Properties

Label 1134.2.h.s.541.1
Level $1134$
Weight $2$
Character 1134.541
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1134.541
Dual form 1134.2.h.s.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} -4.24264 q^{11} +(-3.12132 - 5.40629i) q^{13} +(2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 - 3.67423i) q^{22} -7.24264 q^{23} -5.00000 q^{25} +(3.12132 - 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(-2.12132 + 3.67423i) q^{29} +(-0.378680 + 0.655892i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} -6.24264 q^{38} +(-2.74264 - 4.75039i) q^{41} +(3.24264 - 5.61642i) q^{43} +(2.12132 - 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} +(6.62132 + 11.4685i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-2.50000 - 4.33013i) q^{50} +6.24264 q^{52} +(2.12132 + 3.67423i) q^{53} +(-1.00000 + 2.44949i) q^{56} -4.24264 q^{58} +(-3.12132 - 5.40629i) q^{61} -0.757359 q^{62} +1.00000 q^{64} +(4.12132 - 7.13834i) q^{67} +7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +4.00000 q^{74} +(-3.12132 - 5.40629i) q^{76} +(-4.24264 + 10.3923i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(2.74264 - 4.75039i) q^{82} +(3.87868 - 6.71807i) q^{83} +6.48528 q^{86} +4.24264 q^{88} +(-2.74264 + 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(3.62132 - 6.27231i) q^{92} +(-6.62132 + 11.4685i) q^{94} +(6.24264 - 10.8126i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} - 4q^{13} + 2q^{14} - 2q^{16} - 4q^{19} - 12q^{23} - 20q^{25} + 4q^{26} - 2q^{28} - 10q^{31} + 2q^{32} + 8q^{37} - 8q^{38} + 6q^{41} - 4q^{43} - 6q^{46} + 18q^{47} - 20q^{49} - 10q^{50} + 8q^{52} - 4q^{56} - 4q^{61} - 20q^{62} + 4q^{64} + 8q^{67} + 12q^{71} + 14q^{73} + 16q^{74} - 4q^{76} - 10q^{79} - 6q^{82} + 24q^{83} - 8q^{86} + 6q^{89} - 40q^{91} + 6q^{92} - 18q^{94} + 8q^{97} - 10q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 1.00000 2.44949i 0.377964 0.925820i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −4.24264 −1.27920 −0.639602 0.768706i \(-0.720901\pi\)
−0.639602 + 0.768706i \(0.720901\pi\)
\(12\) 0 0
\(13\) −3.12132 5.40629i −0.865699 1.49943i −0.866352 0.499434i \(-0.833541\pi\)
0.000653431 1.00000i \(-0.499792\pi\)
\(14\) 2.62132 0.358719i 0.700577 0.0958718i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −3.12132 + 5.40629i −0.716080 + 1.24029i 0.246462 + 0.969153i \(0.420732\pi\)
−0.962542 + 0.271134i \(0.912601\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.12132 3.67423i −0.452267 0.783349i
\(23\) −7.24264 −1.51019 −0.755097 0.655613i \(-0.772410\pi\)
−0.755097 + 0.655613i \(0.772410\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 3.12132 5.40629i 0.612141 1.06026i
\(27\) 0 0
\(28\) 1.62132 + 2.09077i 0.306401 + 0.395118i
\(29\) −2.12132 + 3.67423i −0.393919 + 0.682288i −0.992963 0.118428i \(-0.962214\pi\)
0.599043 + 0.800717i \(0.295548\pi\)
\(30\) 0 0
\(31\) −0.378680 + 0.655892i −0.0680129 + 0.117802i −0.898027 0.439941i \(-0.854999\pi\)
0.830014 + 0.557743i \(0.188333\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −6.24264 −1.01269
\(39\) 0 0
\(40\) 0 0
\(41\) −2.74264 4.75039i −0.428329 0.741887i 0.568396 0.822755i \(-0.307564\pi\)
−0.996725 + 0.0808682i \(0.974231\pi\)
\(42\) 0 0
\(43\) 3.24264 5.61642i 0.494498 0.856496i −0.505482 0.862837i \(-0.668685\pi\)
0.999980 + 0.00634147i \(0.00201857\pi\)
\(44\) 2.12132 3.67423i 0.319801 0.553912i
\(45\) 0 0
\(46\) −3.62132 6.27231i −0.533935 0.924802i
\(47\) 6.62132 + 11.4685i 0.965819 + 1.67285i 0.707399 + 0.706815i \(0.249869\pi\)
0.258420 + 0.966033i \(0.416798\pi\)
\(48\) 0 0
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) −2.50000 4.33013i −0.353553 0.612372i
\(51\) 0 0
\(52\) 6.24264 0.865699
\(53\) 2.12132 + 3.67423i 0.291386 + 0.504695i 0.974138 0.225955i \(-0.0725503\pi\)
−0.682752 + 0.730650i \(0.739217\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 + 2.44949i −0.133631 + 0.327327i
\(57\) 0 0
\(58\) −4.24264 −0.557086
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) −3.12132 5.40629i −0.399644 0.692204i 0.594038 0.804437i \(-0.297533\pi\)
−0.993682 + 0.112233i \(0.964200\pi\)
