Properties

Label 3150.2.bp.g.899.7
Level 3150
Weight 2
Character 3150.899
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.7
Character \(\chi\) \(=\) 3150.899
Dual form 3150.2.bp.g.1349.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.04195 + 2.43194i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.04195 + 2.43194i) q^{7} +1.00000 q^{8} +(-1.38605 - 0.800236i) q^{11} +0.770726 q^{13} +(1.58515 - 2.11833i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.05027 - 1.76107i) q^{17} +(-3.06818 + 1.77141i) q^{19} +1.60047i q^{22} +(-1.61385 - 2.79527i) q^{23} +(-0.385363 - 0.667468i) q^{26} +(-2.62710 - 0.313613i) q^{28} -0.700774i q^{29} +(1.13725 + 0.656589i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.52215i q^{34} +(-0.792101 + 0.457320i) q^{37} +(3.06818 + 1.77141i) q^{38} -4.88167 q^{41} -9.26963i q^{43} +(1.38605 - 0.800236i) q^{44} +(-1.61385 + 2.79527i) q^{46} +(-2.31462 + 1.33635i) q^{47} +(-4.82867 + 5.06793i) q^{49} +(-0.385363 + 0.667468i) q^{52} +(4.64520 - 8.04572i) q^{53} +(1.04195 + 2.43194i) q^{56} +(-0.606888 + 0.350387i) q^{58} +(1.56198 - 2.70542i) q^{59} +(-9.43214 + 5.44565i) q^{61} -1.31318i q^{62} +1.00000 q^{64} +(5.90314 + 3.40818i) q^{67} +(3.05027 - 1.76107i) q^{68} -6.47930i q^{71} +(5.51852 - 9.55835i) q^{73} +(0.792101 + 0.457320i) q^{74} -3.54282i q^{76} +(0.501930 - 4.20460i) q^{77} +(1.45086 + 2.51296i) q^{79} +(2.44083 + 4.22765i) q^{82} -11.9777i q^{83} +(-8.02773 + 4.63481i) q^{86} +(-1.38605 - 0.800236i) q^{88} +(4.40369 + 7.62742i) q^{89} +(0.803059 + 1.87436i) q^{91} +3.22770 q^{92} +(2.31462 + 1.33635i) q^{94} +5.31224 q^{97} +(6.80329 + 1.64779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} - 12q^{16} + 24q^{17} - 12q^{19} - 8q^{23} - 12q^{32} + 12q^{38} - 8q^{46} - 24q^{47} + 52q^{49} - 32q^{53} - 12q^{61} + 24q^{64} - 24q^{68} - 16q^{77} - 4q^{79} + 68q^{91} + 16q^{92} + 24q^{94} - 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 1.04195 + 2.43194i 0.393821 + 0.919187i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.38605 0.800236i −0.417910 0.241280i 0.276273 0.961079i \(-0.410901\pi\)
−0.694183 + 0.719799i \(0.744234\pi\)
\(12\) 0 0
\(13\) 0.770726 0.213761 0.106880 0.994272i \(-0.465914\pi\)
0.106880 + 0.994272i \(0.465914\pi\)
\(14\) 1.58515 2.11833i 0.423648 0.566147i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.05027 1.76107i −0.739799 0.427123i 0.0821974 0.996616i \(-0.473806\pi\)
−0.821996 + 0.569493i \(0.807140\pi\)
\(18\) 0 0
\(19\) −3.06818 + 1.77141i −0.703888 + 0.406390i −0.808794 0.588092i \(-0.799879\pi\)
0.104906 + 0.994482i \(0.466546\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.60047i 0.341222i
\(23\) −1.61385 2.79527i −0.336511 0.582854i 0.647263 0.762267i \(-0.275914\pi\)
−0.983774 + 0.179413i \(0.942580\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.385363 0.667468i −0.0755759 0.130901i
\(27\) 0 0
\(28\) −2.62710 0.313613i −0.496475 0.0592674i
\(29\) 0.700774i 0.130131i −0.997881 0.0650653i \(-0.979274\pi\)
0.997881 0.0650653i \(-0.0207256\pi\)
\(30\) 0 0
\(31\) 1.13725 + 0.656589i 0.204255 + 0.117927i 0.598639 0.801019i \(-0.295708\pi\)
−0.394383 + 0.918946i \(0.629042\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.52215i 0.604043i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.792101 + 0.457320i −0.130221 + 0.0751829i −0.563695 0.825983i \(-0.690621\pi\)
0.433475 + 0.901166i \(0.357287\pi\)
\(38\) 3.06818 + 1.77141i 0.497724 + 0.287361i
\(39\) 0 0
\(40\) 0 0
\(41\) −4.88167 −0.762388 −0.381194 0.924495i \(-0.624487\pi\)
−0.381194 + 0.924495i \(0.624487\pi\)
\(42\) 0 0
\(43\) 9.26963i 1.41361i −0.707411 0.706803i \(-0.750137\pi\)
0.707411 0.706803i \(-0.249863\pi\)
\(44\) 1.38605 0.800236i 0.208955 0.120640i
\(45\) 0 0
\(46\) −1.61385 + 2.79527i −0.237949 + 0.412140i
\(47\) −2.31462 + 1.33635i −0.337623 + 0.194926i −0.659220 0.751950i \(-0.729113\pi\)
0.321598 + 0.946876i \(0.395780\pi\)
\(48\) 0 0
\(49\) −4.82867 + 5.06793i −0.689810 + 0.723990i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.385363 + 0.667468i −0.0534402 + 0.0925612i
\(53\) 4.64520 8.04572i 0.638067 1.10516i −0.347789 0.937573i \(-0.613068\pi\)
0.985856 0.167592i \(-0.0535991\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.04195 + 2.43194i 0.139237 + 0.324982i
\(57\) 0 0
