Properties

Label 1064.2.q.n.457.6
Level $1064$
Weight $2$
Character 1064.457
Analytic conductor $8.496$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.49608277506\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + 4560 x^{6} + 1376 x^{5} + 4688 x^{4} + 736 x^{3} + 1280 x^{2} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 457.6
Root \(0.670757 + 1.16179i\) of defining polynomial
Character \(\chi\) \(=\) 1064.457
Dual form 1064.2.q.n.305.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +O(q^{10})\) \(q+(0.670757 + 1.16179i) q^{3} +(-1.45434 + 2.51900i) q^{5} +(-2.59748 - 0.503078i) q^{7} +(0.600170 - 1.03952i) q^{9} +(-2.49731 - 4.32547i) q^{11} +1.55217 q^{13} -3.90205 q^{15} +(-3.09564 - 5.36181i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-1.15781 - 3.35516i) q^{21} +(-3.39198 + 5.87509i) q^{23} +(-1.73024 - 2.99686i) q^{25} +5.63482 q^{27} +0.707720 q^{29} +(-4.78494 - 8.28777i) q^{31} +(3.35018 - 5.80268i) q^{33} +(5.04489 - 5.81141i) q^{35} +(-2.12203 + 3.67547i) q^{37} +(1.04113 + 1.80329i) q^{39} -2.00000 q^{41} -1.25818 q^{43} +(1.74571 + 3.02365i) q^{45} +(6.17715 - 10.6991i) q^{47} +(6.49383 + 2.61347i) q^{49} +(4.15285 - 7.19295i) q^{51} +(-0.445867 - 0.772264i) q^{53} +14.5278 q^{55} -1.34151 q^{57} +(-5.28845 - 9.15987i) q^{59} +(5.91457 - 10.2443i) q^{61} +(-2.08189 + 2.39821i) q^{63} +(-2.25739 + 3.90992i) q^{65} +(-0.994841 - 1.72312i) q^{67} -9.10079 q^{69} -12.4174 q^{71} +(3.50344 + 6.06814i) q^{73} +(2.32114 - 4.02033i) q^{75} +(4.31068 + 12.4917i) q^{77} +(-8.46797 + 14.6670i) q^{79} +(1.97908 + 3.42787i) q^{81} -0.494217 q^{83} +18.0085 q^{85} +(0.474708 + 0.822219i) q^{87} +(1.69022 - 2.92754i) q^{89} +(-4.03174 - 0.780862i) q^{91} +(6.41907 - 11.1182i) q^{93} +(-1.45434 - 2.51900i) q^{95} -10.0685 q^{97} -5.99524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{5} + 5 q^{7} - 6 q^{9} + O(q^{10}) \) \( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 0.670757 + 1.16179i 0.387262 + 0.670757i 0.992080 0.125606i \(-0.0400876\pi\)
−0.604818 + 0.796363i \(0.706754\pi\)
\(4\) 0 0
\(5\) −1.45434 + 2.51900i −0.650403 + 1.12653i 0.332622 + 0.943060i \(0.392067\pi\)
−0.983025 + 0.183471i \(0.941267\pi\)
\(6\) 0 0
\(7\) −2.59748 0.503078i −0.981756 0.190145i
\(8\) 0 0
\(9\) 0.600170 1.03952i 0.200057 0.346508i
\(10\) 0 0
\(11\) −2.49731 4.32547i −0.752968 1.30418i −0.946378 0.323061i \(-0.895288\pi\)
0.193410 0.981118i \(-0.438045\pi\)
\(12\) 0 0
\(13\) 1.55217 0.430495 0.215247 0.976560i \(-0.430944\pi\)
0.215247 + 0.976560i \(0.430944\pi\)
\(14\) 0 0
\(15\) −3.90205 −1.00750
\(16\) 0 0
\(17\) −3.09564 5.36181i −0.750804 1.30043i −0.947434 0.319953i \(-0.896333\pi\)
0.196630 0.980478i \(-0.437000\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i
\(20\) 0 0
\(21\) −1.15781 3.35516i −0.252655 0.732156i
\(22\) 0 0
\(23\) −3.39198 + 5.87509i −0.707278 + 1.22504i 0.258586 + 0.965988i \(0.416744\pi\)
−0.965863 + 0.259052i \(0.916590\pi\)
\(24\) 0 0
\(25\) −1.73024 2.99686i −0.346047 0.599372i
\(26\) 0 0
\(27\) 5.63482 1.08442
\(28\) 0 0
\(29\) 0.707720 0.131420 0.0657102 0.997839i \(-0.479069\pi\)
0.0657102 + 0.997839i \(0.479069\pi\)
\(30\) 0 0
\(31\) −4.78494 8.28777i −0.859401 1.48853i −0.872501 0.488613i \(-0.837503\pi\)
0.0130995 0.999914i \(-0.495830\pi\)
\(32\) 0 0
\(33\) 3.35018 5.80268i 0.583192 1.01012i
\(34\) 0 0
\(35\) 5.04489 5.81141i 0.852741 0.982307i
\(36\) 0 0
\(37\) −2.12203 + 3.67547i −0.348860 + 0.604243i −0.986047 0.166466i \(-0.946764\pi\)
0.637187 + 0.770709i \(0.280098\pi\)
\(38\) 0 0
\(39\) 1.04113 + 1.80329i 0.166714 + 0.288757i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −1.25818 −0.191871 −0.0959355 0.995388i \(-0.530584\pi\)
−0.0959355 + 0.995388i \(0.530584\pi\)
\(44\) 0 0
\(45\) 1.74571 + 3.02365i 0.260235 + 0.450740i
\(46\) 0 0
\(47\) 6.17715 10.6991i 0.901030 1.56063i 0.0748706 0.997193i \(-0.476146\pi\)
0.826159 0.563436i \(-0.190521\pi\)
\(48\) 0 0
\(49\) 6.49383 + 2.61347i 0.927689 + 0.373353i
\(50\) 0 0
\(51\) 4.15285 7.19295i 0.581515 1.00721i
\(52\) 0 0
\(53\) −0.445867 0.772264i −0.0612445 0.106079i 0.833777 0.552101i \(-0.186174\pi\)
