Properties

Label 441.2.h.b.373.3
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.3
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.b.214.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +O(q^{10})\) \(q+1.69963 q^{2} +(-1.29418 + 1.15113i) q^{3} +0.888736 q^{4} +(-1.79418 - 3.10761i) q^{5} +(-2.19963 + 1.95649i) q^{6} -1.88874 q^{8} +(0.349814 - 2.97954i) q^{9} +(-3.04944 - 5.28179i) q^{10} +(1.40545 - 2.43430i) q^{11} +(-1.15019 + 1.02305i) q^{12} +(0.500000 - 0.866025i) q^{13} +(5.89926 + 1.95649i) q^{15} -4.98762 q^{16} +(-2.05563 - 3.56046i) q^{17} +(0.594554 - 5.06410i) q^{18} +(-0.444368 + 0.769668i) q^{19} +(-1.59455 - 2.76185i) q^{20} +(2.38874 - 4.13741i) q^{22} +(-2.93818 - 5.08907i) q^{23} +(2.44437 - 2.17417i) q^{24} +(-3.93818 + 6.82112i) q^{25} +(0.849814 - 1.47192i) q^{26} +(2.97710 + 4.25874i) q^{27} +(0.849814 + 1.47192i) q^{29} +(10.0265 + 3.32530i) q^{30} +6.98762 q^{31} -4.69963 q^{32} +(0.983290 + 4.76828i) q^{33} +(-3.49381 - 6.05146i) q^{34} +(0.310892 - 2.64802i) q^{36} +(-2.38255 + 4.12669i) q^{37} +(-0.755260 + 1.30815i) q^{38} +(0.349814 + 1.69636i) q^{39} +(3.38874 + 5.86946i) q^{40} +(-2.70582 + 4.68661i) q^{41} +(-2.60507 - 4.51212i) q^{43} +(1.24907 - 2.16345i) q^{44} +(-9.88688 + 4.25874i) q^{45} +(-4.99381 - 8.64953i) q^{46} +2.66621 q^{47} +(6.45489 - 5.74138i) q^{48} +(-6.69344 + 11.5934i) q^{50} +(6.75890 + 2.24159i) q^{51} +(0.444368 - 0.769668i) q^{52} +(0.0618219 + 0.107079i) q^{53} +(5.05996 + 7.23828i) q^{54} -10.0865 q^{55} +(-0.310892 - 1.50761i) q^{57} +(1.44437 + 2.50172i) q^{58} +8.87636 q^{59} +(5.24288 + 1.73880i) q^{60} -3.87636 q^{61} +11.8764 q^{62} +1.98762 q^{64} -3.58836 q^{65} +(1.67123 + 8.10430i) q^{66} +12.3090 q^{67} +(-1.82691 - 3.16431i) q^{68} +(9.66071 + 3.20397i) q^{69} -2.87636 q^{71} +(-0.660706 + 5.62755i) q^{72} +(-5.32072 - 9.21576i) q^{73} +(-4.04944 + 7.01384i) q^{74} +(-2.75526 - 13.3611i) q^{75} +(-0.394926 + 0.684031i) q^{76} +(0.594554 + 2.88318i) q^{78} -7.08650 q^{79} +(8.94870 + 15.4996i) q^{80} +(-8.75526 - 2.08457i) q^{81} +(-4.59888 + 7.96550i) q^{82} +(-2.05563 - 3.56046i) q^{83} +(-7.37636 + 12.7762i) q^{85} +(-4.42766 - 7.66893i) q^{86} +(-2.79418 - 0.926690i) q^{87} +(-2.65452 + 4.59776i) q^{88} +(4.80470 - 8.32199i) q^{89} +(-16.8040 + 7.23828i) q^{90} +(-2.61126 - 4.52284i) q^{92} +(-9.04325 + 8.04364i) q^{93} +4.53156 q^{94} +3.18911 q^{95} +(6.08217 - 5.40987i) q^{96} +(3.66071 + 6.34053i) q^{97} +(-6.76145 - 5.03913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} - 13q^{12} + 3q^{13} + 11q^{15} + 6q^{16} - 12q^{17} + 10q^{18} - 3q^{19} - 16q^{20} + 15q^{22} + 15q^{24} - 6q^{25} - q^{26} + 7q^{27} - q^{29} + 31q^{30} + 6q^{31} - 16q^{32} + 13q^{33} - 3q^{34} - 11q^{36} + 3q^{37} + 8q^{38} - 4q^{39} + 21q^{40} - 22q^{41} + 3q^{43} - 23q^{44} + q^{45} - 12q^{46} + 18q^{47} + 14q^{48} - 10q^{50} - 12q^{51} + 3q^{52} + 18q^{53} - 13q^{54} + 12q^{55} + 11q^{57} + 9q^{58} + 18q^{59} - 17q^{60} + 12q^{61} + 36q^{62} - 24q^{64} - 10q^{65} - 34q^{66} + 6q^{68} + 39q^{69} + 18q^{71} + 15q^{72} + 3q^{73} - 6q^{74} - 4q^{75} - 21q^{76} + 10q^{78} + 30q^{79} + 11q^{80} - 40q^{81} + 9q^{82} - 12q^{83} - 9q^{85} - 34q^{86} - 11q^{87} + 21q^{88} - 2q^{89} - 73q^{90} - 15q^{92} - 18q^{93} - 48q^{94} + 32q^{95} + 7q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.69963 1.20182 0.600909 0.799317i \(-0.294805\pi\)
0.600909 + 0.799317i \(0.294805\pi\)
\(3\) −1.29418 + 1.15113i −0.747196 + 0.664603i
\(4\) 0.888736 0.444368
\(5\) −1.79418 3.10761i −0.802383 1.38977i −0.918044 0.396479i \(-0.870232\pi\)
0.115661 0.993289i \(-0.463101\pi\)
\(6\) −2.19963 + 1.95649i −0.897994 + 0.798733i
\(7\) 0 0
\(8\) −1.88874 −0.667769
\(9\) 0.349814 2.97954i 0.116605 0.993178i
\(10\) −3.04944 5.28179i −0.964318 1.67025i
\(11\) 1.40545 2.43430i 0.423758 0.733970i −0.572546 0.819873i \(-0.694044\pi\)
0.996304 + 0.0859026i \(0.0273774\pi\)
\(12\) −1.15019 + 1.02305i −0.332030 + 0.295328i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 5.89926 + 1.95649i 1.52318 + 0.505163i
\(16\) −4.98762 −1.24691
\(17\) −2.05563 3.56046i −0.498564 0.863538i 0.501435 0.865196i \(-0.332806\pi\)
−0.999999 + 0.00165734i \(0.999472\pi\)
\(18\) 0.594554 5.06410i 0.140138 1.19362i
\(19\) −0.444368 + 0.769668i −0.101945 + 0.176574i −0.912486 0.409108i \(-0.865840\pi\)
0.810541 + 0.585682i \(0.199173\pi\)
\(20\) −1.59455 2.76185i −0.356553 0.617568i
\(21\) 0 0
\(22\) 2.38874 4.13741i 0.509280 0.882099i
\(23\) −2.93818 5.08907i −0.612652 1.06115i −0.990792 0.135396i \(-0.956769\pi\)
0.378139 0.925749i \(-0.376564\pi\)
\(24\) 2.44437 2.17417i 0.498955 0.443802i
\(25\) −3.93818 + 6.82112i −0.787636 + 1.36422i
\(26\) 0.849814 1.47192i 0.166662 0.288667i
\(27\) 2.97710 + 4.25874i 0.572943 + 0.819595i
\(28\) 0 0
\(29\) 0.849814 + 1.47192i 0.157807 + 0.273329i 0.934077 0.357071i \(-0.116224\pi\)
−0.776271 + 0.630399i \(0.782891\pi\)
\(30\) 10.0265 + 3.32530i 1.83059 + 0.607114i
\(31\) 6.98762 1.25501 0.627507 0.778611i \(-0.284075\pi\)
0.627507 + 0.778611i \(0.284075\pi\)
\(32\) −4.69963 −0.830785
\(33\) 0.983290 + 4.76828i 0.171169 + 0.830051i
\(34\) −3.49381 6.05146i −0.599183 1.03782i
\(35\) 0 0
\(36\) 0.310892 2.64802i 0.0518154 0.441337i
\(37\) −2.38255 + 4.12669i −0.391688 + 0.678424i −0.992672 0.120837i \(-0.961442\pi\)
0.600984 + 0.799261i \(0.294775\pi\)
\(38\) −0.755260 + 1.30815i −0.122519 + 0.212210i
