Properties

Label 804.2.q.b.193.5
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 193.5
Character \(\chi\) = 804.193
Dual form 804.2.q.b.25.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.654861 + 0.755750i) q^{3} +(1.69814 + 1.09133i) q^{5} +(-0.693468 + 4.82317i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.654861 + 0.755750i) q^{3} +(1.69814 + 1.09133i) q^{5} +(-0.693468 + 4.82317i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.656414 + 0.421852i) q^{11} +(0.749561 + 1.64131i) q^{13} +(0.287274 + 1.99804i) q^{15} +(-4.81748 + 1.41454i) q^{17} +(-0.841566 - 5.85322i) q^{19} +(-4.09924 + 2.63442i) q^{21} +(-4.58797 - 5.29480i) q^{23} +(-0.384395 - 0.841709i) q^{25} +(-0.841254 + 0.540641i) q^{27} +4.90421 q^{29} +(-4.31097 + 9.43970i) q^{31} +(0.111046 + 0.772339i) q^{33} +(-6.44127 + 7.43362i) q^{35} +8.86088 q^{37} +(-0.749561 + 1.64131i) q^{39} +(9.14557 - 2.68538i) q^{41} +(-0.967308 + 0.284027i) q^{43} +(-1.32189 + 1.52554i) q^{45} +(-2.68948 - 3.10382i) q^{47} +(-16.0657 - 4.71730i) q^{49} +(-4.22381 - 2.71448i) q^{51} +(12.5726 + 3.69164i) q^{53} +(0.654304 + 1.43273i) q^{55} +(3.87246 - 4.46906i) q^{57} +(-0.517190 + 1.13249i) q^{59} +(-0.873249 + 0.561203i) q^{61} +(-4.67539 - 1.37282i) q^{63} +(-0.518348 + 3.60519i) q^{65} +(3.64682 + 7.32808i) q^{67} +(0.997061 - 6.93471i) q^{69} +(15.7387 + 4.62130i) q^{71} +(-0.241827 + 0.155413i) q^{73} +(0.384395 - 0.841709i) q^{75} +(-2.48987 + 2.87346i) q^{77} +(-1.73759 - 3.80479i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(12.5737 + 8.08062i) q^{83} +(-9.72447 - 2.85536i) q^{85} +(3.21157 + 3.70635i) q^{87} +(-2.07902 + 2.39932i) q^{89} +(-8.43612 + 2.47707i) q^{91} +(-9.95713 + 2.92368i) q^{93} +(4.95869 - 10.8580i) q^{95} -0.952015 q^{97} +(-0.510975 + 0.589697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

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
\(5\) 1.69814 + 1.09133i 0.759431 + 0.488057i 0.862150 0.506654i \(-0.169118\pi\)
−0.102719 + 0.994710i \(0.532754\pi\)
\(6\) 0 0
\(7\) −0.693468 + 4.82317i −0.262106 + 1.82299i 0.254855 + 0.966979i \(0.417972\pi\)
−0.516961 + 0.856009i \(0.672937\pi\)
\(8\) 0 0
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0 0
\(11\) 0.656414 + 0.421852i 0.197916 + 0.127193i 0.635845 0.771816i \(-0.280652\pi\)
−0.437929 + 0.899009i \(0.644288\pi\)
\(12\) 0 0
\(13\) 0.749561 + 1.64131i 0.207891 + 0.455217i 0.984641 0.174591i \(-0.0558605\pi\)
−0.776750 + 0.629809i \(0.783133\pi\)
\(14\) 0 0
\(15\) 0.287274 + 1.99804i 0.0741739 + 0.515890i
\(16\) 0 0
\(17\) −4.81748 + 1.41454i −1.16841 + 0.343076i −0.807695 0.589600i \(-0.799285\pi\)
−0.360714 + 0.932676i \(0.617467\pi\)
\(18\) 0 0
\(19\) −0.841566 5.85322i −0.193069 1.34282i −0.823827 0.566842i \(-0.808165\pi\)
0.630758 0.775980i \(-0.282744\pi\)
\(20\) 0 0
\(21\) −4.09924 + 2.63442i −0.894527 + 0.574877i
\(22\) 0 0
\(23\) −4.58797 5.29480i −0.956658 1.10404i −0.994498 0.104758i \(-0.966593\pi\)
0.0378397 0.999284i \(-0.487952\pi\)
\(24\) 0 0
\(25\) −0.384395 0.841709i −0.0768791 0.168342i
\(26\) 0 0
\(27\) −0.841254 + 0.540641i −0.161899 + 0.104046i
\(28\) 0 0
\(29\) 4.90421 0.910689 0.455344 0.890315i \(-0.349516\pi\)
0.455344 + 0.890315i \(0.349516\pi\)
\(30\) 0 0
\(31\) −4.31097 + 9.43970i −0.774272 + 1.69542i −0.0572601 + 0.998359i \(0.518236\pi\)
−0.717012 + 0.697061i \(0.754491\pi\)
\(32\) 0 0
\(33\) 0.111046 + 0.772339i 0.0193305 + 0.134447i
\(34\) 0 0
\(35\) −6.44127 + 7.43362i −1.08877 + 1.25651i
\(36\) 0 0
\(37\) 8.86088 1.45672 0.728360 0.685195i \(-0.240283\pi\)
0.728360 + 0.685195i \(0.240283\pi\)
\(38\) 0 0
\(39\) −0.749561 + 1.64131i −0.120026 + 0.262820i
\(40\) 0 0
\(41\) 9.14557 2.68538i 1.42830 0.419386i 0.525995 0.850488i \(-0.323693\pi\)
0.902303 + 0.431102i \(0.141875\pi\)
\(42\) 0 0
\(43\) −0.967308 + 0.284027i −0.147513 + 0.0433138i −0.354655 0.934997i \(-0.615402\pi\)
0.207142 + 0.978311i \(0.433584\pi\)
\(44\) 0 0
\(45\) −1.32189 + 1.52554i −0.197056 + 0.227414i
\(46\) 0 0
\(47\) −2.68948 3.10382i −0.392300 0.452739i 0.524901 0.851164i \(-0.324102\pi\)
−0.917201 + 0.398425i \(0.869557\pi\)
\(48\) 0 0
\(49\) −16.0657 4.71730i −2.29509 0.673900i
\(50\) 0 0
\(51\) −4.22381 2.71448i −0.591452 0.380103i
\(52\) 0 0
\(53\) 12.5726 + 3.69164i 1.72698 + 0.507086i 0.986326 0.164805i \(-0.0526996\pi\)
