Properties

Label 280.2.bo.a.17.5
Level $280$
Weight $2$
Character 280.17
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 17.5
Character \(\chi\) \(=\) 280.17
Dual form 280.2.bo.a.33.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16710 + 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(-2.59977 + 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +O(q^{10})\) \(q+(-1.16710 + 0.312724i) q^{3} +(-0.121837 - 2.23275i) q^{5} +(-2.59977 + 0.491095i) q^{7} +(-1.33374 + 0.770036i) q^{9} +(-1.67933 + 2.90869i) q^{11} +(-2.92389 - 2.92389i) q^{13} +(0.840431 + 2.56774i) q^{15} +(0.0694548 + 0.259209i) q^{17} +(-0.458405 - 0.793981i) q^{19} +(2.88063 - 1.38617i) q^{21} +(-7.58021 - 2.03111i) q^{23} +(-4.97031 + 0.544063i) q^{25} +(3.87894 - 3.87894i) q^{27} -1.31878i q^{29} +(3.25671 + 1.88026i) q^{31} +(1.05034 - 3.91991i) q^{33} +(1.41324 + 5.74480i) q^{35} +(2.11773 - 7.90347i) q^{37} +(4.32685 + 2.49811i) q^{39} +5.65819i q^{41} +(-2.61631 + 2.61631i) q^{43} +(1.88180 + 2.88409i) q^{45} +(-0.911807 - 0.244318i) q^{47} +(6.51765 - 2.55347i) q^{49} +(-0.162122 - 0.280803i) q^{51} +(3.49525 + 13.0444i) q^{53} +(6.69897 + 3.39514i) q^{55} +(0.783303 + 0.783303i) q^{57} +(3.91972 - 6.78916i) q^{59} +(9.70077 - 5.60074i) q^{61} +(3.08927 - 2.65691i) q^{63} +(-6.17206 + 6.88454i) q^{65} +(5.37983 - 1.44152i) q^{67} +9.48206 q^{69} -13.5245 q^{71} +(-7.33366 + 1.96505i) q^{73} +(5.63073 - 2.18932i) q^{75} +(2.93744 - 8.38665i) q^{77} +(-1.87245 + 1.08106i) q^{79} +(-1.00398 + 1.73894i) q^{81} +(-5.49970 - 5.49970i) q^{83} +(0.570285 - 0.186656i) q^{85} +(0.412415 + 1.53915i) q^{87} +(-1.34818 - 2.33512i) q^{89} +(9.03736 + 6.16554i) q^{91} +(-4.38892 - 1.17601i) q^{93} +(-1.71691 + 1.12024i) q^{95} +(-10.1018 + 10.1018i) q^{97} -5.17259i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −1.16710 + 0.312724i −0.673828 + 0.180552i −0.579478 0.814988i \(-0.696744\pi\)
−0.0943492 + 0.995539i \(0.530077\pi\)
\(4\) 0 0
\(5\) −0.121837 2.23275i −0.0544873 0.998514i
\(6\) 0 0
\(7\) −2.59977 + 0.491095i −0.982622 + 0.185617i
\(8\) 0 0
\(9\) −1.33374 + 0.770036i −0.444581 + 0.256679i
\(10\) 0 0
\(11\) −1.67933 + 2.90869i −0.506338 + 0.877003i 0.493635 + 0.869669i \(0.335668\pi\)
−0.999973 + 0.00733373i \(0.997666\pi\)
\(12\) 0 0
\(13\) −2.92389 2.92389i −0.810941 0.810941i 0.173834 0.984775i \(-0.444384\pi\)
−0.984775 + 0.173834i \(0.944384\pi\)
\(14\) 0 0
\(15\) 0.840431 + 2.56774i 0.216998 + 0.662989i
\(16\) 0 0
\(17\) 0.0694548 + 0.259209i 0.0168453 + 0.0628674i 0.973837 0.227248i \(-0.0729729\pi\)
−0.956992 + 0.290116i \(0.906306\pi\)
\(18\) 0 0
\(19\) −0.458405 0.793981i −0.105165 0.182152i 0.808640 0.588303i \(-0.200204\pi\)
−0.913806 + 0.406152i \(0.866871\pi\)
\(20\) 0 0
\(21\) 2.88063 1.38617i 0.628605 0.302488i
\(22\) 0 0
\(23\) −7.58021 2.03111i −1.58058 0.423516i −0.641476 0.767143i \(-0.721678\pi\)
−0.939106 + 0.343627i \(0.888344\pi\)
\(24\) 0 0
\(25\) −4.97031 + 0.544063i −0.994062 + 0.108813i
\(26\) 0 0
\(27\) 3.87894 3.87894i 0.746503 0.746503i
\(28\) 0 0
\(29\) 1.31878i 0.244892i −0.992475 0.122446i \(-0.960926\pi\)
0.992475 0.122446i \(-0.0390737\pi\)
\(30\) 0 0
\(31\) 3.25671 + 1.88026i 0.584923 + 0.337705i 0.763087 0.646295i \(-0.223683\pi\)
−0.178165 + 0.984001i \(0.557016\pi\)
\(32\) 0 0
\(33\) 1.05034 3.91991i 0.182840 0.682369i
\(34\) 0 0
\(35\) 1.41324 + 5.74480i 0.238881 + 0.971049i
\(36\) 0 0
\(37\) 2.11773 7.90347i 0.348153 1.29932i −0.540733 0.841194i \(-0.681853\pi\)
0.888886 0.458129i \(-0.151480\pi\)
\(38\) 0 0
\(39\) 4.32685 + 2.49811i 0.692851 + 0.400018i
\(40\) 0 0
\(41\) 5.65819i 0.883661i 0.897098 + 0.441831i \(0.145671\pi\)
−0.897098 + 0.441831i \(0.854329\pi\)
\(42\) 0 0
\(43\) −2.61631 + 2.61631i −0.398984 + 0.398984i −0.877875 0.478891i \(-0.841039\pi\)
0.478891 + 0.877875i \(0.341039\pi\)
\(44\) 0 0
\(45\) 1.88180 + 2.88409i 0.280521 + 0.429934i
\(46\) 0 0
\(47\) −0.911807 0.244318i −0.133001 0.0356374i 0.191705 0.981453i \(-0.438598\pi\)
−0.324705 + 0.945815i \(0.605265\pi\)
\(48\) 0 0
\(49\) 6.51765 2.55347i 0.931093 0.364782i
\(50\) 0 0
\(51\) −0.162122 0.280803i −0.0227016 0.0393203i
\(52\) 0 0
\(53\) 3.49525 + 13.0444i 0.480109 + 1.79179i 0.601140 + 0.799144i \(0.294713\pi\)
−0.121031 + 0.992649i \(0.538620\pi\)
\(54\) 0 0
\(55\) 6.69897 + 3.39514i 0.903289 + 0.457800i
\(56\) 0 0
