Properties

Label 804.2.q.b.193.2
Level 804
Weight 2
Character 804.193
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 193.2
Character \(\chi\) = 804.193
Dual form 804.2.q.b.25.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 + 0.755750i) q^{3} +(-1.48760 - 0.956023i) q^{5} +(-0.105071 + 0.730785i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.50272 - 1.60840i) q^{11} +(-2.69174 - 5.89410i) q^{13} +(-0.251658 - 1.75032i) q^{15} +(-3.71302 + 1.09024i) q^{17} +(-0.939824 - 6.53662i) q^{19} +(-0.621097 + 0.399155i) q^{21} +(4.18984 + 4.83534i) q^{23} +(-0.778098 - 1.70380i) q^{25} +(-0.841254 + 0.540641i) q^{27} +7.01799 q^{29} +(2.16207 - 4.73427i) q^{31} +(-0.423385 - 2.94471i) q^{33} +(0.854951 - 0.986666i) q^{35} -4.77012 q^{37} +(2.69174 - 5.89410i) q^{39} +(-5.36252 + 1.57458i) q^{41} +(-4.08414 + 1.19921i) q^{43} +(1.15800 - 1.33640i) q^{45} +(-3.54575 - 4.09201i) q^{47} +(6.19344 + 1.81856i) q^{49} +(-3.25546 - 2.09216i) q^{51} +(-12.4504 - 3.65577i) q^{53} +(2.18538 + 4.78532i) q^{55} +(4.32459 - 4.99085i) q^{57} +(-0.638345 + 1.39778i) q^{59} +(-4.33100 + 2.78336i) q^{61} +(-0.708393 - 0.208003i) q^{63} +(-1.63065 + 11.3414i) q^{65} +(2.02680 - 7.93045i) q^{67} +(-0.910540 + 6.33294i) q^{69} +(9.87363 + 2.89916i) q^{71} +(13.8272 - 8.88621i) q^{73} +(0.778098 - 1.70380i) q^{75} +(1.43836 - 1.65995i) q^{77} +(-0.387067 - 0.847559i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-8.20888 - 5.27553i) q^{83} +(6.56580 + 1.92789i) q^{85} +(4.59581 + 5.30384i) q^{87} +(-2.24252 + 2.58801i) q^{89} +(4.59014 - 1.34779i) q^{91} +(4.99377 - 1.46630i) q^{93} +(-4.85108 + 10.6224i) q^{95} -5.05052 q^{97} +(1.94820 - 2.24835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{6}{11}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.654861 + 0.755750i 0.378084 + 0.436332i
\(4\) 0 0
\(5\) −1.48760 0.956023i −0.665276 0.427547i 0.163944 0.986470i \(-0.447578\pi\)
−0.829220 + 0.558923i \(0.811215\pi\)
\(6\) 0 0
\(7\) −0.105071 + 0.730785i −0.0397131 + 0.276211i −0.999996 0.00281747i \(-0.999103\pi\)
0.960283 + 0.279028i \(0.0900123\pi\)
\(8\) 0 0
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0 0
\(11\) −2.50272 1.60840i −0.754598 0.484951i 0.105917 0.994375i \(-0.466222\pi\)
−0.860516 + 0.509424i \(0.829858\pi\)
\(12\) 0 0
\(13\) −2.69174 5.89410i −0.746555 1.63473i −0.772460 0.635064i \(-0.780974\pi\)
0.0259045 0.999664i \(-0.491753\pi\)
\(14\) 0 0
\(15\) −0.251658 1.75032i −0.0649777 0.451930i
\(16\) 0 0
\(17\) −3.71302 + 1.09024i −0.900540 + 0.264423i −0.699054 0.715069i \(-0.746395\pi\)
−0.201486 + 0.979491i \(0.564577\pi\)
\(18\) 0 0
\(19\) −0.939824 6.53662i −0.215610 1.49960i −0.753982 0.656895i \(-0.771869\pi\)
0.538371 0.842708i \(-0.319040\pi\)
\(20\) 0 0
\(21\) −0.621097 + 0.399155i −0.135534 + 0.0871027i
\(22\) 0 0
\(23\) 4.18984 + 4.83534i 0.873643 + 1.00824i 0.999868 + 0.0162358i \(0.00516824\pi\)
−0.126226 + 0.992002i \(0.540286\pi\)
\(24\) 0 0
\(25\) −0.778098 1.70380i −0.155620 0.340759i
\(26\) 0 0
\(27\) −0.841254 + 0.540641i −0.161899 + 0.104046i
\(28\) 0 0
\(29\) 7.01799 1.30321 0.651604 0.758559i \(-0.274096\pi\)
0.651604 + 0.758559i \(0.274096\pi\)
\(30\) 0 0
\(31\) 2.16207 4.73427i 0.388319 0.850299i −0.610004 0.792399i \(-0.708832\pi\)
0.998322 0.0579007i \(-0.0184407\pi\)
\(32\) 0 0
\(33\) −0.423385 2.94471i −0.0737019 0.512608i
\(34\) 0 0
\(35\) 0.854951 0.986666i 0.144513 0.166777i
\(36\) 0 0
\(37\) −4.77012 −0.784203 −0.392101 0.919922i \(-0.628252\pi\)
−0.392101 + 0.919922i \(0.628252\pi\)
\(38\) 0 0
\(39\) 2.69174 5.89410i 0.431024 0.943811i
\(40\) 0 0
\(41\) −5.36252 + 1.57458i −0.837484 + 0.245908i −0.672229 0.740343i \(-0.734663\pi\)
−0.165255 + 0.986251i \(0.552845\pi\)
\(42\) 0 0
\(43\) −4.08414 + 1.19921i −0.622826 + 0.182878i −0.577894 0.816112i \(-0.696125\pi\)
−0.0449320 + 0.998990i \(0.514307\pi\)
\(44\) 0 0
\(45\) 1.15800 1.33640i 0.172624 0.199219i
\(46\) 0 0
\(47\) −3.54575 4.09201i −0.517200 0.596881i 0.435727 0.900079i \(-0.356491\pi\)
−0.952928 + 0.303198i \(0.901946\pi\)
\(48\) 0 0
\(49\) 6.19344 + 1.81856i 0.884778 + 0.259794i
\(50\) 0 0
\(51\) −3.25546 2.09216i −0.455856 0.292961i
\(52\) 0 0
\(53\) −12.4504 3.65577i −1.71019 0.502158i −0.727299 0.686321i \(-0.759225\pi\)
−0.982896 + 0.184163i \(0.941043\pi\)
