Properties

Label 336.4.bc.d.257.5
Level $336$
Weight $4$
Character 336.257
Analytic conductor $19.825$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} - 29 x^{9} + 6 x^{8} - 49 x^{7} + 1564 x^{6} - 441 x^{5} + 486 x^{4} - 21141 x^{3} - 59049 x + 531441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.5
Root \(2.85284 - 0.928053i\) of defining polynomial
Character \(\chi\) \(=\) 336.257
Dual form 336.4.bc.d.17.5

$q$-expansion

\(f(q)\) \(=\) \(q+(3.47555 + 3.86271i) q^{3} +(0.623706 - 1.08029i) q^{5} +(-10.0808 + 15.5363i) q^{7} +(-2.84113 + 26.8501i) q^{9} +O(q^{10})\) \(q+(3.47555 + 3.86271i) q^{3} +(0.623706 - 1.08029i) q^{5} +(-10.0808 + 15.5363i) q^{7} +(-2.84113 + 26.8501i) q^{9} +(-35.2392 + 20.3453i) q^{11} -19.5973i q^{13} +(6.34057 - 1.34540i) q^{15} +(-52.3592 - 90.6889i) q^{17} +(-35.0345 - 20.2272i) q^{19} +(-95.0487 + 15.0578i) q^{21} +(-69.6324 - 40.2023i) q^{23} +(61.7220 + 106.906i) q^{25} +(-113.589 + 82.3444i) q^{27} +211.712i q^{29} +(86.6242 - 50.0125i) q^{31} +(-201.064 - 65.4076i) q^{33} +(10.4962 + 20.5803i) q^{35} +(94.9875 - 164.523i) q^{37} +(75.6987 - 68.1113i) q^{39} -186.753 q^{41} -158.618 q^{43} +(27.2339 + 19.8158i) q^{45} +(-179.034 + 310.097i) q^{47} +(-139.753 - 313.238i) q^{49} +(168.328 - 517.442i) q^{51} +(-366.460 + 211.576i) q^{53} +50.7580i q^{55} +(-43.6323 - 205.629i) q^{57} +(-312.781 - 541.753i) q^{59} +(699.575 + 403.900i) q^{61} +(-388.510 - 314.812i) q^{63} +(-21.1708 - 12.2229i) q^{65} +(149.272 + 258.547i) q^{67} +(-86.7208 - 408.695i) q^{69} +455.386i q^{71} +(-434.467 + 250.840i) q^{73} +(-198.428 + 609.970i) q^{75} +(39.1491 - 752.584i) q^{77} +(-30.9561 + 53.6176i) q^{79} +(-712.856 - 152.569i) q^{81} +73.1180 q^{83} -130.627 q^{85} +(-817.783 + 735.816i) q^{87} +(57.3723 - 99.3717i) q^{89} +(304.469 + 197.557i) q^{91} +(494.251 + 160.784i) q^{93} +(-43.7025 + 25.2316i) q^{95} +1416.51i q^{97} +(-446.156 - 1003.98i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} + O(q^{10}) \) \( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) 3.47555 + 3.86271i 0.668870 + 0.743380i
\(4\) 0 0
\(5\) 0.623706 1.08029i 0.0557859 0.0966240i −0.836784 0.547533i \(-0.815567\pi\)
0.892570 + 0.450909i \(0.148900\pi\)
\(6\) 0 0
\(7\) −10.0808 + 15.5363i −0.544314 + 0.838881i
\(8\) 0 0
\(9\) −2.84113 + 26.8501i −0.105227 + 0.994448i
\(10\) 0 0
\(11\) −35.2392 + 20.3453i −0.965910 + 0.557668i −0.897987 0.440022i \(-0.854971\pi\)
−0.0679230 + 0.997691i \(0.521637\pi\)
\(12\) 0 0
\(13\) 19.5973i 0.418101i −0.977905 0.209050i \(-0.932963\pi\)
0.977905 0.209050i \(-0.0670373\pi\)
\(14\) 0 0
\(15\) 6.34057 1.34540i 0.109142 0.0231588i
\(16\) 0 0
\(17\) −52.3592 90.6889i −0.746999 1.29384i −0.949255 0.314507i \(-0.898161\pi\)
0.202256 0.979333i \(-0.435173\pi\)
\(18\) 0 0
\(19\) −35.0345 20.2272i −0.423025 0.244234i 0.273346 0.961916i \(-0.411870\pi\)
−0.696371 + 0.717682i \(0.745203\pi\)
\(20\) 0 0
\(21\) −95.0487 + 15.0578i −0.987683 + 0.156470i
\(22\) 0 0
\(23\) −69.6324 40.2023i −0.631276 0.364467i 0.149970 0.988691i \(-0.452082\pi\)
−0.781246 + 0.624223i \(0.785416\pi\)
\(24\) 0 0
\(25\) 61.7220 + 106.906i 0.493776 + 0.855245i
\(26\) 0 0
\(27\) −113.589 + 82.3444i −0.809636 + 0.586933i
\(28\) 0 0
\(29\) 211.712i 1.35565i 0.735222 + 0.677827i \(0.237078\pi\)
−0.735222 + 0.677827i \(0.762922\pi\)
\(30\) 0 0
\(31\) 86.6242 50.0125i 0.501876 0.289758i −0.227612 0.973752i \(-0.573092\pi\)
0.729488 + 0.683994i \(0.239758\pi\)
\(32\) 0 0
\(33\) −201.064 65.4076i −1.06063 0.345030i
\(34\) 0 0
\(35\) 10.4962 + 20.5803i 0.0506910 + 0.0993916i
\(36\) 0 0
\(37\) 94.9875 164.523i 0.422050 0.731012i −0.574090 0.818792i \(-0.694644\pi\)
0.996140 + 0.0877801i \(0.0279773\pi\)
\(38\) 0 0
\(39\) 75.6987 68.1113i 0.310808 0.279655i
\(40\) 0 0
\(41\) −186.753 −0.711362 −0.355681 0.934607i \(-0.615751\pi\)
−0.355681 + 0.934607i \(0.615751\pi\)
\(42\) 0 0
\(43\) −158.618 −0.562536 −0.281268 0.959629i \(-0.590755\pi\)
−0.281268 + 0.959629i \(0.590755\pi\)
\(44\) 0 0
\(45\) 27.2339 + 19.8158i 0.0902174 + 0.0656437i
\(46\) 0 0
\(47\) −179.034 + 310.097i −0.555635 + 0.962388i 0.442219 + 0.896907i \(0.354191\pi\)
−0.997854 + 0.0654808i \(0.979142\pi\)
\(48\) 0 0
\(49\) −139.753 313.238i −0.407444 0.913230i
\(50\) 0 0
