Properties

Label 1064.2.q.n.305.6
Level $1064$
Weight $2$
Character 1064.305
Analytic conductor $8.496$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 305.6
Root \(0.670757 - 1.16179i\) of defining polynomial
Character \(\chi\) \(=\) 1064.305
Dual form 1064.2.q.n.457.6

$q$-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 \(\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times\).

\(n\) \(533\) \(799\) \(913\) \(1009\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.604818 0.796363i \(-0.706754\pi\)
0.992080 + 0.125606i \(0.0400876\pi\)
\(4\) 0 0
\(5\) −1.45434 2.51900i −0.650403 1.12653i −0.983025 0.183471i \(-0.941267\pi\)
0.332622 0.943060i \(-0.392067\pi\)
\(6\) 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 0.193410 + 0.981118i \(0.438045\pi\)
−0.946378 + 0.323061i \(0.895288\pi\)
\(12\) 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 0.196630 + 0.980478i \(0.437000\pi\)
−0.947434 + 0.319953i \(0.896333\pi\)
\(18\) 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 −0.965863 0.259052i \(-0.916590\pi\)
0.258586 0.965988i \(-0.416744\pi\)
\(24\) 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 0.0130995 + 0.999914i \(0.495830\pi\)
−0.872501 + 0.488613i \(0.837503\pi\)
\(32\) 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 0.637187 0.770709i \(-0.280098\pi\)
−0.986047 + 0.166466i \(0.946764\pi\)
\(38\) 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 0.826159 + 0.563436i \(0.190521\pi\)
0.0748706 + 0.997193i \(0.476146\pi\)
\(48\) 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 −0.895022 0.446022i \(-0.852840\pi\)
0.833777 + 0.552101i \(0.186174\pi\)
\(54\) 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 0.283826 + 0.958876i \(0.408396\pi\)
−0.972324 + 0.233638i \(0.924937\pi\)
\(60\) 0 0
\(61\) 5.91457 + 10.2443i 0.757283 + 1.31165i 0.944231 + 0.329283i \(0.106807\pi\)
−0.186948 + 0.982370i \(0.559860\pi\)
\(62\) 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 −0.920375 0.391037i \(-0.872116\pi\)
0.798836 + 0.601549i \(0.205450\pi\)
\(68\) 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 −0.584848 0.811143i \(-0.698846\pi\)
0.994894 + 0.100921i \(0.0321790\pi\)
\(74\) 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 −0.739498 0.673158i \(-0.764937\pi\)
−0.213223 0.977004i \(-0.568396\pi\)
\(80\) 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 0.941594 0.336750i \(-0.109328\pi\)
−0.762431 + 0.647069i \(0.775995\pi\)
\(90\) 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 −0.922893 0.385057i \(-0.874182\pi\)
0.794916 + 0.606720i \(0.207515\pi\)
\(102\) 0 0
\(103\) −3.21853 5.57466i −0.317131 0.549288i 0.662757 0.748835i \(-0.269386\pi\)
−0.979888 + 0.199547i \(0.936053\pi\)
\(104\) 0 0
\(105\) 10.1355 1.96303i 0.989124 0.191572i
\(106\) 0 0
\(107\) −1.19930 2.07724i −0.115940 0.200815i 0.802215 0.597035i \(-0.203655\pi\)
−0.918155 + 0.396221i \(0.870322\pi\)
\(108\) 0 0
\(109\) 7.12729 12.3448i 0.682670 1.18242i −0.291493 0.956573i \(-0.594152\pi\)
0.974163 0.225847i \(-0.0725148\pi\)
\(110\) 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 0.969080 0.246747i \(-0.0793616\pi\)
−0.698229 + 0.715875i \(0.746028\pi\)
\(132\) 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 0.179928 + 0.983680i \(0.442414\pi\)
−0.941856 + 0.336018i \(0.890920\pi\)
\(138\) 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 0.633981 0.773349i \(-0.281420\pi\)
−0.986730 + 0.162369i \(0.948087\pi\)
\(150\) 0 0
\(151\) −8.63199 + 14.9510i −0.702461 + 1.21670i 0.265139 + 0.964210i \(0.414582\pi\)
−0.967600 + 0.252488i \(0.918751\pi\)
\(152\) 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 −0.299704 0.954032i \(-0.596888\pi\)
0.976068 0.217465i \(-0.0697788\pi\)
\(158\) 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 0.976097 + 0.217335i \(0.0697365\pi\)
−0.299831 + 0.953992i \(0.596930\pi\)
\(164\) 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 0.701925 0.712251i \(-0.252324\pi\)
−0.967790 + 0.251760i \(0.918991\pi\)
\(174\) 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 0.176808 + 0.984245i \(0.443423\pi\)
−0.940785 + 0.339002i \(0.889910\pi\)
\(180\) 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 −0.999538 0.0304008i \(-0.990322\pi\)
0.473441 0.880826i \(-0.343012\pi\)
\(192\) 0 0
\(193\) 7.85414 13.6038i 0.565353 0.979220i −0.431664 0.902035i \(-0.642073\pi\)
0.997017 0.0771858i \(-0.0245935\pi\)
