Properties

Label 684.3.m.a.353.3
Level $684$
Weight $3$
Character 684.353
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.m (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 353.3
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.88193 + 0.833354i) q^{3} -7.26979i q^{5} +(3.75776 - 6.50863i) q^{7} +(7.61104 - 4.80334i) q^{9} +O(q^{10})\) \(q+(-2.88193 + 0.833354i) q^{3} -7.26979i q^{5} +(3.75776 - 6.50863i) q^{7} +(7.61104 - 4.80334i) q^{9} +(-14.6898 - 8.48117i) q^{11} +(10.1476 - 17.5762i) q^{13} +(6.05831 + 20.9510i) q^{15} +(12.9313 + 7.46590i) q^{17} +(-17.9208 - 6.31229i) q^{19} +(-5.40560 + 21.8890i) q^{21} +(28.8029 + 16.6293i) q^{23} -27.8498 q^{25} +(-17.9316 + 20.1856i) q^{27} +30.3086i q^{29} +(-23.8575 - 41.3223i) q^{31} +(49.4028 + 12.2003i) q^{33} +(-47.3163 - 27.3181i) q^{35} +25.1099 q^{37} +(-14.5975 + 59.1098i) q^{39} -5.04512i q^{41} +(-24.8411 - 43.0261i) q^{43} +(-34.9192 - 55.3306i) q^{45} +62.4682i q^{47} +(-3.74149 - 6.48044i) q^{49} +(-43.4889 - 10.7398i) q^{51} +(47.5227 - 27.4372i) q^{53} +(-61.6563 + 106.792i) q^{55} +(56.9069 + 3.25720i) q^{57} -73.6284i q^{59} -95.3512 q^{61} +(-2.66269 - 67.5872i) q^{63} +(-127.775 - 73.7709i) q^{65} +(0.588665 - 1.01960i) q^{67} +(-96.8660 - 23.9216i) q^{69} +(-12.3658 - 7.13938i) q^{71} +(-59.5390 + 103.125i) q^{73} +(80.2611 - 23.2087i) q^{75} +(-110.401 + 63.7403i) q^{77} +(0.0750630 + 0.130013i) q^{79} +(34.8559 - 73.1168i) q^{81} +(-41.9662 - 24.2292i) q^{83} +(54.2755 - 94.0079i) q^{85} +(-25.2578 - 87.3472i) q^{87} +(67.4096 - 38.9190i) q^{89} +(-76.2645 - 132.094i) q^{91} +(103.192 + 99.2064i) q^{93} +(-45.8890 + 130.280i) q^{95} +(-47.2818 - 81.8945i) q^{97} +(-152.543 + 6.00963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.88193 + 0.833354i −0.960643 + 0.277785i
\(4\) 0 0
\(5\) 7.26979i 1.45396i −0.686660 0.726979i \(-0.740924\pi\)
0.686660 0.726979i \(-0.259076\pi\)
\(6\) 0 0
\(7\) 3.75776 6.50863i 0.536823 0.929804i −0.462250 0.886750i \(-0.652958\pi\)
0.999073 0.0430544i \(-0.0137089\pi\)
\(8\) 0 0
\(9\) 7.61104 4.80334i 0.845671 0.533704i
\(10\) 0 0
\(11\) −14.6898 8.48117i −1.33544 0.771015i −0.349310 0.937007i \(-0.613584\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(12\) 0 0
\(13\) 10.1476 17.5762i 0.780585 1.35201i −0.151016 0.988531i \(-0.548255\pi\)
0.931601 0.363482i \(-0.118412\pi\)
\(14\) 0 0
\(15\) 6.05831 + 20.9510i 0.403887 + 1.39673i
\(16\) 0 0
\(17\) 12.9313 + 7.46590i 0.760666 + 0.439170i 0.829535 0.558455i \(-0.188606\pi\)
−0.0688691 + 0.997626i \(0.521939\pi\)
\(18\) 0 0
\(19\) −17.9208 6.31229i −0.943200 0.332226i
\(20\) 0 0
\(21\) −5.40560 + 21.8890i −0.257410 + 1.04233i
\(22\) 0 0
\(23\) 28.8029 + 16.6293i 1.25230 + 0.723015i 0.971565 0.236771i \(-0.0760891\pi\)
0.280733 + 0.959786i \(0.409422\pi\)
\(24\) 0 0
\(25\) −27.8498 −1.11399
\(26\) 0 0
\(27\) −17.9316 + 20.1856i −0.664133 + 0.747614i
\(28\) 0 0
\(29\) 30.3086i 1.04512i 0.852601 + 0.522562i \(0.175024\pi\)
−0.852601 + 0.522562i \(0.824976\pi\)
\(30\) 0 0
\(31\) −23.8575 41.3223i −0.769596 1.33298i −0.937782 0.347224i \(-0.887124\pi\)
0.168187 0.985755i \(-0.446209\pi\)
\(32\) 0 0
\(33\) 49.4028 + 12.2003i 1.49706 + 0.369706i
\(34\) 0 0
\(35\) −47.3163 27.3181i −1.35190 0.780517i
\(36\) 0 0
\(37\) 25.1099 0.678647 0.339324 0.940670i \(-0.389802\pi\)
0.339324 + 0.940670i \(0.389802\pi\)
\(38\) 0 0
\(39\) −14.5975 + 59.1098i −0.374295 + 1.51564i
\(40\) 0 0
\(41\) 5.04512i 0.123052i −0.998105 0.0615258i \(-0.980403\pi\)
0.998105 0.0615258i \(-0.0195967\pi\)
\(42\) 0 0
\(43\) −24.8411 43.0261i −0.577701 1.00061i −0.995742 0.0921791i \(-0.970617\pi\)
0.418042 0.908428i \(-0.362717\pi\)
\(44\) 0 0
\(45\) −34.9192 55.3306i −0.775983 1.22957i
\(46\) 0 0
\(47\) 62.4682i 1.32911i 0.747239 + 0.664555i \(0.231379\pi\)
−0.747239 + 0.664555i \(0.768621\pi\)
\(48\) 0 0
\(49\) −3.74149 6.48044i −0.0763569 0.132254i
\(50\) 0 0
\(51\) −43.4889 10.7398i −0.852723 0.210585i
\(52\) 0 0
\(53\) 47.5227 27.4372i 0.896654 0.517684i 0.0205412 0.999789i \(-0.493461\pi\)
0.876113 + 0.482105i \(0.160128\pi\)
\(54\) 0 0
\(55\) −61.6563 + 106.792i −1.12102 + 1.94167i
\(56\) 0 0
\(57\) 56.9069 + 3.25720i 0.998366 + 0.0571438i
\(58\) 0 0
