 + 0.347471i \(0.887041\pi\)
\(608\) 3599.75 + 6234.96i 0.240114 + 0.415890i
\(609\) 0 0
\(610\) −5123.29 + 8873.80i −0.340059 + 0.588999i
\(611\) 19205.8 1.27166
\(612\) 0 0
\(613\) 19450.0 1.28153 0.640766 0.767736i \(-0.278617\pi\)
0.640766 + 0.767736i \(0.278617\pi\)
\(614\) 12777.6 22131.5i 0.839843 1.45465i
\(615\) 0 0
\(616\) −302.618 524.149i −0.0197935 0.0342834i
\(617\) −1009.02 1747.68i −0.0658375 0.114034i 0.831228 0.555932i \(-0.187639\pi\)
−0.897065 + 0.441898i \(0.854305\pi\)
\(618\) 0 0
\(619\) −4548.76 + 7878.69i −0.295364 + 0.511585i −0.975069 0.221900i \(-0.928774\pi\)
0.679706 + 0.733485i \(0.262108\pi\)
\(620\) −6509.88 −0.421682
\(621\) 0 0
\(622\) −8613.93 −0.555285
\(623\) −5924.95 + 10262.3i −0.381025 + 0.659954i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 2530.01 + 4382.10i 0.161533 + 0.279783i
\(627\) 0 0
\(628\) 1518.86 2630.74i 0.0965113 0.167163i
\(629\) −19243.6 −1.21986
\(630\) 0 0
\(631\) 3118.35 0.196735 0.0983674 0.995150i \(-0.468638\pi\)
0.0983674 + 0.995150i \(0.468638\pi\)
\(632\) −178.986 + 310.013i −0.0112653 + 0.0195121i
\(633\) 0 0
\(634\) −1810.52 3135.91i −0.113415 0.196440i
\(635\) −6008.58 10407.2i −0.375501 0.650387i
\(636\) 0 0
\(637\) 14483.4 25085.9i 0.900867 1.56035i
\(638\) −3284.70 −0.203828
\(639\) 0 0
\(640\) 2864.91 0.176946
\(641\) −5227.12 + 9053.64i −0.322089 + 0.557874i −0.980919 0.194418i \(-0.937718\pi\)
0.658830 + 0.752292i \(0.271052\pi\)
\(642\) 0 0
\(643\) −8062.80 13965.2i −0.494504 0.856506i 0.505476 0.862841i \(-0.331317\pi\)
−0.999980 + 0.00633487i \(0.997984\pi\)
\(644\) −8828.49 15291.4i −0.540204 0.935661i
\(645\) 0 0
\(646\) −3023.67 + 5237.15i −0.184156 + 0.318967i
\(647\) −13627.3 −0.828045 −0.414022 0.910267i \(-0.635877\pi\)
−0.414022 + 0.910267i \(0.635877\pi\)
\(648\) 0 0
\(649\) 772.220 0.0467061
\(650\) −3981.24 + 6895.72i −0.240242 + 0.416111i
\(651\) 0 0
\(652\) 8645.39 + 14974.3i 0.519294 + 0.899443i
\(653\) −1327.33 2299.01i −0.0795446 0.137775i 0.823509 0.567303i \(-0.192013\pi\)
−0.903054 + 0.429528i \(0.858680\pi\)
\(654\) 0 0
\(655\) 4087.02 7078.92i 0.243806 0.422285i
\(656\) −8045.68 −0.478858
\(657\) 0 0
\(658\) −23535.9 −1.39441
\(659\) −9128.39 + 15810.8i −0.539593 + 0.934602i 0.459333 + 0.888264i \(0.348088\pi\)
−0.998926 + 0.0463379i \(0.985245\pi\)
\(660\) 0 0
\(661\) 3519.17 + 6095.38i 0.207080 + 0.358673i 0.950793 0.309825i \(-0.100271\pi\)
−0.743713 + 0.668499i \(0.766937\pi\)
\(662\) −4317.05 7477.35i −0.253455 0.438996i
