Properties

Label 1050.2.d.h.1049.9
Level $1050$
Weight $2$
Character 1050.1049
Analytic conductor $8.384$
Analytic rank $0$
Dimension $12$
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.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 4 x^{8} - 30 x^{6} + 36 x^{4} + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.9
Root \(-1.06864 - 1.36309i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.h.1049.10

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.36309 - 1.06864i) q^{3} +1.00000 q^{4} +(1.36309 - 1.06864i) q^{6} +(0.294447 + 2.62932i) q^{7} +1.00000 q^{8} +(0.716015 - 2.91330i) q^{9} +1.43203i q^{11} +(1.36309 - 1.06864i) q^{12} +4.73625 q^{13} +(0.294447 + 2.62932i) q^{14} +1.00000 q^{16} -2.59897i q^{17} +(0.716015 - 2.91330i) q^{18} -2.72617i q^{19} +(3.21115 + 3.26933i) q^{21} +1.43203i q^{22} -2.82660 q^{23} +(1.36309 - 1.06864i) q^{24} +4.73625 q^{26} +(-2.13728 - 4.73625i) q^{27} +(0.294447 + 2.62932i) q^{28} +2.82660i q^{29} +5.91403i q^{31} +1.00000 q^{32} +(1.53032 + 1.95198i) q^{33} -2.59897i q^{34} +(0.716015 - 2.91330i) q^{36} +2.39457i q^{37} -2.72617i q^{38} +(6.45592 - 5.06134i) q^{39} +11.1481 q^{41} +(3.21115 + 3.26933i) q^{42} +0.432029i q^{43} +1.43203i q^{44} -2.82660 q^{46} -10.3158i q^{47} +(1.36309 - 1.06864i) q^{48} +(-6.82660 + 1.54839i) q^{49} +(-2.77736 - 3.54262i) q^{51} +4.73625 q^{52} -5.69066 q^{53} +(-2.13728 - 4.73625i) q^{54} +(0.294447 + 2.62932i) q^{56} +(-2.91330 - 3.71601i) q^{57} +2.82660i q^{58} -10.7775 q^{59} +1.05058i q^{61} +5.91403i q^{62} +(7.87082 + 1.02482i) q^{63} +1.00000 q^{64} +(1.53032 + 1.95198i) q^{66} -9.82660i q^{67} -2.59897i q^{68} +(-3.85291 + 3.02062i) q^{69} +13.2586i q^{71} +(0.716015 - 2.91330i) q^{72} +7.58963 q^{73} +2.39457i q^{74} -2.72617i q^{76} +(-3.76526 + 0.421657i) q^{77} +(6.45592 - 5.06134i) q^{78} -16.5173 q^{79} +(-7.97465 - 4.17193i) q^{81} +11.1481 q^{82} -12.9148i q^{83} +(3.21115 + 3.26933i) q^{84} +0.432029i q^{86} +(3.02062 + 3.85291i) q^{87} +1.43203i q^{88} -3.90396 q^{89} +(1.39457 + 12.4531i) q^{91} -2.82660 q^{92} +(6.31998 + 8.06134i) q^{93} -10.3158i q^{94} +(1.36309 - 1.06864i) q^{96} -14.0015 q^{97} +(-6.82660 + 1.54839i) q^{98} +(4.17193 + 1.02535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 12q^{2} + 12q^{4} + 12q^{8} + O(q^{10}) \) \( 12q + 12q^{2} + 12q^{4} + 12q^{8} + 12q^{16} + 14q^{21} + 20q^{23} + 12q^{32} - 12q^{39} + 14q^{42} + 20q^{46} - 28q^{49} + 28q^{51} + 20q^{53} - 8q^{57} + 30q^{63} + 12q^{64} - 44q^{77} - 12q^{78} - 56q^{79} - 16q^{81} + 14q^{84} - 20q^{91} + 20q^{92} - 48q^{93} - 28q^{98} - 48q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.36309 1.06864i 0.786979 0.616980i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.36309 1.06864i 0.556478 0.436271i
\(7\) 0.294447 + 2.62932i 0.111290 + 0.993788i
\(8\) 1.00000 0.353553
\(9\) 0.716015 2.91330i 0.238672 0.971100i
\(10\) 0 0
\(11\) 1.43203i 0.431773i 0.976418 + 0.215887i \(0.0692641\pi\)
−0.976418 + 0.215887i \(0.930736\pi\)
\(12\) 1.36309 1.06864i 0.393489 0.308490i
\(13\) 4.73625 1.31360 0.656799 0.754066i \(-0.271910\pi\)
0.656799 + 0.754066i \(0.271910\pi\)
\(14\) 0.294447 + 2.62932i 0.0786942 + 0.702714i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.59897i 0.630342i −0.949035 0.315171i \(-0.897938\pi\)
0.949035 0.315171i \(-0.102062\pi\)
\(18\) 0.716015 2.91330i 0.168766 0.686672i
\(19\) 2.72617i 0.625427i −0.949847 0.312714i \(-0.898762\pi\)
0.949847 0.312714i \(-0.101238\pi\)
\(20\) 0 0
\(21\) 3.21115 + 3.26933i 0.700730 + 0.713426i
\(22\) 1.43203i 0.305310i
\(23\) −2.82660 −0.589387 −0.294694 0.955592i \(-0.595218\pi\)
−0.294694 + 0.955592i \(0.595218\pi\)
\(24\) 1.36309 1.06864i 0.278239 0.218135i
\(25\) 0 0
\(26\) 4.73625 0.928854
\(27\) −2.13728 4.73625i −0.411320 0.911491i
\(28\) 0.294447 + 2.62932i 0.0556452 + 0.496894i
\(29\) 2.82660i 0.524887i 0.964947 + 0.262443i \(0.0845283\pi\)
−0.964947 + 0.262443i \(0.915472\pi\)
\(30\) 0 0
\(31\) 5.91403i 1.06219i 0.847312 + 0.531096i \(0.178220\pi\)
−0.847312 + 0.531096i \(0.821780\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.53032 + 1.95198i 0.266395 + 0.339796i
\(34\) 2.59897i 0.445719i
\(35\) 0 0
\(36\) 0.716015 2.91330i 0.119336 0.485550i
\(37\) 2.39457i 0.393665i 0.980437 + 0.196833i \(0.0630656\pi\)
−0.980437 + 0.196833i \(0.936934\pi\)
\(38\) 2.72617i 0.442244i
\(39\) 6.45592 5.06134i 1.03377 0.810464i
\(40\) 0 0
\(41\) 11.1481 1.74104 0.870520 0.492134i \(-0.163783\pi\)
0.870520 + 0.492134i \(0.163783\pi\)
\(42\) 3.21115 + 3.26933i 0.495491 + 0.504468i
\(43\) 0.432029i 0.0658838i 0.999457 + 0.0329419i \(0.0104876\pi\)
