Properties

Label 756.2.ck.a.5.6
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 5.6
Character \(\chi\) = 756.5
Dual form 756.2.ck.a.605.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +O(q^{10})\) \(q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +(3.93578 - 0.693985i) q^{11} +(1.87975 - 2.24020i) q^{13} +(-4.57548 + 5.12720i) q^{15} +7.25945 q^{17} +2.16772i q^{19} +(1.44981 - 4.34719i) q^{21} +(-0.423740 + 0.504993i) q^{23} +(-10.0933 - 3.67365i) q^{25} +(0.474237 - 5.17447i) q^{27} +(-5.27940 - 6.29175i) q^{29} +(-0.711008 - 1.95348i) q^{31} +(-6.42955 - 2.56454i) q^{33} +(10.4796 - 0.604570i) q^{35} +(-0.0940596 - 0.162916i) q^{37} +(-4.81025 + 1.58660i) q^{39} +(0.931145 + 0.781324i) q^{41} +(-0.546157 - 0.198785i) q^{43} +(11.4118 - 3.38228i) q^{45} +(-7.42893 - 2.70391i) q^{47} +(-6.25889 + 3.13470i) q^{49} +(-10.6926 - 6.61564i) q^{51} +(-5.15055 + 2.97367i) q^{53} -15.8561i q^{55} +(1.97547 - 3.19288i) q^{57} +(10.3271 + 8.66550i) q^{59} +(3.62963 - 9.97232i) q^{61} +(-6.09711 + 5.08186i) q^{63} +(-7.45790 - 8.88798i) q^{65} +(1.33647 - 7.57947i) q^{67} +(1.08434 - 0.357657i) q^{69} +(-0.923830 - 0.533373i) q^{71} +(2.88569 + 1.66605i) q^{73} +(11.5188 + 14.6092i) q^{75} +(4.18269 + 9.71128i) q^{77} +(2.48404 + 14.0877i) q^{79} +(-5.41408 + 7.18942i) q^{81} +(6.12280 - 5.13764i) q^{83} +(5.00139 - 28.3643i) q^{85} +(2.04241 + 14.0785i) q^{87} +8.66443 q^{89} +(6.91226 + 3.47624i) q^{91} +(-0.732970 + 3.52528i) q^{93} +(8.46975 + 1.49345i) q^{95} +(3.49318 - 9.59744i) q^{97} +(7.13314 + 9.63672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} - 6q^{11} + 12q^{15} + 33q^{21} + 21q^{23} - 6q^{29} + 27q^{35} + 39q^{39} - 54q^{47} + 18q^{49} - 9q^{51} - 45q^{53} + 3q^{57} + 45q^{59} + 39q^{63} + 24q^{65} - 36q^{69} + 36q^{71} + 45q^{75} + 21q^{77} - 18q^{79} + 18q^{81} + 36q^{85} - 45q^{87} + 9q^{91} - 48q^{93} - 66q^{95} + O(q^{100}) \)

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
\(3\) −1.47292 0.911314i −0.850394 0.526147i
\(4\) 0 0
\(5\) 0.688949 3.90722i 0.308107 1.74736i −0.300398 0.953814i \(-0.597120\pi\)
0.608506 0.793550i \(-0.291769\pi\)
\(6\) 0 0
\(7\) 0.608733 + 2.57477i 0.230079 + 0.973172i
\(8\) 0 0
\(9\) 1.33902 + 2.68459i 0.446338 + 0.894864i
\(10\) 0 0
\(11\) 3.93578 0.693985i 1.18668 0.209244i 0.454749 0.890620i \(-0.349729\pi\)
0.731934 + 0.681376i \(0.238618\pi\)
\(12\) 0 0
\(13\) 1.87975 2.24020i 0.521349 0.621319i −0.439550 0.898218i \(-0.644862\pi\)
0.960899 + 0.276899i \(0.0893066\pi\)
\(14\) 0 0
\(15\) −4.57548 + 5.12720i −1.18138 + 1.32384i
\(16\) 0 0
\(17\) 7.25945 1.76068 0.880338 0.474347i \(-0.157316\pi\)
0.880338 + 0.474347i \(0.157316\pi\)
\(18\) 0 0
\(19\) 2.16772i 0.497308i 0.968592 + 0.248654i \(0.0799882\pi\)
−0.968592 + 0.248654i \(0.920012\pi\)
\(20\) 0 0
\(21\) 1.44981 4.34719i 0.316373 0.948635i
\(22\) 0 0
\(23\) −0.423740 + 0.504993i −0.0883558 + 0.105298i −0.808411 0.588618i \(-0.799672\pi\)
0.720055 + 0.693917i \(0.244116\pi\)
\(24\) 0 0
\(25\) −10.0933 3.67365i −2.01866 0.734731i
\(26\) 0 0
\(27\) 0.474237 5.17447i 0.0912669 0.995826i
\(28\) 0 0
\(29\) −5.27940 6.29175i −0.980360 1.16835i −0.985725 0.168362i \(-0.946152\pi\)
0.00536483 0.999986i \(-0.498292\pi\)
\(30\) 0 0
\(31\) −0.711008 1.95348i −0.127701 0.350855i 0.859322 0.511435i \(-0.170886\pi\)
−0.987023 + 0.160580i \(0.948664\pi\)
\(32\) 0 0
\(33\) −6.42955 2.56454i −1.11924 0.446430i
\(34\) 0 0
\(35\) 10.4796 0.604570i 1.77137 0.102191i
\(36\) 0 0
\(37\) −0.0940596 0.162916i −0.0154633 0.0267832i 0.858190 0.513332i \(-0.171589\pi\)
−0.873654 + 0.486549i \(0.838256\pi\)
\(38\) 0 0
\(39\) −4.81025 + 1.58660i −0.770257 + 0.254060i
\(40\) 0 0
\(41\) 0.931145 + 0.781324i 0.145420 + 0.122022i 0.712596 0.701575i \(-0.247519\pi\)
−0.567175 + 0.823597i \(0.691964\pi\)
\(42\) 0 0
\(43\) −0.546157 0.198785i −0.0832882 0.0303144i 0.300040 0.953927i \(-0.403000\pi\)
−0.383328 + 0.923612i \(0.625222\pi\)
\(44\) 0 0
\(45\) 11.4118 3.38228i 1.70117 0.504201i
\(46\) 0 0
\(47\) −7.42893 2.70391i −1.08362 0.394406i −0.262367 0.964968i \(-0.584503\pi\)
−0.821254 + 0.570563i \(0.806725\pi\)
\(48\) 0 0
\(49\) −6.25889 + 3.13470i −0.894127 + 0.447814i
\(50\) 0 0
\(51\) −10.6926 6.61564i −1.49727 0.926375i
\(52\) 0 0
\(53\) −5.15055 + 2.97367i −0.707482 + 0.408465i −0.810128 0.586253i \(-0.800602\pi\)
