Properties

Label 804.2.y.b.49.5
Level 804
Weight 2
Character 804.49
Analytic conductor 6.420
Analytic rank 0
Dimension 120
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.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 49.5
Character \(\chi\) = 804.49
Dual form 804.2.y.b.361.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +(1.12351 + 0.449787i) q^{11} +(-1.87649 - 1.78923i) q^{13} +(1.08168 - 2.36856i) q^{15} +(-0.432922 + 1.25085i) q^{17} +(-2.72887 + 0.260576i) q^{19} +(-3.99710 - 3.14336i) q^{21} +(-0.334601 + 7.02413i) q^{23} +(-1.70800 + 0.501514i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-0.475676 + 0.823894i) q^{29} +(2.66411 - 2.54023i) q^{31} +(-0.701987 - 0.985803i) q^{33} +(0.630019 + 13.2257i) q^{35} +(-0.0722595 - 0.125157i) q^{37} +(0.611273 + 2.51970i) q^{39} +(2.86735 - 0.552636i) q^{41} +(2.29395 + 2.64736i) q^{43} +(-2.19051 + 1.40776i) q^{45} +(-2.68982 + 1.38670i) q^{47} +(18.5167 + 3.56881i) q^{49} +(1.04046 - 0.818224i) q^{51} +(3.84849 - 4.44139i) q^{53} +(-0.742925 + 3.06238i) q^{55} +(2.43655 + 1.25613i) q^{57} +(9.06210 + 2.66087i) q^{59} +(-10.6901 + 4.27966i) q^{61} +(1.66315 + 4.80536i) q^{63} +(3.91612 - 5.49942i) q^{65} +(-1.01038 - 8.12275i) q^{67} +(4.07902 - 5.72818i) q^{69} +(1.79677 + 5.19142i) q^{71} +(8.52691 - 3.41366i) q^{73} +(1.70800 + 0.501514i) q^{75} +(5.46983 + 2.81989i) q^{77} +(-3.37120 + 13.8963i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-9.03833 + 7.10782i) q^{83} +(-3.38431 - 0.652272i) q^{85} +(0.845595 - 0.435934i) q^{87} +(5.42733 - 3.48794i) q^{89} +(-8.63395 - 9.96411i) q^{91} +(-3.61455 + 0.696647i) q^{93} +(-1.68283 - 6.93673i) q^{95} +(-4.30471 - 7.45598i) q^{97} +(0.0575838 + 1.20883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{33}\right)\) \(1\)

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
\(3\) −0.841254 0.540641i −0.485698 0.312139i
\(4\) 0 0
\(5\) 0.370568 + 2.57736i 0.165723 + 1.15263i 0.887602 + 0.460611i \(0.152370\pi\)
−0.721879 + 0.692020i \(0.756721\pi\)
\(6\) 0 0
\(7\) 5.06200 + 0.483363i 1.91326 + 0.182694i 0.982923 0.184017i \(-0.0589102\pi\)
0.930335 + 0.366711i \(0.119516\pi\)
\(8\) 0 0
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 0 0
\(11\) 1.12351 + 0.449787i 0.338752 + 0.135616i 0.534801 0.844978i \(-0.320387\pi\)
−0.196048 + 0.980594i \(0.562811\pi\)
\(12\) 0 0
\(13\) −1.87649 1.78923i −0.520445 0.496243i 0.383707 0.923455i \(-0.374647\pi\)
−0.904152 + 0.427212i \(0.859496\pi\)
\(14\) 0 0
\(15\) 1.08168 2.36856i 0.279290 0.611559i
\(16\) 0 0
\(17\) −0.432922 + 1.25085i −0.104999 + 0.303375i −0.985247 0.171140i \(-0.945255\pi\)
0.880248 + 0.474514i \(0.157376\pi\)
\(18\) 0 0
\(19\) −2.72887 + 0.260576i −0.626046 + 0.0597802i −0.403258 0.915087i \(-0.632122\pi\)
−0.222789 + 0.974867i \(0.571516\pi\)
\(20\) 0 0
\(21\) −3.99710 3.14336i −0.872239 0.685937i
\(22\) 0 0
\(23\) −0.334601 + 7.02413i −0.0697690 + 1.46463i 0.644416 + 0.764675i \(0.277101\pi\)
−0.714185 + 0.699957i \(0.753202\pi\)
\(24\) 0 0
\(25\) −1.70800 + 0.501514i −0.341600 + 0.100303i
\(26\) 0 0
\(27\) 0.142315 0.989821i 0.0273885 0.190491i
\(28\) 0 0
\(29\) −0.475676 + 0.823894i −0.0883307 + 0.152993i −0.906806 0.421549i \(-0.861487\pi\)
0.818475 + 0.574542i \(0.194820\pi\)
\(30\) 0 0
\(31\) 2.66411 2.54023i 0.478489 0.456238i −0.412039 0.911166i \(-0.635183\pi\)
0.890528 + 0.454928i \(0.150335\pi\)
\(32\) 0 0
\(33\) −0.701987 0.985803i −0.122200 0.171606i
\(34\) 0 0
\(35\) 0.630019 + 13.2257i 0.106493 + 2.23556i
\(36\) 0 0
\(37\) −0.0722595 0.125157i −0.0118794 0.0205757i 0.860025 0.510253i \(-0.170448\pi\)
−0.871904 + 0.489677i \(0.837115\pi\)
\(38\) 0 0
\(39\) 0.611273 + 2.51970i 0.0978821 + 0.403475i
\(40\) 0 0
\(41\) 2.86735 0.552636i 0.447805 0.0863073i 0.0396369 0.999214i \(-0.487380\pi\)
0.408168 + 0.912907i \(0.366168\pi\)
\(42\) 0 0
\(43\) 2.29395 + 2.64736i 0.349824 + 0.403719i 0.903205 0.429210i \(-0.141208\pi\)
−0.553381 + 0.832929i \(0.686662\pi\)
\(44\) 0 0
\(45\) −2.19051 + 1.40776i −0.326542 + 0.209856i
\(46\) 0 0
\(47\) −2.68982 + 1.38670i −0.392350 + 0.202271i −0.643101 0.765781i \(-0.722353\pi\)
0.250751 + 0.968052i \(0.419322\pi\)
\(48\) 0 0
\(49\) 18.5167 + 3.56881i 2.64525 + 0.509830i
\(50\) 0 0
\(51\) 1.04046 0.818224i 0.145693 0.114574i
\(52\) 0 0
\(53\) 3.84849 4.44139i 0.528630 0.610072i −0.427140 0.904185i \(-0.640479\pi\)
