Properties

Label 384.2.n.a.337.8
Level $384$
Weight $2$
Character 384.337
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 337.8
Character \(\chi\) \(=\) 384.337
Dual form 384.2.n.a.49.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923880 + 0.382683i) q^{3} +(1.36206 + 3.28830i) q^{5} +(2.73097 - 2.73097i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(0.923880 + 0.382683i) q^{3} +(1.36206 + 3.28830i) q^{5} +(2.73097 - 2.73097i) q^{7} +(0.707107 + 0.707107i) q^{9} +(-3.01609 + 1.24931i) q^{11} +(0.932498 - 2.25125i) q^{13} +3.55923i q^{15} +0.517450i q^{17} +(-1.52739 + 3.68744i) q^{19} +(3.56818 - 1.47799i) q^{21} +(-2.39792 - 2.39792i) q^{23} +(-5.42220 + 5.42220i) q^{25} +(0.382683 + 0.923880i) q^{27} +(7.09056 + 2.93701i) q^{29} +1.50132 q^{31} -3.26460 q^{33} +(12.7000 + 5.26051i) q^{35} +(-3.40814 - 8.22797i) q^{37} +(1.72303 - 1.72303i) q^{39} +(-3.21656 - 3.21656i) q^{41} +(1.31346 - 0.544054i) q^{43} +(-1.36206 + 3.28830i) q^{45} -4.67448i q^{47} -7.91635i q^{49} +(-0.198019 + 0.478061i) q^{51} +(-4.19534 + 1.73777i) q^{53} +(-8.21621 - 8.21621i) q^{55} +(-2.82224 + 2.82224i) q^{57} +(0.680868 + 1.64376i) q^{59} +(6.71487 + 2.78139i) q^{61} +3.86217 q^{63} +8.67291 q^{65} +(-11.1312 - 4.61070i) q^{67} +(-1.29774 - 3.13303i) q^{69} +(-1.86620 + 1.86620i) q^{71} +(-9.06859 - 9.06859i) q^{73} +(-7.08445 + 2.93447i) q^{75} +(-4.82504 + 11.6487i) q^{77} +10.4412i q^{79} +1.00000i q^{81} +(1.89340 - 4.57106i) q^{83} +(-1.70153 + 0.704798i) q^{85} +(5.42688 + 5.42688i) q^{87} +(-2.70762 + 2.70762i) q^{89} +(-3.60147 - 8.69471i) q^{91} +(1.38704 + 0.574529i) q^{93} -14.2058 q^{95} +3.73293 q^{97} +(-3.01609 - 1.24931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(1\)

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
\(5\) 1.36206 + 3.28830i 0.609132 + 1.47057i 0.863946 + 0.503584i \(0.167986\pi\)
−0.254814 + 0.966990i \(0.582014\pi\)
\(6\) 0 0
\(7\) 2.73097 2.73097i 1.03221 1.03221i 0.0327442 0.999464i \(-0.489575\pi\)
0.999464 0.0327442i \(-0.0104247\pi\)
\(8\) 0 0
\(9\) 0.707107 + 0.707107i 0.235702 + 0.235702i
\(10\) 0 0
\(11\) −3.01609 + 1.24931i −0.909387 + 0.376680i −0.787822 0.615903i \(-0.788791\pi\)
−0.121565 + 0.992583i \(0.538791\pi\)
\(12\) 0 0
\(13\) 0.932498 2.25125i 0.258628 0.624384i −0.740220 0.672365i \(-0.765279\pi\)
0.998848 + 0.0479806i \(0.0152786\pi\)
\(14\) 0 0
\(15\) 3.55923i 0.918990i
\(16\) 0 0
\(17\) 0.517450i 0.125500i 0.998029 + 0.0627500i \(0.0199871\pi\)
−0.998029 + 0.0627500i \(0.980013\pi\)
\(18\) 0 0
\(19\) −1.52739 + 3.68744i −0.350407 + 0.845956i 0.646163 + 0.763199i \(0.276373\pi\)
−0.996570 + 0.0827570i \(0.973627\pi\)
\(20\) 0 0
\(21\) 3.56818 1.47799i 0.778640 0.322523i
\(22\) 0 0
\(23\) −2.39792 2.39792i −0.500000 0.500000i 0.411438 0.911438i \(-0.365027\pi\)
−0.911438 + 0.411438i \(0.865027\pi\)
\(24\) 0 0
\(25\) −5.42220 + 5.42220i −1.08444 + 1.08444i
\(26\) 0 0
\(27\) 0.382683 + 0.923880i 0.0736475 + 0.177801i
\(28\) 0 0
\(29\) 7.09056 + 2.93701i 1.31668 + 0.545389i 0.926828 0.375487i \(-0.122524\pi\)
0.389857 + 0.920875i \(0.372524\pi\)
\(30\) 0 0
\(31\) 1.50132 0.269644 0.134822 0.990870i \(-0.456954\pi\)
0.134822 + 0.990870i \(0.456954\pi\)
\(32\) 0 0
\(33\) −3.26460 −0.568293
\(34\) 0 0
\(35\) 12.7000 + 5.26051i 2.14669 + 0.889188i
\(36\) 0 0
\(37\) −3.40814 8.22797i −0.560294 1.35267i −0.909531 0.415635i \(-0.863559\pi\)
0.349237 0.937034i \(-0.386441\pi\)
\(38\) 0 0
\(39\) 1.72303 1.72303i 0.275906 0.275906i
\(40\) 0 0
\(41\) −3.21656 3.21656i −0.502342 0.502342i 0.409823 0.912165i \(-0.365590\pi\)
−0.912165 + 0.409823i \(0.865590\pi\)
\(42\) 0 0
\(43\) 1.31346 0.544054i 0.200301 0.0829675i −0.280278 0.959919i \(-0.590427\pi\)
0.480579 + 0.876951i \(0.340427\pi\)
\(44\) 0 0
\(45\) −1.36206 + 3.28830i −0.203044 + 0.490191i
\(46\) 0 0
\(47\) 4.67448i 0.681843i −0.940092 0.340921i \(-0.889261\pi\)
0.940092 0.340921i \(-0.110739\pi\)
\(48\) 0 0
\(49\) 7.91635i 1.13091i
\(50\) 0 0
\(51\) −0.198019 + 0.478061i −0.0277283 + 0.0669419i
\(52\) 0 0
\(53\) −4.19534 + 1.73777i −0.576275 + 0.238701i −0.651733 0.758448i \(-0.725958\pi\)
0.0754586 + 0.997149i \(0.475958\pi\)
\(54\) 0 0
\(55\) −8.21621 8.21621i −1.10787 1.10787i
