Properties

Label 1680.2.cz.d.97.4
Level 1680
Weight 2
Character 1680.97
Analytic conductor 13.415
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.cz (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.4
Root \(-1.40927 + 0.118126i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 1680.97
Dual form 1680.2.cz.d.433.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{3} +(2.23450 + 0.0836010i) q^{5} +(2.64501 + 0.0627175i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{3} +(2.23450 + 0.0836010i) q^{5} +(2.64501 + 0.0627175i) q^{7} +1.00000i q^{9} -3.98602 q^{11} +(0.500437 + 0.500437i) q^{13} +(-1.52092 - 1.63915i) q^{15} +(-1.67840 + 1.67840i) q^{17} +7.21850 q^{19} +(-1.82596 - 1.91465i) q^{21} +(5.16007 - 5.16007i) q^{23} +(4.98602 + 0.373614i) q^{25} +(0.707107 - 0.707107i) q^{27} -3.65191i q^{29} +4.93821i q^{31} +(2.81854 + 2.81854i) q^{33} +(5.90504 + 0.361268i) q^{35} +(0.292275 + 0.292275i) q^{37} -0.707725i q^{39} +7.63184i q^{41} +(-3.65191 + 3.65191i) q^{43} +(-0.0836010 + 2.23450i) q^{45} +(0.305303 - 0.305303i) q^{47} +(6.99213 + 0.331777i) q^{49} +2.37361 q^{51} +(5.39653 - 5.39653i) q^{53} +(-8.90678 - 0.333235i) q^{55} +(-5.10425 - 5.10425i) q^{57} -6.10959 q^{59} -7.11047i q^{61} +(-0.0627175 + 2.64501i) q^{63} +(1.07639 + 1.16007i) q^{65} +(-0.944185 - 0.944185i) q^{67} -7.29744 q^{69} -1.19297 q^{71} +(1.38298 + 1.38298i) q^{73} +(-3.26147 - 3.78983i) q^{75} +(-10.5431 - 0.249993i) q^{77} -8.64027i q^{79} -1.00000 q^{81} +(11.9895 + 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +(-2.58229 + 2.58229i) q^{87} +7.82581 q^{89} +(1.29227 + 1.35505i) q^{91} +(3.49184 - 3.49184i) q^{93} +(16.1298 + 0.603474i) q^{95} +(7.43671 - 7.43671i) q^{97} -3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 0 0
\(5\) 2.23450 + 0.0836010i 0.999301 + 0.0373875i
\(6\) 0 0
\(7\) 2.64501 + 0.0627175i 0.999719 + 0.0237050i
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −3.98602 −1.20183 −0.600915 0.799313i \(-0.705197\pi\)
−0.600915 + 0.799313i \(0.705197\pi\)
\(12\) 0 0
\(13\) 0.500437 + 0.500437i 0.138796 + 0.138796i 0.773091 0.634295i \(-0.218709\pi\)
−0.634295 + 0.773091i \(0.718709\pi\)
\(14\) 0 0
\(15\) −1.52092 1.63915i −0.392699 0.423226i
\(16\) 0 0
\(17\) −1.67840 + 1.67840i −0.407071 + 0.407071i −0.880716 0.473645i \(-0.842938\pi\)
0.473645 + 0.880716i \(0.342938\pi\)
\(18\) 0 0
\(19\) 7.21850 1.65604 0.828019 0.560700i \(-0.189468\pi\)
0.828019 + 0.560700i \(0.189468\pi\)
\(20\) 0 0
\(21\) −1.82596 1.91465i −0.398456 0.417811i
\(22\) 0 0
\(23\) 5.16007 5.16007i 1.07595 1.07595i 0.0790800 0.996868i \(-0.474802\pi\)
0.996868 0.0790800i \(-0.0251983\pi\)
\(24\) 0 0
\(25\) 4.98602 + 0.373614i 0.997204 + 0.0747227i
\(26\) 0 0
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0 0
\(29\) 3.65191i 0.678143i −0.940761 0.339071i \(-0.889887\pi\)
0.940761 0.339071i \(-0.110113\pi\)
\(30\) 0 0
\(31\) 4.93821i 0.886929i 0.896292 + 0.443465i \(0.146251\pi\)
−0.896292 + 0.443465i \(0.853749\pi\)
\(32\) 0 0
\(33\) 2.81854 + 2.81854i 0.490645 + 0.490645i
\(34\) 0 0
\(35\) 5.90504 + 0.361268i 0.998134 + 0.0610654i
\(36\) 0 0
\(37\) 0.292275 + 0.292275i 0.0480497 + 0.0480497i 0.730723 0.682674i \(-0.239183\pi\)
−0.682674 + 0.730723i \(0.739183\pi\)
\(38\) 0 0
\(39\) 0.707725i 0.113327i
\(40\) 0 0
\(41\) 7.63184i 1.19189i 0.803024 + 0.595947i \(0.203223\pi\)
−0.803024 + 0.595947i \(0.796777\pi\)
\(42\) 0 0
\(43\) −3.65191 + 3.65191i −0.556911 + 0.556911i −0.928427 0.371516i \(-0.878838\pi\)
0.371516 + 0.928427i \(0.378838\pi\)
\(44\) 0 0
\(45\) −0.0836010 + 2.23450i −0.0124625 + 0.333100i
\(46\) 0 0
\(47\) 0.305303 0.305303i 0.0445331 0.0445331i −0.684490 0.729023i \(-0.739975\pi\)
0.729023 + 0.684490i \(0.239975\pi\)
\(48\) 0 0
\(49\) 6.99213 + 0.331777i 0.998876 + 0.0473967i
\(50\) 0 0
\(51\) 2.37361 0.332372
\(52\) 0 0
\(53\) 5.39653 5.39653i 0.741270 0.741270i −0.231553 0.972822i \(-0.574381\pi\)
0.972822 + 0.231553i \(0.0743805\pi\)
\(54\) 0 0
\(55\) −8.90678 0.333235i −1.20099 0.0449335i
\(56\) 0 0
\(57\) −5.10425 5.10425i −0.676075 0.676075i