\(39\) 0.349814 + 1.69636i 0.0560151 + 0.271635i
\(40\) 3.38874 + 5.86946i 0.535806 + 0.928044i
\(41\) −2.70582 + 4.68661i −0.422578 + 0.731926i −0.996191 0.0872002i \(-0.972208\pi\)
0.573613 + 0.819126i \(0.305541\pi\)
\(42\) 0 0
\(43\) −2.60507 4.51212i −0.397270 0.688092i 0.596118 0.802897i \(-0.296709\pi\)
−0.993388 + 0.114805i \(0.963376\pi\)
\(44\) 1.24907 2.16345i 0.188304 0.326153i
\(45\) −9.88688 + 4.25874i −1.47385 + 0.634856i
\(46\) −4.99381 8.64953i −0.736297 1.27530i
\(47\) 2.66621 0.388906 0.194453 0.980912i \(-0.437707\pi\)
0.194453 + 0.980912i \(0.437707\pi\)
\(48\) 6.45489 5.74138i 0.931683 0.828697i
\(49\) 0 0
\(50\) −6.69344 + 11.5934i −0.946595 + 1.63955i
\(51\) 6.75890 + 2.24159i 0.946436 + 0.313885i
\(52\) 0.444368 0.769668i 0.0616227 0.106734i
\(53\) 0.0618219 + 0.107079i 0.00849190 + 0.0147084i 0.870240 0.492628i \(-0.163964\pi\)
−0.861748 + 0.507336i \(0.830630\pi\)
\(54\) 5.05996 + 7.23828i 0.688574 + 0.985005i
\(55\) −10.0865 −1.36006
\(56\) 0 0
\(57\) −0.310892 1.50761i −0.0411787 0.199688i
\(58\) 1.44437 + 2.50172i 0.189655 + 0.328492i
\(59\) 8.87636 1.15560 0.577802 0.816177i \(-0.303911\pi\)
0.577802 + 0.816177i \(0.303911\pi\)
\(60\) 5.24288 + 1.73880i 0.676853 + 0.224478i
\(61\) −3.87636 −0.496317 −0.248158 0.968720i \(-0.579825\pi\)
−0.248158 + 0.968720i \(0.579825\pi\)
\(62\) 11.8764 1.50830
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) −3.58836 −0.445082
\(66\) 1.67123 + 8.10430i 0.205714 + 0.997571i
\(67\) 12.3090 1.50379 0.751894 0.659284i \(-0.229141\pi\)
0.751894 + 0.659284i \(0.229141\pi\)
\(68\) −1.82691 3.16431i −0.221546 0.383729i
\(69\) 9.66071 + 3.20397i 1.16301 + 0.385713i
\(70\) 0 0
\(71\) −2.87636 −0.341361 −0.170680 0.985326i \(-0.554597\pi\)
−0.170680 + 0.985326i \(0.554597\pi\)
\(72\) −0.660706 + 5.62755i −0.0778650 + 0.663214i
\(73\) −5.32072 9.21576i −0.622744 1.07862i −0.988973 0.148099i \(-0.952685\pi\)
0.366229 0.930525i \(-0.380649\pi\)
\(74\) −4.04944 + 7.01384i −0.470738 + 0.815342i
\(75\) −2.75526 13.3611i −0.318150 1.54281i
\(76\) −0.394926 + 0.684031i −0.0453011 + 0.0784638i
\(77\) 0 0
\(78\) 0.594554 + 2.88318i 0.0673200 + 0.326456i
\(79\) −7.08650 −0.797294 −0.398647 0.917104i \(-0.630520\pi\)
−0.398647 + 0.917104i \(0.630520\pi\)
\(80\) 8.94870 + 15.4996i 1.00049 + 1.73291i
\(81\) −8.75526 2.08457i −0.972807 0.231619i
\(82\) −4.59888 + 7.96550i −0.507862 + 0.879642i
\(83\) −2.05563 3.56046i −0.225635 0.390811i 0.730875 0.682512i \(-0.239112\pi\)
−0.956510 + 0.291700i \(0.905779\pi\)
\(84\) 0 0
\(85\) −7.37636 + 12.7762i −0.800078 + 1.38578i
\(86\) −4.42766 7.66893i −0.477447 0.826962i
\(87\) −2.79418 0.926690i −0.299568 0.0993516i
\(88\) −2.65452 + 4.59776i −0.282972 + 0.490123i
\(89\) 4.80470 8.32199i 0.509297 0.882129i −0.490645 0.871360i \(-0.663239\pi\)
0.999942 0.0107692i \(-0.00342802\pi\)
\(90\) −16.8040 + 7.23828i −1.77130 + 0.762981i
\(91\) 0 0
\(92\) −2.61126 4.52284i −0.272243 0.471539i
\(93\) −9.04325 + 8.04364i −0.937742 + 0.834086i
\(94\) 4.53156 0.467395
\(95\) 3.18911 0.327196
\(96\) 6.08217 5.40987i 0.620759 0.552142i
\(97\) 3.66071 + 6.34053i 0.371688 + 0.643783i 0.989825 0.142287i \(-0.0454456\pi\)
−0.618137 + 0.786070i \(0.712112\pi\)
\(98\) 0 0
\(99\) −6.76145 5.03913i −0.679551 0.506452i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) 1.73236 3.00054i 0.172376 0.298564i −0.766874 0.641798i \(-0.778189\pi\)
0.939250 + 0.343233i \(0.111522\pi\)
\(102\) 11.4876 + 3.80987i 1.13744 + 0.377233i
\(103\) −7.93818 13.7493i −0.782172 1.35476i −0.930674 0.365849i \(-0.880779\pi\)
0.148502 0.988912i \(-0.452555\pi\)
\(104\) −0.944368 + 1.63569i −0.0926029 + 0.160393i
\(105\) 0 0
\(106\) 0.105074 + 0.181994i 0.0102057 + 0.0176768i
\(107\) 2.67673 4.63623i 0.258769 0.448201i −0.707143 0.707070i \(-0.750016\pi\)
0.965912 + 0.258869i \(0.0833498\pi\)
\(108\) 2.64586 + 3.78490i 0.254598 + 0.364202i
\(109\) 9.43199 + 16.3367i 0.903421 + 1.56477i 0.823023 + 0.568008i \(0.192286\pi\)
0.0803973 + 0.996763i \(0.474381\pi\)
\(110\) −17.1433 −1.63455
\(111\) −1.66690 8.08330i −0.158215 0.767233i
\(112\) 0 0
\(113\) 9.27561 16.0658i 0.872576 1.51135i 0.0132538 0.999912i \(-0.495781\pi\)
0.859322 0.511434i \(-0.170886\pi\)
\(114\) −0.528401 2.56238i −0.0494893 0.239989i
\(115\) −10.5433 + 18.2614i −0.983163 + 1.70289i
\(116\) 0.755260 + 1.30815i 0.0701242 + 0.121459i
\(117\) −2.40545 1.79272i −0.222384 0.165737i
\(118\) 15.0865 1.38883
\(119\) 0 0
\(120\) −11.1421 3.69529i −1.01713 0.337332i
\(121\) 1.54944 + 2.68371i 0.140858 + 0.243974i
\(122\) −6.58836 −0.596482
\(123\) −1.89307 9.18007i −0.170692 0.827739i
\(124\) 6.21015 0.557688
\(125\) 10.3214 0.923175
\(126\) 0 0
\(127\) 9.98762 0.886258 0.443129 0.896458i \(-0.353868\pi\)
0.443129 + 0.896458i \(0.353868\pi\)
\(128\) 12.7775 1.12938
\(129\) 8.56546 + 2.84073i 0.754147 + 0.250113i
\(130\) −6.09888 −0.534908
\(131\) 8.02654 + 13.9024i 0.701282 + 1.21466i 0.968017 + 0.250886i \(0.0807220\pi\)
−0.266734 + 0.963770i \(0.585945\pi\)
\(132\) 0.873885 + 4.23774i 0.0760619 + 0.368848i
\(133\) 0 0
\(134\) 20.9208 1.80728
\(135\) 7.89307 16.8926i 0.679327 1.45389i
\(136\) 3.88255 + 6.72477i 0.332926 + 0.576644i
\(137\) 6.49381 11.2476i 0.554804 0.960948i −0.443115 0.896465i \(-0.646127\pi\)
0.997919 0.0644834i \(-0.0205400\pi\)
\(138\) 16.4196 + 5.44556i 1.39773 + 0.463557i
