Properties

Label 336.4.bc.d.17.5
Level $336$
Weight $4$
Character 336.17
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 17.5
Root \(2.85284 + 0.928053i\) of defining polynomial
Character \(\chi\) \(=\) 336.17
Dual form 336.4.bc.d.257.5

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

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

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 0.892570 0.450909i \(-0.148900\pi\)
−0.836784 + 0.547533i \(0.815567\pi\)
\(6\) 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 −0.0679230 0.997691i \(-0.521637\pi\)
−0.897987 + 0.440022i \(0.854971\pi\)
\(12\) 0 0
\(13\) 19.5973i 0.418101i 0.977905 + 0.209050i \(0.0670373\pi\)
−0.977905 + 0.209050i \(0.932963\pi\)
\(14\) 0 0
\(15\) 6.34057 + 1.34540i 0.109142 + 0.0231588i
\(16\) 0 0
\(17\) −52.3592 + 90.6889i −0.746999 + 1.29384i 0.202256 + 0.979333i \(0.435173\pi\)
−0.949255 + 0.314507i \(0.898161\pi\)
\(18\) 0 0
\(19\) −35.0345 + 20.2272i −0.423025 + 0.244234i −0.696371 0.717682i \(-0.745203\pi\)
0.273346 + 0.961916i \(0.411870\pi\)
\(20\) 0 0
\(21\) −95.0487 15.0578i −0.987683 0.156470i
\(22\) 0 0
\(23\) −69.6324 + 40.2023i −0.631276 + 0.364467i −0.781246 0.624223i \(-0.785416\pi\)
0.149970 + 0.988691i \(0.452082\pi\)
\(24\) 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 \(-0.762922\pi\)
0.735222 0.677827i \(-0.237078\pi\)
\(30\) 0 0
\(31\) 86.6242 + 50.0125i 0.501876 + 0.289758i 0.729488 0.683994i \(-0.239758\pi\)
−0.227612 + 0.973752i \(0.573092\pi\)
\(32\) 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 0.996140 0.0877801i \(-0.0279773\pi\)
−0.574090 + 0.818792i \(0.694644\pi\)
\(38\) 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 −0.997854 0.0654808i \(-0.979142\pi\)
0.442219 0.896907i \(-0.354191\pi\)
\(48\) 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 −0.0567521 0.998388i \(-0.518074\pi\)
−0.893006 + 0.450045i \(0.851408\pi\)
\(54\) 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 0.281599 + 0.959532i \(0.409135\pi\)
−0.971779 + 0.235895i \(0.924198\pi\)
\(60\) 0 0
\(61\) 699.575 403.900i 1.46838 0.847772i 0.469011 0.883192i \(-0.344611\pi\)
0.999372 + 0.0354209i \(0.0112772\pi\)
\(62\) 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 −0.697235 0.716843i \(-0.745587\pi\)
0.969421 + 0.245402i \(0.0789199\pi\)
\(68\) 0 0
\(69\) −86.7208 + 408.695i −0.151304 + 0.713059i
\(70\) 0 0
\(71\) 455.386i 0.761189i −0.924742 0.380594i \(-0.875719\pi\)
0.924742 0.380594i \(-0.124281\pi\)
\(72\) 0 0
\(73\) −434.467 250.840i −0.696582 0.402172i 0.109491 0.993988i \(-0.465078\pi\)
−0.806073 + 0.591816i \(0.798411\pi\)
\(74\) 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 0.843140 0.537694i \(-0.180704\pi\)
−0.887227 + 0.461334i \(0.847371\pi\)
\(80\) 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 0.898167 0.439655i \(-0.144899\pi\)
−0.829836 + 0.558008i \(0.811566\pi\)
\(90\) 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 \(-0.734178\pi\)
0.671101 0.741366i \(-0.265822\pi\)
\(98\) 0 0
\(99\) −446.156 + 1003.98i −0.452933 + 1.01923i
\(100\) 0 0
\(101\) 120.406 208.549i 0.118622 0.205459i −0.800600 0.599199i \(-0.795486\pi\)
0.919222 + 0.393740i \(0.128819\pi\)
\(102\) 0 0
\(103\) 960.453 554.518i 0.918799 0.530469i 0.0355471 0.999368i \(-0.488683\pi\)
0.883252 + 0.468899i \(0.155349\pi\)
\(104\) 0 0
