Properties

Label 384.2.n.a.49.5
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 49.5
Character \(\chi\) \(=\) 384.49
Dual form 384.2.n.a.337.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923880 - 0.382683i) q^{3} +(-1.48656 + 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(0.923880 - 0.382683i) q^{3} +(-1.48656 + 3.58888i) q^{5} +(-1.03821 - 1.03821i) q^{7} +(0.707107 - 0.707107i) q^{9} +(2.98911 + 1.23813i) q^{11} +(1.33971 + 3.23434i) q^{13} +3.88457i q^{15} +5.31367i q^{17} +(0.339726 + 0.820171i) q^{19} +(-1.35649 - 0.561876i) q^{21} +(-4.32186 + 4.32186i) q^{23} +(-7.13463 - 7.13463i) q^{25} +(0.382683 - 0.923880i) q^{27} +(5.78209 - 2.39502i) q^{29} +1.42287 q^{31} +3.23539 q^{33} +(5.26938 - 2.18265i) q^{35} +(0.646238 - 1.56016i) q^{37} +(2.47546 + 2.47546i) q^{39} +(3.42644 - 3.42644i) q^{41} +(-6.50505 - 2.69448i) q^{43} +(1.48656 + 3.58888i) q^{45} -10.5764i q^{47} -4.84423i q^{49} +(2.03345 + 4.90919i) q^{51} +(6.63468 + 2.74817i) q^{53} +(-8.88700 + 8.88700i) q^{55} +(0.627732 + 0.627732i) q^{57} +(0.185450 - 0.447716i) q^{59} +(-3.16624 + 1.31150i) q^{61} -1.46825 q^{63} -13.5992 q^{65} +(6.09277 - 2.52371i) q^{67} +(-2.33898 + 5.64679i) q^{69} +(-2.91549 - 2.91549i) q^{71} +(1.02065 - 1.02065i) q^{73} +(-9.32184 - 3.86123i) q^{75} +(-1.81789 - 4.38878i) q^{77} -12.8099i q^{79} -1.00000i q^{81} +(6.41532 + 15.4879i) q^{83} +(-19.0701 - 7.89910i) q^{85} +(4.42542 - 4.42542i) q^{87} +(-0.991462 - 0.991462i) q^{89} +(1.96703 - 4.74883i) q^{91} +(1.31456 - 0.544508i) q^{93} -3.44851 q^{95} +14.5301 q^{97} +(2.98911 - 1.23813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91} + O(q^{100}) \)

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
\(5\) −1.48656 + 3.58888i −0.664810 + 1.60499i 0.125364 + 0.992111i \(0.459990\pi\)
−0.790174 + 0.612883i \(0.790010\pi\)
\(6\) 0 0
\(7\) −1.03821 1.03821i −0.392407 0.392407i 0.483137 0.875545i \(-0.339497\pi\)
−0.875545 + 0.483137i \(0.839497\pi\)
\(8\) 0 0
\(9\) 0.707107 0.707107i 0.235702 0.235702i
\(10\) 0 0
\(11\) 2.98911 + 1.23813i 0.901252 + 0.373311i 0.784701 0.619874i \(-0.212816\pi\)
0.116550 + 0.993185i \(0.462816\pi\)
\(12\) 0 0
\(13\) 1.33971 + 3.23434i 0.371568 + 0.897045i 0.993485 + 0.113962i \(0.0363541\pi\)
−0.621917 + 0.783083i \(0.713646\pi\)
\(14\) 0 0
\(15\) 3.88457i 1.00299i
\(16\) 0 0
\(17\) 5.31367i 1.28876i 0.764708 + 0.644378i \(0.222883\pi\)
−0.764708 + 0.644378i \(0.777117\pi\)
\(18\) 0 0
\(19\) 0.339726 + 0.820171i 0.0779385 + 0.188160i 0.958046 0.286614i \(-0.0925297\pi\)
−0.880108 + 0.474774i \(0.842530\pi\)
\(20\) 0 0
\(21\) −1.35649 0.561876i −0.296010 0.122611i
\(22\) 0 0
\(23\) −4.32186 + 4.32186i −0.901171 + 0.901171i −0.995537 0.0943668i \(-0.969917\pi\)
0.0943668 + 0.995537i \(0.469917\pi\)
\(24\) 0 0
\(25\) −7.13463 7.13463i −1.42693 1.42693i
\(26\) 0 0
\(27\) 0.382683 0.923880i 0.0736475 0.177801i
\(28\) 0 0
\(29\) 5.78209 2.39502i 1.07371 0.444744i 0.225410 0.974264i \(-0.427628\pi\)
0.848298 + 0.529520i \(0.177628\pi\)
\(30\) 0 0
\(31\) 1.42287 0.255555 0.127777 0.991803i \(-0.459216\pi\)
0.127777 + 0.991803i \(0.459216\pi\)
\(32\) 0 0
\(33\) 3.23539 0.563210
\(34\) 0 0
\(35\) 5.26938 2.18265i 0.890687 0.368935i
\(36\) 0 0
\(37\) 0.646238 1.56016i 0.106241 0.256488i −0.861815 0.507223i \(-0.830672\pi\)
0.968056 + 0.250735i \(0.0806721\pi\)
\(38\) 0 0
\(39\) 2.47546 + 2.47546i 0.396390 + 0.396390i
\(40\) 0 0
\(41\) 3.42644 3.42644i 0.535120 0.535120i −0.386972 0.922092i \(-0.626479\pi\)
0.922092 + 0.386972i \(0.126479\pi\)
\(42\) 0 0
\(43\) −6.50505 2.69448i −0.992010 0.410904i −0.173149 0.984896i \(-0.555394\pi\)
−0.818861 + 0.573991i \(0.805394\pi\)
\(44\) 0 0
\(45\) 1.48656 + 3.58888i 0.221603 + 0.534998i
\(46\) 0 0
\(47\) 10.5764i 1.54273i −0.636391 0.771366i \(-0.719574\pi\)
0.636391 0.771366i \(-0.280426\pi\)
\(48\) 0 0
\(49\) 4.84423i 0.692033i
\(50\) 0 0
\(51\) 2.03345 + 4.90919i 0.284741 + 0.687425i
\(52\) 0 0
\(53\) 6.63468 + 2.74817i 0.911344 + 0.377491i 0.788571 0.614944i \(-0.210821\pi\)
0.122773 + 0.992435i \(0.460821\pi\)
\(54\) 0 0
\(55\) −8.88700 + 8.88700i −1.19832 + 1.19832i
\(56\) 0 0
\(57\) 0.627732 + 0.627732i 0.0831451 + 0.0831451i
\(58\) 0 0
