Properties

Label 756.2.ck.a.5.11
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 5.11
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +O(q^{10})\) \(q+(-0.230632 - 1.71663i) q^{3} +(0.315692 - 1.79038i) q^{5} +(0.645961 + 2.56568i) q^{7} +(-2.89362 + 0.791819i) q^{9} +(-5.18280 + 0.913868i) q^{11} +(-4.33786 + 5.16966i) q^{13} +(-3.14622 - 0.129007i) q^{15} -5.78942 q^{17} +1.82961i q^{19} +(4.25534 - 1.70060i) q^{21} +(3.09892 - 3.69315i) q^{23} +(1.59267 + 0.579685i) q^{25} +(2.02662 + 4.78464i) q^{27} +(0.0973787 + 0.116051i) q^{29} +(-2.86208 - 7.86351i) q^{31} +(2.76409 + 8.68617i) q^{33} +(4.79747 - 0.346549i) q^{35} +(-2.28287 - 3.95404i) q^{37} +(9.87483 + 6.25420i) q^{39} +(4.02366 + 3.37625i) q^{41} +(-0.904658 - 0.329269i) q^{43} +(0.504163 + 5.43064i) q^{45} +(-10.7114 - 3.89862i) q^{47} +(-6.16547 + 3.31466i) q^{49} +(1.33523 + 9.93828i) q^{51} +(1.23298 - 0.711859i) q^{53} +9.56767i q^{55} +(3.14076 - 0.421968i) q^{57} +(-5.70576 - 4.78770i) q^{59} +(-5.09450 + 13.9970i) q^{61} +(-3.90072 - 6.91262i) q^{63} +(7.88622 + 9.39843i) q^{65} +(1.25272 - 7.10453i) q^{67} +(-7.05447 - 4.46793i) q^{69} +(5.35129 + 3.08957i) q^{71} +(6.14864 + 3.54992i) q^{73} +(0.627782 - 2.86772i) q^{75} +(-5.69258 - 12.7071i) q^{77} +(-0.525918 - 2.98263i) q^{79} +(7.74605 - 4.58244i) q^{81} +(3.88765 - 3.26213i) q^{83} +(-1.82767 + 10.3652i) q^{85} +(0.176758 - 0.193928i) q^{87} +8.80084 q^{89} +(-16.0658 - 7.79018i) q^{91} +(-12.8386 + 6.72671i) q^{93} +(3.27570 + 0.577594i) q^{95} +(-0.860050 + 2.36297i) q^{97} +(14.2734 - 6.74822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −0.230632 1.71663i −0.133156 0.991095i
\(4\) 0 0
\(5\) 0.315692 1.79038i 0.141182 0.800681i −0.829172 0.558993i \(-0.811188\pi\)
0.970354 0.241688i \(-0.0777011\pi\)
\(6\) 0 0
\(7\) 0.645961 + 2.56568i 0.244150 + 0.969737i
\(8\) 0 0
\(9\) −2.89362 + 0.791819i −0.964539 + 0.263940i
\(10\) 0 0
\(11\) −5.18280 + 0.913868i −1.56267 + 0.275541i −0.887039 0.461695i \(-0.847241\pi\)
−0.675635 + 0.737237i \(0.736130\pi\)
\(12\) 0 0
\(13\) −4.33786 + 5.16966i −1.20311 + 1.43381i −0.331601 + 0.943420i \(0.607589\pi\)
−0.871505 + 0.490387i \(0.836856\pi\)
\(14\) 0 0
\(15\) −3.14622 0.129007i −0.812350 0.0333094i
\(16\) 0 0
\(17\) −5.78942 −1.40414 −0.702070 0.712108i \(-0.747741\pi\)
−0.702070 + 0.712108i \(0.747741\pi\)
\(18\) 0 0
\(19\) 1.82961i 0.419742i 0.977729 + 0.209871i \(0.0673044\pi\)
−0.977729 + 0.209871i \(0.932696\pi\)
\(20\) 0 0
\(21\) 4.25534 1.70060i 0.928592 0.371102i
\(22\) 0 0
\(23\) 3.09892 3.69315i 0.646170 0.770075i −0.339161 0.940728i \(-0.610143\pi\)
0.985331 + 0.170653i \(0.0545878\pi\)
\(24\) 0 0
\(25\) 1.59267 + 0.579685i 0.318534 + 0.115937i
\(26\) 0 0
\(27\) 2.02662 + 4.78464i 0.390023 + 0.920805i
\(28\) 0 0
\(29\) 0.0973787 + 0.116051i 0.0180828 + 0.0215502i 0.775010 0.631949i \(-0.217745\pi\)
−0.756927 + 0.653499i \(0.773300\pi\)
\(30\) 0 0
\(31\) −2.86208 7.86351i −0.514045 1.41233i −0.876986 0.480515i \(-0.840450\pi\)
0.362941 0.931812i \(-0.381773\pi\)
\(32\) 0 0
\(33\) 2.76409 + 8.68617i 0.481166 + 1.51207i
\(34\) 0 0
\(35\) 4.79747 0.346549i 0.810920 0.0585774i
\(36\) 0 0
\(37\) −2.28287 3.95404i −0.375301 0.650041i 0.615071 0.788472i \(-0.289127\pi\)
−0.990372 + 0.138431i \(0.955794\pi\)
\(38\) 0 0
\(39\) 9.87483 + 6.25420i 1.58124 + 1.00147i
\(40\) 0 0
\(41\) 4.02366 + 3.37625i 0.628390 + 0.527282i 0.900428 0.435005i \(-0.143253\pi\)
−0.272038 + 0.962286i \(0.587698\pi\)
\(42\) 0 0
\(43\) −0.904658 0.329269i −0.137959 0.0502130i 0.272118 0.962264i \(-0.412276\pi\)
−0.410077 + 0.912051i \(0.634498\pi\)
\(44\) 0 0
\(45\) 0.504163 + 5.43064i 0.0751562 + 0.809552i
\(46\) 0 0
\(47\) −10.7114 3.89862i −1.56242 0.568673i −0.591127 0.806578i \(-0.701317\pi\)
−0.971288 + 0.237906i \(0.923539\pi\)
\(48\) 0 0
\(49\) −6.16547 + 3.31466i −0.880781 + 0.473523i
\(50\) 0 0
\(51\) 1.33523 + 9.93828i 0.186969 + 1.39164i
\(52\) 0 0
\(53\) 1.23298 0.711859i 0.169362 0.0977814i −0.412923 0.910766i \(-0.635492\pi\)
0.582285 + 0.812985i \(0.302159\pi\)
\(54\) 0 0
\(55\) 9.56767i 1.29010i
\(56\) 0 0
\(57\) 3.14076 0.421968i 0.416004 0.0558910i
\(58\) 0 0
\(59\) −5.70576 4.78770i −0.742826 0.623305i 0.190769 0.981635i \(-0.438902\pi\)
−0.933595 + 0.358330i \(0.883346\pi\)
