Properties

Label 225.4.h.d.46.12
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.12
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +O(q^{10})\) \(q+(0.856692 - 2.63663i) q^{2} +(0.254251 + 0.184724i) q^{4} +(7.75979 + 8.04895i) q^{5} -7.15708 q^{7} +(18.6477 - 13.5483i) q^{8} +(27.8698 - 13.5642i) q^{10} +(-15.3917 + 47.3707i) q^{11} +(16.6242 + 51.1641i) q^{13} +(-6.13142 + 18.8706i) q^{14} +(-18.9696 - 58.3826i) q^{16} +(10.7434 - 7.80553i) q^{17} +(124.404 - 90.3850i) q^{19} +(0.486099 + 3.47988i) q^{20} +(111.713 + 81.1643i) q^{22} +(-66.4882 + 204.630i) q^{23} +(-4.57128 + 124.916i) q^{25} +149.143 q^{26} +(-1.81970 - 1.32209i) q^{28} +(56.2588 + 40.8744i) q^{29} +(122.680 - 89.1322i) q^{31} +14.2140 q^{32} +(-11.3765 - 35.0133i) q^{34} +(-55.5375 - 57.6070i) q^{35} +(-92.0967 - 283.445i) q^{37} +(-131.735 - 405.440i) q^{38} +(253.752 + 44.9620i) q^{40} +(-110.882 - 341.260i) q^{41} +451.178 q^{43} +(-12.6639 + 9.20084i) q^{44} +(482.572 + 350.609i) q^{46} +(-124.804 - 90.6754i) q^{47} -291.776 q^{49} +(325.442 + 119.068i) q^{50} +(-5.22453 + 16.0794i) q^{52} +(-39.5720 - 28.7507i) q^{53} +(-500.721 + 243.700i) q^{55} +(-133.463 + 96.9665i) q^{56} +(155.967 - 113.317i) q^{58} +(9.36171 + 28.8124i) q^{59} +(175.261 - 539.399i) q^{61} +(-129.909 - 399.820i) q^{62} +(163.934 - 504.537i) q^{64} +(-282.817 + 530.831i) q^{65} +(-557.154 + 404.796i) q^{67} +4.17339 q^{68} +(-199.467 + 97.0802i) q^{70} +(684.549 + 497.354i) q^{71} +(-110.215 + 339.207i) q^{73} -826.236 q^{74} +48.3262 q^{76} +(110.160 - 339.036i) q^{77} +(-158.437 - 115.111i) q^{79} +(322.718 - 605.722i) q^{80} -994.767 q^{82} +(-580.078 + 421.451i) q^{83} +(146.193 + 25.9038i) q^{85} +(386.521 - 1189.59i) q^{86} +(354.775 + 1091.88i) q^{88} +(-371.049 + 1141.97i) q^{89} +(-118.981 - 366.186i) q^{91} +(-54.7048 + 39.7453i) q^{92} +(-345.996 + 251.381i) q^{94} +(1692.85 + 299.955i) q^{95} +(-1001.28 - 727.475i) q^{97} +(-249.962 + 769.305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.856692 2.63663i 0.302886 0.932189i −0.677571 0.735457i \(-0.736967\pi\)
0.980457 0.196731i \(-0.0630327\pi\)
\(3\) 0 0
\(4\) 0.254251 + 0.184724i 0.0317814 + 0.0230905i
\(5\) 7.75979 + 8.04895i 0.694057 + 0.719920i
\(6\) 0 0
\(7\) −7.15708 −0.386446 −0.193223 0.981155i \(-0.561894\pi\)
−0.193223 + 0.981155i \(0.561894\pi\)
\(8\) 18.6477 13.5483i 0.824118 0.598757i
\(9\) 0 0
\(10\) 27.8698 13.5642i 0.881322 0.428938i
\(11\) −15.3917 + 47.3707i −0.421888 + 1.29844i 0.484055 + 0.875037i \(0.339163\pi\)
−0.905943 + 0.423400i \(0.860837\pi\)
\(12\) 0 0
\(13\) 16.6242 + 51.1641i 0.354672 + 1.09157i 0.956200 + 0.292716i \(0.0945589\pi\)
−0.601528 + 0.798852i \(0.705441\pi\)
\(14\) −6.13142 + 18.8706i −0.117049 + 0.360241i
\(15\) 0 0
\(16\) −18.9696 58.3826i −0.296401 0.912228i
\(17\) 10.7434 7.80553i 0.153274 0.111360i −0.508505 0.861059i \(-0.669802\pi\)
0.661779 + 0.749699i \(0.269802\pi\)
\(18\) 0 0
\(19\) 124.404 90.3850i 1.50212 1.09135i 0.532593 0.846372i \(-0.321218\pi\)
0.969527 0.244983i \(-0.0787822\pi\)
\(20\) 0.486099 + 3.47988i 0.00543475 + 0.0389062i
\(21\) 0 0
\(22\) 111.713 + 81.1643i 1.08260 + 0.786558i
\(23\) −66.4882 + 204.630i −0.602772 + 1.85514i −0.0913347 + 0.995820i \(0.529113\pi\)
−0.511437 + 0.859321i \(0.670887\pi\)
\(24\) 0 0
\(25\) −4.57128 + 124.916i −0.0365702 + 0.999331i
\(26\) 149.143 1.12497
\(27\) 0 0
\(28\) −1.81970 1.32209i −0.0122818 0.00892325i
\(29\) 56.2588 + 40.8744i 0.360241 + 0.261730i 0.753153 0.657846i \(-0.228532\pi\)
−0.392912 + 0.919576i \(0.628532\pi\)
\(30\) 0 0
\(31\) 122.680 89.1322i 0.710773 0.516407i −0.172650 0.984983i \(-0.555233\pi\)
0.883423 + 0.468576i \(0.155233\pi\)
\(32\) 14.2140 0.0785218
\(33\) 0 0
\(34\) −11.3765 35.0133i −0.0573839 0.176610i
\(35\) −55.5375 57.6070i −0.268216 0.278210i
\(36\) 0 0
\(37\) −92.0967 283.445i −0.409206 1.25941i −0.917332 0.398123i \(-0.869662\pi\)
0.508127 0.861282i \(-0.330338\pi\)
\(38\) −131.735 405.440i −0.562376 1.73082i
\(39\) 0 0
\(40\) 253.752 + 44.9620i 1.00304 + 0.177728i
\(41\) −110.882 341.260i −0.422363 1.29990i −0.905497 0.424352i \(-0.860502\pi\)
0.483135 0.875546i \(-0.339498\pi\)
\(42\) 0 0
\(43\) 451.178 1.60009 0.800047 0.599937i \(-0.204808\pi\)
0.800047 + 0.599937i \(0.204808\pi\)
\(44\) −12.6639 + 9.20084i −0.0433898 + 0.0315245i
\(45\) 0 0
\(46\) 482.572 + 350.609i 1.54677 + 1.12379i
\(47\) −124.804 90.6754i −0.387330 0.281412i 0.377030 0.926201i \(-0.376945\pi\)
−0.764361 + 0.644789i \(0.776945\pi\)
\(48\) 0 0
\(49\) −291.776 −0.850659
\(50\) 325.442 + 119.068i 0.920489 + 0.336774i
\(51\) 0 0
\(52\) −5.22453 + 16.0794i −0.0139329 + 0.0428811i
\(53\) −39.5720 28.7507i −0.102559 0.0745135i 0.535324 0.844647i \(-0.320190\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(54\) 0 0
\(55\) −500.721 + 243.700i −1.22759 + 0.597464i