\(59\) 0.185450 0.447716i 0.0241435 0.0582877i −0.911348 0.411637i \(-0.864957\pi\)
0.935492 + 0.353349i \(0.114957\pi\)
\(60\) 0 0
\(61\) −3.16624 + 1.31150i −0.405396 + 0.167920i −0.576057 0.817409i \(-0.695410\pi\)
0.170662 + 0.985330i \(0.445410\pi\)
\(62\) 0 0
\(63\) −1.46825 −0.184983
\(64\) 0 0
\(65\) −13.5992 −1.68677
\(66\) 0 0
\(67\) 6.09277 2.52371i 0.744350 0.308320i 0.0219162 0.999760i \(-0.493023\pi\)
0.722434 + 0.691440i \(0.243023\pi\)
\(68\) 0 0
\(69\) −2.33898 + 5.64679i −0.281580 + 0.679793i
\(70\) 0 0
\(71\) −2.91549 2.91549i −0.346005 0.346005i 0.512614 0.858619i \(-0.328677\pi\)
−0.858619 + 0.512614i \(0.828677\pi\)
\(72\) 0 0
\(73\) 1.02065 1.02065i 0.119458 0.119458i −0.644851 0.764309i \(-0.723080\pi\)
0.764309 + 0.644851i \(0.223080\pi\)
\(74\) 0 0
\(75\) −9.32184 3.86123i −1.07639 0.445857i
\(76\) 0 0
\(77\) −1.81789 4.38878i −0.207168 0.500147i
\(78\) 0 0
\(79\) 12.8099i 1.44122i −0.693338 0.720612i \(-0.743861\pi\)
0.693338 0.720612i \(-0.256139\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 6.41532 + 15.4879i 0.704173 + 1.70002i 0.714072 + 0.700072i \(0.246849\pi\)
−0.00989955 + 0.999951i \(0.503151\pi\)
\(84\) 0 0
\(85\) −19.0701 7.89910i −2.06844 0.856778i
\(86\) 0 0
\(87\) 4.42542 4.42542i 0.474455 0.474455i
\(88\) 0 0
\(89\) −0.991462 0.991462i −0.105095 0.105095i 0.652604 0.757699i \(-0.273676\pi\)
−0.757699 + 0.652604i \(0.773676\pi\)
\(90\) 0 0
\(91\) 1.96703 4.74883i 0.206201 0.497813i
\(92\) 0 0
\(93\) 1.31456 0.544508i 0.136313 0.0564628i
\(94\) 0 0
\(95\) −3.44851 −0.353810
\(96\) 0 0
\(97\) 14.5301 1.47530 0.737652 0.675182i \(-0.235935\pi\)
0.737652 + 0.675182i \(0.235935\pi\)
\(98\) 0 0
\(99\) 2.98911 1.23813i 0.300417 0.124437i
\(100\) 0 0
\(101\) 0.742560 1.79270i 0.0738875 0.178380i −0.882621 0.470086i \(-0.844223\pi\)
0.956508 + 0.291706i \(0.0942229\pi\)
\(102\) 0 0
\(103\) 2.11500 + 2.11500i 0.208397 + 0.208397i 0.803586 0.595189i \(-0.202923\pi\)
−0.595189 + 0.803586i \(0.702923\pi\)
\(104\) 0 0
\(105\) 4.03301 4.03301i 0.393581 0.393581i
\(106\) 0 0
\(107\) −4.62290 1.91487i −0.446913 0.185117i 0.147865 0.989008i \(-0.452760\pi\)
−0.594778 + 0.803890i \(0.702760\pi\)
\(108\) 0 0
\(109\) 0.135885 + 0.328056i 0.0130155 + 0.0314221i 0.930254 0.366917i \(-0.119587\pi\)
−0.917238 + 0.398339i \(0.869587\pi\)
\(110\) 0 0
\(111\) 1.68870i 0.160284i
\(112\) 0 0
\(113\) 2.38693i 0.224543i 0.993678 + 0.112272i \(0.0358127\pi\)
−0.993678 + 0.112272i \(0.964187\pi\)
\(114\) 0 0
\(115\) −9.08591 21.9353i −0.847266 2.04548i
\(116\) 0 0
\(117\) 3.23434 + 1.33971i 0.299015 + 0.123856i
\(118\) 0 0
\(119\) 5.51672 5.51672i 0.505717 0.505717i
\(120\) 0 0
\(121\) −0.376343 0.376343i −0.0342130 0.0342130i
\(122\) 0 0
\(123\) 1.85438 4.47686i 0.167203 0.403665i
\(124\) 0 0
\(125\) 18.2670 7.56643i 1.63385 0.676762i
\(126\) 0 0
\(127\) 13.4220 1.19101 0.595507 0.803350i \(-0.296951\pi\)
0.595507 + 0.803350i \(0.296951\pi\)
\(128\) 0 0
\(129\) −7.04101 −0.619927
\(130\) 0 0
\(131\) −7.38818 + 3.06028i −0.645508 + 0.267378i −0.681326 0.731980i \(-0.738596\pi\)
0.0358180 + 0.999358i \(0.488596\pi\)
\(132\) 0 0
\(133\) 0.498804 1.20422i 0.0432518 0.104419i
\(134\) 0 0
\(135\) 2.74681 + 2.74681i 0.236407 + 0.236407i
\(136\) 0 0
\(137\) −10.6802 + 10.6802i −0.912474 + 0.912474i −0.996466 0.0839927i \(-0.973233\pi\)
0.0839927 + 0.996466i \(0.473233\pi\)
\(138\) 0 0
\(139\) 4.00214 + 1.65774i 0.339457 + 0.140608i 0.545899 0.837851i \(-0.316188\pi\)
−0.206441 + 0.978459i \(0.566188\pi\)
\(140\) 0 0
\(141\) −4.04743 9.77136i −0.340855 0.822897i
\(142\) 0 0
\(143\) 11.3265i 0.947173i
\(144\) 0 0
\(145\) 24.3116i 2.01896i
\(146\) 0 0
\(147\) −1.85381 4.47549i −0.152899 0.369132i
\(148\) 0 0
\(149\) −17.5080 7.25206i −1.43431 0.594112i −0.475901 0.879499i \(-0.657878\pi\)
−0.958412 + 0.285387i \(0.907878\pi\)
\(150\) 0 0
\(151\) −1.13128 + 1.13128i −0.0920621 + 0.0920621i −0.751638 0.659576i \(-0.770736\pi\)
0.659576 + 0.751638i \(0.270736\pi\)
\(152\) 0 0
\(153\) 3.75733 + 3.75733i 0.303762 + 0.303762i
\(154\) 0 0
\(155\) −2.11518 + 5.10649i −0.169895 + 0.410163i
\(156\) 0 0
\(157\) 1.69192 0.700815i 0.135030 0.0559311i −0.314145 0.949375i \(-0.601718\pi\)
