Properties

Label 624.4.bv.a.49.1
Level $624$
Weight $4$
Character 624.49
Analytic conductor $36.817$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(36.8171918436\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 624.49
Dual form 624.4.bv.a.433.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{3} +5.19615i q^{5} +(-9.00000 - 5.19615i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{3} +5.19615i q^{5} +(-9.00000 - 5.19615i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-45.0000 + 25.9808i) q^{11} +(-32.5000 + 33.7750i) q^{13} +(13.5000 - 7.79423i) q^{15} +(58.5000 - 101.325i) q^{17} +(21.0000 + 12.1244i) q^{19} +31.1769i q^{21} +(9.00000 + 15.5885i) q^{23} +98.0000 q^{25} +27.0000 q^{27} +(49.5000 + 85.7365i) q^{29} -193.990i q^{31} +(135.000 + 77.9423i) q^{33} +(27.0000 - 46.7654i) q^{35} +(97.5000 - 56.2917i) q^{37} +(136.500 + 33.7750i) q^{39} +(-31.5000 + 18.1865i) q^{41} +(-41.0000 + 71.0141i) q^{43} +(-40.5000 - 23.3827i) q^{45} +72.7461i q^{47} +(-117.500 - 203.516i) q^{49} -351.000 q^{51} -261.000 q^{53} +(-135.000 - 233.827i) q^{55} -72.7461i q^{57} +(684.000 + 394.908i) q^{59} +(359.500 - 622.672i) q^{61} +(81.0000 - 46.7654i) q^{63} +(-175.500 - 168.875i) q^{65} +(609.000 - 351.606i) q^{67} +(27.0000 - 46.7654i) q^{69} +(405.000 + 233.827i) q^{71} +684.160i q^{73} +(-147.000 - 254.611i) q^{75} +540.000 q^{77} +440.000 q^{79} +(-40.5000 - 70.1481i) q^{81} -1195.12i q^{83} +(526.500 + 303.975i) q^{85} +(148.500 - 257.210i) q^{87} +(1314.00 - 758.638i) q^{89} +(468.000 - 135.100i) q^{91} +(-504.000 + 290.985i) q^{93} +(-63.0000 + 109.119i) q^{95} +(-1002.00 - 578.505i) q^{97} -467.654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{3} - 18 q^{7} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{3} - 18 q^{7} - 9 q^{9} - 90 q^{11} - 65 q^{13} + 27 q^{15} + 117 q^{17} + 42 q^{19} + 18 q^{23} + 196 q^{25} + 54 q^{27} + 99 q^{29} + 270 q^{33} + 54 q^{35} + 195 q^{37} + 273 q^{39} - 63 q^{41} - 82 q^{43} - 81 q^{45} - 235 q^{49} - 702 q^{51} - 522 q^{53} - 270 q^{55} + 1368 q^{59} + 719 q^{61} + 162 q^{63} - 351 q^{65} + 1218 q^{67} + 54 q^{69} + 810 q^{71} - 294 q^{75} + 1080 q^{77} + 880 q^{79} - 81 q^{81} + 1053 q^{85} + 297 q^{87} + 2628 q^{89} + 936 q^{91} - 1008 q^{93} - 126 q^{95} - 2004 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 0 0
\(5\) 5.19615i 0.464758i 0.972625 + 0.232379i \(0.0746510\pi\)
−0.972625 + 0.232379i \(0.925349\pi\)
\(6\) 0 0
\(7\) −9.00000 5.19615i −0.485954 0.280566i 0.236940 0.971524i \(-0.423855\pi\)
−0.722895 + 0.690958i \(0.757189\pi\)
\(8\) 0 0
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −45.0000 + 25.9808i −1.23346 + 0.712136i −0.967749 0.251918i \(-0.918939\pi\)
−0.265707 + 0.964054i \(0.585605\pi\)
\(12\) 0 0
\(13\) −32.5000 + 33.7750i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) 13.5000 7.79423i 0.232379 0.134164i
\(16\) 0 0
\(17\) 58.5000 101.325i 0.834608 1.44558i −0.0597414 0.998214i \(-0.519028\pi\)
0.894349 0.447369i \(-0.147639\pi\)
\(18\) 0 0
\(19\) 21.0000 + 12.1244i 0.253565 + 0.146396i 0.621395 0.783497i \(-0.286566\pi\)
−0.367831 + 0.929893i \(0.619899\pi\)
\(20\) 0 0
\(21\) 31.1769i 0.323970i
\(22\) 0 0
\(23\) 9.00000 + 15.5885i 0.0815926 + 0.141323i 0.903934 0.427672i \(-0.140666\pi\)
−0.822342 + 0.568994i \(0.807333\pi\)
\(24\) 0 0
\(25\) 98.0000 0.784000
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 49.5000 + 85.7365i 0.316963 + 0.548996i 0.979853 0.199721i \(-0.0640037\pi\)
−0.662890 + 0.748717i \(0.730670\pi\)
\(30\) 0 0
\(31\) 193.990i 1.12392i −0.827164 0.561961i \(-0.810047\pi\)
0.827164 0.561961i \(-0.189953\pi\)
\(32\) 0 0
\(33\) 135.000 + 77.9423i 0.712136 + 0.411152i
\(34\) 0 0
\(35\) 27.0000 46.7654i 0.130395 0.225851i
\(36\) 0 0
\(37\) 97.5000 56.2917i 0.433214 0.250116i −0.267501 0.963558i \(-0.586198\pi\)
0.700715 + 0.713442i \(0.252865\pi\)
\(38\) 0 0
\(39\) 136.500 + 33.7750i 0.560449 + 0.138675i
\(40\) 0 0
\(41\) −31.5000 + 18.1865i −0.119987 + 0.0692746i −0.558792 0.829308i \(-0.688735\pi\)
0.438805 + 0.898582i \(0.355402\pi\)
\(42\) 0 0
\(43\) −41.0000 + 71.0141i −0.145406 + 0.251850i −0.929524 0.368761i \(-0.879782\pi\)
