Properties

Label 756.2.ck.a.5.1
Level 756
Weight 2
Character 756.5
Analytic conductor 6.037
Analytic rank 0
Dimension 144
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.ck (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.03669039281\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.70107 - 0.326131i) q^{3} +(-0.752649 + 4.26848i) q^{5} +(-2.02371 - 1.70429i) q^{7} +(2.78728 + 1.10954i) q^{9} +O(q^{10})\) \(q+(-1.70107 - 0.326131i) q^{3} +(-0.752649 + 4.26848i) q^{5} +(-2.02371 - 1.70429i) q^{7} +(2.78728 + 1.10954i) q^{9} +(4.32943 - 0.763395i) q^{11} +(-1.92336 + 2.29217i) q^{13} +(2.67239 - 7.01553i) q^{15} -2.90177 q^{17} +7.24080i q^{19} +(2.88665 + 3.55911i) q^{21} +(0.613310 - 0.730915i) q^{23} +(-12.9550 - 4.71524i) q^{25} +(-4.37950 - 2.79643i) q^{27} +(-1.81160 - 2.15898i) q^{29} +(-3.48739 - 9.58153i) q^{31} +(-7.61363 - 0.113372i) q^{33} +(8.79786 - 7.35545i) q^{35} +(-1.55745 - 2.69759i) q^{37} +(4.01932 - 3.27188i) q^{39} +(-1.60343 - 1.34544i) q^{41} +(-6.51659 - 2.37185i) q^{43} +(-6.83391 + 11.0624i) q^{45} +(-6.33367 - 2.30527i) q^{47} +(1.19081 + 6.89797i) q^{49} +(4.93612 + 0.946358i) q^{51} +(-3.91722 + 2.26161i) q^{53} +19.0547i q^{55} +(2.36145 - 12.3171i) q^{57} +(-2.94386 - 2.47019i) q^{59} +(0.378045 - 1.03867i) q^{61} +(-3.74966 - 6.99571i) q^{63} +(-8.33648 - 9.93503i) q^{65} +(-2.23922 + 12.6992i) q^{67} +(-1.28166 + 1.04332i) q^{69} +(1.85714 + 1.07222i) q^{71} +(3.23289 + 1.86651i) q^{73} +(20.4996 + 12.2460i) q^{75} +(-10.0626 - 5.83370i) q^{77} +(1.72657 + 9.79189i) q^{79} +(6.53783 + 6.18521i) q^{81} +(12.4261 - 10.4268i) q^{83} +(2.18402 - 12.3862i) q^{85} +(2.37755 + 4.26340i) q^{87} +2.59484 q^{89} +(7.79884 - 1.36073i) q^{91} +(2.80746 + 17.4362i) q^{93} +(-30.9073 - 5.44978i) q^{95} +(1.09651 - 3.01263i) q^{97} +(12.9143 + 2.67589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.70107 0.326131i −0.982113 0.188292i
\(4\) 0 0
\(5\) −0.752649 + 4.26848i −0.336595 + 1.90892i 0.0742902 + 0.997237i \(0.476331\pi\)
−0.410885 + 0.911687i \(0.634780\pi\)
\(6\) 0 0
\(7\) −2.02371 1.70429i −0.764891 0.644160i
\(8\) 0 0
\(9\) 2.78728 + 1.10954i 0.929092 + 0.369848i
\(10\) 0 0
\(11\) 4.32943 0.763395i 1.30537 0.230172i 0.522652 0.852546i \(-0.324943\pi\)
0.782720 + 0.622374i \(0.213832\pi\)
\(12\) 0 0
\(13\) −1.92336 + 2.29217i −0.533444 + 0.635734i −0.963705 0.266971i \(-0.913977\pi\)
0.430260 + 0.902705i \(0.358422\pi\)
\(14\) 0 0
\(15\) 2.67239 7.01553i 0.690009 1.81140i
\(16\) 0 0
\(17\) −2.90177 −0.703783 −0.351892 0.936041i \(-0.614461\pi\)
−0.351892 + 0.936041i \(0.614461\pi\)
\(18\) 0 0
\(19\) 7.24080i 1.66115i 0.556904 + 0.830577i \(0.311989\pi\)
−0.556904 + 0.830577i \(0.688011\pi\)
\(20\) 0 0
\(21\) 2.88665 + 3.55911i 0.629919 + 0.776661i
\(22\) 0 0
\(23\) 0.613310 0.730915i 0.127884 0.152406i −0.698303 0.715802i \(-0.746061\pi\)
0.826187 + 0.563396i \(0.190506\pi\)
\(24\) 0 0
\(25\) −12.9550 4.71524i −2.59100 0.943047i
\(26\) 0 0
\(27\) −4.37950 2.79643i −0.842835 0.538173i
\(28\) 0 0
\(29\) −1.81160 2.15898i −0.336406 0.400913i 0.571149 0.820847i \(-0.306498\pi\)
−0.907555 + 0.419933i \(0.862054\pi\)
\(30\) 0 0
\(31\) −3.48739 9.58153i −0.626354 1.72089i −0.690872 0.722977i \(-0.742773\pi\)
0.0645186 0.997917i \(-0.479449\pi\)
\(32\) 0 0
\(33\) −7.61363 0.113372i −1.32536 0.0197355i
\(34\) 0 0
\(35\) 8.79786 7.35545i 1.48711 1.24330i
\(36\) 0 0
\(37\) −1.55745 2.69759i −0.256044 0.443481i 0.709135 0.705073i \(-0.249086\pi\)
−0.965178 + 0.261592i \(0.915752\pi\)
\(38\) 0 0
\(39\) 4.01932 3.27188i 0.643606 0.523920i
\(40\) 0 0
\(41\) −1.60343 1.34544i −0.250414 0.210122i 0.508936 0.860804i \(-0.330039\pi\)
−0.759351 + 0.650682i \(0.774483\pi\)
\(42\) 0 0
\(43\) −6.51659 2.37185i −0.993771 0.361703i −0.206592 0.978427i \(-0.566237\pi\)
−0.787179 + 0.616724i \(0.788459\pi\)
\(44\) 0 0
\(45\) −6.83391 + 11.0624i −1.01874 + 1.64908i
\(46\) 0 0
\(47\) −6.33367 2.30527i −0.923861 0.336258i −0.164087 0.986446i \(-0.552468\pi\)
−0.759773 + 0.650188i \(0.774690\pi\)
\(48\) 0 0
\(49\) 1.19081 + 6.89797i 0.170116 + 0.985424i
\(50\) 0 0
\(51\) 4.93612 + 0.946358i 0.691195 + 0.132517i
\(52\) 0 0
\(53\) −3.91722 + 2.26161i −0.538071 + 0.310655i −0.744297 0.667849i \(-0.767215\pi\)
0.206226 + 0.978504i \(0.433882\pi\)
\(54\) 0 0
