Properties

Label 280.2.bo.a.17.2
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 17.2
Character \(\chi\) \(=\) 280.17
Dual form 280.2.bo.a.33.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.30560 + 0.617784i) q^{3} +(1.37859 - 1.76054i) q^{5} +(-0.755351 + 2.53563i) q^{7} +(2.33607 - 1.34873i) q^{9} +O(q^{10})\) \(q+(-2.30560 + 0.617784i) q^{3} +(1.37859 - 1.76054i) q^{5} +(-0.755351 + 2.53563i) q^{7} +(2.33607 - 1.34873i) q^{9} +(2.18726 - 3.78844i) q^{11} +(4.36695 + 4.36695i) q^{13} +(-2.09085 + 4.91077i) q^{15} +(0.438132 + 1.63513i) q^{17} +(3.56560 + 6.17580i) q^{19} +(0.175064 - 6.31281i) q^{21} +(4.91851 + 1.31791i) q^{23} +(-1.19897 - 4.85412i) q^{25} +(0.510640 - 0.510640i) q^{27} -1.33053i q^{29} +(-1.90109 - 1.09759i) q^{31} +(-2.70251 + 10.0859i) q^{33} +(3.42276 + 4.82543i) q^{35} +(-0.224926 + 0.839435i) q^{37} +(-12.7663 - 7.37062i) q^{39} +5.69781i q^{41} +(3.40535 - 3.40535i) q^{43} +(0.845995 - 5.97207i) q^{45} +(-9.84549 - 2.63809i) q^{47} +(-5.85889 - 3.83059i) q^{49} +(-2.02031 - 3.49929i) q^{51} +(-0.541299 - 2.02016i) q^{53} +(-3.65436 - 9.07346i) q^{55} +(-12.0362 - 12.0362i) q^{57} +(2.56679 - 4.44580i) q^{59} +(6.21535 - 3.58843i) q^{61} +(1.65533 + 6.94217i) q^{63} +(13.7084 - 1.66793i) q^{65} +(-7.11586 + 1.90669i) q^{67} -12.1543 q^{69} +4.31969 q^{71} +(-14.2630 + 3.82176i) q^{73} +(5.76315 + 10.4510i) q^{75} +(7.95396 + 8.40770i) q^{77} +(4.82649 - 2.78658i) q^{79} +(-4.90805 + 8.50099i) q^{81} +(-0.272283 - 0.272283i) q^{83} +(3.48271 + 1.48283i) q^{85} +(0.821982 + 3.06768i) q^{87} +(1.79506 + 3.10913i) q^{89} +(-14.3716 + 7.77441i) q^{91} +(5.06123 + 1.35615i) q^{93} +(15.7882 + 2.23653i) q^{95} +(0.325781 - 0.325781i) q^{97} -11.8001i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

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
\(3\) −2.30560 + 0.617784i −1.33114 + 0.356678i −0.853140 0.521682i \(-0.825305\pi\)
−0.478000 + 0.878360i \(0.658638\pi\)
\(4\) 0 0
\(5\) 1.37859 1.76054i 0.616525 0.787336i
\(6\) 0 0
\(7\) −0.755351 + 2.53563i −0.285496 + 0.958380i
\(8\) 0 0
\(9\) 2.33607 1.34873i 0.778688 0.449576i
\(10\) 0 0
\(11\) 2.18726 3.78844i 0.659483 1.14226i −0.321266 0.946989i \(-0.604108\pi\)
0.980750 0.195270i \(-0.0625583\pi\)
\(12\) 0 0
\(13\) 4.36695 + 4.36695i 1.21117 + 1.21117i 0.970641 + 0.240533i \(0.0773224\pi\)
0.240533 + 0.970641i \(0.422678\pi\)
\(14\) 0 0
\(15\) −2.09085 + 4.91077i −0.539855 + 1.26795i
\(16\) 0 0
\(17\) 0.438132 + 1.63513i 0.106263 + 0.396577i 0.998485 0.0550183i \(-0.0175217\pi\)
−0.892223 + 0.451595i \(0.850855\pi\)
\(18\) 0 0
\(19\) 3.56560 + 6.17580i 0.818004 + 1.41682i 0.907151 + 0.420806i \(0.138253\pi\)
−0.0891466 + 0.996019i \(0.528414\pi\)
\(20\) 0 0
\(21\) 0.175064 6.31281i 0.0382021 1.37757i
\(22\) 0 0
\(23\) 4.91851 + 1.31791i 1.02558 + 0.274803i 0.732125 0.681170i \(-0.238529\pi\)
0.293454 + 0.955973i \(0.405195\pi\)
\(24\) 0 0
\(25\) −1.19897 4.85412i −0.239795 0.970824i
\(26\) 0 0
\(27\) 0.510640 0.510640i 0.0982727 0.0982727i
\(28\) 0 0
\(29\) 1.33053i 0.247074i −0.992340 0.123537i \(-0.960576\pi\)
0.992340 0.123537i \(-0.0394237\pi\)
\(30\) 0 0
\(31\) −1.90109 1.09759i −0.341446 0.197134i 0.319465 0.947598i \(-0.396497\pi\)
−0.660911 + 0.750464i \(0.729830\pi\)
\(32\) 0 0
\(33\) −2.70251 + 10.0859i −0.470446 + 1.75573i
\(34\) 0 0
\(35\) 3.42276 + 4.82543i 0.578551 + 0.815646i
\(36\) 0 0
\(37\) −0.224926 + 0.839435i −0.0369776 + 0.138002i −0.981947 0.189157i \(-0.939425\pi\)
0.944969 + 0.327159i \(0.106091\pi\)
\(38\) 0 0
\(39\) −12.7663 7.37062i −2.04424 1.18024i
\(40\) 0 0
\(41\) 5.69781i 0.889849i 0.895568 + 0.444924i \(0.146769\pi\)
−0.895568 + 0.444924i \(0.853231\pi\)
\(42\) 0 0
\(43\) 3.40535 3.40535i 0.519312 0.519312i −0.398051 0.917363i \(-0.630313\pi\)
0.917363 + 0.398051i \(0.130313\pi\)
\(44\) 0 0
\(45\) 0.845995 5.97207i 0.126113 0.890264i
\(46\) 0 0
\(47\) −9.84549 2.63809i −1.43611 0.384805i −0.544942 0.838474i \(-0.683448\pi\)
−0.891170 + 0.453669i \(0.850115\pi\)
\(48\) 0 0
\(49\) −5.85889 3.83059i −0.836984 0.547227i
\(50\) 0 0
\(51\) −2.02031 3.49929i −0.282901 0.489998i
\(52\) 0 0
\(53\) −0.541299 2.02016i −0.0743531 0.277490i 0.918733 0.394880i \(-0.129214\pi\)
−0.993086 + 0.117390i \(0.962547\pi\)
\(54\) 0 0
\(55\) −3.65436 9.07346i −0.492753 1.22347i
\(56\) 0 0
\(57\) −12.0362 12.0362i −1.59423 1.59423i
