Properties

Label 1050.2.bc.f.607.1
Level $1050$
Weight $2$
Character 1050.607
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 607.1
Root \(1.44378 + 0.833568i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.f.493.1

$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 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 0.987192 0.159535i \(-0.0509996\pi\)
−0.631758 + 0.775166i \(0.717666\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) 0.0968928 + 0.0968928i 0.0268732 + 0.0268732i 0.720416 0.693542i \(-0.243951\pi\)
−0.693542 + 0.720416i \(0.743951\pi\)
\(14\) 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 \(-0.544386\pi\)
−0.615517 + 0.788124i \(0.711053\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) −0.434539 + 0.752644i −0.0996901 + 0.172668i −0.911556 0.411175i \(-0.865118\pi\)
0.811866 + 0.583843i \(0.198452\pi\)
\(20\) 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 0.996751 + 0.0805432i \(0.0256655\pi\)
−0.822940 + 0.568128i \(0.807668\pi\)
\(24\) 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 \(0.123786\pi\)
−0.925333 + 0.379156i \(0.876214\pi\)
\(30\) 0 0
\(31\) −0.747356 + 0.431486i −0.134229 + 0.0774973i −0.565611 0.824672i \(-0.691360\pi\)
0.431382 + 0.902170i \(0.358026\pi\)
\(32\) −0.258819 + 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 \(-0.883519\pi\)
−0.629774 + 0.776778i \(0.716853\pi\)
\(38\) 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 \(0.180031\pi\)
−0.844276 + 0.535908i \(0.819969\pi\)
\(42\) 0.258819 2.63306i 0.0399366 0.406290i
\(43\) −2.57551 + 2.57551i −0.392761 + 0.392761i −0.875670 0.482909i \(-0.839580\pi\)
0.482909 + 0.875670i \(0.339580\pi\)
\(44\) 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 \(-0.103381\pi\)
−0.980301 + 0.197512i \(0.936714\pi\)
\(48\) −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 \(-0.222054\pi\)
0.342516 + 0.939512i \(0.388721\pi\)
\(54\) 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 0.969327 + 0.245776i \(0.0790426\pi\)
−0.271815 + 0.962349i \(0.587624\pi\)
\(60\) 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
\(63\) 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 0.410604 + 0.911814i \(0.365318\pi\)
−0.811501 + 0.584352i \(0.801349\pi\)
\(68\) −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 −0.0516512 0.998665i \(-0.516448\pi\)
0.544064 0.839044i \(-0.316885\pi\)
\(74\) 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 0.256486 0.966548i \(-0.417435\pi\)
−0.708812 + 0.705397i \(0.750769\pi\)
\(80\) 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 \(-0.0633258\pi\)
−0.197634 + 0.980276i \(0.563326\pi\)
\(84\) 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 0.471007 + 0.882130i \(0.343891\pi\)
−0.999450 + 0.0331611i \(0.989443\pi\)
\(90\) 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 −0.175504 + 0.984479i \(0.556155\pi\)
−0.984479 + 0.175504i \(0.943845\pi\)
\(98\) −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 −0.526972 0.849882i \(-0.676673\pi\)
0.472534 + 0.881313i \(0.343340\pi\)
\(102\) 0.833568 3.11092i 0.0825355 0.308027i
\(103\) −1.57614 + 0.422325i −0.155302 + 0.0416130i −0.335632 0.941993i \(-0.608950\pi\)
0.180331 + 0.983606i \(0.442283\pi\)
\(104\) −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 \(-0.322734\pi\)
0.882192 + 0.470889i \(0.156067\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) −7.45905 + 4.30648i −0.714447 + 0.412486i −0.812705 0.582675i \(-0.802006\pi\)
0.0982585 + 0.995161i \(0.468673\pi\)
\(110\) 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 −0.186919 + 0.982375i \(0.559850\pi\)
−0.982375 + 0.186919i \(0.940150\pi\)
\(114\) −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 \(-0.0436898\pi\)
−0.136825 + 0.990595i \(0.543690\pi\)
\(128\) 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 −0.0671030 0.997746i \(-0.521376\pi\)
−0.897625 + 0.440760i \(0.854709\pi\)
\(132\) 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 0.627525 + 0.778597i \(0.284068\pi\)
−0.932751 + 0.360522i \(0.882598\pi\)
\(138\) −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 −0.383523 0.923531i \(-0.625289\pi\)
