Properties

Label 756.2.ck.a.5.18
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.18
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +O(q^{10})\) \(q+(1.11789 + 1.32299i) q^{3} +(-0.682386 + 3.87000i) q^{5} +(2.62129 + 0.358920i) q^{7} +(-0.500623 + 2.95793i) q^{9} +(0.639761 - 0.112807i) q^{11} +(2.79383 - 3.32955i) q^{13} +(-5.88282 + 3.42346i) q^{15} +4.23325 q^{17} -1.27018i q^{19} +(2.45548 + 3.86919i) q^{21} +(-3.69805 + 4.40717i) q^{23} +(-9.81281 - 3.57157i) q^{25} +(-4.47297 + 2.64434i) q^{27} +(-0.340590 - 0.405899i) q^{29} +(-1.83445 - 5.04012i) q^{31} +(0.864428 + 0.720293i) q^{33} +(-3.17775 + 9.89949i) q^{35} +(1.16130 + 2.01143i) q^{37} +(7.52818 - 0.0258750i) q^{39} +(-6.14659 - 5.15760i) q^{41} +(-0.264517 - 0.0962762i) q^{43} +(-11.1056 - 3.95587i) q^{45} +(-8.79969 - 3.20283i) q^{47} +(6.74235 + 1.88167i) q^{49} +(4.73233 + 5.60056i) q^{51} +(8.85622 - 5.11314i) q^{53} +2.55285i q^{55} +(1.68044 - 1.41993i) q^{57} +(0.258559 + 0.216957i) q^{59} +(-4.56709 + 12.5480i) q^{61} +(-2.37394 + 7.57393i) q^{63} +(10.9789 + 13.0842i) q^{65} +(1.70373 - 9.66231i) q^{67} +(-9.96468 + 0.0342494i) q^{69} +(9.11650 + 5.26341i) q^{71} +(-2.00088 - 1.15521i) q^{73} +(-6.24452 - 16.9749i) q^{75} +(1.71749 - 0.0660776i) q^{77} +(-2.46001 - 13.9514i) q^{79} +(-8.49875 - 2.96162i) q^{81} +(12.6075 - 10.5789i) q^{83} +(-2.88871 + 16.3827i) q^{85} +(0.156258 - 0.904351i) q^{87} +4.00479 q^{89} +(8.51848 - 7.72498i) q^{91} +(4.61732 - 8.06129i) q^{93} +(4.91560 + 0.866753i) q^{95} +(3.15648 - 8.67235i) q^{97} +(0.0133968 + 1.94884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 1.11789 + 1.32299i 0.645417 + 0.763831i
\(4\) 0 0
\(5\) −0.682386 + 3.87000i −0.305172 + 1.73072i 0.317520 + 0.948251i \(0.397150\pi\)
−0.622693 + 0.782467i \(0.713961\pi\)
\(6\) 0 0
\(7\) 2.62129 + 0.358920i 0.990756 + 0.135659i
\(8\) 0 0
\(9\) −0.500623 + 2.95793i −0.166874 + 0.985978i
\(10\) 0 0
\(11\) 0.639761 0.112807i 0.192895 0.0340126i −0.0763658 0.997080i \(-0.524332\pi\)
0.269261 + 0.963067i \(0.413221\pi\)
\(12\) 0 0
\(13\) 2.79383 3.32955i 0.774868 0.923452i −0.223821 0.974630i \(-0.571853\pi\)
0.998690 + 0.0511781i \(0.0162976\pi\)
\(14\) 0 0
\(15\) −5.88282 + 3.42346i −1.51894 + 0.883934i
\(16\) 0 0
\(17\) 4.23325 1.02671 0.513357 0.858175i \(-0.328402\pi\)
0.513357 + 0.858175i \(0.328402\pi\)
\(18\) 0 0
\(19\) 1.27018i 0.291399i −0.989329 0.145700i \(-0.953457\pi\)
0.989329 0.145700i \(-0.0465433\pi\)
\(20\) 0 0
\(21\) 2.45548 + 3.86919i 0.535830 + 0.844326i
\(22\) 0 0
\(23\) −3.69805 + 4.40717i −0.771097 + 0.918957i −0.998495 0.0548445i \(-0.982534\pi\)
0.227398 + 0.973802i \(0.426978\pi\)
\(24\) 0 0
\(25\) −9.81281 3.57157i −1.96256 0.714314i
\(26\) 0 0
\(27\) −4.47297 + 2.64434i −0.860824 + 0.508903i
\(28\) 0 0
\(29\) −0.340590 0.405899i −0.0632459 0.0753736i 0.733494 0.679696i \(-0.237888\pi\)
−0.796740 + 0.604322i \(0.793444\pi\)
\(30\) 0 0
\(31\) −1.83445 5.04012i −0.329477 0.905232i −0.988244 0.152884i \(-0.951144\pi\)
0.658767 0.752347i \(-0.271078\pi\)
\(32\) 0 0
\(33\) 0.864428 + 0.720293i 0.150478 + 0.125387i
\(34\) 0 0
\(35\) −3.17775 + 9.89949i −0.537138 + 1.67332i
\(36\) 0 0
\(37\) 1.16130 + 2.01143i 0.190917 + 0.330677i 0.945554 0.325464i \(-0.105521\pi\)
−0.754638 + 0.656142i \(0.772187\pi\)
\(38\) 0 0
\(39\) 7.52818 0.0258750i 1.20547 0.00414331i
\(40\) 0 0
\(41\) −6.14659 5.15760i −0.959936 0.805482i 0.0210065 0.999779i \(-0.493313\pi\)
−0.980943 + 0.194297i \(0.937757\pi\)
\(42\) 0 0
\(43\) −0.264517 0.0962762i −0.0403384 0.0146820i 0.321772 0.946817i \(-0.395721\pi\)
−0.362111 + 0.932135i \(0.617944\pi\)
\(44\) 0 0
\(45\) −11.1056 3.95587i −1.65552 0.589706i
\(46\) 0 0
\(47\) −8.79969 3.20283i −1.28357 0.467180i −0.391957 0.919984i \(-0.628202\pi\)
−0.891610 + 0.452803i \(0.850424\pi\)
\(48\) 0 0
\(49\) 6.74235 + 1.88167i 0.963193 + 0.268810i
\(50\) 0 0
\(51\) 4.73233 + 5.60056i 0.662658 + 0.784235i
\(52\) 0 0
\(53\) 8.85622 5.11314i 1.21650 0.702344i 0.252329 0.967642i \(-0.418803\pi\)
0.964167 + 0.265297i \(0.0854701\pi\)
\(54\) 0 0
\(55\) 2.55285i 0.344227i
\(56\) 0 0
\(57\) 1.68044 1.41993i 0.222580 0.188074i
\(58\) 0 0
\(59\) 0.258559 + 0.216957i 0.0336616 + 0.0282454i 0.659463 0.751737i \(-0.270784\pi\)
−0.625802 + 0.779982i \(0.715228\pi\)
