Properties

Label 690.2.d.c.139.3
Level $690$
Weight $2$
Character 690.139
Analytic conductor $5.510$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 139.3
Root \(1.45161 + 1.45161i\) of defining polynomial
Character \(\chi\) \(=\) 690.139
Dual form 690.2.d.c.139.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} -0.622216i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.21432 + 0.311108i) q^{5} -1.00000 q^{6} -0.622216i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(0.311108 - 2.21432i) q^{10} +4.42864 q^{11} +1.00000i q^{12} +1.37778i q^{13} -0.622216 q^{14} +(0.311108 - 2.21432i) q^{15} +1.00000 q^{16} -6.42864i q^{17} +1.00000i q^{18} +1.37778 q^{19} +(-2.21432 - 0.311108i) q^{20} -0.622216 q^{21} -4.42864i q^{22} +1.00000i q^{23} +1.00000 q^{24} +(4.80642 + 1.37778i) q^{25} +1.37778 q^{26} +1.00000i q^{27} +0.622216i q^{28} +4.23506 q^{29} +(-2.21432 - 0.311108i) q^{30} -4.00000 q^{31} -1.00000i q^{32} -4.42864i q^{33} -6.42864 q^{34} +(0.193576 - 1.37778i) q^{35} +1.00000 q^{36} -11.8064i q^{37} -1.37778i q^{38} +1.37778 q^{39} +(-0.311108 + 2.21432i) q^{40} -10.8573 q^{41} +0.622216i q^{42} -1.05086i q^{43} -4.42864 q^{44} +(-2.21432 - 0.311108i) q^{45} +1.00000 q^{46} +11.6128i q^{47} -1.00000i q^{48} +6.61285 q^{49} +(1.37778 - 4.80642i) q^{50} -6.42864 q^{51} -1.37778i q^{52} +3.37778i q^{53} +1.00000 q^{54} +(9.80642 + 1.37778i) q^{55} +0.622216 q^{56} -1.37778i q^{57} -4.23506i q^{58} -9.61285 q^{59} +(-0.311108 + 2.21432i) q^{60} +8.66370 q^{61} +4.00000i q^{62} +0.622216i q^{63} -1.00000 q^{64} +(-0.428639 + 3.05086i) q^{65} -4.42864 q^{66} -11.8064i q^{67} +6.42864i q^{68} +1.00000 q^{69} +(-1.37778 - 0.193576i) q^{70} -6.99063 q^{71} -1.00000i q^{72} +2.75557i q^{73} -11.8064 q^{74} +(1.37778 - 4.80642i) q^{75} -1.37778 q^{76} -2.75557i q^{77} -1.37778i q^{78} -12.0415 q^{79} +(2.21432 + 0.311108i) q^{80} +1.00000 q^{81} +10.8573i q^{82} +2.19358i q^{83} +0.622216 q^{84} +(2.00000 - 14.2351i) q^{85} -1.05086 q^{86} -4.23506i q^{87} +4.42864i q^{88} -2.75557 q^{89} +(-0.311108 + 2.21432i) q^{90} +0.857279 q^{91} -1.00000i q^{92} +4.00000i q^{93} +11.6128 q^{94} +(3.05086 + 0.428639i) q^{95} -1.00000 q^{96} +2.13335i q^{97} -6.61285i q^{98} -4.42864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + O(q^{10}) \) \( 6q - 6q^{4} - 6q^{6} - 6q^{9} + 2q^{10} - 4q^{14} + 2q^{15} + 6q^{16} + 8q^{19} - 4q^{21} + 6q^{24} + 2q^{25} + 8q^{26} - 28q^{29} - 24q^{31} - 12q^{34} + 28q^{35} + 6q^{36} + 8q^{39} - 2q^{40} - 12q^{41} + 6q^{46} - 14q^{49} + 8q^{50} - 12q^{51} + 6q^{54} + 32q^{55} + 4q^{56} - 4q^{59} - 2q^{60} - 28q^{61} - 6q^{64} + 24q^{65} + 6q^{69} - 8q^{70} + 12q^{71} - 44q^{74} + 8q^{75} - 8q^{76} + 8q^{79} + 6q^{81} + 4q^{84} + 12q^{85} + 20q^{86} - 16q^{89} - 2q^{90} - 48q^{91} + 16q^{94} - 8q^{95} - 6q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.21432 + 0.311108i 0.990274 + 0.139132i
\(6\) −1.00000 −0.408248
\(7\) 0.622216i 0.235175i −0.993063 0.117588i \(-0.962484\pi\)
0.993063 0.117588i \(-0.0375161\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 0.311108 2.21432i 0.0983809 0.700229i
\(11\) 4.42864 1.33529 0.667643 0.744482i \(-0.267303\pi\)
0.667643 + 0.744482i \(0.267303\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.37778i 0.382129i 0.981578 + 0.191064i \(0.0611939\pi\)
−0.981578 + 0.191064i \(0.938806\pi\)
\(14\) −0.622216 −0.166294
\(15\) 0.311108 2.21432i 0.0803277 0.571735i
\(16\) 1.00000 0.250000
\(17\) 6.42864i 1.55917i −0.626294 0.779587i \(-0.715429\pi\)
0.626294 0.779587i \(-0.284571\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.37778 0.316085 0.158043 0.987432i \(-0.449482\pi\)
0.158043 + 0.987432i \(0.449482\pi\)
\(20\) −2.21432 0.311108i −0.495137 0.0695658i
\(21\) −0.622216 −0.135779
\(22\) 4.42864i 0.944189i
\(23\) 1.00000i 0.208514i
\(24\) 1.00000 0.204124
\(25\) 4.80642 + 1.37778i 0.961285 + 0.275557i
\(26\) 1.37778 0.270206
\(27\) 1.00000i 0.192450i
\(28\) 0.622216i 0.117588i
\(29\) 4.23506 0.786432 0.393216 0.919446i \(-0.371363\pi\)
0.393216 + 0.919446i \(0.371363\pi\)
\(30\) −2.21432 0.311108i −0.404278 0.0568003i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.42864i 0.770927i
\(34\) −6.42864 −1.10250
\(35\) 0.193576 1.37778i 0.0327203 0.232888i
\(36\) 1.00000 0.166667
\(37\) 11.8064i 1.94096i −0.241173 0.970482i \(-0.577532\pi\)
0.241173 0.970482i \(-0.422468\pi\)
\(38\) 1.37778i 0.223506i
\(39\) 1.37778 0.220622
\(40\) −0.311108 + 2.21432i −0.0491905 + 0.350115i
\(41\) −10.8573 −1.69562 −0.847811 0.530298i \(-0.822080\pi\)
−0.847811 + 0.530298i \(0.822080\pi\)
\(42\) 0.622216i 0.0960100i
\(43\) 1.05086i 0.160254i −0.996785 0.0801270i \(-0.974467\pi\)
