Properties

Label 560.2.ci.c.353.1
Level $560$
Weight $2$
Character 560.353
Analytic conductor $4.472$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.ci (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.1
Root \(-0.144868 + 1.25092i\) of defining polynomial
Character \(\chi\) \(=\) 560.353
Dual form 560.2.ci.c.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +O(q^{10})\) \(q+(-0.523277 - 1.95290i) q^{3} +(-2.03078 + 0.935904i) q^{5} +(-1.83959 - 1.90155i) q^{7} +(-0.941911 + 0.543813i) q^{9} +(-2.01999 + 3.49872i) q^{11} +(0.204875 - 0.204875i) q^{13} +(2.89039 + 3.47617i) q^{15} +(-1.97024 + 0.527924i) q^{17} +(3.10166 + 5.37224i) q^{19} +(-2.75092 + 4.58757i) q^{21} +(-1.17456 + 4.38350i) q^{23} +(3.24817 - 3.80124i) q^{25} +(-2.73397 - 2.73397i) q^{27} +7.15869i q^{29} +(-6.33287 - 3.65628i) q^{31} +(7.88965 + 2.11403i) q^{33} +(5.51548 + 2.13996i) q^{35} +(-4.46814 - 1.19723i) q^{37} +(-0.507306 - 0.292893i) q^{39} -2.58745i q^{41} +(4.97801 + 4.97801i) q^{43} +(1.40386 - 1.98590i) q^{45} +(0.0815604 - 0.304388i) q^{47} +(-0.231803 + 6.99616i) q^{49} +(2.06196 + 3.57142i) q^{51} +(-8.00039 + 2.14370i) q^{53} +(0.827689 - 8.99566i) q^{55} +(8.86840 - 8.86840i) q^{57} +(-0.427702 + 0.740802i) q^{59} +(-5.99356 + 3.46038i) q^{61} +(2.76682 + 0.790700i) q^{63} +(-0.224313 + 0.607800i) q^{65} +(0.817530 + 3.05106i) q^{67} +9.17514 q^{69} -7.12240 q^{71} +(-2.98311 - 11.1331i) q^{73} +(-9.12312 - 4.35423i) q^{75} +(10.3690 - 2.59511i) q^{77} +(4.39618 - 2.53813i) q^{79} +(-5.53997 + 9.59552i) q^{81} +(3.85372 - 3.85372i) q^{83} +(3.50704 - 2.91605i) q^{85} +(13.9802 - 3.74598i) q^{87} +(-1.53615 - 2.66069i) q^{89} +(-0.766467 - 0.0126942i) q^{91} +(-3.82650 + 14.2807i) q^{93} +(-11.3267 - 8.00700i) q^{95} +(-6.63103 - 6.63103i) q^{97} -4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 12q^{5} - 8q^{7} + O(q^{10}) \) \( 16q - 12q^{5} - 8q^{7} + 12q^{11} - 16q^{15} - 36q^{17} - 28q^{21} + 4q^{23} + 12q^{25} - 24q^{31} + 48q^{33} - 8q^{35} + 4q^{37} + 8q^{43} - 12q^{45} - 12q^{47} + 16q^{51} - 28q^{53} + 8q^{57} - 12q^{61} + 36q^{63} - 8q^{65} - 32q^{67} - 16q^{71} - 12q^{73} + 48q^{75} + 16q^{77} + 24q^{85} + 24q^{87} + 16q^{91} + 28q^{93} - 20q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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
\(3\) −0.523277 1.95290i −0.302114 1.12751i −0.935401 0.353588i \(-0.884961\pi\)
0.633287 0.773917i \(-0.281705\pi\)
\(4\) 0 0
\(5\) −2.03078 + 0.935904i −0.908194 + 0.418549i
\(6\) 0 0
\(7\) −1.83959 1.90155i −0.695300 0.718719i
\(8\) 0 0
\(9\) −0.941911 + 0.543813i −0.313970 + 0.181271i
\(10\) 0 0
\(11\) −2.01999 + 3.49872i −0.609049 + 1.05490i 0.382349 + 0.924018i \(0.375115\pi\)
−0.991397 + 0.130886i \(0.958218\pi\)
\(12\) 0 0
\(13\) 0.204875 0.204875i 0.0568221 0.0568221i −0.678125 0.734947i \(-0.737207\pi\)
0.734947 + 0.678125i \(0.237207\pi\)
\(14\) 0 0
\(15\) 2.89039 + 3.47617i 0.746295 + 0.897544i
\(16\) 0 0
\(17\) −1.97024 + 0.527924i −0.477853 + 0.128040i −0.489703 0.871890i \(-0.662895\pi\)
0.0118498 + 0.999930i \(0.496228\pi\)
\(18\) 0 0
\(19\) 3.10166 + 5.37224i 0.711571 + 1.23248i 0.964267 + 0.264931i \(0.0853491\pi\)
−0.252697 + 0.967545i \(0.581318\pi\)
\(20\) 0 0
\(21\) −2.75092 + 4.58757i −0.600300 + 1.00109i
\(22\) 0 0
\(23\) −1.17456 + 4.38350i −0.244912 + 0.914023i 0.728516 + 0.685029i \(0.240210\pi\)
−0.973428 + 0.228994i \(0.926456\pi\)
\(24\) 0 0
\(25\) 3.24817 3.80124i 0.649633 0.760248i
\(26\) 0 0
\(27\) −2.73397 2.73397i −0.526152 0.526152i
\(28\) 0 0
\(29\) 7.15869i 1.32934i 0.747139 + 0.664668i \(0.231427\pi\)
−0.747139 + 0.664668i \(0.768573\pi\)
\(30\) 0 0
\(31\) −6.33287 3.65628i −1.13742 0.656688i −0.191627 0.981468i \(-0.561376\pi\)
−0.945790 + 0.324780i \(0.894710\pi\)
\(32\) 0 0
\(33\) 7.88965 + 2.11403i 1.37341 + 0.368005i
\(34\) 0 0
\(35\) 5.51548 + 2.13996i 0.932287 + 0.361719i
\(36\) 0 0
\(37\) −4.46814 1.19723i −0.734558 0.196824i −0.127900 0.991787i \(-0.540824\pi\)
−0.606658 + 0.794963i \(0.707490\pi\)
\(38\) 0 0
\(39\) −0.507306 0.292893i −0.0812340 0.0469005i
\(40\) 0 0
\(41\) 2.58745i 0.404093i −0.979376 0.202046i \(-0.935241\pi\)
0.979376 0.202046i \(-0.0647591\pi\)
\(42\) 0 0
\(43\) 4.97801 + 4.97801i 0.759140 + 0.759140i 0.976166 0.217026i \(-0.0696356\pi\)
−0.217026 + 0.976166i \(0.569636\pi\)
\(44\) 0 0
\(45\) 1.40386 1.98590i 0.209275 0.296041i
\(46\) 0 0
