Properties

Label 450.2.h.e.271.1
Level $450$
Weight $2$
Character 450.271
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 271.1
Root \(1.17421 - 0.0566033i\) of defining polynomial
Character \(\chi\) \(=\) 450.271
Dual form 450.2.h.e.181.1

$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.828599 0.559842i \(-0.810862\pi\)
0.999418 + 0.0341166i \(0.0108618\pi\)
\(12\) 0 0
\(13\) −0.747156 2.29951i −0.207224 0.637769i −0.999615 0.0277557i \(-0.991164\pi\)
0.792391 0.610014i \(-0.208836\pi\)
\(14\) −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 −0.280060 0.959983i \(-0.590354\pi\)
0.826455 + 0.563003i \(0.190354\pi\)
\(18\) 0 0
\(19\) 1.35294 0.982966i 0.310385 0.225508i −0.421677 0.906746i \(-0.638558\pi\)
0.732062 + 0.681238i \(0.238558\pi\)
\(20\) 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 −0.307929 0.951409i \(-0.599636\pi\)
0.808344 0.588710i \(-0.200364\pi\)
\(24\) 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 0.987039 0.160483i \(-0.0513052\pi\)
0.152383 + 0.988321i \(0.451305\pi\)
\(30\) 0 0
\(31\) 4.28304 3.11181i 0.769256 0.558897i −0.132479 0.991186i \(-0.542294\pi\)
0.901735 + 0.432288i \(0.142294\pi\)
\(32\) −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 0.912086 0.409998i \(-0.134471\pi\)
−0.978884 + 0.204416i \(0.934471\pi\)
\(38\) 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 0.829711 0.558194i \(-0.188505\pi\)
−0.999348 + 0.0361034i \(0.988505\pi\)
\(42\) 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 0.690682 0.723158i \(-0.257310\pi\)
−0.474332 + 0.880346i \(0.657310\pi\)
\(48\) 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 0.163485 0.986546i \(-0.447727\pi\)
−0.887741 + 0.460342i \(0.847727\pi\)
\(54\) 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 0.950291 + 0.311364i \(0.100786\pi\)
−0.585786 + 0.810466i \(0.699214\pi\)
\(60\) 0 0
\(61\) 0.799717 2.46127i 0.102393 0.315134i −0.886717 0.462313i \(-0.847019\pi\)
0.989110 + 0.147180i \(0.0470195\pi\)
\(62\) 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 −0.948171 0.317761i \(-0.897069\pi\)
0.00920814 + 0.999958i \(0.497069\pi\)
\(68\) −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 0.602355 0.798229i \(-0.294229\pi\)
−0.573023 + 0.819540i \(0.694229\pi\)
\(72\) 0 0
\(73\) 4.61920 14.2164i 0.540636 1.66391i −0.190509 0.981685i \(-0.561014\pi\)
0.731145 0.682222i \(-0.238986\pi\)
\(74\) 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 0.734041 0.679106i \(-0.237632\pi\)
−0.419037 + 0.907969i \(0.637632\pi\)
\(80\) −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 −0.833612 0.552351i \(-0.813731\pi\)
0.267717 + 0.963498i \(0.413731\pi\)
\(84\) 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 −0.881832 0.471565i \(-0.843689\pi\)
0.990595 + 0.136824i \(0.0436894\pi\)
\(90\) 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 0.0302807 0.999541i \(-0.490360\pi\)
−0.941263 + 0.337674i \(0.890360\pi\)
\(98\) 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 0.687770 0.725929i \(-0.258590\pi\)
−0.477867 + 0.878432i \(0.658590\pi\)
\(104\) −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 0.979625 + 0.200833i \(0.0643649\pi\)
−0.674487 + 0.738287i \(0.735635\pi\)
\(110\) −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 0.823615 0.567149i \(-0.191954\pi\)
−0.999681 + 0.0252760i \(0.991954\pi\)
\(114\) 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 −0.946383 0.323046i \(-0.895293\pi\)
0.955522 + 0.294921i \(0.0952932\pi\)
\(128\) 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 −0.755552 0.655089i \(-0.772631\pi\)
0.389548 + 0.921006i \(0.372631\pi\)
\(132\) 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 0.782493 + 0.622660i \(0.213948\pi\)