\(56\) 0 0
\(57\) −2.82224 + 2.82224i −0.373815 + 0.373815i
\(58\) 0 0
\(59\) 0.680868 + 1.64376i 0.0886415 + 0.213999i 0.961983 0.273109i \(-0.0880518\pi\)
−0.873342 + 0.487108i \(0.838052\pi\)
\(60\) 0 0
\(61\) 6.71487 + 2.78139i 0.859751 + 0.356121i 0.768610 0.639717i \(-0.220949\pi\)
0.0911409 + 0.995838i \(0.470949\pi\)
\(62\) 0 0
\(63\) 3.86217 0.486587
\(64\) 0 0
\(65\) 8.67291 1.07574
\(66\) 0 0
\(67\) −11.1312 4.61070i −1.35989 0.563286i −0.420864 0.907124i \(-0.638273\pi\)
−0.939029 + 0.343837i \(0.888273\pi\)
\(68\) 0 0
\(69\) −1.29774 3.13303i −0.156230 0.377172i
\(70\) 0 0
\(71\) −1.86620 + 1.86620i −0.221477 + 0.221477i −0.809120 0.587643i \(-0.800056\pi\)
0.587643 + 0.809120i \(0.300056\pi\)
\(72\) 0 0
\(73\) −9.06859 9.06859i −1.06140 1.06140i −0.997988 0.0634101i \(-0.979802\pi\)
−0.0634101 0.997988i \(-0.520198\pi\)
\(74\) 0 0
\(75\) −7.08445 + 2.93447i −0.818042 + 0.338844i
\(76\) 0 0
\(77\) −4.82504 + 11.6487i −0.549864 + 1.32749i
\(78\) 0 0
\(79\) 10.4412i 1.17473i 0.809323 + 0.587364i \(0.199834\pi\)
−0.809323 + 0.587364i \(0.800166\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 1.89340 4.57106i 0.207827 0.501739i −0.785253 0.619175i \(-0.787467\pi\)
0.993081 + 0.117435i \(0.0374673\pi\)
\(84\) 0 0
\(85\) −1.70153 + 0.704798i −0.184557 + 0.0764460i
\(86\) 0 0
\(87\) 5.42688 + 5.42688i 0.581823 + 0.581823i
\(88\) 0 0
\(89\) −2.70762 + 2.70762i −0.287007 + 0.287007i −0.835896 0.548888i \(-0.815051\pi\)
0.548888 + 0.835896i \(0.315051\pi\)
\(90\) 0 0
\(91\) −3.60147 8.69471i −0.377536 0.911453i
\(92\) 0 0
\(93\) 1.38704 + 0.574529i 0.143829 + 0.0595759i
\(94\) 0 0
\(95\) −14.2058 −1.45749
\(96\) 0 0
\(97\) 3.73293 0.379022 0.189511 0.981879i \(-0.439310\pi\)
0.189511 + 0.981879i \(0.439310\pi\)
\(98\) 0 0
\(99\) −3.01609 1.24931i −0.303129 0.125560i
\(100\) 0 0
\(101\) −6.36949 15.3773i −0.633788 1.53010i −0.834824 0.550517i \(-0.814431\pi\)
0.201036 0.979584i \(-0.435569\pi\)
\(102\) 0 0
\(103\) 7.42244 7.42244i 0.731355 0.731355i −0.239533 0.970888i \(-0.576994\pi\)
0.970888 + 0.239533i \(0.0769944\pi\)
\(104\) 0 0
\(105\) 9.72015 + 9.72015i 0.948589 + 0.948589i
\(106\) 0 0
\(107\) −7.85343 + 3.25300i −0.759220 + 0.314479i −0.728497 0.685049i \(-0.759781\pi\)
−0.0307226 + 0.999528i \(0.509781\pi\)
\(108\) 0 0
\(109\) 3.33028 8.04001i 0.318983 0.770094i −0.680325 0.732910i \(-0.738161\pi\)
0.999308 0.0371832i \(-0.0118385\pi\)
\(110\) 0 0
\(111\) 8.90589i 0.845310i
\(112\) 0 0
\(113\) 17.4463i 1.64121i −0.571494 0.820606i \(-0.693636\pi\)
0.571494 0.820606i \(-0.306364\pi\)
\(114\) 0 0
\(115\) 4.61897 11.1512i 0.430721 1.03985i
\(116\) 0 0
\(117\) 2.25125 0.932498i 0.208128 0.0862095i
\(118\) 0 0
\(119\) 1.41314 + 1.41314i 0.129542 + 0.129542i
\(120\) 0 0
\(121\) −0.242116 + 0.242116i −0.0220105 + 0.0220105i
\(122\) 0 0
\(123\) −1.74079 4.20263i −0.156962 0.378939i
\(124\) 0 0
\(125\) −8.77369 3.63418i −0.784743 0.325051i
\(126\) 0 0
\(127\) −1.84791 −0.163975 −0.0819876 0.996633i \(-0.526127\pi\)
−0.0819876 + 0.996633i \(0.526127\pi\)
\(128\) 0 0
\(129\) 1.42168 0.125172
\(130\) 0 0
\(131\) 7.59353 + 3.14534i 0.663450 + 0.274810i 0.688889 0.724866i \(-0.258099\pi\)
−0.0254395 + 0.999676i \(0.508099\pi\)
\(132\) 0 0
\(133\) 5.89902 + 14.2415i 0.511510 + 1.23490i
\(134\) 0 0
\(135\) −2.51676 + 2.51676i −0.216608 + 0.216608i
\(136\) 0 0
\(137\) 7.98582 + 7.98582i 0.682274 + 0.682274i 0.960512 0.278238i \(-0.0897503\pi\)
−0.278238 + 0.960512i \(0.589750\pi\)
\(138\) 0 0
\(139\) −1.52261 + 0.630686i −0.129146 + 0.0534941i −0.446321 0.894873i \(-0.647266\pi\)
0.317174 + 0.948367i \(0.397266\pi\)
\(140\) 0 0
\(141\) 1.78885 4.31865i 0.150648 0.363696i
\(142\) 0 0
\(143\) 7.95496i 0.665227i
\(144\) 0 0
\(145\) 27.3163i 2.26850i
\(146\) 0 0
\(147\) 3.02945 7.31375i 0.249865 0.603228i
\(148\) 0 0
\(149\) −3.85004 + 1.59474i −0.315408 + 0.130646i −0.534771 0.844997i \(-0.679602\pi\)
0.219363 + 0.975643i \(0.429602\pi\)
\(150\) 0 0
\(151\) 0.409447 + 0.409447i 0.0333203 + 0.0333203i 0.723571 0.690250i \(-0.242500\pi\)
−0.690250 + 0.723571i \(0.742500\pi\)
\(152\) 0 0
\(153\) −0.365892 + 0.365892i −0.0295806 + 0.0295806i
\(154\) 0 0
\(155\) 2.04488 + 4.93678i 0.164249 + 0.396532i
