Properties

Label 450.2.h.e.181.1
Level $450$
Weight $2$
Character 450.181
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.1
Root \(1.17421 + 0.0566033i\) of defining polynomial
Character \(\chi\) \(=\) 450.181
Dual form 450.2.h.e.271.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-2.15743 + 0.587785i) q^{5} +1.83337 q^{7} +(0.809017 + 0.587785i) q^{8} +(1.22570 + 1.87020i) q^{10} +(0.566541 + 1.74363i) q^{11} +(-0.747156 + 2.29951i) q^{13} +(-0.566541 - 1.74363i) q^{14} +(0.309017 - 0.951057i) q^{16} +(2.25284 + 1.63679i) q^{17} +(1.35294 + 0.982966i) q^{19} +(1.39991 - 1.74363i) q^{20} +(1.48322 - 1.07763i) q^{22} +(2.39991 + 7.38615i) q^{23} +(4.30902 - 2.53621i) q^{25} +2.41785 q^{26} +(-1.48322 + 1.07763i) q^{28} +(6.13597 - 4.45805i) q^{29} +(4.28304 + 3.11181i) q^{31} -1.00000 q^{32} +(0.860510 - 2.64838i) q^{34} +(-3.95536 + 1.07763i) q^{35} +(-0.406315 + 1.25051i) q^{37} +(0.516776 - 1.59047i) q^{38} +(-2.09089 - 0.792578i) q^{40} +(-1.08621 + 3.34301i) q^{41} -4.30550 q^{43} +(-1.48322 - 1.07763i) q^{44} +(6.28304 - 4.56489i) q^{46} +(1.48322 - 1.07763i) q^{47} -3.63877 q^{49} +(-3.74364 - 3.31439i) q^{50} +(-0.747156 - 2.29951i) q^{52} +(-5.27267 + 3.83082i) q^{53} +(-2.24716 - 3.42877i) q^{55} +(1.48322 + 1.07763i) q^{56} +(-6.13597 - 4.45805i) q^{58} +(2.79981 - 8.61694i) q^{59} +(0.799717 + 2.46127i) q^{61} +(1.63597 - 5.03501i) q^{62} +(0.309017 + 0.951057i) q^{64} +(0.260320 - 5.40020i) q^{65} +(-7.68574 - 5.58402i) q^{67} -2.78467 q^{68} +(2.24716 + 3.42877i) q^{70} +(0.247156 - 0.179569i) q^{71} +(4.61920 + 14.2164i) q^{73} +1.31486 q^{74} -1.67232 q^{76} +(1.03868 + 3.19672i) q^{77} +(2.79981 - 2.03418i) q^{79} +(-0.107666 + 2.23347i) q^{80} +3.51505 q^{82} +(-5.15555 - 3.74572i) q^{83} +(-5.82243 - 2.20707i) q^{85} +(1.33047 + 4.09478i) q^{86} +(-0.566541 + 1.74363i) q^{88} +(1.02608 + 3.15794i) q^{89} +(-1.36981 + 4.21584i) q^{91} +(-6.28304 - 4.56489i) q^{92} +(-1.48322 - 1.07763i) q^{94} +(-3.49664 - 1.32545i) q^{95} +(-8.97214 + 6.51864i) q^{97} +(1.12444 + 3.46068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) 0 0
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) −2.15743 + 0.587785i −0.964832 + 0.262866i
\(6\) 0 0
\(7\) 1.83337 0.692947 0.346474 0.938060i \(-0.387379\pi\)
0.346474 + 0.938060i \(0.387379\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 0 0
\(10\) 1.22570 + 1.87020i 0.387600 + 0.591410i
\(11\) 0.566541 + 1.74363i 0.170819 + 0.525726i 0.999418 0.0341166i \(-0.0108618\pi\)
−0.828599 + 0.559842i \(0.810862\pi\)
\(12\) 0 0
\(13\) −0.747156 + 2.29951i −0.207224 + 0.637769i 0.792391 + 0.610014i \(0.208836\pi\)
−0.999615 + 0.0277557i \(0.991164\pi\)
\(14\) −0.566541 1.74363i −0.151414 0.466006i
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 2.25284 + 1.63679i 0.546395 + 0.396979i 0.826455 0.563003i \(-0.190354\pi\)
−0.280060 + 0.959983i \(0.590354\pi\)
\(18\) 0 0
\(19\) 1.35294 + 0.982966i 0.310385 + 0.225508i 0.732062 0.681238i \(-0.238558\pi\)
−0.421677 + 0.906746i \(0.638558\pi\)
\(20\) 1.39991 1.74363i 0.313029 0.389889i
\(21\) 0 0
\(22\) 1.48322 1.07763i 0.316224 0.229750i
\(23\) 2.39991 + 7.38615i 0.500415 + 1.54012i 0.808344 + 0.588710i \(0.200364\pi\)
−0.307929 + 0.951409i \(0.599636\pi\)
\(24\) 0 0
\(25\) 4.30902 2.53621i 0.861803 0.507242i
\(26\) 2.41785 0.474179
\(27\) 0 0
\(28\) −1.48322 + 1.07763i −0.280303 + 0.203652i
\(29\) 6.13597 4.45805i 1.13942 0.827838i 0.152383 0.988321i \(-0.451305\pi\)
0.987039 + 0.160483i \(0.0513052\pi\)
\(30\) 0 0
\(31\) 4.28304 + 3.11181i 0.769256 + 0.558897i 0.901735 0.432288i \(-0.142294\pi\)
−0.132479 + 0.991186i \(0.542294\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 0.860510 2.64838i 0.147576 0.454193i
\(35\) −3.95536 + 1.07763i −0.668578 + 0.182152i
\(36\) 0 0
\(37\) −0.406315 + 1.25051i −0.0667977 + 0.205582i −0.978884 0.204416i \(-0.934471\pi\)
0.912086 + 0.409998i \(0.134471\pi\)
\(38\) 0.516776 1.59047i 0.0838321 0.258009i
\(39\) 0 0
\(40\) −2.09089 0.792578i −0.330599 0.125318i
\(41\) −1.08621 + 3.34301i −0.169637 + 0.522090i −0.999348 0.0361034i \(-0.988505\pi\)
0.829711 + 0.558194i \(0.188505\pi\)
\(42\) 0 0
\(43\) −4.30550 −0.656583 −0.328291 0.944576i \(-0.606473\pi\)
−0.328291 + 0.944576i \(0.606473\pi\)
\(44\) −1.48322 1.07763i −0.223604 0.162458i
\(45\) 0 0
\(46\) 6.28304 4.56489i 0.926383 0.673057i
\(47\) 1.48322 1.07763i 0.216350 0.157188i −0.474332 0.880346i \(-0.657310\pi\)
0.690682 + 0.723158i \(0.257310\pi\)
\(48\) 0 0
\(49\) −3.63877 −0.519824
\(50\) −3.74364 3.31439i −0.529431 0.468725i
\(51\) 0 0
\(52\) −0.747156 2.29951i −0.103612 0.318885i
\(53\) −5.27267 + 3.83082i −0.724257 + 0.526203i −0.887741 0.460342i \(-0.847727\pi\)
0.163485 + 0.986546i \(0.447727\pi\)
\(54\) 0 0
\(55\) −2.24716 3.42877i −0.303006 0.462335i