\(60\) 0 0
\(61\) −5.09450 + 13.9970i −0.652284 + 1.79214i −0.0431508 + 0.999069i \(0.513740\pi\)
−0.609133 + 0.793068i \(0.708483\pi\)
\(62\) 0 0
\(63\) −3.90072 6.91262i −0.491445 0.870909i
\(64\) 0 0
\(65\) 7.88622 + 9.39843i 0.978165 + 1.16573i
\(66\) 0 0
\(67\) 1.25272 7.10453i 0.153044 0.867957i −0.807508 0.589857i \(-0.799184\pi\)
0.960552 0.278100i \(-0.0897047\pi\)
\(68\) 0 0
\(69\) −7.05447 4.46793i −0.849259 0.537876i
\(70\) 0 0
\(71\) 5.35129 + 3.08957i 0.635082 + 0.366665i 0.782717 0.622377i \(-0.213833\pi\)
−0.147636 + 0.989042i \(0.547166\pi\)
\(72\) 0 0
\(73\) 6.14864 + 3.54992i 0.719643 + 0.415486i 0.814621 0.579993i \(-0.196945\pi\)
−0.0949780 + 0.995479i \(0.530278\pi\)
\(74\) 0 0
\(75\) 0.627782 2.86772i 0.0724900 0.331136i
\(76\) 0 0
\(77\) −5.69258 12.7071i −0.648730 1.44811i
\(78\) 0 0
\(79\) −0.525918 2.98263i −0.0591704 0.335572i 0.940824 0.338895i \(-0.110053\pi\)
−0.999994 + 0.00332345i \(0.998942\pi\)
\(80\) 0 0
\(81\) 7.74605 4.58244i 0.860672 0.509160i
\(82\) 0 0
\(83\) 3.88765 3.26213i 0.426725 0.358065i −0.403989 0.914764i \(-0.632377\pi\)
0.830714 + 0.556699i \(0.187932\pi\)
\(84\) 0 0
\(85\) −1.82767 + 10.3652i −0.198239 + 1.12427i
\(86\) 0 0
\(87\) 0.176758 0.193928i 0.0189505 0.0207913i
\(88\) 0 0
\(89\) 8.80084 0.932887 0.466443 0.884551i \(-0.345535\pi\)
0.466443 + 0.884551i \(0.345535\pi\)
\(90\) 0 0
\(91\) −16.0658 7.79018i −1.68415 0.816633i
\(92\) 0 0
\(93\) −12.8386 + 6.72671i −1.33130 + 0.697527i
\(94\) 0 0
\(95\) 3.27570 + 0.577594i 0.336080 + 0.0592599i
\(96\) 0 0
\(97\) −0.860050 + 2.36297i −0.0873249 + 0.239923i −0.975666 0.219260i \(-0.929636\pi\)
0.888342 + 0.459183i \(0.151858\pi\)
\(98\) 0 0
\(99\) 14.2734 6.74822i 1.43453 0.678222i
\(100\) 0 0
\(101\) −1.40806 + 1.18150i −0.140107 + 0.117564i −0.710148 0.704053i \(-0.751372\pi\)
0.570041 + 0.821617i \(0.306927\pi\)
\(102\) 0 0
\(103\) −11.5504 2.03665i −1.13809 0.200677i −0.427322 0.904100i \(-0.640543\pi\)
−0.710772 + 0.703423i \(0.751654\pi\)
\(104\) 0 0
\(105\) −1.70135 8.15554i −0.166034 0.795899i
\(106\) 0 0
\(107\) −0.729358 0.421095i −0.0705097 0.0407088i 0.464331 0.885662i \(-0.346295\pi\)
−0.534840 + 0.844953i \(0.679628\pi\)
\(108\) 0 0
\(109\) −1.56999 2.71930i −0.150378 0.260462i 0.780989 0.624545i \(-0.214716\pi\)
−0.931366 + 0.364084i \(0.881382\pi\)
\(110\) 0 0
\(111\) −6.26111 + 4.83076i −0.594279 + 0.458516i
\(112\) 0 0
\(113\) 1.91026 + 5.24839i 0.179702 + 0.493727i 0.996538 0.0831437i \(-0.0264960\pi\)
−0.816836 + 0.576870i \(0.804274\pi\)
\(114\) 0 0
\(115\) −5.63383 6.71414i −0.525357 0.626096i
\(116\) 0 0
\(117\) 8.45868 18.3938i 0.782005 1.70051i
\(118\) 0 0
\(119\) −3.73974 14.8538i −0.342821 1.36165i
\(120\) 0 0
\(121\) 15.6897 5.71057i 1.42633 0.519142i
\(122\) 0 0
\(123\) 4.86778 7.68580i 0.438913 0.693005i
\(124\) 0 0
\(125\) 6.08564 10.5406i 0.544316 0.942784i
\(126\) 0 0
\(127\) 7.84663 + 13.5908i 0.696276 + 1.20598i 0.969749 + 0.244105i \(0.0784943\pi\)
−0.273473 + 0.961880i \(0.588172\pi\)
\(128\) 0 0
\(129\) −0.356588 + 1.62890i −0.0313958 + 0.143417i
\(130\) 0 0
\(131\) −13.7132 11.5067i −1.19813 1.00535i −0.999682 0.0252344i \(-0.991967\pi\)
−0.198444 0.980112i \(-0.563589\pi\)
\(132\) 0 0
\(133\) −4.69421 + 1.18186i −0.407040 + 0.102480i
\(134\) 0 0
\(135\) 9.20611 2.11794i 0.792335 0.182283i
\(136\) 0 0
\(137\) −4.00541 + 11.0048i −0.342205 + 0.940202i 0.642548 + 0.766245i \(0.277877\pi\)
−0.984753 + 0.173956i \(0.944345\pi\)
\(138\) 0 0
\(139\) −8.72732 1.53886i −0.740241 0.130525i −0.209203 0.977872i \(-0.567087\pi\)
−0.531038 + 0.847348i \(0.678198\pi\)
\(140\) 0 0
\(141\) −4.22209 + 19.2866i −0.355565 + 1.62422i
\(142\) 0 0
\(143\) 17.7579 30.7576i 1.48499 2.57208i
\(144\) 0 0
\(145\) 0.238517 0.137708i 0.0198078 0.0114360i
\(146\) 0 0
\(147\) 7.11200 + 9.81934i 0.586588 + 0.809886i
\(148\) 0 0
\(149\) 0.302146 + 0.830140i 0.0247528 + 0.0680077i 0.951454 0.307792i \(-0.0995902\pi\)
−0.926701 + 0.375800i \(0.877368\pi\)
\(150\) 0 0
\(151\) 1.39213 + 7.89518i 0.113290 + 0.642501i 0.987583 + 0.157101i \(0.0502148\pi\)
−0.874292 + 0.485400i \(0.838674\pi\)
\(152\) 0 0
\(153\) 16.7524 4.58417i 1.35435 0.370608i
\(154\) 0 0
\(155\) −14.9822 + 2.64176i −1.20340 + 0.212192i
\(156\) 0 0
\(157\) −1.89950 + 2.26374i −0.151597 + 0.180666i −0.836498 0.547970i \(-0.815401\pi\)
