Properties

Label 225.4.e.f.76.2
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.2
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.f.151.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +O(q^{10})\) \(q+(-2.16773 - 3.75461i) q^{2} +(-0.193913 + 5.19253i) q^{3} +(-5.39807 + 9.34974i) q^{4} +(19.9163 - 10.5279i) q^{6} +(-6.50075 - 11.2596i) q^{7} +12.1226 q^{8} +(-26.9248 - 2.01380i) q^{9} +(17.2761 + 29.9230i) q^{11} +(-47.5021 - 29.8427i) q^{12} +(3.77884 - 6.54514i) q^{13} +(-28.1837 + 48.8156i) q^{14} +(16.9062 + 29.2824i) q^{16} -82.0901 q^{17} +(50.8046 + 105.458i) q^{18} +146.406 q^{19} +(59.7265 - 31.5720i) q^{21} +(74.8995 - 129.730i) q^{22} +(93.9451 - 162.718i) q^{23} +(-2.35072 + 62.9468i) q^{24} -32.7659 q^{26} +(15.6778 - 139.417i) q^{27} +140.366 q^{28} +(-21.8589 - 37.8607i) q^{29} +(29.3391 - 50.8168i) q^{31} +(121.786 - 210.940i) q^{32} +(-158.726 + 83.9041i) q^{33} +(177.949 + 308.216i) q^{34} +(164.171 - 240.869i) q^{36} +329.358 q^{37} +(-317.368 - 549.697i) q^{38} +(33.2531 + 20.8909i) q^{39} +(86.4845 - 149.796i) q^{41} +(-248.011 - 155.811i) q^{42} +(78.3437 + 135.695i) q^{43} -373.030 q^{44} -814.589 q^{46} +(84.6230 + 146.571i) q^{47} +(-155.328 + 82.1077i) q^{48} +(86.9806 - 150.655i) q^{49} +(15.9183 - 426.255i) q^{51} +(40.7969 + 70.6623i) q^{52} -609.837 q^{53} +(-557.443 + 243.355i) q^{54} +(-78.8058 - 136.496i) q^{56} +(-28.3899 + 760.217i) q^{57} +(-94.7682 + 164.143i) q^{58} +(297.215 - 514.792i) q^{59} +(-162.538 - 281.525i) q^{61} -254.396 q^{62} +(152.357 + 316.254i) q^{63} -785.498 q^{64} +(659.102 + 414.075i) q^{66} +(344.191 - 596.156i) q^{67} +(443.128 - 767.521i) q^{68} +(826.700 + 519.366i) q^{69} -515.170 q^{71} +(-326.398 - 24.4124i) q^{72} +1088.37 q^{73} +(-713.959 - 1236.61i) q^{74} +(-790.310 + 1368.86i) q^{76} +(224.615 - 389.044i) q^{77} +(6.35373 - 170.138i) q^{78} +(262.896 + 455.349i) q^{79} +(720.889 + 108.442i) q^{81} -749.899 q^{82} +(179.006 + 310.048i) q^{83} +(-27.2188 + 728.855i) q^{84} +(339.655 - 588.300i) q^{86} +(200.832 - 106.161i) q^{87} +(209.430 + 362.744i) q^{88} +1517.67 q^{89} -98.2610 q^{91} +(1014.25 + 1756.72i) q^{92} +(258.179 + 162.198i) q^{93} +(366.879 - 635.453i) q^{94} +(1071.70 + 673.283i) q^{96} +(197.680 + 342.393i) q^{97} -754.200 q^{98} +(-404.896 - 840.462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16773 3.75461i −0.766407 1.32746i −0.939500 0.342550i \(-0.888709\pi\)
0.173093 0.984906i \(-0.444624\pi\)
\(3\) −0.193913 + 5.19253i −0.0373185 + 0.999303i
\(4\) −5.39807 + 9.34974i −0.674759 + 1.16872i
\(5\) 0 0
\(6\) 19.9163 10.5279i 1.35513 0.716334i
\(7\) −6.50075 11.2596i −0.351007 0.607963i 0.635419 0.772168i \(-0.280827\pi\)
−0.986426 + 0.164205i \(0.947494\pi\)
\(8\) 12.1226 0.535747
\(9\) −26.9248 2.01380i −0.997215 0.0745850i
\(10\) 0 0
\(11\) 17.2761 + 29.9230i 0.473539 + 0.820194i 0.999541 0.0302897i \(-0.00964297\pi\)
−0.526002 + 0.850483i \(0.676310\pi\)
\(12\) −47.5021 29.8427i −1.14272 0.717904i
\(13\) 3.77884 6.54514i 0.0806200 0.139638i −0.822896 0.568191i \(-0.807643\pi\)
0.903516 + 0.428553i \(0.140977\pi\)
\(14\) −28.1837 + 48.8156i −0.538029 + 0.931894i
\(15\) 0 0
\(16\) 16.9062 + 29.2824i 0.264159 + 0.457537i
\(17\) −82.0901 −1.17116 −0.585581 0.810614i \(-0.699134\pi\)
−0.585581 + 0.810614i \(0.699134\pi\)
\(18\) 50.8046 + 105.458i 0.665264 + 1.38092i
\(19\) 146.406 1.76778 0.883890 0.467696i \(-0.154916\pi\)
0.883890 + 0.467696i \(0.154916\pi\)
\(20\) 0 0
\(21\) 59.7265 31.5720i 0.620638 0.328075i
\(22\) 74.8995 129.730i 0.725847 1.25720i
\(23\) 93.9451 162.718i 0.851691 1.47517i −0.0279894 0.999608i \(-0.508910\pi\)
0.879681 0.475565i \(-0.157756\pi\)
\(24\) −2.35072 + 62.9468i −0.0199933 + 0.535374i
\(25\) 0 0
\(26\) −32.7659 −0.247151
\(27\) 15.6778 139.417i 0.111748 0.993737i
\(28\) 140.366 0.947382
\(29\) −21.8589 37.8607i −0.139969 0.242433i 0.787516 0.616295i \(-0.211367\pi\)
−0.927485 + 0.373861i \(0.878034\pi\)
\(30\) 0 0
\(31\) 29.3391 50.8168i 0.169982 0.294418i −0.768431 0.639933i \(-0.778962\pi\)
0.938413 + 0.345514i \(0.112296\pi\)
\(32\) 121.786 210.940i 0.672780 1.16529i
\(33\) −158.726 + 83.9041i −0.837294 + 0.442601i
\(34\) 177.949 + 308.216i 0.897587 + 1.55467i
\(35\) 0 0
\(36\) 164.171 240.869i 0.760049 1.11514i
\(37\) 329.358 1.46341 0.731705 0.681621i \(-0.238725\pi\)
0.731705 + 0.681621i \(0.238725\pi\)
\(38\) −317.368 549.697i −1.35484 2.34665i
\(39\) 33.2531 + 20.8909i 0.136532 + 0.0857750i
\(40\) 0 0
\(41\) 86.4845 149.796i 0.329429 0.570588i −0.652969 0.757384i \(-0.726477\pi\)
0.982399 + 0.186796i \(0.0598103\pi\)
\(42\) −248.011 155.811i −0.911166 0.572431i
\(43\) 78.3437 + 135.695i 0.277844 + 0.481240i 0.970849 0.239693i \(-0.0770467\pi\)
−0.693004 + 0.720933i \(0.743713\pi\)
\(44\) −373.030 −1.27810
\(45\) 0 0
\(46\) −814.589 −2.61097
\(47\) 84.6230 + 146.571i 0.262628 + 0.454886i 0.966940 0.255006i \(-0.0820774\pi\)
−0.704311 + 0.709891i \(0.748744\pi\)
\(48\) −155.328 + 82.1077i −0.467076 + 0.246900i
\(49\) 86.9806 150.655i 0.253588 0.439227i
\(50\) 0 0
\(51\) 15.9183 426.255i 0.0437061 1.17035i
