Properties

Label 384.2.n.a.49.8
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 49.8
Character \(\chi\) \(=\) 384.49
Dual form 384.2.n.a.337.8

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.36206 3.28830i 0.609132 1.47057i −0.254814 0.966990i \(-0.582014\pi\)
0.863946 0.503584i \(-0.167986\pi\)
\(6\) 0 0
\(7\) 2.73097 + 2.73097i 1.03221 + 1.03221i 0.999464 + 0.0327442i \(0.0104247\pi\)
0.0327442 + 0.999464i \(0.489575\pi\)
\(8\) 0 0
\(9\) 0.707107 0.707107i 0.235702 0.235702i
\(10\) 0 0
\(11\) −3.01609 1.24931i −0.909387 0.376680i −0.121565 0.992583i \(-0.538791\pi\)
−0.787822 + 0.615903i \(0.788791\pi\)
\(12\) 0 0
\(13\) 0.932498 + 2.25125i 0.258628 + 0.624384i 0.998848 0.0479806i \(-0.0152786\pi\)
−0.740220 + 0.672365i \(0.765279\pi\)
\(14\) 0 0
\(15\) 3.55923i 0.918990i
\(16\) 0 0
\(17\) 0.517450i 0.125500i −0.998029 0.0627500i \(-0.980013\pi\)
0.998029 0.0627500i \(-0.0199871\pi\)
\(18\) 0 0
\(19\) −1.52739 3.68744i −0.350407 0.845956i −0.996570 0.0827570i \(-0.973627\pi\)
0.646163 0.763199i \(-0.276373\pi\)
\(20\) 0 0
\(21\) 3.56818 + 1.47799i 0.778640 + 0.322523i
\(22\) 0 0
\(23\) −2.39792 + 2.39792i −0.500000 + 0.500000i −0.911438 0.411438i \(-0.865027\pi\)
0.411438 + 0.911438i \(0.365027\pi\)
\(24\) 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 0.389857 0.920875i \(-0.372524\pi\)
0.926828 + 0.375487i \(0.122524\pi\)
\(30\) 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 0.349237 + 0.937034i \(0.386441\pi\)
−0.909531 + 0.415635i \(0.863559\pi\)
\(38\) 0 0
\(39\) 1.72303 + 1.72303i 0.275906 + 0.275906i
\(40\) 0 0
\(41\) −3.21656 + 3.21656i −0.502342 + 0.502342i −0.912165 0.409823i \(-0.865590\pi\)
0.409823 + 0.912165i \(0.365590\pi\)
\(42\) 0 0
\(43\) 1.31346 + 0.544054i 0.200301 + 0.0829675i 0.480579 0.876951i \(-0.340427\pi\)
−0.280278 + 0.959919i \(0.590427\pi\)
\(44\) 0 0
\(45\) −1.36206 3.28830i −0.203044 0.490191i
\(46\) 0 0
\(47\) 4.67448i 0.681843i 0.940092 + 0.340921i \(0.110739\pi\)
−0.940092 + 0.340921i \(0.889261\pi\)
\(48\) 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 0.0754586 0.997149i \(-0.475958\pi\)
−0.651733 + 0.758448i \(0.725958\pi\)
\(54\) 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 −0.873342 0.487108i \(-0.838052\pi\)
0.961983 + 0.273109i \(0.0880518\pi\)
\(60\) 0 0
\(61\) 6.71487 2.78139i 0.859751 0.356121i 0.0911409 0.995838i \(-0.470949\pi\)
0.768610 + 0.639717i \(0.220949\pi\)
\(62\) 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 −0.939029 0.343837i \(-0.888273\pi\)
−0.420864 + 0.907124i \(0.638273\pi\)
\(68\) 0 0
\(69\) −1.29774 + 3.13303i −0.156230 + 0.377172i
\(70\) 0 0
\(71\) −1.86620 1.86620i −0.221477 0.221477i 0.587643 0.809120i \(-0.300056\pi\)
−0.809120 + 0.587643i \(0.800056\pi\)
\(72\) 0 0
\(73\) −9.06859 + 9.06859i −1.06140 + 1.06140i −0.0634101 + 0.997988i \(0.520198\pi\)
−0.997988 + 0.0634101i \(0.979802\pi\)
\(74\) 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 \(-0.800166\pi\)
0.809323 0.587364i \(-0.199834\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 1.89340 + 4.57106i 0.207827 + 0.501739i 0.993081 0.117435i \(-0.0374673\pi\)
−0.785253 + 0.619175i \(0.787467\pi\)
\(84\) 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 0.548888 0.835896i \(-0.315051\pi\)
−0.835896 + 0.548888i \(0.815051\pi\)
\(90\) 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 0.201036 + 0.979584i \(0.435569\pi\)
−0.834824 + 0.550517i \(0.814431\pi\)
\(102\) 0 0
\(103\) 7.42244 + 7.42244i 0.731355 + 0.731355i 0.970888 0.239533i \(-0.0769944\pi\)