\(54\) 0 0
\(55\) 2.18538 + 4.78532i 0.294677 + 0.645252i
\(56\) 0 0
\(57\) 4.32459 4.99085i 0.572806 0.661054i
\(58\) 0 0
\(59\) −0.638345 + 1.39778i −0.0831054 + 0.181975i −0.946623 0.322344i \(-0.895529\pi\)
0.863517 + 0.504319i \(0.168257\pi\)
\(60\) 0 0
\(61\) −4.33100 + 2.78336i −0.554528 + 0.356373i −0.787697 0.616063i \(-0.788727\pi\)
0.233169 + 0.972436i \(0.425090\pi\)
\(62\) 0 0
\(63\) −0.708393 0.208003i −0.0892491 0.0262059i
\(64\) 0 0
\(65\) −1.63065 + 11.3414i −0.202258 + 1.40673i
\(66\) 0 0
\(67\) 2.02680 7.93045i 0.247614 0.968859i
\(68\) 0 0
\(69\) −0.910540 + 6.33294i −0.109616 + 0.762397i
\(70\) 0 0
\(71\) 9.87363 + 2.89916i 1.17178 + 0.344067i 0.809002 0.587806i \(-0.200008\pi\)
0.362783 + 0.931874i \(0.381827\pi\)
\(72\) 0 0
\(73\) 13.8272 8.88621i 1.61835 1.04005i 0.661308 0.750114i \(-0.270002\pi\)
0.957045 0.289938i \(-0.0936348\pi\)
\(74\) 0 0
\(75\) 0.778098 1.70380i 0.0898470 0.196737i
\(76\) 0 0
\(77\) 1.43836 1.65995i 0.163916 0.189169i
\(78\) 0 0
\(79\) −0.387067 0.847559i −0.0435485 0.0953578i 0.886607 0.462523i \(-0.153056\pi\)
−0.930156 + 0.367165i \(0.880328\pi\)
\(80\) 0 0
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0 0
\(83\) −8.20888 5.27553i −0.901042 0.579064i 0.00605745 0.999982i \(-0.498072\pi\)
−0.907099 + 0.420917i \(0.861708\pi\)
\(84\) 0 0
\(85\) 6.56580 + 1.92789i 0.712161 + 0.209109i
\(86\) 0 0
\(87\) 4.59581 + 5.30384i 0.492722 + 0.568632i
\(88\) 0 0
\(89\) −2.24252 + 2.58801i −0.237707 + 0.274328i −0.862051 0.506821i \(-0.830821\pi\)
0.624345 + 0.781149i \(0.285366\pi\)
\(90\) 0 0
\(91\) 4.59014 1.34779i 0.481177 0.141286i
\(92\) 0 0
\(93\) 4.99377 1.46630i 0.517830 0.152049i
\(94\) 0 0
\(95\) −4.85108 + 10.6224i −0.497710 + 1.08983i
\(96\) 0 0
\(97\) −5.05052 −0.512802 −0.256401 0.966570i \(-0.582537\pi\)
−0.256401 + 0.966570i \(0.582537\pi\)
\(98\) 0 0
\(99\) 1.94820 2.24835i 0.195802 0.225967i
\(100\) 0 0
\(101\) 0.494284 + 3.43782i 0.0491831 + 0.342076i 0.999524 + 0.0308641i \(0.00982589\pi\)
−0.950340 + 0.311212i \(0.899265\pi\)
\(102\) 0 0
\(103\) −3.76865 + 8.25219i −0.371336 + 0.813112i 0.628053 + 0.778170i \(0.283852\pi\)
−0.999389 + 0.0349420i \(0.988875\pi\)
\(104\) 0 0
\(105\) 1.30555 0.127408
\(106\) 0 0
\(107\) 13.3015 8.54836i 1.28591 0.826401i 0.294301 0.955713i \(-0.404913\pi\)
0.991604 + 0.129312i \(0.0412768\pi\)
\(108\) 0 0
\(109\) 6.13972 + 13.4441i 0.588079 + 1.28771i 0.936596 + 0.350410i \(0.113958\pi\)
−0.348518 + 0.937302i \(0.613315\pi\)
\(110\) 0 0
\(111\) −3.12376 3.60502i −0.296495 0.342173i
\(112\) 0 0
\(113\) −9.11915 + 5.86052i −0.857857 + 0.551311i −0.894016 0.448035i \(-0.852124\pi\)
0.0361590 + 0.999346i \(0.488488\pi\)
\(114\) 0 0
\(115\) −1.61012 11.1986i −0.150145 1.04428i
\(116\) 0 0
\(117\) 6.21718 1.82553i 0.574778 0.168770i
\(118\) 0 0
\(119\) −0.406601 2.82797i −0.0372731 0.259240i
\(120\) 0 0
\(121\) −0.892911 1.95520i −0.0811738 0.177746i
\(122\) 0 0
\(123\) −4.70169 3.02159i −0.423937 0.272448i
\(124\) 0 0
\(125\) −1.72966 + 12.0300i −0.154705 + 1.07600i
\(126\) 0 0
\(127\) −2.08379 + 14.4930i −0.184906 + 1.28605i 0.660053 + 0.751219i \(0.270534\pi\)
−0.844959 + 0.534831i \(0.820375\pi\)
\(128\) 0 0
\(129\) −3.58085 2.30127i −0.315276 0.202616i
\(130\) 0 0
\(131\) −9.65506 11.1425i −0.843566 0.973527i 0.156333 0.987704i \(-0.450033\pi\)
−0.999900 + 0.0141770i \(0.995487\pi\)
\(132\) 0 0
\(133\) 4.87561 0.422769
\(134\) 0 0
\(135\) 1.76832 0.152192
\(136\) 0 0
\(137\) 11.2791 + 13.0168i 0.963637 + 1.11210i 0.993646 + 0.112547i \(0.0359008\pi\)
−0.0300096 + 0.999550i \(0.509554\pi\)
\(138\) 0 0
\(139\) −16.7655 10.7746i −1.42203 0.913886i −0.999973 0.00731819i \(-0.997671\pi\)
−0.422061 0.906568i \(-0.638693\pi\)
\(140\) 0 0
\(141\) 0.770564 5.35939i 0.0648932 0.451342i
\(142\) 0 0
\(143\) −2.74339 + 19.0807i −0.229413 + 1.59561i
\(144\) 0 0
\(145\) −10.4400 6.70936i −0.866992 0.557182i
\(146\) 0 0
\(147\) 2.68147 + 5.87160i 0.221164 + 0.484281i
\(148\) 0 0
\(149\) 1.44779 + 10.0696i 0.118607 + 0.824932i 0.959092 + 0.283096i \(0.0913614\pi\)
−0.840484 + 0.541836i \(0.817729\pi\)
\(150\) 0 0
\(151\) −2.00719 + 0.589364i −0.163343 + 0.0479618i −0.362381 0.932030i \(-0.618036\pi\)
0.199039 + 0.979992i \(0.436218\pi\)
\(152\) 0 0
\(153\) −0.550727 3.83039i −0.0445236 0.309669i