\(58\) 0 0
\(59\) 2.56679 4.44580i 0.334167 0.578794i −0.649157 0.760654i \(-0.724878\pi\)
0.983324 + 0.181860i \(0.0582117\pi\)
\(60\) 0 0
\(61\) 6.21535 3.58843i 0.795794 0.459452i −0.0462043 0.998932i \(-0.514713\pi\)
0.841998 + 0.539480i \(0.181379\pi\)
\(62\) 0 0
\(63\) 1.65533 + 6.94217i 0.208552 + 0.874631i
\(64\) 0 0
\(65\) 13.7084 1.66793i 1.70032 0.206882i
\(66\) 0 0
\(67\) −7.11586 + 1.90669i −0.869341 + 0.232939i −0.665803 0.746128i \(-0.731911\pi\)
−0.203538 + 0.979067i \(0.565244\pi\)
\(68\) 0 0
\(69\) −12.1543 −1.46321
\(70\) 0 0
\(71\) 4.31969 0.512653 0.256326 0.966590i \(-0.417488\pi\)
0.256326 + 0.966590i \(0.417488\pi\)
\(72\) 0 0
\(73\) −14.2630 + 3.82176i −1.66936 + 0.447303i −0.964937 0.262481i \(-0.915459\pi\)
−0.704420 + 0.709784i \(0.748793\pi\)
\(74\) 0 0
\(75\) 5.76315 + 10.4510i 0.665471 + 1.20677i
\(76\) 0 0
\(77\) 7.95396 + 8.40770i 0.906438 + 0.958146i
\(78\) 0 0
\(79\) 4.82649 2.78658i 0.543023 0.313514i −0.203280 0.979121i \(-0.565160\pi\)
0.746303 + 0.665606i \(0.231827\pi\)
\(80\) 0 0
\(81\) −4.90805 + 8.50099i −0.545339 + 0.944555i
\(82\) 0 0
\(83\) −0.272283 0.272283i −0.0298869 0.0298869i 0.692005 0.721892i \(-0.256727\pi\)
−0.721892 + 0.692005i \(0.756727\pi\)
\(84\) 0 0
\(85\) 3.48271 + 1.48283i 0.377753 + 0.160835i
\(86\) 0 0
\(87\) 0.821982 + 3.06768i 0.0881257 + 0.328890i
\(88\) 0 0
\(89\) 1.79506 + 3.10913i 0.190276 + 0.329567i 0.945342 0.326082i \(-0.105729\pi\)
−0.755066 + 0.655649i \(0.772395\pi\)
\(90\) 0 0
\(91\) −14.3716 + 7.77441i −1.50655 + 0.814980i
\(92\) 0 0
\(93\) 5.06123 + 1.35615i 0.524825 + 0.140627i
\(94\) 0 0
\(95\) 15.7882 + 2.23653i 1.61984 + 0.229464i
\(96\) 0 0
\(97\) 0.325781 0.325781i 0.0330781 0.0330781i −0.690374 0.723452i \(-0.742554\pi\)
0.723452 + 0.690374i \(0.242554\pi\)
\(98\) 0 0
\(99\) 11.8001i 1.18595i
\(100\) 0 0
\(101\) 10.6907 + 6.17228i 1.06376 + 0.614165i 0.926471 0.376365i \(-0.122826\pi\)
0.137294 + 0.990530i \(0.456160\pi\)
\(102\) 0 0
\(103\) −1.41652 + 5.28651i −0.139573 + 0.520895i 0.860364 + 0.509681i \(0.170236\pi\)
−0.999937 + 0.0112145i \(0.996430\pi\)
\(104\) 0 0
\(105\) −10.8726 9.01099i −1.06106 0.879382i
\(106\) 0 0
\(107\) 0.926726 3.45859i 0.0895900 0.334354i −0.906554 0.422090i \(-0.861297\pi\)
0.996144 + 0.0877359i \(0.0279632\pi\)
\(108\) 0 0
\(109\) 5.80975 + 3.35426i 0.556473 + 0.321280i 0.751729 0.659472i \(-0.229220\pi\)
−0.195255 + 0.980752i \(0.562554\pi\)
\(110\) 0 0
\(111\) 2.07436i 0.196889i
\(112\) 0 0
\(113\) 5.75259 5.75259i 0.541158 0.541158i −0.382710 0.923869i \(-0.625009\pi\)
0.923869 + 0.382710i \(0.125009\pi\)
\(114\) 0 0
\(115\) 9.10083 6.84235i 0.848657 0.638052i
\(116\) 0 0
\(117\) 16.0913 + 4.31165i 1.48764 + 0.398613i
\(118\) 0 0
\(119\) −4.47703 0.124155i −0.410409 0.0113813i
\(120\) 0 0
\(121\) −4.06820 7.04634i −0.369837 0.640576i
\(122\) 0 0
\(123\) −3.52002 13.1369i −0.317389 1.18451i
\(124\) 0 0
\(125\) −10.1987 4.58101i −0.912203 0.409738i
\(126\) 0 0
\(127\) 3.47621 + 3.47621i 0.308464 + 0.308464i 0.844314 0.535849i \(-0.180009\pi\)
−0.535849 + 0.844314i \(0.680009\pi\)
\(128\) 0 0
\(129\) −5.74762 + 9.95516i −0.506049 + 0.876503i
\(130\) 0 0
\(131\) −4.72880 + 2.73018i −0.413157 + 0.238537i −0.692145 0.721758i \(-0.743334\pi\)
0.278988 + 0.960295i \(0.410001\pi\)
\(132\) 0 0
\(133\) −18.3528 + 4.37616i −1.59139 + 0.379461i
\(134\) 0 0
\(135\) −0.195036 1.60296i −0.0167860 0.137961i
\(136\) 0 0
\(137\) −16.6760 + 4.46833i −1.42473 + 0.381756i −0.887160 0.461463i \(-0.847325\pi\)
−0.537571 + 0.843218i \(0.680658\pi\)
\(138\) 0 0
\(139\) −4.33475 −0.367669 −0.183834 0.982957i \(-0.558851\pi\)
−0.183834 + 0.982957i \(0.558851\pi\)
\(140\) 0 0
\(141\) 24.3295 2.04892
\(142\) 0 0
\(143\) 26.0956 6.99230i 2.18222 0.584725i
\(144\) 0 0
\(145\) −2.34245 1.83426i −0.194530 0.152327i
\(146\) 0 0
\(147\) 15.8747 + 5.21229i 1.30933 + 0.429902i
\(148\) 0 0
\(149\) −2.22537 + 1.28482i −0.182309 + 0.105256i −0.588377 0.808587i \(-0.700233\pi\)
0.406068 + 0.913843i \(0.366900\pi\)
\(150\) 0 0
\(151\) −0.516263 + 0.894194i −0.0420129 + 0.0727685i −0.886267 0.463174i \(-0.846710\pi\)
0.844254 + 0.535943i \(0.180044\pi\)
\(152\) 0 0
\(153\) 3.22885 + 3.22885i 0.261037 + 0.261037i
\(154\) 0 0
\(155\) −4.55318 + 1.83380i −0.365720 + 0.147295i
\(156\) 0 0
