Properties

Label 570.2.m.b.37.1
Level $570$
Weight $2$
Character 570.37
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 37.1
Root \(0.339574 - 0.339574i\) of defining polynomial
Character \(\chi\) \(=\) 570.37
Dual form 570.2.m.b.493.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.29975 + 1.81952i) q^{5} -1.00000 q^{6} +(-0.728588 - 0.728588i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-0.367533 - 2.20566i) q^{10} -4.80832 q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.531491 - 0.531491i) q^{13} +1.03038 q^{14} +(-2.20566 + 0.367533i) q^{15} -1.00000 q^{16} +(-3.72984 - 3.72984i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(2.90517 + 3.24961i) q^{19} +(1.81952 + 1.29975i) q^{20} -1.03038i q^{21} +(3.39999 - 3.39999i) q^{22} +(-4.07973 + 4.07973i) q^{23} +1.00000i q^{24} +(-1.62130 - 4.72984i) q^{25} +0.751642 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.728588 + 0.728588i) q^{28} -0.494819 q^{29} +(1.29975 - 1.81952i) q^{30} -8.62312i q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.39999 - 3.39999i) q^{33} +5.27479 q^{34} +(2.27266 - 0.378698i) q^{35} +1.00000 q^{36} +(-5.47836 + 5.47836i) q^{37} +(-4.35209 - 0.243552i) q^{38} -0.751642i q^{39} +(-2.20566 + 0.367533i) q^{40} +5.82553i q^{41} +(0.728588 + 0.728588i) q^{42} +(-3.04079 + 3.04079i) q^{43} +4.80832i q^{44} +(-1.81952 - 1.29975i) q^{45} -5.76961i q^{46} +(0.910451 + 0.910451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -5.93832i q^{49} +(4.49094 + 2.19807i) q^{50} -5.27479i q^{51} +(-0.531491 + 0.531491i) q^{52} +(-3.53266 - 3.53266i) q^{53} -1.00000i q^{54} +(6.24961 - 8.74883i) q^{55} -1.03038i q^{56} +(-0.243552 + 4.35209i) q^{57} +(0.349890 - 0.349890i) q^{58} +12.1307 q^{59} +(0.367533 + 2.20566i) q^{60} -5.32419 q^{61} +(6.09747 + 6.09747i) q^{62} +(0.728588 - 0.728588i) q^{63} +1.00000i q^{64} +(1.65786 - 0.276253i) q^{65} +4.80832 q^{66} +(-9.19128 + 9.19128i) q^{67} +(-3.72984 + 3.72984i) q^{68} -5.76961 q^{69} +(-1.33924 + 1.87480i) q^{70} +2.06076i q^{71} +(-0.707107 + 0.707107i) q^{72} +(3.31160 - 3.31160i) q^{73} -7.74758i q^{74} +(2.19807 - 4.49094i) q^{75} +(3.24961 - 2.90517i) q^{76} +(3.50328 + 3.50328i) q^{77} +(0.531491 + 0.531491i) q^{78} -2.77074 q^{79} +(1.29975 - 1.81952i) q^{80} -1.00000 q^{81} +(-4.11927 - 4.11927i) q^{82} +(-3.57770 + 3.57770i) q^{83} -1.03038 q^{84} +(11.6344 - 1.93866i) q^{85} -4.30033i q^{86} +(-0.349890 - 0.349890i) q^{87} +(-3.39999 - 3.39999i) q^{88} -1.08630 q^{89} +(2.20566 - 0.367533i) q^{90} +0.774476i q^{91} +(4.07973 + 4.07973i) q^{92} +(6.09747 - 6.09747i) q^{93} -1.28757 q^{94} +(-9.68873 + 1.06234i) q^{95} +1.00000 q^{96} +(-2.81665 + 2.81665i) q^{97} +(4.19903 + 4.19903i) q^{98} -4.80832i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −1.29975 + 1.81952i −0.581266 + 0.813714i
\(6\) −1.00000 −0.408248
\(7\) −0.728588 0.728588i −0.275380 0.275380i 0.555881 0.831262i \(-0.312381\pi\)
−0.831262 + 0.555881i \(0.812381\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −0.367533 2.20566i −0.116224 0.697490i
\(11\) −4.80832 −1.44976 −0.724881 0.688874i \(-0.758105\pi\)
−0.724881 + 0.688874i \(0.758105\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) −0.531491 0.531491i −0.147409 0.147409i 0.629550 0.776960i \(-0.283239\pi\)
−0.776960 + 0.629550i \(0.783239\pi\)
\(14\) 1.03038 0.275380
\(15\) −2.20566 + 0.367533i −0.569498 + 0.0948965i
\(16\) −1.00000 −0.250000
\(17\) −3.72984 3.72984i −0.904619 0.904619i 0.0912125 0.995831i \(-0.470926\pi\)
−0.995831 + 0.0912125i \(0.970926\pi\)
\(18\) −0.707107 0.707107i −0.166667 0.166667i
\(19\) 2.90517 + 3.24961i 0.666493 + 0.745511i
\(20\) 1.81952 + 1.29975i 0.406857 + 0.290633i
\(21\) 1.03038i 0.224847i
\(22\) 3.39999 3.39999i 0.724881 0.724881i
\(23\) −4.07973 + 4.07973i −0.850682 + 0.850682i −0.990217 0.139535i \(-0.955439\pi\)
0.139535 + 0.990217i \(0.455439\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −1.62130 4.72984i −0.324260 0.945968i
\(26\) 0.751642 0.147409
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −0.728588 + 0.728588i −0.137690 + 0.137690i
\(29\) −0.494819 −0.0918856 −0.0459428 0.998944i \(-0.514629\pi\)
−0.0459428 + 0.998944i \(0.514629\pi\)
\(30\) 1.29975 1.81952i 0.237301 0.332197i
\(31\) 8.62312i 1.54876i −0.632722 0.774379i \(-0.718062\pi\)
0.632722 0.774379i \(-0.281938\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.39999 3.39999i −0.591863 0.591863i
\(34\) 5.27479 0.904619
\(35\) 2.27266 0.378698i 0.384150 0.0640117i
\(36\) 1.00000 0.166667
\(37\) −5.47836 + 5.47836i −0.900637 + 0.900637i −0.995491 0.0948538i \(-0.969762\pi\)
0.0948538 + 0.995491i \(0.469762\pi\)
\(38\) −4.35209 0.243552i −0.706002 0.0395093i
\(39\) 0.751642i 0.120359i
\(40\) −2.20566 + 0.367533i −0.348745 + 0.0581120i
\(41\) 5.82553i 0.909794i 0.890544 + 0.454897i \(0.150324\pi\)
−0.890544 + 0.454897i \(0.849676\pi\)
\(42\) 0.728588 + 0.728588i 0.112424 + 0.112424i
\(43\) −3.04079 + 3.04079i −0.463716 + 0.463716i −0.899871 0.436155i \(-0.856340\pi\)
0.436155 + 0.899871i \(0.356340\pi\)
\(44\) 4.80832i 0.724881i
\(45\) −1.81952 1.29975i −0.271238 0.193755i
\(46\) 5.76961i 0.850682i
\(47\) 0.910451 + 0.910451i 0.132803 + 0.132803i 0.770384 0.637581i \(-0.220065\pi\)
−0.637581 + 0.770384i \(0.720065\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) 5.93832i 0.848331i
\(50\) 4.49094 + 2.19807i 0.635114 + 0.310854i
\(51\) 5.27479i 0.738618i
\(52\) −0.531491 + 0.531491i −0.0737046 + 0.0737046i