−0.239533 + 0.970888i \(0.576994\pi\)
\(104\) 0 0
\(105\) 9.72015 9.72015i 0.948589 0.948589i
\(106\) 0 0
\(107\) −7.85343 3.25300i −0.759220 0.314479i −0.0307226 0.999528i \(-0.509781\pi\)
−0.728497 + 0.685049i \(0.759781\pi\)
\(108\) 0 0
\(109\) 3.33028 + 8.04001i 0.318983 + 0.770094i 0.999308 + 0.0371832i \(0.0118385\pi\)
−0.680325 + 0.732910i \(0.738161\pi\)
\(110\) 0 0
\(111\) 8.90589i 0.845310i
\(112\) 0 0
\(113\) 17.4463i 1.64121i 0.571494 + 0.820606i \(0.306364\pi\)
−0.571494 + 0.820606i \(0.693636\pi\)
\(114\) 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 −0.0254395 0.999676i \(-0.508099\pi\)
0.688889 + 0.724866i \(0.258099\pi\)
\(132\) 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 −0.278238 0.960512i \(-0.589750\pi\)
0.960512 + 0.278238i \(0.0897503\pi\)
\(138\) 0 0
\(139\) −1.52261 0.630686i −0.129146 0.0534941i 0.317174 0.948367i \(-0.397266\pi\)
−0.446321 + 0.894873i \(0.647266\pi\)
\(140\) 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 0.219363 0.975643i \(-0.429602\pi\)
−0.534771 + 0.844997i \(0.679602\pi\)
\(150\) 0 0
\(151\) 0.409447 0.409447i 0.0333203 0.0333203i −0.690250 0.723571i \(-0.742500\pi\)
0.723571 + 0.690250i \(0.242500\pi\)
\(152\) 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 −0.810461 0.585793i \(-0.800783\pi\)
−0.158864 + 0.987301i \(0.550783\pi\)
\(158\) 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 0.324177 0.945996i \(-0.394913\pi\)
0.898148 + 0.439693i \(0.144913\pi\)
\(164\) 0 0
\(165\) −4.44658 + 10.7350i −0.346166 + 0.835718i
\(166\) 0 0
\(167\) 3.65825 + 3.65825i 0.283084 + 0.283084i 0.834338 0.551254i \(-0.185850\pi\)
−0.551254 + 0.834338i \(0.685850\pi\)
\(168\) 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 −0.995697 0.0926640i \(-0.970462\pi\)
0.638541 0.769588i \(-0.279538\pi\)
\(174\) 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 0.816318 0.577602i \(-0.196011\pi\)
−0.985651 + 0.168798i \(0.946011\pi\)
\(180\) 0 0
\(181\) −14.5765 6.03777i −1.08346 0.448784i −0.231738 0.972778i \(-0.574441\pi\)
−0.851722 + 0.523994i \(0.824441\pi\)
\(182\) 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 −0.501220 0.865320i \(-0.667115\pi\)
0.966290 0.257458i \(-0.0828847\pi\)
\(198\) 0 0
\(199\) −5.80270 5.80270i −0.411343 0.411343i 0.470863 0.882206i \(-0.343942\pi\)
−0.882206 + 0.470863i \(0.843942\pi\)
\(200\) 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 −0.933510 0.358552i \(-0.883271\pi\)
0.406557 0.913626i \(-0.366729\pi\)
\(212\) 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 −0.982165 0.188022i \(-0.939792\pi\)
−0.561544 + 0.827447i \(0.689792\pi\)
\(228\) 0 0
\(229\) 2.92749 7.06760i 0.193454 0.467040i −0.797153 0.603777i \(-0.793662\pi\)
0.990607 + 0.136737i \(0.0436616\pi\)
\(230\) 0 0
\(231\) −8.91550 8.91550i −0.586597 0.586597i
\(232\) 0 0
\(233\) 13.0873 13.0873i 0.857375 0.857375i −0.133653 0.991028i \(-0.542671\pi\)
0.991028 + 0.133653i \(0.0426708\pi\)
\(234\) 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 \(0.0424281\pi\)
−0.991130 + 0.132897i \(0.957572\pi\)
\(240\) 0 0
\(241\) 14.2144i 0.915632i −0.889047 0.457816i \(-0.848632\pi\)
0.889047 0.457816i \(-0.151368\pi\)
\(242\) 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 −0.980840 0.194816i \(-0.937589\pi\)
0.831314 + 0.555803i \(0.187589\pi\)
\(252\) 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 0.0487861 0.998809i \(-0.484465\pi\)
−0.998809 + 0.0487861i \(0.984465\pi\)
\(264\) 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 0.800812 0.598916i \(-0.204402\pi\)
