Properties

Label 546.2.c.e.337.2
Level $546$
Weight $2$
Character 546.337
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{17})\)
Defining polynomial: \(x^{4} + 9 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.2
Root \(1.56155i\) of defining polynomial
Character \(\chi\) \(=\) 546.337
Dual form 546.2.c.e.337.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +0.561553 q^{10} -1.43845i q^{11} +1.00000 q^{12} +(-0.561553 - 3.56155i) q^{13} +1.00000 q^{14} -0.561553i q^{15} +1.00000 q^{16} +5.68466 q^{17} -1.00000i q^{18} -2.56155i q^{19} -0.561553i q^{20} -1.00000i q^{21} -1.43845 q^{22} +5.68466 q^{23} -1.00000i q^{24} +4.68466 q^{25} +(-3.56155 + 0.561553i) q^{26} -1.00000 q^{27} -1.00000i q^{28} -2.56155 q^{29} -0.561553 q^{30} -10.2462i q^{31} -1.00000i q^{32} +1.43845i q^{33} -5.68466i q^{34} -0.561553 q^{35} -1.00000 q^{36} +1.68466i q^{37} -2.56155 q^{38} +(0.561553 + 3.56155i) q^{39} -0.561553 q^{40} -4.00000i q^{41} -1.00000 q^{42} -10.5616 q^{43} +1.43845i q^{44} +0.561553i q^{45} -5.68466i q^{46} -6.24621i q^{47} -1.00000 q^{48} -1.00000 q^{49} -4.68466i q^{50} -5.68466 q^{51} +(0.561553 + 3.56155i) q^{52} +13.1231 q^{53} +1.00000i q^{54} +0.807764 q^{55} -1.00000 q^{56} +2.56155i q^{57} +2.56155i q^{58} +12.2462i q^{59} +0.561553i q^{60} +2.56155 q^{61} -10.2462 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(2.00000 - 0.315342i) q^{65} +1.43845 q^{66} -7.12311i q^{67} -5.68466 q^{68} -5.68466 q^{69} +0.561553i q^{70} +15.3693i q^{71} +1.00000i q^{72} -7.43845i q^{73} +1.68466 q^{74} -4.68466 q^{75} +2.56155i q^{76} +1.43845 q^{77} +(3.56155 - 0.561553i) q^{78} +16.0000 q^{79} +0.561553i q^{80} +1.00000 q^{81} -4.00000 q^{82} +2.00000i q^{83} +1.00000i q^{84} +3.19224i q^{85} +10.5616i q^{86} +2.56155 q^{87} +1.43845 q^{88} +8.00000i q^{89} +0.561553 q^{90} +(3.56155 - 0.561553i) q^{91} -5.68466 q^{92} +10.2462i q^{93} -6.24621 q^{94} +1.43845 q^{95} +1.00000i q^{96} -10.0000i q^{97} +1.00000i q^{98} -1.43845i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 4q^{4} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 4q^{4} + 4q^{9} - 6q^{10} + 4q^{12} + 6q^{13} + 4q^{14} + 4q^{16} - 2q^{17} - 14q^{22} - 2q^{23} - 6q^{25} - 6q^{26} - 4q^{27} - 2q^{29} + 6q^{30} + 6q^{35} - 4q^{36} - 2q^{38} - 6q^{39} + 6q^{40} - 4q^{42} - 34q^{43} - 4q^{48} - 4q^{49} + 2q^{51} - 6q^{52} + 36q^{53} - 38q^{55} - 4q^{56} + 2q^{61} - 8q^{62} - 4q^{64} + 8q^{65} + 14q^{66} + 2q^{68} + 2q^{69} - 18q^{74} + 6q^{75} + 14q^{77} + 6q^{78} + 64q^{79} + 4q^{81} - 16q^{82} + 2q^{87} + 14q^{88} - 6q^{90} + 6q^{91} + 2q^{92} + 8q^{94} + 14q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 0.561553i 0.251134i 0.992085 + 0.125567i \(0.0400750\pi\)
−0.992085 + 0.125567i \(0.959925\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) 0.561553 0.177579
\(11\) 1.43845i 0.433708i −0.976204 0.216854i \(-0.930420\pi\)
0.976204 0.216854i \(-0.0695796\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.561553 3.56155i −0.155747 0.987797i
\(14\) 1.00000 0.267261
\(15\) 0.561553i 0.144992i
\(16\) 1.00000 0.250000
\(17\) 5.68466 1.37873 0.689366 0.724413i \(-0.257889\pi\)
0.689366 + 0.724413i \(0.257889\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 2.56155i 0.587661i −0.955858 0.293830i \(-0.905070\pi\)
0.955858 0.293830i \(-0.0949300\pi\)
\(20\) 0.561553i 0.125567i
\(21\) 1.00000i 0.218218i
\(22\) −1.43845 −0.306678
\(23\) 5.68466 1.18533 0.592667 0.805448i \(-0.298075\pi\)
0.592667 + 0.805448i \(0.298075\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.68466 0.936932
\(26\) −3.56155 + 0.561553i −0.698478 + 0.110130i
\(27\) −1.00000 −0.192450
\(28\) 1.00000i 0.188982i
\(29\) −2.56155 −0.475668 −0.237834 0.971306i \(-0.576437\pi\)
−0.237834 + 0.971306i \(0.576437\pi\)
\(30\) −0.561553 −0.102525
\(31\) 10.2462i 1.84027i −0.391597 0.920137i \(-0.628077\pi\)
0.391597 0.920137i \(-0.371923\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.43845i 0.250402i
\(34\) 5.68466i 0.974911i
\(35\) −0.561553 −0.0949197
\(36\) −1.00000 −0.166667
\(37\) 1.68466i 0.276956i 0.990366 + 0.138478i \(0.0442210\pi\)
−0.990366 + 0.138478i \(0.955779\pi\)
\(38\) −2.56155 −0.415539
\(39\) 0.561553 + 3.56155i 0.0899204 + 0.570305i
\(40\) −0.561553 −0.0887893
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) −1.00000 −0.154303