\(62\) −0.757359 −0.0961847
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.12132 7.13834i 0.503499 0.872087i −0.496492 0.868041i \(-0.665379\pi\)
0.999992 0.00404550i \(-0.00128773\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.24264 0.859543 0.429772 0.902938i \(-0.358594\pi\)
0.429772 + 0.902938i \(0.358594\pi\)
\(72\) 0 0
\(73\) 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i \(-0.0323196\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −3.12132 5.40629i −0.358040 0.620143i
\(77\) −4.24264 + 10.3923i −0.483494 + 1.18431i
\(78\) 0 0
\(79\) −4.62132 8.00436i −0.519939 0.900561i −0.999731 0.0231789i \(-0.992621\pi\)
0.479792 0.877382i \(-0.340712\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 2.74264 4.75039i 0.302874 0.524593i
\(83\) 3.87868 6.71807i 0.425740 0.737404i −0.570749 0.821125i \(-0.693347\pi\)
0.996489 + 0.0837207i \(0.0266803\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.48528 0.699326
\(87\) 0 0
\(88\) 4.24264 0.452267
\(89\) −2.74264 + 4.75039i −0.290719 + 0.503541i −0.973980 0.226634i \(-0.927228\pi\)
0.683261 + 0.730175i \(0.260561\pi\)
\(90\) 0 0
\(91\) −16.3640 + 2.23936i −1.71541 + 0.234748i
\(92\) 3.62132 6.27231i 0.377549 0.653934i
\(93\) 0 0
\(94\) −6.62132 + 11.4685i −0.682937 + 1.18288i
\(95\) 0 0
\(96\) 0 0
\(97\) 6.24264 10.8126i 0.633844 1.09785i −0.352915 0.935656i \(-0.614809\pi\)
0.986759 0.162195i \(-0.0518573\pi\)
\(98\) 1.74264 6.77962i 0.176033 0.684845i
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −7.75736 −0.771886 −0.385943 0.922523i \(-0.626124\pi\)
−0.385943 + 0.922523i \(0.626124\pi\)
\(102\) 0 0
\(103\) 0.757359 0.0746248 0.0373124 0.999304i \(-0.488120\pi\)
0.0373124 + 0.999304i \(0.488120\pi\)
\(104\) 3.12132 + 5.40629i 0.306071 + 0.530130i
\(105\) 0 0
\(106\) −2.12132 + 3.67423i −0.206041 + 0.356873i
\(107\) −1.24264 + 2.15232i −0.120131 + 0.208072i −0.919819 0.392343i \(-0.871665\pi\)
0.799688 + 0.600415i \(0.204998\pi\)
\(108\) 0 0
\(109\) 1.12132 + 1.94218i 0.107403 + 0.186027i 0.914717 0.404094i \(-0.132413\pi\)
−0.807314 + 0.590122i \(0.799080\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.62132 + 0.358719i −0.247691 + 0.0338958i
\(113\) −10.2426 17.7408i −0.963547 1.66891i −0.713470 0.700686i \(-0.752878\pi\)
−0.250076 0.968226i \(-0.580456\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.12132 3.67423i −0.196960 0.341144i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 3.12132 5.40629i 0.282591 0.489462i
\(123\) 0 0
\(124\) −0.378680 0.655892i −0.0340064 0.0589009i
\(125\) 0 0
\(126\) 0 0
\(127\) 6.75736 0.599619 0.299809 0.953999i \(-0.403077\pi\)
0.299809 + 0.953999i \(0.403077\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.75736 0.677764 0.338882 0.940829i \(-0.389951\pi\)
0.338882 + 0.940829i \(0.389951\pi\)
\(132\) 0 0
\(133\) 10.1213 + 13.0519i 0.877630 + 1.13175i
\(134\) 8.24264 0.712056
\(135\) 0 0
\(136\) 0 0
\(137\) 19.9706 1.70620 0.853100 0.521747i \(-0.174720\pi\)
0.853100 + 0.521747i \(0.174720\pi\)
\(138\) 0 0
\(139\) 2.36396 + 4.09450i 0.200509 + 0.347291i 0.948692 0.316200i \(-0.102407\pi\)
−0.748184 + 0.663491i \(0.769074\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.62132 + 6.27231i 0.303894 + 0.526361i
\(143\) 13.2426 + 22.9369i 1.10741 + 1.91808i
\(144\) 0 0
\(145\) 0 0
\(146\) −3.50000 + 6.06218i −0.289662 + 0.501709i
\(147\) 0 0
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) −16.2426 −1.33065 −0.665324 0.746554i \(-0.731707\pi\)
−0.665324 + 0.746554i \(0.731707\pi\)
\(150\) 0 0
\(151\) −2.75736 −0.224391 −0.112195 0.993686i \(-0.535788\pi\)
−0.112195 + 0.993686i \(0.535788\pi\)
\(152\) 3.12132 5.40629i 0.253173 0.438508i
\(153\) 0 0
\(154\) −11.1213 + 1.52192i −0.896182 + 0.122640i
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 4.62132 8.00436i 0.367653 0.636793i
\(159\) 0 0
\(160\) 0 0
\(161\) −7.24264 + 17.7408i −0.570800 + 1.39817i
\(162\) 0 0
\(163\) 5.87868 10.1822i 0.460454 0.797529i −0.538530 0.842606i \(-0.681020\pi\)
0.998984 + 0.0450772i \(0.0143534\pi\)
\(164\) 5.48528 0.428329
\(165\) 0 0
\(166\) 7.75736 0.602088
