Properties

Label 225.4.p.b.32.6
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 32.6
Character \(\chi\) \(=\) 225.32
Dual form 225.4.p.b.218.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +O(q^{10})\) \(q+(-1.43923 - 0.385641i) q^{2} +(2.38802 + 4.61491i) q^{3} +(-5.00553 - 2.88994i) q^{4} +(-1.65722 - 7.56285i) q^{6} +(-6.62758 + 24.7344i) q^{7} +(14.5184 + 14.5184i) q^{8} +(-15.5947 + 22.0410i) q^{9} +(11.8937 - 6.86683i) q^{11} +(1.38352 - 30.0013i) q^{12} +(-21.6449 - 80.7799i) q^{13} +(19.0773 - 33.0428i) q^{14} +(7.82311 + 13.5500i) q^{16} +(-19.6420 + 19.6420i) q^{17} +(30.9444 - 25.7081i) q^{18} +23.7249i q^{19} +(-129.974 + 28.4807i) q^{21} +(-19.7659 + 5.29627i) q^{22} +(-74.1658 + 19.8727i) q^{23} +(-32.3308 + 101.671i) q^{24} +124.608i q^{26} +(-138.958 - 19.3339i) q^{27} +(104.656 - 104.656i) q^{28} +(-103.697 - 179.609i) q^{29} +(-16.4679 + 28.5232i) q^{31} +(-48.5466 - 181.178i) q^{32} +(60.0922 + 38.4902i) q^{33} +(35.8441 - 20.6946i) q^{34} +(141.757 - 65.2589i) q^{36} +(-156.441 - 156.441i) q^{37} +(9.14932 - 34.1457i) q^{38} +(321.103 - 292.793i) q^{39} +(-247.106 - 142.667i) q^{41} +(198.046 + 9.13295i) q^{42} +(122.522 + 32.8295i) q^{43} -79.3790 q^{44} +114.406 q^{46} +(-332.652 - 89.1338i) q^{47} +(-43.8503 + 68.4606i) q^{48} +(-270.821 - 156.359i) q^{49} +(-137.551 - 43.7404i) q^{51} +(-125.105 + 466.899i) q^{52} +(-169.925 - 169.925i) q^{53} +(192.536 + 81.4138i) q^{54} +(-455.326 + 262.882i) q^{56} +(-109.488 + 56.6556i) q^{57} +(79.9798 + 298.489i) q^{58} +(-219.565 + 380.298i) q^{59} +(138.080 + 239.161i) q^{61} +(34.7009 - 34.7009i) q^{62} +(-441.816 - 531.805i) q^{63} +154.310i q^{64} +(-71.6433 - 78.5704i) q^{66} +(912.635 - 244.540i) q^{67} +(155.083 - 41.5543i) q^{68} +(-268.820 - 294.812i) q^{69} +112.676i q^{71} +(-546.409 + 93.5891i) q^{72} +(474.023 - 474.023i) q^{73} +(164.825 + 285.485i) q^{74} +(68.5637 - 118.756i) q^{76} +(91.0209 + 339.695i) q^{77} +(-575.056 + 297.567i) q^{78} +(-286.620 + 165.480i) q^{79} +(-242.609 - 687.446i) q^{81} +(300.625 + 300.625i) q^{82} +(-388.308 + 1449.19i) q^{83} +(732.896 + 233.056i) q^{84} +(-163.677 - 94.4988i) q^{86} +(581.246 - 907.461i) q^{87} +(272.373 + 72.9820i) q^{88} -598.425 q^{89} +2141.50 q^{91} +(428.670 + 114.862i) q^{92} +(-170.958 - 7.88376i) q^{93} +(444.390 + 256.569i) q^{94} +(720.191 - 656.695i) q^{96} +(-77.4097 + 288.897i) q^{97} +(329.477 + 329.477i) q^{98} +(-34.1273 + 369.235i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.43923 0.385641i −0.508846 0.136345i −0.00474347 0.999989i \(-0.501510\pi\)
−0.504102 + 0.863644i \(0.668177\pi\)
\(3\) 2.38802 + 4.61491i 0.459575 + 0.888139i
\(4\) −5.00553 2.88994i −0.625691 0.361243i
\(5\) 0 0
\(6\) −1.65722 7.56285i −0.112759 0.514587i
\(7\) −6.62758 + 24.7344i −0.357855 + 1.33553i 0.518997 + 0.854776i \(0.326305\pi\)
−0.876853 + 0.480759i \(0.840361\pi\)
\(8\) 14.5184 + 14.5184i 0.641628 + 0.641628i
\(9\) −15.5947 + 22.0410i −0.577582 + 0.816332i
\(10\) 0 0
\(11\) 11.8937 6.86683i 0.326008 0.188221i −0.328059 0.944657i \(-0.606395\pi\)
0.654067 + 0.756436i \(0.273061\pi\)
\(12\) 1.38352 30.0013i 0.0332823 0.721719i
\(13\) −21.6449 80.7799i −0.461786 1.72341i −0.667331 0.744761i \(-0.732563\pi\)
0.205545 0.978648i \(-0.434103\pi\)
\(14\) 19.0773 33.0428i 0.364186 0.630789i
\(15\) 0 0
\(16\) 7.82311 + 13.5500i 0.122236 + 0.211719i
\(17\) −19.6420 + 19.6420i −0.280228 + 0.280228i −0.833200 0.552972i \(-0.813494\pi\)
0.552972 + 0.833200i \(0.313494\pi\)
\(18\) 30.9444 25.7081i 0.405203 0.336637i
\(19\) 23.7249i 0.286467i 0.989689 + 0.143233i \(0.0457500\pi\)
−0.989689 + 0.143233i \(0.954250\pi\)
\(20\) 0 0
\(21\) −129.974 + 28.4807i −1.35060 + 0.295952i
\(22\) −19.7659 + 5.29627i −0.191551 + 0.0513258i
\(23\) −74.1658 + 19.8727i −0.672375 + 0.180162i −0.578825 0.815452i \(-0.696488\pi\)
−0.0935508 + 0.995615i \(0.529822\pi\)
\(24\) −32.3308 + 101.671i −0.274979 + 0.864731i
\(25\) 0 0
\(26\) 124.608i 0.939911i
\(27\) −138.958 19.3339i −0.990459 0.137808i
\(28\) 104.656 104.656i 0.706360 0.706360i
\(29\) −103.697 179.609i −0.664002 1.15009i −0.979555 0.201178i \(-0.935523\pi\)
0.315552 0.948908i \(-0.397810\pi\)
\(30\) 0 0
\(31\) −16.4679 + 28.5232i −0.0954104 + 0.165256i −0.909780 0.415091i \(-0.863750\pi\)
0.814369 + 0.580347i \(0.197083\pi\)
\(32\) −48.5466 181.178i −0.268185 1.00088i
\(33\) 60.0922 + 38.4902i 0.316991 + 0.203039i
\(34\) 35.8441 20.6946i 0.180800 0.104385i
\(35\) 0 0
\(36\) 141.757 65.2589i 0.656283 0.302124i
\(37\) −156.441 156.441i −0.695101 0.695101i 0.268249 0.963350i \(-0.413555\pi\)
−0.963350 + 0.268249i \(0.913555\pi\)
\(38\) 9.14932 34.1457i 0.0390583 0.145768i
\(39\) 321.103 292.793i 1.31840 1.20216i
\(40\) 0 0
\(41\) −247.106 142.667i −0.941255 0.543434i −0.0509015 0.998704i \(-0.516209\pi\)
−0.890354 + 0.455270i \(0.849543\pi\)
\(42\) 198.046 + 9.13295i 0.727600 + 0.0335535i
\(43\) 122.522 + 32.8295i 0.434520 + 0.116429i 0.469447 0.882961i \(-0.344453\pi\)
−0.0349271 + 0.999390i \(0.511120\pi\)
\(44\) −79.3790 −0.271974
\(45\) 0 0
\(46\) 114.406 0.366700
\(47\) −332.652 89.1338i −1.03239 0.276628i −0.297433 0.954743i \(-0.596130\pi\)
−0.734956 + 0.678115i \(0.762797\pi\)
\(48\) −43.8503 + 68.4606i −0.131859 + 0.205863i
\(49\) −270.821 156.359i −0.789567 0.455857i
\(50\) 0 0
\(51\) −137.551 43.7404i −0.377667 0.120096i