\(43\) −10.5616 −1.61062 −0.805311 0.592853i \(-0.798002\pi\)
−0.805311 + 0.592853i \(0.798002\pi\)
\(44\) 1.43845i 0.216854i
\(45\) 0.561553i 0.0837114i
\(46\) 5.68466i 0.838157i
\(47\) 6.24621i 0.911104i −0.890209 0.455552i \(-0.849442\pi\)
0.890209 0.455552i \(-0.150558\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.00000 −0.142857
\(50\) 4.68466i 0.662511i
\(51\) −5.68466 −0.796011
\(52\) 0.561553 + 3.56155i 0.0778734 + 0.493899i
\(53\) 13.1231 1.80260 0.901299 0.433198i \(-0.142615\pi\)
0.901299 + 0.433198i \(0.142615\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 0.807764 0.108919
\(56\) −1.00000 −0.133631
\(57\) 2.56155i 0.339286i
\(58\) 2.56155i 0.336348i
\(59\) 12.2462i 1.59432i 0.603768 + 0.797160i \(0.293666\pi\)
−0.603768 + 0.797160i \(0.706334\pi\)
\(60\) 0.561553i 0.0724962i
\(61\) 2.56155 0.327973 0.163987 0.986463i \(-0.447565\pi\)
0.163987 + 0.986463i \(0.447565\pi\)
\(62\) −10.2462 −1.30127
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 2.00000 0.315342i 0.248069 0.0391133i
\(66\) 1.43845 0.177061
\(67\) 7.12311i 0.870226i −0.900376 0.435113i \(-0.856708\pi\)
0.900376 0.435113i \(-0.143292\pi\)
\(68\) −5.68466 −0.689366
\(69\) −5.68466 −0.684352
\(70\) 0.561553i 0.0671184i
\(71\) 15.3693i 1.82400i 0.410188 + 0.912001i \(0.365463\pi\)
−0.410188 + 0.912001i \(0.634537\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 7.43845i 0.870604i −0.900284 0.435302i \(-0.856642\pi\)
0.900284 0.435302i \(-0.143358\pi\)
\(74\) 1.68466 0.195838
\(75\) −4.68466 −0.540938
\(76\) 2.56155i 0.293830i
\(77\) 1.43845 0.163926
\(78\) 3.56155 0.561553i 0.403266 0.0635833i
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 0.561553i 0.0627835i
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) 2.00000i 0.219529i 0.993958 + 0.109764i \(0.0350096\pi\)
−0.993958 + 0.109764i \(0.964990\pi\)
\(84\) 1.00000i 0.109109i
\(85\) 3.19224i 0.346247i
\(86\) 10.5616i 1.13888i
\(87\) 2.56155 0.274627
\(88\) 1.43845 0.153339
\(89\) 8.00000i 0.847998i 0.905663 + 0.423999i \(0.139374\pi\)
−0.905663 + 0.423999i \(0.860626\pi\)
\(90\) 0.561553 0.0591929
\(91\) 3.56155 0.561553i 0.373352 0.0588667i
\(92\) −5.68466 −0.592667
\(93\) 10.2462i 1.06248i
\(94\) −6.24621 −0.644247
\(95\) 1.43845 0.147582
\(96\) 1.00000i 0.102062i
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 1.43845i 0.144569i
\(100\) −4.68466 −0.468466
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 5.68466i 0.562865i
\(103\) −18.8078 −1.85318 −0.926592 0.376068i \(-0.877276\pi\)
−0.926592 + 0.376068i \(0.877276\pi\)
\(104\) 3.56155 0.561553i 0.349239 0.0550648i
\(105\) 0.561553 0.0548019
\(106\) 13.1231i 1.27463i
\(107\) −13.1231 −1.26866 −0.634329 0.773063i \(-0.718724\pi\)
−0.634329 + 0.773063i \(0.718724\pi\)
\(108\) 1.00000 0.0962250
\(109\) 15.9309i 1.52590i 0.646457 + 0.762950i \(0.276250\pi\)
−0.646457 + 0.762950i \(0.723750\pi\)
\(110\) 0.807764i 0.0770173i
\(111\) 1.68466i 0.159901i
\(112\) 1.00000i 0.0944911i
\(113\) 3.75379 0.353127 0.176563 0.984289i \(-0.443502\pi\)
0.176563 + 0.984289i \(0.443502\pi\)
\(114\) 2.56155 0.239911
\(115\) 3.19224i 0.297678i
\(116\) 2.56155 0.237834
\(117\) −0.561553 3.56155i −0.0519156 0.329266i
\(118\) 12.2462 1.12736
\(119\) 5.68466i 0.521112i
\(120\) 0.561553 0.0512625
\(121\) 8.93087 0.811897
\(122\) 2.56155i 0.231912i
\(123\) 4.00000i 0.360668i
\(124\) 10.2462i 0.920137i
\(125\) 5.43845i 0.486430i
\(126\) 1.00000 0.0890871
\(127\) −6.24621 −0.554262 −0.277131 0.960832i \(-0.589384\pi\)
−0.277131 + 0.960832i \(0.589384\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.5616 0.929893
\(130\) −0.315342 2.00000i −0.0276573 0.175412i
\(131\) 2.56155 0.223804 0.111902 0.993719i \(-0.464306\pi\)
0.111902 + 0.993719i \(0.464306\pi\)
\(132\) 1.43845i 0.125201i
\(133\) 2.56155 0.222115
\(134\) −7.12311 −0.615343
\(135\) 0.561553i 0.0483308i
\(136\) 5.68466i 0.487455i
\(137\) 5.68466i 0.485673i 0.970067 + 0.242837i \(0.0780779\pi\)
−0.970067 + 0.242837i \(0.921922\pi\)
\(138\) 5.68466i 0.483910i
\(139\) −6.24621 −0.529797 −0.264898 0.964276i \(-0.585338\pi\)
−0.264898 + 0.964276i \(0.585338\pi\)
\(140\) 0.561553 0.0474599
\(141\) 6.24621i 0.526026i
\(142\) 15.3693 1.28976
\(143\) −5.12311 + 0.807764i −0.428416 + 0.0675486i
\(144\) 1.00000 0.0833333
\(145\) 1.43845i 0.119457i
\(146\) −7.43845 −0.615610
