Properties

Label 1512.2.j.c.323.29
Level 1512
Weight 2
Character 1512.323
Analytic conductor 12.073
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.29
Character \(\chi\) = 1512.323
Dual form 1512.2.j.c.323.30

$q$-expansion

\(f(q)\) \(=\) \(q+(1.33436 - 0.468477i) q^{2} +(1.56106 - 1.25024i) q^{4} +3.47003 q^{5} -1.00000i q^{7} +(1.49731 - 2.39959i) q^{8} +O(q^{10})\) \(q+(1.33436 - 0.468477i) q^{2} +(1.56106 - 1.25024i) q^{4} +3.47003 q^{5} -1.00000i q^{7} +(1.49731 - 2.39959i) q^{8} +(4.63028 - 1.62563i) q^{10} +5.11891i q^{11} +0.268602i q^{13} +(-0.468477 - 1.33436i) q^{14} +(0.873805 - 3.90339i) q^{16} +1.96616i q^{17} +0.909926 q^{19} +(5.41692 - 4.33836i) q^{20} +(2.39809 + 6.83050i) q^{22} +5.86455 q^{23} +7.04110 q^{25} +(0.125834 + 0.358413i) q^{26} +(-1.25024 - 1.56106i) q^{28} -7.19959 q^{29} +4.57491i q^{31} +(-0.662675 - 5.61791i) q^{32} +(0.921102 + 2.62358i) q^{34} -3.47003i q^{35} -6.98312i q^{37} +(1.21417 - 0.426280i) q^{38} +(5.19572 - 8.32666i) q^{40} -8.34605i q^{41} -9.25237 q^{43} +(6.39986 + 7.99092i) q^{44} +(7.82544 - 2.74741i) q^{46} -6.49316 q^{47} -1.00000 q^{49} +(9.39539 - 3.29859i) q^{50} +(0.335817 + 0.419304i) q^{52} +4.54325 q^{53} +17.7628i q^{55} +(-2.39959 - 1.49731i) q^{56} +(-9.60688 + 3.37285i) q^{58} +3.50524i q^{59} -1.96254i q^{61} +(2.14324 + 6.10459i) q^{62} +(-3.51611 - 7.18589i) q^{64} +0.932057i q^{65} -11.0280 q^{67} +(2.45817 + 3.06929i) q^{68} +(-1.62563 - 4.63028i) q^{70} +1.20092 q^{71} -9.01697 q^{73} +(-3.27143 - 9.31802i) q^{74} +(1.42045 - 1.13762i) q^{76} +5.11891 q^{77} +13.5570i q^{79} +(3.03213 - 13.5449i) q^{80} +(-3.90994 - 11.1367i) q^{82} -4.96335i q^{83} +6.82263i q^{85} +(-12.3460 + 4.33452i) q^{86} +(12.2833 + 7.66461i) q^{88} -18.2032i q^{89} +0.268602 q^{91} +(9.15490 - 7.33208i) q^{92} +(-8.66424 + 3.04190i) q^{94} +3.15747 q^{95} +3.39139 q^{97} +(-1.33436 + 0.468477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 8q^{4} + O(q^{10}) \) \( 32q + 8q^{4} - 8q^{10} - 8q^{16} - 64q^{19} + 24q^{22} - 16q^{25} - 8q^{28} + 8q^{34} - 24q^{40} - 48q^{43} - 8q^{46} - 32q^{49} - 24q^{52} - 96q^{58} - 40q^{64} + 16q^{67} - 16q^{70} - 16q^{73} + 16q^{76} + 24q^{82} + 72q^{88} + 16q^{91} - 56q^{94} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33436 0.468477i 0.943538 0.331263i
\(3\) 0 0
\(4\) 1.56106 1.25024i 0.780529 0.625119i
\(5\) 3.47003 1.55184 0.775922 0.630829i \(-0.217285\pi\)
0.775922 + 0.630829i \(0.217285\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 1.49731 2.39959i 0.529380 0.848385i
\(9\) 0 0
\(10\) 4.63028 1.62563i 1.46422 0.514069i
\(11\) 5.11891i 1.54341i 0.635981 + 0.771705i \(0.280596\pi\)
−0.635981 + 0.771705i \(0.719404\pi\)
\(12\) 0 0
\(13\) 0.268602i 0.0744968i 0.999306 + 0.0372484i \(0.0118593\pi\)
−0.999306 + 0.0372484i \(0.988141\pi\)
\(14\) −0.468477 1.33436i −0.125206 0.356624i
\(15\) 0 0
\(16\) 0.873805 3.90339i 0.218451 0.975848i
\(17\) 1.96616i 0.476864i 0.971159 + 0.238432i \(0.0766334\pi\)
−0.971159 + 0.238432i \(0.923367\pi\)
\(18\) 0 0
\(19\) 0.909926 0.208751 0.104376 0.994538i \(-0.466716\pi\)
0.104376 + 0.994538i \(0.466716\pi\)
\(20\) 5.41692 4.33836i 1.21126 0.970088i
\(21\) 0 0
\(22\) 2.39809 + 6.83050i 0.511275 + 1.45627i
\(23\) 5.86455 1.22284 0.611421 0.791305i \(-0.290598\pi\)
0.611421 + 0.791305i \(0.290598\pi\)
\(24\) 0 0
\(25\) 7.04110 1.40822
\(26\) 0.125834 + 0.358413i 0.0246781 + 0.0702906i
\(27\) 0 0
\(28\) −1.25024 1.56106i −0.236273 0.295012i
\(29\) −7.19959 −1.33693 −0.668466 0.743743i \(-0.733049\pi\)
−0.668466 + 0.743743i \(0.733049\pi\)
\(30\) 0 0
\(31\) 4.57491i 0.821678i 0.911708 + 0.410839i \(0.134764\pi\)
−0.911708 + 0.410839i \(0.865236\pi\)
\(32\) −0.662675 5.61791i −0.117145 0.993115i
\(33\) 0 0
\(34\) 0.921102 + 2.62358i 0.157968 + 0.449940i
\(35\) 3.47003i 0.586542i
\(36\) 0 0
\(37\) 6.98312i 1.14802i −0.818849 0.574009i \(-0.805388\pi\)
0.818849 0.574009i \(-0.194612\pi\)
\(38\) 1.21417 0.426280i 0.196965 0.0691517i
\(39\) 0 0
\(40\) 5.19572 8.32666i 0.821515 1.31656i
\(41\) 8.34605i 1.30343i −0.758462 0.651717i \(-0.774049\pi\)
0.758462 0.651717i \(-0.225951\pi\)
\(42\) 0 0
\(43\) −9.25237 −1.41097 −0.705487 0.708723i \(-0.749272\pi\)
−0.705487 + 0.708723i \(0.749272\pi\)
\(44\) 6.39986 + 7.99092i 0.964816 + 1.20468i
\(45\) 0 0
\(46\) 7.82544 2.74741i 1.15380 0.405083i
