Properties

Label 684.3.m.a.353.14
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 353.14
Character \(\chi\) \(=\) 684.353
Dual form 684.3.m.a.653.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +O(q^{10})\) \(q+(-1.60029 - 2.53754i) q^{3} +1.56237i q^{5} +(-4.59594 + 7.96040i) q^{7} +(-3.87817 + 8.12156i) q^{9} +(-18.3761 - 10.6095i) q^{11} +(0.163320 - 0.282878i) q^{13} +(3.96458 - 2.50024i) q^{15} +(22.8775 + 13.2083i) q^{17} +(8.51862 - 16.9833i) q^{19} +(27.5546 - 1.07655i) q^{21} +(-2.17715 - 1.25698i) q^{23} +22.5590 q^{25} +(26.8149 - 3.15581i) q^{27} -52.9670i q^{29} +(-4.11110 - 7.12064i) q^{31} +(2.48516 + 63.6082i) q^{33} +(-12.4371 - 7.18057i) q^{35} +30.2712 q^{37} +(-0.979172 + 0.0382561i) q^{39} +10.9070i q^{41} +(30.7940 + 53.3368i) q^{43} +(-12.6889 - 6.05915i) q^{45} +41.4547i q^{47} +(-17.7453 - 30.7358i) q^{49} +(-3.09392 - 79.1895i) q^{51} +(54.4144 - 31.4162i) q^{53} +(16.5759 - 28.7104i) q^{55} +(-56.7280 + 5.56184i) q^{57} -78.8050i q^{59} -57.7876 q^{61} +(-46.8270 - 68.1980i) q^{63} +(0.441962 + 0.255167i) q^{65} +(30.3656 - 52.5947i) q^{67} +(0.294435 + 7.53613i) q^{69} +(48.8284 + 28.1911i) q^{71} +(30.1874 - 52.2860i) q^{73} +(-36.1008 - 57.2442i) q^{75} +(168.911 - 97.5209i) q^{77} +(-34.6994 - 60.1011i) q^{79} +(-50.9195 - 62.9937i) q^{81} +(1.98665 + 1.14700i) q^{83} +(-20.6363 + 35.7431i) q^{85} +(-134.406 + 84.7623i) q^{87} +(92.6623 - 53.4986i) q^{89} +(1.50122 + 2.60018i) q^{91} +(-11.4899 + 21.8271i) q^{93} +(26.5343 + 13.3093i) q^{95} +(13.8646 + 24.0142i) q^{97} +(157.431 - 108.098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99} + O(q^{100}) \)

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
\(3\) −1.60029 2.53754i −0.533428 0.845845i
\(4\) 0 0
\(5\) 1.56237i 0.312475i 0.987720 + 0.156237i \(0.0499365\pi\)
−0.987720 + 0.156237i \(0.950064\pi\)
\(6\) 0 0
\(7\) −4.59594 + 7.96040i −0.656563 + 1.13720i 0.324937 + 0.945736i \(0.394657\pi\)
−0.981500 + 0.191464i \(0.938676\pi\)
\(8\) 0 0
\(9\) −3.87817 + 8.12156i −0.430908 + 0.902396i
\(10\) 0 0
\(11\) −18.3761 10.6095i −1.67056 0.964496i −0.967326 0.253535i \(-0.918407\pi\)
−0.703231 0.710962i \(-0.748260\pi\)
\(12\) 0 0
\(13\) 0.163320 0.282878i 0.0125631 0.0217599i −0.859676 0.510840i \(-0.829334\pi\)
0.872239 + 0.489081i \(0.162668\pi\)
\(14\) 0 0
\(15\) 3.96458 2.50024i 0.264305 0.166683i
\(16\) 0 0
\(17\) 22.8775 + 13.2083i 1.34573 + 0.776960i 0.987642 0.156727i \(-0.0500942\pi\)
0.358092 + 0.933686i \(0.383428\pi\)
\(18\) 0 0
\(19\) 8.51862 16.9833i 0.448349 0.893859i
\(20\) 0 0
\(21\) 27.5546 1.07655i 1.31212 0.0512644i
\(22\) 0 0
\(23\) −2.17715 1.25698i −0.0946589 0.0546513i 0.451923 0.892057i \(-0.350738\pi\)
−0.546582 + 0.837405i \(0.684071\pi\)
\(24\) 0 0
\(25\) 22.5590 0.902360
\(26\) 0 0
\(27\) 26.8149 3.15581i 0.993146 0.116882i
\(28\) 0 0
\(29\) 52.9670i 1.82645i −0.407458 0.913224i \(-0.633585\pi\)
0.407458 0.913224i \(-0.366415\pi\)
\(30\) 0 0
\(31\) −4.11110 7.12064i −0.132616 0.229698i 0.792068 0.610433i \(-0.209004\pi\)
−0.924684 + 0.380735i \(0.875671\pi\)
\(32\) 0 0
\(33\) 2.48516 + 63.6082i 0.0753079 + 1.92752i
\(34\) 0 0
\(35\) −12.4371 7.18057i −0.355346 0.205159i
\(36\) 0 0
\(37\) 30.2712 0.818141 0.409071 0.912503i \(-0.365853\pi\)
0.409071 + 0.912503i \(0.365853\pi\)
\(38\) 0 0
\(39\) −0.979172 + 0.0382561i −0.0251070 + 0.000980925i
\(40\) 0 0
\(41\) 10.9070i 0.266025i 0.991114 + 0.133012i \(0.0424650\pi\)
−0.991114 + 0.133012i \(0.957535\pi\)
\(42\) 0 0
\(43\) 30.7940 + 53.3368i 0.716140 + 1.24039i 0.962518 + 0.271218i \(0.0874263\pi\)
−0.246378 + 0.969174i \(0.579240\pi\)
\(44\) 0 0
\(45\) −12.6889 6.05915i −0.281976 0.134648i
\(46\) 0 0
\(47\) 41.4547i 0.882015i 0.897503 + 0.441008i \(0.145379\pi\)
−0.897503 + 0.441008i \(0.854621\pi\)
\(48\) 0 0
\(49\) −17.7453 30.7358i −0.362149 0.627261i
\(50\) 0 0
\(51\) −3.09392 79.1895i −0.0606650 1.55273i
\(52\) 0 0
\(53\) 54.4144 31.4162i 1.02669 0.592758i 0.110653 0.993859i \(-0.464706\pi\)
0.916034 + 0.401101i \(0.131372\pi\)
\(54\) 0 0
\(55\) 16.5759 28.7104i 0.301381 0.522007i
\(56\) 0 0
\(57\) −56.7280 + 5.56184i −0.995228 + 0.0975762i
\(58\) 0 0
\(59\) 78.8050i 1.33568i −0.744305 0.667839i \(-0.767219\pi\)
