Properties

Label 804.2.y.b.157.2
Level 804
Weight 2
Character 804.157
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 157.2
Character \(\chi\) = 804.157
Dual form 804.2.y.b.169.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.19502 - 2.61673i) q^{5} +(-1.34977 + 1.28701i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\) \(q+(0.142315 - 0.989821i) q^{3} +(-1.19502 - 2.61673i) q^{5} +(-1.34977 + 1.28701i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-4.03738 - 0.385523i) q^{11} +(4.55479 + 0.877865i) q^{13} +(-2.76016 + 0.810456i) q^{15} +(-4.03473 - 2.08005i) q^{17} +(0.436555 + 0.416254i) q^{19} +(1.08181 + 1.51919i) q^{21} +(-4.41195 + 1.76628i) q^{23} +(-2.14488 + 2.47533i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-0.934423 + 1.61847i) q^{29} +(-8.97739 + 1.73025i) q^{31} +(-0.956177 + 3.94142i) q^{33} +(4.98075 + 1.99399i) q^{35} +(-2.34904 - 4.06866i) q^{37} +(1.51714 - 4.38350i) q^{39} +(0.430155 + 9.03006i) q^{41} +(3.06430 - 1.96930i) q^{43} +(0.409395 + 2.84741i) q^{45} +(6.26934 + 4.93026i) q^{47} +(-0.167571 + 3.51774i) q^{49} +(-2.63308 + 3.69764i) q^{51} +(-8.74113 - 5.61758i) q^{53} +(3.81593 + 11.0254i) q^{55} +(0.474145 - 0.372872i) q^{57} +(-7.56473 - 8.73016i) q^{59} +(7.89708 - 0.754080i) q^{61} +(1.65769 - 0.854598i) q^{63} +(-3.14593 - 12.9677i) q^{65} +(-4.96592 + 6.50689i) q^{67} +(1.12041 + 4.61841i) q^{69} +(1.67654 - 0.864316i) q^{71} +(-1.31904 + 0.125953i) q^{73} +(2.14488 + 2.47533i) q^{75} +(5.94571 - 4.67576i) q^{77} +(-3.04218 - 8.78980i) q^{79} +(0.841254 + 0.540641i) q^{81} +(2.64677 - 3.71687i) q^{83} +(-0.621337 + 13.0435i) q^{85} +(1.46901 + 1.15524i) q^{87} +(-1.52653 - 10.6173i) q^{89} +(-7.27776 + 4.67713i) q^{91} +(0.435023 + 9.13225i) q^{93} +(0.567532 - 1.63978i) q^{95} +(-6.97677 - 12.0841i) q^{97} +(3.76522 + 1.50737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{14}{33}\right)\) \(1\)

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
\(3\) 0.142315 0.989821i 0.0821655 0.571474i
\(4\) 0 0
\(5\) −1.19502 2.61673i −0.534429 1.17024i −0.963682 0.267052i \(-0.913951\pi\)
0.429254 0.903184i \(-0.358777\pi\)
\(6\) 0 0
\(7\) −1.34977 + 1.28701i −0.510166 + 0.486443i −0.900879 0.434070i \(-0.857077\pi\)
0.390713 + 0.920513i \(0.372229\pi\)
\(8\) 0 0
\(9\) −0.959493 0.281733i −0.319831 0.0939109i
\(10\) 0 0
\(11\) −4.03738 0.385523i −1.21731 0.116239i −0.533439 0.845838i \(-0.679101\pi\)
−0.683875 + 0.729599i \(0.739707\pi\)
\(12\) 0 0
\(13\) 4.55479 + 0.877865i 1.26327 + 0.243476i 0.776536 0.630073i \(-0.216975\pi\)
0.486737 + 0.873549i \(0.338187\pi\)
\(14\) 0 0
\(15\) −2.76016 + 0.810456i −0.712670 + 0.209259i
\(16\) 0 0
\(17\) −4.03473 2.08005i −0.978565 0.504486i −0.106732 0.994288i \(-0.534039\pi\)
−0.871834 + 0.489802i \(0.837069\pi\)
\(18\) 0 0
\(19\) 0.436555 + 0.416254i 0.100152 + 0.0954952i 0.738501 0.674252i \(-0.235534\pi\)
−0.638349 + 0.769747i \(0.720382\pi\)
\(20\) 0 0
\(21\) 1.08181 + 1.51919i 0.236071 + 0.331515i
\(22\) 0 0
\(23\) −4.41195 + 1.76628i −0.919956 + 0.368295i −0.782813 0.622257i \(-0.786216\pi\)
−0.137142 + 0.990551i \(0.543792\pi\)
\(24\) 0 0
\(25\) −2.14488 + 2.47533i −0.428977 + 0.495065i
\(26\) 0 0
\(27\) −0.415415 + 0.909632i −0.0799467 + 0.175059i
\(28\) 0 0
\(29\) −0.934423 + 1.61847i −0.173518 + 0.300542i −0.939647 0.342144i \(-0.888847\pi\)
0.766129 + 0.642686i \(0.222180\pi\)
\(30\) 0 0
\(31\) −8.97739 + 1.73025i −1.61239 + 0.310762i −0.914234 0.405187i \(-0.867206\pi\)
−0.698152 + 0.715949i \(0.745994\pi\)
\(32\) 0 0
\(33\) −0.956177 + 3.94142i −0.166449 + 0.686113i
\(34\) 0 0
\(35\) 4.98075 + 1.99399i 0.841900 + 0.337046i
\(36\) 0 0
\(37\) −2.34904 4.06866i −0.386180 0.668883i 0.605752 0.795653i \(-0.292872\pi\)
−0.991932 + 0.126770i \(0.959539\pi\)
\(38\) 0 0
\(39\) 1.51714 4.38350i 0.242937 0.701922i
\(40\) 0 0
\(41\) 0.430155 + 9.03006i 0.0671789 + 1.41026i 0.741070 + 0.671428i \(0.234319\pi\)
−0.673891 + 0.738831i \(0.735378\pi\)
\(42\) 0 0
\(43\) 3.06430 1.96930i 0.467301 0.300316i −0.285720 0.958313i \(-0.592233\pi\)
0.753020 + 0.657997i \(0.228596\pi\)
\(44\) 0 0
\(45\) 0.409395 + 2.84741i 0.0610290 + 0.424466i
\(46\) 0 0
\(47\) 6.26934 + 4.93026i 0.914478 + 0.719153i 0.960056 0.279808i \(-0.0902707\pi\)
−0.0455786 + 0.998961i \(0.514513\pi\)
\(48\) 0 0
\(49\) −0.167571 + 3.51774i −0.0239386 + 0.502534i
\(50\) 0 0
