Properties

Label 225.4.p.b.32.10
Level $225$
Weight $4$
Character 225.32
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.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.10
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +O(q^{10})\) \(q+(1.60134 + 0.429078i) q^{2} +(1.67949 - 4.91725i) q^{3} +(-4.54802 - 2.62580i) q^{4} +(4.79931 - 7.15356i) q^{6} +(-8.15082 + 30.4193i) q^{7} +(-15.5344 - 15.5344i) q^{8} +(-21.3587 - 16.5169i) q^{9} +(-31.0214 + 17.9102i) q^{11} +(-20.5500 + 17.9537i) q^{12} +(14.3888 + 53.6997i) q^{13} +(-26.1045 + 45.2143i) q^{14} +(2.79604 + 4.84288i) q^{16} +(29.9510 - 29.9510i) q^{17} +(-27.1155 - 35.6137i) q^{18} -17.7095i q^{19} +(135.890 + 91.1683i) q^{21} +(-57.3607 + 15.3698i) q^{22} +(-101.925 + 27.3107i) q^{23} +(-102.476 + 50.2966i) q^{24} +92.1654i q^{26} +(-117.089 + 77.2859i) q^{27} +(116.945 - 116.945i) q^{28} +(26.5786 + 46.0355i) q^{29} +(-19.1014 + 33.0846i) q^{31} +(47.8872 + 178.717i) q^{32} +(35.9690 + 182.620i) q^{33} +(60.8131 - 35.1104i) q^{34} +(53.7695 + 131.203i) q^{36} +(75.1697 + 75.1697i) q^{37} +(7.59877 - 28.3590i) q^{38} +(288.220 + 19.4346i) q^{39} +(-126.863 - 73.2444i) q^{41} +(178.488 + 204.299i) q^{42} +(-526.075 - 140.961i) q^{43} +188.114 q^{44} -174.935 q^{46} +(-161.279 - 43.2145i) q^{47} +(28.5095 - 5.61527i) q^{48} +(-561.849 - 324.384i) q^{49} +(-96.9742 - 197.579i) q^{51} +(75.5641 - 282.009i) q^{52} +(-170.746 - 170.746i) q^{53} +(-220.661 + 73.5208i) q^{54} +(599.162 - 345.926i) q^{56} +(-87.0821 - 29.7429i) q^{57} +(22.8086 + 85.1228i) q^{58} +(-28.0525 + 48.5883i) q^{59} +(187.285 + 324.386i) q^{61} +(-44.7838 + 44.7838i) q^{62} +(676.522 - 515.089i) q^{63} +261.998i q^{64} +(-20.7596 + 307.870i) q^{66} +(-110.806 + 29.6904i) q^{67} +(-214.863 + 57.5724i) q^{68} +(-36.8879 + 547.058i) q^{69} -921.281i q^{71} +(75.2138 + 588.372i) q^{72} +(-373.434 + 373.434i) q^{73} +(88.1187 + 152.626i) q^{74} +(-46.5016 + 80.5432i) q^{76} +(-291.966 - 1089.63i) q^{77} +(453.200 + 154.791i) q^{78} +(492.922 - 284.589i) q^{79} +(183.385 + 705.557i) q^{81} +(-171.723 - 171.723i) q^{82} +(-117.674 + 439.165i) q^{83} +(-378.640 - 771.455i) q^{84} +(-781.941 - 451.454i) q^{86} +(271.006 - 53.3777i) q^{87} +(760.121 + 203.674i) q^{88} +148.257 q^{89} -1750.79 q^{91} +(535.269 + 143.425i) q^{92} +(130.605 + 149.492i) q^{93} +(-239.720 - 138.402i) q^{94} +(959.224 + 64.6801i) q^{96} +(-83.7049 + 312.391i) q^{97} +(-760.526 - 760.526i) q^{98} +(958.396 + 129.839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} + O(q^{10}) \) \( 64 q + 6 q^{2} - 24 q^{6} + 2 q^{7} - 36 q^{11} + 138 q^{12} + 2 q^{13} + 316 q^{16} + 480 q^{18} + 480 q^{21} + 34 q^{22} - 306 q^{23} - 180 q^{27} + 232 q^{28} - 4 q^{31} + 1770 q^{32} + 294 q^{33} - 216 q^{36} - 136 q^{37} - 114 q^{38} + 1992 q^{41} - 1698 q^{42} + 2 q^{43} - 952 q^{46} - 3462 q^{47} - 4326 q^{48} - 2496 q^{51} + 242 q^{52} - 7128 q^{56} + 2544 q^{57} - 534 q^{58} + 32 q^{61} + 4038 q^{63} + 2892 q^{66} - 610 q^{67} + 2694 q^{68} + 1854 q^{72} + 8 q^{73} + 1368 q^{76} + 6486 q^{77} - 1434 q^{78} + 3012 q^{81} + 3784 q^{82} - 2814 q^{83} + 12480 q^{86} - 4830 q^{87} + 1338 q^{88} + 992 q^{91} - 13152 q^{92} - 8310 q^{93} - 7932 q^{96} - 358 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.60134 + 0.429078i 0.566160 + 0.151702i 0.530535 0.847663i \(-0.321991\pi\)
0.0356249 + 0.999365i \(0.488658\pi\)
\(3\) 1.67949 4.91725i 0.323217 0.946325i
\(4\) −4.54802 2.62580i −0.568502 0.328225i
\(5\) 0 0
\(6\) 4.79931 7.15356i 0.326552 0.486738i
\(7\) −8.15082 + 30.4193i −0.440103 + 1.64249i 0.288449 + 0.957495i \(0.406860\pi\)
−0.728552 + 0.684991i \(0.759806\pi\)
\(8\) −15.5344 15.5344i −0.686528 0.686528i
\(9\) −21.3587 16.5169i −0.791061 0.611737i
\(10\) 0 0
\(11\) −31.0214 + 17.9102i −0.850300 + 0.490921i −0.860752 0.509025i \(-0.830006\pi\)
0.0104522 + 0.999945i \(0.496673\pi\)
\(12\) −20.5500 + 17.9537i −0.494357 + 0.431900i
\(13\) 14.3888 + 53.6997i 0.306979 + 1.14566i 0.931228 + 0.364437i \(0.118739\pi\)
−0.624249 + 0.781226i \(0.714595\pi\)
\(14\) −26.1045 + 45.2143i −0.498337 + 0.863145i
\(15\) 0 0
\(16\) 2.79604 + 4.84288i 0.0436881 + 0.0756700i
\(17\) 29.9510 29.9510i 0.427305 0.427305i −0.460404 0.887709i \(-0.652296\pi\)
0.887709 + 0.460404i \(0.152296\pi\)
\(18\) −27.1155 35.6137i −0.355065 0.466346i
\(19\) 17.7095i 0.213834i −0.994268 0.106917i \(-0.965902\pi\)
0.994268 0.106917i \(-0.0340979\pi\)
\(20\) 0 0
\(21\) 135.890 + 91.1683i 1.41208 + 0.947360i
\(22\) −57.3607 + 15.3698i −0.555879 + 0.148947i
\(23\) −101.925 + 27.3107i −0.924036 + 0.247595i −0.689310 0.724467i \(-0.742086\pi\)
−0.234726 + 0.972062i \(0.575419\pi\)
\(24\) −102.476 + 50.2966i −0.871576 + 0.427781i
\(25\) 0 0
\(26\) 92.1654i 0.695197i
\(27\) −117.089 + 77.2859i −0.834586 + 0.550877i
\(28\) 116.945 116.945i 0.789304 0.789304i
\(29\) 26.5786 + 46.0355i 0.170190 + 0.294779i 0.938486 0.345316i \(-0.112228\pi\)
−0.768296 + 0.640095i \(0.778895\pi\)
\(30\) 0 0
\(31\) −19.1014 + 33.0846i −0.110668 + 0.191683i −0.916040 0.401087i \(-0.868632\pi\)
0.805372 + 0.592770i \(0.201966\pi\)
\(32\) 47.8872 + 178.717i 0.264542 + 0.987284i
\(33\) 35.9690 + 182.620i 0.189739 + 0.963334i
\(34\) 60.8131 35.1104i 0.306746 0.177100i
\(35\) 0 0
\(36\) 53.7695 + 131.203i 0.248933 + 0.607420i
\(37\) 75.1697 + 75.1697i 0.333995 + 0.333995i 0.854102 0.520106i \(-0.174108\pi\)
−0.520106 + 0.854102i \(0.674108\pi\)
