Properties

Label 441.2.h.b.214.3
Level $441$
Weight $2$
Character 441.214
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 214.3
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.b.373.3

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.115661 + 0.993289i \(0.463101\pi\)
−0.918044 + 0.396479i \(0.870232\pi\)
\(6\) −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 0.996304 0.0859026i \(-0.0273774\pi\)
−0.572546 + 0.819873i \(0.694044\pi\)
\(12\) −1.15019 1.02305i −0.332030 0.295328i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 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 −0.999999 0.00165734i \(-0.999472\pi\)
0.501435 + 0.865196i \(0.332806\pi\)
\(18\) 0.594554 + 5.06410i 0.140138 + 1.19362i
\(19\) −0.444368 0.769668i −0.101945 0.176574i 0.810541 0.585682i \(-0.199173\pi\)
−0.912486 + 0.409108i \(0.865840\pi\)
\(20\) −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 0.378139 + 0.925749i \(0.376564\pi\)
−0.990792 + 0.135396i \(0.956769\pi\)
\(24\) 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 −0.776271 0.630399i \(-0.782891\pi\)
0.934077 + 0.357071i \(0.116224\pi\)
\(30\) 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 0.600984 0.799261i \(-0.294775\pi\)
−0.992672 + 0.120837i \(0.961442\pi\)
\(38\) −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 0.573613 0.819126i \(-0.305541\pi\)
−0.996191 + 0.0872002i \(0.972208\pi\)
\(42\) 0 0
\(43\) −2.60507 + 4.51212i −0.397270 + 0.688092i −0.993388 0.114805i \(-0.963376\pi\)
0.596118 + 0.802897i \(0.296709\pi\)
\(44\) 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 −0.861748 0.507336i \(-0.830630\pi\)
0.870240 + 0.492628i \(0.163964\pi\)
\(54\) 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 0.366229 + 0.930525i \(0.380649\pi\)
−0.988973 + 0.148099i \(0.952685\pi\)
\(74\) −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 −0.956510 0.291700i \(-0.905779\pi\)
0.730875 + 0.682512i \(0.239112\pi\)
\(84\) 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 0.999942 + 0.0107692i \(0.00342802\pi\)
−0.490645 + 0.871360i \(0.663239\pi\)
\(90\) −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 −0.618137 0.786070i \(-0.712112\pi\)
0.989825 + 0.142287i \(0.0454456\pi\)
\(98\) 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 0.939250 0.343233i \(-0.111522\pi\)
−0.766874 + 0.641798i \(0.778189\pi\)
\(102\) 11.4876 3.80987i 1.13744 0.377233i
\(103\) −7.93818 + 13.7493i −0.782172 + 1.35476i 0.148502 + 0.988912i \(0.452555\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(104\) −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 0.965912 0.258869i \(-0.0833498\pi\)
−0.707143 + 0.707070i \(0.750016\pi\)
\(108\) 2.64586 3.78490i 0.254598 0.364202i
\(109\) 9.43199 16.3367i 0.903421 1.56477i 0.0803973 0.996763i \(-0.474381\pi\)
0.823023 0.568008i \(-0.192286\pi\)
\(110\) −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 0.859322 + 0.511434i \(0.170886\pi\)
0.0132538 + 0.999912i \(0.495781\pi\)
\(114\) −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 −0.266734 0.963770i \(-0.585945\pi\)
0.968017 0.250886i \(-0.0807220\pi\)
\(132\) 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 0.997919 + 0.0644834i \(0.0205400\pi\)
−0.443115 + 0.896465i \(0.646127\pi\)
\(138\) 16.4196 5.44556i 1.39773 0.463557i
\(139\) 0.555632 + 0.962383i 0.0471281 + 0.0816283i 0.888627 0.458630i \(-0.151660\pi\)
−0.841499 + 0.540259i \(0.818326\pi\)
\(140\) 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 −0.985429 0.170086i \(-0.945595\pi\)
0.640013 + 0.768364i \(0.278929\pi\)
\(150\) −4.68292 + 22.7089i −0.382359 + 1.85418i
\(151\) 7.42580 + 12.8619i 0.604303 + 1.04668i 0.992161 + 0.124964i \(0.0398816\pi\)
−0.387858 + 0.921719i \(0.626785\pi\)
\(152\) 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 0.994173 0.107796i \(-0.0343792\pi\)
−0.590440 + 0.807081i \(0.701046\pi\)
\(164\) −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 0.999418 0.0341045i \(-0.0108579\pi\)
−0.529244 + 0.848469i \(0.677525\pi\)
\(168\) 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 −0.785239 0.619193i \(-0.787460\pi\)
0.928856 + 0.370440i \(0.120793\pi\)
\(180\) −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 −0.978518 0.206160i \(-0.933903\pi\)
0.667799 + 0.744342i \(0.267237\pi\)
\(200\) 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 0.625902 0.779902i \(-0.284731\pi\)
−0.988366 + 0.152096i \(0.951398\pi\)