\(154\) 0 0
\(155\) −7.74236 + 4.97571i −0.621882 + 0.399659i
\(156\) 0 0
\(157\) −0.271501 0.313329i −0.0216681 0.0250064i 0.744812 0.667274i \(-0.232539\pi\)
−0.766480 + 0.642268i \(0.777994\pi\)
\(158\) 0 0
\(159\) −5.39044 11.8034i −0.427489 0.936071i
\(160\) 0 0
\(161\) −3.97382 + 2.55382i −0.313181 + 0.201269i
\(162\) 0 0
\(163\) 21.5970 1.69160 0.845802 0.533497i \(-0.179122\pi\)
0.845802 + 0.533497i \(0.179122\pi\)
\(164\) 0 0
\(165\) −2.18538 + 4.78532i −0.170132 + 0.372536i
\(166\) 0 0
\(167\) −2.92030 20.3111i −0.225980 1.57172i −0.714794 0.699335i \(-0.753480\pi\)
0.488814 0.872388i \(-0.337430\pi\)
\(168\) 0 0
\(169\) −18.9817 + 21.9060i −1.46013 + 1.68508i
\(170\) 0 0
\(171\) 6.60384 0.505008
\(172\) 0 0
\(173\) −8.68144 + 19.0097i −0.660038 + 1.44528i 0.222449 + 0.974944i \(0.428595\pi\)
−0.882487 + 0.470337i \(0.844132\pi\)
\(174\) 0 0
\(175\) 1.32686 0.389602i 0.100301 0.0294512i
\(176\) 0 0
\(177\) −1.47440 + 0.432923i −0.110823 + 0.0325404i
\(178\) 0 0
\(179\) 11.4291 13.1899i 0.854252 0.985859i −0.145742 0.989323i \(-0.546557\pi\)
0.999994 + 0.00346358i \(0.00110250\pi\)
\(180\) 0 0
\(181\) 9.84190 + 11.3582i 0.731543 + 0.844246i 0.992644 0.121066i \(-0.0386312\pi\)
−0.261102 + 0.965311i \(0.584086\pi\)
\(182\) 0 0
\(183\) −4.93973 1.45044i −0.365155 0.107219i
\(184\) 0 0
\(185\) 7.09604 + 4.56035i 0.521711 + 0.335283i
\(186\) 0 0
\(187\) 11.0462 + 3.24346i 0.807778 + 0.237185i
\(188\) 0 0
\(189\) −0.306701 0.671581i −0.0223092 0.0488503i
\(190\) 0 0
\(191\) 2.71479 3.13303i 0.196435 0.226698i −0.648984 0.760802i \(-0.724806\pi\)
0.845419 + 0.534104i \(0.179351\pi\)
\(192\) 0 0
\(193\) 9.97110 21.8337i 0.717736 1.57162i −0.0993153 0.995056i \(-0.531665\pi\)
0.817051 0.576566i \(-0.195607\pi\)
\(194\) 0 0
\(195\) −9.63914 + 6.19470i −0.690273 + 0.443611i
\(196\) 0 0
\(197\) 15.7553 + 4.62617i 1.12252 + 0.329601i 0.789763 0.613412i \(-0.210204\pi\)
0.332755 + 0.943013i \(0.392022\pi\)
\(198\) 0 0
\(199\) 1.51142 10.5121i 0.107141 0.745185i −0.863447 0.504440i \(-0.831699\pi\)
0.970588 0.240745i \(-0.0773918\pi\)
\(200\) 0 0
\(201\) 7.32071 3.66158i 0.516363 0.258268i
\(202\) 0 0
\(203\) −0.737387 + 5.12864i −0.0517544 + 0.359960i
\(204\) 0 0
\(205\) 9.48262 + 2.78435i 0.662295 + 0.194467i
\(206\) 0 0
\(207\) −5.38240 + 3.45906i −0.374102 + 0.240421i
\(208\) 0 0
\(209\) −8.16138 + 17.8709i −0.564535 + 1.23616i
\(210\) 0 0
\(211\) −2.59792 + 2.99816i −0.178848 + 0.206402i −0.838094 0.545526i \(-0.816330\pi\)
0.659246 + 0.751927i \(0.270876\pi\)
\(212\) 0 0
\(213\) 4.27482 + 9.36054i 0.292906 + 0.641374i
\(214\) 0 0
\(215\) 7.22205 + 2.12059i 0.492540 + 0.144623i
\(216\) 0 0
\(217\) 3.23256 + 2.07744i 0.219440 + 0.141026i
\(218\) 0 0
\(219\) 15.7707 + 4.63068i 1.06568 + 0.312912i
\(220\) 0 0
\(221\) 16.4205 + 18.9503i 1.10456 + 1.27473i
\(222\) 0 0
\(223\) −0.404679 + 0.467024i −0.0270993 + 0.0312743i −0.769137 0.639083i \(-0.779314\pi\)
0.742038 + 0.670358i \(0.233859\pi\)
\(224\) 0 0
\(225\) 1.79719 0.527702i 0.119813 0.0351802i
\(226\) 0 0
\(227\) −6.26085 + 1.83835i −0.415547 + 0.122016i −0.482821 0.875719i \(-0.660388\pi\)
0.0672741 + 0.997735i \(0.478570\pi\)
\(228\) 0 0
\(229\) 0.264402 0.578959i 0.0174721 0.0382587i −0.900695 0.434452i \(-0.856942\pi\)
0.918167 + 0.396194i \(0.129669\pi\)
\(230\) 0 0
\(231\) 2.19643 0.144515
\(232\) 0 0
\(233\) −6.32624 + 7.30087i −0.414446 + 0.478296i −0.924137 0.382062i \(-0.875214\pi\)
0.509691 + 0.860357i \(0.329760\pi\)
\(234\) 0 0
\(235\) 1.36260 + 9.47710i 0.0888863 + 0.618218i
\(236\) 0 0
\(237\) 0.387067 0.847559i 0.0251427 0.0550549i
\(238\) 0 0
\(239\) 0.455619 0.0294716 0.0147358 0.999891i \(-0.495309\pi\)
0.0147358 + 0.999891i \(0.495309\pi\)
\(240\) 0 0
\(241\) 13.6846 8.79457i 0.881503 0.566508i −0.0197478 0.999805i \(-0.506286\pi\)
0.901251 + 0.433297i \(0.142650\pi\)
\(242\) 0 0
\(243\) −0.415415 0.909632i −0.0266489 0.0583529i
\(244\) 0 0
\(245\) −7.47479 8.62637i −0.477547 0.551119i
\(246\) 0 0
\(247\) −35.9977 + 23.1343i −2.29048 + 1.47200i
\(248\) 0 0
\(249\) −1.38870 9.65859i −0.0880050 0.612088i
\(250\) 0 0
\(251\) 5.45796 1.60260i 0.344503 0.101155i −0.104904 0.994482i \(-0.533453\pi\)
0.449407 + 0.893327i \(0.351635\pi\)
\(252\) 0 0
\(253\) −2.70885 18.8404i −0.170304 1.18449i
\(254\) 0 0