\(52\) 40.7969 + 70.6623i 0.108798 + 0.188444i
\(53\) −609.837 −1.58052 −0.790259 0.612772i \(-0.790054\pi\)
−0.790259 + 0.612772i \(0.790054\pi\)
\(54\) −557.443 + 243.355i −1.40479 + 0.613267i
\(55\) 0 0
\(56\) −78.8058 136.496i −0.188051 0.325714i
\(57\) −28.3899 + 760.217i −0.0659709 + 1.76655i
\(58\) −94.7682 + 164.143i −0.214546 + 0.371605i
\(59\) 297.215 514.792i 0.655833 1.13594i −0.325852 0.945421i \(-0.605651\pi\)
0.981684 0.190514i \(-0.0610156\pi\)
\(60\) 0 0
\(61\) −162.538 281.525i −0.341163 0.590911i 0.643486 0.765458i \(-0.277487\pi\)
−0.984649 + 0.174547i \(0.944154\pi\)
\(62\) −254.396 −0.521103
\(63\) 152.357 + 316.254i 0.304685 + 0.632449i
\(64\) −785.498 −1.53418
\(65\) 0 0
\(66\) 659.102 + 414.075i 1.22924 + 0.772258i
\(67\) 344.191 596.156i 0.627606 1.08705i −0.360425 0.932788i \(-0.617368\pi\)
0.988031 0.154257i \(-0.0492985\pi\)
\(68\) 443.128 767.521i 0.790253 1.36876i
\(69\) 826.700 + 519.366i 1.44236 + 0.906149i
\(70\) 0 0
\(71\) −515.170 −0.861119 −0.430560 0.902562i \(-0.641684\pi\)
−0.430560 + 0.902562i \(0.641684\pi\)
\(72\) −326.398 24.4124i −0.534255 0.0399587i
\(73\) 1088.37 1.74499 0.872497 0.488619i \(-0.162499\pi\)
0.872497 + 0.488619i \(0.162499\pi\)
\(74\) −713.959 1236.61i −1.12157 1.94261i
\(75\) 0 0
\(76\) −790.310 + 1368.86i −1.19283 + 2.06603i
\(77\) 224.615 389.044i 0.332431 0.575788i
\(78\) 6.35373 170.138i 0.00922331 0.246979i
\(79\) 262.896 + 455.349i 0.374406 + 0.648491i 0.990238 0.139387i \(-0.0445131\pi\)
−0.615832 + 0.787878i \(0.711180\pi\)
\(80\) 0 0
\(81\) 720.889 + 108.442i 0.988874 + 0.148755i
\(82\) −749.899 −1.00991
\(83\) 179.006 + 310.048i 0.236729 + 0.410027i 0.959774 0.280775i \(-0.0905913\pi\)
−0.723045 + 0.690801i \(0.757258\pi\)
\(84\) −27.2188 + 728.855i −0.0353549 + 0.946722i
\(85\) 0 0
\(86\) 339.655 588.300i 0.425884 0.737652i
\(87\) 200.832 106.161i 0.247488 0.130824i
\(88\) 209.430 + 362.744i 0.253697 + 0.439416i
\(89\) 1517.67 1.80756 0.903779 0.427999i \(-0.140781\pi\)
0.903779 + 0.427999i \(0.140781\pi\)
\(90\) 0 0
\(91\) −98.2610 −0.113193
\(92\) 1014.25 + 1756.72i 1.14937 + 1.99077i
\(93\) 258.179 + 162.198i 0.287870 + 0.180851i
\(94\) 366.879 635.453i 0.402560 0.697255i
\(95\) 0 0
\(96\) 1071.70 + 673.283i 1.13937 + 0.715798i
\(97\) 197.680 + 342.393i 0.206922 + 0.358399i 0.950743 0.309979i \(-0.100322\pi\)
−0.743822 + 0.668378i \(0.766989\pi\)
\(98\) −754.200 −0.777405
\(99\) −404.896 840.462i −0.411046 0.853228i
\(100\) 0 0
\(101\) −166.629 288.610i −0.164160 0.284334i 0.772197 0.635384i \(-0.219158\pi\)
−0.936357 + 0.351050i \(0.885825\pi\)
\(102\) −1634.93 + 864.238i −1.58708 + 0.838944i
\(103\) −815.444 + 1412.39i −0.780078 + 1.35114i 0.151817 + 0.988409i \(0.451487\pi\)
−0.931896 + 0.362727i \(0.881846\pi\)
\(104\) 45.8092 79.3439i 0.0431919 0.0748106i
\(105\) 0 0
\(106\) 1321.96 + 2289.70i 1.21132 + 2.09807i
\(107\) −688.472 −0.622029 −0.311015 0.950405i \(-0.600669\pi\)
−0.311015 + 0.950405i \(0.600669\pi\)
\(108\) 1218.89 + 899.168i 1.08599 + 0.801134i
\(109\) −1188.95 −1.04478 −0.522390 0.852707i \(-0.674959\pi\)
−0.522390 + 0.852707i \(0.674959\pi\)
\(110\) 0 0
\(111\) −63.8668 + 1710.20i −0.0546123 + 1.46239i
\(112\) 219.806 380.715i 0.185444 0.321198i
\(113\) −134.208 + 232.455i −0.111727 + 0.193518i −0.916467 0.400111i \(-0.868972\pi\)
0.804739 + 0.593628i \(0.202305\pi\)
\(114\) 2915.86 1541.35i 2.39557 1.26632i
\(115\) 0 0
\(116\) 471.984 0.377781
\(117\) −114.925 + 168.617i −0.0908104 + 0.133236i
\(118\) −2577.12 −2.01054
\(119\) 533.647 + 924.303i 0.411087 + 0.712023i
\(120\) 0 0
\(121\) 68.5754 118.776i 0.0515217 0.0892382i
\(122\) −704.678 + 1220.54i −0.522939 + 0.905756i
\(123\) 761.048 + 478.121i 0.557897 + 0.350493i
\(124\) 316.749 + 548.625i 0.229394 + 0.397323i
\(125\) 0 0
\(126\) 857.144 1257.59i 0.606036 0.889169i
\(127\) −145.302 −0.101523 −0.0507616 0.998711i \(-0.516165\pi\)
−0.0507616 + 0.998711i \(0.516165\pi\)
\(128\) 728.455 + 1261.72i 0.503023 + 0.871261i
\(129\) −719.794 + 380.489i −0.491274 + 0.259692i
\(130\) 0 0
\(131\) 134.659 233.237i 0.0898110 0.155557i −0.817620 0.575758i \(-0.804707\pi\)
0.907431 + 0.420201i \(0.138040\pi\)
\(132\) 72.3352 1936.97i 0.0476968 1.27721i
\(133\) −951.747 1648.47i −0.620504 1.07474i
\(134\) −2984.45 −1.92401
\(135\) 0 0
\(136\) −995.143 −0.627447
\(137\) 413.688 + 716.528i 0.257984 + 0.446841i 0.965702 0.259654i \(-0.0836086\pi\)
−0.707718 + 0.706495i \(0.750275\pi\)
\(138\) 157.959 4229.78i 0.0974375 2.60915i
\(139\) 84.9350 147.112i 0.0518280 0.0897687i −0.838947 0.544212i \(-0.816829\pi\)
0.890775 + 0.454444i \(0.150162\pi\)
\(140\) 0 0
\(141\) −777.486 + 410.986i −0.464370 + 0.245470i
\(142\) 1116.75 + 1934.26i 0.659968 + 1.14310i
\(143\) 261.134 0.152707
\(144\) −396.227 822.467i −0.229298 0.475965i
\(145\) 0 0
\(146\) −2359.30 4086.42i −1.33738 2.31640i
\(147\) 765.413 + 480.863i 0.429457 + 0.269802i
\(148\) −1777.90 + 3079.41i −0.987450 + 1.71031i
\(149\) −873.174 + 1512.38i −0.480089 + 0.831538i −0.999739 0.0228410i \(-0.992729\pi\)
0.519650 + 0.854379i \(0.326062\pi\)
\(150\) 0 0
\(151\) −171.419 296.906i −0.0923832 0.160012i 0.816130 0.577868i \(-0.196115\pi\)