\(52\) −125.105 + 466.899i −0.333634 + 1.24514i
\(53\) −169.925 169.925i −0.440397 0.440397i 0.451748 0.892145i \(-0.350800\pi\)
−0.892145 + 0.451748i \(0.850800\pi\)
\(54\) 192.536 + 81.4138i 0.485201 + 0.205167i
\(55\) 0 0
\(56\) −455.326 + 262.882i −1.08653 + 0.627306i
\(57\) −109.488 + 56.6556i −0.254423 + 0.131653i
\(58\) 79.9798 + 298.489i 0.181067 + 0.675750i
\(59\) −219.565 + 380.298i −0.484491 + 0.839162i −0.999841 0.0178172i \(-0.994328\pi\)
0.515351 + 0.856979i \(0.327662\pi\)
\(60\) 0 0
\(61\) 138.080 + 239.161i 0.289824 + 0.501990i 0.973768 0.227545i \(-0.0730698\pi\)
−0.683943 + 0.729535i \(0.739736\pi\)
\(62\) 34.7009 34.7009i 0.0710810 0.0710810i
\(63\) −441.816 531.805i −0.883549 1.06351i
\(64\) 154.310i 0.301386i
\(65\) 0 0
\(66\) −71.6433 78.5704i −0.133616 0.146536i
\(67\) 912.635 244.540i 1.66412 0.445900i 0.700605 0.713549i \(-0.252913\pi\)
0.963516 + 0.267649i \(0.0862468\pi\)
\(68\) 155.083 41.5543i 0.276567 0.0741058i
\(69\) −268.820 294.812i −0.469016 0.514365i
\(70\) 0 0
\(71\) 112.676i 0.188341i 0.995556 + 0.0941705i \(0.0300199\pi\)
−0.995556 + 0.0941705i \(0.969980\pi\)
\(72\) −546.409 + 93.5891i −0.894374 + 0.153189i
\(73\) 474.023 474.023i 0.760002 0.760002i −0.216320 0.976322i \(-0.569405\pi\)
0.976322 + 0.216320i \(0.0694055\pi\)
\(74\) 164.825 + 285.485i 0.258926 + 0.448473i
\(75\) 0 0
\(76\) 68.5637 118.756i 0.103484 0.179240i
\(77\) 91.0209 + 339.695i 0.134712 + 0.502751i
\(78\) −575.056 + 297.567i −0.834772 + 0.431959i
\(79\) −286.620 + 165.480i −0.408194 + 0.235671i −0.690013 0.723797i \(-0.742395\pi\)
0.281820 + 0.959467i \(0.409062\pi\)
\(80\) 0 0
\(81\) −242.609 687.446i −0.332797 0.942998i
\(82\) 300.625 + 300.625i 0.404859 + 0.404859i
\(83\) −388.308 + 1449.19i −0.513523 + 1.91649i −0.135202 + 0.990818i \(0.543168\pi\)
−0.378321 + 0.925674i \(0.623498\pi\)
\(84\) 732.896 + 233.056i 0.951971 + 0.302721i
\(85\) 0 0
\(86\) −163.677 94.4988i −0.205229 0.118489i
\(87\) 581.246 907.461i 0.716278 1.11828i
\(88\) 272.373 + 72.9820i 0.329943 + 0.0884080i
\(89\) −598.425 −0.712730 −0.356365 0.934347i \(-0.615984\pi\)
−0.356365 + 0.934347i \(0.615984\pi\)
\(90\) 0 0
\(91\) 2141.50 2.46692
\(92\) 428.670 + 114.862i 0.485782 + 0.130165i
\(93\) −170.958 7.88376i −0.190618 0.00879041i
\(94\) 444.390 + 256.569i 0.487610 + 0.281522i
\(95\) 0 0
\(96\) 720.191 656.695i 0.765669 0.698164i
\(97\) −77.4097 + 288.897i −0.0810285 + 0.302402i −0.994533 0.104427i \(-0.966699\pi\)
0.913504 + 0.406830i \(0.133366\pi\)
\(98\) 329.477 + 329.477i 0.339614 + 0.339614i
\(99\) −34.1273 + 369.235i −0.0346457 + 0.374844i
\(100\) 0 0
\(101\) −72.2861 + 41.7344i −0.0712152 + 0.0411161i −0.535185 0.844735i \(-0.679758\pi\)
0.463970 + 0.885851i \(0.346425\pi\)
\(102\) 181.100 + 115.998i 0.175800 + 0.112603i
\(103\) −67.7920 253.003i −0.0648519 0.242031i 0.925889 0.377795i \(-0.123318\pi\)
−0.990741 + 0.135764i \(0.956651\pi\)
\(104\) 858.544 1487.04i 0.809492 1.40208i
\(105\) 0 0
\(106\) 179.032 + 310.092i 0.164048 + 0.284140i
\(107\) −278.425 + 278.425i −0.251555 + 0.251555i −0.821608 0.570053i \(-0.806923\pi\)
0.570053 + 0.821608i \(0.306923\pi\)
\(108\) 639.682 + 498.356i 0.569939 + 0.444022i
\(109\) 1231.78i 1.08242i 0.840889 + 0.541208i \(0.182033\pi\)
−0.840889 + 0.541208i \(0.817967\pi\)
\(110\) 0 0
\(111\) 348.376 1095.54i 0.297896 0.936797i
\(112\) −387.000 + 103.696i −0.326501 + 0.0874857i
\(113\) 90.0361 24.1251i 0.0749547 0.0200841i −0.221147 0.975241i \(-0.570980\pi\)
0.296102 + 0.955156i \(0.404313\pi\)
\(114\) 179.428 39.3174i 0.147412 0.0323019i
\(115\) 0 0
\(116\) 1198.72i 0.959465i
\(117\) 2118.01 + 782.665i 1.67359 + 0.618440i
\(118\) 462.664 462.664i 0.360946 0.360946i
\(119\) −355.654 616.012i −0.273973 0.474535i
\(120\) 0 0
\(121\) −571.193 + 989.336i −0.429146 + 0.743303i
\(122\) −106.498 397.457i −0.0790321 0.294952i
\(123\) 68.2995 1481.06i 0.0500680 1.08571i
\(124\) 164.861 95.1827i 0.119395 0.0689327i
\(125\) 0 0
\(126\) 430.790 + 935.774i 0.304586 + 0.661630i
\(127\) 394.695 + 394.695i 0.275776 + 0.275776i 0.831420 0.555644i \(-0.187528\pi\)
−0.555644 + 0.831420i \(0.687528\pi\)
\(128\) −328.864 + 1227.34i −0.227092 + 0.847519i
\(129\) 141.079 + 643.823i 0.0962889 + 0.439422i
\(130\) 0 0
\(131\) 566.164 + 326.875i 0.377603 + 0.218009i 0.676775 0.736190i \(-0.263377\pi\)
−0.299172 + 0.954199i \(0.596710\pi\)
\(132\) −189.559 366.327i −0.124992 0.241550i
\(133\) −586.823 157.239i −0.382587 0.102514i
\(134\) −1407.80 −0.907577
\(135\) 0 0
\(136\) −570.339 −0.359604
\(137\) 9.89738 + 2.65200i 0.00617219 + 0.00165383i 0.261904 0.965094i \(-0.415650\pi\)
−0.255732 + 0.966748i \(0.582316\pi\)
\(138\) 273.203 + 527.971i 0.168526 + 0.325680i
\(139\) 1435.50 + 828.789i 0.875956 + 0.505734i 0.869323 0.494244i \(-0.164555\pi\)
0.00663323 + 0.999978i \(0.497889\pi\)
\(140\) 0 0
\(141\) −383.035 1748.01i −0.228776 1.04404i
\(142\) 43.4526 162.167i 0.0256793 0.0958366i
\(143\) −812.140 812.140i −0.474927 0.474927i
\(144\) −420.655 38.8799i −0.243435 0.0224999i
\(145\) 0 0
\(146\) −865.032 + 499.427i −0.490346 + 0.283102i
\(147\) 74.8545 1623.20i 0.0419993 0.910745i
\(148\) 330.964 + 1235.18i 0.183818 + 0.686019i
\(149\) 763.694 1322.76i 0.419894 0.727278i −0.576034 0.817426i \(-0.695400\pi\)
0.995928 + 0.0901473i \(0.0287338\pi\)
\(150\) 0 0
