Properties

Label 1050.2.bc.e.943.4
Level $1050$
Weight $2$
Character 1050.943
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 28 x^{14} + 519 x^{12} - 5404 x^{10} + 40705 x^{8} - 194544 x^{6} + 672624 x^{4} - 1306368 x^{2} + 1679616\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 943.4
Root \(1.44378 - 0.833568i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.e.157.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.258819 + 2.63306i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +1.00000i q^{6} +(-0.258819 + 2.63306i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.17884 + 2.04182i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-0.0968928 + 0.0968928i) q^{13} +(-2.61033 + 0.431486i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.833568 + 3.11092i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(0.434539 - 0.752644i) q^{19} +(-0.931486 + 2.47635i) q^{21} +(-1.66714 + 1.66714i) q^{22} +(-3.11092 + 0.833568i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.118669 - 0.0685135i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.09239 - 2.40971i) q^{28} -4.08363i q^{29} +(-0.747356 + 0.431486i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.610214 + 2.27735i) q^{33} -3.22066 q^{34} -1.00000 q^{36} +(2.54841 + 9.51079i) q^{37} +(0.839465 + 0.224934i) q^{38} +(-0.118669 + 0.0685135i) q^{39} +6.86297i q^{41} +(-2.63306 - 0.258819i) q^{42} +(-2.57551 - 2.57551i) q^{43} +(-2.04182 - 1.17884i) q^{44} +(-1.61033 - 2.78917i) q^{46} +(-0.833568 + 0.223354i) q^{47} +(0.707107 - 0.707107i) q^{48} +(-6.86603 - 1.36297i) q^{49} +(-1.61033 + 2.78917i) q^{51} +(0.0354652 - 0.132358i) q^{52} +(-2.16313 + 8.07290i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.04487 - 1.67884i) q^{56} +(0.614531 - 0.614531i) q^{57} +(3.94449 - 1.05692i) q^{58} +(-5.35769 - 9.27978i) q^{59} +(-7.44351 - 4.29751i) q^{61} +(-0.610214 - 0.610214i) q^{62} +(-1.54067 + 2.15089i) q^{63} +1.00000i q^{64} +(-2.04182 + 1.17884i) q^{66} +(12.2466 + 3.28148i) q^{67} +(-0.833568 - 3.11092i) q^{68} -3.22066 q^{69} +5.13703 q^{71} +(-0.258819 - 0.965926i) q^{72} +(15.7014 + 4.20718i) q^{73} +(-8.52714 + 4.92315i) q^{74} +0.869078i q^{76} +(-5.68133 + 2.57551i) q^{77} +(-0.0968928 - 0.0968928i) q^{78} +(4.02036 + 2.32116i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-6.62912 + 1.77627i) q^{82} +(-7.13020 + 7.13020i) q^{83} +(-0.431486 - 2.61033i) q^{84} +(1.82116 - 3.15434i) q^{86} +(1.05692 - 3.94449i) q^{87} +(0.610214 - 2.27735i) q^{88} +(4.98532 - 8.63484i) q^{89} +(-0.230047 - 0.280202i) q^{91} +(2.27735 - 2.27735i) q^{92} +(-0.833568 + 0.223354i) q^{93} +(-0.431486 - 0.747356i) q^{94} +(0.866025 + 0.500000i) q^{96} +(11.4245 + 11.4245i) q^{97} +(-0.460527 - 6.98483i) q^{98} +2.35769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 4q^{11} - 8q^{14} + 8q^{16} + 4q^{19} - 4q^{21} - 8q^{24} + 16q^{34} - 16q^{36} + 12q^{44} + 8q^{46} - 96q^{49} + 8q^{51} - 8q^{54} - 4q^{56} - 40q^{59} - 24q^{61} + 12q^{66} + 16q^{69} + 104q^{71} + 48q^{74} + 12q^{79} + 8q^{81} + 4q^{84} + 52q^{86} - 60q^{89} - 52q^{91} + 4q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 + 0.965926i 0.183013 + 0.683013i
\(3\) 0.965926 + 0.258819i 0.557678 + 0.149429i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) −0.258819 + 2.63306i −0.0978244 + 0.995204i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) 1.17884 + 2.04182i 0.355435 + 0.615631i 0.987192 0.159535i \(-0.0509996\pi\)
−0.631758 + 0.775166i \(0.717666\pi\)
\(12\) −0.965926 + 0.258819i −0.278839 + 0.0747146i
\(13\) −0.0968928 + 0.0968928i −0.0268732 + 0.0268732i −0.720416 0.693542i \(-0.756049\pi\)
0.693542 + 0.720416i \(0.256049\pi\)
\(14\) −2.61033 + 0.431486i −0.697640 + 0.115320i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −0.833568 + 3.11092i −0.202170 + 0.754508i 0.788124 + 0.615517i \(0.211053\pi\)
−0.990294 + 0.138991i \(0.955614\pi\)
\(18\) −0.258819 + 0.965926i −0.0610042 + 0.227671i
\(19\) 0.434539 0.752644i 0.0996901 0.172668i −0.811866 0.583843i \(-0.801548\pi\)
0.911556 + 0.411175i \(0.134882\pi\)
\(20\) 0 0
\(21\) −0.931486 + 2.47635i −0.203267 + 0.540385i
\(22\) −1.66714 + 1.66714i −0.355435 + 0.355435i
\(23\) −3.11092 + 0.833568i −0.648671 + 0.173811i −0.568128 0.822940i \(-0.692332\pi\)
−0.0805432 + 0.996751i \(0.525665\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −0.118669 0.0685135i −0.0232729 0.0134366i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −1.09239 2.40971i −0.206442 0.455392i
\(29\) 4.08363i 0.758311i −0.925333 0.379156i \(-0.876214\pi\)
0.925333 0.379156i \(-0.123786\pi\)
\(30\) 0 0
\(31\) −0.747356 + 0.431486i −0.134229 + 0.0774973i −0.565611 0.824672i \(-0.691360\pi\)
0.431382 + 0.902170i \(0.358026\pi\)
\(32\) 0.965926 + 0.258819i 0.170753 + 0.0457532i
\(33\) 0.610214 + 2.27735i 0.106225 + 0.396436i
\(34\) −3.22066 −0.552338
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 2.54841 + 9.51079i 0.418956 + 1.56356i 0.776778 + 0.629774i \(0.216853\pi\)
−0.357822 + 0.933790i \(0.616481\pi\)
\(38\) 0.839465 + 0.224934i 0.136179 + 0.0364891i
\(39\) −0.118669 + 0.0685135i −0.0190022 + 0.0109709i
\(40\) 0 0
\(41\) 6.86297i 1.07182i 0.844276 + 0.535908i \(0.180031\pi\)
−0.844276 + 0.535908i \(0.819969\pi\)
\(42\) −2.63306 0.258819i −0.406290 0.0399366i
\(43\) −2.57551 2.57551i −0.392761 0.392761i 0.482909 0.875670i \(-0.339580\pi\)