\(59\) 73.6284i 1.24794i −0.781449 0.623969i \(-0.785519\pi\)
0.781449 0.623969i \(-0.214481\pi\)
\(60\) 0 0
\(61\) −95.3512 −1.56314 −0.781568 0.623821i \(-0.785580\pi\)
−0.781568 + 0.623821i \(0.785580\pi\)
\(62\) 0 0
\(63\) −2.66269 67.5872i −0.0422650 1.07281i
\(64\) 0 0
\(65\) −127.775 73.7709i −1.96577 1.13494i
\(66\) 0 0
\(67\) 0.588665 1.01960i 0.00878605 0.0152179i −0.861599 0.507590i \(-0.830537\pi\)
0.870385 + 0.492372i \(0.163870\pi\)
\(68\) 0 0
\(69\) −96.8660 23.9216i −1.40385 0.346690i
\(70\) 0 0
\(71\) −12.3658 7.13938i −0.174166 0.100555i 0.410383 0.911913i \(-0.365395\pi\)
−0.584549 + 0.811359i \(0.698728\pi\)
\(72\) 0 0
\(73\) −59.5390 + 103.125i −0.815603 + 1.41267i 0.0932911 + 0.995639i \(0.470261\pi\)
−0.908894 + 0.417027i \(0.863072\pi\)
\(74\) 0 0
\(75\) 80.2611 23.2087i 1.07015 0.309450i
\(76\) 0 0
\(77\) −110.401 + 63.7403i −1.43379 + 0.827796i
\(78\) 0 0
\(79\) 0.0750630 + 0.130013i 0.000950165 + 0.00164573i 0.866500 0.499177i \(-0.166364\pi\)
−0.865550 + 0.500823i \(0.833031\pi\)
\(80\) 0 0
\(81\) 34.8559 73.1168i 0.430319 0.902677i
\(82\) 0 0
\(83\) −41.9662 24.2292i −0.505617 0.291918i 0.225413 0.974263i \(-0.427627\pi\)
−0.731030 + 0.682345i \(0.760960\pi\)
\(84\) 0 0
\(85\) 54.2755 94.0079i 0.638535 1.10598i
\(86\) 0 0
\(87\) −25.2578 87.3472i −0.290320 1.00399i
\(88\) 0 0
\(89\) 67.4096 38.9190i 0.757412 0.437292i −0.0709540 0.997480i \(-0.522604\pi\)
0.828366 + 0.560188i \(0.189271\pi\)
\(90\) 0 0
\(91\) −76.2645 132.094i −0.838071 1.45158i
\(92\) 0 0
\(93\) 103.192 + 99.2064i 1.10959 + 1.06674i
\(94\) 0 0
\(95\) −45.8890 + 130.280i −0.483042 + 1.37137i
\(96\) 0 0
\(97\) −47.2818 81.8945i −0.487441 0.844273i 0.512455 0.858714i \(-0.328736\pi\)
−0.999896 + 0.0144414i \(0.995403\pi\)
\(98\) 0 0
\(99\) −152.543 + 6.00963i −1.54083 + 0.0607034i
\(100\) 0 0
\(101\) 84.7721i 0.839328i 0.907680 + 0.419664i \(0.137852\pi\)
−0.907680 + 0.419664i \(0.862148\pi\)
\(102\) 0 0
\(103\) −3.50170 6.06512i −0.0339971 0.0588846i 0.848526 0.529153i \(-0.177490\pi\)
−0.882523 + 0.470269i \(0.844157\pi\)
\(104\) 0 0
\(105\) 159.128 + 39.2976i 1.51550 + 0.374262i
\(106\) 0 0
\(107\) 97.9295i 0.915229i 0.889151 + 0.457614i \(0.151296\pi\)
−0.889151 + 0.457614i \(0.848704\pi\)
\(108\) 0 0
\(109\) 75.3829 130.567i 0.691587 1.19786i −0.279731 0.960078i \(-0.590245\pi\)
0.971318 0.237785i \(-0.0764213\pi\)
\(110\) 0 0
\(111\) −72.3651 + 20.9255i −0.651938 + 0.188518i
\(112\) 0 0
\(113\) 39.6676 22.9021i 0.351041 0.202674i −0.314103 0.949389i \(-0.601704\pi\)
0.665144 + 0.746715i \(0.268370\pi\)
\(114\) 0 0
\(115\) 120.892 209.391i 1.05123 1.82079i
\(116\) 0 0
\(117\) −7.19045 182.515i −0.0614568 1.55996i
\(118\) 0 0
\(119\) 97.1855 56.1101i 0.816685 0.471513i
\(120\) 0 0
\(121\) 83.3603 + 144.384i 0.688928 + 1.19326i
\(122\) 0 0
\(123\) 4.20437 + 14.5397i 0.0341819 + 0.118209i
\(124\) 0 0
\(125\) 20.7173i 0.165739i
\(126\) 0 0
\(127\) −14.0912 24.4067i −0.110955 0.192179i 0.805201 0.593002i \(-0.202058\pi\)
−0.916155 + 0.400823i \(0.868724\pi\)
\(128\) 0 0
\(129\) 107.446 + 103.297i 0.832918 + 0.800750i
\(130\) 0 0
\(131\) 252.087i 1.92433i 0.272466 + 0.962166i \(0.412161\pi\)
−0.272466 + 0.962166i \(0.587839\pi\)
\(132\) 0 0
\(133\) −108.426 + 92.9197i −0.815236 + 0.698645i
\(134\) 0 0
\(135\) 146.745 + 130.359i 1.08700 + 0.965622i
\(136\) 0 0
\(137\) 86.3432i 0.630242i −0.949051 0.315121i \(-0.897955\pi\)
0.949051 0.315121i \(-0.102045\pi\)
\(138\) 0 0
\(139\) −82.7671 + 143.357i −0.595447 + 1.03134i 0.398037 + 0.917369i \(0.369692\pi\)
−0.993484 + 0.113974i \(0.963642\pi\)
\(140\) 0 0
\(141\) −52.0582 180.029i −0.369207 1.27680i
\(142\) 0 0
\(143\) −298.133 + 172.127i −2.08484 + 1.20369i
\(144\) 0 0
\(145\) 220.337 1.51957
\(146\) 0 0
\(147\) 16.1832 + 15.5582i 0.110090 + 0.105838i
\(148\) 0 0
\(149\) 196.064i 1.31587i 0.753076 + 0.657934i \(0.228569\pi\)
−0.753076 + 0.657934i \(0.771431\pi\)
\(150\) 0 0
\(151\) 0.412875 0.715121i 0.00273427 0.00473590i −0.864655 0.502366i \(-0.832463\pi\)
0.867389 + 0.497630i \(0.165796\pi\)
\(152\) 0 0
\(153\) 134.282 5.29023i 0.877660 0.0345767i
\(154\) 0 0
\(155\) −300.405 + 173.439i −1.93809 + 1.11896i
\(156\) 0 0
\(157\) −128.511 −0.818541 −0.409271 0.912413i \(-0.634217\pi\)