\(51\) 168.328 517.442i 0.462170 1.42071i
\(52\) 0 0
\(53\) −366.460 + 211.576i −0.949758 + 0.548343i −0.893006 0.450045i \(-0.851408\pi\)
−0.0567521 + 0.998388i \(0.518074\pi\)
\(54\) 0 0
\(55\) 50.7580i 0.124440i
\(56\) 0 0
\(57\) −43.6323 205.629i −0.101390 0.477829i
\(58\) 0 0
\(59\) −312.781 541.753i −0.690180 1.19543i −0.971779 0.235895i \(-0.924198\pi\)
0.281599 0.959532i \(-0.409135\pi\)
\(60\) 0 0
\(61\) 699.575 + 403.900i 1.46838 + 0.847772i 0.999372 0.0354209i \(-0.0112772\pi\)
0.469011 + 0.883192i \(0.344611\pi\)
\(62\) 0 0
\(63\) −388.510 314.812i −0.776948 0.629565i
\(64\) 0 0
\(65\) −21.1708 12.2229i −0.0403986 0.0233241i
\(66\) 0 0
\(67\) 149.272 + 258.547i 0.272187 + 0.471441i 0.969421 0.245402i \(-0.0789199\pi\)
−0.697235 + 0.716843i \(0.745587\pi\)
\(68\) 0 0
\(69\) −86.7208 408.695i −0.151304 0.713059i
\(70\) 0 0
\(71\) 455.386i 0.761189i 0.924742 + 0.380594i \(0.124281\pi\)
−0.924742 + 0.380594i \(0.875719\pi\)
\(72\) 0 0
\(73\) −434.467 + 250.840i −0.696582 + 0.402172i −0.806073 0.591816i \(-0.798411\pi\)
0.109491 + 0.993988i \(0.465078\pi\)
\(74\) 0 0
\(75\) −198.428 + 609.970i −0.305500 + 0.939110i
\(76\) 0 0
\(77\) 39.1491 752.584i 0.0579410 1.11383i
\(78\) 0 0
\(79\) −30.9561 + 53.6176i −0.0440865 + 0.0763601i −0.887227 0.461334i \(-0.847371\pi\)
0.843140 + 0.537694i \(0.180704\pi\)
\(80\) 0 0
\(81\) −712.856 152.569i −0.977855 0.209285i
\(82\) 0 0
\(83\) 73.1180 0.0966957 0.0483478 0.998831i \(-0.484604\pi\)
0.0483478 + 0.998831i \(0.484604\pi\)
\(84\) 0 0
\(85\) −130.627 −0.166688
\(86\) 0 0
\(87\) −817.783 + 735.816i −1.00777 + 0.906755i
\(88\) 0 0
\(89\) 57.3723 99.3717i 0.0683309 0.118353i −0.829836 0.558008i \(-0.811566\pi\)
0.898167 + 0.439655i \(0.144899\pi\)
\(90\) 0 0
\(91\) 304.469 + 197.557i 0.350737 + 0.227578i
\(92\) 0 0
\(93\) 494.251 + 160.784i 0.551090 + 0.179274i
\(94\) 0 0
\(95\) −43.7025 + 25.2316i −0.0471977 + 0.0272496i
\(96\) 0 0
\(97\) 1416.51i 1.48273i 0.671101 + 0.741366i \(0.265822\pi\)
−0.671101 + 0.741366i \(0.734178\pi\)
\(98\) 0 0
\(99\) −446.156 1003.98i −0.452933 1.01923i
\(100\) 0 0
\(101\) 120.406 + 208.549i 0.118622 + 0.205459i 0.919222 0.393740i \(-0.128819\pi\)
−0.800600 + 0.599199i \(0.795486\pi\)
\(102\) 0 0
\(103\) 960.453 + 554.518i 0.918799 + 0.530469i 0.883252 0.468899i \(-0.155349\pi\)
0.0355471 + 0.999368i \(0.488683\pi\)
\(104\) 0 0
\(105\) −43.0157 + 112.072i −0.0399800 + 0.104163i
\(106\) 0 0
\(107\) −924.644 533.843i −0.835408 0.482323i 0.0202926 0.999794i \(-0.493540\pi\)
−0.855701 + 0.517471i \(0.826874\pi\)
\(108\) 0 0
\(109\) −5.04376 8.73604i −0.00443215 0.00767671i 0.863801 0.503833i \(-0.168077\pi\)
−0.868233 + 0.496157i \(0.834744\pi\)
\(110\) 0 0
\(111\) 965.640 204.899i 0.825716 0.175208i
\(112\) 0 0
\(113\) 884.294i 0.736171i 0.929792 + 0.368086i \(0.119987\pi\)
−0.929792 + 0.368086i \(0.880013\pi\)
\(114\) 0 0
\(115\) −86.8602 + 50.1487i −0.0704326 + 0.0406643i
\(116\) 0 0
\(117\) 526.189 + 55.6784i 0.415780 + 0.0439954i
\(118\) 0 0
\(119\) 1936.79 + 100.751i 1.49198 + 0.0776122i
\(120\) 0 0
\(121\) 162.366 281.226i 0.121988 0.211289i
\(122\) 0 0
\(123\) −649.067 721.372i −0.475808 0.528812i
\(124\) 0 0
\(125\) 309.912 0.221755
\(126\) 0 0
\(127\) 840.132 0.587005 0.293503 0.955958i \(-0.405179\pi\)
0.293503 + 0.955958i \(0.405179\pi\)
\(128\) 0 0
\(129\) −551.285 612.697i −0.376263 0.418178i
\(130\) 0 0
\(131\) 258.951 448.517i 0.172707 0.299138i −0.766658 0.642056i \(-0.778082\pi\)
0.939366 + 0.342918i \(0.111415\pi\)
\(132\) 0 0
\(133\) 667.434 340.400i 0.435142 0.221928i
\(134\) 0 0
\(135\) 18.1098 + 174.067i 0.0115455 + 0.110973i
\(136\) 0 0
\(137\) 950.957 549.035i 0.593034 0.342389i −0.173262 0.984876i \(-0.555431\pi\)
0.766296 + 0.642487i \(0.222097\pi\)
\(138\) 0 0
\(139\) 828.268i 0.505416i 0.967543 + 0.252708i \(0.0813212\pi\)
−0.967543 + 0.252708i \(0.918679\pi\)
\(140\) 0 0
\(141\) −1820.06 + 386.197i −1.08707 + 0.230664i
\(142\) 0 0
\(143\) 398.714 + 690.592i 0.233162 + 0.403848i
\(144\) 0 0
\(145\) 228.710 + 132.046i 0.130989 + 0.0756264i
\(146\) 0 0
\(147\) 724.230 1628.50i 0.406350 0.913717i
\(148\) 0 0
\(149\) 773.007 + 446.296i 0.425015 + 0.245382i 0.697221 0.716857i \(-0.254420\pi\)
−0.272206 + 0.962239i \(0.587753\pi\)
\(150\) 0 0