\(212\) 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 −0.945172 0.326574i \(-0.894106\pi\)
0.755407 + 0.655256i \(0.227439\pi\)
\(224\) 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 0.620975 0.783830i \(-0.286737\pi\)
−0.989304 + 0.145865i \(0.953403\pi\)
\(228\) −0.276301 + 1.33987i −0.0182985 + 0.0887351i
\(229\) 9.82141 17.0112i 0.649017 1.12413i −0.334341 0.942452i \(-0.608514\pi\)
0.983358 0.181679i \(-0.0581530\pi\)
\(230\) −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 0.681067 0.732221i \(-0.261516\pi\)
−0.974656 + 0.223711i \(0.928183\pi\)
\(234\) −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 0.625484 0.780237i \(-0.284901\pi\)
−0.988447 + 0.151567i \(0.951568\pi\)
\(240\) −29.4233 + 9.75822i −1.89926 + 0.629890i
\(241\) −3.49312 6.05026i −0.225012 0.389732i 0.731311 0.682044i \(-0.238909\pi\)
−0.956323 + 0.292312i \(0.905575\pi\)
\(242\) 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 −0.887378 0.461043i \(-0.847475\pi\)
0.842964 + 0.537970i \(0.180809\pi\)
\(258\) 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 −0.999999 0.00163692i \(-0.999479\pi\)
0.498582 0.866843i \(-0.333854\pi\)
\(264\) −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 0.428026 + 0.903767i \(0.359209\pi\)
−0.996698 + 0.0812022i \(0.974124\pi\)
\(270\) 13.4153 + 28.7112i 0.816428 + 1.74731i
\(271\) 1.98143 + 3.43194i 0.120363 + 0.208475i 0.919911 0.392127i \(-0.128261\pi\)
−0.799548 + 0.600603i \(0.794927\pi\)
\(272\) 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 0.898950 0.438051i \(-0.144331\pi\)
−0.828838 + 0.559488i \(0.810998\pi\)
\(278\) 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 0.0589978 + 0.998258i \(0.481210\pi\)
−0.894016 + 0.448035i \(0.852124\pi\)
\(282\) −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 −0.831765 0.555127i \(-0.812670\pi\)
−0.0648718 0.997894i \(-0.520664\pi\)
\(294\) 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 0.997799 0.0663093i \(-0.0211224\pi\)
−0.556325 + 0.830965i \(0.687789\pi\)
\(338\) 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 −0.868660 0.495409i \(-0.835018\pi\)
0.863367 + 0.504577i \(0.168352\pi\)
\(350\) 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 0.650338 0.759645i \(-0.274627\pi\)
−0.983041 + 0.183386i \(0.941294\pi\)
\(354\) −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 −0.999456 0.0329908i \(-0.989497\pi\)
0.471157 0.882049i \(-0.343837\pi\)
\(360\) 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 0.929063 + 0.369921i \(0.120615\pi\)
−0.144171 + 0.989553i \(0.546052\pi\)
\(368\) 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 −0.942406 0.334470i \(-0.891443\pi\)
0.760863 + 0.648913i \(0.224776\pi\)
\(374\) −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 −0.822100 0.569343i \(-0.807198\pi\)
0.904116 + 0.427288i \(0.140531\pi\)
\(384\) −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 0.793552 0.608503i \(-0.208230\pi\)
−0.923755 + 0.382984i \(0.874896\pi\)
\(390\) 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 0.995975 + 0.0896370i \(0.0285707\pi\)
−0.420359 + 0.907358i \(0.638096\pi\)
\(398\) −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 −0.543984 0.839095i \(-0.683085\pi\)
0.998670 + 0.0515566i \(0.0164183\pi\)
\(402\) −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 0.965748 0.259481i \(-0.0835513\pi\)
−0.707591 + 0.706622i \(0.750218\pi\)
\(420\) 0 0
\(421\) 18.0858 31.3256i 0.881449 1.52671i 0.0317181 0.999497i \(-0.489902\pi\)
0.849731 0.527217i \(-0.176765\pi\)
\(422\) −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 0.0400101 + 0.999199i \(0.487261\pi\)
−0.885337 + 0.464950i \(0.846072\pi\)
\(432\) −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 0.0976463 0.995221i \(-0.468869\pi\)
0.813064 0.582175i \(-0.197798\pi\)
\(462\) 0 0
\(463\) −10.9382 18.9455i −0.508340 0.880471i −0.999953 0.00965741i \(-0.996926\pi\)
0.491613 0.870814i \(-0.336407\pi\)
\(464\) −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 0.687570 0.726118i \(-0.258677\pi\)
−0.972622 + 0.232394i \(0.925344\pi\)
\(468\) −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 0.977963 0.208777i \(-0.0669484\pi\)
−0.669788 + 0.742552i \(0.733615\pi\)
\(480\) −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 −0.938743 0.344617i \(-0.888009\pi\)
0.767819 + 0.640667i \(0.221342\pi\)
\(488\) 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 0.988645 0.150270i \(-0.0480143\pi\)