0.744305 0.667839i \(-0.232781\pi\)
\(60\) 0 0
\(61\) −57.7876 −0.947337 −0.473669 0.880703i \(-0.657071\pi\)
−0.473669 + 0.880703i \(0.657071\pi\)
\(62\) 0 0
\(63\) −46.8270 68.1980i −0.743286 1.08251i
\(64\) 0 0
\(65\) 0.441962 + 0.255167i 0.00679941 + 0.00392564i
\(66\) 0 0
\(67\) 30.3656 52.5947i 0.453218 0.784996i −0.545366 0.838198i \(-0.683609\pi\)
0.998584 + 0.0532020i \(0.0169427\pi\)
\(68\) 0 0
\(69\) 0.294435 + 7.53613i 0.00426717 + 0.109219i
\(70\) 0 0
\(71\) 48.8284 + 28.1911i 0.687724 + 0.397058i 0.802759 0.596304i \(-0.203365\pi\)
−0.115035 + 0.993361i \(0.536698\pi\)
\(72\) 0 0
\(73\) 30.1874 52.2860i 0.413526 0.716247i −0.581747 0.813370i \(-0.697631\pi\)
0.995272 + 0.0971226i \(0.0309639\pi\)
\(74\) 0 0
\(75\) −36.1008 57.2442i −0.481344 0.763257i
\(76\) 0 0
\(77\) 168.911 97.5209i 2.19365 1.26650i
\(78\) 0 0
\(79\) −34.6994 60.1011i −0.439232 0.760773i 0.558398 0.829573i \(-0.311416\pi\)
−0.997630 + 0.0688003i \(0.978083\pi\)
\(80\) 0 0
\(81\) −50.9195 62.9937i −0.628636 0.777699i
\(82\) 0 0
\(83\) 1.98665 + 1.14700i 0.0239356 + 0.0138192i 0.511920 0.859033i \(-0.328934\pi\)
−0.487984 + 0.872852i \(0.662268\pi\)
\(84\) 0 0
\(85\) −20.6363 + 35.7431i −0.242780 + 0.420507i
\(86\) 0 0
\(87\) −134.406 + 84.7623i −1.54489 + 0.974279i
\(88\) 0 0
\(89\) 92.6623 53.4986i 1.04115 0.601108i 0.120991 0.992654i \(-0.461393\pi\)
0.920159 + 0.391545i \(0.128059\pi\)
\(90\) 0 0
\(91\) 1.50122 + 2.60018i 0.0164969 + 0.0285734i
\(92\) 0 0
\(93\) −11.4899 + 21.8271i −0.123548 + 0.234700i
\(94\) 0 0
\(95\) 26.5343 + 13.3093i 0.279308 + 0.140098i
\(96\) 0 0
\(97\) 13.8646 + 24.0142i 0.142934 + 0.247569i 0.928600 0.371082i \(-0.121013\pi\)
−0.785666 + 0.618650i \(0.787680\pi\)
\(98\) 0 0
\(99\) 157.431 108.098i 1.59021 1.09189i
\(100\) 0 0
\(101\) 14.4308i 0.142879i 0.997445 + 0.0714394i \(0.0227593\pi\)
−0.997445 + 0.0714394i \(0.977241\pi\)
\(102\) 0 0
\(103\) 83.0455 + 143.839i 0.806267 + 1.39650i 0.915432 + 0.402472i \(0.131849\pi\)
−0.109165 + 0.994024i \(0.534818\pi\)
\(104\) 0 0
\(105\) 1.68198 + 43.0506i 0.0160188 + 0.410006i
\(106\) 0 0
\(107\) 131.867i 1.23241i −0.787587 0.616203i \(-0.788670\pi\)
0.787587 0.616203i \(-0.211330\pi\)
\(108\) 0 0
\(109\) −73.6078 + 127.492i −0.675301 + 1.16965i 0.301080 + 0.953599i \(0.402653\pi\)
−0.976381 + 0.216056i \(0.930681\pi\)
\(110\) 0 0
\(111\) −48.4426 76.8143i −0.436420 0.692021i
\(112\) 0 0
\(113\) 7.71947 4.45684i 0.0683139 0.0394411i −0.465454 0.885072i \(-0.654109\pi\)
0.533768 + 0.845631i \(0.320776\pi\)
\(114\) 0 0
\(115\) 1.96387 3.40153i 0.0170771 0.0295785i
\(116\) 0 0
\(117\) 1.66403 + 2.42346i 0.0142225 + 0.0207134i
\(118\) 0 0
\(119\) −210.287 + 121.409i −1.76712 + 1.02025i
\(120\) 0 0
\(121\) 164.621 + 285.132i 1.36051 + 2.35647i
\(122\) 0 0
\(123\) 27.6769 17.4543i 0.225016 0.141905i
\(124\) 0 0
\(125\) 74.3049i 0.594439i
\(126\) 0 0
\(127\) −54.7983 94.9135i −0.431483 0.747351i 0.565518 0.824736i \(-0.308676\pi\)
−0.997001 + 0.0773852i \(0.975343\pi\)
\(128\) 0 0
\(129\) 86.0649 163.495i 0.667170 1.26740i
\(130\) 0 0
\(131\) 36.4161i 0.277985i −0.990293 0.138993i \(-0.955614\pi\)
0.990293 0.138993i \(-0.0443864\pi\)
\(132\) 0 0
\(133\) 96.0429 + 145.866i 0.722127 + 1.09674i
\(134\) 0 0
\(135\) 4.93056 + 41.8949i 0.0365226 + 0.310333i
\(136\) 0 0
\(137\) 219.638i 1.60320i −0.597860 0.801600i \(-0.703982\pi\)
0.597860 0.801600i \(-0.296018\pi\)
\(138\) 0 0
\(139\) −66.5128 + 115.204i −0.478509 + 0.828803i −0.999696 0.0246398i \(-0.992156\pi\)
0.521187 + 0.853443i \(0.325489\pi\)
\(140\) 0 0
\(141\) 105.193 66.3394i 0.746048 0.470492i
\(142\) 0 0
\(143\) −6.00237 + 3.46547i −0.0419746 + 0.0242341i
\(144\) 0 0
\(145\) 82.7542 0.570718
\(146\) 0 0
\(147\) −49.5956 + 94.2154i −0.337385 + 0.640921i
\(148\) 0 0
\(149\) 93.6039i 0.628214i −0.949388 0.314107i \(-0.898295\pi\)
0.949388 0.314107i \(-0.101705\pi\)
\(150\) 0 0
\(151\) −1.49138 + 2.58314i −0.00987668 + 0.0171069i −0.870922 0.491422i \(-0.836477\pi\)
0.861045 + 0.508529i \(0.169811\pi\)
\(152\) 0 0
\(153\) −195.995 + 134.577i −1.28101 + 0.879586i
\(154\) 0 0
\(155\) 11.1251 6.42307i 0.0717748 0.0414392i
\(156\) 0 0
\(157\) −40.0109 −0.254847 −0.127423 0.991848i \(-0.540671\pi\)