\(151\) 712.518 + 1234.12i 0.383999 + 0.665106i 0.991630 0.129113i \(-0.0412131\pi\)
−0.607630 + 0.794220i \(0.707880\pi\)
\(152\) 0 0
\(153\) 2583.76 1148.19i 1.36526 0.606705i
\(154\) 0 0
\(155\) 124.772i 0.0646577i
\(156\) 0 0
\(157\) −244.872 + 141.377i −0.124477 + 0.0718670i −0.560946 0.827853i \(-0.689562\pi\)
0.436468 + 0.899720i \(0.356229\pi\)
\(158\) 0 0
\(159\) −2090.91 680.189i −1.04289 0.339261i
\(160\) 0 0
\(161\) 1326.55 676.557i 0.649358 0.331181i
\(162\) 0 0
\(163\) 1158.07 2005.83i 0.556484 0.963858i −0.441303 0.897358i \(-0.645484\pi\)
0.997786 0.0664997i \(-0.0211832\pi\)
\(164\) 0 0
\(165\) −196.064 + 176.412i −0.0925063 + 0.0832342i
\(166\) 0 0
\(167\) 2344.70 1.08646 0.543229 0.839585i \(-0.317202\pi\)
0.543229 + 0.839585i \(0.317202\pi\)
\(168\) 0 0
\(169\) 1812.95 0.825192
\(170\) 0 0
\(171\) 642.640 883.213i 0.287391 0.394977i
\(172\) 0 0
\(173\) 516.901 895.298i 0.227163 0.393458i −0.729803 0.683657i \(-0.760388\pi\)
0.956966 + 0.290199i \(0.0937216\pi\)
\(174\) 0 0
\(175\) −2283.13 118.767i −0.986218 0.0513026i
\(176\) 0 0
\(177\) 1005.55 3091.07i 0.427016 1.31265i
\(178\) 0 0
\(179\) 125.472 72.4412i 0.0523922 0.0302486i −0.473575 0.880753i \(-0.657037\pi\)
0.525967 + 0.850505i \(0.323703\pi\)
\(180\) 0 0
\(181\) 2057.17i 0.844797i 0.906410 + 0.422398i \(0.138812\pi\)
−0.906410 + 0.422398i \(0.861188\pi\)
\(182\) 0 0
\(183\) 871.257 + 4106.03i 0.351941 + 1.65862i
\(184\) 0 0
\(185\) −118.489 205.228i −0.0470889 0.0815604i
\(186\) 0 0
\(187\) 3690.19 + 2130.53i 1.44307 + 0.833155i
\(188\) 0 0
\(189\) −134.257 2594.85i −0.0516706 0.998664i
\(190\) 0 0
\(191\) 2553.66 + 1474.36i 0.967417 + 0.558538i 0.898448 0.439080i \(-0.144696\pi\)
0.0689690 + 0.997619i \(0.478029\pi\)
\(192\) 0 0
\(193\) 1135.40 + 1966.57i 0.423460 + 0.733455i 0.996275 0.0862300i \(-0.0274820\pi\)
−0.572815 + 0.819685i \(0.694149\pi\)
\(194\) 0 0
\(195\) −26.3662 124.258i −0.00968270 0.0456323i
\(196\) 0 0
\(197\) 495.849i 0.179329i 0.995972 + 0.0896645i \(0.0285795\pi\)
−0.995972 + 0.0896645i \(0.971421\pi\)
\(198\) 0 0
\(199\) −727.207 + 419.853i −0.259047 + 0.149561i −0.623900 0.781504i \(-0.714453\pi\)
0.364853 + 0.931065i \(0.381119\pi\)
\(200\) 0 0
\(201\) −479.890 + 1475.19i −0.168402 + 0.517670i
\(202\) 0 0
\(203\) −3289.22 2134.24i −1.13723 0.737902i
\(204\) 0 0
\(205\) −116.479 + 201.747i −0.0396840 + 0.0687347i
\(206\) 0 0
\(207\) 1277.27 1755.42i 0.428871 0.589420i
\(208\) 0 0
\(209\) 1646.12 0.544805
\(210\) 0 0
\(211\) −4001.71 −1.30564 −0.652818 0.757514i \(-0.726414\pi\)
−0.652818 + 0.757514i \(0.726414\pi\)
\(212\) 0 0
\(213\) −1759.03 + 1582.72i −0.565852 + 0.509136i
\(214\) 0 0
\(215\) −98.9311 + 171.354i −0.0313816 + 0.0543545i
\(216\) 0 0
\(217\) −96.2355 + 1849.99i −0.0301055 + 0.578734i
\(218\) 0 0
\(219\) −2478.93 806.416i −0.764889 0.248825i
\(220\) 0 0
\(221\) −1777.26 + 1026.10i −0.540955 + 0.312321i
\(222\) 0 0
\(223\) 3040.54i 0.913047i 0.889711 + 0.456523i \(0.150905\pi\)
−0.889711 + 0.456523i \(0.849095\pi\)
\(224\) 0 0
\(225\) −3045.79 + 1353.51i −0.902455 + 0.401040i
\(226\) 0 0
\(227\) −2198.24 3807.46i −0.642741 1.11326i −0.984818 0.173588i \(-0.944464\pi\)
0.342078 0.939672i \(-0.388869\pi\)
\(228\) 0 0
\(229\) −1717.81 991.778i −0.495703 0.286194i 0.231234 0.972898i \(-0.425724\pi\)
−0.726937 + 0.686704i \(0.759057\pi\)
\(230\) 0 0
\(231\) 3043.08 2464.42i 0.866754 0.701935i
\(232\) 0 0
\(233\) −3787.78 2186.87i −1.06500 0.614879i −0.138191 0.990406i \(-0.544129\pi\)
−0.926812 + 0.375526i \(0.877462\pi\)
\(234\) 0 0
\(235\) 223.329 + 386.818i 0.0619932 + 0.107375i
\(236\) 0 0
\(237\) −314.699 + 66.7758i −0.0862527 + 0.0183019i
\(238\) 0 0
\(239\) 3826.41i 1.03561i 0.855500 + 0.517803i \(0.173250\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(240\) 0 0
\(241\) 2979.03 1719.94i 0.796250 0.459715i −0.0459083 0.998946i \(-0.514618\pi\)
0.842158 + 0.539231i \(0.181285\pi\)
\(242\) 0 0
\(243\) −1888.24 3283.82i −0.498479 0.866902i
\(244\) 0 0
\(245\) −425.553 44.3943i −0.110970 0.0115765i
\(246\) 0 0
\(247\) −396.398 + 686.582i −0.102114 + 0.176867i
\(248\) 0 0
\(249\) 254.125 + 282.434i 0.0646768 + 0.0718816i
\(250\) 0 0
\(251\) 2046.61 0.514664 0.257332 0.966323i \(-0.417157\pi\)
0.257332 + 0.966323i \(0.417157\pi\)
\(252\) 0 0
\(253\) 3271.72 0.813008
