Properties

Label 768.2.n.b.97.4
Level $768$
Weight $2$
Character 768.97
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
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 97.4
Character \(\chi\) \(=\) 768.97
Dual form 768.2.n.b.673.4

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\)

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 \(-0.540010\pi\)
0.790174 0.612883i \(-0.209990\pi\)
\(6\) 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 −0.116550 0.993185i \(-0.537184\pi\)
−0.784701 + 0.619874i \(0.787184\pi\)
\(12\) 0 0
\(13\) −1.33971 3.23434i −0.371568 0.897045i −0.993485 0.113962i \(-0.963646\pi\)
0.621917 0.783083i \(-0.286354\pi\)
\(14\) 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 0.880108 0.474774i \(-0.157470\pi\)
−0.958046 + 0.286614i \(0.907470\pi\)
\(20\) 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 −0.848298 0.529520i \(-0.822372\pi\)
−0.225410 + 0.974264i \(0.572372\pi\)
\(30\) 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 −0.968056 0.250735i \(-0.919328\pi\)
0.861815 + 0.507223i \(0.169328\pi\)
\(38\) 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 0.818861 0.573991i \(-0.194606\pi\)
0.173149 + 0.984896i \(0.444606\pi\)
\(44\) 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 −0.122773 0.992435i \(-0.539179\pi\)
−0.788571 + 0.614944i \(0.789179\pi\)
\(54\) 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 −0.935492 0.353349i \(-0.885043\pi\)
0.911348 + 0.411637i \(0.135043\pi\)
\(60\) 0 0
\(61\) 3.16624 1.31150i 0.405396 0.167920i −0.170662 0.985330i \(-0.554590\pi\)
0.576057 + 0.817409i \(0.304590\pi\)
\(62\) 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 −0.722434 0.691440i \(-0.756977\pi\)
−0.0219162 + 0.999760i \(0.506977\pi\)
\(68\) 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 \(-0.753151\pi\)
0.00989955 0.999951i \(-0.496849\pi\)
\(84\) 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 −0.956508 0.291706i \(-0.905777\pi\)
0.882621 + 0.470086i \(0.155777\pi\)
\(102\) 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 0.594778 0.803890i \(-0.297240\pi\)
−0.147865 + 0.989008i \(0.547240\pi\)
\(108\) 0 0
\(109\) −0.135885 0.328056i −0.0130155 0.0314221i 0.917238 0.398339i \(-0.130413\pi\)
−0.930254 + 0.366917i \(0.880413\pi\)
\(110\) 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 −0.0358180 0.999358i \(-0.511404\pi\)
0.681326 + 0.731980i \(0.261404\pi\)
\(132\) 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 0.206441 0.978459i \(-0.433812\pi\)
−0.545899 + 0.837851i \(0.683812\pi\)
\(140\) 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 0.958412 0.285387i \(-0.0921222\pi\)
0.475901 + 0.879499i \(0.342122\pi\)
\(150\) 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 −0.449175 0.893444i \(-0.648282\pi\)
0.314145 + 0.949375i \(0.398282\pi\)
\(158\) 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 0.592632 0.805473i \(-0.298089\pi\)
0.988610 + 0.150501i \(0.0480887\pi\)
\(164\) 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 0.999974 0.00724669i \(-0.00230671\pi\)
−0.712212 + 0.701964i \(0.752307\pi\)
\(174\) 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 \(-0.882985\pi\)
0.405738 0.913989i \(-0.367015\pi\)
\(180\) 0 0
\(181\) −17.3885 7.20257i −1.29248 0.535363i −0.372757 0.927929i \(-0.621587\pi\)
−0.919724 + 0.392566i \(0.871587\pi\)
\(182\) 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 \(0.294864\pi\)
−0.990084 + 0.140478i \(0.955136\pi\)
\(198\) 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 0.714871 0.699256i \(-0.246485\pi\)
−0.999939 + 0.0110418i \(0.996485\pi\)
\(212\) 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 −0.864578 0.502499i \(-0.832414\pi\)
−0.256029 + 0.966669i \(0.582414\pi\)
\(228\) 0 0
\(229\) −3.92011 + 9.46398i −0.259048 + 0.625397i −0.998876 0.0473987i \(-0.984907\pi\)
0.739828 + 0.672796i \(0.234907\pi\)
\(230\) 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 −0.957582 0.288162i \(-0.906956\pi\)
0.880874 + 0.473351i \(0.156956\pi\)
\(252\) 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 0.796561 0.604558i \(-0.206650\pi\)
−0.990741 + 0.135767i \(0.956650\pi\)
\(270\) 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 −0.0588078 0.998269i \(-0.518730\pi\)
−0.747466 + 0.664300i \(0.768730\pi\)
\(278\) 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 \(-0.580730\pi\)
0.861907 0.507067i \(-0.169270\pi\)
\(284\) 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 −0.710333 0.703865i \(-0.751456\pi\)
0.999990 + 0.00457366i \(0.00145584\pi\)
\(294\) 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 \(0.0897044\pi\)
−0.482567 + 0.875859i \(0.660296\pi\)
\(308\) 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 0.241660 0.970361i \(-0.422308\pi\)
0.857028 + 0.515269i \(0.172308\pi\)
\(318\) 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 0.407886 0.913033i \(-0.366266\pi\)
−0.357192 + 0.934031i \(0.616266\pi\)
\(332\) 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 \(0.405712\pi\)