\(167\) 12.1066 + 20.9692i 0.936837 + 1.62265i 0.771325 + 0.636441i \(0.219594\pi\)
0.165512 + 0.986208i \(0.447072\pi\)
\(168\) 0 0
\(169\) −12.9853 + 22.4912i −0.998868 + 1.73009i
\(170\) 0 0
\(171\) 0 0
\(172\) 3.24264 + 5.61642i 0.247249 + 0.428248i
\(173\) −5.48528 9.50079i −0.417038 0.722331i 0.578602 0.815610i \(-0.303599\pi\)
−0.995640 + 0.0932788i \(0.970265\pi\)
\(174\) 0 0
\(175\) −5.00000 + 12.2474i −0.377964 + 0.925820i
\(176\) 2.12132 + 3.67423i 0.159901 + 0.276956i
\(177\) 0 0
\(178\) −5.48528 −0.411139
\(179\) −8.12132 14.0665i −0.607016 1.05138i −0.991729 0.128346i \(-0.959033\pi\)
0.384713 0.923036i \(-0.374300\pi\)
\(180\) 0 0
\(181\) −20.2426 −1.50462 −0.752312 0.658807i \(-0.771061\pi\)
−0.752312 + 0.658807i \(0.771061\pi\)
\(182\) −10.1213 13.0519i −0.750242 0.967473i
\(183\) 0 0
\(184\) 7.24264 0.533935
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −13.2426 −0.965819
\(189\) 0 0
\(190\) 0 0
\(191\) 4.24264 + 7.34847i 0.306987 + 0.531717i 0.977702 0.209999i \(-0.0673460\pi\)
−0.670715 + 0.741715i \(0.734013\pi\)
\(192\) 0 0
\(193\) 2.25736 3.90986i 0.162488 0.281438i −0.773272 0.634074i \(-0.781381\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) 12.4853 0.896391
\(195\) 0 0
\(196\) 6.74264 1.88064i 0.481617 0.134331i
\(197\) −16.9706 −1.20910 −0.604551 0.796566i \(-0.706648\pi\)
−0.604551 + 0.796566i \(0.706648\pi\)
\(198\) 0 0
\(199\) 7.37868 + 12.7802i 0.523061 + 0.905968i 0.999640 + 0.0268362i \(0.00854325\pi\)
−0.476579 + 0.879132i \(0.658123\pi\)
\(200\) 5.00000 0.353553
\(201\) 0 0
\(202\) −3.87868 6.71807i −0.272903 0.472682i
\(203\) 6.87868 + 8.87039i 0.482789 + 0.622579i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.378680 + 0.655892i 0.0263839 + 0.0456982i
\(207\) 0 0
\(208\) −3.12132 + 5.40629i −0.216425 + 0.374858i
\(209\) 13.2426 22.9369i 0.916013 1.58658i
\(210\) 0 0
\(211\) 3.24264 + 5.61642i 0.223233 + 0.386650i 0.955788 0.294058i \(-0.0950057\pi\)
−0.732555 + 0.680708i \(0.761672\pi\)
\(212\) −4.24264 −0.291386
\(213\) 0 0
\(214\) −2.48528 −0.169890
\(215\) 0 0
\(216\) 0 0
\(217\) 1.22792 + 1.58346i 0.0833568 + 0.107493i
\(218\) −1.12132 + 1.94218i −0.0759454 + 0.131541i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −5.86396 + 10.1567i −0.392680 + 0.680141i −0.992802 0.119767i \(-0.961785\pi\)
0.600122 + 0.799908i \(0.295119\pi\)
\(224\) −1.62132 2.09077i −0.108329 0.139695i
\(225\) 0 0
\(226\) 10.2426 17.7408i 0.681330 1.18010i
\(227\) −26.4853 −1.75789 −0.878945 0.476923i \(-0.841752\pi\)
−0.878945 + 0.476923i \(0.841752\pi\)
\(228\) 0 0
\(229\) 24.9706 1.65010 0.825051 0.565059i \(-0.191147\pi\)
0.825051 + 0.565059i \(0.191147\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.12132 3.67423i 0.139272 0.241225i
\(233\) 10.2426 17.7408i 0.671018 1.16224i −0.306598 0.951839i \(-0.599191\pi\)
0.977616 0.210398i \(-0.0674759\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.86396 + 3.22848i 0.120570 + 0.208833i 0.919992 0.391936i \(-0.128195\pi\)
−0.799423 + 0.600769i \(0.794861\pi\)
\(240\) 0 0
\(241\) 8.51472 0.548481 0.274241 0.961661i \(-0.411574\pi\)
0.274241 + 0.961661i \(0.411574\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 0 0
\(244\) 6.24264 0.399644
\(245\) 0 0
\(246\) 0 0
\(247\) 38.9706 2.47964
\(248\) 0.378680 0.655892i 0.0240462 0.0416492i
\(249\) 0 0
\(250\) 0 0
\(251\) −18.7279 −1.18210 −0.591048 0.806636i \(-0.701286\pi\)
−0.591048 + 0.806636i \(0.701286\pi\)
\(252\) 0 0
\(253\) 30.7279 1.93185
\(254\) 3.37868 + 5.85204i 0.211997 + 0.367190i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.48528 −0.342162 −0.171081 0.985257i \(-0.554726\pi\)
−0.171081 + 0.985257i \(0.554726\pi\)
\(258\) 0 0
\(259\) −6.48528 8.36308i −0.402976 0.519657i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.87868 + 6.71807i 0.239626 + 0.415044i
\(263\) −22.9706 −1.41643 −0.708213 0.705999i \(-0.750498\pi\)
−0.708213 + 0.705999i \(0.750498\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −6.24264 + 15.2913i −0.382761 + 0.937569i
\(267\) 0 0
\(268\) 4.12132 + 7.13834i 0.251750 + 0.436043i