\(147\) 1.00000 0.0824786
\(148\) 1.68466i 0.138478i
\(149\) 10.0000i 0.819232i −0.912258 0.409616i \(-0.865663\pi\)
0.912258 0.409616i \(-0.134337\pi\)
\(150\) 4.68466i 0.382501i
\(151\) 4.31534i 0.351178i −0.984464 0.175589i \(-0.943817\pi\)
0.984464 0.175589i \(-0.0561829\pi\)
\(152\) 2.56155 0.207769
\(153\) 5.68466 0.459577
\(154\) 1.43845i 0.115913i
\(155\) 5.75379 0.462155
\(156\) −0.561553 3.56155i −0.0449602 0.285152i
\(157\) 8.80776 0.702936 0.351468 0.936200i \(-0.385683\pi\)
0.351468 + 0.936200i \(0.385683\pi\)
\(158\) 16.0000i 1.27289i
\(159\) −13.1231 −1.04073
\(160\) 0.561553 0.0443946
\(161\) 5.68466i 0.448014i
\(162\) 1.00000i 0.0785674i
\(163\) 0.876894i 0.0686837i −0.999410 0.0343418i \(-0.989067\pi\)
0.999410 0.0343418i \(-0.0109335\pi\)
\(164\) 4.00000i 0.312348i
\(165\) −0.807764 −0.0628843
\(166\) 2.00000 0.155230
\(167\) 8.80776i 0.681565i −0.940142 0.340783i \(-0.889308\pi\)
0.940142 0.340783i \(-0.110692\pi\)
\(168\) 1.00000 0.0771517
\(169\) −12.3693 + 4.00000i −0.951486 + 0.307692i
\(170\) 3.19224 0.244833
\(171\) 2.56155i 0.195887i
\(172\) 10.5616 0.805311
\(173\) −20.2462 −1.53929 −0.769645 0.638471i \(-0.779567\pi\)
−0.769645 + 0.638471i \(0.779567\pi\)
\(174\) 2.56155i 0.194191i
\(175\) 4.68466i 0.354127i
\(176\) 1.43845i 0.108427i
\(177\) 12.2462i 0.920482i
\(178\) 8.00000 0.599625
\(179\) 2.87689 0.215029 0.107515 0.994204i \(-0.465711\pi\)
0.107515 + 0.994204i \(0.465711\pi\)
\(180\) 0.561553i 0.0418557i
\(181\) 11.3693 0.845075 0.422537 0.906346i \(-0.361140\pi\)
0.422537 + 0.906346i \(0.361140\pi\)
\(182\) −0.561553 3.56155i −0.0416251 0.264000i
\(183\) −2.56155 −0.189355
\(184\) 5.68466i 0.419079i
\(185\) −0.946025 −0.0695531
\(186\) 10.2462 0.751289
\(187\) 8.17708i 0.597967i
\(188\) 6.24621i 0.455552i
\(189\) 1.00000i 0.0727393i
\(190\) 1.43845i 0.104356i
\(191\) 13.0540 0.944553 0.472276 0.881451i \(-0.343432\pi\)
0.472276 + 0.881451i \(0.343432\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000i 0.863779i 0.901927 + 0.431889i \(0.142153\pi\)
−0.901927 + 0.431889i \(0.857847\pi\)
\(194\) −10.0000 −0.717958
\(195\) −2.00000 + 0.315342i −0.143223 + 0.0225821i
\(196\) 1.00000 0.0714286
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) −1.43845 −0.102226
\(199\) −23.9309 −1.69641 −0.848207 0.529665i \(-0.822318\pi\)
−0.848207 + 0.529665i \(0.822318\pi\)
\(200\) 4.68466i 0.331255i
\(201\) 7.12311i 0.502425i
\(202\) 6.00000i 0.422159i
\(203\) 2.56155i 0.179786i
\(204\) 5.68466 0.398006
\(205\) 2.24621 0.156882
\(206\) 18.8078i 1.31040i
\(207\) 5.68466 0.395111
\(208\) −0.561553 3.56155i −0.0389367 0.246949i
\(209\) −3.68466 −0.254873
\(210\) 0.561553i 0.0387508i
\(211\) −12.8078 −0.881723 −0.440861 0.897575i \(-0.645327\pi\)
−0.440861 + 0.897575i \(0.645327\pi\)
\(212\) −13.1231 −0.901299
\(213\) 15.3693i 1.05309i
\(214\) 13.1231i 0.897077i
\(215\) 5.93087i 0.404482i
\(216\) 1.00000i 0.0680414i
\(217\) 10.2462 0.695558
\(218\) 15.9309 1.07897
\(219\) 7.43845i 0.502644i
\(220\) −0.807764 −0.0544594
\(221\) −3.19224 20.2462i −0.214733 1.36191i
\(222\) −1.68466 −0.113067
\(223\) 18.2462i 1.22186i 0.791686 + 0.610928i \(0.209204\pi\)
−0.791686 + 0.610928i \(0.790796\pi\)
\(224\) 1.00000 0.0668153
\(225\) 4.68466 0.312311
\(226\) 3.75379i 0.249698i
\(227\) 23.6155i 1.56742i −0.621128 0.783709i \(-0.713325\pi\)
0.621128 0.783709i \(-0.286675\pi\)
\(228\) 2.56155i 0.169643i
\(229\) 2.00000i 0.132164i −0.997814 0.0660819i \(-0.978950\pi\)
0.997814 0.0660819i \(-0.0210498\pi\)
\(230\) 3.19224 0.210490
\(231\) −1.43845 −0.0946429
\(232\) 2.56155i 0.168174i
\(233\) 2.00000 0.131024 0.0655122 0.997852i \(-0.479132\pi\)
0.0655122 + 0.997852i \(0.479132\pi\)
\(234\) −3.56155 + 0.561553i −0.232826 + 0.0367099i
\(235\) 3.50758 0.228809
\(236\) 12.2462i 0.797160i
\(237\) −16.0000 −1.03931
\(238\) 5.68466 0.368482
\(239\) 2.24621i 0.145295i 0.997358 + 0.0726477i \(0.0231449\pi\)
−0.997358 + 0.0726477i \(0.976855\pi\)
\(240\) 0.561553i 0.0362481i
\(241\) 6.00000i 0.386494i −0.981150 0.193247i \(-0.938098\pi\)
0.981150 0.193247i \(-0.0619019\pi\)
\(242\) 8.93087i 0.574098i
\(243\) −1.00000 −0.0641500
\(244\) −2.56155 −0.163987
\(245\) 0.561553i 0.0358763i
\(246\) 4.00000 0.255031
\(247\) −9.12311 + 1.43845i −0.580489 + 0.0915262i
\(248\) 10.2462 0.650635
\(249\) 2.00000i 0.126745i
\(250\) 5.43845 0.343958