\(57\) 0.783303 + 0.783303i 0.103751 + 0.103751i
\(58\) 0 0
\(59\) 3.91972 6.78916i 0.510304 0.883873i −0.489624 0.871933i \(-0.662866\pi\)
0.999929 0.0119396i \(-0.00380059\pi\)
\(60\) 0 0
\(61\) 9.70077 5.60074i 1.24206 0.717102i 0.272544 0.962143i \(-0.412135\pi\)
0.969513 + 0.245042i \(0.0788017\pi\)
\(62\) 0 0
\(63\) 3.08927 2.65691i 0.389211 0.334740i
\(64\) 0 0
\(65\) −6.17206 + 6.88454i −0.765550 + 0.853922i
\(66\) 0 0
\(67\) 5.37983 1.44152i 0.657251 0.176110i 0.0852461 0.996360i \(-0.472832\pi\)
0.572005 + 0.820250i \(0.306166\pi\)
\(68\) 0 0
\(69\) 9.48206 1.14151
\(70\) 0 0
\(71\) −13.5245 −1.60506 −0.802532 0.596609i \(-0.796514\pi\)
−0.802532 + 0.596609i \(0.796514\pi\)
\(72\) 0 0
\(73\) −7.33366 + 1.96505i −0.858340 + 0.229992i −0.661039 0.750351i \(-0.729884\pi\)
−0.197301 + 0.980343i \(0.563218\pi\)
\(74\) 0 0
\(75\) 5.63073 2.18932i 0.650180 0.252800i
\(76\) 0 0
\(77\) 2.93744 8.38665i 0.334753 0.955747i
\(78\) 0 0
\(79\) −1.87245 + 1.08106i −0.210667 + 0.121629i −0.601621 0.798781i \(-0.705478\pi\)
0.390954 + 0.920410i \(0.372145\pi\)
\(80\) 0 0
\(81\) −1.00398 + 1.73894i −0.111553 + 0.193216i
\(82\) 0 0
\(83\) −5.49970 5.49970i −0.603671 0.603671i 0.337614 0.941285i \(-0.390380\pi\)
−0.941285 + 0.337614i \(0.890380\pi\)
\(84\) 0 0
\(85\) 0.570285 0.186656i 0.0618561 0.0202457i
\(86\) 0 0
\(87\) 0.412415 + 1.53915i 0.0442155 + 0.165015i
\(88\) 0 0
\(89\) −1.34818 2.33512i −0.142907 0.247523i 0.785683 0.618629i \(-0.212312\pi\)
−0.928590 + 0.371107i \(0.878978\pi\)
\(90\) 0 0
\(91\) 9.03736 + 6.16554i 0.947372 + 0.646324i
\(92\) 0 0
\(93\) −4.38892 1.17601i −0.455110 0.121946i
\(94\) 0 0
\(95\) −1.71691 + 1.12024i −0.176151 + 0.114934i
\(96\) 0 0
\(97\) −10.1018 + 10.1018i −1.02568 + 1.02568i −0.0260207 + 0.999661i \(0.508284\pi\)
−0.999661 + 0.0260207i \(0.991716\pi\)
\(98\) 0 0
\(99\) 5.17259i 0.519865i
\(100\) 0 0
\(101\) −14.7714 8.52827i −1.46981 0.848594i −0.470382 0.882463i \(-0.655884\pi\)
−0.999426 + 0.0338687i \(0.989217\pi\)
\(102\) 0 0
\(103\) 4.62827 17.2729i 0.456037 1.70195i −0.228985 0.973430i \(-0.573541\pi\)
0.685022 0.728522i \(-0.259793\pi\)
\(104\) 0 0
\(105\) −3.44594 6.26282i −0.336289 0.611189i
\(106\) 0 0
\(107\) 2.05577 7.67224i 0.198739 0.741703i −0.792528 0.609835i \(-0.791236\pi\)
0.991267 0.131868i \(-0.0420976\pi\)
\(108\) 0 0
\(109\) 12.5649 + 7.25433i 1.20350 + 0.694839i 0.961331 0.275396i \(-0.0888089\pi\)
0.242166 + 0.970235i \(0.422142\pi\)
\(110\) 0 0
\(111\) 9.88644i 0.938379i
\(112\) 0 0
\(113\) −5.46472 + 5.46472i −0.514078 + 0.514078i −0.915773 0.401696i \(-0.868421\pi\)
0.401696 + 0.915773i \(0.368421\pi\)
\(114\) 0 0
\(115\) −3.61140 + 17.1721i −0.336765 + 1.60131i
\(116\) 0 0
\(117\) 6.15121 + 1.64821i 0.568680 + 0.152377i
\(118\) 0 0
\(119\) −0.307863 0.639775i −0.0282217 0.0586481i
\(120\) 0 0
\(121\) −0.140314 0.243031i −0.0127558 0.0220938i
\(122\) 0 0
\(123\) −1.76946 6.60370i −0.159546 0.595435i
\(124\) 0 0
\(125\) 1.82032 + 11.0312i 0.162815 + 0.986657i
\(126\) 0 0
\(127\) 4.91615 + 4.91615i 0.436238 + 0.436238i 0.890744 0.454506i \(-0.150184\pi\)
−0.454506 + 0.890744i \(0.650184\pi\)
\(128\) 0 0
\(129\) 2.23532 3.87169i 0.196809 0.340884i
\(130\) 0 0
\(131\) −11.7319 + 6.77343i −1.02502 + 0.591797i −0.915555 0.402193i \(-0.868248\pi\)
−0.109468 + 0.993990i \(0.534915\pi\)
\(132\) 0 0
\(133\) 1.58167 + 1.83905i 0.137148 + 0.159466i
\(134\) 0 0
\(135\) −9.13330 8.18810i −0.786069 0.704719i
\(136\) 0 0
\(137\) −14.9165 + 3.99687i −1.27441 + 0.341476i −0.831717 0.555200i \(-0.812642\pi\)
−0.442688 + 0.896676i \(0.645975\pi\)
\(138\) 0 0
\(139\) −10.4513 −0.886472 −0.443236 0.896405i \(-0.646170\pi\)
−0.443236 + 0.896405i \(0.646170\pi\)
\(140\) 0 0
\(141\) 1.14058 0.0960540
\(142\) 0 0
\(143\) 13.4149 3.59450i 1.12181 0.300587i
\(144\) 0 0
\(145\) −2.94450 + 0.160677i −0.244528 + 0.0133435i
\(146\) 0 0
\(147\) −6.80824 + 5.01840i −0.561534 + 0.413910i
\(148\) 0 0
\(149\) −13.7158 + 7.91884i −1.12364 + 0.648737i −0.942329 0.334688i \(-0.891369\pi\)
−0.181316 + 0.983425i \(0.558036\pi\)
\(150\) 0 0
\(151\) 8.90977 15.4322i 0.725067 1.25585i −0.233880 0.972265i \(-0.575142\pi\)
0.958947 0.283587i \(-0.0915244\pi\)
\(152\) 0 0
\(153\) −0.292235 0.292235i −0.0236258 0.0236258i
\(154\) 0 0
\(155\) 3.80136 7.50050i 0.305333 0.602454i
\(156\) 0 0