0.740650 + 0.671891i \(0.234518\pi\)
\(54\) 0 0
\(55\) 0.654304 + 1.43273i 0.0882263 + 0.193189i
\(56\) 0 0
\(57\) 3.87246 4.46906i 0.512920 0.591941i
\(58\) 0 0
\(59\) −0.517190 + 1.13249i −0.0673324 + 0.147437i −0.940306 0.340330i \(-0.889461\pi\)
0.872974 + 0.487767i \(0.162189\pi\)
\(60\) 0 0
\(61\) −0.873249 + 0.561203i −0.111808 + 0.0718547i −0.595350 0.803467i \(-0.702987\pi\)
0.483542 + 0.875321i \(0.339350\pi\)
\(62\) 0 0
\(63\) −4.67539 1.37282i −0.589044 0.172959i
\(64\) 0 0
\(65\) −0.518348 + 3.60519i −0.0642931 + 0.447169i
\(66\) 0 0
\(67\) 3.64682 + 7.32808i 0.445530 + 0.895267i
\(68\) 0 0
\(69\) 0.997061 6.93471i 0.120032 0.834841i
\(70\) 0 0
\(71\) 15.7387 + 4.62130i 1.86784 + 0.548448i 0.998531 + 0.0541797i \(0.0172544\pi\)
0.869310 + 0.494268i \(0.164564\pi\)
\(72\) 0 0
\(73\) −0.241827 + 0.155413i −0.0283037 + 0.0181897i −0.554716 0.832040i \(-0.687173\pi\)
0.526412 + 0.850229i \(0.323537\pi\)
\(74\) 0 0
\(75\) 0.384395 0.841709i 0.0443862 0.0971921i
\(76\) 0 0
\(77\) −2.48987 + 2.87346i −0.283746 + 0.327461i
\(78\) 0 0
\(79\) −1.73759 3.80479i −0.195494 0.428072i 0.786345 0.617787i \(-0.211971\pi\)
−0.981839 + 0.189715i \(0.939244\pi\)
\(80\) 0 0
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 0 0
\(83\) 12.5737 + 8.08062i 1.38014 + 0.886964i 0.999290 0.0376723i \(-0.0119943\pi\)
0.380852 + 0.924636i \(0.375631\pi\)
\(84\) 0 0
\(85\) −9.72447 2.85536i −1.05477 0.309707i
\(86\) 0 0
\(87\) 3.21157 + 3.70635i 0.344317 + 0.397363i
\(88\) 0 0
\(89\) −2.07902 + 2.39932i −0.220376 + 0.254327i −0.855162 0.518361i \(-0.826543\pi\)
0.634787 + 0.772687i \(0.281088\pi\)
\(90\) 0 0
\(91\) −8.43612 + 2.47707i −0.884346 + 0.259667i
\(92\) 0 0
\(93\) −9.95713 + 2.92368i −1.03251 + 0.303171i
\(94\) 0 0
\(95\) 4.95869 10.8580i 0.508751 1.11401i
\(96\) 0 0
\(97\) −0.952015 −0.0966625 −0.0483312 0.998831i \(-0.515390\pi\)
−0.0483312 + 0.998831i \(0.515390\pi\)
\(98\) 0 0
\(99\) −0.510975 + 0.589697i −0.0513549 + 0.0592668i
\(100\) 0 0
\(101\) −0.562569 3.91275i −0.0559777 0.389334i −0.998479 0.0551314i \(-0.982442\pi\)
0.942501 0.334202i \(-0.108467\pi\)
\(102\) 0 0
\(103\) −7.06490 + 15.4700i −0.696126 + 1.52430i 0.148481 + 0.988915i \(0.452562\pi\)
−0.844607 + 0.535387i \(0.820166\pi\)
\(104\) 0 0
\(105\) −9.83608 −0.959904
\(106\) 0 0
\(107\) −0.540581 + 0.347410i −0.0522599 + 0.0335854i −0.566510 0.824055i \(-0.691707\pi\)
0.514250 + 0.857640i \(0.328070\pi\)
\(108\) 0 0
\(109\) 0.199094 + 0.435955i 0.0190697 + 0.0417569i 0.918927 0.394427i \(-0.129057\pi\)
−0.899857 + 0.436184i \(0.856330\pi\)
\(110\) 0 0
\(111\) 5.80264 + 6.69660i 0.550762 + 0.635613i
\(112\) 0 0
\(113\) 5.27425 3.38956i 0.496160 0.318863i −0.268519 0.963274i \(-0.586534\pi\)
0.764679 + 0.644412i \(0.222898\pi\)
\(114\) 0 0
\(115\) −2.01265 13.9983i −0.187681 1.30535i
\(116\) 0 0
\(117\) −1.73128 + 0.508349i −0.160057 + 0.0469969i
\(118\) 0 0
\(119\) −3.48180 24.2165i −0.319176 2.21992i
\(120\) 0 0
\(121\) −4.31664 9.45213i −0.392422 0.859285i
\(122\) 0 0
\(123\) 8.01855 + 5.15321i 0.723008 + 0.464649i
\(124\) 0 0
\(125\) 1.70219 11.8390i 0.152249 1.05891i
\(126\) 0 0
\(127\) −1.22297 + 8.50596i −0.108521 + 0.754782i 0.860793 + 0.508956i \(0.169968\pi\)
−0.969314 + 0.245826i \(0.920941\pi\)
\(128\) 0 0
\(129\) −0.848106 0.545044i −0.0746715 0.0479885i
\(130\) 0 0
\(131\) −5.57733 6.43659i −0.487294 0.562367i 0.457847 0.889031i \(-0.348621\pi\)
−0.945141 + 0.326664i \(0.894075\pi\)
\(132\) 0 0
\(133\) 28.8147 2.49855
\(134\) 0 0
\(135\) −2.01858 −0.173732
\(136\) 0 0
\(137\) 1.82918 + 2.11099i 0.156278 + 0.180354i 0.828489 0.560005i \(-0.189201\pi\)
−0.672211 + 0.740359i \(0.734655\pi\)
\(138\) 0 0
\(139\) −2.73377 1.75689i −0.231875 0.149017i 0.419544 0.907735i \(-0.362190\pi\)
−0.651420 + 0.758718i \(0.725826\pi\)
\(140\) 0 0
\(141\) 0.584479 4.06514i 0.0492220 0.342347i
\(142\) 0 0
\(143\) −0.200367 + 1.39358i −0.0167555 + 0.116537i
\(144\) 0 0
\(145\) 8.32803 + 5.35210i 0.691605 + 0.444468i
\(146\) 0 0
\(147\) −6.95567 15.2308i −0.573694 1.25621i
\(148\) 0 0
\(149\) 1.48716 + 10.3434i 0.121833 + 0.847367i 0.955477 + 0.295065i \(0.0953414\pi\)
−0.833644 + 0.552302i \(0.813750\pi\)
\(150\) 0 0
\(151\) −8.69841 + 2.55408i −0.707867 + 0.207848i −0.615798 0.787904i \(-0.711166\pi\)