\(269\) −5.48528 9.50079i −0.334444 0.579273i 0.648934 0.760844i \(-0.275215\pi\)
−0.983378 + 0.181571i \(0.941882\pi\)
\(270\) 0 0
\(271\) 6.24264 10.8126i 0.379213 0.656817i −0.611735 0.791063i \(-0.709528\pi\)
0.990948 + 0.134246i \(0.0428613\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 9.98528 + 17.2950i 0.603233 + 1.04483i
\(275\) 21.2132 1.27920
\(276\) 0 0
\(277\) −19.2132 −1.15441 −0.577205 0.816599i \(-0.695857\pi\)
−0.577205 + 0.816599i \(0.695857\pi\)
\(278\) −2.36396 + 4.09450i −0.141781 + 0.245572i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.2279 19.4473i 0.669802 1.16013i −0.308158 0.951335i \(-0.599712\pi\)
0.977959 0.208795i \(-0.0669542\pi\)
\(282\) 0 0
\(283\) −12.4853 + 21.6251i −0.742173 + 1.28548i 0.209331 + 0.977845i \(0.432871\pi\)
−0.951504 + 0.307636i \(0.900462\pi\)
\(284\) −3.62132 + 6.27231i −0.214886 + 0.372193i
\(285\) 0 0
\(286\) −13.2426 + 22.9369i −0.783054 + 1.35629i
\(287\) −14.3787 + 1.96768i −0.848747 + 0.116148i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 −0.409644
\(293\) −5.48528 9.50079i −0.320454 0.555042i 0.660128 0.751153i \(-0.270502\pi\)
−0.980582 + 0.196111i \(0.937169\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) −8.12132 14.0665i −0.470455 0.814853i
\(299\) 22.6066 + 39.1558i 1.30737 + 2.26444i
\(300\) 0 0
\(301\) −10.5147 13.5592i −0.606058 0.781541i
\(302\) −1.37868 2.38794i −0.0793341 0.137411i
\(303\) 0 0
\(304\) 6.24264 0.358040
\(305\) 0 0
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −6.87868 8.87039i −0.391949 0.505437i
\(309\) 0 0
\(310\) 0 0
\(311\) −5.48528 + 9.50079i −0.311042 + 0.538740i −0.978588 0.205828i \(-0.934011\pi\)
0.667546 + 0.744568i \(0.267345\pi\)
\(312\) 0 0
\(313\) 8.98528 + 15.5630i 0.507878 + 0.879671i 0.999958 + 0.00912090i \(0.00290331\pi\)
−0.492080 + 0.870550i \(0.663763\pi\)
\(314\) −14.0000 −0.790066
\(315\) 0 0
\(316\) 9.24264 0.519939
\(317\) −8.48528 14.6969i −0.476581 0.825462i 0.523059 0.852296i \(-0.324791\pi\)
−0.999640 + 0.0268342i \(0.991457\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) −18.9853 + 2.59808i −1.05801 + 0.144785i
\(323\) 0 0
\(324\) 0 0
\(325\) 15.6066 + 27.0314i 0.865699 + 1.49943i
\(326\) 11.7574 0.651180
\(327\) 0 0
\(328\) 2.74264 + 4.75039i 0.151437 + 0.262297i
\(329\) 34.7132 4.75039i 1.91380 0.261898i
\(330\) 0 0
\(331\) 9.24264 + 16.0087i 0.508021 + 0.879919i 0.999957 + 0.00928730i \(0.00295628\pi\)
−0.491935 + 0.870632i \(0.663710\pi\)
\(332\) 3.87868 + 6.71807i 0.212870 + 0.368702i
\(333\) 0 0
\(334\) −12.1066 + 20.9692i −0.662444 + 1.14739i
\(335\) 0 0
\(336\) 0 0
\(337\) −2.24264 3.88437i −0.122164 0.211595i 0.798457 0.602052i \(-0.205650\pi\)
−0.920621 + 0.390457i \(0.872317\pi\)
\(338\) −25.9706 −1.41261
\(339\) 0 0
\(340\) 0 0
\(341\) 1.60660 2.78272i 0.0870024 0.150693i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) −3.24264 + 5.61642i −0.174831 + 0.302817i
\(345\) 0 0
\(346\) 5.48528 9.50079i 0.294891 0.510765i
\(347\) −3.36396 + 5.82655i −0.180587 + 0.312786i −0.942081 0.335387i \(-0.891133\pi\)
0.761494 + 0.648172i \(0.224466\pi\)
\(348\) 0 0
\(349\) −12.4853 + 21.6251i −0.668322 + 1.15757i 0.310051 + 0.950720i \(0.399654\pi\)
−0.978373 + 0.206848i \(0.933680\pi\)
\(350\) −13.1066 + 1.79360i −0.700577 + 0.0958718i
\(351\) 0 0
\(352\) −2.12132 + 3.67423i −0.113067 + 0.195837i
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −2.74264 4.75039i −0.145360 0.251770i
\(357\) 0 0
\(358\) 8.12132 14.0665i 0.429225 0.743440i
\(359\) 5.37868 9.31615i 0.283876 0.491687i −0.688460 0.725274i \(-0.741713\pi\)
0.972336 + 0.233587i \(0.0750463\pi\)
\(360\) 0 0
\(361\) −9.98528 17.2950i −0.525541 0.910264i
\(362\) −10.1213 17.5306i −0.531965 0.921390i
\(363\) 0 0
\(364\) 6.24264 15.2913i 0.327203 0.801481i
\(365\) 0 0
\(366\) 0 0
\(367\) 11.7279 0.612193 0.306096 0.952001i \(-0.400977\pi\)
0.306096 + 0.952001i \(0.400977\pi\)
\(368\) 3.62132 + 6.27231i 0.188774 + 0.326967i
\(369\) 0 0
\(370\) 0 0
\(371\) 11.1213 1.52192i 0.577390 0.0790140i
\(372\) 0 0
\(373\) −7.21320 −0.373486 −0.186743 0.982409i \(-0.559793\pi\)