−0.989757 + 0.142762i \(0.954402\pi\)
\(270\) 0 0
\(271\) 28.7832i 1.74846i 0.485515 + 0.874228i \(0.338632\pi\)
−0.485515 + 0.874228i \(0.661368\pi\)
\(272\) 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 −0.0135158 0.999909i \(-0.504302\pi\)
−0.716599 + 0.697485i \(0.754302\pi\)
\(278\) 0 0
\(279\) 1.06159 1.06159i 0.0635558 0.0635558i
\(280\) 0 0
\(281\) −21.6306 21.6306i −1.29037 1.29037i −0.934555 0.355820i \(-0.884202\pi\)
−0.355820 0.934555i \(-0.615798\pi\)
\(282\) 0 0
\(283\) 11.4777 27.7097i 0.682281 1.64717i −0.0775002 0.996992i \(-0.524694\pi\)
0.759781 0.650179i \(-0.225306\pi\)
\(284\) 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 −0.968519 0.248942i \(-0.919917\pi\)
0.860874 + 0.508818i \(0.169917\pi\)
\(294\) 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 −0.781519 0.623881i \(-0.785555\pi\)
0.111467 0.993768i \(-0.464445\pi\)
\(308\) 0 0
\(309\) 9.69789 + 4.01700i 0.551694 + 0.228519i
\(310\) 0 0
\(311\) −11.6121 + 11.6121i −0.658459 + 0.658459i −0.955015 0.296556i \(-0.904162\pi\)
0.296556 + 0.955015i \(0.404162\pi\)
\(312\) 0 0
\(313\) −6.84409 6.84409i −0.386851 0.386851i 0.486712 0.873563i \(-0.338196\pi\)
−0.873563 + 0.486712i \(0.838196\pi\)
\(314\) 0 0
\(315\) 5.26051 12.7000i 0.296396 0.715563i
\(316\) 0 0
\(317\) −23.6795 + 9.80835i −1.32997 + 0.550892i −0.930647 0.365918i \(-0.880755\pi\)
−0.399324 + 0.916810i \(0.630755\pi\)
\(318\) 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 0.888837 0.458224i \(-0.151514\pi\)
0.304489 + 0.952516i \(0.401514\pi\)
\(332\) 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 \(0.229529\pi\)
−0.751088 + 0.660202i \(0.770471\pi\)
\(338\) 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 −0.881092 0.472945i \(-0.843191\pi\)
0.957449 + 0.288604i \(0.0931910\pi\)
\(348\) 0 0
\(349\) 3.17452 1.31493i 0.169928 0.0703866i −0.296098 0.955158i \(-0.595685\pi\)
0.466026 + 0.884771i \(0.345685\pi\)
\(350\) 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 0.772462 0.635062i \(-0.219025\pi\)
−0.635062 + 0.772462i \(0.719025\pi\)
\(360\) 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 \(0.0117734\pi\)
−0.999316 + 0.0369787i \(0.988227\pi\)
\(368\) 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 0.991025 0.133674i \(-0.0426774\pi\)
0.606239 + 0.795282i \(0.292677\pi\)
\(374\) 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 −0.751357 0.659896i \(-0.770600\pi\)
0.997907 + 0.0646720i \(0.0206001\pi\)
\(380\) 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 −0.953547 0.301243i \(-0.902598\pi\)
0.887271 + 0.461248i \(0.152598\pi\)
\(390\) 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 0.839521 0.543327i \(-0.182836\pi\)
−0.977821 + 0.209441i \(0.932836\pi\)
\(398\) 0 0
\(399\) 15.4149i 0.771710i
\(400\) 0 0
\(401\) 22.5969i 1.12844i −0.825626 0.564218i \(-0.809178\pi\)
0.825626 0.564218i \(-0.190822\pi\)
\(402\) 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 0.615644 0.788024i \(-0.288896\pi\)
−0.788024 + 0.615644i \(0.788896\pi\)
\(410\) 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 −0.593805 0.804609i \(-0.702375\pi\)
0.149061 + 0.988828i \(0.452375\pi\)
\(420\) 0 0
\(421\) −0.766817 + 1.85126i −0.0373724 + 0.0902249i −0.941464 0.337114i \(-0.890549\pi\)
0.904091 + 0.427339i \(0.140549\pi\)
\(422\) 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 \(-0.910263\pi\)
0.960524 0.278197i \(-0.0897368\pi\)
\(432\) 0 0
\(433\) 3.12797i 0.150321i −0.997171 0.0751603i \(-0.976053\pi\)