\(156\) 0 0
\(157\) −12.1456 5.03087i −0.969324 0.401507i −0.158864 0.987301i \(-0.550783\pi\)
−0.810461 + 0.585793i \(0.800783\pi\)
\(158\) 0 0
\(159\) −4.54101 −0.360125
\(160\) 0 0
\(161\) −13.0973 −1.03221
\(162\) 0 0
\(163\) 15.6056 + 6.46405i 1.22233 + 0.506304i 0.898148 0.439693i \(-0.144913\pi\)
0.324177 + 0.945996i \(0.394913\pi\)
\(164\) 0 0
\(165\) −4.44658 10.7350i −0.346166 0.835718i
\(166\) 0 0
\(167\) 3.65825 3.65825i 0.283084 0.283084i −0.551254 0.834338i \(-0.685850\pi\)
0.834338 + 0.551254i \(0.185850\pi\)
\(168\) 0 0
\(169\) 4.99382 + 4.99382i 0.384140 + 0.384140i
\(170\) 0 0
\(171\) −3.68744 + 1.52739i −0.281985 + 0.116802i
\(172\) 0 0
\(173\) −4.69766 + 11.3412i −0.357156 + 0.862252i 0.638541 + 0.769588i \(0.279538\pi\)
−0.995697 + 0.0926640i \(0.970462\pi\)
\(174\) 0 0
\(175\) 29.6157i 2.23874i
\(176\) 0 0
\(177\) 1.77919i 0.133732i
\(178\) 0 0
\(179\) −2.26551 + 5.46943i −0.169332 + 0.408804i −0.985651 0.168798i \(-0.946011\pi\)
0.816318 + 0.577602i \(0.196011\pi\)
\(180\) 0 0
\(181\) −14.5765 + 6.03777i −1.08346 + 0.448784i −0.851722 0.523994i \(-0.824441\pi\)
−0.231738 + 0.972778i \(0.574441\pi\)
\(182\) 0 0
\(183\) 5.13934 + 5.13934i 0.379911 + 0.379911i
\(184\) 0 0
\(185\) 22.4140 22.4140i 1.64791 1.64791i
\(186\) 0 0
\(187\) −0.646454 1.56068i −0.0472734 0.114128i
\(188\) 0 0
\(189\) 3.56818 + 1.47799i 0.259547 + 0.107508i
\(190\) 0 0
\(191\) 12.3765 0.895535 0.447768 0.894150i \(-0.352219\pi\)
0.447768 + 0.894150i \(0.352219\pi\)
\(192\) 0 0
\(193\) 21.9343 1.57887 0.789434 0.613835i \(-0.210374\pi\)
0.789434 + 0.613835i \(0.210374\pi\)
\(194\) 0 0
\(195\) 8.01273 + 3.31898i 0.573803 + 0.237677i
\(196\) 0 0
\(197\) 6.52756 + 15.7589i 0.465070 + 1.12278i 0.966290 + 0.257458i \(0.0828847\pi\)
−0.501220 + 0.865320i \(0.667115\pi\)
\(198\) 0 0
\(199\) −5.80270 + 5.80270i −0.411343 + 0.411343i −0.882206 0.470863i \(-0.843942\pi\)
0.470863 + 0.882206i \(0.343942\pi\)
\(200\) 0 0
\(201\) −8.51946 8.51946i −0.600916 0.600916i
\(202\) 0 0
\(203\) 27.3850 11.3432i 1.92205 0.796138i
\(204\) 0 0
\(205\) 6.19587 14.9582i 0.432738 1.04472i
\(206\) 0 0
\(207\) 3.39117i 0.235702i
\(208\) 0 0
\(209\) 13.0298i 0.901293i
\(210\) 0 0
\(211\) −7.65444 + 18.4794i −0.526953 + 1.27218i 0.406557 + 0.913626i \(0.366729\pi\)
−0.933510 + 0.358552i \(0.883271\pi\)
\(212\) 0 0
\(213\) −2.43831 + 1.00998i −0.167070 + 0.0692026i
\(214\) 0 0
\(215\) 3.57803 + 3.57803i 0.244020 + 0.244020i
\(216\) 0 0
\(217\) 4.10004 4.10004i 0.278329 0.278329i
\(218\) 0 0
\(219\) −4.90788 11.8487i −0.331644 0.800659i
\(220\) 0 0
\(221\) 1.16491 + 0.482521i 0.0783602 + 0.0324579i
\(222\) 0 0
\(223\) 29.0773 1.94716 0.973580 0.228346i \(-0.0733317\pi\)
0.973580 + 0.228346i \(0.0733317\pi\)
\(224\) 0 0
\(225\) −7.66815 −0.511210
\(226\) 0 0
\(227\) −23.2583 9.63391i −1.54371 0.639425i −0.561544 0.827447i \(-0.689792\pi\)
−0.982165 + 0.188022i \(0.939792\pi\)
\(228\) 0 0
\(229\) 2.92749 + 7.06760i 0.193454 + 0.467040i 0.990607 0.136737i \(-0.0436616\pi\)
−0.797153 + 0.603777i \(0.793662\pi\)
\(230\) 0 0
\(231\) −8.91550 + 8.91550i −0.586597 + 0.586597i
\(232\) 0 0
\(233\) 13.0873 + 13.0873i 0.857375 + 0.857375i 0.991028 0.133653i \(-0.0426708\pi\)
−0.133653 + 0.991028i \(0.542671\pi\)
\(234\) 0 0
\(235\) 15.3711 6.36692i 1.00270 0.415332i
\(236\) 0 0
\(237\) −3.99568 + 9.64642i −0.259547 + 0.626602i
\(238\) 0 0
\(239\) 4.10909i 0.265795i −0.991130 0.132897i \(-0.957572\pi\)
0.991130 0.132897i \(-0.0424281\pi\)
\(240\) 0 0
\(241\) 14.2144i 0.915632i 0.889047 + 0.457816i \(0.151368\pi\)
−0.889047 + 0.457816i \(0.848632\pi\)
\(242\) 0 0
\(243\) −0.382683 + 0.923880i −0.0245492 + 0.0592669i
\(244\) 0 0
\(245\) 26.0314 10.7825i 1.66308 0.688871i
\(246\) 0 0
\(247\) 6.87706 + 6.87706i 0.437577 + 0.437577i
\(248\) 0 0
\(249\) 3.49854 3.49854i 0.221711 0.221711i
\(250\) 0 0
\(251\) −2.36893 5.71910i −0.149525 0.360986i 0.831314 0.555803i \(-0.187589\pi\)
−0.980840 + 0.194816i \(0.937589\pi\)
\(252\) 0 0
\(253\) 10.2281 + 4.23661i 0.643034 + 0.266353i
\(254\) 0 0
\(255\) −1.84172 −0.115333
\(256\) 0 0
\(257\) −8.28191 −0.516612 −0.258306 0.966063i \(-0.583164\pi\)
−0.258306 + 0.966063i \(0.583164\pi\)
\(258\) 0 0
