Properties

Label 1050.2.bc.f.493.4
Level $1050$
Weight $2$
Character 1050.493
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 493.4
Root \(-1.44378 + 0.833568i\) of defining polynomial
Character \(\chi\) \(=\) 1050.493
Dual form 1050.2.bc.f.607.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(2.63306 - 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.17884 - 2.04182i) q^{11} +(0.258819 - 0.965926i) q^{12} +(-0.0968928 + 0.0968928i) q^{13} +(2.61033 + 0.431486i) q^{14} +(0.500000 + 0.866025i) q^{16} +(3.11092 - 0.833568i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-0.434539 - 0.752644i) q^{19} +(-0.931486 - 2.47635i) q^{21} +(1.66714 - 1.66714i) q^{22} +(-0.833568 + 3.11092i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.118669 + 0.0685135i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.40971 + 1.09239i) q^{28} -4.08363i q^{29} +(-0.747356 - 0.431486i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.27735 - 0.610214i) q^{33} +3.22066 q^{34} -1.00000 q^{36} +(9.51079 + 2.54841i) q^{37} +(-0.224934 - 0.839465i) q^{38} +(0.118669 + 0.0685135i) q^{39} -6.86297i q^{41} +(-0.258819 - 2.63306i) q^{42} +(2.57551 + 2.57551i) q^{43} +(2.04182 - 1.17884i) q^{44} +(-1.61033 + 2.78917i) q^{46} +(0.223354 - 0.833568i) q^{47} +(0.707107 - 0.707107i) q^{48} +(6.86603 - 1.36297i) q^{49} +(-1.61033 - 2.78917i) q^{51} +(-0.132358 + 0.0354652i) q^{52} +(-8.07290 + 2.16313i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.04487 + 1.67884i) q^{56} +(-0.614531 + 0.614531i) q^{57} +(1.05692 - 3.94449i) q^{58} +(5.35769 - 9.27978i) q^{59} +(-7.44351 + 4.29751i) q^{61} +(-0.610214 - 0.610214i) q^{62} +(-2.15089 + 1.54067i) q^{63} +1.00000i q^{64} +(-2.04182 - 1.17884i) q^{66} +(3.28148 + 12.2466i) q^{67} +(3.11092 + 0.833568i) q^{68} +3.22066 q^{69} +5.13703 q^{71} +(-0.965926 - 0.258819i) q^{72} +(-4.20718 - 15.7014i) q^{73} +(8.52714 + 4.92315i) q^{74} -0.869078i q^{76} +(2.57551 - 5.68133i) q^{77} +(0.0968928 + 0.0968928i) q^{78} +(-4.02036 + 2.32116i) q^{79} +(0.500000 - 0.866025i) q^{81} +(1.77627 - 6.62912i) q^{82} +(-7.13020 + 7.13020i) q^{83} +(0.431486 - 2.61033i) q^{84} +(1.82116 + 3.15434i) q^{86} +(-3.94449 + 1.05692i) q^{87} +(2.27735 - 0.610214i) q^{88} +(-4.98532 - 8.63484i) q^{89} +(-0.230047 + 0.280202i) q^{91} +(-2.27735 + 2.27735i) q^{92} +(-0.223354 + 0.833568i) q^{93} +(0.431486 - 0.747356i) q^{94} +(0.866025 - 0.500000i) q^{96} +(11.4245 + 11.4245i) q^{97} +(6.98483 + 0.460527i) 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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 2.63306 0.258819i 0.995204 0.0978244i
\(8\) 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 −0.631758 0.775166i \(-0.717666\pi\)
0.987192 + 0.159535i \(0.0509996\pi\)
\(12\) 0.258819 0.965926i 0.0747146 0.278839i
\(13\) −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
\(17\) 3.11092 0.833568i 0.754508 0.202170i 0.138991 0.990294i \(-0.455614\pi\)
0.615517 + 0.788124i \(0.288947\pi\)
\(18\) −0.965926 + 0.258819i −0.227671 + 0.0610042i
\(19\) −0.434539 0.752644i −0.0996901 0.172668i 0.811866 0.583843i \(-0.198452\pi\)
−0.911556 + 0.411175i \(0.865118\pi\)
\(20\) 0 0
\(21\) −0.931486 2.47635i −0.203267 0.540385i
\(22\) 1.66714 1.66714i 0.355435 0.355435i
\(23\) −0.833568 + 3.11092i −0.173811 + 0.648671i 0.822940 + 0.568128i \(0.192332\pi\)
−0.996751 + 0.0805432i \(0.974335\pi\)
\(24\) 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
\(28\) 2.40971 + 1.09239i 0.455392 + 0.206442i
\(29\) 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 0.431382 0.902170i \(-0.358026\pi\)
−0.565611 + 0.824672i \(0.691360\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) −2.27735 0.610214i −0.396436 0.106225i
\(34\) 3.22066 0.552338
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 9.51079 + 2.54841i 1.56356 + 0.418956i 0.933790 0.357822i \(-0.116481\pi\)
0.629774 + 0.776778i \(0.283147\pi\)
\(38\) −0.224934 0.839465i −0.0364891 0.136179i
\(39\) 0.118669 + 0.0685135i 0.0190022 + 0.0109709i
\(40\) 0 0
\(41\) 6.86297i 1.07182i −0.844276 0.535908i \(-0.819969\pi\)
0.844276 0.535908i \(-0.180031\pi\)
\(42\) −0.258819 2.63306i −0.0399366 0.406290i
\(43\) 2.57551 + 2.57551i 0.392761 + 0.392761i 0.875670 0.482909i \(-0.160420\pi\)
−0.482909 + 0.875670i \(0.660420\pi\)
\(44\) 2.04182 1.17884i 0.307815 0.177717i
\(45\) 0 0
\(46\) −1.61033 + 2.78917i −0.237430 + 0.411241i