\(56\) 1.48322 + 1.07763i 0.198204 + 0.144004i
\(57\) 0 0
\(58\) −6.13597 4.45805i −0.805693 0.585370i
\(59\) 2.79981 8.61694i 0.364505 1.12183i −0.585786 0.810466i \(-0.699214\pi\)
0.950291 0.311364i \(-0.100786\pi\)
\(60\) 0 0
\(61\) 0.799717 + 2.46127i 0.102393 + 0.315134i 0.989110 0.147180i \(-0.0470195\pi\)
−0.886717 + 0.462313i \(0.847019\pi\)
\(62\) 1.63597 5.03501i 0.207769 0.639447i
\(63\) 0 0
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 0.260320 5.40020i 0.0322887 0.669812i
\(66\) 0 0
\(67\) −7.68574 5.58402i −0.938963 0.682196i 0.00920814 0.999958i \(-0.497069\pi\)
−0.948171 + 0.317761i \(0.897069\pi\)
\(68\) −2.78467 −0.337691
\(69\) 0 0
\(70\) 2.24716 + 3.42877i 0.268587 + 0.409816i
\(71\) 0.247156 0.179569i 0.0293320 0.0213110i −0.573023 0.819540i \(-0.694229\pi\)
0.602355 + 0.798229i \(0.294229\pi\)
\(72\) 0 0
\(73\) 4.61920 + 14.2164i 0.540636 + 1.66391i 0.731145 + 0.682222i \(0.238986\pi\)
−0.190509 + 0.981685i \(0.561014\pi\)
\(74\) 1.31486 0.152850
\(75\) 0 0
\(76\) −1.67232 −0.191829
\(77\) 1.03868 + 3.19672i 0.118368 + 0.364300i
\(78\) 0 0
\(79\) 2.79981 2.03418i 0.315004 0.228864i −0.419037 0.907969i \(-0.637632\pi\)
0.734041 + 0.679106i \(0.237632\pi\)
\(80\) −0.107666 + 2.23347i −0.0120374 + 0.249710i
\(81\) 0 0
\(82\) 3.51505 0.388172
\(83\) −5.15555 3.74572i −0.565895 0.411147i 0.267717 0.963498i \(-0.413731\pi\)
−0.833612 + 0.552351i \(0.813731\pi\)
\(84\) 0 0
\(85\) −5.82243 2.20707i −0.631532 0.239390i
\(86\) 1.33047 + 4.09478i 0.143469 + 0.441551i
\(87\) 0 0
\(88\) −0.566541 + 1.74363i −0.0603935 + 0.185872i
\(89\) 1.02608 + 3.15794i 0.108764 + 0.334741i 0.990595 0.136824i \(-0.0436894\pi\)
−0.881832 + 0.471565i \(0.843689\pi\)
\(90\) 0 0
\(91\) −1.36981 + 4.21584i −0.143595 + 0.441940i
\(92\) −6.28304 4.56489i −0.655052 0.475923i
\(93\) 0 0
\(94\) −1.48322 1.07763i −0.152983 0.111149i
\(95\) −3.49664 1.32545i −0.358748 0.135988i
\(96\) 0 0
\(97\) −8.97214 + 6.51864i −0.910982 + 0.661867i −0.941263 0.337674i \(-0.890360\pi\)
0.0302807 + 0.999541i \(0.490360\pi\)
\(98\) 1.12444 + 3.46068i 0.113586 + 0.349581i
\(99\) 0 0
\(100\) −1.99532 + 4.58462i −0.199532 + 0.458462i
\(101\) 13.1807 1.31152 0.655762 0.754968i \(-0.272347\pi\)
0.655762 + 0.754968i \(0.272347\pi\)
\(102\) 0 0
\(103\) 2.13029 1.54774i 0.209903 0.152504i −0.477867 0.878432i \(-0.658590\pi\)
0.687770 + 0.725929i \(0.258590\pi\)
\(104\) −1.95608 + 1.42118i −0.191809 + 0.139358i
\(105\) 0 0
\(106\) 5.27267 + 3.83082i 0.512127 + 0.372082i
\(107\) −18.8045 −1.81790 −0.908949 0.416908i \(-0.863114\pi\)
−0.908949 + 0.416908i \(0.863114\pi\)
\(108\) 0 0
\(109\) 3.18574 9.80470i 0.305139 0.939120i −0.674487 0.738287i \(-0.735635\pi\)
0.979625 0.200833i \(-0.0643649\pi\)
\(110\) −2.56654 + 3.19672i −0.244710 + 0.304795i
\(111\) 0 0
\(112\) 0.566541 1.74363i 0.0535331 0.164758i
\(113\) −1.87160 + 5.76019i −0.176065 + 0.541873i −0.999681 0.0252760i \(-0.991954\pi\)
0.823615 + 0.567149i \(0.191954\pi\)
\(114\) 0 0
\(115\) −9.51911 14.5245i −0.887661 1.35442i
\(116\) −2.34373 + 7.21327i −0.217610 + 0.669735i
\(117\) 0 0
\(118\) −9.06039 −0.834076
\(119\) 4.13029 + 3.00083i 0.378623 + 0.275086i
\(120\) 0 0
\(121\) 6.17989 4.48996i 0.561809 0.408178i
\(122\) 2.09369 1.52115i 0.189553 0.137719i
\(123\) 0 0
\(124\) −5.29413 −0.475427
\(125\) −7.80566 + 8.00448i −0.698159 + 0.715942i
\(126\) 0 0
\(127\) 0.102986 + 0.316957i 0.00913850 + 0.0281254i 0.955522 0.294921i \(-0.0952932\pi\)
−0.946383 + 0.323046i \(0.895293\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) 0 0
\(130\) −5.21634 + 1.42118i −0.457503 + 0.124645i
\(131\) −4.18910 3.04356i −0.366003 0.265917i 0.389548 0.921006i \(-0.372631\pi\)
−0.755552 + 0.655089i \(0.772631\pi\)
\(132\) 0 0
\(133\) 2.48043 + 1.80214i 0.215080 + 0.156265i
\(134\) −2.93569 + 9.03513i −0.253605 + 0.780516i
\(135\) 0 0
\(136\) 0.860510 + 2.64838i 0.0737881 + 0.227096i
\(137\) 6.03299 18.5676i 0.515433 1.58634i −0.267060 0.963680i \(-0.586052\pi\)
0.782493 0.622660i \(-0.213948\pi\)
\(138\) 0 0
\(139\) −2.45825 7.56572i −0.208506 0.641716i −0.999551 0.0299582i \(-0.990463\pi\)
0.791045 0.611758i \(-0.209537\pi\)
\(140\) 2.56654 3.19672i 0.216912 0.270172i
\(141\) 0 0
\(142\) −0.247156 0.179569i −0.0207409 0.0150691i
\(143\) −4.43280 −0.370689
\(144\) 0 0
\(145\) −10.6176 + 13.2246i −0.881741 + 1.09824i
\(146\) 12.0932 8.78624i 1.00084 0.727154i
\(147\) 0 0
\(148\) −0.406315 1.25051i −0.0333989 0.102791i
\(149\) 1.67955 0.137594 0.0687969 0.997631i \(-0.478084\pi\)
0.0687969 + 0.997631i \(0.478084\pi\)
\(150\) 0 0
\(151\) −21.2664 −1.73063 −0.865316 0.501227i \(-0.832882\pi\)
−0.865316 + 0.501227i \(0.832882\pi\)
\(152\) 0.516776 + 1.59047i 0.0419161 + 0.129004i
\(153\) 0 0
\(154\) 2.71929 1.97568i 0.219127 0.159205i
\(155\) −11.0694 4.19601i −0.889118 0.337031i
\(156\) 0 0