\(194\) 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 −0.490238 0.871589i \(-0.663090\pi\)
0.999937 0.0112361i \(-0.00357663\pi\)
\(200\) 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 −0.966521 0.256586i \(-0.917402\pi\)
0.705471 + 0.708739i \(0.250736\pi\)
\(228\) 0 0
\(229\) 14.3345 + 24.8281i 0.947252 + 1.64069i 0.751177 + 0.660101i \(0.229486\pi\)
0.196075 + 0.980589i \(0.437180\pi\)
\(230\) 0 0
\(231\) −11.6212 13.3870i −0.764621 0.880798i
\(232\) 0 0
\(233\) −1.52152 2.63535i −0.0996781 0.172647i 0.811873 0.583834i \(-0.198448\pi\)
−0.911551 + 0.411186i \(0.865115\pi\)
\(234\) 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 −0.682962 0.730454i \(-0.739309\pi\)
0.974073 + 0.226236i \(0.0726420\pi\)
\(242\) 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 −0.963150 0.268964i \(-0.913319\pi\)
0.248646 0.968595i \(-0.420015\pi\)
\(258\) 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 0.453833 + 0.891087i \(0.350056\pi\)
−0.998620 + 0.0525124i \(0.983277\pi\)
\(264\) 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 −0.637690 0.770293i \(-0.720110\pi\)
0.985938 + 0.167109i \(0.0534432\pi\)
\(270\) 0 0
\(271\) 2.52461 + 4.37276i 0.153359 + 0.265626i 0.932460 0.361272i \(-0.117657\pi\)
−0.779101 + 0.626898i \(0.784324\pi\)
\(272\) 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 −0.946565 0.322513i \(-0.895472\pi\)
0.752587 + 0.658493i \(0.228806\pi\)
\(278\) 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 −0.326433 0.945220i \(-0.605847\pi\)
0.981801 0.189910i \(-0.0608198\pi\)
\(284\) 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 −0.307182 0.951651i \(-0.599386\pi\)
0.977745 0.209798i \(-0.0672805\pi\)
\(312\) 0 0
\(313\) 13.3560 + 23.1333i 0.754927 + 1.30757i 0.945411 + 0.325882i \(0.105661\pi\)
−0.190483 + 0.981690i \(0.561006\pi\)
\(314\) 0 0
\(315\) −3.01331 + 8.73211i −0.169781 + 0.491999i
\(316\) 0 0
\(317\) 13.5370 + 23.4468i 0.760314 + 1.31690i 0.942689 + 0.333674i \(0.108288\pi\)
−0.182374 + 0.983229i \(0.558378\pi\)
\(318\) 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 0.819647 0.572869i \(-0.194170\pi\)
−0.905943 + 0.423400i \(0.860836\pi\)
\(332\) 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 −0.829520 0.558477i \(-0.811386\pi\)
0.898415 + 0.439147i \(0.144719\pi\)
\(348\) 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 −0.573644 0.819105i \(-0.694471\pi\)
0.996188 + 0.0872380i \(0.0278040\pi\)
\(354\) 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 −0.999393 0.0348477i \(-0.988905\pi\)
0.469517 0.882923i \(-0.344428\pi\)
\(360\) 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 −0.909008 0.416779i \(-0.863159\pi\)
0.815445 + 0.578834i \(0.196492\pi\)
\(368\) 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 −0.971649 0.236427i \(-0.924024\pi\)
0.281073 0.959686i \(-0.409310\pi\)
\(374\) 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 0.991347 0.131266i \(-0.0419042\pi\)
−0.609353 + 0.792899i \(0.708571\pi\)
\(384\) 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 −0.142061 + 0.989858i \(0.545373\pi\)
−0.786211 + 0.617958i \(0.787960\pi\)
\(390\) 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 0.999998 0.00210848i \(-0.000671150\pi\)
−0.501825 + 0.864969i \(0.667338\pi\)
\(398\) 0 0
\(399\) 3.48456 0.674886i 0.174446 0.0337866i
\(400\) 0 0
\(401\) −2.31504 4.00977i −0.115608 0.200238i 0.802415 0.596767i \(-0.203548\pi\)
−0.918023 + 0.396528i \(0.870215\pi\)
\(402\) 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 −0.915405 0.402534i \(-0.868130\pi\)
0.806307 + 0.591497i \(0.201463\pi\)
\(410\) 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 −0.839371 0.543559i \(-0.817076\pi\)
0.890421 + 0.455137i \(0.150410\pi\)
\(432\) 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 0.996911 + 0.0785439i \(0.0250271\pi\)
−0.430434 + 0.902622i \(0.641640\pi\)
\(440\) 0 0
\(441\) 6.61416 + 5.18196i 0.314960 + 0.246760i
\(442\) 0 0
\(443\) 5.32007 + 9.21464i 0.252764 + 0.437801i 0.964286 0.264864i \(-0.0853269\pi\)
−0.711522 + 0.702664i \(0.751994\pi\)
\(444\) 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 0.947670 0.319251i \(-0.103431\pi\)
−0.750315 + 0.661081i \(0.770098\pi\)
\(458\) 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 −0.998985 0.0450398i \(-0.985659\pi\)
0.460487 0.887666i \(-0.347675\pi\)
\(468\) 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 −0.911927 0.410353i \(-0.865406\pi\)