\(53\) −3.53266 3.53266i −0.485248 0.485248i 0.421555 0.906803i \(-0.361484\pi\)
−0.906803 + 0.421555i \(0.861484\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 6.24961 8.74883i 0.842697 1.17969i
\(56\) 1.03038i 0.137690i
\(57\) −0.243552 + 4.35209i −0.0322592 + 0.576448i
\(58\) 0.349890 0.349890i 0.0459428 0.0459428i
\(59\) 12.1307 1.57928 0.789641 0.613569i \(-0.210267\pi\)
0.789641 + 0.613569i \(0.210267\pi\)
\(60\) 0.367533 + 2.20566i 0.0474483 + 0.284749i
\(61\) −5.32419 −0.681692 −0.340846 0.940119i \(-0.610713\pi\)
−0.340846 + 0.940119i \(0.610713\pi\)
\(62\) 6.09747 + 6.09747i 0.774379 + 0.774379i
\(63\) 0.728588 0.728588i 0.0917935 0.0917935i
\(64\) 1.00000i 0.125000i
\(65\) 1.65786 0.276253i 0.205633 0.0342650i
\(66\) 4.80832 0.591863
\(67\) −9.19128 + 9.19128i −1.12289 + 1.12289i −0.131590 + 0.991304i \(0.542008\pi\)
−0.991304 + 0.131590i \(0.957992\pi\)
\(68\) −3.72984 + 3.72984i −0.452309 + 0.452309i
\(69\) −5.76961 −0.694579
\(70\) −1.33924 + 1.87480i −0.160069 + 0.224081i
\(71\) 2.06076i 0.244567i 0.992495 + 0.122284i \(0.0390217\pi\)
−0.992495 + 0.122284i \(0.960978\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) 3.31160 3.31160i 0.387594 0.387594i −0.486235 0.873828i \(-0.661630\pi\)
0.873828 + 0.486235i \(0.161630\pi\)
\(74\) 7.74758i 0.900637i
\(75\) 2.19807 4.49094i 0.253811 0.518569i
\(76\) 3.24961 2.90517i 0.372756 0.333246i
\(77\) 3.50328 + 3.50328i 0.399236 + 0.399236i
\(78\) 0.531491 + 0.531491i 0.0601795 + 0.0601795i
\(79\) −2.77074 −0.311733 −0.155866 0.987778i \(-0.549817\pi\)
−0.155866 + 0.987778i \(0.549817\pi\)
\(80\) 1.29975 1.81952i 0.145316 0.203428i
\(81\) −1.00000 −0.111111
\(82\) −4.11927 4.11927i −0.454897 0.454897i
\(83\) −3.57770 + 3.57770i −0.392703 + 0.392703i −0.875650 0.482947i \(-0.839567\pi\)
0.482947 + 0.875650i \(0.339567\pi\)
\(84\) −1.03038 −0.112424
\(85\) 11.6344 1.93866i 1.26192 0.210277i
\(86\) 4.30033i 0.463716i
\(87\) −0.349890 0.349890i −0.0375122 0.0375122i
\(88\) −3.39999 3.39999i −0.362441 0.362441i
\(89\) −1.08630 −0.115147 −0.0575736 0.998341i \(-0.518336\pi\)
−0.0575736 + 0.998341i \(0.518336\pi\)
\(90\) 2.20566 0.367533i 0.232497 0.0387414i
\(91\) 0.774476i 0.0811872i
\(92\) 4.07973 + 4.07973i 0.425341 + 0.425341i
\(93\) 6.09747 6.09747i 0.632278 0.632278i
\(94\) −1.28757 −0.132803
\(95\) −9.68873 + 1.06234i −0.994042 + 0.108994i
\(96\) 1.00000 0.102062
\(97\) −2.81665 + 2.81665i −0.285988 + 0.285988i −0.835491 0.549503i \(-0.814817\pi\)
0.549503 + 0.835491i \(0.314817\pi\)
\(98\) 4.19903 + 4.19903i 0.424166 + 0.424166i
\(99\) 4.80832i 0.483254i
\(100\) −4.72984 + 1.62130i −0.472984 + 0.162130i
\(101\) −14.0592 −1.39894 −0.699470 0.714662i \(-0.746581\pi\)
−0.699470 + 0.714662i \(0.746581\pi\)
\(102\) 3.72984 + 3.72984i 0.369309 + 0.369309i
\(103\) 6.63327 + 6.63327i 0.653596 + 0.653596i 0.953857 0.300261i \(-0.0970739\pi\)
−0.300261 + 0.953857i \(0.597074\pi\)
\(104\) 0.751642i 0.0737046i
\(105\) 1.87480 + 1.33924i 0.182961 + 0.130696i
\(106\) 4.99593 0.485248
\(107\) −1.54262 + 1.54262i −0.149131 + 0.149131i −0.777730 0.628599i \(-0.783629\pi\)
0.628599 + 0.777730i \(0.283629\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) 18.4286 1.76514 0.882569 0.470183i \(-0.155812\pi\)
0.882569 + 0.470183i \(0.155812\pi\)
\(110\) 1.76721 + 10.6055i 0.168497 + 1.01119i
\(111\) −7.74758 −0.735367
\(112\) 0.728588 + 0.728588i 0.0688451 + 0.0688451i
\(113\) 5.25913 + 5.25913i 0.494738 + 0.494738i 0.909795 0.415058i \(-0.136239\pi\)
−0.415058 + 0.909795i \(0.636239\pi\)
\(114\) −2.90517 3.24961i −0.272095 0.304354i
\(115\) −2.12052 12.7258i −0.197740 1.18668i
\(116\) 0.494819i 0.0459428i
\(117\) 0.531491 0.531491i 0.0491364 0.0491364i
\(118\) −8.57770 + 8.57770i −0.789641 + 0.789641i
\(119\) 5.43503i 0.498229i
\(120\) −1.81952 1.29975i −0.166099 0.118650i
\(121\) 12.1199 1.10181
\(122\) 3.76477 3.76477i 0.340846 0.340846i
\(123\) −4.11927 + 4.11927i −0.371422 + 0.371422i
\(124\) −8.62312 −0.774379
\(125\) 10.7133 + 3.19762i 0.958229 + 0.286004i
\(126\) 1.03038i 0.0917935i
\(127\) −9.35800 + 9.35800i −0.830388 + 0.830388i −0.987570 0.157181i \(-0.949759\pi\)
0.157181 + 0.987570i \(0.449759\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −4.30033 −0.378623
\(130\) −0.976946 + 1.36763i −0.0856839 + 0.119949i
\(131\) 12.6267 1.10320 0.551601 0.834108i \(-0.314017\pi\)
0.551601 + 0.834108i \(0.314017\pi\)
\(132\) −3.39999 + 3.39999i −0.295931 + 0.295931i
\(133\) 0.250951 4.48430i 0.0217602 0.388838i
\(134\) 12.9984i 1.12289i
\(135\) −0.367533 2.20566i −0.0316322 0.189833i
\(136\) 5.27479i 0.452309i
\(137\) 0.378698 + 0.378698i 0.0323544 + 0.0323544i 0.723099 0.690745i \(-0.242717\pi\)
−0.690745 + 0.723099i \(0.742717\pi\)
\(138\) 4.07973 4.07973i 0.347290 0.347290i
\(139\) 22.7942i 1.93338i 0.255957 + 0.966688i \(0.417609\pi\)
−0.255957 + 0.966688i \(0.582391\pi\)
\(140\) −0.378698 2.27266i −0.0320058 0.192075i
\(141\) 1.28757i 0.108433i
\(142\) −1.45718 1.45718i −0.122284 0.122284i
\(143\) 2.55558 + 2.55558i 0.213708 + 0.213708i
\(144\) 1.00000i 0.0833333i
\(145\) 0.643141 0.900333i 0.0534100 0.0747686i
\(146\) 4.68331i 0.387594i
\(147\) 4.19903 4.19903i 0.346330 0.346330i
\(148\) 5.47836 + 5.47836i 0.450319 + 0.450319i
\(149\) 15.8801i 1.30095i 0.759529 + 0.650473i \(0.225429\pi\)
−0.759529 + 0.650473i \(0.774571\pi\)
\(150\) 1.62130 + 4.72984i 0.132379 + 0.386190i
\(151\) 13.3507i 1.08646i 0.839583 + 0.543231i \(0.182799\pi\)