−0.875670 + 0.482909i \(0.839580\pi\)
\(44\) −2.04182 1.17884i −0.307815 0.177717i
\(45\) 0 0
\(46\) −1.61033 2.78917i −0.237430 0.411241i
\(47\) −0.833568 + 0.223354i −0.121588 + 0.0325795i −0.319100 0.947721i \(-0.603381\pi\)
0.197512 + 0.980301i \(0.436714\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) −6.86603 1.36297i −0.980861 0.194710i
\(50\) 0 0
\(51\) −1.61033 + 2.78917i −0.225491 + 0.390562i
\(52\) 0.0354652 0.132358i 0.00491814 0.0183548i
\(53\) −2.16313 + 8.07290i −0.297129 + 1.10890i 0.642384 + 0.766383i \(0.277946\pi\)
−0.939512 + 0.342516i \(0.888721\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 2.04487 1.67884i 0.273257 0.224345i
\(57\) 0.614531 0.614531i 0.0813966 0.0813966i
\(58\) 3.94449 1.05692i 0.517936 0.138781i
\(59\) −5.35769 9.27978i −0.697511 1.20812i −0.969327 0.245776i \(-0.920957\pi\)
0.271815 0.962349i \(-0.412376\pi\)
\(60\) 0 0
\(61\) −7.44351 4.29751i −0.953044 0.550240i −0.0590186 0.998257i \(-0.518797\pi\)
−0.894025 + 0.448017i \(0.852130\pi\)
\(62\) −0.610214 0.610214i −0.0774973 0.0774973i
\(63\) −1.54067 + 2.15089i −0.194107 + 0.270986i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −2.04182 + 1.17884i −0.251330 + 0.145106i
\(67\) 12.2466 + 3.28148i 1.49617 + 0.400896i 0.911814 0.410604i \(-0.134682\pi\)
0.584352 + 0.811501i \(0.301349\pi\)
\(68\) −0.833568 3.11092i −0.101085 0.377254i
\(69\) −3.22066 −0.387722
\(70\) 0 0
\(71\) 5.13703 0.609653 0.304826 0.952408i \(-0.401402\pi\)
0.304826 + 0.952408i \(0.401402\pi\)
\(72\) −0.258819 0.965926i −0.0305021 0.113835i
\(73\) 15.7014 + 4.20718i 1.83771 + 0.492413i 0.998665 0.0516512i \(-0.0164484\pi\)
0.839044 + 0.544064i \(0.183115\pi\)
\(74\) −8.52714 + 4.92315i −0.991260 + 0.572304i
\(75\) 0 0
\(76\) 0.869078i 0.0996901i
\(77\) −5.68133 + 2.57551i −0.647448 + 0.293506i
\(78\) −0.0968928 0.0968928i −0.0109709 0.0109709i
\(79\) 4.02036 + 2.32116i 0.452326 + 0.261151i 0.708812 0.705397i \(-0.249231\pi\)
−0.256486 + 0.966548i \(0.582565\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −6.62912 + 1.77627i −0.732064 + 0.196156i
\(83\) −7.13020 + 7.13020i −0.782642 + 0.782642i −0.980276 0.197634i \(-0.936674\pi\)
0.197634 + 0.980276i \(0.436674\pi\)
\(84\) −0.431486 2.61033i −0.0470790 0.284810i
\(85\) 0 0
\(86\) 1.82116 3.15434i 0.196380 0.340141i
\(87\) 1.05692 3.94449i 0.113314 0.422893i
\(88\) 0.610214 2.27735i 0.0650490 0.242766i
\(89\) 4.98532 8.63484i 0.528443 0.915291i −0.471007 0.882130i \(-0.656109\pi\)
0.999450 0.0331611i \(-0.0105574\pi\)
\(90\) 0 0
\(91\) −0.230047 0.280202i −0.0241155 0.0293732i
\(92\) 2.27735 2.27735i 0.237430 0.237430i
\(93\) −0.833568 + 0.223354i −0.0864370 + 0.0231607i
\(94\) −0.431486 0.747356i −0.0445044 0.0770839i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 11.4245 + 11.4245i 1.15998 + 1.15998i 0.984479 + 0.175504i \(0.0561555\pi\)
0.175504 + 0.984479i \(0.443845\pi\)
\(98\) −0.460527 6.98483i −0.0465203 0.705575i
\(99\) 2.35769i 0.236956i
\(100\) 0 0
\(101\) −0.547103 + 0.315870i −0.0544388 + 0.0314302i −0.526972 0.849882i \(-0.676673\pi\)
0.472534 + 0.881313i \(0.343340\pi\)
\(102\) −3.11092 0.833568i −0.308027 0.0825355i
\(103\) −0.422325 1.57614i −0.0416130 0.155302i 0.941993 0.335632i \(-0.108950\pi\)
−0.983606 + 0.180331i \(0.942283\pi\)
\(104\) 0.137027 0.0134366
\(105\) 0 0
\(106\) −8.35769 −0.811770
\(107\) −3.91015 14.5929i −0.378009 1.41075i −0.848898 0.528556i \(-0.822734\pi\)
0.470889 0.882192i \(-0.343933\pi\)
\(108\) −0.965926 0.258819i −0.0929463 0.0249049i
\(109\) 7.45905 4.30648i 0.714447 0.412486i −0.0982585 0.995161i \(-0.531327\pi\)
0.812705 + 0.582675i \(0.197994\pi\)
\(110\) 0 0
\(111\) 9.84629i 0.934569i
\(112\) 2.15089 + 1.54067i 0.203240 + 0.145580i
\(113\) −12.4298 12.4298i −1.16929 1.16929i −0.982375 0.186919i \(-0.940150\pi\)
−0.186919 0.982375i \(-0.559850\pi\)
\(114\) 0.752644 + 0.434539i 0.0704915 + 0.0406983i
\(115\) 0 0
\(116\) 2.04182 + 3.53653i 0.189578 + 0.328358i
\(117\) −0.132358 + 0.0354652i −0.0122365 + 0.00327876i
\(118\) 7.57691 7.57691i 0.697511 0.697511i
\(119\) −7.97549 3.00000i −0.731112 0.275010i
\(120\) 0 0
\(121\) 2.72066 4.71232i 0.247333 0.428393i
\(122\) 2.22456 8.30216i 0.201402 0.751642i
\(123\) −1.77627 + 6.62912i −0.160161 + 0.597728i
\(124\) 0.431486 0.747356i 0.0387486 0.0671146i
\(125\) 0 0
\(126\) −2.47635 0.931486i −0.220611 0.0829834i
\(127\) 9.62150 9.62150i 0.853770 0.853770i −0.136825 0.990595i \(-0.543690\pi\)
0.990595 + 0.136825i \(0.0436898\pi\)
\(128\) −0.965926 + 0.258819i −0.0853766 + 0.0228766i
\(129\) −1.82116 3.15434i −0.160344 0.277724i
\(130\) 0 0
\(131\) −11.0418 6.37500i −0.964728 0.556986i −0.0671030 0.997746i \(-0.521376\pi\)
−0.897625 + 0.440760i \(0.854709\pi\)
\(132\) −1.66714 1.66714i −0.145106 0.145106i
\(133\) 1.86929 + 1.33897i 0.162088 + 0.116103i
\(134\) 12.6787i 1.09527i
\(135\) 0 0
\(136\) 2.78917 1.61033i 0.239170 0.138085i
\(137\) 13.3330 + 3.57258i 1.13912 + 0.305226i 0.778597 0.627525i \(-0.215932\pi\)
0.360522 + 0.932751i \(0.382598\pi\)
\(138\) −0.833568 3.11092i −0.0709580 0.264819i
\(139\) 13.9299 1.18152 0.590760 0.806847i \(-0.298828\pi\)
0.590760 + 0.806847i \(0.298828\pi\)
\(140\) 0 0
\(141\) −0.862973 −0.0726754
\(142\) 1.32956 + 4.96199i 0.111574 + 0.416401i
\(143\) −0.312059 0.0836158i −0.0260957 0.00699231i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 16.2553i 1.34530i