0.784119 + 0.620611i \(0.213115\pi\)
\(44\) 0 0
\(45\) −40.5000 23.3827i −0.134164 0.0774597i
\(46\) 0 0
\(47\) 72.7461i 0.225768i 0.993608 + 0.112884i \(0.0360089\pi\)
−0.993608 + 0.112884i \(0.963991\pi\)
\(48\) 0 0
\(49\) −117.500 203.516i −0.342566 0.593341i
\(50\) 0 0
\(51\) −351.000 −0.963722
\(52\) 0 0
\(53\) −261.000 −0.676436 −0.338218 0.941068i \(-0.609824\pi\)
−0.338218 + 0.941068i \(0.609824\pi\)
\(54\) 0 0
\(55\) −135.000 233.827i −0.330971 0.573258i
\(56\) 0 0
\(57\) 72.7461i 0.169043i
\(58\) 0 0
\(59\) 684.000 + 394.908i 1.50931 + 0.871400i 0.999941 + 0.0108508i \(0.00345397\pi\)
0.509368 + 0.860549i \(0.329879\pi\)
\(60\) 0 0
\(61\) 359.500 622.672i 0.754578 1.30697i −0.191006 0.981589i \(-0.561175\pi\)
0.945584 0.325379i \(-0.105492\pi\)
\(62\) 0 0
\(63\) 81.0000 46.7654i 0.161985 0.0935220i
\(64\) 0 0
\(65\) −175.500 168.875i −0.334894 0.322252i
\(66\) 0 0
\(67\) 609.000 351.606i 1.11047 0.641128i 0.171516 0.985181i \(-0.445134\pi\)
0.938950 + 0.344054i \(0.111800\pi\)
\(68\) 0 0
\(69\) 27.0000 46.7654i 0.0471075 0.0815926i
\(70\) 0 0
\(71\) 405.000 + 233.827i 0.676967 + 0.390847i 0.798711 0.601714i \(-0.205515\pi\)
−0.121744 + 0.992561i \(0.538849\pi\)
\(72\) 0 0
\(73\) 684.160i 1.09692i 0.836178 + 0.548458i \(0.184785\pi\)
−0.836178 + 0.548458i \(0.815215\pi\)
\(74\) 0 0
\(75\) −147.000 254.611i −0.226321 0.392000i
\(76\) 0 0
\(77\) 540.000 0.799204
\(78\) 0 0
\(79\) 440.000 0.626631 0.313316 0.949649i \(-0.398560\pi\)
0.313316 + 0.949649i \(0.398560\pi\)
\(80\) 0 0
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 1195.12i 1.58049i −0.612789 0.790247i \(-0.709952\pi\)
0.612789 0.790247i \(-0.290048\pi\)
\(84\) 0 0
\(85\) 526.500 + 303.975i 0.671846 + 0.387891i
\(86\) 0 0
\(87\) 148.500 257.210i 0.182999 0.316963i
\(88\) 0 0
\(89\) 1314.00 758.638i 1.56499 0.903545i 0.568246 0.822859i \(-0.307622\pi\)
0.996740 0.0806862i \(-0.0257112\pi\)
\(90\) 0 0
\(91\) 468.000 135.100i 0.539118 0.155630i
\(92\) 0 0
\(93\) −504.000 + 290.985i −0.561961 + 0.324448i
\(94\) 0 0
\(95\) −63.0000 + 109.119i −0.0680386 + 0.117846i
\(96\) 0 0
\(97\) −1002.00 578.505i −1.04884 0.605549i −0.126517 0.991964i \(-0.540380\pi\)
−0.922325 + 0.386415i \(0.873713\pi\)
\(98\) 0 0
\(99\) 467.654i 0.474757i
\(100\) 0 0
\(101\) −787.500 1363.99i −0.775833 1.34378i −0.934325 0.356423i \(-0.883996\pi\)
0.158491 0.987360i \(-0.449337\pi\)
\(102\) 0 0
\(103\) −794.000 −0.759565 −0.379782 0.925076i \(-0.624001\pi\)
−0.379782 + 0.925076i \(0.624001\pi\)
\(104\) 0 0
\(105\) −162.000 −0.150567
\(106\) 0 0
\(107\) 225.000 + 389.711i 0.203286 + 0.352101i 0.949585 0.313509i \(-0.101505\pi\)
−0.746299 + 0.665610i \(0.768171\pi\)
\(108\) 0 0
\(109\) 595.825i 0.523576i 0.965125 + 0.261788i \(0.0843120\pi\)
−0.965125 + 0.261788i \(0.915688\pi\)
\(110\) 0 0
\(111\) −292.500 168.875i −0.250116 0.144405i
\(112\) 0 0
\(113\) 850.500 1473.11i 0.708038 1.22636i −0.257546 0.966266i \(-0.582914\pi\)
0.965584 0.260092i \(-0.0837529\pi\)
\(114\) 0 0
\(115\) −81.0000 + 46.7654i −0.0656808 + 0.0379208i
\(116\) 0 0
\(117\) −117.000 405.300i −0.0924500 0.320256i
\(118\) 0 0
\(119\) −1053.00 + 607.950i −0.811163 + 0.468325i
\(120\) 0 0
\(121\) 684.500 1185.59i 0.514275 0.890750i
\(122\) 0 0
\(123\) 94.5000 + 54.5596i 0.0692746 + 0.0399957i
\(124\) 0 0
\(125\) 1158.74i 0.829128i
\(126\) 0 0
\(127\) −832.000 1441.07i −0.581323 1.00688i −0.995323 0.0966044i \(-0.969202\pi\)
0.414000 0.910277i \(-0.364132\pi\)
\(128\) 0 0
\(129\) 246.000 0.167900
\(130\) 0 0
\(131\) 1476.00 0.984418 0.492209 0.870477i \(-0.336190\pi\)
0.492209 + 0.870477i \(0.336190\pi\)
\(132\) 0 0
\(133\) −126.000 218.238i −0.0821473 0.142283i
\(134\) 0 0
\(135\) 140.296i 0.0894427i
\(136\) 0 0
\(137\) 877.500 + 506.625i 0.547225 + 0.315941i 0.748002 0.663696i \(-0.231013\pi\)
−0.200777 + 0.979637i \(0.564347\pi\)
\(138\) 0 0
\(139\) 562.000 973.413i 0.342937 0.593984i −0.642040 0.766671i \(-0.721912\pi\)
0.984977 + 0.172687i \(0.0552450\pi\)
\(140\) 0 0
\(141\) 189.000 109.119i 0.112884 0.0651737i
\(142\) 0 0
\(143\) 585.000 2364.25i 0.342099 1.38258i
\(144\) 0 0