\(157\) −4.71159 17.5839i −0.376026 1.40335i −0.851841 0.523801i \(-0.824513\pi\)
0.475815 0.879545i \(-0.342153\pi\)
\(158\) 0 0
\(159\) 2.49604 + 4.32327i 0.197949 + 0.342857i
\(160\) 0 0
\(161\) −7.05694 + 11.4760i −0.556164 + 0.904439i
\(162\) 0 0
\(163\) −8.44026 2.26156i −0.661092 0.177139i −0.0873531 0.996177i \(-0.527841\pi\)
−0.573739 + 0.819038i \(0.694508\pi\)
\(164\) 0 0
\(165\) 14.0309 + 18.6622i 1.09231 + 1.45285i
\(166\) 0 0
\(167\) 12.3783 12.3783i 0.957862 0.957862i −0.0412856 0.999147i \(-0.513145\pi\)
0.999147 + 0.0412856i \(0.0131454\pi\)
\(168\) 0 0
\(169\) 25.1405i 1.93389i
\(170\) 0 0
\(171\) 16.6589 + 9.61804i 1.27394 + 0.735510i
\(172\) 0 0
\(173\) −0.746705 + 2.78674i −0.0567709 + 0.211872i −0.988485 0.151322i \(-0.951647\pi\)
0.931714 + 0.363194i \(0.118314\pi\)
\(174\) 0 0
\(175\) 13.2139 + 0.626405i 0.998878 + 0.0473518i
\(176\) 0 0
\(177\) −3.17144 + 11.8360i −0.238380 + 0.889646i
\(178\) 0 0
\(179\) −6.47526 3.73849i −0.483984 0.279428i 0.238092 0.971243i \(-0.423478\pi\)
−0.722075 + 0.691815i \(0.756812\pi\)
\(180\) 0 0
\(181\) 21.7307i 1.61523i −0.589708 0.807617i \(-0.700757\pi\)
0.589708 0.807617i \(-0.299243\pi\)
\(182\) 0 0
\(183\) −12.1132 + 12.1132i −0.895437 + 0.895437i
\(184\) 0 0
\(185\) 1.16777 + 1.55323i 0.0858565 + 0.114196i
\(186\) 0 0
\(187\) 7.15290 + 1.91661i 0.523072 + 0.140157i
\(188\) 0 0
\(189\) 0.909084 + 1.68051i 0.0661261 + 0.122239i
\(190\) 0 0
\(191\) −5.73369 9.93104i −0.414875 0.718585i 0.580540 0.814232i \(-0.302841\pi\)
−0.995415 + 0.0956469i \(0.969508\pi\)
\(192\) 0 0
\(193\) −1.43727 5.36396i −0.103457 0.386106i 0.894709 0.446650i \(-0.147383\pi\)
−0.998166 + 0.0605441i \(0.980716\pi\)
\(194\) 0 0
\(195\) −30.5757 + 12.3144i −2.18957 + 0.881855i
\(196\) 0 0
\(197\) −12.5995 12.5995i −0.897678 0.897678i 0.0975523 0.995230i \(-0.468899\pi\)
−0.995230 + 0.0975523i \(0.968899\pi\)
\(198\) 0 0
\(199\) 2.02418 3.50598i 0.143490 0.248532i −0.785318 0.619092i \(-0.787501\pi\)
0.928809 + 0.370560i \(0.120834\pi\)
\(200\) 0 0
\(201\) 15.2284 8.79213i 1.07413 0.620149i
\(202\) 0 0
\(203\) 3.37375 + 1.00502i 0.236790 + 0.0705385i
\(204\) 0 0
\(205\) 10.0312 + 7.85495i 0.700610 + 0.548614i
\(206\) 0 0
\(207\) 13.2674 3.55500i 0.922151 0.247090i
\(208\) 0 0
\(209\) 31.1955 2.15784
\(210\) 0 0
\(211\) −21.3214 −1.46783 −0.733913 0.679244i \(-0.762308\pi\)
−0.733913 + 0.679244i \(0.762308\pi\)
\(212\) 0 0
\(213\) −9.95948 + 2.66863i −0.682412 + 0.182852i
\(214\) 0 0
\(215\) −1.30066 10.6898i −0.0887041 0.729041i
\(216\) 0 0
\(217\) 4.21909 3.99140i 0.286410 0.270954i
\(218\) 0 0
\(219\) 30.5238 17.6229i 2.06260 1.19084i
\(220\) 0 0
\(221\) −5.22723 + 9.05383i −0.351622 + 0.609026i
\(222\) 0 0
\(223\) 19.7653 + 19.7653i 1.32358 + 1.32358i 0.910854 + 0.412730i \(0.135425\pi\)
0.412730 + 0.910854i \(0.364575\pi\)
\(224\) 0 0
\(225\) −9.34776 9.72245i −0.623184 0.648163i
\(226\) 0 0
\(227\) 0.760893 + 2.83969i 0.0505022 + 0.188477i 0.986569 0.163346i \(-0.0522287\pi\)
−0.936067 + 0.351823i \(0.885562\pi\)
\(228\) 0 0
\(229\) −12.0300 20.8366i −0.794965 1.37692i −0.922861 0.385133i \(-0.874156\pi\)
0.127896 0.991788i \(-0.459178\pi\)
\(230\) 0 0
\(231\) −23.5328 14.4710i −1.54834 0.952120i
\(232\) 0 0
\(233\) 2.37700 + 0.636915i 0.155722 + 0.0417257i 0.335838 0.941920i \(-0.390981\pi\)
−0.180116 + 0.983645i \(0.557647\pi\)
\(234\) 0 0
\(235\) −18.2174 + 13.6965i −1.18837 + 0.893460i
\(236\) 0 0
\(237\) −9.40647 + 9.40647i −0.611016 + 0.611016i
\(238\) 0 0
\(239\) 15.4754i 1.00102i 0.865730 + 0.500511i \(0.166855\pi\)
−0.865730 + 0.500511i \(0.833145\pi\)
\(240\) 0 0
\(241\) −13.8765 8.01160i −0.893864 0.516073i −0.0186595 0.999826i \(-0.505940\pi\)
−0.875204 + 0.483753i \(0.839273\pi\)
\(242\) 0 0
\(243\) 5.50351 20.5394i 0.353050 1.31760i
\(244\) 0 0
\(245\) −14.8209 + 5.03397i −0.946873 + 0.321608i
\(246\) 0 0
\(247\) −11.3986 + 42.5402i −0.725276 + 2.70677i
\(248\) 0 0
\(249\) 0.795987 + 0.459563i 0.0504436 + 0.0291237i
\(250\) 0 0
\(251\) 0.592810i 0.0374178i −0.999825 0.0187089i \(-0.994044\pi\)
0.999825 0.0187089i \(-0.00595558\pi\)
\(252\) 0 0
\(253\) 15.7509 15.7509i 0.990249 0.990249i
\(254\) 0 0
\(255\) −8.94581 1.26725i −0.560208 0.0793582i
\(256\) 0 0
\(257\) −18.7358 5.02024i −1.16871 0.313154i −0.378269 0.925696i \(-0.623480\pi\)
−0.790438 + 0.612542i \(0.790147\pi\)
\(258\) 0 0
