Properties

Label 3150.2.bp.g.1349.11
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 1349.11
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.g.899.11

$q$-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 −0.433795 0.901011i \(-0.642826\pi\)
0.563401 + 0.826184i \(0.309493\pi\)
\(12\) 0 0
\(13\) −2.74440 −0.761160 −0.380580 0.924748i \(-0.624276\pi\)
−0.380580 + 0.924748i \(0.624276\pi\)
\(14\) −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 \(0.308515\pi\)
−0.565937 + 0.824449i \(0.691485\pi\)
\(30\) 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 0.327973 0.944687i \(-0.393634\pi\)
−0.654136 + 0.756377i \(0.726968\pi\)
\(38\) 3.12125 1.80205i 0.506334 0.292332i
\(39\) 0 0
\(40\) 0 0
\(41\) −2.22816 −0.347980 −0.173990 0.984747i \(-0.555666\pi\)
−0.173990 + 0.984747i \(0.555666\pi\)
\(42\) 0 0
\(43\) 2.22575i 0.339424i −0.985494 0.169712i \(-0.945716\pi\)
0.985494 0.169712i \(-0.0542838\pi\)
\(44\) −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 0.993395 0.114742i \(-0.0366040\pi\)
−0.596067 + 0.802935i \(0.703271\pi\)
\(60\) 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 −0.000534152 1.00000i \(-0.500170\pi\)
0.865758 + 0.500463i \(0.166837\pi\)
\(68\) −3.16952 1.82992i −0.384360 0.221911i
\(69\) 0 0
\(70\) 0 0
\(71\) 10.3761i 1.23141i 0.787975 + 0.615707i \(0.211129\pi\)
−0.787975 + 0.615707i \(0.788871\pi\)
\(72\) 0 0
\(73\) −6.53361 11.3165i −0.764701 1.32450i −0.940405 0.340058i \(-0.889553\pi\)
0.175704 0.984443i \(-0.443780\pi\)
\(74\) 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 −0.902741 0.430184i \(-0.858449\pi\)
0.823921 + 0.566704i \(0.191782\pi\)
\(90\) 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 \(-0.348017\pi\)
0.459532 + 0.888161i \(0.348017\pi\)
\(98\) −5.14181 + 4.74992i −0.519401 + 0.479815i
\(99\) 0 0
\(100\) 0 0
\(101\) 1.50180 + 2.60119i 0.149434 + 0.258828i 0.931019 0.364972i \(-0.118921\pi\)
−0.781584 + 0.623800i \(0.785588\pi\)
\(102\) 0 0
\(103\) 7.18752 12.4491i 0.708207 1.22665i −0.257314 0.966328i \(-0.582838\pi\)
0.965522 0.260323i \(-0.0838291\pi\)
\(104\) −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 \(0.0106427\pi\)
−0.999441 + 0.0334287i \(0.989357\pi\)
\(128\) −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 \(-0.645919\pi\)
0.997876 0.0651355i \(-0.0207479\pi\)
\(132\) 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 0.957097 0.289768i \(-0.0935783\pi\)
0.227602 + 0.973754i \(0.426912\pi\)
\(150\) 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 \(0.0345645\pi\)
−0.403200 + 0.915112i \(0.632102\pi\)
\(158\) −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 −0.122473 0.992472i \(-0.539082\pi\)
−0.920742 + 0.390171i \(0.872416\pi\)
\(164\) 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 −0.558229 0.829687i \(-0.688519\pi\)
0.439416 + 0.898284i \(0.355186\pi\)
\(180\) 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 0.223933 0.974605i \(-0.428110\pi\)
−0.732066 + 0.681234i \(0.761444\pi\)
\(192\) 0 0
\(193\) 10.4356 6.02502i 0.751174 0.433691i −0.0749438 0.997188i \(-0.523878\pi\)
0.826118 + 0.563497i \(0.190544\pi\)
\(194\) −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 \(-0.789049\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(224\) −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 \(-0.825428\pi\)
0.853342 0.521351i \(-0.174572\pi\)
\(240\) 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 \(-0.561287\pi\)
−0.191352 + 0.981522i \(0.561287\pi\)
\(252\) 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 0.875355 0.483480i \(-0.160627\pi\)
−0.856384 + 0.516340i \(0.827294\pi\)
\(270\) 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 −0.468797 0.883306i \(-0.655312\pi\)
0.530567 + 0.847643i \(0.321979\pi\)
\(278\) −0.0590003 0.0340638i −0.00353860 0.00204301i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.97593i 0.117874i 0.998262 + 0.0589370i \(0.0187711\pi\)
−0.998262 + 0.0589370i \(0.981229\pi\)
\(282\) 0 0
\(283\) 13.5654 + 23.4960i 0.806382 + 1.39669i 0.915354 + 0.402650i \(0.131911\pi\)
−0.108972 + 0.994045i \(0.534756\pi\)
\(284\) 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 \(-0.367827\pi\)
0.403404 + 0.915022i \(0.367827\pi\)
\(308\) −1.02582 0.819908i −0.0584515 0.0467186i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.32643 + 5.76155i 0.188625 + 0.326708i 0.944792 0.327671i \(-0.106264\pi\)
−0.756167 + 0.654378i \(0.772930\pi\)
\(312\) 0 0
\(313\) 6.07282 10.5184i 0.343256 0.594537i −0.641779 0.766890i \(-0.721803\pi\)
0.985035 + 0.172352i \(0.0551367\pi\)
\(314\) −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 \(-0.939691\pi\)