−0.908513 + 0.417856i \(0.862782\pi\)
\(152\) 1774.82 0.947082
\(153\) 2210.26 + 165.313i 1.16790 + 0.0873512i
\(154\) −1947.61 −1.01911
\(155\) 0 0
\(156\) −374.827 + 198.137i −0.192373 + 0.101690i
\(157\) 1747.85 3027.36i 0.888494 1.53892i 0.0468373 0.998903i \(-0.485086\pi\)
0.841656 0.540014i \(-0.181581\pi\)
\(158\) 1139.77 1974.15i 0.573895 0.994016i
\(159\) 118.255 3166.60i 0.0589826 1.57942i
\(160\) 0 0
\(161\) −2442.85 −1.19580
\(162\) −1155.53 2941.73i −0.560415 1.42669i
\(163\) 663.542 0.318851 0.159425 0.987210i \(-0.449036\pi\)
0.159425 + 0.987210i \(0.449036\pi\)
\(164\) 933.699 + 1617.21i 0.444571 + 0.770020i
\(165\) 0 0
\(166\) 776.074 1344.20i 0.362862 0.628495i
\(167\) −1229.82 + 2130.11i −0.569858 + 0.987023i 0.426721 + 0.904383i \(0.359669\pi\)
−0.996579 + 0.0826401i \(0.973665\pi\)
\(168\) 724.039 382.733i 0.332505 0.175765i
\(169\) 1069.94 + 1853.19i 0.487001 + 0.843510i
\(170\) 0 0
\(171\) −3941.95 294.831i −1.76286 0.131850i
\(172\) −1691.62 −0.749912
\(173\) 763.873 + 1323.07i 0.335701 + 0.581451i 0.983619 0.180259i \(-0.0576936\pi\)
−0.647918 + 0.761710i \(0.724360\pi\)
\(174\) −833.943 523.917i −0.363339 0.228264i
\(175\) 0 0
\(176\) −584.144 + 1011.77i −0.250179 + 0.433323i
\(177\) 2615.44 + 1643.12i 1.11067 + 0.697767i
\(178\) −3289.89 5698.26i −1.38533 2.39945i
\(179\) 1006.17 0.420137 0.210069 0.977687i \(-0.432631\pi\)
0.210069 + 0.977687i \(0.432631\pi\)
\(180\) 0 0
\(181\) 591.861 0.243053 0.121527 0.992588i \(-0.461221\pi\)
0.121527 + 0.992588i \(0.461221\pi\)
\(182\) 213.003 + 368.932i 0.0867518 + 0.150259i
\(183\) 1493.35 789.395i 0.603231 0.318873i
\(184\) 1138.86 1972.56i 0.456291 0.790319i
\(185\) 0 0
\(186\) 49.3307 1320.96i 0.0194468 0.520740i
\(187\) −1418.19 2456.38i −0.554591 0.960580i
\(188\) −1827.20 −0.708843
\(189\) −1671.70 + 729.792i −0.643379 + 0.280870i
\(190\) 0 0
\(191\) −1822.29 3156.29i −0.690345 1.19571i −0.971725 0.236117i \(-0.924125\pi\)
0.281379 0.959597i \(-0.409208\pi\)
\(192\) 152.318 4078.72i 0.0572531 1.53311i
\(193\) −6.70078 + 11.6061i −0.00249913 + 0.00432862i −0.867272 0.497834i \(-0.834129\pi\)
0.864773 + 0.502163i \(0.167462\pi\)
\(194\) 857.034 1484.43i 0.317173 0.549359i
\(195\) 0 0
\(196\) 939.055 + 1626.49i 0.342221 + 0.592745i
\(197\) −63.1983 −0.0228563 −0.0114281 0.999935i \(-0.503638\pi\)
−0.0114281 + 0.999935i \(0.503638\pi\)
\(198\) −2277.90 + 3342.12i −0.817594 + 1.19957i
\(199\) −4902.79 −1.74648 −0.873240 0.487291i \(-0.837985\pi\)
−0.873240 + 0.487291i \(0.837985\pi\)
\(200\) 0 0
\(201\) 3028.82 + 1902.82i 1.06287 + 0.667736i
\(202\) −722.411 + 1251.25i −0.251627 + 0.435831i
\(203\) −284.198 + 492.246i −0.0982602 + 0.170192i
\(204\) 3899.45 + 2449.79i 1.33831 + 0.840783i
\(205\) 0 0
\(206\) 7070.64 2.39143
\(207\) −2857.13 + 4191.95i −0.959345 + 1.40754i
\(208\) 255.543 0.0851861
\(209\) 2529.32 + 4380.90i 0.837112 + 1.44992i
\(210\) 0 0
\(211\) 1556.11 2695.26i 0.507711 0.879381i −0.492249 0.870454i \(-0.663825\pi\)
0.999960 0.00892670i \(-0.00284149\pi\)
\(212\) 3291.94 5701.81i 1.06647 1.84718i
\(213\) 99.8980 2675.04i 0.0321357 0.860519i
\(214\) 1492.42 + 2584.95i 0.476728 + 0.825717i
\(215\) 0 0
\(216\) 190.055 1690.10i 0.0598685 0.532391i
\(217\) −762.904 −0.238660
\(218\) 2577.32 + 4464.06i 0.800727 + 1.38690i
\(219\) −211.050 + 5651.42i −0.0651206 + 1.74378i
\(220\) 0 0
\(221\) −310.205 + 537.291i −0.0944192 + 0.163539i
\(222\) 6559.60 3467.46i 1.98311 1.04829i
\(223\) 2434.71 + 4217.05i 0.731123 + 1.26634i 0.956404 + 0.292048i \(0.0943368\pi\)
−0.225281 + 0.974294i \(0.572330\pi\)
\(224\) −3166.81 −0.944603
\(225\) 0 0
\(226\) 1163.70 0.342515
\(227\) −3293.59 5704.67i −0.963011 1.66798i −0.714867 0.699260i \(-0.753513\pi\)
−0.248144 0.968723i \(-0.579820\pi\)
\(228\) −6954.58 4369.15i −2.02008 1.26910i
\(229\) −8.21503 + 14.2288i −0.00237059 + 0.00410598i −0.867208 0.497946i \(-0.834088\pi\)
0.864838 + 0.502052i \(0.167421\pi\)
\(230\) 0 0
\(231\) 1976.57 + 1241.76i 0.562981 + 0.353687i
\(232\) −264.986 458.969i −0.0749879 0.129883i
\(233\) −707.542 −0.198938 −0.0994692 0.995041i \(-0.531714\pi\)
−0.0994692 + 0.995041i \(0.531714\pi\)
\(234\) 882.216 + 65.9839i 0.246463 + 0.0184338i
\(235\) 0 0
\(236\) 3208.78 + 5557.77i 0.885058 + 1.53297i
\(237\) −2415.39 + 1276.80i −0.662012 + 0.349945i
\(238\) 2313.60 4007.27i 0.630120 1.09140i
\(239\) 3056.02 5293.18i 0.827102 1.43258i −0.0731999 0.997317i \(-0.523321\pi\)
0.900302 0.435266i \(-0.143346\pi\)
\(240\) 0 0
\(241\) −1544.12 2674.49i −0.412719 0.714850i 0.582467 0.812854i \(-0.302087\pi\)
−0.995186 + 0.0980044i \(0.968754\pi\)
\(242\) −594.611 −0.157946
\(243\) −702.879 + 3722.21i −0.185554 + 0.982634i
\(244\) 3509.58 0.920810
\(245\) 0 0
\(246\) 145.415 3893.87i 0.0376883 1.00920i
\(247\) 553.244 958.246i 0.142518 0.246849i
\(248\) 355.665 616.030i 0.0910676 0.157734i
\(249\) −1644.65 + 869.375i −0.418575 + 0.221263i
\(250\) 0 0
\(251\) 2743.28 0.689859 0.344929 0.938629i \(-0.387903\pi\)
0.344929 + 0.938629i \(0.387903\pi\)
\(252\) −3779.33 282.669i −0.944743 0.0706605i
\(253\) 6492.00 1.61324