0.997171 0.0751603i \(-0.0239468\pi\)
\(434\) 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 −0.873618 0.486612i \(-0.838232\pi\)
0.486612 + 0.873618i \(0.338232\pi\)
\(440\) 0 0
\(441\) 5.59770 + 5.59770i 0.266557 + 0.266557i
\(442\) 0 0
\(443\) −9.34973 + 22.5722i −0.444219 + 1.07244i 0.530235 + 0.847851i \(0.322104\pi\)
−0.974454 + 0.224588i \(0.927896\pi\)
\(444\) 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 −0.993076 0.117474i \(-0.962520\pi\)
0.117474 + 0.993076i \(0.462520\pi\)
\(458\) 0 0
\(459\) −0.478061 0.198019i −0.0223140 0.00924275i
\(460\) 0 0
\(461\) 2.60820 + 6.29674i 0.121476 + 0.293268i 0.972907 0.231198i \(-0.0742647\pi\)
−0.851431 + 0.524467i \(0.824265\pi\)
\(462\) 0 0
\(463\) 5.96406i 0.277174i 0.990350 + 0.138587i \(0.0442560\pi\)
−0.990350 + 0.138587i \(0.955744\pi\)
\(464\) 0 0
\(465\) 5.34354i 0.247801i
\(466\) 0 0
\(467\) −8.88493 21.4501i −0.411146 0.992593i −0.984831 0.173518i \(-0.944487\pi\)
0.573685 0.819076i \(-0.305513\pi\)
\(468\) 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 0.641058 0.767492i \(-0.278496\pi\)
−0.767492 + 0.641058i \(0.778496\pi\)
\(488\) 0 0
\(489\) 11.9440 11.9440i 0.540127 0.540127i
\(490\) 0 0
\(491\) −19.9243 8.25292i −0.899172 0.372449i −0.115270 0.993334i \(-0.536773\pi\)
−0.783902 + 0.620885i \(0.786773\pi\)
\(492\) 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 0.795907 + 0.605419i \(0.206995\pi\)
−0.134695 + 0.990887i \(0.543005\pi\)
\(500\) 0 0
\(501\) 4.77973 + 1.97983i 0.213543 + 0.0884523i
\(502\) 0 0
\(503\) 26.5194 26.5194i 1.18244 1.18244i 0.203333 0.979110i \(-0.434823\pi\)
0.979110 0.203333i \(-0.0651773\pi\)
\(504\) 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 0.498750 0.866746i \(-0.333793\pi\)
0.965551 + 0.260212i \(0.0837926\pi\)
\(510\) 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 −0.760066 0.649846i \(-0.774833\pi\)
0.649846 + 0.760066i \(0.274833\pi\)
\(522\) 0 0
\(523\) −21.6449 8.96561i −0.946465 0.392039i −0.144564 0.989495i \(-0.546178\pi\)
−0.801901 + 0.597457i \(0.796178\pi\)
\(524\) 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 −0.159923 0.987130i \(-0.551125\pi\)
0.584924 + 0.811088i \(0.301125\pi\)
\(542\) 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 −0.274901 0.961473i \(-0.588645\pi\)
0.485479 + 0.874248i \(0.338645\pi\)
\(548\) 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 0.879015 0.476793i \(-0.158201\pi\)
−0.958702 + 0.284414i \(0.908201\pi\)
\(558\) 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 0.987002 0.160705i \(-0.0513768\pi\)
−0.811552 + 0.584281i \(0.801377\pi\)
\(564\) 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 0.675228 0.737609i \(-0.264045\pi\)
−0.737609 + 0.675228i \(0.764045\pi\)
\(570\) 0 0
\(571\) 10.9476 26.4299i 0.458145 1.10606i −0.511003 0.859579i \(-0.670726\pi\)
0.969148 0.246480i \(-0.0792740\pi\)
\(572\) 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 0.854731 0.519072i \(-0.173722\pi\)
0.237347 + 0.971425i \(0.423722\pi\)
\(588\) 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 \(0.00879924\pi\)
−0.999618 + 0.0276401i \(0.991201\pi\)
\(594\) 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 −0.515697 0.856771i \(-0.672467\pi\)
0.856771 + 0.515697i \(0.172467\pi\)
\(600\) 0 0
\(601\) −25.9145 25.9145i −1.05707 1.05707i −0.998270 0.0588044i \(-0.981271\pi\)
−0.0588044 0.998270i \(-0.518729\pi\)
\(602\) 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 0.642602 + 0.766200i \(0.277855\pi\)