\(254\) 0 0
\(255\) −454.000 504.575i −0.111493 0.123913i
\(256\) 0 0
\(257\) −3025.57 + 5240.44i −0.734357 + 1.27194i 0.220648 + 0.975354i \(0.429183\pi\)
−0.955005 + 0.296590i \(0.904150\pi\)
\(258\) 0 0
\(259\) 1598.53 + 3134.29i 0.383505 + 0.751950i
\(260\) 0 0
\(261\) −5684.49 601.501i −1.34813 0.142651i
\(262\) 0 0
\(263\) −5433.69 + 3137.14i −1.27398 + 0.735530i −0.975734 0.218960i \(-0.929733\pi\)
−0.298242 + 0.954490i \(0.596400\pi\)
\(264\) 0 0
\(265\) 527.844i 0.122359i
\(266\) 0 0
\(267\) 583.245 123.758i 0.133685 0.0283666i
\(268\) 0 0
\(269\) −1668.18 2889.37i −0.378106 0.654899i 0.612681 0.790331i \(-0.290091\pi\)
−0.990787 + 0.135432i \(0.956758\pi\)
\(270\) 0 0
\(271\) −2462.26 1421.59i −0.551925 0.318654i 0.197973 0.980207i \(-0.436564\pi\)
−0.749898 + 0.661553i \(0.769897\pi\)
\(272\) 0 0
\(273\) 295.091 + 1862.70i 0.0654202 + 0.412951i
\(274\) 0 0
\(275\) −4350.06 2511.51i −0.953886 0.550726i
\(276\) 0 0
\(277\) −3174.17 5497.82i −0.688510 1.19253i −0.972320 0.233654i \(-0.924932\pi\)
0.283809 0.958881i \(-0.408402\pi\)
\(278\) 0 0
\(279\) 1096.73 + 2467.96i 0.235339 + 0.529580i
\(280\) 0 0
\(281\) 3735.88i 0.793110i 0.918011 + 0.396555i \(0.129794\pi\)
−0.918011 + 0.396555i \(0.870206\pi\)
\(282\) 0 0
\(283\) 4777.96 2758.56i 1.00361 0.579432i 0.0942927 0.995545i \(-0.469941\pi\)
0.909313 + 0.416112i \(0.136608\pi\)
\(284\) 0 0
\(285\) −249.353 81.1164i −0.0518259 0.0168594i
\(286\) 0 0
\(287\) 1882.62 2901.44i 0.387205 0.596748i
\(288\) 0 0
\(289\) −3026.48 + 5242.01i −0.616014 + 1.06697i
\(290\) 0 0
\(291\) −5471.58 + 4923.16i −1.10223 + 0.991755i
\(292\) 0 0
\(293\) 7574.50 1.51026 0.755131 0.655574i \(-0.227573\pi\)
0.755131 + 0.655574i \(0.227573\pi\)
\(294\) 0 0
\(295\) −780.333 −0.154009
\(296\) 0 0
\(297\) 2327.45 5212.75i 0.454721 1.01843i
\(298\) 0 0
\(299\) −787.855 + 1364.61i −0.152384 + 0.263937i
\(300\) 0 0
\(301\) 1599.01 2464.34i 0.306196 0.471901i
\(302\) 0 0
\(303\) −387.088 + 1189.91i −0.0733915 + 0.225606i
\(304\) 0 0
\(305\) 872.657 503.829i 0.163830 0.0945874i
\(306\) 0 0
\(307\) 10635.6i 1.97723i −0.150480 0.988613i \(-0.548082\pi\)
0.150480 0.988613i \(-0.451918\pi\)
\(308\) 0 0
\(309\) 1196.16 + 5637.21i 0.220217 + 1.03783i
\(310\) 0 0
\(311\) 2885.59 + 4997.99i 0.526132 + 0.911287i 0.999537 + 0.0304419i \(0.00969146\pi\)
−0.473405 + 0.880845i \(0.656975\pi\)
\(312\) 0 0
\(313\) −2030.41 1172.26i −0.366664 0.211694i 0.305336 0.952245i \(-0.401231\pi\)
−0.672000 + 0.740551i \(0.734565\pi\)
\(314\) 0 0
\(315\) −582.404 + 223.354i −0.104174 + 0.0399509i
\(316\) 0 0
\(317\) −6852.10 3956.06i −1.21405 0.700929i −0.250407 0.968141i \(-0.580565\pi\)
−0.963638 + 0.267211i \(0.913898\pi\)
\(318\) 0 0
\(319\) −4307.36 7460.56i −0.756005 1.30944i
\(320\) 0 0
\(321\) −1151.56 5427.03i −0.200230 0.943637i
\(322\) 0 0
\(323\) 4236.32i 0.729769i
\(324\) 0 0
\(325\) 2095.06 1209.58i 0.357579 0.206448i
\(326\) 0 0
\(327\) 16.2150 49.8451i 0.00274218 0.00842949i
\(328\) 0 0
\(329\) −3012.94 5907.57i −0.504889 0.989953i
\(330\) 0 0
\(331\) −2440.02 + 4226.23i −0.405182 + 0.701797i −0.994343 0.106220i \(-0.966125\pi\)
0.589160 + 0.808016i \(0.299459\pi\)
\(332\) 0 0
\(333\) 4147.59 + 3017.86i 0.682543 + 0.496629i
\(334\) 0 0
\(335\) 372.407 0.0607367
\(336\) 0 0
\(337\) −4136.39 −0.668616 −0.334308 0.942464i \(-0.608503\pi\)
−0.334308 + 0.942464i \(0.608503\pi\)
\(338\) 0 0
\(339\) −3415.77 + 3073.41i −0.547255 + 0.492403i
\(340\) 0 0
\(341\) −2035.04 + 3524.80i −0.323178 + 0.559761i
\(342\) 0 0
\(343\) 6275.39 + 986.454i 0.987869 + 0.155287i
\(344\) 0 0
\(345\) −495.597 161.222i −0.0773393 0.0251591i
\(346\) 0 0
\(347\) −2009.83 + 1160.38i −0.310933 + 0.179517i −0.647344 0.762198i \(-0.724120\pi\)
0.336411 + 0.941715i \(0.390787\pi\)
\(348\) 0 0
\(349\) 226.795i 0.0347853i 0.999849 + 0.0173926i \(0.00553653\pi\)
−0.999849 + 0.0173926i \(0.994463\pi\)
\(350\) 0 0
\(351\) 1613.73 + 2226.03i 0.245397 + 0.338509i
\(352\) 0 0
\(353\) 742.854 + 1286.66i 0.112006 + 0.194000i 0.916579 0.399854i \(-0.130939\pi\)
−0.804573 + 0.593854i \(0.797606\pi\)
\(354\) 0 0
\(355\) 491.949 + 284.027i 0.0735491 + 0.0424636i
\(356\) 0 0
\(357\) 6342.25 + 7831.45i 0.940245 + 1.16102i
\(358\) 0 0
\(359\) −9419.94 5438.60i −1.38486 0.799550i −0.392131 0.919909i \(-0.628262\pi\)