−0.999457 + 0.0329419i \(0.989512\pi\)
\(44\) 1.43203i 0.215887i
\(45\) 0 0
\(46\) −2.82660 −0.416760
\(47\) 10.3158i 1.50471i −0.658755 0.752357i \(-0.728917\pi\)
0.658755 0.752357i \(-0.271083\pi\)
\(48\) 1.36309 1.06864i 0.196745 0.154245i
\(49\) −6.82660 + 1.54839i −0.975229 + 0.221198i
\(50\) 0 0
\(51\) −2.77736 3.54262i −0.388908 0.496066i
\(52\) 4.73625 0.656799
\(53\) −5.69066 −0.781672 −0.390836 0.920460i \(-0.627814\pi\)
−0.390836 + 0.920460i \(0.627814\pi\)
\(54\) −2.13728 4.73625i −0.290847 0.644521i
\(55\) 0 0
\(56\) 0.294447 + 2.62932i 0.0393471 + 0.351357i
\(57\) −2.91330 3.71601i −0.385876 0.492198i
\(58\) 2.82660i 0.371151i
\(59\) −10.7775 −1.40311 −0.701555 0.712615i \(-0.747510\pi\)
−0.701555 + 0.712615i \(0.747510\pi\)
\(60\) 0 0
\(61\) 1.05058i 0.134513i 0.997736 + 0.0672563i \(0.0214245\pi\)
−0.997736 + 0.0672563i \(0.978575\pi\)
\(62\) 5.91403i 0.751083i
\(63\) 7.87082 + 1.02482i 0.991630 + 0.129115i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.53032 + 1.95198i 0.188370 + 0.240272i
\(67\) 9.82660i 1.20051i −0.799808 0.600255i \(-0.795066\pi\)
0.799808 0.600255i \(-0.204934\pi\)
\(68\) 2.59897i 0.315171i
\(69\) −3.85291 + 3.02062i −0.463835 + 0.363640i
\(70\) 0 0
\(71\) 13.2586i 1.57351i 0.617265 + 0.786755i \(0.288240\pi\)
−0.617265 + 0.786755i \(0.711760\pi\)
\(72\) 0.716015 2.91330i 0.0843831 0.343336i
\(73\) 7.58963 0.888299 0.444150 0.895953i \(-0.353506\pi\)
0.444150 + 0.895953i \(0.353506\pi\)
\(74\) 2.39457i 0.278363i
\(75\) 0 0
\(76\) 2.72617i 0.312714i
\(77\) −3.76526 + 0.421657i −0.429091 + 0.0480522i
\(78\) 6.45592 5.06134i 0.730989 0.573084i
\(79\) −16.5173 −1.85834 −0.929169 0.369656i \(-0.879475\pi\)
−0.929169 + 0.369656i \(0.879475\pi\)
\(80\) 0 0
\(81\) −7.97465 4.17193i −0.886072 0.463548i
\(82\) 11.1481 1.23110
\(83\) 12.9148i 1.41758i −0.705419 0.708790i \(-0.749241\pi\)
0.705419 0.708790i \(-0.250759\pi\)
\(84\) 3.21115 + 3.26933i 0.350365 + 0.356713i
\(85\) 0 0
\(86\) 0.432029i 0.0465869i
\(87\) 3.02062 + 3.85291i 0.323845 + 0.413075i
\(88\) 1.43203i 0.152655i
\(89\) −3.90396 −0.413819 −0.206910 0.978360i \(-0.566341\pi\)
−0.206910 + 0.978360i \(0.566341\pi\)
\(90\) 0 0
\(91\) 1.39457 + 12.4531i 0.146191 + 1.30544i
\(92\) −2.82660 −0.294694
\(93\) 6.31998 + 8.06134i 0.655351 + 0.835923i
\(94\) 10.3158i 1.06399i
\(95\) 0 0
\(96\) 1.36309 1.06864i 0.139120 0.109068i
\(97\) −14.0015 −1.42163 −0.710817 0.703377i \(-0.751675\pi\)
−0.710817 + 0.703377i \(0.751675\pi\)
\(98\) −6.82660 + 1.54839i −0.689591 + 0.156411i
\(99\) 4.17193 + 1.02535i 0.419295 + 0.103052i
\(100\) 0 0
\(101\) −10.3158 −1.02646 −0.513231 0.858251i \(-0.671551\pi\)
−0.513231 + 0.858251i \(0.671551\pi\)
\(102\) −2.77736 3.54262i −0.275000 0.350771i
\(103\) −13.8743 −1.36707 −0.683536 0.729917i \(-0.739559\pi\)
−0.683536 + 0.729917i \(0.739559\pi\)
\(104\) 4.73625 0.464427
\(105\) 0 0
\(106\) −5.69066 −0.552726
\(107\) 15.9493 1.54188 0.770938 0.636910i \(-0.219788\pi\)
0.770938 + 0.636910i \(0.219788\pi\)
\(108\) −2.13728 4.73625i −0.205660 0.455746i
\(109\) 10.7891 1.03341 0.516706 0.856163i \(-0.327158\pi\)
0.516706 + 0.856163i \(0.327158\pi\)
\(110\) 0 0
\(111\) 2.55894 + 3.26401i 0.242884 + 0.309806i
\(112\) 0.294447 + 2.62932i 0.0278226 + 0.248447i
\(113\) −14.3439 −1.34936 −0.674679 0.738112i \(-0.735718\pi\)
−0.674679 + 0.738112i \(0.735718\pi\)
\(114\) −2.91330 3.71601i −0.272856 0.348037i
\(115\) 0 0
\(116\) 2.82660i 0.262443i
\(117\) 3.39122 13.7981i 0.313519 1.27564i
\(118\) −10.7775 −0.992148
\(119\) 6.83350 0.765257i 0.626426 0.0701510i
\(120\) 0 0
\(121\) 8.94929 0.813572
\(122\) 1.05058i 0.0951148i
\(123\) 15.1958 11.9133i 1.37016 1.07419i
\(124\) 5.91403i 0.531096i
\(125\) 0 0
\(126\) 7.87082 + 1.02482i 0.701188 + 0.0912979i
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.461684 + 0.588894i 0.0406490 + 0.0518492i
\(130\) 0 0
\(131\) −17.2804 −1.50980 −0.754899 0.655842i \(-0.772314\pi\)
−0.754899 + 0.655842i \(0.772314\pi\)
\(132\) 1.53032 + 1.95198i 0.133198 + 0.169898i
\(133\) 7.16797 0.802714i 0.621542 0.0696041i
\(134\) 9.82660i 0.848889i
\(135\) 0 0
\(136\) 2.59897i 0.222859i
\(137\) −3.03746 −0.259507 −0.129754 0.991546i \(-0.541419\pi\)
−0.129754 + 0.991546i \(0.541419\pi\)
\(138\) −3.85291 + 3.02062i −0.327981 + 0.257132i
\(139\) 20.7478i 1.75980i 0.475155 + 0.879902i \(0.342392\pi\)
−0.475155 + 0.879902i \(0.657608\pi\)
\(140\) 0 0
\(141\) −11.0239 14.0613i −0.928379 1.18418i
\(142\) 13.2586i 1.11264i
\(143\) 6.78244i 0.567176i
\(144\) 0.716015 2.91330i 0.0596679 0.242775i
\(145\) 0 0
\(146\) 7.58963 0.628122
\(147\) −7.65059 + 9.40577i −0.631010 + 0.775775i