\(47\) 0.223354 0.833568i 0.0325795 0.121588i −0.947721 0.319100i \(-0.896619\pi\)
0.980301 + 0.197512i \(0.0632861\pi\)
\(48\) 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
\(52\) −0.132358 + 0.0354652i −0.0183548 + 0.00491814i
\(53\) −8.07290 + 2.16313i −1.10890 + 0.297129i −0.766383 0.642384i \(-0.777946\pi\)
−0.342516 + 0.939512i \(0.611279\pi\)
\(54\) 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
\(58\) 1.05692 3.94449i 0.138781 0.517936i
\(59\) 5.35769 9.27978i 0.697511 1.20812i −0.271815 0.962349i \(-0.587624\pi\)
0.969327 0.245776i \(-0.0790426\pi\)
\(60\) 0 0
\(61\) −7.44351 + 4.29751i −0.953044 + 0.550240i −0.894025 0.448017i \(-0.852130\pi\)
−0.0590186 + 0.998257i \(0.518797\pi\)
\(62\) −0.610214 0.610214i −0.0774973 0.0774973i
\(63\) −2.15089 + 1.54067i −0.270986 + 0.194107i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −2.04182 1.17884i −0.251330 0.145106i
\(67\) 3.28148 + 12.2466i 0.400896 + 1.49617i 0.811501 + 0.584352i \(0.198651\pi\)
−0.410604 + 0.911814i \(0.634682\pi\)
\(68\) 3.11092 + 0.833568i 0.377254 + 0.101085i
\(69\) 3.22066 0.387722
\(70\) 0 0
\(71\) 5.13703 0.609653 0.304826 0.952408i \(-0.401402\pi\)
0.304826 + 0.952408i \(0.401402\pi\)
\(72\) −0.965926 0.258819i −0.113835 0.0305021i
\(73\) −4.20718 15.7014i −0.492413 1.83771i −0.544064 0.839044i \(-0.683115\pi\)
0.0516512 0.998665i \(-0.483552\pi\)
\(74\) 8.52714 + 4.92315i 0.991260 + 0.572304i
\(75\) 0 0
\(76\) 0.869078i 0.0996901i
\(77\) 2.57551 5.68133i 0.293506 0.647448i
\(78\) 0.0968928 + 0.0968928i 0.0109709 + 0.0109709i
\(79\) −4.02036 + 2.32116i −0.452326 + 0.261151i −0.708812 0.705397i \(-0.750769\pi\)
0.256486 + 0.966548i \(0.417435\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 1.77627 6.62912i 0.196156 0.732064i
\(83\) −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
\(87\) −3.94449 + 1.05692i −0.422893 + 0.113314i
\(88\) 2.27735 0.610214i 0.242766 0.0650490i
\(89\) −4.98532 8.63484i −0.528443 0.915291i −0.999450 0.0331611i \(-0.989443\pi\)
0.471007 0.882130i \(-0.343891\pi\)
\(90\) 0 0
\(91\) −0.230047 + 0.280202i −0.0241155 + 0.0293732i
\(92\) −2.27735 + 2.27735i −0.237430 + 0.237430i
\(93\) −0.223354 + 0.833568i −0.0231607 + 0.0864370i
\(94\) 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 \(0.443845\pi\)
\(98\) 6.98483 + 0.460527i 0.705575 + 0.0465203i
\(99\) 2.35769i 0.236956i
\(100\) 0 0
\(101\) −0.547103 0.315870i −0.0544388 0.0314302i 0.472534 0.881313i \(-0.343340\pi\)
−0.526972 + 0.849882i \(0.676673\pi\)
\(102\) −0.833568 3.11092i −0.0825355 0.308027i
\(103\) 1.57614 + 0.422325i 0.155302 + 0.0416130i 0.335632 0.941993i \(-0.391050\pi\)
−0.180331 + 0.983606i \(0.557717\pi\)
\(104\) −0.137027 −0.0134366
\(105\) 0 0
\(106\) −8.35769 −0.811770
\(107\) −14.5929 3.91015i −1.41075 0.378009i −0.528556 0.848898i \(-0.677266\pi\)
−0.882192 + 0.470889i \(0.843933\pi\)
\(108\) 0.258819 + 0.965926i 0.0249049 + 0.0929463i
\(109\) −7.45905 4.30648i −0.714447 0.412486i 0.0982585 0.995161i \(-0.468673\pi\)
−0.812705 + 0.582675i \(0.802006\pi\)
\(110\) 0 0
\(111\) 9.84629i 0.934569i
\(112\) 1.54067 + 2.15089i 0.145580 + 0.203240i
\(113\) 12.4298 + 12.4298i 1.16929 + 1.16929i 0.982375 + 0.186919i \(0.0598501\pi\)
0.186919 + 0.982375i \(0.440150\pi\)
\(114\) −0.752644 + 0.434539i −0.0704915 + 0.0406983i
\(115\) 0 0
\(116\) 2.04182 3.53653i 0.189578 0.328358i
\(117\) 0.0354652 0.132358i 0.00327876 0.0122365i
\(118\) 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
\(122\) −8.30216 + 2.22456i −0.751642 + 0.201402i
\(123\) −6.62912 + 1.77627i −0.597728 + 0.160161i
\(124\) −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 −0.990595 0.136825i \(-0.956310\pi\)
0.136825 + 0.990595i \(0.456310\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) 1.82116 3.15434i 0.160344 0.277724i
\(130\) 0 0
\(131\) −11.0418 + 6.37500i −0.964728 + 0.556986i −0.897625 0.440760i \(-0.854709\pi\)
−0.0671030 + 0.997746i \(0.521376\pi\)
\(132\) −1.66714 1.66714i −0.145106 0.145106i
\(133\) −1.33897 1.86929i −0.116103 0.162088i
\(134\) 12.6787i 1.09527i
\(135\) 0 0
\(136\) 2.78917 + 1.61033i 0.239170 + 0.138085i
\(137\) 3.57258 + 13.3330i 0.305226 + 1.13912i 0.932751 + 0.360522i \(0.117402\pi\)
−0.627525 + 0.778597i \(0.715932\pi\)
\(138\) 3.11092 + 0.833568i 0.264819 + 0.0709580i
\(139\) −13.9299 −1.18152 −0.590760 0.806847i \(-0.701172\pi\)
−0.590760 + 0.806847i \(0.701172\pi\)
\(140\) 0 0
