Properties

Label 684.3.s.a.445.6
Level $684$
Weight $3$
Character 684.445
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 445.6
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.67140 + 1.36514i) q^{3} +(-4.45215 - 7.71135i) q^{5} +(-2.28143 - 3.95155i) q^{7} +(5.27278 - 7.29368i) q^{9} +O(q^{10})\) \(q+(-2.67140 + 1.36514i) q^{3} +(-4.45215 - 7.71135i) q^{5} +(-2.28143 - 3.95155i) q^{7} +(5.27278 - 7.29368i) q^{9} +(-0.526632 - 0.912153i) q^{11} -16.8563i q^{13} +(22.4206 + 14.5223i) q^{15} +(3.48650 - 6.03879i) q^{17} +(17.6720 - 6.97862i) q^{19} +(11.4890 + 7.44171i) q^{21} -8.67438 q^{23} +(-27.1433 + 47.0136i) q^{25} +(-4.12881 + 26.6824i) q^{27} +(-32.0106 - 18.4813i) q^{29} +(-9.57498 - 5.52812i) q^{31} +(2.65206 + 1.71780i) q^{33} +(-20.3145 + 35.1858i) q^{35} -11.0819i q^{37} +(23.0113 + 45.0301i) q^{39} +(-18.4835 + 10.6715i) q^{41} +51.1871 q^{43} +(-79.7193 - 8.18769i) q^{45} +(-13.8872 + 24.0533i) q^{47} +(14.0902 - 24.4049i) q^{49} +(-1.07004 + 20.8916i) q^{51} +(-11.4429 + 6.60656i) q^{53} +(-4.68929 + 8.12209i) q^{55} +(-37.6822 + 42.7674i) q^{57} +(-23.2263 + 13.4097i) q^{59} +(-0.965926 + 1.67303i) q^{61} +(-40.8508 - 4.19564i) q^{63} +(-129.985 + 75.0470i) q^{65} -23.9413i q^{67} +(23.1728 - 11.8418i) q^{69} +(-102.629 - 59.2527i) q^{71} +(-46.1686 + 79.9664i) q^{73} +(8.33051 - 162.647i) q^{75} +(-2.40295 + 4.16203i) q^{77} +38.4785i q^{79} +(-25.3956 - 76.9160i) q^{81} +(36.8320 + 63.7949i) q^{83} -62.0896 q^{85} +(110.743 + 5.67208i) q^{87} +(86.6168 - 50.0082i) q^{89} +(-66.6087 + 38.4566i) q^{91} +(33.1253 + 1.69663i) q^{93} +(-132.493 - 105.205i) q^{95} +143.029i q^{97} +(-9.42977 - 0.968498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.67140 + 1.36514i −0.890467 + 0.455047i
\(4\) 0 0
\(5\) −4.45215 7.71135i −0.890430 1.54227i −0.839361 0.543575i \(-0.817070\pi\)
−0.0510696 0.998695i \(-0.516263\pi\)
\(6\) 0 0
\(7\) −2.28143 3.95155i −0.325918 0.564507i 0.655779 0.754953i \(-0.272340\pi\)
−0.981698 + 0.190445i \(0.939007\pi\)
\(8\) 0 0
\(9\) 5.27278 7.29368i 0.585864 0.810409i
\(10\) 0 0
\(11\) −0.526632 0.912153i −0.0478756 0.0829230i 0.841095 0.540888i \(-0.181912\pi\)
−0.888970 + 0.457965i \(0.848578\pi\)
\(12\) 0 0
\(13\) 16.8563i 1.29664i −0.761367 0.648321i \(-0.775471\pi\)
0.761367 0.648321i \(-0.224529\pi\)
\(14\) 0 0
\(15\) 22.4206 + 14.5223i 1.49470 + 0.968154i
\(16\) 0 0
\(17\) 3.48650 6.03879i 0.205088 0.355223i −0.745073 0.666983i \(-0.767585\pi\)
0.950161 + 0.311760i \(0.100919\pi\)
\(18\) 0 0
\(19\) 17.6720 6.97862i 0.930104 0.367296i
\(20\) 0 0
\(21\) 11.4890 + 7.44171i 0.547097 + 0.354367i
\(22\) 0 0
\(23\) −8.67438 −0.377147 −0.188573 0.982059i \(-0.560386\pi\)
−0.188573 + 0.982059i \(0.560386\pi\)
\(24\) 0 0
\(25\) −27.1433 + 47.0136i −1.08573 + 1.88054i
\(26\) 0 0
\(27\) −4.12881 + 26.6824i −0.152919 + 0.988239i
\(28\) 0 0
\(29\) −32.0106 18.4813i −1.10381 0.637287i −0.166593 0.986026i \(-0.553277\pi\)
−0.937220 + 0.348739i \(0.886610\pi\)
\(30\) 0 0
\(31\) −9.57498 5.52812i −0.308870 0.178326i 0.337551 0.941307i \(-0.390402\pi\)
−0.646421 + 0.762981i \(0.723735\pi\)
\(32\) 0 0
\(33\) 2.65206 + 1.71780i 0.0803656 + 0.0520546i
\(34\) 0 0
\(35\) −20.3145 + 35.1858i −0.580415 + 1.00531i
\(36\) 0 0
\(37\) 11.0819i 0.299510i −0.988723 0.149755i \(-0.952152\pi\)
0.988723 0.149755i \(-0.0478484\pi\)
\(38\) 0 0
\(39\) 23.0113 + 45.0301i 0.590033 + 1.15462i
\(40\) 0 0
\(41\) −18.4835 + 10.6715i −0.450818 + 0.260280i −0.708176 0.706036i \(-0.750482\pi\)
0.257357 + 0.966316i \(0.417148\pi\)
\(42\) 0 0
\(43\) 51.1871 1.19040 0.595199 0.803578i \(-0.297073\pi\)
0.595199 + 0.803578i \(0.297073\pi\)
\(44\) 0 0
\(45\) −79.7193 8.18769i −1.77154 0.181949i
\(46\) 0 0
\(47\) −13.8872 + 24.0533i −0.295472 + 0.511772i −0.975094 0.221790i \(-0.928810\pi\)
0.679623 + 0.733562i \(0.262143\pi\)
\(48\) 0 0
\(49\) 14.0902 24.4049i 0.287554 0.498059i
\(50\) 0 0
\(51\) −1.07004 + 20.8916i −0.0209811 + 0.409639i
\(52\) 0 0
\(53\) −11.4429 + 6.60656i −0.215904 + 0.124652i −0.604052 0.796945i \(-0.706448\pi\)
0.388148 + 0.921597i \(0.373115\pi\)
\(54\) 0 0
\(55\) −4.68929 + 8.12209i −0.0852598 + 0.147674i
\(56\) 0 0
\(57\) −37.6822 + 42.7674i −0.661091 + 0.750306i