\(145\) −445.500 + 257.210i −0.255150 + 0.147311i
\(146\) 0 0
\(147\) −352.500 + 610.548i −0.197780 + 0.342566i
\(148\) 0 0
\(149\) 2830.50 + 1634.19i 1.55627 + 0.898510i 0.997609 + 0.0691115i \(0.0220164\pi\)
0.558657 + 0.829399i \(0.311317\pi\)
\(150\) 0 0
\(151\) 1638.52i 0.883052i 0.897248 + 0.441526i \(0.145563\pi\)
−0.897248 + 0.441526i \(0.854437\pi\)
\(152\) 0 0
\(153\) 526.500 + 911.925i 0.278203 + 0.481861i
\(154\) 0 0
\(155\) 1008.00 0.522352
\(156\) 0 0
\(157\) 1259.00 0.639995 0.319997 0.947418i \(-0.396318\pi\)
0.319997 + 0.947418i \(0.396318\pi\)
\(158\) 0 0
\(159\) 391.500 + 678.098i 0.195270 + 0.338218i
\(160\) 0 0
\(161\) 187.061i 0.0915684i
\(162\) 0 0
\(163\) −2556.00 1475.71i −1.22823 0.709118i −0.261570 0.965185i \(-0.584240\pi\)
−0.966659 + 0.256066i \(0.917574\pi\)
\(164\) 0 0
\(165\) −405.000 + 701.481i −0.191086 + 0.330971i
\(166\) 0 0
\(167\) 2718.00 1569.24i 1.25943 0.727133i 0.286468 0.958090i \(-0.407519\pi\)
0.972964 + 0.230956i \(0.0741855\pi\)
\(168\) 0 0
\(169\) −84.5000 2195.37i −0.0384615 0.999260i
\(170\) 0 0
\(171\) −189.000 + 109.119i −0.0845216 + 0.0487986i
\(172\) 0 0
\(173\) −2133.00 + 3694.46i −0.937393 + 1.62361i −0.167083 + 0.985943i \(0.553435\pi\)
−0.770310 + 0.637669i \(0.779899\pi\)
\(174\) 0 0
\(175\) −882.000 509.223i −0.380988 0.219964i
\(176\) 0 0
\(177\) 2369.45i 1.00621i
\(178\) 0 0
\(179\) 1503.00 + 2603.27i 0.627595 + 1.08703i 0.988033 + 0.154243i \(0.0492939\pi\)
−0.360438 + 0.932783i \(0.617373\pi\)
\(180\) 0 0
\(181\) −1873.00 −0.769166 −0.384583 0.923090i \(-0.625655\pi\)
−0.384583 + 0.923090i \(0.625655\pi\)
\(182\) 0 0
\(183\) −2157.00 −0.871312
\(184\) 0 0
\(185\) 292.500 + 506.625i 0.116243 + 0.201339i
\(186\) 0 0
\(187\) 6079.50i 2.37742i
\(188\) 0 0
\(189\) −243.000 140.296i −0.0935220 0.0539949i
\(190\) 0 0
\(191\) −1368.00 + 2369.45i −0.518246 + 0.897629i 0.481529 + 0.876430i \(0.340082\pi\)
−0.999775 + 0.0211985i \(0.993252\pi\)
\(192\) 0 0
\(193\) −2254.50 + 1301.64i −0.840842 + 0.485460i −0.857550 0.514400i \(-0.828015\pi\)
0.0167085 + 0.999860i \(0.494681\pi\)
\(194\) 0 0
\(195\) −175.500 + 709.275i −0.0644503 + 0.260473i
\(196\) 0 0
\(197\) 3222.00 1860.22i 1.16527 0.672768i 0.212708 0.977116i \(-0.431772\pi\)
0.952561 + 0.304347i \(0.0984384\pi\)
\(198\) 0 0
\(199\) 599.000 1037.50i 0.213377 0.369579i −0.739392 0.673275i \(-0.764887\pi\)
0.952769 + 0.303695i \(0.0982205\pi\)
\(200\) 0 0
\(201\) −1827.00 1054.82i −0.641128 0.370155i
\(202\) 0 0
\(203\) 1028.84i 0.355716i
\(204\) 0 0
\(205\) −94.5000 163.679i −0.0321959 0.0557650i
\(206\) 0 0
\(207\) −162.000 −0.0543951
\(208\) 0 0
\(209\) −1260.00 −0.417014
\(210\) 0 0
\(211\) 1196.00 + 2071.53i 0.390218 + 0.675878i 0.992478 0.122422i \(-0.0390662\pi\)
−0.602260 + 0.798300i \(0.705733\pi\)
\(212\) 0 0
\(213\) 1402.96i 0.451311i
\(214\) 0 0
\(215\) −369.000 213.042i −0.117049 0.0675784i
\(216\) 0 0
\(217\) −1008.00 + 1745.91i −0.315334 + 0.546175i
\(218\) 0 0
\(219\) 1777.50 1026.24i 0.548458 0.316652i
\(220\) 0 0
\(221\) 1521.00 + 5268.90i 0.462957 + 1.60373i
\(222\) 0 0
\(223\) 1764.00 1018.45i 0.529714 0.305830i −0.211186 0.977446i \(-0.567733\pi\)
0.740900 + 0.671615i \(0.234399\pi\)
\(224\) 0 0
\(225\) −441.000 + 763.834i −0.130667 + 0.226321i
\(226\) 0 0
\(227\) −1863.00 1075.60i −0.544721 0.314495i 0.202269 0.979330i \(-0.435168\pi\)
−0.746990 + 0.664835i \(0.768502\pi\)
\(228\) 0 0
\(229\) 3471.03i 1.00162i 0.865556 + 0.500812i \(0.166965\pi\)
−0.865556 + 0.500812i \(0.833035\pi\)
\(230\) 0 0
\(231\) −810.000 1402.96i −0.230710 0.399602i
\(232\) 0 0
\(233\) −1854.00 −0.521286 −0.260643 0.965435i \(-0.583935\pi\)
−0.260643 + 0.965435i \(0.583935\pi\)
\(234\) 0 0
\(235\) −378.000 −0.104928
\(236\) 0 0
\(237\) −660.000 1143.15i −0.180893 0.313316i
\(238\) 0 0
\(239\) 4458.30i 1.20662i 0.797505 + 0.603312i \(0.206153\pi\)
−0.797505 + 0.603312i \(0.793847\pi\)
\(240\) 0 0
\(241\) −361.500 208.712i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 1057.50 610.548i 0.275760 0.159210i
\(246\) 0 0
\(247\) −1092.00 + 315.233i −0.281305 + 0.0812057i
\(248\) 0 0
\(249\) −3105.00 + 1792.67i −0.790247 + 0.456249i
\(250\) 0 0
