Properties

Label 1050.2.bc.g.607.2
Level $1050$
Weight $2$
Character 1050.607
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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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: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 607.2
Root \(2.69978 + 0.355433i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.g.493.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.942805 + 2.47207i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +1.00000i q^{6} +(0.942805 + 2.47207i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.55390 + 2.69144i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-3.40812 - 3.40812i) q^{13} +(-1.55050 - 2.14382i) q^{14} +(0.500000 - 0.866025i) q^{16} +(5.14616 + 1.37891i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-3.61673 + 6.26436i) q^{19} +(2.63185 - 0.270861i) q^{21} +(-2.19755 - 2.19755i) q^{22} +(1.36289 + 5.08638i) q^{23} +(0.500000 + 0.866025i) q^{24} +(4.17408 + 2.40991i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(2.05253 + 1.66947i) q^{28} -4.49359i q^{29} +(-7.98911 + 4.61252i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.00191 - 0.804359i) q^{33} -5.32769 q^{34} -1.00000 q^{36} +(-3.47079 + 0.929997i) q^{37} +(1.87216 - 6.98699i) q^{38} +(-4.17408 + 2.40991i) q^{39} +2.51851i q^{41} +(-2.47207 + 0.942805i) q^{42} +(3.86848 - 3.86848i) q^{43} +(2.69144 + 1.55390i) q^{44} +(-2.63291 - 4.56033i) q^{46} +(1.05713 + 3.94526i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-5.22224 + 4.66135i) q^{49} +(2.66385 - 4.61392i) q^{51} +(-4.65558 - 1.24746i) q^{52} +(3.32222 + 0.890187i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.41468 - 1.08135i) q^{56} +(5.11483 + 5.11483i) q^{57} +(1.16303 + 4.34047i) q^{58} +(0.666188 + 1.15387i) q^{59} +(10.8719 + 6.27689i) q^{61} +(6.52308 - 6.52308i) q^{62} +(0.419541 - 2.61228i) q^{63} -1.00000i q^{64} +(-2.69144 + 1.55390i) q^{66} +(1.72448 - 6.43584i) q^{67} +(5.14616 - 1.37891i) q^{68} +5.26581 q^{69} +9.22738 q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.13063 + 7.95163i) q^{73} +(3.11183 - 1.79662i) q^{74} +7.23346i q^{76} +(-5.18839 + 6.37885i) q^{77} +(3.40812 - 3.40812i) q^{78} +(1.65789 + 0.957181i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-0.651839 - 2.43270i) q^{82} +(8.97250 + 8.97250i) q^{83} +(2.14382 - 1.55050i) q^{84} +(-2.73543 + 4.73790i) q^{86} +(-4.34047 - 1.16303i) q^{87} +(-3.00191 - 0.804359i) q^{88} +(2.03677 - 3.52779i) q^{89} +(5.21191 - 11.6383i) q^{91} +(3.72349 + 3.72349i) q^{92} +(2.38761 + 8.91070i) q^{93} +(-2.04222 - 3.53723i) q^{94} +(0.866025 + 0.500000i) q^{96} +(2.69423 - 2.69423i) q^{97} +(3.83785 - 5.85414i) q^{98} -3.10780i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

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
\(7\) 0.942805 + 2.47207i 0.356347 + 0.934354i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 0 0
\(11\) 1.55390 + 2.69144i 0.468519 + 0.811499i 0.999353 0.0359771i \(-0.0114543\pi\)
−0.530833 + 0.847476i \(0.678121\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) −3.40812 3.40812i −0.945243 0.945243i 0.0533341 0.998577i \(-0.483015\pi\)
−0.998577 + 0.0533341i \(0.983015\pi\)
\(14\) −1.55050 2.14382i −0.414388 0.572960i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 5.14616 + 1.37891i 1.24813 + 0.334434i 0.821612 0.570047i \(-0.193075\pi\)
0.426514 + 0.904481i \(0.359742\pi\)
\(18\) 0.965926 + 0.258819i 0.227671 + 0.0610042i
\(19\) −3.61673 + 6.26436i −0.829735 + 1.43714i 0.0685112 + 0.997650i \(0.478175\pi\)
−0.898246 + 0.439493i \(0.855158\pi\)
\(20\) 0 0
\(21\) 2.63185 0.270861i 0.574317 0.0591067i
\(22\) −2.19755 2.19755i −0.468519 0.468519i
\(23\) 1.36289 + 5.08638i 0.284183 + 1.06058i 0.949435 + 0.313965i \(0.101657\pi\)
−0.665252 + 0.746619i \(0.731676\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) 4.17408 + 2.40991i 0.818604 + 0.472621i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 2.05253 + 1.66947i 0.387891 + 0.315500i
\(29\) 4.49359i 0.834438i −0.908806 0.417219i \(-0.863005\pi\)
0.908806 0.417219i \(-0.136995\pi\)
\(30\) 0 0
\(31\) −7.98911 + 4.61252i −1.43489 + 0.828432i −0.997488 0.0708354i \(-0.977433\pi\)
−0.437399 + 0.899268i \(0.644100\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) 3.00191 0.804359i 0.522565 0.140021i
\(34\) −5.32769 −0.913692
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −3.47079 + 0.929997i −0.570595 + 0.152890i −0.532569 0.846386i \(-0.678773\pi\)
−0.0380256 + 0.999277i \(0.512107\pi\)
\(38\) 1.87216 6.98699i 0.303704 1.13344i
\(39\) −4.17408 + 2.40991i −0.668387 + 0.385894i
\(40\) 0 0
\(41\) 2.51851i 0.393326i 0.980471 + 0.196663i \(0.0630104\pi\)
−0.980471 + 0.196663i \(0.936990\pi\)
\(42\) −2.47207 + 0.942805i −0.381448 + 0.145478i
\(43\) 3.86848 3.86848i 0.589938 0.589938i −0.347677 0.937615i \(-0.613029\pi\)
0.937615 + 0.347677i \(0.113029\pi\)
\(44\) 2.69144 + 1.55390i 0.405750 + 0.234260i
\(45\) 0 0
\(46\) −2.63291 4.56033i −0.388201 0.672383i
\(47\) 1.05713 + 3.94526i 0.154198 + 0.575476i 0.999173 + 0.0406690i \(0.0129489\pi\)
−0.844974 + 0.534807i \(0.820384\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −5.22224 + 4.66135i −0.746034 + 0.665908i
\(50\) 0 0
\(51\) 2.66385 4.61392i 0.373013 0.646078i
