Properties

Label 3150.2.bp.g.1349.2
Level 3150
Weight 2
Character 3150.1349
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 1349.2
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.g.899.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.61577 - 0.397202i) q^{7} +1.00000 q^{8} +(-0.429853 + 0.248176i) q^{11} +2.74440 q^{13} +(1.65187 - 2.06672i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.16952 - 1.82992i) q^{17} +(-3.12125 - 1.80205i) q^{19} -0.496352i q^{22} +(-3.21210 + 5.56351i) q^{23} +(-1.37220 + 2.37672i) q^{26} +(0.963896 + 2.46392i) q^{28} -8.87959i q^{29} +(-6.90736 + 3.98797i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.65984i q^{34} +(1.98397 + 1.14545i) q^{37} +(3.12125 - 1.80205i) q^{38} +2.22816 q^{41} +2.22575i q^{43} +(0.429853 + 0.248176i) q^{44} +(-3.21210 - 5.56351i) q^{46} +(5.66749 + 3.27213i) q^{47} +(6.68446 + 2.07798i) q^{49} +(-1.37220 - 2.37672i) q^{52} +(3.88322 + 6.72594i) q^{53} +(-2.61577 - 0.397202i) q^{56} +(7.68995 + 4.43979i) q^{58} +(-3.05194 - 5.28611i) q^{59} +(3.24271 + 1.87218i) q^{61} -7.97593i q^{62} +1.00000 q^{64} +(-7.08216 + 4.08889i) q^{67} +(-3.16952 - 1.82992i) q^{68} -10.3761i q^{71} +(6.53361 + 11.3165i) q^{73} +(-1.98397 + 1.14545i) q^{74} +3.60411i q^{76} +(1.22297 - 0.478431i) q^{77} +(-4.44344 + 7.69627i) q^{79} +(-1.11408 + 1.92964i) q^{82} +4.79091i q^{83} +(-1.92756 - 1.11288i) q^{86} +(-0.429853 + 0.248176i) q^{88} +(0.743586 - 1.28793i) q^{89} +(-7.17871 - 1.09008i) q^{91} +6.42419 q^{92} +(-5.66749 + 3.27213i) q^{94} -9.05174 q^{97} +(-5.14181 + 4.74992i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 12q^{2} - 12q^{4} + 24q^{8} - 12q^{16} + 24q^{17} - 12q^{19} - 8q^{23} - 12q^{32} + 12q^{38} - 8q^{46} - 24q^{47} + 52q^{49} - 32q^{53} - 12q^{61} + 24q^{64} - 24q^{68} - 16q^{77} - 4q^{79} + 68q^{91} + 16q^{92} + 24q^{94} - 20q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(7\) −2.61577 0.397202i −0.988667 0.150128i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −0.429853 + 0.248176i −0.129606 + 0.0748278i −0.563401 0.826184i \(-0.690507\pi\)
0.433795 + 0.901011i \(0.357174\pi\)
\(12\) 0 0
\(13\) 2.74440 0.761160 0.380580 0.924748i \(-0.375724\pi\)
0.380580 + 0.924748i \(0.375724\pi\)
\(14\) 1.65187 2.06672i 0.441481 0.552354i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.16952 1.82992i 0.768721 0.443821i −0.0636974 0.997969i \(-0.520289\pi\)
0.832418 + 0.554148i \(0.186956\pi\)
\(18\) 0 0
\(19\) −3.12125 1.80205i −0.716064 0.413420i 0.0972384 0.995261i \(-0.468999\pi\)
−0.813302 + 0.581841i \(0.802332\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.496352i 0.105823i
\(23\) −3.21210 + 5.56351i −0.669768 + 1.16007i 0.308200 + 0.951321i \(0.400273\pi\)
−0.977969 + 0.208751i \(0.933060\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.37220 + 2.37672i −0.269111 + 0.466114i
\(27\) 0 0
\(28\) 0.963896 + 2.46392i 0.182159 + 0.465637i
\(29\) 8.87959i 1.64890i −0.565937 0.824449i \(-0.691485\pi\)
0.565937 0.824449i \(-0.308515\pi\)
\(30\) 0 0
\(31\) −6.90736 + 3.98797i −1.24060 + 0.716260i −0.969216 0.246211i \(-0.920814\pi\)
−0.271383 + 0.962472i \(0.587481\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.65984i 0.627658i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.98397 + 1.14545i 0.326163 + 0.188311i 0.654136 0.756377i \(-0.273032\pi\)
−0.327973 + 0.944687i \(0.606366\pi\)
\(38\) 3.12125 1.80205i 0.506334 0.292332i
\(39\) 0 0
\(40\) 0 0
\(41\) 2.22816 0.347980 0.173990 0.984747i \(-0.444334\pi\)
0.173990 + 0.984747i \(0.444334\pi\)
\(42\) 0 0
\(43\) 2.22575i 0.339424i 0.985494 + 0.169712i \(0.0542838\pi\)
−0.985494 + 0.169712i \(0.945716\pi\)
\(44\) 0.429853 + 0.248176i 0.0648028 + 0.0374139i
\(45\) 0 0
\(46\) −3.21210 5.56351i −0.473598 0.820295i
\(47\) 5.66749 + 3.27213i 0.826688 + 0.477289i 0.852717 0.522373i \(-0.174953\pi\)
−0.0260292 + 0.999661i \(0.508286\pi\)
\(48\) 0 0
\(49\) 6.68446 + 2.07798i 0.954923 + 0.296854i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.37220 2.37672i −0.190290 0.329592i
\(53\) 3.88322 + 6.72594i 0.533402 + 0.923879i 0.999239 + 0.0390085i \(0.0124199\pi\)
−0.465837 + 0.884870i \(0.654247\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.61577 0.397202i −0.349546 0.0530784i
\(57\) 0 0
