Properties

Label 280.2.bo.a.33.2
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 33.2
Character \(\chi\) \(=\) 280.33
Dual form 280.2.bo.a.17.2

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

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

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
\(3\) −2.30560 0.617784i −1.33114 0.356678i −0.478000 0.878360i \(-0.658638\pi\)
−0.853140 + 0.521682i \(0.825305\pi\)
\(4\) 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 0.980750 + 0.195270i \(0.0625583\pi\)
−0.321266 + 0.946989i \(0.604108\pi\)
\(12\) 0 0
\(13\) 4.36695 4.36695i 1.21117 1.21117i 0.240533 0.970641i \(-0.422678\pi\)
0.970641 0.240533i \(-0.0773224\pi\)
\(14\) 0 0
\(15\) −2.09085 4.91077i −0.539855 1.26795i
\(16\) 0 0
\(17\) 0.438132 1.63513i 0.106263 0.396577i −0.892223 0.451595i \(-0.850855\pi\)
0.998485 + 0.0550183i \(0.0175217\pi\)
\(18\) 0 0
\(19\) 3.56560 6.17580i 0.818004 1.41682i −0.0891466 0.996019i \(-0.528414\pi\)
0.907151 0.420806i \(-0.138253\pi\)
\(20\) 0 0
\(21\) 0.175064 + 6.31281i 0.0382021 + 1.37757i
\(22\) 0 0
\(23\) 4.91851 1.31791i 1.02558 0.274803i 0.293454 0.955973i \(-0.405195\pi\)
0.732125 + 0.681170i \(0.238529\pi\)
\(24\) 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 \(0.0394237\pi\)
−0.992340 + 0.123537i \(0.960576\pi\)
\(30\) 0 0
\(31\) −1.90109 + 1.09759i −0.341446 + 0.197134i −0.660911 0.750464i \(-0.729830\pi\)
0.319465 + 0.947598i \(0.396497\pi\)
\(32\) 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 0.944969 0.327159i \(-0.106091\pi\)
−0.981947 + 0.189157i \(0.939425\pi\)
\(38\) 0 0
\(39\) −12.7663 + 7.37062i −2.04424 + 1.18024i
\(40\) 0 0
\(41\) 5.69781i 0.889849i −0.895568 0.444924i \(-0.853231\pi\)
0.895568 0.444924i \(-0.146769\pi\)
\(42\) 0 0
\(43\) 3.40535 + 3.40535i 0.519312 + 0.519312i 0.917363 0.398051i \(-0.130313\pi\)
−0.398051 + 0.917363i \(0.630313\pi\)
\(44\) 0 0
\(45\) 0.845995 + 5.97207i 0.126113 + 0.890264i
\(46\) 0 0
\(47\) −9.84549 + 2.63809i −1.43611 + 0.384805i −0.891170 0.453669i \(-0.850115\pi\)
−0.544942 + 0.838474i \(0.683448\pi\)
\(48\) 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 −0.993086 0.117390i \(-0.962547\pi\)
0.918733 + 0.394880i \(0.129214\pi\)
\(54\) 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 0.983324 0.181860i \(-0.0582117\pi\)
−0.649157 + 0.760654i \(0.724878\pi\)
\(60\) 0 0
\(61\) 6.21535 + 3.58843i 0.795794 + 0.459452i 0.841998 0.539480i \(-0.181379\pi\)
−0.0462043 + 0.998932i \(0.514713\pi\)
\(62\) 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 −0.203538 0.979067i \(-0.565244\pi\)
−0.665803 + 0.746128i \(0.731911\pi\)
\(68\) 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 −0.704420 0.709784i \(-0.748793\pi\)
−0.964937 + 0.262481i \(0.915459\pi\)
\(74\) 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 0.746303 0.665606i \(-0.231827\pi\)
−0.203280 + 0.979121i \(0.565160\pi\)
\(80\) 0 0
\(81\) −4.90805 8.50099i −0.545339 0.944555i
\(82\) 0 0
\(83\) −0.272283 + 0.272283i −0.0298869 + 0.0298869i −0.721892 0.692005i \(-0.756727\pi\)
0.692005 + 0.721892i \(0.256727\pi\)
