Properties

Label 804.2.q.b.241.2
Level 804
Weight 2
Character 804.241
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 241.2
Character \(\chi\) = 804.241
Dual form 804.2.q.b.397.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(-1.77661 - 0.521660i) q^{5} +(0.707286 + 0.816251i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(-1.77661 - 0.521660i) q^{5} +(0.707286 + 0.816251i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-6.30285 - 1.85068i) q^{11} +(4.21329 + 2.70772i) q^{13} +(1.21255 - 1.39936i) q^{15} +(-0.520776 - 3.62208i) q^{17} +(4.73554 - 5.46510i) q^{19} +(-1.03631 + 0.304287i) q^{21} +(2.13944 - 4.68472i) q^{23} +(-1.32205 - 0.849633i) q^{25} +(0.959493 - 0.281733i) q^{27} +3.56041 q^{29} +(-2.55994 + 1.64517i) q^{31} +(4.30174 - 4.96447i) q^{33} +(-0.830765 - 1.81912i) q^{35} -5.91644 q^{37} +(-4.21329 + 2.70772i) q^{39} +(0.936661 + 6.51462i) q^{41} +(-1.17480 - 8.17090i) q^{43} +(0.769188 + 1.68429i) q^{45} +(5.39652 - 11.8167i) q^{47} +(0.830191 - 5.77410i) q^{49} +(3.51110 + 1.03095i) q^{51} +(-0.207822 + 1.44544i) q^{53} +(10.2323 + 6.57588i) q^{55} +(3.00402 + 6.57788i) q^{57} +(-1.12909 + 0.725625i) q^{59} +(0.203291 - 0.0596917i) q^{61} +(0.153708 - 1.06906i) q^{63} +(-6.07287 - 7.00847i) q^{65} +(-8.00742 - 1.69742i) q^{67} +(3.37262 + 3.89221i) q^{69} +(1.41822 - 9.86395i) q^{71} +(11.6575 - 3.42296i) q^{73} +(1.32205 - 0.849633i) q^{75} +(-2.94729 - 6.45367i) q^{77} +(0.266249 + 0.171108i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(4.67588 + 1.37296i) q^{83} +(-0.964276 + 6.70668i) q^{85} +(-1.47905 + 3.23866i) q^{87} +(-2.91449 - 6.38185i) q^{89} +(0.769823 + 5.35424i) q^{91} +(-0.433064 - 3.01203i) q^{93} +(-11.2641 + 7.23901i) q^{95} +0.508626 q^{97} +(2.72883 + 5.97531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(1\)

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
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) −1.77661 0.521660i −0.794524 0.233293i −0.140812 0.990036i \(-0.544971\pi\)
−0.653712 + 0.756743i \(0.726789\pi\)
\(6\) 0 0
\(7\) 0.707286 + 0.816251i 0.267329 + 0.308514i 0.873504 0.486817i \(-0.161842\pi\)
−0.606175 + 0.795331i \(0.707297\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) −6.30285 1.85068i −1.90038 0.558002i −0.989327 0.145712i \(-0.953453\pi\)
−0.911053 0.412289i \(-0.864729\pi\)
\(12\) 0 0
\(13\) 4.21329 + 2.70772i 1.16856 + 0.750986i 0.973248 0.229755i \(-0.0737926\pi\)
0.195309 + 0.980742i \(0.437429\pi\)
\(14\) 0 0
\(15\) 1.21255 1.39936i 0.313079 0.361312i
\(16\) 0 0
\(17\) −0.520776 3.62208i −0.126307 0.878483i −0.950178 0.311706i \(-0.899099\pi\)
0.823872 0.566776i \(-0.191810\pi\)
\(18\) 0 0
\(19\) 4.73554 5.46510i 1.08641 1.25378i 0.121106 0.992640i \(-0.461356\pi\)
0.965301 0.261141i \(-0.0840987\pi\)
\(20\) 0 0
\(21\) −1.03631 + 0.304287i −0.226140 + 0.0664008i
\(22\) 0 0
\(23\) 2.13944 4.68472i 0.446104 0.976832i −0.544333 0.838869i \(-0.683217\pi\)
0.990437 0.137963i \(-0.0440555\pi\)
\(24\) 0 0
\(25\) −1.32205 0.849633i −0.264411 0.169927i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) 3.56041 0.661151 0.330575 0.943780i \(-0.392757\pi\)
0.330575 + 0.943780i \(0.392757\pi\)
\(30\) 0 0
\(31\) −2.55994 + 1.64517i −0.459778 + 0.295481i −0.749952 0.661493i \(-0.769923\pi\)
0.290174 + 0.956974i \(0.406287\pi\)
\(32\) 0 0
\(33\) 4.30174 4.96447i 0.748836 0.864203i
\(34\) 0 0
\(35\) −0.830765 1.81912i −0.140425 0.307488i
\(36\) 0 0
\(37\) −5.91644 −0.972657 −0.486328 0.873776i \(-0.661664\pi\)
−0.486328 + 0.873776i \(0.661664\pi\)
\(38\) 0 0
\(39\) −4.21329 + 2.70772i −0.674667 + 0.433582i
\(40\) 0 0
\(41\) 0.936661 + 6.51462i 0.146282 + 1.01741i 0.922237 + 0.386625i \(0.126359\pi\)
−0.775955 + 0.630788i \(0.782732\pi\)
\(42\) 0 0
\(43\) −1.17480 8.17090i −0.179155 1.24605i −0.858724 0.512438i \(-0.828742\pi\)
0.679569 0.733612i \(-0.262167\pi\)
\(44\) 0 0
\(45\) 0.769188 + 1.68429i 0.114664 + 0.251079i
\(46\) 0 0
\(47\) 5.39652 11.8167i 0.787163 1.72365i 0.102563 0.994727i \(-0.467296\pi\)
0.684600 0.728919i \(-0.259977\pi\)
\(48\) 0 0
\(49\) 0.830191 5.77410i 0.118599 0.824872i
\(50\) 0 0
\(51\) 3.51110 + 1.03095i 0.491652 + 0.144362i
\(52\) 0 0
\(53\) −0.207822 + 1.44544i −0.0285466 + 0.198546i −0.999104 0.0423243i \(-0.986524\pi\)
0.970557 + 0.240870i \(0.0774328\pi\)