0.996785 0.0801270i \(-0.0255326\pi\)
\(44\) −4.42864 −0.667643
\(45\) −2.21432 0.311108i −0.330091 0.0463772i
\(46\) 1.00000 0.147442
\(47\) 11.6128i 1.69391i 0.531666 + 0.846954i \(0.321566\pi\)
−0.531666 + 0.846954i \(0.678434\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.61285 0.944693
\(50\) 1.37778 4.80642i 0.194848 0.679731i
\(51\) −6.42864 −0.900190
\(52\) 1.37778i 0.191064i
\(53\) 3.37778i 0.463974i 0.972719 + 0.231987i \(0.0745227\pi\)
−0.972719 + 0.231987i \(0.925477\pi\)
\(54\) 1.00000 0.136083
\(55\) 9.80642 + 1.37778i 1.32230 + 0.185780i
\(56\) 0.622216 0.0831471
\(57\) 1.37778i 0.182492i
\(58\) 4.23506i 0.556091i
\(59\) −9.61285 −1.25149 −0.625743 0.780029i \(-0.715204\pi\)
−0.625743 + 0.780029i \(0.715204\pi\)
\(60\) −0.311108 + 2.21432i −0.0401638 + 0.285867i
\(61\) 8.66370 1.10927 0.554637 0.832093i \(-0.312857\pi\)
0.554637 + 0.832093i \(0.312857\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0.622216i 0.0783918i
\(64\) −1.00000 −0.125000
\(65\) −0.428639 + 3.05086i −0.0531662 + 0.378412i
\(66\) −4.42864 −0.545128
\(67\) 11.8064i 1.44238i −0.692735 0.721192i \(-0.743594\pi\)
0.692735 0.721192i \(-0.256406\pi\)
\(68\) 6.42864i 0.779587i
\(69\) 1.00000 0.120386
\(70\) −1.37778 0.193576i −0.164677 0.0231368i
\(71\) −6.99063 −0.829635 −0.414818 0.909905i \(-0.636155\pi\)
−0.414818 + 0.909905i \(0.636155\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 2.75557i 0.322515i 0.986912 + 0.161257i \(0.0515550\pi\)
−0.986912 + 0.161257i \(0.948445\pi\)
\(74\) −11.8064 −1.37247
\(75\) 1.37778 4.80642i 0.159093 0.554998i
\(76\) −1.37778 −0.158043
\(77\) 2.75557i 0.314026i
\(78\) 1.37778i 0.156003i
\(79\) −12.0415 −1.35477 −0.677387 0.735627i \(-0.736888\pi\)
−0.677387 + 0.735627i \(0.736888\pi\)
\(80\) 2.21432 + 0.311108i 0.247568 + 0.0347829i
\(81\) 1.00000 0.111111
\(82\) 10.8573i 1.19899i
\(83\) 2.19358i 0.240776i 0.992727 + 0.120388i \(0.0384139\pi\)
−0.992727 + 0.120388i \(0.961586\pi\)
\(84\) 0.622216 0.0678893
\(85\) 2.00000 14.2351i 0.216930 1.54401i
\(86\) −1.05086 −0.113317
\(87\) 4.23506i 0.454046i
\(88\) 4.42864i 0.472095i
\(89\) −2.75557 −0.292090 −0.146045 0.989278i \(-0.546654\pi\)
−0.146045 + 0.989278i \(0.546654\pi\)
\(90\) −0.311108 + 2.21432i −0.0327936 + 0.233410i
\(91\) 0.857279 0.0898673
\(92\) 1.00000i 0.104257i
\(93\) 4.00000i 0.414781i
\(94\) 11.6128 1.19777
\(95\) 3.05086 + 0.428639i 0.313011 + 0.0439775i
\(96\) −1.00000 −0.102062
\(97\) 2.13335i 0.216609i 0.994118 + 0.108305i \(0.0345422\pi\)
−0.994118 + 0.108305i \(0.965458\pi\)
\(98\) 6.61285i 0.667998i
\(99\) −4.42864 −0.445095
\(100\) −4.80642 1.37778i −0.480642 0.137778i
\(101\) 16.2351 1.61545 0.807725 0.589560i \(-0.200699\pi\)
0.807725 + 0.589560i \(0.200699\pi\)
\(102\) 6.42864i 0.636530i
\(103\) 12.2351i 1.20556i 0.797909 + 0.602778i \(0.205940\pi\)
−0.797909 + 0.602778i \(0.794060\pi\)
\(104\) −1.37778 −0.135103
\(105\) −1.37778 0.193576i −0.134458 0.0188911i
\(106\) 3.37778 0.328079
\(107\) 10.6637i 1.03090i 0.856920 + 0.515450i \(0.172375\pi\)
−0.856920 + 0.515450i \(0.827625\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 15.1526 1.45135 0.725676 0.688036i \(-0.241527\pi\)
0.725676 + 0.688036i \(0.241527\pi\)
\(110\) 1.37778 9.80642i 0.131367 0.935006i
\(111\) −11.8064 −1.12062
\(112\) 0.622216i 0.0587939i
\(113\) 14.4286i 1.35733i 0.734447 + 0.678666i \(0.237442\pi\)
−0.734447 + 0.678666i \(0.762558\pi\)
\(114\) −1.37778 −0.129041
\(115\) −0.311108 + 2.21432i −0.0290110 + 0.206486i
\(116\) −4.23506 −0.393216
\(117\) 1.37778i 0.127376i
\(118\) 9.61285i 0.884934i
\(119\) −4.00000 −0.366679
\(120\) 2.21432 + 0.311108i 0.202139 + 0.0284001i
\(121\) 8.61285 0.782986
\(122\) 8.66370i 0.784375i
\(123\) 10.8573i 0.978968i
\(124\) 4.00000 0.359211
\(125\) 10.2143 + 4.54617i 0.913597 + 0.406622i
\(126\) 0.622216 0.0554314
\(127\) 4.99063i 0.442847i 0.975178 + 0.221423i \(0.0710703\pi\)
−0.975178 + 0.221423i \(0.928930\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −1.05086 −0.0925226
\(130\) 3.05086 + 0.428639i 0.267578 + 0.0375942i
\(131\) 0.755569 0.0660143 0.0330072 0.999455i \(-0.489492\pi\)
0.0330072 + 0.999455i \(0.489492\pi\)
\(132\) 4.42864i 0.385464i
\(133\) 0.857279i 0.0743355i
\(134\) −11.8064 −1.01992
\(135\) −0.311108 + 2.21432i −0.0267759 + 0.190578i
\(136\) 6.42864 0.551251
\(137\) 12.9175i 1.10362i −0.833971 0.551808i \(-0.813938\pi\)
0.833971 0.551808i \(-0.186062\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) 14.1017 1.19609 0.598046 0.801462i \(-0.295944\pi\)
0.598046 + 0.801462i \(0.295944\pi\)
\(140\) −0.193576 + 1.37778i −0.0163602 + 0.116444i
\(141\) 11.6128 0.977978
\(142\) 6.99063i 0.586641i