0.684901 + 0.728636i \(0.259845\pi\)
\(158\) 0 0
\(159\) −1.50636 1.95238i −0.119462 0.154834i
\(160\) 0 0
\(161\) 11.4772 + 5.56522i 0.904533 + 0.438601i
\(162\) 0 0
\(163\) −4.81113 + 8.33312i −0.376837 + 0.652700i −0.990600 0.136790i \(-0.956321\pi\)
0.613764 + 0.789490i \(0.289655\pi\)
\(164\) 0 0
\(165\) 16.4241 2.20661i 1.27862 0.171785i
\(166\) 0 0
\(167\) −1.38609 + 0.504495i −0.107259 + 0.0390390i −0.395092 0.918642i \(-0.629287\pi\)
0.287833 + 0.957681i \(0.407065\pi\)
\(168\) 0 0
\(169\) −5.65094 32.0480i −0.434687 2.46523i
\(170\) 0 0
\(171\) −1.44872 5.29420i −0.110787 0.404858i
\(172\) 0 0
\(173\) −9.17580 + 7.69941i −0.697623 + 0.585375i −0.921096 0.389335i \(-0.872705\pi\)
0.223473 + 0.974710i \(0.428260\pi\)
\(174\) 0 0
\(175\) −0.458485 + 4.46075i −0.0346582 + 0.337201i
\(176\) 0 0
\(177\) −6.90276 + 10.8989i −0.518844 + 0.819208i
\(178\) 0 0
\(179\) 19.8615i 1.48452i −0.670115 0.742258i \(-0.733755\pi\)
0.670115 0.742258i \(-0.266245\pi\)
\(180\) 0 0
\(181\) −10.5009 + 6.06267i −0.780523 + 0.450635i −0.836616 0.547791i \(-0.815469\pi\)
0.0560928 + 0.998426i \(0.482136\pi\)
\(182\) 0 0
\(183\) 25.2026 + 5.51720i 1.86303 + 0.407843i
\(184\) 0 0
\(185\) −7.79991 + 2.83894i −0.573461 + 0.208723i
\(186\) 0 0
\(187\) 30.0054 5.29076i 2.19421 0.386899i
\(188\) 0 0
\(189\) −10.9668 + 8.29036i −0.797715 + 0.603035i
\(190\) 0 0
\(191\) 21.1412 3.72777i 1.52972 0.269732i 0.655478 0.755214i \(-0.272467\pi\)
0.874246 + 0.485483i \(0.161356\pi\)
\(192\) 0 0
\(193\) −1.19954 + 0.436597i −0.0863449 + 0.0314270i −0.384831 0.922987i \(-0.625740\pi\)
0.298487 + 0.954414i \(0.403518\pi\)
\(194\) 0 0
\(195\) 14.3148 15.7053i 1.02510 1.12468i
\(196\) 0 0
\(197\) −21.5364 + 12.4340i −1.53440 + 0.885889i −0.535253 + 0.844692i \(0.679784\pi\)
−0.999151 + 0.0411970i \(0.986883\pi\)
\(198\) 0 0
\(199\) 12.5210i 0.887593i 0.896127 + 0.443797i \(0.146369\pi\)
−0.896127 + 0.443797i \(0.853631\pi\)
\(200\) 0 0
\(201\) −12.4847 0.511921i −0.880606 0.0361081i
\(202\) 0 0
\(203\) −0.234848 + 0.324808i −0.0164831 + 0.0227970i
\(204\) 0 0
\(205\) 7.31500 6.13802i 0.510902 0.428698i
\(206\) 0 0
\(207\) −6.04279 + 13.1403i −0.420003 + 0.913317i
\(208\) 0 0
\(209\) −1.67202 9.48252i −0.115656 0.655920i
\(210\) 0 0
\(211\) −17.7817 + 6.47201i −1.22414 + 0.445552i −0.871588 0.490239i \(-0.836909\pi\)
−0.352555 + 0.935791i \(0.614687\pi\)
\(212\) 0 0
\(213\) 4.06946 9.89873i 0.278835 0.678250i
\(214\) 0 0
\(215\) −0.875108 + 1.51573i −0.0596819 + 0.103372i
\(216\) 0 0
\(217\) 18.3265 12.4227i 1.24408 0.843309i
\(218\) 0 0
\(219\) 4.67581 11.3736i 0.315962 0.768559i
\(220\) 0 0
\(221\) 25.1137 29.9293i 1.68933 2.01327i
\(222\) 0 0
\(223\) 27.2213 4.79986i 1.82288 0.321422i 0.845669 0.533708i \(-0.179202\pi\)
0.977208 + 0.212286i \(0.0680909\pi\)
\(224\) 0 0
\(225\) −5.06759 0.416280i −0.337839 0.0277520i
\(226\) 0 0
\(227\) −1.81605 10.2993i −0.120535 0.683590i −0.983860 0.178941i \(-0.942733\pi\)
0.863325 0.504649i \(-0.168378\pi\)
\(228\) 0 0
\(229\) −6.09555 16.7474i −0.402805 1.10670i −0.960894 0.276917i \(-0.910687\pi\)
0.558089 0.829781i \(-0.311535\pi\)
\(230\) 0 0
\(231\) −20.5005 + 12.7027i −1.34883 + 0.835777i
\(232\) 0 0
\(233\) −17.9372 + 10.3560i −1.17510 + 0.678446i −0.954877 0.297002i \(-0.904013\pi\)
−0.220227 + 0.975449i \(0.570680\pi\)
\(234\) 0 0
\(235\) −10.3615 + 17.9467i −0.675910 + 1.17071i
\(236\) 0 0
\(237\) −4.99877 + 1.59069i −0.324705 + 0.103327i
\(238\) 0 0
\(239\) 4.70161 + 0.829021i 0.304122 + 0.0536249i 0.323627 0.946185i \(-0.395098\pi\)
−0.0195046 + 0.999810i \(0.506209\pi\)
\(240\) 0 0
\(241\) 2.94531 8.09217i 0.189724 0.521263i −0.807963 0.589233i \(-0.799430\pi\)
0.997687 + 0.0679702i \(0.0216523\pi\)
\(242\) 0 0
\(243\) −9.65283 12.2402i −0.619229 0.785210i
\(244\) 0 0
\(245\) 3.98811 + 12.0849i 0.254791 + 0.772078i
\(246\) 0 0
\(247\) −9.45849 7.93661i −0.601829 0.504994i
\(248\) 0 0
\(249\) −6.49647 5.92129i −0.411697 0.375247i
\(250\) 0 0
\(251\) 10.1667 + 17.6092i 0.641715 + 1.11148i 0.985050 + 0.172270i \(0.0551101\pi\)
−0.343335 + 0.939213i \(0.611557\pi\)
\(252\) 0 0
\(253\) −12.6860 + 21.9729i −0.797564 + 1.38142i
\(254\) 0 0
\(255\) 18.2148 + 0.746874i 1.14065 + 0.0467710i
\(256\) 0 0