\(147\) −6.27931 3.09359i −0.517909 0.255155i
\(148\) −6.96238 6.96238i −0.572304 0.572304i
\(149\) 16.7851 + 9.69087i 1.37509 + 0.793907i 0.991563 0.129625i \(-0.0413772\pi\)
0.383523 + 0.923531i \(0.374711\pi\)
\(150\) 0 0
\(151\) 1.57380 + 2.72590i 0.128074 + 0.221831i 0.922930 0.384967i \(-0.125787\pi\)
−0.794856 + 0.606798i \(0.792454\pi\)
\(152\) −0.839465 + 0.224934i −0.0680896 + 0.0182445i
\(153\) −2.27735 + 2.27735i −0.184113 + 0.184113i
\(154\) −3.95818 4.82116i −0.318960 0.388500i
\(155\) 0 0
\(156\) 0.0685135 0.118669i 0.00548547 0.00950112i
\(157\) 1.59734 5.96135i 0.127482 0.475768i −0.872434 0.488731i \(-0.837460\pi\)
0.999916 + 0.0129635i \(0.00412653\pi\)
\(158\) −1.20152 + 4.48413i −0.0955877 + 0.356738i
\(159\) −4.17884 + 7.23797i −0.331404 + 0.574008i
\(160\) 0 0
\(161\) −1.38967 8.40698i −0.109521 0.662563i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −2.67874 + 0.717766i −0.209815 + 0.0562198i −0.362196 0.932102i \(-0.617973\pi\)
0.152380 + 0.988322i \(0.451306\pi\)
\(164\) −3.43149 5.94351i −0.267954 0.464110i
\(165\) 0 0
\(166\) −8.73268 5.04182i −0.677788 0.391321i
\(167\) −12.1316 12.1316i −0.938772 0.938772i 0.0594585 0.998231i \(-0.481063\pi\)
−0.998231 + 0.0594585i \(0.981063\pi\)
\(168\) 2.40971 1.09239i 0.185913 0.0842795i
\(169\) 12.9812i 0.998556i
\(170\) 0 0
\(171\) 0.752644 0.434539i 0.0575561 0.0332300i
\(172\) 3.51821 + 0.942700i 0.268261 + 0.0718802i
\(173\) −0.332486 1.24086i −0.0252785 0.0943405i 0.952134 0.305681i \(-0.0988839\pi\)
−0.977413 + 0.211340i \(0.932217\pi\)
\(174\) 4.08363 0.309579
\(175\) 0 0
\(176\) 2.35769 0.177717
\(177\) −2.77334 10.3503i −0.208457 0.777973i
\(178\) 9.63091 + 2.58059i 0.721867 + 0.193424i
\(179\) 16.7851 9.69087i 1.25458 0.724329i 0.282560 0.959249i \(-0.408816\pi\)
0.972015 + 0.234920i \(0.0754829\pi\)
\(180\) 0 0
\(181\) 25.1913i 1.87246i −0.351394 0.936228i \(-0.614292\pi\)
0.351394 0.936228i \(-0.385708\pi\)
\(182\) 0.211114 0.294730i 0.0156488 0.0218468i
\(183\) −6.07760 6.07760i −0.449269 0.449269i
\(184\) 2.78917 + 1.61033i 0.205621 + 0.118715i
\(185\) 0 0
\(186\) −0.431486 0.747356i −0.0316381 0.0547988i
\(187\) −7.33457 + 1.96529i −0.536357 + 0.143716i
\(188\) 0.610214 0.610214i 0.0445044 0.0445044i
\(189\) −2.04487 + 1.67884i −0.148742 + 0.122118i
\(190\) 0 0
\(191\) −3.43149 + 5.94351i −0.248294 + 0.430057i −0.963052 0.269314i \(-0.913203\pi\)
0.714759 + 0.699371i \(0.246536\pi\)
\(192\) −0.258819 + 0.965926i −0.0186787 + 0.0697097i
\(193\) −0.719346 + 2.68464i −0.0517797 + 0.193244i −0.986971 0.160899i \(-0.948561\pi\)
0.935191 + 0.354143i \(0.115227\pi\)
\(194\) −8.07834 + 13.9921i −0.579991 + 1.00457i
\(195\) 0 0
\(196\) 6.62764 2.25264i 0.473403 0.160903i
\(197\) −17.3662 + 17.3662i −1.23729 + 1.23729i −0.276190 + 0.961103i \(0.589072\pi\)
−0.961103 + 0.276190i \(0.910928\pi\)
\(198\) −2.27735 + 0.610214i −0.161844 + 0.0433660i
\(199\) 5.26553 + 9.12016i 0.373263 + 0.646511i 0.990065 0.140607i \(-0.0449055\pi\)
−0.616802 + 0.787118i \(0.711572\pi\)
\(200\) 0 0
\(201\) 10.9800 + 6.33933i 0.774472 + 0.447142i
\(202\) −0.446708 0.446708i −0.0314302 0.0314302i
\(203\) 10.7525 + 1.05692i 0.754674 + 0.0741814i
\(204\) 3.22066i 0.225491i
\(205\) 0 0
\(206\) 1.41313 0.815870i 0.0984573 0.0568444i
\(207\) −3.11092 0.833568i −0.216224 0.0579370i
\(208\) 0.0354652 + 0.132358i 0.00245907 + 0.00917738i
\(209\) 2.04901 0.141733
\(210\) 0 0
\(211\) 13.6726 0.941257 0.470629 0.882331i \(-0.344027\pi\)
0.470629 + 0.882331i \(0.344027\pi\)
\(212\) −2.16313 8.07290i −0.148564 0.554449i
\(213\) 4.96199 + 1.32956i 0.339990 + 0.0911000i
\(214\) 13.0836 7.55384i 0.894379 0.516370i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −0.942700 2.07951i −0.0639947 0.141167i
\(218\) 6.09028 + 6.09028i 0.412486 + 0.412486i
\(219\) 14.0775 + 8.12764i 0.951268 + 0.549215i
\(220\) 0 0
\(221\) −0.220659 0.382192i −0.0148431 0.0257090i
\(222\) −9.51079 + 2.54841i −0.638322 + 0.171038i
\(223\) −6.42310 + 6.42310i −0.430122 + 0.430122i −0.888670 0.458547i \(-0.848370\pi\)
0.458547 + 0.888670i \(0.348370\pi\)
\(224\) −0.931486 + 2.47635i −0.0622376 + 0.165458i
\(225\) 0 0
\(226\) 8.78917 15.2233i 0.584647 1.01264i
\(227\) 4.02438 15.0192i 0.267107 0.996858i −0.693841 0.720128i \(-0.744083\pi\)
0.960948 0.276729i \(-0.0892505\pi\)
\(228\) −0.224934 + 0.839465i −0.0148966 + 0.0555949i
\(229\) 5.40393 9.35988i 0.357102 0.618518i −0.630374 0.776292i \(-0.717098\pi\)
0.987475 + 0.157774i \(0.0504317\pi\)
\(230\) 0 0
\(231\) −6.15434 + 1.01731i −0.404926 + 0.0669341i
\(232\) −2.88756 + 2.88756i −0.189578 + 0.189578i
\(233\) 12.1316 3.25066i 0.794768 0.212958i 0.161483 0.986876i \(-0.448372\pi\)
0.633286 + 0.773918i \(0.281706\pi\)
\(234\) −0.0685135 0.118669i −0.00447887 0.00775763i
\(235\) 0 0
\(236\) 9.27978 + 5.35769i 0.604062 + 0.348756i
\(237\) 3.28261 + 3.28261i 0.213229 + 0.213229i
\(238\) 0.833568 8.48019i 0.0540322 0.549689i
\(239\) 15.9706i 1.03306i 0.856270 + 0.516528i \(0.172776\pi\)
−0.856270 + 0.516528i \(0.827224\pi\)
\(240\) 0 0
\(241\) 23.6526 13.6558i 1.52360 0.879649i 0.523987 0.851726i \(-0.324444\pi\)
0.999610 0.0279230i \(-0.00888932\pi\)
\(242\) 5.25591 + 1.40832i 0.337863 + 0.0905300i
\(243\) 0.258819 + 0.965926i 0.0166032 + 0.0619642i
\(244\) 8.59502 0.550240
\(245\) 0 0
\(246\) −6.86297 −0.437567
\(247\) 0.0308220 + 0.115029i 0.00196116 + 0.00731915i