−0.186743 + 0.982409i \(0.559793\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.62132 11.4685i −0.341469 0.591441i
\(377\) 26.4853 1.36406
\(378\) 0 0
\(379\) 1.27208 0.0653423 0.0326711 0.999466i \(-0.489599\pi\)
0.0326711 + 0.999466i \(0.489599\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.24264 + 7.34847i −0.217072 + 0.375980i
\(383\) 24.2132 1.23724 0.618618 0.785692i \(-0.287693\pi\)
0.618618 + 0.785692i \(0.287693\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.51472 0.229793
\(387\) 0 0
\(388\) 6.24264 + 10.8126i 0.316922 + 0.548925i
\(389\) −10.2426 −0.519322 −0.259661 0.965700i \(-0.583611\pi\)
−0.259661 + 0.965700i \(0.583611\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.00000 + 4.89898i 0.252538 + 0.247436i
\(393\) 0 0
\(394\) −8.48528 14.6969i −0.427482 0.740421i
\(395\) 0 0
\(396\) 0 0
\(397\) 10.1213 17.5306i 0.507975 0.879838i −0.491983 0.870605i \(-0.663728\pi\)
0.999957 0.00923278i \(-0.00293893\pi\)
\(398\) −7.37868 + 12.7802i −0.369860 + 0.640616i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) −29.4853 −1.47242 −0.736212 0.676751i \(-0.763388\pi\)
−0.736212 + 0.676751i \(0.763388\pi\)
\(402\) 0 0
\(403\) 4.72792 0.235515
\(404\) 3.87868 6.71807i 0.192972 0.334236i
\(405\) 0 0
\(406\) −4.24264 + 10.3923i −0.210559 + 0.515761i
\(407\) −8.48528 + 14.6969i −0.420600 + 0.728500i
\(408\) 0 0
\(409\) −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i \(0.499551\pi\)
−0.866730 + 0.498778i \(0.833782\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.378680 + 0.655892i −0.0186562 + 0.0323135i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −6.24264 −0.306071
\(417\) 0 0
\(418\) 26.4853 1.29544
\(419\) −3.87868 6.71807i −0.189486 0.328199i 0.755593 0.655041i \(-0.227349\pi\)
−0.945079 + 0.326842i \(0.894015\pi\)
\(420\) 0 0
\(421\) 7.12132 12.3345i 0.347072 0.601146i −0.638656 0.769492i \(-0.720509\pi\)
0.985728 + 0.168346i \(0.0538426\pi\)
\(422\) −3.24264 + 5.61642i −0.157849 + 0.273403i
\(423\) 0 0
\(424\) −2.12132 3.67423i −0.103020 0.178437i
\(425\) 0 0
\(426\) 0 0
\(427\) −16.3640 + 2.23936i −0.791908 + 0.108370i
\(428\) −1.24264 2.15232i −0.0600653 0.104036i
\(429\) 0 0
\(430\) 0 0
\(431\) −18.6213 32.2531i −0.896957 1.55358i −0.831363 0.555729i \(-0.812439\pi\)
−0.0655943 0.997846i \(-0.520894\pi\)
\(432\) 0 0
\(433\) 3.97056 0.190813 0.0954065 0.995438i \(-0.469585\pi\)
0.0954065 + 0.995438i \(0.469585\pi\)
\(434\) −0.757359 + 1.85514i −0.0363544 + 0.0890498i
\(435\) 0 0
\(436\) −2.24264 −0.107403
\(437\) 22.6066 39.1558i 1.08142 1.87308i
\(438\) 0 0
\(439\) −5.86396 10.1567i −0.279872 0.484752i 0.691481 0.722395i \(-0.256959\pi\)
−0.971353 + 0.237643i \(0.923625\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.75736 + 8.23999i 0.226029 + 0.391494i 0.956628 0.291313i \(-0.0940923\pi\)
−0.730599 + 0.682807i \(0.760759\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −11.7279 −0.555333
\(447\) 0 0
\(448\) 1.00000 2.44949i 0.0472456 0.115728i
\(449\) 4.97056 0.234575 0.117288 0.993098i \(-0.462580\pi\)
0.117288 + 0.993098i \(0.462580\pi\)
\(450\) 0 0
\(451\) 11.6360 + 20.1542i 0.547920 + 0.949025i
\(452\) 20.4853 0.963547
\(453\) 0 0
\(454\) −13.2426 22.9369i −0.621508 1.07648i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.75736 9.97204i −0.269318 0.466472i 0.699368 0.714762i \(-0.253465\pi\)
−0.968686 + 0.248290i \(0.920132\pi\)
\(458\) 12.4853 + 21.6251i 0.583399 + 1.01048i
\(459\) 0 0
\(460\) 0 0
\(461\) 17.1213 29.6550i 0.797419 1.38117i −0.123872 0.992298i \(-0.539531\pi\)
0.921291 0.388873i \(-0.127135\pi\)
\(462\) 0 0
\(463\) 4.37868 + 7.58410i 0.203495 + 0.352463i 0.949652 0.313307i \(-0.101437\pi\)
−0.746158 + 0.665769i \(0.768103\pi\)
\(464\) 4.24264 0.196960
\(465\) 0 0
\(466\) 20.4853 0.948962
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 0 0
\(469\) −13.3640 17.2335i −0.617090 0.795768i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −13.7574 + 23.8284i −0.632564 + 1.09563i
\(474\) 0 0
\(475\) 15.6066 27.0314i 0.716080 1.24029i
\(476\) 0 0
\(477\) 0 0
\(478\) −1.86396 + 3.22848i −0.0852556 + 0.147667i
\(479\) 13.2426 0.605072 0.302536 0.953138i \(-0.402167\pi\)