−0.895022 + 0.446022i \(0.852840\pi\)
\(54\) 0 0
\(55\) 14.5278 1.95893
\(56\) 0 0
\(57\) −1.34151 −0.177688
\(58\) 0 0
\(59\) −5.28845 9.15987i −0.688498 1.19251i −0.972324 0.233638i \(-0.924937\pi\)
0.283826 0.958876i \(-0.408396\pi\)
\(60\) 0 0
\(61\) 5.91457 10.2443i 0.757283 1.31165i −0.186948 0.982370i \(-0.559860\pi\)
0.944231 0.329283i \(-0.106807\pi\)
\(62\) 0 0
\(63\) −2.08189 + 2.39821i −0.262294 + 0.302147i
\(64\) 0 0
\(65\) −2.25739 + 3.90992i −0.279995 + 0.484965i
\(66\) 0 0
\(67\) −0.994841 1.72312i −0.121539 0.210512i 0.798836 0.601549i \(-0.205450\pi\)
−0.920375 + 0.391037i \(0.872116\pi\)
\(68\) 0 0
\(69\) −9.10079 −1.09561
\(70\) 0 0
\(71\) −12.4174 −1.47368 −0.736839 0.676068i \(-0.763683\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(72\) 0 0
\(73\) 3.50344 + 6.06814i 0.410047 + 0.710222i 0.994894 0.100921i \(-0.0321790\pi\)
−0.584848 + 0.811143i \(0.698846\pi\)
\(74\) 0 0
\(75\) 2.32114 4.02033i 0.268022 0.464228i
\(76\) 0 0
\(77\) 4.31068 + 12.4917i 0.491247 + 1.42356i
\(78\) 0 0
\(79\) −8.46797 + 14.6670i −0.952721 + 1.65016i −0.213223 + 0.977004i \(0.568396\pi\)
−0.739498 + 0.673158i \(0.764937\pi\)
\(80\) 0 0
\(81\) 1.97908 + 3.42787i 0.219898 + 0.380875i
\(82\) 0 0
\(83\) −0.494217 −0.0542474 −0.0271237 0.999632i \(-0.508635\pi\)
−0.0271237 + 0.999632i \(0.508635\pi\)
\(84\) 0 0
\(85\) 18.0085 1.95330
\(86\) 0 0
\(87\) 0.474708 + 0.822219i 0.0508941 + 0.0881511i
\(88\) 0 0
\(89\) 1.69022 2.92754i 0.179163 0.310319i −0.762431 0.647069i \(-0.775995\pi\)
0.941594 + 0.336750i \(0.109328\pi\)
\(90\) 0 0
\(91\) −4.03174 0.780862i −0.422641 0.0818566i
\(92\) 0 0
\(93\) 6.41907 11.1182i 0.665627 1.15290i
\(94\) 0 0
\(95\) −1.45434 2.51900i −0.149213 0.258444i
\(96\) 0 0
\(97\) −10.0685 −1.02230 −0.511152 0.859491i \(-0.670781\pi\)
−0.511152 + 0.859491i \(0.670781\pi\)
\(98\) 0 0
\(99\) −5.99524 −0.602545
\(100\) 0 0
\(101\) −1.28615 2.22768i −0.127977 0.221663i 0.794916 0.606720i \(-0.207515\pi\)
−0.922893 + 0.385057i \(0.874182\pi\)
\(102\) 0 0
\(103\) −3.21853 + 5.57466i −0.317131 + 0.549288i −0.979888 0.199547i \(-0.936053\pi\)
0.662757 + 0.748835i \(0.269386\pi\)
\(104\) 0 0
\(105\) 10.1355 + 1.96303i 0.989124 + 0.191572i
\(106\) 0 0
\(107\) −1.19930 + 2.07724i −0.115940 + 0.200815i −0.918155 0.396221i \(-0.870322\pi\)
0.802215 + 0.597035i \(0.203655\pi\)
\(108\) 0 0
\(109\) 7.12729 + 12.3448i 0.682670 + 1.18242i 0.974163 + 0.225847i \(0.0725148\pi\)
−0.291493 + 0.956573i \(0.594152\pi\)
\(110\) 0 0
\(111\) −5.69348 −0.540401
\(112\) 0 0
\(113\) −0.713643 −0.0671338 −0.0335669 0.999436i \(-0.510687\pi\)
−0.0335669 + 0.999436i \(0.510687\pi\)
\(114\) 0 0
\(115\) −9.86623 17.0888i −0.920031 1.59354i
\(116\) 0 0
\(117\) 0.931566 1.61352i 0.0861233 0.149170i
\(118\) 0 0
\(119\) 5.34347 + 15.4846i 0.489835 + 1.41947i
\(120\) 0 0
\(121\) −6.97314 + 12.0778i −0.633922 + 1.09798i
\(122\) 0 0
\(123\) −1.34151 2.32357i −0.120960 0.209509i
\(124\) 0 0
\(125\) −4.47800 −0.400525
\(126\) 0 0
\(127\) −8.73364 −0.774985 −0.387493 0.921873i \(-0.626659\pi\)
−0.387493 + 0.921873i \(0.626659\pi\)
\(128\) 0 0
\(129\) −0.843935 1.46174i −0.0743043 0.128699i
\(130\) 0 0
\(131\) 3.10003 5.36941i 0.270851 0.469128i −0.698229 0.715875i \(-0.746028\pi\)
0.969080 + 0.246747i \(0.0793616\pi\)
\(132\) 0 0
\(133\) 1.73442 1.99795i 0.150393 0.173244i
\(134\) 0 0
\(135\) −8.19496 + 14.1941i −0.705310 + 1.22163i
\(136\) 0 0
\(137\) −8.91814 15.4467i −0.761928 1.31970i −0.941856 0.336018i \(-0.890920\pi\)
0.179928 0.983680i \(-0.442414\pi\)
\(138\) 0 0
\(139\) −15.1484 −1.28487 −0.642435 0.766340i \(-0.722076\pi\)
−0.642435 + 0.766340i \(0.722076\pi\)
\(140\) 0 0
\(141\) 16.5735 1.39574
\(142\) 0 0
\(143\) −3.87625 6.71387i −0.324149 0.561442i
\(144\) 0 0
\(145\) −1.02927 + 1.78275i −0.0854762 + 0.148049i
\(146\) 0 0
\(147\) 1.31949 + 9.29744i 0.108830 + 0.766840i
\(148\) 0 0
\(149\) −4.30586 + 7.45796i −0.352749 + 0.610980i −0.986730 0.162369i \(-0.948087\pi\)
0.633981 + 0.773349i \(0.281420\pi\)
\(150\) 0 0
\(151\) −8.63199 14.9510i −0.702461 1.21670i −0.967600 0.252488i \(-0.918751\pi\)
0.265139 0.964210i \(-0.414582\pi\)
\(152\) 0 0
\(153\) −7.43165 −0.600813