\(251\) 2052.00 3554.17i 0.516020 0.893773i −0.483807 0.875175i \(-0.660746\pi\)
0.999827 0.0185985i \(-0.00592043\pi\)
\(252\) 0 0
\(253\) −810.000 467.654i −0.201282 0.116210i
\(254\) 0 0
\(255\) 1823.85i 0.447898i
\(256\) 0 0
\(257\) −994.500 1722.52i −0.241382 0.418086i 0.719726 0.694258i \(-0.244267\pi\)
−0.961108 + 0.276172i \(0.910934\pi\)
\(258\) 0 0
\(259\) −1170.00 −0.280696
\(260\) 0 0
\(261\) −891.000 −0.211308
\(262\) 0 0
\(263\) 369.000 + 639.127i 0.0865153 + 0.149849i 0.906036 0.423201i \(-0.139094\pi\)
−0.819521 + 0.573050i \(0.805760\pi\)
\(264\) 0 0
\(265\) 1356.20i 0.314379i
\(266\) 0 0
\(267\) −3942.00 2275.91i −0.903545 0.521662i
\(268\) 0 0
\(269\) 1053.00 1823.85i 0.238671 0.413391i −0.721662 0.692246i \(-0.756622\pi\)
0.960333 + 0.278855i \(0.0899549\pi\)
\(270\) 0 0
\(271\) −594.000 + 342.946i −0.133147 + 0.0768727i −0.565094 0.825026i \(-0.691160\pi\)
0.431947 + 0.901899i \(0.357827\pi\)
\(272\) 0 0
\(273\) −1053.00 1013.25i −0.233445 0.224632i
\(274\) 0 0
\(275\) −4410.00 + 2546.11i −0.967029 + 0.558315i
\(276\) 0 0
\(277\) −1832.50 + 3173.98i −0.397488 + 0.688470i −0.993415 0.114569i \(-0.963451\pi\)
0.595927 + 0.803039i \(0.296785\pi\)
\(278\) 0 0
\(279\) 1512.00 + 872.954i 0.324448 + 0.187320i
\(280\) 0 0
\(281\) 1719.93i 0.365132i −0.983194 0.182566i \(-0.941560\pi\)
0.983194 0.182566i \(-0.0584404\pi\)
\(282\) 0 0
\(283\) −913.000 1581.36i −0.191775 0.332163i 0.754064 0.656801i \(-0.228091\pi\)
−0.945838 + 0.324638i \(0.894758\pi\)
\(284\) 0 0
\(285\) 378.000 0.0785642
\(286\) 0 0
\(287\) 378.000 0.0777444
\(288\) 0 0
\(289\) −4388.00 7600.24i −0.893141 1.54696i
\(290\) 0 0
\(291\) 3471.03i 0.699228i
\(292\) 0 0
\(293\) −436.500 252.013i −0.0870328 0.0502484i 0.455852 0.890056i \(-0.349335\pi\)
−0.542885 + 0.839807i \(0.682668\pi\)
\(294\) 0 0
\(295\) −2052.00 + 3554.17i −0.404990 + 0.701463i
\(296\) 0 0
\(297\) −1215.00 + 701.481i −0.237379 + 0.137051i
\(298\) 0 0
\(299\) −819.000 202.650i −0.158408 0.0391958i
\(300\) 0 0
\(301\) 738.000 426.084i 0.141321 0.0815917i
\(302\) 0 0
\(303\) −2362.50 + 4091.97i −0.447928 + 0.775833i
\(304\) 0 0
\(305\) 3235.50 + 1868.02i 0.607424 + 0.350696i
\(306\) 0 0
\(307\) 1950.29i 0.362570i −0.983431 0.181285i \(-0.941974\pi\)
0.983431 0.181285i \(-0.0580256\pi\)
\(308\) 0 0
\(309\) 1191.00 + 2062.87i 0.219267 + 0.379782i
\(310\) 0 0
\(311\) 3798.00 0.692491 0.346246 0.938144i \(-0.387456\pi\)
0.346246 + 0.938144i \(0.387456\pi\)
\(312\) 0 0
\(313\) 1378.00 0.248847 0.124424 0.992229i \(-0.460292\pi\)
0.124424 + 0.992229i \(0.460292\pi\)
\(314\) 0 0
\(315\) 243.000 + 420.888i 0.0434651 + 0.0752837i
\(316\) 0 0
\(317\) 7103.14i 1.25852i 0.777193 + 0.629262i \(0.216643\pi\)
−0.777193 + 0.629262i \(0.783357\pi\)
\(318\) 0 0
\(319\) −4455.00 2572.10i −0.781919 0.451441i
\(320\) 0 0
\(321\) 675.000 1169.13i 0.117367 0.203286i
\(322\) 0 0
\(323\) 2457.00 1418.55i 0.423254 0.244366i
\(324\) 0 0
\(325\) −3185.00 + 3309.95i −0.543606 + 0.564932i
\(326\) 0 0
\(327\) 1548.00 893.738i 0.261788 0.151143i
\(328\) 0 0
\(329\) 378.000 654.715i 0.0633429 0.109713i
\(330\) 0 0
\(331\) −8724.00 5036.80i −1.44868 0.836398i −0.450281 0.892887i \(-0.648676\pi\)
−0.998403 + 0.0564889i \(0.982009\pi\)
\(332\) 0 0
\(333\) 1013.25i 0.166744i
\(334\) 0 0
\(335\) 1827.00 + 3164.46i 0.297969 + 0.516098i
\(336\) 0 0
\(337\) 9001.00 1.45494 0.727471 0.686138i \(-0.240695\pi\)
0.727471 + 0.686138i \(0.240695\pi\)
\(338\) 0 0
\(339\) −5103.00 −0.817572
\(340\) 0 0
\(341\) 5040.00 + 8729.54i 0.800385 + 1.38631i
\(342\) 0 0
\(343\) 6006.75i 0.945581i
\(344\) 0 0
\(345\) 243.000 + 140.296i 0.0379208 + 0.0218936i
\(346\) 0 0
\(347\) 1647.00 2852.69i 0.254800 0.441327i −0.710041 0.704160i \(-0.751324\pi\)
0.964841 + 0.262834i \(0.0846570\pi\)
\(348\) 0 0
\(349\) −9132.00 + 5272.36i −1.40064 + 0.808662i −0.994459 0.105129i \(-0.966475\pi\)
−0.406185 + 0.913791i \(0.633141\pi\)
\(350\) 0 0
\(351\) −877.500 + 911.925i −0.133440 + 0.138675i
\(352\) 0 0
\(353\) −2146.50 + 1239.28i −0.323645 + 0.186856i −0.653016 0.757344i \(-0.726497\pi\)
0.329371 + 0.944201i \(0.393163\pi\)
\(354\) 0 0