−0.127423 + 0.991848i \(0.540671\pi\)
\(158\) 0 0
\(159\) −166.798 87.8036i −1.04905 0.552224i
\(160\) 0 0
\(161\) 20.0121 11.5540i 0.124299 0.0717640i
\(162\) 0 0
\(163\) −73.5546 −0.451255 −0.225628 0.974214i \(-0.572443\pi\)
−0.225628 + 0.974214i \(0.572443\pi\)
\(164\) 0 0
\(165\) −99.3798 + 3.88275i −0.602302 + 0.0235318i
\(166\) 0 0
\(167\) −85.1627 49.1687i −0.509956 0.294423i 0.222860 0.974851i \(-0.428461\pi\)
−0.732816 + 0.680427i \(0.761794\pi\)
\(168\) 0 0
\(169\) 84.4467 + 146.266i 0.499684 + 0.865479i
\(170\) 0 0
\(171\) 104.894 + 135.049i 0.613417 + 0.789759i
\(172\) 0 0
\(173\) −40.7061 + 23.5017i −0.235296 + 0.135848i −0.613013 0.790073i \(-0.710043\pi\)
0.377717 + 0.925921i \(0.376709\pi\)
\(174\) 0 0
\(175\) −103.680 + 179.579i −0.592456 + 1.02616i
\(176\) 0 0
\(177\) −199.971 + 126.111i −1.12978 + 0.712489i
\(178\) 0 0
\(179\) 250.921i 1.40179i −0.713262 0.700897i \(-0.752783\pi\)
0.713262 0.700897i \(-0.247217\pi\)
\(180\) 0 0
\(181\) 122.712 + 212.544i 0.677969 + 1.17428i 0.975591 + 0.219594i \(0.0704732\pi\)
−0.297622 + 0.954684i \(0.596193\pi\)
\(182\) 0 0
\(183\) 92.4766 + 146.638i 0.505337 + 0.801301i
\(184\) 0 0
\(185\) 47.2949i 0.255648i
\(186\) 0 0
\(187\) −280.266 485.435i −1.49875 2.59591i
\(188\) 0 0
\(189\) −98.1183 + 227.962i −0.519144 + 1.20615i
\(190\) 0 0
\(191\) 240.460 + 138.830i 1.25895 + 0.726857i 0.972871 0.231348i \(-0.0743137\pi\)
0.286082 + 0.958205i \(0.407647\pi\)
\(192\) 0 0
\(193\) 229.151 1.18731 0.593654 0.804720i \(-0.297685\pi\)
0.593654 + 0.804720i \(0.297685\pi\)
\(194\) 0 0
\(195\) −0.0597702 1.52983i −0.000306514 0.00784529i
\(196\) 0 0
\(197\) 174.829i 0.887455i 0.896162 + 0.443727i \(0.146344\pi\)
−0.896162 + 0.443727i \(0.853656\pi\)
\(198\) 0 0
\(199\) 163.425 + 283.060i 0.821230 + 1.42241i 0.904767 + 0.425907i \(0.140045\pi\)
−0.0835370 + 0.996505i \(0.526622\pi\)
\(200\) 0 0
\(201\) −182.055 + 7.11283i −0.905744 + 0.0353872i
\(202\) 0 0
\(203\) 421.638 + 243.433i 2.07704 + 1.19918i
\(204\) 0 0
\(205\) −17.0408 −0.0831259
\(206\) 0 0
\(207\) 18.6520 12.8071i 0.0901064 0.0618701i
\(208\) 0 0
\(209\) −336.723 + 221.710i −1.61112 + 1.06081i
\(210\) 0 0
\(211\) 60.2414 0.285504 0.142752 0.989758i \(-0.454405\pi\)
0.142752 + 0.989758i \(0.454405\pi\)
\(212\) 0 0
\(213\) −6.60348 169.018i −0.0310023 0.793510i
\(214\) 0 0
\(215\) −83.3320 + 48.1118i −0.387591 + 0.223776i
\(216\) 0 0
\(217\) 75.5775 0.348283
\(218\) 0 0
\(219\) −180.986 + 7.07109i −0.826421 + 0.0322881i
\(220\) 0 0
\(221\) 7.47269 4.31436i 0.0338131 0.0195220i
\(222\) 0 0
\(223\) −130.050 225.254i −0.583185 1.01011i −0.995099 0.0988836i \(-0.968473\pi\)
0.411914 0.911223i \(-0.364860\pi\)
\(224\) 0 0
\(225\) −87.4877 + 183.214i −0.388834 + 0.814286i
\(226\) 0 0
\(227\) −143.205 82.6796i −0.630860 0.364227i 0.150225 0.988652i \(-0.452000\pi\)
−0.781085 + 0.624425i \(0.785333\pi\)
\(228\) 0 0
\(229\) −166.723 288.773i −0.728048 1.26102i −0.957707 0.287745i \(-0.907095\pi\)
0.229659 0.973271i \(-0.426239\pi\)
\(230\) 0 0
\(231\) −517.769 272.557i −2.24142 1.17990i
\(232\) 0 0
\(233\) −46.3651 26.7689i −0.198992 0.114888i 0.397193 0.917735i \(-0.369984\pi\)
−0.596185 + 0.802847i \(0.703318\pi\)
\(234\) 0 0
\(235\) −64.7677 −0.275607
\(236\) 0 0
\(237\) −96.9797 + 184.230i −0.409197 + 0.777341i
\(238\) 0 0
\(239\) 364.835 210.637i 1.52651 0.881328i 0.527000 0.849865i \(-0.323317\pi\)
0.999505 0.0314631i \(-0.0100167\pi\)
\(240\) 0 0
\(241\) 141.455 0.586949 0.293475 0.955967i \(-0.405188\pi\)
0.293475 + 0.955967i \(0.405188\pi\)
\(242\) 0 0
\(243\) −78.3628 + 230.018i −0.322481 + 0.946576i
\(244\) 0 0
\(245\) 48.0208 27.7248i 0.196003 0.113162i
\(246\) 0 0
\(247\) −3.41295 5.18345i −0.0138176 0.0209856i
\(248\) 0 0
\(249\) −0.268672 6.87672i −0.00107900 0.0276174i
\(250\) 0 0
\(251\) 111.588 64.4253i 0.444573 0.256675i −0.260962 0.965349i \(-0.584040\pi\)
0.705536 + 0.708674i \(0.250706\pi\)
\(252\) 0 0
\(253\) 26.6718 + 46.1969i 0.105422 + 0.182596i
\(254\) 0 0
\(255\) 123.723 4.83385i 0.485190 0.0189563i
\(256\) 0 0
\(257\) −4.49375 2.59447i −0.0174854 0.0100952i 0.491232 0.871029i \(-0.336547\pi\)
−0.508717 + 0.860934i \(0.669880\pi\)
\(258\) 0 0
\(259\) −139.125 + 240.971i −0.537161 + 0.930390i