0.449175 + 0.893444i \(0.351718\pi\)
\(158\) 0 0
\(159\) 7.18133 0.569516
\(160\) 0 0
\(161\) 8.97402 0.707252
\(162\) 0 0
\(163\) −20.1880 + 8.36212i −1.58124 + 0.654972i −0.988610 0.150501i \(-0.951911\pi\)
−0.592632 + 0.805473i \(0.701911\pi\)
\(164\) 0 0
\(165\) −4.80961 + 11.6114i −0.374428 + 0.903948i
\(166\) 0 0
\(167\) 2.40472 + 2.40472i 0.186083 + 0.186083i 0.794000 0.607917i \(-0.207995\pi\)
−0.607917 + 0.794000i \(0.707995\pi\)
\(168\) 0 0
\(169\) 0.526247 0.526247i 0.0404805 0.0404805i
\(170\) 0 0
\(171\) 0.820171 + 0.339726i 0.0627200 + 0.0259795i
\(172\) 0 0
\(173\) −3.78491 9.13758i −0.287761 0.694717i 0.712212 0.701964i \(-0.247693\pi\)
−0.999974 + 0.00724669i \(0.997693\pi\)
\(174\) 0 0
\(175\) 14.8145i 1.11987i
\(176\) 0 0
\(177\) 0.484604i 0.0364251i
\(178\) 0 0
\(179\) 7.05680 + 17.0366i 0.527450 + 1.27338i 0.933188 + 0.359388i \(0.117015\pi\)
−0.405738 + 0.913989i \(0.632985\pi\)
\(180\) 0 0
\(181\) 17.3885 + 7.20257i 1.29248 + 0.535363i 0.919724 0.392566i \(-0.128413\pi\)
0.372757 + 0.927929i \(0.378413\pi\)
\(182\) 0 0
\(183\) −2.42334 + 2.42334i −0.179138 + 0.179138i
\(184\) 0 0
\(185\) 4.63854 + 4.63854i 0.341032 + 0.341032i
\(186\) 0 0
\(187\) −6.57903 + 15.8832i −0.481106 + 1.16149i
\(188\) 0 0
\(189\) −1.35649 + 0.561876i −0.0986701 + 0.0408705i
\(190\) 0 0
\(191\) −9.91467 −0.717400 −0.358700 0.933453i \(-0.616780\pi\)
−0.358700 + 0.933453i \(0.616780\pi\)
\(192\) 0 0
\(193\) 9.84834 0.708899 0.354450 0.935075i \(-0.384668\pi\)
0.354450 + 0.935075i \(0.384668\pi\)
\(194\) 0 0
\(195\) −12.5640 + 5.20419i −0.899728 + 0.372680i
\(196\) 0 0
\(197\) 5.46439 13.1922i 0.389322 0.939905i −0.600762 0.799428i \(-0.705136\pi\)
0.990084 0.140478i \(-0.0448638\pi\)
\(198\) 0 0
\(199\) 6.14473 + 6.14473i 0.435588 + 0.435588i 0.890524 0.454936i \(-0.150338\pi\)
−0.454936 + 0.890524i \(0.650338\pi\)
\(200\) 0 0
\(201\) 4.66320 4.66320i 0.328917 0.328917i
\(202\) 0 0
\(203\) −8.48958 3.51650i −0.595852 0.246810i
\(204\) 0 0
\(205\) 7.20345 + 17.3907i 0.503111 + 1.21462i
\(206\) 0 0
\(207\) 6.11204i 0.424816i
\(208\) 0 0
\(209\) 2.87221i 0.198675i
\(210\) 0 0
\(211\) 4.14085 + 9.99689i 0.285068 + 0.688214i 0.999939 0.0110418i \(-0.00351479\pi\)
−0.714871 + 0.699256i \(0.753515\pi\)
\(212\) 0 0
\(213\) −3.80927 1.57785i −0.261007 0.108113i
\(214\) 0 0
\(215\) 19.3403 19.3403i 1.31900 1.31900i
\(216\) 0 0
\(217\) −1.47724 1.47724i −0.100281 0.100281i
\(218\) 0 0
\(219\) 0.552372 1.33355i 0.0373259 0.0901126i
\(220\) 0 0
\(221\) −17.1862 + 7.11877i −1.15607 + 0.478860i
\(222\) 0 0
\(223\) 14.1199 0.945540 0.472770 0.881186i \(-0.343254\pi\)
0.472770 + 0.881186i \(0.343254\pi\)
\(224\) 0 0
\(225\) −10.0899 −0.672659
\(226\) 0 0
\(227\) 16.8836 6.99343i 1.12061 0.464170i 0.256029 0.966669i \(-0.417586\pi\)
0.864578 + 0.502499i \(0.167586\pi\)
\(228\) 0 0
\(229\) 3.92011 9.46398i 0.259048 0.625397i −0.739828 0.672796i \(-0.765093\pi\)
0.998876 + 0.0473987i \(0.0150931\pi\)
\(230\) 0 0
\(231\) −3.35902 3.35902i −0.221008 0.221008i
\(232\) 0 0
\(233\) 3.06027 3.06027i 0.200485 0.200485i −0.599723 0.800208i \(-0.704722\pi\)
0.800208 + 0.599723i \(0.204722\pi\)
\(234\) 0 0
\(235\) 37.9575 + 15.7225i 2.47608 + 1.02562i
\(236\) 0 0
\(237\) −4.90213 11.8348i −0.318428 0.768752i
\(238\) 0 0
\(239\) 0.210325i 0.0136048i −0.999977 0.00680240i \(-0.997835\pi\)
0.999977 0.00680240i \(-0.00216529\pi\)
\(240\) 0 0
\(241\) 13.0724i 0.842068i −0.907045 0.421034i \(-0.861667\pi\)
0.907045 0.421034i \(-0.138333\pi\)
\(242\) 0 0
\(243\) −0.382683 0.923880i −0.0245492 0.0592669i
\(244\) 0 0
\(245\) 17.3853 + 7.20125i 1.11071 + 0.460071i
\(246\) 0 0
\(247\) −2.19758 + 2.19758i −0.139829 + 0.139829i
\(248\) 0 0
\(249\) 11.8540 + 11.8540i 0.751214 + 0.751214i
\(250\) 0 0
\(251\) 1.21528 2.93395i 0.0767079 0.185189i −0.880874 0.473351i \(-0.843044\pi\)
0.957582 + 0.288162i \(0.0930442\pi\)
\(252\) 0 0
\(253\) −18.2696 + 7.56751i −1.14860 + 0.475765i
\(254\) 0 0
\(255\) −20.6413 −1.29261
\(256\) 0 0
\(257\) 2.57305 0.160502 0.0802512 0.996775i \(-0.474428\pi\)
0.0802512 + 0.996775i \(0.474428\pi\)
\(258\) 0 0
\(259\) −2.29071 + 0.948841i −0.142338 + 0.0589581i
\(260\) 0 0
\(261\) 2.39502 5.78209i 0.148248 0.357903i