\(139\) 0.555632 0.962383i 0.0471281 0.0816283i −0.841499 0.540259i \(-0.818326\pi\)
0.888627 + 0.458630i \(0.151660\pi\)
\(140\) 0 0
\(141\) −3.45056 + 3.06914i −0.290589 + 0.258468i
\(142\) −4.88874 −0.410254
\(143\) −1.40545 2.43430i −0.117529 0.203567i
\(144\) −1.74474 + 14.8608i −0.145395 + 1.23840i
\(145\) 3.04944 5.28179i 0.253242 0.438629i
\(146\) −9.04325 15.6634i −0.748425 1.29631i
\(147\) 0 0
\(148\) −2.11745 + 3.66754i −0.174054 + 0.301470i
\(149\) −4.21634 7.30291i −0.345416 0.598278i 0.640013 0.768364i \(-0.278929\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(150\) −4.68292 22.7089i −0.382359 1.85418i
\(151\) 7.42580 12.8619i 0.604303 1.04668i −0.387858 0.921719i \(-0.626785\pi\)
0.992161 0.124964i \(-0.0398816\pi\)
\(152\) 0.839294 1.45370i 0.0680757 0.117911i
\(153\) −11.3276 + 4.87933i −0.915782 + 0.394470i
\(154\) 0 0
\(155\) −12.5371 21.7148i −1.00700 1.74418i
\(156\) 0.310892 + 1.50761i 0.0248913 + 0.120706i
\(157\) −2.88874 −0.230546 −0.115273 0.993334i \(-0.536774\pi\)
−0.115273 + 0.993334i \(0.536774\pi\)
\(158\) −12.0444 −0.958203
\(159\) −0.203270 0.0674145i −0.0161204 0.00534632i
\(160\) 8.43199 + 14.6046i 0.666607 + 1.15460i
\(161\) 0 0
\(162\) −14.8807 3.54299i −1.16914 0.278363i
\(163\) 5.15452 8.92788i 0.403733 0.699286i −0.590440 0.807081i \(-0.701046\pi\)
0.994173 + 0.107796i \(0.0343792\pi\)
\(164\) −2.40476 + 4.16516i −0.187780 + 0.325245i
\(165\) 13.0538 11.6108i 1.01623 0.903903i
\(166\) −3.49381 6.05146i −0.271172 0.469684i
\(167\) 6.07598 10.5239i 0.470174 0.814365i −0.529244 0.848469i \(-0.677525\pi\)
0.999418 + 0.0341045i \(0.0108579\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −12.5371 + 21.7148i −0.961549 + 1.66545i
\(171\) 2.13781 + 1.59325i 0.163482 + 0.121839i
\(172\) −2.31522 4.01008i −0.176534 0.305766i
\(173\) 6.60940 0.502504 0.251252 0.967922i \(-0.419158\pi\)
0.251252 + 0.967922i \(0.419158\pi\)
\(174\) −4.74907 1.57503i −0.360026 0.119403i
\(175\) 0 0
\(176\) −7.00983 + 12.1414i −0.528386 + 0.915191i
\(177\) −11.4876 + 10.2178i −0.863462 + 0.768018i
\(178\) 8.16621 14.1443i 0.612083 1.06016i
\(179\) 1.92147 + 3.32808i 0.143617 + 0.248752i 0.928856 0.370440i \(-0.120793\pi\)
−0.785239 + 0.619193i \(0.787460\pi\)
\(180\) −8.78682 + 3.78490i −0.654931 + 0.282109i
\(181\) −18.5426 −1.37826 −0.689129 0.724639i \(-0.742007\pi\)
−0.689129 + 0.724639i \(0.742007\pi\)
\(182\) 0 0
\(183\) 5.01671 4.46218i 0.370846 0.329854i
\(184\) 5.54944 + 9.61192i 0.409110 + 0.708600i
\(185\) 17.0989 1.25713
\(186\) −15.3702 + 13.6712i −1.12700 + 1.00242i
\(187\) −11.5563 −0.845082
\(188\) 2.36955 0.172818
\(189\) 0 0
\(190\) 5.42030 0.393230
\(191\) 4.63416 0.335316 0.167658 0.985845i \(-0.446380\pi\)
0.167658 + 0.985845i \(0.446380\pi\)
\(192\) −2.57234 + 2.28800i −0.185643 + 0.165122i
\(193\) −25.2967 −1.82089 −0.910446 0.413627i \(-0.864262\pi\)
−0.910446 + 0.413627i \(0.864262\pi\)
\(194\) 6.22184 + 10.7765i 0.446702 + 0.773711i
\(195\) 4.64400 4.13066i 0.332563 0.295803i
\(196\) 0 0
\(197\) 10.7207 0.763816 0.381908 0.924200i \(-0.375267\pi\)
0.381908 + 0.924200i \(0.375267\pi\)
\(198\) −11.4920 8.56465i −0.816697 0.608663i
\(199\) −4.38323 7.59199i −0.310719 0.538182i 0.667799 0.744342i \(-0.267237\pi\)
−0.978518 + 0.206160i \(0.933903\pi\)
\(200\) 7.43818 12.8833i 0.525959 0.910987i
\(201\) −15.9301 + 14.1693i −1.12362 + 0.999422i
\(202\) 2.94437 5.09979i 0.207165 0.358820i
\(203\) 0 0
\(204\) 6.00688 + 1.99218i 0.420566 + 0.139481i
\(205\) 19.4189 1.35628
\(206\) −13.4920 23.3687i −0.940029 1.62818i
\(207\) −16.1909 + 6.97418i −1.12534 + 0.484739i
\(208\) −2.49381 + 4.31941i −0.172915 + 0.299497i
\(209\) 1.24907 + 2.16345i 0.0864000 + 0.149649i
\(210\) 0 0
\(211\) −5.26509 + 9.11941i −0.362464 + 0.627806i −0.988366 0.152096i \(-0.951398\pi\)
0.625902 + 0.779902i \(0.284731\pi\)
\(212\) 0.0549434 + 0.0951647i 0.00377353 + 0.00653594i
\(213\) 3.72253 3.31105i 0.255063 0.226869i
\(214\) 4.54944 7.87987i 0.310993 0.538656i
\(215\) −9.34795 + 16.1911i −0.637525 + 1.10423i
\(216\) −5.62296 8.04364i −0.382594 0.547300i
\(217\) 0 0
\(218\) 16.0309 + 27.7663i 1.08575 + 1.88057i
\(219\) 17.4945 + 5.80205i 1.18217 + 0.392066i
\(220\) −8.96424 −0.604369
\(221\) −4.11126 −0.276554
\(222\) −2.83310 13.7386i −0.190145 0.922075i
\(223\) −2.83379 4.90827i −0.189765 0.328682i 0.755407 0.655256i \(-0.227439\pi\)
−0.945172 + 0.326574i \(0.894106\pi\)
\(224\) 0 0
\(225\) 18.9462 + 14.1201i 1.26308 + 0.941338i
\(226\) 15.7651 27.3059i 1.04868 1.81636i
\(227\) −5.54944 + 9.61192i −0.368329 + 0.637965i −0.989304 0.145865i \(-0.953403\pi\)
0.620975 + 0.783830i \(0.286737\pi\)
\(228\) −0.276301 1.33987i −0.0182985 0.0887351i
\(229\) 9.82141 + 17.0112i 0.649017 + 1.12413i 0.983358 + 0.181679i \(0.0581530\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(230\) −17.9196 + 31.0377i −1.18158 + 2.04656i
\(231\) 0 0
\(232\) −1.60507 2.78007i −0.105378 0.182521i
\(233\) −4.48143 + 7.76207i −0.293588 + 0.508510i −0.974656 0.223711i \(-0.928183\pi\)
0.681067 + 0.732221i \(0.261516\pi\)
\(234\) −4.08836 3.04695i −0.267265 0.199185i
\(235\) −4.78366 8.28554i −0.312052 0.540489i
\(236\) 7.88874 0.513513
\(237\) 9.17123 8.15747i 0.595735 0.529884i
\(238\) 0 0
\(239\) −5.61126 + 9.71899i −0.362963 + 0.628670i −0.988447 0.151567i \(-0.951568\pi\)
0.625484 + 0.780237i \(0.284901\pi\)
\(240\) −29.4233 9.75822i −1.89926 0.629890i