−0.0920688 + 0.995753i \(0.529348\pi\)
\(152\) 0 0
\(153\) −0.714542 4.96975i −0.0577673 0.401780i
\(154\) 0 0
\(155\) −17.6224 + 11.3252i −1.41547 + 0.909665i
\(156\) 0 0
\(157\) 1.03551 + 1.19505i 0.0826430 + 0.0953751i 0.795565 0.605868i \(-0.207174\pi\)
−0.712922 + 0.701243i \(0.752629\pi\)
\(158\) 0 0
\(159\) 5.44333 + 11.9192i 0.431684 + 0.945256i
\(160\) 0 0
\(161\) 28.7193 18.4568i 2.26340 1.45460i
\(162\) 0 0
\(163\) 14.2474 1.11594 0.557971 0.829860i \(-0.311580\pi\)
0.557971 + 0.829860i \(0.311580\pi\)
\(164\) 0 0
\(165\) −0.654304 + 1.43273i −0.0509375 + 0.111538i
\(166\) 0 0
\(167\) −0.641035 4.45850i −0.0496048 0.345009i −0.999476 0.0323675i \(-0.989695\pi\)
0.949871 0.312641i \(-0.101214\pi\)
\(168\) 0 0
\(169\) 6.38113 7.36422i 0.490856 0.566478i
\(170\) 0 0
\(171\) 5.91341 0.452210
\(172\) 0 0
\(173\) 10.2562 22.4578i 0.779761 1.70744i 0.0758829 0.997117i \(-0.475822\pi\)
0.703878 0.710321i \(-0.251450\pi\)
\(174\) 0 0
\(175\) 4.32627 1.27031i 0.327035 0.0960263i
\(176\) 0 0
\(177\) −1.19456 + 0.350756i −0.0897889 + 0.0263644i
\(178\) 0 0
\(179\) 13.7752 15.8974i 1.02961 1.18823i 0.0477008 0.998862i \(-0.484811\pi\)
0.981906 0.189368i \(-0.0606440\pi\)
\(180\) 0 0
\(181\) −14.8676 17.1581i −1.10510 1.27535i −0.958168 0.286207i \(-0.907605\pi\)
−0.146932 0.989147i \(-0.546940\pi\)
\(182\) 0 0
\(183\) −0.995986 0.292448i −0.0736254 0.0216184i
\(184\) 0 0
\(185\) 15.0470 + 9.67012i 1.10628 + 0.710961i
\(186\) 0 0
\(187\) −3.75898 1.10374i −0.274884 0.0807132i
\(188\) 0 0
\(189\) −2.02422 4.43243i −0.147240 0.322412i
\(190\) 0 0
\(191\) 5.24895 6.05761i 0.379800 0.438313i −0.533376 0.845879i \(-0.679077\pi\)
0.913176 + 0.407565i \(0.133622\pi\)
\(192\) 0 0
\(193\) −9.74788 + 21.3449i −0.701668 + 1.53644i 0.136269 + 0.990672i \(0.456489\pi\)
−0.837937 + 0.545767i \(0.816239\pi\)
\(194\) 0 0
\(195\) −3.06407 + 1.96916i −0.219422 + 0.141014i
\(196\) 0 0
\(197\) −10.3475 3.03831i −0.737232 0.216471i −0.108504 0.994096i \(-0.534606\pi\)
−0.628728 + 0.777625i \(0.716424\pi\)
\(198\) 0 0
\(199\) 0.502079 3.49204i 0.0355914 0.247544i −0.964257 0.264970i \(-0.914638\pi\)
0.999848 + 0.0174259i \(0.00554712\pi\)
\(200\) 0 0
\(201\) −3.15003 + 7.55495i −0.222186 + 0.532885i
\(202\) 0 0
\(203\) −3.40091 + 23.6538i −0.238697 + 1.66017i
\(204\) 0 0
\(205\) 18.4611 + 5.42066i 1.28938 + 0.378595i
\(206\) 0 0
\(207\) 5.89384 3.78774i 0.409650 0.263266i
\(208\) 0 0
\(209\) 1.91678 4.19715i 0.132586 0.290323i
\(210\) 0 0
\(211\) −8.17700 + 9.43676i −0.562928 + 0.649653i −0.963846 0.266461i \(-0.914146\pi\)
0.400918 + 0.916114i \(0.368691\pi\)
\(212\) 0 0
\(213\) 6.81411 + 14.9208i 0.466895 + 1.02236i
\(214\) 0 0
\(215\) −1.95259 0.573332i −0.133166 0.0391009i
\(216\) 0 0
\(217\) −42.5398 27.3387i −2.88779 1.85587i
\(218\) 0 0
\(219\) −0.275816 0.0809868i −0.0186379 0.00547258i
\(220\) 0 0
\(221\) −5.93269 6.84669i −0.399076 0.460558i
\(222\) 0 0
\(223\) 15.5541 17.9504i 1.04158 1.20205i 0.0626089 0.998038i \(-0.480058\pi\)
0.978969 0.204007i \(-0.0653966\pi\)
\(224\) 0 0
\(225\) 0.887847 0.260695i 0.0591898 0.0173797i
\(226\) 0 0
\(227\) −26.4985 + 7.78065i −1.75877 + 0.516420i −0.992081 0.125603i \(-0.959913\pi\)
−0.766685 + 0.642023i \(0.778095\pi\)
\(228\) 0 0
\(229\) 3.05444 6.68830i 0.201843 0.441975i −0.781459 0.623957i \(-0.785524\pi\)
0.983302 + 0.181982i \(0.0582512\pi\)
\(230\) 0 0
\(231\) −3.80213 −0.250162
\(232\) 0 0
\(233\) 0.809277 0.933956i 0.0530175 0.0611855i −0.728621 0.684917i \(-0.759839\pi\)
0.781639 + 0.623731i \(0.214384\pi\)
\(234\) 0 0
\(235\) −1.17982 8.20582i −0.0769629 0.535289i
\(236\) 0 0
\(237\) 1.73759 3.80479i 0.112869 0.247148i
\(238\) 0 0
\(239\) 8.34297 0.539662 0.269831 0.962908i \(-0.413032\pi\)
0.269831 + 0.962908i \(0.413032\pi\)
\(240\) 0 0
\(241\) 20.3678 13.0896i 1.31201 0.843176i 0.317542 0.948244i \(-0.397142\pi\)
0.994465 + 0.105068i \(0.0335061\pi\)
\(242\) 0 0
\(243\) −0.415415 0.909632i −0.0266489 0.0583529i
\(244\) 0 0
\(245\) −22.1336 25.5435i −1.41406 1.63192i
\(246\) 0 0
\(247\) 8.97615 5.76862i 0.571139 0.367048i
\(248\) 0 0
\(249\) 2.12709 + 14.7942i 0.134799 + 0.937547i
\(250\) 0 0
\(251\) −11.4967 + 3.37573i −0.725664 + 0.213074i −0.623645 0.781708i \(-0.714349\pi\)
−0.102020 + 0.994782i \(0.532531\pi\)
\(252\) 0 0
\(253\) −0.777988 5.41102i −0.0489117 0.340188i
