Properties

Label 280.2.bo.a.33.5
Level $280$
Weight $2$
Character 280.33
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 33.5
Character \(\chi\) \(=\) 280.33
Dual form 280.2.bo.a.17.5

$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 −0.0943492 0.995539i \(-0.530077\pi\)
−0.579478 + 0.814988i \(0.696744\pi\)
\(4\) 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 −0.999973 0.00733373i \(-0.997666\pi\)
0.493635 0.869669i \(-0.335668\pi\)
\(12\) 0 0
\(13\) −2.92389 + 2.92389i −0.810941 + 0.810941i −0.984775 0.173834i \(-0.944384\pi\)
0.173834 + 0.984775i \(0.444384\pi\)
\(14\) 0 0
\(15\) 0.840431 2.56774i 0.216998 0.662989i
\(16\) 0 0
\(17\) 0.0694548 0.259209i 0.0168453 0.0628674i −0.956992 0.290116i \(-0.906306\pi\)
0.973837 + 0.227248i \(0.0729729\pi\)
\(18\) 0 0
\(19\) −0.458405 + 0.793981i −0.105165 + 0.182152i −0.913806 0.406152i \(-0.866871\pi\)
0.808640 + 0.588303i \(0.200204\pi\)
\(20\) 0 0
\(21\) 2.88063 + 1.38617i 0.628605 + 0.302488i
\(22\) 0 0
\(23\) −7.58021 + 2.03111i −1.58058 + 0.423516i −0.939106 0.343627i \(-0.888344\pi\)
−0.641476 + 0.767143i \(0.721678\pi\)
\(24\) 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 \(0.0390737\pi\)
−0.992475 + 0.122446i \(0.960926\pi\)
\(30\) 0 0
\(31\) 3.25671 1.88026i 0.584923 0.337705i −0.178165 0.984001i \(-0.557016\pi\)
0.763087 + 0.646295i \(0.223683\pi\)
\(32\) 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 0.888886 + 0.458129i \(0.151480\pi\)
−0.540733 + 0.841194i \(0.681853\pi\)
\(38\) 0 0
\(39\) 4.32685 2.49811i 0.692851 0.400018i
\(40\) 0 0
\(41\) 5.65819i 0.883661i −0.897098 0.441831i \(-0.854329\pi\)
0.897098 0.441831i \(-0.145671\pi\)
\(42\) 0 0
\(43\) −2.61631 2.61631i −0.398984 0.398984i 0.478891 0.877875i \(-0.341039\pi\)
−0.877875 + 0.478891i \(0.841039\pi\)
\(44\) 0 0
\(45\) 1.88180 2.88409i 0.280521 0.429934i
\(46\) 0 0
\(47\) −0.911807 + 0.244318i −0.133001 + 0.0356374i −0.324705 0.945815i \(-0.605265\pi\)
0.191705 + 0.981453i \(0.438598\pi\)
\(48\) 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 −0.121031 0.992649i \(-0.538620\pi\)
0.601140 0.799144i \(-0.294713\pi\)
\(54\) 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 0.999929 + 0.0119396i \(0.00380059\pi\)
−0.489624 + 0.871933i \(0.662866\pi\)
\(60\) 0 0
\(61\) 9.70077 + 5.60074i 1.24206 + 0.717102i 0.969513 0.245042i \(-0.0788017\pi\)
0.272544 + 0.962143i \(0.412135\pi\)
\(62\) 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 0.572005 0.820250i \(-0.306166\pi\)
0.0852461 + 0.996360i \(0.472832\pi\)
\(68\) 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 −0.197301 0.980343i \(-0.563218\pi\)
−0.661039 + 0.750351i \(0.729884\pi\)
\(74\) 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 0.390954 0.920410i \(-0.372145\pi\)
−0.601621 + 0.798781i \(0.705478\pi\)
\(80\) 0 0
\(81\) −1.00398 1.73894i −0.111553 0.193216i
\(82\) 0 0
\(83\) −5.49970 + 5.49970i −0.603671 + 0.603671i −0.941285 0.337614i \(-0.890380\pi\)
0.337614 + 0.941285i \(0.390380\pi\)
\(84\) 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 −0.928590 0.371107i \(-0.878978\pi\)