\(151\) −219.184 379.637i −0.118125 0.204599i 0.800900 0.598799i \(-0.204355\pi\)
−0.919025 + 0.394200i \(0.871022\pi\)
\(152\) −344.448 + 344.448i −0.183805 + 0.183805i
\(153\) −126.617 739.239i −0.0669044 0.390614i
\(154\) 524.001i 0.274190i
\(155\) 0 0
\(156\) −2453.45 + 537.615i −1.25919 + 0.275921i
\(157\) −1472.31 + 394.505i −0.748430 + 0.200541i −0.612821 0.790221i \(-0.709965\pi\)
−0.135608 + 0.990763i \(0.543299\pi\)
\(158\) 476.330 127.632i 0.239840 0.0642650i
\(159\) 378.405 1189.97i 0.188739 0.593529i
\(160\) 0 0
\(161\) 1966.16i 0.962453i
\(162\) 84.0636 + 1082.96i 0.0407695 + 0.525216i
\(163\) −1347.15 + 1347.15i −0.647345 + 0.647345i −0.952350 0.305006i \(-0.901342\pi\)
0.305006 + 0.952350i \(0.401342\pi\)
\(164\) 824.597 + 1428.24i 0.392623 + 0.680044i
\(165\) 0 0
\(166\) 1117.73 1935.97i 0.522608 0.905183i
\(167\) 30.5750 + 114.108i 0.0141675 + 0.0528737i 0.972648 0.232285i \(-0.0746203\pi\)
−0.958480 + 0.285159i \(0.907954\pi\)
\(168\) −2300.50 1473.52i −1.05647 0.676692i
\(169\) −4154.23 + 2398.45i −1.89087 + 1.09169i
\(170\) 0 0
\(171\) −522.921 369.984i −0.233852 0.165458i
\(172\) −518.410 518.410i −0.229816 0.229816i
\(173\) 127.211 474.757i 0.0559056 0.208642i −0.932323 0.361626i \(-0.882222\pi\)
0.988229 + 0.152984i \(0.0488883\pi\)
\(174\) −1186.50 + 1081.90i −0.516946 + 0.471370i
\(175\) 0 0
\(176\) 186.091 + 107.440i 0.0796998 + 0.0460147i
\(177\) −2279.37 105.114i −0.967952 0.0446374i
\(178\) 861.274 + 230.778i 0.362670 + 0.0971770i
\(179\) −641.856 −0.268015 −0.134007 0.990980i \(-0.542785\pi\)
−0.134007 + 0.990980i \(0.542785\pi\)
\(180\) 0 0
\(181\) −1243.05 −0.510470 −0.255235 0.966879i \(-0.582153\pi\)
−0.255235 + 0.966879i \(0.582153\pi\)
\(182\) −3082.12 825.851i −1.25528 0.336352i
\(183\) −773.968 + 1208.35i −0.312641 + 0.488106i
\(184\) −1365.29 788.248i −0.547012 0.315817i
\(185\) 0 0
\(186\) 243.008 + 77.2750i 0.0957968 + 0.0304628i
\(187\) −98.7376 + 368.494i −0.0386118 + 0.144101i
\(188\) 1407.51 + 1407.51i 0.546027 + 0.546027i
\(189\) 1399.17 3308.90i 0.538488 1.27348i
\(190\) 0 0
\(191\) −3517.42 + 2030.79i −1.33252 + 0.769332i −0.985686 0.168593i \(-0.946078\pi\)
−0.346837 + 0.937925i \(0.612744\pi\)
\(192\) −712.125 + 368.495i −0.267673 + 0.138509i
\(193\) −661.892 2470.21i −0.246860 0.921295i −0.972439 0.233156i \(-0.925095\pi\)
0.725579 0.688139i \(-0.241572\pi\)
\(194\) 222.821 385.938i 0.0824620 0.142828i
\(195\) 0 0
\(196\) 903.736 + 1565.32i 0.329350 + 0.570451i
\(197\) 1350.59 1350.59i 0.488454 0.488454i −0.419364 0.907818i \(-0.637747\pi\)
0.907818 + 0.419364i \(0.137747\pi\)
\(198\) 191.510 518.255i 0.0687373 0.186014i
\(199\) 4890.58i 1.74213i −0.491167 0.871065i \(-0.663430\pi\)
0.491167 0.871065i \(-0.336570\pi\)
\(200\) 0 0
\(201\) 3307.92 + 3627.76i 1.16081 + 1.27305i
\(202\) 120.131 32.1890i 0.0418435 0.0112119i
\(203\) 5129.78 1374.52i 1.77360 0.475234i
\(204\) 562.109 + 616.459i 0.192919 + 0.211572i
\(205\) 0 0
\(206\) 390.274i 0.131999i
\(207\) 718.582 1944.59i 0.241280 0.652941i
\(208\) 925.239 925.239i 0.308432 0.308432i
\(209\) 162.915 + 282.177i 0.0539190 + 0.0933905i
\(210\) 0 0
\(211\) −1481.97 + 2566.85i −0.483522 + 0.837484i −0.999821 0.0189240i \(-0.993976\pi\)
0.516299 + 0.856408i \(0.327309\pi\)
\(212\) 359.492 + 1341.64i 0.116462 + 0.434643i
\(213\) −519.991 + 269.073i −0.167273 + 0.0865568i
\(214\) 508.090 293.346i 0.162301 0.0937043i
\(215\) 0 0
\(216\) −1736.74 2298.14i −0.547085 0.723927i
\(217\) −596.365 596.365i −0.186562 0.186562i
\(218\) 475.026 1772.82i 0.147582 0.550782i
\(219\) 3319.55 + 1055.60i 1.02427 + 0.325710i
\(220\) 0 0
\(221\) 2011.82 + 1161.53i 0.612353 + 0.353542i
\(222\) −923.882 + 1442.40i −0.279310 + 0.436069i
\(223\) 2259.54 + 605.443i 0.678521 + 0.181809i 0.581590 0.813482i \(-0.302431\pi\)
0.0969311 + 0.995291i \(0.469097\pi\)
\(224\) 4803.09 1.43268
\(225\) 0 0
\(226\) −138.887 −0.0408787
\(227\) −1979.99 530.537i −0.578928 0.155123i −0.0425397 0.999095i \(-0.513545\pi\)
−0.536388 + 0.843972i \(0.680212\pi\)
\(228\) 711.779 + 32.8239i 0.206749 + 0.00953427i
\(229\) 3464.76 + 2000.38i 0.999815 + 0.577244i 0.908194 0.418550i \(-0.137462\pi\)
0.0916215 + 0.995794i \(0.470795\pi\)
\(230\) 0 0
\(231\) −1350.30 + 1231.25i −0.384602 + 0.350694i
\(232\) 1102.11 4113.14i 0.311885 1.16397i
\(233\) −4906.70 4906.70i −1.37961 1.37961i −0.845271 0.534337i \(-0.820561\pi\)
−0.534337 0.845271i \(-0.679439\pi\)
\(234\) −2746.49 1943.23i −0.767280 0.542876i
\(235\) 0 0
\(236\) 2198.08 1269.06i 0.606283 0.350038i
\(237\) −1448.13 927.556i −0.396904 0.254225i
\(238\) 274.310 + 1023.74i 0.0747096 + 0.278820i
\(239\) −2501.24 + 4332.28i −0.676954 + 1.17252i 0.298939 + 0.954272i \(0.403367\pi\)
−0.975894 + 0.218247i \(0.929966\pi\)
\(240\) 0 0
\(241\) −1825.14 3161.24i −0.487834 0.844952i 0.512069 0.858945i \(-0.328879\pi\)
−0.999902 + 0.0139921i \(0.995546\pi\)
\(242\) 1203.61 1203.61i 0.319715 0.319715i
\(243\) 2593.14 2761.25i 0.684569 0.728948i
\(244\) 1596.17i 0.418788i
\(245\) 0 0
\(246\) −669.458 + 2105.25i −0.173508 + 0.545634i
\(247\) 1916.50 513.524i 0.493700 0.132286i
\(248\) −653.199 + 175.024i −0.167251 + 0.0448147i
\(249\) −7615.15 + 1668.68i −1.93811 + 0.424692i
\(250\) 0 0
\(251\) 3563.08i 0.896013i −0.894030 0.448007i \(-0.852134\pi\)
0.894030 0.448007i \(-0.147866\pi\)
\(252\) 674.637 + 3938.79i 0.168643 + 0.984605i
