Properties

Label 1148.2.ba.a.113.17
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.17
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.4

$q$-expansion

\(f(q)\) \(=\) \(q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +O(q^{10})\) \(q+2.28455i q^{3} +(1.15282 + 3.54801i) q^{5} +(0.587785 + 0.809017i) q^{7} -2.21915 q^{9} +(-0.170591 - 0.0554285i) q^{11} +(-1.72999 + 2.38113i) q^{13} +(-8.10559 + 2.63367i) q^{15} +(2.20009 + 0.714853i) q^{17} +(-0.238808 - 0.328691i) q^{19} +(-1.84824 + 1.34282i) q^{21} +(0.682118 + 0.495588i) q^{23} +(-7.21429 + 5.24149i) q^{25} +1.78389i q^{27} +(4.71296 - 1.53133i) q^{29} +(1.43394 - 4.41323i) q^{31} +(0.126629 - 0.389724i) q^{33} +(-2.19279 + 3.01812i) q^{35} +(1.20270 + 3.70154i) q^{37} +(-5.43980 - 3.95225i) q^{39} +(1.75557 - 6.15776i) q^{41} +(-0.780429 - 0.567015i) q^{43} +(-2.55827 - 7.87356i) q^{45} +(7.77005 - 10.6946i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.63312 + 5.02621i) q^{51} +(-10.8610 + 3.52896i) q^{53} -0.669158i q^{55} +(0.750909 - 0.545568i) q^{57} +(-1.25990 - 0.915373i) q^{59} +(1.80030 - 1.30800i) q^{61} +(-1.30438 - 1.79533i) q^{63} +(-10.4426 - 3.39302i) q^{65} +(3.84279 - 1.24860i) q^{67} +(-1.13219 + 1.55833i) q^{69} +(-0.775836 - 0.252084i) q^{71} +13.2778 q^{73} +(-11.9744 - 16.4814i) q^{75} +(-0.0554285 - 0.170591i) q^{77} -8.02141i q^{79} -10.7328 q^{81} -14.2863 q^{83} +8.63004i q^{85} +(3.49840 + 10.7670i) q^{87} +(-5.60107 - 7.70921i) q^{89} -2.94324 q^{91} +(10.0822 + 3.27591i) q^{93} +(0.890896 - 1.22621i) q^{95} +(-1.78899 + 0.581279i) q^{97} +(0.378567 + 0.123004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.28455i 1.31898i 0.751712 + 0.659492i \(0.229228\pi\)
−0.751712 + 0.659492i \(0.770772\pi\)
\(4\) 0 0
\(5\) 1.15282 + 3.54801i 0.515556 + 1.58672i 0.782268 + 0.622942i \(0.214063\pi\)
−0.266712 + 0.963776i \(0.585937\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −2.21915 −0.739716
\(10\) 0 0
\(11\) −0.170591 0.0554285i −0.0514352 0.0167123i 0.283186 0.959065i \(-0.408608\pi\)
−0.334622 + 0.942353i \(0.608608\pi\)
\(12\) 0 0
\(13\) −1.72999 + 2.38113i −0.479814 + 0.660407i −0.978469 0.206393i \(-0.933827\pi\)
0.498655 + 0.866800i \(0.333827\pi\)
\(14\) 0 0
\(15\) −8.10559 + 2.63367i −2.09285 + 0.680009i
\(16\) 0 0
\(17\) 2.20009 + 0.714853i 0.533601 + 0.173377i 0.563409 0.826178i \(-0.309490\pi\)
−0.0298081 + 0.999556i \(0.509490\pi\)
\(18\) 0 0
\(19\) −0.238808 0.328691i −0.0547863 0.0754069i 0.780745 0.624850i \(-0.214840\pi\)
−0.835531 + 0.549443i \(0.814840\pi\)
\(20\) 0 0
\(21\) −1.84824 + 1.34282i −0.403318 + 0.293028i
\(22\) 0 0
\(23\) 0.682118 + 0.495588i 0.142231 + 0.103337i 0.656626 0.754217i \(-0.271983\pi\)
−0.514394 + 0.857554i \(0.671983\pi\)
\(24\) 0 0
\(25\) −7.21429 + 5.24149i −1.44286 + 1.04830i
\(26\) 0 0
\(27\) 1.78389i 0.343310i
\(28\) 0 0
\(29\) 4.71296 1.53133i 0.875174 0.284361i 0.163222 0.986589i \(-0.447811\pi\)
0.711952 + 0.702228i \(0.247811\pi\)
\(30\) 0 0
\(31\) 1.43394 4.41323i 0.257544 0.792639i −0.735774 0.677227i \(-0.763181\pi\)
0.993318 0.115411i \(-0.0368187\pi\)
\(32\) 0 0
\(33\) 0.126629 0.389724i 0.0220433 0.0678422i
\(34\) 0 0
\(35\) −2.19279 + 3.01812i −0.370649 + 0.510155i
\(36\) 0 0
\(37\) 1.20270 + 3.70154i 0.197723 + 0.608529i 0.999934 + 0.0114885i \(0.00365698\pi\)
−0.802211 + 0.597041i \(0.796343\pi\)
\(38\) 0 0
\(39\) −5.43980 3.95225i −0.871066 0.632866i
\(40\) 0 0
\(41\) 1.75557 6.15776i 0.274174 0.961680i
\(42\) 0 0
\(43\) −0.780429 0.567015i −0.119014 0.0864690i 0.526686 0.850060i \(-0.323434\pi\)
−0.645700 + 0.763591i \(0.723434\pi\)
\(44\) 0 0
\(45\) −2.55827 7.87356i −0.381365 1.17372i
\(46\) 0 0
\(47\) 7.77005 10.6946i 1.13338 1.55996i 0.351888 0.936042i \(-0.385540\pi\)
0.781489 0.623919i \(-0.214460\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −1.63312 + 5.02621i −0.228682 + 0.703810i
\(52\) 0 0
\(53\) −10.8610 + 3.52896i −1.49188 + 0.484740i −0.937637 0.347617i \(-0.886991\pi\)
−0.554240 + 0.832357i \(0.686991\pi\)
\(54\) 0 0
\(55\) 0.669158i 0.0902293i
\(56\) 0 0
\(57\) 0.750909 0.545568i 0.0994604 0.0722622i
\(58\) 0 0
\(59\) −1.25990 0.915373i −0.164025 0.119171i 0.502745 0.864435i \(-0.332324\pi\)
−0.666770 + 0.745264i \(0.732324\pi\)