\(52\) −4.65558 1.24746i −0.645613 0.172991i
\(53\) 3.32222 + 0.890187i 0.456342 + 0.122277i 0.479665 0.877451i \(-0.340758\pi\)
−0.0233232 + 0.999728i \(0.507425\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.41468 1.08135i −0.322675 0.144502i
\(57\) 5.11483 + 5.11483i 0.677476 + 0.677476i
\(58\) 1.16303 + 4.34047i 0.152713 + 0.569932i
\(59\) 0.666188 + 1.15387i 0.0867303 + 0.150221i 0.906127 0.423005i \(-0.139025\pi\)
−0.819397 + 0.573227i \(0.805691\pi\)
\(60\) 0 0
\(61\) 10.8719 + 6.27689i 1.39200 + 0.803673i 0.993537 0.113510i \(-0.0362095\pi\)
0.398466 + 0.917183i \(0.369543\pi\)
\(62\) 6.52308 6.52308i 0.828432 0.828432i
\(63\) 0.419541 2.61228i 0.0528572 0.329116i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −2.69144 + 1.55390i −0.331293 + 0.191272i
\(67\) 1.72448 6.43584i 0.210679 0.786263i −0.776965 0.629544i \(-0.783242\pi\)
0.987643 0.156719i \(-0.0500916\pi\)
\(68\) 5.14616 1.37891i 0.624063 0.167217i
\(69\) 5.26581 0.633929
\(70\) 0 0
\(71\) 9.22738 1.09509 0.547544 0.836777i \(-0.315563\pi\)
0.547544 + 0.836777i \(0.315563\pi\)
\(72\) 0.965926 0.258819i 0.113835 0.0305021i
\(73\) −2.13063 + 7.95163i −0.249372 + 0.930667i 0.721764 + 0.692139i \(0.243332\pi\)
−0.971136 + 0.238528i \(0.923335\pi\)
\(74\) 3.11183 1.79662i 0.361743 0.208852i
\(75\) 0 0
\(76\) 7.23346i 0.829735i
\(77\) −5.18839 + 6.37885i −0.591272 + 0.726938i
\(78\) 3.40812 3.40812i 0.385894 0.385894i
\(79\) 1.65789 + 0.957181i 0.186527 + 0.107691i 0.590356 0.807143i \(-0.298988\pi\)
−0.403829 + 0.914835i \(0.632321\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.651839 2.43270i −0.0719836 0.268646i
\(83\) 8.97250 + 8.97250i 0.984860 + 0.984860i 0.999887 0.0150269i \(-0.00478339\pi\)
−0.0150269 + 0.999887i \(0.504783\pi\)
\(84\) 2.14382 1.55050i 0.233910 0.169173i
\(85\) 0 0
\(86\) −2.73543 + 4.73790i −0.294969 + 0.510901i
\(87\) −4.34047 1.16303i −0.465347 0.124689i
\(88\) −3.00191 0.804359i −0.320005 0.0857450i
\(89\) 2.03677 3.52779i 0.215897 0.373945i −0.737653 0.675181i \(-0.764066\pi\)
0.953550 + 0.301236i \(0.0973991\pi\)
\(90\) 0 0
\(91\) 5.21191 11.6383i 0.546357 1.22003i
\(92\) 3.72349 + 3.72349i 0.388201 + 0.388201i
\(93\) 2.38761 + 8.91070i 0.247584 + 0.923996i
\(94\) −2.04222 3.53723i −0.210639 0.364837i
\(95\) 0 0
\(96\) 0.866025 + 0.500000i 0.0883883 + 0.0510310i
\(97\) 2.69423 2.69423i 0.273558 0.273558i −0.556973 0.830531i \(-0.688037\pi\)
0.830531 + 0.556973i \(0.188037\pi\)
\(98\) 3.83785 5.85414i 0.387681 0.591357i
\(99\) 3.10780i 0.312346i
\(100\) 0 0
\(101\) −6.80907 + 3.93122i −0.677528 + 0.391171i −0.798923 0.601433i \(-0.794597\pi\)
0.121395 + 0.992604i \(0.461263\pi\)
\(102\) −1.37891 + 5.14616i −0.136532 + 0.509545i
\(103\) −11.4280 + 3.06212i −1.12603 + 0.301720i −0.773322 0.634013i \(-0.781407\pi\)
−0.352710 + 0.935732i \(0.614740\pi\)
\(104\) 4.81981 0.472621
\(105\) 0 0
\(106\) −3.43942 −0.334066
\(107\) −2.08859 + 0.559635i −0.201911 + 0.0541020i −0.358357 0.933585i \(-0.616663\pi\)
0.156446 + 0.987687i \(0.449996\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 0.489782 0.282776i 0.0469126 0.0270850i −0.476360 0.879250i \(-0.658044\pi\)
0.523273 + 0.852165i \(0.324711\pi\)
\(110\) 0 0
\(111\) 3.59323i 0.341054i
\(112\) 2.61228 + 0.419541i 0.246837 + 0.0396429i
\(113\) −9.98231 + 9.98231i −0.939057 + 0.939057i −0.998247 0.0591899i \(-0.981148\pi\)
0.0591899 + 0.998247i \(0.481148\pi\)
\(114\) −6.26436 3.61673i −0.586711 0.338738i
\(115\) 0 0
\(116\) −2.24679 3.89156i −0.208610 0.361322i
\(117\) 1.24746 + 4.65558i 0.115328 + 0.430408i
\(118\) −0.942132 0.942132i −0.0867303 0.0867303i
\(119\) 1.44306 + 14.0217i 0.132285 + 1.28537i
\(120\) 0 0
\(121\) 0.670774 1.16181i 0.0609795 0.105620i
\(122\) −12.1260 3.24916i −1.09784 0.294165i
\(123\) 2.43270 + 0.651839i 0.219349 + 0.0587744i
\(124\) −4.61252 + 7.98911i −0.414216 + 0.717443i
\(125\) 0 0
\(126\) 0.270861 + 2.63185i 0.0241302 + 0.234464i
\(127\) 2.14534 + 2.14534i 0.190368 + 0.190368i 0.795855 0.605487i \(-0.207022\pi\)
−0.605487 + 0.795855i \(0.707022\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −2.73543 4.73790i −0.240841 0.417149i
\(130\) 0 0
\(131\) 7.59798 + 4.38669i 0.663838 + 0.383267i 0.793738 0.608260i \(-0.208132\pi\)
−0.129900 + 0.991527i \(0.541466\pi\)
\(132\) 2.19755 2.19755i 0.191272 0.191272i
\(133\) −18.8958 3.03474i −1.63847 0.263145i
\(134\) 6.66287i 0.575584i
\(135\) 0 0
\(136\) −4.61392 + 2.66385i −0.395640 + 0.228423i
\(137\) 3.52127 13.1416i 0.300843 1.12276i −0.635622 0.772000i \(-0.719256\pi\)
0.936465 0.350760i \(-0.114077\pi\)
\(138\) −5.08638 + 1.36289i −0.432982 + 0.116017i
\(139\) 10.9145 0.925753 0.462876 0.886423i \(-0.346817\pi\)
0.462876 + 0.886423i \(0.346817\pi\)
\(140\) 0 0
\(141\) 4.08444 0.343972
\(142\) −8.91296 + 2.38822i −0.747959 + 0.200415i
\(143\) 3.87686 14.4686i 0.324199 1.20993i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 8.23213i 0.681296i
\(147\) 3.15091 + 6.25074i 0.259882 + 0.515553i
\(148\) −2.54080 + 2.54080i −0.208852 + 0.208852i
\(149\) 1.81017 + 1.04510i 0.148295 + 0.0856183i 0.572312 0.820036i \(-0.306047\pi\)
−0.424016 + 0.905655i \(0.639380\pi\)
\(150\) 0 0
\(151\) −2.02118 3.50079i −0.164481 0.284890i 0.771990 0.635635i \(-0.219262\pi\)
−0.936471 + 0.350745i \(0.885928\pi\)