\(257\) −24.5648 + 8.94086i −1.53231 + 0.557715i −0.964186 0.265227i \(-0.914553\pi\)
−0.568124 + 0.822943i \(0.692331\pi\)
\(258\) 0 0
\(259\) 8.67018 8.41127i 0.538739 0.522651i
\(260\) 0 0
\(261\) −0.373668 0.258702i −0.0231295 0.0160133i
\(262\) 0 0
\(263\) 1.08151 + 1.28890i 0.0666890 + 0.0794768i 0.798358 0.602184i \(-0.205703\pi\)
−0.731669 + 0.681661i \(0.761258\pi\)
\(264\) 0 0
\(265\) −0.885256 2.43222i −0.0543809 0.149410i
\(266\) 0 0
\(267\) −2.02976 15.1078i −0.124219 0.924580i
\(268\) 0 0
\(269\) −0.872457 1.51114i −0.0531946 0.0921358i 0.838202 0.545360i \(-0.183607\pi\)
−0.891397 + 0.453224i \(0.850274\pi\)
\(270\) 0 0
\(271\) 12.3127 + 7.10874i 0.747943 + 0.431825i 0.824950 0.565206i \(-0.191203\pi\)
−0.0770073 + 0.997031i \(0.524536\pi\)
\(272\) 0 0
\(273\) −9.66754 + 29.3757i −0.585106 + 1.77790i
\(274\) 0 0
\(275\) −8.78426 1.54890i −0.529711 0.0934023i
\(276\) 0 0
\(277\) 13.1335 11.0203i 0.789114 0.662145i −0.156412 0.987692i \(-0.549993\pi\)
0.945526 + 0.325547i \(0.105548\pi\)
\(278\) 0 0
\(279\) 14.5082 + 20.4877i 0.868586 + 1.22657i
\(280\) 0 0
\(281\) 2.63156 7.23016i 0.156986 0.431315i −0.836118 0.548549i \(-0.815180\pi\)
0.993104 + 0.117234i \(0.0374027\pi\)
\(282\) 0 0
\(283\) 10.3777 + 1.82987i 0.616890 + 0.108774i 0.473356 0.880871i \(-0.343042\pi\)
0.143533 + 0.989645i \(0.454154\pi\)
\(284\) 0 0
\(285\) 0.236032 5.75637i 0.0139813 0.340978i
\(286\) 0 0
\(287\) −6.06327 + 12.5044i −0.357903 + 0.738109i
\(288\) 0 0
\(289\) 16.5174 0.971611
\(290\) 0 0
\(291\) 4.25469 + 0.931409i 0.249414 + 0.0546002i
\(292\) 0 0
\(293\) −1.28836 + 7.30665i −0.0752668 + 0.426859i 0.923769 + 0.382951i \(0.125092\pi\)
−0.999036 + 0.0439083i \(0.986019\pi\)
\(294\) 0 0
\(295\) −10.3731 + 8.70402i −0.603942 + 0.506768i
\(296\) 0 0
\(297\) −14.8761 22.9458i −0.863198 1.33145i
\(298\) 0 0
\(299\) 5.64965 + 32.0407i 0.326728 + 1.85296i
\(300\) 0 0
\(301\) 0.260425 2.53376i 0.0150107 0.146044i
\(302\) 0 0
\(303\) 2.35295 + 2.14462i 0.135173 + 0.123205i
\(304\) 0 0
\(305\) 23.4517 + 13.5398i 1.34284 + 0.775289i
\(306\) 0 0
\(307\) 9.63531 + 5.56295i 0.549916 + 0.317494i 0.749088 0.662470i \(-0.230492\pi\)
−0.199172 + 0.979965i \(0.563825\pi\)
\(308\) 0 0
\(309\) −0.832269 + 20.2974i −0.0473462 + 1.15468i
\(310\) 0 0
\(311\) 4.05426 22.9929i 0.229896 1.30381i −0.623205 0.782059i \(-0.714170\pi\)
0.853101 0.521746i \(-0.174719\pi\)
\(312\) 0 0
\(313\) 10.7008 + 12.7528i 0.604847 + 0.720828i 0.978386 0.206786i \(-0.0663003\pi\)
−0.373539 + 0.927614i \(0.621856\pi\)
\(314\) 0 0
\(315\) −13.6076 + 4.80151i −0.766703 + 0.270534i
\(316\) 0 0
\(317\) −4.90817 + 13.4851i −0.275670 + 0.757398i 0.722170 + 0.691715i \(0.243145\pi\)
−0.997841 + 0.0656825i \(0.979078\pi\)
\(318\) 0 0
\(319\) −0.610750 0.512480i −0.0341954 0.0286934i
\(320\) 0 0
\(321\) −0.554650 + 1.34915i −0.0309576 + 0.0753025i
\(322\) 0 0
\(323\) 10.5924i 0.589377i
\(324\) 0 0
\(325\) −9.90557 + 5.71898i −0.549462 + 0.317232i
\(326\) 0 0
\(327\) −4.30593 + 3.32224i −0.238119 + 0.183720i
\(328\) 0 0
\(329\) 3.08350 30.0004i 0.169999 1.65397i
\(330\) 0 0
\(331\) 1.26284 + 0.459636i 0.0694120 + 0.0252639i 0.376493 0.926420i \(-0.377130\pi\)
−0.307081 + 0.951683i \(0.599352\pi\)
\(332\) 0 0
\(333\) 9.73663 + 9.63387i 0.533564 + 0.527933i
\(334\) 0 0
\(335\) −12.3243 4.48569i −0.673350 0.245079i
\(336\) 0 0
\(337\) −18.4097 15.4476i −1.00284 0.841483i −0.0154653 0.999880i \(-0.504923\pi\)
−0.987375 + 0.158397i \(0.949367\pi\)
\(338\) 0 0
\(339\) 8.56895 4.48964i 0.465402 0.243844i
\(340\) 0 0
\(341\) 22.0198 + 38.1394i 1.19244 + 2.06537i
\(342\) 0 0
\(343\) −12.4870 13.6775i −0.674236 0.738516i
\(344\) 0 0
\(345\) −10.2263 + 11.2197i −0.550567 + 0.604047i
\(346\) 0 0
\(347\) 2.11988 + 5.82432i 0.113801 + 0.312666i 0.983498 0.180921i \(-0.0579078\pi\)
−0.869697 + 0.493587i \(0.835686\pi\)
\(348\) 0 0
\(349\) −14.8710 17.7226i −0.796028 0.948669i 0.203510 0.979073i \(-0.434765\pi\)
−0.999538 + 0.0304036i \(0.990321\pi\)
\(350\) 0 0
\(351\) −33.5262 10.2782i −1.78950 0.548609i
\(352\) 0 0
\(353\) 12.0988 + 4.40361i 0.643955 + 0.234380i 0.643294 0.765619i \(-0.277567\pi\)
0.000661077 1.00000i \(0.499790\pi\)
\(354\) 0 0
\(355\) 7.22086 8.60548i 0.383243 0.456732i
\(356\) 0 0
\(357\) −24.6360 + 9.84551i −1.30387 + 0.521080i