\(54\) 0 0
\(55\) 10.2323 + 6.57588i 1.37972 + 0.886692i
\(56\) 0 0
\(57\) 3.00402 + 6.57788i 0.397892 + 0.871262i
\(58\) 0 0
\(59\) −1.12909 + 0.725625i −0.146996 + 0.0944683i −0.612071 0.790803i \(-0.709663\pi\)
0.465076 + 0.885271i \(0.346027\pi\)
\(60\) 0 0
\(61\) 0.203291 0.0596917i 0.0260288 0.00764274i −0.268692 0.963226i \(-0.586591\pi\)
0.294721 + 0.955583i \(0.404773\pi\)
\(62\) 0 0
\(63\) 0.153708 1.06906i 0.0193654 0.134689i
\(64\) 0 0
\(65\) −6.07287 7.00847i −0.753247 0.869293i
\(66\) 0 0
\(67\) −8.00742 1.69742i −0.978262 0.207373i
\(68\) 0 0
\(69\) 3.37262 + 3.89221i 0.406015 + 0.468567i
\(70\) 0 0
\(71\) 1.41822 9.86395i 0.168312 1.17064i −0.714060 0.700084i \(-0.753146\pi\)
0.882372 0.470552i \(-0.155945\pi\)
\(72\) 0 0
\(73\) 11.6575 3.42296i 1.36441 0.400627i 0.484095 0.875016i \(-0.339149\pi\)
0.880316 + 0.474388i \(0.157331\pi\)
\(74\) 0 0
\(75\) 1.32205 0.849633i 0.152658 0.0981072i
\(76\) 0 0
\(77\) −2.94729 6.45367i −0.335875 0.735464i
\(78\) 0 0
\(79\) 0.266249 + 0.171108i 0.0299553 + 0.0192511i 0.555533 0.831495i \(-0.312514\pi\)
−0.525577 + 0.850746i \(0.676151\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) 4.67588 + 1.37296i 0.513244 + 0.150702i 0.528091 0.849188i \(-0.322908\pi\)
−0.0148469 + 0.999890i \(0.504726\pi\)
\(84\) 0 0
\(85\) −0.964276 + 6.70668i −0.104590 + 0.727442i
\(86\) 0 0
\(87\) −1.47905 + 3.23866i −0.158570 + 0.347221i
\(88\) 0 0
\(89\) −2.91449 6.38185i −0.308936 0.676475i 0.689941 0.723866i \(-0.257637\pi\)
−0.998876 + 0.0473910i \(0.984909\pi\)
\(90\) 0 0
\(91\) 0.769823 + 5.35424i 0.0806994 + 0.561277i
\(92\) 0 0
\(93\) −0.433064 3.01203i −0.0449067 0.312333i
\(94\) 0 0
\(95\) −11.2641 + 7.23901i −1.15567 + 0.742707i
\(96\) 0 0
\(97\) 0.508626 0.0516432 0.0258216 0.999667i \(-0.491780\pi\)
0.0258216 + 0.999667i \(0.491780\pi\)
\(98\) 0 0
\(99\) 2.72883 + 5.97531i 0.274258 + 0.600542i
\(100\) 0 0
\(101\) −10.0015 + 11.5424i −0.995189 + 1.14851i −0.00628108 + 0.999980i \(0.501999\pi\)
−0.988908 + 0.148529i \(0.952546\pi\)
\(102\) 0 0
\(103\) −9.45292 + 6.07503i −0.931424 + 0.598590i −0.915951 0.401290i \(-0.868562\pi\)
−0.0154733 + 0.999880i \(0.504925\pi\)
\(104\) 0 0
\(105\) 1.99984 0.195165
\(106\) 0 0
\(107\) −9.62937 + 2.82744i −0.930906 + 0.273339i −0.711816 0.702366i \(-0.752127\pi\)
−0.219090 + 0.975705i \(0.570309\pi\)
\(108\) 0 0
\(109\) 4.61414 + 2.96533i 0.441954 + 0.284027i 0.742633 0.669699i \(-0.233577\pi\)
−0.300679 + 0.953726i \(0.597213\pi\)
\(110\) 0 0
\(111\) 2.45778 5.38178i 0.233282 0.510816i
\(112\) 0 0
\(113\) 0.455474 0.133739i 0.0428474 0.0125811i −0.260239 0.965544i \(-0.583801\pi\)
0.303086 + 0.952963i \(0.401983\pi\)
\(114\) 0 0
\(115\) −6.24478 + 7.20686i −0.582329 + 0.672043i
\(116\) 0 0
\(117\) −0.712763 4.95737i −0.0658950 0.458309i
\(118\) 0 0
\(119\) 2.58819 2.98693i 0.237259 0.273811i
\(120\) 0 0
\(121\) 27.0471 + 17.3821i 2.45882 + 1.58019i
\(122\) 0 0
\(123\) −6.31501 1.85425i −0.569405 0.167192i
\(124\) 0 0
\(125\) 7.96830 + 9.19591i 0.712706 + 0.822507i
\(126\) 0 0
\(127\) −2.57508 2.97180i −0.228501 0.263704i 0.629908 0.776670i \(-0.283092\pi\)
−0.858409 + 0.512965i \(0.828547\pi\)
\(128\) 0 0
\(129\) 7.92054 + 2.32568i 0.697364 + 0.204765i
\(130\) 0 0
\(131\) −8.67599 + 18.9978i −0.758025 + 1.65984i −0.00664048 + 0.999978i \(0.502114\pi\)
−0.751384 + 0.659865i \(0.770614\pi\)
\(132\) 0 0
\(133\) 7.81028 0.677237
\(134\) 0 0
\(135\) −1.85161 −0.159361
\(136\) 0 0
\(137\) 3.28591 7.19515i 0.280735 0.614723i −0.715763 0.698343i \(-0.753921\pi\)
0.996498 + 0.0836201i \(0.0266482\pi\)
\(138\) 0 0
\(139\) −21.0011 6.16648i −1.78129 0.523034i −0.785850 0.618418i \(-0.787774\pi\)
−0.995441 + 0.0953838i \(0.969592\pi\)
\(140\) 0 0
\(141\) 8.50707 + 9.81769i 0.716425 + 0.826798i
\(142\) 0 0
\(143\) −21.5446 24.8638i −1.80165 2.07922i
\(144\) 0 0
\(145\) −6.32545 1.85732i −0.525300 0.154242i
\(146\) 0 0
\(147\) 4.90744 + 3.15382i 0.404759 + 0.260123i
\(148\) 0 0
\(149\) −7.46522 + 8.61532i −0.611575 + 0.705795i −0.974084 0.226185i \(-0.927375\pi\)
0.362510 + 0.931980i \(0.381920\pi\)
\(150\) 0 0
\(151\) −0.810852 5.63960i −0.0659862 0.458944i −0.995848 0.0910344i \(-0.970983\pi\)
0.929862 0.367910i \(-0.119926\pi\)
\(152\) 0 0
\(153\) −2.39635 + 2.76553i −0.193733 + 0.223580i
