Properties

Label 684.3.m.a.353.10
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 353.10
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +O(q^{10})\) \(q+(-2.11779 - 2.12485i) q^{3} +8.55202i q^{5} +(-5.68709 + 9.85033i) q^{7} +(-0.0299448 + 8.99995i) q^{9} +(12.9413 + 7.47166i) q^{11} +(-0.847351 + 1.46766i) q^{13} +(18.1717 - 18.1114i) q^{15} +(-22.9277 - 13.2373i) q^{17} +(1.22562 + 18.9604i) q^{19} +(32.9745 - 8.77672i) q^{21} +(-2.95885 - 1.70829i) q^{23} -48.1370 q^{25} +(19.1869 - 18.9964i) q^{27} -11.0579i q^{29} +(-18.4894 - 32.0245i) q^{31} +(-11.5308 - 43.3216i) q^{33} +(-84.2401 - 48.6361i) q^{35} +55.7350 q^{37} +(4.91305 - 1.30769i) q^{39} -45.0347i q^{41} +(12.0594 + 20.8875i) q^{43} +(-76.9677 - 0.256089i) q^{45} +88.7028i q^{47} +(-40.1859 - 69.6041i) q^{49} +(20.4288 + 76.7517i) q^{51} +(-49.9793 + 28.8555i) q^{53} +(-63.8977 + 110.674i) q^{55} +(37.6924 - 42.7584i) q^{57} -23.5787i q^{59} +32.3568 q^{61} +(-88.4821 - 51.4785i) q^{63} +(-12.5514 - 7.24656i) q^{65} +(-28.6083 + 49.5510i) q^{67} +(2.63636 + 9.90491i) q^{69} +(51.0876 + 29.4954i) q^{71} +(39.1711 - 67.8463i) q^{73} +(101.944 + 102.284i) q^{75} +(-147.197 + 84.9839i) q^{77} +(26.4100 + 45.7434i) q^{79} +(-80.9982 - 0.539004i) q^{81} +(-60.4098 - 34.8776i) q^{83} +(113.206 - 196.078i) q^{85} +(-23.4963 + 23.4182i) q^{87} +(-9.10392 + 5.25615i) q^{89} +(-9.63792 - 16.6934i) q^{91} +(-28.8906 + 107.108i) q^{93} +(-162.150 + 10.4815i) q^{95} +(-41.4092 - 71.7229i) q^{97} +(-67.6321 + 116.247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

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
\(3\) −2.11779 2.12485i −0.705929 0.708282i
\(4\) 0 0
\(5\) 8.55202i 1.71040i 0.518296 + 0.855202i \(0.326567\pi\)
−0.518296 + 0.855202i \(0.673433\pi\)
\(6\) 0 0
\(7\) −5.68709 + 9.85033i −0.812441 + 1.40719i 0.0987097 + 0.995116i \(0.468528\pi\)
−0.911151 + 0.412073i \(0.864805\pi\)
\(8\) 0 0
\(9\) −0.0299448 + 8.99995i −0.00332720 + 0.999994i
\(10\) 0 0
\(11\) 12.9413 + 7.47166i 1.17648 + 0.679242i 0.955198 0.295968i \(-0.0956422\pi\)
0.221283 + 0.975210i \(0.428976\pi\)
\(12\) 0 0
\(13\) −0.847351 + 1.46766i −0.0651809 + 0.112897i −0.896774 0.442488i \(-0.854096\pi\)
0.831593 + 0.555385i \(0.187429\pi\)
\(14\) 0 0
\(15\) 18.1717 18.1114i 1.21145 1.20742i
\(16\) 0 0
\(17\) −22.9277 13.2373i −1.34869 0.778666i −0.360625 0.932711i \(-0.617436\pi\)
−0.988064 + 0.154045i \(0.950770\pi\)
\(18\) 0 0
\(19\) 1.22562 + 18.9604i 0.0645064 + 0.997917i
\(20\) 0 0
\(21\) 32.9745 8.77672i 1.57021 0.417939i
\(22\) 0 0
\(23\) −2.95885 1.70829i −0.128646 0.0742736i 0.434296 0.900770i \(-0.356997\pi\)
−0.562942 + 0.826497i \(0.690330\pi\)
\(24\) 0 0
\(25\) −48.1370 −1.92548
\(26\) 0 0
\(27\) 19.1869 18.9964i 0.710627 0.703569i
\(28\) 0 0
\(29\) 11.0579i 0.381306i −0.981658 0.190653i \(-0.938940\pi\)
0.981658 0.190653i \(-0.0610605\pi\)
\(30\) 0 0
\(31\) −18.4894 32.0245i −0.596431 1.03305i −0.993343 0.115192i \(-0.963252\pi\)
0.396912 0.917857i \(-0.370082\pi\)
\(32\) 0 0
\(33\) −11.5308 43.3216i −0.349418 1.31278i
\(34\) 0 0
\(35\) −84.2401 48.6361i −2.40686 1.38960i
\(36\) 0 0
\(37\) 55.7350 1.50635 0.753176 0.657819i \(-0.228521\pi\)
0.753176 + 0.657819i \(0.228521\pi\)
\(38\) 0 0
\(39\) 4.91305 1.30769i 0.125976 0.0335306i
\(40\) 0 0
\(41\) 45.0347i 1.09841i −0.835688 0.549204i \(-0.814931\pi\)
0.835688 0.549204i \(-0.185069\pi\)
\(42\) 0 0
\(43\) 12.0594 + 20.8875i 0.280451 + 0.485755i 0.971496 0.237057i \(-0.0761827\pi\)
−0.691045 + 0.722812i \(0.742849\pi\)
\(44\) 0 0
\(45\) −76.9677 0.256089i −1.71039 0.00569086i
\(46\) 0 0
\(47\) 88.7028i 1.88729i 0.330954 + 0.943647i \(0.392629\pi\)
−0.330954 + 0.943647i \(0.607371\pi\)
\(48\) 0 0
\(49\) −40.1859 69.6041i −0.820121 1.42049i
\(50\) 0 0
\(51\) 20.4288 + 76.7517i 0.400564 + 1.50493i
\(52\) 0 0
\(53\) −49.9793 + 28.8555i −0.943005 + 0.544444i −0.890901 0.454197i \(-0.849926\pi\)
−0.0521040 + 0.998642i \(0.516593\pi\)
\(54\) 0 0
\(55\) −63.8977 + 110.674i −1.16178 + 2.01226i
\(56\) 0 0
\(57\) 37.6924 42.7584i 0.661270 0.750148i
\(58\) 0 0
\(59\) 23.5787i 0.399640i −0.979833 0.199820i \(-0.935964\pi\)
0.979833 0.199820i \(-0.0640357\pi\)
\(60\) 0 0
