Properties

Label 39.4.j.a.4.1
Level $39$
Weight $4$
Character 39.4
Analytic conductor $2.301$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 39.4
Dual form 39.4.j.a.10.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +(-4.00000 - 6.92820i) q^{4} -5.19615i q^{5} +(9.00000 - 5.19615i) q^{7} +(-4.50000 - 7.79423i) q^{9} +(45.0000 + 25.9808i) q^{11} -24.0000 q^{12} +(-32.5000 - 33.7750i) q^{13} +(-13.5000 - 7.79423i) q^{15} +(-32.0000 + 55.4256i) q^{16} +(58.5000 + 101.325i) q^{17} +(-21.0000 + 12.1244i) q^{19} +(-36.0000 + 20.7846i) q^{20} -31.1769i q^{21} +(-9.00000 + 15.5885i) q^{23} +98.0000 q^{25} -27.0000 q^{27} +(-72.0000 - 41.5692i) q^{28} +(49.5000 - 85.7365i) q^{29} -193.990i q^{31} +(135.000 - 77.9423i) q^{33} +(-27.0000 - 46.7654i) q^{35} +(-36.0000 + 62.3538i) q^{36} +(97.5000 + 56.2917i) q^{37} +(-136.500 + 33.7750i) q^{39} +(-31.5000 - 18.1865i) q^{41} +(41.0000 + 71.0141i) q^{43} -415.692i q^{44} +(-40.5000 + 23.3827i) q^{45} +72.7461i q^{47} +(96.0000 + 166.277i) q^{48} +(-117.500 + 203.516i) q^{49} +351.000 q^{51} +(-104.000 + 360.267i) q^{52} -261.000 q^{53} +(135.000 - 233.827i) q^{55} +72.7461i q^{57} +(-684.000 + 394.908i) q^{59} +124.708i q^{60} +(359.500 + 622.672i) q^{61} +(-81.0000 - 46.7654i) q^{63} +512.000 q^{64} +(-175.500 + 168.875i) q^{65} +(-609.000 - 351.606i) q^{67} +(468.000 - 810.600i) q^{68} +(27.0000 + 46.7654i) q^{69} +(-405.000 + 233.827i) q^{71} -684.160i q^{73} +(147.000 - 254.611i) q^{75} +(168.000 + 96.9948i) q^{76} +540.000 q^{77} -440.000 q^{79} +(288.000 + 166.277i) q^{80} +(-40.5000 + 70.1481i) q^{81} -1195.12i q^{83} +(-216.000 + 124.708i) q^{84} +(526.500 - 303.975i) q^{85} +(-148.500 - 257.210i) q^{87} +(1314.00 + 758.638i) q^{89} +(-468.000 - 135.100i) q^{91} +144.000 q^{92} +(-504.000 - 290.985i) q^{93} +(63.0000 + 109.119i) q^{95} +(-1002.00 + 578.505i) q^{97} -467.654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} - 8 q^{4} + 18 q^{7} - 9 q^{9} + 90 q^{11} - 48 q^{12} - 65 q^{13} - 27 q^{15} - 64 q^{16} + 117 q^{17} - 42 q^{19} - 72 q^{20} - 18 q^{23} + 196 q^{25} - 54 q^{27} - 144 q^{28} + 99 q^{29} + 270 q^{33} - 54 q^{35} - 72 q^{36} + 195 q^{37} - 273 q^{39} - 63 q^{41} + 82 q^{43} - 81 q^{45} + 192 q^{48} - 235 q^{49} + 702 q^{51} - 208 q^{52} - 522 q^{53} + 270 q^{55} - 1368 q^{59} + 719 q^{61} - 162 q^{63} + 1024 q^{64} - 351 q^{65} - 1218 q^{67} + 936 q^{68} + 54 q^{69} - 810 q^{71} + 294 q^{75} + 336 q^{76} + 1080 q^{77} - 880 q^{79} + 576 q^{80} - 81 q^{81} - 432 q^{84} + 1053 q^{85} - 297 q^{87} + 2628 q^{89} - 936 q^{91} + 288 q^{92} - 1008 q^{93} + 126 q^{95} - 2004 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −4.00000 6.92820i −0.500000 0.866025i
\(5\) 5.19615i 0.464758i −0.972625 0.232379i \(-0.925349\pi\)
0.972625 0.232379i \(-0.0746510\pi\)
\(6\) 0 0
\(7\) 9.00000 5.19615i 0.485954 0.280566i −0.236940 0.971524i \(-0.576145\pi\)
0.722895 + 0.690958i \(0.242811\pi\)
\(8\) 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 \(-0.0810613\pi\)
0.265707 + 0.964054i \(0.414395\pi\)
\(12\) −24.0000 −0.577350
\(13\) −32.5000 33.7750i −0.693375 0.720577i
\(14\) 0 0
\(15\) −13.5000 7.79423i −0.232379 0.134164i
\(16\) −32.0000 + 55.4256i −0.500000 + 0.866025i
\(17\) 58.5000 + 101.325i 0.834608 + 1.44558i 0.894349 + 0.447369i \(0.147639\pi\)
−0.0597414 + 0.998214i \(0.519028\pi\)
\(18\) 0 0
\(19\) −21.0000 + 12.1244i −0.253565 + 0.146396i −0.621395 0.783497i \(-0.713434\pi\)
0.367831 + 0.929893i \(0.380101\pi\)
\(20\) −36.0000 + 20.7846i −0.402492 + 0.232379i
\(21\) 31.1769i 0.323970i
\(22\) 0 0
\(23\) −9.00000 + 15.5885i −0.0815926 + 0.141323i −0.903934 0.427672i \(-0.859334\pi\)
0.822342 + 0.568994i \(0.192667\pi\)
\(24\) 0 0
\(25\) 98.0000 0.784000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) −72.0000 41.5692i −0.485954 0.280566i