−0.409271 + 0.912413i \(0.634217\pi\)
\(158\) 0 0
\(159\) −114.092 + 118.675i −0.717560 + 0.746386i
\(160\) 0 0
\(161\) 216.468 124.978i 1.34452 0.776261i
\(162\) 0 0
\(163\) 236.259 1.44944 0.724722 0.689041i \(-0.241968\pi\)
0.724722 + 0.689041i \(0.241968\pi\)
\(164\) 0 0
\(165\) 88.6936 359.148i 0.537537 2.17665i
\(166\) 0 0
\(167\) 144.149 + 83.2244i 0.863167 + 0.498350i 0.865072 0.501648i \(-0.167273\pi\)
−0.00190452 + 0.999998i \(0.500606\pi\)
\(168\) 0 0
\(169\) −121.448 210.354i −0.718626 1.24470i
\(170\) 0 0
\(171\) −166.716 + 38.0366i −0.974947 + 0.222436i
\(172\) 0 0
\(173\) −58.6776 + 33.8776i −0.339177 + 0.195824i −0.659908 0.751346i \(-0.729405\pi\)
0.320731 + 0.947170i \(0.396071\pi\)
\(174\) 0 0
\(175\) −104.653 + 181.264i −0.598016 + 1.03579i
\(176\) 0 0
\(177\) 61.3585 + 212.192i 0.346658 + 1.19882i
\(178\) 0 0
\(179\) 60.5311i 0.338163i −0.985602 0.169081i \(-0.945920\pi\)
0.985602 0.169081i \(-0.0540801\pi\)
\(180\) 0 0
\(181\) 83.4816 + 144.594i 0.461224 + 0.798864i 0.999022 0.0442096i \(-0.0140769\pi\)
−0.537798 + 0.843074i \(0.680744\pi\)
\(182\) 0 0
\(183\) 274.796 79.4614i 1.50162 0.434215i
\(184\) 0 0
\(185\) 182.544i 0.986724i
\(186\) 0 0
\(187\) −126.639 219.345i −0.677214 1.17297i
\(188\) 0 0
\(189\) 63.9978 + 192.563i 0.338613 + 1.01885i
\(190\) 0 0
\(191\) 133.030 + 76.8050i 0.696493 + 0.402120i 0.806040 0.591861i \(-0.201607\pi\)
−0.109547 + 0.993982i \(0.534940\pi\)
\(192\) 0 0
\(193\) 238.302 1.23473 0.617364 0.786678i \(-0.288201\pi\)
0.617364 + 0.786678i \(0.288201\pi\)
\(194\) 0 0
\(195\) 429.716 + 106.121i 2.20367 + 0.544209i
\(196\) 0 0
\(197\) 109.602i 0.556357i −0.960529 0.278178i \(-0.910269\pi\)
0.960529 0.278178i \(-0.0897306\pi\)
\(198\) 0 0
\(199\) −126.692 219.437i −0.636643 1.10270i −0.986165 0.165770i \(-0.946989\pi\)
0.349522 0.936928i \(-0.386344\pi\)
\(200\) 0 0
\(201\) −0.846806 + 3.42898i −0.00421296 + 0.0170596i
\(202\) 0 0
\(203\) 197.267 + 113.892i 0.971760 + 0.561046i
\(204\) 0 0
\(205\) −36.6769 −0.178912
\(206\) 0 0
\(207\) 299.096 11.7833i 1.44491 0.0569242i
\(208\) 0 0
\(209\) 209.718 + 244.716i 1.00343 + 1.17089i
\(210\) 0 0
\(211\) 394.462 1.86949 0.934745 0.355320i \(-0.115628\pi\)
0.934745 + 0.355320i \(0.115628\pi\)
\(212\) 0 0
\(213\) 41.5869 + 10.2701i 0.195244 + 0.0482165i
\(214\) 0 0
\(215\) −312.791 + 180.590i −1.45484 + 0.839952i
\(216\) 0 0
\(217\) −358.602 −1.65255
\(218\) 0 0
\(219\) 85.6479 346.815i 0.391086 1.58363i
\(220\) 0 0
\(221\) 262.444 151.522i 1.18753 0.685620i
\(222\) 0 0
\(223\) 97.6081 + 169.062i 0.437705 + 0.758127i 0.997512 0.0704962i \(-0.0224583\pi\)
−0.559807 + 0.828623i \(0.689125\pi\)
\(224\) 0 0
\(225\) −211.966 + 133.772i −0.942070 + 0.594542i
\(226\) 0 0
\(227\) −253.263 146.222i −1.11570 0.644148i −0.175398 0.984498i \(-0.556121\pi\)
−0.940299 + 0.340349i \(0.889455\pi\)
\(228\) 0 0
\(229\) −70.4763 122.069i −0.307757 0.533050i 0.670114 0.742258i \(-0.266245\pi\)
−0.977871 + 0.209207i \(0.932912\pi\)
\(230\) 0 0
\(231\) 265.051 275.699i 1.14741 1.19350i
\(232\) 0 0
\(233\) −198.955 114.867i −0.853885 0.492991i 0.00807462 0.999967i \(-0.497430\pi\)
−0.861960 + 0.506977i \(0.830763\pi\)
\(234\) 0 0
\(235\) 454.130 1.93247
\(236\) 0 0
\(237\) −0.324673 0.312134i −0.00136993 0.00131702i
\(238\) 0 0
\(239\) −203.641 + 117.572i −0.852053 + 0.491933i −0.861343 0.508024i \(-0.830376\pi\)
0.00929033 + 0.999957i \(0.497043\pi\)
\(240\) 0 0
\(241\) 69.1883 0.287089 0.143544 0.989644i \(-0.454150\pi\)
0.143544 + 0.989644i \(0.454150\pi\)
\(242\) 0 0
\(243\) −39.5200 + 239.765i −0.162634 + 0.986687i
\(244\) 0 0
\(245\) −47.1114 + 27.1998i −0.192292 + 0.111020i
\(246\) 0 0
\(247\) −292.799 + 250.924i −1.18542 + 1.01589i
\(248\) 0 0
\(249\) 141.135 + 34.8542i 0.566808 + 0.139977i
\(250\) 0 0
\(251\) −18.6371 + 10.7602i −0.0742515 + 0.0428692i −0.536666 0.843795i \(-0.680317\pi\)
0.462415 + 0.886664i \(0.346983\pi\)
\(252\) 0 0
\(253\) −282.072 488.564i −1.11491 1.93108i
\(254\) 0 0
\(255\) −78.0762 + 316.155i −0.306181 + 1.23982i
\(256\) 0 0
\(257\) −252.333 145.684i −0.981839 0.566865i −0.0790144 0.996873i \(-0.525177\pi\)
−0.902825 + 0.430008i \(0.858511\pi\)
\(258\) 0 0