0.955771 + 0.294113i \(0.0950243\pi\)
\(54\) 0 0
\(55\) −0.742925 + 3.06238i −0.100176 + 0.412931i
\(56\) 0 0
\(57\) 2.43655 + 1.25613i 0.322729 + 0.166378i
\(58\) 0 0
\(59\) 9.06210 + 2.66087i 1.17978 + 0.346416i 0.812091 0.583531i \(-0.198329\pi\)
0.367694 + 0.929947i \(0.380148\pi\)
\(60\) 0 0
\(61\) −10.6901 + 4.27966i −1.36872 + 0.547954i −0.935498 0.353332i \(-0.885049\pi\)
−0.433225 + 0.901286i \(0.642624\pi\)
\(62\) 0 0
\(63\) 1.66315 + 4.80536i 0.209537 + 0.605418i
\(64\) 0 0
\(65\) 3.91612 5.49942i 0.485735 0.682120i
\(66\) 0 0
\(67\) −1.01038 8.12275i −0.123438 0.992352i
\(68\) 0 0
\(69\) 4.07902 5.72818i 0.491056 0.689591i
\(70\) 0 0
\(71\) 1.79677 + 5.19142i 0.213237 + 0.616109i 0.999999 0.00114777i \(-0.000365348\pi\)
−0.786762 + 0.617256i \(0.788244\pi\)
\(72\) 0 0
\(73\) 8.52691 3.41366i 0.997999 0.399538i 0.185590 0.982627i \(-0.440580\pi\)
0.812408 + 0.583089i \(0.198156\pi\)
\(74\) 0 0
\(75\) 1.70800 + 0.501514i 0.197223 + 0.0579099i
\(76\) 0 0
\(77\) 5.46983 + 2.81989i 0.623345 + 0.321356i
\(78\) 0 0
\(79\) −3.37120 + 13.8963i −0.379289 + 1.56345i 0.387696 + 0.921787i \(0.373271\pi\)
−0.766985 + 0.641665i \(0.778244\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) 0 0
\(83\) −9.03833 + 7.10782i −0.992086 + 0.780185i −0.975572 0.219679i \(-0.929499\pi\)
−0.0165138 + 0.999864i \(0.505257\pi\)
\(84\) 0 0
\(85\) −3.38431 0.652272i −0.367080 0.0707489i
\(86\) 0 0
\(87\) 0.845595 0.435934i 0.0906573 0.0467371i
\(88\) 0 0
\(89\) 5.42733 3.48794i 0.575296 0.369720i −0.220406 0.975408i \(-0.570738\pi\)
0.795702 + 0.605688i \(0.207102\pi\)
\(90\) 0 0
\(91\) −8.63395 9.96411i −0.905084 1.04452i
\(92\) 0 0
\(93\) −3.61455 + 0.696647i −0.374811 + 0.0722389i
\(94\) 0 0
\(95\) −1.68283 6.93673i −0.172655 0.711693i
\(96\) 0 0
\(97\) −4.30471 7.45598i −0.437077 0.757040i 0.560385 0.828232i \(-0.310653\pi\)
−0.997463 + 0.0711919i \(0.977320\pi\)
\(98\) 0 0
\(99\) 0.0575838 + 1.20883i 0.00578739 + 0.121492i
\(100\) 0 0
\(101\) −8.85696 12.4379i −0.881301 1.23761i −0.970379 0.241589i \(-0.922331\pi\)
0.0890778 0.996025i \(-0.471608\pi\)
\(102\) 0 0
\(103\) 2.14835 2.04844i 0.211683 0.201839i −0.576818 0.816872i \(-0.695706\pi\)
0.788501 + 0.615033i \(0.210857\pi\)
\(104\) 0 0
\(105\) 6.62036 11.4668i 0.646081 1.11905i
\(106\) 0 0
\(107\) −0.782903 + 5.44521i −0.0756861 + 0.526408i 0.916343 + 0.400395i \(0.131127\pi\)
−0.992029 + 0.126013i \(0.959782\pi\)
\(108\) 0 0
\(109\) 13.8640 4.07083i 1.32793 0.389915i 0.460581 0.887618i \(-0.347641\pi\)
0.867348 + 0.497703i \(0.165823\pi\)
\(110\) 0 0
\(111\) −0.00687649 + 0.144355i −0.000652687 + 0.0137016i
\(112\) 0 0
\(113\) −8.89916 6.99837i −0.837162 0.658352i 0.104643 0.994510i \(-0.466630\pi\)
−0.941806 + 0.336158i \(0.890872\pi\)
\(114\) 0 0
\(115\) −18.2277 + 1.74054i −1.69974 + 0.162306i
\(116\) 0 0
\(117\) 0.848018 2.45019i 0.0783993 0.226520i
\(118\) 0 0
\(119\) −2.79607 + 6.12253i −0.256315 + 0.561252i
\(120\) 0 0
\(121\) −6.90110 6.58018i −0.627373 0.598198i
\(122\) 0 0
\(123\) −2.71095 1.08530i −0.244438 0.0978581i
\(124\) 0 0
\(125\) 3.48291 + 7.62650i 0.311521 + 0.682135i
\(126\) 0 0
\(127\) −8.06798 0.770399i −0.715917 0.0683618i −0.269261 0.963067i \(-0.586779\pi\)
−0.446657 + 0.894705i \(0.647385\pi\)
\(128\) 0 0
\(129\) −0.498523 3.46730i −0.0438925 0.305279i
\(130\) 0 0
\(131\) −8.27935 5.32081i −0.723370 0.464882i 0.126438 0.991975i \(-0.459646\pi\)
−0.849808 + 0.527093i \(0.823282\pi\)
\(132\) 0 0
\(133\) −13.9395 −1.20871
\(134\) 0 0
\(135\) 2.60386 0.224105
\(136\) 0 0
\(137\) 13.1755 + 8.46737i 1.12566 + 0.723416i 0.964649 0.263537i \(-0.0848892\pi\)
0.161008 + 0.986953i \(0.448526\pi\)
\(138\) 0 0
\(139\) −1.21327 8.43848i −0.102908 0.715742i −0.974316 0.225184i \(-0.927702\pi\)
0.871408 0.490559i \(-0.163207\pi\)
\(140\) 0 0
\(141\) 3.01252 + 0.287661i 0.253700 + 0.0242254i
\(142\) 0 0
\(143\) −1.30349 2.85425i −0.109003 0.238684i
\(144\) 0 0
\(145\) −2.29974 0.920678i −0.190983 0.0764582i
\(146\) 0 0
\(147\) −13.6478 13.0132i −1.12565 1.07331i
\(148\) 0 0
\(149\) −6.29448 + 13.7830i −0.515664 + 1.12915i 0.455392 + 0.890291i \(0.349499\pi\)
−0.971055 + 0.238855i \(0.923228\pi\)
\(150\) 0 0
\(151\) −2.64275 + 7.63574i −0.215064 + 0.621388i 0.784934 + 0.619579i \(0.212697\pi\)
−0.999998 + 0.00180825i \(0.999424\pi\)
\(152\) 0 0
\(153\) −1.31765 + 0.125821i −0.106526 + 0.0101720i