\(60\) 0 0
\(61\) −4.56709 + 12.5480i −0.584756 + 1.60660i 0.195197 + 0.980764i \(0.437465\pi\)
−0.779953 + 0.625839i \(0.784757\pi\)
\(62\) 0 0
\(63\) −2.37394 + 7.57393i −0.299089 + 0.954225i
\(64\) 0 0
\(65\) 10.9789 + 13.0842i 1.36177 + 1.62289i
\(66\) 0 0
\(67\) 1.70373 9.66231i 0.208143 1.18044i −0.684273 0.729226i \(-0.739880\pi\)
0.892416 0.451213i \(-0.149009\pi\)
\(68\) 0 0
\(69\) −9.96468 + 0.0342494i −1.19961 + 0.00412314i
\(70\) 0 0
\(71\) 9.11650 + 5.26341i 1.08193 + 0.624652i 0.931416 0.363956i \(-0.118574\pi\)
0.150513 + 0.988608i \(0.451907\pi\)
\(72\) 0 0
\(73\) −2.00088 1.15521i −0.234185 0.135207i 0.378316 0.925676i \(-0.376503\pi\)
−0.612501 + 0.790470i \(0.709837\pi\)
\(74\) 0 0
\(75\) −6.24452 16.9749i −0.721055 1.96010i
\(76\) 0 0
\(77\) 1.71749 0.0660776i 0.195726 0.00753025i
\(78\) 0 0
\(79\) −2.46001 13.9514i −0.276772 1.56965i −0.733275 0.679932i \(-0.762009\pi\)
0.456503 0.889722i \(-0.349102\pi\)
\(80\) 0 0
\(81\) −8.49875 2.96162i −0.944306 0.329069i
\(82\) 0 0
\(83\) 12.6075 10.5789i 1.38385 1.16119i 0.416085 0.909326i \(-0.363402\pi\)
0.967763 0.251861i \(-0.0810425\pi\)
\(84\) 0 0
\(85\) −2.88871 + 16.3827i −0.313325 + 1.77695i
\(86\) 0 0
\(87\) 0.156258 0.904351i 0.0167527 0.0969566i
\(88\) 0 0
\(89\) 4.00479 0.424507 0.212254 0.977215i \(-0.431920\pi\)
0.212254 + 0.977215i \(0.431920\pi\)
\(90\) 0 0
\(91\) 8.51848 7.72498i 0.892980 0.809798i
\(92\) 0 0
\(93\) 4.61732 8.06129i 0.478793 0.835917i
\(94\) 0 0
\(95\) 4.91560 + 0.866753i 0.504330 + 0.0889270i
\(96\) 0 0
\(97\) 3.15648 8.67235i 0.320492 0.880543i −0.669925 0.742429i \(-0.733674\pi\)
0.990416 0.138114i \(-0.0441041\pi\)
\(98\) 0 0
\(99\) 0.0133968 + 1.94884i 0.00134643 + 0.195866i
\(100\) 0 0
\(101\) −9.22907 + 7.74411i −0.918327 + 0.770568i −0.973685 0.227899i \(-0.926814\pi\)
0.0553581 + 0.998467i \(0.482370\pi\)
\(102\) 0 0
\(103\) 12.3318 + 2.17442i 1.21508 + 0.214252i 0.744209 0.667947i \(-0.232827\pi\)
0.470876 + 0.882199i \(0.343938\pi\)
\(104\) 0 0
\(105\) −16.6494 + 6.86244i −1.62481 + 0.669705i
\(106\) 0 0
\(107\) 3.09467 + 1.78671i 0.299173 + 0.172728i 0.642071 0.766645i \(-0.278075\pi\)
−0.342898 + 0.939373i \(0.611409\pi\)
\(108\) 0 0
\(109\) 6.37741 + 11.0460i 0.610845 + 1.05801i 0.991098 + 0.133132i \(0.0425034\pi\)
−0.380254 + 0.924882i \(0.624163\pi\)
\(110\) 0 0
\(111\) −1.36290 + 3.78496i −0.129361 + 0.359253i
\(112\) 0 0
\(113\) 3.18210 + 8.74275i 0.299347 + 0.822449i 0.994609 + 0.103693i \(0.0330659\pi\)
−0.695262 + 0.718756i \(0.744712\pi\)
\(114\) 0 0
\(115\) −14.5322 17.3189i −1.35514 1.61499i
\(116\) 0 0
\(117\) 8.44995 + 9.93081i 0.781198 + 0.918104i
\(118\) 0 0
\(119\) 11.0966 + 1.51940i 1.01722 + 0.139283i
\(120\) 0 0
\(121\) −9.94005 + 3.61788i −0.903641 + 0.328898i
\(122\) 0 0
\(123\) −0.0477670 13.8976i −0.00430700 1.25310i
\(124\) 0 0
\(125\) 10.6939 18.5223i 0.956487 1.65668i
\(126\) 0 0
\(127\) 5.81728 + 10.0758i 0.516200 + 0.894084i 0.999823 + 0.0188080i \(0.00598712\pi\)
−0.483623 + 0.875276i \(0.660680\pi\)
\(128\) 0 0
\(129\) −0.168329 0.457581i −0.0148205 0.0402877i
\(130\) 0 0
\(131\) −0.330003 0.276906i −0.0288325 0.0241934i 0.628258 0.778005i \(-0.283768\pi\)
−0.657090 + 0.753812i \(0.728213\pi\)
\(132\) 0 0
\(133\) 0.455893 3.32951i 0.0395309 0.288706i
\(134\) 0 0
\(135\) −7.18130 19.1149i −0.618068 1.64515i
\(136\) 0 0
\(137\) −4.94778 + 13.5939i −0.422717 + 1.16141i 0.527429 + 0.849599i \(0.323156\pi\)
−0.950146 + 0.311806i \(0.899066\pi\)
\(138\) 0 0
\(139\) −15.9851 2.81861i −1.35584 0.239071i −0.551965 0.833868i \(-0.686122\pi\)
−0.803876 + 0.594796i \(0.797233\pi\)
\(140\) 0 0
\(141\) −5.59981 15.2224i −0.471589 1.28195i
\(142\) 0 0
\(143\) 1.41178 2.44528i 0.118059 0.204485i
\(144\) 0 0
\(145\) 1.80324 1.04110i 0.149751 0.0864590i
\(146\) 0 0
\(147\) 5.04781 + 11.0236i 0.416336 + 0.909211i
\(148\) 0 0
\(149\) 0.174749 + 0.480118i 0.0143160 + 0.0393328i 0.946645 0.322279i \(-0.104449\pi\)
−0.932329 + 0.361612i \(0.882227\pi\)
\(150\) 0 0
\(151\) −0.273788 1.55273i −0.0222806 0.126359i 0.971639 0.236470i \(-0.0759905\pi\)
−0.993919 + 0.110111i \(0.964879\pi\)
\(152\) 0 0
\(153\) −2.11926 + 12.5217i −0.171332 + 1.01232i
\(154\) 0 0
\(155\) 20.7571 3.66003i 1.66725 0.293981i
\(156\) 0 0