\(29\) 49.5000 85.7365i 0.316963 0.548996i −0.662890 0.748717i \(-0.730670\pi\)
0.979853 + 0.199721i \(0.0640037\pi\)
\(30\) 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
\(36\) −36.0000 + 62.3538i −0.166667 + 0.288675i
\(37\) 97.5000 + 56.2917i 0.433214 + 0.250116i 0.700715 0.713442i \(-0.252865\pi\)
−0.267501 + 0.963558i \(0.586198\pi\)
\(38\) 0 0
\(39\) −136.500 + 33.7750i −0.560449 + 0.138675i
\(40\) 0 0
\(41\) −31.5000 18.1865i −0.119987 0.0692746i 0.438805 0.898582i \(-0.355402\pi\)
−0.558792 + 0.829308i \(0.688735\pi\)
\(42\) 0 0
\(43\) 41.0000 + 71.0141i 0.145406 + 0.251850i 0.929524 0.368761i \(-0.120218\pi\)
−0.784119 + 0.620611i \(0.786885\pi\)
\(44\) 415.692i 1.42427i
\(45\) −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 \(0.963991\pi\)
\(48\) 96.0000 + 166.277i 0.288675 + 0.500000i
\(49\) −117.500 + 203.516i −0.342566 + 0.593341i
\(50\) 0 0
\(51\) 351.000 0.963722
\(52\) −104.000 + 360.267i −0.277350 + 0.960769i
\(53\) −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 −0.509368 + 0.860549i \(0.670121\pi\)
−0.999941 + 0.0108508i \(0.996546\pi\)
\(60\) 124.708i 0.268328i
\(61\) 359.500 + 622.672i 0.754578 + 1.30697i 0.945584 + 0.325379i \(0.105492\pi\)
−0.191006 + 0.981589i \(0.561175\pi\)
\(62\) 0 0
\(63\) −81.0000 46.7654i −0.161985 0.0935220i
\(64\) 512.000 1.00000
\(65\) −175.500 + 168.875i −0.334894 + 0.322252i
\(66\) 0 0
\(67\) −609.000 351.606i −1.11047 0.641128i −0.171516 0.985181i \(-0.554866\pi\)
−0.938950 + 0.344054i \(0.888200\pi\)
\(68\) 468.000 810.600i 0.834608 1.44558i
\(69\) 27.0000 + 46.7654i 0.0471075 + 0.0815926i
\(70\) 0 0
\(71\) −405.000 + 233.827i −0.676967 + 0.390847i −0.798711 0.601714i \(-0.794485\pi\)
0.121744 + 0.992561i \(0.461151\pi\)
\(72\) 0 0
\(73\) 684.160i 1.09692i −0.836178 0.548458i \(-0.815215\pi\)
0.836178 0.548458i \(-0.184785\pi\)
\(74\) 0 0
\(75\) 147.000 254.611i 0.226321 0.392000i
\(76\) 168.000 + 96.9948i 0.253565 + 0.146396i
\(77\) 540.000 0.799204
\(78\) 0 0
\(79\) −440.000 −0.626631 −0.313316 0.949649i \(-0.601440\pi\)
−0.313316 + 0.949649i \(0.601440\pi\)
\(80\) 288.000 + 166.277i 0.402492 + 0.232379i
\(81\) −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 \(-0.290048\pi\)
\(84\) −216.000 + 124.708i −0.280566 + 0.161985i
\(85\) 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 0.996740 + 0.0806862i \(0.0257112\pi\)
0.568246 + 0.822859i \(0.307622\pi\)
\(90\) 0 0
\(91\) −468.000 135.100i −0.539118 0.155630i
\(92\) 144.000 0.163185
\(93\) −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 −0.922325 0.386415i \(-0.873713\pi\)
−0.126517 + 0.991964i \(0.540380\pi\)
\(98\) 0 0
\(99\) 467.654i 0.474757i
\(100\) −392.000 678.964i −0.392000 0.678964i
\(101\) −787.500 + 1363.99i −0.775833 + 1.34378i 0.158491 + 0.987360i \(0.449337\pi\)
−0.934325 + 0.356423i \(0.883996\pi\)
\(102\) 0 0
\(103\) 794.000 0.759565 0.379782 0.925076i \(-0.375999\pi\)
0.379782 + 0.925076i \(0.375999\pi\)
\(104\) 0 0
\(105\) −162.000 −0.150567
\(106\) 0 0
\(107\) −225.000 + 389.711i −0.203286 + 0.352101i −0.949585 0.313509i \(-0.898495\pi\)
0.746299 + 0.665610i \(0.231829\pi\)
\(108\) 108.000 + 187.061i 0.0962250 + 0.166667i
\(109\) 595.825i 0.523576i −0.965125 0.261788i \(-0.915688\pi\)
0.965125 0.261788i \(-0.0843120\pi\)
\(110\) 0 0
\(111\) 292.500 168.875i 0.250116 0.144405i
\(112\) 665.108i 0.561132i
\(113\) 850.500 + 1473.11i 0.708038 + 1.22636i 0.965584 + 0.260092i \(0.0837529\pi\)
−0.257546 + 0.966266i \(0.582914\pi\)
\(114\) 0 0
\(115\) 81.0000 + 46.7654i 0.0656808 + 0.0379208i
\(116\) −792.000 −0.633925
\(117\) −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
\(124\) −1344.00 + 775.959i −0.973345 + 0.561961i
\(125\) 1158.74i 0.829128i
\(126\) 0 0
\(127\) 832.000 1441.07i 0.581323 1.00688i −0.414000 0.910277i \(-0.635868\pi\)
0.995323 0.0966044i \(-0.0307982\pi\)
\(128\) 0 0
\(129\) 246.000 0.167900
\(130\) 0 0