\(260\) 0 0
\(261\) 430.175 + 205.415i 1.64818 + 0.787031i
\(262\) 0 0
\(263\) −18.3290 + 10.5822i −0.0696919 + 0.0402366i −0.534441 0.845206i \(-0.679478\pi\)
0.464749 + 0.885442i \(0.346145\pi\)
\(264\) 0 0
\(265\) 49.0838 + 85.0156i 0.185222 + 0.320813i
\(266\) 0 0
\(267\) −284.041 149.521i −1.06382 0.560003i
\(268\) 0 0
\(269\) −180.342 104.121i −0.670418 0.387066i 0.125817 0.992053i \(-0.459845\pi\)
−0.796235 + 0.604988i \(0.793178\pi\)
\(270\) 0 0
\(271\) 150.784 261.165i 0.556398 0.963710i −0.441395 0.897313i \(-0.645516\pi\)
0.997793 0.0663970i \(-0.0211504\pi\)
\(272\) 0 0
\(273\) 4.19568 7.97043i 0.0153688 0.0291957i
\(274\) 0 0
\(275\) −414.547 239.339i −1.50744 0.870323i
\(276\) 0 0
\(277\) −106.417 + 184.320i −0.384177 + 0.665414i −0.991655 0.128923i \(-0.958848\pi\)
0.607478 + 0.794337i \(0.292181\pi\)
\(278\) 0 0
\(279\) 73.7743 5.77350i 0.264424 0.0206936i
\(280\) 0 0
\(281\) 242.264i 0.862150i −0.902316 0.431075i \(-0.858134\pi\)
0.902316 0.431075i \(-0.141866\pi\)
\(282\) 0 0
\(283\) 336.324 1.18843 0.594213 0.804308i \(-0.297464\pi\)
0.594213 + 0.804308i \(0.297464\pi\)
\(284\) 0 0
\(285\) −8.68967 88.6303i −0.0304901 0.310983i
\(286\) 0 0
\(287\) −86.8242 50.1280i −0.302523 0.174662i
\(288\) 0 0
\(289\) 204.419 + 354.064i 0.707333 + 1.22514i
\(290\) 0 0
\(291\) 38.7495 73.6114i 0.133160 0.252960i
\(292\) 0 0
\(293\) 179.353 103.550i 0.612127 0.353412i −0.161670 0.986845i \(-0.551688\pi\)
0.773797 + 0.633433i \(0.218355\pi\)
\(294\) 0 0
\(295\) 123.123 0.417366
\(296\) 0 0
\(297\) −526.236 226.500i −1.77184 0.762628i
\(298\) 0 0
\(299\) −0.711145 + 0.410580i −0.00237841 + 0.00137318i
\(300\) 0 0
\(301\) −566.110 −1.88076
\(302\) 0 0
\(303\) 36.6186 23.0933i 0.120853 0.0762156i
\(304\) 0 0
\(305\) 90.2858i 0.296019i
\(306\) 0 0
\(307\) 137.863 238.786i 0.449066 0.777806i −0.549259 0.835652i \(-0.685090\pi\)
0.998325 + 0.0578463i \(0.0184233\pi\)
\(308\) 0 0
\(309\) 232.100 440.915i 0.751133 1.42691i
\(310\) 0 0
\(311\) 237.877 137.339i 0.764879 0.441603i −0.0661657 0.997809i \(-0.521077\pi\)
0.831045 + 0.556205i \(0.187743\pi\)
\(312\) 0 0
\(313\) −485.034 −1.54963 −0.774815 0.632189i \(-0.782157\pi\)
−0.774815 + 0.632189i \(0.782157\pi\)
\(314\) 0 0
\(315\) 106.551 73.1613i 0.338256 0.232258i
\(316\) 0 0
\(317\) 406.534i 1.28244i 0.767357 + 0.641220i \(0.221571\pi\)
−0.767357 + 0.641220i \(0.778429\pi\)
\(318\) 0 0
\(319\) −561.951 + 973.328i −1.76160 + 3.05118i
\(320\) 0 0
\(321\) −334.618 + 211.026i −1.04243 + 0.657401i
\(322\) 0 0
\(323\) 419.206 276.019i 1.29785 0.854547i
\(324\) 0 0
\(325\) 3.68433 6.38145i 0.0113364 0.0196352i
\(326\) 0 0
\(327\) 441.310 17.2419i 1.34957 0.0527275i
\(328\) 0 0
\(329\) −329.996 190.523i −1.00303 0.579098i
\(330\) 0 0
\(331\) −114.803 + 198.845i −0.346838 + 0.600741i −0.985686 0.168592i \(-0.946078\pi\)
0.638848 + 0.769333i \(0.279411\pi\)
\(332\) 0 0
\(333\) −117.397 + 245.850i −0.352544 + 0.738287i
\(334\) 0 0
\(335\) 82.1726 + 47.4424i 0.245291 + 0.141619i
\(336\) 0 0
\(337\) 444.001 1.31751 0.658755 0.752358i \(-0.271083\pi\)
0.658755 + 0.752358i \(0.271083\pi\)
\(338\) 0 0
\(339\) −23.6627 12.4562i −0.0698016 0.0367440i
\(340\) 0 0
\(341\) 174.466i 0.511631i
\(342\) 0 0
\(343\) −124.176 −0.362030
\(344\) 0 0
\(345\) −11.7742 + 0.460017i −0.0341283 + 0.00133338i
\(346\) 0 0
\(347\) 53.3296i 0.153688i 0.997043 + 0.0768439i \(0.0244843\pi\)
−0.997043 + 0.0768439i \(0.975516\pi\)
\(348\) 0 0
\(349\) −174.035 + 301.437i −0.498666 + 0.863715i −0.999999 0.00153938i \(-0.999510\pi\)
0.501333 + 0.865255i \(0.332843\pi\)
\(350\) 0 0
\(351\) 3.48670 8.10077i 0.00993362 0.0230791i
\(352\) 0 0
\(353\) −155.310 89.6686i −0.439973 0.254019i 0.263613 0.964628i \(-0.415086\pi\)
−0.703586 + 0.710610i \(0.748419\pi\)
\(354\) 0 0
\(355\) −44.0450 + 76.2882i −0.124070 + 0.214896i
\(356\) 0 0
\(357\) 644.599 + 339.321i 1.80560 + 0.950479i
\(358\) 0 0
\(359\) 192.832 + 111.332i 0.537138 + 0.310117i 0.743918 0.668271i \(-0.232965\pi\)
−0.206780 + 0.978387i \(0.566299\pi\)
\(360\) 0 0
\(361\) −215.866 289.349i −0.597967 0.801521i
\(362\) 0 0
\(363\) 460.093 874.026i 1.26747 2.40778i
\(364\) 0 0
\(365\) 81.6903 + 47.1639i 0.223809 + 0.129216i