−0.624460 + 0.781057i \(0.714681\pi\)
\(492\) −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 −0.280694 0.959797i \(-0.590565\pi\)
0.971556 0.236810i \(-0.0761019\pi\)
\(500\) 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 −0.675226 0.737611i \(-0.735954\pi\)
0.976403 + 0.215957i \(0.0692870\pi\)
\(510\) −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 0.0156383 + 0.999878i \(0.495022\pi\)
−0.873739 + 0.486396i \(0.838311\pi\)
\(522\) 7.95922 + 3.42841i 0.348366 + 0.150057i
\(523\) 9.56182 + 16.5616i 0.418109 + 0.724187i 0.995749 0.0921051i \(-0.0293596\pi\)
−0.577640 + 0.816292i \(0.696026\pi\)
\(524\) 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 0.837548 0.546363i \(-0.183988\pi\)
−0.891939 + 0.452156i \(0.850655\pi\)
\(542\) 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 −0.991297 0.131646i \(-0.957974\pi\)
0.609657 + 0.792665i \(0.291307\pi\)
\(548\) 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 −0.0208360 + 0.999783i \(0.506633\pi\)
−0.855419 + 0.517936i \(0.826701\pi\)
\(558\) 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 −0.803946 0.594702i \(-0.797270\pi\)
0.917000 + 0.398887i \(0.130603\pi\)
\(578\) 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 −0.232994 0.972478i \(-0.574852\pi\)
0.958688 0.284461i \(-0.0918145\pi\)
\(588\) 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 −0.972490 0.232943i \(-0.925164\pi\)
0.284511 0.958673i \(-0.408169\pi\)
\(594\) 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 −0.541783 0.840519i \(-0.682250\pi\)
0.998802 + 0.0489384i \(0.0155838\pi\)
\(602\) 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 −0.673496 0.739191i \(-0.735208\pi\)
0.976906 + 0.213669i \(0.0685413\pi\)
\(608\) 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 0.253740 + 0.967272i \(0.418339\pi\)
−0.964553 + 0.263891i \(0.914994\pi\)
\(614\) 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 0.885568 0.464509i \(-0.153769\pi\)
−0.845061 + 0.534670i \(0.820436\pi\)
\(618\) 44.3614 14.7125i 1.78448 0.591822i
\(619\) 19.6909 + 34.1056i 0.791444 + 1.37082i 0.925073 + 0.379789i \(0.124004\pi\)
−0.133629 + 0.991031i \(0.542663\pi\)
\(620\) −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 0.975208 0.221291i \(-0.0710270\pi\)
−0.679247 + 0.733909i \(0.737694\pi\)
\(642\) 3.18292 15.4350i 0.125620 0.609169i
\(643\) −5.32691 9.22649i −0.210073 0.363857i 0.741664 0.670771i \(-0.234037\pi\)
−0.951737 + 0.306914i \(0.900703\pi\)
\(644\) 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 −0.844336 0.535814i \(-0.820005\pi\)
0.886197 + 0.463309i \(0.153338\pi\)
\(648\) 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 −0.954377 0.298604i \(-0.903479\pi\)
0.735787 + 0.677213i \(0.236812\pi\)
\(654\) −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 −0.734621 0.678478i \(-0.762640\pi\)
0.954890 + 0.296961i \(0.0959733\pi\)
\(660\) 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 −0.533569 0.845756i \(-0.679150\pi\)
0.999231 + 0.0392063i \(0.0124830\pi\)
\(674\) 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 0.101207 0.994865i \(-0.467729\pi\)
0.810975 0.585081i \(-0.198937\pi\)
\(684\) 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 0.875866 0.482554i \(-0.160291\pi\)
−0.855837 + 0.517245i \(0.826957\pi\)
\(720\) 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 −0.527850 0.849338i \(-0.677002\pi\)
0.999473 + 0.0324628i \(0.0103350\pi\)
\(728\) 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 −0.951856 0.306545i \(-0.900827\pi\)
0.741404 + 0.671059i \(0.234160\pi\)
\(734\) 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 −0.447556 0.894256i \(-0.647705\pi\)
0.998226 0.0595336i \(-0.0189613\pi\)
\(740\) 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 0.985991 0.166796i \(-0.0533420\pi\)
−0.637445 + 0.770496i \(0.720009\pi\)
\(744\) 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 −0.866264 0.499587i \(-0.833485\pi\)
0.865787 + 0.500413i \(0.166818\pi\)
\(752\) −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 −0.967669 0.252225i \(-0.918838\pi\)
0.702268 + 0.711913i \(0.252171\pi\)
\(762\) −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 0.844658 + 0.535306i \(0.179804\pi\)
0.0412592 + 0.999148i \(0.486863\pi\)
\(770\) 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 −0.732199 0.681090i \(-0.761506\pi\)
0.955941 + 0.293558i \(0.0948394\pi\)
\(774\) −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 + 3.67107i