0.302536 + 0.953138i \(0.402167\pi\)
\(480\) 0 0
\(481\) −24.9706 −1.13856
\(482\) 4.25736 + 7.37396i 0.193917 + 0.335875i
\(483\) 0 0
\(484\) −3.50000 + 6.06218i −0.159091 + 0.275554i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.37868 + 2.38794i 0.0624739 + 0.108208i 0.895571 0.444919i \(-0.146768\pi\)
−0.833097 + 0.553127i \(0.813434\pi\)
\(488\) 3.12132 + 5.40629i 0.141296 + 0.244731i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.36396 + 5.82655i 0.151813 + 0.262949i 0.931894 0.362730i \(-0.118155\pi\)
−0.780081 + 0.625679i \(0.784822\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 19.4853 + 33.7495i 0.876684 + 1.51846i
\(495\) 0 0
\(496\) 0.757359 0.0340064
\(497\) 7.24264 17.7408i 0.324877 0.795782i
\(498\) 0 0
\(499\) −10.7279 −0.480248 −0.240124 0.970742i \(-0.577188\pi\)
−0.240124 + 0.970742i \(0.577188\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −9.36396 16.2189i −0.417934 0.723883i
\(503\) 24.2132 1.07961 0.539807 0.841789i \(-0.318497\pi\)
0.539807 + 0.841789i \(0.318497\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 15.3640 + 26.6112i 0.683011 + 1.18301i
\(507\) 0 0
\(508\) −3.37868 + 5.85204i −0.149905 + 0.259643i
\(509\) −7.75736 −0.343839 −0.171919 0.985111i \(-0.554997\pi\)
−0.171919 + 0.985111i \(0.554997\pi\)
\(510\) 0 0
\(511\) 18.3492 2.51104i 0.811723 0.111082i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −2.74264 4.75039i −0.120973 0.209531i
\(515\) 0 0
\(516\) 0 0
\(517\) −28.0919 48.6566i −1.23548 2.13991i
\(518\) 4.00000 9.79796i 0.175750 0.430498i
\(519\) 0 0
\(520\) 0 0
\(521\) 8.22792 + 14.2512i 0.360472 + 0.624355i 0.988039 0.154207i \(-0.0492824\pi\)
−0.627567 + 0.778563i \(0.715949\pi\)
\(522\) 0 0
\(523\) 10.1213 17.5306i 0.442574 0.766561i −0.555305 0.831647i \(-0.687399\pi\)
0.997880 + 0.0650852i \(0.0207319\pi\)
\(524\) −3.87868 + 6.71807i −0.169441 + 0.293480i
\(525\) 0 0
\(526\) −11.4853 19.8931i −0.500782 0.867380i
\(527\) 0 0
\(528\) 0 0
\(529\) 29.4558 1.28069
\(530\) 0 0
\(531\) 0 0
\(532\) −16.3640 + 2.23936i −0.709468 + 0.0970884i
\(533\) −17.1213 + 29.6550i −0.741607 + 1.28450i
\(534\) 0 0
\(535\) 0 0
\(536\) −4.12132 + 7.13834i −0.178014 + 0.308329i
\(537\) 0 0
\(538\) 5.48528 9.50079i 0.236487 0.409608i
\(539\) 21.2132 + 20.7846i 0.913717 + 0.895257i
\(540\) 0 0
\(541\) 7.48528 12.9649i 0.321817 0.557404i −0.659046 0.752103i \(-0.729040\pi\)
0.980863 + 0.194699i \(0.0623730\pi\)
\(542\) 12.4853 0.536289
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 3.24264 5.61642i 0.138645 0.240141i −0.788339 0.615241i \(-0.789059\pi\)
0.926984 + 0.375101i \(0.122392\pi\)
\(548\) −9.98528 + 17.2950i −0.426550 + 0.738806i
\(549\) 0 0
\(550\) 10.6066 + 18.3712i 0.452267 + 0.783349i
\(551\) −13.2426 22.9369i −0.564155 0.977146i
\(552\) 0 0
\(553\) −24.2279 + 3.31552i −1.03028 + 0.140990i
\(554\) −9.60660 16.6391i −0.408145 0.706929i
\(555\) 0 0
\(556\) −4.72792 −0.200509
\(557\) −20.4853 35.4815i −0.867989 1.50340i −0.864048 0.503409i \(-0.832079\pi\)
−0.00394110 0.999992i \(-0.501254\pi\)
\(558\) 0 0
\(559\) −40.4853 −1.71234
\(560\) 0 0
\(561\) 0 0
\(562\) 22.4558 0.947243
\(563\) 9.36396 16.2189i 0.394644 0.683543i −0.598412 0.801189i \(-0.704201\pi\)
0.993056 + 0.117645i \(0.0375346\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −24.9706 −1.04959
\(567\) 0 0
\(568\) −7.24264 −0.303894
\(569\) 12.4706 + 21.5996i 0.522793 + 0.905504i 0.999648 + 0.0265224i \(0.00844333\pi\)
−0.476855 + 0.878982i \(0.658223\pi\)
\(570\) 0 0
\(571\) 10.4853 18.1610i 0.438795 0.760016i −0.558801 0.829301i \(-0.688739\pi\)
0.997597 + 0.0692856i \(0.0220720\pi\)
\(572\) −26.4853 −1.10741
\(573\) 0 0
\(574\) −8.89340 11.4685i −0.371203 0.478684i
\(575\) 36.2132 1.51019
\(576\) 0 0
\(577\) −17.9706 31.1259i −0.748124 1.29579i −0.948721 0.316115i \(-0.897621\pi\)
0.200596 0.979674i \(-0.435712\pi\)
\(578\) 17.0000 0.707107
\(579\) 0 0
\(580\) 0 0
\(581\) −12.5772 16.2189i −0.521789 0.672872i
\(582\) 0 0
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) −3.50000 6.06218i −0.144831 0.250855i
\(585\) 0 0