\(366\) 0 0
\(367\) 466.936 1.27231 0.636153 0.771563i \(-0.280525\pi\)
0.636153 + 0.771563i \(0.280525\pi\)
\(368\) 0 0
\(369\) −88.5820 42.2993i −0.240060 0.114632i
\(370\) 0 0
\(371\) 577.547i 1.55673i
\(372\) 0 0
\(373\) −29.7770 51.5752i −0.0798310 0.138271i 0.823346 0.567540i \(-0.192105\pi\)
−0.903177 + 0.429269i \(0.858771\pi\)
\(374\) 0 0
\(375\) 188.551 118.909i 0.502803 0.317091i
\(376\) 0 0
\(377\) −14.9832 8.65056i −0.0397433 0.0229458i
\(378\) 0 0
\(379\) 61.2909 0.161717 0.0808587 0.996726i \(-0.474234\pi\)
0.0808587 + 0.996726i \(0.474234\pi\)
\(380\) 0 0
\(381\) −153.153 + 290.941i −0.401978 + 0.763626i
\(382\) 0 0
\(383\) 202.153i 0.527814i 0.964548 + 0.263907i \(0.0850112\pi\)
−0.964548 + 0.263907i \(0.914989\pi\)
\(384\) 0 0
\(385\) 152.364 + 263.902i 0.395751 + 0.685460i
\(386\) 0 0
\(387\) −552.603 + 43.2462i −1.42791 + 0.111747i
\(388\) 0 0
\(389\) 773.464i 1.98834i −0.107826 0.994170i \(-0.534389\pi\)
0.107826 0.994170i \(-0.465611\pi\)
\(390\) 0 0
\(391\) −33.2052 57.5131i −0.0849237 0.147092i
\(392\) 0 0
\(393\) −92.4070 + 58.2761i −0.235132 + 0.148285i
\(394\) 0 0
\(395\) 93.9003 54.2133i 0.237722 0.137249i
\(396\) 0 0
\(397\) 111.155 192.525i 0.279986 0.484951i −0.691395 0.722477i \(-0.743003\pi\)
0.971381 + 0.237527i \(0.0763367\pi\)
\(398\) 0 0
\(399\) 216.444 477.139i 0.542466 1.19584i
\(400\) 0 0
\(401\) 495.758i 1.23630i 0.786058 + 0.618152i \(0.212119\pi\)
−0.786058 + 0.618152i \(0.787881\pi\)
\(402\) 0 0
\(403\) −2.68570 −0.00666427
\(404\) 0 0
\(405\) 98.4196 79.5553i 0.243011 0.196433i
\(406\) 0 0
\(407\) −556.268 321.161i −1.36675 0.789094i
\(408\) 0 0
\(409\) 403.387 698.686i 0.986275 1.70828i 0.350149 0.936694i \(-0.386131\pi\)
0.636126 0.771585i \(-0.280536\pi\)
\(410\) 0 0
\(411\) −557.340 + 351.484i −1.35606 + 0.855193i
\(412\) 0 0
\(413\) 627.320 + 362.183i 1.51893 + 0.876957i
\(414\) 0 0
\(415\) −1.79203 + 3.10389i −0.00431815 + 0.00747926i
\(416\) 0 0
\(417\) 398.773 15.5800i 0.956289 0.0373620i
\(418\) 0 0
\(419\) 235.914 136.205i 0.563041 0.325072i −0.191324 0.981527i \(-0.561278\pi\)
0.754365 + 0.656455i \(0.227945\pi\)
\(420\) 0 0
\(421\) 400.333 + 693.396i 0.950909 + 1.64702i 0.743465 + 0.668775i \(0.233181\pi\)
0.207444 + 0.978247i \(0.433486\pi\)
\(422\) 0 0
\(423\) −336.677 160.769i −0.795927 0.380068i
\(424\) 0 0
\(425\) 516.093 + 297.966i 1.21434 + 0.701097i
\(426\) 0 0
\(427\) 265.588 460.012i 0.621987 1.07731i
\(428\) 0 0
\(429\) 18.3993 + 9.68549i 0.0428887 + 0.0225769i
\(430\) 0 0
\(431\) 76.3653 44.0895i 0.177182 0.102296i −0.408786 0.912630i \(-0.634048\pi\)
0.585968 + 0.810334i \(0.300714\pi\)
\(432\) 0 0
\(433\) −405.267 701.944i −0.935952 1.62112i −0.772927 0.634495i \(-0.781208\pi\)
−0.163026 0.986622i \(-0.552125\pi\)
\(434\) 0 0
\(435\) −132.430 209.992i −0.304437 0.482739i
\(436\) 0 0
\(437\) −39.8940 + 26.2675i −0.0912907 + 0.0601088i
\(438\) 0 0
\(439\) 4.18943 + 7.25630i 0.00954312 + 0.0165292i 0.870758 0.491713i \(-0.163629\pi\)
−0.861214 + 0.508242i \(0.830296\pi\)
\(440\) 0 0
\(441\) 318.442 24.9210i 0.722091 0.0565101i
\(442\) 0 0
\(443\) 93.4493i 0.210947i 0.994422 + 0.105473i \(0.0336358\pi\)
−0.994422 + 0.105473i \(0.966364\pi\)
\(444\) 0 0
\(445\) 83.5848 + 144.773i 0.187831 + 0.325333i
\(446\) 0 0
\(447\) −237.523 + 149.793i −0.531372 + 0.335107i
\(448\) 0 0
\(449\) 122.697i 0.273268i 0.990622 + 0.136634i \(0.0436284\pi\)
−0.990622 + 0.136634i \(0.956372\pi\)
\(450\) 0 0
\(451\) 115.717 200.429i 0.256580 0.444409i
\(452\) 0 0
\(453\) 8.94145 0.349341i 0.0197383 0.000771172i
\(454\) 0 0
\(455\) −4.06246 + 2.34546i −0.00892848 + 0.00515486i
\(456\) 0 0
\(457\) 213.401 369.622i 0.466962 0.808801i −0.532326 0.846539i \(-0.678682\pi\)
0.999288 + 0.0377382i \(0.0120153\pi\)
\(458\) 0 0
\(459\) 655.141 + 281.983i 1.42732 + 0.614342i
\(460\) 0 0
\(461\) 144.545 83.4531i 0.313546 0.181026i −0.334966 0.942230i \(-0.608725\pi\)
0.648512 + 0.761204i \(0.275391\pi\)
\(462\) 0 0
\(463\) −422.303 731.450i −0.912101 1.57980i −0.811092 0.584919i \(-0.801126\pi\)
−0.101009 0.994886i \(-0.532207\pi\)
\(464\) 0 0
\(465\) −34.1021 17.9516i −0.0733378 0.0386055i
\(466\) 0 0
\(467\) 612.701i 1.31199i 0.754764 + 0.655997i \(0.227752\pi\)
