Properties

Label 147.4.c.b.146.3
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.3
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.21

$q$-expansion

\(f(q)\) \(=\) \(q-4.84485i q^{2} +(-5.11673 + 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 + 24.7898i) q^{6} +36.2033i q^{8} +(25.3618 - 9.26169i) q^{9} +O(q^{10})\) \(q-4.84485i q^{2} +(-5.11673 + 0.905040i) q^{3} -15.4725 q^{4} -17.3012 q^{5} +(4.38478 + 24.7898i) q^{6} +36.2033i q^{8} +(25.3618 - 9.26169i) q^{9} +83.8216i q^{10} -27.8490i q^{11} +(79.1688 - 14.0033i) q^{12} -16.3036i q^{13} +(88.5254 - 15.6583i) q^{15} +51.6191 q^{16} +40.8263 q^{17} +(-44.8715 - 122.874i) q^{18} +68.1627i q^{19} +267.693 q^{20} -134.924 q^{22} +71.7749i q^{23} +(-32.7654 - 185.242i) q^{24} +174.331 q^{25} -78.9883 q^{26} +(-121.387 + 70.3430i) q^{27} +216.426i q^{29} +(-75.8619 - 428.892i) q^{30} -157.351i q^{31} +39.5396i q^{32} +(25.2044 + 142.496i) q^{33} -197.797i q^{34} +(-392.412 + 143.302i) q^{36} -348.489 q^{37} +330.238 q^{38} +(14.7554 + 83.4209i) q^{39} -626.360i q^{40} +153.371 q^{41} +427.584 q^{43} +430.894i q^{44} +(-438.789 + 160.238i) q^{45} +347.738 q^{46} +16.8103 q^{47} +(-264.121 + 46.7174i) q^{48} -844.606i q^{50} +(-208.897 + 36.9495i) q^{51} +252.258i q^{52} -192.526i q^{53} +(340.801 + 588.103i) q^{54} +481.820i q^{55} +(-61.6899 - 348.770i) q^{57} +1048.55 q^{58} -287.422 q^{59} +(-1369.71 + 242.273i) q^{60} +224.297i q^{61} -762.340 q^{62} +604.516 q^{64} +282.071i q^{65} +(690.370 - 122.112i) q^{66} -172.206 q^{67} -631.687 q^{68} +(-64.9591 - 367.252i) q^{69} +1068.78i q^{71} +(335.304 + 918.181i) q^{72} +1078.22i q^{73} +1688.38i q^{74} +(-892.004 + 157.776i) q^{75} -1054.65i q^{76} +(404.161 - 71.4875i) q^{78} +52.0336 q^{79} -893.072 q^{80} +(557.442 - 469.786i) q^{81} -743.059i q^{82} -1023.07 q^{83} -706.344 q^{85} -2071.58i q^{86} +(-195.874 - 1107.39i) q^{87} +1008.23 q^{88} +668.570 q^{89} +(776.329 + 2125.87i) q^{90} -1110.54i q^{92} +(142.409 + 805.121i) q^{93} -81.4431i q^{94} -1179.29i q^{95} +(-35.7849 - 202.313i) q^{96} -1358.39i q^{97} +(-257.929 - 706.300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.84485i 1.71291i −0.516220 0.856456i \(-0.672661\pi\)
0.516220 0.856456i \(-0.327339\pi\)
\(3\) −5.11673 + 0.905040i −0.984715 + 0.174175i
\(4\) −15.4725 −1.93407
\(5\) −17.3012 −1.54746 −0.773732 0.633513i \(-0.781612\pi\)
−0.773732 + 0.633513i \(0.781612\pi\)
\(6\) 4.38478 + 24.7898i 0.298346 + 1.68673i
\(7\) 0 0
\(8\) 36.2033i 1.59998i
\(9\) 25.3618 9.26169i 0.939326 0.343025i
\(10\) 83.8216i 2.65067i
\(11\) 27.8490i 0.763344i −0.924298 0.381672i \(-0.875348\pi\)
0.924298 0.381672i \(-0.124652\pi\)
\(12\) 79.1688 14.0033i 1.90450 0.336866i
\(13\) 16.3036i 0.347830i −0.984761 0.173915i \(-0.944358\pi\)
0.984761 0.173915i \(-0.0556419\pi\)
\(14\) 0 0
\(15\) 88.5254 15.6583i 1.52381 0.269530i
\(16\) 51.6191 0.806549
\(17\) 40.8263 0.582461 0.291231 0.956653i \(-0.405935\pi\)
0.291231 + 0.956653i \(0.405935\pi\)
\(18\) −44.8715 122.874i −0.587572 1.60898i
\(19\) 68.1627i 0.823031i 0.911403 + 0.411515i \(0.135000\pi\)
−0.911403 + 0.411515i \(0.865000\pi\)
\(20\) 267.693 2.99290
\(21\) 0 0
\(22\) −134.924 −1.30754
\(23\) 71.7749i 0.650700i 0.945594 + 0.325350i \(0.105482\pi\)
−0.945594 + 0.325350i \(0.894518\pi\)
\(24\) −32.7654 185.242i −0.278676 1.57552i
\(25\) 174.331 1.39465
\(26\) −78.9883 −0.595803
\(27\) −121.387 + 70.3430i −0.865222 + 0.501389i
\(28\) 0 0
\(29\) 216.426i 1.38584i 0.721014 + 0.692920i \(0.243676\pi\)
−0.721014 + 0.692920i \(0.756324\pi\)
\(30\) −75.8619 428.892i −0.461681 2.61015i
\(31\) 157.351i 0.911646i −0.890070 0.455823i \(-0.849345\pi\)
0.890070 0.455823i \(-0.150655\pi\)
\(32\) 39.5396i 0.218428i
\(33\) 25.2044 + 142.496i 0.132955 + 0.751676i
\(34\) 197.797i 0.997705i
\(35\) 0 0
\(36\) −392.412 + 143.302i −1.81672 + 0.663434i
\(37\) −348.489 −1.54841 −0.774207 0.632933i \(-0.781851\pi\)
−0.774207 + 0.632933i \(0.781851\pi\)
\(38\) 330.238 1.40978
\(39\) 14.7554 + 83.4209i 0.0605834 + 0.342514i
\(40\) 626.360i 2.47590i
\(41\) 153.371 0.584208 0.292104 0.956387i \(-0.405645\pi\)
0.292104 + 0.956387i \(0.405645\pi\)
\(42\) 0 0
\(43\) 427.584 1.51642 0.758208 0.652012i \(-0.226075\pi\)
0.758208 + 0.652012i \(0.226075\pi\)
\(44\) 430.894i 1.47636i
\(45\) −438.789 + 160.238i −1.45357 + 0.530820i
\(46\) 347.738 1.11459
\(47\) 16.8103 0.0521708 0.0260854 0.999660i \(-0.491696\pi\)
0.0260854 + 0.999660i \(0.491696\pi\)
\(48\) −264.121 + 46.7174i −0.794221 + 0.140481i