\(56\) −133.463 + 96.9665i −0.318477 + 0.231387i
\(57\) 0 0
\(58\) 155.967 113.317i 0.353094 0.256538i
\(59\) 9.36171 + 28.8124i 0.0206575 + 0.0635772i 0.960854 0.277056i \(-0.0893587\pi\)
−0.940196 + 0.340633i \(0.889359\pi\)
\(60\) 0 0
\(61\) 175.261 539.399i 0.367868 1.13218i −0.580298 0.814404i \(-0.697064\pi\)
0.948166 0.317776i \(-0.102936\pi\)
\(62\) −129.909 399.820i −0.266105 0.818987i
\(63\) 0 0
\(64\) 163.934 504.537i 0.320184 0.985425i
\(65\) −282.817 + 530.831i −0.539679 + 1.01295i
\(66\) 0 0
\(67\) −557.154 + 404.796i −1.01593 + 0.738115i −0.965444 0.260610i \(-0.916076\pi\)
−0.0504840 + 0.998725i \(0.516076\pi\)
\(68\) 4.17339 0.00744262
\(69\) 0 0
\(70\) −199.467 + 97.0802i −0.340584 + 0.165761i
\(71\) 684.549 + 497.354i 1.14424 + 0.831339i 0.987704 0.156333i \(-0.0499674\pi\)
0.156536 + 0.987672i \(0.449967\pi\)
\(72\) 0 0
\(73\) −110.215 + 339.207i −0.176708 + 0.543851i −0.999707 0.0241912i \(-0.992299\pi\)
0.822999 + 0.568042i \(0.192299\pi\)
\(74\) −826.236 −1.29795
\(75\) 0 0
\(76\) 48.3262 0.0729394
\(77\) 110.160 339.036i 0.163037 0.501776i
\(78\) 0 0
\(79\) −158.437 115.111i −0.225640 0.163937i 0.469222 0.883080i \(-0.344535\pi\)
−0.694862 + 0.719143i \(0.744535\pi\)
\(80\) 322.718 605.722i 0.451012 0.846523i
\(81\) 0 0
\(82\) −994.767 −1.33968
\(83\) −580.078 + 421.451i −0.767130 + 0.557353i −0.901089 0.433634i \(-0.857231\pi\)
0.133959 + 0.990987i \(0.457231\pi\)
\(84\) 0 0
\(85\) 146.193 + 25.9038i 0.186551 + 0.0330548i
\(86\) 386.521 1189.59i 0.484647 1.49159i
\(87\) 0 0
\(88\) 354.775 + 1091.88i 0.429763 + 1.32267i
\(89\) −371.049 + 1141.97i −0.441922 + 1.36010i 0.443902 + 0.896076i \(0.353594\pi\)
−0.885824 + 0.464022i \(0.846406\pi\)
\(90\) 0 0
\(91\) −118.981 366.186i −0.137062 0.421832i
\(92\) −54.7048 + 39.7453i −0.0619931 + 0.0450406i
\(93\) 0 0
\(94\) −345.996 + 251.381i −0.379646 + 0.275829i
\(95\) 1692.85 + 299.955i 1.82824 + 0.323945i
\(96\) 0 0
\(97\) −1001.28 727.475i −1.04809 0.761483i −0.0762433 0.997089i \(-0.524293\pi\)
−0.971849 + 0.235606i \(0.924293\pi\)
\(98\) −249.962 + 769.305i −0.257653 + 0.792975i
\(99\) 0 0
\(100\) −24.2373 + 30.9157i −0.0242373 + 0.0309157i
\(101\) 365.423 0.360010 0.180005 0.983666i \(-0.442389\pi\)
0.180005 + 0.983666i \(0.442389\pi\)
\(102\) 0 0
\(103\) −157.043 114.098i −0.150232 0.109150i 0.510130 0.860097i \(-0.329597\pi\)
−0.660362 + 0.750947i \(0.729597\pi\)
\(104\) 1003.19 + 728.861i 0.945875 + 0.687218i
\(105\) 0 0
\(106\) −109.706 + 79.7060i −0.100524 + 0.0730352i
\(107\) 286.289 0.258660 0.129330 0.991602i \(-0.458717\pi\)
0.129330 + 0.991602i \(0.458717\pi\)
\(108\) 0 0
\(109\) −437.785 1347.36i −0.384699 1.18398i −0.936699 0.350137i \(-0.886135\pi\)
0.552000 0.833844i \(-0.313865\pi\)
\(110\) 213.582 + 1528.99i 0.185130 + 1.32530i
\(111\) 0 0
\(112\) 135.767 + 417.849i 0.114543 + 0.352527i
\(113\) −348.438 1072.38i −0.290074 0.892755i −0.984832 0.173512i \(-0.944489\pi\)
0.694758 0.719244i \(-0.255511\pi\)
\(114\) 0 0
\(115\) −2162.99 + 1052.72i −1.75391 + 0.853626i
\(116\) 6.75336 + 20.7847i 0.00540547 + 0.0166363i
\(117\) 0 0
\(118\) 83.9877 0.0655228
\(119\) −76.8914 + 55.8648i −0.0592321 + 0.0430346i
\(120\) 0 0
\(121\) −930.279 675.887i −0.698933 0.507804i
\(122\) −1272.05 924.198i −0.943983 0.685844i
\(123\) 0 0
\(124\) 47.6564 0.0345135
\(125\) −1040.92 + 932.531i −0.744820 + 0.667265i
\(126\) 0 0
\(127\) −294.997 + 907.909i −0.206116 + 0.634361i 0.793549 + 0.608506i \(0.208231\pi\)
−0.999666 + 0.0258551i \(0.991769\pi\)
\(128\) −1097.84 797.629i −0.758097 0.550790i
\(129\) 0 0
\(130\) 1157.32 + 1200.44i 0.780795 + 0.809890i
\(131\) 1193.22 866.926i 0.795818 0.578196i −0.113866 0.993496i \(-0.536323\pi\)
0.909684 + 0.415300i \(0.136323\pi\)
\(132\) 0 0
\(133\) −890.371 + 646.893i −0.580489 + 0.421750i
\(134\) 589.987 + 1815.79i 0.380352 + 1.17060i
\(135\) 0 0
\(136\) 94.5873 291.110i 0.0596382 0.183547i
\(137\) −286.735 882.480i −0.178813 0.550331i 0.820974 0.570966i \(-0.193431\pi\)
−0.999787 + 0.0206352i \(0.993431\pi\)
\(138\) 0 0
\(139\) 285.429 878.460i 0.174171 0.536043i −0.825424 0.564514i \(-0.809064\pi\)
0.999595 + 0.0284706i \(0.00906369\pi\)
\(140\) −3.47905 24.9058i −0.00210024 0.0150352i
\(141\) 0 0
\(142\) 1897.79 1378.82i 1.12154 0.814846i
\(143\) −2679.56 −1.56696
\(144\) 0 0
\(145\) 107.560 + 770.001i 0.0616027 + 0.441001i
\(146\) 799.941 + 581.191i 0.453449 + 0.329450i
\(147\) 0 0
\(148\) 28.9434 89.0786i 0.0160752 0.0494744i
\(149\) −1993.74 −1.09620 −0.548098 0.836414i \(-0.684648\pi\)
−0.548098 + 0.836414i \(0.684648\pi\)
\(150\) 0 0
\(151\) 1706.75 0.919825 0.459913 0.887964i \(-0.347881\pi\)
0.459913 + 0.887964i \(0.347881\pi\)
\(152\) 1095.28 3370.94i 0.584469 1.79881i
\(153\) 0 0
\(154\) −799.539 580.899i −0.418368 0.303962i
