Properties

Label 1078.2.i.d.901.13
Level $1078$
Weight $2$
Character 1078.901
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 901.13
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.d.1011.13

$q$-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} +(-3.14127 - 1.06416i) 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} +(2.48935 - 0.496755i) 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} +(-0.649042 - 3.25250i) 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} +(2.40422 + 0.814474i) 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} +(1.06416 - 3.14127i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{9} + O(q^{10}) \) \( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) −0.662827 + 0.382683i −0.382683 + 0.220942i −0.678985 0.734152i \(-0.737580\pi\)
0.296302 + 0.955094i \(0.404247\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.77675 + 1.02581i 0.794586 + 0.458755i 0.841575 0.540141i \(-0.181629\pi\)
−0.0469885 + 0.998895i \(0.514962\pi\)
\(6\) −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
\(11\) −3.14127 1.06416i −0.947128 0.320857i
\(12\) −0.662827 0.382683i −0.191342 0.110471i
\(13\) 6.59694 1.82966 0.914830 0.403838i \(-0.132324\pi\)
0.914830 + 0.403838i \(0.132324\pi\)
\(14\) 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 \(-0.0223863\pi\)
−0.559620 + 0.828749i \(0.689053\pi\)
\(18\) −2.09077 + 1.20711i −0.492799 + 0.284518i
\(19\) 0.439269 0.760837i 0.100775 0.174548i −0.811229 0.584729i \(-0.801201\pi\)
0.912004 + 0.410181i \(0.134534\pi\)
\(20\) 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 0.281690 + 0.959505i \(0.409105\pi\)
−0.971801 + 0.235802i \(0.924228\pi\)
\(24\) −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 −0.910753 0.412952i \(-0.864498\pi\)
−0.0977497 + 0.995211i \(0.531164\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 2.48935 0.496755i 0.433341 0.0864740i
\(34\) 3.61108i 0.619295i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) 5.52454 9.56878i 0.908229 1.57310i 0.0917046 0.995786i \(-0.470768\pi\)
0.816524 0.577312i \(-0.195898\pi\)
\(38\) 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 \(-0.559215\pi\)
−0.184960 + 0.982746i \(0.559215\pi\)
\(42\) 0 0
\(43\) 7.81288i 1.19145i 0.803188 + 0.595726i \(0.203136\pi\)
−0.803188 + 0.595726i \(0.796864\pi\)
\(44\) −0.649042 3.25250i −0.0978468 0.490333i
\(45\) −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 0.816955 0.576702i \(-0.195661\pi\)
−0.0909611 + 0.995854i \(0.528994\pi\)
\(48\) 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 0.850890 0.525344i \(-0.176063\pi\)
−0.880406 + 0.474220i \(0.842730\pi\)
\(54\) 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 −0.670339 0.742055i \(-0.733851\pi\)
0.307469 + 0.951558i \(0.400518\pi\)
\(60\) −0.785118 1.35986i −0.101358 0.175558i
\(61\) 5.66711 9.81572i 0.725599 1.25677i −0.233129 0.972446i \(-0.574896\pi\)
0.958727 0.284328i \(-0.0917704\pi\)
\(62\) −6.48376 −0.823439
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 11.7211 + 6.76718i 1.45382 + 0.839365i
\(66\) 2.40422 + 0.814474i 0.295939 + 0.100255i
\(67\) −1.48123 2.56556i −0.180961 0.313434i 0.761247 0.648462i \(-0.224587\pi\)
−0.942208 + 0.335028i \(0.891254\pi\)
\(68\) −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 0.986831 + 0.161754i \(0.0517152\pi\)
−0.353332 + 0.935498i \(0.614951\pi\)
\(74\) 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 \(-0.491730\pi\)