\(157\) 10.4514 0.834113 0.417056 0.908881i \(-0.363062\pi\)
0.417056 + 0.908881i \(0.363062\pi\)
\(158\) −2.79981 2.03418i −0.222741 0.161831i
\(159\) 0 0
\(160\) 2.15743 0.587785i 0.170560 0.0464685i
\(161\) 4.39991 + 13.5415i 0.346761 + 1.06722i
\(162\) 0 0
\(163\) 3.21706 9.90109i 0.251980 0.775513i −0.742430 0.669923i \(-0.766327\pi\)
0.994410 0.105590i \(-0.0336731\pi\)
\(164\) −1.08621 3.34301i −0.0848187 0.261045i
\(165\) 0 0
\(166\) −1.96924 + 6.06071i −0.152843 + 0.470402i
\(167\) 1.71650 + 1.24711i 0.132826 + 0.0965041i 0.652215 0.758034i \(-0.273840\pi\)
−0.519388 + 0.854538i \(0.673840\pi\)
\(168\) 0 0
\(169\) 5.78772 + 4.20502i 0.445209 + 0.323463i
\(170\) −0.299814 + 6.21949i −0.0229947 + 0.477013i
\(171\) 0 0
\(172\) 3.48322 2.53071i 0.265593 0.192965i
\(173\) 5.59774 + 17.2281i 0.425588 + 1.30983i 0.902430 + 0.430837i \(0.141782\pi\)
−0.476841 + 0.878989i \(0.658218\pi\)
\(174\) 0 0
\(175\) 7.90000 4.64980i 0.597184 0.351492i
\(176\) 1.83337 0.138195
\(177\) 0 0
\(178\) 2.68630 1.95171i 0.201347 0.146287i
\(179\) 8.54361 6.20730i 0.638579 0.463955i −0.220782 0.975323i \(-0.570861\pi\)
0.859362 + 0.511368i \(0.170861\pi\)
\(180\) 0 0
\(181\) −14.6886 10.6719i −1.09180 0.793237i −0.112096 0.993697i \(-0.535756\pi\)
−0.979702 + 0.200460i \(0.935756\pi\)
\(182\) 4.43280 0.328581
\(183\) 0 0
\(184\) −2.39991 + 7.38615i −0.176923 + 0.544514i
\(185\) 0.141566 2.93671i 0.0104081 0.215911i
\(186\) 0 0
\(187\) −1.57763 + 4.85544i −0.115368 + 0.355065i
\(188\) −0.566541 + 1.74363i −0.0413193 + 0.127168i
\(189\) 0 0
\(190\) −0.180052 + 3.73509i −0.0130623 + 0.270972i
\(191\) 6.76906 20.8330i 0.489792 1.50742i −0.335127 0.942173i \(-0.608779\pi\)
0.824919 0.565251i \(-0.191221\pi\)
\(192\) 0 0
\(193\) 27.4248 1.97408 0.987041 0.160465i \(-0.0512995\pi\)
0.987041 + 0.160465i \(0.0512995\pi\)
\(194\) 8.97214 + 6.51864i 0.644162 + 0.468011i
\(195\) 0 0
\(196\) 2.94383 2.13882i 0.210273 0.152773i
\(197\) −0.909110 + 0.660507i −0.0647714 + 0.0470592i −0.619700 0.784839i \(-0.712746\pi\)
0.554928 + 0.831898i \(0.312746\pi\)
\(198\) 0 0
\(199\) 25.4992 1.80759 0.903794 0.427968i \(-0.140770\pi\)
0.903794 + 0.427968i \(0.140770\pi\)
\(200\) 4.97682 + 0.480938i 0.351914 + 0.0340074i
\(201\) 0 0
\(202\) −4.07305 12.5355i −0.286579 0.881998i
\(203\) 11.2495 8.17323i 0.789559 0.573648i
\(204\) 0 0
\(205\) 0.378451 7.85077i 0.0264321 0.548322i
\(206\) −2.13029 1.54774i −0.148424 0.107836i
\(207\) 0 0
\(208\) 1.95608 + 1.42118i 0.135630 + 0.0985408i
\(209\) −0.947439 + 2.91592i −0.0655358 + 0.201698i
\(210\) 0 0
\(211\) 6.58341 + 20.2617i 0.453221 + 1.39487i 0.873211 + 0.487342i \(0.162033\pi\)
−0.419990 + 0.907529i \(0.637967\pi\)
\(212\) 2.01398 6.19839i 0.138321 0.425708i
\(213\) 0 0
\(214\) 5.81090 + 17.8841i 0.397225 + 1.22253i
\(215\) 9.28882 2.53071i 0.633492 0.172593i
\(216\) 0 0
\(217\) 7.85237 + 5.70508i 0.533054 + 0.387286i
\(218\) −10.3093 −0.698232
\(219\) 0 0
\(220\) 3.83337 + 1.45309i 0.258445 + 0.0979670i
\(221\) −5.44703 + 3.95750i −0.366407 + 0.266210i
\(222\) 0 0
\(223\) 1.00280 + 3.08629i 0.0671522 + 0.206673i 0.979002 0.203851i \(-0.0653458\pi\)
−0.911850 + 0.410524i \(0.865346\pi\)
\(224\) −1.83337 −0.122497
\(225\) 0 0
\(226\) 6.05662 0.402880
\(227\) −5.06085 15.5757i −0.335901 1.03380i −0.966277 0.257506i \(-0.917099\pi\)
0.630376 0.776290i \(-0.282901\pi\)
\(228\) 0 0
\(229\) 4.11788 2.99181i 0.272117 0.197705i −0.443355 0.896346i \(-0.646212\pi\)
0.715472 + 0.698642i \(0.246212\pi\)
\(230\) −10.8720 + 13.5415i −0.716881 + 0.892901i
\(231\) 0 0
\(232\) 7.58448 0.497946
\(233\) −1.34536 0.977464i −0.0881378 0.0640358i 0.542844 0.839834i \(-0.317348\pi\)
−0.630981 + 0.775798i \(0.717348\pi\)
\(234\) 0 0
\(235\) −2.56654 + 3.19672i −0.167423 + 0.208531i
\(236\) 2.79981 + 8.61694i 0.182252 + 0.560915i
\(237\) 0 0
\(238\) 1.57763 4.85544i 0.102263 0.314732i
\(239\) −3.95536 12.1733i −0.255851 0.787428i −0.993661 0.112420i \(-0.964140\pi\)
0.737810 0.675009i \(-0.235860\pi\)
\(240\) 0 0
\(241\) 0.122209 0.376121i 0.00787219 0.0242281i −0.947043 0.321106i \(-0.895945\pi\)
0.954915 + 0.296878i \(0.0959454\pi\)
\(242\) −6.17989 4.48996i −0.397259 0.288625i
\(243\) 0 0
\(244\) −2.09369 1.52115i −0.134034 0.0973817i
\(245\) 7.85040 2.13882i 0.501543 0.136644i
\(246\) 0 0
\(247\) −3.27120 + 2.37666i −0.208141 + 0.151223i
\(248\) 1.63597 + 5.03501i 0.103885 + 0.319724i
\(249\) 0 0
\(250\) 10.0248 + 4.95010i 0.634024 + 0.313072i
\(251\) −9.36589 −0.591170 −0.295585 0.955316i \(-0.595515\pi\)
−0.295585 + 0.955316i \(0.595515\pi\)
\(252\) 0 0
\(253\) −11.5191 + 8.36912i −0.724200 + 0.526162i
\(254\) 0.269620 0.195890i 0.0169175 0.0122913i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 4.97926 0.310598 0.155299 0.987868i \(-0.450366\pi\)
0.155299 + 0.987868i \(0.450366\pi\)
\(258\) 0 0
