Properties

Label 384.2.n.a.337.4
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 337.4
Character \(\chi\) \(=\) 384.337
Dual form 384.2.n.a.49.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.923880 - 0.382683i) q^{3} +(0.750897 + 1.81283i) q^{5} +(-0.638460 + 0.638460i) q^{7} +(0.707107 + 0.707107i) q^{9} +(0.343096 - 0.142115i) q^{11} +(-1.56981 + 3.78987i) q^{13} -1.96219i q^{15} -1.52272i q^{17} +(-3.15404 + 7.61453i) q^{19} +(0.834188 - 0.345532i) q^{21} +(6.00496 + 6.00496i) q^{23} +(0.813044 - 0.813044i) q^{25} +(-0.382683 - 0.923880i) q^{27} +(-0.647232 - 0.268092i) q^{29} +3.66460 q^{31} -0.371365 q^{33} +(-1.63683 - 0.677999i) q^{35} +(3.69013 + 8.90877i) q^{37} +(2.90064 - 2.90064i) q^{39} +(-8.19959 - 8.19959i) q^{41} +(1.86276 - 0.771580i) q^{43} +(-0.750897 + 1.81283i) q^{45} -3.21602i q^{47} +6.18474i q^{49} +(-0.582718 + 1.40681i) q^{51} +(7.71461 - 3.19550i) q^{53} +(0.515260 + 0.515260i) q^{55} +(5.82791 - 5.82791i) q^{57} +(-2.78703 - 6.72848i) q^{59} +(-10.4842 - 4.34269i) q^{61} -0.902919 q^{63} -8.04913 q^{65} +(-6.56831 - 2.72068i) q^{67} +(-3.24986 - 7.84586i) q^{69} +(-0.957148 + 0.957148i) q^{71} +(-2.14406 - 2.14406i) q^{73} +(-1.06229 + 0.440016i) q^{75} +(-0.128318 + 0.309788i) q^{77} -0.628155i q^{79} +1.00000i q^{81} +(4.17789 - 10.0863i) q^{83} +(2.76042 - 1.14340i) q^{85} +(0.495370 + 0.495370i) q^{87} +(8.70474 - 8.70474i) q^{89} +(-1.41741 - 3.42194i) q^{91} +(-3.38565 - 1.40238i) q^{93} -16.1722 q^{95} +10.2387 q^{97} +(0.343096 + 0.142115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

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
\(5\) 0.750897 + 1.81283i 0.335811 + 0.810720i 0.998108 + 0.0614789i \(0.0195817\pi\)
−0.662297 + 0.749241i \(0.730418\pi\)
\(6\) 0 0
\(7\) −0.638460 + 0.638460i −0.241315 + 0.241315i −0.817394 0.576079i \(-0.804582\pi\)
0.576079 + 0.817394i \(0.304582\pi\)
\(8\) 0 0
\(9\) 0.707107 + 0.707107i 0.235702 + 0.235702i
\(10\) 0 0
\(11\) 0.343096 0.142115i 0.103447 0.0428493i −0.330360 0.943855i \(-0.607170\pi\)
0.433807 + 0.901006i \(0.357170\pi\)
\(12\) 0 0
\(13\) −1.56981 + 3.78987i −0.435388 + 1.05112i 0.542135 + 0.840291i \(0.317616\pi\)
−0.977523 + 0.210828i \(0.932384\pi\)
\(14\) 0 0
\(15\) 1.96219i 0.506635i
\(16\) 0 0
\(17\) 1.52272i 0.369313i −0.982803 0.184656i \(-0.940883\pi\)
0.982803 0.184656i \(-0.0591172\pi\)
\(18\) 0 0
\(19\) −3.15404 + 7.61453i −0.723587 + 1.74689i −0.0607223 + 0.998155i \(0.519340\pi\)
−0.662865 + 0.748739i \(0.730660\pi\)
\(20\) 0 0
\(21\) 0.834188 0.345532i 0.182035 0.0754013i
\(22\) 0 0
\(23\) 6.00496 + 6.00496i 1.25212 + 1.25212i 0.954767 + 0.297355i \(0.0961043\pi\)
0.297355 + 0.954767i \(0.403896\pi\)
\(24\) 0 0
\(25\) 0.813044 0.813044i 0.162609 0.162609i
\(26\) 0 0
\(27\) −0.382683 0.923880i −0.0736475 0.177801i
\(28\) 0 0
\(29\) −0.647232 0.268092i −0.120188 0.0497835i 0.321779 0.946815i \(-0.395719\pi\)
−0.441967 + 0.897031i \(0.645719\pi\)
\(30\) 0 0
\(31\) 3.66460 0.658181 0.329091 0.944298i \(-0.393258\pi\)
0.329091 + 0.944298i \(0.393258\pi\)
\(32\) 0 0
\(33\) −0.371365 −0.0646463
\(34\) 0 0
\(35\) −1.63683 0.677999i −0.276676 0.114603i
\(36\) 0 0
\(37\) 3.69013 + 8.90877i 0.606654 + 1.46459i 0.866617 + 0.498974i \(0.166290\pi\)
−0.259963 + 0.965619i \(0.583710\pi\)
\(38\) 0 0
\(39\) 2.90064 2.90064i 0.464474 0.464474i
\(40\) 0 0
\(41\) −8.19959 8.19959i −1.28056 1.28056i −0.940349 0.340211i \(-0.889501\pi\)
−0.340211 0.940349i \(-0.610499\pi\)
\(42\) 0 0
\(43\) 1.86276 0.771580i 0.284068 0.117665i −0.236100 0.971729i \(-0.575869\pi\)
0.520168 + 0.854064i \(0.325869\pi\)
\(44\) 0 0
\(45\) −0.750897 + 1.81283i −0.111937 + 0.270240i
\(46\) 0 0
\(47\) 3.21602i 0.469105i −0.972103 0.234552i \(-0.924638\pi\)
0.972103 0.234552i \(-0.0753624\pi\)
\(48\) 0 0
\(49\) 6.18474i 0.883534i
\(50\) 0 0
\(51\) −0.582718 + 1.40681i −0.0815969 + 0.196992i
\(52\) 0 0
\(53\) 7.71461 3.19550i 1.05968 0.438935i 0.216344 0.976317i \(-0.430587\pi\)
0.843339 + 0.537382i \(0.180587\pi\)
\(54\) 0 0
\(55\) 0.515260 + 0.515260i 0.0694776 + 0.0694776i
\(56\) 0 0
\(57\) 5.82791 5.82791i 0.771926 0.771926i
\(58\) 0 0
\(59\) −2.78703 6.72848i −0.362840 0.875973i −0.994882 0.101039i \(-0.967783\pi\)