\(586\) 5.48528 9.50079i 0.226595 0.392474i
\(587\) −1.60660 + 2.78272i −0.0663115 + 0.114855i −0.897275 0.441472i \(-0.854456\pi\)
0.830963 + 0.556327i \(0.187790\pi\)
\(588\) 0 0
\(589\) −2.36396 4.09450i −0.0974053 0.168711i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) −2.74264 + 4.75039i −0.112627 + 0.195075i −0.916829 0.399281i \(-0.869260\pi\)
0.804202 + 0.594356i \(0.202593\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.12132 14.0665i 0.332662 0.576188i
\(597\) 0 0
\(598\) −22.6066 + 39.1558i −0.924453 + 1.60120i
\(599\) 11.4853 19.8931i 0.469276 0.812810i −0.530107 0.847931i \(-0.677848\pi\)
0.999383 + 0.0351210i \(0.0111817\pi\)
\(600\) 0 0
\(601\) 8.98528 15.5630i 0.366517 0.634827i −0.622501 0.782619i \(-0.713883\pi\)
0.989018 + 0.147792i \(0.0472167\pi\)
\(602\) 6.48528 15.8856i 0.264320 0.647450i
\(603\) 0 0
\(604\) 1.37868 2.38794i 0.0560977 0.0971640i
\(605\) 0 0
\(606\) 0 0
\(607\) −38.9706 −1.58177 −0.790883 0.611967i \(-0.790378\pi\)
−0.790883 + 0.611967i \(0.790378\pi\)
\(608\) 3.12132 + 5.40629i 0.126586 + 0.219254i
\(609\) 0 0
\(610\) 0 0
\(611\) 41.3345 71.5935i 1.67222 2.89636i
\(612\) 0 0
\(613\) 18.9706 + 32.8580i 0.766214 + 1.32712i 0.939602 + 0.342268i \(0.111195\pi\)
−0.173389 + 0.984853i \(0.555472\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 0 0
\(616\) 4.24264 10.3923i 0.170941 0.418718i
\(617\) −14.2279 24.6435i −0.572795 0.992109i −0.996277 0.0862052i \(-0.972526\pi\)
0.423483 0.905904i \(-0.360807\pi\)
\(618\) 0 0
\(619\) −1.51472 −0.0608817 −0.0304408 0.999537i \(-0.509691\pi\)
−0.0304408 + 0.999537i \(0.509691\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −10.9706 −0.439879
\(623\) 8.89340 + 11.4685i 0.356306 + 0.459474i
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −8.98528 + 15.5630i −0.359124 + 0.622021i
\(627\) 0 0
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 0 0
\(630\) 0 0
\(631\) −24.4853 −0.974744 −0.487372 0.873195i \(-0.662044\pi\)
−0.487372 + 0.873195i \(0.662044\pi\)
\(632\) 4.62132 + 8.00436i 0.183826 + 0.318396i
\(633\) 0 0
\(634\) 8.48528 14.6969i 0.336994 0.583690i
\(635\) 0 0
\(636\) 0 0
\(637\) −10.8787 + 42.3227i −0.431029 + 1.67689i
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) 4.45584 0.175995 0.0879976 0.996121i \(-0.471953\pi\)
0.0879976 + 0.996121i \(0.471953\pi\)
\(642\) 0 0
\(643\) 23.3640 + 40.4676i 0.921385 + 1.59589i 0.797275 + 0.603617i \(0.206274\pi\)
0.124110 + 0.992268i \(0.460392\pi\)
\(644\) −11.7426 15.1427i −0.462725 0.596706i
\(645\) 0 0
\(646\) 0 0
\(647\) 1.13604 + 1.96768i 0.0446623 + 0.0773574i 0.887492 0.460822i \(-0.152445\pi\)
−0.842830 + 0.538180i \(0.819112\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −15.6066 + 27.0314i −0.612141 + 1.06026i
\(651\) 0 0
\(652\) 5.87868 + 10.1822i 0.230227 + 0.398765i
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.74264 + 4.75039i −0.107082 + 0.185472i
\(657\) 0 0
\(658\) 21.4706 + 27.6873i 0.837010 + 1.07936i
\(659\) −19.6066 + 33.9596i −0.763765 + 1.32288i 0.177132 + 0.984187i \(0.443318\pi\)
−0.940897 + 0.338692i \(0.890015\pi\)
\(660\) 0 0
\(661\) 21.0919 36.5322i 0.820379 1.42094i −0.0850210 0.996379i \(-0.527096\pi\)
0.905400 0.424559i \(-0.139571\pi\)
\(662\) −9.24264 + 16.0087i −0.359225 + 0.622197i
\(663\) 0 0
\(664\) −3.87868 + 6.71807i −0.150522 + 0.260712i
\(665\) 0 0
\(666\) 0 0
\(667\) 15.3640 26.6112i 0.594895 1.03039i
\(668\) −24.2132 −0.936837
\(669\) 0 0
\(670\) 0 0
\(671\) 13.2426 + 22.9369i 0.511226 + 0.885470i
\(672\) 0 0
\(673\) 13.7426 23.8030i 0.529740 0.917536i −0.469658 0.882848i \(-0.655623\pi\)
0.999398 0.0346881i \(-0.0110438\pi\)
\(674\) 2.24264 3.88437i 0.0863833 0.149620i
\(675\) 0 0
\(676\) −12.9853 22.4912i −0.499434 0.865045i
\(677\) 17.1213 + 29.6550i 0.658026 + 1.13973i 0.981126 + 0.193369i \(0.0619416\pi\)
−0.323100 + 0.946365i \(0.604725\pi\)
\(678\) 0 0
\(679\) −20.2426 26.1039i −0.776841 1.00177i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.21320 0.123040
\(683\) 20.8492 + 36.1119i 0.797774 + 1.38179i 0.921063 + 0.389414i \(0.127323\pi\)