\(60\) 0 0
\(61\) 1.80030 1.30800i 0.230505 0.167472i −0.466538 0.884501i \(-0.654499\pi\)
0.697043 + 0.717030i \(0.254499\pi\)
\(62\) 0 0
\(63\) −1.30438 1.79533i −0.164337 0.226190i
\(64\) 0 0
\(65\) −10.4426 3.39302i −1.29525 0.420852i
\(66\) 0 0
\(67\) 3.84279 1.24860i 0.469471 0.152540i −0.0647212 0.997903i \(-0.520616\pi\)
0.534192 + 0.845363i \(0.320616\pi\)
\(68\) 0 0
\(69\) −1.13219 + 1.55833i −0.136300 + 0.187601i
\(70\) 0 0
\(71\) −0.775836 0.252084i −0.0920748 0.0299169i 0.262617 0.964900i \(-0.415414\pi\)
−0.354692 + 0.934983i \(0.615414\pi\)
\(72\) 0 0
\(73\) 13.2778 1.55405 0.777027 0.629468i \(-0.216727\pi\)
0.777027 + 0.629468i \(0.216727\pi\)
\(74\) 0 0
\(75\) −11.9744 16.4814i −1.38269 1.90311i
\(76\) 0 0
\(77\) −0.0554285 0.170591i −0.00631666 0.0194407i
\(78\) 0 0
\(79\) 8.02141i 0.902480i −0.892403 0.451240i \(-0.850982\pi\)
0.892403 0.451240i \(-0.149018\pi\)
\(80\) 0 0
\(81\) −10.7328 −1.19254
\(82\) 0 0
\(83\) −14.2863 −1.56812 −0.784062 0.620683i \(-0.786856\pi\)
−0.784062 + 0.620683i \(0.786856\pi\)
\(84\) 0 0
\(85\) 8.63004i 0.936060i
\(86\) 0 0
\(87\) 3.49840 + 10.7670i 0.375068 + 1.15434i
\(88\) 0 0
\(89\) −5.60107 7.70921i −0.593712 0.817175i 0.401402 0.915902i \(-0.368523\pi\)
−0.995115 + 0.0987270i \(0.968523\pi\)
\(90\) 0 0
\(91\) −2.94324 −0.308535
\(92\) 0 0
\(93\) 10.0822 + 3.27591i 1.04548 + 0.339696i
\(94\) 0 0
\(95\) 0.890896 1.22621i 0.0914040 0.125807i
\(96\) 0 0
\(97\) −1.78899 + 0.581279i −0.181645 + 0.0590199i −0.398427 0.917200i \(-0.630444\pi\)
0.216782 + 0.976220i \(0.430444\pi\)
\(98\) 0 0
\(99\) 0.378567 + 0.123004i 0.0380475 + 0.0123624i
\(100\) 0 0
\(101\) 5.72207 + 7.87576i 0.569368 + 0.783667i 0.992480 0.122410i \(-0.0390623\pi\)
−0.423112 + 0.906077i \(0.639062\pi\)
\(102\) 0 0
\(103\) 5.73658 4.16787i 0.565242 0.410672i −0.268132 0.963382i \(-0.586406\pi\)
0.833374 + 0.552710i \(0.186406\pi\)
\(104\) 0 0
\(105\) −6.89503 5.00953i −0.672886 0.488880i
\(106\) 0 0
\(107\) 0.956235 0.694746i 0.0924428 0.0671636i −0.540604 0.841277i \(-0.681804\pi\)
0.633047 + 0.774114i \(0.281804\pi\)
\(108\) 0 0
\(109\) 18.4121i 1.76356i 0.471658 + 0.881782i \(0.343656\pi\)
−0.471658 + 0.881782i \(0.656344\pi\)
\(110\) 0 0
\(111\) −8.45634 + 2.74763i −0.802640 + 0.260794i
\(112\) 0 0
\(113\) −1.89249 + 5.82449i −0.178031 + 0.547922i −0.999759 0.0219574i \(-0.993010\pi\)
0.821728 + 0.569880i \(0.193010\pi\)
\(114\) 0 0
\(115\) −0.971992 + 2.99148i −0.0906387 + 0.278957i
\(116\) 0 0
\(117\) 3.83911 5.28408i 0.354926 0.488514i
\(118\) 0 0
\(119\) 0.714853 + 2.20009i 0.0655305 + 0.201682i
\(120\) 0 0
\(121\) −8.87316 6.44673i −0.806651 0.586066i
\(122\) 0 0
\(123\) 14.0677 + 4.01069i 1.26844 + 0.361631i
\(124\) 0 0
\(125\) −11.8230 8.58994i −1.05748 0.768307i
\(126\) 0 0
\(127\) 1.41857 + 4.36590i 0.125878 + 0.387411i 0.994060 0.108834i \(-0.0347117\pi\)
−0.868182 + 0.496245i \(0.834712\pi\)
\(128\) 0 0
\(129\) 1.29537 1.78293i 0.114051 0.156978i
\(130\) 0 0
\(131\) 2.21263 6.80979i 0.193319 0.594974i −0.806673 0.590998i \(-0.798734\pi\)
0.999992 0.00397639i \(-0.00126573\pi\)
\(132\) 0 0
\(133\) 0.125549 0.386399i 0.0108865 0.0335051i
\(134\) 0 0
\(135\) −6.32926 + 2.05650i −0.544736 + 0.176995i
\(136\) 0 0
\(137\) 19.1845i 1.63905i 0.573046 + 0.819523i \(0.305762\pi\)
−0.573046 + 0.819523i \(0.694238\pi\)
\(138\) 0 0
\(139\) 14.0484 10.2067i 1.19157 0.865723i 0.198137 0.980174i \(-0.436511\pi\)
0.993429 + 0.114451i \(0.0365110\pi\)
\(140\) 0 0
\(141\) 24.4322 + 17.7510i 2.05756 + 1.49491i
\(142\) 0 0
\(143\) 0.427104 0.310309i 0.0357162 0.0259494i
\(144\) 0 0
\(145\) 10.8664 + 14.9563i 0.902402 + 1.24205i
\(146\) 0 0
\(147\) −2.17273 0.705963i −0.179204 0.0582269i
\(148\) 0 0
\(149\) 0.214659 0.0697470i 0.0175856 0.00571390i −0.300211 0.953873i \(-0.597057\pi\)
0.317797 + 0.948159i \(0.397057\pi\)
\(150\) 0 0
\(151\) −2.15187 + 2.96179i −0.175116 + 0.241027i −0.887549 0.460714i \(-0.847593\pi\)
0.712432 + 0.701741i \(0.247593\pi\)
\(152\) 0 0
\(153\) −4.88233 1.58637i −0.394713 0.128250i
\(154\) 0 0
\(155\) 17.3112 1.39047
\(156\) 0 0
\(157\) 4.49536 + 6.18734i 0.358769 + 0.493803i 0.949805 0.312842i \(-0.101281\pi\)
−0.591036 + 0.806645i \(0.701281\pi\)
\(158\) 0 0
\(159\) −8.06207 24.8125i −0.639364 1.96776i