\(105\) −43.0157 112.072i −0.0399800 0.104163i
\(106\) 0 0
\(107\) −924.644 + 533.843i −0.835408 + 0.482323i −0.855701 0.517471i \(-0.826874\pi\)
0.0202926 + 0.999794i \(0.493540\pi\)
\(108\) 0 0
\(109\) −5.04376 + 8.73604i −0.00443215 + 0.00767671i −0.868233 0.496157i \(-0.834744\pi\)
0.863801 + 0.503833i \(0.168077\pi\)
\(110\) 0 0
\(111\) 965.640 + 204.899i 0.825716 + 0.175208i
\(112\) 0 0
\(113\) 884.294i 0.736171i −0.929792 0.368086i \(-0.880013\pi\)
0.929792 0.368086i \(-0.119987\pi\)
\(114\) 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 0.939366 0.342918i \(-0.111415\pi\)
−0.766658 + 0.642056i \(0.778082\pi\)
\(132\) 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 0.766296 0.642487i \(-0.222097\pi\)
−0.173262 + 0.984876i \(0.555431\pi\)
\(138\) 0 0
\(139\) 828.268i 0.505416i −0.967543 0.252708i \(-0.918679\pi\)
0.967543 0.252708i \(-0.0813212\pi\)
\(140\) 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 −0.272206 0.962239i \(-0.587753\pi\)
0.697221 + 0.716857i \(0.254420\pi\)
\(150\) 0 0
\(151\) 712.518 1234.12i 0.383999 0.665106i −0.607630 0.794220i \(-0.707880\pi\)
0.991630 + 0.129113i \(0.0412131\pi\)
\(152\) 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 0.436468 0.899720i \(-0.356229\pi\)
−0.560946 + 0.827853i \(0.689562\pi\)
\(158\) 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 0.997786 + 0.0664997i \(0.0211832\pi\)
−0.441303 + 0.897358i \(0.645484\pi\)
\(164\) 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 0.956966 0.290199i \(-0.0937216\pi\)
−0.729803 + 0.683657i \(0.760388\pi\)
\(174\) 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 0.525967 0.850505i \(-0.323703\pi\)
−0.473575 + 0.880753i \(0.657037\pi\)
\(180\) 0 0
\(181\) 2057.17i 0.844797i −0.906410 0.422398i \(-0.861188\pi\)
0.906410 0.422398i \(-0.138812\pi\)
\(182\) 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 0.0689690 0.997619i \(-0.478029\pi\)
0.898448 + 0.439080i \(0.144696\pi\)
\(192\) 0 0
\(193\) 1135.40 1966.57i 0.423460 0.733455i −0.572815 0.819685i \(-0.694149\pi\)
0.996275 + 0.0862300i \(0.0274820\pi\)
\(194\) 0 0
\(195\) −26.3662 + 124.258i −0.00968270 + 0.0456323i
\(196\) 0 0
\(197\) 495.849i 0.179329i −0.995972 0.0896645i \(-0.971421\pi\)
0.995972 0.0896645i \(-0.0285795\pi\)
\(198\) 0 0
\(199\) −727.207 419.853i −0.259047 0.149561i 0.364853 0.931065i \(-0.381119\pi\)
−0.623900 + 0.781504i \(0.714453\pi\)
\(200\) 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 \(-0.849095\pi\)
0.889711 0.456523i \(-0.150905\pi\)
\(224\) 0 0
\(225\) −3045.79 1353.51i −0.902455 0.401040i
\(226\) 0 0
\(227\) −2198.24 + 3807.46i −0.642741 + 1.11326i 0.342078 + 0.939672i \(0.388869\pi\)
−0.984818 + 0.173588i \(0.944464\pi\)
\(228\) 0 0
\(229\) −1717.81 + 991.778i −0.495703 + 0.286194i −0.726937 0.686704i \(-0.759057\pi\)
0.231234 + 0.972898i \(0.425724\pi\)
\(230\) 0 0
\(231\) 3043.08 + 2464.42i 0.866754 + 0.701935i
\(232\) 0 0
\(233\) −3787.78 + 2186.87i −1.06500 + 0.614879i −0.926812 0.375526i \(-0.877462\pi\)
−0.138191 + 0.990406i \(0.544129\pi\)
\(234\) 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 \(-0.826750\pi\)
0.855500 0.517803i \(-0.173250\pi\)
\(240\) 0 0
\(241\) 2979.03 + 1719.94i 0.796250 + 0.459715i 0.842158 0.539231i \(-0.181285\pi\)
−0.0459083 + 0.998946i \(0.514618\pi\)
\(242\) 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 −0.955005 0.296590i \(-0.904150\pi\)