\(157\) 7.62298 9.08472i 0.608380 0.725040i −0.370646 0.928774i \(-0.620864\pi\)
0.979026 + 0.203735i \(0.0653080\pi\)
\(158\) 0 0
\(159\) 16.6650 + 6.00077i 1.32162 + 0.475892i
\(160\) 0 0
\(161\) −11.2755 + 10.2252i −0.888633 + 0.805856i
\(162\) 0 0
\(163\) 11.9778 20.7461i 0.938172 1.62496i 0.169295 0.985565i \(-0.445851\pi\)
0.768877 0.639397i \(-0.220816\pi\)
\(164\) 0 0
\(165\) −3.37741 + 2.85382i −0.262931 + 0.222170i
\(166\) 0 0
\(167\) −22.6351 + 8.23851i −1.75156 + 0.637515i −0.999761 0.0218801i \(-0.993035\pi\)
−0.751797 + 0.659395i \(0.770813\pi\)
\(168\) 0 0
\(169\) −1.02303 5.80190i −0.0786947 0.446300i
\(170\) 0 0
\(171\) 3.75711 + 0.635882i 0.287313 + 0.0486271i
\(172\) 0 0
\(173\) 13.9125 11.6740i 1.05775 0.887559i 0.0638639 0.997959i \(-0.479658\pi\)
0.993887 + 0.110400i \(0.0352132\pi\)
\(174\) 0 0
\(175\) −24.4403 12.8841i −1.84752 0.973950i
\(176\) 0 0
\(177\) 0.00200934 + 0.584608i 0.000151031 + 0.0439418i
\(178\) 0 0
\(179\) 15.1291i 1.13080i −0.824817 0.565400i \(-0.808722\pi\)
0.824817 0.565400i \(-0.191278\pi\)
\(180\) 0 0
\(181\) 8.68681 5.01533i 0.645685 0.372787i −0.141116 0.989993i \(-0.545069\pi\)
0.786801 + 0.617206i \(0.211736\pi\)
\(182\) 0 0
\(183\) −21.7064 + 7.98508i −1.60458 + 0.590274i
\(184\) 0 0
\(185\) −8.57670 + 3.12166i −0.630572 + 0.229509i
\(186\) 0 0
\(187\) 2.70827 0.477540i 0.198048 0.0349212i
\(188\) 0 0
\(189\) −12.6741 + 5.32615i −0.921903 + 0.387420i
\(190\) 0 0
\(191\) −1.98847 + 0.350621i −0.143881 + 0.0253701i −0.245125 0.969492i \(-0.578829\pi\)
0.101244 + 0.994862i \(0.467718\pi\)
\(192\) 0 0
\(193\) −12.8234 + 4.66733i −0.923048 + 0.335962i −0.759451 0.650565i \(-0.774532\pi\)
−0.163598 + 0.986527i \(0.552310\pi\)
\(194\) 0 0
\(195\) −5.03699 + 29.1517i −0.360706 + 2.08760i
\(196\) 0 0
\(197\) 7.10485 4.10199i 0.506200 0.292255i −0.225070 0.974343i \(-0.572261\pi\)
0.731270 + 0.682088i \(0.238928\pi\)
\(198\) 0 0
\(199\) 18.3216i 1.29878i 0.760455 + 0.649391i \(0.224976\pi\)
−0.760455 + 0.649391i \(0.775024\pi\)
\(200\) 0 0
\(201\) 14.6878 8.54743i 1.03599 0.602889i
\(202\) 0 0
\(203\) −0.747100 1.18622i −0.0524362 0.0832567i
\(204\) 0 0
\(205\) 24.1543 20.2678i 1.68701 1.41557i
\(206\) 0 0
\(207\) −11.1848 13.1449i −0.777396 0.913635i
\(208\) 0 0
\(209\) −0.143285 0.812612i −0.00991125 0.0562095i
\(210\) 0 0
\(211\) 4.56276 1.66071i 0.314113 0.114328i −0.180153 0.983639i \(-0.557659\pi\)
0.494266 + 0.869311i \(0.335437\pi\)
\(212\) 0 0
\(213\) 3.22782 + 17.9450i 0.221167 + 1.22957i
\(214\) 0 0
\(215\) 0.553092 0.957983i 0.0377205 0.0653339i
\(216\) 0 0
\(217\) −2.99964 13.8700i −0.203629 0.941560i
\(218\) 0 0
\(219\) −0.708439 3.93855i −0.0478719 0.266143i
\(220\) 0 0
\(221\) 11.8270 14.0948i 0.795568 0.948121i
\(222\) 0 0
\(223\) 20.2250 3.56621i 1.35436 0.238811i 0.551102 0.834438i \(-0.314207\pi\)
0.803261 + 0.595627i \(0.203096\pi\)
\(224\) 0 0
\(225\) 15.4770 27.2376i 1.03180 1.81584i
\(226\) 0 0
\(227\) −0.608939 3.45347i −0.0404167 0.229215i 0.957908 0.287076i \(-0.0926831\pi\)
−0.998325 + 0.0578610i \(0.981572\pi\)
\(228\) 0 0
\(229\) 4.61818 + 12.6884i 0.305178 + 0.838470i 0.993579 + 0.113140i \(0.0360907\pi\)
−0.688401 + 0.725330i \(0.741687\pi\)
\(230\) 0 0
\(231\) 2.00739 + 2.19836i 0.132077 + 0.144641i
\(232\) 0 0
\(233\) −4.98374 + 2.87737i −0.326496 + 0.188502i −0.654284 0.756249i \(-0.727030\pi\)
0.327788 + 0.944751i \(0.393697\pi\)
\(234\) 0 0
\(235\) 18.3997 31.8693i 1.20027 2.07892i
\(236\) 0 0
\(237\) 15.7076 18.8508i 1.02032 1.22449i
\(238\) 0 0
\(239\) 10.7739 + 1.89974i 0.696908 + 0.122884i 0.510869 0.859659i \(-0.329324\pi\)
0.186039 + 0.982542i \(0.440435\pi\)
\(240\) 0 0
\(241\) 5.92681 16.2838i 0.381779 1.04893i −0.588827 0.808259i \(-0.700410\pi\)
0.970607 0.240671i \(-0.0773675\pi\)
\(242\) 0 0
\(243\) −5.58250 14.5546i −0.358118 0.933676i
\(244\) 0 0
\(245\) −11.8829 + 24.8089i −0.759174 + 1.58498i
\(246\) 0 0
\(247\) −4.22913 3.54867i −0.269093 0.225796i
\(248\) 0 0
\(249\) 28.0896 + 4.85347i 1.78011 + 0.307576i
\(250\) 0 0
\(251\) −8.96226 15.5231i −0.565693 0.979809i −0.996985 0.0775963i \(-0.975275\pi\)
0.431292 0.902212i \(-0.358058\pi\)
\(252\) 0 0
\(253\) −1.86871 + 3.23670i −0.117485 + 0.203489i
\(254\) 0 0
\(255\) −24.9035 + 14.4924i −1.55952 + 0.907548i
\(256\) 0 0