0.102646 + 0.994718i \(0.467269\pi\)
\(54\) 0 0
\(55\) 15.8561i 2.13804i
\(56\) 0 0
\(57\) 1.97547 3.19288i 0.261657 0.422908i
\(58\) 0 0
\(59\) 10.3271 + 8.66550i 1.34448 + 1.12815i 0.980451 + 0.196765i \(0.0630435\pi\)
0.364029 + 0.931388i \(0.381401\pi\)
\(60\) 0 0
\(61\) 3.62963 9.97232i 0.464726 1.27682i −0.457167 0.889381i \(-0.651136\pi\)
0.921893 0.387444i \(-0.126642\pi\)
\(62\) 0 0
\(63\) −6.09711 + 5.08186i −0.768163 + 0.640254i
\(64\) 0 0
\(65\) −7.45790 8.88798i −0.925039 1.10242i
\(66\) 0 0
\(67\) 1.33647 7.57947i 0.163275 0.925980i −0.787550 0.616251i \(-0.788651\pi\)
0.950825 0.309729i \(-0.100238\pi\)
\(68\) 0 0
\(69\) 1.08434 0.357657i 0.130540 0.0430569i
\(70\) 0 0
\(71\) −0.923830 0.533373i −0.109638 0.0632998i 0.444178 0.895939i \(-0.353496\pi\)
−0.553816 + 0.832639i \(0.686829\pi\)
\(72\) 0 0
\(73\) 2.88569 + 1.66605i 0.337744 + 0.194997i 0.659274 0.751903i \(-0.270864\pi\)
−0.321530 + 0.946899i \(0.604197\pi\)
\(74\) 0 0
\(75\) 11.5188 + 14.6092i 1.33008 + 1.68692i
\(76\) 0 0
\(77\) 4.18269 + 9.71128i 0.476662 + 1.10670i
\(78\) 0 0
\(79\) 2.48404 + 14.0877i 0.279476 + 1.58499i 0.724375 + 0.689406i \(0.242128\pi\)
−0.444899 + 0.895581i \(0.646760\pi\)
\(80\) 0 0
\(81\) −5.41408 + 7.18942i −0.601564 + 0.798825i
\(82\) 0 0
\(83\) 6.12280 5.13764i 0.672064 0.563929i −0.241611 0.970373i \(-0.577676\pi\)
0.913676 + 0.406444i \(0.133231\pi\)
\(84\) 0 0
\(85\) 5.00139 28.3643i 0.542477 3.07654i
\(86\) 0 0
\(87\) 2.04241 + 14.0785i 0.218969 + 1.50937i
\(88\) 0 0
\(89\) 8.66443 0.918428 0.459214 0.888326i \(-0.348131\pi\)
0.459214 + 0.888326i \(0.348131\pi\)
\(90\) 0 0
\(91\) 6.91226 + 3.47624i 0.724602 + 0.364409i
\(92\) 0 0
\(93\) −0.732970 + 3.52528i −0.0760054 + 0.365554i
\(94\) 0 0
\(95\) 8.46975 + 1.49345i 0.868978 + 0.153224i
\(96\) 0 0
\(97\) 3.49318 9.59744i 0.354679 0.974472i −0.626167 0.779689i \(-0.715377\pi\)
0.980846 0.194783i \(-0.0624004\pi\)
\(98\) 0 0
\(99\) 7.13314 + 9.63672i 0.716907 + 0.968526i
\(100\) 0 0
\(101\) −8.98912 + 7.54277i −0.894451 + 0.750534i −0.969098 0.246676i \(-0.920662\pi\)
0.0746466 + 0.997210i \(0.476217\pi\)
\(102\) 0 0
\(103\) −6.28666 1.10851i −0.619443 0.109224i −0.144885 0.989449i \(-0.546281\pi\)
−0.474558 + 0.880224i \(0.657392\pi\)
\(104\) 0 0
\(105\) −15.9866 8.65971i −1.56013 0.845101i
\(106\) 0 0
\(107\) 11.1821 + 6.45600i 1.08102 + 0.624125i 0.931170 0.364584i \(-0.118789\pi\)
0.149846 + 0.988709i \(0.452122\pi\)
\(108\) 0 0
\(109\) 1.15230 + 1.99583i 0.110370 + 0.191166i 0.915919 0.401362i \(-0.131463\pi\)
−0.805550 + 0.592528i \(0.798130\pi\)
\(110\) 0 0
\(111\) −0.00992484 + 0.325681i −0.000942024 + 0.0309122i
\(112\) 0 0
\(113\) −5.63872 15.4922i −0.530446 1.45739i −0.858542 0.512744i \(-0.828629\pi\)
0.328096 0.944644i \(-0.393593\pi\)
\(114\) 0 0
\(115\) 1.68119 + 2.00356i 0.156771 + 0.186833i
\(116\) 0 0
\(117\) 8.53103 + 2.04670i 0.788694 + 0.189218i
\(118\) 0 0
\(119\) 4.41907 + 18.6914i 0.405095 + 1.71344i
\(120\) 0 0
\(121\) 4.67215 1.70052i 0.424740 0.154593i
\(122\) 0 0
\(123\) −0.659476 1.99940i −0.0594630 0.180280i
\(124\) 0 0
\(125\) −11.3888 + 19.7260i −1.01865 + 1.76435i
\(126\) 0 0
\(127\) −2.99863 5.19378i −0.266085 0.460873i 0.701762 0.712411i \(-0.252397\pi\)
−0.967847 + 0.251538i \(0.919064\pi\)
\(128\) 0 0
\(129\) 0.623293 + 0.790516i 0.0548779 + 0.0696010i
\(130\) 0 0
\(131\) −5.03254 4.22280i −0.439695 0.368948i 0.395900 0.918293i \(-0.370433\pi\)
−0.835595 + 0.549346i \(0.814877\pi\)
\(132\) 0 0
\(133\) −5.58137 + 1.31956i −0.483966 + 0.114420i
\(134\) 0 0
\(135\) −19.8911 5.41789i −1.71195 0.466298i
\(136\) 0 0
\(137\) −5.48611 + 15.0730i −0.468710 + 1.28777i 0.450067 + 0.892995i \(0.351400\pi\)
−0.918777 + 0.394776i \(0.870822\pi\)
\(138\) 0 0
\(139\) −22.1082 3.89827i −1.87519 0.330647i −0.884476 0.466587i \(-0.845484\pi\)
−0.990717 + 0.135939i \(0.956595\pi\)
\(140\) 0 0
\(141\) 8.47814 + 10.7527i 0.713989 + 0.905544i
\(142\) 0 0
\(143\) 5.84362 10.1214i 0.488668 0.846398i
\(144\) 0 0
\(145\) −28.2205 + 16.2931i −2.34358 + 1.35307i
\(146\) 0 0
\(147\) 12.0756 + 1.08664i 0.995976 + 0.0896244i
\(148\) 0 0
\(149\) 0.744457 + 2.04538i 0.0609883 + 0.167564i 0.966444 0.256876i \(-0.0826932\pi\)
−0.905456 + 0.424440i \(0.860471\pi\)
\(150\) 0 0