0.632042 0.774934i \(-0.282217\pi\)
\(60\) 0 0
\(61\) −10.4842 4.34269i −1.34236 0.556024i −0.408205 0.912890i \(-0.633845\pi\)
−0.934155 + 0.356866i \(0.883845\pi\)
\(62\) 0 0
\(63\) −0.902919 −0.113757
\(64\) 0 0
\(65\) −8.04913 −0.998372
\(66\) 0 0
\(67\) −6.56831 2.72068i −0.802447 0.332384i −0.0565107 0.998402i \(-0.517997\pi\)
−0.745936 + 0.666018i \(0.767997\pi\)
\(68\) 0 0
\(69\) −3.24986 7.84586i −0.391238 0.944531i
\(70\) 0 0
\(71\) −0.957148 + 0.957148i −0.113593 + 0.113593i −0.761618 0.648026i \(-0.775595\pi\)
0.648026 + 0.761618i \(0.275595\pi\)
\(72\) 0 0
\(73\) −2.14406 2.14406i −0.250944 0.250944i 0.570414 0.821357i \(-0.306783\pi\)
−0.821357 + 0.570414i \(0.806783\pi\)
\(74\) 0 0
\(75\) −1.06229 + 0.440016i −0.122663 + 0.0508087i
\(76\) 0 0
\(77\) −0.128318 + 0.309788i −0.0146232 + 0.0353036i
\(78\) 0 0
\(79\) 0.628155i 0.0706729i −0.999375 0.0353365i \(-0.988750\pi\)
0.999375 0.0353365i \(-0.0112503\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 4.17789 10.0863i 0.458583 1.10712i −0.510388 0.859944i \(-0.670498\pi\)
0.968971 0.247174i \(-0.0795018\pi\)
\(84\) 0 0
\(85\) 2.76042 1.14340i 0.299409 0.124019i
\(86\) 0 0
\(87\) 0.495370 + 0.495370i 0.0531092 + 0.0531092i
\(88\) 0 0
\(89\) 8.70474 8.70474i 0.922701 0.922701i −0.0745189 0.997220i \(-0.523742\pi\)
0.997220 + 0.0745189i \(0.0237421\pi\)
\(90\) 0 0
\(91\) −1.41741 3.42194i −0.148585 0.358717i
\(92\) 0 0
\(93\) −3.38565 1.40238i −0.351075 0.145420i
\(94\) 0 0
\(95\) −16.1722 −1.65923
\(96\) 0 0
\(97\) 10.2387 1.03959 0.519793 0.854292i \(-0.326009\pi\)
0.519793 + 0.854292i \(0.326009\pi\)
\(98\) 0 0
\(99\) 0.343096 + 0.142115i 0.0344825 + 0.0142831i
\(100\) 0 0
\(101\) 1.36634 + 3.29864i 0.135956 + 0.328227i 0.977165 0.212484i \(-0.0681553\pi\)
−0.841208 + 0.540711i \(0.818155\pi\)
\(102\) 0 0
\(103\) 2.02375 2.02375i 0.199406 0.199406i −0.600340 0.799745i \(-0.704968\pi\)
0.799745 + 0.600340i \(0.204968\pi\)
\(104\) 0 0
\(105\) 1.25278 + 1.25278i 0.122259 + 0.122259i
\(106\) 0 0
\(107\) 8.80292 3.64629i 0.851010 0.352500i 0.0858251 0.996310i \(-0.472647\pi\)
0.765185 + 0.643810i \(0.222647\pi\)
\(108\) 0 0
\(109\) 3.58112 8.64559i 0.343009 0.828097i −0.654399 0.756149i \(-0.727078\pi\)
0.997408 0.0719480i \(-0.0229216\pi\)
\(110\) 0 0
\(111\) 9.64278i 0.915253i
\(112\) 0 0
\(113\) 10.5067i 0.988391i 0.869351 + 0.494195i \(0.164537\pi\)
−0.869351 + 0.494195i \(0.835463\pi\)
\(114\) 0 0
\(115\) −6.37684 + 15.3951i −0.594644 + 1.43560i
\(116\) 0 0
\(117\) −3.78987 + 1.56981i −0.350373 + 0.145129i
\(118\) 0 0
\(119\) 0.972194 + 0.972194i 0.0891208 + 0.0891208i
\(120\) 0 0
\(121\) −7.68066 + 7.68066i −0.698241 + 0.698241i
\(122\) 0 0
\(123\) 4.43758 + 10.7133i 0.400124 + 0.965984i
\(124\) 0 0
\(125\) 11.1485 + 4.61788i 0.997156 + 0.413036i
\(126\) 0 0
\(127\) −2.30939 −0.204925 −0.102462 0.994737i \(-0.532672\pi\)
−0.102462 + 0.994737i \(0.532672\pi\)
\(128\) 0 0
\(129\) −2.01624 −0.177520
\(130\) 0 0
\(131\) −4.80498 1.99029i −0.419813 0.173892i 0.162769 0.986664i \(-0.447958\pi\)
−0.582582 + 0.812772i \(0.697958\pi\)
\(132\) 0 0
\(133\) −2.84785 6.87531i −0.246940 0.596165i
\(134\) 0 0
\(135\) 1.38748 1.38748i 0.119415 0.119415i
\(136\) 0 0
\(137\) 6.45738 + 6.45738i 0.551691 + 0.551691i 0.926929 0.375238i \(-0.122439\pi\)
−0.375238 + 0.926929i \(0.622439\pi\)
\(138\) 0 0
\(139\) 13.8089 5.71982i 1.17125 0.485149i 0.289646 0.957134i \(-0.406462\pi\)
0.881607 + 0.471985i \(0.156462\pi\)
\(140\) 0 0
\(141\) −1.23072 + 2.97121i −0.103645 + 0.250221i
\(142\) 0 0
\(143\) 1.52338i 0.127392i
\(144\) 0 0
\(145\) 1.37463i 0.114157i
\(146\) 0 0
\(147\) 2.36680 5.71395i 0.195210 0.471279i
\(148\) 0 0
\(149\) 6.65965 2.75852i 0.545580 0.225987i −0.0928315 0.995682i \(-0.529592\pi\)
0.638412 + 0.769695i \(0.279592\pi\)
\(150\) 0 0
\(151\) −4.80906 4.80906i −0.391355 0.391355i 0.483815 0.875170i \(-0.339251\pi\)
−0.875170 + 0.483815i \(0.839251\pi\)
\(152\) 0 0
\(153\) 1.07672 1.07672i 0.0870479 0.0870479i
\(154\) 0 0
\(155\) 2.75174 + 6.64328i 0.221025 + 0.533601i
\(156\) 0 0
\(157\) −8.75017 3.62444i −0.698340 0.289262i 0.00513017 0.999987i \(-0.498367\pi\)
−0.703470 + 0.710725i \(0.748367\pi\)
\(158\) 0 0