\(148\) 2.39457i 0.196833i
\(149\) 18.9493i 1.55239i 0.630495 + 0.776193i \(0.282852\pi\)
−0.630495 + 0.776193i \(0.717148\pi\)
\(150\) 0 0
\(151\) 5.25863 0.427941 0.213971 0.976840i \(-0.431360\pi\)
0.213971 + 0.976840i \(0.431360\pi\)
\(152\) 2.72617i 0.221122i
\(153\) −7.57157 1.86090i −0.612125 0.150445i
\(154\) −3.76526 + 0.421657i −0.303413 + 0.0339781i
\(155\) 0 0
\(156\) 6.45592 5.06134i 0.516887 0.405232i
\(157\) 6.29566 0.502449 0.251224 0.967929i \(-0.419167\pi\)
0.251224 + 0.967929i \(0.419167\pi\)
\(158\) −16.5173 −1.31404
\(159\) −7.75687 + 6.08127i −0.615160 + 0.482276i
\(160\) 0 0
\(161\) −0.832284 7.43203i −0.0655932 0.585726i
\(162\) −7.97465 4.17193i −0.626547 0.327778i
\(163\) 0.605427i 0.0474207i −0.999719 0.0237104i \(-0.992452\pi\)
0.999719 0.0237104i \(-0.00754795\pi\)
\(164\) 11.1481 0.870520
\(165\) 0 0
\(166\) 12.9148i 1.00238i
\(167\) 12.0825i 0.934971i 0.884001 + 0.467485i \(0.154840\pi\)
−0.884001 + 0.467485i \(0.845160\pi\)
\(168\) 3.21115 + 3.26933i 0.247746 + 0.252234i
\(169\) 9.43203 0.725541
\(170\) 0 0
\(171\) −7.94217 1.95198i −0.607353 0.149272i
\(172\) 0.432029i 0.0329419i
\(173\) 15.5137i 1.17949i 0.807590 + 0.589744i \(0.200771\pi\)
−0.807590 + 0.589744i \(0.799229\pi\)
\(174\) 3.02062 + 3.85291i 0.228993 + 0.292088i
\(175\) 0 0
\(176\) 1.43203i 0.107943i
\(177\) −14.6907 + 11.5173i −1.10422 + 0.865690i
\(178\) −3.90396 −0.292614
\(179\) 4.56797i 0.341426i 0.985321 + 0.170713i \(0.0546071\pi\)
−0.985321 + 0.170713i \(0.945393\pi\)
\(180\) 0 0
\(181\) 7.80792i 0.580358i −0.956972 0.290179i \(-0.906285\pi\)
0.956972 0.290179i \(-0.0937149\pi\)
\(182\) 1.39457 + 12.4531i 0.103373 + 0.923084i
\(183\) 1.12269 + 1.43203i 0.0829916 + 0.105859i
\(184\) −2.82660 −0.208380
\(185\) 0 0
\(186\) 6.31998 + 8.06134i 0.463403 + 0.591086i
\(187\) 3.72179 0.272165
\(188\) 10.3158i 0.752357i
\(189\) 11.8238 7.01416i 0.860053 0.510205i
\(190\) 0 0
\(191\) 7.22117i 0.522506i 0.965270 + 0.261253i \(0.0841357\pi\)
−0.965270 + 0.261253i \(0.915864\pi\)
\(192\) 1.36309 1.06864i 0.0983724 0.0771225i
\(193\) 7.60250i 0.547240i −0.961838 0.273620i \(-0.911779\pi\)
0.961838 0.273620i \(-0.0882210\pi\)
\(194\) −14.0015 −1.00525
\(195\) 0 0
\(196\) −6.82660 + 1.54839i −0.487614 + 0.110599i
\(197\) 21.7384 1.54880 0.774400 0.632697i \(-0.218052\pi\)
0.774400 + 0.632697i \(0.218052\pi\)
\(198\) 4.17193 + 1.02535i 0.296486 + 0.0728687i
\(199\) 6.04124i 0.428252i 0.976806 + 0.214126i \(0.0686904\pi\)
−0.976806 + 0.214126i \(0.931310\pi\)
\(200\) 0 0
\(201\) −10.5011 13.3945i −0.740691 0.944776i
\(202\) −10.3158 −0.725818
\(203\) −7.43203 + 0.832284i −0.521626 + 0.0584149i
\(204\) −2.77736 3.54262i −0.194454 0.248033i
\(205\) 0 0
\(206\) −13.8743 −0.966666
\(207\) −2.02389 + 8.23474i −0.140670 + 0.572354i
\(208\) 4.73625 0.328400
\(209\) 3.90396 0.270043
\(210\) 0 0
\(211\) 16.7759 1.15490 0.577450 0.816426i \(-0.304048\pi\)
0.577450 + 0.816426i \(0.304048\pi\)
\(212\) −5.69066 −0.390836
\(213\) 14.1687 + 18.0727i 0.970824 + 1.23832i
\(214\) 15.9493 1.09027
\(215\) 0 0
\(216\) −2.13728 4.73625i −0.145424 0.322261i
\(217\) −15.5499 + 1.74137i −1.05559 + 0.118212i
\(218\) 10.7891 0.730733
\(219\) 10.3453 8.11059i 0.699073 0.548063i
\(220\) 0 0
\(221\) 12.3093i 0.828016i
\(222\) 2.55894 + 3.26401i 0.171745 + 0.219066i
\(223\) −11.1120 −0.744112 −0.372056 0.928210i \(-0.621347\pi\)
−0.372056 + 0.928210i \(0.621347\pi\)
\(224\) 0.294447 + 2.62932i 0.0196736 + 0.175679i
\(225\) 0 0
\(226\) −14.3439 −0.954140
\(227\) 7.24413i 0.480810i 0.970673 + 0.240405i \(0.0772802\pi\)
−0.970673 + 0.240405i \(0.922720\pi\)
\(228\) −2.91330 3.71601i −0.192938 0.246099i
\(229\) 27.1596i 1.79476i −0.441259 0.897380i \(-0.645468\pi\)
0.441259 0.897380i \(-0.354532\pi\)
\(230\) 0 0
\(231\) −4.68178 + 4.59846i −0.308038 + 0.302557i
\(232\) 2.82660i 0.185576i
\(233\) −5.38132 −0.352542 −0.176271 0.984342i \(-0.556404\pi\)
−0.176271 + 0.984342i \(0.556404\pi\)
\(234\) 3.39122 13.7981i 0.221691 0.902011i
\(235\) 0 0
\(236\) −10.7775 −0.701555
\(237\) −22.5145 + 17.6510i −1.46247 + 1.14656i
\(238\) 6.83350 0.765257i 0.442950 0.0496043i
\(239\) 2.51726i 0.162828i 0.996680 + 0.0814141i \(0.0259436\pi\)
−0.996680 + 0.0814141i \(0.974056\pi\)
\(240\) 0 0
\(241\) 16.8077i 1.08268i −0.840804 0.541340i \(-0.817917\pi\)
0.840804 0.541340i \(-0.182083\pi\)
\(242\) 8.94929 0.575282
\(243\) −15.3284 + 2.83532i −0.983320 + 0.181886i
\(244\) 1.05058i 0.0672563i
\(245\) 0 0
\(246\) 15.1958 11.9133i 0.968850 0.759564i
\(247\) 12.9118i 0.821560i
\(248\) 5.91403i 0.375542i
\(249\) −13.8012 17.6040i −0.874619 1.11561i