\(154\) 0 0
\(155\) 27.8358 2.23583
\(156\) 0 0
\(157\) 8.47482 + 14.6788i 0.676364 + 1.17150i 0.976068 + 0.217465i \(0.0697788\pi\)
−0.299704 + 0.954032i \(0.596888\pi\)
\(158\) 0 0
\(159\) 0.598137 1.03600i 0.0474353 0.0821604i
\(160\) 0 0
\(161\) 11.7662 13.5540i 0.927310 1.06821i
\(162\) 0 0
\(163\) 8.63399 14.9545i 0.676266 1.17133i −0.299831 0.953992i \(-0.596930\pi\)
0.976097 0.217335i \(-0.0697365\pi\)
\(164\) 0 0
\(165\) 9.74463 + 16.8782i 0.758619 + 1.31397i
\(166\) 0 0
\(167\) 8.74790 0.676933 0.338466 0.940979i \(-0.390092\pi\)
0.338466 + 0.940979i \(0.390092\pi\)
\(168\) 0 0
\(169\) −10.5908 −0.814674
\(170\) 0 0
\(171\) 0.600170 + 1.03952i 0.0458961 + 0.0794944i
\(172\) 0 0
\(173\) −3.49691 + 6.05682i −0.265865 + 0.460491i −0.967790 0.251760i \(-0.918991\pi\)
0.701925 + 0.712251i \(0.252324\pi\)
\(174\) 0 0
\(175\) 2.98661 + 8.65473i 0.225766 + 0.654236i
\(176\) 0 0
\(177\) 7.09454 12.2881i 0.533258 0.923630i
\(178\) 0 0
\(179\) −10.2213 17.7038i −0.763977 1.32325i −0.940785 0.339002i \(-0.889910\pi\)
0.176808 0.984245i \(-0.443423\pi\)
\(180\) 0 0
\(181\) 9.96247 0.740505 0.370252 0.928931i \(-0.379271\pi\)
0.370252 + 0.928931i \(0.379271\pi\)
\(182\) 0 0
\(183\) 15.8690 1.17307
\(184\) 0 0
\(185\) −6.17234 10.6908i −0.453799 0.786003i
\(186\) 0 0
\(187\) −15.4616 + 26.7802i −1.13066 + 1.95837i
\(188\) 0 0
\(189\) −14.6363 2.83475i −1.06464 0.206198i
\(190\) 0 0
\(191\) −7.27080 + 12.5934i −0.526097 + 0.911226i 0.473441 + 0.880826i \(0.343012\pi\)
−0.999538 + 0.0304008i \(0.990322\pi\)
\(192\) 0 0
\(193\) 7.85414 + 13.6038i 0.565353 + 0.979220i 0.997017 + 0.0771858i \(0.0245935\pi\)
−0.431664 + 0.902035i \(0.642073\pi\)
\(194\) 0 0
\(195\) −6.05665 −0.433725
\(196\) 0 0
\(197\) 0.726728 0.0517772 0.0258886 0.999665i \(-0.491758\pi\)
0.0258886 + 0.999665i \(0.491758\pi\)
\(198\) 0 0
\(199\) 7.19019 + 12.4538i 0.509699 + 0.882825i 0.999937 + 0.0112361i \(0.00357663\pi\)
−0.490238 + 0.871589i \(0.663090\pi\)
\(200\) 0 0
\(201\) 1.33459 2.31158i 0.0941350 0.163047i
\(202\) 0 0
\(203\) −1.83829 0.356038i −0.129023 0.0249890i
\(204\) 0 0
\(205\) 2.90869 5.03800i 0.203152 0.351869i
\(206\) 0 0
\(207\) 4.07153 + 7.05210i 0.282991 + 0.490155i
\(208\) 0 0
\(209\) 4.99462 0.345485
\(210\) 0 0
\(211\) −20.8134 −1.43285 −0.716427 0.697662i \(-0.754224\pi\)
−0.716427 + 0.697662i \(0.754224\pi\)
\(212\) 0 0
\(213\) −8.32908 14.4264i −0.570699 0.988480i
\(214\) 0 0
\(215\) 1.82983 3.16936i 0.124793 0.216148i
\(216\) 0 0
\(217\) 8.25942 + 23.9345i 0.560686 + 1.62478i
\(218\) 0 0
\(219\) −4.69992 + 8.14050i −0.317591 + 0.550084i
\(220\) 0 0
\(221\) −4.80497 8.32245i −0.323217 0.559828i
\(222\) 0 0
\(223\) 6.02432 0.403418 0.201709 0.979445i \(-0.435350\pi\)
0.201709 + 0.979445i \(0.435350\pi\)
\(224\) 0 0
\(225\) −4.15374 −0.276916
\(226\) 0 0
\(227\) −3.93313 6.81237i −0.261051 0.452153i 0.705471 0.708739i \(-0.250736\pi\)
−0.966521 + 0.256586i \(0.917402\pi\)
\(228\) 0 0
\(229\) 14.3345 24.8281i 0.947252 1.64069i 0.196075 0.980589i \(-0.437180\pi\)
0.751177 0.660101i \(-0.229486\pi\)
\(230\) 0 0
\(231\) −11.6212 + 13.3870i −0.764621 + 0.880798i
\(232\) 0 0
\(233\) −1.52152 + 2.63535i −0.0996781 + 0.172647i −0.911551 0.411186i \(-0.865115\pi\)
0.811873 + 0.583834i \(0.198448\pi\)
\(234\) 0 0
\(235\) 17.9674 + 31.1205i 1.17206 + 2.03008i
\(236\) 0 0
\(237\) −22.7198 −1.47581
\(238\) 0 0
\(239\) 9.23545 0.597392 0.298696 0.954348i \(-0.403448\pi\)
0.298696 + 0.954348i \(0.403448\pi\)
\(240\) 0 0
\(241\) 4.51925 + 7.82757i 0.291110 + 0.504218i 0.974073 0.226236i \(-0.0726420\pi\)
−0.682962 + 0.730454i \(0.739309\pi\)
\(242\) 0 0
\(243\) 5.79725 10.0411i 0.371894 0.644139i
\(244\) 0 0
\(245\) −16.0276 + 12.5571i −1.02397 + 0.802241i
\(246\) 0 0
\(247\) −0.776085 + 1.34422i −0.0493811 + 0.0855306i
\(248\) 0 0
\(249\) −0.331500 0.574174i −0.0210079 0.0363868i
\(250\) 0 0
\(251\) −2.91027 −0.183695 −0.0918473 0.995773i \(-0.529277\pi\)
−0.0918473 + 0.995773i \(0.529277\pi\)
\(252\) 0 0
\(253\) 33.8834 2.13023
\(254\) 0 0
\(255\) 12.0794 + 20.9221i 0.756438 + 1.31019i
\(256\) 0 0
\(257\) −11.4544 + 19.8396i −0.714505 + 1.23756i 0.248646 + 0.968595i \(0.420015\pi\)