\(248\) 0.833568 + 0.223354i 0.0529316 + 0.0141830i
\(249\) −8.73268 + 5.04182i −0.553411 + 0.319512i
\(250\) 0 0
\(251\) 3.45189i 0.217881i −0.994048 0.108941i \(-0.965254\pi\)
0.994048 0.108941i \(-0.0347459\pi\)
\(252\) 0.258819 2.63306i 0.0163041 0.165867i
\(253\) −5.36927 5.36927i −0.337563 0.337563i
\(254\) 11.7839 + 6.80343i 0.739387 + 0.426885i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.44226 + 1.99415i −0.464236 + 0.124392i −0.483353 0.875426i \(-0.660581\pi\)
0.0191171 + 0.999817i \(0.493914\pi\)
\(258\) 2.57551 2.57551i 0.160344 0.160344i
\(259\) −25.7021 + 4.24854i −1.59705 + 0.263992i
\(260\) 0 0
\(261\) 2.04182 3.53653i 0.126385 0.218906i
\(262\) 3.29994 12.3155i 0.203871 0.760857i
\(263\) −5.49231 + 20.4976i −0.338670 + 1.26394i 0.561164 + 0.827704i \(0.310354\pi\)
−0.899835 + 0.436231i \(0.856313\pi\)
\(264\) 1.17884 2.04182i 0.0725528 0.125665i
\(265\) 0 0
\(266\) −0.809534 + 2.15215i −0.0496357 + 0.131956i
\(267\) 7.05031 7.05031i 0.431472 0.431472i
\(268\) −12.2466 + 3.28148i −0.748083 + 0.200448i
\(269\) 0.595654 + 1.03170i 0.0363177 + 0.0629041i 0.883613 0.468218i \(-0.155104\pi\)
−0.847295 + 0.531122i \(0.821771\pi\)
\(270\) 0 0
\(271\) −7.05603 4.07380i −0.428623 0.247466i 0.270137 0.962822i \(-0.412931\pi\)
−0.698760 + 0.715356i \(0.746264\pi\)
\(272\) 2.27735 + 2.27735i 0.138085 + 0.138085i
\(273\) −0.149687 0.330195i −0.00905944 0.0199843i
\(274\) 13.8034i 0.833893i
\(275\) 0 0
\(276\) 2.78917 1.61033i 0.167888 0.0969304i
\(277\) 16.2147 + 4.34472i 0.974248 + 0.261049i 0.710620 0.703576i \(-0.248414\pi\)
0.263627 + 0.964625i \(0.415081\pi\)
\(278\) 3.60533 + 13.4553i 0.216233 + 0.806994i
\(279\) −0.862973 −0.0516648
\(280\) 0 0
\(281\) 10.5053 0.626693 0.313346 0.949639i \(-0.398550\pi\)
0.313346 + 0.949639i \(0.398550\pi\)
\(282\) −0.223354 0.833568i −0.0133005 0.0496382i
\(283\) 24.1532 + 6.47184i 1.43576 + 0.384711i 0.891047 0.453911i \(-0.149972\pi\)
0.544714 + 0.838622i \(0.316638\pi\)
\(284\) −4.44880 + 2.56851i −0.263987 + 0.152413i
\(285\) 0 0
\(286\) 0.323067i 0.0191033i
\(287\) −18.0706 1.77627i −1.06668 0.104850i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 5.73946 + 3.31368i 0.337615 + 0.194922i
\(290\) 0 0
\(291\) 8.07834 + 13.9921i 0.473561 + 0.820232i
\(292\) −15.7014 + 4.20718i −0.918855 + 0.246206i
\(293\) 8.66269 8.66269i 0.506080 0.506080i −0.407241 0.913321i \(-0.633509\pi\)
0.913321 + 0.407241i \(0.133509\pi\)
\(294\) 1.36297 6.86603i 0.0794902 0.400435i
\(295\) 0 0
\(296\) 4.92315 8.52714i 0.286152 0.495630i
\(297\) −0.610214 + 2.27735i −0.0354082 + 0.132145i
\(298\) −5.01636 + 18.7213i −0.290590 + 1.08450i
\(299\) 0.220659 0.382192i 0.0127610 0.0221027i
\(300\) 0 0
\(301\) 7.44805 6.11487i 0.429299 0.352455i
\(302\) −2.22569 + 2.22569i −0.128074 + 0.128074i
\(303\) −0.610214 + 0.163506i −0.0350559 + 0.00939319i
\(304\) −0.434539 0.752644i −0.0249225 0.0431671i
\(305\) 0 0
\(306\) −2.78917 1.61033i −0.159446 0.0920564i
\(307\) −6.28097 6.28097i −0.358474 0.358474i 0.504776 0.863250i \(-0.331575\pi\)
−0.863250 + 0.504776i \(0.831575\pi\)
\(308\) 3.63243 5.07112i 0.206977 0.288954i
\(309\) 1.63174i 0.0928264i
\(310\) 0 0
\(311\) −12.1714 + 7.02714i −0.690175 + 0.398473i −0.803678 0.595065i \(-0.797126\pi\)
0.113503 + 0.993538i \(0.463793\pi\)
\(312\) 0.132358 + 0.0354652i 0.00749330 + 0.00200782i
\(313\) −5.09785 19.0255i −0.288148 1.07538i −0.946508 0.322679i \(-0.895416\pi\)
0.658361 0.752703i \(-0.271250\pi\)
\(314\) 6.17165 0.348286
\(315\) 0 0
\(316\) −4.64231 −0.261151
\(317\) −0.615688 2.29778i −0.0345805 0.129056i 0.946478 0.322769i \(-0.104614\pi\)
−0.981058 + 0.193713i \(0.937947\pi\)
\(318\) −8.07290 2.16313i −0.452706 0.121302i
\(319\) 8.33802 4.81396i 0.466840 0.269530i
\(320\) 0 0
\(321\) 15.1077i 0.843228i
\(322\) 7.76085 3.51821i 0.432495 0.196062i
\(323\) 1.97919 + 1.97919i 0.110125 + 0.110125i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 0 0
\(326\) −1.38662 2.40169i −0.0767977 0.133017i
\(327\) 8.31948 2.22920i 0.460069 0.123275i
\(328\) 4.85285 4.85285i 0.267954 0.267954i
\(329\) −0.372361 2.25264i −0.0205289 0.124192i
\(330\) 0 0
\(331\) −13.8430 + 23.9768i −0.760881 + 1.31788i 0.181516 + 0.983388i \(0.441899\pi\)
−0.942397 + 0.334496i \(0.891434\pi\)
\(332\) 2.60984 9.74004i 0.143233 0.534554i
\(333\) −2.54841 + 9.51079i −0.139652 + 0.521188i
\(334\) 8.57834 14.8581i 0.469386 0.813001i
\(335\) 0 0
\(336\) 1.67884 + 2.04487i 0.0915884 + 0.111557i
\(337\) −3.18572 + 3.18572i −0.173537 + 0.173537i −0.788532 0.614994i \(-0.789158\pi\)
0.614994 + 0.788532i \(0.289158\pi\)
\(338\) −12.5389 + 3.35979i −0.682026 + 0.182748i
\(339\) −8.78917 15.2233i −0.477362 0.826816i
\(340\) 0 0
\(341\) −1.76203 1.01731i −0.0954194 0.0550904i
\(342\) 0.614531 + 0.614531i 0.0332300 + 0.0332300i
\(343\) 5.36585 17.7259i 0.289729 0.957109i
\(344\) 3.64231i 0.196380i
\(345\) 0 0
\(346\) 1.11252 0.642314i 0.0598095 0.0345310i
\(347\) −5.59119 1.49816i −0.300151 0.0804252i 0.105601 0.994409i \(-0.466324\pi\)
−0.405752 + 0.913983i \(0.632990\pi\)
\(348\) 1.05692 + 3.94449i 0.0566569 + 0.211447i
\(349\) −19.6326 −1.05091 −0.525455 0.850821i \(-0.676105\pi\)
−0.525455 + 0.850821i \(0.676105\pi\)
\(350\) 0 0
\(351\) −0.137027 −0.00731396
\(352\) 0.610214 + 2.27735i 0.0325245 + 0.121383i
\(353\) 25.1461 + 6.73787i 1.33839 + 0.358621i 0.855837 0.517246i \(-0.173043\pi\)
0.482554 + 0.875866i \(0.339709\pi\)