\(58\) 7.68995 + 4.43979i 1.00974 + 0.582973i
\(59\) −3.05194 5.28611i −0.397328 0.688193i 0.596067 0.802935i \(-0.296729\pi\)
−0.993395 + 0.114742i \(0.963396\pi\)
\(60\) 0 0
\(61\) 3.24271 + 1.87218i 0.415187 + 0.239708i 0.693016 0.720922i \(-0.256282\pi\)
−0.277829 + 0.960630i \(0.589615\pi\)
\(62\) 7.97593i 1.01294i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.08216 + 4.08889i −0.865224 + 0.499537i −0.865758 0.500463i \(-0.833163\pi\)
0.000534152 1.00000i \(0.499830\pi\)
\(68\) −3.16952 1.82992i −0.384360 0.221911i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.3761i 1.23141i −0.787975 0.615707i \(-0.788871\pi\)
0.787975 0.615707i \(-0.211129\pi\)
\(72\) 0 0
\(73\) 6.53361 + 11.3165i 0.764701 + 1.32450i 0.940405 + 0.340058i \(0.110447\pi\)
−0.175704 + 0.984443i \(0.556220\pi\)
\(74\) −1.98397 + 1.14545i −0.230632 + 0.133156i
\(75\) 0 0
\(76\) 3.60411i 0.413420i
\(77\) 1.22297 0.478431i 0.139370 0.0545223i
\(78\) 0 0
\(79\) −4.44344 + 7.69627i −0.499926 + 0.865898i −1.00000 8.52501e-5i \(-0.999973\pi\)
0.500074 + 0.865983i \(0.333306\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.11408 + 1.92964i −0.123030 + 0.213093i
\(83\) 4.79091i 0.525871i 0.964813 + 0.262935i \(0.0846906\pi\)
−0.964813 + 0.262935i \(0.915309\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.92756 1.11288i −0.207854 0.120005i
\(87\) 0 0
\(88\) −0.429853 + 0.248176i −0.0458225 + 0.0264556i
\(89\) 0.743586 1.28793i 0.0788199 0.136520i −0.823921 0.566704i \(-0.808218\pi\)
0.902741 + 0.430184i \(0.141551\pi\)
\(90\) 0 0
\(91\) −7.17871 1.09008i −0.752534 0.114272i
\(92\) 6.42419 0.669768
\(93\) 0 0
\(94\) −5.66749 + 3.27213i −0.584557 + 0.337494i
\(95\) 0 0
\(96\) 0 0
\(97\) −9.05174 −0.919064 −0.459532 0.888161i \(-0.651983\pi\)
−0.459532 + 0.888161i \(0.651983\pi\)
\(98\) −5.14181 + 4.74992i −0.519401 + 0.479815i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.50180 2.60119i −0.149434 0.258828i 0.781584 0.623800i \(-0.214412\pi\)
−0.931019 + 0.364972i \(0.881079\pi\)
\(102\) 0 0
\(103\) −7.18752 + 12.4491i −0.708207 + 1.22665i 0.257314 + 0.966328i \(0.417162\pi\)
−0.965522 + 0.260323i \(0.916171\pi\)
\(104\) 2.74440 0.269111
\(105\) 0 0
\(106\) −7.76645 −0.754344
\(107\) 1.06314 1.84141i 0.102778 0.178016i −0.810050 0.586360i \(-0.800560\pi\)
0.912828 + 0.408344i \(0.133894\pi\)
\(108\) 0 0
\(109\) 3.95181 + 6.84474i 0.378515 + 0.655607i 0.990846 0.134994i \(-0.0431015\pi\)
−0.612331 + 0.790601i \(0.709768\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.65187 2.06672i 0.156087 0.195287i
\(113\) −12.2968 −1.15678 −0.578391 0.815760i \(-0.696319\pi\)
−0.578391 + 0.815760i \(0.696319\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −7.68995 + 4.43979i −0.713994 + 0.412224i
\(117\) 0 0
\(118\) 6.10388 0.561907
\(119\) −9.01756 + 3.52771i −0.826638 + 0.323384i
\(120\) 0 0
\(121\) −5.37682 + 9.31292i −0.488802 + 0.846629i
\(122\) −3.24271 + 1.87218i −0.293581 + 0.169499i
\(123\) 0 0
\(124\) 6.90736 + 3.98797i 0.620299 + 0.358130i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.753445i 0.0668574i −0.999441 0.0334287i \(-0.989357\pi\)
0.999441 0.0334287i \(-0.0106427\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −6.35624 + 11.0093i −0.555347 + 0.961890i 0.442529 + 0.896754i \(0.354081\pi\)
−0.997876 + 0.0651355i \(0.979252\pi\)
\(132\) 0 0
\(133\) 7.44868 + 5.95352i 0.645882 + 0.516236i
\(134\) 8.17778i 0.706452i
\(135\) 0 0
\(136\) 3.16952 1.82992i 0.271784 0.156914i
\(137\) −2.15740 3.73673i −0.184319 0.319250i 0.759028 0.651058i \(-0.225675\pi\)
−0.943347 + 0.331808i \(0.892341\pi\)
\(138\) 0 0
\(139\) 0.0681276i 0.00577851i 0.999996 + 0.00288926i \(0.000919680\pi\)
−0.999996 + 0.00288926i \(0.999080\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.98595 + 5.18804i 0.754084 + 0.435371i
\(143\) −1.17969 + 0.681094i −0.0986507 + 0.0569560i
\(144\) 0 0
\(145\) 0 0
\(146\) −13.0672 −1.08145
\(147\) 0 0
\(148\) 2.29090i 0.188311i
\(149\) −14.4611 8.34911i −1.18470 0.683986i −0.227602 0.973754i \(-0.573088\pi\)
−0.957097 + 0.289768i \(0.906422\pi\)
\(150\) 0 0
\(151\) 6.51016 + 11.2759i 0.529789 + 0.917622i 0.999396 + 0.0347463i \(0.0110623\pi\)
−0.469607 + 0.882876i \(0.655604\pi\)
\(152\) −3.12125 1.80205i −0.253167 0.146166i
\(153\) 0 0
\(154\) −0.197152 + 1.29834i −0.0158870 + 0.104623i