\(152\) −1.87216 6.98699i −0.151852 0.566720i
\(153\) −3.76725 3.76725i −0.304564 0.304564i
\(154\) 3.36063 7.50435i 0.270807 0.604718i
\(155\) 0 0
\(156\) −2.40991 + 4.17408i −0.192947 + 0.334194i
\(157\) −0.874716 0.234379i −0.0698099 0.0187055i 0.223745 0.974648i \(-0.428172\pi\)
−0.293555 + 0.955942i \(0.594838\pi\)
\(158\) −1.84913 0.495474i −0.147109 0.0394178i
\(159\) 1.71971 2.97862i 0.136382 0.236220i
\(160\) 0 0
\(161\) −11.2889 + 8.16463i −0.889693 + 0.643463i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 1.91065 + 7.13062i 0.149653 + 0.558514i 0.999504 + 0.0314902i \(0.0100253\pi\)
−0.849851 + 0.527023i \(0.823308\pi\)
\(164\) 1.25926 + 2.18110i 0.0983314 + 0.170315i
\(165\) 0 0
\(166\) −10.9890 6.34452i −0.852914 0.492430i
\(167\) −0.610646 + 0.610646i −0.0472532 + 0.0472532i −0.730339 0.683085i \(-0.760638\pi\)
0.683085 + 0.730339i \(0.260638\pi\)
\(168\) −1.66947 + 2.05253i −0.128803 + 0.158356i
\(169\) 10.2306i 0.786967i
\(170\) 0 0
\(171\) 6.26436 3.61673i 0.479048 0.276578i
\(172\) 1.41596 5.28444i 0.107966 0.402935i
\(173\) 3.37831 0.905215i 0.256848 0.0688222i −0.128097 0.991762i \(-0.540887\pi\)
0.384945 + 0.922939i \(0.374220\pi\)
\(174\) 4.49359 0.340658
\(175\) 0 0
\(176\) 3.10780 0.234260
\(177\) 1.28698 0.344844i 0.0967351 0.0259201i
\(178\) −1.05431 + 3.93474i −0.0790239 + 0.294921i
\(179\) 15.6420 9.03091i 1.16914 0.675002i 0.215661 0.976468i \(-0.430810\pi\)
0.953477 + 0.301467i \(0.0974762\pi\)
\(180\) 0 0
\(181\) 21.7257i 1.61486i −0.589965 0.807429i \(-0.700858\pi\)
0.589965 0.807429i \(-0.299142\pi\)
\(182\) −2.02211 + 12.5907i −0.149889 + 0.933283i
\(183\) 8.87686 8.87686i 0.656196 0.656196i
\(184\) −4.56033 2.63291i −0.336192 0.194100i
\(185\) 0 0
\(186\) −4.61252 7.98911i −0.338206 0.585790i
\(187\) 4.28538 + 15.9932i 0.313378 + 1.16954i
\(188\) 2.88813 + 2.88813i 0.210639 + 0.210639i
\(189\) −2.41468 1.08135i −0.175642 0.0786568i
\(190\) 0 0
\(191\) −8.29123 + 14.3608i −0.599932 + 1.03911i 0.392898 + 0.919582i \(0.371473\pi\)
−0.992830 + 0.119531i \(0.961861\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) −2.04533 0.548044i −0.147226 0.0394491i 0.184453 0.982841i \(-0.440949\pi\)
−0.331679 + 0.943392i \(0.607615\pi\)
\(194\) −1.90511 + 3.29975i −0.136779 + 0.236908i
\(195\) 0 0
\(196\) −2.19191 + 6.64797i −0.156565 + 0.474855i
\(197\) 1.22531 + 1.22531i 0.0872995 + 0.0872995i 0.749408 0.662108i \(-0.230338\pi\)
−0.662108 + 0.749408i \(0.730338\pi\)
\(198\) 0.804359 + 3.00191i 0.0571633 + 0.213336i
\(199\) −3.93901 6.82256i −0.279229 0.483638i 0.691964 0.721932i \(-0.256745\pi\)
−0.971193 + 0.238293i \(0.923412\pi\)
\(200\) 0 0
\(201\) −5.77022 3.33144i −0.407000 0.234981i
\(202\) 5.55958 5.55958i 0.391171 0.391171i
\(203\) 11.1085 4.23657i 0.779661 0.297349i
\(204\) 5.32769i 0.373013i
\(205\) 0 0
\(206\) 10.2461 5.91556i 0.713876 0.412157i
\(207\) 1.36289 5.08638i 0.0947276 0.353528i
\(208\) −4.65558 + 1.24746i −0.322806 + 0.0864957i
\(209\) −22.4802 −1.55499
\(210\) 0 0
\(211\) −15.9995 −1.10145 −0.550724 0.834687i \(-0.685648\pi\)
−0.550724 + 0.834687i \(0.685648\pi\)
\(212\) 3.32222 0.890187i 0.228171 0.0611383i
\(213\) 2.38822 8.91296i 0.163638 0.610706i
\(214\) 1.87258 1.08113i 0.128007 0.0739047i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −18.9346 15.4009i −1.28537 1.04548i
\(218\) −0.399905 + 0.399905i −0.0270850 + 0.0270850i
\(219\) 7.12923 + 4.11606i 0.481749 + 0.278138i
\(220\) 0 0
\(221\) −12.8392 22.2382i −0.863660 1.49590i
\(222\) −0.929997 3.47079i −0.0624173 0.232944i
\(223\) −1.20707 1.20707i −0.0808314 0.0808314i 0.665535 0.746367i \(-0.268203\pi\)
−0.746367 + 0.665535i \(0.768203\pi\)
\(224\) −2.63185 + 0.270861i −0.175848 + 0.0180977i
\(225\) 0 0
\(226\) 7.05856 12.2258i 0.469528 0.813247i
\(227\) −6.58082 1.76332i −0.436784 0.117036i 0.0337248 0.999431i \(-0.489263\pi\)
−0.470509 + 0.882395i \(0.655930\pi\)
\(228\) 6.98699 + 1.87216i 0.462725 + 0.123987i
\(229\) −9.90714 + 17.1597i −0.654682 + 1.13394i 0.327291 + 0.944924i \(0.393864\pi\)
−0.981973 + 0.189019i \(0.939469\pi\)
\(230\) 0 0
\(231\) 4.81864 + 6.66257i 0.317043 + 0.438365i
\(232\) 3.17745 + 3.17745i 0.208610 + 0.208610i
\(233\) −4.65807 17.3842i −0.305161 1.13887i −0.932807 0.360376i \(-0.882648\pi\)
0.627647 0.778498i \(-0.284018\pi\)
\(234\) −2.40991 4.17408i −0.157540 0.272868i
\(235\) 0 0
\(236\) 1.15387 + 0.666188i 0.0751107 + 0.0433652i
\(237\) 1.35366 1.35366i 0.0879296 0.0879296i
\(238\) −5.02297 13.1704i −0.325591 0.853711i
\(239\) 26.6409i 1.72325i −0.507542 0.861627i \(-0.669446\pi\)
0.507542 0.861627i \(-0.330554\pi\)
\(240\) 0 0
\(241\) −12.4923 + 7.21241i −0.804697 + 0.464592i −0.845111 0.534591i \(-0.820466\pi\)
0.0404137 + 0.999183i \(0.487132\pi\)
\(242\) −0.347218 + 1.29584i −0.0223200 + 0.0832995i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 12.5538 0.803673
\(245\) 0 0
\(246\) −2.51851 −0.160575
\(247\) 33.6760 9.02344i 2.14275 0.574148i
\(248\) 2.38761 8.91070i 0.151614 0.565830i
\(249\) 10.9890 6.34452i 0.696401 0.402067i
\(250\) 0 0
\(251\) 26.4573i 1.66997i −0.550271 0.834986i \(-0.685476\pi\)
0.550271 0.834986i \(-0.314524\pi\)
\(252\) −0.942805 2.47207i −0.0593911 0.155726i
\(253\) −11.5719 + 11.5719i −0.727518 + 0.727518i