\(160\) 0 0
\(161\) 0.843144i 0.0664491i
\(162\) 0 0
\(163\) −14.6940 −1.15092 −0.575461 0.817829i \(-0.695177\pi\)
−0.575461 + 0.817829i \(0.695177\pi\)
\(164\) 0 0
\(165\) 1.52872 0.119011
\(166\) 0 0
\(167\) 3.80519i 0.294454i 0.989103 + 0.147227i \(0.0470348\pi\)
−0.989103 + 0.147227i \(0.952965\pi\)
\(168\) 0 0
\(169\) 1.34031 + 4.12506i 0.103101 + 0.317312i
\(170\) 0 0
\(171\) 0.529950 + 0.729414i 0.0405263 + 0.0557797i
\(172\) 0 0
\(173\) −1.68081 −0.127789 −0.0638947 0.997957i \(-0.520352\pi\)
−0.0638947 + 0.997957i \(0.520352\pi\)
\(174\) 0 0
\(175\) −8.48091 2.75561i −0.641096 0.208305i
\(176\) 0 0
\(177\) 2.09121 2.87830i 0.157185 0.216347i
\(178\) 0 0
\(179\) 0.732335 0.237950i 0.0547373 0.0177852i −0.281520 0.959555i \(-0.590839\pi\)
0.336258 + 0.941770i \(0.390839\pi\)
\(180\) 0 0
\(181\) 5.80624 + 1.88656i 0.431574 + 0.140227i 0.516745 0.856139i \(-0.327144\pi\)
−0.0851708 + 0.996366i \(0.527144\pi\)
\(182\) 0 0
\(183\) 2.98818 + 4.11288i 0.220893 + 0.304032i
\(184\) 0 0
\(185\) −11.7466 + 8.53440i −0.863627 + 0.627462i
\(186\) 0 0
\(187\) −0.335693 0.243896i −0.0245483 0.0178354i
\(188\) 0 0
\(189\) −1.44320 + 1.04854i −0.104977 + 0.0762704i
\(190\) 0 0
\(191\) 24.3882i 1.76466i −0.470627 0.882332i \(-0.655972\pi\)
0.470627 0.882332i \(-0.344028\pi\)
\(192\) 0 0
\(193\) −4.58839 + 1.49086i −0.330280 + 0.107314i −0.469463 0.882952i \(-0.655552\pi\)
0.139183 + 0.990267i \(0.455552\pi\)
\(194\) 0 0
\(195\) 7.75151 23.8567i 0.555097 1.70841i
\(196\) 0 0
\(197\) 4.25268 13.0884i 0.302991 0.932510i −0.677428 0.735589i \(-0.736906\pi\)
0.980419 0.196921i \(-0.0630943\pi\)
\(198\) 0 0
\(199\) 7.32961 10.0883i 0.519582 0.715143i −0.465916 0.884829i \(-0.654275\pi\)
0.985498 + 0.169686i \(0.0542752\pi\)
\(200\) 0 0
\(201\) 2.85248 + 8.77902i 0.201198 + 0.619225i
\(202\) 0 0
\(203\) 4.00908 + 2.91277i 0.281382 + 0.204436i
\(204\) 0 0
\(205\) 23.8716 0.869983i 1.66727 0.0607622i
\(206\) 0 0
\(207\) −1.51372 1.09978i −0.105211 0.0764402i
\(208\) 0 0
\(209\) 0.0225197 + 0.0693086i 0.00155772 + 0.00479417i
\(210\) 0 0
\(211\) −0.421975 + 0.580799i −0.0290500 + 0.0399839i −0.823295 0.567614i \(-0.807867\pi\)
0.794245 + 0.607598i \(0.207867\pi\)
\(212\) 0 0
\(213\) 0.575898 1.77243i 0.0394599 0.121445i
\(214\) 0 0
\(215\) 1.11208 3.42263i 0.0758433 0.233422i
\(216\) 0 0
\(217\) 4.41323 1.43394i 0.299589 0.0973425i
\(218\) 0 0
\(219\) 30.3338i 2.04977i
\(220\) 0 0
\(221\) −5.50830 + 4.00202i −0.370529 + 0.269205i
\(222\) 0 0
\(223\) 1.98086 + 1.43918i 0.132648 + 0.0963747i 0.652131 0.758106i \(-0.273875\pi\)
−0.519483 + 0.854481i \(0.673875\pi\)
\(224\) 0 0
\(225\) 16.0096 11.6316i 1.06731 0.775443i
\(226\) 0 0
\(227\) 12.1759 + 16.7587i 0.808142 + 1.11231i 0.991607 + 0.129286i \(0.0412685\pi\)
−0.183465 + 0.983026i \(0.558731\pi\)
\(228\) 0 0
\(229\) 16.6982 + 5.42559i 1.10345 + 0.358533i 0.803430 0.595400i \(-0.203006\pi\)
0.300021 + 0.953933i \(0.403006\pi\)
\(230\) 0 0
\(231\) 0.389724 0.126629i 0.0256419 0.00833157i
\(232\) 0 0
\(233\) −5.65958 + 7.78974i −0.370771 + 0.510323i −0.953110 0.302623i \(-0.902138\pi\)
0.582339 + 0.812946i \(0.302138\pi\)
\(234\) 0 0
\(235\) 46.9018 + 15.2393i 3.05954 + 0.994104i
\(236\) 0 0
\(237\) 18.3253 1.19036
\(238\) 0 0
\(239\) −3.49935 4.81644i −0.226354 0.311550i 0.680701 0.732561i \(-0.261675\pi\)
−0.907055 + 0.421011i \(0.861675\pi\)
\(240\) 0 0
\(241\) 5.75805 + 17.7215i 0.370908 + 1.14154i 0.946198 + 0.323589i \(0.104889\pi\)
−0.575289 + 0.817950i \(0.695111\pi\)
\(242\) 0 0
\(243\) 19.1680i 1.22963i
\(244\) 0 0
\(245\) −3.73060 −0.238339
\(246\) 0 0
\(247\) 1.19579 0.0760864
\(248\) 0 0
\(249\) 32.6377i 2.06833i
\(250\) 0 0
\(251\) 5.28543 + 16.2669i 0.333613 + 1.02676i 0.967401 + 0.253249i \(0.0814992\pi\)
−0.633788 + 0.773507i \(0.718501\pi\)
\(252\) 0 0
\(253\) −0.0888937 0.122352i −0.00558870 0.00769219i
\(254\) 0 0
\(255\) −19.7157 −1.23465
\(256\) 0 0
\(257\) 19.6529 + 6.38562i 1.22591 + 0.398324i 0.849233 0.528019i \(-0.177065\pi\)
0.376682 + 0.926343i \(0.377065\pi\)
\(258\) 0 0
\(259\) −2.28768 + 3.14872i −0.142149 + 0.195652i
\(260\) 0 0
\(261\) −10.4588 + 3.39826i −0.647381 + 0.210347i
\(262\) 0 0
\(263\) 4.30906 + 1.40010i 0.265708 + 0.0863337i 0.438841 0.898565i \(-0.355389\pi\)