\(254\) 314.974 + 545.552i 0.0778081 + 0.134768i
\(255\) 0 0
\(256\) 16.1888 28.0399i 0.00395235 0.00684568i
\(257\) 360.023 623.578i 0.0873838 0.151353i −0.819021 0.573764i \(-0.805483\pi\)
0.906404 + 0.422411i \(0.138816\pi\)
\(258\) 2988.91 + 1877.75i 0.721245 + 0.453115i
\(259\) −2141.08 3708.45i −0.513668 0.889699i
\(260\) 0 0
\(261\) 512.303 + 1063.41i 0.121497 + 0.252197i
\(262\) −1167.62 −0.275327
\(263\) −2614.08 4527.72i −0.612894 1.06156i −0.990750 0.135699i \(-0.956672\pi\)
0.377857 0.925864i \(-0.376661\pi\)
\(264\) −1924.17 + 1017.13i −0.448578 + 0.237122i
\(265\) 0 0
\(266\) −4126.26 + 7146.88i −0.951116 + 1.64738i
\(267\) −294.295 + 7880.55i −0.0674554 + 1.80630i
\(268\) 3715.94 + 6436.19i 0.846966 + 1.46699i
\(269\) 320.400 0.0726213 0.0363107 0.999341i \(-0.488439\pi\)
0.0363107 + 0.999341i \(0.488439\pi\)
\(270\) 0 0
\(271\) −1044.06 −0.234029 −0.117014 0.993130i \(-0.537332\pi\)
−0.117014 + 0.993130i \(0.537332\pi\)
\(272\) −1387.83 2403.79i −0.309373 0.535850i
\(273\) 19.0541 510.224i 0.00422419 0.113114i
\(274\) 1793.52 3106.48i 0.395441 0.684923i
\(275\) 0 0
\(276\) −9318.52 + 4925.85i −2.03228 + 1.07428i
\(277\) 1665.66 + 2885.01i 0.361299 + 0.625789i 0.988175 0.153330i \(-0.0489999\pi\)
−0.626876 + 0.779119i \(0.715667\pi\)
\(278\) −736.463 −0.158885
\(279\) −892.283 + 1309.15i −0.191468 + 0.280920i
\(280\) 0 0
\(281\) 2800.64 + 4850.86i 0.594563 + 1.02981i 0.993608 + 0.112883i \(0.0360084\pi\)
−0.399045 + 0.916931i \(0.630658\pi\)
\(282\) 3228.47 + 2028.25i 0.681746 + 0.428300i
\(283\) 3133.92 5428.11i 0.658277 1.14017i −0.322785 0.946472i \(-0.604619\pi\)
0.981062 0.193696i \(-0.0620476\pi\)
\(284\) 2780.93 4816.71i 0.581048 1.00640i
\(285\) 0 0
\(286\) −566.066 980.455i −0.117036 0.202712i
\(287\) −2248.85 −0.462529
\(288\) −3703.86 + 5434.26i −0.757819 + 1.11186i
\(289\) 1825.78 0.371622
\(290\) 0 0
\(291\) −1816.22 + 960.068i −0.365871 + 0.193403i
\(292\) −5875.12 + 10176.0i −1.17745 + 2.03940i
\(293\) 1051.43 1821.13i 0.209642 0.363111i −0.741960 0.670445i \(-0.766103\pi\)
0.951602 + 0.307334i \(0.0994368\pi\)
\(294\) 146.249 3916.21i 0.0290116 0.776864i
\(295\) 0 0
\(296\) 3992.67 0.784018
\(297\) 4442.64 1939.46i 0.867973 0.378918i
\(298\) 7571.21 1.47177
\(299\) −710.006 1229.77i −0.137327 0.237857i
\(300\) 0 0
\(301\) 1018.59 1764.24i 0.195051 0.337838i
\(302\) −743.178 + 1287.22i −0.141606 + 0.245269i
\(303\) 1530.93 809.260i 0.290262 0.153435i
\(304\) 2475.16 + 4287.11i 0.466975 + 0.808824i
\(305\) 0 0
\(306\) −4170.55 8657.02i −0.779132 1.61728i
\(307\) −2020.07 −0.375543 −0.187771 0.982213i \(-0.560126\pi\)
−0.187771 + 0.982213i \(0.560126\pi\)
\(308\) 2424.97 + 4200.18i 0.448622 + 0.777037i
\(309\) −7175.76 4508.10i −1.32108 0.829957i
\(310\) 0 0
\(311\) −2696.66 + 4670.75i −0.491684 + 0.851621i −0.999954 0.00957637i \(-0.996952\pi\)
0.508270 + 0.861198i \(0.330285\pi\)
\(312\) 403.113 + 253.252i 0.0731467 + 0.0459537i
\(313\) −1555.89 2694.87i −0.280971 0.486656i 0.690653 0.723186i \(-0.257323\pi\)
−0.971624 + 0.236530i \(0.923990\pi\)
\(314\) −15155.4 −2.72379
\(315\) 0 0
\(316\) −5676.53 −1.01054
\(317\) 2466.79 + 4272.60i 0.437062 + 0.757013i 0.997461 0.0712090i \(-0.0226857\pi\)
−0.560399 + 0.828222i \(0.689352\pi\)
\(318\) −12145.7 + 6420.31i −2.14181 + 1.13218i
\(319\) 755.271 1308.17i 0.132561 0.229603i
\(320\) 0 0
\(321\) 133.504 3574.92i 0.0232132 0.621596i
\(322\) 5295.44 + 9171.96i 0.916469 + 1.58737i
\(323\) −12018.5 −2.07036
\(324\) −4905.32 + 6154.75i −0.841104 + 1.05534i
\(325\) 0 0
\(326\) −1438.38 2491.34i −0.244369 0.423260i
\(327\) 230.553 6173.68i 0.0389896 1.04405i
\(328\) 1048.41 1815.91i 0.176491 0.305691i
\(329\) 1100.23 1905.65i 0.184369 0.319336i
\(330\) 0 0
\(331\) −4386.39 7597.45i −0.728392 1.26161i −0.957563 0.288226i \(-0.906935\pi\)
0.229171 0.973386i \(-0.426399\pi\)
\(332\) −3865.16 −0.638940
\(333\) −8867.91 663.260i −1.45933 0.109148i
\(334\) 10663.7 1.74697
\(335\) 0 0
\(336\) 1934.25 + 1215.17i 0.314053 + 0.197301i
\(337\) 5171.06 8956.54i 0.835863 1.44776i −0.0574635 0.998348i \(-0.518301\pi\)
0.893326 0.449409i \(-0.148365\pi\)
\(338\) 4638.68 8034.43i 0.746482 1.29294i
\(339\) −1181.00 741.954i −0.189213 0.118871i
\(340\) 0 0
\(341\) 2027.46 0.321973
\(342\) 7438.09 + 15439.6i 1.17604 + 2.44116i
\(343\) −6721.27 −1.05806
\(344\) 949.727 + 1644.98i 0.148854 + 0.257823i
\(345\) 0 0
\(346\) 3311.74 5736.10i 0.514567 0.891256i
\(347\) −669.161 + 1159.02i −0.103523 + 0.179307i −0.913134 0.407660i \(-0.866345\pi\)
0.809611 + 0.586967i \(0.199678\pi\)
\(348\) −91.5236 + 2450.79i −0.0140982 + 0.377518i
\(349\) −5056.17 8757.55i −0.775503 1.34321i −0.934511 0.355934i \(-0.884163\pi\)
0.159008 0.987277i \(-0.449170\pi\)
\(350\) 0 0
\(351\) −853.262 629.448i −0.129754 0.0957193i
\(352\) 8415.95 1.27435
\(353\) −822.140 1423.99i −0.123961 0.214706i 0.797366 0.603497i \(-0.206226\pi\)
−0.921326 + 0.388791i \(0.872893\pi\)
\(354\) 499.737 13381.8i 0.0750303 2.00914i
\(355\) 0 0
\(356\) −8192.50 + 14189.8i −1.21967 + 2.11253i
\(357\) −4902.96 + 2591.74i −0.726868 + 0.384229i