−0.882717 + 0.469906i \(0.844288\pi\)
\(348\) 0 0
\(349\) 6.12429 2.53676i 0.327826 0.135790i −0.212700 0.977118i \(-0.568226\pi\)
0.540525 + 0.841328i \(0.318226\pi\)
\(350\) 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 0.353247 0.935530i \(-0.385078\pi\)
−0.411736 + 0.911303i \(0.635078\pi\)
\(374\) 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 \(0.448573\pi\)
−0.811644 + 0.584152i \(0.801427\pi\)
\(380\) 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 −0.920105 0.391673i \(-0.871897\pi\)
0.927567 + 0.373658i \(0.121897\pi\)
\(390\) 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 \(0.122591\pi\)
−0.389666 + 0.920956i \(0.627409\pi\)
\(398\) 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 0.510356 0.859963i \(-0.329514\pi\)
0.968962 + 0.247210i \(0.0795136\pi\)
\(420\) 0 0
\(421\) 14.0297 33.8706i 0.683764 1.65075i −0.0732174 0.997316i \(-0.523327\pi\)
0.756981 0.653436i \(-0.226673\pi\)
\(422\) 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 \(-0.725315\pi\)
0.996994 0.0774732i \(-0.0246852\pi\)
\(444\) 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 0.998335 0.0576867i \(-0.0183724\pi\)
−0.746720 + 0.665139i \(0.768372\pi\)
\(462\) 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 0.999953 0.00968289i \(-0.00308221\pi\)
−0.713920 + 0.700227i \(0.753082\pi\)
\(468\) 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 0.100688 0.994918i \(-0.467896\pi\)
−0.632316 + 0.774711i \(0.717896\pi\)
\(492\) 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 0.966005 0.258524i \(-0.0832360\pi\)
−0.865873 + 0.500265i \(0.833236\pi\)
\(500\) 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 −0.498305 0.867002i \(-0.666044\pi\)
0.260708 + 0.965418i \(0.416044\pi\)
\(510\) 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 0.255386 0.966839i \(-0.417797\pi\)
−0.503073 + 0.864244i \(0.667797\pi\)
\(524\) 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 −0.507230 0.861811i \(-0.669331\pi\)
0.250726 + 0.968058i \(0.419331\pi\)
\(542\) 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 0.443996 0.896029i \(-0.353560\pi\)
0.947541 + 0.319635i \(0.103560\pi\)
\(548\) 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 0.999353 0.0359756i \(-0.0114539\pi\)
−0.732088 + 0.681210i \(0.761454\pi\)
\(558\) 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 0.846031 0.533134i \(-0.178986\pi\)
−0.975217 + 0.221251i \(0.928986\pi\)
\(564\) 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 −0.966385 0.257098i \(-0.917234\pi\)
0.865133 + 0.501542i \(0.167234\pi\)
\(572\) 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 0.893036 0.449985i \(-0.148571\pi\)
0.313284 + 0.949659i \(0.398571\pi\)
\(588\) 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 −0.784745 0.619819i \(-0.787206\pi\)
0.993177 + 0.116620i \(0.0372061\pi\)
\(614\) 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 0.978524 0.206131i \(-0.0660872\pi\)
0.546165 + 0.837678i \(0.316087\pi\)
\(620\) 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 −0.786570 0.617501i \(-0.788145\pi\)
−0.119550 + 0.992828i \(0.538145\pi\)
\(644\) 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 \(-0.926349\pi\)
0.526108 0.850418i \(-0.323651\pi\)
\(654\) 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 0.808507 0.588486i \(-0.200276\pi\)
−0.987824 + 0.155579i \(0.950276\pi\)
\(660\) 0 0
\(661\) 18.8580 + 7.81122i 0.733490 + 0.303821i 0.717985 0.696058i \(-0.245065\pi\)
0.0155046 + 0.999880i \(0.495065\pi\)
\(662\) 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 −0.728412 0.685140i \(-0.759741\pi\)
0.999532 + 0.0305981i \(0.00974121\pi\)
\(678\) 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 0.945129 0.326697i \(-0.105936\pi\)
0.437297 + 0.899317i \(0.355936\pi\)
\(684\) 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 \(-0.935919\pi\)
0.551434 0.834219i \(-0.314081\pi\)
\(692\) 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 0.0526339 0.998614i \(-0.483238\pi\)
0.743344 + 0.668909i \(0.233238\pi\)
\(702\) 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 −0.935045 0.354528i \(-0.884641\pi\)
0.911866 + 0.410487i \(0.134641\pi\)
\(710\) 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 −0.539607 0.841917i \(-0.681427\pi\)
0.213765 + 0.976885i \(0.431427\pi\)
\(734\) 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 −0.335313 0.942107i \(-0.608842\pi\)
0.429068 + 0.903272i \(0.358842\pi\)
\(740\) 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 −0.0411358 0.999154i \(-0.513098\pi\)
−0.735596 + 0.677421i \(0.763098\pi\)
\(758\) 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 \(0.494279\pi\)
−0.719701 + 0.694284i \(0.755721\pi\)
\(774\) 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 \(0.0363266\pi\)
−0.621985 + 0.783029i \(0.713673\pi\)
\(788\) 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 −0.575482 0.817814i \(-0.695186\pi\)
0.171355 + 0.985209i \(0.445186\pi\)
\(798\) 0