\(131\) −1476.00 −0.984418 −0.492209 0.870477i \(-0.663810\pi\)
−0.492209 + 0.870477i \(0.663810\pi\)
\(132\) −1080.00 623.538i −0.712136 0.411152i
\(133\) −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 −0.200777 0.979637i \(-0.564347\pi\)
0.748002 + 0.663696i \(0.231013\pi\)
\(138\) 0 0
\(139\) −562.000 973.413i −0.342937 0.593984i 0.642040 0.766671i \(-0.278088\pi\)
−0.984977 + 0.172687i \(0.944755\pi\)
\(140\) −216.000 + 374.123i −0.130395 + 0.225851i
\(141\) 189.000 + 109.119i 0.112884 + 0.0651737i
\(142\) 0 0
\(143\) −585.000 2364.25i −0.342099 1.38258i
\(144\) 576.000 0.333333
\(145\) −445.500 257.210i −0.255150 0.147311i
\(146\) 0 0
\(147\) 352.500 + 610.548i 0.197780 + 0.342566i
\(148\) 900.666i 0.500232i
\(149\) 2830.50 1634.19i 1.55627 0.898510i 0.558657 0.829399i \(-0.311317\pi\)
0.997609 0.0691115i \(-0.0220164\pi\)
\(150\) 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
\(156\) 780.000 + 810.600i 0.400320 + 0.416025i
\(157\) 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 \(-0.415760\pi\)
0.966659 + 0.256066i \(0.0824264\pi\)
\(164\) 290.985i 0.138549i
\(165\) −405.000 701.481i −0.191086 0.330971i
\(166\) 0 0
\(167\) −2718.00 1569.24i −1.25943 0.727133i −0.286468 0.958090i \(-0.592481\pi\)
−0.972964 + 0.230956i \(0.925815\pi\)
\(168\) 0 0
\(169\) −84.5000 + 2195.37i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 189.000 + 109.119i 0.0845216 + 0.0487986i
\(172\) 328.000 568.113i 0.145406 0.251850i
\(173\) −2133.00 3694.46i −0.937393 1.62361i −0.770310 0.637669i \(-0.779899\pi\)
−0.167083 0.985943i \(-0.553435\pi\)
\(174\) 0 0
\(175\) 882.000 509.223i 0.380988 0.219964i
\(176\) −2880.00 + 1662.77i −1.23346 + 0.712136i
\(177\) 2369.45i 1.00621i
\(178\) 0 0
\(179\) −1503.00 + 2603.27i −0.627595 + 1.08703i 0.360438 + 0.932783i \(0.382627\pi\)
−0.988033 + 0.154243i \(0.950706\pi\)
\(180\) 324.000 + 187.061i 0.134164 + 0.0774597i
\(181\) −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
\(188\) 504.000 290.985i 0.195521 0.112884i
\(189\) −243.000 + 140.296i −0.0935220 + 0.0539949i
\(190\) 0 0
\(191\) 1368.00 + 2369.45i 0.518246 + 0.897629i 0.999775 + 0.0211985i \(0.00674821\pi\)
−0.481529 + 0.876430i \(0.659918\pi\)
\(192\) 768.000 1330.22i 0.288675 0.500000i
\(193\) −2254.50 1301.64i −0.840842 0.485460i 0.0167085 0.999860i \(-0.494681\pi\)
−0.857550 + 0.514400i \(0.828015\pi\)
\(194\) 0 0
\(195\) 175.500 + 709.275i 0.0644503 + 0.260473i
\(196\) 1880.00 0.685131
\(197\) 3222.00 + 1860.22i 1.16527 + 0.672768i 0.952561 0.304347i \(-0.0984384\pi\)
0.212708 + 0.977116i \(0.431772\pi\)
\(198\) 0 0
\(199\) −599.000 1037.50i −0.213377 0.369579i 0.739392 0.673275i \(-0.235113\pi\)
−0.952769 + 0.303695i \(0.901780\pi\)
\(200\) 0 0
\(201\) −1827.00 + 1054.82i −0.641128 + 0.370155i
\(202\) 0 0
\(203\) 1028.84i 0.355716i
\(204\) −1404.00 2431.80i −0.481861 0.834608i
\(205\) −94.5000 + 163.679i −0.0321959 + 0.0557650i
\(206\) 0 0
\(207\) 162.000 0.0543951
\(208\) 2912.00 720.533i 0.970725 0.240192i
\(209\) −1260.00 −0.417014
\(210\) 0 0
\(211\) −1196.00 + 2071.53i −0.390218 + 0.675878i −0.992478 0.122422i \(-0.960934\pi\)
0.602260 + 0.798300i \(0.294267\pi\)
\(212\) 1044.00 + 1808.26i 0.338218 + 0.585811i
\(213\) 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
\(220\) −2160.00 −0.661942
\(221\) 1521.00 5268.90i 0.462957 1.60373i
\(222\) 0 0
\(223\) −1764.00 1018.45i −0.529714 0.305830i 0.211186 0.977446i \(-0.432267\pi\)
−0.740900 + 0.671615i \(0.765601\pi\)
\(224\) 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 \(-0.564832\pi\)
0.746990 + 0.664835i \(0.231498\pi\)
\(228\) 504.000 290.985i 0.146396 0.0845216i
\(229\) 3471.03i 1.00162i −0.865556 0.500812i \(-0.833035\pi\)
0.865556 0.500812i \(-0.166965\pi\)
\(230\) 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
\(236\) 5472.00 + 3159.26i 1.50931 + 0.871400i