−0.839583 + 0.543231i \(0.817201\pi\)
\(152\) −0.243552 + 4.35209i −0.0197547 + 0.353001i
\(153\) 3.72984 3.72984i 0.301540 0.301540i
\(154\) −4.95439 −0.399236
\(155\) 15.6899 + 11.2079i 1.26025 + 0.900240i
\(156\) −0.751642 −0.0601795
\(157\) 11.7372 + 11.7372i 0.936727 + 0.936727i 0.998114 0.0613870i \(-0.0195524\pi\)
−0.0613870 + 0.998114i \(0.519552\pi\)
\(158\) 1.95921 1.95921i 0.155866 0.155866i
\(159\) 4.99593i 0.396203i
\(160\) 0.367533 + 2.20566i 0.0290560 + 0.174372i
\(161\) 5.94489 0.468523
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −0.988668 + 0.988668i −0.0774384 + 0.0774384i −0.744765 0.667327i \(-0.767438\pi\)
0.667327 + 0.744765i \(0.267438\pi\)
\(164\) 5.82553 0.454897
\(165\) 10.6055 1.76721i 0.825637 0.137577i
\(166\) 5.05963i 0.392703i
\(167\) −7.42584 + 7.42584i −0.574629 + 0.574629i −0.933418 0.358790i \(-0.883189\pi\)
0.358790 + 0.933418i \(0.383189\pi\)
\(168\) 0.728588 0.728588i 0.0562118 0.0562118i
\(169\) 12.4350i 0.956541i
\(170\) −6.85591 + 9.59758i −0.525824 + 0.736101i
\(171\) −3.24961 + 2.90517i −0.248504 + 0.222164i
\(172\) 3.04079 + 3.04079i 0.231858 + 0.231858i
\(173\) −11.0462 11.0462i −0.839825 0.839825i 0.149011 0.988836i \(-0.452391\pi\)
−0.988836 + 0.149011i \(0.952391\pi\)
\(174\) 0.494819 0.0375122
\(175\) −2.26484 + 4.62737i −0.171206 + 0.349796i
\(176\) 4.80832 0.362441
\(177\) 8.57770 + 8.57770i 0.644739 + 0.644739i
\(178\) 0.768128 0.768128i 0.0575736 0.0575736i
\(179\) 19.0425 1.42330 0.711652 0.702532i \(-0.247947\pi\)
0.711652 + 0.702532i \(0.247947\pi\)
\(180\) −1.29975 + 1.81952i −0.0968776 + 0.135619i
\(181\) 1.78110i 0.132388i −0.997807 0.0661941i \(-0.978914\pi\)
0.997807 0.0661941i \(-0.0210857\pi\)
\(182\) −0.547637 0.547637i −0.0405936 0.0405936i
\(183\) −3.76477 3.76477i −0.278300 0.278300i
\(184\) −5.76961 −0.425341
\(185\) −2.84749 17.0885i −0.209351 1.25637i
\(186\) 8.62312i 0.632278i
\(187\) 17.9343 + 17.9343i 1.31148 + 1.31148i
\(188\) 0.910451 0.910451i 0.0664014 0.0664014i
\(189\) 1.03038 0.0749491
\(190\) 6.09977 7.60215i 0.442524 0.551518i
\(191\) −14.8650 −1.07559 −0.537797 0.843075i \(-0.680743\pi\)
−0.537797 + 0.843075i \(0.680743\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −5.04632 5.04632i −0.363242 0.363242i 0.501763 0.865005i \(-0.332685\pi\)
−0.865005 + 0.501763i \(0.832685\pi\)
\(194\) 3.98335i 0.285988i
\(195\) 1.36763 + 0.976946i 0.0979378 + 0.0699606i
\(196\) −5.93832 −0.424166
\(197\) −7.66209 7.66209i −0.545901 0.545901i 0.379351 0.925253i \(-0.376147\pi\)
−0.925253 + 0.379351i \(0.876147\pi\)
\(198\) 3.39999 + 3.39999i 0.241627 + 0.241627i
\(199\) 20.9302i 1.48370i 0.670565 + 0.741851i \(0.266052\pi\)
−0.670565 + 0.741851i \(0.733948\pi\)
\(200\) 2.19807 4.49094i 0.155427 0.317557i
\(201\) −12.9984 −0.916839
\(202\) 9.94134 9.94134i 0.699470 0.699470i
\(203\) 0.360520 + 0.360520i 0.0253035 + 0.0253035i
\(204\) −5.27479 −0.369309
\(205\) −10.5997 7.57173i −0.740312 0.528832i
\(206\) −9.38086 −0.653596
\(207\) −4.07973 4.07973i −0.283561 0.283561i
\(208\) 0.531491 + 0.531491i 0.0368523 + 0.0368523i
\(209\) −13.9690 15.6252i −0.966256 1.08081i
\(210\) −2.27266 + 0.378698i −0.156829 + 0.0261327i
\(211\) 27.6388i 1.90273i −0.308062 0.951366i \(-0.599681\pi\)
0.308062 0.951366i \(-0.400319\pi\)
\(212\) −3.53266 + 3.53266i −0.242624 + 0.242624i
\(213\) −1.45718 + 1.45718i −0.0998441 + 0.0998441i
\(214\) 2.18160i 0.149131i
\(215\) −1.58051 9.48504i −0.107790 0.646875i
\(216\) −1.00000 −0.0680414
\(217\) −6.28270 + 6.28270i −0.426498 + 0.426498i
\(218\) −13.0310 + 13.0310i −0.882569 + 0.882569i
\(219\) 4.68331 0.316469
\(220\) −8.74883 6.24961i −0.589846 0.421349i
\(221\) 3.96475i 0.266698i
\(222\) 5.47836 5.47836i 0.367684 0.367684i
\(223\) 8.04571 + 8.04571i 0.538781 + 0.538781i 0.923171 0.384390i \(-0.125588\pi\)
−0.384390 + 0.923171i \(0.625588\pi\)
\(224\) −1.03038 −0.0688451
\(225\) 4.72984 1.62130i 0.315323 0.108087i
\(226\) −7.43754 −0.494738
\(227\) 1.98330 1.98330i 0.131636 0.131636i −0.638219 0.769855i \(-0.720329\pi\)
0.769855 + 0.638219i \(0.220329\pi\)
\(228\) 4.35209 + 0.243552i 0.288224 + 0.0161296i
\(229\) 19.6443i 1.29813i −0.760732 0.649066i \(-0.775160\pi\)
0.760732 0.649066i \(-0.224840\pi\)
\(230\) 10.4979 + 7.49905i 0.692212 + 0.494473i
\(231\) 4.95439i 0.325975i
\(232\) −0.349890 0.349890i −0.0229714 0.0229714i
\(233\) −4.73992 + 4.73992i −0.310523 + 0.310523i −0.845112 0.534589i \(-0.820466\pi\)
0.534589 + 0.845112i \(0.320466\pi\)
\(234\) 0.751642i 0.0491364i
\(235\) −2.83994 + 0.473225i −0.185257 + 0.0308698i
\(236\) 12.1307i 0.789641i
\(237\) −1.95921 1.95921i −0.127264 0.127264i
\(238\) −3.84315 3.84315i −0.249114 0.249114i
\(239\) 21.1851i 1.37035i −0.728378 0.685176i \(-0.759725\pi\)
0.728378 0.685176i \(-0.240275\pi\)
\(240\) 2.20566 0.367533i 0.142375 0.0237241i
\(241\) 16.2784i 1.04859i −0.851538 0.524293i \(-0.824329\pi\)
0.851538 0.524293i \(-0.175671\pi\)
\(242\) −8.57008 + 8.57008i −0.550905 + 0.550905i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 5.32419i 0.340846i
\(245\) 10.8049 + 7.71833i 0.690299 + 0.493106i
\(246\) 5.82553i 0.371422i
\(247\) 0.183064 3.27121i 0.0116481 0.208142i
\(248\) 6.09747 6.09747i 0.387190 0.387190i
\(249\) −5.05963 −0.320641
\(250\) −9.83652 + 5.31441i −0.622116 + 0.336113i
\(251\) 5.24992 0.331372 0.165686 0.986179i \(-0.447016\pi\)
0.165686 + 0.986179i \(0.447016\pi\)
\(252\) −0.728588 0.728588i −0.0458967 0.0458967i