\(58\) 0 0
\(59\) −23.2263 + 13.4097i −0.393667 + 0.227284i −0.683748 0.729718i \(-0.739651\pi\)
0.290081 + 0.957002i \(0.406318\pi\)
\(60\) 0 0
\(61\) −0.965926 + 1.67303i −0.0158349 + 0.0274268i −0.873834 0.486224i \(-0.838374\pi\)
0.857999 + 0.513651i \(0.171707\pi\)
\(62\) 0 0
\(63\) −40.8508 4.19564i −0.648426 0.0665975i
\(64\) 0 0
\(65\) −129.985 + 75.0470i −1.99977 + 1.15457i
\(66\) 0 0
\(67\) 23.9413i 0.357333i −0.983910 0.178666i \(-0.942822\pi\)
0.983910 0.178666i \(-0.0571782\pi\)
\(68\) 0 0
\(69\) 23.1728 11.8418i 0.335837 0.171620i
\(70\) 0 0
\(71\) −102.629 59.2527i −1.44547 0.834545i −0.447267 0.894401i \(-0.647603\pi\)
−0.998207 + 0.0598559i \(0.980936\pi\)
\(72\) 0 0
\(73\) −46.1686 + 79.9664i −0.632447 + 1.09543i 0.354603 + 0.935017i \(0.384616\pi\)
−0.987050 + 0.160413i \(0.948717\pi\)
\(74\) 0 0
\(75\) 8.33051 162.647i 0.111073 2.16862i
\(76\) 0 0
\(77\) −2.40295 + 4.16203i −0.0312071 + 0.0540523i
\(78\) 0 0
\(79\) 38.4785i 0.487070i 0.969892 + 0.243535i \(0.0783071\pi\)
−0.969892 + 0.243535i \(0.921693\pi\)
\(80\) 0 0
\(81\) −25.3956 76.9160i −0.313526 0.949580i
\(82\) 0 0
\(83\) 36.8320 + 63.7949i 0.443759 + 0.768613i 0.997965 0.0637666i \(-0.0203113\pi\)
−0.554206 + 0.832380i \(0.686978\pi\)
\(84\) 0 0
\(85\) −62.0896 −0.730466
\(86\) 0 0
\(87\) 110.743 + 5.67208i 1.27291 + 0.0651963i
\(88\) 0 0
\(89\) 86.6168 50.0082i 0.973222 0.561890i 0.0730051 0.997332i \(-0.476741\pi\)
0.900217 + 0.435442i \(0.143408\pi\)
\(90\) 0 0
\(91\) −66.6087 + 38.4566i −0.731964 + 0.422599i
\(92\) 0 0
\(93\) 33.1253 + 1.69663i 0.356186 + 0.0182433i
\(94\) 0 0
\(95\) −132.493 105.205i −1.39466 1.10742i
\(96\) 0 0
\(97\) 143.029i 1.47452i 0.675607 + 0.737262i \(0.263882\pi\)
−0.675607 + 0.737262i \(0.736118\pi\)
\(98\) 0 0
\(99\) −9.42977 0.968498i −0.0952502 0.00978281i
\(100\) 0 0
\(101\) −16.5909 + 28.7362i −0.164266 + 0.284517i −0.936394 0.350950i \(-0.885859\pi\)
0.772128 + 0.635467i \(0.219192\pi\)
\(102\) 0 0
\(103\) 140.802 + 81.2919i 1.36701 + 0.789241i 0.990545 0.137191i \(-0.0438073\pi\)
0.376462 + 0.926432i \(0.377141\pi\)
\(104\) 0 0
\(105\) 6.23470 121.728i 0.0593781 1.15931i
\(106\) 0 0
\(107\) 126.606i 1.18323i −0.806220 0.591616i \(-0.798490\pi\)
0.806220 0.591616i \(-0.201510\pi\)
\(108\) 0 0
\(109\) −91.6855 52.9346i −0.841151 0.485639i 0.0165041 0.999864i \(-0.494746\pi\)
−0.857655 + 0.514225i \(0.828080\pi\)
\(110\) 0 0
\(111\) 15.1283 + 29.6041i 0.136291 + 0.266704i
\(112\) 0 0
\(113\) −51.1065 29.5063i −0.452270 0.261118i 0.256519 0.966539i \(-0.417425\pi\)
−0.708788 + 0.705421i \(0.750758\pi\)
\(114\) 0 0
\(115\) 38.6196 + 66.8912i 0.335823 + 0.581663i
\(116\) 0 0
\(117\) −122.945 88.8798i −1.05081 0.759657i
\(118\) 0 0
\(119\) −31.8168 −0.267368
\(120\) 0 0
\(121\) 59.9453 103.828i 0.495416 0.858085i
\(122\) 0 0
\(123\) 34.8089 53.7405i 0.282999 0.436914i
\(124\) 0 0
\(125\) 260.777 2.08621
\(126\) 0 0
\(127\) −205.351 + 118.560i −1.61694 + 0.933541i −0.629234 + 0.777216i \(0.716631\pi\)
−0.987706 + 0.156325i \(0.950035\pi\)
\(128\) 0 0
\(129\) −136.741 + 69.8777i −1.06001 + 0.541687i
\(130\) 0 0
\(131\) 61.9051 + 107.223i 0.472558 + 0.818494i 0.999507 0.0314029i \(-0.00999751\pi\)
−0.526949 + 0.849897i \(0.676664\pi\)
\(132\) 0 0
\(133\) −67.8937 53.9105i −0.510479 0.405342i
\(134\) 0 0
\(135\) 224.140 86.9555i 1.66029 0.644115i
\(136\) 0 0
\(137\) −74.0078 + 128.185i −0.540203 + 0.935658i 0.458689 + 0.888597i \(0.348319\pi\)
−0.998892 + 0.0470616i \(0.985014\pi\)
\(138\) 0 0
\(139\) 151.636 1.09091 0.545453 0.838142i \(-0.316358\pi\)
0.545453 + 0.838142i \(0.316358\pi\)
\(140\) 0 0
\(141\) 4.26209 83.2139i 0.0302276 0.590170i
\(142\) 0 0
\(143\) −15.3756 + 8.87709i −0.107522 + 0.0620776i
\(144\) 0 0
\(145\) 329.126i 2.26984i
\(146\) 0 0
\(147\) −4.32440 + 84.4303i −0.0294177 + 0.574356i
\(148\) 0 0
\(149\) 41.0582 + 71.1149i 0.275559 + 0.477281i 0.970276 0.242001i \(-0.0778039\pi\)
−0.694717 + 0.719283i \(0.744471\pi\)
\(150\) 0 0
\(151\) 155.595 89.8330i 1.03043 0.594921i 0.113324 0.993558i \(-0.463850\pi\)
0.917109 + 0.398637i \(0.130517\pi\)
\(152\) 0 0
\(153\) −25.6615 57.2706i −0.167722 0.374318i
\(154\) 0 0
\(155\) 98.4480i 0.635149i
\(156\) 0 0