\(38\) 7.59877 28.3590i 0.0324390 0.121064i
\(39\) 288.220 + 19.4346i 1.18339 + 0.0797955i
\(40\) 0 0
\(41\) −126.863 73.2444i −0.483236 0.278996i 0.238528 0.971136i \(-0.423335\pi\)
−0.721764 + 0.692139i \(0.756668\pi\)
\(42\) 178.488 + 204.299i 0.655744 + 0.750572i
\(43\) −526.075 140.961i −1.86571 0.499916i −0.865712 0.500542i \(-0.833134\pi\)
−1.00000 0.000626116i \(0.999801\pi\)
\(44\) 188.114 0.644530
\(45\) 0 0
\(46\) −174.935 −0.560712
\(47\) −161.279 43.2145i −0.500530 0.134117i −0.000284175 1.00000i \(-0.500090\pi\)
−0.500246 + 0.865883i \(0.666757\pi\)
\(48\) 28.5095 5.61527i 0.0857291 0.0168853i
\(49\) −561.849 324.384i −1.63804 0.945725i
\(50\) 0 0
\(51\) −96.9742 197.579i −0.266257 0.542481i
\(52\) 75.5641 282.009i 0.201517 0.752070i
\(53\) −170.746 170.746i −0.442525 0.442525i 0.450335 0.892860i \(-0.351305\pi\)
−0.892860 + 0.450335i \(0.851305\pi\)
\(54\) −220.661 + 73.5208i −0.556078 + 0.185276i
\(55\) 0 0
\(56\) 599.162 345.926i 1.42976 0.825470i
\(57\) −87.0821 29.7429i −0.202356 0.0691147i
\(58\) 22.8086 + 85.1228i 0.0516365 + 0.192710i
\(59\) −28.0525 + 48.5883i −0.0619004 + 0.107215i −0.895315 0.445434i \(-0.853049\pi\)
0.833414 + 0.552648i \(0.186383\pi\)
\(60\) 0 0
\(61\) 187.285 + 324.386i 0.393104 + 0.680876i 0.992857 0.119309i \(-0.0380679\pi\)
−0.599753 + 0.800185i \(0.704735\pi\)
\(62\) −44.7838 + 44.7838i −0.0917346 + 0.0917346i
\(63\) 676.522 515.089i 1.35292 1.03008i
\(64\) 261.998i 0.511716i
\(65\) 0 0
\(66\) −20.7596 + 307.870i −0.0387170 + 0.574185i
\(67\) −110.806 + 29.6904i −0.202046 + 0.0541382i −0.358423 0.933559i \(-0.616685\pi\)
0.156376 + 0.987698i \(0.450019\pi\)
\(68\) −214.863 + 57.5724i −0.383176 + 0.102672i
\(69\) −36.8879 + 547.058i −0.0643592 + 0.954465i
\(70\) 0 0
\(71\) 921.281i 1.53994i −0.638079 0.769971i \(-0.720271\pi\)
0.638079 0.769971i \(-0.279729\pi\)
\(72\) 75.2138 + 588.372i 0.123111 + 0.963060i
\(73\) −373.434 + 373.434i −0.598729 + 0.598729i −0.939974 0.341246i \(-0.889151\pi\)
0.341246 + 0.939974i \(0.389151\pi\)
\(74\) 88.1187 + 152.626i 0.138427 + 0.239762i
\(75\) 0 0
\(76\) −46.5016 + 80.5432i −0.0701856 + 0.121565i
\(77\) −291.966 1089.63i −0.432111 1.61266i
\(78\) 453.200 + 154.791i 0.657883 + 0.224700i
\(79\) 492.922 284.589i 0.702000 0.405300i −0.106092 0.994356i \(-0.533834\pi\)
0.808092 + 0.589056i \(0.200500\pi\)
\(80\) 0 0
\(81\) 183.385 + 705.557i 0.251556 + 0.967843i
\(82\) −171.723 171.723i −0.231264 0.231264i
\(83\) −117.674 + 439.165i −0.155619 + 0.580779i 0.843432 + 0.537235i \(0.180531\pi\)
−0.999052 + 0.0435432i \(0.986135\pi\)
\(84\) −378.640 771.455i −0.491822 1.00205i
\(85\) 0 0
\(86\) −781.941 451.454i −0.980452 0.566065i
\(87\) 271.006 53.3777i 0.333965 0.0657780i
\(88\) 760.121 + 203.674i 0.920786 + 0.246724i
\(89\) 148.257 0.176575 0.0882874 0.996095i \(-0.471861\pi\)
0.0882874 + 0.996095i \(0.471861\pi\)
\(90\) 0 0
\(91\) −1750.79 −2.01684
\(92\) 535.269 + 143.425i 0.606583 + 0.162533i
\(93\) 130.605 + 149.492i 0.145625 + 0.166683i
\(94\) −239.720 138.402i −0.263034 0.151863i
\(95\) 0 0
\(96\) 959.224 + 64.6801i 1.01980 + 0.0687644i
\(97\) −83.7049 + 312.391i −0.0876180 + 0.326995i −0.995797 0.0915871i \(-0.970806\pi\)
0.908179 + 0.418582i \(0.137473\pi\)
\(98\) −760.526 760.526i −0.783926 0.783926i
\(99\) 958.396 + 129.839i 0.972954 + 0.131811i
\(100\) 0 0
\(101\) −225.111 + 129.968i −0.221776 + 0.128043i −0.606773 0.794875i \(-0.707536\pi\)
0.384996 + 0.922918i \(0.374203\pi\)
\(102\) −70.5121 358.000i −0.0684484 0.347523i
\(103\) 304.307 + 1135.69i 0.291109 + 1.08643i 0.944259 + 0.329205i \(0.106781\pi\)
−0.653149 + 0.757229i \(0.726553\pi\)
\(104\) 610.670 1057.71i 0.575780 0.997280i
\(105\) 0 0
\(106\) −200.160 346.687i −0.183408 0.317671i
\(107\) 832.828 832.828i 0.752453 0.752453i −0.222483 0.974937i \(-0.571416\pi\)
0.974937 + 0.222483i \(0.0714162\pi\)
\(108\) 735.461 44.0451i 0.655276 0.0392430i
\(109\) 494.550i 0.434581i −0.976107 0.217290i \(-0.930278\pi\)
0.976107 0.217290i \(-0.0697219\pi\)
\(110\) 0 0
\(111\) 495.874 243.382i 0.424021 0.208115i
\(112\) −170.107 + 45.5800i −0.143514 + 0.0384545i
\(113\) 1593.14 426.881i 1.32629 0.355377i 0.474957 0.880009i \(-0.342464\pi\)
0.851329 + 0.524632i \(0.175797\pi\)
\(114\) −126.686 84.9935i −0.104081 0.0698278i
\(115\) 0 0
\(116\) 279.160i 0.223443i
\(117\) 579.627 1384.61i 0.458004 1.09408i
\(118\) −65.7698 + 65.7698i −0.0513102 + 0.0513102i
\(119\) 666.962 + 1155.21i 0.513784 + 0.889900i
\(120\) 0 0
\(121\) −23.9492 + 41.4813i −0.0179934 + 0.0311655i
\(122\) 160.719 + 599.813i 0.119269 + 0.445119i
\(123\) −573.225 + 500.804i −0.420211 + 0.367122i
\(124\) 173.747 100.313i 0.125830 0.0726482i
\(125\) 0 0
\(126\) 1304.36 534.552i 0.922232 0.377950i
\(127\) −944.231 944.231i −0.659740 0.659740i 0.295579 0.955318i \(-0.404488\pi\)
−0.955318 + 0.295579i \(0.904488\pi\)
\(128\) 270.680 1010.19i 0.186914 0.697571i
\(129\) −1576.68 + 2350.10i −1.07611 + 1.60399i
\(130\) 0 0
\(131\) 1480.35 + 854.679i 0.987317 + 0.570028i 0.904471 0.426535i \(-0.140266\pi\)
0.0828457 + 0.996562i \(0.473599\pi\)
\(132\) 315.935 925.005i 0.208323 0.609935i
\(133\) 538.711 + 144.347i 0.351219 + 0.0941089i
\(134\) −190.178 −0.122603
\(135\) 0 0
\(136\) −930.539 −0.586714
\(137\) 1380.02 + 369.776i 0.860608 + 0.230599i 0.662022 0.749484i \(-0.269698\pi\)
0.198586 + 0.980083i \(0.436365\pi\)
\(138\) −293.801 + 860.199i −0.181232 + 0.530616i
