Properties

Label 1078.2.i.d.1011.7
Level $1078$
Weight $2$
Character 1078.1011
Analytic conductor $8.608$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1011.7
Character \(\chi\) \(=\) 1078.1011
Dual form 1078.2.i.d.901.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.77675 - 1.02581i) q^{5} +0.765367 q^{6} +1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(-1.02581 + 1.77675i) q^{10} +(0.649042 + 3.25250i) q^{11} +(-0.662827 + 0.382683i) q^{12} -6.59694 q^{13} -1.57024 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.80554 + 3.12729i) q^{17} +(2.09077 + 1.20711i) q^{18} +(-0.439269 - 0.760837i) q^{19} -2.05161i q^{20} +(-2.18834 - 2.49222i) q^{22} +(-3.30966 - 5.73249i) q^{23} +(0.382683 - 0.662827i) q^{24} +(-0.395443 + 0.684927i) q^{25} +(5.71311 - 3.29847i) q^{26} +4.14386i q^{27} +6.18955i q^{29} +(1.35986 - 0.785118i) q^{30} +(-5.61510 - 3.24188i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.814474 - 2.40422i) q^{33} -3.61108i q^{34} -2.41421 q^{36} +(5.52454 + 9.56878i) q^{37} +(0.760837 + 0.439269i) q^{38} +(4.37263 + 2.52454i) q^{39} +(1.02581 + 1.77675i) q^{40} +2.36864 q^{41} +7.81288i q^{43} +(3.14127 + 1.06416i) q^{44} +(-4.28945 - 2.47652i) q^{45} +(5.73249 + 3.30966i) q^{46} +(4.97716 - 2.87357i) q^{47} +0.765367i q^{48} -0.790886i q^{50} +(2.39352 - 1.38190i) q^{51} +(-3.29847 + 5.71311i) q^{52} +(-0.214882 + 0.372186i) q^{53} +(-2.07193 - 3.58869i) q^{54} +(4.48962 + 5.11308i) q^{55} +0.672404i q^{57} +(-3.09477 - 5.36031i) q^{58} +(-2.78725 - 1.60922i) q^{59} +(-0.785118 + 1.35986i) q^{60} +(-5.66711 - 9.81572i) q^{61} +6.48376 q^{62} -1.00000 q^{64} +(-11.7211 + 6.76718i) q^{65} +(0.496755 + 2.48935i) q^{66} +(-1.48123 + 2.56556i) q^{67} +(1.80554 + 3.12729i) q^{68} +5.06620i q^{69} -2.13403 q^{71} +(2.09077 - 1.20711i) q^{72} +(-5.41262 + 9.37493i) q^{73} +(-9.56878 - 5.52454i) q^{74} +(0.524221 - 0.302659i) q^{75} -0.878539 q^{76} -5.04908 q^{78} +(7.34847 - 4.24264i) q^{79} +(-1.77675 - 1.02581i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(-2.05130 + 1.18432i) q^{82} -12.3153 q^{83} +7.40854i q^{85} +(-3.90644 - 6.76615i) q^{86} +(2.36864 - 4.10260i) q^{87} +(-3.25250 + 0.649042i) q^{88} +(-5.82684 + 3.36413i) q^{89} +4.95303 q^{90} -6.61931 q^{92} +(2.48123 + 4.29762i) q^{93} +(-2.87357 + 4.97716i) q^{94} +(-1.56094 - 0.901211i) q^{95} +(-0.382683 - 0.662827i) q^{96} -9.23880i q^{97} +(6.01676 - 5.28311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.662827 0.382683i −0.382683 0.220942i 0.296302 0.955094i \(-0.404247\pi\)
−0.678985 + 0.734152i \(0.737580\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.77675 1.02581i 0.794586 0.458755i −0.0469885 0.998895i \(-0.514962\pi\)
0.841575 + 0.540141i \(0.181629\pi\)
\(6\) 0.765367 0.312460
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.20711 2.09077i −0.402369 0.696923i
\(10\) −1.02581 + 1.77675i −0.324388 + 0.561857i
\(11\) 0.649042 + 3.25250i 0.195694 + 0.980665i
\(12\) −0.662827 + 0.382683i −0.191342 + 0.110471i
\(13\) −6.59694 −1.82966 −0.914830 0.403838i \(-0.867676\pi\)
−0.914830 + 0.403838i \(0.867676\pi\)
\(14\) 0 0
\(15\) −1.57024 −0.405433
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.80554 + 3.12729i −0.437908 + 0.758478i −0.997528 0.0702708i \(-0.977614\pi\)
0.559620 + 0.828749i \(0.310947\pi\)
\(18\) 2.09077 + 1.20711i 0.492799 + 0.284518i
\(19\) −0.439269 0.760837i −0.100775 0.174548i 0.811229 0.584729i \(-0.198799\pi\)
−0.912004 + 0.410181i \(0.865466\pi\)
\(20\) 2.05161i 0.458755i
\(21\) 0 0
\(22\) −2.18834 2.49222i −0.466555 0.531344i
\(23\) −3.30966 5.73249i −0.690111 1.19531i −0.971801 0.235802i \(-0.924228\pi\)
0.281690 0.959505i \(-0.409105\pi\)
\(24\) 0.382683 0.662827i 0.0781149 0.135299i
\(25\) −0.395443 + 0.684927i −0.0790886 + 0.136985i
\(26\) 5.71311 3.29847i 1.12043 0.646883i
\(27\) 4.14386i 0.797486i
\(28\) 0 0
\(29\) 6.18955i 1.14937i 0.818375 + 0.574685i \(0.194876\pi\)
−0.818375 + 0.574685i \(0.805124\pi\)
\(30\) 1.35986 0.785118i 0.248276 0.143342i
\(31\) −5.61510 3.24188i −1.00850 0.582259i −0.0977497 0.995211i \(-0.531164\pi\)
−0.910753 + 0.412952i \(0.864498\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.814474 2.40422i 0.141782 0.418521i
\(34\) 3.61108i 0.619295i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) 5.52454 + 9.56878i 0.908229 + 1.57310i 0.816524 + 0.577312i \(0.195898\pi\)
0.0917046 + 0.995786i \(0.470768\pi\)
\(38\) 0.760837 + 0.439269i 0.123424 + 0.0712589i
\(39\) 4.37263 + 2.52454i 0.700181 + 0.404250i
\(40\) 1.02581 + 1.77675i 0.162194 + 0.280929i
\(41\) 2.36864 0.369919 0.184960 0.982746i \(-0.440785\pi\)
0.184960 + 0.982746i \(0.440785\pi\)
\(42\) 0 0
\(43\) 7.81288i 1.19145i 0.803188 + 0.595726i \(0.203136\pi\)
−0.803188 + 0.595726i \(0.796864\pi\)
\(44\) 3.14127 + 1.06416i 0.473564 + 0.160428i
\(45\) −4.28945 2.47652i −0.639434 0.369177i
\(46\) 5.73249 + 3.30966i 0.845210 + 0.487982i
\(47\) 4.97716 2.87357i 0.725994 0.419153i −0.0909611 0.995854i \(-0.528994\pi\)
0.816955 + 0.576702i \(0.195661\pi\)
\(48\) 0.765367i 0.110471i
\(49\) 0 0
\(50\) 0.790886i 0.111848i
\(51\) 2.39352 1.38190i 0.335160 0.193505i
\(52\) −3.29847 + 5.71311i −0.457415 + 0.792266i