−0.173133 + 0.984898i \(0.555389\pi\)
\(264\) 0 0
\(265\) −25.0416 34.4668i −1.53829 2.11728i
\(266\) 0 0
\(267\) 17.6120 12.7959i 1.07784 0.783096i
\(268\) 0 0
\(269\) −23.4546 17.0408i −1.43005 1.03899i −0.990007 0.141017i \(-0.954963\pi\)
−0.440044 0.897976i \(-0.645037\pi\)
\(270\) 0 0
\(271\) −20.8873 + 15.1755i −1.26882 + 0.921849i −0.999155 0.0411066i \(-0.986912\pi\)
−0.269661 + 0.962955i \(0.586912\pi\)
\(272\) 0 0
\(273\) 6.72397i 0.406953i
\(274\) 0 0
\(275\) 1.52122 0.494275i 0.0917332 0.0298059i
\(276\) 0 0
\(277\) 1.98487 6.10881i 0.119259 0.367043i −0.873552 0.486731i \(-0.838189\pi\)
0.992812 + 0.119688i \(0.0381894\pi\)
\(278\) 0 0
\(279\) −3.18214 + 9.79361i −0.190509 + 0.586328i
\(280\) 0 0
\(281\) 1.57844 2.17253i 0.0941617 0.129603i −0.759337 0.650698i \(-0.774476\pi\)
0.853498 + 0.521095i \(0.174476\pi\)
\(282\) 0 0
\(283\) 1.61238 + 4.96239i 0.0958459 + 0.294983i 0.987473 0.157787i \(-0.0504359\pi\)
−0.891627 + 0.452770i \(0.850436\pi\)
\(284\) 0 0
\(285\) 2.80134 + 2.03529i 0.165937 + 0.120560i
\(286\) 0 0
\(287\) 6.01363 2.19915i 0.354973 0.129812i
\(288\) 0 0
\(289\) −9.42390 6.84686i −0.554347 0.402757i
\(290\) 0 0
\(291\) −1.32796 4.08703i −0.0778462 0.239586i
\(292\) 0 0
\(293\) −11.6486 + 16.0329i −0.680518 + 0.936652i −0.999940 0.0109602i \(-0.996511\pi\)
0.319422 + 0.947612i \(0.396511\pi\)
\(294\) 0 0
\(295\) 1.79531 5.52540i 0.104527 0.321701i
\(296\) 0 0
\(297\) 0.0988783 0.304316i 0.00573750 0.0176582i
\(298\) 0 0
\(299\) −2.36012 + 0.766849i −0.136489 + 0.0443480i
\(300\) 0 0
\(301\) 0.964663i 0.0556023i
\(302\) 0 0
\(303\) −17.9925 + 13.0723i −1.03364 + 0.750986i
\(304\) 0 0
\(305\) 6.71621 + 4.87961i 0.384569 + 0.279406i
\(306\) 0 0
\(307\) 4.18354 3.03952i 0.238767 0.173475i −0.461967 0.886897i \(-0.652856\pi\)
0.700734 + 0.713423i \(0.252856\pi\)
\(308\) 0 0
\(309\) 9.52169 + 13.1055i 0.541670 + 0.745545i
\(310\) 0 0
\(311\) 1.88893 + 0.613751i 0.107111 + 0.0348026i 0.362082 0.932146i \(-0.382066\pi\)
−0.254971 + 0.966949i \(0.582066\pi\)
\(312\) 0 0
\(313\) 7.15404 2.32449i 0.404370 0.131388i −0.0997681 0.995011i \(-0.531810\pi\)
0.504139 + 0.863623i \(0.331810\pi\)
\(314\) 0 0
\(315\) 4.86613 6.69765i 0.274175 0.377370i
\(316\) 0 0
\(317\) 15.5713 + 5.05943i 0.874572 + 0.284166i 0.711702 0.702482i \(-0.247925\pi\)
0.162870 + 0.986647i \(0.447925\pi\)
\(318\) 0 0
\(319\) −0.888869 −0.0497671
\(320\) 0 0
\(321\) 1.58718 + 2.18456i 0.0885876 + 0.121930i
\(322\) 0 0
\(323\) −0.290434 0.893863i −0.0161602 0.0497359i
\(324\) 0 0
\(325\) 26.2459i 1.45586i
\(326\) 0 0
\(327\) −42.0634 −2.32611
\(328\) 0 0
\(329\) 13.2192 0.728798
\(330\) 0 0
\(331\) 23.7322i 1.30444i 0.758031 + 0.652219i \(0.226162\pi\)
−0.758031 + 0.652219i \(0.773838\pi\)
\(332\) 0 0
\(333\) −2.66898 8.21427i −0.146259 0.450139i
\(334\) 0 0
\(335\) 8.86007 + 12.1948i 0.484077 + 0.666275i
\(336\) 0 0
\(337\) 23.9523 1.30477 0.652383 0.757889i \(-0.273769\pi\)
0.652383 + 0.757889i \(0.273769\pi\)
\(338\) 0 0
\(339\) −13.3063 4.32349i −0.722700 0.234820i
\(340\) 0 0
\(341\) −0.489237 + 0.673377i −0.0264937 + 0.0364654i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) −6.83418 2.22056i −0.367940 0.119551i
\(346\) 0 0
\(347\) −9.10198 12.5278i −0.488620 0.672528i 0.491513 0.870870i \(-0.336444\pi\)
−0.980133 + 0.198343i \(0.936444\pi\)
\(348\) 0 0
\(349\) 24.7336 17.9700i 1.32396 0.961914i 0.324087 0.946027i \(-0.394943\pi\)
0.999874 0.0158869i \(-0.00505718\pi\)
\(350\) 0 0
\(351\) −4.24768 3.08612i −0.226724 0.164725i
\(352\) 0 0
\(353\) −21.4939 + 15.6162i −1.14400 + 0.831168i −0.987672 0.156536i \(-0.949967\pi\)
−0.156333 + 0.987704i \(0.549967\pi\)
\(354\) 0 0
\(355\) 3.04328i 0.161520i
\(356\) 0 0
\(357\) −5.02621 + 1.63312i −0.266015 + 0.0864336i
\(358\) 0 0
\(359\) 2.41790 7.44154i 0.127612 0.392750i −0.866756 0.498733i \(-0.833799\pi\)
0.994368 + 0.105983i \(0.0337989\pi\)
\(360\) 0 0
\(361\) 5.82031 17.9131i 0.306332 0.942794i
\(362\) 0 0
\(363\) 14.7278 20.2711i 0.773011 1.06396i
\(364\) 0 0
\(365\) 15.3069 + 47.1099i 0.801201 + 2.46584i
\(366\) 0 0
\(367\) 20.3452 + 14.7816i 1.06201 + 0.771595i 0.974459 0.224565i \(-0.0720963\pi\)
0.0875499 + 0.996160i \(0.472096\pi\)
\(368\) 0 0