\(141\) −0.862973 −0.0726754
\(142\) 4.96199 + 1.32956i 0.416401 + 0.111574i
\(143\) 0.0836158 + 0.312059i 0.00699231 + 0.0260957i
\(144\) −0.866025 0.500000i −0.0721688 0.0416667i
\(145\) 0 0
\(146\) 16.2553i 1.34530i
\(147\) −3.09359 6.27931i −0.255155 0.517909i
\(148\) 6.96238 + 6.96238i 0.572304 + 0.572304i
\(149\) −16.7851 + 9.69087i −1.37509 + 0.793907i −0.991563 0.129625i \(-0.958623\pi\)
−0.383523 + 0.923531i \(0.625289\pi\)
\(150\) 0 0
\(151\) 1.57380 2.72590i 0.128074 0.221831i −0.794856 0.606798i \(-0.792454\pi\)
0.922930 + 0.384967i \(0.125787\pi\)
\(152\) 0.224934 0.839465i 0.0182445 0.0680896i
\(153\) −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
\(157\) −5.96135 + 1.59734i −0.475768 + 0.127482i −0.488731 0.872434i \(-0.662540\pi\)
0.0129635 + 0.999916i \(0.495873\pi\)
\(158\) −4.48413 + 1.20152i −0.356738 + 0.0955877i
\(159\) 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
\(163\) −0.717766 + 2.67874i −0.0562198 + 0.209815i −0.988322 0.152380i \(-0.951306\pi\)
0.932102 + 0.362196i \(0.117973\pi\)
\(164\) 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 \(0.981063\pi\)
\(168\) 1.09239 2.40971i 0.0842795 0.185913i
\(169\) 12.9812i 0.998556i
\(170\) 0 0
\(171\) 0.752644 + 0.434539i 0.0575561 + 0.0332300i
\(172\) 0.942700 + 3.51821i 0.0718802 + 0.268261i
\(173\) 1.24086 + 0.332486i 0.0943405 + 0.0252785i 0.305681 0.952134i \(-0.401116\pi\)
−0.211340 + 0.977413i \(0.567783\pi\)
\(174\) −4.08363 −0.309579
\(175\) 0 0
\(176\) 2.35769 0.177717
\(177\) −10.3503 2.77334i −0.777973 0.208457i
\(178\) −2.58059 9.63091i −0.193424 0.721867i
\(179\) −16.7851 9.69087i −1.25458 0.724329i −0.282560 0.959249i \(-0.591184\pi\)
−0.972015 + 0.234920i \(0.924517\pi\)
\(180\) 0 0
\(181\) 25.1913i 1.87246i 0.351394 + 0.936228i \(0.385708\pi\)
−0.351394 + 0.936228i \(0.614292\pi\)
\(182\) −0.294730 + 0.211114i −0.0218468 + 0.0156488i
\(183\) 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
\(187\) 1.96529 7.33457i 0.143716 0.536357i
\(188\) 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 0.714759 0.699371i \(-0.246536\pi\)
−0.963052 + 0.269314i \(0.913203\pi\)
\(192\) 0.965926 0.258819i 0.0697097 0.0186787i
\(193\) −2.68464 + 0.719346i −0.193244 + 0.0517797i −0.354143 0.935191i \(-0.615227\pi\)
0.160899 + 0.986971i \(0.448561\pi\)
\(194\) 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 \(-0.410928\pi\)
0.961103 0.276190i \(-0.0890720\pi\)
\(198\) −0.610214 + 2.27735i −0.0433660 + 0.161844i
\(199\) −5.26553 + 9.12016i −0.373263 + 0.646511i −0.990065 0.140607i \(-0.955095\pi\)
0.616802 + 0.787118i \(0.288428\pi\)
\(200\) 0 0
\(201\) 10.9800 6.33933i 0.774472 0.447142i
\(202\) −0.446708 0.446708i −0.0314302 0.0314302i
\(203\) −1.05692 10.7525i −0.0741814 0.754674i
\(204\) 3.22066i 0.225491i
\(205\) 0 0
\(206\) 1.41313 + 0.815870i 0.0984573 + 0.0568444i
\(207\) −0.833568 3.11092i −0.0579370 0.216224i
\(208\) −0.132358 0.0354652i −0.00917738 0.00245907i
\(209\) −2.04901 −0.141733
\(210\) 0 0
\(211\) 13.6726 0.941257 0.470629 0.882331i \(-0.344027\pi\)
0.470629 + 0.882331i \(0.344027\pi\)
\(212\) −8.07290 2.16313i −0.554449 0.148564i
\(213\) −1.32956 4.96199i −0.0911000 0.339990i
\(214\) −13.0836 7.55384i −0.894379 0.516370i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −2.07951 0.942700i −0.141167 0.0639947i
\(218\) −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
\(222\) 2.54841 9.51079i 0.171038 0.638322i
\(223\) −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
\(227\) −15.0192 + 4.02438i −0.996858 + 0.267107i −0.720128 0.693841i \(-0.755917\pi\)
−0.276729 + 0.960948i \(0.589250\pi\)
\(228\) −0.839465 + 0.224934i −0.0555949 + 0.0148966i
\(229\) −5.40393 9.35988i −0.357102 0.618518i 0.630374 0.776292i \(-0.282902\pi\)
−0.987475 + 0.157774i \(0.949568\pi\)
\(230\) 0 0
\(231\) −6.15434 1.01731i −0.404926 0.0669341i
\(232\) 2.88756 2.88756i 0.189578 0.189578i
\(233\) 3.25066 12.1316i 0.212958 0.794768i −0.773918 0.633286i \(-0.781706\pi\)
0.986876 0.161483i \(-0.0516275\pi\)
\(234\) 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
\(238\) 8.48019 0.833568i 0.549689 0.0540322i
\(239\) 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 0.999610 + 0.0279230i \(0.00888932\pi\)
0.523987 + 0.851726i \(0.324444\pi\)
\(242\) 1.40832 + 5.25591i 0.0905300 + 0.337863i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) −8.59502 −0.550240
\(245\) 0 0
\(246\) −6.86297 −0.437567