\(53\) −0.214882 + 0.372186i −0.0295163 + 0.0511237i −0.880406 0.474220i \(-0.842730\pi\)
0.850890 + 0.525344i \(0.176063\pi\)
\(54\) −2.07193 3.58869i −0.281954 0.488359i
\(55\) 4.48962 + 5.11308i 0.605380 + 0.689448i
\(56\) 0 0
\(57\) 0.672404i 0.0890621i
\(58\) −3.09477 5.36031i −0.406364 0.703843i
\(59\) −2.78725 1.60922i −0.362870 0.209503i 0.307469 0.951558i \(-0.400518\pi\)
−0.670339 + 0.742055i \(0.733851\pi\)
\(60\) −0.785118 + 1.35986i −0.101358 + 0.175558i
\(61\) −5.66711 9.81572i −0.725599 1.25677i −0.958727 0.284328i \(-0.908230\pi\)
0.233129 0.972446i \(-0.425104\pi\)
\(62\) 6.48376 0.823439
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −11.7211 + 6.76718i −1.45382 + 0.839365i
\(66\) 0.496755 + 2.48935i 0.0611464 + 0.306418i
\(67\) −1.48123 + 2.56556i −0.180961 + 0.313434i −0.942208 0.335028i \(-0.891254\pi\)
0.761247 + 0.648462i \(0.224587\pi\)
\(68\) 1.80554 + 3.12729i 0.218954 + 0.379239i
\(69\) 5.06620i 0.609899i
\(70\) 0 0
\(71\) −2.13403 −0.253263 −0.126631 0.991950i \(-0.540417\pi\)
−0.126631 + 0.991950i \(0.540417\pi\)
\(72\) 2.09077 1.20711i 0.246400 0.142259i
\(73\) −5.41262 + 9.37493i −0.633499 + 1.09725i 0.353332 + 0.935498i \(0.385049\pi\)
−0.986831 + 0.161754i \(0.948285\pi\)
\(74\) −9.56878 5.52454i −1.11235 0.642215i
\(75\) 0.524221 0.302659i 0.0605318 0.0349480i
\(76\) −0.878539 −0.100775
\(77\) 0 0
\(78\) −5.04908 −0.571695
\(79\) 7.34847 4.24264i 0.826767 0.477334i −0.0259772 0.999663i \(-0.508270\pi\)
0.852745 + 0.522328i \(0.174936\pi\)
\(80\) −1.77675 1.02581i −0.198647 0.114689i
\(81\) −2.03553 + 3.52565i −0.226170 + 0.391739i
\(82\) −2.05130 + 1.18432i −0.226528 + 0.130786i
\(83\) −12.3153 −1.35178 −0.675892 0.737001i \(-0.736241\pi\)
−0.675892 + 0.737001i \(0.736241\pi\)
\(84\) 0 0
\(85\) 7.40854i 0.803569i
\(86\) −3.90644 6.76615i −0.421242 0.729613i
\(87\) 2.36864 4.10260i 0.253945 0.439845i
\(88\) −3.25250 + 0.649042i −0.346717 + 0.0691881i
\(89\) −5.82684 + 3.36413i −0.617644 + 0.356597i −0.775951 0.630793i \(-0.782730\pi\)
0.158307 + 0.987390i \(0.449396\pi\)
\(90\) 4.95303 0.522095
\(91\) 0 0
\(92\) −6.61931 −0.690111
\(93\) 2.48123 + 4.29762i 0.257291 + 0.445642i
\(94\) −2.87357 + 4.97716i −0.296386 + 0.513355i
\(95\) −1.56094 0.901211i −0.160149 0.0924622i
\(96\) −0.382683 0.662827i −0.0390575 0.0676495i
\(97\) 9.23880i 0.938058i −0.883183 0.469029i \(-0.844604\pi\)
0.883183 0.469029i \(-0.155396\pi\)
\(98\) 0 0
\(99\) 6.01676 5.28311i 0.604707 0.530973i
\(100\) 0.395443 + 0.684927i 0.0395443 + 0.0684927i
\(101\) 0.929830 1.61051i 0.0925216 0.160252i −0.816050 0.577981i \(-0.803841\pi\)
0.908572 + 0.417729i \(0.137174\pi\)
\(102\) −1.38190 + 2.39352i −0.136829 + 0.236994i
\(103\) −5.81112 + 3.35505i −0.572587 + 0.330583i −0.758182 0.652043i \(-0.773912\pi\)
0.185595 + 0.982626i \(0.440579\pi\)
\(104\) 6.59694i 0.646883i
\(105\) 0 0
\(106\) 0.429764i 0.0417423i
\(107\) −12.7768 + 7.37667i −1.23518 + 0.713130i −0.968105 0.250547i \(-0.919390\pi\)
−0.267073 + 0.963676i \(0.586056\pi\)
\(108\) 3.58869 + 2.07193i 0.345322 + 0.199372i
\(109\) 5.19615 + 3.00000i 0.497701 + 0.287348i 0.727764 0.685828i \(-0.240560\pi\)
−0.230063 + 0.973176i \(0.573893\pi\)
\(110\) −6.44466 2.18325i −0.614475 0.208165i
\(111\) 8.45660i 0.802665i
\(112\) 0 0
\(113\) −0.597322 −0.0561913 −0.0280956 0.999605i \(-0.508944\pi\)
−0.0280956 + 0.999605i \(0.508944\pi\)
\(114\) −0.336202 0.582319i −0.0314882 0.0545392i
\(115\) −11.7609 6.79013i −1.09671 0.633183i
\(116\) 5.36031 + 3.09477i 0.497692 + 0.287343i
\(117\) 7.96321 + 13.7927i 0.736199 + 1.27513i
\(118\) 3.21844 0.296282
\(119\) 0 0
\(120\) 1.57024i 0.143342i
\(121\) −10.1575 + 4.22202i −0.923408 + 0.383820i
\(122\) 9.81572 + 5.66711i 0.888673 + 0.513076i
\(123\) −1.57000 0.906438i −0.141562 0.0817308i
\(124\) −5.61510 + 3.24188i −0.504251 + 0.291130i
\(125\) 11.8807i 1.06264i
\(126\) 0 0
\(127\) 7.33002i 0.650434i −0.945639 0.325217i \(-0.894563\pi\)
0.945639 0.325217i \(-0.105437\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 2.98986 5.17859i 0.263242 0.455949i
\(130\) 6.76718 11.7211i 0.593521 1.02801i
\(131\) −4.41025 7.63878i −0.385325 0.667403i 0.606489 0.795092i \(-0.292577\pi\)
−0.991814 + 0.127689i \(0.959244\pi\)
\(132\) −1.67488 1.90747i −0.145780 0.166024i
\(133\) 0 0
\(134\) 2.96246i 0.255917i
\(135\) 4.25080 + 7.36260i 0.365850 + 0.633671i
\(136\) −3.12729 1.80554i −0.268163 0.154824i
\(137\) −1.61810 + 2.80263i −0.138244 + 0.239445i −0.926832 0.375477i \(-0.877479\pi\)
0.788588 + 0.614922i \(0.210812\pi\)
\(138\) −2.53310 4.38746i −0.215632 0.373485i
\(139\) 2.47122 0.209606 0.104803 0.994493i \(-0.466579\pi\)
0.104803 + 0.994493i \(0.466579\pi\)
\(140\) 0 0
\(141\) −4.39866 −0.370434
\(142\) 1.84813 1.06702i 0.155091 0.0895420i
\(143\) −4.28169 21.4565i −0.358053 1.79428i
\(144\) −1.20711 + 2.09077i −0.100592 + 0.174231i
\(145\) 6.34928 + 10.9973i 0.527279 + 0.913274i
\(146\) 10.8252i 0.895903i
\(147\) 0 0
\(148\) 11.0491 0.908229
\(149\) 3.38495 1.95430i 0.277306 0.160103i −0.354897 0.934905i \(-0.615484\pi\)
0.632203 + 0.774803i \(0.282151\pi\)
\(150\) −0.302659 + 0.524221i −0.0247120 + 0.0428024i
\(151\) −20.9488 12.0948i −1.70479 0.984259i −0.940760 0.339074i \(-0.889886\pi\)