\(154\) 0 0
\(155\) 7.53432 + 5.92506i 0.605171 + 0.475912i
\(156\) 0 0
\(157\) 0.606027 12.7221i 0.0483663 1.01533i −0.836056 0.548645i \(-0.815144\pi\)
0.884422 0.466688i \(-0.154553\pi\)
\(158\) 0 0
\(159\) −5.63875 + 1.65569i −0.447182 + 0.131305i
\(160\) 0 0
\(161\) −5.08895 + 35.3944i −0.401066 + 2.78947i
\(162\) 0 0
\(163\) 7.73805 13.4027i 0.606091 1.04978i −0.385787 0.922588i \(-0.626070\pi\)
0.991878 0.127192i \(-0.0405966\pi\)
\(164\) 0 0
\(165\) 2.28064 2.17458i 0.177547 0.169291i
\(166\) 0 0
\(167\) 10.3247 + 14.4991i 0.798953 + 1.12197i 0.990094 + 0.140409i \(0.0448418\pi\)
−0.191141 + 0.981563i \(0.561219\pi\)
\(168\) 0 0
\(169\) −0.298693 6.27033i −0.0229764 0.482333i
\(170\) 0 0
\(171\) −1.37064 2.37402i −0.104816 0.181546i
\(172\) 0 0
\(173\) −5.65157 23.2961i −0.429681 1.77117i −0.615038 0.788498i \(-0.710859\pi\)
0.185357 0.982671i \(-0.440656\pi\)
\(174\) 0 0
\(175\) −8.88832 + 1.71308i −0.671894 + 0.129497i
\(176\) 0 0
\(177\) −6.18494 7.13781i −0.464889 0.536510i
\(178\) 0 0
\(179\) 4.97089 3.19460i 0.371542 0.238775i −0.341523 0.939873i \(-0.610943\pi\)
0.713065 + 0.701098i \(0.247306\pi\)
\(180\) 0 0
\(181\) −6.30900 + 3.25251i −0.468944 + 0.241757i −0.676467 0.736473i \(-0.736490\pi\)
0.207523 + 0.978230i \(0.433460\pi\)
\(182\) 0 0
\(183\) 11.3068 + 2.17921i 0.835824 + 0.161092i
\(184\) 0 0
\(185\) 0.295798 0.232618i 0.0217475 0.0171024i
\(186\) 0 0
\(187\) −1.04901 + 1.21062i −0.0767112 + 0.0885294i
\(188\) 0 0
\(189\) 1.19884 4.94169i 0.0872029 0.359455i
\(190\) 0 0
\(191\) −24.0238 12.3851i −1.73830 0.896155i −0.965056 0.262044i \(-0.915603\pi\)
−0.773242 0.634111i \(-0.781366\pi\)
\(192\) 0 0
\(193\) 14.3949 + 4.22671i 1.03616 + 0.304245i 0.755215 0.655477i \(-0.227532\pi\)
0.280950 + 0.959723i \(0.409351\pi\)
\(194\) 0 0
\(195\) −6.26766 + 2.50919i −0.448837 + 0.179687i
\(196\) 0 0
\(197\) 0.246166 + 0.711249i 0.0175386 + 0.0506744i 0.953430 0.301613i \(-0.0975251\pi\)
−0.935892 + 0.352288i \(0.885404\pi\)
\(198\) 0 0
\(199\) 0.166767 0.234192i 0.0118218 0.0166014i −0.808623 0.588328i \(-0.799787\pi\)
0.820445 + 0.571726i \(0.193726\pi\)
\(200\) 0 0
\(201\) −3.54150 + 7.37955i −0.249798 + 0.520513i
\(202\) 0 0
\(203\) −2.80611 + 3.94063i −0.196950 + 0.276578i
\(204\) 0 0
\(205\) 2.48689 + 7.18541i 0.173692 + 0.501850i
\(206\) 0 0
\(207\) −6.52837 + 2.61357i −0.453753 + 0.181655i
\(208\) 0 0
\(209\) −3.18313 0.934652i −0.220182 0.0646513i
\(210\) 0 0
\(211\) −10.1264 5.22055i −0.697133 0.359397i 0.0729543 0.997335i \(-0.476757\pi\)
−0.770088 + 0.637938i \(0.779788\pi\)
\(212\) 0 0
\(213\) 1.29516 5.33871i 0.0887427 0.365802i
\(214\) 0 0
\(215\) −5.97314 + 6.89337i −0.407364 + 0.470124i
\(216\) 0 0
\(217\) 14.7136 11.5709i 0.998825 0.785485i
\(218\) 0 0
\(219\) −9.01885 1.73824i −0.609438 0.117459i
\(220\) 0 0
\(221\) 3.05043 1.57260i 0.205194 0.105785i
\(222\) 0 0
\(223\) 14.2642 9.16706i 0.955203 0.613872i 0.0325368 0.999471i \(-0.489641\pi\)
0.922667 + 0.385599i \(0.126005\pi\)
\(224\) 0 0
\(225\) −1.16572 1.34532i −0.0777149 0.0896877i
\(226\) 0 0
\(227\) 26.7183 5.14952i 1.77335 0.341786i 0.805364 0.592780i \(-0.201970\pi\)
0.967989 + 0.250994i \(0.0807575\pi\)
\(228\) 0 0
\(229\) −2.80822 11.5756i −0.185572 0.764940i −0.986170 0.165738i \(-0.947000\pi\)
0.800597 0.599203i \(-0.204516\pi\)
\(230\) 0 0
\(231\) −3.07696 5.32946i −0.202449 0.350652i
\(232\) 0 0
\(233\) 0.0987032 + 2.07203i 0.00646626 + 0.135744i 0.999792 + 0.0203998i \(0.00649391\pi\)
−0.993326 + 0.115344i \(0.963203\pi\)
\(234\) 0 0
\(235\) −4.57078 6.41876i −0.298165 0.418714i
\(236\) 0 0
\(237\) 10.3489 9.86768i 0.672235 0.640975i
\(238\) 0 0
\(239\) 11.6048 20.1001i 0.750652 1.30017i −0.196854 0.980433i \(-0.563073\pi\)
0.947507 0.319736i \(-0.103594\pi\)
\(240\) 0 0
\(241\) 3.73281 25.9622i 0.240451 1.67237i −0.409432 0.912341i \(-0.634273\pi\)
0.649883 0.760034i \(-0.274818\pi\)
\(242\) 0 0
\(243\) 0.959493 0.281733i 0.0615515 0.0180732i
\(244\) 0 0
\(245\) −2.33639 + 49.0468i −0.149266 + 3.13349i
\(246\) 0 0
\(247\) 5.58693 + 4.39361i 0.355488 + 0.279559i
\(248\) 0 0
\(249\) 11.4463 1.09299i 0.725380 0.0692654i
\(250\) 0 0
\(251\) 8.97241 25.9241i 0.566333 1.63631i −0.189746 0.981833i \(-0.560767\pi\)
0.756080 0.654480i \(-0.227112\pi\)
\(252\) 0 0
\(253\) −3.53530 + 7.74122i −0.222262 + 0.486686i
\(254\) 0 0