\(257\) −10.6659 + 3.88206i −0.665319 + 0.242156i −0.652531 0.757762i \(-0.726293\pi\)
−0.0127881 + 0.999918i \(0.504071\pi\)
\(258\) 0 0
\(259\) 2.32217 + 5.68936i 0.144292 + 0.353520i
\(260\) 0 0
\(261\) 1.37113 0.804240i 0.0848708 0.0497812i
\(262\) 0 0
\(263\) 0.155958 + 0.185863i 0.00961677 + 0.0114608i 0.770831 0.637039i \(-0.219841\pi\)
−0.761215 + 0.648500i \(0.775397\pi\)
\(264\) 0 0
\(265\) 13.7445 + 37.7627i 0.844319 + 2.31975i
\(266\) 0 0
\(267\) 4.47693 + 5.29831i 0.273984 + 0.324251i
\(268\) 0 0
\(269\) −8.65220 14.9860i −0.527534 0.913715i −0.999485 0.0320906i \(-0.989784\pi\)
0.471951 0.881625i \(-0.343550\pi\)
\(270\) 0 0
\(271\) −8.44600 4.87630i −0.513058 0.296214i 0.221032 0.975267i \(-0.429058\pi\)
−0.734090 + 0.679053i \(0.762391\pi\)
\(272\) 0 0
\(273\) 19.7429 + 2.63419i 1.19489 + 0.159428i
\(274\) 0 0
\(275\) −6.68075 1.17800i −0.402864 0.0710359i
\(276\) 0 0
\(277\) −18.7307 + 15.7169i −1.12542 + 0.944336i −0.998865 0.0476243i \(-0.984835\pi\)
−0.126550 + 0.991960i \(0.540391\pi\)
\(278\) 0 0
\(279\) 15.8267 2.90299i 0.947520 0.173797i
\(280\) 0 0
\(281\) −4.28951 + 11.7853i −0.255891 + 0.703054i 0.743520 + 0.668714i \(0.233155\pi\)
−0.999410 + 0.0343397i \(0.989067\pi\)
\(282\) 0 0
\(283\) −22.5040 3.96806i −1.33772 0.235876i −0.541408 0.840760i \(-0.682109\pi\)
−0.796314 + 0.604883i \(0.793220\pi\)
\(284\) 0 0
\(285\) 4.34842 + 7.47225i 0.257578 + 0.442618i
\(286\) 0 0
\(287\) −14.2608 15.7257i −0.841791 0.928260i
\(288\) 0 0
\(289\) 0.920395 0.0541409
\(290\) 0 0
\(291\) 15.0021 5.51877i 0.879437 0.323516i
\(292\) 0 0
\(293\) −0.331036 + 1.87740i −0.0193393 + 0.109679i −0.992949 0.118539i \(-0.962179\pi\)
0.973610 + 0.228218i \(0.0732899\pi\)
\(294\) 0 0
\(295\) −1.01606 + 0.852577i −0.0591574 + 0.0496390i
\(296\) 0 0
\(297\) −2.56333 + 2.19633i −0.148740 + 0.127444i
\(298\) 0 0
\(299\) 4.34218 + 24.6257i 0.251115 + 1.42414i
\(300\) 0 0
\(301\) −0.658820 0.347308i −0.0379738 0.0200185i
\(302\) 0 0
\(303\) −20.5625 3.55290i −1.18129 0.204109i
\(304\) 0 0
\(305\) −45.4442 26.2372i −2.60212 1.50234i
\(306\) 0 0
\(307\) −12.7896 7.38406i −0.729939 0.421430i 0.0884610 0.996080i \(-0.471805\pi\)
−0.818400 + 0.574649i \(0.805138\pi\)
\(308\) 0 0
\(309\) 10.9089 + 18.7456i 0.620584 + 1.06640i
\(310\) 0 0
\(311\) −2.02677 + 11.4944i −0.114928 + 0.651788i 0.871858 + 0.489758i \(0.162915\pi\)
−0.986786 + 0.162029i \(0.948196\pi\)
\(312\) 0 0
\(313\) 1.14698 + 1.36692i 0.0648312 + 0.0772629i 0.797485 0.603338i \(-0.206163\pi\)
−0.732654 + 0.680601i \(0.761719\pi\)
\(314\) 0 0
\(315\) −27.6912 14.3555i −1.56022 0.808841i
\(316\) 0 0
\(317\) −10.5347 + 28.9437i −0.591685 + 1.62564i 0.175692 + 0.984445i \(0.443784\pi\)
−0.767377 + 0.641196i \(0.778438\pi\)
\(318\) 0 0
\(319\) −0.263684 0.221257i −0.0147635 0.0123880i
\(320\) 0 0
\(321\) 1.09571 + 6.09158i 0.0611566 + 0.339999i
\(322\) 0 0
\(323\) 5.37699i 0.299184i
\(324\) 0 0
\(325\) −39.3070 + 22.6939i −2.18036 + 1.25883i
\(326\) 0 0
\(327\) −7.48451 + 20.7855i −0.413894 + 1.14944i
\(328\) 0 0
\(329\) −21.9170 11.5539i −1.20832 0.636989i
\(330\) 0 0
\(331\) 11.6294 + 4.23276i 0.639210 + 0.232653i 0.641235 0.767345i \(-0.278422\pi\)
−0.00202526 + 0.999998i \(0.500645\pi\)
\(332\) 0 0
\(333\) −6.53106 + 2.42808i −0.357900 + 0.133058i
\(334\) 0 0
\(335\) 36.2306 + 13.1868i 1.97949 + 0.720475i
\(336\) 0 0
\(337\) 16.3396 + 13.7106i 0.890075 + 0.746862i 0.968225 0.250080i \(-0.0804569\pi\)
−0.0781501 + 0.996942i \(0.524901\pi\)
\(338\) 0 0
\(339\) −8.00935 + 13.9834i −0.435008 + 0.759473i
\(340\) 0 0
\(341\) −1.74217 3.01753i −0.0943439 0.163408i
\(342\) 0 0
\(343\) 16.9983 + 7.35237i 0.917823 + 0.396990i
\(344\) 0 0
\(345\) 6.66721 38.5867i 0.358951 2.07744i
\(346\) 0 0
\(347\) −0.760701 2.09001i −0.0408366 0.112198i 0.917598 0.397509i \(-0.130125\pi\)
−0.958435 + 0.285311i \(0.907903\pi\)
\(348\) 0 0
\(349\) 11.8201 + 14.0867i 0.632718 + 0.754043i 0.983201 0.182525i \(-0.0584272\pi\)
−0.350484 + 0.936569i \(0.613983\pi\)
\(350\) 0 0
\(351\) −3.69225 + 22.2808i −0.197078 + 1.18926i
\(352\) 0 0
\(353\) −26.2308 9.54724i −1.39613 0.508148i −0.469100 0.883145i \(-0.655421\pi\)
−0.927026 + 0.374997i \(0.877644\pi\)
\(354\) 0 0
\(355\) −26.5904 + 31.6892i −1.41127 + 1.68189i
\(356\) 0 0
\(357\) 10.3947 + 16.3792i 0.550144 + 0.866881i