\(250\) 0 0
\(251\) −1.75565 −0.110816 −0.0554079 0.998464i \(-0.517646\pi\)
−0.0554079 + 0.998464i \(0.517646\pi\)
\(252\) 7.87082 + 1.02482i 0.495815 + 0.0645574i
\(253\) 4.04778i 0.254482i
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 21.9366i 1.36837i −0.729309 0.684184i \(-0.760159\pi\)
0.729309 0.684184i \(-0.239841\pi\)
\(258\) 0.461684 + 0.588894i 0.0287432 + 0.0366629i
\(259\) −6.29609 + 0.705074i −0.391220 + 0.0438112i
\(260\) 0 0
\(261\) 8.23474 + 2.02389i 0.509718 + 0.125276i
\(262\) −17.2804 −1.06759
\(263\) 4.08523 0.251906 0.125953 0.992036i \(-0.459801\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(264\) 1.53032 + 1.95198i 0.0941850 + 0.120136i
\(265\) 0 0
\(266\) 7.16797 0.802714i 0.439497 0.0492175i
\(267\) −5.32144 + 4.17193i −0.325667 + 0.255318i
\(268\) 9.82660i 0.600255i
\(269\) 6.96461 0.424640 0.212320 0.977200i \(-0.431898\pi\)
0.212320 + 0.977200i \(0.431898\pi\)
\(270\) 0 0
\(271\) 23.4740i 1.42594i −0.701194 0.712971i \(-0.747349\pi\)
0.701194 0.712971i \(-0.252651\pi\)
\(272\) 2.59897i 0.157585i
\(273\) 15.2088 + 15.4843i 0.920478 + 0.937155i
\(274\) −3.03746 −0.183499
\(275\) 0 0
\(276\) −3.85291 + 3.02062i −0.231918 + 0.181820i
\(277\) 14.1227i 0.848550i −0.905533 0.424275i \(-0.860529\pi\)
0.905533 0.424275i \(-0.139471\pi\)
\(278\) 20.7478i 1.24437i
\(279\) 17.2294 + 4.23453i 1.03149 + 0.253515i
\(280\) 0 0
\(281\) 23.6532i 1.41103i 0.708694 + 0.705516i \(0.249285\pi\)
−0.708694 + 0.705516i \(0.750715\pi\)
\(282\) −11.0239 14.0613i −0.656463 0.837341i
\(283\) 0.807187 0.0479823 0.0239912 0.999712i \(-0.492363\pi\)
0.0239912 + 0.999712i \(0.492363\pi\)
\(284\) 13.2586i 0.786755i
\(285\) 0 0
\(286\) 6.78244i 0.401054i
\(287\) 3.28252 + 29.3118i 0.193761 + 1.73022i
\(288\) 0.716015 2.91330i 0.0421916 0.171668i
\(289\) 10.2454 0.602669
\(290\) 0 0
\(291\) −19.0852 + 14.9625i −1.11880 + 0.877120i
\(292\) 7.58963 0.444150
\(293\) 14.6704i 0.857055i 0.903529 + 0.428528i \(0.140968\pi\)
−0.903529 + 0.428528i \(0.859032\pi\)
\(294\) −7.65059 + 9.40577i −0.446191 + 0.548556i
\(295\) 0 0
\(296\) 2.39457i 0.139182i
\(297\) 6.78244 3.06065i 0.393557 0.177597i
\(298\) 18.9493i 1.09770i
\(299\) −13.3875 −0.774218
\(300\) 0 0
\(301\) −1.13594 + 0.127210i −0.0654746 + 0.00733224i
\(302\) 5.25863 0.302600
\(303\) −14.0613 + 11.0239i −0.807803 + 0.633306i
\(304\) 2.72617i 0.156357i
\(305\) 0 0
\(306\) −7.57157 1.86090i −0.432838 0.106380i
\(307\) −10.0975 −0.576295 −0.288148 0.957586i \(-0.593039\pi\)
−0.288148 + 0.957586i \(0.593039\pi\)
\(308\) −3.76526 + 0.421657i −0.214545 + 0.0240261i
\(309\) −18.9118 + 14.8266i −1.07586 + 0.843456i
\(310\) 0 0
\(311\) 4.27456 0.242388 0.121194 0.992629i \(-0.461328\pi\)
0.121194 + 0.992629i \(0.461328\pi\)
\(312\) 6.45592 5.06134i 0.365494 0.286542i
\(313\) 0.923368 0.0521918 0.0260959 0.999659i \(-0.491692\pi\)
0.0260959 + 0.999659i \(0.491692\pi\)
\(314\) 6.29566 0.355285
\(315\) 0 0
\(316\) −16.5173 −0.929169
\(317\) −15.7384 −0.883959 −0.441979 0.897025i \(-0.645724\pi\)
−0.441979 + 0.897025i \(0.645724\pi\)
\(318\) −7.75687 + 6.08127i −0.434984 + 0.341021i
\(319\) −4.04778 −0.226632
\(320\) 0 0
\(321\) 21.7403 17.0441i 1.21342 0.951307i
\(322\) −0.832284 7.43203i −0.0463814 0.414171i
\(323\) −7.08523 −0.394233
\(324\) −7.97465 4.17193i −0.443036 0.231774i
\(325\) 0 0
\(326\) 0.605427i 0.0335315i
\(327\) 14.7065 11.5297i 0.813274 0.637595i
\(328\) 11.1481 0.615550
\(329\) 27.1235 3.03746i 1.49537 0.167460i
\(330\) 0 0
\(331\) −12.6054 −0.692857 −0.346428 0.938076i \(-0.612606\pi\)
−0.346428 + 0.938076i \(0.612606\pi\)
\(332\) 12.9148i 0.708790i
\(333\) 6.97611 + 1.71455i 0.382289 + 0.0939567i
\(334\) 12.0825i 0.661124i
\(335\) 0 0
\(336\) 3.21115 + 3.26933i 0.175183 + 0.178357i
\(337\) 18.8986i 1.02947i −0.857349 0.514736i \(-0.827890\pi\)
0.857349 0.514736i \(-0.172110\pi\)
\(338\) 9.43203 0.513035
\(339\) −19.5519 + 15.3284i −1.06192 + 0.832526i
\(340\) 0 0
\(341\) −8.46907 −0.458626
\(342\) −7.94217 1.95198i −0.429463 0.105551i
\(343\) −6.08127 17.4934i −0.328358 0.944553i
\(344\) 0.432029i 0.0232935i
\(345\) 0 0
\(346\) 15.5137i 0.834024i
\(347\) −30.7384 −1.65013 −0.825063 0.565041i \(-0.808860\pi\)
−0.825063 + 0.565041i \(0.808860\pi\)
\(348\) 3.02062 + 3.85291i 0.161922 + 0.206537i
\(349\) 0.970523i 0.0519509i 0.999663 + 0.0259754i \(0.00826917\pi\)
−0.999663 + 0.0259754i \(0.991731\pi\)
\(350\) 0 0
\(351\) −10.1227 22.4320i −0.540309 1.19733i
\(352\) 1.43203i 0.0763274i
\(353\) 16.3570i 0.870598i 0.900286 + 0.435299i \(0.143357\pi\)
−0.900286 + 0.435299i \(0.856643\pi\)
\(354\) −14.6907 + 11.5173i −0.780800 + 0.612136i