\(49\) 0 0
\(50\) 844.606i 2.38891i
\(51\) −208.897 + 36.9495i −0.573558 + 0.101450i
\(52\) 252.258i 0.672727i
\(53\) 192.526i 0.498971i −0.968379 0.249486i \(-0.919738\pi\)
0.968379 0.249486i \(-0.0802615\pi\)
\(54\) 340.801 + 588.103i 0.858836 + 1.48205i
\(55\) 481.820i 1.18125i
\(56\) 0 0
\(57\) −61.6899 348.770i −0.143351 0.810451i
\(58\) 1048.55 2.37382
\(59\) −287.422 −0.634224 −0.317112 0.948388i \(-0.602713\pi\)
−0.317112 + 0.948388i \(0.602713\pi\)
\(60\) −1369.71 + 242.273i −2.94715 + 0.521289i
\(61\) 224.297i 0.470792i 0.971900 + 0.235396i \(0.0756387\pi\)
−0.971900 + 0.235396i \(0.924361\pi\)
\(62\) −762.340 −1.56157
\(63\) 0 0
\(64\) 604.516 1.18070
\(65\) 282.071i 0.538255i
\(66\) 690.370 122.112i 1.28755 0.227741i
\(67\) −172.206 −0.314004 −0.157002 0.987598i \(-0.550183\pi\)
−0.157002 + 0.987598i \(0.550183\pi\)
\(68\) −631.687 −1.12652
\(69\) −64.9591 367.252i −0.113336 0.640754i
\(70\) 0 0
\(71\) 1068.78i 1.78649i 0.449569 + 0.893246i \(0.351578\pi\)
−0.449569 + 0.893246i \(0.648422\pi\)
\(72\) 335.304 + 918.181i 0.548832 + 1.50290i
\(73\) 1078.22i 1.72871i 0.502881 + 0.864356i \(0.332274\pi\)
−0.502881 + 0.864356i \(0.667726\pi\)
\(74\) 1688.38i 2.65230i
\(75\) −892.004 + 157.776i −1.37333 + 0.242913i
\(76\) 1054.65i 1.59180i
\(77\) 0 0
\(78\) 404.161 71.4875i 0.586696 0.103774i
\(79\) 52.0336 0.0741043 0.0370521 0.999313i \(-0.488203\pi\)
0.0370521 + 0.999313i \(0.488203\pi\)
\(80\) −893.072 −1.24811
\(81\) 557.442 469.786i 0.764667 0.644426i
\(82\) 743.059i 1.00070i
\(83\) −1023.07 −1.35298 −0.676488 0.736454i \(-0.736499\pi\)
−0.676488 + 0.736454i \(0.736499\pi\)
\(84\) 0 0
\(85\) −706.344 −0.901338
\(86\) 2071.58i 2.59749i
\(87\) −195.874 1107.39i −0.241379 1.36466i
\(88\) 1008.23 1.22133
\(89\) 668.570 0.796272 0.398136 0.917326i \(-0.369657\pi\)
0.398136 + 0.917326i \(0.369657\pi\)
\(90\) 776.329 + 2125.87i 0.909247 + 2.48984i
\(91\) 0 0
\(92\) 1110.54i 1.25850i
\(93\) 142.409 + 805.121i 0.158786 + 0.897711i
\(94\) 81.4431i 0.0893640i
\(95\) 1179.29i 1.27361i
\(96\) −35.7849 202.313i −0.0380446 0.215089i
\(97\) 1358.39i 1.42190i −0.703244 0.710949i \(-0.748266\pi\)
0.703244 0.710949i \(-0.251734\pi\)
\(98\) 0 0
\(99\) −257.929 706.300i −0.261846 0.717029i
\(100\) −2697.34 −2.69734
\(101\) 29.0959 0.0286649 0.0143324 0.999897i \(-0.495438\pi\)
0.0143324 + 0.999897i \(0.495438\pi\)
\(102\) 179.015 + 1012.08i 0.173775 + 0.982455i
\(103\) 300.909i 0.287859i −0.989588 0.143929i \(-0.954026\pi\)
0.989588 0.143929i \(-0.0459738\pi\)
\(104\) 590.243 0.556520
\(105\) 0 0
\(106\) −932.759 −0.854694
\(107\) 523.431i 0.472916i 0.971642 + 0.236458i \(0.0759866\pi\)
−0.971642 + 0.236458i \(0.924013\pi\)
\(108\) 1878.17 1088.38i 1.67340 0.969721i
\(109\) −62.6812 −0.0550805 −0.0275402 0.999621i \(-0.508767\pi\)
−0.0275402 + 0.999621i \(0.508767\pi\)
\(110\) 2334.35 2.02337
\(111\) 1783.13 315.397i 1.52475 0.269695i
\(112\) 0 0
\(113\) 84.9426i 0.0707144i −0.999375 0.0353572i \(-0.988743\pi\)
0.999375 0.0353572i \(-0.0112569\pi\)
\(114\) −1689.74 + 298.878i −1.38823 + 0.245548i
\(115\) 1241.79i 1.00693i
\(116\) 3348.66i 2.68031i
\(117\) −150.998 413.488i −0.119315 0.326726i
\(118\) 1392.52i 1.08637i
\(119\) 0 0
\(120\) 566.881 + 3204.91i 0.431241 + 2.43806i
\(121\) 555.434 0.417306
\(122\) 1086.69 0.806425
\(123\) −784.758 + 138.807i −0.575278 + 0.101754i
\(124\) 2434.62i 1.76318i
\(125\) −853.482 −0.610702
\(126\) 0 0
\(127\) −1842.84 −1.28760 −0.643802 0.765192i \(-0.722644\pi\)
−0.643802 + 0.765192i \(0.722644\pi\)
\(128\) 2612.47i 1.80400i
\(129\) −2187.83 + 386.981i −1.49324 + 0.264122i
\(130\) 1366.59 0.921984
\(131\) −97.8698 −0.0652742 −0.0326371 0.999467i \(-0.510391\pi\)
−0.0326371 + 0.999467i \(0.510391\pi\)
\(132\) −389.977 2204.77i −0.257145 1.45379i
\(133\) 0 0
\(134\) 834.310i 0.537861i
\(135\) 2100.14 1217.02i 1.33890 0.775882i
\(136\) 1478.05i 0.931924i
\(137\) 1693.85i 1.05631i 0.849147 + 0.528157i \(0.177117\pi\)
−0.849147 + 0.528157i \(0.822883\pi\)
\(138\) −1779.28 + 314.717i −1.09755 + 0.194134i
\(139\) 1821.25i 1.11134i 0.831402 + 0.555672i \(0.187539\pi\)
−0.831402 + 0.555672i \(0.812461\pi\)
\(140\) 0 0
\(141\) −86.0135 + 15.2139i −0.0513733 + 0.00908685i
\(142\) 5178.08 3.06010
\(143\) −454.038 −0.265514
\(144\) 1309.15 478.080i 0.757613 0.276667i
\(145\) 3744.43i 2.14454i
\(146\) 5223.80 2.96113
\(147\) 0 0
\(148\) 5392.02 2.99474
\(149\) 1798.00i 0.988574i 0.869299 + 0.494287i \(0.164571\pi\)
−0.869299 + 0.494287i \(0.835429\pi\)