\(151\) 3.62566 + 20.5621i 0.295052 + 1.67332i 0.666992 + 0.745065i \(0.267582\pi\)
−0.371940 + 0.928257i \(0.621307\pi\)
\(152\) 0 0
\(153\) 9.72052 + 19.4887i 0.785857 + 1.57557i
\(154\) 0 0
\(155\) −8.12252 + 1.43222i −0.652417 + 0.115039i
\(156\) 0 0
\(157\) −8.45553 + 10.0769i −0.674825 + 0.804225i −0.989432 0.144997i \(-0.953683\pi\)
0.314607 + 0.949222i \(0.398127\pi\)
\(158\) 0 0
\(159\) 10.2963 + 0.313771i 0.816551 + 0.0248837i
\(160\) 0 0
\(161\) −1.55819 0.783626i −0.122802 0.0617584i
\(162\) 0 0
\(163\) −2.50840 + 4.34468i −0.196473 + 0.340302i −0.947383 0.320104i \(-0.896282\pi\)
0.750909 + 0.660405i \(0.229616\pi\)
\(164\) 0 0
\(165\) −14.4499 + 23.3548i −1.12492 + 1.81817i
\(166\) 0 0
\(167\) 3.96921 1.44467i 0.307147 0.111792i −0.183848 0.982955i \(-0.558856\pi\)
0.490995 + 0.871162i \(0.336633\pi\)
\(168\) 0 0
\(169\) 0.772396 + 4.38048i 0.0594151 + 0.336960i
\(170\) 0 0
\(171\) −5.81943 + 2.90260i −0.445023 + 0.221968i
\(172\) 0 0
\(173\) 11.7887 9.89186i 0.896275 0.752064i −0.0731834 0.997318i \(-0.523316\pi\)
0.969459 + 0.245254i \(0.0788714\pi\)
\(174\) 0 0
\(175\) 3.31470 28.2242i 0.250568 2.13355i
\(176\) 0 0
\(177\) −7.31412 22.1749i −0.549763 1.66677i
\(178\) 0 0
\(179\) 4.06742i 0.304013i −0.988379 0.152007i \(-0.951426\pi\)
0.988379 0.152007i \(-0.0485735\pi\)
\(180\) 0 0
\(181\) −6.60441 + 3.81306i −0.490902 + 0.283422i −0.724948 0.688803i \(-0.758136\pi\)
0.234047 + 0.972225i \(0.424803\pi\)
\(182\) 0 0
\(183\) −14.4341 + 11.3807i −1.06700 + 0.841289i
\(184\) 0 0
\(185\) −0.701351 + 0.255271i −0.0515644 + 0.0187679i
\(186\) 0 0
\(187\) 28.5716 5.03795i 2.08936 0.368411i
\(188\) 0 0
\(189\) 13.6117 1.92882i 0.990109 0.140301i
\(190\) 0 0
\(191\) 15.7820 2.78279i 1.14194 0.201356i 0.429488 0.903072i \(-0.358694\pi\)
0.712456 + 0.701717i \(0.247583\pi\)
\(192\) 0 0
\(193\) 17.2269 6.27007i 1.24002 0.451329i 0.363000 0.931789i \(-0.381752\pi\)
0.877017 + 0.480460i \(0.159530\pi\)
\(194\) 0 0
\(195\) 2.88519 + 19.8878i 0.206613 + 1.42420i
\(196\) 0 0
\(197\) 8.35914 4.82615i 0.595564 0.343849i −0.171731 0.985144i \(-0.554936\pi\)
0.767294 + 0.641295i \(0.221603\pi\)
\(198\) 0 0
\(199\) 10.5741i 0.749581i 0.927110 + 0.374790i \(0.122285\pi\)
−0.927110 + 0.374790i \(0.877715\pi\)
\(200\) 0 0
\(201\) −8.87579 + 9.94605i −0.626050 + 0.701540i
\(202\) 0 0
\(203\) 12.9861 17.4232i 0.911443 1.22287i
\(204\) 0 0
\(205\) 3.69432 3.09990i 0.258022 0.216506i
\(206\) 0 0
\(207\) −1.92310 0.461375i −0.133664 0.0320678i
\(208\) 0 0
\(209\) 1.50436 + 8.53166i 0.104059 + 0.590147i
\(210\) 0 0
\(211\) −17.5093 + 6.37285i −1.20539 + 0.438725i −0.865101 0.501597i \(-0.832746\pi\)
−0.340286 + 0.940322i \(0.610524\pi\)
\(212\) 0 0
\(213\) 0.874661 + 1.62752i 0.0599308 + 0.111516i
\(214\) 0 0
\(215\) −1.15297 + 1.99701i −0.0786320 + 0.136195i
\(216\) 0 0
\(217\) 4.59694 3.01983i 0.312061 0.204999i
\(218\) 0 0
\(219\) −2.73210 5.08373i −0.184618 0.343527i
\(220\) 0 0
\(221\) 13.6460 16.2626i 0.917926 1.09394i
\(222\) 0 0
\(223\) −13.0786 + 2.30611i −0.875808 + 0.154429i −0.593440 0.804878i \(-0.702231\pi\)
−0.282367 + 0.959306i \(0.591120\pi\)
\(224\) 0 0
\(225\) −3.65279 32.0154i −0.243520 2.13436i
\(226\) 0 0
\(227\) −2.26914 12.8689i −0.150608 0.854141i −0.962692 0.270600i \(-0.912778\pi\)
0.812084 0.583541i \(-0.198333\pi\)
\(228\) 0 0
\(229\) 4.91506 + 13.5040i 0.324796 + 0.892370i 0.989405 + 0.145179i \(0.0463758\pi\)
−0.664609 + 0.747191i \(0.731402\pi\)
\(230\) 0 0
\(231\) 2.68923 18.1157i 0.176939 1.19193i
\(232\) 0 0
\(233\) −6.49516 + 3.74998i −0.425512 + 0.245669i −0.697433 0.716650i \(-0.745674\pi\)
0.271921 + 0.962320i \(0.412341\pi\)
\(234\) 0 0
\(235\) −15.6829 + 27.1636i −1.02304 + 1.77196i
\(236\) 0 0
\(237\) 9.17949 23.0138i 0.596272 1.49491i
\(238\) 0 0
\(239\) −2.35845 0.415858i −0.152555 0.0268996i 0.0968488 0.995299i \(-0.469124\pi\)
−0.249404 + 0.968399i \(0.580235\pi\)
\(240\) 0 0
\(241\) 8.28691 22.7681i 0.533807 1.46662i −0.320700 0.947181i \(-0.603918\pi\)
0.854506 0.519441i \(-0.173860\pi\)
\(242\) 0 0
\(243\) 14.5263 5.65556i 0.931865 0.362804i
\(244\) 0 0
\(245\) 7.93590 + 26.6145i 0.507006 + 1.70034i
\(246\) 0 0
\(247\) 4.85611 + 4.07476i 0.308987 + 0.259271i
\(248\) 0 0
\(249\) −13.7004 + 1.98757i −0.868229 + 0.125957i
\(250\) 0 0
\(251\) 14.5178 + 25.1456i 0.916356 + 1.58717i 0.804904 + 0.593405i \(0.202217\pi\)