\(47\) −6.49316 −0.947125 −0.473562 0.880760i \(-0.657032\pi\)
−0.473562 + 0.880760i \(0.657032\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 9.39539 3.29859i 1.32871 0.466491i
\(51\) 0 0
\(52\) 0.335817 + 0.419304i 0.0465694 + 0.0581470i
\(53\) 4.54325 0.624063 0.312032 0.950072i \(-0.398990\pi\)
0.312032 + 0.950072i \(0.398990\pi\)
\(54\) 0 0
\(55\) 17.7628i 2.39513i
\(56\) −2.39959 1.49731i −0.320659 0.200087i
\(57\) 0 0
\(58\) −9.60688 + 3.37285i −1.26145 + 0.442876i
\(59\) 3.50524i 0.456344i 0.973621 + 0.228172i \(0.0732748\pi\)
−0.973621 + 0.228172i \(0.926725\pi\)
\(60\) 0 0
\(61\) 1.96254i 0.251278i −0.992076 0.125639i \(-0.959902\pi\)
0.992076 0.125639i \(-0.0400980\pi\)
\(62\) 2.14324 + 6.10459i 0.272192 + 0.775284i
\(63\) 0 0
\(64\) −3.51611 7.18589i −0.439514 0.898236i
\(65\) 0.932057i 0.115607i
\(66\) 0 0
\(67\) −11.0280 −1.34728 −0.673641 0.739059i \(-0.735271\pi\)
−0.673641 + 0.739059i \(0.735271\pi\)
\(68\) 2.45817 + 3.06929i 0.298097 + 0.372206i
\(69\) 0 0
\(70\) −1.62563 4.63028i −0.194300 0.553425i
\(71\) 1.20092 0.142523 0.0712616 0.997458i \(-0.477297\pi\)
0.0712616 + 0.997458i \(0.477297\pi\)
\(72\) 0 0
\(73\) −9.01697 −1.05536 −0.527679 0.849444i \(-0.676937\pi\)
−0.527679 + 0.849444i \(0.676937\pi\)
\(74\) −3.27143 9.31802i −0.380296 1.08320i
\(75\) 0 0
\(76\) 1.42045 1.13762i 0.162937 0.130495i
\(77\) 5.11891 0.583354
\(78\) 0 0
\(79\) 13.5570i 1.52528i 0.646825 + 0.762638i \(0.276096\pi\)
−0.646825 + 0.762638i \(0.723904\pi\)
\(80\) 3.03213 13.5449i 0.339002 1.51436i
\(81\) 0 0
\(82\) −3.90994 11.1367i −0.431780 1.22984i
\(83\) 4.96335i 0.544799i −0.962184 0.272399i \(-0.912183\pi\)
0.962184 0.272399i \(-0.0878172\pi\)
\(84\) 0 0
\(85\) 6.82263i 0.740019i
\(86\) −12.3460 + 4.33452i −1.33131 + 0.467404i
\(87\) 0 0
\(88\) 12.2833 + 7.66461i 1.30941 + 0.817050i
\(89\) 18.2032i 1.92954i −0.263100 0.964769i \(-0.584745\pi\)
0.263100 0.964769i \(-0.415255\pi\)
\(90\) 0 0
\(91\) 0.268602 0.0281572
\(92\) 9.15490 7.33208i 0.954464 0.764423i
\(93\) 0 0
\(94\) −8.66424 + 3.04190i −0.893649 + 0.313748i
\(95\) 3.15747 0.323949
\(96\) 0 0
\(97\) 3.39139 0.344344 0.172172 0.985067i \(-0.444922\pi\)
0.172172 + 0.985067i \(0.444922\pi\)
\(98\) −1.33436 + 0.468477i −0.134791 + 0.0473233i
\(99\) 0 0
\(100\) 10.9916 8.80305i 1.09916 0.880305i
\(101\) 8.18671 0.814608 0.407304 0.913293i \(-0.366469\pi\)
0.407304 + 0.913293i \(0.366469\pi\)
\(102\) 0 0
\(103\) 16.5624i 1.63194i −0.578093 0.815971i \(-0.696203\pi\)
0.578093 0.815971i \(-0.303797\pi\)
\(104\) 0.644536 + 0.402181i 0.0632020 + 0.0394371i
\(105\) 0 0
\(106\) 6.06235 2.12841i 0.588828 0.206729i
\(107\) 15.1480i 1.46441i 0.681083 + 0.732206i \(0.261509\pi\)
−0.681083 + 0.732206i \(0.738491\pi\)
\(108\) 0 0
\(109\) 7.70038i 0.737562i 0.929516 + 0.368781i \(0.120225\pi\)
−0.929516 + 0.368781i \(0.879775\pi\)
\(110\) 8.32145 + 23.7020i 0.793419 + 2.25990i
\(111\) 0 0
\(112\) −3.90339 0.873805i −0.368836 0.0825668i
\(113\) 14.5822i 1.37178i −0.727706 0.685889i \(-0.759413\pi\)
0.727706 0.685889i \(-0.240587\pi\)
\(114\) 0 0
\(115\) 20.3501 1.89766
\(116\) −11.2390 + 9.00121i −1.04351 + 0.835742i
\(117\) 0 0
\(118\) 1.64213 + 4.67727i 0.151170 + 0.430578i
\(119\) 1.96616 0.180238
\(120\) 0 0
\(121\) −15.2033 −1.38211
\(122\) −0.919406 2.61874i −0.0832391 0.237090i
\(123\) 0 0
\(124\) 5.71973 + 7.14170i 0.513647 + 0.641343i
\(125\) 7.08266 0.633492
\(126\) 0 0
\(127\) 13.7782i 1.22262i 0.791392 + 0.611309i \(0.209357\pi\)
−0.791392 + 0.611309i \(0.790643\pi\)
\(128\) −8.05820 7.94138i −0.712251 0.701925i
\(129\) 0 0
\(130\) 0.436648 + 1.24370i 0.0382965 + 0.109080i
\(131\) 11.4226i 0.997997i −0.866603 0.498999i \(-0.833701\pi\)
0.866603 0.498999i \(-0.166299\pi\)
\(132\) 0 0
\(133\) 0.909926i 0.0789006i
\(134\) −14.7153 + 5.16636i −1.27121 + 0.446305i
\(135\) 0 0
\(136\) 4.71799 + 2.94396i 0.404564 + 0.252442i
\(137\) 5.89343i 0.503510i 0.967791 + 0.251755i \(0.0810077\pi\)
−0.967791 + 0.251755i \(0.918992\pi\)
\(138\) 0 0
\(139\) 3.67309 0.311547 0.155774 0.987793i \(-0.450213\pi\)
0.155774 + 0.987793i \(0.450213\pi\)
\(140\) −4.33836 5.41692i −0.366659 0.457813i
\(141\) 0 0
\(142\) 1.60247 0.562604i 0.134476 0.0472127i
\(143\) −1.37495 −0.114979
\(144\) 0 0
\(145\) −24.9828 −2.07471
\(146\) −12.0319 + 4.22425i −0.995770 + 0.349601i
\(147\) 0 0