\(143\) 6.10171i 0.510251i
\(144\) −1.00000 −0.0833333
\(145\) 9.37778 + 1.31756i 0.778783 + 0.109418i
\(146\) 2.75557 0.228052
\(147\) 6.61285i 0.545418i
\(148\) 11.8064i 0.970482i
\(149\) −12.4286 −1.01819 −0.509097 0.860709i \(-0.670021\pi\)
−0.509097 + 0.860709i \(0.670021\pi\)
\(150\) −4.80642 1.37778i −0.392443 0.112496i
\(151\) −4.85728 −0.395280 −0.197640 0.980275i \(-0.563328\pi\)
−0.197640 + 0.980275i \(0.563328\pi\)
\(152\) 1.37778i 0.111753i
\(153\) 6.42864i 0.519725i
\(154\) −2.75557 −0.222050
\(155\) −8.85728 1.24443i −0.711434 0.0999551i
\(156\) −1.37778 −0.110311
\(157\) 9.90813i 0.790755i 0.918519 + 0.395378i \(0.129386\pi\)
−0.918519 + 0.395378i \(0.870614\pi\)
\(158\) 12.0415i 0.957969i
\(159\) 3.37778 0.267876
\(160\) 0.311108 2.21432i 0.0245952 0.175057i
\(161\) 0.622216 0.0490375
\(162\) 1.00000i 0.0785674i
\(163\) 10.1017i 0.791227i 0.918417 + 0.395614i \(0.129468\pi\)
−0.918417 + 0.395614i \(0.870532\pi\)
\(164\) 10.8573 0.847811
\(165\) 1.37778 9.80642i 0.107260 0.763429i
\(166\) 2.19358 0.170255
\(167\) 1.89829i 0.146894i −0.997299 0.0734470i \(-0.976600\pi\)
0.997299 0.0734470i \(-0.0234000\pi\)
\(168\) 0.622216i 0.0480050i
\(169\) 11.1017 0.853978
\(170\) −14.2351 2.00000i −1.09178 0.153393i
\(171\) −1.37778 −0.105362
\(172\) 1.05086i 0.0801270i
\(173\) 21.2257i 1.61376i 0.590716 + 0.806880i \(0.298846\pi\)
−0.590716 + 0.806880i \(0.701154\pi\)
\(174\) −4.23506 −0.321059
\(175\) 0.857279 2.99063i 0.0648042 0.226071i
\(176\) 4.42864 0.333821
\(177\) 9.61285i 0.722546i
\(178\) 2.75557i 0.206539i
\(179\) −0.488863 −0.0365393 −0.0182697 0.999833i \(-0.505816\pi\)
−0.0182697 + 0.999833i \(0.505816\pi\)
\(180\) 2.21432 + 0.311108i 0.165046 + 0.0231886i
\(181\) −20.9304 −1.55575 −0.777873 0.628422i \(-0.783701\pi\)
−0.777873 + 0.628422i \(0.783701\pi\)
\(182\) 0.857279i 0.0635457i
\(183\) 8.66370i 0.640439i
\(184\) −1.00000 −0.0737210
\(185\) 3.67307 26.1432i 0.270050 1.92209i
\(186\) 4.00000 0.293294
\(187\) 28.4701i 2.08194i
\(188\) 11.6128i 0.846954i
\(189\) 0.622216 0.0452595
\(190\) 0.428639 3.05086i 0.0310968 0.221332i
\(191\) 18.9590 1.37182 0.685912 0.727684i \(-0.259403\pi\)
0.685912 + 0.727684i \(0.259403\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 1.24443i 0.0895761i −0.998997 0.0447881i \(-0.985739\pi\)
0.998997 0.0447881i \(-0.0142613\pi\)
\(194\) 2.13335 0.153166
\(195\) 3.05086 + 0.428639i 0.218476 + 0.0306955i
\(196\) −6.61285 −0.472346
\(197\) 15.2444i 1.08612i 0.839694 + 0.543060i \(0.182735\pi\)
−0.839694 + 0.543060i \(0.817265\pi\)
\(198\) 4.42864i 0.314730i
\(199\) 14.5303 1.03003 0.515015 0.857181i \(-0.327786\pi\)
0.515015 + 0.857181i \(0.327786\pi\)
\(200\) −1.37778 + 4.80642i −0.0974241 + 0.339865i
\(201\) −11.8064 −0.832761
\(202\) 16.2351i 1.14230i
\(203\) 2.63512i 0.184949i
\(204\) 6.42864 0.450095
\(205\) −24.0415 3.37778i −1.67913 0.235915i
\(206\) 12.2351 0.852457
\(207\) 1.00000i 0.0695048i
\(208\) 1.37778i 0.0955322i
\(209\) 6.10171 0.422064
\(210\) −0.193576 + 1.37778i −0.0133580 + 0.0950762i
\(211\) 0.266706 0.0183608 0.00918041 0.999958i \(-0.497078\pi\)
0.00918041 + 0.999958i \(0.497078\pi\)
\(212\) 3.37778i 0.231987i
\(213\) 6.99063i 0.478990i
\(214\) 10.6637 0.728956
\(215\) 0.326929 2.32693i 0.0222964 0.158695i
\(216\) −1.00000 −0.0680414
\(217\) 2.48886i 0.168955i
\(218\) 15.1526i 1.02626i
\(219\) 2.75557 0.186204
\(220\) −9.80642 1.37778i −0.661149 0.0928902i
\(221\) 8.85728 0.595805
\(222\) 11.8064i 0.792395i
\(223\) 0.990632i 0.0663376i −0.999450 0.0331688i \(-0.989440\pi\)
0.999450 0.0331688i \(-0.0105599\pi\)
\(224\) −0.622216 −0.0415735
\(225\) −4.80642 1.37778i −0.320428 0.0918523i
\(226\) 14.4286 0.959779
\(227\) 17.1526i 1.13846i 0.822180 + 0.569228i \(0.192758\pi\)
−0.822180 + 0.569228i \(0.807242\pi\)
\(228\) 1.37778i 0.0912460i
\(229\) −7.15257 −0.472655 −0.236327 0.971673i \(-0.575944\pi\)
−0.236327 + 0.971673i \(0.575944\pi\)
\(230\) 2.21432 + 0.311108i 0.146008 + 0.0205138i
\(231\) −2.75557 −0.181303
\(232\) 4.23506i 0.278046i
\(233\) 3.71456i 0.243349i −0.992570 0.121674i \(-0.961174\pi\)
0.992570 0.121674i \(-0.0388264\pi\)
\(234\) −1.37778 −0.0900686
\(235\) −3.61285 + 25.7146i −0.235676 + 1.67743i
\(236\) 9.61285 0.625743
\(237\) 12.0415i 0.782179i
\(238\) 4.00000i 0.259281i
\(239\) −27.8479 −1.80133 −0.900666 0.434512i \(-0.856921\pi\)
−0.900666 + 0.434512i \(0.856921\pi\)
\(240\) 0.311108 2.21432i 0.0200819 0.142934i
\(241\) −7.12399 −0.458896 −0.229448 0.973321i \(-0.573692\pi\)
−0.229448 + 0.973321i \(0.573692\pi\)
\(242\) 8.61285i 0.553655i
\(243\) 1.00000i 0.0641500i
\(244\) −8.66370 −0.554637
\(245\) 14.6430 + 2.05731i 0.935504 + 0.131437i
\(246\) 10.8573 0.692235