0.785683 + 0.618629i \(0.212312\pi\)
\(90\) 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 −0.999661 0.0260207i \(-0.991716\pi\)
−0.0260207 0.999661i \(-0.508284\pi\)
\(98\) 0 0
\(99\) 5.17259i 0.519865i
\(100\) 0 0
\(101\) −14.7714 + 8.52827i −1.46981 + 0.848594i −0.999426 0.0338687i \(-0.989217\pi\)
−0.470382 + 0.882463i \(0.655884\pi\)
\(102\) 0 0
\(103\) 4.62827 + 17.2729i 0.456037 + 1.70195i 0.685022 + 0.728522i \(0.259793\pi\)
−0.228985 + 0.973430i \(0.573541\pi\)
\(104\) 0 0
\(105\) −3.44594 + 6.26282i −0.336289 + 0.611189i
\(106\) 0 0
\(107\) 2.05577 + 7.67224i 0.198739 + 0.741703i 0.991267 + 0.131868i \(0.0420976\pi\)
−0.792528 + 0.609835i \(0.791236\pi\)
\(108\) 0 0
\(109\) 12.5649 7.25433i 1.20350 0.694839i 0.242166 0.970235i \(-0.422142\pi\)
0.961331 + 0.275396i \(0.0888089\pi\)
\(110\) 0 0
\(111\) 9.88644i 0.938379i
\(112\) 0 0
\(113\) −5.46472 5.46472i −0.514078 0.514078i 0.401696 0.915773i \(-0.368421\pi\)
−0.915773 + 0.401696i \(0.868421\pi\)
\(114\) 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 −0.454506 0.890744i \(-0.650184\pi\)
0.890744 + 0.454506i \(0.150184\pi\)
\(128\) 0 0
\(129\) 2.23532 + 3.87169i 0.196809 + 0.340884i
\(130\) 0 0
\(131\) −11.7319 6.77343i −1.02502 0.591797i −0.109468 0.993990i \(-0.534915\pi\)
−0.915555 + 0.402193i \(0.868248\pi\)
\(132\) 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 −0.442688 0.896676i \(-0.645975\pi\)
−0.831717 + 0.555200i \(0.812642\pi\)
\(138\) 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 −0.181316 0.983425i \(-0.558036\pi\)
−0.942329 + 0.334688i \(0.891369\pi\)
\(150\) 0 0
\(151\) 8.90977 + 15.4322i 0.725067 + 1.25585i 0.958947 + 0.283587i \(0.0915244\pi\)
−0.233880 + 0.972265i \(0.575142\pi\)
\(152\) 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 0.802693 + 0.596392i \(0.203400\pi\)
−0.993349 + 0.115144i \(0.963267\pi\)
\(158\) 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 −0.592380 0.805659i \(-0.701812\pi\)
−0.110187 + 0.993911i \(0.535145\pi\)
\(164\) 0 0
\(165\) −8.88013 + 1.86754i −0.691317 + 0.145388i
\(166\) 0 0
\(167\) 2.96983 + 2.96983i 0.229812 + 0.229812i 0.812614 0.582802i \(-0.198044\pi\)
−0.582802 + 0.812614i \(0.698044\pi\)
\(168\) 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 0.906325 0.422582i \(-0.138876\pi\)
−0.996191 + 0.0871956i \(0.972209\pi\)
\(174\) 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 −0.744777 0.667313i \(-0.767444\pi\)
0.205522 + 0.978653i \(0.434111\pi\)
\(180\) 0 0
\(181\) 19.1591i 1.42409i 0.702135 + 0.712043i \(0.252230\pi\)
−0.702135 + 0.712043i \(0.747770\pi\)
\(182\) 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 −0.772078 0.635527i \(-0.780783\pi\)
0.936422 + 0.350876i \(0.114116\pi\)
\(192\) 0 0
\(193\) 2.32967 8.69445i 0.167693 0.625840i −0.829988 0.557781i \(-0.811653\pi\)
0.997681 0.0680587i \(-0.0216805\pi\)
\(194\) 0 0
\(195\) 5.05047 + 9.96512i 0.361672 + 0.713617i
\(196\) 0 0
\(197\) 5.71540 5.71540i 0.407205 0.407205i −0.473558 0.880763i \(-0.657030\pi\)