\(253\) 19.6166 19.6166i 1.23329 1.23329i
\(254\) 13.2342i 0.830388i
\(255\) 9.59758 + 6.85591i 0.601024 + 0.429333i
\(256\) 1.00000 0.0625000
\(257\) 16.0320 16.0320i 1.00005 1.00005i 4.94079e−5 1.00000i \(-0.499984\pi\)
1.00000 4.94079e-5i \(-1.57270e-5\pi\)
\(258\) 3.04079 3.04079i 0.189311 0.189311i
\(259\) 7.98294 0.496036
\(260\) −0.276253 1.65786i −0.0171325 0.102816i
\(261\) 0.494819i 0.0306285i
\(262\) −8.92844 + 8.92844i −0.551601 + 0.551601i
\(263\) −5.94999 + 5.94999i −0.366892 + 0.366892i −0.866342 0.499450i \(-0.833535\pi\)
0.499450 + 0.866342i \(0.333535\pi\)
\(264\) 4.80832i 0.295931i
\(265\) 11.0193 1.83617i 0.676911 0.112795i
\(266\) 2.99343 + 3.34833i 0.183539 + 0.205299i
\(267\) −0.768128 0.768128i −0.0470087 0.0470087i
\(268\) 9.19128 + 9.19128i 0.561447 + 0.561447i
\(269\) −26.2880 −1.60281 −0.801404 0.598123i \(-0.795913\pi\)
−0.801404 + 0.598123i \(0.795913\pi\)
\(270\) 1.81952 + 1.29975i 0.110732 + 0.0791002i
\(271\) −11.9318 −0.724802 −0.362401 0.932022i \(-0.618043\pi\)
−0.362401 + 0.932022i \(0.618043\pi\)
\(272\) 3.72984 + 3.72984i 0.226155 + 0.226155i
\(273\) −0.547637 + 0.547637i −0.0331445 + 0.0331445i
\(274\) −0.535560 −0.0323544
\(275\) 7.79573 + 22.7426i 0.470100 + 1.37143i
\(276\) 5.76961i 0.347290i
\(277\) −13.1943 13.1943i −0.792771 0.792771i 0.189173 0.981944i \(-0.439419\pi\)
−0.981944 + 0.189173i \(0.939419\pi\)
\(278\) −16.1179 16.1179i −0.966688 0.966688i
\(279\) 8.62312 0.516253
\(280\) 1.87480 + 1.33924i 0.112040 + 0.0800346i
\(281\) 25.4814i 1.52009i −0.649870 0.760045i \(-0.725177\pi\)
0.649870 0.760045i \(-0.274823\pi\)
\(282\) −0.910451 0.910451i −0.0542165 0.0542165i
\(283\) −14.9451 + 14.9451i −0.888392 + 0.888392i −0.994369 0.105977i \(-0.966203\pi\)
0.105977 + 0.994369i \(0.466203\pi\)
\(284\) 2.06076 0.122284
\(285\) −7.60215 6.09977i −0.450313 0.361319i
\(286\) −3.61413 −0.213708
\(287\) 4.24441 4.24441i 0.250540 0.250540i
\(288\) 0.707107 + 0.707107i 0.0416667 + 0.0416667i
\(289\) 10.8234i 0.636671i
\(290\) 0.181862 + 1.09140i 0.0106793 + 0.0640893i
\(291\) −3.98335 −0.233508
\(292\) −3.31160 3.31160i −0.193797 0.193797i
\(293\) −19.3388 19.3388i −1.12978 1.12978i −0.990212 0.139570i \(-0.955428\pi\)
−0.139570 0.990212i \(-0.544572\pi\)
\(294\) 5.93832i 0.346330i
\(295\) −15.7669 + 22.0720i −0.917982 + 1.28508i
\(296\) −7.74758 −0.450319
\(297\) 3.39999 3.39999i 0.197288 0.197288i
\(298\) −11.2289 11.2289i −0.650473 0.650473i
\(299\) 4.33668 0.250797
\(300\) −4.49094 2.19807i −0.259284 0.126906i
\(301\) 4.43097 0.255397
\(302\) −9.44035 9.44035i −0.543231 0.543231i
\(303\) −9.94134 9.94134i −0.571115 0.571115i
\(304\) −2.90517 3.24961i −0.166623 0.186378i
\(305\) 6.92011 9.68746i 0.396244 0.554702i
\(306\) 5.27479i 0.301540i
\(307\) −0.00353863 + 0.00353863i −0.000201960 + 0.000201960i −0.707208 0.707006i \(-0.750045\pi\)
0.707006 + 0.707208i \(0.250045\pi\)
\(308\) 3.50328 3.50328i 0.199618 0.199618i
\(309\) 9.38086i 0.533659i
\(310\) −19.0196 + 3.16928i −1.08024 + 0.180003i
\(311\) −11.6925 −0.663019 −0.331509 0.943452i \(-0.607558\pi\)
−0.331509 + 0.943452i \(0.607558\pi\)
\(312\) 0.531491 0.531491i 0.0300898 0.0300898i
\(313\) −16.6688 + 16.6688i −0.942174 + 0.942174i −0.998417 0.0562432i \(-0.982088\pi\)
0.0562432 + 0.998417i \(0.482088\pi\)
\(314\) −16.5988 −0.936727
\(315\) 0.378698 + 2.27266i 0.0213372 + 0.128050i
\(316\) 2.77074i 0.155866i
\(317\) 6.96737 6.96737i 0.391327 0.391327i −0.483834 0.875160i \(-0.660756\pi\)
0.875160 + 0.483834i \(0.160756\pi\)
\(318\) 3.53266 + 3.53266i 0.198102 + 0.198102i
\(319\) 2.37925 0.133212
\(320\) −1.81952 1.29975i −0.101714 0.0726582i
\(321\) −2.18160 −0.121765
\(322\) −4.20367 + 4.20367i −0.234261 + 0.234261i
\(323\) 1.28468 22.9564i 0.0714818 1.27733i
\(324\) 1.00000i 0.0555556i
\(325\) −1.65216 + 3.37558i −0.0916454 + 0.187243i
\(326\) 1.39819i 0.0774384i
\(327\) 13.0310 + 13.0310i 0.720614 + 0.720614i
\(328\) −4.11927 + 4.11927i −0.227449 + 0.227449i
\(329\) 1.32669i 0.0731426i
\(330\) −6.24961 + 8.74883i −0.344030 + 0.481607i
\(331\) 12.2381i 0.672669i 0.941743 + 0.336335i \(0.109187\pi\)
−0.941743 + 0.336335i \(0.890813\pi\)
\(332\) 3.57770 + 3.57770i 0.196352 + 0.196352i
\(333\) −5.47836 5.47836i −0.300212 0.300212i
\(334\) 10.5017i 0.574629i
\(335\) −4.77735 28.6701i −0.261015 1.56641i
\(336\) 1.03038i 0.0562118i
\(337\) 18.9918 18.9918i 1.03455 1.03455i 0.0351664 0.999381i \(-0.488804\pi\)
0.999381 0.0351664i \(-0.0111961\pi\)
\(338\) 8.79290 + 8.79290i 0.478271 + 0.478271i
\(339\) 7.43754i 0.403952i
\(340\) −1.93866 11.6344i −0.105138 0.630962i
\(341\) 41.4627i 2.24533i
\(342\) 0.243552 4.35209i 0.0131698 0.235334i
\(343\) −9.42671 + 9.42671i −0.508994 + 0.508994i
\(344\) −4.30033 −0.231858
\(345\) 7.49905 10.4979i 0.403735 0.565189i
\(346\) 15.6216 0.839825
\(347\) 1.51527 + 1.51527i 0.0813438 + 0.0813438i 0.746608 0.665264i \(-0.231681\pi\)
−0.665264 + 0.746608i \(0.731681\pi\)
\(348\) −0.349890 + 0.349890i −0.0187561 + 0.0187561i
\(349\) 21.3136i 1.14089i 0.821336 + 0.570444i \(0.193229\pi\)
−0.821336 + 0.570444i \(0.806771\pi\)
\(350\) −1.67056 4.87353i −0.0892950 0.260501i
\(351\) 0.751642 0.0401197
\(352\) −3.39999 + 3.39999i −0.181220 + 0.181220i
\(353\) 9.37463 9.37463i 0.498961 0.498961i −0.412153 0.911115i \(-0.635223\pi\)
0.911115 + 0.412153i \(0.135223\pi\)
\(354\) −12.1307 −0.644739
\(355\) −3.74959 2.67847i −0.199008 0.142158i
\(356\) 1.08630i 0.0575736i
\(357\) −3.84315 + 3.84315i −0.203401 + 0.203401i
