Properties

Label 63.4.e.a.46.1
Level $63$
Weight $4$
Character 63.46
Analytic conductor $3.717$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.46
Dual form 63.4.e.a.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-3.50000 - 18.1865i) q^{7} -21.0000 q^{8} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-3.50000 - 18.1865i) q^{7} -21.0000 q^{8} +(-4.50000 + 7.79423i) q^{10} +(-7.50000 + 12.9904i) q^{11} -64.0000 q^{13} +(-42.0000 + 36.3731i) q^{14} +(35.5000 + 61.4878i) q^{16} +(42.0000 - 72.7461i) q^{17} +(8.00000 + 13.8564i) q^{19} +3.00000 q^{20} +45.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(58.0000 - 100.459i) q^{25} +(96.0000 + 166.277i) q^{26} +(17.5000 + 6.06218i) q^{28} +297.000 q^{29} +(126.500 - 219.104i) q^{31} +(22.5000 - 38.9711i) q^{32} -252.000 q^{34} +(-42.0000 + 36.3731i) q^{35} +(158.000 + 273.664i) q^{37} +(24.0000 - 41.5692i) q^{38} +(31.5000 + 54.5596i) q^{40} -360.000 q^{41} +26.0000 q^{43} +(-7.50000 - 12.9904i) q^{44} +(-126.000 + 218.238i) q^{46} +(-15.0000 - 25.9808i) q^{47} +(-318.500 + 127.306i) q^{49} -348.000 q^{50} +(32.0000 - 55.4256i) q^{52} +(181.500 - 314.367i) q^{53} +45.0000 q^{55} +(73.5000 + 381.917i) q^{56} +(-445.500 - 771.629i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(59.0000 + 102.191i) q^{61} -759.000 q^{62} +433.000 q^{64} +(96.0000 + 166.277i) q^{65} +(185.000 - 320.429i) q^{67} +(42.0000 + 72.7461i) q^{68} +(157.500 + 54.5596i) q^{70} +342.000 q^{71} +(-181.000 + 313.501i) q^{73} +(474.000 - 820.992i) q^{74} -16.0000 q^{76} +(262.500 + 90.9327i) q^{77} +(-233.500 - 404.434i) q^{79} +(106.500 - 184.463i) q^{80} +(540.000 + 935.307i) q^{82} -477.000 q^{83} -252.000 q^{85} +(-39.0000 - 67.5500i) q^{86} +(157.500 - 272.798i) q^{88} +(453.000 + 784.619i) q^{89} +(224.000 + 1163.94i) q^{91} +84.0000 q^{92} +(-45.0000 + 77.9423i) q^{94} +(24.0000 - 41.5692i) q^{95} +503.000 q^{97} +(808.500 + 636.529i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - q^{4} - 3q^{5} - 7q^{7} - 42q^{8} + O(q^{10}) \) \( 2q - 3q^{2} - q^{4} - 3q^{5} - 7q^{7} - 42q^{8} - 9q^{10} - 15q^{11} - 128q^{13} - 84q^{14} + 71q^{16} + 84q^{17} + 16q^{19} + 6q^{20} + 90q^{22} - 84q^{23} + 116q^{25} + 192q^{26} + 35q^{28} + 594q^{29} + 253q^{31} + 45q^{32} - 504q^{34} - 84q^{35} + 316q^{37} + 48q^{38} + 63q^{40} - 720q^{41} + 52q^{43} - 15q^{44} - 252q^{46} - 30q^{47} - 637q^{49} - 696q^{50} + 64q^{52} + 363q^{53} + 90q^{55} + 147q^{56} - 891q^{58} - 15q^{59} + 118q^{61} - 1518q^{62} + 866q^{64} + 192q^{65} + 370q^{67} + 84q^{68} + 315q^{70} + 684q^{71} - 362q^{73} + 948q^{74} - 32q^{76} + 525q^{77} - 467q^{79} + 213q^{80} + 1080q^{82} - 954q^{83} - 504q^{85} - 78q^{86} + 315q^{88} + 906q^{89} + 448q^{91} + 168q^{92} - 90q^{94} + 48q^{95} + 1006q^{97} + 1617q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i \(-0.988735\pi\)
0.469044 0.883175i \(-0.344599\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) −1.50000 2.59808i −0.134164 0.232379i 0.791114 0.611669i \(-0.209502\pi\)
−0.925278 + 0.379290i \(0.876168\pi\)
\(6\) 0 0
\(7\) −3.50000 18.1865i −0.188982 0.981981i
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) −4.50000 + 7.79423i −0.142302 + 0.246475i
\(11\) −7.50000 + 12.9904i −0.205576 + 0.356068i −0.950316 0.311287i \(-0.899240\pi\)
0.744740 + 0.667355i \(0.232573\pi\)
\(12\) 0 0
\(13\) −64.0000 −1.36542 −0.682708 0.730691i \(-0.739198\pi\)
−0.682708 + 0.730691i \(0.739198\pi\)
\(14\) −42.0000 + 36.3731i −0.801784 + 0.694365i
\(15\) 0 0
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) 42.0000 72.7461i 0.599206 1.03785i −0.393733 0.919225i \(-0.628817\pi\)
0.992939 0.118630i \(-0.0378502\pi\)
\(18\) 0 0
\(19\) 8.00000 + 13.8564i 0.0965961 + 0.167309i 0.910274 0.414007i \(-0.135871\pi\)
−0.813678 + 0.581317i \(0.802538\pi\)
\(20\) 3.00000 0.0335410
\(21\) 0 0
\(22\) 45.0000 0.436092
\(23\) −42.0000 72.7461i −0.380765 0.659505i 0.610406 0.792088i \(-0.291006\pi\)
−0.991172 + 0.132583i \(0.957673\pi\)
\(24\) 0 0
\(25\) 58.0000 100.459i 0.464000 0.803672i
\(26\) 96.0000 + 166.277i 0.724121 + 1.25421i
\(27\) 0 0
\(28\) 17.5000 + 6.06218i 0.118114 + 0.0409159i
\(29\) 297.000 1.90178 0.950888 0.309535i \(-0.100173\pi\)
0.950888 + 0.309535i \(0.100173\pi\)
\(30\) 0 0
\(31\) 126.500 219.104i 0.732906 1.26943i −0.222731 0.974880i \(-0.571497\pi\)
0.955636 0.294550i \(-0.0951696\pi\)
\(32\) 22.5000 38.9711i 0.124296 0.215287i
\(33\) 0 0
\(34\) −252.000 −1.27111
\(35\) −42.0000 + 36.3731i −0.202837 + 0.175662i
\(36\) 0 0
\(37\) 158.000 + 273.664i 0.702028 + 1.21595i 0.967753 + 0.251900i \(0.0810553\pi\)
−0.265725 + 0.964049i \(0.585611\pi\)
\(38\) 24.0000 41.5692i 0.102456 0.177458i
\(39\) 0 0
\(40\) 31.5000 + 54.5596i 0.124515 + 0.215666i