\(47\) 0.0815604 0.304388i 0.0118968 0.0443995i −0.959722 0.280950i \(-0.909350\pi\)
0.971619 + 0.236551i \(0.0760170\pi\)
\(48\) 0 0
\(49\) −0.231803 + 6.99616i −0.0331148 + 0.999452i
\(50\) 0 0
\(51\) 2.06196 + 3.57142i 0.288732 + 0.500099i
\(52\) 0 0
\(53\) −8.00039 + 2.14370i −1.09894 + 0.294460i −0.762332 0.647186i \(-0.775946\pi\)
−0.336606 + 0.941646i \(0.609279\pi\)
\(54\) 0 0
\(55\) 0.827689 8.99566i 0.111606 1.21297i
\(56\) 0 0
\(57\) 8.86840 8.86840i 1.17465 1.17465i
\(58\) 0 0
\(59\) −0.427702 + 0.740802i −0.0556821 + 0.0964442i −0.892523 0.451002i \(-0.851067\pi\)
0.836841 + 0.547446i \(0.184400\pi\)
\(60\) 0 0
\(61\) −5.99356 + 3.46038i −0.767397 + 0.443057i −0.831945 0.554858i \(-0.812773\pi\)
0.0645484 + 0.997915i \(0.479439\pi\)
\(62\) 0 0
\(63\) 2.76682 + 0.790700i 0.348587 + 0.0996189i
\(64\) 0 0
\(65\) −0.224313 + 0.607800i −0.0278226 + 0.0753883i
\(66\) 0 0
\(67\) 0.817530 + 3.05106i 0.0998772 + 0.372747i 0.997714 0.0675822i \(-0.0215285\pi\)
−0.897837 + 0.440329i \(0.854862\pi\)
\(68\) 0 0
\(69\) 9.17514 1.10456
\(70\) 0 0
\(71\) −7.12240 −0.845273 −0.422637 0.906299i \(-0.638895\pi\)
−0.422637 + 0.906299i \(0.638895\pi\)
\(72\) 0 0
\(73\) −2.98311 11.1331i −0.349147 1.30303i −0.887692 0.460438i \(-0.847693\pi\)
0.538545 0.842597i \(-0.318974\pi\)
\(74\) 0 0
\(75\) −9.12312 4.35423i −1.05345 0.502783i
\(76\) 0 0
\(77\) 10.3690 2.59511i 1.18165 0.295740i
\(78\) 0 0
\(79\) 4.39618 2.53813i 0.494609 0.285562i −0.231876 0.972745i \(-0.574486\pi\)
0.726484 + 0.687183i \(0.241153\pi\)
\(80\) 0 0
\(81\) −5.53997 + 9.59552i −0.615553 + 1.06617i
\(82\) 0 0
\(83\) 3.85372 3.85372i 0.423001 0.423001i −0.463235 0.886236i \(-0.653311\pi\)
0.886236 + 0.463235i \(0.153311\pi\)
\(84\) 0 0
\(85\) 3.50704 2.91605i 0.380392 0.316290i
\(86\) 0 0
\(87\) 13.9802 3.74598i 1.49883 0.401611i
\(88\) 0 0
\(89\) −1.53615 2.66069i −0.162832 0.282033i 0.773051 0.634343i \(-0.218729\pi\)
−0.935883 + 0.352310i \(0.885396\pi\)
\(90\) 0 0
\(91\) −0.766467 0.0126942i −0.0803475 0.00133071i
\(92\) 0 0
\(93\) −3.82650 + 14.2807i −0.396789 + 1.48084i
\(94\) 0 0
\(95\) −11.3267 8.00700i −1.16210 0.821501i
\(96\) 0 0
\(97\) −6.63103 6.63103i −0.673279 0.673279i 0.285191 0.958471i \(-0.407943\pi\)
−0.958471 + 0.285191i \(0.907943\pi\)
\(98\) 0 0
\(99\) 4.39398i 0.441611i
\(100\) 0 0
\(101\) −8.56364 4.94422i −0.852114 0.491968i 0.00924966 0.999957i \(-0.497056\pi\)
−0.861364 + 0.507989i \(0.830389\pi\)
\(102\) 0 0
\(103\) −4.13612 1.10827i −0.407544 0.109201i 0.0492221 0.998788i \(-0.484326\pi\)
−0.456766 + 0.889587i \(0.650992\pi\)
\(104\) 0 0
\(105\) 1.29299 11.8910i 0.126183 1.16044i
\(106\) 0 0
\(107\) −14.3653 3.84918i −1.38875 0.372114i −0.514457 0.857516i \(-0.672007\pi\)
−0.874291 + 0.485402i \(0.838673\pi\)
\(108\) 0 0
\(109\) −11.4586 6.61564i −1.09754 0.633664i −0.161964 0.986797i \(-0.551783\pi\)
−0.935573 + 0.353133i \(0.885116\pi\)
\(110\) 0 0
\(111\) 9.35230i 0.887681i
\(112\) 0 0
\(113\) 9.75336 + 9.75336i 0.917519 + 0.917519i 0.996848 0.0793296i \(-0.0252780\pi\)
−0.0793296 + 0.996848i \(0.525278\pi\)
\(114\) 0 0
\(115\) −1.71727 10.0012i −0.160136 0.932618i
\(116\) 0 0
\(117\) −0.0815604 + 0.304388i −0.00754026 + 0.0281406i
\(118\) 0 0
\(119\) 4.62831 + 2.77535i 0.424276 + 0.254416i
\(120\) 0 0
\(121\) −2.66069 4.60846i −0.241881 0.418951i
\(122\) 0 0
\(123\) −5.05303 + 1.35396i −0.455617 + 0.122082i
\(124\) 0 0
\(125\) −3.03873 + 10.7595i −0.271792 + 0.962356i
\(126\) 0 0
\(127\) 2.19984 2.19984i 0.195204 0.195204i −0.602736 0.797940i \(-0.705923\pi\)
0.797940 + 0.602736i \(0.205923\pi\)
\(128\) 0 0
\(129\) 7.11667 12.3264i 0.626587 1.08528i
\(130\) 0 0
\(131\) 6.32091 3.64938i 0.552260 0.318848i −0.197773 0.980248i \(-0.563371\pi\)
0.750033 + 0.661400i \(0.230037\pi\)
\(132\) 0 0
\(133\) 4.50980 15.7807i 0.391049 1.36836i
\(134\) 0 0
\(135\) 8.11083 + 2.99337i 0.698069 + 0.257628i
\(136\) 0 0
\(137\) 1.85804 + 6.93431i 0.158743 + 0.592438i 0.998756 + 0.0498710i \(0.0158810\pi\)
−0.840012 + 0.542567i \(0.817452\pi\)
\(138\) 0 0
\(139\) −12.4172 −1.05321 −0.526605 0.850110i \(-0.676535\pi\)
−0.526605 + 0.850110i \(0.676535\pi\)
\(140\) 0 0
\(141\) −0.637116 −0.0536549
\(142\) 0 0
\(143\) 0.302955 + 1.13064i 0.0253344 + 0.0945492i
\(144\) 0 0
\(145\) −6.69985 14.5378i −0.556392 1.20730i
\(146\) 0 0
\(147\) 13.7841 3.20824i 1.13689 0.264611i
\(148\) 0 0
