Properties

Label 384.2.n.a.49.1
Level $384$
Weight $2$
Character 384.49
Analytic conductor $3.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 384.49
Dual form 384.2.n.a.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.923880 + 0.382683i) q^{3} +(-1.35803 + 3.27858i) q^{5} +(-2.48546 - 2.48546i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.923880 + 0.382683i) q^{3} +(-1.35803 + 3.27858i) q^{5} +(-2.48546 - 2.48546i) q^{7} +(0.707107 - 0.707107i) q^{9} +(-0.420646 - 0.174237i) q^{11} +(-1.98881 - 4.80141i) q^{13} -3.54871i q^{15} -4.75470i q^{17} +(0.402518 + 0.971765i) q^{19} +(3.24741 + 1.34512i) q^{21} +(-0.739125 + 0.739125i) q^{23} +(-5.36930 - 5.36930i) q^{25} +(-0.382683 + 0.923880i) q^{27} +(-0.153117 + 0.0634229i) q^{29} -8.57458 q^{31} +0.455304 q^{33} +(11.5241 - 4.77344i) q^{35} +(-2.67583 + 6.46002i) q^{37} +(3.67484 + 3.67484i) q^{39} +(-1.39247 + 1.39247i) q^{41} +(-2.84883 - 1.18002i) q^{43} +(1.35803 + 3.27858i) q^{45} +0.715661i q^{47} +5.35501i q^{49} +(1.81955 + 4.39277i) q^{51} +(-10.4455 - 4.32668i) q^{53} +(1.14250 - 1.14250i) q^{55} +(-0.743756 - 0.743756i) q^{57} +(-2.09568 + 5.05941i) q^{59} +(-2.81202 + 1.16478i) q^{61} -3.51497 q^{63} +18.4427 q^{65} +(5.39384 - 2.23420i) q^{67} +(0.400012 - 0.965714i) q^{69} +(8.26068 + 8.26068i) q^{71} +(4.37354 - 4.37354i) q^{73} +(7.01532 + 2.90584i) q^{75} +(0.612439 + 1.47856i) q^{77} -9.46948i q^{79} -1.00000i q^{81} +(-2.85195 - 6.88522i) q^{83} +(15.5887 + 6.45704i) q^{85} +(0.117190 - 0.117190i) q^{87} +(8.60493 + 8.60493i) q^{89} +(-6.99060 + 16.8768i) q^{91} +(7.92188 - 3.28135i) q^{93} -3.73264 q^{95} -10.2117 q^{97} +(-0.420646 + 0.174237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(1\)

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 0
\(3\) −0.923880 + 0.382683i −0.533402 + 0.220942i
\(4\) 0 0
\(5\) −1.35803 + 3.27858i −0.607330 + 1.46623i 0.258562 + 0.965995i \(0.416751\pi\)
−0.865892 + 0.500230i \(0.833249\pi\)
\(6\) 0 0
\(7\) −2.48546 2.48546i −0.939415 0.939415i 0.0588516 0.998267i \(-0.481256\pi\)
−0.998267 + 0.0588516i \(0.981256\pi\)
\(8\) 0 0
\(9\) 0.707107 0.707107i 0.235702 0.235702i
\(10\) 0 0
\(11\) −0.420646 0.174237i −0.126829 0.0525345i 0.318366 0.947968i \(-0.396866\pi\)
−0.445196 + 0.895433i \(0.646866\pi\)
\(12\) 0 0
\(13\) −1.98881 4.80141i −0.551596 1.33167i −0.916280 0.400539i \(-0.868823\pi\)
0.364684 0.931131i \(-0.381177\pi\)
\(14\) 0 0
\(15\) 3.54871i 0.916273i
\(16\) 0 0
\(17\) 4.75470i 1.15318i −0.817032 0.576592i \(-0.804382\pi\)
0.817032 0.576592i \(-0.195618\pi\)
\(18\) 0 0
\(19\) 0.402518 + 0.971765i 0.0923440 + 0.222938i 0.963302 0.268419i \(-0.0865011\pi\)
−0.870958 + 0.491357i \(0.836501\pi\)
\(20\) 0 0
\(21\) 3.24741 + 1.34512i 0.708643 + 0.293529i
\(22\) 0 0
\(23\) −0.739125 + 0.739125i −0.154118 + 0.154118i −0.779955 0.625836i \(-0.784758\pi\)
0.625836 + 0.779955i \(0.284758\pi\)
\(24\) 0 0
\(25\) −5.36930 5.36930i −1.07386 1.07386i
\(26\) 0 0
\(27\) −0.382683 + 0.923880i −0.0736475 + 0.177801i
\(28\) 0 0
\(29\) −0.153117 + 0.0634229i −0.0284330 + 0.0117773i −0.396855 0.917881i \(-0.629898\pi\)
0.368422 + 0.929659i \(0.379898\pi\)
\(30\) 0 0
\(31\) −8.57458 −1.54004 −0.770020 0.638020i \(-0.779754\pi\)
−0.770020 + 0.638020i \(0.779754\pi\)
\(32\) 0 0
\(33\) 0.455304 0.0792582
\(34\) 0 0
\(35\) 11.5241 4.77344i 1.94793 0.806859i
\(36\) 0 0
\(37\) −2.67583 + 6.46002i −0.439903 + 1.06202i 0.536079 + 0.844168i \(0.319905\pi\)
−0.975982 + 0.217852i \(0.930095\pi\)
\(38\) 0 0
\(39\) 3.67484 + 3.67484i 0.588445 + 0.588445i
\(40\) 0 0
\(41\) −1.39247 + 1.39247i −0.217467 + 0.217467i −0.807430 0.589963i \(-0.799142\pi\)
0.589963 + 0.807430i \(0.299142\pi\)
\(42\) 0 0
\(43\) −2.84883 1.18002i −0.434443 0.179952i 0.154734 0.987956i \(-0.450548\pi\)
−0.589177 + 0.808004i \(0.700548\pi\)
\(44\) 0 0
\(45\) 1.35803 + 3.27858i 0.202443 + 0.488742i
\(46\) 0 0
\(47\) 0.715661i 0.104390i 0.998637 + 0.0521949i \(0.0166217\pi\)
−0.998637 + 0.0521949i \(0.983378\pi\)
\(48\) 0 0
\(49\) 5.35501i 0.765002i
\(50\) 0 0
\(51\) 1.81955 + 4.39277i 0.254787 + 0.615111i
\(52\) 0 0
\(53\) −10.4455 4.32668i −1.43480 0.594316i −0.476272 0.879298i \(-0.658012\pi\)
−0.958533 + 0.284982i \(0.908012\pi\)