\(58\) −0.606888 + 0.350387i −0.0796883 + 0.0460081i
\(59\) 1.56198 2.70542i 0.203352 0.352216i −0.746254 0.665661i \(-0.768150\pi\)
0.949606 + 0.313445i \(0.101483\pi\)
\(60\) 0 0
\(61\) −9.43214 + 5.44565i −1.20766 + 0.697244i −0.962248 0.272175i \(-0.912257\pi\)
−0.245414 + 0.969418i \(0.578924\pi\)
\(62\) 1.31318i 0.166774i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 5.90314 + 3.40818i 0.721183 + 0.416375i 0.815188 0.579196i \(-0.196634\pi\)
−0.0940048 + 0.995572i \(0.529967\pi\)
\(68\) 3.05027 1.76107i 0.369899 0.213561i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.47930i 0.768951i −0.923135 0.384475i \(-0.874382\pi\)
0.923135 0.384475i \(-0.125618\pi\)
\(72\) 0 0
\(73\) 5.51852 9.55835i 0.645894 1.11872i −0.338201 0.941074i \(-0.609818\pi\)
0.984094 0.177647i \(-0.0568484\pi\)
\(74\) 0.792101 + 0.457320i 0.0920799 + 0.0531623i
\(75\) 0 0
\(76\) 3.54282i 0.406390i
\(77\) 0.501930 4.20460i 0.0572002 0.479158i
\(78\) 0 0
\(79\) 1.45086 + 2.51296i 0.163234 + 0.282730i 0.936027 0.351928i \(-0.114474\pi\)
−0.772792 + 0.634659i \(0.781141\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.44083 + 4.22765i 0.269545 + 0.466865i
\(83\) 11.9777i 1.31472i −0.753576 0.657361i \(-0.771673\pi\)
0.753576 0.657361i \(-0.228327\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.02773 + 4.63481i −0.865653 + 0.499785i
\(87\) 0 0
\(88\) −1.38605 0.800236i −0.147753 0.0853055i
\(89\) 4.40369 + 7.62742i 0.466791 + 0.808505i 0.999280 0.0379313i \(-0.0120768\pi\)
−0.532490 + 0.846437i \(0.678743\pi\)
\(90\) 0 0
\(91\) 0.803059 + 1.87436i 0.0841835 + 0.196486i
\(92\) 3.22770 0.336511
\(93\) 0 0
\(94\) 2.31462 + 1.33635i 0.238735 + 0.137834i
\(95\) 0 0
\(96\) 0 0
\(97\) 5.31224 0.539376 0.269688 0.962948i \(-0.413079\pi\)
0.269688 + 0.962948i \(0.413079\pi\)
\(98\) 6.80329 + 1.64779i 0.687236 + 0.166452i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.62663 8.01356i 0.460367 0.797379i −0.538612 0.842554i \(-0.681051\pi\)
0.998979 + 0.0451749i \(0.0143845\pi\)
\(102\) 0 0
\(103\) −7.91290 13.7055i −0.779681 1.35045i −0.932125 0.362136i \(-0.882048\pi\)
0.152444 0.988312i \(-0.451286\pi\)
\(104\) 0.770726 0.0755759
\(105\) 0 0
\(106\) −9.29040 −0.902363
\(107\) −6.20735 10.7514i −0.600087 1.03938i −0.992807 0.119724i \(-0.961799\pi\)
0.392720 0.919658i \(-0.371534\pi\)
\(108\) 0 0
\(109\) −5.51750 + 9.55659i −0.528480 + 0.915355i 0.470968 + 0.882150i \(0.343905\pi\)
−0.999449 + 0.0332048i \(0.989429\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.58515 2.11833i 0.149782 0.200163i
\(113\) 15.0301 1.41391 0.706957 0.707256i \(-0.250067\pi\)
0.706957 + 0.707256i \(0.250067\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.606888 + 0.350387i 0.0563482 + 0.0325326i
\(117\) 0 0
\(118\) −3.12395 −0.287583
\(119\) 1.10459 9.25303i 0.101258 0.848223i
\(120\) 0 0
\(121\) −4.21924 7.30795i −0.383568 0.664359i
\(122\) 9.43214 + 5.44565i 0.853946 + 0.493026i
\(123\) 0 0
\(124\) −1.13725 + 0.656589i −0.102128 + 0.0589634i
\(125\) 0 0
\(126\) 0 0
\(127\) 2.66506i 0.236486i −0.992985 0.118243i \(-0.962274\pi\)
0.992985 0.118243i \(-0.0377262\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −7.10987 12.3147i −0.621192 1.07594i −0.989264 0.146139i \(-0.953315\pi\)
0.368071 0.929797i \(-0.380018\pi\)
\(132\) 0 0
\(133\) −7.50486 5.61590i −0.650754 0.486960i
\(134\) 6.81636i 0.588844i
\(135\) 0 0
\(136\) −3.05027 1.76107i −0.261558 0.151011i
\(137\) −0.0650662 + 0.112698i −0.00555898 + 0.00962843i −0.868792 0.495178i \(-0.835103\pi\)
0.863233 + 0.504806i \(0.168436\pi\)
\(138\) 0 0
\(139\) 3.63572i 0.308378i −0.988041 0.154189i \(-0.950724\pi\)
0.988041 0.154189i \(-0.0492765\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.61123 + 3.23965i −0.470884 + 0.271865i
\(143\) −1.06826 0.616762i −0.0893327 0.0515763i
\(144\) 0 0
\(145\) 0 0
\(146\) −11.0370 −0.913432
\(147\) 0 0
\(148\) 0.914639i 0.0751829i
\(149\) −2.53957 + 1.46622i −0.208049 + 0.120117i −0.600405 0.799696i \(-0.704994\pi\)
0.392355 + 0.919814i \(0.371660\pi\)
\(150\) 0 0
\(151\) −3.56919 + 6.18201i −0.290456 + 0.503085i −0.973918 0.226902i \(-0.927140\pi\)
0.683461 + 0.729987i \(0.260474\pi\)
\(152\) −3.06818 + 1.77141i −0.248862 + 0.143681i
\(153\) 0 0
\(154\) −3.89225 + 1.66762i −0.313647 + 0.134380i
\(155\) 0 0
\(156\) 0 0
\(157\) 7.15702 12.3963i 0.571192 0.989334i −0.425252 0.905075i \(-0.639814\pi\)