\(355\) −1215.00 + 2104.44i −0.181649 + 0.314626i
\(356\) 0 0
\(357\) 3159.00 + 1823.85i 0.468325 + 0.270388i
\(358\) 0 0
\(359\) 5414.39i 0.795991i 0.917387 + 0.397995i \(0.130294\pi\)
−0.917387 + 0.397995i \(0.869706\pi\)
\(360\) 0 0
\(361\) −3135.50 5430.85i −0.457137 0.791784i
\(362\) 0 0
\(363\) −4107.00 −0.593834
\(364\) 0 0
\(365\) −3555.00 −0.509801
\(366\) 0 0
\(367\) −4973.00 8613.49i −0.707326 1.22512i −0.965846 0.259118i \(-0.916568\pi\)
0.258520 0.966006i \(-0.416765\pi\)
\(368\) 0 0
\(369\) 327.358i 0.0461831i
\(370\) 0 0
\(371\) 2349.00 + 1356.20i 0.328717 + 0.189785i
\(372\) 0 0
\(373\) 3650.50 6322.85i 0.506745 0.877707i −0.493225 0.869902i \(-0.664182\pi\)
0.999970 0.00780555i \(-0.00248461\pi\)
\(374\) 0 0
\(375\) 3010.50 1738.11i 0.414564 0.239349i
\(376\) 0 0
\(377\) −4504.50 1114.57i −0.615368 0.152264i
\(378\) 0 0
\(379\) 2964.00 1711.27i 0.401716 0.231931i −0.285508 0.958376i \(-0.592162\pi\)
0.687224 + 0.726445i \(0.258829\pi\)
\(380\) 0 0
\(381\) −2496.00 + 4323.20i −0.335627 + 0.581323i
\(382\) 0 0
\(383\) 5004.00 + 2889.06i 0.667604 + 0.385442i 0.795168 0.606389i \(-0.207382\pi\)
−0.127564 + 0.991830i \(0.540716\pi\)
\(384\) 0 0
\(385\) 2805.92i 0.371436i
\(386\) 0 0
\(387\) −369.000 639.127i −0.0484685 0.0839500i
\(388\) 0 0
\(389\) 9153.00 1.19300 0.596498 0.802614i \(-0.296558\pi\)
0.596498 + 0.802614i \(0.296558\pi\)
\(390\) 0 0
\(391\) 2106.00 0.272391
\(392\) 0 0
\(393\) −2214.00 3834.76i −0.284177 0.492209i
\(394\) 0 0
\(395\) 2286.31i 0.291232i
\(396\) 0 0
\(397\) 1752.00 + 1011.52i 0.221487 + 0.127876i 0.606639 0.794978i \(-0.292518\pi\)
−0.385152 + 0.922853i \(0.625851\pi\)
\(398\) 0 0
\(399\) −378.000 + 654.715i −0.0474277 + 0.0821473i
\(400\) 0 0
\(401\) 7195.50 4154.32i 0.896075 0.517349i 0.0201504 0.999797i \(-0.493586\pi\)
0.875925 + 0.482448i \(0.160252\pi\)
\(402\) 0 0
\(403\) 6552.00 + 6304.66i 0.809872 + 0.779300i
\(404\) 0 0
\(405\) 364.500 210.444i 0.0447214 0.0258199i
\(406\) 0 0
\(407\) −2925.00 + 5066.25i −0.356233 + 0.617014i
\(408\) 0 0
\(409\) −9022.50 5209.14i −1.09079 0.629769i −0.157005 0.987598i \(-0.550184\pi\)
−0.933787 + 0.357829i \(0.883517\pi\)
\(410\) 0 0
\(411\) 3039.75i 0.364817i
\(412\) 0 0
\(413\) −4104.00 7108.34i −0.488970 0.846921i
\(414\) 0 0
\(415\) 6210.00 0.734547
\(416\) 0 0
\(417\) −3372.00 −0.395989
\(418\) 0 0
\(419\) 2088.00 + 3616.52i 0.243450 + 0.421667i 0.961695 0.274123i \(-0.0883875\pi\)
−0.718245 + 0.695790i \(0.755054\pi\)
\(420\) 0 0
\(421\) 14471.3i 1.67527i 0.546233 + 0.837633i \(0.316061\pi\)
−0.546233 + 0.837633i \(0.683939\pi\)
\(422\) 0 0
\(423\) −567.000 327.358i −0.0651737 0.0376281i
\(424\) 0 0
\(425\) 5733.00 9929.85i 0.654333 1.13334i
\(426\) 0 0
\(427\) −6471.00 + 3736.03i −0.733381 + 0.423418i
\(428\) 0 0
\(429\) −7020.00 + 2026.50i −0.790044 + 0.228066i
\(430\) 0 0
\(431\) 5697.00 3289.16i 0.636693 0.367595i −0.146646 0.989189i \(-0.546848\pi\)
0.783340 + 0.621594i \(0.213515\pi\)
\(432\) 0 0
\(433\) 3302.50 5720.10i 0.366531 0.634851i −0.622489 0.782628i \(-0.713879\pi\)
0.989021 + 0.147778i \(0.0472120\pi\)
\(434\) 0 0
\(435\) 1336.50 + 771.629i 0.147311 + 0.0850500i
\(436\) 0 0
\(437\) 436.477i 0.0477792i
\(438\) 0 0
\(439\) −4271.00 7397.59i −0.464336 0.804254i 0.534835 0.844957i \(-0.320374\pi\)
−0.999171 + 0.0407023i \(0.987040\pi\)
\(440\) 0 0
\(441\) 2115.00 0.228377
\(442\) 0 0
\(443\) 14328.0 1.53667 0.768334 0.640049i \(-0.221086\pi\)
0.768334 + 0.640049i \(0.221086\pi\)
\(444\) 0 0
\(445\) 3942.00 + 6827.74i 0.419930 + 0.727340i
\(446\) 0 0
\(447\) 9805.14i 1.03751i
\(448\) 0 0
\(449\) 2610.00 + 1506.88i 0.274329 + 0.158384i 0.630853 0.775902i \(-0.282705\pi\)
−0.356525 + 0.934286i \(0.616038\pi\)
\(450\) 0 0
\(451\) 945.000 1636.79i 0.0986659 0.170894i
\(452\) 0 0
\(453\) 4257.00 2457.78i 0.441526 0.254915i
\(454\) 0 0
\(455\) 702.000 + 2431.80i 0.0723303 + 0.250559i
\(456\) 0 0
\(457\) −2500.50 + 1443.66i −0.255948 + 0.147772i −0.622485 0.782632i \(-0.713877\pi\)
0.366536 + 0.930404i \(0.380543\pi\)
\(458\) 0 0
\(459\) 1579.50 2735.77i 0.160620 0.278203i
\(460\) 0 0
\(461\) 3118.50 + 1800.47i 0.315061 + 0.181900i 0.649189 0.760627i \(-0.275108\pi\)