\(155\) 1669.39 + 295.798i 0.865088 + 0.153284i
\(156\) 0 0
\(157\) 489.227 0.248692 0.124346 0.992239i \(-0.460317\pi\)
0.124346 + 0.992239i \(0.460317\pi\)
\(158\) −439.238 + 319.125i −0.221164 + 0.160685i
\(159\) 0 0
\(160\) 110.297 + 114.408i 0.0544986 + 0.0565295i
\(161\) 475.862 1464.55i 0.232939 0.716912i
\(162\) 0 0
\(163\) −1064.87 3277.32i −0.511698 1.57485i −0.789210 0.614123i \(-0.789510\pi\)
0.277512 0.960722i \(-0.410490\pi\)
\(164\) 34.8471 107.248i 0.0165921 0.0510652i
\(165\) 0 0
\(166\) 614.262 + 1890.50i 0.287205 + 0.883925i
\(167\) 748.980 544.166i 0.347053 0.252148i −0.400579 0.916262i \(-0.631191\pi\)
0.747632 + 0.664114i \(0.231191\pi\)
\(168\) 0 0
\(169\) −563.993 + 409.765i −0.256710 + 0.186511i
\(170\) 193.541 363.265i 0.0873171 0.163889i
\(171\) 0 0
\(172\) 114.713 + 83.3436i 0.0508532 + 0.0369470i
\(173\) −200.254 + 616.317i −0.0880058 + 0.270854i −0.985368 0.170441i \(-0.945481\pi\)
0.897362 + 0.441295i \(0.145481\pi\)
\(174\) 0 0
\(175\) 32.7170 894.037i 0.0141324 0.386188i
\(176\) 3057.60 1.30952
\(177\) 0 0
\(178\) 2693.08 + 1956.64i 1.13401 + 0.823910i
\(179\) −1657.52 1204.26i −0.692115 0.502851i 0.185240 0.982693i \(-0.440694\pi\)
−0.877355 + 0.479842i \(0.840694\pi\)
\(180\) 0 0
\(181\) 729.361 529.912i 0.299519 0.217614i −0.427867 0.903842i \(-0.640735\pi\)
0.727386 + 0.686228i \(0.240735\pi\)
\(182\) −1067.43 −0.434741
\(183\) 0 0
\(184\) 1532.54 + 4716.67i 0.614023 + 1.88977i
\(185\) 1566.78 2940.75i 0.622659 1.16869i
\(186\) 0 0
\(187\) 204.395 + 629.062i 0.0799295 + 0.245998i
\(188\) −14.9816 46.1086i −0.00581195 0.0178873i
\(189\) 0 0
\(190\) 2241.13 4206.46i 0.855728 1.60615i
\(191\) −899.058 2767.02i −0.340594 1.04824i −0.963900 0.266264i \(-0.914211\pi\)
0.623306 0.781978i \(-0.285789\pi\)
\(192\) 0 0
\(193\) 184.846 0.0689406 0.0344703 0.999406i \(-0.489026\pi\)
0.0344703 + 0.999406i \(0.489026\pi\)
\(194\) −2775.87 + 2016.79i −1.02730 + 0.746377i
\(195\) 0 0
\(196\) −74.1844 53.8981i −0.0270351 0.0196422i
\(197\) −2578.89 1873.67i −0.932682 0.677633i 0.0139660 0.999902i \(-0.495554\pi\)
−0.946648 + 0.322269i \(0.895554\pi\)
\(198\) 0 0
\(199\) 2048.58 0.729749 0.364874 0.931057i \(-0.381112\pi\)
0.364874 + 0.931057i \(0.381112\pi\)
\(200\) 1607.16 + 2391.33i 0.568218 + 0.845463i
\(201\) 0 0
\(202\) 313.055 963.485i 0.109042 0.335597i
\(203\) −402.649 292.541i −0.139214 0.101145i
\(204\) 0 0
\(205\) 1886.36 3540.59i 0.642679 1.20627i
\(206\) −435.373 + 316.317i −0.147252 + 0.106985i
\(207\) 0 0
\(208\) 2671.74 1941.13i 0.890633 0.647083i
\(209\) 2366.81 + 7284.29i 0.783329 + 2.41084i
\(210\) 0 0
\(211\) −921.101 + 2834.86i −0.300527 + 0.924927i 0.680782 + 0.732487i \(0.261640\pi\)
−0.981309 + 0.192441i \(0.938360\pi\)
\(212\) −4.75026 14.6198i −0.00153891 0.00473628i
\(213\) 0 0
\(214\) 245.261 754.837i 0.0783445 0.241120i
\(215\) 3501.05 + 3631.51i 1.11056 + 1.15194i
\(216\) 0 0
\(217\) −878.030 + 637.926i −0.274676 + 0.199563i
\(218\) −3927.54 −1.22021
\(219\) 0 0
\(220\) −172.326 30.5343i −0.0528101 0.00935737i
\(221\) 577.964 + 419.915i 0.175919 + 0.127812i
\(222\) 0 0
\(223\) −575.194 + 1770.27i −0.172726 + 0.531595i −0.999522 0.0309059i \(-0.990161\pi\)
0.826797 + 0.562501i \(0.190161\pi\)
\(224\) −101.731 −0.0303445
\(225\) 0 0
\(226\) −3125.98 −0.920076
\(227\) 405.456 1247.86i 0.118551 0.364862i −0.874120 0.485710i \(-0.838561\pi\)
0.992671 + 0.120848i \(0.0385612\pi\)
\(228\) 0 0
\(229\) 3473.56 + 2523.69i 1.00236 + 0.728255i 0.962592 0.270955i \(-0.0873393\pi\)
0.0397643 + 0.999209i \(0.487339\pi\)
\(230\) 922.623 + 6604.86i 0.264504 + 1.89353i
\(231\) 0 0
\(232\) 1602.87 0.453594
\(233\) −355.013 + 257.932i −0.0998184 + 0.0725223i −0.636575 0.771215i \(-0.719649\pi\)
0.536756 + 0.843737i \(0.319649\pi\)
\(234\) 0 0
\(235\) −238.611 1708.16i −0.0662351 0.474163i
\(236\) −2.94212 + 9.05492i −0.000811508 + 0.00249756i
\(237\) 0 0
\(238\) 81.4226 + 250.593i 0.0221758 + 0.0682501i
\(239\) 1047.42 3223.62i 0.283480 0.872462i −0.703370 0.710824i \(-0.748322\pi\)
0.986850 0.161638i \(-0.0516777\pi\)
\(240\) 0 0
\(241\) −850.354 2617.12i −0.227287 0.699517i −0.998051 0.0623969i \(-0.980126\pi\)
0.770765 0.637120i \(-0.219874\pi\)
\(242\) −2579.03 + 1873.77i −0.685067 + 0.497730i
\(243\) 0 0
\(244\) 144.201 104.768i 0.0378340 0.0274880i
\(245\) −2264.12 2348.49i −0.590406 0.612407i
\(246\) 0 0
\(247\) 6692.59 + 4862.45i 1.72405 + 1.25259i
\(248\) 1080.10 3324.21i 0.276559 0.851160i
\(249\) 0 0
\(250\) 1566.99 + 3543.41i 0.396421 + 0.896419i
\(251\) 3369.50 0.847334 0.423667 0.905818i \(-0.360743\pi\)
0.423667 + 0.905818i \(0.360743\pi\)
\(252\) 0 0
\(253\) −8670.09 6299.19i −2.15448 1.56532i
\(254\) 2141.10 + 1555.60i 0.528914 + 0.384279i
\(255\) 0 0
\(256\) 389.919 283.293i 0.0951951 0.0691633i
\(257\) 4556.70 1.10599 0.552994 0.833185i \(-0.313485\pi\)