\(148\) −8.73056 10.9010i −0.717648 0.896061i
\(149\) 23.0240 1.88620 0.943102 0.332504i \(-0.107894\pi\)
0.943102 + 0.332504i \(0.107894\pi\)
\(150\) 0 0
\(151\) 1.33860i 0.108934i 0.998516 + 0.0544669i \(0.0173459\pi\)
−0.998516 + 0.0544669i \(0.982654\pi\)
\(152\) 1.36244 2.18345i 0.110509 0.177101i
\(153\) 0 0
\(154\) 6.83050 2.39809i 0.550417 0.193244i
\(155\) 15.8751i 1.27512i
\(156\) 0 0
\(157\) 21.7839i 1.73854i 0.494333 + 0.869272i \(0.335412\pi\)
−0.494333 + 0.869272i \(0.664588\pi\)
\(158\) 6.35112 + 18.0899i 0.505268 + 1.43916i
\(159\) 0 0
\(160\) −2.29950 19.4943i −0.181792 1.54116i
\(161\) 5.86455i 0.462191i
\(162\) 0 0
\(163\) −20.2710 −1.58775 −0.793875 0.608082i \(-0.791939\pi\)
−0.793875 + 0.608082i \(0.791939\pi\)
\(164\) −10.4346 13.0287i −0.814802 1.01737i
\(165\) 0 0
\(166\) −2.32522 6.62292i −0.180472 0.514039i
\(167\) 6.57632 0.508891 0.254445 0.967087i \(-0.418107\pi\)
0.254445 + 0.967087i \(0.418107\pi\)
\(168\) 0 0
\(169\) 12.9279 0.994450
\(170\) 3.19625 + 9.10388i 0.245141 + 0.698236i
\(171\) 0 0
\(172\) −14.4435 + 11.5677i −1.10131 + 0.882027i
\(173\) −13.3399 −1.01421 −0.507105 0.861884i \(-0.669284\pi\)
−0.507105 + 0.861884i \(0.669284\pi\)
\(174\) 0 0
\(175\) 7.04110i 0.532257i
\(176\) 19.9811 + 4.47293i 1.50613 + 0.337160i
\(177\) 0 0
\(178\) −8.52779 24.2897i −0.639185 1.82059i
\(179\) 9.82571i 0.734408i 0.930140 + 0.367204i \(0.119685\pi\)
−0.930140 + 0.367204i \(0.880315\pi\)
\(180\) 0 0
\(181\) 4.88753i 0.363287i 0.983364 + 0.181643i \(0.0581417\pi\)
−0.983364 + 0.181643i \(0.941858\pi\)
\(182\) 0.358413 0.125834i 0.0265674 0.00932744i
\(183\) 0 0
\(184\) 8.78106 14.0725i 0.647348 1.03744i
\(185\) 24.2316i 1.78154i
\(186\) 0 0
\(187\) −10.0646 −0.735997
\(188\) −10.1362 + 8.11800i −0.739258 + 0.592066i
\(189\) 0 0
\(190\) 4.21322 1.47920i 0.305659 0.107313i
\(191\) 11.6129 0.840281 0.420141 0.907459i \(-0.361981\pi\)
0.420141 + 0.907459i \(0.361981\pi\)
\(192\) 0 0
\(193\) −12.8166 −0.922562 −0.461281 0.887254i \(-0.652610\pi\)
−0.461281 + 0.887254i \(0.652610\pi\)
\(194\) 4.52536 1.58879i 0.324902 0.114069i
\(195\) 0 0
\(196\) −1.56106 + 1.25024i −0.111504 + 0.0893028i
\(197\) 4.69147 0.334253 0.167127 0.985935i \(-0.446551\pi\)
0.167127 + 0.985935i \(0.446551\pi\)
\(198\) 0 0
\(199\) 15.3555i 1.08852i 0.838915 + 0.544262i \(0.183190\pi\)
−0.838915 + 0.544262i \(0.816810\pi\)
\(200\) 10.5427 16.8958i 0.745483 1.19471i
\(201\) 0 0
\(202\) 10.9241 3.83529i 0.768614 0.269850i
\(203\) 7.19959i 0.505312i
\(204\) 0 0
\(205\) 28.9610i 2.02273i
\(206\) −7.75911 22.1003i −0.540603 1.53980i
\(207\) 0 0
\(208\) 1.04846 + 0.234706i 0.0726976 + 0.0162739i
\(209\) 4.65783i 0.322189i
\(210\) 0 0
\(211\) 5.09850 0.350995 0.175497 0.984480i \(-0.443847\pi\)
0.175497 + 0.984480i \(0.443847\pi\)
\(212\) 7.09228 5.68015i 0.487100 0.390114i
\(213\) 0 0
\(214\) 7.09649 + 20.2130i 0.485106 + 1.38173i
\(215\) −32.1060 −2.18961
\(216\) 0 0
\(217\) 4.57491 0.310565
\(218\) 3.60745 + 10.2751i 0.244327 + 0.695918i
\(219\) 0 0
\(220\) 22.2077 + 27.7287i 1.49724 + 1.86947i
\(221\) −0.528115 −0.0355249
\(222\) 0 0
\(223\) 29.5118i 1.97625i −0.153636 0.988127i \(-0.549098\pi\)
0.153636 0.988127i \(-0.450902\pi\)
\(224\) −5.61791 + 0.662675i −0.375362 + 0.0442768i
\(225\) 0 0
\(226\) −6.83143 19.4580i −0.454420 1.29433i
\(227\) 14.4769i 0.960868i −0.877031 0.480434i \(-0.840479\pi\)
0.877031 0.480434i \(-0.159521\pi\)
\(228\) 0 0
\(229\) 11.9120i 0.787168i 0.919289 + 0.393584i \(0.128765\pi\)
−0.919289 + 0.393584i \(0.871235\pi\)
\(230\) 27.1545 9.53358i 1.79052 0.628625i
\(231\) 0 0
\(232\) −10.7800 + 17.2761i −0.707744 + 1.13423i
\(233\) 13.2938i 0.870904i 0.900212 + 0.435452i \(0.143411\pi\)
−0.900212 + 0.435452i \(0.856589\pi\)
\(234\) 0 0
\(235\) −22.5315 −1.46979
\(236\) 4.38239 + 5.47189i 0.285269 + 0.356190i
\(237\) 0 0
\(238\) 2.62358 0.921102i 0.170061 0.0597062i
\(239\) −11.7744 −0.761624 −0.380812 0.924652i \(-0.624356\pi\)
−0.380812 + 0.924652i \(0.624356\pi\)
\(240\) 0 0
\(241\) −23.3009 −1.50094 −0.750471 0.660903i \(-0.770173\pi\)
−0.750471 + 0.660903i \(0.770173\pi\)
\(242\) −20.2867 + 7.12238i −1.30408 + 0.457844i
\(243\) 0 0
\(244\) −2.45364 3.06364i −0.157079 0.196129i
\(245\) −3.47003 −0.221692
\(246\) 0 0
\(247\) 0.244408i 0.0155513i
\(248\) 10.9779 + 6.85007i 0.697099 + 0.434980i
\(249\) 0 0