\(358\) 0 0
\(359\) 17.1001i 0.902507i 0.892396 + 0.451253i \(0.149023\pi\)
−0.892396 + 0.451253i \(0.850977\pi\)
\(360\) 0 0
\(361\) 17.3866 0.915086
\(362\) 0 0
\(363\) −15.8984 9.10621i −0.834448 0.477952i
\(364\) 0 0
\(365\) 5.83603 6.95511i 0.305472 0.364047i
\(366\) 0 0
\(367\) −23.2623 + 4.10177i −1.21428 + 0.214110i −0.743862 0.668333i \(-0.767008\pi\)
−0.470418 + 0.882443i \(0.655897\pi\)
\(368\) 0 0
\(369\) 18.3330 15.5992i 0.954377 0.812062i
\(370\) 0 0
\(371\) 25.0500 10.2244i 1.30053 0.530823i
\(372\) 0 0
\(373\) 0.125883 0.713915i 0.00651795 0.0369651i −0.981375 0.192100i \(-0.938470\pi\)
0.987893 + 0.155135i \(0.0495813\pi\)
\(374\) 0 0
\(375\) 36.4595 6.55808i 1.88276 0.338658i
\(376\) 0 0
\(377\) −2.30301 −0.118611
\(378\) 0 0
\(379\) 8.15560 0.418925 0.209462 0.977817i \(-0.432829\pi\)
0.209462 + 0.977817i \(0.432829\pi\)
\(380\) 0 0
\(381\) −6.82714 + 18.9599i −0.349765 + 0.971346i
\(382\) 0 0
\(383\) 0.822617 4.66529i 0.0420338 0.238385i −0.956551 0.291564i \(-0.905824\pi\)
0.998585 + 0.0531790i \(0.0169354\pi\)
\(384\) 0 0
\(385\) −0.916270 + 6.69178i −0.0466974 + 0.341045i
\(386\) 0 0
\(387\) 0.417202 0.734225i 0.0212076 0.0373228i
\(388\) 0 0
\(389\) 30.2267 5.32978i 1.53255 0.270231i 0.657201 0.753715i \(-0.271740\pi\)
0.875353 + 0.483485i \(0.160629\pi\)
\(390\) 0 0
\(391\) −15.6548 + 18.6566i −0.791696 + 0.943506i
\(392\) 0 0
\(393\) −0.00256455 0.746143i −0.000129365 0.0376380i
\(394\) 0 0
\(395\) 55.6706 2.80109
\(396\) 0 0
\(397\) 30.3514i 1.52329i 0.647992 + 0.761647i \(0.275609\pi\)
−0.647992 + 0.761647i \(0.724391\pi\)
\(398\) 0 0
\(399\) 4.91457 3.11890i 0.246036 0.156140i
\(400\) 0 0
\(401\) 3.04703 3.63131i 0.152161 0.181339i −0.684579 0.728939i \(-0.740014\pi\)
0.836740 + 0.547600i \(0.184458\pi\)
\(402\) 0 0
\(403\) −21.9065 7.97331i −1.09124 0.397179i
\(404\) 0 0
\(405\) 17.2609 30.8692i 0.857702 1.53390i
\(406\) 0 0
\(407\) 0.969858 + 1.15583i 0.0480741 + 0.0572925i
\(408\) 0 0
\(409\) 3.67133 + 10.0869i 0.181536 + 0.498765i 0.996765 0.0803734i \(-0.0256113\pi\)
−0.815229 + 0.579139i \(0.803389\pi\)
\(410\) 0 0
\(411\) −23.5157 + 8.65067i −1.15995 + 0.426706i
\(412\) 0 0
\(413\) 0.599890 + 0.661510i 0.0295187 + 0.0325508i
\(414\) 0 0
\(415\) 32.3373 + 56.0098i 1.58737 + 2.74941i
\(416\) 0 0
\(417\) −14.1407 24.2991i −0.692472 1.18993i
\(418\) 0 0
\(419\) −8.97960 7.53478i −0.438682 0.368098i 0.396534 0.918020i \(-0.370213\pi\)
−0.835216 + 0.549922i \(0.814657\pi\)
\(420\) 0 0
\(421\) −15.3936 5.60280i −0.750236 0.273064i −0.0615311 0.998105i \(-0.519598\pi\)
−0.688705 + 0.725041i \(0.741821\pi\)
\(422\) 0 0
\(423\) 13.8791 24.4255i 0.674824 1.18761i
\(424\) 0 0
\(425\) −41.5401 15.1193i −2.01499 0.733396i
\(426\) 0 0
\(427\) −16.4754 + 31.2527i −0.797300 + 1.51242i
\(428\) 0 0
\(429\) 4.81332 0.865786i 0.232389 0.0418006i
\(430\) 0 0
\(431\) −7.17094 + 4.14015i −0.345412 + 0.199424i −0.662663 0.748918i \(-0.730574\pi\)
0.317251 + 0.948342i \(0.397240\pi\)
\(432\) 0 0
\(433\) 5.95449i 0.286154i −0.989712 0.143077i \(-0.954300\pi\)
0.989712 0.143077i \(-0.0456997\pi\)
\(434\) 0 0
\(435\) 3.39321 + 1.22184i 0.162692 + 0.0585826i
\(436\) 0 0
\(437\) 5.59789 + 4.69719i 0.267784 + 0.224697i
\(438\) 0 0
\(439\) 9.17660 25.2125i 0.437975 1.20333i −0.502832 0.864384i \(-0.667709\pi\)
0.940807 0.338943i \(-0.110069\pi\)
\(440\) 0 0
\(441\) −8.94123 + 19.0014i −0.425773 + 0.904830i
\(442\) 0 0
\(443\) −9.94463 11.8515i −0.472484 0.563084i 0.476189 0.879343i \(-0.342018\pi\)
−0.948673 + 0.316259i \(0.897573\pi\)
\(444\) 0 0
\(445\) −2.73281 + 15.4986i −0.129548 + 0.734702i
\(446\) 0 0
\(447\) −0.439842 + 0.767912i −0.0208038 + 0.0363210i
\(448\) 0 0
\(449\) −6.95141 4.01340i −0.328058 0.189404i 0.326921 0.945052i \(-0.393989\pi\)
−0.654978 + 0.755648i \(0.727322\pi\)
\(450\) 0 0
\(451\) −4.51416 2.60625i −0.212564 0.122724i
\(452\) 0 0
\(453\) 1.74818 2.09801i 0.0821369 0.0985730i
\(454\) 0 0
\(455\) 24.0828 + 38.2380i 1.12902 + 1.79262i
\(456\) 0 0
\(457\) 5.90878 + 33.5104i 0.276401 + 1.56755i 0.734475 + 0.678635i \(0.237428\pi\)
−0.458074 + 0.888914i \(0.651461\pi\)
\(458\) 0 0
\(459\) −18.9352 + 11.1941i −0.883820 + 0.522498i
\(460\) 0 0
\(461\) 11.2017 9.39934i 0.521715 0.437771i −0.343514 0.939148i \(-0.611617\pi\)