0.996444 0.0842589i \(-0.0268523\pi\)
\(158\) 1.45086 2.51296i 0.115424 0.199921i
\(159\) 0 0
\(160\) 0 0
\(161\) 5.11638 6.83732i 0.403227 0.538857i
\(162\) 0 0
\(163\) −6.24313 + 3.60448i −0.489000 + 0.282324i −0.724160 0.689632i \(-0.757772\pi\)
0.235159 + 0.971957i \(0.424439\pi\)
\(164\) 2.44083 4.22765i 0.190597 0.330124i
\(165\) 0 0
\(166\) −10.3730 + 5.98884i −0.805099 + 0.464824i
\(167\) 13.8952i 1.07524i 0.843187 + 0.537620i \(0.180677\pi\)
−0.843187 + 0.537620i \(0.819323\pi\)
\(168\) 0 0
\(169\) −12.4060 −0.954306
\(170\) 0 0
\(171\) 0 0
\(172\) 8.02773 + 4.63481i 0.612109 + 0.353401i
\(173\) −2.05023 + 1.18370i −0.155876 + 0.0899951i −0.575909 0.817514i \(-0.695352\pi\)
0.420033 + 0.907509i \(0.362018\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.60047i 0.120640i
\(177\) 0 0
\(178\) 4.40369 7.62742i 0.330071 0.571700i
\(179\) −15.4837 8.93953i −1.15731 0.668172i −0.206650 0.978415i \(-0.566256\pi\)
−0.950657 + 0.310243i \(0.899590\pi\)
\(180\) 0 0
\(181\) 16.6673i 1.23887i 0.785049 + 0.619434i \(0.212638\pi\)
−0.785049 + 0.619434i \(0.787362\pi\)
\(182\) 1.22171 1.63265i 0.0905594 0.121020i
\(183\) 0 0
\(184\) −1.61385 2.79527i −0.118975 0.206070i
\(185\) 0 0
\(186\) 0 0
\(187\) 2.81855 + 4.88187i 0.206113 + 0.356998i
\(188\) 2.67270i 0.194926i
\(189\) 0 0
\(190\) 0 0
\(191\) 21.4359 12.3760i 1.55104 0.895496i 0.552987 0.833190i \(-0.313488\pi\)
0.998057 0.0623063i \(-0.0198456\pi\)
\(192\) 0 0
\(193\) −10.8917 6.28835i −0.784005 0.452645i 0.0538428 0.998549i \(-0.482853\pi\)
−0.837848 + 0.545904i \(0.816186\pi\)
\(194\) −2.65612 4.60054i −0.190698 0.330299i
\(195\) 0 0
\(196\) −1.97462 6.71572i −0.141044 0.479694i
\(197\) −19.7360 −1.40613 −0.703066 0.711125i \(-0.748186\pi\)
−0.703066 + 0.711125i \(0.748186\pi\)
\(198\) 0 0
\(199\) −9.82275 5.67117i −0.696316 0.402018i 0.109658 0.993969i \(-0.465025\pi\)
−0.805974 + 0.591951i \(0.798358\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −9.25326 −0.651057
\(203\) 1.70424 0.730173i 0.119614 0.0512481i
\(204\) 0 0
\(205\) 0 0
\(206\) −7.91290 + 13.7055i −0.551318 + 0.954911i
\(207\) 0 0
\(208\) −0.385363 0.667468i −0.0267201 0.0462806i
\(209\) 5.67019 0.392215
\(210\) 0 0
\(211\) 16.0647 1.10594 0.552970 0.833201i \(-0.313494\pi\)
0.552970 + 0.833201i \(0.313494\pi\)
\(212\) 4.64520 + 8.04572i 0.319034 + 0.552582i
\(213\) 0 0
\(214\) −6.20735 + 10.7514i −0.424326 + 0.734954i
\(215\) 0 0
\(216\) 0 0
\(217\) −0.411830 + 3.44985i −0.0279569 + 0.234191i
\(218\) 11.0350 0.747384
\(219\) 0 0
\(220\) 0 0
\(221\) −2.35092 1.35730i −0.158140 0.0913022i
\(222\) 0 0
\(223\) 2.00917 0.134544 0.0672720 0.997735i \(-0.478570\pi\)
0.0672720 + 0.997735i \(0.478570\pi\)
\(224\) −2.62710 0.313613i −0.175530 0.0209542i
\(225\) 0 0
\(226\) −7.51506 13.0165i −0.499894 0.865842i
\(227\) 3.38249 + 1.95288i 0.224504 + 0.129617i 0.608034 0.793911i \(-0.291958\pi\)
−0.383530 + 0.923528i \(0.625292\pi\)
\(228\) 0 0
\(229\) −11.5904 + 6.69174i −0.765918 + 0.442203i −0.831416 0.555650i \(-0.812470\pi\)
0.0654987 + 0.997853i \(0.479136\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.700774i 0.0460081i
\(233\) −5.14808 8.91673i −0.337262 0.584154i 0.646655 0.762783i \(-0.276167\pi\)
−0.983917 + 0.178628i \(0.942834\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.56198 + 2.70542i 0.101676 + 0.176108i
\(237\) 0 0
\(238\) −8.56565 + 3.66991i −0.555229 + 0.237885i
\(239\) 17.5460i 1.13495i −0.823389 0.567477i \(-0.807920\pi\)
0.823389 0.567477i \(-0.192080\pi\)
\(240\) 0 0
\(241\) 8.66068 + 5.00024i 0.557883 + 0.322094i 0.752295 0.658826i \(-0.228947\pi\)
−0.194412 + 0.980920i \(0.562280\pi\)
\(242\) −4.21924 + 7.30795i −0.271223 + 0.469773i
\(243\) 0 0
\(244\) 10.8913i 0.697244i
\(245\) 0 0
\(246\) 0 0
\(247\) −2.36472 + 1.36527i −0.150464 + 0.0868702i
\(248\) 1.13725 + 0.656589i 0.0722152 + 0.0416935i
\(249\) 0 0
\(250\) 0 0
\(251\) −3.55412 −0.224334 −0.112167 0.993689i \(-0.535779\pi\)
−0.112167 + 0.993689i \(0.535779\pi\)
\(252\) 0 0
\(253\) 5.16584i 0.324774i
\(254\) −2.30801 + 1.33253i −0.144818 + 0.0836105i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.15756 + 3.55507i −0.384098 + 0.221759i −0.679600 0.733583i \(-0.737847\pi\)
0.295502 + 0.955342i \(0.404513\pi\)
\(258\) 0 0