\(61\) 32.3568 0.530439 0.265220 0.964188i \(-0.414556\pi\)
0.265220 + 0.964188i \(0.414556\pi\)
\(62\) 0 0
\(63\) −88.4821 51.4785i −1.40448 0.817119i
\(64\) 0 0
\(65\) −12.5514 7.24656i −0.193099 0.111486i
\(66\) 0 0
\(67\) −28.6083 + 49.5510i −0.426989 + 0.739567i −0.996604 0.0823446i \(-0.973759\pi\)
0.569615 + 0.821912i \(0.307093\pi\)
\(68\) 0 0
\(69\) 2.63636 + 9.90491i 0.0382081 + 0.143549i
\(70\) 0 0
\(71\) 51.0876 + 29.4954i 0.719543 + 0.415429i 0.814585 0.580045i \(-0.196965\pi\)
−0.0950412 + 0.995473i \(0.530298\pi\)
\(72\) 0 0
\(73\) 39.1711 67.8463i 0.536590 0.929401i −0.462495 0.886622i \(-0.653046\pi\)
0.999085 0.0427787i \(-0.0136210\pi\)
\(74\) 0 0
\(75\) 101.944 + 102.284i 1.35925 + 1.36378i
\(76\) 0 0
\(77\) −147.197 + 84.9839i −1.91164 + 1.10369i
\(78\) 0 0
\(79\) 26.4100 + 45.7434i 0.334303 + 0.579030i 0.983351 0.181718i \(-0.0581657\pi\)
−0.649047 + 0.760748i \(0.724832\pi\)
\(80\) 0 0
\(81\) −80.9982 0.539004i −0.999978 0.00665437i
\(82\) 0 0
\(83\) −60.4098 34.8776i −0.727828 0.420212i 0.0897988 0.995960i \(-0.471378\pi\)
−0.817627 + 0.575748i \(0.804711\pi\)
\(84\) 0 0
\(85\) 113.206 196.078i 1.33183 2.30680i
\(86\) 0 0
\(87\) −23.4963 + 23.4182i −0.270072 + 0.269175i
\(88\) 0 0
\(89\) −9.10392 + 5.25615i −0.102291 + 0.0590579i −0.550273 0.834985i \(-0.685476\pi\)
0.447982 + 0.894043i \(0.352143\pi\)
\(90\) 0 0
\(91\) −9.63792 16.6934i −0.105911 0.183444i
\(92\) 0 0
\(93\) −28.8906 + 107.108i −0.310652 + 1.15170i
\(94\) 0 0
\(95\) −162.150 + 10.4815i −1.70684 + 0.110332i
\(96\) 0 0
\(97\) −41.4092 71.7229i −0.426899 0.739412i 0.569696 0.821855i \(-0.307061\pi\)
−0.996596 + 0.0824438i \(0.973728\pi\)
\(98\) 0 0
\(99\) −67.6321 + 116.247i −0.683152 + 1.17421i
\(100\) 0 0
\(101\) 60.8711i 0.602684i 0.953516 + 0.301342i \(0.0974346\pi\)
−0.953516 + 0.301342i \(0.902565\pi\)
\(102\) 0 0
\(103\) −63.9370 110.742i −0.620747 1.07517i −0.989347 0.145578i \(-0.953496\pi\)
0.368599 0.929588i \(-0.379837\pi\)
\(104\) 0 0
\(105\) 75.0586 + 281.998i 0.714844 + 2.68570i
\(106\) 0 0
\(107\) 7.27245i 0.0679668i 0.999422 + 0.0339834i \(0.0108193\pi\)
−0.999422 + 0.0339834i \(0.989181\pi\)
\(108\) 0 0
\(109\) 57.9610 100.391i 0.531752 0.921022i −0.467561 0.883961i \(-0.654867\pi\)
0.999313 0.0370607i \(-0.0117995\pi\)
\(110\) 0 0
\(111\) −118.035 118.428i −1.06338 1.06692i
\(112\) 0 0
\(113\) −162.932 + 94.0691i −1.44188 + 0.832469i −0.997975 0.0636047i \(-0.979740\pi\)
−0.443904 + 0.896074i \(0.646407\pi\)
\(114\) 0 0
\(115\) 14.6093 25.3041i 0.127038 0.220036i
\(116\) 0 0
\(117\) −13.1835 7.67007i −0.112679 0.0655561i
\(118\) 0 0
\(119\) 260.784 150.564i 2.19146 1.26524i
\(120\) 0 0
\(121\) 51.1513 + 88.5967i 0.422738 + 0.732204i
\(122\) 0 0
\(123\) −95.6919 + 95.3740i −0.777983 + 0.775399i
\(124\) 0 0
\(125\) 197.868i 1.58294i
\(126\) 0 0
\(127\) 52.5288 + 90.9825i 0.413612 + 0.716398i 0.995282 0.0970277i \(-0.0309336\pi\)
−0.581669 + 0.813425i \(0.697600\pi\)
\(128\) 0 0
\(129\) 18.8434 69.8596i 0.146073 0.541547i
\(130\) 0 0
\(131\) 31.2636i 0.238654i −0.992855 0.119327i \(-0.961926\pi\)
0.992855 0.119327i \(-0.0380736\pi\)
\(132\) 0 0
\(133\) −193.737 95.7569i −1.45667 0.719976i
\(134\) 0 0
\(135\) 162.457 + 164.087i 1.20339 + 1.21546i
\(136\) 0 0
\(137\) 46.3064i 0.338003i 0.985616 + 0.169001i \(0.0540543\pi\)
−0.985616 + 0.169001i \(0.945946\pi\)
\(138\) 0 0
\(139\) 7.87782 13.6448i 0.0566749 0.0981639i −0.836296 0.548278i \(-0.815283\pi\)
0.892971 + 0.450114i \(0.148617\pi\)
\(140\) 0 0
\(141\) 188.480 187.854i 1.33674 1.33230i
\(142\) 0 0
\(143\) −21.9316 + 12.6622i −0.153368 + 0.0885471i
\(144\) 0 0
\(145\) 94.5670 0.652186
\(146\) 0 0
\(147\) −62.7927 + 232.796i −0.427161 + 1.58364i
\(148\) 0 0
\(149\) 259.890i 1.74423i −0.489305 0.872113i \(-0.662749\pi\)
0.489305 0.872113i \(-0.337251\pi\)
\(150\) 0 0
\(151\) 55.7981 96.6452i 0.369524 0.640035i −0.619967 0.784628i \(-0.712854\pi\)
0.989491 + 0.144593i \(0.0461874\pi\)
\(152\) 0 0
\(153\) 119.822 205.952i 0.783149 1.34609i
\(154\) 0 0
\(155\) 273.874 158.121i 1.76693 1.02014i
\(156\) 0 0
\(157\) 69.6329 0.443522 0.221761 0.975101i \(-0.428820\pi\)
0.221761 + 0.975101i \(0.428820\pi\)
\(158\) 0 0