\(149\) 20.7399 11.9742i 1.69908 0.980963i 0.752440 0.658661i \(-0.228877\pi\)
0.946637 0.322302i \(-0.104457\pi\)
\(150\) 0 0
\(151\) −1.77167 + 3.06862i −0.144176 + 0.249721i −0.929065 0.369916i \(-0.879387\pi\)
0.784889 + 0.619636i \(0.212720\pi\)
\(152\) 0 0
\(153\) 1.56870 1.56870i 0.126822 0.126822i
\(154\) 0 0
\(155\) 16.2826 + 1.49816i 1.30785 + 0.120335i
\(156\) 0 0
\(157\) −5.91389 + 1.58462i −0.471980 + 0.126467i −0.486966 0.873421i \(-0.661896\pi\)
0.0149859 + 0.999888i \(0.495230\pi\)
\(158\) 0 0
\(159\) 8.37284 + 14.5022i 0.664010 + 1.15010i
\(160\) 0 0
\(161\) 10.4962 5.83037i 0.827213 0.459498i
\(162\) 0 0
\(163\) 4.28549 15.9937i 0.335666 1.25272i −0.567480 0.823387i \(-0.692082\pi\)
0.903146 0.429334i \(-0.141252\pi\)
\(164\) 0 0
\(165\) −18.0007 + 3.09083i −1.40135 + 0.240621i
\(166\) 0 0
\(167\) 10.2873 + 10.2873i 0.796056 + 0.796056i 0.982471 0.186415i \(-0.0596869\pi\)
−0.186415 + 0.982471i \(0.559687\pi\)
\(168\) 0 0
\(169\) 12.9161i 0.993543i
\(170\) 0 0
\(171\) −5.84298 3.37345i −0.446824 0.257974i
\(172\) 0 0
\(173\) 7.50720 + 2.01155i 0.570762 + 0.152935i 0.532646 0.846338i \(-0.321198\pi\)
0.0381159 + 0.999273i \(0.487864\pi\)
\(174\) 0 0
\(175\) −13.2036 + 0.816171i −0.998095 + 0.0616967i
\(176\) 0 0
\(177\) 1.67052 + 0.447613i 0.125564 + 0.0336447i
\(178\) 0 0
\(179\) −3.34695 1.93236i −0.250163 0.144431i 0.369676 0.929161i \(-0.379469\pi\)
−0.619839 + 0.784729i \(0.712802\pi\)
\(180\) 0 0
\(181\) 6.99107i 0.519642i 0.965657 + 0.259821i \(0.0836636\pi\)
−0.965657 + 0.259821i \(0.916336\pi\)
\(182\) 0 0
\(183\) 9.89407 + 9.89407i 0.731390 + 0.731390i
\(184\) 0 0
\(185\) 10.1943 1.75043i 0.749502 0.128694i
\(186\) 0 0
\(187\) 2.13280 7.95971i 0.155966 0.582071i
\(188\) 0 0
\(189\) −0.169398 + 10.2282i −0.0123219 + 0.743990i
\(190\) 0 0
\(191\) 2.23721 + 3.87496i 0.161879 + 0.280383i 0.935543 0.353214i \(-0.114911\pi\)
−0.773664 + 0.633597i \(0.781578\pi\)
\(192\) 0 0
\(193\) 19.3907 5.19573i 1.39577 0.373997i 0.518949 0.854805i \(-0.326324\pi\)
0.876825 + 0.480809i \(0.159657\pi\)
\(194\) 0 0
\(195\) 1.30435 + 0.120013i 0.0934064 + 0.00859431i
\(196\) 0 0
\(197\) −7.84901 + 7.84901i −0.559219 + 0.559219i −0.929085 0.369866i \(-0.879404\pi\)
0.369866 + 0.929085i \(0.379404\pi\)
\(198\) 0 0
\(199\) 5.40103 9.35485i 0.382869 0.663148i −0.608602 0.793475i \(-0.708270\pi\)
0.991471 + 0.130327i \(0.0416028\pi\)
\(200\) 0 0
\(201\) 5.53062 3.19310i 0.390100 0.225224i
\(202\) 0 0
\(203\) 13.6126 13.1691i 0.955419 0.924288i
\(204\) 0 0
\(205\) 2.42161 + 5.25456i 0.169133 + 0.366995i
\(206\) 0 0
\(207\) −1.27748 4.76761i −0.0887908 0.331372i
\(208\) 0 0
\(209\) −25.0613 −1.73353
\(210\) 0 0
\(211\) −7.56555 −0.520834 −0.260417 0.965496i \(-0.583860\pi\)
−0.260417 + 0.965496i \(0.583860\pi\)
\(212\) 0 0
\(213\) 3.72699 + 13.9093i 0.255369 + 0.953050i
\(214\) 0 0
\(215\) −14.7682 5.45032i −1.00718 0.371709i
\(216\) 0 0
\(217\) 4.69728 + 18.7683i 0.318872 + 1.27408i
\(218\) 0 0
\(219\) −20.1809 + 11.6514i −1.36370 + 0.787330i
\(220\) 0 0
\(221\) −0.295494 + 0.511811i −0.0198771 + 0.0344281i
\(222\) 0 0
\(223\) −9.35230 + 9.35230i −0.626277 + 0.626277i −0.947129 0.320853i \(-0.896031\pi\)
0.320853 + 0.947129i \(0.396031\pi\)
\(224\) 0 0
\(225\) −0.992322 + 5.34682i −0.0661548 + 0.356455i
\(226\) 0 0
\(227\) −15.6420 + 4.19127i −1.03820 + 0.278184i −0.737367 0.675493i \(-0.763931\pi\)
−0.300832 + 0.953677i \(0.597264\pi\)
\(228\) 0 0
\(229\) 5.88820 + 10.1987i 0.389103 + 0.673947i 0.992329 0.123624i \(-0.0394515\pi\)
−0.603226 + 0.797570i \(0.706118\pi\)
\(230\) 0 0
\(231\) −10.4938 18.8915i −0.690442 1.24297i
\(232\) 0 0
\(233\) −1.48154 + 5.52920i −0.0970591 + 0.362230i −0.997324 0.0731138i \(-0.976706\pi\)
0.900264 + 0.435343i \(0.143373\pi\)
\(234\) 0 0
\(235\) 0.119246 + 0.694478i 0.00777876 + 0.0453028i
\(236\) 0 0
\(237\) −7.25713 7.25713i −0.471402 0.471402i
\(238\) 0 0
\(239\) 8.33794i 0.539337i 0.962953 + 0.269668i \(0.0869141\pi\)
−0.962953 + 0.269668i \(0.913086\pi\)
\(240\) 0 0
\(241\) 2.56723 + 1.48219i 0.165370 + 0.0954763i 0.580401 0.814331i \(-0.302896\pi\)
−0.415031 + 0.909807i \(0.636229\pi\)
\(242\) 0 0
\(243\) 10.4340 + 2.79578i 0.669340 + 0.179349i
\(244\) 0 0
\(245\) −6.07700 14.4246i −0.388245 0.921556i
\(246\) 0 0
\(247\) 1.73609 + 0.465184i 0.110465 + 0.0295989i
\(248\) 0 0
\(249\) −9.54248 5.50936i −0.604730 0.349141i
\(250\) 0 0
\(251\) 16.1800i 1.02127i 0.859796 + 0.510637i \(0.170590\pi\)