0.220648 0.975354i \(-0.429183\pi\)
\(258\) 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 −0.298242 0.954490i \(-0.596400\pi\)
−0.975734 + 0.218960i \(0.929733\pi\)
\(264\) 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 −0.990787 0.135432i \(-0.956758\pi\)
0.612681 + 0.790331i \(0.290091\pi\)
\(270\) 0 0
\(271\) −2462.26 + 1421.59i −0.551925 + 0.318654i −0.749898 0.661553i \(-0.769897\pi\)
0.197973 + 0.980207i \(0.436564\pi\)
\(272\) 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 0.283809 + 0.958881i \(0.408402\pi\)
−0.972320 + 0.233654i \(0.924932\pi\)
\(278\) 0 0
\(279\) 1096.73 2467.96i 0.235339 0.529580i
\(280\) 0 0
\(281\) 3735.88i 0.793110i −0.918011 0.396555i \(-0.870206\pi\)
0.918011 0.396555i \(-0.129794\pi\)
\(282\) 0 0
\(283\) 4777.96 + 2758.56i 1.00361 + 0.579432i 0.909313 0.416112i \(-0.136608\pi\)
0.0942927 + 0.995545i \(0.469941\pi\)
\(284\) 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 \(0.451918\pi\)
−0.150480 + 0.988613i \(0.548082\pi\)
\(308\) 0 0
\(309\) 1196.16 5637.21i 0.220217 1.03783i
\(310\) 0 0
\(311\) 2885.59 4997.99i 0.526132 0.911287i −0.473405 0.880845i \(-0.656975\pi\)
0.999537 0.0304419i \(-0.00969146\pi\)
\(312\) 0 0
\(313\) −2030.41 + 1172.26i −0.366664 + 0.211694i −0.672000 0.740551i \(-0.734565\pi\)
0.305336 + 0.952245i \(0.401231\pi\)
\(314\) 0 0
\(315\) −582.404 223.354i −0.104174 0.0399509i
\(316\) 0 0
\(317\) −6852.10 + 3956.06i −1.21405 + 0.700929i −0.963638 0.267211i \(-0.913898\pi\)
−0.250407 + 0.968141i \(0.580565\pi\)
\(318\) 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 0.589160 0.808016i \(-0.299459\pi\)
−0.994343 + 0.106220i \(0.966125\pi\)
\(332\) 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 0.336411 0.941715i \(-0.390787\pi\)
−0.647344 + 0.762198i \(0.724120\pi\)
\(348\) 0 0
\(349\) 226.795i 0.0347853i −0.999849 0.0173926i \(-0.994463\pi\)
0.999849 0.0173926i \(-0.00553653\pi\)
\(350\) 0 0
\(351\) 1613.73 2226.03i 0.245397 0.338509i
\(352\) 0 0
\(353\) 742.854 1286.66i 0.112006 0.194000i −0.804573 0.593854i \(-0.797606\pi\)
0.916579 + 0.399854i \(0.130939\pi\)
\(354\) 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 −0.992730 0.120359i \(-0.961595\pi\)
−0.392131 + 0.919909i \(0.628262\pi\)
\(360\) 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 0.715957 0.698144i \(-0.245991\pi\)
−0.246632 + 0.969109i \(0.579324\pi\)
\(368\) 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 0.976185 + 0.216938i \(0.0696070\pi\)
−0.300219 + 0.953870i \(0.597060\pi\)
\(374\) 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 0.974171 0.225812i \(-0.0725034\pi\)
−0.682644 + 0.730751i \(0.739170\pi\)
\(384\) 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 −0.998288 0.0584981i \(-0.981369\pi\)
−0.549805 0.835293i \(-0.685298\pi\)
\(390\) 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 −0.631520 0.775360i \(-0.717568\pi\)
0.355722 + 0.934592i \(0.384235\pi\)
\(398\) 0 0
\(399\) 3634.57 1395.03i 0.456030 0.175035i
\(400\) 0 0
\(401\) −2268.96 + 1309.98i −0.282560 + 0.163136i −0.634582 0.772856i \(-0.718828\pi\)
0.352022 + 0.935992i \(0.385494\pi\)
\(402\) 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 −0.458952 0.888461i \(-0.651775\pi\)
−0.998906 + 0.0467669i \(0.985108\pi\)
\(410\) 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 0.834220 0.551432i \(-0.185918\pi\)