\(157\) 118.748 + 205.678i 0.756358 + 1.31005i 0.944696 + 0.327946i \(0.106357\pi\)
−0.188338 + 0.982104i \(0.560310\pi\)
\(158\) 0 0
\(159\) 21.5497 33.2699i 0.135533 0.209245i
\(160\) 0 0
\(161\) 19.7900 + 34.2772i 0.122919 + 0.212902i
\(162\) 0 0
\(163\) 223.745 1.37267 0.686335 0.727286i \(-0.259219\pi\)
0.686335 + 0.727286i \(0.259219\pi\)
\(164\) 0 0
\(165\) 1.43918 28.0989i 0.00872233 0.170296i
\(166\) 0 0
\(167\) 5.81572i 0.0348247i −0.999848 0.0174123i \(-0.994457\pi\)
0.999848 0.0174123i \(-0.00554280\pi\)
\(168\) 0 0
\(169\) −115.136 −0.681281
\(170\) 0 0
\(171\) 42.2806 165.691i 0.247255 0.968950i
\(172\) 0 0
\(173\) 282.198i 1.63120i −0.578613 0.815602i \(-0.696406\pi\)
0.578613 0.815602i \(-0.303594\pi\)
\(174\) 0 0
\(175\) 247.702 1.41544
\(176\) 0 0
\(177\) 43.7407 67.5300i 0.247123 0.381526i
\(178\) 0 0
\(179\) 25.2455i 0.141036i 0.997510 + 0.0705181i \(0.0224653\pi\)
−0.997510 + 0.0705181i \(0.977535\pi\)
\(180\) 0 0
\(181\) −136.039 + 78.5424i −0.751599 + 0.433936i −0.826271 0.563272i \(-0.809542\pi\)
0.0746723 + 0.997208i \(0.476209\pi\)
\(182\) 0 0
\(183\) 0.296451 5.78797i 0.00161995 0.0316283i
\(184\) 0 0
\(185\) −85.4561 + 49.3381i −0.461925 + 0.266692i
\(186\) 0 0
\(187\) −7.34440 −0.0392749
\(188\) 0 0
\(189\) 114.857 44.5589i 0.607707 0.235761i
\(190\) 0 0
\(191\) −107.270 185.798i −0.561625 0.972763i −0.997355 0.0726857i \(-0.976843\pi\)
0.435730 0.900078i \(-0.356490\pi\)
\(192\) 0 0
\(193\) −268.141 + 154.811i −1.38933 + 0.802132i −0.993240 0.116079i \(-0.962967\pi\)
−0.396093 + 0.918211i \(0.629634\pi\)
\(194\) 0 0
\(195\) 244.793 377.929i 1.25535 1.93810i
\(196\) 0 0
\(197\) 376.293 1.91012 0.955060 0.296414i \(-0.0957908\pi\)
0.955060 + 0.296414i \(0.0957908\pi\)
\(198\) 0 0
\(199\) −37.6504 65.2123i −0.189198 0.327700i 0.755785 0.654820i \(-0.227255\pi\)
−0.944983 + 0.327119i \(0.893922\pi\)
\(200\) 0 0
\(201\) 32.6832 + 63.9568i 0.162603 + 0.318193i
\(202\) 0 0
\(203\) 168.655i 0.830814i
\(204\) 0 0
\(205\) 164.583 + 95.0221i 0.802844 + 0.463522i
\(206\) 0 0
\(207\) −45.7381 + 63.2682i −0.220957 + 0.305643i
\(208\) 0 0
\(209\) −15.6722 12.4444i −0.0749866 0.0595426i
\(210\) 0 0
\(211\) 279.402 161.313i 1.32418 0.764516i 0.339788 0.940502i \(-0.389645\pi\)
0.984393 + 0.175986i \(0.0563113\pi\)
\(212\) 0 0
\(213\) 355.051 + 18.1852i 1.66690 + 0.0853763i
\(214\) 0 0
\(215\) −227.893 394.722i −1.05997 1.83592i
\(216\) 0 0
\(217\) 50.4480i 0.232479i
\(218\) 0 0
\(219\) 14.1695 276.649i 0.0647011 1.26324i
\(220\) 0 0
\(221\) −101.792 58.7696i −0.460597 0.265926i
\(222\) 0 0
\(223\) 48.2068i 0.216174i −0.994141 0.108087i \(-0.965527\pi\)
0.994141 0.108087i \(-0.0344725\pi\)
\(224\) 0 0
\(225\) 199.781 + 445.867i 0.887917 + 1.98163i
\(226\) 0 0
\(227\) −137.892 + 79.6118i −0.607453 + 0.350713i −0.771968 0.635662i \(-0.780727\pi\)
0.164515 + 0.986375i \(0.447394\pi\)
\(228\) 0 0
\(229\) 30.7008 53.1753i 0.134065 0.232207i −0.791175 0.611590i \(-0.790530\pi\)
0.925240 + 0.379383i \(0.123864\pi\)
\(230\) 0 0
\(231\) 0.737485 14.3988i 0.00319258 0.0623325i
\(232\) 0 0
\(233\) −123.485 + 213.882i −0.529977 + 0.917947i 0.469412 + 0.882979i \(0.344466\pi\)
−0.999388 + 0.0349674i \(0.988867\pi\)
\(234\) 0 0
\(235\) 247.311 1.05239
\(236\) 0 0
\(237\) −52.5286 102.792i −0.221640 0.433720i
\(238\) 0 0
\(239\) 140.849 243.957i 0.589325 1.02074i −0.404996 0.914319i \(-0.632727\pi\)
0.994321 0.106423i \(-0.0339396\pi\)
\(240\) 0 0
\(241\) −72.7517 42.0032i −0.301874 0.174287i 0.341410 0.939914i \(-0.389095\pi\)
−0.643285 + 0.765627i \(0.722429\pi\)
\(242\) 0 0
\(243\) 172.843 + 170.805i 0.711288 + 0.702901i
\(244\) 0 0
\(245\) −250.926 −1.02419
\(246\) 0 0
\(247\) −117.634 297.885i −0.476251 1.20601i
\(248\) 0 0
\(249\) −185.482 120.141i −0.744908 0.482494i
\(250\) 0 0
\(251\) −12.0665 20.8998i −0.0480738 0.0832663i 0.840987 0.541055i \(-0.181975\pi\)
−0.889061 + 0.457789i \(0.848642\pi\)
\(252\) 0 0
\(253\) 4.56821 + 7.91236i 0.0180562 + 0.0312742i
\(254\) 0 0
\(255\) 165.866 84.7611i 0.650457 0.332397i
\(256\) 0 0
\(257\) 109.226i 0.425002i −0.977161 0.212501i \(-0.931839\pi\)
0.977161 0.212501i \(-0.0681609\pi\)
\(258\) 0 0
\(259\) −43.7905 + 25.2825i −0.169075 + 0.0976157i
\(260\) 0 0