\(84\) 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 −0.755066 0.655649i \(-0.772395\pi\)
0.945342 + 0.326082i \(0.105729\pi\)
\(90\) 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 0.723452 0.690374i \(-0.242554\pi\)
−0.690374 + 0.723452i \(0.742554\pi\)
\(98\) 0 0
\(99\) 11.8001i 1.18595i
\(100\) 0 0
\(101\) 10.6907 6.17228i 1.06376 0.614165i 0.137294 0.990530i \(-0.456160\pi\)
0.926471 + 0.376365i \(0.122826\pi\)
\(102\) 0 0
\(103\) −1.41652 5.28651i −0.139573 0.520895i −0.999937 0.0112145i \(-0.996430\pi\)
0.860364 0.509681i \(-0.170236\pi\)
\(104\) 0 0
\(105\) −10.8726 + 9.01099i −1.06106 + 0.879382i
\(106\) 0 0
\(107\) 0.926726 + 3.45859i 0.0895900 + 0.334354i 0.996144 0.0877359i \(-0.0279632\pi\)
−0.906554 + 0.422090i \(0.861297\pi\)
\(108\) 0 0
\(109\) 5.80975 3.35426i 0.556473 0.321280i −0.195255 0.980752i \(-0.562554\pi\)
0.751729 + 0.659472i \(0.229220\pi\)
\(110\) 0 0
\(111\) 2.07436i 0.196889i
\(112\) 0 0
\(113\) 5.75259 + 5.75259i 0.541158 + 0.541158i 0.923869 0.382710i \(-0.125009\pi\)
−0.382710 + 0.923869i \(0.625009\pi\)
\(114\) 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 −0.535849 0.844314i \(-0.680009\pi\)
0.844314 + 0.535849i \(0.180009\pi\)
\(128\) 0 0
\(129\) −5.74762 9.95516i −0.506049 0.876503i
\(130\) 0 0
\(131\) −4.72880 2.73018i −0.413157 0.238537i 0.278988 0.960295i \(-0.410001\pi\)
−0.692145 + 0.721758i \(0.743334\pi\)
\(132\) 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 −0.537571 0.843218i \(-0.680658\pi\)
−0.887160 + 0.461463i \(0.847325\pi\)
\(138\) 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 0.406068 0.913843i \(-0.366900\pi\)
−0.588377 + 0.808587i \(0.700233\pi\)
\(150\) 0 0
\(151\) −0.516263 0.894194i −0.0420129 0.0727685i 0.844254 0.535943i \(-0.180044\pi\)
−0.886267 + 0.463174i \(0.846710\pi\)
\(152\) 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 0.475815 + 0.879545i \(0.342153\pi\)
−0.851841 + 0.523801i \(0.824513\pi\)
\(158\) 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 −0.573739 0.819038i \(-0.694508\pi\)
−0.0873531 + 0.996177i \(0.527841\pi\)
\(164\) 0 0
\(165\) 14.0309 18.6622i 1.09231 1.45285i
\(166\) 0 0
\(167\) 12.3783 + 12.3783i 0.957862 + 0.957862i 0.999147 0.0412856i \(-0.0131454\pi\)
−0.0412856 + 0.999147i \(0.513145\pi\)
\(168\) 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 0.931714 0.363194i \(-0.118314\pi\)
−0.988485 + 0.151322i \(0.951647\pi\)
\(174\) 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 −0.722075 0.691815i \(-0.756812\pi\)
0.238092 + 0.971243i \(0.423478\pi\)
\(180\) 0 0
\(181\) 21.7307i 1.61523i 0.589708 + 0.807617i \(0.299243\pi\)
−0.589708 + 0.807617i \(0.700757\pi\)
\(182\) 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 −0.995415 0.0956469i \(-0.969508\pi\)
0.580540 + 0.814232i \(0.302841\pi\)
\(192\) 0 0
\(193\) −1.43727 + 5.36396i −0.103457 + 0.386106i −0.998166 0.0605441i \(-0.980716\pi\)
0.894709 + 0.446650i \(0.147383\pi\)
\(194\) 0 0
\(195\) −30.5757 12.3144i −2.18957 0.881855i
\(196\) 0 0
\(197\) −12.5995 + 12.5995i −0.897678 + 0.897678i −0.995230 0.0975523i \(-0.968899\pi\)