\(150\) 764.402 + 4321.62i 0.416088 + 2.35239i
\(151\) −2089.84 −1.12628 −0.563141 0.826361i \(-0.690407\pi\)
−0.563141 + 0.826361i \(0.690407\pi\)
\(152\) −2467.71 −1.31683
\(153\) 1035.43 378.121i 0.547121 0.199799i
\(154\) 0 0
\(155\) 2722.35i 1.41074i
\(156\) −228.303 1290.73i −0.117172 0.662445i
\(157\) 1090.34i 0.554258i −0.960833 0.277129i \(-0.910617\pi\)
0.960833 0.277129i \(-0.0893829\pi\)
\(158\) 252.095i 0.126934i
\(159\) 174.244 + 985.103i 0.0869083 + 0.491344i
\(160\) 684.082i 0.338009i
\(161\) 0 0
\(162\) −2276.04 2700.72i −1.10384 1.30981i
\(163\) −1940.53 −0.932478 −0.466239 0.884659i \(-0.654391\pi\)
−0.466239 + 0.884659i \(0.654391\pi\)
\(164\) −2373.04 −1.12990
\(165\) −436.067 2465.34i −0.205744 1.16319i
\(166\) 4956.64i 2.31753i
\(167\) −2664.87 −1.23481 −0.617406 0.786645i \(-0.711816\pi\)
−0.617406 + 0.786645i \(0.711816\pi\)
\(168\) 0 0
\(169\) 1931.19 0.879014
\(170\) 3422.13i 1.54391i
\(171\) 631.301 + 1728.73i 0.282320 + 0.773094i
\(172\) −6615.81 −2.93285
\(173\) 3096.19 1.36069 0.680343 0.732894i \(-0.261831\pi\)
0.680343 + 0.732894i \(0.261831\pi\)
\(174\) −5365.16 + 948.982i −2.33754 + 0.413461i
\(175\) 0 0
\(176\) 1437.54i 0.615674i
\(177\) 1470.66 260.129i 0.624529 0.110466i
\(178\) 3239.12i 1.36394i
\(179\) 902.641i 0.376908i 0.982082 + 0.188454i \(0.0603476\pi\)
−0.982082 + 0.188454i \(0.939652\pi\)
\(180\) 6789.18 2479.29i 2.81131 1.02664i
\(181\) 3496.01i 1.43567i 0.696213 + 0.717835i \(0.254867\pi\)
−0.696213 + 0.717835i \(0.745133\pi\)
\(182\) 0 0
\(183\) −202.998 1147.67i −0.0820002 0.463596i
\(184\) −2598.49 −1.04110
\(185\) 6029.28 2.39612
\(186\) 3900.69 689.948i 1.53770 0.271986i
\(187\) 1136.97i 0.444618i
\(188\) −260.097 −0.100902
\(189\) 0 0
\(190\) −5713.50 −2.18158
\(191\) 354.514i 0.134302i 0.997743 + 0.0671512i \(0.0213910\pi\)
−0.997743 + 0.0671512i \(0.978609\pi\)
\(192\) −3093.15 + 547.112i −1.16265 + 0.205648i
\(193\) 2839.88 1.05917 0.529584 0.848258i \(-0.322348\pi\)
0.529584 + 0.848258i \(0.322348\pi\)
\(194\) −6581.21 −2.43559
\(195\) −255.285 1443.28i −0.0937506 0.530028i
\(196\) 0 0
\(197\) 3058.25i 1.10605i −0.833165 0.553024i \(-0.813474\pi\)
0.833165 0.553024i \(-0.186526\pi\)
\(198\) −3421.92 + 1249.62i −1.22821 + 0.448520i
\(199\) 1839.48i 0.655264i 0.944805 + 0.327632i \(0.106251\pi\)
−0.944805 + 0.327632i \(0.893749\pi\)
\(200\) 6311.35i 2.23140i
\(201\) 881.129 155.853i 0.309204 0.0546916i
\(202\) 140.965i 0.0491004i
\(203\) 0 0
\(204\) 3232.17 571.702i 1.10930 0.196212i
\(205\) −2653.50 −0.904041
\(206\) −1457.86 −0.493077
\(207\) 664.756 + 1820.34i 0.223207 + 0.611219i
\(208\) 841.576i 0.280542i
\(209\) 1898.26 0.628256
\(210\) 0 0
\(211\) −644.694 −0.210344 −0.105172 0.994454i \(-0.533539\pi\)
−0.105172 + 0.994454i \(0.533539\pi\)
\(212\) 2978.86i 0.965044i
\(213\) −967.289 5468.66i −0.311162 1.75918i
\(214\) 2535.94 0.810063
\(215\) −7397.71 −2.34660
\(216\) −2546.65 4394.62i −0.802210 1.38433i
\(217\) 0 0
\(218\) 303.681i 0.0943480i
\(219\) −975.831 5516.95i −0.301098 1.70229i
\(220\) 7454.98i 2.28461i
\(221\) 665.615i 0.202598i
\(222\) −1528.05 8638.97i −0.461964 2.61176i
\(223\) 3760.55i 1.12926i −0.825344 0.564630i \(-0.809019\pi\)
0.825344 0.564630i \(-0.190981\pi\)
\(224\) 0 0
\(225\) 4421.35 1614.60i 1.31003 0.478399i
\(226\) −411.534 −0.121128
\(227\) −2836.86 −0.829467 −0.414733 0.909943i \(-0.636125\pi\)
−0.414733 + 0.909943i \(0.636125\pi\)
\(228\) 954.500 + 5396.35i 0.277251 + 1.56747i
\(229\) 5207.86i 1.50282i 0.659837 + 0.751409i \(0.270625\pi\)
−0.659837 + 0.751409i \(0.729375\pi\)
\(230\) −6016.28 −1.72479
\(231\) 0 0
\(232\) −7835.35 −2.21731
\(233\) 2185.90i 0.614604i −0.951612 0.307302i \(-0.900574\pi\)
0.951612 0.307302i \(-0.0994262\pi\)
\(234\) −2003.28 + 731.565i −0.559653 + 0.204376i
\(235\) −290.837 −0.0807325
\(236\) 4447.15 1.22663
\(237\) −266.242 + 47.0925i −0.0729716 + 0.0129071i
\(238\) 0 0
\(239\) 1921.87i 0.520148i 0.965589 + 0.260074i \(0.0837469\pi\)
−0.965589 + 0.260074i \(0.916253\pi\)
\(240\) 4569.61 808.266i 1.22903 0.217389i
\(241\) 4476.26i 1.19644i 0.801333 + 0.598218i \(0.204124\pi\)
−0.801333 + 0.598218i \(0.795876\pi\)
\(242\) 2690.99i 0.714809i
\(243\) −2427.11 + 2908.28i −0.640736 + 0.767761i
\(244\) 3470.45i 0.910543i
\(245\) 0 0
\(246\) 672.498 + 3802.03i 0.174296 + 0.985401i
\(247\) 1111.29 0.286275
\(248\) 5696.62 1.45861
\(249\) 5234.79 925.923i 1.33230 0.235655i
\(250\) 4134.99i 1.04608i
\(251\) 3296.51 0.828980 0.414490 0.910054i \(-0.363960\pi\)