\(41\) −360.000 −1.37128 −0.685641 0.727940i \(-0.740478\pi\)
−0.685641 + 0.727940i \(0.740478\pi\)
\(42\) 0 0
\(43\) 26.0000 0.0922084 0.0461042 0.998937i \(-0.485319\pi\)
0.0461042 + 0.998937i \(0.485319\pi\)
\(44\) −7.50000 12.9904i −0.0256970 0.0445085i
\(45\) 0 0
\(46\) −126.000 + 218.238i −0.403863 + 0.699511i
\(47\) −15.0000 25.9808i −0.0465527 0.0806316i 0.841810 0.539774i \(-0.181490\pi\)
−0.888363 + 0.459142i \(0.848157\pi\)
\(48\) 0 0
\(49\) −318.500 + 127.306i −0.928571 + 0.371154i
\(50\) −348.000 −0.984293
\(51\) 0 0
\(52\) 32.0000 55.4256i 0.0853385 0.147811i
\(53\) 181.500 314.367i 0.470395 0.814748i −0.529032 0.848602i \(-0.677445\pi\)
0.999427 + 0.0338538i \(0.0107781\pi\)
\(54\) 0 0
\(55\) 45.0000 0.110324
\(56\) 73.5000 + 381.917i 0.175390 + 0.911354i
\(57\) 0 0
\(58\) −445.500 771.629i −1.00857 1.74689i
\(59\) −7.50000 + 12.9904i −0.0165494 + 0.0286645i −0.874182 0.485599i \(-0.838601\pi\)
0.857632 + 0.514264i \(0.171935\pi\)
\(60\) 0 0
\(61\) 59.0000 + 102.191i 0.123839 + 0.214495i 0.921279 0.388903i \(-0.127146\pi\)
−0.797440 + 0.603399i \(0.793813\pi\)
\(62\) −759.000 −1.55473
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 96.0000 + 166.277i 0.183190 + 0.317294i
\(66\) 0 0
\(67\) 185.000 320.429i 0.337334 0.584279i −0.646597 0.762832i \(-0.723808\pi\)
0.983930 + 0.178553i \(0.0571417\pi\)
\(68\) 42.0000 + 72.7461i 0.0749007 + 0.129732i
\(69\) 0 0
\(70\) 157.500 + 54.5596i 0.268926 + 0.0931589i
\(71\) 342.000 0.571661 0.285831 0.958280i \(-0.407731\pi\)
0.285831 + 0.958280i \(0.407731\pi\)
\(72\) 0 0
\(73\) −181.000 + 313.501i −0.290198 + 0.502638i −0.973856 0.227165i \(-0.927054\pi\)
0.683658 + 0.729802i \(0.260388\pi\)
\(74\) 474.000 820.992i 0.744613 1.28971i
\(75\) 0 0
\(76\) −16.0000 −0.0241490
\(77\) 262.500 + 90.9327i 0.388502 + 0.134581i
\(78\) 0 0
\(79\) −233.500 404.434i −0.332542 0.575979i 0.650468 0.759534i \(-0.274573\pi\)
−0.983010 + 0.183555i \(0.941240\pi\)
\(80\) 106.500 184.463i 0.148838 0.257795i
\(81\) 0 0
\(82\) 540.000 + 935.307i 0.727232 + 1.25960i
\(83\) −477.000 −0.630814 −0.315407 0.948957i \(-0.602141\pi\)
−0.315407 + 0.948957i \(0.602141\pi\)
\(84\) 0 0
\(85\) −252.000 −0.321568
\(86\) −39.0000 67.5500i −0.0489009 0.0846989i
\(87\) 0 0
\(88\) 157.500 272.798i 0.190790 0.330459i
\(89\) 453.000 + 784.619i 0.539527 + 0.934488i 0.998929 + 0.0462600i \(0.0147303\pi\)
−0.459402 + 0.888228i \(0.651936\pi\)
\(90\) 0 0
\(91\) 224.000 + 1163.94i 0.258039 + 1.34081i
\(92\) 84.0000 0.0951914
\(93\) 0 0
\(94\) −45.0000 + 77.9423i −0.0493765 + 0.0855227i
\(95\) 24.0000 41.5692i 0.0259195 0.0448938i
\(96\) 0 0
\(97\) 503.000 0.526515 0.263257 0.964726i \(-0.415203\pi\)
0.263257 + 0.964726i \(0.415203\pi\)
\(98\) 808.500 + 636.529i 0.833376 + 0.656113i
\(99\) 0 0
\(100\) 58.0000 + 100.459i 0.0580000 + 0.100459i
\(101\) −543.000 + 940.504i −0.534956 + 0.926570i 0.464210 + 0.885725i \(0.346338\pi\)
−0.999165 + 0.0408451i \(0.986995\pi\)
\(102\) 0 0
\(103\) −868.000 1503.42i −0.830355 1.43822i −0.897757 0.440491i \(-0.854804\pi\)
0.0674017 0.997726i \(-0.478529\pi\)
\(104\) 1344.00 1.26721
\(105\) 0 0
\(106\) −1089.00 −0.997859
\(107\) −676.500 1171.73i −0.611212 1.05865i −0.991036 0.133592i \(-0.957349\pi\)
0.379824 0.925059i \(-0.375985\pi\)
\(108\) 0 0
\(109\) 185.000 320.429i 0.162567 0.281574i −0.773222 0.634136i \(-0.781356\pi\)
0.935789 + 0.352562i \(0.114689\pi\)
\(110\) −67.5000 116.913i −0.0585079 0.101339i
\(111\) 0 0
\(112\) 994.000 860.829i 0.838609 0.726256i
\(113\) 648.000 0.539458 0.269729 0.962936i \(-0.413066\pi\)
0.269729 + 0.962936i \(0.413066\pi\)
\(114\) 0 0
\(115\) −126.000 + 218.238i −0.102170 + 0.176964i
\(116\) −148.500 + 257.210i −0.118861 + 0.205873i
\(117\) 0 0
\(118\) 45.0000 0.0351067
\(119\) −1470.00 509.223i −1.13239 0.392272i
\(120\) 0 0
\(121\) 553.000 + 957.824i 0.415477 + 0.719627i
\(122\) 177.000 306.573i 0.131351 0.227507i
\(123\) 0 0
\(124\) 126.500 + 219.104i 0.0916132 + 0.158679i
\(125\) −723.000 −0.517337
\(126\) 0 0
\(127\) 377.000 0.263412 0.131706 0.991289i \(-0.457954\pi\)
0.131706 + 0.991289i \(0.457954\pi\)
\(128\) −829.500 1436.74i −0.572798 0.992115i
\(129\) 0 0
\(130\) 288.000 498.831i 0.194302 0.336541i
\(131\) −325.500 563.783i −0.217092 0.376015i 0.736826 0.676083i \(-0.236324\pi\)
−0.953918 + 0.300068i \(0.902991\pi\)
\(132\) 0 0
\(133\) 224.000 193.990i 0.146040 0.126474i
\(134\) −1110.00 −0.715593
\(135\) 0 0
\(136\) −882.000 + 1527.67i −0.556109 + 0.963210i
\(137\) −885.000 + 1532.86i −0.551903 + 0.955923i 0.446235 + 0.894916i \(0.352765\pi\)
−0.998137 + 0.0610074i \(0.980569\pi\)
\(138\) 0 0
\(139\) −1558.00 −0.950704 −0.475352 0.879796i \(-0.657679\pi\)
−0.475352 + 0.879796i \(0.657679\pi\)