\(139\) −304.149 175.600i −0.185594 0.107153i 0.404324 0.914616i \(-0.367507\pi\)
−0.589918 + 0.807463i \(0.700840\pi\)
\(140\) 0 0
\(141\) −483.362 + 720.469i −0.288698 + 0.430315i
\(142\) 395.301 1475.28i 0.233612 0.871853i
\(143\) −1408.13 1408.13i −0.823454 0.823454i
\(144\) 20.2697 149.619i 0.0117301 0.0865852i
\(145\) 0 0
\(146\) −758.228 + 437.763i −0.429804 + 0.248148i
\(147\) −2538.69 + 2217.95i −1.42441 + 1.24445i
\(148\) −144.493 539.254i −0.0802515 0.299503i
\(149\) 817.396 1415.77i 0.449421 0.778419i −0.548928 0.835870i \(-0.684964\pi\)
0.998348 + 0.0574504i \(0.0182971\pi\)
\(150\) 0 0
\(151\) −238.948 413.869i −0.128777 0.223048i 0.794426 0.607361i \(-0.207772\pi\)
−0.923203 + 0.384313i \(0.874438\pi\)
\(152\) −275.106 + 275.106i −0.146803 + 0.146803i
\(153\) −1134.41 + 145.016i −0.599423 + 0.0766263i
\(154\) 1870.15i 0.978576i
\(155\) 0 0
\(156\) −1259.80 845.198i −0.646569 0.433782i
\(157\) −1668.57 + 447.091i −0.848192 + 0.227272i −0.656634 0.754209i \(-0.728020\pi\)
−0.191557 + 0.981481i \(0.561354\pi\)
\(158\) 911.447 244.221i 0.458929 0.122970i
\(159\) −1126.37 + 552.836i −0.561804 + 0.275741i
\(160\) 0 0
\(161\) 3323.09i 1.62668i
\(162\) −9.07787 + 1208.52i −0.00440262 + 0.586115i
\(163\) −2222.14 + 2222.14i −1.06780 + 1.06780i −0.0702721 + 0.997528i \(0.522387\pi\)
−0.997528 + 0.0702721i \(0.977613\pi\)
\(164\) 384.650 + 666.234i 0.183147 + 0.317220i
\(165\) 0 0
\(166\) −376.872 + 652.762i −0.176211 + 0.305206i
\(167\) 436.939 + 1630.68i 0.202463 + 0.755603i 0.990208 + 0.139601i \(0.0445821\pi\)
−0.787744 + 0.616002i \(0.788751\pi\)
\(168\) −694.721 3527.20i −0.319041 1.61982i
\(169\) −773.962 + 446.847i −0.352281 + 0.203390i
\(170\) 0 0
\(171\) −292.506 + 378.252i −0.130810 + 0.169156i
\(172\) 2022.46 + 2022.46i 0.896576 + 0.896576i
\(173\) −706.777 + 2637.73i −0.310609 + 1.15921i 0.617400 + 0.786649i \(0.288186\pi\)
−0.928009 + 0.372558i \(0.878481\pi\)
\(174\) 456.877 + 30.8070i 0.199056 + 0.0134223i
\(175\) 0 0
\(176\) −173.474 100.155i −0.0742959 0.0428948i
\(177\) 191.807 + 219.544i 0.0814526 + 0.0932315i
\(178\) 237.409 + 63.6136i 0.0999696 + 0.0267868i
\(179\) −484.184 −0.202177 −0.101088 0.994877i \(-0.532232\pi\)
−0.101088 + 0.994877i \(0.532232\pi\)
\(180\) 0 0
\(181\) 2651.62 1.08891 0.544456 0.838789i \(-0.316736\pi\)
0.544456 + 0.838789i \(0.316736\pi\)
\(182\) −2803.61 751.224i −1.14185 0.305958i
\(183\) 1909.63 376.123i 0.771388 0.151933i
\(184\) 2007.59 + 1159.08i 0.804357 + 0.464396i
\(185\) 0 0
\(186\) 144.999 + 295.427i 0.0571606 + 0.116461i
\(187\) −392.693 + 1465.55i −0.153564 + 0.573110i
\(188\) 620.026 + 620.026i 0.240532 + 0.240532i
\(189\) −1396.61 4191.71i −0.537505 1.61324i
\(190\) 0 0
\(191\) 785.170 453.318i 0.297450 0.171733i −0.343847 0.939026i \(-0.611730\pi\)
0.641297 + 0.767293i \(0.278397\pi\)
\(192\) 1288.31 + 440.022i 0.484249 + 0.165395i
\(193\) −702.651 2622.33i −0.262062 0.978028i −0.964024 0.265814i \(-0.914359\pi\)
0.701963 0.712214i \(-0.252307\pi\)
\(194\) −268.080 + 464.328i −0.0992115 + 0.171839i
\(195\) 0 0
\(196\) 1703.53 + 2950.61i 0.620821 + 1.07529i
\(197\) 749.196 749.196i 0.270954 0.270954i −0.558530 0.829484i \(-0.688634\pi\)
0.829484 + 0.558530i \(0.188634\pi\)
\(198\) 1479.01 + 619.143i 0.530851 + 0.222225i
\(199\) 4679.84i 1.66706i 0.552473 + 0.833531i \(0.313684\pi\)
−0.552473 + 0.833531i \(0.686316\pi\)
\(200\) 0 0
\(201\) −40.1021 + 594.725i −0.0140726 + 0.208700i
\(202\) −416.247 + 111.533i −0.144985 + 0.0388487i
\(203\) −1617.00 + 433.275i −0.559071 + 0.149803i
\(204\) −77.7616 + 1153.23i −0.0266882 + 0.395794i
\(205\) 0 0
\(206\) 1949.20i 0.659257i
\(207\) 2628.07 + 1100.16i 0.882432 + 0.369404i
\(208\) −219.830 + 219.830i −0.0732809 + 0.0732809i
\(209\) 317.181 + 549.374i 0.104975 + 0.181823i
\(210\) 0 0
\(211\) −2264.65 + 3922.50i −0.738887 + 1.27979i 0.214109 + 0.976810i \(0.431315\pi\)
−0.952997 + 0.302981i \(0.902018\pi\)
\(212\) 328.212 + 1224.90i 0.106329 + 0.396824i
\(213\) −4530.17 1547.28i −1.45729 0.497736i
\(214\) 1690.99 976.293i 0.540157 0.311860i
\(215\) 0 0
\(216\) 3019.49 + 618.318i 0.951160 + 0.194774i
\(217\) −850.718 850.718i −0.266131 0.266131i
\(218\) 212.201 791.944i 0.0659268 0.246042i
\(219\) 1209.09 + 2463.45i 0.373072 + 0.760111i
\(220\) 0 0
\(221\) 2039.32 + 1177.40i 0.620721 + 0.358373i
\(222\) 898.494 176.968i 0.271635 0.0535015i
\(223\) 304.776 + 81.6646i 0.0915217 + 0.0245232i 0.304289 0.952580i \(-0.401581\pi\)
−0.212768 + 0.977103i \(0.568248\pi\)
\(224\) −5826.77 −1.73803
\(225\) 0 0
\(226\) 2734.33 0.804801
\(227\) −4521.76 1211.60i −1.32211 0.354259i −0.472343 0.881415i \(-0.656592\pi\)
−0.849769 + 0.527156i \(0.823258\pi\)
\(228\) 317.952 + 363.931i 0.0923548 + 0.105710i
\(229\) −3088.47 1783.13i −0.891231 0.514552i −0.0168860 0.999857i \(-0.505375\pi\)
−0.874345 + 0.485305i \(0.838709\pi\)
\(230\) 0 0
\(231\) −5848.34 394.351i −1.66577 0.112322i
\(232\) 302.250 1128.01i 0.0855332 0.319214i
\(233\) −32.0022 32.0022i −0.00899801 0.00899801i 0.702593 0.711591i \(-0.252025\pi\)
−0.711591 + 0.702593i \(0.752025\pi\)
\(234\) 1522.29 1968.53i 0.425278 0.549944i
\(235\) 0 0
\(236\) 255.166 147.320i 0.0703810 0.0406345i
\(237\) −571.538 2901.78i −0.156647 0.795320i
\(238\) 572.358 + 2136.07i 0.155884 + 0.581768i
\(239\) 171.781 297.534i 0.0464921 0.0805267i −0.841843 0.539723i \(-0.818529\pi\)
0.888335 + 0.459196i \(0.151862\pi\)
\(240\) 0 0
\(241\) −2279.51 3948.22i −0.609277 1.05530i −0.991360 0.131171i \(-0.958126\pi\)