\(259\) −31.7778 13.1628i −1.97458 0.817896i
\(260\) 0 0
\(261\) 2.93701 + 7.09056i 0.181796 + 0.438895i
\(262\) 0 0
\(263\) −15.4068 + 15.4068i −0.950023 + 0.950023i −0.998809 0.0487861i \(-0.984465\pi\)
0.0487861 + 0.998809i \(0.484465\pi\)
\(264\) 0 0
\(265\) −11.4286 11.4286i −0.702055 0.702055i
\(266\) 0 0
\(267\) −3.53768 + 1.46535i −0.216502 + 0.0896782i
\(268\) 0 0
\(269\) −3.09893 + 7.48148i −0.188945 + 0.456154i −0.989757 0.142762i \(-0.954402\pi\)
0.800812 + 0.598916i \(0.204402\pi\)
\(270\) 0 0
\(271\) 28.7832i 1.74846i −0.485515 0.874228i \(-0.661368\pi\)
0.485515 0.874228i \(-0.338632\pi\)
\(272\) 0 0
\(273\) 9.41108i 0.569585i
\(274\) 0 0
\(275\) 9.57988 23.1279i 0.577688 1.39466i
\(276\) 0 0
\(277\) −12.1515 + 5.03333i −0.730115 + 0.302424i −0.716599 0.697485i \(-0.754302\pi\)
−0.0135158 + 0.999909i \(0.504302\pi\)
\(278\) 0 0
\(279\) 1.06159 + 1.06159i 0.0635558 + 0.0635558i
\(280\) 0 0
\(281\) −21.6306 + 21.6306i −1.29037 + 1.29037i −0.355820 + 0.934555i \(0.615798\pi\)
−0.934555 + 0.355820i \(0.884202\pi\)
\(282\) 0 0
\(283\) 11.4777 + 27.7097i 0.682281 + 1.64717i 0.759781 + 0.650179i \(0.225306\pi\)
−0.0775002 + 0.996992i \(0.524694\pi\)
\(284\) 0 0
\(285\) −13.1245 5.43633i −0.777426 0.322020i
\(286\) 0 0
\(287\) −17.5686 −1.03704
\(288\) 0 0
\(289\) 16.7322 0.984250
\(290\) 0 0
\(291\) 3.44878 + 1.42853i 0.202171 + 0.0837420i
\(292\) 0 0
\(293\) −1.84257 4.44836i −0.107644 0.259876i 0.860874 0.508818i \(-0.169917\pi\)
−0.968519 + 0.248942i \(0.919917\pi\)
\(294\) 0 0
\(295\) −4.47780 + 4.47780i −0.260708 + 0.260708i
\(296\) 0 0
\(297\) −2.30842 2.30842i −0.133948 0.133948i
\(298\) 0 0
\(299\) −7.63436 + 3.16226i −0.441507 + 0.182878i
\(300\) 0 0
\(301\) 2.10123 5.07282i 0.121113 0.292392i
\(302\) 0 0
\(303\) 16.6443i 0.956190i
\(304\) 0 0
\(305\) 25.8690i 1.48125i
\(306\) 0 0
\(307\) −11.7403 + 28.3435i −0.670052 + 1.61765i 0.111467 + 0.993768i \(0.464445\pi\)
−0.781519 + 0.623881i \(0.785555\pi\)
\(308\) 0 0
\(309\) 9.69789 4.01700i 0.551694 0.228519i
\(310\) 0 0
\(311\) −11.6121 11.6121i −0.658459 0.658459i 0.296556 0.955015i \(-0.404162\pi\)
−0.955015 + 0.296556i \(0.904162\pi\)
\(312\) 0 0
\(313\) −6.84409 + 6.84409i −0.386851 + 0.386851i −0.873563 0.486712i \(-0.838196\pi\)
0.486712 + 0.873563i \(0.338196\pi\)
\(314\) 0 0
\(315\) 5.26051 + 12.7000i 0.296396 + 0.715563i
\(316\) 0 0
\(317\) −23.6795 9.80835i −1.32997 0.550892i −0.399324 0.916810i \(-0.630755\pi\)
−0.930647 + 0.365918i \(0.880755\pi\)
\(318\) 0 0
\(319\) −25.0550 −1.40281
\(320\) 0 0
\(321\) −8.50049 −0.474451
\(322\) 0 0
\(323\) −1.90806 0.790346i −0.106167 0.0439760i
\(324\) 0 0
\(325\) 7.15054 + 17.2629i 0.396640 + 0.957575i
\(326\) 0 0
\(327\) 6.15356 6.15356i 0.340293 0.340293i
\(328\) 0 0
\(329\) −12.7658 12.7658i −0.703803 0.703803i
\(330\) 0 0
\(331\) 21.7107 8.99285i 1.19333 0.494292i 0.304489 0.952516i \(-0.401514\pi\)
0.888837 + 0.458224i \(0.151514\pi\)
\(332\) 0 0
\(333\) 3.40814 8.22797i 0.186765 0.450890i
\(334\) 0 0
\(335\) 42.8828i 2.34294i
\(336\) 0 0
\(337\) 24.2394i 1.32040i −0.751088 0.660202i \(-0.770471\pi\)
0.751088 0.660202i \(-0.229529\pi\)
\(338\) 0 0
\(339\) 6.67642 16.1183i 0.362613 0.875426i
\(340\) 0 0
\(341\) −4.52811 + 1.87561i −0.245211 + 0.101570i
\(342\) 0 0
\(343\) −2.50251 2.50251i −0.135123 0.135123i
\(344\) 0 0
\(345\) 8.53475 8.53475i 0.459495 0.459495i
\(346\) 0 0
\(347\) 1.42236 + 3.43389i 0.0763565 + 0.184341i 0.957449 0.288604i \(-0.0931910\pi\)
−0.881092 + 0.472945i \(0.843191\pi\)
\(348\) 0 0
\(349\) 3.17452 + 1.31493i 0.169928 + 0.0703866i 0.466026 0.884771i \(-0.345685\pi\)
−0.296098 + 0.955158i \(0.595685\pi\)
\(350\) 0 0
\(351\) 2.43674 0.130063
\(352\) 0 0
\(353\) −7.88845 −0.419860 −0.209930 0.977716i \(-0.567324\pi\)
−0.209930 + 0.977716i \(0.567324\pi\)
\(354\) 0 0
\(355\) −8.67850 3.59475i −0.460607 0.190790i
\(356\) 0 0
\(357\) 0.764784 + 1.84635i 0.0404767 + 0.0977193i
\(358\) 0 0
\(359\) 2.60336 2.60336i 0.137400 0.137400i −0.635062 0.772462i \(-0.719025\pi\)
0.772462 + 0.635062i \(0.219025\pi\)
\(360\) 0 0
\(361\) 2.17074 + 2.17074i 0.114250 + 0.114250i
\(362\) 0 0
\(363\) −0.316339 + 0.131032i −0.0166035 + 0.00687740i
\(364\) 0 0
\(365\) 17.4683 42.1722i 0.914333 2.20740i