\(58\) 0 0
\(59\) −6.10959 −0.795401 −0.397701 0.917515i \(-0.630192\pi\)
−0.397701 + 0.917515i \(0.630192\pi\)
\(60\) 0 0
\(61\) 7.11047i 0.910402i −0.890389 0.455201i \(-0.849567\pi\)
0.890389 0.455201i \(-0.150433\pi\)
\(62\) 0 0
\(63\) −0.0627175 + 2.64501i −0.00790166 + 0.333240i
\(64\) 0 0
\(65\) 1.07639 + 1.16007i 0.133510 + 0.143889i
\(66\) 0 0
\(67\) −0.944185 0.944185i −0.115351 0.115351i 0.647075 0.762426i \(-0.275992\pi\)
−0.762426 + 0.647075i \(0.775992\pi\)
\(68\) 0 0
\(69\) −7.29744 −0.878508
\(70\) 0 0
\(71\) −1.19297 −0.141579 −0.0707897 0.997491i \(-0.522552\pi\)
−0.0707897 + 0.997491i \(0.522552\pi\)
\(72\) 0 0
\(73\) 1.38298 + 1.38298i 0.161865 + 0.161865i 0.783393 0.621527i \(-0.213487\pi\)
−0.621527 + 0.783393i \(0.713487\pi\)
\(74\) 0 0
\(75\) −3.26147 3.78983i −0.376602 0.437612i
\(76\) 0 0
\(77\) −10.5431 0.249993i −1.20149 0.0284894i
\(78\) 0 0
\(79\) 8.64027i 0.972106i −0.873929 0.486053i \(-0.838436\pi\)
0.873929 0.486053i \(-0.161564\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) 11.9895 + 11.9895i 1.31602 + 1.31602i 0.916898 + 0.399122i \(0.130685\pi\)
0.399122 + 0.916898i \(0.369315\pi\)
\(84\) 0 0
\(85\) −3.89070 + 3.61007i −0.422006 + 0.391567i
\(86\) 0 0
\(87\) −2.58229 + 2.58229i −0.276851 + 0.276851i
\(88\) 0 0
\(89\) 7.82581 0.829534 0.414767 0.909928i \(-0.363863\pi\)
0.414767 + 0.909928i \(0.363863\pi\)
\(90\) 0 0
\(91\) 1.29227 + 1.35505i 0.135467 + 0.142048i
\(92\) 0 0
\(93\) 3.49184 3.49184i 0.362087 0.362087i
\(94\) 0 0
\(95\) 16.1298 + 0.603474i 1.65488 + 0.0619151i
\(96\) 0 0
\(97\) 7.43671 7.43671i 0.755083 0.755083i −0.220340 0.975423i \(-0.570717\pi\)
0.975423 + 0.220340i \(0.0707167\pi\)
\(98\) 0 0
\(99\) 3.98602i 0.400610i
\(100\) 0 0
\(101\) 6.31633i 0.628498i −0.949341 0.314249i \(-0.898247\pi\)
0.949341 0.314249i \(-0.101753\pi\)
\(102\) 0 0
\(103\) 12.5410 + 12.5410i 1.23570 + 1.23570i 0.961743 + 0.273954i \(0.0883316\pi\)
0.273954 + 0.961743i \(0.411668\pi\)
\(104\) 0 0
\(105\) −3.92004 4.43095i −0.382557 0.432416i
\(106\) 0 0
\(107\) −7.48020 7.48020i −0.723138 0.723138i 0.246105 0.969243i \(-0.420849\pi\)
−0.969243 + 0.246105i \(0.920849\pi\)
\(108\) 0 0
\(109\) 0.668223i 0.0640042i 0.999488 + 0.0320021i \(0.0101883\pi\)
−0.999488 + 0.0320021i \(0.989812\pi\)
\(110\) 0 0
\(111\) 0.413339i 0.0392324i
\(112\) 0 0
\(113\) −3.39653 + 3.39653i −0.319518 + 0.319518i −0.848582 0.529064i \(-0.822543\pi\)
0.529064 + 0.848582i \(0.322543\pi\)
\(114\) 0 0
\(115\) 11.9616 11.0988i 1.11542 1.03497i
\(116\) 0 0
\(117\) −0.500437 + 0.500437i −0.0462655 + 0.0462655i
\(118\) 0 0
\(119\) −4.54464 + 4.33411i −0.416607 + 0.397307i
\(120\) 0 0
\(121\) 4.88837 0.444397
\(122\) 0 0
\(123\) 5.39653 5.39653i 0.486588 0.486588i
\(124\) 0 0
\(125\) 11.1101 + 1.25168i 0.993713 + 0.111953i
\(126\) 0 0
\(127\) 5.88837 + 5.88837i 0.522508 + 0.522508i 0.918328 0.395820i \(-0.129540\pi\)
−0.395820 + 0.918328i \(0.629540\pi\)
\(128\) 0 0
\(129\) 5.16458 0.454716
\(130\) 0 0
\(131\) 18.8144i 1.64383i −0.569613 0.821913i \(-0.692907\pi\)
0.569613 0.821913i \(-0.307093\pi\)
\(132\) 0 0
\(133\) 19.0930 + 0.452726i 1.65557 + 0.0392564i
\(134\) 0 0
\(135\) 1.63915 1.52092i 0.141075 0.130900i
\(136\) 0 0
\(137\) −0.811977 0.811977i −0.0693719 0.0693719i 0.671570 0.740941i \(-0.265620\pi\)
−0.740941 + 0.671570i \(0.765620\pi\)
\(138\) 0 0
\(139\) 0.442439 0.0375272 0.0187636 0.999824i \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) 0 0
\(141\) −0.431764 −0.0363611
\(142\) 0 0
\(143\) −1.99475 1.99475i −0.166810 0.166810i
\(144\) 0 0
\(145\) 0.305303 8.16021i 0.0253541 0.677669i
\(146\) 0 0
\(147\) −4.70958 5.17879i −0.388440 0.427139i
\(148\) 0 0
\(149\) 3.14114i 0.257332i −0.991688 0.128666i \(-0.958930\pi\)
0.991688 0.128666i \(-0.0410696\pi\)
\(150\) 0 0
\(151\) 14.7239 1.19822 0.599109 0.800668i \(-0.295522\pi\)
0.599109 + 0.800668i \(0.295522\pi\)
\(152\) 0 0
\(153\) −1.67840 1.67840i −0.135690 0.135690i
\(154\) 0 0
\(155\) −0.412839 + 11.0345i −0.0331601 + 0.886309i
\(156\) 0 0