\(250\) 9.45085 3.31806i 0.597724 0.209853i
\(251\) 18.5562i 1.17126i 0.810579 + 0.585629i \(0.199153\pi\)
−0.810579 + 0.585629i \(0.800847\pi\)
\(252\) 0 0
\(253\) 30.0201i 1.88735i
\(254\) 6.45477 + 18.3851i 0.405009 + 1.15359i
\(255\) 0 0
\(256\) −14.4729 6.82161i −0.904558 0.426351i
\(257\) 12.7179i 0.793318i −0.917966 0.396659i \(-0.870169\pi\)
0.917966 0.396659i \(-0.129831\pi\)
\(258\) 0 0
\(259\) −6.98312 −0.433910
\(260\) 1.16529 + 1.45500i 0.0722685 + 0.0902350i
\(261\) 0 0
\(262\) −5.35123 15.2419i −0.330600 0.941648i
\(263\) −4.04929 −0.249690 −0.124845 0.992176i \(-0.539843\pi\)
−0.124845 + 0.992176i \(0.539843\pi\)
\(264\) 0 0
\(265\) 15.7652 0.968449
\(266\) −0.426280 1.21417i −0.0261369 0.0744457i
\(267\) 0 0
\(268\) −17.2153 + 13.7876i −1.05159 + 0.842212i
\(269\) −22.6641 −1.38185 −0.690926 0.722925i \(-0.742797\pi\)
−0.690926 + 0.722925i \(0.742797\pi\)
\(270\) 0 0
\(271\) 0.0619260i 0.00376174i −0.999998 0.00188087i \(-0.999401\pi\)
0.999998 0.00188087i \(-0.000598699\pi\)
\(272\) 7.67470 + 1.71804i 0.465347 + 0.104172i
\(273\) 0 0
\(274\) 2.76094 + 7.86399i 0.166794 + 0.475081i
\(275\) 36.0427i 2.17346i
\(276\) 0 0
\(277\) 24.9177i 1.49716i 0.663045 + 0.748580i \(0.269264\pi\)
−0.663045 + 0.748580i \(0.730736\pi\)
\(278\) 4.90124 1.72076i 0.293957 0.103204i
\(279\) 0 0
\(280\) −8.32666 5.19572i −0.497613 0.310503i
\(281\) 8.26290i 0.492923i 0.969153 + 0.246462i \(0.0792679\pi\)
−0.969153 + 0.246462i \(0.920732\pi\)
\(282\) 0 0
\(283\) 23.4764 1.39553 0.697763 0.716329i \(-0.254179\pi\)
0.697763 + 0.716329i \(0.254179\pi\)
\(284\) 1.87471 1.50144i 0.111243 0.0890940i
\(285\) 0 0
\(286\) −1.83469 + 0.644133i −0.108487 + 0.0380884i
\(287\) −8.34605 −0.492652
\(288\) 0 0
\(289\) 13.1342 0.772601
\(290\) −33.3362 + 11.7039i −1.95757 + 0.687275i
\(291\) 0 0
\(292\) −14.0760 + 11.2734i −0.823737 + 0.659724i
\(293\) 6.18958 0.361599 0.180800 0.983520i \(-0.442131\pi\)
0.180800 + 0.983520i \(0.442131\pi\)
\(294\) 0 0
\(295\) 12.1633i 0.708174i
\(296\) −16.7566 10.4559i −0.973960 0.607737i
\(297\) 0 0
\(298\) 30.7225 10.7862i 1.77971 0.624830i
\(299\) 1.57523i 0.0910979i
\(300\) 0 0
\(301\) 9.25237i 0.533298i
\(302\) 0.627104 + 1.78618i 0.0360858 + 0.102783i
\(303\) 0 0
\(304\) 0.795098 3.55180i 0.0456020 0.203710i
\(305\) 6.81007i 0.389944i
\(306\) 0 0
\(307\) −25.4140 −1.45045 −0.725226 0.688511i \(-0.758265\pi\)
−0.725226 + 0.688511i \(0.758265\pi\)
\(308\) 7.99092 6.39986i 0.455325 0.364666i
\(309\) 0 0
\(310\) 7.43710 + 21.1831i 0.422399 + 1.20312i
\(311\) −7.55273 −0.428276 −0.214138 0.976803i \(-0.568694\pi\)
−0.214138 + 0.976803i \(0.568694\pi\)
\(312\) 0 0
\(313\) 2.49790 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(314\) 10.2053 + 29.0677i 0.575916 + 1.64038i
\(315\) 0 0
\(316\) 16.9494 + 21.1632i 0.953480 + 1.19052i
\(317\) 10.9643 0.615815 0.307908 0.951416i \(-0.400371\pi\)
0.307908 + 0.951416i \(0.400371\pi\)
\(318\) 0 0
\(319\) 36.8541i 2.06343i
\(320\) −12.2010 24.9352i −0.682057 1.39392i
\(321\) 0 0
\(322\) −2.74741 7.82544i −0.153107 0.436095i
\(323\) 1.78906i 0.0995460i
\(324\) 0 0
\(325\) 1.89125i 0.104908i
\(326\) −27.0489 + 9.49651i −1.49810 + 0.525963i
\(327\) 0 0
\(328\) −20.0271 12.4967i −1.10581 0.690012i
\(329\) 6.49316i 0.357980i
\(330\) 0 0
\(331\) 35.6043 1.95699 0.978494 0.206275i \(-0.0661341\pi\)
0.978494 + 0.206275i \(0.0661341\pi\)
\(332\) −6.20538 7.74808i −0.340564 0.425231i
\(333\) 0 0
\(334\) 8.77521 3.08086i 0.480158 0.168577i
\(335\) −38.2674 −2.09077
\(336\) 0 0
\(337\) 18.4308 1.00399 0.501995 0.864871i \(-0.332600\pi\)
0.501995 + 0.864871i \(0.332600\pi\)
\(338\) 17.2505 6.05640i 0.938302 0.329425i
\(339\) 0 0
\(340\) 8.52992 + 10.6505i 0.462600 + 0.577606i
\(341\) −23.4185 −1.26819
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −13.8537 + 22.2019i −0.746941 + 1.19705i
\(345\) 0 0
\(346\) −17.8002 + 6.24942i −0.956946 + 0.335971i
\(347\) 25.2141i 1.35356i 0.736184 + 0.676782i \(0.236626\pi\)
−0.736184 + 0.676782i \(0.763374\pi\)
\(348\) 0 0
\(349\) 4.82396i 0.258221i 0.991630 + 0.129110i \(0.0412121\pi\)
−0.991630 + 0.129110i \(0.958788\pi\)
\(350\) −3.29859 9.39539i −0.176317 0.502205i
\(351\) 0 0
\(352\) 28.7576 3.39217i 1.53278 0.180804i
\(353\) 21.2660i 1.13187i −0.824448 0.565937i \(-0.808514\pi\)
0.824448 0.565937i \(-0.191486\pi\)
\(354\) 0 0