\(51\) −2.63308 + 3.69764i −0.368705 + 0.517773i
\(52\) 0 0
\(53\) −8.74113 5.61758i −1.20069 0.771635i −0.221612 0.975135i \(-0.571132\pi\)
−0.979075 + 0.203500i \(0.934768\pi\)
\(54\) 0 0
\(55\) 3.81593 + 11.0254i 0.514540 + 1.48667i
\(56\) 0 0
\(57\) 0.474145 0.372872i 0.0628021 0.0493881i
\(58\) 0 0
\(59\) −7.56473 8.73016i −0.984843 1.13657i −0.990628 0.136587i \(-0.956387\pi\)
0.00578483 0.999983i \(-0.498159\pi\)
\(60\) 0 0
\(61\) 7.89708 0.754080i 1.01112 0.0965500i 0.423674 0.905815i \(-0.360740\pi\)
0.587444 + 0.809265i \(0.300134\pi\)
\(62\) 0 0
\(63\) 1.65769 0.854598i 0.208849 0.107669i
\(64\) 0 0
\(65\) −3.14593 12.9677i −0.390205 1.60845i
\(66\) 0 0
\(67\) −4.96592 + 6.50689i −0.606683 + 0.794944i
\(68\) 0 0
\(69\) 1.12041 + 4.61841i 0.134882 + 0.555992i
\(70\) 0 0
\(71\) 1.67654 0.864316i 0.198969 0.102575i −0.355863 0.934538i \(-0.615813\pi\)
0.554832 + 0.831963i \(0.312783\pi\)
\(72\) 0 0
\(73\) −1.31904 + 0.125953i −0.154382 + 0.0147417i −0.171961 0.985104i \(-0.555010\pi\)
0.0175788 + 0.999845i \(0.494404\pi\)
\(74\) 0 0
\(75\) 2.14488 + 2.47533i 0.247670 + 0.285826i
\(76\) 0 0
\(77\) 5.94571 4.67576i 0.677577 0.532852i
\(78\) 0 0
\(79\) −3.04218 8.78980i −0.342272 0.988929i −0.976450 0.215743i \(-0.930783\pi\)
0.634179 0.773187i \(-0.281338\pi\)
\(80\) 0 0
\(81\) 0.841254 + 0.540641i 0.0934726 + 0.0600712i
\(82\) 0 0
\(83\) 2.64677 3.71687i 0.290521 0.407980i −0.643360 0.765564i \(-0.722460\pi\)
0.933881 + 0.357584i \(0.116399\pi\)
\(84\) 0 0
\(85\) −0.621337 + 13.0435i −0.0673935 + 1.41476i
\(86\) 0 0
\(87\) 1.46901 + 1.15524i 0.157495 + 0.123855i
\(88\) 0 0
\(89\) −1.52653 10.6173i −0.161812 1.12543i −0.895215 0.445635i \(-0.852978\pi\)
0.733403 0.679794i \(-0.237931\pi\)
\(90\) 0 0
\(91\) −7.27776 + 4.67713i −0.762916 + 0.490296i
\(92\) 0 0
\(93\) 0.435023 + 9.13225i 0.0451097 + 0.946970i
\(94\) 0 0
\(95\) 0.567532 1.63978i 0.0582275 0.168237i
\(96\) 0 0
\(97\) −6.97677 12.0841i −0.708383 1.22696i −0.965457 0.260564i \(-0.916092\pi\)
0.257073 0.966392i \(-0.417242\pi\)
\(98\) 0 0
\(99\) 3.76522 + 1.50737i 0.378419 + 0.151496i
\(100\) 0 0
\(101\) 2.21161 9.11638i 0.220063 0.907114i −0.749447 0.662064i \(-0.769681\pi\)
0.969511 0.245050i \(-0.0788042\pi\)
\(102\) 0 0
\(103\) −9.31730 + 1.79576i −0.918061 + 0.176942i −0.626329 0.779558i \(-0.715444\pi\)
−0.291732 + 0.956500i \(0.594231\pi\)
\(104\) 0 0
\(105\) 2.68253 4.64628i 0.261788 0.453430i
\(106\) 0 0
\(107\) −0.578222 + 1.26613i −0.0558989 + 0.122401i −0.935520 0.353273i \(-0.885069\pi\)
0.879621 + 0.475674i \(0.157796\pi\)
\(108\) 0 0
\(109\) 4.92924 5.68865i 0.472136 0.544874i −0.468869 0.883268i \(-0.655338\pi\)
0.941005 + 0.338394i \(0.109884\pi\)
\(110\) 0 0
\(111\) −4.36155 + 1.74610i −0.413980 + 0.165732i
\(112\) 0 0
\(113\) −3.30446 4.64046i −0.310857 0.436538i 0.629360 0.777114i \(-0.283317\pi\)
−0.940217 + 0.340576i \(0.889378\pi\)
\(114\) 0 0
\(115\) 9.89424 + 9.43414i 0.922642 + 0.879738i
\(116\) 0 0
\(117\) −4.12297 2.12554i −0.381169 0.196506i
\(118\) 0 0
\(119\) 8.12300 2.38513i 0.744634 0.218644i
\(120\) 0 0
\(121\) 5.35057 + 1.03124i 0.486415 + 0.0937489i
\(122\) 0 0
\(123\) 8.99937 + 0.859335i 0.811445 + 0.0774836i
\(124\) 0 0
\(125\) −4.76037 1.39777i −0.425781 0.125021i
\(126\) 0 0
\(127\) 9.12722 8.70278i 0.809909 0.772247i −0.166987 0.985959i \(-0.553404\pi\)
0.976897 + 0.213712i \(0.0685554\pi\)
\(128\) 0 0
\(129\) −1.51316 3.31337i −0.133227 0.291726i
\(130\) 0 0
\(131\) −1.66634 + 11.5897i −0.145589 + 1.01259i 0.777741 + 0.628585i \(0.216366\pi\)
−0.923330 + 0.384008i \(0.874543\pi\)
\(132\) 0 0
\(133\) −1.12497 −0.0975474
\(134\) 0 0
\(135\) 2.87669 0.247586
\(136\) 0 0
\(137\) 2.41103 16.7691i 0.205989 1.43268i −0.580089 0.814553i \(-0.696982\pi\)
0.786077 0.618128i \(-0.212109\pi\)
\(138\) 0 0
\(139\) 4.50079 + 9.85536i 0.381752 + 0.835921i 0.998799 + 0.0489942i \(0.0156016\pi\)
−0.617047 + 0.786926i \(0.711671\pi\)
\(140\) 0 0
\(141\) 5.77230 5.50388i 0.486116 0.463510i
\(142\) 0 0
\(143\) −18.0510 5.30025i −1.50950 0.443229i
\(144\) 0 0
\(145\) 5.35174 + 0.511029i 0.444438 + 0.0424387i
\(146\) 0 0
\(147\) 3.45809 + 0.666491i 0.285218 + 0.0549713i
\(148\) 0 0
\(149\) 18.2670 5.36368i 1.49649 0.439410i 0.571886 0.820333i \(-0.306212\pi\)
0.924607 + 0.380923i \(0.124394\pi\)
\(150\) 0 0
\(151\) −21.0271 10.8402i −1.71116 0.882164i −0.979750 0.200224i \(-0.935833\pi\)