\(259\) 94.3571 163.431i 0.364313 0.631009i
\(260\) 0 0
\(261\) 145.582 + 230.680i 0.557787 + 0.883831i
\(262\) 0 0
\(263\) −140.817 + 81.3007i −0.535426 + 0.309128i −0.743223 0.669044i \(-0.766704\pi\)
0.207797 + 0.978172i \(0.433371\pi\)
\(264\) 0 0
\(265\) −199.463 345.480i −0.752690 1.30370i
\(266\) 0 0
\(267\) −161.837 + 168.338i −0.606129 + 0.630479i
\(268\) 0 0
\(269\) 29.2134 + 16.8664i 0.108600 + 0.0627003i 0.553316 0.832971i \(-0.313362\pi\)
−0.444716 + 0.895672i \(0.646695\pi\)
\(270\) 0 0
\(271\) −88.5330 + 153.344i −0.326690 + 0.565844i −0.981853 0.189644i \(-0.939267\pi\)
0.655163 + 0.755488i \(0.272600\pi\)
\(272\) 0 0
\(273\) 329.870 + 317.130i 1.20831 + 1.16165i
\(274\) 0 0
\(275\) 409.108 + 236.199i 1.48767 + 0.858904i
\(276\) 0 0
\(277\) 88.8575 153.906i 0.320785 0.555616i −0.659865 0.751384i \(-0.729387\pi\)
0.980650 + 0.195768i \(0.0627199\pi\)
\(278\) 0 0
\(279\) −380.065 199.911i −1.36224 0.716525i
\(280\) 0 0
\(281\) 336.283i 1.19674i −0.801221 0.598369i \(-0.795816\pi\)
0.801221 0.598369i \(-0.204184\pi\)
\(282\) 0 0
\(283\) 31.1149 0.109947 0.0549733 0.998488i \(-0.482493\pi\)
0.0549733 + 0.998488i \(0.482493\pi\)
\(284\) 0 0
\(285\) 23.6791 413.701i 0.0830846 1.45158i
\(286\) 0 0
\(287\) −32.8368 18.9583i −0.114414 0.0660569i
\(288\) 0 0
\(289\) −33.0207 57.1936i −0.114259 0.197902i
\(290\) 0 0
\(291\) 204.510 + 196.612i 0.702783 + 0.675641i
\(292\) 0 0
\(293\) 180.338 104.118i 0.615487 0.355351i −0.159623 0.987178i \(-0.551028\pi\)
0.775110 + 0.631827i \(0.217695\pi\)
\(294\) 0 0
\(295\) −535.263 −1.81445
\(296\) 0 0
\(297\) 434.609 144.441i 1.46333 0.486335i
\(298\) 0 0
\(299\) 584.560 337.496i 1.95505 1.12875i
\(300\) 0 0
\(301\) −373.388 −1.24049
\(302\) 0 0
\(303\) −70.6452 244.307i −0.233153 0.806295i
\(304\) 0 0
\(305\) 693.183i 2.27273i
\(306\) 0 0
\(307\) 251.455 435.532i 0.819071 1.41867i −0.0872974 0.996182i \(-0.527823\pi\)
0.906368 0.422489i \(-0.138844\pi\)
\(308\) 0 0
\(309\) 15.1460 + 14.5611i 0.0490163 + 0.0471233i
\(310\) 0 0
\(311\) 241.751 139.575i 0.777334 0.448794i −0.0581507 0.998308i \(-0.518520\pi\)
0.835485 + 0.549514i \(0.185187\pi\)
\(312\) 0 0
\(313\) −113.259 −0.361850 −0.180925 0.983497i \(-0.557909\pi\)
−0.180925 + 0.983497i \(0.557909\pi\)
\(314\) 0 0
\(315\) −491.345 + 19.3572i −1.55982 + 0.0614515i
\(316\) 0 0
\(317\) 109.393i 0.345089i −0.985002 0.172544i \(-0.944801\pi\)
0.985002 0.172544i \(-0.0551988\pi\)
\(318\) 0 0
\(319\) 257.052 445.227i 0.805806 1.39570i
\(320\) 0 0
\(321\) −81.6100 282.226i −0.254237 0.879209i
\(322\) 0 0
\(323\) −184.613 215.421i −0.571556 0.666938i
\(324\) 0 0
\(325\) −282.609 + 489.492i −0.869565 + 1.50613i
\(326\) 0 0
\(327\) −108.440 + 439.106i −0.331620 + 1.34283i
\(328\) 0 0
\(329\) 406.582 + 234.740i 1.23581 + 0.713497i
\(330\) 0 0
\(331\) −50.5317 + 87.5235i −0.152664 + 0.264422i −0.932206 0.361928i \(-0.882119\pi\)
0.779542 + 0.626350i \(0.215452\pi\)
\(332\) 0 0
\(333\) 191.113 120.612i 0.573912 0.362197i
\(334\) 0 0
\(335\) −7.41226 4.27947i −0.0221262 0.0127745i
\(336\) 0 0
\(337\) −560.509 −1.66323 −0.831616 0.555351i \(-0.812584\pi\)
−0.831616 + 0.555351i \(0.812584\pi\)
\(338\) 0 0
\(339\) −95.2337 + 99.0595i −0.280925 + 0.292211i
\(340\) 0 0
\(341\) 809.357i 2.37348i
\(342\) 0 0
\(343\) 312.022 0.909685
\(344\) 0 0
\(345\) −173.905 + 704.195i −0.504072 + 2.04114i
\(346\) 0 0
\(347\) 106.009i 0.305501i 0.988265 + 0.152751i \(0.0488132\pi\)
−0.988265 + 0.152751i \(0.951187\pi\)
\(348\) 0 0
\(349\) 120.332 208.421i 0.344791 0.597196i −0.640525 0.767938i \(-0.721283\pi\)
0.985316 + 0.170742i \(0.0546164\pi\)
\(350\) 0 0
\(351\) 172.822 + 520.004i 0.492371 + 1.48149i
\(352\) 0 0
\(353\) −438.326 253.068i −1.24172 0.716906i −0.272274 0.962220i \(-0.587776\pi\)
−0.969444 + 0.245314i \(0.921109\pi\)
\(354\) 0 0
\(355\) −51.9018 + 89.8965i −0.146202 + 0.253229i
\(356\) 0 0
\(357\) −233.322 + 242.695i −0.653564 + 0.679819i
\(358\) 0 0
\(359\) −481.722 278.122i −1.34184 0.774714i −0.354766 0.934955i \(-0.615439\pi\)
−0.987078 + 0.160242i \(0.948773\pi\)
\(360\) 0 0
\(361\) 281.310 + 226.243i 0.779252 + 0.626711i
\(362\) 0 0
\(363\) −360.562 346.637i −0.993284 0.954922i
\(364\) 0 0
\(365\) 749.694 + 432.836i 2.05396 + 1.18585i