\(259\) −0.744923 + 2.29264i −0.0462873 + 0.142458i
\(260\) 2.96356 + 4.52187i 0.183792 + 0.280434i
\(261\) 0 0
\(262\) −1.60009 + 4.92458i −0.0988541 + 0.304242i
\(263\) 6.12199 18.8416i 0.377498 1.16182i −0.564279 0.825584i \(-0.690846\pi\)
0.941778 0.336236i \(-0.109154\pi\)
\(264\) 0 0
\(265\) 9.12372 11.3639i 0.560466 0.698080i
\(266\) 0.947439 2.91592i 0.0580912 0.178786i
\(267\) 0 0
\(268\) 9.50010 0.580311
\(269\) 11.9685 + 8.69564i 0.729734 + 0.530183i 0.889479 0.456976i \(-0.151067\pi\)
−0.159745 + 0.987158i \(0.551067\pi\)
\(270\) 0 0
\(271\) 10.1583 7.38047i 0.617075 0.448331i −0.234823 0.972038i \(-0.575451\pi\)
0.851899 + 0.523707i \(0.175451\pi\)
\(272\) 2.25284 1.63679i 0.136599 0.0992448i
\(273\) 0 0
\(274\) −19.5232 −1.17944
\(275\) 6.86346 + 6.07648i 0.413882 + 0.366426i
\(276\) 0 0
\(277\) −1.95664 6.02193i −0.117563 0.361823i 0.874910 0.484286i \(-0.160921\pi\)
−0.992473 + 0.122463i \(0.960921\pi\)
\(278\) −6.43579 + 4.67587i −0.385993 + 0.280440i
\(279\) 0 0
\(280\) −3.83337 1.45309i −0.229087 0.0868384i
\(281\) −16.2525 11.8082i −0.969545 0.704416i −0.0141971 0.999899i \(-0.504519\pi\)
−0.955348 + 0.295484i \(0.904519\pi\)
\(282\) 0 0
\(283\) −1.46981 1.06788i −0.0873709 0.0634787i 0.543242 0.839576i \(-0.317197\pi\)
−0.630613 + 0.776097i \(0.717197\pi\)
\(284\) −0.0944052 + 0.290549i −0.00560192 + 0.0172409i
\(285\) 0 0
\(286\) 1.36981 + 4.21584i 0.0809986 + 0.249288i
\(287\) −1.99142 + 6.12896i −0.117550 + 0.361781i
\(288\) 0 0
\(289\) −2.85705 8.79311i −0.168062 0.517242i
\(290\) 15.8583 + 6.01129i 0.931232 + 0.352995i
\(291\) 0 0
\(292\) −12.0932 8.78624i −0.707702 0.514176i
\(293\) 6.85931 0.400725 0.200363 0.979722i \(-0.435788\pi\)
0.200363 + 0.979722i \(0.435788\pi\)
\(294\) 0 0
\(295\) −0.975494 + 20.2361i −0.0567955 + 1.17819i
\(296\) −1.06375 + 0.772856i −0.0618290 + 0.0449214i
\(297\) 0 0
\(298\) −0.519009 1.59734i −0.0300654 0.0925317i
\(299\) −18.7776 −1.08594
\(300\) 0 0
\(301\) −7.89356 −0.454977
\(302\) 6.57167 + 20.2255i 0.378157 + 1.16385i
\(303\) 0 0
\(304\) 1.35294 0.982966i 0.0775963 0.0563770i
\(305\) −3.17203 4.83997i −0.181630 0.277136i
\(306\) 0 0
\(307\) −2.89526 −0.165241 −0.0826206 0.996581i \(-0.526329\pi\)
−0.0826206 + 0.996581i \(0.526329\pi\)
\(308\) −2.71929 1.97568i −0.154946 0.112575i
\(309\) 0 0
\(310\) −0.569997 + 11.8243i −0.0323736 + 0.671575i
\(311\) 6.38090 + 19.6384i 0.361828 + 1.11359i 0.951944 + 0.306272i \(0.0990819\pi\)
−0.590116 + 0.807318i \(0.700918\pi\)
\(312\) 0 0
\(313\) 5.07629 15.6232i 0.286929 0.883076i −0.698885 0.715234i \(-0.746320\pi\)
0.985814 0.167842i \(-0.0536798\pi\)
\(314\) −3.22966 9.93987i −0.182260 0.560939i
\(315\) 0 0
\(316\) −1.06943 + 3.29138i −0.0601603 + 0.185154i
\(317\) 13.3535 + 9.70191i 0.750009 + 0.544914i 0.895830 0.444397i \(-0.146582\pi\)
−0.145820 + 0.989311i \(0.546582\pi\)
\(318\) 0 0
\(319\) 11.2495 + 8.17323i 0.629850 + 0.457613i
\(320\) −1.22570 1.87020i −0.0685187 0.104548i
\(321\) 0 0
\(322\) 11.5191 8.36912i 0.641935 0.466393i
\(323\) 1.43905 + 4.42894i 0.0800709 + 0.246433i
\(324\) 0 0
\(325\) 2.61254 + 11.8036i 0.144917 + 0.654744i
\(326\) −10.4106 −0.576591
\(327\) 0 0
\(328\) −2.84373 + 2.06609i −0.157019 + 0.114081i
\(329\) 2.71929 1.97568i 0.149919 0.108923i
\(330\) 0 0
\(331\) −22.2245 16.1471i −1.22157 0.887522i −0.225340 0.974280i \(-0.572349\pi\)
−0.996229 + 0.0867577i \(0.972349\pi\)
\(332\) 6.37261 0.349742
\(333\) 0 0
\(334\) 0.655643 2.01786i 0.0358752 0.110413i
\(335\) 19.8637 + 7.52957i 1.08527 + 0.411384i
\(336\) 0 0
\(337\) −0.848317 + 2.61085i −0.0462108 + 0.142222i −0.971500 0.237041i \(-0.923822\pi\)
0.925289 + 0.379263i \(0.123822\pi\)
\(338\) 2.21071 6.80387i 0.120247 0.370082i
\(339\) 0 0
\(340\) 6.00773 1.63679i 0.325815 0.0887672i
\(341\) −2.99934 + 9.23102i −0.162423 + 0.499888i
\(342\) 0 0
\(343\) −19.5048 −1.05316
\(344\) −3.48322 2.53071i −0.187803 0.136447i
\(345\) 0 0
\(346\) 14.6551 10.6475i 0.787862 0.572415i
\(347\) −17.2637 + 12.5428i −0.926762 + 0.673332i −0.945198 0.326498i \(-0.894131\pi\)
0.0184361 + 0.999830i \(0.494131\pi\)
\(348\) 0 0
\(349\) −16.7650 −0.897411 −0.448705 0.893680i \(-0.648115\pi\)
−0.448705 + 0.893680i \(0.648115\pi\)
\(350\) −6.86346 6.07648i −0.366867 0.324802i
\(351\) 0 0
\(352\) −0.566541 1.74363i −0.0301967 0.0929360i
\(353\) 2.41785 1.75667i 0.128689 0.0934981i −0.521579 0.853203i \(-0.674657\pi\)
0.650268 + 0.759705i \(0.274657\pi\)
\(354\) 0 0
\(355\) −0.427674 + 0.532683i −0.0226986 + 0.0282719i
\(356\) −2.68630 1.95171i −0.142374 0.103441i
\(357\) 0 0
\(358\) −8.54361 6.20730i −0.451544 0.328066i
\(359\) −2.07194 + 6.37678i −0.109353 + 0.336554i −0.990727 0.135865i \(-0.956619\pi\)
0.881375 + 0.472418i \(0.156619\pi\)
\(360\) 0 0
\(361\) −5.00711 15.4103i −0.263532 0.811068i
\(362\) −5.61056 + 17.2675i −0.294884 + 0.907561i