\(259\) −1.93751 1.44984i −0.120391 0.0900885i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.10987 + 12.3147i −0.439249 + 0.760802i
\(263\) −14.2752 + 24.7253i −0.880245 + 1.52463i −0.0291760 + 0.999574i \(0.509288\pi\)
−0.851069 + 0.525054i \(0.824045\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.11108 + 9.30735i −0.0681245 + 0.570670i
\(267\) 0 0
\(268\) −5.90314 + 3.40818i −0.360592 + 0.208188i
\(269\) −12.9628 + 22.4523i −0.790359 + 1.36894i 0.135386 + 0.990793i \(0.456772\pi\)
−0.925745 + 0.378149i \(0.876561\pi\)
\(270\) 0 0
\(271\) −24.1643 + 13.9513i −1.46788 + 0.847479i −0.999353 0.0359726i \(-0.988547\pi\)
−0.468523 + 0.883451i \(0.655214\pi\)
\(272\) 3.52215i 0.213561i
\(273\) 0 0
\(274\) 0.130132 0.00786158
\(275\) 0 0
\(276\) 0 0
\(277\) 8.98042 + 5.18485i 0.539581 + 0.311527i 0.744909 0.667166i \(-0.232493\pi\)
−0.205328 + 0.978693i \(0.565826\pi\)
\(278\) −3.14863 + 1.81786i −0.188842 + 0.109028i
\(279\) 0 0
\(280\) 0 0
\(281\) 21.0412i 1.25521i −0.778530 0.627607i \(-0.784035\pi\)
0.778530 0.627607i \(-0.215965\pi\)
\(282\) 0 0
\(283\) 13.6859 23.7046i 0.813541 1.40909i −0.0968293 0.995301i \(-0.530870\pi\)
0.910371 0.413794i \(-0.135797\pi\)
\(284\) 5.61123 + 3.23965i 0.332965 + 0.192238i
\(285\) 0 0
\(286\) 1.23352i 0.0729399i
\(287\) −5.08646 11.8719i −0.300244 0.700777i
\(288\) 0 0
\(289\) −2.29724 3.97894i −0.135132 0.234055i
\(290\) 0 0
\(291\) 0 0
\(292\) 5.51852 + 9.55835i 0.322947 + 0.559360i
\(293\) 16.9059i 0.987654i −0.869560 0.493827i \(-0.835598\pi\)
0.869560 0.493827i \(-0.164402\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.792101 + 0.457320i −0.0460399 + 0.0265812i
\(297\) 0 0
\(298\) 2.53957 + 1.46622i 0.147113 + 0.0849358i
\(299\) −1.24384 2.15439i −0.0719328 0.124591i
\(300\) 0 0
\(301\) 22.5432 9.65851i 1.29937 0.556707i
\(302\) 7.13837 0.410767
\(303\) 0 0
\(304\) 3.06818 + 1.77141i 0.175972 + 0.101597i
\(305\) 0 0
\(306\) 0 0
\(307\) −14.0139 −0.799813 −0.399906 0.916556i \(-0.630957\pi\)
−0.399906 + 0.916556i \(0.630957\pi\)
\(308\) 3.39032 + 2.53698i 0.193182 + 0.144558i
\(309\) 0 0
\(310\) 0 0
\(311\) −6.72211 + 11.6430i −0.381176 + 0.660216i −0.991231 0.132143i \(-0.957814\pi\)
0.610055 + 0.792359i \(0.291147\pi\)
\(312\) 0 0
\(313\) 2.12904 + 3.68760i 0.120340 + 0.208436i 0.919902 0.392149i \(-0.128268\pi\)
−0.799562 + 0.600584i \(0.794935\pi\)
\(314\) −14.3140 −0.807788
\(315\) 0 0
\(316\) −2.90172 −0.163234
\(317\) −0.0987910 0.171111i −0.00554866 0.00961055i 0.863238 0.504798i \(-0.168433\pi\)
−0.868786 + 0.495187i \(0.835100\pi\)
\(318\) 0 0
\(319\) −0.560785 + 0.971308i −0.0313979 + 0.0543828i
\(320\) 0 0
\(321\) 0 0
\(322\) −8.47948 1.01225i −0.472543 0.0564105i
\(323\) 12.4783 0.694314
\(324\) 0 0
\(325\) 0 0
\(326\) 6.24313 + 3.60448i 0.345775 + 0.199633i
\(327\) 0 0
\(328\) −4.88167 −0.269545
\(329\) −5.66165 4.23662i −0.312137 0.233572i
\(330\) 0 0
\(331\) −2.29740 3.97922i −0.126277 0.218718i 0.795955 0.605356i \(-0.206969\pi\)
−0.922231 + 0.386639i \(0.873636\pi\)
\(332\) 10.3730 + 5.98884i 0.569291 + 0.328680i
\(333\) 0 0
\(334\) 12.0336 6.94758i 0.658447 0.380155i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.05076i 0.329606i −0.986327 0.164803i \(-0.947301\pi\)
0.986327 0.164803i \(-0.0526988\pi\)
\(338\) 6.20299 + 10.7439i 0.337398 + 0.584391i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.05085 1.82013i −0.0569069 0.0985656i
\(342\) 0 0
\(343\) −17.3562 6.46250i −0.937144 0.348942i
\(344\) 9.26963i 0.499785i
\(345\) 0 0
\(346\) 2.05023 + 1.18370i 0.110221 + 0.0636362i
\(347\) −1.59102 + 2.75573i −0.0854104 + 0.147935i −0.905566 0.424205i \(-0.860553\pi\)
0.820156 + 0.572140i \(0.193887\pi\)
\(348\) 0 0
\(349\) 29.0573i 1.55540i −0.628636 0.777700i \(-0.716386\pi\)
0.628636 0.777700i \(-0.283614\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.38605 0.800236i 0.0738767 0.0426527i
\(353\) 6.63942 + 3.83327i 0.353381 + 0.204025i 0.666173 0.745797i \(-0.267931\pi\)
−0.312792 + 0.949822i \(0.601264\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −8.80739 −0.466791
\(357\) 0 0
\(358\) 17.8791i 0.944938i
\(359\) −19.6694 + 11.3561i −1.03811 + 0.599353i −0.919297 0.393564i \(-0.871242\pi\)
−0.118812 + 0.992917i \(0.537909\pi\)
\(360\) 0 0
\(361\) −3.22420 + 5.58447i −0.169695 + 0.293920i
\(362\) 14.4343 8.33363i 0.758649 0.438006i
\(363\) 0 0