0.552994 + 0.833185i \(0.313485\pi\)
\(258\) 0 0
\(259\) 659.144 + 2028.64i 0.158136 + 0.486692i
\(260\) −169.964 + 82.7211i −0.0405412 + 0.0197313i
\(261\) 0 0
\(262\) −1263.54 3888.77i −0.297945 0.916981i
\(263\) 1302.86 + 4009.78i 0.305466 + 0.940129i 0.979503 + 0.201431i \(0.0645590\pi\)
−0.674036 + 0.738698i \(0.735441\pi\)
\(264\) 0 0
\(265\) −75.6570 541.612i −0.0175380 0.125551i
\(266\) 942.841 + 2901.77i 0.217328 + 0.668867i
\(267\) 0 0
\(268\) −216.433 −0.0493311
\(269\) 525.519 381.812i 0.119113 0.0865408i −0.526634 0.850092i \(-0.676546\pi\)
0.645747 + 0.763551i \(0.276546\pi\)
\(270\) 0 0
\(271\) −1185.38 861.228i −0.265707 0.193047i 0.446952 0.894558i \(-0.352509\pi\)
−0.712659 + 0.701510i \(0.752509\pi\)
\(272\) −659.505 479.159i −0.147016 0.106813i
\(273\) 0 0
\(274\) −2572.41 −0.567172
\(275\) −5847.02 2139.22i −1.28214 0.469090i
\(276\) 0 0
\(277\) 711.145 2188.68i 0.154255 0.474747i −0.843830 0.536611i \(-0.819704\pi\)
0.998085 + 0.0618637i \(0.0197044\pi\)
\(278\) −2071.65 1505.14i −0.446939 0.324721i
\(279\) 0 0
\(280\) −1816.12 321.797i −0.387622 0.0686823i
\(281\) 6769.19 4918.10i 1.43707 1.04409i 0.448423 0.893822i \(-0.351986\pi\)
0.988645 0.150269i \(-0.0480140\pi\)
\(282\) 0 0
\(283\) −470.418 + 341.779i −0.0988108 + 0.0717903i −0.636094 0.771612i \(-0.719451\pi\)
0.537283 + 0.843402i \(0.319451\pi\)
\(284\) 82.1740 + 252.906i 0.0171695 + 0.0528422i
\(285\) 0 0
\(286\) −2295.56 + 7064.99i −0.474612 + 1.46071i
\(287\) 793.592 + 2442.43i 0.163220 + 0.502341i
\(288\) 0 0
\(289\) −1463.71 + 4504.82i −0.297925 + 0.916919i
\(290\) 2122.35 + 376.057i 0.429754 + 0.0761478i
\(291\) 0 0
\(292\) −90.6819 + 65.8843i −0.0181738 + 0.0132041i
\(293\) −2079.50 −0.414627 −0.207313 0.978275i \(-0.566472\pi\)
−0.207313 + 0.978275i \(0.566472\pi\)
\(294\) 0 0
\(295\) −159.265 + 298.930i −0.0314330 + 0.0589979i
\(296\) −5557.58 4037.82i −1.09131 0.792884i
\(297\) 0 0
\(298\) −1708.02 + 5256.74i −0.332023 + 1.02186i
\(299\) −11575.0 −2.23880
\(300\) 0 0
\(301\) −3229.12 −0.618350
\(302\) 1462.16 4500.07i 0.278603 0.857451i
\(303\) 0 0
\(304\) −7636.81 5548.47i −1.44079 1.04680i
\(305\) 5701.59 2774.95i 1.07040 0.520962i
\(306\) 0 0
\(307\) 5017.05 0.932698 0.466349 0.884601i \(-0.345569\pi\)
0.466349 + 0.884601i \(0.345569\pi\)
\(308\) 90.6364 65.8512i 0.0167678 0.0121825i
\(309\) 0 0
\(310\) 2210.06 4148.16i 0.404913 0.759998i
\(311\) −926.375 + 2851.09i −0.168906 + 0.519841i −0.999303 0.0373323i \(-0.988114\pi\)
0.830396 + 0.557173i \(0.188114\pi\)
\(312\) 0 0
\(313\) −1432.91 4410.05i −0.258763 0.796392i −0.993065 0.117568i \(-0.962490\pi\)
0.734302 0.678823i \(-0.237510\pi\)
\(314\) 419.117 1289.91i 0.0753253 0.231827i
\(315\) 0 0
\(316\) −19.0190 58.5344i −0.00338576 0.0104203i
\(317\) −1121.63 + 814.913i −0.198729 + 0.144385i −0.682699 0.730699i \(-0.739194\pi\)
0.483971 + 0.875084i \(0.339194\pi\)
\(318\) 0 0
\(319\) −2802.17 + 2035.89i −0.491822 + 0.357329i
\(320\) 5333.09 2595.61i 0.931653 0.453434i
\(321\) 0 0
\(322\) −3453.81 2509.34i −0.597743 0.434286i
\(323\) 631.021 1942.08i 0.108703 0.334552i
\(324\) 0 0
\(325\) −6467.23 + 1842.75i −1.10381 + 0.314516i
\(326\) −9553.34 −1.62304
\(327\) 0 0
\(328\) −6691.19 4861.43i −1.12640 0.818377i
\(329\) 893.232 + 648.971i 0.149682 + 0.108751i
\(330\) 0 0
\(331\) −6494.76 + 4718.72i −1.07850 + 0.783578i −0.977421 0.211300i \(-0.932230\pi\)
−0.101081 + 0.994878i \(0.532230\pi\)
\(332\) −225.338 −0.0372500
\(333\) 0 0
\(334\) −793.117 2440.96i −0.129932 0.399891i
\(335\) −7581.58 1343.37i −1.23650 0.219093i
\(336\) 0 0
\(337\) 2266.96 + 6976.97i 0.366436 + 1.12777i 0.949077 + 0.315045i \(0.102019\pi\)
−0.582641 + 0.812730i \(0.697981\pi\)
\(338\) 597.229 + 1838.08i 0.0961094 + 0.295794i
\(339\) 0 0
\(340\) 32.3846 + 33.5914i 0.00516560 + 0.00535809i
\(341\) 2334.00 + 7183.33i 0.370655 + 1.14076i
\(342\) 0 0
\(343\) 4543.15 0.715180
\(344\) 8413.42 6112.71i 1.31867 0.958067i
\(345\) 0 0
\(346\) 1453.44 + 1055.99i 0.225831 + 0.164076i
\(347\) −5317.34 3863.27i −0.822621 0.597669i 0.0948410 0.995492i \(-0.469766\pi\)
−0.917462 + 0.397823i \(0.869766\pi\)
\(348\) 0 0
\(349\) 11655.8 1.78774 0.893868 0.448331i \(-0.147981\pi\)
0.893868 + 0.448331i \(0.147981\pi\)
\(350\) −2329.21 852.177i −0.355719 0.130145i
\(351\) 0 0
\(352\) −218.777 + 673.326i −0.0331274 + 0.101956i
\(353\) 569.531 + 413.788i 0.0858727 + 0.0623902i 0.629893 0.776682i \(-0.283099\pi\)
−0.544021 + 0.839072i \(0.683099\pi\)
\(354\) 0 0
\(355\) 1308.78 + 9369.27i 0.195670 + 1.40076i
\(356\) −305.289 + 221.806i −0.0454503 + 0.0330216i
\(357\) 0 0
\(358\) −4595.16 + 3338.58i −0.678384 + 0.492875i
\(359\) 1732.60 + 5332.39i 0.254716 + 0.783935i 0.993885 + 0.110416i \(0.0352182\pi\)
−0.739170 + 0.673519i \(0.764782\pi\)
\(360\) 0 0
\(361\) 5187.42 15965.2i 0.756294 2.32763i