\(159\) −8.35023 −0.662217
\(160\) 0 0
\(161\) −7.66786 −0.604312
\(162\) 0 0
\(163\) 15.2806 + 6.32945i 1.19687 + 0.495761i 0.889987 0.455986i \(-0.150713\pi\)
0.306885 + 0.951747i \(0.400713\pi\)
\(164\) 0 0
\(165\) −0.278856 0.673219i −0.0217089 0.0524100i
\(166\) 0 0
\(167\) −7.16635 + 7.16635i −0.554549 + 0.554549i −0.927750 0.373201i \(-0.878260\pi\)
0.373201 + 0.927750i \(0.378260\pi\)
\(168\) 0 0
\(169\) −2.70638 2.70638i −0.208183 0.208183i
\(170\) 0 0
\(171\) −7.61453 + 3.15404i −0.582298 + 0.241196i
\(172\) 0 0
\(173\) −4.47280 + 10.7983i −0.340061 + 0.820979i 0.657648 + 0.753325i \(0.271551\pi\)
−0.997709 + 0.0676539i \(0.978449\pi\)
\(174\) 0 0
\(175\) 1.03819i 0.0784800i
\(176\) 0 0
\(177\) 7.28285i 0.547413i
\(178\) 0 0
\(179\) 1.44741 3.49435i 0.108184 0.261180i −0.860511 0.509431i \(-0.829856\pi\)
0.968696 + 0.248251i \(0.0798558\pi\)
\(180\) 0 0
\(181\) −10.1985 + 4.22436i −0.758049 + 0.313994i −0.728021 0.685555i \(-0.759560\pi\)
−0.0300283 + 0.999549i \(0.509560\pi\)
\(182\) 0 0
\(183\) 8.02424 + 8.02424i 0.593169 + 0.593169i
\(184\) 0 0
\(185\) −13.3791 + 13.3791i −0.983654 + 0.983654i
\(186\) 0 0
\(187\) −0.216401 0.522438i −0.0158248 0.0382044i
\(188\) 0 0
\(189\) 0.834188 + 0.345532i 0.0606783 + 0.0251338i
\(190\) 0 0
\(191\) 1.23454 0.0893282 0.0446641 0.999002i \(-0.485778\pi\)
0.0446641 + 0.999002i \(0.485778\pi\)
\(192\) 0 0
\(193\) 11.6382 0.837739 0.418869 0.908047i \(-0.362427\pi\)
0.418869 + 0.908047i \(0.362427\pi\)
\(194\) 0 0
\(195\) 7.43643 + 3.08027i 0.532534 + 0.220583i
\(196\) 0 0
\(197\) −7.96962 19.2404i −0.567812 1.37082i −0.903395 0.428809i \(-0.858933\pi\)
0.335583 0.942011i \(-0.391067\pi\)
\(198\) 0 0
\(199\) −10.3810 + 10.3810i −0.735892 + 0.735892i −0.971780 0.235888i \(-0.924200\pi\)
0.235888 + 0.971780i \(0.424200\pi\)
\(200\) 0 0
\(201\) 5.02717 + 5.02717i 0.354589 + 0.354589i
\(202\) 0 0
\(203\) 0.584398 0.242066i 0.0410167 0.0169897i
\(204\) 0 0
\(205\) 8.70738 21.0215i 0.608149 1.46820i
\(206\) 0 0
\(207\) 8.49230i 0.590256i
\(208\) 0 0
\(209\) 3.06075i 0.211717i
\(210\) 0 0
\(211\) 0.213911 0.516427i 0.0147262 0.0355523i −0.916345 0.400389i \(-0.868875\pi\)
0.931072 + 0.364836i \(0.118875\pi\)
\(212\) 0 0
\(213\) 1.25057 0.518005i 0.0856879 0.0354931i
\(214\) 0 0
\(215\) 2.79748 + 2.79748i 0.190787 + 0.190787i
\(216\) 0 0
\(217\) −2.33970 + 2.33970i −0.158829 + 0.158829i
\(218\) 0 0
\(219\) 1.16036 + 2.80135i 0.0784098 + 0.189298i
\(220\) 0 0
\(221\) 5.77089 + 2.39038i 0.388192 + 0.160794i
\(222\) 0 0
\(223\) 23.4290 1.56892 0.784460 0.620179i \(-0.212940\pi\)
0.784460 + 0.620179i \(0.212940\pi\)
\(224\) 0 0
\(225\) 1.14982 0.0766545
\(226\) 0 0
\(227\) 11.5345 + 4.77773i 0.765568 + 0.317109i 0.731076 0.682296i \(-0.239019\pi\)
0.0344925 + 0.999405i \(0.489019\pi\)
\(228\) 0 0
\(229\) 7.39995 + 17.8651i 0.489002 + 1.18056i 0.955223 + 0.295888i \(0.0956154\pi\)
−0.466220 + 0.884669i \(0.654385\pi\)
\(230\) 0 0
\(231\) 0.237101 0.237101i 0.0156001 0.0156001i
\(232\) 0 0
\(233\) 7.86004 + 7.86004i 0.514928 + 0.514928i 0.916033 0.401104i \(-0.131373\pi\)
−0.401104 + 0.916033i \(0.631373\pi\)
\(234\) 0 0
\(235\) 5.83008 2.41490i 0.380313 0.157531i
\(236\) 0 0
\(237\) −0.240384 + 0.580339i −0.0156146 + 0.0376971i
\(238\) 0 0
\(239\) 26.1171i 1.68937i 0.535262 + 0.844686i \(0.320213\pi\)
−0.535262 + 0.844686i \(0.679787\pi\)
\(240\) 0 0
\(241\) 12.8873i 0.830144i −0.909788 0.415072i \(-0.863756\pi\)
0.909788 0.415072i \(-0.136244\pi\)
\(242\) 0 0
\(243\) 0.382683 0.923880i 0.0245492 0.0592669i
\(244\) 0 0
\(245\) −11.2118 + 4.64410i −0.716299 + 0.296701i
\(246\) 0 0
\(247\) −23.9068 23.9068i −1.52115 1.52115i
\(248\) 0 0
\(249\) −7.71974 + 7.71974i −0.489218 + 0.489218i
\(250\) 0 0
\(251\) −0.265442 0.640835i −0.0167546 0.0404491i 0.915281 0.402816i \(-0.131969\pi\)
−0.932035 + 0.362367i \(0.881969\pi\)
\(252\) 0 0
\(253\) 2.91368 + 1.20688i 0.183181 + 0.0758761i
\(254\) 0 0
\(255\) −2.98786 −0.187107
\(256\) 0 0
\(257\) −10.6839 −0.666442 −0.333221 0.942849i \(-0.608136\pi\)
−0.333221 + 0.942849i \(0.608136\pi\)
\(258\) 0 0
\(259\) −8.04390 3.33189i −0.499824 0.207034i
\(260\) 0 0
\(261\) −0.268092 0.647232i −0.0165945 0.0400627i