\(54\) 0 0
\(55\) 1.14250 1.14250i 0.154055 0.154055i
\(56\) 0 0
\(57\) −0.743756 0.743756i −0.0985130 0.0985130i
\(58\) 0 0
\(59\) −2.09568 + 5.05941i −0.272834 + 0.658679i −0.999602 0.0282033i \(-0.991021\pi\)
0.726768 + 0.686883i \(0.241021\pi\)
\(60\) 0 0
\(61\) −2.81202 + 1.16478i −0.360042 + 0.149134i −0.555369 0.831604i \(-0.687423\pi\)
0.195327 + 0.980738i \(0.437423\pi\)
\(62\) 0 0
\(63\) −3.51497 −0.442845
\(64\) 0 0
\(65\) 18.4427 2.28753
\(66\) 0 0
\(67\) 5.39384 2.23420i 0.658962 0.272951i −0.0280395 0.999607i \(-0.508926\pi\)
0.687002 + 0.726656i \(0.258926\pi\)
\(68\) 0 0
\(69\) 0.400012 0.965714i 0.0481558 0.116258i
\(70\) 0 0
\(71\) 8.26068 + 8.26068i 0.980363 + 0.980363i 0.999811 0.0194483i \(-0.00619097\pi\)
−0.0194483 + 0.999811i \(0.506191\pi\)
\(72\) 0 0
\(73\) 4.37354 4.37354i 0.511884 0.511884i −0.403219 0.915103i \(-0.632109\pi\)
0.915103 + 0.403219i \(0.132109\pi\)
\(74\) 0 0
\(75\) 7.01532 + 2.90584i 0.810060 + 0.335538i
\(76\) 0 0
\(77\) 0.612439 + 1.47856i 0.0697938 + 0.168497i
\(78\) 0 0
\(79\) 9.46948i 1.06540i −0.846304 0.532700i \(-0.821177\pi\)
0.846304 0.532700i \(-0.178823\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) −2.85195 6.88522i −0.313042 0.755751i −0.999589 0.0286653i \(-0.990874\pi\)
0.686547 0.727086i \(-0.259126\pi\)
\(84\) 0 0
\(85\) 15.5887 + 6.45704i 1.69083 + 0.700364i
\(86\) 0 0
\(87\) 0.117190 0.117190i 0.0125641 0.0125641i
\(88\) 0 0
\(89\) 8.60493 + 8.60493i 0.912120 + 0.912120i 0.996439 0.0843186i \(-0.0268713\pi\)
−0.0843186 + 0.996439i \(0.526871\pi\)
\(90\) 0 0
\(91\) −6.99060 + 16.8768i −0.732814 + 1.76917i
\(92\) 0 0
\(93\) 7.92188 3.28135i 0.821460 0.340260i
\(94\) 0 0
\(95\) −3.73264 −0.382961
\(96\) 0 0
\(97\) −10.2117 −1.03684 −0.518420 0.855126i \(-0.673480\pi\)
−0.518420 + 0.855126i \(0.673480\pi\)
\(98\) 0 0
\(99\) −0.420646 + 0.174237i −0.0422765 + 0.0175115i
\(100\) 0 0
\(101\) −1.92210 + 4.64035i −0.191256 + 0.461732i −0.990197 0.139677i \(-0.955394\pi\)
0.798941 + 0.601409i \(0.205394\pi\)
\(102\) 0 0
\(103\) 2.99647 + 2.99647i 0.295251 + 0.295251i 0.839150 0.543900i \(-0.183053\pi\)
−0.543900 + 0.839150i \(0.683053\pi\)
\(104\) 0 0
\(105\) −8.82017 + 8.82017i −0.860760 + 0.860760i
\(106\) 0 0
\(107\) 0.420364 + 0.174120i 0.0406381 + 0.0168328i 0.402910 0.915240i \(-0.367999\pi\)
−0.362272 + 0.932072i \(0.617999\pi\)
\(108\) 0 0
\(109\) −1.97979 4.77963i −0.189629 0.457806i 0.800259 0.599655i \(-0.204695\pi\)
−0.989888 + 0.141849i \(0.954695\pi\)
\(110\) 0 0
\(111\) 6.99227i 0.663677i
\(112\) 0 0
\(113\) 6.63496i 0.624164i 0.950055 + 0.312082i \(0.101026\pi\)
−0.950055 + 0.312082i \(0.898974\pi\)
\(114\) 0 0
\(115\) −1.41953 3.42704i −0.132371 0.319573i
\(116\) 0 0
\(117\) −4.80141 1.98881i −0.443890 0.183865i
\(118\) 0 0
\(119\) −11.8176 + 11.8176i −1.08332 + 1.08332i
\(120\) 0 0
\(121\) −7.63159 7.63159i −0.693781 0.693781i
\(122\) 0 0
\(123\) 0.753600 1.81935i 0.0679498 0.164045i
\(124\) 0 0
\(125\) 8.50244 3.52183i 0.760481 0.315002i
\(126\) 0 0
\(127\) 19.1639 1.70052 0.850262 0.526360i \(-0.176443\pi\)
0.850262 + 0.526360i \(0.176443\pi\)
\(128\) 0 0
\(129\) 3.08355 0.271492
\(130\) 0 0
\(131\) −16.6367 + 6.89115i −1.45356 + 0.602083i −0.963042 0.269350i \(-0.913191\pi\)
−0.490514 + 0.871433i \(0.663191\pi\)
\(132\) 0 0
\(133\) 1.41484 3.41572i 0.122682 0.296181i
\(134\) 0 0
\(135\) −2.50932 2.50932i −0.215968 0.215968i
\(136\) 0 0
\(137\) −4.17579 + 4.17579i −0.356762 + 0.356762i −0.862618 0.505856i \(-0.831177\pi\)
0.505856 + 0.862618i \(0.331177\pi\)
\(138\) 0 0
\(139\) −17.1703 7.11217i −1.45636 0.603246i −0.492661 0.870221i \(-0.663976\pi\)
−0.963703 + 0.266975i \(0.913976\pi\)
\(140\) 0 0
\(141\) −0.273872 0.661185i −0.0230642 0.0556818i
\(142\) 0 0
\(143\) 2.36622i 0.197873i
\(144\) 0 0
\(145\) 0.588135i 0.0488420i
\(146\) 0 0
\(147\) −2.04927 4.94739i −0.169021 0.408054i
\(148\) 0 0
\(149\) 7.65604 + 3.17123i 0.627207 + 0.259798i 0.673566 0.739127i \(-0.264762\pi\)
−0.0463589 + 0.998925i \(0.514762\pi\)
\(150\) 0 0
\(151\) 8.34642 8.34642i 0.679222 0.679222i −0.280602 0.959824i \(-0.590534\pi\)
0.959824 + 0.280602i \(0.0905341\pi\)
\(152\) 0 0
\(153\) −3.36208 3.36208i −0.271808 0.271808i
\(154\) 0 0