−0.859796 + 0.510637i \(0.829410\pi\)
\(252\) 0 0
\(253\) −12.9641 12.9641i −0.815043 0.815043i
\(254\) 0 0
\(255\) −7.52990 5.32298i −0.471541 0.333338i
\(256\) 0 0
\(257\) −1.50754 + 5.62621i −0.0940377 + 0.350954i −0.996872 0.0790355i \(-0.974816\pi\)
0.902834 + 0.429989i \(0.141483\pi\)
\(258\) 0 0
\(259\) 5.94295 + 10.6988i 0.369277 + 0.664793i
\(260\) 0 0
\(261\) −3.89299 6.74285i −0.240970 0.417372i
\(262\) 0 0
\(263\) 1.67793 0.449601i 0.103466 0.0277236i −0.206715 0.978401i \(-0.566277\pi\)
0.310180 + 0.950678i \(0.399611\pi\)
\(264\) 0 0
\(265\) 14.2408 11.8410i 0.874803 0.727386i
\(266\) 0 0
\(267\) −4.39223 + 4.39223i −0.268800 + 0.268800i
\(268\) 0 0
\(269\) −1.89169 + 3.27650i −0.115338 + 0.199772i −0.917915 0.396777i \(-0.870128\pi\)
0.802577 + 0.596549i \(0.203462\pi\)
\(270\) 0 0
\(271\) 18.4029 10.6249i 1.11789 0.645416i 0.177032 0.984205i \(-0.443351\pi\)
0.940862 + 0.338789i \(0.110017\pi\)
\(272\) 0 0
\(273\) 0.376284 + 1.50347i 0.0227737 + 0.0909943i
\(274\) 0 0
\(275\) 6.73822 + 19.0429i 0.406330 + 1.14833i
\(276\) 0 0
\(277\) −1.26567 4.72353i −0.0760465 0.283810i 0.917422 0.397916i \(-0.130266\pi\)
−0.993469 + 0.114106i \(0.963600\pi\)
\(278\) 0 0
\(279\) 7.95333 0.476153
\(280\) 0 0
\(281\) −29.4776 −1.75849 −0.879243 0.476373i \(-0.841951\pi\)
−0.879243 + 0.476373i \(0.841951\pi\)
\(282\) 0 0
\(283\) 2.92041 + 10.8991i 0.173601 + 0.647886i 0.996786 + 0.0801133i \(0.0255282\pi\)
−0.823185 + 0.567773i \(0.807805\pi\)
\(284\) 0 0
\(285\) −9.70983 + 26.3098i −0.575161 + 1.55846i
\(286\) 0 0
\(287\) −4.92018 + 4.75986i −0.290429 + 0.280966i
\(288\) 0 0
\(289\) −11.1193 + 6.41973i −0.654076 + 0.377631i
\(290\) 0 0
\(291\) −9.47985 + 16.4196i −0.555719 + 0.962533i
\(292\) 0 0
\(293\) −7.23407 + 7.23407i −0.422619 + 0.422619i −0.886105 0.463485i \(-0.846599\pi\)
0.463485 + 0.886105i \(0.346599\pi\)
\(294\) 0 0
\(295\) 0.175251 1.90470i 0.0102035 0.110896i
\(296\) 0 0
\(297\) 15.0880 4.04281i 0.875493 0.234588i
\(298\) 0 0
\(299\) 0.657432 + 1.13871i 0.0380203 + 0.0658531i
\(300\) 0 0
\(301\) 0.308440 18.6235i 0.0177782 1.07344i
\(302\) 0 0
\(303\) −5.17439 + 19.3111i −0.297261 + 1.10939i
\(304\) 0 0
\(305\) 8.93304 12.6367i 0.511504 0.723575i
\(306\) 0 0
\(307\) 1.07859 + 1.07859i 0.0615584 + 0.0615584i 0.737216 0.675657i \(-0.236140\pi\)
−0.675657 + 0.737216i \(0.736140\pi\)
\(308\) 0 0
\(309\) 8.65735i 0.492500i
\(310\) 0 0
\(311\) 8.33830 + 4.81412i 0.472821 + 0.272984i 0.717420 0.696641i \(-0.245323\pi\)
−0.244599 + 0.969624i \(0.578656\pi\)
\(312\) 0 0
\(313\) 2.92361 + 0.783378i 0.165252 + 0.0442791i 0.340496 0.940246i \(-0.389405\pi\)
−0.175244 + 0.984525i \(0.556072\pi\)
\(314\) 0 0
\(315\) −6.35883 + 0.983739i −0.358280 + 0.0554274i
\(316\) 0 0
\(317\) −1.88227 0.504353i −0.105719 0.0283273i 0.205572 0.978642i \(-0.434095\pi\)
−0.311291 + 0.950315i \(0.600761\pi\)
\(318\) 0 0
\(319\) −25.0463 14.4605i −1.40232 0.809631i
\(320\) 0 0
\(321\) 30.0682i 1.67824i
\(322\) 0 0
\(323\) −8.94715 8.94715i −0.497833 0.497833i
\(324\) 0 0
\(325\) −0.113311 1.44425i −0.00628535 0.0801124i
\(326\) 0 0
\(327\) −6.92363 + 25.8393i −0.382878 + 1.42892i
\(328\) 0 0
\(329\) −0.728847 + 0.404858i −0.0401826 + 0.0223205i
\(330\) 0 0
\(331\) −14.4468 25.0225i −0.794066 1.37536i −0.923431 0.383765i \(-0.874627\pi\)
0.129365 0.991597i \(-0.458706\pi\)
\(332\) 0 0
\(333\) 4.85966 1.30214i 0.266308 0.0713570i
\(334\) 0 0
\(335\) −4.51573 5.43092i −0.246721 0.296723i
\(336\) 0 0
\(337\) −0.823226 + 0.823226i −0.0448440 + 0.0448440i −0.729173 0.684329i \(-0.760095\pi\)
0.684329 + 0.729173i \(0.260095\pi\)
\(338\) 0 0
\(339\) 13.9436 24.1510i 0.757312 1.31170i
\(340\) 0 0
\(341\) 25.5846 14.7713i 1.38548 0.799910i
\(342\) 0 0
\(343\) 13.7300 12.4293i 0.741350 0.671119i
\(344\) 0 0
\(345\) −18.6327 + 8.58706i −1.00315 + 0.462312i
\(346\) 0 0
\(347\) 4.32336 + 16.1350i 0.232090 + 0.866172i 0.979439 + 0.201740i \(0.0646597\pi\)
−0.747349 + 0.664432i \(0.768674\pi\)
\(348\) 0 0
\(349\) 36.7146 1.96529 0.982644 0.185503i \(-0.0593916\pi\)
0.982644 + 0.185503i \(0.0593916\pi\)
\(350\) 0 0
\(351\) −1.12024 −0.0597942
\(352\) 0 0
\(353\) −3.69356 13.7845i −0.196588 0.733677i −0.991850 0.127411i \(-0.959333\pi\)
0.795262 0.606266i \(-0.207333\pi\)
\(354\) 0 0
\(355\) 14.4640 6.66588i 0.767672 0.353788i
\(356\) 0 0
\(357\) 2.99808 10.4909i 0.158675 0.555236i
