Properties

Label 1050.2.b.e.251.8
Level $1050$
Weight $2$
Character 1050.251
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.b (of order \(2\), degree \(1\), 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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.8
Root \(-1.06864 + 1.36309i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.e.251.2

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.06864 1.36309i −0.616980 0.786979i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 1.36309 1.06864i 0.556478 0.436271i
\(7\) −2.62932 + 0.294447i −0.993788 + 0.111290i
\(8\) 1.00000i 0.353553i
\(9\) −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 \(0.930736\pi\)
\(12\) 1.06864 + 1.36309i 0.308490 + 0.393489i
\(13\) 4.73625i 1.31360i −0.754066 0.656799i \(-0.771910\pi\)
0.754066 0.656799i \(-0.228090\pi\)
\(14\) −0.294447 2.62932i −0.0786942 0.702714i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.59897 0.630342 0.315171 0.949035i \(-0.397938\pi\)
0.315171 + 0.949035i \(0.397938\pi\)
\(18\) −2.91330 0.716015i −0.686672 0.168766i
\(19\) 2.72617i 0.625427i 0.949847 + 0.312714i \(0.101238\pi\)
−0.949847 + 0.312714i \(0.898762\pi\)
\(20\) 0 0
\(21\) 3.21115 + 3.26933i 0.700730 + 0.713426i
\(22\) −1.43203 −0.305310
\(23\) 2.82660i 0.589387i 0.955592 + 0.294694i \(0.0952176\pi\)
−0.955592 + 0.294694i \(0.904782\pi\)
\(24\) −1.36309 + 1.06864i −0.278239 + 0.218135i
\(25\) 0 0
\(26\) 4.73625 0.928854
\(27\) 4.73625 2.13728i 0.911491 0.411320i
\(28\) 2.62932 0.294447i 0.496894 0.0556452i
\(29\) 2.82660i 0.524887i −0.964947 0.262443i \(-0.915472\pi\)
0.964947 0.262443i \(-0.0845283\pi\)
\(30\) 0 0
\(31\) 5.91403i 1.06219i 0.847312 + 0.531096i \(0.178220\pi\)
−0.847312 + 0.531096i \(0.821780\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.95198 1.53032i 0.339796 0.266395i
\(34\) 2.59897i 0.445719i
\(35\) 0 0
\(36\) 0.716015 2.91330i 0.119336 0.485550i
\(37\) −2.39457 −0.393665 −0.196833 0.980437i \(-0.563066\pi\)
−0.196833 + 0.980437i \(0.563066\pi\)
\(38\) −2.72617 −0.442244
\(39\) −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 \(0.163783\pi\)
\(42\) −3.26933 + 3.21115i −0.504468 + 0.495491i
\(43\) 0.432029 0.0658838 0.0329419 0.999457i \(-0.489512\pi\)
0.0329419 + 0.999457i \(0.489512\pi\)
\(44\) 1.43203i 0.215887i
\(45\) 0 0
\(46\) −2.82660 −0.416760
\(47\) 10.3158 1.50471 0.752357 0.658755i \(-0.228917\pi\)
0.752357 + 0.658755i \(0.228917\pi\)
\(48\) −1.06864 1.36309i −0.154245 0.196745i
\(49\) 6.82660 1.54839i 0.975229 0.221198i
\(50\) 0 0
\(51\) −2.77736 3.54262i −0.388908 0.496066i
\(52\) 4.73625i 0.656799i
\(53\) 5.69066i 0.781672i 0.920460 + 0.390836i \(0.127814\pi\)
−0.920460 + 0.390836i \(0.872186\pi\)
\(54\) 2.13728 + 4.73625i 0.290847 + 0.644521i
\(55\) 0 0
\(56\) 0.294447 + 2.62932i 0.0393471 + 0.351357i
\(57\) 3.71601 2.91330i 0.492198 0.385876i
\(58\) 2.82660 0.371151
\(59\) 10.7775 1.40311 0.701555 0.712615i \(-0.252490\pi\)
0.701555 + 0.712615i \(0.252490\pi\)
\(60\) 0 0
\(61\) 1.05058i 0.134513i 0.997736 + 0.0672563i \(0.0214245\pi\)
−0.997736 + 0.0672563i \(0.978575\pi\)
\(62\) −5.91403 −0.751083
\(63\) 1.02482 7.87082i 0.129115 0.991630i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 1.53032 + 1.95198i 0.188370 + 0.240272i
\(67\) 9.82660 1.20051 0.600255 0.799808i \(-0.295066\pi\)
0.600255 + 0.799808i \(0.295066\pi\)
\(68\) −2.59897 −0.315171
\(69\) 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 \(0.711760\pi\)
\(72\) 2.91330 + 0.716015i 0.343336 + 0.0843831i
\(73\) 7.58963i 0.888299i −0.895953 0.444150i \(-0.853506\pi\)
0.895953 0.444150i \(-0.146494\pi\)
\(74\) 2.39457i 0.278363i
\(75\) 0 0
\(76\) 2.72617i 0.312714i
\(77\) −0.421657 3.76526i −0.0480522 0.429091i
\(78\) −5.06134 6.45592i −0.573084 0.730989i
\(79\) 16.5173 1.85834 0.929169 0.369656i \(-0.120525\pi\)
0.929169 + 0.369656i \(0.120525\pi\)
\(80\) 0 0
\(81\) −7.97465 4.17193i −0.886072 0.463548i
\(82\) 11.1481i 1.23110i
\(83\) −12.9148 −1.41758 −0.708790 0.705419i \(-0.750759\pi\)
−0.708790 + 0.705419i \(0.750759\pi\)
\(84\) −3.21115 3.26933i −0.350365 0.356713i
\(85\) 0 0
\(86\) 0.432029i 0.0465869i