−0.754764 + 0.655997i \(0.772248\pi\)
\(468\) 0 0
\(469\) 279.117 + 483.444i 0.595132 + 1.03080i
\(470\) 0 0
\(471\) 64.0289 + 101.529i 0.135942 + 0.215561i
\(472\) 0 0
\(473\) 1306.83i 2.76286i
\(474\) 0 0
\(475\) 192.172 383.126i 0.404572 0.806582i
\(476\) 0 0
\(477\) 44.1199 + 563.767i 0.0924945 + 1.18190i
\(478\) 0 0
\(479\) 138.380i 0.288892i −0.989513 0.144446i \(-0.953860\pi\)
0.989513 0.144446i \(-0.0461401\pi\)
\(480\) 0 0
\(481\) 4.94389 8.56308i 0.0102784 0.0178027i
\(482\) 0 0
\(483\) −61.3438 32.2918i −0.127006 0.0668567i
\(484\) 0 0
\(485\) −37.5191 + 21.6616i −0.0773589 + 0.0446632i
\(486\) 0 0
\(487\) −767.796 −1.57658 −0.788291 0.615302i \(-0.789034\pi\)
−0.788291 + 0.615302i \(0.789034\pi\)
\(488\) 0 0
\(489\) 117.708 + 186.647i 0.240712 + 0.381692i
\(490\) 0 0
\(491\) 20.6719i 0.0421017i 0.999778 + 0.0210508i \(0.00670118\pi\)
−0.999778 + 0.0210508i \(0.993299\pi\)
\(492\) 0 0
\(493\) 699.605 1211.75i 1.41908 2.45791i
\(494\) 0 0
\(495\) 168.889 + 245.966i 0.341189 + 0.496901i
\(496\) 0 0
\(497\) −448.825 + 259.129i −0.903068 + 0.521387i
\(498\) 0 0
\(499\) −821.607 −1.64651 −0.823253 0.567674i \(-0.807843\pi\)
−0.823253 + 0.567674i \(0.807843\pi\)
\(500\) 0 0
\(501\) 11.5173 + 294.787i 0.0229886 + 0.588398i
\(502\) 0 0
\(503\) −331.574 + 191.434i −0.659192 + 0.380585i −0.791969 0.610561i \(-0.790944\pi\)
0.132777 + 0.991146i \(0.457611\pi\)
\(504\) 0 0
\(505\) −22.5462 −0.0446460
\(506\) 0 0
\(507\) 236.016 448.354i 0.465515 0.884327i
\(508\) 0 0
\(509\) −483.713 279.272i −0.950321 0.548668i −0.0571400 0.998366i \(-0.518198\pi\)
−0.893180 + 0.449698i \(0.851531\pi\)
\(510\) 0 0
\(511\) 277.479 + 480.607i 0.543011 + 0.940523i
\(512\) 0 0
\(513\) 174.830 482.290i 0.340800 0.940136i
\(514\) 0 0
\(515\) −224.730 + 129.748i −0.436369 + 0.251938i
\(516\) 0 0
\(517\) 439.812 761.777i 0.850701 1.47346i
\(518\) 0 0
\(519\) 124.778 + 65.6838i 0.240420 + 0.126558i
\(520\) 0 0
\(521\) 1013.96i 1.94618i 0.230417 + 0.973092i \(0.425991\pi\)
−0.230417 + 0.973092i \(0.574009\pi\)
\(522\) 0 0
\(523\) 400.647 + 693.941i 0.766056 + 1.32685i 0.939687 + 0.342036i \(0.111117\pi\)
−0.173631 + 0.984811i \(0.555550\pi\)
\(524\) 0 0
\(525\) 621.604 24.2859i 1.18401 0.0462589i
\(526\) 0 0
\(527\) 217.203i 0.412150i
\(528\) 0 0
\(529\) −261.340 452.654i −0.494026 0.855679i
\(530\) 0 0
\(531\) 640.020 + 305.620i 1.20531 + 0.575555i
\(532\) 0 0
\(533\) 3.08536 + 1.78133i 0.00578866 + 0.00334209i
\(534\) 0 0
\(535\) 206.026 0.385096
\(536\) 0 0
\(537\) −636.721 + 401.546i −1.18570 + 0.747757i
\(538\) 0 0
\(539\) 753.073i 1.39717i
\(540\) 0 0
\(541\) −12.7450 22.0750i −0.0235582 0.0408040i 0.854006 0.520263i \(-0.174166\pi\)
−0.877564 + 0.479459i \(0.840833\pi\)
\(542\) 0 0
\(543\) 342.964 651.519i 0.631609 1.19985i
\(544\) 0 0
\(545\) −199.191 115.003i −0.365487 0.211014i
\(546\) 0 0
\(547\) 7.32208 0.0133859 0.00669295 0.999978i \(-0.497870\pi\)
0.00669295 + 0.999978i \(0.497870\pi\)
\(548\) 0 0
\(549\) 224.110 469.325i 0.408215 0.854873i
\(550\) 0 0
\(551\) −899.555 451.206i −1.63259 0.818885i
\(552\) 0 0
\(553\) 637.905 1.15353
\(554\) 0 0
\(555\) 120.013 75.6854i 0.216239 0.136370i
\(556\) 0 0
\(557\) 235.341 135.874i 0.422514 0.243939i −0.273638 0.961833i \(-0.588227\pi\)
0.696153 + 0.717894i \(0.254894\pi\)
\(558\) 0 0
\(559\) 20.1171 0.0359877
\(560\) 0 0
\(561\) −783.303 + 1488.02i −1.39626 + 2.65244i
\(562\) 0 0
\(563\) −125.587 + 72.5078i −0.223068 + 0.128788i −0.607370 0.794419i \(-0.707775\pi\)
0.384302 + 0.923207i \(0.374442\pi\)
\(564\) 0 0
\(565\) 6.96324 + 12.0607i 0.0123243 + 0.0213464i
\(566\) 0 0
\(567\) 735.478 115.825i 1.29714 0.204277i
\(568\) 0 0
\(569\) −944.345 545.218i −1.65966 0.958204i −0.972872 0.231344i \(-0.925688\pi\)
−0.686785 0.726860i \(-0.740979\pi\)
\(570\) 0 0
\(571\) −234.969 406.979i −0.411505 0.712748i 0.583549 0.812078i \(-0.301663\pi\)
−0.995055 + 0.0993297i \(0.968330\pi\)
\(572\) 0 0
\(573\) −32.5195 832.343i −0.0567530 1.45261i
\(574\) 0 0
\(575\) −49.1144 28.3562i −0.0854163 0.0493151i
\(576\) 0 0
\(577\) −43.8582 −0.0760107 −0.0380053 0.999278i \(-0.512100\pi\)
−0.0380053 + 0.999278i \(0.512100\pi\)
\(578\) 0 0
\(579\) −366.706 581.478i −0.633344 1.00428i