−0.334128 + 0.942528i \(0.608442\pi\)
\(462\) 0 0
\(463\) 2677.75i 0.268781i −0.990928 0.134391i \(-0.957092\pi\)
0.990928 0.134391i \(-0.0429077\pi\)
\(464\) 0 0
\(465\) −1512.00 2618.86i −0.150790 0.261176i
\(466\) 0 0
\(467\) −13878.0 −1.37515 −0.687577 0.726111i \(-0.741326\pi\)
−0.687577 + 0.726111i \(0.741326\pi\)
\(468\) 0 0
\(469\) −7308.00 −0.719514
\(470\) 0 0
\(471\) −1888.50 3270.98i −0.184751 0.319997i
\(472\) 0 0
\(473\) 4260.84i 0.414194i
\(474\) 0 0
\(475\) 2058.00 + 1188.19i 0.198795 + 0.114774i
\(476\) 0 0
\(477\) 1174.50 2034.29i 0.112739 0.195270i
\(478\) 0 0
\(479\) −954.000 + 550.792i −0.0910008 + 0.0525393i −0.544810 0.838560i \(-0.683398\pi\)
0.453809 + 0.891099i \(0.350065\pi\)
\(480\) 0 0
\(481\) −1267.50 + 5122.54i −0.120152 + 0.485588i
\(482\) 0 0
\(483\) −486.000 + 280.592i −0.0457842 + 0.0264335i
\(484\) 0 0
\(485\) 3006.00 5206.54i 0.281434 0.487458i
\(486\) 0 0
\(487\) 14829.0 + 8561.53i 1.37981 + 0.796632i 0.992136 0.125166i \(-0.0399462\pi\)
0.387671 + 0.921798i \(0.373280\pi\)
\(488\) 0 0
\(489\) 8854.24i 0.818820i
\(490\) 0 0
\(491\) 225.000 + 389.711i 0.0206805 + 0.0358196i 0.876180 0.481983i \(-0.160083\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(492\) 0 0
\(493\) 11583.0 1.05816
\(494\) 0 0
\(495\) 2430.00 0.220647
\(496\) 0 0
\(497\) −2430.00 4208.88i −0.219317 0.379868i
\(498\) 0 0
\(499\) 13219.0i 1.18590i −0.805239 0.592950i \(-0.797963\pi\)
0.805239 0.592950i \(-0.202037\pi\)
\(500\) 0 0
\(501\) −8154.00 4707.71i −0.727133 0.419811i
\(502\) 0 0
\(503\) 2673.00 4629.77i 0.236945 0.410400i −0.722891 0.690962i \(-0.757187\pi\)
0.959836 + 0.280561i \(0.0905206\pi\)
\(504\) 0 0
\(505\) 7087.50 4091.97i 0.624534 0.360575i
\(506\) 0 0
\(507\) −5577.00 + 3512.60i −0.488527 + 0.307692i
\(508\) 0 0
\(509\) −5080.50 + 2933.23i −0.442415 + 0.255428i −0.704621 0.709583i \(-0.748883\pi\)
0.262207 + 0.965012i \(0.415550\pi\)
\(510\) 0 0
\(511\) 3555.00 6157.44i 0.307757 0.533051i
\(512\) 0 0
\(513\) 567.000 + 327.358i 0.0487986 + 0.0281739i
\(514\) 0 0
\(515\) 4125.75i 0.353014i
\(516\) 0 0
\(517\) −1890.00 3273.58i −0.160778 0.278475i
\(518\) 0 0
\(519\) 12798.0 1.08241
\(520\) 0 0
\(521\) −9657.00 −0.812055 −0.406028 0.913861i \(-0.633086\pi\)
−0.406028 + 0.913861i \(0.633086\pi\)
\(522\) 0 0
\(523\) 10813.0 + 18728.7i 0.904053 + 1.56586i 0.822184 + 0.569222i \(0.192755\pi\)
0.0818685 + 0.996643i \(0.473911\pi\)
\(524\) 0 0
\(525\) 3055.34i 0.253992i
\(526\) 0 0
\(527\) −19656.0 11348.4i −1.62472 0.938034i
\(528\) 0 0
\(529\) 5921.50 10256.3i 0.486685 0.842964i
\(530\) 0 0
\(531\) −6156.00 + 3554.17i −0.503103 + 0.290467i
\(532\) 0 0
\(533\) 409.500 1654.97i 0.0332785 0.134493i
\(534\) 0 0
\(535\) −2025.00 + 1169.13i −0.163642 + 0.0944787i
\(536\) 0 0
\(537\) 4509.00 7809.82i 0.362342 0.627595i
\(538\) 0 0
\(539\) 10575.0 + 6105.48i 0.845079 + 0.487906i
\(540\) 0 0
\(541\) 5371.09i 0.426841i −0.976960 0.213421i \(-0.931540\pi\)
0.976960 0.213421i \(-0.0684605\pi\)
\(542\) 0 0
\(543\) 2809.50 + 4866.20i 0.222039 + 0.384583i
\(544\) 0 0
\(545\) −3096.00 −0.243336
\(546\) 0 0
\(547\) −16946.0 −1.32460 −0.662302 0.749237i \(-0.730421\pi\)
−0.662302 + 0.749237i \(0.730421\pi\)
\(548\) 0 0
\(549\) 3235.50 + 5604.05i 0.251526 + 0.435656i
\(550\) 0 0
\(551\) 2400.62i 0.185608i
\(552\) 0 0
\(553\) −3960.00 2286.31i −0.304514 0.175811i
\(554\) 0 0
\(555\) 877.500 1519.87i 0.0671132 0.116243i
\(556\) 0 0
\(557\) 3343.50 1930.37i 0.254342 0.146845i −0.367409 0.930060i \(-0.619755\pi\)
0.621751 + 0.783215i \(0.286422\pi\)
\(558\) 0 0
\(559\) −1066.00 3692.73i −0.0806565 0.279402i
\(560\) 0 0
\(561\) 15795.0 9119.25i 1.18871 0.686301i
\(562\) 0 0
\(563\) 10836.0 18768.5i 0.811160 1.40497i −0.100893 0.994897i \(-0.532170\pi\)
0.912053 0.410073i \(-0.134497\pi\)
\(564\) 0 0
\(565\) 7654.50 + 4419.33i 0.569960 + 0.329066i
\(566\) 0 0
\(567\) 841.777i 0.0623480i
\(568\) 0 0
\(569\) 693.000 + 1200.31i 0.0510581 + 0.0884353i 0.890425 0.455130i \(-0.150407\pi\)
−0.839367 + 0.543565i \(0.817074\pi\)
\(570\) 0 0
\(571\) −1162.00 −0.0851632 −0.0425816 0.999093i \(-0.513558\pi\)