\(87\) −3.85291 + 3.02062i −0.413075 + 0.323845i
\(88\) 1.43203 0.152655
\(89\) 3.90396 0.413819 0.206910 0.978360i \(-0.433659\pi\)
0.206910 + 0.978360i \(0.433659\pi\)
\(90\) 0 0
\(91\) 1.39457 + 12.4531i 0.146191 + 1.30544i
\(92\) 2.82660i 0.294694i
\(93\) 8.06134 6.31998i 0.835923 0.655351i
\(94\) 10.3158i 1.06399i
\(95\) 0 0
\(96\) 1.36309 1.06864i 0.139120 0.109068i
\(97\) 14.0015i 1.42163i −0.703377 0.710817i \(-0.748325\pi\)
0.703377 0.710817i \(-0.251675\pi\)
\(98\) 1.54839 + 6.82660i 0.156411 + 0.689591i
\(99\) −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 \(0.671551\pi\)
\(102\) 3.54262 2.77736i 0.350771 0.275000i
\(103\) 13.8743i 1.36707i 0.729917 + 0.683536i \(0.239559\pi\)
−0.729917 + 0.683536i \(0.760441\pi\)
\(104\) −4.73625 −0.464427
\(105\) 0 0
\(106\) −5.69066 −0.552726
\(107\) 15.9493i 1.54188i 0.636910 + 0.770938i \(0.280212\pi\)
−0.636910 + 0.770938i \(0.719788\pi\)
\(108\) −4.73625 + 2.13728i −0.455746 + 0.205660i
\(109\) −10.7891 −1.03341 −0.516706 0.856163i \(-0.672842\pi\)
−0.516706 + 0.856163i \(0.672842\pi\)
\(110\) 0 0
\(111\) 2.55894 + 3.26401i 0.242884 + 0.309806i
\(112\) −2.62932 + 0.294447i −0.248447 + 0.0278226i
\(113\) 14.3439i 1.34936i 0.738112 + 0.674679i \(0.235718\pi\)
−0.738112 + 0.674679i \(0.764282\pi\)
\(114\) 2.91330 + 3.71601i 0.272856 + 0.348037i
\(115\) 0 0
\(116\) 2.82660i 0.262443i
\(117\) 13.7981 + 3.39122i 1.27564 + 0.313519i
\(118\) 10.7775i 0.992148i
\(119\) −6.83350 + 0.765257i −0.626426 + 0.0701510i
\(120\) 0 0
\(121\) 8.94929 0.813572
\(122\) −1.05058 −0.0951148
\(123\) −11.9133 15.1958i −1.07419 1.37016i
\(124\) 5.91403i 0.531096i
\(125\) 0 0
\(126\) 7.87082 + 1.02482i 0.701188 + 0.0912979i
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −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 \(0.772314\pi\)
\(132\) −1.95198 + 1.53032i −0.169898 + 0.133198i
\(133\) −0.802714 7.16797i −0.0696041 0.621542i
\(134\) 9.82660i 0.848889i
\(135\) 0 0
\(136\) 2.59897i 0.222859i
\(137\) 3.03746i 0.259507i −0.991546 0.129754i \(-0.958581\pi\)
0.991546 0.129754i \(-0.0414187\pi\)
\(138\) 3.02062 + 3.85291i 0.257132 + 0.327981i
\(139\) 20.7478i 1.75980i −0.475155 0.879902i \(-0.657608\pi\)
0.475155 0.879902i \(-0.342392\pi\)
\(140\) 0 0
\(141\) −11.0239 14.0613i −0.928379 1.18418i
\(142\) −13.2586 −1.11264
\(143\) 6.78244 0.567176
\(144\) −0.716015 + 2.91330i −0.0596679 + 0.242775i
\(145\) 0 0
\(146\) 7.58963 0.628122
\(147\) −9.40577 7.65059i −0.775775 0.631010i
\(148\) 2.39457 0.196833
\(149\) 18.9493i 1.55239i −0.630495 0.776193i \(-0.717148\pi\)
0.630495 0.776193i \(-0.282852\pi\)
\(150\) 0 0
\(151\) 5.25863 0.427941 0.213971 0.976840i \(-0.431360\pi\)
0.213971 + 0.976840i \(0.431360\pi\)
\(152\) 2.72617 0.221122
\(153\) −1.86090 + 7.57157i −0.150445 + 0.612125i
\(154\) 3.76526 0.421657i 0.303413 0.0339781i
\(155\) 0 0
\(156\) 6.45592 5.06134i 0.516887 0.405232i
\(157\) 6.29566i 0.502449i 0.967929 + 0.251224i \(0.0808332\pi\)
−0.967929 + 0.251224i \(0.919167\pi\)
\(158\) 16.5173i 1.31404i
\(159\) 7.75687 6.08127i 0.615160 0.482276i
\(160\) 0 0
\(161\) −0.832284 7.43203i −0.0655932 0.585726i
\(162\) 4.17193 7.97465i 0.327778 0.626547i
\(163\) −0.605427 −0.0474207 −0.0237104 0.999719i \(-0.507548\pi\)
−0.0237104 + 0.999719i \(0.507548\pi\)
\(164\) −11.1481 −0.870520
\(165\) 0 0
\(166\) 12.9148i 1.00238i
\(167\) −12.0825 −0.934971 −0.467485 0.884001i \(-0.654840\pi\)
−0.467485 + 0.884001i \(0.654840\pi\)
\(168\) 3.26933 3.21115i 0.252234 0.247746i
\(169\) −9.43203 −0.725541
\(170\) 0 0
\(171\) −7.94217 1.95198i −0.607353 0.149272i
\(172\) −0.432029 −0.0329419
\(173\) 15.5137 1.17949 0.589744 0.807590i \(-0.299229\pi\)
0.589744 + 0.807590i \(0.299229\pi\)
\(174\) −3.02062 3.85291i −0.228993 0.292088i
\(175\) 0 0
\(176\) 1.43203i 0.107943i
\(177\) −11.5173 14.6907i −0.865690 1.10422i
\(178\) 3.90396i 0.292614i
\(179\) 4.56797i 0.341426i −0.985321 0.170713i \(-0.945393\pi\)
0.985321 0.170713i \(-0.0546071\pi\)
\(180\) 0 0
\(181\) 7.80792i 0.580358i −0.956972 0.290179i \(-0.906285\pi\)
0.956972 0.290179i \(-0.0937149\pi\)
\(182\) −12.4531 + 1.39457i −0.923084 + 0.103373i