\(140\) −10.5000 54.5596i −0.00633866 0.0329366i
\(141\) 0 0
\(142\) −513.000 888.542i −0.303169 0.525104i
\(143\) 480.000 831.384i 0.280697 0.486181i
\(144\) 0 0
\(145\) −445.500 771.629i −0.255150 0.441933i
\(146\) 1086.00 0.615603
\(147\) 0 0
\(148\) −316.000 −0.175507
\(149\) 1227.00 + 2125.23i 0.674629 + 1.16849i 0.976577 + 0.215168i \(0.0690298\pi\)
−0.301948 + 0.953324i \(0.597637\pi\)
\(150\) 0 0
\(151\) −629.500 + 1090.33i −0.339258 + 0.587612i −0.984293 0.176540i \(-0.943509\pi\)
0.645035 + 0.764153i \(0.276843\pi\)
\(152\) −168.000 290.985i −0.0896487 0.155276i
\(153\) 0 0
\(154\) −157.500 818.394i −0.0824137 0.428234i
\(155\) −759.000 −0.393318
\(156\) 0 0
\(157\) 98.0000 169.741i 0.0498169 0.0862854i −0.840042 0.542522i \(-0.817470\pi\)
0.889859 + 0.456236i \(0.150803\pi\)
\(158\) −700.500 + 1213.30i −0.352714 + 0.610918i
\(159\) 0 0
\(160\) −135.000 −0.0667043
\(161\) −1176.00 + 1018.45i −0.575663 + 0.498539i
\(162\) 0 0
\(163\) 626.000 + 1084.26i 0.300810 + 0.521019i 0.976320 0.216332i \(-0.0694095\pi\)
−0.675509 + 0.737351i \(0.736076\pi\)
\(164\) 180.000 311.769i 0.0857051 0.148446i
\(165\) 0 0
\(166\) 715.500 + 1239.28i 0.334540 + 0.579440i
\(167\) 2646.00 1.22607 0.613035 0.790056i \(-0.289949\pi\)
0.613035 + 0.790056i \(0.289949\pi\)
\(168\) 0 0
\(169\) 1899.00 0.864360
\(170\) 378.000 + 654.715i 0.170537 + 0.295379i
\(171\) 0 0
\(172\) −13.0000 + 22.5167i −0.00576303 + 0.00998186i
\(173\) −393.000 680.696i −0.172712 0.299147i 0.766655 0.642059i \(-0.221920\pi\)
−0.939367 + 0.342913i \(0.888586\pi\)
\(174\) 0 0
\(175\) −2030.00 703.213i −0.876878 0.303759i
\(176\) −1065.00 −0.456122
\(177\) 0 0
\(178\) 1359.00 2353.86i 0.572255 0.991174i
\(179\) 1446.00 2504.55i 0.603794 1.04580i −0.388447 0.921471i \(-0.626988\pi\)
0.992241 0.124331i \(-0.0396784\pi\)
\(180\) 0 0
\(181\) 1352.00 0.555212 0.277606 0.960695i \(-0.410459\pi\)
0.277606 + 0.960695i \(0.410459\pi\)
\(182\) 2688.00 2327.88i 1.09477 0.948097i
\(183\) 0 0
\(184\) 882.000 + 1527.67i 0.353380 + 0.612072i
\(185\) 474.000 820.992i 0.188374 0.326273i
\(186\) 0 0
\(187\) 630.000 + 1091.19i 0.246365 + 0.426716i
\(188\) 30.0000 0.0116382
\(189\) 0 0
\(190\) −144.000 −0.0549835
\(191\) 1956.00 + 3387.89i 0.741001 + 1.28345i 0.952040 + 0.305974i \(0.0989820\pi\)
−0.211039 + 0.977478i \(0.567685\pi\)
\(192\) 0 0
\(193\) −746.500 + 1292.98i −0.278416 + 0.482230i −0.970991 0.239115i \(-0.923143\pi\)
0.692575 + 0.721345i \(0.256476\pi\)
\(194\) −754.500 1306.83i −0.279227 0.483635i
\(195\) 0 0
\(196\) 49.0000 339.482i 0.0178571 0.123718i
\(197\) 4086.00 1.47774 0.738872 0.673846i \(-0.235359\pi\)
0.738872 + 0.673846i \(0.235359\pi\)
\(198\) 0 0
\(199\) 1778.00 3079.59i 0.633362 1.09702i −0.353497 0.935436i \(-0.615008\pi\)
0.986860 0.161580i \(-0.0516590\pi\)
\(200\) −1218.00 + 2109.64i −0.430628 + 0.745870i
\(201\) 0 0
\(202\) 3258.00 1.13481
\(203\) −1039.50 5401.40i −0.359402 1.86751i
\(204\) 0 0
\(205\) 540.000 + 935.307i 0.183977 + 0.318657i
\(206\) −2604.00 + 4510.26i −0.880725 + 1.52546i
\(207\) 0 0
\(208\) −2272.00 3935.22i −0.757379 1.31182i
\(209\) −240.000 −0.0794313
\(210\) 0 0
\(211\) 1250.00 0.407837 0.203918 0.978988i \(-0.434632\pi\)
0.203918 + 0.978988i \(0.434632\pi\)
\(212\) 181.500 + 314.367i 0.0587994 + 0.101844i
\(213\) 0 0
\(214\) −2029.50 + 3515.20i −0.648289 + 1.12287i
\(215\) −39.0000 67.5500i −0.0123711 0.0214273i
\(216\) 0 0
\(217\) −4427.50 1533.73i −1.38506 0.479799i
\(218\) −1110.00 −0.344856
\(219\) 0 0
\(220\) −22.5000 + 38.9711i −0.00689523 + 0.0119429i
\(221\) −2688.00 + 4655.75i −0.818165 + 1.41710i
\(222\) 0 0
\(223\) 425.000 0.127624 0.0638119 0.997962i \(-0.479674\pi\)
0.0638119 + 0.997962i \(0.479674\pi\)
\(224\) −787.500 272.798i −0.234898 0.0813709i
\(225\) 0 0
\(226\) −972.000 1683.55i −0.286091 0.495523i
\(227\) 1927.50 3338.53i 0.563580 0.976149i −0.433600 0.901105i \(-0.642757\pi\)
0.997180 0.0750439i \(-0.0239097\pi\)
\(228\) 0 0
\(229\) 1094.00 + 1894.86i 0.315692 + 0.546795i 0.979584 0.201033i \(-0.0644299\pi\)
−0.663892 + 0.747828i \(0.731097\pi\)
\(230\) 756.000 0.216735
\(231\) 0 0
\(232\) −6237.00 −1.76500
\(233\) 426.000 + 737.854i 0.119778 + 0.207461i 0.919679 0.392670i \(-0.128449\pi\)
−0.799902 + 0.600131i \(0.795115\pi\)
\(234\) 0 0
\(235\) −45.0000 + 77.9423i −0.0124914 + 0.0216357i
\(236\) −7.50000 12.9904i −0.00206868 0.00358306i
\(237\) 0 0
\(238\) 882.000 + 4583.01i 0.240217 + 1.24820i
\(239\) −5508.00 −1.49072 −0.745362 0.666660i \(-0.767723\pi\)
−0.745362 + 0.666660i \(0.767723\pi\)
\(240\) 0 0
\(241\) −395.500 + 685.026i −0.105711 + 0.183097i −0.914029 0.405650i \(-0.867045\pi\)
0.808317 + 0.588747i \(0.200379\pi\)
\(242\) 1659.00 2873.47i 0.440680 0.763280i