\(253\) −745.643 + 745.643i −0.185289 + 0.185289i
\(254\) −415.847 720.268i −0.102727 0.177928i
\(255\) 0 0
\(256\) 1563.86 2708.69i 0.381803 0.661302i
\(257\) 1785.37 + 6663.08i 0.433339 + 1.61724i 0.745010 + 0.667053i \(0.232444\pi\)
−0.311672 + 0.950190i \(0.600889\pi\)
\(258\) 45.2399 981.017i 0.0109167 0.236727i
\(259\) 4906.30 2832.66i 1.17708 0.679586i
\(260\) 0 0
\(261\) 5575.88 + 515.362i 1.32237 + 0.122223i
\(262\) −688.785 688.785i −0.162417 0.162417i
\(263\) −1321.88 + 4933.33i −0.309927 + 1.15666i 0.618694 + 0.785632i \(0.287662\pi\)
−0.928621 + 0.371030i \(0.879005\pi\)
\(264\) 313.626 + 1431.26i 0.0731149 + 0.333666i
\(265\) 0 0
\(266\) 783.937 + 452.607i 0.180700 + 0.104327i
\(267\) −1429.05 2761.68i −0.327553 0.633003i
\(268\) −5274.93 1413.41i −1.20230 0.322157i
\(269\) −6950.52 −1.57539 −0.787696 0.616064i \(-0.788726\pi\)
−0.787696 + 0.616064i \(0.788726\pi\)
\(270\) 0 0
\(271\) −5694.64 −1.27648 −0.638238 0.769839i \(-0.720336\pi\)
−0.638238 + 0.769839i \(0.720336\pi\)
\(272\) −419.810 112.488i −0.0935836 0.0250756i
\(273\) 5113.94 + 9882.82i 1.13374 + 2.19097i
\(274\) −13.2219 7.63368i −0.00291520 0.00168309i
\(275\) 0 0
\(276\) 493.596 + 2252.56i 0.107648 + 0.491262i
\(277\) −742.484 + 2770.99i −0.161052 + 0.601056i 0.837458 + 0.546501i \(0.184041\pi\)
−0.998511 + 0.0545548i \(0.982626\pi\)
\(278\) −1746.41 1746.41i −0.376772 0.376772i
\(279\) −371.868 807.781i −0.0797962 0.173335i
\(280\) 0 0
\(281\) 5092.45 2940.13i 1.08110 0.624176i 0.149910 0.988700i \(-0.452102\pi\)
0.931194 + 0.364524i \(0.118768\pi\)
\(282\) −122.828 + 2663.51i −0.0259373 + 0.562446i
\(283\) 470.532 + 1756.05i 0.0988348 + 0.368856i 0.997573 0.0696293i \(-0.0221817\pi\)
−0.898738 + 0.438486i \(0.855515\pi\)
\(284\) 325.628 564.005i 0.0680369 0.117843i
\(285\) 0 0
\(286\) 855.664 + 1482.05i 0.176911 + 0.306418i
\(287\) 5166.49 5166.49i 1.06261 1.06261i
\(288\) 4750.42 + 1755.41i 0.971948 + 0.359162i
\(289\) 4141.39i 0.842945i
\(290\) 0 0
\(291\) −1518.09 + 332.653i −0.305814 + 0.0670119i
\(292\) −3742.63 + 1002.84i −0.750072 + 0.200981i
\(293\) −6655.60 + 1783.36i −1.32705 + 0.355581i −0.851613 0.524172i \(-0.824375\pi\)
−0.475432 + 0.879752i \(0.657708\pi\)
\(294\) −733.707 + 2307.30i −0.145547 + 0.457703i
\(295\) 0 0
\(296\) 4542.54i 0.891992i
\(297\) −1785.48 + 724.246i −0.348836 + 0.141498i
\(298\) −1609.24 + 1609.24i −0.312822 + 0.312822i
\(299\) 3210.62 + 5560.96i 0.620987 + 1.07558i
\(300\) 0 0
\(301\) −1624.04 + 2812.92i −0.310991 + 0.538652i
\(302\) 169.052 + 630.912i 0.0322115 + 0.120215i
\(303\) −365.221 233.931i −0.0692455 0.0443531i
\(304\) −321.473 + 185.603i −0.0606505 + 0.0350166i
\(305\) 0 0
\(306\) −102.850 + 1112.77i −0.0192141 + 0.207884i
\(307\) 1580.63 + 1580.63i 0.293848 + 0.293848i 0.838598 0.544750i \(-0.183376\pi\)
−0.544750 + 0.838598i \(0.683376\pi\)
\(308\) 526.091 1963.40i 0.0973273 0.363230i
\(309\) 1005.70 917.031i 0.185153 0.168829i
\(310\) 0 0
\(311\) −1301.03 751.148i −0.237217 0.136957i 0.376680 0.926343i \(-0.377066\pi\)
−0.613897 + 0.789386i \(0.710399\pi\)
\(312\) 8912.78 + 411.015i 1.61727 + 0.0745806i
\(313\) −3778.34 1012.40i −0.682314 0.182825i −0.0990184 0.995086i \(-0.531570\pi\)
−0.583295 + 0.812260i \(0.698237\pi\)
\(314\) 2271.14 0.408178
\(315\) 0 0
\(316\) 1912.92 0.340538
\(317\) 3726.04 + 998.390i 0.660175 + 0.176893i 0.573325 0.819328i \(-0.305653\pi\)
0.0868500 + 0.996221i \(0.472320\pi\)
\(318\) −1003.52 + 1566.72i −0.176963 + 0.276281i
\(319\) −2466.68 1424.14i −0.432940 0.249958i
\(320\) 0 0
\(321\) −1949.79 620.020i −0.339024 0.107807i
\(322\) −758.232 + 2829.76i −0.131225 + 0.489740i
\(323\) −466.004 466.004i −0.0802761 0.0802761i
\(324\) −772.293 + 4142.16i −0.132423 + 0.710247i
\(325\) 0 0
\(326\) 2458.39 1419.35i 0.417661 0.241136i
\(327\) −5684.56 + 2941.52i −0.961335 + 0.497451i
\(328\) −1516.29 5658.87i −0.255253 0.952618i
\(329\) 4409.35 7637.22i 0.738892 1.27980i
\(330\) 0 0
\(331\) −3448.09 5972.26i −0.572580 0.991738i −0.996300 0.0859446i \(-0.972609\pi\)
0.423720 0.905793i \(-0.360724\pi\)
\(332\) 6131.76 6131.76i 1.01363 1.01363i
\(333\) 5887.76 1008.46i 0.968912 0.165955i
\(334\) 176.018i 0.0288362i
\(335\) 0 0
\(336\) −1402.71 1538.34i −0.227751 0.249772i
\(337\) 6614.22 1772.28i 1.06914 0.286475i 0.318999 0.947755i \(-0.396653\pi\)
0.750139 + 0.661280i \(0.229987\pi\)
\(338\) 6903.85 1849.88i 1.11101 0.297693i
\(339\) 326.343 + 357.897i 0.0522847 + 0.0573401i
\(340\) 0 0
\(341\) 452.329i 0.0718329i
\(342\) 609.924 + 734.153i 0.0964354 + 0.116077i
\(343\) −548.319 + 548.319i −0.0863162 + 0.0863162i
\(344\) 1302.18 + 2255.45i 0.204096 + 0.353504i
\(345\) 0 0
\(346\) −366.172 + 634.229i −0.0568946 + 0.0985444i
\(347\) 69.6922 + 260.095i 0.0107818 + 0.0402381i 0.971107 0.238644i \(-0.0767029\pi\)
−0.960325 + 0.278882i \(0.910036\pi\)
\(348\) −5531.96 + 2862.56i −0.852138 + 0.440946i
\(349\) 8184.76 4725.48i 1.25536 0.724782i 0.283190 0.959064i \(-0.408607\pi\)
0.972169 + 0.234282i \(0.0752738\pi\)
\(350\) 0 0
\(351\) 1445.93 + 11643.5i 0.219881 + 1.77060i
\(352\) −1821.52 1821.52i −0.275816 0.275816i
\(353\) −91.7954 + 342.585i −0.0138407 + 0.0516543i −0.972501 0.232899i \(-0.925179\pi\)
0.958660 + 0.284554i \(0.0918454\pi\)
\(354\) 3240.00 + 1030.30i 0.486452 + 0.154689i
\(355\) 0 0