−0.267060 + 0.963680i \(0.586052\pi\)
\(138\) 0 0
\(139\) −2.45825 + 7.56572i −0.208506 + 0.641716i 0.791045 + 0.611758i \(0.209537\pi\)
−0.999551 + 0.0299582i \(0.990463\pi\)
\(140\) 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 0.994410 + 0.105590i \(0.0336731\pi\)
−0.742430 + 0.669923i \(0.766327\pi\)
\(164\) −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 −0.519388 0.854538i \(-0.673840\pi\)
0.652215 + 0.758034i \(0.273840\pi\)
\(168\) 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 −0.476841 0.878989i \(-0.658218\pi\)
0.902430 0.430837i \(-0.141782\pi\)
\(174\) 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 0.859362 0.511368i \(-0.170861\pi\)
−0.220782 + 0.975323i \(0.570861\pi\)
\(180\) 0 0
\(181\) −14.6886 + 10.6719i −1.09180 + 0.793237i −0.979702 0.200460i \(-0.935756\pi\)
−0.112096 + 0.993697i \(0.535756\pi\)
\(182\) 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 0.824919 + 0.565251i \(0.191221\pi\)
−0.335127 + 0.942173i \(0.608779\pi\)
\(192\) 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 0.554928 0.831898i \(-0.312746\pi\)
−0.619700 + 0.784839i \(0.712746\pi\)
\(198\) 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 −0.419990 0.907529i \(-0.637967\pi\)
0.873211 0.487342i \(-0.162033\pi\)
\(212\) 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 −0.911850 0.410524i \(-0.865346\pi\)
0.979002 + 0.203851i \(0.0653458\pi\)
\(224\) −1.83337 −0.122497
\(225\) 0 0
\(226\) 6.05662 0.402880
\(227\) −5.06085 + 15.5757i −0.335901 + 1.03380i 0.630376 + 0.776290i \(0.282901\pi\)
−0.966277 + 0.257506i \(0.917099\pi\)
\(228\) 0 0
\(229\) 4.11788 + 2.99181i 0.272117 + 0.197705i 0.715472 0.698642i \(-0.246212\pi\)
−0.443355 + 0.896346i \(0.646212\pi\)
\(230\) −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 −0.630981 0.775798i \(-0.717348\pi\)
0.542844 + 0.839834i \(0.317348\pi\)
\(234\) 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 0.737810 + 0.675009i \(0.235860\pi\)
−0.993661 + 0.112420i \(0.964140\pi\)
\(240\) 0 0
\(241\) 0.122209 + 0.376121i 0.00787219 + 0.0242281i 0.954915 0.296878i \(-0.0959454\pi\)
−0.947043 + 0.321106i \(0.895945\pi\)
\(242\) −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 0.941778 + 0.336236i \(0.109154\pi\)
−0.564279 + 0.825584i \(0.690846\pi\)
\(264\) 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 −0.159745 0.987158i \(-0.551067\pi\)
0.889479 + 0.456976i \(0.151067\pi\)
\(270\) 0 0
\(271\) 10.1583 + 7.38047i 0.617075 + 0.448331i 0.851899 0.523707i \(-0.175451\pi\)
−0.234823 + 0.972038i \(0.575451\pi\)
\(272\) 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 −0.992473 0.122463i \(-0.960921\pi\)
0.874910 + 0.484286i \(0.160921\pi\)
\(278\) −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 −0.955348 0.295484i \(-0.904519\pi\)
−0.0141971 + 0.999899i \(0.504519\pi\)
\(282\) 0 0
\(283\) −1.46981 + 1.06788i −0.0873709 + 0.0634787i −0.630613 0.776097i \(-0.717197\pi\)
0.543242 + 0.839576i \(0.317197\pi\)
\(284\) −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 −0.590116 0.807318i \(-0.700918\pi\)
0.951944 0.306272i \(-0.0990819\pi\)
\(312\) 0 0
\(313\) 5.07629 + 15.6232i 0.286929 + 0.883076i 0.985814 + 0.167842i \(0.0536798\pi\)
−0.698885 + 0.715234i \(0.746320\pi\)
\(314\) −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 −0.145820 0.989311i \(-0.546582\pi\)
0.895830 + 0.444397i \(0.146582\pi\)
\(318\) 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 −0.996229 0.0867577i \(-0.972349\pi\)
−0.225340 + 0.974280i \(0.572349\pi\)
\(332\) 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 0.925289 0.379263i \(-0.123822\pi\)
−0.971500 + 0.237041i \(0.923822\pi\)