0.382082 0.924128i \(-0.375207\pi\)
\(242\) −56.1496 + 56.1496i −0.0149150 + 0.0149150i
\(243\) 3777.39 + 283.226i 0.997201 + 0.0747692i
\(244\) 1967.09i 0.516106i
\(245\) 0 0
\(246\) −1132.81 + 556.000i −0.293600 + 0.144103i
\(247\) 950.996 254.819i 0.244981 0.0656426i
\(248\) 810.677 217.220i 0.207573 0.0556189i
\(249\) 1961.85 + 1316.20i 0.499306 + 0.334984i
\(250\) 0 0
\(251\) 6166.99i 1.55083i 0.631455 + 0.775413i \(0.282458\pi\)
−0.631455 + 0.775413i \(0.717542\pi\)
\(252\) −4429.35 + 566.220i −1.10723 + 0.141542i
\(253\) 2672.71 2672.71i 0.664158 0.664158i
\(254\) −1106.89 1917.18i −0.273434 0.473602i
\(255\) 0 0
\(256\) 1914.90 3316.70i 0.467504 0.809740i
\(257\) 1495.68 + 5581.97i 0.363028 + 1.35484i 0.870075 + 0.492920i \(0.164071\pi\)
−0.507047 + 0.861919i \(0.669263\pi\)
\(258\) −3533.17 + 3086.79i −0.852580 + 0.744865i
\(259\) −2899.30 + 1673.91i −0.695575 + 0.401590i
\(260\) 0 0
\(261\) 192.680 1422.25i 0.0456957 0.337300i
\(262\) 2003.82 + 2003.82i 0.472505 + 0.472505i
\(263\) −639.642 + 2387.18i −0.149970 + 0.559694i 0.849514 + 0.527566i \(0.176895\pi\)
−0.999484 + 0.0321282i \(0.989772\pi\)
\(264\) 2278.13 3395.64i 0.531095 0.791617i
\(265\) 0 0
\(266\) 800.723 + 462.298i 0.184570 + 0.106561i
\(267\) 248.995 729.014i 0.0570720 0.167097i
\(268\) 581.909 + 155.922i 0.132633 + 0.0355390i
\(269\) 5983.06 1.35611 0.678055 0.735012i \(-0.262823\pi\)
0.678055 + 0.735012i \(0.262823\pi\)
\(270\) 0 0
\(271\) 228.531 0.0512260 0.0256130 0.999672i \(-0.491846\pi\)
0.0256130 + 0.999672i \(0.491846\pi\)
\(272\) 228.793 + 61.3049i 0.0510023 + 0.0136660i
\(273\) −2940.42 + 8609.05i −0.651876 + 1.90858i
\(274\) 2051.22 + 1184.28i 0.452259 + 0.261112i
\(275\) 0 0
\(276\) 1604.23 2391.17i 0.349867 0.521491i
\(277\) −877.084 + 3273.32i −0.190249 + 0.710017i 0.803197 + 0.595713i \(0.203131\pi\)
−0.993446 + 0.114304i \(0.963536\pi\)
\(278\) −411.700 411.700i −0.0888206 0.0888206i
\(279\) 954.436 391.147i 0.204805 0.0839332i
\(280\) 0 0
\(281\) −7217.53 + 4167.04i −1.53225 + 0.884644i −0.532990 + 0.846122i \(0.678932\pi\)
−0.999258 + 0.0385220i \(0.987735\pi\)
\(282\) −1083.16 + 946.317i −0.228729 + 0.199831i
\(283\) −2149.82 8023.23i −0.451567 1.68527i −0.697990 0.716107i \(-0.745922\pi\)
0.246423 0.969162i \(-0.420745\pi\)
\(284\) −2419.10 + 4190.00i −0.505447 + 0.875461i
\(285\) 0 0
\(286\) −1650.70 2859.10i −0.341287 0.591126i
\(287\) 3262.08 3262.08i 0.670921 0.670921i
\(288\) 1929.05 4608.11i 0.394689 0.942832i
\(289\) 3118.88i 0.634821i
\(290\) 0 0
\(291\) 1395.52 + 936.254i 0.281124 + 0.188605i
\(292\) 2678.95 717.822i 0.536896 0.143861i
\(293\) 8898.62 2384.38i 1.77428 0.475416i 0.784755 0.619806i \(-0.212789\pi\)
0.989521 + 0.144390i \(0.0461221\pi\)
\(294\) −5016.99 + 2462.40i −0.995227 + 0.488470i
\(295\) 0 0
\(296\) 2335.43i 0.458594i
\(297\) 2248.06 4494.61i 0.439211 0.878127i
\(298\) 1916.41 1916.41i 0.372532 0.372532i
\(299\) −2933.15 5080.37i −0.567320 0.982627i
\(300\) 0 0
\(301\) 8575.88 14853.9i 1.64221 2.84439i
\(302\) −205.054 765.273i −0.0390714 0.145816i
\(303\) 261.014 + 1325.21i 0.0494881 + 0.251258i
\(304\) 85.7651 49.5165i 0.0161808 0.00934199i
\(305\) 0 0
\(306\) −1878.80 254.531i −0.350993 0.0475509i
\(307\) 1803.17 + 1803.17i 0.335219 + 0.335219i 0.854564 0.519346i \(-0.173824\pi\)
−0.519346 + 0.854564i \(0.673824\pi\)
\(308\) −1533.29 + 5722.30i −0.283659 + 1.05863i
\(309\) 6095.54 + 411.020i 1.12221 + 0.0756702i
\(310\) 0 0
\(311\) −250.629 144.701i −0.0456974 0.0263834i 0.476977 0.878916i \(-0.341732\pi\)
−0.522675 + 0.852532i \(0.675066\pi\)
\(312\) −4175.42 4779.22i −0.757649 0.867213i
\(313\) −1884.83 505.039i −0.340373 0.0912028i 0.0845834 0.996416i \(-0.473044\pi\)
−0.424957 + 0.905214i \(0.639711\pi\)
\(314\) −2863.78 −0.514690
\(315\) 0 0
\(316\) −2989.09 −0.532118
\(317\) −4329.75 1160.15i −0.767139 0.205554i −0.146032 0.989280i \(-0.546650\pi\)
−0.621107 + 0.783726i \(0.713317\pi\)
\(318\) −2040.91 + 401.979i −0.359901 + 0.0708864i
\(319\) −1649.01 952.056i −0.289426 0.167100i
\(320\) 0 0
\(321\) −2696.50 5493.94i −0.468860 0.955271i
\(322\) 1425.86 5321.40i 0.246771 0.920962i
\(323\) −530.418 530.418i −0.0913722 0.0913722i
\(324\) 1018.62 3690.42i 0.174660 0.632788i
\(325\) 0 0
\(326\) −4511.87 + 2604.93i −0.766533 + 0.442558i
\(327\) −2431.83 830.590i −0.411255 0.140464i
\(328\) 832.931 + 3108.54i 0.140216 + 0.523294i
\(329\) 2629.11 4553.75i 0.440570 0.763089i
\(330\) 0 0
\(331\) 4301.37 + 7450.20i 0.714274 + 1.23716i 0.963239 + 0.268647i \(0.0865765\pi\)
−0.248964 + 0.968513i \(0.580090\pi\)
\(332\) 1688.34 1688.34i 0.279096 0.279096i
\(333\) −363.954 2847.09i −0.0598936 0.468528i
\(334\) 2798.76i 0.458506i
\(335\) 0 0
\(336\) −61.5638 + 913.008i −0.00999577 + 0.148240i
\(337\) 6513.21 1745.21i 1.05281 0.282100i 0.309397 0.950933i \(-0.399873\pi\)
0.743412 + 0.668833i \(0.233206\pi\)
\(338\) −1431.11 + 383.465i −0.230302 + 0.0617093i
\(339\) 576.579 8550.82i 0.0923760 1.36996i
\(340\) 0 0
\(341\) 1368.44i 0.217317i
\(342\) −630.702 + 480.202i −0.0997206 + 0.0759250i
\(343\) 6808.97 6808.97i 1.07187 1.07187i
\(344\) 5982.49 + 10362.0i 0.937657 + 1.62407i
\(345\) 0 0
\(346\) −2263.58 + 3920.64i −0.351708 + 0.609176i
\(347\) −3049.05 11379.2i −0.471705 1.76043i −0.633643 0.773626i \(-0.718441\pi\)
0.161938 0.986801i \(-0.448226\pi\)
\(348\) −1372.70 468.846i −0.211450 0.0722206i
\(349\) 6061.28 3499.48i 0.929664 0.536742i 0.0429588 0.999077i \(-0.486322\pi\)