\(262\) 0 0
\(263\) −12.8467 12.8467i −0.792159 0.792159i 0.189686 0.981845i \(-0.439253\pi\)
−0.981845 + 0.189686i \(0.939253\pi\)
\(264\) 0 0
\(265\) −19.7257 + 19.7257i −1.21174 + 1.21174i
\(266\) 0 0
\(267\) −1.29541 0.536575i −0.0792776 0.0328379i
\(268\) 0 0
\(269\) 3.18478 + 7.68874i 0.194180 + 0.468791i 0.990741 0.135767i \(-0.0433499\pi\)
−0.796561 + 0.604558i \(0.793350\pi\)
\(270\) 0 0
\(271\) 29.7589i 1.80772i −0.427823 0.903862i \(-0.640719\pi\)
0.427823 0.903862i \(-0.359281\pi\)
\(272\) 0 0
\(273\) 5.14010i 0.311093i
\(274\) 0 0
\(275\) −12.4926 30.1598i −0.753333 1.81871i
\(276\) 0 0
\(277\) 13.4191 + 5.55836i 0.806274 + 0.333970i 0.747466 0.664300i \(-0.231270\pi\)
0.0588078 + 0.998269i \(0.481270\pi\)
\(278\) 0 0
\(279\) 1.00612 1.00612i 0.0602348 0.0602348i
\(280\) 0 0
\(281\) 0.428981 + 0.428981i 0.0255909 + 0.0255909i 0.719786 0.694196i \(-0.244240\pi\)
−0.694196 + 0.719786i \(0.744240\pi\)
\(282\) 0 0
\(283\) −10.2786 + 24.8146i −0.610997 + 1.47508i 0.250910 + 0.968010i \(0.419270\pi\)
−0.861907 + 0.507067i \(0.830730\pi\)
\(284\) 0 0
\(285\) −3.18601 + 1.31969i −0.188723 + 0.0781716i
\(286\) 0 0
\(287\) −7.11474 −0.419970
\(288\) 0 0
\(289\) −11.2351 −0.660890
\(290\) 0 0
\(291\) 13.4240 5.56041i 0.786930 0.325957i
\(292\) 0 0
\(293\) −4.95811 + 11.9699i −0.289656 + 0.699292i −0.999990 0.00457366i \(-0.998544\pi\)
0.710333 + 0.703865i \(0.248544\pi\)
\(294\) 0 0
\(295\) 1.33111 + 1.33111i 0.0775005 + 0.0775005i
\(296\) 0 0
\(297\) 2.28777 2.28777i 0.132750 0.132750i
\(298\) 0 0
\(299\) −19.7684 8.18834i −1.14324 0.473544i
\(300\) 0 0
\(301\) 3.95618 + 9.55106i 0.228030 + 0.550514i
\(302\) 0 0
\(303\) 1.94040i 0.111473i
\(304\) 0 0
\(305\) 13.3129i 0.762293i
\(306\) 0 0
\(307\) −8.37498 20.2190i −0.477985 1.15396i −0.960552 0.278099i \(-0.910296\pi\)
0.482567 0.875859i \(-0.339704\pi\)
\(308\) 0 0
\(309\) 2.76338 + 1.14463i 0.157203 + 0.0651157i
\(310\) 0 0
\(311\) −5.71820 + 5.71820i −0.324249 + 0.324249i −0.850395 0.526145i \(-0.823637\pi\)
0.526145 + 0.850395i \(0.323637\pi\)
\(312\) 0 0
\(313\) 11.6027 + 11.6027i 0.655823 + 0.655823i 0.954389 0.298566i \(-0.0965083\pi\)
−0.298566 + 0.954389i \(0.596508\pi\)
\(314\) 0 0
\(315\) 2.18265 5.26938i 0.122978 0.296896i
\(316\) 0 0
\(317\) −19.5616 + 8.10268i −1.09869 + 0.455092i −0.857028 0.515269i \(-0.827692\pi\)
−0.241660 + 0.970361i \(0.577692\pi\)
\(318\) 0 0
\(319\) 20.2487 1.13371
\(320\) 0 0
\(321\) −5.00379 −0.279284
\(322\) 0 0
\(323\) −4.35812 + 1.80519i −0.242492 + 0.100444i
\(324\) 0 0
\(325\) 13.5175 32.6341i 0.749816 1.81022i
\(326\) 0 0
\(327\) 0.251083 + 0.251083i 0.0138849 + 0.0138849i
\(328\) 0 0
\(329\) −10.9806 + 10.9806i −0.605379 + 0.605379i
\(330\) 0 0
\(331\) −0.922294 0.382027i −0.0506939 0.0209981i 0.357192 0.934031i \(-0.383734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(332\) 0 0
\(333\) −0.646238 1.56016i −0.0354136 0.0854961i
\(334\) 0 0
\(335\) 25.6178i 1.39965i
\(336\) 0 0
\(337\) 32.5245i 1.77172i −0.463949 0.885862i \(-0.653568\pi\)
0.463949 0.885862i \(-0.346432\pi\)
\(338\) 0 0
\(339\) 0.913437 + 2.20523i 0.0496111 + 0.119772i
\(340\) 0 0
\(341\) 4.25311 + 1.76170i 0.230319 + 0.0954012i
\(342\) 0 0
\(343\) −12.2968 + 12.2968i −0.663966 + 0.663966i
\(344\) 0 0
\(345\) −16.7886 16.7886i −0.903867 0.903867i
\(346\) 0 0
\(347\) 11.0057 26.5700i 0.590815 1.42635i −0.291901 0.956448i \(-0.594288\pi\)
0.882717 0.469906i \(-0.155712\pi\)
\(348\) 0 0
\(349\) −6.12429 + 2.53676i −0.327826 + 0.135790i −0.540525 0.841328i \(-0.681774\pi\)
0.212700 + 0.977118i \(0.431774\pi\)
\(350\) 0 0
\(351\) 3.50082 0.186860
\(352\) 0 0
\(353\) −27.1372 −1.44437 −0.722185 0.691700i \(-0.756862\pi\)
−0.722185 + 0.691700i \(0.756862\pi\)
\(354\) 0 0
\(355\) 14.7974 6.12928i 0.785364 0.325309i
\(356\) 0 0
\(357\) 2.98563 7.20794i 0.158016 0.381485i
\(358\) 0 0
\(359\) 6.86522 + 6.86522i 0.362332 + 0.362332i 0.864671 0.502339i \(-0.167527\pi\)
−0.502339 + 0.864671i \(0.667527\pi\)
\(360\) 0 0
\(361\) 12.8778 12.8778i 0.677777 0.677777i
\(362\) 0 0
\(363\) −0.491715 0.203675i −0.0258084 0.0106902i
\(364\) 0 0
\(365\) 2.14573 + 5.18025i 0.112313 + 0.271147i
\(366\) 0 0