0.111452 + 0.993770i \(0.464450\pi\)
\(252\) 0 0
\(253\) −1.31729 + 2.28161i −0.0828173 + 0.143444i
\(254\) 0 0
\(255\) −33.2155 + 37.2207i −2.08003 + 2.33085i
\(256\) 0 0
\(257\) 13.6563 4.97049i 0.851857 0.310051i 0.121060 0.992645i \(-0.461371\pi\)
0.730797 + 0.682594i \(0.239148\pi\)
\(258\) 0 0
\(259\) 0.362214 0.341354i 0.0225069 0.0212107i
\(260\) 0 0
\(261\) 9.82158 22.5978i 0.607940 1.39877i
\(262\) 0 0
\(263\) −8.03518 9.57596i −0.495471 0.590479i 0.459129 0.888369i \(-0.348161\pi\)
−0.954600 + 0.297891i \(0.903717\pi\)
\(264\) 0 0
\(265\) 8.07033 + 22.1730i 0.495756 + 1.36208i
\(266\) 0 0
\(267\) −12.7621 7.89602i −0.781025 0.483228i
\(268\) 0 0
\(269\) 9.04697 + 15.6698i 0.551604 + 0.955406i 0.998159 + 0.0606497i \(0.0193173\pi\)
−0.446555 + 0.894756i \(0.647349\pi\)
\(270\) 0 0
\(271\) −10.9167 6.30277i −0.663143 0.382866i 0.130330 0.991471i \(-0.458396\pi\)
−0.793474 + 0.608605i \(0.791730\pi\)
\(272\) 0 0
\(273\) −7.01330 11.4195i −0.424464 0.691138i
\(274\) 0 0
\(275\) −42.2744 7.45412i −2.54924 0.449500i
\(276\) 0 0
\(277\) −12.1089 + 10.1606i −0.727555 + 0.610491i −0.929464 0.368914i \(-0.879730\pi\)
0.201909 + 0.979404i \(0.435285\pi\)
\(278\) 0 0
\(279\) 4.29224 4.52450i 0.256970 0.270875i
\(280\) 0 0
\(281\) 0.386386 1.06159i 0.0230499 0.0633290i −0.927634 0.373490i \(-0.878161\pi\)
0.950684 + 0.310161i \(0.100383\pi\)
\(282\) 0 0
\(283\) 19.0304 + 3.35557i 1.13124 + 0.199468i 0.707770 0.706443i \(-0.249701\pi\)
0.423469 + 0.905911i \(0.360812\pi\)
\(284\) 0 0
\(285\) −11.1143 9.91833i −0.658355 0.587511i
\(286\) 0 0
\(287\) −1.44491 + 2.87310i −0.0852904 + 0.169594i
\(288\) 0 0
\(289\) 35.6997 2.09998
\(290\) 0 0
\(291\) −13.8915 + 10.9529i −0.814332 + 0.642071i
\(292\) 0 0
\(293\) 3.55249 20.1472i 0.207539 1.17701i −0.685856 0.727738i \(-0.740572\pi\)
0.893394 0.449273i \(-0.148317\pi\)
\(294\) 0 0
\(295\) 40.9729 34.3804i 2.38554 2.00170i
\(296\) 0 0
\(297\) −1.72451 20.6947i −0.100066 1.20083i
\(298\) 0 0
\(299\) 0.334761 + 1.89852i 0.0193597 + 0.109794i
\(300\) 0 0
\(301\) 0.179362 1.52724i 0.0103382 0.0880285i
\(302\) 0 0
\(303\) 20.1141 2.91802i 1.15553 0.167636i
\(304\) 0 0
\(305\) −36.4634 21.0522i −2.08789 1.20544i
\(306\) 0 0
\(307\) −24.4057 14.0906i −1.39291 0.804194i −0.399269 0.916834i \(-0.630736\pi\)
−0.993636 + 0.112640i \(0.964069\pi\)
\(308\) 0 0
\(309\) 8.24958 + 7.36187i 0.469302 + 0.418802i
\(310\) 0 0
\(311\) −1.80190 + 10.2191i −0.102176 + 0.579470i 0.890135 + 0.455698i \(0.150610\pi\)
−0.992311 + 0.123772i \(0.960501\pi\)
\(312\) 0 0
\(313\) 13.1554 + 15.6780i 0.743586 + 0.886171i 0.996692 0.0812672i \(-0.0258967\pi\)
−0.253106 + 0.967438i \(0.581452\pi\)
\(314\) 0 0
\(315\) 15.6554 + 27.3239i 0.882079 + 1.53953i
\(316\) 0 0
\(317\) −1.39302 + 3.82728i −0.0782396 + 0.214962i −0.972645 0.232295i \(-0.925377\pi\)
0.894406 + 0.447256i \(0.147599\pi\)
\(318\) 0 0
\(319\) −25.1449 21.0991i −1.40785 1.18132i
\(320\) 0 0
\(321\) −10.5870 19.6996i −0.590908 1.09953i
\(322\) 0 0
\(323\) 15.7364i 0.875598i
\(324\) 0 0
\(325\) −27.2026 + 15.7054i −1.50893 + 0.871179i
\(326\) 0 0
\(327\) 0.121586 3.98981i 0.00672373 0.220637i
\(328\) 0 0
\(329\) 2.43971 20.7737i 0.134506 1.14529i
\(330\) 0 0
\(331\) 3.67758 + 1.33853i 0.202138 + 0.0735722i 0.441105 0.897455i \(-0.354587\pi\)
−0.238967 + 0.971028i \(0.576809\pi\)
\(332\) 0 0
\(333\) 0.311416 0.470659i 0.0170655 0.0257919i
\(334\) 0 0
\(335\) −28.6939 10.4437i −1.56772 0.570602i
\(336\) 0 0
\(337\) 7.46671 + 6.26531i 0.406737 + 0.341293i 0.823091 0.567910i \(-0.192248\pi\)
−0.416354 + 0.909203i \(0.636692\pi\)
\(338\) 0 0
\(339\) −5.81289 + 27.9576i −0.315713 + 1.51845i
\(340\) 0 0
\(341\) −4.15406 7.19503i −0.224955 0.389633i
\(342\) 0 0
\(343\) −11.8811 14.2070i −0.641520 0.767106i
\(344\) 0 0
\(345\) −0.650390 4.48318i −0.0350158 0.241366i
\(346\) 0 0
\(347\) −0.307897 0.845941i −0.0165288 0.0454125i 0.931154 0.364627i \(-0.118803\pi\)
−0.947683 + 0.319214i \(0.896581\pi\)
\(348\) 0 0
\(349\) 14.2878 + 17.0276i 0.764810 + 0.911465i 0.998142 0.0609324i \(-0.0194074\pi\)
−0.233332 + 0.972397i \(0.574963\pi\)
\(350\) 0 0
\(351\) −10.7004 10.7891i −0.571144 0.575879i
\(352\) 0 0
\(353\) 25.6896 + 9.35025i 1.36732 + 0.497663i 0.918309 0.395863i \(-0.129555\pi\)
0.449010 + 0.893527i \(0.351777\pi\)