\(580\) 0 0
\(581\) −18.2611 + 10.5430i −0.0314304 + 0.0181464i
\(582\) 0 0
\(583\) −1333.23 −2.28685
\(584\) 0 0
\(585\) −3.78635 + 2.59984i −0.00647240 + 0.00444417i
\(586\) 0 0
\(587\) 373.819 215.824i 0.636829 0.367674i −0.146563 0.989201i \(-0.546821\pi\)
0.783392 + 0.621528i \(0.213488\pi\)
\(588\) 0 0
\(589\) −155.953 + 9.16212i −0.264776 + 0.0155554i
\(590\) 0 0
\(591\) 443.634 279.776i 0.750650 0.473394i
\(592\) 0 0
\(593\) 839.777 484.845i 1.41615 0.817614i 0.420191 0.907435i \(-0.361963\pi\)
0.995958 + 0.0898213i \(0.0286296\pi\)
\(594\) 0 0
\(595\) −189.686 328.547i −0.318801 0.552179i
\(596\) 0 0
\(597\) 456.748 867.673i 0.765073 1.45339i
\(598\) 0 0
\(599\) −721.606 416.619i −1.20468 0.695525i −0.243091 0.970003i \(-0.578161\pi\)
−0.961593 + 0.274479i \(0.911495\pi\)
\(600\) 0 0
\(601\) −39.4076 + 68.2560i −0.0655701 + 0.113571i −0.896947 0.442139i \(-0.854220\pi\)
0.831377 + 0.555709i \(0.187553\pi\)
\(602\) 0 0
\(603\) 309.388 + 450.587i 0.513082 + 0.747243i
\(604\) 0 0
\(605\) −445.483 + 257.200i −0.736336 + 0.425124i
\(606\) 0 0
\(607\) −237.075 410.626i −0.390568 0.676484i 0.601956 0.798529i \(-0.294388\pi\)
−0.992525 + 0.122045i \(0.961055\pi\)
\(608\) 0 0
\(609\) −57.0218 1459.48i −0.0936318 2.39653i
\(610\) 0 0
\(611\) 11.7266 + 6.77038i 0.0191925 + 0.0110808i
\(612\) 0 0
\(613\) 197.970 342.894i 0.322953 0.559370i −0.658143 0.752893i \(-0.728658\pi\)
0.981096 + 0.193522i \(0.0619912\pi\)
\(614\) 0 0
\(615\) 27.2702 + 43.2417i 0.0443417 + 0.0703117i
\(616\) 0 0
\(617\) −657.897 379.837i −1.06628 0.615619i −0.139120 0.990276i \(-0.544427\pi\)
−0.927164 + 0.374657i \(0.877761\pi\)
\(618\) 0 0
\(619\) 267.269 462.924i 0.431776 0.747857i −0.565251 0.824919i \(-0.691221\pi\)
0.997026 + 0.0770618i \(0.0245539\pi\)
\(620\) 0 0
\(621\) −62.3470 26.8352i −0.100398 0.0432128i
\(622\) 0 0
\(623\) 983.506i 1.57866i
\(624\) 0 0
\(625\) 447.883 0.716613
\(626\) 0 0
\(627\) 1101.45 + 499.648i 1.75670 + 0.796887i
\(628\) 0 0
\(629\) 692.529 + 399.832i 1.10100 + 0.635663i
\(630\) 0 0
\(631\) −316.906 548.898i −0.502229 0.869886i −0.999997 0.00257536i \(-0.999180\pi\)
0.497768 0.867310i \(-0.334153\pi\)
\(632\) 0 0
\(633\) −96.4035 152.865i −0.152296 0.241493i
\(634\) 0 0
\(635\) 148.290 85.6154i 0.233528 0.134827i
\(636\) 0 0
\(637\) −11.5927 −0.0181988
\(638\) 0 0
\(639\) −418.321 + 287.233i −0.654649 + 0.449504i
\(640\) 0 0
\(641\) −7.78120 + 4.49248i −0.0121392 + 0.00700855i −0.506057 0.862500i \(-0.668898\pi\)
0.493918 + 0.869508i \(0.335564\pi\)
\(642\) 0 0
\(643\) 396.064 0.615963 0.307982 0.951392i \(-0.400346\pi\)
0.307982 + 0.951392i \(0.400346\pi\)
\(644\) 0 0
\(645\) 255.440 + 134.465i 0.396032 + 0.208474i
\(646\) 0 0
\(647\) 749.207i 1.15797i 0.815338 + 0.578985i \(0.196551\pi\)
−0.815338 + 0.578985i \(0.803449\pi\)
\(648\) 0 0
\(649\) −836.079 + 1448.13i −1.28826 + 2.23133i
\(650\) 0 0
\(651\) −120.946 191.781i −0.185784 0.294594i
\(652\) 0 0
\(653\) 411.871 237.794i 0.630737 0.364156i −0.150301 0.988640i \(-0.548024\pi\)
0.781037 + 0.624484i \(0.214691\pi\)
\(654\) 0 0
\(655\) 56.8955 0.0868633
\(656\) 0 0
\(657\) 307.573 + 447.943i 0.468147 + 0.681801i
\(658\) 0 0
\(659\) 69.8374i 0.105975i −0.998595 0.0529874i \(-0.983126\pi\)
0.998595 0.0529874i \(-0.0168743\pi\)
\(660\) 0 0
\(661\) −185.179 + 320.740i −0.280150 + 0.485234i −0.971421 0.237361i \(-0.923718\pi\)
0.691272 + 0.722595i \(0.257051\pi\)
\(662\) 0 0
\(663\) −22.9063 12.0580i −0.0345495 0.0181871i
\(664\) 0 0
\(665\) −227.897 + 150.055i −0.342702 + 0.225646i
\(666\) 0 0
\(667\) −66.5785 + 115.317i −0.0998178 + 0.172889i
\(668\) 0 0
\(669\) −363.472 + 690.478i −0.543306 + 1.03210i
\(670\) 0 0
\(671\) 1061.91 + 613.095i 1.58258 + 0.913704i
\(672\) 0 0
\(673\) 96.0890 166.431i 0.142777 0.247297i −0.785764 0.618526i \(-0.787730\pi\)
0.928541 + 0.371229i \(0.121063\pi\)
\(674\) 0 0
\(675\) 604.918 71.1920i 0.896175 0.105470i
\(676\) 0 0
\(677\) −610.979 352.749i −0.902480 0.521047i −0.0244761 0.999700i \(-0.507792\pi\)
−0.878004 + 0.478653i \(0.841125\pi\)
\(678\) 0 0
\(679\) −254.883 −0.375380
\(680\) 0 0
\(681\) 19.3669 + 495.699i 0.0284389 + 0.727899i
\(682\) 0 0
\(683\) 563.037i 0.824358i 0.911103 + 0.412179i \(0.135232\pi\)