\(358\) 0 0
\(359\) 10.8382i 0.572021i 0.958227 + 0.286010i \(0.0923292\pi\)
−0.958227 + 0.286010i \(0.907671\pi\)
\(360\) 0 0
\(361\) 15.6525 0.823816
\(362\) 0 0
\(363\) −13.4215 25.6162i −0.704444 1.34450i
\(364\) 0 0
\(365\) 8.29677 9.88770i 0.434273 0.517546i
\(366\) 0 0
\(367\) −36.3151 + 6.40333i −1.89563 + 0.334251i −0.994962 0.100253i \(-0.968035\pi\)
−0.900670 + 0.434504i \(0.856924\pi\)
\(368\) 0 0
\(369\) −14.3163 6.58357i −0.745277 0.342727i
\(370\) 0 0
\(371\) 2.62286 + 2.70359i 0.136172 + 0.140364i
\(372\) 0 0
\(373\) 0.0371083 0.210452i 0.00192140 0.0108968i −0.983832 0.179094i \(-0.942683\pi\)
0.985753 + 0.168197i \(0.0537945\pi\)
\(374\) 0 0
\(375\) −19.4979 8.01577i −1.00687 0.413932i
\(376\) 0 0
\(377\) −1.02236 −0.0526543
\(378\) 0 0
\(379\) 5.01195 0.257447 0.128723 0.991681i \(-0.458912\pi\)
0.128723 + 0.991681i \(0.458912\pi\)
\(380\) 0 0
\(381\) 21.5206 16.6042i 1.10253 0.850659i
\(382\) 0 0
\(383\) −2.18975 + 12.4187i −0.111891 + 0.634564i 0.876352 + 0.481671i \(0.159970\pi\)
−0.988243 + 0.152893i \(0.951141\pi\)
\(384\) 0 0
\(385\) −24.5476 + 6.18034i −1.25106 + 0.314980i
\(386\) 0 0
\(387\) 2.87846 + 0.236452i 0.146320 + 0.0120195i
\(388\) 0 0
\(389\) 3.73108 0.657890i 0.189173 0.0333564i −0.0782587 0.996933i \(-0.524936\pi\)
0.267432 + 0.963577i \(0.413825\pi\)
\(390\) 0 0
\(391\) −17.9410 + 21.3812i −0.907313 + 1.08129i
\(392\) 0 0
\(393\) −16.5900 + 26.1942i −0.836857 + 1.32132i
\(394\) 0 0
\(395\) −5.50606 −0.277040
\(396\) 0 0
\(397\) 27.7630i 1.39338i 0.717370 + 0.696692i \(0.245346\pi\)
−0.717370 + 0.696692i \(0.754654\pi\)
\(398\) 0 0
\(399\) 3.11145 + 7.78564i 0.155767 + 0.389769i
\(400\) 0 0
\(401\) −9.88822 + 11.7843i −0.493794 + 0.588481i −0.954178 0.299239i \(-0.903267\pi\)
0.460384 + 0.887720i \(0.347712\pi\)
\(402\) 0 0
\(403\) 53.0670 + 19.3148i 2.64345 + 0.962139i
\(404\) 0 0
\(405\) −5.75894 15.3150i −0.286164 0.761008i
\(406\) 0 0
\(407\) 15.4451 + 18.4068i 0.765586 + 0.912390i
\(408\) 0 0
\(409\) −1.53558 4.21896i −0.0759293 0.208614i 0.895921 0.444214i \(-0.146517\pi\)
−0.971850 + 0.235600i \(0.924295\pi\)
\(410\) 0 0
\(411\) 19.8149 + 4.33774i 0.977396 + 0.213965i
\(412\) 0 0
\(413\) 8.59803 17.7318i 0.423081 0.872527i
\(414\) 0 0
\(415\) −4.61314 7.99019i −0.226450 0.392223i
\(416\) 0 0
\(417\) −0.628851 + 15.3365i −0.0307950 + 0.751030i
\(418\) 0 0
\(419\) −27.2205 22.8408i −1.32981 1.11584i −0.984122 0.177495i \(-0.943201\pi\)
−0.345689 0.938349i \(-0.612355\pi\)
\(420\) 0 0
\(421\) 13.9948 + 5.09367i 0.682063 + 0.248250i 0.659733 0.751500i \(-0.270669\pi\)
0.0223297 + 0.999751i \(0.492892\pi\)
\(422\) 0 0
\(423\) 34.0816 + 2.79965i 1.65711 + 0.136124i
\(424\) 0 0
\(425\) −9.22065 3.35604i −0.447267 0.162792i
\(426\) 0 0
\(427\) −39.2028 4.02935i −1.89716 0.194994i
\(428\) 0 0
\(429\) −56.8948 23.3900i −2.74691 1.12928i
\(430\) 0 0
\(431\) −30.2447 + 17.4618i −1.45684 + 0.841105i −0.998854 0.0478566i \(-0.984761\pi\)
−0.457982 + 0.888961i \(0.651428\pi\)
\(432\) 0 0
\(433\) 31.8455i 1.53040i −0.643795 0.765198i \(-0.722641\pi\)
0.643795 0.765198i \(-0.277359\pi\)
\(434\) 0 0
\(435\) −0.291403 0.377686i −0.0139717 0.0181086i
\(436\) 0 0
\(437\) 6.75704 + 5.66983i 0.323233 + 0.271225i
\(438\) 0 0
\(439\) 8.72292 23.9660i 0.416322 1.14384i −0.537448 0.843297i \(-0.680611\pi\)
0.953770 0.300538i \(-0.0971664\pi\)
\(440\) 0 0
\(441\) 15.2159 14.4733i 0.724566 0.689205i
\(442\) 0 0
\(443\) 1.72020 + 2.05006i 0.0817294 + 0.0974013i 0.805360 0.592787i \(-0.201972\pi\)
−0.723630 + 0.690188i \(0.757528\pi\)
\(444\) 0 0
\(445\) 2.77835 15.7568i 0.131707 0.746945i
\(446\) 0 0
\(447\) 1.35536 0.710129i 0.0641062 0.0335880i
\(448\) 0 0
\(449\) 26.1501 + 15.0977i 1.23410 + 0.712507i 0.967882 0.251407i \(-0.0808932\pi\)
0.266216 + 0.963913i \(0.414226\pi\)
\(450\) 0 0
\(451\) −23.9393 13.8213i −1.12726 0.650822i
\(452\) 0 0
\(453\) 13.2320 4.21066i 0.621694 0.197834i
\(454\) 0 0
\(455\) −19.0192 + 26.3046i −0.891634 + 1.23318i
\(456\) 0 0
\(457\) −0.604538 3.42851i −0.0282791 0.160379i 0.967398 0.253261i \(-0.0815031\pi\)
−0.995677 + 0.0928822i \(0.970392\pi\)
\(458\) 0 0
\(459\) −11.7329 27.7003i −0.547647 1.29294i
\(460\) 0 0
\(461\) −30.1613 + 25.3083i −1.40475 + 1.17873i −0.445807 + 0.895129i \(0.647083\pi\)