\(366\) 0 0
\(367\) 608.527 1.65811 0.829056 0.559165i \(-0.188878\pi\)
0.829056 + 0.559165i \(0.188878\pi\)
\(368\) 0 0
\(369\) −24.2334 38.3986i −0.0656732 0.104061i
\(370\) 0 0
\(371\) 412.410i 1.11162i
\(372\) 0 0
\(373\) 61.6756 + 106.825i 0.165350 + 0.286395i 0.936780 0.349920i \(-0.113791\pi\)
−0.771429 + 0.636315i \(0.780458\pi\)
\(374\) 0 0
\(375\) −17.2649 59.7059i −0.0460397 0.159216i
\(376\) 0 0
\(377\) 532.709 + 307.560i 1.41302 + 0.815808i
\(378\) 0 0
\(379\) −358.690 −0.946412 −0.473206 0.880952i \(-0.656903\pi\)
−0.473206 + 0.880952i \(0.656903\pi\)
\(380\) 0 0
\(381\) 60.9495 + 58.5955i 0.159972 + 0.153794i
\(382\) 0 0
\(383\) 366.840i 0.957806i −0.877868 0.478903i \(-0.841035\pi\)
0.877868 0.478903i \(-0.158965\pi\)
\(384\) 0 0
\(385\) 463.379 + 802.595i 1.20358 + 2.08466i
\(386\) 0 0
\(387\) −395.736 208.153i −1.02257 0.537863i
\(388\) 0 0
\(389\) 190.120i 0.488740i 0.969682 + 0.244370i \(0.0785812\pi\)
−0.969682 + 0.244370i \(0.921419\pi\)
\(390\) 0 0
\(391\) 248.306 + 430.078i 0.635054 + 1.09995i
\(392\) 0 0
\(393\) −210.078 726.498i −0.534550 1.84860i
\(394\) 0 0
\(395\) 0.945166 0.545692i 0.00239283 0.00138150i
\(396\) 0 0
\(397\) 115.434 199.937i 0.290765 0.503619i −0.683226 0.730207i \(-0.739424\pi\)
0.973991 + 0.226588i \(0.0727570\pi\)
\(398\) 0 0
\(399\) 235.042 358.146i 0.589078 0.897608i
\(400\) 0 0
\(401\) 439.408i 1.09578i 0.836551 + 0.547890i \(0.184569\pi\)
−0.836551 + 0.547890i \(0.815431\pi\)
\(402\) 0 0
\(403\) −968.385 −2.40294
\(404\) 0 0
\(405\) −531.544 253.395i −1.31245 0.625666i
\(406\) 0 0
\(407\) −368.860 212.962i −0.906291 0.523247i
\(408\) 0 0
\(409\) 131.307 227.431i 0.321045 0.556065i −0.659659 0.751565i \(-0.729299\pi\)
0.980704 + 0.195499i \(0.0626328\pi\)
\(410\) 0 0
\(411\) 71.9545 + 248.835i 0.175072 + 0.605438i
\(412\) 0 0
\(413\) −479.220 276.678i −1.16034 0.669922i
\(414\) 0 0
\(415\) −176.141 + 305.086i −0.424437 + 0.735146i
\(416\) 0 0
\(417\) 119.062 482.119i 0.285520 1.15616i
\(418\) 0 0
\(419\) 490.534 283.210i 1.17072 0.675918i 0.216874 0.976200i \(-0.430414\pi\)
0.953851 + 0.300281i \(0.0970806\pi\)
\(420\) 0 0
\(421\) 239.616 + 415.027i 0.569158 + 0.985811i 0.996649 + 0.0817918i \(0.0260642\pi\)
−0.427491 + 0.904020i \(0.640602\pi\)
\(422\) 0 0
\(423\) 300.056 + 475.448i 0.709352 + 1.12399i
\(424\) 0 0
\(425\) −360.134 207.924i −0.847375 0.489232i
\(426\) 0 0
\(427\) −358.307 + 620.606i −0.839126 + 1.45341i
\(428\) 0 0
\(429\) 715.755 744.508i 1.66843 1.73545i
\(430\) 0 0
\(431\) 480.030 277.145i 1.11376 0.643029i 0.173958 0.984753i \(-0.444344\pi\)
0.939800 + 0.341724i \(0.111011\pi\)
\(432\) 0 0
\(433\) −116.826 202.348i −0.269805 0.467316i 0.699006 0.715116i \(-0.253626\pi\)
−0.968811 + 0.247799i \(0.920293\pi\)
\(434\) 0 0
\(435\) −634.996 + 183.619i −1.45976 + 0.422112i
\(436\) 0 0
\(437\) −411.201 479.823i −0.940964 1.09799i
\(438\) 0 0
\(439\) −100.290 173.707i −0.228451 0.395688i 0.728898 0.684622i \(-0.240033\pi\)
−0.957349 + 0.288934i \(0.906699\pi\)
\(440\) 0 0
\(441\) −59.6044 31.3513i −0.135157 0.0710914i
\(442\) 0 0
\(443\) 296.907i 0.670219i −0.942179 0.335110i \(-0.891227\pi\)
0.942179 0.335110i \(-0.108773\pi\)
\(444\) 0 0
\(445\) −282.933 490.054i −0.635804 1.10124i
\(446\) 0 0
\(447\) −163.391 565.043i −0.365528 1.26408i
\(448\) 0 0
\(449\) 392.134i 0.873349i 0.899620 + 0.436675i \(0.143844\pi\)
−0.899620 + 0.436675i \(0.856156\pi\)
\(450\) 0 0
\(451\) −42.7885 + 74.1118i −0.0948747 + 0.164328i
\(452\) 0 0
\(453\) −0.593928 + 2.40500i −0.00131110 + 0.00530905i
\(454\) 0 0
\(455\) −960.295 + 554.426i −2.11054 + 1.21852i
\(456\) 0 0
\(457\) 101.699 176.148i 0.222537 0.385445i −0.733041 0.680184i \(-0.761900\pi\)
0.955578 + 0.294740i \(0.0952330\pi\)
\(458\) 0 0
\(459\) −382.583 + 127.151i −0.833513 + 0.277017i
\(460\) 0 0
\(461\) −121.048 + 69.8873i −0.262578 + 0.151599i −0.625510 0.780216i \(-0.715109\pi\)
0.362932 + 0.931816i \(0.381776\pi\)
\(462\) 0 0
\(463\) 94.0240 + 162.854i 0.203076 + 0.351737i 0.949518 0.313713i \(-0.101573\pi\)
−0.746442 + 0.665450i \(0.768240\pi\)
\(464\) 0 0
\(465\) 721.209 750.182i 1.55099 1.61329i
\(466\) 0 0
\(467\) 370.749i 0.793896i −0.917841 0.396948i \(-0.870069\pi\)
