Properties

Label 756.2.ck.a.5.8
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 5.8
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +O(q^{10})\) \(q+(-0.792956 + 1.53988i) q^{3} +(-0.192493 + 1.09168i) q^{5} +(-0.137506 - 2.64218i) q^{7} +(-1.74244 - 2.44211i) q^{9} +(2.56116 - 0.451601i) q^{11} +(2.84782 - 3.39390i) q^{13} +(-1.52842 - 1.16207i) q^{15} +2.17412 q^{17} -1.97804i q^{19} +(4.17766 + 1.88339i) q^{21} +(-0.918430 + 1.09454i) q^{23} +(3.54375 + 1.28982i) q^{25} +(5.14223 - 0.746660i) q^{27} +(-1.56472 - 1.86476i) q^{29} +(0.482623 + 1.32600i) q^{31} +(-1.33548 + 4.30197i) q^{33} +(2.91088 + 0.358487i) q^{35} +(1.48594 + 2.57372i) q^{37} +(2.96799 + 7.07650i) q^{39} +(7.49508 + 6.28912i) q^{41} +(-10.5897 - 3.85434i) q^{43} +(3.00141 - 1.43210i) q^{45} +(9.93706 + 3.61679i) q^{47} +(-6.96218 + 0.726628i) q^{49} +(-1.72398 + 3.34787i) q^{51} +(3.97427 - 2.29454i) q^{53} +2.88290i q^{55} +(3.04594 + 1.56850i) q^{57} +(-1.11622 - 0.936622i) q^{59} +(2.84554 - 7.81804i) q^{61} +(-6.21289 + 4.93964i) q^{63} +(3.15687 + 3.76221i) q^{65} +(0.0822020 - 0.466191i) q^{67} +(-0.957186 - 2.28219i) q^{69} +(-8.36281 - 4.82827i) q^{71} +(12.9594 + 7.48209i) q^{73} +(-4.79620 + 4.43417i) q^{75} +(-1.54538 - 6.70493i) q^{77} +(-1.17523 - 6.66506i) q^{79} +(-2.92780 + 8.51046i) q^{81} +(0.735605 - 0.617246i) q^{83} +(-0.418502 + 2.37344i) q^{85} +(4.11225 - 0.930801i) q^{87} +16.3867 q^{89} +(-9.35887 - 7.05776i) q^{91} +(-2.42457 - 0.308277i) q^{93} +(2.15939 + 0.380759i) q^{95} +(4.74751 - 13.0437i) q^{97} +(-5.56553 - 5.46774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −0.792956 + 1.53988i −0.457813 + 0.889048i
\(4\) 0 0
\(5\) −0.192493 + 1.09168i −0.0860854 + 0.488214i 0.911032 + 0.412336i \(0.135287\pi\)
−0.997117 + 0.0758781i \(0.975824\pi\)
\(6\) 0 0
\(7\) −0.137506 2.64218i −0.0519722 0.998649i
\(8\) 0 0
\(9\) −1.74244 2.44211i −0.580814 0.814036i
\(10\) 0 0
\(11\) 2.56116 0.451601i 0.772219 0.136163i 0.226364 0.974043i \(-0.427316\pi\)
0.545855 + 0.837880i \(0.316205\pi\)
\(12\) 0 0
\(13\) 2.84782 3.39390i 0.789843 0.941298i −0.209490 0.977811i \(-0.567180\pi\)
0.999333 + 0.0365127i \(0.0116249\pi\)
\(14\) 0 0
\(15\) −1.52842 1.16207i −0.394635 0.300045i
\(16\) 0 0
\(17\) 2.17412 0.527301 0.263650 0.964618i \(-0.415073\pi\)
0.263650 + 0.964618i \(0.415073\pi\)
\(18\) 0 0
\(19\) 1.97804i 0.453794i −0.973919 0.226897i \(-0.927142\pi\)
0.973919 0.226897i \(-0.0728582\pi\)
\(20\) 0 0
\(21\) 4.17766 + 1.88339i 0.911640 + 0.410989i
\(22\) 0 0
\(23\) −0.918430 + 1.09454i −0.191506 + 0.228228i −0.853250 0.521502i \(-0.825372\pi\)
0.661744 + 0.749730i \(0.269816\pi\)
\(24\) 0 0
\(25\) 3.54375 + 1.28982i 0.708750 + 0.257964i
\(26\) 0 0
\(27\) 5.14223 0.746660i 0.989622 0.143695i
\(28\) 0 0
\(29\) −1.56472 1.86476i −0.290561 0.346277i 0.600942 0.799293i \(-0.294792\pi\)
−0.891502 + 0.453016i \(0.850348\pi\)
\(30\) 0 0
\(31\) 0.482623 + 1.32600i 0.0866817 + 0.238156i 0.975458 0.220185i \(-0.0706661\pi\)
−0.888776 + 0.458341i \(0.848444\pi\)
\(32\) 0 0
\(33\) −1.33548 + 4.30197i −0.232477 + 0.748877i
\(34\) 0 0
\(35\) 2.91088 + 0.358487i 0.492029 + 0.0605954i
\(36\) 0 0
\(37\) 1.48594 + 2.57372i 0.244287 + 0.423117i 0.961931 0.273293i \(-0.0881129\pi\)
−0.717644 + 0.696410i \(0.754780\pi\)
\(38\) 0 0
\(39\) 2.96799 + 7.07650i 0.475259 + 1.13315i
\(40\) 0 0
\(41\) 7.49508 + 6.28912i 1.17054 + 0.982196i 0.999995 0.00315517i \(-0.00100432\pi\)
0.170540 + 0.985351i \(0.445449\pi\)
\(42\) 0 0
\(43\) −10.5897 3.85434i −1.61492 0.587782i −0.632513 0.774550i \(-0.717977\pi\)
−0.982404 + 0.186768i \(0.940199\pi\)
\(44\) 0 0
\(45\) 3.00141 1.43210i 0.447424 0.213485i
\(46\) 0 0
\(47\) 9.93706 + 3.61679i 1.44947 + 0.527564i 0.942443 0.334367i \(-0.108522\pi\)
0.507026 + 0.861931i \(0.330745\pi\)
\(48\) 0 0
\(49\) −6.96218 + 0.726628i −0.994598 + 0.103804i
\(50\) 0 0
\(51\) −1.72398 + 3.34787i −0.241405 + 0.468796i
\(52\) 0 0
\(53\) 3.97427 2.29454i 0.545907 0.315180i −0.201562 0.979476i \(-0.564602\pi\)
0.747470 + 0.664296i \(0.231269\pi\)
\(54\) 0 0
\(55\) 2.88290i 0.388730i
\(56\) 0 0
\(57\) 3.04594 + 1.56850i 0.403445 + 0.207753i
\(58\) 0 0
\(59\) −1.11622 0.936622i −0.145320 0.121938i 0.567230 0.823560i \(-0.308015\pi\)
−0.712549 + 0.701622i \(0.752460\pi\)