\(362\) −772.342 2377.03i −0.112137 0.345121i
\(363\) 0 0
\(364\) 37.3924 115.082i 0.00538432 0.0165712i
\(365\) −3585.50 + 1745.06i −0.514175 + 0.250248i
\(366\) 0 0
\(367\) −1908.15 + 1386.35i −0.271402 + 0.197185i −0.715159 0.698962i \(-0.753646\pi\)
0.443756 + 0.896147i \(0.353646\pi\)
\(368\) 13208.1 1.87097
\(369\) 0 0
\(370\) −6411.42 6650.34i −0.900848 0.934418i
\(371\) 283.220 + 205.771i 0.0396335 + 0.0287954i
\(372\) 0 0
\(373\) −1665.42 + 5125.62i −0.231185 + 0.711514i 0.766420 + 0.642340i \(0.222036\pi\)
−0.997605 + 0.0691739i \(0.977964\pi\)
\(374\) 1833.71 0.253526
\(375\) 0 0
\(376\) −3555.80 −0.487703
\(377\) −1156.04 + 3557.94i −0.157929 + 0.486056i
\(378\) 0 0
\(379\) 2275.81 + 1653.47i 0.308445 + 0.224098i 0.731229 0.682132i \(-0.238947\pi\)
−0.422784 + 0.906230i \(0.638947\pi\)
\(380\) 375.001 + 388.975i 0.0506241 + 0.0525106i
\(381\) 0 0
\(382\) −8065.81 −1.08032
\(383\) −7657.03 + 5563.16i −1.02156 + 0.742204i −0.966601 0.256285i \(-0.917501\pi\)
−0.0549545 + 0.998489i \(0.517501\pi\)
\(384\) 0 0
\(385\) 3583.70 1744.18i 0.474396 0.230888i
\(386\) 158.357 487.371i 0.0208812 0.0642657i
\(387\) 0 0
\(388\) −120.195 369.923i −0.0157268 0.0484020i
\(389\) 4368.83 13445.9i 0.569431 1.75253i −0.0849726 0.996383i \(-0.527080\pi\)
0.654404 0.756145i \(-0.272920\pi\)
\(390\) 0 0
\(391\) 882.934 + 2717.39i 0.114199 + 0.351469i
\(392\) −5440.94 + 3953.08i −0.701044 + 0.509338i
\(393\) 0 0
\(394\) −7149.50 + 5194.41i −0.914179 + 0.664190i
\(395\) −302.914 2168.49i −0.0385854 0.276225i
\(396\) 0 0
\(397\) −11467.9 8331.93i −1.44977 1.05332i −0.985885 0.167423i \(-0.946455\pi\)
−0.463884 0.885896i \(-0.653545\pi\)
\(398\) 1755.00 5401.34i 0.221031 0.680264i
\(399\) 0 0
\(400\) 7379.65 2102.74i 0.922457 0.262842i
\(401\) −5740.98 −0.714940 −0.357470 0.933925i \(-0.616361\pi\)
−0.357470 + 0.933925i \(0.616361\pi\)
\(402\) 0 0
\(403\) 6599.83 + 4795.06i 0.815784 + 0.592702i
\(404\) 92.9092 + 67.5025i 0.0114416 + 0.00831281i
\(405\) 0 0
\(406\) −1116.27 + 811.017i −0.136452 + 0.0991382i
\(407\) 14844.5 1.80790
\(408\) 0 0
\(409\) 312.072 + 960.459i 0.0377285 + 0.116117i 0.968147 0.250382i \(-0.0805563\pi\)
−0.930418 + 0.366499i \(0.880556\pi\)
\(410\) −7719.18 8006.83i −0.929813 0.964462i
\(411\) 0 0
\(412\) −18.8516 58.0193i −0.00225425 0.00693788i
\(413\) −67.0026 206.213i −0.00798300 0.0245692i
\(414\) 0 0
\(415\) −7893.52 1398.65i −0.933681 0.165438i
\(416\) 236.296 + 727.246i 0.0278495 + 0.0857119i
\(417\) 0 0
\(418\) 21233.6 2.48462
\(419\) 1306.11 948.947i 0.152286 0.110642i −0.509033 0.860747i \(-0.669997\pi\)
0.661319 + 0.750105i \(0.269997\pi\)
\(420\) 0 0
\(421\) 7924.08 + 5757.18i 0.917330 + 0.666480i 0.942858 0.333195i \(-0.108127\pi\)
−0.0255276 + 0.999674i \(0.508127\pi\)
\(422\) 6685.36 + 4857.20i 0.771181 + 0.560296i
\(423\) 0 0
\(424\) −1127.45 −0.129136
\(425\) 925.928 + 1377.71i 0.105680 + 0.157244i
\(426\) 0 0
\(427\) −1254.36 + 3860.53i −0.142161 + 0.437527i
\(428\) 72.7893 + 52.8845i 0.00822057 + 0.00597259i
\(429\) 0 0
\(430\) 12574.3 6119.88i 1.41020 0.686341i
\(431\) −2915.55 + 2118.27i −0.325840 + 0.236736i −0.738663 0.674075i \(-0.764543\pi\)
0.412824 + 0.910811i \(0.364543\pi\)
\(432\) 0 0
\(433\) 8305.22 6034.09i 0.921763 0.669700i −0.0221993 0.999754i \(-0.507067\pi\)
0.943962 + 0.330054i \(0.107067\pi\)
\(434\) 929.773 + 2861.55i 0.102835 + 0.316494i
\(435\) 0 0
\(436\) 137.583 423.438i 0.0151125 0.0465115i
\(437\) 10224.0 + 31466.3i 1.11918 + 3.44448i
\(438\) 0 0
\(439\) 4195.10 12911.2i 0.456084 1.40368i −0.413773 0.910380i \(-0.635789\pi\)
0.869858 0.493303i \(-0.164211\pi\)
\(440\) −6035.55 + 11328.4i −0.653940 + 1.22741i
\(441\) 0 0
\(442\) 1602.30 1164.14i 0.172429 0.125277i
\(443\) 16740.4 1.79540 0.897699 0.440609i \(-0.145238\pi\)
0.897699 + 0.440609i \(0.145238\pi\)
\(444\) 0 0
\(445\) −12070.9 + 5874.90i −1.28588 + 0.625836i
\(446\) 4174.77 + 3033.15i 0.443231 + 0.322026i
\(447\) 0 0
\(448\) −1173.29 + 3611.02i −0.123734 + 0.380814i
\(449\) −18160.7 −1.90882 −0.954408 0.298505i \(-0.903512\pi\)
−0.954408 + 0.298505i \(0.903512\pi\)
\(450\) 0 0
\(451\) 17872.4 1.86603
\(452\) 109.504 337.020i 0.0113952 0.0350710i
\(453\) 0 0
\(454\) −2942.80 2138.07i −0.304213 0.221024i
\(455\) 2024.15 3799.20i 0.208557 0.391449i
\(456\) 0 0
\(457\) 2032.75 0.208070 0.104035 0.994574i \(-0.466825\pi\)
0.104035 + 0.994574i \(0.466825\pi\)
\(458\) 9629.81 6996.47i 0.982471 0.713807i
\(459\) 0 0
\(460\) −744.406 131.901i −0.0754524 0.0133693i
\(461\) −1858.95 + 5721.26i −0.187809 + 0.578017i −0.999985 0.00539516i \(-0.998283\pi\)
0.812176 + 0.583412i \(0.198283\pi\)
\(462\) 0 0
\(463\) 1811.95 + 5576.62i 0.181876 + 0.559757i 0.999881 0.0154550i \(-0.00491968\pi\)
−0.818005 + 0.575212i \(0.804920\pi\)
\(464\) 1319.14 4059.90i 0.131982 0.406199i