\(354\) 9.27978 5.35769i 0.493215 0.284758i
\(355\) 0 0
\(356\) 9.97065i 0.528443i
\(357\) −6.92728 4.96199i −0.366630 0.262616i
\(358\) 13.7050 + 13.7050i 0.724329 + 0.724329i
\(359\) 6.41108 + 3.70144i 0.338364 + 0.195355i 0.659548 0.751662i \(-0.270748\pi\)
−0.321184 + 0.947017i \(0.604081\pi\)
\(360\) 0 0
\(361\) 9.12235 + 15.8004i 0.480124 + 0.831599i
\(362\) 24.3329 6.51999i 1.27891 0.342683i
\(363\) 3.84759 3.84759i 0.201946 0.201946i
\(364\) 0.339328 + 0.127639i 0.0177856 + 0.00669010i
\(365\) 0 0
\(366\) 4.29751 7.44351i 0.224635 0.389078i
\(367\) 3.12375 11.6580i 0.163058 0.608542i −0.835222 0.549914i \(-0.814661\pi\)
0.998280 0.0586284i \(-0.0186727\pi\)
\(368\) −0.833568 + 3.11092i −0.0434527 + 0.162168i
\(369\) −3.43149 + 5.94351i −0.178636 + 0.309407i
\(370\) 0 0
\(371\) −20.6966 7.78507i −1.07451 0.404181i
\(372\) 0.610214 0.610214i 0.0316381 0.0316381i
\(373\) −0.115029 + 0.0308220i −0.00595600 + 0.00159590i −0.261796 0.965123i \(-0.584315\pi\)
0.255840 + 0.966719i \(0.417648\pi\)
\(374\) −3.79665 6.57599i −0.196320 0.340036i
\(375\) 0 0
\(376\) 0.747356 + 0.431486i 0.0385420 + 0.0222522i
\(377\) 0.395674 + 0.395674i 0.0203783 + 0.0203783i
\(378\) −2.15089 1.54067i −0.110630 0.0792438i
\(379\) 8.83801i 0.453978i 0.973897 + 0.226989i \(0.0728881\pi\)
−0.973897 + 0.226989i \(0.927112\pi\)
\(380\) 0 0
\(381\) 11.7839 6.80343i 0.603707 0.348550i
\(382\) −6.62912 1.77627i −0.339175 0.0908818i
\(383\) −10.0127 37.3678i −0.511624 1.90941i −0.402625 0.915365i \(-0.631902\pi\)
−0.108999 0.994042i \(-0.534764\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −2.77934 −0.141465
\(387\) −0.942700 3.51821i −0.0479201 0.178840i
\(388\) −15.6062 4.18166i −0.792283 0.212292i
\(389\) 26.3005 15.1846i 1.33349 0.769888i 0.347654 0.937623i \(-0.386979\pi\)
0.985832 + 0.167735i \(0.0536452\pi\)
\(390\) 0 0
\(391\) 10.3726i 0.524567i
\(392\) 3.89125 + 5.81878i 0.196538 + 0.293893i
\(393\) −9.01560 9.01560i −0.454777 0.454777i
\(394\) −21.2692 12.2798i −1.07153 0.618647i
\(395\) 0 0
\(396\) −1.17884 2.04182i −0.0592391 0.102605i
\(397\) −26.0335 + 6.97566i −1.30658 + 0.350098i −0.843936 0.536444i \(-0.819767\pi\)
−0.462648 + 0.886542i \(0.653101\pi\)
\(398\) −7.44658 + 7.44658i −0.373263 + 0.373263i
\(399\) 1.45905 + 1.77715i 0.0730436 + 0.0889688i
\(400\) 0 0
\(401\) −6.86297 + 11.8870i −0.342721 + 0.593609i −0.984937 0.172914i \(-0.944682\pi\)
0.642216 + 0.766523i \(0.278015\pi\)
\(402\) −3.28148 + 12.2466i −0.163665 + 0.610807i
\(403\) 0.0306055 0.114221i 0.00152457 0.00568977i
\(404\) 0.315870 0.547103i 0.0157151 0.0272194i
\(405\) 0 0
\(406\) 1.76203 + 10.6596i 0.0874482 + 0.529028i
\(407\) −16.4151 + 16.4151i −0.813667 + 0.813667i
\(408\) 3.11092 0.833568i 0.154013 0.0412678i
\(409\) −2.11119 3.65669i −0.104392 0.180812i 0.809098 0.587674i \(-0.199956\pi\)
−0.913489 + 0.406862i \(0.866623\pi\)
\(410\) 0 0
\(411\) 11.9541 + 6.90169i 0.589651 + 0.340435i
\(412\) 1.15381 + 1.15381i 0.0568444 + 0.0568444i
\(413\) 25.8209 11.7053i 1.27056 0.575982i
\(414\) 3.22066i 0.158287i
\(415\) 0 0
\(416\) −0.118669 + 0.0685135i −0.00581822 + 0.00335915i
\(417\) 13.4553 + 3.60533i 0.658908 + 0.176554i
\(418\) 0.530323 + 1.97919i 0.0259390 + 0.0968056i
\(419\) −28.1807 −1.37672 −0.688359 0.725370i \(-0.741669\pi\)
−0.688359 + 0.725370i \(0.741669\pi\)
\(420\) 0 0
\(421\) −3.31486 −0.161557 −0.0807783 0.996732i \(-0.525741\pi\)
−0.0807783 + 0.996732i \(0.525741\pi\)
\(422\) 3.53872 + 13.2067i 0.172262 + 0.642891i
\(423\) −0.833568 0.223354i −0.0405295 0.0108598i
\(424\) 7.23797 4.17884i 0.351507 0.202943i
\(425\) 0 0
\(426\) 5.13703i 0.248890i
\(427\) 13.2421 18.4869i 0.640832 0.894646i
\(428\) 10.6827 + 10.6827i 0.516370 + 0.516370i
\(429\) −0.279784 0.161533i −0.0135081 0.00779891i
\(430\) 0 0
\(431\) −2.08773 3.61606i −0.100563 0.174179i 0.811354 0.584555i \(-0.198731\pi\)
−0.911917 + 0.410376i \(0.865398\pi\)
\(432\) 0.965926 0.258819i 0.0464731 0.0124524i
\(433\) −4.81820 + 4.81820i −0.231548 + 0.231548i −0.813339 0.581791i \(-0.802352\pi\)
0.581791 + 0.813339i \(0.302352\pi\)
\(434\) 1.76467 1.44880i 0.0847067 0.0695444i
\(435\) 0 0
\(436\) −4.30648 + 7.45905i −0.206243 + 0.357223i
\(437\) −0.724435 + 2.70363i −0.0346544 + 0.129332i
\(438\) −4.20718 + 15.7014i −0.201027 + 0.750242i
\(439\) −1.24102 + 2.14951i −0.0592307 + 0.102591i −0.894120 0.447827i \(-0.852198\pi\)
0.834890 + 0.550417i \(0.185531\pi\)
\(440\) 0 0
\(441\) −5.26467 4.61338i −0.250698 0.219685i
\(442\) 0.312059 0.312059i 0.0148431 0.0148431i
\(443\) −14.2947 + 3.83026i −0.679164 + 0.181981i −0.581879 0.813275i \(-0.697682\pi\)
−0.0972845 + 0.995257i \(0.531016\pi\)
\(444\) −4.92315 8.52714i −0.233642 0.404680i
\(445\) 0 0
\(446\) −7.86666 4.54182i −0.372497 0.215061i
\(447\) 13.7050 + 13.7050i 0.648222 + 0.648222i
\(448\) −2.63306 0.258819i −0.124400 0.0122281i
\(449\) 0.554300i 0.0261590i −0.999914 0.0130795i \(-0.995837\pi\)
0.999914 0.0130795i \(-0.00416346\pi\)
\(450\) 0 0
\(451\) −14.0129 + 8.09037i −0.659843 + 0.380961i
\(452\) 16.9794 + 4.54961i 0.798643 + 0.213996i
\(453\) 0.814659 + 3.04035i 0.0382760 + 0.142848i
\(454\) 15.5490 0.729750
\(455\) 0 0
\(456\) −0.869078 −0.0406983
\(457\) 8.30331 + 30.9884i 0.388413 + 1.44958i 0.832717 + 0.553699i \(0.186784\pi\)
−0.444304 + 0.895876i \(0.646549\pi\)
\(458\) 10.4396 + 2.79728i 0.487810 + 0.130708i