\(60\) 0 0
\(61\) 2.84554 7.81804i 0.364333 1.00100i −0.613146 0.789969i \(-0.710096\pi\)
0.977480 0.211029i \(-0.0676813\pi\)
\(62\) 0 0
\(63\) −6.21289 + 4.93964i −0.782750 + 0.622336i
\(64\) 0 0
\(65\) 3.15687 + 3.76221i 0.391561 + 0.466645i
\(66\) 0 0
\(67\) 0.0822020 0.466191i 0.0100426 0.0569543i −0.979375 0.202053i \(-0.935239\pi\)
0.989417 + 0.145098i \(0.0463499\pi\)
\(68\) 0 0
\(69\) −0.957186 2.28219i −0.115232 0.274744i
\(70\) 0 0
\(71\) −8.36281 4.82827i −0.992483 0.573010i −0.0864676 0.996255i \(-0.527558\pi\)
−0.906016 + 0.423244i \(0.860891\pi\)
\(72\) 0 0
\(73\) 12.9594 + 7.48209i 1.51678 + 0.875713i 0.999806 + 0.0197110i \(0.00627461\pi\)
0.516973 + 0.856002i \(0.327059\pi\)
\(74\) 0 0
\(75\) −4.79620 + 4.43417i −0.553818 + 0.512014i
\(76\) 0 0
\(77\) −1.54538 6.70493i −0.176113 0.764098i
\(78\) 0 0
\(79\) −1.17523 6.66506i −0.132224 0.749877i −0.976753 0.214368i \(-0.931231\pi\)
0.844529 0.535509i \(-0.179880\pi\)
\(80\) 0 0
\(81\) −2.92780 + 8.51046i −0.325311 + 0.945607i
\(82\) 0 0
\(83\) 0.735605 0.617246i 0.0807431 0.0677515i −0.601523 0.798856i \(-0.705439\pi\)
0.682266 + 0.731104i \(0.260995\pi\)
\(84\) 0 0
\(85\) −0.418502 + 2.37344i −0.0453929 + 0.257436i
\(86\) 0 0
\(87\) 4.11225 0.930801i 0.440879 0.0997924i
\(88\) 0 0
\(89\) 16.3867 1.73699 0.868493 0.495702i \(-0.165089\pi\)
0.868493 + 0.495702i \(0.165089\pi\)
\(90\) 0 0
\(91\) −9.35887 7.05776i −0.981076 0.739854i
\(92\) 0 0
\(93\) −2.42457 0.308277i −0.251416 0.0319668i
\(94\) 0 0
\(95\) 2.15939 + 0.380759i 0.221549 + 0.0390651i
\(96\) 0 0
\(97\) 4.74751 13.0437i 0.482037 1.32439i −0.425707 0.904861i \(-0.639974\pi\)
0.907744 0.419525i \(-0.137803\pi\)
\(98\) 0 0
\(99\) −5.56553 5.46774i −0.559357 0.549529i
\(100\) 0 0
\(101\) 7.96739 6.68543i 0.792785 0.665226i −0.153648 0.988126i \(-0.549102\pi\)
0.946433 + 0.322900i \(0.104658\pi\)
\(102\) 0 0
\(103\) −11.6309 2.05085i −1.14603 0.202076i −0.431788 0.901975i \(-0.642117\pi\)
−0.714241 + 0.699899i \(0.753228\pi\)
\(104\) 0 0
\(105\) −2.86023 + 4.19813i −0.279130 + 0.409696i
\(106\) 0 0
\(107\) 7.14243 + 4.12369i 0.690485 + 0.398652i 0.803794 0.594908i \(-0.202812\pi\)
−0.113309 + 0.993560i \(0.536145\pi\)
\(108\) 0 0
\(109\) −0.0911298 0.157841i −0.00872865 0.0151185i 0.861628 0.507540i \(-0.169445\pi\)
−0.870357 + 0.492422i \(0.836112\pi\)
\(110\) 0 0
\(111\) −5.14150 + 0.247315i −0.488009 + 0.0234741i
\(112\) 0 0
\(113\) −2.98486 8.20082i −0.280792 0.771469i −0.997269 0.0738581i \(-0.976469\pi\)
0.716477 0.697611i \(-0.245753\pi\)
\(114\) 0 0
\(115\) −1.01810 1.21332i −0.0949383 0.113143i
\(116\) 0 0
\(117\) −13.2504 1.04102i −1.22500 0.0962419i
\(118\) 0 0
\(119\) −0.298953 5.74440i −0.0274050 0.526588i
\(120\) 0 0
\(121\) −3.98103 + 1.44898i −0.361911 + 0.131725i
\(122\) 0 0
\(123\) −15.6277 + 6.55451i −1.40911 + 0.591000i
\(124\) 0 0
\(125\) −4.86152 + 8.42040i −0.434828 + 0.753144i
\(126\) 0 0
\(127\) −1.91309 3.31356i −0.169759 0.294031i 0.768576 0.639758i \(-0.220966\pi\)
−0.938335 + 0.345727i \(0.887632\pi\)
\(128\) 0 0
\(129\) 14.3324 13.2505i 1.26190 1.16665i
\(130\) 0 0
\(131\) −5.32055 4.46447i −0.464859 0.390063i 0.380056 0.924963i \(-0.375905\pi\)
−0.844915 + 0.534901i \(0.820349\pi\)
\(132\) 0 0
\(133\) −5.22634 + 0.271992i −0.453181 + 0.0235847i
\(134\) 0 0
\(135\) −0.174727 + 5.75740i −0.0150381 + 0.495518i
\(136\) 0 0
\(137\) −7.38768 + 20.2975i −0.631172 + 1.73413i 0.0466563 + 0.998911i \(0.485143\pi\)
−0.677828 + 0.735220i \(0.737079\pi\)
\(138\) 0 0
\(139\) −12.3574 2.17894i −1.04814 0.184815i −0.377050 0.926193i \(-0.623062\pi\)
−0.671088 + 0.741378i \(0.734173\pi\)
\(140\) 0 0
\(141\) −13.4491 + 12.4339i −1.13262 + 1.04712i
\(142\) 0 0
\(143\) 5.76103 9.97839i 0.481761 0.834435i
\(144\) 0 0
\(145\) 2.33692 1.34922i 0.194070 0.112047i
\(146\) 0 0
\(147\) 4.40179 11.2971i 0.363053 0.931768i
\(148\) 0 0
\(149\) −3.33358 9.15893i −0.273097 0.750328i −0.998102 0.0615845i \(-0.980385\pi\)
0.725005 0.688744i \(-0.241838\pi\)
\(150\) 0 0
\(151\) 0.556841 + 3.15800i 0.0453150 + 0.256994i 0.999046 0.0436665i \(-0.0139039\pi\)
−0.953731 + 0.300661i \(0.902793\pi\)
\(152\) 0 0
\(153\) −3.78827 5.30943i −0.306264 0.429242i
\(154\) 0 0
\(155\) −1.54047 + 0.271626i −0.123733 + 0.0218175i
\(156\) 0 0