\(354\) 0 0
\(355\) −2.72048 + 3.24214i −0.144388 + 0.172075i
\(356\) 0 0
\(357\) 10.5248 31.5582i 0.557031 1.67024i
\(358\) 0 0
\(359\) 2.55839i 0.135027i 0.997718 + 0.0675135i \(0.0215066\pi\)
−0.997718 + 0.0675135i \(0.978493\pi\)
\(360\) 0 0
\(361\) 14.3010 0.752685
\(362\) 0 0
\(363\) −8.43143 1.75305i −0.442535 0.0920112i
\(364\) 0 0
\(365\) 8.49772 10.1272i 0.444791 0.530082i
\(366\) 0 0
\(367\) −5.82671 + 1.02741i −0.304152 + 0.0536302i −0.323641 0.946180i \(-0.604907\pi\)
0.0194893 + 0.999810i \(0.493796\pi\)
\(368\) 0 0
\(369\) −0.850718 + 3.54595i −0.0442866 + 0.184595i
\(370\) 0 0
\(371\) −10.7918 11.4513i −0.560284 0.594522i
\(372\) 0 0
\(373\) −3.00818 + 17.0603i −0.155758 + 0.883346i 0.802332 + 0.596878i \(0.203592\pi\)
−0.958090 + 0.286468i \(0.907519\pi\)
\(374\) 0 0
\(375\) 34.7514 18.6761i 1.79455 0.964430i
\(376\) 0 0
\(377\) −24.0187 −1.23703
\(378\) 0 0
\(379\) −33.5463 −1.72316 −0.861579 0.507623i \(-0.830524\pi\)
−0.861579 + 0.507623i \(0.830524\pi\)
\(380\) 0 0
\(381\) −0.316405 + 10.3827i −0.0162099 + 0.531924i
\(382\) 0 0
\(383\) 0.383922 2.17733i 0.0196175 0.111256i −0.973427 0.228999i \(-0.926455\pi\)
0.993044 + 0.117743i \(0.0375658\pi\)
\(384\) 0 0
\(385\) 40.8258 9.65213i 2.08068 0.491918i
\(386\) 0 0
\(387\) −0.197656 1.73239i −0.0100474 0.0880621i
\(388\) 0 0
\(389\) −33.7290 + 5.94734i −1.71013 + 0.301542i −0.941215 0.337808i \(-0.890315\pi\)
−0.768916 + 0.639350i \(0.779203\pi\)
\(390\) 0 0
\(391\) −3.07612 + 3.66597i −0.155566 + 0.185396i
\(392\) 0 0
\(393\) 3.56425 + 10.8061i 0.179793 + 0.545095i
\(394\) 0 0
\(395\) 56.7551 2.85566
\(396\) 0 0
\(397\) 21.5352i 1.08082i −0.841401 0.540411i \(-0.818269\pi\)
0.841401 0.540411i \(-0.181731\pi\)
\(398\) 0 0
\(399\) 9.42347 + 3.14277i 0.471764 + 0.157335i
\(400\) 0 0
\(401\) −16.6603 + 19.8550i −0.831975 + 0.991509i 0.168008 + 0.985786i \(0.446266\pi\)
−0.999984 + 0.00572381i \(0.998178\pi\)
\(402\) 0 0
\(403\) −5.71270 2.07925i −0.284570 0.103575i
\(404\) 0 0
\(405\) 24.3607 + 26.1072i 1.21049 + 1.29727i
\(406\) 0 0
\(407\) −0.483259 0.575926i −0.0239543 0.0285476i
\(408\) 0 0
\(409\) 3.98666 + 10.9532i 0.197127 + 0.541603i 0.998391 0.0567086i \(-0.0180606\pi\)
−0.801263 + 0.598312i \(0.795838\pi\)
\(410\) 0 0
\(411\) 21.8168 17.2018i 1.07615 0.848502i
\(412\) 0 0
\(413\) −16.0252 + 31.8650i −0.788549 + 1.56797i
\(414\) 0 0
\(415\) −15.8556 27.4627i −0.778321 1.34809i
\(416\) 0 0
\(417\) 29.0112 + 25.8894i 1.42068 + 1.26781i
\(418\) 0 0
\(419\) −6.52747 5.47720i −0.318888 0.267579i 0.469266 0.883057i \(-0.344518\pi\)
−0.788154 + 0.615478i \(0.788963\pi\)
\(420\) 0 0
\(421\) 21.6891 + 7.89419i 1.05706 + 0.384739i 0.811324 0.584597i \(-0.198747\pi\)
0.245739 + 0.969336i \(0.420969\pi\)
\(422\) 0 0
\(423\) −2.68855 23.5642i −0.130722 1.14573i
\(424\) 0 0
\(425\) −73.2717 26.6687i −3.55420 1.29362i
\(426\) 0 0
\(427\) 27.8859 + 3.27498i 1.34949 + 0.158487i
\(428\) 0 0
\(429\) −17.8310 + 9.58276i −0.860890 + 0.462660i
\(430\) 0 0
\(431\) 4.15301 2.39774i 0.200043 0.115495i −0.396632 0.917978i \(-0.629821\pi\)
0.596676 + 0.802482i \(0.296488\pi\)
\(432\) 0 0
\(433\) 21.7041i 1.04303i 0.853242 + 0.521516i \(0.174633\pi\)
−0.853242 + 0.521516i \(0.825367\pi\)
\(434\) 0 0
\(435\) 56.4148 + 1.71919i 2.70488 + 0.0824290i
\(436\) 0 0
\(437\) −1.09468 0.918547i −0.0523657 0.0439401i
\(438\) 0 0
\(439\) −6.09546 + 16.7471i −0.290921 + 0.799298i 0.705012 + 0.709195i \(0.250942\pi\)
−0.995933 + 0.0901022i \(0.971281\pi\)
\(440\) 0 0
\(441\) −16.7961 12.6052i −0.799816 0.600246i
\(442\) 0 0
\(443\) 14.9000 + 17.7571i 0.707919 + 0.843666i 0.993398 0.114720i \(-0.0365969\pi\)
−0.285478 + 0.958385i \(0.592153\pi\)
\(444\) 0 0
\(445\) 5.96935 33.8539i 0.282974 1.60483i
\(446\) 0 0
\(447\) 0.767452 3.69112i 0.0362992 0.174584i
\(448\) 0 0
\(449\) 10.5855 + 6.11156i 0.499563 + 0.288423i 0.728533 0.685011i \(-0.240203\pi\)
−0.228970 + 0.973433i \(0.573536\pi\)
\(450\) 0 0
\(451\) 4.20701 + 2.42892i 0.198100 + 0.114373i
\(452\) 0 0
\(453\) 13.3982 33.5906i 0.629503 1.57822i
\(454\) 0 0
\(455\) 18.3446 24.6128i 0.860010 1.15387i
\(456\) 0 0
\(457\) 2.69680 + 15.2943i 0.126151 + 0.715438i 0.980618 + 0.195932i \(0.0627731\pi\)
−0.854467 + 0.519506i \(0.826116\pi\)
\(458\) 0 0
\(459\) 3.44270 37.5638i 0.160691 1.75333i
\(460\) 0 0