0.865229 + 0.501377i \(0.167173\pi\)
\(462\) 0 0
\(463\) 5.10869 28.9728i 0.237421 1.34648i −0.600033 0.799975i \(-0.704846\pi\)
0.837454 0.546507i \(-0.184043\pi\)
\(464\) 0 0
\(465\) 28.0464 + 23.3699i 1.30062 + 1.08375i
\(466\) 0 0
\(467\) −14.2525 −0.659527 −0.329763 0.944064i \(-0.606969\pi\)
−0.329763 + 0.944064i \(0.606969\pi\)
\(468\) 0 0
\(469\) 7.93396 24.7162i 0.366356 1.14129i
\(470\) 0 0
\(471\) 20.5407 0.0706000i 0.946466 0.00325308i
\(472\) 0 0
\(473\) −0.180088 0.0317544i −0.00828046 0.00146007i
\(474\) 0 0
\(475\) −4.53654 + 12.4640i −0.208151 + 0.571889i
\(476\) 0 0
\(477\) 10.6907 + 28.7559i 0.489494 + 1.31664i
\(478\) 0 0
\(479\) −2.86649 + 2.40527i −0.130973 + 0.109900i −0.705921 0.708290i \(-0.749467\pi\)
0.574948 + 0.818190i \(0.305022\pi\)
\(480\) 0 0
\(481\) 9.94164 + 1.75298i 0.453300 + 0.0799290i
\(482\) 0 0
\(483\) −26.1326 3.48674i −1.18908 0.158652i
\(484\) 0 0
\(485\) 31.4081 + 18.1335i 1.42617 + 0.823398i
\(486\) 0 0
\(487\) 11.0027 + 19.0573i 0.498581 + 0.863568i 0.999999 0.00163760i \(-0.000521265\pi\)
−0.501418 + 0.865205i \(0.667188\pi\)
\(488\) 0 0
\(489\) 40.8369 7.34546i 1.84671 0.332173i
\(490\) 0 0
\(491\) −8.03487 22.0756i −0.362609 0.996259i −0.978104 0.208118i \(-0.933266\pi\)
0.615495 0.788141i \(-0.288956\pi\)
\(492\) 0 0
\(493\) −1.44180 1.71827i −0.0649355 0.0773871i
\(494\) 0 0
\(495\) −7.55118 1.27802i −0.339400 0.0574426i
\(496\) 0 0
\(497\) 22.0079 + 17.0690i 0.987188 + 0.765651i
\(498\) 0 0
\(499\) −4.45052 + 1.61986i −0.199233 + 0.0725147i −0.439709 0.898140i \(-0.644918\pi\)
0.240477 + 0.970655i \(0.422696\pi\)
\(500\) 0 0
\(501\) −36.2032 20.7363i −1.61744 0.926430i
\(502\) 0 0
\(503\) −9.45110 + 16.3698i −0.421404 + 0.729893i −0.996077 0.0884900i \(-0.971796\pi\)
0.574673 + 0.818383i \(0.305129\pi\)
\(504\) 0 0
\(505\) −23.6719 41.0010i −1.05339 1.82452i
\(506\) 0 0
\(507\) 6.53223 7.83938i 0.290107 0.348159i
\(508\) 0 0
\(509\) −28.0651 23.5494i −1.24396 1.04381i −0.997204 0.0747321i \(-0.976190\pi\)
−0.246759 0.969077i \(-0.579366\pi\)
\(510\) 0 0
\(511\) −4.83026 3.74629i −0.213678 0.165726i
\(512\) 0 0
\(513\) 3.35879 + 5.68148i 0.148294 + 0.250844i
\(514\) 0 0
\(515\) −16.8300 + 46.2402i −0.741620 + 2.03758i
\(516\) 0 0
\(517\) −5.99100 1.05638i −0.263484 0.0464593i
\(518\) 0 0
\(519\) 30.9974 + 5.35589i 1.36063 + 0.235098i
\(520\) 0 0
\(521\) 16.4028 28.4105i 0.718621 1.24469i −0.242925 0.970045i \(-0.578107\pi\)
0.961546 0.274643i \(-0.0885598\pi\)
\(522\) 0 0
\(523\) 3.12916 1.80662i 0.136829 0.0789980i −0.430023 0.902818i \(-0.641495\pi\)
0.566852 + 0.823820i \(0.308161\pi\)
\(524\) 0 0
\(525\) −10.2761 46.7375i −0.448485 2.03979i
\(526\) 0 0
\(527\) −7.76569 21.3361i −0.338279 0.929414i
\(528\) 0 0
\(529\) −1.75362 9.94526i −0.0762442 0.432403i
\(530\) 0 0
\(531\) −0.771186 + 0.656188i −0.0334666 + 0.0284761i
\(532\) 0 0
\(533\) −34.3450 + 6.05596i −1.48765 + 0.262313i
\(534\) 0 0
\(535\) −9.02633 + 10.7572i −0.390242 + 0.465073i
\(536\) 0 0
\(537\) 20.0157 16.9127i 0.863740 0.729837i
\(538\) 0 0
\(539\) 4.52576 + 0.443232i 0.194938 + 0.0190913i
\(540\) 0 0
\(541\) 8.45105 14.6376i 0.363339 0.629321i −0.625169 0.780489i \(-0.714970\pi\)
0.988508 + 0.151168i \(0.0483034\pi\)
\(542\) 0 0
\(543\) 16.3462 + 5.88598i 0.701482 + 0.252591i
\(544\) 0 0
\(545\) −47.0999 + 17.1430i −2.01754 + 0.734323i
\(546\) 0 0
\(547\) 1.82850 + 10.3699i 0.0781810 + 0.443386i 0.998621 + 0.0525021i \(0.0167196\pi\)
−0.920440 + 0.390884i \(0.872169\pi\)
\(548\) 0 0
\(549\) −34.8297 19.7909i −1.48649 0.844657i
\(550\) 0 0
\(551\) −0.515565 + 0.432610i −0.0219638 + 0.0184298i
\(552\) 0 0
\(553\) −1.44097 37.4536i −0.0612762 1.59269i
\(554\) 0 0
\(555\) −13.7178 7.85723i −0.582288 0.333521i
\(556\) 0 0
\(557\) 4.74008i 0.200844i 0.994945 + 0.100422i \(0.0320192\pi\)
−0.994945 + 0.100422i \(0.967981\pi\)
\(558\) 0 0
\(559\) −1.05957 + 0.611744i −0.0448151 + 0.0258740i
\(560\) 0 0
\(561\) 3.65934 + 3.04918i 0.154497 + 0.128736i
\(562\) 0 0
\(563\) 15.4903 5.63801i 0.652839 0.237614i 0.00569722 0.999984i \(-0.498187\pi\)
0.647142 + 0.762370i \(0.275964\pi\)
\(564\) 0 0
\(565\) −36.0059 + 6.34881i −1.51478 + 0.267097i
\(566\) 0 0
\(567\) −21.2147 10.8136i −0.890935 0.454131i
\(568\) 0 0