−0.963150 + 0.268964i \(0.913319\pi\)
\(258\) 0 0
\(259\) 7.36099 8.47942i 0.457390 0.526885i
\(260\) 0 0
\(261\) 0.424752 0.735692i 0.0262915 0.0455382i
\(262\) 0 0
\(263\) −8.83496 15.3026i −0.544787 0.943599i −0.998620 0.0525124i \(-0.983277\pi\)
0.453833 0.891087i \(-0.350056\pi\)
\(264\) 0 0
\(265\) 2.59378 0.159334
\(266\) 0 0
\(267\) 4.53490 0.277531
\(268\) 0 0
\(269\) 5.71170 + 9.89295i 0.348248 + 0.603184i 0.985938 0.167109i \(-0.0534432\pi\)
−0.637690 + 0.770293i \(0.720110\pi\)
\(270\) 0 0
\(271\) 2.52461 4.37276i 0.153359 0.265626i −0.779101 0.626898i \(-0.784324\pi\)
0.932460 + 0.361272i \(0.117657\pi\)
\(272\) 0 0
\(273\) −1.79712 5.20778i −0.108767 0.315189i
\(274\) 0 0
\(275\) −8.64189 + 14.9682i −0.521125 + 0.902616i
\(276\) 0 0
\(277\) −3.22844 5.59182i −0.193978 0.335980i 0.752587 0.658493i \(-0.228806\pi\)
−0.946565 + 0.322513i \(0.895472\pi\)
\(278\) 0 0
\(279\) −11.4871 −0.687715
\(280\) 0 0
\(281\) −10.2877 −0.613711 −0.306856 0.951756i \(-0.599277\pi\)
−0.306856 + 0.951756i \(0.599277\pi\)
\(282\) 0 0
\(283\) 11.0250 + 19.0959i 0.655368 + 1.13513i 0.981801 + 0.189910i \(0.0608198\pi\)
−0.326433 + 0.945220i \(0.605847\pi\)
\(284\) 0 0
\(285\) 1.95102 3.37927i 0.115569 0.200171i
\(286\) 0 0
\(287\) 5.19496 + 1.00616i 0.306649 + 0.0593915i
\(288\) 0 0
\(289\) −10.6660 + 18.4741i −0.627413 + 1.08671i
\(290\) 0 0
\(291\) −6.75353 11.6975i −0.395899 0.685717i
\(292\) 0 0
\(293\) −20.5297 −1.19936 −0.599680 0.800240i \(-0.704705\pi\)
−0.599680 + 0.800240i \(0.704705\pi\)
\(294\) 0 0
\(295\) 30.7649 1.79120
\(296\) 0 0
\(297\) −14.0719 24.3732i −0.816534 1.41428i
\(298\) 0 0
\(299\) −5.26494 + 9.11914i −0.304479 + 0.527374i
\(300\) 0 0
\(301\) 3.26810 + 0.632963i 0.188370 + 0.0364834i
\(302\) 0 0
\(303\) 1.72539 2.98847i 0.0991212 0.171683i
\(304\) 0 0
\(305\) 17.2037 + 29.7976i 0.985078 + 1.70621i
\(306\) 0 0
\(307\) 21.5830 1.23181 0.615904 0.787821i \(-0.288791\pi\)
0.615904 + 0.787821i \(0.288791\pi\)
\(308\) 0 0
\(309\) −8.63541 −0.491251
\(310\) 0 0
\(311\) 11.8255 + 20.4824i 0.670562 + 1.16145i 0.977745 + 0.209798i \(0.0672805\pi\)
−0.307182 + 0.951651i \(0.599386\pi\)
\(312\) 0 0
\(313\) 13.3560 23.1333i 0.754927 1.30757i −0.190483 0.981690i \(-0.561006\pi\)
0.945411 0.325882i \(-0.105661\pi\)
\(314\) 0 0
\(315\) −3.01331 8.73211i −0.169781 0.491999i
\(316\) 0 0
\(317\) 13.5370 23.4468i 0.760314 1.31690i −0.182374 0.983229i \(-0.558378\pi\)
0.942689 0.333674i \(-0.108288\pi\)
\(318\) 0 0
\(319\) −1.76740 3.06122i −0.0989553 0.171396i
\(320\) 0 0
\(321\) −3.21775 −0.179597
\(322\) 0 0
\(323\) 6.19129 0.344492
\(324\) 0 0
\(325\) −2.68562 4.65164i −0.148972 0.258026i
\(326\) 0 0
\(327\) −9.56136 + 16.5608i −0.528744 + 0.915812i
\(328\) 0 0
\(329\) −21.4275 + 24.6832i −1.18134 + 1.36083i
\(330\) 0 0
\(331\) −1.57001 + 2.71934i −0.0862957 + 0.149469i −0.905943 0.423400i \(-0.860836\pi\)
0.819647 + 0.572869i \(0.194170\pi\)
\(332\) 0 0
\(333\) 2.54716 + 4.41181i 0.139583 + 0.241766i
\(334\) 0 0
\(335\) 5.78737 0.316198
\(336\) 0 0
\(337\) 21.6417 1.17890 0.589449 0.807805i \(-0.299345\pi\)
0.589449 + 0.807805i \(0.299345\pi\)
\(338\) 0 0
\(339\) −0.478681 0.829100i −0.0259984 0.0450305i
\(340\) 0 0
\(341\) −23.8990 + 41.3943i −1.29420 + 2.24163i
\(342\) 0 0
\(343\) −15.5528 10.0553i −0.839773 0.542937i
\(344\) 0 0
\(345\) 13.2357 22.9249i 0.712586 1.23423i
\(346\) 0 0
\(347\) 1.28338 + 2.22288i 0.0688955 + 0.119330i 0.898415 0.439147i \(-0.144719\pi\)
−0.829520 + 0.558477i \(0.811386\pi\)
\(348\) 0 0
\(349\) 1.91567 0.102543 0.0512716 0.998685i \(-0.483673\pi\)
0.0512716 + 0.998685i \(0.483673\pi\)
\(350\) 0 0
\(351\) 8.74619 0.466837
\(352\) 0 0
\(353\) 7.93887 + 13.7505i 0.422543 + 0.731867i 0.996188 0.0872380i \(-0.0278040\pi\)
−0.573644 + 0.819105i \(0.694471\pi\)
\(354\) 0 0
\(355\) 18.0592 31.2795i 0.958485 1.66014i
\(356\) 0 0
\(357\) −14.4056 + 16.5943i −0.762423 + 0.878266i
\(358\) 0 0
\(359\) −10.0397 + 17.3893i −0.529875 + 0.917771i 0.469517 + 0.882923i \(0.344428\pi\)
−0.999393 + 0.0348477i \(0.988905\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.0263158 0.0455803i