\(663\) 0 0
\(664\) −3229.52 + 5593.69i −0.188749 + 0.326923i
\(665\) −3930.95 −0.229226
\(666\) 0 0
\(667\) 16502.7 0.958003
\(668\) 7389.39 12798.8i 0.428000 0.741318i
\(669\) 0 0
\(670\) −5904.46 10226.8i −0.340461 0.589696i
\(671\) 1351.90 + 2341.56i 0.0777789 + 0.134717i
\(672\) 0 0
\(673\) 5021.54 8697.56i 0.287617 0.498167i −0.685624 0.727956i \(-0.740470\pi\)
0.973240 + 0.229789i \(0.0738038\pi\)
\(674\) 12027.0 0.687331
\(675\) 0 0
\(676\) 31705.9 1.80393
\(677\) 12999.6 22516.0i 0.737984 1.27823i −0.215417 0.976522i \(-0.569111\pi\)
0.953402 0.301704i \(-0.0975555\pi\)
\(678\) 0 0
\(679\) 18915.2 + 32762.1i 1.06907 + 1.85168i
\(680\) 595.044 + 1030.65i 0.0335572 + 0.0581228i
\(681\) 0 0
\(682\) −1865.70 + 3231.49i −0.104753 + 0.181437i
\(683\) 13619.4 0.763004 0.381502 0.924368i \(-0.375407\pi\)
0.381502 + 0.924368i \(0.375407\pi\)
\(684\) 0 0
\(685\) 12631.9 0.704584
\(686\) −363.618 + 629.805i −0.0202376 + 0.0350525i
\(687\) 0 0
\(688\) −14534.0 25173.6i −0.805382 1.39496i
\(689\) 16979.6 + 29409.6i 0.938857 + 1.62615i
\(690\) 0 0
\(691\) 6861.47 11884.4i 0.377746 0.654275i −0.612988 0.790092i \(-0.710033\pi\)
0.990734 + 0.135817i \(0.0433659\pi\)
\(692\) −9306.80 −0.511259
\(693\) 0 0
\(694\) −41283.8 −2.25808
\(695\) 4727.11 8187.60i 0.257999 0.446868i
\(696\) 0 0
\(697\) −2937.91 5088.61i −0.159657 0.276535i
\(698\) −11746.5 20345.6i −0.636982 1.10328i
\(699\) 0 0
\(700\) 2246.02 3890.23i 0.121274 0.210053i
\(701\) 11103.4 0.598244 0.299122 0.954215i \(-0.403306\pi\)
0.299122 + 0.954215i \(0.403306\pi\)
\(702\) 0 0
\(703\) 10925.1 0.586129
\(704\) −894.410 + 1549.16i −0.0478826 + 0.0829351i
\(705\) 0 0
\(706\) 19883.9 + 34440.0i 1.05997 + 1.83593i
\(707\) 24314.5 + 42114.0i 1.29341 + 2.24026i
\(708\) 0 0
\(709\) 1531.80 2653.15i 0.0811395 0.140538i −0.822600 0.568620i \(-0.807477\pi\)
0.903740 + 0.428082i \(0.140811\pi\)
\(710\) 7968.90 0.421222
\(711\) 0 0
\(712\) −2036.75 −0.107206
\(713\) 9373.50 16235.4i 0.492343 0.852763i
\(714\) 0 0
\(715\) 1050.55 + 1819.60i 0.0549486 + 0.0951737i
\(716\) −4088.96 7082.29i −0.213424 0.369662i
\(717\) 0 0
\(718\) −2160.65 + 3742.35i −0.112305 + 0.194517i
\(719\) 31506.0 1.63418 0.817089 0.576511i \(-0.195586\pi\)
0.817089 + 0.576511i \(0.195586\pi\)
\(720\) 0 0
\(721\) −1257.25 −0.0649411
\(722\) −11487.9 + 19897.7i −0.592156 + 1.02564i
\(723\) 0 0
\(724\) −3747.21 6490.36i −0.192354 0.333166i
\(725\) 2099.20 + 3635.92i 0.107534 + 0.186255i
\(726\) 0 0