\(55\) 19.0547i 2.56933i
\(56\) 0 0
\(57\) 2.36145 12.3171i 0.312782 1.63144i
\(58\) 0 0
\(59\) −2.94386 2.47019i −0.383257 0.321591i 0.430722 0.902485i \(-0.358259\pi\)
−0.813980 + 0.580893i \(0.802703\pi\)
\(60\) 0 0
\(61\) 0.378045 1.03867i 0.0484037 0.132988i −0.913135 0.407657i \(-0.866346\pi\)
0.961539 + 0.274669i \(0.0885682\pi\)
\(62\) 0 0
\(63\) −3.74966 6.99571i −0.472413 0.881377i
\(64\) 0 0
\(65\) −8.33648 9.93503i −1.03401 1.23229i
\(66\) 0 0
\(67\) −2.23922 + 12.6992i −0.273564 + 1.55146i 0.469921 + 0.882708i \(0.344282\pi\)
−0.743486 + 0.668752i \(0.766829\pi\)
\(68\) 0 0
\(69\) −1.28166 + 1.04332i −0.154293 + 0.125601i
\(70\) 0 0
\(71\) 1.85714 + 1.07222i 0.220402 + 0.127249i 0.606136 0.795361i \(-0.292719\pi\)
−0.385735 + 0.922610i \(0.626052\pi\)
\(72\) 0 0
\(73\) 3.23289 + 1.86651i 0.378381 + 0.218458i 0.677113 0.735879i \(-0.263231\pi\)
−0.298733 + 0.954337i \(0.596564\pi\)
\(74\) 0 0
\(75\) 20.4996 + 12.2460i 2.36709 + 1.41404i
\(76\) 0 0
\(77\) −10.0626 5.83370i −1.14673 0.664811i
\(78\) 0 0
\(79\) 1.72657 + 9.79189i 0.194255 + 1.10167i 0.913476 + 0.406893i \(0.133388\pi\)
−0.719221 + 0.694781i \(0.755501\pi\)
\(80\) 0 0
\(81\) 6.53783 + 6.18521i 0.726425 + 0.687245i
\(82\) 0 0
\(83\) 12.4261 10.4268i 1.36395 1.14449i 0.389205 0.921151i \(-0.372750\pi\)
0.974742 0.223336i \(-0.0716947\pi\)
\(84\) 0 0
\(85\) 2.18402 12.3862i 0.236890 1.34347i
\(86\) 0 0
\(87\) 2.37755 + 4.26340i 0.254900 + 0.457085i
\(88\) 0 0
\(89\) 2.59484 0.275052 0.137526 0.990498i \(-0.456085\pi\)
0.137526 + 0.990498i \(0.456085\pi\)
\(90\) 0 0
\(91\) 7.79884 1.36073i 0.817541 0.142644i
\(92\) 0 0
\(93\) 2.80746 + 17.4362i 0.291120 + 1.80805i
\(94\) 0 0
\(95\) −30.9073 5.44978i −3.17102 0.559136i
\(96\) 0 0
\(97\) 1.09651 3.01263i 0.111334 0.305887i −0.871496 0.490403i \(-0.836850\pi\)
0.982829 + 0.184516i \(0.0590719\pi\)
\(98\) 0 0
\(99\) 12.9143 + 2.67589i 1.29794 + 0.268937i
\(100\) 0 0
\(101\) −1.88932 + 1.58532i −0.187994 + 0.157746i −0.731927 0.681383i \(-0.761379\pi\)
0.543933 + 0.839128i \(0.316934\pi\)
\(102\) 0 0
\(103\) −13.6220 2.40193i −1.34222 0.236669i −0.544023 0.839070i \(-0.683100\pi\)
−0.798194 + 0.602401i \(0.794211\pi\)
\(104\) 0 0
\(105\) −17.3646 + 9.64287i −1.69461 + 0.941048i
\(106\) 0 0
\(107\) −0.786735 0.454221i −0.0760565 0.0439112i 0.461489 0.887146i \(-0.347315\pi\)
−0.537546 + 0.843234i \(0.680649\pi\)
\(108\) 0 0
\(109\) −1.61722 2.80111i −0.154902 0.268298i 0.778121 0.628114i \(-0.216173\pi\)
−0.933023 + 0.359816i \(0.882839\pi\)
\(110\) 0 0
\(111\) 1.76957 + 5.09672i 0.167960 + 0.483759i
\(112\) 0 0
\(113\) 4.89305 + 13.4435i 0.460299 + 1.26466i 0.925261 + 0.379331i \(0.123846\pi\)
−0.464962 + 0.885331i \(0.653932\pi\)
\(114\) 0 0
\(115\) 2.65829 + 3.16803i 0.247887 + 0.295420i
\(116\) 0 0
\(117\) −7.90420 + 4.25487i −0.730744 + 0.393363i
\(118\) 0 0
\(119\) 5.87235 + 4.94545i 0.538317 + 0.453349i
\(120\) 0 0
\(121\) 7.82456 2.84791i 0.711324 0.258901i
\(122\) 0 0
\(123\) 2.28876 + 2.81162i 0.206371 + 0.253515i
\(124\) 0 0
\(125\) 19.0417 32.9811i 1.70314 2.94992i
\(126\) 0 0
\(127\) −0.308792 0.534844i −0.0274009 0.0474597i 0.852000 0.523542i \(-0.175390\pi\)
−0.879401 + 0.476082i \(0.842056\pi\)
\(128\) 0 0
\(129\) 10.3116 + 6.15994i 0.907890 + 0.542352i
\(130\) 0 0
\(131\) −2.14776 1.80218i −0.187651 0.157458i 0.544123 0.839006i \(-0.316863\pi\)
−0.731773 + 0.681548i \(0.761307\pi\)
\(132\) 0 0
\(133\) 12.3404 14.6533i 1.07005 1.27060i
\(134\) 0 0
\(135\) 15.2327 16.5891i 1.31102 1.42776i
\(136\) 0 0
\(137\) −0.761525 + 2.09227i −0.0650615 + 0.178755i −0.967963 0.251092i \(-0.919210\pi\)
0.902902 + 0.429847i \(0.141433\pi\)
\(138\) 0 0
\(139\) 3.14112 + 0.553864i 0.266426 + 0.0469781i 0.305265 0.952267i \(-0.401255\pi\)
−0.0388391 + 0.999245i \(0.512366\pi\)
\(140\) 0 0
\(141\) 10.0222 + 5.98703i 0.844021 + 0.504199i
\(142\) 0 0
\(143\) −6.57722 + 11.3921i −0.550015 + 0.952653i
\(144\) 0 0
\(145\) 10.5791 6.10784i 0.878546 0.507229i
\(146\) 0 0
\(147\) 0.223986 12.1223i 0.0184740 0.999829i
\(148\) 0 0
\(149\) −1.48706 4.08565i −0.121824 0.334710i 0.863758 0.503907i \(-0.168105\pi\)
−0.985582 + 0.169197i \(0.945882\pi\)
\(150\) 0 0
\(151\) −1.64956 9.35512i −0.134239 0.761309i −0.975386 0.220503i \(-0.929230\pi\)
0.841147 0.540806i \(-0.181881\pi\)
\(152\) 0 0