\(183\) 1.43203 1.12269i 0.105859 0.0829916i
\(184\) 2.82660 0.208380
\(185\) 0 0
\(186\) 6.31998 + 8.06134i 0.463403 + 0.591086i
\(187\) 3.72179i 0.272165i
\(188\) −10.3158 −0.752357
\(189\) −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 \(0.915864\pi\)
\(192\) 1.06864 + 1.36309i 0.0771225 + 0.0983724i
\(193\) −7.60250 −0.547240 −0.273620 0.961838i \(-0.588221\pi\)
−0.273620 + 0.961838i \(0.588221\pi\)
\(194\) 14.0015 1.00525
\(195\) 0 0
\(196\) −6.82660 + 1.54839i −0.487614 + 0.110599i
\(197\) 21.7384i 1.54880i 0.632697 + 0.774400i \(0.281948\pi\)
−0.632697 + 0.774400i \(0.718052\pi\)
\(198\) 1.02535 4.17193i 0.0728687 0.296486i
\(199\) 6.04124i 0.428252i −0.976806 0.214126i \(-0.931310\pi\)
0.976806 0.214126i \(-0.0686904\pi\)
\(200\) 0 0
\(201\) −10.5011 13.3945i −0.740691 0.944776i
\(202\) 10.3158i 0.725818i
\(203\) 0.832284 + 7.43203i 0.0584149 + 0.521626i
\(204\) 2.77736 + 3.54262i 0.194454 + 0.248033i
\(205\) 0 0
\(206\) −13.8743 −0.966666
\(207\) −8.23474 2.02389i −0.572354 0.140670i
\(208\) 4.73625i 0.328400i
\(209\) −3.90396 −0.270043
\(210\) 0 0
\(211\) 16.7759 1.15490 0.577450 0.816426i \(-0.304048\pi\)
0.577450 + 0.816426i \(0.304048\pi\)
\(212\) 5.69066i 0.390836i
\(213\) 18.0727 14.1687i 1.23832 0.970824i
\(214\) −15.9493 −1.09027
\(215\) 0 0
\(216\) −2.13728 4.73625i −0.145424 0.322261i
\(217\) −1.74137 15.5499i −0.118212 1.05559i
\(218\) 10.7891i 0.730733i
\(219\) −10.3453 + 8.11059i −0.699073 + 0.548063i
\(220\) 0 0
\(221\) 12.3093i 0.828016i
\(222\) −3.26401 + 2.55894i −0.219066 + 0.171745i
\(223\) 11.1120i 0.744112i 0.928210 + 0.372056i \(0.121347\pi\)
−0.928210 + 0.372056i \(0.878653\pi\)
\(224\) −0.294447 2.62932i −0.0196736 0.175679i
\(225\) 0 0
\(226\) −14.3439 −0.954140
\(227\) −7.24413 −0.480810 −0.240405 0.970673i \(-0.577280\pi\)
−0.240405 + 0.970673i \(0.577280\pi\)
\(228\) −3.71601 + 2.91330i −0.246099 + 0.192938i
\(229\) 27.1596i 1.79476i 0.441259 + 0.897380i \(0.354532\pi\)
−0.441259 + 0.897380i \(0.645468\pi\)
\(230\) 0 0
\(231\) −4.68178 + 4.59846i −0.308038 + 0.302557i
\(232\) −2.82660 −0.185576
\(233\) 5.38132i 0.352542i 0.984342 + 0.176271i \(0.0564035\pi\)
−0.984342 + 0.176271i \(0.943596\pi\)
\(234\) −3.39122 + 13.7981i −0.221691 + 0.902011i
\(235\) 0 0
\(236\) −10.7775 −0.701555
\(237\) −17.6510 22.5145i −1.14656 1.46247i
\(238\) −0.765257 6.83350i −0.0496043 0.442950i
\(239\) 2.51726i 0.162828i −0.996680 0.0814141i \(-0.974056\pi\)
0.996680 0.0814141i \(-0.0259436\pi\)
\(240\) 0 0
\(241\) 16.8077i 1.08268i −0.840804 0.541340i \(-0.817917\pi\)
0.840804 0.541340i \(-0.182083\pi\)
\(242\) 8.94929i 0.575282i
\(243\) 2.83532 + 15.3284i 0.181886 + 0.983320i
\(244\) 1.05058i 0.0672563i
\(245\) 0 0
\(246\) 15.1958 11.9133i 0.968850 0.759564i
\(247\) 12.9118 0.821560
\(248\) 5.91403 0.375542
\(249\) 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 \(0.517646\pi\)
\(252\) −1.02482 + 7.87082i −0.0645574 + 0.495815i
\(253\) −4.04778 −0.254482
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 21.9366 1.36837 0.684184 0.729309i \(-0.260159\pi\)
0.684184 + 0.729309i \(0.260159\pi\)
\(258\) 0.588894 0.461684i 0.0366629 0.0287432i
\(259\) 6.29609 0.705074i 0.391220 0.0438112i
\(260\) 0 0
\(261\) 8.23474 + 2.02389i 0.509718 + 0.125276i
\(262\) 17.2804i 1.06759i
\(263\) 4.08523i 0.251906i −0.992036 0.125953i \(-0.959801\pi\)
0.992036 0.125953i \(-0.0401989\pi\)
\(264\) −1.53032 1.95198i −0.0941850 0.120136i
\(265\) 0 0
\(266\) 7.16797 0.802714i 0.439497 0.0492175i
\(267\) −4.17193 5.32144i −0.255318 0.325667i
\(268\) −9.82660 −0.600255
\(269\) −6.96461 −0.424640 −0.212320 0.977200i \(-0.568102\pi\)
−0.212320 + 0.977200i \(0.568102\pi\)
\(270\) 0 0
\(271\) 23.4740i 1.42594i −0.701194 0.712971i \(-0.747349\pi\)
0.701194 0.712971i \(-0.252651\pi\)
\(272\) 2.59897 0.157585
\(273\) 15.4843 15.2088i 0.937155 0.920478i
\(274\) 3.03746 0.183499
\(275\) 0 0
\(276\) −3.85291 + 3.02062i −0.231918 + 0.181820i
\(277\) 14.1227 0.848550 0.424275 0.905533i \(-0.360529\pi\)
0.424275 + 0.905533i \(0.360529\pi\)
\(278\) 20.7478 1.24437
\(279\) −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 \(0.750715\pi\)