\(255\) 2.84268 + 6.22460i 0.178015 + 0.389799i
\(256\) 0 0
\(257\) 0.483698 + 0.310854i 0.0301723 + 0.0193905i 0.555640 0.831423i \(-0.312473\pi\)
−0.525468 + 0.850814i \(0.676110\pi\)
\(258\) 0 0
\(259\) 0.501201 3.48593i 0.0311431 0.216605i
\(260\) 0 0
\(261\) −0.998764 + 6.94656i −0.0618219 + 0.429981i
\(262\) 0 0
\(263\) −13.5317 8.69627i −0.834398 0.536235i 0.0522745 0.998633i \(-0.483353\pi\)
−0.886673 + 0.462398i \(0.846989\pi\)
\(264\) 0 0
\(265\) 15.0262 + 17.3412i 0.923055 + 1.06526i
\(266\) 0 0
\(267\) −3.42442 −0.209571
\(268\) 0 0
\(269\) 3.87866 0.236486 0.118243 0.992985i \(-0.462274\pi\)
0.118243 + 0.992985i \(0.462274\pi\)
\(270\) 0 0
\(271\) 4.95964 + 5.72373i 0.301277 + 0.347692i 0.886121 0.463453i \(-0.153390\pi\)
−0.584844 + 0.811145i \(0.698844\pi\)
\(272\) 0 0
\(273\) 4.02449 + 2.58638i 0.243573 + 0.156535i
\(274\) 0 0
\(275\) −0.793026 + 5.51562i −0.0478213 + 0.332604i
\(276\) 0 0
\(277\) 3.39594 23.6193i 0.204042 1.41915i −0.588090 0.808796i \(-0.700120\pi\)
0.792132 0.610350i \(-0.208971\pi\)
\(278\) 0 0
\(279\) 4.37838 + 2.81382i 0.262127 + 0.168459i
\(280\) 0 0
\(281\) −5.09748 11.1619i −0.304090 0.665864i 0.694469 0.719522i \(-0.255639\pi\)
−0.998559 + 0.0536581i \(0.982912\pi\)
\(282\) 0 0
\(283\) 1.71507 + 11.9286i 0.101950 + 0.709081i 0.975122 + 0.221668i \(0.0711501\pi\)
−0.873172 + 0.487413i \(0.837941\pi\)
\(284\) 0 0
\(285\) −11.2046 + 3.28998i −0.663705 + 0.194881i
\(286\) 0 0
\(287\) −0.587232 4.08429i −0.0346632 0.241088i
\(288\) 0 0
\(289\) −1.70339 + 1.09471i −0.100200 + 0.0643944i
\(290\) 0 0
\(291\) −3.30739 3.81693i −0.193882 0.223752i
\(292\) 0 0
\(293\) −6.39464 14.0023i −0.373579 0.818023i −0.999279 0.0379600i \(-0.987914\pi\)
0.625700 0.780063i \(-0.284813\pi\)
\(294\) 0 0
\(295\) 2.28591 1.46907i 0.133091 0.0855324i
\(296\) 0 0
\(297\) 2.97499 0.172626
\(298\) 0 0
\(299\) 17.2220 37.7108i 0.995971 2.18087i
\(300\) 0 0
\(301\) −0.447241 3.11063i −0.0257786 0.179294i
\(302\) 0 0
\(303\) −2.27445 + 2.62485i −0.130664 + 0.150794i
\(304\) 0 0
\(305\) 9.10376 0.521280
\(306\) 0 0
\(307\) 9.96207 21.8139i 0.568565 1.24498i −0.378993 0.925400i \(-0.623729\pi\)
0.947558 0.319584i \(-0.103543\pi\)
\(308\) 0 0
\(309\) −8.70453 + 2.55588i −0.495183 + 0.145399i
\(310\) 0 0
\(311\) 23.5974 6.92883i 1.33809 0.392898i 0.467100 0.884204i \(-0.345299\pi\)
0.870987 + 0.491307i \(0.163481\pi\)
\(312\) 0 0
\(313\) −11.1285 + 12.8430i −0.629022 + 0.725930i −0.977394 0.211426i \(-0.932189\pi\)
0.348372 + 0.937356i \(0.386735\pi\)
\(314\) 0 0
\(315\) 0.854951 + 0.986666i 0.0481710 + 0.0555923i
\(316\) 0 0
\(317\) −2.20012 0.646013i −0.123571 0.0362837i 0.219362 0.975643i \(-0.429602\pi\)
−0.342933 + 0.939360i \(0.611420\pi\)
\(318\) 0 0
\(319\) −17.5641 11.2877i −0.983398 0.631992i
\(320\) 0 0
\(321\) 15.1711 + 4.45462i 0.846766 + 0.248633i
\(322\) 0 0
\(323\) 10.6161 + 23.2460i 0.590695 + 1.29344i
\(324\) 0 0
\(325\) −7.94790 + 9.17236i −0.440870 + 0.508791i
\(326\) 0 0
\(327\) −6.13972 + 13.4441i −0.339527 + 0.743461i
\(328\) 0 0
\(329\) 3.36293 2.16123i 0.185404 0.119152i
\(330\) 0 0
\(331\) 8.57734 + 2.51853i 0.471453 + 0.138431i 0.508824 0.860870i \(-0.330080\pi\)
−0.0373712 + 0.999301i \(0.511898\pi\)
\(332\) 0 0
\(333\) 0.678859 4.72157i 0.0372012 0.258740i
\(334\) 0 0
\(335\) −10.5968 + 9.85968i −0.578964 + 0.538692i
\(336\) 0 0
\(337\) 2.27861 15.8481i 0.124124 0.863302i −0.828682 0.559720i \(-0.810909\pi\)
0.952806 0.303581i \(-0.0981824\pi\)
\(338\) 0 0
\(339\) −10.4009 3.05397i −0.564897 0.165869i
\(340\) 0 0
\(341\) −13.0256 + 8.37107i −0.705378 + 0.453319i
\(342\) 0 0
\(343\) −4.12663 + 9.03606i −0.222817 + 0.487901i
\(344\) 0 0
\(345\) 7.40896 8.55040i 0.398885 0.460338i
\(346\) 0 0
\(347\) −11.5827 25.3626i −0.621792 1.36154i −0.914208 0.405244i \(-0.867186\pi\)
0.292416 0.956291i \(-0.405541\pi\)
\(348\) 0 0
\(349\) 13.5873 + 3.98958i 0.727310 + 0.213558i 0.624369 0.781130i \(-0.285356\pi\)
0.102942 + 0.994687i \(0.467174\pi\)
\(350\) 0 0
\(351\) 5.45103 + 3.50316i 0.290954 + 0.186985i
\(352\) 0 0
\(353\) −22.6461 6.64949i −1.20533 0.353917i −0.383441 0.923565i \(-0.625261\pi\)
−0.821889 + 0.569648i \(0.807079\pi\)
\(354\) 0 0
\(355\) −11.9164 13.7522i −0.632455 0.729892i
\(356\) 0 0
\(357\) 1.87097 2.15922i 0.0990224 0.114278i
\(358\) 0 0