−0.731408 0.681940i \(-0.761137\pi\)
\(152\) 0 0
\(153\) 3.28528 + 3.13251i 0.265599 + 0.253248i
\(154\) 0 0
\(155\) 15.2557 + 21.4237i 1.22537 + 1.72079i
\(156\) 0 0
\(157\) 15.1716 6.07380i 1.21083 0.484742i 0.323652 0.946176i \(-0.395089\pi\)
0.887174 + 0.461434i \(0.152665\pi\)
\(158\) 0 0
\(159\) −6.80440 + 7.85269i −0.539624 + 0.622759i
\(160\) 0 0
\(161\) 3.68192 8.06229i 0.290176 0.635397i
\(162\) 0 0
\(163\) −9.70461 + 16.8089i −0.760124 + 1.31657i 0.182663 + 0.983176i \(0.441528\pi\)
−0.942786 + 0.333397i \(0.891805\pi\)
\(164\) 0 0
\(165\) 11.4563 2.20801i 0.891869 0.171894i
\(166\) 0 0
\(167\) 0.931492 3.83966i 0.0720810 0.297122i −0.924349 0.381549i \(-0.875391\pi\)
0.996430 + 0.0844269i \(0.0269060\pi\)
\(168\) 0 0
\(169\) 7.90672 + 3.16537i 0.608209 + 0.243490i
\(170\) 0 0
\(171\) −0.301599 0.522384i −0.0230638 0.0399477i
\(172\) 0 0
\(173\) −1.67945 + 4.85245i −0.127686 + 0.368925i −0.990666 0.136314i \(-0.956474\pi\)
0.862979 + 0.505239i \(0.168596\pi\)
\(174\) 0 0
\(175\) −0.290655 6.10161i −0.0219715 0.461238i
\(176\) 0 0
\(177\) −9.71787 + 6.24530i −0.730440 + 0.469425i
\(178\) 0 0
\(179\) 1.42366 + 9.90179i 0.106410 + 0.740094i 0.971252 + 0.238052i \(0.0765088\pi\)
−0.864843 + 0.502042i \(0.832582\pi\)
\(180\) 0 0
\(181\) −13.6389 10.7257i −1.01377 0.797238i −0.0344197 0.999407i \(-0.510958\pi\)
−0.979350 + 0.202170i \(0.935201\pi\)
\(182\) 0 0
\(183\) 0.377467 7.92402i 0.0279032 0.585760i
\(184\) 0 0
\(185\) −7.83941 + 11.0089i −0.576365 + 0.809392i
\(186\) 0 0
\(187\) 15.4878 + 9.95341i 1.13258 + 0.727866i
\(188\) 0 0
\(189\) −0.609986 1.76244i −0.0443699 0.128199i
\(190\) 0 0
\(191\) 14.5778 11.4641i 1.05481 0.829512i 0.0690409 0.997614i \(-0.478006\pi\)
0.985770 + 0.168102i \(0.0537637\pi\)
\(192\) 0 0
\(193\) 5.94841 + 6.86483i 0.428176 + 0.494141i 0.928310 0.371807i \(-0.121262\pi\)
−0.500135 + 0.865948i \(0.666716\pi\)
\(194\) 0 0
\(195\) −13.2834 + 1.26841i −0.951246 + 0.0908330i
\(196\) 0 0
\(197\) −3.04557 + 1.57010i −0.216988 + 0.111865i −0.563294 0.826257i \(-0.690466\pi\)
0.346306 + 0.938122i \(0.387436\pi\)
\(198\) 0 0
\(199\) 1.56994 + 6.47140i 0.111290 + 0.458745i 1.00000 0.000274706i \(8.74415e-5\pi\)
−0.888710 + 0.458471i \(0.848397\pi\)
\(200\) 0 0
\(201\) 5.73394 + 5.84140i 0.404441 + 0.412021i
\(202\) 0 0
\(203\) −0.821719 3.38717i −0.0576734 0.237733i
\(204\) 0 0
\(205\) 23.1152 11.9167i 1.61443 0.832298i
\(206\) 0 0
\(207\) 4.73086 0.451742i 0.328817 0.0313982i
\(208\) 0 0
\(209\) −1.60206 1.84888i −0.110817 0.127889i
\(210\) 0 0
\(211\) 5.85986 4.60825i 0.403410 0.317245i −0.395756 0.918356i \(-0.629517\pi\)
0.799166 + 0.601111i \(0.205275\pi\)
\(212\) 0 0
\(213\) −0.616922 1.78248i −0.0422708 0.122133i
\(214\) 0 0
\(215\) −8.81502 5.66507i −0.601179 0.386354i
\(216\) 0 0
\(217\) 9.89059 13.8894i 0.671417 0.942874i
\(218\) 0 0
\(219\) −0.0630480 + 1.32354i −0.00426039 + 0.0894365i
\(220\) 0 0
\(221\) −16.5514 13.0161i −1.11336 0.875560i
\(222\) 0 0
\(223\) −2.09690 14.5842i −0.140418 0.976632i −0.931194 0.364525i \(-0.881231\pi\)
0.790775 0.612107i \(-0.209678\pi\)
\(224\) 0 0
\(225\) 2.75538 1.77078i 0.183692 0.118052i
\(226\) 0 0
\(227\) 0.248861 + 5.22424i 0.0165175 + 0.346745i 0.991965 + 0.126513i \(0.0403785\pi\)
−0.975447 + 0.220232i \(0.929318\pi\)
\(228\) 0 0
\(229\) 1.70756 4.93367i 0.112839 0.326026i −0.874415 0.485178i \(-0.838755\pi\)
0.987254 + 0.159152i \(0.0508760\pi\)
\(230\) 0 0
\(231\) −3.78200 6.55062i −0.248838 0.430999i
\(232\) 0 0
\(233\) 18.8674 + 7.55336i 1.23604 + 0.494837i 0.895361 0.445342i \(-0.146918\pi\)
0.340682 + 0.940179i \(0.389342\pi\)
\(234\) 0 0
\(235\) 5.40917 22.2969i 0.352856 1.45449i
\(236\) 0 0
\(237\) −9.13327 + 1.76029i −0.593270 + 0.114343i
\(238\) 0 0
\(239\) 3.93905 6.82263i 0.254796 0.441319i −0.710044 0.704157i \(-0.751325\pi\)
0.964840 + 0.262838i \(0.0846585\pi\)
\(240\) 0 0
\(241\) −7.78131 + 17.0387i −0.501238 + 1.09756i 0.474827 + 0.880079i \(0.342511\pi\)
−0.976065 + 0.217479i \(0.930217\pi\)
\(242\) 0 0
\(243\) 0.654861 0.755750i 0.0420093 0.0484814i
\(244\) 0 0
\(245\) 9.40521 3.76528i 0.600877 0.240555i
\(246\) 0 0
\(247\) 1.62300 + 2.27919i 0.103269 + 0.145021i
\(248\) 0 0
\(249\) −3.30236 3.14880i −0.209279 0.199547i
\(250\) 0 0
\(251\) −11.4912 5.92415i −0.725321 0.373929i 0.0556884 0.998448i \(-0.482265\pi\)