\(159\) 167.159 + 45.0883i 1.05132 + 0.283574i
\(160\) 0 0
\(161\) 33.6545 19.4304i 0.209034 0.120686i
\(162\) 0 0
\(163\) −201.458 −1.23594 −0.617969 0.786203i \(-0.712044\pi\)
−0.617969 + 0.786203i \(0.712044\pi\)
\(164\) 0 0
\(165\) 370.487 98.6115i 2.24538 0.597645i
\(166\) 0 0
\(167\) 87.5324 + 50.5369i 0.524146 + 0.302616i 0.738629 0.674112i \(-0.235473\pi\)
−0.214483 + 0.976728i \(0.568807\pi\)
\(168\) 0 0
\(169\) 83.0640 + 143.871i 0.491503 + 0.851308i
\(170\) 0 0
\(171\) −170.680 + 10.4628i −0.998126 + 0.0611858i
\(172\) 0 0
\(173\) −135.808 + 78.4086i −0.785016 + 0.453229i −0.838205 0.545355i \(-0.816395\pi\)
0.0531893 + 0.998584i \(0.483061\pi\)
\(174\) 0 0
\(175\) 273.759 474.165i 1.56434 2.70951i
\(176\) 0 0
\(177\) −50.1012 + 49.9348i −0.283058 + 0.282117i
\(178\) 0 0
\(179\) 211.533i 1.18175i 0.806764 + 0.590874i \(0.201217\pi\)
−0.806764 + 0.590874i \(0.798783\pi\)
\(180\) 0 0
\(181\) −149.964 259.745i −0.828529 1.43505i −0.899192 0.437554i \(-0.855845\pi\)
0.0706634 0.997500i \(-0.477488\pi\)
\(182\) 0 0
\(183\) −68.5248 68.7532i −0.374453 0.375701i
\(184\) 0 0
\(185\) 476.647i 2.57647i
\(186\) 0 0
\(187\) −197.809 342.616i −1.05780 1.83217i
\(188\) 0 0
\(189\) 78.0026 + 297.031i 0.412712 + 1.57160i
\(190\) 0 0
\(191\) −2.94629 1.70104i −0.0154256 0.00890598i 0.492267 0.870444i \(-0.336168\pi\)
−0.507693 + 0.861538i \(0.669502\pi\)
\(192\) 0 0
\(193\) −117.968 −0.611233 −0.305617 0.952155i \(-0.598863\pi\)
−0.305617 + 0.952155i \(0.598863\pi\)
\(194\) 0 0
\(195\) 11.1834 + 42.0165i 0.0573508 + 0.215469i
\(196\) 0 0
\(197\) 211.815i 1.07520i 0.843200 + 0.537600i \(0.180669\pi\)
−0.843200 + 0.537600i \(0.819331\pi\)
\(198\) 0 0
\(199\) 17.4240 + 30.1792i 0.0875576 + 0.151654i 0.906478 0.422253i \(-0.138760\pi\)
−0.818921 + 0.573907i \(0.805427\pi\)
\(200\) 0 0
\(201\) 165.875 44.1503i 0.825247 0.219653i
\(202\) 0 0
\(203\) 108.924 + 62.8870i 0.536569 + 0.309788i
\(204\) 0 0
\(205\) 385.138 1.87872
\(206\) 0 0
\(207\) 15.4632 26.5784i 0.0747012 0.128398i
\(208\) 0 0
\(209\) −125.805 + 254.530i −0.601936 + 1.21785i
\(210\) 0 0
\(211\) 221.862 1.05148 0.525740 0.850645i \(-0.323788\pi\)
0.525740 + 0.850645i \(0.323788\pi\)
\(212\) 0 0
\(213\) −45.5194 171.018i −0.213706 0.802903i
\(214\) 0 0
\(215\) −178.630 + 103.132i −0.830837 + 0.479684i
\(216\) 0 0
\(217\) 420.602 1.93826
\(218\) 0 0
\(219\) −227.119 + 60.4515i −1.03707 + 0.276034i
\(220\) 0 0
\(221\) 38.8556 22.4333i 0.175817 0.101508i
\(222\) 0 0
\(223\) 159.876 + 276.914i 0.716934 + 1.24177i 0.962209 + 0.272312i \(0.0877884\pi\)
−0.245275 + 0.969454i \(0.578878\pi\)
\(224\) 0 0
\(225\) 1.44145 433.230i 0.00640646 1.92547i
\(226\) 0 0
\(227\) −150.571 86.9322i −0.663308 0.382961i 0.130228 0.991484i \(-0.458429\pi\)
−0.793536 + 0.608523i \(0.791762\pi\)
\(228\) 0 0
\(229\) 156.869 + 271.705i 0.685017 + 1.18648i 0.973432 + 0.228978i \(0.0735384\pi\)
−0.288415 + 0.957506i \(0.593128\pi\)
\(230\) 0 0
\(231\) 492.309 + 132.792i 2.13121 + 0.574857i
\(232\) 0 0
\(233\) −41.0716 23.7127i −0.176273 0.101771i 0.409268 0.912414i \(-0.365784\pi\)
−0.585540 + 0.810643i \(0.699118\pi\)
\(234\) 0 0
\(235\) −758.588 −3.22803
\(236\) 0 0
\(237\) 41.2670 152.992i 0.174122 0.645536i
\(238\) 0 0
\(239\) −15.4509 + 8.92060i −0.0646483 + 0.0373247i −0.531976 0.846760i \(-0.678550\pi\)
0.467327 + 0.884084i \(0.345217\pi\)
\(240\) 0 0
\(241\) 248.187 1.02982 0.514912 0.857243i \(-0.327825\pi\)
0.514912 + 0.857243i \(0.327825\pi\)
\(242\) 0 0
\(243\) 170.392 + 173.250i 0.701201 + 0.712964i
\(244\) 0 0
\(245\) 595.255 343.671i 2.42961 1.40274i
\(246\) 0 0
\(247\) −28.8659 14.2674i −0.116866 0.0577626i
\(248\) 0 0
\(249\) 53.8256 + 202.225i 0.216167 + 0.812148i
\(250\) 0 0
\(251\) −172.100 + 99.3621i −0.685658 + 0.395865i −0.801984 0.597346i \(-0.796222\pi\)
0.116325 + 0.993211i \(0.462889\pi\)
\(252\) 0 0
\(253\) −25.5276 44.2150i −0.100899 0.174763i
\(254\) 0 0
\(255\) −656.382 + 174.707i −2.57405 + 0.685126i
\(256\) 0 0
\(257\) −279.705 161.488i −1.08835 0.628357i −0.155210 0.987881i \(-0.549605\pi\)
−0.933135 + 0.359525i \(0.882939\pi\)
\(258\) 0 0
\(259\) −316.970 + 549.008i −1.22382 + 2.11972i
\(260\) 0 0
\(261\) 99.5202 + 0.331126i 0.381304 + 0.00126868i