\(358\) −2181.10 3777.77i −0.321996 0.557714i
\(359\) 11283.0 1.65876 0.829379 0.558686i \(-0.188694\pi\)
0.829379 + 0.558686i \(0.188694\pi\)
\(360\) 0 0
\(361\) 14575.7 2.12504
\(362\) −1282.99 2222.21i −0.186278 0.322643i
\(363\) 603.451 + 379.112i 0.0872533 + 0.0548160i
\(364\) 530.420 918.715i 0.0763780 0.132291i
\(365\) 0 0
\(366\) −6201.04 3895.74i −0.885610 0.556376i
\(367\) 139.011 + 240.774i 0.0197720 + 0.0342461i 0.875742 0.482779i \(-0.160373\pi\)
−0.855970 + 0.517025i \(0.827039\pi\)
\(368\) 6353.01 0.899928
\(369\) −2630.23 + 3859.05i −0.371069 + 0.544429i
\(370\) 0 0
\(371\) 3964.39 + 6866.53i 0.554774 + 0.960896i
\(372\) −2910.18 + 1538.34i −0.405607 + 0.214407i
\(373\) −4916.70 + 8515.98i −0.682513 + 1.18215i 0.291699 + 0.956510i \(0.405780\pi\)
−0.974212 + 0.225637i \(0.927554\pi\)
\(374\) −6148.51 + 10649.5i −0.850085 + 1.47239i
\(375\) 0 0
\(376\) 1025.85 + 1776.82i 0.140702 + 0.243704i
\(377\) −330.405 −0.0451372
\(378\) 6363.88 + 4694.61i 0.865933 + 0.638796i
\(379\) 13511.9 1.83129 0.915644 0.401990i \(-0.131681\pi\)
0.915644 + 0.401990i \(0.131681\pi\)
\(380\) 0 0
\(381\) 28.1758 754.484i 0.00378869 0.101452i
\(382\) −7900.43 + 13683.9i −1.05817 + 1.83281i
\(383\) 694.822 1203.47i 0.0926991 0.160559i −0.815947 0.578127i \(-0.803784\pi\)
0.908646 + 0.417567i \(0.137117\pi\)
\(384\) −6692.78 + 3537.86i −0.889426 + 0.470158i
\(385\) 0 0
\(386\) 58.1018 0.00766141
\(387\) −1836.13 3811.34i −0.241177 0.500623i
\(388\) −4268.38 −0.558490
\(389\) 453.369 + 785.258i 0.0590918 + 0.102350i 0.894058 0.447951i \(-0.147846\pi\)
−0.834966 + 0.550301i \(0.814513\pi\)
\(390\) 0 0
\(391\) −7711.96 + 13357.5i −0.997469 + 1.72767i
\(392\) 1054.43 1826.32i 0.135859 0.235314i
\(393\) 1184.98 + 744.450i 0.152097 + 0.0955536i
\(394\) 136.997 + 237.285i 0.0175172 + 0.0303407i
\(395\) 0 0
\(396\) 10043.8 + 751.206i 1.27454 + 0.0953271i
\(397\) 1904.52 0.240769 0.120384 0.992727i \(-0.461587\pi\)
0.120384 + 0.992727i \(0.461587\pi\)
\(398\) 10627.9 + 18408.1i 1.33851 + 2.31837i
\(399\) 8744.32 4622.32i 1.09715 0.579963i
\(400\) 0 0
\(401\) 5206.91 9018.64i 0.648431 1.12312i −0.335067 0.942194i \(-0.608759\pi\)
0.983498 0.180921i \(-0.0579078\pi\)
\(402\) 578.722 15496.8i 0.0718011 1.92267i
\(403\) −221.735 384.057i −0.0274080 0.0474720i
\(404\) 3597.90 0.443075
\(405\) 0 0
\(406\) 2464.26 0.301229
\(407\) 5690.02 + 9855.40i 0.692982 + 1.20028i
\(408\) 192.971 5167.31i 0.0234154 0.627010i
\(409\) −3124.74 + 5412.21i −0.377771 + 0.654319i −0.990738 0.135790i \(-0.956643\pi\)
0.612966 + 0.790109i \(0.289976\pi\)
\(410\) 0 0
\(411\) −3800.82 + 2009.14i −0.456157 + 0.241128i
\(412\) −8803.65 15248.4i −1.05273 1.82338i
\(413\) −7728.48 −0.920808
\(414\) 21932.6 + 1640.42i 2.60370 + 0.194739i
\(415\) 0 0
\(416\) −920.420 1594.21i −0.108479 0.187891i
\(417\) 747.413 + 469.555i 0.0877721 + 0.0551419i
\(418\) 10965.7 18993.2i 1.28314 2.22246i
\(419\) −1495.14 + 2589.65i −0.174325 + 0.301940i −0.939927 0.341374i \(-0.889108\pi\)
0.765602 + 0.643314i \(0.222441\pi\)
\(420\) 0 0
\(421\) 2346.32 + 4063.95i 0.271622 + 0.470463i 0.969277 0.245971i \(-0.0791067\pi\)
−0.697656 + 0.716433i \(0.745773\pi\)
\(422\) −13492.9 −1.55645
\(423\) −1983.29 4116.82i −0.227969 0.473207i
\(424\) −7392.79 −0.846758
\(425\) 0 0
\(426\) −10260.3 + 5423.67i −1.16693 + 0.616849i
\(427\) −2113.24 + 3660.24i −0.239501 + 0.414828i
\(428\) 3716.43 6437.04i 0.419720 0.726977i
\(429\) −50.6371 + 1355.94i −0.00569879 + 0.152601i
\(430\) 0 0
\(431\) 817.709 0.0913866 0.0456933 0.998956i \(-0.485450\pi\)
0.0456933 + 0.998956i \(0.485450\pi\)
\(432\) 4347.52 1897.93i 0.484190 0.211376i
\(433\) 5547.29 0.615671 0.307836 0.951440i \(-0.400395\pi\)
0.307836 + 0.951440i \(0.400395\pi\)
\(434\) 1653.77 + 2864.41i 0.182911 + 0.316811i
\(435\) 0 0
\(436\) 6418.06 11116.4i 0.704975 1.22105i
\(437\) 13754.1 23822.8i 1.50560 2.60778i
\(438\) 21676.4 11458.3i 2.36470 1.25000i
\(439\) −6690.82 11588.8i −0.727416 1.25992i −0.957972 0.286862i \(-0.907388\pi\)
0.230556 0.973059i \(-0.425946\pi\)
\(440\) 0 0
\(441\) −2645.32 + 3881.19i −0.285641 + 0.419089i
\(442\) 2689.76 0.289454
\(443\) 5418.44 + 9385.00i 0.581123 + 1.00654i 0.995347 + 0.0963598i \(0.0307199\pi\)
−0.414223 + 0.910175i \(0.635947\pi\)
\(444\) −15645.2 9828.95i −1.67227 1.05059i
\(445\) 0 0
\(446\) 10555.6 18282.8i 1.12068 1.94107i
\(447\) −7683.77 4827.26i −0.813043 0.510786i
\(448\) 5106.32 + 8844.41i 0.538507 + 0.932721i
\(449\) 2970.62 0.312232 0.156116 0.987739i \(-0.450103\pi\)
0.156116 + 0.987739i \(0.450103\pi\)
\(450\) 0 0
\(451\) 5976.44 0.623991
\(452\) −1448.93 2509.61i −0.150778 0.261155i
\(453\) 1574.94 832.524i 0.163349 0.0863475i
\(454\) −14279.2 + 24732.3i −1.47612 + 2.55671i
\(455\) 0 0
\(456\) −344.159 + 9215.79i −0.0353437 + 0.946423i
\(457\) −8088.16 14009.1i −0.827896 1.43396i −0.899686 0.436538i \(-0.856204\pi\)
0.0717901 0.997420i \(-0.477129\pi\)
\(458\) 71.2317 0.00726733
\(459\) −1286.99 + 11444.8i −0.130875 + 1.16383i
\(460\) 0 0
\(461\) −2865.91 4963.90i −0.289541 0.501500i 0.684159 0.729333i \(-0.260169\pi\)
−0.973700 + 0.227833i \(0.926836\pi\)