−0.992730 + 0.120359i \(0.961595\pi\)
\(360\) 0 0
\(361\) −2611.22 4522.77i −0.380700 0.659392i
\(362\) 0 0
\(363\) 1650.61 350.241i 0.238662 0.0506416i
\(364\) 0 0
\(365\) 625.800i 0.0897421i
\(366\) 0 0
\(367\) 3299.69 1905.08i 0.469325 0.270965i −0.246632 0.969109i \(-0.579324\pi\)
0.715957 + 0.698144i \(0.245991\pi\)
\(368\) 0 0
\(369\) 530.587 5014.32i 0.0748544 0.707413i
\(370\) 0 0
\(371\) 407.121 7826.30i 0.0569721 1.09521i
\(372\) 0 0
\(373\) 4869.55 8434.30i 0.675967 1.17081i −0.300219 0.953870i \(-0.597060\pi\)
0.976185 0.216938i \(-0.0696070\pi\)
\(374\) 0 0
\(375\) 1077.11 + 1197.10i 0.148325 + 0.164848i
\(376\) 0 0
\(377\) 4148.98 0.566800
\(378\) 0 0
\(379\) −320.171 −0.0433933 −0.0216967 0.999765i \(-0.506907\pi\)
−0.0216967 + 0.999765i \(0.506907\pi\)
\(380\) 0 0
\(381\) 2919.92 + 3245.19i 0.392630 + 0.436368i
\(382\) 0 0
\(383\) 2185.13 3784.75i 0.291527 0.504939i −0.682644 0.730751i \(-0.739170\pi\)
0.974171 + 0.225812i \(0.0725034\pi\)
\(384\) 0 0
\(385\) −788.592 511.683i −0.104391 0.0677346i
\(386\) 0 0
\(387\) 450.654 4258.92i 0.0591939 0.559413i
\(388\) 0 0
\(389\) −11877.4 + 6857.42i −1.54809 + 0.893791i −0.549805 + 0.835293i \(0.685298\pi\)
−0.998288 + 0.0584981i \(0.981369\pi\)
\(390\) 0 0
\(391\) 8419.84i 1.08903i
\(392\) 0 0
\(393\) 2632.49 558.587i 0.337892 0.0716971i
\(394\) 0 0
\(395\) 38.6150 + 66.8832i 0.00491882 + 0.00851964i
\(396\) 0 0
\(397\) −2181.61 1259.55i −0.275798 0.159232i 0.355722 0.934592i \(-0.384235\pi\)
−0.631520 + 0.775360i \(0.717568\pi\)
\(398\) 0 0
\(399\) 3634.57 + 1395.03i 0.456030 + 0.175035i
\(400\) 0 0
\(401\) −2268.96 1309.98i −0.282560 0.163136i 0.352022 0.935992i \(-0.385494\pi\)
−0.634582 + 0.772856i \(0.718828\pi\)
\(402\) 0 0
\(403\) −980.109 1697.60i −0.121148 0.209835i
\(404\) 0 0
\(405\) −609.431 + 674.933i −0.0747725 + 0.0828091i
\(406\) 0 0
\(407\) 7730.22i 0.941456i
\(408\) 0 0
\(409\) −12058.7 + 6962.09i −1.45786 + 0.841694i −0.998906 0.0467669i \(-0.985108\pi\)
−0.458952 + 0.888461i \(0.651775\pi\)
\(410\) 0 0
\(411\) 5425.86 + 1765.08i 0.651187 + 0.211836i
\(412\) 0 0
\(413\) 11569.9 + 601.863i 1.37850 + 0.0717088i
\(414\) 0 0
\(415\) 45.6041 78.9886i 0.00539426 0.00934313i
\(416\) 0 0
\(417\) −3199.36 + 2878.69i −0.375716 + 0.338057i
\(418\) 0 0
\(419\) 15171.1 1.76887 0.884433 0.466666i \(-0.154545\pi\)
0.884433 + 0.466666i \(0.154545\pi\)
\(420\) 0 0
\(421\) −1052.53 −0.121846 −0.0609228 0.998142i \(-0.519404\pi\)
−0.0609228 + 0.998142i \(0.519404\pi\)
\(422\) 0 0
\(423\) −7817.47 5688.11i −0.898577 0.653819i
\(424\) 0 0
\(425\) 6463.43 11195.0i 0.737700 1.27773i
\(426\) 0 0
\(427\) −13327.4 + 6797.16i −1.51044 + 0.770345i
\(428\) 0 0
\(429\) −1281.81 + 3940.30i −0.144258 + 0.443449i
\(430\) 0 0
\(431\) 6923.58 3997.33i 0.773776 0.446740i −0.0604442 0.998172i \(-0.519252\pi\)
0.834220 + 0.551432i \(0.185918\pi\)
\(432\) 0 0
\(433\) 12889.4i 1.43055i 0.698845 + 0.715273i \(0.253697\pi\)
−0.698845 + 0.715273i \(0.746303\pi\)
\(434\) 0 0
\(435\) 284.838 + 1342.38i 0.0313953 + 0.147959i
\(436\) 0 0
\(437\) 1626.36 + 2816.94i 0.178030 + 0.308358i
\(438\) 0 0
\(439\) −12456.7 7191.89i −1.35427 0.781891i −0.365430 0.930839i \(-0.619078\pi\)
−0.988845 + 0.148948i \(0.952411\pi\)
\(440\) 0 0
\(441\) 8807.53 2862.44i 0.951034 0.309085i
\(442\) 0 0
\(443\) 3432.16 + 1981.56i 0.368097 + 0.212521i 0.672627 0.739982i \(-0.265166\pi\)
−0.304530 + 0.952503i \(0.598499\pi\)
\(444\) 0 0
\(445\) −71.5668 123.957i −0.00762380 0.0132048i
\(446\) 0 0
\(447\) 962.710 + 4537.03i 0.101867 + 0.480076i
\(448\) 0 0
\(449\) 13479.1i 1.41675i 0.705838 + 0.708373i \(0.250570\pi\)
−0.705838 + 0.708373i \(0.749430\pi\)
\(450\) 0 0
\(451\) 6581.00 3799.54i 0.687112 0.396704i
\(452\) 0 0
\(453\) −2290.65 + 7041.49i −0.237581 + 0.730327i
\(454\) 0 0
\(455\) 403.318 205.698i 0.0415557 0.0211940i
\(456\) 0 0
\(457\) −1989.79 + 3446.42i −0.203673 + 0.352772i −0.949709 0.313134i \(-0.898621\pi\)
0.746036 + 0.665905i \(0.231955\pi\)
\(458\) 0 0
\(459\) 13415.1 + 5989.74i 1.36419 + 0.609101i
\(460\) 0 0
\(461\) 9053.72 0.914694 0.457347 0.889288i \(-0.348800\pi\)
0.457347 + 0.889288i \(0.348800\pi\)
\(462\) 0 0
\(463\) 5736.10 0.575764 0.287882 0.957666i \(-0.407049\pi\)
0.287882 + 0.957666i \(0.407049\pi\)