\(356\) 2995.44 + 1729.42i 0.445949 + 0.257469i
\(357\) 1993.53 3112.36i 0.295542 0.461411i
\(358\) 923.781 + 247.526i 0.136378 + 0.0365424i
\(359\) −2385.59 −0.350715 −0.175358 0.984505i \(-0.556108\pi\)
−0.175358 + 0.984505i \(0.556108\pi\)
\(360\) 0 0
\(361\) 6296.13 0.917937
\(362\) 1789.04 + 479.371i 0.259750 + 0.0695999i
\(363\) −5929.71 273.450i −0.857381 0.0395383i
\(364\) −10719.3 6188.81i −1.54353 0.891159i
\(365\) 0 0
\(366\) 1579.91 1440.62i 0.225637 0.205744i
\(367\) 859.169 3206.46i 0.122202 0.456065i −0.877522 0.479536i \(-0.840805\pi\)
0.999725 + 0.0234708i \(0.00747167\pi\)
\(368\) −849.482 849.482i −0.120332 0.120332i
\(369\) 6998.06 3221.61i 0.987275 0.454499i
\(370\) 0 0
\(371\) 5329.20 3076.82i 0.745764 0.430567i
\(372\) 832.951 + 533.521i 0.116093 + 0.0743596i
\(373\) 2837.71 + 10590.5i 0.393917 + 1.47012i 0.823618 + 0.567145i \(0.191952\pi\)
−0.429701 + 0.902971i \(0.641381\pi\)
\(374\) 284.213 492.271i 0.0392949 0.0680608i
\(375\) 0 0
\(376\) −3535.49 6123.65i −0.484917 0.839901i
\(377\) −12264.3 + 12264.3i −1.67544 + 1.67544i
\(378\) −3289.77 + 4222.70i −0.447640 + 0.574583i
\(379\) 1340.48i 0.181677i 0.995866 + 0.0908385i \(0.0289547\pi\)
−0.995866 + 0.0908385i \(0.971045\pi\)
\(380\) 0 0
\(381\) −878.940 + 2764.02i −0.118188 + 0.371666i
\(382\) 5845.55 1566.31i 0.782943 0.209789i
\(383\) 13746.2 3683.28i 1.83394 0.491401i 0.835614 0.549318i \(-0.185112\pi\)
0.998321 + 0.0579162i \(0.0184456\pi\)
\(384\) −6449.39 + 1413.23i −0.857081 + 0.187809i
\(385\) 0 0
\(386\) 3810.47i 0.502455i
\(387\) −2634.28 + 2188.53i −0.346016 + 0.287465i
\(388\) 1222.37 1222.37i 0.159940 0.159940i
\(389\) 5939.24 + 10287.1i 0.774116 + 1.34081i 0.935290 + 0.353883i \(0.115139\pi\)
−0.161174 + 0.986926i \(0.551528\pi\)
\(390\) 0 0
\(391\) 1066.42 1847.10i 0.137932 0.238905i
\(392\) −1661.81 6201.96i −0.214118 0.799098i
\(393\) −156.486 + 3393.38i −0.0200857 + 0.435555i
\(394\) −2464.66 + 1422.97i −0.315146 + 0.181950i
\(395\) 0 0
\(396\) 1237.89 1749.59i 0.157087 0.222021i
\(397\) −1019.37 1019.37i −0.128869 0.128869i 0.639731 0.768599i \(-0.279046\pi\)
−0.768599 + 0.639731i \(0.779046\pi\)
\(398\) −1886.01 + 7038.68i −0.237530 + 0.886476i
\(399\) −675.703 3083.62i −0.0847806 0.386903i
\(400\) 0 0
\(401\) 8126.77 + 4691.99i 1.01205 + 0.584306i 0.911791 0.410655i \(-0.134700\pi\)
0.100257 + 0.994962i \(0.468033\pi\)
\(402\) −3361.85 6496.86i −0.417100 0.806055i
\(403\) 2660.55 + 712.893i 0.328862 + 0.0881184i
\(404\) 482.440 0.0594116
\(405\) 0 0
\(406\) −7913.02 −0.967283
\(407\) −2934.92 786.408i −0.357441 0.0957760i
\(408\) −1361.98 2632.06i −0.165265 0.319378i
\(409\) −2717.07 1568.70i −0.328485 0.189651i 0.326683 0.945134i \(-0.394069\pi\)
−0.655168 + 0.755483i \(0.727402\pi\)
\(410\) 0 0
\(411\) 11.3964 + 52.0085i 0.00136775 + 0.00624183i
\(412\) −391.830 + 1462.33i −0.0468546 + 0.174864i
\(413\) −7951.27 7951.27i −0.947353 0.947353i
\(414\) −1784.12 + 2521.61i −0.211799 + 0.299349i
\(415\) 0 0
\(416\) −13584.8 + 7843.18i −1.60108 + 0.924383i
\(417\) −396.770 + 8603.88i −0.0465946 + 1.01039i
\(418\) −125.654 468.946i −0.0147032 0.0548729i
\(419\) −1590.40 + 2754.66i −0.185433 + 0.321179i −0.943722 0.330739i \(-0.892702\pi\)
0.758290 + 0.651918i \(0.226035\pi\)
\(420\) 0 0
\(421\) 1402.60 + 2429.37i 0.162372 + 0.281236i 0.935719 0.352747i \(-0.114752\pi\)
−0.773347 + 0.633983i \(0.781419\pi\)
\(422\) 3122.79 3122.79i 0.360225 0.360225i
\(423\) 7152.21 5941.96i 0.822110 0.682997i
\(424\) 4934.08i 0.565142i
\(425\) 0 0
\(426\) 852.154 186.729i 0.0969178 0.0212372i
\(427\) −6830.64 + 1830.27i −0.774141 + 0.207430i
\(428\) 2198.30 589.032i 0.248268 0.0665232i
\(429\) 1808.54 5687.36i 0.203537 0.640066i
\(430\) 0 0
\(431\) 14909.0i 1.66623i −0.553103 0.833113i \(-0.686556\pi\)
0.553103 0.833113i \(-0.313444\pi\)
\(432\) −825.105 2034.13i −0.0918932 0.226544i
\(433\) −3778.79 + 3778.79i −0.419393 + 0.419393i −0.884994 0.465602i \(-0.845838\pi\)
0.465602 + 0.884994i \(0.345838\pi\)
\(434\) 628.325 + 1088.29i 0.0694944 + 0.120368i
\(435\) 0 0
\(436\) 3559.78 6165.72i 0.391015 0.677258i
\(437\) −471.478 1759.58i −0.0516106 0.192613i
\(438\) −4370.52 2799.40i −0.476784 0.305390i
\(439\) −1424.98 + 822.711i −0.154921 + 0.0894438i −0.575457 0.817832i \(-0.695176\pi\)
0.420535 + 0.907276i \(0.361842\pi\)
\(440\) 0 0
\(441\) 7669.69 3530.80i 0.828170 0.381254i
\(442\) −2447.55 2447.55i −0.263389 0.263389i
\(443\) 1770.56 6607.83i 0.189891 0.708685i −0.803639 0.595117i \(-0.797106\pi\)
0.993530 0.113567i \(-0.0362277\pi\)
\(444\) −4909.87 + 4476.99i −0.524802 + 0.478533i
\(445\) 0 0
\(446\) −3018.53 1742.75i −0.320474 0.185026i
\(447\) 7928.12 + 365.607i 0.838897 + 0.0386860i
\(448\) −3816.77 1022.70i −0.402512 0.107853i
\(449\) −7775.18 −0.817224 −0.408612 0.912708i \(-0.633987\pi\)
−0.408612 + 0.912708i \(0.633987\pi\)
\(450\) 0 0
\(451\) −3918.67 −0.409142
\(452\) −520.399 139.440i −0.0541537 0.0145104i
\(453\) 1228.57 1918.09i 0.127425 0.198940i
\(454\) 2645.07 + 1527.13i 0.273435 + 0.157868i
\(455\) 0 0
\(456\) −2412.14 767.046i −0.247717 0.0787724i
\(457\) 616.297 2300.05i 0.0630834 0.235431i −0.927184 0.374605i \(-0.877778\pi\)
0.990268 + 0.139175i \(0.0444449\pi\)
\(458\) −4215.17 4215.17i −0.430048 0.430048i
\(459\) 3109.15 2349.64i 0.316172 0.238937i
\(460\) 0 0