\(157\) −2.48933 + 2.96666i −0.198670 + 0.236766i −0.856177 0.516683i \(-0.827167\pi\)
0.657507 + 0.753449i \(0.271611\pi\)
\(158\) 0 0
\(159\) 0.381896 + 7.93935i 0.0302863 + 0.629632i
\(160\) 0 0
\(161\) 3.01826 + 2.27615i 0.237872 + 0.179386i
\(162\) 0 0
\(163\) 1.66040 2.87591i 0.130053 0.225258i −0.793644 0.608383i \(-0.791819\pi\)
0.923697 + 0.383124i \(0.125152\pi\)
\(164\) 0 0
\(165\) −4.43931 2.28601i −0.345600 0.177966i
\(166\) 0 0
\(167\) −7.24079 + 2.63543i −0.560309 + 0.203936i −0.606621 0.794991i \(-0.707475\pi\)
0.0463118 + 0.998927i \(0.485253\pi\)
\(168\) 0 0
\(169\) −1.15105 6.52791i −0.0885421 0.502147i
\(170\) 0 0
\(171\) −4.83060 + 3.44663i −0.369405 + 0.263570i
\(172\) 0 0
\(173\) −19.1231 + 16.0462i −1.45390 + 1.21997i −0.524229 + 0.851577i \(0.675646\pi\)
−0.929671 + 0.368390i \(0.879909\pi\)
\(174\) 0 0
\(175\) 2.92064 9.54057i 0.220780 0.721199i
\(176\) 0 0
\(177\) 2.32740 0.976145i 0.174938 0.0733715i
\(178\) 0 0
\(179\) 10.2768i 0.768121i 0.923308 + 0.384060i \(0.125475\pi\)
−0.923308 + 0.384060i \(0.874525\pi\)
\(180\) 0 0
\(181\) −0.236613 + 0.136609i −0.0175873 + 0.0101540i −0.508768 0.860904i \(-0.669899\pi\)
0.491181 + 0.871058i \(0.336566\pi\)
\(182\) 0 0
\(183\) 9.78244 + 10.5811i 0.723139 + 0.782180i
\(184\) 0 0
\(185\) −3.09571 + 1.12675i −0.227601 + 0.0828401i
\(186\) 0 0
\(187\) 5.56826 0.981835i 0.407192 0.0717989i
\(188\) 0 0
\(189\) −2.67989 13.4840i −0.194933 0.980816i
\(190\) 0 0
\(191\) 10.2790 1.81247i 0.743765 0.131146i 0.211091 0.977466i \(-0.432298\pi\)
0.532674 + 0.846321i \(0.321187\pi\)
\(192\) 0 0
\(193\) 3.65214 1.32927i 0.262887 0.0956831i −0.207214 0.978296i \(-0.566440\pi\)
0.470101 + 0.882613i \(0.344217\pi\)
\(194\) 0 0
\(195\) −8.29660 + 1.87792i −0.594132 + 0.134481i
\(196\) 0 0
\(197\) 15.4374 8.91279i 1.09987 0.635010i 0.163683 0.986513i \(-0.447663\pi\)
0.936187 + 0.351503i \(0.114329\pi\)
\(198\) 0 0
\(199\) 1.02772i 0.0728533i 0.999336 + 0.0364266i \(0.0115975\pi\)
−0.999336 + 0.0364266i \(0.988402\pi\)
\(200\) 0 0
\(201\) 0.652694 + 0.496250i 0.0460375 + 0.0350027i
\(202\) 0 0
\(203\) −4.71186 + 4.39067i −0.330708 + 0.308165i
\(204\) 0 0
\(205\) −8.30846 + 6.97163i −0.580288 + 0.486919i
\(206\) 0 0
\(207\) 4.27330 + 0.335731i 0.297015 + 0.0233349i
\(208\) 0 0
\(209\) −0.893288 5.06609i −0.0617900 0.350429i
\(210\) 0 0
\(211\) −12.2463 + 4.45728i −0.843068 + 0.306852i −0.727211 0.686414i \(-0.759184\pi\)
−0.115857 + 0.993266i \(0.536962\pi\)
\(212\) 0 0
\(213\) 14.0663 9.04909i 0.963806 0.620034i
\(214\) 0 0
\(215\) 6.24616 10.8187i 0.425984 0.737827i
\(216\) 0 0
\(217\) 3.43715 1.45751i 0.233329 0.0989420i
\(218\) 0 0
\(219\) −21.7977 + 14.0229i −1.47295 + 0.947577i
\(220\) 0 0
\(221\) 6.19149 7.37873i 0.416485 0.496347i
\(222\) 0 0
\(223\) 8.52773 1.50367i 0.571059 0.100693i 0.119340 0.992853i \(-0.461922\pi\)
0.451719 + 0.892160i \(0.350811\pi\)
\(224\) 0 0
\(225\) −3.02490 10.9017i −0.201660 0.726777i
\(226\) 0 0
\(227\) 5.20218 + 29.5031i 0.345281 + 1.95819i 0.278578 + 0.960414i \(0.410137\pi\)
0.0667035 + 0.997773i \(0.478752\pi\)
\(228\) 0 0
\(229\) −5.43169 14.9234i −0.358936 0.986169i −0.979399 0.201933i \(-0.935278\pi\)
0.620463 0.784236i \(-0.286945\pi\)
\(230\) 0 0
\(231\) 11.5502 + 2.93702i 0.759947 + 0.193242i
\(232\) 0 0
\(233\) −3.53816 + 2.04276i −0.231793 + 0.133826i −0.611399 0.791323i \(-0.709393\pi\)
0.379606 + 0.925148i \(0.376060\pi\)
\(234\) 0 0
\(235\) −5.86120 + 10.1519i −0.382342 + 0.662236i
\(236\) 0 0
\(237\) 11.1953 + 3.47539i 0.727211 + 0.225751i
\(238\) 0 0
\(239\) −22.6228 3.98901i −1.46335 0.258028i −0.615445 0.788180i \(-0.711024\pi\)
−0.847903 + 0.530152i \(0.822135\pi\)
\(240\) 0 0
\(241\) 1.77041 4.86416i 0.114042 0.313328i −0.869520 0.493897i \(-0.835572\pi\)
0.983562 + 0.180569i \(0.0577940\pi\)
\(242\) 0 0
\(243\) −10.7835 11.2569i −0.691759 0.722129i
\(244\) 0 0
\(245\) 0.546925 7.74035i 0.0349417 0.494513i
\(246\) 0 0
\(247\) −6.71328 5.63311i −0.427156 0.358426i
\(248\) 0 0
\(249\) 0.367180 + 1.62219i 0.0232691 + 0.102802i
\(250\) 0 0
\(251\) −2.34715 4.06538i −0.148151 0.256604i 0.782393 0.622785i \(-0.213999\pi\)
−0.930544 + 0.366180i \(0.880665\pi\)
\(252\) 0 0
\(253\) −1.85795 + 3.21806i −0.116808 + 0.202318i
\(254\) 0 0
\(255\) −3.32295 2.52648i −0.208091 0.158214i