\(465\) 0 0
\(466\) 375.934 + 1157.01i 0.0373709 + 0.115016i
\(467\) −7272.50 + 5283.78i −0.720624 + 0.523564i −0.886583 0.462569i \(-0.846928\pi\)
0.165960 + 0.986133i \(0.446928\pi\)
\(468\) 0 0
\(469\) 3987.60 2897.16i 0.392602 0.285242i
\(470\) −4708.21 834.242i −0.462071 0.0818739i
\(471\) 0 0
\(472\) 564.933 + 410.448i 0.0550915 + 0.0400263i
\(473\) −6944.39 + 21372.6i −0.675060 + 2.07762i
\(474\) 0 0
\(475\) 10721.9 + 15953.3i 1.03569 + 1.54103i
\(476\) −29.8693 −0.00287617
\(477\) 0 0
\(478\) −7602.16 5523.30i −0.727437 0.528514i
\(479\) 5375.66 + 3905.65i 0.512777 + 0.372554i 0.813876 0.581039i \(-0.197353\pi\)
−0.301099 + 0.953593i \(0.597353\pi\)
\(480\) 0 0
\(481\) 12971.2 9424.10i 1.22959 0.893351i
\(482\) −7628.87 −0.720924
\(483\) 0 0
\(484\) −111.672 343.690i −0.0104876 0.0322774i
\(485\) −1914.34 13704.3i −0.179228 1.28306i
\(486\) 0 0
\(487\) 2239.85 + 6893.56i 0.208414 + 0.641431i 0.999556 + 0.0297992i \(0.00948677\pi\)
−0.791142 + 0.611632i \(0.790513\pi\)
\(488\) −4039.74 12433.0i −0.374734 1.15331i
\(489\) 0 0
\(490\) −8131.76 + 3957.71i −0.749705 + 0.364880i
\(491\) −4273.47 13152.4i −0.392788 1.20888i −0.930671 0.365858i \(-0.880776\pi\)
0.537883 0.843020i \(-0.319224\pi\)
\(492\) 0 0
\(493\) 923.456 0.0843618
\(494\) 18554.0 13480.2i 1.68984 1.22774i
\(495\) 0 0
\(496\) −7530.96 5471.56i −0.681754 0.495323i
\(497\) −4899.38 3559.61i −0.442187 0.321268i
\(498\) 0 0
\(499\) 9216.11 0.826793 0.413397 0.910551i \(-0.364342\pi\)
0.413397 + 0.910551i \(0.364342\pi\)
\(500\) −436.916 + 44.8142i −0.0390789 + 0.00400831i
\(501\) 0 0
\(502\) 2886.62 8884.12i 0.256646 0.789876i
\(503\) 10276.2 + 7466.09i 0.910919 + 0.661822i 0.941247 0.337718i \(-0.109655\pi\)
−0.0303278 + 0.999540i \(0.509655\pi\)
\(504\) 0 0
\(505\) 2835.61 + 2941.27i 0.249867 + 0.259178i
\(506\) −24036.2 + 17463.3i −2.11174 + 1.53427i
\(507\) 0 0
\(508\) −242.716 + 176.344i −0.0211984 + 0.0154015i
\(509\) −2793.42 8597.26i −0.243254 0.748658i −0.995919 0.0902544i \(-0.971232\pi\)
0.752665 0.658404i \(-0.228768\pi\)
\(510\) 0 0
\(511\) 788.817 2427.73i 0.0682881 0.210169i
\(512\) −3767.60 11595.5i −0.325207 1.00088i
\(513\) 0 0
\(514\) 3903.69 12014.3i 0.334989 1.03099i
\(515\) −300.248 2149.41i −0.0256903 0.183911i
\(516\) 0 0
\(517\) 6216.30 4516.41i 0.528806 0.384200i
\(518\) 5913.44 0.501586
\(519\) 0 0
\(520\) 1917.99 + 13730.4i 0.161749 + 1.15792i
\(521\) −10554.5 7668.29i −0.887526 0.644825i 0.0477059 0.998861i \(-0.484809\pi\)
−0.935232 + 0.354036i \(0.884809\pi\)
\(522\) 0 0
\(523\) −3201.49 + 9853.17i −0.267670 + 0.823803i 0.723396 + 0.690433i \(0.242580\pi\)
−0.991066 + 0.133370i \(0.957420\pi\)
\(524\) 463.520 0.0386431
\(525\) 0 0
\(526\) 11688.5 0.968899
\(527\) 622.274 1915.16i 0.0514359 0.158303i
\(528\) 0 0
\(529\) −27609.3 20059.3i −2.26920 1.64867i
\(530\) −1492.84 264.516i −0.122349 0.0216789i
\(531\) 0 0
\(532\) −345.875 −0.0281872
\(533\) 15616.9 11346.4i 1.26913 0.922074i
\(534\) 0 0
\(535\) 2221.54 + 2304.33i 0.179525 + 0.186214i
\(536\) −4905.31 + 15097.0i −0.395293 + 1.21659i
\(537\) 0 0
\(538\) −556.487 1712.69i −0.0445946 0.137248i
\(539\) 4490.92 13821.6i 0.358883 1.10453i
\(540\) 0 0
\(541\) −1162.41 3577.53i −0.0923770 0.284307i 0.894184 0.447699i \(-0.147756\pi\)
−0.986561 + 0.163392i \(0.947756\pi\)
\(542\) −3286.24 + 2387.59i −0.260436 + 0.189218i
\(543\) 0 0
\(544\) 152.706 110.948i 0.0120353 0.00874419i
\(545\) 7447.74 13979.0i 0.585369 1.09870i
\(546\) 0 0
\(547\) 7890.38 + 5732.70i 0.616761 + 0.448103i 0.851789 0.523886i \(-0.175518\pi\)
−0.235028 + 0.971989i \(0.575518\pi\)
\(548\) 90.1127 277.338i 0.00702449 0.0216192i
\(549\) 0 0
\(550\) −10649.4 + 13583.8i −0.825623 + 1.05312i
\(551\) 10693.3 0.826766
\(552\) 0 0
\(553\) 1133.95 + 823.861i 0.0871978 + 0.0633529i
\(554\) −5161.50 3750.05i −0.395832 0.287589i
\(555\) 0 0
\(556\) 234.844 170.624i 0.0179129 0.0130145i
\(557\) 16009.1 1.21783 0.608913 0.793237i \(-0.291606\pi\)
0.608913 + 0.793237i \(0.291606\pi\)
\(558\) 0 0
\(559\) 7500.49 + 23084.1i 0.567508 + 1.74661i
\(560\) −2309.72 + 4335.21i −0.174292 + 0.327135i
\(561\) 0 0
\(562\) −7168.10 22061.1i −0.538021 1.65586i
\(563\) −850.464 2617.46i −0.0636639 0.195937i 0.914165 0.405342i \(-0.132847\pi\)
−0.977829 + 0.209404i \(0.932847\pi\)
\(564\) 0 0
\(565\) 5927.75 11126.0i 0.441385 0.828453i
\(566\) 498.140 + 1533.12i 0.0369936 + 0.113855i
\(567\) 0 0
\(568\) 19503.6 1.44076
\(569\) 4062.83 2951.82i 0.299337 0.217481i −0.427971 0.903793i \(-0.640771\pi\)
0.727308 + 0.686312i \(0.240771\pi\)
\(570\) 0 0
\(571\) 10.2190 + 7.42452i 0.000748950 + 0.000544144i 0.588160 0.808745i \(-0.299853\pi\)
−0.587411 + 0.809289i \(0.699853\pi\)
\(572\) −681.280 494.979i −0.0498003 0.0361820i
\(573\) 0 0
\(574\) 7119.63 0.517714
\(575\) −25257.7 9240.89i −1.83186 0.670212i