−0.852745 + 0.522328i \(0.825064\pi\)
\(80\) −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 \(-0.263759\pi\)
0.675892 + 0.737001i \(0.263759\pi\)
\(84\) 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
\(88\) 1.06416 3.14127i 0.113440 0.334860i
\(89\) −5.82684 3.36413i −0.617644 0.356597i 0.158307 0.987390i \(-0.449396\pi\)
−0.775951 + 0.630793i \(0.782730\pi\)
\(90\) −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 \(0.155396\pi\)
−0.883183 + 0.469029i \(0.844604\pi\)
\(98\) 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 \(-0.196159\pi\)
−0.908572 + 0.417729i \(0.862826\pi\)
\(102\) −1.38190 2.39352i −0.136829 0.236994i
\(103\) −5.81112 3.35505i −0.572587 0.330583i 0.185595 0.982626i \(-0.440579\pi\)
−0.758182 + 0.652043i \(0.773912\pi\)
\(104\) 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 \(-0.0806103\pi\)
0.267073 + 0.963676i \(0.413944\pi\)
\(108\) 3.58869 2.07193i 0.345322 0.199372i
\(109\) −5.19615 + 3.00000i −0.497701 + 0.287348i −0.727764 0.685828i \(-0.759440\pi\)
0.230063 + 0.973176i \(0.426107\pi\)
\(110\) −1.33158 6.67287i −0.126961 0.636233i
\(111\) 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
\(121\) 8.73512 + 6.68563i 0.794102 + 0.607785i
\(122\) 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 \(-0.707423\pi\)
0.991814 + 0.127689i \(0.0407559\pi\)
\(132\) 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 0.788588 0.614922i \(-0.210812\pi\)
−0.926832 + 0.375477i \(0.877479\pi\)
\(138\) 2.53310 4.38746i 0.215632 0.373485i
\(139\) −2.47122 −0.209606 −0.104803 0.994493i \(-0.533421\pi\)
−0.104803 + 0.994493i \(0.533421\pi\)
\(140\) 0 0
\(141\) −4.39866 −0.370434
\(142\) −1.84813 1.06702i −0.155091 0.0895420i
\(143\) −20.7227 7.02021i −1.73292 0.587059i
\(144\) −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 \(-0.384516\pi\)
−0.632203 + 0.774803i \(0.717849\pi\)
\(150\) 0.302659 + 0.524221i 0.0247120 + 0.0428024i
\(151\) 20.9488 12.0948i 1.70479 0.984259i 0.764027 0.645185i \(-0.223220\pi\)
0.940760 0.339074i \(-0.110114\pi\)
\(152\) 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 0.408534 0.912743i \(-0.366040\pi\)
0.994726 + 0.102571i \(0.0327068\pi\)
\(158\) −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 −0.480422 0.877038i \(-0.659516\pi\)
0.999748 0.0224612i \(-0.00715023\pi\)
\(164\) −1.18432 2.05130i −0.0924798 0.160180i
\(165\) 4.93253 + 1.67099i 0.383997 + 0.130086i
\(166\) 10.6654 + 6.15767i 0.827795 + 0.477928i
\(167\) 20.4160 1.57984 0.789920 0.613210i \(-0.210122\pi\)
0.789920 + 0.613210i \(0.210122\pi\)
\(168\) 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 −0.401830 0.915714i \(-0.631626\pi\)
0.993947 0.109863i \(-0.0350411\pi\)
\(174\) 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 0.937798 0.347180i \(-0.112861\pi\)
−0.769566 + 0.638567i \(0.779527\pi\)
\(180\) −4.28945 2.47652i −0.319717 0.184589i
\(181\) 8.18338i 0.608266i −0.952630 0.304133i \(-0.901633\pi\)
0.952630 0.304133i \(-0.0983667\pi\)
\(182\) 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
\(187\) −2.34374 11.7450i −0.171391 0.858882i
\(188\) 5.74713i 0.419153i
\(189\) 0 0
\(190\) 1.80242 0.130761
\(191\) −5.18311 + 8.97741i −0.375037 + 0.649582i −0.990333 0.138714i \(-0.955703\pi\)
0.615296 + 0.788296i \(0.289037\pi\)
\(192\) 0.662827 0.382683i 0.0478354 0.0276178i
\(193\) 1.40584 0.811664i 0.101195 0.0584248i −0.448549 0.893758i \(-0.648059\pi\)