\(155\) 0 0
\(156\) 0 0
\(157\) −7.40408 12.8242i −0.590910 1.02349i −0.994110 0.108374i \(-0.965436\pi\)
0.403200 0.915112i \(-0.367898\pi\)
\(158\) −4.44344 7.69627i −0.353501 0.612282i
\(159\) 0 0
\(160\) 0 0
\(161\) 10.6119 13.2770i 0.836337 1.04637i
\(162\) 0 0
\(163\) 13.3189 + 7.68966i 1.04322 + 0.602301i 0.920742 0.390171i \(-0.127584\pi\)
0.122473 + 0.992472i \(0.460918\pi\)
\(164\) −1.11408 1.92964i −0.0869950 0.150680i
\(165\) 0 0
\(166\) −4.14905 2.39546i −0.322029 0.185923i
\(167\) 24.5161i 1.89712i 0.316603 + 0.948558i \(0.397458\pi\)
−0.316603 + 0.948558i \(0.602542\pi\)
\(168\) 0 0
\(169\) −5.46825 −0.420635
\(170\) 0 0
\(171\) 0 0
\(172\) 1.92756 1.11288i 0.146975 0.0848561i
\(173\) 10.8463 + 6.26213i 0.824631 + 0.476101i 0.852011 0.523524i \(-0.175383\pi\)
−0.0273795 + 0.999625i \(0.508716\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.496352i 0.0374139i
\(177\) 0 0
\(178\) 0.743586 + 1.28793i 0.0557341 + 0.0965343i
\(179\) 1.58961 0.917762i 0.118813 0.0685968i −0.439416 0.898284i \(-0.644814\pi\)
0.558229 + 0.829687i \(0.311481\pi\)
\(180\) 0 0
\(181\) 23.6564i 1.75837i 0.476481 + 0.879185i \(0.341912\pi\)
−0.476481 + 0.879185i \(0.658088\pi\)
\(182\) 4.53340 5.67191i 0.336038 0.420430i
\(183\) 0 0
\(184\) −3.21210 + 5.56351i −0.236799 + 0.410148i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.908284 + 1.57319i −0.0664203 + 0.115043i
\(188\) 6.54425i 0.477289i
\(189\) 0 0
\(190\) 0 0
\(191\) 7.02253 + 4.05446i 0.508133 + 0.293371i 0.732066 0.681234i \(-0.238556\pi\)
−0.223933 + 0.974605i \(0.571890\pi\)
\(192\) 0 0
\(193\) −10.4356 + 6.02502i −0.751174 + 0.433691i −0.826118 0.563497i \(-0.809456\pi\)
0.0749438 + 0.997188i \(0.476122\pi\)
\(194\) 4.52587 7.83903i 0.324938 0.562810i
\(195\) 0 0
\(196\) −1.54265 6.82790i −0.110189 0.487707i
\(197\) 12.7463 0.908137 0.454068 0.890967i \(-0.349972\pi\)
0.454068 + 0.890967i \(0.349972\pi\)
\(198\) 0 0
\(199\) −16.4954 + 9.52361i −1.16933 + 0.675111i −0.953521 0.301325i \(-0.902571\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.00359 0.211332
\(203\) −3.52699 + 23.2269i −0.247546 + 1.63021i
\(204\) 0 0
\(205\) 0 0
\(206\) −7.18752 12.4491i −0.500778 0.867373i
\(207\) 0 0
\(208\) −1.37220 + 2.37672i −0.0951450 + 0.164796i
\(209\) 1.78891 0.123741
\(210\) 0 0
\(211\) −8.92057 −0.614117 −0.307059 0.951691i \(-0.599345\pi\)
−0.307059 + 0.951691i \(0.599345\pi\)
\(212\) 3.88322 6.72594i 0.266701 0.461939i
\(213\) 0 0
\(214\) 1.06314 + 1.84141i 0.0726748 + 0.125876i
\(215\) 0 0
\(216\) 0 0
\(217\) 19.6521 7.68797i 1.33407 0.521893i
\(218\) −7.90363 −0.535301
\(219\) 0 0
\(220\) 0 0
\(221\) 8.69843 5.02204i 0.585120 0.337819i
\(222\) 0 0
\(223\) 23.5443 1.57664 0.788320 0.615265i \(-0.210951\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(224\) 0.963896 + 2.46392i 0.0644030 + 0.164628i
\(225\) 0 0
\(226\) 6.14838 10.6493i 0.408984 0.708382i
\(227\) 8.07522 4.66223i 0.535971 0.309443i −0.207473 0.978241i \(-0.566524\pi\)
0.743445 + 0.668797i \(0.233191\pi\)
\(228\) 0 0
\(229\) −20.1545 11.6362i −1.33185 0.768944i −0.346266 0.938136i \(-0.612551\pi\)
−0.985583 + 0.169193i \(0.945884\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.87959i 0.582973i
\(233\) −6.31017 + 10.9295i −0.413393 + 0.716018i −0.995258 0.0972676i \(-0.968990\pi\)
0.581865 + 0.813285i \(0.302323\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.05194 + 5.28611i −0.198664 + 0.344097i
\(237\) 0 0
\(238\) 1.45370 9.57329i 0.0942292 0.620544i
\(239\) 16.1198i 1.04270i 0.853342 + 0.521351i \(0.174572\pi\)
−0.853342 + 0.521351i \(0.825428\pi\)
\(240\) 0 0
\(241\) −18.3222 + 10.5783i −1.18024 + 0.681411i −0.956070 0.293140i \(-0.905300\pi\)
−0.224168 + 0.974550i \(0.571966\pi\)
\(242\) −5.37682 9.31292i −0.345635 0.598657i
\(243\) 0 0
\(244\) 3.74436i 0.239708i
\(245\) 0 0
\(246\) 0 0
\(247\) −8.56597 4.94556i −0.545039 0.314679i
\(248\) −6.90736 + 3.98797i −0.438618 + 0.253236i
\(249\) 0 0
\(250\) 0 0
\(251\) 6.06317 0.382704 0.191352 0.981522i \(-0.438713\pi\)
0.191352 + 0.981522i \(0.438713\pi\)
\(252\) 0 0
\(253\) 3.18866i 0.200469i
\(254\) 0.652503 + 0.376723i 0.0409416 + 0.0236377i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.51357 5.49266i −0.593440 0.342623i 0.173016 0.984919i \(-0.444649\pi\)