\(262\) 0 0
\(263\) −0.733161 + 0.733161i −0.0452086 + 0.0452086i −0.729350 0.684141i \(-0.760177\pi\)
0.684141 + 0.729350i \(0.260177\pi\)
\(264\) 0 0
\(265\) 11.5858 + 11.5858i 0.711707 + 0.711707i
\(266\) 0 0
\(267\) −11.3733 + 4.71097i −0.696034 + 0.288307i
\(268\) 0 0
\(269\) 0.757304 1.82829i 0.0461736 0.111473i −0.899110 0.437723i \(-0.855785\pi\)
0.945284 + 0.326250i \(0.105785\pi\)
\(270\) 0 0
\(271\) 4.80909i 0.292131i −0.989275 0.146066i \(-0.953339\pi\)
0.989275 0.146066i \(-0.0466611\pi\)
\(272\) 0 0
\(273\) 3.70388i 0.224169i
\(274\) 0 0
\(275\) 0.163406 0.394498i 0.00985378 0.0237891i
\(276\) 0 0
\(277\) 8.34968 3.45855i 0.501684 0.207804i −0.117466 0.993077i \(-0.537477\pi\)
0.619150 + 0.785273i \(0.287477\pi\)
\(278\) 0 0
\(279\) 2.59126 + 2.59126i 0.155135 + 0.155135i
\(280\) 0 0
\(281\) 8.76860 8.76860i 0.523091 0.523091i −0.395413 0.918504i \(-0.629398\pi\)
0.918504 + 0.395413i \(0.129398\pi\)
\(282\) 0 0
\(283\) −7.62757 18.4146i −0.453412 1.09463i −0.971016 0.239013i \(-0.923176\pi\)
0.517605 0.855620i \(-0.326824\pi\)
\(284\) 0 0
\(285\) 14.9411 + 6.18883i 0.885037 + 0.366594i
\(286\) 0 0
\(287\) 10.4702 0.618038
\(288\) 0 0
\(289\) 14.6813 0.863608
\(290\) 0 0
\(291\) −9.45936 3.91819i −0.554517 0.229689i
\(292\) 0 0
\(293\) 3.54788 + 8.56535i 0.207270 + 0.500393i 0.992991 0.118187i \(-0.0377082\pi\)
−0.785722 + 0.618580i \(0.787708\pi\)
\(294\) 0 0
\(295\) 10.1048 10.1048i 0.588323 0.588323i
\(296\) 0 0
\(297\) −0.262594 0.262594i −0.0152373 0.0152373i
\(298\) 0 0
\(299\) −32.1847 + 13.3313i −1.86129 + 0.770971i
\(300\) 0 0
\(301\) −0.696674 + 1.68192i −0.0401556 + 0.0969443i
\(302\) 0 0
\(303\) 3.57042i 0.205116i
\(304\) 0 0
\(305\) 22.2669i 1.27500i
\(306\) 0 0
\(307\) 10.9217 26.3674i 0.623336 1.50487i −0.224427 0.974491i \(-0.572051\pi\)
0.847763 0.530375i \(-0.177949\pi\)
\(308\) 0 0
\(309\) −2.64415 + 1.09524i −0.150420 + 0.0623062i
\(310\) 0 0
\(311\) −10.0285 10.0285i −0.568665 0.568665i 0.363089 0.931754i \(-0.381722\pi\)
−0.931754 + 0.363089i \(0.881722\pi\)
\(312\) 0 0
\(313\) −13.6930 + 13.6930i −0.773973 + 0.773973i −0.978799 0.204826i \(-0.934337\pi\)
0.204826 + 0.978799i \(0.434337\pi\)
\(314\) 0 0
\(315\) −0.677999 1.63683i −0.0382009 0.0922252i
\(316\) 0 0
\(317\) −3.88745 1.61024i −0.218341 0.0904398i 0.270832 0.962627i \(-0.412701\pi\)
−0.489173 + 0.872187i \(0.662701\pi\)
\(318\) 0 0
\(319\) −0.260163 −0.0145663
\(320\) 0 0
\(321\) −9.52821 −0.531813
\(322\) 0 0
\(323\) 11.5948 + 4.80271i 0.645150 + 0.267230i
\(324\) 0 0
\(325\) 1.80500 + 4.35765i 0.100123 + 0.241719i
\(326\) 0 0
\(327\) −6.61705 + 6.61705i −0.365924 + 0.365924i
\(328\) 0 0
\(329\) 2.05330 + 2.05330i 0.113202 + 0.113202i
\(330\) 0 0
\(331\) −24.2486 + 10.0441i −1.33283 + 0.552074i −0.931460 0.363844i \(-0.881464\pi\)
−0.401365 + 0.915918i \(0.631464\pi\)
\(332\) 0 0
\(333\) −3.69013 + 8.90877i −0.202218 + 0.488198i
\(334\) 0 0
\(335\) 13.9501i 0.762178i
\(336\) 0 0
\(337\) 28.8246i 1.57018i −0.619383 0.785089i \(-0.712617\pi\)
0.619383 0.785089i \(-0.287383\pi\)
\(338\) 0 0
\(339\) 4.02075 9.70696i 0.218377 0.527210i
\(340\) 0 0
\(341\) 1.25731 0.520795i 0.0680871 0.0282026i
\(342\) 0 0
\(343\) −8.41793 8.41793i −0.454525 0.454525i
\(344\) 0 0
\(345\) 11.7829 11.7829i 0.634368 0.634368i
\(346\) 0 0
\(347\) 9.62155 + 23.2285i 0.516512 + 1.24697i 0.940033 + 0.341084i \(0.110794\pi\)
−0.423521 + 0.905886i \(0.639206\pi\)
\(348\) 0 0
\(349\) −0.998904 0.413760i −0.0534701 0.0221480i 0.355788 0.934567i \(-0.384212\pi\)
−0.409258 + 0.912419i \(0.634212\pi\)
\(350\) 0 0
\(351\) 4.10212 0.218955
\(352\) 0 0
\(353\) 0.259074 0.0137891 0.00689456 0.999976i \(-0.497805\pi\)
0.00689456 + 0.999976i \(0.497805\pi\)
\(354\) 0 0
\(355\) −2.45386 1.01642i −0.130237 0.0539461i
\(356\) 0 0
\(357\) −0.526147 1.27023i −0.0278467 0.0672278i
\(358\) 0 0
\(359\) 19.4929 19.4929i 1.02879 1.02879i 0.0292206 0.999573i \(-0.490697\pi\)
0.999573 0.0292206i \(-0.00930254\pi\)
\(360\) 0 0
\(361\) −34.5981 34.5981i −1.82095 1.82095i
\(362\) 0 0
\(363\) 10.0353 4.15674i 0.526715 0.218172i
\(364\) 0 0
\(365\) 2.27684 5.49678i 0.119175 0.287715i
\(366\) 0 0
\(367\) 20.4476i 1.06735i 0.845689 + 0.533677i \(0.179190\pi\)