\(363\) 0 0
\(364\) −1.36981 4.21584i −0.0717976 0.220970i
\(365\) −18.3218 27.9559i −0.959007 1.46328i
\(366\) 0 0
\(367\) −3.24949 2.36089i −0.169622 0.123237i 0.499736 0.866178i \(-0.333430\pi\)
−0.669357 + 0.742941i \(0.733430\pi\)
\(368\) 7.76626 0.404844
\(369\) 0 0
\(370\) −2.83672 + 0.772856i −0.147474 + 0.0401789i
\(371\) −9.66673 + 7.02329i −0.501872 + 0.364631i
\(372\) 0 0
\(373\) 8.21467 + 25.2822i 0.425340 + 1.30906i 0.902669 + 0.430336i \(0.141605\pi\)
−0.477329 + 0.878725i \(0.658395\pi\)
\(374\) 5.10532 0.263990
\(375\) 0 0
\(376\) 1.83337 0.0945486
\(377\) 5.66679 + 17.4406i 0.291855 + 0.898236i
\(378\) 0 0
\(379\) 12.6431 9.18578i 0.649435 0.471842i −0.213644 0.976912i \(-0.568533\pi\)
0.863079 + 0.505070i \(0.168533\pi\)
\(380\) 3.60792 0.982966i 0.185082 0.0504251i
\(381\) 0 0
\(382\) −21.9051 −1.12076
\(383\) 10.8776 + 7.90306i 0.555821 + 0.403828i 0.829927 0.557872i \(-0.188382\pi\)
−0.274106 + 0.961699i \(0.588382\pi\)
\(384\) 0 0
\(385\) −4.11986 6.28618i −0.209967 0.320374i
\(386\) −8.47474 26.0826i −0.431353 1.32757i
\(387\) 0 0
\(388\) 3.42705 10.5474i 0.173982 0.535462i
\(389\) 7.75991 + 23.8826i 0.393443 + 1.21089i 0.930167 + 0.367136i \(0.119662\pi\)
−0.536724 + 0.843758i \(0.680338\pi\)
\(390\) 0 0
\(391\) −6.68294 + 20.5680i −0.337971 + 1.04017i
\(392\) −2.94383 2.13882i −0.148686 0.108026i
\(393\) 0 0
\(394\) 0.909110 + 0.660507i 0.0458003 + 0.0332759i
\(395\) −4.84474 + 6.03430i −0.243765 + 0.303619i
\(396\) 0 0
\(397\) −2.84628 + 2.06794i −0.142850 + 0.103787i −0.656915 0.753964i \(-0.728139\pi\)
0.514065 + 0.857751i \(0.328139\pi\)
\(398\) −7.87968 24.2511i −0.394972 1.21560i
\(399\) 0 0
\(400\) −1.08052 4.88185i −0.0540261 0.244093i
\(401\) −29.8696 −1.49161 −0.745807 0.666162i \(-0.767936\pi\)
−0.745807 + 0.666162i \(0.767936\pi\)
\(402\) 0 0
\(403\) −10.3557 + 7.52388i −0.515856 + 0.374791i
\(404\) −10.6634 + 7.74739i −0.530523 + 0.385447i
\(405\) 0 0
\(406\) −11.2495 8.17323i −0.558303 0.405631i
\(407\) −2.41062 −0.119490
\(408\) 0 0
\(409\) −11.9784 + 36.8656i −0.592291 + 1.82289i −0.0245200 + 0.999699i \(0.507806\pi\)
−0.567771 + 0.823186i \(0.692194\pi\)
\(410\) −7.58347 + 2.06609i −0.374521 + 0.102037i
\(411\) 0 0
\(412\) −0.813697 + 2.50430i −0.0400880 + 0.123378i
\(413\) 5.13308 15.7980i 0.252582 0.777369i
\(414\) 0 0
\(415\) 13.3244 + 5.05079i 0.654070 + 0.247933i
\(416\) 0.747156 2.29951i 0.0366323 0.112743i
\(417\) 0 0
\(418\) 3.06598 0.149962
\(419\) −15.2988 11.1152i −0.747395 0.543014i 0.147624 0.989044i \(-0.452838\pi\)
−0.895018 + 0.446030i \(0.852838\pi\)
\(420\) 0 0
\(421\) 17.8414 12.9625i 0.869536 0.631755i −0.0609265 0.998142i \(-0.519406\pi\)
0.930462 + 0.366388i \(0.119406\pi\)
\(422\) 17.2356 12.5224i 0.839016 0.609581i
\(423\) 0 0
\(424\) −6.51738 −0.316512
\(425\) 13.8588 + 1.33925i 0.672250 + 0.0649633i
\(426\) 0 0
\(427\) 1.46617 + 4.51242i 0.0709531 + 0.218371i
\(428\) 15.2131 11.0530i 0.735355 0.534267i
\(429\) 0 0
\(430\) −5.27725 8.05216i −0.254492 0.388310i
\(431\) −7.44763 5.41102i −0.358740 0.260640i 0.393787 0.919202i \(-0.371165\pi\)
−0.752526 + 0.658562i \(0.771165\pi\)
\(432\) 0 0
\(433\) −28.1516 20.4533i −1.35288 0.982923i −0.998862 0.0476837i \(-0.984816\pi\)
−0.354015 0.935240i \(-0.615184\pi\)
\(434\) 2.99934 9.23102i 0.143973 0.443103i
\(435\) 0 0
\(436\) 3.18574 + 9.80470i 0.152569 + 0.469560i
\(437\) −4.01342 + 12.3520i −0.191988 + 0.590878i
\(438\) 0 0
\(439\) −2.58025 7.94118i −0.123148 0.379012i 0.870411 0.492326i \(-0.163853\pi\)
−0.993559 + 0.113314i \(0.963853\pi\)
\(440\) 0.197391 4.09478i 0.00941024 0.195211i
\(441\) 0 0
\(442\) 5.44703 + 3.95750i 0.259089 + 0.188239i
\(443\) 1.19887 0.0569599 0.0284799 0.999594i \(-0.490933\pi\)
0.0284799 + 0.999594i \(0.490933\pi\)
\(444\) 0 0
\(445\) −4.06988 6.20992i −0.192931 0.294379i
\(446\) 2.62535 1.90743i 0.124314 0.0903194i
\(447\) 0 0
\(448\) 0.566541 + 1.74363i 0.0267666 + 0.0823790i
\(449\) −32.7953 −1.54771 −0.773853 0.633365i \(-0.781673\pi\)
−0.773853 + 0.633365i \(0.781673\pi\)
\(450\) 0 0
\(451\) −6.44437 −0.303453
\(452\) −1.87160 5.76019i −0.0880326 0.270936i
\(453\) 0 0
\(454\) −13.2495 + 9.62631i −0.621829 + 0.451785i
\(455\) 0.477261 9.90054i 0.0223743 0.464145i
\(456\) 0 0
\(457\) 19.7884 0.925664 0.462832 0.886446i \(-0.346833\pi\)
0.462832 + 0.886446i \(0.346833\pi\)
\(458\) −4.11788 2.99181i −0.192416 0.139798i
\(459\) 0 0
\(460\) 16.2384 + 6.15537i 0.757119 + 0.286995i
\(461\) −2.90468 8.93970i −0.135285 0.416363i 0.860350 0.509704i \(-0.170245\pi\)
−0.995634 + 0.0933412i \(0.970245\pi\)
\(462\) 0 0
\(463\) 5.47977 16.8650i 0.254666 0.783783i −0.739229 0.673454i \(-0.764810\pi\)
0.993895 0.110328i \(-0.0351902\pi\)
\(464\) −2.34373 7.21327i −0.108805 0.334868i
\(465\) 0 0
\(466\) −0.513883 + 1.58157i −0.0238052 + 0.0732649i