\(247\) 0.115029 + 0.0308220i 0.00731915 + 0.00196116i
\(248\) −0.223354 0.833568i −0.0141830 0.0529316i
\(249\) 8.73268 + 5.04182i 0.553411 + 0.319512i
\(250\) 0 0
\(251\) 3.45189i 0.217881i 0.994048 + 0.108941i \(0.0347459\pi\)
−0.994048 + 0.108941i \(0.965254\pi\)
\(252\) −2.63306 + 0.258819i −0.165867 + 0.0163041i
\(253\) 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
\(257\) 1.99415 7.44226i 0.124392 0.464236i −0.875426 0.483353i \(-0.839419\pi\)
0.999817 + 0.0191171i \(0.00608554\pi\)
\(258\) 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
\(262\) −12.3155 + 3.29994i −0.760857 + 0.203871i
\(263\) −20.4976 + 5.49231i −1.26394 + 0.338670i −0.827704 0.561164i \(-0.810354\pi\)
−0.436231 + 0.899835i \(0.643687\pi\)
\(264\) −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
\(268\) −3.28148 + 12.2466i −0.200448 + 0.748083i
\(269\) −0.595654 + 1.03170i −0.0363177 + 0.0629041i −0.883613 0.468218i \(-0.844896\pi\)
0.847295 + 0.531122i \(0.178229\pi\)
\(270\) 0 0
\(271\) −7.05603 + 4.07380i −0.428623 + 0.247466i −0.698760 0.715356i \(-0.746264\pi\)
0.270137 + 0.962822i \(0.412931\pi\)
\(272\) 2.27735 + 2.27735i 0.138085 + 0.138085i
\(273\) 0.330195 + 0.149687i 0.0199843 + 0.00905944i
\(274\) 13.8034i 0.833893i
\(275\) 0 0
\(276\) 2.78917 + 1.61033i 0.167888 + 0.0969304i
\(277\) 4.34472 + 16.2147i 0.261049 + 0.974248i 0.964625 + 0.263627i \(0.0849189\pi\)
−0.703576 + 0.710620i \(0.748414\pi\)
\(278\) −13.4553 3.60533i −0.806994 0.216233i
\(279\) 0.862973 0.0516648
\(280\) 0 0
\(281\) 10.5053 0.626693 0.313346 0.949639i \(-0.398550\pi\)
0.313346 + 0.949639i \(0.398550\pi\)
\(282\) −0.833568 0.223354i −0.0496382 0.0133005i
\(283\) −6.47184 24.1532i −0.384711 1.43576i −0.838622 0.544714i \(-0.816638\pi\)
0.453911 0.891047i \(-0.350028\pi\)
\(284\) 4.44880 + 2.56851i 0.263987 + 0.152413i
\(285\) 0 0
\(286\) 0.323067i 0.0191033i
\(287\) −1.77627 18.0706i −0.104850 1.06668i
\(288\) −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
\(292\) 4.20718 15.7014i 0.246206 0.918855i
\(293\) 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
\(297\) 2.27735 0.610214i 0.132145 0.0354082i
\(298\) −18.7213 + 5.01636i −1.08450 + 0.290590i
\(299\) −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
\(303\) −0.163506 + 0.610214i −0.00939319 + 0.0350559i
\(304\) 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 \(0.831575\pi\)
\(308\) 5.07112 3.63243i 0.288954 0.206977i
\(309\) 1.63174i 0.0928264i
\(310\) 0 0
\(311\) −12.1714 7.02714i −0.690175 0.398473i 0.113503 0.993538i \(-0.463793\pi\)
−0.803678 + 0.595065i \(0.797126\pi\)
\(312\) 0.0354652 + 0.132358i 0.00200782 + 0.00749330i
\(313\) 19.0255 + 5.09785i 1.07538 + 0.288148i 0.752703 0.658361i \(-0.228750\pi\)
0.322679 + 0.946508i \(0.395416\pi\)
\(314\) −6.17165 −0.348286
\(315\) 0 0
\(316\) −4.64231 −0.261151
\(317\) −2.29778 0.615688i −0.129056 0.0345805i 0.193713 0.981058i \(-0.437947\pi\)
−0.322769 + 0.946478i \(0.604614\pi\)
\(318\) 2.16313 + 8.07290i 0.121302 + 0.452706i
\(319\) −8.33802 4.81396i −0.466840 0.269530i
\(320\) 0 0
\(321\) 15.1077i 0.843228i
\(322\) −3.51821 + 7.76085i −0.196062 + 0.432495i
\(323\) −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
\(327\) −2.22920 + 8.31948i −0.123275 + 0.460069i
\(328\) 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 −0.942397 0.334496i \(-0.891434\pi\)
0.181516 0.983388i \(-0.441899\pi\)
\(332\) −9.74004 + 2.60984i −0.534554 + 0.143233i
\(333\) −9.51079 + 2.54841i −0.521188 + 0.139652i
\(334\) −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 −0.614994 0.788532i \(-0.710842\pi\)
0.788532 + 0.614994i \(0.210842\pi\)
\(338\) −3.35979 + 12.5389i −0.182748 + 0.682026i
\(339\) 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
\(343\) 17.7259 5.36585i 0.957109 0.289729i
\(344\) 3.64231i 0.196380i
\(345\) 0 0
\(346\) 1.11252 + 0.642314i 0.0598095 + 0.0345310i
\(347\) −1.49816 5.59119i −0.0804252 0.300151i 0.913983 0.405752i \(-0.132990\pi\)
−0.994409 + 0.105601i \(0.966324\pi\)
\(348\) −3.94449 1.05692i −0.211447 0.0566569i
\(349\) 19.6326 1.05091 0.525455 0.850821i \(-0.323895\pi\)
0.525455 + 0.850821i \(0.323895\pi\)
\(350\) 0 0
\(351\) −0.137027 −0.00731396
\(352\) 2.27735 + 0.610214i 0.121383 + 0.0325245i
\(353\) −6.73787 25.1461i −0.358621 1.33839i −0.875866 0.482554i \(-0.839709\pi\)
0.517246 0.855837i \(-0.326957\pi\)
\(354\) −9.27978 5.35769i −0.493215 0.284758i