\(154\) 0 0
\(155\) 5.40623 1.58741i 0.434239 0.127504i
\(156\) 0 0
\(157\) 1.28348 2.81042i 0.102433 0.224296i −0.851476 0.524394i \(-0.824292\pi\)
0.953908 + 0.300098i \(0.0970193\pi\)
\(158\) 0 0
\(159\) −1.22848 0.789498i −0.0974250 0.0626113i
\(160\) 0 0
\(161\) 5.33711 1.56712i 0.420623 0.123506i
\(162\) 0 0
\(163\) −11.7855 −0.923110 −0.461555 0.887112i \(-0.652708\pi\)
−0.461555 + 0.887112i \(0.652708\pi\)
\(164\) 0 0
\(165\) −10.2323 + 6.57588i −0.796581 + 0.511932i
\(166\) 0 0
\(167\) 7.28198 8.40386i 0.563497 0.650310i −0.400477 0.916307i \(-0.631156\pi\)
0.963974 + 0.265997i \(0.0857010\pi\)
\(168\) 0 0
\(169\) 5.01971 + 10.9916i 0.386131 + 0.845510i
\(170\) 0 0
\(171\) −7.23137 −0.552996
\(172\) 0 0
\(173\) −1.33481 + 0.857833i −0.101484 + 0.0652199i −0.590398 0.807112i \(-0.701029\pi\)
0.488914 + 0.872332i \(0.337393\pi\)
\(174\) 0 0
\(175\) −0.241557 1.68006i −0.0182600 0.127001i
\(176\) 0 0
\(177\) −0.191009 1.32850i −0.0143571 0.0998559i
\(178\) 0 0
\(179\) −0.482924 1.05746i −0.0360954 0.0790380i 0.890725 0.454542i \(-0.150197\pi\)
−0.926821 + 0.375504i \(0.877470\pi\)
\(180\) 0 0
\(181\) 7.93138 17.3673i 0.589535 1.29090i −0.346188 0.938165i \(-0.612524\pi\)
0.935723 0.352736i \(-0.114749\pi\)
\(182\) 0 0
\(183\) −0.0301528 + 0.209717i −0.00222896 + 0.0155027i
\(184\) 0 0
\(185\) 10.5112 + 3.08637i 0.772799 + 0.226914i
\(186\) 0 0
\(187\) −3.42094 + 23.7932i −0.250164 + 1.73993i
\(188\) 0 0
\(189\) 0.908600 + 0.583922i 0.0660909 + 0.0424741i
\(190\) 0 0
\(191\) −4.85212 10.6247i −0.351087 0.768774i −0.999969 0.00788471i \(-0.997490\pi\)
0.648882 0.760889i \(-0.275237\pi\)
\(192\) 0 0
\(193\) −17.8992 + 11.5031i −1.28841 + 0.828012i −0.991901 0.127017i \(-0.959460\pi\)
−0.296512 + 0.955029i \(0.595823\pi\)
\(194\) 0 0
\(195\) 8.89789 2.61266i 0.637191 0.187096i
\(196\) 0 0
\(197\) 1.42272 9.89523i 0.101365 0.705006i −0.874244 0.485487i \(-0.838642\pi\)
0.975608 0.219519i \(-0.0704487\pi\)
\(198\) 0 0
\(199\) −7.24130 8.35690i −0.513322 0.592405i 0.438624 0.898671i \(-0.355466\pi\)
−0.951946 + 0.306265i \(0.900920\pi\)
\(200\) 0 0
\(201\) 4.87043 6.57867i 0.343534 0.464024i
\(202\) 0 0
\(203\) 2.51822 + 2.90619i 0.176745 + 0.203974i
\(204\) 0 0
\(205\) 1.73433 12.0626i 0.121131 0.842485i
\(206\) 0 0
\(207\) −4.94151 + 1.45096i −0.343459 + 0.100849i
\(208\) 0 0
\(209\) −39.9615 + 25.6817i −2.76420 + 1.77644i
\(210\) 0 0
\(211\) 9.17122 + 20.0822i 0.631373 + 1.38251i 0.906951 + 0.421235i \(0.138403\pi\)
−0.275578 + 0.961279i \(0.588869\pi\)
\(212\) 0 0
\(213\) 8.38342 + 5.38769i 0.574422 + 0.369159i
\(214\) 0 0
\(215\) −2.17527 + 15.1293i −0.148352 + 1.03181i
\(216\) 0 0
\(217\) −3.15348 0.925945i −0.214072 0.0628573i
\(218\) 0 0
\(219\) −1.72908 + 12.0260i −0.116840 + 0.812642i
\(220\) 0 0
\(221\) 7.61339 16.6710i 0.512132 1.12141i
\(222\) 0 0
\(223\) 9.62261 + 21.0706i 0.644377 + 1.41099i 0.896390 + 0.443266i \(0.146180\pi\)
−0.252013 + 0.967724i \(0.581092\pi\)
\(224\) 0 0
\(225\) 0.223652 + 1.55553i 0.0149101 + 0.103702i
\(226\) 0 0
\(227\) 3.51482 + 24.4461i 0.233287 + 1.62254i 0.683727 + 0.729738i \(0.260358\pi\)
−0.450440 + 0.892807i \(0.648733\pi\)
\(228\) 0 0
\(229\) 11.9149 7.65725i 0.787359 0.506005i −0.0841093 0.996457i \(-0.526804\pi\)
0.871468 + 0.490452i \(0.163168\pi\)
\(230\) 0 0
\(231\) 7.09481 0.466804
\(232\) 0 0
\(233\) 10.2538 + 22.4527i 0.671748 + 1.47092i 0.871156 + 0.491006i \(0.163371\pi\)
−0.199408 + 0.979917i \(0.563902\pi\)
\(234\) 0 0
\(235\) −15.7518 + 18.1786i −1.02753 + 1.18584i
\(236\) 0 0
\(237\) −0.266249 + 0.171108i −0.0172947 + 0.0111146i
\(238\) 0 0
\(239\) 22.2021 1.43614 0.718068 0.695973i \(-0.245027\pi\)
0.718068 + 0.695973i \(0.245027\pi\)
\(240\) 0 0
\(241\) 22.0047 6.46117i 1.41745 0.416200i 0.518810 0.854890i \(-0.326375\pi\)
0.898639 + 0.438689i \(0.144557\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) −4.48704 + 9.82525i −0.286667 + 0.627712i
\(246\) 0 0
\(247\) 34.7502 10.2036i 2.21110 0.649238i
\(248\) 0 0
\(249\) −3.19132 + 3.68298i −0.202242 + 0.233399i
\(250\) 0 0
\(251\) −3.72323 25.8956i −0.235008 1.63452i −0.675927 0.736969i \(-0.736256\pi\)
0.440919 0.897547i \(-0.354653\pi\)
\(252\) 0 0
\(253\) −22.1545 + 25.5677i −1.39284 + 1.60743i
\(254\) 0 0
\(255\) −5.70004 3.66319i −0.356950 0.229398i