\(254\) 0 0
\(255\) −4.21023 9.21913i −0.263655 0.577324i
\(256\) 0 0
\(257\) 12.3112 + 7.91193i 0.767952 + 0.493533i 0.865015 0.501745i \(-0.167309\pi\)
−0.0970634 + 0.995278i \(0.530945\pi\)
\(258\) 0 0
\(259\) −6.14473 + 42.7375i −0.381815 + 2.65558i
\(260\) 0 0
\(261\) −0.697942 + 4.85429i −0.0432015 + 0.300473i
\(262\) 0 0
\(263\) −9.11311 5.85664i −0.561939 0.361136i 0.228626 0.973514i \(-0.426577\pi\)
−0.790565 + 0.612378i \(0.790213\pi\)
\(264\) 0 0
\(265\) 17.3212 + 19.9897i 1.06403 + 1.22796i
\(266\) 0 0
\(267\) −3.17475 −0.194292
\(268\) 0 0
\(269\) −1.15339 −0.0703235 −0.0351617 0.999382i \(-0.511195\pi\)
−0.0351617 + 0.999382i \(0.511195\pi\)
\(270\) 0 0
\(271\) −4.00442 4.62134i −0.243251 0.280727i 0.620975 0.783830i \(-0.286737\pi\)
−0.864226 + 0.503104i \(0.832191\pi\)
\(272\) 0 0
\(273\) −7.39653 4.75346i −0.447658 0.287692i
\(274\) 0 0
\(275\) 0.102754 0.714667i 0.00619628 0.0430961i
\(276\) 0 0
\(277\) 0.484910 3.37262i 0.0291354 0.202641i −0.970054 0.242888i \(-0.921905\pi\)
0.999190 + 0.0402467i \(0.0128144\pi\)
\(278\) 0 0
\(279\) −8.73010 5.61050i −0.522658 0.335892i
\(280\) 0 0
\(281\) −2.02477 4.43362i −0.120787 0.264488i 0.839574 0.543245i \(-0.182805\pi\)
−0.960361 + 0.278758i \(0.910077\pi\)
\(282\) 0 0
\(283\) −3.06644 21.3276i −0.182281 1.26779i −0.851352 0.524594i \(-0.824217\pi\)
0.669071 0.743198i \(-0.266692\pi\)
\(284\) 0 0
\(285\) 11.4532 3.36296i 0.678428 0.199204i
\(286\) 0 0
\(287\) 6.60990 + 45.9729i 0.390170 + 2.71369i
\(288\) 0 0
\(289\) 6.90584 4.43811i 0.406226 0.261066i
\(290\) 0 0
\(291\) −0.623437 0.719485i −0.0365465 0.0421770i
\(292\) 0 0
\(293\) −0.249125 0.545507i −0.0145540 0.0318688i 0.902215 0.431286i \(-0.141940\pi\)
−0.916769 + 0.399417i \(0.869213\pi\)
\(294\) 0 0
\(295\) −2.11417 + 1.35870i −0.123092 + 0.0791064i
\(296\) 0 0
\(297\) −0.780281 −0.0452765
\(298\) 0 0
\(299\) 5.25144 11.4991i 0.303699 0.665008i
\(300\) 0 0
\(301\) −0.699116 4.86246i −0.0402964 0.280267i
\(302\) 0 0
\(303\) 2.58866 2.98747i 0.148715 0.171626i
\(304\) 0 0
\(305\) −2.09535 −0.119980
\(306\) 0 0
\(307\) 2.89730 6.34419i 0.165357 0.362082i −0.808755 0.588145i \(-0.799858\pi\)
0.974113 + 0.226063i \(0.0725856\pi\)
\(308\) 0 0
\(309\) −16.3180 + 4.79139i −0.928296 + 0.272572i
\(310\) 0 0
\(311\) −13.4896 + 3.96090i −0.764924 + 0.224602i −0.640845 0.767670i \(-0.721416\pi\)
−0.124079 + 0.992272i \(0.539598\pi\)
\(312\) 0 0
\(313\) −19.9896 + 23.0692i −1.12988 + 1.30395i −0.182728 + 0.983163i \(0.558493\pi\)
−0.947151 + 0.320787i \(0.896053\pi\)
\(314\) 0 0
\(315\) −6.44127 7.43362i −0.362924 0.418837i
\(316\) 0 0
\(317\) 26.4579 + 7.76875i 1.48603 + 0.436336i 0.921271 0.388922i \(-0.127152\pi\)
0.564755 + 0.825259i \(0.308971\pi\)
\(318\) 0 0
\(319\) 3.21919 + 2.06885i 0.180240 + 0.115833i
\(320\) 0 0
\(321\) −0.616560 0.181038i −0.0344130 0.0101046i
\(322\) 0 0
\(323\) 12.3338 + 27.0073i 0.686273 + 1.50273i
\(324\) 0 0
\(325\) 1.09338 1.26182i 0.0606496 0.0699934i
\(326\) 0 0
\(327\) −0.199094 + 0.435955i −0.0110099 + 0.0241084i
\(328\) 0 0
\(329\) 16.8353 10.8194i 0.928162 0.596493i
\(330\) 0 0
\(331\) −15.0585 4.42157i −0.827690 0.243032i −0.159665 0.987171i \(-0.551042\pi\)
−0.668024 + 0.744140i \(0.732860\pi\)
\(332\) 0 0
\(333\) −1.26103 + 8.77069i −0.0691042 + 0.480631i
\(334\) 0 0
\(335\) −1.80453 + 16.4240i −0.0985920 + 0.897337i
\(336\) 0 0
\(337\) −2.18286 + 15.1821i −0.118908 + 0.827024i 0.839854 + 0.542813i \(0.182641\pi\)
−0.958762 + 0.284211i \(0.908268\pi\)
\(338\) 0 0
\(339\) 6.01556 + 1.76633i 0.326720 + 0.0959337i
\(340\) 0 0
\(341\) −6.81193 + 4.37776i −0.368887 + 0.237069i
\(342\) 0 0
\(343\) 19.7238 43.1891i 1.06499 2.33199i
\(344\) 0 0
\(345\) 9.26119 10.6880i 0.498606 0.575422i
\(346\) 0 0
\(347\) −8.78288 19.2318i −0.471490 1.03242i −0.984716 0.174165i \(-0.944277\pi\)
0.513227 0.858253i \(-0.328450\pi\)
\(348\) 0 0
\(349\) 0.531914 + 0.156184i 0.0284727 + 0.00836034i 0.295938 0.955207i \(-0.404368\pi\)
−0.267465 + 0.963568i \(0.586186\pi\)
\(350\) 0 0
\(351\) −1.51793 0.975514i −0.0810211 0.0520691i
\(352\) 0 0
\(353\) 5.65818 + 1.66139i 0.301154 + 0.0884269i 0.428819 0.903391i \(-0.358930\pi\)
−0.127664 + 0.991817i \(0.540748\pi\)
\(354\) 0 0
\(355\) 21.6832 + 25.0237i 1.15082 + 1.32812i
\(356\) 0 0
\(357\) 16.0215 18.4898i 0.847947 0.978583i