\(256\) 0 0
\(257\) −17.3371 + 6.31020i −1.08146 + 0.393620i −0.820451 0.571716i \(-0.806278\pi\)
−0.261010 + 0.965336i \(0.584056\pi\)
\(258\) 0 0
\(259\) 6.59590 4.28001i 0.409849 0.265947i
\(260\) 0 0
\(261\) −1.82751 + 7.07044i −0.113120 + 0.437649i
\(262\) 0 0
\(263\) 16.6777 + 19.8757i 1.02839 + 1.22559i 0.973878 + 0.227072i \(0.0729154\pi\)
0.0545106 + 0.998513i \(0.482640\pi\)
\(264\) 0 0
\(265\) 1.73989 + 4.78031i 0.106881 + 0.293652i
\(266\) 0 0
\(267\) −12.9939 + 25.2335i −0.795215 + 1.54426i
\(268\) 0 0
\(269\) −13.5863 23.5321i −0.828369 1.43478i −0.899317 0.437297i \(-0.855936\pi\)
0.0709484 0.997480i \(-0.477397\pi\)
\(270\) 0 0
\(271\) 8.32385 + 4.80578i 0.505638 + 0.291930i 0.731039 0.682336i \(-0.239036\pi\)
−0.225401 + 0.974266i \(0.572369\pi\)
\(272\) 0 0
\(273\) 18.2892 8.81501i 1.10692 0.533509i
\(274\) 0 0
\(275\) 9.65859 + 1.70307i 0.582435 + 0.102699i
\(276\) 0 0
\(277\) 7.11640 5.97137i 0.427583 0.358785i −0.403456 0.914999i \(-0.632191\pi\)
0.831039 + 0.556214i \(0.187747\pi\)
\(278\) 0 0
\(279\) 2.39729 3.48909i 0.143522 0.208886i
\(280\) 0 0
\(281\) −5.95969 + 16.3741i −0.355526 + 0.976798i 0.625038 + 0.780595i \(0.285084\pi\)
−0.980563 + 0.196204i \(0.937139\pi\)
\(282\) 0 0
\(283\) 9.35523 + 1.64958i 0.556111 + 0.0980573i 0.444638 0.895710i \(-0.353332\pi\)
0.111472 + 0.993768i \(0.464443\pi\)
\(284\) 0 0
\(285\) −2.29863 + 3.02327i −0.136159 + 0.179083i
\(286\) 0 0
\(287\) 15.5863 20.6681i 0.920033 1.22000i
\(288\) 0 0
\(289\) −12.2732 −0.721954
\(290\) 0 0
\(291\) 16.3211 + 17.6537i 0.956760 + 1.03488i
\(292\) 0 0
\(293\) −3.63421 + 20.6107i −0.212313 + 1.20409i 0.673196 + 0.739464i \(0.264921\pi\)
−0.885509 + 0.464623i \(0.846190\pi\)
\(294\) 0 0
\(295\) 1.23736 1.03827i 0.0720417 0.0604501i
\(296\) 0 0
\(297\) 12.8329 4.23455i 0.744639 0.245714i
\(298\) 0 0
\(299\) 1.09924 + 6.23412i 0.0635709 + 0.360528i
\(300\) 0 0
\(301\) −8.72771 + 28.5099i −0.503057 + 1.64328i
\(302\) 0 0
\(303\) 3.97695 + 17.5701i 0.228470 + 1.00937i
\(304\) 0 0
\(305\) 7.98706 + 4.61133i 0.457338 + 0.264044i
\(306\) 0 0
\(307\) 3.82657 + 2.20927i 0.218394 + 0.126090i 0.605206 0.796069i \(-0.293091\pi\)
−0.386813 + 0.922158i \(0.626424\pi\)
\(308\) 0 0
\(309\) 12.3809 16.2840i 0.704323 0.926362i
\(310\) 0 0
\(311\) 0.494496 2.80443i 0.0280403 0.159024i −0.967572 0.252594i \(-0.918716\pi\)
0.995613 + 0.0935690i \(0.0298276\pi\)
\(312\) 0 0
\(313\) 7.42776 + 8.85206i 0.419842 + 0.500348i 0.933963 0.357370i \(-0.116326\pi\)
−0.514121 + 0.857718i \(0.671882\pi\)
\(314\) 0 0
\(315\) −4.19657 7.73333i −0.236450 0.435724i
\(316\) 0 0
\(317\) 6.33865 17.4153i 0.356014 0.978141i −0.624384 0.781117i \(-0.714650\pi\)
0.980399 0.197024i \(-0.0631277\pi\)
\(318\) 0 0
\(319\) −4.84962 4.06931i −0.271526 0.227838i
\(320\) 0 0
\(321\) −12.0136 + 7.72857i −0.670534 + 0.431367i
\(322\) 0 0
\(323\) 4.30050i 0.239286i
\(324\) 0 0
\(325\) 14.4695 8.35395i 0.802622 0.463394i
\(326\) 0 0
\(327\) 0.315318 0.0151673i 0.0174371 0.000838756i
\(328\) 0 0
\(329\) 8.18981 26.7528i 0.451519 1.47493i
\(330\) 0 0
\(331\) −27.2952 9.93463i −1.50028 0.546057i −0.544146 0.838991i \(-0.683146\pi\)
−0.956133 + 0.292934i \(0.905368\pi\)
\(332\) 0 0
\(333\) 3.69615 8.11338i 0.202548 0.444610i
\(334\) 0 0
\(335\) 0.493108 + 0.179477i 0.0269414 + 0.00980586i
\(336\) 0 0
\(337\) 10.6404 + 8.92833i 0.579618 + 0.486357i 0.884822 0.465930i \(-0.154280\pi\)
−0.305204 + 0.952287i \(0.598725\pi\)
\(338\) 0 0
\(339\) 14.9951 + 1.90658i 0.814423 + 0.103551i
\(340\) 0 0
\(341\) 1.83490 + 3.17813i 0.0993652 + 0.172106i
\(342\) 0 0
\(343\) 2.87722 + 18.2954i 0.155355 + 0.987859i
\(344\) 0 0
\(345\) 2.67568 0.605636i 0.144054 0.0326063i
\(346\) 0 0
\(347\) −3.18039 8.73805i −0.170732 0.469083i 0.824586 0.565737i \(-0.191408\pi\)
−0.995318 + 0.0966539i \(0.969186\pi\)
\(348\) 0 0
\(349\) 18.3394 + 21.8561i 0.981686 + 1.16993i 0.985455 + 0.169936i \(0.0543559\pi\)
−0.00376869 + 0.999993i \(0.501200\pi\)
\(350\) 0 0
\(351\) 12.1100 19.5785i 0.646386 1.04503i
\(352\) 0 0
\(353\) −23.9298 8.70972i −1.27365 0.463572i −0.385325 0.922781i \(-0.625911\pi\)
−0.888328 + 0.459209i \(0.848133\pi\)
\(354\) 0 0
\(355\) 6.88071 8.20011i 0.365190 0.435217i
\(356\) 0 0
\(357\) 9.08273 + 4.09471i 0.480709 + 0.216715i
\(358\) 0 0