\(157\) −2.38891 8.91553i −0.190656 0.711537i −0.993349 0.115144i \(-0.963267\pi\)
0.802693 0.596392i \(-0.203400\pi\)
\(158\) 0 0
\(159\) −8.15863 14.1312i −0.647022 1.12067i
\(160\) 0 0
\(161\) 20.7043 + 1.55783i 1.63173 + 0.122774i
\(162\) 0 0
\(163\) −8.96978 2.40344i −0.702567 0.188252i −0.110187 0.993911i \(-0.535145\pi\)
−0.592380 + 0.805659i \(0.701812\pi\)
\(164\) 0 0
\(165\) −8.88013 1.86754i −0.691317 0.145388i
\(166\) 0 0
\(167\) 2.96983 2.96983i 0.229812 0.229812i −0.582802 0.812614i \(-0.698044\pi\)
0.812614 + 0.582802i \(0.198044\pi\)
\(168\) 0 0
\(169\) 4.09824i 0.315250i
\(170\) 0 0
\(171\) 1.22279 + 0.705977i 0.0935089 + 0.0539874i
\(172\) 0 0
\(173\) −1.18201 + 4.41132i −0.0898665 + 0.335386i −0.996191 0.0871956i \(-0.972209\pi\)
0.906325 + 0.422582i \(0.138876\pi\)
\(174\) 0 0
\(175\) 12.6545 3.85534i 0.956590 0.291436i
\(176\) 0 0
\(177\) −2.45159 + 9.14944i −0.184272 + 0.687714i
\(178\) 0 0
\(179\) −7.21474 4.16543i −0.539255 0.311339i 0.205522 0.978653i \(-0.434111\pi\)
−0.744777 + 0.667313i \(0.767444\pi\)
\(180\) 0 0
\(181\) 19.1591i 1.42409i −0.702135 0.712043i \(-0.747770\pi\)
0.702135 0.712043i \(-0.252230\pi\)
\(182\) 0 0
\(183\) −9.57031 + 9.57031i −0.707458 + 0.707458i
\(184\) 0 0
\(185\) −17.9045 3.76541i −1.31636 0.276839i
\(186\) 0 0
\(187\) −0.870595 0.233275i −0.0636642 0.0170588i
\(188\) 0 0
\(189\) −8.17945 + 11.9893i −0.594967 + 0.872094i
\(190\) 0 0
\(191\) 2.27127 + 3.93396i 0.164344 + 0.284652i 0.936422 0.350876i \(-0.114116\pi\)
−0.772078 + 0.635527i \(0.780783\pi\)
\(192\) 0 0
\(193\) 2.32967 + 8.69445i 0.167693 + 0.625840i 0.997681 + 0.0680587i \(0.0216805\pi\)
−0.829988 + 0.557781i \(0.811653\pi\)
\(194\) 0 0
\(195\) 5.05047 9.96512i 0.361672 0.713617i
\(196\) 0 0
\(197\) 5.71540 + 5.71540i 0.407205 + 0.407205i 0.880763 0.473558i \(-0.157030\pi\)
−0.473558 + 0.880763i \(0.657030\pi\)
\(198\) 0 0
\(199\) −6.85652 + 11.8758i −0.486046 + 0.841856i −0.999871 0.0160388i \(-0.994894\pi\)
0.513826 + 0.857895i \(0.328228\pi\)
\(200\) 0 0
\(201\) −5.82803 + 3.36481i −0.411077 + 0.237336i
\(202\) 0 0
\(203\) 0.647647 + 3.42853i 0.0454559 + 0.240636i
\(204\) 0 0
\(205\) 12.6333 0.689379i 0.882349 0.0481483i
\(206\) 0 0
\(207\) 11.6741 3.12806i 0.811404 0.217415i
\(208\) 0 0
\(209\) 3.07926 0.212997
\(210\) 0 0
\(211\) −7.27456 −0.500802 −0.250401 0.968142i \(-0.580562\pi\)
−0.250401 + 0.968142i \(0.580562\pi\)
\(212\) 0 0
\(213\) 15.7845 4.22945i 1.08154 0.289797i
\(214\) 0 0
\(215\) 6.16033 + 5.52280i 0.420131 + 0.376652i
\(216\) 0 0
\(217\) −9.39010 3.28890i −0.637442 0.223265i
\(218\) 0 0
\(219\) 7.94462 4.58683i 0.536848 0.309949i
\(220\) 0 0
\(221\) 0.554819 0.960975i 0.0373212 0.0646422i
\(222\) 0 0
\(223\) 3.13514 + 3.13514i 0.209945 + 0.209945i 0.804244 0.594299i \(-0.202571\pi\)
−0.594299 + 0.804244i \(0.702571\pi\)
\(224\) 0 0
\(225\) 6.21016 4.55296i 0.414011 0.303531i
\(226\) 0 0
\(227\) 0.113469 + 0.423472i 0.00753121 + 0.0281069i 0.969589 0.244738i \(-0.0787020\pi\)
−0.962058 + 0.272845i \(0.912035\pi\)
\(228\) 0 0
\(229\) −6.98055 12.0907i −0.461288 0.798974i 0.537738 0.843112i \(-0.319279\pi\)
−0.999025 + 0.0441386i \(0.985946\pi\)
\(230\) 0 0
\(231\) −0.805590 + 10.7067i −0.0530039 + 0.704449i
\(232\) 0 0
\(233\) 10.7647 + 2.88438i 0.705217 + 0.188962i 0.593566 0.804785i \(-0.297720\pi\)
0.111651 + 0.993748i \(0.464386\pi\)
\(234\) 0 0
\(235\) −0.434408 + 2.06560i −0.0283377 + 0.134745i
\(236\) 0 0
\(237\) 1.84727 1.84727i 0.119993 0.119993i
\(238\) 0 0
\(239\) 2.45924i 0.159075i −0.996832 0.0795376i \(-0.974656\pi\)
0.996832 0.0795376i \(-0.0253444\pi\)
\(240\) 0 0
\(241\) −15.7270 9.07999i −1.01307 0.584893i −0.100978 0.994889i \(-0.532197\pi\)
−0.912088 + 0.409995i \(0.865530\pi\)
\(242\) 0 0
\(243\) −3.63144 + 13.5527i −0.232957 + 0.869407i
\(244\) 0 0
\(245\) −6.49535 14.2412i −0.414973 0.909834i
\(246\) 0 0
\(247\) −0.981186 + 3.66184i −0.0624314 + 0.232997i
\(248\) 0 0
\(249\) 8.13862 + 4.69883i 0.515764 + 0.297776i
\(250\) 0 0
\(251\) 12.5983i 0.795196i 0.917560 + 0.397598i \(0.130156\pi\)
−0.917560 + 0.397598i \(0.869844\pi\)
\(252\) 0 0
\(253\) 18.6376 18.6376i 1.17173 1.17173i
\(254\) 0 0
\(255\) −0.607210 + 0.396189i −0.0380250 + 0.0248103i
\(256\) 0 0
\(257\) 21.0068 + 5.62876i 1.31037 + 0.351113i 0.845362 0.534194i \(-0.179385\pi\)
0.465008 + 0.885306i \(0.346051\pi\)