\(569\) −31.0763 + 5.47959i −1.30279 + 0.229716i −0.781629 0.623744i \(-0.785611\pi\)
−0.521158 + 0.853460i \(0.674500\pi\)
\(570\) 0 0
\(571\) 31.0241 11.2918i 1.29832 0.472549i 0.401870 0.915697i \(-0.368361\pi\)
0.896449 + 0.443148i \(0.146138\pi\)
\(572\) 0 0
\(573\) −2.68677 2.23878i −0.112241 0.0935262i
\(574\) 0 0
\(575\) 52.0288 30.0388i 2.16975 1.25271i
\(576\) 0 0
\(577\) 15.9807i 0.665285i 0.943053 + 0.332642i \(0.107940\pi\)
−0.943053 + 0.332642i \(0.892060\pi\)
\(578\) 0 0
\(579\) −20.5101 11.7477i −0.852369 0.488217i
\(580\) 0 0
\(581\) 36.8448 23.2054i 1.52858 0.962721i
\(582\) 0 0
\(583\) 5.08906 4.27023i 0.210768 0.176855i
\(584\) 0 0
\(585\) −44.1984 + 25.9247i −1.82738 + 1.07185i
\(586\) 0 0
\(587\) −2.71350 15.3890i −0.111998 0.635174i −0.988193 0.153216i \(-0.951037\pi\)
0.876195 0.481958i \(-0.160074\pi\)
\(588\) 0 0
\(589\) −6.40186 + 2.33009i −0.263784 + 0.0960095i
\(590\) 0 0
\(591\) 13.3694 + 4.81408i 0.549943 + 0.198025i
\(592\) 0 0
\(593\) −0.551611 + 0.955418i −0.0226520 + 0.0392343i −0.877129 0.480255i \(-0.840544\pi\)
0.854477 + 0.519489i \(0.173878\pi\)
\(594\) 0 0
\(595\) −13.4522 + 41.9070i −0.551487 + 1.71802i
\(596\) 0 0
\(597\) −24.2393 + 20.4816i −0.992049 + 0.838255i
\(598\) 0 0
\(599\) −0.973078 + 1.15967i −0.0397589 + 0.0473828i −0.785557 0.618789i \(-0.787624\pi\)
0.745799 + 0.666172i \(0.232068\pi\)
\(600\) 0 0
\(601\) −40.4782 + 7.13740i −1.65114 + 0.291141i −0.920243 0.391347i \(-0.872009\pi\)
−0.730897 + 0.682488i \(0.760898\pi\)
\(602\) 0 0
\(603\) 27.7276 + 9.87669i 1.12915 + 0.402210i
\(604\) 0 0
\(605\) −7.21827 40.9368i −0.293464 1.66432i
\(606\) 0 0
\(607\) 12.3909 + 34.0439i 0.502933 + 1.38180i 0.888398 + 0.459075i \(0.151819\pi\)
−0.385464 + 0.922723i \(0.625959\pi\)
\(608\) 0 0
\(609\) 0.734188 2.31448i 0.0297508 0.0937876i
\(610\) 0 0
\(611\) −35.2488 + 20.3509i −1.42601 + 0.823310i
\(612\) 0 0
\(613\) 4.15491 7.19651i 0.167815 0.290664i −0.769836 0.638241i \(-0.779662\pi\)
0.937651 + 0.347577i \(0.112996\pi\)
\(614\) 0 0
\(615\) 53.8162 + 9.29864i 2.17008 + 0.374957i
\(616\) 0 0
\(617\) −29.6763 5.23273i −1.19472 0.210662i −0.459306 0.888278i \(-0.651902\pi\)
−0.735416 + 0.677616i \(0.763013\pi\)
\(618\) 0 0
\(619\) 7.51408 20.6448i 0.302016 0.829783i −0.692133 0.721770i \(-0.743329\pi\)
0.994149 0.108013i \(-0.0344488\pi\)
\(620\) 0 0
\(621\) 4.88724 29.4920i 0.196118 1.18347i
\(622\) 0 0
\(623\) 10.4977 + 1.43740i 0.420583 + 0.0575882i
\(624\) 0 0
\(625\) 24.3866 + 20.4628i 0.975465 + 0.818512i
\(626\) 0 0
\(627\) 0.914902 1.09798i 0.0365377 0.0438491i
\(628\) 0 0
\(629\) 4.91607 + 8.51489i 0.196017 + 0.339511i
\(630\) 0 0
\(631\) 13.1731 22.8165i 0.524414 0.908311i −0.475182 0.879887i \(-0.657618\pi\)
0.999596 0.0284238i \(-0.00904880\pi\)
\(632\) 0 0
\(633\) 7.29779 + 4.18000i 0.290061 + 0.166140i
\(634\) 0 0
\(635\) −42.9631 + 15.6373i −1.70494 + 0.620546i
\(636\) 0 0
\(637\) 25.1021 17.1920i 0.994581 0.681171i
\(638\) 0 0
\(639\) −20.1328 + 24.3310i −0.796440 + 0.962520i
\(640\) 0 0
\(641\) −27.9668 33.3296i −1.10462 1.31644i −0.944193 0.329393i \(-0.893156\pi\)
−0.160431 0.987047i \(-0.551288\pi\)
\(642\) 0 0
\(643\) −6.28983 17.2812i −0.248047 0.681503i −0.999758 0.0220101i \(-0.992993\pi\)
0.751711 0.659493i \(-0.229229\pi\)
\(644\) 0 0
\(645\) 1.88570 0.339187i 0.0742495 0.0133555i
\(646\) 0 0
\(647\) −16.2772 28.1929i −0.639922 1.10838i −0.985449 0.169969i \(-0.945633\pi\)
0.345527 0.938409i \(-0.387700\pi\)
\(648\) 0 0
\(649\) 0.189891 + 0.109633i 0.00745385 + 0.00430348i
\(650\) 0 0
\(651\) 14.9967 19.4737i 0.587767 0.763236i
\(652\) 0 0
\(653\) −22.5933 3.98381i −0.884145 0.155899i −0.286903 0.957960i \(-0.592626\pi\)
−0.597242 + 0.802061i \(0.703737\pi\)
\(654\) 0 0
\(655\) 1.29682 1.08816i 0.0506708 0.0425178i
\(656\) 0 0
\(657\) 4.41872 5.34015i 0.172391 0.208339i
\(658\) 0 0
\(659\) 3.24389 8.91251i 0.126364 0.347182i −0.860338 0.509725i \(-0.829747\pi\)
0.986702 + 0.162543i \(0.0519695\pi\)
\(660\) 0 0
\(661\) 24.9854 + 4.40561i 0.971821 + 0.171358i 0.636949 0.770906i \(-0.280196\pi\)
0.334871 + 0.942264i \(0.391307\pi\)
\(662\) 0 0
\(663\) 31.8687 0.109535i 1.23768 0.00425399i
\(664\) 0 0
\(665\) 12.5741 + 4.03632i 0.487604 + 0.156522i
\(666\) 0 0
\(667\) 3.04838 0.118034
\(668\) 0 0
\(669\) 27.3274 + 22.7708i 1.05654 + 0.880372i