\(259\) −1.95860 1.20440i −0.121702 0.0748377i
\(260\) 0 0
\(261\) −1.79453 3.10821i −0.111078 0.192393i
\(262\) 0 0
\(263\) −6.58626 24.5803i −0.406126 1.51568i −0.801969 0.597366i \(-0.796214\pi\)
0.395843 0.918318i \(-0.370453\pi\)
\(264\) 0 0
\(265\) −4.30279 1.83199i −0.264318 0.112538i
\(266\) 0 0
\(267\) −6.05945 6.05945i −0.370833 0.370833i
\(268\) 0 0
\(269\) −6.17421 + 10.6940i −0.376448 + 0.652027i −0.990543 0.137205i \(-0.956188\pi\)
0.614095 + 0.789232i \(0.289521\pi\)
\(270\) 0 0
\(271\) −10.0880 + 5.82432i −0.612803 + 0.353802i −0.774062 0.633110i \(-0.781778\pi\)
0.161259 + 0.986912i \(0.448445\pi\)
\(272\) 0 0
\(273\) 28.3322 26.8032i 1.71474 1.62221i
\(274\) 0 0
\(275\) −21.0120 6.07497i −1.26707 0.366334i
\(276\) 0 0
\(277\) 18.2575 4.89207i 1.09698 0.293936i 0.335448 0.942059i \(-0.391112\pi\)
0.761536 + 0.648123i \(0.224446\pi\)
\(278\) 0 0
\(279\) −5.92143 −0.354506
\(280\) 0 0
\(281\) 21.9795 1.31119 0.655594 0.755114i \(-0.272418\pi\)
0.655594 + 0.755114i \(0.272418\pi\)
\(282\) 0 0
\(283\) −23.1631 + 6.20653i −1.37690 + 0.368940i −0.869995 0.493061i \(-0.835878\pi\)
−0.506907 + 0.862001i \(0.669211\pi\)
\(284\) 0 0
\(285\) −37.7830 + 4.59715i −2.23807 + 0.272312i
\(286\) 0 0
\(287\) −14.4476 4.30385i −0.852813 0.254048i
\(288\) 0 0
\(289\) 12.2407 7.06720i 0.720044 0.415717i
\(290\) 0 0
\(291\) −0.549859 + 0.952384i −0.0322333 + 0.0558298i
\(292\) 0 0
\(293\) 0.297685 + 0.297685i 0.0173909 + 0.0173909i 0.715749 0.698358i \(-0.246086\pi\)
−0.698358 + 0.715749i \(0.746086\pi\)
\(294\) 0 0
\(295\) −4.28845 10.6479i −0.249683 0.619943i
\(296\) 0 0
\(297\) −0.817629 3.05143i −0.0474436 0.177062i
\(298\) 0 0
\(299\) 15.7236 + 27.2341i 0.909321 + 1.57499i
\(300\) 0 0
\(301\) 6.06250 + 11.2070i 0.349436 + 0.645959i
\(302\) 0 0
\(303\) −28.4616 7.62627i −1.63508 0.438118i
\(304\) 0 0
\(305\) 2.25086 15.8893i 0.128884 0.909820i
\(306\) 0 0
\(307\) 5.95890 5.95890i 0.340093 0.340093i −0.516309 0.856402i \(-0.672695\pi\)
0.856402 + 0.516309i \(0.172695\pi\)
\(308\) 0 0
\(309\) 13.0637i 0.743167i
\(310\) 0 0
\(311\) 9.70989 + 5.60601i 0.550598 + 0.317888i 0.749363 0.662159i \(-0.230360\pi\)
−0.198765 + 0.980047i \(0.563693\pi\)
\(312\) 0 0
\(313\) −0.0792166 + 0.295640i −0.00447759 + 0.0167106i −0.968128 0.250454i \(-0.919420\pi\)
0.963651 + 0.267165i \(0.0860868\pi\)
\(314\) 0 0
\(315\) 14.5040 + 6.65614i 0.817206 + 0.375031i
\(316\) 0 0
\(317\) 5.75358 21.4727i 0.323153 1.20603i −0.593002 0.805201i \(-0.702057\pi\)
0.916155 0.400824i \(-0.131276\pi\)
\(318\) 0 0
\(319\) −5.04065 2.91022i −0.282222 0.162941i
\(320\) 0 0
\(321\) 8.54664i 0.477027i
\(322\) 0 0
\(323\) −8.53602 + 8.53602i −0.474957 + 0.474957i
\(324\) 0 0
\(325\) 15.9618 26.4336i 0.885403 1.46627i
\(326\) 0 0
\(327\) −15.4672 4.14442i −0.855337 0.229187i
\(328\) 0 0
\(329\) 14.1260 22.9719i 0.778794 1.26648i
\(330\) 0 0
\(331\) 7.04614 + 12.2043i 0.387291 + 0.670808i 0.992084 0.125575i \(-0.0400775\pi\)
−0.604793 + 0.796383i \(0.706744\pi\)
\(332\) 0 0
\(333\) 0.606728 + 2.26434i 0.0332485 + 0.124085i
\(334\) 0 0
\(335\) −6.45307 + 15.1563i −0.352569 + 0.828076i
\(336\) 0 0
\(337\) 19.3301 + 19.3301i 1.05298 + 1.05298i 0.998516 + 0.0544630i \(0.0173447\pi\)
0.0544630 + 0.998516i \(0.482655\pi\)
\(338\) 0 0
\(339\) −9.70933 + 16.8170i −0.527338 + 0.913377i
\(340\) 0 0
\(341\) −8.31635 + 4.80145i −0.450356 + 0.260013i
\(342\) 0 0
\(343\) 14.1385 11.9626i 0.763407 0.645918i
\(344\) 0 0
\(345\) −16.7558 + 21.3981i −0.902102 + 1.15203i
\(346\) 0 0
\(347\) 31.4736 8.43333i 1.68959 0.452725i 0.719308 0.694691i \(-0.244459\pi\)
0.970285 + 0.241966i \(0.0777922\pi\)
\(348\) 0 0
\(349\) 18.5313 0.991957 0.495978 0.868335i \(-0.334810\pi\)
0.495978 + 0.868335i \(0.334810\pi\)
\(350\) 0 0
\(351\) 4.45988 0.238051
\(352\) 0 0
\(353\) −26.0688 + 6.98512i −1.38750 + 0.371780i −0.873841 0.486212i \(-0.838378\pi\)
−0.513662 + 0.857992i \(0.671712\pi\)
\(354\) 0 0
\(355\) 5.95508 7.60496i 0.316063 0.403630i
\(356\) 0 0
\(357\) 10.3990 2.47959i 0.550371 0.131234i
\(358\) 0 0
\(359\) −21.1575 + 12.2153i −1.11665 + 0.644698i −0.940543 0.339673i \(-0.889683\pi\)
−0.176106 + 0.984371i \(0.556350\pi\)
\(360\) 0 0
\(361\) −15.9270 + 27.5863i −0.838261 + 1.45191i
\(362\) 0 0
\(363\) 13.7328 + 13.7328i 0.720784 + 0.720784i
\(364\) 0 0
\(365\) −12.9345 + 30.3791i −0.677022 + 1.59012i