\(366\) 0 0
\(367\) 1.41682i 0.0739575i −0.999316 0.0369787i \(-0.988227\pi\)
0.999316 0.0369787i \(-0.0117734\pi\)
\(368\) 0 0
\(369\) 4.54890i 0.236806i
\(370\) 0 0
\(371\) −6.71155 + 16.2031i −0.348447 + 0.841224i
\(372\) 0 0
\(373\) 30.8483 12.7778i 1.59726 0.661609i 0.606239 0.795282i \(-0.292677\pi\)
0.991025 + 0.133674i \(0.0426774\pi\)
\(374\) 0 0
\(375\) −6.71510 6.71510i −0.346766 0.346766i
\(376\) 0 0
\(377\) 13.2239 13.2239i 0.681064 0.681064i
\(378\) 0 0
\(379\) 4.79982 + 11.5878i 0.246550 + 0.595224i 0.997907 0.0646720i \(-0.0206001\pi\)
−0.751357 + 0.659896i \(0.770600\pi\)
\(380\) 0 0
\(381\) −1.70724 0.707163i −0.0874647 0.0362291i
\(382\) 0 0
\(383\) 13.2502 0.677053 0.338527 0.940957i \(-0.390071\pi\)
0.338527 + 0.940957i \(0.390071\pi\)
\(384\) 0 0
\(385\) −44.8763 −2.28711
\(386\) 0 0
\(387\) 1.31346 + 0.544054i 0.0667671 + 0.0276558i
\(388\) 0 0
\(389\) −1.30717 3.15579i −0.0662762 0.160005i 0.887271 0.461248i \(-0.152598\pi\)
−0.953547 + 0.301243i \(0.902598\pi\)
\(390\) 0 0
\(391\) 1.24080 1.24080i 0.0627500 0.0627500i
\(392\) 0 0
\(393\) 5.81184 + 5.81184i 0.293168 + 0.293168i
\(394\) 0 0
\(395\) −34.3339 + 14.2215i −1.72752 + 0.715564i
\(396\) 0 0
\(397\) −2.75561 + 6.65262i −0.138300 + 0.333886i −0.977821 0.209441i \(-0.932836\pi\)
0.839521 + 0.543327i \(0.182836\pi\)
\(398\) 0 0
\(399\) 15.4149i 0.771710i
\(400\) 0 0
\(401\) 22.5969i 1.12844i 0.825626 + 0.564218i \(0.190822\pi\)
−0.825626 + 0.564218i \(0.809178\pi\)
\(402\) 0 0
\(403\) 1.39997 3.37984i 0.0697377 0.168362i
\(404\) 0 0
\(405\) −3.28830 + 1.36206i −0.163397 + 0.0676813i
\(406\) 0 0
\(407\) 20.5585 + 20.5585i 1.01905 + 1.01905i
\(408\) 0 0
\(409\) −3.48618 + 3.48618i −0.172380 + 0.172380i −0.788024 0.615644i \(-0.788896\pi\)
0.615644 + 0.788024i \(0.288896\pi\)
\(410\) 0 0
\(411\) 4.32189 + 10.4340i 0.213183 + 0.514670i
\(412\) 0 0
\(413\) 6.34848 + 2.62963i 0.312388 + 0.129395i
\(414\) 0 0
\(415\) 17.6100 0.864439
\(416\) 0 0
\(417\) −1.64806 −0.0807059
\(418\) 0 0
\(419\) −9.10369 3.77087i −0.444744 0.184219i 0.149061 0.988828i \(-0.452375\pi\)
−0.593805 + 0.804609i \(0.702375\pi\)
\(420\) 0 0
\(421\) −0.766817 1.85126i −0.0373724 0.0902249i 0.904091 0.427339i \(-0.140549\pi\)
−0.941464 + 0.337114i \(0.890549\pi\)
\(422\) 0 0
\(423\) 3.30535 3.30535i 0.160712 0.160712i
\(424\) 0 0
\(425\) −2.80572 2.80572i −0.136097 0.136097i
\(426\) 0 0
\(427\) 25.9340 10.7422i 1.25503 0.519851i
\(428\) 0 0
\(429\) −3.04423 + 7.34942i −0.146977 + 0.354834i
\(430\) 0 0
\(431\) 11.5510i 0.556394i 0.960524 + 0.278197i \(0.0897368\pi\)
−0.960524 + 0.278197i \(0.910263\pi\)
\(432\) 0 0
\(433\) 3.12797i 0.150321i 0.997171 + 0.0751603i \(0.0239468\pi\)
−0.997171 + 0.0751603i \(0.976053\pi\)
\(434\) 0 0
\(435\) −10.4535 + 25.2370i −0.501207 + 1.21002i
\(436\) 0 0
\(437\) 12.5047 5.17962i 0.598182 0.247775i
\(438\) 0 0
\(439\) −8.10867 8.10867i −0.387006 0.387006i 0.486612 0.873618i \(-0.338232\pi\)
−0.873618 + 0.486612i \(0.838232\pi\)
\(440\) 0 0
\(441\) 5.59770 5.59770i 0.266557 0.266557i
\(442\) 0 0
\(443\) −9.34973 22.5722i −0.444219 1.07244i −0.974454 0.224588i \(-0.927896\pi\)
0.530235 0.847851i \(-0.322104\pi\)
\(444\) 0 0
\(445\) −12.5914 5.21554i −0.596891 0.247240i
\(446\) 0 0
\(447\) −4.16726 −0.197105
\(448\) 0 0
\(449\) −28.6259 −1.35094 −0.675469 0.737388i \(-0.736059\pi\)
−0.675469 + 0.737388i \(0.736059\pi\)
\(450\) 0 0
\(451\) 13.7199 + 5.68297i 0.646045 + 0.267601i
\(452\) 0 0
\(453\) 0.221591 + 0.534968i 0.0104113 + 0.0251350i
\(454\) 0 0
\(455\) 23.6854 23.6854i 1.11039 1.11039i
\(456\) 0 0
\(457\) −18.7182 18.7182i −0.875602 0.875602i 0.117474 0.993076i \(-0.462520\pi\)
−0.993076 + 0.117474i \(0.962520\pi\)
\(458\) 0 0
\(459\) −0.478061 + 0.198019i −0.0223140 + 0.00924275i
\(460\) 0 0
\(461\) 2.60820 6.29674i 0.121476 0.293268i −0.851431 0.524467i \(-0.824265\pi\)
0.972907 + 0.231198i \(0.0742647\pi\)
\(462\) 0 0
\(463\) 5.96406i 0.277174i −0.990350 0.138587i \(-0.955744\pi\)
0.990350 0.138587i \(-0.0442560\pi\)
\(464\) 0 0
\(465\) 5.34354i 0.247801i
\(466\) 0 0
\(467\) −8.88493 + 21.4501i −0.411146 + 0.992593i 0.573685 + 0.819076i \(0.305513\pi\)
−0.984831 + 0.173518i \(0.944487\pi\)
\(468\) 0 0