−0.764027 0.645185i \(-0.776780\pi\)
\(152\) 0.760837 0.439269i 0.0617120 0.0356294i
\(153\) 8.71792 0.704802
\(154\) 0 0
\(155\) −13.3022 −1.06846
\(156\) 4.37263 2.52454i 0.350090 0.202125i
\(157\) 17.5828 + 10.1514i 1.40326 + 0.810172i 0.994726 0.102571i \(-0.0327068\pi\)
0.408534 + 0.912743i \(0.366040\pi\)
\(158\) −4.24264 + 7.34847i −0.337526 + 0.584613i
\(159\) 0.284859 0.164463i 0.0225908 0.0130428i
\(160\) 2.05161 0.162194
\(161\) 0 0
\(162\) 4.07107i 0.319853i
\(163\) 6.63031 + 11.4840i 0.519326 + 0.899499i 0.999748 + 0.0224612i \(0.00715023\pi\)
−0.480422 + 0.877038i \(0.659516\pi\)
\(164\) 1.18432 2.05130i 0.0924798 0.160180i
\(165\) −1.01915 5.10719i −0.0793407 0.397594i
\(166\) 10.6654 6.15767i 0.827795 0.477928i
\(167\) −20.4160 −1.57984 −0.789920 0.613210i \(-0.789878\pi\)
−0.789920 + 0.613210i \(0.789878\pi\)
\(168\) 0 0
\(169\) 30.5196 2.34766
\(170\) −3.70427 6.41598i −0.284104 0.492083i
\(171\) −1.06049 + 1.83682i −0.0810977 + 0.140465i
\(172\) 6.76615 + 3.90644i 0.515914 + 0.297863i
\(173\) −7.78809 13.4894i −0.592117 1.02558i −0.993947 0.109863i \(-0.964959\pi\)
0.401830 0.915714i \(-0.368374\pi\)
\(174\) 4.73728i 0.359132i
\(175\) 0 0
\(176\) 2.49222 2.18834i 0.187859 0.164952i
\(177\) 1.23165 + 2.13327i 0.0925761 + 0.160347i
\(178\) 3.36413 5.82684i 0.252152 0.436740i
\(179\) 2.25080 3.89850i 0.168232 0.291387i −0.769566 0.638567i \(-0.779527\pi\)
0.937798 + 0.347180i \(0.112861\pi\)
\(180\) −4.28945 + 2.47652i −0.319717 + 0.184589i
\(181\) 8.18338i 0.608266i 0.952630 + 0.304133i \(0.0983667\pi\)
−0.952630 + 0.304133i \(0.901633\pi\)
\(182\) 0 0
\(183\) 8.67483i 0.641262i
\(184\) 5.73249 3.30966i 0.422605 0.243991i
\(185\) 19.6314 + 11.3342i 1.44333 + 0.833308i
\(186\) −4.29762 2.48123i −0.315116 0.181933i
\(187\) −11.3434 3.84277i −0.829509 0.281011i
\(188\) 5.74713i 0.419153i
\(189\) 0 0
\(190\) 1.80242 0.130761
\(191\) −5.18311 8.97741i −0.375037 0.649582i 0.615296 0.788296i \(-0.289037\pi\)
−0.990333 + 0.138714i \(0.955703\pi\)
\(192\) 0.662827 + 0.382683i 0.0478354 + 0.0276178i
\(193\) −1.40584 0.811664i −0.101195 0.0584248i 0.448549 0.893758i \(-0.351941\pi\)
−0.549743 + 0.835334i \(0.685274\pi\)
\(194\) 4.61940 + 8.00103i 0.331653 + 0.574441i
\(195\) 10.3587 0.741805
\(196\) 0 0
\(197\) 4.38713i 0.312570i −0.987712 0.156285i \(-0.950048\pi\)
0.987712 0.156285i \(-0.0499518\pi\)
\(198\) −2.56911 + 7.58369i −0.182579 + 0.538949i
\(199\) 17.3760 + 10.0320i 1.23175 + 0.711151i 0.967394 0.253275i \(-0.0815077\pi\)
0.264355 + 0.964426i \(0.414841\pi\)
\(200\) −0.684927 0.395443i −0.0484317 0.0279620i
\(201\) 1.96360 1.13368i 0.138502 0.0799639i
\(202\) 1.85966i 0.130845i
\(203\) 0 0
\(204\) 2.76380i 0.193505i
\(205\) 4.20847 2.42976i 0.293933 0.169702i
\(206\) 3.35505 5.81112i 0.233758 0.404880i
\(207\) −7.99022 + 13.8395i −0.555359 + 0.961909i
\(208\) 3.29847 + 5.71311i 0.228708 + 0.396133i
\(209\) 2.18952 1.92254i 0.151452 0.132985i
\(210\) 0 0
\(211\) 8.56380i 0.589556i −0.955566 0.294778i \(-0.904754\pi\)
0.955566 0.294778i \(-0.0952457\pi\)
\(212\) 0.214882 + 0.372186i 0.0147581 + 0.0255619i
\(213\) 1.41449 + 0.816659i 0.0969195 + 0.0559565i
\(214\) 7.37667 12.7768i 0.504259 0.873402i
\(215\) 8.01450 + 13.8815i 0.546584 + 0.946712i
\(216\) −4.14386 −0.281954
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 7.17526 4.14264i 0.484859 0.279934i
\(220\) 6.67287 1.33158i 0.449885 0.0897753i
\(221\) 11.9110 20.6305i 0.801223 1.38776i
\(222\) 4.22830 + 7.32363i 0.283785 + 0.491530i
\(223\) 8.24084i 0.551848i 0.961180 + 0.275924i \(0.0889837\pi\)
−0.961180 + 0.275924i \(0.911016\pi\)
\(224\) 0 0
\(225\) 1.90937 0.127291
\(226\) 0.517296 0.298661i 0.0344100 0.0198666i
\(227\) 13.7397 23.7979i 0.911938 1.57952i 0.100614 0.994926i \(-0.467919\pi\)
0.811324 0.584597i \(-0.198747\pi\)
\(228\) 0.582319 + 0.336202i 0.0385650 + 0.0222655i
\(229\) 0.0903638 0.0521716i 0.00597141 0.00344759i −0.497011 0.867744i \(-0.665569\pi\)
0.502983 + 0.864296i \(0.332236\pi\)
\(230\) 13.5803 0.895456
\(231\) 0 0
\(232\) −6.18955 −0.406364
\(233\) 13.1269 7.57884i 0.859974 0.496507i −0.00402925 0.999992i \(-0.501283\pi\)
0.864004 + 0.503485i \(0.167949\pi\)
\(234\) −13.7927 7.96321i −0.901656 0.520571i
\(235\) 5.89544 10.2112i 0.384576 0.666106i
\(236\) −2.78725 + 1.60922i −0.181435 + 0.104751i
\(237\) −6.49435 −0.421854
\(238\) 0 0
\(239\) 25.9135i 1.67620i −0.545515 0.838101i \(-0.683666\pi\)
0.545515 0.838101i \(-0.316334\pi\)
\(240\) 0.785118 + 1.35986i 0.0506792 + 0.0877789i
\(241\) −3.65554 + 6.33158i −0.235474 + 0.407853i −0.959410 0.282014i \(-0.908998\pi\)
0.723936 + 0.689867i \(0.242331\pi\)
\(242\) 6.68563 8.73512i 0.429769 0.561515i
\(243\) 13.4645 7.77372i 0.863747 0.498684i
\(244\) −11.3342 −0.725599
\(245\) 0 0
\(246\) 1.81288 0.115585
\(247\) 2.89783 + 5.01919i 0.184385 + 0.319364i
\(248\) 3.24188 5.61510i 0.205860 0.356560i
\(249\) 8.16294 + 4.71287i 0.517305 + 0.298666i
\(250\) −5.94033 10.2889i −0.375699 0.650730i
\(251\) 10.0161i 0.632208i −0.948724 0.316104i \(-0.897625\pi\)
0.948724 0.316104i \(-0.102375\pi\)
\(252\) 0 0
\(253\) 16.4968 14.4853i 1.03715 0.910682i
\(254\) 3.66501 + 6.34799i 0.229963 + 0.398308i