\(258\) 0 0
\(259\) −1.62426 + 21.5872i −0.100927 + 1.34137i
\(260\) 0 0
\(261\) 1.01551 + 1.75891i 0.0628584 + 0.108874i
\(262\) 0 0
\(263\) 6.53630 + 24.3938i 0.403046 + 1.50419i 0.807632 + 0.589687i \(0.200749\pi\)
−0.404586 + 0.914500i \(0.632584\pi\)
\(264\) 0 0
\(265\) 28.6991 9.39330i 1.76297 0.577026i
\(266\) 0 0
\(267\) 2.30372 + 2.30372i 0.140985 + 0.140985i
\(268\) 0 0
\(269\) 4.20486 7.28303i 0.256375 0.444054i −0.708893 0.705316i \(-0.750805\pi\)
0.965268 + 0.261262i \(0.0841386\pi\)
\(270\) 0 0
\(271\) −6.55088 + 3.78215i −0.397938 + 0.229749i −0.685594 0.727984i \(-0.740457\pi\)
0.287656 + 0.957734i \(0.407124\pi\)
\(272\) 0 0
\(273\) −12.4756 4.36962i −0.755060 0.264462i
\(274\) 0 0
\(275\) 6.76429 15.3708i 0.407902 0.926891i
\(276\) 0 0
\(277\) −14.7982 + 3.96518i −0.889140 + 0.238244i −0.674347 0.738415i \(-0.735575\pi\)
−0.214794 + 0.976659i \(0.568908\pi\)
\(278\) 0 0
\(279\) −5.79148 −0.346727
\(280\) 0 0
\(281\) 24.6162 1.46848 0.734239 0.678891i \(-0.237539\pi\)
0.734239 + 0.678891i \(0.237539\pi\)
\(282\) 0 0
\(283\) 23.6426 6.33503i 1.40541 0.376578i 0.525125 0.851025i \(-0.324018\pi\)
0.880284 + 0.474447i \(0.157352\pi\)
\(284\) 0 0
\(285\) 1.65348 1.84435i 0.0979438 0.109250i
\(286\) 0 0
\(287\) −2.77871 14.7100i −0.164022 0.868305i
\(288\) 0 0
\(289\) 14.6601 8.46399i 0.862357 0.497882i
\(290\) 0 0
\(291\) 8.63076 14.9489i 0.505944 0.876321i
\(292\) 0 0
\(293\) −5.69984 5.69984i −0.332988 0.332988i 0.520732 0.853720i \(-0.325659\pi\)
−0.853720 + 0.520732i \(0.825659\pi\)
\(294\) 0 0
\(295\) −15.6360 7.92457i −0.910365 0.461386i
\(296\) 0 0
\(297\) 4.76860 + 17.7967i 0.276702 + 1.03267i
\(298\) 0 0
\(299\) 16.2249 + 28.1024i 0.938312 + 1.62520i
\(300\) 0 0
\(301\) 5.51697 8.08668i 0.317993 0.466109i
\(302\) 0 0
\(303\) 19.9067 + 5.33400i 1.14361 + 0.306430i
\(304\) 0 0
\(305\) −13.6870 20.9770i −0.783713 1.20114i
\(306\) 0 0
\(307\) −0.652734 + 0.652734i −0.0372535 + 0.0372535i −0.725488 0.688235i \(-0.758386\pi\)
0.688235 + 0.725488i \(0.258386\pi\)
\(308\) 0 0
\(309\) 21.6067i 1.22916i
\(310\) 0 0
\(311\) −6.75054 3.89743i −0.382788 0.221003i 0.296243 0.955113i \(-0.404266\pi\)
−0.679031 + 0.734110i \(0.737600\pi\)
\(312\) 0 0
\(313\) −0.897622 + 3.34997i −0.0507366 + 0.189352i −0.986643 0.162897i \(-0.947916\pi\)
0.935906 + 0.352249i \(0.114583\pi\)
\(314\) 0 0
\(315\) −6.30860 6.57384i −0.355450 0.370394i
\(316\) 0 0
\(317\) −0.210260 + 0.784701i −0.0118094 + 0.0440732i −0.971579 0.236715i \(-0.923929\pi\)
0.959770 + 0.280788i \(0.0905959\pi\)
\(318\) 0 0
\(319\) 3.83592 + 2.21467i 0.214771 + 0.123998i
\(320\) 0 0
\(321\) 9.59719i 0.535663i
\(322\) 0 0
\(323\) 0.173968 0.173968i 0.00967986 0.00967986i
\(324\) 0 0
\(325\) 16.1234 + 12.9419i 0.894366 + 0.717885i
\(326\) 0 0
\(327\) −16.9331 4.53721i −0.936403 0.250909i
\(328\) 0 0
\(329\) 2.49048 + 0.187388i 0.137304 + 0.0103310i
\(330\) 0 0
\(331\) 7.79902 + 13.5083i 0.428673 + 0.742483i 0.996756 0.0804881i \(-0.0256479\pi\)
−0.568083 + 0.822972i \(0.692315\pi\)
\(332\) 0 0
\(333\) 3.26146 + 12.1719i 0.178727 + 0.667017i
\(334\) 0 0
\(335\) −3.87402 11.8362i −0.211660 0.646679i
\(336\) 0 0
\(337\) −12.2052 12.2052i −0.664861 0.664861i 0.291661 0.956522i \(-0.405792\pi\)
−0.956522 + 0.291661i \(0.905792\pi\)
\(338\) 0 0
\(339\) 4.66894 8.08685i 0.253582 0.439217i
\(340\) 0 0
\(341\) −10.9382 + 6.31517i −0.592337 + 0.341986i
\(342\) 0 0
\(343\) −15.6904 + 9.83924i −0.847203 + 0.531269i
\(344\) 0 0
\(345\) −1.15527 21.1710i −0.0621976 1.13981i
\(346\) 0 0
\(347\) −14.7477 + 3.95163i −0.791697 + 0.212134i −0.631935 0.775021i \(-0.717739\pi\)
−0.159761 + 0.987156i \(0.551072\pi\)
\(348\) 0 0
\(349\) −35.5955 −1.90538 −0.952692 0.303938i \(-0.901698\pi\)
−0.952692 + 0.303938i \(0.901698\pi\)
\(350\) 0 0
\(351\) −22.6832 −1.21074
\(352\) 0 0
\(353\) 6.13426 1.64367i 0.326494 0.0874838i −0.0918490 0.995773i \(-0.529278\pi\)
0.418343 + 0.908289i \(0.362611\pi\)
\(354\) 0 0
\(355\) 1.64779 + 30.1968i 0.0874556 + 1.60268i
\(356\) 0 0
\(357\) 0.559381 + 0.650408i 0.0296056 + 0.0344232i
\(358\) 0 0
\(359\) −26.6079 + 15.3621i −1.40431 + 0.810780i −0.994832 0.101539i \(-0.967623\pi\)
−0.409481 + 0.912319i \(0.634290\pi\)
\(360\) 0 0
\(361\) 9.07973 15.7266i 0.477881 0.827713i
\(362\) 0 0
\(363\) 0.239763 + 0.239763i 0.0125843 + 0.0125843i
\(364\) 0 0