−0.781009 + 0.624519i \(0.785295\pi\)
\(252\) 0 0
\(253\) 18.4937 5.43023i 1.16269 0.341395i
\(254\) 0 0
\(255\) 12.8223 + 2.47129i 0.802963 + 0.154758i
\(256\) 0 0
\(257\) 6.35637 + 0.606960i 0.396500 + 0.0378611i 0.291402 0.956601i \(-0.405878\pi\)
0.105098 + 0.994462i \(0.466484\pi\)
\(258\) 0 0
\(259\) 8.40706 + 2.46853i 0.522389 + 0.153387i
\(260\) 0 0
\(261\) 1.35255 1.28965i 0.0837206 0.0798274i
\(262\) 0 0
\(263\) 4.17725 + 9.14690i 0.257580 + 0.564022i 0.993602 0.112935i \(-0.0360253\pi\)
−0.736022 + 0.676958i \(0.763298\pi\)
\(264\) 0 0
\(265\) −4.25386 + 29.5863i −0.261313 + 1.81747i
\(266\) 0 0
\(267\) −10.7265 −0.656448
\(268\) 0 0
\(269\) −7.24161 −0.441529 −0.220764 0.975327i \(-0.570855\pi\)
−0.220764 + 0.975327i \(0.570855\pi\)
\(270\) 0 0
\(271\) 4.34254 30.2030i 0.263791 1.83470i −0.239873 0.970804i \(-0.577106\pi\)
0.503663 0.863900i \(-0.331985\pi\)
\(272\) 0 0
\(273\) 3.59379 + 7.86930i 0.217506 + 0.476272i
\(274\) 0 0
\(275\) 9.61400 9.16693i 0.579746 0.552787i
\(276\) 0 0
\(277\) 4.54685 + 1.33508i 0.273194 + 0.0802169i 0.415460 0.909612i \(-0.363621\pi\)
−0.142266 + 0.989828i \(0.545439\pi\)
\(278\) 0 0
\(279\) 9.10121 + 0.869060i 0.544875 + 0.0520292i
\(280\) 0 0
\(281\) −5.18852 1.00000i −0.309521 0.0596553i 0.0321254 0.999484i \(-0.489772\pi\)
−0.341646 + 0.939829i \(0.610985\pi\)
\(282\) 0 0
\(283\) −20.4236 + 5.99690i −1.21406 + 0.356479i −0.825211 0.564825i \(-0.808944\pi\)
−0.388844 + 0.921304i \(0.627126\pi\)
\(284\) 0 0
\(285\) −1.54232 0.795119i −0.0913590 0.0470988i
\(286\) 0 0
\(287\) −12.2024 11.6349i −0.720282 0.686788i
\(288\) 0 0
\(289\) 2.09147 + 2.93706i 0.123028 + 0.172768i
\(290\) 0 0
\(291\) −12.9540 + 5.18600i −0.759378 + 0.304009i
\(292\) 0 0
\(293\) −7.67437 + 8.85670i −0.448342 + 0.517414i −0.934261 0.356590i \(-0.883939\pi\)
0.485919 + 0.874004i \(0.338485\pi\)
\(294\) 0 0
\(295\) −13.8044 + 30.2275i −0.803726 + 1.75991i
\(296\) 0 0
\(297\) 2.02787 3.51238i 0.117669 0.203809i
\(298\) 0 0
\(299\) −21.6461 + 4.17194i −1.25183 + 0.241270i
\(300\) 0 0
\(301\) −1.60160 + 6.60188i −0.0923146 + 0.380526i
\(302\) 0 0
\(303\) −8.70884 3.48650i −0.500310 0.200294i
\(304\) 0 0
\(305\) −11.4104 19.7634i −0.653357 1.13165i
\(306\) 0 0
\(307\) −6.21136 + 17.9465i −0.354501 + 1.02426i 0.616946 + 0.787006i \(0.288370\pi\)
−0.971447 + 0.237258i \(0.923751\pi\)
\(308\) 0 0
\(309\) 0.451494 + 9.47803i 0.0256846 + 0.539186i
\(310\) 0 0
\(311\) 0.870718 0.559577i 0.0493739 0.0317307i −0.515721 0.856757i \(-0.672476\pi\)
0.565095 + 0.825026i \(0.308840\pi\)
\(312\) 0 0
\(313\) 3.81862 + 26.5591i 0.215841 + 1.50121i 0.753165 + 0.657832i \(0.228526\pi\)
−0.537324 + 0.843376i \(0.680565\pi\)
\(314\) 0 0
\(315\) −4.21722 3.31646i −0.237613 0.186861i
\(316\) 0 0
\(317\) −1.50358 + 31.5640i −0.0844494 + 1.77281i 0.418234 + 0.908340i \(0.362649\pi\)
−0.502683 + 0.864471i \(0.667654\pi\)
\(318\) 0 0
\(319\) 4.39657 6.17412i 0.246161 0.345684i
\(320\) 0 0
\(321\) 1.17095 + 0.752526i 0.0653562 + 0.0420019i
\(322\) 0 0
\(323\) −0.895552 2.58753i −0.0498298 0.143974i
\(324\) 0 0
\(325\) −11.9425 + 9.39169i −0.662451 + 0.520957i
\(326\) 0 0
\(327\) −4.92924 5.68865i −0.272588 0.314583i
\(328\) 0 0
\(329\) −14.8075 + 1.41394i −0.816362 + 0.0779531i
\(330\) 0 0
\(331\) −2.09251 + 1.07876i −0.115015 + 0.0592941i −0.514774 0.857326i \(-0.672124\pi\)
0.399759 + 0.916620i \(0.369094\pi\)
\(332\) 0 0
\(333\) 1.10761 + 4.56565i 0.0606969 + 0.250196i
\(334\) 0 0
\(335\) 22.9611 + 5.21859i 1.25450 + 0.285122i
\(336\) 0 0
\(337\) −4.41376 18.1938i −0.240433 0.991077i −0.956194 0.292732i \(-0.905435\pi\)
0.715762 0.698345i \(-0.246080\pi\)
\(338\) 0 0
\(339\) −5.06350 + 2.61042i −0.275012 + 0.141778i
\(340\) 0 0
\(341\) 36.9121 3.52468i 1.99890 0.190872i
\(342\) 0 0
\(343\) −12.8504 14.8302i −0.693858 0.800755i
\(344\) 0 0
\(345\) 10.7462 8.45091i 0.578556 0.454982i
\(346\) 0 0
\(347\) 7.46155 + 21.5587i 0.400557 + 1.15733i 0.947387 + 0.320090i \(0.103713\pi\)
−0.546830 + 0.837244i \(0.684166\pi\)
\(348\) 0 0
\(349\) 16.3819 + 10.5280i 0.876903 + 0.563551i 0.899857 0.436185i \(-0.143671\pi\)
−0.0229542 + 0.999737i \(0.507307\pi\)
\(350\) 0 0
\(351\) −2.69066 + 3.77851i −0.143617 + 0.201682i
\(352\) 0 0
\(353\) −0.155515 + 3.26467i −0.00827725 + 0.173761i 0.990943 + 0.134282i \(0.0428728\pi\)
−0.999220 + 0.0394788i \(0.987430\pi\)
\(354\) 0 0