−0.991563 + 0.129625i \(0.958623\pi\)
\(150\) 0 0
\(151\) 1.57380 + 2.72590i 0.128074 + 0.221831i 0.922930 0.384967i \(-0.125787\pi\)
−0.794856 + 0.606798i \(0.792454\pi\)
\(152\) −0.224934 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 \(-0.337460\pi\)
−0.0129635 + 0.999916i \(0.504127\pi\)
\(158\) 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 \(-0.0486939\pi\)
−0.932102 + 0.362196i \(0.882027\pi\)
\(164\) 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 \(-0.518937\pi\)
0.998231 + 0.0594585i \(0.0189374\pi\)
\(168\) −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 \(-0.598884\pi\)
0.211340 + 0.977413i \(0.432217\pi\)
\(174\) −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 −0.972015 0.234920i \(-0.924517\pi\)
−0.282560 + 0.959249i \(0.591184\pi\)
\(180\) 0 0
\(181\) 25.1913i 1.87246i −0.351394 0.936228i \(-0.614292\pi\)
0.351394 0.936228i \(-0.385708\pi\)
\(182\) 0.294730 + 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 −0.963052 0.269314i \(-0.913203\pi\)
0.714759 + 0.699371i \(0.246536\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 2.68464 + 0.719346i 0.193244 + 0.0517797i 0.354143 0.935191i \(-0.384773\pi\)
−0.160899 + 0.986971i \(0.551439\pi\)
\(194\) 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 −0.961103 0.276190i \(-0.910928\pi\)
−0.276190 0.961103i \(-0.589072\pi\)
\(198\) 0.610214 + 2.27735i 0.0433660 + 0.161844i
\(199\) −5.26553 9.12016i −0.373263 0.646511i 0.616802 0.787118i \(-0.288428\pi\)
−0.990065 + 0.140607i \(0.955095\pi\)
\(200\) 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 \(-0.151630\pi\)
−0.458547 + 0.888670i \(0.651630\pi\)
\(224\) 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 \(-0.244083\pi\)
0.276729 + 0.960948i \(0.410750\pi\)
\(228\) 0.839465 + 0.224934i 0.0555949 + 0.0148966i
\(229\) −5.40393 + 9.35988i −0.357102 + 0.618518i −0.987475 0.157774i \(-0.949568\pi\)
0.630374 + 0.776292i \(0.282902\pi\)
\(230\) 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 −0.986876 0.161483i \(-0.948372\pi\)
0.773918 0.633286i \(-0.218294\pi\)
\(234\) 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 \(-0.827224\pi\)
0.856270 0.516528i \(-0.172776\pi\)
\(240\) 0 0
\(241\) 23.6526 13.6558i 1.52360 0.879649i 0.523987 0.851726i \(-0.324444\pi\)
0.999610 0.0279230i \(-0.00888932\pi\)
\(242\) −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 \(-0.965254\pi\)
0.994048 0.108941i \(-0.0347459\pi\)
\(252\) 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 \(-0.160581\pi\)
−0.999817 + 0.0191171i \(0.993914\pi\)
\(258\) −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 \(-0.189646\pi\)
0.436231 + 0.899835i \(0.356313\pi\)
\(264\) −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 0.847295 0.531122i \(-0.178229\pi\)
−0.883613 + 0.468218i \(0.844896\pi\)
\(270\) 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
\(273\) −0.330195 + 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 0.703576 + 0.710620i \(0.251586\pi\)
−0.964625 + 0.263627i \(0.915081\pi\)
\(278\) 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 −0.453911 0.891047i \(-0.649972\pi\)
0.838622 0.544714i \(-0.183362\pi\)
\(284\) 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 \(-0.366491\pi\)
−0.913321 + 0.407241i \(0.866491\pi\)
\(294\) −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 \(-0.668425\pi\)
0.863250 + 0.504776i \(0.168425\pi\)
\(308\) −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 −0.803678 0.595065i \(-0.797126\pi\)
0.113503 + 0.993538i \(0.463793\pi\)
\(312\) −0.0354652 + 0.132358i −0.00200782 + 0.00749330i
\(313\) −19.0255 + 5.09785i −1.07538 + 0.288148i −0.752703 0.658361i \(-0.771250\pi\)
−0.322679 + 0.946508i \(0.604584\pi\)
\(314\) −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 \(-0.562053\pi\)
0.322769 + 0.946478i \(0.395386\pi\)
\(318\) −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 0.181516 + 0.983388i \(0.441899\pi\)
−0.942397 + 0.334496i \(0.891434\pi\)
\(332\) 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 \(-0.289158\pi\)
−0.788532 + 0.614994i \(0.789158\pi\)
\(338\) 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 \(-0.867010\pi\)