\(241\) −3.49312 + 6.05026i −0.225012 + 0.389732i −0.956323 0.292312i \(-0.905575\pi\)
0.731311 + 0.682044i \(0.238909\pi\)
\(242\) 2.63348 + 4.56131i 0.169286 + 0.293212i
\(243\) 13.7305 7.38061i 0.880812 0.473466i
\(244\) −3.44506 −0.220547
\(245\) 0 0
\(246\) −3.21751 15.6027i −0.205141 0.994792i
\(247\) 0.444368 + 0.769668i 0.0282745 + 0.0489728i
\(248\) −13.1978 −0.838059
\(249\) 6.75890 + 2.24159i 0.428328 + 0.142055i
\(250\) 17.5426 1.10949
\(251\) −4.62041 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(252\) 0 0
\(253\) −16.5178 −1.03847
\(254\) 16.9752 1.06512
\(255\) −5.16071 25.0259i −0.323176 1.56718i
\(256\) 17.7417 1.10886
\(257\) −0.712008 1.23323i −0.0444138 0.0769270i 0.842964 0.537970i \(-0.180809\pi\)
−0.887378 + 0.461043i \(0.847475\pi\)
\(258\) 14.5581 + 4.82819i 0.906348 + 0.300590i
\(259\) 0 0
\(260\) −3.18911 −0.197780
\(261\) 4.68292 2.01715i 0.289865 0.124859i
\(262\) 13.6421 + 23.6289i 0.842814 + 1.45980i
\(263\) −8.13162 + 14.0844i −0.501417 + 0.868480i 0.498582 + 0.866843i \(0.333854\pi\)
−0.999999 + 0.00163692i \(0.999479\pi\)
\(264\) −1.85717 9.00602i −0.114301 0.554282i
\(265\) 0.221840 0.384237i 0.0136275 0.0236035i
\(266\) 0 0
\(267\) 3.36151 + 16.3010i 0.205721 + 0.997604i
\(268\) 10.9395 0.668235
\(269\) −9.32691 16.1547i −0.568672 0.984969i −0.996698 0.0812022i \(-0.974124\pi\)
0.428026 0.903767i \(-0.359209\pi\)
\(270\) 13.4153 28.7112i 0.816428 1.74731i
\(271\) 1.98143 3.43194i 0.120363 0.208475i −0.799548 0.600603i \(-0.794927\pi\)
0.919911 + 0.392127i \(0.128261\pi\)
\(272\) 10.2527 + 17.7582i 0.621662 + 1.07675i
\(273\) 0 0
\(274\) 11.0371 19.1168i 0.666773 1.15489i
\(275\) 11.0698 + 19.1734i 0.667534 + 1.15620i
\(276\) 8.58582 + 2.84748i 0.516805 + 0.171398i
\(277\) 1.16690 2.02112i 0.0701120 0.121438i −0.828838 0.559488i \(-0.810998\pi\)
0.898950 + 0.438051i \(0.144331\pi\)
\(278\) 0.944368 1.63569i 0.0566394 0.0981024i
\(279\) 2.44437 20.8199i 0.146340 1.24645i
\(280\) 0 0
\(281\) −13.9975 24.2443i −0.835018 1.44629i −0.894016 0.448035i \(-0.852124\pi\)
0.0589978 0.998258i \(-0.481210\pi\)
\(282\) −5.86467 + 5.21640i −0.349236 + 0.310632i
\(283\) −10.3200 −0.613462 −0.306731 0.951796i \(-0.599235\pi\)
−0.306731 + 0.951796i \(0.599235\pi\)
\(284\) −2.55632 −0.151690
\(285\) −4.12729 + 3.67107i −0.244479 + 0.217455i
\(286\) −2.38874 4.13741i −0.141249 0.244650i
\(287\) 0 0
\(288\) −1.64400 + 14.0027i −0.0968734 + 0.825117i
\(289\) 0.0487535 0.0844436i 0.00286785 0.00496727i
\(290\) 5.18292 8.97708i 0.304351 0.527152i
\(291\) −12.0364 3.99186i −0.705585 0.234007i
\(292\) −4.72872 8.19038i −0.276727 0.479306i
\(293\) −15.3480 + 26.5834i −0.896637 + 1.55302i −0.0648718 + 0.997894i \(0.520664\pi\)
−0.831765 + 0.555127i \(0.812670\pi\)
\(294\) 0 0
\(295\) −15.9258 27.5843i −0.927236 1.60602i
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) 14.5512 1.26174i 0.844348 0.0732133i
\(298\) −7.16621 12.4122i −0.415127 0.719021i
\(299\) −5.87636 −0.339838
\(300\) −2.44870 11.8745i −0.141376 0.685575i
\(301\) 0 0
\(302\) 12.6211 21.8604i 0.726262 1.25792i
\(303\) 1.21201 + 5.87741i 0.0696280 + 0.337648i
\(304\) 2.21634 3.83881i 0.127116 0.220171i
\(305\) 6.95489 + 12.0462i 0.398236 + 0.689765i
\(306\) −19.2527 + 8.29305i −1.10060 + 0.474082i
\(307\) 11.4437 0.653125 0.326563 0.945176i \(-0.394110\pi\)
0.326563 + 0.945176i \(0.394110\pi\)
\(308\) 0 0
\(309\) 26.1007 + 8.65628i 1.48482 + 0.492439i
\(310\) −21.3083 36.9071i −1.21023 2.09618i
\(311\) −11.9629 −0.678352 −0.339176 0.940723i \(-0.610148\pi\)
−0.339176 + 0.940723i \(0.610148\pi\)
\(312\) −0.660706 3.20397i −0.0374051 0.181389i
\(313\) 13.5439 0.765549 0.382774 0.923842i \(-0.374969\pi\)
0.382774 + 0.923842i \(0.374969\pi\)
\(314\) −4.90978 −0.277075
\(315\) 0 0
\(316\) −6.29803 −0.354292
\(317\) −29.9629 −1.68288 −0.841441 0.540349i \(-0.818292\pi\)
−0.841441 + 0.540349i \(0.818292\pi\)
\(318\) −0.345483 0.114580i −0.0193738 0.00642530i
\(319\) 4.77747 0.267487
\(320\) −3.56615 6.17676i −0.199354 0.345291i
\(321\) 1.87271 + 9.08138i 0.104525 + 0.506873i
\(322\) 0 0
\(323\) 3.65383 0.203304
\(324\) −7.78111 1.85263i −0.432284 0.102924i
\(325\) 3.93818 + 6.82112i 0.218451 + 0.378368i
\(326\) 8.76076 15.1741i 0.485214 0.840415i
\(327\) −31.0123 10.2852i −1.71498 0.568774i
\(328\) 5.11058 8.85178i 0.282184 0.488758i
\(329\) 0 0
\(330\) 22.1866 19.7341i 1.22133 1.08633i
\(331\) 2.08650 0.114685 0.0573423 0.998355i \(-0.481737\pi\)
0.0573423 + 0.998355i \(0.481737\pi\)
\(332\) −1.82691 3.16431i −0.100265 0.173664i
\(333\) 11.4622 + 8.54245i 0.628123 + 0.468124i
\(334\) 10.3269 17.8867i 0.565064 0.978719i
\(335\) −22.0846 38.2517i −1.20661 2.08992i
\(336\) 0 0
\(337\) 8.10439 14.0372i 0.441474 0.764655i −0.556325 0.830965i \(-0.687789\pi\)
0.997799 + 0.0663093i \(0.0211224\pi\)
\(338\) 10.1978 + 17.6631i 0.554686 + 0.960743i
\(339\) 6.48948 + 31.4695i 0.352460 + 1.70919i
\(340\) −6.55563 + 11.3547i −0.355529 + 0.615794i
\(341\) 9.82072 17.0100i 0.531822 0.921143i
\(342\) 3.63348 + 2.70793i 0.196476 + 0.146428i
\(343\) 0 0
\(344\) 4.92030 + 8.52220i 0.265285 + 0.459486i
\(345\) −7.37636 35.7703i −0.397130 1.92581i
\(346\) 11.2335 0.603918
\(347\) 11.2670 0.604842 0.302421 0.953175i \(-0.402205\pi\)
0.302421 + 0.953175i \(0.402205\pi\)
\(348\) −2.48329 0.823583i −0.133118 0.0441487i
\(349\) −0.0988844 0.171273i −0.00529316 0.00916803i 0.863367 0.504577i \(-0.168352\pi\)