\(366\) 0 0
\(367\) −0.168542 0.629007i −0.00879781 0.0328339i 0.961387 0.275199i \(-0.0887436\pi\)
−0.970185 + 0.242365i \(0.922077\pi\)
\(368\) 0 0
\(369\) 7.68480 + 13.3105i 0.400055 + 0.692915i
\(370\) 0 0
\(371\) 5.53125 + 0.153390i 0.287168 + 0.00796362i
\(372\) 0 0
\(373\) 0.0933104 + 0.0250025i 0.00483143 + 0.00129458i 0.261234 0.965276i \(-0.415871\pi\)
−0.256403 + 0.966570i \(0.582537\pi\)
\(374\) 0 0
\(375\) 26.3443 + 4.26136i 1.36041 + 0.220056i
\(376\) 0 0
\(377\) 5.81037 5.81037i 0.299249 0.299249i
\(378\) 0 0
\(379\) 10.4991i 0.539303i 0.962958 + 0.269651i \(0.0869085\pi\)
−0.962958 + 0.269651i \(0.913092\pi\)
\(380\) 0 0
\(381\) −10.1623 5.86721i −0.520631 0.300586i
\(382\) 0 0
\(383\) 2.86065 10.6761i 0.146172 0.545522i −0.853528 0.521047i \(-0.825542\pi\)
0.999700 0.0244754i \(-0.00779155\pi\)
\(384\) 0 0
\(385\) 25.7673 2.41246i 1.31322 0.122950i
\(386\) 0 0
\(387\) 3.36223 12.5480i 0.170912 0.637852i
\(388\) 0 0
\(389\) 6.30536 + 3.64040i 0.319695 + 0.184576i 0.651256 0.758858i \(-0.274242\pi\)
−0.331562 + 0.943433i \(0.607576\pi\)
\(390\) 0 0
\(391\) 8.61981i 0.435923i
\(392\) 0 0
\(393\) 9.21608 9.21608i 0.464890 0.464890i
\(394\) 0 0
\(395\) 1.74789 12.3388i 0.0879459 0.620831i
\(396\) 0 0
\(397\) 23.7390 + 6.36084i 1.19142 + 0.319241i 0.799449 0.600734i \(-0.205125\pi\)
0.391976 + 0.919976i \(0.371792\pi\)
\(398\) 0 0
\(399\) 39.6108 21.4278i 1.98302 1.07273i
\(400\) 0 0
\(401\) −6.84060 11.8483i −0.341603 0.591674i 0.643127 0.765759i \(-0.277637\pi\)
−0.984731 + 0.174085i \(0.944303\pi\)
\(402\) 0 0
\(403\) −3.50882 13.0951i −0.174787 0.652314i
\(404\) 0 0
\(405\) 8.20011 + 20.3602i 0.407467 + 1.01171i
\(406\) 0 0
\(407\) 2.68818 + 2.68818i 0.133248 + 0.133248i
\(408\) 0 0
\(409\) −6.44604 + 11.1649i −0.318736 + 0.552067i −0.980225 0.197888i \(-0.936592\pi\)
0.661489 + 0.749955i \(0.269925\pi\)
\(410\) 0 0
\(411\) 35.6879 20.6044i 1.76035 1.01634i
\(412\) 0 0
\(413\) 9.33411 + 9.86658i 0.459302 + 0.485503i
\(414\) 0 0
\(415\) −0.854730 + 0.103997i −0.0419570 + 0.00510501i
\(416\) 0 0
\(417\) 9.99421 2.67794i 0.489419 0.131139i
\(418\) 0 0
\(419\) −8.27208 −0.404117 −0.202059 0.979373i \(-0.564763\pi\)
−0.202059 + 0.979373i \(0.564763\pi\)
\(420\) 0 0
\(421\) −21.7954 −1.06224 −0.531121 0.847296i \(-0.678229\pi\)
−0.531121 + 0.847296i \(0.678229\pi\)
\(422\) 0 0
\(423\) −26.5578 + 7.11613i −1.29128 + 0.345998i
\(424\) 0 0
\(425\) 7.41180 4.08722i 0.359525 0.198259i
\(426\) 0 0
\(427\) 4.40419 + 18.4704i 0.213134 + 0.893845i
\(428\) 0 0
\(429\) −55.8463 + 32.2429i −2.69629 + 1.55670i
\(430\) 0 0
\(431\) −0.922967 + 1.59863i −0.0444578 + 0.0770031i −0.887398 0.461004i \(-0.847489\pi\)
0.842940 + 0.538007i \(0.180823\pi\)
\(432\) 0 0
\(433\) −28.5087 28.5087i −1.37004 1.37004i −0.860370 0.509670i \(-0.829767\pi\)
−0.509670 0.860370i \(-0.670233\pi\)
\(434\) 0 0
\(435\) 6.53393 + 2.78194i 0.313278 + 0.133384i
\(436\) 0 0
\(437\) 9.39827 + 35.0748i 0.449580 + 1.67786i
\(438\) 0 0
\(439\) −10.1088 17.5090i −0.482469 0.835660i 0.517329 0.855787i \(-0.326926\pi\)
−0.999797 + 0.0201265i \(0.993593\pi\)
\(440\) 0 0
\(441\) −18.8532 1.04646i −0.897770 0.0498315i
\(442\) 0 0
\(443\) 23.1032 + 6.19049i 1.09767 + 0.294119i 0.761815 0.647795i \(-0.224309\pi\)
0.335853 + 0.941914i \(0.390975\pi\)
\(444\) 0 0
\(445\) 7.94838 + 1.12596i 0.376789 + 0.0533754i
\(446\) 0 0
\(447\) 4.33708 4.33708i 0.205137 0.205137i
\(448\) 0 0
\(449\) 15.9935i 0.754782i 0.926054 + 0.377391i \(0.123179\pi\)
−0.926054 + 0.377391i \(0.876821\pi\)
\(450\) 0 0
\(451\) 21.5858 + 12.4626i 1.01644 + 0.586840i
\(452\) 0 0
\(453\) 0.637878 2.38059i 0.0299701 0.111850i
\(454\) 0 0
\(455\) −6.12539 + 36.0194i −0.287163 + 1.68862i
\(456\) 0 0
\(457\) 3.93478 14.6848i 0.184061 0.686925i −0.810769 0.585367i \(-0.800950\pi\)
0.994830 0.101558i \(-0.0323829\pi\)
\(458\) 0 0
\(459\) 1.05869 + 0.611235i 0.0494154 + 0.0285300i
\(460\) 0 0
\(461\) 24.4079i 1.13679i −0.822756 0.568395i \(-0.807564\pi\)
0.822756 0.568395i \(-0.192436\pi\)
\(462\) 0 0
\(463\) 5.25987 5.25987i 0.244447 0.244447i −0.574240 0.818687i \(-0.694702\pi\)
0.818687 + 0.574240i \(0.194702\pi\)
\(464\) 0 0
\(465\) 9.36492 7.04090i 0.434288 0.326514i
\(466\) 0 0
\(467\) −35.7255 9.57262i −1.65318 0.442968i −0.692679 0.721246i \(-0.743570\pi\)
−0.960501 + 0.278278i \(0.910236\pi\)
\(468\) 0 0