\(237\) −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 \(0.793847\pi\)
\(240\) 864.000 498.831i 0.232379 0.134164i
\(241\) −361.500 + 208.712i −0.0966235 + 0.0557856i −0.547533 0.836784i \(-0.684433\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 2876.00 4981.38i 0.754578 1.30697i
\(245\) 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 −0.999827 0.0185985i \(-0.994080\pi\)
0.483807 0.875175i \(-0.339254\pi\)
\(252\) 748.246i 0.187044i
\(253\) −810.000 + 467.654i −0.201282 + 0.116210i
\(254\) 0 0
\(255\) 1823.85i 0.447898i
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) −994.500 + 1722.52i −0.241382 + 0.418086i −0.961108 0.276172i \(-0.910934\pi\)
0.719726 + 0.694258i \(0.244267\pi\)
\(258\) 0 0
\(259\) 1170.00 0.280696
\(260\) 1872.00 + 540.400i 0.446525 + 0.128901i
\(261\) −891.000 −0.211308
\(262\) 0 0
\(263\) −369.000 + 639.127i −0.0865153 + 0.149849i −0.906036 0.423201i \(-0.860906\pi\)
0.819521 + 0.573050i \(0.194240\pi\)
\(264\) 0 0
\(265\) 1356.20i 0.314379i
\(266\) 0 0
\(267\) 3942.00 2275.91i 0.903545 0.521662i
\(268\) 5625.70i 1.28226i
\(269\) 1053.00 + 1823.85i 0.238671 + 0.413391i 0.960333 0.278855i \(-0.0899549\pi\)
−0.721662 + 0.692246i \(0.756622\pi\)
\(270\) 0 0
\(271\) 594.000 + 342.946i 0.133147 + 0.0768727i 0.565094 0.825026i \(-0.308840\pi\)
−0.431947 + 0.901899i \(0.642173\pi\)
\(272\) −7488.00 −1.66922
\(273\) −1053.00 + 1013.25i −0.233445 + 0.224632i
\(274\) 0 0
\(275\) 4410.00 + 2546.11i 0.967029 + 0.558315i
\(276\) 216.000 374.123i 0.0471075 0.0815926i
\(277\) −1832.50 3173.98i −0.397488 0.688470i 0.595927 0.803039i \(-0.296785\pi\)
−0.993415 + 0.114569i \(0.963451\pi\)
\(278\) 0 0
\(279\) −1512.00 + 872.954i −0.324448 + 0.187320i
\(280\) 0 0
\(281\) 1719.93i 0.365132i 0.983194 + 0.182566i \(0.0584404\pi\)
−0.983194 + 0.182566i \(0.941560\pi\)
\(282\) 0 0
\(283\) 913.000 1581.36i 0.191775 0.332163i −0.754064 0.656801i \(-0.771909\pi\)
0.945838 + 0.324638i \(0.105242\pi\)
\(284\) 3240.00 + 1870.61i 0.676967 + 0.390847i
\(285\) 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
\(292\) −4740.00 + 2736.64i −0.949957 + 0.548458i
\(293\) −436.500 + 252.013i −0.0870328 + 0.0502484i −0.542885 0.839807i \(-0.682668\pi\)
0.455852 + 0.890056i \(0.349335\pi\)
\(294\) 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
\(300\) −2352.00 −0.452643
\(301\) 738.000 + 426.084i 0.141321 + 0.0815917i
\(302\) 0 0
\(303\) 2362.50 + 4091.97i 0.447928 + 0.775833i
\(304\) 1551.92i 0.292791i
\(305\) 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 \(-0.0580256\pi\)
\(308\) −2160.00 3741.23i −0.399602 0.692131i
\(309\) 1191.00 2062.87i 0.219267 0.379782i
\(310\) 0 0
\(311\) −3798.00 −0.692491 −0.346246 0.938144i \(-0.612544\pi\)
−0.346246 + 0.938144i \(0.612544\pi\)
\(312\) 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
\(316\) 1760.00 + 3048.41i 0.313316 + 0.542679i
\(317\) 7103.14i 1.25852i −0.777193 0.629262i \(-0.783357\pi\)
0.777193 0.629262i \(-0.216643\pi\)
\(318\) 0 0
\(319\) 4455.00 2572.10i 0.781919 0.451441i
\(320\) 2660.43i 0.464758i
\(321\) 675.000 + 1169.13i 0.117367 + 0.203286i
\(322\) 0 0
\(323\) −2457.00 1418.55i −0.423254 0.244366i
\(324\) 648.000 0.111111
\(325\) −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 \(-0.351324\pi\)
0.998403 + 0.0564889i \(0.0179906\pi\)
\(332\) −8280.00 + 4780.46i −1.36875 + 0.790247i
\(333\) 1013.25i 0.166744i
\(334\) 0 0
\(335\) −1827.00 + 3164.46i −0.297969 + 0.516098i
\(336\) 1728.00 + 997.661i 0.280566 + 0.161985i
\(337\) 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
\(340\) −4212.00 2431.80i −0.671846 0.387891i
\(341\) 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 \(-0.248676\pi\)
−0.964841 + 0.262834i \(0.915343\pi\)
\(348\) −1188.00 + 2057.68i −0.182999 + 0.316963i
\(349\) −9132.00 5272.36i −1.40064 0.808662i −0.406185 0.913791i \(-0.633141\pi\)