\(367\) 32.3050i 1.68631i 0.537671 + 0.843154i \(0.319304\pi\)
−0.537671 + 0.843154i \(0.680696\pi\)
\(368\) 0 0
\(369\) 4.84572i 0.252258i
\(370\) 0 0
\(371\) −4.03502 9.74139i −0.209488 0.505748i
\(372\) 0 0
\(373\) 1.12962 + 0.467902i 0.0584893 + 0.0242271i 0.411736 0.911303i \(-0.364922\pi\)
−0.353247 + 0.935530i \(0.614922\pi\)
\(374\) 0 0
\(375\) 13.9809 13.9809i 0.721973 0.721973i
\(376\) 0 0
\(377\) 15.4926 + 15.4926i 0.797911 + 0.797911i
\(378\) 0 0
\(379\) 12.6694 30.5866i 0.650783 1.57113i −0.160861 0.986977i \(-0.551427\pi\)
0.811644 0.584152i \(-0.198573\pi\)
\(380\) 0 0
\(381\) 12.4004 5.13640i 0.635289 0.263145i
\(382\) 0 0
\(383\) −9.01248 −0.460516 −0.230258 0.973130i \(-0.573957\pi\)
−0.230258 + 0.973130i \(0.573957\pi\)
\(384\) 0 0
\(385\) 18.4532 0.940461
\(386\) 0 0
\(387\) −6.50505 + 2.69448i −0.330670 + 0.136968i
\(388\) 0 0
\(389\) −0.147171 + 0.355303i −0.00746188 + 0.0180146i −0.927567 0.373658i \(-0.878103\pi\)
0.920105 + 0.391673i \(0.128103\pi\)
\(390\) 0 0
\(391\) −22.9650 22.9650i −1.16139 1.16139i
\(392\) 0 0
\(393\) −5.65467 + 5.65467i −0.285240 + 0.285240i
\(394\) 0 0
\(395\) 45.9731 + 19.0427i 2.31316 + 0.958141i
\(396\) 0 0
\(397\) −10.7013 25.8353i −0.537084 1.29664i −0.926750 0.375679i \(-0.877409\pi\)
0.389666 0.920956i \(-0.372591\pi\)
\(398\) 0 0
\(399\) 1.30344i 0.0652535i
\(400\) 0 0
\(401\) 39.5351i 1.97429i −0.159825 0.987145i \(-0.551093\pi\)
0.159825 0.987145i \(-0.448907\pi\)
\(402\) 0 0
\(403\) 1.90623 + 4.60204i 0.0949559 + 0.229244i
\(404\) 0 0
\(405\) 3.58888 + 1.48656i 0.178333 + 0.0738678i
\(406\) 0 0
\(407\) 3.86336 3.86336i 0.191500 0.191500i
\(408\) 0 0
\(409\) −16.6530 16.6530i −0.823439 0.823439i 0.163160 0.986600i \(-0.447831\pi\)
−0.986600 + 0.163160i \(0.947831\pi\)
\(410\) 0 0
\(411\) −5.78010 + 13.9544i −0.285111 + 0.688319i
\(412\) 0 0
\(413\) −0.657361 + 0.272288i −0.0323466 + 0.0133984i
\(414\) 0 0
\(415\) −65.1211 −3.19667
\(416\) 0 0
\(417\) 4.33189 0.212133
\(418\) 0 0
\(419\) −30.2809 + 12.5428i −1.47932 + 0.612754i −0.968962 0.247210i \(-0.920486\pi\)
−0.510356 + 0.859963i \(0.670486\pi\)
\(420\) 0 0
\(421\) −14.0297 + 33.8706i −0.683764 + 1.65075i 0.0732174 + 0.997316i \(0.476673\pi\)
−0.756981 + 0.653436i \(0.773327\pi\)
\(422\) 0 0
\(423\) −7.47867 7.47867i −0.363626 0.363626i
\(424\) 0 0
\(425\) 37.9111 37.9111i 1.83896 1.83896i
\(426\) 0 0
\(427\) 4.64885 + 1.92561i 0.224973 + 0.0931870i
\(428\) 0 0
\(429\) 4.33448 + 10.4644i 0.209271 + 0.505224i
\(430\) 0 0
\(431\) 11.0244i 0.531027i −0.964107 0.265513i \(-0.914459\pi\)
0.964107 0.265513i \(-0.0855414\pi\)
\(432\) 0 0
\(433\) 26.0973i 1.25416i 0.778956 + 0.627079i \(0.215750\pi\)
−0.778956 + 0.627079i \(0.784250\pi\)
\(434\) 0 0
\(435\) 9.30363 + 22.4609i 0.446075 + 1.07692i
\(436\) 0 0
\(437\) −5.01291 2.07642i −0.239800 0.0993285i
\(438\) 0 0
\(439\) 9.89316 9.89316i 0.472175 0.472175i −0.430443 0.902618i \(-0.641643\pi\)
0.902618 + 0.430443i \(0.141643\pi\)
\(440\) 0 0
\(441\) −3.42539 3.42539i −0.163114 0.163114i
\(442\) 0 0
\(443\) −7.29919 + 17.6218i −0.346795 + 0.837237i 0.650200 + 0.759763i \(0.274685\pi\)
−0.996994 + 0.0774732i \(0.975315\pi\)
\(444\) 0 0
\(445\) 5.03210 2.08436i 0.238544 0.0988083i
\(446\) 0 0
\(447\) −18.9505 −0.896330
\(448\) 0 0
\(449\) 7.16414 0.338096 0.169048 0.985608i \(-0.445931\pi\)
0.169048 + 0.985608i \(0.445931\pi\)
\(450\) 0 0
\(451\) 14.4844 5.99964i 0.682044 0.282512i
\(452\) 0 0
\(453\) −0.612243 + 1.47809i −0.0287657 + 0.0694465i
\(454\) 0 0
\(455\) 14.1189 + 14.1189i 0.661902 + 0.661902i
\(456\) 0 0
\(457\) −15.2704 + 15.2704i −0.714317 + 0.714317i −0.967435 0.253118i \(-0.918544\pi\)
0.253118 + 0.967435i \(0.418544\pi\)
\(458\) 0 0
\(459\) 4.90919 + 2.03345i 0.229142 + 0.0949135i
\(460\) 0 0
\(461\) −5.40240 13.0425i −0.251615 0.607452i 0.746720 0.665139i \(-0.231628\pi\)
−0.998335 + 0.0576867i \(0.981628\pi\)
\(462\) 0 0
\(463\) 13.5410i 0.629305i 0.949207 + 0.314652i \(0.101888\pi\)
−0.949207 + 0.314652i \(0.898112\pi\)
\(464\) 0 0
\(465\) 5.52723i 0.256319i
\(466\) 0 0
\(467\) −6.18122 14.9228i −0.286033 0.690544i 0.713920 0.700227i \(-0.246918\pi\)
−0.999953 + 0.00968289i \(0.996918\pi\)
\(468\) 0 0
\(469\) −8.94573 3.70544i −0.413075 0.171101i