\(157\) −7.96508 + 7.96508i −0.635682 + 0.635682i −0.949487 0.313805i \(-0.898396\pi\)
0.313805 + 0.949487i \(0.398396\pi\)
\(158\) 0 0
\(159\) −7.63184 −0.605244
\(160\) 0 0
\(161\) 13.9720 13.3248i 1.10115 1.05014i
\(162\) 0 0
\(163\) −10.4450 + 10.4450i −0.818113 + 0.818113i −0.985834 0.167722i \(-0.946359\pi\)
0.167722 + 0.985834i \(0.446359\pi\)
\(164\) 0 0
\(165\) 6.06241 + 6.53368i 0.471958 + 0.508646i
\(166\) 0 0
\(167\) −4.63621 + 4.63621i −0.358761 + 0.358761i −0.863356 0.504595i \(-0.831642\pi\)
0.504595 + 0.863356i \(0.331642\pi\)
\(168\) 0 0
\(169\) 12.4991i 0.961471i
\(170\) 0 0
\(171\) 7.21850i 0.552013i
\(172\) 0 0
\(173\) −2.48531 2.48531i −0.188954 0.188954i 0.606290 0.795244i \(-0.292657\pi\)
−0.795244 + 0.606290i \(0.792657\pi\)
\(174\) 0 0
\(175\) 13.1646 + 1.30092i 0.995153 + 0.0983404i
\(176\) 0 0
\(177\) 4.32013 + 4.32013i 0.324721 + 0.324721i
\(178\) 0 0
\(179\) 22.1109i 1.65264i −0.563199 0.826321i \(-0.690430\pi\)
0.563199 0.826321i \(-0.309570\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 0 0
\(183\) −5.02786 + 5.02786i −0.371670 + 0.371670i
\(184\) 0 0
\(185\) 0.628655 + 0.677524i 0.0462196 + 0.0498125i
\(186\) 0 0
\(187\) 6.69013 6.69013i 0.489231 0.489231i
\(188\) 0 0
\(189\) 1.91465 1.82596i 0.139270 0.132819i
\(190\) 0 0
\(191\) −15.2898 −1.10633 −0.553167 0.833070i \(-0.686581\pi\)
−0.553167 + 0.833070i \(0.686581\pi\)
\(192\) 0 0
\(193\) −8.92787 + 8.92787i −0.642642 + 0.642642i −0.951204 0.308562i \(-0.900152\pi\)
0.308562 + 0.951204i \(0.400152\pi\)
\(194\) 0 0
\(195\) 0.0591665 1.58142i 0.00423700 0.113248i
\(196\) 0 0
\(197\) −2.68715 2.68715i −0.191451 0.191451i 0.604872 0.796323i \(-0.293224\pi\)
−0.796323 + 0.604872i \(0.793224\pi\)
\(198\) 0 0
\(199\) −0.616637 −0.0437122 −0.0218561 0.999761i \(-0.506958\pi\)
−0.0218561 + 0.999761i \(0.506958\pi\)
\(200\) 0 0
\(201\) 1.33528i 0.0941833i
\(202\) 0 0
\(203\) 0.229039 9.65933i 0.0160754 0.677952i
\(204\) 0 0
\(205\) −0.638029 + 17.0534i −0.0445619 + 1.19106i
\(206\) 0 0
\(207\) 5.16007 + 5.16007i 0.358649 + 0.358649i
\(208\) 0 0
\(209\) −28.7731 −1.99028
\(210\) 0 0
\(211\) −9.30849 −0.640823 −0.320411 0.947278i \(-0.603821\pi\)
−0.320411 + 0.947278i \(0.603821\pi\)
\(212\) 0 0
\(213\) 0.843557 + 0.843557i 0.0577996 + 0.0577996i
\(214\) 0 0
\(215\) −8.46551 + 7.85491i −0.577343 + 0.535700i
\(216\) 0 0
\(217\) −0.309712 + 13.0616i −0.0210246 + 0.886680i
\(218\) 0 0
\(219\) 1.95583i 0.132163i
\(220\) 0 0
\(221\) −1.67987 −0.113000
\(222\) 0 0
\(223\) 1.35505 + 1.35505i 0.0907407 + 0.0907407i 0.751020 0.660279i \(-0.229562\pi\)
−0.660279 + 0.751020i \(0.729562\pi\)
\(224\) 0 0
\(225\) −0.373614 + 4.98602i −0.0249076 + 0.332401i
\(226\) 0 0
\(227\) −4.15437 + 4.15437i −0.275735 + 0.275735i −0.831404 0.555668i \(-0.812462\pi\)
0.555668 + 0.831404i \(0.312462\pi\)
\(228\) 0 0
\(229\) 12.9900 0.858403 0.429202 0.903209i \(-0.358795\pi\)
0.429202 + 0.903209i \(0.358795\pi\)
\(230\) 0 0
\(231\) 7.27830 + 7.63184i 0.478877 + 0.502138i
\(232\) 0 0
\(233\) −16.4639 + 16.4639i −1.07859 + 1.07859i −0.0819485 + 0.996637i \(0.526114\pi\)
−0.996637 + 0.0819485i \(0.973886\pi\)
\(234\) 0 0
\(235\) 0.707725 0.656678i 0.0461669 0.0428370i
\(236\) 0 0
\(237\) −6.10959 + 6.10959i −0.396861 + 0.396861i
\(238\) 0 0
\(239\) 5.48048i 0.354503i −0.984166 0.177251i \(-0.943279\pi\)
0.984166 0.177251i \(-0.0567205\pi\)
\(240\) 0 0
\(241\) 14.6507i 0.943737i −0.881669 0.471868i \(-0.843580\pi\)
0.881669 0.471868i \(-0.156420\pi\)
\(242\) 0 0
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 15.5962 + 1.32591i 0.996406 + 0.0847090i
\(246\) 0 0
\(247\) 3.61241 + 3.61241i 0.229852 + 0.229852i
\(248\) 0 0
\(249\) 16.9557i 1.07453i
\(250\) 0 0
\(251\) 21.1506i 1.33501i −0.744604 0.667507i \(-0.767361\pi\)
0.744604 0.667507i \(-0.232639\pi\)
\(252\) 0 0
\(253\) −20.5681 + 20.5681i −1.29311 + 1.29311i
\(254\) 0 0
\(255\) 5.30385 + 0.198436i 0.332140 + 0.0124266i
\(256\) 0 0
\(257\) −9.39248 + 9.39248i −0.585887 + 0.585887i −0.936515 0.350628i \(-0.885968\pi\)
0.350628 + 0.936515i \(0.385968\pi\)
\(258\) 0 0