\(362\) 0 0
\(363\) −18.7091 −0.981975
\(364\) 0 0
\(365\) −20.3808 −1.06678
\(366\) 0 0
\(367\) −1.79240 3.10453i −0.0935626 0.162055i 0.815445 0.578834i \(-0.196492\pi\)
−0.909008 + 0.416779i \(0.863159\pi\)
\(368\) 0 0
\(369\) −1.20034 + 2.07905i −0.0624872 + 0.108231i
\(370\) 0 0
\(371\) 0.769622 + 2.23025i 0.0399568 + 0.115789i
\(372\) 0 0
\(373\) −13.3372 + 23.1008i −0.690576 + 1.19611i 0.281073 + 0.959686i \(0.409310\pi\)
−0.971649 + 0.236427i \(0.924024\pi\)
\(374\) 0 0
\(375\) −3.00365 5.20248i −0.155108 0.268655i
\(376\) 0 0
\(377\) 1.09850 0.0565758
\(378\) 0 0
\(379\) 18.9451 0.973146 0.486573 0.873640i \(-0.338247\pi\)
0.486573 + 0.873640i \(0.338247\pi\)
\(380\) 0 0
\(381\) −5.85815 10.1466i −0.300122 0.519827i
\(382\) 0 0
\(383\) 7.47577 12.9484i 0.381994 0.661633i −0.609353 0.792899i \(-0.708571\pi\)
0.991347 + 0.131266i \(0.0419042\pi\)
\(384\) 0 0
\(385\) −37.7357 7.30862i −1.92319 0.372482i
\(386\) 0 0
\(387\) −0.755123 + 1.30791i −0.0383850 + 0.0664848i
\(388\) 0 0
\(389\) −18.3084 31.7111i −0.928273 1.60782i −0.786211 0.617958i \(-0.787960\pi\)
−0.142061 0.989858i \(-0.545373\pi\)
\(390\) 0 0
\(391\) 42.0015 2.12411
\(392\) 0 0
\(393\) 8.31748 0.419561
\(394\) 0 0
\(395\) −24.6307 42.6616i −1.23931 2.14654i
\(396\) 0 0
\(397\) 9.92602 17.1924i 0.498173 0.862861i −0.501825 0.864969i \(-0.667338\pi\)
0.999998 + 0.00210848i \(0.000671150\pi\)
\(398\) 0 0
\(399\) 3.48456 + 0.674886i 0.174446 + 0.0337866i
\(400\) 0 0
\(401\) −2.31504 + 4.00977i −0.115608 + 0.200238i −0.918023 0.396528i \(-0.870215\pi\)
0.802415 + 0.596767i \(0.203548\pi\)
\(402\) 0 0
\(403\) −7.42705 12.8640i −0.369968 0.640803i
\(404\) 0 0
\(405\) −11.5131 −0.572090
\(406\) 0 0
\(407\) 21.1975 1.05072
\(408\) 0 0
\(409\) −2.20637 3.82155i −0.109098 0.188963i 0.806307 0.591497i \(-0.201463\pi\)
−0.915405 + 0.402534i \(0.868130\pi\)
\(410\) 0 0
\(411\) 11.9638 20.7219i 0.590131 1.02214i
\(412\) 0 0
\(413\) 9.12854 + 26.4531i 0.449186 + 1.30167i
\(414\) 0 0
\(415\) 0.718762 1.24493i 0.0352826 0.0611113i
\(416\) 0 0
\(417\) −10.1609 17.5992i −0.497581 0.861836i
\(418\) 0 0
\(419\) 32.8148 1.60311 0.801554 0.597922i \(-0.204007\pi\)
0.801554 + 0.597922i \(0.204007\pi\)
\(420\) 0 0
\(421\) 10.3765 0.505721 0.252861 0.967503i \(-0.418629\pi\)
0.252861 + 0.967503i \(0.418629\pi\)
\(422\) 0 0
\(423\) −7.41468 12.8426i −0.360514 0.624428i
\(424\) 0 0
\(425\) −10.7124 + 18.5544i −0.519628 + 0.900021i
\(426\) 0 0
\(427\) −20.5167 + 23.6340i −0.992872 + 1.14373i
\(428\) 0 0
\(429\) 5.20005 9.00675i 0.251061 0.434850i
\(430\) 0 0
\(431\) 1.05984 + 1.83569i 0.0510505 + 0.0884220i 0.890421 0.455137i \(-0.150410\pi\)
−0.839371 + 0.543559i \(0.817076\pi\)
\(432\) 0 0
\(433\) −4.23274 −0.203413 −0.101706 0.994814i \(-0.532430\pi\)
−0.101706 + 0.994814i \(0.532430\pi\)
\(434\) 0 0
\(435\) −2.76156 −0.132407
\(436\) 0 0
\(437\) −3.39198 5.87509i −0.162261 0.281044i
\(438\) 0 0
\(439\) 11.8690 20.5577i 0.566476 0.981166i −0.430434 0.902622i \(-0.641640\pi\)
0.996911 0.0785439i \(-0.0250271\pi\)
\(440\) 0 0
\(441\) 6.61416 5.18196i 0.314960 0.246760i
\(442\) 0 0
\(443\) 5.32007 9.21464i 0.252764 0.437801i −0.711522 0.702664i \(-0.751994\pi\)
0.964286 + 0.264864i \(0.0853269\pi\)
\(444\) 0 0
\(445\) 4.91631 + 8.51530i 0.233056 + 0.403664i
\(446\) 0 0
\(447\) −11.5527 −0.546426
\(448\) 0 0
\(449\) 18.4650 0.871418 0.435709 0.900088i \(-0.356498\pi\)
0.435709 + 0.900088i \(0.356498\pi\)
\(450\) 0 0
\(451\) 4.99462 + 8.65094i 0.235188 + 0.407357i
\(452\) 0 0
\(453\) 11.5799 20.0570i 0.544073 0.942362i
\(454\) 0 0
\(455\) 7.83052 9.02029i 0.367101 0.422878i
\(456\) 0 0
\(457\) 4.21897 7.30748i 0.197355 0.341829i −0.750315 0.661081i \(-0.770098\pi\)
0.947670 + 0.319251i \(0.103431\pi\)
\(458\) 0 0
\(459\) −17.4434 30.2128i −0.814187 1.41021i
\(460\) 0 0
\(461\) −18.8951 −0.880034 −0.440017 0.897990i \(-0.645028\pi\)
−0.440017 + 0.897990i \(0.645028\pi\)
\(462\) 0 0
\(463\) 27.5602 1.28083 0.640415 0.768029i \(-0.278762\pi\)
0.640415 + 0.768029i \(0.278762\pi\)
\(464\) 0 0
\(465\) 18.6711 + 32.3393i 0.865851 + 1.49970i
\(466\) 0 0
\(467\) −11.6370 + 20.1560i −0.538498 + 0.932706i 0.460487 + 0.887666i \(0.347675\pi\)