0.414490 + 0.910054i \(0.363960\pi\)
\(252\) 0 0
\(253\) 1998.86 0.496708
\(254\) 8928.28i 2.20555i
\(255\) 3614.17 639.270i 0.887561 0.156991i
\(256\) −7820.90 −1.90940
\(257\) 7110.67 1.72588 0.862940 0.505307i \(-0.168621\pi\)
0.862940 + 0.505307i \(0.168621\pi\)
\(258\) 1874.86 + 10599.7i 0.452418 + 2.55779i
\(259\) 0 0
\(260\) 4364.35i 1.04102i
\(261\) 2004.47 + 5488.96i 0.475378 + 1.30176i
\(262\) 474.164i 0.111809i
\(263\) 6808.88i 1.59640i 0.602391 + 0.798201i \(0.294215\pi\)
−0.602391 + 0.798201i \(0.705785\pi\)
\(264\) −5158.81 + 912.484i −1.20266 + 0.212725i
\(265\) 3330.93i 0.772140i
\(266\) 0 0
\(267\) −3420.89 + 605.082i −0.784101 + 0.138691i
\(268\) 2664.46 0.607305
\(269\) 3603.91 0.816856 0.408428 0.912791i \(-0.366077\pi\)
0.408428 + 0.912791i \(0.366077\pi\)
\(270\) −5896.26 10174.9i −1.32902 2.29342i
\(271\) 3376.15i 0.756777i 0.925647 + 0.378388i \(0.123522\pi\)
−0.925647 + 0.378388i \(0.876478\pi\)
\(272\) 2107.42 0.469784
\(273\) 0 0
\(274\) 8206.42 1.80937
\(275\) 4854.94i 1.06460i
\(276\) 1005.08 + 5682.33i 0.219199 + 1.23926i
\(277\) −6940.10 −1.50538 −0.752690 0.658375i \(-0.771244\pi\)
−0.752690 + 0.658375i \(0.771244\pi\)
\(278\) 8823.70 1.90363
\(279\) −1457.33 3990.70i −0.312718 0.856333i
\(280\) 0 0
\(281\) 3834.00i 0.813940i −0.913441 0.406970i \(-0.866585\pi\)
0.913441 0.406970i \(-0.133415\pi\)
\(282\) 73.7093 + 416.722i 0.0155650 + 0.0879980i
\(283\) 6443.70i 1.35349i 0.736217 + 0.676746i \(0.236610\pi\)
−0.736217 + 0.676746i \(0.763390\pi\)
\(284\) 16536.7i 3.45519i
\(285\) 1067.31 + 6034.13i 0.221831 + 1.25414i
\(286\) 2199.74i 0.454802i
\(287\) 0 0
\(288\) 366.203 + 1002.80i 0.0749262 + 0.205175i
\(289\) −3246.21 −0.660739
\(290\) −18141.2 −3.67341
\(291\) 1229.40 + 6950.54i 0.247659 + 1.40016i
\(292\) 16682.8i 3.34344i
\(293\) 1443.22 0.287760 0.143880 0.989595i \(-0.454042\pi\)
0.143880 + 0.989595i \(0.454042\pi\)
\(294\) 0 0
\(295\) 4972.74 0.981439
\(296\) 12616.5i 2.47742i
\(297\) 1958.98 + 3380.51i 0.382733 + 0.660462i
\(298\) 8711.01 1.69334
\(299\) 1170.19 0.226333
\(300\) 13801.6 2441.20i 2.65611 0.469809i
\(301\) 0 0
\(302\) 10124.9i 1.92922i
\(303\) −148.876 + 26.3330i −0.0282267 + 0.00499271i
\(304\) 3518.50i 0.663815i
\(305\) 3880.61i 0.728534i
\(306\) −1831.94 5016.50i −0.342238 0.937170i
\(307\) 5504.32i 1.02328i 0.859199 + 0.511642i \(0.170962\pi\)
−0.859199 + 0.511642i \(0.829038\pi\)
\(308\) 0 0
\(309\) 272.335 + 1539.67i 0.0501378 + 0.283459i
\(310\) 13189.4 2.41647
\(311\) −2419.45 −0.441140 −0.220570 0.975371i \(-0.570792\pi\)
−0.220570 + 0.975371i \(0.570792\pi\)
\(312\) −3020.11 + 534.193i −0.548013 + 0.0969319i
\(313\) 1190.38i 0.214966i −0.994207 0.107483i \(-0.965721\pi\)
0.994207 0.107483i \(-0.0342791\pi\)
\(314\) −5282.52 −0.949395
\(315\) 0 0
\(316\) −805.092 −0.143323
\(317\) 6628.17i 1.17437i −0.809453 0.587185i \(-0.800236\pi\)
0.809453 0.587185i \(-0.199764\pi\)
\(318\) 4772.67 844.184i 0.841629 0.148866i
\(319\) 6027.25 1.05787
\(320\) −10458.8 −1.82709
\(321\) −473.726 2678.25i −0.0823701 0.465687i
\(322\) 0 0
\(323\) 2782.83i 0.479384i
\(324\) −8625.05 + 7268.78i −1.47892 + 1.24636i
\(325\) 2842.21i 0.485101i
\(326\) 9401.56i 1.59725i
\(327\) 320.723 56.7290i 0.0542385 0.00959364i
\(328\) 5552.54i 0.934718i
\(329\) 0 0
\(330\) −11944.2 + 2112.68i −1.99245 + 0.352421i
\(331\) −7185.16 −1.19315 −0.596574 0.802558i \(-0.703472\pi\)
−0.596574 + 0.802558i \(0.703472\pi\)
\(332\) 15829.6 2.61675
\(333\) −8838.32 + 3227.60i −1.45447 + 0.531145i
\(334\) 12910.9i 2.11512i
\(335\) 2979.36 0.485910
\(336\) 0 0
\(337\) −7214.56 −1.16618 −0.583090 0.812408i \(-0.698156\pi\)
−0.583090 + 0.812408i \(0.698156\pi\)
\(338\) 9356.34i 1.50567i
\(339\) 76.8764 + 434.628i 0.0123167 + 0.0696335i
\(340\) 10928.9 1.74325
\(341\) −4382.06 −0.695899
\(342\) 8375.42 3058.56i 1.32424 0.483590i
\(343\) 0 0
\(344\) 15479.9i 2.42623i
\(345\) 1123.87 + 6353.90i 0.175383 + 0.991543i
\(346\) 15000.6i 2.33074i
\(347\) 8151.04i 1.26101i −0.776185 0.630505i \(-0.782848\pi\)
0.776185 0.630505i \(-0.217152\pi\)
\(348\) 3030.68 + 17134.2i 0.466843 + 2.63934i
\(349\) 491.916i 0.0754489i −0.999288 0.0377245i \(-0.987989\pi\)
0.999288 0.0377245i \(-0.0120109\pi\)
\(350\) 0 0
\(351\) 1146.84 + 1979.04i 0.174398 + 0.300950i
\(352\) 1101.14 0.166735
\(353\) −2923.64 −0.440820 −0.220410 0.975407i \(-0.570740\pi\)
−0.220410 + 0.975407i \(0.570740\pi\)
\(354\) −1260.28 7125.13i −0.189218 1.06976i
\(355\) 18491.2i 2.76453i
\(356\) −10344.5 −1.54004