\(153\) −8.08805 3.21964i −0.653880 0.260293i
\(154\) 0 0
\(155\) 43.5234 7.67434i 3.49588 0.616418i
\(156\) 0 0
\(157\) −7.53512 + 8.98000i −0.601368 + 0.716682i −0.977748 0.209783i \(-0.932724\pi\)
0.376380 + 0.926465i \(0.377169\pi\)
\(158\) 0 0
\(159\) 7.40104 2.56962i 0.586940 0.203784i
\(160\) 0 0
\(161\) −2.48685 + 0.433903i −0.195991 + 0.0341964i
\(162\) 0 0
\(163\) 5.42078 9.38907i 0.424588 0.735408i −0.571794 0.820397i \(-0.693752\pi\)
0.996382 + 0.0849891i \(0.0270855\pi\)
\(164\) 0 0
\(165\) 6.21431 32.4133i 0.483784 2.52337i
\(166\) 0 0
\(167\) 8.96909 3.26448i 0.694049 0.252613i 0.0291811 0.999574i \(-0.490710\pi\)
0.664868 + 0.746961i \(0.268488\pi\)
\(168\) 0 0
\(169\) 0.702691 + 3.98516i 0.0540532 + 0.306551i
\(170\) 0 0
\(171\) −8.03398 + 20.1821i −0.614374 + 1.54337i
\(172\) 0 0
\(173\) −2.14560 + 1.80038i −0.163127 + 0.136880i −0.720697 0.693250i \(-0.756178\pi\)
0.557570 + 0.830130i \(0.311734\pi\)
\(174\) 0 0
\(175\) 18.1811 + 31.6213i 1.37436 + 2.39035i
\(176\) 0 0
\(177\) 4.20210 + 5.16205i 0.315849 + 0.388003i
\(178\) 0 0
\(179\) 5.74007i 0.429033i −0.976720 0.214516i \(-0.931182\pi\)
0.976720 0.214516i \(-0.0688176\pi\)
\(180\) 0 0
\(181\) −12.3552 + 7.13329i −0.918356 + 0.530213i −0.883110 0.469166i \(-0.844555\pi\)
−0.0352458 + 0.999379i \(0.511221\pi\)
\(182\) 0 0
\(183\) −0.981824 + 1.64356i −0.0725785 + 0.121495i
\(184\) 0 0
\(185\) 12.6868 4.61762i 0.932753 0.339494i
\(186\) 0 0
\(187\) −12.5630 + 2.21520i −0.918699 + 0.161991i
\(188\) 0 0
\(189\) 4.09692 + 13.1231i 0.298007 + 0.954564i
\(190\) 0 0
\(191\) −12.4959 + 2.20336i −0.904172 + 0.159430i −0.606356 0.795193i \(-0.707369\pi\)
−0.297816 + 0.954623i \(0.596258\pi\)
\(192\) 0 0
\(193\) −18.1759 + 6.61549i −1.30833 + 0.476193i −0.899701 0.436507i \(-0.856215\pi\)
−0.408630 + 0.912700i \(0.633993\pi\)
\(194\) 0 0
\(195\) 10.9408 + 19.6190i 0.783488 + 1.40494i
\(196\) 0 0
\(197\) −16.8427 + 9.72416i −1.20000 + 0.692818i −0.960554 0.278093i \(-0.910298\pi\)
−0.239442 + 0.970911i \(0.576964\pi\)
\(198\) 0 0
\(199\) 2.05689i 0.145809i −0.997339 0.0729045i \(-0.976773\pi\)
0.997339 0.0729045i \(-0.0232268\pi\)
\(200\) 0 0
\(201\) 7.95069 20.8720i 0.560798 1.47220i
\(202\) 0 0
\(203\) −0.0133679 + 7.45665i −0.000938244 + 0.523354i
\(204\) 0 0
\(205\) 6.94981 5.83159i 0.485396 0.407296i
\(206\) 0 0
\(207\) 2.52045 1.35677i 0.175183 0.0943019i
\(208\) 0 0
\(209\) 5.52759 + 31.3485i 0.382352 + 2.16842i
\(210\) 0 0
\(211\) −15.5379 + 5.65535i −1.06968 + 0.389330i −0.816055 0.577974i \(-0.803844\pi\)
−0.253620 + 0.967304i \(0.581621\pi\)
\(212\) 0 0
\(213\) −2.80944 2.42959i −0.192499 0.166473i
\(214\) 0 0
\(215\) 15.0289 26.0308i 1.02496 1.77529i
\(216\) 0 0
\(217\) −9.27220 + 25.3338i −0.629438 + 1.71977i
\(218\) 0 0
\(219\) −4.89064 4.22940i −0.330479 0.285797i
\(220\) 0 0
\(221\) 5.58115 6.65136i 0.375429 0.447419i
\(222\) 0 0
\(223\) −17.4743 + 3.08118i −1.17016 + 0.206331i −0.724762 0.688999i \(-0.758050\pi\)
−0.445402 + 0.895331i \(0.646939\pi\)
\(224\) 0 0
\(225\) −30.8774 27.5168i −2.05850 1.83445i
\(226\) 0 0
\(227\) 4.57912 + 25.9695i 0.303927 + 1.72366i 0.628512 + 0.777800i \(0.283664\pi\)
−0.324585 + 0.945856i \(0.605225\pi\)
\(228\) 0 0
\(229\) 6.47887 + 17.8006i 0.428136 + 1.17629i 0.946943 + 0.321402i \(0.104154\pi\)
−0.518807 + 0.854891i \(0.673624\pi\)
\(230\) 0 0
\(231\) 15.2146 + 13.2052i 1.00104 + 0.868841i
\(232\) 0 0
\(233\) 7.05865 4.07531i 0.462427 0.266983i −0.250637 0.968081i \(-0.580640\pi\)
0.713064 + 0.701099i \(0.247307\pi\)
\(234\) 0 0
\(235\) 14.6070 25.3001i 0.952857 1.65040i
\(236\) 0 0
\(237\) 0.256414 17.2198i 0.0166559 1.11855i
\(238\) 0 0
\(239\) 15.2709 + 2.69267i 0.987792 + 0.174174i 0.644128 0.764918i \(-0.277221\pi\)
0.343665 + 0.939092i \(0.388332\pi\)
\(240\) 0 0
\(241\) −6.27100 + 17.2294i −0.403951 + 1.10985i 0.556367 + 0.830937i \(0.312195\pi\)
−0.960318 + 0.278909i \(0.910027\pi\)
\(242\) 0 0
\(243\) −9.10412 12.6537i −0.584029 0.811732i
\(244\) 0 0
\(245\) −30.3401 0.108785i −1.93836 0.00695002i
\(246\) 0 0
\(247\) −16.5972 13.9267i −1.05605 0.886133i
\(248\) 0 0
\(249\) −24.5382 + 13.6841i −1.55505 + 0.867196i
\(250\) 0 0
\(251\) 2.09345 + 3.62596i 0.132137 + 0.228869i 0.924500 0.381181i \(-0.124483\pi\)
−0.792363 + 0.610050i \(0.791149\pi\)
\(252\) 0 0