\(369\) −3.89588 + 13.6650i −0.202811 + 0.711370i
\(370\) 0 0
\(371\) −9.23894 6.71248i −0.479662 0.348495i
\(372\) 0 0
\(373\) −4.44324 13.6749i −0.230062 0.708059i −0.997738 0.0672208i \(-0.978587\pi\)
0.767676 0.640839i \(-0.221413\pi\)
\(374\) 0 0
\(375\) 19.6241 27.0103i 1.01338 1.39480i
\(376\) 0 0
\(377\) −4.50708 + 13.8714i −0.232126 + 0.714412i
\(378\) 0 0
\(379\) −1.96540 + 6.04889i −0.100956 + 0.310710i −0.988760 0.149511i \(-0.952230\pi\)
0.887804 + 0.460222i \(0.152230\pi\)
\(380\) 0 0
\(381\) −9.97411 + 3.24078i −0.510989 + 0.166030i
\(382\) 0 0
\(383\) 23.7977i 1.21601i −0.793934 0.608004i \(-0.791971\pi\)
0.793934 0.608004i \(-0.208029\pi\)
\(384\) 0 0
\(385\) 0.541360 0.393321i 0.0275903 0.0200455i
\(386\) 0 0
\(387\) 1.73189 + 1.25829i 0.0880368 + 0.0639625i
\(388\) 0 0
\(389\) −3.24816 + 2.35993i −0.164688 + 0.119653i −0.667077 0.744989i \(-0.732455\pi\)
0.502389 + 0.864642i \(0.332455\pi\)
\(390\) 0 0
\(391\) 1.14645 + 1.57795i 0.0579785 + 0.0798005i
\(392\) 0 0
\(393\) 15.5573 + 5.05486i 0.784761 + 0.254984i
\(394\) 0 0
\(395\) 28.4600 9.24723i 1.43198 0.465279i
\(396\) 0 0
\(397\) 6.92956 9.53772i 0.347785 0.478684i −0.598910 0.800816i \(-0.704399\pi\)
0.946695 + 0.322132i \(0.104399\pi\)
\(398\) 0 0
\(399\) 0.882747 + 0.286822i 0.0441926 + 0.0143591i
\(400\) 0 0
\(401\) 5.25865 0.262604 0.131302 0.991342i \(-0.458084\pi\)
0.131302 + 0.991342i \(0.458084\pi\)
\(402\) 0 0
\(403\) 8.02776 + 11.0493i 0.399891 + 0.550403i
\(404\) 0 0
\(405\) −12.3730 38.0802i −0.614819 1.89222i
\(406\) 0 0
\(407\) 0.698114i 0.0346042i
\(408\) 0 0
\(409\) 33.0146 1.63247 0.816234 0.577722i \(-0.196058\pi\)
0.816234 + 0.577722i \(0.196058\pi\)
\(410\) 0 0
\(411\) −43.8280 −2.16187
\(412\) 0 0
\(413\) 1.55733i 0.0766310i
\(414\) 0 0
\(415\) −16.4695 50.6879i −0.808455 2.48817i
\(416\) 0 0
\(417\) 23.3177 + 32.0941i 1.14187 + 1.57165i
\(418\) 0 0
\(419\) −38.1555 −1.86402 −0.932009 0.362434i \(-0.881946\pi\)
−0.932009 + 0.362434i \(0.881946\pi\)
\(420\) 0 0
\(421\) 11.3278 + 3.68061i 0.552081 + 0.179382i 0.571755 0.820424i \(-0.306263\pi\)
−0.0196738 + 0.999806i \(0.506263\pi\)
\(422\) 0 0
\(423\) −17.2429 + 23.7328i −0.838378 + 1.15393i
\(424\) 0 0
\(425\) −19.6190 + 6.37460i −0.951662 + 0.309214i
\(426\) 0 0
\(427\) 2.11638 + 0.687655i 0.102419 + 0.0332779i
\(428\) 0 0
\(429\) 0.708916 + 0.975739i 0.0342268 + 0.0471091i
\(430\) 0 0
\(431\) −18.7745 + 13.6405i −0.904335 + 0.657038i −0.939576 0.342341i \(-0.888780\pi\)
0.0352410 + 0.999379i \(0.488780\pi\)
\(432\) 0 0
\(433\) −5.81215 4.22278i −0.279314 0.202934i 0.439304 0.898338i \(-0.355225\pi\)
−0.718618 + 0.695405i \(0.755225\pi\)
\(434\) 0 0
\(435\) −34.1683 + 24.8247i −1.63824 + 1.19025i
\(436\) 0 0
\(437\) 0.342556i 0.0163867i
\(438\) 0 0
\(439\) −9.36014 + 3.04130i −0.446735 + 0.145153i −0.523741 0.851878i \(-0.675464\pi\)
0.0770057 + 0.997031i \(0.475464\pi\)
\(440\) 0 0
\(441\) 0.685755 2.11054i 0.0326550 0.100502i
\(442\) 0 0
\(443\) 10.9339 33.6511i 0.519486 1.59881i −0.255482 0.966814i \(-0.582234\pi\)
0.774968 0.632000i \(-0.217766\pi\)
\(444\) 0 0
\(445\) 20.8953 28.7600i 0.990534 1.36335i
\(446\) 0 0
\(447\) 0.159340 + 0.490399i 0.00753653 + 0.0231951i
\(448\) 0 0
\(449\) 14.0963 + 10.2415i 0.665243 + 0.483328i 0.868430 0.495813i \(-0.165130\pi\)
−0.203186 + 0.979140i \(0.565130\pi\)
\(450\) 0 0
\(451\) −0.640801 + 0.953151i −0.0301741 + 0.0448821i
\(452\) 0 0
\(453\) −6.76634 4.91603i −0.317910 0.230975i
\(454\) 0 0
\(455\) −3.39302 10.4426i −0.159067 0.489559i
\(456\) 0 0
\(457\) −13.8422 + 19.0521i −0.647509 + 0.891220i −0.998988 0.0449757i \(-0.985679\pi\)
0.351479 + 0.936196i \(0.385679\pi\)
\(458\) 0 0
\(459\) −1.27522 + 3.92472i −0.0595222 + 0.183190i
\(460\) 0 0
\(461\) 0.867571 2.67011i 0.0404068 0.124359i −0.928818 0.370536i \(-0.879174\pi\)
0.969225 + 0.246176i \(0.0791742\pi\)
\(462\) 0 0
\(463\) 21.9126 7.11984i 1.01837 0.330887i 0.248185 0.968713i \(-0.420166\pi\)
0.770181 + 0.637826i \(0.220166\pi\)
\(464\) 0 0
\(465\) 39.5483i 1.83401i
\(466\) 0 0
\(467\) −18.8079 + 13.6647i −0.870325 + 0.632328i −0.930674 0.365849i \(-0.880779\pi\)
0.0603491 + 0.998177i \(0.480779\pi\)
\(468\) 0 0
\(469\) 3.26887 + 2.37497i 0.150942 + 0.109666i
\(470\) 0 0