−0.766457 + 0.642296i \(0.777982\pi\)
\(258\) 0 0
\(259\) −4.73464 3.78426i −0.294196 0.235143i
\(260\) 0 0
\(261\) 0 0
\(262\) −6.35624 11.0093i −0.392690 0.680159i
\(263\) −0.669365 1.15937i −0.0412748 0.0714901i 0.844650 0.535319i \(-0.179809\pi\)
−0.885925 + 0.463829i \(0.846475\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.88024 + 3.47399i −0.544482 + 0.213004i
\(267\) 0 0
\(268\) 7.08216 + 4.08889i 0.432612 + 0.249769i
\(269\) −0.311161 0.538946i −0.0189718 0.0328601i 0.856384 0.516340i \(-0.172706\pi\)
−0.875355 + 0.483480i \(0.839373\pi\)
\(270\) 0 0
\(271\) 18.4634 + 10.6598i 1.12157 + 0.647539i 0.941801 0.336170i \(-0.109132\pi\)
0.179769 + 0.983709i \(0.442465\pi\)
\(272\) 3.65984i 0.221911i
\(273\) 0 0
\(274\) 4.31480 0.260667
\(275\) 0 0
\(276\) 0 0
\(277\) −1.02805 + 0.593544i −0.0617694 + 0.0356626i −0.530567 0.847643i \(-0.678021\pi\)
0.468797 + 0.883306i \(0.344688\pi\)
\(278\) −0.0590003 0.0340638i −0.00353860 0.00204301i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.97593i 0.117874i −0.998262 0.0589370i \(-0.981229\pi\)
0.998262 0.0589370i \(-0.0187711\pi\)
\(282\) 0 0
\(283\) −13.5654 23.4960i −0.806382 1.39669i −0.915354 0.402650i \(-0.868089\pi\)
0.108972 0.994045i \(-0.465244\pi\)
\(284\) −8.98595 + 5.18804i −0.533218 + 0.307853i
\(285\) 0 0
\(286\) 1.36219i 0.0805479i
\(287\) −5.82835 0.885030i −0.344036 0.0522417i
\(288\) 0 0
\(289\) −1.80278 + 3.12250i −0.106046 + 0.183677i
\(290\) 0 0
\(291\) 0 0
\(292\) 6.53361 11.3165i 0.382350 0.662250i
\(293\) 10.3808i 0.606456i −0.952918 0.303228i \(-0.901936\pi\)
0.952918 0.303228i \(-0.0980643\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.98397 + 1.14545i 0.115316 + 0.0665778i
\(297\) 0 0
\(298\) 14.4611 8.34911i 0.837708 0.483651i
\(299\) −8.81529 + 15.2685i −0.509801 + 0.883002i
\(300\) 0 0
\(301\) 0.884074 5.82205i 0.0509572 0.335577i
\(302\) −13.0203 −0.749235
\(303\) 0 0
\(304\) 3.12125 1.80205i 0.179016 0.103355i
\(305\) 0 0
\(306\) 0 0
\(307\) −14.1364 −0.806808 −0.403404 0.915022i \(-0.632173\pi\)
−0.403404 + 0.915022i \(0.632173\pi\)
\(308\) −1.02582 0.819908i −0.0584515 0.0467186i
\(309\) 0 0
\(310\) 0 0
\(311\) −3.32643 5.76155i −0.188625 0.326708i 0.756167 0.654378i \(-0.227070\pi\)
−0.944792 + 0.327671i \(0.893736\pi\)
\(312\) 0 0
\(313\) −6.07282 + 10.5184i −0.343256 + 0.594537i −0.985035 0.172352i \(-0.944863\pi\)
0.641779 + 0.766890i \(0.278197\pi\)
\(314\) 14.8082 0.835673
\(315\) 0 0
\(316\) 8.88688 0.499926
\(317\) −15.3605 + 26.6051i −0.862730 + 1.49429i 0.00655283 + 0.999979i \(0.497914\pi\)
−0.869283 + 0.494314i \(0.835419\pi\)
\(318\) 0 0
\(319\) 2.20370 + 3.81692i 0.123383 + 0.213706i
\(320\) 0 0
\(321\) 0 0
\(322\) 6.19225 + 15.8287i 0.345081 + 0.882099i
\(323\) −13.1905 −0.733937
\(324\) 0 0
\(325\) 0 0
\(326\) −13.3189 + 7.68966i −0.737665 + 0.425891i
\(327\) 0 0
\(328\) 2.22816 0.123030
\(329\) −13.5251 10.8103i −0.745664 0.595989i
\(330\) 0 0
\(331\) 15.5140 26.8710i 0.852724 1.47696i −0.0260166 0.999662i \(-0.508282\pi\)
0.878741 0.477300i \(-0.158384\pi\)
\(332\) 4.14905 2.39546i 0.227709 0.131468i
\(333\) 0 0
\(334\) −21.2316 12.2581i −1.16174 0.670732i
\(335\) 0 0
\(336\) 0 0
\(337\) 6.91470i 0.376668i 0.982105 + 0.188334i \(0.0603087\pi\)
−0.982105 + 0.188334i \(0.939691\pi\)
\(338\) 2.73413 4.73565i 0.148717 0.257585i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.97943 3.42848i 0.107192 0.185663i
\(342\) 0 0
\(343\) −16.6596 8.09058i −0.899534 0.436850i
\(344\) 2.22575i 0.120005i
\(345\) 0 0
\(346\) −10.8463 + 6.26213i −0.583103 + 0.336654i
\(347\) 3.74704 + 6.49006i 0.201152 + 0.348405i 0.948900 0.315578i \(-0.102198\pi\)
−0.747748 + 0.663982i \(0.768865\pi\)
\(348\) 0 0
\(349\) 12.4552i 0.666714i −0.942801 0.333357i \(-0.891819\pi\)
0.942801 0.333357i \(-0.108181\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.429853 + 0.248176i 0.0229113 + 0.0132278i
\(353\) 16.4027 9.47011i 0.873028 0.504043i 0.00467471 0.999989i \(-0.498512\pi\)
0.868353 + 0.495946i \(0.165179\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.48717 −0.0788199
\(357\) 0 0
\(358\) 1.83552i 0.0970105i
\(359\) 23.0590 + 13.3131i 1.21701 + 0.702639i 0.964277 0.264898i \(-0.0853381\pi\)
0.252730 + 0.967537i \(0.418671\pi\)
\(360\) 0 0
\(361\) −3.00520 5.20516i −0.158168 0.273956i