0.917841 0.396948i \(-0.129931\pi\)
\(468\) 0 0
\(469\) −4.42412 7.66281i −0.00943310 0.0163386i
\(470\) 0 0
\(471\) 370.360 107.095i 0.786326 0.227378i
\(472\) 0 0
\(473\) 842.727i 1.78166i
\(474\) 0 0
\(475\) 499.090 + 175.796i 1.05072 + 0.370097i
\(476\) 0 0
\(477\) 229.907 437.093i 0.481985 0.916338i
\(478\) 0 0
\(479\) 330.120i 0.689185i −0.938752 0.344592i \(-0.888017\pi\)
0.938752 0.344592i \(-0.111983\pi\)
\(480\) 0 0
\(481\) 254.806 441.337i 0.529742 0.917540i
\(482\) 0 0
\(483\) −519.696 + 540.573i −1.07597 + 1.11920i
\(484\) 0 0
\(485\) −595.355 + 343.729i −1.22754 + 0.708719i
\(486\) 0 0
\(487\) 709.032 1.45592 0.727959 0.685621i \(-0.240469\pi\)
0.727959 + 0.685621i \(0.240469\pi\)
\(488\) 0 0
\(489\) −680.883 + 196.888i −1.39240 + 0.402634i
\(490\) 0 0
\(491\) 363.330i 0.739980i −0.929036 0.369990i \(-0.879361\pi\)
0.929036 0.369990i \(-0.120639\pi\)
\(492\) 0 0
\(493\) −226.281 + 391.930i −0.458988 + 0.794990i
\(494\) 0 0
\(495\) 43.6887 + 1108.95i 0.0882601 + 2.24031i
\(496\) 0 0
\(497\) −92.9351 + 53.6561i −0.186992 + 0.107960i
\(498\) 0 0
\(499\) −743.071 −1.48912 −0.744560 0.667556i \(-0.767341\pi\)
−0.744560 + 0.667556i \(0.767341\pi\)
\(500\) 0 0
\(501\) −484.782 119.720i −0.967630 0.238962i
\(502\) 0 0
\(503\) −319.580 + 184.509i −0.635348 + 0.366818i −0.782820 0.622248i \(-0.786220\pi\)
0.147473 + 0.989066i \(0.452886\pi\)
\(504\) 0 0
\(505\) 616.275 1.22035
\(506\) 0 0
\(507\) 525.303 + 505.016i 1.03610 + 0.996086i
\(508\) 0 0
\(509\) −106.451 61.4595i −0.209137 0.120746i 0.391773 0.920062i \(-0.371862\pi\)
−0.600910 + 0.799316i \(0.705195\pi\)
\(510\) 0 0
\(511\) 447.466 + 775.035i 0.875668 + 1.51670i
\(512\) 0 0
\(513\) 448.766 248.552i 0.874787 0.484507i
\(514\) 0 0
\(515\) −44.0921 + 25.4566i −0.0856157 + 0.0494303i
\(516\) 0 0
\(517\) 529.803 917.646i 1.02476 1.77494i
\(518\) 0 0
\(519\) 140.873 146.532i 0.271431 0.282335i
\(520\) 0 0
\(521\) 883.174i 1.69515i −0.530674 0.847576i \(-0.678061\pi\)
0.530674 0.847576i \(-0.321939\pi\)
\(522\) 0 0
\(523\) 82.8317 + 143.469i 0.158378 + 0.274319i 0.934284 0.356530i \(-0.116040\pi\)
−0.775906 + 0.630849i \(0.782707\pi\)
\(524\) 0 0
\(525\) 150.545 609.603i 0.286752 1.16115i
\(526\) 0 0
\(527\) 712.470i 1.35193i
\(528\) 0 0
\(529\) 288.570 + 499.818i 0.545501 + 0.944835i
\(530\) 0 0
\(531\) −353.662 560.389i −0.666030 1.05535i
\(532\) 0 0
\(533\) −88.6738 51.1959i −0.166367 0.0960523i
\(534\) 0 0
\(535\) 711.926 1.33070
\(536\) 0 0
\(537\) 50.4439 + 174.446i 0.0939364 + 0.324854i
\(538\) 0 0
\(539\) 126.929i 0.235489i
\(540\) 0 0
\(541\) −239.705 415.182i −0.443079 0.767435i 0.554838 0.831959i \(-0.312780\pi\)
−0.997916 + 0.0645241i \(0.979447\pi\)
\(542\) 0 0
\(543\) −361.087 347.141i −0.664985 0.639302i
\(544\) 0 0
\(545\) −949.195 548.018i −1.74164 1.00554i
\(546\) 0 0
\(547\) 323.732 0.591831 0.295916 0.955214i \(-0.404375\pi\)
0.295916 + 0.955214i \(0.404375\pi\)
\(548\) 0 0
\(549\) −725.722 + 458.004i −1.32190 + 0.834252i
\(550\) 0 0
\(551\) 191.317 543.154i 0.347217 0.985761i
\(552\) 0 0
\(553\) 1.12827 0.00204028
\(554\) 0 0
\(555\) 152.124 + 526.079i 0.274097 + 0.947890i
\(556\) 0 0
\(557\) −139.331 + 80.4425i −0.250145 + 0.144421i −0.619830 0.784736i \(-0.712799\pi\)
0.369686 + 0.929157i \(0.379465\pi\)
\(558\) 0 0
\(559\) −1008.31 −1.80378
\(560\) 0 0
\(561\) 547.757 + 526.602i 0.976394 + 0.938685i
\(562\) 0 0
\(563\) −351.195 + 202.763i −0.623793 + 0.360147i −0.778344 0.627838i \(-0.783940\pi\)
0.154551 + 0.987985i \(0.450607\pi\)
\(564\) 0 0
\(565\) −166.493 288.375i −0.294679 0.510398i
\(566\) 0 0
\(567\) −344.910 501.619i −0.608307 0.884690i
\(568\) 0 0
\(569\) 937.203 + 541.095i 1.64711 + 0.950957i 0.978214 + 0.207597i \(0.0665644\pi\)
0.668892 + 0.743360i \(0.266769\pi\)
\(570\) 0 0
\(571\) −275.915 477.899i −0.483214 0.836951i 0.516600 0.856227i \(-0.327197\pi\)
−0.999814 + 0.0192758i \(0.993864\pi\)
\(572\) 0 0
\(573\) −447.389 110.485i −0.780784 0.192819i
\(574\) 0 0
\(575\) −802.154 463.124i −1.39505 0.805432i
\(576\) 0 0
\(577\) −7.66081 −0.0132770 −0.00663848 0.999978i \(-0.502113\pi\)
−0.00663848 + 0.999978i \(0.502113\pi\)
\(578\) 0 0
\(579\) −686.771 + 198.590i −1.18613 + 0.342988i