\(358\) 0 0
\(359\) −17.5469 + 5.15225i −0.926092 + 0.271925i −0.709800 0.704403i \(-0.751215\pi\)
−0.216292 + 0.976329i \(0.569396\pi\)
\(360\) 0 0
\(361\) −15.3216 + 4.49883i −0.806401 + 0.236781i
\(362\) 0 0
\(363\) 4.31664 9.45213i 0.226565 0.496108i
\(364\) 0 0
\(365\) −0.580261 −0.0303723
\(366\) 0 0
\(367\) 17.5323 20.2334i 0.915180 1.05617i −0.0830404 0.996546i \(-0.526463\pi\)
0.998221 0.0596282i \(-0.0189915\pi\)
\(368\) 0 0
\(369\) 1.35650 + 9.43465i 0.0706165 + 0.491148i
\(370\) 0 0
\(371\) −26.5241 + 58.0797i −1.37706 + 3.01535i
\(372\) 0 0
\(373\) −18.1521 −0.939882 −0.469941 0.882698i \(-0.655725\pi\)
−0.469941 + 0.882698i \(0.655725\pi\)
\(374\) 0 0
\(375\) 10.0620 6.46647i 0.519601 0.333927i
\(376\) 0 0
\(377\) 3.67600 + 8.04933i 0.189324 + 0.414561i
\(378\) 0 0
\(379\) 0.595678 + 0.687449i 0.0305979 + 0.0353119i 0.770842 0.637026i \(-0.219836\pi\)
−0.740244 + 0.672338i \(0.765290\pi\)
\(380\) 0 0
\(381\) −7.22925 + 4.64596i −0.370366 + 0.238020i
\(382\) 0 0
\(383\) 2.30968 + 16.0642i 0.118019 + 0.820843i 0.959732 + 0.280917i \(0.0906386\pi\)
−0.841713 + 0.539926i \(0.818452\pi\)
\(384\) 0 0
\(385\) −7.36402 + 2.16227i −0.375305 + 0.110200i
\(386\) 0 0
\(387\) −0.143474 0.997884i −0.00729319 0.0507253i
\(388\) 0 0
\(389\) −1.82491 3.99599i −0.0925264 0.202605i 0.857710 0.514133i \(-0.171886\pi\)
−0.950237 + 0.311529i \(0.899159\pi\)
\(390\) 0 0
\(391\) 29.5921 + 19.0177i 1.49654 + 0.961767i
\(392\) 0 0
\(393\) 1.21207 8.43014i 0.0611409 0.425244i
\(394\) 0 0
\(395\) 1.20160 8.35734i 0.0604593 0.420503i
\(396\) 0 0
\(397\) −9.37733 6.02645i −0.470635 0.302459i 0.283741 0.958901i \(-0.408424\pi\)
−0.754376 + 0.656442i \(0.772061\pi\)
\(398\) 0 0
\(399\) 18.8696 + 21.7767i 0.944663 + 1.09020i
\(400\) 0 0
\(401\) 1.76059 0.0879196 0.0439598 0.999033i \(-0.486003\pi\)
0.0439598 + 0.999033i \(0.486003\pi\)
\(402\) 0 0
\(403\) −18.7248 −0.932749
\(404\) 0 0
\(405\) −1.32189 1.52554i −0.0656852 0.0758048i
\(406\) 0 0
\(407\) 5.81640 + 3.73797i 0.288308 + 0.185285i
\(408\) 0 0
\(409\) −2.41312 + 16.7837i −0.119321 + 0.829898i 0.838985 + 0.544155i \(0.183150\pi\)
−0.958306 + 0.285743i \(0.907760\pi\)
\(410\) 0 0
\(411\) −0.397519 + 2.76481i −0.0196082 + 0.136378i
\(412\) 0 0
\(413\) −5.10353 3.27984i −0.251128 0.161390i
\(414\) 0 0
\(415\) 12.5333 + 27.4440i 0.615234 + 1.34717i
\(416\) 0 0
\(417\) −0.462471 3.21656i −0.0226473 0.157516i
\(418\) 0 0
\(419\) −38.2174 + 11.2217i −1.86704 + 0.548214i −0.868417 + 0.495834i \(0.834862\pi\)
−0.998627 + 0.0523795i \(0.983319\pi\)
\(420\) 0 0
\(421\) 2.42240 + 16.8482i 0.118061 + 0.821130i 0.959687 + 0.281070i \(0.0906894\pi\)
−0.841627 + 0.540060i \(0.818402\pi\)
\(422\) 0 0
\(423\) 3.45498 2.22038i 0.167987 0.107959i
\(424\) 0 0
\(425\) 3.04245 + 3.51117i 0.147580 + 0.170317i
\(426\) 0 0
\(427\) −2.10121 4.60101i −0.101685 0.222658i
\(428\) 0 0
\(429\) −1.18441 + 0.761175i −0.0571839 + 0.0367499i
\(430\) 0 0
\(431\) −16.7065 −0.804725 −0.402363 0.915480i \(-0.631811\pi\)
−0.402363 + 0.915480i \(0.631811\pi\)
\(432\) 0 0
\(433\) 1.75990 3.85364i 0.0845754 0.185194i −0.862619 0.505854i \(-0.831177\pi\)
0.947194 + 0.320660i \(0.103905\pi\)
\(434\) 0 0
\(435\) 1.40885 + 9.79878i 0.0675493 + 0.469816i
\(436\) 0 0
\(437\) −27.1306 + 31.3103i −1.29783 + 1.49778i
\(438\) 0 0
\(439\) −22.0099 −1.05048 −0.525239 0.850955i \(-0.676024\pi\)
−0.525239 + 0.850955i \(0.676024\pi\)
\(440\) 0 0
\(441\) 6.95567 15.2308i 0.331222 0.725275i
\(442\) 0 0
\(443\) 17.8577 5.24351i 0.848447 0.249127i 0.171524 0.985180i \(-0.445131\pi\)
0.676923 + 0.736053i \(0.263313\pi\)
\(444\) 0 0
\(445\) −6.14890 + 1.80548i −0.291486 + 0.0855880i
\(446\) 0 0
\(447\) −6.84316 + 7.89743i −0.323671 + 0.373536i
\(448\) 0 0
\(449\) −15.1683 17.5051i −0.715835 0.826117i 0.274965 0.961454i \(-0.411334\pi\)
−0.990800 + 0.135337i \(0.956788\pi\)
\(450\) 0 0
\(451\) 7.13611 + 2.09535i 0.336026 + 0.0986663i
\(452\) 0 0
\(453\) −7.62649 4.90125i −0.358324 0.230281i
\(454\) 0 0
\(455\) −17.0290 5.00016i −0.798331 0.234411i
\(456\) 0 0
\(457\) 8.50451 + 18.6223i 0.397824 + 0.871114i 0.997486 + 0.0708603i \(0.0225744\pi\)
−0.599662 + 0.800253i \(0.704698\pi\)
\(458\) 0 0
\(459\) 3.28796 3.79451i 0.153469 0.177113i
\(460\) 0 0
\(461\) 5.85350 12.8174i 0.272624 0.596964i −0.722954 0.690896i \(-0.757216\pi\)