−0.0425816 + 0.999093i \(0.513558\pi\)
\(572\) 0 0
\(573\) 8208.00 0.598419
\(574\) 0 0
\(575\) 882.000 + 1527.67i 0.0639686 + 0.110797i
\(576\) 0 0
\(577\) 8045.38i 0.580474i −0.956955 0.290237i \(-0.906266\pi\)
0.956955 0.290237i \(-0.0937341\pi\)
\(578\) 0 0
\(579\) 6763.50 + 3904.91i 0.485460 + 0.280281i
\(580\) 0 0
\(581\) −6210.00 + 10756.0i −0.443432 + 0.768047i
\(582\) 0 0
\(583\) 11745.0 6780.98i 0.834354 0.481714i
\(584\) 0 0
\(585\) 2106.00 607.950i 0.148842 0.0429669i
\(586\) 0 0
\(587\) 23922.0 13811.4i 1.68206 0.971135i 0.721763 0.692140i \(-0.243332\pi\)
0.960293 0.278995i \(-0.0900013\pi\)
\(588\) 0 0
\(589\) 2352.00 4073.78i 0.164537 0.284987i
\(590\) 0 0
\(591\) −9666.00 5580.67i −0.672768 0.388423i
\(592\) 0 0
\(593\) 275.396i 0.0190711i −0.999955 0.00953555i \(-0.996965\pi\)
0.999955 0.00953555i \(-0.00303531\pi\)
\(594\) 0 0
\(595\) −3159.00 5471.55i −0.217658 0.376994i
\(596\) 0 0
\(597\) −3594.00 −0.246386
\(598\) 0 0
\(599\) −22356.0 −1.52494 −0.762472 0.647021i \(-0.776014\pi\)
−0.762472 + 0.647021i \(0.776014\pi\)
\(600\) 0 0
\(601\) 9041.50 + 15660.3i 0.613661 + 1.06289i 0.990618 + 0.136662i \(0.0436373\pi\)
−0.376956 + 0.926231i \(0.623029\pi\)
\(602\) 0 0
\(603\) 6328.91i 0.427418i
\(604\) 0 0
\(605\) 6160.50 + 3556.77i 0.413983 + 0.239013i
\(606\) 0 0
\(607\) 2740.00 4745.82i 0.183218 0.317342i −0.759757 0.650207i \(-0.774682\pi\)
0.942975 + 0.332865i \(0.108015\pi\)
\(608\) 0 0
\(609\) −2673.00 + 1543.26i −0.177858 + 0.102686i
\(610\) 0 0
\(611\) −2457.00 2364.25i −0.162683 0.156542i
\(612\) 0 0
\(613\) 15361.5 8868.97i 1.01215 0.584362i 0.100326 0.994955i \(-0.468011\pi\)
0.911819 + 0.410592i \(0.134678\pi\)
\(614\) 0 0
\(615\) −283.500 + 491.036i −0.0185883 + 0.0321959i
\(616\) 0 0
\(617\) 8545.50 + 4933.75i 0.557583 + 0.321921i 0.752175 0.658963i \(-0.229005\pi\)
−0.194592 + 0.980884i \(0.562338\pi\)
\(618\) 0 0
\(619\) 4115.35i 0.267221i −0.991034 0.133611i \(-0.957343\pi\)
0.991034 0.133611i \(-0.0426572\pi\)
\(620\) 0 0
\(621\) 243.000 + 420.888i 0.0157025 + 0.0271975i
\(622\) 0 0
\(623\) −15768.0 −1.01402
\(624\) 0 0
\(625\) 6229.00 0.398656
\(626\) 0 0
\(627\) 1890.00 + 3273.58i 0.120382 + 0.208507i
\(628\) 0 0
\(629\) 13172.2i 0.834995i
\(630\) 0 0
\(631\) 10968.0 + 6332.38i 0.691964 + 0.399506i 0.804347 0.594159i \(-0.202515\pi\)
−0.112383 + 0.993665i \(0.535849\pi\)
\(632\) 0 0
\(633\) 3588.00 6214.60i 0.225293 0.390218i
\(634\) 0 0
\(635\) 7488.00 4323.20i 0.467956 0.270175i
\(636\) 0 0
\(637\) 10692.5 + 2645.71i 0.665074 + 0.164563i
\(638\) 0 0
\(639\) −3645.00 + 2104.44i −0.225656 + 0.130282i
\(640\) 0 0
\(641\) 1894.50 3281.37i 0.116737 0.202194i −0.801736 0.597678i \(-0.796090\pi\)
0.918473 + 0.395484i \(0.129423\pi\)
\(642\) 0 0
\(643\) −14646.0 8455.87i −0.898261 0.518611i −0.0216255 0.999766i \(-0.506884\pi\)
−0.876636 + 0.481155i \(0.840217\pi\)
\(644\) 0 0
\(645\) 1278.25i 0.0780328i
\(646\) 0 0
\(647\) −13896.0 24068.6i −0.844371 1.46249i −0.886166 0.463368i \(-0.846641\pi\)
0.0417951 0.999126i \(-0.486692\pi\)
\(648\) 0 0
\(649\) −41040.0 −2.48222
\(650\) 0 0
\(651\) 6048.00 0.364116
\(652\) 0 0
\(653\) 297.000 + 514.419i 0.0177986 + 0.0308281i 0.874788 0.484507i \(-0.161001\pi\)
−0.856989 + 0.515335i \(0.827668\pi\)
\(654\) 0 0
\(655\) 7669.52i 0.457516i
\(656\) 0 0
\(657\) −5332.50 3078.72i −0.316652 0.182819i
\(658\) 0 0
\(659\) 8874.00 15370.2i 0.524555 0.908556i −0.475036 0.879966i \(-0.657565\pi\)
0.999591 0.0285901i \(-0.00910174\pi\)
\(660\) 0 0
\(661\) 13675.5 7895.55i 0.804713 0.464601i −0.0404035 0.999183i \(-0.512864\pi\)
0.845117 + 0.534582i \(0.179531\pi\)
\(662\) 0 0
\(663\) 11407.5 11855.0i 0.668221 0.694436i
\(664\) 0 0
\(665\) 1134.00 654.715i 0.0661273 0.0381786i
\(666\) 0 0
\(667\) −891.000 + 1543.26i −0.0517236 + 0.0895879i
\(668\) 0 0
\(669\) −5292.00 3055.34i −0.305830 0.176571i
\(670\) 0 0
\(671\) 37360.3i 2.14945i
\(672\) 0 0
\(673\) −10466.5 18128.5i −0.599486 1.03834i −0.992897 0.118977i \(-0.962038\pi\)
0.393411 0.919363i \(-0.371295\pi\)
\(674\) 0 0
\(675\) 2646.00 0.150881
\(676\) 0 0
\(677\) 3402.00 0.193131 0.0965653 0.995327i \(-0.469214\pi\)