0.880763 + 0.473558i \(0.157030\pi\)
\(198\) 0 0
\(199\) −6.85652 11.8758i −0.486046 0.841856i 0.513826 0.857895i \(-0.328228\pi\)
−0.999871 + 0.0160388i \(0.994894\pi\)
\(200\) 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 −0.594299 0.804244i \(-0.702571\pi\)
0.804244 + 0.594299i \(0.202571\pi\)
\(224\) 0 0
\(225\) 6.21016 + 4.55296i 0.414011 + 0.303531i
\(226\) 0 0
\(227\) 0.113469 0.423472i 0.00753121 0.0281069i −0.962058 0.272845i \(-0.912035\pi\)
0.969589 + 0.244738i \(0.0787020\pi\)
\(228\) 0 0
\(229\) −6.98055 + 12.0907i −0.461288 + 0.798974i −0.999025 0.0441386i \(-0.985946\pi\)
0.537738 + 0.843112i \(0.319279\pi\)
\(230\) 0 0
\(231\) −0.805590 10.7067i −0.0530039 0.704449i
\(232\) 0 0
\(233\) 10.7647 2.88438i 0.705217 0.188962i 0.111651 0.993748i \(-0.464386\pi\)
0.593566 + 0.804785i \(0.297720\pi\)
\(234\) 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 \(0.0253444\pi\)
−0.996832 + 0.0795376i \(0.974656\pi\)
\(240\) 0 0
\(241\) −15.7270 + 9.07999i −1.01307 + 0.584893i −0.912088 0.409995i \(-0.865530\pi\)
−0.100978 + 0.994889i \(0.532197\pi\)
\(242\) 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 \(-0.869844\pi\)
0.917560 0.397598i \(-0.130156\pi\)
\(252\) 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 0.465008 0.885306i \(-0.346051\pi\)
0.845362 + 0.534194i \(0.179385\pi\)
\(258\) 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 −0.404586 0.914500i \(-0.632584\pi\)
0.807632 0.589687i \(-0.200749\pi\)
\(264\) 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 0.965268 0.261262i \(-0.0841386\pi\)
−0.708893 + 0.705316i \(0.750805\pi\)
\(270\) 0 0
\(271\) −6.55088 3.78215i −0.397938 0.229749i 0.287656 0.957734i \(-0.407124\pi\)
−0.685594 + 0.727984i \(0.740457\pi\)
\(272\) 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 −0.214794 0.976659i \(-0.568908\pi\)
−0.674347 + 0.738415i \(0.735575\pi\)
\(278\) 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 0.880284 0.474447i \(-0.157352\pi\)
0.525125 + 0.851025i \(0.324018\pi\)
\(284\) 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 −0.853720 0.520732i \(-0.825659\pi\)
0.520732 + 0.853720i \(0.325659\pi\)
\(294\) 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 0.688235 0.725488i \(-0.258386\pi\)
−0.725488 + 0.688235i \(0.758386\pi\)
\(308\) 0 0
\(309\) 21.6067i 1.22916i
\(310\) 0 0
\(311\) −6.75054 + 3.89743i −0.382788 + 0.221003i −0.679031 0.734110i \(-0.737600\pi\)
0.296243 + 0.955113i \(0.404266\pi\)
\(312\) 0 0
\(313\) −0.897622 3.34997i −0.0507366 0.189352i 0.935906 0.352249i \(-0.114583\pi\)
−0.986643 + 0.162897i \(0.947916\pi\)
\(314\) 0 0
\(315\) −6.30860 + 6.57384i −0.355450 + 0.370394i
\(316\) 0 0
\(317\) −0.210260 0.784701i −0.0118094 0.0440732i 0.959770 0.280788i \(-0.0905959\pi\)
−0.971579 + 0.236715i \(0.923929\pi\)
\(318\) 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 −0.568083 0.822972i \(-0.692315\pi\)
0.996756 + 0.0804881i \(0.0256479\pi\)
\(332\) 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 −0.956522 0.291661i \(-0.905792\pi\)
0.291661 + 0.956522i \(0.405792\pi\)