\(259\) 0.754738 + 0.791399i 0.0468971 + 0.0491752i
\(260\) 0 0
\(261\) 3.65191 0.226048
\(262\) 0 0
\(263\) −15.3779 + 15.3779i −0.948241 + 0.948241i −0.998725 0.0504843i \(-0.983924\pi\)
0.0504843 + 0.998725i \(0.483924\pi\)
\(264\) 0 0
\(265\) 12.5097 11.6074i 0.768466 0.713037i
\(266\) 0 0
\(267\) −5.53368 5.53368i −0.338656 0.338656i
\(268\) 0 0
\(269\) −22.9851 −1.40143 −0.700714 0.713442i \(-0.747135\pi\)
−0.700714 + 0.713442i \(0.747135\pi\)
\(270\) 0 0
\(271\) 15.7596i 0.957330i −0.877998 0.478665i \(-0.841121\pi\)
0.877998 0.478665i \(-0.158879\pi\)
\(272\) 0 0
\(273\) 0.0443868 1.87194i 0.00268641 0.113295i
\(274\) 0 0
\(275\) −19.8744 1.48923i −1.19847 0.0898041i
\(276\) 0 0
\(277\) 4.80771 + 4.80771i 0.288867 + 0.288867i 0.836632 0.547765i \(-0.184521\pi\)
−0.547765 + 0.836632i \(0.684521\pi\)
\(278\) 0 0
\(279\) −4.93821 −0.295643
\(280\) 0 0
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) 0 0
\(283\) −14.9095 14.9095i −0.886278 0.886278i 0.107885 0.994163i \(-0.465592\pi\)
−0.994163 + 0.107885i \(0.965592\pi\)
\(284\) 0 0
\(285\) −10.9788 11.8322i −0.650325 0.700879i
\(286\) 0 0
\(287\) −0.478650 + 20.1863i −0.0282538 + 1.19156i
\(288\) 0 0
\(289\) 11.3660i 0.668586i
\(290\) 0 0
\(291\) −10.5171 −0.616523
\(292\) 0 0
\(293\) 4.79236 + 4.79236i 0.279973 + 0.279973i 0.833098 0.553125i \(-0.186565\pi\)
−0.553125 + 0.833098i \(0.686565\pi\)
\(294\) 0 0
\(295\) −13.6519 0.510768i −0.794845 0.0297381i
\(296\) 0 0
\(297\) −2.81854 + 2.81854i −0.163548 + 0.163548i
\(298\) 0 0
\(299\) 5.16458 0.298675
\(300\) 0 0
\(301\) −9.88837 + 9.43029i −0.569956 + 0.543553i
\(302\) 0 0
\(303\) −4.46632 + 4.46632i −0.256583 + 0.256583i
\(304\) 0 0
\(305\) 0.594442 15.8884i 0.0340377 0.909765i
\(306\) 0 0
\(307\) −9.85063 + 9.85063i −0.562205 + 0.562205i −0.929933 0.367728i \(-0.880136\pi\)
0.367728 + 0.929933i \(0.380136\pi\)
\(308\) 0 0
\(309\) 17.7356i 1.00894i
\(310\) 0 0
\(311\) 27.3063i 1.54840i 0.632941 + 0.774200i \(0.281848\pi\)
−0.632941 + 0.774200i \(0.718152\pi\)
\(312\) 0 0
\(313\) 18.5080 + 18.5080i 1.04613 + 1.04613i 0.998883 + 0.0472492i \(0.0150455\pi\)
0.0472492 + 0.998883i \(0.484955\pi\)
\(314\) 0 0
\(315\) −0.361268 + 5.90504i −0.0203551 + 0.332711i
\(316\) 0 0
\(317\) −21.8793 21.8793i −1.22887 1.22887i −0.964393 0.264473i \(-0.914802\pi\)
−0.264473 0.964393i \(-0.585198\pi\)
\(318\) 0 0
\(319\) 14.5566i 0.815013i
\(320\) 0 0
\(321\) 10.5786i 0.590440i
\(322\) 0 0
\(323\) −12.1155 + 12.1155i −0.674126 + 0.674126i
\(324\) 0 0
\(325\) 2.30822 + 2.68216i 0.128037 + 0.148780i
\(326\) 0 0
\(327\) 0.472505 0.472505i 0.0261296 0.0261296i
\(328\) 0 0
\(329\) 0.826678 0.788382i 0.0455762 0.0434649i
\(330\) 0 0
\(331\) 16.6913 0.917438 0.458719 0.888581i \(-0.348309\pi\)
0.458719 + 0.888581i \(0.348309\pi\)
\(332\) 0 0
\(333\) −0.292275 + 0.292275i −0.0160166 + 0.0160166i
\(334\) 0 0
\(335\) −2.03085 2.18872i −0.110957 0.119583i
\(336\) 0 0
\(337\) 2.54028 + 2.54028i 0.138378 + 0.138378i 0.772903 0.634525i \(-0.218804\pi\)
−0.634525 + 0.772903i \(0.718804\pi\)
\(338\) 0 0
\(339\) 4.80341 0.260886
\(340\) 0 0
\(341\) 19.6838i 1.06594i
\(342\) 0 0
\(343\) 18.4734 + 1.31608i 0.997472 + 0.0710617i
\(344\) 0 0
\(345\) −16.3062 0.610073i −0.877894 0.0328452i
\(346\) 0 0
\(347\) −13.6980 13.6980i −0.735348 0.735348i 0.236326 0.971674i \(-0.424057\pi\)
−0.971674 + 0.236326i \(0.924057\pi\)
\(348\) 0 0
\(349\) 0.508601 0.0272248 0.0136124 0.999907i \(-0.495667\pi\)
0.0136124 + 0.999907i \(0.495667\pi\)
\(350\) 0 0
\(351\) 0.707725 0.0377756
\(352\) 0 0
\(353\) 10.9217 + 10.9217i 0.581305 + 0.581305i 0.935262 0.353957i \(-0.115164\pi\)
−0.353957 + 0.935262i \(0.615164\pi\)
\(354\) 0 0
\(355\) −2.66570 0.0997335i −0.141480 0.00529330i
\(356\) 0 0
\(357\) 6.27823 + 0.148867i 0.332279 + 0.00787888i
\(358\) 0 0
\(359\) 15.9860i 0.843710i 0.906663 + 0.421855i \(0.138621\pi\)
−0.906663 + 0.421855i \(0.861379\pi\)
\(360\) 0 0
\(361\) 33.1068 1.74246
\(362\) 0 0
\(363\) −3.45660 3.45660i −0.181424 0.181424i
\(364\) 0 0
\(365\) 2.97465 + 3.20589i 0.155701 + 0.167804i