\(470\) 0 0
\(471\) 1.29494 1.29494i 0.0596676 0.0596676i
\(472\) 0 0
\(473\) −16.1082 16.1082i −0.740656 0.740656i
\(474\) 0 0
\(475\) 3.42780 8.27543i 0.157278 0.379703i
\(476\) 0 0
\(477\) 6.63468 2.74817i 0.303781 0.125830i
\(478\) 0 0
\(479\) 6.44443 0.294453 0.147227 0.989103i \(-0.452965\pi\)
0.147227 + 0.989103i \(0.452965\pi\)
\(480\) 0 0
\(481\) 5.91185 0.269557
\(482\) 0 0
\(483\) 8.29091 3.43421i 0.377250 0.156262i
\(484\) 0 0
\(485\) −21.5998 + 52.1465i −0.980797 + 2.36785i
\(486\) 0 0
\(487\) −4.42962 4.42962i −0.200725 0.200725i 0.599585 0.800311i \(-0.295332\pi\)
−0.800311 + 0.599585i \(0.795332\pi\)
\(488\) 0 0
\(489\) −15.4512 + 15.4512i −0.698727 + 0.698727i
\(490\) 0 0
\(491\) 11.7801 + 4.87947i 0.531628 + 0.220207i 0.632316 0.774711i \(-0.282104\pi\)
−0.100688 + 0.994918i \(0.532104\pi\)
\(492\) 0 0
\(493\) 12.7264 + 30.7242i 0.573167 + 1.38375i
\(494\) 0 0
\(495\) 12.5681i 0.564895i
\(496\) 0 0
\(497\) 6.05380i 0.271550i
\(498\) 0 0
\(499\) −2.23679 5.40009i −0.100132 0.241741i 0.865873 0.500265i \(-0.166764\pi\)
−0.966005 + 0.258524i \(0.916764\pi\)
\(500\) 0 0
\(501\) 3.14192 + 1.30143i 0.140371 + 0.0581434i
\(502\) 0 0
\(503\) −2.89565 + 2.89565i −0.129111 + 0.129111i −0.768709 0.639598i \(-0.779101\pi\)
0.639598 + 0.768709i \(0.279101\pi\)
\(504\) 0 0
\(505\) 5.32991 + 5.32991i 0.237178 + 0.237178i
\(506\) 0 0
\(507\) 0.284803 0.687575i 0.0126485 0.0305363i
\(508\) 0 0
\(509\) 5.36042 2.22036i 0.237596 0.0984156i −0.260708 0.965418i \(-0.583956\pi\)
0.498305 + 0.867002i \(0.333956\pi\)
\(510\) 0 0
\(511\) −2.11930 −0.0937525
\(512\) 0 0
\(513\) 0.887747 0.0391950
\(514\) 0 0
\(515\) −10.7345 + 4.44639i −0.473020 + 0.195931i
\(516\) 0 0
\(517\) 13.0950 31.6142i 0.575919 1.39039i
\(518\) 0 0
\(519\) −6.99360 6.99360i −0.306985 0.306985i
\(520\) 0 0
\(521\) 18.2831 18.2831i 0.800998 0.800998i −0.182254 0.983252i \(-0.558339\pi\)
0.983252 + 0.182254i \(0.0583392\pi\)
\(522\) 0 0
\(523\) 5.66441 + 2.34627i 0.247687 + 0.102595i 0.503073 0.864244i \(-0.332203\pi\)
−0.255386 + 0.966839i \(0.582203\pi\)
\(524\) 0 0
\(525\) 5.66927 + 13.6868i 0.247427 + 0.597342i
\(526\) 0 0
\(527\) 7.56065i 0.329347i
\(528\) 0 0
\(529\) 14.3570i 0.624217i
\(530\) 0 0
\(531\) −0.185450 0.447716i −0.00804785 0.0194292i
\(532\) 0 0
\(533\) 15.6727 + 6.49185i 0.678860 + 0.281193i
\(534\) 0 0
\(535\) 13.7445 13.7445i 0.594224 0.594224i
\(536\) 0 0
\(537\) 13.0393 + 13.0393i 0.562686 + 0.562686i
\(538\) 0 0
\(539\) 5.99780 14.4800i 0.258343 0.623696i
\(540\) 0 0
\(541\) 5.96613 2.47125i 0.256504 0.106247i −0.250726 0.968058i \(-0.580669\pi\)
0.507230 + 0.861811i \(0.330669\pi\)
\(542\) 0 0
\(543\) 18.8212 0.807696
\(544\) 0 0
\(545\) −1.37936 −0.0590851
\(546\) 0 0
\(547\) −32.5453 + 13.4807i −1.39154 + 0.576393i −0.947541 0.319635i \(-0.896440\pi\)
−0.443996 + 0.896029i \(0.646440\pi\)
\(548\) 0 0
\(549\) −1.31150 + 3.16624i −0.0559735 + 0.135132i
\(550\) 0 0
\(551\) 3.92865 + 3.92865i 0.167366 + 0.167366i
\(552\) 0 0
\(553\) −13.2994 + 13.2994i −0.565547 + 0.565547i
\(554\) 0 0
\(555\) 6.06054 + 2.51036i 0.257256 + 0.106559i
\(556\) 0 0
\(557\) −6.30768 15.2281i −0.267265 0.645235i 0.732088 0.681210i \(-0.238546\pi\)
−0.999353 + 0.0359756i \(0.988546\pi\)
\(558\) 0 0
\(559\) 24.6494i 1.04256i
\(560\) 0 0
\(561\) 17.1918i 0.725839i
\(562\) 0 0
\(563\) 3.06528 + 7.40024i 0.129186 + 0.311883i 0.975217 0.221251i \(-0.0710141\pi\)
−0.846031 + 0.533134i \(0.821014\pi\)
\(564\) 0 0
\(565\) −8.56638 3.54831i −0.360390 0.149279i
\(566\) 0 0
\(567\) −1.03821 + 1.03821i −0.0436008 + 0.0436008i
\(568\) 0 0
\(569\) 17.9001 + 17.9001i 0.750410 + 0.750410i 0.974556 0.224146i \(-0.0719591\pi\)
−0.224146 + 0.974556i \(0.571959\pi\)
\(570\) 0 0
\(571\) 2.41948 5.84113i 0.101252 0.244444i −0.865133 0.501542i \(-0.832766\pi\)
0.966385 + 0.257098i \(0.0827663\pi\)
\(572\) 0 0
\(573\) −9.15996 + 3.79418i −0.382663 + 0.158504i
\(574\) 0 0
\(575\) 61.6698 2.57181
\(576\) 0 0
\(577\) −24.5768 −1.02314 −0.511572 0.859240i \(-0.670937\pi\)
−0.511572 + 0.859240i \(0.670937\pi\)
\(578\) 0 0
\(579\) 9.09868 3.76880i 0.378128 0.156626i
\(580\) 0 0
\(581\) 9.41931 22.7402i 0.390779 0.943424i
\(582\) 0 0