\(254\) −2.62750 1.51699i −0.164864 0.0951842i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 2.90266 + 10.8329i 0.181063 + 0.675736i 0.995439 + 0.0953987i \(0.0304126\pi\)
−0.814376 + 0.580337i \(0.802921\pi\)
\(258\) 3.86848 + 3.86848i 0.240841 + 0.240841i
\(259\) −5.57130 7.70323i −0.346183 0.478656i
\(260\) 0 0
\(261\) −2.24679 + 3.89156i −0.139073 + 0.240882i
\(262\) −8.47444 2.27072i −0.523553 0.140286i
\(263\) −6.62539 1.77527i −0.408539 0.109468i 0.0486959 0.998814i \(-0.484493\pi\)
−0.457235 + 0.889346i \(0.651160\pi\)
\(264\) −1.55390 + 2.69144i −0.0956361 + 0.165647i
\(265\) 0 0
\(266\) 19.0374 1.95926i 1.16726 0.120130i
\(267\) −2.88043 2.88043i −0.176279 0.176279i
\(268\) −1.72448 6.43584i −0.105339 0.393131i
\(269\) −4.49032 7.77746i −0.273780 0.474200i 0.696047 0.717996i \(-0.254941\pi\)
−0.969827 + 0.243796i \(0.921607\pi\)
\(270\) 0 0
\(271\) 7.76980 + 4.48590i 0.471982 + 0.272499i 0.717069 0.697002i \(-0.245483\pi\)
−0.245087 + 0.969501i \(0.578817\pi\)
\(272\) 3.76725 3.76725i 0.228423 0.228423i
\(273\) −9.89279 8.04653i −0.598739 0.486998i
\(274\) 13.6052i 0.821918i
\(275\) 0 0
\(276\) 4.56033 2.63291i 0.274499 0.158482i
\(277\) 6.39571 23.8691i 0.384281 1.43416i −0.455016 0.890483i \(-0.650367\pi\)
0.839297 0.543673i \(-0.182967\pi\)
\(278\) −10.5426 + 2.82487i −0.632301 + 0.169424i
\(279\) 9.22503 0.552288
\(280\) 0 0
\(281\) 18.4916 1.10312 0.551558 0.834137i \(-0.314034\pi\)
0.551558 + 0.834137i \(0.314034\pi\)
\(282\) −3.94526 + 1.05713i −0.234937 + 0.0629512i
\(283\) −1.44208 + 5.38190i −0.0857226 + 0.319921i −0.995450 0.0952849i \(-0.969624\pi\)
0.909727 + 0.415206i \(0.136290\pi\)
\(284\) 7.99114 4.61369i 0.474187 0.273772i
\(285\) 0 0
\(286\) 14.9790i 0.885729i
\(287\) −6.22594 + 2.37447i −0.367505 + 0.140160i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 9.85909 + 5.69215i 0.579947 + 0.334832i
\(290\) 0 0
\(291\) −1.90511 3.29975i −0.111679 0.193434i
\(292\) 2.13063 + 7.95163i 0.124686 + 0.465334i
\(293\) −17.6465 17.6465i −1.03092 1.03092i −0.999507 0.0314115i \(-0.990000\pi\)
−0.0314115 0.999507i \(-0.510000\pi\)
\(294\) −4.66135 5.22224i −0.271856 0.304567i
\(295\) 0 0
\(296\) 1.79662 3.11183i 0.104426 0.180871i
\(297\) −3.00191 0.804359i −0.174188 0.0466736i
\(298\) −2.01899 0.540986i −0.116957 0.0313385i
\(299\) 12.6901 21.9799i 0.733888 1.27113i
\(300\) 0 0
\(301\) 13.2104 + 5.91593i 0.761433 + 0.340988i
\(302\) 2.85838 + 2.85838i 0.164481 + 0.164481i
\(303\) 2.03495 + 7.59453i 0.116905 + 0.436295i
\(304\) 3.61673 + 6.26436i 0.207434 + 0.359286i
\(305\) 0 0
\(306\) 4.61392 + 2.66385i 0.263760 + 0.152282i
\(307\) −11.4807 + 11.4807i −0.655239 + 0.655239i −0.954250 0.299011i \(-0.903343\pi\)
0.299011 + 0.954250i \(0.403343\pi\)
\(308\) −1.30385 + 8.11844i −0.0742939 + 0.462591i
\(309\) 11.8311i 0.673049i
\(310\) 0 0
\(311\) −11.3751 + 6.56743i −0.645024 + 0.372405i −0.786547 0.617530i \(-0.788133\pi\)
0.141523 + 0.989935i \(0.454800\pi\)
\(312\) 1.24746 4.65558i 0.0706234 0.263570i
\(313\) 24.5811 6.58648i 1.38940 0.372290i 0.514877 0.857264i \(-0.327838\pi\)
0.874528 + 0.484974i \(0.161171\pi\)
\(314\) 0.905573 0.0511044
\(315\) 0 0
\(316\) 1.91436 0.107691
\(317\) 18.3779 4.92434i 1.03220 0.276578i 0.297325 0.954776i \(-0.403906\pi\)
0.734879 + 0.678198i \(0.237239\pi\)
\(318\) −0.890187 + 3.32222i −0.0499192 + 0.186301i
\(319\) 12.0942 6.98260i 0.677146 0.390950i
\(320\) 0 0
\(321\) 2.16226i 0.120686i
\(322\) 8.79112 10.8082i 0.489910 0.602318i
\(323\) −27.2502 + 27.2502i −1.51624 + 1.51624i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) 0 0
\(326\) −3.69108 6.39314i −0.204430 0.354083i
\(327\) −0.146375 0.546281i −0.00809458 0.0302094i
\(328\) −1.78086 1.78086i −0.0983314 0.0983314i
\(329\) −8.75629 + 6.33291i −0.482750 + 0.349145i
\(330\) 0 0
\(331\) 10.4690 18.1329i 0.575430 0.996674i −0.420565 0.907263i \(-0.638168\pi\)
0.995995 0.0894115i \(-0.0284986\pi\)
\(332\) 12.2567 + 3.28416i 0.672672 + 0.180242i
\(333\) 3.47079 + 0.929997i 0.190198 + 0.0509635i
\(334\) 0.431792 0.747886i 0.0236266 0.0409225i
\(335\) 0 0
\(336\) 1.08135 2.41468i 0.0589926 0.131732i
\(337\) −0.272770 0.272770i −0.0148587 0.0148587i 0.699638 0.714497i \(-0.253344\pi\)
−0.714497 + 0.699638i \(0.753344\pi\)
\(338\) −2.64787 9.88197i −0.144025 0.537508i
\(339\) 7.05856 + 12.2258i 0.383368 + 0.664013i
\(340\) 0 0
\(341\) −24.8286 14.3348i −1.34454 0.776273i
\(342\) −5.11483 + 5.11483i −0.276578 + 0.276578i
\(343\) −16.4467 8.51498i −0.888040 0.459766i
\(344\) 5.47086i 0.294969i
\(345\) 0 0
\(346\) −3.02891 + 1.74874i −0.162835 + 0.0940129i
\(347\) 3.91516 14.6116i 0.210177 0.784391i −0.777632 0.628720i \(-0.783579\pi\)
0.987809 0.155671i \(-0.0497540\pi\)
\(348\) −4.34047 + 1.16303i −0.232674 + 0.0623447i
\(349\) −15.2733 −0.817563 −0.408781 0.912632i \(-0.634046\pi\)
−0.408781 + 0.912632i \(0.634046\pi\)
\(350\) 0 0
\(351\) 4.81981 0.257262
\(352\) −3.00191 + 0.804359i −0.160002 + 0.0428725i
\(353\) −7.77147 + 29.0035i −0.413634 + 1.54370i 0.373923 + 0.927460i \(0.378012\pi\)
−0.787557 + 0.616242i \(0.788654\pi\)
\(354\) −1.15387 + 0.666188i −0.0613276 + 0.0354075i
\(355\) 0 0
\(356\) 4.07354i 0.215897i
\(357\) 13.9174 + 2.23519i 0.736587 + 0.118299i
\(358\) −12.7716 + 12.7716i −0.675002 + 0.675002i
\(359\) −10.1537 5.86222i −0.535890 0.309396i 0.207522 0.978230i \(-0.433460\pi\)