\(261\) −303.582 + 136.027i −1.16315 + 0.521177i
\(262\) 0 0
\(263\) −374.488 −1.42391 −0.711955 0.702225i \(-0.752190\pi\)
−0.711955 + 0.702225i \(0.752190\pi\)
\(264\) 0 0
\(265\) 101.891 + 58.8268i 0.384494 + 0.221988i
\(266\) 0 0
\(267\) −163.120 + 251.836i −0.610936 + 0.943207i
\(268\) 0 0
\(269\) −464.481 268.168i −1.72670 0.996909i −0.902632 0.430413i \(-0.858368\pi\)
−0.824065 0.566496i \(-0.808299\pi\)
\(270\) 0 0
\(271\) 123.546 213.989i 0.455891 0.789626i −0.542848 0.839831i \(-0.682654\pi\)
0.998739 + 0.0502050i \(0.0159875\pi\)
\(272\) 0 0
\(273\) 125.440 193.663i 0.459487 0.709389i
\(274\) 0 0
\(275\) 57.1781 0.207920
\(276\) 0 0
\(277\) −224.160 388.257i −0.809243 1.40165i −0.913389 0.407087i \(-0.866544\pi\)
0.104147 0.994562i \(-0.466789\pi\)
\(278\) 0 0
\(279\) −90.8071 + 40.6883i −0.325473 + 0.145836i
\(280\) 0 0
\(281\) 303.885 + 175.448i 1.08144 + 0.624371i 0.931285 0.364291i \(-0.118689\pi\)
0.150158 + 0.988662i \(0.452022\pi\)
\(282\) 0 0
\(283\) 82.4426 + 142.795i 0.291316 + 0.504575i 0.974121 0.226026i \(-0.0725734\pi\)
−0.682805 + 0.730601i \(0.739240\pi\)
\(284\) 0 0
\(285\) 497.561 + 100.173i 1.74583 + 0.351485i
\(286\) 0 0
\(287\) 84.3378 + 48.6924i 0.293860 + 0.169660i
\(288\) 0 0
\(289\) 120.189 + 208.173i 0.415878 + 0.720321i
\(290\) 0 0
\(291\) −195.255 382.088i −0.670978 1.31302i
\(292\) 0 0
\(293\) −56.9902 32.9033i −0.194506 0.112298i 0.399584 0.916696i \(-0.369154\pi\)
−0.594090 + 0.804398i \(0.702488\pi\)
\(294\) 0 0
\(295\) 206.814 + 119.404i 0.701066 + 0.404760i
\(296\) 0 0
\(297\) 26.5128 10.2857i 0.0892688 0.0346321i
\(298\) 0 0
\(299\) 146.218i 0.489025i
\(300\) 0 0
\(301\) −116.780 202.269i −0.387973 0.671989i
\(302\) 0 0
\(303\) 5.09188 99.4148i 0.0168049 0.328102i
\(304\) 0 0
\(305\) 17.2018 0.0563993
\(306\) 0 0
\(307\) −256.227 147.933i −0.834615 0.481865i 0.0208149 0.999783i \(-0.493374\pi\)
−0.855430 + 0.517918i \(0.826707\pi\)
\(308\) 0 0
\(309\) −487.113 24.9492i −1.57642 0.0807417i
\(310\) 0 0
\(311\) −102.633 + 177.766i −0.330010 + 0.571594i −0.982513 0.186192i \(-0.940385\pi\)
0.652504 + 0.757786i \(0.273719\pi\)
\(312\) 0 0
\(313\) 182.485 316.073i 0.583018 1.00982i −0.412101 0.911138i \(-0.635205\pi\)
0.995119 0.0986790i \(-0.0314617\pi\)
\(314\) 0 0
\(315\) 149.520 + 333.695i 0.474666 + 1.05935i
\(316\) 0 0
\(317\) −248.263 143.335i −0.783164 0.452160i 0.0543863 0.998520i \(-0.482680\pi\)
−0.837551 + 0.546360i \(0.816013\pi\)
\(318\) 0 0
\(319\) 38.9314i 0.122042i
\(320\) 0 0
\(321\) 172.835 + 338.215i 0.538427 + 1.05363i
\(322\) 0 0
\(323\) 19.4709 131.048i 0.0602814 0.405722i
\(324\) 0 0
\(325\) 792.477 + 457.537i 2.43839 + 1.40781i
\(326\) 0 0
\(327\) 317.192 + 16.2461i 0.970006 + 0.0496823i
\(328\) 0 0
\(329\) 126.730 0.385198
\(330\) 0 0
\(331\) −105.392 + 60.8478i −0.318403 + 0.183830i −0.650681 0.759351i \(-0.725516\pi\)
0.332277 + 0.943182i \(0.392183\pi\)
\(332\) 0 0
\(333\) −80.8275 58.4322i −0.242725 0.175472i
\(334\) 0 0
\(335\) −184.620 + 106.590i −0.551103 + 0.318180i
\(336\) 0 0
\(337\) 2.64151 1.52507i 0.00783829 0.00452544i −0.496076 0.868279i \(-0.665226\pi\)
0.503914 + 0.863754i \(0.331893\pi\)
\(338\) 0 0
\(339\) 176.806 + 9.05575i 0.521552 + 0.0267131i
\(340\) 0 0
\(341\) 11.6451i 0.0341500i
\(342\) 0 0
\(343\) −352.163 −1.02671
\(344\) 0 0
\(345\) −194.485 125.972i −0.563723 0.365136i
\(346\) 0 0
\(347\) −114.632 198.548i −0.330352 0.572186i 0.652229 0.758022i \(-0.273834\pi\)
−0.982581 + 0.185836i \(0.940501\pi\)
\(348\) 0 0
\(349\) −102.794 178.045i −0.294540 0.510158i 0.680338 0.732899i \(-0.261833\pi\)
−0.974878 + 0.222741i \(0.928500\pi\)
\(350\) 0 0
\(351\) 449.769 + 69.5967i 1.28139 + 0.198281i
\(352\) 0 0
\(353\) −171.317 296.730i −0.485318 0.840595i 0.514540 0.857466i \(-0.327963\pi\)
−0.999858 + 0.0168717i \(0.994629\pi\)
\(354\) 0 0
\(355\) 1055.21i 2.97241i
\(356\) 0 0
\(357\) 84.9954 43.4344i 0.238082 0.121665i
\(358\) 0 0
\(359\) −177.982 + 308.274i −0.495772 + 0.858702i −0.999988 0.00487566i \(-0.998448\pi\)
0.504217 + 0.863577i \(0.331781\pi\)
\(360\) 0 0
\(361\) 263.598 246.652i 0.730188 0.683247i
\(362\) 0 0
\(363\) −18.3977 + 359.201i −0.0506825 + 0.989535i
\(364\) 0 0
\(365\) 822.198 2.25260
\(366\) 0 0