\(256\) 0 0
\(257\) −7.77514 2.28299i −0.485000 0.142409i 0.0300863 0.999547i \(-0.490422\pi\)
−0.515086 + 0.857139i \(0.672240\pi\)
\(258\) 0 0
\(259\) −4.18461 4.82930i −0.260019 0.300078i
\(260\) 0 0
\(261\) −2.33157 2.69077i −0.144321 0.166555i
\(262\) 0 0
\(263\) 3.00315 + 0.881805i 0.185182 + 0.0543744i 0.373009 0.927828i \(-0.378326\pi\)
−0.187827 + 0.982202i \(0.560144\pi\)
\(264\) 0 0
\(265\) 1.12325 2.45956i 0.0690004 0.151090i
\(266\) 0 0
\(267\) 7.01586 0.429364
\(268\) 0 0
\(269\) −4.50112 −0.274438 −0.137219 0.990541i \(-0.543816\pi\)
−0.137219 + 0.990541i \(0.543816\pi\)
\(270\) 0 0
\(271\) 3.63644 7.96269i 0.220898 0.483699i −0.766443 0.642312i \(-0.777975\pi\)
0.987341 + 0.158614i \(0.0507024\pi\)
\(272\) 0 0
\(273\) −5.19018 1.52398i −0.314124 0.0922352i
\(274\) 0 0
\(275\) 6.76031 + 7.80181i 0.407662 + 0.470467i
\(276\) 0 0
\(277\) −15.8811 18.3277i −0.954200 1.10121i −0.994781 0.102029i \(-0.967466\pi\)
0.0405815 0.999176i \(-0.487079\pi\)
\(278\) 0 0
\(279\) 2.91974 + 0.857313i 0.174800 + 0.0513260i
\(280\) 0 0
\(281\) −3.01093 1.93501i −0.179617 0.115433i 0.447743 0.894163i \(-0.352228\pi\)
−0.627360 + 0.778729i \(0.715864\pi\)
\(282\) 0 0
\(283\) 1.92622 2.22298i 0.114502 0.132142i −0.695605 0.718425i \(-0.744864\pi\)
0.810107 + 0.586282i \(0.199409\pi\)
\(284\) 0 0
\(285\) −1.90555 13.2534i −0.112875 0.785064i
\(286\) 0 0
\(287\) −4.65508 + 5.37225i −0.274781 + 0.317114i
\(288\) 0 0
\(289\) 3.46315 1.01687i 0.203714 0.0598160i
\(290\) 0 0
\(291\) −0.211291 + 0.462663i −0.0123861 + 0.0271218i
\(292\) 0 0
\(293\) −12.4449 7.99786i −0.727040 0.467240i 0.124040 0.992277i \(-0.460415\pi\)
−0.851079 + 0.525037i \(0.824051\pi\)
\(294\) 0 0
\(295\) 2.38449 0.700149i 0.138830 0.0407643i
\(296\) 0 0
\(297\) −6.56894 −0.381168
\(298\) 0 0
\(299\) 21.6990 13.9451i 1.25489 0.806466i
\(300\) 0 0
\(301\) 5.83859 6.73809i 0.336531 0.388377i
\(302\) 0 0
\(303\) −6.34453 13.8926i −0.364484 0.798108i
\(304\) 0 0
\(305\) −0.392308 −0.0224635
\(306\) 0 0
\(307\) 27.6458 17.7669i 1.57783 1.01401i 0.601197 0.799101i \(-0.294691\pi\)
0.976634 0.214909i \(-0.0689455\pi\)
\(308\) 0 0
\(309\) −1.59915 11.1223i −0.0909725 0.632728i
\(310\) 0 0
\(311\) −3.71480 25.8370i −0.210647 1.46508i −0.771005 0.636829i \(-0.780246\pi\)
0.560358 0.828251i \(-0.310664\pi\)
\(312\) 0 0
\(313\) 6.00882 + 13.1575i 0.339638 + 0.743704i 0.999974 0.00726673i \(-0.00231309\pi\)
−0.660335 + 0.750971i \(0.729586\pi\)
\(314\) 0 0
\(315\) −0.830765 + 1.81912i −0.0468083 + 0.102496i
\(316\) 0 0
\(317\) −0.816861 + 5.68139i −0.0458795 + 0.319099i 0.953938 + 0.300003i \(0.0969878\pi\)
−0.999818 + 0.0190956i \(0.993921\pi\)
\(318\) 0 0
\(319\) −22.4407 6.58918i −1.25644 0.368923i
\(320\) 0 0
\(321\) 1.42826 9.93374i 0.0797175 0.554447i
\(322\) 0 0
\(323\) −22.2612 14.3064i −1.23865 0.796029i
\(324\) 0 0
\(325\) −3.26964 7.15951i −0.181367 0.397138i
\(326\) 0 0
\(327\) −4.61414 + 2.96533i −0.255162 + 0.163983i
\(328\) 0 0
\(329\) 13.4623 3.95289i 0.742200 0.217930i
\(330\) 0 0
\(331\) −1.85936 + 12.9321i −0.102200 + 0.710814i 0.872714 + 0.488232i \(0.162358\pi\)
−0.974914 + 0.222583i \(0.928551\pi\)
\(332\) 0 0
\(333\) 3.87444 + 4.47135i 0.212318 + 0.245028i
\(334\) 0 0
\(335\) 13.3406 + 7.19280i 0.728874 + 0.392985i
\(336\) 0 0
\(337\) 8.12315 + 9.37462i 0.442496 + 0.510668i 0.932558 0.361020i \(-0.117571\pi\)
−0.490062 + 0.871688i \(0.663026\pi\)
\(338\) 0 0
\(339\) −0.0675573 + 0.469871i −0.00366921 + 0.0255199i
\(340\) 0 0
\(341\) 19.1796 5.63163i 1.03863 0.304970i
\(342\) 0 0
\(343\) 11.6605 7.49375i 0.629608 0.404625i
\(344\) 0 0
\(345\) −3.96142 8.67429i −0.213276 0.467008i
\(346\) 0 0
\(347\) −11.5268 7.40784i −0.618792 0.397673i 0.193353 0.981129i \(-0.438064\pi\)
−0.812145 + 0.583456i \(0.801700\pi\)
\(348\) 0 0
\(349\) 0.418591 2.91137i 0.0224067 0.155842i −0.975546 0.219794i \(-0.929461\pi\)
0.997953 + 0.0639522i \(0.0203705\pi\)
\(350\) 0 0
\(351\) 4.80548 + 1.41102i 0.256498 + 0.0753145i
\(352\) 0 0
\(353\) −1.18195 + 8.22064i −0.0629089 + 0.437541i 0.933888 + 0.357566i \(0.116393\pi\)
−0.996797 + 0.0799751i \(0.974516\pi\)
\(354\) 0 0
\(355\) −7.66525 + 16.7846i −0.406829 + 0.890832i
\(356\) 0 0
\(357\) 1.64183 + 3.59511i 0.0868950 + 0.190274i
\(358\) 0 0