\(362\) −20.4871 11.8282i −1.07678 0.621677i
\(363\) 0 0
\(364\) 2.64532 + 6.76199i 0.138652 + 0.354425i
\(365\) 0 0
\(366\) 0 0
\(367\) −5.45606 9.45017i −0.284804 0.493295i 0.687758 0.725940i \(-0.258595\pi\)
−0.972562 + 0.232646i \(0.925262\pi\)
\(368\) −3.21210 5.56351i −0.167442 0.290018i
\(369\) 0 0
\(370\) 0 0
\(371\) −7.48604 19.1359i −0.388656 0.993487i
\(372\) 0 0
\(373\) 19.4924 + 11.2539i 1.00928 + 0.582707i 0.910980 0.412450i \(-0.135327\pi\)
0.0982976 + 0.995157i \(0.468660\pi\)
\(374\) −0.908284 1.57319i −0.0469663 0.0813480i
\(375\) 0 0
\(376\) 5.66749 + 3.27213i 0.292278 + 0.168747i
\(377\) 24.3692i 1.25508i
\(378\) 0 0
\(379\) 3.25909 0.167408 0.0837040 0.996491i \(-0.473325\pi\)
0.0837040 + 0.996491i \(0.473325\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −7.02253 + 4.05446i −0.359304 + 0.207444i
\(383\) −15.0013 8.66098i −0.766528 0.442555i 0.0651064 0.997878i \(-0.479261\pi\)
−0.831635 + 0.555323i \(0.812595\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.0500i 0.613331i
\(387\) 0 0
\(388\) 4.52587 + 7.83903i 0.229766 + 0.397967i
\(389\) −27.4515 + 15.8491i −1.39185 + 0.803582i −0.993520 0.113662i \(-0.963742\pi\)
−0.398326 + 0.917244i \(0.630409\pi\)
\(390\) 0 0
\(391\) 23.5115i 1.18903i
\(392\) 6.68446 + 2.07798i 0.337616 + 0.104954i
\(393\) 0 0
\(394\) −6.37315 + 11.0386i −0.321075 + 0.556118i
\(395\) 0 0
\(396\) 0 0
\(397\) −16.7561 + 29.0224i −0.840964 + 1.45659i 0.0481170 + 0.998842i \(0.484678\pi\)
−0.889081 + 0.457750i \(0.848655\pi\)
\(398\) 19.0472i 0.954751i
\(399\) 0 0
\(400\) 0 0
\(401\) 31.0404 + 17.9212i 1.55008 + 0.894940i 0.998134 + 0.0610611i \(0.0194485\pi\)
0.551947 + 0.833879i \(0.313885\pi\)
\(402\) 0 0
\(403\) −18.9566 + 10.9446i −0.944295 + 0.545189i
\(404\) −1.50180 + 2.60119i −0.0747171 + 0.129414i
\(405\) 0 0
\(406\) −18.3516 14.6679i −0.910775 0.727957i
\(407\) −1.13709 −0.0563635
\(408\) 0 0
\(409\) 21.3474 12.3249i 1.05556 0.609429i 0.131361 0.991335i \(-0.458065\pi\)
0.924201 + 0.381905i \(0.124732\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.3750 0.708207
\(413\) 5.88350 + 15.0395i 0.289508 + 0.740044i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.37220 2.37672i −0.0672777 0.116528i
\(417\) 0 0
\(418\) −0.894453 + 1.54924i −0.0437491 + 0.0757757i
\(419\) 10.6574 0.520646 0.260323 0.965522i \(-0.416171\pi\)
0.260323 + 0.965522i \(0.416171\pi\)
\(420\) 0 0
\(421\) 22.6815 1.10543 0.552714 0.833371i \(-0.313592\pi\)
0.552714 + 0.833371i \(0.313592\pi\)
\(422\) 4.46028 7.72544i 0.217123 0.376068i
\(423\) 0 0
\(424\) 3.88322 + 6.72594i 0.188586 + 0.326641i
\(425\) 0 0
\(426\) 0 0
\(427\) −7.73854 6.18520i −0.374494 0.299323i
\(428\) −2.12628 −0.102778
\(429\) 0 0
\(430\) 0 0
\(431\) 26.0439 15.0364i 1.25449 0.724279i 0.282491 0.959270i \(-0.408839\pi\)
0.971998 + 0.234991i \(0.0755061\pi\)
\(432\) 0 0
\(433\) −14.9203 −0.717025 −0.358512 0.933525i \(-0.616716\pi\)
−0.358512 + 0.933525i \(0.616716\pi\)
\(434\) −3.16806 + 20.8632i −0.152072 + 1.00146i
\(435\) 0 0
\(436\) 3.95181 6.84474i 0.189258 0.327804i
\(437\) 20.0515 11.5767i 0.959194 0.553791i
\(438\) 0 0
\(439\) −11.1126 6.41586i −0.530375 0.306212i 0.210794 0.977530i \(-0.432395\pi\)
−0.741169 + 0.671318i \(0.765728\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 10.0441i 0.477748i
\(443\) −10.2071 + 17.6792i −0.484953 + 0.839963i −0.999851 0.0172887i \(-0.994497\pi\)
0.514898 + 0.857252i \(0.327830\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.7721 + 20.3899i −0.557426 + 0.965491i
\(447\) 0 0
\(448\) −2.61577 0.397202i −0.123583 0.0187660i
\(449\) 20.8404i 0.983519i −0.870731 0.491760i \(-0.836354\pi\)
0.870731 0.491760i \(-0.163646\pi\)
\(450\) 0 0
\(451\) −0.957782 + 0.552976i −0.0451002 + 0.0260386i
\(452\) 6.14838 + 10.6493i 0.289196 + 0.500901i
\(453\) 0 0
\(454\) 9.32446i 0.437619i
\(455\) 0 0
\(456\) 0 0
\(457\) 13.8811 + 8.01424i 0.649329 + 0.374890i 0.788199 0.615420i \(-0.211014\pi\)
−0.138870 + 0.990311i \(0.544347\pi\)
\(458\) 20.1545 11.6362i 0.941760 0.543725i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.98400 0.0924039 0.0462020 0.998932i \(-0.485288\pi\)
0.0462020 + 0.998932i \(0.485288\pi\)
\(462\) 0 0
\(463\) 36.3987i 1.69159i −0.533506 0.845796i \(-0.679126\pi\)