\(357\) 0 0
\(358\) 4373.16 0.645610
\(359\) 4802.16i 0.705985i −0.935626 0.352992i \(-0.885164\pi\)
0.935626 0.352992i \(-0.114836\pi\)
\(360\) −5801.15 15885.6i −0.849298 2.32568i
\(361\) 2212.85 0.322620
\(362\) 16937.6 2.45918
\(363\) −2842.01 + 502.690i −0.410927 + 0.0726843i
\(364\) 0 0
\(365\) 18654.5i 2.67512i
\(366\) −5560.27 + 983.494i −0.794099 + 0.140459i
\(367\) 8957.91i 1.27411i −0.770817 0.637056i \(-0.780152\pi\)
0.770817 0.637056i \(-0.219848\pi\)
\(368\) 3704.96i 0.524821i
\(369\) 3889.77 1420.47i 0.548762 0.200398i
\(370\) 29210.9i 4.10434i
\(371\) 0 0
\(372\) −2203.42 12457.3i −0.307103 1.73623i
\(373\) −5072.83 −0.704186 −0.352093 0.935965i \(-0.614530\pi\)
−0.352093 + 0.935965i \(0.614530\pi\)
\(374\) −5508.45 −0.761592
\(375\) 4367.04 772.435i 0.601367 0.106369i
\(376\) 608.587i 0.0834720i
\(377\) 3528.52 0.482037
\(378\) 0 0
\(379\) −855.835 −0.115993 −0.0579964 0.998317i \(-0.518471\pi\)
−0.0579964 + 0.998317i \(0.518471\pi\)
\(380\) 18246.7i 2.46325i
\(381\) 9429.31 1667.84i 1.26792 0.224268i
\(382\) 1717.57 0.230048
\(383\) −7080.61 −0.944653 −0.472326 0.881424i \(-0.656586\pi\)
−0.472326 + 0.881424i \(0.656586\pi\)
\(384\) 2364.39 + 13367.3i 0.314212 + 1.77643i
\(385\) 0 0
\(386\) 13758.8i 1.81426i
\(387\) 10844.3 3960.15i 1.42441 0.520170i
\(388\) 21017.8i 2.75005i
\(389\) 2073.59i 0.270270i −0.990827 0.135135i \(-0.956853\pi\)
0.990827 0.135135i \(-0.0431468\pi\)
\(390\) −6992.47 + 1236.82i −0.907891 + 0.160587i
\(391\) 2930.31i 0.379007i
\(392\) 0 0
\(393\) 500.773 88.5761i 0.0642765 0.0113691i
\(394\) −14816.8 −1.89456
\(395\) −900.243 −0.114674
\(396\) 3990.81 + 10928.3i 0.506429 + 1.38678i
\(397\) 5722.06i 0.723380i 0.932298 + 0.361690i \(0.117800\pi\)
−0.932298 + 0.361690i \(0.882200\pi\)
\(398\) 8912.01 1.12241
\(399\) 0 0
\(400\) 8998.81 1.12485
\(401\) 11728.9i 1.46064i 0.683107 + 0.730319i \(0.260628\pi\)
−0.683107 + 0.730319i \(0.739372\pi\)
\(402\) −755.084 4268.94i −0.0936820 0.529640i
\(403\) −2565.38 −0.317098
\(404\) −450.188 −0.0554398
\(405\) −9644.41 + 8127.86i −1.18330 + 0.997226i
\(406\) 0 0
\(407\) 9705.08i 1.18197i
\(408\) −1337.69 7562.77i −0.162318 0.917679i
\(409\) 2623.53i 0.317176i 0.987345 + 0.158588i \(0.0506942\pi\)
−0.987345 + 0.158588i \(0.949306\pi\)
\(410\) 12855.8i 1.54854i
\(411\) −1533.00 8666.95i −0.183983 1.04017i
\(412\) 4655.83i 0.556738i
\(413\) 0 0
\(414\) 8819.27 3220.64i 1.04696 0.382333i
\(415\) 17700.4 2.09368
\(416\) 644.637 0.0759757
\(417\) −1648.31 9318.86i −0.193568 1.09436i
\(418\) 9196.78i 1.07615i
\(419\) −2183.62 −0.254598 −0.127299 0.991864i \(-0.540631\pi\)
−0.127299 + 0.991864i \(0.540631\pi\)
\(420\) 0 0
\(421\) −12921.5 −1.49586 −0.747929 0.663778i \(-0.768952\pi\)
−0.747929 + 0.663778i \(0.768952\pi\)
\(422\) 3123.44i 0.360300i
\(423\) 426.338 155.691i 0.0490054 0.0178959i
\(424\) 6970.07 0.798341
\(425\) 7117.29 0.812328
\(426\) −26494.8 + 4686.37i −3.01333 + 0.532993i
\(427\) 0 0
\(428\) 8098.81i 0.914651i
\(429\) 2323.19 410.922i 0.261456 0.0462459i
\(430\) 35840.8i 4.01952i
\(431\) 12619.8i 1.41038i 0.709018 + 0.705190i \(0.249138\pi\)
−0.709018 + 0.705190i \(0.750862\pi\)
\(432\) −6265.91 + 3631.04i −0.697844 + 0.404395i
\(433\) 14180.4i 1.57382i −0.617066 0.786912i \(-0.711679\pi\)
0.617066 0.786912i \(-0.288321\pi\)
\(434\) 0 0
\(435\) 3388.86 + 19159.2i 0.373525 + 2.11176i
\(436\) 969.837 0.106529
\(437\) −4892.36 −0.535546
\(438\) −26728.8 + 4727.75i −2.91587 + 0.515755i
\(439\) 7467.03i 0.811804i −0.913917 0.405902i \(-0.866957\pi\)
0.913917 0.405902i \(-0.133043\pi\)
\(440\) −17443.5 −1.88997
\(441\) 0 0
\(442\) −3224.80 −0.347032
\(443\) 363.788i 0.0390160i 0.999810 + 0.0195080i \(0.00620998\pi\)
−0.999810 + 0.0195080i \(0.993790\pi\)
\(444\) −27589.5 + 4879.99i −2.94896 + 0.521608i
\(445\) −11567.0 −1.23220
\(446\) −18219.3 −1.93432
\(447\) −1627.26 9199.85i −0.172185 0.973463i
\(448\) 0 0
\(449\) 5444.69i 0.572273i 0.958189 + 0.286136i \(0.0923711\pi\)
−0.958189 + 0.286136i \(0.907629\pi\)
\(450\) −7822.48 21420.7i −0.819456 2.24396i
\(451\) 4271.23i 0.445952i
\(452\) 1314.28i 0.136766i
\(453\) 10693.1 1891.39i 1.10907 0.196170i
\(454\) 13744.1i 1.42080i
\(455\) 0 0
\(456\) 12626.6 2233.38i 1.29670 0.229359i
\(457\) 2305.66 0.236005 0.118003 0.993013i \(-0.462351\pi\)
0.118003 + 0.993013i \(0.462351\pi\)
\(458\) 25231.3 2.57419
\(459\) −4955.80 + 2871.85i −0.503958 + 0.292040i
\(460\) 19213.6i 1.94748i
\(461\) 585.754 0.0591785 0.0295892 0.999562i \(-0.490580\pi\)