\(462\) 377.667 10113.0i 0.0380317 1.01840i
\(463\) −7020.03 + 12159.1i −0.704641 + 1.22047i 0.262181 + 0.965019i \(0.415558\pi\)
−0.966821 + 0.255454i \(0.917775\pi\)
\(464\) 739.101 1280.16i 0.0739481 0.128082i
\(465\) 0 0
\(466\) 1533.76 + 2656.55i 0.152468 + 0.264082i
\(467\) 3.48921 0.000345742 0.000172871 1.00000i \(-0.499945\pi\)
0.000172871 1.00000i \(0.499945\pi\)
\(468\) −956.148 1984.72i −0.0944401 0.196034i
\(469\) −8949.99 −0.881177
\(470\) 0 0
\(471\) 15380.7 + 9662.80i 1.50469 + 0.945305i
\(472\) 3603.01 6240.60i 0.351360 0.608574i
\(473\) −2706.94 + 4688.56i −0.263140 + 0.455772i
\(474\) 10029.8 + 6301.12i 0.971907 + 0.610591i
\(475\) 0 0
\(476\) −11522.7 −1.10954
\(477\) 16419.7 + 1228.09i 1.57612 + 0.117883i
\(478\) −26498.4 −2.53559
\(479\) 1825.54 + 3161.93i 0.174136 + 0.301612i 0.939862 0.341555i \(-0.110954\pi\)
−0.765726 + 0.643167i \(0.777620\pi\)
\(480\) 0 0
\(481\) 1244.59 2155.69i 0.117980 0.204348i
\(482\) −6694.44 + 11595.1i −0.632621 + 1.09573i
\(483\) 473.700 12684.6i 0.0446255 1.19497i
\(484\) 740.350 + 1282.32i 0.0695295 + 0.120429i
\(485\) 0 0
\(486\) 15499.1 5429.70i 1.44661 0.506782i
\(487\) −13646.8 −1.26981 −0.634903 0.772592i \(-0.718960\pi\)
−0.634903 + 0.772592i \(0.718960\pi\)
\(488\) −1970.38 3412.80i −0.182777 0.316579i
\(489\) −128.669 + 3445.46i −0.0118990 + 0.318628i
\(490\) 0 0
\(491\) −20.8492 + 36.1118i −0.00191631 + 0.00331915i −0.866982 0.498340i \(-0.833943\pi\)
0.865066 + 0.501659i \(0.167277\pi\)
\(492\) −8578.50 + 4534.67i −0.786074 + 0.415525i
\(493\) 1794.40 + 3107.99i 0.163926 + 0.283929i
\(494\) −4797.12 −0.436908
\(495\) 0 0
\(496\) 1984.05 0.179610
\(497\) 3348.99 + 5800.62i 0.302259 + 0.523528i
\(498\) 6829.31 + 4290.45i 0.614515 + 0.386063i
\(499\) 1196.47 2072.34i 0.107337 0.185913i −0.807354 0.590068i \(-0.799101\pi\)
0.914691 + 0.404155i \(0.132434\pi\)
\(500\) 0 0
\(501\) −10822.2 6798.94i −0.965070 0.606295i
\(502\) −5946.69 10300.0i −0.528713 0.915757i
\(503\) −1254.89 −0.111238 −0.0556190 0.998452i \(-0.517713\pi\)
−0.0556190 + 0.998452i \(0.517713\pi\)
\(504\) 1846.95 + 3833.81i 0.163234 + 0.338833i
\(505\) 0 0
\(506\) −14072.9 24375.0i −1.23640 2.14150i
\(507\) −9830.23 + 5196.35i −0.861097 + 0.455183i
\(508\) 784.349 1358.53i 0.0685037 0.118652i
\(509\) −273.965 + 474.521i −0.0238571 + 0.0413217i −0.877707 0.479197i \(-0.840928\pi\)
0.853850 + 0.520519i \(0.174261\pi\)
\(510\) 0 0
\(511\) −7075.25 12254.7i −0.612506 1.06089i
\(512\) 11514.9 0.993929
\(513\) 2295.32 20411.5i 0.197545 1.75671i
\(514\) −3121.73 −0.267886
\(515\) 0 0
\(516\) 328.027 8783.80i 0.0279856 0.749390i
\(517\) −2923.90 + 5064.35i −0.248729 + 0.430812i
\(518\) −9282.53 + 16077.8i −0.787357 + 1.36374i
\(519\) −7018.20 + 3709.88i −0.593573 + 0.313768i
\(520\) 0 0
\(521\) 12151.4 1.02181 0.510903 0.859638i \(-0.329311\pi\)
0.510903 + 0.859638i \(0.329311\pi\)
\(522\) 2882.17 4228.68i 0.241665 0.354568i
\(523\) −18913.8 −1.58134 −0.790672 0.612241i \(-0.790268\pi\)
−0.790672 + 0.612241i \(0.790268\pi\)
\(524\) 1453.80 + 2518.06i 0.121202 + 0.209927i
\(525\) 0 0
\(526\) −11333.2 + 19629.7i −0.939452 + 1.62718i
\(527\) −2408.45 + 4171.55i −0.199077 + 0.344812i
\(528\) −5140.37 3229.38i −0.423685 0.266176i
\(529\) −11567.9 20036.1i −0.950757 1.64676i
\(530\) 0 0
\(531\) −9039.14 + 13262.1i −0.738730 + 1.08386i
\(532\) 20550.4 1.67476
\(533\) −653.621 1132.11i −0.0531172 0.0920017i
\(534\) 30226.4 15977.9i 2.44948 1.29482i
\(535\) 0 0
\(536\) 4172.48 7226.94i 0.336238 0.582381i
\(537\) −195.109 + 5224.56i −0.0156789 + 0.419845i
\(538\) −694.540 1202.98i −0.0556575 0.0964016i
\(539\) 6010.73 0.480335
\(540\) 0 0
\(541\) −9936.16 −0.789628 −0.394814 0.918761i \(-0.629191\pi\)
−0.394814 + 0.918761i \(0.629191\pi\)
\(542\) 2263.23 + 3920.02i 0.179361 + 0.310663i
\(543\) −114.769 + 3073.26i −0.00907039 + 0.242884i
\(544\) −9997.44 + 17316.1i −0.787935 + 1.36474i
\(545\) 0 0
\(546\) −1957.00 + 1034.48i −0.153391 + 0.0810840i
\(547\) 6359.84 + 11015.6i 0.497125 + 0.861045i 0.999994 0.00331677i \(-0.00105576\pi\)
−0.502870 + 0.864362i \(0.667722\pi\)
\(548\) −8932.47 −0.696307
\(549\) 3809.38 + 7907.32i 0.296139 + 0.614711i
\(550\) 0 0
\(551\) −3200.27 5543.03i −0.247434 0.428568i
\(552\) 10021.7 + 6296.05i 0.772741 + 0.485467i
\(553\) 3418.04 5920.22i 0.262839 0.455250i
\(554\) 7221.40 12507.8i 0.553805 0.959218i
\(555\) 0 0
\(556\) 916.971 + 1588.24i 0.0699429 + 0.121145i
\(557\) 16006.5 1.21763 0.608813 0.793314i \(-0.291646\pi\)
0.608813 + 0.793314i \(0.291646\pi\)
\(558\) 6849.57 + 512.302i 0.519651 + 0.0388665i
\(559\) 1184.19 0.0895993
\(560\) 0 0
\(561\) 13029.9 6887.69i 0.980608 0.518358i
\(562\) 12142.1 21030.7i 0.911355 1.57851i
\(563\) 2313.29 4006.74i 0.173168 0.299936i −0.766358 0.642414i \(-0.777933\pi\)
0.939526 + 0.342478i \(0.111266\pi\)
\(564\) 354.318 9487.82i 0.0264530 0.708350i
\(565\) 0 0
\(566\) −27173.9 −2.01803
\(567\) −3465.30 8821.90i −0.256665 0.653412i
\(568\) −6245.19 −0.461342
\(569\) −8429.52 14600.4i −0.621061 1.07571i −0.989288 0.145974i \(-0.953369\pi\)
0.368227 0.929736i \(-0.379965\pi\)
\(570\) 0 0