\(155\) 11.6445 28.1124i 0.935313 2.25804i
\(156\) 0 0
\(157\) 1.13210 0.468931i 0.0903514 0.0374248i −0.337050 0.941487i \(-0.609429\pi\)
0.427401 + 0.904062i \(0.359429\pi\)
\(158\) 0 0
\(159\) 11.3062 0.896637
\(160\) 0 0
\(161\) 3.67413 0.289562
\(162\) 0 0
\(163\) 12.5235 5.18742i 0.980920 0.406310i 0.166154 0.986100i \(-0.446865\pi\)
0.814766 + 0.579790i \(0.196865\pi\)
\(164\) 0 0
\(165\) −0.618317 + 1.49275i −0.0481359 + 0.116210i
\(166\) 0 0
\(167\) 6.60580 + 6.60580i 0.511172 + 0.511172i 0.914886 0.403713i \(-0.132281\pi\)
−0.403713 + 0.914886i \(0.632281\pi\)
\(168\) 0 0
\(169\) −9.90575 + 9.90575i −0.761981 + 0.761981i
\(170\) 0 0
\(171\) 0.971765 + 0.402518i 0.0743127 + 0.0307813i
\(172\) 0 0
\(173\) −7.14385 17.2468i −0.543137 1.31125i −0.922499 0.386000i \(-0.873856\pi\)
0.379361 0.925249i \(-0.376144\pi\)
\(174\) 0 0
\(175\) 26.6903i 2.01760i
\(176\) 0 0
\(177\) 5.47627i 0.411622i
\(178\) 0 0
\(179\) −3.80659 9.18993i −0.284518 0.686887i 0.715412 0.698703i \(-0.246239\pi\)
−0.999930 + 0.0118153i \(0.996239\pi\)
\(180\) 0 0
\(181\) −5.55971 2.30291i −0.413250 0.171174i 0.166365 0.986064i \(-0.446797\pi\)
−0.579615 + 0.814890i \(0.696797\pi\)
\(182\) 0 0
\(183\) 2.15222 2.15222i 0.159097 0.159097i
\(184\) 0 0
\(185\) −17.5458 17.5458i −1.28999 1.28999i
\(186\) 0 0
\(187\) −0.828446 + 2.00005i −0.0605820 + 0.146258i
\(188\) 0 0
\(189\) 3.24741 1.34512i 0.236214 0.0978431i
\(190\) 0 0
\(191\) −5.75185 −0.416190 −0.208095 0.978109i \(-0.566726\pi\)
−0.208095 + 0.978109i \(0.566726\pi\)
\(192\) 0 0
\(193\) −2.02898 −0.146049 −0.0730246 0.997330i \(-0.523265\pi\)
−0.0730246 + 0.997330i \(0.523265\pi\)
\(194\) 0 0
\(195\) −17.0388 + 7.05770i −1.22017 + 0.505412i
\(196\) 0 0
\(197\) 3.54890 8.56781i 0.252849 0.610431i −0.745583 0.666413i \(-0.767829\pi\)
0.998432 + 0.0559816i \(0.0178288\pi\)
\(198\) 0 0
\(199\) −12.7457 12.7457i −0.903520 0.903520i 0.0922191 0.995739i \(-0.470604\pi\)
−0.995739 + 0.0922191i \(0.970604\pi\)
\(200\) 0 0
\(201\) −4.12827 + 4.12827i −0.291185 + 0.291185i
\(202\) 0 0
\(203\) 0.538200 + 0.222930i 0.0377742 + 0.0156466i
\(204\) 0 0
\(205\) −2.67431 6.45635i −0.186782 0.450931i
\(206\) 0 0
\(207\) 1.04528i 0.0726521i
\(208\) 0 0
\(209\) 0.478902i 0.0331264i
\(210\) 0 0
\(211\) 8.49277 + 20.5034i 0.584666 + 1.41151i 0.888541 + 0.458798i \(0.151720\pi\)
−0.303874 + 0.952712i \(0.598280\pi\)
\(212\) 0 0
\(213\) −10.7931 4.47065i −0.739531 0.306324i
\(214\) 0 0
\(215\) 7.73761 7.73761i 0.527700 0.527700i
\(216\) 0 0
\(217\) 21.3118 + 21.3118i 1.44674 + 1.44674i
\(218\) 0 0
\(219\) −2.36694 + 5.71430i −0.159943 + 0.386137i
\(220\) 0 0
\(221\) −22.8293 + 9.45619i −1.53566 + 0.636092i
\(222\) 0 0
\(223\) −1.93870 −0.129825 −0.0649123 0.997891i \(-0.520677\pi\)
−0.0649123 + 0.997891i \(0.520677\pi\)
\(224\) 0 0
\(225\) −7.59333 −0.506222
\(226\) 0 0
\(227\) −19.8529 + 8.22334i −1.31768 + 0.545802i −0.927117 0.374773i \(-0.877721\pi\)
−0.390566 + 0.920575i \(0.627721\pi\)
\(228\) 0 0
\(229\) 9.21270 22.2414i 0.608792 1.46975i −0.255522 0.966803i \(-0.582247\pi\)
0.864315 0.502951i \(-0.167753\pi\)
\(230\) 0 0
\(231\) −1.13164 1.13164i −0.0744564 0.0744564i
\(232\) 0 0
\(233\) 7.56463 7.56463i 0.495575 0.495575i −0.414482 0.910057i \(-0.636037\pi\)
0.910057 + 0.414482i \(0.136037\pi\)
\(234\) 0 0
\(235\) −2.34635 0.971890i −0.153059 0.0633991i
\(236\) 0 0
\(237\) 3.62381 + 8.74866i 0.235392 + 0.568287i
\(238\) 0 0
\(239\) 21.0655i 1.36261i −0.731997 0.681307i \(-0.761412\pi\)
0.731997 0.681307i \(-0.238588\pi\)
\(240\) 0 0
\(241\) 24.1957i 1.55858i 0.626664 + 0.779289i \(0.284420\pi\)
−0.626664 + 0.779289i \(0.715580\pi\)
\(242\) 0 0
\(243\) 0.382683 + 0.923880i 0.0245492 + 0.0592669i
\(244\) 0 0
\(245\) −17.5568 7.27228i −1.12166 0.464609i
\(246\) 0 0
\(247\) 3.86531 3.86531i 0.245943 0.245943i
\(248\) 0 0
\(249\) 5.26972 + 5.26972i 0.333955 + 0.333955i
\(250\) 0 0
\(251\) −0.0707278 + 0.170752i −0.00446430 + 0.0107778i −0.926096 0.377288i \(-0.876857\pi\)
0.921632 + 0.388066i \(0.126857\pi\)
\(252\) 0 0
\(253\) 0.439693 0.182127i 0.0276433 0.0114502i
\(254\) 0 0
\(255\) −16.8731 −1.05663
\(256\) 0 0
\(257\) −29.7460 −1.85550 −0.927751 0.373199i \(-0.878261\pi\)
−0.927751 + 0.373199i \(0.878261\pi\)