\(459\) −2.78917 + 1.61033i −0.130187 + 0.0751637i
\(460\) 0 0
\(461\) 0.441317i 0.0205542i 0.999947 + 0.0102771i \(0.00327136\pi\)
−0.999947 + 0.0102771i \(0.996729\pi\)
\(462\) −2.57551 5.68133i −0.119823 0.264320i
\(463\) −26.0183 26.0183i −1.20917 1.20917i −0.971295 0.237877i \(-0.923548\pi\)
−0.237877 0.971295i \(-0.576452\pi\)
\(464\) −3.53653 2.04182i −0.164179 0.0947889i
\(465\) 0 0
\(466\) 6.27978 + 10.8769i 0.290905 + 0.503863i
\(467\) 18.9052 5.06565i 0.874831 0.234410i 0.206655 0.978414i \(-0.433742\pi\)
0.668175 + 0.744004i \(0.267076\pi\)
\(468\) 0.0968928 0.0968928i 0.00447887 0.00447887i
\(469\) −11.8100 + 31.3968i −0.545335 + 1.44977i
\(470\) 0 0
\(471\) 3.08582 5.34480i 0.142187 0.246275i
\(472\) −2.77334 + 10.3503i −0.127653 + 0.476409i
\(473\) 2.22259 8.29482i 0.102195 0.381396i
\(474\) −2.32116 + 4.02036i −0.106614 + 0.184661i
\(475\) 0 0
\(476\) 8.40698 1.38967i 0.385333 0.0636954i
\(477\) −5.90978 + 5.90978i −0.270590 + 0.270590i
\(478\) −15.4265 + 4.13351i −0.705590 + 0.189062i
\(479\) −15.3363 26.5632i −0.700732 1.21370i −0.968210 0.250140i \(-0.919523\pi\)
0.267477 0.963564i \(-0.413810\pi\)
\(480\) 0 0
\(481\) −1.16845 0.674604i −0.0532767 0.0307593i
\(482\) 19.3123 + 19.3123i 0.879649 + 0.879649i
\(483\) 0.833568 8.48019i 0.0379286 0.385862i
\(484\) 5.44132i 0.247333i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) −23.7975 6.37653i −1.07837 0.288948i −0.324441 0.945906i \(-0.605176\pi\)
−0.753927 + 0.656958i \(0.771843\pi\)
\(488\) 2.22456 + 8.30216i 0.100701 + 0.375821i
\(489\) −2.77324 −0.125410
\(490\) 0 0
\(491\) 3.08275 0.139122 0.0695612 0.997578i \(-0.477840\pi\)
0.0695612 + 0.997578i \(0.477840\pi\)
\(492\) −1.77627 6.62912i −0.0800804 0.298864i
\(493\) 12.7038 + 3.40398i 0.572152 + 0.153308i
\(494\) −0.103133 + 0.0595436i −0.00464015 + 0.00267899i
\(495\) 0 0
\(496\) 0.862973i 0.0387486i
\(497\) −1.32956 + 13.5261i −0.0596389 + 0.606729i
\(498\) −7.13020 7.13020i −0.319512 0.319512i
\(499\) −28.7283 16.5863i −1.28605 0.742503i −0.308105 0.951352i \(-0.599695\pi\)
−0.977948 + 0.208849i \(0.933028\pi\)
\(500\) 0 0
\(501\) −8.57834 14.8581i −0.383252 0.663812i
\(502\) 3.33427 0.893415i 0.148816 0.0398751i
\(503\) −23.7377 + 23.7377i −1.05841 + 1.05841i −0.0602259 + 0.998185i \(0.519182\pi\)
−0.998185 + 0.0602259i \(0.980818\pi\)
\(504\) 2.61033 0.431486i 0.116273 0.0192199i
\(505\) 0 0
\(506\) 3.79665 6.57599i 0.168782 0.292339i
\(507\) −3.35979 + 12.5389i −0.149213 + 0.556872i
\(508\) −3.52171 + 13.1432i −0.156251 + 0.583136i
\(509\) −13.6202 + 23.5908i −0.603703 + 1.04564i 0.388552 + 0.921427i \(0.372975\pi\)
−0.992255 + 0.124217i \(0.960358\pi\)
\(510\) 0 0
\(511\) −15.1416 + 40.2538i −0.669824 + 1.78072i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.839465 0.224934i 0.0370633 0.00993107i
\(514\) −3.85240 6.67255i −0.169922 0.294314i
\(515\) 0 0
\(516\) 3.15434 + 1.82116i 0.138862 + 0.0801720i
\(517\) −1.43869 1.43869i −0.0632736 0.0632736i
\(518\) −10.7560 23.7267i −0.472590 1.04249i
\(519\) 1.28463i 0.0563889i
\(520\) 0 0
\(521\) −10.8599 + 6.26995i −0.475780 + 0.274692i −0.718656 0.695366i \(-0.755242\pi\)
0.242876 + 0.970057i \(0.421909\pi\)
\(522\) 3.94449 + 1.05692i 0.172645 + 0.0462602i
\(523\) 0.432274 + 1.61327i 0.0189020 + 0.0705433i 0.974733 0.223375i \(-0.0717074\pi\)
−0.955831 + 0.293918i \(0.905041\pi\)
\(524\) 12.7500 0.556986
\(525\) 0 0
\(526\) −21.2207 −0.925265
\(527\) −0.719346 2.68464i −0.0313352 0.116945i
\(528\) 2.27735 + 0.610214i 0.0991089 + 0.0265562i
\(529\) −10.9356 + 6.31368i −0.475461 + 0.274508i
\(530\) 0 0
\(531\) 10.7154i 0.465008i
\(532\) −2.28834 0.224934i −0.0992119 0.00975212i
\(533\) −0.664973 0.664973i −0.0288032 0.0288032i
\(534\) 8.63484 + 4.98532i 0.373666 + 0.215736i
\(535\) 0 0
\(536\) −6.33933 10.9800i −0.273817 0.474265i
\(537\) 18.7213 5.01636i 0.807884 0.216472i
\(538\) −0.842382 + 0.842382i −0.0363177 + 0.0363177i
\(539\) −5.31103 15.6259i −0.228762 0.673055i
\(540\) 0 0
\(541\) −13.9661 + 24.1900i −0.600450 + 1.04001i 0.392303 + 0.919836i \(0.371678\pi\)
−0.992753 + 0.120174i \(0.961655\pi\)
\(542\) 2.10875 7.86998i 0.0905788 0.338045i
\(543\) 6.51999 24.3329i 0.279800 1.04423i
\(544\) −1.61033 + 2.78917i −0.0690423 + 0.119585i
\(545\) 0 0
\(546\) 0.280202 0.230047i 0.0119916 0.00984510i
\(547\) 3.01203 3.01203i 0.128785 0.128785i −0.639776 0.768561i \(-0.720973\pi\)
0.768561 + 0.639776i \(0.220973\pi\)
\(548\) −13.3330 + 3.57258i −0.569560 + 0.152613i
\(549\) −4.29751 7.44351i −0.183413 0.317681i
\(550\) 0 0
\(551\) −3.07352 1.77450i −0.130936 0.0755961i
\(552\) 2.27735 + 2.27735i 0.0969304 + 0.0969304i
\(553\) −7.15230 + 9.98510i −0.304147 + 0.424610i
\(554\) 16.7867i 0.713199i
\(555\) 0 0
\(556\) −12.0637 + 6.96496i −0.511614 + 0.295380i
\(557\) 20.8352 + 5.58276i 0.882814 + 0.236549i 0.671621 0.740895i \(-0.265598\pi\)
0.211193 + 0.977444i \(0.432265\pi\)
\(558\) −0.223354 0.833568i −0.00945532 0.0352877i
\(559\) 0.499096 0.0211095
\(560\) 0 0
\(561\) −7.59330 −0.320589
\(562\) 2.71897 + 10.1473i 0.114693 + 0.428039i
\(563\) −30.1081 8.06743i −1.26890 0.340002i −0.439293 0.898344i \(-0.644771\pi\)
−0.829611 + 0.558342i \(0.811438\pi\)
\(564\) 0.747356 0.431486i 0.0314694 0.0181689i
\(565\) 0 0
\(566\) 25.0053i 1.05105i
\(567\) −2.40971 + 1.09239i −0.101198 + 0.0458759i
\(568\) −3.63243 3.63243i −0.152413 0.152413i
\(569\) 2.12720 + 1.22814i 0.0891767 + 0.0514862i 0.543925 0.839134i \(-0.316938\pi\)