\(359\) 1.12157 + 7.80070i 0.0591943 + 0.411705i 0.997776 + 0.0666495i \(0.0212309\pi\)
−0.938582 + 0.345056i \(0.887860\pi\)
\(360\) 0 0
\(361\) −4.73804 32.9538i −0.249371 1.73441i
\(362\) 0 0
\(363\) −27.0471 + 17.3821i −1.41960 + 0.912323i
\(364\) 0 0
\(365\) −22.4965 −1.17752
\(366\) 0 0
\(367\) 0.297957 + 0.652435i 0.0155532 + 0.0340568i 0.917249 0.398314i \(-0.130404\pi\)
−0.901696 + 0.432371i \(0.857677\pi\)
\(368\) 0 0
\(369\) 4.31004 4.97405i 0.224372 0.258939i
\(370\) 0 0
\(371\) −1.32683 + 0.852702i −0.0688856 + 0.0442701i
\(372\) 0 0
\(373\) 13.6530 0.706926 0.353463 0.935449i \(-0.385004\pi\)
0.353463 + 0.935449i \(0.385004\pi\)
\(374\) 0 0
\(375\) −11.6750 + 3.42810i −0.602897 + 0.177026i
\(376\) 0 0
\(377\) 15.0010 + 9.64058i 0.772593 + 0.496515i
\(378\) 0 0
\(379\) 6.38225 13.9752i 0.327834 0.717856i −0.671906 0.740636i \(-0.734524\pi\)
0.999741 + 0.0227795i \(0.00725158\pi\)
\(380\) 0 0
\(381\) 3.77297 1.10784i 0.193295 0.0567565i
\(382\) 0 0
\(383\) 11.4782 13.2465i 0.586507 0.676866i −0.382483 0.923962i \(-0.624931\pi\)
0.968991 + 0.247097i \(0.0794765\pi\)
\(384\) 0 0
\(385\) 1.86957 + 13.0031i 0.0952820 + 0.662701i
\(386\) 0 0
\(387\) −5.40582 + 6.23865i −0.274793 + 0.317128i
\(388\) 0 0
\(389\) 25.5214 + 16.4016i 1.29399 + 0.831595i 0.992544 0.121889i \(-0.0388952\pi\)
0.301443 + 0.953484i \(0.402532\pi\)
\(390\) 0 0
\(391\) −18.0826 5.30953i −0.914476 0.268514i
\(392\) 0 0
\(393\) −13.6768 15.7839i −0.689905 0.796193i
\(394\) 0 0
\(395\) −0.383760 0.442883i −0.0193091 0.0222839i
\(396\) 0 0
\(397\) −31.7750 9.32999i −1.59474 0.468259i −0.640666 0.767820i \(-0.721342\pi\)
−0.954077 + 0.299561i \(0.903160\pi\)
\(398\) 0 0
\(399\) −3.24451 + 7.10448i −0.162428 + 0.355669i
\(400\) 0 0
\(401\) 8.62132 0.430528 0.215264 0.976556i \(-0.430939\pi\)
0.215264 + 0.976556i \(0.430939\pi\)
\(402\) 0 0
\(403\) −15.2404 −0.759180
\(404\) 0 0
\(405\) 0.769188 1.68429i 0.0382212 0.0836929i
\(406\) 0 0
\(407\) 37.2904 + 10.9495i 1.84842 + 0.542744i
\(408\) 0 0
\(409\) −17.1503 19.7925i −0.848028 0.978676i 0.151925 0.988392i \(-0.451453\pi\)
−0.999953 + 0.00971574i \(0.996907\pi\)
\(410\) 0 0
\(411\) 5.17992 + 5.97795i 0.255507 + 0.294870i
\(412\) 0 0
\(413\) −1.39088 0.408401i −0.0684410 0.0200961i
\(414\) 0 0
\(415\) −7.59099 4.87843i −0.372627 0.239473i
\(416\) 0 0
\(417\) 14.3334 16.5416i 0.701910 0.810047i
\(418\) 0 0
\(419\) −3.56496 24.7949i −0.174160 1.21131i −0.869978 0.493090i \(-0.835867\pi\)
0.695818 0.718218i \(-0.255042\pi\)
\(420\) 0 0
\(421\) 10.3091 11.8973i 0.502433 0.579839i −0.446712 0.894678i \(-0.647405\pi\)
0.949145 + 0.314839i \(0.101951\pi\)
\(422\) 0 0
\(423\) −12.4644 + 3.65989i −0.606042 + 0.177950i
\(424\) 0 0
\(425\) −2.38894 + 5.23105i −0.115881 + 0.253743i
\(426\) 0 0
\(427\) 0.192509 + 0.123718i 0.00931614 + 0.00598712i
\(428\) 0 0
\(429\) 31.5669 9.26887i 1.52406 0.447505i
\(430\) 0 0
\(431\) 29.4346 1.41781 0.708907 0.705302i \(-0.249189\pi\)
0.708907 + 0.705302i \(0.249189\pi\)
\(432\) 0 0
\(433\) −13.4260 + 8.62834i −0.645210 + 0.414652i −0.821913 0.569613i \(-0.807093\pi\)
0.176703 + 0.984264i \(0.443457\pi\)
\(434\) 0 0
\(435\) 4.31716 4.98227i 0.206992 0.238882i
\(436\) 0 0
\(437\) −15.4711 33.8769i −0.740082 1.62055i
\(438\) 0 0
\(439\) −17.1229 −0.817229 −0.408615 0.912707i \(-0.633988\pi\)
−0.408615 + 0.912707i \(0.633988\pi\)
\(440\) 0 0
\(441\) −4.90744 + 3.15382i −0.233687 + 0.150182i
\(442\) 0 0
\(443\) −0.280265 1.94928i −0.0133158 0.0926133i 0.982080 0.188466i \(-0.0603514\pi\)
−0.995396 + 0.0958524i \(0.969442\pi\)
\(444\) 0 0
\(445\) 1.84876 + 12.8584i 0.0876398 + 0.609548i
\(446\) 0 0
\(447\) −4.73561 10.3695i −0.223987 0.490462i
\(448\) 0 0
\(449\) 1.16035 2.54082i 0.0547604 0.119909i −0.880274 0.474466i \(-0.842641\pi\)
0.935034 + 0.354557i \(0.115368\pi\)
\(450\) 0 0
\(451\) 6.15286 42.7941i 0.289727 2.01510i
\(452\) 0 0
\(453\) 5.46680 + 1.60520i 0.256853 + 0.0754187i
\(454\) 0 0
\(455\) 1.42541 9.91398i 0.0668245 0.464774i
\(456\) 0 0
\(457\) 3.41726 + 2.19614i 0.159853 + 0.102731i 0.618122 0.786083i \(-0.287894\pi\)
−0.458269 + 0.888814i \(0.651530\pi\)
\(458\) 0 0
\(459\) −1.52014 3.32864i −0.0709540 0.155368i
\(460\) 0 0
\(461\) 8.53402 5.48448i 0.397469 0.255438i −0.326604 0.945161i \(-0.605904\pi\)
0.724073 + 0.689723i \(0.242268\pi\)
\(462\) 0 0