\(461\) 26.6254 22.3413i 1.24007 1.04054i 0.242547 0.970140i \(-0.422017\pi\)
0.997519 0.0703997i \(-0.0224275\pi\)
\(462\) 0 0
\(463\) 4.43131 25.1312i 0.205941 1.16795i −0.690012 0.723798i \(-0.742395\pi\)
0.895953 0.444149i \(-0.146494\pi\)
\(464\) 0 0
\(465\) 13.2691 + 5.29261i 0.615338 + 0.245439i
\(466\) 0 0
\(467\) −13.5982 −0.629249 −0.314625 0.949216i \(-0.601879\pi\)
−0.314625 + 0.949216i \(0.601879\pi\)
\(468\) 0 0
\(469\) 20.3289 1.17278i 0.938704 0.0541541i
\(470\) 0 0
\(471\) 21.6376 7.13689i 0.997008 0.328851i
\(472\) 0 0
\(473\) −2.28751 0.403350i −0.105180 0.0185460i
\(474\) 0 0
\(475\) 7.96344 21.8794i 0.365388 1.00389i
\(476\) 0 0
\(477\) −14.8798 9.84533i −0.681297 0.450787i
\(478\) 0 0
\(479\) −19.3576 + 16.2429i −0.884470 + 0.742159i −0.967093 0.254422i \(-0.918115\pi\)
0.0826230 + 0.996581i \(0.473670\pi\)
\(480\) 0 0
\(481\) −0.541772 0.0955291i −0.0247027 0.00435575i
\(482\) 0 0
\(483\) 1.58096 + 2.57422i 0.0719363 + 0.117131i
\(484\) 0 0
\(485\) −35.0927 20.2608i −1.59348 0.919995i
\(486\) 0 0
\(487\) 4.72827 + 8.18961i 0.214258 + 0.371107i 0.953043 0.302835i \(-0.0979332\pi\)
−0.738784 + 0.673942i \(0.764600\pi\)
\(488\) 0 0
\(489\) 7.65406 4.11345i 0.346128 0.186017i
\(490\) 0 0
\(491\) 11.9824 + 32.9213i 0.540757 + 1.48572i 0.845863 + 0.533400i \(0.179086\pi\)
−0.305106 + 0.952319i \(0.598692\pi\)
\(492\) 0 0
\(493\) −38.3256 45.6746i −1.72610 2.05708i
\(494\) 0 0
\(495\) 42.5672 21.2316i 1.91325 0.954288i
\(496\) 0 0
\(497\) 0.810948 2.70333i 0.0363760 0.121261i
\(498\) 0 0
\(499\) −27.3282 + 9.94666i −1.22338 + 0.445274i −0.871325 0.490706i \(-0.836739\pi\)
−0.352054 + 0.935980i \(0.614517\pi\)
\(500\) 0 0
\(501\) −7.16290 1.48930i −0.320015 0.0665369i
\(502\) 0 0
\(503\) 4.77536 8.27117i 0.212923 0.368793i −0.739705 0.672931i \(-0.765035\pi\)
0.952628 + 0.304138i \(0.0983684\pi\)
\(504\) 0 0
\(505\) 23.2782 + 40.3191i 1.03587 + 1.79418i
\(506\) 0 0
\(507\) 2.85431 7.15601i 0.126764 0.317809i
\(508\) 0 0
\(509\) −15.5398 13.0395i −0.688791 0.577964i 0.229770 0.973245i \(-0.426203\pi\)
−0.918560 + 0.395281i \(0.870647\pi\)
\(510\) 0 0
\(511\) −2.53309 + 8.44416i −0.112057 + 0.373548i
\(512\) 0 0
\(513\) 11.2168 + 1.02801i 0.495233 + 0.0453878i
\(514\) 0 0
\(515\) −8.66237 + 23.7997i −0.381710 + 1.04874i
\(516\) 0 0
\(517\) −31.1151 5.48643i −1.36844 0.241293i
\(518\) 0 0
\(519\) −26.3784 + 3.82680i −1.15788 + 0.167978i
\(520\) 0 0
\(521\) 7.07494 12.2542i 0.309959 0.536864i −0.668394 0.743807i \(-0.733018\pi\)
0.978353 + 0.206943i \(0.0663514\pi\)
\(522\) 0 0
\(523\) −27.6390 + 15.9574i −1.20857 + 0.697767i −0.962446 0.271472i \(-0.912489\pi\)
−0.246121 + 0.969239i \(0.579156\pi\)
\(524\) 0 0
\(525\) −30.6034 + 38.5513i −1.33564 + 1.68252i
\(526\) 0 0
\(527\) −5.16153 14.1812i −0.224840 0.617742i
\(528\) 0 0
\(529\) 3.91845 + 22.2226i 0.170367 + 0.966200i
\(530\) 0 0
\(531\) −9.43514 + 39.3274i −0.409450 + 1.70666i
\(532\) 0 0
\(533\) 3.50064 0.617257i 0.151630 0.0267364i
\(534\) 0 0
\(535\) 32.9290 39.2432i 1.42364 1.69663i
\(536\) 0 0
\(537\) −3.70670 + 5.99101i −0.159956 + 0.258531i
\(538\) 0 0
\(539\) −22.4582 + 16.6811i −0.967343 + 0.718504i
\(540\) 0 0
\(541\) 6.59562 11.4239i 0.283568 0.491154i −0.688693 0.725053i \(-0.741815\pi\)
0.972261 + 0.233899i \(0.0751486\pi\)
\(542\) 0 0
\(543\) 13.2027 + 0.402340i 0.566581 + 0.0172661i
\(544\) 0 0
\(545\) 8.59204 3.12725i 0.368043 0.133957i
\(546\) 0 0
\(547\) 1.86468 + 10.5751i 0.0797281 + 0.452161i 0.998370 + 0.0570699i \(0.0181758\pi\)
−0.918642 + 0.395091i \(0.870713\pi\)
\(548\) 0 0
\(549\) 31.6317 3.60902i 1.35001 0.154029i
\(550\) 0 0
\(551\) 13.6387 11.4442i 0.581029 0.487541i
\(552\) 0 0
\(553\) −34.7604 + 14.9715i −1.47816 + 0.636651i
\(554\) 0 0
\(555\) 1.26567 + 0.263156i 0.0537247 + 0.0111703i
\(556\) 0 0
\(557\) 32.7388i 1.38719i 0.720367 + 0.693593i \(0.243974\pi\)
−0.720367 + 0.693593i \(0.756026\pi\)
\(558\) 0 0
\(559\) −1.47196 + 0.849835i −0.0622571 + 0.0359442i
\(560\) 0 0
\(561\) −46.6750 18.6172i −1.97062 0.786018i
\(562\) 0 0
\(563\) −8.37882 + 3.04964i −0.353125 + 0.128527i −0.512491 0.858693i \(-0.671277\pi\)
0.159366 + 0.987220i \(0.449055\pi\)
\(564\) 0 0
\(565\) −64.4165 + 11.3584i −2.71002 + 0.477850i
\(566\) 0 0
\(567\) −21.8068 9.56357i −0.915801 0.401632i
\(568\) 0 0