\(358\) 0 0
\(359\) 23.4596 13.5444i 1.23815 0.714847i 0.269435 0.963019i \(-0.413163\pi\)
0.968716 + 0.248172i \(0.0798298\pi\)
\(360\) 0 0
\(361\) −9.74064 + 16.8713i −0.512665 + 0.887962i
\(362\) 0 0
\(363\) −7.60756 + 7.60756i −0.399293 + 0.399293i
\(364\) 0 0
\(365\) 16.4776 + 19.8171i 0.862477 + 1.03727i
\(366\) 0 0
\(367\) −21.8990 + 5.86782i −1.14312 + 0.306298i −0.780204 0.625525i \(-0.784885\pi\)
−0.362914 + 0.931823i \(0.618218\pi\)
\(368\) 0 0
\(369\) 1.40709 + 2.43715i 0.0732502 + 0.126873i
\(370\) 0 0
\(371\) 18.7938 + 11.2696i 0.975726 + 0.585090i
\(372\) 0 0
\(373\) −3.32215 + 12.3984i −0.172014 + 0.641966i 0.825027 + 0.565094i \(0.191160\pi\)
−0.997041 + 0.0768720i \(0.975507\pi\)
\(374\) 0 0
\(375\) 22.6022 + 0.304135i 1.16717 + 0.0157055i
\(376\) 0 0
\(377\) 1.46664 + 1.46664i 0.0755356 + 0.0755356i
\(378\) 0 0
\(379\) 14.4739i 0.743476i 0.928338 + 0.371738i \(0.121238\pi\)
−0.928338 + 0.371738i \(0.878762\pi\)
\(380\) 0 0
\(381\) −5.44718 3.14493i −0.279068 0.161120i
\(382\) 0 0
\(383\) −1.69189 0.453341i −0.0864517 0.0231647i 0.215334 0.976540i \(-0.430916\pi\)
−0.301786 + 0.953376i \(0.597583\pi\)
\(384\) 0 0
\(385\) −18.6283 + 14.9744i −0.949387 + 0.763168i
\(386\) 0 0
\(387\) −7.39595 1.98174i −0.375957 0.100737i
\(388\) 0 0
\(389\) −2.40954 1.39115i −0.122169 0.0705341i 0.437670 0.899135i \(-0.355804\pi\)
−0.559839 + 0.828601i \(0.689137\pi\)
\(390\) 0 0
\(391\) 9.25661i 0.468127i
\(392\) 0 0
\(393\) −10.4344 10.4344i −0.526348 0.526348i
\(394\) 0 0
\(395\) −6.55224 + 9.26881i −0.329679 + 0.466364i
\(396\) 0 0
\(397\) 10.2668 38.3163i 0.515277 1.92304i 0.165486 0.986212i \(-0.447081\pi\)
0.349791 0.936828i \(-0.386253\pi\)
\(398\) 0 0
\(399\) −33.1780 0.549491i −1.66098 0.0275089i
\(400\) 0 0
\(401\) 9.98528 + 17.2950i 0.498641 + 0.863672i 0.999999 0.00156835i \(-0.000499221\pi\)
−0.501358 + 0.865240i \(0.667166\pi\)
\(402\) 0 0
\(403\) −2.04653 + 0.548365i −0.101945 + 0.0273160i
\(404\) 0 0
\(405\) 2.27000 24.6713i 0.112797 1.22593i
\(406\) 0 0
\(407\) 13.2144 13.2144i 0.655012 0.655012i
\(408\) 0 0
\(409\) −7.65280 + 13.2550i −0.378407 + 0.655419i −0.990831 0.135110i \(-0.956861\pi\)
0.612424 + 0.790529i \(0.290195\pi\)
\(410\) 0 0
\(411\) 12.5697 7.25713i 0.620019 0.357968i
\(412\) 0 0
\(413\) 2.19547 0.549475i 0.108032 0.0270379i
\(414\) 0 0
\(415\) −4.21936 + 11.4328i −0.207120 + 0.561214i
\(416\) 0 0
\(417\) 6.49762 + 24.2495i 0.318190 + 1.18750i
\(418\) 0 0
\(419\) 27.7027 1.35337 0.676684 0.736274i \(-0.263416\pi\)
0.676684 + 0.736274i \(0.263416\pi\)
\(420\) 0 0
\(421\) 33.0159 1.60910 0.804549 0.593887i \(-0.202407\pi\)
0.804549 + 0.593887i \(0.202407\pi\)
\(422\) 0 0
\(423\) 0.0887072 + 0.331060i 0.00431309 + 0.0160967i
\(424\) 0 0
\(425\) −4.39289 + 9.20413i −0.213087 + 0.446466i
\(426\) 0 0
\(427\) 17.6058 + 5.03138i 0.852005 + 0.243485i
\(428\) 0 0
\(429\) 2.04950 1.18328i 0.0989509 0.0571293i
\(430\) 0 0
\(431\) 11.9586 20.7129i 0.576027 0.997708i −0.419902 0.907569i \(-0.637936\pi\)
0.995929 0.0901384i \(-0.0287309\pi\)
\(432\) 0 0
\(433\) −13.2515 + 13.2515i −0.636829 + 0.636829i −0.949772 0.312943i \(-0.898685\pi\)
0.312943 + 0.949772i \(0.398685\pi\)
\(434\) 0 0
\(435\) −24.8849 + 20.6914i −1.19314 + 0.992077i
\(436\) 0 0
\(437\) −27.1923 + 7.28615i −1.30078 + 0.348544i
\(438\) 0 0
\(439\) 7.05383 + 12.2176i 0.336661 + 0.583114i 0.983802 0.179256i \(-0.0573690\pi\)
−0.647141 + 0.762370i \(0.724036\pi\)
\(440\) 0 0
\(441\) −3.58626 6.71582i −0.170774 0.319801i
\(442\) 0 0
\(443\) −5.45161 + 20.3457i −0.259014 + 0.966652i 0.706800 + 0.707414i \(0.250138\pi\)
−0.965813 + 0.259238i \(0.916528\pi\)
\(444\) 0 0
\(445\) 5.60975 + 3.96560i 0.265928 + 0.187988i
\(446\) 0 0
\(447\) −34.2370 34.2370i −1.61936 1.61936i
\(448\) 0 0
\(449\) 31.3247i 1.47831i −0.673538 0.739153i \(-0.735226\pi\)
0.673538 0.739153i \(-0.264774\pi\)
\(450\) 0 0
\(451\) 9.05278 + 5.22662i 0.426279 + 0.246112i
\(452\) 0 0
\(453\) 6.91977 + 1.85415i 0.325119 + 0.0871154i
\(454\) 0 0
\(455\) 1.56841 0.691560i 0.0735281 0.0324209i
\(456\) 0 0
\(457\) 2.76404 + 0.740622i 0.129296 + 0.0346448i 0.322887 0.946438i \(-0.395347\pi\)
−0.193591 + 0.981082i \(0.562013\pi\)
\(458\) 0 0
\(459\) 6.82989 + 3.94324i 0.318792 + 0.184055i
\(460\) 0 0
\(461\) 3.02674i 0.140969i 0.997513 + 0.0704846i \(0.0224546\pi\)
−0.997513 + 0.0704846i \(0.977545\pi\)
\(462\) 0 0