\(338\) 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 −0.159761 0.987156i \(-0.551072\pi\)
−0.631935 + 0.775021i \(0.717739\pi\)
\(348\) 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 0.418343 0.908289i \(-0.362611\pi\)
−0.0918490 + 0.995773i \(0.529278\pi\)
\(354\) 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 −0.409481 0.912319i \(-0.634290\pi\)
−0.994832 + 0.101539i \(0.967623\pi\)
\(360\) 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 −0.0664728 0.997788i \(-0.521175\pi\)
0.556461 0.830874i \(-0.312159\pi\)
\(368\) 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 0.142937 0.989732i \(-0.454345\pi\)
0.618653 + 0.785664i \(0.287679\pi\)
\(374\) 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 \(0.302184\pi\)
−0.582221 + 0.813030i \(0.697816\pi\)
\(380\) 0 0
\(381\) −7.27506 + 4.20026i −0.372713 + 0.215186i
\(382\) 0 0
\(383\) 5.44366 + 20.3160i 0.278158 + 1.03810i 0.953695 + 0.300774i \(0.0972450\pi\)
−0.675537 + 0.737326i \(0.736088\pi\)
\(384\) 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 −0.987119 0.159986i \(-0.948855\pi\)
−0.355007 + 0.934864i \(0.615522\pi\)
\(390\) 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 −0.349980 0.936757i \(-0.613812\pi\)
0.165287 + 0.986245i \(0.447145\pi\)
\(398\) 0 0
\(399\) −2.42109 + 1.65174i −0.121206 + 0.0826902i
\(400\) 0 0
\(401\) 5.34357 9.25534i 0.266845 0.462190i −0.701200 0.712964i \(-0.747352\pi\)
0.968045 + 0.250775i \(0.0806854\pi\)
\(402\) 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 0.951666 0.307136i \(-0.0993707\pi\)
−0.741820 + 0.670599i \(0.766037\pi\)
\(410\) 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 0.954389 + 0.298567i \(0.0965087\pi\)
−0.218628 + 0.975808i \(0.570158\pi\)
\(432\) 0 0
\(433\) −15.7711 + 15.7711i −0.757910 + 0.757910i −0.975942 0.218032i \(-0.930036\pi\)
0.218032 + 0.975942i \(0.430036\pi\)
\(434\) 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 −0.427273 0.904123i \(-0.640526\pi\)
0.996630 0.0820326i \(-0.0261412\pi\)
\(440\) 0 0
\(441\) −6.72660 8.42450i −0.320314 0.401167i
\(442\) 0 0
\(443\) 25.7705 6.90519i 1.22439 0.328075i 0.411999 0.911184i \(-0.364831\pi\)
0.812394 + 0.583109i \(0.198164\pi\)
\(444\) 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 \(0.0616533\pi\)
−0.981301 + 0.192481i \(0.938347\pi\)
\(450\) 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 0.947774 0.318944i \(-0.103328\pi\)
−0.980268 + 0.197673i \(0.936661\pi\)
\(458\) 0 0
\(459\) 1.27487 0.736045i 0.0595057 0.0343556i
\(460\) 0 0
\(461\) 18.0493i 0.840641i −0.907376 0.420321i \(-0.861918\pi\)
0.907376 0.420321i \(-0.138082\pi\)
\(462\) 0 0
\(463\) 13.2907 + 13.2907i 0.617672 + 0.617672i 0.944934 0.327261i \(-0.106126\pi\)
−0.327261 + 0.944934i \(0.606126\pi\)
\(464\) 0 0
\(465\) −2.09099 9.94263i −0.0969675 0.461079i
\(466\) 0 0
\(467\) 2.71031 0.726226i 0.125418 0.0336057i −0.195564 0.980691i \(-0.562654\pi\)
0.320982 + 0.947085i \(0.395987\pi\)
\(468\) 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 0.988803 + 0.149224i \(0.0476777\pi\)