\(355\) 4.16723 0.221174
\(356\) −22.7584 28.4163i −1.20619 1.50606i
\(357\) 0 0
\(358\) 4.60312 + 13.1111i 0.243282 + 0.692942i
\(359\) −24.9785 −1.31832 −0.659158 0.752004i \(-0.729087\pi\)
−0.659158 + 0.752004i \(0.729087\pi\)
\(360\) 0 0
\(361\) −18.1720 −0.956423
\(362\) 2.28969 + 6.52174i 0.120344 + 0.342775i
\(363\) 0 0
\(364\) 0.419304 0.335817i 0.0219775 0.0176016i
\(365\) −31.2892 −1.63775
\(366\) 0 0
\(367\) 13.8851i 0.724795i −0.932024 0.362397i \(-0.881958\pi\)
0.932024 0.362397i \(-0.118042\pi\)
\(368\) 5.12447 22.8916i 0.267132 1.19331i
\(369\) 0 0
\(370\) −11.3520 32.3338i −0.590160 1.68095i
\(371\) 4.54325i 0.235874i
\(372\) 0 0
\(373\) 0.513970i 0.0266123i 0.999911 + 0.0133062i \(0.00423561\pi\)
−0.999911 + 0.0133062i \(0.995764\pi\)
\(374\) −13.4299 + 4.71504i −0.694441 + 0.243809i
\(375\) 0 0
\(376\) −9.72229 + 15.5810i −0.501389 + 0.803526i
\(377\) 1.93383i 0.0995972i
\(378\) 0 0
\(379\) −7.97711 −0.409757 −0.204878 0.978787i \(-0.565680\pi\)
−0.204878 + 0.978787i \(0.565680\pi\)
\(380\) 4.92899 3.94759i 0.252852 0.202507i
\(381\) 0 0
\(382\) 15.4959 5.44039i 0.792837 0.278354i
\(383\) −8.03401 −0.410519 −0.205259 0.978708i \(-0.565804\pi\)
−0.205259 + 0.978708i \(0.565804\pi\)
\(384\) 0 0
\(385\) 17.7628 0.905275
\(386\) −17.1021 + 6.00430i −0.870472 + 0.305611i
\(387\) 0 0
\(388\) 5.29416 4.24005i 0.268770 0.215256i
\(389\) −6.60733 −0.335005 −0.167503 0.985872i \(-0.553570\pi\)
−0.167503 + 0.985872i \(0.553570\pi\)
\(390\) 0 0
\(391\) 11.5306i 0.583130i
\(392\) −1.49731 + 2.39959i −0.0756257 + 0.121198i
\(393\) 0 0
\(394\) 6.26013 2.19785i 0.315381 0.110726i
\(395\) 47.0430i 2.36699i
\(396\) 0 0
\(397\) 17.4642i 0.876502i −0.898853 0.438251i \(-0.855598\pi\)
0.898853 0.438251i \(-0.144402\pi\)
\(398\) 7.19372 + 20.4899i 0.360588 + 1.02706i
\(399\) 0 0
\(400\) 6.15255 27.4842i 0.307627 1.37421i
\(401\) 18.6133i 0.929503i 0.885441 + 0.464751i \(0.153856\pi\)
−0.885441 + 0.464751i \(0.846144\pi\)
\(402\) 0 0
\(403\) −1.22883 −0.0612124
\(404\) 12.7799 10.2353i 0.635825 0.509227i
\(405\) 0 0
\(406\) 3.37285 + 9.60688i 0.167392 + 0.476782i
\(407\) 35.7460 1.77186
\(408\) 0 0
\(409\) 3.72844 0.184359 0.0921797 0.995742i \(-0.470617\pi\)
0.0921797 + 0.995742i \(0.470617\pi\)
\(410\) −13.5676 38.6446i −0.670055 1.90852i
\(411\) 0 0
\(412\) −20.7070 25.8549i −1.02016 1.27378i
\(413\) 3.50524 0.172482
\(414\) 0 0
\(415\) 17.2230i 0.845443i
\(416\) 1.50898 0.177996i 0.0739839 0.00872697i
\(417\) 0 0
\(418\) 2.18209 + 6.21525i 0.106729 + 0.303998i
\(419\) 30.1591i 1.47337i 0.676237 + 0.736684i \(0.263609\pi\)
−0.676237 + 0.736684i \(0.736391\pi\)
\(420\) 0 0
\(421\) 4.17416i 0.203436i −0.994813 0.101718i \(-0.967566\pi\)
0.994813 0.101718i \(-0.0324340\pi\)
\(422\) 6.80325 2.38853i 0.331177 0.116272i
\(423\) 0 0
\(424\) 6.80266 10.9020i 0.330367 0.529446i
\(425\) 13.8439i 0.671529i
\(426\) 0 0
\(427\) −1.96254 −0.0949740
\(428\) 18.9386 + 23.6469i 0.915433 + 1.14302i
\(429\) 0 0
\(430\) −42.8411 + 15.0409i −2.06598 + 0.725338i
\(431\) 20.3147 0.978524 0.489262 0.872137i \(-0.337266\pi\)
0.489262 + 0.872137i \(0.337266\pi\)
\(432\) 0 0
\(433\) 37.5740 1.80569 0.902847 0.429963i \(-0.141473\pi\)
0.902847 + 0.429963i \(0.141473\pi\)
\(434\) 6.10459 2.14324i 0.293030 0.102879i
\(435\) 0 0
\(436\) 9.62731 + 12.0207i 0.461064 + 0.575689i
\(437\) 5.33630 0.255270
\(438\) 0 0
\(439\) 12.2219i 0.583317i −0.956522 0.291659i \(-0.905793\pi\)
0.956522 0.291659i \(-0.0942072\pi\)
\(440\) 42.6234 + 26.5964i 2.03199 + 1.26793i
\(441\) 0 0
\(442\) −0.704698 + 0.247410i −0.0335191 + 0.0117681i
\(443\) 2.13132i 0.101262i −0.998717 0.0506311i \(-0.983877\pi\)
0.998717 0.0506311i \(-0.0161233\pi\)
\(444\) 0 0
\(445\) 63.1657i 2.99434i
\(446\) −13.8256 39.3795i −0.654661 1.86467i
\(447\) 0 0
\(448\) −7.18589 + 3.51611i −0.339501 + 0.166121i
\(449\) 24.6873i 1.16506i −0.812807 0.582532i \(-0.802062\pi\)
0.812807 0.582532i \(-0.197938\pi\)
\(450\) 0 0
\(451\) 42.7227 2.01173
\(452\) −18.2312 22.7637i −0.857526 1.07071i
\(453\) 0 0
\(454\) −6.78211 19.3175i −0.318300 0.906615i
\(455\) 0.932057 0.0436955
\(456\) 0 0
\(457\) −33.2814 −1.55684 −0.778419 0.627745i \(-0.783978\pi\)
−0.778419 + 0.627745i \(0.783978\pi\)
\(458\) 5.58051 + 15.8950i 0.260760 + 0.742723i
\(459\) 0 0
\(460\) 31.7678 25.4425i 1.48118 1.18626i