\(463\) −19.2889 19.2889i −0.896431 0.896431i 0.0986876 0.995118i \(-0.468536\pi\)
−0.995118 + 0.0986876i \(0.968536\pi\)
\(464\) 0 0
\(465\) −5.59457 32.5822i −0.259442 1.51096i
\(466\) 0 0
\(467\) 6.50385 24.2727i 0.300962 1.12321i −0.635403 0.772180i \(-0.719166\pi\)
0.936366 0.351026i \(-0.114167\pi\)
\(468\) 0 0
\(469\) 4.29784 7.16729i 0.198456 0.330955i
\(470\) 0 0
\(471\) 6.18921 + 10.7200i 0.285184 + 0.493953i
\(472\) 0 0
\(473\) −27.4722 + 7.36115i −1.26317 + 0.338466i
\(474\) 0 0
\(475\) 30.4959 + 5.65976i 1.39925 + 0.259688i
\(476\) 0 0
\(477\) 6.36989 6.36989i 0.291657 0.291657i
\(478\) 0 0
\(479\) 4.14346 7.17668i 0.189319 0.327911i −0.755704 0.654913i \(-0.772705\pi\)
0.945024 + 0.327002i \(0.106039\pi\)
\(480\) 0 0
\(481\) −1.16069 + 0.670127i −0.0529231 + 0.0305551i
\(482\) 0 0
\(483\) −16.8785 17.4470i −0.767999 0.793867i
\(484\) 0 0
\(485\) 19.6722 + 7.26018i 0.893269 + 0.329668i
\(486\) 0 0
\(487\) −2.76375 10.3144i −0.125237 0.467392i 0.874611 0.484826i \(-0.161117\pi\)
−0.999848 + 0.0174340i \(0.994450\pi\)
\(488\) 0 0
\(489\) −33.4765 −1.51386
\(490\) 0 0
\(491\) −25.7259 −1.16100 −0.580498 0.814262i \(-0.697142\pi\)
−0.580498 + 0.814262i \(0.697142\pi\)
\(492\) 0 0
\(493\) −3.77924 14.1043i −0.170209 0.635227i
\(494\) 0 0
\(495\) 4.11234 + 8.92322i 0.184836 + 0.401069i
\(496\) 0 0
\(497\) 13.1023 + 13.5436i 0.587719 + 0.607514i
\(498\) 0 0
\(499\) 12.6429 7.29940i 0.565975 0.326766i −0.189565 0.981868i \(-0.560708\pi\)
0.755540 + 0.655102i \(0.227374\pi\)
\(500\) 0 0
\(501\) 14.7069 25.4732i 0.657058 1.13806i
\(502\) 0 0
\(503\) −13.9891 + 13.9891i −0.623744 + 0.623744i −0.946487 0.322743i \(-0.895395\pi\)
0.322743 + 0.946487i \(0.395395\pi\)
\(504\) 0 0
\(505\) 22.0182 + 2.02589i 0.979798 + 0.0901510i
\(506\) 0 0
\(507\) 25.2237 6.75868i 1.12022 0.300163i
\(508\) 0 0
\(509\) 1.42883 + 2.47481i 0.0633319 + 0.109694i 0.895953 0.444149i \(-0.146494\pi\)
−0.832621 + 0.553843i \(0.813161\pi\)
\(510\) 0 0
\(511\) −15.6825 + 26.1530i −0.693754 + 1.15694i
\(512\) 0 0
\(513\) 6.20768 23.1674i 0.274076 1.02287i
\(514\) 0 0
\(515\) 9.43680 1.62036i 0.415835 0.0714015i
\(516\) 0 0
\(517\) 0.900216 + 0.900216i 0.0395914 + 0.0395914i
\(518\) 0 0
\(519\) 15.7134i 0.689741i
\(520\) 0 0
\(521\) 24.7917 + 14.3135i 1.08614 + 0.627084i 0.932547 0.361049i \(-0.117581\pi\)
0.153595 + 0.988134i \(0.450915\pi\)
\(522\) 0 0
\(523\) −30.5069 8.17429i −1.33397 0.357437i −0.479777 0.877390i \(-0.659283\pi\)
−0.854195 + 0.519954i \(0.825949\pi\)
\(524\) 0 0
\(525\) 8.50302 + 25.3581i 0.371102 + 1.10672i
\(526\) 0 0
\(527\) 14.4075 + 3.86048i 0.627600 + 0.168165i
\(528\) 0 0
\(529\) 2.08308 + 1.20267i 0.0905687 + 0.0522899i
\(530\) 0 0
\(531\) 0.930359i 0.0403742i
\(532\) 0 0
\(533\) −0.530105 0.530105i −0.0229614 0.0229614i
\(534\) 0 0
\(535\) 32.7753 5.62772i 1.41700 0.243308i
\(536\) 0 0
\(537\) −2.02232 + 7.54741i −0.0872696 + 0.325695i
\(538\) 0 0
\(539\) −24.0094 14.9432i −1.03416 0.643648i
\(540\) 0 0
\(541\) −18.4994 32.0420i −0.795353 1.37759i −0.922615 0.385722i \(-0.873952\pi\)
0.127262 0.991869i \(-0.459381\pi\)
\(542\) 0 0
\(543\) 13.6528 3.65827i 0.585899 0.156991i
\(544\) 0 0
\(545\) 29.4616 + 2.71076i 1.26200 + 0.116116i
\(546\) 0 0
\(547\) 20.0765 20.0765i 0.858409 0.858409i −0.132742 0.991151i \(-0.542378\pi\)
0.991151 + 0.132742i \(0.0423781\pi\)
\(548\) 0 0
\(549\) 3.76360 6.51875i 0.160627 0.278213i
\(550\) 0 0
\(551\) −38.4582 + 22.2039i −1.63838 + 0.945916i
\(552\) 0 0
\(553\) −12.9136 3.69043i −0.549141 0.156933i
\(554\) 0 0
\(555\) −8.75286 18.9925i −0.371538 0.806187i
\(556\) 0 0
\(557\) −6.65499 24.8367i −0.281981 1.05237i −0.951017 0.309137i \(-0.899960\pi\)
0.669037 0.743229i \(-0.266707\pi\)
\(558\) 0 0
\(559\) 2.03974 0.0862718
\(560\) 0 0
\(561\) −16.6605 −0.703408
\(562\) 0 0
\(563\) −1.38907 5.18407i −0.0585422 0.218482i 0.930458 0.366400i \(-0.119410\pi\)
−0.989000 + 0.147917i \(0.952743\pi\)
\(564\) 0 0
\(565\) −28.9352 10.6788i −1.21731 0.449258i
\(566\) 0 0
\(567\) 28.4377 7.11728i 1.19427 0.298898i
\(568\) 0 0
\(569\) 22.0839 12.7502i 0.925806 0.534514i 0.0403234 0.999187i \(-0.487161\pi\)
0.885483 + 0.464672i \(0.153828\pi\)
\(570\) 0 0
\(571\) 7.95235 13.7739i 0.332795 0.576419i −0.650263 0.759709i \(-0.725341\pi\)
0.983059 + 0.183290i \(0.0586748\pi\)
\(572\) 0 0
\(573\) 6.39672 6.39672i 0.267227 0.267227i
\(574\) 0 0
\(575\) 12.8476 + 18.7031i 0.535781 + 0.779973i