0.0975523 + 0.995230i \(0.468899\pi\)
\(198\) 0 0
\(199\) 2.02418 + 3.50598i 0.143490 + 0.248532i 0.928809 0.370560i \(-0.120834\pi\)
−0.785318 + 0.619092i \(0.787501\pi\)
\(200\) 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 0.412730 0.910854i \(-0.364575\pi\)
0.910854 0.412730i \(-0.135425\pi\)
\(224\) 0 0
\(225\) −9.34776 + 9.72245i −0.623184 + 0.648163i
\(226\) 0 0
\(227\) 0.760893 2.83969i 0.0505022 0.188477i −0.936067 0.351823i \(-0.885562\pi\)
0.986569 + 0.163346i \(0.0522287\pi\)
\(228\) 0 0
\(229\) −12.0300 + 20.8366i −0.794965 + 1.37692i 0.127896 + 0.991788i \(0.459178\pi\)
−0.922861 + 0.385133i \(0.874156\pi\)
\(230\) 0 0
\(231\) −23.5328 + 14.4710i −1.54834 + 0.952120i
\(232\) 0 0
\(233\) 2.37700 0.636915i 0.155722 0.0417257i −0.180116 0.983645i \(-0.557647\pi\)
0.335838 + 0.941920i \(0.390981\pi\)
\(234\) 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 \(-0.833145\pi\)
0.865730 0.500511i \(-0.166855\pi\)
\(240\) 0 0
\(241\) −13.8765 + 8.01160i −0.893864 + 0.516073i −0.875204 0.483753i \(-0.839273\pi\)
−0.0186595 + 0.999826i \(0.505940\pi\)
\(242\) 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 \(0.00595558\pi\)
−0.999825 + 0.0187089i \(0.994044\pi\)
\(252\) 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 −0.790438 0.612542i \(-0.790147\pi\)
−0.378269 + 0.925696i \(0.623480\pi\)
\(258\) 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 0.395843 + 0.918318i \(0.370453\pi\)
−0.801969 + 0.597366i \(0.796214\pi\)
\(264\) 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 0.614095 0.789232i \(-0.289521\pi\)
−0.990543 + 0.137205i \(0.956188\pi\)
\(270\) 0 0
\(271\) −10.0880 5.82432i −0.612803 0.353802i 0.161259 0.986912i \(-0.448445\pi\)
−0.774062 + 0.633110i \(0.781778\pi\)
\(272\) 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 0.761536 0.648123i \(-0.224446\pi\)
0.335448 + 0.942059i \(0.391112\pi\)
\(278\) 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 −0.506907 0.862001i \(-0.669211\pi\)
−0.869995 + 0.493061i \(0.835878\pi\)
\(284\) 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 −0.698358 0.715749i \(-0.746086\pi\)
0.715749 + 0.698358i \(0.246086\pi\)
\(294\) 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 0.856402 0.516309i \(-0.172695\pi\)
−0.516309 + 0.856402i \(0.672695\pi\)
\(308\) 0 0
\(309\) 13.0637i 0.743167i
\(310\) 0 0
\(311\) 9.70989 5.60601i 0.550598 0.317888i −0.198765 0.980047i \(-0.563693\pi\)
0.749363 + 0.662159i \(0.230360\pi\)
\(312\) 0 0
\(313\) −0.0792166 0.295640i −0.00447759 0.0167106i 0.963651 0.267165i \(-0.0860868\pi\)
−0.968128 + 0.250454i \(0.919420\pi\)
\(314\) 0 0
\(315\) 14.5040 6.65614i 0.817206 0.375031i
\(316\) 0 0
\(317\) 5.75358 + 21.4727i 0.323153 + 1.20603i 0.916155 + 0.400824i \(0.131276\pi\)
−0.593002 + 0.805201i \(0.702057\pi\)
\(318\) 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 −0.604793 0.796383i \(-0.706744\pi\)
0.992084 + 0.125575i \(0.0400775\pi\)
\(332\) 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 0.0544630 0.998516i \(-0.482655\pi\)