\(461\) 15.2279 0.709233 0.354617 0.935012i \(-0.384611\pi\)
0.354617 + 0.935012i \(0.384611\pi\)
\(462\) 0 0
\(463\) 3.21883i 0.149592i −0.997199 0.0747959i \(-0.976169\pi\)
0.997199 0.0747959i \(-0.0238305\pi\)
\(464\) −6.29104 + 28.1028i −0.292054 + 1.30464i
\(465\) 0 0
\(466\) 6.22783 + 17.7387i 0.288499 + 0.821731i
\(467\) 22.5827i 1.04500i −0.852638 0.522502i \(-0.824999\pi\)
0.852638 0.522502i \(-0.175001\pi\)
\(468\) 0 0
\(469\) 11.0280i 0.509225i
\(470\) −30.0652 + 10.5555i −1.38680 + 0.486888i
\(471\) 0 0
\(472\) 8.41117 + 5.24845i 0.387155 + 0.241579i
\(473\) 47.3621i 2.17771i
\(474\) 0 0
\(475\) 6.40688 0.293968
\(476\) 3.06929 2.45817i 0.140681 0.112670i
\(477\) 0 0
\(478\) −15.7114 + 5.51605i −0.718622 + 0.252298i
\(479\) 28.0140 1.27999 0.639995 0.768379i \(-0.278936\pi\)
0.639995 + 0.768379i \(0.278936\pi\)
\(480\) 0 0
\(481\) 1.87568 0.0855237
\(482\) −31.0919 + 10.9159i −1.41620 + 0.497207i
\(483\) 0 0
\(484\) −23.7332 + 19.0077i −1.07878 + 0.863987i
\(485\) 11.7682 0.534368
\(486\) 0 0
\(487\) 2.55321i 0.115697i 0.998325 + 0.0578485i \(0.0184240\pi\)
−0.998325 + 0.0578485i \(0.981576\pi\)
\(488\) −4.70930 2.93854i −0.213180 0.133021i
\(489\) 0 0
\(490\) −4.63028 + 1.62563i −0.209175 + 0.0734384i
\(491\) 0.803432i 0.0362584i −0.999836 0.0181292i \(-0.994229\pi\)
0.999836 0.0181292i \(-0.00577102\pi\)
\(492\) 0 0
\(493\) 14.1556i 0.637534i
\(494\) 0.114500 + 0.326130i 0.00515158 + 0.0146733i
\(495\) 0 0
\(496\) 17.8577 + 3.99758i 0.801832 + 0.179497i
\(497\) 1.20092i 0.0538687i
\(498\) 0 0
\(499\) 32.6029 1.45950 0.729752 0.683712i \(-0.239635\pi\)
0.729752 + 0.683712i \(0.239635\pi\)
\(500\) 11.0564 8.85502i 0.494459 0.396008i
\(501\) 0 0
\(502\) 8.69317 + 24.7608i 0.387995 + 1.10513i
\(503\) −11.6962 −0.521508 −0.260754 0.965405i \(-0.583971\pi\)
−0.260754 + 0.965405i \(0.583971\pi\)
\(504\) 0 0
\(505\) 28.4081 1.26414
\(506\) 14.0637 + 40.0578i 0.625209 + 1.78078i
\(507\) 0 0
\(508\) 17.2260 + 21.5086i 0.764282 + 0.954289i
\(509\) 40.0087 1.77335 0.886676 0.462391i \(-0.153008\pi\)
0.886676 + 0.462391i \(0.153008\pi\)
\(510\) 0 0
\(511\) 9.01697i 0.398887i
\(512\) −22.5079 2.32228i −0.994719 0.102631i
\(513\) 0 0
\(514\) −5.95803 16.9703i −0.262797 0.748526i
\(515\) 57.4720i 2.53252i
\(516\) 0 0
\(517\) 33.2379i 1.46180i
\(518\) −9.31802 + 3.27143i −0.409410 + 0.143738i
\(519\) 0 0
\(520\) 2.23656 + 1.39558i 0.0980796 + 0.0612003i
\(521\) 5.13277i 0.224871i 0.993659 + 0.112435i \(0.0358651\pi\)
−0.993659 + 0.112435i \(0.964135\pi\)
\(522\) 0 0
\(523\) 35.3652 1.54641 0.773207 0.634154i \(-0.218652\pi\)
0.773207 + 0.634154i \(0.218652\pi\)
\(524\) −14.2810 17.8313i −0.623867 0.778966i
\(525\) 0 0
\(526\) −5.40324 + 1.89700i −0.235592 + 0.0827132i
\(527\) −8.99500 −0.391829
\(528\) 0 0
\(529\) 11.3929 0.495344
\(530\) 21.0365 7.38564i 0.913769 0.320812i
\(531\) 0 0
\(532\) −1.13762 1.42045i −0.0493223 0.0615842i
\(533\) 2.24177 0.0971018
\(534\) 0 0
\(535\) 52.5640i 2.27254i
\(536\) −16.5123 + 26.4627i −0.713224 + 1.14301i
\(537\) 0 0
\(538\) −30.2421 + 10.6176i −1.30383 + 0.457757i
\(539\) 5.11891i 0.220487i
\(540\) 0 0
\(541\) 30.7038i 1.32006i 0.751240 + 0.660029i \(0.229456\pi\)
−0.751240 + 0.660029i \(0.770544\pi\)
\(542\) −0.0290109 0.0826319i −0.00124613 0.00354934i
\(543\) 0 0
\(544\) 11.0457 1.30293i 0.473581 0.0558625i
\(545\) 26.7205i 1.14458i
\(546\) 0 0
\(547\) −2.21526 −0.0947175 −0.0473588 0.998878i \(-0.515080\pi\)
−0.0473588 + 0.998878i \(0.515080\pi\)
\(548\) 7.36820 + 9.19999i 0.314754 + 0.393004i
\(549\) 0 0
\(550\) 16.8852 + 48.0942i 0.719988 + 2.05074i
\(551\) −6.55110 −0.279086
\(552\) 0 0
\(553\) 13.5570 0.576500
\(554\) 11.6734 + 33.2493i 0.495954 + 1.41263i
\(555\) 0 0
\(556\) 5.73390 4.59224i 0.243172 0.194754i
\(557\) 8.88158 0.376325 0.188162 0.982138i \(-0.439747\pi\)
0.188162 + 0.982138i \(0.439747\pi\)
\(558\) 0 0
\(559\) 2.48521i 0.105113i
\(560\) −13.5449 3.03213i −0.572376 0.128131i
\(561\) 0 0
\(562\) 3.87098 + 11.0257i 0.163287 + 0.465092i
\(563\) 28.9398i 1.21967i −0.792529 0.609834i \(-0.791236\pi\)
0.792529 0.609834i \(-0.208764\pi\)
\(564\) 0 0
\(565\) 50.6007i 2.12879i
\(566\) 31.3260 10.9981i 1.31673 0.462287i
\(567\) 0 0
\(568\) 1.79815 2.88173i 0.0754489 0.120915i
\(569\) 30.8816i 1.29463i 0.762224 + 0.647313i \(0.224107\pi\)
−0.762224 + 0.647313i \(0.775893\pi\)