\(576\) 0 0
\(577\) −5786.32 + 17808.5i −0.417483 + 1.28488i 0.492528 + 0.870296i \(0.336073\pi\)
−0.910011 + 0.414584i \(0.863927\pi\)
\(578\) 10623.6 + 7718.50i 0.764504 + 0.555445i
\(579\) 0 0
\(580\) −114.891 + 215.643i −0.00822512 + 0.0154381i
\(581\) 4151.66 3016.36i 0.296455 0.215387i
\(582\) 0 0
\(583\) 1971.02 1432.03i 0.140019 0.101730i
\(584\) 2540.43 + 7818.64i 0.180006 + 0.554002i
\(585\) 0 0
\(586\) −1781.49 + 5482.86i −0.125585 + 0.386510i
\(587\) 5487.34 + 16888.3i 0.385838 + 1.18749i 0.935871 + 0.352344i \(0.114615\pi\)
−0.550033 + 0.835143i \(0.685385\pi\)
\(588\) 0 0
\(589\) 7205.69 22176.8i 0.504084 1.55141i
\(590\) 651.727 + 676.013i 0.0454765 + 0.0471712i
\(591\) 0 0
\(592\) −14801.2 + 10753.7i −1.02758 + 0.746577i
\(593\) −22731.1 −1.57413 −0.787063 0.616873i \(-0.788399\pi\)
−0.787063 + 0.616873i \(0.788399\pi\)
\(594\) 0 0
\(595\) −1046.31 185.395i −0.0720919 0.0127739i
\(596\) −506.909 368.291i −0.0348386 0.0253117i
\(597\) 0 0
\(598\) −9916.23 + 30519.0i −0.678102 + 2.08698i
\(599\) −13575.9 −0.926036 −0.463018 0.886349i \(-0.653233\pi\)
−0.463018 + 0.886349i \(0.653233\pi\)
\(600\) 0 0
\(601\) −28512.0 −1.93516 −0.967578 0.252573i \(-0.918723\pi\)
−0.967578 + 0.252573i \(0.918723\pi\)
\(602\) −2766.36 + 8513.99i −0.187290 + 0.576419i
\(603\) 0 0
\(604\) 433.944 + 315.279i 0.0292333 + 0.0212393i
\(605\) −1778.59 12732.5i −0.119520 0.855621i
\(606\) 0 0
\(607\) −23489.6 −1.57070 −0.785349 0.619053i \(-0.787517\pi\)
−0.785349 + 0.619053i \(0.787517\pi\)
\(608\) 1768.28 1284.73i 0.117949 0.0856951i
\(609\) 0 0
\(610\) −2432.01 17410.3i −0.161425 1.15561i
\(611\) 2564.56 7892.89i 0.169805 0.522606i
\(612\) 0 0
\(613\) −6495.01 19989.6i −0.427946 1.31708i −0.900145 0.435590i \(-0.856540\pi\)
0.472199 0.881492i \(-0.343460\pi\)
\(614\) 4298.07 13228.1i 0.282502 0.869451i
\(615\) 0 0
\(616\) −2539.15 7814.71i −0.166080 0.511142i
\(617\) −3053.20 + 2218.28i −0.199217 + 0.144740i −0.682922 0.730492i \(-0.739291\pi\)
0.483704 + 0.875231i \(0.339291\pi\)
\(618\) 0 0
\(619\) −13979.6 + 10156.8i −0.907736 + 0.659509i −0.940441 0.339956i \(-0.889588\pi\)
0.0327052 + 0.999465i \(0.489588\pi\)
\(620\) 369.804 + 383.584i 0.0239543 + 0.0248469i
\(621\) 0 0
\(622\) 6723.64 + 4885.01i 0.433430 + 0.314905i
\(623\) 2655.63 8173.18i 0.170779 0.525604i
\(624\) 0 0
\(625\) −15583.2 1142.05i −0.997325 0.0730915i
\(626\) −12855.2 −0.820763
\(627\) 0 0
\(628\) 124.387 + 90.3721i 0.00790376 + 0.00574242i
\(629\) −3201.87 2326.29i −0.202968 0.147465i
\(630\) 0 0
\(631\) 7560.47 5493.00i 0.476985 0.346550i −0.323172 0.946340i \(-0.604749\pi\)
0.800157 + 0.599790i \(0.204749\pi\)
\(632\) −4514.05 −0.284113
\(633\) 0 0
\(634\) 1187.73 + 3655.45i 0.0744018 + 0.228985i
\(635\) −9596.83 + 4670.76i −0.599746 + 0.291895i
\(636\) 0 0
\(637\) −4850.55 14928.5i −0.301705 0.928552i
\(638\) 2967.30 + 9132.40i 0.184132 + 0.566701i
\(639\) 0 0
\(640\) −2098.95 15025.9i −0.129638 0.928049i
\(641\) 1411.17 + 4343.13i 0.0869544 + 0.267618i 0.985074 0.172134i \(-0.0550663\pi\)
−0.898119 + 0.439752i \(0.855066\pi\)
\(642\) 0 0
\(643\) −752.275 −0.0461381 −0.0230691 0.999734i \(-0.507344\pi\)
−0.0230691 + 0.999734i \(0.507344\pi\)
\(644\) 391.527 284.461i 0.0239570 0.0174058i
\(645\) 0 0
\(646\) −4579.96 3327.53i −0.278941 0.202663i
\(647\) 20747.7 + 15074.1i 1.26070 + 0.915956i 0.998792 0.0491360i \(-0.0156468\pi\)
0.261913 + 0.965092i \(0.415647\pi\)
\(648\) 0 0
\(649\) −1508.96 −0.0912661
\(650\) −681.772 + 18630.4i −0.0411405 + 1.12422i
\(651\) 0 0
\(652\) 334.657 1029.97i 0.0201015 0.0618661i
\(653\) 8512.09 + 6184.40i 0.510113 + 0.370619i 0.812866 0.582450i \(-0.197906\pi\)
−0.302753 + 0.953069i \(0.597906\pi\)
\(654\) 0 0
\(655\) 16237.0 + 2877.02i 0.968598 + 0.171625i
\(656\) −17820.2 + 12947.2i −1.06061 + 0.770582i
\(657\) 0 0
\(658\) 2476.32 1799.15i 0.146713 0.106593i
\(659\) 2193.75 + 6751.65i 0.129676 + 0.399100i 0.994724 0.102588i \(-0.0327124\pi\)
−0.865048 + 0.501688i \(0.832712\pi\)
\(660\) 0 0
\(661\) −6944.82 + 21373.9i −0.408657 + 1.25772i 0.509146 + 0.860680i \(0.329961\pi\)
−0.917803 + 0.397036i \(0.870039\pi\)
\(662\) 6877.50 + 21166.8i 0.403779 + 1.24270i
\(663\) 0 0
\(664\) −5107.14 + 15718.2i −0.298487 + 0.918649i
\(665\) −12115.9 2146.81i −0.706518 0.125187i
\(666\) 0 0
\(667\) −12104.7 + 8794.55i −0.702690 + 0.510534i
\(668\) 290.950 0.0168521
\(669\) 0 0
\(670\) −10037.1 + 18839.0i −0.578754 + 1.08629i
\(671\) 22854.2 + 16604.5i 1.31487 + 0.955306i
\(672\) 0 0
\(673\) −9009.19 + 27727.4i −0.516016 + 1.58813i 0.265409 + 0.964136i \(0.414493\pi\)
−0.781426 + 0.623999i \(0.785507\pi\)
\(674\) 20337.8 1.16229
\(675\) 0 0
\(676\) −219.089 −0.0124653
\(677\) 4869.04 14985.4i 0.276414 0.850716i −0.712428 0.701746i \(-0.752404\pi\)
0.988842 0.148970i \(-0.0475957\pi\)