\(576\) 0 0
\(577\) −22.2641 + 5.96565i −0.926867 + 0.248353i −0.690518 0.723315i \(-0.742617\pi\)
−0.236349 + 0.971668i \(0.575951\pi\)
\(578\) 0 0
\(579\) −20.2934 35.1493i −0.843366 1.46075i
\(580\) 0 0
\(581\) −14.4173 0.238779i −0.598132 0.00990621i
\(582\) 0 0
\(583\) 8.66048 32.3214i 0.358681 1.33861i
\(584\) 0 0
\(585\) −0.119246 0.694478i −0.00493022 0.0287131i
\(586\) 0 0
\(587\) −28.2277 28.2277i −1.16508 1.16508i −0.983348 0.181734i \(-0.941829\pi\)
−0.181734 0.983348i \(-0.558171\pi\)
\(588\) 0 0
\(589\) 45.3622i 1.86912i
\(590\) 0 0
\(591\) 19.4355 + 11.2211i 0.799471 + 0.461575i
\(592\) 0 0
\(593\) −34.2220 9.16977i −1.40533 0.376557i −0.525075 0.851056i \(-0.675963\pi\)
−0.880256 + 0.474499i \(0.842629\pi\)
\(594\) 0 0
\(595\) −11.9965 1.30447i −0.491811 0.0534782i
\(596\) 0 0
\(597\) −21.0953 5.65247i −0.863373 0.231340i
\(598\) 0 0
\(599\) −14.5339 8.39115i −0.593839 0.342853i 0.172775 0.984961i \(-0.444727\pi\)
−0.766614 + 0.642108i \(0.778060\pi\)
\(600\) 0 0
\(601\) 1.73528i 0.0707833i 0.999374 + 0.0353917i \(0.0112679\pi\)
−0.999374 + 0.0353917i \(0.988732\pi\)
\(602\) 0 0
\(603\) −2.42925 2.42925i −0.0989266 0.0989266i
\(604\) 0 0
\(605\) 9.71637 + 6.86862i 0.395027 + 0.279249i
\(606\) 0 0
\(607\) −10.2070 + 38.0930i −0.414288 + 1.54615i 0.371968 + 0.928245i \(0.378683\pi\)
−0.786257 + 0.617900i \(0.787984\pi\)
\(608\) 0 0
\(609\) −32.8410 19.6930i −1.33079 0.798000i
\(610\) 0 0
\(611\) −0.0456517 0.0790711i −0.00184687 0.00319887i
\(612\) 0 0
\(613\) −0.330293 + 0.0885018i −0.0133404 + 0.00357455i −0.265483 0.964116i \(-0.585531\pi\)
0.252143 + 0.967690i \(0.418865\pi\)
\(614\) 0 0
\(615\) 8.99444 7.47875i 0.362691 0.301572i
\(616\) 0 0
\(617\) 11.1876 11.1876i 0.450397 0.450397i −0.445089 0.895486i \(-0.646828\pi\)
0.895486 + 0.445089i \(0.146828\pi\)
\(618\) 0 0
\(619\) −18.2682 + 31.6414i −0.734260 + 1.27178i 0.220787 + 0.975322i \(0.429138\pi\)
−0.955047 + 0.296454i \(0.904196\pi\)
\(620\) 0 0
\(621\) 15.1956 8.77316i 0.609777 0.352055i
\(622\) 0 0
\(623\) −2.23356 + 7.81566i −0.0894855 + 0.313128i
\(624\) 0 0
\(625\) −3.89884 24.6941i −0.155953 0.987764i
\(626\) 0 0
\(627\) 13.1140 + 48.9421i 0.523723 + 1.95456i
\(628\) 0 0
\(629\) 9.43535 0.376212
\(630\) 0 0
\(631\) 35.8189 1.42593 0.712964 0.701201i \(-0.247352\pi\)
0.712964 + 0.701201i \(0.247352\pi\)
\(632\) 0 0
\(633\) 3.95888 + 14.7747i 0.157351 + 0.587243i
\(634\) 0 0
\(635\) −2.40856 + 6.52623i −0.0955807 + 0.258986i
\(636\) 0 0
\(637\) 1.38585 + 1.48083i 0.0549093 + 0.0586726i
\(638\) 0 0
\(639\) 6.70867 3.87325i 0.265391 0.153223i
\(640\) 0 0
\(641\) 7.16573 12.4114i 0.283029 0.490221i −0.689100 0.724666i \(-0.741994\pi\)
0.972129 + 0.234445i \(0.0753272\pi\)
\(642\) 0 0
\(643\) −7.65201 + 7.65201i −0.301766 + 0.301766i −0.841704 0.539939i \(-0.818447\pi\)
0.539939 + 0.841704i \(0.318447\pi\)
\(644\) 0 0
\(645\) −2.91605 + 31.6928i −0.114819 + 1.24790i
\(646\) 0 0
\(647\) −31.2468 + 8.37254i −1.22844 + 0.329159i −0.813971 0.580906i \(-0.802698\pi\)
−0.414466 + 0.910065i \(0.636032\pi\)
\(648\) 0 0
\(649\) −1.72791 2.99282i −0.0678262 0.117478i
\(650\) 0 0
\(651\) 34.1947 18.9943i 1.34019 0.744447i
\(652\) 0 0
\(653\) −0.132578 + 0.494788i −0.00518818 + 0.0193625i −0.968471 0.249125i \(-0.919857\pi\)
0.963283 + 0.268487i \(0.0865237\pi\)
\(654\) 0 0
\(655\) −9.42093 + 13.3269i −0.368106 + 0.520724i
\(656\) 0 0
\(657\) 8.86417 + 8.86417i 0.345824 + 0.345824i
\(658\) 0 0
\(659\) 19.5542i 0.761723i 0.924632 + 0.380862i \(0.124373\pi\)
−0.924632 + 0.380862i \(0.875627\pi\)
\(660\) 0 0
\(661\) 34.0324 + 19.6486i 1.32371 + 0.764242i 0.984318 0.176405i \(-0.0564468\pi\)
0.339388 + 0.940647i \(0.389780\pi\)
\(662\) 0 0
\(663\) 1.15414 + 0.309250i 0.0448230 + 0.0120103i
\(664\) 0 0
\(665\) 5.61080 + 36.2679i 0.217578 + 1.40641i
\(666\) 0 0
\(667\) −31.3801 8.40828i −1.21504 0.325570i
\(668\) 0 0
\(669\) 23.1579 + 13.3702i 0.895337 + 0.516923i
\(670\) 0 0
\(671\) 27.9597i 1.07937i
\(672\) 0 0
\(673\) 18.4813 + 18.4813i 0.712401 + 0.712401i 0.967037 0.254636i \(-0.0819556\pi\)
−0.254636 + 0.967037i \(0.581956\pi\)
\(674\) 0 0
\(675\) −19.2729 + 1.51208i −0.741812 + 0.0582002i
\(676\) 0 0
\(677\) −10.6631 + 39.7951i −0.409815 + 1.52945i 0.385183 + 0.922840i \(0.374138\pi\)
−0.794999 + 0.606611i \(0.792528\pi\)
\(678\) 0 0
\(679\) −0.410862 + 24.8076i −0.0157674 + 0.952030i
\(680\) 0 0