0.549743 + 0.835334i \(0.314726\pi\)
\(194\) −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 \(-0.0499518\pi\)
\(198\) 7.85223 1.56693i 0.558033 0.111357i
\(199\) 17.3760 10.0320i 1.23175 0.711151i 0.264355 0.964426i \(-0.414841\pi\)
0.967394 + 0.253275i \(0.0815077\pi\)
\(200\) 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
\(220\) 2.18325 6.44466i 0.147195 0.434499i
\(221\) 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 \(-0.911016\pi\)
0.961180 0.275924i \(-0.0889837\pi\)
\(224\) 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 −0.811324 0.584597i \(-0.801253\pi\)
−0.100614 0.994926i \(-0.532081\pi\)
\(228\) −0.582319 + 0.336202i −0.0385650 + 0.0222655i
\(229\) 0.0903638 + 0.0521716i 0.00597141 + 0.00344759i 0.502983 0.864296i \(-0.332236\pi\)
−0.497011 + 0.867744i \(0.665569\pi\)
\(230\) −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 \(-0.498717\pi\)
−0.864004 + 0.503485i \(0.832051\pi\)
\(234\) −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 \(-0.0910024\pi\)
−0.723936 + 0.689867i \(0.757669\pi\)
\(242\) 4.22202 + 10.1575i 0.271402 + 0.652948i
\(243\) 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 \(0.102375\pi\)
−0.948724 + 0.316104i \(0.897625\pi\)
\(252\) 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 −0.0541598 0.998532i \(-0.517248\pi\)
−0.891834 + 0.452362i \(0.850581\pi\)
\(258\) 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 \(-0.582412\pi\)
0.709150 + 0.705058i \(0.249079\pi\)
\(264\) 0.496755 + 2.48935i 0.0305732 + 0.153209i
\(265\) 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 −0.310936 0.950431i \(-0.600643\pi\)
0.667629 + 0.744494i \(0.267309\pi\)
\(270\) 7.36260 4.25080i 0.448073 0.258695i
\(271\) −9.77158 + 16.9249i −0.593581 + 1.02811i 0.400164 + 0.916443i \(0.368953\pi\)
−0.993745 + 0.111669i \(0.964380\pi\)
\(272\) −3.61108 −0.218954
\(273\) 0 0
\(274\) 3.23620i 0.195506i
\(275\) 0.513318 + 2.57235i 0.0309543 + 0.155119i
\(276\) 4.38746 2.53310i 0.264094 0.152475i
\(277\) −23.1011 + 13.3374i −1.38801 + 0.801368i −0.993091 0.117348i \(-0.962561\pi\)
−0.394919 + 0.918716i \(0.629227\pi\)
\(278\) −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 \(-0.0699836\pi\)
−0.676838 + 0.736132i \(0.736650\pi\)
\(284\) −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 \(-0.166760\pi\)
0.865879 + 0.500253i \(0.166760\pi\)
\(294\) 0 0
\(295\) −6.60300 −0.384442
\(296\) 9.56878 + 5.52454i 0.556174 + 0.321107i
\(297\) −4.40974 + 13.0170i −0.255879 + 0.755321i
\(298\) −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 \(-0.652847\pi\)
−0.461941 + 0.886910i \(0.652847\pi\)
\(308\) 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 −0.464568 0.885538i \(-0.653790\pi\)
0.534614 + 0.845096i \(0.320457\pi\)
\(312\) −2.52454 4.37263i −0.142924 0.247551i
\(313\) −9.99982 5.77340i −0.565223 0.326332i 0.190016 0.981781i \(-0.439146\pi\)
−0.755239 + 0.655449i \(0.772479\pi\)
\(314\) 20.3029 1.14576
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) −15.8620 + 27.4737i −0.890896 + 1.54308i −0.0520931 + 0.998642i \(0.516589\pi\)
−0.838803 + 0.544435i \(0.816744\pi\)
\(318\) 0.164463 + 0.284859i 0.00922265 + 0.0159741i
\(319\) 6.58668 19.4430i 0.368783 1.08860i
\(320\) −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 −0.0231086 + 0.999733i \(0.507356\pi\)
−0.854240 + 0.519879i \(0.825977\pi\)
\(332\) 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