\(364\) −2.02477 0.241710i −0.106127 0.0126690i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.37433 16.2368i 0.489336 0.847555i −0.510589 0.859825i \(-0.670573\pi\)
0.999925 + 0.0122703i \(0.00390585\pi\)
\(368\) −1.61385 + 2.79527i −0.0841277 + 0.145713i
\(369\) 0 0
\(370\) 0 0
\(371\) 24.4068 + 2.91359i 1.26714 + 0.151266i
\(372\) 0 0
\(373\) −2.46050 + 1.42057i −0.127400 + 0.0735545i −0.562346 0.826902i \(-0.690101\pi\)
0.434946 + 0.900457i \(0.356768\pi\)
\(374\) 2.81855 4.88187i 0.145744 0.252435i
\(375\) 0 0
\(376\) −2.31462 + 1.33635i −0.119368 + 0.0689169i
\(377\) 0.540105i 0.0278168i
\(378\) 0 0
\(379\) 27.2750 1.40102 0.700510 0.713642i \(-0.252956\pi\)
0.700510 + 0.713642i \(0.252956\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −21.4359 12.3760i −1.09675 0.633211i
\(383\) −26.1843 + 15.1175i −1.33796 + 0.772469i −0.986504 0.163737i \(-0.947645\pi\)
−0.351451 + 0.936206i \(0.614312\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.5767i 0.640137i
\(387\) 0 0
\(388\) −2.65612 + 4.60054i −0.134844 + 0.233557i
\(389\) 4.29588 + 2.48023i 0.217810 + 0.125752i 0.604936 0.796274i \(-0.293199\pi\)
−0.387126 + 0.922027i \(0.626532\pi\)
\(390\) 0 0
\(391\) 11.3684i 0.574926i
\(392\) −4.82867 + 5.06793i −0.243885 + 0.255969i
\(393\) 0 0
\(394\) 9.86800 + 17.0919i 0.497143 + 0.861077i
\(395\) 0 0
\(396\) 0 0
\(397\) 7.30213 + 12.6477i 0.366483 + 0.634768i 0.989013 0.147828i \(-0.0472283\pi\)
−0.622530 + 0.782596i \(0.713895\pi\)
\(398\) 11.3423i 0.568540i
\(399\) 0 0
\(400\) 0 0
\(401\) 17.5622 10.1395i 0.877014 0.506345i 0.00734158 0.999973i \(-0.497663\pi\)
0.869673 + 0.493629i \(0.164330\pi\)
\(402\) 0 0
\(403\) 0.876505 + 0.506050i 0.0436618 + 0.0252082i
\(404\) 4.62663 + 8.01356i 0.230183 + 0.398689i
\(405\) 0 0
\(406\) −1.48447 1.11083i −0.0736730 0.0551296i
\(407\) 1.46385 0.0725606
\(408\) 0 0
\(409\) −4.26877 2.46458i −0.211077 0.121865i 0.390735 0.920503i \(-0.372221\pi\)
−0.601812 + 0.798638i \(0.705554\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.8258 0.779681
\(413\) 8.20693 + 0.979714i 0.403837 + 0.0482086i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.385363 + 0.667468i −0.0188940 + 0.0327253i
\(417\) 0 0
\(418\) −2.83510 4.91053i −0.138669 0.240182i
\(419\) −24.0686 −1.17583 −0.587913 0.808924i \(-0.700050\pi\)
−0.587913 + 0.808924i \(0.700050\pi\)
\(420\) 0 0
\(421\) 16.0657 0.782995 0.391498 0.920179i \(-0.371957\pi\)
0.391498 + 0.920179i \(0.371957\pi\)
\(422\) −8.03236 13.9125i −0.391009 0.677248i
\(423\) 0 0
\(424\) 4.64520 8.04572i 0.225591 0.390735i
\(425\) 0 0
\(426\) 0 0
\(427\) −23.0713 17.2643i −1.11650 0.835478i
\(428\) 12.4147 0.600087
\(429\) 0 0
\(430\) 0 0
\(431\) 0.373691 + 0.215751i 0.0180001 + 0.0103923i 0.508973 0.860782i \(-0.330025\pi\)
−0.490973 + 0.871175i \(0.663359\pi\)
\(432\) 0 0
\(433\) 30.5287 1.46711 0.733557 0.679628i \(-0.237859\pi\)
0.733557 + 0.679628i \(0.237859\pi\)
\(434\) 3.19357 1.36827i 0.153296 0.0656790i
\(435\) 0 0
\(436\) −5.51750 9.55659i −0.264240 0.457677i
\(437\) 9.90315 + 5.71759i 0.473732 + 0.273509i
\(438\) 0 0
\(439\) 32.9059 18.9982i 1.57051 0.906735i 0.574406 0.818571i \(-0.305233\pi\)
0.996106 0.0881648i \(-0.0281002\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.71461i 0.129121i
\(443\) −11.6503 20.1789i −0.553522 0.958728i −0.998017 0.0629464i \(-0.979950\pi\)
0.444495 0.895781i \(-0.353383\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.00459 1.73999i −0.0475685 0.0823911i
\(447\) 0 0
\(448\) 1.04195 + 2.43194i 0.0492276 + 0.114898i
\(449\) 21.9119i 1.03409i 0.855960 + 0.517043i \(0.172967\pi\)
−0.855960 + 0.517043i \(0.827033\pi\)
\(450\) 0 0
\(451\) 6.76623 + 3.90648i 0.318609 + 0.183949i
\(452\) −7.51506 + 13.0165i −0.353479 + 0.612243i
\(453\) 0 0
\(454\) 3.90576i 0.183306i
\(455\) 0 0
\(456\) 0 0
\(457\) −34.0904 + 19.6821i −1.59468 + 0.920691i −0.602195 + 0.798349i \(0.705707\pi\)
−0.992488 + 0.122341i \(0.960960\pi\)
\(458\) 11.5904 + 6.69174i 0.541586 + 0.312685i
\(459\) 0 0
\(460\) 0 0
\(461\) −2.35282 −0.109582 −0.0547909 0.998498i \(-0.517449\pi\)
−0.0547909 + 0.998498i \(0.517449\pi\)
\(462\) 0 0
\(463\) 2.24550i 0.104357i −0.998638 0.0521787i \(-0.983383\pi\)
0.998638 0.0521787i \(-0.0166165\pi\)
\(464\) −0.606888 + 0.350387i −0.0281741 + 0.0162663i
\(465\) 0 0
\(466\) −5.14808 + 8.91673i −0.238480 + 0.413059i