\(365\) 5.28097 + 16.1348i 0.276418 + 0.844533i
\(366\) 0 0
\(367\) 9.38683 + 35.0321i 0.489988 + 1.82866i 0.556461 + 0.830874i \(0.312159\pi\)
−0.0664728 + 0.997788i \(0.521175\pi\)
\(368\) 0 0
\(369\) −4.35701 7.54657i −0.226817 0.392859i
\(370\) 0 0
\(371\) −15.4929 32.1961i −0.804352 1.67154i
\(372\) 0 0
\(373\) 14.7087 + 3.94120i 0.761590 + 0.204067i 0.618653 0.785664i \(-0.287679\pi\)
0.142937 + 0.989732i \(0.454345\pi\)
\(374\) 0 0
\(375\) −5.57422 12.3052i −0.287851 0.635440i
\(376\) 0 0
\(377\) −3.85597 + 3.85597i −0.198592 + 0.198592i
\(378\) 0 0
\(379\) 31.6560i 1.62606i −0.582221 0.813030i \(-0.697816\pi\)
0.582221 0.813030i \(-0.302184\pi\)
\(380\) 0 0
\(381\) −7.27506 4.20026i −0.372713 0.215186i
\(382\) 0 0
\(383\) 5.44366 20.3160i 0.278158 1.03810i −0.675537 0.737326i \(-0.736088\pi\)
0.953695 0.300774i \(-0.0972450\pi\)
\(384\) 0 0
\(385\) −19.0831 5.53676i −0.972567 0.282179i
\(386\) 0 0
\(387\) 1.47483 5.50414i 0.0749699 0.279791i
\(388\) 0 0
\(389\) −26.4709 15.2830i −1.34213 0.774877i −0.355007 0.934864i \(-0.615522\pi\)
−0.987119 + 0.159986i \(0.948855\pi\)
\(390\) 0 0
\(391\) 2.10593i 0.106501i
\(392\) 0 0
\(393\) 11.5742 11.5742i 0.583839 0.583839i
\(394\) 0 0
\(395\) 2.64187 + 4.04899i 0.132927 + 0.203727i
\(396\) 0 0
\(397\) −3.67997 0.986045i −0.184692 0.0494882i 0.165287 0.986245i \(-0.447145\pi\)
−0.349980 + 0.936757i \(0.613812\pi\)
\(398\) 0 0
\(399\) −2.42109 1.65174i −0.121206 0.0826902i
\(400\) 0 0
\(401\) 5.34357 + 9.25534i 0.266845 + 0.462190i 0.968045 0.250775i \(-0.0806854\pi\)
−0.701200 + 0.712964i \(0.747352\pi\)
\(402\) 0 0
\(403\) −4.02458 15.0199i −0.200479 0.748196i
\(404\) 0 0
\(405\) 4.00494 + 2.02976i 0.199007 + 0.100860i
\(406\) 0 0
\(407\) 19.4324 + 19.4324i 0.963227 + 0.963227i
\(408\) 0 0
\(409\) 4.24386 7.35057i 0.209845 0.363463i −0.741820 0.670599i \(-0.766037\pi\)
0.951666 + 0.307136i \(0.0993707\pi\)
\(410\) 0 0
\(411\) 16.1592 9.32953i 0.797075 0.460192i
\(412\) 0 0
\(413\) −6.85627 + 19.5752i −0.337375 + 0.963234i
\(414\) 0 0
\(415\) −11.6094 + 12.9495i −0.569882 + 0.635667i
\(416\) 0 0
\(417\) 12.1978 3.26839i 0.597329 0.160054i
\(418\) 0 0
\(419\) −23.6626 −1.15599 −0.577997 0.816039i \(-0.696165\pi\)
−0.577997 + 0.816039i \(0.696165\pi\)
\(420\) 0 0
\(421\) −18.3661 −0.895110 −0.447555 0.894256i \(-0.647705\pi\)
−0.447555 + 0.894256i \(0.647705\pi\)
\(422\) 0 0
\(423\) 1.40425 0.376267i 0.0682769 0.0182948i
\(424\) 0 0
\(425\) −0.486238 1.25056i −0.0235860 0.0606611i
\(426\) 0 0
\(427\) −22.4693 + 19.3247i −1.08737 + 0.935186i
\(428\) 0 0
\(429\) −14.5324 + 8.39031i −0.701633 + 0.405088i
\(430\) 0 0
\(431\) 15.2748 26.4567i 0.735761 1.27438i −0.218628 0.975808i \(-0.570158\pi\)
0.954389 0.298567i \(-0.0965087\pi\)
\(432\) 0 0
\(433\) −15.7711 15.7711i −0.757910 0.757910i 0.218032 0.975942i \(-0.430036\pi\)
−0.975942 + 0.218032i \(0.930036\pi\)
\(434\) 0 0
\(435\) 3.38629 1.10834i 0.162360 0.0531411i
\(436\) 0 0
\(437\) 1.86214 + 6.94961i 0.0890783 + 0.332445i
\(438\) 0 0
\(439\) 11.9294 + 20.6623i 0.569357 + 0.986155i 0.996630 + 0.0820326i \(0.0261412\pi\)
−0.427273 + 0.904123i \(0.640526\pi\)
\(440\) 0 0
\(441\) −6.72660 + 8.42450i −0.320314 + 0.401167i
\(442\) 0 0
\(443\) 25.7705 + 6.90519i 1.22439 + 0.328075i 0.812394 0.583109i \(-0.198164\pi\)
0.411999 + 0.911184i \(0.364831\pi\)
\(444\) 0 0
\(445\) −5.04948 + 3.29466i −0.239368 + 0.156182i
\(446\) 0 0
\(447\) 13.5314 13.5314i 0.640012 0.640012i
\(448\) 0 0
\(449\) 8.15718i 0.384961i −0.981301 0.192481i \(-0.938347\pi\)
0.981301 0.192481i \(-0.0616533\pi\)
\(450\) 0 0
\(451\) −16.4579 9.50199i −0.774973 0.447431i
\(452\) 0 0
\(453\) −5.57261 + 20.7972i −0.261824 + 0.977140i
\(454\) 0 0
\(455\) 12.6650 20.9293i 0.593745 0.981181i
\(456\) 0 0
\(457\) −0.694650 + 2.59247i −0.0324943 + 0.121271i −0.980268 0.197673i \(-0.936661\pi\)
0.947774 + 0.318944i \(0.103328\pi\)
\(458\) 0 0
\(459\) 1.27487 + 0.736045i 0.0595057 + 0.0343556i
\(460\) 0 0
\(461\) 18.0493i 0.840641i 0.907376 + 0.420321i \(0.138082\pi\)
−0.907376 + 0.420321i \(0.861918\pi\)
\(462\) 0 0
\(463\) 13.2907 13.2907i 0.617672 0.617672i −0.327261 0.944934i \(-0.606126\pi\)
0.944934 + 0.327261i \(0.106126\pi\)
\(464\) 0 0
\(465\) −2.09099 + 9.94263i −0.0969675 + 0.461079i
\(466\) 0 0
\(467\) 2.71031 + 0.726226i 0.125418 + 0.0336057i 0.320982 0.947085i \(-0.395987\pi\)