\(366\) 0 0
\(367\) −0.410036 + 0.410036i −0.0214037 + 0.0214037i −0.717728 0.696324i \(-0.754818\pi\)
0.696324 + 0.717728i \(0.254818\pi\)
\(368\) 0 0
\(369\) −7.63184 −0.397298
\(370\) 0 0
\(371\) 14.6123 13.9354i 0.758633 0.723490i
\(372\) 0 0
\(373\) −3.44496 + 3.44496i −0.178373 + 0.178373i −0.790646 0.612273i \(-0.790255\pi\)
0.612273 + 0.790646i \(0.290255\pi\)
\(374\) 0 0
\(375\) −6.97092 8.74106i −0.359977 0.451387i
\(376\) 0 0
\(377\) 1.82755 1.82755i 0.0941237 0.0941237i
\(378\) 0 0
\(379\) 12.9179i 0.663547i 0.943359 + 0.331773i \(0.107647\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(380\) 0 0
\(381\) 8.32741i 0.426626i
\(382\) 0 0
\(383\) 10.0770 + 10.0770i 0.514910 + 0.514910i 0.916027 0.401117i \(-0.131378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(384\) 0 0
\(385\) −23.5376 1.44002i −1.19959 0.0733903i
\(386\) 0 0
\(387\) −3.65191 3.65191i −0.185637 0.185637i
\(388\) 0 0
\(389\) 24.3300i 1.23358i 0.787127 + 0.616791i \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(390\) 0 0
\(391\) 17.3213i 0.875976i
\(392\) 0 0
\(393\) −13.3038 + 13.3038i −0.671089 + 0.671089i
\(394\) 0 0
\(395\) 0.722335 19.3067i 0.0363446 0.971426i
\(396\) 0 0
\(397\) 6.80633 6.80633i 0.341600 0.341600i −0.515369 0.856969i \(-0.672345\pi\)
0.856969 + 0.515369i \(0.172345\pi\)
\(398\) 0 0
\(399\) −13.1807 13.8209i −0.659858 0.691911i
\(400\) 0 0
\(401\) −8.83090 −0.440994 −0.220497 0.975388i \(-0.570768\pi\)
−0.220497 + 0.975388i \(0.570768\pi\)
\(402\) 0 0
\(403\) −2.47127 + 2.47127i −0.123103 + 0.123103i
\(404\) 0 0
\(405\) −2.23450 0.0836010i −0.111033 0.00415417i
\(406\) 0 0
\(407\) −1.16501 1.16501i −0.0577476 0.0577476i
\(408\) 0 0
\(409\) −23.1985 −1.14709 −0.573546 0.819174i \(-0.694432\pi\)
−0.573546 + 0.819174i \(0.694432\pi\)
\(410\) 0 0
\(411\) 1.14831i 0.0566419i
\(412\) 0 0
\(413\) −16.1599 0.383178i −0.795178 0.0188550i
\(414\) 0 0
\(415\) 25.7883 + 27.7930i 1.26590 + 1.36430i
\(416\) 0 0
\(417\) −0.312852 0.312852i −0.0153204 0.0153204i
\(418\) 0 0
\(419\) −13.0393 −0.637009 −0.318505 0.947921i \(-0.603181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(420\) 0 0
\(421\) −31.3549 −1.52814 −0.764071 0.645132i \(-0.776802\pi\)
−0.764071 + 0.645132i \(0.776802\pi\)
\(422\) 0 0
\(423\) 0.305303 + 0.305303i 0.0148444 + 0.0148444i
\(424\) 0 0
\(425\) −8.99560 + 7.74146i −0.436351 + 0.375516i
\(426\) 0 0
\(427\) 0.445951 18.8072i 0.0215811 0.910146i
\(428\) 0 0
\(429\) 2.82101i 0.136200i
\(430\) 0 0
\(431\) 22.5558 1.08648 0.543238 0.839579i \(-0.317198\pi\)
0.543238 + 0.839579i \(0.317198\pi\)
\(432\) 0 0
\(433\) −19.9639 19.9639i −0.959405 0.959405i 0.0398028 0.999208i \(-0.487327\pi\)
−0.999208 + 0.0398028i \(0.987327\pi\)
\(434\) 0 0
\(435\) −5.98602 + 5.55426i −0.287008 + 0.266306i
\(436\) 0 0
\(437\) 37.2479 37.2479i 1.78181 1.78181i
\(438\) 0 0
\(439\) −30.1943 −1.44110 −0.720548 0.693405i \(-0.756110\pi\)
−0.720548 + 0.693405i \(0.756110\pi\)
\(440\) 0 0
\(441\) −0.331777 + 6.99213i −0.0157989 + 0.332959i
\(442\) 0 0
\(443\) 12.7423 12.7423i 0.605404 0.605404i −0.336337 0.941742i \(-0.609188\pi\)
0.941742 + 0.336337i \(0.109188\pi\)
\(444\) 0 0
\(445\) 17.4868 + 0.654245i 0.828954 + 0.0310142i
\(446\) 0 0
\(447\) −2.22112 + 2.22112i −0.105056 + 0.105056i
\(448\) 0 0
\(449\) 30.4170i 1.43547i 0.696318 + 0.717734i \(0.254820\pi\)
−0.696318 + 0.717734i \(0.745180\pi\)
\(450\) 0 0
\(451\) 30.4207i 1.43245i
\(452\) 0 0
\(453\) −10.4114 10.4114i −0.489170 0.489170i
\(454\) 0 0
\(455\) 2.77431 + 3.13589i 0.130062 + 0.147013i
\(456\) 0 0
\(457\) 1.31546 + 1.31546i 0.0615348 + 0.0615348i 0.737204 0.675670i \(-0.236145\pi\)
−0.675670 + 0.737204i \(0.736145\pi\)
\(458\) 0 0
\(459\) 2.37361i 0.110791i
\(460\) 0 0
\(461\) 1.29957i 0.0605272i −0.999542 0.0302636i \(-0.990365\pi\)
0.999542 0.0302636i \(-0.00963467\pi\)
\(462\) 0 0
\(463\) −16.5240 + 16.5240i −0.767934 + 0.767934i −0.977742 0.209809i \(-0.932716\pi\)
0.209809 + 0.977742i \(0.432716\pi\)
\(464\) 0 0
\(465\) 8.09446 7.51062i 0.375372 0.348297i
\(466\) 0 0