\(355\) 0 0
\(356\) −3.90396 −0.206910
\(357\) 8.49687 8.34567i 0.449702 0.441700i
\(358\) 4.56797i 0.241425i
\(359\) 9.81335i 0.517929i −0.965887 0.258964i \(-0.916619\pi\)
0.965887 0.258964i \(-0.0833812\pi\)
\(360\) 0 0
\(361\) 11.5680 0.608841
\(362\) 7.80792i 0.410375i
\(363\) 12.1987 9.56358i 0.640264 0.501958i
\(364\) 1.39457 + 12.4531i 0.0730955 + 0.652719i
\(365\) 0 0
\(366\) 1.12269 + 1.43203i 0.0586839 + 0.0748534i
\(367\) 33.9970 1.77463 0.887315 0.461163i \(-0.152568\pi\)
0.887315 + 0.461163i \(0.152568\pi\)
\(368\) −2.82660 −0.147347
\(369\) 7.98220 32.4777i 0.415537 1.69072i
\(370\) 0 0
\(371\) −1.67560 14.9625i −0.0869927 0.776817i
\(372\) 6.31998 + 8.06134i 0.327676 + 0.417961i
\(373\) 26.5650i 1.37549i −0.725954 0.687743i \(-0.758602\pi\)
0.725954 0.687743i \(-0.241398\pi\)
\(374\) 3.72179 0.192449
\(375\) 0 0
\(376\) 10.3158i 0.531997i
\(377\) 13.3875i 0.689490i
\(378\) 11.8238 7.01416i 0.608149 0.360769i
\(379\) −8.25863 −0.424217 −0.212109 0.977246i \(-0.568033\pi\)
−0.212109 + 0.977246i \(0.568033\pi\)
\(380\) 0 0
\(381\) 2.13728 + 2.72617i 0.109496 + 0.139666i
\(382\) 7.22117i 0.369467i
\(383\) 32.6920i 1.67049i −0.549882 0.835243i \(-0.685327\pi\)
0.549882 0.835243i \(-0.314673\pi\)
\(384\) 1.36309 1.06864i 0.0695598 0.0545338i
\(385\) 0 0
\(386\) 7.60250i 0.386957i
\(387\) 1.25863 + 0.309339i 0.0639798 + 0.0157246i
\(388\) −14.0015 −0.710817
\(389\) 1.33354i 0.0676134i 0.999428 + 0.0338067i \(0.0107631\pi\)
−0.999428 + 0.0338067i \(0.989237\pi\)
\(390\) 0 0
\(391\) 7.34624i 0.371515i
\(392\) −6.82660 + 1.54839i −0.344795 + 0.0782054i
\(393\) −23.5547 + 18.4666i −1.18818 + 0.931514i
\(394\) 21.7384 1.09517
\(395\) 0 0
\(396\) 4.17193 + 1.02535i 0.209647 + 0.0515260i
\(397\) 23.0123 1.15495 0.577477 0.816407i \(-0.304037\pi\)
0.577477 + 0.816407i \(0.304037\pi\)
\(398\) 6.04124i 0.302820i
\(399\) 8.91276 8.75416i 0.446196 0.438256i
\(400\) 0 0
\(401\) 17.5547i 0.876641i 0.898819 + 0.438320i \(0.144426\pi\)
−0.898819 + 0.438320i \(0.855574\pi\)
\(402\) −10.5011 13.3945i −0.523748 0.668058i
\(403\) 28.0103i 1.39529i
\(404\) −10.3158 −0.513231
\(405\) 0 0
\(406\) −7.43203 + 0.832284i −0.368845 + 0.0413056i
\(407\) −3.42910 −0.169974
\(408\) −2.77736 3.54262i −0.137500 0.175386i
\(409\) 9.94521i 0.491759i 0.969300 + 0.245879i \(0.0790767\pi\)
−0.969300 + 0.245879i \(0.920923\pi\)
\(410\) 0 0
\(411\) −4.14032 + 3.24595i −0.204227 + 0.160111i
\(412\) −13.8743 −0.683536
\(413\) −3.17340 28.3374i −0.156153 1.39439i
\(414\) −2.02389 + 8.23474i −0.0994687 + 0.404716i
\(415\) 0 0
\(416\) 4.73625 0.232214
\(417\) 22.1719 + 28.2811i 1.08576 + 1.38493i
\(418\) 3.90396 0.190949
\(419\) 7.71684 0.376992 0.188496 0.982074i \(-0.439639\pi\)
0.188496 + 0.982074i \(0.439639\pi\)
\(420\) 0 0
\(421\) 11.2109 0.546384 0.273192 0.961960i \(-0.411921\pi\)
0.273192 + 0.961960i \(0.411921\pi\)
\(422\) 16.7759 0.816638
\(423\) −30.0530 7.38627i −1.46123 0.359133i
\(424\) −5.69066 −0.276363
\(425\) 0 0
\(426\) 14.1687 + 18.0727i 0.686476 + 0.875624i
\(427\) −2.76230 + 0.309339i −0.133677 + 0.0149700i
\(428\) 15.9493 0.770938
\(429\) 7.24799 + 9.24506i 0.349936 + 0.446356i
\(430\) 0 0
\(431\) 26.2079i 1.26239i −0.775624 0.631196i \(-0.782565\pi\)
0.775624 0.631196i \(-0.217435\pi\)
\(432\) −2.13728 4.73625i −0.102830 0.227873i
\(433\) 23.4378 1.12635 0.563175 0.826337i \(-0.309580\pi\)
0.563175 + 0.826337i \(0.309580\pi\)
\(434\) −15.5499 + 1.74137i −0.746417 + 0.0835884i
\(435\) 0 0
\(436\) 10.7891 0.516706
\(437\) 7.70581i 0.368619i
\(438\) 10.3453 8.11059i 0.494319 0.387539i
\(439\) 25.0334i 1.19478i −0.801952 0.597389i \(-0.796205\pi\)
0.801952 0.597389i \(-0.203795\pi\)
\(440\) 0 0
\(441\) −0.377028 + 20.9966i −0.0179537 + 0.999839i
\(442\) 12.3093i 0.585496i
\(443\) 18.4666 0.877373 0.438686 0.898640i \(-0.355444\pi\)
0.438686 + 0.898640i \(0.355444\pi\)
\(444\) 2.55894 + 3.26401i 0.121442 + 0.154903i
\(445\) 0 0
\(446\) −11.1120 −0.526167
\(447\) 20.2500 + 25.8295i 0.957791 + 1.22170i
\(448\) 0.294447 + 2.62932i 0.0139113 + 0.124223i
\(449\) 32.3439i 1.52640i −0.646162 0.763201i \(-0.723627\pi\)
0.646162 0.763201i \(-0.276373\pi\)
\(450\) 0 0
\(451\) 15.9644i 0.751734i
\(452\) −14.3439 −0.674679
\(453\) 7.16797 5.61959i 0.336781 0.264031i
\(454\) 7.24413i 0.339984i
\(455\) 0 0
\(456\) −2.91330 3.71601i −0.136428 0.174018i
\(457\) 10.9251i 0.511054i −0.966802 0.255527i \(-0.917751\pi\)
0.966802 0.255527i \(-0.0822490\pi\)
\(458\) 27.1596i 1.26909i
\(459\) −12.3093 + 5.55472i −0.574551 + 0.259272i
\(460\) 0 0
\(461\) 26.6729 1.24228 0.621139 0.783700i \(-0.286670\pi\)