0.533506 0.845796i \(-0.320874\pi\)
\(464\) 7.68995 + 4.43979i 0.356997 + 0.206112i
\(465\) 0 0
\(466\) −6.31017 10.9295i −0.292313 0.506301i
\(467\) −26.9113 15.5372i −1.24530 0.718977i −0.275136 0.961405i \(-0.588723\pi\)
−0.970169 + 0.242428i \(0.922056\pi\)
\(468\) 0 0
\(469\) 20.1494 7.88253i 0.930413 0.363981i
\(470\) 0 0
\(471\) 0 0
\(472\) −3.05194 5.28611i −0.140477 0.243313i
\(473\) −0.552378 0.956747i −0.0253984 0.0439913i
\(474\) 0 0
\(475\) 0 0
\(476\) 7.56386 + 6.04558i 0.346689 + 0.277099i
\(477\) 0 0
\(478\) −13.9601 8.05990i −0.638522 0.368651i
\(479\) 18.2404 + 31.5933i 0.833426 + 1.44354i 0.895305 + 0.445453i \(0.146957\pi\)
−0.0618788 + 0.998084i \(0.519709\pi\)
\(480\) 0 0
\(481\) 5.44483 + 3.14357i 0.248263 + 0.143335i
\(482\) 21.1567i 0.963660i
\(483\) 0 0
\(484\) 10.7536 0.488802
\(485\) 0 0
\(486\) 0 0
\(487\) 12.2399 7.06672i 0.554644 0.320224i −0.196349 0.980534i \(-0.562909\pi\)
0.750993 + 0.660310i \(0.229575\pi\)
\(488\) 3.24271 + 1.87218i 0.146791 + 0.0847496i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.5466i 1.46881i −0.678714 0.734403i \(-0.737462\pi\)
0.678714 0.734403i \(-0.262538\pi\)
\(492\) 0 0
\(493\) −16.2489 28.1440i −0.731815 1.26754i
\(494\) 8.56597 4.94556i 0.385401 0.222511i
\(495\) 0 0
\(496\) 7.97593i 0.358130i
\(497\) −4.12140 + 27.1414i −0.184870 + 1.21746i
\(498\) 0 0
\(499\) 5.87396 10.1740i 0.262955 0.455451i −0.704071 0.710130i \(-0.748636\pi\)
0.967026 + 0.254679i \(0.0819697\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.03158 + 5.25086i −0.135306 + 0.234357i
\(503\) 24.5250i 1.09352i −0.837291 0.546758i \(-0.815862\pi\)
0.837291 0.546758i \(-0.184138\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 2.76146 + 1.59433i 0.122762 + 0.0708766i
\(507\) 0 0
\(508\) −0.652503 + 0.376723i −0.0289501 + 0.0167144i
\(509\) −5.84634 + 10.1262i −0.259135 + 0.448834i −0.966010 0.258503i \(-0.916771\pi\)
0.706876 + 0.707338i \(0.250104\pi\)
\(510\) 0 0
\(511\) −12.5954 32.1966i −0.557189 1.42429i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 9.51357 5.49266i 0.419626 0.242271i
\(515\) 0 0
\(516\) 0 0
\(517\) −3.24825 −0.142858
\(518\) 5.64459 2.20819i 0.248009 0.0970221i
\(519\) 0 0
\(520\) 0 0
\(521\) 14.8674 + 25.7511i 0.651354 + 1.12818i 0.982795 + 0.184702i \(0.0591319\pi\)
−0.331441 + 0.943476i \(0.607535\pi\)
\(522\) 0 0
\(523\) −2.82915 + 4.90024i −0.123710 + 0.214272i −0.921228 0.389023i \(-0.872813\pi\)
0.797518 + 0.603295i \(0.206146\pi\)
\(524\) 12.7125 0.555347
\(525\) 0 0
\(526\) 1.33873 0.0583714
\(527\) −14.5953 + 25.2799i −0.635783 + 1.10121i
\(528\) 0 0
\(529\) −9.13513 15.8225i −0.397179 0.687935i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.43156 9.42751i 0.0620660 0.408734i
\(533\) 6.11497 0.264869
\(534\) 0 0
\(535\) 0 0
\(536\) −7.08216 + 4.08889i −0.305903 + 0.176613i
\(537\) 0 0
\(538\) 0.622322 0.0268302
\(539\) −3.38904 + 0.765697i −0.145976 + 0.0329809i
\(540\) 0 0
\(541\) 17.6742 30.6126i 0.759874 1.31614i −0.183041 0.983105i \(-0.558594\pi\)
0.942915 0.333035i \(-0.108073\pi\)
\(542\) −18.4634 + 10.6598i −0.793070 + 0.457879i
\(543\) 0 0
\(544\) −3.16952 1.82992i −0.135892 0.0784572i
\(545\) 0 0
\(546\) 0 0
\(547\) 21.4806i 0.918445i −0.888321 0.459223i \(-0.848128\pi\)
0.888321 0.459223i \(-0.151872\pi\)
\(548\) −2.15740 + 3.73673i −0.0921595 + 0.159625i
\(549\) 0 0
\(550\) 0 0
\(551\) −16.0015 + 27.7154i −0.681687 + 1.18072i
\(552\) 0 0
\(553\) 14.6800 18.3667i 0.624256 0.781031i
\(554\) 1.18709i 0.0504345i
\(555\) 0 0
\(556\) 0.0590003 0.0340638i 0.00250217 0.00144463i
\(557\) −19.9150 34.4939i −0.843828 1.46155i −0.886635 0.462469i \(-0.846964\pi\)
0.0428076 0.999083i \(-0.486370\pi\)
\(558\) 0 0
\(559\) 6.10836i 0.258356i
\(560\) 0 0
\(561\) 0 0
\(562\) 1.71120 + 0.987964i 0.0721828 + 0.0416747i
\(563\) 8.95567 5.17056i 0.377437 0.217913i −0.299266 0.954170i \(-0.596742\pi\)
0.676702 + 0.736257i \(0.263408\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 27.1309 1.14040
\(567\) 0 0
\(568\) 10.3761i 0.435371i
\(569\) −24.3464 14.0564i −1.02065 0.589275i −0.106361 0.994328i \(-0.533920\pi\)
−0.914293 + 0.405053i \(0.867253\pi\)
\(570\) 0 0
\(571\) 13.7146 + 23.7544i 0.573938 + 0.994090i 0.996156 + 0.0875958i \(0.0279184\pi\)
−0.422218 + 0.906494i \(0.638748\pi\)