\(247\) 1.89829i 0.120785i
\(248\) 4.00000i 0.254000i
\(249\) 2.19358 0.139012
\(250\) 4.54617 10.2143i 0.287525 0.646010i
\(251\) −22.4099 −1.41450 −0.707250 0.706963i \(-0.750065\pi\)
−0.707250 + 0.706963i \(0.750065\pi\)
\(252\) 0.622216i 0.0391959i
\(253\) 4.42864i 0.278426i
\(254\) 4.99063 0.313140
\(255\) −14.2351 2.00000i −0.891434 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 11.7146i 0.730734i −0.930864 0.365367i \(-0.880943\pi\)
0.930864 0.365367i \(-0.119057\pi\)
\(258\) 1.05086i 0.0654234i
\(259\) −7.34614 −0.456467
\(260\) 0.428639 3.05086i 0.0265831 0.189206i
\(261\) −4.23506 −0.262144
\(262\) 0.755569i 0.0466792i
\(263\) 8.47013i 0.522290i 0.965300 + 0.261145i \(0.0841001\pi\)
−0.965300 + 0.261145i \(0.915900\pi\)
\(264\) 4.42864 0.272564
\(265\) −1.05086 + 7.47949i −0.0645535 + 0.459462i
\(266\) −0.857279 −0.0525631
\(267\) 2.75557i 0.168638i
\(268\) 11.8064i 0.721192i
\(269\) −28.8256 −1.75753 −0.878765 0.477255i \(-0.841632\pi\)
−0.878765 + 0.477255i \(0.841632\pi\)
\(270\) 2.21432 + 0.311108i 0.134759 + 0.0189334i
\(271\) −13.8350 −0.840417 −0.420208 0.907428i \(-0.638043\pi\)
−0.420208 + 0.907428i \(0.638043\pi\)
\(272\) 6.42864i 0.389794i
\(273\) 0.857279i 0.0518849i
\(274\) −12.9175 −0.780375
\(275\) 21.2859 + 6.10171i 1.28359 + 0.367947i
\(276\) −1.00000 −0.0601929
\(277\) 2.88892i 0.173578i 0.996227 + 0.0867892i \(0.0276607\pi\)
−0.996227 + 0.0867892i \(0.972339\pi\)
\(278\) 14.1017i 0.845764i
\(279\) 4.00000 0.239474
\(280\) 1.37778 + 0.193576i 0.0823384 + 0.0115684i
\(281\) 5.51114 0.328767 0.164383 0.986397i \(-0.447437\pi\)
0.164383 + 0.986397i \(0.447437\pi\)
\(282\) 11.6128i 0.691535i
\(283\) 8.19358i 0.487058i −0.969894 0.243529i \(-0.921695\pi\)
0.969894 0.243529i \(-0.0783050\pi\)
\(284\) 6.99063 0.414818
\(285\) 0.428639 3.05086i 0.0253904 0.180717i
\(286\) 6.10171 0.360802
\(287\) 6.75557i 0.398769i
\(288\) 1.00000i 0.0589256i
\(289\) −24.3274 −1.43102
\(290\) 1.31756 9.37778i 0.0773699 0.550682i
\(291\) 2.13335 0.125059
\(292\) 2.75557i 0.161257i
\(293\) 12.6222i 0.737398i −0.929549 0.368699i \(-0.879803\pi\)
0.929549 0.368699i \(-0.120197\pi\)
\(294\) −6.61285 −0.385669
\(295\) −21.2859 2.99063i −1.23931 0.174121i
\(296\) 11.8064 0.686234
\(297\) 4.42864i 0.256976i
\(298\) 12.4286i 0.719972i
\(299\) −1.37778 −0.0796793
\(300\) −1.37778 + 4.80642i −0.0795464 + 0.277499i
\(301\) −0.653858 −0.0376878
\(302\) 4.85728i 0.279505i
\(303\) 16.2351i 0.932680i
\(304\) 1.37778 0.0790214
\(305\) 19.1842 + 2.69535i 1.09848 + 0.154335i
\(306\) 6.42864 0.367501
\(307\) 0.653858i 0.0373177i −0.999826 0.0186588i \(-0.994060\pi\)
0.999826 0.0186588i \(-0.00593964\pi\)
\(308\) 2.75557i 0.157013i
\(309\) 12.2351 0.696028
\(310\) −1.24443 + 8.85728i −0.0706789 + 0.503060i
\(311\) −13.0923 −0.742399 −0.371199 0.928553i \(-0.621053\pi\)
−0.371199 + 0.928553i \(0.621053\pi\)
\(312\) 1.37778i 0.0780017i
\(313\) 11.2573i 0.636302i −0.948040 0.318151i \(-0.896938\pi\)
0.948040 0.318151i \(-0.103062\pi\)
\(314\) 9.90813 0.559148
\(315\) −0.193576 + 1.37778i −0.0109068 + 0.0776294i
\(316\) 12.0415 0.677387
\(317\) 22.4701i 1.26205i −0.775763 0.631024i \(-0.782635\pi\)
0.775763 0.631024i \(-0.217365\pi\)
\(318\) 3.37778i 0.189417i
\(319\) 18.7556 1.05011
\(320\) −2.21432 0.311108i −0.123784 0.0173915i
\(321\) 10.6637 0.595190
\(322\) 0.622216i 0.0346747i
\(323\) 8.85728i 0.492832i
\(324\) −1.00000 −0.0555556
\(325\) −1.89829 + 6.62222i −0.105298 + 0.367334i
\(326\) 10.1017 0.559482
\(327\) 15.1526i 0.837939i
\(328\) 10.8573i 0.599493i
\(329\) 7.22570 0.398365
\(330\) −9.80642 1.37778i −0.539826 0.0758445i
\(331\) −29.4479 −1.61860 −0.809300 0.587395i \(-0.800153\pi\)
−0.809300 + 0.587395i \(0.800153\pi\)
\(332\) 2.19358i 0.120388i
\(333\) 11.8064i 0.646988i
\(334\) −1.89829 −0.103870
\(335\) 3.67307 26.1432i 0.200681 1.42836i
\(336\) −0.622216 −0.0339446
\(337\) 24.6222i 1.34126i −0.741793 0.670629i \(-0.766024\pi\)
0.741793 0.670629i \(-0.233976\pi\)
\(338\) 11.1017i 0.603853i
\(339\) 14.4286 0.783656
\(340\) −2.00000 + 14.2351i −0.108465 + 0.772005i
\(341\) −17.7146 −0.959297
\(342\) 1.37778i 0.0745020i
\(343\) 8.47013i 0.457344i
\(344\) 1.05086 0.0566583
\(345\) 2.21432 + 0.311108i 0.119215 + 0.0167495i
\(346\) 21.2257 1.14110
\(347\) 26.1017i 1.40121i 0.713548 + 0.700607i \(0.247087\pi\)
−0.713548 + 0.700607i \(0.752913\pi\)
\(348\) 4.23506i 0.227023i
\(349\) 21.2257 1.13619 0.568093 0.822965i \(-0.307681\pi\)
0.568093 + 0.822965i \(0.307681\pi\)
\(350\) −2.99063 0.857279i −0.159856 0.0458235i
\(351\) −1.37778 −0.0735407
\(352\) 4.42864i 0.236047i
\(353\) 4.28544i 0.228091i 0.993476 + 0.114046i \(0.0363810\pi\)