\(467\) 17.6857 + 12.8494i 0.818398 + 0.594601i 0.916253 0.400599i \(-0.131198\pi\)
−0.0978549 + 0.995201i \(0.531198\pi\)
\(468\) 0 0
\(469\) −14.0908 10.2375i −0.650651 0.472726i
\(470\) 3.83337 + 1.45309i 0.176820 + 0.0670258i
\(471\) 0 0
\(472\) 7.33001 5.32556i 0.337391 0.245129i
\(473\) −2.43924 7.50722i −0.112157 0.345182i
\(474\) 0 0
\(475\) 8.32284 + 0.804283i 0.381878 + 0.0369030i
\(476\) −5.10532 −0.234002
\(477\) 0 0
\(478\) −10.3553 + 7.52354i −0.473639 + 0.344119i
\(479\) −4.94352 + 3.59168i −0.225875 + 0.164108i −0.694967 0.719041i \(-0.744581\pi\)
0.469092 + 0.883149i \(0.344581\pi\)
\(480\) 0 0
\(481\) −2.57198 1.86865i −0.117272 0.0852031i
\(482\) −0.395477 −0.0180135
\(483\) 0 0
\(484\) −2.36051 + 7.26490i −0.107296 + 0.330223i
\(485\) 15.5252 19.3372i 0.704963 0.878057i
\(486\) 0 0
\(487\) 1.56421 4.81415i 0.0708812 0.218150i −0.909340 0.416053i \(-0.863413\pi\)
0.980222 + 0.197903i \(0.0634131\pi\)
\(488\) −0.799717 + 2.46127i −0.0362015 + 0.111417i
\(489\) 0 0
\(490\) −4.46004 6.80524i −0.201484 0.307429i
\(491\) −0.736165 + 2.26568i −0.0332227 + 0.102249i −0.966293 0.257446i \(-0.917119\pi\)
0.933070 + 0.359695i \(0.117119\pi\)
\(492\) 0 0
\(493\) 21.1203 0.951209
\(494\) 3.27120 + 2.37666i 0.147178 + 0.106931i
\(495\) 0 0
\(496\) 4.28304 3.11181i 0.192314 0.139724i
\(497\) 0.453127 0.329216i 0.0203255 0.0147674i
\(498\) 0 0
\(499\) −0.0503313 −0.00225314 −0.00112657 0.999999i \(-0.500359\pi\)
−0.00112657 + 0.999999i \(0.500359\pi\)
\(500\) 1.61000 11.0638i 0.0720012 0.494789i
\(501\) 0 0
\(502\) 2.89422 + 8.90749i 0.129175 + 0.397561i
\(503\) −4.37744 + 3.18040i −0.195181 + 0.141807i −0.681083 0.732206i \(-0.738491\pi\)
0.485903 + 0.874013i \(0.338491\pi\)
\(504\) 0 0
\(505\) −28.4364 + 7.74739i −1.26540 + 0.344755i
\(506\) 11.5191 + 8.36912i 0.512087 + 0.372053i
\(507\) 0 0
\(508\) −0.269620 0.195890i −0.0119625 0.00869123i
\(509\) −5.85472 + 18.0190i −0.259506 + 0.798678i 0.733402 + 0.679795i \(0.237931\pi\)
−0.992908 + 0.118883i \(0.962069\pi\)
\(510\) 0 0
\(511\) 8.46868 + 26.0639i 0.374632 + 1.15300i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 0 0
\(514\) −1.53868 4.73556i −0.0678681 0.208877i
\(515\) −3.68621 + 4.59130i −0.162434 + 0.202317i
\(516\) 0 0
\(517\) 2.71929 + 1.97568i 0.119594 + 0.0868904i
\(518\) 2.41062 0.105917
\(519\) 0 0
\(520\) 3.38476 4.21584i 0.148432 0.184877i
\(521\) 31.0817 22.5822i 1.36171 0.989342i 0.363379 0.931642i \(-0.381623\pi\)
0.998334 0.0577005i \(-0.0183768\pi\)
\(522\) 0 0
\(523\) −3.79057 11.6662i −0.165750 0.510127i 0.833341 0.552760i \(-0.186425\pi\)
−0.999091 + 0.0426332i \(0.986425\pi\)
\(524\) 5.17801 0.226202
\(525\) 0 0
\(526\) −19.8112 −0.863809
\(527\) 4.55565 + 14.0208i 0.198447 + 0.610757i
\(528\) 0 0
\(529\) −30.1883 + 21.9331i −1.31254 + 0.953613i
\(530\) −13.6271 5.16553i −0.591924 0.224376i
\(531\) 0 0
\(532\) −3.06598 −0.132927
\(533\) −6.87572 4.99550i −0.297820 0.216379i
\(534\) 0 0
\(535\) 40.5694 11.0530i 1.75397 0.477863i
\(536\) −2.93569 9.03513i −0.126803 0.390258i
\(537\) 0 0
\(538\) 4.57157 14.0698i 0.197094 0.606594i
\(539\) −2.06151 6.34468i −0.0887957 0.273285i
\(540\) 0 0
\(541\) 12.9872 39.9704i 0.558362 1.71846i −0.128534 0.991705i \(-0.541027\pi\)
0.686896 0.726756i \(-0.258973\pi\)
\(542\) −10.1583 7.38047i −0.436338 0.317018i
\(543\) 0 0
\(544\) −2.25284 1.63679i −0.0965899 0.0701767i
\(545\) −1.10996 + 23.0255i −0.0475453 + 0.986304i
\(546\) 0 0
\(547\) −15.6719 + 11.3863i −0.670080 + 0.486842i −0.870052 0.492960i \(-0.835915\pi\)
0.199972 + 0.979802i \(0.435915\pi\)
\(548\) 6.03299 + 18.5676i 0.257717 + 0.793170i
\(549\) 0 0
\(550\) 3.65815 8.40528i 0.155984 0.358402i
\(551\) 12.6837 0.540344
\(552\) 0 0
\(553\) 5.13308 3.72940i 0.218281 0.158590i
\(554\) −5.12256 + 3.72176i −0.217637 + 0.158122i
\(555\) 0 0
\(556\) 6.43579 + 4.67587i 0.272938 + 0.198301i
\(557\) −8.54685 −0.362142 −0.181071 0.983470i \(-0.557956\pi\)
−0.181071 + 0.983470i \(0.557956\pi\)
\(558\) 0 0
\(559\) 3.21688 9.90054i 0.136060 0.418748i
\(560\) −0.197391 + 4.09478i −0.00834129 + 0.173036i
\(561\) 0 0
\(562\) −6.20792 + 19.1060i −0.261865 + 0.805938i
\(563\) 7.24949 22.3116i 0.305529 0.940323i −0.673950 0.738777i \(-0.735404\pi\)
0.979479 0.201546i \(-0.0645964\pi\)
\(564\) 0 0
\(565\) 0.652091 13.5273i 0.0274337 0.569098i
\(566\) −0.561416 + 1.72786i −0.0235981 + 0.0726274i
\(567\) 0 0
\(568\) 0.305502 0.0128186
\(569\) −5.74445 4.17359i −0.240820 0.174966i 0.460829 0.887489i \(-0.347552\pi\)
−0.701649 + 0.712523i \(0.747552\pi\)
\(570\) 0 0
\(571\) 9.67745 7.03108i 0.404989 0.294241i −0.366581 0.930386i \(-0.619472\pi\)
0.771570 + 0.636145i \(0.219472\pi\)
\(572\) 3.58621 2.60553i 0.149947 0.108943i
\(573\) 0 0
\(574\) 6.44437 0.268983
\(575\) 29.0741 + 25.7404i 1.21247 + 1.07345i
\(576\) 0 0