−0.743411 + 0.668834i \(0.766794\pi\)
\(360\) 0 0
\(361\) −16.6615 28.8585i −0.876920 1.51887i
\(362\) 5.62302 + 20.9854i 0.295540 + 1.10297i
\(363\) −0.948618 0.948618i −0.0497895 0.0497895i
\(364\) −1.30550 12.6850i −0.0684267 0.664876i
\(365\) 0 0
\(366\) −6.27689 + 10.8719i −0.328098 + 0.568283i
\(367\) −29.3629 7.86775i −1.53273 0.410693i −0.608821 0.793308i \(-0.708357\pi\)
−0.923908 + 0.382615i \(0.875024\pi\)
\(368\) 5.08638 + 1.36289i 0.265146 + 0.0710457i
\(369\) 1.25926 2.18110i 0.0655543 0.113543i
\(370\) 0 0
\(371\) 0.931604 + 9.05203i 0.0483665 + 0.469958i
\(372\) 6.52308 + 6.52308i 0.338206 + 0.338206i
\(373\) −7.80742 29.1377i −0.404253 1.50869i −0.805429 0.592692i \(-0.798065\pi\)
0.401176 0.916001i \(-0.368601\pi\)
\(374\) −8.27871 14.3392i −0.428082 0.741460i
\(375\) 0 0
\(376\) −3.53723 2.04222i −0.182419 0.105319i
\(377\) −15.3147 + 15.3147i −0.788746 + 0.788746i
\(378\) 2.61228 + 0.419541i 0.134361 + 0.0215789i
\(379\) 4.44115i 0.228127i −0.993473 0.114063i \(-0.963613\pi\)
0.993473 0.114063i \(-0.0363867\pi\)
\(380\) 0 0
\(381\) 2.62750 1.51699i 0.134611 0.0777176i
\(382\) 4.29186 16.0174i 0.219590 0.819523i
\(383\) 21.5032 5.76177i 1.09876 0.294413i 0.336502 0.941683i \(-0.390756\pi\)
0.762261 + 0.647270i \(0.224089\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 2.11748 0.107777
\(387\) −5.28444 + 1.41596i −0.268623 + 0.0719774i
\(388\) 0.986157 3.68039i 0.0500645 0.186843i
\(389\) −10.9881 + 6.34400i −0.557120 + 0.321653i −0.751989 0.659176i \(-0.770905\pi\)
0.194869 + 0.980829i \(0.437572\pi\)
\(390\) 0 0
\(391\) 28.0546i 1.41878i
\(392\) 0.396606 6.98876i 0.0200316 0.352985i
\(393\) 6.20372 6.20372i 0.312936 0.312936i
\(394\) −1.50069 0.866423i −0.0756036 0.0436498i
\(395\) 0 0
\(396\) −1.55390 2.69144i −0.0780865 0.135250i
\(397\) −5.63565 21.0326i −0.282845 1.05559i −0.950399 0.311032i \(-0.899325\pi\)
0.667554 0.744561i \(-0.267341\pi\)
\(398\) 5.57060 + 5.57060i 0.279229 + 0.279229i
\(399\) −7.82192 + 17.4665i −0.391586 + 0.874418i
\(400\) 0 0
\(401\) −13.1539 + 22.7832i −0.656872 + 1.13774i 0.324549 + 0.945869i \(0.394788\pi\)
−0.981421 + 0.191867i \(0.938546\pi\)
\(402\) 6.43584 + 1.72448i 0.320990 + 0.0860091i
\(403\) 42.9479 + 11.5078i 2.13939 + 0.573247i
\(404\) −3.93122 + 6.80907i −0.195585 + 0.338764i
\(405\) 0 0
\(406\) −9.63343 + 6.96730i −0.478099 + 0.345781i
\(407\) −7.89630 7.89630i −0.391405 0.391405i
\(408\) 1.37891 + 5.14616i 0.0682661 + 0.254773i
\(409\) 1.17325 + 2.03214i 0.0580137 + 0.100483i 0.893574 0.448917i \(-0.148190\pi\)
−0.835560 + 0.549399i \(0.814857\pi\)
\(410\) 0 0
\(411\) −11.7824 6.80258i −0.581184 0.335547i
\(412\) −8.36587 + 8.36587i −0.412157 + 0.412157i
\(413\) −2.22436 + 2.73474i −0.109454 + 0.134568i
\(414\) 5.26581i 0.258800i
\(415\) 0 0
\(416\) 4.17408 2.40991i 0.204651 0.118155i
\(417\) 2.82487 10.5426i 0.138335 0.516271i
\(418\) 21.7142 5.81830i 1.06208 0.284582i
\(419\) 1.03087 0.0503614 0.0251807 0.999683i \(-0.491984\pi\)
0.0251807 + 0.999683i \(0.491984\pi\)
\(420\) 0 0
\(421\) 28.6945 1.39849 0.699243 0.714884i \(-0.253521\pi\)
0.699243 + 0.714884i \(0.253521\pi\)
\(422\) 15.4543 4.14097i 0.752304 0.201579i
\(423\) 1.05713 3.94526i 0.0513994 0.191825i
\(424\) −2.97862 + 1.71971i −0.144655 + 0.0835164i
\(425\) 0 0
\(426\) 9.22738i 0.447068i
\(427\) −5.26683 + 32.7939i −0.254880 + 1.58701i
\(428\) −1.52895 + 1.52895i −0.0739047 + 0.0739047i
\(429\) −12.9722 7.48952i −0.626305 0.361597i
\(430\) 0 0
\(431\) 12.1388 + 21.0250i 0.584704 + 1.01274i 0.994912 + 0.100745i \(0.0321227\pi\)
−0.410208 + 0.911992i \(0.634544\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) 19.1704 + 19.1704i 0.921271 + 0.921271i 0.997119 0.0758481i \(-0.0241664\pi\)
−0.0758481 + 0.997119i \(0.524166\pi\)
\(434\) 22.2755 + 9.97551i 1.06926 + 0.478840i
\(435\) 0 0
\(436\) 0.282776 0.489782i 0.0135425 0.0234563i
\(437\) −36.7922 9.85843i −1.76001 0.471593i
\(438\) −7.95163 2.13063i −0.379943 0.101806i
\(439\) 7.29947 12.6431i 0.348385 0.603420i −0.637578 0.770386i \(-0.720064\pi\)
0.985963 + 0.166966i \(0.0533969\pi\)
\(440\) 0 0
\(441\) 6.85327 1.42573i 0.326346 0.0678920i
\(442\) 18.1574 + 18.1574i 0.863660 + 0.863660i
\(443\) 5.88534 + 21.9644i 0.279621 + 1.04356i 0.952681 + 0.303971i \(0.0983127\pi\)
−0.673060 + 0.739587i \(0.735021\pi\)
\(444\) 1.79662 + 3.11183i 0.0852636 + 0.147681i
\(445\) 0 0
\(446\) 1.47835 + 0.853528i 0.0700021 + 0.0404157i
\(447\) 1.47800 1.47800i 0.0699071 0.0699071i
\(448\) 2.47207 0.942805i 0.116794 0.0445433i
\(449\) 41.8564i 1.97532i 0.156600 + 0.987662i \(0.449947\pi\)
−0.156600 + 0.987662i \(0.550053\pi\)
\(450\) 0 0
\(451\) −6.77842 + 3.91352i −0.319183 + 0.184281i
\(452\) −3.65378 + 13.6361i −0.171859 + 0.641388i
\(453\) −3.90462 + 1.04624i −0.183455 + 0.0491566i
\(454\) 6.81296 0.319748
\(455\) 0 0
\(456\) −7.23346 −0.338738
\(457\) 25.6536 6.87387i 1.20003 0.321546i 0.397185 0.917739i \(-0.369987\pi\)
0.802841 + 0.596193i \(0.203321\pi\)
\(458\) 5.12831 19.1391i 0.239630 0.894313i
\(459\) −4.61392 + 2.66385i −0.215359 + 0.124338i
\(460\) 0 0
\(461\) 16.5608i 0.771313i −0.922642 0.385656i \(-0.873975\pi\)
0.922642 0.385656i \(-0.126025\pi\)
\(462\) −6.37885 5.18839i −0.296771 0.241386i