\(341\) 21.0884 4.20824i 1.14200 0.227889i
\(342\) 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 \(-0.570916\pi\)
0.734145 + 0.678993i \(0.237583\pi\)
\(348\) 2.36864 4.10260i 0.126972 0.219923i
\(349\) −15.5762 −0.833773 −0.416887 0.908958i \(-0.636879\pi\)
−0.416887 + 0.908958i \(0.636879\pi\)
\(350\) 0 0
\(351\) 27.3368i 1.45913i
\(352\) 3.25250 0.649042i 0.173359 0.0345941i
\(353\) 5.44549 3.14396i 0.289834 0.167336i −0.348033 0.937482i \(-0.613150\pi\)
0.637867 + 0.770146i \(0.279817\pi\)
\(354\) 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 \(-0.420847\pi\)
−0.716332 + 0.697759i \(0.754180\pi\)
\(360\) −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 −0.598706 0.800969i \(-0.704318\pi\)
0.394306 + 0.918979i \(0.370985\pi\)
\(368\) −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 \(-0.162745\pi\)
0.0123213 + 0.999924i \(0.496078\pi\)
\(374\) 3.84277 11.3434i 0.198705 0.586551i
\(375\) 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 0.895399 0.445265i \(-0.146890\pi\)
0.0620891 + 0.998071i \(0.480224\pi\)
\(384\) 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 0.954567 0.297998i \(-0.0963188\pi\)
−0.735357 + 0.677680i \(0.762985\pi\)
\(390\) −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
\(396\) 7.58369 + 2.56911i 0.381095 + 0.129103i
\(397\) −31.3257 18.0859i −1.57219 0.907705i −0.995900 0.0904617i \(-0.971166\pi\)
−0.576292 0.817244i \(-0.695501\pi\)
\(398\) 20.0640 1.00572
\(399\) 0 0
\(400\) 0.790886 0.0395443
\(401\) 4.49678 7.78865i 0.224558 0.388947i −0.731628 0.681704i \(-0.761239\pi\)
0.956187 + 0.292757i \(0.0945727\pi\)
\(402\) 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 \(-0.0905290\pi\)
−0.722909 + 0.690943i \(0.757196\pi\)
\(410\) −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
\(418\) −2.85745 + 0.570209i −0.139762 + 0.0278898i
\(419\) 37.9064i 1.85185i 0.377709 + 0.925924i \(0.376712\pi\)
−0.377709 + 0.925924i \(0.623288\pi\)
\(420\) 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
\(429\) 16.4221 3.27706i 0.792867 0.158218i
\(430\) −13.8815 + 8.01450i −0.669426 + 0.386493i
\(431\) −28.0651 + 16.2034i −1.35185 + 0.780490i −0.988508 0.151167i \(-0.951697\pi\)
−0.363339 + 0.931657i \(0.618363\pi\)
\(432\) 3.58869 + 2.07193i 0.172661 + 0.0996858i
\(433\) 10.2319i 0.491714i 0.969306 + 0.245857i \(0.0790694\pi\)
−0.969306 + 0.245857i \(0.920931\pi\)
\(434\) 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 −0.283152 0.959075i \(-0.591380\pi\)
0.972159 0.234321i \(-0.0752867\pi\)
\(440\) 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 −0.746251 0.665665i \(-0.768148\pi\)
0.949608 + 0.313439i \(0.101481\pi\)
\(444\) −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
\(451\) 7.44052 + 2.52061i 0.350361 + 0.118691i
\(452\) −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 \(-0.526564\pi\)
−0.904689 + 0.426072i \(0.859897\pi\)
\(458\) 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 \(-0.508391\pi\)
−0.0263579 + 0.999653i \(0.508391\pi\)
\(462\) 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 0.997122 0.0758078i \(-0.0241536\pi\)
0.432910 + 0.901437i \(0.357487\pi\)
\(468\) −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
\(473\) 8.31417 24.5423i 0.382286 1.12846i
\(474\) 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 \(-0.0814285\pi\)
−0.702863 + 0.711325i \(0.748095\pi\)