\(358\) −13.4651 + 13.4651i −0.711652 + 0.711652i
\(359\) 30.1209i 1.58972i −0.606792 0.794861i \(-0.707544\pi\)
0.606792 0.794861i \(-0.292456\pi\)
\(360\) −0.367533 2.20566i −0.0193707 0.116248i
\(361\) −2.11992 + 18.8814i −0.111575 + 0.993756i
\(362\) 1.25943 + 1.25943i 0.0661941 + 0.0661941i
\(363\) 8.57008 + 8.57008i 0.449812 + 0.449812i
\(364\) 0.774476 0.0405936
\(365\) 1.72127 + 10.3298i 0.0900954 + 0.540685i
\(366\) 5.32419 0.278300
\(367\) −10.0986 10.0986i −0.527140 0.527140i 0.392578 0.919719i \(-0.371583\pi\)
−0.919719 + 0.392578i \(0.871583\pi\)
\(368\) 4.07973 4.07973i 0.212671 0.212671i
\(369\) −5.82553 −0.303265
\(370\) 14.0969 + 10.0699i 0.732861 + 0.523510i
\(371\) 5.14771i 0.267256i
\(372\) −6.09747 6.09747i −0.316139 0.316139i
\(373\) 11.5759 + 11.5759i 0.599377 + 0.599377i 0.940147 0.340770i \(-0.110688\pi\)
−0.340770 + 0.940147i \(0.610688\pi\)
\(374\) −25.3629 −1.31148
\(375\) 5.31441 + 9.83652i 0.274435 + 0.507956i
\(376\) 1.28757i 0.0664014i
\(377\) 0.262992 + 0.262992i 0.0135448 + 0.0135448i
\(378\) −0.728588 + 0.728588i −0.0374745 + 0.0374745i
\(379\) 30.6895 1.57641 0.788206 0.615412i \(-0.211010\pi\)
0.788206 + 0.615412i \(0.211010\pi\)
\(380\) 1.06234 + 9.68873i 0.0544971 + 0.497021i
\(381\) −13.2342 −0.678009
\(382\) 10.5111 10.5111i 0.537797 0.537797i
\(383\) −6.71232 6.71232i −0.342983 0.342983i 0.514504 0.857488i \(-0.327976\pi\)
−0.857488 + 0.514504i \(0.827976\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −10.9277 + 1.82090i −0.556926 + 0.0928017i
\(386\) 7.13657 0.363242
\(387\) −3.04079 3.04079i −0.154572 0.154572i
\(388\) 2.81665 + 2.81665i 0.142994 + 0.142994i
\(389\) 1.69598i 0.0859894i 0.999075 + 0.0429947i \(0.0136899\pi\)
−0.999075 + 0.0429947i \(0.986310\pi\)
\(390\) −1.65786 + 0.276253i −0.0839492 + 0.0139886i
\(391\) 30.4335 1.53909
\(392\) 4.19903 4.19903i 0.212083 0.212083i
\(393\) 8.92844 + 8.92844i 0.450380 + 0.450380i
\(394\) 10.8358 0.545901
\(395\) 3.60127 5.04142i 0.181199 0.253661i
\(396\) −4.80832 −0.241627
\(397\) −17.6346 17.6346i −0.885057 0.885057i 0.108986 0.994043i \(-0.465240\pi\)
−0.994043 + 0.108986i \(0.965240\pi\)
\(398\) −14.7999 14.7999i −0.741851 0.741851i
\(399\) 3.34833 2.99343i 0.167626 0.149859i
\(400\) 1.62130 + 4.72984i 0.0810651 + 0.236492i
\(401\) 1.30146i 0.0649918i −0.999472 0.0324959i \(-0.989654\pi\)
0.999472 0.0324959i \(-0.0103456\pi\)
\(402\) 9.19128 9.19128i 0.458420 0.458420i
\(403\) −4.58311 + 4.58311i −0.228301 + 0.228301i
\(404\) 14.0592i 0.699470i
\(405\) 1.29975 1.81952i 0.0645851 0.0904126i
\(406\) −0.509852 −0.0253035
\(407\) 26.3417 26.3417i 1.30571 1.30571i
\(408\) 3.72984 3.72984i 0.184655 0.184655i
\(409\) 18.8682 0.932971 0.466485 0.884529i \(-0.345520\pi\)
0.466485 + 0.884529i \(0.345520\pi\)
\(410\) 12.8491 2.14107i 0.634572 0.105740i
\(411\) 0.535560i 0.0264172i
\(412\) 6.63327 6.63327i 0.326798 0.326798i
\(413\) −8.83828 8.83828i −0.434903 0.434903i
\(414\) 5.76961 0.283561
\(415\) −1.85958 11.1598i −0.0912831 0.547813i
\(416\) −0.751642 −0.0368523
\(417\) −16.1179 + 16.1179i −0.789298 + 0.789298i
\(418\) 20.9262 + 1.17107i 1.02354 + 0.0572791i
\(419\) 20.1568i 0.984725i 0.870390 + 0.492363i \(0.163867\pi\)
−0.870390 + 0.492363i \(0.836133\pi\)
\(420\) 1.33924 1.87480i 0.0653480 0.0914806i
\(421\) 8.85286i 0.431462i 0.976453 + 0.215731i \(0.0692134\pi\)
−0.976453 + 0.215731i \(0.930787\pi\)
\(422\) 19.5436 + 19.5436i 0.951366 + 0.951366i
\(423\) −0.910451 + 0.910451i −0.0442676 + 0.0442676i
\(424\) 4.99593i 0.242624i
\(425\) −11.5943 + 23.6887i −0.562408 + 1.14907i
\(426\) 2.06076i 0.0998441i
\(427\) 3.87914 + 3.87914i 0.187725 + 0.187725i
\(428\) 1.54262 + 1.54262i 0.0745656 + 0.0745656i
\(429\) 3.61413i 0.174492i
\(430\) 7.82453 + 5.58935i 0.377332 + 0.269542i
\(431\) 25.3047i 1.21889i 0.792830 + 0.609443i \(0.208607\pi\)
−0.792830 + 0.609443i \(0.791393\pi\)
\(432\) 0.707107 0.707107i 0.0340207 0.0340207i
\(433\) 6.00560 + 6.00560i 0.288611 + 0.288611i 0.836531 0.547920i \(-0.184580\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(434\) 8.88509i 0.426498i
\(435\) 1.09140 0.181862i 0.0523287 0.00871963i
\(436\) 18.4286i 0.882569i
\(437\) −25.1099 1.40520i −1.20117 0.0672198i
\(438\) −3.31160 + 3.31160i −0.158234 + 0.158234i
\(439\) −38.4260 −1.83397 −0.916986 0.398919i \(-0.869386\pi\)
−0.916986 + 0.398919i \(0.869386\pi\)
\(440\) 10.6055 1.76721i 0.505597 0.0842486i
\(441\) 5.93832 0.282777
\(442\) −2.80350 2.80350i −0.133349 0.133349i
\(443\) 27.7457 27.7457i 1.31824 1.31824i 0.403066 0.915171i \(-0.367945\pi\)
0.915171 0.403066i \(-0.132055\pi\)
\(444\) 7.74758i 0.367684i
\(445\) 1.41191 1.97654i 0.0669311 0.0936969i
\(446\) −11.3784 −0.538781
\(447\) −11.2289 + 11.2289i −0.531109 + 0.531109i
\(448\) 0.728588 0.728588i 0.0344226 0.0344226i
\(449\) 28.1598 1.32894 0.664472 0.747313i \(-0.268656\pi\)
0.664472 + 0.747313i \(0.268656\pi\)
\(450\) −2.19807 + 4.49094i −0.103618 + 0.211705i
\(451\) 28.0110i 1.31899i
\(452\) 5.25913 5.25913i 0.247369 0.247369i
\(453\) −9.44035 + 9.44035i −0.443546 + 0.443546i
\(454\) 2.80480i 0.131636i
\(455\) −1.40917 1.00663i −0.0660631 0.0471913i
\(456\) −3.24961 + 2.90517i −0.152177 + 0.136047i
\(457\) −19.5575 19.5575i −0.914859 0.914859i 0.0817904 0.996650i \(-0.473936\pi\)
−0.996650 + 0.0817904i \(0.973936\pi\)
\(458\) 13.8906 + 13.8906i 0.649066 + 0.649066i
\(459\) 5.27479 0.246206
\(460\) −12.7258 + 2.12052i −0.593342 + 0.0988698i