\(355\) −4.26517 3.35417i −0.226372 0.178021i
\(356\) 0 0
\(357\) −1.20483 8.37976i −0.0637662 0.443504i
\(358\) 0 0
\(359\) −12.8182 + 8.23776i −0.676519 + 0.434773i −0.833270 0.552866i \(-0.813534\pi\)
0.156751 + 0.987638i \(0.449898\pi\)
\(360\) 0 0
\(361\) −0.886744 18.6150i −0.0466707 0.979739i
\(362\) 0 0
\(363\) 1.78221 5.14935i 0.0935416 0.270271i
\(364\) 0 0
\(365\) 1.90586 + 3.30105i 0.0997575 + 0.172785i
\(366\) 0 0
\(367\) 0.484492 + 0.193962i 0.0252903 + 0.0101247i 0.384273 0.923219i \(-0.374452\pi\)
−0.358983 + 0.933344i \(0.616876\pi\)
\(368\) 0 0
\(369\) 2.13133 8.78547i 0.110953 0.457353i
\(370\) 0 0
\(371\) 19.0284 3.66743i 0.987906 0.190403i
\(372\) 0 0
\(373\) −6.71847 + 11.6367i −0.347869 + 0.602527i −0.985871 0.167508i \(-0.946428\pi\)
0.638002 + 0.770035i \(0.279761\pi\)
\(374\) 0 0
\(375\) −2.06102 + 4.51300i −0.106430 + 0.233050i
\(376\) 0 0
\(377\) −5.67690 + 6.55149i −0.292375 + 0.337419i
\(378\) 0 0
\(379\) 26.1231 10.4581i 1.34186 0.537198i 0.414048 0.910255i \(-0.364115\pi\)
0.927808 + 0.373057i \(0.121690\pi\)
\(380\) 0 0
\(381\) −7.31526 10.2728i −0.374772 0.526294i
\(382\) 0 0
\(383\) 14.2059 + 13.5453i 0.725889 + 0.692134i 0.959976 0.280082i \(-0.0903617\pi\)
−0.234087 + 0.972216i \(0.575210\pi\)
\(384\) 0 0
\(385\) −19.3404 9.97068i −0.985679 0.508153i
\(386\) 0 0
\(387\) −3.49499 + 1.02622i −0.177660 + 0.0521657i
\(388\) 0 0
\(389\) −28.8371 5.55789i −1.46210 0.281796i −0.604701 0.796453i \(-0.706707\pi\)
−0.857396 + 0.514657i \(0.827919\pi\)
\(390\) 0 0
\(391\) 21.4750 + 2.05061i 1.08604 + 0.103704i
\(392\) 0 0
\(393\) 11.2346 + 3.29876i 0.566708 + 0.166401i
\(394\) 0 0
\(395\) −19.3650 + 18.4645i −0.974360 + 0.929051i
\(396\) 0 0
\(397\) −9.97163 21.8348i −0.500462 1.09586i −0.976319 0.216336i \(-0.930589\pi\)
0.475857 0.879523i \(-0.342138\pi\)
\(398\) 0 0
\(399\) −0.160100 + 1.11352i −0.00801503 + 0.0557458i
\(400\) 0 0
\(401\) −20.3950 −1.01848 −0.509239 0.860625i \(-0.670073\pi\)
−0.509239 + 0.860625i \(0.670073\pi\)
\(402\) 0 0
\(403\) −42.4091 −2.11255
\(404\) 0 0
\(405\) 0.409395 2.84741i 0.0203430 0.141489i
\(406\) 0 0
\(407\) 7.91540 + 17.3323i 0.392352 + 0.859131i
\(408\) 0 0
\(409\) −17.2059 + 16.4058i −0.850778 + 0.811215i −0.983682 0.179914i \(-0.942418\pi\)
0.132904 + 0.991129i \(0.457570\pi\)
\(410\) 0 0
\(411\) −16.2553 4.77299i −0.801815 0.235434i
\(412\) 0 0
\(413\) 21.4464 + 2.04789i 1.05531 + 0.100770i
\(414\) 0 0
\(415\) −12.8890 2.48415i −0.632695 0.121942i
\(416\) 0 0
\(417\) 10.3956 3.05242i 0.509073 0.149477i
\(418\) 0 0
\(419\) −6.15672 3.17401i −0.300776 0.155061i 0.301232 0.953551i \(-0.402602\pi\)
−0.602008 + 0.798490i \(0.705632\pi\)
\(420\) 0 0
\(421\) −7.71084 7.35227i −0.375803 0.358328i 0.478514 0.878080i \(-0.341176\pi\)
−0.854317 + 0.519752i \(0.826024\pi\)
\(422\) 0 0
\(423\) −4.62637 6.49683i −0.224942 0.315887i
\(424\) 0 0
\(425\) 13.8028 5.52582i 0.669535 0.268041i
\(426\) 0 0
\(427\) −9.68876 + 11.1814i −0.468872 + 0.541107i
\(428\) 0 0
\(429\) −7.81522 + 17.1129i −0.377322 + 0.826221i
\(430\) 0 0
\(431\) −6.62300 + 11.4714i −0.319018 + 0.552556i −0.980284 0.197596i \(-0.936687\pi\)
0.661265 + 0.750152i \(0.270020\pi\)
\(432\) 0 0
\(433\) −29.5366 + 5.69271i −1.41944 + 0.273574i −0.840507 0.541801i \(-0.817742\pi\)
−0.578932 + 0.815376i \(0.696530\pi\)
\(434\) 0 0
\(435\) 1.26746 5.22454i 0.0607700 0.250497i
\(436\) 0 0
\(437\) −2.66128 1.06542i −0.127306 0.0509657i
\(438\) 0 0
\(439\) −10.0159 17.3480i −0.478031 0.827975i 0.521651 0.853159i \(-0.325316\pi\)
−0.999683 + 0.0251839i \(0.991983\pi\)
\(440\) 0 0
\(441\) 1.15184 3.32804i 0.0548497 0.158478i
\(442\) 0 0
\(443\) 1.80741 + 37.9423i 0.0858729 + 1.80269i 0.473413 + 0.880841i \(0.343022\pi\)
−0.387540 + 0.921853i \(0.626675\pi\)
\(444\) 0 0
\(445\) −25.9583 + 16.6824i −1.23054 + 0.790820i
\(446\) 0 0
\(447\) −2.70942 18.8444i −0.128151 0.891311i
\(448\) 0 0
\(449\) −9.58226 7.53558i −0.452215 0.355626i 0.365926 0.930644i \(-0.380752\pi\)
−0.818141 + 0.575018i \(0.804995\pi\)
\(450\) 0 0
\(451\) 1.74460 36.6236i 0.0821499 1.72454i
\(452\) 0 0
\(453\) −13.7223 + 19.2703i −0.644731 + 0.905399i
\(454\) 0 0
\(455\) 20.9358 + 13.4546i 0.981487 + 0.630763i
\(456\) 0 0
\(457\) 7.58828 + 21.9249i 0.354965 + 1.02560i 0.971246 + 0.238077i \(0.0765172\pi\)
−0.616281 + 0.787526i \(0.711362\pi\)
\(458\) 0 0
\(459\) 3.56816 2.80604i 0.166548 0.130975i