\(243\) 0 0
\(244\) −118.000 −0.0309597
\(245\) 808.500 + 636.529i 0.210829 + 0.165985i
\(246\) 0 0
\(247\) −512.000 886.810i −0.131894 0.228447i
\(248\) −2656.50 + 4601.19i −0.680193 + 1.17813i
\(249\) 0 0
\(250\) 1084.50 + 1878.41i 0.274359 + 0.475204i
\(251\) −5265.00 −1.32400 −0.662000 0.749504i \(-0.730292\pi\)
−0.662000 + 0.749504i \(0.730292\pi\)
\(252\) 0 0
\(253\) 1260.00 0.313105
\(254\) −565.500 979.475i −0.139695 0.241959i
\(255\) 0 0
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) −3435.00 5949.59i −0.833733 1.44407i −0.895058 0.445950i \(-0.852866\pi\)
0.0613246 0.998118i \(-0.480468\pi\)
\(258\) 0 0
\(259\) 4424.00 3831.30i 1.06137 0.919171i
\(260\) −192.000 −0.0457974
\(261\) 0 0
\(262\) −976.500 + 1691.35i −0.230261 + 0.398824i
\(263\) −111.000 + 192.258i −0.0260249 + 0.0450765i −0.878745 0.477292i \(-0.841618\pi\)
0.852720 + 0.522369i \(0.174952\pi\)
\(264\) 0 0
\(265\) −1089.00 −0.252441
\(266\) −840.000 290.985i −0.193623 0.0670730i
\(267\) 0 0
\(268\) 185.000 + 320.429i 0.0421667 + 0.0730349i
\(269\) 3925.50 6799.17i 0.889747 1.54109i 0.0495729 0.998771i \(-0.484214\pi\)
0.840174 0.542317i \(-0.182453\pi\)
\(270\) 0 0
\(271\) −2591.50 4488.61i −0.580895 1.00614i −0.995374 0.0960800i \(-0.969370\pi\)
0.414479 0.910059i \(-0.363964\pi\)
\(272\) 5964.00 1.32949
\(273\) 0 0
\(274\) 5310.00 1.17076
\(275\) 870.000 + 1506.88i 0.190774 + 0.330431i
\(276\) 0 0
\(277\) 2480.00 4295.49i 0.537938 0.931736i −0.461077 0.887360i \(-0.652537\pi\)
0.999015 0.0443755i \(-0.0141298\pi\)
\(278\) 2337.00 + 4047.80i 0.504187 + 0.873277i
\(279\) 0 0
\(280\) 882.000 763.834i 0.188249 0.163028i
\(281\) 774.000 0.164317 0.0821583 0.996619i \(-0.473819\pi\)
0.0821583 + 0.996619i \(0.473819\pi\)
\(282\) 0 0
\(283\) −1849.00 + 3202.56i −0.388380 + 0.672695i −0.992232 0.124402i \(-0.960299\pi\)
0.603852 + 0.797097i \(0.293632\pi\)
\(284\) −171.000 + 296.181i −0.0357288 + 0.0618841i
\(285\) 0 0
\(286\) −2880.00 −0.595447
\(287\) 1260.00 + 6547.15i 0.259148 + 1.34657i
\(288\) 0 0
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) −1336.50 + 2314.89i −0.270628 + 0.468741i
\(291\) 0 0
\(292\) −181.000 313.501i −0.0362747 0.0628297i
\(293\) 6273.00 1.25076 0.625380 0.780321i \(-0.284944\pi\)
0.625380 + 0.780321i \(0.284944\pi\)
\(294\) 0 0
\(295\) 45.0000 0.00888136
\(296\) −3318.00 5746.94i −0.651537 1.12849i
\(297\) 0 0
\(298\) 3681.00 6375.68i 0.715552 1.23937i
\(299\) 2688.00 + 4655.75i 0.519903 + 0.900499i
\(300\) 0 0
\(301\) −91.0000 472.850i −0.0174258 0.0905469i
\(302\) 3777.00 0.719675
\(303\) 0 0
\(304\) −568.000 + 983.805i −0.107161 + 0.185609i
\(305\) 177.000 306.573i 0.0332295 0.0575551i
\(306\) 0 0
\(307\) −1684.00 −0.313065 −0.156533 0.987673i \(-0.550032\pi\)
−0.156533 + 0.987673i \(0.550032\pi\)
\(308\) −210.000 + 181.865i −0.0388502 + 0.0336453i
\(309\) 0 0
\(310\) 1138.50 + 1971.94i 0.208589 + 0.361286i
\(311\) −660.000 + 1143.15i −0.120338 + 0.208432i −0.919901 0.392151i \(-0.871731\pi\)
0.799563 + 0.600582i \(0.205065\pi\)
\(312\) 0 0
\(313\) 4251.50 + 7363.81i 0.767760 + 1.32980i 0.938775 + 0.344531i \(0.111962\pi\)
−0.171014 + 0.985269i \(0.554704\pi\)
\(314\) −588.000 −0.105678
\(315\) 0 0
\(316\) 467.000 0.0831355
\(317\) −1288.50 2231.75i −0.228295 0.395418i 0.729008 0.684505i \(-0.239982\pi\)
−0.957303 + 0.289087i \(0.906648\pi\)
\(318\) 0 0
\(319\) −2227.50 + 3858.14i −0.390959 + 0.677162i
\(320\) −649.500 1124.97i −0.113463 0.196524i
\(321\) 0 0
\(322\) 4410.00 + 1527.67i 0.763229 + 0.264390i
\(323\) 1344.00 0.231524
\(324\) 0 0
\(325\) −3712.00 + 6429.37i −0.633553 + 1.09735i
\(326\) 1878.00 3252.79i 0.319058 0.552624i
\(327\) 0 0
\(328\) 7560.00 1.27266
\(329\) −420.000 + 363.731i −0.0703810 + 0.0609517i
\(330\) 0 0
\(331\) 242.000 + 419.156i 0.0401859 + 0.0696040i 0.885419 0.464794i \(-0.153872\pi\)
−0.845233 + 0.534398i \(0.820538\pi\)
\(332\) 238.500 413.094i 0.0394259 0.0682876i
\(333\) 0 0
\(334\) −3969.00 6874.51i −0.650222 1.12622i
\(335\) −1110.00 −0.181032
\(336\) 0 0
\(337\) −8359.00 −1.35117 −0.675584 0.737283i \(-0.736109\pi\)
−0.675584 + 0.737283i \(0.736109\pi\)
\(338\) −2848.50 4933.75i −0.458396 0.793966i
\(339\) 0 0
\(340\) 126.000 218.238i 0.0200980 0.0348107i
\(341\) 1897.50 + 3286.57i 0.301335 + 0.521928i
\(342\) 0 0
\(343\) 3430.00 + 5346.84i 0.539949 + 0.841698i
\(344\) −546.000 −0.0855766
\(345\) 0 0
\(346\) −1179.00 + 2042.09i −0.183189 + 0.317293i
\(347\) −930.000 + 1610.81i −0.143876 + 0.249201i −0.928953 0.370197i \(-0.879290\pi\)
0.785077 + 0.619398i \(0.212623\pi\)
\(348\) 0 0
\(349\) −1918.00 −0.294178 −0.147089 0.989123i \(-0.546990\pi\)
−0.147089 + 0.989123i \(0.546990\pi\)
\(350\) 1218.00 + 6328.91i 0.186014 + 0.966556i