\(727\) −7528.24 + 13039.3i −0.384054 + 0.665200i −0.991637 0.129055i \(-0.958806\pi\)
0.607584 + 0.794256i \(0.292139\pi\)
\(728\) 9855.55 0.501746
\(729\) 0 0
\(730\) −2203.98 −0.111744
\(731\) 10614.3 18384.5i 0.537049 0.930197i
\(732\) 0 0
\(733\) −10133.7 17552.1i −0.510637 0.884449i −0.999924 0.0123261i \(-0.996076\pi\)
0.489287 0.872123i \(-0.337257\pi\)
\(734\) −7013.05 12147.0i −0.352666 0.610835i
\(735\) 0 0
\(736\) 11846.2 20518.2i 0.593283 1.02760i
\(737\) −3116.06 −0.155742
\(738\) 0 0
\(739\) −22434.4 −1.11673 −0.558365 0.829595i \(-0.688571\pi\)
−0.558365 + 0.829595i \(0.688571\pi\)
\(740\) −6242.28 + 10811.9i −0.310096 + 0.537101i
\(741\) 0 0
\(742\) −20807.8 36040.2i −1.02949 1.78312i
\(743\) −18623.1 32256.2i −0.919538 1.59269i −0.800118 0.599843i \(-0.795230\pi\)
−0.119420 0.992844i \(-0.538103\pi\)
\(744\) 0 0
\(745\) 697.253 1207.68i 0.0342891 0.0593904i
\(746\) −36709.9 −1.80167
\(747\) 0 0
\(748\) −1823.51 −0.0891365
\(749\) 24213.9 41939.7i 1.18125 2.04598i
\(750\) 0 0
\(751\) 11115.5 + 19252.6i 0.540093 + 0.935468i 0.998898 + 0.0469310i \(0.0149441\pi\)
−0.458806 + 0.888537i \(0.651723\pi\)
\(752\) −8360.78 14481.3i −0.405434 0.702232i
\(753\) 0 0
\(754\) 26743.7 46321.5i 1.29171 2.23731i
\(755\) 2159.76 0.104108
\(756\) 0 0
\(757\) −11212.1 −0.538324 −0.269162 0.963095i \(-0.586747\pi\)
−0.269162 + 0.963095i \(0.586747\pi\)
\(758\) 20843.2 36101.5i 0.998760 1.72990i
\(759\) 0 0
\(760\) −337.824 585.128i −0.0161239 0.0279274i
\(761\) 6841.43 + 11849.7i 0.325889 + 0.564456i 0.981692 0.190476i \(-0.0610031\pi\)
−0.655803 + 0.754932i \(0.727670\pi\)
\(762\) 0 0
\(763\) 7360.81 12749.3i 0.349252 0.604922i
\(764\) 8531.05 0.403982
\(765\) 0 0
\(766\) −25695.8 −1.21205
\(767\) −6287.35 + 10890.0i −0.295988 + 0.512667i
\(768\) 0 0
\(769\) −6837.13 11842.3i −0.320616 0.555322i 0.660000 0.751266i \(-0.270556\pi\)
−0.980615 + 0.195944i \(0.937223\pi\)
\(770\) −1287.40 2229.84i −0.0602528 0.104361i
\(771\) 0 0
\(772\) −11061.2 + 19158.5i −0.515674 + 0.893173i
\(773\) −28378.8 −1.32046 −0.660230 0.751064i \(-0.729541\pi\)
−0.660230 + 0.751064i \(0.729541\pi\)
\(774\) 0 0
\(775\) 4769.35 0.221058
\(776\) −3251.12 + 5631.11i −0.150398 + 0.260496i
\(777\) 0 0
\(778\) 2431.46 + 4211.41i 0.112046 + 0.194070i
\(779\) 1667.93 + 2888.95i 0.0767137 + 0.132872i
\(780\) 0 0
\(781\) 1051.39 1821.07i 0.0481713 0.0834352i
\(782\) 19900.8 0.910040
\(783\) 0 0
\(784\) −25219.9 −1.14887
\(785\) −1112.77 + 1927.37i −0.0505941 + 0.0876316i
\(786\) 0