\(464\) 0 0
\(465\) 481.960 433.652i 0.0480653 0.0432476i
\(466\) 0 0
\(467\) −6196.30 + 10732.3i −0.613984 + 1.06345i 0.376578 + 0.926385i \(0.377101\pi\)
−0.990562 + 0.137067i \(0.956232\pi\)
\(468\) 0 0
\(469\) −5521.65 287.234i −0.543638 0.0282798i
\(470\) 0 0
\(471\) −1397.17 454.509i −0.136684 0.0444643i
\(472\) 0 0
\(473\) 5589.57 3227.14i 0.543359 0.313709i
\(474\) 0 0
\(475\) 4993.85i 0.482387i
\(476\) 0 0
\(477\) −4639.67 10440.6i −0.445359 1.00219i
\(478\) 0 0
\(479\) −4133.87 7160.07i −0.394324 0.682989i 0.598691 0.800980i \(-0.295688\pi\)
−0.993015 + 0.117991i \(0.962355\pi\)
\(480\) 0 0
\(481\) −3224.21 1861.50i −0.305637 0.176460i
\(482\) 0 0
\(483\) 7223.82 + 2772.67i 0.680529 + 0.261202i
\(484\) 0 0
\(485\) 1530.24 + 883.487i 0.143268 + 0.0827156i
\(486\) 0 0
\(487\) 470.075 + 814.194i 0.0437395 + 0.0757590i 0.887066 0.461642i \(-0.152740\pi\)
−0.843327 + 0.537401i \(0.819406\pi\)
\(488\) 0 0
\(489\) 11772.9 2498.08i 1.08873 0.231017i
\(490\) 0 0
\(491\) 1057.30i 0.0971801i 0.998819 + 0.0485900i \(0.0154728\pi\)
−0.998819 + 0.0485900i \(0.984527\pi\)
\(492\) 0 0
\(493\) 19199.9 11085.1i 1.75400 1.01267i
\(494\) 0 0
\(495\) −1362.86 144.210i −0.123749 0.0130944i
\(496\) 0 0
\(497\) −7075.02 4590.68i −0.638547 0.414326i
\(498\) 0 0
\(499\) −3086.65 + 5346.23i −0.276909 + 0.479620i −0.970615 0.240638i \(-0.922643\pi\)
0.693706 + 0.720258i \(0.255977\pi\)
\(500\) 0 0
\(501\) 8149.12 + 9056.91i 0.726699 + 0.807651i
\(502\) 0 0
\(503\) 4284.28 0.379775 0.189887 0.981806i \(-0.439188\pi\)
0.189887 + 0.981806i \(0.439188\pi\)
\(504\) 0 0
\(505\) 300.390 0.0264697
\(506\) 0 0
\(507\) 6300.98 + 7002.89i 0.551946 + 0.613431i
\(508\) 0 0
\(509\) 7550.52 13077.9i 0.657507 1.13884i −0.323752 0.946142i \(-0.604944\pi\)
0.981259 0.192693i \(-0.0617223\pi\)
\(510\) 0 0
\(511\) 482.673 9278.68i 0.0417851 0.803258i
\(512\) 0 0
\(513\) 5645.13 587.315i 0.485845 0.0505470i
\(514\) 0 0
\(515\) 1198.08 691.712i 0.102512 0.0591854i
\(516\) 0 0
\(517\) 14570.1i 1.23944i
\(518\) 0 0
\(519\) 5254.79 1115.01i 0.444431 0.0943037i
\(520\) 0 0
\(521\) −6894.00 11940.8i −0.579715 1.00410i −0.995512 0.0946385i \(-0.969830\pi\)
0.415796 0.909458i \(-0.363503\pi\)
\(522\) 0 0
\(523\) 832.513 + 480.652i 0.0696047 + 0.0401863i 0.534398 0.845233i \(-0.320538\pi\)
−0.464794 + 0.885419i \(0.653872\pi\)
\(524\) 0 0
\(525\) −7476.36 9231.85i −0.621514 0.767449i
\(526\) 0 0
\(527\) −9071.15 5237.23i −0.749802 0.432898i
\(528\) 0 0
\(529\) −2851.06 4938.17i −0.234327 0.405866i
\(530\) 0 0
\(531\) 15434.8 6859.02i 1.26142 0.560557i
\(532\) 0 0
\(533\) 3659.84i 0.297421i
\(534\) 0 0
\(535\) −1153.41 + 665.922i −0.0932080 + 0.0538137i
\(536\) 0 0
\(537\) 715.903 + 232.889i 0.0575298 + 0.0187149i
\(538\) 0 0
\(539\) 11297.7 + 8194.92i 0.902834 + 0.654880i
\(540\) 0 0
\(541\) 597.846 1035.50i 0.0475109 0.0822913i −0.841292 0.540581i \(-0.818204\pi\)
0.888803 + 0.458290i \(0.151538\pi\)
\(542\) 0 0
\(543\) −7946.26 + 7149.79i −0.628005 + 0.565059i
\(544\) 0 0
\(545\) −12.5833 −0.000989006
\(546\) 0 0
\(547\) −18601.8 −1.45403 −0.727014 0.686622i \(-0.759093\pi\)
−0.727014 + 0.686622i \(0.759093\pi\)
\(548\) 0 0
\(549\) −12832.3 + 17636.1i −0.997578 + 1.37102i
\(550\) 0 0
\(551\) 4282.34 7417.24i 0.331096 0.573475i
\(552\) 0 0
\(553\) −520.955 1021.45i −0.0400601 0.0785473i
\(554\) 0 0
\(555\) 380.925 1170.97i 0.0291340 0.0895582i
\(556\) 0 0
\(557\) 5908.09 3411.04i 0.449432 0.259480i −0.258158 0.966103i \(-0.583116\pi\)
0.707590 + 0.706623i \(0.249782\pi\)
\(558\) 0 0
\(559\) 3108.49i 0.235197i
\(560\) 0 0
\(561\) 4595.80 + 21658.9i 0.345873 + 1.63002i
\(562\) 0 0
\(563\) 5679.80 + 9837.71i 0.425178 + 0.736430i 0.996437 0.0843399i \(-0.0268782\pi\)
−0.571259 + 0.820770i \(0.693545\pi\)
\(564\) 0 0
\(565\) 955.293 + 551.539i 0.0711318 + 0.0410680i
\(566\) 0 0
\(567\) 9556.55 9537.12i 0.707826 0.706387i
\(568\) 0 0
\(569\) 18467.2 + 10662.1i 1.36061 + 0.785549i 0.989705 0.143122i \(-0.0457141\pi\)
0.370905 + 0.928671i \(0.379047\pi\)
\(570\) 0 0
\(571\) −7384.00 12789.5i −0.541175 0.937343i −0.998837 0.0482163i \(-0.984646\pi\)
0.457662 0.889126i \(-0.348687\pi\)
\(572\) 0 0
\(573\) 3180.36 + 14988.3i 0.231870 + 1.09275i
\(574\) 0 0
\(575\) 9925.45i 0.719861i
\(576\) 0 0