0.995579 + 0.0939317i \(0.0299435\pi\)
\(462\) 0 0
\(463\) 11.2181 7.20943i 0.521349 0.335051i −0.253356 0.967373i \(-0.581535\pi\)
0.774705 + 0.632322i \(0.217898\pi\)
\(464\) 0 0
\(465\) −20.0993 5.90168i −0.932082 0.273684i
\(466\) 0 0
\(467\) −1.11098 + 7.72707i −0.0514102 + 0.357566i 0.947836 + 0.318757i \(0.103265\pi\)
−0.999247 + 0.0388089i \(0.987644\pi\)
\(468\) 0 0
\(469\) −37.8735 + 12.5074i −1.74884 + 0.577540i
\(470\) 0 0
\(471\) −0.225039 + 1.56518i −0.0103692 + 0.0721196i
\(472\) 0 0
\(473\) −0.754772 0.221621i −0.0347044 0.0101901i
\(474\) 0 0
\(475\) −4.60321 + 2.95831i −0.211210 + 0.135736i
\(476\) 0 0
\(477\) −5.44333 + 11.9192i −0.249233 + 0.545744i
\(478\) 0 0
\(479\) 19.6750 22.7062i 0.898975 1.03747i −0.100121 0.994975i \(-0.531923\pi\)
0.999097 0.0424974i \(-0.0135314\pi\)
\(480\) 0 0
\(481\) 6.64177 + 14.5434i 0.302839 + 0.663124i
\(482\) 0 0
\(483\) 32.7559 + 9.61800i 1.49044 + 0.437634i
\(484\) 0 0
\(485\) −1.61665 1.03896i −0.0734085 0.0471768i
\(486\) 0 0
\(487\) 26.5014 + 7.78152i 1.20089 + 0.352614i 0.820195 0.572084i \(-0.193865\pi\)
0.380700 + 0.924699i \(0.375683\pi\)
\(488\) 0 0
\(489\) 9.33006 + 10.7675i 0.421920 + 0.486922i
\(490\) 0 0
\(491\) 3.91167 4.51430i 0.176531 0.203728i −0.660588 0.750749i \(-0.729693\pi\)
0.837119 + 0.547021i \(0.184238\pi\)
\(492\) 0 0
\(493\) −23.6259 + 6.93719i −1.06406 + 0.312435i
\(494\) 0 0
\(495\) −1.51126 + 0.443746i −0.0679260 + 0.0199449i
\(496\) 0 0
\(497\) −33.2036 + 72.7058i −1.48939 + 3.26130i
\(498\) 0 0
\(499\) 3.47258 0.155454 0.0777269 0.996975i \(-0.475234\pi\)
0.0777269 + 0.996975i \(0.475234\pi\)
\(500\) 0 0
\(501\) 2.94972 3.40416i 0.131784 0.152086i
\(502\) 0 0
\(503\) −5.95885 41.4447i −0.265692 1.84793i −0.487863 0.872920i \(-0.662223\pi\)
0.222171 0.975008i \(-0.428686\pi\)
\(504\) 0 0
\(505\) 3.31478 7.25835i 0.147506 0.322992i
\(506\) 0 0
\(507\) 9.74426 0.432758
\(508\) 0 0
\(509\) 17.8823 11.4923i 0.792621 0.509387i −0.0805792 0.996748i \(-0.525677\pi\)
0.873200 + 0.487362i \(0.162041\pi\)
\(510\) 0 0
\(511\) −0.581883 1.27415i −0.0257410 0.0563649i
\(512\) 0 0
\(513\) 3.87246 + 4.46906i 0.170973 + 0.197314i
\(514\) 0 0
\(515\) −28.8800 + 18.5601i −1.27261 + 0.817854i
\(516\) 0 0
\(517\) −0.456058 3.17195i −0.0200574 0.139502i
\(518\) 0 0
\(519\) 23.6889 6.95567i 1.03983 0.305320i
\(520\) 0 0
\(521\) −2.96176 20.5995i −0.129757 0.902479i −0.945860 0.324574i \(-0.894779\pi\)
0.816103 0.577906i \(-0.196130\pi\)
\(522\) 0 0
\(523\) 6.04314 + 13.2326i 0.264248 + 0.578623i 0.994521 0.104532i \(-0.0333346\pi\)
−0.730273 + 0.683155i \(0.760607\pi\)
\(524\) 0 0
\(525\) 3.79314 + 2.43770i 0.165546 + 0.106390i
\(526\) 0 0
\(527\) 7.41516 51.5735i 0.323009 2.24658i
\(528\) 0 0
\(529\) −3.71220 + 25.8189i −0.161400 + 1.12256i
\(530\) 0 0
\(531\) −1.04736 0.673095i −0.0454514 0.0292098i
\(532\) 0 0
\(533\) 11.2627 + 12.9979i 0.487842 + 0.563000i
\(534\) 0 0
\(535\) −1.29712 −0.0560794
\(536\) 0 0
\(537\) 21.0353 0.907741
\(538\) 0 0
\(539\) −8.55572 9.87382i −0.368521 0.425296i
\(540\) 0 0
\(541\) 1.32937 + 0.854337i 0.0571543 + 0.0367308i 0.568906 0.822403i \(-0.307367\pi\)
−0.511752 + 0.859133i \(0.671003\pi\)
\(542\) 0 0
\(543\) 3.23104 22.4724i 0.138657 0.964382i
\(544\) 0 0
\(545\) −0.137680 + 0.957589i −0.00589758 + 0.0410186i
\(546\) 0 0
\(547\) 10.7454 + 6.90563i 0.459439 + 0.295264i 0.749813 0.661650i \(-0.230143\pi\)
−0.290374 + 0.956913i \(0.593780\pi\)
\(548\) 0 0
\(549\) −0.431215 0.944228i −0.0184038 0.0402987i
\(550\) 0 0
\(551\) −4.12722 28.7054i −0.175825 1.22289i
\(552\) 0 0
\(553\) 19.5561 5.74219i 0.831611 0.244183i
\(554\) 0 0
\(555\) 2.54550 + 17.7043i 0.108050 + 0.751507i
\(556\) 0 0
\(557\) −17.6492 + 11.3425i −0.747821 + 0.480595i −0.858214 0.513293i \(-0.828426\pi\)
0.110393 + 0.993888i \(0.464789\pi\)
\(558\) 0 0
\(559\) −1.19123 1.37476i −0.0503838 0.0581460i
\(560\) 0 0
\(561\) −1.62746 3.56364i −0.0687115 0.150457i
\(562\) 0 0
\(563\) 12.7710 8.20746i 0.538236 0.345903i −0.243113 0.969998i \(-0.578169\pi\)
0.781348 + 0.624095i \(0.214532\pi\)
\(564\) 0 0
\(565\) 12.6555 0.532422
\(566\) 0 0
\(567\) 2.02422 4.43243i 0.0850093 0.186144i
\(568\) 0 0
\(569\) −0.609586 4.23976i −0.0255552 0.177740i 0.973046 0.230610i \(-0.0740722\pi\)
−0.998601 + 0.0528700i \(0.983163\pi\)