\(463\) 19.0305 19.0305i 0.884424 0.884424i −0.109557 0.993981i \(-0.534943\pi\)
0.993981 + 0.109557i \(0.0349431\pi\)
\(464\) −3.89156 2.24679i −0.180661 0.104305i
\(465\) 0 0
\(466\) 8.99871 + 15.5862i 0.416857 + 0.722018i
\(467\) 3.52162 + 13.1429i 0.162961 + 0.608179i 0.998291 + 0.0584309i \(0.0186097\pi\)
−0.835330 + 0.549748i \(0.814724\pi\)
\(468\) 3.40812 + 3.40812i 0.157540 + 0.157540i
\(469\) 17.5357 1.80471i 0.809722 0.0833339i
\(470\) 0 0
\(471\) −0.452786 + 0.784249i −0.0208633 + 0.0361363i
\(472\) −1.28698 0.344844i −0.0592379 0.0158727i
\(473\) 16.4230 + 4.40054i 0.755131 + 0.202337i
\(474\) −0.957181 + 1.65789i −0.0439648 + 0.0761493i
\(475\) 0 0
\(476\) 8.26057 + 11.4216i 0.378623 + 0.523508i
\(477\) −2.43203 2.43203i −0.111355 0.111355i
\(478\) 6.89516 + 25.7331i 0.315377 + 1.17700i
\(479\) 0.662643 + 1.14773i 0.0302769 + 0.0524412i 0.880767 0.473550i \(-0.157028\pi\)
−0.850490 + 0.525991i \(0.823694\pi\)
\(480\) 0 0
\(481\) 14.9984 + 8.65935i 0.683869 + 0.394832i
\(482\) 10.1999 10.1999i 0.464592 0.464592i
\(483\) 4.96463 + 13.0174i 0.225899 + 0.592314i
\(484\) 1.34155i 0.0609795i
\(485\) 0 0
\(486\) −0.866025 + 0.500000i −0.0392837 + 0.0226805i
\(487\) −8.29304 + 30.9501i −0.375794 + 1.40248i 0.476388 + 0.879235i \(0.341946\pi\)
−0.852182 + 0.523246i \(0.824721\pi\)
\(488\) −12.1260 + 3.24916i −0.548919 + 0.147082i
\(489\) 7.38217 0.333833
\(490\) 0 0
\(491\) −22.3460 −1.00846 −0.504231 0.863569i \(-0.668224\pi\)
−0.504231 + 0.863569i \(0.668224\pi\)
\(492\) 2.43270 0.651839i 0.109674 0.0293872i
\(493\) 6.19624 23.1247i 0.279065 1.04148i
\(494\) −30.1930 + 17.4320i −1.35845 + 0.784301i
\(495\) 0 0
\(496\) 9.22503i 0.414216i
\(497\) 8.69961 + 22.8107i 0.390231 + 1.02320i
\(498\) −8.97250 + 8.97250i −0.402067 + 0.402067i
\(499\) 9.39838 + 5.42616i 0.420729 + 0.242908i 0.695389 0.718633i \(-0.255232\pi\)
−0.274660 + 0.961541i \(0.588565\pi\)
\(500\) 0 0
\(501\) 0.431792 + 0.747886i 0.0192910 + 0.0334131i
\(502\) 6.84766 + 25.5558i 0.305626 + 1.14061i
\(503\) 2.64043 + 2.64043i 0.117731 + 0.117731i 0.763518 0.645787i \(-0.223471\pi\)
−0.645787 + 0.763518i \(0.723471\pi\)
\(504\) 1.55050 + 2.14382i 0.0690647 + 0.0954933i
\(505\) 0 0
\(506\) 8.18256 14.1726i 0.363759 0.630049i
\(507\) 9.88197 + 2.64787i 0.438874 + 0.117596i
\(508\) 2.93059 + 0.785250i 0.130024 + 0.0348398i
\(509\) −8.70464 + 15.0769i −0.385827 + 0.668271i −0.991883 0.127150i \(-0.959417\pi\)
0.606057 + 0.795421i \(0.292750\pi\)
\(510\) 0 0
\(511\) −21.6657 + 2.22976i −0.958435 + 0.0986389i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −1.87216 6.98699i −0.0826578 0.308483i
\(514\) −5.60751 9.71249i −0.247337 0.428399i
\(515\) 0 0
\(516\) −4.73790 2.73543i −0.208575 0.120421i
\(517\) −8.97575 + 8.97575i −0.394753 + 0.394753i
\(518\) 7.37520 + 5.99880i 0.324048 + 0.263572i
\(519\) 3.49748i 0.153522i
\(520\) 0 0
\(521\) 6.14512 3.54789i 0.269223 0.155436i −0.359312 0.933218i \(-0.616989\pi\)
0.628534 + 0.777782i \(0.283655\pi\)
\(522\) 1.16303 4.34047i 0.0509043 0.189977i
\(523\) −3.40450 + 0.912232i −0.148868 + 0.0398891i −0.332484 0.943109i \(-0.607887\pi\)
0.183615 + 0.982998i \(0.441220\pi\)
\(524\) 8.77339 0.383267
\(525\) 0 0
\(526\) 6.85911 0.299071
\(527\) −47.4734 + 12.7205i −2.06798 + 0.554112i
\(528\) 0.804359 3.00191i 0.0350052 0.130641i
\(529\) −4.09523 + 2.36438i −0.178053 + 0.102799i
\(530\) 0 0
\(531\) 1.33238i 0.0578202i
\(532\) −17.8816 + 6.81974i −0.775266 + 0.295673i
\(533\) 8.58340 8.58340i 0.371788 0.371788i
\(534\) 3.52779 + 2.03677i 0.152662 + 0.0881397i
\(535\) 0 0
\(536\) 3.33144 + 5.77022i 0.143896 + 0.249235i
\(537\) −4.67474 17.4464i −0.201730 0.752867i
\(538\) 6.35027 + 6.35027i 0.273780 + 0.273780i
\(539\) −20.6606 6.81204i −0.889915 0.293415i
\(540\) 0 0
\(541\) −10.1975 + 17.6627i −0.438426 + 0.759377i −0.997568 0.0696952i \(-0.977797\pi\)
0.559142 + 0.829072i \(0.311131\pi\)
\(542\) −8.66609 2.32207i −0.372240 0.0997415i
\(543\) −20.9854 5.62302i −0.900570 0.241307i
\(544\) −2.66385 + 4.61392i −0.114211 + 0.197820i
\(545\) 0 0
\(546\) 11.6383 + 5.21191i 0.498073 + 0.223049i
\(547\) 8.79499 + 8.79499i 0.376047 + 0.376047i 0.869674 0.493627i \(-0.164329\pi\)
−0.493627 + 0.869674i \(0.664329\pi\)
\(548\) −3.52127 13.1416i −0.150421 0.561380i
\(549\) −6.27689 10.8719i −0.267891 0.464001i
\(550\) 0 0
\(551\) 28.1495 + 16.2521i 1.19921 + 0.692363i
\(552\) −3.72349 + 3.72349i −0.158482 + 0.158482i
\(553\) −0.803154 + 5.00084i −0.0341536 + 0.212658i
\(554\) 24.7111i 1.04988i
\(555\) 0 0
\(556\) 9.45220 5.45723i 0.400863 0.231438i
\(557\) 4.64933 17.3515i 0.196999 0.735208i −0.794742 0.606947i \(-0.792394\pi\)
0.991740 0.128261i \(-0.0409395\pi\)
\(558\) −8.91070 + 2.38761i −0.377220 + 0.101076i
\(559\) −26.3685 −1.11527
\(560\) 0 0
\(561\) 16.5574 0.699055
\(562\) −17.8615 + 4.78598i −0.753442 + 0.201884i
\(563\) 11.2652 42.0423i 0.474771 1.77187i −0.147493 0.989063i \(-0.547120\pi\)
0.622264 0.782807i \(-0.286213\pi\)
\(564\) 3.53723 2.04222i 0.148944 0.0859929i
\(565\) 0 0
\(566\) 5.57176i 0.234198i
\(567\) −1.66947 + 2.05253i −0.0701112 + 0.0861980i
\(568\) −6.52474 + 6.52474i −0.273772 + 0.273772i
\(569\) 15.7466 + 9.09131i 0.660132 + 0.381128i 0.792327 0.610096i \(-0.208869\pi\)
−0.132195 + 0.991224i \(0.542203\pi\)
\(570\) 0 0
