Properties

Label 3150.2.bp.h.899.6
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 \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 899.6
Character \(\chi\) = 3150.899
Dual form 3150.2.bp.h.1349.6

$q$-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 \(-0.534086\pi\)
−0.106880 + 0.994272i \(0.534086\pi\)
\(14\) 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 0.821996 0.569493i \(-0.192860\pi\)
−0.0821974 + 0.996616i \(0.526194\pi\)
\(18\) 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 0.983774 0.179413i \(-0.0574198\pi\)
−0.647263 + 0.762267i \(0.724086\pi\)
\(24\) 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 −0.433475 0.901166i \(-0.642713\pi\)
0.563695 + 0.825983i \(0.309379\pi\)
\(38\) −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 \(0.249863\pi\)
−0.707411 + 0.706803i \(0.750137\pi\)
\(44\) 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 −0.321598 0.946876i \(-0.604220\pi\)
0.659220 + 0.751950i \(0.270887\pi\)
\(48\) 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 \(0.386932\pi\)
−0.985856 + 0.167592i \(0.946401\pi\)
\(54\) 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 0.0940048 0.995572i \(-0.470033\pi\)
−0.815188 + 0.579196i \(0.803366\pi\)
\(68\) −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 \(0.390182\pi\)
−0.984094 + 0.177647i \(0.943152\pi\)
\(74\) 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 \(0.228327\pi\)
−0.753576 + 0.657361i \(0.771673\pi\)
\(84\) 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 \(-0.586921\pi\)
−0.269688 + 0.962948i \(0.586921\pi\)
\(98\) −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 \(0.117952\pi\)
−0.152444 + 0.988312i \(0.548714\pi\)
\(104\) 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 \(0.0382009\pi\)
−0.392720 + 0.919658i \(0.628466\pi\)
\(108\) 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 \(-0.749933\pi\)
−0.706957 + 0.707256i \(0.749933\pi\)
\(114\) 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 \(0.0377262\pi\)
−0.992985 + 0.118243i \(0.962274\pi\)
\(128\) 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 −0.863233 0.504806i \(-0.831564\pi\)
0.868792 + 0.495178i \(0.164897\pi\)
\(138\) 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 \(0.360186\pi\)
−0.996444 + 0.0842589i \(0.973148\pi\)
\(158\) −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 −0.235159 0.971957i \(-0.575561\pi\)
0.724160 + 0.689632i \(0.242228\pi\)
\(164\) 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 \(-0.819323\pi\)
0.843187 0.537620i \(-0.180677\pi\)
\(168\) 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 −0.420033 0.907509i \(-0.637982\pi\)
0.575909 + 0.817514i \(0.304648\pi\)
\(174\) 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 0.837848 0.545904i \(-0.183814\pi\)
−0.0538428 + 0.998549i \(0.517147\pi\)
\(194\) −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 \(-0.251814\pi\)
0.703066 + 0.711125i \(0.251814\pi\)
\(198\) 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 \(-0.521430\pi\)
−0.0672720 + 0.997735i \(0.521430\pi\)
\(224\) −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 0.383530 0.923528i \(-0.374708\pi\)
−0.608034 + 0.793911i \(0.708042\pi\)
\(228\) 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 0.983917 0.178628i \(-0.0571660\pi\)
−0.646655 + 0.762783i \(0.723833\pi\)
\(234\) 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 −0.295502 0.955342i \(-0.595487\pi\)
0.679600 + 0.733583i \(0.262153\pi\)
\(258\) 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 \(-0.490712\pi\)
0.851069 0.525054i \(-0.175955\pi\)
\(264\) 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 0.205328 0.978693i \(-0.434174\pi\)
−0.744909 + 0.667166i \(0.767507\pi\)
\(278\) 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 \(0.469130\pi\)
−0.910371 + 0.413794i \(0.864203\pi\)
\(284\) 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 \(0.164402\pi\)
−0.869560 + 0.493827i \(0.835598\pi\)
\(294\) 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 \(-0.369043\pi\)
0.399906 + 0.916556i \(0.369043\pi\)
\(308\) −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 0.799562 0.600584i \(-0.205065\pi\)
−0.919902 + 0.392149i \(0.871732\pi\)
\(314\) −14.3140 −0.807788
\(315\) 0 0
\(316\) −2.90172 −0.163234
\(317\) 0.0987910 + 0.171111i 0.00554866 + 0.00961055i 0.868786 0.495187i \(-0.164900\pi\)
−0.863238 + 0.504798i \(0.831567\pi\)
\(318\) 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 \(0.0526988\pi\)