0.998516 0.0544630i \(-0.0173447\pi\)
\(338\) 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 0.970285 0.241966i \(-0.0777922\pi\)
0.719308 + 0.694691i \(0.244459\pi\)
\(348\) 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 −0.513662 0.857992i \(-0.671712\pi\)
−0.873841 + 0.486212i \(0.838378\pi\)
\(354\) 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 −0.176106 0.984371i \(-0.556350\pi\)
−0.940543 + 0.339673i \(0.889683\pi\)
\(360\) 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 −0.970185 0.242365i \(-0.922077\pi\)
0.961387 + 0.275199i \(0.0887436\pi\)
\(368\) 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 −0.256403 0.966570i \(-0.582537\pi\)
0.261234 + 0.965276i \(0.415871\pi\)
\(374\) 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 \(-0.913092\pi\)
0.962958 0.269651i \(-0.0869085\pi\)
\(380\) 0 0
\(381\) −10.1623 + 5.86721i −0.520631 + 0.300586i
\(382\) 0 0
\(383\) 2.86065 + 10.6761i 0.146172 + 0.545522i 0.999700 + 0.0244754i \(0.00779155\pi\)
−0.853528 + 0.521047i \(0.825542\pi\)
\(384\) 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 −0.331562 0.943433i \(-0.607576\pi\)
0.651256 + 0.758858i \(0.274242\pi\)
\(390\) 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 0.391976 0.919976i \(-0.371792\pi\)
0.799449 + 0.600734i \(0.205125\pi\)
\(398\) 0 0
\(399\) 39.6108 + 21.4278i 1.98302 + 1.07273i
\(400\) 0 0
\(401\) −6.84060 + 11.8483i −0.341603 + 0.591674i −0.984731 0.174085i \(-0.944303\pi\)
0.643127 + 0.765759i \(0.277637\pi\)
\(402\) 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 0.661489 0.749955i \(-0.269925\pi\)
−0.980225 + 0.197888i \(0.936592\pi\)
\(410\) 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 0.842940 0.538007i \(-0.180823\pi\)
−0.887398 + 0.461004i \(0.847489\pi\)
\(432\) 0 0
\(433\) −28.5087 + 28.5087i −1.37004 + 1.37004i −0.509670 + 0.860370i \(0.670233\pi\)
−0.860370 + 0.509670i \(0.829767\pi\)
\(434\) 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 −0.999797 0.0201265i \(-0.993593\pi\)
0.517329 + 0.855787i \(0.326926\pi\)
\(440\) 0 0
\(441\) −18.8532 + 1.04646i −0.897770 + 0.0498315i
\(442\) 0 0
\(443\) 23.1032 6.19049i 1.09767 0.294119i 0.335853 0.941914i \(-0.390975\pi\)
0.761815 + 0.647795i \(0.224309\pi\)
\(444\) 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 \(-0.876821\pi\)
0.926054 0.377391i \(-0.123179\pi\)
\(450\) 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 0.994830 + 0.101558i \(0.0323829\pi\)
−0.810769 + 0.585367i \(0.800950\pi\)
\(458\) 0 0
\(459\) 1.05869 0.611235i 0.0494154 0.0285300i
\(460\) 0 0
\(461\) 24.4079i 1.13679i 0.822756 + 0.568395i \(0.192436\pi\)
−0.822756 + 0.568395i \(0.807564\pi\)
\(462\) 0 0
\(463\) 5.25987 + 5.25987i 0.244447 + 0.244447i 0.818687 0.574240i \(-0.194702\pi\)
−0.574240 + 0.818687i \(0.694702\pi\)
\(464\) 0 0
\(465\) 9.36492 + 7.04090i 0.434288 + 0.326514i
\(466\) 0 0
\(467\) −35.7255 + 9.57262i −1.65318 + 0.442968i −0.960501 0.278278i \(-0.910236\pi\)
−0.692679 + 0.721246i \(0.743570\pi\)
\(468\) 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 −0.999993 0.00380219i \(-0.998790\pi\)