\(355\) 0 0
\(356\) 9.97065i 0.528443i
\(357\) −4.96199 6.92728i −0.262616 0.366630i
\(358\) −13.7050 13.7050i −0.724329 0.724329i
\(359\) −6.41108 + 3.70144i −0.338364 + 0.195355i −0.659548 0.751662i \(-0.729252\pi\)
0.321184 + 0.947017i \(0.395919\pi\)
\(360\) 0 0
\(361\) 9.12235 15.8004i 0.480124 0.831599i
\(362\) −6.51999 + 24.3329i −0.342683 + 1.27891i
\(363\) 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
\(367\) −11.6580 + 3.12375i −0.608542 + 0.163058i −0.549914 0.835222i \(-0.685339\pi\)
−0.0586284 + 0.998280i \(0.518673\pi\)
\(368\) −3.11092 + 0.833568i −0.162168 + 0.0434527i
\(369\) 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
\(373\) −0.0308220 + 0.115029i −0.00159590 + 0.00595600i −0.966719 0.255840i \(-0.917648\pi\)
0.965123 + 0.261796i \(0.0843147\pi\)
\(374\) 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
\(378\) 1.54067 + 2.15089i 0.0792438 + 0.110630i
\(379\) 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
\(382\) −1.77627 6.62912i −0.0908818 0.339175i
\(383\) 37.3678 + 10.0127i 1.90941 + 0.511624i 0.994042 + 0.108999i \(0.0347644\pi\)
0.915365 + 0.402625i \(0.131902\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −2.77934 −0.141465
\(387\) −3.51821 0.942700i −0.178840 0.0479201i
\(388\) 4.18166 + 15.6062i 0.212292 + 0.792283i
\(389\) −26.3005 15.1846i −1.33349 0.769888i −0.347654 0.937623i \(-0.613021\pi\)
−0.985832 + 0.167735i \(0.946355\pi\)
\(390\) 0 0
\(391\) 10.3726i 0.524567i
\(392\) 5.81878 + 3.89125i 0.293893 + 0.196538i
\(393\) 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
\(397\) 6.97566 26.0335i 0.350098 1.30658i −0.536444 0.843936i \(-0.680233\pi\)
0.886542 0.462648i \(-0.153101\pi\)
\(398\) −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 0.642216 0.766523i \(-0.278015\pi\)
−0.984937 + 0.172914i \(0.944682\pi\)
\(402\) 12.2466 3.28148i 0.610807 0.163665i
\(403\) 0.114221 0.0306055i 0.00568977 0.00152457i
\(404\) −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
\(408\) 0.833568 3.11092i 0.0412678 0.154013i
\(409\) 2.11119 3.65669i 0.104392 0.180812i −0.809098 0.587674i \(-0.800044\pi\)
0.913489 + 0.406862i \(0.133377\pi\)
\(410\) 0 0
\(411\) 11.9541 6.90169i 0.589651 0.340435i
\(412\) 1.15381 + 1.15381i 0.0568444 + 0.0568444i
\(413\) 11.7053 25.8209i 0.575982 1.27056i
\(414\) 3.22066i 0.158287i
\(415\) 0 0
\(416\) −0.118669 0.0685135i −0.00581822 0.00335915i
\(417\) 3.60533 + 13.4553i 0.176554 + 0.658908i
\(418\) −1.97919 0.530323i −0.0968056 0.0259390i
\(419\) 28.1807 1.37672 0.688359 0.725370i \(-0.258331\pi\)
0.688359 + 0.725370i \(0.258331\pi\)
\(420\) 0 0
\(421\) −3.31486 −0.161557 −0.0807783 0.996732i \(-0.525741\pi\)
−0.0807783 + 0.996732i \(0.525741\pi\)
\(422\) 13.2067 + 3.53872i 0.642891 + 0.172262i
\(423\) 0.223354 + 0.833568i 0.0108598 + 0.0405295i
\(424\) −7.23797 4.17884i −0.351507 0.202943i
\(425\) 0 0
\(426\) 5.13703i 0.248890i
\(427\) −18.4869 + 13.2421i −0.894646 + 0.640832i
\(428\) −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 −0.911917 0.410376i \(-0.865398\pi\)
0.811354 + 0.584555i \(0.198731\pi\)
\(432\) −0.258819 + 0.965926i −0.0124524 + 0.0464731i
\(433\) −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
\(437\) 2.70363 0.724435i 0.129332 0.0346544i
\(438\) −15.7014 + 4.20718i −0.750242 + 0.201027i
\(439\) 1.24102 + 2.14951i 0.0592307 + 0.102591i 0.894120 0.447827i \(-0.147802\pi\)
−0.834890 + 0.550417i \(0.814469\pi\)
\(440\) 0 0
\(441\) −5.26467 + 4.61338i −0.250698 + 0.219685i
\(442\) −0.312059 + 0.312059i −0.0148431 + 0.0148431i
\(443\) −3.83026 + 14.2947i −0.181981 + 0.679164i 0.813275 + 0.581879i \(0.197682\pi\)
−0.995257 + 0.0972845i \(0.968984\pi\)
\(444\) 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
\(448\) 0.258819 + 2.63306i 0.0122281 + 0.124400i
\(449\) 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
\(452\) 4.54961 + 16.9794i 0.213996 + 0.798643i
\(453\) −3.04035 0.814659i −0.142848 0.0382760i
\(454\) −15.5490 −0.729750
\(455\) 0 0
\(456\) −0.869078 −0.0406983
\(457\) 30.9884 + 8.30331i 1.44958 + 0.388413i 0.895876 0.444304i \(-0.146549\pi\)
0.553699 + 0.832717i \(0.313216\pi\)
\(458\) −2.79728 10.4396i −0.130708 0.487810i
\(459\) 2.78917 + 1.61033i 0.130187 + 0.0751637i
\(460\) 0 0
\(461\) 0.441317i 0.0205542i −0.999947 0.0102771i \(-0.996729\pi\)
0.999947 0.0102771i \(-0.00327136\pi\)
\(462\) −5.68133 2.57551i −0.264320 0.119823i