\(359\) 6.90425i 0.364392i −0.983262 0.182196i \(-0.941679\pi\)
0.983262 0.182196i \(-0.0583206\pi\)
\(360\) 0 0
\(361\) 15.0873 0.794071
\(362\) 0 0
\(363\) 0.925536 7.27926i 0.0485780 0.382062i
\(364\) 0 0
\(365\) −10.6626 + 12.7072i −0.558108 + 0.665127i
\(366\) 0 0
\(367\) −1.94103 + 0.342257i −0.101321 + 0.0178657i −0.224079 0.974571i \(-0.571937\pi\)
0.122758 + 0.992437i \(0.460826\pi\)
\(368\) 0 0
\(369\) 2.29898 29.2622i 0.119680 1.52333i
\(370\) 0 0
\(371\) −6.60907 10.1852i −0.343126 0.528789i
\(372\) 0 0
\(373\) −2.81578 + 15.9691i −0.145796 + 0.826849i 0.820929 + 0.571030i \(0.193456\pi\)
−0.966725 + 0.255819i \(0.917655\pi\)
\(374\) 0 0
\(375\) −9.11141 14.1632i −0.470511 0.731382i
\(376\) 0 0
\(377\) −10.7848 −0.555447
\(378\) 0 0
\(379\) 18.2120 0.935489 0.467744 0.883864i \(-0.345067\pi\)
0.467744 + 0.883864i \(0.345067\pi\)
\(380\) 0 0
\(381\) 6.61947 0.318408i 0.339126 0.0163125i
\(382\) 0 0
\(383\) −0.688493 + 3.90464i −0.0351804 + 0.199518i −0.997332 0.0729961i \(-0.976744\pi\)
0.962152 + 0.272514i \(0.0878550\pi\)
\(384\) 0 0
\(385\) 7.61712 0.396414i 0.388205 0.0202032i
\(386\) 0 0
\(387\) 9.03924 + 32.5772i 0.459490 + 1.65599i
\(388\) 0 0
\(389\) −22.3307 + 3.93751i −1.13221 + 0.199640i −0.708197 0.706015i \(-0.750491\pi\)
−0.424016 + 0.905655i \(0.639380\pi\)
\(390\) 0 0
\(391\) −1.99678 + 2.37966i −0.100981 + 0.120345i
\(392\) 0 0
\(393\) 11.0937 4.65286i 0.559603 0.234706i
\(394\) 0 0
\(395\) 7.50234 0.377483
\(396\) 0 0
\(397\) 6.21045i 0.311694i 0.987781 + 0.155847i \(0.0498106\pi\)
−0.987781 + 0.155847i \(0.950189\pi\)
\(398\) 0 0
\(399\) 3.72542 8.26360i 0.186504 0.413697i
\(400\) 0 0
\(401\) 9.61370 11.4572i 0.480085 0.572143i −0.470582 0.882356i \(-0.655956\pi\)
0.950667 + 0.310213i \(0.100400\pi\)
\(402\) 0 0
\(403\) 5.87472 + 2.13822i 0.292641 + 0.106512i
\(404\) 0 0
\(405\) −8.72713 4.83442i −0.433655 0.240224i
\(406\) 0 0
\(407\) 4.96802 + 5.92065i 0.246256 + 0.293476i
\(408\) 0 0
\(409\) 3.02910 + 8.32239i 0.149780 + 0.411516i 0.991779 0.127962i \(-0.0408437\pi\)
−0.841999 + 0.539478i \(0.818621\pi\)
\(410\) 0 0
\(411\) −25.3975 27.4711i −1.25277 1.35505i
\(412\) 0 0
\(413\) −2.32123 + 3.07805i −0.114220 + 0.151461i
\(414\) 0 0
\(415\) 0.532237 + 0.921861i 0.0261265 + 0.0452524i
\(416\) 0 0
\(417\) 13.1541 17.3010i 0.644161 0.847235i
\(418\) 0 0
\(419\) −1.66306 1.39547i −0.0812457 0.0681732i 0.601260 0.799053i \(-0.294665\pi\)
−0.682506 + 0.730880i \(0.739110\pi\)
\(420\) 0 0
\(421\) −12.3900 4.50961i −0.603854 0.219785i 0.0219579 0.999759i \(-0.493010\pi\)
−0.625812 + 0.779974i \(0.715232\pi\)
\(422\) 0 0
\(423\) −8.48214 30.5694i −0.412416 1.48634i
\(424\) 0 0
\(425\) 7.70453 + 2.80422i 0.373725 + 0.136025i
\(426\) 0 0
\(427\) −21.0479 6.44338i −1.01858 0.311817i
\(428\) 0 0
\(429\) 10.7973 + 16.7837i 0.521296 + 0.810325i
\(430\) 0 0
\(431\) 18.2641 10.5448i 0.879749 0.507923i 0.00917317 0.999958i \(-0.497080\pi\)
0.870576 + 0.492035i \(0.163747\pi\)
\(432\) 0 0
\(433\) 24.5525i 1.17992i 0.807433 + 0.589959i \(0.200856\pi\)
−0.807433 + 0.589959i \(0.799144\pi\)
\(434\) 0 0
\(435\) 0.224560 + 4.66843i 0.0107668 + 0.223834i
\(436\) 0 0
\(437\) 2.16505 + 1.81670i 0.103569 + 0.0869044i
\(438\) 0 0
\(439\) 12.6349 34.7140i 0.603030 1.65681i −0.142069 0.989857i \(-0.545375\pi\)
0.745099 0.666954i \(-0.232402\pi\)
\(440\) 0 0
\(441\) 13.9057 + 15.7363i 0.662176 + 0.749348i
\(442\) 0 0
\(443\) 14.6233 + 17.4273i 0.694772 + 0.827997i 0.991924 0.126833i \(-0.0404812\pi\)
−0.297152 + 0.954830i \(0.596037\pi\)
\(444\) 0 0
\(445\) −3.15432 + 17.8890i −0.149529 + 0.848021i
\(446\) 0 0
\(447\) 16.7470 + 2.12933i 0.792106 + 0.100714i
\(448\) 0 0
\(449\) −23.3226 13.4653i −1.10066 0.635468i −0.164268 0.986416i \(-0.552526\pi\)
−0.936395 + 0.350948i \(0.885859\pi\)
\(450\) 0 0
\(451\) 22.0363 + 12.7226i 1.03765 + 0.599086i
\(452\) 0 0
\(453\) −5.30448 1.64669i −0.249226 0.0773682i
\(454\) 0 0
\(455\) 9.50633 8.85833i 0.445664 0.415285i
\(456\) 0 0
\(457\) −2.17866 12.3558i −0.101913 0.577979i −0.992408 0.122986i \(-0.960753\pi\)
0.890495 0.454993i \(-0.150358\pi\)
\(458\) 0 0
\(459\) 11.1798 1.62333i 0.521829 0.0757704i
\(460\) 0 0
\(461\) −12.3292 + 10.3454i −0.574229 + 0.481835i −0.883046 0.469286i \(-0.844511\pi\)
0.308817 + 0.951121i \(0.400067\pi\)