0.496704 0.867920i \(-0.334544\pi\)
\(480\) 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 0.570792 0.821094i \(-0.306636\pi\)
0.0837736 + 0.996485i \(0.473303\pi\)
\(488\) 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 0.361983 0.932185i \(-0.382100\pi\)
−0.626304 + 0.779579i \(0.715433\pi\)
\(500\) 0 0
\(501\) −20.8923 36.1865i −0.933400 1.61670i
\(502\) 0 0
\(503\) −13.8531 + 13.8531i −0.617679 + 0.617679i −0.944936 0.327256i \(-0.893876\pi\)
0.327256 + 0.944936i \(0.393876\pi\)
\(504\) 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 −0.395882 + 0.918301i \(0.629561\pi\)
−0.597332 + 0.801994i \(0.703772\pi\)
\(510\) 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 0.386236 0.922400i \(-0.373775\pi\)
0.991940 + 0.126710i \(0.0404418\pi\)
\(522\) 0 0
\(523\) −4.05288 15.1255i −0.177220 0.661394i −0.996163 0.0875187i \(-0.972106\pi\)
0.818943 0.573875i \(-0.194560\pi\)
\(524\) 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 −0.981677 0.190553i \(-0.938972\pi\)
0.655862 + 0.754881i \(0.272305\pi\)
\(542\) 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 0.0303138 0.999540i \(-0.490349\pi\)
0.999540 0.0303138i \(-0.00965066\pi\)
\(548\) 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 0.751101 0.660187i \(-0.229523\pi\)
0.320379 + 0.947289i \(0.396190\pi\)
\(558\) 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 0.347145 0.937812i \(-0.387151\pi\)
−0.168270 + 0.985741i \(0.553818\pi\)
\(564\) 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 0.289550 0.957163i \(-0.406494\pi\)
−0.684153 + 0.729339i \(0.739828\pi\)
\(570\) 0 0
\(571\) −22.5354 39.0325i −0.943078 1.63346i −0.759555 0.650444i \(-0.774583\pi\)
−0.183523 0.983015i \(-0.558750\pi\)
\(572\) 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 −0.717660 0.696394i \(-0.754787\pi\)
0.969709 0.244265i \(-0.0785467\pi\)
\(578\) 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 0.380110 0.924941i \(-0.375886\pi\)
−0.924941 + 0.380110i \(0.875886\pi\)
\(588\) 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 0.947161 0.320758i \(-0.103938\pi\)
−0.980645 + 0.195796i \(0.937271\pi\)
\(594\) 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 −0.176745 0.984257i \(-0.556557\pi\)
0.764019 + 0.645194i \(0.223223\pi\)
\(600\) 0 0
\(601\) 10.4871i 0.427778i −0.976858 0.213889i \(-0.931387\pi\)
0.976858 0.213889i \(-0.0686131\pi\)
\(602\) 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 −0.826230 0.563332i \(-0.809519\pi\)
−0.433870 + 0.900975i \(0.642852\pi\)
\(608\) 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 −0.727951 0.685630i \(-0.759527\pi\)
0.973238 0.229797i \(-0.0738064\pi\)
\(614\) 0 0
\(615\) −27.9806 + 11.9133i −1.12829 + 0.480390i
\(616\) 0 0
\(617\) −24.6695 + 24.6695i −0.993158 + 0.993158i −0.999977 0.00681844i \(-0.997830\pi\)
0.00681844 + 0.999977i \(0.497830\pi\)
\(618\) 0 0
\(619\) 12.1208 + 20.9938i 0.487174 + 0.843811i 0.999891 0.0147470i \(-0.00469428\pi\)
−0.512717 + 0.858558i \(0.671361\pi\)