\(469\) −42.9906 + 17.8073i −1.98512 + 0.822264i
\(470\) 0 0
\(471\) −9.29584 9.29584i −0.428330 0.428330i
\(472\) 0 0
\(473\) −3.28184 + 3.28184i −0.150899 + 0.150899i
\(474\) 0 0
\(475\) −11.7122 28.2758i −0.537394 1.29738i
\(476\) 0 0
\(477\) −4.19534 1.73777i −0.192092 0.0795669i
\(478\) 0 0
\(479\) 22.6413 1.03451 0.517254 0.855832i \(-0.326954\pi\)
0.517254 + 0.855832i \(0.326954\pi\)
\(480\) 0 0
\(481\) −21.7013 −0.989494
\(482\) 0 0
\(483\) −12.1003 5.01210i −0.550582 0.228059i
\(484\) 0 0
\(485\) 5.08448 + 12.2750i 0.230874 + 0.557380i
\(486\) 0 0
\(487\) −2.79015 + 2.79015i −0.126434 + 0.126434i −0.767492 0.641058i \(-0.778496\pi\)
0.641058 + 0.767492i \(0.278496\pi\)
\(488\) 0 0
\(489\) 11.9440 + 11.9440i 0.540127 + 0.540127i
\(490\) 0 0
\(491\) −19.9243 + 8.25292i −0.899172 + 0.372449i −0.783902 0.620885i \(-0.786773\pi\)
−0.115270 + 0.993334i \(0.536773\pi\)
\(492\) 0 0
\(493\) −1.51975 + 3.66901i −0.0684463 + 0.165244i
\(494\) 0 0
\(495\) 11.6195i 0.522256i
\(496\) 0 0
\(497\) 10.1930i 0.457221i
\(498\) 0 0
\(499\) 14.7704 35.6588i 0.661212 1.59631i −0.134695 0.990887i \(-0.543005\pi\)
0.795907 0.605419i \(-0.206995\pi\)
\(500\) 0 0
\(501\) 4.77973 1.97983i 0.213543 0.0884523i
\(502\) 0 0
\(503\) 26.5194 + 26.5194i 1.18244 + 1.18244i 0.979110 + 0.203333i \(0.0651773\pi\)
0.203333 + 0.979110i \(0.434823\pi\)
\(504\) 0 0
\(505\) 41.8897 41.8897i 1.86407 1.86407i
\(506\) 0 0
\(507\) 2.70263 + 6.52473i 0.120028 + 0.289774i
\(508\) 0 0
\(509\) 33.0361 + 13.6840i 1.46430 + 0.606534i 0.965551 0.260212i \(-0.0837926\pi\)
0.498750 + 0.866746i \(0.333793\pi\)
\(510\) 0 0
\(511\) −49.5320 −2.19117
\(512\) 0 0
\(513\) −3.99125 −0.176218
\(514\) 0 0
\(515\) 34.5171 + 14.2974i 1.52100 + 0.630020i
\(516\) 0 0
\(517\) 5.83986 + 14.0987i 0.256837 + 0.620059i
\(518\) 0 0
\(519\) −8.68014 + 8.68014i −0.381016 + 0.381016i
\(520\) 0 0
\(521\) −2.51581 2.51581i −0.110220 0.110220i 0.649846 0.760066i \(-0.274833\pi\)
−0.760066 + 0.649846i \(0.774833\pi\)
\(522\) 0 0
\(523\) −21.6449 + 8.96561i −0.946465 + 0.392039i −0.801901 0.597457i \(-0.796178\pi\)
−0.144564 + 0.989495i \(0.546178\pi\)
\(524\) 0 0
\(525\) −11.3334 + 27.3613i −0.494632 + 1.19415i
\(526\) 0 0
\(527\) 0.776856i 0.0338404i
\(528\) 0 0
\(529\) 11.5000i 0.500000i
\(530\) 0 0
\(531\) −0.680868 + 1.64376i −0.0295472 + 0.0713331i
\(532\) 0 0
\(533\) −10.2407 + 4.24184i −0.443574 + 0.183734i
\(534\) 0 0
\(535\) −21.3937 21.3937i −0.924930 0.924930i
\(536\) 0 0
\(537\) −4.18612 + 4.18612i −0.180644 + 0.180644i
\(538\) 0 0
\(539\) 9.88995 + 23.8764i 0.425990 + 1.02843i
\(540\) 0 0
\(541\) 9.88526 + 4.09461i 0.425001 + 0.176041i 0.584924 0.811088i \(-0.301125\pi\)
−0.159923 + 0.987130i \(0.551125\pi\)
\(542\) 0 0
\(543\) −15.7775 −0.677075
\(544\) 0 0
\(545\) 30.9741 1.32678
\(546\) 0 0
\(547\) 4.92501 + 2.04001i 0.210578 + 0.0872244i 0.485479 0.874248i \(-0.338645\pi\)
−0.274901 + 0.961473i \(0.588645\pi\)
\(548\) 0 0
\(549\) 2.78139 + 6.71487i 0.118707 + 0.286584i
\(550\) 0 0
\(551\) −21.6601 + 21.6601i −0.922750 + 0.922750i
\(552\) 0 0
\(553\) 28.5146 + 28.5146i 1.21256 + 1.21256i
\(554\) 0 0
\(555\) 29.2853 12.1304i 1.24309 0.514905i
\(556\) 0 0
\(557\) −1.88066 + 4.54032i −0.0796862 + 0.192380i −0.958702 0.284414i \(-0.908201\pi\)
0.879015 + 0.476793i \(0.158201\pi\)
\(558\) 0 0
\(559\) 3.46426i 0.146523i
\(560\) 0 0
\(561\) 1.68926i 0.0713208i
\(562\) 0 0
\(563\) 4.16303 10.0504i 0.175451 0.423575i −0.811552 0.584281i \(-0.801377\pi\)
0.987002 + 0.160705i \(0.0513768\pi\)
\(564\) 0 0
\(565\) 57.3688 23.7630i 2.41353 0.999715i
\(566\) 0 0
\(567\) 2.73097 + 2.73097i 0.114690 + 0.114690i
\(568\) 0 0
\(569\) −1.48801 + 1.48801i −0.0623805 + 0.0623805i −0.737609 0.675228i \(-0.764045\pi\)
0.675228 + 0.737609i \(0.264045\pi\)
\(570\) 0 0
\(571\) 10.9476 + 26.4299i 0.458145 + 1.10606i 0.969148 + 0.246480i \(0.0792740\pi\)
−0.511003 + 0.859579i \(0.670726\pi\)
\(572\) 0 0
\(573\) 11.4344 + 4.73630i 0.477680 + 0.197862i
\(574\) 0 0
\(575\) 26.0040 1.08444
\(576\) 0 0
\(577\) 28.1723 1.17283 0.586413 0.810012i \(-0.300539\pi\)
0.586413 + 0.810012i \(0.300539\pi\)
\(578\) 0 0
\(579\) 20.2647 + 8.39391i 0.842172 + 0.348839i
\(580\) 0 0