\(572\) 1.17969 + 0.681094i 0.0493253 + 0.0284780i
\(573\) 0 0
\(574\) 3.68063 4.60498i 0.153627 0.192208i
\(575\) 0 0
\(576\) 0 0
\(577\) 6.51910 + 11.2914i 0.271394 + 0.470068i 0.969219 0.246200i \(-0.0791821\pi\)
−0.697825 + 0.716268i \(0.745849\pi\)
\(578\) −1.80278 3.12250i −0.0749857 0.129879i
\(579\) 0 0
\(580\) 0 0
\(581\) 1.90296 12.5319i 0.0789481 0.519911i
\(582\) 0 0
\(583\) −3.33843 1.92744i −0.138264 0.0798266i
\(584\) 6.53361 + 11.3165i 0.270363 + 0.468282i
\(585\) 0 0
\(586\) 8.99008 + 5.19042i 0.371377 + 0.214414i
\(587\) 35.0223i 1.44553i 0.691096 + 0.722763i \(0.257128\pi\)
−0.691096 + 0.722763i \(0.742872\pi\)
\(588\) 0 0
\(589\) 28.7461 1.18446
\(590\) 0 0
\(591\) 0 0
\(592\) −1.98397 + 1.14545i −0.0815409 + 0.0470776i
\(593\) 14.1919 + 8.19370i 0.582792 + 0.336475i 0.762242 0.647292i \(-0.224099\pi\)
−0.179450 + 0.983767i \(0.557432\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.6982i 0.683986i
\(597\) 0 0
\(598\) −8.81529 15.2685i −0.360484 0.624376i
\(599\) 26.0718 15.0526i 1.06527 0.615032i 0.138382 0.990379i \(-0.455810\pi\)
0.926884 + 0.375347i \(0.122476\pi\)
\(600\) 0 0
\(601\) 1.75569i 0.0716162i 0.999359 + 0.0358081i \(0.0114005\pi\)
−0.999359 + 0.0358081i \(0.988599\pi\)
\(602\) 4.60001 + 3.67666i 0.187482 + 0.149849i
\(603\) 0 0
\(604\) 6.51016 11.2759i 0.264895 0.458811i
\(605\) 0 0
\(606\) 0 0
\(607\) −9.03616 + 15.6511i −0.366766 + 0.635258i −0.989058 0.147528i \(-0.952868\pi\)
0.622292 + 0.782785i \(0.286202\pi\)
\(608\) 3.60411i 0.146166i
\(609\) 0 0
\(610\) 0 0
\(611\) 15.5539 + 8.98003i 0.629242 + 0.363293i
\(612\) 0 0
\(613\) −11.1285 + 6.42507i −0.449478 + 0.259506i −0.707610 0.706604i \(-0.750226\pi\)
0.258132 + 0.966110i \(0.416893\pi\)
\(614\) 7.06821 12.2425i 0.285250 0.494067i
\(615\) 0 0
\(616\) 1.22297 0.478431i 0.0492749 0.0192765i
\(617\) 37.3633 1.50419 0.752094 0.659055i \(-0.229044\pi\)
0.752094 + 0.659055i \(0.229044\pi\)
\(618\) 0 0
\(619\) −23.7213 + 13.6955i −0.953439 + 0.550468i −0.894147 0.447773i \(-0.852217\pi\)
−0.0592911 + 0.998241i \(0.518884\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.65287 0.266756
\(623\) −2.45661 + 3.07356i −0.0984222 + 0.123140i
\(624\) 0 0
\(625\) 0 0
\(626\) −6.07282 10.5184i −0.242719 0.420401i
\(627\) 0 0
\(628\) −7.40408 + 12.8242i −0.295455 + 0.511743i
\(629\) 8.38432 0.334305
\(630\) 0 0
\(631\) −4.09420 −0.162987 −0.0814937 0.996674i \(-0.525969\pi\)
−0.0814937 + 0.996674i \(0.525969\pi\)
\(632\) −4.44344 + 7.69627i −0.176751 + 0.306141i
\(633\) 0 0
\(634\) −15.3605 26.6051i −0.610043 1.05662i
\(635\) 0 0
\(636\) 0 0
\(637\) 18.3449 + 5.70280i 0.726850 + 0.225953i
\(638\) −4.40740 −0.174491
\(639\) 0 0
\(640\) 0 0
\(641\) −28.4700 + 16.4371i −1.12450 + 0.649228i −0.942545 0.334080i \(-0.891574\pi\)
−0.181951 + 0.983308i \(0.558241\pi\)
\(642\) 0 0
\(643\) −48.1790 −1.89999 −0.949996 0.312261i \(-0.898914\pi\)
−0.949996 + 0.312261i \(0.898914\pi\)
\(644\) −16.8042 2.55170i −0.662178 0.100551i
\(645\) 0 0
\(646\) 6.59524 11.4233i 0.259486 0.449443i
\(647\) −4.58478 + 2.64703i −0.180246 + 0.104065i −0.587408 0.809291i \(-0.699852\pi\)
0.407162 + 0.913356i \(0.366518\pi\)
\(648\) 0 0
\(649\) 2.62377 + 1.51483i 0.102992 + 0.0594625i
\(650\) 0 0
\(651\) 0 0
\(652\) 15.3793i 0.602301i
\(653\) 25.0603 43.4057i 0.980686 1.69860i 0.320956 0.947094i \(-0.395996\pi\)
0.659729 0.751503i \(-0.270671\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.11408 + 1.92964i −0.0434975 + 0.0753399i
\(657\) 0 0
\(658\) 16.1245 6.30798i 0.628599 0.245911i
\(659\) 2.20149i 0.0857579i −0.999080 0.0428790i \(-0.986347\pi\)
0.999080 0.0428790i \(-0.0136530\pi\)
\(660\) 0 0
\(661\) −33.7612 + 19.4921i −1.31316 + 0.758153i −0.982618 0.185638i \(-0.940565\pi\)
−0.330542 + 0.943791i \(0.607231\pi\)
\(662\) 15.5140 + 26.8710i 0.602967 + 1.04437i
\(663\) 0 0
\(664\) 4.79091i 0.185923i
\(665\) 0 0
\(666\) 0 0
\(667\) 49.4017 + 28.5221i 1.91284 + 1.10438i
\(668\) 21.2316 12.2581i 0.821475 0.474279i
\(669\) 0 0
\(670\) 0 0
\(671\) −1.85852 −0.0717473
\(672\) 0 0
\(673\) 43.4830i 1.67615i −0.545556 0.838074i \(-0.683682\pi\)
0.545556 0.838074i \(-0.316318\pi\)
\(674\) −5.98830 3.45735i −0.230661 0.133172i
\(675\) 0 0
\(676\) 2.73413 + 4.73565i 0.105159 + 0.182140i
\(677\) 36.0802 + 20.8309i 1.38668 + 0.800597i 0.992939 0.118626i \(-0.0378489\pi\)