\(471\) −14.1353 + 10.2699i −0.651318 + 0.473210i
\(472\) 0 0
\(473\) 0.101706 + 0.139986i 0.00467643 + 0.00643655i
\(474\) 0 0
\(475\) 3.44566 + 1.11956i 0.158098 + 0.0513691i
\(476\) 0 0
\(477\) 24.1022 7.83129i 1.10357 0.358570i
\(478\) 0 0
\(479\) −6.56209 + 9.03194i −0.299829 + 0.412680i −0.932176 0.362006i \(-0.882092\pi\)
0.632346 + 0.774686i \(0.282092\pi\)
\(480\) 0 0
\(481\) −10.8945 3.53984i −0.496747 0.161403i
\(482\) 0 0
\(483\) −1.92620 −0.0876452
\(484\) 0 0
\(485\) −4.12476 5.67725i −0.187296 0.257791i
\(486\) 0 0
\(487\) −8.97216 27.6135i −0.406567 1.25129i −0.919579 0.392904i \(-0.871470\pi\)
0.513012 0.858381i \(-0.328530\pi\)
\(488\) 0 0
\(489\) 33.5691i 1.51805i
\(490\) 0 0
\(491\) −0.754777 −0.0340626 −0.0170313 0.999855i \(-0.505421\pi\)
−0.0170313 + 0.999855i \(0.505421\pi\)
\(492\) 0 0
\(493\) 11.4636 0.516295
\(494\) 0 0
\(495\) 1.48496i 0.0667441i
\(496\) 0 0
\(497\) −0.252084 0.775836i −0.0113075 0.0348010i
\(498\) 0 0
\(499\) −15.7563 21.6867i −0.705349 0.970830i −0.999885 0.0151895i \(-0.995165\pi\)
0.294535 0.955641i \(-0.404835\pi\)
\(500\) 0 0
\(501\) −8.69312 −0.388380
\(502\) 0 0
\(503\) −18.4766 6.00341i −0.823830 0.267679i −0.133386 0.991064i \(-0.542585\pi\)
−0.690444 + 0.723386i \(0.742585\pi\)
\(504\) 0 0
\(505\) −21.3468 + 29.3813i −0.949918 + 1.30745i
\(506\) 0 0
\(507\) −9.42388 + 3.06200i −0.418529 + 0.135988i
\(508\) 0 0
\(509\) −31.2628 10.1579i −1.38570 0.450241i −0.481162 0.876632i \(-0.659785\pi\)
−0.904539 + 0.426391i \(0.859785\pi\)
\(510\) 0 0
\(511\) 7.80452 + 10.7420i 0.345252 + 0.475198i
\(512\) 0 0
\(513\) 0.586348 0.426007i 0.0258879 0.0188087i
\(514\) 0 0
\(515\) 21.4009 + 15.5486i 0.943035 + 0.685155i
\(516\) 0 0
\(517\) −1.91828 + 1.39372i −0.0843661 + 0.0612955i
\(518\) 0 0
\(519\) 3.83988i 0.168552i
\(520\) 0 0
\(521\) −29.8695 + 9.70518i −1.30860 + 0.425192i −0.878567 0.477619i \(-0.841500\pi\)
−0.430038 + 0.902811i \(0.641500\pi\)
\(522\) 0 0
\(523\) −11.4946 + 35.3767i −0.502623 + 1.54691i 0.302108 + 0.953274i \(0.402310\pi\)
−0.804731 + 0.593640i \(0.797690\pi\)
\(524\) 0 0
\(525\) 6.29533 19.3750i 0.274751 0.845595i
\(526\) 0 0
\(527\) 6.30962 8.68445i 0.274851 0.378300i
\(528\) 0 0
\(529\) −6.88771 21.1982i −0.299466 0.921661i
\(530\) 0 0
\(531\) 2.79591 + 2.03135i 0.121332 + 0.0881530i
\(532\) 0 0
\(533\) 11.6253 + 14.8331i 0.503547 + 0.642494i
\(534\) 0 0
\(535\) 3.56733 + 2.59182i 0.154229 + 0.112054i
\(536\) 0 0
\(537\) 0.543608 + 1.67305i 0.0234584 + 0.0721976i
\(538\) 0 0
\(539\) 0.105431 0.145114i 0.00454124 0.00625049i
\(540\) 0 0
\(541\) 8.04716 24.7666i 0.345974 1.06480i −0.615086 0.788460i \(-0.710879\pi\)
0.961060 0.276339i \(-0.0891214\pi\)
\(542\) 0 0
\(543\) −4.30993 + 13.2646i −0.184957 + 0.569239i
\(544\) 0 0
\(545\) −65.3264 + 21.2258i −2.79828 + 0.909215i
\(546\) 0 0
\(547\) 22.1714i 0.947981i 0.880530 + 0.473990i \(0.157187\pi\)
−0.880530 + 0.473990i \(0.842813\pi\)
\(548\) 0 0
\(549\) −3.99514 + 2.90264i −0.170508 + 0.123882i
\(550\) 0 0
\(551\) −1.62883 1.18341i −0.0693903 0.0504150i
\(552\) 0 0
\(553\) 6.48946 4.71487i 0.275960 0.200497i
\(554\) 0 0
\(555\) −19.4972 26.8356i −0.827611 1.13911i
\(556\) 0 0
\(557\) 0.936148 + 0.304173i 0.0396659 + 0.0128882i 0.328783 0.944406i \(-0.393362\pi\)
−0.289117 + 0.957294i \(0.593362\pi\)
\(558\) 0 0
\(559\) 2.70027 0.877372i 0.114209 0.0371089i
\(560\) 0 0
\(561\) 0.557190 0.766907i 0.0235246 0.0323788i
\(562\) 0 0
\(563\) 38.0456 + 12.3618i 1.60343 + 0.520986i 0.967953 0.251132i \(-0.0808029\pi\)
0.635478 + 0.772119i \(0.280803\pi\)
\(564\) 0 0
\(565\) −22.8471 −0.961183
\(566\) 0 0
\(567\) −6.30860 8.68304i −0.264936 0.364653i
\(568\) 0 0
\(569\) 5.02089 + 15.4527i 0.210486 + 0.647811i 0.999443 + 0.0333622i \(0.0106215\pi\)
−0.788957 + 0.614449i \(0.789379\pi\)
\(570\) 0 0
\(571\) 8.72115i 0.364969i 0.983209 + 0.182484i \(0.0584139\pi\)
−0.983209 + 0.182484i \(0.941586\pi\)
\(572\) 0 0
\(573\) 55.7158 2.32756
\(574\) 0 0
\(575\) −7.51862 −0.313548
\(576\) 0 0
\(577\) 11.3683i 0.473269i −0.971599 0.236634i \(-0.923956\pi\)
0.971599 0.236634i \(-0.0760443\pi\)
\(578\) 0 0
\(579\) −3.40594 10.4824i −0.141546 0.435633i
\(580\) 0 0
\(581\) −8.39727 11.5579i −0.348377 0.479500i
\(582\) 0 0
\(583\) 2.04840 0.0848361