\(251\) −15.0540 −0.950198 −0.475099 0.879932i \(-0.657588\pi\)
−0.475099 + 0.879932i \(0.657588\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 8.17708i 0.514089i
\(254\) 6.24621i 0.391922i
\(255\) 3.19224i 0.199906i
\(256\) 1.00000 0.0625000
\(257\) −26.0000 −1.62184 −0.810918 0.585160i \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) 10.5616i 0.657534i
\(259\) −1.68466 −0.104680
\(260\) −2.00000 + 0.315342i −0.124035 + 0.0195567i
\(261\) −2.56155 −0.158556
\(262\) 2.56155i 0.158253i
\(263\) 1.36932 0.0844357 0.0422178 0.999108i \(-0.486558\pi\)
0.0422178 + 0.999108i \(0.486558\pi\)
\(264\) −1.43845 −0.0885303
\(265\) 7.36932i 0.452694i
\(266\) 2.56155i 0.157059i
\(267\) 8.00000i 0.489592i
\(268\) 7.12311i 0.435113i
\(269\) 6.63068 0.404280 0.202140 0.979357i \(-0.435210\pi\)
0.202140 + 0.979357i \(0.435210\pi\)
\(270\) −0.561553 −0.0341750
\(271\) 8.00000i 0.485965i 0.970031 + 0.242983i \(0.0781258\pi\)
−0.970031 + 0.242983i \(0.921874\pi\)
\(272\) 5.68466 0.344683
\(273\) −3.56155 + 0.561553i −0.215555 + 0.0339867i
\(274\) 5.68466 0.343423
\(275\) 6.73863i 0.406355i
\(276\) 5.68466 0.342176
\(277\) −19.1231 −1.14900 −0.574498 0.818506i \(-0.694803\pi\)
−0.574498 + 0.818506i \(0.694803\pi\)
\(278\) 6.24621i 0.374623i
\(279\) 10.2462i 0.613425i
\(280\) 0.561553i 0.0335592i
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) 6.24621 0.371956
\(283\) −13.1231 −0.780088 −0.390044 0.920796i \(-0.627540\pi\)
−0.390044 + 0.920796i \(0.627540\pi\)
\(284\) 15.3693i 0.912001i
\(285\) −1.43845 −0.0852063
\(286\) 0.807764 + 5.12311i 0.0477641 + 0.302936i
\(287\) 4.00000 0.236113
\(288\) 1.00000i 0.0589256i
\(289\) 15.3153 0.900902
\(290\) −1.43845 −0.0844685
\(291\) 10.0000i 0.586210i
\(292\) 7.43845i 0.435302i
\(293\) 24.2462i 1.41648i 0.705972 + 0.708239i \(0.250510\pi\)
−0.705972 + 0.708239i \(0.749490\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −6.87689 −0.400388
\(296\) −1.68466 −0.0979188
\(297\) 1.43845i 0.0834672i
\(298\) −10.0000 −0.579284
\(299\) −3.19224 20.2462i −0.184612 1.17087i
\(300\) 4.68466 0.270469
\(301\) 10.5616i 0.608758i
\(302\) −4.31534 −0.248320
\(303\) −6.00000 −0.344691
\(304\) 2.56155i 0.146915i
\(305\) 1.43845i 0.0823652i
\(306\) 5.68466i 0.324970i
\(307\) 9.75379i 0.556678i −0.960483 0.278339i \(-0.910216\pi\)
0.960483 0.278339i \(-0.0897839\pi\)
\(308\) −1.43845 −0.0819631
\(309\) 18.8078 1.06994
\(310\) 5.75379i 0.326793i
\(311\) 32.4924 1.84248 0.921238 0.388999i \(-0.127179\pi\)
0.921238 + 0.388999i \(0.127179\pi\)
\(312\) −3.56155 + 0.561553i −0.201633 + 0.0317917i
\(313\) 15.7538 0.890457 0.445228 0.895417i \(-0.353122\pi\)
0.445228 + 0.895417i \(0.353122\pi\)
\(314\) 8.80776i 0.497051i
\(315\) −0.561553 −0.0316399
\(316\) −16.0000 −0.900070
\(317\) 21.3693i 1.20022i −0.799917 0.600110i \(-0.795123\pi\)
0.799917 0.600110i \(-0.204877\pi\)
\(318\) 13.1231i 0.735907i
\(319\) 3.68466i 0.206301i
\(320\) 0.561553i 0.0313918i
\(321\) 13.1231 0.732460
\(322\) 5.68466 0.316794
\(323\) 14.5616i 0.810226i
\(324\) −1.00000 −0.0555556
\(325\) −2.63068 16.6847i −0.145924 0.925498i
\(326\) −0.876894 −0.0485667
\(327\) 15.9309i 0.880979i
\(328\) 4.00000 0.220863
\(329\) 6.24621 0.344365
\(330\) 0.807764i 0.0444659i
\(331\) 7.12311i 0.391521i −0.980652 0.195761i \(-0.937282\pi\)
0.980652 0.195761i \(-0.0627176\pi\)
\(332\) 2.00000i 0.109764i
\(333\) 1.68466i 0.0923187i
\(334\) −8.80776 −0.481939
\(335\) 4.00000 0.218543
\(336\) 1.00000i 0.0545545i
\(337\) −17.0540 −0.928989 −0.464495 0.885576i \(-0.653764\pi\)
−0.464495 + 0.885576i \(0.653764\pi\)
\(338\) 4.00000 + 12.3693i 0.217571 + 0.672802i
\(339\) −3.75379 −0.203878
\(340\) 3.19224i 0.173123i
\(341\) −14.7386 −0.798142
\(342\) −2.56155 −0.138513
\(343\) 1.00000i 0.0539949i
\(344\) 10.5616i 0.569441i
\(345\) 3.19224i 0.171864i
\(346\) 20.2462i 1.08844i
\(347\) 8.49242 0.455897 0.227949 0.973673i \(-0.426798\pi\)
0.227949 + 0.973673i \(0.426798\pi\)
\(348\) −2.56155 −0.137314
\(349\) 21.3693i 1.14387i 0.820298 + 0.571937i \(0.193808\pi\)
−0.820298 + 0.571937i \(0.806192\pi\)
\(350\) 4.68466 0.250406
\(351\) 0.561553 + 3.56155i 0.0299735 + 0.190102i
\(352\) −1.43845 −0.0766695
\(353\) 1.75379i 0.0933448i 0.998910 + 0.0466724i \(0.0148617\pi\)
−0.998910 + 0.0466724i \(0.985138\pi\)
\(354\) −12.2462 −0.650879
\(355\) −8.63068 −0.458069