\(255\) 2.49442 + 2.37842i 0.156206 + 0.148943i
\(256\) 0 0
\(257\) −20.3242 8.13657i −1.26779 0.507545i −0.362356 0.932040i \(-0.618027\pi\)
−0.905430 + 0.424495i \(0.860452\pi\)
\(258\) 0 0
\(259\) −0.305281 0.668473i −0.0189693 0.0415369i
\(260\) 0 0
\(261\) −0.947043 0.0904317i −0.0586205 0.00559758i
\(262\) 0 0
\(263\) −1.09377 7.60733i −0.0674447 0.469088i −0.995354 0.0962824i \(-0.969305\pi\)
0.927909 0.372806i \(-0.121604\pi\)
\(264\) 0 0
\(265\) 12.8732 + 8.27310i 0.790794 + 0.508213i
\(266\) 0 0
\(267\) −6.45148 −0.394824
\(268\) 0 0
\(269\) −18.0212 −1.09877 −0.549386 0.835568i \(-0.685138\pi\)
−0.549386 + 0.835568i \(0.685138\pi\)
\(270\) 0 0
\(271\) 2.05234 + 1.31896i 0.124671 + 0.0801209i 0.601490 0.798880i \(-0.294574\pi\)
−0.476819 + 0.879001i \(0.658210\pi\)
\(272\) 0 0
\(273\) 1.87634 + 13.0502i 0.113561 + 0.789835i
\(274\) 0 0
\(275\) −2.14454 0.204779i −0.129321 0.0123486i
\(276\) 0 0
\(277\) −1.59627 3.49535i −0.0959107 0.210015i 0.855595 0.517645i \(-0.173191\pi\)
−0.951506 + 0.307630i \(0.900464\pi\)
\(278\) 0 0
\(279\) 3.41739 + 1.36811i 0.204594 + 0.0819069i
\(280\) 0 0
\(281\) −23.0547 21.9826i −1.37533 1.31137i −0.902801 0.430058i \(-0.858493\pi\)
−0.472528 0.881316i \(-0.656658\pi\)
\(282\) 0 0
\(283\) −9.67117 + 21.1769i −0.574891 + 1.25884i 0.369261 + 0.929326i \(0.379611\pi\)
−0.944152 + 0.329511i \(0.893116\pi\)
\(284\) 0 0
\(285\) −2.33459 + 6.74536i −0.138289 + 0.399560i
\(286\) 0 0
\(287\) 14.7817 1.41148i 0.872534 0.0833169i
\(288\) 0 0
\(289\) 11.9857 + 9.42566i 0.705042 + 0.554451i
\(290\) 0 0
\(291\) −0.409653 + 8.59967i −0.0240143 + 0.504122i
\(292\) 0 0
\(293\) 7.53424 2.21225i 0.440155 0.129241i −0.0541438 0.998533i \(-0.517243\pi\)
0.494299 + 0.869292i \(0.335425\pi\)
\(294\) 0 0
\(295\) −3.49990 + 24.3423i −0.203772 + 1.41726i
\(296\) 0 0
\(297\) 0.605102 1.04807i 0.0351116 0.0608151i
\(298\) 0 0
\(299\) 13.1957 12.5820i 0.763125 0.727638i
\(300\) 0 0
\(301\) 10.3324 + 14.5098i 0.595547 + 0.836329i
\(302\) 0 0
\(303\) 0.726534 + 15.2518i 0.0417383 + 0.876195i
\(304\) 0 0
\(305\) −14.9916 25.9663i −0.858418 1.48682i
\(306\) 0 0
\(307\) −0.457844 1.88726i −0.0261305 0.107711i 0.957253 0.289252i \(-0.0934067\pi\)
−0.983383 + 0.181541i \(0.941892\pi\)
\(308\) 0 0
\(309\) −2.91477 + 0.561777i −0.165816 + 0.0319584i
\(310\) 0 0
\(311\) −0.886652 1.02325i −0.0502774 0.0580232i 0.730054 0.683390i \(-0.239495\pi\)
−0.780331 + 0.625366i \(0.784950\pi\)
\(312\) 0 0
\(313\) 5.10202 3.27887i 0.288383 0.185333i −0.388449 0.921470i \(-0.626989\pi\)
0.676832 + 0.736138i \(0.263353\pi\)
\(314\) 0 0
\(315\) −11.7688 + 6.06725i −0.663098 + 0.341851i
\(316\) 0 0
\(317\) −3.72444 0.717828i −0.209186 0.0403172i 0.0835818 0.996501i \(-0.473364\pi\)
−0.292767 + 0.956184i \(0.594576\pi\)
\(318\) 0 0
\(319\) −0.905006 + 0.711705i −0.0506706 + 0.0398478i
\(320\) 0 0
\(321\) 3.60252 4.15753i 0.201073 0.232051i
\(322\) 0 0
\(323\) 0.855449 3.52621i 0.0475985 0.196204i
\(324\) 0 0
\(325\) 4.10237 + 2.11492i 0.227559 + 0.117315i
\(326\) 0 0
\(327\) −13.8640 4.07083i −0.766680 0.225118i
\(328\) 0 0
\(329\) −14.2861 + 5.71931i −0.787621 + 0.315316i
\(330\) 0 0
\(331\) 4.71666 + 13.6279i 0.259251 + 0.749056i 0.997240 + 0.0742437i \(0.0236543\pi\)
−0.737989 + 0.674812i \(0.764225\pi\)
\(332\) 0 0
\(333\) 0.0838292 0.117722i 0.00459381 0.00645111i
\(334\) 0 0
\(335\) 20.5608 5.61416i 1.12336 0.306734i
\(336\) 0 0
\(337\) −5.08101 + 7.13528i −0.276780 + 0.388683i −0.929443 0.368965i \(-0.879712\pi\)
0.652663 + 0.757648i \(0.273652\pi\)
\(338\) 0 0
\(339\) 3.70284 + 10.6987i 0.201111 + 0.581071i
\(340\) 0 0
\(341\) 4.13574 1.65570i 0.223963 0.0896611i
\(342\) 0 0
\(343\) 57.8535 + 16.9873i 3.12379 + 0.917229i
\(344\) 0 0
\(345\) 16.2751 + 8.39041i 0.876224 + 0.451725i
\(346\) 0 0
\(347\) −8.07631 + 33.2910i −0.433559 + 1.78716i 0.165237 + 0.986254i \(0.447161\pi\)
−0.598797 + 0.800901i \(0.704354\pi\)
\(348\) 0 0
\(349\) −3.88577 + 4.48442i −0.208001 + 0.240045i −0.850158 0.526527i \(-0.823494\pi\)
0.642158 + 0.766572i \(0.278039\pi\)
\(350\) 0 0
\(351\) −2.03807 + 1.60276i −0.108784 + 0.0855488i
\(352\) 0 0
\(353\) −22.7398 4.38274i −1.21032 0.233270i −0.456121 0.889918i \(-0.650761\pi\)
−0.754197 + 0.656648i \(0.771974\pi\)
\(354\) 0 0
\(355\) −12.7143 + 6.55470i −0.674807 + 0.347887i
\(356\) 0 0
\(357\) 5.66229 3.63893i 0.299680 0.192593i