\(255\) 2.83512 4.91058i 0.177542 0.307512i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −15.1654 + 8.75577i −0.945994 + 0.546170i −0.891834 0.452362i \(-0.850581\pi\)
−0.0541598 + 0.998532i \(0.517248\pi\)
\(258\) 5.97972i 0.372281i
\(259\) 0 0
\(260\) 13.5344i 0.839365i
\(261\) 12.9409 7.47145i 0.801023 0.462471i
\(262\) 7.63878 + 4.41025i 0.471925 + 0.272466i
\(263\) −7.34847 4.24264i −0.453126 0.261612i 0.256023 0.966671i \(-0.417588\pi\)
−0.709150 + 0.705058i \(0.750921\pi\)
\(264\) 2.40422 + 0.814474i 0.147970 + 0.0501274i
\(265\) 0.881709i 0.0541629i
\(266\) 0 0
\(267\) 5.14958 0.315149
\(268\) 1.48123 + 2.56556i 0.0904805 + 0.156717i
\(269\) 5.85020 + 3.37761i 0.356693 + 0.205937i 0.667629 0.744494i \(-0.267309\pi\)
−0.310936 + 0.950431i \(0.600643\pi\)
\(270\) −7.36260 4.25080i −0.448073 0.258695i
\(271\) 9.77158 + 16.9249i 0.593581 + 1.02811i 0.993745 + 0.111669i \(0.0356197\pi\)
−0.400164 + 0.916443i \(0.631047\pi\)
\(272\) 3.61108 0.218954
\(273\) 0 0
\(274\) 3.23620i 0.195506i
\(275\) −2.48438 0.841631i −0.149814 0.0507522i
\(276\) 4.38746 + 2.53310i 0.264094 + 0.152475i
\(277\) 23.1011 + 13.3374i 1.38801 + 0.801368i 0.993091 0.117348i \(-0.0374394\pi\)
0.394919 + 0.918716i \(0.370773\pi\)
\(278\) −2.14014 + 1.23561i −0.128357 + 0.0741070i
\(279\) 15.6532i 0.937132i
\(280\) 0 0
\(281\) 20.9533i 1.24997i 0.780636 + 0.624986i \(0.214895\pi\)
−0.780636 + 0.624986i \(0.785105\pi\)
\(282\) 3.80935 2.19933i 0.226844 0.130968i
\(283\) −5.03147 + 8.71476i −0.299090 + 0.518039i −0.975928 0.218093i \(-0.930016\pi\)
0.676838 + 0.736132i \(0.263350\pi\)
\(284\) −1.06702 + 1.84813i −0.0633157 + 0.109666i
\(285\) 0.689757 + 1.19469i 0.0408577 + 0.0707675i
\(286\) 14.4363 + 16.4410i 0.853637 + 0.972180i
\(287\) 0 0
\(288\) 2.41421i 0.142259i
\(289\) 1.98005 + 3.42955i 0.116474 + 0.201738i
\(290\) −10.9973 6.34928i −0.645782 0.372842i
\(291\) −3.53553 + 6.12372i −0.207257 + 0.358979i
\(292\) 5.41262 + 9.37493i 0.316749 + 0.548626i
\(293\) −29.6429 −1.73176 −0.865879 0.500253i \(-0.833240\pi\)
−0.865879 + 0.500253i \(0.833240\pi\)
\(294\) 0 0
\(295\) −6.60300 −0.384442
\(296\) −9.56878 + 5.52454i −0.556174 + 0.321107i
\(297\) −13.4779 + 2.68954i −0.782067 + 0.156063i
\(298\) −1.95430 + 3.38495i −0.113210 + 0.196085i
\(299\) 21.8336 + 37.8169i 1.26267 + 2.18701i
\(300\) 0.605318i 0.0349480i
\(301\) 0 0
\(302\) 24.1895 1.39195
\(303\) −1.23263 + 0.711661i −0.0708129 + 0.0408839i
\(304\) −0.439269 + 0.760837i −0.0251938 + 0.0436370i
\(305\) −20.1380 11.6267i −1.15310 0.665743i
\(306\) −7.54994 + 4.35896i −0.431601 + 0.249185i
\(307\) 16.1877 0.923883 0.461941 0.886910i \(-0.347153\pi\)
0.461941 + 0.886910i \(0.347153\pi\)
\(308\) 0 0
\(309\) 5.13569 0.292159
\(310\) 11.5200 6.65109i 0.654293 0.377756i
\(311\) 1.23529 + 0.713195i 0.0700469 + 0.0404416i 0.534614 0.845096i \(-0.320457\pi\)
−0.464568 + 0.885538i \(0.653790\pi\)
\(312\) −2.52454 + 4.37263i −0.142924 + 0.247551i
\(313\) −9.99982 + 5.77340i −0.565223 + 0.326332i −0.755239 0.655449i \(-0.772479\pi\)
0.190016 + 0.981781i \(0.439146\pi\)
\(314\) −20.3029 −1.14576
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) −15.8620 27.4737i −0.890896 1.54308i −0.838803 0.544435i \(-0.816744\pi\)
−0.0520931 0.998642i \(-0.516589\pi\)
\(318\) −0.164463 + 0.284859i −0.00922265 + 0.0159741i
\(319\) −20.1315 + 4.01728i −1.12715 + 0.224924i
\(320\) −1.77675 + 1.02581i −0.0993233 + 0.0573443i
\(321\) 11.2917 0.630242
\(322\) 0 0
\(323\) 3.17247 0.176521
\(324\) 2.03553 + 3.52565i 0.113085 + 0.195869i
\(325\) 2.60871 4.51842i 0.144705 0.250637i
\(326\) −11.4840 6.63031i −0.636042 0.367219i
\(327\) −2.29610 3.97696i −0.126975 0.219927i
\(328\) 2.36864i 0.130786i
\(329\) 0 0
\(330\) 3.43620 + 3.91338i 0.189157 + 0.215425i
\(331\) −15.9620 27.6469i −0.877348 1.51961i −0.854240 0.519879i \(-0.825977\pi\)
−0.0231086 0.999733i \(-0.507356\pi\)
\(332\) −6.15767 + 10.6654i −0.337946 + 0.585339i
\(333\) 13.3374 23.1011i 0.730886 1.26593i
\(334\) 17.6808 10.2080i 0.967450 0.558558i
\(335\) 6.07782i 0.332067i
\(336\) 0 0
\(337\) 1.40854i 0.0767278i −0.999264 0.0383639i \(-0.987785\pi\)
0.999264 0.0383639i \(-0.0122146\pi\)
\(338\) −26.4307 + 15.2598i −1.43764 + 0.830023i
\(339\) 0.395921 + 0.228585i 0.0215035 + 0.0124150i
\(340\) 6.41598 + 3.70427i 0.347955 + 0.200892i
\(341\) 6.89978 20.3672i 0.373644 1.10295i
\(342\) 2.12098i 0.114689i
\(343\) 0 0
\(344\) −7.81288 −0.421242
\(345\) 5.19694 + 9.00137i 0.279794 + 0.484617i
\(346\) 13.4894 + 7.78809i 0.725193 + 0.418690i
\(347\) −9.55973 5.51931i −0.513193 0.296292i 0.220952 0.975285i \(-0.429084\pi\)
−0.734145 + 0.678993i \(0.762417\pi\)
\(348\) −2.36864 4.10260i −0.126972 0.219923i
\(349\) 15.5762 0.833773 0.416887 0.908958i \(-0.363121\pi\)
0.416887 + 0.908958i \(0.363121\pi\)
\(350\) 0 0
\(351\) 27.3368i 1.45913i
\(352\) −1.06416 + 3.14127i −0.0567200 + 0.167430i
\(353\) 5.44549 + 3.14396i 0.289834 + 0.167336i 0.637867 0.770146i \(-0.279817\pi\)
−0.348033 + 0.937482i \(0.613150\pi\)
\(354\) −2.13327 1.23165i −0.113382 0.0654612i
\(355\) −3.79164 + 2.18910i −0.201239 + 0.116186i
\(356\) 6.72825i 0.356597i
\(357\) 0 0
\(358\) 4.50159i 0.237917i
\(359\) 8.90941 5.14385i 0.470221 0.271482i −0.246111 0.969242i \(-0.579153\pi\)