\(356\) 8.00000i 0.423999i
\(357\) 5.68466i 0.300864i
\(358\) 2.87689i 0.152049i
\(359\) 17.6155i 0.929712i 0.885386 + 0.464856i \(0.153894\pi\)
−0.885386 + 0.464856i \(0.846106\pi\)
\(360\) −0.561553 −0.0295964
\(361\) 12.4384 0.654655
\(362\) 11.3693i 0.597558i
\(363\) −8.93087 −0.468749
\(364\) −3.56155 + 0.561553i −0.186676 + 0.0294334i
\(365\) 4.17708 0.218638
\(366\) 2.56155i 0.133895i
\(367\) 25.3693 1.32427 0.662134 0.749386i \(-0.269651\pi\)
0.662134 + 0.749386i \(0.269651\pi\)
\(368\) 5.68466 0.296333
\(369\) 4.00000i 0.208232i
\(370\) 0.946025i 0.0491815i
\(371\) 13.1231i 0.681318i
\(372\) 10.2462i 0.531241i
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) −8.17708 −0.422827
\(375\) 5.43845i 0.280840i
\(376\) 6.24621 0.322124
\(377\) 1.43845 + 9.12311i 0.0740838 + 0.469864i
\(378\) −1.00000 −0.0514344
\(379\) 27.1231i 1.39322i 0.717450 + 0.696610i \(0.245309\pi\)
−0.717450 + 0.696610i \(0.754691\pi\)
\(380\) −1.43845 −0.0737908
\(381\) 6.24621 0.320003
\(382\) 13.0540i 0.667899i
\(383\) 13.4384i 0.686673i −0.939213 0.343336i \(-0.888443\pi\)
0.939213 0.343336i \(-0.111557\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0.807764i 0.0411675i
\(386\) 12.0000 0.610784
\(387\) −10.5616 −0.536874
\(388\) 10.0000i 0.507673i
\(389\) 18.8769 0.957097 0.478548 0.878061i \(-0.341163\pi\)
0.478548 + 0.878061i \(0.341163\pi\)
\(390\) 0.315342 + 2.00000i 0.0159679 + 0.101274i
\(391\) 32.3153 1.63426
\(392\) 1.00000i 0.0505076i
\(393\) −2.56155 −0.129213
\(394\) 6.00000 0.302276
\(395\) 8.98485i 0.452077i
\(396\) 1.43845i 0.0722847i
\(397\) 9.36932i 0.470233i 0.971967 + 0.235116i \(0.0755471\pi\)
−0.971967 + 0.235116i \(0.924453\pi\)
\(398\) 23.9309i 1.19955i
\(399\) −2.56155 −0.128238
\(400\) 4.68466 0.234233
\(401\) 34.9848i 1.74706i −0.486771 0.873530i \(-0.661825\pi\)
0.486771 0.873530i \(-0.338175\pi\)
\(402\) 7.12311 0.355268
\(403\) −36.4924 + 5.75379i −1.81782 + 0.286617i
\(404\) −6.00000 −0.298511
\(405\) 0.561553i 0.0279038i
\(406\) −2.56155 −0.127128
\(407\) 2.42329 0.120118
\(408\) 5.68466i 0.281433i
\(409\) 6.80776i 0.336622i 0.985734 + 0.168311i \(0.0538313\pi\)
−0.985734 + 0.168311i \(0.946169\pi\)
\(410\) 2.24621i 0.110932i
\(411\) 5.68466i 0.280404i
\(412\) 18.8078 0.926592
\(413\) −12.2462 −0.602597
\(414\) 5.68466i 0.279386i
\(415\) −1.12311 −0.0551311
\(416\) −3.56155 + 0.561553i −0.174619 + 0.0275324i
\(417\) 6.24621 0.305878
\(418\) 3.68466i 0.180223i
\(419\) −8.31534 −0.406231 −0.203116 0.979155i \(-0.565107\pi\)
−0.203116 + 0.979155i \(0.565107\pi\)
\(420\) −0.561553 −0.0274010
\(421\) 10.0000i 0.487370i 0.969854 + 0.243685i \(0.0783563\pi\)
−0.969854 + 0.243685i \(0.921644\pi\)
\(422\) 12.8078i 0.623472i
\(423\) 6.24621i 0.303701i
\(424\) 13.1231i 0.637314i
\(425\) 26.6307 1.29178
\(426\) −15.3693 −0.744646
\(427\) 2.56155i 0.123962i
\(428\) 13.1231 0.634329
\(429\) 5.12311 0.807764i 0.247346 0.0389992i
\(430\) −5.93087 −0.286012
\(431\) 27.8617i 1.34205i 0.741433 + 0.671026i \(0.234146\pi\)
−0.741433 + 0.671026i \(0.765854\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −1.36932 −0.0658052 −0.0329026 0.999459i \(-0.510475\pi\)
−0.0329026 + 0.999459i \(0.510475\pi\)
\(434\) 10.2462i 0.491834i
\(435\) 1.43845i 0.0689683i
\(436\) 15.9309i 0.762950i
\(437\) 14.5616i 0.696574i
\(438\) 7.43845 0.355423
\(439\) 19.9309 0.951249 0.475624 0.879649i \(-0.342222\pi\)
0.475624 + 0.879649i \(0.342222\pi\)
\(440\) 0.807764i 0.0385086i
\(441\) −1.00000 −0.0476190
\(442\) −20.2462 + 3.19224i −0.963014 + 0.151839i
\(443\) 31.3693 1.49040 0.745201 0.666840i \(-0.232354\pi\)
0.745201 + 0.666840i \(0.232354\pi\)
\(444\) 1.68466i 0.0799504i
\(445\) −4.49242 −0.212961
\(446\) 18.2462 0.863983
\(447\) 10.0000i 0.472984i
\(448\) 1.00000i 0.0472456i
\(449\) 21.6847i 1.02336i 0.859175 + 0.511681i \(0.170977\pi\)
−0.859175 + 0.511681i \(0.829023\pi\)
\(450\) 4.68466i 0.220837i
\(451\) −5.75379 −0.270935
\(452\) −3.75379 −0.176563
\(453\) 4.31534i 0.202752i
\(454\) −23.6155 −1.10833
\(455\) 0.315342 + 2.00000i 0.0147834 + 0.0937614i
\(456\) −2.56155 −0.119956
\(457\) 16.0000i 0.748448i 0.927338 + 0.374224i \(0.122091\pi\)
−0.927338 + 0.374224i \(0.877909\pi\)
\(458\) −2.00000 −0.0934539
\(459\) −5.68466 −0.265337
\(460\) 3.19224i 0.148839i
\(461\) 8.06913i 0.375817i −0.982187 0.187908i \(-0.939829\pi\)