−0.365170 + 0.930941i \(0.618989\pi\)
\(480\) 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 −0.473666 0.880705i \(-0.657070\pi\)
−0.850559 + 0.525880i \(0.823736\pi\)
\(488\) 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 0.953729 0.300666i \(-0.0972090\pi\)
0.216480 + 0.976287i \(0.430542\pi\)
\(500\) 0 0
\(501\) −2.53736 4.39484i −0.113361 0.196347i
\(502\) 0 0
\(503\) −10.2304 + 10.2304i −0.456149 + 0.456149i −0.897389 0.441240i \(-0.854539\pi\)
0.441240 + 0.897389i \(0.354539\pi\)
\(504\) 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 −0.955100 0.296284i \(-0.904253\pi\)
0.734139 + 0.678999i \(0.237586\pi\)
\(510\) 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 −0.731894 0.681419i \(-0.761363\pi\)
0.224179 + 0.974548i \(0.428030\pi\)
\(522\) 0 0
\(523\) −3.31005 12.3533i −0.144739 0.540172i −0.999767 0.0215904i \(-0.993127\pi\)
0.855028 0.518581i \(-0.173540\pi\)
\(524\) 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 −0.885016 0.465561i \(-0.845853\pi\)
0.845695 + 0.533666i \(0.179186\pi\)
\(542\) 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 −0.765222 0.643766i \(-0.777371\pi\)
0.643766 + 0.765222i \(0.277371\pi\)
\(548\) 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 0.686516 0.727115i \(-0.259139\pi\)
0.230982 + 0.972958i \(0.425806\pi\)
\(558\) 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 0.323779 0.946133i \(-0.395047\pi\)
−0.192665 + 0.981264i \(0.561713\pi\)
\(564\) 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 0.875195 0.483771i \(-0.160733\pi\)
0.0186397 + 0.999826i \(0.494066\pi\)
\(570\) 0 0
\(571\) 18.2044 + 31.5310i 0.761831 + 1.31953i 0.941906 + 0.335877i \(0.109033\pi\)
−0.180074 + 0.983653i \(0.557634\pi\)
\(572\) 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 −0.933372 0.358909i \(-0.883149\pi\)
0.987779 + 0.155862i \(0.0498155\pi\)
\(578\) 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 0.964730 0.263242i \(-0.0847917\pi\)
−0.263242 + 0.964730i \(0.584792\pi\)
\(588\) 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 −0.984345 0.176254i \(-0.943602\pi\)
0.764341 0.644813i \(-0.223065\pi\)
\(594\) 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 0.195656 0.980673i \(-0.437316\pi\)
0.947115 + 0.320893i \(0.103983\pi\)
\(600\) 0 0
\(601\) 25.1960i 1.02777i −0.857861 0.513883i \(-0.828207\pi\)
0.857861 0.513883i \(-0.171793\pi\)
\(602\) 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 −0.875488 + 0.483240i \(0.839460\pi\)
−0.999815 + 0.0192458i \(0.993873\pi\)
\(608\) 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 0.795138 + 0.606428i \(0.207398\pi\)
−0.991824 + 0.127613i \(0.959268\pi\)
\(614\) 0 0
\(615\) −14.5288 4.75532i −0.585858 0.191753i
\(616\) 0 0
\(617\) −4.50888 + 4.50888i −0.181521 + 0.181521i −0.792018 0.610497i \(-0.790970\pi\)
0.610497 + 0.792018i \(0.290970\pi\)
\(618\) 0 0
\(619\) 5.79025 + 10.0290i 0.232730 + 0.403100i 0.958610 0.284721i \(-0.0919009\pi\)
−0.725881 + 0.687821i \(0.758568\pi\)
\(620\) 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 0.869288 0.494305i \(-0.164578\pi\)