\(463\) −0.0372962 + 0.0109512i −0.00173330 + 0.000508943i −0.282599 0.959238i \(-0.591197\pi\)
0.280866 + 0.959747i \(0.409378\pi\)
\(464\) 0 0
\(465\) −0.801868 + 5.57711i −0.0371857 + 0.258632i
\(466\) 0 0
\(467\) 10.5560 + 12.1823i 0.488474 + 0.563729i 0.945457 0.325746i \(-0.105615\pi\)
−0.456983 + 0.889475i \(0.651070\pi\)
\(468\) 0 0
\(469\) −4.27801 7.73663i −0.197540 0.357244i
\(470\) 0 0
\(471\) 2.02328 + 2.33498i 0.0932276 + 0.107590i
\(472\) 0 0
\(473\) −7.71717 + 53.6741i −0.354836 + 2.46794i
\(474\) 0 0
\(475\) −10.9040 + 3.20170i −0.500309 + 0.146904i
\(476\) 0 0
\(477\) 1.22848 0.789498i 0.0562484 0.0361486i
\(478\) 0 0
\(479\) 11.0837 + 24.2699i 0.506427 + 1.10892i 0.974327 + 0.225138i \(0.0722834\pi\)
−0.467900 + 0.883781i \(0.654989\pi\)
\(480\) 0 0
\(481\) −24.9277 16.0201i −1.13661 0.730452i
\(482\) 0 0
\(483\) −0.791616 + 5.50581i −0.0360198 + 0.250523i
\(484\) 0 0
\(485\) −0.903631 0.265330i −0.0410317 0.0120480i
\(486\) 0 0
\(487\) 6.22412 43.2897i 0.282042 1.96164i 0.00784481 0.999969i \(-0.497503\pi\)
0.274197 0.961674i \(-0.411588\pi\)
\(488\) 0 0
\(489\) 4.89586 10.7204i 0.221399 0.484795i
\(490\) 0 0
\(491\) 11.3020 + 24.7478i 0.510050 + 1.11685i 0.973071 + 0.230507i \(0.0740385\pi\)
−0.463020 + 0.886348i \(0.653234\pi\)
\(492\) 0 0
\(493\) −1.85417 12.8961i −0.0835078 0.580809i
\(494\) 0 0
\(495\) −1.73099 12.0393i −0.0778024 0.541127i
\(496\) 0 0
\(497\) 9.05455 5.81901i 0.406152 0.261018i
\(498\) 0 0
\(499\) 14.7062 0.658339 0.329169 0.944271i \(-0.393231\pi\)
0.329169 + 0.944271i \(0.393231\pi\)
\(500\) 0 0
\(501\) 4.61937 + 10.1150i 0.206378 + 0.451906i
\(502\) 0 0
\(503\) −20.5152 + 23.6758i −0.914729 + 1.05565i 0.0835205 + 0.996506i \(0.473384\pi\)
−0.998249 + 0.0591472i \(0.981162\pi\)
\(504\) 0 0
\(505\) 23.7900 15.2889i 1.05864 0.680347i
\(506\) 0 0
\(507\) −12.0836 −0.536651
\(508\) 0 0
\(509\) 7.30156 2.14393i 0.323636 0.0950281i −0.115879 0.993263i \(-0.536968\pi\)
0.439515 + 0.898235i \(0.355150\pi\)
\(510\) 0 0
\(511\) 11.0392 + 7.09446i 0.488345 + 0.313841i
\(512\) 0 0
\(513\) 3.00402 6.57788i 0.132631 0.290421i
\(514\) 0 0
\(515\) 19.9632 5.86174i 0.879686 0.258299i
\(516\) 0 0
\(517\) −55.8824 + 64.4917i −2.45771 + 2.83634i
\(518\) 0 0
\(519\) −0.225811 1.57055i −0.00991198 0.0689394i
\(520\) 0 0
\(521\) 14.5179 16.7546i 0.636041 0.734031i −0.342628 0.939471i \(-0.611317\pi\)
0.978670 + 0.205440i \(0.0658627\pi\)
\(522\) 0 0
\(523\) −20.0776 12.9031i −0.877931 0.564212i 0.0222380 0.999753i \(-0.492921\pi\)
−0.900169 + 0.435541i \(0.856557\pi\)
\(524\) 0 0
\(525\) 1.62858 + 0.478196i 0.0710773 + 0.0208702i
\(526\) 0 0
\(527\) 7.29209 + 8.41552i 0.317648 + 0.366586i
\(528\) 0 0
\(529\) −2.30762 2.66313i −0.100331 0.115788i
\(530\) 0 0
\(531\) 1.28779 + 0.378129i 0.0558853 + 0.0164094i
\(532\) 0 0
\(533\) −13.6933 + 29.9842i −0.593124 + 1.29876i
\(534\) 0 0
\(535\) 18.5826 0.803395
\(536\) 0 0
\(537\) 1.16251 0.0501660
\(538\) 0 0
\(539\) −15.9186 + 34.8569i −0.685663 + 1.50139i
\(540\) 0 0
\(541\) 25.8313 + 7.58477i 1.11058 + 0.326095i 0.785046 0.619437i \(-0.212639\pi\)
0.325530 + 0.945532i \(0.394457\pi\)
\(542\) 0 0
\(543\) 12.5030 + 14.4293i 0.536557 + 0.619220i
\(544\) 0 0
\(545\) −6.65063 7.67523i −0.284882 0.328771i
\(546\) 0 0
\(547\) −12.6118 3.70316i −0.539242 0.158336i 0.000759759 1.00000i \(-0.499758\pi\)
−0.540002 + 0.841664i \(0.681576\pi\)
\(548\) 0 0
\(549\) −0.178240 0.114548i −0.00760708 0.00488877i
\(550\) 0 0
\(551\) 16.8604 19.4580i 0.718279 0.828938i
\(552\) 0 0
\(553\) 0.0486471 + 0.338348i 0.00206869 + 0.0143880i
\(554\) 0 0
\(555\) −7.17397 + 8.27920i −0.304518 + 0.351433i
\(556\) 0 0
\(557\) −24.8846 + 7.30677i −1.05439 + 0.309598i −0.762591 0.646881i \(-0.776073\pi\)
−0.291802 + 0.956479i \(0.594255\pi\)
\(558\) 0 0
\(559\) 17.1747 37.6074i 0.726414 1.59062i
\(560\) 0 0
\(561\) −20.2219 12.9958i −0.853771 0.548685i
\(562\) 0 0
\(563\) 18.0781 5.30821i 0.761901 0.223714i 0.122375 0.992484i \(-0.460949\pi\)
0.639526 + 0.768770i \(0.279131\pi\)
\(564\) 0 0
\(565\) −0.878966 −0.0369784
\(566\) 0 0
\(567\) −0.908600 + 0.583922i −0.0381576 + 0.0245224i
\(568\) 0 0
\(569\) −6.21332 + 7.17055i −0.260476 + 0.300605i −0.870891 0.491477i \(-0.836457\pi\)
0.610415 + 0.792082i \(0.291003\pi\)
\(570\) 0 0