0.0295892 + 0.999562i \(0.490580\pi\)
\(462\) 0 0
\(463\) 11321.6 1.13641 0.568205 0.822887i \(-0.307638\pi\)
0.568205 + 0.822887i \(0.307638\pi\)
\(464\) 11171.7i 1.11775i
\(465\) −2463.84 13929.5i −0.245716 1.38918i
\(466\) −10590.3 −1.05276
\(467\) −9958.30 −0.986756 −0.493378 0.869815i \(-0.664238\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(468\) 2336.33 + 6397.71i 0.230763 + 0.631910i
\(469\) 0 0
\(470\) 1409.06i 0.138288i
\(471\) 986.800 + 5578.97i 0.0965379 + 0.545786i
\(472\) 10405.6i 1.01474i
\(473\) 11907.8i 1.15755i
\(474\) 228.156 + 1289.90i 0.0221088 + 0.124994i
\(475\) 11882.9i 1.14784i
\(476\) 0 0
\(477\) −1783.11 4882.81i −0.171160 0.468697i
\(478\) 9311.16 0.890967
\(479\) −13832.0 −1.31942 −0.659709 0.751521i \(-0.729320\pi\)
−0.659709 + 0.751521i \(0.729320\pi\)
\(480\) 619.122 + 3500.26i 0.0588727 + 0.332842i
\(481\) 5681.62i 0.538585i
\(482\) 21686.8 2.04939
\(483\) 0 0
\(484\) −8593.98 −0.807098
\(485\) 23501.8i 2.20034i
\(486\) 14090.1 + 11759.0i 1.31511 + 1.09752i
\(487\) 456.178 0.0424464 0.0212232 0.999775i \(-0.493244\pi\)
0.0212232 + 0.999775i \(0.493244\pi\)
\(488\) −8120.30 −0.753256
\(489\) 9929.15 1756.26i 0.918224 0.162414i
\(490\) 0 0
\(491\) 17039.5i 1.56616i −0.621922 0.783079i \(-0.713648\pi\)
0.621922 0.783079i \(-0.286352\pi\)
\(492\) 12142.2 2147.70i 1.11263 0.196800i
\(493\) 8835.90i 0.807198i
\(494\) 5384.05i 0.490364i
\(495\) 4462.47 + 12219.8i 0.405198 + 1.10958i
\(496\) 8122.31i 0.735287i
\(497\) 0 0
\(498\) −4485.96 25361.8i −0.403656 2.28210i
\(499\) −1855.54 −0.166463 −0.0832317 0.996530i \(-0.526524\pi\)
−0.0832317 + 0.996530i \(0.526524\pi\)
\(500\) 13205.5 1.18114
\(501\) 13635.4 2411.81i 1.21594 0.215073i
\(502\) 15971.1i 1.41997i
\(503\) 5860.64 0.519509 0.259754 0.965675i \(-0.416358\pi\)
0.259754 + 0.965675i \(0.416358\pi\)
\(504\) 0 0
\(505\) −503.394 −0.0443579
\(506\) 9684.15i 0.850816i
\(507\) −9881.39 + 1747.81i −0.865578 + 0.153102i
\(508\) 28513.4 2.49031
\(509\) 5456.88 0.475191 0.237595 0.971364i \(-0.423641\pi\)
0.237595 + 0.971364i \(0.423641\pi\)
\(510\) −3097.16 17510.1i −0.268911 1.52031i
\(511\) 0 0
\(512\) 16991.3i 1.46663i
\(513\) −4794.76 8274.08i −0.412659 0.712104i
\(514\) 34450.1i 2.95628i
\(515\) 5206.08i 0.445451i
\(516\) 33851.3 5987.57i 2.88802 0.510830i
\(517\) 468.148i 0.0398243i
\(518\) 0 0
\(519\) −15842.4 + 2802.17i −1.33989 + 0.236998i
\(520\) −10211.9 −0.861195
\(521\) −7285.24 −0.612614 −0.306307 0.951933i \(-0.599093\pi\)
−0.306307 + 0.951933i \(0.599093\pi\)
\(522\) 26593.2 9711.36i 2.22979 0.814281i
\(523\) 3415.29i 0.285545i −0.989756 0.142772i \(-0.954398\pi\)
0.989756 0.142772i \(-0.0456017\pi\)
\(524\) 1514.29 0.126245
\(525\) 0 0
\(526\) 32988.0 2.73450
\(527\) 6424.06i 0.530999i
\(528\) 1301.03 + 7355.50i 0.107235 + 0.606264i
\(529\) 7015.37 0.576590
\(530\) 16137.8 1.32261
\(531\) −7289.55 + 2662.01i −0.595743 + 0.217555i
\(532\) 0 0
\(533\) 2500.49i 0.203205i
\(534\) 2931.53 + 16573.7i 0.237565 + 1.34310i
\(535\) 9055.98i 0.731821i
\(536\) 6234.41i 0.502398i
\(537\) −816.926 4618.57i −0.0656480 0.371147i
\(538\) 17460.4i 1.39920i
\(539\) 0 0
\(540\) −32494.5 + 18830.3i −2.58952 + 1.50061i
\(541\) −2381.89 −0.189289 −0.0946447 0.995511i \(-0.530172\pi\)
−0.0946447 + 0.995511i \(0.530172\pi\)
\(542\) 16356.9 1.29629
\(543\) −3164.03 17888.1i −0.250058 1.41373i
\(544\) 1614.26i 0.127226i
\(545\) 1084.46 0.0852351
\(546\) 0 0
\(547\) −1376.55 −0.107600 −0.0537998 0.998552i \(-0.517133\pi\)
−0.0537998 + 0.998552i \(0.517133\pi\)
\(548\) 26208.1i 2.04298i
\(549\) 2077.37 + 5688.58i 0.161494 + 0.442227i
\(550\) −23521.4 −1.82356
\(551\) −14752.2 −1.14059
\(552\) 13295.8 2351.73i 1.02519 0.181334i
\(553\) 0 0
\(554\) 33623.7i 2.57858i
\(555\) −30850.2 + 5456.74i −2.35949 + 0.417344i
\(556\) 28179.4i 2.14941i
\(557\) 2037.41i 0.154987i 0.996993 + 0.0774935i \(0.0246917\pi\)
−0.996993 + 0.0774935i \(0.975308\pi\)
\(558\) −19334.3 + 7060.56i −1.46682 + 0.535658i
\(559\) 6971.14i 0.527456i
\(560\) 0 0
\(561\) 1029.01 + 5817.58i 0.0774414 + 0.437822i
\(562\) −18575.1 −1.39421
\(563\) 2394.19 0.179224 0.0896118 0.995977i \(-0.471437\pi\)
0.0896118 + 0.995977i \(0.471437\pi\)
\(564\) 1330.85 235.398i 0.0993595 0.0175746i
\(565\) 1469.61i 0.109428i
\(566\) 31218.7 2.31841
\(567\) 0 0
\(568\) −38693.4 −2.85834
\(569\) 7635.14i 0.562534i −0.959630 0.281267i \(-0.909245\pi\)
0.959630 0.281267i \(-0.0907546\pi\)
\(570\) 29234.4 5170.95i 2.14824 0.379977i