0.811339 + 0.584576i \(0.198739\pi\)
\(480\) 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 −0.448885 0.893590i \(-0.648179\pi\)
0.998314 0.0580489i \(-0.0184879\pi\)
\(488\) 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 0.556940 0.830553i \(-0.311976\pi\)
−0.997750 + 0.0670472i \(0.978642\pi\)
\(500\) 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 0.992745 0.120236i \(-0.0383652\pi\)
−0.600500 + 0.799625i \(0.705032\pi\)
\(510\) 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 −0.0347205 + 0.999397i \(0.511054\pi\)
−0.848143 + 0.529767i \(0.822279\pi\)
\(522\) 0 0
\(523\) −0.978350 1.69455i −0.0427803 0.0740976i 0.843842 0.536591i \(-0.180288\pi\)
−0.886623 + 0.462493i \(0.846955\pi\)
\(524\) 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 0.978497 + 0.206263i \(0.0661301\pi\)
−0.310620 + 0.950534i \(0.600537\pi\)
\(542\) 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 −0.999958 0.00911734i \(-0.997098\pi\)
0.507875 + 0.861431i \(0.330431\pi\)
\(558\) 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 0.493077 + 0.869986i \(0.335872\pi\)
−0.999968 + 0.00797592i \(0.997461\pi\)
\(564\) 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 0.989495 + 0.144567i \(0.0461790\pi\)
−0.369548 + 0.929211i \(0.620488\pi\)
\(570\) 0 0
\(571\) 13.2462 22.9431i 0.554337 0.960141i −0.443617 0.896216i \(-0.646305\pi\)
0.997955 0.0639243i \(-0.0203616\pi\)
\(572\) 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 0.466793 + 0.884367i \(0.345409\pi\)
−0.999280 + 0.0379287i \(0.987924\pi\)
\(578\) 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 0.845795 0.533508i \(-0.179127\pi\)
−0.884929 + 0.465725i \(0.845793\pi\)
\(594\) 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 −0.585236 0.810863i \(-0.698998\pi\)
0.994846 + 0.101397i \(0.0323313\pi\)
\(600\) 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 0.523125 0.852256i \(-0.324766\pi\)
−0.999638 + 0.0269121i \(0.991433\pi\)
\(608\) 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 0.446259 + 0.894904i \(0.352756\pi\)
−0.998139 + 0.0609799i \(0.980577\pi\)
\(614\) 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 −0.880620 0.473823i \(-0.842874\pi\)
0.850653 + 0.525728i \(0.176207\pi\)
\(620\) 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 −0.837016 0.547179i \(-0.815702\pi\)
0.892379 + 0.451288i \(0.149035\pi\)
\(642\) 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 −0.914012 0.405687i \(-0.867032\pi\)
0.808341 + 0.588714i \(0.200366\pi\)
\(648\) 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 0.998252 + 0.0590999i \(0.0188231\pi\)
−0.447944 + 0.894062i \(0.647844\pi\)
\(654\) 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 0.0398248 + 0.999207i \(0.487320\pi\)
−0.885251 + 0.465114i \(0.846013\pi\)
\(662\) 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 −0.870227 0.492650i \(-0.836028\pi\)
0.00846617 0.999964i \(-0.497305\pi\)
\(678\) 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 −0.421196 0.906970i \(-0.638390\pi\)
0.996057 0.0887184i \(-0.0282771\pi\)
\(684\) 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 0.986557 0.163418i \(-0.0522520\pi\)
−0.634803 + 0.772674i \(0.718919\pi\)
\(692\) 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 −0.963999 0.265907i \(-0.914329\pi\)
0.251718 0.967801i \(-0.419005\pi\)
\(710\) 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 0.870020 0.493016i \(-0.164106\pi\)
−0.861974 + 0.506952i \(0.830772\pi\)
\(720\) 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 0.969261 0.246033i \(-0.0791273\pi\)
−0.697702 + 0.716388i \(0.745794\pi\)
\(734\) 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 −0.694482 0.719510i \(-0.744366\pi\)
0.970355 + 0.241684i \(0.0776996\pi\)
\(740\) 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 0.822684 0.568499i \(-0.192476\pi\)
−0.903676 + 0.428216i \(0.859142\pi\)
\(752\) 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 0.717579 0.696477i \(-0.245250\pi\)
−0.961956 + 0.273203i \(0.911917\pi\)
\(762\) 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 −0.205341 0.978690i \(-0.565830\pi\)
0.950241 0.311514i \(-0.100836\pi\)
\(774\) 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 −0.335632 0.941993i \(-0.608950\pi\)
0.983606 0.180331i \(-0.0577169\pi\)
\(788\) 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 0.153359