\(258\) 0 0
\(259\) 22.7068 9.40545i 1.41093 0.584426i
\(260\) 0 0
\(261\) −0.0634229 + 0.153117i −0.00392578 + 0.00947768i
\(262\) 0 0
\(263\) −0.211270 0.211270i −0.0130275 0.0130275i 0.700563 0.713591i \(-0.252932\pi\)
−0.713591 + 0.700563i \(0.752932\pi\)
\(264\) 0 0
\(265\) 28.3707 28.3707i 1.74280 1.74280i
\(266\) 0 0
\(267\) −11.2429 4.65695i −0.688053 0.285001i
\(268\) 0 0
\(269\) 9.18492 + 22.1744i 0.560014 + 1.35199i 0.909754 + 0.415148i \(0.136270\pi\)
−0.349740 + 0.936847i \(0.613730\pi\)
\(270\) 0 0
\(271\) 15.5563i 0.944979i 0.881336 + 0.472489i \(0.156644\pi\)
−0.881336 + 0.472489i \(0.843356\pi\)
\(272\) 0 0
\(273\) 18.2673i 1.10559i
\(274\) 0 0
\(275\) 1.32304 + 3.19410i 0.0797824 + 0.192612i
\(276\) 0 0
\(277\) 24.1714 + 10.0121i 1.45232 + 0.601570i 0.962750 0.270394i \(-0.0871539\pi\)
0.489570 + 0.871964i \(0.337154\pi\)
\(278\) 0 0
\(279\) −6.06314 + 6.06314i −0.362991 + 0.362991i
\(280\) 0 0
\(281\) 18.5324 + 18.5324i 1.10555 + 1.10555i 0.993729 + 0.111820i \(0.0356679\pi\)
0.111820 + 0.993729i \(0.464332\pi\)
\(282\) 0 0
\(283\) 3.60189 8.69574i 0.214110 0.516908i −0.779937 0.625858i \(-0.784749\pi\)
0.994047 + 0.108950i \(0.0347489\pi\)
\(284\) 0 0
\(285\) 3.44851 1.42842i 0.204272 0.0846123i
\(286\) 0 0
\(287\) 6.92186 0.408584
\(288\) 0 0
\(289\) −5.60720 −0.329836
\(290\) 0 0
\(291\) 9.43437 3.90784i 0.553052 0.229082i
\(292\) 0 0
\(293\) 8.32183 20.0907i 0.486167 1.17371i −0.470467 0.882417i \(-0.655915\pi\)
0.956634 0.291293i \(-0.0940854\pi\)
\(294\) 0 0
\(295\) −13.7417 13.7417i −0.800072 0.800072i
\(296\) 0 0
\(297\) 0.321948 0.321948i 0.0186813 0.0186813i
\(298\) 0 0
\(299\) 5.01882 + 2.07886i 0.290246 + 0.120224i
\(300\) 0 0
\(301\) 4.14775 + 10.0136i 0.239072 + 0.577172i
\(302\) 0 0
\(303\) 5.02268i 0.288545i
\(304\) 0 0
\(305\) 10.8012i 0.618476i
\(306\) 0 0
\(307\) −11.7750 28.4274i −0.672036 1.62244i −0.778146 0.628083i \(-0.783840\pi\)
0.106111 0.994354i \(-0.466160\pi\)
\(308\) 0 0
\(309\) −3.91507 1.62168i −0.222721 0.0922539i
\(310\) 0 0
\(311\) 1.08506 1.08506i 0.0615284 0.0615284i −0.675673 0.737201i \(-0.736147\pi\)
0.737201 + 0.675673i \(0.236147\pi\)
\(312\) 0 0
\(313\) 3.44537 + 3.44537i 0.194744 + 0.194744i 0.797742 0.602998i \(-0.206027\pi\)
−0.602998 + 0.797742i \(0.706027\pi\)
\(314\) 0 0
\(315\) 4.77344 11.5241i 0.268953 0.649310i
\(316\) 0 0
\(317\) 1.87234 0.775548i 0.105161 0.0435591i −0.329483 0.944162i \(-0.606874\pi\)
0.434644 + 0.900603i \(0.356874\pi\)
\(318\) 0 0
\(319\) 0.0754585 0.00422486
\(320\) 0 0
\(321\) −0.454998 −0.0253955
\(322\) 0 0
\(323\) 4.62045 1.91385i 0.257089 0.106490i
\(324\) 0 0
\(325\) −15.1017 + 36.4587i −0.837690 + 2.02236i
\(326\) 0 0
\(327\) 3.65817 + 3.65817i 0.202297 + 0.202297i
\(328\) 0 0
\(329\) 1.77875 1.77875i 0.0980654 0.0980654i
\(330\) 0 0
\(331\) 27.3713 + 11.3376i 1.50446 + 0.623168i 0.974406 0.224795i \(-0.0721712\pi\)
0.530055 + 0.847963i \(0.322171\pi\)
\(332\) 0 0
\(333\) 2.67583 + 6.46002i 0.146634 + 0.354007i
\(334\) 0 0
\(335\) 20.7182i 1.13196i
\(336\) 0 0
\(337\) 8.28014i 0.451048i 0.974238 + 0.225524i \(0.0724094\pi\)
−0.974238 + 0.225524i \(0.927591\pi\)
\(338\) 0 0
\(339\) −2.53909 6.12990i −0.137904 0.332930i
\(340\) 0 0
\(341\) 3.60686 + 1.49401i 0.195322 + 0.0809052i
\(342\) 0 0
\(343\) −4.08855 + 4.08855i −0.220761 + 0.220761i
\(344\) 0 0
\(345\) 2.62294 + 2.62294i 0.141214 + 0.141214i
\(346\) 0 0
\(347\) −7.72315 + 18.6453i −0.414601 + 1.00093i 0.569286 + 0.822140i \(0.307220\pi\)
−0.983886 + 0.178795i \(0.942780\pi\)
\(348\) 0 0
\(349\) −1.13179 + 0.468804i −0.0605835 + 0.0250945i −0.412769 0.910836i \(-0.635438\pi\)
0.352186 + 0.935930i \(0.385438\pi\)
\(350\) 0 0
\(351\) 5.19700 0.277396
\(352\) 0 0
\(353\) −11.9551 −0.636306 −0.318153 0.948039i \(-0.603063\pi\)
−0.318153 + 0.948039i \(0.603063\pi\)
\(354\) 0 0
\(355\) −38.3016 + 15.8650i −2.03284 + 0.842028i
\(356\) 0 0
\(357\) 6.39565 15.4405i 0.338494 0.817196i
\(358\) 0 0
\(359\) −5.02082 5.02082i −0.264989 0.264989i 0.562088 0.827077i \(-0.309998\pi\)
−0.827077 + 0.562088i \(0.809998\pi\)
\(360\) 0 0
\(361\) 12.6527 12.6527i 0.665933 0.665933i
\(362\) 0 0
\(363\) 9.97115 + 4.13019i 0.523350 + 0.216779i
\(364\) 0 0