\(570\) 0 0
\(571\) −7.58639 + 8.75516i −0.317481 + 0.366392i −0.891950 0.452134i \(-0.850663\pi\)
0.574470 + 0.818526i \(0.305208\pi\)
\(572\) 0 0
\(573\) 8.01536 0.334847
\(574\) 0 0
\(575\) −2.69308 + 5.89703i −0.112309 + 0.245923i
\(576\) 0 0
\(577\) −2.75241 + 0.808181i −0.114584 + 0.0336450i −0.338522 0.940958i \(-0.609927\pi\)
0.223938 + 0.974603i \(0.428109\pi\)
\(578\) 0 0
\(579\) −22.5149 + 6.61097i −0.935687 + 0.274743i
\(580\) 0 0
\(581\) −47.6937 + 55.0415i −1.97867 + 2.28350i
\(582\) 0 0
\(583\) 6.69549 + 7.72700i 0.277299 + 0.320020i
\(584\) 0 0
\(585\) −3.49472 1.02614i −0.144489 0.0424258i
\(586\) 0 0
\(587\) −29.7151 19.0967i −1.22647 0.788207i −0.243135 0.969992i \(-0.578176\pi\)
−0.983338 + 0.181786i \(0.941812\pi\)
\(588\) 0 0
\(589\) 58.8806 + 17.2889i 2.42613 + 0.712377i
\(590\) 0 0
\(591\) −4.48000 9.80983i −0.184283 0.403522i
\(592\) 0 0
\(593\) 8.67864 10.0157i 0.356389 0.411295i −0.549038 0.835798i \(-0.685006\pi\)
0.905427 + 0.424503i \(0.139551\pi\)
\(594\) 0 0
\(595\) 20.5155 44.9227i 0.841054 1.84165i
\(596\) 0 0
\(597\) 2.96790 1.90735i 0.121468 0.0780627i
\(598\) 0 0
\(599\) 28.1855 + 8.27600i 1.15163 + 0.338148i 0.801174 0.598432i \(-0.204209\pi\)
0.350454 + 0.936580i \(0.386027\pi\)
\(600\) 0 0
\(601\) 4.67780 32.5348i 0.190811 1.32712i −0.639056 0.769160i \(-0.720675\pi\)
0.829867 0.557961i \(-0.188416\pi\)
\(602\) 0 0
\(603\) −7.77248 + 2.56680i −0.316520 + 0.104528i
\(604\) 0 0
\(605\) 2.98511 20.7619i 0.121362 0.844092i
\(606\) 0 0
\(607\) −16.0373 4.70898i −0.650935 0.191132i −0.0604384 0.998172i \(-0.519250\pi\)
−0.590496 + 0.807040i \(0.701068\pi\)
\(608\) 0 0
\(609\) −20.1035 + 12.9197i −0.814635 + 0.523534i
\(610\) 0 0
\(611\) 3.07841 6.74077i 0.124539 0.272702i
\(612\) 0 0
\(613\) 6.11279 7.05454i 0.246893 0.284930i −0.618754 0.785585i \(-0.712362\pi\)
0.865647 + 0.500655i \(0.166907\pi\)
\(614\) 0 0
\(615\) 7.99277 + 17.5017i 0.322300 + 0.705738i
\(616\) 0 0
\(617\) −25.5246 7.49469i −1.02758 0.301725i −0.275854 0.961200i \(-0.588961\pi\)
−0.751727 + 0.659474i \(0.770779\pi\)
\(618\) 0 0
\(619\) −13.6915 8.79900i −0.550308 0.353662i 0.235750 0.971814i \(-0.424245\pi\)
−0.786059 + 0.618152i \(0.787882\pi\)
\(620\) 0 0
\(621\) 6.72223 + 1.97383i 0.269754 + 0.0792069i
\(622\) 0 0
\(623\) −10.1306 11.6913i −0.405873 0.468403i
\(624\) 0 0
\(625\) 12.7810 14.7501i 0.511240 0.590002i
\(626\) 0 0
\(627\) 4.42722 1.29995i 0.176806 0.0519149i
\(628\) 0 0
\(629\) −42.6871 + 12.5340i −1.70204 + 0.499765i
\(630\) 0 0
\(631\) 18.1424 39.7262i 0.722236 1.58148i −0.0885083 0.996075i \(-0.528210\pi\)
0.810744 0.585401i \(-0.199063\pi\)
\(632\) 0 0
\(633\) −12.4866 −0.496299
\(634\) 0 0
\(635\) −11.3596 + 13.1096i −0.450791 + 0.520240i
\(636\) 0 0
\(637\) −4.29963 29.9046i −0.170358 1.18486i
\(638\) 0 0
\(639\) −6.81411 + 14.9208i −0.269562 + 0.590259i
\(640\) 0 0
\(641\) 25.9495 1.02495 0.512473 0.858704i \(-0.328730\pi\)
0.512473 + 0.858704i \(0.328730\pi\)
\(642\) 0 0
\(643\) 19.6379 12.6205i 0.774442 0.497704i −0.0927426 0.995690i \(-0.529563\pi\)
0.867185 + 0.497986i \(0.165927\pi\)
\(644\) 0 0
\(645\) −0.845379 1.85112i −0.0332868 0.0728879i
\(646\) 0 0
\(647\) −20.8555 24.0685i −0.819915 0.946232i 0.179380 0.983780i \(-0.442591\pi\)
−0.999295 + 0.0375477i \(0.988045\pi\)
\(648\) 0 0
\(649\) −0.817232 + 0.525203i −0.0320792 + 0.0206160i
\(650\) 0 0
\(651\) −7.19645 50.0524i −0.282051 1.96171i
\(652\) 0 0
\(653\) 29.8833 8.77452i 1.16942 0.343374i 0.361335 0.932436i \(-0.382321\pi\)
0.808088 + 0.589062i \(0.200503\pi\)
\(654\) 0 0
\(655\) −2.44666 17.0169i −0.0955990 0.664906i
\(656\) 0 0
\(657\) −0.119415 0.261483i −0.00465883 0.0102014i
\(658\) 0 0
\(659\) −8.45305 5.43244i −0.329284 0.211618i 0.365544 0.930794i \(-0.380883\pi\)
−0.694828 + 0.719176i \(0.744519\pi\)
\(660\) 0 0
\(661\) 3.67476 25.5585i 0.142932 0.994112i −0.784502 0.620126i \(-0.787082\pi\)
0.927434 0.373986i \(-0.122009\pi\)
\(662\) 0 0
\(663\) 1.28930 8.96725i 0.0500721 0.348259i
\(664\) 0 0
\(665\) 48.9314 + 31.4463i 1.89748 + 1.21943i
\(666\) 0 0
\(667\) −22.5004 25.9668i −0.871218 1.00544i
\(668\) 0 0
\(669\) 23.7517 0.918295
\(670\) 0 0
\(671\) −0.809957 −0.0312681
\(672\) 0 0
\(673\) 13.3837 + 15.4457i 0.515905 + 0.595386i 0.952601 0.304223i \(-0.0983968\pi\)