0.716332 + 0.697759i \(0.245820\pi\)
\(360\) 2.47652 4.28945i 0.130524 0.226074i
\(361\) 9.11408 15.7861i 0.479689 0.830845i
\(362\) −4.09169 7.08701i −0.215054 0.372485i
\(363\) 8.34836 + 1.08864i 0.438175 + 0.0571385i
\(364\) 0 0
\(365\) 22.2092i 1.16248i
\(366\) −4.33742 7.51262i −0.226720 0.392691i
\(367\) −3.91575 2.26076i −0.204401 0.118011i 0.394306 0.918979i \(-0.370985\pi\)
−0.598706 + 0.800969i \(0.704318\pi\)
\(368\) −3.30966 + 5.73249i −0.172528 + 0.298827i
\(369\) −2.85920 4.95228i −0.148844 0.257805i
\(370\) −22.6684 −1.17848
\(371\) 0 0
\(372\) 4.96246 0.257291
\(373\) −17.0814 + 9.86195i −0.884442 + 0.510633i −0.872120 0.489291i \(-0.837255\pi\)
−0.0123213 + 0.999924i \(0.503922\pi\)
\(374\) 11.7450 2.34374i 0.607321 0.121192i
\(375\) 4.54653 7.87482i 0.234782 0.406654i
\(376\) 2.87357 + 4.97716i 0.148193 + 0.256677i
\(377\) 40.8321i 2.10296i
\(378\) 0 0
\(379\) −35.6268 −1.83003 −0.915014 0.403423i \(-0.867820\pi\)
−0.915014 + 0.403423i \(0.867820\pi\)
\(380\) −1.56094 + 0.901211i −0.0800747 + 0.0462311i
\(381\) −2.80508 + 4.85854i −0.143708 + 0.248910i
\(382\) 8.97741 + 5.18311i 0.459324 + 0.265191i
\(383\) 18.7384 10.8186i 0.957488 0.552806i 0.0620891 0.998071i \(-0.480224\pi\)
0.895399 + 0.445265i \(0.146890\pi\)
\(384\) −0.765367 −0.0390575
\(385\) 0 0
\(386\) 1.62333 0.0826252
\(387\) 16.3349 9.43098i 0.830351 0.479403i
\(388\) −8.00103 4.61940i −0.406191 0.234514i
\(389\) 4.32349 7.48851i 0.219210 0.379682i −0.735357 0.677680i \(-0.762985\pi\)
0.954567 + 0.297998i \(0.0963188\pi\)
\(390\) −8.97094 + 5.17937i −0.454261 + 0.262268i
\(391\) 23.9029 1.20882
\(392\) 0 0
\(393\) 6.75092i 0.340539i
\(394\) 2.19356 + 3.79936i 0.110510 + 0.191409i
\(395\) 8.70426 15.0762i 0.437959 0.758567i
\(396\) −1.56693 7.85223i −0.0787410 0.394589i
\(397\) −31.3257 + 18.0859i −1.57219 + 0.907705i −0.576292 + 0.817244i \(0.695501\pi\)
−0.995900 + 0.0904617i \(0.971166\pi\)
\(398\) −20.0640 −1.00572
\(399\) 0 0
\(400\) 0.790886 0.0395443
\(401\) 4.49678 + 7.78865i 0.224558 + 0.388947i 0.956187 0.292757i \(-0.0945727\pi\)
−0.731628 + 0.681704i \(0.761239\pi\)
\(402\) −1.13368 + 1.96360i −0.0565430 + 0.0979354i
\(403\) 37.0425 + 21.3865i 1.84522 + 1.06534i
\(404\) −0.929830 1.61051i −0.0462608 0.0801260i
\(405\) 8.35225i 0.415027i
\(406\) 0 0
\(407\) −27.5368 + 24.1791i −1.36495 + 1.19851i
\(408\) 1.38190 + 2.39352i 0.0684143 + 0.118497i
\(409\) −4.79140 + 8.29894i −0.236919 + 0.410356i −0.959829 0.280587i \(-0.909471\pi\)
0.722909 + 0.690943i \(0.242804\pi\)
\(410\) −2.42976 + 4.20847i −0.119997 + 0.207842i
\(411\) 2.14504 1.23844i 0.105807 0.0610877i
\(412\) 6.71011i 0.330583i
\(413\) 0 0
\(414\) 15.9804i 0.785396i
\(415\) −21.8813 + 12.6331i −1.07411 + 0.620137i
\(416\) −5.71311 3.29847i −0.280108 0.161721i
\(417\) −1.63799 0.945695i −0.0802128 0.0463109i
\(418\) −0.934908 + 2.75972i −0.0457278 + 0.134983i
\(419\) 37.9064i 1.85185i −0.377709 0.925924i \(-0.623288\pi\)
0.377709 0.925924i \(-0.376712\pi\)
\(420\) 0 0
\(421\) 2.88394 0.140555 0.0702774 0.997527i \(-0.477612\pi\)
0.0702774 + 0.997527i \(0.477612\pi\)
\(422\) 4.28190 + 7.41646i 0.208440 + 0.361028i
\(423\) −12.0159 6.93740i −0.584235 0.337308i
\(424\) −0.372186 0.214882i −0.0180750 0.0104356i
\(425\) −1.42798 2.47333i −0.0692670 0.119974i
\(426\) −1.63332 −0.0791345
\(427\) 0 0
\(428\) 14.7533i 0.713130i
\(429\) −5.37304 + 15.8605i −0.259413 + 0.765752i
\(430\) −13.8815 8.01450i −0.669426 0.386493i
\(431\) 28.0651 + 16.2034i 1.35185 + 0.780490i 0.988508 0.151167i \(-0.0483032\pi\)
0.363339 + 0.931657i \(0.381637\pi\)
\(432\) 3.58869 2.07193i 0.172661 0.0996858i
\(433\) 10.2319i 0.491714i −0.969306 0.245857i \(-0.920931\pi\)
0.969306 0.245857i \(-0.0790694\pi\)
\(434\) 0 0
\(435\) 9.71905i 0.465993i
\(436\) 5.19615 3.00000i 0.248851 0.143674i
\(437\) −2.90766 + 5.03622i −0.139092 + 0.240915i
\(438\) −4.14264 + 7.17526i −0.197943 + 0.342847i
\(439\) −14.4363 25.0044i −0.689008 1.19340i −0.972159 0.234321i \(-0.924713\pi\)
0.283152 0.959075i \(-0.408620\pi\)
\(440\) −5.11308 + 4.48962i −0.243757 + 0.214034i
\(441\) 0 0
\(442\) 23.8221i 1.13310i
\(443\) 4.28018 + 7.41349i 0.203358 + 0.352226i 0.949608 0.313439i \(-0.101481\pi\)
−0.746251 + 0.665665i \(0.768148\pi\)
\(444\) −7.32363 4.22830i −0.347564 0.200666i
\(445\) −6.90188 + 11.9544i −0.327181 + 0.566694i
\(446\) −4.12042 7.13678i −0.195108 0.337936i
\(447\) −2.99152 −0.141494
\(448\) 0 0
\(449\) −10.8089 −0.510102 −0.255051 0.966928i \(-0.582092\pi\)
−0.255051 + 0.966928i \(0.582092\pi\)
\(450\) −1.65356 + 0.954684i −0.0779496 + 0.0450042i
\(451\) 1.53735 + 7.70399i 0.0723908 + 0.362767i
\(452\) −0.298661 + 0.517296i −0.0140478 + 0.0243315i
\(453\) 9.25694 + 16.0335i 0.434929 + 0.753319i
\(454\) 27.4795i 1.28967i
\(455\) 0 0
\(456\) −0.672404 −0.0314882
\(457\) 21.1220 12.1948i 0.988044 0.570448i 0.0833551 0.996520i \(-0.473436\pi\)
0.904689 + 0.426072i \(0.140103\pi\)
\(458\) −0.0521716 + 0.0903638i −0.00243782 + 0.00422242i
\(459\) −12.9590 7.48190i −0.604876 0.349225i
\(460\) −11.7609 + 6.79013i −0.548353 + 0.316592i
\(461\) 1.13186 0.0527158 0.0263579 0.999653i \(-0.491609\pi\)
0.0263579 + 0.999653i \(0.491609\pi\)