\(571\) 17.7351 + 38.8346i 0.742193 + 1.62518i 0.779914 + 0.625887i \(0.215263\pi\)
−0.0377207 + 0.999288i \(0.512010\pi\)
\(572\) 0 0
\(573\) 11.6802 0.487947
\(574\) 0 0
\(575\) −6.80875 + 4.37572i −0.283945 + 0.182480i
\(576\) 0 0
\(577\) −4.10699 28.5647i −0.170976 1.18916i −0.876828 0.480805i \(-0.840345\pi\)
0.705852 0.708360i \(-0.250565\pi\)
\(578\) 0 0
\(579\) −3.02801 21.0603i −0.125840 0.875234i
\(580\) 0 0
\(581\) 2.18650 + 4.78777i 0.0907113 + 0.198630i
\(582\) 0 0
\(583\) 3.98492 8.72575i 0.165038 0.361384i
\(584\) 0 0
\(585\) −1.31976 + 9.17914i −0.0545654 + 0.379511i
\(586\) 0 0
\(587\) 0.103554 + 0.0304062i 0.00427413 + 0.00125500i 0.283869 0.958863i \(-0.408382\pi\)
−0.279595 + 0.960118i \(0.590200\pi\)
\(588\) 0 0
\(589\) −3.13165 + 21.7811i −0.129037 + 0.897474i
\(590\) 0 0
\(591\) 8.41000 + 5.40478i 0.345941 + 0.222323i
\(592\) 0 0
\(593\) −5.75662 12.6052i −0.236396 0.517635i 0.753836 0.657062i \(-0.228201\pi\)
−0.990232 + 0.139427i \(0.955474\pi\)
\(594\) 0 0
\(595\) −6.15636 + 3.95645i −0.252386 + 0.162199i
\(596\) 0 0
\(597\) 10.6099 3.11533i 0.434232 0.127502i
\(598\) 0 0
\(599\) 2.65164 18.4426i 0.108343 0.753543i −0.861137 0.508373i \(-0.830247\pi\)
0.969480 0.245170i \(-0.0788438\pi\)
\(600\) 0 0
\(601\) 14.5061 + 16.7409i 0.591715 + 0.682875i 0.970081 0.242781i \(-0.0780595\pi\)
−0.378366 + 0.925656i \(0.623514\pi\)
\(602\) 0 0
\(603\) 3.96092 + 7.16318i 0.161301 + 0.291707i
\(604\) 0 0
\(605\) −38.9845 44.9906i −1.58495 1.82913i
\(606\) 0 0
\(607\) −6.12585 + 42.6062i −0.248641 + 1.72933i 0.357445 + 0.933934i \(0.383648\pi\)
−0.606085 + 0.795400i \(0.707261\pi\)
\(608\) 0 0
\(609\) −3.68967 + 1.08338i −0.149513 + 0.0439009i
\(610\) 0 0
\(611\) 54.7335 35.1751i 2.21428 1.42303i
\(612\) 0 0
\(613\) 5.59468 + 12.2506i 0.225967 + 0.494799i 0.988326 0.152356i \(-0.0486861\pi\)
−0.762359 + 0.647155i \(0.775959\pi\)
\(614\) 0 0
\(615\) 10.2520 + 6.58857i 0.413401 + 0.265677i
\(616\) 0 0
\(617\) 0.546163 3.79865i 0.0219877 0.152928i −0.975870 0.218354i \(-0.929931\pi\)
0.997857 + 0.0654256i \(0.0208405\pi\)
\(618\) 0 0
\(619\) −13.1539 3.86232i −0.528699 0.155240i 0.00647978 0.999979i \(-0.497937\pi\)
−0.535178 + 0.844739i \(0.679756\pi\)
\(620\) 0 0
\(621\) 0.732940 5.09771i 0.0294119 0.204564i
\(622\) 0 0
\(623\) 3.14781 6.89275i 0.126115 0.276152i
\(624\) 0 0
\(625\) −6.09524 13.3467i −0.243809 0.533868i
\(626\) 0 0
\(627\) −6.76029 47.0189i −0.269980 1.87775i
\(628\) 0 0
\(629\) 3.08114 + 21.4298i 0.122853 + 0.854462i
\(630\) 0 0
\(631\) −14.3046 + 9.19299i −0.569456 + 0.365967i −0.793461 0.608621i \(-0.791723\pi\)
0.224005 + 0.974588i \(0.428087\pi\)
\(632\) 0 0
\(633\) −22.0773 −0.877492
\(634\) 0 0
\(635\) 3.02464 + 6.62304i 0.120029 + 0.262827i
\(636\) 0 0
\(637\) 19.1325 22.0801i 0.758057 0.874844i
\(638\) 0 0
\(639\) −8.38342 + 5.38769i −0.331643 + 0.213134i
\(640\) 0 0
\(641\) 4.66303 0.184179 0.0920893 0.995751i \(-0.470645\pi\)
0.0920893 + 0.995751i \(0.470645\pi\)
\(642\) 0 0
\(643\) 22.7653 6.68450i 0.897776 0.263611i 0.199889 0.979819i \(-0.435942\pi\)
0.697887 + 0.716208i \(0.254124\pi\)
\(644\) 0 0
\(645\) −12.8585 8.26365i −0.506302 0.325381i
\(646\) 0 0
\(647\) −1.66057 + 3.63614i −0.0652837 + 0.142951i −0.939461 0.342655i \(-0.888674\pi\)
0.874178 + 0.485606i \(0.161401\pi\)
\(648\) 0 0
\(649\) 8.45941 2.48391i 0.332061 0.0975019i
\(650\) 0 0
\(651\) 2.15227 2.48385i 0.0843542 0.0973499i
\(652\) 0 0
\(653\) 1.02272 + 7.11316i 0.0400220 + 0.278359i 0.999999 0.00172121i \(-0.000547878\pi\)
−0.959976 + 0.280081i \(0.909639\pi\)
\(654\) 0 0
\(655\) 25.3242 29.2257i 0.989499 1.14194i
\(656\) 0 0
\(657\) −10.2210 6.56861i −0.398758 0.256266i
\(658\) 0 0
\(659\) −9.59738 2.81805i −0.373861 0.109775i 0.0894037 0.995995i \(-0.471504\pi\)
−0.463265 + 0.886220i \(0.653322\pi\)
\(660\) 0 0
\(661\) 2.11853 + 2.44492i 0.0824013 + 0.0950962i 0.795453 0.606015i \(-0.207233\pi\)
−0.713052 + 0.701111i \(0.752688\pi\)
\(662\) 0 0
\(663\) 12.0018 + 13.8508i 0.466109 + 0.537919i
\(664\) 0 0
\(665\) −13.8758 4.07431i −0.538081 0.157995i
\(666\) 0 0
\(667\) 7.61728 16.6795i 0.294942 0.645833i
\(668\) 0 0
\(669\) −23.1638 −0.895566
\(670\) 0 0
\(671\) −1.39178 −0.0537292
\(672\) 0 0
\(673\) −18.7166 + 40.9837i −0.721473 + 1.57981i 0.0903556 + 0.995910i \(0.471200\pi\)