\(253\) 2.09731 3.63264i 0.131856 0.228382i
\(254\) 0 0
\(255\) −7.75468 + 20.3575i −0.485617 + 1.27483i
\(256\) 0 0
\(257\) 22.5787 8.21799i 1.40842 0.512624i 0.477757 0.878492i \(-0.341450\pi\)
0.930667 + 0.365868i \(0.119228\pi\)
\(258\) 0 0
\(259\) −1.44563 + 8.11348i −0.0898270 + 0.504147i
\(260\) 0 0
\(261\) −2.65395 8.02774i −0.164276 0.496905i
\(262\) 0 0
\(263\) 10.8318 + 12.9088i 0.667917 + 0.795993i 0.988499 0.151228i \(-0.0483229\pi\)
−0.320582 + 0.947221i \(0.603878\pi\)
\(264\) 0 0
\(265\) −6.70534 18.4228i −0.411906 1.13170i
\(266\) 0 0
\(267\) −4.41400 0.846257i −0.270133 0.0517901i
\(268\) 0 0
\(269\) 13.0831 + 22.6606i 0.797690 + 1.38164i 0.921117 + 0.389286i \(0.127278\pi\)
−0.123427 + 0.992354i \(0.539389\pi\)
\(270\) 0 0
\(271\) −17.1840 9.92120i −1.04385 0.602670i −0.122932 0.992415i \(-0.539230\pi\)
−0.920923 + 0.389745i \(0.872563\pi\)
\(272\) 0 0
\(273\) −13.7102 0.228738i −0.829776 0.0138439i
\(274\) 0 0
\(275\) −59.6874 10.5245i −3.59928 0.634651i
\(276\) 0 0
\(277\) 16.7162 14.0265i 1.00438 0.842773i 0.0167929 0.999859i \(-0.494654\pi\)
0.987585 + 0.157086i \(0.0502100\pi\)
\(278\) 0 0
\(279\) 0.910790 30.5758i 0.0545276 1.83052i
\(280\) 0 0
\(281\) −10.6039 + 29.1339i −0.632575 + 1.73799i 0.0413070 + 0.999147i \(0.486848\pi\)
−0.673882 + 0.738839i \(0.735374\pi\)
\(282\) 0 0
\(283\) −7.29589 1.28646i −0.433695 0.0764722i −0.0474615 0.998873i \(-0.515113\pi\)
−0.386234 + 0.922401i \(0.626224\pi\)
\(284\) 0 0
\(285\) 50.7981 + 19.3503i 3.00902 + 1.14621i
\(286\) 0 0
\(287\) 0.951869 + 5.45549i 0.0561871 + 0.322028i
\(288\) 0 0
\(289\) −8.57971 −0.504689
\(290\) 0 0
\(291\) −2.84775 + 4.76709i −0.166938 + 0.279452i
\(292\) 0 0
\(293\) 0.184679 1.04737i 0.0107891 0.0611878i −0.978938 0.204158i \(-0.934554\pi\)
0.989727 + 0.142970i \(0.0456654\pi\)
\(294\) 0 0
\(295\) 12.7597 10.7066i 0.742896 0.623363i
\(296\) 0 0
\(297\) −21.0955 8.76364i −1.22408 0.508518i
\(298\) 0 0
\(299\) 0.495765 + 2.81162i 0.0286708 + 0.162600i
\(300\) 0 0
\(301\) 9.14539 + 15.9061i 0.527132 + 0.916811i
\(302\) 0 0
\(303\) 3.73088 2.08058i 0.214333 0.119526i
\(304\) 0 0
\(305\) 4.14901 + 2.39543i 0.237572 + 0.137162i
\(306\) 0 0
\(307\) 21.3745 + 12.3406i 1.21991 + 0.704313i 0.964898 0.262625i \(-0.0845883\pi\)
0.255009 + 0.966939i \(0.417922\pi\)
\(308\) 0 0
\(309\) 22.3887 + 8.52841i 1.27365 + 0.485164i
\(310\) 0 0
\(311\) 3.38324 19.1873i 0.191846 1.08801i −0.724994 0.688755i \(-0.758157\pi\)
0.916840 0.399256i \(-0.130731\pi\)
\(312\) 0 0
\(313\) −0.941625 1.12219i −0.0532238 0.0634297i 0.738776 0.673951i \(-0.235404\pi\)
−0.792000 + 0.610522i \(0.790960\pi\)
\(314\) 0 0
\(315\) 32.6833 10.7401i 1.84149 0.605134i
\(316\) 0 0
\(317\) −5.51824 + 15.1612i −0.309935 + 0.851541i 0.682733 + 0.730668i \(0.260791\pi\)
−0.992668 + 0.120872i \(0.961431\pi\)
\(318\) 0 0
\(319\) −9.49136 7.96420i −0.531414 0.445910i
\(320\) 0 0
\(321\) 1.19016 + 1.02924i 0.0664280 + 0.0574466i
\(322\) 0 0
\(323\) 21.0112i 1.16909i
\(324\) 0 0
\(325\) 35.7253 20.6260i 1.98168 1.14412i
\(326\) 0 0
\(327\) 1.83748 + 5.29231i 0.101613 + 0.292665i
\(328\) 0 0
\(329\) 8.88868 + 15.4596i 0.490049 + 0.852315i
\(330\) 0 0
\(331\) −2.87169 1.04521i −0.157842 0.0574500i 0.261891 0.965098i \(-0.415654\pi\)
−0.419733 + 0.907648i \(0.637876\pi\)
\(332\) 0 0
\(333\) −1.34796 9.24698i −0.0738680 0.506731i
\(334\) 0 0
\(335\) −52.5212 19.1161i −2.86954 1.04443i
\(336\) 0 0
\(337\) 2.25773 + 1.89446i 0.122986 + 0.103198i 0.702206 0.711973i \(-0.252198\pi\)
−0.579220 + 0.815171i \(0.696643\pi\)
\(338\) 0 0
\(339\) −3.93906 24.4642i −0.213941 1.32871i
\(340\) 0 0
\(341\) −22.4129 38.8203i −1.21373 2.10224i
\(342\) 0 0
\(343\) 9.34626 15.9890i 0.504650 0.863324i
\(344\) 0 0
\(345\) −3.48875 6.25598i −0.187828 0.336811i
\(346\) 0 0
\(347\) −6.74241 18.5246i −0.361952 0.994454i −0.978339 0.207011i \(-0.933627\pi\)
0.616387 0.787443i \(-0.288596\pi\)
\(348\) 0 0
\(349\) −10.9431 13.0415i −0.585773 0.698097i 0.389014 0.921232i \(-0.372816\pi\)
−0.974788 + 0.223134i \(0.928371\pi\)
\(350\) 0 0
\(351\) 14.8332 4.66002i 0.791740 0.248734i
\(352\) 0 0
\(353\) 31.5747 + 11.4922i 1.68055 + 0.611670i 0.993385 0.114830i \(-0.0366325\pi\)
0.687166 + 0.726501i \(0.258855\pi\)
\(354\) 0 0
\(355\) −5.97452 + 7.12015i −0.317094 + 0.377898i