\(620\) 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 0.964178 + 0.265257i \(0.0854568\pi\)
−0.252370 + 0.967631i \(0.581210\pi\)
\(642\) 0 0
\(643\) 16.5722 16.5722i 0.653545 0.653545i −0.300300 0.953845i \(-0.597087\pi\)
0.953845 + 0.300300i \(0.0970868\pi\)
\(644\) 0 0
\(645\) 9.60281 23.8430i 0.378110 0.938816i
\(646\) 0 0
\(647\) −7.11698 + 26.5609i −0.279797 + 1.04422i 0.672760 + 0.739860i \(0.265108\pi\)
−0.952558 + 0.304358i \(0.901558\pi\)
\(648\) 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 −0.477907 0.878410i \(-0.658604\pi\)
0.0253256 + 0.999679i \(0.491938\pi\)
\(654\) 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 \(0.362198\pi\)
−0.419521 + 0.907746i \(0.637802\pi\)
\(660\) 0 0
\(661\) 2.27963 1.31614i 0.0886673 0.0511921i −0.455011 0.890486i \(-0.650365\pi\)
0.543678 + 0.839294i \(0.317031\pi\)
\(662\) 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 0.117383 0.993087i \(-0.462549\pi\)
−0.993087 + 0.117383i \(0.962549\pi\)
\(674\) 0 0
\(675\) −3.09095 + 1.86646i −0.118971 + 0.0718402i
\(676\) 0 0
\(677\) −10.0751 + 2.69961i −0.387216 + 0.103754i −0.447175 0.894447i \(-0.647570\pi\)
0.0599584 + 0.998201i \(0.480903\pi\)
\(678\) 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 −0.901289 0.433218i \(-0.857378\pi\)
0.997148 + 0.0754672i \(0.0240448\pi\)
\(684\) 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 0.826987 0.562221i \(-0.190053\pi\)
−0.0734041 + 0.997302i \(0.523386\pi\)
\(692\) 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 0.993989 0.109480i \(-0.0349187\pi\)
0.402182 + 0.915560i \(0.368252\pi\)
\(710\) 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 −0.590493 0.807042i \(-0.701067\pi\)
0.994166 + 0.107861i \(0.0344002\pi\)
\(720\) 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 0.794808 0.606861i \(-0.207572\pi\)
−0.606861 + 0.794808i \(0.707572\pi\)
\(728\) 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 −0.934754 0.355295i \(-0.884380\pi\)
0.631873 0.775072i \(-0.282286\pi\)
\(734\) 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 −0.744244 0.667908i \(-0.767190\pi\)
0.206303 + 0.978488i \(0.433857\pi\)
\(740\) 0 0
\(741\) 105.123i 3.86177i
\(742\) 0 0
\(743\) −23.6519 23.6519i −0.867703 0.867703i 0.124515 0.992218i \(-0.460262\pi\)
−0.992218 + 0.124515i \(0.960262\pi\)
\(744\) 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 −0.780584 0.625051i \(-0.785078\pi\)
0.931602 + 0.363480i \(0.118411\pi\)
\(752\) 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 −0.195304 0.980743i \(-0.562569\pi\)
0.980743 + 0.195304i \(0.0625693\pi\)
\(758\) 0 0
\(759\) −26.5846 46.0459i −0.964960 1.67136i
\(760\) 0 0
\(761\) −18.9354 10.9324i −0.686408 0.396298i 0.115857 0.993266i \(-0.463038\pi\)
−0.802265 + 0.596968i \(0.796372\pi\)
\(762\) 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 0.567173 0.823599i \(-0.308037\pi\)
0.0793867 + 0.996844i \(0.474704\pi\)
\(774\) 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 −0.733018 0.680210i \(-0.761889\pi\)
0.974917 0.222570i \(-0.0714446\pi\)
\(788\) 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