\(462\) 0 0
\(463\) 6.38388 0.296684 0.148342 0.988936i \(-0.452606\pi\)
0.148342 + 0.988936i \(0.452606\pi\)
\(464\) 5.36031 3.09477i 0.248846 0.143671i
\(465\) 8.81704 + 5.09052i 0.408881 + 0.236067i
\(466\) −7.57884 + 13.1269i −0.351083 + 0.608094i
\(467\) 30.9033 17.8420i 1.43003 0.825629i 0.432910 0.901437i \(-0.357487\pi\)
0.997122 + 0.0758078i \(0.0241536\pi\)
\(468\) 15.9264 0.736199
\(469\) 0 0
\(470\) 11.7909i 0.543873i
\(471\) −7.76957 13.4573i −0.358003 0.620079i
\(472\) 1.60922 2.78725i 0.0740704 0.128294i
\(473\) −25.4114 + 5.07089i −1.16842 + 0.233160i
\(474\) 5.62427 3.24718i 0.258331 0.149148i
\(475\) 0.694824 0.0318807
\(476\) 0 0
\(477\) 1.03754 0.0475058
\(478\) 12.9567 + 22.4417i 0.592627 + 1.02646i
\(479\) −5.79094 + 10.0302i −0.264595 + 0.458291i −0.967457 0.253034i \(-0.918571\pi\)
0.702863 + 0.711325i \(0.251905\pi\)
\(480\) −1.35986 0.785118i −0.0620690 0.0358356i
\(481\) −36.4450 63.1246i −1.66175 2.87824i
\(482\) 7.31108i 0.333011i
\(483\) 0 0
\(484\) −1.42237 + 10.9077i −0.0646532 + 0.495802i
\(485\) −9.47721 16.4150i −0.430338 0.745368i
\(486\) −7.77372 + 13.4645i −0.352623 + 0.610761i
\(487\) −20.0319 + 34.6963i −0.907732 + 1.57224i −0.0905248 + 0.995894i \(0.528854\pi\)
−0.817207 + 0.576344i \(0.804479\pi\)
\(488\) 9.81572 5.66711i 0.444337 0.256538i
\(489\) 10.1492i 0.458964i
\(490\) 0 0
\(491\) 19.7876i 0.893003i −0.894783 0.446502i \(-0.852670\pi\)
0.894783 0.446502i \(-0.147330\pi\)
\(492\) −1.57000 + 0.906438i −0.0707810 + 0.0408654i
\(493\) −19.3565 11.1755i −0.871773 0.503318i
\(494\) −5.01919 2.89783i −0.225824 0.130380i
\(495\) 5.27083 15.5588i 0.236906 0.699316i
\(496\) 6.48376i 0.291130i
\(497\) 0 0
\(498\) −9.42575 −0.422378
\(499\) 13.3276 + 23.0841i 0.596627 + 1.03339i 0.993315 + 0.115435i \(0.0368260\pi\)
−0.396688 + 0.917953i \(0.629841\pi\)
\(500\) 10.2889 + 5.94033i 0.460136 + 0.265660i
\(501\) 13.5323 + 7.81288i 0.604579 + 0.349054i
\(502\) 5.00803 + 8.67417i 0.223519 + 0.387147i
\(503\) −10.9142 −0.486638 −0.243319 0.969946i \(-0.578236\pi\)
−0.243319 + 0.969946i \(0.578236\pi\)
\(504\) 0 0
\(505\) 3.81530i 0.169779i
\(506\) −7.04402 + 20.7930i −0.313145 + 0.924363i
\(507\) −20.2292 11.6793i −0.898410 0.518697i
\(508\) −6.34799 3.66501i −0.281646 0.162609i
\(509\) −19.4284 + 11.2170i −0.861149 + 0.497184i −0.864397 0.502810i \(-0.832299\pi\)
0.00324816 + 0.999995i \(0.498966\pi\)
\(510\) 5.67025i 0.251083i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 3.15280 1.82027i 0.139200 0.0803669i
\(514\) 8.75577 15.1654i 0.386200 0.668919i
\(515\) −6.88327 + 11.9222i −0.303313 + 0.525354i
\(516\) −2.98986 5.17859i −0.131621 0.227975i
\(517\) 12.5767 + 14.3231i 0.553121 + 0.629931i
\(518\) 0 0
\(519\) 11.9215i 0.523295i
\(520\) −6.76718 11.7211i −0.296760 0.514004i
\(521\) 33.9574 + 19.6053i 1.48770 + 0.858925i 0.999902 0.0140307i \(-0.00446624\pi\)
0.487800 + 0.872955i \(0.337800\pi\)
\(522\) −7.47145 + 12.9409i −0.327016 + 0.566409i
\(523\) 9.04494 + 15.6663i 0.395508 + 0.685039i 0.993166 0.116712i \(-0.0372353\pi\)
−0.597658 + 0.801751i \(0.703902\pi\)
\(524\) −8.82050 −0.385325
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) 20.2766 11.7067i 0.883262 0.509952i
\(528\) −2.48935 + 0.496755i −0.108335 + 0.0216185i
\(529\) −10.4077 + 18.0266i −0.452507 + 0.783764i
\(530\) −0.440854 0.763582i −0.0191495 0.0331679i
\(531\) 7.77001i 0.337190i
\(532\) 0 0
\(533\) −15.6258 −0.676827
\(534\) −4.45967 + 2.57479i −0.192989 + 0.111422i
\(535\) −15.1341 + 26.2130i −0.654303 + 1.13329i
\(536\) −2.56556 1.48123i −0.110816 0.0639794i
\(537\) −2.98378 + 1.72269i −0.128760 + 0.0743394i
\(538\) −6.75523 −0.291238
\(539\) 0 0
\(540\) 8.50159 0.365850
\(541\) 8.33615 4.81288i 0.358399 0.206922i −0.309979 0.950743i \(-0.600322\pi\)
0.668378 + 0.743822i \(0.266989\pi\)
\(542\) −16.9249 9.77158i −0.726985 0.419725i
\(543\) 3.13164 5.42416i 0.134392 0.232773i
\(544\) −3.12729 + 1.80554i −0.134081 + 0.0774119i
\(545\) 12.3097 0.527289
\(546\) 0 0
\(547\) 10.2834i 0.439685i −0.975535 0.219843i \(-0.929446\pi\)
0.975535 0.219843i \(-0.0705544\pi\)
\(548\) 1.61810 + 2.80263i 0.0691218 + 0.119722i
\(549\) −13.6816 + 23.6972i −0.583917 + 1.01137i
\(550\) 2.57235 0.513318i 0.109686 0.0218880i
\(551\) 4.70924 2.71888i 0.200620 0.115828i
\(552\) −5.06620 −0.215632
\(553\) 0 0
\(554\) −26.6748 −1.13330
\(555\) −8.67483 15.0252i −0.368226 0.637786i
\(556\) 1.23561 2.14014i 0.0524016 0.0907622i
\(557\) 32.2426 + 18.6153i 1.36616 + 0.788755i 0.990436 0.137974i \(-0.0440591\pi\)
0.375729 + 0.926730i \(0.377392\pi\)
\(558\) −7.82660 13.5561i −0.331326 0.573874i
\(559\) 51.5411i 2.17995i
\(560\) 0 0
\(561\) 6.04812 + 6.88801i 0.255352 + 0.290812i
\(562\) −10.4767 18.1461i −0.441932 0.765448i
\(563\) −8.09387 + 14.0190i −0.341116 + 0.590830i −0.984640 0.174596i \(-0.944138\pi\)
0.643524 + 0.765426i \(0.277471\pi\)
\(564\) −2.19933 + 3.80935i −0.0926086 + 0.160403i
\(565\) −1.06129 + 0.612736i −0.0446488 + 0.0257780i
\(566\) 10.0629i 0.422977i
\(567\) 0 0
\(568\) 2.13403i 0.0895420i
\(569\) −26.4052 + 15.2451i −1.10696 + 0.639106i −0.938042 0.346523i \(-0.887362\pi\)
−0.168923 + 0.985629i \(0.554029\pi\)
\(570\) −1.19469 0.689757i −0.0500402 0.0288907i