\(356\) 0 0
\(357\) −8.37641 10.3277i −0.443327 0.546601i
\(358\) 0 0
\(359\) 35.8639i 1.89282i −0.322963 0.946412i \(-0.604679\pi\)
0.322963 0.946412i \(-0.395321\pi\)
\(360\) 0 0
\(361\) −33.4292 −1.75943
\(362\) 0 0
\(363\) −14.2389 + 2.29266i −0.747349 + 0.120333i
\(364\) 0 0
\(365\) −10.4004 + 12.3947i −0.544381 + 0.648768i
\(366\) 0 0
\(367\) −10.2889 + 1.81421i −0.537075 + 0.0947008i −0.435605 0.900138i \(-0.643466\pi\)
−0.101470 + 0.994839i \(0.532354\pi\)
\(368\) 0 0
\(369\) −2.97639 5.52919i −0.154945 0.287838i
\(370\) 0 0
\(371\) 11.7817 + 2.09922i 0.611677 + 0.108986i
\(372\) 0 0
\(373\) −3.57682 + 20.2851i −0.185200 + 1.05032i 0.740497 + 0.672060i \(0.234590\pi\)
−0.925698 + 0.378264i \(0.876521\pi\)
\(374\) 0 0
\(375\) −43.1473 + 49.8931i −2.22812 + 2.57647i
\(376\) 0 0
\(377\) 8.43313 0.434328
\(378\) 0 0
\(379\) 17.6242 0.905295 0.452647 0.891690i \(-0.350480\pi\)
0.452647 + 0.891690i \(0.350480\pi\)
\(380\) 0 0
\(381\) 0.350848 + 1.01051i 0.0179745 + 0.0517702i
\(382\) 0 0
\(383\) −3.38965 + 19.2237i −0.173203 + 0.982283i 0.766994 + 0.641654i \(0.221751\pi\)
−0.940198 + 0.340630i \(0.889360\pi\)
\(384\) 0 0
\(385\) 32.4746 38.5611i 1.65506 1.96526i
\(386\) 0 0
\(387\) −15.5319 13.8414i −0.789530 0.703599i
\(388\) 0 0
\(389\) 19.1065 3.36900i 0.968739 0.170815i 0.333177 0.942864i \(-0.391879\pi\)
0.635562 + 0.772049i \(0.280768\pi\)
\(390\) 0 0
\(391\) −1.77969 + 2.12095i −0.0900026 + 0.107261i
\(392\) 0 0
\(393\) 3.06574 + 3.76609i 0.154646 + 0.189974i
\(394\) 0 0
\(395\) −43.0960 −2.16840
\(396\) 0 0
\(397\) 14.2349i 0.714430i −0.934022 0.357215i \(-0.883726\pi\)
0.934022 0.357215i \(-0.116274\pi\)
\(398\) 0 0
\(399\) −25.7708 + 20.9017i −1.29015 + 1.04639i
\(400\) 0 0
\(401\) −5.44418 + 6.48813i −0.271870 + 0.324002i −0.884654 0.466249i \(-0.845605\pi\)
0.612784 + 0.790250i \(0.290050\pi\)
\(402\) 0 0
\(403\) 28.6700 + 10.4350i 1.42815 + 0.519806i
\(404\) 0 0
\(405\) −31.3221 + 23.2513i −1.55641 + 1.15537i
\(406\) 0 0
\(407\) −8.80220 10.4901i −0.436309 0.519973i
\(408\) 0 0
\(409\) −7.95252 21.8494i −0.393227 1.08038i −0.965519 0.260332i \(-0.916168\pi\)
0.572293 0.820049i \(-0.306054\pi\)
\(410\) 0 0
\(411\) 1.97776 3.31075i 0.0975558 0.163307i
\(412\) 0 0
\(413\) 1.74760 + 10.0161i 0.0859940 + 0.492861i
\(414\) 0 0
\(415\) 35.1540 + 60.8885i 1.72564 + 2.98890i
\(416\) 0 0
\(417\) −5.16263 1.96658i −0.252815 0.0963037i
\(418\) 0 0
\(419\) 22.3451 + 18.7498i 1.09163 + 0.915986i 0.996834 0.0795111i \(-0.0253359\pi\)
0.0947953 + 0.995497i \(0.469780\pi\)
\(420\) 0 0
\(421\) 0.0754834 + 0.0274737i 0.00367883 + 0.00133899i 0.343859 0.939021i \(-0.388266\pi\)
−0.340180 + 0.940360i \(0.610488\pi\)
\(422\) 0 0
\(423\) −15.0959 13.4529i −0.733988 0.654102i
\(424\) 0 0
\(425\) 37.5925 + 13.6825i 1.82350 + 0.663701i
\(426\) 0 0
\(427\) −2.53525 + 1.45767i −0.122689 + 0.0705417i
\(428\) 0 0
\(429\) 14.9036 17.2337i 0.719553 0.832050i
\(430\) 0 0
\(431\) −5.28143 + 3.04924i −0.254398 + 0.146877i −0.621776 0.783195i \(-0.713589\pi\)
0.367379 + 0.930072i \(0.380255\pi\)
\(432\) 0 0
\(433\) 14.5293i 0.698233i 0.937079 + 0.349117i \(0.113518\pi\)
−0.937079 + 0.349117i \(0.886482\pi\)
\(434\) 0 0
\(435\) −19.9877 + 6.93970i −0.958338 + 0.332733i
\(436\) 0 0
\(437\) 5.29241 + 4.44086i 0.253170 + 0.212435i
\(438\) 0 0
\(439\) −5.60029 + 15.3867i −0.267287 + 0.734366i 0.731341 + 0.682012i \(0.238895\pi\)
−0.998629 + 0.0523540i \(0.983328\pi\)
\(440\) 0 0
\(441\) −4.33447 + 20.5478i −0.206403 + 0.978467i
\(442\) 0 0
\(443\) 9.21074 + 10.9769i 0.437615 + 0.521530i 0.939103 0.343635i \(-0.111658\pi\)
−0.501488 + 0.865165i \(0.667214\pi\)
\(444\) 0 0
\(445\) −1.95300 + 11.0760i −0.0925812 + 0.525054i
\(446\) 0 0
\(447\) 1.19713 + 7.43496i 0.0566222 + 0.351661i
\(448\) 0 0
\(449\) 0.400129 + 0.231014i 0.0188832 + 0.0109022i 0.509412 0.860523i \(-0.329863\pi\)
−0.490529 + 0.871425i \(0.663196\pi\)
\(450\) 0 0
\(451\) −7.96905 4.60093i −0.375248 0.216650i
\(452\) 0 0
\(453\) −0.244977 + 16.4517i −0.0115100 + 0.772968i
\(454\) 0 0
\(455\) −0.0615154 + 34.3134i −0.00288388 + 1.60864i
\(456\) 0 0
\(457\) −3.13328 17.7697i −0.146569 0.831233i −0.966094 0.258190i \(-0.916874\pi\)
0.819525 0.573043i \(-0.194237\pi\)
\(458\) 0 0
\(459\) 12.7083 + 8.11460i 0.593173 + 0.378757i
\(460\) 0 0