\(367\) −238.486 + 413.069i −0.649825 + 1.12553i 0.333340 + 0.942807i \(0.391824\pi\)
−0.983165 + 0.182722i \(0.941509\pi\)
\(368\) 0 0
\(369\) −19.6253 + 191.082i −0.0531851 + 0.517836i
\(370\) 0 0
\(371\) 52.2123 + 30.1448i 0.140734 + 0.0812528i
\(372\) 0 0
\(373\) 113.432 + 65.4898i 0.304106 + 0.175576i 0.644286 0.764785i \(-0.277155\pi\)
−0.340180 + 0.940360i \(0.610488\pi\)
\(374\) 0 0
\(375\) −696.639 + 355.997i −1.85770 + 0.949325i
\(376\) 0 0
\(377\) −311.528 + 539.582i −0.826333 + 1.43125i
\(378\) 0 0
\(379\) 121.104i 0.319534i 0.987155 + 0.159767i \(0.0510743\pi\)
−0.987155 + 0.159767i \(0.948926\pi\)
\(380\) 0 0
\(381\) 386.725 597.054i 1.01503 1.56707i
\(382\) 0 0
\(383\) −417.409 + 240.991i −1.08984 + 0.629220i −0.933534 0.358489i \(-0.883292\pi\)
−0.156307 + 0.987709i \(0.549959\pi\)
\(384\) 0 0
\(385\) 42.7931 0.111151
\(386\) 0 0
\(387\) 269.899 373.343i 0.697412 0.964710i
\(388\) 0 0
\(389\) −273.111 + 473.042i −0.702085 + 1.21605i 0.265649 + 0.964070i \(0.414414\pi\)
−0.967733 + 0.251977i \(0.918919\pi\)
\(390\) 0 0
\(391\) −30.2432 + 52.3828i −0.0773483 + 0.133971i
\(392\) 0 0
\(393\) −311.747 201.926i −0.793250 0.513806i
\(394\) 0 0
\(395\) 296.721 171.312i 0.751193 0.433702i
\(396\) 0 0
\(397\) 27.6892 47.9590i 0.0697460 0.120804i −0.829043 0.559184i \(-0.811114\pi\)
0.898789 + 0.438381i \(0.144448\pi\)
\(398\) 0 0
\(399\) 254.967 + 51.3321i 0.639015 + 0.128652i
\(400\) 0 0
\(401\) −457.086 + 263.899i −1.13987 + 0.658102i −0.946397 0.323004i \(-0.895307\pi\)
−0.193469 + 0.981106i \(0.561974\pi\)
\(402\) 0 0
\(403\) −93.1839 + 161.399i −0.231226 + 0.400494i
\(404\) 0 0
\(405\) −480.061 + 538.276i −1.18534 + 1.32908i
\(406\) 0 0
\(407\) −10.1084 + 5.83606i −0.0248362 + 0.0143392i
\(408\) 0 0
\(409\) 241.831i 0.591275i −0.955300 0.295637i \(-0.904468\pi\)
0.955300 0.295637i \(-0.0955320\pi\)
\(410\) 0 0
\(411\) 22.7136 443.465i 0.0552643 1.07899i
\(412\) 0 0
\(413\) 105.978 + 61.1867i 0.256606 + 0.148152i
\(414\) 0 0
\(415\) 327.963 568.049i 0.790273 1.36879i
\(416\) 0 0
\(417\) −405.080 + 207.004i −0.971416 + 0.496413i
\(418\) 0 0
\(419\) 62.5857 108.402i 0.149369 0.258715i −0.781625 0.623748i \(-0.785609\pi\)
0.930994 + 0.365033i \(0.118942\pi\)
\(420\) 0 0
\(421\) 453.417i 1.07700i −0.842625 0.538500i \(-0.818991\pi\)
0.842625 0.538500i \(-0.181009\pi\)
\(422\) 0 0
\(423\) 102.213 + 228.116i 0.241638 + 0.539282i
\(424\) 0 0
\(425\) 189.270 + 327.825i 0.445341 + 0.771354i
\(426\) 0 0
\(427\) 8.81477 0.0206435
\(428\) 0 0
\(429\) 28.9559 44.7041i 0.0674962 0.104205i
\(430\) 0 0
\(431\) 696.599 402.182i 1.61624 0.933136i 0.628358 0.777925i \(-0.283728\pi\)
0.987881 0.155211i \(-0.0496058\pi\)
\(432\) 0 0
\(433\) −53.8698 + 31.1017i −0.124411 + 0.0718285i −0.560914 0.827874i \(-0.689550\pi\)
0.436503 + 0.899703i \(0.356217\pi\)
\(434\) 0 0
\(435\) −449.304 879.229i −1.03288 2.02122i
\(436\) 0 0
\(437\) −153.293 + 60.5352i −0.350786 + 0.138524i
\(438\) 0 0
\(439\) 465.349i 1.06002i −0.847991 0.530011i \(-0.822188\pi\)
0.847991 0.530011i \(-0.177812\pi\)
\(440\) 0 0
\(441\) −103.707 231.451i −0.235164 0.524832i
\(442\) 0 0
\(443\) 278.441 482.274i 0.628535 1.08865i −0.359311 0.933218i \(-0.616988\pi\)
0.987846 0.155437i \(-0.0496785\pi\)
\(444\) 0 0
\(445\) −771.262 445.288i −1.73317 1.00065i
\(446\) 0 0
\(447\) −206.765 133.926i −0.462561 0.299611i
\(448\) 0 0
\(449\) 445.457i 0.992109i −0.868291 0.496054i \(-0.834782\pi\)
0.868291 0.496054i \(-0.165218\pi\)
\(450\) 0 0
\(451\) 19.4681 + 11.2399i 0.0431664 + 0.0249221i
\(452\) 0 0
\(453\) −293.023 + 452.390i −0.646850 + 0.998653i
\(454\) 0 0
\(455\) 593.104 + 342.429i 1.30353 + 0.752591i
\(456\) 0 0
\(457\) −265.110 459.184i −0.580110 1.00478i −0.995466 0.0951208i \(-0.969676\pi\)
0.415356 0.909659i \(-0.363657\pi\)
\(458\) 0 0
\(459\) 146.735 + 117.961i 0.319683 + 0.256996i
\(460\) 0 0
\(461\) 738.736 1.60246 0.801232 0.598354i \(-0.204178\pi\)
0.801232 + 0.598354i \(0.204178\pi\)
\(462\) 0 0
\(463\) −450.313 + 779.964i −0.972597 + 1.68459i −0.284951 + 0.958542i \(0.591977\pi\)
−0.687646 + 0.726046i \(0.741356\pi\)
\(464\) 0 0
\(465\) −134.395 262.994i −0.289023 0.565579i
\(466\) 0 0
\(467\) −20.7828 −0.0445027 −0.0222514 0.999752i \(-0.507083\pi\)