\(461\) −7507.21 + 4334.29i −0.758451 + 0.437892i −0.828739 0.559635i \(-0.810941\pi\)
0.0702886 + 0.997527i \(0.477608\pi\)
\(462\) 2418.22 1251.33i 0.243519 0.126011i
\(463\) −1323.45 4939.17i −0.132842 0.495772i 0.867156 0.498037i \(-0.165946\pi\)
−0.999997 + 0.00226497i \(0.999279\pi\)
\(464\) 1622.47 2810.20i 0.162330 0.281164i
\(465\) 0 0
\(466\) 5169.66 + 8954.12i 0.513906 + 0.890111i
\(467\) −4104.76 + 4104.76i −0.406736 + 0.406736i −0.880599 0.473863i \(-0.842859\pi\)
0.473863 + 0.880599i \(0.342859\pi\)
\(468\) −8339.92 10038.6i −0.823746 0.991526i
\(469\) 24194.2i 2.38206i
\(470\) 0 0
\(471\) −5336.52 5852.50i −0.522068 0.572546i
\(472\) −8709.04 + 2333.58i −0.849292 + 0.227567i
\(473\) 1682.67 450.870i 0.163571 0.0438288i
\(474\) 1726.49 + 1893.43i 0.167301 + 0.183477i
\(475\) 0 0
\(476\) 4111.29i 0.395883i
\(477\) 6395.26 1095.38i 0.613876 0.105145i
\(478\) 5270.58 5270.58i 0.504332 0.504332i
\(479\) −7608.37 13178.1i −0.725752 1.25704i −0.958664 0.284541i \(-0.908159\pi\)
0.232912 0.972498i \(-0.425175\pi\)
\(480\) 0 0
\(481\) −9251.13 + 16023.4i −0.876955 + 1.51893i
\(482\) 1407.70 + 5253.62i 0.133027 + 0.496464i
\(483\) 9073.63 4695.22i 0.854792 0.442319i
\(484\) 5718.25 3301.43i 0.537026 0.310052i
\(485\) 0 0
\(486\) −4796.99 + 2974.06i −0.447728 + 0.277585i
\(487\) −1399.75 1399.75i −0.130244 0.130244i 0.638980 0.769223i \(-0.279357\pi\)
−0.769223 + 0.638980i \(0.779357\pi\)
\(488\) −1467.54 + 5476.92i −0.136132 + 0.508050i
\(489\) −9434.01 2999.96i −0.872435 0.277429i
\(490\) 0 0
\(491\) −10186.1 5880.94i −0.936235 0.540536i −0.0474571 0.998873i \(-0.515112\pi\)
−0.888778 + 0.458338i \(0.848445\pi\)
\(492\) −4622.06 + 7216.12i −0.423534 + 0.661235i
\(493\) 5564.68 + 1491.05i 0.508358 + 0.136214i
\(494\) −2956.32 −0.269254
\(495\) 0 0
\(496\) −515.321 −0.0466504
\(497\) −2786.99 746.771i −0.251536 0.0673989i
\(498\) 11603.5 + 535.098i 1.04411 + 0.0481492i
\(499\) 13118.8 + 7574.16i 1.17691 + 0.679491i 0.955298 0.295644i \(-0.0955342\pi\)
0.221614 + 0.975134i \(0.428867\pi\)
\(500\) 0 0
\(501\) −453.582 + 413.592i −0.0404482 + 0.0368821i
\(502\) −1374.07 + 5128.10i −0.122167 + 0.455933i
\(503\) 10418.9 + 10418.9i 0.923572 + 0.923572i 0.997280 0.0737075i \(-0.0234831\pi\)
−0.0737075 + 0.997280i \(0.523483\pi\)
\(504\) 1306.49 14135.4i 0.115468 1.24929i
\(505\) 0 0
\(506\) 1360.71 785.604i 0.119547 0.0690205i
\(507\) −20989.0 13443.9i −1.83857 1.17764i
\(508\) −835.011 3116.30i −0.0729284 0.272172i
\(509\) 5758.26 9973.60i 0.501435 0.868511i −0.498564 0.866853i \(-0.666139\pi\)
0.999999 0.00165784i \(-0.000527706\pi\)
\(510\) 0 0
\(511\) 8583.07 + 14866.3i 0.743038 + 1.28698i
\(512\) 3892.45 3892.45i 0.335983 0.335983i
\(513\) 458.696 3296.76i 0.0394774 0.283734i
\(514\) 10278.2i 0.882011i
\(515\) 0 0
\(516\) 1154.44 3630.38i 0.0984910 0.309726i
\(517\) −4568.53 + 1224.13i −0.388634 + 0.104134i
\(518\) −8153.71 + 2184.78i −0.691609 + 0.185316i
\(519\) 2494.74 546.664i 0.210996 0.0462348i
\(520\) 0 0
\(521\) 17652.9i 1.48443i 0.670162 + 0.742215i \(0.266225\pi\)
−0.670162 + 0.742215i \(0.733775\pi\)
\(522\) −7826.24 2892.02i −0.656217 0.242491i
\(523\) −3650.39 + 3650.39i −0.305202 + 0.305202i −0.843045 0.537843i \(-0.819239\pi\)
0.537843 + 0.843045i \(0.319239\pi\)
\(524\) −1889.30 3272.36i −0.157508 0.272813i
\(525\) 0 0
\(526\) 3804.99 6590.44i 0.315410 0.546306i
\(527\) −236.791 883.714i −0.0195726 0.0730459i
\(528\) −51.4353 + 1115.36i −0.00423946 + 0.0919317i
\(529\) −5431.29 + 3135.76i −0.446395 + 0.257726i
\(530\) 0 0
\(531\) −4958.08 10770.1i −0.405202 0.880191i
\(532\) 2482.95 + 2482.95i 0.202349 + 0.202349i
\(533\) −6176.01 + 23049.2i −0.501900 + 1.87312i
\(534\) 991.721 + 4525.80i 0.0803670 + 0.366761i
\(535\) 0 0
\(536\) 16800.3 + 9699.66i 1.35385 + 0.781645i
\(537\) −1532.77 2962.11i −0.123173 0.238034i
\(538\) 10003.4 + 2680.41i 0.801632 + 0.214797i
\(539\) −4294.76 −0.343207
\(540\) 0 0
\(541\) 572.214 0.0454739 0.0227370 0.999741i \(-0.492762\pi\)
0.0227370 + 0.999741i \(0.492762\pi\)
\(542\) 8195.92 + 2196.09i 0.649529 + 0.174041i
\(543\) −2968.42 5736.55i −0.234599 0.453368i
\(544\) 4512.25 + 2605.15i 0.355627 + 0.205321i
\(545\) 0 0
\(546\) −3548.93 16195.8i −0.278169 1.26945i
\(547\) 5037.74 18801.1i 0.393781 1.46961i −0.430066 0.902797i \(-0.641510\pi\)
0.823847 0.566812i \(-0.191823\pi\)
\(548\) −41.8775 41.8775i −0.00326445 0.00326445i
\(549\) −7424.65 686.239i −0.577188 0.0533478i
\(550\) 0 0
\(551\) 4261.20 2460.21i 0.329462 0.190215i
\(552\) 377.362 8183.02i 0.0290971 0.630964i
\(553\) −2193.47 8186.13i −0.168672 0.629493i
\(554\) 2137.22 3701.77i 0.163902 0.283886i
\(555\) 0 0
\(556\) −4790.31 8297.06i −0.365385 0.632866i
\(557\) −7665.26 + 7665.26i −0.583101 + 0.583101i −0.935754 0.352653i \(-0.885280\pi\)
0.352653 + 0.935754i \(0.385280\pi\)
\(558\) 223.691 + 1305.99i 0.0169706 + 0.0990808i
\(559\) 10607.9i 0.802621i
\(560\) 0 0
\(561\) −1936.35 + 424.305i −0.145727 + 0.0319326i
\(562\) −8463.06 + 2267.67i −0.635218 + 0.170206i
\(563\) −6711.58 + 1798.36i −0.502415 + 0.134622i −0.501121 0.865378i \(-0.667079\pi\)
−0.00129433 + 0.999999i \(0.500412\pi\)
\(564\) −3134.36 + 9856.67i −0.234008 + 0.735888i
\(565\) 0 0
\(566\) 2708.82i 0.201167i
\(567\) 18611.5 1444.70i 1.37850 0.107005i
\(568\) −1635.88 + 1635.88i −0.120845 + 0.120845i
\(569\) −1142.29 1978.50i −0.0841603 0.145770i 0.820873 0.571111i \(-0.193487\pi\)