\(577\) 16718.5 9652.44i 1.20624 0.696424i 0.244305 0.969698i \(-0.421440\pi\)
0.961936 + 0.273275i \(0.0881068\pi\)
\(578\) 0 0
\(579\) −3650.16 + 11220.6i −0.261996 + 0.805377i
\(580\) 0 0
\(581\) −737.091 + 1135.98i −0.0526328 + 0.0811162i
\(582\) 0 0
\(583\) 8609.17 14911.5i 0.611587 1.05930i
\(584\) 0 0
\(585\) 388.336 533.710i 0.0274457 0.0377200i
\(586\) 0 0
\(587\) −4397.46 −0.309204 −0.154602 0.987977i \(-0.549410\pi\)
−0.154602 + 0.987977i \(0.549410\pi\)
\(588\) 0 0
\(589\) −4046.45 −0.283075
\(590\) 0 0
\(591\) −1915.32 + 1723.35i −0.133310 + 0.119948i
\(592\) 0 0
\(593\) −10970.1 + 19000.8i −0.759677 + 1.31580i 0.183339 + 0.983050i \(0.441309\pi\)
−0.943015 + 0.332749i \(0.892024\pi\)
\(594\) 0 0
\(595\) 1316.83 2029.46i 0.0907307 0.139832i
\(596\) 0 0
\(597\) −4149.21 1349.77i −0.284449 0.0925335i
\(598\) 0 0
\(599\) 4765.07 2751.12i 0.325034 0.187659i −0.328600 0.944469i \(-0.606577\pi\)
0.653634 + 0.756810i \(0.273243\pi\)
\(600\) 0 0
\(601\) 5814.58i 0.394645i 0.980339 + 0.197322i \(0.0632246\pi\)
−0.980339 + 0.197322i \(0.936775\pi\)
\(602\) 0 0
\(603\) −7366.11 + 3273.41i −0.497465 + 0.221067i
\(604\) 0 0
\(605\) −202.537 350.804i −0.0136104 0.0235739i
\(606\) 0 0
\(607\) 11510.7 + 6645.69i 0.769693 + 0.444382i 0.832765 0.553627i \(-0.186756\pi\)
−0.0630721 + 0.998009i \(0.520090\pi\)
\(608\) 0 0
\(609\) −3187.91 20123.0i −0.212119 1.33896i
\(610\) 0 0
\(611\) 6077.05 + 3508.59i 0.402375 + 0.232311i
\(612\) 0 0
\(613\) −9797.17 16969.2i −0.645520 1.11807i −0.984181 0.177166i \(-0.943307\pi\)
0.338661 0.940909i \(-0.390026\pi\)
\(614\) 0 0
\(615\) −1184.12 + 251.257i −0.0776394 + 0.0164743i
\(616\) 0 0
\(617\) 348.388i 0.0227319i −0.999935 0.0113660i \(-0.996382\pi\)
0.999935 0.0113660i \(-0.00361797\pi\)
\(618\) 0 0
\(619\) −5867.68 + 3387.71i −0.381005 + 0.219973i −0.678255 0.734826i \(-0.737264\pi\)
0.297251 + 0.954799i \(0.403930\pi\)
\(620\) 0 0
\(621\) 11219.9 1167.31i 0.725022 0.0754307i
\(622\) 0 0
\(623\) 965.508 + 1893.10i 0.0620903 + 0.121742i
\(624\) 0 0
\(625\) −7521.95 + 13028.4i −0.481405 + 0.833818i
\(626\) 0 0
\(627\) 5721.16 + 6358.48i 0.364404 + 0.404997i
\(628\) 0 0
\(629\) −19893.9 −1.26108
\(630\) 0 0
\(631\) 7326.82 0.462244 0.231122 0.972925i \(-0.425760\pi\)
0.231122 + 0.972925i \(0.425760\pi\)
\(632\) 0 0
\(633\) −13908.2 15457.5i −0.873301 0.970584i
\(634\) 0 0
\(635\) 523.995 907.586i 0.0327466 0.0567188i
\(636\) 0 0
\(637\) −6138.62 + 2738.79i −0.381822 + 0.170353i
\(638\) 0 0
\(639\) −12227.2 1293.81i −0.756963 0.0800975i
\(640\) 0 0
\(641\) −2433.38 + 1404.91i −0.149942 + 0.0865689i −0.573094 0.819490i \(-0.694257\pi\)
0.423152 + 0.906059i \(0.360924\pi\)
\(642\) 0 0
\(643\) 27485.5i 1.68573i 0.538128 + 0.842863i \(0.319132\pi\)
−0.538128 + 0.842863i \(0.680868\pi\)
\(644\) 0 0
\(645\) −1005.73 + 213.405i −0.0613962 + 0.0130276i
\(646\) 0 0
\(647\) −14659.9 25391.7i −0.890790 1.54289i −0.838930 0.544239i \(-0.816819\pi\)
−0.0518595 0.998654i \(-0.516515\pi\)
\(648\) 0 0
\(649\) 22044.3 + 12727.3i 1.33330 + 0.769783i
\(650\) 0 0
\(651\) −7480.44 + 6057.99i −0.450356 + 0.364718i
\(652\) 0 0
\(653\) −14500.6 8371.91i −0.868992 0.501713i −0.00197863 0.999998i \(-0.500630\pi\)
−0.867013 + 0.498285i \(0.833963\pi\)
\(654\) 0 0
\(655\) −323.019 559.485i −0.0192693 0.0333754i
\(656\) 0 0
\(657\) −5500.69 12378.1i −0.326640 0.735034i
\(658\) 0 0
\(659\) 9520.47i 0.562769i 0.959595 + 0.281385i \(0.0907937\pi\)
−0.959595 + 0.281385i \(0.909206\pi\)
\(660\) 0 0
\(661\) −20217.5 + 11672.6i −1.18966 + 0.686853i −0.958230 0.285998i \(-0.907675\pi\)
−0.231434 + 0.972851i \(0.574342\pi\)
\(662\) 0 0
\(663\) −10140.5 3298.77i −0.594002 0.193233i
\(664\) 0 0
\(665\) 48.5515 933.331i 0.00283120 0.0544256i
\(666\) 0 0
\(667\) 8511.31 14742.0i 0.494092 0.855792i
\(668\) 0 0
\(669\) −11744.7 + 10567.5i −0.678740 + 0.610709i
\(670\) 0 0
\(671\) −32869.9 −1.89110
\(672\) 0 0
\(673\) −12283.5 −0.703559 −0.351780 0.936083i \(-0.614423\pi\)
−0.351780 + 0.936083i \(0.614423\pi\)
\(674\) 0 0
\(675\) −15814.0 7060.82i −0.901750 0.402624i
\(676\) 0 0
\(677\) −6495.88 + 11251.2i −0.368769 + 0.638727i −0.989373 0.145397i \(-0.953554\pi\)
0.620604 + 0.784124i \(0.286887\pi\)
\(678\) 0 0
\(679\) −22007.4 14279.6i −1.24384 0.807072i
\(680\) 0 0