\(462\) 0 0
\(463\) −0.398483 + 2.25991i −0.0185191 + 0.105027i −0.992666 0.120888i \(-0.961426\pi\)
0.974147 + 0.225915i \(0.0725370\pi\)
\(464\) 0 0
\(465\) 0.803252 2.58752i 0.0372499 0.119993i
\(466\) 0 0
\(467\) 3.76536 0.174240 0.0871201 0.996198i \(-0.472234\pi\)
0.0871201 + 0.996198i \(0.472234\pi\)
\(468\) 0 0
\(469\) −1.24306 0.153088i −0.0573992 0.00706896i
\(470\) 0 0
\(471\) −2.59437 6.18569i −0.119542 0.285022i
\(472\) 0 0
\(473\) −28.8626 5.08925i −1.32710 0.234004i
\(474\) 0 0
\(475\) 2.55132 7.00969i 0.117063 0.321627i
\(476\) 0 0
\(477\) −12.5285 5.70748i −0.573638 0.261328i
\(478\) 0 0
\(479\) 6.83095 5.73185i 0.312114 0.261895i −0.473251 0.880928i \(-0.656920\pi\)
0.785365 + 0.619033i \(0.212475\pi\)
\(480\) 0 0
\(481\) 12.9666 + 2.28637i 0.591227 + 0.104249i
\(482\) 0 0
\(483\) −5.89834 + 2.84287i −0.268384 + 0.129355i
\(484\) 0 0
\(485\) 13.3257 + 7.69359i 0.605088 + 0.349348i
\(486\) 0 0
\(487\) 17.0344 + 29.5044i 0.771901 + 1.33697i 0.936520 + 0.350615i \(0.114027\pi\)
−0.164618 + 0.986357i \(0.552639\pi\)
\(488\) 0 0
\(489\) 3.11191 + 4.83729i 0.140726 + 0.218750i
\(490\) 0 0
\(491\) 6.27488 + 17.2401i 0.283181 + 0.778034i 0.996978 + 0.0776816i \(0.0247518\pi\)
−0.713797 + 0.700353i \(0.753026\pi\)
\(492\) 0 0
\(493\) −3.40188 4.05420i −0.153213 0.182592i
\(494\) 0 0
\(495\) 7.04035 5.02328i 0.316440 0.225780i
\(496\) 0 0
\(497\) −11.6072 + 22.7599i −0.520655 + 1.02092i
\(498\) 0 0
\(499\) −20.9598 + 7.62873i −0.938287 + 0.341509i −0.765489 0.643449i \(-0.777503\pi\)
−0.172798 + 0.984957i \(0.555281\pi\)
\(500\) 0 0
\(501\) 1.68339 13.2397i 0.0752082 0.591506i
\(502\) 0 0
\(503\) −3.88720 + 6.73283i −0.173322 + 0.300202i −0.939579 0.342331i \(-0.888783\pi\)
0.766257 + 0.642534i \(0.222117\pi\)
\(504\) 0 0
\(505\) 5.76469 + 9.98474i 0.256526 + 0.444315i
\(506\) 0 0
\(507\) 10.9649 + 3.40388i 0.486969 + 0.151172i
\(508\) 0 0
\(509\) −0.434346 0.364459i −0.0192520 0.0161544i 0.633111 0.774061i \(-0.281778\pi\)
−0.652363 + 0.757907i \(0.726222\pi\)
\(510\) 0 0
\(511\) 17.9870 35.2697i 0.795699 1.56024i
\(512\) 0 0
\(513\) −1.47693 10.1716i −0.0652079 0.449085i
\(514\) 0 0
\(515\) 4.47774 12.3025i 0.197313 0.542112i
\(516\) 0 0
\(517\) 27.0837 + 4.77560i 1.19114 + 0.210030i
\(518\) 0 0
\(519\) −9.54536 42.1711i −0.418995 1.85111i
\(520\) 0 0
\(521\) −21.7562 + 37.6828i −0.953155 + 1.65091i −0.214621 + 0.976697i \(0.568851\pi\)
−0.738535 + 0.674216i \(0.764482\pi\)
\(522\) 0 0
\(523\) 26.5254 15.3144i 1.15987 0.669654i 0.208600 0.978001i \(-0.433109\pi\)
0.951274 + 0.308347i \(0.0997758\pi\)
\(524\) 0 0
\(525\) 12.3754 + 12.0627i 0.540105 + 0.526459i
\(526\) 0 0
\(527\) 1.04928 + 2.88287i 0.0457073 + 0.125580i
\(528\) 0 0
\(529\) 3.63940 + 20.6401i 0.158235 + 0.897394i
\(530\) 0 0
\(531\) −0.342381 + 4.35794i −0.0148581 + 0.189119i
\(532\) 0 0
\(533\) 42.6893 7.52727i 1.84908 0.326042i
\(534\) 0 0
\(535\) −5.87662 + 7.00348i −0.254068 + 0.302787i
\(536\) 0 0
\(537\) −15.8249 8.14901i −0.682896 0.351656i
\(538\) 0 0
\(539\) −17.5031 + 5.00514i −0.753913 + 0.215587i
\(540\) 0 0
\(541\) 19.4663 33.7166i 0.836921 1.44959i −0.0555351 0.998457i \(-0.517686\pi\)
0.892456 0.451134i \(-0.148980\pi\)
\(542\) 0 0
\(543\) −0.0227367 0.472679i −0.000975724 0.0202846i
\(544\) 0 0
\(545\) 0.189854 0.0691013i 0.00813246 0.00295997i
\(546\) 0 0
\(547\) 7.64697 + 43.3681i 0.326961 + 1.85429i 0.495523 + 0.868595i \(0.334977\pi\)
−0.168562 + 0.985691i \(0.553912\pi\)
\(548\) 0 0
\(549\) −24.0507 + 6.67338i −1.02646 + 0.284813i
\(550\) 0 0
\(551\) −3.68857 + 3.09508i −0.157138 + 0.131855i
\(552\) 0 0
\(553\) −17.4486 + 4.02164i −0.741992 + 0.171018i
\(554\) 0 0
\(555\) 0.719712 5.66048i 0.0305501 0.240274i
\(556\) 0 0
\(557\) 19.4237i 0.823010i 0.911407 + 0.411505i \(0.134997\pi\)
−0.911407 + 0.411505i \(0.865003\pi\)
\(558\) 0 0
\(559\) −43.2389 + 24.9640i −1.82881 + 1.05586i
\(560\) 0 0
\(561\) −2.90348 + 9.35299i −0.122585 + 0.394883i
\(562\) 0 0
\(563\) −24.7668 + 9.01439i −1.04380 + 0.379911i −0.806319 0.591481i \(-0.798543\pi\)
−0.237479 + 0.971393i \(0.576321\pi\)
\(564\) 0 0
\(565\) 9.52724 1.67991i 0.400814 0.0706744i
\(566\) 0 0
\(567\) 22.8887 + 6.56551i 0.961236 + 0.275726i
\(568\) 0 0
\(569\) −37.5823 + 6.62677i −1.57553 + 0.277809i −0.891974 0.452087i \(-0.850680\pi\)