−0.994459 + 0.105129i \(0.966475\pi\)
\(350\) 0 0
\(351\) 877.500 + 911.925i 0.133440 + 0.138675i
\(352\) 0 0
\(353\) −2146.50 1239.28i −0.323645 0.186856i 0.329371 0.944201i \(-0.393163\pi\)
−0.653016 + 0.757344i \(0.726497\pi\)
\(354\) 0 0
\(355\) 1215.00 + 2104.44i 0.181649 + 0.314626i
\(356\) 12138.2i 1.80709i
\(357\) 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
\(364\) 936.000 + 3782.80i 0.134779 + 0.544705i
\(365\) −3555.00 −0.509801
\(366\) 0 0
\(367\) 4973.00 8613.49i 0.707326 1.22512i −0.258520 0.966006i \(-0.583235\pi\)
0.965846 0.259118i \(-0.0834318\pi\)
\(368\) −576.000 997.661i −0.0815926 0.141323i
\(369\) 327.358i 0.0461831i
\(370\) 0 0
\(371\) −2349.00 + 1356.20i −0.328717 + 0.189785i
\(372\) 4655.75i 0.648897i
\(373\) 3650.50 + 6322.85i 0.506745 + 0.877707i 0.999970 + 0.00780555i \(0.00248461\pi\)
−0.493225 + 0.869902i \(0.664182\pi\)
\(374\) 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 \(-0.407838\pi\)
−0.687224 + 0.726445i \(0.741171\pi\)
\(380\) 504.000 872.954i 0.0680386 0.117846i
\(381\) −2496.00 4323.20i −0.335627 0.581323i
\(382\) 0 0
\(383\) −5004.00 + 2889.06i −0.667604 + 0.385442i −0.795168 0.606389i \(-0.792618\pi\)
0.127564 + 0.991830i \(0.459284\pi\)
\(384\) 0 0
\(385\) 2805.92i 0.371436i
\(386\) 0 0
\(387\) 369.000 639.127i 0.0484685 0.0839500i
\(388\) 8016.00 + 4628.04i 1.04884 + 0.605549i
\(389\) 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
\(396\) −3240.00 + 1870.61i −0.411152 + 0.237379i
\(397\) 1752.00 1011.52i 0.221487 0.127876i −0.385152 0.922853i \(-0.625851\pi\)
0.606639 + 0.794978i \(0.292518\pi\)
\(398\) 0 0
\(399\) 378.000 + 654.715i 0.0474277 + 0.0821473i
\(400\) −3136.00 + 5431.71i −0.392000 + 0.678964i
\(401\) 7195.50 + 4154.32i 0.896075 + 0.517349i 0.875925 0.482448i \(-0.160252\pi\)
0.0201504 + 0.999797i \(0.493586\pi\)
\(402\) 0 0
\(403\) −6552.00 + 6304.66i −0.809872 + 0.779300i
\(404\) 12600.0 1.55167
\(405\) 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 −0.933787 0.357829i \(-0.883517\pi\)
−0.157005 + 0.987598i \(0.550184\pi\)
\(410\) 0 0
\(411\) 3039.75i 0.364817i
\(412\) −3176.00 5500.99i −0.379782 0.657802i
\(413\) −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 \(-0.911612\pi\)
0.718245 + 0.695790i \(0.244946\pi\)
\(420\) 648.000 + 1122.37i 0.0752837 + 0.130395i
\(421\) 14471.3i 1.67527i −0.546233 0.837633i \(-0.683939\pi\)
0.546233 0.837633i \(-0.316061\pi\)
\(422\) 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
\(428\) 3600.00 0.406571
\(429\) −7020.00 2026.50i −0.790044 0.228066i
\(430\) 0 0
\(431\) −5697.00 3289.16i −0.636693 0.367595i 0.146646 0.989189i \(-0.453152\pi\)
−0.783340 + 0.621594i \(0.786485\pi\)
\(432\) 864.000 1496.49i 0.0962250 0.166667i
\(433\) 3302.50 + 5720.10i 0.366531 + 0.634851i 0.989021 0.147778i \(-0.0472120\pi\)
−0.622489 + 0.782628i \(0.713879\pi\)
\(434\) 0 0
\(435\) −1336.50 + 771.629i −0.147311 + 0.0850500i
\(436\) −4128.00 + 2383.30i −0.453430 + 0.261788i
\(437\) 436.477i 0.0477792i
\(438\) 0 0
\(439\) 4271.00 7397.59i 0.464336 0.804254i −0.534835 0.844957i \(-0.679626\pi\)
0.999171 + 0.0407023i \(0.0129595\pi\)
\(440\) 0 0
\(441\) 2115.00 0.228377
\(442\) 0 0
\(443\) −14328.0 −1.53667 −0.768334 0.640049i \(-0.778914\pi\)
−0.768334 + 0.640049i \(0.778914\pi\)
\(444\) −2340.00 1351.00i −0.250116 0.144405i
\(445\) 3942.00 6827.74i 0.419930 0.727340i
\(446\) 0 0
\(447\) 9805.14i 1.03751i
\(448\) 4608.00 2660.43i 0.485954 0.280566i
\(449\) 2610.00 1506.88i 0.274329 0.158384i −0.356525 0.934286i \(-0.616038\pi\)
0.630853 + 0.775902i \(0.282705\pi\)
\(450\) 0 0
\(451\) −945.000 1636.79i −0.0986659 0.170894i
\(452\) 6804.00 11784.9i 0.708038 1.22636i
\(453\) 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 0.366536 0.930404i \(-0.380543\pi\)
−0.622485 + 0.782632i \(0.713877\pi\)
\(458\) 0 0
\(459\) −1579.50 2735.77i −0.160620 0.278203i