\(571\) −35.0634 20.2439i −1.46736 0.847179i −0.468025 0.883715i \(-0.655034\pi\)
−0.999332 + 0.0365365i \(0.988367\pi\)
\(572\) −20.7227 7.02021i −0.866461 0.293530i
\(573\) 7.93396i 0.331446i
\(574\) 0 0
\(575\) 5.23512 0.218320
\(576\) 1.20711 + 2.09077i 0.0502961 + 0.0871154i
\(577\) −22.1360 12.7802i −0.921533 0.532047i −0.0374092 0.999300i \(-0.511910\pi\)
−0.884124 + 0.467253i \(0.845244\pi\)
\(578\) −3.42955 1.98005i −0.142651 0.0823594i
\(579\) 0.621221 + 1.07599i 0.0258170 + 0.0447164i
\(580\) 12.6986 0.527279
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) −1.35000 0.457338i −0.0559114 0.0189410i
\(584\) −9.37493 5.41262i −0.387937 0.223976i
\(585\) 28.2972 + 16.3374i 1.16995 + 0.675469i
\(586\) 25.6715 14.8215i 1.06048 0.612269i
\(587\) 7.18094i 0.296389i 0.988958 + 0.148195i \(0.0473462\pi\)
−0.988958 + 0.148195i \(0.952654\pi\)
\(588\) 0 0
\(589\) 5.69624i 0.234709i
\(590\) 5.71837 3.30150i 0.235421 0.135921i
\(591\) −1.67888 + 2.90791i −0.0690599 + 0.119615i
\(592\) 5.52454 9.56878i 0.227057 0.393274i
\(593\) −9.88857 17.1275i −0.406075 0.703343i 0.588371 0.808591i \(-0.299770\pi\)
−0.994446 + 0.105249i \(0.966436\pi\)
\(594\) 10.3274 9.06816i 0.423740 0.372071i
\(595\) 0 0
\(596\) 3.90860i 0.160103i
\(597\) −7.67817 13.2990i −0.314247 0.544291i
\(598\) −37.8169 21.8336i −1.54645 0.892842i
\(599\) 6.87989 11.9163i 0.281105 0.486888i −0.690552 0.723282i \(-0.742632\pi\)
0.971657 + 0.236395i \(0.0759658\pi\)
\(600\) 0.302659 + 0.524221i 0.0123560 + 0.0214012i
\(601\) 11.0384 0.450266 0.225133 0.974328i \(-0.427718\pi\)
0.225133 + 0.974328i \(0.427718\pi\)
\(602\) 0 0
\(603\) 7.15201 0.291252
\(604\) −20.9488 + 12.0948i −0.852393 + 0.492129i
\(605\) −13.7163 + 17.9211i −0.557648 + 0.728595i
\(606\) 0.711661 1.23263i 0.0289093 0.0500723i
\(607\) 5.90718 + 10.2315i 0.239765 + 0.415285i 0.960647 0.277773i \(-0.0895963\pi\)
−0.720882 + 0.693058i \(0.756263\pi\)
\(608\) 0.878539i 0.0356294i
\(609\) 0 0
\(610\) 23.2534 0.941503
\(611\) −32.8340 + 18.9567i −1.32832 + 0.766907i
\(612\) 4.35896 7.54994i 0.176200 0.305188i
\(613\) 18.3140 + 10.5736i 0.739697 + 0.427064i 0.821959 0.569546i \(-0.192881\pi\)
−0.0822621 + 0.996611i \(0.526214\pi\)
\(614\) −14.0190 + 8.09387i −0.565760 + 0.326642i
\(615\) −3.71932 −0.149978
\(616\) 0 0
\(617\) −43.8743 −1.76631 −0.883157 0.469078i \(-0.844586\pi\)
−0.883157 + 0.469078i \(0.844586\pi\)
\(618\) −4.44764 + 2.56785i −0.178910 + 0.103294i
\(619\) 4.12964 + 2.38425i 0.165984 + 0.0958310i 0.580691 0.814124i \(-0.302782\pi\)
−0.414707 + 0.909955i \(0.636116\pi\)
\(620\) −6.65109 + 11.5200i −0.267114 + 0.462655i
\(621\) 23.7546 13.7148i 0.953241 0.550354i
\(622\) −1.42639 −0.0571931
\(623\) 0 0
\(624\) 5.04908i 0.202125i
\(625\) 10.2100 + 17.6843i 0.408401 + 0.707372i
\(626\) 5.77340 9.99982i 0.230751 0.399673i
\(627\) −2.18699 + 0.436419i −0.0873401 + 0.0174289i
\(628\) 17.5828 10.1514i 0.701630 0.405086i
\(629\) −39.8991 −1.59088
\(630\) 0 0
\(631\) −6.66195 −0.265208 −0.132604 0.991169i \(-0.542334\pi\)
−0.132604 + 0.991169i \(0.542334\pi\)
\(632\) 4.24264 + 7.34847i 0.168763 + 0.292306i
\(633\) −3.27722 + 5.67632i −0.130258 + 0.225613i
\(634\) 27.4737 + 15.8620i 1.09112 + 0.629959i
\(635\) −7.51918 13.0236i −0.298390 0.516826i
\(636\) 0.328927i 0.0130428i
\(637\) 0 0
\(638\) 15.4257 13.5448i 0.610711 0.536244i
\(639\) 2.57600 + 4.46177i 0.101905 + 0.176505i
\(640\) 1.02581 1.77675i 0.0405486 0.0702322i
\(641\) 5.76074 9.97789i 0.227535 0.394103i −0.729542 0.683936i \(-0.760267\pi\)
0.957077 + 0.289833i \(0.0935999\pi\)
\(642\) −9.77892 + 5.64586i −0.385943 + 0.222824i
\(643\) 21.7793i 0.858892i 0.903093 + 0.429446i \(0.141291\pi\)
−0.903093 + 0.429446i \(0.858709\pi\)
\(644\) 0 0
\(645\) 12.2681i 0.483055i
\(646\) −2.74744 + 1.58624i −0.108097 + 0.0624096i
\(647\) −15.2087 8.78075i −0.597916 0.345207i 0.170306 0.985391i \(-0.445525\pi\)
−0.768221 + 0.640185i \(0.778858\pi\)
\(648\) −3.52565 2.03553i −0.138501 0.0799633i
\(649\) 3.42495 10.1100i 0.134441 0.396852i
\(650\) 5.21742i 0.204644i
\(651\) 0 0
\(652\) 13.2606 0.519326
\(653\) −13.2213 22.9000i −0.517390 0.896146i −0.999796 0.0201984i \(-0.993570\pi\)
0.482406 0.875948i \(-0.339763\pi\)
\(654\) 3.97696 + 2.29610i 0.155512 + 0.0897846i
\(655\) −15.6718 9.04812i −0.612348 0.353539i
\(656\) −1.18432 2.05130i −0.0462399 0.0800898i
\(657\) 26.1344 1.01960
\(658\) 0 0
\(659\) 38.9324i 1.51659i 0.651910 + 0.758296i \(0.273968\pi\)
−0.651910 + 0.758296i \(0.726032\pi\)
\(660\) −4.93253 1.67099i −0.191999 0.0650430i
\(661\) 10.2982 + 5.94569i 0.400555 + 0.231261i 0.686723 0.726919i \(-0.259048\pi\)
−0.286168 + 0.958179i \(0.592382\pi\)
\(662\) 27.6469 + 15.9620i 1.07453 + 0.620379i
\(663\) −15.7899 + 9.11631i −0.613229 + 0.354048i
\(664\) 12.3153i 0.477928i
\(665\) 0 0
\(666\) 26.6748i 1.03363i
\(667\) 35.4815 20.4853i 1.37385 0.793193i
\(668\) −10.2080 + 17.6808i −0.394960 + 0.684091i
\(669\) 3.15363 5.46225i 0.121927 0.211183i
\(670\) −3.03891 5.26354i −0.117403 0.203348i
\(671\) 28.2474 24.8031i 1.09048 0.957512i
\(672\) 0 0
\(673\) 17.4386i 0.672210i 0.941825 + 0.336105i \(0.109110\pi\)
−0.941825 + 0.336105i \(0.890890\pi\)