−0.845689 + 0.533677i \(0.820810\pi\)
\(368\) 0 0
\(369\) 11.5960i 0.603662i
\(370\) 0 0
\(371\) −2.88527 + 6.96567i −0.149796 + 0.361640i
\(372\) 0 0
\(373\) −9.59680 + 3.97512i −0.496903 + 0.205824i −0.617038 0.786934i \(-0.711667\pi\)
0.120134 + 0.992758i \(0.461667\pi\)
\(374\) 0 0
\(375\) −8.53273 8.53273i −0.440628 0.440628i
\(376\) 0 0
\(377\) 2.03207 2.03207i 0.104657 0.104657i
\(378\) 0 0
\(379\) −2.18850 5.28351i −0.112416 0.271396i 0.857652 0.514231i \(-0.171923\pi\)
−0.970068 + 0.242835i \(0.921923\pi\)
\(380\) 0 0
\(381\) 2.13360 + 0.883764i 0.109307 + 0.0452766i
\(382\) 0 0
\(383\) 25.5047 1.30323 0.651614 0.758550i \(-0.274092\pi\)
0.651614 + 0.758550i \(0.274092\pi\)
\(384\) 0 0
\(385\) −0.657945 −0.0335320
\(386\) 0 0
\(387\) 1.86276 + 0.771580i 0.0946893 + 0.0392216i
\(388\) 0 0
\(389\) −10.0662 24.3021i −0.510379 1.23216i −0.943664 0.330907i \(-0.892646\pi\)
0.433285 0.901257i \(-0.357354\pi\)
\(390\) 0 0
\(391\) 9.14386 9.14386i 0.462425 0.462425i
\(392\) 0 0
\(393\) 3.67758 + 3.67758i 0.185509 + 0.185509i
\(394\) 0 0
\(395\) 1.13873 0.471679i 0.0572960 0.0237328i
\(396\) 0 0
\(397\) 0.0155261 0.0374832i 0.000779230 0.00188123i −0.923489 0.383624i \(-0.874676\pi\)
0.924269 + 0.381743i \(0.124676\pi\)
\(398\) 0 0
\(399\) 7.44178i 0.372555i
\(400\) 0 0
\(401\) 7.24998i 0.362047i −0.983479 0.181023i \(-0.942059\pi\)
0.983479 0.181023i \(-0.0579410\pi\)
\(402\) 0 0
\(403\) −5.75274 + 13.8883i −0.286564 + 0.691827i
\(404\) 0 0
\(405\) −1.81283 + 0.750897i −0.0900800 + 0.0373124i
\(406\) 0 0
\(407\) 2.53214 + 2.53214i 0.125514 + 0.125514i
\(408\) 0 0
\(409\) 4.79664 4.79664i 0.237179 0.237179i −0.578502 0.815681i \(-0.696363\pi\)
0.815681 + 0.578502i \(0.196363\pi\)
\(410\) 0 0
\(411\) −3.49471 8.43697i −0.172381 0.416165i
\(412\) 0 0
\(413\) 6.07527 + 2.51646i 0.298945 + 0.123827i
\(414\) 0 0
\(415\) 21.4219 1.05156
\(416\) 0 0
\(417\) −14.9466 −0.731939
\(418\) 0 0
\(419\) −25.2331 10.4519i −1.23272 0.510608i −0.331285 0.943531i \(-0.607482\pi\)
−0.901431 + 0.432923i \(0.857482\pi\)
\(420\) 0 0
\(421\) −4.02613 9.71993i −0.196222 0.473721i 0.794890 0.606753i \(-0.207528\pi\)
−0.991112 + 0.133033i \(0.957528\pi\)
\(422\) 0 0
\(423\) 2.27407 2.27407i 0.110569 0.110569i
\(424\) 0 0
\(425\) −1.23804 1.23804i −0.0600535 0.0600535i
\(426\) 0 0
\(427\) 9.46636 3.92109i 0.458109 0.189755i
\(428\) 0 0
\(429\) 0.582973 1.40742i 0.0281462 0.0679510i
\(430\) 0 0
\(431\) 32.0275i 1.54271i −0.636404 0.771356i \(-0.719579\pi\)
0.636404 0.771356i \(-0.280421\pi\)
\(432\) 0 0
\(433\) 15.7159i 0.755258i −0.925957 0.377629i \(-0.876739\pi\)
0.925957 0.377629i \(-0.123261\pi\)
\(434\) 0 0
\(435\) −0.526048 + 1.26999i −0.0252221 + 0.0608914i
\(436\) 0 0
\(437\) −64.6649 + 26.7851i −3.09334 + 1.28130i
\(438\) 0 0
\(439\) 15.0452 + 15.0452i 0.718067 + 0.718067i 0.968209 0.250143i \(-0.0804775\pi\)
−0.250143 + 0.968209i \(0.580477\pi\)
\(440\) 0 0
\(441\) −4.37327 + 4.37327i −0.208251 + 0.208251i
\(442\) 0 0
\(443\) −0.935563 2.25865i −0.0444499 0.107312i 0.900095 0.435693i \(-0.143497\pi\)
−0.944545 + 0.328382i \(0.893497\pi\)
\(444\) 0 0
\(445\) 22.3165 + 9.24381i 1.05791 + 0.438199i
\(446\) 0 0
\(447\) −7.20836 −0.340944
\(448\) 0 0
\(449\) 39.2374 1.85173 0.925865 0.377855i \(-0.123338\pi\)
0.925865 + 0.377855i \(0.123338\pi\)
\(450\) 0 0
\(451\) −3.97853 1.64796i −0.187342 0.0775995i
\(452\) 0 0
\(453\) 2.60264 + 6.28333i 0.122283 + 0.295217i
\(454\) 0 0
\(455\) 5.13905 5.13905i 0.240922 0.240922i
\(456\) 0 0
\(457\) 25.5724 + 25.5724i 1.19623 + 1.19623i 0.975287 + 0.220940i \(0.0709125\pi\)
0.220940 + 0.975287i \(0.429088\pi\)
\(458\) 0 0
\(459\) −1.40681 + 0.582718i −0.0656641 + 0.0271990i
\(460\) 0 0
\(461\) −6.04846 + 14.6023i −0.281705 + 0.680096i −0.999876 0.0157709i \(-0.994980\pi\)
0.718171 + 0.695867i \(0.244980\pi\)
\(462\) 0 0
\(463\) 18.8446i 0.875785i 0.899027 + 0.437892i \(0.144275\pi\)
−0.899027 + 0.437892i \(0.855725\pi\)
\(464\) 0 0
\(465\) 7.19063i 0.333458i
\(466\) 0 0
\(467\) 8.99695 21.7206i 0.416329 1.00511i −0.567073 0.823668i \(-0.691924\pi\)
0.983402 0.181440i \(-0.0580758\pi\)
\(468\) 0 0
\(469\) 5.93065 2.45656i 0.273852 0.113433i
\(470\) 0 0