\(670\) 0 0
\(671\) −1.50634 + 8.54290i −0.0581517 + 0.329795i
\(672\) 0 0
\(673\) −7.51664 + 6.30721i −0.289745 + 0.243125i −0.776061 0.630658i \(-0.782785\pi\)
0.486315 + 0.873783i \(0.338341\pi\)
\(674\) 0 0
\(675\) 53.3369 9.97285i 2.05294 0.383855i
\(676\) 0 0
\(677\) −6.52377 36.9981i −0.250729 1.42195i −0.806803 0.590821i \(-0.798804\pi\)
0.556074 0.831133i \(-0.312307\pi\)
\(678\) 0 0
\(679\) 11.3867 21.5998i 0.436982 0.828926i
\(680\) 0 0
\(681\) 3.88818 4.66623i 0.148995 0.178810i
\(682\) 0 0
\(683\) −2.32361 1.34154i −0.0889104 0.0513324i 0.454886 0.890550i \(-0.349680\pi\)
−0.543796 + 0.839217i \(0.683013\pi\)
\(684\) 0 0
\(685\) −49.2321 28.4242i −1.88106 1.08603i
\(686\) 0 0
\(687\) −11.6240 + 20.2941i −0.443482 + 0.774267i
\(688\) 0 0
\(689\) 7.71827 43.7725i 0.294043 1.66760i
\(690\) 0 0
\(691\) 15.9156 + 18.9675i 0.605459 + 0.721558i 0.978498 0.206258i \(-0.0661287\pi\)
−0.373039 + 0.927816i \(0.621684\pi\)
\(692\) 0 0
\(693\) −0.664362 + 5.11330i −0.0252370 + 0.194238i
\(694\) 0 0
\(695\) 21.8161 59.9391i 0.827530 2.27362i
\(696\) 0 0
\(697\) −26.0200 21.8334i −0.985580 0.826999i
\(698\) 0 0
\(699\) −9.37804 3.37687i −0.354710 0.127725i
\(700\) 0 0
\(701\) 39.7674i 1.50200i 0.660305 + 0.750998i \(0.270427\pi\)
−0.660305 + 0.750998i \(0.729573\pi\)
\(702\) 0 0
\(703\) 2.55488 1.47506i 0.0963592 0.0556330i
\(704\) 0 0
\(705\) 62.7318 11.2838i 2.36262 0.424971i
\(706\) 0 0
\(707\) −26.9716 + 16.9871i −1.01437 + 0.638865i
\(708\) 0 0
\(709\) 33.8905 + 12.3351i 1.27279 + 0.463256i 0.888040 0.459766i \(-0.152067\pi\)
0.384746 + 0.923022i \(0.374289\pi\)
\(710\) 0 0
\(711\) 42.4988 0.292147i 1.59383 0.0109564i
\(712\) 0 0
\(713\) 28.9965 + 10.5539i 1.08593 + 0.395246i
\(714\) 0 0
\(715\) 8.49987 + 7.13223i 0.317877 + 0.266730i
\(716\) 0 0
\(717\) 9.53079 + 16.3776i 0.355934 + 0.611631i
\(718\) 0 0
\(719\) −14.2473 24.6770i −0.531333 0.920296i −0.999331 0.0365666i \(-0.988358\pi\)
0.467998 0.883730i \(-0.344975\pi\)
\(720\) 0 0
\(721\) 31.5447 + 10.1259i 1.17479 + 0.377109i
\(722\) 0 0
\(723\) 28.1689 10.3624i 1.04761 0.385382i
\(724\) 0 0
\(725\) 1.89245 + 5.19945i 0.0702837 + 0.193103i
\(726\) 0 0
\(727\) −13.6895 16.3145i −0.507716 0.605072i 0.449915 0.893071i \(-0.351454\pi\)
−0.957631 + 0.287999i \(0.907010\pi\)
\(728\) 0 0
\(729\) 13.0150 23.6561i 0.482035 0.876152i
\(730\) 0 0
\(731\) −1.11977 0.407561i −0.0414160 0.0150742i
\(732\) 0 0
\(733\) 30.0632 35.8280i 1.11041 1.32334i 0.169175 0.985586i \(-0.445890\pi\)
0.941236 0.337750i \(-0.109666\pi\)
\(734\) 0 0
\(735\) −46.1059 + 12.0127i −1.70064 + 0.443094i
\(736\) 0 0
\(737\) 6.37376i 0.234780i
\(738\) 0 0
\(739\) 8.16282 0.300274 0.150137 0.988665i \(-0.452028\pi\)
0.150137 + 0.988665i \(0.452028\pi\)
\(740\) 0 0
\(741\) −0.0328659 9.56215i −0.00120736 0.351274i
\(742\) 0 0
\(743\) −11.9198 + 14.2055i −0.437295 + 0.521148i −0.939012 0.343884i \(-0.888257\pi\)
0.501717 + 0.865032i \(0.332702\pi\)
\(744\) 0 0
\(745\) −1.97730 + 0.348652i −0.0724428 + 0.0127736i
\(746\) 0 0
\(747\) 24.9801 + 42.5881i 0.913976 + 1.55822i
\(748\) 0 0
\(749\) 7.47075 + 5.79423i 0.272975 + 0.211716i
\(750\) 0 0
\(751\) −1.93571 + 10.9779i −0.0706350 + 0.400591i 0.928907 + 0.370314i \(0.120750\pi\)
−0.999542 + 0.0302768i \(0.990361\pi\)
\(752\) 0 0
\(753\) 10.5181 29.2102i 0.383300 1.06448i
\(754\) 0 0
\(755\) 6.19590 0.225492
\(756\) 0 0
\(757\) 14.8985 0.541494 0.270747 0.962651i \(-0.412729\pi\)
0.270747 + 0.962651i \(0.412729\pi\)
\(758\) 0 0
\(759\) −6.37115 + 1.14600i −0.231258 + 0.0415971i
\(760\) 0 0
\(761\) −5.84310 + 33.1379i −0.211812 + 1.20125i 0.674541 + 0.738237i \(0.264341\pi\)
−0.886353 + 0.463009i \(0.846770\pi\)
\(762\) 0 0
\(763\) 12.7524 + 31.2438i 0.461669 + 1.13110i
\(764\) 0 0
\(765\) −47.0128 16.7462i −1.69975 0.605459i
\(766\) 0 0
\(767\) 1.44474 0.254747i 0.0521666 0.00919838i
\(768\) 0 0
\(769\) 2.31424 2.75800i 0.0834536 0.0994561i −0.722702 0.691160i \(-0.757100\pi\)
0.806155 + 0.591704i \(0.201544\pi\)
\(770\) 0 0
\(771\) −17.0593 9.77115i −0.614375 0.351900i
\(772\) 0 0
\(773\) −39.3835 −1.41653 −0.708263 0.705948i \(-0.750521\pi\)
−0.708263 + 0.705948i \(0.750521\pi\)
\(774\) 0 0
\(775\) 56.0096i 2.01192i
\(776\) 0 0
\(777\) −4.93106 + 9.43232i −0.176901 + 0.338383i