0.982187 0.187908i \(-0.0601708\pi\)
\(462\) 1.43845i 0.0669226i
\(463\) 39.5464i 1.83788i −0.394401 0.918938i \(-0.629048\pi\)
0.394401 0.918938i \(-0.370952\pi\)
\(464\) −2.56155 −0.118917
\(465\) −5.75379 −0.266826
\(466\) 2.00000i 0.0926482i
\(467\) −2.56155 −0.118535 −0.0592673 0.998242i \(-0.518876\pi\)
−0.0592673 + 0.998242i \(0.518876\pi\)
\(468\) 0.561553 + 3.56155i 0.0259578 + 0.164633i
\(469\) 7.12311 0.328914
\(470\) 3.50758i 0.161792i
\(471\) −8.80776 −0.405840
\(472\) −12.2462 −0.563678
\(473\) 15.1922i 0.698540i
\(474\) 16.0000i 0.734904i
\(475\) 12.0000i 0.550598i
\(476\) 5.68466i 0.260556i
\(477\) 13.1231 0.600866
\(478\) 2.24621 0.102739
\(479\) 41.3002i 1.88705i 0.331296 + 0.943527i \(0.392514\pi\)
−0.331296 + 0.943527i \(0.607486\pi\)
\(480\) −0.561553 −0.0256313
\(481\) 6.00000 0.946025i 0.273576 0.0431350i
\(482\) −6.00000 −0.273293
\(483\) 5.68466i 0.258661i
\(484\) −8.93087 −0.405949
\(485\) 5.61553 0.254988
\(486\) 1.00000i 0.0453609i
\(487\) 30.2462i 1.37059i 0.728267 + 0.685293i \(0.240326\pi\)
−0.728267 + 0.685293i \(0.759674\pi\)
\(488\) 2.56155i 0.115956i
\(489\) 0.876894i 0.0396545i
\(490\) −0.561553 −0.0253684
\(491\) 6.24621 0.281888 0.140944 0.990018i \(-0.454986\pi\)
0.140944 + 0.990018i \(0.454986\pi\)
\(492\) 4.00000i 0.180334i
\(493\) −14.5616 −0.655819
\(494\) 1.43845 + 9.12311i 0.0647188 + 0.410468i
\(495\) 0.807764 0.0363063
\(496\) 10.2462i 0.460068i
\(497\) −15.3693 −0.689408
\(498\) −2.00000 −0.0896221
\(499\) 34.4924i 1.54409i 0.635566 + 0.772046i \(0.280767\pi\)
−0.635566 + 0.772046i \(0.719233\pi\)
\(500\) 5.43845i 0.243215i
\(501\) 8.80776i 0.393502i
\(502\) 15.0540i 0.671892i
\(503\) −5.61553 −0.250384 −0.125192 0.992133i \(-0.539955\pi\)
−0.125192 + 0.992133i \(0.539955\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 3.36932i 0.149933i
\(506\) −8.17708 −0.363516
\(507\) 12.3693 4.00000i 0.549341 0.177646i
\(508\) 6.24621 0.277131
\(509\) 9.68466i 0.429265i 0.976695 + 0.214632i \(0.0688554\pi\)
−0.976695 + 0.214632i \(0.931145\pi\)
\(510\) −3.19224 −0.141355
\(511\) 7.43845 0.329058
\(512\) 1.00000i 0.0441942i
\(513\) 2.56155i 0.113095i
\(514\) 26.0000i 1.14681i
\(515\) 10.5616i 0.465398i
\(516\) −10.5616 −0.464946
\(517\) −8.98485 −0.395153
\(518\) 1.68466i 0.0740196i
\(519\) 20.2462 0.888710
\(520\) 0.315342 + 2.00000i 0.0138286 + 0.0877058i
\(521\) −29.0540 −1.27288 −0.636439 0.771327i \(-0.719593\pi\)
−0.636439 + 0.771327i \(0.719593\pi\)
\(522\) 2.56155i 0.112116i
\(523\) 24.4924 1.07098 0.535489 0.844542i \(-0.320127\pi\)
0.535489 + 0.844542i \(0.320127\pi\)
\(524\) −2.56155 −0.111902
\(525\) 4.68466i 0.204455i
\(526\) 1.36932i 0.0597051i
\(527\) 58.2462i 2.53724i
\(528\) 1.43845i 0.0626004i
\(529\) 9.31534 0.405015
\(530\) 7.36932 0.320103
\(531\) 12.2462i 0.531440i
\(532\) −2.56155 −0.111057
\(533\) −14.2462 + 2.24621i −0.617072 + 0.0972942i
\(534\) −8.00000 −0.346194
\(535\) 7.36932i 0.318603i
\(536\) 7.12311 0.307671
\(537\) −2.87689 −0.124147
\(538\) 6.63068i 0.285869i
\(539\) 1.43845i 0.0619583i
\(540\) 0.561553i 0.0241654i
\(541\) 26.8078i 1.15256i 0.817254 + 0.576278i \(0.195495\pi\)
−0.817254 + 0.576278i \(0.804505\pi\)
\(542\) 8.00000 0.343629
\(543\) −11.3693 −0.487904
\(544\) 5.68466i 0.243728i
\(545\) −8.94602 −0.383206
\(546\) 0.561553 + 3.56155i 0.0240322 + 0.152420i
\(547\) −36.9848 −1.58136 −0.790679 0.612231i \(-0.790272\pi\)
−0.790679 + 0.612231i \(0.790272\pi\)
\(548\) 5.68466i 0.242837i
\(549\) 2.56155 0.109324
\(550\) −6.73863 −0.287336
\(551\) 6.56155i 0.279532i
\(552\) 5.68466i 0.241955i
\(553\) 16.0000i 0.680389i
\(554\) 19.1231i 0.812463i
\(555\) 0.946025 0.0401565
\(556\) 6.24621 0.264898
\(557\) 0.246211i 0.0104323i 0.999986 + 0.00521615i \(0.00166036\pi\)
−0.999986 + 0.00521615i \(0.998340\pi\)
\(558\) −10.2462 −0.433757
\(559\) 5.93087 + 37.6155i 0.250849 + 1.59097i
\(560\) −0.561553 −0.0237299
\(561\) 8.17708i 0.345237i
\(562\) −6.00000 −0.253095
\(563\) 0.946025 0.0398702 0.0199351 0.999801i \(-0.493654\pi\)
0.0199351 + 0.999801i \(0.493654\pi\)
\(564\) 6.24621i 0.263013i
\(565\) 2.10795i 0.0886821i
\(566\) 13.1231i 0.551605i
\(567\) 1.00000i 0.0419961i
\(568\) −15.3693 −0.644882
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 1.43845i 0.0602499i
\(571\) −1.75379 −0.0733938 −0.0366969 0.999326i \(-0.511684\pi\)