\(351\) 0 0
\(352\) 337.500 + 584.567i 0.0511046 + 0.0885157i
\(353\) −1524.00 + 2639.65i −0.229786 + 0.398000i −0.957744 0.287620i \(-0.907136\pi\)
0.727959 + 0.685621i \(0.240469\pi\)
\(354\) 0 0
\(355\) −513.000 888.542i −0.0766964 0.132842i
\(356\) −906.000 −0.134882
\(357\) 0 0
\(358\) −8676.00 −1.28084
\(359\) −15.0000 25.9808i −0.00220521 0.00381953i 0.864921 0.501909i \(-0.167369\pi\)
−0.867126 + 0.498089i \(0.834035\pi\)
\(360\) 0 0
\(361\) 3301.50 5718.37i 0.481338 0.833703i
\(362\) −2028.00 3512.60i −0.294446 0.509995i
\(363\) 0 0
\(364\) −1120.00 387.979i −0.161275 0.0558672i
\(365\) 1086.00 0.155737
\(366\) 0 0
\(367\) 5655.50 9795.61i 0.804400 1.39326i −0.112296 0.993675i \(-0.535820\pi\)
0.916696 0.399586i \(-0.130846\pi\)
\(368\) 2982.00 5164.98i 0.422412 0.731638i
\(369\) 0 0
\(370\) −2844.00 −0.399601
\(371\) −6352.50 2200.57i −0.888963 0.307946i
\(372\) 0 0
\(373\) −604.000 1046.16i −0.0838443 0.145223i 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(374\) 1890.00 3273.58i 0.261309 0.452600i
\(375\) 0 0
\(376\) 315.000 + 545.596i 0.0432045 + 0.0748324i
\(377\) −19008.0 −2.59672
\(378\) 0 0
\(379\) 7640.00 1.03546 0.517731 0.855543i \(-0.326777\pi\)
0.517731 + 0.855543i \(0.326777\pi\)
\(380\) 24.0000 + 41.5692i 0.00323993 + 0.00561173i
\(381\) 0 0
\(382\) 5868.00 10163.7i 0.785950 1.36131i
\(383\) 6375.00 + 11041.8i 0.850515 + 1.47314i 0.880744 + 0.473592i \(0.157043\pi\)
−0.0302291 + 0.999543i \(0.509624\pi\)
\(384\) 0 0
\(385\) −157.500 818.394i −0.0208492 0.108336i
\(386\) 4479.00 0.590609
\(387\) 0 0
\(388\) −251.500 + 435.611i −0.0329072 + 0.0569969i
\(389\) 1563.00 2707.20i 0.203720 0.352854i −0.746004 0.665942i \(-0.768030\pi\)
0.949724 + 0.313087i \(0.101363\pi\)
\(390\) 0 0
\(391\) −7056.00 −0.912627
\(392\) 6688.50 2673.42i 0.861786 0.344459i
\(393\) 0 0
\(394\) −6129.00 10615.7i −0.783692 1.35739i
\(395\) −700.500 + 1213.30i −0.0892303 + 0.154551i
\(396\) 0 0
\(397\) 2966.00 + 5137.26i 0.374960 + 0.649450i 0.990321 0.138795i \(-0.0443230\pi\)
−0.615361 + 0.788246i \(0.710990\pi\)
\(398\) −10668.0 −1.34356
\(399\) 0 0
\(400\) 8236.00 1.02950
\(401\) 804.000 + 1392.57i 0.100124 + 0.173420i 0.911736 0.410777i \(-0.134743\pi\)
−0.811611 + 0.584198i \(0.801409\pi\)
\(402\) 0 0
\(403\) −8096.00 + 14022.7i −1.00072 + 1.73330i
\(404\) −543.000 940.504i −0.0668695 0.115821i
\(405\) 0 0
\(406\) −12474.0 + 10802.8i −1.52481 + 1.32053i
\(407\) −4740.00 −0.577280
\(408\) 0 0
\(409\) 2232.50 3866.80i 0.269902 0.467484i −0.698934 0.715186i \(-0.746342\pi\)
0.968836 + 0.247702i \(0.0796753\pi\)
\(410\) 1620.00 2805.92i 0.195137 0.337987i
\(411\) 0 0
\(412\) 1736.00 0.207589
\(413\) 262.500 + 90.9327i 0.0312755 + 0.0108342i
\(414\) 0 0
\(415\) 715.500 + 1239.28i 0.0846326 + 0.146588i
\(416\) −1440.00 + 2494.15i −0.169716 + 0.293957i
\(417\) 0 0
\(418\) 360.000 + 623.538i 0.0421248 + 0.0729623i
\(419\) 1584.00 0.184686 0.0923430 0.995727i \(-0.470564\pi\)
0.0923430 + 0.995727i \(0.470564\pi\)
\(420\) 0 0
\(421\) −1330.00 −0.153967 −0.0769837 0.997032i \(-0.524529\pi\)
−0.0769837 + 0.997032i \(0.524529\pi\)
\(422\) −1875.00 3247.60i −0.216288 0.374622i
\(423\) 0 0
\(424\) −3811.50 + 6601.71i −0.436563 + 0.756150i
\(425\) −4872.00 8438.55i −0.556063 0.963129i
\(426\) 0 0
\(427\) 1652.00 1430.67i 0.187227 0.162143i
\(428\) 1353.00 0.152803
\(429\) 0 0
\(430\) −117.000 + 202.650i −0.0131215 + 0.0227271i
\(431\) 4794.00 8303.45i 0.535775 0.927989i −0.463351 0.886175i \(-0.653353\pi\)
0.999125 0.0418139i \(-0.0133137\pi\)
\(432\) 0 0
\(433\) 494.000 0.0548271 0.0274135 0.999624i \(-0.491273\pi\)
0.0274135 + 0.999624i \(0.491273\pi\)
\(434\) 2656.50 + 13803.6i 0.293816 + 1.52671i
\(435\) 0 0
\(436\) 185.000 + 320.429i 0.0203209 + 0.0351968i
\(437\) 672.000 1163.94i 0.0735609 0.127411i
\(438\) 0 0
\(439\) 8004.50 + 13864.2i 0.870237 + 1.50729i 0.861752 + 0.507330i \(0.169368\pi\)
0.00848508 + 0.999964i \(0.497299\pi\)
\(440\) −945.000 −0.102389
\(441\) 0 0
\(442\) 16128.0 1.73559
\(443\) 3886.50 + 6731.62i 0.416824 + 0.721961i 0.995618 0.0935130i \(-0.0298097\pi\)
−0.578794 + 0.815474i \(0.696476\pi\)
\(444\) 0 0
\(445\) 1359.00 2353.86i 0.144770 0.250749i
\(446\) −637.500 1104.18i −0.0676827 0.117230i
\(447\) 0 0
\(448\) −1515.50 7874.77i −0.159823 0.830464i
\(449\) −864.000 −0.0908122 −0.0454061 0.998969i \(-0.514458\pi\)
−0.0454061 + 0.998969i \(0.514458\pi\)
\(450\) 0 0
\(451\) 2700.00 4676.54i 0.281903 0.488269i
\(452\) −324.000 + 561.184i −0.0337161 + 0.0583980i
\(453\) 0 0
\(454\) −11565.0 −1.19553
\(455\) 2688.00 2327.88i 0.276957 0.239852i
\(456\) 0 0
\(457\) −1259.50 2181.52i −0.128921 0.223298i 0.794338 0.607476i \(-0.207818\pi\)
−0.923259 + 0.384179i \(0.874485\pi\)