−0.683558 + 0.729896i \(0.739568\pi\)
\(570\) 0 0
\(571\) −33.6216 + 12.2373i −1.40702 + 0.512114i −0.930254 0.366916i \(-0.880414\pi\)
−0.476767 + 0.879030i \(0.658191\pi\)
\(572\) 0 0
\(573\) −5.35984 + 17.2657i −0.223911 + 0.721283i
\(574\) 0 0
\(575\) −4.66645 + 2.69418i −0.194604 + 0.112355i
\(576\) 0 0
\(577\) 33.1855i 1.38153i 0.723079 + 0.690765i \(0.242726\pi\)
−0.723079 + 0.690765i \(0.757274\pi\)
\(578\) 0 0
\(579\) −0.849075 + 6.67791i −0.0352864 + 0.277524i
\(580\) 0 0
\(581\) −1.73202 1.85872i −0.0718564 0.0771128i
\(582\) 0 0
\(583\) 9.14251 7.67147i 0.378644 0.317720i
\(584\) 0 0
\(585\) 3.68707 14.2648i 0.152442 0.589779i
\(586\) 0 0
\(587\) −6.48754 36.7927i −0.267769 1.51860i −0.761032 0.648715i \(-0.775307\pi\)
0.493262 0.869881i \(-0.335804\pi\)
\(588\) 0 0
\(589\) 2.62288 0.954650i 0.108074 0.0393357i
\(590\) 0 0
\(591\) 1.48342 + 30.8392i 0.0610196 + 1.26855i
\(592\) 0 0
\(593\) −15.3436 + 26.5758i −0.630084 + 1.09134i 0.357450 + 0.933932i \(0.383646\pi\)
−0.987534 + 0.157406i \(0.949687\pi\)
\(594\) 0 0
\(595\) 6.32860 + 0.779394i 0.259447 + 0.0319520i
\(596\) 0 0
\(597\) −1.58257 0.814938i −0.0647701 0.0333532i
\(598\) 0 0
\(599\) −9.81363 + 11.6954i −0.400974 + 0.477862i −0.928317 0.371790i \(-0.878744\pi\)
0.527343 + 0.849653i \(0.323188\pi\)
\(600\) 0 0
\(601\) 4.22303 0.744633i 0.172261 0.0303742i −0.0868524 0.996221i \(-0.527681\pi\)
0.259113 + 0.965847i \(0.416570\pi\)
\(602\) 0 0
\(603\) −1.28172 + 0.611564i −0.0521957 + 0.0249048i
\(604\) 0 0
\(605\) −0.815499 4.62493i −0.0331548 0.188030i
\(606\) 0 0
\(607\) 3.37027 + 9.25974i 0.136795 + 0.375841i 0.989108 0.147191i \(-0.0470231\pi\)
−0.852313 + 0.523032i \(0.824801\pi\)
\(608\) 0 0
\(609\) −3.02480 10.7373i −0.122571 0.435097i
\(610\) 0 0
\(611\) 40.5740 23.4254i 1.64145 0.947690i
\(612\) 0 0
\(613\) 19.1652 33.1951i 0.774074 1.34074i −0.161239 0.986915i \(-0.551549\pi\)
0.935313 0.353820i \(-0.115118\pi\)
\(614\) 0 0
\(615\) −4.14720 18.3222i −0.167231 0.738822i
\(616\) 0 0
\(617\) −26.7808 4.72218i −1.07816 0.190108i −0.393756 0.919215i \(-0.628824\pi\)
−0.684399 + 0.729107i \(0.739936\pi\)
\(618\) 0 0
\(619\) −4.97533 + 13.6696i −0.199976 + 0.549428i −0.998628 0.0523642i \(-0.983324\pi\)
0.798653 + 0.601792i \(0.205547\pi\)
\(620\) 0 0
\(621\) −3.90553 + 6.31414i −0.156723 + 0.253378i
\(622\) 0 0
\(623\) −2.25326 43.2965i −0.0902750 1.73464i
\(624\) 0 0
\(625\) 6.18788 + 5.19224i 0.247515 + 0.207690i
\(626\) 0 0
\(627\) 8.50949 + 2.64163i 0.339836 + 0.105497i
\(628\) 0 0
\(629\) 3.23060 + 5.59557i 0.128813 + 0.223110i
\(630\) 0 0
\(631\) 0.991846 1.71793i 0.0394847 0.0683896i −0.845608 0.533805i \(-0.820762\pi\)
0.885092 + 0.465415i \(0.154095\pi\)
\(632\) 0 0
\(633\) 2.84710 22.3922i 0.113162 0.890009i
\(634\) 0 0
\(635\) 3.98561 1.45064i 0.158164 0.0575670i
\(636\) 0 0
\(637\) −17.3609 + 25.6983i −0.687865 + 1.01820i
\(638\) 0 0
\(639\) 2.78054 + 28.8359i 0.109997 + 1.14073i
\(640\) 0 0
\(641\) 2.57561 + 3.06949i 0.101730 + 0.121238i 0.814507 0.580153i \(-0.197007\pi\)
−0.712777 + 0.701391i \(0.752563\pi\)
\(642\) 0 0
\(643\) −6.23306 17.1252i −0.245808 0.675351i −0.999829 0.0185010i \(-0.994111\pi\)
0.754021 0.656850i \(-0.228112\pi\)
\(644\) 0 0
\(645\) 11.7065 + 18.1970i 0.460942 + 0.716507i
\(646\) 0 0
\(647\) −13.6102 23.5735i −0.535072 0.926771i −0.999160 0.0409821i \(-0.986951\pi\)
0.464088 0.885789i \(-0.346382\pi\)
\(648\) 0 0
\(649\) −3.28180 1.89475i −0.128822 0.0743754i
\(650\) 0 0
\(651\) −0.481129 + 6.44853i −0.0188569 + 0.252738i
\(652\) 0 0
\(653\) −15.6291 2.75583i −0.611614 0.107844i −0.140743 0.990046i \(-0.544949\pi\)
−0.470871 + 0.882202i \(0.656060\pi\)
\(654\) 0 0
\(655\) 5.89794 4.94896i 0.230452 0.193372i
\(656\) 0 0
\(657\) −4.30885 44.6853i −0.168104 1.74334i
\(658\) 0 0
\(659\) −15.1582 + 41.6467i −0.590478 + 1.62232i 0.179142 + 0.983823i \(0.442668\pi\)
−0.769620 + 0.638502i \(0.779554\pi\)
\(660\) 0 0
\(661\) −1.36845 0.241294i −0.0532263 0.00938524i 0.146972 0.989141i \(-0.453047\pi\)
−0.200198 + 0.979755i \(0.564159\pi\)
\(662\) 0 0
\(663\) 6.45276 + 15.3851i 0.250604 + 0.597510i
\(664\) 0 0
\(665\) 0.709104 5.75785i 0.0274979 0.223280i
\(666\) 0 0
\(667\) 3.47814 0.134674
\(668\) 0 0