\(469\) 0.540307 19.4834i 0.0249490 0.899662i
\(470\) 0 0
\(471\) 21.7261 + 37.6307i 1.00109 + 1.73393i
\(472\) 0 0
\(473\) −5.45260 20.3494i −0.250711 0.935666i
\(474\) 0 0
\(475\) 25.7030 24.7124i 1.17933 1.13388i
\(476\) 0 0
\(477\) −3.98915 3.98915i −0.182651 0.182651i
\(478\) 0 0
\(479\) −11.0150 + 19.0786i −0.503289 + 0.871722i 0.496704 + 0.867920i \(0.334544\pi\)
−0.999993 + 0.00380219i \(0.998790\pi\)
\(480\) 0 0
\(481\) −4.64801 + 2.68353i −0.211931 + 0.122359i
\(482\) 0 0
\(483\) 9.18076 30.8189i 0.417739 1.40231i
\(484\) 0 0
\(485\) −0.124431 1.02267i −0.00565010 0.0464370i
\(486\) 0 0
\(487\) 14.4450 3.87053i 0.654566 0.175390i 0.0837736 0.996485i \(-0.473303\pi\)
0.570792 + 0.821094i \(0.306636\pi\)
\(488\) 0 0
\(489\) 20.8570 0.943187
\(490\) 0 0
\(491\) −13.9698 −0.630449 −0.315224 0.949017i \(-0.602080\pi\)
−0.315224 + 0.949017i \(0.602080\pi\)
\(492\) 0 0
\(493\) 2.17559 0.582948i 0.0979838 0.0262547i
\(494\) 0 0
\(495\) −20.7744 16.2675i −0.933742 0.731168i
\(496\) 0 0
\(497\) −3.26288 + 10.9531i −0.146360 + 0.491316i
\(498\) 0 0
\(499\) −5.90449 + 3.40896i −0.264321 + 0.152606i −0.626304 0.779579i \(-0.715433\pi\)
0.361983 + 0.932185i \(0.382100\pi\)
\(500\) 0 0
\(501\) −20.8923 + 36.1865i −0.933400 + 1.61670i
\(502\) 0 0
\(503\) −13.8531 13.8531i −0.617679 0.617679i 0.327256 0.944936i \(-0.393876\pi\)
−0.944936 + 0.327256i \(0.893876\pi\)
\(504\) 0 0
\(505\) 25.6046 10.3123i 1.13939 0.458892i
\(506\) 0 0
\(507\) −15.5314 57.9640i −0.689774 2.57427i
\(508\) 0 0
\(509\) −22.4079 38.8116i −0.993213 1.72030i −0.597332 0.801994i \(-0.703772\pi\)
−0.395882 0.918301i \(-0.629561\pi\)
\(510\) 0 0
\(511\) 1.08299 39.0525i 0.0479085 1.72758i
\(512\) 0 0
\(513\) 4.97434 + 1.33287i 0.219623 + 0.0588477i
\(514\) 0 0
\(515\) 7.35429 + 9.78176i 0.324069 + 0.431036i
\(516\) 0 0
\(517\) −31.5289 + 31.5289i −1.38664 + 1.38664i
\(518\) 0 0
\(519\) 6.88642i 0.302280i
\(520\) 0 0
\(521\) 31.4574 + 18.1620i 1.37818 + 0.795690i 0.991940 0.126710i \(-0.0404418\pi\)
0.386236 + 0.922400i \(0.373775\pi\)
\(522\) 0 0
\(523\) −4.05288 + 15.1255i −0.177220 + 0.661394i 0.818943 + 0.573875i \(0.194560\pi\)
−0.996163 + 0.0875187i \(0.972106\pi\)
\(524\) 0 0
\(525\) −30.8530 + 6.71911i −1.34654 + 0.293246i
\(526\) 0 0
\(527\) 0.961782 3.58942i 0.0418959 0.156358i
\(528\) 0 0
\(529\) 2.53622 + 1.46429i 0.110271 + 0.0636647i
\(530\) 0 0
\(531\) 13.8476i 0.600934i
\(532\) 0 0
\(533\) −24.8821 + 24.8821i −1.07776 + 1.07776i
\(534\) 0 0
\(535\) −4.81139 6.39951i −0.208015 0.276675i
\(536\) 0 0
\(537\) 17.2389 + 4.61916i 0.743916 + 0.199332i
\(538\) 0 0
\(539\) −27.3269 + 13.8176i −1.17705 + 0.595165i
\(540\) 0 0
\(541\) −7.57826 13.1259i −0.325815 0.564328i 0.655862 0.754881i \(-0.272305\pi\)
−0.981677 + 0.190553i \(0.938972\pi\)
\(542\) 0 0
\(543\) 13.4249 + 50.1024i 0.576118 + 2.15010i
\(544\) 0 0
\(545\) 13.9146 5.60412i 0.596035 0.240054i
\(546\) 0 0
\(547\) 24.0863 + 24.0863i 1.02985 + 1.02985i 0.999540 + 0.0303138i \(0.00965066\pi\)
0.0303138 + 0.999540i \(0.490349\pi\)
\(548\) 0 0
\(549\) 9.67964 16.7656i 0.413117 0.715540i
\(550\) 0 0
\(551\) 8.21710 4.74414i 0.350060 0.202107i
\(552\) 0 0
\(553\) 3.42004 + 14.3431i 0.145435 + 0.609929i
\(554\) 0 0
\(555\) −3.65198 2.85969i −0.155018 0.121387i
\(556\) 0 0
\(557\) 25.2878 6.77586i 1.07148 0.287102i 0.320379 0.947289i \(-0.396190\pi\)
0.751101 + 0.660187i \(0.229523\pi\)
\(558\) 0 0
\(559\) 29.7420 1.25795
\(560\) 0 0
\(561\) −17.6758 −0.746273
\(562\) 0 0
\(563\) 4.24428 1.13725i 0.178875 0.0479294i −0.168270 0.985741i \(-0.553818\pi\)
0.347145 + 0.937812i \(0.387151\pi\)
\(564\) 0 0
\(565\) −2.19717 18.0581i −0.0924358 0.759711i
\(566\) 0 0
\(567\) −17.8481 18.8663i −0.749550 0.792308i
\(568\) 0 0
\(569\) −9.41275 + 5.43445i −0.394603 + 0.227824i −0.684153 0.729339i \(-0.739828\pi\)
0.289550 + 0.957163i \(0.406494\pi\)
\(570\) 0 0
\(571\) −22.5354 + 39.0325i −0.943078 + 1.63346i −0.183523 + 0.983015i \(0.558750\pi\)
−0.759555 + 0.650444i \(0.774583\pi\)
\(572\) 0 0
\(573\) 19.3548 + 19.3548i 0.808560 + 0.808560i
\(574\) 0 0
\(575\) 0.500131 25.4551i 0.0208569 1.06155i
\(576\) 0 0
\(577\) 6.05442 + 22.5954i 0.252049 + 0.940659i 0.969709 + 0.244265i \(0.0785467\pi\)
−0.717660 + 0.696394i \(0.754787\pi\)
\(578\) 0 0
\(579\) 6.62753 + 11.4792i 0.275431 + 0.477060i
\(580\) 0 0