\(262\) 0 0
\(263\) −281.674 + 162.624i −1.07100 + 0.618343i −0.928455 0.371445i \(-0.878863\pi\)
−0.142547 + 0.989788i \(0.545529\pi\)
\(264\) 0 0
\(265\) −246.773 427.423i −0.931219 1.61292i
\(266\) 0 0
\(267\) 30.4487 + 8.21301i 0.114040 + 0.0307604i
\(268\) 0 0
\(269\) −341.263 197.028i −1.26864 0.732448i −0.293907 0.955834i \(-0.594956\pi\)
−0.974730 + 0.223386i \(0.928289\pi\)
\(270\) 0 0
\(271\) 31.9450 55.3304i 0.117878 0.204171i −0.801048 0.598600i \(-0.795724\pi\)
0.918927 + 0.394428i \(0.129057\pi\)
\(272\) 0 0
\(273\) −15.0598 + 55.8321i −0.0551640 + 0.204513i
\(274\) 0 0
\(275\) −622.954 359.663i −2.26529 1.30787i
\(276\) 0 0
\(277\) −99.8043 + 172.866i −0.360304 + 0.624066i −0.988011 0.154385i \(-0.950661\pi\)
0.627706 + 0.778450i \(0.283994\pi\)
\(278\) 0 0
\(279\) 288.773 165.444i 1.03503 0.592990i
\(280\) 0 0
\(281\) 388.747i 1.38344i 0.722166 + 0.691720i \(0.243147\pi\)
−0.722166 + 0.691720i \(0.756853\pi\)
\(282\) 0 0
\(283\) 431.751 1.52562 0.762811 0.646621i \(-0.223819\pi\)
0.762811 + 0.646621i \(0.223819\pi\)
\(284\) 0 0
\(285\) 365.671 + 322.346i 1.28306 + 1.13104i
\(286\) 0 0
\(287\) 443.607 + 256.116i 1.54567 + 0.892392i
\(288\) 0 0
\(289\) 205.953 + 356.721i 0.712640 + 1.23433i
\(290\) 0 0
\(291\) −64.7042 + 239.882i −0.222351 + 0.824338i
\(292\) 0 0
\(293\) 329.972 190.510i 1.12618 0.650203i 0.183212 0.983073i \(-0.441350\pi\)
0.942973 + 0.332870i \(0.108017\pi\)
\(294\) 0 0
\(295\) 201.646 0.683545
\(296\) 0 0
\(297\) 390.238 102.479i 1.31393 0.345048i
\(298\) 0 0
\(299\) 5.01437 2.89505i 0.0167705 0.00968244i
\(300\) 0 0
\(301\) −274.331 −0.911399
\(302\) 0 0
\(303\) 129.342 128.912i 0.426870 0.425452i
\(304\) 0 0
\(305\) 276.716i 0.907265i
\(306\) 0 0
\(307\) −201.382 + 348.804i −0.655968 + 1.13617i 0.325682 + 0.945479i \(0.394406\pi\)
−0.981650 + 0.190690i \(0.938927\pi\)
\(308\) 0 0
\(309\) −99.9050 + 370.385i −0.323317 + 1.19866i
\(310\) 0 0
\(311\) −6.94866 + 4.01181i −0.0223430 + 0.0128997i −0.511130 0.859503i \(-0.670773\pi\)
0.488787 + 0.872403i \(0.337440\pi\)
\(312\) 0 0
\(313\) 481.944 1.53976 0.769879 0.638190i \(-0.220317\pi\)
0.769879 + 0.638190i \(0.220317\pi\)
\(314\) 0 0
\(315\) 440.245 756.701i 1.39760 2.40222i
\(316\) 0 0
\(317\) 5.80886i 0.0183245i 0.999958 + 0.00916225i \(0.00291647\pi\)
−0.999958 + 0.00916225i \(0.997084\pi\)
\(318\) 0 0
\(319\) 82.6206 143.103i 0.258999 0.448599i
\(320\) 0 0
\(321\) 15.4528 15.4015i 0.0481397 0.0479798i
\(322\) 0 0
\(323\) 222.884 450.943i 0.690045 1.39611i
\(324\) 0 0
\(325\) 40.7889 70.6485i 0.125504 0.217380i
\(326\) 0 0
\(327\) −336.065 + 89.4495i −1.02772 + 0.273546i
\(328\) 0 0
\(329\) −873.751 504.461i −2.65578 1.53331i
\(330\) 0 0
\(331\) 190.031 329.143i 0.574110 0.994388i −0.422027 0.906583i \(-0.638681\pi\)
0.996138 0.0878052i \(-0.0279853\pi\)
\(332\) 0 0
\(333\) −1.66898 + 501.612i −0.00501194 + 1.50634i
\(334\) 0 0
\(335\) −423.761 244.659i −1.26496 0.730324i
\(336\) 0 0
\(337\) −91.0767 −0.270257 −0.135129 0.990828i \(-0.543145\pi\)
−0.135129 + 0.990828i \(0.543145\pi\)
\(338\) 0 0
\(339\) 544.939 + 146.988i 1.60749 + 0.433593i
\(340\) 0 0
\(341\) 552.585i 1.62048i
\(342\) 0 0
\(343\) 356.829 1.04032
\(344\) 0 0
\(345\) −84.7069 + 22.5462i −0.245527 + 0.0653512i
\(346\) 0 0
\(347\) 515.909i 1.48677i 0.668863 + 0.743385i \(0.266781\pi\)
−0.668863 + 0.743385i \(0.733219\pi\)
\(348\) 0 0
\(349\) −83.2922 + 144.266i −0.238660 + 0.413371i −0.960330 0.278866i \(-0.910041\pi\)
0.721670 + 0.692237i \(0.243375\pi\)
\(350\) 0 0
\(351\) 11.6220 + 44.2564i 0.0331112 + 0.126087i
\(352\) 0 0
\(353\) −323.433 186.734i −0.916241 0.528992i −0.0338071 0.999428i \(-0.510763\pi\)
−0.882434 + 0.470436i \(0.844097\pi\)
\(354\) 0 0
\(355\) −252.245 + 436.902i −0.710550 + 1.23071i
\(356\) 0 0
\(357\) −872.209 235.264i −2.44316 0.659002i
\(358\) 0 0
\(359\) −425.053 245.405i −1.18399 0.683578i −0.227058 0.973881i \(-0.572911\pi\)
−0.956935 + 0.290303i \(0.906244\pi\)
\(360\) 0 0
\(361\) −357.996 + 46.4766i −0.991678 + 0.128744i
\(362\) 0 0
\(363\) 79.9267 296.318i 0.220184 0.816302i
\(364\) 0 0
\(365\) 580.222 + 334.991i 1.58965 + 0.917785i
\(366\) 0 0
\(367\) 582.904 1.58829 0.794147 0.607726i \(-0.207918\pi\)