\(584\) 0 0
\(585\) 23.1738 + 7.52962i 0.958118 + 0.311311i
\(586\) 0 0
\(587\) −11.4326 + 15.7357i −0.471876 + 0.649481i −0.976918 0.213613i \(-0.931477\pi\)
0.505043 + 0.863094i \(0.331477\pi\)
\(588\) 0 0
\(589\) −1.79302 + 0.582589i −0.0738803 + 0.0240052i
\(590\) 0 0
\(591\) 29.9010 + 9.71544i 1.22996 + 0.399640i
\(592\) 0 0
\(593\) 16.3478 + 22.5007i 0.671322 + 0.923995i 0.999789 0.0205202i \(-0.00653223\pi\)
−0.328468 + 0.944515i \(0.606532\pi\)
\(594\) 0 0
\(595\) −6.98185 + 5.07261i −0.286228 + 0.207957i
\(596\) 0 0
\(597\) 23.0473 + 16.7448i 0.943262 + 0.685320i
\(598\) 0 0
\(599\) −23.2031 + 16.8580i −0.948053 + 0.688801i −0.950346 0.311196i \(-0.899270\pi\)
0.00229229 + 0.999997i \(0.499270\pi\)
\(600\) 0 0
\(601\) 34.0639i 1.38950i 0.719253 + 0.694748i \(0.244484\pi\)
−0.719253 + 0.694748i \(0.755516\pi\)
\(602\) 0 0
\(603\) −8.52772 + 2.77082i −0.347276 + 0.112837i
\(604\) 0 0
\(605\) 12.6439 38.9139i 0.514048 1.58208i
\(606\) 0 0
\(607\) 9.98901 30.7430i 0.405441 1.24782i −0.515085 0.857139i \(-0.672240\pi\)
0.920526 0.390681i \(-0.127760\pi\)
\(608\) 0 0
\(609\) −6.65435 + 9.15893i −0.269648 + 0.371139i
\(610\) 0 0
\(611\) 12.0230 + 37.0030i 0.486399 + 1.49698i
\(612\) 0 0
\(613\) −1.32095 0.959724i −0.0533525 0.0387629i 0.560789 0.827959i \(-0.310498\pi\)
−0.614142 + 0.789196i \(0.710498\pi\)
\(614\) 0 0
\(615\) 1.98752 + 54.5358i 0.0801444 + 2.19910i
\(616\) 0 0
\(617\) 2.95859 + 2.14954i 0.119108 + 0.0865374i 0.645745 0.763553i \(-0.276547\pi\)
−0.526636 + 0.850091i \(0.676547\pi\)
\(618\) 0 0
\(619\) 4.24265 + 13.0575i 0.170526 + 0.524826i 0.999401 0.0346084i \(-0.0110184\pi\)
−0.828875 + 0.559434i \(0.811018\pi\)
\(620\) 0 0
\(621\) −0.884074 + 1.21682i −0.0354767 + 0.0488294i
\(622\) 0 0
\(623\) 2.94466 9.06272i 0.117975 0.363090i
\(624\) 0 0
\(625\) 3.06930 9.44632i 0.122772 0.377853i
\(626\) 0 0
\(627\) −0.158339 + 0.0514473i −0.00632343 + 0.00205461i
\(628\) 0 0
\(629\) 9.00349i 0.358992i
\(630\) 0 0
\(631\) −11.6797 + 8.48579i −0.464961 + 0.337814i −0.795474 0.605988i \(-0.792778\pi\)
0.330513 + 0.943801i \(0.392778\pi\)
\(632\) 0 0
\(633\) −1.32686 0.964022i −0.0527380 0.0383164i
\(634\) 0 0
\(635\) −13.8549 + 10.0662i −0.549816 + 0.399464i
\(636\) 0 0
\(637\) −1.72999 2.38113i −0.0685448 0.0943438i
\(638\) 0 0
\(639\) 1.72170 + 0.559413i 0.0681092 + 0.0221300i
\(640\) 0 0
\(641\) −35.4448 + 11.5167i −1.39998 + 0.454883i −0.909186 0.416390i \(-0.863295\pi\)
−0.490799 + 0.871273i \(0.663295\pi\)
\(642\) 0 0
\(643\) 4.46353 6.14353i 0.176025 0.242277i −0.711884 0.702297i \(-0.752158\pi\)
0.887908 + 0.460020i \(0.152158\pi\)
\(644\) 0 0
\(645\) 7.81916 + 2.54060i 0.307879 + 0.100036i
\(646\) 0 0
\(647\) −11.9327 −0.469123 −0.234562 0.972101i \(-0.575365\pi\)
−0.234562 + 0.972101i \(0.575365\pi\)
\(648\) 0 0
\(649\) 0.164191 + 0.225989i 0.00644505 + 0.00887085i
\(650\) 0 0
\(651\) 3.27591 + 10.0822i 0.128393 + 0.395153i
\(652\) 0 0
\(653\) 40.5099i 1.58527i −0.609694 0.792637i \(-0.708708\pi\)
0.609694 0.792637i \(-0.291292\pi\)
\(654\) 0 0
\(655\) 26.7120 1.04372
\(656\) 0 0
\(657\) −29.4655 −1.14956
\(658\) 0 0
\(659\) 45.8040i 1.78427i 0.451769 + 0.892135i \(0.350793\pi\)
−0.451769 + 0.892135i \(0.649207\pi\)
\(660\) 0 0
\(661\) −7.70088 23.7009i −0.299530 0.921858i −0.981662 0.190629i \(-0.938947\pi\)
0.682132 0.731229i \(-0.261053\pi\)
\(662\) 0 0
\(663\) −9.14279 12.5840i −0.355077 0.488721i
\(664\) 0 0
\(665\) 1.51568 0.0587757
\(666\) 0 0
\(667\) 3.97370 + 1.29113i 0.153862 + 0.0499929i
\(668\) 0 0
\(669\) −3.28787 + 4.52537i −0.127117 + 0.174961i
\(670\) 0 0
\(671\) −0.379616 + 0.123345i −0.0146549 + 0.00476167i
\(672\) 0 0
\(673\) −43.7580 14.2178i −1.68675 0.548057i −0.700546 0.713608i \(-0.747060\pi\)
−0.986201 + 0.165550i \(0.947060\pi\)
\(674\) 0 0
\(675\) −9.35024 12.8695i −0.359891 0.495347i
\(676\) 0 0
\(677\) 8.90078 6.46679i 0.342085 0.248539i −0.403456 0.914999i \(-0.632191\pi\)
0.745541 + 0.666460i \(0.232191\pi\)
\(678\) 0 0
\(679\) −1.52181 1.10566i −0.0584016 0.0424312i
\(680\) 0 0
\(681\) −38.2860 + 27.8164i −1.46712 + 1.06593i
\(682\) 0 0
\(683\) 37.0709i 1.41848i −0.704967 0.709240i \(-0.749038\pi\)
0.704967 0.709240i \(-0.250962\pi\)
\(684\) 0 0
\(685\) −68.0669 + 22.1163i −2.60070 + 0.845020i