\(359\) 7.11892 2.09030i 0.375722 0.110322i −0.0884186 0.996083i \(-0.528181\pi\)
0.464141 + 0.885761i \(0.346363\pi\)
\(360\) 0 0
\(361\) −23.6137 + 6.93362i −1.24283 + 0.364927i
\(362\) 0 0
\(363\) 0.892911 1.95520i 0.0468657 0.102622i
\(364\) 0 0
\(365\) −29.0648 −1.52132
\(366\) 0 0
\(367\) 17.5729 20.2803i 0.917300 1.05862i −0.0807827 0.996732i \(-0.525742\pi\)
0.998083 0.0618893i \(-0.0197126\pi\)
\(368\) 0 0
\(369\) −0.795384 5.53202i −0.0414061 0.287985i
\(370\) 0 0
\(371\) 3.97976 8.71445i 0.206619 0.452432i
\(372\) 0 0
\(373\) −18.4066 −0.953057 −0.476529 0.879159i \(-0.658105\pi\)
−0.476529 + 0.879159i \(0.658105\pi\)
\(374\) 0 0
\(375\) −10.2244 + 6.57081i −0.527984 + 0.339315i
\(376\) 0 0
\(377\) −18.8906 41.3647i −0.972917 2.13039i
\(378\) 0 0
\(379\) 0.297421 + 0.343242i 0.0152775 + 0.0176312i 0.763337 0.646001i \(-0.223560\pi\)
−0.748059 + 0.663632i \(0.769014\pi\)
\(380\) 0 0
\(381\) −12.3177 + 7.91611i −0.631055 + 0.405554i
\(382\) 0 0
\(383\) 1.85580 + 12.9074i 0.0948271 + 0.659537i 0.980687 + 0.195584i \(0.0626603\pi\)
−0.885860 + 0.463953i \(0.846431\pi\)
\(384\) 0 0
\(385\) −3.72666 + 1.09424i −0.189928 + 0.0557679i
\(386\) 0 0
\(387\) −0.605772 4.21324i −0.0307931 0.214171i
\(388\) 0 0
\(389\) −8.19821 17.9516i −0.415666 0.910181i −0.995439 0.0954030i \(-0.969586\pi\)
0.579773 0.814778i \(-0.303141\pi\)
\(390\) 0 0
\(391\) −20.8287 13.3858i −1.05335 0.676948i
\(392\) 0 0
\(393\) 2.09824 14.5936i 0.105842 0.736150i
\(394\) 0 0
\(395\) −0.234485 + 1.63088i −0.0117982 + 0.0820583i
\(396\) 0 0
\(397\) 10.7991 + 6.94018i 0.541993 + 0.348318i 0.782818 0.622251i \(-0.213782\pi\)
−0.240825 + 0.970569i \(0.577418\pi\)
\(398\) 0 0
\(399\) 3.19284 + 3.68474i 0.159842 + 0.184468i
\(400\) 0 0
\(401\) 9.40988 0.469907 0.234953 0.972007i \(-0.424506\pi\)
0.234953 + 0.972007i \(0.424506\pi\)
\(402\) 0 0
\(403\) −33.7239 −1.67991
\(404\) 0 0
\(405\) 1.15800 + 1.33640i 0.0575415 + 0.0664064i
\(406\) 0 0
\(407\) 11.9383 + 7.67226i 0.591758 + 0.380300i
\(408\) 0 0
\(409\) 1.90931 13.2795i 0.0944093 0.656631i −0.886581 0.462574i \(-0.846926\pi\)
0.980990 0.194057i \(-0.0621648\pi\)
\(410\) 0 0
\(411\) −2.45118 + 17.0483i −0.120908 + 0.840932i
\(412\) 0 0
\(413\) −0.954405 0.613359i −0.0469632 0.0301814i
\(414\) 0 0
\(415\) 7.16801 + 15.6958i 0.351864 + 0.770475i
\(416\) 0 0
\(417\) −2.83622 19.7264i −0.138891 0.966005i
\(418\) 0 0
\(419\) 18.4016 5.40321i 0.898979 0.263964i 0.200584 0.979677i \(-0.435716\pi\)
0.698395 + 0.715713i \(0.253898\pi\)
\(420\) 0 0
\(421\) −2.85477 19.8554i −0.139133 0.967692i −0.933071 0.359693i \(-0.882881\pi\)
0.793938 0.607999i \(-0.208028\pi\)
\(422\) 0 0
\(423\) 4.55497 2.92730i 0.221470 0.142330i
\(424\) 0 0
\(425\) 4.74665 + 5.47792i 0.230246 + 0.265718i
\(426\) 0 0
\(427\) −1.57898 3.45748i −0.0764121 0.167319i
\(428\) 0 0
\(429\) −16.2167 + 10.4219i −0.782952 + 0.503173i
\(430\) 0 0
\(431\) 17.5968 0.847608 0.423804 0.905754i \(-0.360695\pi\)
0.423804 + 0.905754i \(0.360695\pi\)
\(432\) 0 0
\(433\) −15.7576 + 34.5043i −0.757261 + 1.65817i −0.00440120 + 0.999990i \(0.501401\pi\)
−0.752860 + 0.658181i \(0.771326\pi\)
\(434\) 0 0
\(435\) −1.76613 12.2837i −0.0846794 0.588958i
\(436\) 0 0
\(437\) 27.6690 31.9318i 1.32359 1.52750i
\(438\) 0 0
\(439\) 27.2447 1.30032 0.650160 0.759798i \(-0.274702\pi\)
0.650160 + 0.759798i \(0.274702\pi\)
\(440\) 0 0
\(441\) −2.68147 + 5.87160i −0.127689 + 0.279600i
\(442\) 0 0
\(443\) 3.97896 1.16833i 0.189046 0.0555090i −0.185839 0.982580i \(-0.559500\pi\)
0.374885 + 0.927071i \(0.377682\pi\)
\(444\) 0 0
\(445\) 5.81017 1.70602i 0.275428 0.0808731i
\(446\) 0 0
\(447\) −6.66198 + 7.68833i −0.315101 + 0.363646i
\(448\) 0 0
\(449\) −14.7109 16.9773i −0.694249 0.801206i 0.293715 0.955893i \(-0.405108\pi\)
−0.987963 + 0.154687i \(0.950563\pi\)
\(450\) 0 0
\(451\) 15.9534 + 4.68435i 0.751217 + 0.220577i
\(452\) 0 0
\(453\) −1.75984 1.13098i −0.0826846 0.0531381i
\(454\) 0 0
\(455\) −8.11681 2.38331i −0.380522 0.111731i
\(456\) 0 0
\(457\) −5.99493 13.1271i −0.280431 0.614058i 0.716034 0.698065i \(-0.245955\pi\)
−0.996465 + 0.0840069i \(0.973228\pi\)
\(458\) 0 0
\(459\) 2.53416 2.92458i 0.118285 0.136508i
\(460\) 0 0
\(461\) 14.6836 32.1525i 0.683882 1.49749i −0.174596 0.984640i \(-0.555862\pi\)
0.858477 0.512852i \(-0.171411\pi\)