−0.436696 + 0.899609i \(0.643851\pi\)
\(674\) 0 0
\(675\) 0.778436 + 0.500271i 0.0299620 + 0.0192554i
\(676\) 0 0
\(677\) −6.53198 + 45.4309i −0.251044 + 1.74605i 0.340925 + 0.940090i \(0.389260\pi\)
−0.591969 + 0.805960i \(0.701649\pi\)
\(678\) 0 0
\(679\) 0.660192 4.59173i 0.0253358 0.176215i
\(680\) 0 0
\(681\) −23.2330 14.9310i −0.890292 0.572156i
\(682\) 0 0
\(683\) 10.4938 + 22.9783i 0.401535 + 0.879240i 0.997112 + 0.0759416i \(0.0241963\pi\)
−0.595577 + 0.803298i \(0.703076\pi\)
\(684\) 0 0
\(685\) 0.802425 + 5.58099i 0.0306591 + 0.213239i
\(686\) 0 0
\(687\) 7.05491 2.07151i 0.269162 0.0790330i
\(688\) 0 0
\(689\) 3.36479 + 23.4026i 0.128188 + 0.891568i
\(690\) 0 0
\(691\) −9.26787 + 5.95610i −0.352566 + 0.226581i −0.704921 0.709286i \(-0.749017\pi\)
0.352355 + 0.935867i \(0.385381\pi\)
\(692\) 0 0
\(693\) −2.48987 2.87346i −0.0945822 0.109154i
\(694\) 0 0
\(695\) −2.72498 5.96687i −0.103364 0.226336i
\(696\) 0 0
\(697\) −40.2600 + 25.8735i −1.52496 + 0.980029i
\(698\) 0 0
\(699\) 1.23580 0.0467423
\(700\) 0 0
\(701\) −1.94442 + 4.25768i −0.0734395 + 0.160810i −0.942791 0.333384i \(-0.891809\pi\)
0.869352 + 0.494194i \(0.164537\pi\)
\(702\) 0 0
\(703\) −7.45702 51.8647i −0.281247 1.95611i
\(704\) 0 0
\(705\) 5.42893 6.26532i 0.204465 0.235965i
\(706\) 0 0
\(707\) 19.2620 0.724423
\(708\) 0 0
\(709\) −0.854364 + 1.87080i −0.0320863 + 0.0702592i −0.924997 0.379976i \(-0.875932\pi\)
0.892910 + 0.450235i \(0.148660\pi\)
\(710\) 0 0
\(711\) 4.01335 1.17842i 0.150512 0.0441944i
\(712\) 0 0
\(713\) 69.7599 20.4834i 2.61253 0.767108i
\(714\) 0 0
\(715\) −1.86111 + 2.14783i −0.0696014 + 0.0803243i
\(716\) 0 0
\(717\) 5.46348 + 6.30519i 0.204037 + 0.235472i
\(718\) 0 0
\(719\) −9.58930 2.81567i −0.357621 0.105007i 0.0979867 0.995188i \(-0.468760\pi\)
−0.455607 + 0.890181i \(0.650578\pi\)
\(720\) 0 0
\(721\) −69.7151 44.8032i −2.59633 1.66856i
\(722\) 0 0
\(723\) 23.2306 + 6.82111i 0.863954 + 0.253680i
\(724\) 0 0
\(725\) −1.88516 4.12791i −0.0700129 0.153307i
\(726\) 0 0
\(727\) 1.47923 1.70712i 0.0548615 0.0633136i −0.727655 0.685943i \(-0.759390\pi\)
0.782517 + 0.622629i \(0.213935\pi\)
\(728\) 0 0
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) 0 0
\(731\) 4.25822 2.73659i 0.157496 0.101216i
\(732\) 0 0
\(733\) −18.6844 5.48623i −0.690124 0.202639i −0.0821785 0.996618i \(-0.526188\pi\)
−0.607945 + 0.793979i \(0.708006\pi\)
\(734\) 0 0
\(735\) 4.81009 33.4549i 0.177423 1.23400i
\(736\) 0 0
\(737\) −0.697539 + 6.34867i −0.0256942 + 0.233856i
\(738\) 0 0
\(739\) −5.93100 + 41.2510i −0.218175 + 1.51744i 0.526592 + 0.850118i \(0.323470\pi\)
−0.744767 + 0.667325i \(0.767439\pi\)
\(740\) 0 0
\(741\) 10.2378 + 3.00608i 0.376093 + 0.110431i
\(742\) 0 0
\(743\) −23.3711 + 15.0197i −0.857404 + 0.551020i −0.893876 0.448314i \(-0.852025\pi\)
0.0364716 + 0.999335i \(0.488388\pi\)
\(744\) 0 0
\(745\) −8.76267 + 19.1876i −0.321039 + 0.702978i
\(746\) 0 0
\(747\) −9.78780 + 11.2957i −0.358117 + 0.413289i
\(748\) 0 0
\(749\) −1.30074 2.84823i −0.0475282 0.104072i
\(750\) 0 0
\(751\) 37.2009 + 10.9232i 1.35748 + 0.398592i 0.877873 0.478893i \(-0.158962\pi\)
0.479605 + 0.877484i \(0.340780\pi\)
\(752\) 0 0
\(753\) −10.0799 6.47798i −0.367333 0.236071i
\(754\) 0 0
\(755\) −17.5584 5.15563i −0.639017 0.187632i
\(756\) 0 0
\(757\) −2.57616 2.97305i −0.0936322 0.108057i 0.707000 0.707214i \(-0.250048\pi\)
−0.800632 + 0.599156i \(0.795503\pi\)
\(758\) 0 0
\(759\) 3.57991 4.13143i 0.129942 0.149961i
\(760\) 0 0
\(761\) −34.3144 + 10.0756i −1.24390 + 0.365241i −0.836478 0.548000i \(-0.815389\pi\)
−0.407419 + 0.913241i \(0.633571\pi\)
\(762\) 0 0
\(763\) −2.24075 + 0.657944i −0.0811206 + 0.0238192i
\(764\) 0 0
\(765\) 4.21023 9.21913i 0.152221 0.333318i
\(766\) 0 0
\(767\) −2.24643 −0.0811138
\(768\) 0 0
\(769\) 20.8718 24.0873i 0.752656 0.868612i −0.242167 0.970235i \(-0.577858\pi\)
0.994823 + 0.101623i \(0.0324036\pi\)
\(770\) 0 0
\(771\) 2.08269 + 14.4854i 0.0750061 + 0.521679i
\(772\) 0 0
\(773\) −5.44363 + 11.9199i −0.195794 + 0.428729i −0.981910 0.189351i \(-0.939362\pi\)
0.786116 + 0.618079i \(0.212089\pi\)
\(774\) 0 0
\(775\) 9.60259 0.344935
\(776\) 0 0
\(777\) −36.3228 + 23.3433i −1.30307 + 0.837435i
\(778\) 0 0
\(779\) −23.4147 51.2711i −0.838920 1.83698i
\(780\) 0 0
\(781\) 8.38160 + 9.67289i 0.299917 +