\(580\) 0 0
\(581\) −315.398 + 182.095i −0.542854 + 0.313417i
\(582\) 0 0
\(583\) −930.799 −1.59657
\(584\) 0 0
\(585\) −1326.85 + 52.2730i −2.26811 + 0.0893556i
\(586\) 0 0
\(587\) −686.241 + 396.201i −1.16906 + 0.674960i −0.953459 0.301521i \(-0.902506\pi\)
−0.215605 + 0.976481i \(0.569172\pi\)
\(588\) 0 0
\(589\) 166.706 + 891.125i 0.283033 + 1.51295i
\(590\) 0 0
\(591\) 91.3376 + 315.866i 0.154547 + 0.534460i
\(592\) 0 0
\(593\) −541.981 + 312.913i −0.913965 + 0.527678i −0.881705 0.471802i \(-0.843604\pi\)
−0.0322602 + 0.999480i \(0.510271\pi\)
\(594\) 0 0
\(595\) −407.908 706.518i −0.685560 1.18742i
\(596\) 0 0
\(597\) 547.986 + 526.822i 0.917899 + 0.882450i
\(598\) 0 0
\(599\) −150.471 86.8742i −0.251203 0.145032i 0.369112 0.929385i \(-0.379662\pi\)
−0.620315 + 0.784353i \(0.712995\pi\)
\(600\) 0 0
\(601\) −138.816 + 240.436i −0.230975 + 0.400060i −0.958095 0.286450i \(-0.907525\pi\)
0.727120 + 0.686510i \(0.240858\pi\)
\(602\) 0 0
\(603\) −0.417120 10.5878i −0.000691741 0.0175585i
\(604\) 0 0
\(605\) 1049.64 606.012i 1.73495 1.00167i
\(606\) 0 0
\(607\) 236.591 + 409.787i 0.389770 + 0.675102i 0.992418 0.122905i \(-0.0392211\pi\)
−0.602648 + 0.798007i \(0.705888\pi\)
\(608\) 0 0
\(609\) −663.423 163.836i −1.08937 0.269025i
\(610\) 0 0
\(611\) 1097.95 + 633.903i 1.79697 + 1.03748i
\(612\) 0 0
\(613\) 412.386 714.274i 0.672735 1.16521i −0.304391 0.952547i \(-0.598453\pi\)
0.977126 0.212663i \(-0.0682137\pi\)
\(614\) 0 0
\(615\) 105.700 30.5649i 0.171870 0.0496990i
\(616\) 0 0
\(617\) 449.661 + 259.612i 0.728786 + 0.420765i 0.817978 0.575250i \(-0.195095\pi\)
−0.0891918 + 0.996014i \(0.528428\pi\)
\(618\) 0 0
\(619\) 515.153 892.272i 0.832235 1.44147i −0.0640275 0.997948i \(-0.520395\pi\)
0.896262 0.443525i \(-0.146272\pi\)
\(620\) 0 0
\(621\) −852.154 + 283.212i −1.37223 + 0.456058i
\(622\) 0 0
\(623\) 584.992i 0.938992i
\(624\) 0 0
\(625\) −545.634 −0.873015
\(626\) 0 0
\(627\) −808.326 530.484i −1.28920 0.846067i
\(628\) 0 0
\(629\) 324.705 + 187.468i 0.516224 + 0.298042i
\(630\) 0 0
\(631\) 282.848 + 489.908i 0.448254 + 0.776399i 0.998273 0.0587536i \(-0.0187126\pi\)
−0.550018 + 0.835153i \(0.685379\pi\)
\(632\) 0 0
\(633\) −1136.81 + 328.727i −1.79591 + 0.519316i
\(634\) 0 0
\(635\) −177.432 + 102.440i −0.279420 + 0.161323i
\(636\) 0 0
\(637\) −151.868 −0.238412
\(638\) 0 0
\(639\) −128.409 + 5.05886i −0.200953 + 0.00791684i
\(640\) 0 0
\(641\) 427.649 246.903i 0.667159 0.385184i −0.127840 0.991795i \(-0.540805\pi\)
0.794999 + 0.606610i \(0.207471\pi\)
\(642\) 0 0
\(643\) 921.506 1.43314 0.716568 0.697518i \(-0.245712\pi\)
0.716568 + 0.697518i \(0.245712\pi\)
\(644\) 0 0
\(645\) 750.945 781.112i 1.16426 1.21103i
\(646\) 0 0
\(647\) 838.370i 1.29578i −0.761734 0.647890i \(-0.775652\pi\)
0.761734 0.647890i \(-0.224348\pi\)
\(648\) 0 0
\(649\) −624.454 + 1081.59i −0.962179 + 1.66654i
\(650\) 0 0
\(651\) 1033.47 298.843i 1.58751 0.459052i
\(652\) 0 0
\(653\) 671.238 387.539i 1.02793 0.593475i 0.111539 0.993760i \(-0.464422\pi\)
0.916391 + 0.400285i \(0.131089\pi\)
\(654\) 0 0
\(655\) 1832.62 2.79789
\(656\) 0 0
\(657\) 42.1885 + 1070.87i 0.0642139 + 1.62994i
\(658\) 0 0
\(659\) 82.4435i 0.125104i −0.998042 0.0625520i \(-0.980076\pi\)
0.998042 0.0625520i \(-0.0199239\pi\)
\(660\) 0 0
\(661\) −434.594 + 752.739i −0.657479 + 1.13879i 0.323787 + 0.946130i \(0.395044\pi\)
−0.981266 + 0.192657i \(0.938289\pi\)
\(662\) 0 0
\(663\) −630.073 + 655.384i −0.950336 + 0.988513i
\(664\) 0 0
\(665\) 675.507 + 788.236i 1.01580 + 1.18532i
\(666\) 0 0
\(667\) −504.012 + 872.974i −0.755640 + 1.30881i
\(668\) 0 0
\(669\) −422.189 405.883i −0.631074 0.606702i
\(670\) 0 0
\(671\) 1400.69 + 808.690i 2.08747 + 1.20520i
\(672\) 0 0
\(673\) −379.173 + 656.747i −0.563407 + 0.975850i 0.433789 + 0.901015i \(0.357176\pi\)
−0.997196 + 0.0748351i \(0.976157\pi\)
\(674\) 0 0
\(675\) 499.391 562.164i 0.739839 0.832836i
\(676\) 0 0
\(677\) 910.405 + 525.622i 1.34476 + 0.776400i 0.987502 0.157605i \(-0.0503773\pi\)
0.357261 + 0.934005i \(0.383711\pi\)
\(678\) 0 0
\(679\) −710.694 −1.04668
\(680\) 0 0
\(681\) 851.742 + 210.342i 1.25072 + 0.308873i
\(682\) 0 0
\(683\) 834.766i 1.22221i −0.791551 0.611103i \(-0.790726\pi\)