0.794147 + 0.607726i \(0.207918\pi\)
\(368\) 0 0
\(369\) 405.310 + 1.34856i 1.09840 + 0.00365463i
\(370\) 0 0
\(371\) 656.416i 1.76932i
\(372\) 0 0
\(373\) −230.863 399.867i −0.618936 1.07203i −0.989680 0.143293i \(-0.954231\pi\)
0.370744 0.928735i \(-0.379103\pi\)
\(374\) 0 0
\(375\) −420.439 + 419.042i −1.12117 + 1.11745i
\(376\) 0 0
\(377\) 16.2291 + 9.36989i 0.0430481 + 0.0248538i
\(378\) 0 0
\(379\) 117.960 0.311240 0.155620 0.987817i \(-0.450262\pi\)
0.155620 + 0.987817i \(0.450262\pi\)
\(380\) 0 0
\(381\) 82.0790 304.297i 0.215430 0.798680i
\(382\) 0 0
\(383\) 532.359i 1.38997i −0.719024 0.694986i \(-0.755411\pi\)
0.719024 0.694986i \(-0.244589\pi\)
\(384\) 0 0
\(385\) −726.784 1258.83i −1.88775 3.26968i
\(386\) 0 0
\(387\) −188.347 + 107.908i −0.486686 + 0.278833i
\(388\) 0 0
\(389\) 204.479i 0.525653i −0.964843 0.262826i \(-0.915345\pi\)
0.964843 0.262826i \(-0.0846546\pi\)
\(390\) 0 0
\(391\) 45.2264 + 78.3345i 0.115669 + 0.200344i
\(392\) 0 0
\(393\) −66.4304 + 66.2097i −0.169034 + 0.168473i
\(394\) 0 0
\(395\) −391.198 + 225.858i −0.990375 + 0.571793i
\(396\) 0 0
\(397\) 139.246 241.180i 0.350745 0.607508i −0.635635 0.771989i \(-0.719262\pi\)
0.986380 + 0.164482i \(0.0525952\pi\)
\(398\) 0 0
\(399\) 206.825 + 614.453i 0.518357 + 1.53998i
\(400\) 0 0
\(401\) 792.290i 1.97579i 0.155139 + 0.987893i \(0.450417\pi\)
−0.155139 + 0.987893i \(0.549583\pi\)
\(402\) 0 0
\(403\) 62.6679 0.155504
\(404\) 0 0
\(405\) 4.60957 692.698i 0.0113817 1.71037i
\(406\) 0 0
\(407\) 721.283 + 416.433i 1.77219 + 1.02318i
\(408\) 0 0
\(409\) −340.011 + 588.917i −0.831324 + 1.43989i 0.0656652 + 0.997842i \(0.479083\pi\)
−0.896989 + 0.442053i \(0.854250\pi\)
\(410\) 0 0
\(411\) 98.3940 98.0672i 0.239401 0.238606i
\(412\) 0 0
\(413\) 232.258 + 134.094i 0.562369 + 0.324684i
\(414\) 0 0
\(415\) 298.274 516.625i 0.718732 1.24488i
\(416\) 0 0
\(417\) −45.6766 + 12.1576i −0.109536 + 0.0291549i
\(418\) 0 0
\(419\) −53.3836 + 30.8210i −0.127407 + 0.0735586i −0.562349 0.826900i \(-0.690102\pi\)
0.434942 + 0.900459i \(0.356769\pi\)
\(420\) 0 0
\(421\) 223.104 + 386.427i 0.529938 + 0.917880i 0.999390 + 0.0349216i \(0.0111182\pi\)
−0.469452 + 0.882958i \(0.655549\pi\)
\(422\) 0 0
\(423\) −798.321 2.65619i −1.88728 0.00627941i
\(424\) 0 0
\(425\) 1103.67 + 637.204i 2.59687 + 1.49930i
\(426\) 0 0
\(427\) −184.016 + 318.725i −0.430951 + 0.746428i
\(428\) 0 0
\(429\) 73.3519 + 19.7854i 0.170983 + 0.0461199i
\(430\) 0 0
\(431\) −43.4486 + 25.0851i −0.100809 + 0.0582020i −0.549557 0.835456i \(-0.685203\pi\)
0.448748 + 0.893658i \(0.351870\pi\)
\(432\) 0 0
\(433\) −281.978 488.400i −0.651219 1.12794i −0.982827 0.184527i \(-0.940925\pi\)
0.331609 0.943417i \(-0.392409\pi\)
\(434\) 0 0
\(435\) −200.273 200.940i −0.460398 0.461932i
\(436\) 0 0
\(437\) 28.7635 58.1948i 0.0658205 0.133169i
\(438\) 0 0
\(439\) 208.341 + 360.857i 0.474581 + 0.821998i 0.999576 0.0291067i \(-0.00926627\pi\)
−0.524995 + 0.851105i \(0.675933\pi\)
\(440\) 0 0
\(441\) 627.637 359.587i 1.42321 0.815390i
\(442\) 0 0
\(443\) 331.474i 0.748249i 0.927378 + 0.374125i \(0.122057\pi\)
−0.927378 + 0.374125i \(0.877943\pi\)
\(444\) 0 0
\(445\) −44.9507 77.8568i −0.101013 0.174959i
\(446\) 0 0
\(447\) −552.226 + 550.391i −1.23540 + 1.23130i
\(448\) 0 0
\(449\) 482.323i 1.07422i −0.843513 0.537108i \(-0.819517\pi\)
0.843513 0.537108i \(-0.180483\pi\)
\(450\) 0 0
\(451\) 336.484 582.807i 0.746084 1.29226i
\(452\) 0 0
\(453\) −323.525 + 86.1116i −0.714183 + 0.190092i
\(454\) 0 0
\(455\) 142.762 82.4237i 0.313763 0.181151i
\(456\) 0 0
\(457\) −164.410 + 284.767i −0.359760 + 0.623122i −0.987921 0.154961i \(-0.950475\pi\)
0.628161 + 0.778084i \(0.283808\pi\)
\(458\) 0 0
\(459\) −691.373 + 181.560i −1.50626 + 0.395554i
\(460\) 0 0
\(461\) −84.5382 + 48.8081i −0.183380 + 0.105874i −0.588880 0.808221i \(-0.700431\pi\)
0.405500 + 0.914095i \(0.367098\pi\)
\(462\) 0 0
\(463\) 460.726 + 798.001i 0.995089 + 1.72354i 0.583270 + 0.812278i \(0.301773\pi\)
0.411818 + 0.911266i \(0.364894\pi\)
\(464\) 0 0
\(465\) −915.991 247.073i −1.96987 0.531340i
\(466\) 0 0
\(467\) 483.678i 1.03571i −0.855467 0.517857i \(-0.826730\pi\)
0.855467 0.517857i \(-0.173270\pi\)