\(571\) 2512.52 0.184143 0.0920715 0.995752i \(-0.470651\pi\)
0.0920715 + 0.995752i \(0.470651\pi\)
\(572\) 7025.11 0.513522
\(573\) −320.850 1813.95i −0.0233921 0.132249i
\(574\) 0 0
\(575\) 12512.6i 0.907496i
\(576\) 15331.6 5598.84i 1.10906 0.405009i
\(577\) 10906.9i 0.786929i 0.919340 + 0.393465i \(0.128724\pi\)
−0.919340 + 0.393465i \(0.871276\pi\)
\(578\) 15727.4i 1.13179i
\(579\) −14530.9 + 2570.21i −1.04298 + 0.184480i
\(580\) 57935.9i 4.14768i
\(581\) 0 0
\(582\) 33674.3 5956.26i 2.39836 0.424218i
\(583\) −5361.65 −0.380887
\(584\) −39035.1 −2.76590
\(585\) 2612.45 + 7153.83i 0.184635 + 0.505597i
\(586\) 6992.18i 0.492908i
\(587\) −25367.7 −1.78371 −0.891855 0.452321i \(-0.850596\pi\)
−0.891855 + 0.452321i \(0.850596\pi\)
\(588\) 0 0
\(589\) 10725.4 0.750313
\(590\) 24092.2i 1.68112i
\(591\) 2767.84 + 15648.2i 0.192646 + 1.08914i
\(592\) −17988.7 −1.24887
\(593\) −9834.38 −0.681028 −0.340514 0.940239i \(-0.610601\pi\)
−0.340514 + 0.940239i \(0.610601\pi\)
\(594\) 16378.1 9490.96i 1.13131 0.655587i
\(595\) 0 0
\(596\) 27819.5i 1.91197i
\(597\) −1664.81 9412.13i −0.114131 0.645248i
\(598\) 5669.37i 0.387689i
\(599\) 6922.43i 0.472192i −0.971730 0.236096i \(-0.924132\pi\)
0.971730 0.236096i \(-0.0758679\pi\)
\(600\) −5712.03 32293.5i −0.388654 2.19729i
\(601\) 15144.9i 1.02791i 0.857817 + 0.513955i \(0.171820\pi\)
−0.857817 + 0.513955i \(0.828180\pi\)
\(602\) 0 0
\(603\) −4367.44 + 1594.91i −0.294952 + 0.107711i
\(604\) 32335.1 2.17830
\(605\) −9609.67 −0.645766
\(606\) 127.579 + 721.281i 0.00855207 + 0.0483499i
\(607\) 27601.0i 1.84562i 0.385259 + 0.922809i \(0.374112\pi\)
−0.385259 + 0.922809i \(0.625888\pi\)
\(608\) −2695.12 −0.179773
\(609\) 0 0
\(610\) −18800.9 −1.24791
\(611\) 274.067i 0.0181466i
\(612\) −16020.7 + 5850.49i −1.05817 + 0.386425i
\(613\) 12162.1 0.801342 0.400671 0.916222i \(-0.368777\pi\)
0.400671 + 0.916222i \(0.368777\pi\)
\(614\) 26667.6 1.75279
\(615\) 13577.2 2401.52i 0.890223 0.157461i
\(616\) 0 0
\(617\) 17715.1i 1.15589i 0.816077 + 0.577944i \(0.196145\pi\)
−0.816077 + 0.577944i \(0.803855\pi\)
\(618\) 7459.46 1319.42i 0.485540 0.0858816i
\(619\) 4569.82i 0.296731i 0.988933 + 0.148366i \(0.0474013\pi\)
−0.988933 + 0.148366i \(0.952599\pi\)
\(620\) 42121.7i 2.72847i
\(621\) −5048.86 8712.55i −0.326254 0.563000i
\(622\) 11721.9i 0.755634i
\(623\) 0 0
\(624\) 761.660 + 4306.11i 0.0488635 + 0.276254i
\(625\) −7025.11 −0.449607
\(626\) −5767.21 −0.368218
\(627\) −9712.88 + 1718.00i −0.618652 + 0.109426i
\(628\) 16870.3i 1.07197i
\(629\) −14227.6 −0.901891
\(630\) 0 0
\(631\) −1677.26 −0.105817 −0.0529086 0.998599i \(-0.516849\pi\)
−0.0529086 + 0.998599i \(0.516849\pi\)
\(632\) 1883.79i 0.118565i
\(633\) 3298.72 583.474i 0.207129 0.0366366i
\(634\) −32112.5 −2.01159
\(635\) 31883.3 1.99252
\(636\) −2695.99 15242.0i −0.168087 0.950293i
\(637\) 0 0
\(638\) 29201.1i 1.81204i
\(639\) 9898.71 + 27106.2i 0.612812 + 1.67810i
\(640\) 45198.9i 2.79163i
\(641\) 27279.5i 1.68093i −0.541868 0.840464i \(-0.682283\pi\)
0.541868 0.840464i \(-0.317717\pi\)
\(642\) −12975.7 + 2295.13i −0.797681 + 0.141093i
\(643\) 19330.9i 1.18559i −0.805353 0.592796i \(-0.798024\pi\)
0.805353 0.592796i \(-0.201976\pi\)
\(644\) 0 0
\(645\) 37852.0 6695.22i 2.31073 0.408719i
\(646\) 13482.4 0.821142
\(647\) 19942.3 1.21177 0.605884 0.795553i \(-0.292819\pi\)
0.605884 + 0.795553i \(0.292819\pi\)
\(648\) 17007.8 + 20181.3i 1.03106 + 1.22345i
\(649\) 8004.42i 0.484131i
\(650\) −13770.1 −0.830935
\(651\) 0 0
\(652\) 30024.9 1.80347
\(653\) 12834.9i 0.769171i 0.923089 + 0.384586i \(0.125656\pi\)
−0.923089 + 0.384586i \(0.874344\pi\)
\(654\) −274.843 1553.85i −0.0164331 0.0929059i
\(655\) 1693.26 0.101010
\(656\) 7916.88 0.471193
\(657\) 9986.12 + 27345.6i 0.592992 + 1.62382i
\(658\) 0 0
\(659\) 11112.6i 0.656880i −0.944525 0.328440i \(-0.893477\pi\)
0.944525 0.328440i \(-0.106523\pi\)
\(660\) 6747.06 + 38145.1i 0.397922 + 2.24969i
\(661\) 3297.94i 0.194062i 0.995281 + 0.0970312i \(0.0309346\pi\)
−0.995281 + 0.0970312i \(0.969065\pi\)
\(662\) 34811.0i 2.04376i
\(663\) 602.408 + 3405.77i 0.0352875 + 0.199501i
\(664\) 37038.7i 2.16473i
\(665\) 0 0
\(666\) 15637.2 + 42820.3i 0.909805 + 2.49137i
\(667\) −15534.0 −0.901766
\(668\) 41232.2 2.38821
\(669\) 3403.45 + 19241.7i 0.196689 + 1.11200i
\(670\) 14434.5i 0.832321i
\(671\) 6246.45 0.359376
\(672\) 0 0
\(673\) 527.753 0.0302279 0.0151140 0.999886i \(-0.495189\pi\)
0.0151140 + 0.999886i \(0.495189\pi\)
\(674\) 34953.5i 1.99756i
\(675\) −21161.5 + 12263.0i −1.20668 + 0.699261i