−0.454749 + 0.890620i \(0.650271\pi\)
\(570\) 0 0
\(571\) 4.62235 + 8.00615i 0.193439 + 0.335047i 0.946388 0.323033i \(-0.104702\pi\)
−0.752948 + 0.658080i \(0.771369\pi\)
\(572\) 0.312059 0.0836158i 0.0130478 0.00349615i
\(573\) −4.85285 + 4.85285i −0.202731 + 0.202731i
\(574\) −2.96128 17.9146i −0.123601 0.747742i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 12.0756 45.0669i 0.502715 1.87616i 0.0210977 0.999777i \(-0.493284\pi\)
0.481618 0.876381i \(-0.340049\pi\)
\(578\) −1.71529 + 6.40154i −0.0713465 + 0.266269i
\(579\) −1.38967 + 2.40698i −0.0577527 + 0.100031i
\(580\) 0 0
\(581\) −16.9288 20.6197i −0.702326 0.855449i
\(582\) −11.4245 + 11.4245i −0.473561 + 0.473561i
\(583\) −19.0334 + 5.09998i −0.788282 + 0.211219i
\(584\) −8.12764 14.0775i −0.336324 0.582530i
\(585\) 0 0
\(586\) 10.6096 + 6.12545i 0.438278 + 0.253040i
\(587\) −0.512695 0.512695i −0.0211612 0.0211612i 0.696447 0.717608i \(-0.254763\pi\)
−0.717608 + 0.696447i \(0.754763\pi\)
\(588\) 6.98483 0.460527i 0.288050 0.0189918i
\(589\) 0.749991i 0.0309028i
\(590\) 0 0
\(591\) −21.2692 + 12.2798i −0.874898 + 0.505123i
\(592\) 9.51079 + 2.54841i 0.390891 + 0.104739i
\(593\) −6.05324 22.5910i −0.248577 0.927701i −0.971552 0.236827i \(-0.923893\pi\)
0.722975 0.690874i \(-0.242774\pi\)
\(594\) −2.35769 −0.0967370
\(595\) 0 0
\(596\) −19.3817 −0.793907
\(597\) 2.72564 + 10.1722i 0.111553 + 0.416321i
\(598\) 0.426280 + 0.114221i 0.0174319 + 0.00467086i
\(599\) −9.39922 + 5.42664i −0.384042 + 0.221727i −0.679575 0.733606i \(-0.737836\pi\)
0.295534 + 0.955332i \(0.404503\pi\)
\(600\) 0 0
\(601\) 23.5701i 0.961443i −0.876873 0.480721i \(-0.840375\pi\)
0.876873 0.480721i \(-0.159625\pi\)
\(602\) 7.83421 + 5.61162i 0.319299 + 0.228713i
\(603\) 8.96516 + 8.96516i 0.365090 + 0.365090i
\(604\) −2.72590 1.57380i −0.110915 0.0640370i
\(605\) 0 0
\(606\) −0.315870 0.547103i −0.0128313 0.0222245i
\(607\) −28.3006 + 7.58314i −1.14869 + 0.307790i −0.782439 0.622727i \(-0.786025\pi\)
−0.366249 + 0.930517i \(0.619358\pi\)
\(608\) 0.614531 0.614531i 0.0249225 0.0249225i
\(609\) 10.1125 + 3.80385i 0.409780 + 0.154140i
\(610\) 0 0
\(611\) 0.0591253 0.102408i 0.00239195 0.00414299i
\(612\) 0.833568 3.11092i 0.0336950 0.125751i
\(613\) −0.813525 + 3.03612i −0.0328580 + 0.122628i −0.980407 0.196983i \(-0.936886\pi\)
0.947549 + 0.319611i \(0.103552\pi\)
\(614\) 4.44132 7.69259i 0.179237 0.310448i
\(615\) 0 0
\(616\) 5.83847 + 2.19615i 0.235239 + 0.0884855i
\(617\) −26.2183 + 26.2183i −1.05551 + 1.05551i −0.0571445 + 0.998366i \(0.518200\pi\)
−0.998366 + 0.0571445i \(0.981800\pi\)
\(618\) 1.57614 0.422325i 0.0634016 0.0169884i
\(619\) −11.7918 20.4240i −0.473953 0.820910i 0.525603 0.850730i \(-0.323840\pi\)
−0.999555 + 0.0298201i \(0.990507\pi\)
\(620\) 0 0
\(621\) −2.78917 1.61033i −0.111926 0.0646203i
\(622\) −9.93788 9.93788i −0.398473 0.398473i
\(623\) 21.4458 + 15.3615i 0.859206 + 0.615447i
\(624\) 0.137027i 0.00548547i
\(625\) 0 0
\(626\) 17.0578 9.84830i 0.681765 0.393617i
\(627\) 1.97919 + 0.530323i 0.0790414 + 0.0211791i
\(628\) 1.59734 + 5.96135i 0.0637408 + 0.237884i
\(629\) −31.7116 −1.26442
\(630\) 0 0
\(631\) −8.97684 −0.357362 −0.178681 0.983907i \(-0.557183\pi\)
−0.178681 + 0.983907i \(0.557183\pi\)
\(632\) −1.20152 4.48413i −0.0477939 0.178369i
\(633\) 13.2067 + 3.53872i 0.524918 + 0.140651i
\(634\) 2.06013 1.18942i 0.0818182 0.0472378i
\(635\) 0 0
\(636\) 8.35769i 0.331404i
\(637\) 0.797331 0.533206i 0.0315914 0.0211264i
\(638\) 6.80797 + 6.80797i 0.269530 + 0.269530i
\(639\) 4.44880 + 2.56851i 0.175992 + 0.101609i
\(640\) 0 0
\(641\) 6.96802 + 12.0690i 0.275220 + 0.476695i 0.970191 0.242343i \(-0.0779160\pi\)
−0.694971 + 0.719038i \(0.744583\pi\)
\(642\) 14.5929 3.91015i 0.575936 0.154321i
\(643\) −25.1156 + 25.1156i −0.990461 + 0.990461i −0.999955 0.00949415i \(-0.996978\pi\)
0.00949415 + 0.999955i \(0.496978\pi\)
\(644\) 5.40698 + 6.58582i 0.213065 + 0.259518i
\(645\) 0 0
\(646\) −1.39950 + 2.42401i −0.0550627 + 0.0953713i
\(647\) −11.0458 + 41.2236i −0.434256 + 1.62067i 0.308583 + 0.951197i \(0.400145\pi\)
−0.742839 + 0.669470i \(0.766521\pi\)
\(648\) 0.258819 0.965926i 0.0101674 0.0379452i
\(649\) 12.6317 21.8788i 0.495839 0.858819i
\(650\) 0 0
\(651\) −0.372361 2.25264i −0.0145940 0.0882881i
\(652\) 1.96097 1.96097i 0.0767977 0.0767977i
\(653\) 29.4978 7.90392i 1.15434 0.309304i 0.369637 0.929176i \(-0.379482\pi\)
0.784703 + 0.619872i \(0.212815\pi\)
\(654\) 4.30648 + 7.45905i 0.168397 + 0.291672i
\(655\) 0 0
\(656\) 5.94351 + 3.43149i 0.232055 + 0.133977i
\(657\) 11.4942 + 11.4942i 0.448432 + 0.448432i
\(658\) 2.07951 0.942700i 0.0810678 0.0367503i
\(659\) 29.4442i 1.14698i −0.819211 0.573492i \(-0.805588\pi\)
0.819211 0.573492i \(-0.194412\pi\)
\(660\) 0 0
\(661\) 11.4306 6.59945i 0.444598 0.256689i −0.260948 0.965353i \(-0.584035\pi\)
0.705546 + 0.708664i \(0.250702\pi\)
\(662\) −26.7426 7.16567i −1.03938 0.278502i
\(663\) −0.114221 0.426280i −0.00443599 0.0165553i
\(664\) 10.0836 0.391321
\(665\) 0 0
\(666\) −9.84629 −0.381536
\(667\) 3.40398 + 12.7038i 0.131803 + 0.491895i
\(668\) 16.5721 + 4.44048i 0.641193 + 0.171807i
\(669\) −7.86666 + 4.54182i −0.304142 + 0.175597i
\(670\) 0 0
\(671\) 20.2644i 0.782297i
\(672\) −1.54067 + 2.15089i −0.0594328 + 0.0829723i
\(673\) −8.91749 8.91749i −0.343744 0.343744i 0.514029 0.857773i \(-0.328152\pi\)