−0.998985 + 0.0450398i \(0.985659\pi\)
\(468\) 0 0
\(469\) 1.71722 + 4.97625i 0.0792939 + 0.229782i
\(470\) 0 0
\(471\) −11.3691 + 19.6918i −0.523860 + 0.907352i
\(472\) 0 0
\(473\) 3.14207 + 5.44223i 0.144473 + 0.250234i
\(474\) 0 0
\(475\) 3.46047 0.158777
\(476\) 0 0
\(477\) −1.07038 −0.0490095
\(478\) 0 0
\(479\) −2.20147 3.81305i −0.100588 0.174223i 0.811339 0.584576i \(-0.198739\pi\)
−0.911927 + 0.410353i \(0.865406\pi\)
\(480\) 0 0
\(481\) −3.29376 + 5.70496i −0.150182 + 0.260124i
\(482\) 0 0
\(483\) 23.6391 + 4.57840i 1.07562 + 0.208325i
\(484\) 0 0
\(485\) 14.6431 25.3626i 0.664909 1.15166i
\(486\) 0 0
\(487\) 12.1248 + 21.0008i 0.549429 + 0.951638i 0.998314 + 0.0580489i \(0.0184879\pi\)
−0.448885 + 0.893590i \(0.648179\pi\)
\(488\) 0 0
\(489\) 23.1652 1.04757
\(490\) 0 0
\(491\) −27.0129 −1.21908 −0.609538 0.792757i \(-0.708645\pi\)
−0.609538 + 0.792757i \(0.708645\pi\)
\(492\) 0 0
\(493\) −2.19085 3.79466i −0.0986709 0.170903i
\(494\) 0 0
\(495\) 8.71915 15.1020i 0.391897 0.678785i
\(496\) 0 0
\(497\) 32.2541 + 6.24693i 1.44679 + 0.280213i
\(498\) 0 0
\(499\) −9.84696 + 17.0554i −0.440810 + 0.763506i −0.997750 0.0670472i \(-0.978642\pi\)
0.556940 + 0.830553i \(0.311976\pi\)
\(500\) 0 0
\(501\) 5.86772 + 10.1632i 0.262150 + 0.454057i
\(502\) 0 0
\(503\) 0.561980 0.0250574 0.0125287 0.999922i \(-0.496012\pi\)
0.0125287 + 0.999922i \(0.496012\pi\)
\(504\) 0 0
\(505\) 7.48204 0.332946
\(506\) 0 0
\(507\) −7.10383 12.3042i −0.315492 0.546449i
\(508\) 0 0
\(509\) 8.84945 15.3277i 0.392245 0.679388i −0.600500 0.799625i \(-0.705032\pi\)
0.992745 + 0.120236i \(0.0383652\pi\)
\(510\) 0 0
\(511\) −6.04738 17.5244i −0.267520 0.775233i
\(512\) 0 0
\(513\) −2.81741 + 4.87989i −0.124392 + 0.215453i
\(514\) 0 0
\(515\) −9.36171 16.2150i −0.412526 0.714516i
\(516\) 0 0
\(517\) −61.7051 −2.71379
\(518\) 0 0
\(519\) −9.38230 −0.411837
\(520\) 0 0
\(521\) −20.1517 34.9038i −0.882863 1.52916i −0.848143 0.529767i \(-0.822279\pi\)
−0.0347205 0.999397i \(-0.511054\pi\)
\(522\) 0 0
\(523\) −0.978350 + 1.69455i −0.0427803 + 0.0740976i −0.886623 0.462493i \(-0.846955\pi\)
0.843842 + 0.536591i \(0.180288\pi\)
\(524\) 0 0
\(525\) −8.05165 + 9.27502i −0.351403 + 0.404795i
\(526\) 0 0
\(527\) −29.6250 + 51.3119i −1.29048 + 2.23518i
\(528\) 0 0
\(529\) −11.5111 19.9378i −0.500483 0.866862i
\(530\) 0 0
\(531\) −12.6959 −0.550954
\(532\) 0 0
\(533\) −3.10434 −0.134464
\(534\) 0 0
\(535\) −3.48838 6.04206i −0.150816 0.261221i
\(536\) 0 0
\(537\) 13.7121 23.7500i 0.591719 1.02489i
\(538\) 0 0
\(539\) −4.91262 34.6155i −0.211601 1.49100i
\(540\) 0 0
\(541\) 15.5344 26.9064i 0.667877 1.15680i −0.310620 0.950534i \(-0.600537\pi\)
0.978497 0.206263i \(-0.0661301\pi\)
\(542\) 0 0
\(543\) 6.68240 + 11.5743i 0.286769 + 0.496699i
\(544\) 0 0
\(545\) −41.4621 −1.77604
\(546\) 0 0
\(547\) 36.8556 1.57583 0.787917 0.615782i \(-0.211160\pi\)
0.787917 + 0.615782i \(0.211160\pi\)
\(548\) 0 0
\(549\) −7.09949 12.2967i −0.302999 0.524810i
\(550\) 0 0
\(551\) −0.353860 + 0.612904i −0.0150749 + 0.0261106i
\(552\) 0 0
\(553\) 29.3740 33.8371i 1.24911 1.43890i
\(554\) 0 0
\(555\) 8.28028 14.3419i 0.351478 0.608778i
\(556\) 0 0
\(557\) −11.6136 20.1153i −0.492083 0.852313i 0.507875 0.861431i \(-0.330431\pi\)
−0.999958 + 0.00911734i \(0.997098\pi\)
\(558\) 0 0
\(559\) −1.95291 −0.0825994
\(560\) 0 0
\(561\) −41.4839 −1.75145
\(562\) 0 0
\(563\) −12.0273 20.8319i −0.506891 0.877962i −0.999968 0.00797592i \(-0.997461\pi\)
0.493077 0.869986i \(-0.335872\pi\)
\(564\) 0 0
\(565\) 1.03788 1.79766i 0.0436640 0.0756283i
\(566\) 0 0
\(567\) −3.41615 9.89948i −0.143465 0.415739i
\(568\) 0 0
\(569\) 14.7880 25.6136i 0.619946 1.07378i −0.369548 0.929211i \(-0.620488\pi\)
0.989495 0.144567i \(-0.0461790\pi\)
\(570\) 0 0
\(571\) 13.2462 + 22.9431i 0.554337 + 0.960141i 0.997955 + 0.0639243i \(0.0203616\pi\)
−0.443617 + 0.896216i \(0.646305\pi\)
\(572\) 0 0
\(573\) −19.5078 −0.814949
\(574\) 0 0
\(575\) 23.4757 0.979006
\(576\) 0 0
\(577\) −12.7908 22.1543i −0.532487 0.922295i −0.999280 0.0379287i \(-0.987924\pi\)
0.466793 0.884367i \(-0.345409\pi\)
\(578\) 0 0