\(581\) −7.31261 17.6542i −0.303378 0.732420i
\(582\) 0 0
\(583\) 10.4825 10.4825i 0.434143 0.434143i
\(584\) 0 0
\(585\) 6.13268 + 6.13268i 0.253555 + 0.253555i
\(586\) 0 0
\(587\) 26.4589 10.9597i 1.09208 0.452353i 0.237347 0.971425i \(-0.423722\pi\)
0.854731 + 0.519072i \(0.173722\pi\)
\(588\) 0 0
\(589\) −2.29309 + 5.53601i −0.0944851 + 0.228107i
\(590\) 0 0
\(591\) 17.0573i 0.701645i
\(592\) 0 0
\(593\) 1.34616i 0.0552802i −0.999618 0.0276401i \(-0.991201\pi\)
0.999618 0.0276401i \(-0.00879924\pi\)
\(594\) 0 0
\(595\) −2.72205 + 6.57160i −0.111593 + 0.269409i
\(596\) 0 0
\(597\) −7.58160 + 3.14040i −0.310294 + 0.128528i
\(598\) 0 0
\(599\) 8.34761 + 8.34761i 0.341074 + 0.341074i 0.856771 0.515697i \(-0.172467\pi\)
−0.515697 + 0.856771i \(0.672467\pi\)
\(600\) 0 0
\(601\) −25.9145 + 25.9145i −1.05707 + 1.05707i −0.0588044 + 0.998270i \(0.518729\pi\)
−0.998270 + 0.0588044i \(0.981271\pi\)
\(602\) 0 0
\(603\) −4.61070 11.1312i −0.187762 0.453298i
\(604\) 0 0
\(605\) −1.12593 0.466374i −0.0457754 0.0189608i
\(606\) 0 0
\(607\) 2.09569 0.0850615 0.0425307 0.999095i \(-0.486458\pi\)
0.0425307 + 0.999095i \(0.486458\pi\)
\(608\) 0 0
\(609\) 29.6413 1.20112
\(610\) 0 0
\(611\) −10.5234 4.35894i −0.425732 0.176344i
\(612\) 0 0
\(613\) −8.75402 21.1341i −0.353572 0.853597i −0.996174 0.0873972i \(-0.972145\pi\)
0.642602 0.766200i \(-0.277855\pi\)
\(614\) 0 0
\(615\) 11.4485 11.4485i 0.461647 0.461647i
\(616\) 0 0
\(617\) 7.54724 + 7.54724i 0.303841 + 0.303841i 0.842514 0.538674i \(-0.181074\pi\)
−0.538674 + 0.842514i \(0.681074\pi\)
\(618\) 0 0
\(619\) −30.8044 + 12.7596i −1.23813 + 0.512851i −0.903130 0.429366i \(-0.858737\pi\)
−0.335002 + 0.942217i \(0.608737\pi\)
\(620\) 0 0
\(621\) 1.29774 3.13303i 0.0520766 0.125724i
\(622\) 0 0
\(623\) 14.7888i 0.592502i
\(624\) 0 0
\(625\) 4.54021i 0.181608i
\(626\) 0 0
\(627\) 4.98630 12.0380i 0.199134 0.480751i
\(628\) 0 0
\(629\) 4.25756 1.76354i 0.169760 0.0703169i
\(630\) 0 0
\(631\) −4.03006 4.03006i −0.160434 0.160434i 0.622325 0.782759i \(-0.286188\pi\)
−0.782759 + 0.622325i \(0.786188\pi\)
\(632\) 0 0
\(633\) −14.1436 + 14.1436i −0.562156 + 0.562156i
\(634\) 0 0
\(635\) −2.51696 6.07648i −0.0998825 0.241138i
\(636\) 0 0
\(637\) −17.8217 7.38198i −0.706120 0.292485i
\(638\) 0 0
\(639\) −2.63920 −0.104405
\(640\) 0 0
\(641\) 10.3489 0.408757 0.204378 0.978892i \(-0.434483\pi\)
0.204378 + 0.978892i \(0.434483\pi\)
\(642\) 0 0
\(643\) 8.10100 + 3.35554i 0.319472 + 0.132330i 0.536656 0.843801i \(-0.319687\pi\)
−0.217184 + 0.976131i \(0.569687\pi\)
\(644\) 0 0
\(645\) 1.93642 + 4.67493i 0.0762464 + 0.184075i
\(646\) 0 0
\(647\) −20.0358 + 20.0358i −0.787689 + 0.787689i −0.981115 0.193426i \(-0.938040\pi\)
0.193426 + 0.981115i \(0.438040\pi\)
\(648\) 0 0
\(649\) −4.10712 4.10712i −0.161219 0.161219i
\(650\) 0 0
\(651\) 5.35696 2.21893i 0.209956 0.0869666i
\(652\) 0 0
\(653\) 11.1811 26.9936i 0.437552 1.05634i −0.539240 0.842152i \(-0.681289\pi\)
0.976792 0.214191i \(-0.0687115\pi\)
\(654\) 0 0
\(655\) 29.2540i 1.14305i
\(656\) 0 0
\(657\) 12.8249i 0.500348i
\(658\) 0 0
\(659\) 10.0306 24.2161i 0.390738 0.943325i −0.599041 0.800718i \(-0.704451\pi\)
0.989779 0.142607i \(-0.0455486\pi\)
\(660\) 0 0
\(661\) −13.8010 + 5.71657i −0.536798 + 0.222349i −0.634578 0.772859i \(-0.718826\pi\)
0.0977799 + 0.995208i \(0.468826\pi\)
\(662\) 0 0
\(663\) 0.891582 + 0.891582i 0.0346262 + 0.0346262i
\(664\) 0 0
\(665\) −38.7956 + 38.7956i −1.50443 + 1.50443i
\(666\) 0 0
\(667\) −9.95988 24.0453i −0.385648 0.931037i
\(668\) 0 0
\(669\) 26.8639 + 11.1274i 1.03862 + 0.430210i
\(670\) 0 0
\(671\) −23.7275 −0.915990
\(672\) 0 0
\(673\) 31.4646 1.21287 0.606436 0.795132i \(-0.292599\pi\)
0.606436 + 0.795132i \(0.292599\pi\)
\(674\) 0 0
\(675\) −7.08445 2.93447i −0.272681 0.112948i
\(676\) 0 0
\(677\) −6.25070 15.0905i −0.240234 0.579976i 0.757072 0.653332i \(-0.226629\pi\)
−0.997306 + 0.0733553i \(0.976629\pi\)
\(678\) 0 0
\(679\) 10.1945 10.1945i 0.391229 0.391229i
\(680\) 0 0
\(681\) −17.8011 17.8011i −0.682141 0.682141i
\(682\) 0 0
\(683\) 13.3397 5.52548i 0.510429 0.211426i −0.112578 0.993643i \(-0.535911\pi\)
0.623007 + 0.782216i \(0.285911\pi\)
\(684\) 0 0
\(685\) −15.3826 + 37.1370i −0.587740 + 1.41893i