−0.0366969 + 0.999326i \(0.511684\pi\)
\(572\) 5.12311 0.807764i 0.214208 0.0337743i
\(573\) −13.0540 −0.545338
\(574\) 4.00000i 0.166957i
\(575\) 26.6307 1.11058
\(576\) −1.00000 −0.0416667
\(577\) 24.2462i 1.00938i −0.863300 0.504691i \(-0.831606\pi\)
0.863300 0.504691i \(-0.168394\pi\)
\(578\) 15.3153i 0.637034i
\(579\) 12.0000i 0.498703i
\(580\) 1.43845i 0.0597283i
\(581\) −2.00000 −0.0829740
\(582\) 10.0000 0.414513
\(583\) 18.8769i 0.781801i
\(584\) 7.43845 0.307805
\(585\) 2.00000 0.315342i 0.0826898 0.0130378i
\(586\) 24.2462 1.00160
\(587\) 28.8769i 1.19188i 0.803030 + 0.595938i \(0.203220\pi\)
−0.803030 + 0.595938i \(0.796780\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −26.2462 −1.08146
\(590\) 6.87689i 0.283117i
\(591\) 6.00000i 0.246807i
\(592\) 1.68466i 0.0692390i
\(593\) 28.0000i 1.14982i 0.818216 + 0.574911i \(0.194963\pi\)
−0.818216 + 0.574911i \(0.805037\pi\)
\(594\) 1.43845 0.0590202
\(595\) −3.19224 −0.130869
\(596\) 10.0000i 0.409616i
\(597\) 23.9309 0.979425
\(598\) −20.2462 + 3.19224i −0.827929 + 0.130540i
\(599\) −23.3002 −0.952020 −0.476010 0.879440i \(-0.657917\pi\)
−0.476010 + 0.879440i \(0.657917\pi\)
\(600\) 4.68466i 0.191250i
\(601\) 25.8617 1.05492 0.527461 0.849579i \(-0.323144\pi\)
0.527461 + 0.849579i \(0.323144\pi\)
\(602\) −10.5616 −0.430457
\(603\) 7.12311i 0.290075i
\(604\) 4.31534i 0.175589i
\(605\) 5.01515i 0.203895i
\(606\) 6.00000i 0.243733i
\(607\) 41.5464 1.68632 0.843158 0.537666i \(-0.180694\pi\)
0.843158 + 0.537666i \(0.180694\pi\)
\(608\) −2.56155 −0.103885
\(609\) 2.56155i 0.103799i
\(610\) 1.43845 0.0582410
\(611\) −22.2462 + 3.50758i −0.899985 + 0.141901i
\(612\) −5.68466 −0.229789
\(613\) 18.8078i 0.759638i −0.925061 0.379819i \(-0.875986\pi\)
0.925061 0.379819i \(-0.124014\pi\)
\(614\) −9.75379 −0.393631
\(615\) −2.24621 −0.0905760
\(616\) 1.43845i 0.0579567i
\(617\) 26.8078i 1.07924i −0.841909 0.539620i \(-0.818568\pi\)
0.841909 0.539620i \(-0.181432\pi\)
\(618\) 18.8078i 0.756559i
\(619\) 2.06913i 0.0831654i 0.999135 + 0.0415827i \(0.0132400\pi\)
−0.999135 + 0.0415827i \(0.986760\pi\)
\(620\) −5.75379 −0.231078
\(621\) −5.68466 −0.228117
\(622\) 32.4924i 1.30283i
\(623\) −8.00000 −0.320513
\(624\) 0.561553 + 3.56155i 0.0224801 + 0.142576i
\(625\) 20.3693 0.814773
\(626\) 15.7538i 0.629648i
\(627\) 3.68466 0.147151
\(628\) −8.80776 −0.351468
\(629\) 9.57671i 0.381848i
\(630\) 0.561553i 0.0223728i
\(631\) 0.315342i 0.0125535i −0.999980 0.00627677i \(-0.998002\pi\)
0.999980 0.00627677i \(-0.00199797\pi\)
\(632\) 16.0000i 0.636446i
\(633\) 12.8078 0.509063
\(634\) −21.3693 −0.848684
\(635\) 3.50758i 0.139194i
\(636\) 13.1231 0.520365
\(637\) 0.561553 + 3.56155i 0.0222495 + 0.141114i
\(638\) 3.68466 0.145877
\(639\) 15.3693i 0.608001i
\(640\) −0.561553 −0.0221973
\(641\) −44.1080 −1.74216 −0.871080 0.491142i \(-0.836580\pi\)
−0.871080 + 0.491142i \(0.836580\pi\)
\(642\) 13.1231i 0.517928i
\(643\) 20.8078i 0.820578i 0.911956 + 0.410289i \(0.134572\pi\)
−0.911956 + 0.410289i \(0.865428\pi\)
\(644\) 5.68466i 0.224007i
\(645\) 5.93087i 0.233528i
\(646\) −14.5616 −0.572917
\(647\) 35.3693 1.39051 0.695256 0.718763i \(-0.255291\pi\)
0.695256 + 0.718763i \(0.255291\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 17.6155 0.691470
\(650\) −16.6847 + 2.63068i −0.654426 + 0.103184i
\(651\) −10.2462 −0.401581
\(652\) 0.876894i 0.0343418i
\(653\) −25.4384 −0.995483 −0.497742 0.867325i \(-0.665837\pi\)
−0.497742 + 0.867325i \(0.665837\pi\)
\(654\) −15.9309 −0.622946
\(655\) 1.43845i 0.0562048i
\(656\) 4.00000i 0.156174i
\(657\) 7.43845i 0.290201i
\(658\) 6.24621i 0.243503i
\(659\) 21.1231 0.822839 0.411420 0.911446i \(-0.365033\pi\)
0.411420 + 0.911446i \(0.365033\pi\)
\(660\) 0.807764 0.0314422
\(661\) 4.73863i 0.184311i −0.995745 0.0921557i \(-0.970624\pi\)
0.995745 0.0921557i \(-0.0293758\pi\)
\(662\) −7.12311 −0.276847
\(663\) 3.19224 + 20.2462i 0.123976 + 0.786298i
\(664\) −2.00000 −0.0776151
\(665\) 1.43845i 0.0557806i
\(666\) 1.68466 0.0652792
\(667\) −14.5616 −0.563826
\(668\) 8.80776i 0.340783i
\(669\) 18.2462i 0.705439i
\(670\) 4.00000i 0.154533i
\(671\) 3.68466i 0.142245i
\(672\) −1.00000 −0.0385758
\(673\) 17.1922 0.662712 0.331356 0.943506i \(-0.392494\pi\)
0.331356 + 0.943506i \(0.392494\pi\)
\(674\) 17.0540i 0.656895i
\(675\) −4.68466 −0.180313