\(460\) 748.246i 0.0758416i
\(461\) 3118.50 1800.47i 0.315061 0.181900i −0.334128 0.942528i \(-0.608442\pi\)
0.649189 + 0.760627i \(0.275108\pi\)
\(462\) 0 0
\(463\) 2677.75i 0.268781i −0.990928 0.134391i \(-0.957092\pi\)
0.990928 0.134391i \(-0.0429077\pi\)
\(464\) 3168.00 + 5487.14i 0.316963 + 0.548996i
\(465\) −1512.00 + 2618.86i −0.150790 + 0.261176i
\(466\) 0 0
\(467\) 13878.0 1.37515 0.687577 0.726111i \(-0.258674\pi\)
0.687577 + 0.726111i \(0.258674\pi\)
\(468\) 3276.00 810.600i 0.323575 0.0800641i
\(469\) −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
\(476\) 9727.20i 0.936650i
\(477\) 1174.50 + 2034.29i 0.112739 + 0.195270i
\(478\) 0 0
\(479\) 954.000 + 550.792i 0.0910008 + 0.0525393i 0.544810 0.838560i \(-0.316602\pi\)
−0.453809 + 0.891099i \(0.649935\pi\)
\(480\) 0 0
\(481\) −1267.50 5122.54i −0.120152 0.485588i
\(482\) 0 0
\(483\) 486.000 + 280.592i 0.0457842 + 0.0264335i
\(484\) 5476.00 9484.71i 0.514275 0.890750i
\(485\) 3006.00 + 5206.54i 0.281434 + 0.487458i
\(486\) 0 0
\(487\) −14829.0 + 8561.53i −1.37981 + 0.796632i −0.992136 0.125166i \(-0.960054\pi\)
−0.387671 + 0.921798i \(0.626720\pi\)
\(488\) 0 0
\(489\) 8854.24i 0.818820i
\(490\) 0 0
\(491\) −225.000 + 389.711i −0.0206805 + 0.0358196i −0.876180 0.481983i \(-0.839917\pi\)
0.855500 + 0.517803i \(0.173250\pi\)
\(492\) 756.000 + 436.477i 0.0692746 + 0.0399957i
\(493\) 11583.0 1.05816
\(494\) 0 0
\(495\) −2430.00 −0.220647
\(496\) 10752.0 + 6207.67i 0.973345 + 0.561961i
\(497\) −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 \(-0.202037\pi\)
\(500\) −8028.00 + 4634.97i −0.718046 + 0.414564i
\(501\) −8154.00 + 4707.71i −0.727133 + 0.419811i
\(502\) 0 0
\(503\) −2673.00 4629.77i −0.236945 0.410400i 0.722891 0.690962i \(-0.242813\pi\)
−0.959836 + 0.280561i \(0.909479\pi\)
\(504\) 0 0
\(505\) 7087.50 + 4091.97i 0.624534 + 0.360575i
\(506\) 0 0
\(507\) 5577.00 + 3512.60i 0.488527 + 0.307692i
\(508\) −13312.0 −1.16265
\(509\) −5080.50 2933.23i −0.442415 0.255428i 0.262207 0.965012i \(-0.415550\pi\)
−0.704621 + 0.709583i \(0.748883\pi\)
\(510\) 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
\(516\) −984.000 1704.34i −0.0839500 0.145406i
\(517\) −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 −0.0818685 + 0.996643i \(0.526089\pi\)
−0.822184 + 0.569222i \(0.807245\pi\)
\(524\) 5904.00 + 10226.0i 0.492209 + 0.852531i
\(525\) 3055.34i 0.253992i
\(526\) 0 0
\(527\) 19656.0 11348.4i 1.62472 0.938034i
\(528\) 9976.61i 0.822304i
\(529\) 5921.50 + 10256.3i 0.486685 + 0.842964i
\(530\) 0 0
\(531\) 6156.00 + 3554.17i 0.503103 + 0.290467i
\(532\) 2016.00 0.164295
\(533\) 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
\(540\) 972.000 561.184i 0.0774597 0.0447214i
\(541\) 5371.09i 0.426841i 0.976960 + 0.213421i \(0.0684605\pi\)
−0.976960 + 0.213421i \(0.931540\pi\)
\(542\) 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 \(-0.269579\pi\)
0.662302 + 0.749237i \(0.269579\pi\)
\(548\) −7020.00 4053.00i −0.547225 0.315941i
\(549\) 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
\(556\) −4496.00 + 7787.30i −0.342937 + 0.593984i
\(557\) 3343.50 + 1930.37i 0.254342 + 0.146845i 0.621751 0.783215i \(-0.286422\pi\)
−0.367409 + 0.930060i \(0.619755\pi\)
\(558\) 0 0
\(559\) 1066.00 3692.73i 0.0806565 0.279402i
\(560\) 3456.00 0.260790
\(561\) 15795.0 + 9119.25i 1.18871 + 0.686301i
\(562\) 0 0
\(563\) −10836.0 18768.5i −0.811160 1.40497i −0.912053 0.410073i \(-0.865503\pi\)
0.100893 0.994897i \(-0.467830\pi\)
\(564\) 1745.91i 0.130347i
\(565\) 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 −0.839367 0.543565i \(-0.817074\pi\)
0.890425 + 0.455130i \(0.150407\pi\)
\(570\) 0 0
\(571\) 1162.00 0.0851632 0.0425816 0.999093i \(-0.486442\pi\)
0.0425816 + 0.999093i \(0.486442\pi\)
\(572\) −14040.0 + 13510.0i −1.02630 + 0.987555i
\(573\) 8208.00 0.598419
\(574\) 0 0