\(282\) 14.0613 11.0239i 0.837341 0.656463i
\(283\) 0.807187i 0.0479823i −0.999712 0.0239912i \(-0.992363\pi\)
0.999712 0.0239912i \(-0.00763735\pi\)
\(284\) 13.2586i 0.786755i
\(285\) 0 0
\(286\) 6.78244i 0.401054i
\(287\) −29.3118 + 3.28252i −1.73022 + 0.193761i
\(288\) −2.91330 0.716015i −0.171668 0.0421916i
\(289\) −10.2454 −0.602669
\(290\) 0 0
\(291\) −19.0852 + 14.9625i −1.11880 + 0.877120i
\(292\) 7.58963i 0.444150i
\(293\) 14.6704 0.857055 0.428528 0.903529i \(-0.359032\pi\)
0.428528 + 0.903529i \(0.359032\pi\)
\(294\) 7.65059 9.40577i 0.446191 0.548556i
\(295\) 0 0
\(296\) 2.39457i 0.139182i
\(297\) 3.06065 + 6.78244i 0.177597 + 0.393557i
\(298\) 18.9493 1.09770
\(299\) 13.3875 0.774218
\(300\) 0 0
\(301\) −1.13594 + 0.127210i −0.0654746 + 0.00733224i
\(302\) 5.25863i 0.302600i
\(303\) 11.0239 + 14.0613i 0.633306 + 0.807803i
\(304\) 2.72617i 0.156357i
\(305\) 0 0
\(306\) −7.57157 1.86090i −0.432838 0.106380i
\(307\) 10.0975i 0.576295i −0.957586 0.288148i \(-0.906961\pi\)
0.957586 0.288148i \(-0.0930394\pi\)
\(308\) 0.421657 + 3.76526i 0.0240261 + 0.214545i
\(309\) 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 \(0.461328\pi\)
\(312\) 5.06134 + 6.45592i 0.286542 + 0.365494i
\(313\) 0.923368i 0.0521918i −0.999659 0.0260959i \(-0.991692\pi\)
0.999659 0.0260959i \(-0.00830753\pi\)
\(314\) −6.29566 −0.355285
\(315\) 0 0
\(316\) −16.5173 −0.929169
\(317\) 15.7384i 0.883959i −0.897025 0.441979i \(-0.854276\pi\)
0.897025 0.441979i \(-0.145724\pi\)
\(318\) 6.08127 + 7.75687i 0.341021 + 0.434984i
\(319\) 4.04778 0.226632
\(320\) 0 0
\(321\) 21.7403 17.0441i 1.21342 0.951307i
\(322\) 7.43203 0.832284i 0.414171 0.0463814i
\(323\) 7.08523i 0.394233i
\(324\) 7.97465 + 4.17193i 0.443036 + 0.231774i
\(325\) 0 0
\(326\) 0.605427i 0.0335315i
\(327\) 11.5297 + 14.7065i 0.637595 + 0.813274i
\(328\) 11.1481i 0.615550i
\(329\) −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 \(0.612606\pi\)
\(332\) 12.9148 0.708790
\(333\) 1.71455 6.97611i 0.0939567 0.382289i
\(334\) 12.0825i 0.661124i
\(335\) 0 0
\(336\) 3.21115 + 3.26933i 0.175183 + 0.178357i
\(337\) 18.8986 1.02947 0.514736 0.857349i \(-0.327890\pi\)
0.514736 + 0.857349i \(0.327890\pi\)
\(338\) 9.43203i 0.513035i
\(339\) 19.5519 15.3284i 1.06192 0.832526i
\(340\) 0 0
\(341\) −8.46907 −0.458626
\(342\) 1.95198 7.94217i 0.105551 0.429463i
\(343\) −17.4934 + 6.08127i −0.944553 + 0.328358i
\(344\) 0.432029i 0.0232935i
\(345\) 0 0
\(346\) 15.5137i 0.834024i
\(347\) 30.7384i 1.65013i −0.565041 0.825063i \(-0.691140\pi\)
0.565041 0.825063i \(-0.308860\pi\)
\(348\) 3.85291 3.02062i 0.206537 0.161922i
\(349\) 0.970523i 0.0519509i −0.999663 0.0259754i \(-0.991731\pi\)
0.999663 0.0259754i \(-0.00826917\pi\)
\(350\) 0 0
\(351\) −10.1227 22.4320i −0.540309 1.19733i
\(352\) −1.43203 −0.0763274
\(353\) 16.3570 0.870598 0.435299 0.900286i \(-0.356643\pi\)
0.435299 + 0.900286i \(0.356643\pi\)
\(354\) 14.6907 11.5173i 0.780800 0.612136i
\(355\) 0 0
\(356\) −3.90396 −0.206910
\(357\) 8.34567 + 8.49687i 0.441700 + 0.449702i
\(358\) 4.56797 0.241425
\(359\) 9.81335i 0.517929i 0.965887 + 0.258964i \(0.0833812\pi\)
−0.965887 + 0.258964i \(0.916619\pi\)
\(360\) 0 0
\(361\) 11.5680 0.608841
\(362\) 7.80792 0.410375
\(363\) −9.56358 12.1987i −0.501958 0.640264i
\(364\) −1.39457 12.4531i −0.0730955 0.652719i
\(365\) 0 0
\(366\) 1.12269 + 1.43203i 0.0586839 + 0.0748534i
\(367\) 33.9970i 1.77463i 0.461163 + 0.887315i \(0.347432\pi\)
−0.461163 + 0.887315i \(0.652568\pi\)
\(368\) 2.82660i 0.147347i
\(369\) −7.98220 + 32.4777i −0.415537 + 1.69072i
\(370\) 0 0
\(371\) −1.67560 14.9625i −0.0869927 0.776817i
\(372\) −8.06134 + 6.31998i −0.417961 + 0.327676i
\(373\) −26.5650 −1.37549 −0.687743 0.725954i \(-0.741398\pi\)
−0.687743 + 0.725954i \(0.741398\pi\)
\(374\) −3.72179 −0.192449
\(375\) 0 0
\(376\) 10.3158i 0.531997i
\(377\) −13.3875 −0.689490
\(378\) −7.01416 11.8238i −0.360769 0.608149i
\(379\) 8.25863 0.424217 0.212109 0.977246i \(-0.431967\pi\)
0.212109 + 0.977246i \(0.431967\pi\)
\(380\) 0 0
\(381\) 2.13728 + 2.72617i 0.109496 + 0.139666i
\(382\) −7.22117 −0.369467