\(468\) 0 0
\(469\) −325.396 563.602i −0.693808 1.20171i
\(470\) 0 0
\(471\) −147.468 147.959i −0.313095 0.314139i
\(472\) 0 0
\(473\) 360.414i 0.761976i
\(474\) 0 0
\(475\) −58.9977 912.698i −0.124206 1.92147i
\(476\) 0 0
\(477\) −258.202 450.675i −0.541304 0.944811i
\(478\) 0 0
\(479\) 722.222i 1.50777i 0.657006 + 0.753886i \(0.271823\pi\)
−0.657006 + 0.753886i \(0.728177\pi\)
\(480\) 0 0
\(481\) −47.2271 + 81.7998i −0.0981853 + 0.170062i
\(482\) 0 0
\(483\) −112.560 30.3611i −0.233043 0.0628594i
\(484\) 0 0
\(485\) 613.376 354.133i 1.26469 0.730170i
\(486\) 0 0
\(487\) −461.951 −0.948564 −0.474282 0.880373i \(-0.657292\pi\)
−0.474282 + 0.880373i \(0.657292\pi\)
\(488\) 0 0
\(489\) 426.645 + 428.067i 0.872485 + 0.875393i
\(490\) 0 0
\(491\) 372.061i 0.757761i 0.925446 + 0.378881i \(0.123691\pi\)
−0.925446 + 0.378881i \(0.876309\pi\)
\(492\) 0 0
\(493\) −146.376 + 253.531i −0.296910 + 0.514262i
\(494\) 0 0
\(495\) −994.148 578.391i −2.00838 1.16847i
\(496\) 0 0
\(497\) −581.079 + 335.486i −1.16917 + 0.675022i
\(498\) 0 0
\(499\) −500.410 −1.00283 −0.501413 0.865208i \(-0.667186\pi\)
−0.501413 + 0.865208i \(0.667186\pi\)
\(500\) 0 0
\(501\) −77.9920 293.019i −0.155673 0.584869i
\(502\) 0 0
\(503\) −427.105 + 246.589i −0.849115 + 0.490237i −0.860352 0.509700i \(-0.829756\pi\)
0.0112372 + 0.999937i \(0.496423\pi\)
\(504\) 0 0
\(505\) −520.571 −1.03083
\(506\) 0 0
\(507\) 129.792 481.187i 0.256000 0.949086i
\(508\) 0 0
\(509\) −236.316 136.437i −0.464275 0.268049i 0.249565 0.968358i \(-0.419712\pi\)
−0.713840 + 0.700309i \(0.753046\pi\)
\(510\) 0 0
\(511\) 445.538 + 771.695i 0.871895 + 1.51017i
\(512\) 0 0
\(513\) 383.695 + 340.510i 0.747944 + 0.663762i
\(514\) 0 0
\(515\) 947.068 546.790i 1.83897 1.06173i
\(516\) 0 0
\(517\) −662.757 + 1147.93i −1.28193 + 2.22036i
\(518\) 0 0
\(519\) 454.218 + 122.518i 0.875180 + 0.236065i
\(520\) 0 0
\(521\) 355.563i 0.682463i 0.939979 + 0.341231i \(0.110844\pi\)
−0.939979 + 0.341231i \(0.889156\pi\)
\(522\) 0 0
\(523\) −13.8818 24.0441i −0.0265427 0.0459734i 0.852449 0.522811i \(-0.175116\pi\)
−0.878992 + 0.476837i \(0.841783\pi\)
\(524\) 0 0
\(525\) −1587.29 + 422.484i −3.02341 + 0.804732i
\(526\) 0 0
\(527\) 978.998i 1.85768i
\(528\) 0 0
\(529\) −258.663 448.018i −0.488967 0.846915i
\(530\) 0 0
\(531\) 212.207 + 0.706061i 0.399637 + 0.00132968i
\(532\) 0 0
\(533\) 66.0955 + 38.1602i 0.124006 + 0.0715952i
\(534\) 0 0
\(535\) −62.1941 −0.116251
\(536\) 0 0
\(537\) 449.475 447.982i 0.837011 0.834230i
\(538\) 0 0
\(539\) 1201.02i 2.22824i
\(540\) 0 0
\(541\) 312.904 + 541.966i 0.578381 + 1.00178i 0.995665 + 0.0930090i \(0.0296485\pi\)
−0.417284 + 0.908776i \(0.637018\pi\)
\(542\) 0 0
\(543\) −234.326 + 868.734i −0.431540 + 1.59988i
\(544\) 0 0
\(545\) 858.548 + 495.683i 1.57532 + 0.909510i
\(546\) 0 0
\(547\) −799.520 −1.46165 −0.730823 0.682567i \(-0.760863\pi\)
−0.730823 + 0.682567i \(0.760863\pi\)
\(548\) 0 0
\(549\) −0.968918 + 291.209i −0.00176488 + 0.530436i
\(550\) 0 0
\(551\) 209.662 13.5528i 0.380511 0.0245967i
\(552\) 0 0
\(553\) −600.783 −1.08641
\(554\) 0 0
\(555\) 1012.80 1009.44i 1.82487 1.81881i
\(556\) 0 0
\(557\) 418.721 241.749i 0.751744 0.434019i −0.0745799 0.997215i \(-0.523762\pi\)
0.826324 + 0.563196i \(0.190428\pi\)
\(558\) 0 0
\(559\) −40.8741 −0.0731201
\(560\) 0 0
\(561\) −309.088 + 1145.90i −0.550959 + 2.04261i
\(562\) 0 0
\(563\) −487.316 + 281.352i −0.865571 + 0.499738i −0.865874 0.500262i \(-0.833237\pi\)
0.000302975 1.00000i \(0.499904\pi\)
\(564\) 0 0
\(565\) −804.480 1393.40i −1.42386 2.46620i
\(566\) 0 0
\(567\) 465.953 794.793i 0.821787 1.40175i
\(568\) 0 0
\(569\) 104.072 + 60.0860i 0.182903 + 0.105599i 0.588656 0.808384i \(-0.299657\pi\)
−0.405753 + 0.913983i \(0.632991\pi\)
\(570\) 0 0
\(571\) −29.2018 50.5790i −0.0511415 0.0885797i 0.839321 0.543636i \(-0.182953\pi\)
−0.890463 + 0.455056i \(0.849619\pi\)
\(572\) 0 0
\(573\) 2.62517 + 9.86286i 0.00458144 + 0.0172127i
\(574\) 0 0
\(575\) 142.430 + 82.2321i 0.247705 + 0.143012i
\(576\) 0 0
\(577\) −370.132 −0.641477 −0.320739 0.947168i \(-0.603931\pi\)
−0.320739 + 0.947168i \(0.603931\pi\)
\(578\) 0 0
\(579\) 249.831 + 250.664i 0.431488 + 0.432926i
\(580\) 0 0