\(575\) −882.000 + 1527.67i −0.0639686 + 0.110797i
\(576\) −2304.00 3990.65i −0.166667 0.288675i
\(577\) 8045.38i 0.580474i 0.956955 + 0.290237i \(0.0937341\pi\)
−0.956955 + 0.290237i \(0.906266\pi\)
\(578\) 0 0
\(579\) −6763.50 + 3904.91i −0.485460 + 0.280281i
\(580\) 4115.35i 0.294622i
\(581\) −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 −0.960293 0.278995i \(-0.909999\pi\)
−0.721763 0.692140i \(-0.756668\pi\)
\(588\) 2820.00 4884.38i 0.197780 0.342566i
\(589\) 2352.00 + 4073.78i 0.164537 + 0.284987i
\(590\) 0 0
\(591\) 9666.00 5580.67i 0.672768 0.388423i
\(592\) −6240.00 + 3602.67i −0.433214 + 0.250116i
\(593\) 275.396i 0.0190711i 0.999955 + 0.00953555i \(0.00303531\pi\)
−0.999955 + 0.00953555i \(0.996965\pi\)
\(594\) 0 0
\(595\) 3159.00 5471.55i 0.217658 0.376994i
\(596\) −22644.0 13073.5i −1.55627 0.898510i
\(597\) −3594.00 −0.246386
\(598\) 0 0
\(599\) 22356.0 1.52494 0.762472 0.647021i \(-0.223986\pi\)
0.762472 + 0.647021i \(0.223986\pi\)
\(600\) 0 0
\(601\) 9041.50 15660.3i 0.613661 1.06289i −0.376956 0.926231i \(-0.623029\pi\)
0.990618 0.136662i \(-0.0436373\pi\)
\(602\) 0 0
\(603\) 6328.91i 0.427418i
\(604\) 11352.0 6554.08i 0.764746 0.441526i
\(605\) 6160.50 3556.77i 0.413983 0.239013i
\(606\) 0 0
\(607\) −2740.00 4745.82i −0.183218 0.317342i 0.759757 0.650207i \(-0.225318\pi\)
−0.942975 + 0.332865i \(0.891985\pi\)
\(608\) 0 0
\(609\) −2673.00 1543.26i −0.177858 0.102686i
\(610\) 0 0
\(611\) 2457.00 2364.25i 0.162683 0.156542i
\(612\) −8424.00 −0.556405
\(613\) 15361.5 + 8868.97i 1.01215 + 0.584362i 0.911819 0.410592i \(-0.134678\pi\)
0.100326 + 0.994955i \(0.468011\pi\)
\(614\) 0 0
\(615\) 283.500 + 491.036i 0.0185883 + 0.0321959i
\(616\) 0 0
\(617\) 8545.50 4933.75i 0.557583 0.321921i −0.194592 0.980884i \(-0.562338\pi\)
0.752175 + 0.658963i \(0.229005\pi\)
\(618\) 0 0
\(619\) 4115.35i 0.267221i −0.991034 0.133611i \(-0.957343\pi\)
0.991034 0.133611i \(-0.0426572\pi\)
\(620\) 4032.00 + 6983.63i 0.261176 + 0.452370i
\(621\) 243.000 420.888i 0.0157025 0.0271975i
\(622\) 0 0
\(623\) 15768.0 1.01402
\(624\) 2496.00 8646.40i 0.160128 0.554700i
\(625\) 6229.00 0.398656
\(626\) 0 0
\(627\) −1890.00 + 3273.58i −0.120382 + 0.208507i
\(628\) −5036.00 8722.61i −0.319997 0.554252i
\(629\) 13172.2i 0.834995i
\(630\) 0 0
\(631\) −10968.0 + 6332.38i −0.691964 + 0.399506i −0.804347 0.594159i \(-0.797485\pi\)
0.112383 + 0.993665i \(0.464151\pi\)
\(632\) 0 0
\(633\) 3588.00 + 6214.60i 0.225293 + 0.390218i
\(634\) 0 0
\(635\) −7488.00 4323.20i −0.467956 0.270175i
\(636\) 6264.00 0.390540
\(637\) 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 0.918473 0.395484i \(-0.129423\pi\)
−0.801736 + 0.597678i \(0.796090\pi\)
\(642\) 0 0
\(643\) 14646.0 8455.87i 0.898261 0.518611i 0.0216255 0.999766i \(-0.493116\pi\)
0.876636 + 0.481155i \(0.159783\pi\)
\(644\) 1296.00 748.246i 0.0793006 0.0457842i
\(645\) 1278.25i 0.0780328i
\(646\) 0 0
\(647\) 13896.0 24068.6i 0.844371 1.46249i −0.0417951 0.999126i \(-0.513308\pi\)
0.886166 0.463368i \(-0.153359\pi\)
\(648\) 0 0
\(649\) −41040.0 −2.48222
\(650\) 0 0
\(651\) −6048.00 −0.364116
\(652\) −20448.0 11805.7i −1.22823 0.709118i
\(653\) 297.000 514.419i 0.0177986 0.0308281i −0.856989 0.515335i \(-0.827668\pi\)
0.874788 + 0.484507i \(0.161001\pi\)
\(654\) 0 0
\(655\) 7669.52i 0.457516i
\(656\) 2016.00 1163.94i 0.119987 0.0692746i
\(657\) −5332.50 + 3078.72i −0.316652 + 0.182819i
\(658\) 0 0
\(659\) −8874.00 15370.2i −0.524555 0.908556i −0.999591 0.0285901i \(-0.990898\pi\)
0.475036 0.879966i \(-0.342435\pi\)
\(660\) −3240.00 + 5611.84i −0.191086 + 0.330971i
\(661\) 13675.5 + 7895.55i 0.804713 + 0.464601i 0.845117 0.534582i \(-0.179531\pi\)
−0.0404035 + 0.999183i \(0.512864\pi\)
\(662\) 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
\(668\) 25107.8i 1.45427i
\(669\) −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 0.393411 + 0.919363i \(0.371295\pi\)