\(571\) 13.6567 + 23.6541i 0.571516 + 0.989894i 0.996411 + 0.0846515i \(0.0269777\pi\)
−0.424895 + 0.905243i \(0.639689\pi\)
\(572\) −3.87686 14.4686i −0.162100 0.604964i
\(573\) 11.7256 + 11.7256i 0.489843 + 0.489843i
\(574\) 5.39923 3.90495i 0.225360 0.162989i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −23.9084 6.40624i −0.995320 0.266695i −0.275836 0.961205i \(-0.588955\pi\)
−0.719484 + 0.694509i \(0.755621\pi\)
\(578\) −10.9964 2.94647i −0.457390 0.122557i
\(579\) −1.05874 + 1.83379i −0.0439997 + 0.0762098i
\(580\) 0 0
\(581\) −13.7213 + 30.6400i −0.569256 + 1.27116i
\(582\) 2.69423 + 2.69423i 0.111679 + 0.111679i
\(583\) 2.76653 + 10.3248i 0.114578 + 0.427610i
\(584\) −4.11606 7.12923i −0.170324 0.295010i
\(585\) 0 0
\(586\) 21.6124 + 12.4779i 0.892801 + 0.515459i
\(587\) 25.7187 25.7187i 1.06153 1.06153i 0.0635463 0.997979i \(-0.479759\pi\)
0.997979 0.0635463i \(-0.0202411\pi\)
\(588\) 5.85414 + 3.83785i 0.241421 + 0.158270i
\(589\) 66.7289i 2.74952i
\(590\) 0 0
\(591\) 1.50069 0.866423i 0.0617301 0.0356399i
\(592\) −0.929997 + 3.47079i −0.0382226 + 0.142649i
\(593\) −26.7446 + 7.16619i −1.09827 + 0.294280i −0.762059 0.647507i \(-0.775812\pi\)
−0.336209 + 0.941787i \(0.609145\pi\)
\(594\) 3.10780 0.127515
\(595\) 0 0
\(596\) 2.09021 0.0856183
\(597\) −7.60958 + 2.03898i −0.311439 + 0.0834499i
\(598\) −6.56888 + 24.5154i −0.268622 + 1.00251i
\(599\) 19.0168 10.9793i 0.777004 0.448603i −0.0583635 0.998295i \(-0.518588\pi\)
0.835367 + 0.549692i \(0.185255\pi\)
\(600\) 0 0
\(601\) 7.04092i 0.287205i 0.989635 + 0.143603i \(0.0458687\pi\)
−0.989635 + 0.143603i \(0.954131\pi\)
\(602\) −14.2914 2.29525i −0.582474 0.0935475i
\(603\) −4.71136 + 4.71136i −0.191861 + 0.191861i
\(604\) −3.50079 2.02118i −0.142445 0.0822407i
\(605\) 0 0
\(606\) −3.93122 6.80907i −0.159695 0.276600i
\(607\) −6.10130 22.7704i −0.247644 0.924221i −0.972036 0.234832i \(-0.924546\pi\)
0.724392 0.689388i \(-0.242121\pi\)
\(608\) −5.11483 5.11483i −0.207434 0.207434i
\(609\) −1.21714 11.8264i −0.0493209 0.479232i
\(610\) 0 0
\(611\) 9.84311 17.0488i 0.398209 0.689719i
\(612\) −5.14616 1.37891i −0.208021 0.0557391i
\(613\) −13.4583 3.60613i −0.543574 0.145650i −0.0234247 0.999726i \(-0.507457\pi\)
−0.520149 + 0.854075i \(0.674124\pi\)
\(614\) 8.11809 14.0609i 0.327620 0.567454i
\(615\) 0 0
\(616\) −0.841783 8.17928i −0.0339164 0.329552i
\(617\) −9.68360 9.68360i −0.389847 0.389847i 0.484786 0.874633i \(-0.338898\pi\)
−0.874633 + 0.484786i \(0.838898\pi\)
\(618\) −3.06212 11.4280i −0.123177 0.459701i
\(619\) 6.20950 + 10.7552i 0.249581 + 0.432287i 0.963410 0.268033i \(-0.0863738\pi\)
−0.713829 + 0.700320i \(0.753040\pi\)
\(620\) 0 0
\(621\) −4.56033 2.63291i −0.183000 0.105655i
\(622\) 9.28775 9.28775i 0.372405 0.372405i
\(623\) 10.6412 + 1.70902i 0.426331 + 0.0684704i
\(624\) 4.81981i 0.192947i
\(625\) 0 0
\(626\) −22.0388 + 12.7241i −0.880847 + 0.508557i
\(627\) −5.81830 + 21.7142i −0.232361 + 0.867181i
\(628\) −0.874716 + 0.234379i −0.0349050 + 0.00935276i
\(629\) −19.1436 −0.763306
\(630\) 0 0
\(631\) −0.546516 −0.0217565 −0.0108782 0.999941i \(-0.503463\pi\)
−0.0108782 + 0.999941i \(0.503463\pi\)
\(632\) −1.84913 + 0.495474i −0.0735545 + 0.0197089i
\(633\) −4.14097 + 15.4543i −0.164589 + 0.614253i
\(634\) −16.4772 + 9.51309i −0.654391 + 0.377813i
\(635\) 0 0
\(636\) 3.43942i 0.136382i
\(637\) 33.6845 + 1.91156i 1.33463 + 0.0757389i
\(638\) −9.87488 + 9.87488i −0.390950 + 0.390950i
\(639\) −7.99114 4.61369i −0.316125 0.182515i
\(640\) 0 0
\(641\) −4.37559 7.57874i −0.172825 0.299342i 0.766581 0.642147i \(-0.221956\pi\)
−0.939407 + 0.342805i \(0.888623\pi\)
\(642\) −0.559635 2.08859i −0.0220870 0.0824300i
\(643\) 10.2080 + 10.2080i 0.402565 + 0.402565i 0.879136 0.476571i \(-0.158121\pi\)
−0.476571 + 0.879136i \(0.658121\pi\)
\(644\) −5.69420 + 12.7152i −0.224383 + 0.501051i
\(645\) 0 0
\(646\) 19.2688 33.3746i 0.758122 1.31311i
\(647\) 23.1835 + 6.21201i 0.911438 + 0.244219i 0.683922 0.729555i \(-0.260273\pi\)
0.227516 + 0.973774i \(0.426940\pi\)
\(648\) −0.965926 0.258819i −0.0379452 0.0101674i
\(649\) −2.07038 + 3.58601i −0.0812696 + 0.140763i
\(650\) 0 0
\(651\) −19.7768 + 14.3034i −0.775114 + 0.560594i
\(652\) 5.21998 + 5.21998i 0.204430 + 0.204430i
\(653\) 9.71382 + 36.2525i 0.380131 + 1.41867i 0.845701 + 0.533657i \(0.179183\pi\)
−0.465570 + 0.885011i \(0.654151\pi\)
\(654\) 0.282776 + 0.489782i 0.0110574 + 0.0191520i
\(655\) 0 0
\(656\) 2.18110 + 1.25926i 0.0851575 + 0.0491657i
\(657\) 5.82099 5.82099i 0.227099 0.227099i
\(658\) 6.81885 8.38342i 0.265826 0.326820i
\(659\) 30.4591i 1.18652i 0.805011 + 0.593259i \(0.202159\pi\)
−0.805011 + 0.593259i \(0.797841\pi\)
\(660\) 0 0
\(661\) −23.8795 + 13.7868i −0.928805 + 0.536246i −0.886434 0.462856i \(-0.846825\pi\)
−0.0423719 + 0.999102i \(0.513491\pi\)
\(662\) −5.41917 + 20.2246i −0.210622 + 0.786052i
\(663\) −24.8035 + 6.64608i −0.963288 + 0.258112i
\(664\) −12.6890 −0.492430
\(665\) 0 0
\(666\) −3.59323 −0.139235
\(667\) 22.8561 6.12427i 0.884992 0.237133i
\(668\) −0.223512 + 0.834158i −0.00864794 + 0.0322746i
\(669\) −1.47835 + 0.853528i −0.0571565 + 0.0329993i
\(670\) 0 0
\(671\) 39.0147i 1.50615i
\(672\) −0.419541 + 2.61228i −0.0161842 + 0.100771i
\(673\) 8.77420 8.77420i 0.338221 0.338221i −0.517477 0.855697i \(-0.673129\pi\)