\(471\) 6.69709 + 6.69709i 0.308586 + 0.308586i
\(472\) 0 0
\(473\) 0.529452 0.529452i 0.0243442 0.0243442i
\(474\) 0 0
\(475\) 3.62657 + 8.75533i 0.166399 + 0.401722i
\(476\) 0 0
\(477\) 7.71461 + 3.19550i 0.353228 + 0.146312i
\(478\) 0 0
\(479\) −37.2438 −1.70171 −0.850857 0.525397i \(-0.823917\pi\)
−0.850857 + 0.525397i \(0.823917\pi\)
\(480\) 0 0
\(481\) −39.5559 −1.80359
\(482\) 0 0
\(483\) 7.08418 + 2.93436i 0.322341 + 0.133518i
\(484\) 0 0
\(485\) 7.68823 + 18.5610i 0.349105 + 0.842813i
\(486\) 0 0
\(487\) −27.2623 + 27.2623i −1.23537 + 1.23537i −0.273503 + 0.961871i \(0.588182\pi\)
−0.961871 + 0.273503i \(0.911818\pi\)
\(488\) 0 0
\(489\) −11.6953 11.6953i −0.528879 0.528879i
\(490\) 0 0
\(491\) −26.3108 + 10.8983i −1.18739 + 0.491832i −0.886904 0.461955i \(-0.847148\pi\)
−0.300484 + 0.953787i \(0.597148\pi\)
\(492\) 0 0
\(493\) −0.408229 + 0.985551i −0.0183857 + 0.0443870i
\(494\) 0 0
\(495\) 0.728687i 0.0327520i
\(496\) 0 0
\(497\) 1.22220i 0.0548232i
\(498\) 0 0
\(499\) −2.00327 + 4.83631i −0.0896785 + 0.216503i −0.962355 0.271796i \(-0.912382\pi\)
0.872676 + 0.488299i \(0.162382\pi\)
\(500\) 0 0
\(501\) 9.36329 3.87840i 0.418321 0.173274i
\(502\) 0 0
\(503\) 9.33046 + 9.33046i 0.416024 + 0.416024i 0.883831 0.467806i \(-0.154956\pi\)
−0.467806 + 0.883831i \(0.654956\pi\)
\(504\) 0 0
\(505\) −4.95388 + 4.95388i −0.220445 + 0.220445i
\(506\) 0 0
\(507\) 1.46468 + 3.53605i 0.0650488 + 0.157042i
\(508\) 0 0
\(509\) −4.91588 2.03622i −0.217893 0.0902541i 0.271067 0.962560i \(-0.412623\pi\)
−0.488960 + 0.872306i \(0.662623\pi\)
\(510\) 0 0
\(511\) 2.73780 0.121113
\(512\) 0 0
\(513\) 8.24191 0.363889
\(514\) 0 0
\(515\) 5.18832 + 2.14907i 0.228625 + 0.0946995i
\(516\) 0 0
\(517\) −0.457045 1.10340i −0.0201008 0.0485276i
\(518\) 0 0
\(519\) 8.26466 8.26466i 0.362778 0.362778i
\(520\) 0 0
\(521\) 10.3057 + 10.3057i 0.451502 + 0.451502i 0.895853 0.444351i \(-0.146566\pi\)
−0.444351 + 0.895853i \(0.646566\pi\)
\(522\) 0 0
\(523\) 1.09031 0.451621i 0.0476759 0.0197480i −0.358718 0.933446i \(-0.616786\pi\)
0.406394 + 0.913698i \(0.366786\pi\)
\(524\) 0 0
\(525\) 0.397299 0.959165i 0.0173396 0.0418614i
\(526\) 0 0
\(527\) 5.58014i 0.243075i
\(528\) 0 0
\(529\) 49.1192i 2.13562i
\(530\) 0 0
\(531\) 2.78703 6.72848i 0.120947 0.291991i
\(532\) 0 0
\(533\) 43.9472 18.2035i 1.90356 0.788481i
\(534\) 0 0
\(535\) 13.2202 + 13.2202i 0.571558 + 0.571558i
\(536\) 0 0
\(537\) −2.67446 + 2.67446i −0.115412 + 0.115412i
\(538\) 0 0
\(539\) 0.878944 + 2.12196i 0.0378588 + 0.0913993i
\(540\) 0 0
\(541\) 29.9414 + 12.4021i 1.28728 + 0.533209i 0.918174 0.396177i \(-0.129663\pi\)
0.369107 + 0.929387i \(0.379663\pi\)
\(542\) 0 0
\(543\) 11.0388 0.473720
\(544\) 0 0
\(545\) 18.3620 0.786541
\(546\) 0 0
\(547\) −7.78227 3.22352i −0.332746 0.137828i 0.210054 0.977690i \(-0.432636\pi\)
−0.542800 + 0.839862i \(0.682636\pi\)
\(548\) 0 0
\(549\) −4.34269 10.4842i −0.185341 0.447454i
\(550\) 0 0
\(551\) 4.08280 4.08280i 0.173933 0.173933i
\(552\) 0 0
\(553\) 0.401052 + 0.401052i 0.0170545 + 0.0170545i
\(554\) 0 0
\(555\) 17.4807 7.24074i 0.742014 0.307352i
\(556\) 0 0
\(557\) 5.41814 13.0806i 0.229574 0.554241i −0.766551 0.642183i \(-0.778029\pi\)
0.996126 + 0.0879419i \(0.0280290\pi\)
\(558\) 0 0
\(559\) 8.27084i 0.349819i
\(560\) 0 0
\(561\) 0.565483i 0.0238747i
\(562\) 0 0
\(563\) −10.5280 + 25.4168i −0.443702 + 1.07119i 0.530938 + 0.847411i \(0.321840\pi\)
−0.974640 + 0.223780i \(0.928160\pi\)
\(564\) 0 0
\(565\) −19.0469 + 7.88947i −0.801308 + 0.331913i
\(566\) 0 0
\(567\) −0.638460 0.638460i −0.0268128 0.0268128i
\(568\) 0 0
\(569\) −0.593219 + 0.593219i −0.0248690 + 0.0248690i −0.719432 0.694563i \(-0.755598\pi\)
0.694563 + 0.719432i \(0.255598\pi\)
\(570\) 0 0
\(571\) 8.10194 + 19.5598i 0.339056 + 0.818553i 0.997807 + 0.0661921i \(0.0210850\pi\)
−0.658751 + 0.752361i \(0.728915\pi\)
\(572\) 0 0
\(573\) −1.14057 0.472438i −0.0476479 0.0197364i
\(574\) 0 0
\(575\) 9.76460 0.407212
\(576\) 0 0
\(577\) −11.2774 −0.469484 −0.234742 0.972058i \(-0.575424\pi\)
−0.234742 + 0.972058i \(0.575424\pi\)
\(578\) 0 0
\(579\) −10.7523 4.45376i −0.446852 0.185092i
\(580\) 0 0
\(581\) 3.77230 + 9.10713i 0.156501 + 0.377828i
\(582\) 0 0