\(480\) 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 −0.817207 0.576344i \(-0.804479\pi\)
−0.0905248 0.995894i \(-0.528854\pi\)
\(488\) 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
\(495\) 16.1097 3.21473i 0.724078 0.144491i
\(496\) 6.48376i 0.291130i
\(497\) 0 0
\(498\) −9.42575 −0.422378
\(499\) 13.3276 23.0841i 0.596627 1.03339i −0.396688 0.917953i \(-0.629841\pi\)
0.993315 0.115435i \(-0.0368260\pi\)
\(500\) 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 \(-0.421764\pi\)
0.243319 + 0.969946i \(0.421764\pi\)
\(504\) 0 0
\(505\) 3.81530i 0.169779i
\(506\) 21.5293 4.29621i 0.957094 0.190990i
\(507\) −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 0.00324816 0.999995i \(-0.498966\pi\)
−0.864397 + 0.502810i \(0.832299\pi\)
\(510\) 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 0.487800 0.872955i \(-0.337800\pi\)
0.999902 + 0.0140307i \(0.00446624\pi\)
\(522\) −7.47145 12.9409i −0.327016 0.566409i
\(523\) −9.04494 + 15.6663i −0.395508 + 0.685039i −0.993166 0.116712i \(-0.962765\pi\)
0.597658 + 0.801751i \(0.296098\pi\)
\(524\) 8.82050 0.385325
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) −20.2766 11.7067i −0.883262 0.509952i
\(528\) −0.814474 + 2.40422i −0.0354454 + 0.104630i
\(529\) −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 \(-0.399678\pi\)
−0.668378 + 0.743822i \(0.733011\pi\)
\(542\) −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
\(550\) −0.841631 + 2.48438i −0.0358873 + 0.105934i
\(551\) 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 \(-0.955941\pi\)
−0.375729 + 0.926730i \(0.622608\pi\)
\(558\) 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 \(-0.0558618\pi\)
−0.643524 + 0.765426i \(0.722529\pi\)
\(564\) −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 \(-0.112638\pi\)
0.168923 + 0.985629i \(0.445971\pi\)
\(570\) −1.19469 + 0.689757i −0.0500402 + 0.0288907i
\(571\) 35.0634 20.2439i 1.46736 0.847179i 0.468025 0.883715i \(-0.344966\pi\)
0.999332 + 0.0365365i \(0.0116325\pi\)
\(572\) −4.28169 21.4565i −0.179026 0.897142i
\(573\) 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 −0.884124 0.467253i \(-0.845244\pi\)
−0.0374092 + 0.999300i \(0.511910\pi\)
\(578\) 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
\(583\) 0.278935 + 1.39781i 0.0115523 + 0.0578912i
\(584\) −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 \(-0.952654\pi\)
0.988958 0.148195i \(-0.0473462\pi\)
\(588\) 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 \(-0.700230\pi\)
0.994446 + 0.105249i \(0.0335638\pi\)
\(594\) −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 0.971657 0.236395i \(-0.0759658\pi\)
−0.690552 + 0.723282i \(0.742632\pi\)
\(600\) −0.302659 + 0.524221i −0.0123560 + 0.0214012i
\(601\) −11.0384 −0.450266 −0.225133 0.974328i \(-0.572282\pi\)
−0.225133 + 0.974328i \(0.572282\pi\)
\(602\) 0 0
\(603\) 7.15201 0.291252
\(604\) 20.9488 + 12.0948i 0.852393 + 0.492129i
\(605\) 8.66194 + 20.8392i 0.352158 + 0.847235i
\(606\) 0.711661 + 1.23263i 0.0289093 + 0.0500723i
\(607\) −5.90718 + 10.2315i −0.239765 + 0.415285i −0.960647 0.277773i \(-0.910404\pi\)
0.720882 + 0.693058i \(0.243737\pi\)
\(608\) 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 \(-0.807119\pi\)
0.0822621 + 0.996611i \(0.473786\pi\)
\(614\) −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 −0.414707 0.909955i \(-0.636116\pi\)
0.580691 + 0.814124i \(0.302782\pi\)
\(620\) −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