−0.857773 + 0.514029i \(0.828152\pi\)
\(674\) −3.90169 2.25264i −0.150288 0.0867686i
\(675\) 0 0
\(676\) −6.49061 11.2421i −0.249639 0.432387i
\(677\) 40.5930 10.8769i 1.56011 0.418031i 0.627415 0.778685i \(-0.284113\pi\)
0.932700 + 0.360654i \(0.117446\pi\)
\(678\) 12.4298 12.4298i 0.477362 0.477362i
\(679\) −33.0383 + 27.1245i −1.26789 + 1.04094i
\(680\) 0 0
\(681\) 7.77450 13.4658i 0.297919 0.516011i
\(682\) 0.526598 1.96529i 0.0201645 0.0752549i
\(683\) 1.11168 4.14885i 0.0425373 0.158751i −0.941390 0.337319i \(-0.890480\pi\)
0.983928 + 0.178568i \(0.0571465\pi\)
\(684\) −0.434539 + 0.752644i −0.0166150 + 0.0287780i
\(685\) 0 0
\(686\) 18.5107 + 0.595211i 0.706742 + 0.0227253i
\(687\) 7.64231 7.64231i 0.291572 0.291572i
\(688\) −3.51821 + 0.942700i −0.134130 + 0.0359401i
\(689\) −0.572615 0.991798i −0.0218149 0.0377845i
\(690\) 0 0
\(691\) 32.4983 + 18.7629i 1.23629 + 0.713773i 0.968334 0.249657i \(-0.0803180\pi\)
0.267958 + 0.963431i \(0.413651\pi\)
\(692\) 0.908369 + 0.908369i 0.0345310 + 0.0345310i
\(693\) −6.20793 0.610214i −0.235820 0.0231801i
\(694\) 5.78843i 0.219726i
\(695\) 0 0
\(696\) −3.53653 + 2.04182i −0.134052 + 0.0773948i
\(697\) −21.3501 5.72075i −0.808694 0.216689i
\(698\) −5.08130 18.9637i −0.192330 0.717785i
\(699\) 12.5596 0.475046
\(700\) 0 0
\(701\) 12.7644 0.482104 0.241052 0.970512i \(-0.422508\pi\)
0.241052 + 0.970512i \(0.422508\pi\)
\(702\) −0.0354652 0.132358i −0.00133855 0.00499553i
\(703\) 8.26562 + 2.21477i 0.311744 + 0.0835315i
\(704\) −2.04182 + 1.17884i −0.0769538 + 0.0444293i
\(705\) 0 0
\(706\) 26.0331i 0.979770i
\(707\) −0.690104 1.52231i −0.0259541 0.0572523i
\(708\) 7.57691 + 7.57691i 0.284758 + 0.284758i
\(709\) −43.1134 24.8916i −1.61916 0.934822i −0.987138 0.159872i \(-0.948892\pi\)
−0.632022 0.774951i \(-0.717775\pi\)
\(710\) 0 0
\(711\) 2.32116 + 4.02036i 0.0870502 + 0.150775i
\(712\) −9.63091 + 2.58059i −0.360934 + 0.0967118i
\(713\) 1.96529 1.96529i 0.0736007 0.0736007i
\(714\) 3.00000 7.97549i 0.112272 0.298475i
\(715\) 0 0
\(716\) −9.69087 + 16.7851i −0.362165 + 0.627288i
\(717\) −4.13351 + 15.4265i −0.154369 + 0.576112i
\(718\) −1.91601 + 7.15063i −0.0715047 + 0.266859i
\(719\) −23.1988 + 40.1815i −0.865169 + 1.49852i 0.00171077 + 0.999999i \(0.499455\pi\)
−0.866880 + 0.498518i \(0.833878\pi\)
\(720\) 0 0
\(721\) 4.25938 0.704074i 0.158628 0.0262211i
\(722\) −12.9010 + 12.9010i −0.480124 + 0.480124i
\(723\) 26.3810 7.06878i 0.981121 0.262891i
\(724\) 12.5957 + 21.8163i 0.468114 + 0.810797i
\(725\) 0 0
\(726\) 4.71232 + 2.72066i 0.174891 + 0.100973i
\(727\) −16.5504 16.5504i −0.613820 0.613820i 0.330119 0.943939i \(-0.392911\pi\)
−0.943939 + 0.330119i \(0.892911\pi\)
\(728\) −0.0354652 + 0.360801i −0.00131443 + 0.0133722i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 10.1590 5.86533i 0.375746 0.216937i
\(732\) 8.30216 + 2.22456i 0.306856 + 0.0822219i
\(733\) 10.0281 + 37.4254i 0.370396 + 1.38234i 0.859956 + 0.510368i \(0.170491\pi\)
−0.489560 + 0.871970i \(0.662842\pi\)
\(734\) 12.0692 0.445484
\(735\) 0 0
\(736\) −3.22066 −0.118715
\(737\) 7.73669 + 28.8737i 0.284985 + 1.06358i
\(738\) −6.62912 1.77627i −0.244021 0.0653853i
\(739\) 34.4840 19.9093i 1.26851 0.732377i 0.293807 0.955865i \(-0.405078\pi\)
0.974707 + 0.223488i \(0.0717444\pi\)
\(740\) 0 0
\(741\) 0.119087i 0.00437478i
\(742\) 2.16313 22.0063i 0.0794109 0.807877i
\(743\) −28.0880 28.0880i −1.03045 1.03045i −0.999522 0.0309276i \(-0.990154\pi\)
−0.0309276 0.999522i \(-0.509846\pi\)
\(744\) 0.747356 + 0.431486i 0.0273994 + 0.0158191i
\(745\) 0 0
\(746\) −0.0595436 0.103133i −0.00218005 0.00377595i
\(747\) −9.74004 + 2.60984i −0.356369 + 0.0954889i
\(748\) 5.36927 5.36927i 0.196320 0.196320i
\(749\) 39.4360 6.51876i 1.44096 0.238190i
\(750\) 0 0
\(751\) −16.5445 + 28.6558i −0.603716 + 1.04567i 0.388538 + 0.921433i \(0.372980\pi\)
−0.992253 + 0.124233i \(0.960353\pi\)
\(752\) −0.223354 + 0.833568i −0.00814488 + 0.0303971i
\(753\) 0.893415 3.33427i 0.0325579 0.121508i
\(754\) −0.279784 + 0.484600i −0.0101891 + 0.0176481i
\(755\) 0 0
\(756\) 0.931486 2.47635i 0.0338778 0.0900642i
\(757\) −8.48469 + 8.48469i −0.308381 + 0.308381i −0.844281 0.535900i \(-0.819972\pi\)
0.535900 + 0.844281i \(0.319972\pi\)
\(758\) −8.53686 + 2.28744i −0.310073 + 0.0830837i
\(759\) −3.79665 6.57599i −0.137810 0.238693i
\(760\) 0 0
\(761\) 25.4199 + 14.6762i 0.921471 + 0.532011i 0.884104 0.467290i \(-0.154770\pi\)
0.0373669 + 0.999302i \(0.488103\pi\)
\(762\) 9.62150 + 9.62150i 0.348550 + 0.348550i
\(763\) 9.40869 + 20.7547i 0.340617 + 0.751371i
\(764\) 6.86297i 0.248294i
\(765\) 0 0
\(766\) 33.5031 19.3430i 1.21052 0.698891i
\(767\) 1.41827 + 0.380023i 0.0512106 + 0.0137218i
\(768\) −0.258819 0.965926i −0.00933933 0.0348548i
\(769\) 21.4307 0.772812 0.386406 0.922329i \(-0.373716\pi\)
0.386406 + 0.922329i \(0.373716\pi\)
\(770\) 0 0
\(771\) −7.70480 −0.277482
\(772\) −0.719346 2.68464i −0.0258898 0.0966222i
\(773\) 11.0747 + 2.96745i 0.398329 + 0.106732i 0.452422 0.891804i \(-0.350560\pi\)
−0.0540931 + 0.998536i \(0.517227\pi\)
\(774\) 3.15434 1.82116i 0.113380 0.0654601i
\(775\) 0 0
\(776\) 16.1567i 0.579991i
\(777\) −25.9259 2.54841i −0.930086 0.0914236i
\(778\) 21.4742 + 21.4742i 0.769888 + 0.769888i
\(779\) 5.16537 + 2.98223i 0.185069 + 0.106849i
\(780\) 0 0
\(781\) 6.05575 + 10.4889i 0.216692 + 0.375321i
\(782\) 10.0192 2.68464i 0.358286