\(458\) 3282.00 5684.59i 0.334842 0.579964i
\(459\) 0 0
\(460\) −126.000 218.238i −0.0127713 0.0221205i
\(461\) 342.000 0.0345521 0.0172761 0.999851i \(-0.494501\pi\)
0.0172761 + 0.999851i \(0.494501\pi\)
\(462\) 0 0
\(463\) −4336.00 −0.435229 −0.217614 0.976035i \(-0.569828\pi\)
−0.217614 + 0.976035i \(0.569828\pi\)
\(464\) 10543.5 + 18261.9i 1.05489 + 1.82713i
\(465\) 0 0
\(466\) 1278.00 2213.56i 0.127043 0.220046i
\(467\) 9318.00 + 16139.2i 0.923310 + 1.59922i 0.794257 + 0.607581i \(0.207860\pi\)
0.129052 + 0.991638i \(0.458806\pi\)
\(468\) 0 0
\(469\) −6475.00 2243.01i −0.637500 0.220837i
\(470\) 270.000 0.0264982
\(471\) 0 0
\(472\) 157.500 272.798i 0.0153592 0.0266029i
\(473\) −195.000 + 337.750i −0.0189558 + 0.0328325i
\(474\) 0 0
\(475\) 1856.00 0.179282
\(476\) 1176.00 1018.45i 0.113239 0.0980680i
\(477\) 0 0
\(478\) 8262.00 + 14310.2i 0.790575 + 1.36932i
\(479\) 7539.00 13057.9i 0.719135 1.24558i −0.242208 0.970224i \(-0.577872\pi\)
0.961343 0.275354i \(-0.0887951\pi\)
\(480\) 0 0
\(481\) −10112.0 17514.5i −0.958560 1.66028i
\(482\) 2373.00 0.224247
\(483\) 0 0
\(484\) −1106.00 −0.103869
\(485\) −754.500 1306.83i −0.0706393 0.122351i
\(486\) 0 0
\(487\) −3110.50 + 5387.54i −0.289425 + 0.501300i −0.973673 0.227950i \(-0.926798\pi\)
0.684247 + 0.729250i \(0.260131\pi\)
\(488\) −1239.00 2146.01i −0.114932 0.199068i
\(489\) 0 0
\(490\) 441.000 3055.34i 0.0406579 0.281686i
\(491\) 7371.00 0.677492 0.338746 0.940878i \(-0.389997\pi\)
0.338746 + 0.940878i \(0.389997\pi\)
\(492\) 0 0
\(493\) 12474.0 21605.6i 1.13956 1.97377i
\(494\) −1536.00 + 2660.43i −0.139895 + 0.242304i
\(495\) 0 0
\(496\) 17963.0 1.62613
\(497\) −1197.00 6219.79i −0.108034 0.561360i
\(498\) 0 0
\(499\) −2137.00 3701.39i −0.191714 0.332058i 0.754104 0.656755i \(-0.228071\pi\)
−0.945818 + 0.324696i \(0.894738\pi\)
\(500\) 361.500 626.136i 0.0323335 0.0560033i
\(501\) 0 0
\(502\) 7897.50 + 13678.9i 0.702157 + 1.21617i
\(503\) 2520.00 0.223382 0.111691 0.993743i \(-0.464373\pi\)
0.111691 + 0.993743i \(0.464373\pi\)
\(504\) 0 0
\(505\) 3258.00 0.287087
\(506\) −1890.00 3273.58i −0.166049 0.287605i
\(507\) 0 0
\(508\) −188.500 + 326.492i −0.0164633 + 0.0285152i
\(509\) −7138.50 12364.2i −0.621628 1.07669i −0.989183 0.146689i \(-0.953138\pi\)
0.367555 0.930002i \(-0.380195\pi\)
\(510\) 0 0
\(511\) 6335.00 + 2194.51i 0.548423 + 0.189979i
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) −10305.0 + 17848.8i −0.884308 + 1.53167i
\(515\) −2604.00 + 4510.26i −0.222808 + 0.385914i
\(516\) 0 0
\(517\) 450.000 0.0382804
\(518\) −16590.0 5746.94i −1.40719 0.487464i
\(519\) 0 0
\(520\) −2016.00 3491.81i −0.170014 0.294473i
\(521\) −3153.00 + 5461.16i −0.265135 + 0.459228i −0.967599 0.252492i \(-0.918750\pi\)
0.702464 + 0.711719i \(0.252083\pi\)
\(522\) 0 0
\(523\) −4036.00 6990.56i −0.337442 0.584466i 0.646509 0.762906i \(-0.276228\pi\)
−0.983951 + 0.178440i \(0.942895\pi\)
\(524\) 651.000 0.0542730
\(525\) 0 0
\(526\) 666.000 0.0552072
\(527\) −10626.0 18404.8i −0.878322 1.52130i
\(528\) 0 0
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) 1633.50 + 2829.30i 0.133877 + 0.231881i
\(531\) 0 0
\(532\) 56.0000 + 290.985i 0.00456374 + 0.0237139i
\(533\) 23040.0 1.87237
\(534\) 0 0
\(535\) −2029.50 + 3515.20i −0.164005 + 0.284066i
\(536\) −3885.00 + 6729.02i −0.313072 + 0.542256i
\(537\) 0 0
\(538\) −23553.0 −1.88744
\(539\) 735.000 5092.23i 0.0587360 0.406935i
\(540\) 0 0
\(541\) 11429.0 + 19795.6i 0.908264 + 1.57316i 0.816474 + 0.577382i \(0.195926\pi\)
0.0917903 + 0.995778i \(0.470741\pi\)
\(542\) −7774.50 + 13465.8i −0.616132 + 1.06717i
\(543\) 0 0
\(544\) −1890.00 3273.58i −0.148958 0.258003i
\(545\) −1110.00 −0.0872425
\(546\) 0 0
\(547\) −24724.0 −1.93258 −0.966291 0.257454i \(-0.917116\pi\)
−0.966291 + 0.257454i \(0.917116\pi\)
\(548\) −885.000 1532.86i −0.0689878 0.119490i
\(549\) 0 0
\(550\) 2610.00 4520.65i 0.202347 0.350475i
\(551\) 2376.00 + 4115.35i 0.183704 + 0.318185i
\(552\) 0 0
\(553\) −6538.00 + 5662.07i −0.502756 + 0.435399i
\(554\) −14880.0 −1.14114
\(555\) 0 0
\(556\) 779.000 1349.27i 0.0594190 0.102917i
\(557\) −4921.50 + 8524.29i −0.374382 + 0.648448i −0.990234 0.139413i \(-0.955478\pi\)
0.615853 + 0.787861i \(0.288812\pi\)
\(558\) 0 0
\(559\) −1664.00 −0.125903
\(560\) −3727.50 1291.24i −0.281278 0.0974375i
\(561\) 0 0
\(562\) −1161.00 2010.91i −0.0871420 0.150934i
\(563\) −6685.50 + 11579.6i −0.500462 + 0.866826i 0.499538 + 0.866292i \(0.333503\pi\)
−1.00000 0.000533812i \(0.999830\pi\)
\(564\) 0 0
\(565\) −972.000 1683.55i −0.0723758 0.125359i
\(566\) 11094.0 0.823879
\(567\) 0 0
\(568\) −7182.00 −0.530546
\(569\) −2616.00 4531.04i −0.192739 0.333834i 0.753418 0.657542i \(-0.228404\pi\)