\(467\) −20.1009 + 20.1009i −0.930157 + 0.930157i −0.997715 0.0675588i \(-0.978479\pi\)
0.0675588 + 0.997715i \(0.478479\pi\)
\(468\) 0 0
\(469\) −2.43816 2.55659i −0.112584 0.118052i
\(470\) 0 0
\(471\) 11.2643 0.519032
\(472\) 0 0
\(473\) 14.5566 14.5566i 0.669313 0.669313i
\(474\) 0 0
\(475\) 35.9916 + 2.69693i 1.65141 + 0.123744i
\(476\) 0 0
\(477\) 5.39653 + 5.39653i 0.247090 + 0.247090i
\(478\) 0 0
\(479\) 11.0836 0.506425 0.253212 0.967411i \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(480\) 0 0
\(481\) 0.292530i 0.0133382i
\(482\) 0 0
\(483\) −19.3018 0.457677i −0.878261 0.0208250i
\(484\) 0 0
\(485\) 17.2391 15.9956i 0.782786 0.726325i
\(486\) 0 0
\(487\) 13.6519 + 13.6519i 0.618627 + 0.618627i 0.945179 0.326552i \(-0.105887\pi\)
−0.326552 + 0.945179i \(0.605887\pi\)
\(488\) 0 0
\(489\) 14.7714 0.667986
\(490\) 0 0
\(491\) −32.1155 −1.44935 −0.724677 0.689089i \(-0.758011\pi\)
−0.724677 + 0.689089i \(0.758011\pi\)
\(492\) 0 0
\(493\) 6.12936 + 6.12936i 0.276052 + 0.276052i
\(494\) 0 0
\(495\) 0.333235 8.90678i 0.0149778 0.400330i
\(496\) 0 0
\(497\) −3.15541 0.0748201i −0.141540 0.00335614i
\(498\) 0 0
\(499\) 4.27431i 0.191344i −0.995413 0.0956722i \(-0.969500\pi\)
0.995413 0.0956722i \(-0.0305000\pi\)
\(500\) 0 0
\(501\) 6.55659 0.292927
\(502\) 0 0
\(503\) −17.5637 17.5637i −0.783128 0.783128i 0.197229 0.980357i \(-0.436806\pi\)
−0.980357 + 0.197229i \(0.936806\pi\)
\(504\) 0 0
\(505\) 0.528051 14.1139i 0.0234980 0.628059i
\(506\) 0 0
\(507\) −8.83822 + 8.83822i −0.392519 + 0.392519i
\(508\) 0 0
\(509\) −27.9162 −1.23736 −0.618682 0.785641i \(-0.712333\pi\)
−0.618682 + 0.785641i \(0.712333\pi\)
\(510\) 0 0
\(511\) 3.57125 + 3.74473i 0.157983 + 0.165657i
\(512\) 0 0
\(513\) 5.10425 5.10425i 0.225358 0.225358i
\(514\) 0 0
\(515\) 26.9744 + 29.0713i 1.18863 + 1.28103i
\(516\) 0 0
\(517\) −1.21695 + 1.21695i −0.0535212 + 0.0535212i
\(518\) 0 0
\(519\) 3.51476i 0.154281i
\(520\) 0 0
\(521\) 28.8647i 1.26458i 0.774730 + 0.632292i \(0.217886\pi\)
−0.774730 + 0.632292i \(0.782114\pi\)
\(522\) 0 0
\(523\) 3.54707 + 3.54707i 0.155103 + 0.155103i 0.780392 0.625290i \(-0.215019\pi\)
−0.625290 + 0.780392i \(0.715019\pi\)
\(524\) 0 0
\(525\) −8.38891 10.2287i −0.366122 0.446417i
\(526\) 0 0
\(527\) −8.28829 8.28829i −0.361043 0.361043i
\(528\) 0 0
\(529\) 30.2526i 1.31533i
\(530\) 0 0
\(531\) 6.10959i 0.265134i
\(532\) 0 0
\(533\) −3.81926 + 3.81926i −0.165430 + 0.165430i
\(534\) 0 0
\(535\) −16.0892 17.3399i −0.695596 0.749669i
\(536\) 0 0
\(537\) −15.6347 + 15.6347i −0.674688 + 0.674688i
\(538\) 0 0
\(539\) −27.8708 1.32247i −1.20048 0.0569628i
\(540\) 0 0
\(541\) −4.08698 −0.175713 −0.0878565 0.996133i \(-0.528002\pi\)
−0.0878565 + 0.996133i \(0.528002\pi\)
\(542\) 0 0
\(543\) 6.00000 6.00000i 0.257485 0.257485i
\(544\) 0 0
\(545\) −0.0558641 + 1.49315i −0.00239296 + 0.0639594i
\(546\) 0 0
\(547\) −28.2200 28.2200i −1.20660 1.20660i −0.972121 0.234482i \(-0.924661\pi\)
−0.234482 0.972121i \(-0.575339\pi\)
\(548\) 0 0
\(549\) 7.11047 0.303467
\(550\) 0 0
\(551\) 26.3613i 1.12303i
\(552\) 0 0
\(553\) 0.541896 22.8536i 0.0230438 0.971833i
\(554\) 0 0
\(555\) 0.0345555 0.923607i 0.00146680 0.0392050i
\(556\) 0 0
\(557\) 28.1616 + 28.1616i 1.19325 + 1.19325i 0.976150 + 0.217096i \(0.0696584\pi\)
0.217096 + 0.976150i \(0.430342\pi\)
\(558\) 0 0
\(559\) −3.65510 −0.154594
\(560\) 0 0
\(561\) −9.46128 −0.399455
\(562\) 0 0
\(563\) 27.3645 + 27.3645i 1.15328 + 1.15328i 0.985891 + 0.167386i \(0.0535326\pi\)
0.167386 + 0.985891i \(0.446467\pi\)
\(564\) 0 0
\(565\) −7.87351 + 7.30560i −0.331241 + 0.307349i
\(566\) 0 0
\(567\) −2.64501 0.0627175i −0.111080 0.00263389i
\(568\) 0 0
\(569\) 17.7767i 0.745240i −0.927984 0.372620i \(-0.878460\pi\)
0.927984 0.372620i \(-0.121540\pi\)
\(570\) 0 0
\(571\) 16.8866 0.706683 0.353342 0.935494i \(-0.385045\pi\)
0.353342 + 0.935494i \(0.385045\pi\)
\(572\) 0 0
\(573\) 10.8116 + 10.8116i 0.451659 + 0.451659i
\(574\) 0 0
\(575\) 27.6561 23.8003i 1.15334 0.992543i
\(576\) 0 0
\(577\) 3.89677 3.89677i 0.162225 0.162225i −0.621327 0.783552i \(-0.713406\pi\)