\(686\) 0 0
\(687\) 7.64991i 0.291862i
\(688\) 0 0
\(689\) 11.0652i 0.421552i
\(690\) 0 0
\(691\) 9.47463 22.8738i 0.360432 0.870160i −0.634805 0.772673i \(-0.718919\pi\)
0.995237 0.0974874i \(-0.0310806\pi\)
\(692\) 0 0
\(693\) −11.6487 + 4.82504i −0.442496 + 0.183288i
\(694\) 0 0
\(695\) −4.14777 4.14777i −0.157334 0.157334i
\(696\) 0 0
\(697\) 1.66441 1.66441i 0.0630439 0.0630439i
\(698\) 0 0
\(699\) 7.08278 + 17.0993i 0.267895 + 0.646756i
\(700\) 0 0
\(701\) −5.36748 2.22328i −0.202727 0.0839723i 0.279010 0.960288i \(-0.409994\pi\)
−0.481737 + 0.876316i \(0.659994\pi\)
\(702\) 0 0
\(703\) 35.5457 1.34063
\(704\) 0 0
\(705\) 16.6376 0.626607
\(706\) 0 0
\(707\) −59.3898 24.6001i −2.23358 0.925180i
\(708\) 0 0
\(709\) −14.4269 34.8295i −0.541812 1.30805i −0.923443 0.383735i \(-0.874638\pi\)
0.381631 0.924315i \(-0.375362\pi\)
\(710\) 0 0
\(711\) −7.38305 + 7.38305i −0.276886 + 0.276886i
\(712\) 0 0
\(713\) −3.60003 3.60003i −0.134822 0.134822i
\(714\) 0 0
\(715\) −26.1583 + 10.8351i −0.978266 + 0.405211i
\(716\) 0 0
\(717\) 1.57248 3.79630i 0.0587254 0.141776i
\(718\) 0 0
\(719\) 38.6849i 1.44270i 0.692569 + 0.721351i \(0.256479\pi\)
−0.692569 + 0.721351i \(0.743521\pi\)
\(720\) 0 0
\(721\) 40.5409i 1.50982i
\(722\) 0 0
\(723\) −5.43963 + 13.1324i −0.202302 + 0.488400i
\(724\) 0 0
\(725\) −54.3715 + 22.5214i −2.01931 + 0.836425i
\(726\) 0 0
\(727\) 31.8871 + 31.8871i 1.18263 + 1.18263i 0.979061 + 0.203566i \(0.0652532\pi\)
0.203566 + 0.979061i \(0.434747\pi\)
\(728\) 0 0
\(729\) −0.707107 + 0.707107i −0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) 0.281521 + 0.679651i 0.0104124 + 0.0251378i
\(732\) 0 0
\(733\) −18.4333 7.63532i −0.680849 0.282017i 0.0153326 0.999882i \(-0.495119\pi\)
−0.696182 + 0.717865i \(0.745119\pi\)
\(734\) 0 0
\(735\) 28.1761 1.03929
\(736\) 0 0
\(737\) 39.3330 1.44885
\(738\) 0 0
\(739\) 19.0069 + 7.87292i 0.699180 + 0.289610i 0.703819 0.710379i \(-0.251477\pi\)
−0.00463865 + 0.999989i \(0.501477\pi\)
\(740\) 0 0
\(741\) 3.72184 + 8.98531i 0.136725 + 0.330084i
\(742\) 0 0
\(743\) 17.5266 17.5266i 0.642987 0.642987i −0.308302 0.951289i \(-0.599761\pi\)
0.951289 + 0.308302i \(0.0997606\pi\)
\(744\) 0 0
\(745\) −10.4880 10.4880i −0.384250 0.384250i
\(746\) 0 0
\(747\) 4.57106 1.89340i 0.167246 0.0692757i
\(748\) 0 0
\(749\) −12.5636 + 30.3313i −0.459065 + 1.10828i
\(750\) 0 0
\(751\) 40.4908i 1.47753i −0.673963 0.738765i \(-0.735409\pi\)
0.673963 0.738765i \(-0.264591\pi\)
\(752\) 0 0
\(753\) 6.19031i 0.225587i
\(754\) 0 0
\(755\) −0.788695 + 1.90408i −0.0287035 + 0.0692965i
\(756\) 0 0
\(757\) −29.7102 + 12.3064i −1.07984 + 0.447283i −0.850452 0.526053i \(-0.823671\pi\)
−0.229385 + 0.973336i \(0.573671\pi\)
\(758\) 0 0
\(759\) 7.82823 + 7.82823i 0.284147 + 0.284147i
\(760\) 0 0
\(761\) −15.8052 + 15.8052i −0.572939 + 0.572939i −0.932949 0.360010i \(-0.882773\pi\)
0.360010 + 0.932949i \(0.382773\pi\)
\(762\) 0 0
\(763\) −12.8621 31.0519i −0.465640 1.12415i
\(764\) 0 0
\(765\) −1.70153 0.704798i −0.0615190 0.0254820i
\(766\) 0 0
\(767\) 4.33542 0.156543
\(768\) 0 0
\(769\) 2.99003 0.107823 0.0539116 0.998546i \(-0.482831\pi\)
0.0539116 + 0.998546i \(0.482831\pi\)
\(770\) 0 0
\(771\) −7.65149 3.16935i −0.275562 0.114141i
\(772\) 0 0
\(773\) 1.59236 + 3.84429i 0.0572731 + 0.138269i 0.949926 0.312476i \(-0.101158\pi\)
−0.892653 + 0.450745i \(0.851158\pi\)
\(774\) 0 0
\(775\) −8.14044 + 8.14044i −0.292413 + 0.292413i
\(776\) 0 0
\(777\) −24.3217 24.3217i −0.872535 0.872535i
\(778\) 0 0
\(779\) 16.7738 6.94792i 0.600983 0.248935i
\(780\) 0 0
\(781\) 3.29718 7.96009i 0.117982 0.284834i
\(782\) 0 0
\(783\) 7.67477i 0.274274i
\(784\) 0 0
\(785\) 46.7908i 1.67003i
\(786\) 0 0
\(787\) −3.14740 + 7.59851i −0.112193 + 0.270857i −0.969996 0.243121i \(-0.921829\pi\)
0.857803 + 0.513978i \(0.171829\pi\)
\(788\) 0 0
\(789\) −20.1299 + 8.33809i −0.716645 + 0.296844i
\(790\) 0 0
\(791\) −47.6453 47.6453i −1.69407 1.69407i
\(792\) 0 0
\(793\) 12.5232 12.5232i 0.444712 0.444712i
\(794\) 0 0
\(795\) −6.18513 14.9322i −0.219364 0.529591i
\(796\) 0 0
\(797\) −13.9175 5.76480i −0.492982 0.204200i 0.122321 0.992491i \(-0.460966\pi\)
−0.615303 + 0.788291i \(0.710966\pi\)
\(798\) 0