\(463\) 26.0183 + 26.0183i 1.20917 + 1.20917i 0.971295 + 0.237877i \(0.0764516\pi\)
0.237877 + 0.971295i \(0.423548\pi\)
\(464\) 3.53653 2.04182i 0.164179 0.0947889i
\(465\) 0 0
\(466\) 6.27978 10.8769i 0.290905 0.503863i
\(467\) −5.06565 + 18.9052i −0.234410 + 0.874831i 0.744004 + 0.668175i \(0.232924\pi\)
−0.978414 + 0.206655i \(0.933742\pi\)
\(468\) 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
\(472\) 10.3503 2.77334i 0.476409 0.127653i
\(473\) 8.29482 2.22259i 0.381396 0.102195i
\(474\) 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
\(478\) −4.13351 + 15.4265i −0.189062 + 0.705590i
\(479\) 15.3363 26.5632i 0.700732 1.21370i −0.267477 0.963564i \(-0.586190\pi\)
0.968210 0.250140i \(-0.0804766\pi\)
\(480\) 0 0
\(481\) −1.16845 + 0.674604i −0.0532767 + 0.0307593i
\(482\) 19.3123 + 19.3123i 0.879649 + 0.879649i
\(483\) 8.48019 0.833568i 0.385862 0.0379286i
\(484\) 5.44132i 0.247333i
\(485\) 0 0
\(486\) −0.866025 0.500000i −0.0392837 0.0226805i
\(487\) −6.37653 23.7975i −0.288948 1.07837i −0.945906 0.324441i \(-0.894824\pi\)
0.656958 0.753927i \(-0.271843\pi\)
\(488\) −8.30216 2.22456i −0.375821 0.100701i
\(489\) 2.77324 0.125410
\(490\) 0 0
\(491\) 3.08275 0.139122 0.0695612 0.997578i \(-0.477840\pi\)
0.0695612 + 0.997578i \(0.477840\pi\)
\(492\) −6.62912 1.77627i −0.298864 0.0800804i
\(493\) −3.40398 12.7038i −0.153308 0.572152i
\(494\) 0.103133 + 0.0595436i 0.00464015 + 0.00267899i
\(495\) 0 0
\(496\) 0.862973i 0.0387486i
\(497\) 13.5261 1.32956i 0.606729 0.0596389i
\(498\) 7.13020 + 7.13020i 0.319512 + 0.319512i
\(499\) 28.7283 16.5863i 1.28605 0.742503i 0.308105 0.951352i \(-0.400305\pi\)
0.977948 + 0.208849i \(0.0669717\pi\)
\(500\) 0 0
\(501\) −8.57834 + 14.8581i −0.383252 + 0.663812i
\(502\) −0.893415 + 3.33427i −0.0398751 + 0.148816i
\(503\) −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
\(507\) 12.5389 3.35979i 0.556872 0.149213i
\(508\) −13.1432 + 3.52171i −0.583136 + 0.156251i
\(509\) 13.6202 + 23.5908i 0.603703 + 1.04564i 0.992255 + 0.124217i \(0.0396420\pi\)
−0.388552 + 0.921427i \(0.627025\pi\)
\(510\) 0 0
\(511\) −15.1416 40.2538i −0.669824 1.78072i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0.224934 0.839465i 0.00993107 0.0370633i
\(514\) 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
\(518\) 23.7267 + 10.7560i 1.04249 + 0.472590i
\(519\) 1.28463i 0.0563889i
\(520\) 0 0
\(521\) −10.8599 6.26995i −0.475780 0.274692i 0.242876 0.970057i \(-0.421909\pi\)
−0.718656 + 0.695366i \(0.755242\pi\)
\(522\) 1.05692 + 3.94449i 0.0462602 + 0.172645i
\(523\) −1.61327 0.432274i −0.0705433 0.0189020i 0.223375 0.974733i \(-0.428293\pi\)
−0.293918 + 0.955831i \(0.594959\pi\)
\(524\) −12.7500 −0.556986
\(525\) 0 0
\(526\) −21.2207 −0.925265
\(527\) −2.68464 0.719346i −0.116945 0.0313352i
\(528\) −0.610214 2.27735i −0.0265562 0.0991089i
\(529\) 10.9356 + 6.31368i 0.475461 + 0.274508i
\(530\) 0 0
\(531\) 10.7154i 0.465008i
\(532\) −0.224934 2.28834i −0.00975212 0.0992119i
\(533\) 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
\(537\) −5.01636 + 18.7213i −0.216472 + 0.807884i
\(538\) −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 −0.992753 0.120174i \(-0.961655\pi\)
0.392303 0.919836i \(-0.371678\pi\)
\(542\) −7.86998 + 2.10875i −0.338045 + 0.0905788i
\(543\) 24.3329 6.51999i 1.04423 0.279800i
\(544\) 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 −0.768561 0.639776i \(-0.779027\pi\)
0.639776 + 0.768561i \(0.279027\pi\)
\(548\) −3.57258 + 13.3330i −0.152613 + 0.569560i
\(549\) 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
\(553\) −9.98510 + 7.15230i −0.424610 + 0.304147i
\(554\) 16.7867i 0.713199i
\(555\) 0 0
\(556\) −12.0637 6.96496i −0.511614 0.295380i
\(557\) 5.58276 + 20.8352i 0.236549 + 0.882814i 0.977444 + 0.211193i \(0.0677349\pi\)
−0.740895 + 0.671621i \(0.765598\pi\)
\(558\) 0.833568 + 0.223354i 0.0352877 + 0.00945532i
\(559\) −0.499096 −0.0211095
\(560\) 0 0
\(561\) −7.59330 −0.320589
\(562\) 10.1473 + 2.71897i 0.428039 + 0.114693i
\(563\) 8.06743 + 30.1081i 0.340002 + 1.26890i 0.898344 + 0.439293i \(0.144771\pi\)
−0.558342 + 0.829611i \(0.688562\pi\)
\(564\) −0.747356 0.431486i −0.0314694 0.0181689i
\(565\) 0 0
\(566\) 25.0053i 1.05105i
\(567\) 1.09239 2.40971i 0.0458759 0.101198i
\(568\) 3.63243 + 3.63243i 0.152413 + 0.152413i
\(569\) −2.12720 + 1.22814i −0.0891767 + 0.0514862i −0.543925 0.839134i \(-0.683062\pi\)
0.454749 + 0.890620i \(0.349729\pi\)