\(358\) 0 0
\(359\) 8.17560 + 9.43514i 0.431491 + 0.497968i 0.929303 0.369317i \(-0.120408\pi\)
−0.497812 + 0.867285i \(0.665863\pi\)
\(360\) 0 0
\(361\) −11.2778 + 2.17362i −0.593568 + 0.114401i
\(362\) 0 0
\(363\) 2.24806 + 9.26662i 0.117992 + 0.486371i
\(364\) 0 0
\(365\) 11.9580 + 20.7119i 0.625912 + 1.08411i
\(366\) 0 0
\(367\) −0.592003 12.4277i −0.0309023 0.648719i −0.960187 0.279356i \(-0.909879\pi\)
0.929285 0.369363i \(-0.120424\pi\)
\(368\) 0 0
\(369\) 1.69384 + 2.37866i 0.0881776 + 0.123828i
\(370\) 0 0
\(371\) 21.6279 20.6221i 1.12286 1.07065i
\(372\) 0 0
\(373\) −0.271346 + 0.469985i −0.0140497 + 0.0243349i −0.872965 0.487783i \(-0.837806\pi\)
0.858915 + 0.512118i \(0.171139\pi\)
\(374\) 0 0
\(375\) 1.19319 8.29882i 0.0616161 0.428549i
\(376\) 0 0
\(377\) 2.36674 0.694937i 0.121893 0.0357911i
\(378\) 0 0
\(379\) −1.31960 + 27.7018i −0.0677833 + 1.42295i 0.667209 + 0.744870i \(0.267489\pi\)
−0.734992 + 0.678075i \(0.762814\pi\)
\(380\) 0 0
\(381\) 6.37071 + 5.00998i 0.326381 + 0.256669i
\(382\) 0 0
\(383\) 17.7168 1.69175i 0.905287 0.0864445i 0.367983 0.929833i \(-0.380049\pi\)
0.537305 + 0.843388i \(0.319443\pi\)
\(384\) 0 0
\(385\) −5.24093 + 15.1427i −0.267103 + 0.771742i
\(386\) 0 0
\(387\) −1.45518 + 3.18640i −0.0739711 + 0.161974i
\(388\) 0 0
\(389\) −6.32465 6.03054i −0.320673 0.305761i 0.512595 0.858630i \(-0.328684\pi\)
−0.833268 + 0.552870i \(0.813533\pi\)
\(390\) 0 0
\(391\) −8.64125 3.45944i −0.437007 0.174951i
\(392\) 0 0
\(393\) 4.08838 + 8.95231i 0.206232 + 0.451584i
\(394\) 0 0
\(395\) −37.0650 3.53927i −1.86494 0.178080i
\(396\) 0 0
\(397\) −1.36545 9.49691i −0.0685299 0.476636i −0.994968 0.100190i \(-0.968055\pi\)
0.926438 0.376446i \(-0.122854\pi\)
\(398\) 0 0
\(399\) 11.7267 + 7.53627i 0.587068 + 0.377286i
\(400\) 0 0
\(401\) −8.91046 −0.444967 −0.222484 0.974936i \(-0.571416\pi\)
−0.222484 + 0.974936i \(0.571416\pi\)
\(402\) 0 0
\(403\) −9.54424 −0.475432
\(404\) 0 0
\(405\) −2.19051 1.40776i −0.108847 0.0699519i
\(406\) 0 0
\(407\) −0.0248905 0.173117i −0.00123378 0.00858110i
\(408\) 0 0
\(409\) 3.79478 + 0.362357i 0.187640 + 0.0179174i 0.188453 0.982082i \(-0.439653\pi\)
−0.000813102 1.00000i \(0.500259\pi\)
\(410\) 0 0
\(411\) −6.50611 14.2464i −0.320923 0.702723i
\(412\) 0 0
\(413\) 44.5862 + 17.8496i 2.19394 + 0.878322i
\(414\) 0 0
\(415\) −21.6687 20.6611i −1.06368 1.01421i
\(416\) 0 0
\(417\) −3.54152 + 7.75484i −0.173429 + 0.379756i
\(418\) 0 0
\(419\) 5.70812 16.4925i 0.278860 0.805712i −0.715400 0.698716i \(-0.753755\pi\)
0.994259 0.106997i \(-0.0341235\pi\)
\(420\) 0 0
\(421\) −14.9859 + 1.43098i −0.730368 + 0.0697417i −0.453613 0.891199i \(-0.649865\pi\)
−0.276755 + 0.960941i \(0.589259\pi\)
\(422\) 0 0
\(423\) −2.37877 1.87069i −0.115660 0.0909560i
\(424\) 0 0
\(425\) 0.112114 2.35356i 0.00543833 0.114165i
\(426\) 0 0
\(427\) −56.1818 + 16.4965i −2.71883 + 0.798320i
\(428\) 0 0
\(429\) −0.446556 + 3.10587i −0.0215599 + 0.149953i
\(430\) 0 0
\(431\) 13.0662 22.6314i 0.629379 1.09012i −0.358298 0.933607i \(-0.616643\pi\)
0.987677 0.156509i \(-0.0500240\pi\)
\(432\) 0 0
\(433\) 10.5696 10.0781i 0.507942 0.484322i −0.392223 0.919870i \(-0.628294\pi\)
0.900165 + 0.435548i \(0.143445\pi\)
\(434\) 0 0
\(435\) 1.43691 + 2.01786i 0.0688946 + 0.0967489i
\(436\) 0 0
\(437\) −0.917236 19.2552i −0.0438773 0.921099i
\(438\) 0 0
\(439\) 17.4413 + 30.2092i 0.832427 + 1.44181i 0.896108 + 0.443836i \(0.146383\pi\)
−0.0636808 + 0.997970i \(0.520284\pi\)
\(440\) 0 0
\(441\) 4.44583 + 18.3260i 0.211706 + 0.872665i
\(442\) 0 0
\(443\) −6.93574 + 1.33675i −0.329527 + 0.0635111i −0.351331 0.936251i \(-0.614271\pi\)
0.0218046 + 0.999762i \(0.493059\pi\)
\(444\) 0 0
\(445\) 11.0009 + 12.6957i 0.521491 + 0.601833i
\(446\) 0 0
\(447\) 12.7469 8.19193i 0.602907 0.387465i
\(448\) 0 0
\(449\) −4.57360 + 2.35786i −0.215842 + 0.111274i −0.562757 0.826622i \(-0.690259\pi\)
0.346915 + 0.937896i \(0.387229\pi\)
\(450\) 0 0
\(451\) 3.47008 + 0.668803i 0.163400 + 0.0314927i
\(452\) 0 0
\(453\) 6.35142 4.99481i 0.298416 0.234677i
\(454\) 0 0
\(455\) 22.4816 25.9452i 1.05396 1.21633i
\(456\) 0 0
\(457\) 4.22750 17.4260i 0.197754 0.815153i −0.783336 0.621599i \(-0.786483\pi\)
0.981090 0.193554i \(-0.0620015\pi\)
\(458\) 0 0
\(459\) 1.17650 + 0.606530i 0.0549145 + 0.0283104i
\(460\) 0 0
\(461\) 12.8005 + 3.75855i 0.596177 + 0.175053i 0.565880 0.824488i \(-0.308537\pi\)