\(462\) 0 0
\(463\) 16.6526 10.7020i 0.773913 0.497364i −0.0930952 0.995657i \(-0.529676\pi\)
0.867009 + 0.498293i \(0.166040\pi\)
\(464\) 0 0
\(465\) −8.83056 2.59289i −0.409508 0.120242i
\(466\) 0 0
\(467\) 3.92532 27.3012i 0.181642 1.26335i −0.671237 0.741243i \(-0.734237\pi\)
0.852880 0.522108i \(-0.174854\pi\)
\(468\) 0 0
\(469\) 5.58249 + 2.31442i 0.257776 + 0.106870i
\(470\) 0 0
\(471\) 0.0590028 0.410373i 0.00271871 0.0189090i
\(472\) 0 0
\(473\) 12.1503 + 3.56764i 0.558670 + 0.164040i
\(474\) 0 0
\(475\) −10.4058 + 6.68740i −0.477450 + 0.306839i
\(476\) 0 0
\(477\) 5.39044 11.8034i 0.246811 0.540441i
\(478\) 0 0
\(479\) −23.3361 + 26.9313i −1.06625 + 1.23052i −0.0942520 + 0.995548i \(0.530046\pi\)
−0.972002 + 0.234974i \(0.924500\pi\)
\(480\) 0 0
\(481\) 12.8399 + 28.1155i 0.585451 + 1.28196i
\(482\) 0 0
\(483\) −4.53235 1.33082i −0.206229 0.0605543i
\(484\) 0 0
\(485\) 7.51316 + 4.82841i 0.341155 + 0.219247i
\(486\) 0 0
\(487\) −9.21644 2.70619i −0.417637 0.122629i 0.0661612 0.997809i \(-0.478925\pi\)
−0.483798 + 0.875180i \(0.660743\pi\)
\(488\) 0 0
\(489\) 14.1430 + 16.3219i 0.639568 + 0.738101i
\(490\) 0 0
\(491\) −13.3516 + 15.4086i −0.602551 + 0.695381i −0.972296 0.233752i \(-0.924900\pi\)
0.369745 + 0.929133i \(0.379445\pi\)
\(492\) 0 0
\(493\) −26.0580 + 7.65131i −1.17359 + 0.344598i
\(494\) 0 0
\(495\) −5.04762 + 1.48212i −0.226874 + 0.0666161i
\(496\) 0 0
\(497\) −3.15609 + 6.91088i −0.141570 + 0.309995i
\(498\) 0 0
\(499\) −27.0208 −1.20962 −0.604808 0.796371i \(-0.706750\pi\)
−0.604808 + 0.796371i \(0.706750\pi\)
\(500\) 0 0
\(501\) 13.4377 15.5080i 0.600354 0.692846i
\(502\) 0 0
\(503\) −2.74180 19.0696i −0.122251 0.850272i −0.954997 0.296617i \(-0.904142\pi\)
0.832746 0.553655i \(-0.186767\pi\)
\(504\) 0 0
\(505\) 2.55134 5.58666i 0.113533 0.248603i
\(506\) 0 0
\(507\) −28.9859 −1.28731
\(508\) 0 0
\(509\) 23.9309 15.3795i 1.06072 0.681682i 0.110693 0.993855i \(-0.464693\pi\)
0.950026 + 0.312172i \(0.101057\pi\)
\(510\) 0 0
\(511\) 5.04107 + 11.0384i 0.223004 + 0.488310i
\(512\) 0 0
\(513\) 4.32459 + 4.99085i 0.190935 + 0.220351i
\(514\) 0 0
\(515\) 13.4955 8.67305i 0.594684 0.382180i
\(516\) 0 0
\(517\) 2.29242 + 15.9441i 0.100821 + 0.701222i
\(518\) 0 0
\(519\) −20.0517 + 5.88771i −0.880173 + 0.258442i
\(520\) 0 0
\(521\) −2.42440 16.8621i −0.106215 0.738740i −0.971428 0.237336i \(-0.923726\pi\)
0.865213 0.501405i \(-0.167183\pi\)
\(522\) 0 0
\(523\) 4.13778 + 9.06048i 0.180933 + 0.396187i 0.978267 0.207351i \(-0.0664843\pi\)
−0.797334 + 0.603538i \(0.793757\pi\)
\(524\) 0 0
\(525\) 1.16335 + 0.747641i 0.0507729 + 0.0326297i
\(526\) 0 0
\(527\) −2.86631 + 19.9356i −0.124858 + 0.868409i
\(528\) 0 0
\(529\) −2.55245 + 17.7527i −0.110976 + 0.771857i
\(530\) 0 0
\(531\) −1.29271 0.830772i −0.0560987 0.0360524i
\(532\) 0 0
\(533\) 23.7152 + 27.3688i 1.02722 + 1.18548i
\(534\) 0 0
\(535\) −27.9598 −1.20881
\(536\) 0 0
\(537\) 17.4527 0.753141
\(538\) 0 0
\(539\) −12.5755 14.5129i −0.541664 0.625114i
\(540\) 0 0
\(541\) 29.5525 + 18.9922i 1.27056 + 0.816539i 0.989693 0.143207i \(-0.0457415\pi\)
0.280867 + 0.959747i \(0.409378\pi\)
\(542\) 0 0
\(543\) −2.13885 + 14.8760i −0.0917868 + 0.638392i
\(544\) 0 0
\(545\) 3.71943 25.8692i 0.159323 1.10811i
\(546\) 0 0
\(547\) −7.96729 5.12027i −0.340657 0.218927i 0.359115 0.933293i \(-0.383079\pi\)
−0.699772 + 0.714366i \(0.746715\pi\)
\(548\) 0 0
\(549\) −2.13867 4.68303i −0.0912762 0.199867i
\(550\) 0 0
\(551\) −6.59567 45.8739i −0.280985 1.95429i
\(552\) 0 0
\(553\) 0.660053 0.193809i 0.0280683 0.00824160i
\(554\) 0 0
\(555\) 1.20044 + 8.34922i 0.0509557 + 0.354405i
\(556\) 0 0
\(557\) −17.9883 + 11.5604i −0.762190 + 0.489830i −0.863080 0.505068i \(-0.831467\pi\)
0.100890 + 0.994898i \(0.467831\pi\)
\(558\) 0 0
\(559\) 18.0617 + 20.8444i 0.763930 + 0.881623i
\(560\) 0 0
\(561\) 4.78248 + 10.4722i 0.201917 + 0.442136i
\(562\) 0 0
\(563\) 20.0815 12.9056i 0.846336 0.543907i −0.0440943 0.999027i \(-0.514040\pi\)
0.890430 + 0.455121i \(0.150404\pi\)
\(564\) 0 0
\(565\) 19.1685 0.806423
\(566\) 0 0
\(567\) 0.306701 0.671581i 0.0128802 0.0282037i
\(568\) 0 0
\(569\) −5.79090 40.2766i −0.242767 1.68848i −0.638108 0.769947i \(-0.720283\pi\)
0.395341 0.918535i \(-0.370627\pi\)
\(570\) 0 0