0.393736 + 0.919223i \(0.371182\pi\)
\(678\) 0 0
\(679\) 23.6772 + 3.59537i 0.908648 + 0.137978i
\(680\) 0 0
\(681\) 0 0
\(682\) 1.97943 + 3.42848i 0.0757965 + 0.131283i
\(683\) 23.8637 + 41.3332i 0.913120 + 1.58157i 0.809630 + 0.586940i \(0.199668\pi\)
0.103490 + 0.994631i \(0.466999\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 15.3365 10.3824i 0.585548 0.396400i
\(687\) 0 0
\(688\) −1.92756 1.11288i −0.0734875 0.0424280i
\(689\) 10.6571 + 18.4587i 0.406004 + 0.703220i
\(690\) 0 0
\(691\) 33.6953 + 19.4540i 1.28183 + 0.740066i 0.977183 0.212399i \(-0.0681277\pi\)
0.304648 + 0.952465i \(0.401461\pi\)
\(692\) 12.5243i 0.476101i
\(693\) 0 0
\(694\) −7.49408 −0.284471
\(695\) 0 0
\(696\) 0 0
\(697\) 7.06219 4.07736i 0.267500 0.154441i
\(698\) 10.7866 + 6.22762i 0.408277 + 0.235719i
\(699\) 0 0
\(700\) 0 0
\(701\) 8.73610i 0.329958i 0.986297 + 0.164979i \(0.0527556\pi\)
−0.986297 + 0.164979i \(0.947244\pi\)
\(702\) 0 0
\(703\) −4.12832 7.15046i −0.155703 0.269685i
\(704\) −0.429853 + 0.248176i −0.0162007 + 0.00935348i
\(705\) 0 0
\(706\) 18.9402i 0.712824i
\(707\) 2.89515 + 7.40061i 0.108883 + 0.278329i
\(708\) 0 0
\(709\) 8.25544 14.2988i 0.310039 0.537004i −0.668331 0.743864i \(-0.732991\pi\)
0.978371 + 0.206860i \(0.0663244\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.743586 1.28793i 0.0278671 0.0482671i
\(713\) 51.2389i 1.91891i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.58961 0.917762i −0.0594066 0.0342984i
\(717\) 0 0
\(718\) −23.0590 + 13.3131i −0.860554 + 0.496841i
\(719\) 22.5570 39.0699i 0.841234 1.45706i −0.0476171 0.998866i \(-0.515163\pi\)
0.888852 0.458195i \(-0.151504\pi\)
\(720\) 0 0
\(721\) 23.7457 29.7092i 0.884336 1.10643i
\(722\) 6.01040 0.223684
\(723\) 0 0
\(724\) 20.4871 11.8282i 0.761396 0.439592i
\(725\) 0 0
\(726\) 0 0
\(727\) −31.9760 −1.18593 −0.592963 0.805230i \(-0.702042\pi\)
−0.592963 + 0.805230i \(0.702042\pi\)
\(728\) −7.17871 1.09008i −0.266061 0.0404012i
\(729\) 0 0
\(730\) 0 0
\(731\) 4.07295 + 7.05456i 0.150644 + 0.260922i
\(732\) 0 0
\(733\) −23.3606 + 40.4618i −0.862844 + 1.49449i 0.00632839 + 0.999980i \(0.497986\pi\)
−0.869172 + 0.494509i \(0.835348\pi\)
\(734\) 10.9121 0.402773
\(735\) 0 0
\(736\) 6.42419 0.236799
\(737\) 2.02953 3.51524i 0.0747586 0.129486i
\(738\) 0 0
\(739\) −4.59353 7.95623i −0.168976 0.292675i 0.769084 0.639147i \(-0.220713\pi\)
−0.938060 + 0.346473i \(0.887379\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 20.3152 + 3.08485i 0.745795 + 0.113248i
\(743\) 28.5353 1.04686 0.523430 0.852069i \(-0.324652\pi\)
0.523430 + 0.852069i \(0.324652\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −19.4924 + 11.2539i −0.713667 + 0.412036i
\(747\) 0 0
\(748\) 1.81657 0.0664203
\(749\) −3.51234 + 4.39442i −0.128338 + 0.160569i
\(750\) 0 0
\(751\) 21.4749 37.1956i 0.783629 1.35729i −0.146185 0.989257i \(-0.546700\pi\)
0.929814 0.368029i \(-0.119967\pi\)
\(752\) −5.66749 + 3.27213i −0.206672 + 0.119322i
\(753\) 0 0
\(754\) 21.1043 + 12.1846i 0.768574 + 0.443736i
\(755\) 0 0
\(756\) 0 0
\(757\) 19.4415i 0.706612i 0.935508 + 0.353306i \(0.114943\pi\)
−0.935508 + 0.353306i \(0.885057\pi\)
\(758\) −1.62954 + 2.82245i −0.0591877 + 0.102516i
\(759\) 0 0
\(760\) 0 0
\(761\) −24.9154 + 43.1547i −0.903182 + 1.56436i −0.0798434 + 0.996807i \(0.525442\pi\)
−0.823339 + 0.567550i \(0.807891\pi\)
\(762\) 0 0
\(763\) −7.61827 19.4739i −0.275800 0.705003i
\(764\) 8.10892i 0.293371i
\(765\) 0 0
\(766\) 15.0013 8.66098i 0.542017 0.312934i
\(767\) −8.37575 14.5072i −0.302431 0.523825i
\(768\) 0 0
\(769\) 29.5025i 1.06389i −0.846779 0.531944i \(-0.821462\pi\)
0.846779 0.531944i \(-0.178538\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.4356 + 6.02502i 0.375587 + 0.216845i
\(773\) 21.9349 12.6641i 0.788945 0.455498i −0.0506458 0.998717i \(-0.516128\pi\)
0.839591 + 0.543219i \(0.182795\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −9.05174 −0.324938
\(777\) 0 0
\(778\) 31.6982i 1.13644i
\(779\) −6.95465 4.01527i −0.249176 0.143862i
\(780\) 0 0
\(781\) 2.57509 + 4.46019i 0.0921440 + 0.159598i
\(782\) −20.3616 11.7558i −0.728129 0.420385i
\(783\) 0 0
\(784\) −5.14181 + 4.74992i −0.183636 + 0.169640i
\(785\) 0 0
\(786\) 0 0
\(787\) −3.40220 5.89278i −0.121275 0.210055i