\(571\) −8074.57 + 13985.6i −0.591787 + 1.02501i 0.402205 + 0.915550i \(0.368244\pi\)
−0.993992 + 0.109455i \(0.965089\pi\)
\(572\) −1409.62 + 2441.53i −0.103040 + 0.178471i
\(573\) 16742.5 8850.23i 1.22064 0.645242i
\(574\) 4874.90 + 8443.58i 0.354485 + 0.613986i
\(575\) 0 0
\(576\) 21149.4 + 1581.83i 1.52990 + 0.114427i
\(577\) −7430.10 −0.536082 −0.268041 0.963408i \(-0.586376\pi\)
−0.268041 + 0.963408i \(0.586376\pi\)
\(578\) −3957.79 6855.10i −0.284814 0.493312i
\(579\) −58.9656 37.0446i −0.00423234 0.00265893i
\(580\) 0 0
\(581\) 2327.35 4031.09i 0.166187 0.287845i
\(582\) 7541.75 + 4738.03i 0.537140 + 0.337453i
\(583\) −10535.6 18248.2i −0.748437 1.29633i
\(584\) 13193.9 0.934875
\(585\) 0 0
\(586\) −9116.84 −0.642685
\(587\) 8576.06 + 14854.2i 0.603019 + 1.04446i 0.992361 + 0.123366i \(0.0393689\pi\)
−0.389343 + 0.921093i \(0.627298\pi\)
\(588\) −8627.70 + 4560.68i −0.605103 + 0.319863i
\(589\) 4295.41 7439.87i 0.300491 0.520466i
\(590\) 0 0
\(591\) 12.2549 328.159i 0.000852963 0.0228404i
\(592\) 5568.19 + 9644.39i 0.386573 + 0.669564i
\(593\) 15477.7 1.07183 0.535913 0.844273i \(-0.319967\pi\)
0.535913 + 0.844273i \(0.319967\pi\)
\(594\) −16912.3 12476.2i −1.16822 0.861790i
\(595\) 0 0
\(596\) −9426.92 16327.9i −0.647889 1.12218i
\(597\) 950.713 25457.9i 0.0651760 1.74526i
\(598\) −3078.20 + 5331.59i −0.210496 + 0.364590i
\(599\) −9479.61 + 16419.2i −0.646622 + 1.11998i 0.337302 + 0.941396i \(0.390486\pi\)
−0.983924 + 0.178586i \(0.942848\pi\)
\(600\) 0 0
\(601\) 1046.80 + 1813.12i 0.0710482 + 0.123059i 0.899361 0.437207i \(-0.144032\pi\)
−0.828313 + 0.560266i \(0.810699\pi\)
\(602\) −8832.06 −0.597953
\(603\) −10467.8 + 15358.3i −0.706935 + 1.03721i
\(604\) 3701.33 0.249346
\(605\) 0 0
\(606\) −6357.09 3993.78i −0.426137 0.267716i
\(607\) −3067.63 + 5313.28i −0.205125 + 0.355288i −0.950173 0.311724i \(-0.899094\pi\)
0.745047 + 0.667012i \(0.232427\pi\)
\(608\) 17830.2 30882.8i 1.18933 2.05997i
\(609\) −2500.89 1571.16i −0.166406 0.104543i
\(610\) 0 0
\(611\) 1279.11 0.0846924
\(612\) −13476.8 + 19773.0i −0.890141 + 1.30600i
\(613\) 12762.8 0.840922 0.420461 0.907311i \(-0.361868\pi\)
0.420461 + 0.907311i \(0.361868\pi\)
\(614\) 4378.96 + 7584.59i 0.287819 + 0.498516i
\(615\) 0 0
\(616\) 2722.91 4716.21i 0.178099 0.308477i
\(617\) 367.040 635.732i 0.0239489 0.0414807i −0.853803 0.520597i \(-0.825709\pi\)
0.877751 + 0.479116i \(0.159043\pi\)
\(618\) −1371.09 + 36714.5i −0.0892446 + 2.38976i
\(619\) 5324.85 + 9222.91i 0.345757 + 0.598869i 0.985491 0.169727i \(-0.0542887\pi\)
−0.639734 + 0.768597i \(0.720955\pi\)
\(620\) 0 0
\(621\) −21212.8 15648.6i −1.37076 1.01120i
\(622\) 23382.5 1.50732
\(623\) −9865.99 17088.4i −0.634466 1.09893i
\(624\) −49.5530 + 1326.91i −0.00317902 + 0.0851267i
\(625\) 0 0
\(626\) −6745.47 + 11683.5i −0.430676 + 0.745952i
\(627\) −23238.5 + 12284.0i −1.48015 + 0.782420i
\(628\) 18870.0 + 32683.9i 1.19904 + 2.07680i
\(629\) −27037.1 −1.71389
\(630\) 0 0
\(631\) −3465.43 −0.218632 −0.109316 0.994007i \(-0.534866\pi\)
−0.109316 + 0.994007i \(0.534866\pi\)
\(632\) 3186.98 + 5520.00i 0.200587 + 0.347427i
\(633\) 13693.5 + 8602.79i 0.859821 + 0.540174i
\(634\) 10694.6 18523.7i 0.669935 1.16036i
\(635\) 0 0
\(636\) 28968.5 + 18199.2i 1.80609 + 1.13466i
\(637\) −657.371 1138.60i −0.0408885 0.0708209i
\(638\) −6548.89 −0.406384
\(639\) 13870.9 + 1037.45i 0.858721 + 0.0642266i
\(640\) 0 0
\(641\) 14605.0 + 25296.7i 0.899945 + 1.55875i 0.827563 + 0.561373i \(0.189727\pi\)
0.0723819 + 0.997377i \(0.476940\pi\)
\(642\) −13711.8 + 7248.19i −0.842932 + 0.445581i
\(643\) −8512.87 + 14744.7i −0.522107 + 0.904316i 0.477562 + 0.878598i \(0.341521\pi\)
−0.999669 + 0.0257183i \(0.991813\pi\)
\(644\) 13186.7 22840.0i 0.806877 1.39755i
\(645\) 0 0
\(646\) 26052.7 + 45124.7i 1.58674 + 2.74831i
\(647\) −8673.26 −0.527019 −0.263509 0.964657i \(-0.584880\pi\)
−0.263509 + 0.964657i \(0.584880\pi\)
\(648\) 8739.03 + 1314.60i 0.529786 + 0.0796948i
\(649\) 20538.8 1.24225
\(650\) 0 0
\(651\) 147.937 3961.40i 0.00890645 0.238494i
\(652\) −3581.85 + 6203.95i −0.215147 + 0.372646i
\(653\) −540.335 + 935.888i −0.0323812 + 0.0560859i −0.881762 0.471695i \(-0.843642\pi\)
0.849381 + 0.527781i \(0.176976\pi\)
\(654\) −23679.5 + 12517.2i −1.41582 + 0.748412i
\(655\) 0 0
\(656\) 5848.49 0.348087
\(657\) −29304.3 2191.76i −1.74013 0.130150i
\(658\) −9539.95 −0.565206
\(659\) −3484.81 6035.86i −0.205992 0.356789i 0.744456 0.667671i \(-0.232709\pi\)
−0.950448 + 0.310882i \(0.899375\pi\)
\(660\) 0 0
\(661\) −5448.66 + 9437.36i −0.320618 + 0.555326i −0.980616 0.195941i \(-0.937224\pi\)
0.659998 + 0.751267i \(0.270557\pi\)
\(662\) −19017.0 + 32938.4i −1.11649 + 1.93382i
\(663\) −2729.75 1714.94i −0.159901 0.100456i
\(664\) 2170.02 + 3758.58i 0.126827 + 0.219671i
\(665\) 0 0
\(666\) 16732.9 + 34733.3i 0.973554 + 2.02085i
\(667\) −8214.14 −0.476841
\(668\) −13277.3 22997.0i −0.769034 1.33201i
\(669\) −22369.3 + 11824.6i −1.29274 + 0.683356i
\(670\) 0 0
\(671\) 5616.05 9727.28i 0.323108 0.559639i
\(672\) 614.084 16443.7i 0.0352512 0.943945i
\(673\) 14803.9 + 25641.2i 0.847919 + 1.46864i 0.883062 + 0.469257i \(0.155478\pi\)