−0.993476 + 0.114046i \(0.963619\pi\)
\(354\) 9.61285 0.510917
\(355\) −15.4795 2.17484i −0.821566 0.115429i
\(356\) 2.75557 0.146045
\(357\) 4.00000i 0.211702i
\(358\) 0.488863i 0.0258372i
\(359\) 4.65386 0.245621 0.122811 0.992430i \(-0.460809\pi\)
0.122811 + 0.992430i \(0.460809\pi\)
\(360\) 0.311108 2.21432i 0.0163968 0.116705i
\(361\) −17.1017 −0.900090
\(362\) 20.9304i 1.10008i
\(363\) 8.61285i 0.452057i
\(364\) −0.857279 −0.0449336
\(365\) −0.857279 + 6.10171i −0.0448720 + 0.319378i
\(366\) −8.66370 −0.452859
\(367\) 4.88892i 0.255200i 0.991826 + 0.127600i \(0.0407273\pi\)
−0.991826 + 0.127600i \(0.959273\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 10.8573 0.565207
\(370\) −26.1432 3.67307i −1.35912 0.190954i
\(371\) 2.10171 0.109115
\(372\) 4.00000i 0.207390i
\(373\) 23.4193i 1.21260i −0.795235 0.606302i \(-0.792652\pi\)
0.795235 0.606302i \(-0.207348\pi\)
\(374\) −28.4701 −1.47216
\(375\) 4.54617 10.2143i 0.234763 0.527465i
\(376\) −11.6128 −0.598887
\(377\) 5.83500i 0.300518i
\(378\) 0.622216i 0.0320033i
\(379\) 4.90766 0.252089 0.126045 0.992025i \(-0.459772\pi\)
0.126045 + 0.992025i \(0.459772\pi\)
\(380\) −3.05086 0.428639i −0.156506 0.0219887i
\(381\) 4.99063 0.255678
\(382\) 18.9590i 0.970026i
\(383\) 19.8796i 1.01580i 0.861417 + 0.507899i \(0.169578\pi\)
−0.861417 + 0.507899i \(0.830422\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.857279 6.10171i 0.0436910 0.310972i
\(386\) −1.24443 −0.0633399
\(387\) 1.05086i 0.0534180i
\(388\) 2.13335i 0.108305i
\(389\) 0.161933 0.00821034 0.00410517 0.999992i \(-0.498693\pi\)
0.00410517 + 0.999992i \(0.498693\pi\)
\(390\) 0.428639 3.05086i 0.0217050 0.154486i
\(391\) 6.42864 0.325110
\(392\) 6.61285i 0.333999i
\(393\) 0.755569i 0.0381134i
\(394\) 15.2444 0.768003
\(395\) −26.6637 3.74620i −1.34160 0.188492i
\(396\) 4.42864 0.222548
\(397\) 1.76494i 0.0885796i 0.999019 + 0.0442898i \(0.0141025\pi\)
−0.999019 + 0.0442898i \(0.985898\pi\)
\(398\) 14.5303i 0.728341i
\(399\) −0.857279 −0.0429176
\(400\) 4.80642 + 1.37778i 0.240321 + 0.0688892i
\(401\) −31.3461 −1.56535 −0.782676 0.622430i \(-0.786146\pi\)
−0.782676 + 0.622430i \(0.786146\pi\)
\(402\) 11.8064i 0.588851i
\(403\) 5.51114i 0.274529i
\(404\) −16.2351 −0.807725
\(405\) 2.21432 + 0.311108i 0.110030 + 0.0154591i
\(406\) −2.63512 −0.130779
\(407\) 52.2864i 2.59174i
\(408\) 6.42864i 0.318265i
\(409\) 3.51114 0.173615 0.0868073 0.996225i \(-0.472334\pi\)
0.0868073 + 0.996225i \(0.472334\pi\)
\(410\) −3.37778 + 24.0415i −0.166817 + 1.18732i
\(411\) −12.9175 −0.637173
\(412\) 12.2351i 0.602778i
\(413\) 5.98126i 0.294319i
\(414\) −1.00000 −0.0491473
\(415\) −0.682439 + 4.85728i −0.0334996 + 0.238434i
\(416\) 1.37778 0.0675514
\(417\) 14.1017i 0.690564i
\(418\) 6.10171i 0.298444i
\(419\) 19.7748 0.966061 0.483031 0.875603i \(-0.339536\pi\)
0.483031 + 0.875603i \(0.339536\pi\)
\(420\) 1.37778 + 0.193576i 0.0672290 + 0.00944555i
\(421\) 11.8064 0.575410 0.287705 0.957719i \(-0.407108\pi\)
0.287705 + 0.957719i \(0.407108\pi\)
\(422\) 0.266706i 0.0129831i
\(423\) 11.6128i 0.564636i
\(424\) −3.37778 −0.164040
\(425\) 8.85728 30.8988i 0.429641 1.49881i
\(426\) 6.99063 0.338697
\(427\) 5.39069i 0.260874i
\(428\) 10.6637i 0.515450i
\(429\) 6.10171 0.294593
\(430\) −2.32693 0.326929i −0.112214 0.0157659i
\(431\) 24.9403 1.20133 0.600665 0.799501i \(-0.294903\pi\)
0.600665 + 0.799501i \(0.294903\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 32.0513i 1.54029i 0.637870 + 0.770144i \(0.279816\pi\)
−0.637870 + 0.770144i \(0.720184\pi\)
\(434\) 2.48886 0.119469
\(435\) 1.31756 9.37778i 0.0631722 0.449630i
\(436\) −15.1526 −0.725676
\(437\) 1.37778i 0.0659084i
\(438\) 2.75557i 0.131666i
\(439\) −0.470127 −0.0224379 −0.0112190 0.999937i \(-0.503571\pi\)
−0.0112190 + 0.999937i \(0.503571\pi\)
\(440\) −1.37778 + 9.80642i −0.0656833 + 0.467503i
\(441\) −6.61285 −0.314898
\(442\) 8.85728i 0.421298i
\(443\) 0.653858i 0.0310658i 0.999879 + 0.0155329i \(0.00494447\pi\)
−0.999879 + 0.0155329i \(0.995056\pi\)
\(444\) 11.8064 0.560308
\(445\) −6.10171 0.857279i −0.289249 0.0406389i
\(446\) −0.990632 −0.0469078
\(447\) 12.4286i 0.587854i
\(448\) 0.622216i 0.0293969i
\(449\) −17.1427 −0.809015 −0.404508 0.914535i \(-0.632557\pi\)
−0.404508 + 0.914535i \(0.632557\pi\)
\(450\) −1.37778 + 4.80642i −0.0649494 + 0.226577i
\(451\) −48.0830 −2.26414
\(452\) 14.4286i 0.678666i
\(453\) 4.85728i 0.228215i
\(454\) 17.1526 0.805010
\(455\) 1.89829 + 0.266706i 0.0889932 + 0.0125034i
\(456\) 1.37778 0.0645207
\(457\) 1.00937i 0.0472162i 0.999721 + 0.0236081i \(0.00751540\pi\)
−0.999721 + 0.0236081i \(0.992485\pi\)
\(458\) 7.15257i 0.334217i
\(459\) 6.42864 0.300063