−0.811829 + 0.583896i \(0.801528\pi\)
\(674\) 0 0
\(675\) −1.50787 0.442751i −0.0580380 0.0170415i
\(676\) 0 0
\(677\) 2.44945 + 2.82681i 0.0941399 + 0.108643i 0.800865 0.598845i \(-0.204374\pi\)
−0.706725 + 0.707489i \(0.749828\pi\)
\(678\) 0 0
\(679\) 0.359744 + 0.415167i 0.0138057 + 0.0159326i
\(680\) 0 0
\(681\) −23.6971 6.95808i −0.908073 0.266634i
\(682\) 0 0
\(683\) 14.3418 + 9.21694i 0.548775 + 0.352676i 0.785462 0.618910i \(-0.212425\pi\)
−0.236687 + 0.971586i \(0.576062\pi\)
\(684\) 0 0
\(685\) −9.59121 + 11.0688i −0.366461 + 0.422919i
\(686\) 0 0
\(687\) 2.01564 + 14.0191i 0.0769016 + 0.534863i
\(688\) 0 0
\(689\) −4.78946 + 5.52733i −0.182464 + 0.210574i
\(690\) 0 0
\(691\) −29.6452 + 8.70462i −1.12776 + 0.331139i −0.791826 0.610747i \(-0.790869\pi\)
−0.335932 + 0.941886i \(0.609051\pi\)
\(692\) 0 0
\(693\) −2.94729 + 6.45367i −0.111958 + 0.245155i
\(694\) 0 0
\(695\) 34.0940 + 21.9109i 1.29326 + 0.831126i
\(696\) 0 0
\(697\) 23.1087 6.78532i 0.875303 0.257012i
\(698\) 0 0
\(699\) −24.6832 −0.933606
\(700\) 0 0
\(701\) −11.7482 + 7.55013i −0.443725 + 0.285164i −0.743363 0.668888i \(-0.766770\pi\)
0.299638 + 0.954053i \(0.403134\pi\)
\(702\) 0 0
\(703\) −28.0175 + 32.3340i −1.05670 + 1.21950i
\(704\) 0 0
\(705\) −9.99226 21.8800i −0.376330 0.824048i
\(706\) 0 0
\(707\) −16.4954 −0.620374
\(708\) 0 0
\(709\) 11.9925 7.70714i 0.450389 0.289448i −0.295716 0.955276i \(-0.595558\pi\)
0.746105 + 0.665828i \(0.231922\pi\)
\(710\) 0 0
\(711\) −0.0450413 0.313269i −0.00168918 0.0117485i
\(712\) 0 0
\(713\) 2.23034 + 15.5123i 0.0835268 + 0.580942i
\(714\) 0 0
\(715\) 25.3059 + 55.4123i 0.946388 + 2.07230i
\(716\) 0 0
\(717\) −9.22310 + 20.1958i −0.344443 + 0.754225i
\(718\) 0 0
\(719\) −6.47060 + 45.0040i −0.241313 + 1.67837i 0.404243 + 0.914652i \(0.367535\pi\)
−0.645555 + 0.763714i \(0.723374\pi\)
\(720\) 0 0
\(721\) −11.6447 3.41918i −0.433670 0.127337i
\(722\) 0 0
\(723\) −3.26380 + 22.7003i −0.121382 + 0.844232i
\(724\) 0 0
\(725\) −4.70705 3.02504i −0.174816 0.112347i
\(726\) 0 0
\(727\) 3.47740 + 7.61444i 0.128970 + 0.282404i 0.963091 0.269178i \(-0.0867518\pi\)
−0.834121 + 0.551581i \(0.814025\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) −28.9838 + 8.51041i −1.07200 + 0.314769i
\(732\) 0 0
\(733\) −2.43843 + 16.9596i −0.0900653 + 0.626418i 0.893928 + 0.448211i \(0.147939\pi\)
−0.983993 + 0.178207i \(0.942970\pi\)
\(734\) 0 0
\(735\) −7.07338 8.16311i −0.260906 0.301101i
\(736\) 0 0
\(737\) 47.3281 + 25.5178i 1.74335 + 0.939960i
\(738\) 0 0
\(739\) 14.6066 + 16.8569i 0.537313 + 0.620092i 0.957880 0.287169i \(-0.0927143\pi\)
−0.420567 + 0.907261i \(0.638169\pi\)
\(740\) 0 0
\(741\) −5.15425 + 35.8486i −0.189346 + 1.31693i
\(742\) 0 0
\(743\) −17.9183 + 5.26128i −0.657358 + 0.193018i −0.593366 0.804933i \(-0.702201\pi\)
−0.0639919 + 0.997950i \(0.520383\pi\)
\(744\) 0 0
\(745\) 17.7570 11.4118i 0.650568 0.418095i
\(746\) 0 0
\(747\) −2.02443 4.43289i −0.0740702 0.162191i
\(748\) 0 0
\(749\) −9.11861 5.86018i −0.333187 0.214126i
\(750\) 0 0
\(751\) 3.63994 25.3163i 0.132823 0.923807i −0.809026 0.587772i \(-0.800005\pi\)
0.941850 0.336034i \(-0.109086\pi\)
\(752\) 0 0
\(753\) 25.1022 + 7.37066i 0.914773 + 0.268602i
\(754\) 0 0
\(755\) −1.50138 + 10.4424i −0.0546410 + 0.380036i
\(756\) 0 0
\(757\) 20.4627 44.8072i 0.743731 1.62854i −0.0335870 0.999436i \(-0.510693\pi\)
0.777318 0.629108i \(-0.216580\pi\)
\(758\) 0 0
\(759\) −14.0538 30.7736i −0.510122 1.11701i
\(760\) 0 0
\(761\) 4.47973 + 31.1572i 0.162390 + 1.12945i 0.894111 + 0.447845i \(0.147808\pi\)
−0.731721 + 0.681604i \(0.761283\pi\)
\(762\) 0 0
\(763\) 0.843062 + 5.86363i 0.0305209 + 0.212278i
\(764\) 0 0
\(765\) 5.70004 3.66319i 0.206085 0.132443i
\(766\) 0 0
\(767\) −6.72200 −0.242717
\(768\) 0 0
\(769\) −17.6486 38.6450i −0.636424 1.39357i −0.902950 0.429746i \(-0.858603\pi\)
0.266526 0.963828i \(-0.414124\pi\)
\(770\) 0 0
\(771\) 5.30658 6.12413i 0.191112 0.220555i
\(772\) 0 0
\(773\) 9.10646 5.85237i 0.327537 0.210495i −0.366529 0.930407i \(-0.619454\pi\)
0.694066 + 0.719912i \(0.255818\pi\)
\(774\) 0 0
\(775\) 4.78217 0.171781
\(776\) 0 0
\(777\) 6.13124 1.80029i 0.219957 0.0645852i
\(778\) 0 0
\(779\) 40.0387 + 25.7313i 1.43453 + 0.921919i
\(780\) 0 0
\(781\) −27.1939 + 59.5463i −0.973074 + 2.13073i