\(674\) 0.704268 + 1.21983i 0.0271274 + 0.0469860i
\(675\) −2.83824 1.63866i −0.109244 0.0630720i
\(676\) 15.2598 26.4307i 0.586915 1.01657i
\(677\) 20.7150 + 35.8794i 0.796141 + 1.37896i 0.922112 + 0.386923i \(0.126462\pi\)
−0.125970 + 0.992034i \(0.540204\pi\)
\(678\) −0.457170 −0.0175575
\(679\) 0 0
\(680\) −7.40854 −0.284104
\(681\) −18.2141 + 10.5159i −0.697967 + 0.402971i
\(682\) 4.20824 + 21.0884i 0.161142 + 0.807518i
\(683\) −10.7076 + 18.5462i −0.409717 + 0.709650i −0.994858 0.101281i \(-0.967706\pi\)
0.585141 + 0.810931i \(0.301039\pi\)
\(684\) 1.06049 + 1.83682i 0.0405488 + 0.0702327i
\(685\) 6.63943i 0.253679i
\(686\) 0 0
\(687\) −0.0798608 −0.00304688
\(688\) 6.76615 3.90644i 0.257957 0.148932i
\(689\) 1.41756 2.45529i 0.0540048 0.0935391i
\(690\) −9.00137 5.19694i −0.342676 0.197844i
\(691\) 11.6732 6.73955i 0.444071 0.256384i −0.261252 0.965271i \(-0.584135\pi\)
0.705323 + 0.708886i \(0.250802\pi\)
\(692\) −15.5762 −0.592117
\(693\) 0 0
\(694\) 11.0386 0.419020
\(695\) 4.39074 2.53499i 0.166550 0.0961578i
\(696\) 4.10260 + 2.36864i 0.155509 + 0.0897830i
\(697\) −4.27667 + 7.40741i −0.161990 + 0.280576i
\(698\) −13.4894 + 7.78809i −0.510580 + 0.294783i
\(699\) −11.6012 −0.438797
\(700\) 0 0
\(701\) 26.4644i 0.999545i −0.866157 0.499773i \(-0.833417\pi\)
0.866157 0.499773i \(-0.166583\pi\)
\(702\) 13.6684 + 23.6743i 0.515880 + 0.893531i
\(703\) 4.85352 8.40654i 0.183054 0.317059i
\(704\) −0.649042 3.25250i −0.0244617 0.122583i
\(705\) −7.81532 + 4.51218i −0.294342 + 0.169938i
\(706\) −6.28791 −0.236649
\(707\) 0 0
\(708\) 2.46329 0.0925761
\(709\) −9.38888 16.2620i −0.352607 0.610733i 0.634099 0.773252i \(-0.281371\pi\)
−0.986705 + 0.162519i \(0.948038\pi\)
\(710\) 2.18910 3.79164i 0.0821556 0.142298i
\(711\) −17.7408 10.2426i −0.665331 0.384129i
\(712\) −3.36413 5.82684i −0.126076 0.218370i
\(713\) 42.9181i 1.60729i
\(714\) 0 0
\(715\) −29.6177 33.7307i −1.10764 1.26146i
\(716\) −2.25080 3.89850i −0.0841162 0.145694i
\(717\) −9.91665 + 17.1761i −0.370344 + 0.641455i
\(718\) −5.14385 + 8.90941i −0.191967 + 0.332496i
\(719\) −3.00287 + 1.73371i −0.111988 + 0.0646564i −0.554948 0.831885i \(-0.687262\pi\)
0.442960 + 0.896542i \(0.353928\pi\)
\(720\) 4.95303i 0.184589i
\(721\) 0 0
\(722\) 18.2282i 0.678382i
\(723\) 4.84598 2.79783i 0.180224 0.104052i
\(724\) 7.08701 + 4.09169i 0.263387 + 0.152066i
\(725\) −4.23939 2.44761i −0.157447 0.0909021i
\(726\) −7.77421 + 3.23139i −0.288528 + 0.119928i
\(727\) 21.6647i 0.803500i 0.915749 + 0.401750i \(0.131598\pi\)
−0.915749 + 0.401750i \(0.868402\pi\)
\(728\) 0 0
\(729\) 0.313708 0.0116188
\(730\) −11.1046 19.2337i −0.410999 0.711872i
\(731\) −24.4331 14.1065i −0.903691 0.521746i
\(732\) 7.51262 + 4.33742i 0.277675 + 0.160315i
\(733\) 7.45423 + 12.9111i 0.275328 + 0.476883i 0.970218 0.242234i \(-0.0778801\pi\)
−0.694890 + 0.719116i \(0.744547\pi\)
\(734\) 4.52152 0.166892
\(735\) 0 0
\(736\) 6.61931i 0.243991i
\(737\) −9.30587 3.15254i −0.342786 0.116125i
\(738\) 4.95228 + 2.85920i 0.182296 + 0.105249i
\(739\) −4.11862 2.37789i −0.151506 0.0874719i 0.422331 0.906442i \(-0.361212\pi\)
−0.573836 + 0.818970i \(0.694545\pi\)
\(740\) 19.6314 11.3342i 0.721666 0.416654i
\(741\) 4.43581i 0.162954i
\(742\) 0 0
\(743\) 14.8792i 0.545864i 0.962033 + 0.272932i \(0.0879934\pi\)
−0.962033 + 0.272932i \(0.912007\pi\)
\(744\) −4.29762 + 2.48123i −0.157558 + 0.0909663i
\(745\) 4.00947 6.94461i 0.146896 0.254431i
\(746\) 9.86195 17.0814i 0.361072 0.625395i
\(747\) 14.8659 + 25.7485i 0.543916 + 0.942090i
\(748\) −8.99962 + 7.90226i −0.329059 + 0.288935i
\(749\) 0 0
\(750\) 9.09306i 0.332032i
\(751\) −8.24101 14.2739i −0.300719 0.520860i 0.675580 0.737287i \(-0.263893\pi\)
−0.976299 + 0.216426i \(0.930560\pi\)
\(752\) −4.97716 2.87357i −0.181498 0.104788i
\(753\) −3.83298 + 6.63892i −0.139682 + 0.241936i
\(754\) 20.4160 + 35.3616i 0.743508 + 1.28779i
\(755\) −49.6276 −1.80613
\(756\) 0 0
\(757\) −3.82008 −0.138843 −0.0694216 0.997587i \(-0.522115\pi\)
−0.0694216 + 0.997587i \(0.522115\pi\)
\(758\) 30.8537 17.8134i 1.12066 0.647012i
\(759\) −16.4778 + 3.28818i −0.598107 + 0.119353i
\(760\) 0.901211 1.56094i 0.0326903 0.0566213i
\(761\) −0.927001 1.60561i −0.0336038 0.0582034i 0.848734 0.528819i \(-0.177365\pi\)
−0.882338 + 0.470616i \(0.844032\pi\)
\(762\) 5.61016i 0.203235i
\(763\) 0 0
\(764\) −10.3662 −0.375037
\(765\) 15.4895 8.94289i 0.560026 0.323331i
\(766\) −10.8186 + 18.7384i −0.390893 + 0.677046i
\(767\) 18.3873 + 10.6159i 0.663928 + 0.383319i
\(768\) 0.662827 0.382683i 0.0239177 0.0138089i
\(769\) −8.92308 −0.321775 −0.160887 0.986973i \(-0.551436\pi\)
−0.160887 + 0.986973i \(0.551436\pi\)
\(770\) 0 0
\(771\) 13.4028 0.482688
\(772\) −1.40584 + 0.811664i −0.0505974 + 0.0292124i
\(773\) 17.6034 + 10.1633i 0.633151 + 0.365550i 0.781971 0.623315i \(-0.214214\pi\)
−0.148821 + 0.988864i \(0.547548\pi\)
\(774\) −9.43098 + 16.3349i −0.338989 + 0.587147i
\(775\) 4.44091 2.56396i 0.159522 0.0921001i
\(776\) 9.23880 0.331653
\(777\) 0 0
\(778\) 8.64698i 0.310009i
\(779\) −1.04047 1.80215i −0.0372787 0.0645686i
\(780\) 5.17937 8.97094i 0.185451 0.321211i
\(781\) −1.38508 6.94093i −0.0495619 0.248366i
\(782\) −20.7005 + 11.9514i −0.740248 + 0.427382i