−0.946157 + 0.323708i \(0.895070\pi\)
\(570\) 0 0
\(571\) 7199.00 12469.0i 0.527616 0.913858i −0.471866 0.881670i \(-0.656419\pi\)
0.999482 0.0321874i \(-0.0102474\pi\)
\(572\) 480.000 + 831.384i 0.0350871 + 0.0607726i
\(573\) 0 0
\(574\) 15120.0 13094.3i 1.09947 0.952170i
\(575\) −9744.00 −0.706701
\(576\) 0 0
\(577\) −9935.50 + 17208.8i −0.716846 + 1.24161i 0.245397 + 0.969423i \(0.421082\pi\)
−0.962243 + 0.272191i \(0.912252\pi\)
\(578\) −3214.50 + 5567.68i −0.231325 + 0.400666i
\(579\) 0 0
\(580\) 891.000 0.0637875
\(581\) 1669.50 + 8674.98i 0.119213 + 0.619447i
\(582\) 0 0
\(583\) 2722.50 + 4715.51i 0.193404 + 0.334985i
\(584\) 3801.00 6583.53i 0.269326 0.466487i
\(585\) 0 0
\(586\) −9409.50 16297.7i −0.663315 1.14890i
\(587\) 16137.0 1.13466 0.567330 0.823491i \(-0.307976\pi\)
0.567330 + 0.823491i \(0.307976\pi\)
\(588\) 0 0
\(589\) 4048.00 0.283183
\(590\) −67.5000 116.913i −0.00471005 0.00815805i
\(591\) 0 0
\(592\) −11218.0 + 19430.1i −0.778812 + 1.34894i
\(593\) −10662.0 18467.1i −0.738340 1.27884i −0.953242 0.302207i \(-0.902276\pi\)
0.214902 0.976636i \(-0.431057\pi\)
\(594\) 0 0
\(595\) 882.000 + 4583.01i 0.0607705 + 0.315773i
\(596\) −2454.00 −0.168657
\(597\) 0 0
\(598\) 8064.00 13967.3i 0.551441 0.955123i
\(599\) −4323.00 + 7487.66i −0.294880 + 0.510747i −0.974957 0.222394i \(-0.928613\pi\)
0.680077 + 0.733141i \(0.261946\pi\)
\(600\) 0 0
\(601\) 11195.0 0.759823 0.379911 0.925023i \(-0.375954\pi\)
0.379911 + 0.925023i \(0.375954\pi\)
\(602\) −1092.00 + 945.700i −0.0739312 + 0.0640263i
\(603\) 0 0
\(604\) −629.500 1090.33i −0.0424073 0.0734515i
\(605\) 1659.00 2873.47i 0.111484 0.193096i
\(606\) 0 0
\(607\) 4485.50 + 7769.11i 0.299935 + 0.519503i 0.976121 0.217228i \(-0.0697015\pi\)
−0.676185 + 0.736731i \(0.736368\pi\)
\(608\) 720.000 0.0480261
\(609\) 0 0
\(610\) −1062.00 −0.0704904
\(611\) 960.000 + 1662.77i 0.0635637 + 0.110096i
\(612\) 0 0
\(613\) 6386.00 11060.9i 0.420764 0.728784i −0.575251 0.817977i \(-0.695096\pi\)
0.996014 + 0.0891932i \(0.0284288\pi\)
\(614\) 2526.00 + 4375.16i 0.166028 + 0.287569i
\(615\) 0 0
\(616\) −5512.50 1909.59i −0.360560 0.124902i
\(617\) −12762.0 −0.832705 −0.416352 0.909203i \(-0.636692\pi\)
−0.416352 + 0.909203i \(0.636692\pi\)
\(618\) 0 0
\(619\) −6421.00 + 11121.5i −0.416933 + 0.722150i −0.995629 0.0933936i \(-0.970229\pi\)
0.578696 + 0.815543i \(0.303562\pi\)
\(620\) 379.500 657.313i 0.0245824 0.0425780i
\(621\) 0 0
\(622\) 3960.00 0.255276
\(623\) 12684.0 10984.7i 0.815688 0.706407i
\(624\) 0 0
\(625\) −6165.50 10679.0i −0.394592 0.683453i
\(626\) 12754.5 22091.4i 0.814333 1.41047i
\(627\) 0 0
\(628\) 98.0000 + 169.741i 0.00622711 + 0.0107857i
\(629\) 26544.0 1.68264
\(630\) 0 0
\(631\) 21365.0 1.34790 0.673952 0.738775i \(-0.264596\pi\)
0.673952 + 0.738775i \(0.264596\pi\)
\(632\) 4903.50 + 8493.11i 0.308625 + 0.534554i
\(633\) 0 0
\(634\) −3865.50 + 6695.24i −0.242143 + 0.419404i
\(635\) −565.500 979.475i −0.0353404 0.0612114i
\(636\) 0 0
\(637\) 20384.0 8147.57i 1.26789 0.506779i
\(638\) 13365.0 0.829350
\(639\) 0 0
\(640\) −2488.50 + 4310.21i −0.153698 + 0.266212i
\(641\) 4137.00 7165.49i 0.254917 0.441529i −0.709956 0.704246i \(-0.751285\pi\)
0.964873 + 0.262717i \(0.0846186\pi\)
\(642\) 0 0
\(643\) 27998.0 1.71716 0.858580 0.512680i \(-0.171347\pi\)
0.858580 + 0.512680i \(0.171347\pi\)
\(644\) −294.000 1527.67i −0.0179895 0.0934761i
\(645\) 0 0
\(646\) −2016.00 3491.81i −0.122784 0.212668i
\(647\) −8733.00 + 15126.0i −0.530649 + 0.919110i 0.468712 + 0.883351i \(0.344718\pi\)
−0.999360 + 0.0357592i \(0.988615\pi\)
\(648\) 0 0
\(649\) −112.500 194.856i −0.00680433 0.0117854i
\(650\) 22272.0 1.34397
\(651\) 0 0
\(652\) −1252.00 −0.0752026
\(653\) 1078.50 + 1868.02i 0.0646324 + 0.111947i 0.896531 0.442981i \(-0.146079\pi\)
−0.831898 + 0.554928i \(0.812746\pi\)
\(654\) 0 0
\(655\) −976.500 + 1691.35i −0.0582519 + 0.100895i
\(656\) −12780.0 22135.6i −0.760633 1.31745i
\(657\) 0 0
\(658\) 1575.00 + 545.596i 0.0933129 + 0.0323245i
\(659\) −19944.0 −1.17892 −0.589460 0.807798i \(-0.700659\pi\)
−0.589460 + 0.807798i \(0.700659\pi\)
\(660\) 0 0
\(661\) −13753.0 + 23820.9i −0.809273 + 1.40170i 0.104095 + 0.994567i \(0.466806\pi\)
−0.913368 + 0.407135i \(0.866528\pi\)
\(662\) 726.000 1257.47i 0.0426236 0.0738262i
\(663\) 0 0
\(664\) 10017.0 0.585444
\(665\) −840.000 290.985i −0.0489832 0.0169683i
\(666\) 0 0
\(667\) −12474.0 21605.6i −0.724131 1.25423i
\(668\) −1323.00 + 2291.50i −0.0766294 + 0.132726i
\(669\) 0 0
\(670\) 1665.00 + 2883.86i 0.0960068 + 0.166289i
\(671\) −1770.00 −0.101833
\(672\) 0 0
\(673\) −19123.0 −1.09530 −0.547650 0.836707i \(-0.684478\pi\)
−0.547650 + 0.836707i \(0.684478\pi\)
\(674\) 12538.5 + 21717.3i 0.716565 + 1.24113i