\(681\) 7067.05 21724.2i 0.397665 1.22243i
\(682\) 0 0
\(683\) −7366.62 + 4253.12i −0.412703 + 0.238274i −0.691950 0.721945i \(-0.743248\pi\)
0.279248 + 0.960219i \(0.409915\pi\)
\(684\) 0 0
\(685\) 1369.74i 0.0764018i
\(686\) 0 0
\(687\) −2139.38 10082.4i −0.118810 0.559923i
\(688\) 0 0
\(689\) 4146.31 + 7181.62i 0.229263 + 0.397095i
\(690\) 0 0
\(691\) 22372.0 + 12916.5i 1.23165 + 0.711093i 0.967374 0.253354i \(-0.0815336\pi\)
0.264276 + 0.964447i \(0.414867\pi\)
\(692\) 0 0
\(693\) 20095.7 + 3189.34i 1.10155 + 0.174824i
\(694\) 0 0
\(695\) 894.770 + 516.595i 0.0488353 + 0.0281951i
\(696\) 0 0
\(697\) 9778.22 + 16936.4i 0.531387 + 0.920389i
\(698\) 0 0
\(699\) −4717.33 22231.7i −0.255259 1.20298i
\(700\) 0 0
\(701\) 22607.8i 1.21810i −0.793134 0.609048i \(-0.791552\pi\)
0.793134 0.609048i \(-0.208448\pi\)
\(702\) 0 0
\(703\) −6655.69 + 3842.67i −0.357076 + 0.206158i
\(704\) 0 0
\(705\) −717.975 + 2207.06i −0.0383553 + 0.117905i
\(706\) 0 0
\(707\) −4453.86 231.688i −0.236923 0.0123246i
\(708\) 0 0
\(709\) 5472.41 9478.50i 0.289874 0.502077i −0.683905 0.729571i \(-0.739720\pi\)
0.973779 + 0.227494i \(0.0730532\pi\)
\(710\) 0 0
\(711\) −1351.69 983.509i −0.0712971 0.0518769i
\(712\) 0 0
\(713\) −8042.46 −0.422430
\(714\) 0 0
\(715\) 994.720 0.0520285
\(716\) 0 0
\(717\) −14780.3 + 13298.9i −0.769849 + 0.692685i
\(718\) 0 0
\(719\) −12885.3 + 22317.9i −0.668344 + 1.15761i 0.310023 + 0.950729i \(0.399663\pi\)
−0.978367 + 0.206877i \(0.933670\pi\)
\(720\) 0 0
\(721\) −18297.3 + 9331.88i −0.945116 + 0.482021i
\(722\) 0 0
\(723\) 16997.4 + 5529.40i 0.874330 + 0.284427i
\(724\) 0 0
\(725\) −22633.2 + 13067.3i −1.15942 + 0.669389i
\(726\) 0 0
\(727\) 15593.1i 0.795485i 0.917497 + 0.397742i \(0.130206\pi\)
−0.917497 + 0.397742i \(0.869794\pi\)
\(728\) 0 0
\(729\) 6121.81 18706.8i 0.311020 0.950403i
\(730\) 0 0
\(731\) 8305.13 + 14384.9i 0.420214 + 0.727832i
\(732\) 0 0
\(733\) 692.858 + 400.022i 0.0349131 + 0.0201571i 0.517355 0.855771i \(-0.326917\pi\)
−0.482442 + 0.875928i \(0.660250\pi\)
\(734\) 0 0
\(735\) −1307.55 1798.08i −0.0656185 0.0902358i
\(736\) 0 0
\(737\) −10520.5 6073.99i −0.525815 0.303580i
\(738\) 0 0
\(739\) −454.445 787.122i −0.0226211 0.0391810i 0.854493 0.519463i \(-0.173868\pi\)
−0.877114 + 0.480282i \(0.840534\pi\)
\(740\) 0 0
\(741\) −4029.77 + 855.076i −0.199781 + 0.0423914i
\(742\) 0 0
\(743\) 8109.00i 0.400391i 0.979756 + 0.200195i \(0.0641577\pi\)
−0.979756 + 0.200195i \(0.935842\pi\)
\(744\) 0 0
\(745\) 964.258 556.715i 0.0474197 0.0273778i
\(746\) 0 0
\(747\) −207.737 + 1963.22i −0.0101750 + 0.0961588i
\(748\) 0 0
\(749\) 17615.1 8983.95i 0.859337 0.438273i
\(750\) 0 0
\(751\) −10382.2 + 17982.5i −0.504463 + 0.873756i 0.495524 + 0.868594i \(0.334976\pi\)
−0.999987 + 0.00516122i \(0.998357\pi\)
\(752\) 0 0
\(753\) 7113.09 + 7905.46i 0.344243 + 0.382591i
\(754\) 0 0
\(755\) 1777.61 0.0856870
\(756\) 0 0
\(757\) 23295.6 1.11848 0.559242 0.829005i \(-0.311092\pi\)
0.559242 + 0.829005i \(0.311092\pi\)
\(758\) 0 0
\(759\) 11371.0 + 12637.7i 0.543796 + 0.604374i
\(760\) 0 0
\(761\) 5014.38 8685.16i 0.238858 0.413715i −0.721529 0.692385i \(-0.756560\pi\)
0.960387 + 0.278670i \(0.0898935\pi\)
\(762\) 0 0
\(763\) 186.571 + 9.70535i 0.00885233 + 0.000460494i
\(764\) 0 0
\(765\) 371.128 3507.35i 0.0175401 0.165763i
\(766\) 0 0
\(767\) −10616.9 + 6129.66i −0.499809 + 0.288565i
\(768\) 0 0
\(769\) 13500.3i 0.633074i 0.948580 + 0.316537i \(0.102520\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(770\) 0 0
\(771\) −30757.8 + 6526.49i −1.43673 + 0.304858i
\(772\) 0 0
\(773\) 11644.9 + 20169.5i 0.541833 + 0.938482i 0.998799 + 0.0489979i \(0.0156028\pi\)
−0.456966 + 0.889484i \(0.651064\pi\)
\(774\) 0 0
\(775\) 10693.2 + 6173.74i 0.495629 + 0.286151i
\(776\) 0 0
\(777\) −6551.10 + 17068.0i −0.302470 + 0.788046i
\(778\) 0 0
\(779\) 6542.79 + 3777.48i 0.300924 + 0.173739i
\(780\) 0 0
\(781\) −9264.99 16047.4i −0.424491 0.735240i
\(782\) 0 0
\(783\) −17433.3 24048.1i −0.795677 1.09759i
\(784\) 0 0
\(785\) 352.711i 0.0160367i
\(786\) 0 0
\(787\) 20635.4 11913.8i 0.934653 0.539622i 0.0463726 0.998924i \(-0.485234\pi\)
0.888280 + 0.459302i \(0.151901\pi\)
\(788\) 0 0
\(789\) −31002.9 10085.5i −1.39890 0.455074i
\(790\) 0 0
\(791\) −13738.7 8914.42i −0.617560 0.400709i