\(365\) 8.39959 + 20.2784i 0.439655 + 1.06142i
\(366\) 0 0
\(367\) 23.7760i 1.24109i 0.784169 + 0.620547i \(0.213090\pi\)
−0.784169 + 0.620547i \(0.786910\pi\)
\(368\) 0 0
\(369\) 1.96925i 0.102515i
\(370\) 0 0
\(371\) 15.2082 + 36.7157i 0.789568 + 1.90619i
\(372\) 0 0
\(373\) 3.85917 + 1.59852i 0.199820 + 0.0827683i 0.480349 0.877077i \(-0.340510\pi\)
−0.280529 + 0.959846i \(0.590510\pi\)
\(374\) 0 0
\(375\) −6.50749 + 6.50749i −0.336045 + 0.336045i
\(376\) 0 0
\(377\) 0.609039 + 0.609039i 0.0313671 + 0.0313671i
\(378\) 0 0
\(379\) 3.43755 8.29899i 0.176575 0.426290i −0.810669 0.585505i \(-0.800896\pi\)
0.987244 + 0.159215i \(0.0508962\pi\)
\(380\) 0 0
\(381\) −17.7052 + 7.33372i −0.907063 + 0.375718i
\(382\) 0 0
\(383\) 9.61765 0.491439 0.245720 0.969341i \(-0.420976\pi\)
0.245720 + 0.969341i \(0.420976\pi\)
\(384\) 0 0
\(385\) −5.67928 −0.289443
\(386\) 0 0
\(387\) −2.84883 + 1.18002i −0.144814 + 0.0599840i
\(388\) 0 0
\(389\) −11.3406 + 27.3786i −0.574991 + 1.38815i 0.322269 + 0.946648i \(0.395555\pi\)
−0.897260 + 0.441503i \(0.854445\pi\)
\(390\) 0 0
\(391\) 3.51432 + 3.51432i 0.177727 + 0.177727i
\(392\) 0 0
\(393\) 12.7332 12.7332i 0.642305 0.642305i
\(394\) 0 0
\(395\) 31.0465 + 12.8599i 1.56212 + 0.647050i
\(396\) 0 0
\(397\) 0.283457 + 0.684326i 0.0142263 + 0.0343453i 0.930833 0.365445i \(-0.119083\pi\)
−0.916607 + 0.399790i \(0.869083\pi\)
\(398\) 0 0
\(399\) 3.69715i 0.185089i
\(400\) 0 0
\(401\) 4.48635i 0.224038i −0.993706 0.112019i \(-0.964268\pi\)
0.993706 0.112019i \(-0.0357317\pi\)
\(402\) 0 0
\(403\) 17.0532 + 41.1700i 0.849480 + 2.05083i
\(404\) 0 0
\(405\) 3.27858 + 1.35803i 0.162914 + 0.0674811i
\(406\) 0 0
\(407\) 2.25115 2.25115i 0.111585 0.111585i
\(408\) 0 0
\(409\) −15.2251 15.2251i −0.752833 0.752833i 0.222174 0.975007i \(-0.428685\pi\)
−0.975007 + 0.222174i \(0.928685\pi\)
\(410\) 0 0
\(411\) 2.25992 5.45593i 0.111474 0.269121i
\(412\) 0 0
\(413\) 17.7837 7.36624i 0.875078 0.362469i
\(414\) 0 0
\(415\) 26.4468 1.29822
\(416\) 0 0
\(417\) 18.5850 0.910111
\(418\) 0 0
\(419\) 13.2128 5.47292i 0.645487 0.267369i −0.0358301 0.999358i \(-0.511408\pi\)
0.681317 + 0.731988i \(0.261408\pi\)
\(420\) 0 0
\(421\) 5.77775 13.9487i 0.281590 0.679819i −0.718283 0.695751i \(-0.755072\pi\)
0.999873 + 0.0159320i \(0.00507152\pi\)
\(422\) 0 0
\(423\) 0.506049 + 0.506049i 0.0246049 + 0.0246049i
\(424\) 0 0
\(425\) −25.5294 + 25.5294i −1.23836 + 1.23836i
\(426\) 0 0
\(427\) 9.88415 + 4.09415i 0.478328 + 0.198130i
\(428\) 0 0
\(429\) −0.905512 2.18610i −0.0437185 0.105546i
\(430\) 0 0
\(431\) 30.9700i 1.49177i −0.666073 0.745886i \(-0.732026\pi\)
0.666073 0.745886i \(-0.267974\pi\)
\(432\) 0 0
\(433\) 38.8143i 1.86529i −0.360790 0.932647i \(-0.617493\pi\)
0.360790 0.932647i \(-0.382507\pi\)
\(434\) 0 0
\(435\) 0.225070 + 0.543366i 0.0107913 + 0.0260524i
\(436\) 0 0
\(437\) −1.01577 0.420745i −0.0485907 0.0201269i
\(438\) 0 0
\(439\) 4.15330 4.15330i 0.198226 0.198226i −0.601013 0.799239i \(-0.705236\pi\)
0.799239 + 0.601013i \(0.205236\pi\)
\(440\) 0 0
\(441\) 3.78657 + 3.78657i 0.180313 + 0.180313i
\(442\) 0 0
\(443\) 2.26978 5.47973i 0.107840 0.260350i −0.860742 0.509041i \(-0.830000\pi\)
0.968583 + 0.248691i \(0.0800003\pi\)
\(444\) 0 0
\(445\) −39.8977 + 16.5262i −1.89133 + 0.783415i
\(446\) 0 0
\(447\) −8.28683 −0.391954
\(448\) 0 0
\(449\) 7.31556 0.345243 0.172621 0.984988i \(-0.444776\pi\)
0.172621 + 0.984988i \(0.444776\pi\)
\(450\) 0 0
\(451\) 0.828358 0.343117i 0.0390058 0.0161567i
\(452\) 0 0
\(453\) −4.51705 + 10.9051i −0.212230 + 0.512367i
\(454\) 0 0
\(455\) −45.8385 45.8385i −2.14894 2.14894i
\(456\) 0 0
\(457\) 1.80714 1.80714i 0.0845343 0.0845343i −0.663575 0.748110i \(-0.730962\pi\)
0.748110 + 0.663575i \(0.230962\pi\)
\(458\) 0 0
\(459\) 4.39277 + 1.81955i 0.205037 + 0.0849291i
\(460\) 0 0
\(461\) 5.44672 + 13.1495i 0.253679 + 0.612436i 0.998495 0.0548340i \(-0.0174629\pi\)
−0.744816 + 0.667269i \(0.767463\pi\)
\(462\) 0 0
\(463\) 28.6674i 1.33229i −0.745824 0.666143i \(-0.767944\pi\)
0.745824 0.666143i \(-0.232056\pi\)
\(464\) 0 0
\(465\) 30.4287i 1.41110i
\(466\) 0 0
\(467\) 0.0184119 + 0.0444502i 0.000852000 + 0.00205691i 0.924305 0.381655i \(-0.124646\pi\)
−0.923453 + 0.383712i \(0.874646\pi\)