\(383\) −32.6920 −1.67049 −0.835243 0.549882i \(-0.814673\pi\)
−0.835243 + 0.549882i \(0.814673\pi\)
\(384\) −1.36309 + 1.06864i −0.0695598 + 0.0545338i
\(385\) 0 0
\(386\) 7.60250i 0.386957i
\(387\) −0.309339 + 1.25863i −0.0157246 + 0.0639798i
\(388\) 14.0015i 0.710817i
\(389\) 1.33354i 0.0676134i −0.999428 0.0338067i \(-0.989237\pi\)
0.999428 0.0338067i \(-0.0107631\pi\)
\(390\) 0 0
\(391\) 7.34624i 0.371515i
\(392\) −1.54839 6.82660i −0.0782054 0.344795i
\(393\) 18.4666 + 23.5547i 0.931514 + 1.18818i
\(394\) −21.7384 −1.09517
\(395\) 0 0
\(396\) 4.17193 + 1.02535i 0.209647 + 0.0515260i
\(397\) 23.0123i 1.15495i 0.816407 + 0.577477i \(0.195963\pi\)
−0.816407 + 0.577477i \(0.804037\pi\)
\(398\) 6.04124 0.302820
\(399\) −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 \(0.855574\pi\)
\(402\) 13.3945 10.5011i 0.668058 0.523748i
\(403\) 28.0103 1.39529
\(404\) 10.3158 0.513231
\(405\) 0 0
\(406\) −7.43203 + 0.832284i −0.368845 + 0.0413056i
\(407\) 3.42910i 0.169974i
\(408\) −3.54262 + 2.77736i −0.175386 + 0.137500i
\(409\) 9.94521i 0.491759i −0.969300 0.245879i \(-0.920923\pi\)
0.969300 0.245879i \(-0.0790767\pi\)
\(410\) 0 0
\(411\) −4.14032 + 3.24595i −0.204227 + 0.160111i
\(412\) 13.8743i 0.683536i
\(413\) −28.3374 + 3.17340i −1.39439 + 0.156153i
\(414\) 2.02389 8.23474i 0.0994687 0.404716i
\(415\) 0 0
\(416\) 4.73625 0.232214
\(417\) −28.2811 + 22.1719i −1.38493 + 1.08576i
\(418\) 3.90396i 0.190949i
\(419\) −7.71684 −0.376992 −0.188496 0.982074i \(-0.560361\pi\)
−0.188496 + 0.982074i \(0.560361\pi\)
\(420\) 0 0
\(421\) 11.2109 0.546384 0.273192 0.961960i \(-0.411921\pi\)
0.273192 + 0.961960i \(0.411921\pi\)
\(422\) 16.7759i 0.816638i
\(423\) −7.38627 + 30.0530i −0.359133 + 1.46123i
\(424\) 5.69066 0.276363
\(425\) 0 0
\(426\) 14.1687 + 18.0727i 0.686476 + 0.875624i
\(427\) −0.309339 2.76230i −0.0149700 0.133677i
\(428\) 15.9493i 0.770938i
\(429\) −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 \(-0.217435\pi\)
\(432\) 4.73625 2.13728i 0.227873 0.102830i
\(433\) 23.4378i 1.12635i −0.826337 0.563175i \(-0.809580\pi\)
0.826337 0.563175i \(-0.190420\pi\)
\(434\) 15.5499 1.74137i 0.746417 0.0835884i
\(435\) 0 0
\(436\) 10.7891 0.516706
\(437\) −7.70581 −0.368619
\(438\) −8.11059 10.3453i −0.387539 0.494319i
\(439\) 25.0334i 1.19478i 0.801952 + 0.597389i \(0.203795\pi\)
−0.801952 + 0.597389i \(0.796205\pi\)
\(440\) 0 0
\(441\) −0.377028 + 20.9966i −0.0179537 + 0.999839i
\(442\) 12.3093 0.585496
\(443\) 18.4666i 0.877373i −0.898640 0.438686i \(-0.855444\pi\)
0.898640 0.438686i \(-0.144556\pi\)
\(444\) −2.55894 3.26401i −0.121442 0.154903i
\(445\) 0 0
\(446\) −11.1120 −0.526167
\(447\) −25.8295 + 20.2500i −1.22170 + 0.957791i
\(448\) 2.62932 0.294447i 0.124223 0.0139113i
\(449\) 32.3439i 1.52640i 0.646162 + 0.763201i \(0.276373\pi\)
−0.646162 + 0.763201i \(0.723627\pi\)
\(450\) 0 0
\(451\) 15.9644i 0.751734i
\(452\) 14.3439i 0.674679i
\(453\) −5.61959 7.16797i −0.264031 0.336781i
\(454\) 7.24413i 0.339984i
\(455\) 0 0
\(456\) −2.91330 3.71601i −0.136428 0.174018i
\(457\) 10.9251 0.511054 0.255527 0.966802i \(-0.417751\pi\)
0.255527 + 0.966802i \(0.417751\pi\)
\(458\) −27.1596 −1.26909
\(459\) 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 \(0.286670\pi\)
\(462\) −4.59846 4.68178i −0.213940 0.217816i
\(463\) −8.07491 −0.375273 −0.187637 0.982239i \(-0.560083\pi\)
−0.187637 + 0.982239i \(0.560083\pi\)
\(464\) 2.82660i 0.131222i
\(465\) 0 0
\(466\) −5.38132 −0.249285
\(467\) 41.6228 1.92607 0.963037 0.269371i \(-0.0868156\pi\)
0.963037 + 0.269371i \(0.0868156\pi\)
\(468\) −13.7981 3.39122i −0.637818 0.156759i
\(469\) −25.8372 + 2.89341i −1.19305 + 0.133605i
\(470\) 0 0
\(471\) 8.58154 6.72780i 0.395416 0.310001i
\(472\) 10.7775i 0.496074i
\(473\) 0.618679i 0.0284469i
\(474\) 22.5145 17.6510i 1.03412 0.810738i
\(475\) 0 0
\(476\) 6.83350 0.765257i 0.313213 0.0350755i
\(477\) −16.5786 4.07460i −0.759082 0.186563i
\(478\) 2.51726 0.115137
\(479\) 21.3728 0.976549 0.488274 0.872690i \(-0.337627\pi\)
0.488274 + 0.872690i \(0.337627\pi\)
\(480\) 0 0
\(481\) 11.3413i 0.517118i
\(482\) 16.8077 0.765570