−0.862725 + 0.505673i \(0.831244\pi\)
\(642\) 0 0
\(643\) 16.9157 16.9157i 0.667092 0.667092i −0.289950 0.957042i \(-0.593639\pi\)
0.957042 + 0.289950i \(0.0936387\pi\)
\(644\) 0 0
\(645\) −8.91686 + 4.51919i −0.351101 + 0.177943i
\(646\) 0 0
\(647\) −12.8652 + 48.0136i −0.505784 + 1.88761i −0.0473574 + 0.998878i \(0.515080\pi\)
−0.458426 + 0.888732i \(0.651587\pi\)
\(648\) 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 −0.800524 0.599301i \(-0.795445\pi\)
−0.393624 + 0.919272i \(0.628779\pi\)
\(654\) 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 \(-0.709785\pi\)
0.612374 0.790568i \(-0.290215\pi\)
\(660\) 0 0
\(661\) 17.1349 9.89284i 0.666471 0.384787i −0.128267 0.991740i \(-0.540942\pi\)
0.794738 + 0.606953i \(0.207608\pi\)
\(662\) 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 0.153206 0.988194i \(-0.451040\pi\)
−0.988194 + 0.153206i \(0.951040\pi\)
\(674\) 0 0
\(675\) −17.1692 21.3899i −0.660841 0.823299i
\(676\) 0 0
\(677\) 36.6550 9.82167i 1.40877 0.377477i 0.527281 0.849691i \(-0.323212\pi\)
0.881484 + 0.472214i \(0.156545\pi\)
\(678\) 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 −0.999776 0.0211702i \(-0.993261\pi\)
0.876416 + 0.481554i \(0.159927\pi\)
\(684\) 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 0.494992 0.868898i \(-0.335171\pi\)
−0.504991 + 0.863124i \(0.668504\pi\)
\(692\) 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 0.116683 0.993169i \(-0.462774\pi\)
−0.801768 + 0.597635i \(0.796107\pi\)
\(710\) 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 −0.952976 0.303044i \(-0.901997\pi\)
0.738932 + 0.673780i \(0.235330\pi\)
\(720\) 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 0.892210 + 0.451620i \(0.149154\pi\)
0.451620 + 0.892210i \(0.350846\pi\)
\(728\) 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 0.754121 + 0.656735i \(0.228063\pi\)
−0.324721 + 0.945810i \(0.605270\pi\)
\(734\) 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 −0.473247 0.880930i \(-0.656918\pi\)
0.526284 + 0.850309i \(0.323585\pi\)
\(740\) 0 0
\(741\) 4.58058i 0.168272i
\(742\) 0 0
\(743\) −23.4760 23.4760i −0.861249 0.861249i 0.130234 0.991483i \(-0.458427\pi\)
−0.991483 + 0.130234i \(0.958427\pi\)
\(744\) 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 −0.976809 0.214112i \(-0.931314\pi\)
0.673831 + 0.738886i \(0.264648\pi\)
\(752\) 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 −0.991331 0.131387i \(-0.958057\pi\)
0.131387 + 0.991331i \(0.458057\pi\)
\(758\) 0 0
\(759\) −15.9235 27.5804i −0.577988 1.00110i
\(760\) 0 0
\(761\) 30.6131 + 17.6745i 1.10973 + 0.640700i 0.938758 0.344577i \(-0.111978\pi\)
0.170967 + 0.985277i \(0.445311\pi\)
\(762\) 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 −0.199147 0.979970i \(-0.563817\pi\)
−0.662451 + 0.749105i \(0.730484\pi\)
\(774\) 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 0.783535 + 0.621348i \(0.213415\pi\)
−0.989235 + 0.146336i \(0.953252\pi\)
\(788\) 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