\(461\) 9.61570 0.447848 0.223924 0.974607i \(-0.428113\pi\)
0.223924 + 0.974607i \(0.428113\pi\)
\(462\) −3.50328 3.50328i −0.162988 0.162988i
\(463\) 16.6735 16.6735i 0.774882 0.774882i −0.204074 0.978956i \(-0.565418\pi\)
0.978956 + 0.204074i \(0.0654182\pi\)
\(464\) 0.494819 0.0229714
\(465\) 3.16928 + 19.0196i 0.146972 + 0.882015i
\(466\) 6.70326i 0.310523i
\(467\) −17.1190 17.1190i −0.792171 0.792171i 0.189676 0.981847i \(-0.439256\pi\)
−0.981847 + 0.189676i \(0.939256\pi\)
\(468\) −0.531491 0.531491i −0.0245682 0.0245682i
\(469\) 13.3933 0.618446
\(470\) 1.67352 2.34276i 0.0771938 0.108064i
\(471\) 16.5988i 0.764834i
\(472\) 8.57770 + 8.57770i 0.394820 + 0.394820i
\(473\) 14.6211 14.6211i 0.672278 0.672278i
\(474\) 2.77074 0.127264
\(475\) 10.6600 19.0096i 0.489113 0.872221i
\(476\) 5.43503 0.249114
\(477\) 3.53266 3.53266i 0.161749 0.161749i
\(478\) 14.9801 + 14.9801i 0.685176 + 0.685176i
\(479\) 14.2801i 0.652474i 0.945288 + 0.326237i \(0.105781\pi\)
−0.945288 + 0.326237i \(0.894219\pi\)
\(480\) −1.29975 + 1.81952i −0.0593252 + 0.0830493i
\(481\) 5.82340 0.265524
\(482\) 11.5106 + 11.5106i 0.524293 + 0.524293i
\(483\) 4.20367 + 4.20367i 0.191274 + 0.191274i
\(484\) 12.1199i 0.550905i
\(485\) −1.46401 8.78590i −0.0664774 0.398947i
\(486\) 1.00000 0.0453609
\(487\) −13.6790 + 13.6790i −0.619856 + 0.619856i −0.945494 0.325639i \(-0.894421\pi\)
0.325639 + 0.945494i \(0.394421\pi\)
\(488\) −3.76477 3.76477i −0.170423 0.170423i
\(489\) −1.39819 −0.0632282
\(490\) −13.0979 + 2.18253i −0.591702 + 0.0985965i
\(491\) 6.60655 0.298150 0.149075 0.988826i \(-0.452370\pi\)
0.149075 + 0.988826i \(0.452370\pi\)
\(492\) 4.11927 + 4.11927i 0.185711 + 0.185711i
\(493\) 1.84560 + 1.84560i 0.0831215 + 0.0831215i
\(494\) 2.18365 + 2.44254i 0.0982471 + 0.109895i
\(495\) 8.74883 + 6.24961i 0.393231 + 0.280899i
\(496\) 8.62312i 0.387190i
\(497\) 1.50144 1.50144i 0.0673490 0.0673490i
\(498\) 3.57770 3.57770i 0.160320 0.160320i
\(499\) 35.7269i 1.59935i 0.600430 + 0.799677i \(0.294996\pi\)
−0.600430 + 0.799677i \(0.705004\pi\)
\(500\) 3.19762 10.7133i 0.143002 0.479114i
\(501\) −10.5017 −0.469182
\(502\) −3.71225 + 3.71225i −0.165686 + 0.165686i
\(503\) −8.52003 + 8.52003i −0.379889 + 0.379889i −0.871062 0.491173i \(-0.836568\pi\)
0.491173 + 0.871062i \(0.336568\pi\)
\(504\) 1.03038 0.0458967
\(505\) 18.2734 25.5809i 0.813156 1.13834i
\(506\) 27.7421i 1.23329i
\(507\) 8.79290 8.79290i 0.390506 0.390506i
\(508\) 9.35800 + 9.35800i 0.415194 + 0.415194i
\(509\) −13.4408 −0.595753 −0.297877 0.954604i \(-0.596278\pi\)
−0.297877 + 0.954604i \(0.596278\pi\)
\(510\) −11.6344 + 1.93866i −0.515179 + 0.0858452i
\(511\) −4.82559 −0.213471
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.35209 0.243552i −0.192149 0.0107531i
\(514\) 22.6727i 1.00005i
\(515\) −20.6910 + 3.44777i −0.911752 + 0.151927i
\(516\) 4.30033i 0.189311i
\(517\) −4.37774 4.37774i −0.192533 0.192533i
\(518\) −5.64479 + 5.64479i −0.248018 + 0.248018i
\(519\) 15.6216i 0.685714i
\(520\) 1.36763 + 0.976946i 0.0599744 + 0.0428419i
\(521\) 13.5544i 0.593831i 0.954904 + 0.296916i \(0.0959580\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(522\) 0.349890 + 0.349890i 0.0153143 + 0.0153143i
\(523\) 5.40357 + 5.40357i 0.236282 + 0.236282i 0.815308 0.579027i \(-0.196567\pi\)
−0.579027 + 0.815308i \(0.696567\pi\)
\(524\) 12.6267i 0.551601i
\(525\) −4.87353 + 1.67056i −0.212698 + 0.0729090i
\(526\) 8.41456i 0.366892i
\(527\) −32.1629 + 32.1629i −1.40104 + 1.40104i
\(528\) 3.39999 + 3.39999i 0.147966 + 0.147966i
\(529\) 10.2884i 0.447321i
\(530\) −6.49346 + 9.09020i −0.282058 + 0.394853i
\(531\) 12.1307i 0.526427i
\(532\) −4.48430 0.250951i −0.194419 0.0108801i
\(533\) 3.09622 3.09622i 0.134112 0.134112i
\(534\) 1.08630 0.0470087
\(535\) −0.801810 4.81186i −0.0346653 0.208035i
\(536\) −12.9984 −0.561447
\(537\) 13.4651 + 13.4651i 0.581062 + 0.581062i
\(538\) 18.5884 18.5884i 0.801404 0.801404i
\(539\) 28.5533i 1.22988i
\(540\) −2.20566 + 0.367533i −0.0949163 + 0.0158161i
\(541\) 7.68488 0.330399 0.165200 0.986260i \(-0.447173\pi\)
0.165200 + 0.986260i \(0.447173\pi\)
\(542\) 8.43702 8.43702i 0.362401 0.362401i
\(543\) 1.25943 1.25943i 0.0540473 0.0540473i
\(544\) −5.27479 −0.226155
\(545\) −23.9525 + 33.5312i −1.02601 + 1.43632i
\(546\) 0.774476i 0.0331445i
\(547\) −17.8604 + 17.8604i −0.763656 + 0.763656i −0.976981 0.213325i \(-0.931571\pi\)
0.213325 + 0.976981i \(0.431571\pi\)
\(548\) 0.378698 0.378698i 0.0161772 0.0161772i
\(549\) 5.32419i 0.227231i
\(550\) −21.5938 10.5690i −0.920765 0.450664i
\(551\) −1.43754 1.60797i −0.0612411 0.0685018i
\(552\) −4.07973 4.07973i −0.173645 0.173645i
\(553\) 2.01873 + 2.01873i 0.0858451 + 0.0858451i
\(554\) 18.6596 0.792771
\(555\) 10.0699 14.0969i 0.427444 0.598379i
\(556\) 22.7942 0.966688
\(557\) 12.5198 + 12.5198i 0.530480 + 0.530480i 0.920715 0.390235i \(-0.127606\pi\)
−0.390235 + 0.920715i \(0.627606\pi\)
\(558\) −6.09747 + 6.09747i −0.258126 + 0.258126i
\(559\) 3.23231 0.136712
\(560\) −2.27266 + 0.378698i −0.0960375 + 0.0160029i
\(561\) 25.3629i 1.07082i
\(562\) 18.0180 + 18.0180i 0.760045 + 0.760045i
\(563\) 11.0759 + 11.0759i 0.466791 + 0.466791i 0.900873 0.434082i \(-0.142927\pi\)
−0.434082 + 0.900873i \(0.642927\pi\)
\(564\) 1.28757 0.0542165
\(565\) −16.4046 + 2.73354i −0.690149 + 0.115001i
\(566\) 21.1355i 0.888392i
\(567\) 0.728588 + 0.728588i 0.0305978 + 0.0305978i
\(568\) −1.45718 + 1.45718i −0.0611418 + 0.0611418i