\(483\) −9.24109 + 9.07664i −0.420484 + 0.413002i
\(484\) −8.94929 −0.406786
\(485\) 0 0
\(486\) −15.3284 + 2.83532i −0.695312 + 0.128613i
\(487\) −27.1094 −1.22845 −0.614223 0.789133i \(-0.710530\pi\)
−0.614223 + 0.789133i \(0.710530\pi\)
\(488\) 1.05058 0.0475574
\(489\) 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 \(0.763305\pi\)
\(492\) 11.9133 + 15.1958i 0.537093 + 0.685081i
\(493\) 7.34624i 0.330858i
\(494\) 12.9118i 0.580931i
\(495\) 0 0
\(496\) 5.91403i 0.265548i
\(497\) −3.90396 34.8611i −0.175117 1.56374i
\(498\) −17.6040 + 13.8012i −0.788852 + 0.618449i
\(499\) 8.50694 0.380823 0.190412 0.981704i \(-0.439018\pi\)
0.190412 + 0.981704i \(0.439018\pi\)
\(500\) 0 0
\(501\) 12.9118 + 16.4695i 0.576858 + 0.735802i
\(502\) 1.75565i 0.0783586i
\(503\) −12.1625 −0.542301 −0.271150 0.962537i \(-0.587404\pi\)
−0.271150 + 0.962537i \(0.587404\pi\)
\(504\) −7.87082 1.02482i −0.350594 0.0456489i
\(505\) 0 0
\(506\) 4.04778i 0.179946i
\(507\) 10.0794 + 12.8567i 0.447644 + 0.570985i
\(508\) 2.00000 0.0887357
\(509\) 6.12130 0.271322 0.135661 0.990755i \(-0.456684\pi\)
0.135661 + 0.990755i \(0.456684\pi\)
\(510\) 0 0
\(511\) 2.23474 + 19.9555i 0.0988592 + 0.882781i
\(512\) 1.00000i 0.0441942i
\(513\) 5.82660 + 12.9118i 0.257251 + 0.570071i
\(514\) 21.9366i 0.967582i
\(515\) 0 0
\(516\) 0.461684 + 0.588894i 0.0203245 + 0.0259246i
\(517\) 14.7725i 0.649695i
\(518\) 0.705074 + 6.29609i 0.0309792 + 0.276634i
\(519\) −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 \(0.245801\pi\)
\(522\) −2.02389 + 8.23474i −0.0885832 + 0.360425i
\(523\) 28.5557i 1.24865i 0.781163 + 0.624327i \(0.214627\pi\)
−0.781163 + 0.624327i \(0.785373\pi\)
\(524\) 17.2804 0.754899
\(525\) 0 0
\(526\) 4.08523 0.178125
\(527\) 15.3704i 0.669544i
\(528\) 1.95198 1.53032i 0.0849491 0.0665988i
\(529\) 15.0103 0.652623
\(530\) 0 0
\(531\) −7.71684 + 31.3981i −0.334882 + 1.36256i
\(532\) 0.802714 + 7.16797i 0.0348020 + 0.310771i
\(533\) 52.8001i 2.28703i
\(534\) 5.32144 4.17193i 0.230281 0.180537i
\(535\) 0 0
\(536\) 9.82660i 0.424445i
\(537\) −6.22654 + 4.88152i −0.268695 + 0.210653i
\(538\) 6.96461i 0.300266i
\(539\) 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 \(0.763847\pi\)
\(542\) 23.4740 1.00829
\(543\) −10.6429 + 8.34386i −0.456730 + 0.358070i
\(544\) 2.59897i 0.111430i
\(545\) 0 0
\(546\) 15.2088 + 15.4843i 0.650876 + 0.662669i
\(547\) −26.7759 −1.14485 −0.572427 0.819955i \(-0.693998\pi\)
−0.572427 + 0.819955i \(0.693998\pi\)
\(548\) 3.03746i 0.129754i
\(549\) −3.06065 0.752229i −0.130625 0.0321044i
\(550\) 0 0
\(551\) 7.70581 0.328279
\(552\) −3.02062 3.85291i −0.128566 0.163991i
\(553\) −43.4291 + 4.86346i −1.84679 + 0.206815i
\(554\) 14.1227i 0.600016i
\(555\) 0 0
\(556\) 20.7478i 0.879902i
\(557\) 40.4158i 1.71247i 0.516583 + 0.856237i \(0.327204\pi\)
−0.516583 + 0.856237i \(0.672796\pi\)
\(558\) 4.23453 17.2294i 0.179262 0.729377i
\(559\) 2.04620i 0.0865449i
\(560\) 0 0
\(561\) 5.07313 3.97726i 0.214188 0.167920i
\(562\) −23.6532 −0.997750
\(563\) −8.16750 −0.344219 −0.172109 0.985078i \(-0.555058\pi\)
−0.172109 + 0.985078i \(0.555058\pi\)
\(564\) 11.0239 + 14.0613i 0.464189 + 0.592089i
\(565\) 0 0
\(566\) 0.807187 0.0339286
\(567\) 22.1963 + 8.62122i 0.932156 + 0.362057i
\(568\) 13.2586 0.556320
\(569\) 15.0375i 0.630403i 0.949025 + 0.315201i \(0.102072\pi\)
−0.949025 + 0.315201i \(0.897928\pi\)
\(570\) 0 0
\(571\) 38.6025 1.61546 0.807732 0.589550i \(-0.200695\pi\)
0.807732 + 0.589550i \(0.200695\pi\)
\(572\) −6.78244 −0.283588
\(573\) 9.84309 7.71684i 0.411201 0.322376i
\(574\) −3.28252 29.3118i −0.137010 1.22345i
\(575\) 0 0
\(576\) 0.716015 2.91330i 0.0298339 0.121388i
\(577\) 23.9467i 0.996913i 0.866915 + 0.498457i \(0.166100\pi\)
−0.866915 + 0.498457i \(0.833900\pi\)
\(578\) 10.2454i 0.426152i
\(579\) 8.12434 + 10.3629i 0.337636 + 0.430666i
\(580\) 0 0
\(581\) 33.9570 3.80271i 1.40877 0.157763i
\(582\) −14.9625 19.0852i −0.620217 0.791108i
\(583\) −8.14919 −0.337505
\(584\) −7.58963 −0.314061
\(585\) 0 0
\(586\) 14.6704i 0.606030i
\(587\) −17.9305 −0.740072 −0.370036 0.929017i \(-0.620655\pi\)
−0.370036 + 0.929017i \(0.620655\pi\)