\(676\) 12.3693 4.00000i 0.475743 0.153846i
\(677\) 6.63068 0.254838 0.127419 0.991849i \(-0.459331\pi\)
0.127419 + 0.991849i \(0.459331\pi\)
\(678\) 3.75379i 0.144163i
\(679\) 10.0000 0.383765
\(680\) −3.19224 −0.122417
\(681\) 23.6155i 0.904949i
\(682\) 14.7386i 0.564371i
\(683\) 11.6847i 0.447101i 0.974692 + 0.223551i \(0.0717648\pi\)
−0.974692 + 0.223551i \(0.928235\pi\)
\(684\) 2.56155i 0.0979434i
\(685\) −3.19224 −0.121969
\(686\) −1.00000 −0.0381802
\(687\) 2.00000i 0.0763048i
\(688\) −10.5616 −0.402655
\(689\) −7.36932 46.7386i −0.280749 1.78060i
\(690\) −3.19224 −0.121526
\(691\) 3.50758i 0.133435i −0.997772 0.0667173i \(-0.978747\pi\)
0.997772 0.0667173i \(-0.0212526\pi\)
\(692\) 20.2462 0.769645
\(693\) 1.43845 0.0546421
\(694\) 8.49242i 0.322368i
\(695\) 3.50758i 0.133050i
\(696\) 2.56155i 0.0970954i
\(697\) 22.7386i 0.861287i
\(698\) 21.3693 0.808841
\(699\) −2.00000 −0.0756469
\(700\) 4.68466i 0.177063i
\(701\) 37.6155 1.42072 0.710359 0.703839i \(-0.248532\pi\)
0.710359 + 0.703839i \(0.248532\pi\)
\(702\) 3.56155 0.561553i 0.134422 0.0211944i
\(703\) 4.31534 0.162756
\(704\) 1.43845i 0.0542135i
\(705\) −3.50758 −0.132103
\(706\) 1.75379 0.0660047
\(707\) 6.00000i 0.225653i
\(708\) 12.2462i 0.460241i
\(709\) 48.2462i 1.81192i −0.423358 0.905962i \(-0.639149\pi\)
0.423358 0.905962i \(-0.360851\pi\)
\(710\) 8.63068i 0.323904i
\(711\) 16.0000 0.600047
\(712\) −8.00000 −0.299813
\(713\) 58.2462i 2.18134i
\(714\) −5.68466 −0.212743
\(715\) −0.453602 2.87689i −0.0169638 0.107590i
\(716\) −2.87689 −0.107515
\(717\) 2.24621i 0.0838863i
\(718\) 17.6155 0.657406
\(719\) 30.2462 1.12799 0.563997 0.825777i \(-0.309263\pi\)
0.563997 + 0.825777i \(0.309263\pi\)
\(720\) 0.561553i 0.0209278i
\(721\) 18.8078i 0.700438i
\(722\) 12.4384i 0.462911i
\(723\) 6.00000i 0.223142i
\(724\) −11.3693 −0.422537
\(725\) −12.0000 −0.445669
\(726\) 8.93087i 0.331456i
\(727\) −20.0691 −0.744323 −0.372161 0.928168i \(-0.621383\pi\)
−0.372161 + 0.928168i \(0.621383\pi\)
\(728\) 0.561553 + 3.56155i 0.0208125 + 0.132000i
\(729\) 1.00000 0.0370370
\(730\) 4.17708i 0.154601i
\(731\) −60.0388 −2.22062
\(732\) 2.56155 0.0946777
\(733\) 31.1231i 1.14956i 0.818309 + 0.574779i \(0.194912\pi\)
−0.818309 + 0.574779i \(0.805088\pi\)
\(734\) 25.3693i 0.936399i
\(735\) 0.561553i 0.0207132i
\(736\) 5.68466i 0.209539i
\(737\) −10.2462 −0.377424
\(738\) −4.00000 −0.147242
\(739\) 23.6155i 0.868711i −0.900741 0.434356i \(-0.856976\pi\)
0.900741 0.434356i \(-0.143024\pi\)
\(740\) 0.946025 0.0347766
\(741\) 9.12311 1.43845i 0.335146 0.0528427i
\(742\) 13.1231 0.481764
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) −10.2462 −0.375644
\(745\) 5.61553 0.205737
\(746\) 6.00000i 0.219676i
\(747\) 2.00000i 0.0731762i
\(748\) 8.17708i 0.298984i
\(749\) 13.1231i 0.479508i
\(750\) −5.43845 −0.198584
\(751\) −14.2462 −0.519852 −0.259926 0.965629i \(-0.583698\pi\)
−0.259926 + 0.965629i \(0.583698\pi\)
\(752\) 6.24621i 0.227776i
\(753\) 15.0540 0.548597
\(754\) 9.12311 1.43845i 0.332244 0.0523852i
\(755\) 2.42329 0.0881926
\(756\) 1.00000i 0.0363696i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 27.1231 0.985156
\(759\) 8.17708i 0.296809i
\(760\) 1.43845i 0.0521780i
\(761\) 30.8769i 1.11929i 0.828734 + 0.559643i \(0.189062\pi\)
−0.828734 + 0.559643i \(0.810938\pi\)
\(762\) 6.24621i 0.226276i
\(763\) −15.9309 −0.576736
\(764\) −13.0540 −0.472276
\(765\) 3.19224i 0.115416i
\(766\) −13.4384 −0.485551
\(767\) 43.6155 6.87689i 1.57487 0.248310i
\(768\) −1.00000 −0.0360844
\(769\) 12.5616i 0.452981i 0.974013 + 0.226491i \(0.0727253\pi\)
−0.974013 + 0.226491i \(0.927275\pi\)
\(770\) 0.807764 0.0291098
\(771\) 26.0000 0.936367
\(772\) 12.0000i 0.431889i
\(773\) 15.9309i 0.572994i 0.958081 + 0.286497i \(0.0924908\pi\)
−0.958081 + 0.286497i \(0.907509\pi\)
\(774\) 10.5616i 0.379627i
\(775\) 48.0000i 1.72421i
\(776\) 10.0000 0.358979
\(777\) 1.68466 0.0604368
\(778\) 18.8769i 0.676769i
\(779\) −10.2462 −0.367109
\(780\) 2.00000 0.315342i 0.0716115 0.0112910i
\(781\) 22.1080 0.791085
\(782\) 32.3153i 1.15559i
\(783\) 2.56155 0.0915424
\(784\) −1.00000 −0.0357143
\(785\) 4.94602i 0.176531i
\(786\) 2.56155i 0.0913676i
\(787\) 45.9309i 1.63726i −0.574322 0.818629i \(-0.694734\pi\)
0.574322 0.818629i \(-0.305266\pi\)
\(788\) 6.00000i 0.213741i
\(789\) −1.36932 −0.0487490
\(790\) 8.98485 0.319666