−0.992897 + 0.118977i \(0.962038\pi\)
\(674\) 0 0
\(675\) −2646.00 −0.150881
\(676\) 15548.0 8196.06i 0.884615 0.466321i
\(677\) 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 \(-0.419931\pi\)
0.963221 + 0.268711i \(0.0865976\pi\)
\(684\) 1745.91i 0.0975971i
\(685\) −2632.50 4559.62i −0.146836 0.254327i
\(686\) 0 0
\(687\) −9018.00 5206.54i −0.500812 0.289144i
\(688\) −5248.00 −0.290811
\(689\) 8482.50 + 8815.27i 0.469024 + 0.487424i
\(690\) 0 0
\(691\) 12009.0 + 6933.40i 0.661134 + 0.381706i 0.792709 0.609600i \(-0.208670\pi\)
−0.131575 + 0.991306i \(0.542003\pi\)
\(692\) −17064.0 + 29555.7i −0.937393 + 1.62361i
\(693\) −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
\(700\) −7056.00 4073.78i −0.380988 0.219964i
\(701\) −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
\(704\) 23040.0 + 13302.2i 1.23346 + 0.712136i
\(705\) 567.000 982.073i 0.0302900 0.0524638i
\(706\) 0 0
\(707\) 16367.9i 0.870690i
\(708\) 16416.0 9477.78i 0.871400 0.503103i
\(709\) −11308.5 + 6528.97i −0.599012 + 0.345840i −0.768653 0.639666i \(-0.779073\pi\)
0.169641 + 0.985506i \(0.445739\pi\)
\(710\) 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
\(716\) 24048.0 1.25519
\(717\) 11583.0 + 6687.45i 0.603312 + 0.348323i
\(718\) 0 0
\(719\) 7110.00 + 12314.9i 0.368788 + 0.638759i 0.989376 0.145377i \(-0.0464397\pi\)
−0.620589 + 0.784136i \(0.713106\pi\)
\(720\) 2992.98i 0.154919i
\(721\) 7146.00 4125.75i 0.369114 0.213108i
\(722\) 0 0
\(723\) 1252.27i 0.0644157i
\(724\) 7492.00 + 12976.5i 0.384583 + 0.666117i
\(725\) 4851.00 8402.18i 0.248499 0.430413i
\(726\) 0 0
\(727\) −5282.00 −0.269462 −0.134731 0.990882i \(-0.543017\pi\)
−0.134731 + 0.990882i \(0.543017\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −4797.00 + 8308.65i −0.242713 + 0.420392i
\(732\) −8628.00 14944.1i −0.435656 0.754578i
\(733\) 11419.4i 0.575424i −0.957717 0.287712i \(-0.907105\pi\)
0.957717 0.287712i \(-0.0928945\pi\)
\(734\) 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 \(-0.504094\pi\)
−0.872384 + 0.488822i \(0.837427\pi\)
\(740\) −4680.00 −0.232487
\(741\) 2457.00 2364.25i 0.121809 0.117210i
\(742\) 0 0
\(743\) −18036.0 10413.1i −0.890547 0.514158i −0.0164258 0.999865i \(-0.505229\pi\)
−0.874121 + 0.485707i \(0.838562\pi\)
\(744\) 0 0
\(745\) −8491.50 14707.7i −0.417590 0.723287i
\(746\) 0 0
\(747\) −9315.00 + 5378.02i −0.456249 + 0.263416i
\(748\) 42120.0 24318.0i 2.05890 1.18871i
\(749\) 4676.54i 0.228140i
\(750\) 0 0
\(751\) 2417.00 4186.37i 0.117440 0.203412i −0.801312 0.598246i \(-0.795864\pi\)
0.918753 + 0.394834i \(0.129198\pi\)
\(752\) −4032.00 2327.88i −0.195521 0.112884i
\(753\) −12312.0 −0.595849
\(754\) 0 0
\(755\) 8514.00 0.410406
\(756\) 1944.00 + 1122.37i 0.0935220 + 0.0539949i
\(757\) −4523.00 + 7834.07i −0.217161 + 0.376135i −0.953939 0.300001i \(-0.903013\pi\)
0.736778 + 0.676135i \(0.236346\pi\)
\(758\) 0 0
\(759\) 2805.92i 0.134188i
\(760\) 0 0
\(761\) −10422.0 + 6017.14i −0.496448 + 0.286625i −0.727246 0.686377i \(-0.759200\pi\)
0.230797 + 0.973002i \(0.425867\pi\)
\(762\) 0 0
\(763\) −3096.00 5362.43i −0.146897 0.254434i
\(764\) 10944.0 18955.6i 0.518246 0.897629i
\(765\) −4738.50 2735.77i −0.223949 0.129297i
\(766\) 0 0
\(767\) 35568.0 + 10267.6i 1.67443 + 0.483366i
\(768\) −12288.0 −0.577350
\(769\) 32514.0 + 18772.0i 1.52469 + 0.880279i 0.999572 + 0.0292479i \(0.00931121\pi\)
0.525115 + 0.851031i \(0.324022\pi\)
\(770\) 0 0
\(771\) 2983.50 + 5167.57i 0.139362 + 0.241382i
\(772\) 20826.2i 0.970920i
\(773\) −13608.0 + 7856.58i −0.633177 + 0.365565i −0.781981 0.623302i \(-0.785791\pi\)
0.148804 + 0.988867i \(0.452457\pi\)
\(774\) 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
\(780\) 4212.00 4053.00i 0.193351 0.186052i
\(781\) −24300.0 −1.11334
\(782\) 0 0
\(783\) −1336.50 + 2314.89i −0.0609995 + 0.105654i
\(784\) −7520.00