−0.905033 + 0.425341i \(0.860154\pi\)
\(570\) 0 0
\(571\) 9342.12 16181.0i 0.684686 1.18591i −0.288850 0.957375i \(-0.593273\pi\)
0.973535 0.228536i \(-0.0733939\pi\)
\(572\) 1718.15 + 6412.23i 0.125594 + 0.468722i
\(573\) −17771.6 11383.0i −1.29567 0.829900i
\(574\) −9428.20 + 5443.38i −0.685585 + 0.395823i
\(575\) 0 0
\(576\) −3401.14 2406.42i −0.246031 0.174075i
\(577\) 17462.0 + 17462.0i 1.25989 + 1.25989i 0.951146 + 0.308740i \(0.0999073\pi\)
0.308740 + 0.951146i \(0.400093\pi\)
\(578\) 1597.09 5960.42i 0.114931 0.428929i
\(579\) 9819.20 8953.49i 0.704787 0.642650i
\(580\) 0 0
\(581\) −33271.3 19209.2i −2.37578 1.37165i
\(582\) 2313.17 + 106.672i 0.164749 + 0.00759744i
\(583\) −3187.89 854.193i −0.226465 0.0606810i
\(584\) 13764.1 0.975277
\(585\) 0 0
\(586\) 10266.7 0.723743
\(587\) −22383.6 5997.68i −1.57389 0.421722i −0.636860 0.770980i \(-0.719767\pi\)
−0.937027 + 0.349258i \(0.886434\pi\)
\(588\) −5065.65 + 7908.67i −0.355279 + 0.554673i
\(589\) −676.712 390.700i −0.0473403 0.0273319i
\(590\) 0 0
\(591\) 9458.08 + 3007.61i 0.658297 + 0.209334i
\(592\) 895.924 3343.63i 0.0621997 0.232133i
\(593\) 13119.3 + 13119.3i 0.908505 + 0.908505i 0.996152 0.0876470i \(-0.0279347\pi\)
−0.0876470 + 0.996152i \(0.527935\pi\)
\(594\) 2849.03 353.804i 0.196796 0.0244389i
\(595\) 0 0
\(596\) −7645.39 + 4414.07i −0.525449 + 0.303368i
\(597\) 22569.6 11678.8i 1.54725 0.800639i
\(598\) −2476.30 9241.67i −0.169337 0.631973i
\(599\) −3451.75 + 5978.61i −0.235450 + 0.407812i −0.959403 0.282037i \(-0.908990\pi\)
0.723953 + 0.689849i \(0.242323\pi\)
\(600\) 0 0
\(601\) 9078.32 + 15724.1i 0.616161 + 1.06722i 0.990180 + 0.139801i \(0.0446462\pi\)
−0.374019 + 0.927421i \(0.622021\pi\)
\(602\) 3422.15 3422.15i 0.231689 0.231689i
\(603\) −8842.40 + 23928.9i −0.597165 + 1.61602i
\(604\) 2533.71i 0.170688i
\(605\) 0 0
\(606\) 435.425 + 477.526i 0.0291880 + 0.0320102i
\(607\) 7416.77 1987.32i 0.495943 0.132888i −0.00217355 0.999998i \(-0.500692\pi\)
0.498116 + 0.867110i \(0.334025\pi\)
\(608\) 4298.44 1151.76i 0.286719 0.0768260i
\(609\) 18593.3 + 20391.1i 1.23717 + 1.35679i
\(610\) 0 0
\(611\) 28800.9i 1.90697i
\(612\) −1502.57 + 4066.20i −0.0992450 + 0.268572i
\(613\) 13352.5 13352.5i 0.879776 0.879776i −0.113735 0.993511i \(-0.536282\pi\)
0.993511 + 0.113735i \(0.0362816\pi\)
\(614\) −1665.34 2884.45i −0.109459 0.189588i
\(615\) 0 0
\(616\) −3610.34 + 6253.29i −0.236144 + 0.409013i
\(617\) −3067.84 11449.3i −0.200172 0.747054i −0.990867 0.134843i \(-0.956947\pi\)
0.790695 0.612211i \(-0.209720\pi\)
\(618\) −1801.08 + 931.983i −0.117233 + 0.0606632i
\(619\) −6467.28 + 3733.89i −0.419939 + 0.242452i −0.695051 0.718960i \(-0.744618\pi\)
0.275112 + 0.961412i \(0.411285\pi\)
\(620\) 0 0
\(621\) 10690.1 1327.54i 0.690788 0.0857849i
\(622\) 1582.81 + 1582.81i 0.102033 + 0.102033i
\(623\) 3966.11 14801.7i 0.255054 0.951875i
\(624\) 6479.38 + 2060.40i 0.415677 + 0.132183i
\(625\) 0 0
\(626\) 5047.48 + 2914.17i 0.322265 + 0.186060i
\(627\) −913.177 + 1425.68i −0.0581639 + 0.0908075i
\(628\) 8509.81 + 2280.20i 0.540730 + 0.144888i
\(629\) 6145.61 0.389573
\(630\) 0 0
\(631\) 2875.59 0.181419 0.0907094 0.995877i \(-0.471087\pi\)
0.0907094 + 0.995877i \(0.471087\pi\)
\(632\) −6563.77 1758.76i −0.413121 0.110696i
\(633\) −15384.7 709.472i −0.966017 0.0445481i
\(634\) −4977.63 2873.83i −0.311809 0.180023i
\(635\) 0 0
\(636\) −5333.08 + 4862.89i −0.332500 + 0.303185i
\(637\) −6768.74 + 25261.3i −0.421016 + 1.57125i
\(638\) 3000.93 + 3000.93i 0.186219 + 0.186219i
\(639\) −2483.50 1757.16i −0.153749 0.108782i
\(640\) 0 0
\(641\) 3459.55 1997.37i 0.213173 0.123076i −0.389612 0.920979i \(-0.627391\pi\)
0.602785 + 0.797903i \(0.294058\pi\)
\(642\) 2567.09 + 1644.27i 0.157812 + 0.101081i
\(643\) 4499.32 + 16791.7i 0.275950 + 1.02986i 0.955202 + 0.295955i \(0.0956377\pi\)
−0.679252 + 0.733905i \(0.737696\pi\)
\(644\) −5682.08 + 9841.66i −0.347679 + 0.602198i
\(645\) 0 0
\(646\) 490.978 + 850.399i 0.0299029 + 0.0517934i
\(647\) 7322.01 7322.01i 0.444912 0.444912i −0.448747 0.893659i \(-0.648130\pi\)
0.893659 + 0.448747i \(0.148130\pi\)
\(648\) 6458.31 13502.9i 0.391522 0.818586i
\(649\) 6030.87i 0.364765i
\(650\) 0 0
\(651\) 1328.04 4176.30i 0.0799537 0.251432i
\(652\) 10636.4 2850.02i 0.638887 0.171189i
\(653\) −8188.49 + 2194.10i −0.490720 + 0.131488i −0.495690 0.868499i \(-0.665085\pi\)
0.00496957 + 0.999988i \(0.498418\pi\)
\(654\) 9315.77 2041.33i 0.556996 0.122053i
\(655\) 0 0
\(656\) 4464.39i 0.265709i
\(657\) 3055.67 + 17840.2i 0.181451 + 1.05938i
\(658\) −9291.31 + 9291.31i −0.550476 + 0.550476i
\(659\) −4605.68 7977.27i −0.272249 0.471548i 0.697189 0.716888i \(-0.254434\pi\)
−0.969437 + 0.245339i \(0.921101\pi\)
\(660\) 0 0
\(661\) 7007.31 12137.0i 0.412334 0.714183i −0.582811 0.812608i \(-0.698047\pi\)
0.995145 + 0.0984247i \(0.0313804\pi\)
\(662\) 2659.45 + 9925.20i 0.156137 + 0.582710i
\(663\) −556.064 + 12058.1i −0.0325727 + 0.706333i
\(664\) −26677.4 + 15402.2i −1.55917 + 0.900184i
\(665\) 0 0
\(666\) −8862.77 819.160i −0.515654 0.0476604i
\(667\) 11260.1 + 11260.1i 0.653661 + 0.653661i
\(668\) 176.720 659.529i 0.0102358 0.0382005i
\(669\) 2601.77 + 11873.4i 0.150359 + 0.686176i
\(670\) 0 0
\(671\) 3284.55 + 1896.34i 0.188970 + 0.109102i
\(672\) 11469.9 + 22165.8i 0.658423 + 1.27242i