\(468\) 0 0
\(469\) −18.9592 7.85315i −0.875454 0.362625i
\(470\) 0 0
\(471\) −0.866471 + 0.866471i −0.0399249 + 0.0399249i
\(472\) 0 0
\(473\) 0.992745 + 0.992745i 0.0456465 + 0.0456465i
\(474\) 0 0
\(475\) 3.05645 7.37893i 0.140240 0.338569i
\(476\) 0 0
\(477\) −10.4455 + 4.32668i −0.478268 + 0.198105i
\(478\) 0 0
\(479\) −8.64155 −0.394843 −0.197421 0.980319i \(-0.563257\pi\)
−0.197421 + 0.980319i \(0.563257\pi\)
\(480\) 0 0
\(481\) 36.3389 1.65691
\(482\) 0 0
\(483\) −3.39446 + 1.40603i −0.154453 + 0.0639766i
\(484\) 0 0
\(485\) 13.8678 33.4798i 0.629704 1.52024i
\(486\) 0 0
\(487\) −2.15820 2.15820i −0.0977973 0.0977973i 0.656515 0.754313i \(-0.272030\pi\)
−0.754313 + 0.656515i \(0.772030\pi\)
\(488\) 0 0
\(489\) −9.58511 + 9.58511i −0.433454 + 0.433454i
\(490\) 0 0
\(491\) −24.4583 10.1310i −1.10379 0.457204i −0.244994 0.969525i \(-0.578786\pi\)
−0.858794 + 0.512321i \(0.828786\pi\)
\(492\) 0 0
\(493\) 0.301557 + 0.728024i 0.0135815 + 0.0327885i
\(494\) 0 0
\(495\) 1.61574i 0.0726221i
\(496\) 0 0
\(497\) 41.0632i 1.84193i
\(498\) 0 0
\(499\) −4.98970 12.0462i −0.223370 0.539263i 0.771974 0.635655i \(-0.219270\pi\)
−0.995343 + 0.0963921i \(0.969270\pi\)
\(500\) 0 0
\(501\) −8.63089 3.57503i −0.385600 0.159721i
\(502\) 0 0
\(503\) 7.59295 7.59295i 0.338553 0.338553i −0.517270 0.855823i \(-0.673052\pi\)
0.855823 + 0.517270i \(0.173052\pi\)
\(504\) 0 0
\(505\) −12.6035 12.6035i −0.560848 0.560848i
\(506\) 0 0
\(507\) 5.36096 12.9425i 0.238088 0.574796i
\(508\) 0 0
\(509\) 12.9910 5.38103i 0.575814 0.238510i −0.0757202 0.997129i \(-0.524126\pi\)
0.651534 + 0.758619i \(0.274126\pi\)
\(510\) 0 0
\(511\) −21.7405 −0.961743
\(512\) 0 0
\(513\) −1.05183 −0.0464395
\(514\) 0 0
\(515\) −13.8934 + 5.75485i −0.612218 + 0.253589i
\(516\) 0 0
\(517\) 0.124695 0.301040i 0.00548407 0.0132397i
\(518\) 0 0
\(519\) 13.2001 + 13.2001i 0.579421 + 0.579421i
\(520\) 0 0
\(521\) 17.0333 17.0333i 0.746242 0.746242i −0.227529 0.973771i \(-0.573065\pi\)
0.973771 + 0.227529i \(0.0730647\pi\)
\(522\) 0 0
\(523\) −38.4247 15.9160i −1.68020 0.695960i −0.680860 0.732414i \(-0.738394\pi\)
−0.999335 + 0.0364542i \(0.988394\pi\)
\(524\) 0 0
\(525\) −10.2139 24.6586i −0.445773 1.07619i
\(526\) 0 0
\(527\) 40.7696i 1.77595i
\(528\) 0 0
\(529\) 21.9074i 0.952495i
\(530\) 0 0
\(531\) 2.09568 + 5.05941i 0.0909447 + 0.219560i
\(532\) 0 0
\(533\) 9.45518 + 3.91646i 0.409549 + 0.169641i
\(534\) 0 0
\(535\) −1.14173 + 1.14173i −0.0493615 + 0.0493615i
\(536\) 0 0
\(537\) 7.03367 + 7.03367i 0.303525 + 0.303525i
\(538\) 0 0
\(539\) 0.933042 2.25256i 0.0401890 0.0970248i
\(540\) 0 0
\(541\) −8.78427 + 3.63857i −0.377665 + 0.156434i −0.563437 0.826159i \(-0.690521\pi\)
0.185772 + 0.982593i \(0.440521\pi\)
\(542\) 0 0
\(543\) 6.01779 0.258248
\(544\) 0 0
\(545\) 18.3590 0.786414
\(546\) 0 0
\(547\) −3.07217 + 1.27253i −0.131357 + 0.0544097i −0.447393 0.894337i \(-0.647648\pi\)
0.316037 + 0.948747i \(0.397648\pi\)
\(548\) 0 0
\(549\) −1.16478 + 2.81202i −0.0497114 + 0.120014i
\(550\) 0 0
\(551\) −0.123264 0.123264i −0.00525124 0.00525124i
\(552\) 0 0
\(553\) −23.5360 + 23.5360i −1.00085 + 1.00085i
\(554\) 0 0
\(555\) 22.9247 + 9.49573i 0.973100 + 0.403071i
\(556\) 0 0
\(557\) 0.215669 + 0.520670i 0.00913817 + 0.0220615i 0.928383 0.371625i \(-0.121199\pi\)
−0.919245 + 0.393687i \(0.871199\pi\)
\(558\) 0 0
\(559\) 16.0252i 0.677795i
\(560\) 0 0
\(561\) 2.16483i 0.0913994i
\(562\) 0 0
\(563\) −11.9538 28.8591i −0.503793 1.21626i −0.947403 0.320044i \(-0.896302\pi\)
0.443610 0.896220i \(-0.353698\pi\)
\(564\) 0 0
\(565\) −21.7532 9.01048i −0.915165 0.379074i
\(566\) 0 0
\(567\) −2.48546 + 2.48546i −0.104379 + 0.104379i
\(568\) 0 0
\(569\) −22.2286 22.2286i −0.931873 0.931873i 0.0659498 0.997823i \(-0.478992\pi\)
−0.997823 + 0.0659498i \(0.978992\pi\)
\(570\) 0 0
\(571\) 2.84886 6.87776i 0.119221 0.287825i −0.852991 0.521925i \(-0.825214\pi\)
0.972213 + 0.234099i \(0.0752141\pi\)
\(572\) 0 0
\(573\) 5.31402 2.20114i 0.221996 0.0919539i
\(574\) 0 0
\(575\) 7.93717 0.331003
\(576\) 0 0
\(577\) −31.1728 −1.29774 −0.648871 0.760899i \(-0.724758\pi\)
−0.648871 + 0.760899i \(0.724758\pi\)
\(578\) 0 0
\(579\) 1.87453 0.776457i 0.0779029 0.0322685i
\(580\) 0 0