\(460\) 0.311108 2.21432i 0.0145055 0.103243i
\(461\) 20.3180 0.946305 0.473153 0.880980i \(-0.343116\pi\)
0.473153 + 0.880980i \(0.343116\pi\)
\(462\) 2.75557i 0.128201i
\(463\) 12.4572i 0.578936i −0.957188 0.289468i \(-0.906522\pi\)
0.957188 0.289468i \(-0.0934784\pi\)
\(464\) 4.23506 0.196608
\(465\) −1.24443 + 8.85728i −0.0577091 + 0.410746i
\(466\) −3.71456 −0.172074
\(467\) 15.7877i 0.730567i −0.930896 0.365284i \(-0.880972\pi\)
0.930896 0.365284i \(-0.119028\pi\)
\(468\) 1.37778i 0.0636881i
\(469\) −7.34614 −0.339213
\(470\) 25.7146 + 3.61285i 1.18612 + 0.166648i
\(471\) 9.90813 0.456543
\(472\) 9.61285i 0.442467i
\(473\) 4.65386i 0.213985i
\(474\) 12.0415 0.553084
\(475\) 6.62222 + 1.89829i 0.303848 + 0.0870995i
\(476\) 4.00000 0.183340
\(477\) 3.37778i 0.154658i
\(478\) 27.8479i 1.27373i
\(479\) −5.12399 −0.234121 −0.117060 0.993125i \(-0.537347\pi\)
−0.117060 + 0.993125i \(0.537347\pi\)
\(480\) −2.21432 0.311108i −0.101069 0.0142001i
\(481\) 16.2667 0.741698
\(482\) 7.12399i 0.324489i
\(483\) 0.622216i 0.0283118i
\(484\) −8.61285 −0.391493
\(485\) −0.663703 + 4.72393i −0.0301372 + 0.214502i
\(486\) −1.00000 −0.0453609
\(487\) 23.2128i 1.05187i −0.850524 0.525936i \(-0.823715\pi\)
0.850524 0.525936i \(-0.176285\pi\)
\(488\) 8.66370i 0.392187i
\(489\) 10.1017 0.456815
\(490\) 2.05731 14.6430i 0.0929397 0.661501i
\(491\) −40.1847 −1.81351 −0.906755 0.421658i \(-0.861448\pi\)
−0.906755 + 0.421658i \(0.861448\pi\)
\(492\) 10.8573i 0.489484i
\(493\) 27.2257i 1.22618i
\(494\) 1.89829 0.0854081
\(495\) −9.80642 1.37778i −0.440766 0.0619268i
\(496\) −4.00000 −0.179605
\(497\) 4.34968i 0.195110i
\(498\) 2.19358i 0.0982965i
\(499\) −30.5718 −1.36858 −0.684292 0.729208i \(-0.739888\pi\)
−0.684292 + 0.729208i \(0.739888\pi\)
\(500\) −10.2143 4.54617i −0.456798 0.203311i
\(501\) −1.89829 −0.0848093
\(502\) 22.4099i 1.00020i
\(503\) 23.4291i 1.04465i 0.852746 + 0.522326i \(0.174936\pi\)
−0.852746 + 0.522326i \(0.825064\pi\)
\(504\) −0.622216 −0.0277157
\(505\) 35.9496 + 5.05086i 1.59974 + 0.224760i
\(506\) 4.42864 0.196877
\(507\) 11.1017i 0.493044i
\(508\) 4.99063i 0.221423i
\(509\) 17.2128 0.762943 0.381472 0.924381i \(-0.375417\pi\)
0.381472 + 0.924381i \(0.375417\pi\)
\(510\) −2.00000 + 14.2351i −0.0885615 + 0.630339i
\(511\) 1.71456 0.0758476
\(512\) 1.00000i 0.0441942i
\(513\) 1.37778i 0.0608307i
\(514\) −11.7146 −0.516707
\(515\) −3.80642 + 27.0923i −0.167731 + 1.19383i
\(516\) 1.05086 0.0462613
\(517\) 51.4291i 2.26185i
\(518\) 7.34614i 0.322771i
\(519\) 21.2257 0.931705
\(520\) −3.05086 0.428639i −0.133789 0.0187971i
\(521\) 22.3684 0.979978 0.489989 0.871729i \(-0.337001\pi\)
0.489989 + 0.871729i \(0.337001\pi\)
\(522\) 4.23506i 0.185364i
\(523\) 30.2953i 1.32472i −0.749186 0.662360i \(-0.769555\pi\)
0.749186 0.662360i \(-0.230445\pi\)
\(524\) −0.755569 −0.0330072
\(525\) −2.99063 0.857279i −0.130522 0.0374147i
\(526\) 8.47013 0.369315
\(527\) 25.7146i 1.12014i
\(528\) 4.42864i 0.192732i
\(529\) −1.00000 −0.0434783
\(530\) 7.47949 + 1.05086i 0.324888 + 0.0456462i
\(531\) 9.61285 0.417162
\(532\) 0.857279i 0.0371678i
\(533\) 14.9590i 0.647946i
\(534\) 2.75557 0.119245
\(535\) −3.31756 + 23.6128i −0.143431 + 1.02087i
\(536\) 11.8064 0.509960
\(537\) 0.488863i 0.0210960i
\(538\) 28.8256i 1.24276i
\(539\) 29.2859 1.26143
\(540\) 0.311108 2.21432i 0.0133879 0.0952891i
\(541\) 31.4479 1.35205 0.676024 0.736879i \(-0.263701\pi\)
0.676024 + 0.736879i \(0.263701\pi\)
\(542\) 13.8350i 0.594264i
\(543\) 20.9304i 0.898210i
\(544\) −6.42864 −0.275626
\(545\) 33.5526 + 4.71408i 1.43724 + 0.201929i
\(546\) −0.857279 −0.0366882
\(547\) 20.8573i 0.891793i 0.895085 + 0.445896i \(0.147115\pi\)
−0.895085 + 0.445896i \(0.852885\pi\)
\(548\) 12.9175i 0.551808i
\(549\) −8.66370 −0.369758
\(550\) 6.10171 21.2859i 0.260178 0.907635i
\(551\) 5.83500 0.248580
\(552\) 1.00000i 0.0425628i
\(553\) 7.49240i 0.318609i
\(554\) 2.88892 0.122739
\(555\) −26.1432 3.67307i −1.10972 0.155913i
\(556\) −14.1017 −0.598046
\(557\) 36.3180i 1.53884i 0.638740 + 0.769422i \(0.279456\pi\)
−0.638740 + 0.769422i \(0.720544\pi\)
\(558\) 4.00000i 0.169334i
\(559\) 1.44785 0.0612376
\(560\) 0.193576 1.37778i 0.00818009 0.0582220i
\(561\) −28.4701 −1.20201
\(562\) 5.51114i 0.232473i
\(563\) 2.58073i 0.108765i −0.998520 0.0543824i \(-0.982681\pi\)
0.998520 0.0543824i \(-0.0173190\pi\)
\(564\) −11.6128 −0.488989
\(565\) −4.48886 + 31.9496i −0.188848 + 1.34413i
\(566\) −8.19358 −0.344402
\(567\) 0.622216i 0.0261306i
\(568\) 6.99063i 0.293320i
\(569\) 36.3497 1.52386 0.761929 0.647661i \(-0.224253\pi\)
0.761929 + 0.647661i \(0.224253\pi\)
\(570\) −3.05086 0.428639i −0.127786 0.0179537i