\(460\) 0 0
\(461\) −19.5037 22.5084i −0.908377 1.04832i −0.998626 0.0524034i \(-0.983312\pi\)
0.0902492 0.995919i \(-0.471234\pi\)
\(462\) 0 0
\(463\) 10.3390 0.987253i 0.480493 0.0458815i 0.148000 0.988987i \(-0.452716\pi\)
0.332493 + 0.943106i \(0.392110\pi\)
\(464\) 0 0
\(465\) 23.3767 12.0515i 1.08407 0.558877i
\(466\) 0 0
\(467\) −3.50959 14.4667i −0.162405 0.669441i −0.993551 0.113387i \(-0.963830\pi\)
0.831146 0.556054i \(-0.187685\pi\)
\(468\) 0 0
\(469\) −1.67155 15.1740i −0.0771850 0.700670i
\(470\) 0 0
\(471\) −3.85283 15.8816i −0.177529 0.731785i
\(472\) 0 0
\(473\) −13.1309 + 6.76946i −0.603761 + 0.311260i
\(474\) 0 0
\(475\) −1.96672 + 0.187799i −0.0902395 + 0.00861682i
\(476\) 0 0
\(477\) 6.80440 + 7.85269i 0.311552 + 0.359550i
\(478\) 0 0
\(479\) −7.80563 + 6.13841i −0.356648 + 0.280471i −0.780366 0.625323i \(-0.784967\pi\)
0.423718 + 0.905794i \(0.360725\pi\)
\(480\) 0 0
\(481\) −7.12766 20.5940i −0.324993 0.939007i
\(482\) 0 0
\(483\) −7.45623 4.79183i −0.339270 0.218036i
\(484\) 0 0
\(485\) −23.2834 + 32.6970i −1.05725 + 1.48470i
\(486\) 0 0
\(487\) 1.69173 35.5139i 0.0766598 1.60929i −0.553519 0.832836i \(-0.686715\pi\)
0.630179 0.776450i \(-0.282981\pi\)
\(488\) 0 0
\(489\) 15.2567 + 11.9980i 0.689931 + 0.542568i
\(490\) 0 0
\(491\) −3.11346 21.6546i −0.140508 0.977258i −0.931061 0.364864i \(-0.881116\pi\)
0.790552 0.612394i \(-0.209794\pi\)
\(492\) 0 0
\(493\) 7.13663 4.58643i 0.321418 0.206563i
\(494\) 0 0
\(495\) −0.555143 11.6539i −0.0249518 0.523803i
\(496\) 0 0
\(497\) −1.15057 + 3.32435i −0.0516100 + 0.149117i
\(498\) 0 0
\(499\) 5.71634 + 9.90100i 0.255899 + 0.443230i 0.965139 0.261737i \(-0.0842953\pi\)
−0.709241 + 0.704967i \(0.750962\pi\)
\(500\) 0 0
\(501\) −3.66801 1.46845i −0.163875 0.0656056i
\(502\) 0 0
\(503\) −4.12016 + 16.9835i −0.183709 + 0.757257i 0.803164 + 0.595758i \(0.203148\pi\)
−0.986873 + 0.161500i \(0.948367\pi\)
\(504\) 0 0
\(505\) −26.4980 + 5.10707i −1.17915 + 0.227262i
\(506\) 0 0
\(507\) 4.25840 7.37576i 0.189122 0.327569i
\(508\) 0 0
\(509\) 6.25360 13.6935i 0.277186 0.606953i −0.718922 0.695091i \(-0.755364\pi\)
0.996108 + 0.0881376i \(0.0280915\pi\)
\(510\) 0 0
\(511\) 1.61830 1.86762i 0.0715895 0.0826187i
\(512\) 0 0
\(513\) −0.559989 + 0.224186i −0.0247241 + 0.00989805i
\(514\) 0 0
\(515\) 15.8334 + 22.2349i 0.697702 + 0.979785i
\(516\) 0 0
\(517\) −23.4110 22.3223i −1.02961 0.981734i
\(518\) 0 0
\(519\) 4.56405 + 2.35293i 0.200340 + 0.103282i
\(520\) 0 0
\(521\) 41.2715 12.1184i 1.80814 0.530917i 0.809701 0.586843i \(-0.199629\pi\)
0.998435 + 0.0559264i \(0.0178112\pi\)
\(522\) 0 0
\(523\) 5.24917 + 1.01170i 0.229530 + 0.0442383i 0.302719 0.953080i \(-0.402106\pi\)
−0.0731890 + 0.997318i \(0.523318\pi\)
\(524\) 0 0
\(525\) −6.08087 0.580652i −0.265391 0.0253418i
\(526\) 0 0
\(527\) 39.8203 + 11.6923i 1.73460 + 0.509325i
\(528\) 0 0
\(529\) −0.300302 + 0.286337i −0.0130566 + 0.0124495i
\(530\) 0 0
\(531\) 4.79873 + 10.5078i 0.208247 + 0.455998i
\(532\) 0 0
\(533\) −5.96790 + 41.5077i −0.258499 + 1.79790i
\(534\) 0 0
\(535\) 4.00410 0.173112
\(536\) 0 0
\(537\) 10.0036 0.431688
\(538\) 0 0
\(539\) 2.03271 14.1378i 0.0875552 0.608960i
\(540\) 0 0
\(541\) −8.40727 18.4094i −0.361457 0.791480i −0.999765 0.0216989i \(-0.993092\pi\)
0.638308 0.769781i \(-0.279635\pi\)
\(542\) 0 0
\(543\) −12.5576 + 11.9736i −0.538897 + 0.513838i
\(544\) 0 0
\(545\) −20.7762 6.10044i −0.889954 0.261314i
\(546\) 0 0
\(547\) 12.9980 + 1.24116i 0.555753 + 0.0530680i 0.369154 0.929368i \(-0.379647\pi\)
0.186599 + 0.982436i \(0.440254\pi\)
\(548\) 0 0
\(549\) −7.78964 1.50133i −0.332454 0.0640752i
\(550\) 0 0
\(551\) −1.08162 + 0.317592i −0.0460786 + 0.0135299i
\(552\) 0 0
\(553\) 15.4188 + 7.94893i 0.655673 + 0.338023i
\(554\) 0 0
\(555\) 9.78120 + 9.32635i 0.415189 + 0.395882i
\(556\) 0 0
\(557\) 20.4899 + 28.7740i 0.868184 + 1.21919i 0.974393 + 0.224850i \(0.0721891\pi\)
−0.106210 + 0.994344i \(0.533871\pi\)
\(558\) 0 0
\(559\) 15.6860 6.27973i 0.663448 0.265604i
\(560\) 0 0
\(561\) 12.0562 13.9137i 0.509015 0.587435i
\(562\) 0 0
\(563\) 1.82599 3.99836i 0.0769564 0.168511i −0.867243 0.497885i \(-0.834110\pi\)
0.944200 + 0.329374i \(0.106838\pi\)
\(564\) 0 0
\(565\) −8.19393 + 14.1923i −0.344721 + 0.597075i
\(566\) 0 0
\(567\) −1.83131 + 0.352956i −0.0769078 + 0.0148228i
\(568\) 0 0