\(467\) −27.8740 + 16.0931i −1.28986 + 0.744699i −0.978628 0.205636i \(-0.934074\pi\)
−0.311228 + 0.950335i \(0.600740\pi\)
\(468\) 0 0
\(469\) −2.13770 + 17.9072i −0.0987099 + 0.826880i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.56198 2.70542i 0.0718958 0.124527i
\(473\) −7.41789 + 12.8482i −0.341075 + 0.590759i
\(474\) 0 0
\(475\) 0 0
\(476\) 7.46106 + 5.58312i 0.341977 + 0.255902i
\(477\) 0 0
\(478\) −15.1952 + 8.77298i −0.695014 + 0.401267i
\(479\) −3.30556 + 5.72539i −0.151035 + 0.261600i −0.931608 0.363464i \(-0.881594\pi\)
0.780573 + 0.625064i \(0.214927\pi\)
\(480\) 0 0
\(481\) −0.610493 + 0.352468i −0.0278361 + 0.0160712i
\(482\) 10.0005i 0.455510i
\(483\) 0 0
\(484\) 8.43849 0.383568
\(485\) 0 0
\(486\) 0 0
\(487\) 4.99120 + 2.88167i 0.226173 + 0.130581i 0.608805 0.793320i \(-0.291649\pi\)
−0.382632 + 0.923901i \(0.624982\pi\)
\(488\) −9.43214 + 5.44565i −0.426973 + 0.246513i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.90529i 0.131114i 0.997849 + 0.0655570i \(0.0208824\pi\)
−0.997849 + 0.0655570i \(0.979118\pi\)
\(492\) 0 0
\(493\) −1.23411 + 2.13755i −0.0555817 + 0.0962704i
\(494\) 2.36472 + 1.36527i 0.106394 + 0.0614265i
\(495\) 0 0
\(496\) 1.31318i 0.0589634i
\(497\) 15.7573 6.75111i 0.706810 0.302829i
\(498\) 0 0
\(499\) 1.14104 + 1.97634i 0.0510800 + 0.0884732i 0.890435 0.455111i \(-0.150400\pi\)
−0.839355 + 0.543584i \(0.817067\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.77706 + 3.07796i 0.0793141 + 0.137376i
\(503\) 1.32664i 0.0591520i −0.999563 0.0295760i \(-0.990584\pi\)
0.999563 0.0295760i \(-0.00941571\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.47375 2.58292i 0.198882 0.114825i
\(507\) 0 0
\(508\) 2.30801 + 1.33253i 0.102402 + 0.0591215i
\(509\) 21.5053 + 37.2483i 0.953207 + 1.65100i 0.738419 + 0.674342i \(0.235573\pi\)
0.214788 + 0.976661i \(0.431094\pi\)
\(510\) 0 0
\(511\) 28.9954 + 3.46136i 1.28268 + 0.153122i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 6.15756 + 3.55507i 0.271598 + 0.156807i
\(515\) 0 0
\(516\) 0 0
\(517\) 4.27758 0.188128
\(518\) −0.286843 + 2.40285i −0.0126032 + 0.105575i
\(519\) 0 0
\(520\) 0 0
\(521\) −19.8838 + 34.4397i −0.871124 + 1.50883i −0.0102890 + 0.999947i \(0.503275\pi\)
−0.860835 + 0.508884i \(0.830058\pi\)
\(522\) 0 0
\(523\) 19.8804 + 34.4338i 0.869307 + 1.50568i 0.862706 + 0.505706i \(0.168768\pi\)
0.00660128 + 0.999978i \(0.497899\pi\)
\(524\) 14.2197 0.621192
\(525\) 0 0
\(526\) 28.5503 1.24485
\(527\) −2.31260 4.00555i −0.100739 0.174484i
\(528\) 0 0
\(529\) 6.29098 10.8963i 0.273521 0.473752i
\(530\) 0 0
\(531\) 0 0
\(532\) 8.61594 3.69145i 0.373548 0.160045i
\(533\) −3.76242 −0.162969
\(534\) 0 0
\(535\) 0 0
\(536\) 5.90314 + 3.40818i 0.254977 + 0.147211i
\(537\) 0 0
\(538\) 25.9257 1.11774
\(539\) 10.7483 3.16033i 0.462963 0.136125i
\(540\) 0 0
\(541\) −10.1006 17.4947i −0.434258 0.752157i 0.562977 0.826473i \(-0.309656\pi\)
−0.997235 + 0.0743161i \(0.976323\pi\)
\(542\) 24.1643 + 13.9513i 1.03795 + 0.599258i
\(543\) 0 0
\(544\) 3.05027 1.76107i 0.130779 0.0755054i
\(545\) 0 0
\(546\) 0 0
\(547\) 34.5631i 1.47781i −0.673810 0.738905i \(-0.735343\pi\)
0.673810 0.738905i \(-0.264657\pi\)
\(548\) −0.0650662 0.112698i −0.00277949 0.00481422i
\(549\) 0 0
\(550\) 0 0
\(551\) 1.24136 + 2.15010i 0.0528837 + 0.0915973i
\(552\) 0 0
\(553\) −4.59965 + 6.14679i −0.195597 + 0.261388i
\(554\) 10.3697i 0.440566i
\(555\) 0 0
\(556\) 3.14863 + 1.81786i 0.133532 + 0.0770945i
\(557\) 16.2396 28.1278i 0.688094 1.19181i −0.284360 0.958718i \(-0.591781\pi\)
0.972454 0.233096i \(-0.0748856\pi\)
\(558\) 0 0
\(559\) 7.14434i 0.302173i
\(560\) 0 0
\(561\) 0 0
\(562\) −18.2222 + 10.5206i −0.768658 + 0.443785i
\(563\) −12.4603 7.19395i −0.525139 0.303189i 0.213896 0.976856i \(-0.431385\pi\)
−0.739035 + 0.673668i \(0.764718\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −27.3718 −1.15052
\(567\) 0 0
\(568\) 6.47930i 0.271865i
\(569\) 6.84504 3.95199i 0.286959 0.165676i −0.349611 0.936895i \(-0.613686\pi\)
0.636570 + 0.771219i \(0.280353\pi\)
\(570\) 0 0
\(571\) 18.3198 31.7309i 0.766661 1.32789i −0.172704 0.984974i \(-0.555250\pi\)
0.939364 0.342921i \(-0.111416\pi\)
\(572\) 1.06826 0.616762i 0.0446664 0.0257881i
\(573\) 0 0
\(574\) −7.73815 + 10.3410i −0.322984 + 0.431624i
\(575\) 0 0
\(576\) 0 0