\(581\) 0.896079 0.484740i 0.0371756 0.0201104i
\(582\) 0 0
\(583\) −8.83721 2.36792i −0.366000 0.0980693i
\(584\) 0 0
\(585\) 29.7742 22.3853i 1.23101 0.925519i
\(586\) 0 0
\(587\) −13.2002 + 13.2002i −0.544831 + 0.544831i −0.924941 0.380110i \(-0.875886\pi\)
0.380110 + 0.924941i \(0.375886\pi\)
\(588\) 0 0
\(589\) 15.6543i 0.645025i
\(590\) 0 0
\(591\) 36.8332 + 21.2657i 1.51512 + 0.874753i
\(592\) 0 0
\(593\) −0.815375 + 3.04302i −0.0334835 + 0.124962i −0.980645 0.195796i \(-0.937271\pi\)
0.947161 + 0.320758i \(0.103938\pi\)
\(594\) 0 0
\(595\) −6.39058 + 7.71082i −0.261988 + 0.316113i
\(596\) 0 0
\(597\) −2.50101 + 9.33389i −0.102360 + 0.382011i
\(598\) 0 0
\(599\) 14.3732 + 8.29838i 0.587274 + 0.339063i 0.764019 0.645194i \(-0.223223\pi\)
−0.176745 + 0.984257i \(0.556557\pi\)
\(600\) 0 0
\(601\) 10.4871i 0.427778i 0.976858 + 0.213889i \(0.0686131\pi\)
−0.976858 + 0.213889i \(0.931387\pi\)
\(602\) 0 0
\(603\) −14.0515 + 14.0515i −0.572222 + 0.572222i
\(604\) 0 0
\(605\) −18.0137 2.55180i −0.732362 0.103745i
\(606\) 0 0
\(607\) −31.0456 8.31863i −1.26010 0.337643i −0.433870 0.900975i \(-0.642852\pi\)
−0.826230 + 0.563332i \(0.809519\pi\)
\(608\) 0 0
\(609\) −8.39940 0.232929i −0.340361 0.00943874i
\(610\) 0 0
\(611\) −31.4744 54.5152i −1.27332 2.20545i
\(612\) 0 0
\(613\) 6.07304 + 22.6649i 0.245288 + 0.915427i 0.973238 + 0.229797i \(0.0738064\pi\)
−0.727951 + 0.685630i \(0.759527\pi\)
\(614\) 0 0
\(615\) −27.9806 11.9133i −1.12829 0.480390i
\(616\) 0 0
\(617\) −24.6695 24.6695i −0.993158 0.993158i 0.00681844 0.999977i \(-0.497830\pi\)
−0.999977 + 0.00681844i \(0.997830\pi\)
\(618\) 0 0
\(619\) 12.1208 20.9938i 0.487174 0.843811i −0.512717 0.858558i \(-0.671361\pi\)
0.999891 + 0.0147470i \(0.00469428\pi\)
\(620\) 0 0
\(621\) 3.18456 1.83861i 0.127792 0.0737808i
\(622\) 0 0
\(623\) −9.23951 + 2.20312i −0.370173 + 0.0882663i
\(624\) 0 0
\(625\) −22.1249 + 11.6399i −0.884997 + 0.465597i
\(626\) 0 0
\(627\) −71.9245 + 19.2721i −2.87239 + 0.769654i
\(628\) 0 0
\(629\) −1.47113 −0.0586579
\(630\) 0 0
\(631\) 25.2348 1.00458 0.502291 0.864699i \(-0.332491\pi\)
0.502291 + 0.864699i \(0.332491\pi\)
\(632\) 0 0
\(633\) 49.1586 13.1720i 1.95388 0.523541i
\(634\) 0 0
\(635\) 10.9123 1.32772i 0.433040 0.0526890i
\(636\) 0 0
\(637\) −8.85748 42.3135i −0.350946 1.67652i
\(638\) 0 0
\(639\) 10.0911 5.82608i 0.399197 0.230476i
\(640\) 0 0
\(641\) 18.0215 31.2142i 0.711808 1.23289i −0.252370 0.967631i \(-0.581210\pi\)
0.964178 0.265257i \(-0.0854568\pi\)
\(642\) 0 0
\(643\) 16.5722 + 16.5722i 0.653545 + 0.653545i 0.953845 0.300300i \(-0.0970868\pi\)
−0.300300 + 0.953845i \(0.597087\pi\)
\(644\) 0 0
\(645\) 9.60281 + 23.8430i 0.378110 + 0.938816i
\(646\) 0 0
\(647\) −7.11698 26.5609i −0.279797 1.04422i −0.952558 0.304358i \(-0.901558\pi\)
0.672760 0.739860i \(-0.265108\pi\)
\(648\) 0 0
\(649\) −11.2285 19.4483i −0.440755 0.763411i
\(650\) 0 0
\(651\) −7.26172 + 11.8091i −0.284609 + 0.462834i
\(652\) 0 0
\(653\) −11.5652 3.09889i −0.452581 0.121269i 0.0253256 0.999679i \(-0.491938\pi\)
−0.477907 + 0.878410i \(0.658604\pi\)
\(654\) 0 0
\(655\) −1.71251 + 12.0890i −0.0669134 + 0.472357i
\(656\) 0 0
\(657\) −28.1648 + 28.1648i −1.09881 + 1.09881i
\(658\) 0 0
\(659\) 46.6055i 1.81549i −0.419521 0.907746i \(-0.637802\pi\)
0.419521 0.907746i \(-0.362198\pi\)
\(660\) 0 0
\(661\) 2.27963 + 1.31614i 0.0886673 + 0.0511921i 0.543678 0.839294i \(-0.317031\pi\)
−0.455011 + 0.890486i \(0.650365\pi\)
\(662\) 0 0
\(663\) 6.45860 24.1038i 0.250831 0.936115i
\(664\) 0 0
\(665\) −17.5967 + 38.3438i −0.682370 + 1.48691i
\(666\) 0 0
\(667\) 1.75352 6.54423i 0.0678966 0.253394i
\(668\) 0 0
\(669\) −57.7816 33.3602i −2.23397 1.28978i
\(670\) 0 0
\(671\) 31.3953i 1.21200i
\(672\) 0 0
\(673\) −22.7177 + 22.7177i −0.875704 + 0.875704i −0.993087 0.117383i \(-0.962549\pi\)
0.117383 + 0.993087i \(0.462549\pi\)
\(674\) 0 0
\(675\) −3.09095 1.86646i −0.118971 0.0718402i
\(676\) 0 0
\(677\) −10.0751 2.69961i −0.387216 0.103754i 0.0599584 0.998201i \(-0.480903\pi\)
−0.447175 + 0.894447i \(0.647570\pi\)
\(678\) 0 0
\(679\) 0.579983 + 1.07214i 0.0222577 + 0.0411450i
\(680\) 0 0
\(681\) −3.50863 6.07713i −0.134451 0.232876i
\(682\) 0 0
\(683\) 2.50520 + 9.34955i 0.0958589 + 0.357750i 0.997148 0.0754672i \(-0.0240448\pi\)
−0.901289 + 0.433218i \(0.857378\pi\)
\(684\) 0 0