\(581\) 687.111 396.704i 1.18264 0.682795i
\(582\) 0 0
\(583\) −862.395 −1.47924
\(584\) 0 0
\(585\) 65.5945 112.745i 0.112127 0.192727i
\(586\) 0 0
\(587\) 621.065 358.572i 1.05803 0.610855i 0.133145 0.991097i \(-0.457492\pi\)
0.924887 + 0.380241i \(0.124159\pi\)
\(588\) 0 0
\(589\) 584.537 389.816i 0.992424 0.661827i
\(590\) 0 0
\(591\) 450.073 448.578i 0.761546 0.759016i
\(592\) 0 0
\(593\) 242.517 140.017i 0.408966 0.236116i −0.281380 0.959597i \(-0.590792\pi\)
0.690345 + 0.723480i \(0.257459\pi\)
\(594\) 0 0
\(595\) 1287.62 + 2230.23i 2.16407 + 3.74828i
\(596\) 0 0
\(597\) 27.2259 100.936i 0.0456045 0.169073i
\(598\) 0 0
\(599\) −264.415 152.660i −0.441428 0.254859i 0.262775 0.964857i \(-0.415362\pi\)
−0.704203 + 0.709999i \(0.748696\pi\)
\(600\) 0 0
\(601\) −88.1717 + 152.718i −0.146708 + 0.254106i −0.930009 0.367537i \(-0.880201\pi\)
0.783301 + 0.621643i \(0.213535\pi\)
\(602\) 0 0
\(603\) −445.100 258.957i −0.738143 0.429448i
\(604\) 0 0
\(605\) −757.680 + 437.447i −1.25236 + 0.723053i
\(606\) 0 0
\(607\) −180.879 313.292i −0.297989 0.516132i 0.677687 0.735351i \(-0.262983\pi\)
−0.975676 + 0.219219i \(0.929649\pi\)
\(608\) 0 0
\(609\) −97.0517 364.627i −0.159362 0.598731i
\(610\) 0 0
\(611\) −130.185 75.1624i −0.213069 0.123015i
\(612\) 0 0
\(613\) −27.3251 + 47.3285i −0.0445760 + 0.0772080i −0.887453 0.460899i \(-0.847527\pi\)
0.842877 + 0.538107i \(0.180860\pi\)
\(614\) 0 0
\(615\) −815.640 818.358i −1.32624 1.33066i
\(616\) 0 0
\(617\) 346.644 + 200.135i 0.561822 + 0.324368i 0.753876 0.657016i \(-0.228182\pi\)
−0.192054 + 0.981384i \(0.561515\pi\)
\(618\) 0 0
\(619\) −379.887 + 657.984i −0.613711 + 1.06298i 0.376898 + 0.926255i \(0.376991\pi\)
−0.990609 + 0.136724i \(0.956343\pi\)
\(620\) 0 0
\(621\) −89.2226 + 23.4305i −0.143676 + 0.0377303i
\(622\) 0 0
\(623\) 119.569i 0.191924i
\(624\) 0 0
\(625\) 488.744 0.781990
\(626\) 0 0
\(627\) 807.265 271.725i 1.28750 0.433373i
\(628\) 0 0
\(629\) −1277.88 737.782i −2.03160 1.17294i
\(630\) 0 0
\(631\) −360.320 624.093i −0.571030 0.989053i −0.996461 0.0840620i \(-0.973211\pi\)
0.425430 0.904991i \(-0.360123\pi\)
\(632\) 0 0
\(633\) −469.858 471.423i −0.742271 0.744745i
\(634\) 0 0
\(635\) −778.084 + 449.227i −1.22533 + 0.707444i
\(636\) 0 0
\(637\) 136.206 0.213825
\(638\) 0 0
\(639\) −266.987 + 458.902i −0.417820 + 0.718157i
\(640\) 0 0
\(641\) 953.036 550.236i 1.48680 0.858402i 0.486909 0.873453i \(-0.338124\pi\)
0.999887 + 0.0150504i \(0.00479087\pi\)
\(642\) 0 0
\(643\) 993.537 1.54516 0.772579 0.634919i \(-0.218966\pi\)
0.772579 + 0.634919i \(0.218966\pi\)
\(644\) 0 0
\(645\) 597.440 + 161.149i 0.926264 + 0.249844i
\(646\) 0 0
\(647\) 137.029i 0.211792i −0.994377 0.105896i \(-0.966229\pi\)
0.994377 0.105896i \(-0.0337710\pi\)
\(648\) 0 0
\(649\) 176.172 305.139i 0.271452 0.470168i
\(650\) 0 0
\(651\) −890.747 893.716i −1.36827 1.37284i
\(652\) 0 0
\(653\) −747.785 + 431.734i −1.14515 + 0.661155i −0.947702 0.319158i \(-0.896600\pi\)
−0.197452 + 0.980313i \(0.563267\pi\)
\(654\) 0 0
\(655\) 267.367 0.408194
\(656\) 0 0
\(657\) 609.440 + 354.569i 0.927610 + 0.539679i
\(658\) 0 0
\(659\) 666.363i 1.01117i 0.862776 + 0.505587i \(0.168724\pi\)
−0.862776 + 0.505587i \(0.831276\pi\)
\(660\) 0 0
\(661\) −192.637 + 333.657i −0.291433 + 0.504776i −0.974149 0.225907i \(-0.927465\pi\)
0.682716 + 0.730684i \(0.260799\pi\)
\(662\) 0 0
\(663\) −129.955 35.0532i −0.196011 0.0528707i
\(664\) 0 0
\(665\) 818.914 1656.84i 1.23145 2.49149i
\(666\) 0 0
\(667\) −18.8901 + 32.7186i −0.0283209 + 0.0490533i
\(668\) 0 0
\(669\) 249.815 926.157i 0.373416 1.38439i
\(670\) 0 0
\(671\) 418.739 + 241.759i 0.624051 + 0.360296i
\(672\) 0 0
\(673\) −536.452 + 929.163i −0.797106 + 1.38063i 0.124387 + 0.992234i \(0.460304\pi\)
−0.921493 + 0.388395i \(0.873030\pi\)
\(674\) 0 0
\(675\) −923.601 + 914.427i −1.36830 + 1.35471i
\(676\) 0 0
\(677\) 331.840 + 191.588i 0.490162 + 0.282995i 0.724642 0.689126i \(-0.242005\pi\)
−0.234479 + 0.972121i \(0.575339\pi\)
\(678\) 0 0
\(679\) 941.992 1.38732
\(680\) 0 0
\(681\) 134.160 + 504.044i 0.197004 + 0.740153i
\(682\) 0 0
\(683\) 951.204i 1.39269i −0.717710 0.696343i \(-0.754809\pi\)
0.717710 0.696343i \(-0.245191\pi\)