\(338\) 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 0.0184361 0.999830i \(-0.494131\pi\)
−0.945198 + 0.326498i \(0.894131\pi\)
\(348\) 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 0.650268 0.759705i \(-0.274657\pi\)
−0.521579 + 0.853203i \(0.674657\pi\)
\(354\) 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 0.881375 0.472418i \(-0.156619\pi\)
−0.990727 + 0.135865i \(0.956619\pi\)
\(360\) 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 −0.669357 0.742941i \(-0.733430\pi\)
0.499736 + 0.866178i \(0.333430\pi\)
\(368\) 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 −0.477329 0.878725i \(-0.658395\pi\)
0.902669 0.430336i \(-0.141605\pi\)
\(374\) 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 0.863079 0.505070i \(-0.168533\pi\)
−0.213644 + 0.976912i \(0.568533\pi\)
\(380\) 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 −0.274106 0.961699i \(-0.588382\pi\)
0.829927 + 0.557872i \(0.188382\pi\)
\(384\) 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 −0.536724 0.843758i \(-0.680338\pi\)
0.930167 0.367136i \(-0.119662\pi\)
\(390\) 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 0.514065 0.857751i \(-0.328139\pi\)
−0.656915 + 0.753964i \(0.728139\pi\)
\(398\) −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 −0.567771 0.823186i \(-0.692194\pi\)
−0.0245200 0.999699i \(-0.507806\pi\)
\(410\) −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 −0.895018 0.446030i \(-0.852838\pi\)
0.147624 + 0.989044i \(0.452838\pi\)
\(420\) 0 0
\(421\) 17.8414 + 12.9625i 0.869536 + 0.631755i 0.930462 0.366388i \(-0.119406\pi\)
−0.0609265 + 0.998142i \(0.519406\pi\)
\(422\) 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 −0.752526 0.658562i \(-0.771165\pi\)
0.393787 + 0.919202i \(0.371165\pi\)
\(432\) 0 0
\(433\) −28.1516 + 20.4533i −1.35288 + 0.982923i −0.354015 + 0.935240i \(0.615184\pi\)
−0.998862 + 0.0476837i \(0.984816\pi\)
\(434\) 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 −0.993559 0.113314i \(-0.963853\pi\)
0.870411 + 0.492326i \(0.163853\pi\)
\(440\) 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 −0.995634 0.0933412i \(-0.970245\pi\)
0.860350 + 0.509704i \(0.170245\pi\)
\(462\) 0 0
\(463\) 5.47977 + 16.8650i 0.254666 + 0.783783i 0.993895 + 0.110328i \(0.0351902\pi\)
−0.739229 + 0.673454i \(0.764810\pi\)
\(464\) −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 −0.0978549 0.995201i \(-0.531198\pi\)
0.916253 + 0.400599i \(0.131198\pi\)
\(468\) 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 0.469092 0.883149i \(-0.344581\pi\)
−0.694967 + 0.719041i \(0.744581\pi\)
\(480\) 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 0.980222 0.197903i \(-0.0634131\pi\)
−0.909340 + 0.416053i \(0.863413\pi\)
\(488\) −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 0.933070 0.359695i \(-0.117119\pi\)
−0.966293 + 0.257446i \(0.917119\pi\)
\(492\) 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 0.485903 0.874013i \(-0.338491\pi\)
−0.681083 + 0.732206i \(0.738491\pi\)
\(504\) 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 −0.992908 0.118883i \(-0.962069\pi\)
0.733402 0.679795i \(-0.237931\pi\)
\(510\) 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 0.998334 + 0.0577005i \(0.0183768\pi\)
0.363379 + 0.931642i \(0.381623\pi\)
\(522\) 0 0
\(523\) −3.79057 + 11.6662i −0.165750 + 0.510127i −0.999091 0.0426332i \(-0.986425\pi\)
0.833341 + 0.552760i \(0.186425\pi\)
\(524\) 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 0.686896 + 0.726756i \(0.258973\pi\)
−0.128534 + 0.991705i \(0.541027\pi\)
\(542\) −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 0.199972 0.979802i \(-0.435915\pi\)
−0.870052 + 0.492960i \(0.835915\pi\)
\(548\) 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 0.979479 + 0.201546i \(0.0645964\pi\)