−0.0351426 + 0.999382i \(0.511189\pi\)
\(674\) −44837.8 −2.56244
\(675\) 0 0
\(676\) −23102.5 −1.31443
\(677\) 3193.71 + 5531.66i 0.181306 + 0.314031i 0.942326 0.334698i \(-0.108634\pi\)
−0.761020 + 0.648729i \(0.775301\pi\)
\(678\) −225.657 + 6042.56i −0.0127821 + 0.342276i
\(679\) 2570.14 4451.62i 0.145262 0.251601i
\(680\) 0 0
\(681\) 30260.4 15995.9i 1.70276 0.900093i
\(682\) −4394.97 7612.31i −0.246762 0.427405i
\(683\) 19929.2 1.11650 0.558251 0.829672i \(-0.311473\pi\)
0.558251 + 0.829672i \(0.311473\pi\)
\(684\) 24035.5 35264.7i 1.34360 1.97131i
\(685\) 0 0
\(686\) 14569.9 + 25235.8i 0.810904 + 1.40453i
\(687\) −72.2907 45.4159i −0.00401465 0.00252216i
\(688\) −2648.99 + 4588.18i −0.146790 + 0.254248i
\(689\) −2304.47 + 3991.46i −0.127421 + 0.220700i
\(690\) 0 0
\(691\) −6473.59 11212.6i −0.356392 0.617289i 0.630963 0.775813i \(-0.282660\pi\)
−0.987355 + 0.158524i \(0.949327\pi\)
\(692\) −16493.8 −0.906069
\(693\) −6831.16 + 10022.6i −0.374451 + 0.549390i
\(694\) 5802.23 0.317362
\(695\) 0 0
\(696\) 2434.60 1286.95i 0.132591 0.0700886i
\(697\) −7099.52 + 12296.7i −0.385815 + 0.668252i
\(698\) −21920.8 + 37967.9i −1.18870 + 2.05889i
\(699\) 137.201 3673.94i 0.00742408 0.198800i
\(700\) 0 0
\(701\) −10692.9 −0.576125 −0.288063 0.957612i \(-0.593011\pi\)
−0.288063 + 0.957612i \(0.593011\pi\)
\(702\) −513.696 + 4568.14i −0.0276185 + 0.245603i
\(703\) 48220.0 2.58699
\(704\) −13570.3 23504.5i −0.726492 1.25832i
\(705\) 0 0
\(706\) −3564.35 + 6173.63i −0.190009 + 0.329104i
\(707\) −2166.42 + 3752.35i −0.115243 + 0.199607i
\(708\) −29481.1 + 15584.0i −1.56493 + 0.827234i
\(709\) 11786.7 + 20415.2i 0.624343 + 1.08139i 0.988668 + 0.150122i \(0.0479665\pi\)
−0.364325 + 0.931272i \(0.618700\pi\)
\(710\) 0 0
\(711\) −6161.44 12789.6i −0.324996 0.674610i
\(712\) 18398.1 0.968394
\(713\) −5512.52 9547.97i −0.289545 0.501507i
\(714\) 20359.3 + 12790.5i 1.06712 + 0.670410i
\(715\) 0 0
\(716\) −5431.37 + 9407.41i −0.283492 + 0.491022i
\(717\) 26892.4 + 16894.9i 1.40072 + 0.879988i
\(718\) −24458.5 42363.3i −1.27128 2.20193i
\(719\) 27013.2 1.40114 0.700572 0.713581i \(-0.252928\pi\)
0.700572 + 0.713581i \(0.252928\pi\)
\(720\) 0 0
\(721\) 21204.0 1.09525
\(722\) −31596.1 54726.0i −1.62865 2.82090i
\(723\) 14186.8 7499.25i 0.729754 0.385754i
\(724\) −3194.91 + 5533.74i −0.164003 + 0.284061i
\(725\) 0 0
\(726\) 115.303 3087.54i 0.00589432 0.157836i
\(727\) 8927.02 + 15462.1i 0.455412 + 0.788797i 0.998712 0.0507416i \(-0.0161585\pi\)
−0.543299 + 0.839539i \(0.682825\pi\)
\(728\) −1191.18 −0.0606428
\(729\) −19191.4 4371.50i −0.975025 0.222095i
\(730\) 0 0
\(731\) −6431.24 11139.2i −0.325401 0.563611i
\(732\) −680.552 + 18223.6i −0.0343633 + 0.920169i
\(733\) −4795.40 + 8305.88i −0.241640 + 0.418533i −0.961182 0.275916i \(-0.911019\pi\)
0.719541 + 0.694449i \(0.244352\pi\)
\(734\) 602.676 1043.87i 0.0303068 0.0524929i
\(735\) 0 0
\(736\) −22882.4 39633.5i −1.14600 1.98493i
\(737\) 23785.1 1.18878
\(738\) 20190.9 + 1510.14i 1.00710 + 0.0753240i
\(739\) −6237.43 −0.310484 −0.155242 0.987876i \(-0.549616\pi\)
−0.155242 + 0.987876i \(0.549616\pi\)
\(740\) 0 0
\(741\) 4868.44 + 3058.55i 0.241359 + 0.151631i
\(742\) 17187.4 29769.5i 0.850365 1.47288i
\(743\) 8567.24 14838.9i 0.423017 0.732687i −0.573216 0.819404i \(-0.694304\pi\)
0.996233 + 0.0867173i \(0.0276377\pi\)
\(744\) 3129.79 + 1966.26i 0.154225 + 0.0968905i
\(745\) 0 0
\(746\) 42632.3 2.09233
\(747\) −4195.34 8708.47i −0.205488 0.426541i
\(748\) 30622.1 1.49686
\(749\) 4475.59 + 7751.94i 0.218337 + 0.378171i
\(750\) 0 0
\(751\) −19570.8 + 33897.7i −0.950932 + 1.64706i −0.207518 + 0.978231i \(0.566538\pi\)
−0.743414 + 0.668831i \(0.766795\pi\)
\(752\) −2861.30 + 4955.92i −0.138751 + 0.240324i
\(753\) −531.958 + 14244.6i −0.0257445 + 0.689378i
\(754\) 716.227 + 1240.54i 0.0345934 + 0.0599176i
\(755\) 0 0
\(756\) 2200.63 19569.5i 0.105868 0.941448i
\(757\) 3774.26 0.181212 0.0906062 0.995887i \(-0.471120\pi\)
0.0906062 + 0.995887i \(0.471120\pi\)
\(758\) −29290.0 50731.8i −1.40351 2.43095i
\(759\) −1258.88 + 33709.9i −0.0602036 + 1.61211i
\(760\) 0 0
\(761\) −12998.9 + 22514.8i −0.619200 + 1.07249i 0.370432 + 0.928860i \(0.379210\pi\)
−0.989632 + 0.143627i \(0.954124\pi\)
\(762\) −2893.87 + 1529.73i −0.137577 + 0.0727245i
\(763\) 7729.08 + 13387.2i 0.366725 + 0.635187i
\(764\) 39347.3 1.86327
\(765\) 0 0
\(766\) −6024.73 −0.284181
\(767\) −2246.25 3890.63i −0.105746 0.183158i
\(768\) 142.459 + 89.4984i 0.00669341 + 0.00420507i
\(769\) −7817.68 + 13540.6i −0.366597 + 0.634964i −0.989031 0.147708i \(-0.952810\pi\)
0.622434 + 0.782672i \(0.286144\pi\)
\(770\) 0 0
\(771\) 3168.14 + 1990.35i 0.147987 + 0.0929712i
\(772\) −72.3426 125.301i −0.00337262 0.00584156i
\(773\) −5936.28 −0.276213 −0.138107 0.990417i \(-0.544102\pi\)
−0.138107 + 0.990417i \(0.544102\pi\)
\(774\) −10329.9 + 15155.9i −0.479715 + 0.703833i
\(775\) 0 0
\(776\) 2396.40 + 4150.68i 0.110858 + 0.192011i
\(777\) 19671.4 10398.5i 0.908248 0.480108i
\(778\) 1965.56 3404.45i 0.0905767 0.156883i
\(779\) 12661.8 21930.9i 0.582358 1.00867i
\(780\) 0 0