0.783552 + 0.621327i \(0.213406\pi\)
\(578\) 0 0
\(579\) 12.6259 0.524715
\(580\) 0 0
\(581\) 30.9604 + 32.4643i 1.28445 + 1.34685i
\(582\) 0 0
\(583\) −21.5107 + 21.5107i −0.890881 + 0.890881i
\(584\) 0 0
\(585\) −1.16007 + 1.07639i −0.0479629 + 0.0445034i
\(586\) 0 0
\(587\) 15.1058 15.1058i 0.623484 0.623484i −0.322937 0.946420i \(-0.604670\pi\)
0.946420 + 0.322937i \(0.104670\pi\)
\(588\) 0 0
\(589\) 35.6465i 1.46879i
\(590\) 0 0
\(591\) 3.80020i 0.156319i
\(592\) 0 0
\(593\) −3.43032 3.43032i −0.140866 0.140866i 0.633157 0.774023i \(-0.281759\pi\)
−0.774023 + 0.633157i \(0.781759\pi\)
\(594\) 0 0
\(595\) −10.5174 + 9.30466i −0.431170 + 0.381454i
\(596\) 0 0
\(597\) 0.436028 + 0.436028i 0.0178454 + 0.0178454i
\(598\) 0 0
\(599\) 10.1010i 0.412714i −0.978477 0.206357i \(-0.933839\pi\)
0.978477 0.206357i \(-0.0661608\pi\)
\(600\) 0 0
\(601\) 38.4063i 1.56663i −0.621628 0.783313i \(-0.713528\pi\)
0.621628 0.783313i \(-0.286472\pi\)
\(602\) 0 0
\(603\) 0.944185 0.944185i 0.0384502 0.0384502i
\(604\) 0 0
\(605\) 10.9231 + 0.408673i 0.444087 + 0.0166149i
\(606\) 0 0
\(607\) −10.2931 + 10.2931i −0.417783 + 0.417783i −0.884439 0.466656i \(-0.845459\pi\)
0.466656 + 0.884439i \(0.345459\pi\)
\(608\) 0 0
\(609\) −6.99213 + 6.66822i −0.283336 + 0.270210i
\(610\) 0 0
\(611\) 0.305570 0.0123621
\(612\) 0 0
\(613\) −14.4155 + 14.4155i −0.582235 + 0.582235i −0.935517 0.353282i \(-0.885066\pi\)
0.353282 + 0.935517i \(0.385066\pi\)
\(614\) 0 0
\(615\) 12.5097 11.6074i 0.504440 0.468056i
\(616\) 0 0
\(617\) −25.4196 25.4196i −1.02336 1.02336i −0.999721 0.0236346i \(-0.992476\pi\)
−0.0236346 0.999721i \(-0.507524\pi\)
\(618\) 0 0
\(619\) 11.1991 0.450129 0.225064 0.974344i \(-0.427741\pi\)
0.225064 + 0.974344i \(0.427741\pi\)
\(620\) 0 0
\(621\) 7.29744i 0.292836i
\(622\) 0 0
\(623\) 20.6993 + 0.490815i 0.829301 + 0.0196641i
\(624\) 0 0
\(625\) 24.7208 + 3.72569i 0.988833 + 0.149028i
\(626\) 0 0
\(627\) 20.3457 + 20.3457i 0.812527 + 0.812527i
\(628\) 0 0
\(629\) −0.981107 −0.0391193
\(630\) 0 0
\(631\) −21.2015 −0.844020 −0.422010 0.906591i \(-0.638675\pi\)
−0.422010 + 0.906591i \(0.638675\pi\)
\(632\) 0 0
\(633\) 6.58210 + 6.58210i 0.261615 + 0.261615i
\(634\) 0 0
\(635\) 12.6653 + 13.6499i 0.502608 + 0.541678i
\(636\) 0 0
\(637\) 3.33309 + 3.66516i 0.132062 + 0.145219i
\(638\) 0 0
\(639\) 1.19297i 0.0471931i
\(640\) 0 0
\(641\) −29.8969 −1.18086 −0.590428 0.807090i \(-0.701041\pi\)
−0.590428 + 0.807090i \(0.701041\pi\)
\(642\) 0 0
\(643\) −11.2813 11.2813i −0.444891 0.444891i 0.448761 0.893652i \(-0.351866\pi\)
−0.893652 + 0.448761i \(0.851866\pi\)
\(644\) 0 0
\(645\) 11.5403 + 0.431764i 0.454398 + 0.0170007i
\(646\) 0 0
\(647\) 26.2395 26.2395i 1.03158 1.03158i 0.0320982 0.999485i \(-0.489781\pi\)
0.999485 0.0320982i \(-0.0102189\pi\)
\(648\) 0 0
\(649\) 24.3530 0.955937
\(650\) 0 0
\(651\) 9.45495 9.01695i 0.370569 0.353402i
\(652\) 0 0
\(653\) −1.97641 + 1.97641i −0.0773427 + 0.0773427i −0.744720 0.667377i \(-0.767417\pi\)
0.667377 + 0.744720i \(0.267417\pi\)
\(654\) 0 0
\(655\) 1.57291 42.0410i 0.0614585 1.64268i
\(656\) 0 0
\(657\) −1.38298 + 1.38298i −0.0539552 + 0.0539552i
\(658\) 0 0
\(659\) 15.1044i 0.588385i 0.955746 + 0.294193i \(0.0950507\pi\)
−0.955746 + 0.294193i \(0.904949\pi\)
\(660\) 0 0
\(661\) 1.10054i 0.0428062i −0.999771 0.0214031i \(-0.993187\pi\)
0.999771 0.0214031i \(-0.00681333\pi\)
\(662\) 0 0
\(663\) 1.18785 + 1.18785i 0.0461321 + 0.0461321i
\(664\) 0 0
\(665\) 42.6255 + 2.60781i 1.65295 + 0.101127i
\(666\) 0 0
\(667\) −18.8441 18.8441i −0.729646 0.729646i
\(668\) 0 0
\(669\) 1.91633i 0.0740894i
\(670\) 0 0
\(671\) 28.3425i 1.09415i
\(672\) 0 0
\(673\) −11.4381 + 11.4381i −0.440906 + 0.440906i −0.892316 0.451411i \(-0.850921\pi\)
0.451411 + 0.892316i \(0.350921\pi\)
\(674\) 0 0
\(675\) 3.78983 3.26147i 0.145871 0.125534i
\(676\) 0 0
\(677\) −24.6007 + 24.6007i −0.945481 + 0.945481i −0.998589 0.0531077i \(-0.983087\pi\)
0.0531077 + 0.998589i \(0.483087\pi\)
\(678\) 0 0
\(679\) 20.1366 19.2037i 0.772770 0.736972i
\(680\) 0 0