\(569\) −27.9792 + 4.93349i −1.17295 + 0.206823i −0.725973 0.687723i \(-0.758610\pi\)
−0.446976 + 0.894546i \(0.647499\pi\)
\(570\) 0 0
\(571\) 9.22186 3.35648i 0.385923 0.140464i −0.141770 0.989900i \(-0.545279\pi\)
0.527693 + 0.849435i \(0.323057\pi\)
\(572\) 0 0
\(573\) −25.7817 10.2835i −1.07704 0.429599i
\(574\) 0 0
\(575\) 6.13209 3.54037i 0.255726 0.147643i
\(576\) 0 0
\(577\) 2.15118i 0.0895546i 0.998997 + 0.0447773i \(0.0142578\pi\)
−0.998997 + 0.0447773i \(0.985742\pi\)
\(578\) 0 0
\(579\) −31.0879 6.46374i −1.29197 0.268624i
\(580\) 0 0
\(581\) 16.9554 + 12.6374i 0.703428 + 0.524286i
\(582\) 0 0
\(583\) −18.2077 + 15.2781i −0.754088 + 0.632755i
\(584\) 0 0
\(585\) 13.8744 31.9226i 0.573635 1.31984i
\(586\) 0 0
\(587\) −6.62516 37.5732i −0.273450 1.55081i −0.743844 0.668354i \(-0.766999\pi\)
0.470394 0.882456i \(-0.344112\pi\)
\(588\) 0 0
\(589\) 4.23458 1.54126i 0.174483 0.0635066i
\(590\) 0 0
\(591\) −16.7105 0.509238i −0.687379 0.0209473i
\(592\) 0 0
\(593\) 8.09994 14.0295i 0.332625 0.576123i −0.650401 0.759591i \(-0.725399\pi\)
0.983026 + 0.183468i \(0.0587324\pi\)
\(594\) 0 0
\(595\) 76.0761 4.38885i 3.11882 0.179925i
\(596\) 0 0
\(597\) 9.63635 15.5749i 0.394390 0.637439i
\(598\) 0 0
\(599\) 13.0624 15.5671i 0.533714 0.636056i −0.430052 0.902804i \(-0.641505\pi\)
0.963766 + 0.266748i \(0.0859492\pi\)
\(600\) 0 0
\(601\) 5.94613 1.04846i 0.242548 0.0427677i −0.0510527 0.998696i \(-0.516258\pi\)
0.293600 + 0.955928i \(0.405147\pi\)
\(602\) 0 0
\(603\) 22.1373 6.56116i 0.901502 0.267191i
\(604\) 0 0
\(605\) −3.42545 19.4267i −0.139264 0.789807i
\(606\) 0 0
\(607\) 0.239855 + 0.658996i 0.00973542 + 0.0267478i 0.944465 0.328612i \(-0.106581\pi\)
−0.934730 + 0.355359i \(0.884358\pi\)
\(608\) 0 0
\(609\) −35.0055 + 13.8288i −1.41850 + 0.560370i
\(610\) 0 0
\(611\) −20.0218 + 11.5596i −0.809996 + 0.467651i
\(612\) 0 0
\(613\) −16.1127 + 27.9080i −0.650785 + 1.12719i 0.332148 + 0.943227i \(0.392227\pi\)
−0.982933 + 0.183965i \(0.941107\pi\)
\(614\) 0 0
\(615\) −8.26643 + 1.19924i −0.333335 + 0.0483580i
\(616\) 0 0
\(617\) 18.1880 + 3.20704i 0.732222 + 0.129110i 0.527314 0.849671i \(-0.323199\pi\)
0.204908 + 0.978781i \(0.434310\pi\)
\(618\) 0 0
\(619\) −3.07549 + 8.44985i −0.123615 + 0.339628i −0.986029 0.166575i \(-0.946729\pi\)
0.862414 + 0.506203i \(0.168951\pi\)
\(620\) 0 0
\(621\) 2.41212 + 2.43211i 0.0967949 + 0.0975973i
\(622\) 0 0
\(623\) 5.27433 + 22.3089i 0.211311 + 0.893789i
\(624\) 0 0
\(625\) 28.0869 + 23.5677i 1.12348 + 0.942709i
\(626\) 0 0
\(627\) 5.55920 13.9374i 0.222013 0.556607i
\(628\) 0 0
\(629\) −0.682821 1.18268i −0.0272259 0.0471566i
\(630\) 0 0
\(631\) −5.62050 + 9.73499i −0.223749 + 0.387544i −0.955943 0.293552i \(-0.905163\pi\)
0.732195 + 0.681095i \(0.238496\pi\)
\(632\) 0 0
\(633\) 31.5975 + 6.56970i 1.25589 + 0.261122i
\(634\) 0 0
\(635\) −22.3592 + 8.13807i −0.887296 + 0.322949i
\(636\) 0 0
\(637\) −4.74280 + 19.9136i −0.187917 + 0.789005i
\(638\) 0 0
\(639\) 0.194868 3.19430i 0.00770886 0.126365i
\(640\) 0 0
\(641\) −10.7267 12.7836i −0.423679 0.504920i 0.511409 0.859338i \(-0.329124\pi\)
−0.935087 + 0.354417i \(0.884679\pi\)
\(642\) 0 0
\(643\) 7.25386 + 19.9298i 0.286064 + 0.785955i 0.996607 + 0.0823015i \(0.0262270\pi\)
−0.710543 + 0.703654i \(0.751551\pi\)
\(644\) 0 0
\(645\) 3.51814 1.89072i 0.138527 0.0744470i
\(646\) 0 0
\(647\) −15.2203 26.3623i −0.598371 1.03641i −0.993062 0.117595i \(-0.962482\pi\)
0.394691 0.918814i \(-0.370852\pi\)
\(648\) 0 0
\(649\) 46.6591 + 26.9386i 1.83153 + 1.05743i
\(650\) 0 0
\(651\) −9.52296 + 0.258723i −0.373234 + 0.0101402i
\(652\) 0 0
\(653\) 2.31357 + 0.407944i 0.0905369 + 0.0159641i 0.218733 0.975785i \(-0.429808\pi\)
−0.128196 + 0.991749i \(0.540919\pi\)
\(654\) 0 0
\(655\) −19.9666 + 16.7540i −0.780159 + 0.654631i
\(656\) 0 0
\(657\) −0.608692 + 9.97776i −0.0237473 + 0.389269i
\(658\) 0 0
\(659\) 16.2406 44.6206i 0.632643 1.73817i −0.0410456 0.999157i \(-0.513069\pi\)
0.673689 0.739015i \(-0.264709\pi\)
\(660\) 0 0
\(661\) −7.28366 1.28431i −0.283302 0.0499537i 0.0301917 0.999544i \(-0.490388\pi\)
−0.313493 + 0.949590i \(0.601499\pi\)
\(662\) 0 0
\(663\) −34.9198 + 11.5179i −1.35617 + 0.447317i
\(664\) 0 0
\(665\) 1.31054 + 22.7168i 0.0508204 + 0.880919i
\(666\) 0 0
\(667\) 5.41438 0.209646
\(668\) 0 0