\(673\) 14115.8 + 3782.31i 0.808503 + 0.216638i 0.639314 0.768946i \(-0.279218\pi\)
0.169189 + 0.985584i \(0.445885\pi\)
\(674\) −10202.9 −0.583086
\(675\) 0 0
\(676\) 27725.5 1.57746
\(677\) 17159.0 + 4597.75i 0.974113 + 0.261013i 0.710564 0.703633i \(-0.248440\pi\)
0.263550 + 0.964646i \(0.415107\pi\)
\(678\) −331.664 640.949i −0.0187868 0.0363060i
\(679\) −6632.67 3829.37i −0.374872 0.216433i
\(680\) 0 0
\(681\) −2279.88 10404.4i −0.128289 0.585459i
\(682\) 174.437 651.007i 0.00979404 0.0365519i
\(683\) −15195.5 15195.5i −0.851301 0.851301i 0.138993 0.990293i \(-0.455614\pi\)
−0.990293 + 0.138993i \(0.955614\pi\)
\(684\) 1548.26 + 3363.18i 0.0865487 + 0.188003i
\(685\) 0 0
\(686\) 1000.61 577.705i 0.0556904 0.0321529i
\(687\) −957.652 + 20766.5i −0.0531830 + 1.15326i
\(688\) 513.658 + 1917.00i 0.0284637 + 0.106228i
\(689\) −10048.5 + 17404.6i −0.555615 + 0.962353i
\(690\) 0 0
\(691\) −10015.8 17347.9i −0.551404 0.955060i −0.998174 0.0604108i \(-0.980759\pi\)
0.446770 0.894649i \(-0.352574\pi\)
\(692\) −2008.78 + 2008.78i −0.110350 + 0.110350i
\(693\) −8906.65 3291.25i −0.488219 0.180410i
\(694\) 401.213i 0.0219450i
\(695\) 0 0
\(696\) 21613.6 4736.11i 1.17710 0.257934i
\(697\) 7655.90 2051.39i 0.416051 0.111481i
\(698\) −13602.1 + 3644.68i −0.737605 + 0.197641i
\(699\) 10926.7 34361.3i 0.591251 1.85932i
\(700\) 0 0
\(701\) 16064.1i 0.865523i −0.901508 0.432762i \(-0.857539\pi\)
0.901508 0.432762i \(-0.142461\pi\)
\(702\) 2409.17 17315.3i 0.129527 0.930944i
\(703\) 3711.55 3711.55i 0.199123 0.199123i
\(704\) 1059.62 + 1835.31i 0.0567271 + 0.0982543i
\(705\) 0 0
\(706\) 264.230 457.660i 0.0140856 0.0243970i
\(707\) −553.196 2064.55i −0.0294273 0.109824i
\(708\) 11105.7 + 7113.39i 0.589514 + 0.377595i
\(709\) 15927.0 9195.47i 0.843656 0.487085i −0.0148496 0.999890i \(-0.504727\pi\)
0.858505 + 0.512805i \(0.171394\pi\)
\(710\) 0 0
\(711\) 822.417 8898.01i 0.0433798 0.469341i
\(712\) −8688.16 8688.16i −0.457307 0.457307i
\(713\) 654.522 2442.71i 0.0343788 0.128303i
\(714\) −4069.40 + 3710.63i −0.213296 + 0.194491i
\(715\) 0 0
\(716\) 3212.83 + 1854.93i 0.167694 + 0.0968184i
\(717\) −25966.1 1197.43i −1.35247 0.0623696i
\(718\) 3433.42 + 919.983i 0.178460 + 0.0478182i
\(719\) −4922.15 −0.255306 −0.127653 0.991819i \(-0.540744\pi\)
−0.127653 + 0.991819i \(0.540744\pi\)
\(720\) 0 0
\(721\) 6707.20 0.346448
\(722\) −9061.60 2428.05i −0.467088 0.125156i
\(723\) 10230.4 15972.0i 0.526239 0.821583i
\(724\) 6222.11 + 3592.34i 0.319396 + 0.184404i
\(725\) 0 0
\(726\) 8428.79 + 2680.30i 0.430884 + 0.137018i
\(727\) 3460.69 12915.5i 0.176547 0.658884i −0.819736 0.572742i \(-0.805880\pi\)
0.996283 0.0861414i \(-0.0274537\pi\)
\(728\) 31091.1 + 31091.1i 1.58285 + 1.58285i
\(729\) 18935.4 + 5373.19i 0.962018 + 0.272986i
\(730\) 0 0
\(731\) −3051.40 + 1761.73i −0.154391 + 0.0891379i
\(732\) 7366.17 3811.68i 0.371942 0.192464i
\(733\) 5253.09 + 19604.8i 0.264703 + 0.987886i 0.962432 + 0.271524i \(0.0875275\pi\)
−0.697729 + 0.716362i \(0.745806\pi\)
\(734\) −2473.09 + 4283.51i −0.124364 + 0.215405i
\(735\) 0 0
\(736\) 7200.99 + 12472.5i 0.360641 + 0.624649i
\(737\) 9175.40 9175.40i 0.458589 0.458589i
\(738\) −11314.2 + 1937.90i −0.564339 + 0.0966602i
\(739\) 21111.0i 1.05085i 0.850839 + 0.525427i \(0.176094\pi\)
−0.850839 + 0.525427i \(0.823906\pi\)
\(740\) 0 0
\(741\) 6946.50 + 7618.15i 0.344381 + 0.377679i
\(742\) −8856.51 + 2373.10i −0.438184 + 0.117411i
\(743\) −17034.6 + 4564.40i −0.841101 + 0.225372i −0.653551 0.756883i \(-0.726721\pi\)
−0.187550 + 0.982255i \(0.560055\pi\)
\(744\) −2367.57 2596.49i −0.116666 0.127946i
\(745\) 0 0
\(746\) 16336.5i 0.801771i
\(747\) −25885.9 31158.4i −1.26789 1.52614i
\(748\) 1559.16 1559.16i 0.0762146 0.0762146i
\(749\) −5041.40 8731.96i −0.245940 0.425980i
\(750\) 0 0
\(751\) −1012.62 + 1753.91i −0.0492023 + 0.0852210i −0.889578 0.456784i \(-0.849001\pi\)
0.840375 + 0.542005i \(0.182335\pi\)
\(752\) −1394.61 5204.74i −0.0676278 0.252390i
\(753\) 16443.3 8508.69i 0.795785 0.411785i
\(754\) 22380.7 12921.5i 1.08098 0.624103i
\(755\) 0 0
\(756\) −16566.1 + 12519.3i −0.796962 + 0.602278i
\(757\) −314.843 314.843i −0.0151164 0.0151164i 0.699508 0.714625i \(-0.253402\pi\)
−0.714625 + 0.699508i \(0.753402\pi\)
\(758\) 516.943 1929.26i 0.0247707 0.0924456i
\(759\) −5221.69 1660.46i −0.249717 0.0794085i
\(760\) 0 0
\(761\) 8783.13 + 5070.94i 0.418381 + 0.241553i 0.694385 0.719604i \(-0.255677\pi\)
−0.276003 + 0.961157i \(0.589010\pi\)
\(762\) 2330.92 3639.11i 0.110814 0.173007i
\(763\) −30467.4 8163.72i −1.44560 0.387348i
\(764\) 23475.4 1.11166
\(765\) 0 0
\(766\) −21204.4 −1.00019
\(767\) 35472.9 + 9504.93i 1.66995 + 0.447462i
\(768\) 16234.9 + 748.677i 0.762795 + 0.0351765i
\(769\) −11311.9 6530.95i −0.530454 0.306258i 0.210748 0.977541i \(-0.432410\pi\)
−0.741201 + 0.671283i \(0.765744\pi\)
\(770\) 0 0
\(771\) −26486.0 + 24150.9i −1.23719 + 1.12811i
\(772\) −3825.66 + 14277.6i −0.178353 + 0.665623i
\(773\) −17678.7 17678.7i −0.822587 0.822587i 0.163891 0.986478i \(-0.447595\pi\)
−0.986478 + 0.163891i \(0.947595\pi\)
\(774\) 4635.34 2133.91i 0.215263 0.0990980i
\(775\) 0 0
\(776\) −5318.18 + 3070.45i −0.246020 + 0.142040i
\(777\) 24788.8 + 15877.7i 1.14452 + 0.733088i
\(778\) −4580.83 17095.9i −0.211093 0.787812i
\(779\) 3384.76 5862.57i 0.155676 0.269638i
\(780\) 0