\(583\) 2.19272 2.19272i 0.0908134 0.0908134i
\(584\) 0 0
\(585\) −5.69160 5.69160i −0.235319 0.235319i
\(586\) 0 0
\(587\) 6.13139 2.53970i 0.253070 0.104825i −0.252542 0.967586i \(-0.581267\pi\)
0.505612 + 0.862761i \(0.331267\pi\)
\(588\) 0 0
\(589\) −11.5583 + 27.9042i −0.476251 + 1.14977i
\(590\) 0 0
\(591\) 20.8256i 0.856652i
\(592\) 0 0
\(593\) 26.2096i 1.07630i 0.842849 + 0.538149i \(0.180876\pi\)
−0.842849 + 0.538149i \(0.819124\pi\)
\(594\) 0 0
\(595\) −1.03240 + 2.49243i −0.0423243 + 0.102180i
\(596\) 0 0
\(597\) 13.5635 5.61818i 0.555116 0.229937i
\(598\) 0 0
\(599\) −30.3211 30.3211i −1.23888 1.23888i −0.960457 0.278428i \(-0.910187\pi\)
−0.278428 0.960457i \(-0.589813\pi\)
\(600\) 0 0
\(601\) 9.96259 9.96259i 0.406383 0.406383i −0.474092 0.880475i \(-0.657224\pi\)
0.880475 + 0.474092i \(0.157224\pi\)
\(602\) 0 0
\(603\) −2.72068 6.56831i −0.110795 0.267482i
\(604\) 0 0
\(605\) −19.6911 8.15631i −0.800556 0.331601i
\(606\) 0 0
\(607\) −17.4543 −0.708447 −0.354223 0.935161i \(-0.615255\pi\)
−0.354223 + 0.935161i \(0.615255\pi\)
\(608\) 0 0
\(609\) −0.632548 −0.0256321
\(610\) 0 0
\(611\) 12.1883 + 5.04855i 0.493085 + 0.204243i
\(612\) 0 0
\(613\) 12.6691 + 30.5860i 0.511701 + 1.23536i 0.942893 + 0.333095i \(0.108093\pi\)
−0.431192 + 0.902260i \(0.641907\pi\)
\(614\) 0 0
\(615\) −16.0891 + 16.0891i −0.648776 + 0.648776i
\(616\) 0 0
\(617\) −5.81018 5.81018i −0.233909 0.233909i 0.580413 0.814322i \(-0.302891\pi\)
−0.814322 + 0.580413i \(0.802891\pi\)
\(618\) 0 0
\(619\) 9.00884 3.73158i 0.362096 0.149985i −0.194216 0.980959i \(-0.562216\pi\)
0.556312 + 0.830974i \(0.312216\pi\)
\(620\) 0 0
\(621\) 3.24986 7.84586i 0.130413 0.314844i
\(622\) 0 0
\(623\) 11.1153i 0.445324i
\(624\) 0 0
\(625\) 17.9288i 0.717153i
\(626\) 0 0
\(627\) 1.17130 2.82777i 0.0467772 0.112930i
\(628\) 0 0
\(629\) 13.5655 5.61903i 0.540893 0.224045i
\(630\) 0 0
\(631\) 8.01798 + 8.01798i 0.319191 + 0.319191i 0.848456 0.529266i \(-0.177532\pi\)
−0.529266 + 0.848456i \(0.677532\pi\)
\(632\) 0 0
\(633\) −0.395256 + 0.395256i −0.0157100 + 0.0157100i
\(634\) 0 0
\(635\) −1.73411 4.18652i −0.0688161 0.166137i
\(636\) 0 0
\(637\) −23.4393 9.70889i −0.928700 0.384680i
\(638\) 0 0
\(639\) −1.35361 −0.0535481
\(640\) 0 0
\(641\) −7.70306 −0.304253 −0.152126 0.988361i \(-0.548612\pi\)
−0.152126 + 0.988361i \(0.548612\pi\)
\(642\) 0 0
\(643\) 15.6982 + 6.50239i 0.619075 + 0.256429i 0.670103 0.742268i \(-0.266250\pi\)
−0.0510280 + 0.998697i \(0.516250\pi\)
\(644\) 0 0
\(645\) −1.51398 3.65508i −0.0596131 0.143919i
\(646\) 0 0
\(647\) 4.89235 4.89235i 0.192338 0.192338i −0.604367 0.796706i \(-0.706574\pi\)
0.796706 + 0.604367i \(0.206574\pi\)
\(648\) 0 0
\(649\) −1.91244 1.91244i −0.0750697 0.0750697i
\(650\) 0 0
\(651\) 3.05697 1.26624i 0.119812 0.0496277i
\(652\) 0 0
\(653\) 8.81462 21.2804i 0.344943 0.832766i −0.652258 0.757997i \(-0.726178\pi\)
0.997201 0.0747688i \(-0.0238219\pi\)
\(654\) 0 0
\(655\) 10.2051i 0.398746i
\(656\) 0 0
\(657\) 3.03216i 0.118296i
\(658\) 0 0
\(659\) −6.42799 + 15.5185i −0.250399 + 0.604516i −0.998236 0.0593655i \(-0.981092\pi\)
0.747837 + 0.663882i \(0.231092\pi\)
\(660\) 0 0
\(661\) 34.2088 14.1697i 1.33057 0.551139i 0.399750 0.916624i \(-0.369097\pi\)
0.930817 + 0.365486i \(0.119097\pi\)
\(662\) 0 0
\(663\) −4.41685 4.41685i −0.171536 0.171536i
\(664\) 0 0
\(665\) 10.3253 10.3253i 0.400398 0.400398i
\(666\) 0 0
\(667\) −2.27672 5.49649i −0.0881550 0.212825i
\(668\) 0 0
\(669\) −21.6455 8.96588i −0.836865 0.346641i
\(670\) 0 0
\(671\) −4.21424 −0.162689
\(672\) 0 0
\(673\) 8.37057 0.322662 0.161331 0.986900i \(-0.448421\pi\)
0.161331 + 0.986900i \(0.448421\pi\)
\(674\) 0 0
\(675\) −1.06229 0.440016i −0.0408877 0.0169362i
\(676\) 0 0
\(677\) −3.93149 9.49145i −0.151099 0.364786i 0.830147 0.557545i \(-0.188257\pi\)
−0.981246 + 0.192759i \(0.938257\pi\)
\(678\) 0 0
\(679\) −6.53702 + 6.53702i −0.250868 + 0.250868i
\(680\) 0 0
\(681\) −8.82809 8.82809i −0.338293 0.338293i
\(682\) 0 0
\(683\) 8.70888 3.60734i 0.333236 0.138031i −0.209791 0.977746i \(-0.567278\pi\)
0.543027 + 0.839715i \(0.317278\pi\)
\(684\) 0 0
\(685\) −6.85727 + 16.5549i −0.262003 + 0.632531i
\(686\) 0 0
\(687\) 19.3370i 0.737753i