\(571\) 7.67734 8.86012i 0.321287 0.370784i −0.572014 0.820244i \(-0.693838\pi\)
0.893301 + 0.449459i \(0.148383\pi\)
\(572\) 0 0
\(573\) 4.14559 0.173185
\(574\) 0 0
\(575\) 4.97832 10.9010i 0.207610 0.454603i
\(576\) 0 0
\(577\) −1.18383 + 0.347605i −0.0492836 + 0.0144710i −0.306281 0.951941i \(-0.599085\pi\)
0.256998 + 0.966412i \(0.417267\pi\)
\(578\) 0 0
\(579\) 23.0305 6.76235i 0.957113 0.281034i
\(580\) 0 0
\(581\) 4.71779 5.44462i 0.195727 0.225881i
\(582\) 0 0
\(583\) 25.2799 + 29.1746i 1.04699 + 1.20829i
\(584\) 0 0
\(585\) −10.9939 3.22811i −0.454543 0.133466i
\(586\) 0 0
\(587\) 26.7629 + 17.1995i 1.10462 + 0.709898i 0.960115 0.279605i \(-0.0902035\pi\)
0.144508 + 0.989504i \(0.453840\pi\)
\(588\) 0 0
\(589\) −32.9780 9.68323i −1.35884 0.398990i
\(590\) 0 0
\(591\) 6.82130 + 14.9366i 0.280591 + 0.614408i
\(592\) 0 0
\(593\) −27.6105 + 31.8642i −1.13383 + 1.30851i −0.188615 + 0.982051i \(0.560400\pi\)
−0.945212 + 0.326456i \(0.894146\pi\)
\(594\) 0 0
\(595\) −2.09875 + 4.59562i −0.0860403 + 0.188402i
\(596\) 0 0
\(597\) 8.93430 5.74173i 0.365657 0.234993i
\(598\) 0 0
\(599\) 13.3021 + 3.90585i 0.543509 + 0.159589i 0.541951 0.840410i \(-0.317686\pi\)
0.00155825 + 0.999999i \(0.499504\pi\)
\(600\) 0 0
\(601\) 5.81709 40.4588i 0.237284 1.65035i −0.428016 0.903771i \(-0.640787\pi\)
0.665300 0.746576i \(-0.268304\pi\)
\(602\) 0 0
\(603\) 7.56129 + 3.13480i 0.307919 + 0.127659i
\(604\) 0 0
\(605\) −0.540924 + 3.76221i −0.0219917 + 0.152955i
\(606\) 0 0
\(607\) −5.54600 1.62845i −0.225105 0.0660969i 0.167235 0.985917i \(-0.446516\pi\)
−0.392340 + 0.919820i \(0.628334\pi\)
\(608\) 0 0
\(609\) −4.35885 + 2.80126i −0.176630 + 0.113513i
\(610\) 0 0
\(611\) −14.5745 + 31.9136i −0.589619 + 1.29109i
\(612\) 0 0
\(613\) −8.69243 + 10.0316i −0.351084 + 0.405172i −0.903633 0.428308i \(-0.859110\pi\)
0.552549 + 0.833481i \(0.313655\pi\)
\(614\) 0 0
\(615\) 4.10553 + 8.98985i 0.165551 + 0.362506i
\(616\) 0 0
\(617\) −25.0756 7.36286i −1.00951 0.296418i −0.265155 0.964206i \(-0.585423\pi\)
−0.744351 + 0.667788i \(0.767241\pi\)
\(618\) 0 0
\(619\) −8.70956 5.59730i −0.350067 0.224974i 0.353776 0.935330i \(-0.384898\pi\)
−0.703843 + 0.710356i \(0.748534\pi\)
\(620\) 0 0
\(621\) −6.13890 1.80254i −0.246346 0.0723336i
\(622\) 0 0
\(623\) −1.65565 1.91072i −0.0663323 0.0765515i
\(624\) 0 0
\(625\) 7.94106 9.16447i 0.317642 0.366579i
\(626\) 0 0
\(627\) −18.8505 + 5.53501i −0.752817 + 0.221047i
\(628\) 0 0
\(629\) 17.7116 5.20059i 0.706207 0.207361i
\(630\) 0 0
\(631\) −3.64340 + 7.97794i −0.145042 + 0.317597i −0.968184 0.250237i \(-0.919491\pi\)
0.823143 + 0.567834i \(0.192219\pi\)
\(632\) 0 0
\(633\) −3.96713 −0.157679
\(634\) 0 0
\(635\) 16.9555 19.5677i 0.672860 0.776522i
\(636\) 0 0
\(637\) −5.95240 41.3999i −0.235843 1.64032i
\(638\) 0 0
\(639\) −4.27482 + 9.36054i −0.169109 + 0.370297i
\(640\) 0 0
\(641\) 6.64792 0.262577 0.131288 0.991344i \(-0.458089\pi\)
0.131288 + 0.991344i \(0.458089\pi\)
\(642\) 0 0
\(643\) −25.7116 + 16.5239i −1.01397 + 0.651638i −0.938417 0.345504i \(-0.887708\pi\)
−0.0755507 + 0.997142i \(0.524071\pi\)
\(644\) 0 0
\(645\) 3.12681 + 6.84675i 0.123118 + 0.269591i
\(646\) 0 0
\(647\) −16.0529 18.5260i −0.631105 0.728334i 0.346671 0.937987i \(-0.387312\pi\)
−0.977776 + 0.209653i \(0.932767\pi\)
\(648\) 0 0
\(649\) 3.84579 2.47154i 0.150960 0.0970163i
\(650\) 0 0
\(651\) 0.546852 + 3.80344i 0.0214328 + 0.149068i
\(652\) 0 0
\(653\) −38.5310 + 11.3137i −1.50784 + 0.442741i −0.928183 0.372123i \(-0.878630\pi\)
−0.579652 + 0.814864i \(0.696812\pi\)
\(654\) 0 0
\(655\) 3.71036 + 25.8061i 0.144976 + 1.00833i
\(656\) 0 0
\(657\) 6.82795 + 14.9511i 0.266384 + 0.583299i
\(658\) 0 0
\(659\) 33.0413 + 21.2343i 1.28710 + 0.827172i 0.991746 0.128215i \(-0.0409246\pi\)
0.295358 + 0.955387i \(0.404561\pi\)
\(660\) 0 0
\(661\) 3.38514 23.5441i 0.131667 0.915761i −0.811716 0.584053i \(-0.801466\pi\)
0.943382 0.331708i \(-0.107625\pi\)
\(662\) 0 0
\(663\) −3.56852 + 24.8196i −0.138590 + 0.963912i
\(664\) 0 0
\(665\) −7.25296 4.66120i −0.281258 0.180753i
\(666\) 0 0
\(667\) 29.4043 + 33.9343i 1.13854 + 1.31394i
\(668\) 0 0
\(669\) −0.617962 −0.0238918
\(670\) 0 0
\(671\) 15.3160 0.591269
\(672\) 0 0
\(673\) −6.09943 7.03912i −0.235116 0.271338i 0.625915 0.779892i \(-0.284726\pi\)
−0.861030 + 0.508553i \(0.830180\pi\)