\(684\) 0 0
\(685\) −396.013 −0.578121
\(686\) 0 0
\(687\) 245.116 908.735i 0.356792 1.32276i
\(688\) 0 0
\(689\) 97.8031i 0.141949i
\(690\) 0 0
\(691\) −324.517 + 562.080i −0.469634 + 0.813430i −0.999397 0.0347159i \(-0.988947\pi\)
0.529763 + 0.848145i \(0.322281\pi\)
\(692\) 0 0
\(693\) −760.444 1327.31i −1.09732 1.91530i
\(694\) 0 0
\(695\) 116.690 + 67.3712i 0.167900 + 0.0969370i
\(696\) 0 0
\(697\) −596.139 + 1032.54i −0.855293 + 1.48141i
\(698\) 0 0
\(699\) 36.5951 + 137.489i 0.0523535 + 0.196694i
\(700\) 0 0
\(701\) −96.5605 55.7493i −0.137747 0.0795282i 0.429543 0.903046i \(-0.358675\pi\)
−0.567290 + 0.823518i \(0.692008\pi\)
\(702\) 0 0
\(703\) 68.3101 + 1056.76i 0.0971693 + 1.50321i
\(704\) 0 0
\(705\) 1606.53 + 1611.88i 2.27876 + 2.28636i
\(706\) 0 0
\(707\) −599.600 346.179i −0.848091 0.489645i
\(708\) 0 0
\(709\) 134.935 0.190317 0.0951587 0.995462i \(-0.469664\pi\)
0.0951587 + 0.995462i \(0.469664\pi\)
\(710\) 0 0
\(711\) −412.479 + 236.319i −0.580139 + 0.332375i
\(712\) 0 0
\(713\) 126.341i 0.177196i
\(714\) 0 0
\(715\) −108.288 187.560i −0.151451 0.262321i
\(716\) 0 0
\(717\) 51.6767 + 13.9389i 0.0720735 + 0.0194406i
\(718\) 0 0
\(719\) 1049.29 + 605.806i 1.45937 + 0.842568i 0.998980 0.0451490i \(-0.0143762\pi\)
0.460390 + 0.887717i \(0.347710\pi\)
\(720\) 0 0
\(721\) 1454.46 2.01728
\(722\) 0 0
\(723\) −525.609 527.360i −0.726983 0.729406i
\(724\) 0 0
\(725\) 532.292i 0.734196i
\(726\) 0 0
\(727\) −420.993 729.182i −0.579083 1.00300i −0.995585 0.0938662i \(-0.970077\pi\)
0.416502 0.909135i \(-0.363256\pi\)
\(728\) 0 0
\(729\) 7.27648 728.964i 0.00998146 0.999950i
\(730\) 0 0
\(731\) 638.536i 0.873510i
\(732\) 0 0
\(733\) −240.487 416.537i −0.328087 0.568263i 0.654046 0.756455i \(-0.273070\pi\)
−0.982132 + 0.188193i \(0.939737\pi\)
\(734\) 0 0
\(735\) −1990.87 537.004i −2.70867 0.730618i
\(736\) 0 0
\(737\) −740.456 + 427.503i −1.00469 + 0.580058i
\(738\) 0 0
\(739\) −456.243 + 790.237i −0.617380 + 1.06933i 0.372582 + 0.927999i \(0.378472\pi\)
−0.989962 + 0.141334i \(0.954861\pi\)
\(740\) 0 0
\(741\) 30.8159 + 91.5508i 0.0415870 + 0.123550i
\(742\) 0 0
\(743\) 1221.65i 1.64422i −0.569332 0.822108i \(-0.692798\pi\)
0.569332 0.822108i \(-0.307202\pi\)
\(744\) 0 0
\(745\) 2222.58 2.98333
\(746\) 0 0
\(747\) 315.706 542.640i 0.422631 0.726426i
\(748\) 0 0
\(749\) −71.6360 41.3591i −0.0956422 0.0552191i
\(750\) 0 0
\(751\) −159.165 + 275.682i −0.211938 + 0.367087i −0.952321 0.305098i \(-0.901311\pi\)
0.740383 + 0.672185i \(0.234644\pi\)
\(752\) 0 0
\(753\) 575.601 + 155.259i 0.764411 + 0.206187i
\(754\) 0 0
\(755\) 826.512 + 477.187i 1.09472 + 0.632035i
\(756\) 0 0
\(757\) 162.381 281.252i 0.214506 0.371535i −0.738614 0.674129i \(-0.764519\pi\)
0.953120 + 0.302594i \(0.0978525\pi\)
\(758\) 0 0
\(759\) −39.8882 + 147.880i −0.0525536 + 0.194836i
\(760\) 0 0
\(761\) 380.041 219.417i 0.499397 0.288327i −0.229068 0.973410i \(-0.573568\pi\)
0.728464 + 0.685084i \(0.240234\pi\)
\(762\) 0 0
\(763\) 659.258 + 1141.87i 0.864034 + 1.49655i
\(764\) 0 0
\(765\) 1761.30 + 1024.72i 2.30236 + 1.33950i
\(766\) 0 0
\(767\) 34.6055 + 19.9795i 0.0451179 + 0.0260488i
\(768\) 0 0
\(769\) 411.909 713.448i 0.535643 0.927761i −0.463489 0.886103i \(-0.653403\pi\)
0.999132 0.0416581i \(-0.0132640\pi\)
\(770\) 0 0
\(771\) 249.219 + 936.326i 0.323241 + 1.21443i
\(772\) 0 0
\(773\) −269.588 + 155.647i −0.348756 + 0.201354i −0.664137 0.747611i \(-0.731201\pi\)
0.315381 + 0.948965i \(0.397868\pi\)
\(774\) 0 0
\(775\) 890.022 + 1541.56i 1.14842 + 1.98911i
\(776\) 0 0
\(777\) 1837.83 489.170i 2.36529 0.629563i
\(778\) 0 0
\(779\) 853.878 55.1955i 1.09612 0.0708543i
\(780\) 0 0
\(781\) 440.759 + 763.418i 0.564353 + 0.977488i
\(782\) 0 0
\(783\) −210.059 212.166i −0.268275 0.270966i
\(784\) 0 0
\(785\) 595.502i 0.758601i
\(786\) 0 0
\(787\) 405.386 + 702.149i 0.515103 + 0.892184i 0.999846 + 0.0175280i \(0.00557962\pi\)
−0.484743 + 0.874656i \(0.661087\pi\)
\(788\) 0 0
\(789\) 942.077 + 254.109i 1.19401 + 0.322065i
\(790\) 0 0
\(791\) 2139.92i 2.70533i
\(792\) 0 0
\(793\) −27.4176 + 47.4886i −0.0345745 + 0.0598847i
\(794\) 0 0
\(795\) −385.596 + 1429.55i −0.485027 + 1.79817i
\(796\) 0 0
\(797\) −1228.55 +