\(570\) 0 0
\(571\) 4.62235 8.00615i 0.193439 0.335047i −0.752948 0.658080i \(-0.771369\pi\)
0.946388 + 0.323033i \(0.104702\pi\)
\(572\) −0.0836158 + 0.312059i −0.00349615 + 0.0130478i
\(573\) −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
\(577\) −45.0669 + 12.0756i −1.87616 + 0.502715i −0.876381 + 0.481618i \(0.840049\pi\)
−0.999777 + 0.0210977i \(0.993284\pi\)
\(578\) −6.40154 + 1.71529i −0.266269 + 0.0713465i
\(579\) 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
\(583\) −5.09998 + 19.0334i −0.211219 + 0.788282i
\(584\) 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 \(0.754763\pi\)
\(588\) 0.460527 6.98483i 0.0189918 0.288050i
\(589\) 0.749991i 0.0309028i
\(590\) 0 0
\(591\) −21.2692 12.2798i −0.874898 0.505123i
\(592\) 2.54841 + 9.51079i 0.104739 + 0.390891i
\(593\) 22.5910 + 6.05324i 0.927701 + 0.248577i 0.690874 0.722975i \(-0.257226\pi\)
0.236827 + 0.971552i \(0.423893\pi\)
\(594\) 2.35769 0.0967370
\(595\) 0 0
\(596\) −19.3817 −0.793907
\(597\) 10.1722 + 2.72564i 0.416321 + 0.111553i
\(598\) −0.114221 0.426280i −0.00467086 0.0174319i
\(599\) 9.39922 + 5.42664i 0.384042 + 0.221727i 0.679575 0.733606i \(-0.262164\pi\)
−0.295534 + 0.955332i \(0.595497\pi\)
\(600\) 0 0
\(601\) 23.5701i 0.961443i 0.876873 + 0.480721i \(0.159625\pi\)
−0.876873 + 0.480721i \(0.840375\pi\)
\(602\) 5.61162 + 7.83421i 0.228713 + 0.319299i
\(603\) −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
\(607\) 7.58314 28.3006i 0.307790 1.14869i −0.622727 0.782439i \(-0.713975\pi\)
0.930517 0.366249i \(-0.119358\pi\)
\(608\) 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
\(612\) −3.11092 + 0.833568i −0.125751 + 0.0336950i
\(613\) −3.03612 + 0.813525i −0.122628 + 0.0328580i −0.319611 0.947549i \(-0.603552\pi\)
0.196983 + 0.980407i \(0.436886\pi\)
\(614\) −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 \(-0.481800\pi\)
0.998366 0.0571445i \(-0.0181996\pi\)
\(618\) 0.422325 1.57614i 0.0169884 0.0634016i
\(619\) 11.7918 20.4240i 0.473953 0.820910i −0.525603 0.850730i \(-0.676160\pi\)
0.999555 + 0.0298201i \(0.00949342\pi\)
\(620\) 0 0
\(621\) −2.78917 + 1.61033i −0.111926 + 0.0646203i
\(622\) −9.93788 9.93788i −0.398473 0.398473i
\(623\) −15.3615 21.4458i −0.615447 0.859206i
\(624\) 0.137027i 0.00548547i
\(625\) 0 0
\(626\) 17.0578 + 9.84830i 0.681765 + 0.393617i
\(627\) 0.530323 + 1.97919i 0.0211791 + 0.0790414i
\(628\) −5.96135 1.59734i −0.237884 0.0637408i
\(629\) 31.7116 1.26442
\(630\) 0 0
\(631\) −8.97684 −0.357362 −0.178681 0.983907i \(-0.557183\pi\)
−0.178681 + 0.983907i \(0.557183\pi\)
\(632\) −4.48413 1.20152i −0.178369 0.0477939i
\(633\) −3.53872 13.2067i −0.140651 0.524918i
\(634\) −2.06013 1.18942i −0.0818182 0.0472378i
\(635\) 0 0
\(636\) 8.35769i 0.331404i
\(637\) −0.533206 + 0.797331i −0.0211264 + 0.0315914i
\(638\) −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 −0.694971 0.719038i \(-0.744583\pi\)
0.970191 + 0.242343i \(0.0779160\pi\)
\(642\) −3.91015 + 14.5929i −0.154321 + 0.575936i
\(643\) −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
\(647\) 41.2236 11.0458i 1.62067 0.434256i 0.669470 0.742839i \(-0.266521\pi\)
0.951197 + 0.308583i \(0.0998547\pi\)
\(648\) 0.965926 0.258819i 0.0379452 0.0101674i
\(649\) −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
\(653\) 7.90392 29.4978i 0.309304 1.15434i −0.619872 0.784703i \(-0.712815\pi\)
0.929176 0.369637i \(-0.120518\pi\)
\(654\) −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
\(658\) 0.942700 2.07951i 0.0367503 0.0810678i
\(659\) 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 0.705546 0.708664i \(-0.250702\pi\)
−0.260948 + 0.965353i \(0.584035\pi\)
\(662\) −7.16567 26.7426i −0.278502 1.03938i
\(663\) 0.426280 + 0.114221i 0.0165553 + 0.00443599i
\(664\) −10.0836 −0.391321
\(665\) 0 0
\(666\) −9.84629 −0.381536
\(667\) 12.7038 + 3.40398i 0.491895 + 0.131803i
\(668\) −4.44048 16.5721i −0.171807 0.641193i
\(669\) 7.86666 + 4.54182i 0.304142 + 0.175597i
\(670\) 0 0
\(671\) 20.2644i 0.782297i
\(672\) 2.15089 1.54067i 0.0829723 0.0594328i
\(673\) 8.91749 + 8.91749i 0.343744 + 0.343744i 0.857773 0.514029i \(-0.171848\pi\)
−0.514029 + 0.857773i \(0.671848\pi\)
\(674\) 3.90169 2.25264i 0.150288 0.0867686i
\(675\) 0 0
\(676\) −6.49061 + 11.2421i −0.249639 + 0.432387i
\(677\) −10.8769 + 40.5930i −0.418031 + 1.56011i 0.360654 + 0.932700i \(0.382554\pi\)
−0.778685 + 0.627415i \(0.784113\pi\)