−0.0604442 + 0.998172i \(0.519252\pi\)
\(432\) 0 0
\(433\) 12889.4i 1.43055i −0.698845 0.715273i \(-0.746303\pi\)
0.698845 0.715273i \(-0.253697\pi\)
\(434\) 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 −0.988845 0.148948i \(-0.952411\pi\)
−0.365430 + 0.930839i \(0.619078\pi\)
\(440\) 0 0
\(441\) 8807.53 + 2862.44i 0.951034 + 0.309085i
\(442\) 0 0
\(443\) 3432.16 1981.56i 0.368097 0.212521i −0.304530 0.952503i \(-0.598499\pi\)
0.672627 + 0.739982i \(0.265166\pi\)
\(444\) 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 \(-0.749430\pi\)
0.705838 0.708373i \(-0.250570\pi\)
\(450\) 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 0.746036 0.665905i \(-0.231955\pi\)
−0.949709 + 0.313134i \(0.898621\pi\)
\(458\) 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 −0.990562 0.137067i \(-0.956232\pi\)
0.376578 0.926385i \(-0.377101\pi\)
\(468\) 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 −0.993015 0.117991i \(-0.962355\pi\)
0.598691 + 0.800980i \(0.295688\pi\)
\(480\) 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 −0.843327 0.537401i \(-0.819406\pi\)
0.887066 + 0.461642i \(0.152740\pi\)
\(488\) 0 0
\(489\) 11772.9 + 2498.08i 1.08873 + 0.231017i
\(490\) 0 0
\(491\) 1057.30i 0.0971801i −0.998819 0.0485900i \(-0.984527\pi\)
0.998819 0.0485900i \(-0.0154728\pi\)
\(492\) 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 0.693706 0.720258i \(-0.255977\pi\)
−0.970615 + 0.240638i \(0.922643\pi\)
\(500\) 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 0.981259 + 0.192693i \(0.0617223\pi\)
−0.323752 + 0.946142i \(0.604944\pi\)
\(510\) 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 0.415796 + 0.909458i \(0.363503\pi\)
−0.995512 + 0.0946385i \(0.969830\pi\)
\(522\) 0 0
\(523\) 832.513 480.652i 0.0696047 0.0401863i −0.464794 0.885419i \(-0.653872\pi\)
0.534398 + 0.845233i \(0.320538\pi\)
\(524\) 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 0.888803 0.458290i \(-0.151538\pi\)
−0.841292 + 0.540581i \(0.818204\pi\)
\(542\) 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 0.707590 0.706623i \(-0.249782\pi\)
−0.258158 + 0.966103i \(0.583116\pi\)
\(558\) 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 −0.571259 0.820770i \(-0.693545\pi\)
0.996437 + 0.0843399i \(0.0268782\pi\)
\(564\) 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 0.370905 0.928671i \(-0.379047\pi\)
0.989705 + 0.143122i \(0.0457141\pi\)
\(570\) 0 0
\(571\) −7384.00 + 12789.5i −0.541175 + 0.937343i 0.457662 + 0.889126i \(0.348687\pi\)
−0.998837 + 0.0482163i \(0.984646\pi\)
\(572\) 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 0.961936 0.273275i \(-0.0881068\pi\)
0.244305 + 0.969698i \(0.421440\pi\)
\(578\) 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 −0.943015 0.332749i \(-0.892024\pi\)
0.183339 0.983050i \(-0.441309\pi\)
\(594\) 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 0.653634 0.756810i \(-0.273243\pi\)
−0.328600 + 0.944469i \(0.606577\pi\)
\(600\) 0 0
\(601\) 5814.58i 0.394645i −0.980339 0.197322i \(-0.936775\pi\)
0.980339 0.197322i \(-0.0632246\pi\)
\(602\) 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 −0.0630721 0.998009i \(-0.520090\pi\)
0.832765 + 0.553627i \(0.186756\pi\)
\(608\) 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 0.338661 + 0.940909i \(0.390026\pi\)