−0.958944 + 0.283596i \(0.908472\pi\)
\(462\) 0 0
\(463\) −2.07957 + 11.7939i −0.0966460 + 0.548107i 0.897585 + 0.440842i \(0.145320\pi\)
−0.994231 + 0.107264i \(0.965791\pi\)
\(464\) 0 0
\(465\) 7.99029 + 25.1095i 0.370541 + 1.16443i
\(466\) 0 0
\(467\) −10.4635 −0.484192 −0.242096 0.970252i \(-0.577835\pi\)
−0.242096 + 0.970252i \(0.577835\pi\)
\(468\) 0 0
\(469\) 19.0372 1.37517i 0.879056 0.0634993i
\(470\) 0 0
\(471\) 4.32408 + 2.73865i 0.199243 + 0.126190i
\(472\) 0 0
\(473\) 4.98957 + 0.879796i 0.229421 + 0.0404531i
\(474\) 0 0
\(475\) −1.06060 + 2.91398i −0.0486637 + 0.133702i
\(476\) 0 0
\(477\) −3.00410 + 3.03614i −0.137548 + 0.139015i
\(478\) 0 0
\(479\) −22.7994 + 19.1310i −1.04173 + 0.874117i −0.992200 0.124656i \(-0.960217\pi\)
−0.0495316 + 0.998773i \(0.515773\pi\)
\(480\) 0 0
\(481\) 30.3438 + 5.35044i 1.38356 + 0.243959i
\(482\) 0 0
\(483\) 6.90639 20.9857i 0.314252 0.954881i
\(484\) 0 0
\(485\) 3.95910 + 2.28579i 0.179773 + 0.103792i
\(486\) 0 0
\(487\) 2.80442 + 4.85739i 0.127080 + 0.220109i 0.922544 0.385892i \(-0.126106\pi\)
−0.795464 + 0.606001i \(0.792773\pi\)
\(488\) 0 0
\(489\) 15.4145 + 6.33703i 0.697066 + 0.286570i
\(490\) 0 0
\(491\) −7.88767 21.6712i −0.355965 0.978007i −0.980415 0.196942i \(-0.936899\pi\)
0.624450 0.781065i \(-0.285323\pi\)
\(492\) 0 0
\(493\) −0.563766 0.671870i −0.0253907 0.0302595i
\(494\) 0 0
\(495\) −7.57586 27.6852i −0.340510 1.24436i
\(496\) 0 0
\(497\) −4.47013 + 15.7255i −0.200513 + 0.705384i
\(498\) 0 0
\(499\) 34.5616 12.5794i 1.54719 0.563132i 0.579435 0.815018i \(-0.303273\pi\)
0.967757 + 0.251887i \(0.0810510\pi\)
\(500\) 0 0
\(501\) 1.18571 + 2.26304i 0.0529735 + 0.101105i
\(502\) 0 0
\(503\) −8.09397 + 14.0192i −0.360892 + 0.625083i −0.988108 0.153762i \(-0.950861\pi\)
0.627216 + 0.778846i \(0.284194\pi\)
\(504\) 0 0
\(505\) 1.67082 + 2.89395i 0.0743507 + 0.128779i
\(506\) 0 0
\(507\) −53.7113 + 17.0919i −2.38540 + 0.759076i
\(508\) 0 0
\(509\) 2.79910 + 2.34872i 0.124068 + 0.104105i 0.702710 0.711476i \(-0.251973\pi\)
−0.578643 + 0.815581i \(0.696417\pi\)
\(510\) 0 0
\(511\) −5.13618 + 18.0686i −0.227211 + 0.799306i
\(512\) 0 0
\(513\) −8.75405 + 3.70793i −0.386501 + 0.163709i
\(514\) 0 0
\(515\) −7.29273 + 20.0366i −0.321356 + 0.882918i
\(516\) 0 0
\(517\) 59.0778 + 10.4170i 2.59824 + 0.458139i
\(518\) 0 0
\(519\) 15.3332 + 13.9757i 0.673055 + 0.613465i
\(520\) 0 0
\(521\) 15.6036 27.0262i 0.683605 1.18404i −0.290268 0.956945i \(-0.593744\pi\)
0.973873 0.227093i \(-0.0729222\pi\)
\(522\) 0 0
\(523\) −10.0499 + 5.80229i −0.439450 + 0.253717i −0.703364 0.710830i \(-0.748320\pi\)
0.263914 + 0.964546i \(0.414986\pi\)
\(524\) 0 0
\(525\) 7.76318 0.241744i 0.338813 0.0105506i
\(526\) 0 0
\(527\) 16.5698 + 45.5251i 0.721792 + 1.98311i
\(528\) 0 0
\(529\) −0.0421389 0.238982i −0.00183213 0.0103905i
\(530\) 0 0
\(531\) 20.3013 + 9.33585i 0.881000 + 0.405141i
\(532\) 0 0
\(533\) −34.9082 + 6.15525i −1.51204 + 0.266613i
\(534\) 0 0
\(535\) −0.984172 + 1.17289i −0.0425495 + 0.0507085i
\(536\) 0 0
\(537\) −34.0947 + 4.58069i −1.47130 + 0.197671i
\(538\) 0 0
\(539\) 28.9252 22.8137i 1.24590 0.982654i
\(540\) 0 0
\(541\) 8.29085 14.3602i 0.356451 0.617392i −0.630914 0.775853i \(-0.717320\pi\)
0.987365 + 0.158461i \(0.0506532\pi\)
\(542\) 0 0
\(543\) 12.8292 + 16.6278i 0.550553 + 0.713568i
\(544\) 0 0
\(545\) −5.36420 + 1.95241i −0.229777 + 0.0836321i
\(546\) 0 0
\(547\) 0.477153 + 2.70607i 0.0204016 + 0.115703i 0.993308 0.115497i \(-0.0368460\pi\)
−0.972906 + 0.231200i \(0.925735\pi\)
\(548\) 0 0
\(549\) 3.65843 44.5360i 0.156138 1.90075i
\(550\) 0 0
\(551\) −0.212329 + 0.178165i −0.00904553 + 0.00759010i
\(552\) 0 0
\(553\) 7.31276 3.27600i 0.310970 0.139310i
\(554\) 0 0
\(555\) 6.67231 + 12.7348i 0.283224 + 0.540562i
\(556\) 0 0
\(557\) 31.1083i 1.31810i 0.752098 + 0.659051i \(0.229042\pi\)
−0.752098 + 0.659051i \(0.770958\pi\)
\(558\) 0 0
\(559\) 5.62649 3.24845i 0.237975 0.137395i
\(560\) 0 0
\(561\) −16.0025 50.2879i −0.675625 2.12316i
\(562\) 0 0
\(563\) −3.26144 + 1.18707i −0.137453 + 0.0500289i −0.409831 0.912162i \(-0.634412\pi\)
0.272378 + 0.962190i \(0.412190\pi\)
\(564\) 0 0
\(565\) 9.99964 1.76321i 0.420688 0.0741787i
\(566\) 0 0
\(567\) 16.7607 + 16.9138i 0.703885 + 0.710314i
\(568\) 0 0