0.0302969 + 0.999541i \(0.490355\pi\)
\(462\) 0 0
\(463\) −30.5708 + 12.2387i −1.42074 + 0.568780i −0.949653 0.313305i \(-0.898564\pi\)
−0.471091 + 0.882085i \(0.656140\pi\)
\(464\) 0 0
\(465\) −3.13495 9.05783i −0.145380 0.420047i
\(466\) 0 0
\(467\) −21.4167 + 30.0755i −0.991045 + 1.39173i −0.0720750 + 0.997399i \(0.522962\pi\)
−0.918970 + 0.394328i \(0.870977\pi\)
\(468\) 0 0
\(469\) −1.18833 41.6058i −0.0548721 1.92118i
\(470\) 0 0
\(471\) −7.38790 + 10.3749i −0.340416 + 0.478048i
\(472\) 0 0
\(473\) 1.38654 + 4.00614i 0.0637531 + 0.184202i
\(474\) 0 0
\(475\) 4.53024 1.81363i 0.207862 0.0832152i
\(476\) 0 0
\(477\) 5.63875 + 1.65569i 0.258181 + 0.0758087i
\(478\) 0 0
\(479\) −24.6666 12.7165i −1.12705 0.581032i −0.209161 0.977881i \(-0.567073\pi\)
−0.917884 + 0.396849i \(0.870104\pi\)
\(480\) 0 0
\(481\) −0.0883406 + 0.364145i −0.00402798 + 0.0166036i
\(482\) 0 0
\(483\) 23.4168 27.0244i 1.06550 1.22965i
\(484\) 0 0
\(485\) 17.6216 13.8577i 0.800154 0.629248i
\(486\) 0 0
\(487\) 35.5223 + 6.84636i 1.60967 + 0.310238i 0.913250 0.407399i \(-0.133564\pi\)
0.696417 + 0.717637i \(0.254776\pi\)
\(488\) 0 0
\(489\) −13.7557 + 7.09156i −0.622055 + 0.320691i
\(490\) 0 0
\(491\) 0.788951 0.507028i 0.0356049 0.0228819i −0.522717 0.852506i \(-0.675082\pi\)
0.558322 + 0.829624i \(0.311445\pi\)
\(492\) 0 0
\(493\) −0.824635 0.951679i −0.0371397 0.0428615i
\(494\) 0 0
\(495\) −3.09426 + 0.596370i −0.139077 + 0.0268048i
\(496\) 0 0
\(497\) 6.58591 + 27.1475i 0.295419 + 1.21773i
\(498\) 0 0
\(499\) −3.98180 6.89668i −0.178250 0.308738i 0.763031 0.646361i \(-0.223710\pi\)
−0.941281 + 0.337624i \(0.890377\pi\)
\(500\) 0 0
\(501\) −0.846936 17.7794i −0.0378383 0.794324i
\(502\) 0 0
\(503\) 15.4275 + 21.6648i 0.687876 + 0.965987i 0.999874 + 0.0159039i \(0.00506257\pi\)
−0.311997 + 0.950083i \(0.600998\pi\)
\(504\) 0 0
\(505\) 28.7748 27.4367i 1.28046 1.22092i
\(506\) 0 0
\(507\) −3.13872 + 5.43642i −0.139395 + 0.241440i
\(508\) 0 0
\(509\) 2.43555 16.9396i 0.107954 0.750834i −0.861888 0.507099i \(-0.830718\pi\)
0.969842 0.243736i \(-0.0783729\pi\)
\(510\) 0 0
\(511\) 44.8133 13.1584i 1.98242 0.582092i
\(512\) 0 0
\(513\) −0.130436 + 2.73818i −0.00575887 + 0.120894i
\(514\) 0 0
\(515\) 6.07568 + 4.77797i 0.267727 + 0.210543i
\(516\) 0 0
\(517\) −3.64577 + 0.348129i −0.160341 + 0.0153107i
\(518\) 0 0
\(519\) −7.84041 + 22.6534i −0.344156 + 0.994374i
\(520\) 0 0
\(521\) −1.01120 + 2.21421i −0.0443013 + 0.0970064i −0.930489 0.366321i \(-0.880617\pi\)
0.886187 + 0.463327i \(0.153345\pi\)
\(522\) 0 0
\(523\) −1.20110 1.14524i −0.0525203 0.0500780i 0.663364 0.748296i \(-0.269128\pi\)
−0.715885 + 0.698218i \(0.753976\pi\)
\(524\) 0 0
\(525\) 8.40350 + 3.36425i 0.366759 + 0.146828i
\(526\) 0 0
\(527\) 2.02408 + 4.43212i 0.0881704 + 0.193066i
\(528\) 0 0
\(529\) −26.3306 2.51427i −1.14481 0.109316i
\(530\) 0 0
\(531\) 1.34412 + 9.34854i 0.0583297 + 0.405692i
\(532\) 0 0
\(533\) −6.36935 4.09333i −0.275887 0.177302i
\(534\) 0 0
\(535\) −14.3244 −0.619297
\(536\) 0 0
\(537\) −5.90891 −0.254988
\(538\) 0 0
\(539\) 19.1986 + 12.3382i 0.826944 + 0.531444i
\(540\) 0 0
\(541\) 5.78919 + 40.2647i 0.248897 + 1.73111i 0.604612 + 0.796520i \(0.293328\pi\)
−0.355715 + 0.934595i \(0.615763\pi\)
\(542\) 0 0
\(543\) 7.06591 + 0.674712i 0.303227 + 0.0289547i
\(544\) 0 0
\(545\) 15.6296 + 34.2240i 0.669497 + 1.46599i
\(546\) 0 0
\(547\) 39.4045 + 15.7752i 1.68481 + 0.674498i 0.998600 0.0529010i \(-0.0168468\pi\)
0.686215 + 0.727399i \(0.259271\pi\)
\(548\) 0 0
\(549\) −8.33373 7.94620i −0.355675 0.339135i
\(550\) 0 0
\(551\) 1.08337 2.37225i 0.0461532 0.101061i
\(552\) 0 0
\(553\) −23.7820 + 68.7135i −1.01131 + 2.92199i
\(554\) 0 0
\(555\) −0.374604 + 0.0357703i −0.0159010 + 0.00151837i
\(556\) 0 0
\(557\) 0.201999 + 0.158854i 0.00855898 + 0.00673086i 0.622429 0.782676i \(-0.286146\pi\)
−0.613870 + 0.789407i \(0.710388\pi\)
\(558\) 0 0
\(559\) 0.432160 9.07215i 0.0182784 0.383711i
\(560\) 0 0
\(561\) 1.53699 0.451302i 0.0648920 0.0190540i
\(562\) 0 0
\(563\) 0.0655681 0.456036i 0.00276337 0.0192196i −0.988393 0.151918i \(-0.951455\pi\)
0.991156 + 0.132698i \(0.0423641\pi\)
\(564\) 0 0
\(565\) 14.7396 25.5297i 0.620099 1.07404i
\(566\) 0 0
\(567\) −3.68021 + 3.50907i −0.154554 + 0.147367i
\(568\) 0 0
\(569\) −18.2488 25.6269i −0.765030 1.07433i −0.994876 0.101107i \(-0.967761\pi\)