\(581\) −10.0245 + 24.2013i −0.415887 + 1.00404i
\(582\) 0 0
\(583\) 3.64000 + 3.64000i 0.150754 + 0.150754i
\(584\) 0 0
\(585\) 13.0409 13.0409i 0.539176 0.539176i
\(586\) 0 0
\(587\) 13.5567 + 5.61536i 0.559544 + 0.231771i 0.644487 0.764615i \(-0.277071\pi\)
−0.0849433 + 0.996386i \(0.527071\pi\)
\(588\) 0 0
\(589\) −3.45142 8.33247i −0.142213 0.343334i
\(590\) 0 0
\(591\) 9.27373i 0.381470i
\(592\) 0 0
\(593\) 20.0872i 0.824883i 0.910984 + 0.412442i \(0.135324\pi\)
−0.910984 + 0.412442i \(0.864676\pi\)
\(594\) 0 0
\(595\) −22.6963 54.7937i −0.930457 2.24632i
\(596\) 0 0
\(597\) 16.6531 + 6.89793i 0.681565 + 0.282313i
\(598\) 0 0
\(599\) −22.9392 + 22.9392i −0.937271 + 0.937271i −0.998145 0.0608749i \(-0.980611\pi\)
0.0608749 + 0.998145i \(0.480611\pi\)
\(600\) 0 0
\(601\) 19.0481 + 19.0481i 0.776990 + 0.776990i 0.979318 0.202328i \(-0.0648507\pi\)
−0.202328 + 0.979318i \(0.564851\pi\)
\(602\) 0 0
\(603\) 2.23420 5.39384i 0.0909837 0.219654i
\(604\) 0 0
\(605\) 35.3847 14.6568i 1.43859 0.595885i
\(606\) 0 0
\(607\) −39.8682 −1.61820 −0.809100 0.587672i \(-0.800045\pi\)
−0.809100 + 0.587672i \(0.800045\pi\)
\(608\) 0 0
\(609\) −0.582543 −0.0236059
\(610\) 0 0
\(611\) 3.43618 1.42331i 0.139013 0.0575810i
\(612\) 0 0
\(613\) 7.28252 17.5816i 0.294138 0.710113i −0.705860 0.708351i \(-0.749439\pi\)
0.999998 0.00176143i \(-0.000560680\pi\)
\(614\) 0 0
\(615\) 4.94147 + 4.94147i 0.199259 + 0.199259i
\(616\) 0 0
\(617\) −17.7361 + 17.7361i −0.714027 + 0.714027i −0.967375 0.253348i \(-0.918468\pi\)
0.253348 + 0.967375i \(0.418468\pi\)
\(618\) 0 0
\(619\) −7.84831 3.25088i −0.315450 0.130664i 0.219340 0.975648i \(-0.429609\pi\)
−0.534790 + 0.844985i \(0.679609\pi\)
\(620\) 0 0
\(621\) −0.400012 0.965714i −0.0160519 0.0387528i
\(622\) 0 0
\(623\) 42.7744i 1.71372i
\(624\) 0 0
\(625\) 5.30798i 0.212319i
\(626\) 0 0
\(627\) 0.183268 + 0.442448i 0.00731902 + 0.0176697i
\(628\) 0 0
\(629\) 30.7155 + 12.7228i 1.22471 + 0.507290i
\(630\) 0 0
\(631\) −29.7910 + 29.7910i −1.18596 + 1.18596i −0.207785 + 0.978174i \(0.566626\pi\)
−0.978174 + 0.207785i \(0.933374\pi\)
\(632\) 0 0
\(633\) −15.6926 15.6926i −0.623725 0.623725i
\(634\) 0 0
\(635\) −26.0252 + 62.8305i −1.03278 + 2.49335i
\(636\) 0 0
\(637\) 25.7116 10.6501i 1.01873 0.421972i
\(638\) 0 0
\(639\) 11.6824 0.462147
\(640\) 0 0
\(641\) −25.6481 −1.01304 −0.506520 0.862228i \(-0.669068\pi\)
−0.506520 + 0.862228i \(0.669068\pi\)
\(642\) 0 0
\(643\) 24.6616 10.2152i 0.972559 0.402847i 0.160895 0.986972i \(-0.448562\pi\)
0.811664 + 0.584125i \(0.198562\pi\)
\(644\) 0 0
\(645\) −4.18756 + 10.1097i −0.164885 + 0.398068i
\(646\) 0 0
\(647\) 33.8051 + 33.8051i 1.32902 + 1.32902i 0.906230 + 0.422786i \(0.138948\pi\)
0.422786 + 0.906230i \(0.361052\pi\)
\(648\) 0 0
\(649\) 1.76308 1.76308i 0.0692068 0.0692068i
\(650\) 0 0
\(651\) −27.8452 11.5338i −1.09134 0.452047i
\(652\) 0 0
\(653\) −12.1078 29.2307i −0.473813 1.14389i −0.962465 0.271407i \(-0.912511\pi\)
0.488652 0.872479i \(-0.337489\pi\)
\(654\) 0 0
\(655\) 63.9032i 2.49690i
\(656\) 0 0
\(657\) 6.18512i 0.241304i
\(658\) 0 0
\(659\) 0.896470 + 2.16427i 0.0349215 + 0.0843080i 0.940378 0.340131i \(-0.110471\pi\)
−0.905457 + 0.424439i \(0.860471\pi\)
\(660\) 0 0
\(661\) −24.9607 10.3391i −0.970859 0.402143i −0.159827 0.987145i \(-0.551094\pi\)
−0.811032 + 0.585002i \(0.801094\pi\)
\(662\) 0 0
\(663\) 17.4728 17.4728i 0.678586 0.678586i
\(664\) 0 0
\(665\) 9.27732 + 9.27732i 0.359759 + 0.359759i
\(666\) 0 0
\(667\) 0.0662948 0.160050i 0.00256695 0.00619715i
\(668\) 0 0
\(669\) 1.79112 0.741907i 0.0692487 0.0286838i
\(670\) 0 0
\(671\) 1.38581 0.0534986
\(672\) 0 0
\(673\) −29.0320 −1.11910 −0.559550 0.828797i \(-0.689026\pi\)
−0.559550 + 0.828797i \(0.689026\pi\)
\(674\) 0 0
\(675\) 7.01532 2.90584i 0.270020 0.111846i
\(676\) 0 0
\(677\) 4.97128 12.0017i 0.191062 0.461264i −0.799099 0.601200i \(-0.794690\pi\)
0.990161 + 0.139936i \(0.0446897\pi\)
\(678\) 0 0
\(679\) 25.3807 + 25.3807i 0.974023 + 0.974023i
\(680\) 0 0
\(681\) 15.1947 15.1947i 0.582264 0.582264i
\(682\) 0 0
\(683\) −31.6243 13.0992i −1.21007 0.501227i −0.315830 0.948816i \(-0.602283\pi\)
−0.894239 + 0.447589i \(0.852283\pi\)
\(684\) 0 0
\(685\) −8.01980 19.3615i −0.306421 0.739765i