0.621139 + 0.783700i \(0.286670\pi\)
\(462\) −4.68178 + 4.59846i −0.217816 + 0.213940i
\(463\) 8.07491i 0.375273i −0.982239 0.187637i \(-0.939917\pi\)
0.982239 0.187637i \(-0.0600827\pi\)
\(464\) 2.82660i 0.131222i
\(465\) 0 0
\(466\) −5.38132 −0.249285
\(467\) 41.6228i 1.92607i −0.269371 0.963037i \(-0.586816\pi\)
0.269371 0.963037i \(-0.413184\pi\)
\(468\) 3.39122 13.7981i 0.156759 0.637818i
\(469\) 25.8372 2.89341i 1.19305 0.133605i
\(470\) 0 0
\(471\) 8.58154 6.72780i 0.395416 0.310001i
\(472\) −10.7775 −0.496074
\(473\) −0.618679 −0.0284469
\(474\) −22.5145 + 17.6510i −1.03412 + 0.810738i
\(475\) 0 0
\(476\) 6.83350 0.765257i 0.313213 0.0350755i
\(477\) −4.07460 + 16.5786i −0.186563 + 0.759082i
\(478\) 2.51726i 0.115137i
\(479\) −21.3728 −0.976549 −0.488274 0.872690i \(-0.662373\pi\)
−0.488274 + 0.872690i \(0.662373\pi\)
\(480\) 0 0
\(481\) 11.3413i 0.517118i
\(482\) 16.8077i 0.765570i
\(483\) −9.07664 9.24109i −0.413002 0.420484i
\(484\) 8.94929 0.406786
\(485\) 0 0
\(486\) −15.3284 + 2.83532i −0.695312 + 0.128613i
\(487\) 27.1094i 1.22845i 0.789133 + 0.614223i \(0.210530\pi\)
−0.789133 + 0.614223i \(0.789470\pi\)
\(488\) 1.05058i 0.0475574i
\(489\) −0.646984 0.825250i −0.0292576 0.0373191i
\(490\) 0 0
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) 15.1958 11.9133i 0.685081 0.537093i
\(493\) 7.34624 0.330858
\(494\) 12.9118i 0.580931i
\(495\) 0 0
\(496\) 5.91403i 0.265548i
\(497\) −34.8611 + 3.90396i −1.56374 + 0.175117i
\(498\) −13.8012 17.6040i −0.618449 0.788852i
\(499\) −8.50694 −0.380823 −0.190412 0.981704i \(-0.560982\pi\)
−0.190412 + 0.981704i \(0.560982\pi\)
\(500\) 0 0
\(501\) 12.9118 + 16.4695i 0.576858 + 0.735802i
\(502\) −1.75565 −0.0783586
\(503\) 12.1625i 0.542301i −0.962537 0.271150i \(-0.912596\pi\)
0.962537 0.271150i \(-0.0874041\pi\)
\(504\) 7.87082 + 1.02482i 0.350594 + 0.0456489i
\(505\) 0 0
\(506\) 4.04778i 0.179946i
\(507\) 12.8567 10.0794i 0.570985 0.447644i
\(508\) 2.00000i 0.0887357i
\(509\) −6.12130 −0.271322 −0.135661 0.990755i \(-0.543316\pi\)
−0.135661 + 0.990755i \(0.543316\pi\)
\(510\) 0 0
\(511\) 2.23474 + 19.9555i 0.0988592 + 0.882781i
\(512\) 1.00000 0.0441942
\(513\) −12.9118 + 5.82660i −0.570071 + 0.257251i
\(514\) 21.9366i 0.967582i
\(515\) 0 0
\(516\) 0.461684 + 0.588894i 0.0203245 + 0.0259246i
\(517\) 14.7725 0.649695
\(518\) −6.29609 + 0.705074i −0.276634 + 0.0309792i
\(519\) 16.5786 + 21.1466i 0.727720 + 0.928232i
\(520\) 0 0
\(521\) 32.7031 1.43275 0.716374 0.697717i \(-0.245801\pi\)
0.716374 + 0.697717i \(0.245801\pi\)
\(522\) 8.23474 + 2.02389i 0.360425 + 0.0885832i
\(523\) −28.5557 −1.24865 −0.624327 0.781163i \(-0.714627\pi\)
−0.624327 + 0.781163i \(0.714627\pi\)
\(524\) −17.2804 −0.754899
\(525\) 0 0
\(526\) 4.08523 0.178125
\(527\) 15.3704 0.669544
\(528\) 1.53032 + 1.95198i 0.0665988 + 0.0849491i
\(529\) −15.0103 −0.652623
\(530\) 0 0
\(531\) −7.71684 + 31.3981i −0.334882 + 1.36256i
\(532\) 7.16797 0.802714i 0.310771 0.0348020i
\(533\) 52.8001 2.28703
\(534\) −5.32144 + 4.17193i −0.230281 + 0.180537i
\(535\) 0 0
\(536\) 9.82660i 0.424445i
\(537\) 4.88152 + 6.22654i 0.210653 + 0.268695i
\(538\) 6.96461 0.300266
\(539\) −2.21734 9.77589i −0.0955074 0.421078i
\(540\) 0 0
\(541\) −34.2932 −1.47438 −0.737189 0.675687i \(-0.763847\pi\)
−0.737189 + 0.675687i \(0.763847\pi\)
\(542\) 23.4740i 1.00829i
\(543\) −8.34386 10.6429i −0.358070 0.456730i
\(544\) 2.59897i 0.111430i
\(545\) 0 0
\(546\) 15.2088 + 15.4843i 0.650876 + 0.662669i
\(547\) 26.7759i 1.14485i 0.819955 + 0.572427i \(0.193998\pi\)
−0.819955 + 0.572427i \(0.806002\pi\)
\(548\) −3.03746 −0.129754
\(549\) 3.06065 + 0.752229i 0.130625 + 0.0321044i
\(550\) 0 0
\(551\) 7.70581 0.328279
\(552\) −3.85291 + 3.02062i −0.163991 + 0.128566i
\(553\) −4.86346 43.4291i −0.206815 1.84679i
\(554\) 14.1227i 0.600016i
\(555\) 0 0
\(556\) 20.7478i 0.879902i
\(557\) 40.4158 1.71247 0.856237 0.516583i \(-0.172796\pi\)
0.856237 + 0.516583i \(0.172796\pi\)
\(558\) 17.2294 + 4.23453i 0.729377 + 0.179262i
\(559\) 2.04620i 0.0865449i
\(560\) 0 0
\(561\) 5.07313 3.97726i 0.214188 0.167920i
\(562\) 23.6532i 0.997750i
\(563\) 8.16750i 0.344219i −0.985078 0.172109i \(-0.944942\pi\)
0.985078 0.172109i \(-0.0550583\pi\)
\(564\) −11.0239 14.0613i −0.464189 0.592089i
\(565\) 0 0
\(566\) 0.807187 0.0339286
\(567\) 8.62122 22.1963i 0.362057 0.932156i
\(568\) 13.2586i 0.556320i
\(569\) 15.0375i 0.630403i −0.949025 0.315201i \(-0.897928\pi\)
0.949025 0.315201i \(-0.102072\pi\)
\(570\) 0 0
\(571\) 38.6025 1.61546 0.807732 0.589550i \(-0.200695\pi\)
0.807732 + 0.589550i \(0.200695\pi\)
\(572\) 6.78244i 0.283588i