−0.195564 + 0.980691i \(0.562654\pi\)
\(468\) 0 0
\(469\) −13.2784 + 6.38964i −0.613141 + 0.295046i
\(470\) 0 0
\(471\) 5.57621 + 9.65827i 0.256938 + 0.445030i
\(472\) 0 0
\(473\) −3.21638 12.0037i −0.147889 0.551931i
\(474\) 0 0
\(475\) 2.71039 + 3.69693i 0.124361 + 0.169627i
\(476\) 0 0
\(477\) −14.7065 14.7065i −0.673362 0.673362i
\(478\) 0 0
\(479\) 13.6489 23.6406i 0.623634 1.08017i −0.365170 0.930941i \(-0.618989\pi\)
0.988803 0.149224i \(-0.0476777\pi\)
\(480\) 0 0
\(481\) −29.3009 + 16.9169i −1.33600 + 0.771343i
\(482\) 0 0
\(483\) −24.6512 + 4.65660i −1.12167 + 0.211882i
\(484\) 0 0
\(485\) 23.7855 + 21.3240i 1.08005 + 0.968272i
\(486\) 0 0
\(487\) −29.2231 + 7.83031i −1.32422 + 0.354825i −0.850559 0.525880i \(-0.823736\pi\)
−0.473666 + 0.880705i \(0.657070\pi\)
\(488\) 0 0
\(489\) 11.2203 0.507398
\(490\) 0 0
\(491\) 17.8214 0.804270 0.402135 0.915580i \(-0.368268\pi\)
0.402135 + 0.915580i \(0.368268\pi\)
\(492\) 0 0
\(493\) 0.341840 0.0915956i 0.0153957 0.00412526i
\(494\) 0 0
\(495\) −11.5491 + 0.630214i −0.519092 + 0.0283260i
\(496\) 0 0
\(497\) 35.1607 6.64182i 1.57717 0.297926i
\(498\) 0 0
\(499\) 26.1405 15.0922i 1.17021 0.675621i 0.216480 0.976287i \(-0.430542\pi\)
0.953729 + 0.300666i \(0.0972090\pi\)
\(500\) 0 0
\(501\) −2.53736 + 4.39484i −0.113361 + 0.196347i
\(502\) 0 0
\(503\) −10.2304 10.2304i −0.456149 0.456149i 0.441240 0.897389i \(-0.354539\pi\)
−0.897389 + 0.441240i \(0.854539\pi\)
\(504\) 0 0
\(505\) −17.2417 + 34.0198i −0.767248 + 1.51386i
\(506\) 0 0
\(507\) −1.28162 4.78308i −0.0569188 0.212424i
\(508\) 0 0
\(509\) −4.98510 8.63445i −0.220961 0.382715i 0.734139 0.678999i \(-0.237586\pi\)
−0.955100 + 0.296284i \(0.904253\pi\)
\(510\) 0 0
\(511\) 18.1008 8.71021i 0.800734 0.385317i
\(512\) 0 0
\(513\) −4.85793 1.30168i −0.214483 0.0574705i
\(514\) 0 0
\(515\) −39.1300 8.22926i −1.72427 0.362625i
\(516\) 0 0
\(517\) 2.24187 2.24187i 0.0985974 0.0985974i
\(518\) 0 0
\(519\) 5.51811i 0.242218i
\(520\) 0 0
\(521\) −11.5888 6.69081i −0.507715 0.293130i 0.224179 0.974548i \(-0.428030\pi\)
−0.731894 + 0.681419i \(0.761363\pi\)
\(522\) 0 0
\(523\) −3.31005 + 12.3533i −0.144739 + 0.540172i 0.855028 + 0.518581i \(0.173540\pi\)
−0.999767 + 0.0215904i \(0.993127\pi\)
\(524\) 0 0
\(525\) −13.5635 + 8.45695i −0.591958 + 0.369092i
\(526\) 0 0
\(527\) −0.261186 + 0.974761i −0.0113775 + 0.0424613i
\(528\) 0 0
\(529\) 33.4155 + 19.2925i 1.45285 + 0.838803i
\(530\) 0 0
\(531\) 12.0733i 0.523937i
\(532\) 0 0
\(533\) 16.5439 16.5439i 0.716597 0.716597i
\(534\) 0 0
\(535\) −17.3806 3.65525i −0.751430 0.158030i
\(536\) 0 0
\(537\) 9.72299 + 2.60527i 0.419578 + 0.112426i
\(538\) 0 0
\(539\) −3.51804 + 23.2459i −0.151533 + 1.00127i
\(540\) 0 0
\(541\) −0.914577 1.58409i −0.0393207 0.0681055i 0.845695 0.533666i \(-0.179186\pi\)
−0.885016 + 0.465561i \(0.845853\pi\)
\(542\) 0 0
\(543\) 5.99153 + 22.3607i 0.257121 + 0.959589i
\(544\) 0 0
\(545\) 14.6662 28.9380i 0.628232 1.23957i
\(546\) 0 0
\(547\) −2.84062 2.84062i −0.121456 0.121456i 0.643766 0.765222i \(-0.277371\pi\)
−0.765222 + 0.643766i \(0.777371\pi\)
\(548\) 0 0
\(549\) −8.62555 + 14.9399i −0.368129 + 0.637619i
\(550\) 0 0
\(551\) −1.04709 + 0.604536i −0.0446074 + 0.0257541i
\(552\) 0 0
\(553\) 4.33704 3.73006i 0.184430 0.158618i
\(554\) 0 0
\(555\) 22.0739 1.20454i 0.936985 0.0511297i
\(556\) 0 0
\(557\) 21.6537 5.80210i 0.917498 0.245843i 0.230982 0.972958i \(-0.425806\pi\)
0.686516 + 0.727115i \(0.259139\pi\)
\(558\) 0 0
\(559\) 15.2996 0.647105
\(560\) 0 0
\(561\) 1.08903 0.0459787
\(562\) 0 0
\(563\) 3.11101 0.833593i 0.131114 0.0351318i −0.192665 0.981264i \(-0.561713\pi\)
0.323779 + 0.946133i \(0.395047\pi\)
\(564\) 0 0
\(565\) 12.8671 + 11.5355i 0.541325 + 0.485303i
\(566\) 0 0
\(567\) 1.75613 5.01391i 0.0737507 0.210564i
\(568\) 0 0
\(569\) 21.3213 12.3098i 0.893835 0.516056i 0.0186397 0.999826i \(-0.494066\pi\)
0.875195 + 0.483771i \(0.160733\pi\)
\(570\) 0 0
\(571\) 18.2044 31.5310i 0.761831 1.31953i −0.180074 0.983653i \(-0.557634\pi\)
0.941906 0.335877i \(-0.109033\pi\)
\(572\) 0 0
\(573\) −3.88106 3.88106i −0.162134 0.162134i
\(574\) 0 0
\(575\) 38.7810 + 5.97114i 1.61728 + 0.249014i
\(576\) 0 0
\(577\) 1.30689 + 4.87736i 0.0544064 + 0.203047i 0.987779 0.155862i \(-0.0498155\pi\)
−0.933372 + 0.358909i \(0.883149\pi\)
\(578\) 0 0