0.791551 0.611103i \(-0.209274\pi\)
\(684\) 0 0
\(685\) −627.697 −0.916345
\(686\) 0 0
\(687\) 304.834 + 293.061i 0.443718 + 0.426581i
\(688\) 0 0
\(689\) 1113.69i 1.61638i
\(690\) 0 0
\(691\) 41.2273 71.4077i 0.0596632 0.103340i −0.834651 0.550779i \(-0.814331\pi\)
0.894314 + 0.447439i \(0.147664\pi\)
\(692\) 0 0
\(693\) −534.104 + 1015.43i −0.770713 + 1.46526i
\(694\) 0 0
\(695\) 1042.17 + 601.699i 1.49953 + 0.865754i
\(696\) 0 0
\(697\) 37.6663 65.2400i 0.0540407 0.0936012i
\(698\) 0 0
\(699\) 669.100 + 165.238i 0.957225 + 0.236392i
\(700\) 0 0
\(701\) −44.1386 25.4834i −0.0629652 0.0363530i 0.468187 0.883629i \(-0.344907\pi\)
−0.531152 + 0.847276i \(0.678241\pi\)
\(702\) 0 0
\(703\) −449.990 158.501i −0.640100 0.225464i
\(704\) 0 0
\(705\) −1308.77 + 378.452i −1.85641 + 0.536811i
\(706\) 0 0
\(707\) 551.750 + 318.553i 0.780410 + 0.450570i
\(708\) 0 0
\(709\) −210.795 −0.297313 −0.148657 0.988889i \(-0.547495\pi\)
−0.148657 + 0.988889i \(0.547495\pi\)
\(710\) 0 0
\(711\) 1.19580 + 0.628981i 0.00168186 + 0.000884642i
\(712\) 0 0
\(713\) 1586.94i 2.22572i
\(714\) 0 0
\(715\) 1251.33 + 2167.36i 1.75011 + 3.03127i
\(716\) 0 0
\(717\) 488.899 508.539i 0.681867 0.709259i
\(718\) 0 0
\(719\) 399.243 + 230.503i 0.555276 + 0.320589i 0.751247 0.660021i \(-0.229453\pi\)
−0.195971 + 0.980610i \(0.562786\pi\)
\(720\) 0 0
\(721\) −52.6341 −0.0730015
\(722\) 0 0
\(723\) −199.396 + 57.6584i −0.275790 + 0.0797488i
\(724\) 0 0
\(725\) 844.088i 1.16426i
\(726\) 0 0
\(727\) −267.029 462.507i −0.367302 0.636186i 0.621841 0.783144i \(-0.286385\pi\)
−0.989143 + 0.146958i \(0.953052\pi\)
\(728\) 0 0
\(729\) −85.9153 723.920i −0.117854 0.993031i
\(730\) 0 0
\(731\) 741.845i 1.01484i
\(732\) 0 0
\(733\) 262.174 + 454.098i 0.357672 + 0.619506i 0.987571 0.157171i \(-0.0502372\pi\)
−0.629899 + 0.776677i \(0.716904\pi\)
\(734\) 0 0
\(735\) 113.105 117.648i 0.153884 0.160066i
\(736\) 0 0
\(737\) −17.2948 + 9.98514i −0.0234664 + 0.0135484i
\(738\) 0 0
\(739\) −16.8402 + 29.1681i −0.0227878 + 0.0394696i −0.877194 0.480135i \(-0.840588\pi\)
0.854407 + 0.519605i \(0.173921\pi\)
\(740\) 0 0
\(741\) 634.717 967.152i 0.856569 1.30520i
\(742\) 0 0
\(743\) 12.7053i 0.0171000i 0.999963 + 0.00855001i \(0.00272159\pi\)
−0.999963 + 0.00855001i \(0.997278\pi\)
\(744\) 0 0
\(745\) 1425.35 1.91321
\(746\) 0 0
\(747\) −435.788 + 17.1685i −0.583384 + 0.0229832i
\(748\) 0 0
\(749\) 637.387 + 367.995i 0.850983 + 0.491316i
\(750\) 0 0
\(751\) 734.945 1272.96i 0.978622 1.69502i 0.311197 0.950345i \(-0.399270\pi\)
0.667424 0.744678i \(-0.267397\pi\)
\(752\) 0 0
\(753\) 44.7439 46.5414i 0.0594209 0.0618079i
\(754\) 0 0
\(755\) −5.19877 3.00151i −0.00688579 0.00397551i
\(756\) 0 0
\(757\) −141.145 + 244.470i −0.186453 + 0.322945i −0.944065 0.329759i \(-0.893032\pi\)
0.757612 + 0.652705i \(0.226366\pi\)
\(758\) 0 0
\(759\) 1220.06 + 1172.94i 1.60746 + 1.54538i
\(760\) 0 0
\(761\) 917.495 529.716i 1.20564 0.696079i 0.243839 0.969816i \(-0.421593\pi\)
0.961805 + 0.273737i \(0.0882597\pi\)
\(762\) 0 0
\(763\) −566.542 981.279i −0.742519 1.28608i
\(764\) 0 0
\(765\) −38.4588 976.201i −0.0502730 1.27608i
\(766\) 0 0
\(767\) −1294.10 747.152i −1.68723 0.974122i
\(768\) 0 0
\(769\) 548.055 949.259i 0.712685 1.23441i −0.251160 0.967946i \(-0.580812\pi\)
0.963845 0.266462i \(-0.0858546\pi\)
\(770\) 0 0
\(771\) 848.612 + 209.570i 1.10066 + 0.271815i
\(772\) 0 0
\(773\) −428.849 + 247.596i −0.554786 + 0.320306i −0.751050 0.660245i \(-0.770452\pi\)
0.196264 + 0.980551i \(0.437119\pi\)
\(774\) 0 0
\(775\) 664.425 + 1150.82i 0.857323 + 1.48493i
\(776\) 0 0
\(777\) −135.734 + 549.630i −0.174690 + 0.707375i
\(778\) 0 0
\(779\) −31.8462 + 90.4125i −0.0408809 + 0.116062i
\(780\) 0 0
\(781\) 121.101 + 209.752i 0.155058 + 0.268569i
\(782\) 0 0
\(783\) −611.797 543.482i −0.781349 0.694102i
\(784\) 0 0
\(785\) 934.247i 1.19012i
\(786\) 0 0
\(787\) −134.383 232.757i −0.170753 0.295753i 0.767930 0.640533i \(-0.221287\pi\)
−0.938683 + 0.344781i \(0.887953\pi\)
\(788\) 0 0
\(789\) 338.072 351.654i 0.428482 0.445695i
\(790\) 0 0
\(791\) 344.242i 0.435199i
\(792\) 0 0
\(793\) −967.587 + 1675.91i −1.22016 + 2.11338i
\(794\) 0 0
\(795\) 862.745 + 829.425i 1.08521 + 1.04330i
\(796\) 0 0