\(627\) 0.715547 2.11220i 0.0285762 0.0843532i
\(628\) 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 0.957077 0.289833i \(-0.0935999\pi\)
−0.729542 + 0.683936i \(0.760267\pi\)
\(642\) −9.77892 5.64586i −0.385943 0.222824i
\(643\) 21.7793i 0.858892i −0.903093 0.429446i \(-0.858709\pi\)
0.903093 0.429446i \(-0.141291\pi\)
\(644\) 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 −0.768221 0.640185i \(-0.778858\pi\)
0.170306 + 0.985391i \(0.445525\pi\)
\(648\) 3.52565 2.03553i 0.138501 0.0799633i
\(649\) 10.4680 2.08891i 0.410904 0.0819967i
\(650\) 5.21742i 0.204644i
\(651\) 0 0
\(652\) 13.2606 0.519326
\(653\) −13.2213 + 22.9000i −0.517390 + 0.896146i 0.482406 + 0.875948i \(0.339763\pi\)
−0.999796 + 0.0201984i \(0.993570\pi\)
\(654\) 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 \(0.726032\pi\)
\(660\) 1.01915 + 5.10719i 0.0396703 + 0.198797i
\(661\) 10.2982 5.94569i 0.400555 0.231261i −0.286168 0.958179i \(-0.592382\pi\)
0.686723 + 0.726919i \(0.259048\pi\)
\(662\) −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 0.125970 + 0.992034i \(0.459796\pi\)
−0.922112 + 0.386923i \(0.873538\pi\)
\(678\) 0.457170 0.0175575
\(679\) 0 0
\(680\) −7.40854 −0.284104
\(681\) 18.2141 + 10.5159i 0.697967 + 0.402971i
\(682\) 20.3672 + 6.89978i 0.779902 + 0.264206i
\(683\) −10.7076 18.5462i −0.409717 0.709650i 0.585141 0.810931i \(-0.301039\pi\)
−0.994858 + 0.101281i \(0.967706\pi\)
\(684\) −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 0.705323 0.708886i \(-0.250802\pi\)
−0.261252 + 0.965271i \(0.584135\pi\)
\(692\) 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
\(704\) 3.14127 + 1.06416i 0.118391 + 0.0401071i
\(705\) −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 −0.986705 0.162519i \(-0.948038\pi\)
0.634099 + 0.773252i \(0.281371\pi\)
\(710\) −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 0.442960 0.896542i \(-0.353928\pi\)
−0.554948 + 0.831885i \(0.687262\pi\)
\(720\) 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
\(726\) −6.68557 5.11696i −0.248125 0.189908i
\(727\) 21.6647i 0.803500i −0.915749 0.401750i \(-0.868402\pi\)
0.915749 0.401750i \(-0.131598\pi\)
\(728\) 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 \(-0.922120\pi\)
0.694890 + 0.719116i \(0.255453\pi\)
\(734\) −4.52152 −0.166892
\(735\) 0 0
\(736\) 6.61931i 0.243991i
\(737\) 1.92276 + 9.63539i 0.0708258 + 0.354924i
\(738\) 4.95228 2.85920i 0.182296 0.105249i
\(739\) 4.11862 2.37789i 0.151506 0.0874719i −0.422331 0.906442i \(-0.638788\pi\)
0.573836 + 0.818970i \(0.305455\pi\)
\(740\) 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 −0.976299 0.216426i \(-0.930560\pi\)
0.675580 + 0.737287i \(0.263893\pi\)
\(752\) −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
\(759\) −5.39126 + 15.9143i −0.195690 + 0.577652i
\(760\) 0.901211 + 1.56094i 0.0326903 + 0.0566213i
\(761\) 0.927001 1.60561i 0.0336038 0.0582034i −0.848734 0.528819i \(-0.822635\pi\)
0.882338 + 0.470616i \(0.155968\pi\)
\(762\) 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 \(-0.448564\pi\)
0.160887 + 0.986973i \(0.448564\pi\)
\(770\) 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 −0.148821 0.988864i \(-0.547548\pi\)
0.781971 + 0.623315i \(0.214214\pi\)
\(774\) −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
\(781\) 6.70356 + 2.27096i 0.239872 + 0.0812612i
\(782\) −20.7005 11.9514i −0.740248 0.427382i
\(783\) 25.6486 0.916607