\(669\) 21.3654 + 8.52198i 0.826033 + 0.329479i
\(670\) 0 0
\(671\) 7.36478 41.7678i 0.284314 1.61243i
\(672\) 0 0
\(673\) −14.2500 + 11.9572i −0.549297 + 0.460915i −0.874703 0.484660i \(-0.838943\pi\)
0.325406 + 0.945574i \(0.394499\pi\)
\(674\) 0 0
\(675\) −23.7958 + 50.4852i −0.915901 + 1.94317i
\(676\) 0 0
\(677\) −5.37940 30.5081i −0.206747 1.17252i −0.894667 0.446735i \(-0.852587\pi\)
0.687919 0.725787i \(-0.258524\pi\)
\(678\) 0 0
\(679\) 26.8376 + 3.15186i 1.02993 + 0.120957i
\(680\) 0 0
\(681\) −8.38536 + 21.0229i −0.321328 + 0.805598i
\(682\) 0 0
\(683\) −1.32267 0.763644i −0.0506106 0.0292200i 0.474481 0.880266i \(-0.342636\pi\)
−0.525092 + 0.851046i \(0.675969\pi\)
\(684\) 0 0
\(685\) 55.1138 + 31.8200i 2.10579 + 1.21578i
\(686\) 0 0
\(687\) 5.06688 24.3695i 0.193313 0.929756i
\(688\) 0 0
\(689\) −3.02013 + 17.1280i −0.115058 + 0.652525i
\(690\) 0 0
\(691\) 29.8290 + 35.5488i 1.13475 + 1.35234i 0.927400 + 0.374071i \(0.122038\pi\)
0.207347 + 0.978267i \(0.433517\pi\)
\(692\) 0 0
\(693\) −20.4702 + 24.2324i −0.777597 + 0.920512i
\(694\) 0 0
\(695\) −30.4628 + 83.6960i −1.15552 + 3.17477i
\(696\) 0 0
\(697\) 6.75961 + 5.67198i 0.256038 + 0.214842i
\(698\) 0 0
\(699\) 12.9843 + 0.395685i 0.491111 + 0.0149662i
\(700\) 0 0
\(701\) 13.6944i 0.517231i 0.965980 + 0.258615i \(0.0832662\pi\)
−0.965980 + 0.258615i \(0.916734\pi\)
\(702\) 0 0
\(703\) 0.353155 0.203894i 0.0133195 0.00769002i
\(704\) 0 0
\(705\) 47.8544 25.7179i 1.80230 0.968593i
\(706\) 0 0
\(707\) −24.8929 18.5534i −0.936193 0.697772i
\(708\) 0 0
\(709\) 42.3406 + 15.4107i 1.59013 + 0.578761i 0.977376 0.211510i \(-0.0678380\pi\)
0.612757 + 0.790271i \(0.290060\pi\)
\(710\) 0 0
\(711\) −34.4935 + 25.5322i −1.29361 + 0.957534i
\(712\) 0 0
\(713\) 1.28778 + 0.468712i 0.0482276 + 0.0175534i
\(714\) 0 0
\(715\) −35.5208 29.8055i −1.32840 1.11466i
\(716\) 0 0
\(717\) 3.09484 + 2.76181i 0.115579 + 0.103142i
\(718\) 0 0
\(719\) 6.57011 + 11.3798i 0.245024 + 0.424394i 0.962138 0.272562i \(-0.0878709\pi\)
−0.717115 + 0.696955i \(0.754538\pi\)
\(720\) 0 0
\(721\) −0.972744 16.8615i −0.0362269 0.627955i
\(722\) 0 0
\(723\) −32.9549 + 25.9837i −1.22560 + 0.966345i
\(724\) 0 0
\(725\) 30.1728 + 82.8991i 1.12059 + 3.07879i
\(726\) 0 0
\(727\) 25.2352 + 30.0742i 0.935922 + 1.11539i 0.993129 + 0.117026i \(0.0373361\pi\)
−0.0572067 + 0.998362i \(0.518219\pi\)
\(728\) 0 0
\(729\) −26.5502 4.90784i −0.983341 0.181772i
\(730\) 0 0
\(731\) −3.96480 1.44307i −0.146644 0.0533739i
\(732\) 0 0
\(733\) 2.95168 3.51767i 0.109023 0.129928i −0.708773 0.705436i \(-0.750751\pi\)
0.817796 + 0.575508i \(0.195196\pi\)
\(734\) 0 0
\(735\) 12.5652 46.4333i 0.463474 1.71272i
\(736\) 0 0
\(737\) 30.7586i 1.13301i
\(738\) 0 0
\(739\) 1.73047 0.0636564 0.0318282 0.999493i \(-0.489867\pi\)
0.0318282 + 0.999493i \(0.489867\pi\)
\(740\) 0 0
\(741\) −3.43930 10.4273i −0.126346 0.383055i
\(742\) 0 0
\(743\) −8.04882 + 9.59220i −0.295282 + 0.351904i −0.893205 0.449650i \(-0.851549\pi\)
0.597922 + 0.801554i \(0.295993\pi\)
\(744\) 0 0
\(745\) 8.50464 1.49960i 0.311586 0.0549410i
\(746\) 0 0
\(747\) 21.9910 + 9.55784i 0.804608 + 0.349703i
\(748\) 0 0
\(749\) −9.81580 + 32.7214i −0.358661 + 1.19561i
\(750\) 0 0
\(751\) 7.15576 40.5823i 0.261117 1.48087i −0.518751 0.854926i \(-0.673603\pi\)
0.779868 0.625944i \(-0.215286\pi\)
\(752\) 0 0
\(753\) 1.53187 50.2678i 0.0558244 1.83186i
\(754\) 0 0
\(755\) 82.8387 3.01481
\(756\) 0 0
\(757\) −20.9608 −0.761832 −0.380916 0.924610i \(-0.624391\pi\)
−0.380916 + 0.924610i \(0.624391\pi\)
\(758\) 0 0
\(759\) 4.01953 2.16018i 0.145900 0.0784095i
\(760\) 0 0
\(761\) −5.11286 + 28.9965i −0.185341 + 1.05112i 0.740175 + 0.672414i \(0.234742\pi\)
−0.925516 + 0.378707i \(0.876369\pi\)
\(762\) 0 0
\(763\) −4.43737 + 4.18183i −0.160644 + 0.151392i
\(764\) 0 0
\(765\) 82.8436 24.5535i 2.99521 0.887735i
\(766\) 0 0
\(767\) 38.8249 6.84588i 1.40189 0.247190i
\(768\) 0 0
\(769\) −32.3467 + 38.5493i −1.16645 + 1.39012i −0.261178 + 0.965291i \(0.584111\pi\)
−0.905272 + 0.424832i \(0.860333\pi\)
\(770\) 0 0
\(771\) −24.6444 5.12402i −0.887546 0.184537i
\(772\) 0 0
\(773\) 25.1223 0.903587 0.451793 0.892123i \(-0.350784\pi\)
0.451793 + 0.892123i \(0.350784\pi\)
\(774\) 0 0
\(775\) 22.3290i 0.802081i
\(776\) 0 0
\(777\) −0.844595 + 0.172698i −0.0302997 + 0.00619552i
\(778\) 0