\(461\) −25.2637 + 21.1987i −1.17665 + 0.987324i −0.176651 + 0.984273i \(0.556527\pi\)
−0.999995 + 0.00305036i \(0.999029\pi\)
\(462\) 0 0
\(463\) −0.520482 + 2.95180i −0.0241888 + 0.137182i −0.994511 0.104636i \(-0.966632\pi\)
0.970322 + 0.241817i \(0.0777435\pi\)
\(464\) 0 0
\(465\) −76.5391 1.13972i −3.54942 0.0528532i
\(466\) 0 0
\(467\) −12.8978 −0.596837 −0.298419 0.954435i \(-0.596459\pi\)
−0.298419 + 0.954435i \(0.596459\pi\)
\(468\) 0 0
\(469\) 26.1747 21.8833i 1.20864 1.01048i
\(470\) 0 0
\(471\) 15.7464 12.8182i 0.725556 0.590630i
\(472\) 0 0
\(473\) −30.0238 5.29400i −1.38049 0.243418i
\(474\) 0 0
\(475\) 34.1421 93.8047i 1.56655 4.30405i
\(476\) 0 0
\(477\) −13.4277 + 1.95740i −0.614813 + 0.0896233i
\(478\) 0 0
\(479\) −7.07175 + 5.93390i −0.323117 + 0.271127i −0.789888 0.613251i \(-0.789861\pi\)
0.466772 + 0.884378i \(0.345417\pi\)
\(480\) 0 0
\(481\) 9.17887 + 1.61848i 0.418521 + 0.0737965i
\(482\) 0 0
\(483\) 4.37182 + 0.0729388i 0.198925 + 0.00331883i
\(484\) 0 0
\(485\) 12.0341 + 6.94789i 0.546440 + 0.315487i
\(486\) 0 0
\(487\) 0.254346 + 0.440540i 0.0115255 + 0.0199628i 0.871731 0.489985i \(-0.162998\pi\)
−0.860205 + 0.509948i \(0.829665\pi\)
\(488\) 0 0
\(489\) −12.2832 + 14.2036i −0.555465 + 0.642308i
\(490\) 0 0
\(491\) −5.98576 16.4457i −0.270134 0.742186i −0.998381 0.0568721i \(-0.981887\pi\)
0.728248 0.685314i \(-0.240335\pi\)
\(492\) 0 0
\(493\) 5.25686 + 6.26488i 0.236757 + 0.282156i
\(494\) 0 0
\(495\) −21.1420 + 53.1106i −0.950261 + 2.38715i
\(496\) 0 0
\(497\) −1.93094 5.33495i −0.0866145 0.239305i
\(498\) 0 0
\(499\) −3.27700 + 1.19273i −0.146699 + 0.0533940i −0.414326 0.910129i \(-0.635983\pi\)
0.267627 + 0.963523i \(0.413760\pi\)
\(500\) 0 0
\(501\) −16.3217 + 2.62801i −0.729200 + 0.117411i
\(502\) 0 0
\(503\) −17.1485 + 29.7021i −0.764614 + 1.32435i 0.175836 + 0.984419i \(0.443737\pi\)
−0.940450 + 0.339931i \(0.889596\pi\)
\(504\) 0 0
\(505\) −5.34494 9.25770i −0.237847 0.411962i
\(506\) 0 0
\(507\) 0.104357 7.00820i 0.00463465 0.311245i
\(508\) 0 0
\(509\) −5.27529 4.42649i −0.233823 0.196201i 0.518346 0.855171i \(-0.326548\pi\)
−0.752169 + 0.658970i \(0.770992\pi\)
\(510\) 0 0
\(511\) −3.36136 9.28704i −0.148698 0.410834i
\(512\) 0 0
\(513\) 20.2484 31.7111i 0.893988 1.40008i
\(514\) 0 0
\(515\) 20.5052 56.3375i 0.903566 2.48253i
\(516\) 0 0
\(517\) −29.1810 5.14540i −1.28338 0.226294i
\(518\) 0 0
\(519\) 4.23698 2.36282i 0.185983 0.103716i
\(520\) 0 0
\(521\) 14.2509 24.6832i 0.624341 1.08139i −0.364326 0.931271i \(-0.618701\pi\)
0.988668 0.150120i \(-0.0479659\pi\)
\(522\) 0 0
\(523\) 23.7033 13.6851i 1.03647 0.598408i 0.117641 0.993056i \(-0.462467\pi\)
0.918832 + 0.394648i \(0.129134\pi\)
\(524\) 0 0
\(525\) −20.6146 59.7195i −0.899694 2.60637i
\(526\) 0 0
\(527\) 10.1196 + 27.8034i 0.440817 + 1.21114i
\(528\) 0 0
\(529\) 3.83582 + 21.7540i 0.166775 + 0.945827i
\(530\) 0 0
\(531\) −5.46456 10.1514i −0.237142 0.440535i
\(532\) 0 0
\(533\) 6.16796 1.08758i 0.267164 0.0471082i
\(534\) 0 0
\(535\) 2.53097 3.01629i 0.109423 0.130406i
\(536\) 0 0
\(537\) −1.87201 + 9.76426i −0.0807834 + 0.421359i
\(538\) 0 0
\(539\) 10.4214 + 28.9552i 0.448882 + 1.24719i
\(540\) 0 0
\(541\) 5.53654 9.58956i 0.238034 0.412287i −0.722116 0.691772i \(-0.756830\pi\)
0.960150 + 0.279485i \(0.0901636\pi\)
\(542\) 0 0
\(543\) 23.3435 8.10480i 1.00176 0.347810i
\(544\) 0 0
\(545\) 13.1737 4.79483i 0.564299 0.205388i
\(546\) 0 0
\(547\) 5.69539 + 32.3002i 0.243517 + 1.38105i 0.823911 + 0.566719i \(0.191787\pi\)
−0.580394 + 0.814336i \(0.697101\pi\)
\(548\) 0 0
\(549\) 2.20617 2.47561i 0.0941569 0.105656i
\(550\) 0 0
\(551\) 15.6328 13.1175i 0.665979 0.558823i
\(552\) 0 0
\(553\) 13.1941 22.7585i 0.561070 0.967792i
\(554\) 0 0
\(555\) −23.0871 + 3.71734i −0.979993 + 0.157792i
\(556\) 0 0
\(557\) 21.6610i 0.917804i 0.888487 + 0.458902i \(0.151757\pi\)
−0.888487 + 0.458902i \(0.848243\pi\)
\(558\) 0 0
\(559\) 17.9704 10.3752i 0.760068 0.438825i
\(560\) 0 0
\(561\) 22.0930 + 0.328980i 0.932768 + 0.0138895i
\(562\) 0 0
\(563\) −25.3800 + 9.23755i −1.06964 + 0.389316i −0.816041 0.577994i \(-0.803836\pi\)
−0.253596 + 0.967310i \(0.581614\pi\)
\(564\) 0 0
\(565\) −61.0663 + 10.7676i −2.56908 + 0.452998i
\(566\) 0 0
\(567\) −2.68931 23.6594i −0.112940 0.993602i
\(568\) 0 0