−0.868660 + 0.495409i \(0.835018\pi\)
\(350\) 0 0
\(351\) 5.17673 0.448873i 0.276313 0.0239591i
\(352\) −6.60507 + 11.4403i −0.352052 + 0.609771i
\(353\) −6.25093 + 10.8269i −0.332703 + 0.576259i −0.983041 0.183386i \(-0.941294\pi\)
0.650338 + 0.759645i \(0.274627\pi\)
\(354\) −19.5247 + 17.3665i −1.03773 + 0.923018i
\(355\) 5.16071 + 8.93861i 0.273902 + 0.474412i
\(356\) 4.27011 7.39605i 0.226315 0.391990i
\(357\) 0 0
\(358\) 3.26578 + 5.65650i 0.172602 + 0.298955i
\(359\) −10.0098 + 17.3375i −0.528299 + 0.915040i 0.471157 + 0.882049i \(0.343837\pi\)
−0.999456 + 0.0329908i \(0.989497\pi\)
\(360\) 18.6737 8.04364i 0.984190 0.423937i
\(361\) 9.10507 + 15.7705i 0.479214 + 0.830024i
\(362\) −31.5155 −1.65642
\(363\) −5.09455 1.68961i −0.267395 0.0886814i
\(364\) 0 0
\(365\) −19.0927 + 33.0695i −0.999357 + 1.73094i
\(366\) 8.52654 7.58404i 0.445689 0.396424i
\(367\) 15.0364 26.0438i 0.784892 1.35947i −0.144171 0.989553i \(-0.546052\pi\)
0.929063 0.369921i \(-0.120615\pi\)
\(368\) 14.6545 + 25.3824i 0.763919 + 1.32315i
\(369\) 13.0174 + 9.70152i 0.677659 + 0.505041i
\(370\) 29.0617 1.51085
\(371\) 0 0
\(372\) −8.03706 + 7.14867i −0.416702 + 0.370641i
\(373\) −3.50619 6.07290i −0.181544 0.314443i 0.760863 0.648913i \(-0.224776\pi\)
−0.942406 + 0.334470i \(0.891443\pi\)
\(374\) −19.6414 −1.01564
\(375\) −13.3578 + 11.8813i −0.689793 + 0.613545i
\(376\) −5.03576 −0.259700
\(377\) 1.69963 0.0875353
\(378\) 0 0
\(379\) −19.0741 −0.979772 −0.489886 0.871787i \(-0.662962\pi\)
−0.489886 + 0.871787i \(0.662962\pi\)
\(380\) 2.83427 0.145395
\(381\) −12.9258 + 11.4970i −0.662209 + 0.589010i
\(382\) 7.87636 0.402989
\(383\) 1.60507 + 2.78007i 0.0820155 + 0.142055i 0.904116 0.427288i \(-0.140531\pi\)
−0.822100 + 0.569343i \(0.807198\pi\)
\(384\) −16.5364 + 14.7085i −0.843868 + 0.750590i
\(385\) 0 0
\(386\) −42.9949 −2.18838
\(387\) −14.3553 + 6.18351i −0.729722 + 0.314325i
\(388\) 3.25340 + 5.63506i 0.165166 + 0.286077i
\(389\) −2.56801 + 4.44793i −0.130203 + 0.225519i −0.923755 0.382984i \(-0.874896\pi\)
0.793552 + 0.608503i \(0.208230\pi\)
\(390\) 7.89307 7.02059i 0.399681 0.355501i
\(391\) −12.0796 + 20.9225i −0.610893 + 1.05810i
\(392\) 0 0
\(393\) −26.3912 8.75264i −1.33126 0.441512i
\(394\) 18.2212 0.917968
\(395\) 12.7145 + 22.0221i 0.639735 + 1.10805i
\(396\) −6.00914 4.47846i −0.301971 0.225051i
\(397\) 11.4691 19.8650i 0.575615 0.996995i −0.420359 0.907358i \(-0.638096\pi\)
0.995975 0.0896370i \(-0.0285707\pi\)
\(398\) −7.44987 12.9036i −0.373428 0.646797i
\(399\) 0 0
\(400\) 19.6421 34.0212i 0.982107 1.70106i
\(401\) 9.10507 + 15.7705i 0.454686 + 0.787539i 0.998670 0.0515566i \(-0.0164183\pi\)
−0.543984 + 0.839095i \(0.683085\pi\)
\(402\) −27.0753 + 24.0825i −1.35039 + 1.20112i
\(403\) 3.49381 6.05146i 0.174039 0.301445i
\(404\) 1.53961 2.66668i 0.0765985 0.132672i
\(405\) 9.23050 + 30.9481i 0.458667 + 1.53782i
\(406\) 0 0
\(407\) 6.69708 + 11.5997i 0.331962 + 0.574975i
\(408\) −12.7658 4.23377i −0.632000 0.209603i
\(409\) 15.3324 0.758139 0.379070 0.925368i \(-0.376244\pi\)
0.379070 + 0.925368i \(0.376244\pi\)
\(410\) 33.0049 1.63000
\(411\) 4.54325 + 22.0317i 0.224102 + 1.08674i
\(412\) −7.05494 12.2195i −0.347572 0.602013i
\(413\) 0 0
\(414\) −27.5185 + 11.8535i −1.35246 + 0.582568i
\(415\) −7.37636 + 12.7762i −0.362091 + 0.627160i
\(416\) −2.34981 + 4.07000i −0.115209 + 0.199548i
\(417\) 0.388736 + 1.88510i 0.0190365 + 0.0923138i
\(418\) 2.12296 + 3.67707i 0.103837 + 0.179851i
\(419\) 5.28435 9.15276i 0.258157 0.447142i −0.707591 0.706622i \(-0.750218\pi\)
0.965748 + 0.259481i \(0.0835513\pi\)
\(420\) 0 0
\(421\) 18.0858 + 31.3256i 0.881449 + 1.52671i 0.849731 + 0.527217i \(0.176765\pi\)
0.0317181 + 0.999497i \(0.489902\pi\)
\(422\) −8.94870 + 15.4996i −0.435616 + 0.754509i
\(423\) 0.932677 7.94406i 0.0453483 0.386253i
\(424\) −0.116765 0.202243i −0.00567062 0.00982181i
\(425\) 32.3818 1.57075
\(426\) 6.32691 5.62755i 0.306540 0.272656i
\(427\) 0 0
\(428\) 2.37890 4.12038i 0.114989 0.199166i
\(429\) 4.62110 + 1.53259i 0.223109 + 0.0739939i
\(430\) −15.8880 + 27.5189i −0.766190 + 1.32708i
\(431\) −17.5494 30.3965i −0.845327 1.46415i −0.885337 0.464950i \(-0.846072\pi\)
0.0400101 0.999199i \(-0.487261\pi\)
\(432\) −14.8486 21.2410i −0.714406 1.02196i
\(433\) 41.1730 1.97865 0.989324 0.145731i \(-0.0465533\pi\)
0.989324 + 0.145731i \(0.0465533\pi\)
\(434\) 0 0
\(435\) 2.13348 + 10.3459i 0.102292 + 0.496047i
\(436\) 8.38255 + 14.5190i 0.401451 + 0.695334i
\(437\) 5.22253 0.249827
\(438\) 29.7341 + 9.86132i 1.42075 + 0.471192i
\(439\) 4.67859 0.223297 0.111648 0.993748i \(-0.464387\pi\)
0.111648 + 0.993748i \(0.464387\pi\)
\(440\) 19.0507 0.908209
\(441\) 0 0
\(442\) −6.98762 −0.332367
\(443\) 30.1730 1.43356 0.716781 0.697298i \(-0.245615\pi\)
0.716781 + 0.697298i \(0.245615\pi\)
\(444\) −1.48143 7.18392i −0.0703056 0.340934i
\(445\) −34.4820 −1.63461
\(446\) −4.81639 8.34224i −0.228063 0.395016i
\(447\) 13.8633 + 4.59776i 0.655711 + 0.217466i
\(448\) 0 0
\(449\) 0.333792 0.0157526 0.00787632 0.999969i \(-0.497493\pi\)
0.00787632 + 0.999969i \(0.497493\pi\)
\(450\) 32.2014 + 23.9989i 1.51799 + 1.13132i
\(451\) 7.60576 + 13.1736i 0.358141 + 0.620319i
\(452\) 8.24357 14.2783i 0.387745 0.671594i
\(453\) 5.19530 + 25.1936i 0.244096 + 1.18370i
\(454\) −9.43199 + 16.3367i −0.442665 + 0.766719i
\(455\) 0 0
\(456\) 0.587193 + 2.84748i 0.0274979 + 0.133346i