\(583\) 16.4292 + 16.4292i 0.680429 + 0.680429i
\(584\) 0 0
\(585\) −9.61609 + 9.61609i −0.397576 + 0.397576i
\(586\) 0 0
\(587\) −29.2268 12.1061i −1.20632 0.499674i −0.313284 0.949659i \(-0.601429\pi\)
−0.893036 + 0.449985i \(0.851429\pi\)
\(588\) 0 0
\(589\) 0.483385 + 1.16699i 0.0199175 + 0.0480852i
\(590\) 0 0
\(591\) 14.2791i 0.587365i
\(592\) 0 0
\(593\) 20.8403i 0.855810i 0.903824 + 0.427905i \(0.140748\pi\)
−0.903824 + 0.427905i \(0.859252\pi\)
\(594\) 0 0
\(595\) 11.5979 + 27.9998i 0.475467 + 1.14788i
\(596\) 0 0
\(597\) 8.02847 + 3.32550i 0.328584 + 0.136104i
\(598\) 0 0
\(599\) −31.6901 + 31.6901i −1.29482 + 1.29482i −0.363053 + 0.931768i \(0.618266\pi\)
−0.931768 + 0.363053i \(0.881734\pi\)
\(600\) 0 0
\(601\) −12.9864 12.9864i −0.529726 0.529726i 0.390764 0.920491i \(-0.372211\pi\)
−0.920491 + 0.390764i \(0.872211\pi\)
\(602\) 0 0
\(603\) 2.52371 6.09277i 0.102773 0.248117i
\(604\) 0 0
\(605\) 1.91010 0.791190i 0.0776567 0.0321665i
\(606\) 0 0
\(607\) 7.55886 0.306805 0.153402 0.988164i \(-0.450977\pi\)
0.153402 + 0.988164i \(0.450977\pi\)
\(608\) 0 0
\(609\) −9.18905 −0.372359
\(610\) 0 0
\(611\) 34.2078 14.1693i 1.38390 0.573230i
\(612\) 0 0
\(613\) −5.16053 + 12.4586i −0.208432 + 0.503199i −0.993177 0.116620i \(-0.962794\pi\)
0.784745 + 0.619819i \(0.212794\pi\)
\(614\) 0 0
\(615\) 13.3102 + 13.3102i 0.536721 + 0.536721i
\(616\) 0 0
\(617\) −23.7425 + 23.7425i −0.955835 + 0.955835i −0.999065 0.0432297i \(-0.986235\pi\)
0.0432297 + 0.999065i \(0.486235\pi\)
\(618\) 0 0
\(619\) −37.9338 15.7127i −1.52469 0.631547i −0.546165 0.837678i \(-0.683913\pi\)
−0.978524 + 0.206131i \(0.933913\pi\)
\(620\) 0 0
\(621\) 2.33898 + 5.64679i 0.0938598 + 0.226598i
\(622\) 0 0
\(623\) 2.05869i 0.0824798i
\(624\) 0 0
\(625\) 26.3564i 1.05426i
\(626\) 0 0
\(627\) 1.09915 + 2.65358i 0.0438957 + 0.105974i
\(628\) 0 0
\(629\) 8.29016 + 3.43390i 0.330551 + 0.136919i
\(630\) 0 0
\(631\) 5.63001 5.63001i 0.224127 0.224127i −0.586107 0.810234i \(-0.699340\pi\)
0.810234 + 0.586107i \(0.199340\pi\)
\(632\) 0 0
\(633\) 7.65129 + 7.65129i 0.304111 + 0.304111i
\(634\) 0 0
\(635\) −19.9527 + 48.1701i −0.791798 + 1.91157i
\(636\) 0 0
\(637\) 15.6679 6.48986i 0.620785 0.257137i
\(638\) 0 0
\(639\) −4.12313 −0.163108
\(640\) 0 0
\(641\) 36.4242 1.43867 0.719334 0.694664i \(-0.244447\pi\)
0.719334 + 0.694664i \(0.244447\pi\)
\(642\) 0 0
\(643\) 22.9769 9.51734i 0.906120 0.375327i 0.119550 0.992828i \(-0.461855\pi\)
0.786570 + 0.617501i \(0.211855\pi\)
\(644\) 0 0
\(645\) 10.4669 25.2693i 0.412133 0.994978i
\(646\) 0 0
\(647\) 34.0895 + 34.0895i 1.34020 + 1.34020i 0.895860 + 0.444336i \(0.146560\pi\)
0.444336 + 0.895860i \(0.353440\pi\)
\(648\) 0 0
\(649\) 1.10866 1.10866i 0.0435188 0.0435188i
\(650\) 0 0
\(651\) −1.93010 0.799475i −0.0756468 0.0313339i
\(652\) 0 0
\(653\) 11.4288 + 27.5915i 0.447243 + 1.07974i 0.973351 + 0.229322i \(0.0736508\pi\)
−0.526108 + 0.850418i \(0.676349\pi\)
\(654\) 0 0
\(655\) 31.0645i 1.21379i
\(656\) 0 0
\(657\) 1.44342i 0.0563131i
\(658\) 0 0
\(659\) 4.60322 + 11.1132i 0.179316 + 0.432907i 0.987824 0.155579i \(-0.0497242\pi\)
−0.808507 + 0.588486i \(0.799724\pi\)
\(660\) 0 0
\(661\) −18.8580 7.81122i −0.733490 0.303821i −0.0155046 0.999880i \(-0.504935\pi\)
−0.717985 + 0.696058i \(0.754935\pi\)
\(662\) 0 0
\(663\) −13.1538 + 13.1538i −0.510850 + 0.510850i
\(664\) 0 0
\(665\) 3.58029 + 3.58029i 0.138838 + 0.138838i
\(666\) 0 0
\(667\) −14.6385 + 35.3404i −0.566803 + 1.36838i
\(668\) 0 0
\(669\) 13.0451 5.40346i 0.504353 0.208910i
\(670\) 0 0
\(671\) −11.0881 −0.428050
\(672\) 0 0
\(673\) −46.7689 −1.80281 −0.901404 0.432979i \(-0.857463\pi\)
−0.901404 + 0.432979i \(0.857463\pi\)
\(674\) 0 0
\(675\) −9.32184 + 3.86123i −0.358798 + 0.148619i
\(676\) 0 0
\(677\) −7.05433 + 17.0307i −0.271120 + 0.654541i −0.999532 0.0305981i \(-0.990259\pi\)
0.728412 + 0.685140i \(0.240259\pi\)
\(678\) 0 0
\(679\) −15.0853 15.0853i −0.578920 0.578920i
\(680\) 0 0
\(681\) 12.9222 12.9222i 0.495179 0.495179i
\(682\) 0 0
\(683\) −36.1287 14.9650i −1.38243 0.572620i −0.437297 0.899317i \(-0.644064\pi\)
−0.945129 + 0.326697i \(0.894064\pi\)
\(684\) 0 0
\(685\) −22.4532 54.2068i −0.857893 2.07114i