\(577\) 12.8457 + 39.5350i 0.534774 + 1.64587i 0.744137 + 0.668027i \(0.232861\pi\)
−0.209362 + 0.977838i \(0.567139\pi\)
\(578\) −7.47987 + 5.43444i −0.311121 + 0.226043i
\(579\) 0 0
\(580\) 0.816590 16.9397i 0.0339070 0.703385i
\(581\) −9.45200 6.86728i −0.392135 0.284903i
\(582\) 0 0
\(583\) −9.66673 7.02329i −0.400355 0.290875i
\(584\) −4.61920 + 14.2164i −0.191144 + 0.588280i
\(585\) 0 0
\(586\) −2.11964 6.52359i −0.0875617 0.269487i
\(587\) −5.91072 + 18.1913i −0.243962 + 0.750836i 0.751844 + 0.659341i \(0.229165\pi\)
−0.995806 + 0.0914953i \(0.970835\pi\)
\(588\) 0 0
\(589\) 2.73588 + 8.42016i 0.112730 + 0.346947i
\(590\) 19.5472 5.32556i 0.804744 0.219250i
\(591\) 0 0
\(592\) 1.06375 + 0.772856i 0.0437197 + 0.0317642i
\(593\) −0.538428 −0.0221106 −0.0110553 0.999939i \(-0.503519\pi\)
−0.0110553 + 0.999939i \(0.503519\pi\)
\(594\) 0 0
\(595\) −10.6747 4.04636i −0.437618 0.165885i
\(596\) −1.35878 + 0.987213i −0.0556579 + 0.0404378i
\(597\) 0 0
\(598\) 5.80261 + 17.8586i 0.237286 + 0.730292i
\(599\) 38.4209 1.56983 0.784917 0.619601i \(-0.212705\pi\)
0.784917 + 0.619601i \(0.212705\pi\)
\(600\) 0 0
\(601\) 19.6034 0.799639 0.399820 0.916594i \(-0.369073\pi\)
0.399820 + 0.916594i \(0.369073\pi\)
\(602\) 2.43924 + 7.50722i 0.0994162 + 0.305971i
\(603\) 0 0
\(604\) 17.2048 12.5001i 0.700055 0.508620i
\(605\) −10.6936 + 13.3192i −0.434755 + 0.541503i
\(606\) 0 0
\(607\) −32.4415 −1.31676 −0.658381 0.752685i \(-0.728758\pi\)
−0.658381 + 0.752685i \(0.728758\pi\)
\(608\) −1.35294 0.982966i −0.0548688 0.0398646i
\(609\) 0 0
\(610\) −3.62287 + 4.51242i −0.146686 + 0.182702i
\(611\) 1.36981 + 4.21584i 0.0554166 + 0.170555i
\(612\) 0 0
\(613\) −7.25273 + 22.3216i −0.292935 + 0.901561i 0.690972 + 0.722881i \(0.257183\pi\)
−0.983907 + 0.178680i \(0.942817\pi\)
\(614\) 0.894685 + 2.75356i 0.0361065 + 0.111124i
\(615\) 0 0
\(616\) −1.03868 + 3.19672i −0.0418495 + 0.128799i
\(617\) 14.0876 + 10.2353i 0.567147 + 0.412056i 0.834068 0.551662i \(-0.186006\pi\)
−0.266921 + 0.963718i \(0.586006\pi\)
\(618\) 0 0
\(619\) −10.1801 7.39624i −0.409171 0.297280i 0.364095 0.931362i \(-0.381378\pi\)
−0.773266 + 0.634082i \(0.781378\pi\)
\(620\) 11.4217 3.11181i 0.458707 0.124973i
\(621\) 0 0
\(622\) 16.7054 12.1372i 0.669826 0.486657i
\(623\) 1.88117 + 5.78966i 0.0753676 + 0.231958i
\(624\) 0 0
\(625\) 12.1353 21.8572i 0.485410 0.874287i
\(626\) −16.4272 −0.656563
\(627\) 0 0
\(628\) −8.45536 + 6.14318i −0.337406 + 0.245140i
\(629\) −2.96218 + 2.15215i −0.118110 + 0.0858118i
\(630\) 0 0
\(631\) −33.7653 24.5319i −1.34418 0.976601i −0.999279 0.0379610i \(-0.987914\pi\)
−0.344897 0.938640i \(-0.612086\pi\)
\(632\) 3.46076 0.137662
\(633\) 0 0
\(634\) 5.10060 15.6980i 0.202571 0.623448i
\(635\) −0.408487 0.623280i −0.0162103 0.0247341i
\(636\) 0 0
\(637\) 2.71873 8.36739i 0.107720 0.331528i
\(638\) 4.29692 13.2246i 0.170117 0.523565i
\(639\) 0 0
\(640\) −1.39991 + 1.74363i −0.0553362 + 0.0689232i
\(641\) 4.44926 13.6934i 0.175735 0.540858i −0.823931 0.566690i \(-0.808224\pi\)
0.999666 + 0.0258324i \(0.00822362\pi\)
\(642\) 0 0
\(643\) 30.1666 1.18966 0.594828 0.803853i \(-0.297220\pi\)
0.594828 + 0.803853i \(0.297220\pi\)
\(644\) −11.5191 8.36912i −0.453916 0.329790i
\(645\) 0 0
\(646\) 3.76748 2.73724i 0.148230 0.107695i
\(647\) −8.64660 + 6.28212i −0.339933 + 0.246976i −0.744633 0.667474i \(-0.767376\pi\)
0.404701 + 0.914449i \(0.367376\pi\)
\(648\) 0 0
\(649\) 16.6110 0.652039
\(650\) 10.4185 6.13217i 0.408649 0.240524i
\(651\) 0 0
\(652\) 3.21706 + 9.90109i 0.125990 + 0.387757i
\(653\) 8.22432 5.97532i 0.321843 0.233832i −0.415119 0.909767i \(-0.636260\pi\)
0.736961 + 0.675935i \(0.236260\pi\)
\(654\) 0 0
\(655\) 10.8266 + 4.10398i 0.423032 + 0.160356i
\(656\) 2.84373 + 2.06609i 0.111029 + 0.0806674i
\(657\) 0 0
\(658\) −2.71929 1.97568i −0.106009 0.0770201i
\(659\) −9.61668 + 29.5971i −0.374613 + 1.15294i 0.569127 + 0.822250i \(0.307281\pi\)
−0.943740 + 0.330689i \(0.892719\pi\)
\(660\) 0 0
\(661\) 12.8131 + 39.4347i 0.498372 + 1.53383i 0.811635 + 0.584165i \(0.198578\pi\)
−0.313262 + 0.949667i \(0.601422\pi\)
\(662\) −8.48901 + 26.1265i −0.329935 + 1.01543i
\(663\) 0 0
\(664\) −1.96924 6.06071i −0.0764215 0.235201i
\(665\) −6.41062 2.43003i −0.248593 0.0942324i
\(666\) 0 0
\(667\) 47.6536 + 34.6224i 1.84515 + 1.34058i
\(668\) −2.12171 −0.0820913
\(669\) 0 0
\(670\) 1.02284 21.2182i 0.0395156 0.819732i
\(671\) −3.83849 + 2.78883i −0.148183 + 0.107661i
\(672\) 0 0
\(673\) 0.662831 + 2.03998i 0.0255503 + 0.0786356i 0.963019 0.269435i \(-0.0868369\pi\)
−0.937468 + 0.348071i \(0.886837\pi\)
\(674\) 2.74521 0.105742
\(675\) 0 0
\(676\) −7.15401 −0.275154
\(677\) −12.8391 39.5147i −0.493446 1.51867i −0.819364 0.573274i \(-0.805673\pi\)
0.325918 0.945398i \(-0.394327\pi\)
\(678\) 0 0