\(569\) 2.52733 0.445636i 0.105951 0.0186820i −0.120421 0.992723i \(-0.538425\pi\)
0.226372 + 0.974041i \(0.427313\pi\)
\(570\) 0 0
\(571\) −8.40208 + 3.05811i −0.351616 + 0.127978i −0.511789 0.859111i \(-0.671017\pi\)
0.160173 + 0.987089i \(0.448795\pi\)
\(572\) 0 0
\(573\) 21.9750 + 0.327222i 0.918018 + 0.0136699i
\(574\) 0 0
\(575\) −11.3919 + 6.57710i −0.475074 + 0.274284i
\(576\) 0 0
\(577\) 22.4290i 0.933730i −0.884329 0.466865i \(-0.845383\pi\)
0.884329 0.466865i \(-0.154617\pi\)
\(578\) 0 0
\(579\) 33.0760 5.32569i 1.37459 0.221328i
\(580\) 0 0
\(581\) −42.9171 0.0769398i −1.78050 0.00319200i
\(582\) 0 0
\(583\) −15.2328 + 12.7818i −0.630878 + 0.529370i
\(584\) 0 0
\(585\) −12.2127 36.9414i −0.504935 1.52734i
\(586\) 0 0
\(587\) −0.0953518 0.540767i −0.00393559 0.0223198i 0.982777 0.184797i \(-0.0591627\pi\)
−0.986712 + 0.162477i \(0.948052\pi\)
\(588\) 0 0
\(589\) 69.3780 25.2515i 2.85867 1.04047i
\(590\) 0 0
\(591\) 31.8220 11.0485i 1.30898 0.454476i
\(592\) 0 0
\(593\) 6.42425 11.1271i 0.263812 0.456936i −0.703439 0.710755i \(-0.748353\pi\)
0.967252 + 0.253819i \(0.0816867\pi\)
\(594\) 0 0
\(595\) −25.5294 + 21.3438i −1.04660 + 0.875012i
\(596\) 0 0
\(597\) −0.670815 + 3.49891i −0.0274546 + 0.143201i
\(598\) 0 0
\(599\) −15.6455 + 18.6455i −0.639256 + 0.761836i −0.984252 0.176768i \(-0.943436\pi\)
0.344997 + 0.938604i \(0.387880\pi\)
\(600\) 0 0
\(601\) −11.2471 + 1.98317i −0.458779 + 0.0808951i −0.398261 0.917272i \(-0.630386\pi\)
−0.0605177 + 0.998167i \(0.519275\pi\)
\(602\) 0 0
\(603\) −20.3317 + 32.9118i −0.827970 + 1.34027i
\(604\) 0 0
\(605\) 6.26710 + 35.5425i 0.254794 + 1.44501i
\(606\) 0 0
\(607\) −6.58645 18.0961i −0.267336 0.734499i −0.998625 0.0524309i \(-0.983303\pi\)
0.731289 0.682068i \(-0.238919\pi\)
\(608\) 0 0
\(609\) 2.45458 12.6799i 0.0994648 0.513817i
\(610\) 0 0
\(611\) 17.4660 10.0840i 0.706599 0.407955i
\(612\) 0 0
\(613\) 1.49015 2.58101i 0.0601865 0.104246i −0.834362 0.551217i \(-0.814164\pi\)
0.894549 + 0.446971i \(0.147497\pi\)
\(614\) 0 0
\(615\) −13.7240 + 7.65339i −0.553404 + 0.308614i
\(616\) 0 0
\(617\) 4.17081 + 0.735426i 0.167910 + 0.0296071i 0.256971 0.966419i \(-0.417275\pi\)
−0.0890608 + 0.996026i \(0.528387\pi\)
\(618\) 0 0
\(619\) −5.06792 + 13.9240i −0.203697 + 0.559652i −0.998910 0.0466775i \(-0.985137\pi\)
0.795213 + 0.606330i \(0.207359\pi\)
\(620\) 0 0
\(621\) −4.72994 + 1.48596i −0.189806 + 0.0596296i
\(622\) 0 0
\(623\) −5.25121 4.42235i −0.210385 0.177178i
\(624\) 0 0
\(625\) 73.6426 + 61.7934i 2.94570 + 2.47174i
\(626\) 0 0
\(627\) 0.820905 55.1288i 0.0327838 2.20163i
\(628\) 0 0
\(629\) 4.51937 + 7.82778i 0.180199 + 0.312114i
\(630\) 0 0
\(631\) −17.7526 + 30.7485i −0.706721 + 1.22408i 0.259346 + 0.965785i \(0.416493\pi\)
−0.966067 + 0.258292i \(0.916840\pi\)
\(632\) 0 0
\(633\) 28.2755 4.55274i 1.12385 0.180955i
\(634\) 0 0
\(635\) 2.51538 0.915525i 0.0998200 0.0363315i
\(636\) 0 0
\(637\) −18.1017 10.5377i −0.717215 0.417520i
\(638\) 0 0
\(639\) 3.98668 + 5.04914i 0.157711 + 0.199741i
\(640\) 0 0
\(641\) 27.7797 + 33.1065i 1.09723 + 1.30763i 0.947803 + 0.318857i \(0.103299\pi\)
0.149429 + 0.988772i \(0.452257\pi\)
\(642\) 0 0
\(643\) −5.11111 14.0427i −0.201563 0.553789i 0.797190 0.603729i \(-0.206319\pi\)
−0.998752 + 0.0499403i \(0.984097\pi\)
\(644\) 0 0
\(645\) −34.0546 + 39.3788i −1.34090 + 1.55054i
\(646\) 0 0
\(647\) −11.6483 20.1754i −0.457942 0.793178i 0.540910 0.841080i \(-0.318080\pi\)
−0.998852 + 0.0479021i \(0.984746\pi\)
\(648\) 0 0
\(649\) −14.6309 8.44718i −0.574315 0.331581i
\(650\) 0 0
\(651\) 24.0348 40.0705i 0.941997 1.57049i
\(652\) 0 0
\(653\) −1.35897 0.239623i −0.0531805 0.00937716i 0.146995 0.989137i \(-0.453040\pi\)
−0.200175 + 0.979760i \(0.564151\pi\)
\(654\) 0 0
\(655\) 9.30910 7.81126i 0.363737 0.305211i
\(656\) 0 0
\(657\) 6.93998 + 8.78950i 0.270754 + 0.342911i
\(658\) 0 0
\(659\) 7.35876 20.2180i 0.286657 0.787582i −0.709872 0.704331i \(-0.751247\pi\)
0.996529 0.0832516i \(-0.0265305\pi\)
\(660\) 0 0
\(661\) −16.8878 2.97778i −0.656860 0.115822i −0.164723 0.986340i \(-0.552673\pi\)
−0.492137 + 0.870518i \(0.663784\pi\)
\(662\) 0 0
\(663\) −11.6631 + 9.49424i −0.452959 + 0.368726i
\(664\) 0 0
\(665\) 53.2594 + 63.7036i 2.06531 + 2.47032i
\(666\) 0 0
\(667\) −2.68911 −0.104123
\(668\) 0 0