\(686\) 0 0
\(687\) 24.0739i 0.918478i
\(688\) 0 0
\(689\) 58.7582i 2.23851i
\(690\) 0 0
\(691\) 4.38682 + 10.5907i 0.166883 + 0.402890i 0.985092 0.172031i \(-0.0550328\pi\)
−0.818209 + 0.574921i \(0.805033\pi\)
\(692\) 0 0
\(693\) 1.47856 + 0.612439i 0.0561658 + 0.0232646i
\(694\) 0 0
\(695\) 46.6356 46.6356i 1.76899 1.76899i
\(696\) 0 0
\(697\) 6.62079 + 6.62079i 0.250780 + 0.250780i
\(698\) 0 0
\(699\) −4.09395 + 9.88366i −0.154847 + 0.373834i
\(700\) 0 0
\(701\) 1.31276 0.543761i 0.0495821 0.0205376i −0.357755 0.933816i \(-0.616458\pi\)
0.407337 + 0.913278i \(0.366458\pi\)
\(702\) 0 0
\(703\) −7.35469 −0.277387
\(704\) 0 0
\(705\) 2.53967 0.0956496
\(706\) 0 0
\(707\) 16.3107 6.75611i 0.613427 0.254090i
\(708\) 0 0
\(709\) 2.19698 5.30398i 0.0825094 0.199195i −0.877241 0.480051i \(-0.840618\pi\)
0.959750 + 0.280856i \(0.0906182\pi\)
\(710\) 0 0
\(711\) −6.69594 6.69594i −0.251117 0.251117i
\(712\) 0 0
\(713\) 6.33769 6.33769i 0.237348 0.237348i
\(714\) 0 0
\(715\) −7.75782 3.21340i −0.290126 0.120174i
\(716\) 0 0
\(717\) 8.06142 + 19.4620i 0.301059 + 0.726822i
\(718\) 0 0
\(719\) 7.05462i 0.263093i −0.991310 0.131547i \(-0.958006\pi\)
0.991310 0.131547i \(-0.0419943\pi\)
\(720\) 0 0
\(721\) 14.8952i 0.554726i
\(722\) 0 0
\(723\) −9.25928 22.3539i −0.344356 0.831349i
\(724\) 0 0
\(725\) 1.16266 + 0.481591i 0.0431803 + 0.0178859i
\(726\) 0 0
\(727\) −6.68778 + 6.68778i −0.248036 + 0.248036i −0.820164 0.572128i \(-0.806118\pi\)
0.572128 + 0.820164i \(0.306118\pi\)
\(728\) 0 0
\(729\) −0.707107 0.707107i −0.0261891 0.0261891i
\(730\) 0 0
\(731\) −5.61067 + 13.5453i −0.207518 + 0.500993i
\(732\) 0 0
\(733\) −1.39035 + 0.575901i −0.0513537 + 0.0212714i −0.408212 0.912887i \(-0.633848\pi\)
0.356859 + 0.934158i \(0.383848\pi\)
\(734\) 0 0
\(735\) 19.0034 0.700950
\(736\) 0 0
\(737\) −2.65818 −0.0979152
\(738\) 0 0
\(739\) 4.78590 1.98239i 0.176052 0.0729233i −0.292916 0.956138i \(-0.594626\pi\)
0.468969 + 0.883215i \(0.344626\pi\)
\(740\) 0 0
\(741\) −2.09189 + 5.05026i −0.0768474 + 0.185526i
\(742\) 0 0
\(743\) 5.78338 + 5.78338i 0.212172 + 0.212172i 0.805189 0.593018i \(-0.202064\pi\)
−0.593018 + 0.805189i \(0.702064\pi\)
\(744\) 0 0
\(745\) −20.7943 + 20.7943i −0.761844 + 0.761844i
\(746\) 0 0
\(747\) −6.88522 2.85195i −0.251917 0.104347i
\(748\) 0 0
\(749\) −0.612028 1.47757i −0.0223630 0.0539891i
\(750\) 0 0
\(751\) 16.4504i 0.600283i −0.953895 0.300141i \(-0.902966\pi\)
0.953895 0.300141i \(-0.0970338\pi\)
\(752\) 0 0
\(753\) 0.184821i 0.00673524i
\(754\) 0 0
\(755\) 16.0297 + 38.6991i 0.583380 + 1.40840i
\(756\) 0 0
\(757\) −6.29845 2.60890i −0.228921 0.0948222i 0.265275 0.964173i \(-0.414537\pi\)
−0.494196 + 0.869351i \(0.664537\pi\)
\(758\) 0 0
\(759\) −0.336527 + 0.336527i −0.0122151 + 0.0122151i
\(760\) 0 0
\(761\) −8.75540 8.75540i −0.317383 0.317383i 0.530378 0.847761i \(-0.322050\pi\)
−0.847761 + 0.530378i \(0.822050\pi\)
\(762\) 0 0
\(763\) −6.95890 + 16.8003i −0.251929 + 0.608211i
\(764\) 0 0
\(765\) 15.5887 6.45704i 0.563610 0.233455i
\(766\) 0 0
\(767\) 28.4602 1.02764
\(768\) 0 0
\(769\) 31.9426 1.15188 0.575940 0.817492i \(-0.304636\pi\)
0.575940 + 0.817492i \(0.304636\pi\)
\(770\) 0 0
\(771\) 27.4817 11.3833i 0.989729 0.409959i
\(772\) 0 0
\(773\) −11.4245 + 27.5812i −0.410911 + 0.992027i 0.573983 + 0.818867i \(0.305398\pi\)
−0.984894 + 0.173159i \(0.944602\pi\)
\(774\) 0 0
\(775\) 46.0394 + 46.0394i 1.65379 + 1.65379i
\(776\) 0 0
\(777\) −17.3790 + 17.3790i −0.623468 + 0.623468i
\(778\) 0 0
\(779\) −1.91365 0.792659i −0.0685636 0.0284000i
\(780\) 0 0
\(781\) −2.03550 4.91414i −0.0728360 0.175842i
\(782\) 0 0
\(783\) 0.165732i 0.00592278i
\(784\) 0 0
\(785\) 4.34850i 0.155205i
\(786\) 0 0
\(787\) −4.33415 10.4636i −0.154496 0.372986i 0.827613 0.561299i \(-0.189698\pi\)
−0.982109 + 0.188313i \(0.939698\pi\)
\(788\) 0 0
\(789\) 0.276038 + 0.114338i 0.00982720 + 0.00407056i
\(790\) 0 0
\(791\) 16.4909 16.4909i 0.586349 0.586349i
\(792\) 0 0
\(793\) 11.1851 + 11.1851i 0.397195 + 0.397195i
\(794\) 0 0
\(795\) −15.3541 + 37.0682i −0.544555 + 1.31467i
\(796\) 0 0
\(797\) −46.7451 + 19.3624i −1.65580 + 0.685853i −0.997745 0.0671211i \(-0.978619\pi\)
−0.658050 + 0.752974i \(0.728619\pi\)
\(798\)