−0.984181 + 0.177166i \(0.943307\pi\)
\(614\) 0 0
\(615\) −1184.12 251.257i −0.0776394 0.0164743i
\(616\) 0 0
\(617\) 348.388i 0.0227319i 0.999935 + 0.0113660i \(0.00361797\pi\)
−0.999935 + 0.0113660i \(0.996382\pi\)
\(618\) 0 0
\(619\) −5867.68 3387.71i −0.381005 0.219973i 0.297251 0.954799i \(-0.403930\pi\)
−0.678255 + 0.734826i \(0.737264\pi\)
\(620\) 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 0.423152 0.906059i \(-0.360924\pi\)
−0.573094 + 0.819490i \(0.694257\pi\)
\(642\) 0 0
\(643\) 27485.5i 1.68573i −0.538128 0.842863i \(-0.680868\pi\)
0.538128 0.842863i \(-0.319132\pi\)
\(644\) 0 0
\(645\) −1005.73 213.405i −0.0613962 0.0130276i
\(646\) 0 0
\(647\) −14659.9 + 25391.7i −0.890790 + 1.54289i −0.0518595 + 0.998654i \(0.516515\pi\)
−0.838930 + 0.544239i \(0.816819\pi\)
\(648\) 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 −0.867013 0.498285i \(-0.833963\pi\)
−0.00197863 + 0.999998i \(0.500630\pi\)
\(654\) 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 \(-0.909206\pi\)
0.959595 0.281385i \(-0.0907937\pi\)
\(660\) 0 0
\(661\) −20217.5 11672.6i −1.18966 0.686853i −0.231434 0.972851i \(-0.574342\pi\)
−0.958230 + 0.285998i \(0.907675\pi\)
\(662\) 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 0.620604 0.784124i \(-0.286887\pi\)
−0.989373 + 0.145397i \(0.953554\pi\)
\(678\) 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 0.279248 0.960219i \(-0.409915\pi\)
−0.691950 + 0.721945i \(0.743248\pi\)
\(684\) 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 0.264276 0.964447i \(-0.414867\pi\)
0.967374 + 0.253354i \(0.0815336\pi\)
\(692\) 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 \(0.208448\pi\)
−0.793134 + 0.609048i \(0.791552\pi\)
\(702\) 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 0.973779 0.227494i \(-0.0730532\pi\)
−0.683905 + 0.729571i \(0.739720\pi\)
\(710\) 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 −0.978367 0.206877i \(-0.933670\pi\)
0.310023 0.950729i \(-0.399663\pi\)
\(720\) 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 \(-0.869794\pi\)
0.917497 0.397742i \(-0.130206\pi\)
\(728\) 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 −0.482442 0.875928i \(-0.660250\pi\)
0.517355 + 0.855771i \(0.326917\pi\)
\(734\) 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 −0.877114 0.480282i \(-0.840534\pi\)
0.854493 + 0.519463i \(0.173868\pi\)
\(740\) 0 0
\(741\) −4029.77 855.076i −0.199781 0.0423914i
\(742\) 0 0
\(743\) 8109.00i 0.400391i −0.979756 0.200195i \(-0.935842\pi\)
0.979756 0.200195i \(-0.0641577\pi\)
\(744\) 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 −0.999987 0.00516122i \(-0.998357\pi\)
0.495524 0.868594i \(-0.334976\pi\)
\(752\) 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 0.960387 0.278670i \(-0.0898935\pi\)
−0.721529 + 0.692385i \(0.756560\pi\)
\(762\) 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 \(-0.897480\pi\)
0.948580 0.316537i \(-0.102520\pi\)
\(770\) 0 0
\(771\) −30757.8 6526.49i −1.43673 0.304858i
\(772\) 0 0
\(773\) 11644.9 20169.5i 0.541833 0.938482i −0.456966 0.889484i \(-0.651064\pi\)
0.998799 0.0489979i \(-0.0156028\pi\)
\(774\) 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 0.888280 0.459302i \(-0.151901\pi\)
0.0463726 + 0.998924i \(0.485234\pi\)
\(788\) 0 0
\(789\) −31002.9 + 10085.5i −1.39890 + 0.455074i
\(790\) 0 0
\(791\) −13738.7 + 8914.42i