0.994409 + 0.105601i \(0.0336765\pi\)
\(348\) 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 −0.517246 0.855837i \(-0.673043\pi\)
0.875866 0.482554i \(-0.160291\pi\)
\(354\) −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 0.321184 0.947017i \(-0.395919\pi\)
−0.659548 + 0.751662i \(0.729252\pi\)
\(360\) 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 \(-0.314661\pi\)
0.0586284 + 0.998280i \(0.481327\pi\)
\(368\) 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 \(-0.0823520\pi\)
−0.965123 + 0.261796i \(0.915685\pi\)
\(374\) 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 \(-0.927112\pi\)
0.973897 0.226989i \(-0.0728881\pi\)
\(380\) 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 −0.915365 + 0.402625i \(0.868098\pi\)
−0.994042 + 0.108999i \(0.965236\pi\)
\(384\) 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 −0.985832 0.167735i \(-0.946355\pi\)
−0.347654 + 0.937623i \(0.613021\pi\)
\(390\) 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 −0.886542 0.462648i \(-0.846899\pi\)
0.536444 0.843936i \(-0.319767\pi\)
\(398\) 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 \(0.278015\pi\)
\(402\) −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 0.913489 0.406862i \(-0.133377\pi\)
−0.809098 + 0.587674i \(0.800044\pi\)
\(410\) 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 0.811354 0.584555i \(-0.198731\pi\)
−0.911917 + 0.410376i \(0.865398\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) 4.81820 + 4.81820i 0.231548 + 0.231548i 0.813339 0.581791i \(-0.197648\pi\)
−0.581791 + 0.813339i \(0.697648\pi\)
\(434\) −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 −0.834890 0.550417i \(-0.814469\pi\)
0.894120 + 0.447827i \(0.147802\pi\)
\(440\) 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 0.995257 + 0.0972845i \(0.0310157\pi\)
−0.813275 + 0.581879i \(0.802318\pi\)
\(444\) 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 \(0.00416346\pi\)
−0.999914 + 0.0130795i \(0.995837\pi\)
\(450\) 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 \(-0.853451\pi\)
−0.553699 + 0.832717i \(0.686784\pi\)
\(458\) 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 \(0.00327136\pi\)
−0.999947 + 0.0102771i \(0.996729\pi\)
\(462\) 5.68133 2.57551i 0.264320 0.119823i
\(463\) −26.0183 + 26.0183i −1.20917 + 1.20917i −0.237877 + 0.971295i \(0.576452\pi\)
−0.971295 + 0.237877i \(0.923548\pi\)
\(464\) 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 0.978414 + 0.206655i \(0.0662578\pi\)
−0.744004 + 0.668175i \(0.767076\pi\)
\(468\) −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 0.968210 + 0.250140i \(0.0804766\pi\)
−0.267477 + 0.963564i \(0.586190\pi\)
\(480\) 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 −0.656958 0.753927i \(-0.728157\pi\)
0.945906 0.324441i \(-0.105176\pi\)
\(488\) 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 0.977948 0.208849i \(-0.0669717\pi\)
0.308105 + 0.951352i \(0.400305\pi\)
\(500\) 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 0.998185 + 0.0602259i \(0.0191821\pi\)
0.0602259 + 0.998185i \(0.480818\pi\)
\(504\) −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 −0.388552 0.921427i \(-0.627025\pi\)
0.992255 0.124217i \(-0.0396420\pi\)
\(510\) 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 −0.718656 0.695366i \(-0.755242\pi\)
0.242876 + 0.970057i \(0.421909\pi\)
\(522\) −1.05692 + 3.94449i −0.0462602 + 0.172645i
\(523\) 1.61327 0.432274i 0.0705433 0.0189020i −0.223375 0.974733i \(-0.571707\pi\)
0.293918 + 0.955831i \(0.405041\pi\)
\(524\) −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 0.392303 + 0.919836i \(0.371678\pi\)
−0.992753 + 0.120174i \(0.961655\pi\)
\(542\) 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 \(-0.220973\pi\)
−0.639776 + 0.768561i \(0.720973\pi\)
\(548\) 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 0.740895 + 0.671621i \(0.234402\pi\)
−0.977444 + 0.211193i \(0.932265\pi\)
\(558\) −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 0.558342 + 0.829611i \(0.311438\pi\)
−0.898344 + 0.439293i \(0.855229\pi\)