\(573\) 7.71684 + 9.84309i 0.322376 + 0.411201i
\(574\) 3.28252 + 29.3118i 0.137010 + 1.22345i
\(575\) 0 0
\(576\) 0.716015 2.91330i 0.0298339 0.121388i
\(577\) 23.9467 0.996913 0.498457 0.866915i \(-0.333900\pi\)
0.498457 + 0.866915i \(0.333900\pi\)
\(578\) 10.2454 0.426152
\(579\) −8.12434 10.3629i −0.337636 0.430666i
\(580\) 0 0
\(581\) 33.9570 3.80271i 1.40877 0.157763i
\(582\) −19.0852 + 14.9625i −0.791108 + 0.620217i
\(583\) 8.14919i 0.337505i
\(584\) 7.58963 0.314061
\(585\) 0 0
\(586\) 14.6704i 0.606030i
\(587\) 17.9305i 0.740072i 0.929017 + 0.370036i \(0.120655\pi\)
−0.929017 + 0.370036i \(0.879345\pi\)
\(588\) −7.65059 + 9.40577i −0.315505 + 0.387887i
\(589\) 16.1227 0.664324
\(590\) 0 0
\(591\) 29.6314 23.2306i 1.21887 0.955578i
\(592\) 2.39457i 0.0984163i
\(593\) 18.5744i 0.762759i 0.924419 + 0.381379i \(0.124551\pi\)
−0.924419 + 0.381379i \(0.875449\pi\)
\(594\) 6.78244 3.06065i 0.278287 0.125580i
\(595\) 0 0
\(596\) 18.9493i 0.776193i
\(597\) 6.45592 + 8.23474i 0.264223 + 0.337026i
\(598\) −13.3875 −0.547455
\(599\) 29.3439i 1.19896i 0.800391 + 0.599479i \(0.204625\pi\)
−0.800391 + 0.599479i \(0.795375\pi\)
\(600\) 0 0
\(601\) 22.5145i 0.918385i 0.888337 + 0.459192i \(0.151861\pi\)
−0.888337 + 0.459192i \(0.848139\pi\)
\(602\) −1.13594 + 0.127210i −0.0462975 + 0.00518468i
\(603\) −28.6279 7.03599i −1.16582 0.286528i
\(604\) 5.25863 0.213971
\(605\) 0 0
\(606\) −14.0613 + 11.0239i −0.571203 + 0.447815i
\(607\) 17.5128 0.710822 0.355411 0.934710i \(-0.384341\pi\)
0.355411 + 0.934710i \(0.384341\pi\)
\(608\) 2.72617i 0.110561i
\(609\) −9.24109 + 9.07664i −0.374468 + 0.367804i
\(610\) 0 0
\(611\) 48.8582i 1.97659i
\(612\) −7.57157 1.86090i −0.306062 0.0752223i
\(613\) 32.7626i 1.32327i 0.749826 + 0.661635i \(0.230137\pi\)
−0.749826 + 0.661635i \(0.769863\pi\)
\(614\) −10.0975 −0.407502
\(615\) 0 0
\(616\) −3.76526 + 0.421657i −0.151707 + 0.0169890i
\(617\) 0.693592 0.0279229 0.0139615 0.999903i \(-0.495556\pi\)
0.0139615 + 0.999903i \(0.495556\pi\)
\(618\) −18.9118 + 14.8266i −0.760746 + 0.596413i
\(619\) 18.5305i 0.744802i 0.928072 + 0.372401i \(0.121465\pi\)
−0.928072 + 0.372401i \(0.878535\pi\)
\(620\) 0 0
\(621\) 6.04124 + 13.3875i 0.242427 + 0.537221i
\(622\) 4.27456 0.171394
\(623\) −1.14951 10.2647i −0.0460541 0.411248i
\(624\) 6.45592 5.06134i 0.258444 0.202616i
\(625\) 0 0
\(626\) 0.923368 0.0369052
\(627\) 5.32144 4.17193i 0.212518 0.166611i
\(628\) 6.29566 0.251224
\(629\) 6.22341 0.248144
\(630\) 0 0
\(631\) −8.39457 −0.334183 −0.167091 0.985941i \(-0.553437\pi\)
−0.167091 + 0.985941i \(0.553437\pi\)
\(632\) −16.5173 −0.657021
\(633\) 22.8670 17.9274i 0.908882 0.712550i
\(634\) −15.7384 −0.625053
\(635\) 0 0
\(636\) −7.75687 + 6.08127i −0.307580 + 0.241138i
\(637\) −32.3325 + 7.33354i −1.28106 + 0.290566i
\(638\) −4.04778 −0.160253
\(639\) 38.6264 + 9.49337i 1.52804 + 0.375552i
\(640\) 0 0
\(641\) 23.6532i 0.934245i −0.884193 0.467123i \(-0.845291\pi\)
0.884193 0.467123i \(-0.154709\pi\)
\(642\) 21.7403 17.0441i 0.858020 0.672675i
\(643\) 2.60999 0.102928 0.0514641 0.998675i \(-0.483611\pi\)
0.0514641 + 0.998675i \(0.483611\pi\)
\(644\) −0.832284 7.43203i −0.0327966 0.292863i
\(645\) 0 0
\(646\) −7.08523 −0.278765
\(647\) 4.45673i 0.175212i 0.996155 + 0.0876061i \(0.0279217\pi\)
−0.996155 + 0.0876061i \(0.972078\pi\)
\(648\) −7.97465 4.17193i −0.313274 0.163889i
\(649\) 15.4337i 0.605825i
\(650\) 0 0
\(651\) −19.3349 + 18.9909i −0.757795 + 0.744310i
\(652\) 0.605427i 0.0237104i
\(653\) 30.9118 1.20967 0.604837 0.796349i \(-0.293238\pi\)
0.604837 + 0.796349i \(0.293238\pi\)
\(654\) 14.7065 11.5297i 0.575072 0.450848i
\(655\) 0 0
\(656\) 11.1481 0.435260
\(657\) 5.43429 22.1109i 0.212012 0.862628i
\(658\) 27.1235 3.03746i 1.05738 0.118412i
\(659\) 4.56797i 0.177943i 0.996034 + 0.0889714i \(0.0283580\pi\)
−0.996034 + 0.0889714i \(0.971642\pi\)
\(660\) 0 0
\(661\) 38.0643i 1.48053i −0.672315 0.740266i \(-0.734700\pi\)
0.672315 0.740266i \(-0.265300\pi\)
\(662\) −12.6054 −0.489924
\(663\) −13.1543 16.7787i −0.510869 0.651631i
\(664\) 12.9148i 0.501190i
\(665\) 0 0
\(666\) 6.97611 + 1.71455i 0.270319 + 0.0664374i
\(667\) 7.98968i 0.309362i
\(668\) 12.0825i 0.467485i
\(669\) −15.1466 + 11.8747i −0.585601 + 0.459102i
\(670\) 0 0
\(671\) −1.50446 −0.0580790
\(672\) 3.21115 + 3.26933i 0.123873 + 0.126117i
\(673\) 21.2212i 0.818016i 0.912531 + 0.409008i \(0.134125\pi\)
−0.912531 + 0.409008i \(0.865875\pi\)
\(674\) 18.8986i 0.727946i
\(675\) 0 0
\(676\) 9.43203 0.362770
\(677\) 3.53336i 0.135798i −0.997692 0.0678991i \(-0.978370\pi\)
0.997692 0.0678991i \(-0.0216296\pi\)
\(678\) −19.5519 + 15.3284i −0.750888 + 0.588685i