\(571\) −45.9309 −1.92215 −0.961074 0.276292i \(-0.910894\pi\)
−0.961074 + 0.276292i \(0.910894\pi\)
\(572\) 6.10171i 0.255125i
\(573\) 18.9590i 0.792023i
\(574\) 6.75557 0.281972
\(575\) −1.37778 + 4.80642i −0.0574576 + 0.200442i
\(576\) 1.00000 0.0416667
\(577\) 4.00000i 0.166522i 0.996528 + 0.0832611i \(0.0265335\pi\)
−0.996528 + 0.0832611i \(0.973466\pi\)
\(578\) 24.3274i 1.01189i
\(579\) −1.24443 −0.0517168
\(580\) −9.37778 1.31756i −0.389391 0.0547088i
\(581\) 1.36488 0.0566247
\(582\) 2.13335i 0.0884303i
\(583\) 14.9590i 0.619538i
\(584\) −2.75557 −0.114026
\(585\) 0.428639 3.05086i 0.0177221 0.126137i
\(586\) −12.6222 −0.521419
\(587\) 42.1847i 1.74115i 0.492037 + 0.870574i \(0.336252\pi\)
−0.492037 + 0.870574i \(0.663748\pi\)
\(588\) 6.61285i 0.272709i
\(589\) −5.51114 −0.227082
\(590\) −2.99063 + 21.2859i −0.123122 + 0.876327i
\(591\) 15.2444 0.627072
\(592\) 11.8064i 0.485241i
\(593\) 18.7368i 0.769430i −0.923036 0.384715i \(-0.874300\pi\)
0.923036 0.384715i \(-0.125700\pi\)
\(594\) 4.42864 0.181709
\(595\) −8.85728 1.24443i −0.363113 0.0510167i
\(596\) 12.4286 0.509097
\(597\) 14.5303i 0.594688i
\(598\) 1.37778i 0.0563418i
\(599\) 41.5625 1.69820 0.849098 0.528235i \(-0.177146\pi\)
0.849098 + 0.528235i \(0.177146\pi\)
\(600\) 4.80642 + 1.37778i 0.196221 + 0.0562478i
\(601\) 23.7146 0.967337 0.483668 0.875251i \(-0.339304\pi\)
0.483668 + 0.875251i \(0.339304\pi\)
\(602\) 0.653858i 0.0266493i
\(603\) 11.8064i 0.480795i
\(604\) 4.85728 0.197640
\(605\) 19.0716 + 2.67952i 0.775371 + 0.108938i
\(606\) −16.2351 −0.659504
\(607\) 2.74266i 0.111321i 0.998450 + 0.0556606i \(0.0177265\pi\)
−0.998450 + 0.0556606i \(0.982274\pi\)
\(608\) 1.37778i 0.0558765i
\(609\) −2.63512 −0.106781
\(610\) 2.69535 19.1842i 0.109131 0.776746i
\(611\) −16.0000 −0.647291
\(612\) 6.42864i 0.259862i
\(613\) 24.0731i 0.972305i 0.873874 + 0.486152i \(0.161600\pi\)
−0.873874 + 0.486152i \(0.838400\pi\)
\(614\) −0.653858 −0.0263876
\(615\) −3.37778 + 24.0415i −0.136205 + 0.969446i
\(616\) 2.75557 0.111025
\(617\) 39.4893i 1.58978i −0.606753 0.794890i \(-0.707528\pi\)
0.606753 0.794890i \(-0.292472\pi\)
\(618\) 12.2351i 0.492166i
\(619\) 22.6222 0.909264 0.454632 0.890679i \(-0.349771\pi\)
0.454632 + 0.890679i \(0.349771\pi\)
\(620\) 8.85728 + 1.24443i 0.355717 + 0.0499776i
\(621\) −1.00000 −0.0401286
\(622\) 13.0923i 0.524955i
\(623\) 1.71456i 0.0686923i
\(624\) 1.37778 0.0551555
\(625\) 21.2034 + 13.2444i 0.848137 + 0.529777i
\(626\) −11.2573 −0.449934
\(627\) 6.10171i 0.243679i
\(628\) 9.90813i 0.395378i
\(629\) −75.8992 −3.02630
\(630\) 1.37778 + 0.193576i 0.0548922 + 0.00771226i
\(631\) 5.93978 0.236459 0.118229 0.992986i \(-0.462278\pi\)
0.118229 + 0.992986i \(0.462278\pi\)
\(632\) 12.0415i 0.478985i
\(633\) 0.266706i 0.0106006i
\(634\) −22.4701 −0.892403
\(635\) −1.55262 + 11.0509i −0.0616140 + 0.438540i
\(636\) −3.37778 −0.133938
\(637\) 9.11108i 0.360994i
\(638\) 18.7556i 0.742540i
\(639\) 6.99063 0.276545
\(640\) −0.311108 + 2.21432i −0.0122976 + 0.0875287i
\(641\) 19.8163 0.782696 0.391348 0.920243i \(-0.372009\pi\)
0.391348 + 0.920243i \(0.372009\pi\)
\(642\) 10.6637i 0.420863i
\(643\) 44.7467i 1.76464i −0.470653 0.882318i \(-0.655982\pi\)
0.470653 0.882318i \(-0.344018\pi\)
\(644\) −0.622216 −0.0245187
\(645\) −2.32693 0.326929i −0.0916227 0.0128728i
\(646\) −8.85728 −0.348485
\(647\) 32.9403i 1.29501i 0.762059 + 0.647507i \(0.224189\pi\)
−0.762059 + 0.647507i \(0.775811\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −42.5718 −1.67109
\(650\) 6.62222 + 1.89829i 0.259745 + 0.0744571i
\(651\) 2.48886 0.0975462
\(652\) 10.1017i 0.395614i
\(653\) 37.2257i 1.45675i −0.685177 0.728377i \(-0.740275\pi\)
0.685177 0.728377i \(-0.259725\pi\)
\(654\) −15.1526 −0.592512
\(655\) 1.67307 + 0.235063i 0.0653723 + 0.00918468i
\(656\) −10.8573 −0.423906
\(657\) 2.75557i 0.107505i
\(658\) 7.22570i 0.281687i
\(659\) −24.6953 −0.961994 −0.480997 0.876722i \(-0.659725\pi\)
−0.480997 + 0.876722i \(0.659725\pi\)
\(660\) −1.37778 + 9.80642i −0.0536302 + 0.381715i
\(661\) −14.8287 −0.576770 −0.288385 0.957515i \(-0.593118\pi\)
−0.288385 + 0.957515i \(0.593118\pi\)
\(662\) 29.4479i 1.14452i
\(663\) 8.85728i 0.343988i
\(664\) −2.19358 −0.0851273
\(665\) 0.266706 1.89829i 0.0103424 0.0736125i
\(666\) 11.8064 0.457490
\(667\) 4.23506i 0.163982i
\(668\) 1.89829i 0.0734470i
\(669\) −0.990632 −0.0383000
\(670\) −26.1432 3.67307i −1.01000 0.141903i
\(671\) 38.3684 1.48120
\(672\) 0.622216i 0.0240025i
\(673\) 8.77430i 0.338225i −0.985597 0.169112i \(-0.945910\pi\)
0.985597 0.169112i \(-0.0540901\pi\)
\(674\) −24.6222 −0.948412
\(675\) −1.37778 + 4.80642i −0.0530309 + 0.184999i
\(676\) −11.1017 −0.426989