\(569\) −43.4414 −1.82116 −0.910579 0.413336i \(-0.864364\pi\)
−0.910579 + 0.413336i \(0.864364\pi\)
\(570\) 9.68873 1.06234i 0.405816 0.0444967i
\(571\) 15.6768 0.656052 0.328026 0.944669i \(-0.393617\pi\)
0.328026 + 0.944669i \(0.393617\pi\)
\(572\) 2.55558 2.55558i 0.106854 0.106854i
\(573\) −10.5111 10.5111i −0.439109 0.439109i
\(574\) 6.00250i 0.250540i
\(575\) 25.9109 + 12.6820i 1.08056 + 0.528876i
\(576\) −1.00000 −0.0416667
\(577\) 6.59569 + 6.59569i 0.274582 + 0.274582i 0.830942 0.556359i \(-0.187802\pi\)
−0.556359 + 0.830942i \(0.687802\pi\)
\(578\) −7.65330 7.65330i −0.318335 0.318335i
\(579\) 7.13657i 0.296586i
\(580\) −0.900333 0.643141i −0.0373843 0.0267050i
\(581\) 5.21334 0.216286
\(582\) 2.81665 2.81665i 0.116754 0.116754i
\(583\) 16.9861 + 16.9861i 0.703494 + 0.703494i
\(584\) 4.68331 0.193797
\(585\) 0.276253 + 1.65786i 0.0114217 + 0.0685442i
\(586\) 27.3491 1.12978
\(587\) −23.8623 23.8623i −0.984904 0.984904i 0.0149835 0.999888i \(-0.495230\pi\)
−0.999888 + 0.0149835i \(0.995230\pi\)
\(588\) −4.19903 4.19903i −0.173165 0.173165i
\(589\) 28.0218 25.0517i 1.15462 1.03224i
\(590\) −4.45843 26.7561i −0.183551 1.10153i
\(591\) 10.8358i 0.445727i
\(592\) 5.47836 5.47836i 0.225159 0.225159i
\(593\) 22.7988 22.7988i 0.936236 0.936236i −0.0618495 0.998085i \(-0.519700\pi\)
0.998085 + 0.0618495i \(0.0196999\pi\)
\(594\) 4.80832i 0.197288i
\(595\) −9.88915 7.06418i −0.405416 0.289603i
\(596\) 15.8801 0.650473
\(597\) −14.7999 + 14.7999i −0.605719 + 0.605719i
\(598\) −3.06650 + 3.06650i −0.125398 + 0.125398i
\(599\) −11.4248 −0.466805 −0.233402 0.972380i \(-0.574986\pi\)
−0.233402 + 0.972380i \(0.574986\pi\)
\(600\) 4.72984 1.62130i 0.193095 0.0661894i
\(601\) 7.14156i 0.291310i −0.989335 0.145655i \(-0.953471\pi\)
0.989335 0.145655i \(-0.0465290\pi\)
\(602\) −3.13317 + 3.13317i −0.127698 + 0.127698i
\(603\) −9.19128 9.19128i −0.374298 0.374298i
\(604\) 13.3507 0.543231
\(605\) −15.7529 + 22.0524i −0.640445 + 0.896559i
\(606\) 14.0592 0.571115
\(607\) 6.44190 6.44190i 0.261469 0.261469i −0.564182 0.825651i \(-0.690808\pi\)
0.825651 + 0.564182i \(0.190808\pi\)
\(608\) 4.35209 + 0.243552i 0.176501 + 0.00987733i
\(609\) 0.509852i 0.0206602i
\(610\) 1.95681 + 11.7433i 0.0792290 + 0.475473i
\(611\) 0.967793i 0.0391527i
\(612\) −3.72984 3.72984i −0.150770 0.150770i
\(613\) −21.1379 + 21.1379i −0.853752 + 0.853752i −0.990593 0.136841i \(-0.956305\pi\)
0.136841 + 0.990593i \(0.456305\pi\)
\(614\) 0.00500438i 0.000201960i
\(615\) −2.14107 12.8491i −0.0863363 0.518126i
\(616\) 4.95439i 0.199618i
\(617\) −9.52678 9.52678i −0.383534 0.383534i 0.488840 0.872373i \(-0.337420\pi\)
−0.872373 + 0.488840i \(0.837420\pi\)
\(618\) −6.63327 6.63327i −0.266829 0.266829i
\(619\) 6.57762i 0.264377i −0.991225 0.132188i \(-0.957800\pi\)
0.991225 0.132188i \(-0.0422004\pi\)
\(620\) 11.2079 15.6899i 0.450120 0.630123i
\(621\) 5.76961i 0.231526i
\(622\) 8.26782 8.26782i 0.331509 0.331509i
\(623\) 0.791463 + 0.791463i 0.0317093 + 0.0317093i
\(624\) 0.751642i 0.0300898i
\(625\) −19.7428 + 15.3370i −0.789710 + 0.613480i
\(626\) 23.5732i 0.942174i
\(627\) 1.17107 20.9262i 0.0467682 0.835713i
\(628\) 11.7372 11.7372i 0.468363 0.468363i
\(629\) 40.8668 1.62947
\(630\) −1.87480 1.33924i −0.0746936 0.0533564i
\(631\) −17.0875 −0.680241 −0.340121 0.940382i \(-0.610468\pi\)
−0.340121 + 0.940382i \(0.610468\pi\)
\(632\) −1.95921 1.95921i −0.0779332 0.0779332i
\(633\) 19.5436 19.5436i 0.776787 0.776787i
\(634\) 9.85335i 0.391327i
\(635\) −4.86401 29.1901i −0.193022 1.15837i
\(636\) −4.99593 −0.198102
\(637\) −3.15616 + 3.15616i −0.125052 + 0.125052i
\(638\) −1.68238 + 1.68238i −0.0666062 + 0.0666062i
\(639\) −2.06076 −0.0815224
\(640\) 2.20566 0.367533i 0.0871862 0.0145280i
\(641\) 46.7376i 1.84602i 0.384773 + 0.923011i \(0.374280\pi\)
−0.384773 + 0.923011i \(0.625720\pi\)
\(642\) 1.54262 1.54262i 0.0608825 0.0608825i
\(643\) −7.16897 + 7.16897i −0.282717 + 0.282717i −0.834191 0.551475i \(-0.814065\pi\)
0.551475 + 0.834191i \(0.314065\pi\)
\(644\) 5.94489i 0.234261i
\(645\) 5.58935 7.82453i 0.220080 0.308091i
\(646\) 15.3242 + 17.1410i 0.602922 + 0.674404i
\(647\) −6.19558 6.19558i −0.243574 0.243574i 0.574753 0.818327i \(-0.305098\pi\)
−0.818327 + 0.574753i \(0.805098\pi\)
\(648\) −0.707107 0.707107i −0.0277778 0.0277778i
\(649\) −58.3282 −2.28958
\(650\) −1.21864 3.55515i −0.0477989 0.139444i
\(651\) −8.88509 −0.348234
\(652\) 0.988668 + 0.988668i 0.0387192 + 0.0387192i
\(653\) 17.2336 17.2336i 0.674401 0.674401i −0.284326 0.958728i \(-0.591770\pi\)
0.958728 + 0.284326i \(0.0917699\pi\)
\(654\) −18.4286 −0.720614
\(655\) −16.4116 + 22.9746i −0.641253 + 0.897690i
\(656\) 5.82553i 0.227449i
\(657\) 3.31160 + 3.31160i 0.129198 + 0.129198i
\(658\) 0.938110 + 0.938110i 0.0365713 + 0.0365713i
\(659\) −21.6005 −0.841436 −0.420718 0.907191i \(-0.638222\pi\)
−0.420718 + 0.907191i \(0.638222\pi\)
\(660\) −1.76721 10.6055i −0.0687887 0.412818i
\(661\) 1.49297i 0.0580696i −0.999578 0.0290348i \(-0.990757\pi\)
0.999578 0.0290348i \(-0.00924337\pi\)
\(662\) −8.65367 8.65367i −0.336335 0.336335i
\(663\) −2.80350 + 2.80350i −0.108879 + 0.108879i
\(664\) −5.05963 −0.196352
\(665\) 7.83310 + 6.28508i 0.303755 + 0.243725i
\(666\) 7.74758 0.300212
\(667\) 2.01873 2.01873i 0.0781655 0.0781655i
\(668\) 7.42584 + 7.42584i 0.287314 + 0.287314i
\(669\) 11.3784i 0.439913i
\(670\) 23.6509 + 16.8947i 0.913714 + 0.652700i
\(671\) 25.6004 0.988291