\(675\) 0 0
\(676\) −949.500 + 1644.58i −0.0540225 + 0.0935698i
\(677\) 6928.50 + 12000.5i 0.393329 + 0.681266i 0.992886 0.119066i \(-0.0379899\pi\)
−0.599557 + 0.800332i \(0.704657\pi\)
\(678\) 0 0
\(679\) −1760.50 9147.83i −0.0995019 0.517027i
\(680\) 5292.00 0.298440
\(681\) 0 0
\(682\) 5692.50 9859.70i 0.319615 0.553589i
\(683\) −11122.5 + 19264.7i −0.623120 + 1.07927i 0.365782 + 0.930701i \(0.380802\pi\)
−0.988901 + 0.148574i \(0.952532\pi\)
\(684\) 0 0
\(685\) 5310.00 0.296182
\(686\) 8746.50 16931.7i 0.486797 0.942353i
\(687\) 0 0
\(688\) 923.000 + 1598.68i 0.0511469 + 0.0885890i
\(689\) −11616.0 + 20119.5i −0.642285 + 1.11247i
\(690\) 0 0
\(691\) 320.000 + 554.256i 0.0176170 + 0.0305136i 0.874700 0.484666i \(-0.161059\pi\)
−0.857082 + 0.515179i \(0.827725\pi\)
\(692\) 786.000 0.0431781
\(693\) 0 0
\(694\) 5580.00 0.305207
\(695\) 2337.00 + 4047.80i 0.127550 + 0.220924i
\(696\) 0 0
\(697\) −15120.0 + 26188.6i −0.821680 + 1.42319i
\(698\) 2877.00 + 4983.11i 0.156012 + 0.270220i
\(699\) 0 0
\(700\) 1624.00 1406.43i 0.0876878 0.0759398i
\(701\) 15561.0 0.838418 0.419209 0.907890i \(-0.362307\pi\)
0.419209 + 0.907890i \(0.362307\pi\)
\(702\) 0 0
\(703\) −2528.00 + 4378.62i −0.135626 + 0.234912i
\(704\) −3247.50 + 5624.83i −0.173856 + 0.301128i
\(705\) 0 0
\(706\) 9144.00 0.487449
\(707\) 19005.0 + 6583.53i 1.01097 + 0.350211i
\(708\) 0 0
\(709\) −2767.00 4792.58i −0.146568 0.253864i 0.783389 0.621532i \(-0.213489\pi\)
−0.929957 + 0.367668i \(0.880156\pi\)
\(710\) −1539.00 + 2665.63i −0.0813488 + 0.140900i
\(711\) 0 0
\(712\) −9513.00 16477.0i −0.500723 0.867278i
\(713\) −21252.0 −1.11626
\(714\) 0 0
\(715\) −2880.00 −0.150638
\(716\) 1446.00 + 2504.55i 0.0754742 + 0.130725i
\(717\) 0 0
\(718\) −45.0000 + 77.9423i −0.00233898 + 0.00405123i
\(719\) −10923.0 18919.2i −0.566564 0.981317i −0.996902 0.0786494i \(-0.974939\pi\)
0.430339 0.902667i \(-0.358394\pi\)
\(720\) 0 0
\(721\) −24304.0 + 21047.9i −1.25538 + 1.08719i
\(722\) −19809.0 −1.02107
\(723\) 0 0
\(724\) −676.000 + 1170.87i −0.0347007 + 0.0601035i
\(725\) 17226.0 29836.3i 0.882424 1.52840i
\(726\) 0 0
\(727\) −11089.0 −0.565706 −0.282853 0.959163i \(-0.591281\pi\)
−0.282853 + 0.959163i \(0.591281\pi\)
\(728\) −4704.00 24442.7i −0.239481 1.24438i
\(729\) 0 0
\(730\) −1629.00 2821.51i −0.0825918 0.143053i
\(731\) 1092.00 1891.40i 0.0552518 0.0956990i
\(732\) 0 0
\(733\) −5881.00 10186.2i −0.296343 0.513282i 0.678953 0.734182i \(-0.262434\pi\)
−0.975296 + 0.220900i \(0.929101\pi\)
\(734\) −33933.0 −1.70639
\(735\) 0 0
\(736\) −3780.00 −0.189311
\(737\) 2775.00 + 4806.44i 0.138695 + 0.240227i
\(738\) 0 0
\(739\) 11363.0 19681.3i 0.565622 0.979686i −0.431369 0.902175i \(-0.641969\pi\)
0.996992 0.0775108i \(-0.0246972\pi\)
\(740\) 474.000 + 820.992i 0.0235467 + 0.0407841i
\(741\) 0 0
\(742\) 3811.50 + 19805.1i 0.188578 + 0.979878i
\(743\) −6678.00 −0.329734 −0.164867 0.986316i \(-0.552719\pi\)
−0.164867 + 0.986316i \(0.552719\pi\)
\(744\) 0 0
\(745\) 3681.00 6375.68i 0.181022 0.313539i
\(746\) −1812.00 + 3138.48i −0.0889303 + 0.154032i
\(747\) 0 0
\(748\) −1260.00 −0.0615911
\(749\) −18942.0 + 16404.3i −0.924066 + 0.800265i
\(750\) 0 0
\(751\) 9993.50 + 17309.2i 0.485577 + 0.841043i 0.999863 0.0165754i \(-0.00527637\pi\)
−0.514286 + 0.857619i \(0.671943\pi\)
\(752\) 1065.00 1844.63i 0.0516444 0.0894506i
\(753\) 0 0
\(754\) 28512.0 + 49384.2i 1.37712 + 2.38524i
\(755\) 3777.00 0.182065
\(756\) 0 0
\(757\) 314.000 0.0150760 0.00753799 0.999972i \(-0.497601\pi\)
0.00753799 + 0.999972i \(0.497601\pi\)
\(758\) −11460.0 19849.3i −0.549137 0.951133i
\(759\) 0 0
\(760\) −504.000 + 872.954i −0.0240553 + 0.0416649i
\(761\) −5748.00 9955.83i −0.273804 0.474242i 0.696029 0.718014i \(-0.254949\pi\)
−0.969833 + 0.243772i \(0.921615\pi\)
\(762\) 0 0
\(763\) −6475.00 2243.01i −0.307222 0.106425i
\(764\) −3912.00 −0.185250
\(765\) 0 0
\(766\) 19125.0 33125.5i 0.902107 1.56250i
\(767\) 480.000 831.384i 0.0225969 0.0391389i
\(768\) 0 0
\(769\) 2765.00 0.129660 0.0648299 0.997896i \(-0.479350\pi\)
0.0648299 + 0.997896i \(0.479350\pi\)
\(770\) −1890.00 + 1636.79i −0.0884557 + 0.0766049i
\(771\) 0 0
\(772\) −746.500 1292.98i −0.0348020 0.0602788i
\(773\) −7023.00 + 12164.2i −0.326778 + 0.565997i −0.981871 0.189552i \(-0.939296\pi\)
0.655092 + 0.755549i \(0.272630\pi\)
\(774\) 0 0
\(775\) −14674.0 25416.1i −0.680136 1.17803i
\(776\) −10563.0 −0.488646
\(777\) 0 0
\(778\) −9378.00 −0.432156
\(779\) −2880.00 4988.31i −0.132460 0.229428i
\(780\) 0 0
\(781\) −2565.00 + 4442.71i −0.117520 + 0.203550i
\(782\) 10584.0 + 18332.0i 0.483994 + 0.838302i
\(783\) 0 0
\(784\) −19134.5 15064.5i −0.871652 0.686248i
\(785\) −588.000 −0.0267345
\(786\) 0 0