0.886705 + 0.462335i \(0.152988\pi\)
\(350\) 0 0
\(351\) −5835.00 5175.60i −0.887320 0.787046i
\(352\) −4686.39 4686.39i −0.709618 0.709618i
\(353\) −1840.87 + 6870.23i −0.277563 + 1.03588i 0.676541 + 0.736405i \(0.263478\pi\)
−0.954104 + 0.299475i \(0.903189\pi\)
\(354\) 212.947 + 433.866i 0.0319718 + 0.0651404i
\(355\) 0 0
\(356\) −674.273 389.292i −0.100383 0.0579563i
\(357\) 6800.62 1339.46i 1.00820 0.198576i
\(358\) −775.344 207.753i −0.114464 0.0306706i
\(359\) −10744.0 −1.57951 −0.789755 0.613422i \(-0.789792\pi\)
−0.789755 + 0.613422i \(0.789792\pi\)
\(360\) 0 0
\(361\) 6545.37 0.954275
\(362\) 4246.15 + 1137.75i 0.616498 + 0.165190i
\(363\) 163.751 + 187.432i 0.0236769 + 0.0271009i
\(364\) 7962.60 + 4597.21i 1.14658 + 0.661976i
\(365\) 0 0
\(366\) 3219.36 + 217.080i 0.459777 + 0.0310026i
\(367\) −533.504 + 1991.06i −0.0758820 + 0.283195i −0.993432 0.114425i \(-0.963497\pi\)
0.917550 + 0.397621i \(0.130164\pi\)
\(368\) −417.248 417.248i −0.0591048 0.0591048i
\(369\) 1499.85 + 3659.78i 0.211597 + 0.516316i
\(370\) 0 0
\(371\) 6585.70 3802.25i 0.921597 0.532084i
\(372\) −201.458 1022.83i −0.0280783 0.142557i
\(373\) 2043.27 + 7625.58i 0.283637 + 1.05855i 0.949830 + 0.312767i \(0.101256\pi\)
−0.666193 + 0.745779i \(0.732077\pi\)
\(374\) −1257.67 + 2178.35i −0.173884 + 0.301176i
\(375\) 0 0
\(376\) 1834.05 + 3176.67i 0.251553 + 0.435703i
\(377\) −2089.66 + 2089.66i −0.285472 + 0.285472i
\(378\) −437.876 7311.61i −0.0595818 0.994891i
\(379\) 7547.27i 1.02289i −0.859315 0.511447i \(-0.829110\pi\)
0.859315 0.511447i \(-0.170890\pi\)
\(380\) 0 0
\(381\) −6228.84 + 3057.20i −0.837567 + 0.411089i
\(382\) 1451.83 389.018i 0.194456 0.0521044i
\(383\) 5392.00 1444.78i 0.719369 0.192754i 0.119479 0.992837i \(-0.461878\pi\)
0.599890 + 0.800082i \(0.295211\pi\)
\(384\) −4512.76 3027.60i −0.599715 0.402348i
\(385\) 0 0
\(386\) 4500.74i 0.593475i
\(387\) 8908.00 + 11699.9i 1.17008 + 1.53679i
\(388\) 1200.97 1200.97i 0.157139 0.157139i
\(389\) 3919.49 + 6788.76i 0.510864 + 0.884842i 0.999921 + 0.0125902i \(0.00400769\pi\)
−0.489057 + 0.872252i \(0.662659\pi\)
\(390\) 0 0
\(391\) −2234.77 + 3870.74i −0.289047 + 0.500643i
\(392\) 3688.87 + 13767.1i 0.475297 + 1.77383i
\(393\) 6688.89 5843.81i 0.858549 0.750080i
\(394\) 1521.18 878.255i 0.194508 0.112299i
\(395\) 0 0
\(396\) −4017.87 3107.06i −0.509863 0.394283i
\(397\) −488.460 488.460i −0.0617509 0.0617509i 0.675557 0.737308i \(-0.263903\pi\)
−0.737308 + 0.675557i \(0.763903\pi\)
\(398\) −2008.02 + 7494.03i −0.252897 + 0.943823i
\(399\) 1614.55 2406.55i 0.202578 0.301950i
\(400\) 0 0
\(401\) 7854.07 + 4534.55i 0.978088 + 0.564699i 0.901692 0.432378i \(-0.142325\pi\)
0.0763957 + 0.997078i \(0.475659\pi\)
\(402\) −319.401 + 935.151i −0.0396275 + 0.116023i
\(403\) −2051.48 549.693i −0.253577 0.0679458i
\(404\) 1365.08 0.168107
\(405\) 0 0
\(406\) −2775.28 −0.339249
\(407\) −3678.17 985.563i −0.447961 0.120031i
\(408\) −1562.83 + 4575.69i −0.189636 + 0.555222i
\(409\) −1057.59 610.597i −0.127859 0.0738193i 0.434706 0.900572i \(-0.356852\pi\)
−0.562565 + 0.826753i \(0.690185\pi\)
\(410\) 0 0
\(411\) 4136.01 6164.88i 0.496385 0.739881i
\(412\) 1598.10 5964.18i 0.191098 0.713189i
\(413\) −1249.37 1249.37i −0.148856 0.148856i
\(414\) 3736.38 + 2889.38i 0.443558 + 0.343008i
\(415\) 0 0
\(416\) −8908.03 + 5143.06i −1.04989 + 0.606152i
\(417\) −1374.28 + 1200.66i −0.161389 + 0.140999i
\(418\) 272.191 + 1015.83i 0.0318500 + 0.118866i
\(419\) 8196.06 14196.0i 0.955618 1.65518i 0.222670 0.974894i \(-0.428523\pi\)
0.732948 0.680285i \(-0.238144\pi\)
\(420\) 0 0
\(421\) −815.167 1411.91i −0.0943677 0.163450i 0.814977 0.579494i \(-0.196750\pi\)
−0.909345 + 0.416044i \(0.863416\pi\)
\(422\) −5309.54 + 5309.54i −0.612475 + 0.612475i
\(423\) 2730.93 + 3586.83i 0.313906 + 0.412287i
\(424\) 5304.87i 0.607611i
\(425\) 0 0
\(426\) −6590.44 4421.51i −0.749549 0.502871i
\(427\) −11394.1 + 3053.05i −1.29134 + 0.346012i
\(428\) −5974.55 + 1600.88i −0.674745 + 0.180797i
\(429\) −9289.08 + 4559.20i −1.04541 + 0.513101i
\(430\) 0 0
\(431\) 9676.25i 1.08141i 0.841212 + 0.540706i \(0.181843\pi\)
−0.841212 + 0.540706i \(0.818157\pi\)
\(432\) −701.672 350.954i −0.0781463 0.0390863i
\(433\) −6547.86 + 6547.86i −0.726720 + 0.726720i −0.969965 0.243245i \(-0.921788\pi\)
0.243245 + 0.969965i \(0.421788\pi\)
\(434\) −997.265 1727.31i −0.110300 0.191045i
\(435\) 0 0
\(436\) −1298.59 + 2249.22i −0.142640 + 0.247060i
\(437\) 483.660 + 1805.04i 0.0529441 + 0.197590i
\(438\) 879.158 + 4463.61i 0.0959082 + 0.486940i
\(439\) −14231.6 + 8216.60i −1.54723 + 0.893296i −0.548882 + 0.835900i \(0.684946\pi\)
−0.998352 + 0.0573956i \(0.981720\pi\)
\(440\) 0 0
\(441\) 6642.53 + 16208.4i 0.717259 + 1.75018i
\(442\) 2760.45 + 2760.45i 0.297061 + 0.297061i
\(443\) 1837.42 6857.35i 0.197062 0.735446i −0.794661 0.607053i \(-0.792352\pi\)
0.991723 0.128393i \(-0.0409818\pi\)
\(444\) −2894.32 195.163i −0.309365 0.0208604i
\(445\) 0 0
\(446\) 453.010 + 261.546i 0.0480957 + 0.0277680i
\(447\) −5588.89 6397.11i −0.591377 0.676896i
\(448\) −7969.80 2135.50i −0.840486 0.225207i
\(449\) −15813.2 −1.66207 −0.831037 0.556218i \(-0.812252\pi\)
−0.831037 + 0.556218i \(0.812252\pi\)
\(450\) 0 0
\(451\) 5247.29 0.547861
\(452\) −8366.55 2241.81i −0.870640 0.233287i
\(453\) −2436.41 + 479.877i −0.252698 + 0.0497717i
\(454\) −6721.00 3880.37i −0.694785 0.401134i
\(455\) 0 0