\(457\) −19.3090 −0.903238 −0.451619 0.892211i \(-0.649153\pi\)
−0.451619 + 0.892211i \(0.649153\pi\)
\(458\) 16.6927 + 28.9127i 0.780001 + 1.35100i
\(459\) 9.04325 19.3542i 0.422103 0.903379i
\(460\) −9.37017 + 16.2296i −0.436886 + 0.756709i
\(461\) 19.5538 + 33.8681i 0.910710 + 1.57740i 0.813064 + 0.582175i \(0.197798\pi\)
0.0976463 + 0.995221i \(0.468869\pi\)
\(462\) 0 0
\(463\) −10.9382 + 18.9455i −0.508340 + 0.880471i 0.491613 + 0.870814i \(0.336407\pi\)
−0.999953 + 0.00965741i \(0.996926\pi\)
\(464\) −4.23855 7.34138i −0.196770 0.340815i
\(465\) 41.2218 + 13.6712i 1.91161 + 0.633986i
\(466\) −7.61677 + 13.1926i −0.352840 + 0.611137i
\(467\) −6.16002 + 10.6695i −0.285052 + 0.493724i −0.972622 0.232394i \(-0.925344\pi\)
0.687570 + 0.726118i \(0.258677\pi\)
\(468\) −2.13781 1.59325i −0.0988201 0.0736480i
\(469\) 0 0
\(470\) −8.13045 14.0823i −0.375029 0.649570i
\(471\) 3.73855 3.32530i 0.172263 0.153222i
\(472\) −16.7651 −0.771676
\(473\) −14.6452 −0.673385
\(474\) 15.5877 13.8647i 0.715966 0.636825i
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 0.340671 0.146743i 0.0155983 0.00671890i
\(478\) −9.53706 + 16.5187i −0.436215 + 0.755547i
\(479\) 6.74474 11.6822i 0.308175 0.533775i −0.669788 0.742552i \(-0.733615\pi\)
0.977963 + 0.208777i \(0.0669484\pi\)
\(480\) −27.7243 9.19476i −1.26544 0.419682i
\(481\) 2.38255 + 4.12669i 0.108635 + 0.188161i
\(482\) −5.93701 + 10.2832i −0.270423 + 0.468387i
\(483\) 0 0
\(484\) 1.37704 + 2.38511i 0.0625929 + 0.108414i
\(485\) 13.1359 22.7521i 0.596473 1.03312i
\(486\) 23.3367 12.5443i 1.05858 0.569020i
\(487\) −3.77197 6.53324i −0.170924 0.296050i 0.767819 0.640667i \(-0.221342\pi\)
−0.938743 + 0.344617i \(0.888009\pi\)
\(488\) 7.32141 0.331425
\(489\) 3.60624 + 17.4878i 0.163080 + 0.790826i
\(490\) 0 0
\(491\) 8.06979 13.9773i 0.364185 0.630786i −0.624460 0.781057i \(-0.714681\pi\)
0.988645 + 0.150270i \(0.0480143\pi\)
\(492\) −1.68244 8.15866i −0.0758501 0.367821i
\(493\) 3.49381 6.05146i 0.157353 0.272544i
\(494\) 0.755260 + 1.30815i 0.0339808 + 0.0588564i
\(495\) −3.52840 + 30.0531i −0.158590 + 1.35079i
\(496\) −34.8516 −1.56488
\(497\) 0 0
\(498\) 11.4876 + 3.80987i 0.514773 + 0.170724i
\(499\) 15.4327 + 26.7302i 0.690862 + 1.19661i 0.971556 + 0.236810i \(0.0761019\pi\)
−0.280694 + 0.959797i \(0.590565\pi\)
\(500\) 9.17301 0.410229
\(501\) 4.25093 + 20.6141i 0.189918 + 0.920970i
\(502\) −7.85297 −0.350495
\(503\) −24.6304 −1.09822 −0.549109 0.835751i \(-0.685033\pi\)
−0.549109 + 0.835751i \(0.685033\pi\)
\(504\) 0 0
\(505\) −12.4327 −0.553247
\(506\) −28.0741 −1.24805
\(507\) −19.7280 6.54277i −0.876149 0.290575i
\(508\) 8.87636 0.393825
\(509\) 6.79487 + 11.7691i 0.301177 + 0.521654i 0.976403 0.215957i \(-0.0692870\pi\)
−0.675226 + 0.737611i \(0.735954\pi\)
\(510\) −8.77128 42.5347i −0.388399 1.88347i
\(511\) 0 0
\(512\) 4.59937 0.203265
\(513\) −4.60074 + 0.398930i −0.203128 + 0.0176132i
\(514\) −1.21015 2.09604i −0.0533774 0.0924523i
\(515\) −28.4851 + 49.3376i −1.25520 + 2.17407i
\(516\) 7.61243 + 2.52466i 0.335119 + 0.111142i
\(517\) 3.74721 6.49036i 0.164802 0.285446i
\(518\) 0 0
\(519\) −8.55377 + 7.60826i −0.375469 + 0.333966i
\(520\) 6.77747 0.297212
\(521\) −19.5865 33.9248i −0.858100 1.48627i −0.873739 0.486396i \(-0.838311\pi\)
0.0156383 0.999878i \(-0.495022\pi\)
\(522\) 7.95922 3.42841i 0.348366 0.150057i
\(523\) 9.56182 16.5616i 0.418109 0.724187i −0.577640 0.816292i \(-0.696026\pi\)
0.995749 + 0.0921051i \(0.0293596\pi\)
\(524\) 7.13348 + 12.3555i 0.311627 + 0.539754i
\(525\) 0 0
\(526\) −13.8207 + 23.9382i −0.602612 + 1.04375i
\(527\) −14.3640 24.8791i −0.625705 1.08375i
\(528\) −4.90428 23.7824i −0.213431 1.03499i
\(529\) −5.76578 + 9.98663i −0.250686 + 0.434201i
\(530\) 0.377045 0.653061i 0.0163778 0.0283671i
\(531\) 3.10507 26.4474i 0.134749 1.14772i
\(532\) 0 0
\(533\) 2.70582 + 4.68661i 0.117202 + 0.203000i
\(534\) 5.71331 + 27.7056i 0.247239 + 1.19894i
\(535\) −19.2101 −0.830527
\(536\) −23.2485 −1.00418
\(537\) −6.31777 2.09529i −0.272632 0.0904183i
\(538\) −15.8523 27.4570i −0.683441 1.18375i
\(539\) 0 0
\(540\) 7.01485 15.0131i 0.301871 0.646061i
\(541\) −1.26509 + 2.19120i −0.0543906 + 0.0942072i −0.891939 0.452156i \(-0.850655\pi\)
0.837548 + 0.546363i \(0.183988\pi\)
\(542\) 3.36769 5.83302i 0.144655 0.250550i
\(543\) 23.9975 21.3448i 1.02983 0.915995i
\(544\) 9.66071 + 16.7328i 0.414199 + 0.717414i
\(545\) 33.8454 58.6220i 1.44978 2.51109i
\(546\) 0 0
\(547\) −8.92580 15.4599i −0.381640 0.661019i 0.609657 0.792665i \(-0.291307\pi\)
−0.991297 + 0.131646i \(0.957974\pi\)
\(548\) 5.77128 9.99615i 0.246537 0.427015i
\(549\) −1.35600 + 11.5497i −0.0578728 + 0.492931i
\(550\) 18.8145 + 32.5877i 0.802254 + 1.38955i
\(551\) −1.51052 −0.0643503
\(552\) −18.2465 6.05146i −0.776624 0.257567i
\(553\) 0 0
\(554\) 1.98329 3.43516i 0.0842619 0.145946i
\(555\) −22.1291 + 19.6830i −0.939327 + 0.835496i
\(556\) 0.493810 0.855304i 0.0209422 0.0362730i
\(557\) −20.6804 35.8195i −0.876255 1.51772i −0.855419 0.517936i \(-0.826701\pi\)
−0.0208360 0.999783i \(-0.506633\pi\)
\(558\) 4.15452 35.3860i 0.175875 1.49801i
\(559\) −5.21015 −0.220366
\(560\) 0 0
\(561\) 14.9560 13.3028i 0.631442 0.561644i
\(562\) −23.7905 41.2063i −1.00354 1.73818i
\(563\) 20.7366 0.873944 0.436972 0.899475i \(-0.356051\pi\)
0.436972 + 0.899475i \(0.356051\pi\)
\(564\) −3.06663 + 2.72766i −0.129129 + 0.114855i