−0.996174 + 0.0873972i \(0.972145\pi\)
\(614\) 0 0
\(615\) 11.4485 + 11.4485i 0.461647 + 0.461647i
\(616\) 0 0
\(617\) 7.54724 7.54724i 0.303841 0.303841i −0.538674 0.842514i \(-0.681074\pi\)
0.842514 + 0.538674i \(0.181074\pi\)
\(618\) 0 0
\(619\) −30.8044 12.7596i −1.23813 0.512851i −0.335002 0.942217i \(-0.608737\pi\)
−0.903130 + 0.429366i \(0.858737\pi\)
\(620\) 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 −0.782759 0.622325i \(-0.786188\pi\)
0.622325 + 0.782759i \(0.286188\pi\)
\(632\) 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 −0.217184 0.976131i \(-0.569687\pi\)
0.536656 + 0.843801i \(0.319687\pi\)
\(644\) 0 0
\(645\) 1.93642 4.67493i 0.0762464 0.184075i
\(646\) 0 0
\(647\) −20.0358 20.0358i −0.787689 0.787689i 0.193426 0.981115i \(-0.438040\pi\)
−0.981115 + 0.193426i \(0.938040\pi\)
\(648\) 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 0.976792 + 0.214191i \(0.0687115\pi\)
−0.539240 + 0.842152i \(0.681289\pi\)
\(654\) 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 0.989779 + 0.142607i \(0.0455486\pi\)
−0.599041 + 0.800718i \(0.704451\pi\)
\(660\) 0 0
\(661\) −13.8010 5.71657i −0.536798 0.222349i 0.0977799 0.995208i \(-0.468826\pi\)
−0.634578 + 0.772859i \(0.718826\pi\)
\(662\) 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 −0.997306 0.0733553i \(-0.976629\pi\)
0.757072 + 0.653332i \(0.226629\pi\)
\(678\) 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 0.623007 0.782216i \(-0.285911\pi\)
−0.112578 + 0.993643i \(0.535911\pi\)
\(684\) 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 0.995237 + 0.0974874i \(0.0310806\pi\)
−0.634805 + 0.772673i \(0.718919\pi\)
\(692\) 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 −0.481737 0.876316i \(-0.659994\pi\)
0.279010 + 0.960288i \(0.409994\pi\)
\(702\) 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 0.381631 + 0.924315i \(0.375362\pi\)
−0.923443 + 0.383735i \(0.874638\pi\)
\(710\) 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 \(-0.743521\pi\)
0.692569 0.721351i \(-0.256479\pi\)
\(720\) 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 0.203566 0.979061i \(-0.434747\pi\)
0.979061 0.203566i \(-0.0652532\pi\)
\(728\) 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 −0.696182 0.717865i \(-0.745119\pi\)
0.0153326 + 0.999882i \(0.495119\pi\)
\(734\) 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 −0.00463865 0.999989i \(-0.501477\pi\)
0.703819 + 0.710379i \(0.251477\pi\)
\(740\) 0 0
\(741\) 3.72184 8.98531i 0.136725 0.330084i
\(742\) 0 0
\(743\) 17.5266 + 17.5266i 0.642987 + 0.642987i 0.951289 0.308302i \(-0.0997606\pi\)
−0.308302 + 0.951289i \(0.599761\pi\)
\(744\) 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 \(0.264591\pi\)
−0.673963 + 0.738765i \(0.735409\pi\)
\(752\) 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 −0.229385 0.973336i \(-0.573671\pi\)
−0.850452 + 0.526053i \(0.823671\pi\)
\(758\) 0 0
\(759\) 7.82823 7.82823i 0.284147 0.284147i
\(760\) 0 0
\(761\) −15.8052 15.8052i −0.572939 0.572939i 0.360010 0.932949i \(-0.382773\pi\)
−0.932949 + 0.360010i \(0.882773\pi\)
\(762\) 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 −0.892653 0.450745i \(-0.851158\pi\)
0.949926 + 0.312476i \(0.101158\pi\)
\(774\) 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 0.857803 0.513978i \(-0.171829\pi\)
−0.969996 + 0.243121i \(0.921829\pi\)
\(788\) 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 −0.615303 0.788291i \(-0.710966\pi\)
0.122321 + 0.992491i \(0.460966\pi\)
\(798\)