−0.123289 + 0.992371i \(0.539344\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −14.8640 11.0482i −0.567509 0.421822i
\(687\) 0 0
\(688\) −6.48528 −0.247249
\(689\) 13.2426 22.9369i 0.504504 0.873827i
\(690\) 0 0
\(691\) −3.12132 5.40629i −0.118741 0.205665i 0.800528 0.599295i \(-0.204552\pi\)
−0.919269 + 0.393630i \(0.871219\pi\)
\(692\) 10.9706 0.417038
\(693\) 0 0
\(694\) −6.72792 −0.255388
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −24.9706 −0.945150
\(699\) 0 0
\(700\) −8.10660 10.4539i −0.306401 0.395118i
\(701\) −13.7574 −0.519608 −0.259804 0.965661i \(-0.583658\pi\)
−0.259804 + 0.965661i \(0.583658\pi\)
\(702\) 0 0
\(703\) 12.4853 + 21.6251i 0.470891 + 0.815608i
\(704\) −4.24264 −0.159901
\(705\) 0 0
\(706\) −10.5000 18.1865i −0.395173 0.684459i
\(707\) −7.75736 + 19.0016i −0.291746 + 0.714628i
\(708\) 0 0
\(709\) −12.8492 22.2555i −0.482563 0.835824i 0.517236 0.855843i \(-0.326961\pi\)
−0.999800 + 0.0200183i \(0.993628\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.74264 4.75039i 0.102785 0.178029i
\(713\) 2.74264 4.75039i 0.102713 0.177904i
\(714\) 0 0
\(715\) 0 0
\(716\) 16.2426 0.607016
\(717\) 0 0
\(718\) 10.7574 0.401461
\(719\) −1.13604 + 1.96768i −0.0423671 + 0.0733820i −0.886431 0.462860i \(-0.846823\pi\)
0.844064 + 0.536242i \(0.180157\pi\)
\(720\) 0 0
\(721\) 0.757359 1.85514i 0.0282055 0.0690892i
\(722\) 9.98528 17.2950i 0.371614 0.643654i
\(723\) 0 0
\(724\) 10.1213 17.5306i 0.376156 0.651521i
\(725\) 10.6066 18.3712i 0.393919 0.682288i
\(726\) 0 0
\(727\) 12.8640 22.2810i 0.477098 0.826358i −0.522558 0.852604i \(-0.675022\pi\)
0.999656 + 0.0262462i \(0.00835537\pi\)
\(728\) 16.3640 2.23936i 0.606489 0.0829961i
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −38.9706 −1.43941 −0.719705 0.694280i \(-0.755723\pi\)
−0.719705 + 0.694280i \(0.755723\pi\)
\(734\) 5.86396 + 10.1567i 0.216443 + 0.374890i
\(735\) 0 0
\(736\) −3.62132 + 6.27231i −0.133484 + 0.231200i
\(737\) −17.4853 + 30.2854i −0.644079 + 1.11558i
\(738\) 0 0
\(739\) −5.24264 9.08052i −0.192854 0.334032i 0.753341 0.657630i \(-0.228441\pi\)
−0.946195 + 0.323598i \(0.895108\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 6.87868 + 8.87039i 0.252524 + 0.325642i
\(743\) 17.3787 + 30.1008i 0.637562 + 1.10429i 0.985966 + 0.166945i \(0.0533903\pi\)
−0.348404 + 0.937344i \(0.613276\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −3.60660 6.24682i −0.132047 0.228712i
\(747\) 0 0
\(748\) 0 0
\(749\) 4.02944 + 5.19615i 0.147232 + 0.189863i
\(750\) 0 0
\(751\) −17.2426 −0.629193 −0.314596 0.949226i \(-0.601869\pi\)
−0.314596 + 0.949226i \(0.601869\pi\)
\(752\) 6.62132 11.4685i 0.241455 0.418212i
\(753\) 0 0
\(754\) 13.2426 + 22.9369i 0.482269 + 0.835314i
\(755\) 0 0
\(756\) 0 0
\(757\) 12.9706 0.471423 0.235712 0.971823i \(-0.424258\pi\)
0.235712 + 0.971823i \(0.424258\pi\)
\(758\) 0.636039 + 1.10165i 0.0231020 + 0.0400138i
\(759\) 0 0
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 0 0
\(763\) 5.87868 0.804479i 0.212822 0.0291241i
\(764\) −8.48528 −0.306987
\(765\) 0 0
\(766\) 12.1066 + 20.9692i 0.437429 + 0.757650i
\(767\) 0 0
\(768\) 0 0
\(769\) 6.24264 + 10.8126i 0.225115 + 0.389911i 0.956354 0.292210i \(-0.0943908\pi\)
−0.731239 + 0.682122i \(0.761057\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.25736 + 3.90986i 0.0812441 + 0.140719i
\(773\) −22.6066 39.1558i −0.813103 1.40834i −0.910682 0.413108i \(-0.864443\pi\)
0.0975792 0.995228i \(-0.468890\pi\)
\(774\) 0 0
\(775\) 1.89340 3.27946i 0.0680129 0.117802i
\(776\) −6.24264 + 10.8126i −0.224098 + 0.388149i
\(777\) 0 0
\(778\) −5.12132 8.87039i −0.183608 0.318019i
\(779\) 34.2426 1.22687
\(780\) 0 0
\(781\) −30.7279 −1.09953
\(782\) 0 0
\(783\) 0 0
\(784\) −1.74264 + 6.77962i −0.0622372 + 0.242129i
\(785\) 0 0
\(786\) 0 0
\(787\) 15.6066 27.0314i 0.556315 0.963566i −0.441485 0.897269i \(-0.645548\pi\)
0.997800 0.0662975i \(-0.0211186\pi\)
\(788\) 8.48528 14.6969i 0.302276 0.523557i
\(789\) 0 0
\(790\) 0 0
\(791\) −53.6985 + 7.34847i −1.90930 + 0.261281i
\(792\) 0 0
\(793\) −19.4853 + 33.7495i −0.691943 + 1.19848i
\(794\) 20.2426 0.718384
\(795\) 0 0
\(796\) −14.7574 −0.523061