\(686\) 0 0
\(687\) −12.3950 + 38.1479i −0.472899 + 1.45543i
\(688\) 0 0
\(689\) 10.3866 31.9666i 0.395697 1.21783i
\(690\) 0 0
\(691\) 23.0765 31.7620i 0.877870 1.20828i −0.0991365 0.995074i \(-0.531608\pi\)
0.977006 0.213210i \(-0.0683920\pi\)
\(692\) 0 0
\(693\) 0.123004 + 0.378567i 0.00467254 + 0.0143806i
\(694\) 0 0
\(695\) 52.4087 + 38.0772i 1.98798 + 1.44435i
\(696\) 0 0
\(697\) 8.26432 12.2927i 0.313033 0.465618i
\(698\) 0 0
\(699\) −17.7960 12.9296i −0.673107 0.489041i
\(700\) 0 0
\(701\) −12.1727 37.4636i −0.459755 1.41498i −0.865460 0.500977i \(-0.832974\pi\)
0.405705 0.914004i \(-0.367026\pi\)
\(702\) 0 0
\(703\) 0.929447 1.27927i 0.0350548 0.0482488i
\(704\) 0 0
\(705\) −34.8149 + 107.149i −1.31121 + 4.03548i
\(706\) 0 0
\(707\) −3.00827 + 9.25851i −0.113138 + 0.348202i
\(708\) 0 0
\(709\) −2.96481 + 0.963326i −0.111346 + 0.0361785i −0.364160 0.931336i \(-0.618644\pi\)
0.252814 + 0.967515i \(0.418644\pi\)
\(710\) 0 0
\(711\) 17.8007i 0.667579i
\(712\) 0 0
\(713\) 3.16526 2.29970i 0.118540 0.0861243i
\(714\) 0 0
\(715\) 1.59335 + 1.15764i 0.0595880 + 0.0432932i
\(716\) 0 0
\(717\) 11.0034 7.99442i 0.410929 0.298557i
\(718\) 0 0
\(719\) 10.1144 + 13.9213i 0.377205 + 0.519178i 0.954841 0.297116i \(-0.0960249\pi\)
−0.577637 + 0.816294i \(0.696025\pi\)
\(720\) 0 0
\(721\) 6.74375 + 2.19118i 0.251151 + 0.0816037i
\(722\) 0 0
\(723\) −40.4855 + 13.1545i −1.50567 + 0.489222i
\(724\) 0 0
\(725\) −25.9742 + 35.7504i −0.964657 + 1.32774i
\(726\) 0 0
\(727\) 40.2148 + 13.0666i 1.49149 + 0.484613i 0.937522 0.347927i \(-0.113114\pi\)
0.553964 + 0.832540i \(0.313114\pi\)
\(728\) 0 0
\(729\) 11.5916 0.429319
\(730\) 0 0
\(731\) −1.31168 1.80538i −0.0485144 0.0667743i
\(732\) 0 0
\(733\) −6.79748 20.9205i −0.251070 0.772715i −0.994579 0.103988i \(-0.966839\pi\)
0.743508 0.668727i \(-0.233161\pi\)
\(734\) 0 0
\(735\) 8.52272i 0.314365i
\(736\) 0 0
\(737\) −0.724754 −0.0266967
\(738\) 0 0
\(739\) −18.0296 −0.663230 −0.331615 0.943415i \(-0.607593\pi\)
−0.331615 + 0.943415i \(0.607593\pi\)
\(740\) 0 0
\(741\) 2.73184i 0.100357i
\(742\) 0 0
\(743\) −15.5792 47.9477i −0.571544 1.75903i −0.647657 0.761932i \(-0.724251\pi\)
0.0761131 0.997099i \(-0.475749\pi\)
\(744\) 0 0
\(745\) 0.494926 + 0.681207i 0.0181327 + 0.0249575i
\(746\) 0 0
\(747\) 31.7034 1.15997
\(748\) 0 0
\(749\) 1.12412 + 0.365249i 0.0410745 + 0.0133459i
\(750\) 0 0
\(751\) 28.3366 39.0020i 1.03402 1.42320i 0.132131 0.991232i \(-0.457818\pi\)
0.901887 0.431971i \(-0.142182\pi\)
\(752\) 0 0
\(753\) −37.1624 + 12.0748i −1.35427 + 0.440030i
\(754\) 0 0
\(755\) −12.9892 4.22043i −0.472724 0.153597i
\(756\) 0 0
\(757\) 3.34972 + 4.61050i 0.121748 + 0.167571i 0.865541 0.500839i \(-0.166975\pi\)
−0.743793 + 0.668410i \(0.766975\pi\)
\(758\) 0 0
\(759\) 0.279518 0.203082i 0.0101459 0.00737140i
\(760\) 0 0
\(761\) −21.8766 15.8943i −0.793027 0.576168i 0.115833 0.993269i \(-0.463046\pi\)
−0.908860 + 0.417101i \(0.863046\pi\)
\(762\) 0 0
\(763\) −14.8957 + 10.8224i −0.539262 + 0.391797i
\(764\) 0 0
\(765\) 19.1513i 0.692419i
\(766\) 0 0
\(767\) 4.35924 1.41640i 0.157403 0.0511434i
\(768\) 0 0
\(769\) 14.0293 43.1776i 0.505908 1.55702i −0.293331 0.956011i \(-0.594764\pi\)
0.799239 0.601014i \(-0.205236\pi\)
\(770\) 0 0
\(771\) −14.5882 + 44.8980i −0.525382 + 1.61696i
\(772\) 0 0
\(773\) 19.8092 27.2650i 0.712486 0.980653i −0.287254 0.957854i \(-0.592742\pi\)
0.999740 0.0227982i \(-0.00725751\pi\)
\(774\) 0 0
\(775\) 12.7870 + 39.3543i 0.459322 + 1.41365i
\(776\) 0 0
\(777\) −7.19339 5.22630i −0.258061 0.187493i
\(778\) 0 0
\(779\) −2.44324 + 0.893480i −0.0875383 + 0.0320122i
\(780\) 0 0
\(781\) 0.118378 + 0.0860068i 0.00423590 + 0.00307756i
\(782\) 0 0
\(783\) 2.73173 + 8.40740i 0.0976240 + 0.300456i
\(784\) 0 0
\(785\) −16.7704 + 23.0825i −0.598561 + 0.823848i
\(786\) 0 0
\(787\) −0.537568 + 1.65446i −0.0191622 + 0.0589753i −0.960180 0.279381i \(-0.909871\pi\)
0.941018 + 0.338356i \(0.109871\pi\)
\(788\) 0 0
\(789\) −3.19859 + 9.84424i −0.113873 + 0.350464i
\(790\) 0 0
\(791\) −5.82449 + 1.89249i −0.207095 + 0.0672893i
\(792\) 0 0
\(793\) 6.54958i 0.232583i
\(794\) 0 0
\(795\) 78.7409 57.2086i 2.79265 2.02898i
\(796\) 0 0
\(797\) −27.5997 20.0524i −0.977632 0.710292i