\(681\) 5.87517 0.225137
\(682\) 0 0
\(683\) 13.8654 13.8654i 0.530543 0.530543i −0.390191 0.920734i \(-0.627591\pi\)
0.920734 + 0.390191i \(0.127591\pi\)
\(684\) 0 0
\(685\) −1.74648 1.88225i −0.0667297 0.0719170i
\(686\) 0 0
\(687\) −9.18531 9.18531i −0.350442 0.350442i
\(688\) 0 0
\(689\) 5.40125 0.205771
\(690\) 0 0
\(691\) 12.4060i 0.471947i 0.971759 + 0.235974i \(0.0758279\pi\)
−0.971759 + 0.235974i \(0.924172\pi\)
\(692\) 0 0
\(693\) 0.249993 10.5431i 0.00949646 0.400498i
\(694\) 0 0
\(695\) 0.988633 + 0.0369884i 0.0375010 + 0.00140305i
\(696\) 0 0
\(697\) −12.8093 12.8093i −0.485186 0.485186i
\(698\) 0 0
\(699\) 23.2835 0.880661
\(700\) 0 0
\(701\) 1.45193 0.0548388 0.0274194 0.999624i \(-0.491271\pi\)
0.0274194 + 0.999624i \(0.491271\pi\)
\(702\) 0 0
\(703\) 2.10979 + 2.10979i 0.0795720 + 0.0795720i
\(704\) 0 0
\(705\) −0.964779 0.0360959i −0.0363357 0.00135945i
\(706\) 0 0
\(707\) 0.396144 16.7067i 0.0148985 0.628322i
\(708\) 0 0
\(709\) 48.5284i 1.82252i −0.411827 0.911262i \(-0.635109\pi\)
0.411827 0.911262i \(-0.364891\pi\)
\(710\) 0 0
\(711\) 8.64027 0.324035
\(712\) 0 0
\(713\) 25.4815 + 25.4815i 0.954290 + 0.954290i
\(714\) 0 0
\(715\) −4.29052 4.62405i −0.160457 0.172930i
\(716\) 0 0
\(717\) −3.87528 + 3.87528i −0.144725 + 0.144725i
\(718\) 0 0
\(719\) −43.5872 −1.62553 −0.812764 0.582593i \(-0.802038\pi\)
−0.812764 + 0.582593i \(0.802038\pi\)
\(720\) 0 0
\(721\) 32.3844 + 33.9575i 1.20606 + 1.26464i
\(722\) 0 0
\(723\) −10.3596 + 10.3596i −0.385279 + 0.385279i
\(724\) 0 0
\(725\) 1.36440 18.2085i 0.0506727 0.676247i
\(726\) 0 0
\(727\) −10.4498 + 10.4498i −0.387563 + 0.387563i −0.873817 0.486254i \(-0.838363\pi\)
0.486254 + 0.873817i \(0.338363\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 12.2587i 0.453405i
\(732\) 0 0
\(733\) 18.8687 + 18.8687i 0.696933 + 0.696933i 0.963748 0.266815i \(-0.0859712\pi\)
−0.266815 + 0.963748i \(0.585971\pi\)
\(734\) 0 0
\(735\) −10.0906 11.9657i −0.372199 0.441363i
\(736\) 0 0
\(737\) 3.76354 + 3.76354i 0.138632 + 0.138632i
\(738\) 0 0
\(739\) 20.9689i 0.771354i −0.922634 0.385677i \(-0.873968\pi\)
0.922634 0.385677i \(-0.126032\pi\)
\(740\) 0 0
\(741\) 5.10872i 0.187673i
\(742\) 0 0
\(743\) −9.18724 + 9.18724i −0.337047 + 0.337047i −0.855255 0.518208i \(-0.826599\pi\)
0.518208 + 0.855255i \(0.326599\pi\)
\(744\) 0 0
\(745\) 0.262603 7.01890i 0.00962102 0.257152i
\(746\) 0 0
\(747\) −11.9895 + 11.9895i −0.438673 + 0.438673i
\(748\) 0 0
\(749\) −19.3160 20.2543i −0.705793 0.740077i
\(750\) 0 0
\(751\) −11.1969 −0.408579 −0.204290 0.978910i \(-0.565488\pi\)
−0.204290 + 0.978910i \(0.565488\pi\)
\(752\) 0 0
\(753\) −14.9557 + 14.9557i −0.545017 + 0.545017i
\(754\) 0 0
\(755\) 32.9007 + 1.23094i 1.19738 + 0.0447984i
\(756\) 0 0
\(757\) −13.9324 13.9324i −0.506383 0.506383i 0.407031 0.913414i \(-0.366564\pi\)
−0.913414 + 0.407031i \(0.866564\pi\)
\(758\) 0 0
\(759\) 29.0877 1.05582
\(760\) 0 0
\(761\) 8.78825i 0.318574i −0.987232 0.159287i \(-0.949081\pi\)
0.987232 0.159287i \(-0.0509195\pi\)
\(762\) 0 0
\(763\) −0.0419093 + 1.76746i −0.00151722 + 0.0639862i
\(764\) 0 0
\(765\) −3.61007 3.89070i −0.130522 0.140669i
\(766\) 0 0
\(767\) −3.05747 3.05747i −0.110399 0.110399i
\(768\) 0 0
\(769\) −11.2183 −0.404543 −0.202271 0.979330i \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(770\) 0 0
\(771\) 13.2830 0.478374
\(772\) 0 0
\(773\) 21.5065 + 21.5065i 0.773535 + 0.773535i 0.978723 0.205188i \(-0.0657806\pi\)
−0.205188 + 0.978723i \(0.565781\pi\)
\(774\) 0 0
\(775\) −1.84498 + 24.6220i −0.0662738 + 0.884450i
\(776\) 0 0
\(777\) 0.0259236 1.09328i 0.000930003 0.0392214i
\(778\) 0 0
\(779\) 55.0905i 1.97382i
\(780\) 0 0
\(781\) 4.75520 0.170155
\(782\) 0 0
\(783\) −2.58229 2.58229i −0.0922835 0.0922835i
\(784\) 0 0
\(785\) −18.4639 + 17.1321i −0.659004 + 0.611471i
\(786\) 0 0
\(787\) −37.4673 + 37.4673i −1.33557 + 1.33557i −0.435262 + 0.900304i \(0.643344\pi\)
−0.900304 + 0.435262i \(0.856656\pi\)
\(788\) 0 0
\(789\) 21.7476 0.774235
\(790\) 0 0
\(791\) −9.19686 + 8.77082i −0.327003 + 0.311854i