\(678\) 0 0
\(679\) 7166.27 + 5206.60i 0.405031 + 0.294272i
\(680\) 3077.11 1497.62i 0.173532 0.0844576i
\(681\) 0 0
\(682\) 20939.3 1.17567
\(683\) −9068.24 + 6588.47i −0.508033 + 0.369108i −0.812077 0.583550i \(-0.801663\pi\)
0.304044 + 0.952658i \(0.401663\pi\)
\(684\) 0 0
\(685\) 4878.03 9155.77i 0.272088 0.510692i
\(686\) 3892.08 11978.6i 0.216618 0.666683i
\(687\) 0 0
\(688\) −8558.69 26340.9i −0.474269 1.45965i
\(689\) 813.152 2502.62i 0.0449617 0.138378i
\(690\) 0 0
\(691\) 570.544 + 1755.95i 0.0314103 + 0.0966709i 0.965533 0.260282i \(-0.0838156\pi\)
−0.934122 + 0.356953i \(0.883816\pi\)
\(692\) −164.763 + 119.708i −0.00905111 + 0.00657601i
\(693\) 0 0
\(694\) −14741.3 + 10710.2i −0.806301 + 0.585812i
\(695\) 9285.55 4519.26i 0.506793 0.246655i
\(696\) 0 0
\(697\) −3854.96 2800.79i −0.209494 0.152206i
\(698\) 9985.42 30732.0i 0.541481 1.66651i
\(699\) 0 0
\(700\) 173.469 221.266i 0.00936643 0.0119473i
\(701\) −8002.88 −0.431191 −0.215595 0.976483i \(-0.569169\pi\)
−0.215595 + 0.976483i \(0.569169\pi\)
\(702\) 0 0
\(703\) −37076.3 26937.5i −1.98913 1.44519i
\(704\) 21377.1 + 15531.4i 1.14443 + 0.831477i
\(705\) 0 0
\(706\) 1578.92 1147.15i 0.0841691 0.0611524i
\(707\) −2615.36 −0.139124
\(708\) 0 0
\(709\) −2060.93 6342.89i −0.109168 0.335983i 0.881518 0.472150i \(-0.156522\pi\)
−0.990686 + 0.136166i \(0.956522\pi\)
\(710\) 25824.5 + 4575.82i 1.36504 + 0.241869i
\(711\) 0 0
\(712\) 8552.59 + 26322.2i 0.450171 + 1.38548i
\(713\) 10082.3 + 31030.2i 0.529573 + 1.62986i
\(714\) 0 0
\(715\) −20792.8 21567.6i −1.08756 1.12809i
\(716\) −198.970 612.367i −0.0103853 0.0319626i
\(717\) 0 0
\(718\) 15543.8 0.807926
\(719\) −6078.70 + 4416.43i −0.315295 + 0.229075i −0.734165 0.678971i \(-0.762426\pi\)
0.418870 + 0.908046i \(0.362426\pi\)
\(720\) 0 0
\(721\) 1123.97 + 816.612i 0.0580566 + 0.0421806i
\(722\) −37650.4 27354.6i −1.94072 1.41002i
\(723\) 0 0
\(724\) 283.329 0.0145440
\(725\) −5363.06 + 6840.79i −0.274729 + 0.350429i
\(726\) 0 0
\(727\) 10212.2 31429.8i 0.520974 1.60339i −0.251169 0.967943i \(-0.580815\pi\)
0.772142 0.635449i \(-0.219185\pi\)
\(728\) −7179.92 5216.52i −0.365530 0.265573i
\(729\) 0 0
\(730\) 1529.40 + 10948.6i 0.0775417 + 0.555105i
\(731\) 4847.19 3521.69i 0.245253 0.178186i
\(732\) 0 0
\(733\) 12580.8 9140.51i 0.633948 0.460590i −0.223818 0.974631i \(-0.571852\pi\)
0.857766 + 0.514041i \(0.171852\pi\)
\(734\) 2020.60 + 6218.76i 0.101610 + 0.312723i
\(735\) 0 0
\(736\) −945.062 + 2908.60i −0.0473308 + 0.145669i
\(737\) −10599.9 32623.3i −0.529788 1.63052i
\(738\) 0 0
\(739\) −2576.39 + 7929.33i −0.128247 + 0.394702i −0.994479 0.104940i \(-0.966535\pi\)
0.866232 + 0.499642i \(0.166535\pi\)
\(740\) 941.584 458.267i 0.0467747 0.0227652i
\(741\) 0 0
\(742\) 785.174 570.463i 0.0388472 0.0282242i
\(743\) −9492.12 −0.468684 −0.234342 0.972154i \(-0.575294\pi\)
−0.234342 + 0.972154i \(0.575294\pi\)
\(744\) 0 0
\(745\) −15471.0 16047.5i −0.760822 0.789173i
\(746\) 12087.6 + 8782.17i 0.593243 + 0.431016i
\(747\) 0 0
\(748\) −64.2355 + 197.696i −0.00313995 + 0.00966377i
\(749\) −2048.99 −0.0999581
\(750\) 0 0
\(751\) 8136.39 0.395341 0.197671 0.980269i \(-0.436662\pi\)
0.197671 + 0.980269i \(0.436662\pi\)
\(752\) −2926.37 + 9006.45i −0.141907 + 0.436744i
\(753\) 0 0
\(754\) 8390.58 + 6096.11i 0.405261 + 0.294439i
\(755\) 13244.0 + 13737.6i 0.638411 + 0.662201i
\(756\) 0 0
\(757\) 6875.91 0.330131 0.165066 0.986283i \(-0.447216\pi\)
0.165066 + 0.986283i \(0.447216\pi\)
\(758\) 6309.27 4583.95i 0.302326 0.219653i
\(759\) 0 0
\(760\) 35631.7 17341.9i 1.70065 0.827705i
\(761\) 5507.46 16950.2i 0.262346 0.807417i −0.729947 0.683504i \(-0.760455\pi\)
0.992293 0.123914i \(-0.0395446\pi\)
\(762\) 0 0
\(763\) 3133.26 + 9643.19i 0.148665 + 0.457545i
\(764\) 282.548 869.595i 0.0133799 0.0411791i
\(765\) 0 0
\(766\) 8108.26 + 24954.6i 0.382458 + 1.17709i
\(767\) −1318.53 + 957.968i −0.0620722 + 0.0450981i
\(768\) 0 0
\(769\) −18966.1 + 13779.6i −0.889380 + 0.646173i −0.935716 0.352753i \(-0.885245\pi\)
0.0463361 + 0.998926i \(0.485245\pi\)
\(770\) −1528.63 10943.1i −0.0715427 0.512159i
\(771\) 0 0
\(772\) 46.9974 + 34.1456i 0.00219103 + 0.00159188i
\(773\) −4531.20 + 13945.6i −0.210836 + 0.648886i 0.788587 + 0.614923i \(0.210813\pi\)
−0.999423 + 0.0339629i \(0.989187\pi\)
\(774\) 0 0
\(775\) 10573.3 + 15732.2i 0.490068 + 0.729183i
\(776\) −28527.7 −1.31969
\(777\) 0 0
\(778\) −31709.1 23038.0i −1.46121 1.06163i
\(779\) −44638.9 32432.1i −2.05309 1.49166i
\(780\) 0 0
\(781\) −34096.4 + 24772.5i −1.56218 + 1.13499i
\(782\) 7921.16 0.362225
\(783\) 0 0
\(784\) 5534.89 + 17034.6i 0.252136 + 0.775995i
\(785\) 3796.30 + 3937.77i 0.172606 + 0.179038i
\(786\) 0 0
\(787\) 2673.75 + 8228.97i 0.121104 + 0.372720i 0.993171 0.116666i \(-0.0372207\pi\)
−0.872067 + 0.489387i \(0.837221\pi\)
\(788\)