\(679\) −16.4492 + 11.9510i −0.631263 + 0.458639i
\(680\) −3.41317 5.20790i −0.130889 0.199714i
\(681\) 0 0
\(682\) 9.70607 0.371665
\(683\) −23.3247 16.9464i −0.892495 0.648436i 0.0440323 0.999030i \(-0.485980\pi\)
−0.936527 + 0.350595i \(0.885980\pi\)
\(684\) 0 0
\(685\) −2.10198 + 43.6045i −0.0803124 + 1.66604i
\(686\) 6.02730 + 18.5501i 0.230123 + 0.708247i
\(687\) 0 0
\(688\) −1.33047 + 4.09478i −0.0507238 + 0.156112i
\(689\) −4.86950 14.9868i −0.185513 0.570951i
\(690\) 0 0
\(691\) −15.2050 + 46.7963i −0.578426 + 1.78021i 0.0457774 + 0.998952i \(0.485424\pi\)
−0.624204 + 0.781262i \(0.714576\pi\)
\(692\) −14.6551 10.6475i −0.557103 0.404759i
\(693\) 0 0
\(694\) 17.2637 + 12.5428i 0.655319 + 0.476117i
\(695\) 9.75053 + 14.8776i 0.369859 + 0.564340i
\(696\) 0 0
\(697\) −7.91886 + 5.75339i −0.299948 + 0.217925i
\(698\) 5.18067 + 15.9445i 0.196091 + 0.603507i
\(699\) 0 0
\(700\) −3.65815 + 8.40528i −0.138265 + 0.317690i
\(701\) 24.9783 0.943419 0.471709 0.881754i \(-0.343637\pi\)
0.471709 + 0.881754i \(0.343637\pi\)
\(702\) 0 0
\(703\) −1.77893 + 1.29247i −0.0670935 + 0.0487462i
\(704\) −1.48322 + 1.07763i −0.0559011 + 0.0406145i
\(705\) 0 0
\(706\) −2.41785 1.75667i −0.0909969 0.0661131i
\(707\) 24.1650 0.908817
\(708\) 0 0
\(709\) 3.02602 9.31312i 0.113644 0.349762i −0.878017 0.478629i \(-0.841134\pi\)
0.991662 + 0.128867i \(0.0411340\pi\)
\(710\) 0.638770 + 0.242134i 0.0239726 + 0.00908712i
\(711\) 0 0
\(712\) −1.02608 + 3.15794i −0.0384538 + 0.118349i
\(713\) −12.7054 + 39.1032i −0.475821 + 1.46443i
\(714\) 0 0
\(715\) 9.56346 2.60553i 0.357653 0.0974414i
\(716\) −3.26337 + 10.0436i −0.121958 + 0.375348i
\(717\) 0 0
\(718\) 6.70494 0.250226
\(719\) −6.94474 5.04565i −0.258995 0.188171i 0.450709 0.892671i \(-0.351171\pi\)
−0.709704 + 0.704500i \(0.751171\pi\)
\(720\) 0 0
\(721\) 3.90559 2.83758i 0.145452 0.105677i
\(722\) −13.1088 + 9.52408i −0.487858 + 0.354450i
\(723\) 0 0
\(724\) 18.1561 0.674768
\(725\) 15.1335 34.7719i 0.562043 1.29140i
\(726\) 0 0
\(727\) −7.42142 22.8408i −0.275245 0.847118i −0.989154 0.146880i \(-0.953077\pi\)
0.713909 0.700238i \(-0.246923\pi\)
\(728\) −3.58621 + 2.60553i −0.132914 + 0.0965675i
\(729\) 0 0
\(730\) −20.9259 + 26.0639i −0.774501 + 0.964669i
\(731\) −9.69962 7.04719i −0.358754 0.260650i
\(732\) 0 0
\(733\) 15.3787 + 11.1733i 0.568025 + 0.412695i 0.834387 0.551178i \(-0.185822\pi\)
−0.266362 + 0.963873i \(0.585822\pi\)
\(734\) −1.24119 + 3.82000i −0.0458133 + 0.140999i
\(735\) 0 0
\(736\) −2.39991 7.38615i −0.0884617 0.272257i
\(737\) 5.38220 16.5647i 0.198256 0.610168i
\(738\) 0 0
\(739\) −6.42507 19.7743i −0.236350 0.727411i −0.996939 0.0781776i \(-0.975090\pi\)
0.760589 0.649233i \(-0.224910\pi\)
\(740\) 1.61163 + 2.45906i 0.0592446 + 0.0903968i
\(741\) 0 0
\(742\) 9.66673 + 7.02329i 0.354877 + 0.257833i
\(743\) −6.53365 −0.239696 −0.119848 0.992792i \(-0.538241\pi\)
−0.119848 + 0.992792i \(0.538241\pi\)
\(744\) 0 0
\(745\) −3.62351 + 0.987213i −0.132755 + 0.0361687i
\(746\) 21.5063 15.6252i 0.787401 0.572080i
\(747\) 0 0
\(748\) −1.57763 4.85544i −0.0576838 0.177533i
\(749\) −34.4755 −1.25971
\(750\) 0 0
\(751\) 27.9879 1.02129 0.510646 0.859791i \(-0.329406\pi\)
0.510646 + 0.859791i \(0.329406\pi\)
\(752\) −0.566541 1.74363i −0.0206596 0.0635838i
\(753\) 0 0
\(754\) 14.8359 10.7789i 0.540290 0.392544i
\(755\) 45.8807 12.5001i 1.66977 0.454923i
\(756\) 0 0
\(757\) 4.48558 0.163031 0.0815156 0.996672i \(-0.474024\pi\)
0.0815156 + 0.996672i \(0.474024\pi\)
\(758\) −12.6431 9.18578i −0.459220 0.333643i
\(759\) 0 0
\(760\) −2.04977 3.12758i −0.0743528 0.113449i
\(761\) −0.138770 0.427091i −0.00503042 0.0154820i 0.948510 0.316748i \(-0.102591\pi\)
−0.953540 + 0.301266i \(0.902591\pi\)
\(762\) 0 0
\(763\) 5.84063 17.9756i 0.211445 0.650760i
\(764\) 6.76906 + 20.8330i 0.244896 + 0.753712i
\(765\) 0 0
\(766\) 4.15489 12.7874i 0.150122 0.462028i
\(767\) 17.7228 + 12.8764i 0.639935 + 0.464940i
\(768\) 0 0
\(769\) −16.9783 12.3355i −0.612254 0.444829i 0.237953 0.971277i \(-0.423524\pi\)
−0.850207 + 0.526448i \(0.823524\pi\)
\(770\) −4.70541 + 5.86076i −0.169571 + 0.211207i
\(771\) 0 0
\(772\) −22.1872 + 16.1199i −0.798533 + 0.580168i
\(773\) −10.8283 33.3262i −0.389468 1.19866i −0.933187 0.359392i \(-0.882984\pi\)
0.543718 0.839268i \(-0.317016\pi\)
\(774\) 0 0
\(775\) 26.3479 + 2.54615i 0.946444 + 0.0914602i
\(776\) −11.0902 −0.398114
\(777\) 0 0
\(778\) 20.3157 14.7602i 0.728354 0.529180i
\(779\) −4.75564 + 3.45517i −0.170388 + 0.123794i
\(780\) 0 0
\(781\) 0.453127 + 0.329216i 0.0162142 + 0.0117803i
\(782\) 21.6265 0.773361
\(783\) 0 0
\(784\) −1.12444 + 3.46068i −0.0401586 + 0.123596i
\(785\) −22.5482 + 6.14318i −0.804779 + 0.219259i
\(786\) 0 0
\(787\) 12.1132 37.2807i 0.431790 1.32891i −0.464550 0.885547i \(-0.653784\pi\)
0.896340 0.443367i \(-0.146216\pi\)
\(788\)