\(569\) 36.9880 6.52198i 1.55062 0.273416i 0.668236 0.743949i \(-0.267050\pi\)
0.882382 + 0.470534i \(0.155939\pi\)
\(570\) 0 0
\(571\) 8.86644 3.22712i 0.371049 0.135051i −0.149764 0.988722i \(-0.547851\pi\)
0.520813 + 0.853671i \(0.325629\pi\)
\(572\) 0 0
\(573\) −11.2750 35.4318i −0.471021 1.48019i
\(574\) 0 0
\(575\) 7.07643 4.08558i 0.295108 0.170380i
\(576\) 0 0
\(577\) 16.6185i 0.691838i 0.938264 + 0.345919i \(0.112433\pi\)
−0.938264 + 0.345919i \(0.887567\pi\)
\(578\) 0 0
\(579\) 1.02613 + 1.95847i 0.0426444 + 0.0813913i
\(580\) 0 0
\(581\) 10.8809 + 7.86727i 0.451414 + 0.326390i
\(582\) 0 0
\(583\) −5.73973 + 4.81620i −0.237715 + 0.199467i
\(584\) 0 0
\(585\) −30.2616 20.9510i −1.25116 0.866218i
\(586\) 0 0
\(587\) 1.04950 + 5.95201i 0.0433175 + 0.245666i 0.998776 0.0494593i \(-0.0157498\pi\)
−0.955459 + 0.295125i \(0.904639\pi\)
\(588\) 0 0
\(589\) 14.3872 5.23651i 0.592813 0.215766i
\(590\) 0 0
\(591\) 26.3116 + 34.1023i 1.08231 + 1.40278i
\(592\) 0 0
\(593\) 2.00470 3.47223i 0.0823230 0.142588i −0.821924 0.569597i \(-0.807099\pi\)
0.904247 + 0.427009i \(0.140433\pi\)
\(594\) 0 0
\(595\) −27.7746 + 2.00632i −1.13865 + 0.0822510i
\(596\) 0 0
\(597\) 21.4940 2.88776i 0.879690 0.118188i
\(598\) 0 0
\(599\) −23.8029 + 28.3671i −0.972559 + 1.15905i 0.0146946 + 0.999892i \(0.495322\pi\)
−0.987253 + 0.159158i \(0.949122\pi\)
\(600\) 0 0
\(601\) 12.1383 2.14031i 0.495132 0.0873050i 0.0794939 0.996835i \(-0.474670\pi\)
0.415638 + 0.909530i \(0.363558\pi\)
\(602\) 0 0
\(603\) 2.00061 + 21.5497i 0.0814710 + 0.877573i
\(604\) 0 0
\(605\) −5.27097 29.8932i −0.214296 1.21533i
\(606\) 0 0
\(607\) 7.20692 + 19.8008i 0.292520 + 0.803691i 0.995696 + 0.0926761i \(0.0295421\pi\)
−0.703177 + 0.711015i \(0.748236\pi\)
\(608\) 0 0
\(609\) 0.611737 + 0.328236i 0.0247888 + 0.0133008i
\(610\) 0 0
\(611\) 66.6190 38.4625i 2.69512 1.55603i
\(612\) 0 0
\(613\) 8.07169 13.9806i 0.326012 0.564670i −0.655704 0.755018i \(-0.727628\pi\)
0.981717 + 0.190348i \(0.0609615\pi\)
\(614\) 0 0
\(615\) −12.2238 11.1415i −0.492910 0.449269i
\(616\) 0 0
\(617\) 5.70078 + 1.00520i 0.229505 + 0.0404679i 0.287218 0.957865i \(-0.407270\pi\)
−0.0577128 + 0.998333i \(0.518381\pi\)
\(618\) 0 0
\(619\) 3.07725 8.45468i 0.123685 0.339822i −0.862361 0.506294i \(-0.831015\pi\)
0.986046 + 0.166472i \(0.0532374\pi\)
\(620\) 0 0
\(621\) 23.9507 + 7.34262i 0.961110 + 0.294649i
\(622\) 0 0
\(623\) 5.68500 + 22.5802i 0.227765 + 0.904655i
\(624\) 0 0
\(625\) −10.4587 8.77593i −0.418350 0.351037i
\(626\) 0 0
\(627\) −15.8923 + 5.05722i −0.634679 + 0.201966i
\(628\) 0 0
\(629\) 13.2165 + 22.8916i 0.526976 + 0.912748i
\(630\) 0 0
\(631\) −0.233768 + 0.404898i −0.00930616 + 0.0161187i −0.870641 0.491919i \(-0.836296\pi\)
0.861335 + 0.508038i \(0.169629\pi\)
\(632\) 0 0
\(633\) 15.2111 + 29.0319i 0.604586 + 1.15391i
\(634\) 0 0
\(635\) 26.8097 9.75794i 1.06391 0.387232i
\(636\) 0 0
\(637\) 9.60925 46.2519i 0.380732 1.83257i
\(638\) 0 0
\(639\) −17.9310 4.70278i −0.709338 0.186039i
\(640\) 0 0
\(641\) −16.9589 20.2108i −0.669835 0.798279i 0.318926 0.947780i \(-0.396678\pi\)
−0.988762 + 0.149501i \(0.952233\pi\)
\(642\) 0 0
\(643\) 10.7678 + 29.5842i 0.424639 + 1.16669i 0.949024 + 0.315205i \(0.102073\pi\)
−0.524385 + 0.851481i \(0.675705\pi\)
\(644\) 0 0
\(645\) 2.80377 + 1.15266i 0.110399 + 0.0453859i
\(646\) 0 0
\(647\) −12.0438 20.8605i −0.473491 0.820110i 0.526049 0.850455i \(-0.323673\pi\)
−0.999540 + 0.0303442i \(0.990340\pi\)
\(648\) 0 0
\(649\) 33.9471 + 19.5994i 1.33254 + 0.769343i
\(650\) 0 0
\(651\) −25.5518 28.5947i −1.00146 1.12071i
\(652\) 0 0
\(653\) 22.7631 + 4.01375i 0.890790 + 0.157070i 0.600269 0.799798i \(-0.295060\pi\)
0.290521 + 0.956869i \(0.406171\pi\)
\(654\) 0 0
\(655\) −24.9305 + 20.9192i −0.974116 + 0.817380i
\(656\) 0 0
\(657\) −20.6027 5.40350i −0.803788 0.210810i
\(658\) 0 0
\(659\) 10.3121 28.3323i 0.401703 1.10367i −0.559740 0.828668i \(-0.689099\pi\)
0.961443 0.275003i \(-0.0886788\pi\)
\(660\) 0 0
\(661\) −21.6681 3.82067i −0.842792 0.148607i −0.264448 0.964400i \(-0.585190\pi\)
−0.578344 + 0.815793i \(0.696301\pi\)
\(662\) 0 0
\(663\) −57.1696 36.2082i −2.22028 1.40621i
\(664\) 0 0
\(665\) 0.634051 + 8.77751i 0.0245874 + 0.340377i
\(666\) 0 0
\(667\) 0.730364 0.0282798
\(668\) 0 0
\(669\) −14.5177 45.6219i −0.561286 1.76384i