\(565\) −66.5685 −2.80056
\(566\) −17.5402 −0.737271
\(567\) 0 0
\(568\) 5.43268 0.227950
\(569\) −0.268329 −0.0112489 −0.00562446 0.999984i \(-0.501790\pi\)
−0.00562446 + 0.999984i \(0.501790\pi\)
\(570\) −7.01485 + 6.23945i −0.293820 + 0.261342i
\(571\) 35.9367 1.50391 0.751953 0.659217i \(-0.229112\pi\)
0.751953 + 0.659217i \(0.229112\pi\)
\(572\) −1.24907 2.16345i −0.0522263 0.0904585i
\(573\) −5.99745 + 5.33451i −0.250547 + 0.222852i
\(574\) 0 0
\(575\) 46.2843 1.93019
\(576\) 0.695298 5.92218i 0.0289707 0.246758i
\(577\) 2.71565 + 4.70364i 0.113054 + 0.195815i 0.917000 0.398887i \(-0.130603\pi\)
−0.803946 + 0.594702i \(0.797270\pi\)
\(578\) 0.0828628 0.143523i 0.00344664 0.00596976i
\(579\) 32.7385 29.1197i 1.36056 1.21017i
\(580\) 2.71015 4.69412i 0.112533 0.194913i
\(581\) 0 0
\(582\) −20.4574 6.78468i −0.847985 0.281234i
\(583\) 0.347550 0.0143940
\(584\) 10.0494 + 17.4061i 0.415849 + 0.720271i
\(585\) −1.25526 + 10.6917i −0.0518986 + 0.442046i
\(586\) −26.0858 + 45.1820i −1.07760 + 1.86645i
\(587\) 17.5822 + 30.4532i 0.725694 + 1.25694i 0.958688 + 0.284461i \(0.0918145\pi\)
−0.232994 + 0.972478i \(0.574852\pi\)
\(588\) 0 0
\(589\) −3.10507 + 5.37815i −0.127942 + 0.221603i
\(590\) −27.0679 46.8830i −1.11437 1.93014i
\(591\) −13.8745 + 12.3408i −0.570721 + 0.507635i
\(592\) 11.8832 20.5824i 0.488398 0.845930i
\(593\) −16.7534 + 29.0177i −0.687980 + 1.19162i 0.284511 + 0.958673i \(0.408169\pi\)
−0.972490 + 0.232943i \(0.925164\pi\)
\(594\) 24.7317 2.14448i 1.01475 0.0879891i
\(595\) 0 0
\(596\) −3.74721 6.49036i −0.153492 0.265856i
\(597\) 14.4120 + 4.77975i 0.589846 + 0.195622i
\(598\) −9.98762 −0.408424
\(599\) 6.24729 0.255257 0.127629 0.991822i \(-0.459263\pi\)
0.127629 + 0.991822i \(0.459263\pi\)
\(600\) 5.20396 + 25.2356i 0.212451 + 1.03024i
\(601\) 11.2040 + 19.4058i 0.457019 + 0.791580i 0.998802 0.0489384i \(-0.0155838\pi\)
−0.541783 + 0.840519i \(0.682250\pi\)
\(602\) 0 0
\(603\) 4.30587 36.6752i 0.175349 1.49353i
\(604\) 6.59957 11.4308i 0.268533 0.465112i
\(605\) 5.55996 9.63014i 0.226045 0.391521i
\(606\) 2.05996 + 9.98940i 0.0836803 + 0.405792i
\(607\) 7.47524 + 12.9475i 0.303411 + 0.525523i 0.976906 0.213669i \(-0.0685413\pi\)
−0.673496 + 0.739191i \(0.735208\pi\)
\(608\) 2.08836 3.61715i 0.0846943 0.146695i
\(609\) 0 0
\(610\) 11.8207 + 20.4741i 0.478607 + 0.828972i
\(611\) 1.33310 2.30900i 0.0539316 0.0934123i
\(612\) −10.0672 + 4.33643i −0.406944 + 0.175290i
\(613\) −17.5989 30.4822i −0.710812 1.23116i −0.964553 0.263891i \(-0.914994\pi\)
0.253740 0.967272i \(-0.418339\pi\)
\(614\) 19.4500 0.784938
\(615\) −25.1316 + 22.3536i −1.01340 + 0.901386i
\(616\) 0 0
\(617\) 1.00619 1.74277i 0.0405077 0.0701614i −0.845061 0.534670i \(-0.820436\pi\)
0.885568 + 0.464509i \(0.153769\pi\)
\(618\) 44.3614 + 14.7125i 1.78448 + 0.591822i
\(619\) 19.6909 34.1056i 0.791444 1.37082i −0.133629 0.991031i \(-0.542663\pi\)
0.925073 0.379789i \(-0.124004\pi\)
\(620\) −11.1421 19.2987i −0.447479 0.775056i
\(621\) 12.9258 27.6636i 0.518694 1.11010i
\(622\) −20.3324 −0.815256
\(623\) 0 0
\(624\) −1.74474 8.46079i −0.0698455 0.338703i
\(625\) 1.17240 + 2.03065i 0.0468959 + 0.0812261i
\(626\) 23.0197 0.920051
\(627\) −4.10693 1.36206i −0.164015 0.0543956i
\(628\) −2.56732 −0.102447
\(629\) 19.5906 0.781126
\(630\) 0 0
\(631\) 44.3832 1.76687 0.883433 0.468558i \(-0.155226\pi\)
0.883433 + 0.468558i \(0.155226\pi\)
\(632\) 13.3845 0.532408
\(633\) −3.68361 17.8630i −0.146410 0.709989i
\(634\) −50.9257 −2.02252
\(635\) −17.9196 31.0377i −0.711118 1.23169i
\(636\) −0.180653 0.0599137i −0.00716337 0.00237573i
\(637\) 0 0
\(638\) 8.11993 0.321471
\(639\) −1.00619 + 8.57020i −0.0398043 + 0.339032i
\(640\) −22.9251 39.7075i −0.906195 1.56957i
\(641\) 7.49312 12.9785i 0.295961 0.512619i −0.679247 0.733909i \(-0.737694\pi\)
0.975208 + 0.221291i \(0.0710270\pi\)
\(642\) 3.18292 + 15.4350i 0.125620 + 0.609169i
\(643\) −5.32691 + 9.22649i −0.210073 + 0.363857i −0.951737 0.306914i \(-0.900703\pi\)
0.741664 + 0.670771i \(0.234037\pi\)
\(644\) 0 0
\(645\) −6.54009 31.7150i −0.257516 1.24878i
\(646\) 6.21015 0.244335
\(647\) 1.06478 + 1.84424i 0.0418606 + 0.0725047i 0.886197 0.463309i \(-0.153338\pi\)
−0.844336 + 0.535814i \(0.820005\pi\)
\(648\) 16.5364 + 3.93720i 0.649610 + 0.154668i
\(649\) 12.4752 21.6078i 0.489696 0.848178i
\(650\) 6.69344 + 11.5934i 0.262538 + 0.454730i
\(651\) 0 0
\(652\) 4.58100 7.93453i 0.179406 0.310740i
\(653\) −5.58582 9.67492i −0.218590 0.378609i 0.735787 0.677213i \(-0.236812\pi\)
−0.954377 + 0.298604i \(0.903479\pi\)
\(654\) −52.7094 17.4811i −2.06110 0.683564i
\(655\) 28.8022 49.8868i 1.12539 1.94924i
\(656\) 13.4956 23.3751i 0.526914 0.912642i
\(657\) −29.3200 + 12.6295i −1.14388 + 0.492723i
\(658\) 0 0
\(659\) 5.65452 + 9.79391i 0.220269 + 0.381517i 0.954890 0.296961i \(-0.0959733\pi\)
−0.734621 + 0.678478i \(0.762640\pi\)
\(660\) 11.6014 10.3190i 0.451582 0.401666i
\(661\) −32.3570 −1.25854 −0.629271 0.777186i \(-0.716646\pi\)
−0.629271 + 0.777186i \(0.716646\pi\)
\(662\) 3.54628 0.137830
\(663\) 5.32072 4.73259i 0.206640 0.183798i
\(664\) 3.88255 + 6.72477i 0.150672 + 0.260972i
\(665\) 0 0
\(666\) 19.4814 + 14.5190i 0.754890 + 0.562600i
\(667\) 4.99381 8.64953i 0.193361 0.334911i
\(668\) 5.39995 9.35298i 0.208930 0.361878i
\(669\) 9.31749 + 3.09014i 0.360235 + 0.119472i
\(670\) −37.5357 65.0137i −1.45013 2.51170i