−0.986327 + 0.164803i \(0.947301\pi\)
\(338\) −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 −0.820156 0.572140i \(-0.806113\pi\)
0.905566 + 0.424205i \(0.139447\pi\)
\(348\) 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 0.312792 0.949822i \(-0.398736\pi\)
−0.666173 + 0.745797i \(0.732069\pi\)
\(354\) 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 −0.999925 0.0122703i \(-0.996094\pi\)
0.510589 + 0.859825i \(0.329427\pi\)
\(368\) 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 −0.434946 0.900457i \(-0.643232\pi\)
0.562346 + 0.826902i \(0.309899\pi\)
\(374\) 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 0.351451 0.936206i \(-0.385688\pi\)
0.986504 + 0.163737i \(0.0523549\pi\)
\(384\) 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 0.622530 0.782596i \(-0.286105\pi\)
−0.989013 + 0.147828i \(0.952772\pi\)
\(398\) 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 \(-0.762141\pi\)
−0.733557 + 0.679628i \(0.762141\pi\)
\(434\) 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 \(0.0200497\pi\)
−0.444495 + 0.895781i \(0.646617\pi\)
\(444\) 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 \(-0.294293\pi\)
0.992488 0.122341i \(-0.0390403\pi\)
\(458\) −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 \(0.0166165\pi\)
−0.998638 + 0.0521787i \(0.983383\pi\)
\(464\) −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 0.311228 0.950335i \(-0.399260\pi\)
0.978628 + 0.205636i \(0.0659264\pi\)
\(468\) 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 0.382632 0.923901i \(-0.375018\pi\)
−0.608805 + 0.793320i \(0.708351\pi\)
\(488\) 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 \(0.00941571\pi\)
−0.999563 + 0.0295760i \(0.990584\pi\)
\(504\) 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 \(-0.831232\pi\)
−0.00660128 0.999978i \(-0.502101\pi\)
\(524\) 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 \(0.264657\pi\)
−0.673810 + 0.738905i \(0.735343\pi\)
\(548\) 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 \(0.408219\pi\)
−0.972454 + 0.233096i \(0.925114\pi\)
\(558\) 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 0.739035 0.673668i \(-0.235282\pi\)
−0.213896 + 0.976856i \(0.568615\pi\)
\(564\) 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 −0.999887 0.0150431i \(-0.995211\pi\)
0.512971 + 0.858406i \(0.328545\pi\)
\(578\) 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 \(-0.836740\pi\)
0.871327 0.490704i \(-0.163260\pi\)
\(588\) 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 0.391200 0.920306i \(-0.372060\pi\)
0.992608 + 0.121364i \(0.0387268\pi\)
\(594\) 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 0.860175 0.509999i \(-0.170354\pi\)
−0.871759 + 0.489934i \(0.837021\pi\)
\(608\) 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 −0.235833 0.971794i \(-0.575782\pi\)
−0.959514 + 0.281659i \(0.909115\pi\)
\(614\) 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 \(-0.633088\pi\)
−0.406033 + 0.913858i \(0.633088\pi\)
\(618\) 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 \(-0.667609\pi\)
−0.502560 + 0.864542i \(0.667609\pi\)
\(644\) 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 \(0.0593059\pi\)
0.651768 + 0.758418i \(0.274027\pi\)
\(648\) 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 \(0.190421\pi\)
0.0745575 + 0.997217i \(0.476246\pi\)
\(654\) 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 \(-0.570694\pi\)
0.220270 0.975439i \(-0.429306\pi\)
\(674\) −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 −0.948923 0.315508i \(-0.897825\pi\)
−0.201223 + 0.979545i \(0.564492\pi\)
\(678\) 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 −0.653953 0.756535i \(-0.726891\pi\)
0.982155 + 0.188073i \(0.0602241\pi\)
\(684\) 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 \(-0.474721\pi\)
0.0793325 + 0.996848i \(0.474721\pi\)
\(728\) −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 \(-0.953871\pi\)
0.369696 0.929153i \(-0.379462\pi\)
\(734\) −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 \(-0.415492\pi\)
0.262381 + 0.964964i \(0.415492\pi\)
\(744\) 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 \(0.0169136\pi\)
−0.998589 + 0.0531107i \(0.983086\pi\)
\(758\) 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 −0.285624 0.958342i \(-0.592201\pi\)
−0.972760 + 0.231813i \(0.925534\pi\)
\(774\) 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 \(0.358173\pi\)