\(670\) 0 0
\(671\) 13.6124 77.1995i 0.525499 2.98025i
\(672\) 0 0
\(673\) 27.5418 23.1103i 1.06166 0.890836i 0.0673860 0.997727i \(-0.478534\pi\)
0.994271 + 0.106891i \(0.0340896\pi\)
\(674\) 0 0
\(675\) 0.454152 + 8.79517i 0.0174803 + 0.338526i
\(676\) 0 0
\(677\) −3.13527 17.7810i −0.120498 0.683379i −0.983880 0.178828i \(-0.942769\pi\)
0.863382 0.504550i \(-0.168342\pi\)
\(678\) 0 0
\(679\) −6.61819 0.680231i −0.253983 0.0261049i
\(680\) 0 0
\(681\) −17.2612 + 5.49283i −0.661452 + 0.210486i
\(682\) 0 0
\(683\) −15.3970 8.88943i −0.589148 0.340145i 0.175613 0.984459i \(-0.443809\pi\)
−0.764761 + 0.644315i \(0.777143\pi\)
\(684\) 0 0
\(685\) 18.4382 + 10.6453i 0.704489 + 0.406737i
\(686\) 0 0
\(687\) −27.3432 + 14.3263i −1.04321 + 0.546581i
\(688\) 0 0
\(689\) −1.66841 + 9.46202i −0.0635613 + 0.360474i
\(690\) 0 0
\(691\) −31.7257 37.8092i −1.20690 1.43833i −0.867320 0.497752i \(-0.834159\pi\)
−0.339581 0.940577i \(-0.610285\pi\)
\(692\) 0 0
\(693\) 26.5339 + 32.2620i 1.00794 + 1.22553i
\(694\) 0 0
\(695\) −5.51029 + 15.1394i −0.209017 + 0.574270i
\(696\) 0 0
\(697\) −23.2947 19.5465i −0.882348 0.740378i
\(698\) 0 0
\(699\) 21.9143 + 28.4030i 0.828877 + 1.07430i
\(700\) 0 0
\(701\) 33.0791i 1.24938i −0.780873 0.624690i \(-0.785226\pi\)
0.780873 0.624690i \(-0.214774\pi\)
\(702\) 0 0
\(703\) 7.23437 4.17677i 0.272849 0.157530i
\(704\) 0 0
\(705\) 33.1974 + 13.6478i 1.25029 + 0.514005i
\(706\) 0 0
\(707\) −3.94092 2.84943i −0.148213 0.107164i
\(708\) 0 0
\(709\) 28.2248 + 10.2730i 1.06000 + 0.385810i 0.812430 0.583059i \(-0.198144\pi\)
0.247575 + 0.968869i \(0.420366\pi\)
\(710\) 0 0
\(711\) 3.88350 + 8.21415i 0.145643 + 0.308055i
\(712\) 0 0
\(713\) −37.9105 13.7983i −1.41976 0.516750i
\(714\) 0 0
\(715\) −49.4616 41.5032i −1.84976 1.55213i
\(716\) 0 0
\(717\) 0.338777 8.26212i 0.0126519 0.308554i
\(718\) 0 0
\(719\) −9.32614 16.1534i −0.347806 0.602418i 0.638053 0.769992i \(-0.279740\pi\)
−0.985860 + 0.167574i \(0.946407\pi\)
\(720\) 0 0
\(721\) −2.23571 30.9502i −0.0832624 1.15265i
\(722\) 0 0
\(723\) −14.5705 3.18968i −0.541884 0.118626i
\(724\) 0 0
\(725\) 0.0878190 + 0.241281i 0.00326152 + 0.00896094i
\(726\) 0 0
\(727\) −1.99281 2.37494i −0.0739093 0.0880817i 0.727823 0.685765i \(-0.240532\pi\)
−0.801732 + 0.597684i \(0.796088\pi\)
\(728\) 0 0
\(729\) −18.7856 + 19.3933i −0.695764 + 0.718270i
\(730\) 0 0
\(731\) 5.23744 + 1.90627i 0.193714 + 0.0705061i
\(732\) 0 0
\(733\) −10.8974 + 12.9870i −0.402503 + 0.479685i −0.928782 0.370628i \(-0.879143\pi\)
0.526278 + 0.850312i \(0.323587\pi\)
\(734\) 0 0
\(735\) 19.8255 9.63328i 0.731276 0.355329i
\(736\) 0 0
\(737\) 37.9662i 1.39850i
\(738\) 0 0
\(739\) 18.2858 0.672654 0.336327 0.941745i \(-0.390815\pi\)
0.336327 + 0.941745i \(0.390815\pi\)
\(740\) 0 0
\(741\) −11.4428 + 18.0671i −0.420361 + 0.663713i
\(742\) 0 0
\(743\) 5.10611 6.08522i 0.187325 0.223245i −0.664206 0.747550i \(-0.731230\pi\)
0.851531 + 0.524304i \(0.175675\pi\)
\(744\) 0 0
\(745\) 1.58165 0.278887i 0.0579471 0.0102176i
\(746\) 0 0
\(747\) −8.66636 + 12.5177i −0.317086 + 0.457997i
\(748\) 0 0
\(749\) 0.609260 2.14331i 0.0222619 0.0783150i
\(750\) 0 0
\(751\) 8.65479 49.0838i 0.315818 1.79109i −0.251778 0.967785i \(-0.581015\pi\)
0.567596 0.823307i \(-0.307874\pi\)
\(752\) 0 0
\(753\) 27.8837 21.5136i 1.01614 0.784001i
\(754\) 0 0
\(755\) 14.5748 0.530433
\(756\) 0 0
\(757\) −22.2840 −0.809927 −0.404963 0.914333i \(-0.632716\pi\)
−0.404963 + 0.914333i \(0.632716\pi\)
\(758\) 0 0
\(759\) 40.6450 + 16.7096i 1.47532 + 0.606518i
\(760\) 0 0
\(761\) −4.94389 + 28.0382i −0.179216 + 1.01638i 0.753949 + 0.656933i \(0.228147\pi\)
−0.933164 + 0.359450i \(0.882964\pi\)
\(762\) 0 0
\(763\) 5.96271 5.78465i 0.215865 0.209418i
\(764\) 0 0
\(765\) −2.91881 31.4403i −0.105530 1.13672i
\(766\) 0 0
\(767\) 49.5016 8.72846i 1.78740 0.315167i
\(768\) 0 0
\(769\) −4.26169 + 5.07888i −0.153680 + 0.183149i −0.837391 0.546604i \(-0.815920\pi\)
0.683711 + 0.729753i \(0.260365\pi\)
\(770\) 0 0
\(771\) 21.0135 + 40.1066i 0.756784 + 1.44440i
\(772\) 0 0
\(773\) −38.5225 −1.38556 −0.692778 0.721151i \(-0.743614\pi\)
−0.692778 + 0.721151i \(0.743614\pi\)
\(774\) 0 0
\(775\) 14.1831i 0.509472i
\(776\) 0 0
\(777\) −16.4386 12.9436i −0.589733 0.464347i
\(778\)