\(569\) −0.331472 + 1.36635i −0.0138960 + 0.0572802i −0.978337 0.207016i \(-0.933625\pi\)
0.964441 + 0.264297i \(0.0851398\pi\)
\(570\) 0 0
\(571\) 22.9306 + 9.18004i 0.959617 + 0.384173i 0.797984 0.602678i \(-0.205900\pi\)
0.161633 + 0.986851i \(0.448324\pi\)
\(572\) 0 0
\(573\) −9.27277 16.0609i −0.387375 0.670954i
\(574\) 0 0
\(575\) 5.09100 14.7095i 0.212310 0.613428i
\(576\) 0 0
\(577\) 0.878402 + 18.4399i 0.0365684 + 0.767664i 0.940460 + 0.339904i \(0.110394\pi\)
−0.903892 + 0.427761i \(0.859303\pi\)
\(578\) 0 0
\(579\) 7.64150 4.91089i 0.317570 0.204090i
\(580\) 0 0
\(581\) 1.21109 + 8.42335i 0.0502447 + 0.349459i
\(582\) 0 0
\(583\) 33.1255 + 26.0502i 1.37192 + 1.07889i
\(584\) 0 0
\(585\) −0.634926 + 13.3287i −0.0262510 + 0.551076i
\(586\) 0 0
\(587\) 4.96805 6.97664i 0.205053 0.287957i −0.699224 0.714903i \(-0.746471\pi\)
0.904277 + 0.426946i \(0.140410\pi\)
\(588\) 0 0
\(589\) −4.63934 2.98152i −0.191161 0.122852i
\(590\) 0 0
\(591\) 1.12069 + 3.23801i 0.0460989 + 0.133194i
\(592\) 0 0
\(593\) −29.1476 + 22.9219i −1.19695 + 0.941291i −0.999240 0.0389697i \(-0.987592\pi\)
−0.197709 + 0.980261i \(0.563350\pi\)
\(594\) 0 0
\(595\) −15.9484 18.4054i −0.653819 0.754548i
\(596\) 0 0
\(597\) 6.62896 0.632989i 0.271305 0.0259065i
\(598\) 0 0
\(599\) 28.7615 14.8276i 1.17516 0.605839i 0.243762 0.969835i \(-0.421618\pi\)
0.931400 + 0.363996i \(0.118588\pi\)
\(600\) 0 0
\(601\) −2.69009 11.0887i −0.109731 0.452317i 0.890264 0.455445i \(-0.150520\pi\)
−0.999995 + 0.00312724i \(0.999005\pi\)
\(602\) 0 0
\(603\) 6.59797 4.84426i 0.268690 0.197273i
\(604\) 0 0
\(605\) −3.69556 15.2333i −0.150246 0.619323i
\(606\) 0 0
\(607\) 0.675098 0.348037i 0.0274014 0.0141264i −0.444471 0.895793i \(-0.646608\pi\)
0.471873 + 0.881667i \(0.343578\pi\)
\(608\) 0 0
\(609\) −3.46964 + 0.331310i −0.140597 + 0.0134254i
\(610\) 0 0
\(611\) 24.2275 + 27.9600i 0.980138 + 1.13114i
\(612\) 0 0
\(613\) 8.26184 6.49719i 0.333693 0.262419i −0.437227 0.899351i \(-0.644039\pi\)
0.770920 + 0.636932i \(0.219797\pi\)
\(614\) 0 0
\(615\) −8.50577 24.5758i −0.342986 0.990992i
\(616\) 0 0
\(617\) −17.2571 11.0904i −0.694743 0.446485i 0.145026 0.989428i \(-0.453673\pi\)
−0.839769 + 0.542943i \(0.817310\pi\)
\(618\) 0 0
\(619\) −11.5943 + 16.2819i −0.466012 + 0.654423i −0.978973 0.203989i \(-0.934609\pi\)
0.512961 + 0.858412i \(0.328549\pi\)
\(620\) 0 0
\(621\) 0.226127 4.74699i 0.00907417 0.190490i
\(622\) 0 0
\(623\) 15.7250 + 12.3663i 0.630008 + 0.495444i
\(624\) 0 0
\(625\) 4.36179 + 30.3369i 0.174472 + 1.21348i
\(626\) 0 0
\(627\) −2.05805 + 1.32263i −0.0821908 + 0.0528208i
\(628\) 0 0
\(629\) 1.01474 + 21.3020i 0.0404604 + 0.849368i
\(630\) 0 0
\(631\) −0.311254 + 0.899309i −0.0123908 + 0.0358009i −0.951027 0.309109i \(-0.899969\pi\)
0.938636 + 0.344910i \(0.112090\pi\)
\(632\) 0 0
\(633\) −3.72740 6.45604i −0.148151 0.256605i
\(634\) 0 0
\(635\) −33.6800 13.4834i −1.33655 0.535074i
\(636\) 0 0
\(637\) −3.85135 + 15.8755i −0.152596 + 0.629009i
\(638\) 0 0
\(639\) −1.85213 + 0.356969i −0.0732693 + 0.0141215i
\(640\) 0 0
\(641\) −18.8450 + 32.6405i −0.744333 + 1.28922i 0.206173 + 0.978516i \(0.433899\pi\)
−0.950506 + 0.310707i \(0.899434\pi\)
\(642\) 0 0
\(643\) −2.86236 + 6.26770i −0.112881 + 0.247174i −0.957638 0.287976i \(-0.907018\pi\)
0.844757 + 0.535150i \(0.179745\pi\)
\(644\) 0 0
\(645\) −6.86191 + 7.91907i −0.270188 + 0.311813i
\(646\) 0 0
\(647\) −8.81273 + 3.52808i −0.346464 + 0.138703i −0.538367 0.842711i \(-0.680958\pi\)
0.191903 + 0.981414i \(0.438534\pi\)
\(648\) 0 0
\(649\) 27.1760 + 38.1633i 1.06675 + 1.49804i
\(650\) 0 0
\(651\) −12.3404 11.7666i −0.483660 0.461169i
\(652\) 0 0
\(653\) 25.2957 + 13.0408i 0.989896 + 0.510327i 0.875557 0.483115i \(-0.160495\pi\)
0.114339 + 0.993442i \(0.463525\pi\)
\(654\) 0 0
\(655\) 32.3183 9.48951i 1.26278 0.370786i
\(656\) 0 0
\(657\) 1.30110 + 0.250766i 0.0507606 + 0.00978330i
\(658\) 0 0
\(659\) −31.6100 3.01839i −1.23135 0.117580i −0.540981 0.841035i \(-0.681947\pi\)
−0.690371 + 0.723455i \(0.742553\pi\)
\(660\) 0 0
\(661\) 27.5854 + 8.09981i 1.07295 + 0.315046i 0.770054 0.637978i \(-0.220229\pi\)
0.302894 + 0.953024i \(0.402047\pi\)
\(662\) 0 0
\(663\) −15.2392 + 14.5305i −0.591840 + 0.564318i
\(664\) 0 0
\(665\) 1.34436 + 2.94374i 0.0521321 + 0.114153i
\(666\) 0 0
\(667\) 1.26396 8.79105i 0.0489408 0.340391i
\(668\) 0 0
\(669\) −14.7342 −0.569657
\(670\) 0 0