\(456\) 890.728 + 1814.80i 0.0914741 + 0.186373i
\(457\) −3132.55 + 11690.9i −0.320645 + 1.19666i 0.597973 + 0.801516i \(0.295973\pi\)
−0.918618 + 0.395147i \(0.870694\pi\)
\(458\) −4180.59 4180.59i −0.426520 0.426520i
\(459\) −1192.15 + 5821.73i −0.121230 + 0.592015i
\(460\) 0 0
\(461\) 8677.59 5010.01i 0.876693 0.506159i 0.00712658 0.999975i \(-0.497732\pi\)
0.869567 + 0.493816i \(0.164398\pi\)
\(462\) −9195.97 3140.88i −0.926051 0.316292i
\(463\) −2331.25 8700.34i −0.234001 0.873303i −0.978597 0.205787i \(-0.934025\pi\)
0.744596 0.667515i \(-0.232642\pi\)
\(464\) −148.630 + 257.434i −0.0148706 + 0.0257566i
\(465\) 0 0
\(466\) −37.5150 64.9780i −0.00372929 0.00645933i
\(467\) −2385.09 + 2385.09i −0.236336 + 0.236336i −0.815331 0.578995i \(-0.803445\pi\)
0.578995 + 0.815331i \(0.303445\pi\)
\(468\) −6271.86 + 4775.25i −0.619481 + 0.471659i
\(469\) 3612.64i 0.355685i
\(470\) 0 0
\(471\) −603.875 + 8955.64i −0.0590767 + 0.876123i
\(472\) 1190.57 319.011i 0.116102 0.0311095i
\(473\) 18844.2 5049.29i 1.83183 0.490838i
\(474\) 329.864 4891.98i 0.0319645 0.474042i
\(475\) 0 0
\(476\) 7005.24i 0.674547i
\(477\) 826.714 + 6467.11i 0.0793556 + 0.620773i
\(478\) 402.746 402.746i 0.0385380 0.0385380i
\(479\) 49.6552 + 86.0054i 0.00473654 + 0.00820394i 0.868384 0.495892i \(-0.165159\pi\)
−0.863647 + 0.504096i \(0.831826\pi\)
\(480\) 0 0
\(481\) −2954.99 + 5118.19i −0.280116 + 0.485176i
\(482\) −1956.17 7300.53i −0.184857 0.689897i
\(483\) −16340.4 5581.08i −1.53937 0.525772i
\(484\) 217.843 125.772i 0.0204586 0.0118118i
\(485\) 0 0
\(486\) 5927.37 + 2074.34i 0.553232 + 0.193609i
\(487\) 752.120 + 752.120i 0.0699831 + 0.0699831i 0.741232 0.671249i \(-0.234242\pi\)
−0.671249 + 0.741232i \(0.734242\pi\)
\(488\) 2129.79 7948.48i 0.197564 0.737317i
\(489\) 7194.76 + 14658.9i 0.665354 + 1.35562i
\(490\) 0 0
\(491\) −3533.78 2040.23i −0.324801 0.187524i 0.328729 0.944424i \(-0.393380\pi\)
−0.653531 + 0.756900i \(0.726713\pi\)
\(492\) 3922.05 772.491i 0.359390 0.0707857i
\(493\) 2174.86 + 582.753i 0.198684 + 0.0532371i
\(494\) 1632.21 0.148657
\(495\) 0 0
\(496\) −213.633 −0.0193395
\(497\) 28024.7 + 7509.19i 2.52933 + 0.677733i
\(498\) 2576.84 + 2949.48i 0.231869 + 0.265400i
\(499\) 4377.28 + 2527.22i 0.392693 + 0.226722i 0.683326 0.730113i \(-0.260533\pi\)
−0.290633 + 0.956835i \(0.593866\pi\)
\(500\) 0 0
\(501\) 8752.29 + 590.163i 0.780486 + 0.0526279i
\(502\) −2646.12 + 9875.46i −0.235263 + 0.878014i
\(503\) −4080.19 4080.19i −0.361683 0.361683i 0.502749 0.864432i \(-0.332322\pi\)
−0.864432 + 0.502749i \(0.832322\pi\)
\(504\) −18510.9 2507.77i −1.63600 0.221637i
\(505\) 0 0
\(506\) 5426.73 3133.12i 0.476774 0.275265i
\(507\) 897.401 + 4556.24i 0.0786094 + 0.399112i
\(508\) 1815.02 + 6773.74i 0.158521 + 0.591607i
\(509\) 3668.96 6354.83i 0.319497 0.553385i −0.660886 0.750486i \(-0.729819\pi\)
0.980383 + 0.197101i \(0.0631528\pi\)
\(510\) 0 0
\(511\) −8315.80 14403.4i −0.719901 1.24691i
\(512\) −1426.57 + 1426.57i −0.123137 + 0.123137i
\(513\) 1368.70 + 2073.59i 0.117796 + 0.178463i
\(514\) 9580.40i 0.822127i
\(515\) 0 0
\(516\) 13341.6 6548.25i 1.13824 0.558664i
\(517\) 5777.07 1547.96i 0.491441 0.131681i
\(518\) −5361.01 + 1436.48i −0.454728 + 0.121844i
\(519\) 11783.3 + 7905.43i 0.996592 + 0.668612i
\(520\) 0 0
\(521\) 4773.62i 0.401412i 0.979651 + 0.200706i \(0.0643237\pi\)
−0.979651 + 0.200706i \(0.935676\pi\)
\(522\) 918.804 2194.84i 0.0770401 0.184033i
\(523\) −3198.98 + 3198.98i −0.267460 + 0.267460i −0.828076 0.560616i \(-0.810564\pi\)
0.560616 + 0.828076i \(0.310564\pi\)
\(524\) −4488.43 7774.19i −0.374195 0.648124i
\(525\) 0 0
\(526\) −2048.57 + 3548.23i −0.169813 + 0.294125i
\(527\) 418.811 + 1563.02i 0.0346180 + 0.129196i
\(528\) −783.835 + 684.805i −0.0646061 + 0.0564438i
\(529\) −894.110 + 516.215i −0.0734865 + 0.0424274i
\(530\) 0 0
\(531\) 1401.69 574.442i 0.114554 0.0469466i
\(532\) −2071.04 2071.04i −0.168780 0.168780i
\(533\) 2107.80 7866.40i 0.171292 0.639272i
\(534\) 711.529 1060.56i 0.0576608 0.0859457i
\(535\) 0 0
\(536\) 2182.52 + 1260.08i 0.175878 + 0.101543i
\(537\) −813.181 + 2380.85i −0.0653470 + 0.191325i
\(538\) 9580.91 + 2567.20i 0.767774 + 0.205724i
\(539\) 23239.1 1.85711
\(540\) 0 0
\(541\) −24284.5 −1.92989 −0.964945 0.262452i \(-0.915469\pi\)
−0.964945 + 0.262452i \(0.915469\pi\)
\(542\) 365.955 + 98.0575i 0.0290021 + 0.00777109i
\(543\) 4453.35 13038.7i 0.351955 1.03047i
\(544\) 6787.03 + 3918.50i 0.534911 + 0.308831i
\(545\) 0 0
\(546\) −8402.57 + 12524.4i −0.658602 + 0.981672i
\(547\) −1033.92 + 3858.66i −0.0808180 + 0.301617i −0.994489 0.104837i \(-0.966568\pi\)
0.913671 + 0.406454i \(0.133235\pi\)
\(548\) −5305.41 5305.41i −0.413569 0.413569i
\(549\) 1357.71 10021.8i 0.105547 0.779091i
\(550\) 0 0
\(551\) 815.267 470.694i 0.0630336 0.0363925i
\(552\) 9071.23 7925.17i 0.699451 0.611083i
\(553\) 4639.26 + 17313.9i 0.356747 + 1.33140i
\(554\) −2809.02 + 4865.37i −0.215422 + 0.373122i
\(555\) 0 0
\(556\) 922.183 + 1597.27i 0.0703404 + 0.121833i
\(557\) 12226.1 12226.1i 0.930051 0.930051i −0.0676576 0.997709i \(-0.521553\pi\)
0.997709 + 0.0676576i \(0.0215526\pi\)
\(558\) 1696.21 216.833i 0.128685 0.0164503i
\(559\) 30278.3i 2.29094i
\(560\) 0 0
\(561\) 6546.95 + 4392.34i 0.492714 + 0.330561i
\(562\) −13345.7 + 3575.97i −1.00170 + 0.268404i
\(563\) −12639.6 + 3386.78i −0.946176 + 0.253527i −0.698739 0.715377i \(-0.746255\pi\)
−0.247437 + 0.968904i \(0.579588\pi\)