\(570\) 0 0
\(571\) −31.5945 −1.32219 −0.661094 0.750303i \(-0.729908\pi\)
−0.661094 + 0.750303i \(0.729908\pi\)
\(572\) −2.14638 + 1.71902i −0.0897446 + 0.0718757i
\(573\) 0 0
\(574\) −11.1367 + 3.90994i −0.464836 + 0.163198i
\(575\) 41.2928 1.72203
\(576\) 0 0
\(577\) −37.6007 −1.56534 −0.782669 0.622438i \(-0.786142\pi\)
−0.782669 + 0.622438i \(0.786142\pi\)
\(578\) 17.5258 6.15308i 0.728978 0.255934i
\(579\) 0 0
\(580\) −38.9996 + 31.2345i −1.61937 + 1.29694i
\(581\) −4.96335 −0.205915
\(582\) 0 0
\(583\) 23.2565i 0.963186i
\(584\) −13.5012 + 21.6371i −0.558685 + 0.895349i
\(585\) 0 0
\(586\) 8.25916 2.89968i 0.341183 0.119785i
\(587\) 22.0321i 0.909361i −0.890655 0.454680i \(-0.849754\pi\)
0.890655 0.454680i \(-0.150246\pi\)
\(588\) 0 0
\(589\) 4.16283i 0.171526i
\(590\) 5.69823 + 16.2303i 0.234592 + 0.668190i
\(591\) 0 0
\(592\) −27.2578 6.10188i −1.12029 0.250786i
\(593\) 17.8392i 0.732569i −0.930503 0.366284i \(-0.880630\pi\)
0.930503 0.366284i \(-0.119370\pi\)
\(594\) 0 0
\(595\) 6.82263 0.279701
\(596\) 35.9419 28.7856i 1.47224 1.17910i
\(597\) 0 0
\(598\) 0.737959 + 2.10193i 0.0301774 + 0.0859544i
\(599\) −19.5363 −0.798230 −0.399115 0.916901i \(-0.630683\pi\)
−0.399115 + 0.916901i \(0.630683\pi\)
\(600\) 0 0
\(601\) −20.1240 −0.820877 −0.410438 0.911888i \(-0.634624\pi\)
−0.410438 + 0.911888i \(0.634624\pi\)
\(602\) 4.33452 + 12.3460i 0.176662 + 0.503187i
\(603\) 0 0
\(604\) 1.67357 + 2.08963i 0.0680966 + 0.0850260i
\(605\) −52.7557 −2.14483
\(606\) 0 0
\(607\) 15.3972i 0.624951i 0.949926 + 0.312476i \(0.101158\pi\)
−0.949926 + 0.312476i \(0.898842\pi\)
\(608\) −0.602985 5.11188i −0.0244543 0.207314i
\(609\) 0 0
\(610\) −3.19036 9.08712i −0.129174 0.367927i
\(611\) 1.74408i 0.0705578i
\(612\) 0 0
\(613\) 37.9629i 1.53331i −0.642061 0.766653i \(-0.721921\pi\)
0.642061 0.766653i \(-0.278079\pi\)
\(614\) −33.9115 + 11.9059i −1.36856 + 0.480482i
\(615\) 0 0
\(616\) 7.66461 12.2833i 0.308816 0.494909i
\(617\) 43.0532i 1.73326i −0.498953 0.866629i \(-0.666282\pi\)
0.498953 0.866629i \(-0.333718\pi\)
\(618\) 0 0
\(619\) −6.75463 −0.271491 −0.135746 0.990744i \(-0.543343\pi\)
−0.135746 + 0.990744i \(0.543343\pi\)
\(620\) 19.8476 + 24.7819i 0.797099 + 0.995265i
\(621\) 0 0
\(622\) −10.0781 + 3.53828i −0.404095 + 0.141872i
\(623\) −18.2032 −0.729297
\(624\) 0 0
\(625\) −10.6285 −0.425138
\(626\) 3.33311 1.17021i 0.133218 0.0467710i
\(627\) 0 0
\(628\) 27.2351 + 34.0059i 1.08680 + 1.35698i
\(629\) 13.7299 0.547448
\(630\) 0 0
\(631\) 1.96735i 0.0783189i −0.999233 0.0391594i \(-0.987532\pi\)
0.999233 0.0391594i \(-0.0124680\pi\)
\(632\) 32.5312 + 20.2990i 1.29402 + 0.807451i
\(633\) 0 0
\(634\) 14.6303 5.13652i 0.581045 0.203997i
\(635\) 47.8108i 1.89731i
\(636\) 0 0
\(637\) 0.268602i 0.0106424i
\(638\) −17.2653 49.1768i −0.683540 1.94693i
\(639\) 0 0
\(640\) −27.9622 27.5568i −1.10530 1.08928i
\(641\) 30.2998i 1.19677i −0.801209 0.598385i \(-0.795809\pi\)
0.801209 0.598385i \(-0.204191\pi\)
\(642\) 0 0
\(643\) 3.85901 0.152185 0.0760923 0.997101i \(-0.475756\pi\)
0.0760923 + 0.997101i \(0.475756\pi\)
\(644\) −7.33208 9.15490i −0.288925 0.360754i
\(645\) 0 0
\(646\) 0.838134 + 2.38726i 0.0329760 + 0.0939255i
\(647\) 33.4004 1.31310 0.656552 0.754281i \(-0.272014\pi\)
0.656552 + 0.754281i \(0.272014\pi\)
\(648\) 0 0
\(649\) −17.9430 −0.704326
\(650\) 0.886009 + 2.52362i 0.0347521 + 0.0989846i
\(651\) 0 0
\(652\) −31.6442 + 25.3436i −1.23928 + 0.992533i
\(653\) 26.9899 1.05620 0.528098 0.849184i \(-0.322905\pi\)
0.528098 + 0.849184i \(0.322905\pi\)
\(654\) 0 0
\(655\) 39.6367i 1.54874i
\(656\) −32.5779 7.29283i −1.27195 0.284737i
\(657\) 0 0
\(658\) 3.04190 + 8.66424i 0.118586 + 0.337767i
\(659\) 13.1888i 0.513763i 0.966443 + 0.256881i \(0.0826950\pi\)
−0.966443 + 0.256881i \(0.917305\pi\)
\(660\) 0 0
\(661\) 33.5767i 1.30598i −0.757366 0.652990i \(-0.773514\pi\)
0.757366 0.652990i \(-0.226486\pi\)
\(662\) 47.5091 16.6798i 1.84649 0.648279i
\(663\) 0 0
\(664\) −11.9100 7.43169i −0.462199 0.288406i
\(665\) 3.15747i 0.122441i
\(666\) 0 0
\(667\) −42.2224 −1.63486
\(668\) 10.2660 8.22197i 0.397204 0.318118i
\(669\) 0 0
\(670\) −51.0627 + 17.9274i −1.97272 + 0.692596i
\(671\) 10.0461 0.387824
\(672\) 0 0
\(673\) 13.5269 0.521424 0.260712 0.965417i \(-0.416043\pi\)
0.260712 + 0.965417i \(0.416043\pi\)
\(674\) 24.5934 8.63441i 0.947303 0.332585i