\(588\) 9.40577 + 7.65059i 0.387887 + 0.315505i
\(589\) −16.1227 −0.664324
\(590\) 0 0
\(591\) 29.6314 23.2306i 1.21887 0.955578i
\(592\) −2.39457 −0.0984163
\(593\) 18.5744 0.762759 0.381379 0.924419i \(-0.375449\pi\)
0.381379 + 0.924419i \(0.375449\pi\)
\(594\) −6.78244 + 3.06065i −0.278287 + 0.125580i
\(595\) 0 0
\(596\) 18.9493i 0.776193i
\(597\) −8.23474 + 6.45592i −0.337026 + 0.264223i
\(598\) 13.3875i 0.547455i
\(599\) 29.3439i 1.19896i −0.800391 0.599479i \(-0.795375\pi\)
0.800391 0.599479i \(-0.204625\pi\)
\(600\) 0 0
\(601\) 22.5145i 0.918385i 0.888337 + 0.459192i \(0.151861\pi\)
−0.888337 + 0.459192i \(0.848139\pi\)
\(602\) −0.127210 1.13594i −0.00518468 0.0462975i
\(603\) −7.03599 + 28.6279i −0.286528 + 1.16582i
\(604\) −5.25863 −0.213971
\(605\) 0 0
\(606\) −14.0613 + 11.0239i −0.571203 + 0.447815i
\(607\) 17.5128i 0.710822i 0.934710 + 0.355411i \(0.115659\pi\)
−0.934710 + 0.355411i \(0.884341\pi\)
\(608\) −2.72617 −0.110561
\(609\) 9.24109 9.07664i 0.374468 0.367804i
\(610\) 0 0
\(611\) 48.8582i 1.97659i
\(612\) 1.86090 7.57157i 0.0752223 0.306062i
\(613\) 32.7626 1.32327 0.661635 0.749826i \(-0.269863\pi\)
0.661635 + 0.749826i \(0.269863\pi\)
\(614\) 10.0975 0.407502
\(615\) 0 0
\(616\) −3.76526 + 0.421657i −0.151707 + 0.0169890i
\(617\) 0.693592i 0.0279229i 0.999903 + 0.0139615i \(0.00444422\pi\)
−0.999903 + 0.0139615i \(0.995556\pi\)
\(618\) 14.8266 + 18.9118i 0.596413 + 0.760746i
\(619\) 18.5305i 0.744802i −0.928072 0.372401i \(-0.878535\pi\)
0.928072 0.372401i \(-0.121465\pi\)
\(620\) 0 0
\(621\) 6.04124 + 13.3875i 0.242427 + 0.537221i
\(622\) 4.27456i 0.171394i
\(623\) −10.2647 + 1.14951i −0.411248 + 0.0460541i
\(624\) −6.45592 + 5.06134i −0.258444 + 0.202616i
\(625\) 0 0
\(626\) 0.923368 0.0369052
\(627\) 4.17193 + 5.32144i 0.166611 + 0.212518i
\(628\) 6.29566i 0.251224i
\(629\) −6.22341 −0.248144
\(630\) 0 0
\(631\) −8.39457 −0.334183 −0.167091 0.985941i \(-0.553437\pi\)
−0.167091 + 0.985941i \(0.553437\pi\)
\(632\) 16.5173i 0.657021i
\(633\) −17.9274 22.8670i −0.712550 0.908882i
\(634\) 15.7384 0.625053
\(635\) 0 0
\(636\) −7.75687 + 6.08127i −0.307580 + 0.241138i
\(637\) −7.33354 32.3325i −0.290566 1.28106i
\(638\) 4.04778i 0.160253i
\(639\) −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 \(-0.154709\pi\)
\(642\) 17.0441 + 21.7403i 0.672675 + 0.858020i
\(643\) 2.60999i 0.102928i −0.998675 0.0514641i \(-0.983611\pi\)
0.998675 0.0514641i \(-0.0163888\pi\)
\(644\) 0.832284 + 7.43203i 0.0327966 + 0.292863i
\(645\) 0 0
\(646\) −7.08523 −0.278765
\(647\) −4.45673 −0.175212 −0.0876061 0.996155i \(-0.527922\pi\)
−0.0876061 + 0.996155i \(0.527922\pi\)
\(648\) −4.17193 + 7.97465i −0.163889 + 0.313274i
\(649\) 15.4337i 0.605825i
\(650\) 0 0
\(651\) −19.3349 + 18.9909i −0.757795 + 0.744310i
\(652\) 0.605427 0.0237104
\(653\) 30.9118i 1.20967i −0.796349 0.604837i \(-0.793238\pi\)
0.796349 0.604837i \(-0.206762\pi\)
\(654\) −14.7065 + 11.5297i −0.575072 + 0.450848i
\(655\) 0 0
\(656\) 11.1481 0.435260
\(657\) 22.1109 + 5.43429i 0.862628 + 0.212012i
\(658\) −3.03746 27.1235i −0.118412 1.05738i
\(659\) 4.56797i 0.177943i −0.996034 0.0889714i \(-0.971642\pi\)
0.996034 0.0889714i \(-0.0283580\pi\)
\(660\) 0 0
\(661\) 38.0643i 1.48053i −0.672315 0.740266i \(-0.734700\pi\)
0.672315 0.740266i \(-0.265300\pi\)
\(662\) 12.6054i 0.489924i
\(663\) −16.7787 + 13.1543i −0.651631 + 0.510869i
\(664\) 12.9148i 0.501190i
\(665\) 0 0
\(666\) 6.97611 + 1.71455i 0.270319 + 0.0664374i
\(667\) 7.98968 0.309362
\(668\) 12.0825 0.467485
\(669\) 15.1466 11.8747i 0.585601 0.459102i
\(670\) 0 0
\(671\) −1.50446 −0.0580790
\(672\) −3.26933 + 3.21115i −0.126117 + 0.123873i
\(673\) 21.2212 0.818016 0.409008 0.912531i \(-0.365875\pi\)
0.409008 + 0.912531i \(0.365875\pi\)
\(674\) 18.8986i 0.727946i
\(675\) 0 0
\(676\) 9.43203 0.362770
\(677\) 3.53336 0.135798 0.0678991 0.997692i \(-0.478370\pi\)
0.0678991 + 0.997692i \(0.478370\pi\)
\(678\) 15.3284 + 19.5519i 0.588685 + 0.750888i
\(679\) 4.12269 + 36.8143i 0.158214 + 1.41280i
\(680\) 0 0
\(681\) 7.74137 + 9.87438i 0.296650 + 0.378387i
\(682\) 8.46907i 0.324297i