\(674\) 0 0
\(675\) 1.57572 + 1.01265i 0.0606495 + 0.0389770i
\(676\) 0 0
\(677\) −1.87703 + 13.0550i −0.0721402 + 0.501746i 0.921431 + 0.388541i \(0.127021\pi\)
−0.993572 + 0.113205i \(0.963888\pi\)
\(678\) 0 0
\(679\) 0.530663 3.69084i 0.0203650 0.141641i
\(680\) 0 0
\(681\) −5.48932 3.52777i −0.210351 0.135184i
\(682\) 0 0
\(683\) −12.2310 26.7821i −0.468006 1.02479i −0.985589 0.169157i \(-0.945896\pi\)
0.517583 0.855633i \(-0.326832\pi\)
\(684\) 0 0
\(685\) −4.33446 30.1468i −0.165611 1.15185i
\(686\) 0 0
\(687\) 0.610694 0.179316i 0.0232994 0.00684133i
\(688\) 0 0
\(689\) 11.9658 + 83.2243i 0.455862 + 3.17059i
\(690\) 0 0
\(691\) −1.38214 + 0.888247i −0.0525791 + 0.0337905i −0.566666 0.823947i \(-0.691767\pi\)
0.514087 + 0.857738i \(0.328131\pi\)
\(692\) 0 0
\(693\) 1.43836 + 1.65995i 0.0546387 + 0.0630564i
\(694\) 0 0
\(695\) 14.6397 + 32.0565i 0.555316 + 1.21597i
\(696\) 0 0
\(697\) 18.1945 11.6929i 0.689165 0.442899i
\(698\) 0 0
\(699\) −9.66043 −0.365391
\(700\) 0 0
\(701\) −0.423947 + 0.928314i −0.0160123 + 0.0350619i −0.917469 0.397807i \(-0.869771\pi\)
0.901457 + 0.432869i \(0.142499\pi\)
\(702\) 0 0
\(703\) 4.48307 + 31.1805i 0.169082 + 1.17599i
\(704\) 0 0
\(705\) −6.27000 + 7.23596i −0.236142 + 0.272522i
\(706\) 0 0
\(707\) −2.56424 −0.0964383
\(708\) 0 0
\(709\) −4.78205 + 10.4712i −0.179594 + 0.393255i −0.977923 0.208966i \(-0.932990\pi\)
0.798329 + 0.602221i \(0.205718\pi\)
\(710\) 0 0
\(711\) 0.894018 0.262507i 0.0335283 0.00984479i
\(712\) 0 0
\(713\) 31.9505 9.38151i 1.19656 0.351340i
\(714\) 0 0
\(715\) 22.3226 25.7617i 0.834819 0.963433i
\(716\) 0 0
\(717\) 0.298367 + 0.344334i 0.0111427 + 0.0128594i
\(718\) 0 0
\(719\) 31.7813 + 9.33183i 1.18524 + 0.348018i 0.814193 0.580595i \(-0.197180\pi\)
0.371049 + 0.928613i \(0.378998\pi\)
\(720\) 0 0
\(721\) −5.63460 3.62113i −0.209843 0.134858i
\(722\) 0 0
\(723\) 15.6080 + 4.58292i 0.580468 + 0.170441i
\(724\) 0 0
\(725\) −5.46068 11.9572i −0.202805 0.444080i
\(726\) 0 0
\(727\) −18.3702 + 21.2004i −0.681314 + 0.786279i −0.986102 0.166142i \(-0.946869\pi\)
0.304788 + 0.952420i \(0.401415\pi\)
\(728\) 0 0
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 0 0
\(731\) 13.8571 8.90541i 0.512523 0.329379i
\(732\) 0 0
\(733\) −30.9901 9.09950i −1.14464 0.336098i −0.346196 0.938162i \(-0.612527\pi\)
−0.798448 + 0.602064i \(0.794345\pi\)
\(734\) 0 0
\(735\) 1.62443 11.2981i 0.0599179 0.416738i
\(736\) 0 0
\(737\) −17.8279 + 16.5878i −0.656698 + 0.611019i
\(738\) 0 0
\(739\) 2.05505 14.2932i 0.0755961 0.525783i −0.916474 0.400095i \(-0.868977\pi\)
0.992070 0.125688i \(-0.0401137\pi\)
\(740\) 0 0
\(741\) −41.0572 12.0555i −1.50827 0.442869i
\(742\) 0 0
\(743\) −4.77432 + 3.06827i −0.175153 + 0.112564i −0.625280 0.780401i \(-0.715015\pi\)
0.450127 + 0.892965i \(0.351379\pi\)
\(744\) 0 0
\(745\) 7.47302 16.3636i 0.273790 0.599517i
\(746\) 0 0
\(747\) 6.39007 7.37454i 0.233801 0.269820i
\(748\) 0 0
\(749\) 4.84941 + 10.6187i 0.177193 + 0.388000i
\(750\) 0 0
\(751\) −13.0432 3.82983i −0.475953 0.139752i 0.0349531 0.999389i \(-0.488872\pi\)
−0.510906 + 0.859637i \(0.670690\pi\)
\(752\) 0 0
\(753\) 4.78537 + 3.07537i 0.174389 + 0.112073i
\(754\) 0 0
\(755\) 3.54934 + 1.04218i 0.129174 + 0.0379289i
\(756\) 0 0
\(757\) 24.8713 + 28.7030i 0.903962 + 1.04323i 0.998860 + 0.0477407i \(0.0152021\pi\)
−0.0948978 + 0.995487i \(0.530252\pi\)
\(758\) 0 0
\(759\) 12.4647 14.3851i 0.452441 0.522145i
\(760\) 0 0
\(761\) −8.41179 + 2.46993i −0.304927 + 0.0895347i −0.430617 0.902535i \(-0.641704\pi\)
0.125689 + 0.992070i \(0.459886\pi\)
\(762\) 0 0
\(763\) −10.4699 + 3.07423i −0.379034 + 0.111294i
\(764\) 0 0
\(765\) −2.84268 + 6.22460i −0.102777 + 0.225051i
\(766\) 0 0
\(767\) 9.95691 0.359523
\(768\) 0 0
\(769\) −17.9079 + 20.6668i −0.645776 + 0.745265i −0.980385 0.197092i \(-0.936850\pi\)
0.334609 + 0.942357i \(0.391396\pi\)
\(770\) 0 0
\(771\) 0.0818272 + 0.569121i 0.00294694 + 0.0204964i
\(772\) 0 0
\(773\) 3.97491 8.70384i 0.142968 0.313055i −0.824580 0.565746i \(-0.808588\pi\)
0.967547 + 0.252691i \(0.0813155\pi\)
\(774\) 0 0
\(775\) −9.74852 −0.350177
\(776\) 0 0
\(777\) 2.96271 1.90402i 0.106287 0.0683062i
\(778\) 0 0
\(779\) 15.3322 + 33.5729i 0.549334 + 1.20287i
\(780\) 0 0
\(781\) −20.0479 23.1365i −0.717371 0.827891i