\(577\) 11.6961 20.2583i 0.486916 0.843363i −0.512971 0.858406i \(-0.671455\pi\)
0.999887 + 0.0150431i \(0.00478854\pi\)
\(578\) −2.29724 + 3.97894i −0.0955527 + 0.165502i
\(579\) 0 0
\(580\) 0 0
\(581\) 29.1290 12.4802i 1.20848 0.517765i
\(582\) 0 0
\(583\) −12.8770 + 7.43451i −0.533309 + 0.307906i
\(584\) 5.51852 9.55835i 0.228358 0.395527i
\(585\) 0 0
\(586\) −14.6409 + 8.45295i −0.604812 + 0.349188i
\(587\) 23.7776i 0.981407i 0.871327 + 0.490704i \(0.163260\pi\)
−0.871327 + 0.490704i \(0.836740\pi\)
\(588\) 0 0
\(589\) −4.65236 −0.191697
\(590\) 0 0
\(591\) 0 0
\(592\) 0.792101 + 0.457320i 0.0325551 + 0.0187957i
\(593\) −33.6979 + 19.4555i −1.38381 + 0.798942i −0.992608 0.121364i \(-0.961273\pi\)
−0.391200 + 0.920306i \(0.627940\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.93244i 0.120117i
\(597\) 0 0
\(598\) −1.24384 + 2.15439i −0.0508642 + 0.0880994i
\(599\) 3.09380 + 1.78621i 0.126409 + 0.0729824i 0.561871 0.827225i \(-0.310082\pi\)
−0.435462 + 0.900207i \(0.643415\pi\)
\(600\) 0 0
\(601\) 21.3183i 0.869591i −0.900529 0.434795i \(-0.856821\pi\)
0.900529 0.434795i \(-0.143179\pi\)
\(602\) −19.6361 14.6937i −0.800308 0.598871i
\(603\) 0 0
\(604\) −3.56919 6.18201i −0.145228 0.251543i
\(605\) 0 0
\(606\) 0 0
\(607\) 0.285402 + 0.494331i 0.0115841 + 0.0200643i 0.871759 0.489934i \(-0.162979\pi\)
−0.860175 + 0.509999i \(0.829646\pi\)
\(608\) 3.54282i 0.143681i
\(609\) 0 0
\(610\) 0 0
\(611\) −1.78394 + 1.02996i −0.0721705 + 0.0416676i
\(612\) 0 0
\(613\) 29.5954 + 17.0869i 1.19535 + 0.690134i 0.959514 0.281659i \(-0.0908848\pi\)
0.235833 + 0.971794i \(0.424218\pi\)
\(614\) 7.00693 + 12.1364i 0.282777 + 0.489783i
\(615\) 0 0
\(616\) 0.501930 4.20460i 0.0202233 0.169408i
\(617\) 20.1713 0.812066 0.406033 0.913858i \(-0.366912\pi\)
0.406033 + 0.913858i \(0.366912\pi\)
\(618\) 0 0
\(619\) −13.9621 8.06104i −0.561186 0.324001i 0.192436 0.981310i \(-0.438361\pi\)
−0.753621 + 0.657309i \(0.771695\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 13.4442 0.539064
\(623\) −13.9610 + 18.6569i −0.559336 + 0.747474i
\(624\) 0 0
\(625\) 0 0
\(626\) 2.12904 3.68760i 0.0850935 0.147386i
\(627\) 0 0
\(628\) 7.15702 + 12.3963i 0.285596 + 0.494667i
\(629\) 3.22149 0.128449
\(630\) 0 0
\(631\) 3.10655 0.123670 0.0618350 0.998086i \(-0.480305\pi\)
0.0618350 + 0.998086i \(0.480305\pi\)
\(632\) 1.45086 + 2.51296i 0.0577121 + 0.0999603i
\(633\) 0 0
\(634\) −0.0987910 + 0.171111i −0.00392349 + 0.00679569i
\(635\) 0 0
\(636\) 0 0
\(637\) −3.72158 + 3.90598i −0.147454 + 0.154761i
\(638\) 1.12157 0.0444034
\(639\) 0 0
\(640\) 0 0
\(641\) −18.9248 10.9262i −0.747483 0.431559i 0.0773008 0.997008i \(-0.475370\pi\)
−0.824784 + 0.565448i \(0.808703\pi\)
\(642\) 0 0
\(643\) 25.4873 1.00512 0.502560 0.864542i \(-0.332391\pi\)
0.502560 + 0.864542i \(0.332391\pi\)
\(644\) 3.36311 + 7.84957i 0.132525 + 0.309317i
\(645\) 0 0
\(646\) −6.23917 10.8066i −0.245477 0.425179i
\(647\) −41.5745 24.0030i −1.63446 0.943657i −0.982694 0.185239i \(-0.940694\pi\)
−0.651768 0.758418i \(-0.725973\pi\)
\(648\) 0 0
\(649\) −4.32995 + 2.49990i −0.169966 + 0.0981296i
\(650\) 0 0
\(651\) 0 0
\(652\) 7.20895i 0.282324i
\(653\) −23.0213 39.8741i −0.900894 1.56039i −0.826336 0.563177i \(-0.809579\pi\)
−0.0745575 0.997217i \(-0.523754\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.44083 + 4.22765i 0.0952985 + 0.165062i
\(657\) 0 0
\(658\) −0.838194 + 7.02144i −0.0326762 + 0.273724i
\(659\) 14.8751i 0.579453i −0.957109 0.289727i \(-0.906436\pi\)
0.957109 0.289727i \(-0.0935644\pi\)
\(660\) 0 0
\(661\) 36.7957 + 21.2440i 1.43119 + 0.826296i 0.997211 0.0746297i \(-0.0237775\pi\)
0.433974 + 0.900925i \(0.357111\pi\)
\(662\) −2.29740 + 3.97922i −0.0892911 + 0.154657i
\(663\) 0 0
\(664\) 11.9777i 0.464824i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.95885 + 1.13094i −0.0758471 + 0.0437903i
\(668\) −12.0336 6.94758i −0.465593 0.268810i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.4312 0.672925
\(672\) 0 0
\(673\) 50.6101i 1.95088i 0.220270 + 0.975439i \(0.429306\pi\)
−0.220270 + 0.975439i \(0.570694\pi\)
\(674\) −5.24011 + 3.02538i −0.201841 + 0.116533i
\(675\) 0 0
\(676\) 6.20299 10.7439i 0.238577 0.413227i
\(677\) 29.9259 17.2777i 1.15015 0.664037i 0.201223 0.979545i \(-0.435508\pi\)
0.948923 + 0.315508i \(0.102175\pi\)
\(678\) 0 0