\(683\) 1.70391i 0.0651984i 0.999469 + 0.0325992i \(0.0103785\pi\)
−0.999469 + 0.0325992i \(0.989622\pi\)
\(684\) 7.94217 + 1.95198i 0.303676 + 0.0746359i
\(685\) 0 0
\(686\) −6.08127 17.4934i −0.232184 0.667900i
\(687\) 37.0210 29.0239i 1.41244 1.10733i
\(688\) 0.432029 0.0164710
\(689\) 26.9524 1.02680
\(690\) 0 0
\(691\) 2.21734i 0.0843514i 0.999110 + 0.0421757i \(0.0134289\pi\)
−0.999110 + 0.0421757i \(0.986571\pi\)
\(692\) −15.5137 −0.589744
\(693\) 11.2712 + 1.46757i 0.428159 + 0.0557483i
\(694\) 30.7384 1.16682
\(695\) 0 0
\(696\) 3.02062 + 3.85291i 0.114496 + 0.146044i
\(697\) 28.9735 1.09745
\(698\) 0.970523 0.0367348
\(699\) 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 \(-0.0187644\pi\)
\(702\) 22.4320 10.1227i 0.846642 0.382056i
\(703\) 6.52802i 0.246209i
\(704\) 1.43203i 0.0539716i
\(705\) 0 0
\(706\) 16.3570i 0.615606i
\(707\) 27.1235 3.03746i 1.02008 0.114235i
\(708\) 11.5173 + 14.6907i 0.432845 + 0.552109i
\(709\) 12.8641 0.483120 0.241560 0.970386i \(-0.422341\pi\)
0.241560 + 0.970386i \(0.422341\pi\)
\(710\) 0 0
\(711\) −11.8266 + 48.1198i −0.443532 + 1.80463i
\(712\) 3.90396i 0.146307i
\(713\) −16.7166 −0.626042
\(714\) −8.49687 + 8.34567i −0.317987 + 0.312329i
\(715\) 0 0
\(716\) 4.56797i 0.170713i
\(717\) −3.43125 + 2.69005i −0.128142 + 0.100462i
\(718\) −9.81335 −0.366231
\(719\) −28.5196 −1.06360 −0.531801 0.846870i \(-0.678484\pi\)
−0.531801 + 0.846870i \(0.678484\pi\)
\(720\) 0 0
\(721\) −4.08523 36.4798i −0.152142 1.35858i
\(722\) 11.5680i 0.430515i
\(723\) −22.9104 + 17.9614i −0.852046 + 0.667991i
\(724\) 7.80792i 0.290179i
\(725\) 0 0
\(726\) 12.1987 9.56358i 0.452735 0.354938i
\(727\) 18.9921i 0.704379i 0.935929 + 0.352190i \(0.114563\pi\)
−0.935929 + 0.352190i \(0.885437\pi\)
\(728\) 12.4531 1.39457i 0.461542 0.0516863i
\(729\) 17.8641 20.2454i 0.661632 0.749829i
\(730\) 0 0
\(731\) 1.12283 0.0415293
\(732\) −1.43203 + 1.12269i −0.0529293 + 0.0414958i
\(733\) 27.1345i 1.00224i −0.865379 0.501119i \(-0.832922\pi\)
0.865379 0.501119i \(-0.167078\pi\)
\(734\) −33.9970 −1.25485
\(735\) 0 0
\(736\) −2.82660 −0.104190
\(737\) 14.0720i 0.518348i
\(738\) −32.4777 7.98220i −1.19552 0.293829i
\(739\) 8.67741 0.319204 0.159602 0.987181i \(-0.448979\pi\)
0.159602 + 0.987181i \(0.448979\pi\)
\(740\) 0 0
\(741\) −13.7981 17.6000i −0.506886 0.646551i
\(742\) 14.9625 1.67560i 0.549292 0.0615131i
\(743\) 52.5754i 1.92880i −0.264443 0.964401i \(-0.585188\pi\)
0.264443 0.964401i \(-0.414812\pi\)
\(744\) −6.31998 8.06134i −0.231702 0.295543i
\(745\) 0 0
\(746\) 26.5650i 0.972615i
\(747\) 9.24717 37.6246i 0.338336 1.37661i
\(748\) 3.72179i 0.136082i
\(749\) −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 \(0.489684\pi\)
\(752\) 10.3158 0.376179
\(753\) 1.87616 + 2.39311i 0.0683711 + 0.0872097i
\(754\) 13.3875i 0.487543i
\(755\) 0 0
\(756\) 11.8238 7.01416i 0.430026 0.255103i
\(757\) −4.63995 −0.168642 −0.0843210 0.996439i \(-0.526872\pi\)
−0.0843210 + 0.996439i \(0.526872\pi\)
\(758\) 8.25863i 0.299967i
\(759\) 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 \(0.763983\pi\)
\(762\) −2.72617 + 2.13728i −0.0987589 + 0.0774255i
\(763\) 28.3681 3.17683i 1.02699 0.115009i
\(764\) 7.22117i 0.261253i
\(765\) 0 0
\(766\) 32.6920i 1.18121i
\(767\) 51.0448i 1.84312i
\(768\) −1.06864 1.36309i −0.0385612 0.0491862i
\(769\) 19.2355i 0.693651i 0.937930 + 0.346825i \(0.112740\pi\)
−0.937930 + 0.346825i \(0.887260\pi\)
\(770\) 0 0
\(771\) −23.4423 29.9015i −0.844256 1.07688i
\(772\) 7.60250 0.273620
\(773\) 28.4175 1.02211 0.511053 0.859549i \(-0.329256\pi\)
0.511053 + 0.859549i \(0.329256\pi\)
\(774\) −1.25863 0.309339i −0.0452406 0.0111190i
\(775\) 0 0
\(776\) −14.0015 −0.502624
\(777\) −7.68933 7.82865i −0.275853 0.280851i
\(778\) 1.33354 0.0478099
\(779\) 30.3916i 1.08889i
\(780\) 0 0
\(781\) −18.9867 −0.679399
\(782\) −7.34624 −0.262701
\(783\) −6.04124 13.3875i −0.215896 0.478430i
\(784\) 6.82660 1.54839i 0.243807 0.0552996i
\(785\) 0 0
\(786\) −23.5547 + 18.4666i −0.840169 + 0.658680i
\(787\) 41.6778i 1.48565i −0.669485 0.742826i \(-0.733485\pi\)
0.669485 0.742826i \(-0.266515\pi\)
\(788\) 21.7384i