\(579\) −5.43793 9.41877i −0.225993 0.391431i
\(580\) 0 0
\(581\) 16.9989 + 11.5971i 0.705232 + 0.481129i
\(582\) 0 0
\(583\) −43.8119 11.7394i −1.81450 0.486195i
\(584\) 0 0
\(585\) 2.93059 13.9349i 0.121165 0.576138i
\(586\) 0 0
\(587\) 16.9957 16.9957i 0.701488 0.701488i −0.263242 0.964730i \(-0.584792\pi\)
0.964730 + 0.263242i \(0.0847917\pi\)
\(588\) 0 0
\(589\) 3.44769i 0.142059i
\(590\) 0 0
\(591\) −8.45781 4.88312i −0.347908 0.200865i
\(592\) 0 0
\(593\) −5.35745 + 19.9943i −0.220004 + 0.821067i 0.764341 + 0.644813i \(0.223065\pi\)
−0.984345 + 0.176254i \(0.943602\pi\)
\(594\) 0 0
\(595\) −1.39095 + 0.765328i −0.0570233 + 0.0313754i
\(596\) 0 0
\(597\) 4.28840 16.0045i 0.175513 0.655022i
\(598\) 0 0
\(599\) 27.9687 + 16.1478i 1.14277 + 0.659780i 0.947115 0.320893i \(-0.103983\pi\)
0.195656 + 0.980673i \(0.437316\pi\)
\(600\) 0 0
\(601\) 25.1960i 1.02777i 0.857861 + 0.513883i \(0.171793\pi\)
−0.857861 + 0.513883i \(0.828207\pi\)
\(602\) 0 0
\(603\) −6.06529 + 6.06529i −0.246998 + 0.246998i
\(604\) 0 0
\(605\) −0.525532 + 0.342896i −0.0213659 + 0.0139407i
\(606\) 0 0
\(607\) −46.2025 12.3799i −1.87530 0.502486i −0.999815 0.0192458i \(-0.993873\pi\)
−0.875488 0.483240i \(-0.839460\pi\)
\(608\) 0 0
\(609\) −1.82806 3.79892i −0.0740766 0.153940i
\(610\) 0 0
\(611\) 1.95166 + 3.38038i 0.0789559 + 0.136756i
\(612\) 0 0
\(613\) −4.86971 18.1740i −0.196686 0.734041i −0.991824 0.127613i \(-0.959268\pi\)
0.795138 0.606428i \(-0.207398\pi\)
\(614\) 0 0
\(615\) −14.5288 + 4.75532i −0.585858 + 0.191753i
\(616\) 0 0
\(617\) −4.50888 4.50888i −0.181521 0.181521i 0.610497 0.792018i \(-0.290970\pi\)
−0.792018 + 0.610497i \(0.790970\pi\)
\(618\) 0 0
\(619\) 5.79025 10.0290i 0.232730 0.403100i −0.725881 0.687821i \(-0.758568\pi\)
0.958610 + 0.284721i \(0.0919009\pi\)
\(620\) 0 0
\(621\) −37.2818 + 21.5246i −1.49607 + 0.863754i
\(622\) 0 0
\(623\) 4.65174 + 5.40871i 0.186368 + 0.216695i
\(624\) 0 0
\(625\) 24.4080 5.40833i 0.976320 0.216333i
\(626\) 0 0
\(627\) −3.59381 + 0.962959i −0.143523 + 0.0384569i
\(628\) 0 0
\(629\) 2.19574 0.0875497
\(630\) 0 0
\(631\) 37.5680 1.49556 0.747779 0.663948i \(-0.231120\pi\)
0.747779 + 0.663948i \(0.231120\pi\)
\(632\) 0 0
\(633\) 8.49017 2.27493i 0.337454 0.0904205i
\(634\) 0 0
\(635\) 10.3775 11.5755i 0.411820 0.459359i
\(636\) 0 0
\(637\) −26.5230 11.5908i −1.05088 0.459245i
\(638\) 0 0
\(639\) 18.0382 10.4144i 0.713581 0.411986i
\(640\) 0 0
\(641\) 0.166165 0.287806i 0.00656311 0.0113676i −0.862725 0.505673i \(-0.831244\pi\)
0.869288 + 0.494305i \(0.164578\pi\)
\(642\) 0 0
\(643\) 16.9157 + 16.9157i 0.667092 + 0.667092i 0.957042 0.289950i \(-0.0936387\pi\)
−0.289950 + 0.957042i \(0.593639\pi\)
\(644\) 0 0
\(645\) −8.91686 4.51919i −0.351101 0.177943i
\(646\) 0 0
\(647\) −12.8652 48.0136i −0.505784 1.88761i −0.458426 0.888732i \(-0.651587\pi\)
−0.0473574 0.998878i \(-0.515080\pi\)
\(648\) 0 0
\(649\) 13.1650 + 22.8025i 0.516773 + 0.895077i
\(650\) 0 0
\(651\) 11.9877 + 0.901978i 0.469837 + 0.0353513i
\(652\) 0 0
\(653\) −30.5151 8.17650i −1.19415 0.319971i −0.393624 0.919272i \(-0.628779\pi\)
−0.800524 + 0.599301i \(0.795445\pi\)
\(654\) 0 0
\(655\) 16.5527 + 25.3692i 0.646769 + 0.991255i
\(656\) 0 0
\(657\) 8.26805 8.26805i 0.322567 0.322567i
\(658\) 0 0
\(659\) 40.5893i 1.58114i 0.612374 + 0.790568i \(0.290215\pi\)
−0.612374 + 0.790568i \(0.709785\pi\)
\(660\) 0 0
\(661\) 17.1349 + 9.89284i 0.666471 + 0.384787i 0.794738 0.606953i \(-0.207608\pi\)
−0.128267 + 0.991740i \(0.540942\pi\)
\(662\) 0 0
\(663\) −0.347011 + 1.29506i −0.0134768 + 0.0502961i
\(664\) 0 0
\(665\) 3.91343 3.75553i 0.151756 0.145633i
\(666\) 0 0
\(667\) −2.67859 + 9.99663i −0.103715 + 0.387071i
\(668\) 0 0
\(669\) −4.63947 2.67860i −0.179372 0.103561i
\(670\) 0 0
\(671\) 37.6220i 1.45238i
\(672\) 0 0
\(673\) −21.6615 + 21.6615i −0.834989 + 0.834989i −0.988194 0.153206i \(-0.951040\pi\)
0.153206 + 0.988194i \(0.451040\pi\)
\(674\) 0 0
\(675\) −17.1692 + 21.3899i −0.660841 + 0.823299i
\(676\) 0 0
\(677\) 36.6550 + 9.82167i 1.40877 + 0.377477i 0.881484 0.472214i \(-0.156545\pi\)
0.527281 + 0.849691i \(0.323212\pi\)
\(678\) 0 0
\(679\) 21.3014 31.2233i 0.817475 1.19824i
\(680\) 0 0
\(681\) −0.264860 0.458752i −0.0101495 0.0175794i
\(682\) 0 0
\(683\) −3.22391 12.0318i −0.123359 0.460384i 0.876416 0.481554i \(-0.159927\pi\)