0.982105 0.188334i \(-0.0603087\pi\)
\(338\) 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 −0.252730 0.967537i \(-0.581329\pi\)
−0.964277 + 0.264898i \(0.914662\pi\)
\(360\) 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 0.972562 0.232646i \(-0.0747382\pi\)
−0.687758 + 0.725940i \(0.741405\pi\)
\(368\) −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 −0.0982976 0.995157i \(-0.531340\pi\)
−0.910980 + 0.412450i \(0.864673\pi\)
\(374\) 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 0.398326 0.917244i \(-0.369591\pi\)
0.993520 + 0.113662i \(0.0362580\pi\)
\(390\) 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 \(-0.515322\pi\)
0.889081 0.457750i \(-0.151345\pi\)
\(398\) 19.0472i 0.954751i
\(399\) 0 0
\(400\) 0 0
\(401\) −31.0404 17.9212i −1.55008 0.894940i −0.998134 0.0610611i \(-0.980552\pi\)
−0.551947 0.833879i \(-0.686115\pi\)
\(402\) 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 \(-0.583829\pi\)
−0.260323 + 0.965522i \(0.583829\pi\)
\(420\) 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 −0.971998 0.234991i \(-0.924494\pi\)
−0.282491 + 0.959270i \(0.591161\pi\)
\(432\) 0 0
\(433\) 14.9203 0.717025 0.358512 0.933525i \(-0.383284\pi\)
0.358512 + 0.933525i \(0.383284\pi\)
\(434\) 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 \(0.163646\pi\)
−0.870731 + 0.491760i \(0.836354\pi\)
\(450\) 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 0.138870 0.990311i \(-0.455653\pi\)
−0.788199 + 0.615420i \(0.788986\pi\)
\(458\) 20.1545 11.6362i 0.941760 0.543725i
\(459\) 0 0
\(460\) 0 0
\(461\) −1.98400 −0.0924039 −0.0462020 0.998932i \(-0.514712\pi\)
−0.0462020 + 0.998932i \(0.514712\pi\)
\(462\) 0 0
\(463\) 36.3987i 1.69159i 0.533506 + 0.845796i \(0.320874\pi\)
−0.533506 + 0.845796i \(0.679126\pi\)
\(464\) −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 \(-0.853043\pi\)
0.0618788 0.998084i \(-0.480291\pi\)
\(480\) 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 −0.750993 0.660310i \(-0.770425\pi\)
0.196349 + 0.980534i \(0.437091\pi\)
\(488\) 3.24271 + 1.87218i 0.146791 + 0.0847496i
\(489\) 0 0
\(490\) 0 0
\(491\) 32.5466i 1.46881i 0.678714 + 0.734403i \(0.262538\pi\)
−0.678714 + 0.734403i \(0.737462\pi\)
\(492\) 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 −0.706876 0.707338i \(-0.749896\pi\)
0.966010 + 0.258503i \(0.0832293\pi\)
\(510\) 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 \(-0.940868\pi\)
0.331441 0.943476i \(-0.392465\pi\)
\(522\) 0 0
\(523\) 2.82915 4.90024i 0.123710 0.214272i −0.797518 0.603295i \(-0.793854\pi\)
0.921228 + 0.389023i \(0.127187\pi\)
\(524\) −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 \(0.151872\pi\)
−0.888321 + 0.459223i \(0.848128\pi\)
\(548\) −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 0.914293 0.405053i \(-0.132747\pi\)
0.106361 + 0.994328i \(0.466080\pi\)
\(570\) 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 0.697825 0.716268i \(-0.254151\pi\)
−0.969219 + 0.246200i \(0.920818\pi\)
\(578\) −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 −0.926884 0.375347i \(-0.877524\pi\)
−0.138382 + 0.990379i \(0.544190\pi\)
\(600\) 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 −0.622292 0.782785i \(-0.713798\pi\)
0.989058 + 0.147528i \(0.0471315\pi\)
\(608\) 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 −0.258132 0.966110i \(-0.583107\pi\)
0.707610 + 0.706604i \(0.249774\pi\)
\(614\) −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 0.181951 0.983308i \(-0.441759\pi\)
0.942545 + 0.334080i \(0.108426\pi\)
\(642\) 0 0
\(643\) 48.1790 1.89999 0.949996 0.312261i \(-0.101086\pi\)
0.949996 + 0.312261i \(0.101086\pi\)
\(644\) 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 \(0.0136530\pi\)
−0.999080 + 0.0428790i \(0.986347\pi\)
\(660\) 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 \(0.316318\pi\)
−0.545556 + 0.838074i \(0.683682\pi\)
\(674\) 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 \(-0.947244\pi\)
0.986297 0.164979i \(-0.0527556\pi\)
\(702\) 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 \(0.484837\pi\)
−0.888852 + 0.458195i \(0.848496\pi\)
\(720\) 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 \(-0.297958\pi\)
0.592963 + 0.805230i \(0.297958\pi\)
\(728\) −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 \(-0.502014\pi\)
0.869172 0.494509i \(-0.164652\pi\)
\(734\) −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 \(-0.885057\pi\)
0.935508 0.353306i \(-0.114943\pi\)
\(758\) −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 \(-0.474558\pi\)
0.823339 0.567550i \(-0.192109\pi\)
\(762\) 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 0.920271