\(671\) −5.44801 + 9.43623i −0.210318 + 0.364282i
\(672\) 0 0
\(673\) 12.0803 + 20.9237i 0.465662 + 0.806550i 0.999231 0.0392063i \(-0.0124830\pi\)
−0.533569 + 0.845756i \(0.679150\pi\)
\(674\) 13.7744 23.8580i 0.530572 0.918977i
\(675\) −40.7738 + 3.53549i −1.56938 + 0.136081i
\(676\) 5.33242 + 9.23601i 0.205093 + 0.355231i
\(677\) −25.0741 −0.963677 −0.481838 0.876260i \(-0.660031\pi\)
−0.481838 + 0.876260i \(0.660031\pi\)
\(678\) 11.0297 + 53.4865i 0.423593 + 2.05414i
\(679\) 0 0
\(680\) 13.9320 24.1309i 0.534267 0.925378i
\(681\) −3.88255 18.8277i −0.148779 0.721478i
\(682\) 16.6916 28.9107i 0.639154 1.10705i
\(683\) 23.8392 + 41.2907i 0.912182 + 1.57995i 0.810975 + 0.585081i \(0.198937\pi\)
0.101207 + 0.994865i \(0.467729\pi\)
\(684\) 1.89995 + 1.41598i 0.0726462 + 0.0541413i
\(685\) −46.6043 −1.78066
\(686\) 0 0
\(687\) −32.2927 10.7099i −1.23204 0.408607i
\(688\) 12.9931 + 22.5047i 0.495358 + 0.857985i
\(689\) 0.123644 0.00471046
\(690\) −12.5371 60.7961i −0.477278 2.31447i
\(691\) 24.6800 0.938870 0.469435 0.882967i \(-0.344458\pi\)
0.469435 + 0.882967i \(0.344458\pi\)
\(692\) 5.87402 0.223297
\(693\) 0 0
\(694\) 19.1496 0.726910
\(695\) −3.98762 −0.151259
\(696\) 5.27747 + 1.75027i 0.200042 + 0.0663439i
\(697\) 22.2487 0.842728
\(698\) −0.168067 0.291100i −0.00636142 0.0110183i
\(699\) −3.13533 15.2042i −0.118589 0.575076i
\(700\) 0 0
\(701\) −29.6784 −1.12094 −0.560469 0.828175i \(-0.689379\pi\)
−0.560469 + 0.828175i \(0.689379\pi\)
\(702\) 8.79851 0.762918i 0.332078 0.0287945i
\(703\) −2.11745 3.66754i −0.0798613 0.138324i
\(704\) 2.79349 4.83847i 0.105284 0.182357i
\(705\) 15.7286 + 5.21640i 0.592375 + 0.196461i
\(706\) −10.6243 + 18.4018i −0.399849 + 0.692559i
\(707\) 0 0
\(708\) −10.2095 + 9.08094i −0.383695 + 0.341282i
\(709\) −29.2581 −1.09881 −0.549406 0.835555i \(-0.685146\pi\)
−0.549406 + 0.835555i \(0.685146\pi\)
\(710\) 8.77128 + 15.1923i 0.329180 + 0.570157i
\(711\) −2.47896 + 21.1145i −0.0929682 + 0.791855i
\(712\) −9.07481 + 15.7180i −0.340093 + 0.589058i
\(713\) −20.5309 35.5605i −0.768887 1.33175i
\(714\) 0 0
\(715\) −5.04325 + 8.73517i −0.188607 + 0.326677i
\(716\) 1.70768 + 2.95778i 0.0638189 + 0.110538i
\(717\) −3.92580 19.0374i −0.146612 0.710966i
\(718\) −17.0130 + 29.4674i −0.634919 + 1.09971i
\(719\) 0.537063 0.930220i 0.0200291 0.0346913i −0.855837 0.517245i \(-0.826957\pi\)
0.875866 + 0.482554i \(0.160291\pi\)
\(720\) 49.3120 21.2410i 1.83775 0.791605i
\(721\) 0 0
\(722\) 15.4752 + 26.8039i 0.575929 + 0.997538i
\(723\) −2.44389 11.8512i −0.0908891 0.440750i
\(724\) −16.4794 −0.612454
\(725\) −13.3869 −0.497176
\(726\) −8.65885 2.87171i −0.321360 0.106579i
\(727\) 12.7163 + 22.0253i 0.471623 + 0.816875i 0.999473 0.0324628i \(-0.0103350\pi\)
−0.527850 + 0.849338i \(0.677002\pi\)
\(728\) 0 0
\(729\) −9.27375 + 25.3574i −0.343472 + 0.939163i
\(730\) −32.4505 + 56.2059i −1.20105 + 2.08027i
\(731\) −10.7101 + 18.5505i −0.396129 + 0.686116i
\(732\) 4.45853 3.96570i 0.164792 0.146576i
\(733\) −5.69777 9.86883i −0.210452 0.364513i 0.741404 0.671059i \(-0.234160\pi\)
−0.951856 + 0.306545i \(0.900827\pi\)
\(734\) 25.5562 44.2647i 0.943298 1.63384i
\(735\) 0 0
\(736\) 13.8083 + 23.9168i 0.508982 + 0.881583i
\(737\) 17.2997 29.9639i 0.637242 1.10374i
\(738\) 22.1247 + 16.4890i 0.814423 + 0.606968i
\(739\) 14.9697 + 25.9283i 0.550671 + 0.953790i 0.998226 + 0.0595336i \(0.0189613\pi\)
−0.447556 + 0.894256i \(0.647705\pi\)
\(740\) 15.1964 0.558630
\(741\) −1.46108 0.484566i −0.0536740 0.0178010i
\(742\) 0 0
\(743\) 9.50069 16.4557i 0.348546 0.603700i −0.637445 0.770496i \(-0.720009\pi\)
0.985991 + 0.166796i \(0.0533420\pi\)
\(744\) 17.0803 15.1923i 0.626195 0.556977i
\(745\) −15.1298 + 26.2055i −0.554311 + 0.960096i
\(746\) −5.95922 10.3217i −0.218183 0.377903i
\(747\) −11.3276 + 4.87933i −0.414455 + 0.178525i
\(748\) −10.2705 −0.375527
\(749\) 0 0
\(750\) −22.7033 + 20.1937i −0.829006 + 0.737370i
\(751\) −0.0130684 0.0226352i −0.000476873 0.000825969i 0.865787 0.500413i \(-0.166818\pi\)
−0.866264 + 0.499587i \(0.833485\pi\)
\(752\) −13.2980 −0.484929
\(753\) 5.97965 5.31867i 0.217910 0.193823i
\(754\) 2.88874 0.105202
\(755\) −53.2929 −1.93953
\(756\) 0 0
\(757\) −13.6910 −0.497607 −0.248803 0.968554i \(-0.580037\pi\)
−0.248803 + 0.968554i \(0.580037\pi\)
\(758\) −32.4189 −1.17751
\(759\) 21.3770 19.0141i 0.775938 0.690168i
\(760\) −6.02338 −0.218491
\(761\) −7.32141 12.6811i −0.265401 0.459688i 0.702268 0.711913i \(-0.252171\pi\)
−0.967669 + 0.252225i \(0.918838\pi\)
\(762\) −21.9691 + 19.5407i −0.795855 + 0.707883i
\(763\) 0 0
\(764\) 4.11855 0.149004
\(765\) 35.4869 + 26.4474i 1.28303 + 0.956208i
\(766\) 2.72803 + 4.72509i 0.0985677 + 0.170724i
\(767\) 4.43818 7.68715i 0.160253 0.277567i
\(768\) −22.9610 + 20.4230i −0.828534 + 0.736950i
\(769\) 24.5672 42.5517i 0.885918 1.53445i 0.0412592 0.999148i \(-0.486863\pi\)
0.844658 0.535306i \(-0.179804\pi\)
\(770\) 0 0
\(771\) 2.34108 + 0.776418i 0.0843118 + 0.0279620i
\(772\) −22.4820 −0.809146
\(773\) 6.22067 + 10.7745i 0.223742 + 0.387532i 0.955941 0.293558i \(-0.0948394\pi\)
−0.732199 + 0.681090i \(0.761506\pi\)
\(774\) −24.3987 + 10.5097i −0.876993 + 0.377762i
\(775\) −27.5185 + 47.6634i −0.988493 + 1.71212i
\(776\) −6.91411 11.9756i −0.248202 0.429898i
\(777\) 0 0
\(778\) −4.36467 + 7.55982i −0.156481 + 0.271033i
\(779\) −2.40476 4.16516i −0.0861594 0.149232i
\(780\) 4.12729