\(671\) −32.1742 −1.24207
\(672\) 0 0
\(673\) 5.98465 41.6242i 0.230691 1.60449i −0.464436 0.885607i \(-0.653743\pi\)
0.695127 0.718886i \(-0.255348\pi\)
\(674\) 0 0
\(675\) −1.36062 2.97934i −0.0523703 0.114675i
\(676\) 0 0
\(677\) 6.85195 6.53332i 0.263342 0.251096i −0.546891 0.837204i \(-0.684189\pi\)
0.810233 + 0.586108i \(0.199340\pi\)
\(678\) 0 0
\(679\) 24.9694 + 7.33167i 0.958237 + 0.281364i
\(680\) 0 0
\(681\) 5.20648 + 0.497159i 0.199513 + 0.0190512i
\(682\) 0 0
\(683\) 47.1977 + 9.09661i 1.80597 + 0.348072i 0.977332 0.211714i \(-0.0679044\pi\)
0.828637 + 0.559786i \(0.189117\pi\)
\(684\) 0 0
\(685\) −46.7614 + 13.7304i −1.78666 + 0.524611i
\(686\) 0 0
\(687\) −4.64044 2.39231i −0.177044 0.0912725i
\(688\) 0 0
\(689\) −34.8826 33.2605i −1.32892 1.26712i
\(690\) 0 0
\(691\) −22.3417 31.3745i −0.849919 1.19354i −0.979394 0.201961i \(-0.935269\pi\)
0.129475 0.991583i \(-0.458671\pi\)
\(692\) 0 0
\(693\) −7.02218 + 2.81126i −0.266751 + 0.106791i
\(694\) 0 0
\(695\) 20.4102 23.5547i 0.774205 0.893480i
\(696\) 0 0
\(697\) 17.0474 37.3286i 0.645716 1.41392i
\(698\) 0 0
\(699\) 10.1616 17.6004i 0.384346 0.665707i
\(700\) 0 0
\(701\) 49.7297 9.58461i 1.87826 0.362006i 0.883869 0.467734i \(-0.154929\pi\)
0.994395 + 0.105728i \(0.0337173\pi\)
\(702\) 0 0
\(703\) 0.668110 2.75399i 0.0251983 0.103869i
\(704\) 0 0
\(705\) −21.3002 8.52730i −0.802210 0.321157i
\(706\) 0 0
\(707\) 8.74767 + 15.1514i 0.328990 + 0.569827i
\(708\) 0 0
\(709\) 1.10334 3.18790i 0.0414369 0.119724i −0.922384 0.386273i \(-0.873762\pi\)
0.963821 + 0.266549i \(0.0858834\pi\)
\(710\) 0 0
\(711\) 0.442577 + 9.29083i 0.0165979 + 0.348433i
\(712\) 0 0
\(713\) 36.5517 23.4903i 1.36887 0.879720i
\(714\) 0 0
\(715\) 7.70197 + 53.5684i 0.288037 + 2.00334i
\(716\) 0 0
\(717\) −6.19260 4.86991i −0.231267 0.181870i
\(718\) 0 0
\(719\) 0.875249 18.3737i 0.0326413 0.685225i −0.921951 0.387308i \(-0.873405\pi\)
0.954592 0.297917i \(-0.0962919\pi\)
\(720\) 0 0
\(721\) 10.2651 14.4153i 0.382292 0.536854i
\(722\) 0 0
\(723\) 15.7579 + 10.1270i 0.586041 + 0.376626i
\(724\) 0 0
\(725\) −2.00201 5.78443i −0.0743528 0.214828i
\(726\) 0 0
\(727\) 18.1795 14.2965i 0.674241 0.530229i −0.221301 0.975206i \(-0.571030\pi\)
0.895542 + 0.444976i \(0.146788\pi\)
\(728\) 0 0
\(729\) −0.654861 0.755750i −0.0242541 0.0279907i
\(730\) 0 0
\(731\) −16.4598 + 1.57172i −0.608789 + 0.0581323i
\(732\) 0 0
\(733\) 30.4339 15.6898i 1.12410 0.579514i 0.207068 0.978326i \(-0.433608\pi\)
0.917033 + 0.398812i \(0.130577\pi\)
\(734\) 0 0
\(735\) −2.38845 9.84533i −0.0880994 0.363151i
\(736\) 0 0
\(737\) 22.5578 24.3563i 0.830929 0.897176i
\(738\) 0 0
\(739\) −5.96983 24.6080i −0.219604 0.905220i −0.969780 0.243981i \(-0.921546\pi\)
0.750176 0.661238i \(-0.229969\pi\)
\(740\) 0 0
\(741\) 2.48697 1.28212i 0.0913610 0.0470998i
\(742\) 0 0
\(743\) 1.88517 0.180012i 0.0691602 0.00660400i −0.0604186 0.998173i \(-0.519244\pi\)
0.129579 + 0.991569i \(0.458637\pi\)
\(744\) 0 0
\(745\) −35.8647 41.3901i −1.31398 1.51642i
\(746\) 0 0
\(747\) −3.58672 + 2.82063i −0.131231 + 0.103201i
\(748\) 0 0
\(749\) −0.849049 2.45316i −0.0310236 0.0896367i
\(750\) 0 0
\(751\) 36.7557 + 23.6214i 1.34123 + 0.861959i 0.997036 0.0769387i \(-0.0245146\pi\)
0.344198 + 0.938897i \(0.388151\pi\)
\(752\) 0 0
\(753\) −7.49922 + 10.5312i −0.273287 + 0.383778i
\(754\) 0 0
\(755\) −3.23811 + 67.9763i −0.117847 + 2.47391i
\(756\) 0 0
\(757\) 26.4453 + 20.7968i 0.961171 + 0.755873i 0.969753 0.244090i \(-0.0784892\pi\)
−0.00858144 + 0.999963i \(0.502732\pi\)
\(758\) 0 0
\(759\) −2.74303 19.0782i −0.0995658 0.692495i
\(760\) 0 0
\(761\) −5.89441 + 3.78811i −0.213672 + 0.137319i −0.643099 0.765783i \(-0.722352\pi\)
0.429427 + 0.903101i \(0.358715\pi\)
\(762\) 0 0
\(763\) 0.667967 + 14.0224i 0.0241820 + 0.507643i
\(764\) 0 0
\(765\) 4.27094 12.3401i 0.154416 0.446156i
\(766\) 0 0
\(767\) −26.7919 46.4049i −0.967398 1.67558i
\(768\) 0 0
\(769\) 47.0324 + 18.8289i 1.69603 + 0.678989i 0.999266 0.0383102i \(-0.0121975\pi\)
0.696766 + 0.717299i \(0.254622\pi\)
\(770\) 0 0
\(771\) 1.50539 6.20530i 0.0542152 0.223478i
\(772\) 0 0
\(773\) −14.9147 + 2.87457i −0.536445 + 0.103391i −0.450276 0.892889i \(-0.648674\pi\)
−0.0861686 + 0.996281i \(0.527462\pi\)
\(774\) 0 0
\(775\) 14.9725 25.9331i 0.537828 0.931546i
\(776\) 0 0
\(777\) 3.63986 7.97018i 0.130579 0.285928i
\(778\) 0