−0.0222514 + 0.999752i \(0.507083\pi\)
\(468\) 0 0
\(469\) −94.6052 + 54.6203i −0.201717 + 0.116461i
\(470\) 0 0
\(471\) −598.004 387.340i −1.26965 0.822379i
\(472\) 0 0
\(473\) −26.9568 46.6905i −0.0569911 0.0987115i
\(474\) 0 0
\(475\) −151.586 + 1020.25i −0.319128 + 2.14788i
\(476\) 0 0
\(477\) −12.1497 + 118.296i −0.0254711 + 0.247999i
\(478\) 0 0
\(479\) −379.098 + 656.617i −0.791437 + 1.37081i 0.133640 + 0.991030i \(0.457333\pi\)
−0.925077 + 0.379779i \(0.876000\pi\)
\(480\) 0 0
\(481\) −186.800 −0.388357
\(482\) 0 0
\(483\) −99.6603 64.5522i −0.206336 0.133648i
\(484\) 0 0
\(485\) 1102.95 636.786i 2.27411 1.31296i
\(486\) 0 0
\(487\) 241.518i 0.495930i 0.968769 + 0.247965i \(0.0797617\pi\)
−0.968769 + 0.247965i \(0.920238\pi\)
\(488\) 0 0
\(489\) −597.713 + 305.444i −1.22232 + 0.624629i
\(490\) 0 0
\(491\) −71.9479 124.617i −0.146533 0.253803i 0.783411 0.621505i \(-0.213478\pi\)
−0.929944 + 0.367701i \(0.880145\pi\)
\(492\) 0 0
\(493\) −223.210 + 128.870i −0.452758 + 0.261400i
\(494\) 0 0
\(495\) 34.5143 + 77.0282i 0.0697259 + 0.155612i
\(496\) 0 0
\(497\) 540.723i 1.08797i
\(498\) 0 0
\(499\) −141.590 245.240i −0.283747 0.491464i 0.688558 0.725182i \(-0.258244\pi\)
−0.972304 + 0.233718i \(0.924911\pi\)
\(500\) 0 0
\(501\) 7.93928 + 15.5361i 0.0158469 + 0.0310103i
\(502\) 0 0
\(503\) 269.400 + 466.614i 0.535586 + 0.927661i 0.999135 + 0.0415903i \(0.0132424\pi\)
−0.463549 + 0.886071i \(0.653424\pi\)
\(504\) 0 0
\(505\) 295.460 0.585069
\(506\) 0 0
\(507\) 307.576 157.178i 0.606659 0.310015i
\(508\) 0 0
\(509\) 804.739i 1.58102i 0.612449 + 0.790510i \(0.290184\pi\)
−0.612449 + 0.790510i \(0.709816\pi\)
\(510\) 0 0
\(511\) 421.321 0.824504
\(512\) 0 0
\(513\) 113.242 + 500.345i 0.220745 + 0.975332i
\(514\) 0 0
\(515\) 1447.69i 2.81106i
\(516\) 0 0
\(517\) 29.2537 0.0565836
\(518\) 0 0
\(519\) 385.241 + 753.865i 0.742275 + 1.45253i
\(520\) 0 0
\(521\) 1019.07i 1.95599i −0.208620 0.977997i \(-0.566897\pi\)
0.208620 0.977997i \(-0.433103\pi\)
\(522\) 0 0
\(523\) −586.614 + 338.682i −1.12163 + 0.647575i −0.941817 0.336126i \(-0.890883\pi\)
−0.179815 + 0.983700i \(0.557550\pi\)
\(524\) 0 0
\(525\) −661.711 + 338.148i −1.26040 + 0.644091i
\(526\) 0 0
\(527\) −66.7663 + 38.5475i −0.126691 + 0.0731452i
\(528\) 0 0
\(529\) −453.755 −0.857760
\(530\) 0 0
\(531\) −24.6611 + 240.112i −0.0464427 + 0.452189i
\(532\) 0 0
\(533\) 179.882 + 311.565i 0.337490 + 0.584550i
\(534\) 0 0
\(535\) −976.303 + 563.669i −1.82487 + 1.05359i
\(536\) 0 0
\(537\) −34.4637 67.4409i −0.0641781 0.125588i
\(538\) 0 0
\(539\) −29.6813 −0.0550674
\(540\) 0 0
\(541\) −333.796 578.151i −0.616998 1.06867i −0.990030 0.140853i \(-0.955015\pi\)
0.373033 0.927818i \(-0.378318\pi\)
\(542\) 0 0
\(543\) 256.195 395.531i 0.471813 0.728419i
\(544\) 0 0
\(545\) 942.692i 1.72971i
\(546\) 0 0
\(547\) −387.363 223.644i −0.708159 0.408856i 0.102220 0.994762i \(-0.467405\pi\)
−0.810379 + 0.585906i \(0.800739\pi\)
\(548\) 0 0
\(549\) 7.10946 + 15.8667i 0.0129498 + 0.0289011i
\(550\) 0 0
\(551\) −694.665 103.212i −1.26073 0.187317i
\(552\) 0 0
\(553\) 152.050 87.7860i 0.274954 0.158745i
\(554\) 0 0
\(555\) 160.934 248.461i 0.289971 0.447678i
\(556\) 0 0
\(557\) −465.088 805.556i −0.834988 1.44624i −0.894041 0.447986i \(-0.852141\pi\)
0.0590530 0.998255i \(-0.481192\pi\)
\(558\) 0 0
\(559\) 862.828i 1.54352i
\(560\) 0 0
\(561\) 19.6199 10.0261i 0.0349730 0.0178719i
\(562\) 0 0
\(563\) 615.916 + 355.599i 1.09399 + 0.631615i 0.934636 0.355606i \(-0.115726\pi\)
0.159354 + 0.987222i \(0.449059\pi\)
\(564\) 0 0
\(565\) 525.467i 0.930029i
\(566\) 0 0
\(567\) −245.999 + 275.830i −0.433861 + 0.486473i
\(568\) 0 0
\(569\) 424.190 244.906i 0.745501 0.430415i −0.0785653 0.996909i \(-0.525034\pi\)
0.824066 + 0.566494i \(0.191701\pi\)
\(570\) 0 0
\(571\) −94.8843 + 164.344i −0.166172 + 0.287819i −0.937071 0.349139i \(-0.886474\pi\)
0.770899 + 0.636958i \(0.219807\pi\)
\(572\) 0 0
\(573\) 540.203 + 349.901i 0.942762 + 0.610648i
\(574\) 0 0
\(575\) 235.451 407.813i 0.409480 0.709241i
\(576\) 0 0
\(577\) −852.111 −1.47680 −0.738398 0.674366i \(-0.764417\pi\)
−0.738398 + 0.674366i \(0.764417\pi\)
\(578\) 0 0
\(579\) 504.974 779.614i 0.872148 1.34648i
\(580\) 0 0