\(672\) −0.728588 0.728588i −0.0281059 0.0281059i
\(673\) −8.49705 8.49705i −0.327537 0.327537i 0.524112 0.851649i \(-0.324397\pi\)
−0.851649 + 0.524112i \(0.824397\pi\)
\(674\) 26.8584i 1.03455i
\(675\) 4.49094 + 2.19807i 0.172856 + 0.0846037i
\(676\) −12.4350 −0.478271
\(677\) −5.92660 + 5.92660i −0.227778 + 0.227778i −0.811764 0.583986i \(-0.801492\pi\)
0.583986 + 0.811764i \(0.301492\pi\)
\(678\) −5.25913 5.25913i −0.201976 0.201976i
\(679\) 4.10436 0.157511
\(680\) 9.59758 + 6.85591i 0.368050 + 0.262912i
\(681\) 2.80480 0.107480
\(682\) −29.3186 29.3186i −1.12267 1.12267i
\(683\) 26.3647 + 26.3647i 1.00882 + 1.00882i 0.999961 + 0.00885484i \(0.00281862\pi\)
0.00885484 + 0.999961i \(0.497181\pi\)
\(684\) 2.90517 + 3.24961i 0.111082 + 0.124252i
\(685\) −1.18126 + 0.196836i −0.0451337 + 0.00752071i
\(686\) 13.3314i 0.508994i
\(687\) 13.8906 13.8906i 0.529960 0.529960i
\(688\) 3.04079 3.04079i 0.115929 0.115929i
\(689\) 3.75515i 0.143060i
\(690\) 2.12052 + 12.7258i 0.0807268 + 0.484462i
\(691\) 19.3186 0.734913 0.367456 0.930041i \(-0.380229\pi\)
0.367456 + 0.930041i \(0.380229\pi\)
\(692\) −11.0462 + 11.0462i −0.419912 + 0.419912i
\(693\) −3.50328 + 3.50328i −0.133079 + 0.133079i
\(694\) −2.14291 −0.0813438
\(695\) −41.4744 29.6267i −1.57322 1.12381i
\(696\) 0.494819i 0.0187561i
\(697\) 21.7283 21.7283i 0.823017 0.823017i
\(698\) −15.0710 15.0710i −0.570444 0.570444i
\(699\) −6.70326 −0.253541
\(700\) 4.62737 + 2.26484i 0.174898 + 0.0856031i
\(701\) 8.82340 0.333255 0.166628 0.986020i \(-0.446712\pi\)
0.166628 + 0.986020i \(0.446712\pi\)
\(702\) −0.531491 + 0.531491i −0.0200598 + 0.0200598i
\(703\) −33.7181 1.88694i −1.27170 0.0711672i
\(704\) 4.80832i 0.181220i
\(705\) −2.34276 1.67352i −0.0882335 0.0630284i
\(706\) 13.2577i 0.498961i
\(707\) 10.2434 + 10.2434i 0.385241 + 0.385241i
\(708\) 8.57770 8.57770i 0.322370 0.322370i
\(709\) 1.20583i 0.0452859i 0.999744 + 0.0226429i \(0.00720808\pi\)
−0.999744 + 0.0226429i \(0.992792\pi\)
\(710\) 4.54533 0.757396i 0.170583 0.0284246i
\(711\) 2.77074i 0.103911i
\(712\) −0.768128 0.768128i −0.0287868 0.0287868i
\(713\) 35.1800 + 35.1800i 1.31750 + 1.31750i
\(714\) 5.43503i 0.203401i
\(715\) −7.97154 + 1.32831i −0.298119 + 0.0496761i
\(716\) 19.0425i 0.711652i
\(717\) 14.9801 14.9801i 0.559443 0.559443i
\(718\) 21.2987 + 21.2987i 0.794861 + 0.794861i
\(719\) 9.38938i 0.350165i 0.984554 + 0.175082i \(0.0560192\pi\)
−0.984554 + 0.175082i \(0.943981\pi\)
\(720\) 1.81952 + 1.29975i 0.0678095 + 0.0484388i
\(721\) 9.66585i 0.359975i
\(722\) −11.8521 14.8502i −0.441091 0.552665i
\(723\) 11.5106 11.5106i 0.428084 0.428084i
\(724\) −1.78110 −0.0661941
\(725\) 0.802251 + 2.34042i 0.0297949 + 0.0869209i
\(726\) −12.1199 −0.449812
\(727\) −17.4688 17.4688i −0.647884 0.647884i 0.304597 0.952481i \(-0.401478\pi\)
−0.952481 + 0.304597i \(0.901478\pi\)
\(728\) −0.547637 + 0.547637i −0.0202968 + 0.0202968i
\(729\) 1.00000i 0.0370370i
\(730\) −8.52138 6.08713i −0.315390 0.225295i
\(731\) 22.6833 0.838973
\(732\) −3.76477 + 3.76477i −0.139150 + 0.139150i
\(733\) 13.1840 13.1840i 0.486963 0.486963i −0.420383 0.907347i \(-0.638104\pi\)
0.907347 + 0.420383i \(0.138104\pi\)
\(734\) 14.2815 0.527140
\(735\) 2.18253 + 13.0979i 0.0805037 + 0.483123i
\(736\) 5.76961i 0.212671i
\(737\) 44.1946 44.1946i 1.62793 1.62793i
\(738\) 4.11927 4.11927i 0.151632 0.151632i
\(739\) 47.8710i 1.76096i −0.474080 0.880482i \(-0.657219\pi\)
0.474080 0.880482i \(-0.342781\pi\)
\(740\) −17.0885 + 2.84749i −0.628185 + 0.104676i
\(741\) 2.44254 2.18365i 0.0897290 0.0802184i
\(742\) −3.63998 3.63998i −0.133628 0.133628i
\(743\) 19.4260 + 19.4260i 0.712670 + 0.712670i 0.967093 0.254423i \(-0.0818855\pi\)
−0.254423 + 0.967093i \(0.581886\pi\)
\(744\) 8.62312 0.316139
\(745\) −28.8941 20.6401i −1.05860 0.756196i
\(746\) −16.3708 −0.599377
\(747\) −3.57770 3.57770i −0.130901 0.130901i
\(748\) 17.9343 17.9343i 0.655741 0.655741i
\(749\) 2.24788 0.0821356
\(750\) −10.7133 3.19762i −0.391195 0.116760i
\(751\) 23.5009i 0.857559i −0.903409 0.428779i \(-0.858944\pi\)
0.903409 0.428779i \(-0.141056\pi\)
\(752\) −0.910451 0.910451i −0.0332007 0.0332007i
\(753\) 3.71225 + 3.71225i 0.135282 + 0.135282i
\(754\) −0.371927 −0.0135448
\(755\) −24.2918 17.3525i −0.884069 0.631523i
\(756\) 1.03038i 0.0374745i
\(757\) 19.2062 + 19.2062i 0.698060 + 0.698060i 0.963992 0.265932i \(-0.0856796\pi\)
−0.265932 + 0.963992i \(0.585680\pi\)
\(758\) −21.7007 + 21.7007i −0.788206 + 0.788206i
\(759\) 27.7421 1.00697
\(760\) −7.60215 6.09977i −0.275759 0.221262i
\(761\) −23.7982 −0.862685 −0.431343 0.902188i \(-0.641960\pi\)
−0.431343 + 0.902188i \(0.641960\pi\)
\(762\) 9.35800 9.35800i 0.339005 0.339005i
\(763\) −13.4268 13.4268i −0.486084 0.486084i
\(764\) 14.8650i 0.537797i
\(765\) 1.93866 + 11.6344i 0.0700923 + 0.420642i
\(766\) 9.49265 0.342983
\(767\) −6.44736 6.44736i −0.232801 0.232801i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) 28.9884i 1.04535i 0.852532 + 0.522675i \(0.175066\pi\)
−0.852532 + 0.522675i \(0.824934\pi\)
\(770\) 6.43947 9.01461i 0.232062 0.324864i
\(771\) 22.6727 0.816537
\(772\) −5.04632 + 5.04632i −0.181621 + 0.181621i
\(773\) 29.2365 + 29.2365i 1.05156 + 1.05156i 0.998596 + 0.0529667i \(0.0168677\pi\)
0.0529667 + 0.998596i \(0.483132\pi\)
\(774\) 4.30033 0.154572
\(775\) −40.7860 + 13.9807i −1.46508 + 0.502201i
\(776\) −3.98335 −0.142994
\(777\) 5.64479 + 5.64479i 0.202506 + 0.202506i
\(778\) −1.19924 1.19924i −0.0429947 0.0429947i