\(579\) −10.5364 + 18.2496i −0.437879 + 0.758429i
\(580\) 0 0
\(581\) 1.28372 + 0.248630i 0.0532577 + 0.0103149i
\(582\) 0 0
\(583\) −2.22694 + 3.85717i −0.0922303 + 0.159748i
\(584\) 0 0
\(585\) 2.70963 + 4.69323i 0.112030 + 0.194041i
\(586\) 0 0
\(587\) 27.2213 1.12354 0.561771 0.827293i \(-0.310120\pi\)
0.561771 + 0.827293i \(0.310120\pi\)
\(588\) 0 0
\(589\) 9.56989 0.394320
\(590\) 0 0
\(591\) 0.487458 + 0.844302i 0.0200514 + 0.0347300i
\(592\) 0 0
\(593\) −0.952988 + 1.65062i −0.0391345 + 0.0677830i −0.884929 0.465725i \(-0.845793\pi\)
0.845795 + 0.533508i \(0.179127\pi\)
\(594\) 0 0
\(595\) −46.7768 9.05969i −1.91766 0.371411i
\(596\) 0 0
\(597\) −9.64575 + 16.7069i −0.394774 + 0.683769i
\(598\) 0 0
\(599\) 10.0250 + 17.3638i 0.409610 + 0.709466i 0.994846 0.101397i \(-0.0323313\pi\)
−0.585236 + 0.810863i \(0.698998\pi\)
\(600\) 0 0
\(601\) −14.6961 −0.599466 −0.299733 0.954023i \(-0.596898\pi\)
−0.299733 + 0.954023i \(0.596898\pi\)
\(602\) 0 0
\(603\) −2.38829 −0.0972589
\(604\) 0 0
\(605\) −20.2827 35.1307i −0.824609 1.42826i
\(606\) 0 0
\(607\) −11.7400 + 20.3343i −0.476512 + 0.825344i −0.999638 0.0269121i \(-0.991433\pi\)
0.523125 + 0.852256i \(0.324766\pi\)
\(608\) 0 0
\(609\) −0.819407 2.37451i −0.0332040 0.0962202i
\(610\) 0 0
\(611\) 9.58799 16.6069i 0.387889 0.671843i
\(612\) 0 0
\(613\) −13.6639 23.6666i −0.551880 0.955884i −0.998139 0.0609799i \(-0.980577\pi\)
0.446259 0.894904i \(-0.352756\pi\)
\(614\) 0 0
\(615\) 7.80410 0.314692
\(616\) 0 0
\(617\) −25.5796 −1.02980 −0.514898 0.857252i \(-0.672170\pi\)
−0.514898 + 0.857252i \(0.672170\pi\)
\(618\) 0 0
\(619\) −0.745582 1.29139i −0.0299675 0.0519052i 0.850653 0.525728i \(-0.176207\pi\)
−0.880620 + 0.473823i \(0.842874\pi\)
\(620\) 0 0
\(621\) −19.1132 + 33.1050i −0.766987 + 1.32846i
\(622\) 0 0
\(623\) −5.86309 + 6.75392i −0.234900 + 0.270590i
\(624\) 0 0
\(625\) 15.1637 26.2644i 0.606550 1.05058i
\(626\) 0 0
\(627\) 3.35018 + 5.80268i 0.133793 + 0.231737i
\(628\) 0 0
\(629\) 26.2762 1.04770
\(630\) 0 0
\(631\) −22.0819 −0.879066 −0.439533 0.898226i \(-0.644856\pi\)
−0.439533 + 0.898226i \(0.644856\pi\)
\(632\) 0 0
\(633\) −13.9607 24.1807i −0.554890 0.961097i
\(634\) 0 0
\(635\) 12.7017 22.0000i 0.504052 0.873045i
\(636\) 0 0
\(637\) 10.0795 + 4.05655i 0.399365 + 0.160726i
\(638\) 0 0
\(639\) −7.45257 + 12.9082i −0.294819 + 0.510641i
\(640\) 0 0
\(641\) 1.40167 + 2.42777i 0.0553627 + 0.0958910i 0.892379 0.451288i \(-0.149035\pi\)
−0.837016 + 0.547179i \(0.815702\pi\)
\(642\) 0 0
\(643\) −27.0640 −1.06730 −0.533649 0.845706i \(-0.679180\pi\)
−0.533649 + 0.845706i \(0.679180\pi\)
\(644\) 0 0
\(645\) 4.90949 0.193311
\(646\) 0 0
\(647\) −2.68786 4.65551i −0.105671 0.183027i 0.808341 0.588714i \(-0.200366\pi\)
−0.914012 + 0.405687i \(0.867032\pi\)
\(648\) 0 0
\(649\) −26.4138 + 45.7501i −1.03683 + 1.79585i
\(650\) 0 0
\(651\) −22.2667 + 25.6499i −0.872702 + 1.00530i
\(652\) 0 0
\(653\) 14.0625 24.3570i 0.550308 0.953162i −0.447944 0.894062i \(-0.647844\pi\)
0.998252 0.0590999i \(-0.0188231\pi\)
\(654\) 0 0
\(655\) 9.01703 + 15.6180i 0.352325 + 0.610244i
\(656\) 0 0
\(657\) 8.41064 0.328130
\(658\) 0 0
\(659\) 35.3753 1.37802 0.689012 0.724750i \(-0.258045\pi\)
0.689012 + 0.724750i \(0.258045\pi\)
\(660\) 0 0
\(661\) −21.7358 37.6476i −0.845426 1.46432i −0.885251 0.465114i \(-0.846013\pi\)
0.0398248 0.999207i \(-0.487320\pi\)
\(662\) 0 0
\(663\) 6.44593 11.1647i 0.250339 0.433600i
\(664\) 0 0
\(665\) 2.51038 + 7.27470i 0.0973484 + 0.282101i
\(666\) 0 0
\(667\) −2.40058 + 4.15792i −0.0929507 + 0.160995i
\(668\) 0 0
\(669\) 4.04085 + 6.99896i 0.156228 + 0.270596i
\(670\) 0 0
\(671\) −59.0821 −2.28084
\(672\) 0 0
\(673\) 17.7175 0.682961 0.341481 0.939889i \(-0.389072\pi\)
0.341481 + 0.939889i \(0.389072\pi\)
\(674\) 0 0
\(675\) −9.74957 16.8867i −0.375261 0.649971i
\(676\) 0 0
\(677\) −22.4224 + 38.8367i −0.861761 + 1.49261i 0.00846617 + 0.999964i \(0.497305\pi\)
−0.870227 + 0.492650i \(0.836028\pi\)
\(678\) 0 0
\(679\) 26.1528 + 5.06525i 1.00365 + 0.194386i
\(680\) 0 0
\(681\) 5.27635 9.13890i 0.202190 0.350203i
\(682\) 0 0
\(683\) 15.0236 + 26.0216i 0.574861 + 0.995688i 0.996057 + 0.0887184i \(0.0282771\pi\)