\(679\) −4.12269 36.8143i −0.158214 1.41280i
\(680\) 0 0
\(681\) 7.74137 + 9.87438i 0.296650 + 0.378387i
\(682\) −8.46907 −0.324297
\(683\) −1.70391 −0.0651984 −0.0325992 0.999469i \(-0.510378\pi\)
−0.0325992 + 0.999469i \(0.510378\pi\)
\(684\) −7.94217 1.95198i −0.303676 0.0746359i
\(685\) 0 0
\(686\) −6.08127 17.4934i −0.232184 0.667900i
\(687\) −29.0239 37.0210i −1.10733 1.41244i
\(688\) 0.432029i 0.0164710i
\(689\) −26.9524 −1.02680
\(690\) 0 0
\(691\) 2.21734i 0.0843514i 0.999110 + 0.0421757i \(0.0134289\pi\)
−0.999110 + 0.0421757i \(0.986571\pi\)
\(692\) 15.5137i 0.589744i
\(693\) −1.46757 + 11.2712i −0.0557483 + 0.428159i
\(694\) −30.7384 −1.16682
\(695\) 0 0
\(696\) 3.02062 + 3.85291i 0.114496 + 0.146044i
\(697\) 28.9735i 1.09745i
\(698\) 0.970523i 0.0367348i
\(699\) −7.33521 + 5.75070i −0.277443 + 0.217511i
\(700\) 0 0
\(701\) 3.11976i 0.117832i −0.998263 0.0589158i \(-0.981236\pi\)
0.998263 0.0589158i \(-0.0187644\pi\)
\(702\) −10.1227 22.4320i −0.382056 0.846642i
\(703\) 6.52802 0.246209
\(704\) 1.43203i 0.0539716i
\(705\) 0 0
\(706\) 16.3570i 0.615606i
\(707\) −3.03746 27.1235i −0.114235 1.02008i
\(708\) −14.6907 + 11.5173i −0.552109 + 0.432845i
\(709\) −12.8641 −0.483120 −0.241560 0.970386i \(-0.577659\pi\)
−0.241560 + 0.970386i \(0.577659\pi\)
\(710\) 0 0
\(711\) −11.8266 + 48.1198i −0.443532 + 1.80463i
\(712\) −3.90396 −0.146307
\(713\) 16.7166i 0.626042i
\(714\) 8.49687 8.34567i 0.317987 0.312329i
\(715\) 0 0
\(716\) 4.56797i 0.170713i
\(717\) 2.69005 + 3.43125i 0.100462 + 0.128142i
\(718\) 9.81335i 0.366231i
\(719\) 28.5196 1.06360 0.531801 0.846870i \(-0.321516\pi\)
0.531801 + 0.846870i \(0.321516\pi\)
\(720\) 0 0
\(721\) −4.08523 36.4798i −0.152142 1.35858i
\(722\) 11.5680 0.430515
\(723\) −17.9614 22.9104i −0.667991 0.852046i
\(724\) 7.80792i 0.290179i
\(725\) 0 0
\(726\) 12.1987 9.56358i 0.452735 0.354938i
\(727\) 18.9921 0.704379 0.352190 0.935929i \(-0.385437\pi\)
0.352190 + 0.935929i \(0.385437\pi\)
\(728\) 1.39457 + 12.4531i 0.0516863 + 0.461542i
\(729\) −17.8641 + 20.2454i −0.661632 + 0.749829i
\(730\) 0 0
\(731\) 1.12283 0.0415293
\(732\) 1.12269 + 1.43203i 0.0414958 + 0.0529293i
\(733\) 27.1345 1.00224 0.501119 0.865379i \(-0.332922\pi\)
0.501119 + 0.865379i \(0.332922\pi\)
\(734\) 33.9970 1.25485
\(735\) 0 0
\(736\) −2.82660 −0.104190
\(737\) 14.0720 0.518348
\(738\) 7.98220 32.4777i 0.293829 1.19552i
\(739\) −8.67741 −0.319204 −0.159602 0.987181i \(-0.551021\pi\)
−0.159602 + 0.987181i \(0.551021\pi\)
\(740\) 0 0
\(741\) −13.7981 17.6000i −0.506886 0.646551i
\(742\) −1.67560 14.9625i −0.0615131 0.549292i
\(743\) 52.5754 1.92880 0.964401 0.264443i \(-0.0851879\pi\)
0.964401 + 0.264443i \(0.0851879\pi\)
\(744\) 6.31998 + 8.06134i 0.231702 + 0.295543i
\(745\) 0 0
\(746\) 26.5650i 0.972615i
\(747\) −37.6246 9.24717i −1.37661 0.338336i
\(748\) 3.72179 0.136082
\(749\) 4.69622 + 41.9357i 0.171596 + 1.53230i
\(750\) 0 0
\(751\) 1.77589 0.0648033 0.0324016 0.999475i \(-0.489684\pi\)
0.0324016 + 0.999475i \(0.489684\pi\)
\(752\) 10.3158i 0.376179i
\(753\) −2.39311 + 1.87616i −0.0872097 + 0.0683711i
\(754\) 13.3875i 0.487543i
\(755\) 0 0
\(756\) 11.8238 7.01416i 0.430026 0.255103i
\(757\) 4.63995i 0.168642i 0.996439 + 0.0843210i \(0.0268721\pi\)
−0.996439 + 0.0843210i \(0.973128\pi\)
\(758\) −8.25863 −0.299967
\(759\) −4.32562 5.51747i −0.157010 0.200272i
\(760\) 0 0
\(761\) −40.6884 −1.47495 −0.737477 0.675373i \(-0.763983\pi\)
−0.737477 + 0.675373i \(0.763983\pi\)
\(762\) 2.13728 + 2.72617i 0.0774255 + 0.0987589i
\(763\) 3.17683 + 28.3681i 0.115009 + 1.02699i
\(764\) 7.22117i 0.261253i
\(765\) 0 0
\(766\) 32.6920i 1.18121i
\(767\) −51.0448 −1.84312
\(768\) 1.36309 1.06864i 0.0491862 0.0385612i
\(769\) 19.2355i 0.693651i −0.937930 0.346825i \(-0.887260\pi\)
0.937930 0.346825i \(-0.112740\pi\)
\(770\) 0 0
\(771\) −23.4423 29.9015i −0.844256 1.07688i
\(772\) 7.60250i 0.273620i
\(773\) 28.4175i 1.02211i 0.859549 + 0.511053i \(0.170744\pi\)
−0.859549 + 0.511053i \(0.829256\pi\)
\(774\) 1.25863 + 0.309339i 0.0452406 + 0.0111190i
\(775\) 0 0
\(776\) −14.0015 −0.502624
\(777\) −7.82865 + 7.68933i −0.280851 + 0.275853i
\(778\) 1.33354i 0.0478099i
\(779\) 30.3916i 1.08889i
\(780\) 0 0
\(781\) −18.9867 −0.679399
\(782\) 7.34624i 0.262701i
\(783\) 13.3875 6.04124i 0.478430 0.215896i
\(784\) −6.82660 + 1.54839i −0.243807 + 0.0552996i
\(785\) 0 0
\(786\) −23.5547 + 18.4666i −0.840169 + 0.658680i
\(787\) −41.6778 −1.48565 −0.742826 0.669485i \(-0.766515\pi\)
−0.742826 + 0.669485i \(0.766515\pi\)
\(788\) 21.7384 0.774400
\(789\) 5.56853 4.36565i 0.198245 0.155421i
\(790\) 0 0