\(676\) −29880.5 −1.70007
\(677\) 214.998 0.0122054 0.00610269 0.999981i \(-0.498057\pi\)
0.00610269 + 0.999981i \(0.498057\pi\)
\(678\) 2105.71 372.454i 0.119276 0.0210974i
\(679\) 0 0
\(680\) 25572.0i 1.44212i
\(681\) 14515.4 2567.47i 0.816788 0.144472i
\(682\) 21230.4i 1.19201i
\(683\) 7314.04i 0.409757i 0.978787 + 0.204878i \(0.0656799\pi\)
−0.978787 + 0.204878i \(0.934320\pi\)
\(684\) −9767.83 26747.8i −0.546027 1.49522i
\(685\) 29305.5i 1.63461i
\(686\) 0 0
\(687\) −4713.32 26647.2i −0.261753 1.47985i
\(688\) 22071.5 1.22306
\(689\) −3138.86 −0.173557
\(690\) 30783.7 5444.98i 1.69843 0.300415i
\(691\) 31412.9i 1.72938i 0.502302 + 0.864692i \(0.332486\pi\)
−0.502302 + 0.864692i \(0.667514\pi\)
\(692\) −47905.9 −2.63166
\(693\) 0 0
\(694\) −39490.5 −2.16000
\(695\) 31509.9i 1.71977i
\(696\) 40091.3 7091.30i 2.18342 0.386200i
\(697\) 6261.58 0.340279
\(698\) −2383.26 −0.129237
\(699\) 1978.32 + 11184.6i 0.107049 + 0.605210i
\(700\) 0 0
\(701\) 11496.6i 0.619430i 0.950829 + 0.309715i \(0.100234\pi\)
−0.950829 + 0.309715i \(0.899766\pi\)
\(702\) 9588.17 5556.27i 0.515502 0.298729i
\(703\) 23754.0i 1.27439i
\(704\) 16835.2i 0.901277i
\(705\) 1488.13 263.219i 0.0794984 0.0140616i
\(706\) 14164.6i 0.755087i
\(707\) 0 0
\(708\) −22754.9 + 4024.85i −1.20788 + 0.213649i
\(709\) 21068.2 1.11598 0.557992 0.829847i \(-0.311572\pi\)
0.557992 + 0.829847i \(0.311572\pi\)
\(710\) −89586.8 −4.73540
\(711\) 1319.67 481.919i 0.0696081 0.0254197i
\(712\) 24204.4i 1.27402i
\(713\) 11293.8 0.593208
\(714\) 0 0
\(715\) 7855.39 0.410874
\(716\) 13966.1i 0.728966i
\(717\) −1739.37 9833.68i −0.0905968 0.512197i
\(718\) −23265.7 −1.20929
\(719\) −7492.00 −0.388602 −0.194301 0.980942i \(-0.562244\pi\)
−0.194301 + 0.980942i \(0.562244\pi\)
\(720\) −22649.9 + 8271.35i −1.17238 + 0.428132i
\(721\) 0 0
\(722\) 10720.9i 0.552620i
\(723\) −4051.19 22903.8i −0.208389 1.17815i
\(724\) 54092.1i 2.77668i
\(725\) 37729.8i 1.93276i
\(726\) 2435.46 + 13769.1i 0.124502 + 0.703882i
\(727\) 19637.5i 1.00181i 0.865503 + 0.500904i \(0.166999\pi\)
−0.865503 + 0.500904i \(0.833001\pi\)
\(728\) 0 0
\(729\) 9786.73 17077.5i 0.497217 0.867626i
\(730\) −90378.0 −4.58225
\(731\) 17456.7 0.883254
\(732\) 3140.89 + 17757.3i 0.158594 + 0.896626i
\(733\) 28892.7i 1.45590i −0.685629 0.727951i \(-0.740473\pi\)
0.685629 0.727951i \(-0.259527\pi\)
\(734\) −43399.7 −2.18244
\(735\) 0 0
\(736\) −2837.95 −0.142131
\(737\) 4795.75i 0.239693i
\(738\) −6881.98 18845.3i −0.343265 0.939981i
\(739\) −4114.53 −0.204811 −0.102406 0.994743i \(-0.532654\pi\)
−0.102406 + 0.994743i \(0.532654\pi\)
\(740\) −93288.3 −4.63425
\(741\) −5686.19 + 1005.77i −0.281899 + 0.0498620i
\(742\) 0 0
\(743\) 19095.9i 0.942881i 0.881898 + 0.471441i \(0.156266\pi\)
−0.881898 + 0.471441i \(0.843734\pi\)
\(744\) −29148.0 + 5155.67i −1.43632 + 0.254054i
\(745\) 31107.4i 1.52978i
\(746\) 24577.1i 1.20621i
\(747\) −25947.0 + 9475.40i −1.27089 + 0.464105i
\(748\) 17591.8i 0.859922i
\(749\) 0 0
\(750\) −3742.33 21157.6i −0.182201 1.03009i
\(751\) 27352.7 1.32905 0.664524 0.747267i \(-0.268634\pi\)
0.664524 + 0.747267i \(0.268634\pi\)
\(752\) 867.731 0.0420783
\(753\) −16867.3 + 2983.47i −0.816308 + 0.144388i
\(754\) 17095.1i 0.825687i
\(755\) 36156.7 1.74288
\(756\) 0 0
\(757\) 2016.86 0.0968349 0.0484174 0.998827i \(-0.484582\pi\)
0.0484174 + 0.998827i \(0.484582\pi\)
\(758\) 4146.39i 0.198686i
\(759\) −10227.6 + 1809.05i −0.489115 + 0.0865141i
\(760\) 42694.4 2.03775
\(761\) 28904.7 1.37687 0.688434 0.725299i \(-0.258299\pi\)
0.688434 + 0.725299i \(0.258299\pi\)
\(762\) −8080.45 45683.6i −0.384152 2.17184i
\(763\) 0 0
\(764\) 5485.23i 0.259750i
\(765\) −17914.2 + 6541.94i −0.846651 + 0.309182i
\(766\) 34304.4i 1.61811i
\(767\) 4686.01i 0.220602i
\(768\) 40017.4 7078.23i 1.88021 0.332570i
\(769\) 16726.1i 0.784343i −0.919892 0.392171i \(-0.871724\pi\)
0.919892 0.392171i \(-0.128276\pi\)
\(770\) 0 0
\(771\) −36383.3 + 6435.44i −1.69950 + 0.300605i
\(772\) −43940.2 −2.04850
\(773\) 15197.6 0.707139 0.353570 0.935408i \(-0.384968\pi\)
0.353570 + 0.935408i \(0.384968\pi\)
\(774\) −19186.3 52539.0i −0.891005 2.43989i
\(775\) 27431.1i 1.27142i
\(776\) 49178.4 2.27500
\(777\) 0 0
\(778\) −10046.2 −0.462949
\(779\) 10454.2i 0.480821i
\(780\) 3949.91 + 22331.2i 0.181320 + 1.02511i
\(781\) 29764.4 1.36371
\(782\) 14196.9 0.649206
\(783\) −15224.1 26271.4i −0.694845 1.19906i
\(784\) 0 0
\(785\) 18864.1i 0.857694i
\(786\) −429.138 2426.17i −0.0194743 0.110100i