\(581\) 168.059 291.087i 0.289258 0.501010i
\(582\) 0 0
\(583\) 12.0524 + 6.95845i 0.0206730 + 0.0119356i
\(584\) 0 0
\(585\) −138.015 + 1343.78i −0.235922 + 2.29705i
\(586\) 0 0
\(587\) −661.590 −1.12707 −0.563535 0.826092i \(-0.690559\pi\)
−0.563535 + 0.826092i \(0.690559\pi\)
\(588\) 0 0
\(589\) −207.787 30.8727i −0.352780 0.0524154i
\(590\) 0 0
\(591\) −1005.23 + 513.694i −1.70090 + 0.869194i
\(592\) 0 0
\(593\) −359.755 623.113i −0.606669 1.05078i −0.991785 0.127914i \(-0.959172\pi\)
0.385116 0.922868i \(-0.374161\pi\)
\(594\) 0 0
\(595\) 141.653 + 245.350i 0.238072 + 0.412353i
\(596\) 0 0
\(597\) 189.603 + 122.810i 0.317593 + 0.205712i
\(598\) 0 0
\(599\) 370.363i 0.618302i 0.951013 + 0.309151i \(0.100045\pi\)
−0.951013 + 0.309151i \(0.899955\pi\)
\(600\) 0 0
\(601\) 335.465 193.681i 0.558178 0.322264i −0.194236 0.980955i \(-0.562223\pi\)
0.752414 + 0.658691i \(0.228889\pi\)
\(602\) 0 0
\(603\) −174.620 126.237i −0.289586 0.209348i
\(604\) 0 0
\(605\) −1067.54 −1.76453
\(606\) 0 0
\(607\) 834.955 + 482.061i 1.37554 + 0.794170i 0.991619 0.129194i \(-0.0412391\pi\)
0.383924 + 0.923365i \(0.374572\pi\)
\(608\) 0 0
\(609\) −230.238 450.546i −0.378059 0.739813i
\(610\) 0 0
\(611\) 405.450 + 234.087i 0.663585 + 0.383121i
\(612\) 0 0
\(613\) −75.7056 + 131.126i −0.123500 + 0.213909i −0.921146 0.389218i \(-0.872745\pi\)
0.797645 + 0.603127i \(0.206079\pi\)
\(614\) 0 0
\(615\) −569.386 29.1631i −0.925831 0.0474197i
\(616\) 0 0
\(617\) 392.782 0.636600 0.318300 0.947990i \(-0.396888\pi\)
0.318300 + 0.947990i \(0.396888\pi\)
\(618\) 0 0
\(619\) 488.602 + 846.283i 0.789341 + 1.36718i 0.926371 + 0.376611i \(0.122911\pi\)
−0.137031 + 0.990567i \(0.543756\pi\)
\(620\) 0 0
\(621\) 35.8149 231.454i 0.0576729 0.372711i
\(622\) 0 0
\(623\) −395.220 228.180i −0.634382 0.366261i
\(624\) 0 0
\(625\) −482.434 835.600i −0.771895 1.33696i
\(626\) 0 0
\(627\) 58.8551 + 11.8492i 0.0938678 + 0.0188983i
\(628\) 0 0
\(629\) −66.9210 38.6369i −0.106393 0.0614258i
\(630\) 0 0
\(631\) −365.773 633.537i −0.579672 1.00402i −0.995517 0.0945855i \(-0.969847\pi\)
0.415845 0.909436i \(-0.363486\pi\)
\(632\) 0 0
\(633\) −526.181 + 812.355i −0.831249 + 1.28334i
\(634\) 0 0
\(635\) 1828.51 + 1055.69i 2.87954 + 1.66251i
\(636\) 0 0
\(637\) −411.377 237.509i −0.645804 0.372855i
\(638\) 0 0
\(639\) −973.308 + 436.114i −1.52317 + 0.682495i
\(640\) 0 0
\(641\) 534.564i 0.833952i 0.908917 + 0.416976i \(0.136910\pi\)
−0.908917 + 0.416976i \(0.863090\pi\)
\(642\) 0 0
\(643\) −513.484 889.380i −0.798575 1.38317i −0.920544 0.390638i \(-0.872254\pi\)
0.121969 0.992534i \(-0.461079\pi\)
\(644\) 0 0
\(645\) 1147.64 + 743.355i 1.77929 + 1.15249i
\(646\) 0 0
\(647\) 83.2309 0.128641 0.0643206 0.997929i \(-0.479512\pi\)
0.0643206 + 0.997929i \(0.479512\pi\)
\(648\) 0 0
\(649\) 24.4635 + 14.1240i 0.0376941 + 0.0217627i
\(650\) 0 0
\(651\) −68.8687 134.767i −0.105789 0.207015i
\(652\) 0 0
\(653\) −512.059 + 886.913i −0.784165 + 1.35821i 0.145332 + 0.989383i \(0.453575\pi\)
−0.929497 + 0.368830i \(0.879758\pi\)
\(654\) 0 0
\(655\) 551.221 954.743i 0.841559 1.45762i
\(656\) 0 0
\(657\) 339.812 + 758.384i 0.517218 + 1.15431i
\(658\) 0 0
\(659\) 476.919 + 275.349i 0.723701 + 0.417829i 0.816113 0.577892i \(-0.196124\pi\)
−0.0924121 + 0.995721i \(0.529458\pi\)
\(660\) 0 0
\(661\) 439.526i 0.664942i −0.943114 0.332471i \(-0.892118\pi\)
0.943114 0.332471i \(-0.107882\pi\)
\(662\) 0 0
\(663\) 352.156 + 18.0369i 0.531155 + 0.0272050i
\(664\) 0 0
\(665\) −113.450 + 763.570i −0.170601 + 1.14823i
\(666\) 0 0
\(667\) 277.672 + 160.314i 0.416300 + 0.240351i
\(668\) 0 0
\(669\) 65.8091 + 128.780i 0.0983694 + 0.192496i
\(670\) 0 0
\(671\) 2.03475 0.00303242
\(672\) 0 0
\(673\) 388.654 224.389i 0.577495 0.333417i −0.182642 0.983179i \(-0.558465\pi\)
0.760137 + 0.649763i \(0.225132\pi\)
\(674\) 0 0
\(675\) −1142.37 918.360i −1.69240 1.36053i
\(676\) 0 0
\(677\) 199.246 115.035i 0.294308 0.169919i −0.345575 0.938391i \(-0.612316\pi\)
0.639883 + 0.768472i \(0.278983\pi\)
\(678\) 0 0
\(679\) 565.186 326.310i 0.832379 0.480574i
\(680\) 0 0
\(681\) 259.683 400.917i 0.381326 0.588718i
\(682\) 0 0
\(683\) 980.063i 1.43494i 0.696590 + 0.717469i \(0.254700\pi\)
−0.696590 + 0.717469i \(0.745300\pi\)