−0.911103 + 0.412179i \(0.864768\pi\)
\(684\) 0 0
\(685\) 343.157 0.500959
\(686\) 0 0
\(687\) −465.966 + 885.184i −0.678263 + 1.28848i
\(688\) 0 0
\(689\) 20.5235i 0.0297874i
\(690\) 0 0
\(691\) −533.521 + 924.086i −0.772100 + 1.33732i 0.164310 + 0.986409i \(0.447460\pi\)
−0.936410 + 0.350908i \(0.885873\pi\)
\(692\) 0 0
\(693\) 136.955 + 1750.03i 0.197627 + 2.52529i
\(694\) 0 0
\(695\) −179.991 103.918i −0.258980 0.149522i
\(696\) 0 0
\(697\) −144.063 + 249.525i −0.206690 + 0.357998i
\(698\) 0 0
\(699\) 6.27034 + 160.491i 0.00897045 + 0.229601i
\(700\) 0 0
\(701\) −19.1885 11.0785i −0.0273730 0.0158038i 0.486251 0.873819i \(-0.338364\pi\)
−0.513624 + 0.858015i \(0.671697\pi\)
\(702\) 0 0
\(703\) 257.869 514.106i 0.366812 0.731303i
\(704\) 0 0
\(705\) 103.647 + 164.350i 0.147017 + 0.233121i
\(706\) 0 0
\(707\) −114.875 66.3229i −0.162482 0.0938089i
\(708\) 0 0
\(709\) 499.221 0.704120 0.352060 0.935977i \(-0.385481\pi\)
0.352060 + 0.935977i \(0.385481\pi\)
\(710\) 0 0
\(711\) 622.685 48.7307i 0.875787 0.0685382i
\(712\) 0 0
\(713\) 20.6703i 0.0289906i
\(714\) 0 0
\(715\) −5.41436 9.37795i −0.00757253 0.0131160i
\(716\) 0 0
\(717\) −1118.34 588.701i −1.55975 0.821062i
\(718\) 0 0
\(719\) 802.059 + 463.069i 1.11552 + 0.644046i 0.940254 0.340475i \(-0.110588\pi\)
0.175267 + 0.984521i \(0.443921\pi\)
\(720\) 0 0
\(721\) −1526.69 −2.11746
\(722\) 0 0
\(723\) −226.368 358.947i −0.313095 0.496468i
\(724\) 0 0
\(725\) 1194.88i 1.64811i
\(726\) 0 0
\(727\) 164.277 + 284.536i 0.225965 + 0.391384i 0.956609 0.291376i \(-0.0941130\pi\)
−0.730643 + 0.682759i \(0.760780\pi\)
\(728\) 0 0
\(729\) 709.082 169.246i 0.972677 0.232162i
\(730\) 0 0
\(731\) 1626.95i 2.22565i
\(732\) 0 0
\(733\) −208.671 361.428i −0.284680 0.493080i 0.687851 0.725852i \(-0.258554\pi\)
−0.972532 + 0.232771i \(0.925221\pi\)
\(734\) 0 0
\(735\) −147.200 77.4868i −0.200272 0.105424i
\(736\) 0 0
\(737\) −1116.00 + 644.325i −1.51425 + 0.874253i
\(738\) 0 0
\(739\) 293.870 508.998i 0.397659 0.688766i −0.595778 0.803149i \(-0.703156\pi\)
0.993437 + 0.114384i \(0.0364894\pi\)
\(740\) 0 0
\(741\) −7.69149 + 16.9555i −0.0103799 + 0.0228819i
\(742\) 0 0
\(743\) 308.182i 0.414781i 0.978258 + 0.207390i \(0.0664970\pi\)
−0.978258 + 0.207390i \(0.933503\pi\)
\(744\) 0 0
\(745\) 146.244 0.196301
\(746\) 0 0
\(747\) −17.0200 + 11.6865i −0.0227844 + 0.0156446i
\(748\) 0 0
\(749\) 1049.72 + 606.055i 1.40149 + 0.809152i
\(750\) 0 0
\(751\) 67.4421 116.813i 0.0898031 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(752\) 0 0
\(753\) −342.054 180.059i −0.454255 0.239123i
\(754\) 0 0
\(755\) −4.03584 2.33009i −0.00534548 0.00308621i
\(756\) 0 0
\(757\) −323.700 + 560.665i −0.427609 + 0.740641i −0.996660 0.0816616i \(-0.973977\pi\)
0.569051 + 0.822302i \(0.307311\pi\)
\(758\) 0 0
\(759\) 74.5437 141.609i 0.0982131 0.186573i
\(760\) 0 0
\(761\) −913.138 + 527.201i −1.19992 + 0.692773i −0.960537 0.278152i \(-0.910278\pi\)
−0.239382 + 0.970926i \(0.576945\pi\)
\(762\) 0 0
\(763\) −676.594 1171.89i −0.886754 1.53590i
\(764\) 0 0
\(765\) −210.259 306.217i −0.274848 0.400284i
\(766\) 0 0
\(767\) −22.2922 12.8704i −0.0290642 0.0167802i
\(768\) 0 0
\(769\) 137.478 238.119i 0.178775 0.309647i −0.762686 0.646769i \(-0.776120\pi\)
0.941461 + 0.337121i \(0.109453\pi\)
\(770\) 0 0
\(771\) 0.607728 + 15.5549i 0.000788234 + 0.0201750i
\(772\) 0 0
\(773\) −568.785 + 328.388i −0.735815 + 0.424823i −0.820546 0.571581i \(-0.806330\pi\)
0.0847310 + 0.996404i \(0.472997\pi\)
\(774\) 0 0
\(775\) −92.7423 160.634i −0.119667 0.207270i
\(776\) 0 0
\(777\) 834.112 32.5886i 1.07350 0.0419415i
\(778\) 0 0
\(779\) 185.237 + 92.9127i 0.237788 + 0.119272i
\(780\) 0 0
\(781\) −598.185 1036.09i −0.765922 1.32662i
\(782\) 0 0
\(783\) −167.154 1420.31i −0.213479 1.81393i
\(784\) 0 0
\(785\) 62.5120i 0.0796331i
\(786\) 0 0
\(787\) 266.659 + 461.866i 0.338829 + 0.586869i 0.984213 0.176989i \(-0.0566358\pi\)
−0.645384 + 0.763859i \(0.723302\pi\)
\(788\) 0 0
\(789\) 56.1844 + 29.5758i 0.0712096 + 0.0374852i
\(790\) 0 0
\(791\) 81.9335i 0.103582i
\(792\) 0 0
\(793\) −9.43786 + 16.3469i −0.0119015 + 0.0206139i
\(794\) 0 0
\(795\) 137.182 260.601i 0.172556 0.327800i
\(796\) 0 0