\(564\) 4090.15 2007.50i 0.305366 0.149877i
\(565\) 0 0
\(566\) 13770.4i 1.02264i
\(567\) −22957.3 172.444i −1.70038 0.0127724i
\(568\) −14311.5 + 14311.5i −1.05721 + 1.05721i
\(569\) 4163.99 + 7212.24i 0.306790 + 0.531376i 0.977658 0.210201i \(-0.0674117\pi\)
−0.670868 + 0.741577i \(0.734078\pi\)
\(570\) 0 0
\(571\) −4453.29 + 7713.32i −0.326382 + 0.565311i −0.981791 0.189964i \(-0.939163\pi\)
0.655409 + 0.755274i \(0.272496\pi\)
\(572\) 2706.74 + 10101.7i 0.197857 + 0.738414i
\(573\) −910.396 4622.22i −0.0663741 0.336991i
\(574\) 6623.39 3824.01i 0.481629 0.278068i
\(575\) 0 0
\(576\) 4327.40 5595.93i 0.313035 0.404798i
\(577\) −11134.8 11134.8i −0.803374 0.803374i 0.180248 0.983621i \(-0.442310\pi\)
−0.983621 + 0.180248i \(0.942310\pi\)
\(578\) −1338.24 + 4994.38i −0.0963036 + 0.359410i
\(579\) −14074.7 949.054i −1.01023 0.0681198i
\(580\) 0 0
\(581\) −12399.9 7159.11i −0.885432 0.511205i
\(582\) 1832.98 + 2098.05i 0.130549 + 0.149428i
\(583\) 8354.89 + 2238.68i 0.593523 + 0.159034i
\(584\) 11602.1 0.822088
\(585\) 0 0
\(586\) 15272.8 1.07664
\(587\) −16865.3 4519.05i −1.18587 0.317753i −0.388618 0.921399i \(-0.627048\pi\)
−0.797253 + 0.603646i \(0.793714\pi\)
\(588\) 17369.9 3421.20i 1.21824 0.239945i
\(589\) 585.913 + 338.277i 0.0409883 + 0.0236646i
\(590\) 0 0
\(591\) −2425.72 4942.25i −0.168834 0.343988i
\(592\) −153.860 + 574.215i −0.0106818 + 0.0398650i
\(593\) −4464.48 4464.48i −0.309164 0.309164i 0.535421 0.844585i \(-0.320153\pi\)
−0.844585 + 0.535421i \(0.820153\pi\)
\(594\) 5528.45 6232.81i 0.381877 0.430531i
\(595\) 0 0
\(596\) −7435.06 + 4292.63i −0.510993 + 0.295022i
\(597\) 23011.9 + 7859.73i 1.57758 + 0.538823i
\(598\) −2517.10 9393.96i −0.172127 0.642387i
\(599\) −7836.14 + 13572.6i −0.534517 + 0.925811i 0.464669 + 0.885484i \(0.346173\pi\)
−0.999187 + 0.0403269i \(0.987160\pi\)
\(600\) 0 0
\(601\) −3405.59 5898.65i −0.231143 0.400351i 0.727002 0.686635i \(-0.240913\pi\)
−0.958145 + 0.286284i \(0.907580\pi\)
\(602\) 20106.4 20106.4i 1.36125 1.36125i
\(603\) 2857.06 + 1196.02i 0.192949 + 0.0807726i
\(604\) 2509.71i 0.169071i
\(605\) 0 0
\(606\) −150.645 + 2234.11i −0.0100982 + 0.149760i
\(607\) 832.687 223.118i 0.0556800 0.0149194i −0.230872 0.972984i \(-0.574158\pi\)
0.286552 + 0.958065i \(0.407491\pi\)
\(608\) 3165.00 848.059i 0.211115 0.0565680i
\(609\) −585.214 + 8678.89i −0.0389393 + 0.577481i
\(610\) 0 0
\(611\) 9282.42i 0.614610i
\(612\) 5540.10 + 2319.20i 0.365924 + 0.153183i
\(613\) −2254.58 + 2254.58i −0.148551 + 0.148551i −0.777470 0.628920i \(-0.783497\pi\)
0.628920 + 0.777470i \(0.283497\pi\)
\(614\) 2113.79 + 3661.18i 0.138934 + 0.240641i
\(615\) 0 0
\(616\) −12391.2 + 21462.2i −0.810481 + 1.40379i
\(617\) −5858.87 21865.6i −0.382284 1.42670i −0.842404 0.538847i \(-0.818860\pi\)
0.460120 0.887857i \(-0.347806\pi\)
\(618\) 9584.68 + 3273.65i 0.623871 + 0.213083i
\(619\) −4224.11 + 2438.79i −0.274283 + 0.158357i −0.630832 0.775919i \(-0.717286\pi\)
0.356549 + 0.934276i \(0.383953\pi\)
\(620\) 0 0
\(621\) 9823.58 11075.2i 0.634793 0.715669i
\(622\) −339.255 339.255i −0.0218696 0.0218696i
\(623\) −1208.41 + 4509.86i −0.0777111 + 0.290022i
\(624\) 711.756 + 1450.16i 0.0456619 + 0.0930332i
\(625\) 0 0
\(626\) −2801.55 1617.48i −0.178870 0.103271i
\(627\) 3234.11 636.993i 0.205993 0.0405727i
\(628\) 8762.64 + 2347.94i 0.556795 + 0.149193i
\(629\) 4502.81 0.285436
\(630\) 0 0
\(631\) 3038.06 0.191669 0.0958346 0.995397i \(-0.469448\pi\)
0.0958346 + 0.995397i \(0.469448\pi\)
\(632\) −12078.1 3236.32i −0.760193 0.203693i
\(633\) 15484.4 + 17723.6i 0.972276 + 1.11288i
\(634\) −6435.61 3715.60i −0.403140 0.232753i
\(635\) 0 0
\(636\) 6574.38 + 443.308i 0.409891 + 0.0276388i
\(637\) 9334.98 34838.6i 0.580636 2.16696i
\(638\) −2232.12 2232.12i −0.138512 0.138512i
\(639\) −15216.7 + 19677.3i −0.942039 + 1.21819i
\(640\) 0 0
\(641\) 18662.9 10775.1i 1.14999 0.663946i 0.201104 0.979570i \(-0.435547\pi\)
0.948884 + 0.315624i \(0.102214\pi\)
\(642\) −1960.68 9954.69i −0.120533 0.611963i
\(643\) −2193.22 8185.22i −0.134514 0.502012i −0.999999 0.00107824i \(-0.999657\pi\)
0.865486 0.500933i \(-0.167010\pi\)
\(644\) −8725.76 + 15113.5i −0.533918 + 0.924773i
\(645\) 0 0
\(646\) −621.789 1076.97i −0.0378699 0.0655926i
\(647\) −23205.8 + 23205.8i −1.41007 + 1.41007i −0.650953 + 0.759118i \(0.725630\pi\)
−0.759118 + 0.650953i \(0.774370\pi\)
\(648\) 8111.62 13809.1i 0.491751 0.837152i
\(649\) 2009.70i 0.121553i
\(650\) 0 0
\(651\) −5611.96 + 2754.42i −0.337865 + 0.165829i
\(652\) 15941.2 4271.44i 0.957525 0.256568i
\(653\) −22778.0 + 6103.35i −1.36504 + 0.365762i −0.865666 0.500623i \(-0.833104\pi\)
−0.499377 + 0.866385i \(0.666438\pi\)
\(654\) −3537.79 2373.50i −0.211527 0.141913i
\(655\) 0 0
\(656\) 819.176i 0.0487553i
\(657\) 14144.0 1808.08i 0.839895 0.107367i
\(658\) 6164.01 6164.01i 0.365195 0.365195i
\(659\) −11587.9 20070.8i −0.684976 1.18641i −0.973444 0.228923i \(-0.926480\pi\)
0.288469 0.957489i \(-0.406854\pi\)
\(660\) 0 0
\(661\) 7538.30 13056.7i 0.443580 0.768302i −0.554373 0.832269i \(-0.687042\pi\)
0.997952 + 0.0639664i \(0.0203750\pi\)
\(662\) 3691.25 + 13775.9i 0.216714 + 0.808787i
\(663\) 9214.58 8050.40i 0.539765 0.471571i
\(664\) 8650.14 4994.16i 0.505558 0.291884i
\(665\) 0 0
\(666\) 638.811 4715.33i 0.0371673 0.274348i
\(667\) −3966.29 3966.29i −0.230248 0.230248i
\(668\) 2294.63 8563.67i 0.132907 0.496016i
\(669\) 913.432 1361.51i 0.0527882 0.0786829i
\(670\) 0 0