0.229846 0.973227i \(-0.426178\pi\)
\(570\) 0 0
\(571\) 0.210531 + 4.41959i 0.00881045 + 0.184954i 0.998983 + 0.0450994i \(0.0143605\pi\)
−0.990172 + 0.139855i \(0.955336\pi\)
\(572\) 0 0
\(573\) 13.5142 + 23.4072i 0.564563 + 0.977851i
\(574\) 0 0
\(575\) −2.95120 12.1650i −0.123074 0.507317i
\(576\) 0 0
\(577\) −17.2535 + 3.32534i −0.718272 + 0.138436i −0.535275 0.844678i \(-0.679792\pi\)
−0.182997 + 0.983113i \(0.558580\pi\)
\(578\) 0 0
\(579\) −9.82459 11.3382i −0.408296 0.471199i
\(580\) 0 0
\(581\) −49.1877 + 31.6110i −2.04065 + 1.31145i
\(582\) 0 0
\(583\) 6.32152 3.25897i 0.261810 0.134973i
\(584\) 0 0
\(585\) 6.62927 + 1.27769i 0.274086 + 0.0528258i
\(586\) 0 0
\(587\) 18.2836 14.3784i 0.754646 0.593460i −0.164961 0.986300i \(-0.552750\pi\)
0.919607 + 0.392840i \(0.128507\pi\)
\(588\) 0 0
\(589\) −6.60811 + 7.62616i −0.272282 + 0.314231i
\(590\) 0 0
\(591\) 0.177442 0.731428i 0.00729901 0.0300869i
\(592\) 0 0
\(593\) −14.2831 7.36343i −0.586535 0.302380i 0.139298 0.990250i \(-0.455515\pi\)
−0.725833 + 0.687871i \(0.758546\pi\)
\(594\) 0 0
\(595\) −16.8161 4.93765i −0.689393 0.202424i
\(596\) 0 0
\(597\) −0.266907 + 0.106854i −0.0109238 + 0.00437323i
\(598\) 0 0
\(599\) −6.12830 17.7066i −0.250396 0.723471i −0.998224 0.0595782i \(-0.981024\pi\)
0.747828 0.663893i \(-0.231097\pi\)
\(600\) 0 0
\(601\) 10.5969 14.8812i 0.432256 0.607019i −0.539793 0.841798i \(-0.681497\pi\)
0.972049 + 0.234779i \(0.0754368\pi\)
\(602\) 0 0
\(603\) 6.96899 4.29339i 0.283799 0.174840i
\(604\) 0 0
\(605\) 14.4022 20.2250i 0.585532 0.822264i
\(606\) 0 0
\(607\) 10.3878 + 30.0135i 0.421627 + 1.21821i 0.933321 + 0.359043i \(0.116897\pi\)
−0.511694 + 0.859168i \(0.670982\pi\)
\(608\) 0 0
\(609\) 4.49112 1.79797i 0.181989 0.0728575i
\(610\) 0 0
\(611\) 7.52854 + 2.21058i 0.304572 + 0.0894304i
\(612\) 0 0
\(613\) 40.5561 + 20.9081i 1.63805 + 0.844472i 0.997036 + 0.0769403i \(0.0245151\pi\)
0.641011 + 0.767532i \(0.278515\pi\)
\(614\) 0 0
\(615\) 1.79262 7.38926i 0.0722853 0.297964i
\(616\) 0 0
\(617\) 7.95089 9.17582i 0.320091 0.369404i −0.572786 0.819705i \(-0.694138\pi\)
0.892877 + 0.450300i \(0.148683\pi\)
\(618\) 0 0
\(619\) −14.0746 + 11.0684i −0.565707 + 0.444877i −0.859604 0.510960i \(-0.829290\pi\)
0.293897 + 0.955837i \(0.405048\pi\)
\(620\) 0 0
\(621\) 6.90502 + 1.33083i 0.277089 + 0.0534045i
\(622\) 0 0
\(623\) 29.1591 15.0326i 1.16824 0.602267i
\(624\) 0 0
\(625\) −25.8532 + 16.6148i −1.03413 + 0.664594i
\(626\) 0 0
\(627\) 2.17251 + 2.50721i 0.0867617 + 0.100128i
\(628\) 0 0
\(629\) 0.187835 0.0362022i 0.00748947 0.00144348i
\(630\) 0 0
\(631\) −9.06774 37.3777i −0.360981 1.48798i −0.805706 0.592316i \(-0.798214\pi\)
0.444725 0.895667i \(-0.353302\pi\)
\(632\) 0 0
\(633\) 5.69647 + 9.86657i 0.226414 + 0.392161i
\(634\) 0 0
\(635\) −1.00414 21.0796i −0.0398482 0.836517i
\(636\) 0 0
\(637\) −28.3611 39.8276i −1.12371 1.57803i
\(638\) 0 0
\(639\) −3.97588 + 3.79099i −0.157283 + 0.149969i
\(640\) 0 0
\(641\) −22.2329 + 38.5085i −0.878148 + 1.52100i −0.0247760 + 0.999693i \(0.507887\pi\)
−0.853372 + 0.521303i \(0.825446\pi\)
\(642\) 0 0
\(643\) −4.71859 + 32.8185i −0.186083 + 1.29424i 0.655948 + 0.754806i \(0.272269\pi\)
−0.842031 + 0.539430i \(0.818640\pi\)
\(644\) 0 0
\(645\) 8.75176 2.56975i 0.344600 0.101184i
\(646\) 0 0
\(647\) −0.109205 + 2.29250i −0.00429329 + 0.0901273i −0.999997 0.00246981i \(-0.999214\pi\)
0.995704 + 0.0925971i \(0.0295169\pi\)
\(648\) 0 0
\(649\) 8.98457 + 7.06555i 0.352675 + 0.277347i
\(650\) 0 0
\(651\) −18.6336 + 1.77929i −0.730308 + 0.0697359i
\(652\) 0 0
\(653\) 8.01127 23.1470i 0.313505 0.905814i −0.672646 0.739964i \(-0.734842\pi\)
0.986151 0.165849i \(-0.0530365\pi\)
\(654\) 0 0
\(655\) 10.6456 23.3106i 0.415958 0.910820i
\(656\) 0 0
\(657\) 6.64738 + 6.33826i 0.259339 + 0.247279i
\(658\) 0 0
\(659\) −36.4518 14.5931i −1.41996 0.568466i −0.470513 0.882393i \(-0.655931\pi\)
−0.949447 + 0.313927i \(0.898355\pi\)
\(660\) 0 0
\(661\) −5.44884 11.9313i −0.211935 0.464074i 0.773572 0.633709i \(-0.218468\pi\)
−0.985507 + 0.169635i \(0.945741\pi\)
\(662\) 0 0
\(663\) −3.41640 0.326226i −0.132682 0.0126696i
\(664\) 0 0
\(665\) −5.16555 35.9272i −0.200311 1.39320i
\(666\) 0 0
\(667\) −5.62798 3.61688i −0.217916 0.140046i
\(668\) 0 0
\(669\) −16.9559 −0.655554
\(670\) 0 0
\(671\) −13.9354 −0.537970