\(677\) 12.8256i 0.492929i −0.969152 0.246465i \(-0.920731\pi\)
0.969152 0.246465i \(-0.0792689\pi\)
\(678\) 14.4286i 0.554129i
\(679\) 1.32741 0.0509412
\(680\) 14.2351 + 2.00000i 0.545890 + 0.0766965i
\(681\) 17.1526 0.657288
\(682\) 17.7146i 0.678325i
\(683\) 8.47013i 0.324100i −0.986783 0.162050i \(-0.948189\pi\)
0.986783 0.162050i \(-0.0518106\pi\)
\(684\) 1.37778 0.0526809
\(685\) 4.01874 28.6035i 0.153548 1.09288i
\(686\) −8.47013 −0.323391
\(687\) 7.15257i 0.272887i
\(688\) 1.05086i 0.0400635i
\(689\) −4.65386 −0.177298
\(690\) 0.311108 2.21432i 0.0118437 0.0842977i
\(691\) 25.7975 0.981384 0.490692 0.871333i \(-0.336744\pi\)
0.490692 + 0.871333i \(0.336744\pi\)
\(692\) 21.2257i 0.806880i
\(693\) 2.75557i 0.104675i
\(694\) 26.1017 0.990807
\(695\) 31.2257 + 4.38715i 1.18446 + 0.166414i
\(696\) 4.23506 0.160530
\(697\) 69.7975i 2.64377i
\(698\) 21.2257i 0.803404i
\(699\) −3.71456 −0.140497
\(700\) −0.857279 + 2.99063i −0.0324021 + 0.113035i
\(701\) 7.45091 0.281417 0.140709 0.990051i \(-0.455062\pi\)
0.140709 + 0.990051i \(0.455062\pi\)
\(702\) 1.37778i 0.0520011i
\(703\) 16.2667i 0.613510i
\(704\) −4.42864 −0.166911
\(705\) 25.7146 + 3.61285i 0.968466 + 0.136068i
\(706\) 4.28544 0.161285
\(707\) 10.1017i 0.379914i
\(708\) 9.61285i 0.361273i
\(709\) −13.2543 −0.497775 −0.248887 0.968532i \(-0.580065\pi\)
−0.248887 + 0.968532i \(0.580065\pi\)
\(710\) −2.17484 + 15.4795i −0.0816203 + 0.580935i
\(711\) 12.0415 0.451591
\(712\) 2.75557i 0.103269i
\(713\) 4.00000i 0.149801i
\(714\) 4.00000 0.149696
\(715\) −1.89829 + 13.5111i −0.0709920 + 0.505288i
\(716\) 0.488863 0.0182697
\(717\) 27.8479i 1.04000i
\(718\) 4.65386i 0.173680i
\(719\) 2.33677 0.0871469 0.0435735 0.999050i \(-0.486126\pi\)
0.0435735 + 0.999050i \(0.486126\pi\)
\(720\) −2.21432 0.311108i −0.0825228 0.0115943i
\(721\) 7.61285 0.283517
\(722\) 17.1017i 0.636460i
\(723\) 7.12399i 0.264944i
\(724\) 20.9304 0.777873
\(725\) 20.3555 + 5.83500i 0.755985 + 0.216707i
\(726\) −8.61285 −0.319653
\(727\) 3.37778i 0.125275i −0.998036 0.0626375i \(-0.980049\pi\)
0.998036 0.0626375i \(-0.0199512\pi\)
\(728\) 0.857279i 0.0317729i
\(729\) −1.00000 −0.0370370
\(730\) 6.10171 + 0.857279i 0.225834 + 0.0317293i
\(731\) −6.75557 −0.249864
\(732\) 8.66370i 0.320220i
\(733\) 21.0509i 0.777531i −0.921337 0.388766i \(-0.872902\pi\)
0.921337 0.388766i \(-0.127098\pi\)
\(734\) 4.88892 0.180453
\(735\) 2.05731 14.6430i 0.0758850 0.540114i
\(736\) 1.00000 0.0368605
\(737\) 52.2864i 1.92599i
\(738\) 10.8573i 0.399662i
\(739\) 22.6351 0.832646 0.416323 0.909217i \(-0.363318\pi\)
0.416323 + 0.909217i \(0.363318\pi\)
\(740\) −3.67307 + 26.1432i −0.135025 + 0.961043i
\(741\) 1.89829 0.0697354
\(742\) 2.10171i 0.0771562i
\(743\) 3.87955i 0.142327i 0.997465 + 0.0711635i \(0.0226712\pi\)
−0.997465 + 0.0711635i \(0.977329\pi\)
\(744\) −4.00000 −0.146647
\(745\) −27.5210 3.86665i −1.00829 0.141663i
\(746\) −23.4193 −0.857440
\(747\) 2.19358i 0.0802588i
\(748\) 28.4701i 1.04097i
\(749\) 6.63512 0.242442
\(750\) −10.2143 4.54617i −0.372974 0.166003i
\(751\) 19.7748 0.721592 0.360796 0.932645i \(-0.382505\pi\)
0.360796 + 0.932645i \(0.382505\pi\)
\(752\) 11.6128i 0.423477i
\(753\) 22.4099i 0.816662i
\(754\) 5.83500 0.212498
\(755\) −10.7556 1.51114i −0.391435 0.0549959i
\(756\) −0.622216 −0.0226298
\(757\) 8.19358i 0.297801i 0.988852 + 0.148900i \(0.0475733\pi\)
−0.988852 + 0.148900i \(0.952427\pi\)
\(758\) 4.90766i 0.178254i
\(759\) 4.42864 0.160749
\(760\) −0.428639 + 3.05086i −0.0155484 + 0.110666i
\(761\) −45.1624 −1.63714 −0.818568 0.574410i \(-0.805232\pi\)
−0.818568 + 0.574410i \(0.805232\pi\)
\(762\) 4.99063i 0.180792i
\(763\) 9.42816i 0.341322i
\(764\) −18.9590 −0.685912
\(765\) −2.00000 + 14.2351i −0.0723102 + 0.514670i
\(766\) 19.8796 0.718277
\(767\) 13.2444i 0.478229i
\(768\) 1.00000i 0.0360844i
\(769\) −29.4924 −1.06352 −0.531762 0.846894i \(-0.678470\pi\)
−0.531762 + 0.846894i \(0.678470\pi\)
\(770\) −6.10171 0.857279i −0.219890 0.0308942i
\(771\) −11.7146 −0.421889
\(772\) 1.24443i 0.0447881i
\(773\) 41.0923i 1.47799i 0.673712 + 0.738994i \(0.264699\pi\)
−0.673712 + 0.738994i \(0.735301\pi\)
\(774\) 1.05086 0.0377722
\(775\) −19.2257 5.51114i −0.690607 0.197966i
\(776\) −2.13335 −0.0765829
\(777\) 7.34614i 0.263541i
\(778\) 0.161933i 0.00580559i
\(779\) −14.9590 −0.535961
\(780\) −3.05086 0.428639i −0.109238 0.0153478i
\(781\) −30.9590 −1.10780
\(782\) 6.42864i 0.229888i
\(783\) 4.23506i 0.151349i
\(784\) 6.61285 0.236173
\(785\) −3.08250 + 21.9398i −0.110019 + 0.783064i
\(786\) −0.755569 −0.0269502
\(787\) 10.0919i 0.359736i 0.983691 + 0.179868i \(0.0575671\pi\)
−0.983691 + 0.179868i \(0.942433\pi\)
\(788\) 15.2444i