\(685\) −15.1228 + 35.5188i −0.577812 + 1.35710i
\(686\) 0 0
\(687\) 40.6089 + 40.6089i 1.54933 + 1.54933i
\(688\) 0 0
\(689\) 6.45809 11.1857i 0.246034 0.426143i
\(690\) 0 0
\(691\) 19.8093 11.4369i 0.753583 0.435081i −0.0734041 0.997302i \(-0.523386\pi\)
0.826987 + 0.562221i \(0.190053\pi\)
\(692\) 0 0
\(693\) 29.9207 + 8.91320i 1.13659 + 0.338584i
\(694\) 0 0
\(695\) −5.97585 + 7.63149i −0.226677 + 0.289479i
\(696\) 0 0
\(697\) −9.31666 + 2.49639i −0.352894 + 0.0945576i
\(698\) 0 0
\(699\) −5.87389 −0.222171
\(700\) 0 0
\(701\) −47.3309 −1.78766 −0.893831 0.448403i \(-0.851993\pi\)
−0.893831 + 0.448403i \(0.851993\pi\)
\(702\) 0 0
\(703\) −5.98618 + 1.60399i −0.225773 + 0.0604957i
\(704\) 0 0
\(705\) 33.5405 42.8330i 1.26321 1.61319i
\(706\) 0 0
\(707\) −23.7259 + 22.4455i −0.892304 + 0.844149i
\(708\) 0 0
\(709\) 37.1759 21.4635i 1.39617 0.806079i 0.402182 0.915560i \(-0.368252\pi\)
0.993989 + 0.109480i \(0.0349187\pi\)
\(710\) 0 0
\(711\) 7.51667 13.0192i 0.281897 0.488260i
\(712\) 0 0
\(713\) −7.90399 7.90399i −0.296007 0.296007i
\(714\) 0 0
\(715\) 23.6650 55.5818i 0.885020 2.07864i
\(716\) 0 0
\(717\) −9.56048 35.6802i −0.357043 1.33250i
\(718\) 0 0
\(719\) 10.8241 + 18.7480i 0.403673 + 0.699181i 0.994166 0.107861i \(-0.0344002\pi\)
−0.590493 + 0.807042i \(0.701067\pi\)
\(720\) 0 0
\(721\) −12.3347 7.58494i −0.459368 0.282478i
\(722\) 0 0
\(723\) 36.9431 + 9.89888i 1.37393 + 0.368143i
\(724\) 0 0
\(725\) −6.45856 + 1.59527i −0.239865 + 0.0592470i
\(726\) 0 0
\(727\) 5.06759 5.06759i 0.187947 0.187947i −0.606861 0.794808i \(-0.707572\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(728\) 0 0
\(729\) 21.3073i 0.789159i
\(730\) 0 0
\(731\) 7.06019 + 4.07620i 0.261130 + 0.150764i
\(732\) 0 0
\(733\) −8.20019 + 30.6035i −0.302881 + 1.13037i 0.631873 + 0.775072i \(0.282286\pi\)
−0.934754 + 0.355295i \(0.884380\pi\)
\(734\) 0 0
\(735\) 31.0612 20.7624i 1.14571 0.765834i
\(736\) 0 0
\(737\) −8.34085 + 31.1285i −0.307239 + 1.14663i
\(738\) 0 0
\(739\) −14.6237 8.44299i −0.537941 0.310580i 0.206303 0.978488i \(-0.433857\pi\)
−0.744244 + 0.667908i \(0.767190\pi\)
\(740\) 0 0
\(741\) 105.123i 3.86177i
\(742\) 0 0
\(743\) −23.6519 + 23.6519i −0.867703 + 0.867703i −0.992218 0.124515i \(-0.960262\pi\)
0.124515 + 0.992218i \(0.460262\pi\)
\(744\) 0 0
\(745\) −0.805907 + 5.68908i −0.0295262 + 0.208432i
\(746\) 0 0
\(747\) −1.00331 0.268835i −0.0367090 0.00983615i
\(748\) 0 0
\(749\) 8.06971 + 4.96229i 0.294861 + 0.181318i
\(750\) 0 0
\(751\) 4.13856 + 7.16820i 0.151018 + 0.261571i 0.931602 0.363480i \(-0.118411\pi\)
−0.780584 + 0.625051i \(0.785078\pi\)
\(752\) 0 0
\(753\) 0.366228 + 1.36678i 0.0133461 + 0.0498083i
\(754\) 0 0
\(755\) 0.862545 + 2.14163i 0.0313912 + 0.0779418i
\(756\) 0 0
\(757\) 21.6103 + 21.6103i 0.785439 + 0.785439i 0.980743 0.195304i \(-0.0625693\pi\)
−0.195304 + 0.980743i \(0.562569\pi\)
\(758\) 0 0
\(759\) −26.5846 + 46.0459i −0.964960 + 1.67136i
\(760\) 0 0
\(761\) −18.9354 + 10.9324i −0.686408 + 0.396298i −0.802265 0.596968i \(-0.796372\pi\)
0.115857 + 0.993266i \(0.463038\pi\)
\(762\) 0 0
\(763\) −12.8936 + 12.1978i −0.466779 + 0.441589i
\(764\) 0 0
\(765\) 10.1358 1.23324i 0.366459 0.0445880i
\(766\) 0 0
\(767\) 30.6236 8.20558i 1.10576 0.296286i
\(768\) 0 0
\(769\) −24.3594 −0.878421 −0.439211 0.898384i \(-0.644742\pi\)
−0.439211 + 0.898384i \(0.644742\pi\)
\(770\) 0 0
\(771\) 46.2987 1.66741
\(772\) 0 0
\(773\) 17.9762 4.81671i 0.646560 0.173245i 0.0793867 0.996844i \(-0.474704\pi\)
0.567173 + 0.823599i \(0.308037\pi\)
\(774\) 0 0
\(775\) −3.04850 + 10.5441i −0.109505 + 0.378755i
\(776\) 0 0
\(777\) 5.25982 + 1.56687i 0.188695 + 0.0562111i
\(778\) 0 0
\(779\) −35.1885 + 20.3161i −1.26076 + 0.727900i
\(780\) 0 0
\(781\) 9.44827 16.3649i 0.338086 0.585582i
\(782\) 0 0
\(783\) −0.679423 0.679423i −0.0242806 0.0242806i
\(784\) 0 0
\(785\) −37.4524 15.9461i −1.33673 0.569139i
\(786\) 0 0
\(787\) 6.78612 + 25.3262i 0.241899 + 0.902780i 0.974917 + 0.222570i \(0.0714446\pi\)
−0.733018 + 0.680210i \(0.761889\pi\)
\(788\) 0 0
\(789\) 30.3706 + 52.6034i 1.08122 + 1.87273i
\(790\) 0 0
\(791\) 10.2412 + 18.9317i 0.364137 + 0.673134i
\(792\) 0 0
\(793\) 42.8126 + 11.4716i 1.52032 + 0.407369i
\(794\) 0 0
\(795\) 11.0523 + 1.56565i 0.391984 + 0.0555279i
\(796\) 0 0
\(797\) −12.0225 + 12.0225i −0.425859 + 0.425859