\(681\) 16.3702 + 28.3541i 0.627309 + 1.08653i
\(682\) 0 0
\(683\) −8.81689 + 2.36248i −0.337369 + 0.0903978i −0.423526 0.905884i \(-0.639208\pi\)
0.0861573 + 0.996282i \(0.472541\pi\)
\(684\) 0 0
\(685\) −10.2631 12.3431i −0.392134 0.471607i
\(686\) 0 0
\(687\) 16.8358 16.8358i 0.642325 0.642325i
\(688\) 0 0
\(689\) −1.19989 + 2.07827i −0.0457121 + 0.0791758i
\(690\) 0 0
\(691\) 41.9971 24.2470i 1.59765 0.922401i 0.605706 0.795689i \(-0.292891\pi\)
0.991940 0.126712i \(-0.0404424\pi\)
\(692\) 0 0
\(693\) −8.35538 + 8.08313i −0.317395 + 0.307053i
\(694\) 0 0
\(695\) 25.2166 11.6213i 0.956520 0.440821i
\(696\) 0 0
\(697\) 1.36598 + 5.09790i 0.0517401 + 0.193097i
\(698\) 0 0
\(699\) 11.5732 0.437739
\(700\) 0 0
\(701\) −30.8898 −1.16669 −0.583347 0.812223i \(-0.698257\pi\)
−0.583347 + 0.812223i \(0.698257\pi\)
\(702\) 0 0
\(703\) −7.42684 27.7173i −0.280109 1.04538i
\(704\) 0 0
\(705\) 1.29385 0.596280i 0.0487290 0.0224572i
\(706\) 0 0
\(707\) 6.35191 + 25.3796i 0.238888 + 0.954496i
\(708\) 0 0
\(709\) −12.7354 + 7.35277i −0.478287 + 0.276139i −0.719702 0.694283i \(-0.755722\pi\)
0.241416 + 0.970422i \(0.422388\pi\)
\(710\) 0 0
\(711\) −2.76054 + 4.78140i −0.103528 + 0.179316i
\(712\) 0 0
\(713\) 23.4656 23.4656i 0.878795 0.878795i
\(714\) 0 0
\(715\) −1.67341 2.01256i −0.0625821 0.0752654i
\(716\) 0 0
\(717\) 16.2831 4.36306i 0.608105 0.162941i
\(718\) 0 0
\(719\) −11.7360 20.3273i −0.437679 0.758082i 0.559831 0.828607i \(-0.310866\pi\)
−0.997510 + 0.0705247i \(0.977533\pi\)
\(720\) 0 0
\(721\) 5.50134 + 9.90382i 0.204881 + 0.368837i
\(722\) 0 0
\(723\) 1.55119 5.78913i 0.0576895 0.215300i
\(724\) 0 0
\(725\) 27.2119 + 23.2526i 1.01062 + 0.863581i
\(726\) 0 0
\(727\) 14.1380 + 14.1380i 0.524349 + 0.524349i 0.918882 0.394533i \(-0.129093\pi\)
−0.394533 + 0.918882i \(0.629093\pi\)
\(728\) 0 0
\(729\) 11.4004i 0.422236i
\(730\) 0 0
\(731\) −12.4359 7.17986i −0.459958 0.265557i
\(732\) 0 0
\(733\) −26.7908 7.17859i −0.989543 0.265147i −0.272484 0.962160i \(-0.587845\pi\)
−0.717058 + 0.697013i \(0.754512\pi\)
\(734\) 0 0
\(735\) −24.9899 + 19.4158i −0.921765 + 0.716164i
\(736\) 0 0
\(737\) −12.3262 3.30280i −0.454042 0.121660i
\(738\) 0 0
\(739\) 11.7451 + 6.78102i 0.432050 + 0.249444i 0.700219 0.713928i \(-0.253085\pi\)
−0.268170 + 0.963372i \(0.586419\pi\)
\(740\) 0 0
\(741\) 3.63383i 0.133492i
\(742\) 0 0
\(743\) −13.5961 13.5961i −0.498791 0.498791i 0.412270 0.911062i \(-0.364736\pi\)
−0.911062 + 0.412270i \(0.864736\pi\)
\(744\) 0 0
\(745\) −30.9115 + 43.7275i −1.13251 + 1.60205i
\(746\) 0 0
\(747\) −1.53416 + 5.72557i −0.0561320 + 0.209488i
\(748\) 0 0
\(749\) 19.1069 + 34.3973i 0.698152 + 1.25685i
\(750\) 0 0
\(751\) 21.8309 + 37.8123i 0.796622 + 1.37979i 0.921804 + 0.387656i \(0.126715\pi\)
−0.125182 + 0.992134i \(0.539951\pi\)
\(752\) 0 0
\(753\) 31.5979 8.46663i 1.15149 0.308541i
\(754\) 0 0
\(755\) 0.725941 7.88981i 0.0264197 0.287140i
\(756\) 0 0
\(757\) 7.88896 7.88896i 0.286729 0.286729i −0.549056 0.835785i \(-0.685013\pi\)
0.835785 + 0.549056i \(0.185013\pi\)
\(758\) 0 0
\(759\) −18.5337 + 32.1013i −0.672730 + 1.16520i
\(760\) 0 0
\(761\) −1.70923 + 0.986825i −0.0619596 + 0.0357724i −0.530660 0.847585i \(-0.678056\pi\)
0.468700 + 0.883357i \(0.344722\pi\)
\(762\) 0 0
\(763\) 8.49921 + 33.9593i 0.307692 + 1.22941i
\(764\) 0 0
\(765\) −1.71753 + 4.65384i −0.0620976 + 0.168260i
\(766\) 0 0
\(767\) 0.0641463 + 0.239397i 0.00231619 + 0.00864413i
\(768\) 0 0
\(769\) −17.4914 −0.630756 −0.315378 0.948966i \(-0.602131\pi\)
−0.315378 + 0.948966i \(0.602131\pi\)
\(770\) 0 0
\(771\) 11.7763 0.424112
\(772\) 0 0
\(773\) 11.5736 + 43.1933i 0.416274 + 1.55355i 0.782271 + 0.622939i \(0.214061\pi\)
−0.365997 + 0.930616i \(0.619272\pi\)
\(774\) 0 0
\(775\) −34.4686 + 12.1965i −1.23815 + 0.438112i
\(776\) 0 0
\(777\) 17.7839 17.2044i 0.637994 0.617205i
\(778\) 0 0
\(779\) 13.9004 8.02542i 0.498035 0.287540i
\(780\) 0 0
\(781\) 14.3871 24.9193i 0.514813 0.891682i
\(782\) 0 0
\(783\) 19.5716 19.5716i 0.699433 0.699433i
\(784\) 0 0
\(785\) 10.5268 8.75286i 0.375717 0.312403i
\(786\) 0 0
\(787\) −25.0643 + 6.71595i −0.893445 + 0.239398i −0.676199 0.736719i \(-0.736374\pi\)
−0.217246 + 0.976117i \(0.569707\pi\)
\(788\) 0 0
\(789\) −1.75605 3.04156i −0.0625170 0.108283i
\(790\) 0 0
\(791\) 0.604323 36.4887i 0.0214873 1.29739i
\(792\) 0 0
\(793\) −0.518984 + 1.93688i −0.0184297 + 0.0687805i