\(678\) 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
\(682\) −1.96529 + 0.526598i −0.0752549 + 0.0201645i
\(683\) 4.14885 1.11168i 0.158751 0.0425373i −0.178568 0.983928i \(-0.557146\pi\)
0.337319 + 0.941390i \(0.390480\pi\)
\(684\) 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
\(688\) −0.942700 + 3.51821i −0.0359401 + 0.134130i
\(689\) 0.572615 0.991798i 0.0218149 0.0377845i
\(690\) 0 0
\(691\) 32.4983 18.7629i 1.23629 0.713773i 0.267958 0.963431i \(-0.413651\pi\)
0.968334 + 0.249657i \(0.0803180\pi\)
\(692\) 0.908369 + 0.908369i 0.0345310 + 0.0345310i
\(693\) 0.610214 + 6.20793i 0.0231801 + 0.235820i
\(694\) 5.78843i 0.219726i
\(695\) 0 0
\(696\) −3.53653 2.04182i −0.134052 0.0773948i
\(697\) −5.72075 21.3501i −0.216689 0.808694i
\(698\) 18.9637 + 5.08130i 0.717785 + 0.192330i
\(699\) −12.5596 −0.475046
\(700\) 0 0
\(701\) 12.7644 0.482104 0.241052 0.970512i \(-0.422508\pi\)
0.241052 + 0.970512i \(0.422508\pi\)
\(702\) −0.132358 0.0354652i −0.00499553 0.00133855i
\(703\) −2.21477 8.26562i −0.0835315 0.311744i
\(704\) 2.04182 + 1.17884i 0.0769538 + 0.0444293i
\(705\) 0 0
\(706\) 26.0331i 0.979770i
\(707\) −1.52231 0.690104i −0.0572523 0.0259541i
\(708\) −7.57691 7.57691i −0.284758 0.284758i
\(709\) 43.1134 24.8916i 1.61916 0.934822i 0.632022 0.774951i \(-0.282225\pi\)
0.987138 0.159872i \(-0.0511080\pi\)
\(710\) 0 0
\(711\) 2.32116 4.02036i 0.0870502 0.150775i
\(712\) 2.58059 9.63091i 0.0967118 0.360934i
\(713\) 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
\(717\) 15.4265 4.13351i 0.576112 0.154369i
\(718\) −7.15063 + 1.91601i −0.266859 + 0.0715047i
\(719\) 23.1988 + 40.1815i 0.865169 + 1.49852i 0.866880 + 0.498518i \(0.166122\pi\)
−0.00171077 + 0.999999i \(0.500545\pi\)
\(720\) 0 0
\(721\) 4.25938 + 0.704074i 0.158628 + 0.0262211i
\(722\) 12.9010 12.9010i 0.480124 0.480124i
\(723\) 7.06878 26.3810i 0.262891 0.981121i
\(724\) −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 \(0.892911\pi\)
\(728\) −0.360801 + 0.0354652i −0.0133722 + 0.00131443i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 10.1590 + 5.86533i 0.375746 + 0.216937i
\(732\) 2.22456 + 8.30216i 0.0822219 + 0.306856i
\(733\) −37.4254 10.0281i −1.38234 0.370396i −0.510368 0.859956i \(-0.670491\pi\)
−0.871970 + 0.489560i \(0.837158\pi\)
\(734\) −12.0692 −0.445484
\(735\) 0 0
\(736\) −3.22066 −0.118715
\(737\) 28.8737 + 7.73669i 1.06358 + 0.284985i
\(738\) 1.77627 + 6.62912i 0.0653853 + 0.244021i
\(739\) −34.4840 19.9093i −1.26851 0.732377i −0.293807 0.955865i \(-0.594922\pi\)
−0.974707 + 0.223488i \(0.928256\pi\)
\(740\) 0 0
\(741\) 0.119087i 0.00437478i
\(742\) −22.0063 + 2.16313i −0.807877 + 0.0794109i
\(743\) 28.0880 + 28.0880i 1.03045 + 1.03045i 0.999522 + 0.0309276i \(0.00984614\pi\)
0.0309276 + 0.999522i \(0.490154\pi\)
\(744\) −0.747356 + 0.431486i −0.0273994 + 0.0158191i
\(745\) 0 0
\(746\) −0.0595436 + 0.103133i −0.00218005 + 0.00377595i
\(747\) 2.60984 9.74004i 0.0954889 0.356369i
\(748\) 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 −0.992253 0.124233i \(-0.960353\pi\)
0.388538 0.921433i \(-0.372980\pi\)
\(752\) 0.833568 0.223354i 0.0303971 0.00814488i
\(753\) 3.33427 0.893415i 0.121508 0.0325579i
\(754\) 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 −0.535900 0.844281i \(-0.680028\pi\)
0.844281 + 0.535900i \(0.180028\pi\)
\(758\) −2.28744 + 8.53686i −0.0830837 + 0.310073i
\(759\) 3.79665 6.57599i 0.137810 0.238693i
\(760\) 0 0
\(761\) 25.4199 14.6762i 0.921471 0.532011i 0.0373669 0.999302i \(-0.488103\pi\)
0.884104 + 0.467290i \(0.154770\pi\)
\(762\) 9.62150 + 9.62150i 0.348550 + 0.348550i
\(763\) −20.7547 9.40869i −0.751371 0.340617i
\(764\) 6.86297i 0.248294i
\(765\) 0 0
\(766\) 33.5031 + 19.3430i 1.21052 + 0.698891i
\(767\) 0.380023 + 1.41827i 0.0137218 + 0.0512106i
\(768\) 0.965926 + 0.258819i 0.0348548 + 0.00933933i
\(769\) −21.4307 −0.772812 −0.386406 0.922329i \(-0.626284\pi\)
−0.386406 + 0.922329i \(0.626284\pi\)
\(770\) 0 0
\(771\) −7.70480 −0.277482
\(772\) −2.68464 0.719346i −0.0966222 0.0258898i
\(773\) −2.96745 11.0747i −0.106732 0.398329i 0.891804 0.452422i \(-0.149440\pi\)
−0.998536 + 0.0540931i \(0.982773\pi\)
\(774\) −3.15434 1.82116i −0.113380 0.0654601i
\(775\) 0 0
\(776\) 16.1567i 0.579991i
\(777\) −2.54841 25.9259i −0.0914236 0.930086i
\(778\) −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
\(782\) −2.68464 + 10.0192i −0.0960024 + 0.358286i