\(672\) 0 0
\(673\) 14.6855 + 9.43778i 0.566083 + 0.363800i 0.792163 0.610309i \(-0.208955\pi\)
−0.226080 + 0.974109i \(0.572591\pi\)
\(674\) 0 0
\(675\) 0.253336 + 1.76199i 0.00975090 + 0.0678190i
\(676\) 0 0
\(677\) −24.4573 2.33539i −0.939971 0.0897564i −0.386191 0.922419i \(-0.626209\pi\)
−0.553781 + 0.832663i \(0.686815\pi\)
\(678\) 0 0
\(679\) −18.1865 39.8229i −0.697935 1.52826i
\(680\) 0 0
\(681\) −25.2609 10.1129i −0.967999 0.387528i
\(682\) 0 0
\(683\) −35.0684 33.4376i −1.34185 1.27945i −0.929689 0.368345i \(-0.879925\pi\)
−0.412164 0.911110i \(-0.635227\pi\)
\(684\) 0 0
\(685\) −16.9410 + 37.0957i −0.647284 + 1.41735i
\(686\) 0 0
\(687\) −3.89584 + 11.2563i −0.148636 + 0.429454i
\(688\) 0 0
\(689\) −15.1683 + 1.44840i −0.577867 + 0.0551796i
\(690\) 0 0
\(691\) −32.5304 25.5822i −1.23751 0.973192i −0.999998 0.00180900i \(-0.999424\pi\)
−0.237517 0.971383i \(-0.576333\pi\)
\(692\) 0 0
\(693\) −0.292816 + 6.14695i −0.0111231 + 0.233503i
\(694\) 0 0
\(695\) 21.2994 6.25407i 0.807932 0.237230i
\(696\) 0 0
\(697\) −0.550076 + 3.82586i −0.0208356 + 0.144915i
\(698\) 0 0
\(699\) 1.03719 1.79647i 0.0392302 0.0679487i
\(700\) 0 0
\(701\) −2.84899 + 2.71650i −0.107605 + 0.102601i −0.741972 0.670431i \(-0.766109\pi\)
0.634367 + 0.773032i \(0.281261\pi\)
\(702\) 0 0
\(703\) 0.229800 + 0.322709i 0.00866707 + 0.0121712i
\(704\) 0 0
\(705\) 0.374940 + 7.87096i 0.0141211 + 0.296437i
\(706\) 0 0
\(707\) −38.8220 67.2417i −1.46005 2.52888i
\(708\) 0 0
\(709\) 11.4182 + 47.0664i 0.428819 + 1.76762i 0.618516 + 0.785772i \(0.287734\pi\)
−0.189697 + 0.981843i \(0.560751\pi\)
\(710\) 0 0
\(711\) −14.0409 + 2.70617i −0.526576 + 0.101489i
\(712\) 0 0
\(713\) 16.9515 + 19.5631i 0.634838 + 0.732642i
\(714\) 0 0
\(715\) 6.87339 4.41726i 0.257050 0.165196i
\(716\) 0 0
\(717\) −20.6295 + 10.6353i −0.770424 + 0.397181i
\(718\) 0 0
\(719\) −7.88549 1.51980i −0.294079 0.0566791i 0.0400778 0.999197i \(-0.487239\pi\)
−0.334157 + 0.942517i \(0.608452\pi\)
\(720\) 0 0
\(721\) 11.8651 9.33080i 0.441878 0.347497i
\(722\) 0 0
\(723\) −17.1765 + 19.8227i −0.638800 + 0.737215i
\(724\) 0 0
\(725\) 0.399260 1.64577i 0.0148281 0.0611224i
\(726\) 0 0
\(727\) 14.2289 + 7.33552i 0.527721 + 0.272059i 0.701431 0.712738i \(-0.252545\pi\)
−0.173709 + 0.984797i \(0.555575\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) 0 0
\(731\) −4.30454 + 1.72328i −0.159209 + 0.0637378i
\(732\) 0 0
\(733\) 6.07907 + 17.5643i 0.224535 + 0.648753i 0.999852 + 0.0171803i \(0.00546892\pi\)
−0.775317 + 0.631572i \(0.782410\pi\)
\(734\) 0 0
\(735\) 28.4822 39.9977i 1.05058 1.47534i
\(736\) 0 0
\(737\) 2.51833 9.58049i 0.0927639 0.352902i
\(738\) 0 0
\(739\) 25.8843 36.3495i 0.952171 1.33714i 0.0107361 0.999942i \(-0.496583\pi\)
0.941435 0.337195i \(-0.109478\pi\)
\(740\) 0 0
\(741\) −2.32466 6.71667i −0.0853986 0.246743i
\(742\) 0 0
\(743\) 18.9324 7.57941i 0.694564 0.278061i 0.00260315 0.999997i \(-0.499171\pi\)
0.691961 + 0.721935i \(0.256747\pi\)
\(744\) 0 0
\(745\) −37.8563 11.1156i −1.38695 0.407244i
\(746\) 0 0
\(747\) −10.2202 5.26886i −0.373936 0.192778i
\(748\) 0 0
\(749\) −6.59507 + 27.1852i −0.240979 + 0.993327i
\(750\) 0 0
\(751\) 20.5666 23.7351i 0.750486 0.866107i −0.244129 0.969743i \(-0.578502\pi\)
0.994615 + 0.103636i \(0.0330476\pi\)
\(752\) 0 0
\(753\) −21.5637 + 16.9579i −0.785824 + 0.617979i
\(754\) 0 0
\(755\) −20.6594 3.98177i −0.751872 0.144911i
\(756\) 0 0
\(757\) 30.7784 15.8674i 1.11866 0.576709i 0.203208 0.979136i \(-0.434863\pi\)
0.915452 + 0.402426i \(0.131833\pi\)
\(758\) 0 0
\(759\) 7.15930 4.60100i 0.259866 0.167006i
\(760\) 0 0
\(761\) −21.9926 25.3808i −0.797232 0.920055i 0.200994 0.979592i \(-0.435583\pi\)
−0.998226 + 0.0595378i \(0.981037\pi\)
\(762\) 0 0
\(763\) 72.1472 13.9052i 2.61190 0.503403i
\(764\) 0 0
\(765\) −0.812565 3.34944i −0.0293784 0.121099i
\(766\) 0 0
\(767\) −12.2440 21.2073i −0.442106 0.765750i
\(768\) 0 0
\(769\) −0.998755 20.9664i −0.0360160 0.756069i −0.942576 0.333992i \(-0.891604\pi\)
0.906560 0.422077i \(-0.138699\pi\)
\(770\) 0 0
\(771\) 12.6988 + 17.8330i 0.457336 + 0.642239i
\(772\) 0 0
\(773\) 7.21325 6.87782i 0.259442 0.247378i −0.549182 0.835703i \(-0.685061\pi\)
0.808625 + 0.588325i \(0.200212\pi\)
\(774\) 0 0
\(775\) −3.27635 + 5.67480i −0.117690 + 0.203845i
\(776\) 0 0
\(777\) −0.104585 + 0.727403i −0.00375196 + 0.0260954i