\(686\) 0 0
\(687\) 10.2437i 0.390823i
\(688\) 0 0
\(689\) 25.1406i 0.957779i
\(690\) 0 0
\(691\) 11.2605 + 27.1853i 0.428371 + 1.03418i 0.979804 + 0.199959i \(0.0640810\pi\)
−0.551434 + 0.834219i \(0.685919\pi\)
\(692\) 0 0
\(693\) −4.38878 1.81789i −0.166716 0.0690560i
\(694\) 0 0
\(695\) −11.8989 + 11.8989i −0.451349 + 0.451349i
\(696\) 0 0
\(697\) 18.2070 + 18.2070i 0.689639 + 0.689639i
\(698\) 0 0
\(699\) 1.65621 3.99844i 0.0626435 0.151235i
\(700\) 0 0
\(701\) −21.0746 + 8.72940i −0.795978 + 0.329705i −0.743344 0.668909i \(-0.766762\pi\)
−0.0526339 + 0.998614i \(0.516762\pi\)
\(702\) 0 0
\(703\) 1.49914 0.0565411
\(704\) 0 0
\(705\) 41.0849 1.54735
\(706\) 0 0
\(707\) −2.63214 + 1.09027i −0.0989917 + 0.0410037i
\(708\) 0 0
\(709\) 0.617186 1.49002i 0.0231789 0.0559588i −0.911866 0.410487i \(-0.865359\pi\)
0.935045 + 0.354528i \(0.115359\pi\)
\(710\) 0 0
\(711\) −9.05796 9.05796i −0.339700 0.339700i
\(712\) 0 0
\(713\) −6.14944 + 6.14944i −0.230298 + 0.230298i
\(714\) 0 0
\(715\) −40.6496 16.8376i −1.52021 0.629691i
\(716\) 0 0
\(717\) −0.0804880 0.194315i −0.00300588 0.00725683i
\(718\) 0 0
\(719\) 11.8288i 0.441140i 0.975371 + 0.220570i \(0.0707917\pi\)
−0.975371 + 0.220570i \(0.929208\pi\)
\(720\) 0 0
\(721\) 4.39163i 0.163553i
\(722\) 0 0
\(723\) −5.00259 12.0773i −0.186048 0.449161i
\(724\) 0 0
\(725\) −58.3407 24.1655i −2.16672 0.897484i
\(726\) 0 0
\(727\) 12.9471 12.9471i 0.480182 0.480182i −0.425008 0.905190i \(-0.639729\pi\)
0.905190 + 0.425008i \(0.139729\pi\)
\(728\) 0 0
\(729\) −0.707107 0.707107i −0.0261891 0.0261891i
\(730\) 0 0
\(731\) 14.3176 34.5657i 0.529555 1.27846i
\(732\) 0 0
\(733\) 8.82183 3.65412i 0.325842 0.134968i −0.213765 0.976885i \(-0.568573\pi\)
0.539607 + 0.841917i \(0.318573\pi\)
\(734\) 0 0
\(735\) 18.8178 0.694104
\(736\) 0 0
\(737\) 21.3367 0.785946
\(738\) 0 0
\(739\) −2.54866 + 1.05569i −0.0937540 + 0.0388342i −0.429068 0.903272i \(-0.641158\pi\)
0.335313 + 0.942107i \(0.391158\pi\)
\(740\) 0 0
\(741\) −1.18932 + 2.87127i −0.0436908 + 0.105479i
\(742\) 0 0
\(743\) −14.0090 14.0090i −0.513942 0.513942i 0.401790 0.915732i \(-0.368388\pi\)
−0.915732 + 0.401790i \(0.868388\pi\)
\(744\) 0 0
\(745\) 52.0535 52.0535i 1.90709 1.90709i
\(746\) 0 0
\(747\) 15.4879 + 6.41532i 0.566674 + 0.234724i
\(748\) 0 0
\(749\) 2.81151 + 6.78759i 0.102730 + 0.248013i
\(750\) 0 0
\(751\) 1.69567i 0.0618757i −0.999521 0.0309379i \(-0.990151\pi\)
0.999521 0.0309379i \(-0.00984940\pi\)
\(752\) 0 0
\(753\) 3.17568i 0.115728i
\(754\) 0 0
\(755\) −2.37830 5.74173i −0.0865553 0.208963i
\(756\) 0 0
\(757\) 21.3707 + 8.85204i 0.776731 + 0.321733i 0.735596 0.677421i \(-0.236902\pi\)
0.0411358 + 0.999154i \(0.486902\pi\)
\(758\) 0 0
\(759\) −13.9829 + 13.9829i −0.507548 + 0.507548i
\(760\) 0 0
\(761\) −16.4756 16.4756i −0.597239 0.597239i 0.342338 0.939577i \(-0.388781\pi\)
−0.939577 + 0.342338i \(0.888781\pi\)
\(762\) 0 0
\(763\) 0.199514 0.481670i 0.00722290 0.0174376i
\(764\) 0 0
\(765\) −19.0701 + 7.89910i −0.689481 + 0.285593i
\(766\) 0 0
\(767\) 1.69652 0.0612576
\(768\) 0 0
\(769\) −10.8924 −0.392791 −0.196395 0.980525i \(-0.562924\pi\)
−0.196395 + 0.980525i \(0.562924\pi\)
\(770\) 0 0
\(771\) 2.37719 0.984663i 0.0856123 0.0354618i
\(772\) 0 0
\(773\) 19.5101 47.1015i 0.701728 1.69412i −0.0179727 0.999838i \(-0.505721\pi\)
0.719701 0.694284i \(-0.244279\pi\)
\(774\) 0 0
\(775\) −10.1516 10.1516i −0.364657 0.364657i
\(776\) 0 0
\(777\) −1.75323 + 1.75323i −0.0628968 + 0.0628968i
\(778\) 0 0
\(779\) 3.97432 + 1.64622i 0.142395 + 0.0589818i
\(780\) 0 0
\(781\) −5.10498 12.3245i −0.182670 0.441005i
\(782\) 0 0
\(783\) 6.25849i 0.223660i
\(784\) 0 0
\(785\) 7.11388i 0.253905i
\(786\) 0 0
\(787\) −10.4222 25.1613i −0.371510 0.896905i −0.993495 0.113876i \(-0.963673\pi\)
0.621985 0.783029i \(-0.286327\pi\)
\(788\) 0 0
\(789\) −16.7850 6.95257i −0.597561 0.247518i
\(790\) 0 0
\(791\) 2.47814 2.47814i 0.0881124 0.0881124i
\(792\) 0 0
\(793\) −8.48368 8.48368i −0.301264 0.301264i
\(794\) 0 0
\(795\) −10.6755 + 25.7729i −0.378620 + 0.914070i
\(796\) 0 0
\(797\) 11.4090 4.72576i 0.404128 0.167395i −0.171355 0.985209i \(-0.554814\pi\)
0.575482 + 0.817814i \(0.304814\pi\)
\(798\)