\(669\) −4.44665 + 14.3240i −0.171917 + 0.553798i
\(670\) 0 0
\(671\) 3.75723 21.3083i 0.145046 0.822598i
\(672\) 0 0
\(673\) −6.81767 + 5.72071i −0.262802 + 0.220517i −0.764662 0.644432i \(-0.777094\pi\)
0.501860 + 0.864949i \(0.332649\pi\)
\(674\) 0 0
\(675\) 19.1858 + 3.98657i 0.738463 + 0.153443i
\(676\) 0 0
\(677\) 2.10373 + 11.9308i 0.0808527 + 0.458539i 0.998175 + 0.0603925i \(0.0192352\pi\)
−0.917322 + 0.398146i \(0.869654\pi\)
\(678\) 0 0
\(679\) −35.1165 10.7502i −1.34765 0.412554i
\(680\) 0 0
\(681\) −49.5562 15.3839i −1.89900 0.589512i
\(682\) 0 0
\(683\) −44.4305 25.6519i −1.70009 0.981545i −0.945659 0.325159i \(-0.894582\pi\)
−0.754426 0.656385i \(-0.772085\pi\)
\(684\) 0 0
\(685\) −20.7363 11.9721i −0.792293 0.457431i
\(686\) 0 0
\(687\) 27.2874 + 3.46950i 1.04108 + 0.132370i
\(688\) 0 0
\(689\) 3.53054 20.0227i 0.134503 0.762804i
\(690\) 0 0
\(691\) −28.2860 33.7100i −1.07605 1.28239i −0.957185 0.289478i \(-0.906518\pi\)
−0.118867 0.992910i \(-0.537926\pi\)
\(692\) 0 0
\(693\) −13.6814 + 15.4570i −0.519715 + 0.587161i
\(694\) 0 0
\(695\) 4.75741 13.0709i 0.180459 0.495806i
\(696\) 0 0
\(697\) 16.2952 + 13.6733i 0.617224 + 0.517913i
\(698\) 0 0
\(699\) −0.339990 7.06815i −0.0128596 0.267342i
\(700\) 0 0
\(701\) 45.5828i 1.72164i −0.508909 0.860820i \(-0.669951\pi\)
0.508909 0.860820i \(-0.330049\pi\)
\(702\) 0 0
\(703\) 5.09093 2.93925i 0.192008 0.110856i
\(704\) 0 0
\(705\) −10.9850 17.0755i −0.413719 0.643101i
\(706\) 0 0
\(707\) −18.7597 20.1320i −0.705529 0.757140i
\(708\) 0 0
\(709\) −43.6184 15.8758i −1.63812 0.596228i −0.651415 0.758722i \(-0.725824\pi\)
−0.986710 + 0.162494i \(0.948046\pi\)
\(710\) 0 0
\(711\) −14.2290 + 14.4835i −0.533630 + 0.543174i
\(712\) 0 0
\(713\) −1.89462 0.689584i −0.0709539 0.0258251i
\(714\) 0 0
\(715\) 9.78426 + 8.20997i 0.365911 + 0.307036i
\(716\) 0 0
\(717\) 24.0815 31.6732i 0.899339 1.18286i
\(718\) 0 0
\(719\) 15.0903 + 26.1372i 0.562775 + 0.974754i 0.997253 + 0.0740719i \(0.0235994\pi\)
−0.434478 + 0.900682i \(0.643067\pi\)
\(720\) 0 0
\(721\) −3.81938 + 31.0129i −0.142241 + 1.15498i
\(722\) 0 0
\(723\) 6.08635 + 6.58328i 0.226354 + 0.244835i
\(724\) 0 0
\(725\) −3.13977 8.62644i −0.116608 0.320378i
\(726\) 0 0
\(727\) 13.6781 + 16.3009i 0.507293 + 0.604568i 0.957527 0.288342i \(-0.0931041\pi\)
−0.450235 + 0.892910i \(0.648660\pi\)
\(728\) 0 0
\(729\) 25.8850 7.67899i 0.958704 0.284407i
\(730\) 0 0
\(731\) −23.0233 8.37980i −0.851547 0.309938i
\(732\) 0 0
\(733\) 6.37608 7.59872i 0.235506 0.280665i −0.635328 0.772242i \(-0.719135\pi\)
0.870834 + 0.491577i \(0.163580\pi\)
\(734\) 0 0
\(735\) 11.4855 + 6.97996i 0.423649 + 0.257460i
\(736\) 0 0
\(737\) 1.23111i 0.0453486i
\(738\) 0 0
\(739\) −29.4812 −1.08449 −0.542243 0.840222i \(-0.682425\pi\)
−0.542243 + 0.840222i \(0.682425\pi\)
\(740\) 0 0
\(741\) 13.9976 5.87082i 0.514216 0.215670i
\(742\) 0 0
\(743\) −15.0431 + 17.9277i −0.551879 + 0.657703i −0.967807 0.251694i \(-0.919012\pi\)
0.415928 + 0.909397i \(0.363457\pi\)
\(744\) 0 0
\(745\) 10.6403 1.87617i 0.389831 0.0687377i
\(746\) 0 0
\(747\) −2.78913 0.720913i −0.102049 0.0263768i
\(748\) 0 0
\(749\) 9.91338 19.4386i 0.362227 0.710271i
\(750\) 0 0
\(751\) 5.83197 33.0748i 0.212812 1.20691i −0.671852 0.740685i \(-0.734501\pi\)
0.884664 0.466230i \(-0.154388\pi\)
\(752\) 0 0
\(753\) 8.12136 0.390651i 0.295959 0.0142361i
\(754\) 0 0
\(755\) −3.55471 −0.129369
\(756\) 0 0
\(757\) −52.5640 −1.91047 −0.955235 0.295847i \(-0.904398\pi\)
−0.955235 + 0.295847i \(0.904398\pi\)
\(758\) 0 0
\(759\) −3.48215 5.41280i −0.126394 0.196472i
\(760\) 0 0
\(761\) −5.91832 + 33.5645i −0.214539 + 1.21671i 0.667166 + 0.744909i \(0.267507\pi\)
−0.881705 + 0.471801i \(0.843604\pi\)
\(762\) 0 0
\(763\) −0.404514 + 0.262485i −0.0146444 + 0.00950259i
\(764\) 0 0
\(765\) 6.52542 3.11356i 0.235927 0.112571i
\(766\) 0 0
\(767\) −6.35760 + 1.12102i −0.229560 + 0.0404775i
\(768\) 0 0
\(769\) 31.9548 38.0823i 1.15232 1.37328i 0.236531 0.971624i \(-0.423989\pi\)
0.915789 0.401659i \(-0.131566\pi\)
\(770\) 0 0
\(771\) 4.03065 31.7008i 0.145160 1.14168i
\(772\) 0 0
\(773\) 3.99081 0.143539 0.0717697 0.997421i \(-0.477135\pi\)
0.0717697 + 0.997421i \(0.477135\pi\)
\(774\) 0 0
\(775\) 5.32150i 0.191154i
\(776\) 0 0
\(777\) 1.36043 + 13.5507i 0.0488053 + 0.486130i