−0.999776 + 0.0211702i \(0.993261\pi\)
\(684\) 0 0
\(685\) 10.7414 + 32.8179i 0.410407 + 1.25391i
\(686\) 0 0
\(687\) 11.9281 + 11.9281i 0.455084 + 0.455084i
\(688\) 0 0
\(689\) 27.9208 48.3602i 1.06370 1.84238i
\(690\) 0 0
\(691\) −0.262855 + 0.151759i −0.00999947 + 0.00577320i −0.504991 0.863124i \(-0.668504\pi\)
0.494992 + 0.868898i \(0.335171\pi\)
\(692\) 0 0
\(693\) 2.54023 + 13.4476i 0.0964954 + 0.510831i
\(694\) 0 0
\(695\) 1.27336 + 23.3352i 0.0483014 + 0.885155i
\(696\) 0 0
\(697\) −1.46665 + 0.392989i −0.0555535 + 0.0148855i
\(698\) 0 0
\(699\) −13.4655 −0.509312
\(700\) 0 0
\(701\) −2.82269 −0.106612 −0.0533058 0.998578i \(-0.516976\pi\)
−0.0533058 + 0.998578i \(0.516976\pi\)
\(702\) 0 0
\(703\) −7.24598 + 1.94155i −0.273287 + 0.0732271i
\(704\) 0 0
\(705\) −0.138965 2.54662i −0.00523372 0.0959113i
\(706\) 0 0
\(707\) 42.5905 + 14.9174i 1.60178 + 0.561027i
\(708\) 0 0
\(709\) −18.2418 + 10.5319i −0.685085 + 0.395534i −0.801768 0.597635i \(-0.796107\pi\)
0.116683 + 0.993169i \(0.462774\pi\)
\(710\) 0 0
\(711\) 1.66491 2.88371i 0.0624390 0.108148i
\(712\) 0 0
\(713\) −20.8675 20.8675i −0.781495 0.781495i
\(714\) 0 0
\(715\) −9.66004 29.5140i −0.361265 1.10376i
\(716\) 0 0
\(717\) 0.769066 + 2.87019i 0.0287213 + 0.107189i
\(718\) 0 0
\(719\) −5.73941 9.94096i −0.214044 0.370735i 0.738932 0.673780i \(-0.235330\pi\)
−0.952976 + 0.303044i \(0.901997\pi\)
\(720\) 0 0
\(721\) −3.54980 + 47.1786i −0.132201 + 1.75702i
\(722\) 0 0
\(723\) 21.1946 + 5.67907i 0.788235 + 0.211207i
\(724\) 0 0
\(725\) 0.717500 + 6.55475i 0.0266473 + 0.243437i
\(726\) 0 0
\(727\) 36.2336 36.2336i 1.34383 1.34383i 0.451620 0.892210i \(-0.350846\pi\)
0.892210 0.451620i \(-0.149154\pi\)
\(728\) 0 0
\(729\) 22.9769i 0.850997i
\(730\) 0 0
\(731\) −0.859887 0.496456i −0.0318041 0.0183621i
\(732\) 0 0
\(733\) 11.6256 43.3873i 0.429401 1.60255i −0.324721 0.945810i \(-0.605270\pi\)
0.754121 0.656735i \(-0.228063\pi\)
\(734\) 0 0
\(735\) 12.0343 + 14.5896i 0.443892 + 0.538147i
\(736\) 0 0
\(737\) −4.84159 + 18.0691i −0.178342 + 0.665582i
\(738\) 0 0
\(739\) 1.44181 + 0.832430i 0.0530379 + 0.0306214i 0.526284 0.850309i \(-0.323585\pi\)
−0.473247 + 0.880930i \(0.656918\pi\)
\(740\) 0 0
\(741\) 4.58058i 0.168272i
\(742\) 0 0
\(743\) −23.4760 + 23.4760i −0.861249 + 0.861249i −0.991483 0.130234i \(-0.958427\pi\)
0.130234 + 0.991483i \(0.458427\pi\)
\(744\) 0 0
\(745\) 19.3519 + 29.6592i 0.708997 + 1.08663i
\(746\) 0 0
\(747\) 11.5702 + 3.10021i 0.423330 + 0.113431i
\(748\) 0 0
\(749\) −1.57674 + 20.9557i −0.0576128 + 0.765703i
\(750\) 0 0
\(751\) −8.30294 14.3811i −0.302979 0.524774i 0.673831 0.738886i \(-0.264648\pi\)
−0.976809 + 0.214112i \(0.931314\pi\)
\(752\) 0 0
\(753\) −3.93979 14.7035i −0.143574 0.535825i
\(754\) 0 0
\(755\) −35.5417 18.0130i −1.29349 0.655562i
\(756\) 0 0
\(757\) −23.6602 23.6602i −0.859944 0.859944i 0.131387 0.991331i \(-0.458057\pi\)
−0.991331 + 0.131387i \(0.958057\pi\)
\(758\) 0 0
\(759\) −15.9235 + 27.5804i −0.577988 + 1.00110i
\(760\) 0 0
\(761\) 30.6131 17.6745i 1.10973 0.640700i 0.170967 0.985277i \(-0.445311\pi\)
0.938758 + 0.344577i \(0.111978\pi\)
\(762\) 0 0
\(763\) −36.2284 12.6891i −1.31156 0.459375i
\(764\) 0 0
\(765\) −0.616881 + 0.688091i −0.0223034 + 0.0248780i
\(766\) 0 0
\(767\) −31.3116 + 8.38991i −1.13060 + 0.302942i
\(768\) 0 0
\(769\) −7.73257 −0.278844 −0.139422 0.990233i \(-0.544524\pi\)
−0.139422 + 0.990233i \(0.544524\pi\)
\(770\) 0 0
\(771\) −26.2774 −0.946358
\(772\) 0 0
\(773\) −23.9549 + 6.41870i −0.861598 + 0.230865i −0.662451 0.749105i \(-0.730484\pi\)
−0.199147 + 0.979970i \(0.563817\pi\)
\(774\) 0 0
\(775\) −17.2098 7.57364i −0.618196 0.272053i
\(776\) 0 0
\(777\) −4.85518 25.7025i −0.174179 0.922072i
\(778\) 0 0
\(779\) 4.49250 2.59374i 0.160960 0.0929305i
\(780\) 0 0
\(781\) 22.7122 39.3386i 0.812705 1.40765i
\(782\) 0 0
\(783\) −5.11548 5.11548i −0.182812 0.182812i
\(784\) 0 0
\(785\) −19.6151 + 6.42007i −0.700091 + 0.229142i
\(786\) 0 0
\(787\) −5.77061 21.5362i −0.205700 0.767683i −0.989235 0.146336i \(-0.953252\pi\)
0.783535 0.621348i \(-0.213415\pi\)
\(788\) 0 0
\(789\) −15.2571 26.4260i −0.543167 0.940792i
\(790\) 0 0
\(791\) 11.5233 16.8907i 0.409723 0.600566i
\(792\) 0 0
\(793\) −44.7399 11.9880i −1.58876 0.425707i
\(794\) 0 0
\(795\) −30.5573 + 19.9379i −1.08376 + 0.707123i
\(796\) 0 0
\(797\) −17.2569 +