\(675\) 0 0
\(676\) 20.1811 16.1629i 0.776197 0.621650i
\(677\) 25.3388 0.973850 0.486925 0.873444i \(-0.338118\pi\)
0.486925 + 0.873444i \(0.338118\pi\)
\(678\) 0 0
\(679\) 3.39139i 0.130150i
\(680\) 16.3716 + 10.2156i 0.627821 + 0.391751i
\(681\) 0 0
\(682\) −31.2489 + 10.9711i −1.19658 + 0.420103i
\(683\) 4.74712i 0.181644i 0.995867 + 0.0908218i \(0.0289494\pi\)
−0.995867 + 0.0908218i \(0.971051\pi\)
\(684\) 0 0
\(685\) 20.4504i 0.781369i
\(686\) 0.468477 + 1.33436i 0.0178865 + 0.0509463i
\(687\) 0 0
\(688\) −8.08477 + 36.1156i −0.308229 + 1.37690i
\(689\) 1.22033i 0.0464908i
\(690\) 0 0
\(691\) −46.8908 −1.78381 −0.891904 0.452224i \(-0.850631\pi\)
−0.891904 + 0.452224i \(0.850631\pi\)
\(692\) −20.8243 + 16.6780i −0.791620 + 0.634002i
\(693\) 0 0
\(694\) 11.8122 + 33.6448i 0.448386 + 1.27714i
\(695\) 12.7457 0.483472
\(696\) 0 0
\(697\) 16.4097 0.621561
\(698\) 2.25991 + 6.43692i 0.0855390 + 0.243641i
\(699\) 0 0
\(700\) −8.80305 10.9916i −0.332724 0.415442i
\(701\) 11.8394 0.447166 0.223583 0.974685i \(-0.428225\pi\)
0.223583 + 0.974685i \(0.428225\pi\)
\(702\) 0 0
\(703\) 6.35412i 0.239650i
\(704\) 36.7839 17.9987i 1.38635 0.678350i
\(705\) 0 0
\(706\) −9.96263 28.3766i −0.374949 1.06797i
\(707\) 8.18671i 0.307893i
\(708\) 0 0
\(709\) 3.55487i 0.133506i −0.997770 0.0667530i \(-0.978736\pi\)
0.997770 0.0667530i \(-0.0212639\pi\)
\(710\) 5.56061 1.95225i 0.208686 0.0732668i
\(711\) 0 0
\(712\) −43.6803 27.2559i −1.63699 1.02146i
\(713\) 26.8298i 1.00478i
\(714\) 0 0
\(715\) −4.77112 −0.178430
\(716\) 12.2845 + 15.3385i 0.459093 + 0.573227i
\(717\) 0 0
\(718\) −33.3305 + 11.7019i −1.24388 + 0.436710i
\(719\) 0.174626 0.00651246 0.00325623 0.999995i \(-0.498964\pi\)
0.00325623 + 0.999995i \(0.498964\pi\)
\(720\) 0 0
\(721\) −16.5624 −0.616816
\(722\) −24.2481 + 8.51318i −0.902422 + 0.316828i
\(723\) 0 0
\(724\) 6.11058 + 7.62971i 0.227098 + 0.283556i
\(725\) −50.6930 −1.88269
\(726\) 0 0
\(727\) 8.37928i 0.310770i −0.987854 0.155385i \(-0.950338\pi\)
0.987854 0.155385i \(-0.0496619\pi\)
\(728\) 0.402181 0.644536i 0.0149058 0.0238881i
\(729\) 0 0
\(730\) −41.7511 + 14.6583i −1.54528 + 0.542526i
\(731\) 18.1917i 0.672843i
\(732\) 0 0
\(733\) 15.6312i 0.577351i −0.957427 0.288676i \(-0.906785\pi\)
0.957427 0.288676i \(-0.0932149\pi\)
\(734\) −6.50484 18.5277i −0.240098 0.683872i
\(735\) 0 0
\(736\) −3.88629 32.9465i −0.143250 1.21442i
\(737\) 56.4512i 2.07941i
\(738\) 0 0
\(739\) −25.4382 −0.935760 −0.467880 0.883792i \(-0.654982\pi\)
−0.467880 + 0.883792i \(0.654982\pi\)
\(740\) −30.2953 37.8269i −1.11368 1.39055i
\(741\) 0 0
\(742\) −2.12841 6.06235i −0.0781364 0.222556i
\(743\) 33.0542 1.21264 0.606320 0.795220i \(-0.292645\pi\)
0.606320 + 0.795220i \(0.292645\pi\)
\(744\) 0 0
\(745\) 79.8941 2.92709
\(746\) 0.240783 + 0.685823i 0.00881570 + 0.0251098i
\(747\) 0 0
\(748\) −15.7114 + 12.5832i −0.574467 + 0.460086i
\(749\) 15.1480 0.553496
\(750\) 0 0
\(751\) 40.4075i 1.47449i −0.675625 0.737246i \(-0.736126\pi\)
0.675625 0.737246i \(-0.263874\pi\)
\(752\) −5.67376 + 25.3453i −0.206901 + 0.924250i
\(753\) 0 0
\(754\) −0.905954 2.58043i −0.0329929 0.0939737i
\(755\) 4.64498i 0.169048i
\(756\) 0 0
\(757\) 30.0219i 1.09116i 0.838057 + 0.545582i \(0.183691\pi\)
−0.838057 + 0.545582i \(0.816309\pi\)
\(758\) −10.6444 + 3.73710i −0.386621 + 0.135737i
\(759\) 0 0
\(760\) 4.72772 7.57665i 0.171492 0.274834i
\(761\) 13.9651i 0.506234i −0.967436 0.253117i \(-0.918544\pi\)
0.967436 0.253117i \(-0.0814557\pi\)
\(762\) 0 0
\(763\) 7.70038 0.278772
\(764\) 18.1284 14.5189i 0.655864 0.525276i
\(765\) 0 0
\(766\) −10.7203 + 3.76375i −0.387340 + 0.135990i
\(767\) −0.941516 −0.0339962
\(768\) 0 0
\(769\) 17.9999 0.649094 0.324547 0.945869i \(-0.394788\pi\)
0.324547 + 0.945869i \(0.394788\pi\)
\(770\) 23.7020 8.32145i 0.854161 0.299884i
\(771\) 0 0
\(772\) −20.0075 + 16.0239i −0.720086 + 0.576711i
\(773\) 27.2134 0.978798 0.489399 0.872060i \(-0.337216\pi\)
0.489399 + 0.872060i \(0.337216\pi\)
\(774\) 0 0
\(775\) 32.2124i 1.15710i
\(776\) 5.07798 8.13797i 0.182289 0.292136i
\(777\) 0 0
\(778\) −8.81659 + 3.09539i −0.316090 + 0.110975i
\(779\) 7.59429i 0.272094i
\(780\) 0 0
\(781\) 6.14741i 0.219972i
\(782\) 5.40184 + 15.3861i 0.193170 + 0.550205i
\(783\) 0 0
\(784\) −0.873805 + 3.90339i −0.0312073 + 0.139407i
\(785\)