\(671\) −11619.7 6708.61i −0.668512 0.385966i
\(672\) −9785.98 + 28651.7i −0.561760 + 1.64474i
\(673\) −14112.2 3781.35i −0.808298 0.216583i −0.169074 0.985603i \(-0.554078\pi\)
−0.639224 + 0.769021i \(0.720744\pi\)
\(674\) 11178.7 0.638853
\(675\) 0 0
\(676\) 4693.32 0.267030
\(677\) 9881.83 + 2647.83i 0.560989 + 0.150317i 0.528161 0.849144i \(-0.322882\pi\)
0.0328285 + 0.999461i \(0.489548\pi\)
\(678\) 4592.27 13445.4i 0.260125 0.761603i
\(679\) −8820.44 5092.48i −0.498523 0.287823i
\(680\) 0 0
\(681\) −13552.0 + 20199.7i −0.762573 + 1.13665i
\(682\) 587.168 2191.34i 0.0329675 0.123036i
\(683\) 21858.2 + 21858.2i 1.22457 + 1.22457i 0.965990 + 0.258579i \(0.0832541\pi\)
0.258579 + 0.965990i \(0.416746\pi\)
\(684\) 2323.54 952.232i 0.129887 0.0532303i
\(685\) 0 0
\(686\) 13825.1 7981.91i 0.769451 0.444243i
\(687\) −13955.1 + 12192.0i −0.774995 + 0.677082i
\(688\) −788.266 2941.85i −0.0436807 0.163019i
\(689\) 6712.19 11625.9i 0.371138 0.642830i
\(690\) 0 0
\(691\) 7416.99 + 12846.6i 0.408329 + 0.707247i 0.994703 0.102794i \(-0.0327782\pi\)
−0.586373 + 0.810041i \(0.699445\pi\)
\(692\) 10140.6 10140.6i 0.557062 0.557062i
\(693\) −11761.3 + 28095.4i −0.644698 + 1.54005i
\(694\) 19530.3i 1.06824i
\(695\) 0 0
\(696\) −5039.10 3380.72i −0.274435 0.184118i
\(697\) −5993.42 + 1605.93i −0.325706 + 0.0872725i
\(698\) 11207.7 3003.10i 0.607763 0.162850i
\(699\) −211.110 + 103.616i −0.0114233 + 0.00560673i
\(700\) 0 0
\(701\) 29266.1i 1.57684i −0.615136 0.788421i \(-0.710899\pi\)
0.615136 0.788421i \(-0.289101\pi\)
\(702\) −7123.09 10791.6i −0.382968 0.580202i
\(703\) 1331.22 1331.22i 0.0714195 0.0714195i
\(704\) −4692.44 8127.55i −0.251212 0.435112i
\(705\) 0 0
\(706\) −5895.73 + 10211.7i −0.314290 + 0.544366i
\(707\) −2118.69 7907.07i −0.112704 0.420617i
\(708\) −295.863 1502.14i −0.0157051 0.0797371i
\(709\) −10569.7 + 6102.42i −0.559878 + 0.323246i −0.753096 0.657910i \(-0.771441\pi\)
0.193219 + 0.981156i \(0.438107\pi\)
\(710\) 0 0
\(711\) −15228.7 2063.11i −0.803262 0.108822i
\(712\) −2303.07 2303.07i −0.121224 0.121224i
\(713\) 1043.35 3893.82i 0.0548017 0.204523i
\(714\) 11464.8 + 773.070i 0.600926 + 0.0405202i
\(715\) 0 0
\(716\) 2202.08 + 1271.37i 0.114938 + 0.0663595i
\(717\) −1174.54 1344.40i −0.0611774 0.0700243i
\(718\) −17204.7 4609.99i −0.894255 0.239615i
\(719\) 12947.9 0.671592 0.335796 0.941935i \(-0.390995\pi\)
0.335796 + 0.941935i \(0.390995\pi\)
\(720\) 0 0
\(721\) −37027.2 −1.91257
\(722\) 10481.4 + 2808.48i 0.540272 + 0.144765i
\(723\) −23242.8 + 4577.92i −1.19559 + 0.235484i
\(724\) −12059.6 6962.62i −0.619049 0.357408i
\(725\) 0 0
\(726\) 181.799 + 370.404i 0.00929367 + 0.0189352i
\(727\) 1058.69 3951.09i 0.0540091 0.201565i −0.933649 0.358189i \(-0.883394\pi\)
0.987658 + 0.156624i \(0.0500611\pi\)
\(728\) 27197.3 + 27197.3i 1.38462 + 1.38462i
\(729\) 7736.76 18098.7i 0.393068 0.919509i
\(730\) 0 0
\(731\) −19978.4 + 11534.5i −1.01084 + 0.583611i
\(732\) −9672.66 3303.69i −0.488404 0.166814i
\(733\) −2312.48 8630.30i −0.116526 0.434881i 0.882871 0.469616i \(-0.155608\pi\)
−0.999397 + 0.0347357i \(0.988941\pi\)
\(734\) −1708.64 + 2959.46i −0.0859226 + 0.148822i
\(735\) 0 0
\(736\) −9761.80 16907.9i −0.488892 0.846786i
\(737\) 2905.60 2905.60i 0.145223 0.145223i
\(738\) 831.445 + 6504.12i 0.0414714 + 0.324417i
\(739\) 10810.9i 0.538140i 0.963121 + 0.269070i \(0.0867163\pi\)
−0.963121 + 0.269070i \(0.913284\pi\)
\(740\) 0 0
\(741\) 344.177 5104.25i 0.0170630 0.253049i
\(742\) 12177.4 3262.93i 0.602489 0.161436i
\(743\) −14187.3 + 3801.46i −0.700511 + 0.187701i −0.591460 0.806335i \(-0.701448\pi\)
−0.109052 + 0.994036i \(0.534781\pi\)
\(744\) 293.394 4351.12i 0.0144575 0.214408i
\(745\) 0 0
\(746\) 13087.9i 0.642334i
\(747\) 9767.00 7436.37i 0.478388 0.364234i
\(748\) 5634.21 5634.21i 0.275411 0.275411i
\(749\) 18545.8 + 32122.2i 0.904737 + 1.56705i
\(750\) 0 0
\(751\) 10459.1 18115.7i 0.508201 0.880229i −0.491754 0.870734i \(-0.663644\pi\)
0.999955 0.00949541i \(-0.00302253\pi\)
\(752\) −241.659 901.883i −0.0117186 0.0437344i
\(753\) 30324.6 + 10357.4i 1.46758 + 0.501253i
\(754\) −4242.88 + 2449.63i −0.204929 + 0.118316i
\(755\) 0 0
\(756\) −4654.79 + 22731.2i −0.223933 + 1.09355i
\(757\) 18342.1 + 18342.1i 0.880653 + 0.880653i 0.993601 0.112948i \(-0.0360293\pi\)
−0.112948 + 0.993601i \(0.536029\pi\)
\(758\) 3238.37 12085.7i 0.155175 0.579121i
\(759\) −8653.61 17631.2i −0.413842 0.843177i
\(760\) 0 0
\(761\) 9287.39 + 5362.08i 0.442402 + 0.255421i 0.704616 0.709589i \(-0.251119\pi\)
−0.262214 + 0.965010i \(0.584453\pi\)
\(762\) −11286.3 + 2222.96i −0.536560 + 0.105681i
\(763\) 15043.9 + 4030.99i 0.713793 + 0.191260i
\(764\) −4761.29 −0.225468
\(765\) 0 0
\(766\) 9254.36 0.436519
\(767\) −3012.82 807.283i −0.141834 0.0380043i
\(768\) −13093.0 14986.4i −0.615172 0.704132i
\(769\) 19273.4 + 11127.5i 0.903793 + 0.521805i 0.878429 0.477873i \(-0.158592\pi\)
0.0253640 + 0.999678i \(0.491926\pi\)
\(770\) 0 0
\(771\) 29959.9 + 2020.18i 1.39945 + 0.0943647i
\(772\) −3690.04 + 13771.4i −0.172030 + 0.642026i
\(773\) −20786.4 20786.4i −0.967184 0.967184i 0.0322943 0.999478i \(-0.489719\pi\)
−0.999478 + 0.0322943i \(0.989719\pi\)
\(774\) 9244.60 + 22557.7i 0.429316 + 1.04757i
\(775\) 0 0
\(776\) 6153.09 3552.49i 0.284643 0.164339i
\(777\) 3361.71 + 17067.9i 0.155213 + 0.788040i
\(778\) 3363.53 + 12552.9i 0.154998 + 0.578461i
\(779\) −1297.12 + 2246.68i −0.0596589 + 0.103332i
\(780\) 0