\(684\) 0 0
\(685\) 1317.97 1.92405
\(686\) 0 0
\(687\) −9.42234 + 183.964i −0.0137152 + 0.267778i
\(688\) 0 0
\(689\) 111.362 + 192.885i 0.161629 + 0.279950i
\(690\) 0 0
\(691\) 102.099 + 176.841i 0.147756 + 0.255921i 0.930398 0.366551i \(-0.119462\pi\)
−0.782642 + 0.622472i \(0.786128\pi\)
\(692\) 0 0
\(693\) 17.6863 + 39.4718i 0.0255213 + 0.0569578i
\(694\) 0 0
\(695\) −675.106 1169.32i −0.971375 1.68247i
\(696\) 0 0
\(697\) 148.824i 0.213521i
\(698\) 0 0
\(699\) 37.8985 739.938i 0.0542182 1.05857i
\(700\) 0 0
\(701\) 170.159 294.724i 0.242738 0.420434i −0.718755 0.695263i \(-0.755288\pi\)
0.961493 + 0.274829i \(0.0886212\pi\)
\(702\) 0 0
\(703\) −77.3360 195.838i −0.110009 0.278575i
\(704\) 0 0
\(705\) −660.667 + 337.614i −0.937117 + 0.478886i
\(706\) 0 0
\(707\) 151.403 0.214149
\(708\) 0 0
\(709\) 25.8318 44.7420i 0.0364341 0.0631058i −0.847233 0.531221i \(-0.821733\pi\)
0.883667 + 0.468115i \(0.155067\pi\)
\(710\) 0 0
\(711\) 280.650 + 202.889i 0.394726 + 0.285357i
\(712\) 0 0
\(713\) 83.0570 + 47.9530i 0.116490 + 0.0672552i
\(714\) 0 0
\(715\) 136.909 + 79.0443i 0.191481 + 0.110551i
\(716\) 0 0
\(717\) −43.2277 + 843.986i −0.0602897 + 1.17711i
\(718\) 0 0
\(719\) −320.673 + 555.422i −0.445999 + 0.772492i −0.998121 0.0612706i \(-0.980485\pi\)
0.552122 + 0.833763i \(0.313818\pi\)
\(720\) 0 0
\(721\) 741.846i 1.02891i
\(722\) 0 0
\(723\) 251.689 + 12.8912i 0.348118 + 0.0178301i
\(724\) 0 0
\(725\) 1737.75 1003.29i 2.39689 1.38385i
\(726\) 0 0
\(727\) 494.140 0.679698 0.339849 0.940480i \(-0.389624\pi\)
0.339849 + 0.940480i \(0.389624\pi\)
\(728\) 0 0
\(729\) −694.906 220.334i −0.953232 0.302241i
\(730\) 0 0
\(731\) 178.464 309.108i 0.244137 0.422857i
\(732\) 0 0
\(733\) 427.809 740.986i 0.583641 1.01090i −0.411403 0.911454i \(-0.634961\pi\)
0.995043 0.0994414i \(-0.0317056\pi\)
\(734\) 0 0
\(735\) 670.325 342.550i 0.912007 0.466054i
\(736\) 0 0
\(737\) −21.8381 + 12.6082i −0.0296311 + 0.0171075i
\(738\) 0 0
\(739\) 544.175 942.539i 0.736367 1.27543i −0.217754 0.976004i \(-0.569873\pi\)
0.954121 0.299421i \(-0.0967937\pi\)
\(740\) 0 0
\(741\) 720.903 + 635.184i 0.972878 + 0.857198i
\(742\) 0 0
\(743\) 141.199 81.5216i 0.190040 0.109719i −0.401961 0.915657i \(-0.631671\pi\)
0.592001 + 0.805937i \(0.298338\pi\)
\(744\) 0 0
\(745\) 365.595 633.229i 0.490731 0.849972i
\(746\) 0 0
\(747\) 659.507 + 67.7356i 0.882874 + 0.0906768i
\(748\) 0 0
\(749\) −500.290 + 288.842i −0.667943 + 0.385637i
\(750\) 0 0
\(751\) 978.567i 1.30302i −0.758641 0.651509i \(-0.774136\pi\)
0.758641 0.651509i \(-0.225864\pi\)
\(752\) 0 0
\(753\) 60.7658 + 39.3594i 0.0806983 + 0.0522701i
\(754\) 0 0
\(755\) −1385.47 799.901i −1.83506 1.05947i
\(756\) 0 0
\(757\) 713.647 1236.07i 0.942731 1.63286i 0.182499 0.983206i \(-0.441581\pi\)
0.760232 0.649652i \(-0.225085\pi\)
\(758\) 0 0
\(759\) −23.0050 14.9009i −0.0303096 0.0196322i
\(760\) 0 0
\(761\) 317.545 550.005i 0.417274 0.722740i −0.578390 0.815760i \(-0.696319\pi\)
0.995664 + 0.0930206i \(0.0296522\pi\)
\(762\) 0 0
\(763\) 483.066i 0.633115i
\(764\) 0 0
\(765\) −327.385 + 452.862i −0.427954 + 0.591977i
\(766\) 0 0
\(767\) 226.039 + 391.511i 0.294706 + 0.510445i
\(768\) 0 0
\(769\) −697.716 −0.907302 −0.453651 0.891179i \(-0.649879\pi\)
−0.453651 + 0.891179i \(0.649879\pi\)
\(770\) 0 0
\(771\) 149.108 + 291.785i 0.193396 + 0.378450i
\(772\) 0 0
\(773\) 819.856 473.344i 1.06062 0.612347i 0.135014 0.990844i \(-0.456892\pi\)
0.925603 + 0.378497i \(0.123559\pi\)
\(774\) 0 0
\(775\) 519.793 300.103i 0.670701 0.387229i
\(776\) 0 0
\(777\) 82.4679 127.320i 0.106136 0.163861i
\(778\) 0 0
\(779\) −252.169 + 317.576i −0.323708 + 0.407671i
\(780\) 0 0
\(781\) 124.817i 0.159817i
\(782\) 0 0
\(783\) 625.293 777.815i 0.798586 0.993378i
\(784\) 0 0
\(785\) 1057.37 1831.42i 1.34697 2.33302i
\(786\) 0 0
\(787\) −630.202 363.847i −0.800765 0.462322i 0.0429736 0.999076i \(-0.486317\pi\)
−0.843739 + 0.536754i \(0.819650\pi\)
\(788\) 0 0
\(789\) 1000.41 511.230i 1.26795 0.647946i
\(790\) 0 0
\(791\) 269.266i 0.340413i
\(792\) 0 0
\(793\) 28.2012 + 16.2820i 0.0355627 + 0.0205321i
\(794\) 0 0
\(795\) −352.499 18.0544i −0.443394 0.0227100i
\(796\) 0 0
\(797\) 845.328 + 488.051i 1.06064 +