\(669\) 30.7298 + 0.457588i 1.18808 + 0.0176914i
\(670\) 0 0
\(671\) 0.843803 4.78545i 0.0325747 0.184740i
\(672\) 0 0
\(673\) 10.0604 8.44171i 0.387802 0.325404i −0.427954 0.903800i \(-0.640766\pi\)
0.815756 + 0.578396i \(0.196321\pi\)
\(674\) 0 0
\(675\) 43.5506 + 56.8781i 1.67626 + 2.18924i
\(676\) 0 0
\(677\) −5.88291 33.3637i −0.226099 1.28227i −0.860574 0.509326i \(-0.829895\pi\)
0.634475 0.772943i \(-0.281216\pi\)
\(678\) 0 0
\(679\) −7.35341 + 4.22793i −0.282198 + 0.162253i
\(680\) 0 0
\(681\) 0.680047 45.6693i 0.0260595 1.75005i
\(682\) 0 0
\(683\) 16.6120 + 9.59095i 0.635641 + 0.366988i 0.782934 0.622105i \(-0.213722\pi\)
−0.147292 + 0.989093i \(0.547056\pi\)
\(684\) 0 0
\(685\) −8.35767 4.82531i −0.319330 0.184365i
\(686\) 0 0
\(687\) −5.21570 32.3929i −0.198991 1.23587i
\(688\) 0 0
\(689\) 2.35023 13.3288i 0.0895366 0.507787i
\(690\) 0 0
\(691\) −10.2108 12.1688i −0.388437 0.462921i 0.536021 0.844204i \(-0.319927\pi\)
−0.924458 + 0.381283i \(0.875482\pi\)
\(692\) 0 0
\(693\) −21.5744 27.4250i −0.819544 1.04179i
\(694\) 0 0
\(695\) −4.72832 + 12.9909i −0.179355 + 0.492775i
\(696\) 0 0
\(697\) 4.65280 + 3.90416i 0.176237 + 0.147881i
\(698\) 0 0
\(699\) −13.3363 + 4.63035i −0.504427 + 0.175136i
\(700\) 0 0
\(701\) 19.7654i 0.746528i −0.927725 0.373264i \(-0.878238\pi\)
0.927725 0.373264i \(-0.121762\pi\)
\(702\) 0 0
\(703\) 19.5327 11.2772i 0.736690 0.425328i
\(704\) 0 0
\(705\) −33.0987 + 38.2735i −1.24657 + 1.44146i
\(706\) 0 0
\(707\) 6.52527 + 0.0116982i 0.245408 + 0.000439956i
\(708\) 0 0
\(709\) 6.82226 + 2.48310i 0.256215 + 0.0932547i 0.466934 0.884292i \(-0.345358\pi\)
−0.210719 + 0.977547i \(0.567581\pi\)
\(710\) 0 0
\(711\) −6.05208 + 29.2084i −0.226971 + 1.09540i
\(712\) 0 0
\(713\) −9.14213 3.32746i −0.342375 0.124614i
\(714\) 0 0
\(715\) −43.6765 36.6490i −1.63341 1.37059i
\(716\) 0 0
\(717\) −25.0987 9.56073i −0.937328 0.357052i
\(718\) 0 0
\(719\) 12.6317 + 21.8787i 0.471082 + 0.815937i 0.999453 0.0330761i \(-0.0105304\pi\)
−0.528371 + 0.849013i \(0.677197\pi\)
\(720\) 0 0
\(721\) 23.4734 + 28.0766i 0.874197 + 1.04563i
\(722\) 0 0
\(723\) 16.2865 27.2633i 0.605700 1.01393i
\(724\) 0 0
\(725\) 13.2892 + 36.5118i 0.493549 + 1.35601i
\(726\) 0 0
\(727\) −21.7868 25.9645i −0.808028 0.962970i 0.191801 0.981434i \(-0.438567\pi\)
−0.999830 + 0.0184634i \(0.994123\pi\)
\(728\) 0 0
\(729\) 11.3600 + 24.4939i 0.420740 + 0.907181i
\(730\) 0 0
\(731\) 18.9097 + 6.88256i 0.699399 + 0.254561i
\(732\) 0 0
\(733\) −6.91575 + 8.24187i −0.255439 + 0.304420i −0.878490 0.477761i \(-0.841449\pi\)
0.623051 + 0.782181i \(0.285893\pi\)
\(734\) 0 0
\(735\) 51.5752 + 10.0799i 1.90238 + 0.371803i
\(736\) 0 0
\(737\) 56.6899i 2.08820i
\(738\) 0 0
\(739\) −30.7257 −1.13026 −0.565131 0.825001i \(-0.691174\pi\)
−0.565131 + 0.825001i \(0.691174\pi\)
\(740\) 0 0
\(741\) 23.6910 + 29.1031i 0.870311 + 1.06913i
\(742\) 0 0
\(743\) −7.95620 + 9.48183i −0.291885 + 0.347855i −0.891981 0.452073i \(-0.850685\pi\)
0.600096 + 0.799928i \(0.295129\pi\)
\(744\) 0 0
\(745\) 18.5588 3.27241i 0.679941 0.119892i
\(746\) 0 0
\(747\) 46.2041 15.2750i 1.69052 0.558882i
\(748\) 0 0
\(749\) 0.818000 + 2.26003i 0.0298891 + 0.0825799i
\(750\) 0 0
\(751\) −6.95023 + 39.4167i −0.253618 + 1.43834i 0.545979 + 0.837799i \(0.316158\pi\)
−0.799596 + 0.600538i \(0.794953\pi\)
\(752\) 0 0
\(753\) −2.37857 6.85075i −0.0866798 0.249655i
\(754\) 0 0
\(755\) 41.1737 1.49847
\(756\) 0 0
\(757\) 37.7607 1.37244 0.686218 0.727396i \(-0.259270\pi\)
0.686218 + 0.727396i \(0.259270\pi\)
\(758\) 0 0
\(759\) −4.75238 + 5.49538i −0.172500 + 0.199470i
\(760\) 0 0
\(761\) 5.84612 33.1550i 0.211922 1.20187i −0.674248 0.738505i \(-0.735532\pi\)
0.886169 0.463362i \(-0.153357\pi\)
\(762\) 0 0
\(763\) −1.50111 + 8.42485i −0.0543437 + 0.305000i
\(764\) 0 0
\(765\) 19.8304 32.1004i 0.716971 1.16059i
\(766\) 0 0
\(767\) 11.3242 1.99676i 0.408893 0.0720988i
\(768\) 0 0
\(769\) 5.37628 6.40720i 0.193874 0.231050i −0.660347 0.750961i \(-0.729591\pi\)
0.854220 + 0.519911i \(0.174035\pi\)
\(770\) 0 0
\(771\) −41.0882 + 6.61575i −1.47975 + 0.238260i
\(772\) 0 0
\(773\) 47.4818 1.70780 0.853901 0.520436i \(-0.174230\pi\)
0.853901 + 0.520436i \(0.174230\pi\)
\(774\) 0 0
\(775\) 140.573i 5.04952i
\(776\) 0 0
\(777\) 5.10517 13.3301i 0.183147 0.478216i
\(778\)