0.0965653 + 0.995327i \(0.469214\pi\)
\(678\) 0 0
\(679\) 6012.00 + 10413.1i 0.339793 + 0.588539i
\(680\) 0 0
\(681\) 6453.62i 0.363147i
\(682\) 0 0
\(683\) −21636.0 12491.6i −1.21212 0.699818i −0.248900 0.968529i \(-0.580069\pi\)
−0.963221 + 0.268711i \(0.913402\pi\)
\(684\) 0 0
\(685\) −2632.50 + 4559.62i −0.146836 + 0.254327i
\(686\) 0 0
\(687\) 9018.00 5206.54i 0.500812 0.289144i
\(688\) 0 0
\(689\) 8482.50 8815.27i 0.469024 0.487424i
\(690\) 0 0
\(691\) −12009.0 + 6933.40i −0.661134 + 0.381706i −0.792709 0.609600i \(-0.791330\pi\)
0.131575 + 0.991306i \(0.457997\pi\)
\(692\) 0 0
\(693\) −2430.00 + 4208.88i −0.133201 + 0.230710i
\(694\) 0 0
\(695\) 5058.00 + 2920.24i 0.276059 + 0.159383i
\(696\) 0 0
\(697\) 4255.65i 0.231269i
\(698\) 0 0
\(699\) 2781.00 + 4816.83i 0.150482 + 0.260643i
\(700\) 0 0
\(701\) −21906.0 −1.18028 −0.590141 0.807300i \(-0.700928\pi\)
−0.590141 + 0.807300i \(0.700928\pi\)
\(702\) 0 0
\(703\) 2730.00 0.146464
\(704\) 0 0
\(705\) 567.000 + 982.073i 0.0302900 + 0.0524638i
\(706\) 0 0
\(707\) 16367.9i 0.870690i
\(708\) 0 0
\(709\) −11308.5 6528.97i −0.599012 0.345840i 0.169641 0.985506i \(-0.445739\pi\)
−0.768653 + 0.639666i \(0.779073\pi\)
\(710\) 0 0
\(711\) −1980.00 + 3429.46i −0.104439 + 0.180893i
\(712\) 0 0
\(713\) 3024.00 1745.91i 0.158835 0.0917037i
\(714\) 0 0
\(715\) 12285.0 + 3039.75i 0.642564 + 0.158993i
\(716\) 0 0
\(717\) 11583.0 6687.45i 0.603312 0.348323i
\(718\) 0 0
\(719\) −7110.00 + 12314.9i −0.368788 + 0.638759i −0.989376 0.145377i \(-0.953560\pi\)
0.620589 + 0.784136i \(0.286894\pi\)
\(720\) 0 0
\(721\) 7146.00 + 4125.75i 0.369114 + 0.213108i
\(722\) 0 0
\(723\) 1252.27i 0.0644157i
\(724\) 0 0
\(725\) 4851.00 + 8402.18i 0.248499 + 0.430413i
\(726\) 0 0
\(727\) 5282.00 0.269462 0.134731 0.990882i \(-0.456983\pi\)
0.134731 + 0.990882i \(0.456983\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 4797.00 + 8308.65i 0.242713 + 0.420392i
\(732\) 0 0
\(733\) 11419.4i 0.575424i 0.957717 + 0.287712i \(0.0928945\pi\)
−0.957717 + 0.287712i \(0.907105\pi\)
\(734\) 0 0
\(735\) −3172.50 1831.64i −0.159210 0.0919200i
\(736\) 0 0
\(737\) −18270.0 + 31644.6i −0.913140 + 1.58160i
\(738\) 0 0
\(739\) 17784.0 10267.6i 0.885244 0.511096i 0.0128599 0.999917i \(-0.495906\pi\)
0.872384 + 0.488822i \(0.162573\pi\)
\(740\) 0 0
\(741\) 2457.00 + 2364.25i 0.121809 + 0.117210i
\(742\) 0 0
\(743\) 18036.0 10413.1i 0.890547 0.514158i 0.0164258 0.999865i \(-0.494771\pi\)
0.874121 + 0.485707i \(0.161438\pi\)
\(744\) 0 0
\(745\) −8491.50 + 14707.7i −0.417590 + 0.723287i
\(746\) 0 0
\(747\) 9315.00 + 5378.02i 0.456249 + 0.263416i
\(748\) 0 0
\(749\) 4676.54i 0.228140i
\(750\) 0 0
\(751\) −2417.00 4186.37i −0.117440 0.203412i 0.801312 0.598246i \(-0.204136\pi\)
−0.918753 + 0.394834i \(0.870802\pi\)
\(752\) 0 0
\(753\) −12312.0 −0.595849
\(754\) 0 0
\(755\) −8514.00 −0.410406
\(756\) 0 0
\(757\) −4523.00 7834.07i −0.217161 0.376135i 0.736778 0.676135i \(-0.236346\pi\)
−0.953939 + 0.300001i \(0.903013\pi\)
\(758\) 0 0
\(759\) 2805.92i 0.134188i
\(760\) 0 0
\(761\) −10422.0 6017.14i −0.496448 0.286625i 0.230797 0.973002i \(-0.425867\pi\)
−0.727246 + 0.686377i \(0.759200\pi\)
\(762\) 0 0
\(763\) 3096.00 5362.43i 0.146897 0.254434i
\(764\) 0 0
\(765\) −4738.50 + 2735.77i −0.223949 + 0.129297i
\(766\) 0 0
\(767\) −35568.0 + 10267.6i −1.67443 + 0.483366i
\(768\) 0 0
\(769\) 32514.0 18772.0i 1.52469 0.880279i 0.525115 0.851031i \(-0.324022\pi\)
0.999572 0.0292479i \(-0.00931121\pi\)
\(770\) 0 0
\(771\) −2983.50 + 5167.57i −0.139362 + 0.241382i
\(772\) 0 0
\(773\) −13608.0 7856.58i −0.633177 0.365565i 0.148804 0.988867i \(-0.452457\pi\)
−0.781981 + 0.623302i \(0.785791\pi\)
\(774\) 0 0
\(775\) 19011.0i 0.881155i
\(776\) 0 0
\(777\) 1755.00 + 3039.75i 0.0810300 + 0.140348i
\(778\) 0 0
\(779\) −882.000 −0.0405660
\(780\) 0 0
\(781\) −24300.0 −1.11334
\(782\) 0 0
\(783\) 1336.50 + 2314.89i 0.0609995 + 0.105654i
\(784\) 0 0
\(785\) 6541.96i 0.297443i
\(786\) 0 0
\(787\) 3252.00 + 1877.54i 0.147295 + 0.0850409i 0.571836 0.820368i \(-0.306231\pi\)
−0.424541 + 0.905409i \(0.639565\pi\)
\(788\) 0 0
\(789\) 1107.00 1917.38i 0.0499496 0.0865153i
\(790\)