\(679\) 5.53510 + 12.9191i 0.212418 + 0.495788i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.05085 + 1.82013i −0.0402392 + 0.0696964i
\(683\) −8.57731 + 14.8563i −0.328202 + 0.568462i −0.982155 0.188073i \(-0.939776\pi\)
0.653953 + 0.756535i \(0.273109\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 3.08138 + 18.2621i 0.117648 + 0.697251i
\(687\) 0 0
\(688\) −8.02773 + 4.63481i −0.306055 + 0.176701i
\(689\) 3.58017 6.20104i 0.136394 0.236241i
\(690\) 0 0
\(691\) −30.8635 + 17.8190i −1.17410 + 0.677869i −0.954643 0.297753i \(-0.903763\pi\)
−0.219460 + 0.975622i \(0.570429\pi\)
\(692\) 2.36740i 0.0899951i
\(693\) 0 0
\(694\) 3.18204 0.120788
\(695\) 0 0
\(696\) 0 0
\(697\) 14.8904 + 8.59697i 0.564014 + 0.325633i
\(698\) −25.1643 + 14.5286i −0.952484 + 0.549917i
\(699\) 0 0
\(700\) 0 0
\(701\) 23.0808i 0.871751i 0.900007 + 0.435876i \(0.143561\pi\)
−0.900007 + 0.435876i \(0.856439\pi\)
\(702\) 0 0
\(703\) 1.62020 2.80627i 0.0611071 0.105841i
\(704\) −1.38605 0.800236i −0.0522387 0.0301600i
\(705\) 0 0
\(706\) 7.66655i 0.288534i
\(707\) 24.3092 + 2.90195i 0.914243 + 0.109139i
\(708\) 0 0
\(709\) 4.08362 + 7.07303i 0.153363 + 0.265633i 0.932462 0.361268i \(-0.117656\pi\)
−0.779098 + 0.626902i \(0.784323\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.40369 + 7.62742i 0.165035 + 0.285850i
\(713\) 4.23854i 0.158735i
\(714\) 0 0
\(715\) 0 0
\(716\) 15.4837 8.93953i 0.578654 0.334086i
\(717\) 0 0
\(718\) 19.6694 + 11.3561i 0.734054 + 0.423806i
\(719\) 0.377499 + 0.653847i 0.0140783 + 0.0243844i 0.872979 0.487758i \(-0.162185\pi\)
−0.858900 + 0.512143i \(0.828852\pi\)
\(720\) 0 0
\(721\) 25.0862 33.5242i 0.934260 1.24851i
\(722\) 6.44839 0.239984
\(723\) 0 0
\(724\) −14.4343 8.33363i −0.536446 0.309717i
\(725\) 0 0
\(726\) 0 0
\(727\) −4.27807 −0.158665 −0.0793325 0.996848i \(-0.525279\pi\)
−0.0793325 + 0.996848i \(0.525279\pi\)
\(728\) 0.803059 + 1.87436i 0.0297634 + 0.0694684i
\(729\) 0 0
\(730\) 0 0
\(731\) −16.3245 + 28.2749i −0.603783 + 1.04578i
\(732\) 0 0
\(733\) 16.7810 + 29.0656i 0.619822 + 1.07356i 0.989518 + 0.144410i \(0.0461286\pi\)
−0.369696 + 0.929153i \(0.620538\pi\)
\(734\) −18.7487 −0.692026
\(735\) 0 0
\(736\) 3.22770 0.118975
\(737\) −5.45470 9.44781i −0.200926 0.348015i
\(738\) 0 0
\(739\) 17.3726 30.0902i 0.639060 1.10688i −0.346579 0.938021i \(-0.612657\pi\)
0.985639 0.168864i \(-0.0540099\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −9.68015 22.5937i −0.355369 0.829441i
\(743\) −14.3040 −0.524762 −0.262381 0.964964i \(-0.584508\pi\)
−0.262381 + 0.964964i \(0.584508\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.46050 + 1.42057i 0.0900854 + 0.0520109i
\(747\) 0 0
\(748\) −5.63710 −0.206113
\(749\) 19.6791 26.2984i 0.719060 0.960923i
\(750\) 0 0
\(751\) −21.3172 36.9224i −0.777874 1.34732i −0.933165 0.359449i \(-0.882965\pi\)
0.155290 0.987869i \(-0.450369\pi\)
\(752\) 2.31462 + 1.33635i 0.0844056 + 0.0487316i
\(753\) 0 0
\(754\) −0.467744 + 0.270052i −0.0170342 + 0.00983473i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.92253i 0.106221i −0.998589 0.0531107i \(-0.983086\pi\)
0.998589 0.0531107i \(-0.0169136\pi\)
\(758\) −13.6375 23.6208i −0.495336 0.857946i
\(759\) 0 0
\(760\) 0 0
\(761\) −15.2447 26.4046i −0.552621 0.957167i −0.998084 0.0618669i \(-0.980295\pi\)
0.445464 0.895300i \(-0.353039\pi\)
\(762\) 0 0
\(763\) −28.9900 3.46072i −1.04951 0.125287i
\(764\) 24.7520i 0.895496i
\(765\) 0 0
\(766\) 26.1843 + 15.1175i 0.946077 + 0.546218i
\(767\) 1.20386 2.08514i 0.0434687 0.0752900i
\(768\) 0 0
\(769\) 42.7989i 1.54337i 0.636005 + 0.771685i \(0.280586\pi\)
−0.636005 + 0.771685i \(0.719414\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.8917 6.28835i 0.392002 0.226323i
\(773\) 34.9867 + 20.1996i 1.25838 + 0.726529i 0.972760 0.231813i \(-0.0744657\pi\)
0.285624 + 0.958342i \(0.407799\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 5.31224 0.190698
\(777\) 0 0
\(778\) 4.96045i 0.177841i
\(779\) 14.9778 8.64744i 0.536636 0.309827i
\(780\) 0 0
\(781\) −5.18497 + 8.98062i −0.185533 + 0.321352i
\(782\) 9.84535 5.68421i 0.352069 0.203267i
\(783\) 0 0
\(784\) 6.80329 + 1.64779i 0.242975 + 0.0588495i
\(785\) 0 0
\(786\) 0 0
\(787\) 15.8780 27.5015i 0.565990 0.980323i −0.430967 0.902368i \(-0.641827\pi\)
0.996957 0.0779556i \(-0.0248392\pi\)
\(788\) 9.86800 17.0919i