\(564\) −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 0.454749 0.890620i \(-0.349729\pi\)
−0.543925 + 0.839134i \(0.683062\pi\)
\(570\) 0 0
\(571\) 4.62235 + 8.00615i 0.193439 + 0.335047i 0.946388 0.323033i \(-0.104702\pi\)
−0.752948 + 0.658080i \(0.771369\pi\)
\(572\) 0.0836158 + 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 0.999777 + 0.0210977i \(0.00671609\pi\)
0.876381 + 0.481618i \(0.159951\pi\)
\(578\) 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 \(-0.745237\pi\)
0.717608 + 0.696447i \(0.245237\pi\)
\(588\) −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 \(-0.742774\pi\)
−0.236827 + 0.971552i \(0.576107\pi\)
\(594\) 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 −0.295534 0.955332i \(-0.595497\pi\)
0.679575 + 0.733606i \(0.262164\pi\)
\(600\) 0 0
\(601\) 23.5701i 0.961443i −0.876873 0.480721i \(-0.840375\pi\)
0.876873 0.480721i \(-0.159625\pi\)
\(602\) −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 −0.930517 0.366249i \(-0.880642\pi\)
0.622727 0.782439i \(-0.286025\pi\)
\(608\) −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 \(-0.396448\pi\)
−0.196983 + 0.980407i \(0.563114\pi\)
\(614\) −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 −0.998366 0.0571445i \(-0.981800\pi\)
−0.0571445 0.998366i \(-0.518200\pi\)
\(618\) −0.422325 1.57614i −0.0169884 0.0634016i
\(619\) 11.7918 + 20.4240i 0.473953 + 0.820910i 0.999555 0.0298201i \(-0.00949342\pi\)
−0.525603 + 0.850730i \(0.676160\pi\)
\(620\) 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 0.970191 0.242343i \(-0.0779160\pi\)
−0.694971 + 0.719038i \(0.744583\pi\)
\(642\) 3.91015 + 14.5929i 0.154321 + 0.575936i
\(643\) 25.1156 + 25.1156i 0.990461 + 0.990461i 0.999955 0.00949415i \(-0.00302213\pi\)
−0.00949415 + 0.999955i \(0.503022\pi\)
\(644\) −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 \(-0.733479\pi\)
−0.951197 + 0.308583i \(0.900145\pi\)
\(648\) −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 −0.929176 0.369637i \(-0.879482\pi\)
0.619872 0.784703i \(-0.287185\pi\)
\(654\) −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 \(0.194412\pi\)
−0.819211 + 0.573492i \(0.805588\pi\)
\(660\) 0 0
\(661\) 11.4306 6.59945i 0.444598 0.256689i −0.260948 0.965353i \(-0.584035\pi\)
0.705546 + 0.708664i \(0.250702\pi\)
\(662\) 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 \(-0.828152\pi\)
0.514029 + 0.857773i \(0.328152\pi\)
\(674\) 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 0.778685 + 0.627415i \(0.215887\pi\)
−0.360654 + 0.932700i \(0.617446\pi\)
\(678\) −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 \(-0.442854\pi\)
−0.337319 + 0.941390i \(0.609520\pi\)
\(684\) 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 0.968334 0.249657i \(-0.0803180\pi\)
0.267958 + 0.963431i \(0.413651\pi\)
\(692\) −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 0.987138 + 0.159872i \(0.0511080\pi\)
0.632022 + 0.774951i \(0.282225\pi\)
\(710\) 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 −0.00171077 0.999999i \(-0.500545\pi\)
0.866880 0.498518i \(-0.166122\pi\)
\(720\) 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 \(-0.607089\pi\)
0.943939 + 0.330119i \(0.107089\pi\)
\(728\) 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 \(-0.329509\pi\)
0.871970 + 0.489560i \(0.162842\pi\)
\(734\) −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 −0.974707 0.223488i \(-0.928256\pi\)
−0.293807 + 0.955865i \(0.594922\pi\)
\(740\) 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 −0.0309276 + 0.999522i \(0.509846\pi\)
−0.999522 + 0.0309276i \(0.990154\pi\)
\(744\) −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 0.388538 + 0.921433i \(0.372980\pi\)
−0.992253 + 0.124233i \(0.960353\pi\)
\(752\) −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 \(-0.319972\pi\)
−0.844281 + 0.535900i \(0.819972\pi\)
\(758\) 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 0.884104 0.467290i \(-0.154770\pi\)
0.0373669 + 0.999302i \(0.488103\pi\)
\(762\) −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 \(-0.850560\pi\)
0.998536 + 0.0540931i \(0.0172268\pi\)
\(774\) −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