−0.673950 + 0.738777i \(0.735404\pi\)
\(564\) 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 −0.701649 0.712523i \(-0.747552\pi\)
0.460829 + 0.887489i \(0.347552\pi\)
\(570\) 0 0
\(571\) 9.67745 + 7.03108i 0.404989 + 0.294241i 0.771570 0.636145i \(-0.219472\pi\)
−0.366581 + 0.930386i \(0.619472\pi\)
\(572\) 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 −0.209362 0.977838i \(-0.567139\pi\)
0.744137 0.668027i \(-0.232861\pi\)
\(578\) −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 −0.995806 0.0914953i \(-0.970835\pi\)
0.751844 0.659341i \(-0.229165\pi\)
\(588\) 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 −0.983907 0.178680i \(-0.942817\pi\)
0.690972 0.722881i \(-0.257183\pi\)
\(614\) 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 −0.266921 0.963718i \(-0.586006\pi\)
0.834068 + 0.551662i \(0.186006\pi\)
\(618\) 0 0
\(619\) −10.1801 + 7.39624i −0.409171 + 0.297280i −0.773266 0.634082i \(-0.781378\pi\)
0.364095 + 0.931362i \(0.381378\pi\)
\(620\) 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 −0.344897 + 0.938640i \(0.612086\pi\)
−0.999279 + 0.0379610i \(0.987914\pi\)
\(632\) 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 0.999666 0.0258324i \(-0.00822362\pi\)
−0.823931 + 0.566690i \(0.808224\pi\)
\(642\) 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 0.404701 0.914449i \(-0.367376\pi\)
−0.744633 + 0.667474i \(0.767376\pi\)
\(648\) 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 0.736961 0.675935i \(-0.236260\pi\)
−0.415119 + 0.909767i \(0.636260\pi\)
\(654\) 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 −0.943740 0.330689i \(-0.892719\pi\)
0.569127 0.822250i \(-0.307281\pi\)
\(660\) 0 0
\(661\) 12.8131 39.4347i 0.498372 1.53383i −0.313262 0.949667i \(-0.601422\pi\)
0.811635 0.584165i \(-0.198578\pi\)
\(662\) −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 −0.937468 0.348071i \(-0.886837\pi\)
0.963019 + 0.269435i \(0.0868369\pi\)
\(674\) 2.74521 0.105742
\(675\) 0 0
\(676\) −7.15401 −0.275154
\(677\) −12.8391 + 39.5147i −0.493446 + 1.51867i 0.325918 + 0.945398i \(0.394327\pi\)
−0.819364 + 0.573274i \(0.805673\pi\)
\(678\) 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 −0.936527 0.350595i \(-0.885980\pi\)
0.0440323 + 0.999030i \(0.485980\pi\)
\(684\) 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 −0.624204 0.781262i \(-0.714576\pi\)
0.0457774 0.998952i \(-0.485424\pi\)
\(692\) −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 0.991662 0.128867i \(-0.0411340\pi\)
−0.878017 + 0.478629i \(0.841134\pi\)
\(710\) 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 −0.709704 0.704500i \(-0.751171\pi\)
0.450709 + 0.892671i \(0.351171\pi\)
\(720\) 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 0.713909 + 0.700238i \(0.246923\pi\)
−0.989154 + 0.146880i \(0.953077\pi\)
\(728\) −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 −0.266362 0.963873i \(-0.585822\pi\)
0.834387 + 0.551178i \(0.185822\pi\)
\(734\) −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 0.760589 + 0.649233i \(0.224910\pi\)
−0.996939 + 0.0781776i \(0.975090\pi\)
\(740\) 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 −0.953540 0.301266i \(-0.902591\pi\)
0.948510 + 0.316748i \(0.102591\pi\)
\(762\) 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 −0.850207 0.526448i \(-0.823524\pi\)
0.237953 + 0.971277i \(0.423524\pi\)
\(770\) −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 0.543718 + 0.839268i \(0.317016\pi\)
−0.933187 + 0.359392i \(0.882984\pi\)
\(774\) 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 0.896340 + 0.443367i \(0.146216\pi\)
−0.464550 + 0.885547i \(0.653784\pi\)
\(788\) 0.347249 +