0.855697 + 0.517477i \(0.173129\pi\)
\(674\) 0.334073 + 0.192877i 0.0128680 + 0.00742935i
\(675\) 0 0
\(676\) 5.11529 + 8.85994i 0.196742 + 0.340767i
\(677\) −7.68002 28.6622i −0.295167 1.10158i −0.941085 0.338171i \(-0.890192\pi\)
0.645917 0.763407i \(-0.276475\pi\)
\(678\) −9.98231 9.98231i −0.383368 0.383368i
\(679\) 9.20045 + 4.12019i 0.353081 + 0.158118i
\(680\) 0 0
\(681\) −3.40648 + 5.90020i −0.130537 + 0.226096i
\(682\) 27.6927 + 7.42024i 1.06041 + 0.284136i
\(683\) 40.3297 + 10.8063i 1.54317 + 0.413492i 0.927289 0.374346i \(-0.122133\pi\)
0.615882 + 0.787838i \(0.288800\pi\)
\(684\) 3.61673 6.26436i 0.138289 0.239524i
\(685\) 0 0
\(686\) 18.0902 + 3.96811i 0.690686 + 0.151503i
\(687\) 14.0108 + 14.0108i 0.534546 + 0.534546i
\(688\) −1.41596 5.28444i −0.0539831 0.201468i
\(689\) −8.28867 14.3564i −0.315773 0.546935i
\(690\) 0 0
\(691\) 39.0636 + 22.5534i 1.48605 + 0.857972i 0.999874 0.0158887i \(-0.00505775\pi\)
0.486177 + 0.873860i \(0.338391\pi\)
\(692\) 2.47309 2.47309i 0.0940129 0.0940129i
\(693\) 7.68270 2.93005i 0.291842 0.111304i
\(694\) 15.1270i 0.574214i
\(695\) 0 0
\(696\) 3.89156 2.24679i 0.147509 0.0851645i
\(697\) −3.47280 + 12.9607i −0.131542 + 0.490920i
\(698\) 14.7529 3.95303i 0.558406 0.149624i
\(699\) −17.9974 −0.680725
\(700\) 0 0
\(701\) −2.29359 −0.0866278 −0.0433139 0.999062i \(-0.513792\pi\)
−0.0433139 + 0.999062i \(0.513792\pi\)
\(702\) −4.65558 + 1.24746i −0.175714 + 0.0470823i
\(703\) 6.72709 25.1059i 0.253717 0.946885i
\(704\) 2.69144 1.55390i 0.101437 0.0585649i
\(705\) 0 0
\(706\) 30.0267i 1.13007i
\(707\) −16.1379 13.1261i −0.606927 0.493658i
\(708\) 0.942132 0.942132i 0.0354075 0.0354075i
\(709\) 41.7942 + 24.1299i 1.56961 + 0.906217i 0.996213 + 0.0869427i \(0.0277097\pi\)
0.573401 + 0.819275i \(0.305624\pi\)
\(710\) 0 0
\(711\) −0.957181 1.65789i −0.0358971 0.0621756i
\(712\) 1.05431 + 3.93474i 0.0395119 + 0.147461i
\(713\) −34.3493 34.3493i −1.28639 1.28639i
\(714\) −14.0217 + 1.44306i −0.524748 + 0.0540053i
\(715\) 0 0
\(716\) 9.03091 15.6420i 0.337501 0.584569i
\(717\) −25.7331 6.89516i −0.961020 0.257505i
\(718\) 11.3249 + 3.03451i 0.422643 + 0.113247i
\(719\) 12.5235 21.6914i 0.467048 0.808951i −0.532243 0.846591i \(-0.678651\pi\)
0.999291 + 0.0376405i \(0.0119842\pi\)
\(720\) 0 0
\(721\) −18.3441 25.3638i −0.683171 0.944596i
\(722\) 23.5629 + 23.5629i 0.876920 + 0.876920i
\(723\) 3.73342 + 13.9333i 0.138847 + 0.518185i
\(724\) −10.8628 18.8150i −0.403714 0.699254i
\(725\) 0 0
\(726\) 1.16181 + 0.670774i 0.0431190 + 0.0248948i
\(727\) −17.1495 + 17.1495i −0.636039 + 0.636039i −0.949576 0.313537i \(-0.898486\pi\)
0.313537 + 0.949576i \(0.398486\pi\)
\(728\) 4.54414 + 11.9149i 0.168417 + 0.441596i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 25.2421 14.5735i 0.933612 0.539021i
\(732\) 3.24916 12.1260i 0.120092 0.448190i
\(733\) 7.18102 1.92415i 0.265237 0.0710700i −0.123750 0.992313i \(-0.539492\pi\)
0.388986 + 0.921243i \(0.372825\pi\)
\(734\) 30.3987 1.12204
\(735\) 0 0
\(736\) −5.26581 −0.194100
\(737\) 20.0013 5.35934i 0.736759 0.197414i
\(738\) −0.651839 + 2.43270i −0.0239945 + 0.0895488i
\(739\) 7.23527 4.17729i 0.266154 0.153664i −0.360985 0.932572i \(-0.617559\pi\)
0.627139 + 0.778908i \(0.284226\pi\)
\(740\) 0 0
\(741\) 34.8639i 1.28076i
\(742\) −3.24270 8.50247i −0.119043 0.312136i
\(743\) 20.5565 20.5565i 0.754146 0.754146i −0.221104 0.975250i \(-0.570966\pi\)
0.975250 + 0.221104i \(0.0709661\pi\)
\(744\) −7.98911 4.61252i −0.292895 0.169103i
\(745\) 0 0
\(746\) 15.0828 + 26.1241i 0.552220 + 0.956473i
\(747\) −3.28416 12.2567i −0.120161 0.448448i
\(748\) 11.7079 + 11.7079i 0.428082 + 0.428082i
\(749\) −3.35259 4.63550i −0.122501 0.169378i
\(750\) 0 0
\(751\) 17.3148 29.9902i 0.631828 1.09436i −0.355350 0.934733i \(-0.615638\pi\)
0.987178 0.159625i \(-0.0510283\pi\)
\(752\) 3.94526 + 1.05713i 0.143869 + 0.0385496i
\(753\) −25.5558 6.84766i −0.931306 0.249543i
\(754\) 10.8291 18.7566i 0.394373 0.683075i
\(755\) 0 0
\(756\) −2.63185 + 0.270861i −0.0957195 + 0.00985112i
\(757\) 24.7332 + 24.7332i 0.898945 + 0.898945i 0.995343 0.0963983i \(-0.0307323\pi\)
−0.0963983 + 0.995343i \(0.530732\pi\)
\(758\) 1.14946 + 4.28983i 0.0417501 + 0.155813i
\(759\) 8.18256 + 14.1726i 0.297008 + 0.514433i
\(760\) 0 0
\(761\) −32.5612 18.7992i −1.18034 0.681471i −0.224248 0.974532i \(-0.571993\pi\)
−0.956094 + 0.293061i \(0.905326\pi\)
\(762\) −2.14534 + 2.14534i −0.0777176 + 0.0777176i
\(763\) 1.16081 + 0.944172i 0.0420241 + 0.0341813i
\(764\) 16.5825i 0.599932i
\(765\) 0 0
\(766\) −19.2793 + 11.1309i −0.696588 + 0.402175i
\(767\) 1.66208 6.20298i 0.0600144 0.223977i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) −23.9494 −0.863638 −0.431819 0.901960i \(-0.642128\pi\)
−0.431819 + 0.901960i \(0.642128\pi\)
\(770\) 0 0
\(771\) 11.2150 0.403899
\(772\) −2.04533 + 0.548044i −0.0736130 + 0.0197245i
\(773\) 0.00969506 0.0361824i 0.000348707 0.00130139i −0.965751 0.259470i \(-0.916452\pi\)
0.966100 + 0.258168i \(0.0831189\pi\)
\(774\) 4.73790 2.73543i 0.170300 0.0983230i
\(775\) 0 0
\(776\) 3.81022i 0.136779i
\(777\) −8.88271 + 3.38771i −0.318665 + 0.121534i
\(778\) 8.97176 8.97176i 0.321653 0.321653i
\(779\) −15.7769 9.10878i −0.565265 0.326356i
\(780\) 0 0
\(781\) 14.3384 + 24.8349i 0.513070 + 0.888663i
\(