\(688\) 0 0
\(689\) 34.2537i 1.30496i
\(690\) 0 0
\(691\) −0.128590 + 0.310443i −0.00489178 + 0.0118098i −0.926307 0.376771i \(-0.877034\pi\)
0.921415 + 0.388581i \(0.127034\pi\)
\(692\) 0 0
\(693\) −0.309788 + 0.128318i −0.0117679 + 0.00487441i
\(694\) 0 0
\(695\) 20.7381 + 20.7381i 0.786640 + 0.786640i
\(696\) 0 0
\(697\) −12.4856 + 12.4856i −0.472927 + 0.472927i
\(698\) 0 0
\(699\) −4.25382 10.2696i −0.160894 0.388433i
\(700\) 0 0
\(701\) −29.8219 12.3527i −1.12636 0.466553i −0.259817 0.965658i \(-0.583662\pi\)
−0.866542 + 0.499104i \(0.833662\pi\)
\(702\) 0 0
\(703\) −79.4750 −2.99746
\(704\) 0 0
\(705\) −6.31044 −0.237665
\(706\) 0 0
\(707\) −2.97841 1.23370i −0.112015 0.0463979i
\(708\) 0 0
\(709\) −11.8266 28.5520i −0.444158 1.07229i −0.974476 0.224494i \(-0.927927\pi\)
0.530317 0.847799i \(-0.322073\pi\)
\(710\) 0 0
\(711\) 0.444172 0.444172i 0.0166578 0.0166578i
\(712\) 0 0
\(713\) 22.0058 + 22.0058i 0.824123 + 0.824123i
\(714\) 0 0
\(715\) −2.76163 + 1.14390i −0.103279 + 0.0427795i
\(716\) 0 0
\(717\) 9.99457 24.1290i 0.373254 0.901115i
\(718\) 0 0
\(719\) 34.8049i 1.29801i −0.760786 0.649003i \(-0.775186\pi\)
0.760786 0.649003i \(-0.224814\pi\)
\(720\) 0 0
\(721\) 2.58416i 0.0962392i
\(722\) 0 0
\(723\) −4.93176 + 11.9063i −0.183414 + 0.442801i
\(724\) 0 0
\(725\) −0.744199 + 0.308257i −0.0276389 + 0.0114484i
\(726\) 0 0
\(727\) 4.11603 + 4.11603i 0.152655 + 0.152655i 0.779303 0.626648i \(-0.215573\pi\)
−0.626648 + 0.779303i \(0.715573\pi\)
\(728\) 0 0
\(729\) −0.707107 + 0.707107i −0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) −1.17490 2.83645i −0.0434551 0.104910i
\(732\) 0 0
\(733\) −30.7463 12.7356i −1.13564 0.470398i −0.265947 0.963988i \(-0.585685\pi\)
−0.869695 + 0.493589i \(0.835685\pi\)
\(734\) 0 0
\(735\) 12.1356 0.447629
\(736\) 0 0
\(737\) −2.64021 −0.0972534
\(738\) 0 0
\(739\) 34.5685 + 14.3188i 1.27162 + 0.526724i 0.913458 0.406934i \(-0.133402\pi\)
0.358166 + 0.933658i \(0.383402\pi\)
\(740\) 0 0
\(741\) 12.9383 + 31.2357i 0.475299 + 1.14747i
\(742\) 0 0
\(743\) −10.7639 + 10.7639i −0.394888 + 0.394888i −0.876425 0.481538i \(-0.840078\pi\)
0.481538 + 0.876425i \(0.340078\pi\)
\(744\) 0 0
\(745\) 10.0014 + 10.0014i 0.366424 + 0.366424i
\(746\) 0 0
\(747\) 10.0863 4.17789i 0.369039 0.152861i
\(748\) 0 0
\(749\) −3.29230 + 7.94832i −0.120298 + 0.290425i
\(750\) 0 0
\(751\) 19.3932i 0.707669i −0.935308 0.353835i \(-0.884878\pi\)
0.935308 0.353835i \(-0.115122\pi\)
\(752\) 0 0
\(753\) 0.693634i 0.0252774i
\(754\) 0 0
\(755\) 5.10687 12.3291i 0.185858 0.448701i
\(756\) 0 0
\(757\) −5.99265 + 2.48224i −0.217807 + 0.0902184i −0.488919 0.872329i \(-0.662609\pi\)
0.271112 + 0.962548i \(0.412609\pi\)
\(758\) 0 0
\(759\) −2.23003 2.23003i −0.0809450 0.0809450i
\(760\) 0 0
\(761\) −11.8001 + 11.8001i −0.427755 + 0.427755i −0.887863 0.460108i \(-0.847811\pi\)
0.460108 + 0.887863i \(0.347811\pi\)
\(762\) 0 0
\(763\) 3.23346 + 7.80627i 0.117059 + 0.282606i
\(764\) 0 0
\(765\) 2.76042 + 1.14340i 0.0998031 + 0.0413398i
\(766\) 0 0
\(767\) 29.8751 1.07873
\(768\) 0 0
\(769\) 8.82366 0.318189 0.159095 0.987263i \(-0.449142\pi\)
0.159095 + 0.987263i \(0.449142\pi\)
\(770\) 0 0
\(771\) 9.87062 + 4.08855i 0.355482 + 0.147245i
\(772\) 0 0
\(773\) −7.48121 18.0612i −0.269080 0.649617i 0.730360 0.683062i \(-0.239352\pi\)
−0.999441 + 0.0334448i \(0.989352\pi\)
\(774\) 0 0
\(775\) 2.97948 2.97948i 0.107026 0.107026i
\(776\) 0 0
\(777\) 6.15653 + 6.15653i 0.220864 + 0.220864i
\(778\) 0 0
\(779\) 88.2979 36.5742i 3.16360 1.31041i
\(780\) 0 0
\(781\) −0.192369 + 0.464419i −0.00688349 + 0.0166182i
\(782\) 0 0
\(783\) 0.700559i 0.0250359i
\(784\) 0 0
\(785\) 18.5841i 0.663296i
\(786\) 0 0
\(787\) 5.49189 13.2586i 0.195765 0.472618i −0.795265 0.606263i \(-0.792668\pi\)
0.991029 + 0.133645i \(0.0426681\pi\)
\(788\) 0 0
\(789\) 0.957921 0.396784i 0.0341029 0.0141259i
\(790\) 0 0
\(791\) −6.70813 6.70813i −0.238514 0.238514i
\(792\) 0 0
\(793\) 32.9164 32.9164i 1.16890 1.16890i
\(794\) 0 0
\(795\) −6.27017 15.1375i −0.222380 0.536872i
\(796\) 0 0
\(797\) −32.2565 13.3611i −1.14258 0.473274i −0.270544 0.962708i \(-0.587203\pi\)
−0.872040 + 0.489434i \(0.837203\pi\)
\(798\)