−0.421196 + 0.906970i \(0.638390\pi\)
\(684\) 0 0
\(685\) 51.8802 1.98224
\(686\) 0 0
\(687\) 38.4600 1.46734
\(688\) 0 0
\(689\) −0.692061 1.19869i −0.0263654 0.0456663i
\(690\) 0 0
\(691\) 9.24652 16.0154i 0.351754 0.609256i −0.634803 0.772674i \(-0.718919\pi\)
0.986557 + 0.163418i \(0.0522520\pi\)
\(692\) 0 0
\(693\) 15.5725 + 3.01607i 0.591552 + 0.114571i
\(694\) 0 0
\(695\) 22.0310 38.1588i 0.835683 1.44745i
\(696\) 0 0
\(697\) 6.19129 + 10.7236i 0.234512 + 0.406186i
\(698\) 0 0
\(699\) −4.08228 −0.154406
\(700\) 0 0
\(701\) −26.5282 −1.00196 −0.500978 0.865460i \(-0.667026\pi\)
−0.500978 + 0.865460i \(0.667026\pi\)
\(702\) 0 0
\(703\) −2.12203 3.67547i −0.0800340 0.138623i
\(704\) 0 0
\(705\) −24.1035 + 41.7486i −0.907792 + 1.57234i
\(706\) 0 0
\(707\) 2.22006 + 6.43340i 0.0834940 + 0.241953i
\(708\) 0 0
\(709\) −18.9660 + 32.8500i −0.712281 + 1.23371i 0.251718 + 0.967801i \(0.419005\pi\)
−0.963999 + 0.265907i \(0.914329\pi\)
\(710\) 0 0
\(711\) 10.1644 + 17.6053i 0.381196 + 0.660251i
\(712\) 0 0
\(713\) 64.9218 2.43134
\(714\) 0 0
\(715\) 22.5496 0.843309
\(716\) 0 0
\(717\) 6.19475 + 10.7296i 0.231347 + 0.400705i
\(718\) 0 0
\(719\) 0.215748 0.373686i 0.00804603 0.0139361i −0.861974 0.506952i \(-0.830772\pi\)
0.870020 + 0.493016i \(0.164106\pi\)
\(720\) 0 0
\(721\) 11.1646 12.8609i 0.415790 0.478965i
\(722\) 0 0
\(723\) −6.06264 + 10.5008i −0.225472 + 0.390529i
\(724\) 0 0
\(725\) −1.22452 2.12094i −0.0454777 0.0787696i
\(726\) 0 0
\(727\) −3.14690 −0.116712 −0.0583560 0.998296i \(-0.518586\pi\)
−0.0583560 + 0.998296i \(0.518586\pi\)
\(728\) 0 0
\(729\) 27.4287 1.01588
\(730\) 0 0
\(731\) 3.89488 + 6.74614i 0.144057 + 0.249515i
\(732\) 0 0
\(733\) 7.35219 12.7344i 0.271559 0.470355i −0.697702 0.716388i \(-0.745794\pi\)
0.969261 + 0.246033i \(0.0791273\pi\)
\(734\) 0 0
\(735\) −25.3392 10.1979i −0.934651 0.376155i
\(736\) 0 0
\(737\) −4.96886 + 8.60632i −0.183030 + 0.317018i
\(738\) 0 0
\(739\) 7.49950 + 12.9895i 0.275873 + 0.477827i 0.970355 0.241684i \(-0.0776996\pi\)
−0.694482 + 0.719510i \(0.744366\pi\)
\(740\) 0 0
\(741\) −2.08226 −0.0764937
\(742\) 0 0
\(743\) −31.3454 −1.14995 −0.574975 0.818171i \(-0.694988\pi\)
−0.574975 + 0.818171i \(0.694988\pi\)
\(744\) 0 0
\(745\) −12.5244 21.6929i −0.458858 0.794766i
\(746\) 0 0
\(747\) −0.296614 + 0.513751i −0.0108525 + 0.0187972i
\(748\) 0 0
\(749\) 4.16017 4.79226i 0.152009 0.175106i
\(750\) 0 0
\(751\) −2.21954 + 3.84436i −0.0809923 + 0.140283i −0.903676 0.428216i \(-0.859142\pi\)
0.822684 + 0.568499i \(0.192476\pi\)
\(752\) 0 0
\(753\) −1.95209 3.38111i −0.0711379 0.123215i
\(754\) 0 0
\(755\) 50.2155 1.82753
\(756\) 0 0
\(757\) 7.60936 0.276567 0.138283 0.990393i \(-0.455841\pi\)
0.138283 + 0.990393i \(0.455841\pi\)
\(758\) 0 0
\(759\) 22.7275 + 39.3652i 0.824957 + 1.42887i
\(760\) 0 0
\(761\) −6.74146 + 11.6765i −0.244378 + 0.423274i −0.961956 0.273203i \(-0.911917\pi\)
0.717579 + 0.696477i \(0.245250\pi\)
\(762\) 0 0
\(763\) −12.3026 35.6510i −0.445384 1.29065i
\(764\) 0 0
\(765\) 10.8082 18.7203i 0.390770 0.676834i
\(766\) 0 0
\(767\) −8.20858 14.2177i −0.296395 0.513371i
\(768\) 0 0
\(769\) 21.3561 0.770121 0.385061 0.922891i \(-0.374181\pi\)
0.385061 + 0.922891i \(0.374181\pi\)
\(770\) 0 0
\(771\) −30.7324 −1.10680
\(772\) 0 0
\(773\) 20.7104 + 35.8714i 0.744900 + 1.29020i 0.950241 + 0.311514i \(0.100836\pi\)
−0.205341 + 0.978690i \(0.565830\pi\)
\(774\) 0 0
\(775\) −16.5582 + 28.6796i −0.594787 + 1.03020i
\(776\) 0 0
\(777\) 14.7887 + 2.86426i 0.530542 + 0.102755i
\(778\) 0 0
\(779\) 1.00000 1.73205i 0.0358287 0.0620572i
\(780\) 0 0
\(781\) 31.0102 + 53.7113i 1.10963 + 1.92194i
\(782\) 0 0
\(783\) 3.98787 0.142515
\(784\) 0 0
\(785\) −49.3012 −1.75964
\(786\) 0 0
\(787\) 18.1780 + 31.4851i 0.647974 + 1.12232i 0.983606 + 0.180331i \(0.0577169\pi\)
−0.335632 + 0.941993i \(0.608950\pi\)
\(788\) 0 0
\(789\) 11.8522 20.5287i 0.421951 0.730840i
\(790\) 0 0
\(791\) 1.85367 + 0.359018i 0.0659090 + 0.0127652i
\(792\) 0 0
\(793\) 9.18042 15.9010i 0.326006 0.564660i
\(794\) 0 0
\(795\) 1.73979 + 3.01341i 0.0617041 + 0.106875i
\(796\) 0 0
\(797\) 8.65901 0.306718